LMFDB - Embedded newform 483.2.h.c.160.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 $ x^12 + 17x^10 + 92x^8 + 180x^6 + 92x^4 + 17*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.4
Root			$2.92914i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.c.160.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} -6.97756 q^{10} +3.13874i q^{11} +5.27053i q^{12} +4.69639i q^{13} +(-1.48573 - 6.97756i) q^{14} +2.58774i q^{15} +13.2375 q^{16} -6.97756 q^{17} +2.69639 q^{18} +3.13874 q^{19} +13.6388 q^{20} +(-2.58774 + 0.551006i) q^{21} -8.46329i q^{22} +(-1.27053 - 4.62447i) q^{23} -8.81864i q^{24} +1.69639 q^{25} -12.6633i q^{26} -1.00000i q^{27} +(2.90409 + 13.6388i) q^{28} +3.96693 q^{29} -6.97756i q^{30} -2.57414i q^{31} -18.0561 q^{32} -3.13874 q^{33} +18.8142 q^{34} +(1.42586 + 6.69639i) q^{35} -5.27053 q^{36} -2.90409i q^{37} -8.46329 q^{38} -4.69639 q^{39} -22.8203 q^{40} +5.00000i q^{41} +(6.97756 - 1.48573i) q^{42} -0.785656i q^{43} +16.5429i q^{44} -2.58774 q^{45} +(3.42586 + 12.4694i) q^{46} +12.3597i q^{47} +13.2375i q^{48} +(-6.39279 + 2.85172i) q^{49} -4.57414 q^{50} -6.97756i q^{51} +24.7525i q^{52} -7.52857i q^{53} +2.69639i q^{54} +8.12225i q^{55} +(-4.85912 - 22.8203i) q^{56} +3.13874i q^{57} -10.6964 q^{58} -3.15532i q^{59} +13.6388i q^{60} -8.22864 q^{61} +6.94090i q^{62} +(-0.551006 - 2.58774i) q^{63} +22.2114 q^{64} +12.1530i q^{65} +8.46329 q^{66} -7.76322i q^{67} -36.7755 q^{68} +(4.62447 - 1.27053i) q^{69} +(-3.84468 - 18.0561i) q^{70} +9.23746 q^{71} +8.81864 q^{72} +9.65628i q^{73} +7.83058i q^{74} +1.69639i q^{75} +16.5429 q^{76} +(-8.12225 + 1.72947i) q^{77} +12.6633 q^{78} -1.50395i q^{79} +34.2551 q^{80} +1.00000 q^{81} -13.4820i q^{82} +15.7572 q^{83} +(-13.6388 + 2.90409i) q^{84} -18.0561 q^{85} +2.11844i q^{86} +3.96693i q^{87} -27.6795i q^{88} +2.18580 q^{89} +6.97756 q^{90} +(-12.1530 + 2.58774i) q^{91} +(-6.69639 - 24.3734i) q^{92} +2.57414 q^{93} -33.3266i q^{94} +8.12225 q^{95} -18.0561i q^{96} -7.74499 q^{97} +(17.2375 - 7.68935i) q^{98} -3.13874i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9	$ 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−2.69639			−1.90664			−0.953319	−	0.301966i	$-0.902357\pi$
$2$	−2.69639			−1.90664			−0.953319	+	0.301966i	$0.902357\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	5.27053			2.63527
$5$	2.58774			1.15727			0.578636	−	0.815586i	$-0.303585\pi$
$5$	2.58774			1.15727			0.578636	+	0.815586i	$0.303585\pi$
$6$		−	2.69639i		−	1.10080i
$7$	0.551006	+	2.58774i	0.208261	+	0.978073i
$7$	0.551006	+	2.58774i	0.208261	+	0.978073i
$8$	−8.81864			−3.11786
$9$	−1.00000			−0.333333
$10$	−6.97756			−2.20650
$11$			3.13874i			0.946367i	0.880964	+	0.473184i	$0.156895\pi$
$11$			3.13874i			0.946367i	−0.880964	+	0.473184i	$0.843105\pi$
$12$			5.27053i			1.52147i
$13$			4.69639i			1.30254i	0.758844	+	0.651272i	$0.225765\pi$
$13$			4.69639i			1.30254i	−0.758844	+	0.651272i	$0.774235\pi$
$14$	−1.48573	−	6.97756i	−0.397077	−	1.86483i
$15$			2.58774i			0.668151i
$16$	13.2375			3.30937
$17$	−6.97756			−1.69231			−0.846154	−	0.532939i	$-0.821087\pi$
$17$	−6.97756			−1.69231			−0.846154	+	0.532939i	$0.821087\pi$
$18$	2.69639			0.635546
$19$	3.13874			0.720077			0.360039	−	0.932937i	$-0.382763\pi$
$19$	3.13874			0.720077			0.360039	+	0.932937i	$0.382763\pi$
$20$	13.6388			3.04972
$21$	−2.58774	+	0.551006i	−0.564691	+	0.120239i
$22$		−	8.46329i		−	1.80438i
$23$	−1.27053	−	4.62447i	−0.264925	−	0.964269i
$23$	−1.27053	−	4.62447i	−0.264925	−	0.964269i
$24$		−	8.81864i		−	1.80010i
$25$	1.69639			0.339279
$26$		−	12.6633i		−	2.48348i
$27$		−	1.00000i		−	0.192450i
$28$	2.90409	+	13.6388i	0.548822	+	2.57748i
$29$	3.96693			0.736640			0.368320	−	0.929699i	$-0.379933\pi$
$29$	3.96693			0.736640			0.368320	+	0.929699i	$0.379933\pi$
$30$		−	6.97756i		−	1.27392i
$31$		−	2.57414i		−	0.462329i	−0.972915	−	0.231165i	$-0.925746\pi$
$31$		−	2.57414i		−	0.462329i	0.972915	−	0.231165i	$-0.0742536\pi$
$32$	−18.0561			−3.19190
$33$	−3.13874			−0.546385
$34$	18.8142			3.22662
$35$	1.42586	+	6.69639i	0.241014	+	1.13190i
$36$	−5.27053			−0.878422
$37$		−	2.90409i		−	0.477430i	−0.971090	−	0.238715i	$-0.923274\pi$
$37$		−	2.90409i		−	0.477430i	0.971090	−	0.238715i	$-0.0767262\pi$
$38$	−8.46329			−1.37293
$39$	−4.69639			−0.752025
$40$	−22.8203			−3.60821
$41$			5.00000i			0.780869i	0.920631	+	0.390434i	$0.127675\pi$
$41$			5.00000i			0.780869i	−0.920631	+	0.390434i	$0.872325\pi$
$42$	6.97756	−	1.48573i	1.07666	−	0.229253i
$43$		−	0.785656i		−	0.119811i	−0.998204	−	0.0599057i	$-0.980920\pi$
$43$		−	0.785656i		−	0.119811i	0.998204	−	0.0599057i	$-0.0190800\pi$
$44$			16.5429i			2.49393i
$45$	−2.58774			−0.385757
$46$	3.42586	+	12.4694i	0.505115	+	1.83851i
$47$			12.3597i			1.80285i	0.432936	+	0.901425i	$0.357478\pi$
$47$			12.3597i			1.80285i	−0.432936	+	0.901425i	$0.642522\pi$
$48$			13.2375i			1.91066i
$49$	−6.39279	+	2.85172i	−0.913255	+	0.407388i
$50$	−4.57414			−0.646881
$51$		−	6.97756i		−	0.977054i
$52$			24.7525i			3.43255i
$53$		−	7.52857i		−	1.03413i	−0.855947	−	0.517064i	$-0.827025\pi$
$53$		−	7.52857i		−	1.03413i	0.855947	−	0.517064i	$-0.172975\pi$
$54$			2.69639i			0.366933i
$55$			8.12225i			1.09520i
$56$	−4.85912	−	22.8203i	−0.649328	−	3.04950i
$57$			3.13874i			0.415737i
$58$	−10.6964			−1.40451
$59$		−	3.15532i		−	0.410788i	−0.978679	−	0.205394i	$-0.934152\pi$
$59$		−	3.15532i		−	0.410788i	0.978679	−	0.205394i	$-0.0658476\pi$
$60$			13.6388i			1.76076i
$61$	−8.22864			−1.05357			−0.526785	−	0.849999i	$-0.676603\pi$
$61$	−8.22864			−1.05357			−0.526785	+	0.849999i	$0.676603\pi$
$62$			6.94090i			0.881495i
$63$	−0.551006	−	2.58774i	−0.0694202	−	0.326024i
$64$	22.2114			2.77643
$65$			12.1530i			1.50740i
$66$	8.46329			1.04176
$67$		−	7.76322i		−	0.948428i	−0.880410	−	0.474214i	$-0.842732\pi$
$67$		−	7.76322i		−	0.948428i	0.880410	−	0.474214i	$-0.157268\pi$
$68$	−36.7755			−4.45968
$69$	4.62447	−	1.27053i	0.556721	−	0.152954i
$70$	−3.84468	−	18.0561i	−0.459527	−	2.15812i
$71$	9.23746			1.09628			0.548142	−	0.836385i	$-0.315335\pi$
$71$	9.23746			1.09628			0.548142	+	0.836385i	$0.315335\pi$
$72$	8.81864			1.03929
$73$			9.65628i			1.13018i	0.825029	+	0.565091i	$0.191159\pi$
$73$			9.65628i			1.13018i	−0.825029	+	0.565091i	$0.808841\pi$
$74$			7.83058i			0.910286i
$75$			1.69639i			0.195883i
$76$	16.5429			1.89760
$77$	−8.12225	+	1.72947i	−0.925616	+	0.197091i
$78$	12.6633			1.43384
$79$		−	1.50395i		−	0.169208i	−0.996415	−	0.0846039i	$-0.973038\pi$
$79$		−	1.50395i		−	0.169208i	0.996415	−	0.0846039i	$-0.0269625\pi$
$80$	34.2551			3.82984
$81$	1.00000			0.111111
$82$		−	13.4820i		−	1.48883i
