LMFDB - Embedded newform 1130.2.b.c.679.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1130,2,Mod(679,1130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1130.679"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1130, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1130 = 2 \cdot 5 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1130.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,-22,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.02309542840$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			679.12
Character	$\chi$	$=$	1130.679
Dual form			1130.2.b.c.679.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -2.50893i q^{3} -1.00000 q^{4} +(-1.78890 - 1.34158i) q^{5} +2.50893 q^{6} -2.30395i q^{7} -1.00000i q^{8} -3.29473 q^{9} +(1.34158 - 1.78890i) q^{10} -4.76822 q^{11} +2.50893i q^{12} +1.85725i q^{13} +2.30395 q^{14} +(-3.36592 + 4.48823i) q^{15} +1.00000 q^{16} -2.55782i q^{17} -3.29473i q^{18} +0.479145 q^{19} +(1.78890 + 1.34158i) q^{20} -5.78046 q^{21} -4.76822i q^{22} +1.69375i q^{23} -2.50893 q^{24} +(1.40034 + 4.79990i) q^{25} -1.85725 q^{26} +0.739455i q^{27} +2.30395i q^{28} +5.09785 q^{29} +(-4.48823 - 3.36592i) q^{30} -3.71986 q^{31} +1.00000i q^{32} +11.9631i q^{33} +2.55782 q^{34} +(-3.09093 + 4.12154i) q^{35} +3.29473 q^{36} -5.00749i q^{37} +0.479145i q^{38} +4.65970 q^{39} +(-1.34158 + 1.78890i) q^{40} -5.61415 q^{41} -5.78046i q^{42} +9.87595i q^{43} +4.76822 q^{44} +(5.89395 + 4.42014i) q^{45} -1.69375 q^{46} +9.74729i q^{47} -2.50893i q^{48} +1.69180 q^{49} +(-4.79990 + 1.40034i) q^{50} -6.41740 q^{51} -1.85725i q^{52} +3.54685i q^{53} -0.739455 q^{54} +(8.52988 + 6.39694i) q^{55} -2.30395 q^{56} -1.20214i q^{57} +5.09785i q^{58} -2.12602 q^{59} +(3.36592 - 4.48823i) q^{60} +10.4209 q^{61} -3.71986i q^{62} +7.59090i q^{63} -1.00000 q^{64} +(2.49164 - 3.32243i) q^{65} -11.9631 q^{66} +2.66523i q^{67} +2.55782i q^{68} +4.24949 q^{69} +(-4.12154 - 3.09093i) q^{70} -12.2948 q^{71} +3.29473i q^{72} -14.4107i q^{73} +5.00749 q^{74} +(12.0426 - 3.51335i) q^{75} -0.479145 q^{76} +10.9858i q^{77} +4.65970i q^{78} -11.8784 q^{79} +(-1.78890 - 1.34158i) q^{80} -8.02895 q^{81} -5.61415i q^{82} -7.71935i q^{83} +5.78046 q^{84} +(-3.43152 + 4.57570i) q^{85} -9.87595 q^{86} -12.7902i q^{87} +4.76822i q^{88} -16.9619 q^{89} +(-4.42014 + 5.89395i) q^{90} +4.27901 q^{91} -1.69375i q^{92} +9.33286i q^{93} -9.74729 q^{94} +(-0.857144 - 0.642811i) q^{95} +2.50893 q^{96} +0.0394372i q^{97} +1.69180i q^{98} +15.7100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{4} - 6 q^{5} - 6 q^{6} - 8 q^{9} - 4 q^{10} - 34 q^{11} + 6 q^{14} - 8 q^{15} + 22 q^{16} + 28 q^{19} + 6 q^{20} - 28 q^{21} + 6 q^{24} - 10 q^{25} - 30 q^{26} + 30 q^{29} + 2 q^{30} - 28 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - 22 * q^4 - 6 * q^5 - 6 * q^6 - 8 * q^9 - 4 * q^10 - 34 * q^11 + 6 * q^14 - 8 * q^15 + 22 * q^16 + 28 * q^19 + 6 * q^20 - 28 * q^21 + 6 * q^24 - 10 * q^25 - 30 * q^26 + 30 * q^29 + 2 * q^30 - 28 * q^31 + 2 * q^34 - 4 * q^35 + 8 * q^36 + 52 * q^39 + 4 * q^40 - 78 * q^41 + 34 * q^44 - 12 * q^45 + 4 * q^46 - 12 * q^49 - 8 * q^50 - 32 * q^51 + 12 * q^54 + 6 * q^55 - 6 * q^56 + 64 * q^59 + 8 * q^60 - 72 * q^61 - 22 * q^64 + 8 * q^65 - 20 * q^66 + 24 * q^69 + 26 * q^70 - 66 * q^71 + 36 * q^74 + 20 * q^75 - 28 * q^76 + 10 * q^79 - 6 * q^80 - 66 * q^81 + 28 * q^84 + 48 * q^85 - 26 * q^86 + 88 * q^89 + 32 * q^90 - 68 * q^91 - 76 * q^94 + 4 * q^95 - 6 * q^96 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1130\mathbb{Z}\right)^\times$.

$n$	$227$	$681$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	2.50893i		−	1.44853i	−0.689521	−	0.724266i	$-0.742179\pi$
$3$		−	2.50893i		−	1.44853i	0.689521	−	0.724266i	$-0.257821\pi$
$4$	−1.00000			−0.500000
$5$	−1.78890	−	1.34158i	−0.800021	−	0.599972i
$5$	−1.78890	−	1.34158i	−0.800021	−	0.599972i
$6$	2.50893			1.02427
$7$		−	2.30395i		−	0.870812i	−0.900234	−	0.435406i	$-0.856605\pi$
$7$		−	2.30395i		−	0.870812i	0.900234	−	0.435406i	$-0.143395\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−3.29473			−1.09824
$10$	1.34158	−	1.78890i	0.424244	−	0.565700i
$11$	−4.76822			−1.43767			−0.718836	−	0.695180i	$-0.755325\pi$
$11$	−4.76822			−1.43767			−0.718836	+	0.695180i	$0.755325\pi$
$12$			2.50893i			0.724266i
$13$			1.85725i			0.515107i	0.966264	+	0.257554i	$0.0829164\pi$
$13$			1.85725i			0.515107i	−0.966264	+	0.257554i	$0.917084\pi$
$14$	2.30395			0.615757
$15$	−3.36592	+	4.48823i	−0.869078	+	1.15886i
$16$	1.00000			0.250000
$17$		−	2.55782i		−	0.620364i	−0.950677	−	0.310182i	$-0.899610\pi$
$17$		−	2.55782i		−	0.620364i	0.950677	−	0.310182i	$-0.100390\pi$
$18$		−	3.29473i		−	0.776575i
$19$	0.479145			0.109923			0.0549617	−	0.998488i	$-0.482496\pi$
$19$	0.479145			0.109923			0.0549617	+	0.998488i	$0.482496\pi$
$20$	1.78890	+	1.34158i	0.400011	+	0.299986i
$21$	−5.78046			−1.26140
$22$		−	4.76822i		−	1.01659i
$23$			1.69375i			0.353170i	0.984285	+	0.176585i	$0.0565051\pi$
$23$			1.69375i			0.353170i	−0.984285	+	0.176585i	$0.943495\pi$
$24$	−2.50893			−0.512133
$25$	1.40034	+	4.79990i	0.280068	+	0.959980i
$26$	−1.85725			−0.364236
$27$			0.739455i			0.142308i
$28$			2.30395i			0.435406i
$29$	5.09785			0.946648			0.473324	−	0.880889i	$-0.343054\pi$
$29$	5.09785			0.946648			0.473324	+	0.880889i	$0.343054\pi$
$30$	−4.48823	−	3.36592i	−0.819435	−	0.614531i
$31$	−3.71986			−0.668106			−0.334053	−	0.942554i	$-0.608416\pi$
$31$	−3.71986			−0.668106			−0.334053	+	0.942554i	$0.608416\pi$
$32$			1.00000i			0.176777i
$33$			11.9631i			2.08251i
$34$	2.55782			0.438663
$35$	−3.09093	+	4.12154i	−0.522463	+	0.696668i
$36$	3.29473			0.549122
$37$		−	5.00749i		−	0.823226i	−0.911359	−	0.411613i	$-0.864965\pi$
$37$		−	5.00749i		−	0.823226i	0.911359	−	0.411613i	$-0.135035\pi$
$38$			0.479145i			0.0777276i
$39$	4.65970			0.746149
$40$	−1.34158	+	1.78890i	−0.212122	+	0.282850i
$41$	−5.61415			−0.876784			−0.438392	−	0.898784i	$-0.644452\pi$
$41$	−5.61415			−0.876784			−0.438392	+	0.898784i	$0.644452\pi$
$42$		−	5.78046i		−	0.891944i
$43$			9.87595i			1.50607i	0.657981	+	0.753034i	$0.271411\pi$
$43$			9.87595i			1.50607i	−0.657981	+	0.753034i	$0.728589\pi$
$44$	4.76822			0.718836
$45$	5.89395	+	4.42014i	0.878618	+	0.658915i
$46$	−1.69375			−0.249729
$47$			9.74729i			1.42179i	0.703299	+	0.710894i	$0.251710\pi$
$47$			9.74729i			1.42179i	−0.703299	+	0.710894i	$0.748290\pi$
$48$		−	2.50893i		−	0.362133i
$49$	1.69180			0.241686
$50$	−4.79990	+	1.40034i	−0.678809	+	0.198038i
$51$	−6.41740			−0.898616
$52$		−	1.85725i		−	0.257554i
$53$			3.54685i			0.487197i	0.969876	+	0.243598i	$0.0783279\pi$
$53$			3.54685i			0.487197i	−0.969876	+	0.243598i	$0.921672\pi$
$54$	−0.739455			−0.100627
$55$	8.52988	+	6.39694i	1.15017	+	0.862563i
$56$	−2.30395			−0.307879
$57$		−	1.20214i		−	0.159228i
$58$			5.09785i			0.669381i
$59$	−2.12602			−0.276784			−0.138392	−	0.990378i	$-0.544193\pi$
$59$	−2.12602			−0.276784			−0.138392	+	0.990378i	$0.544193\pi$
$60$	3.36592	−	4.48823i	0.434539	−	0.579428i
