LMFDB - Embedded newform 187.2.d.a.67.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(67,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("187.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 172x^{12} + 700x^{10} + 1492x^{8} + 1620x^{6} + 840x^{4} + 196x^{2} + 16 $ x^16 + 21x^14 + 172x^12 + 700x^10 + 1492x^8 + 1620x^6 + 840x^4 + 196*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.9
Root			$0.420099i$ of defining polynomial
Character	$\chi$	$=$	187.67
Dual form			187.2.d.a.67.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.420099 q^{2} -0.0890922i q^{3} -1.82352 q^{4} +3.34068i q^{5} -0.0374276i q^{6} +2.13044i q^{7} -1.60626 q^{8} +2.99206 q^{9} +O(q^{10})$	\(q+0.420099 q^{2} -0.0890922i q^{3} -1.82352 q^{4} +3.34068i q^{5} -0.0374276i q^{6} +2.13044i q^{7} -1.60626 q^{8} +2.99206 q^{9} +1.40342i q^{10} +1.00000i q^{11} +0.162461i q^{12} -2.81007 q^{13} +0.894998i q^{14} +0.297629 q^{15} +2.97225 q^{16} +(4.03951 + 0.826028i) q^{17} +1.25696 q^{18} -1.49888 q^{19} -6.09179i q^{20} +0.189806 q^{21} +0.420099i q^{22} -7.53789i q^{23} +0.143105i q^{24} -6.16015 q^{25} -1.18051 q^{26} -0.533846i q^{27} -3.88490i q^{28} +5.21426i q^{29} +0.125034 q^{30} +1.28588i q^{31} +4.46115 q^{32} +0.0890922 q^{33} +(1.69700 + 0.347014i) q^{34} -7.11713 q^{35} -5.45608 q^{36} -2.92929i q^{37} -0.629677 q^{38} +0.250355i q^{39} -5.36599i q^{40} -5.86187i q^{41} +0.0797373 q^{42} +5.20419 q^{43} -1.82352i q^{44} +9.99553i q^{45} -3.16666i q^{46} -5.15589 q^{47} -0.264804i q^{48} +2.46121 q^{49} -2.58787 q^{50} +(0.0735927 - 0.359889i) q^{51} +5.12421 q^{52} +11.7626 q^{53} -0.224268i q^{54} -3.34068 q^{55} -3.42204i q^{56} +0.133538i q^{57} +2.19051i q^{58} +2.45417 q^{59} -0.542731 q^{60} +8.34393i q^{61} +0.540198i q^{62} +6.37442i q^{63} -4.07037 q^{64} -9.38754i q^{65} +0.0374276 q^{66} +5.93567 q^{67} +(-7.36612 - 1.50628i) q^{68} -0.671567 q^{69} -2.98990 q^{70} -14.4899i q^{71} -4.80602 q^{72} -5.99444i q^{73} -1.23059i q^{74} +0.548821i q^{75} +2.73323 q^{76} -2.13044 q^{77} +0.105174i q^{78} +10.4774i q^{79} +9.92933i q^{80} +8.92863 q^{81} -2.46257i q^{82} -10.2104 q^{83} -0.346114 q^{84} +(-2.75950 + 13.4947i) q^{85} +2.18628 q^{86} +0.464550 q^{87} -1.60626i q^{88} +7.08143 q^{89} +4.19911i q^{90} -5.98669i q^{91} +13.7455i q^{92} +0.114562 q^{93} -2.16598 q^{94} -5.00727i q^{95} -0.397454i q^{96} +14.3588i q^{97} +1.03395 q^{98} +2.99206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.420099			0.297055			0.148528	−	0.988908i	$-0.452547\pi$
$2$	0.420099			0.297055			0.148528	+	0.988908i	$0.452547\pi$
$3$		−	0.0890922i		−	0.0514374i	−0.999669	−	0.0257187i	$-0.991813\pi$
$3$		−	0.0890922i		−	0.0514374i	0.999669	−	0.0257187i	$-0.00818742\pi$
$4$	−1.82352			−0.911758
$5$			3.34068i			1.49400i	0.664825	+	0.746999i	$0.268506\pi$
$5$			3.34068i			1.49400i	−0.664825	+	0.746999i	$0.731494\pi$
$6$		−	0.0374276i		−	0.0152797i
$7$			2.13044i			0.805232i	0.915369	+	0.402616i	$0.131899\pi$
$7$			2.13044i			0.805232i	−0.915369	+	0.402616i	$0.868101\pi$
$8$	−1.60626			−0.567897
$9$	2.99206			0.997354
$10$			1.40342i			0.443800i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$			0.162461i			0.0468985i
$13$	−2.81007			−0.779373			−0.389686	−	0.920948i	$-0.627417\pi$
$13$	−2.81007			−0.779373			−0.389686	+	0.920948i	$0.627417\pi$
$14$			0.894998i			0.239198i
$15$	0.297629			0.0768474
$16$	2.97225			0.743062
$17$	4.03951	+	0.826028i	0.979726	+	0.200341i
$17$	4.03951	+	0.826028i	0.979726	+	0.200341i
$18$	1.25696			0.296269
$19$	−1.49888			−0.343866			−0.171933	−	0.985109i	$-0.555001\pi$
$19$	−1.49888			−0.343866			−0.171933	+	0.985109i	$0.555001\pi$
$20$		−	6.09179i		−	1.36217i
$21$	0.189806			0.0414190
$22$			0.420099i			0.0895655i
$23$		−	7.53789i		−	1.57176i	−0.618380	−	0.785879i	$-0.712211\pi$
$23$		−	7.53789i		−	1.57176i	0.618380	−	0.785879i	$-0.287789\pi$
$24$			0.143105i			0.0292112i
$25$	−6.16015			−1.23203
$26$	−1.18051			−0.231517
$27$		−	0.533846i		−	0.102739i
$28$		−	3.88490i		−	0.734177i
$29$			5.21426i			0.968263i	0.874995	+	0.484132i	$0.160864\pi$
$29$			5.21426i			0.968263i	−0.874995	+	0.484132i	$0.839136\pi$
$30$	0.125034			0.0228279
$31$			1.28588i			0.230951i	0.993310	+	0.115476i	$0.0368392\pi$
$31$			1.28588i			0.230951i	−0.993310	+	0.115476i	$0.963161\pi$
$32$	4.46115			0.788628
$33$	0.0890922			0.0155090
$34$	1.69700	+	0.347014i	0.291033	+	0.0595124i
$35$	−7.11713			−1.20301
$36$	−5.45608			−0.909346
$37$		−	2.92929i		−	0.481572i	−0.970578	−	0.240786i	$-0.922595\pi$
$37$		−	2.92929i		−	0.481572i	0.970578	−	0.240786i	$-0.0774053\pi$
$38$	−0.629677			−0.102147
$39$			0.250355i			0.0400889i
$40$		−	5.36599i		−	0.848437i
$41$		−	5.86187i		−	0.915470i	−0.889089	−	0.457735i	$-0.848661\pi$
$41$		−	5.86187i		−	0.915470i	0.889089	−	0.457735i	$-0.151339\pi$
$42$	0.0797373			0.0123037
$43$	5.20419			0.793631			0.396816	−	0.917898i	$-0.370115\pi$
$43$	5.20419			0.793631			0.396816	+	0.917898i	$0.370115\pi$
$44$		−	1.82352i		−	0.274905i
$45$			9.99553i			1.49005i
$46$		−	3.16666i		−	0.466899i
$47$	−5.15589			−0.752064			−0.376032	−	0.926607i	$-0.622712\pi$
$47$	−5.15589			−0.752064			−0.376032	+	0.926607i	$0.622712\pi$
$48$		−	0.264804i		−	0.0382212i
$49$	2.46121			0.351602
$50$	−2.58787			−0.365981
$51$	0.0735927	−	0.359889i	0.0103050	−	0.0503946i
$52$	5.12421			0.710600
$53$	11.7626			1.61572			0.807861	−	0.589373i	$-0.200625\pi$
$53$	11.7626			1.61572			0.807861	+	0.589373i	$0.200625\pi$