$83$	15.7572			1.72958			0.864789	−	0.502136i	$-0.167452\pi$
$83$	15.7572			1.72958			0.864789	+	0.502136i	$0.167452\pi$
$84$	−13.6388	+	2.90409i	−1.48811	+	0.316863i
$85$	−18.0561			−1.95846
$86$			2.11844i			0.228437i
$87$			3.96693i			0.425299i
$88$		−	27.6795i		−	2.95064i
$89$	2.18580			0.231694			0.115847	−	0.993267i	$-0.463042\pi$
$89$	2.18580			0.231694			0.115847	+	0.993267i	$0.463042\pi$
$90$	6.97756			0.735499
$91$	−12.1530	+	2.58774i	−1.27398	+	0.271269i
$92$	−6.69639	−	24.3734i	−0.698147	−	2.54111i
$93$	2.57414			0.266926
$94$		−	33.3266i		−	3.43738i
$95$	8.12225			0.833325
$96$		−	18.0561i		−	1.84284i
$97$	−7.74499			−0.786385			−0.393192	−	0.919456i	$-0.628629\pi$
$97$	−7.74499			−0.786385			−0.393192	+	0.919456i	$0.628629\pi$
$98$	17.2375	−	7.68935i	1.74125	−	0.776742i
$99$		−	3.13874i		−	0.315456i
$100$	8.94090			0.894090
$101$			7.38574i			0.734909i	0.930042	+	0.367454i	$0.119771\pi$
$101$			7.38574i			0.734909i	−0.930042	+	0.367454i	$0.880229\pi$
$102$			18.8142i			1.86289i
$103$	5.41013			0.533076			0.266538	−	0.963824i	$-0.414120\pi$
$103$	5.41013			0.533076			0.266538	+	0.963824i	$0.414120\pi$
$104$		−	41.4158i		−	4.06116i
$105$	−6.69639	+	1.42586i	−0.653501	+	0.139150i
$106$			20.3000i			1.97171i
$107$			2.98968i			0.289023i	0.989503	+	0.144512i	$0.0461611\pi$
$107$			2.98968i			0.289023i	−0.989503	+	0.144512i	$0.953839\pi$
$108$		−	5.27053i		−	0.507157i
$109$		−	4.45718i		−	0.426921i	−0.976952	−	0.213460i	$-0.931527\pi$
$109$		−	4.45718i		−	0.426921i	0.976952	−	0.213460i	$-0.0684734\pi$
$110$		−	21.9008i		−	2.08816i
$111$	2.90409			0.275644
$112$	7.29392	+	34.2551i	0.689210	+	3.23680i
$113$			20.6163i			1.93942i	0.244257	+	0.969710i	$0.421456\pi$
$113$			20.6163i			1.93942i	−0.244257	+	0.969710i	$0.578544\pi$
$114$		−	8.46329i		−	0.792660i
$115$	−3.28781	−	11.9669i	−0.306590	−	1.11592i
$116$	20.9078			1.94124
$117$		−	4.69639i		−	0.434182i
$118$			8.50799i			0.783224i
$119$	−3.84468	−	18.0561i	−0.352441	−	1.65520i
$120$		−	22.8203i		−	2.08320i
$121$	1.14828			0.104389
$122$	22.1876			2.00877
$123$	−5.00000			−0.450835
$124$		−	13.5671i		−	1.21836i
$125$	−8.54887			−0.764634
$126$	1.48573	+	6.97756i	0.132359	+	0.621611i
$127$	19.0561			1.69096			0.845478	−	0.534010i	$-0.179316\pi$
$127$	19.0561			1.69096			0.845478	+	0.534010i	$0.179316\pi$
$128$	−23.7785			−2.10174
$129$	0.785656			0.0691732
$130$		−	32.7694i		−	2.87406i
$131$			10.1483i			0.886660i	0.896359	+	0.443330i	$0.146203\pi$
$131$			10.1483i			0.886660i	−0.896359	+	0.443330i	$0.853797\pi$
$132$	−16.5429			−1.43987
$133$	1.72947	+	8.12225i	0.149964	+	0.704289i
$134$			20.9327i			1.80831i
$135$		−	2.58774i		−	0.222717i
$136$	61.5326			5.27638
$137$			4.71006i			0.402407i	0.979549	+	0.201204i	$0.0644853\pi$
$137$			4.71006i			0.402407i	−0.979549	+	0.201204i	$0.935515\pi$
$138$	−12.4694	+	3.42586i	−1.06147	+	0.291628i
$139$			2.43290i			0.206356i	0.994663	+	0.103178i	$0.0329011\pi$
$139$			2.43290i			0.206356i	−0.994663	+	0.103178i	$0.967099\pi$
$140$	7.51504	+	35.2936i	0.635137	+	2.98285i
$141$	−12.3597			−1.04088
$142$	−24.9078			−2.09022
$143$	−14.7408			−1.23269
$144$	−13.2375			−1.10312
$145$	10.2654			0.852493
$146$		−	26.0371i		−	2.15485i
$147$	−2.85172	−	6.39279i	−0.235206	−	0.527268i
$148$		−	15.3061i		−	1.25816i
$149$		−	19.6634i		−	1.61089i	−0.592673	−	0.805443i	$-0.701927\pi$
$149$		−	19.6634i		−	1.61089i	0.592673	−	0.805443i	$-0.298073\pi$
$150$		−	4.57414i		−	0.373477i
$151$	4.72242			0.384305			0.192153	−	0.981365i	$-0.438453\pi$
$151$	4.72242			0.384305			0.192153	+	0.981365i	$0.438453\pi$
$152$	−27.6795			−2.24510
$153$	6.97756			0.564102
$154$	21.9008	−	4.66332i	1.76482	−	0.375781i
$155$		−	6.66121i		−	0.535041i
$156$	−24.7525			−1.98179
$157$	9.48360			0.756873			0.378437	−	0.925627i	$-0.376462\pi$
$157$	9.48360			0.756873			0.378437	+	0.925627i	$0.376462\pi$
$158$			4.05524i			0.322618i
$159$	7.52857			0.597054
$160$	−46.7245			−3.69389
$161$	11.2669	−	5.83592i	0.887953	−	0.459935i
$162$	−2.69639			−0.211849
$163$	−6.54811			−0.512888			−0.256444	−	0.966559i	$-0.582551\pi$
$163$	−6.54811			−0.512888			−0.256444	+	0.966559i	$0.582551\pi$
$164$			26.3527i			2.05780i
$165$	−8.12225			−0.632316
$166$	−42.4876			−3.29768
$167$		−	22.0301i		−	1.70474i	−0.522941	−	0.852369i	$-0.675165\pi$
$167$		−	22.0301i		−	1.70474i	0.522941	−	0.852369i	$-0.324835\pi$
$168$	22.8203	−	4.85912i	1.76063	−	0.374889i
$169$	−9.05611			−0.696623
$170$	48.6864			3.73407
$171$	−3.13874			−0.240026
$172$		−	4.14083i		−	0.315735i
$173$			19.6563i			1.49444i	0.664577	+	0.747220i	$0.268612\pi$
$173$			19.6563i			1.49444i	−0.664577	+	0.747220i	$0.731388\pi$
$174$		−	10.6964i		−	0.810891i
$175$	0.934722	+	4.38982i	0.0706583	+	0.331839i
$176$			41.5490i			3.13187i
$177$	3.15532			0.237169
$178$	−5.89377			−0.441757
$179$	9.51504			0.711187			0.355594	−	0.934641i	$-0.384279\pi$
$179$	9.51504			0.711187			0.355594	+	0.934641i	$0.384279\pi$
$180$	−13.6388			−1.01657
$181$	10.5817			0.786533			0.393267	−	0.919424i	$-0.371345\pi$
$181$	10.5817			0.786533			0.393267	+	0.919424i	$0.371345\pi$
$182$	32.7694	−	6.97756i	2.42903	−	0.517211i
$183$		−	8.22864i		−	0.608278i
$184$	11.2044	+	40.7816i	0.825998	+	3.00646i
$185$		−	7.51504i		−	0.552517i
$186$	−6.94090			−0.508931
$187$		−	21.9008i		−	1.60154i
$188$			65.1423i			4.75099i
$189$	2.58774	−	0.551006i	0.188230	−	0.0400798i
$190$	−21.9008			−1.58885
$191$			11.9857i			0.867258i	0.901091	+	0.433629i	$0.142767\pi$
$191$			11.9857i			0.867258i	−0.901091	+	0.433629i	$0.857233\pi$
$192$			22.2114i			1.60297i
$193$	2.96693			0.213564			0.106782	−	0.994282i	$-0.465945\pi$
$193$	2.96693			0.213564			0.106782	+	0.994282i	$0.465945\pi$
$194$	20.8835			1.49935
$195$	−12.1530			−0.870297
$196$	−33.6934	+	15.0301i	−2.40667	+	1.07358i
$197$	16.9268			1.20599			0.602993	−	0.797747i	$-0.293975\pi$
$197$	16.9268			1.20599			0.602993	+	0.797747i	$0.293975\pi$
$198$			8.46329i			0.601460i
$199$	−15.2062			−1.07794			−0.538969	−	0.842325i	$-0.681186\pi$
$199$	−15.2062			−1.07794			−0.538969	+	0.842325i	$0.681186\pi$
$200$	−14.9599			−1.05782
$201$	7.76322			0.547575
$202$		−	19.9149i		−	1.40121i
$203$	2.18580	+	10.2654i	0.153413	+	0.720488i
$204$		−	36.7755i		−	2.57480i
$205$			12.9387i			0.903678i
$206$	−14.5878			−1.01638
$207$	1.27053	+	4.62447i	0.0883082	+	0.321423i
$208$			62.1683i			4.31060i
$209$			9.85172i			0.681458i
$210$	18.0561	−	3.84468i	1.24599	−	0.265308i
$211$	18.3928			1.26621			0.633106	−	0.774065i	$-0.281780\pi$
$211$	18.3928			1.26621			0.633106	+	0.774065i	$0.281780\pi$
$212$		−	39.6796i		−	2.72520i
$213$			9.23746i			0.632940i