$61$	10.4209			1.33427			0.667133	−	0.744939i	$-0.267521\pi$
$61$	10.4209			1.33427			0.667133	+	0.744939i	$0.267521\pi$
$62$		−	3.71986i		−	0.472422i
$63$			7.59090i			0.956364i
$64$	−1.00000			−0.125000
$65$	2.49164	−	3.32243i	0.309050	−	0.412097i
$66$	−11.9631			−1.47256
$67$			2.66523i			0.325610i	0.986658	+	0.162805i	$0.0520541\pi$
$67$			2.66523i			0.325610i	−0.986658	+	0.162805i	$0.947946\pi$
$68$			2.55782i			0.310182i
$69$	4.24949			0.511578
$70$	−4.12154	−	3.09093i	−0.492619	−	0.369437i
$71$	−12.2948			−1.45912			−0.729561	−	0.683916i	$-0.760276\pi$
$71$	−12.2948			−1.45912			−0.729561	+	0.683916i	$0.760276\pi$
$72$			3.29473i			0.388288i
$73$		−	14.4107i		−	1.68664i	−0.537412	−	0.843320i	$-0.680598\pi$
$73$		−	14.4107i		−	1.68664i	0.537412	−	0.843320i	$-0.319402\pi$
$74$	5.00749			0.582109
$75$	12.0426	−	3.51335i	1.39056	−	0.405687i
$76$	−0.479145			−0.0549617
$77$			10.9858i			1.25194i
$78$			4.65970i			0.527607i
$79$	−11.8784			−1.33642			−0.668212	−	0.743971i	$-0.732940\pi$
$79$	−11.8784			−1.33642			−0.668212	+	0.743971i	$0.732940\pi$
$80$	−1.78890	−	1.34158i	−0.200005	−	0.149993i
$81$	−8.02895			−0.892105
$82$		−	5.61415i		−	0.619980i
$83$		−	7.71935i		−	0.847308i	−0.905824	−	0.423654i	$-0.860747\pi$
$83$		−	7.71935i		−	0.847308i	0.905824	−	0.423654i	$-0.139253\pi$
$84$	5.78046			0.630699
$85$	−3.43152	+	4.57570i	−0.372201	+	0.496304i
$86$	−9.87595			−1.06495
$87$		−	12.7902i		−	1.37125i
$88$			4.76822i			0.508294i
$89$	−16.9619			−1.79796			−0.898981	−	0.437987i	$-0.855691\pi$
$89$	−16.9619			−1.79796			−0.898981	+	0.437987i	$0.855691\pi$
$90$	−4.42014	+	5.89395i	−0.465923	+	0.621276i
$91$	4.27901			0.448562
$92$		−	1.69375i		−	0.176585i
$93$			9.33286i			0.967773i
$94$	−9.74729			−1.00536
$95$	−0.857144	−	0.642811i	−0.0879411	−	0.0659510i
$96$	2.50893			0.256067
$97$			0.0394372i			0.00400424i	0.999998	+	0.00200212i	$0.000637295\pi$
$97$			0.0394372i			0.00400424i	−0.999998	+	0.00200212i	$0.999363\pi$
$98$			1.69180i			0.170898i
$99$	15.7100			1.57891
$100$	−1.40034	−	4.79990i	−0.140034	−	0.479990i
$101$	0.422160			0.0420065			0.0210033	−	0.999779i	$-0.493314\pi$
$101$	0.422160			0.0420065			0.0210033	+	0.999779i	$0.493314\pi$
$102$		−	6.41740i		−	0.635418i
$103$			0.424030i			0.0417809i	0.999782	+	0.0208904i	$0.00665012\pi$
$103$			0.424030i			0.0417809i	−0.999782	+	0.0208904i	$0.993350\pi$
$104$	1.85725			0.182118
$105$	10.3407	+	7.75493i	1.00915	+	0.756804i
$106$	−3.54685			−0.344500
$107$			3.17056i			0.306510i	0.988187	+	0.153255i	$0.0489756\pi$
$107$			3.17056i			0.306510i	−0.988187	+	0.153255i	$0.951024\pi$
$108$		−	0.739455i		−	0.0711541i
$109$	2.96567			0.284060			0.142030	−	0.989862i	$-0.454637\pi$
$109$	2.96567			0.284060			0.142030	+	0.989862i	$0.454637\pi$
$110$	−6.39694	+	8.52988i	−0.609924	+	0.813292i
$111$	−12.5634			−1.19247
$112$		−	2.30395i		−	0.217703i
$113$			1.00000i			0.0940721i
$113$			1.00000i			0.0940721i
$114$	1.20214			0.112591
$115$	2.27229	−	3.02994i	0.211892	−	0.282544i
$116$	−5.09785			−0.473324
$117$		−	6.11912i		−	0.565713i
$118$		−	2.12602i		−	0.195716i
$119$	−5.89311			−0.540220
$120$	4.48823	+	3.36592i	0.409717	+	0.307265i
$121$	11.7359			1.06690
$122$			10.4209i			0.943468i
$123$			14.0855i			1.27005i
$124$	3.71986			0.334053
$125$	3.93437	−	10.4652i	0.351901	−	0.936037i
$126$	−7.59090			−0.676251
$127$			14.7585i			1.30961i	0.755799	+	0.654804i	$0.227249\pi$
$127$			14.7585i			1.30961i	−0.755799	+	0.654804i	$0.772751\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	24.7781			2.18159
$130$	3.32243	+	2.49164i	0.291396	+	0.218531i
$131$	−5.70591			−0.498528			−0.249264	−	0.968436i	$-0.580189\pi$
$131$	−5.70591			−0.498528			−0.249264	+	0.968436i	$0.580189\pi$
$132$		−	11.9631i		−	1.04126i
$133$		−	1.10393i		−	0.0957227i
$134$	−2.66523			−0.230241
$135$	0.992036	−	1.32281i	0.0853809	−	0.113850i
$136$	−2.55782			−0.219332
$137$		−	17.2515i		−	1.47390i	−0.675949	−	0.736948i	$-0.736266\pi$
$137$		−	17.2515i		−	1.47390i	0.675949	−	0.736948i	$-0.263734\pi$
$138$			4.24949i			0.361741i
$139$	−0.897477			−0.0761230			−0.0380615	−	0.999275i	$-0.512118\pi$
$139$	−0.897477			−0.0761230			−0.0380615	+	0.999275i	$0.512118\pi$
$140$	3.09093	−	4.12154i	0.261231	−	0.348334i
$141$	24.4553			2.05951
$142$		−	12.2948i		−	1.03175i
$143$		−	8.85575i		−	0.740555i
$144$	−3.29473			−0.274561
$145$	−9.11956	−	6.83917i	−0.757338	−	0.567962i
$146$	14.4107			1.19263
$147$		−	4.24461i		−	0.350090i
$148$			5.00749i			0.411613i
$149$	−19.3660			−1.58652			−0.793262	−	0.608881i	$-0.791619\pi$
$149$	−19.3660			−1.58652			−0.793262	+	0.608881i	$0.791619\pi$
$150$	3.51335	+	12.0426i	0.286864	+	0.983275i
$151$	−10.0072			−0.814371			−0.407186	−	0.913345i	$-0.633490\pi$
$151$	−10.0072			−0.814371			−0.407186	+	0.913345i	$0.633490\pi$
$152$		−	0.479145i		−	0.0388638i
$153$			8.42734i			0.681310i
$154$	−10.9858			−0.885257
$155$	6.65446	+	4.99048i	0.534499	+	0.400845i
$156$	−4.65970			−0.373074
$157$		−	19.0527i		−	1.52057i	−0.649587	−	0.760287i	$-0.725058\pi$
$157$		−	19.0527i		−	1.52057i	0.649587	−	0.760287i	$-0.274942\pi$
$158$		−	11.8784i		−	0.944994i
$159$	8.89879			0.705720
$160$	1.34158	−	1.78890i	0.106061	−	0.141425i
$161$	3.90231			0.307545
$162$		−	8.02895i		−	0.630814i
$163$			10.0478i			0.787001i	0.919324	+	0.393501i	$0.128736\pi$
$163$			10.0478i			0.787001i	−0.919324	+	0.393501i	$0.871264\pi$
$164$	5.61415			0.438392
$165$	16.0495	−	21.4009i	1.24945	−	1.66605i
$166$	7.71935			0.599137
$167$		−	5.28698i		−	0.409119i	−0.978854	−	0.204560i	$-0.934424\pi$
$167$		−	5.28698i		−	0.409119i	0.978854	−	0.204560i	$-0.0655762\pi$
$168$			5.78046i			0.445972i
$169$	9.55064			0.734665
$170$	−4.57570	−	3.43152i	−0.350940	−	0.263186i
$171$	−1.57865			−0.120723
$172$		−	9.87595i		−	0.753034i
$173$		−	13.2211i		−	1.00518i	−0.864525	−	0.502590i	$-0.832381\pi$
$173$		−	13.2211i		−	1.00518i	0.864525	−	0.502590i	$-0.167619\pi$
$174$	12.7902			0.969619
$175$	11.0587	−	3.22631i	0.835963	−	0.243886i
$176$	−4.76822			−0.359418
$177$			5.33404i			0.400931i
$178$		−	16.9619i		−	1.27135i
$179$	0.867474			0.0648381			0.0324190	−	0.999474i	$-0.489679\pi$
$179$	0.867474			0.0648381			0.0324190	+	0.999474i	$0.489679\pi$
$180$	−5.89395	−	4.42014i	−0.439309	−	0.329457i
$181$	−6.72604			−0.499942			−0.249971	−	0.968253i	$-0.580421\pi$
$181$	−6.72604			−0.499942			−0.249971	+	0.968253i	$0.580421\pi$
$182$			4.27901i			0.317181i
$183$		−	26.1454i		−	1.93272i
$184$	1.69375			0.124865
$185$	−6.71794	+	8.95791i	−0.493913	+	0.658599i
$186$	−9.33286			−0.684319
$187$			12.1963i			0.891879i
$188$		−	9.74729i		−	0.710894i
$189$	1.70367			0.123924
$190$	0.642811	−	0.857144i	0.0466344	−	0.0621837i
$191$	−8.86928			−0.641759			−0.320879	−	0.947120i	$-0.603978\pi$
$191$	−8.86928			−0.641759			−0.320879	+	0.947120i	$0.603978\pi$
$192$			2.50893i			0.181066i
$193$			7.26738i			0.523117i	0.965188	+	0.261559i	$0.0842365\pi$
$193$			7.26738i			0.523117i	−0.965188	+	0.261559i	$0.915764\pi$
$194$	−0.0394372			−0.00283143