$54$		−	0.224268i		−	0.0305190i
$55$	−3.34068			−0.450457
$56$		−	3.42204i		−	0.457289i
$57$			0.133538i			0.0176876i
$58$			2.19051i			0.287627i
$59$	2.45417			0.319505			0.159753	−	0.987157i	$-0.448930\pi$
$59$	2.45417			0.319505			0.159753	+	0.987157i	$0.448930\pi$
$60$	−0.542731			−0.0700662
$61$			8.34393i			1.06833i	0.845380	+	0.534166i	$0.179374\pi$
$61$			8.34393i			1.06833i	−0.845380	+	0.534166i	$0.820626\pi$
$62$			0.540198i			0.0686052i
$63$			6.37442i			0.803101i
$64$	−4.07037			−0.508796
$65$		−	9.38754i		−	1.16438i
$66$	0.0374276			0.00460701
$67$	5.93567			0.725158			0.362579	−	0.931953i	$-0.381896\pi$
$67$	5.93567			0.725158			0.362579	+	0.931953i	$0.381896\pi$
$68$	−7.36612	−	1.50628i	−0.893273	−	0.182663i
$69$	−0.671567			−0.0808471
$70$	−2.98990			−0.357362
$71$		−	14.4899i		−	1.71964i	−0.510599	−	0.859819i	$-0.670576\pi$
$71$		−	14.4899i		−	1.71964i	0.510599	−	0.859819i	$-0.329424\pi$
$72$	−4.80602			−0.566395
$73$		−	5.99444i		−	0.701596i	−0.936451	−	0.350798i	$-0.885910\pi$
$73$		−	5.99444i		−	0.701596i	0.936451	−	0.350798i	$-0.114090\pi$
$74$		−	1.23059i		−	0.143053i
$75$			0.548821i			0.0633724i
$76$	2.73323			0.313523
$77$	−2.13044			−0.242787
$78$			0.105174i			0.0119086i
$79$			10.4774i			1.17880i	0.807842	+	0.589399i	$0.200635\pi$
$79$			10.4774i			1.17880i	−0.807842	+	0.589399i	$0.799365\pi$
$80$			9.92933i			1.11013i
$81$	8.92863			0.992070
$82$		−	2.46257i		−	0.271945i
$83$	−10.2104			−1.12073			−0.560367	−	0.828245i	$-0.689340\pi$
$83$	−10.2104			−1.12073			−0.560367	+	0.828245i	$0.689340\pi$
$84$	−0.346114			−0.0377642
$85$	−2.75950	+	13.4947i	−0.299309	+	1.46371i
$86$	2.18628			0.235752
$87$	0.464550			0.0498049
$88$		−	1.60626i		−	0.171228i
$89$	7.08143			0.750630			0.375315	−	0.926897i	$-0.377535\pi$
$89$	7.08143			0.750630			0.375315	+	0.926897i	$0.377535\pi$
$90$			4.19911i			0.442625i
$91$		−	5.98669i		−	0.627576i
$92$			13.7455i			1.43306i
$93$	0.114562			0.0118795
$94$	−2.16598			−0.223404
$95$		−	5.00727i		−	0.513735i
$96$		−	0.397454i		−	0.0405650i
$97$			14.3588i			1.45791i	0.684560	+	0.728956i	$0.259994\pi$
$97$			14.3588i			1.45791i	−0.684560	+	0.728956i	$0.740006\pi$
$98$	1.03395			0.104445
$99$			2.99206i			0.300714i
$100$	11.2331			1.12331
$101$	−13.0155			−1.29510			−0.647548	−	0.762025i	$-0.724205\pi$
$101$	−13.0155			−1.29510			−0.647548	+	0.762025i	$0.724205\pi$
$102$	0.0309162	−	0.151189i	0.00306116	−	0.0149700i
$103$	−2.21395			−0.218147			−0.109073	−	0.994034i	$-0.534788\pi$
$103$	−2.21395			−0.218147			−0.109073	+	0.994034i	$0.534788\pi$
$104$	4.51369			0.442604
$105$			0.634081i			0.0618800i
$106$	4.94147			0.479958
$107$		−	8.54382i		−	0.825962i	−0.910740	−	0.412981i	$-0.864488\pi$
$107$		−	8.54382i		−	0.825962i	0.910740	−	0.412981i	$-0.135512\pi$
$108$			0.973477i			0.0936729i
$109$			13.4901i			1.29212i	0.763288	+	0.646058i	$0.223584\pi$
$109$			13.4901i			1.29212i	−0.763288	+	0.646058i	$0.776416\pi$
$110$	−1.40342			−0.133811
$111$	−0.260977			−0.0247708
$112$			6.33220i			0.598337i
$113$		−	1.47191i		−	0.138466i	−0.997601	−	0.0692330i	$-0.977945\pi$
$113$		−	1.47191i		−	0.138466i	0.997601	−	0.0692330i	$-0.0220552\pi$
$114$			0.0560993i			0.00525419i
$115$	25.1817			2.34820
$116$		−	9.50829i		−	0.882822i
$117$	−8.40790			−0.777311
$118$	1.03099			0.0949107
$119$	−1.75981	+	8.60596i	−0.161321	+	0.788907i
$120$	−0.478068			−0.0436414
$121$	−1.00000			−0.0909091
$122$			3.50528i			0.317353i
$123$	−0.522246			−0.0470894
$124$		−	2.34483i		−	0.210572i
$125$		−	3.87569i		−	0.346652i
$126$			2.67789i			0.238565i
$127$	7.21406			0.640144			0.320072	−	0.947393i	$-0.396293\pi$
$127$	7.21406			0.640144			0.320072	+	0.947393i	$0.396293\pi$
$128$	−10.6323			−0.939768
$129$		−	0.463653i		−	0.0408223i
$130$		−	3.94370i		−	0.345885i
$131$		−	15.4247i		−	1.34766i	−0.738884	−	0.673832i	$-0.764647\pi$
$131$		−	15.4247i		−	1.34766i	0.738884	−	0.673832i	$-0.235353\pi$
$132$	−0.162461			−0.0141404
$133$		−	3.19327i		−	0.276892i
$134$	2.49357			0.215412
$135$	1.78341			0.153491
$136$	−6.48850	−	1.32681i	−0.556384	−	0.113773i
$137$	−5.57577			−0.476370			−0.238185	−	0.971220i	$-0.576553\pi$
$137$	−5.57577			−0.476370			−0.238185	+	0.971220i	$0.576553\pi$
$138$	−0.282125			−0.0240160
$139$			1.40296i			0.118997i	0.998228	+	0.0594986i	$0.0189502\pi$
$139$			1.40296i			0.118997i	−0.998228	+	0.0594986i	$0.981050\pi$
$140$	12.9782			1.09686
$141$			0.459349i			0.0386842i
$142$		−	6.08721i		−	0.510827i
$143$		−	2.81007i		−	0.234990i
$144$	8.89315			0.741096
$145$	−17.4192			−1.44658
$146$		−	2.51826i		−	0.208413i
$147$		−	0.219275i		−	0.0180855i
$148$			5.34161i			0.439078i
$149$	−13.5489			−1.10997			−0.554984	−	0.831861i	$-0.687276\pi$
$149$	−13.5489			−1.10997			−0.554984	+	0.831861i	$0.687276\pi$
$150$			0.230559i			0.0188251i
$151$	−21.9814			−1.78882			−0.894410	−	0.447248i	$-0.852404\pi$
$151$	−21.9814			−1.78882			−0.894410	+	0.447248i	$0.852404\pi$
$152$	2.40758			0.195281
$153$	12.0865	+	2.47153i	0.977134	+	0.199811i
$154$	−0.894998			−0.0721210
$155$	−4.29572			−0.345041
$156$		−	0.456527i		−	0.0365514i
$157$	−5.98704			−0.477818			−0.238909	−	0.971042i	$-0.576790\pi$
$157$	−5.98704			−0.477818			−0.238909	+	0.971042i	$0.576790\pi$
$158$			4.40154i			0.350168i
$159$		−	1.04796i		−	0.0831085i
$160$			14.9033i			1.17821i
$161$	16.0590			1.26563
$162$	3.75091			0.294699
$163$		−	24.8721i		−	1.94813i	−0.226266	−	0.974066i	$-0.572652\pi$
$163$		−	24.8721i		−	1.94813i	0.226266	−	0.974066i	$-0.427348\pi$