$214$		−	8.06135i		−	0.551062i
$215$		−	2.03307i		−	0.138654i
$216$			8.81864i			0.600033i
$217$	6.66121	−	1.41837i	0.452192	−	0.0962850i
$218$			12.0183i			0.813983i
$219$	−9.65628			−0.652511
$220$			42.8086i			2.88616i
$221$		−	32.7694i		−	2.20431i
$222$	−7.83058			−0.525554
$223$		−	3.02603i		−	0.202638i	−0.994854	−	0.101319i	$-0.967694\pi$
$223$		−	3.02603i		−	0.202638i	0.994854	−	0.101319i	$-0.0323063\pi$
$224$	−9.94902	−	46.7245i	−0.664747	−	3.12191i
$225$	−1.69639			−0.113093
$226$		−	55.5897i		−	3.69777i
$227$	8.53065			0.566199			0.283100	−	0.959091i	$-0.408637\pi$
$227$	8.53065			0.566199			0.283100	+	0.959091i	$0.408637\pi$
$228$			16.5429i			1.09558i
$229$	10.8346			0.715971			0.357985	−	0.933727i	$-0.383464\pi$
$229$	10.8346			0.715971			0.357985	+	0.933727i	$0.383464\pi$
$230$	8.86523	+	32.2675i	0.584556	+	2.12766i
$231$	−1.72947	−	8.12225i	−0.113791	−	0.534405i
$232$	−34.9829			−2.29674
$233$	−9.27053			−0.607333			−0.303666	−	0.952778i	$-0.598211\pi$
$233$	−9.27053			−0.607333			−0.303666	+	0.952778i	$0.598211\pi$
$234$			12.6633i			0.827827i
$235$			31.9837i			2.08639i
$236$		−	16.6302i		−	1.08254i
$237$	1.50395			0.0976921
$238$	10.3668	+	48.6864i	0.671977	+	3.15587i
$239$	−11.8777			−0.768308			−0.384154	−	0.923269i	$-0.625507\pi$
$239$	−11.8777			−0.768308			−0.384154	+	0.923269i	$0.625507\pi$
$240$			34.2551i			2.21116i
$241$	−18.4940			−1.19130			−0.595652	−	0.803243i	$-0.703106\pi$
$241$	−18.4940			−1.19130			−0.595652	+	0.803243i	$0.703106\pi$
$242$	−3.09622			−0.199033
$243$			1.00000i			0.0641500i
$244$	−43.3693			−2.77644
$245$	−16.5429	+	7.37950i	−1.05688	+	0.471459i
$246$	13.4820			0.859579
$247$			14.7408i			0.937933i
$248$			22.7004i			1.44148i
$249$			15.7572i			0.998572i
$250$	23.0511			1.45788
$251$	21.3346			1.34663			0.673315	−	0.739356i	$-0.264870\pi$
$251$	21.3346			1.34663			0.673315	+	0.739356i	$0.264870\pi$
$252$	−2.90409	−	13.6388i	−0.182941	−	0.859162i
$253$	14.5150	−	3.98788i	0.912553	−	0.250716i
$254$	−51.3827			−3.22404
$255$		−	18.0561i		−	1.13072i
$256$	19.6934			1.23084
$257$		−	15.1973i		−	0.947984i	−0.880529	−	0.473992i	$-0.842812\pi$
$257$		−	15.1973i		−	0.947984i	0.880529	−	0.473992i	$-0.157188\pi$
$258$	−2.11844			−0.131888
$259$	7.51504	−	1.60017i	0.466962	−	0.0994299i
$260$			64.0530i			3.97240i
$261$	−3.96693			−0.245547
$262$		−	27.3638i		−	1.69054i
$263$		−	15.2244i		−	0.938778i	−0.882991	−	0.469389i	$-0.844474\pi$
$263$		−	15.2244i		−	0.938778i	0.882991	−	0.469389i	$-0.155526\pi$
$264$	27.6795			1.70355
$265$		−	19.4820i		−	1.19677i
$266$	−4.66332	−	21.9008i	−0.285926	−	1.34282i
$267$			2.18580i			0.133769i
$268$		−	40.9163i		−	2.49936i
$269$		−	19.5481i		−	1.19187i	−0.803033	−	0.595935i	$-0.796782\pi$
$269$		−	19.5481i		−	1.19187i	0.803033	−	0.595935i	$-0.203218\pi$
$270$			6.97756i			0.424641i
$271$		−	9.11521i		−	0.553710i	−0.960912	−	0.276855i	$-0.910708\pi$
$271$		−	9.11521i		−	0.553710i	0.960912	−	0.276855i	$-0.0892921\pi$
$272$	−92.3652			−5.60046
$273$	−2.58774	−	12.1530i	−0.156617	−	0.735535i
$274$		−	12.7002i		−	0.767245i
$275$			5.32454i			0.321082i
$276$	24.3734	−	6.69639i	1.46711	−	0.403075i
$277$	−21.0702			−1.26599			−0.632993	−	0.774158i	$-0.718174\pi$
$277$	−21.0702			−1.26599			−0.632993	+	0.774158i	$0.718174\pi$
$278$		−	6.56006i		−	0.393446i
$279$			2.57414i			0.154110i
$280$	−12.5741	−	59.0531i	−0.751449	−	3.52910i
$281$		−	13.3224i		−	0.794748i	−0.917657	−	0.397374i	$-0.869922\pi$
$281$		−	13.3224i		−	0.794748i	0.917657	−	0.397374i	$-0.130078\pi$
$282$	33.3266			1.98457
$283$	1.01643			0.0604203			0.0302101	−	0.999544i	$-0.490382\pi$
$283$	1.01643			0.0604203			0.0302101	+	0.999544i	$0.490382\pi$
$284$	48.6864			2.88900
$285$			8.12225i			0.481121i
$286$	39.7469			2.35028
$287$	−12.9387	+	2.75503i	−0.763747	+	0.162624i
$288$	18.0561			1.06397
$289$	31.6864			1.86390
$290$	−27.6795			−1.62539
$291$		−	7.74499i		−	0.454020i
$292$			50.8937i			2.97833i
$293$	−7.34305			−0.428986			−0.214493	−	0.976726i	$-0.568810\pi$
$293$	−7.34305			−0.428986			−0.214493	+	0.976726i	$0.568810\pi$
$294$	7.68935	+	17.2375i	0.448452	+	1.00531i
$295$		−	8.16516i		−	0.475394i
$296$			25.6102i			1.48856i
$297$	3.13874			0.182128
$298$			53.0202i			3.07138i
$299$	21.7183	−	5.96693i	1.25600	−	0.345076i
$300$			8.94090i			0.516203i
$301$	2.03307	−	0.432901i	0.117184	−	0.0249520i
$302$	−12.7335			−0.732731
$303$	−7.38574			−0.424300
$304$	41.5490			2.38300
$305$	−21.2936			−1.21927
$306$	−18.8142			−1.07554
$307$		−	9.98101i		−	0.569646i	−0.958580	−	0.284823i	$-0.908065\pi$
$307$		−	9.98101i		−	0.569646i	0.958580	−	0.284823i	$-0.0919349\pi$
$308$	−42.8086	+	9.11521i	−2.43925	+	0.519387i
$309$			5.41013i			0.307771i
$310$			17.9612i			1.02013i
$311$		−	9.95988i		−	0.564773i	−0.959301	−	0.282387i	$-0.908874\pi$
$311$		−	9.95988i		−	0.564773i	0.959301	−	0.282387i	$-0.0911261\pi$
$312$	41.4158			2.34471
$313$	19.6634			1.11144			0.555720	−	0.831370i	$-0.312443\pi$
$313$	19.6634			1.11144			0.555720	+	0.831370i	$0.312443\pi$
$314$	−25.5715			−1.44308
$315$	−1.42586	−	6.69639i	−0.0803380	−	0.377299i
$316$		−	7.92663i		−	0.445908i
$317$	26.0420			1.46267			0.731333	−	0.682021i	$-0.238899\pi$
$317$	26.0420			1.46267			0.731333	+	0.682021i	$0.238899\pi$
$318$	−20.3000			−1.13837
$319$			12.4512i			0.697132i
$320$	57.4774			3.21308
$321$	−2.98968			−0.166868
$322$	−30.3799	+	15.7359i	−1.69300	+	0.876929i
$323$	−21.9008			−1.21859
$324$	5.27053			0.292807
$325$			7.96693i			0.441926i
$326$	17.6563			0.977891
$327$	4.45718			0.246483
$328$		−	44.0932i		−	2.43464i
$329$	−31.9837	+	6.81027i	−1.76332	+	0.375462i
$330$	21.9008			1.20560
$331$	−8.65628			−0.475792			−0.237896	−	0.971291i	$-0.576458\pi$
$331$	−8.65628			−0.475792			−0.237896	+	0.971291i	$0.576458\pi$
$332$	83.0489			4.55790
$333$			2.90409i			0.159143i
$334$			59.4017i			3.25032i
$335$		−	20.0892i		−	1.09759i
$336$	−34.2551	+	7.29392i	−1.86877	+	0.397916i
$337$		−	30.8635i		−	1.68124i	−0.541625	−	0.840620i	$-0.682191\pi$
$337$		−	30.8635i		−	1.68124i	0.541625	−	0.840620i	$-0.317809\pi$
$338$	24.4188			1.32821
$339$	−20.6163			−1.11973
$340$	−95.1653			−5.16106
$341$	8.07957			0.437533
$342$	8.46329			0.457642
$343$	−10.9020	−	14.9715i	−0.588651	−	0.808388i
$344$			6.92842i			0.373556i
$345$	11.9669	−	3.28781i	0.644278	−	0.177010i
$346$		−	53.0010i		−	2.84935i
$347$	−12.5080			−0.671464			−0.335732	−	0.941957i	$-0.608984\pi$
$347$	−12.5080			−0.671464			−0.335732	+	0.941957i	$0.608984\pi$
$348$			20.9078i			1.12078i
$349$			25.2185i			1.34991i	0.737857	+	0.674957i	$0.235838\pi$
$349$			25.2185i			1.34991i	−0.737857	+	0.674957i	$0.764162\pi$