$195$	−8.33574	−	6.25135i	−0.596935	−	0.447668i
$196$	−1.69180			−0.120843
$197$		−	20.0450i		−	1.42815i	−0.700070	−	0.714074i	$-0.746848\pi$
$197$		−	20.0450i		−	1.42815i	0.700070	−	0.714074i	$-0.253152\pi$
$198$			15.7100i			1.11646i
$199$	−21.5949			−1.53082			−0.765412	−	0.643540i	$-0.777465\pi$
$199$	−21.5949			−1.53082			−0.765412	+	0.643540i	$0.777465\pi$
$200$	4.79990	−	1.40034i	0.339404	−	0.0990188i
$201$	6.68688			0.471656
$202$			0.422160i			0.0297031i
$203$		−	11.7452i		−	0.824352i
$204$	6.41740			0.449308
$205$	10.0432	+	7.53182i	0.701445	+	0.526045i
$206$	−0.424030			−0.0295436
$207$		−	5.58043i		−	0.387867i
$208$			1.85725i			0.128777i
$209$	−2.28467			−0.158034
$210$	−7.75493	+	10.3407i	−0.535141	+	0.713574i
$211$	−2.60679			−0.179459			−0.0897293	−	0.995966i	$-0.528600\pi$
$211$	−2.60679			−0.179459			−0.0897293	+	0.995966i	$0.528600\pi$
$212$		−	3.54685i		−	0.243598i
$213$			30.8467i			2.11358i
$214$	−3.17056			−0.216735
$215$	13.2494	−	17.6671i	0.903599	−	1.20489i
$216$	0.739455			0.0503135
$217$			8.57038i			0.581795i
$218$			2.96567i			0.200861i
$219$	−36.1553			−2.44315
$220$	−8.52988	−	6.39694i	−0.575084	−	0.431281i
$221$	4.75051			0.319554
$222$		−	12.5634i		−	0.843203i
$223$		−	11.1681i		−	0.747872i	−0.927455	−	0.373936i	$-0.878008\pi$
$223$		−	11.1681i		−	0.747872i	0.927455	−	0.373936i	$-0.121992\pi$
$224$	2.30395			0.153939
$225$	−4.61373	−	15.8144i	−0.307582	−	1.05429i
$226$	−1.00000			−0.0665190
$227$		−	12.9645i		−	0.860484i	−0.902714	−	0.430242i	$-0.858428\pi$
$227$		−	12.9645i		−	0.860484i	0.902714	−	0.430242i	$-0.141572\pi$
$228$			1.20214i			0.0796138i
$229$	11.8619			0.783858			0.391929	−	0.919995i	$-0.371808\pi$
$229$	11.8619			0.783858			0.391929	+	0.919995i	$0.371808\pi$
$230$	3.02994	+	2.27229i	0.199789	+	0.149830i
$231$	27.5625			1.81348
$232$		−	5.09785i		−	0.334690i
$233$			20.7016i			1.35621i	0.734965	+	0.678105i	$0.237198\pi$
$233$			20.7016i			1.35621i	−0.734965	+	0.678105i	$0.762802\pi$
$234$	6.11912			0.400019
$235$	13.0768	−	17.4369i	0.853033	−	1.13746i
$236$	2.12602			0.138392
$237$			29.8020i			1.93585i
$238$		−	5.89311i		−	0.381993i
$239$	17.6550			1.14201			0.571005	−	0.820946i	$-0.306554\pi$
$239$	17.6550			1.14201			0.571005	+	0.820946i	$0.306554\pi$
$240$	−3.36592	+	4.48823i	−0.217270	+	0.289714i
$241$	17.9663			1.15731			0.578656	−	0.815571i	$-0.303577\pi$
$241$	17.9663			1.15731			0.578656	+	0.815571i	$0.303577\pi$
$242$			11.7359i			0.754413i
$243$			22.3624i			1.43455i
$244$	−10.4209			−0.667133
$245$	−3.02647	−	2.26968i	−0.193354	−	0.145005i
$246$	−14.0855			−0.898060
$247$			0.889890i			0.0566224i
$248$			3.71986i			0.236211i
$249$	−19.3673			−1.22735
$250$	10.4652	+	3.93437i	0.661878	+	0.248832i
$251$	4.19527			0.264803			0.132402	−	0.991196i	$-0.457731\pi$
$251$	4.19527			0.264803			0.132402	+	0.991196i	$0.457731\pi$
$252$		−	7.59090i		−	0.478182i
$253$		−	8.07615i		−	0.507743i
$254$	−14.7585			−0.926032
$255$	11.4801	+	8.60944i	0.718912	+	0.539144i
$256$	1.00000			0.0625000
$257$			27.6300i			1.72351i	0.507324	+	0.861755i	$0.330635\pi$
$257$			27.6300i			1.72351i	−0.507324	+	0.861755i	$0.669365\pi$
$258$			24.7781i			1.54262i
$259$	−11.5370			−0.716876
$260$	−2.49164	+	3.32243i	−0.154525	+	0.206048i
$261$	−16.7960			−1.03965
$262$		−	5.70591i		−	0.352512i
$263$		−	16.2930i		−	1.00467i	−0.864674	−	0.502334i	$-0.832475\pi$
$263$		−	16.2930i		−	1.00467i	0.864674	−	0.502334i	$-0.167525\pi$
$264$	11.9631			0.736280
$265$	4.75837	−	6.34496i	0.292304	−	0.389768i
$266$	1.10393			0.0676862
$267$			42.5563i			2.60440i
$268$		−	2.66523i		−	0.162805i
$269$	15.0945			0.920330			0.460165	−	0.887833i	$-0.347790\pi$
$269$	15.0945			0.920330			0.460165	+	0.887833i	$0.347790\pi$
$270$	1.32281	+	0.992036i	0.0805038	+	0.0603734i
$271$	−3.63226			−0.220644			−0.110322	−	0.993896i	$-0.535188\pi$
$271$	−3.63226			−0.220644			−0.110322	+	0.993896i	$0.535188\pi$
$272$		−	2.55782i		−	0.155091i
$273$		−	10.7357i		−	0.649756i
$274$	17.2515			1.04220
$275$	−6.67712	−	22.8870i	−0.402645	−	1.38014i
$276$	−4.24949			−0.255789
$277$		−	21.6344i		−	1.29988i	−0.759984	−	0.649942i	$-0.774793\pi$
$277$		−	21.6344i		−	1.29988i	0.759984	−	0.649942i	$-0.225207\pi$
$278$		−	0.897477i		−	0.0538271i
$279$	12.2559			0.733743
$280$	4.12154	+	3.09093i	0.246309	+	0.184719i
$281$	−28.9477			−1.72688			−0.863438	−	0.504455i	$-0.831693\pi$
$281$	−28.9477			−1.72688			−0.863438	+	0.504455i	$0.831693\pi$
$282$			24.4553i			1.45629i
$283$		−	7.94805i		−	0.472463i	−0.971697	−	0.236231i	$-0.924088\pi$
$283$		−	7.94805i		−	0.472463i	0.971697	−	0.236231i	$-0.0759123\pi$
$284$	12.2948			0.729561
$285$	−1.61277	+	2.15051i	−0.0955321	+	0.127385i
$286$	8.85575			0.523652
$287$			12.9347i			0.763514i
$288$		−	3.29473i		−	0.194144i
$289$	10.4575			0.615149
$290$	6.83917	−	9.11956i	0.401610	−	0.535519i
$291$	0.0989452			0.00580027
$292$			14.4107i			0.843320i
$293$		−	1.37126i		−	0.0801100i	−0.999197	−	0.0400550i	$-0.987247\pi$
$293$		−	1.37126i		−	0.0801100i	0.999197	−	0.0400550i	$-0.0127533\pi$
$294$	4.24461			0.247551
$295$	3.80324	+	2.85222i	0.221433	+	0.166063i
$296$	−5.00749			−0.291055
$297$		−	3.52588i		−	0.204592i
$298$		−	19.3660i		−	1.12184i
$299$	−3.14570			−0.181921
$300$	−12.0426	+	3.51335i	−0.695281	+	0.202843i
$301$	22.7537			1.31150
$302$		−	10.0072i		−	0.575847i
$303$		−	1.05917i		−	0.0608478i
$304$	0.479145			0.0274809
$305$	−18.6420	−	13.9805i	−1.06744	−	0.800521i
$306$	−8.42734			−0.481759
$307$		−	5.56841i		−	0.317806i	−0.987294	−	0.158903i	$-0.949204\pi$
$307$		−	5.56841i		−	0.317806i	0.987294	−	0.158903i	$-0.0507957\pi$
$308$		−	10.9858i		−	0.625971i
$309$	1.06386			0.0605209
$310$	−4.99048	+	6.65446i	−0.283440	+	0.377948i
$311$	−9.97052			−0.565376			−0.282688	−	0.959212i	$-0.591226\pi$
$311$	−9.97052			−0.565376			−0.282688	+	0.959212i	$0.591226\pi$
$312$		−	4.65970i		−	0.263803i
$313$			12.6094i			0.712726i	0.934348	+	0.356363i	$0.115983\pi$
$313$			12.6094i			0.712726i	−0.934348	+	0.356363i	$0.884017\pi$
$314$	19.0527			1.07521
$315$	10.1838	−	13.5794i	0.573791	−	0.765111i
$316$	11.8784			0.668212
$317$			10.6430i			0.597771i	0.954289	+	0.298886i	$0.0966149\pi$
$317$			10.6430i			0.597771i	−0.954289	+	0.298886i	$0.903385\pi$
$318$			8.89879i			0.499019i
$319$	−24.3077			−1.36097
$320$	1.78890	+	1.34158i	0.100003	+	0.0749965i
$321$	7.95472			0.443989
$322$			3.90231i			0.217467i
$323$		−	1.22557i		−	0.0681925i
$324$	8.02895			0.446053
$325$	−8.91460	+	2.60077i	−0.494493	+	0.144265i
$326$	−10.0478			−0.556494
$327$		−	7.44067i		−	0.411470i
$328$			5.61415i			0.309990i
$329$	22.4573			1.23811
$330$	21.4009	+	16.0495i	1.17808	+	0.883494i
$331$	−6.53916			−0.359425			−0.179712	−	0.983719i	$-0.557517\pi$
$331$	−6.53916			−0.359425			−0.179712	+	0.983719i	$0.557517\pi$
$332$			7.71935i			0.423654i
$333$			16.4983i			0.904103i
$334$	5.28698			0.289291
$335$	3.57562	−	4.76784i	0.195357	−	0.260495i
$336$	−5.78046			−0.315350
$337$			10.6797i			0.581762i	0.956759	+	0.290881i	$0.0939484\pi$