$164$			10.6892i			0.834687i
$165$			0.297629i			0.0231704i
$166$	−4.28937			−0.332920
$167$		−	12.4223i		−	0.961266i	−0.876922	−	0.480633i	$-0.840407\pi$
$167$		−	12.4223i		−	0.961266i	0.876922	−	0.480633i	$-0.159593\pi$
$168$	−0.304877			−0.0235218
$169$	−5.10351			−0.392578
$170$	−1.15926	+	5.66912i	−0.0889114	+	0.434802i
$171$	−4.48474			−0.342956
$172$	−9.48992			−0.723600
$173$		−	24.6065i		−	1.87079i	−0.353599	−	0.935397i	$-0.615042\pi$
$173$		−	24.6065i		−	1.87079i	0.353599	−	0.935397i	$-0.384958\pi$
$174$	0.195157			0.0147948
$175$		−	13.1238i		−	0.992070i
$176$			2.97225i			0.224041i
$177$		−	0.218647i		−	0.0164345i
$178$	2.97490			0.222978
$179$	12.3470			0.922859			0.461430	−	0.887177i	$-0.347337\pi$
$179$	12.3470			0.922859			0.461430	+	0.887177i	$0.347337\pi$
$180$		−	18.2270i		−	1.35856i
$181$			9.06052i			0.673463i	0.941601	+	0.336732i	$0.109322\pi$
$181$			9.06052i			0.673463i	−0.941601	+	0.336732i	$0.890678\pi$
$182$		−	2.51500i		−	0.186425i
$183$	0.743379			0.0549522
$184$			12.1078i			0.892597i
$185$	9.78583			0.719468
$186$	0.0481274			0.00352887
$187$	−0.826028	+	4.03951i	−0.0604052	+	0.295399i
$188$	9.40185			0.685700
$189$	1.13733			0.0827285
$190$		−	2.10355i		−	0.152608i
$191$	17.0736			1.23540			0.617702	−	0.786412i	$-0.288064\pi$
$191$	17.0736			1.23540			0.617702	+	0.786412i	$0.288064\pi$
$192$			0.362638i			0.0261711i
$193$		−	20.7292i		−	1.49212i	−0.665877	−	0.746061i	$-0.731943\pi$
$193$		−	20.7292i		−	1.49212i	0.665877	−	0.746061i	$-0.268057\pi$
$194$			6.03211i			0.433080i
$195$	−0.836357			−0.0598928
$196$	−4.48806			−0.320576
$197$			15.1339i			1.07824i	0.842228	+	0.539122i	$0.181244\pi$
$197$			15.1339i			1.07824i	−0.842228	+	0.539122i	$0.818756\pi$
$198$			1.25696i			0.0893285i
$199$		−	20.5506i		−	1.45679i	−0.685155	−	0.728397i	$-0.740265\pi$
$199$		−	20.5506i		−	1.45679i	0.685155	−	0.728397i	$-0.259735\pi$
$200$	9.89478			0.699666
$201$		−	0.528822i		−	0.0373002i
$202$	−5.46782			−0.384715
$203$	−11.1087			−0.779677
$204$	−0.134197	+	0.656264i	−0.00939570	+	0.0459477i
$205$	19.5826			1.36771
$206$	−0.930077			−0.0648015
$207$		−	22.5538i		−	1.56760i
$208$	−8.35222			−0.579122
$209$		−	1.49888i		−	0.103680i
$210$			0.266377i			0.0183818i
$211$			15.7349i			1.08324i	0.840625	+	0.541618i	$0.182188\pi$
$211$			15.7349i			1.08324i	−0.840625	+	0.541618i	$0.817812\pi$
$212$	−21.4494			−1.47315
$213$	−1.29094			−0.0884537
$214$		−	3.58925i		−	0.245356i
$215$			17.3855i			1.18568i
$216$			0.857494i			0.0583450i
$217$	−2.73950			−0.185969
$218$			5.66717i			0.383829i
$219$	−0.534058			−0.0360883
$220$	6.09179			0.410708
$221$	−11.3513	−	2.32120i	−0.763572	−	0.156141i
$222$	−0.109636			−0.00735830
$223$	−7.41477			−0.496530			−0.248265	−	0.968692i	$-0.579860\pi$
$223$	−7.41477			−0.496530			−0.248265	+	0.968692i	$0.579860\pi$
$224$			9.50423i			0.635028i
$225$	−18.4315			−1.22877
$226$		−	0.618350i		−	0.0411320i
$227$			6.82759i			0.453163i	0.973992	+	0.226582i	$0.0727550\pi$
$227$			6.82759i			0.453163i	−0.973992	+	0.226582i	$0.927245\pi$
$228$		−	0.243509i		−	0.0161268i
$229$	−2.29082			−0.151382			−0.0756909	−	0.997131i	$-0.524116\pi$
$229$	−2.29082			−0.151382			−0.0756909	+	0.997131i	$0.524116\pi$
$230$	10.5788			0.697545
$231$			0.189806i			0.0124883i
$232$		−	8.37543i		−	0.549874i
$233$		−	9.82817i		−	0.643865i	−0.946763	−	0.321932i	$-0.895668\pi$
$233$		−	9.82817i		−	0.643865i	0.946763	−	0.321932i	$-0.104332\pi$
$234$	−3.53215			−0.230904
$235$		−	17.2242i		−	1.12358i
$236$	−4.47522			−0.291312
$237$	0.933453			0.0606343
$238$	−0.739293	+	3.61536i	−0.0479213	+	0.234349i
$239$	1.89256			0.122419			0.0612096	−	0.998125i	$-0.480504\pi$
$239$	1.89256			0.122419			0.0612096	+	0.998125i	$0.480504\pi$
$240$	0.884625			0.0571023
$241$			25.2013i			1.62336i	0.584104	+	0.811679i	$0.301446\pi$
$241$			25.2013i			1.62336i	−0.584104	+	0.811679i	$0.698554\pi$
$242$	−0.420099			−0.0270050
$243$		−	2.39701i		−	0.153768i
$244$		−	15.2153i		−	0.974060i
$245$			8.22212i			0.525292i
$246$	−0.219395			−0.0139881
$247$	4.21195			0.268000
$248$		−	2.06546i		−	0.131157i
$249$			0.909664i			0.0576476i
$250$		−	1.62817i		−	0.102975i
$251$	−7.89903			−0.498582			−0.249291	−	0.968429i	$-0.580198\pi$
$251$	−7.89903			−0.498582			−0.249291	+	0.968429i	$0.580198\pi$
$252$		−	11.6239i		−	0.732234i
$253$	7.53789			0.473903
$254$	3.03062			0.190158
$255$	1.20227	+	0.245850i	0.0752894	+	0.0153957i
$256$	3.67413			0.229633
$257$	12.7284			0.793974			0.396987	−	0.917824i	$-0.370056\pi$
$257$	12.7284			0.793974			0.396987	+	0.917824i	$0.370056\pi$
$258$		−	0.194780i		−	0.0121265i
$259$	6.24069			0.387777
$260$			17.1183i			1.06163i
$261$			15.6014i			0.965702i
$262$		−	6.47991i		−	0.400330i
$263$	−20.8282			−1.28432			−0.642161	−	0.766570i	$-0.721962\pi$
$263$	−20.8282			−1.28432			−0.642161	+	0.766570i	$0.721962\pi$
$264$	−0.143105			−0.00880750
$265$			39.2952i			2.41388i
$266$		−	1.34149i		−	0.0822522i
$267$		−	0.630900i		−	0.0386105i
$268$	−10.8238			−0.661169
$269$			17.2133i			1.04951i	0.851253	+	0.524756i	$0.175843\pi$
$269$			17.2133i			1.04951i	−0.851253	+	0.524756i	$0.824157\pi$
$270$	0.749209			0.0455954
$271$	25.2009			1.53085			0.765423	−	0.643528i	$-0.222530\pi$
$271$	25.2009			1.53085			0.765423	+	0.643528i	$0.222530\pi$
$272$	12.0064	+	2.45516i	0.727997	+	0.148866i
$273$	−0.533368			−0.0322809
$274$	−2.34238			−0.141508
$275$		−	6.16015i		−	0.371471i
$276$	1.22461			0.0737130