$350$	−2.52038	−	11.8367i	−0.134720	−	0.632697i
$351$	4.69639			0.250675
$352$		−	56.6735i		−	3.02071i
$353$			5.98101i			0.318337i	0.987251	+	0.159169i	$0.0508813\pi$
$353$			5.98101i			0.318337i	−0.987251	+	0.159169i	$0.949119\pi$
$354$	−8.50799			−0.452195
$355$	23.9041			1.26870
$356$	11.5203			0.610576
$357$	18.0561	−	3.84468i	0.955630	−	0.203482i
$358$	−25.6563			−1.35598
$359$			2.58774i			0.136576i	0.997666	+	0.0682878i	$0.0217536\pi$
$359$			2.58774i			0.136576i	−0.997666	+	0.0682878i	$0.978246\pi$
$360$	22.8203			1.20274
$361$	−9.14828			−0.481489
$362$	−28.5325			−1.49963
$363$			1.14828i			0.0602692i
$364$	−64.0530	+	13.6388i	−3.35729	+	0.714866i
$365$			24.9879i			1.30793i
$366$			22.1876i			1.15977i
$367$	20.7836			1.08490			0.542448	−	0.840089i	$-0.317498\pi$
$367$	20.7836			1.08490			0.542448	+	0.840089i	$0.317498\pi$
$368$	−16.8186	−	61.2163i	−0.876732	−	3.19112i
$369$		−	5.00000i		−	0.260290i
$370$			20.2635i			1.05345i
$371$	19.4820	−	4.14828i	1.01145	−	0.215368i
$372$	13.5671			0.703421
$373$			2.43479i			0.126069i	0.998011	+	0.0630344i	$0.0200778\pi$
$373$			2.43479i			0.126069i	−0.998011	+	0.0630344i	$0.979922\pi$
$374$			59.0531i			3.05356i
$375$		−	8.54887i		−	0.441462i
$376$		−	108.996i		−	5.62103i
$377$			18.6302i			0.959507i
$378$	−6.97756	+	1.48573i	−0.358887	+	0.0764176i
$379$		−	10.3510i		−	0.531693i	−0.964015	−	0.265846i	$-0.914349\pi$
$379$		−	10.3510i		−	0.531693i	0.964015	−	0.265846i	$-0.0856514\pi$
$380$	42.8086			2.19604
$381$			19.0561i			0.976274i
$382$		−	32.3183i		−	1.65355i
$383$	−4.93695			−0.252266			−0.126133	−	0.992013i	$-0.540257\pi$
$383$	−4.93695			−0.252266			−0.126133	+	0.992013i	$0.540257\pi$
$384$		−	23.7785i		−	1.21344i
$385$	−21.0183	+	4.47541i	−1.07119	+	0.228088i
$386$	−8.00000			−0.407189
$387$			0.785656i			0.0399372i
$388$	−40.8203			−2.07233
$389$		−	15.7572i		−	0.798922i	−0.916750	−	0.399461i	$-0.869197\pi$
$389$		−	15.7572i		−	0.798922i	0.916750	−	0.399461i	$-0.130803\pi$
$390$	32.7694			1.65934
$391$	8.86523	+	32.2675i	0.448334	+	1.63184i
$392$	56.3757	−	25.1483i	2.84740	−	1.27018i
$393$	−10.1483			−0.511913
$394$	−45.6413			−2.29938
$395$		−	3.89183i		−	0.195819i
$396$		−	16.5429i		−	0.831310i
$397$		−	10.4890i		−	0.526428i	−0.964737	−	0.263214i	$-0.915217\pi$
$397$		−	10.4890i		−	0.526428i	0.964737	−	0.263214i	$-0.0847826\pi$
$398$	41.0019			2.05524
$399$	−8.12225	+	1.72947i	−0.406621	+	0.0865816i
$400$	22.4559			1.12280
$401$			20.9962i			1.04850i	0.851565	+	0.524249i	$0.175654\pi$
$401$			20.9962i			1.04850i	−0.851565	+	0.524249i	$0.824346\pi$
$402$	−20.9327			−1.04403
$403$	12.0892			0.602205
$404$			38.9268i			1.93668i
$405$	2.58774			0.128586
$406$	−5.89377	−	27.6795i	−0.292503	−	1.37371i
$407$	9.11521			0.451824
$408$			61.5326i			3.04632i
$409$			14.1453i			0.699439i	0.936854	+	0.349720i	$0.113723\pi$
$409$			14.1453i			0.699439i	−0.936854	+	0.349720i	$0.886277\pi$
$410$		−	34.8878i		−	1.72299i
$411$	−4.71006			−0.232330
$412$	28.5143			1.40480
$413$	8.16516	−	1.73860i	0.401781	−	0.0855510i
$414$	−3.42586	−	12.4694i	−0.168372	−	0.612837i
$415$	40.7755			2.00159
$416$		−	84.7986i		−	4.15759i
$417$	−2.43290			−0.119140
$418$		−	26.5641i		−	1.29929i
$419$	20.9145			1.02174			0.510869	−	0.859659i	$-0.329324\pi$
$419$	20.9145			1.02174			0.510869	+	0.859659i	$0.329324\pi$
$420$	−35.2936	+	7.51504i	−1.72215	+	0.366696i
$421$		−	1.41837i		−	0.0691269i	−0.999403	−	0.0345635i	$-0.988996\pi$
$421$		−	1.41837i		−	0.0691269i	0.999403	−	0.0345635i	$-0.0110041\pi$
$422$	−49.5942			−2.41421
$423$		−	12.3597i		−	0.600950i
$424$			66.3917i			3.22427i
$425$	−11.8367			−0.574163
$426$		−	24.9078i		−	1.20679i
$427$	−4.53403	−	21.2936i	−0.219417	−	1.03047i
$428$			15.7572i			0.761653i
$429$		−	14.7408i		−	0.711691i
$430$			5.48196i			0.264364i
$431$		−	25.0283i		−	1.20557i	−0.797904	−	0.602784i	$-0.794058\pi$
$431$		−	25.0283i		−	1.20557i	0.797904	−	0.602784i	$-0.205942\pi$
$432$		−	13.2375i		−	0.636888i
$433$	26.8717			1.29137			0.645686	−	0.763603i	$-0.276571\pi$
$433$	26.8717			1.29137			0.645686	+	0.763603i	$0.276571\pi$
$434$	−17.9612	+	3.82447i	−0.862166	+	0.183581i
$435$			10.2654i			0.492187i
$436$		−	23.4917i		−	1.12505i
$437$	−3.98788	−	14.5150i	−0.190766	−	0.694348i
$438$	26.0371			1.24410
$439$			20.3898i			0.973151i	0.873638	+	0.486576i	$0.161754\pi$
$439$			20.3898i			0.973151i	−0.873638	+	0.486576i	$0.838246\pi$
$440$		−	71.6272i		−	3.41470i
$441$	6.39279	−	2.85172i	0.304418	−	0.135796i
$442$			88.3591i			4.20281i
$443$	−19.3787			−0.920710			−0.460355	−	0.887735i	$-0.652278\pi$
$443$	−19.3787			−0.920710			−0.460355	+	0.887735i	$0.652278\pi$
$444$	15.3061			0.726397
$445$	5.65628			0.268133
$446$			8.15937i			0.386357i
$447$	19.6634			0.930046
$448$	12.2386	+	57.4774i	0.578221	+	2.71555i
$449$	−14.9599			−0.706001			−0.353000	−	0.935623i	$-0.614839\pi$
$449$	−14.9599			−0.706001			−0.353000	+	0.935623i	$0.614839\pi$
$450$	4.57414			0.215627
$451$	−15.6937			−0.738989
$452$			108.659i			5.11089i
$453$			4.72242i			0.221879i
$454$	−23.0020			−1.07954
$455$	−31.4489	+	6.69639i	−1.47435	+	0.313932i
$456$		−	27.6795i		−	1.29621i
$457$		−	26.5957i		−	1.24409i	−0.782980	−	0.622047i	$-0.786301\pi$
$457$		−	26.5957i		−	1.24409i	0.782980	−	0.622047i	$-0.213699\pi$
$458$	−29.2143			−1.36510
$459$			6.97756i			0.325685i
$460$	−17.3285	−	63.0721i	−0.807946	−	2.94075i
$461$			23.7736i			1.10725i	0.832767	+	0.553624i	$0.186756\pi$
$461$			23.7736i			1.10725i	−0.832767	+	0.553624i	$0.813244\pi$
$462$	4.66332	+	21.9008i	0.216957	+	1.01892i
$463$	26.3407			1.22416			0.612079	−	0.790797i	$-0.290334\pi$
$463$	26.3407			1.22416			0.612079	+	0.790797i	$0.290334\pi$
$464$	52.5120			2.43781
$465$	6.66121			0.308906
$466$	24.9970			1.15796
$467$	9.18158			0.424873			0.212436	−	0.977175i	$-0.431860\pi$
$467$	9.18158			0.424873			0.212436	+	0.977175i	$0.431860\pi$
$468$		−	24.7525i		−	1.14418i
$469$	20.0892	−	4.27758i	0.927632	−	0.197520i
$470$		−	86.2406i		−	3.97798i
$471$			9.48360i			0.436981i
$472$			27.8257i			1.28078i
$473$	2.46597			0.113386
$474$	−4.05524			−0.186263
$475$	5.32454			0.244307
$476$	−20.2635	−	95.1653i	−0.928776	−	4.36190i
$477$			7.52857i			0.344709i
$478$	32.0271			1.46488
$479$	2.73292			0.124871			0.0624353	−	0.998049i	$-0.480113\pi$
$479$	2.73292			0.124871			0.0624353	+	0.998049i	$0.480113\pi$
$480$		−	46.7245i		−	2.13267i
$481$	13.6388			0.621874
$482$	49.8671			2.27138
$483$	5.83592	+	11.2669i	0.265544	+	0.512660i
$484$	6.05206			0.275094
$485$	−20.0420			−0.910061
$486$		−	2.69639i		−	0.122311i
$487$	21.3738			0.968539			0.484270	−	0.874919i	$-0.339085\pi$
$487$	21.3738			0.968539			0.484270	+	0.874919i	$0.339085\pi$