$337$			10.6797i			0.581762i	−0.956759	+	0.290881i	$0.906052\pi$
$338$			9.55064i			0.519486i
$339$	2.50893			0.136266
$340$	3.43152	−	4.57570i	0.186100	−	0.248152i
$341$	17.7371			0.960517
$342$		−	1.57865i		−	0.0853638i
$343$		−	20.0255i		−	1.08128i
$344$	9.87595			0.532476
$345$	−7.60192	−	5.70102i	−0.409274	−	0.306933i
$346$	13.2211			0.710769
$347$		−	9.70400i		−	0.520938i	−0.965482	−	0.260469i	$-0.916123\pi$
$347$		−	9.70400i		−	0.520938i	0.965482	−	0.260469i	$-0.0838772\pi$
$348$			12.7902i			0.685624i
$349$	7.19497			0.385138			0.192569	−	0.981283i	$-0.438318\pi$
$349$	7.19497			0.385138			0.192569	+	0.981283i	$0.438318\pi$
$350$	3.22631	+	11.0587i	0.172454	+	0.591115i
$351$	−1.37335			−0.0733039
$352$		−	4.76822i		−	0.254147i
$353$			21.2202i			1.12944i	0.825284	+	0.564718i	$0.191015\pi$
$353$			21.2202i			1.12944i	−0.825284	+	0.564718i	$0.808985\pi$
$354$	−5.33404			−0.283501
$355$	21.9941	+	16.4944i	1.16733	+	0.875432i
$356$	16.9619			0.898981
$357$			14.7854i			0.782526i
$358$			0.867474i			0.0458474i
$359$	2.67324			0.141088			0.0705441	−	0.997509i	$-0.477526\pi$
$359$	2.67324			0.141088			0.0705441	+	0.997509i	$0.477526\pi$
$360$	4.42014	−	5.89395i	0.232962	−	0.310638i
$361$	−18.7704			−0.987917
$362$		−	6.72604i		−	0.353513i
$363$		−	29.4446i		−	1.54544i
$364$	−4.27901			−0.224281
$365$	−19.3330	+	25.7792i	−1.01194	+	1.34935i
$366$	26.1454			1.36664
$367$			13.5615i			0.707905i	0.935263	+	0.353953i	$0.115163\pi$
$367$			13.5615i			0.707905i	−0.935263	+	0.353953i	$0.884837\pi$
$368$			1.69375i			0.0882926i
$369$	18.4971			0.962921
$370$	−8.95791	−	6.71794i	−0.465699	−	0.349249i
$371$	8.17177			0.424257
$372$		−	9.33286i		−	0.483886i
$373$		−	10.8753i		−	0.563103i	−0.959546	−	0.281551i	$-0.909151\pi$
$373$		−	10.8753i		−	0.563103i	0.959546	−	0.281551i	$-0.0908490\pi$
$374$	−12.1963			−0.630654
$375$	−26.2565	−	9.87107i	−1.35588	−	0.509740i
$376$	9.74729			0.502678
$377$			9.46797i			0.487625i
$378$			1.70367i			0.0876273i
$379$	10.1131			0.519475			0.259737	−	0.965679i	$-0.416364\pi$
$379$	10.1131			0.519475			0.259737	+	0.965679i	$0.416364\pi$
$380$	0.857144	+	0.642811i	0.0439705	+	0.0329755i
$381$	37.0281			1.89701
$382$		−	8.86928i		−	0.453792i
$383$		−	34.1697i		−	1.74599i	−0.487731	−	0.872994i	$-0.662175\pi$
$383$		−	34.1697i		−	1.74599i	0.487731	−	0.872994i	$-0.337825\pi$
$384$	−2.50893			−0.128033
$385$	14.7382	−	19.6524i	0.751130	−	1.00158i
$386$	−7.26738			−0.369900
$387$		−	32.5386i		−	1.65403i
$388$		−	0.0394372i		−	0.00200212i
$389$	29.6193			1.50176			0.750880	−	0.660439i	$-0.229630\pi$
$389$	29.6193			1.50176			0.750880	+	0.660439i	$0.229630\pi$
$390$	6.25135	−	8.33574i	0.316549	−	0.422097i
$391$	4.33231			0.219094
$392$		−	1.69180i		−	0.0854489i
$393$			14.3157i			0.722133i
$394$	20.0450			1.00985
$395$	21.2493	+	15.9358i	1.06917	+	0.801816i
$396$	−15.7100			−0.789457
$397$			31.0048i			1.55609i	0.628211	+	0.778043i	$0.283787\pi$
$397$			31.0048i			1.55609i	−0.628211	+	0.778043i	$0.716213\pi$
$398$		−	21.5949i		−	1.08246i
$399$	−2.76968			−0.138657
$400$	1.40034	+	4.79990i	0.0700169	+	0.239995i
$401$	−30.5717			−1.52668			−0.763340	−	0.645997i	$-0.776442\pi$
$401$	−30.5717			−1.52668			−0.763340	+	0.645997i	$0.776442\pi$
$402$			6.68688i			0.333511i
$403$		−	6.90869i		−	0.344146i
$404$	−0.422160			−0.0210033
$405$	14.3630	+	10.7715i	0.713703	+	0.535238i
$406$	11.7452			0.582905
$407$			23.8768i			1.18353i
$408$			6.41740i			0.317709i
$409$	−4.17007			−0.206197			−0.103098	−	0.994671i	$-0.532876\pi$
$409$	−4.17007			−0.206197			−0.103098	+	0.994671i	$0.532876\pi$
$410$	−7.53182	+	10.0432i	−0.371970	+	0.495997i
$411$	−43.2829			−2.13499
$412$		−	0.424030i		−	0.0208904i
$413$			4.89825i			0.241027i
$414$	5.58043			0.274263
$415$	−10.3561	+	13.8091i	−0.508361	+	0.677864i
$416$	−1.85725			−0.0910590
$417$			2.25171i			0.110267i
$418$		−	2.28467i		−	0.111747i
$419$	−6.41811			−0.313545			−0.156773	−	0.987635i	$-0.550109\pi$
$419$	−6.41811			−0.313545			−0.156773	+	0.987635i	$0.550109\pi$
$420$	−10.3407	−	7.75493i	−0.504573	−	0.378402i
$421$	1.86834			0.0910571			0.0455285	−	0.998963i	$-0.485503\pi$
$421$	1.86834			0.0910571			0.0455285	+	0.998963i	$0.485503\pi$
$422$		−	2.60679i		−	0.126896i
$423$		−	32.1147i		−	1.56147i
$424$	3.54685			0.172250
$425$	12.2773	−	3.58182i	0.595537	−	0.173744i
$426$	−30.8467			−1.49453
$427$		−	24.0094i		−	1.16189i
$428$		−	3.17056i		−	0.153255i
$429$	−22.2185			−1.07272
$430$	17.6671	+	13.2494i	0.851983	+	0.638941i
$431$	−37.9214			−1.82661			−0.913305	−	0.407276i	$-0.866479\pi$
$431$	−37.9214			−1.82661			−0.913305	+	0.407276i	$0.866479\pi$
$432$			0.739455i			0.0355770i
$433$			2.34310i			0.112602i	0.998414	+	0.0563010i	$0.0179307\pi$
$433$			2.34310i			0.112602i	−0.998414	+	0.0563010i	$0.982069\pi$
$434$	−8.57038			−0.411391
$435$	−17.1590	+	22.8803i	−0.822711	+	1.09703i
$436$	−2.96567			−0.142030
$437$			0.811550i			0.0388217i
$438$		−	36.1553i		−	1.72757i
$439$	−9.41453			−0.449331			−0.224666	−	0.974436i	$-0.572129\pi$
$439$	−9.41453			−0.449331			−0.224666	+	0.974436i	$0.572129\pi$
$440$	6.39694	−	8.52988i	0.304962	−	0.406646i
$441$	−5.57403			−0.265430
$442$			4.75051i			0.225959i
$443$		−	3.64970i		−	0.173402i	−0.996234	−	0.0867012i	$-0.972367\pi$
$443$		−	3.64970i		−	0.173402i	0.996234	−	0.0867012i	$-0.0276325\pi$
$444$	12.5634			0.596235
$445$	30.3432	+	22.7558i	1.43841	+	1.07873i
$446$	11.1681			0.528825
$447$			48.5879i			2.29813i
$448$			2.30395i			0.108852i
$449$	−38.9801			−1.83959			−0.919793	−	0.392404i	$-0.871643\pi$
$449$	−38.9801			−1.83959			−0.919793	+	0.392404i	$0.871643\pi$
$450$	15.8144	−	4.61373i	0.745497	−	0.217494i
$451$	26.7695			1.26053
$452$		−	1.00000i		−	0.0470360i
$453$			25.1073i			1.17964i
$454$	12.9645			0.608454
$455$	−7.65472	−	5.74062i	−0.358859	−	0.269124i
$456$	−1.20214			−0.0562955
$457$			13.0967i			0.612638i	0.951929	+	0.306319i	$0.0990974\pi$
$457$			13.0967i			0.612638i	−0.951929	+	0.306319i	$0.900903\pi$
$458$			11.8619i			0.554271i
$459$	1.89140			0.0882828
$460$	−2.27229	+	3.02994i	−0.105946	+	0.141272i
$461$	−6.87060			−0.319996			−0.159998	−	0.987117i	$-0.551149\pi$
$461$	−6.87060			−0.319996			−0.159998	+	0.987117i	$0.551149\pi$
$462$			27.5625i			1.28232i
$463$		−	31.2079i		−	1.45036i	−0.688562	−	0.725178i	$-0.741757\pi$
$463$		−	31.2079i		−	1.45036i	0.688562	−	0.725178i	$-0.258243\pi$
$464$	5.09785			0.236662
$465$	12.5208	−	16.6956i	0.580636	−	0.774238i
$466$	−20.7016			−0.958985
$467$			31.9659i			1.47921i	0.673044	+	0.739603i	$0.264987\pi$
$467$			31.9659i			1.47921i	−0.673044	+	0.739603i	$0.735013\pi$
$468$			6.11912i			0.282856i
$469$	6.14057			0.283545
$470$	17.4369	+	13.0768i	0.804306	+	0.603186i
$471$	−47.8020			−2.20260
$472$			2.12602i			0.0978581i
$473$		−	47.0907i		−	2.16523i
$474$	−29.8020			−1.36885
$475$	0.670965	+	2.29985i	0.0307860	+	0.105524i
$476$	5.89311			0.270110
$477$		−	11.6859i		−	0.535060i
$478$			17.6550i			0.807523i
$479$	29.6350			1.35406			0.677029	−	0.735957i	$-0.263267\pi$