$277$		−	26.4237i		−	1.58765i	−0.608149	−	0.793823i	$-0.708088\pi$
$277$		−	26.4237i		−	1.58765i	0.608149	−	0.793823i	$-0.291912\pi$
$278$			0.589381i			0.0353487i
$279$			3.84744i			0.230340i
$280$	11.4319			0.683189
$281$	24.1420			1.44019			0.720096	−	0.693874i	$-0.244098\pi$
$281$	24.1420			1.44019			0.720096	+	0.693874i	$0.244098\pi$
$282$			0.192972i			0.0114913i
$283$			20.4973i			1.21844i	0.793002	+	0.609219i	$0.208517\pi$
$283$			20.4973i			1.21844i	−0.793002	+	0.609219i	$0.791483\pi$
$284$			26.4226i			1.56789i
$285$	−0.446109			−0.0264252
$286$		−	1.18051i		−	0.0698049i
$287$	12.4884			0.737165
$288$	13.3480			0.786541
$289$	15.6354	+	6.67351i	0.919727	+	0.392559i
$290$	−7.31778			−0.429715
$291$	1.27925			0.0749912
$292$			10.9310i			0.639686i
$293$	8.54045			0.498938			0.249469	−	0.968383i	$-0.419744\pi$
$293$	8.54045			0.498938			0.249469	+	0.968383i	$0.419744\pi$
$294$		−	0.0921171i		−	0.00537238i
$295$			8.19859i			0.477340i
$296$			4.70519i			0.273484i
$297$	0.533846			0.0309769
$298$	−5.69187			−0.329721
$299$			21.1820i			1.22499i
$300$		−	1.00078i		−	0.0577803i
$301$			11.0872i			0.639057i
$302$	−9.23437			−0.531378
$303$			1.15958i			0.0666163i
$304$	−4.45503			−0.255514
$305$	−27.8744			−1.59608
$306$	5.07752	+	1.03829i	0.290263	+	0.0593549i
$307$	−19.3840			−1.10631			−0.553153	−	0.833080i	$-0.686576\pi$
$307$	−19.3840			−1.10631			−0.553153	+	0.833080i	$0.686576\pi$
$308$	3.88490			0.221363
$309$			0.197245i			0.0112209i
$310$	−1.80463			−0.102496
$311$			16.7515i			0.949888i	0.880016	+	0.474944i	$0.157532\pi$
$311$			16.7515i			0.949888i	−0.880016	+	0.474944i	$0.842468\pi$
$312$		−	0.402135i		−	0.0227664i
$313$		−	20.2547i		−	1.14486i	−0.819953	−	0.572431i	$-0.806000\pi$
$313$		−	20.2547i		−	1.14486i	0.819953	−	0.572431i	$-0.194000\pi$
$314$	−2.51515			−0.141938
$315$	−21.2949			−1.19983
$316$		−	19.1057i		−	1.07478i
$317$		−	8.62805i		−	0.484599i	−0.970201	−	0.242300i	$-0.922098\pi$
$317$		−	8.62805i		−	0.484599i	0.970201	−	0.242300i	$-0.0779017\pi$
$318$		−	0.440247i		−	0.0246878i
$319$	−5.21426			−0.291942
$320$		−	13.5978i		−	0.760140i
$321$	−0.761187			−0.0424853
$322$	6.74639			0.375962
$323$	−6.05474	−	1.23812i	−0.336895	−	0.0688906i
$324$	−16.2815			−0.904528
$325$	17.3104			0.960210
$326$		−	10.4487i		−	0.578702i
$327$	1.20186			0.0664631
$328$			9.41566i			0.519893i
$329$		−	10.9843i		−	0.605586i
$330$			0.125034i			0.00688287i
$331$	−31.2792			−1.71926			−0.859630	−	0.510916i	$-0.829306\pi$
$331$	−31.2792			−1.71926			−0.859630	+	0.510916i	$0.829306\pi$
$332$	18.6188			1.02184
$333$		−	8.76462i		−	0.480298i
$334$		−	5.21860i		−	0.285549i
$335$			19.8292i			1.08338i
$336$	0.564150			0.0307769
$337$		−	26.7786i		−	1.45872i	−0.684128	−	0.729362i	$-0.739817\pi$
$337$		−	26.7786i		−	1.45872i	0.684128	−	0.729362i	$-0.260183\pi$
$338$	−2.14398			−0.116617
$339$	−0.131136			−0.00712233
$340$	5.03199	−	24.6079i	0.272898	−	1.33455i
$341$	−1.28588			−0.0696344
$342$	−1.88403			−0.101877
$343$			20.1566i			1.08835i
$344$	−8.35926			−0.450701
$345$		−	2.24349i		−	0.120785i
$346$		−	10.3372i		−	0.555729i
$347$		−	4.23949i		−	0.227588i	−0.993504	−	0.113794i	$-0.963700\pi$
$347$		−	4.23949i		−	0.227588i	0.993504	−	0.113794i	$-0.0363004\pi$
$348$	−0.847114			−0.0454101
$349$	3.71727			0.198981			0.0994904	−	0.995039i	$-0.468279\pi$
$349$	3.71727			0.198981			0.0994904	+	0.995039i	$0.468279\pi$
$350$		−	5.51332i		−	0.294699i
$351$			1.50014i			0.0800718i
$352$			4.46115i			0.237780i
$353$	−21.8301			−1.16190			−0.580950	−	0.813939i	$-0.697319\pi$
$353$	−21.8301			−1.16190			−0.580950	+	0.813939i	$0.697319\pi$
$354$		−	0.0918535i		−	0.00488196i
$355$	48.4062			2.56914
$356$	−12.9131			−0.684393
$357$	0.766724	+	0.156785i	0.0405793	+	0.00829794i
$358$	5.18697			0.274140
$359$	−27.1882			−1.43494			−0.717470	−	0.696589i	$-0.754700\pi$
$359$	−27.1882			−1.43494			−0.717470	+	0.696589i	$0.754700\pi$
$360$		−	16.0554i		−	0.846193i
$361$	−16.7534			−0.881756
$362$			3.80632i			0.200056i
$363$			0.0890922i			0.00467613i
$364$			10.9168i			0.572198i
$365$	20.0255			1.04818
$366$	0.312293			0.0163238
$367$			28.3700i			1.48090i	0.672110	+	0.740451i	$0.265388\pi$
$367$			28.3700i			1.48090i	−0.672110	+	0.740451i	$0.734612\pi$
$368$		−	22.4045i		−	1.16791i
$369$		−	17.5391i		−	0.913047i
$370$	4.11102			0.213722
$371$			25.0596i			1.30103i
$372$	−0.208906			−0.0108313
$373$	9.60655			0.497408			0.248704	−	0.968579i	$-0.419995\pi$
$373$	9.60655			0.497408			0.248704	+	0.968579i	$0.419995\pi$
$374$	−0.347014	+	1.69700i	−0.0179437	+	0.0877496i
$375$	−0.345293			−0.0178309
$376$	8.28168			0.427095
$377$		−	14.6524i		−	0.754638i
$378$	0.477791			0.0245749
$379$		−	14.9152i		−	0.766141i	−0.923719	−	0.383071i	$-0.874867\pi$
$379$		−	14.9152i		−	0.766141i	0.923719	−	0.383071i	$-0.125133\pi$
$380$			9.13085i			0.468403i
$381$		−	0.642716i		−	0.0329273i
$382$	7.17262			0.366983
$383$	23.0508			1.17784			0.588919	−	0.808192i	$-0.299554\pi$
$383$	23.0508			1.17784			0.588919	+	0.808192i	$0.299554\pi$
$384$			0.947251i			0.0483392i
$385$		−	7.11713i		−	0.362723i
$386$		−	8.70833i		−	0.443243i
$387$	15.5713			0.791531
$388$		−	26.1835i		−	1.32926i
$389$	18.2973			0.927710			0.463855	−	0.885911i	$-0.346466\pi$
$389$	18.2973			0.927710			0.463855	+	0.885911i	$0.346466\pi$
$390$	−0.351353			−0.0177914
$391$	6.22651	−	30.4494i	0.314888	−	1.53989i
$392$	−3.95334			−0.199674
$393$	−1.37422			−0.0693204
$394$			6.35773i			0.320298i