$488$	72.5654			3.28488
$489$		−	6.54811i		−	0.296116i
$490$	44.6060	−	19.8980i	2.01510	−	0.898901i
$491$	−21.7785			−0.982851			−0.491426	−	0.870920i	$-0.663524\pi$
$491$	−21.7785			−0.982851			−0.491426	+	0.870920i	$0.663524\pi$
$492$	−26.3527			−1.18807
$493$	−27.6795			−1.24662
$494$		−	39.7469i		−	1.78830i
$495$		−	8.12225i		−	0.365068i
$496$		−	34.0751i		−	1.53002i
$497$	5.08989	+	23.9041i	0.228313	+	1.07225i
$498$		−	42.4876i		−	1.90392i
$499$	−18.1223			−0.811263			−0.405632	−	0.914037i	$-0.632948\pi$
$499$	−18.1223			−0.811263			−0.405632	+	0.914037i	$0.632948\pi$
$500$	−45.0571			−2.01502
$501$	22.0301			0.984231
$502$	−57.5265			−2.56753
$503$	−15.1427			−0.675180			−0.337590	−	0.941293i	$-0.609612\pi$
$503$	−15.1427			−0.675180			−0.337590	+	0.941293i	$0.609612\pi$
$504$	4.85912	+	22.8203i	0.216443	+	1.01650i
$505$			19.1124i			0.850490i
$506$	−39.1382	+	10.7529i	−1.73991	+	0.478025i
$507$		−	9.05611i		−	0.402196i
$508$	100.436			4.45612
$509$			32.2274i			1.42846i	0.699913	+	0.714228i	$0.253222\pi$
$509$			32.2274i			1.42846i	−0.699913	+	0.714228i	$0.746778\pi$
$510$			48.6864i			2.15587i
$511$	−24.9879	+	5.32066i	−1.10540	+	0.235372i
$512$	−5.54407			−0.245015
$513$		−	3.13874i		−	0.138579i
$514$			40.9780i			1.80746i
$515$	14.0000			0.616914
$516$	4.14083			0.182290
$517$	−38.7940			−1.70616
$518$	−20.2635	+	4.31469i	−0.890327	+	0.189577i
$519$	−19.6563			−0.862815
$520$		−	107.173i		−	4.69986i
$521$	12.9878			0.569007			0.284504	−	0.958675i	$-0.408171\pi$
$521$	12.9878			0.569007			0.284504	+	0.958675i	$0.408171\pi$
$522$	10.6964			0.468168
$523$	−19.6998			−0.861413			−0.430707	−	0.902492i	$-0.641736\pi$
$523$	−19.6998			−0.861413			−0.430707	+	0.902492i	$0.641736\pi$
$524$			53.4869i			2.33658i
$525$	−4.38982	+	0.934722i	−0.191588	+	0.0407946i
$526$			41.0510i			1.78991i
$527$			17.9612i			0.782403i
$528$	−41.5490			−1.80819
$529$	−19.7715	+	11.7511i	−0.859630	+	0.510917i
$530$			52.5310i			2.28180i
$531$			3.15532i			0.136929i
$532$	9.11521	+	42.8086i	0.395194	+	1.85599i
$533$	−23.4820			−1.01712
$534$		−	5.89377i		−	0.255048i
$535$			7.73651i			0.334478i
$536$			68.4610i			2.95707i
$537$			9.51504i			0.410604i
$538$			52.7094i			2.27246i
$539$	−8.95081	−	20.0653i	−0.385539	−	0.864275i
$540$		−	13.6388i		−	0.586919i
$541$	−13.5882			−0.584203			−0.292102	−	0.956387i	$-0.594355\pi$
$541$	−13.5882			−0.584203			−0.292102	+	0.956387i	$0.594355\pi$
$542$			24.5782i			1.05572i
$543$			10.5817i			0.454105i
$544$	125.988			5.40167
$545$		−	11.5340i		−	0.494063i
$546$	6.97756	+	32.7694i	0.298612	+	1.40240i
$547$	−3.58118			−0.153120			−0.0765602	−	0.997065i	$-0.524394\pi$
$547$	−3.58118			−0.153120			−0.0765602	+	0.997065i	$0.524394\pi$
$548$			24.8245i			1.06045i
$549$	8.22864			0.351190
$550$		−	14.3571i		−	0.612187i
$551$	12.4512			0.530438
$552$	−40.7816	+	11.2044i	−1.73578	+	0.476890i
$553$	3.89183	−	0.828686i	0.165498	−	0.0352393i
$554$	56.8135			2.41377
$555$	7.51504			0.318996
$556$			12.8227i			0.543803i
$557$		−	19.7269i		−	0.835854i	−0.908481	−	0.417927i	$-0.862757\pi$
$557$		−	19.7269i		−	0.835854i	0.908481	−	0.417927i	$-0.137243\pi$
$558$		−	6.94090i		−	0.293832i
$559$	3.68975			0.156060
$560$	18.8747	+	88.6432i	0.797604	+	3.74586i
$561$	21.9008			0.924652
$562$			35.9225i			1.51530i
$563$	−27.5939			−1.16294			−0.581472	−	0.813567i	$-0.697523\pi$
$563$	−27.5939			−1.16294			−0.581472	+	0.813567i	$0.697523\pi$
$564$	−65.1423			−2.74299
$565$			53.3497i			2.24444i
$566$	−2.74069			−0.115200
$567$	0.551006	+	2.58774i	0.0231401	+	0.108675i
$568$	−81.4619			−3.41806
$569$			20.6307i			0.864883i	0.901662	+	0.432441i	$0.142348\pi$
$569$			20.6307i			0.864883i	−0.901662	+	0.432441i	$0.857652\pi$
$570$		−	21.9008i		−	0.917323i
$571$			32.8185i			1.37341i	0.726935	+	0.686706i	$0.240944\pi$
$571$			32.8185i			1.37341i	−0.726935	+	0.686706i	$0.759056\pi$
$572$	−77.6918			−3.24846
$573$	−11.9857			−0.500712
$574$	34.8878	−	7.42864i	1.45619	−	0.310065i
$575$	−2.15532	−	7.84492i	−0.0898833	−	0.327156i
$576$	−22.2114			−0.925476
$577$		−	5.63729i		−	0.234683i	−0.993092	−	0.117342i	$-0.962563\pi$
$577$		−	5.63729i		−	0.234683i	0.993092	−	0.117342i	$-0.0374373\pi$
$578$	−85.4388			−3.55379
$579$			2.96693i			0.123301i
$580$	54.1040			2.24655
$581$	8.68231	+	40.7755i	0.360203	+	1.69165i
$582$			20.8835i			0.865651i
$583$	23.6302			0.978665
$584$		−	85.1553i		−	3.52375i
$585$		−	12.1530i		−	0.502466i
$586$	19.7998			0.817920
$587$		−	27.6633i		−	1.14179i	−0.821024	−	0.570894i	$-0.806597\pi$
$587$		−	27.6633i		−	1.14179i	0.821024	−	0.570894i	$-0.193403\pi$
$588$	−15.0301	−	33.6934i	−0.619830	−	1.38949i
$589$		−	8.07957i		−	0.332913i
$590$			22.0165i			0.906404i
$591$			16.9268i			0.696276i
$592$		−	38.4428i		−	1.57999i
$593$		−	36.7194i		−	1.50789i	−0.656940	−	0.753943i	$-0.728149\pi$
$593$		−	36.7194i		−	1.50789i	0.656940	−	0.753943i	$-0.271851\pi$
$594$	−8.46329			−0.347253
$595$	−9.94902	−	46.7245i	−0.407870	−	1.91552i
$596$		−	103.637i		−	4.24512i
$597$		−	15.2062i		−	0.622348i
$598$	−58.5612	+	16.0892i	−2.39474	+	0.657935i
$599$	18.3337			0.749094			0.374547	−	0.927208i	$-0.377798\pi$
$599$	18.3337			0.749094			0.374547	+	0.927208i	$0.377798\pi$
$600$		−	14.9599i		−	0.610735i
$601$		−	41.6272i		−	1.69801i	−0.528384	−	0.849005i	$-0.677202\pi$
$601$		−	41.6272i		−	1.69801i	0.528384	−	0.849005i	$-0.322798\pi$
$602$	−5.48196	+	1.16727i	−0.223428	+	0.0475744i
$603$			7.76322i			0.316143i
$604$	24.8897			1.01275
$605$	2.97146			0.120807
$606$	19.9149			0.808986
$607$		−	10.7625i		−	0.436838i	−0.975855	−	0.218419i	$-0.929910\pi$
$607$		−	10.7625i		−	0.436838i	0.975855	−	0.218419i	$-0.0700899\pi$
$608$	−56.6735			−2.29841
$609$	−10.2654	+	2.18580i	−0.415974	+	0.0885730i
$610$	57.4158			2.32470
$611$	−58.0461			−2.34829
$612$	36.7755			1.48656
$613$			30.2181i			1.22050i	0.792210	+	0.610248i	$0.208930\pi$
$613$			30.2181i			1.22050i	−0.792210	+	0.610248i	$0.791070\pi$
$614$			26.9127i			1.08611i
$615$	−12.9387			−0.521739
$616$	71.6272	−	15.2515i	2.88594	−	0.614502i
$617$		−	35.6061i		−	1.43345i	−0.697357	−	0.716724i	$-0.745641\pi$
$617$		−	35.6061i		−	1.43345i	0.697357	−	0.716724i	$-0.254359\pi$
$618$		−	14.5878i		−	0.586809i
$619$	−5.02253			−0.201873			−0.100936	−	0.994893i	$-0.532184\pi$
$619$	−5.02253			−0.201873			−0.100936	+	0.994893i	$0.532184\pi$
$620$		−	35.1081i		−	1.40998i
$621$	−4.62447	+	1.27053i	−0.185574	+	0.0509848i
$622$			26.8558i			1.07682i
$623$	1.20439	+	5.65628i	0.0482528	+	0.226614i
$624$	−62.1683			−2.48872
$625$	−30.6042			−1.22417
$626$	−53.0202			−2.11911
$627$	−9.85172			−0.393440
$628$	49.9836			1.99456