$479$	29.6350			1.35406			0.677029	+	0.735957i	$0.263267\pi$
$480$	−4.48823	−	3.36592i	−0.204859	−	0.153633i
$481$	9.30014			0.424050
$482$			17.9663i			0.818344i
$483$		−	9.79062i		−	0.445489i
$484$	−11.7359			−0.533451
$485$	0.0529081	−	0.0705493i	0.00240243	−	0.00320348i
$486$	−22.3624			−1.01438
$487$			1.33968i			0.0607069i	0.999539	+	0.0303535i	$0.00966329\pi$
$487$			1.33968i			0.0607069i	−0.999539	+	0.0303535i	$0.990337\pi$
$488$		−	10.4209i		−	0.471734i
$489$	25.2091			1.14000
$490$	2.26968	−	3.02647i	0.102534	−	0.136722i
$491$	−30.7491			−1.38769			−0.693843	−	0.720126i	$-0.744084\pi$
$491$	−30.7491			−1.38769			−0.693843	+	0.720126i	$0.744084\pi$
$492$		−	14.0855i		−	0.635024i
$493$		−	13.0394i		−	0.587266i
$494$	−0.889890			−0.0400381
$495$	−28.1036	−	21.0762i	−1.26316	−	0.947304i
$496$	−3.71986			−0.167027
$497$			28.3266i			1.27062i
$498$		−	19.3673i		−	0.867869i
$499$	19.5845			0.876723			0.438361	−	0.898799i	$-0.355559\pi$
$499$	19.5845			0.876723			0.438361	+	0.898799i	$0.355559\pi$
$500$	−3.93437	+	10.4652i	−0.175951	+	0.468019i
$501$	−13.2647			−0.592622
$502$			4.19527i			0.187244i
$503$		−	6.31772i		−	0.281693i	−0.990031	−	0.140847i	$-0.955018\pi$
$503$		−	6.31772i		−	0.281693i	0.990031	−	0.140847i	$-0.0449825\pi$
$504$	7.59090			0.338126
$505$	−0.755203	−	0.566361i	−0.0336061	−	0.0252027i
$506$	8.07615			0.359029
$507$		−	23.9619i		−	1.06418i
$508$		−	14.7585i		−	0.654804i
$509$	−5.56460			−0.246647			−0.123323	−	0.992367i	$-0.539355\pi$
$509$	−5.56460			−0.246647			−0.123323	+	0.992367i	$0.539355\pi$
$510$	−8.60944	+	11.4801i	−0.381233	+	0.508347i
$511$	−33.2015			−1.46875
$512$			1.00000i			0.0441942i
$513$			0.354306i			0.0156430i
$514$	−27.6300			−1.21871
$515$	0.568869	−	0.758548i	0.0250674	−	0.0334256i
$516$	−24.7781			−1.09079
$517$		−	46.4772i		−	2.04407i
$518$		−	11.5370i		−	0.506908i
$519$	−33.1707			−1.45603
$520$	−3.32243	−	2.49164i	−0.145698	−	0.109266i
$521$	−34.8878			−1.52846			−0.764231	−	0.644943i	$-0.776881\pi$
$521$	−34.8878			−1.52846			−0.764231	+	0.644943i	$0.776881\pi$
$522$		−	16.7960i		−	0.735143i
$523$		−	20.9837i		−	0.917553i	−0.888552	−	0.458777i	$-0.848288\pi$
$523$		−	20.9837i		−	0.917553i	0.888552	−	0.458777i	$-0.151712\pi$
$524$	5.70591			0.249264
$525$	−8.09459	−	27.7456i	−0.353277	−	1.21092i
$526$	16.2930			0.710407
$527$			9.51474i			0.414469i
$528$			11.9631i			0.520628i
$529$	20.1312			0.875271
$530$	6.34496	+	4.75837i	0.275607	+	0.206690i
$531$	7.00466			0.303977
$532$			1.10393i			0.0478614i
$533$		−	10.4269i		−	0.451638i
$534$	−42.5563			−1.84159
$535$	4.25356	−	5.67183i	0.183897	−	0.245215i
$536$	2.66523			0.115120
$537$		−	2.17643i		−	0.0939200i
$538$			15.0945i			0.650772i
$539$	−8.06688			−0.347465
$540$	−0.992036	+	1.32281i	−0.0426904	+	0.0569248i
$541$	−42.4888			−1.82674			−0.913369	−	0.407133i	$-0.866529\pi$
$541$	−42.4888			−1.82674			−0.913369	+	0.407133i	$0.866529\pi$
$542$		−	3.63226i		−	0.156019i
$543$			16.8752i			0.724182i
$544$	2.55782			0.109666
$545$	−5.30530	−	3.97868i	−0.227254	−	0.170428i
$546$	10.7357			0.459447
$547$			4.24345i			0.181437i	0.995877	+	0.0907184i	$0.0289163\pi$
$547$			4.24345i			0.181437i	−0.995877	+	0.0907184i	$0.971084\pi$
$548$			17.2515i			0.736948i
$549$	−34.3342			−1.46535
$550$	22.8870	−	6.67712i	0.975904	−	0.284713i
$551$	2.44261			0.104059
$552$		−	4.24949i		−	0.180870i
$553$			27.3673i			1.16377i
$554$	21.6344			0.919156
$555$	22.4748	+	16.8548i	0.954001	+	0.715448i
$556$	0.897477			0.0380615
$557$			10.8691i			0.460539i	0.973127	+	0.230269i	$0.0739608\pi$
$557$			10.8691i			0.460539i	−0.973127	+	0.230269i	$0.926039\pi$
$558$			12.2559i			0.518835i
$559$	−18.3421			−0.775787
$560$	−3.09093	+	4.12154i	−0.130616	+	0.174167i
$561$	30.5996			1.29192
$562$		−	28.9477i		−	1.22109i
$563$			6.26672i			0.264111i	0.991242	+	0.132055i	$0.0421577\pi$
$563$			6.26672i			0.264111i	−0.991242	+	0.132055i	$0.957842\pi$
$564$	−24.4553			−1.02975
$565$	1.34158	−	1.78890i	0.0564406	−	0.0752597i
$566$	7.94805			0.334082
$567$			18.4983i			0.776856i
$568$			12.2948i			0.515877i
$569$	−41.1363			−1.72452			−0.862261	−	0.506463i	$-0.830953\pi$
$569$	−41.1363			−1.72452			−0.862261	+	0.506463i	$0.830953\pi$
$570$	−2.15051	−	1.61277i	−0.0900751	−	0.0675514i
$571$	−6.62270			−0.277151			−0.138576	−	0.990352i	$-0.544252\pi$
$571$	−6.62270			−0.277151			−0.138576	+	0.990352i	$0.544252\pi$
$572$			8.85575i			0.370278i
$573$			22.2524i			0.929607i
$574$	−12.9347			−0.539886
$575$	−8.12981	+	2.37182i	−0.339037	+	0.0989116i
$576$	3.29473			0.137280
$577$		−	21.9451i		−	0.913587i	−0.889573	−	0.456794i	$-0.848998\pi$
$577$		−	21.9451i		−	0.913587i	0.889573	−	0.456794i	$-0.151002\pi$
$578$			10.4575i			0.434976i
$579$	18.2333			0.757752
$580$	9.11956	+	6.83917i	0.378669	+	0.283981i
$581$	−17.7850			−0.737846
$582$			0.0989452i			0.00410141i
$583$		−	16.9121i		−	0.700429i
$584$	−14.4107			−0.596317
$585$	−8.20928	+	10.9465i	−0.339412	+	0.452582i
$586$	1.37126			0.0566463
$587$		−	24.9196i		−	1.02854i	−0.857628	−	0.514271i	$-0.828063\pi$
$587$		−	24.9196i		−	1.02854i	0.857628	−	0.514271i	$-0.171937\pi$
$588$			4.24461i			0.175045i
$589$	−1.78235			−0.0734405
$590$	−2.85222	+	3.80324i	−0.117424	+	0.156577i
$591$	−50.2915			−2.06872
$592$		−	5.00749i		−	0.205807i
$593$			3.51167i			0.144207i	0.997397	+	0.0721035i	$0.0229712\pi$
$593$			3.51167i			0.144207i	−0.997397	+	0.0721035i	$0.977029\pi$
$594$	3.52588			0.144669
$595$	10.5422	+	7.90606i	0.432188	+	0.324117i
$596$	19.3660			0.793262
$597$			54.1802i			2.21745i
$598$		−	3.14570i		−	0.128637i
$599$	−37.7300			−1.54161			−0.770804	−	0.637073i	$-0.780145\pi$
$599$	−37.7300			−1.54161			−0.770804	+	0.637073i	$0.780145\pi$
$600$	−3.51335	−	12.0426i	−0.143432	−	0.491638i
$601$	17.3754			0.708758			0.354379	−	0.935102i	$-0.384692\pi$
$601$	17.3754			0.708758			0.354379	+	0.935102i	$0.384692\pi$
$602$			22.7537i			0.927373i
$603$		−	8.78122i		−	0.357599i
$604$	10.0072			0.407186
$605$	−20.9944	−	15.7446i	−0.853544	−	0.640111i
$606$	1.05917			0.0430259
$607$			12.4194i			0.504089i	0.967716	+	0.252045i	$0.0811029\pi$
$607$			12.4194i			0.504089i	−0.967716	+	0.252045i	$0.918897\pi$
$608$			0.479145i			0.0194319i
$609$	−29.4679			−1.19410
$610$	13.9805	−	18.6420i	0.566054	−	0.754794i
$611$	−18.1031			−0.732374
$612$		−	8.42734i		−	0.340655i
$613$		−	25.2181i		−	1.01855i	−0.860604	−	0.509275i	$-0.829914\pi$
$613$		−	25.2181i		−	1.01855i	0.860604	−	0.509275i	$-0.170086\pi$
$614$	5.56841			0.224723
$615$	18.8968	−	25.1976i	0.761993	−	1.01607i
$616$	10.9858			0.442629
$617$			8.43253i			0.339481i	0.985489	+	0.169740i	$0.0542929\pi$
$617$			8.43253i			0.339481i	−0.985489	+	0.169740i	$0.945707\pi$
$618$			1.06386i			0.0427948i
$619$	11.4958			0.462054			0.231027	−	0.972947i	$-0.425791\pi$
$619$	11.4958			0.462054			0.231027	+	0.972947i	$0.425791\pi$
$620$	−6.65446	−	4.99048i	−0.267249	−	0.200422i
$621$	−1.25245			−0.0502590
$622$		−	9.97052i		−	0.399781i
$623$			39.0795i			1.56569i
$624$	4.65970			0.186537
$625$	−21.0781	+	13.4430i	−0.843124	+	0.537719i