$395$	−35.0016			−1.76112
$396$		−	5.45608i		−	0.274178i
$397$			0.409232i			0.0205388i	0.999947	+	0.0102694i	$0.00326891\pi$
$397$			0.409232i			0.0205388i	−0.999947	+	0.0102694i	$0.996731\pi$
$398$		−	8.63330i		−	0.432748i
$399$	−0.284496			−0.0142426
$400$	−18.3095			−0.915474
$401$		−	7.92981i		−	0.395996i	−0.980202	−	0.197998i	$-0.936556\pi$
$401$		−	7.92981i		−	0.395996i	0.980202	−	0.197998i	$-0.0634439\pi$
$402$		−	0.222158i		−	0.0110802i
$403$		−	3.61342i		−	0.179997i
$404$	23.7341			1.18081
$405$			29.8277i			1.48215i
$406$	−4.66675			−0.231607
$407$	2.92929			0.145200
$408$	−0.118209	+	0.578074i	−0.00585220	+	0.0286189i
$409$	8.02278			0.396701			0.198351	−	0.980131i	$-0.436442\pi$
$409$	8.02278			0.396701			0.198351	+	0.980131i	$0.436442\pi$
$410$	8.22664			0.406285
$411$			0.496758i			0.0245033i
$412$	4.03717			0.198897
$413$			5.22846i			0.257276i
$414$		−	9.47484i		−	0.465663i
$415$		−	34.1096i		−	1.67437i
$416$	−12.5361			−0.614635
$417$	0.124993			0.00612091
$418$		−	0.629677i		−	0.0307985i
$419$			19.3962i			0.947565i	0.880642	+	0.473782i	$0.157112\pi$
$419$			19.3962i			0.947565i	−0.880642	+	0.473782i	$0.842888\pi$
$420$		−	1.15626i		−	0.0564196i
$421$	−7.41456			−0.361364			−0.180682	−	0.983542i	$-0.557830\pi$
$421$	−7.41456			−0.361364			−0.180682	+	0.983542i	$0.557830\pi$
$422$			6.61022i			0.321781i
$423$	−15.4267			−0.750074
$424$	−18.8938			−0.917564
$425$	−24.8840	−	5.08846i	−1.20705	−	0.246826i
$426$	−0.542323			−0.0262756
$427$	−17.7763			−0.860254
$428$			15.5798i			0.753078i
$429$	−0.250355			−0.0120873
$430$			7.30365i			0.352213i
$431$		−	7.11737i		−	0.342831i	−0.985199	−	0.171416i	$-0.945166\pi$
$431$		−	7.11737i		−	0.342831i	0.985199	−	0.171416i	$-0.0548341\pi$
$432$		−	1.58672i		−	0.0763412i
$433$	4.49645			0.216086			0.108043	−	0.994146i	$-0.465542\pi$
$433$	4.49645			0.216086			0.108043	+	0.994146i	$0.465542\pi$
$434$	−1.15086			−0.0552431
$435$			1.55191i			0.0744085i
$436$		−	24.5994i		−	1.17810i
$437$			11.2984i			0.540474i
$438$	−0.224357			−0.0107202
$439$			7.38699i			0.352562i	0.984340	+	0.176281i	$0.0564067\pi$
$439$			7.38699i			0.352562i	−0.984340	+	0.176281i	$0.943593\pi$
$440$	5.36599			0.255814
$441$	7.36410			0.350671
$442$	−4.76868	−	0.975133i	−0.226823	−	0.0463823i
$443$	25.0046			1.18801			0.594003	−	0.804463i	$-0.297547\pi$
$443$	25.0046			1.18801			0.594003	+	0.804463i	$0.297547\pi$
$444$	0.475896			0.0225850
$445$			23.6568i			1.12144i
$446$	−3.11494			−0.147497
$447$			1.20710i			0.0570938i
$448$		−	8.67169i		−	0.409699i
$449$		−	20.6423i		−	0.974168i	−0.873355	−	0.487084i	$-0.838061\pi$
$449$		−	20.6423i		−	0.974168i	0.873355	−	0.487084i	$-0.161939\pi$
$450$	−7.74308			−0.365012
$451$	5.86187			0.276024
$452$			2.68406i			0.126247i
$453$			1.95837i			0.0920123i
$454$			2.86827i			0.134614i
$455$	19.9996			0.937597
$456$		−	0.214497i		−	0.0100447i
$457$	−30.2346			−1.41431			−0.707157	−	0.707056i	$-0.750023\pi$
$457$	−30.2346			−1.41431			−0.707157	+	0.707056i	$0.750023\pi$
$458$	−0.962373			−0.0449687
$459$	0.440972	−	2.15648i	0.0205828	−	0.100656i
$460$	−45.9192			−2.14099
$461$	29.1681			1.35849			0.679247	−	0.733909i	$-0.262306\pi$
$461$	29.1681			1.35849			0.679247	+	0.733909i	$0.262306\pi$
$462$			0.0797373i			0.00370971i
$463$	−9.72292			−0.451862			−0.225931	−	0.974143i	$-0.572542\pi$
$463$	−9.72292			−0.451862			−0.225931	+	0.974143i	$0.572542\pi$
$464$			15.4981i			0.719479i
$465$			0.382715i			0.0177480i
$466$		−	4.12880i		−	0.191263i
$467$	−12.1689			−0.563110			−0.281555	−	0.959545i	$-0.590850\pi$
$467$	−12.1689			−0.563110			−0.281555	+	0.959545i	$0.590850\pi$
$468$	15.3319			0.708720
$469$			12.6456i			0.583920i
$470$		−	7.23586i		−	0.333766i
$471$			0.533399i			0.0245777i
$472$	−3.94202			−0.181446
$473$			5.20419i			0.239289i
$474$	0.392143			0.0180117
$475$	9.23331			0.423653
$476$	3.20904	−	15.6931i	0.147086	−	0.719292i
$477$	35.1945			1.61145
$478$	0.795061			0.0363653
$479$			9.41235i			0.430061i	0.976607	+	0.215031i	$0.0689851\pi$
$479$			9.41235i			0.430061i	−0.976607	+	0.215031i	$0.931015\pi$
$480$	1.32777			0.0606040
$481$			8.23151i			0.375324i
$482$			10.5870i			0.482227i
$483$		−	1.43073i		−	0.0651007i
$484$	1.82352			0.0828871
$485$	−47.9681			−2.17812
$486$		−	1.00698i		−	0.0456776i
$487$		−	3.03498i		−	0.137528i	−0.997633	−	0.0687640i	$-0.978094\pi$
$487$		−	3.03498i		−	0.137528i	0.997633	−	0.0687640i	$-0.0219056\pi$
$488$		−	13.4025i		−	0.606703i
$489$	−2.21591			−0.100207
$490$			3.45411i			0.156041i
$491$	8.61942			0.388989			0.194494	−	0.980904i	$-0.437693\pi$
$491$	8.61942			0.388989			0.194494	+	0.980904i	$0.437693\pi$
$492$	0.952325			0.0429341
$493$	−4.30712	+	21.0631i	−0.193983	+	0.948633i
$494$	1.76944			0.0796107
$495$	−9.99553			−0.449265
$496$			3.82196i			0.171611i
$497$	30.8700			1.38471
$498$			0.382149i			0.0171245i
$499$		−	0.575704i		−	0.0257721i	−0.999917	−	0.0128860i	$-0.995898\pi$
$499$		−	0.575704i		−	0.0257721i	0.999917	−	0.0128860i	$-0.00410186\pi$
$500$			7.06738i			0.316063i
$501$	−1.10673			−0.0494450
$502$	−3.31838			−0.148106
$503$		−	8.31424i		−	0.370714i	−0.982671	−	0.185357i	$-0.940656\pi$
$503$		−	8.31424i		−	0.370714i	0.982671	−	0.185357i	$-0.0593441\pi$
$504$		−	10.2390i		−	0.456079i
$505$		−	43.4808i		−	1.93487i
$506$	3.16666			0.140775
$507$			0.454683i			0.0201932i
$508$	−13.1550			−0.583657
$509$	31.2778			1.38636			0.693182	−	0.720762i	$-0.256208\pi$