$629$			20.2635i			0.807958i
$630$	3.84468	+	18.0561i	0.153176	+	0.719372i
$631$			48.3736i			1.92572i	0.269995	+	0.962862i	$0.412978\pi$
$631$			48.3736i			1.92572i	−0.269995	+	0.962862i	$0.587022\pi$
$632$			13.2628i			0.527566i
$633$			18.3928i			0.731048i
$634$	−70.2195			−2.78877
$635$	49.3122			1.95690
$636$	39.6796			1.57340
$637$	−13.3928	−	30.0230i	−0.530641	−	1.18956i
$638$		−	33.5732i		−	1.32918i
$639$	−9.23746			−0.365428
$640$	−61.5326			−2.43229
$641$		−	18.9142i		−	0.747065i	−0.927617	−	0.373532i	$-0.878146\pi$
$641$		−	18.9142i		−	0.747065i	0.927617	−	0.373532i	$-0.121854\pi$
$642$	8.06135			0.318156
$643$	−2.88975			−0.113961			−0.0569803	−	0.998375i	$-0.518147\pi$
$643$	−2.88975			−0.113961			−0.0569803	+	0.998375i	$0.518147\pi$
$644$	59.3823	−	30.7584i	2.33999	−	1.21205i
$645$	2.03307			0.0800522
$646$	59.0531			2.32341
$647$			3.95798i			0.155604i	0.996969	+	0.0778021i	$0.0247902\pi$
$647$			3.95798i			0.155604i	−0.996969	+	0.0778021i	$0.975210\pi$
$648$	−8.81864			−0.346429
$649$	9.90376			0.388757
$650$		−	21.4820i		−	0.842592i
$651$	1.41837	+	6.66121i	0.0555902	+	0.261073i
$652$	−34.5120			−1.35160
$653$	−14.9219			−0.583939			−0.291970	−	0.956428i	$-0.594311\pi$
$653$	−14.9219			−0.583939			−0.291970	+	0.956428i	$0.594311\pi$
$654$	−12.0183			−0.469953
$655$			26.2611i			1.02611i
$656$			66.1873i			2.58418i
$657$		−	9.65628i		−	0.376727i
$658$	86.2406	−	18.3632i	3.36201	−	0.715871i
$659$		−	6.64298i		−	0.258774i	−0.991594	−	0.129387i	$-0.958699\pi$
$659$		−	6.64298i		−	0.258774i	0.991594	−	0.129387i	$-0.0413009\pi$
$660$	−42.8086			−1.66632
$661$	3.57160			0.138919			0.0694595	−	0.997585i	$-0.477873\pi$
$661$	3.57160			0.138919			0.0694595	+	0.997585i	$0.477873\pi$
$662$	23.3407			0.907163
$663$	32.7694			1.27266
$664$	−138.957			−5.39258
$665$	4.47541	+	21.0183i	0.173549	+	0.815053i
$666$		−	7.83058i		−	0.303429i
$667$	−5.04012	−	18.3449i	−0.195154	−	0.710319i
$668$		−	116.110i		−	4.49244i
$669$	3.02603			0.116993
$670$			54.1683i			2.09270i
$671$		−	25.8276i		−	0.997063i
$672$	46.7245	−	9.94902i	1.80244	−	0.383792i
$673$	−7.91786			−0.305211			−0.152606	−	0.988287i	$-0.548766\pi$
$673$	−7.91786			−0.305211			−0.152606	+	0.988287i	$0.548766\pi$
$674$			83.2200i			3.20552i
$675$		−	1.69639i		−	0.0652942i
$676$	−47.7305			−1.83579
$677$	15.6794			0.602608			0.301304	−	0.953528i	$-0.402578\pi$
$677$	15.6794			0.602608			0.301304	+	0.953528i	$0.402578\pi$
$678$	55.5897			2.13491
$679$	−4.26754	−	20.0420i	−0.163773	−	0.769142i
$680$	159.230			6.10621
$681$			8.53065i			0.326895i
$682$	−21.7857			−0.834218
$683$	18.6864			0.715013			0.357507	−	0.933911i	$-0.383627\pi$
$683$	18.6864			0.715013			0.357507	+	0.933911i	$0.383627\pi$
$684$	−16.5429			−0.632532
$685$			12.1884i			0.465695i
$686$	29.3960	+	40.3692i	1.12234	+	1.54130i
$687$			10.8346i			0.413366i
$688$		−	10.4001i		−	0.396500i
$689$	35.3571			1.34700
$690$	−32.2675	+	8.86523i	−1.22840	+	0.337493i
$691$			32.0089i			1.21768i	0.793294	+	0.608839i	$0.208364\pi$
$691$			32.0089i			1.21768i	−0.793294	+	0.608839i	$0.791636\pi$
$692$			103.599i			3.93825i
$693$	8.12225	−	1.72947i	0.308539	−	0.0656970i
$694$	33.7265			1.28024
$695$			6.29571i			0.238810i
$696$		−	34.9829i		−	1.32602i
$697$		−	34.8878i		−	1.32147i
$698$		−	67.9989i		−	2.57380i
$699$		−	9.27053i		−	0.350644i
$700$	4.92648	+	23.1367i	0.186204	+	0.874485i
$701$		−	2.81463i		−	0.106307i	−0.998586	−	0.0531535i	$-0.983073\pi$
$701$		−	2.81463i		−	0.106307i	0.998586	−	0.0531535i	$-0.0169273\pi$
$702$	−12.6633			−0.477946
$703$		−	9.11521i		−	0.343787i
$704$			69.7160i			2.62752i
$705$	−31.9837			−1.20458
$706$		−	16.1272i		−	0.606954i
$707$	−19.1124	+	4.06959i	−0.718795	+	0.153053i
$708$	16.6302			0.625003
$709$			3.45898i			0.129905i	0.997888	+	0.0649524i	$0.0206895\pi$
$709$			3.45898i			0.129905i	−0.997888	+	0.0649524i	$0.979310\pi$
$710$	−64.4549			−2.41895
$711$			1.50395i			0.0564026i
$712$	−19.2758			−0.722391
$713$	−11.9040	+	3.27053i	−0.445810	+	0.122482i
$714$	−48.6864	+	10.3668i	−1.82204	+	0.387966i
$715$	−38.1453			−1.42655
$716$	50.1493			1.87417
$717$		−	11.8777i		−	0.443583i
$718$		−	6.97756i		−	0.260400i
$719$		−	2.89888i		−	0.108110i	−0.998538	−	0.0540549i	$-0.982785\pi$
$719$		−	2.89888i		−	0.108110i	0.998538	−	0.0540549i	$-0.0172146\pi$
$720$	−34.2551			−1.27661
$721$	2.98101	+	14.0000i	0.111019	+	0.521387i
$722$	24.6674			0.918024
$723$		−	18.4940i		−	0.687800i
$724$	55.7713			2.07273
$725$	6.72947			0.249926
$726$		−	3.09622i		−	0.114912i
$727$	48.9506			1.81548			0.907739	−	0.419536i	$-0.137807\pi$
$727$	48.9506			1.81548			0.907739	+	0.419536i	$0.137807\pi$
$728$	107.173	−	22.8203i	3.97211	−	0.845778i
$729$	−1.00000			−0.0370370
$730$		−	67.3773i		−	2.49374i
$731$			5.48196i			0.202758i
$732$		−	43.3693i		−	1.60298i
$733$	−43.2655			−1.59805			−0.799024	−	0.601299i	$-0.794650\pi$
$733$	−43.2655			−1.59805			−0.799024	+	0.601299i	$0.794650\pi$
$734$	−56.0408			−2.06850
$735$	−7.37950	−	16.5429i	−0.272197	−	0.610193i
$736$	22.9409	+	83.5000i	0.845613	+	3.07785i
$737$	24.3668			0.897561
$738$			13.4820i			0.496278i
$739$	51.0111			1.87647			0.938237	−	0.345994i	$-0.112458\pi$
$739$	51.0111			1.87647			0.938237	+	0.345994i	$0.112458\pi$
$740$		−	39.6083i		−	1.45603i
$741$	−14.7408			−0.541516
$742$	−52.5310	+	11.1854i	−1.92847	+	0.410629i
$743$		−	11.9002i		−	0.436575i	−0.975885	−	0.218287i	$-0.929953\pi$
$743$		−	11.9002i		−	0.436575i	0.975885	−	0.218287i	$-0.0700470\pi$
$744$	−22.7004			−0.832238
$745$		−	50.8837i		−	1.86423i
$746$		−	6.56516i		−	0.240368i
$747$	−15.7572			−0.576526
$748$		−	115.429i		−	4.22050i
$749$	−7.73651	+	1.64733i	−0.282686	+	0.0601921i
$750$			23.0511i			0.841708i
$751$		−	3.82447i		−	0.139557i	−0.997563	−	0.0697785i	$-0.977771\pi$
$751$		−	3.82447i		−	0.139557i	0.997563	−	0.0697785i	$-0.0222292\pi$
$752$			163.611i			5.96629i
$753$			21.3346i			0.777477i
$754$		−	50.2345i		−	1.82943i
$755$	12.2204			0.444746
$756$	13.6388	−	2.90409i	0.496037	−	0.105621i
$757$			14.3935i			0.523141i	0.965184	+	0.261570i	$0.0842404\pi$
$757$			14.3935i			0.523141i	−0.965184	+	0.261570i	$0.915760\pi$
$758$			27.9102i			1.01375i
$759$	3.98788	+	14.5150i	0.144751	+	0.526862i
$760$	−71.6272			−2.59819
$761$		−	26.1814i		−	0.949073i	−0.880236	−	0.474537i	$-0.842616\pi$
$761$		−	26.1814i		−	0.949073i	0.880236	−	0.474537i	$-0.157384\pi$
$762$		−	51.3827i		−	1.86140i
$763$	11.5340	−	2.45593i	0.417560	−	0.0889107i
$764$			63.1713i			2.28546i
$765$	18.0561			0.652820
$766$	13.3119			0.480980
$767$	14.8186			0.535070
$768$			19.6934i			0.710624i
$769$	−39.1998			−1.41358			−0.706790	−	0.707423i	$-0.749858\pi$