$626$	−12.6094			−0.503973
$627$			5.73208i			0.228917i
$628$			19.0527i			0.760287i
$629$	−12.8083			−0.510700
$630$	13.5794	+	10.1838i	0.541015	+	0.405732i
$631$	32.6021			1.29787			0.648935	−	0.760844i	$-0.275215\pi$
$631$	32.6021			1.29787			0.648935	+	0.760844i	$0.275215\pi$
$632$			11.8784i			0.472497i
$633$			6.54025i			0.259952i
$634$	−10.6430			−0.422688
$635$	19.7997	−	26.4016i	0.785728	−	1.04771i
$636$	−8.89879			−0.352860
$637$			3.14209i			0.124494i
$638$		−	24.3077i		−	0.962350i
$639$	40.5080			1.60247
$640$	−1.34158	+	1.78890i	−0.0530305	+	0.0707125i
$641$	42.6947			1.68634			0.843169	−	0.537649i	$-0.180687\pi$
$641$	42.6947			1.68634			0.843169	+	0.537649i	$0.180687\pi$
$642$			7.95472i			0.313948i
$643$			2.12111i			0.0836484i	0.999125	+	0.0418242i	$0.0133169\pi$
$643$			2.12111i			0.0836484i	−0.999125	+	0.0418242i	$0.986683\pi$
$644$	−3.90231			−0.153773
$645$	−44.3255	−	33.2417i	−1.74532	−	1.30889i
$646$	1.22557			0.0482194
$647$		−	10.0240i		−	0.394083i	−0.980395	−	0.197041i	$-0.936867\pi$
$647$		−	10.0240i		−	0.394083i	0.980395	−	0.197041i	$-0.0631333\pi$
$648$			8.02895i			0.315407i
$649$	10.1373			0.397925
$650$	−2.60077	−	8.91460i	−0.102011	−	0.349659i
$651$	21.5025			0.842748
$652$		−	10.0478i		−	0.393501i
$653$		−	48.4997i		−	1.89794i	−0.315366	−	0.948970i	$-0.602127\pi$
$653$		−	48.4997i		−	1.89794i	0.315366	−	0.948970i	$-0.397873\pi$
$654$	7.44067			0.290953
$655$	10.2073	+	7.65492i	0.398833	+	0.299103i
$656$	−5.61415			−0.219196
$657$			47.4792i			1.85234i
$658$			22.4573i			0.875477i
$659$	−1.97417			−0.0769029			−0.0384514	−	0.999260i	$-0.512242\pi$
$659$	−1.97417			−0.0769029			−0.0384514	+	0.999260i	$0.512242\pi$
$660$	−16.0495	+	21.4009i	−0.624725	+	0.833027i
$661$	2.85831			0.111175			0.0555877	−	0.998454i	$-0.482297\pi$
$661$	2.85831			0.111175			0.0555877	+	0.998454i	$0.482297\pi$
$662$		−	6.53916i		−	0.254152i
$663$		−	11.9187i		−	0.462884i
$664$	−7.71935			−0.299569
$665$	−1.48101	+	1.97482i	−0.0574309	+	0.0765802i
$666$	−16.4983			−0.639297
$667$			8.63447i			0.334328i
$668$			5.28698i			0.204560i
$669$	−28.0200			−1.08332
$670$	4.76784	+	3.57562i	0.184198	+	0.138138i
$671$	−49.6893			−1.91824
$672$		−	5.78046i		−	0.222986i
$673$		−	27.9768i		−	1.07843i	−0.842169	−	0.539214i	$-0.818722\pi$
$673$		−	27.9768i		−	1.07843i	0.842169	−	0.539214i	$-0.181278\pi$
$674$	−10.6797			−0.411368
$675$	−3.54931	+	1.03549i	−0.136613	+	0.0398559i
$676$	−9.55064			−0.367332
$677$		−	38.9887i		−	1.49846i	−0.662310	−	0.749230i	$-0.730424\pi$
$677$		−	38.9887i		−	1.49846i	0.662310	−	0.749230i	$-0.269576\pi$
$678$			2.50893i			0.0963549i
$679$	0.0908615			0.00348694
$680$	4.57570	+	3.43152i	0.175470	+	0.131593i
$681$	−32.5270			−1.24644
$682$			17.7371i			0.679188i
$683$			15.5867i			0.596409i	0.954502	+	0.298204i	$0.0963877\pi$
$683$			15.5867i			0.596409i	−0.954502	+	0.298204i	$0.903612\pi$
$684$	1.57865			0.0603613
$685$	−23.1443	+	30.8613i	−0.884297	+	1.17915i
$686$	20.0255			0.764577
$687$		−	29.7607i		−	1.13544i
$688$			9.87595i			0.376517i
$689$	−6.58736			−0.250959
$690$	5.70102	−	7.60192i	0.217034	−	0.289400i
$691$	8.44876			0.321406			0.160703	−	0.987003i	$-0.448624\pi$
$691$	8.44876			0.321406			0.160703	+	0.987003i	$0.448624\pi$
$692$			13.2211i			0.502590i
$693$		−	36.1951i		−	1.37494i
$694$	9.70400			0.368359
$695$	1.60550	+	1.20404i	0.0609000	+	0.0456717i
$696$	−12.7902			−0.484810
$697$			14.3600i			0.543925i
$698$			7.19497i			0.272334i
$699$	51.9389			1.96451
$700$	−11.0587	+	3.22631i	−0.417981	+	0.121943i
$701$	49.5632			1.87197			0.935987	−	0.352034i	$-0.114510\pi$
$701$	49.5632			1.87197			0.935987	+	0.352034i	$0.114510\pi$
$702$		−	1.37335i		−	0.0518337i
$703$		−	2.39932i		−	0.0904919i
$704$	4.76822			0.179709
$705$	−43.7481	−	32.8086i	−1.64765	−	1.23565i
$706$	−21.2202			−0.798632
$707$		−	0.972638i		−	0.0365798i
$708$		−	5.33404i		−	0.200465i
$709$	4.70375			0.176653			0.0883265	−	0.996092i	$-0.471848\pi$
$709$	4.70375			0.176653			0.0883265	+	0.996092i	$0.471848\pi$
$710$	−16.4944	+	21.9941i	−0.619024	+	0.825426i
$711$	39.1361			1.46772
$712$			16.9619i			0.635676i
$713$		−	6.30049i		−	0.235955i
$714$	−14.7854			−0.553329
$715$	−11.8807	+	15.8421i	−0.444312	+	0.592460i
$716$	−0.867474			−0.0324190
$717$		−	44.2953i		−	1.65424i
$718$			2.67324i			0.0997645i
$719$	19.3337			0.721025			0.360513	−	0.932754i	$-0.382602\pi$
$719$	19.3337			0.721025			0.360513	+	0.932754i	$0.382602\pi$
$720$	5.89395	+	4.42014i	0.219654	+	0.164729i
$721$	0.976945			0.0363833
$722$		−	18.7704i		−	0.698563i
$723$		−	45.0762i		−	1.67640i
$724$	6.72604			0.249971
$725$	7.13872	+	24.4692i	0.265125	+	0.908763i
$726$	29.4446			1.09279
$727$		−	23.6982i		−	0.878919i	−0.898262	−	0.439459i	$-0.855170\pi$
$727$		−	23.6982i		−	0.878919i	0.898262	−	0.439459i	$-0.144830\pi$
$728$		−	4.27901i		−	0.158591i
$729$	32.0189			1.18589
$730$	−25.7792	−	19.3330i	−0.954133	−	0.715547i
$731$	25.2610			0.934310
$732$			26.1454i			0.966362i
$733$			46.3571i			1.71224i	0.516779	+	0.856119i	$0.327131\pi$
$733$			46.3571i			1.71224i	−0.516779	+	0.856119i	$0.672869\pi$
$734$	−13.5615			−0.500565
$735$	−5.69448	+	7.59319i	−0.210044	+	0.280079i
$736$	−1.69375			−0.0624323
$737$		−	12.7084i		−	0.468120i
$738$			18.4971i			0.680888i
$739$	17.0783			0.628236			0.314118	−	0.949384i	$-0.398291\pi$
$739$	17.0783			0.628236			0.314118	+	0.949384i	$0.398291\pi$
$740$	6.71794	−	8.95791i	0.246956	−	0.329299i
$741$	2.23267			0.0820193
$742$			8.17177i			0.299995i
$743$		−	23.0830i		−	0.846833i	−0.905935	−	0.423416i	$-0.860831\pi$
$743$		−	23.0830i		−	0.846833i	0.905935	−	0.423416i	$-0.139169\pi$
$744$	9.33286			0.342159
$745$	34.6438	+	25.9810i	1.26925	+	0.951870i
$746$	10.8753			0.398174
$747$			25.4332i			0.930550i
$748$		−	12.1963i		−	0.445940i
$749$	7.30483			0.266913
$750$	9.87107	−	26.2565i	0.360441	−	0.958751i
$751$	35.8886			1.30959			0.654796	−	0.755805i	$-0.272754\pi$
$751$	35.8886			1.30959			0.654796	+	0.755805i	$0.272754\pi$
$752$			9.74729i			0.355447i
$753$		−	10.5256i		−	0.383576i
$754$	−9.46797			−0.344803
$755$	17.9018	+	13.4254i	0.651514	+	0.488600i
$756$	−1.70367			−0.0619618
$757$		−	39.4094i		−	1.43236i	−0.697917	−	0.716179i	$-0.745890\pi$
$757$		−	39.4094i		−	1.43236i	0.697917	−	0.716179i	$-0.254110\pi$
$758$			10.1131i			0.367324i
$759$	−20.2625			−0.735482
$760$	−0.642811	+	0.857144i	−0.0233172	+	0.0310919i
$761$	−40.7642			−1.47770			−0.738851	−	0.673869i	$-0.764631\pi$
$761$	−40.7642			−1.47770			−0.738851	+	0.673869i	$0.764631\pi$
$762$			37.0281i			1.34139i
$763$		−	6.83277i		−	0.247363i
$764$	8.86928			0.320879
$765$	11.3059	−	15.0757i	0.408767	−	0.545062i
$766$	34.1697			1.23460
$767$		−	3.94854i		−	0.142574i
$768$		−	2.50893i		−	0.0905332i
$769$	9.91009			0.357367			0.178683	−	0.983907i	$-0.442816\pi$
$769$	9.91009			0.357367			0.178683	+	0.983907i	$0.442816\pi$
$770$	19.6524	+	14.7382i	0.708224	+	0.531129i
$771$	69.3217			2.49656
$772$		−	7.26738i		−	0.261559i
$773$			16.0461i			0.577137i	0.957459	+	0.288569i	$0.0931793\pi$