$509$	31.2778			1.38636			0.693182	+	0.720762i	$0.256208\pi$
$510$	0.505075	+	0.103281i	0.0223651	+	0.00457337i
$511$	12.7708			0.564947
$512$	22.8080			1.00798
$513$			0.800170i			0.0353284i
$514$	5.34718			0.235854
$515$		−	7.39609i		−	0.325911i
$516$			0.845478i			0.0372201i
$517$		−	5.15589i		−	0.226756i
$518$	2.62171			0.115191
$519$	−2.19224			−0.0962288
$520$			15.0788i			0.661249i
$521$		−	11.0557i		−	0.484357i	−0.970232	−	0.242179i	$-0.922138\pi$
$521$		−	11.0557i		−	0.484357i	0.970232	−	0.242179i	$-0.0778620\pi$
$522$			6.55413i			0.286866i
$523$	33.5485			1.46697			0.733486	−	0.679704i	$-0.237892\pi$
$523$	33.5485			1.46697			0.733486	+	0.679704i	$0.237892\pi$
$524$			28.1272i			1.22874i
$525$	−1.16923			−0.0510295
$526$	−8.74991			−0.381514
$527$	−1.06217	+	5.19434i	−0.0462691	+	0.226269i
$528$	0.264804			0.0115241
$529$	−33.8197			−1.47042
$530$			16.5079i			0.717057i
$531$	7.34302			0.318660
$532$			5.82299i			0.252459i
$533$			16.4722i			0.713492i
$534$		−	0.265041i		−	0.0114694i
$535$	28.5422			1.23399
$536$	−9.53421			−0.411815
$537$		−	1.10002i		−	0.0474695i
$538$			7.23128i			0.311763i
$539$			2.46121i			0.106012i
$540$	−3.25208			−0.139947
$541$			0.0518839i			0.00223066i	0.999999	+	0.00111533i	$0.000355021\pi$
$541$			0.0518839i			0.00223066i	−0.999999	+	0.00111533i	$0.999645\pi$
$542$	10.5869			0.454745
$543$	0.807222			0.0346412
$544$	18.0209	+	3.68504i	0.772639	+	0.157995i
$545$	−45.0661			−1.93042
$546$	−0.224067			−0.00958919
$547$			11.2925i			0.482831i	0.970422	+	0.241415i	$0.0776116\pi$
$547$			11.2925i			0.482831i	−0.970422	+	0.241415i	$0.922388\pi$
$548$	10.1675			0.434335
$549$			24.9656i			1.06550i
$550$		−	2.58787i		−	0.110347i
$551$		−	7.81554i		−	0.332953i
$552$	1.07871			0.0459129
$553$	−22.3215			−0.949205
$554$		−	11.1006i		−	0.471618i
$555$		−	0.871841i		−	0.0370076i
$556$		−	2.55832i		−	0.108497i
$557$	−16.1450			−0.684084			−0.342042	−	0.939685i	$-0.611118\pi$
$557$	−16.1450			−0.684084			−0.342042	+	0.939685i	$0.611118\pi$
$558$			1.61631i			0.0684237i
$559$	−14.6241			−0.618535
$560$	−21.1539			−0.893914
$561$	0.359889	+	0.0735927i	0.0151945	+	0.00310709i
$562$	10.1420			0.427816
$563$	4.97294			0.209585			0.104792	−	0.994494i	$-0.466582\pi$
$563$	4.97294			0.209585			0.104792	+	0.994494i	$0.466582\pi$
$564$		−	0.837631i		−	0.0352706i
$565$	4.91719			0.206868
$566$			8.61089i			0.361943i
$567$			19.0219i			0.798846i
$568$			23.2745i			0.976578i
$569$	35.0006			1.46730			0.733650	−	0.679528i	$-0.237815\pi$
$569$	35.0006			1.46730			0.733650	+	0.679528i	$0.237815\pi$
$570$	−0.187410			−0.00784974
$571$			22.3287i			0.934425i	0.884145	+	0.467213i	$0.154742\pi$
$571$			22.3287i			0.934425i	−0.884145	+	0.467213i	$0.845258\pi$
$572$			5.12421i			0.214254i
$573$		−	1.52113i		−	0.0635460i
$574$	5.24636			0.218979
$575$			46.4345i			1.93645i
$576$	−12.1788			−0.507450
$577$	−28.3996			−1.18229			−0.591145	−	0.806566i	$-0.701324\pi$
$577$	−28.3996			−1.18229			−0.591145	+	0.806566i	$0.701324\pi$
$578$	6.56840	+	2.80354i	0.273209	+	0.116612i
$579$	−1.84681			−0.0767509
$580$	31.7641			1.31893
$581$		−	21.7526i		−	0.902451i
$582$	0.537414			0.0222765
$583$			11.7626i			0.487158i
$584$			9.62861i			0.398435i
$585$		−	28.0881i		−	1.16130i
$586$	3.58783			0.148212
$587$	−22.5993			−0.932774			−0.466387	−	0.884581i	$-0.654445\pi$
$587$	−22.5993			−0.932774			−0.466387	+	0.884581i	$0.654445\pi$
$588$			0.399851i			0.0164896i
$589$		−	1.92738i		−	0.0794163i
$590$			3.44422i			0.141796i
$591$	1.34831			0.0554620
$592$		−	8.70657i		−	0.357838i
$593$	−17.1377			−0.703762			−0.351881	−	0.936045i	$-0.614458\pi$
$593$	−17.1377			−0.703762			−0.351881	+	0.936045i	$0.614458\pi$
$594$	0.224268			0.00920184
$595$	−28.7498	−	5.87895i	−1.17863	−	0.241014i
$596$	24.7066			1.01202
$597$	−1.83090			−0.0749337
$598$			8.89853i			0.363888i
$599$	18.9060			0.772477			0.386238	−	0.922399i	$-0.373774\pi$
$599$	18.9060			0.772477			0.386238	+	0.922399i	$0.373774\pi$
$600$		−	0.881547i		−	0.0359890i
$601$			33.0976i			1.35008i	0.737782	+	0.675039i	$0.235873\pi$
$601$			33.0976i			1.35008i	−0.737782	+	0.675039i	$0.764127\pi$
$602$			4.65774i			0.189835i
$603$	17.7599			0.723239
$604$	40.0834			1.63097
$605$		−	3.34068i		−	0.135818i
$606$			0.487140i			0.0197887i
$607$		−	22.1714i		−	0.899908i	−0.893052	−	0.449954i	$-0.851440\pi$
$607$		−	22.1714i		−	0.899908i	0.893052	−	0.449954i	$-0.148560\pi$
$608$	−6.68672			−0.271182
$609$			0.989697i			0.0401045i
$610$	−11.7100			−0.474125
$611$	14.4884			0.586138
$612$	−22.0399	−	4.50687i	−0.890910	−	0.182180i
$613$	−10.2847			−0.415396			−0.207698	−	0.978193i	$-0.566597\pi$
$613$	−10.2847			−0.415396			−0.207698	+	0.978193i	$0.566597\pi$
$614$	−8.14322			−0.328634
$615$		−	1.74466i		−	0.0703514i
$616$	3.42204			0.137878
$617$		−	6.36379i		−	0.256197i	−0.991761	−	0.128098i	$-0.959113\pi$
$617$		−	6.36379i		−	0.256197i	0.991761	−	0.128098i	$-0.0408873\pi$
$618$			0.0828626i			0.00333322i
$619$		−	22.7974i		−	0.916304i	−0.888874	−	0.458152i	$-0.848512\pi$
$619$		−	22.7974i		−	0.916304i	0.888874	−	0.458152i	$-0.151488\pi$
$620$	7.83332			0.314594
$621$	−4.02407			−0.161480
$622$			7.03727i			0.282169i
$623$			15.0866i			0.604431i
$624$			0.744117i			0.0297885i
$625$	−17.8533			−0.714133
$626$		−	8.50898i		−	0.340087i
$627$	−0.133538			−0.00533301
$628$	10.9175			0.435655
$629$	2.41968	−	11.8329i	0.0964788	−	0.471809i
$630$	−8.94597			−0.356416
$631$	−39.6141			−1.57701			−0.788506	−	0.615027i	$-0.789145\pi$