$769$	−39.1998			−1.41358			−0.706790	+	0.707423i	$0.749858\pi$
$770$	56.6735	−	12.0675i	2.04237	−	0.434881i
$771$	15.1973			0.547319
$772$	15.6373			0.562798
$773$	55.1204			1.98254			0.991272	−	0.131835i	$-0.0420868\pi$
$773$	55.1204			1.98254			0.991272	+	0.131835i	$0.0420868\pi$
$774$		−	2.11844i		−	0.0761457i
$775$		−	4.36675i		−	0.156858i
$776$	68.3003			2.45184
$777$	1.60017	+	7.51504i	0.0574059	+	0.269600i
$778$			42.4876i			1.52325i
$779$			15.6937i			0.562286i
$780$	−64.0530			−2.29347
$781$			28.9940i			1.03749i
$782$	−23.9041	−	87.0059i	−0.854810	−	3.11133i
$783$		−	3.96693i		−	0.141766i
$784$	−84.6242	+	37.7495i	−3.02229	+	1.34820i
$785$	24.5411			0.875908
$786$	27.3638			0.976033
$787$	37.0466			1.32057			0.660284	−	0.751016i	$-0.270436\pi$
$787$	37.0466			1.32057			0.660284	+	0.751016i	$0.270436\pi$
$788$	89.2133			3.17809
$789$	15.2244			0.542004
$790$			10.4939i			0.373357i
$791$	−53.3497	+	11.3597i	−1.89690	+	0.403905i
$792$			27.6795i			0.983547i
$793$		−	38.6449i		−	1.37232i
$794$			28.2825i			1.00371i
$795$	19.4820			0.690954
$796$	−80.1448			−2.84066
$797$	−23.8003			−0.843051			−0.421525	−	0.906817i	$-0.638505\pi$
$797$	−23.8003			−0.843051			−0.421525	+	0.906817i	$0.638505\pi$
$798$	21.9008	−	4.66332i	0.775279	−	0.165080i
$799$		−	86.2406i		−	3.05097i
$800$	−30.6302			−1.08294
$801$	−2.18580			−0.0772314
$802$		−	56.6139i		−	1.99911i
$803$	−30.3086			−1.06957
$804$	40.9163			1.44301
$805$	29.1557	−	15.1018i	1.02760	−	0.532270i
$806$	−32.5972			−1.14819
$807$	19.5481			0.688126
$808$		−	65.1322i		−	2.29134i
$809$	5.76444			0.202667			0.101334	−	0.994853i	$-0.467689\pi$
$809$	5.76444			0.202667			0.101334	+	0.994853i	$0.467689\pi$
$810$	−6.97756			−0.245166
$811$		−	7.04906i		−	0.247526i	−0.992312	−	0.123763i	$-0.960504\pi$
$811$		−	7.04906i		−	0.247526i	0.992312	−	0.123763i	$-0.0394963\pi$
$812$	11.5203	+	54.1040i	0.404284	+	1.89868i
$813$	9.11521			0.319684
$814$	−24.5782			−0.861465
$815$	−16.9448			−0.593550
$816$		−	92.3652i		−	3.23343i
$817$		−	2.46597i		−	0.0862735i
$818$		−	38.1412i		−	1.33358i
$819$	12.1530	−	2.58774i	0.424662	−	0.0904229i
$820$			68.1938i			2.38143i
$821$	7.82164			0.272977			0.136489	−	0.990642i	$-0.456418\pi$
$821$	7.82164			0.272977			0.136489	+	0.990642i	$0.456418\pi$
$822$	12.7002			0.442969
$823$	−32.1995			−1.12240			−0.561202	−	0.827679i	$-0.689661\pi$
$823$	−32.1995			−1.12240			−0.561202	+	0.827679i	$0.689661\pi$
$824$	−47.7100			−1.66206
$825$	−5.32454			−0.185377
$826$	−22.0165	+	4.68795i	−0.766051	+	0.163115i
$827$		−	14.7733i		−	0.513720i	−0.966449	−	0.256860i	$-0.917312\pi$
$827$		−	14.7733i		−	0.513720i	0.966449	−	0.256860i	$-0.0826878\pi$
$828$	6.69639	+	24.3734i	0.232716	+	0.847036i
$829$			14.3958i			0.499986i	0.968248	+	0.249993i	$0.0804284\pi$
$829$			14.3958i			0.499986i	−0.968248	+	0.249993i	$0.919572\pi$
$830$	−109.947			−3.81631
$831$		−	21.0702i		−	0.730917i
$832$			104.314i			3.61642i
$833$	44.6060	−	19.8980i	1.54551	−	0.689426i
$834$	6.56006			0.227156
$835$		−	57.0081i		−	1.97285i
$836$			51.9238i			1.79582i
$837$	−2.57414			−0.0889753
$838$	−56.3936			−1.94808
$839$	−46.8957			−1.61902			−0.809509	−	0.587108i	$-0.800267\pi$
$839$	−46.8957			−1.61902			−0.809509	+	0.587108i	$0.800267\pi$
$840$	59.0531	−	12.5741i	2.03753	−	0.433849i
$841$	−13.2635			−0.457362
$842$			3.82447i			0.131800i
$843$	13.3224			0.458848
$844$	96.9398			3.33681
$845$	−23.4348			−0.806183
$846$			33.3266i			1.14579i
$847$	0.632710	+	2.97146i	0.0217402	+	0.102100i
$848$		−	99.6591i		−	3.42231i
$849$			1.01643i			0.0348837i
$850$	31.9163			1.09472
$851$	−13.4299	+	3.68975i	−0.460371	+	0.126483i
$852$			48.6864i			1.66797i
$853$		−	4.65328i		−	0.159325i	−0.996822	−	0.0796626i	$-0.974616\pi$
$853$		−	4.65328i		−	0.159325i	0.996822	−	0.0796626i	$-0.0253843\pi$
$854$	12.2255	+	57.4158i	0.418348	+	1.96473i
$855$	−8.12225			−0.277775
$856$		−	26.3649i		−	0.901134i
$857$			0.670362i			0.0228991i	0.999934	+	0.0114496i	$0.00364459\pi$
$857$			0.670362i			0.0228991i	−0.999934	+	0.0114496i	$0.996355\pi$
$858$			39.7469i			1.35694i
$859$		−	42.3106i		−	1.44362i	−0.692091	−	0.721810i	$-0.743310\pi$
$859$		−	42.3106i		−	1.44362i	0.692091	−	0.721810i	$-0.256690\pi$
$860$		−	10.7154i		−	0.365391i
$861$	−2.75503	−	12.9387i	−0.0938911	−	0.440950i
$862$			67.4860i			2.29858i
$863$	−5.03007			−0.171226			−0.0856129	−	0.996328i	$-0.527285\pi$
$863$	−5.03007			−0.171226			−0.0856129	+	0.996328i	$0.527285\pi$
$864$			18.0561i			0.614281i
$865$			50.8653i			1.72947i
$866$	−72.4567			−2.46218
$867$			31.6864i			1.07612i
$868$	35.1081	−	7.47555i	1.19165	−	0.253737i
$869$	4.72052			0.160133
$870$		−	27.6795i		−	0.938422i
$871$	36.4591			1.23537
$872$			39.3063i			1.33108i
$873$	7.74499			0.262128
$874$	10.7529	+	39.1382i	0.363722	+	1.32387i
$875$	−4.71048	−	22.1223i	−0.159243	−	0.747869i
$876$	−50.8937			−1.71954
$877$	−47.3377			−1.59848			−0.799241	−	0.601011i	$-0.794765\pi$
$877$	−47.3377			−1.59848			−0.799241	+	0.601011i	$0.794765\pi$
$878$		−	54.9789i		−	1.85545i
$879$		−	7.34305i		−	0.247675i
$880$			107.518i			3.62443i
$881$	2.66556			0.0898051			0.0449026	−	0.998991i	$-0.485702\pi$
$881$	2.66556			0.0898051			0.0449026	+	0.998991i	$0.485702\pi$
$882$	−17.2375	+	7.68935i	−0.580415	+	0.258914i
$883$	28.7945			0.969013			0.484506	−	0.874788i	$-0.338999\pi$
$883$	28.7945			0.969013			0.484506	+	0.874788i	$0.338999\pi$
$884$		−	172.712i		−	5.80893i
$885$	8.16516			0.274469
$886$	52.2526			1.75546
$887$			1.89674i			0.0636862i	0.999493	+	0.0318431i	$0.0101377\pi$
$887$			1.89674i			0.0636862i	−0.999493	+	0.0318431i	$0.989862\pi$
$888$	−25.6102			−0.859421
$889$	10.5000	+	49.3122i	0.352159	+	1.65388i
$890$	−15.2515			−0.511233
$891$			3.13874i			0.105152i
$892$		−	15.9488i		−	0.534005i
$893$			38.7940i			1.29819i
$894$	−53.0202			−1.77326
$895$	24.6224			0.823037
$896$	−13.1021	−	61.5326i	−0.437711	−	2.05566i
$897$	5.96693	+	21.7183i	0.199230	+	0.725154i
$898$	40.3377			1.34609
$899$		−	10.2114i		−	0.340570i
$900$	−8.94090			−0.298030
$901$			52.5310i			1.75006i
$902$	42.3164			1.40898
$903$	0.432901	+	2.03307i	0.0144060	+	0.0676564i
$904$		−	181.808i		−	6.04685i
$905$	27.3827			0.910233
$906$		−	12.7335i		−	0.423043i
$907$			12.9751i			0.430833i	0.976522	+	0.215416i	$0.0691108\pi$
$907$			12.9751i			0.430833i	−0.976522	+	0.215416i	$0.930889\pi$
$908$	44.9611			1.49209
$909$		−	7.38574i		−	0.244970i
$910$	84.7986	−	18.0561i	2.81104	−	0.598554i
$911$		−	26.8082i		−	0.888196i	−0.895978	−	0.444098i	$-0.853524\pi$
$911$		−	26.8082i		−	0.888196i	0.895978	−	0.444098i	$-0.146476\pi$
$912$			41.5490i			1.37583i