$773$			16.0461i			0.577137i	−0.957459	+	0.288569i	$0.906821\pi$
$774$	32.5386			1.16958
$775$	−5.20906	−	17.8549i	−0.187115	−	0.641369i
$776$	0.0394372			0.00141571
$777$			28.9456i			1.03842i
$778$			29.6193i			1.06190i
$779$	−2.69000			−0.0963791
$780$	8.33574	+	6.25135i	0.298467	+	0.223834i
$781$	58.6242			2.09774
$782$			4.33231i			0.154923i
$783$			3.76963i			0.134716i
$784$	1.69180			0.0604215
$785$	−25.5607	+	34.0835i	−0.912302	+	1.21649i
$786$	−14.3157			−0.510625
$787$			27.2678i			0.971993i	0.873961	+	0.485996i	$0.161543\pi$
$787$			27.2678i			0.971993i	−0.873961	+	0.485996i	$0.838457\pi$
$788$			20.0450i			0.714074i
$789$	−40.8779			−1.45529
$790$	−15.9358	+	21.2493i	−0.566970	+	0.756015i
$791$	2.30395			0.0819191
$792$		−	15.7100i		−	0.558230i
$793$			19.3543i			0.687290i
$794$	−31.0048			−1.10032
$795$	−15.9191	−	11.9384i	−0.564591	−	0.423412i
$796$	21.5949			0.765412
$797$		−	2.77006i		−	0.0981207i	−0.998796	−	0.0490603i	$-0.984377\pi$
$797$		−	2.77006i		−	0.0981207i	0.998796	−	0.0490603i	$-0.0156227\pi$
$798$		−	2.76968i		−	0.0980455i
$799$	24.9319			0.882026
$800$	−4.79990	+	1.40034i	−0.169702	+	0.0495094i
$801$	55.8850			1.97460
$802$		−	30.5717i		−	1.07953i
$803$			68.7132i			2.42484i
$804$	−6.68688			−0.235828
$805$	−6.98085	−	5.23525i	−0.246043	−	0.184518i
$806$	6.90869			0.243348
$807$		−	37.8711i		−	1.33313i
$808$		−	0.422160i		−	0.0148516i
$809$	26.1848			0.920608			0.460304	−	0.887761i	$-0.347740\pi$
$809$	26.1848			0.920608			0.460304	+	0.887761i	$0.347740\pi$
$810$	−10.7715	+	14.3630i	−0.378470	+	0.504664i
$811$	−38.2565			−1.34337			−0.671683	−	0.740839i	$-0.734428\pi$
$811$	−38.2565			−1.34337			−0.671683	+	0.740839i	$0.734428\pi$
$812$			11.7452i			0.412176i
$813$			9.11308i			0.319610i
$814$	−23.8768			−0.836882
$815$	13.4798	−	17.9744i	0.472178	−	0.629617i
$816$	−6.41740			−0.224654
$817$			4.73202i			0.165552i
$818$		−	4.17007i		−	0.145803i
$819$	−14.0982			−0.492630
$820$	−10.0432	−	7.53182i	−0.350723	−	0.263023i
$821$	33.1052			1.15538			0.577689	−	0.816257i	$-0.303955\pi$
$821$	33.1052			1.15538			0.577689	+	0.816257i	$0.303955\pi$
$822$		−	43.2829i		−	1.50966i
$823$		−	7.51880i		−	0.262089i	−0.991376	−	0.131044i	$-0.958167\pi$
$823$		−	7.51880i		−	0.262089i	0.991376	−	0.131044i	$-0.0418331\pi$
$824$	0.424030			0.0147718
$825$	−57.4218	+	16.7524i	−1.99917	+	0.583244i
$826$	−4.89825			−0.170432
$827$			43.1094i			1.49906i	0.661971	+	0.749530i	$0.269720\pi$
$827$			43.1094i			1.49906i	−0.661971	+	0.749530i	$0.730280\pi$
$828$			5.58043i			0.193933i
$829$	0.641055			0.0222648			0.0111324	−	0.999938i	$-0.496456\pi$
$829$	0.641055			0.0222648			0.0111324	+	0.999938i	$0.496456\pi$
$830$	−13.8091	−	10.3561i	−0.479323	−	0.359466i
$831$	−54.2791			−1.88292
$832$		−	1.85725i		−	0.0643884i
$833$		−	4.32733i		−	0.149933i
$834$	−2.25171			−0.0779702
$835$	−7.09290	+	9.45790i	−0.245460	+	0.327304i
$836$	2.28467			0.0790170
$837$		−	2.75067i		−	0.0950769i
$838$		−	6.41811i		−	0.221710i
$839$	43.6243			1.50608			0.753039	−	0.657976i	$-0.228587\pi$
$839$	43.6243			1.50608			0.753039	+	0.657976i	$0.228587\pi$
$840$	7.75493	−	10.3407i	0.267571	−	0.356787i
$841$	−3.01189			−0.103858
$842$			1.86834i			0.0643871i
$843$			72.6278i			2.50143i
$844$	2.60679			0.0897293
$845$	−17.0852	−	12.8129i	−0.587747	−	0.440778i
$846$	32.1147			1.10413
$847$		−	27.0390i		−	0.929071i
$848$			3.54685i			0.121799i
$849$	−19.9411			−0.684377
$850$	3.58182	+	12.2773i	0.122855	+	0.421108i
$851$	8.48142			0.290739
$852$		−	30.8467i		−	1.05679i
$853$		−	2.45105i		−	0.0839223i	−0.999119	−	0.0419612i	$-0.986639\pi$
$853$		−	2.45105i		−	0.0839223i	0.999119	−	0.0419612i	$-0.0133606\pi$
$854$	24.0094			0.821583
$855$	2.82406	+	2.11789i	0.0965807	+	0.0724302i
$856$	3.17056			0.108368
$857$			50.4755i			1.72421i	0.506730	+	0.862105i	$0.330854\pi$
$857$			50.4755i			1.72421i	−0.506730	+	0.862105i	$0.669146\pi$
$858$		−	22.2185i		−	0.758526i
$859$	5.47938			0.186954			0.0934770	−	0.995621i	$-0.470202\pi$
$859$	5.47938			0.186954			0.0934770	+	0.995621i	$0.470202\pi$
$860$	−13.2494	+	17.6671i	−0.451799	+	0.602443i
$861$	32.4524			1.10597
$862$		−	37.9214i		−	1.29161i
$863$			20.1024i			0.684295i	0.939646	+	0.342147i	$0.111154\pi$
$863$			20.1024i			0.684295i	−0.939646	+	0.342147i	$0.888846\pi$
$864$	−0.739455			−0.0251568
$865$	−17.7371	+	23.6512i	−0.603079	+	0.804165i
$866$	−2.34310			−0.0796217
$867$		−	26.2372i		−	0.891063i
$868$		−	8.57038i		−	0.290897i
$869$	56.6388			1.92134
$870$	−22.8803	−	17.1590i	−0.775716	−	0.581744i
$871$	−4.94999			−0.167724
$872$		−	2.96567i		−	0.100430i
$873$		−	0.129935i		−	0.00439763i
$874$	−0.811550			−0.0274511
$875$	−24.1114	−	9.06461i	−0.815113	−	0.306440i
$876$	36.1553			1.22158
$877$		−	5.22446i		−	0.176418i	−0.996102	−	0.0882088i	$-0.971886\pi$
$877$		−	5.22446i		−	0.176418i	0.996102	−	0.0882088i	$-0.0281143\pi$
$878$		−	9.41453i		−	0.317725i
$879$	−3.44040			−0.116042
$880$	8.52988	+	6.39694i	0.287542	+	0.215641i
$881$	−54.2428			−1.82749			−0.913743	−	0.406294i	$-0.866821\pi$
$881$	−54.2428			−1.82749			−0.913743	+	0.406294i	$0.866821\pi$
$882$		−	5.57403i		−	0.187687i
$883$			44.5642i			1.49971i	0.661605	+	0.749853i	$0.269876\pi$
$883$			44.5642i			1.49971i	−0.661605	+	0.749853i	$0.730124\pi$
$884$	−4.75051			−0.159777
$885$	7.15603	−	9.54207i	0.240547	−	0.320753i
$886$	3.64970			0.122614
$887$			18.5299i			0.622174i	0.950381	+	0.311087i	$0.100693\pi$
$887$			18.5299i			0.622174i	−0.950381	+	0.311087i	$0.899307\pi$
$888$			12.5634i			0.421602i
$889$	34.0029			1.14042
$890$	−22.7558	+	30.3432i	−0.762775	+	1.01711i
$891$	38.2838			1.28255
$892$			11.1681i			0.373936i
$893$			4.67037i			0.156288i
$894$	−48.5879			−1.62502
$895$	−1.55183	−	1.16378i	−0.0518718	−	0.0389010i
$896$	−2.30395			−0.0769697
$897$			7.89235i			0.263518i
$898$		−	38.9801i		−	1.30078i
$899$	−18.9633			−0.632461
$900$	4.61373	+	15.8144i	0.153791	+	0.527146i
$901$	9.07221			0.302239
$902$			26.7695i			0.891327i
$903$		−	57.0875i		−	1.89975i
$904$	1.00000			0.0332595
$905$	12.0322	+	9.02350i	0.399964	+	0.299951i
$906$	−25.1073			−0.834133
$907$		−	33.1370i		−	1.10030i	−0.835067	−	0.550148i	$-0.814571\pi$
$907$		−	33.1370i		−	1.10030i	0.835067	−	0.550148i	$-0.185429\pi$
$908$			12.9645i			0.430242i
$909$	−1.39090			−0.0461334
$910$	5.74062	−	7.65472i	0.190300	−	0.253752i
$911$	21.1104			0.699420			0.349710	−	0.936858i	$-0.386280\pi$
$911$	21.1104			0.699420			0.349710	+	0.936858i	$0.386280\pi$
$912$		−	1.20214i		−	0.0398069i
$913$			36.8075i			1.21815i
$914$	−13.0967			−0.433201
$915$	−35.0761	+	46.7716i	−1.15958	+	1.54622i
$916$	−11.8619			−0.391929
$917$			13.1461i			0.434124i
$918$			1.89140i			0.0624254i
$919$	−38.5807			−1.27266			−0.636330	−	0.771417i	$-0.719549\pi$
$919$	−38.5807			−1.27266			−0.636330	+	0.771417i	$0.719549\pi$
$920$	−3.02994	−	2.27229i	−0.0998943	−	0.0749152i
$921$	−13.9707			−0.460352
$922$		−	6.87060i		−	0.226271i
$923$		−	22.8344i		−	0.751604i
$924$	−27.5625			−0.906739