$631$	−39.6141			−1.57701			−0.788506	+	0.615027i	$0.789145\pi$
$632$		−	16.8294i		−	0.669436i
$633$	1.40186			0.0557188
$634$		−	3.62464i		−	0.143953i
$635$			24.0999i			0.956374i
$636$			1.91097i			0.0757749i
$637$	−6.91617			−0.274029
$638$	−2.19051			−0.0867229
$639$		−	43.3548i		−	1.71509i
$640$		−	35.5190i		−	1.40401i
$641$		−	33.3856i		−	1.31865i	−0.751856	−	0.659327i	$-0.770841\pi$
$641$		−	33.3856i		−	1.31865i	0.751856	−	0.659327i	$-0.229159\pi$
$642$	−0.319774			−0.0126205
$643$			4.37156i			0.172397i	0.996278	+	0.0861987i	$0.0274720\pi$
$643$			4.37156i			0.172397i	−0.996278	+	0.0861987i	$0.972528\pi$
$644$	−29.2839			−1.15395
$645$	1.54892			0.0609885
$646$	−2.54359	−	0.520131i	−0.100076	−	0.0204643i
$647$	20.5578			0.808212			0.404106	−	0.914712i	$-0.367583\pi$
$647$	20.5578			0.808212			0.404106	+	0.914712i	$0.367583\pi$
$648$	−14.3417			−0.563394
$649$			2.45417i			0.0963345i
$650$	7.27210			0.285235
$651$			0.244068i			0.00956577i
$652$			45.3546i			1.77622i
$653$		−	19.1123i		−	0.747921i	−0.927445	−	0.373961i	$-0.878000\pi$
$653$		−	19.1123i		−	0.747921i	0.927445	−	0.373961i	$-0.122000\pi$
$654$	0.504901			0.0197432
$655$	51.5291			2.01341
$656$		−	17.4229i		−	0.680250i
$657$		−	17.9357i		−	0.699740i
$658$		−	4.61451i		−	0.179892i
$659$	−6.04282			−0.235395			−0.117697	−	0.993050i	$-0.537551\pi$
$659$	−6.04282			−0.235395			−0.117697	+	0.993050i	$0.537551\pi$
$660$		−	0.542731i		−	0.0211258i
$661$	21.6939			0.843795			0.421898	−	0.906643i	$-0.361364\pi$
$661$	21.6939			0.843795			0.421898	+	0.906643i	$0.361364\pi$
$662$	−13.1404			−0.510715
$663$	−0.206800	+	1.01131i	−0.00803146	+	0.0392762i
$664$	16.4005			0.636462
$665$	10.6677			0.413676
$666$		−	3.68201i		−	0.142675i
$667$	39.3045			1.52188
$668$			22.6523i			0.876443i
$669$			0.660598i			0.0255402i
$670$			8.33023i			0.321825i
$671$	−8.34393			−0.322114
$672$	0.846753			0.0326642
$673$		−	7.33990i		−	0.282932i	−0.989943	−	0.141466i	$-0.954818\pi$
$673$		−	7.33990i		−	0.282932i	0.989943	−	0.141466i	$-0.0451816\pi$
$674$		−	11.2497i		−	0.433321i
$675$			3.28857i			0.126577i
$676$	9.30634			0.357936
$677$		−	24.5267i		−	0.942638i	−0.881963	−	0.471319i	$-0.843778\pi$
$677$		−	24.5267i		−	0.942638i	0.881963	−	0.471319i	$-0.156222\pi$
$678$	−0.0550901			−0.00211572
$679$	−30.5905			−1.17396
$680$	4.43246	−	21.6760i	0.169977	−	0.831236i
$681$	0.608285			0.0233095
$682$	−0.540198			−0.0206852
$683$			43.4617i			1.66301i	0.555514	+	0.831507i	$0.312522\pi$
$683$			43.4617i			1.66301i	−0.555514	+	0.831507i	$0.687478\pi$
$684$	8.17799			0.312693
$685$		−	18.6269i		−	0.711696i
$686$			8.46776i			0.323301i
$687$			0.204094i			0.00778669i
$688$	15.4681			0.589717
$689$	−33.0538			−1.25925
$690$		−	0.942488i		−	0.0358799i
$691$			5.25512i			0.199914i	0.994992	+	0.0999571i	$0.0318706\pi$
$691$			5.25512i			0.199914i	−0.994992	+	0.0999571i	$0.968129\pi$
$692$			44.8703i			1.70571i
$693$	−6.37442			−0.242144
$694$		−	1.78101i		−	0.0676061i
$695$	−4.68683			−0.177782
$696$	−0.746186			−0.0282841
$697$	4.84207	−	23.6791i	0.183406	−	0.896909i
$698$	1.56162			0.0591083
$699$	−0.875613			−0.0331187
$700$			23.9316i			0.904528i
$701$	−25.4768			−0.962247			−0.481124	−	0.876653i	$-0.659771\pi$
$701$	−25.4768			−0.962247			−0.481124	+	0.876653i	$0.659771\pi$
$702$			0.630209i			0.0237857i
$703$			4.39065i			0.165596i
$704$		−	4.07037i		−	0.153408i
$705$	−1.53454			−0.0577941
$706$	−9.17081			−0.345148
$707$		−	27.7289i		−	1.04285i
$708$			0.398707i			0.0149843i
$709$		−	33.0135i		−	1.23985i	−0.784661	−	0.619925i	$-0.787163\pi$
$709$		−	33.0135i		−	1.23985i	0.784661	−	0.619925i	$-0.212837\pi$
$710$	20.3354			0.763175
$711$			31.3490i			1.17568i
$712$	−11.3746			−0.426281
$713$	9.69283			0.362999
$714$	0.322100	+	0.0658653i	0.0120543	+	0.00246495i
$715$	9.38754			0.351074
$716$	−22.5150			−0.841425
$717$		−	0.168612i		−	0.00629693i
$718$	−11.4218			−0.426256
$719$		−	11.5472i		−	0.430636i	−0.976544	−	0.215318i	$-0.930921\pi$
$719$		−	11.5472i		−	0.430636i	0.976544	−	0.215318i	$-0.0690788\pi$
$720$			29.7092i			1.10720i
$721$		−	4.71669i		−	0.175659i
$722$	−7.03808			−0.261930
$723$	2.24524			0.0835013
$724$		−	16.5220i		−	0.614036i
$725$		−	32.1206i		−	1.19293i
$726$			0.0374276i			0.00138907i
$727$	3.50071			0.129834			0.0649171	−	0.997891i	$-0.479322\pi$
$727$	3.50071			0.129834			0.0649171	+	0.997891i	$0.479322\pi$
$728$			9.61616i			0.356399i
$729$	26.5723			0.984160
$730$	8.41270			0.311368
$731$	21.0224	+	4.29881i	0.777541	+	0.158997i
$732$	−1.35556			−0.0501031
$733$	23.8165			0.879682			0.439841	−	0.898076i	$-0.355035\pi$
$733$	23.8165			0.879682			0.439841	+	0.898076i	$0.355035\pi$
$734$			11.9182i			0.439910i
$735$	0.732527			0.0270197
$736$		−	33.6276i		−	1.23953i
$737$			5.93567i			0.218643i
$738$		−	7.36815i		−	0.271225i
$739$	−13.0431			−0.479799			−0.239899	−	0.970798i	$-0.577114\pi$
$739$	−13.0431			−0.479799			−0.239899	+	0.970798i	$0.577114\pi$
$740$	−17.8446			−0.655981
$741$		−	0.375252i		−	0.0137852i
$742$			10.5275i			0.386478i
$743$		−	0.202655i		−	0.00743470i	−0.999993	−	0.00371735i	$-0.998817\pi$
$743$		−	0.202655i		−	0.00743470i	0.999993	−	0.00371735i	$-0.00118327\pi$
$744$	−0.184016			−0.00674635
$745$		−	45.2625i		−	1.65829i
$746$	4.03571			0.147758
$747$	−30.5501			−1.11777
$748$	1.50628	−	7.36612i	0.0550749	−	0.269332i
$749$	18.2021			0.665091
$750$	−0.145057			−0.00529675
$751$			44.7298i			1.63221i	0.577901	+	0.816107i	$0.303872\pi$