$913$			49.4578i			1.63682i
$914$			71.7124i			2.37204i
$915$		−	21.2936i		−	0.703944i
$916$	57.1041			1.88677
$917$	−26.2611	+	5.59176i	−0.867218	+	0.184656i
$918$		−	18.8142i		−	0.620963i
$919$			42.9983i			1.41838i	0.705016	+	0.709191i	$0.250940\pi$
$919$			42.9983i			1.41838i	−0.705016	+	0.709191i	$0.749060\pi$
$920$	28.9940	+	105.532i	0.955905	+	3.47929i
$921$	9.98101			0.328886
$922$		−	64.1030i		−	2.11112i
$923$			43.3827i			1.42796i
$924$	−9.11521	−	42.8086i	−0.299868	−	1.40830i
$925$		−	4.92648i		−	0.161982i
$926$	−71.0249			−2.33402
$927$	−5.41013			−0.177692
$928$	−71.6272			−2.35128
$929$			3.74546i			0.122884i	0.998111	+	0.0614422i	$0.0195700\pi$
$929$			3.74546i			0.122884i	−0.998111	+	0.0614422i	$0.980430\pi$
$930$	−17.9612			−0.588972
$931$	−20.0653	+	8.95081i	−0.657614	+	0.293351i
$932$	−48.8607			−1.60048
$933$	9.95988			0.326072
$934$	−24.7572			−0.810079
$935$		−	56.6735i		−	1.85342i
$936$			41.4158i			1.35372i
$937$	−33.4242			−1.09192			−0.545960	−	0.837811i	$-0.683835\pi$
$937$	−33.4242			−1.09192			−0.545960	+	0.837811i	$0.683835\pi$
$938$	−54.1683	+	11.5340i	−1.76866	+	0.376599i
$939$			19.6634i			0.641690i
$940$			168.571i			5.49819i
$941$	26.6813			0.869785			0.434892	−	0.900482i	$-0.356786\pi$
$941$	26.6813			0.869785			0.434892	+	0.900482i	$0.356786\pi$
$942$		−	25.5715i		−	0.833164i
$943$	23.1224	−	6.35267i	0.752968	−	0.206871i
$944$		−	41.7685i		−	1.35945i
$945$	6.69639	−	1.42586i	0.217834	−	0.0463832i
$946$	−6.64924			−0.216185
$947$	27.3266			0.887996			0.443998	−	0.896028i	$-0.353560\pi$
$947$	27.3266			0.887996			0.443998	+	0.896028i	$0.353560\pi$
$948$	7.92663			0.257445
$949$	−45.3497			−1.47211
$950$	−14.3571			−0.465805
$951$			26.0420i			0.844470i
$952$	33.9048	+	159.230i	1.09886	+	5.16069i
$953$			53.2366i			1.72450i	0.506480	+	0.862252i	$0.330946\pi$
$953$			53.2366i			1.72450i	−0.506480	+	0.862252i	$0.669054\pi$
$954$		−	20.3000i		−	0.657236i
$955$			31.0160i			1.00365i
$956$	−62.6021			−2.02470
$957$	−12.4512			−0.402489
$958$	−7.36904			−0.238083
$959$	−12.1884	+	2.59527i	−0.393584	+	0.0838056i
$960$			57.4774i			1.85507i
$961$	24.3738			0.786252
$962$	−36.7755			−1.18569
$963$		−	2.98968i		−	0.0963411i
$964$	−97.4733			−3.13940
$965$	7.67763			0.247152
$966$	−15.7359	−	30.3799i	−0.506295	−	0.977456i
$967$	−18.9639			−0.609839			−0.304919	−	0.952378i	$-0.598630\pi$
$967$	−18.9639			−0.609839			−0.304919	+	0.952378i	$0.598630\pi$
$968$	−10.1263			−0.325471
$969$		−	21.9008i		−	0.703554i
$970$	54.0412			1.73516
$971$	−40.9527			−1.31424			−0.657118	−	0.753788i	$-0.728225\pi$
$971$	−40.9527			−1.31424			−0.657118	+	0.753788i	$0.728225\pi$
$972$			5.27053i			0.169052i
$973$	−6.29571	+	1.34054i	−0.201831	+	0.0429758i
$974$	−57.6322			−1.84665
$975$	−7.96693			−0.255146
$976$	−108.926			−3.48664
$977$		−	3.69363i		−	0.118170i	−0.998253	−	0.0590849i	$-0.981182\pi$
$977$		−	3.69363i		−	0.118170i	0.998253	−	0.0590849i	$-0.0188183\pi$
$978$			17.6563i			0.564585i
$979$			6.86066i			0.219268i
$980$	−87.1897	+	38.8939i	−2.78517	+	1.24242i
$981$			4.45718i			0.142307i
$982$	58.7235			1.87394
$983$	−42.0674			−1.34174			−0.670872	−	0.741574i	$-0.734080\pi$
$983$	−42.0674			−1.34174			−0.670872	+	0.741574i	$0.734080\pi$
$984$	44.0932			1.40564
$985$	43.8022			1.39565
$986$	74.6347			2.37685
$987$	−6.81027	−	31.9837i	−0.216773	−	1.01805i
$988$			77.6918i			2.47170i
$989$	−3.63325	+	0.998203i	−0.115530	+	0.0317410i
$990$			21.9008i			0.696052i
$991$	39.5972			1.25785			0.628923	−	0.777468i	$-0.283496\pi$
$991$	39.5972			1.25785			0.628923	+	0.777468i	$0.283496\pi$
$992$			46.4790i			1.47571i
$993$		−	8.65628i		−	0.274699i
$994$	−13.7244	−	64.4549i	−0.435310	−	2.04439i
$995$	−39.3497			−1.24747
$996$			83.0489i			2.63150i
$997$			13.1814i			0.417458i	0.977974	+	0.208729i	$0.0669326\pi$
$997$			13.1814i			0.417458i	−0.977974	+	0.208729i	$0.933067\pi$
$998$	48.8647			1.54679
$999$	−2.90409			−0.0918815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.c.160.4	yes	12
3.2	odd	2		1449.2.h.e.1126.10		12
7.6	odd	2	inner	483.2.h.c.160.1	✓	12
21.20	even	2		1449.2.h.e.1126.12		12
23.22	odd	2	inner	483.2.h.c.160.3	yes	12
69.68	even	2		1449.2.h.e.1126.11		12
161.160	even	2	inner	483.2.h.c.160.2	yes	12
483.482	odd	2		1449.2.h.e.1126.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.c.160.1	✓	12	7.6	odd	2	inner
483.2.h.c.160.2	yes	12	161.160	even	2	inner
483.2.h.c.160.3	yes	12	23.22	odd	2	inner
483.2.h.c.160.4	yes	12	1.1	even	1	trivial
1449.2.h.e.1126.9		12	483.482	odd	2
1449.2.h.e.1126.10		12	3.2	odd	2
1449.2.h.e.1126.11		12	69.68	even	2
1449.2.h.e.1126.12		12	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.69639 q^{2} +1.00000i q^{3} +5.27053 q^{4} +2.58774 q^{5} -2.69639i q^{6} +(0.551006 + 2.58774i) q^{7} -8.81864 q^{8} -1.00000 q^{9} -6.97756 q^{10} +3.13874i q^{11} +5.27053i q^{12} +4.69639i q^{13} +(-1.48573 - 6.97756i) q^{14} +2.58774i q^{15} +13.2375 q^{16} -6.97756 q^{17} +2.69639 q^{18} +3.13874 q^{19} +13.6388 q^{20} +(-2.58774 + 0.551006i) q^{21} -8.46329i q^{22} +(-1.27053 - 4.62447i) q^{23} -8.81864i q^{24} +1.69639 q^{25} -12.6633i q^{26} -1.00000i q^{27} +(2.90409 + 13.6388i) q^{28} +3.96693 q^{29} -6.97756i q^{30} -2.57414i q^{31} -18.0561 q^{32} -3.13874 q^{33} +18.8142 q^{34} +(1.42586 + 6.69639i) q^{35} -5.27053 q^{36} -2.90409i q^{37} -8.46329 q^{38} -4.69639 q^{39} -22.8203 q^{40} +5.00000i q^{41} +(6.97756 - 1.48573i) q^{42} -0.785656i q^{43} +16.5429i q^{44} -2.58774 q^{45} +(3.42586 + 12.4694i) q^{46} +12.3597i q^{47} +13.2375i q^{48} +(-6.39279 + 2.85172i) q^{49} -4.57414 q^{50} -6.97756i q^{51} +24.7525i q^{52} -7.52857i q^{53} +2.69639i q^{54} +8.12225i q^{55} +(-4.85912 - 22.8203i) q^{56} +3.13874i q^{57} -10.6964 q^{58} -3.15532i q^{59} +13.6388i q^{60} -8.22864 q^{61} +6.94090i q^{62} +(-0.551006 - 2.58774i) q^{63} +22.2114 q^{64} +12.1530i q^{65} +8.46329 q^{66} -7.76322i q^{67} -36.7755 q^{68} +(4.62447 - 1.27053i) q^{69} +(-3.84468 - 18.0561i) q^{70} +9.23746 q^{71} +8.81864 q^{72} +9.65628i q^{73} +7.83058i q^{74} +1.69639i q^{75} +16.5429 q^{76} +(-8.12225 + 1.72947i) q^{77} +12.6633 q^{78} -1.50395i q^{79} +34.2551 q^{80} +1.00000 q^{81} -13.4820i q^{82} +15.7572 q^{83} +(-13.6388 + 2.90409i) q^{84} -18.0561 q^{85} +2.11844i q^{86} +3.96693i q^{87} -27.6795i q^{88} +2.18580 q^{89} +6.97756 q^{90} +(-12.1530 + 2.58774i) q^{91} +(-6.69639 - 24.3734i) q^{92} +2.57414 q^{93} -33.3266i q^{94} +8.12225 q^{95} -18.0561i q^{96} -7.74499 q^{97} +(17.2375 - 7.68935i) q^{98} -3.13874i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9	\( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more