$925$	24.0355	−	7.01218i	0.790281	−	0.230559i
$926$	31.2079			1.02556
$927$		−	1.39706i		−	0.0458856i
$928$			5.09785i			0.167345i
$929$	54.6796			1.79398			0.896990	−	0.442050i	$-0.145749\pi$
$929$	54.6796			1.79398			0.896990	+	0.442050i	$0.145749\pi$
$930$	16.6956	+	12.5208i	0.547469	+	0.410572i
$931$	0.810619			0.0265669
$932$		−	20.7016i		−	0.678105i
$933$			25.0153i			0.818965i
$934$	−31.9659			−1.04596
$935$	16.3622	−	21.8179i	0.535103	−	0.713522i
$936$	−6.11912			−0.200010
$937$			51.3254i			1.67673i	0.545110	+	0.838364i	$0.316488\pi$
$937$			51.3254i			1.67673i	−0.545110	+	0.838364i	$0.683512\pi$
$938$			6.14057i			0.200497i
$939$	31.6361			1.03241
$940$	−13.0768	+	17.4369i	−0.426517	+	0.568730i
$941$	38.0874			1.24161			0.620807	−	0.783964i	$-0.286805\pi$
$941$	38.0874			1.24161			0.620807	+	0.783964i	$0.286805\pi$
$942$		−	47.8020i		−	1.55747i
$943$		−	9.50895i		−	0.309654i
$944$	−2.12602			−0.0691961
$945$	−3.04770	−	2.28560i	−0.0991416	−	0.0743507i
$946$	47.0907			1.53105
$947$		−	18.3160i		−	0.595191i	−0.954692	−	0.297596i	$-0.903815\pi$
$947$		−	18.3160i		−	0.595191i	0.954692	−	0.297596i	$-0.0961847\pi$
$948$		−	29.8020i		−	0.967926i
$949$	26.7641			0.868800
$950$	−2.29985	+	0.670965i	−0.0746170	+	0.0217690i
$951$	26.7026			0.865890
$952$			5.89311i			0.190997i
$953$			15.7776i			0.511088i	0.966797	+	0.255544i	$0.0822545\pi$
$953$			15.7776i			0.511088i	−0.966797	+	0.255544i	$0.917746\pi$
$954$	11.6859			0.378345
$955$	15.8663	+	11.8988i	0.513420	+	0.385037i
$956$	−17.6550			−0.571005
$957$			60.9863i			1.97141i
$958$			29.6350i			0.957463i
$959$	−39.7467			−1.28349
$960$	3.36592	−	4.48823i	0.108635	−	0.144857i
$961$	−17.1627			−0.553634
$962$			9.30014i			0.299849i
$963$		−	10.4462i		−	0.336623i
$964$	−17.9663			−0.578656
$965$	9.74975	−	13.0006i	0.313856	−	0.418505i
$966$	9.79062			0.315008
$967$			17.6418i			0.567322i	0.958925	+	0.283661i	$0.0915490\pi$
$967$			17.6418i			0.567322i	−0.958925	+	0.283661i	$0.908451\pi$
$968$		−	11.7359i		−	0.377207i
$969$	−3.07487			−0.0987790
$970$	0.0705493	+	0.0529081i	0.00226520	+	0.00169878i
$971$	38.4300			1.23328			0.616638	−	0.787247i	$-0.288494\pi$
$971$	38.4300			1.23328			0.616638	+	0.787247i	$0.288494\pi$
$972$		−	22.3624i		−	0.717275i
$973$			2.06774i			0.0662889i
$974$	−1.33968			−0.0429263
$975$	6.52515	+	22.3661i	0.208972	+	0.716288i
$976$	10.4209			0.333566
$977$		−	21.5091i		−	0.688137i	−0.938945	−	0.344069i	$-0.888195\pi$
$977$		−	21.5091i		−	0.688137i	0.938945	−	0.344069i	$-0.111805\pi$
$978$			25.2091i			0.806099i
$979$	80.8783			2.58488
$980$	3.02647	+	2.26968i	0.0966769	+	0.0725024i
$981$	−9.77109			−0.311967
$982$		−	30.7491i		−	0.981243i
$983$		−	54.6053i		−	1.74164i	−0.491603	−	0.870819i	$-0.663589\pi$
$983$		−	54.6053i		−	1.74164i	0.491603	−	0.870819i	$-0.336411\pi$
$984$	14.0855			0.449030
$985$	−26.8920	+	35.8586i	−0.856849	+	1.14255i
$986$	13.0394			0.415260
$987$		−	56.3438i		−	1.79344i
$988$		−	0.889890i		−	0.0283112i
$989$	−16.7274			−0.531899
$990$	21.0762	−	28.1036i	0.669845	−	0.893192i
$991$	−38.4824			−1.22243			−0.611216	−	0.791464i	$-0.709319\pi$
$991$	−38.4824			−1.22243			−0.611216	+	0.791464i	$0.709319\pi$
$992$		−	3.71986i		−	0.118106i
$993$			16.4063i			0.520638i
$994$	−28.3266			−0.898465
$995$	38.6312	+	28.9713i	1.22469	+	0.918452i
$996$	19.3673			0.613676
$997$		−	9.47756i		−	0.300157i	−0.988674	−	0.150079i	$-0.952047\pi$
$997$		−	9.47756i		−	0.300157i	0.988674	−	0.150079i	$-0.0479527\pi$
$998$			19.5845i			0.619937i
$999$	3.70281			0.117152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1130.2.b.c.679.12	yes	22
5.2	odd	4		5650.2.a.ba.1.1		11
5.3	odd	4		5650.2.a.bb.1.11		11
5.4	even	2	inner	1130.2.b.c.679.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1130.2.b.c.679.11	✓	22	5.4	even	2	inner
1130.2.b.c.679.12	yes	22	1.1	even	1	trivial
5650.2.a.ba.1.1		11	5.2	odd	4
5650.2.a.bb.1.11		11	5.3	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:	\( N \)	\(=\)	\( 1130 = 2 \cdot 5 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1130.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.50893i q^{3} -1.00000 q^{4} +(-1.78890 - 1.34158i) q^{5} +2.50893 q^{6} -2.30395i q^{7} -1.00000i q^{8} -3.29473 q^{9} +(1.34158 - 1.78890i) q^{10} -4.76822 q^{11} +2.50893i q^{12} +1.85725i q^{13} +2.30395 q^{14} +(-3.36592 + 4.48823i) q^{15} +1.00000 q^{16} -2.55782i q^{17} -3.29473i q^{18} +0.479145 q^{19} +(1.78890 + 1.34158i) q^{20} -5.78046 q^{21} -4.76822i q^{22} +1.69375i q^{23} -2.50893 q^{24} +(1.40034 + 4.79990i) q^{25} -1.85725 q^{26} +0.739455i q^{27} +2.30395i q^{28} +5.09785 q^{29} +(-4.48823 - 3.36592i) q^{30} -3.71986 q^{31} +1.00000i q^{32} +11.9631i q^{33} +2.55782 q^{34} +(-3.09093 + 4.12154i) q^{35} +3.29473 q^{36} -5.00749i q^{37} +0.479145i q^{38} +4.65970 q^{39} +(-1.34158 + 1.78890i) q^{40} -5.61415 q^{41} -5.78046i q^{42} +9.87595i q^{43} +4.76822 q^{44} +(5.89395 + 4.42014i) q^{45} -1.69375 q^{46} +9.74729i q^{47} -2.50893i q^{48} +1.69180 q^{49} +(-4.79990 + 1.40034i) q^{50} -6.41740 q^{51} -1.85725i q^{52} +3.54685i q^{53} -0.739455 q^{54} +(8.52988 + 6.39694i) q^{55} -2.30395 q^{56} -1.20214i q^{57} +5.09785i q^{58} -2.12602 q^{59} +(3.36592 - 4.48823i) q^{60} +10.4209 q^{61} -3.71986i q^{62} +7.59090i q^{63} -1.00000 q^{64} +(2.49164 - 3.32243i) q^{65} -11.9631 q^{66} +2.66523i q^{67} +2.55782i q^{68} +4.24949 q^{69} +(-4.12154 - 3.09093i) q^{70} -12.2948 q^{71} +3.29473i q^{72} -14.4107i q^{73} +5.00749 q^{74} +(12.0426 - 3.51335i) q^{75} -0.479145 q^{76} +10.9858i q^{77} +4.65970i q^{78} -11.8784 q^{79} +(-1.78890 - 1.34158i) q^{80} -8.02895 q^{81} -5.61415i q^{82} -7.71935i q^{83} +5.78046 q^{84} +(-3.43152 + 4.57570i) q^{85} -9.87595 q^{86} -12.7902i q^{87} +4.76822i q^{88} -16.9619 q^{89} +(-4.42014 + 5.89395i) q^{90} +4.27901 q^{91} -1.69375i q^{92} +9.33286i q^{93} -9.74729 q^{94} +(-0.857144 - 0.642811i) q^{95} +2.50893 q^{96} +0.0394372i q^{97} +1.69180i q^{98} +15.7100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{4} - 6 q^{5} - 6 q^{6} - 8 q^{9} - 4 q^{10} - 34 q^{11} + 6 q^{14} - 8 q^{15} + 22 q^{16} + 28 q^{19} + 6 q^{20} - 28 q^{21} + 6 q^{24} - 10 q^{25} - 30 q^{26} + 30 q^{29} + 2 q^{30} - 28 q^{31}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - 22 * q^4 - 6 * q^5 - 6 * q^6 - 8 * q^9 - 4 * q^10 - 34 * q^11 + 6 * q^14 - 8 * q^15 + 22 * q^16 + 28 * q^19 + 6 * q^20 - 28 * q^21 + 6 * q^24 - 10 * q^25 - 30 * q^26 + 30 * q^29 + 2 * q^30 - 28 * q^31 + 2 * q^34 - 4 * q^35 + 8 * q^36 + 52 * q^39 + 4 * q^40 - 78 * q^41 + 34 * q^44 - 12 * q^45 + 4 * q^46 - 12 * q^49 - 8 * q^50 - 32 * q^51 + 12 * q^54 + 6 * q^55 - 6 * q^56 + 64 * q^59 + 8 * q^60 - 72 * q^61 - 22 * q^64 + 8 * q^65 - 20 * q^66 + 24 * q^69 + 26 * q^70 - 66 * q^71 + 36 * q^74 + 20 * q^75 - 28 * q^76 + 10 * q^79 - 6 * q^80 - 66 * q^81 + 28 * q^84 + 48 * q^85 - 26 * q^86 + 88 * q^89 + 32 * q^90 - 68 * q^91 - 76 * q^94 + 4 * q^95 - 6 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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