$751$			44.7298i			1.63221i	−0.577901	+	0.816107i	$0.696128\pi$
$752$	−15.3246			−0.558830
$753$			0.703742i			0.0256458i
$754$		−	6.15547i		−	0.224169i
$755$		−	73.4328i		−	2.67249i
$756$	−2.07394			−0.0754284
$757$	16.9831			0.617260			0.308630	−	0.951182i	$-0.400130\pi$
$757$	16.9831			0.617260			0.308630	+	0.951182i	$0.400130\pi$
$758$		−	6.26586i		−	0.227586i
$759$		−	0.671567i		−	0.0243763i
$760$			8.04296i			0.291749i
$761$	−43.0108			−1.55914			−0.779571	−	0.626314i	$-0.784563\pi$
$761$	−43.0108			−1.55914			−0.779571	+	0.626314i	$0.784563\pi$
$762$		−	0.270005i		−	0.00978123i
$763$	−28.7399			−1.04045
$764$	−31.1340			−1.12639
$765$	−8.25659	+	40.3771i	−0.298518	+	1.45984i
$766$	9.68360			0.349883
$767$	−6.89638			−0.249014
$768$		−	0.327336i		−	0.0118117i
$769$	20.1757			0.727555			0.363777	−	0.931486i	$-0.381487\pi$
$769$	20.1757			0.727555			0.363777	+	0.931486i	$0.381487\pi$
$770$		−	2.98990i		−	0.107749i
$771$		−	1.13400i		−	0.0408400i
$772$			37.8001i			1.36046i
$773$	−30.3126			−1.09027			−0.545134	−	0.838349i	$-0.683521\pi$
$773$	−30.3126			−1.09027			−0.545134	+	0.838349i	$0.683521\pi$
$774$	6.54147			0.235128
$775$		−	7.92122i		−	0.284539i
$776$		−	23.0639i		−	0.827945i
$777$		−	0.555997i		−	0.0199463i
$778$	7.68669			0.275581
$779$			8.78622i			0.314799i
$780$	1.52511			0.0546077
$781$	14.4899			0.518490
$782$	2.61575	−	12.7918i	0.0935391	−	0.457433i
$783$	2.78361			0.0994781
$784$	7.31532			0.261262
$785$		−	20.0008i		−	0.713859i
$786$	−0.577310			−0.0205920
$787$		−	10.1837i		−	0.363010i	−0.983390	−	0.181505i	$-0.941903\pi$
$787$		−	10.1837i		−	0.363010i	0.983390	−	0.181505i	$-0.0580969\pi$
$788$		−	27.5969i		−	0.983097i
$789$			1.85563i			0.0660621i
$790$	−14.7041			−0.523150
$791$	3.13583			0.111497
$792$		−	4.80602i		−	0.170774i
$793$		−	23.4470i		−	0.832628i
$794$			0.171918i			0.00610115i
$795$	3.50089			0.124164
$796$			37.4744i			1.32824i
$797$	−31.8636			−1.12867			−0.564333	−	0.825547i	$-0.690867\pi$
$797$	−31.8636			−1.12867			−0.564333	+	0.825547i	$0.690867\pi$
$798$	−0.119516			−0.00423084
$799$	−20.8273	−	4.25891i	−0.736816	−	0.150669i
$800$	−27.4814			−0.971613
$801$	21.1881			0.748644
$802$		−	3.33131i		−	0.117632i
$803$	5.99444			0.211539
$804$			0.964316i			0.0340088i
$805$			53.6481i			1.89085i
$806$		−	1.51799i		−	0.0534690i
$807$	1.53357			0.0539842
$808$	20.9063			0.735481
$809$		−	0.299585i		−	0.0105328i	−0.999986	−	0.00526642i	$-0.998324\pi$
$809$		−	0.299585i		−	0.0105328i	0.999986	−	0.00526642i	$-0.00167636\pi$
$810$			12.5306i			0.440280i
$811$			13.4057i			0.470736i	0.971906	+	0.235368i	$0.0756296\pi$
$811$			13.4057i			0.470736i	−0.971906	+	0.235368i	$0.924370\pi$
$812$	20.2569			0.710877
$813$		−	2.24520i		−	0.0787427i
$814$	1.23059			0.0431323
$815$	83.0897			2.91050
$816$	0.218736	−	1.06968i	0.00765728	−	0.0374463i
$817$	−7.80044			−0.272903
$818$	3.37036			0.117842
$819$		−	17.9126i		−	0.625915i
$820$	−35.7092			−1.24702
$821$		−	38.0715i		−	1.32870i	−0.747420	−	0.664352i	$-0.768708\pi$
$821$		−	38.0715i		−	1.32870i	0.747420	−	0.664352i	$-0.231292\pi$
$822$			0.208688i			0.00727882i
$823$			10.4077i			0.362790i	0.983410	+	0.181395i	$0.0580612\pi$
$823$			10.4077i			0.362790i	−0.983410	+	0.181395i	$0.941939\pi$
$824$	3.55617			0.123885
$825$	−0.548821			−0.0191075
$826$			2.19647i			0.0764251i
$827$			22.0710i			0.767483i	0.923441	+	0.383742i	$0.125365\pi$
$827$			22.0710i			0.767483i	−0.923441	+	0.383742i	$0.874635\pi$
$828$			41.1273i			1.42927i
$829$	−4.28264			−0.148742			−0.0743710	−	0.997231i	$-0.523695\pi$
$829$	−4.28264			−0.148742			−0.0743710	+	0.997231i	$0.523695\pi$
$830$		−	14.3294i		−	0.497381i
$831$	−2.35414			−0.0816643
$832$	11.4380			0.396542
$833$	9.94210	+	2.03303i	0.344473	+	0.0704403i
$834$	0.0525093			0.00181825
$835$	41.4989			1.43613
$836$			2.73323i			0.0945307i
$837$	0.686463			0.0237276
$838$			8.14832i			0.281479i
$839$		−	34.0693i		−	1.17620i	−0.808787	−	0.588102i	$-0.799875\pi$
$839$		−	34.0693i		−	1.17620i	0.808787	−	0.588102i	$-0.200125\pi$
$840$		−	1.01850i		−	0.0351415i
$841$	1.81152			0.0624661
$842$	−3.11485			−0.107345
$843$		−	2.15087i		−	0.0740797i
$844$		−	28.6929i		−	0.987649i
$845$		−	17.0492i		−	0.586511i
$846$	−6.48076			−0.222813
$847$		−	2.13044i		−	0.0732029i
$848$	34.9614			1.20058
$849$	1.82615			0.0626732
$850$	−10.4538	−	2.13766i	−0.358561	−	0.0733210i
$851$	−22.0807			−0.756915
$852$	2.35405			0.0806484
$853$			14.6084i			0.500182i	0.968222	+	0.250091i	$0.0804605\pi$
$853$			14.6084i			0.500182i	−0.968222	+	0.250091i	$0.919540\pi$
$854$	−7.46780			−0.255543
$855$		−	14.9821i		−	0.512376i
$856$			13.7236i			0.469062i
$857$		−	34.1152i		−	1.16535i	−0.812704	−	0.582677i	$-0.802005\pi$
$857$		−	34.1152i		−	1.16535i	0.812704	−	0.582677i	$-0.197995\pi$
$858$	−0.105174			−0.00359058
$859$	−42.1275			−1.43737			−0.718686	−	0.695335i	$-0.755256\pi$
$859$	−42.1275			−1.43737			−0.718686	+	0.695335i	$0.755256\pi$
$860$		−	31.7028i		−	1.08106i
$861$		−	1.11262i		−	0.0379179i
$862$		−	2.99000i		−	0.101840i
$863$	−21.9531			−0.747291			−0.373645	−	0.927572i	$-0.621892\pi$
$863$	−21.9531			−0.747291			−0.373645	+	0.927572i	$0.621892\pi$
$864$		−	2.38157i		−	0.0810226i
$865$	82.2023			2.79496
$866$	1.88896			0.0641893
$867$	0.594557	−	1.39299i	0.0201922	−	0.0473084i
$868$	4.99552			0.169559
$869$	−10.4774			−0.355421
$870$			0.651957i			0.0221034i
$871$	−16.6797			−0.565168
$872$		−	21.6685i		−	0.733789i
$873$			42.9623i			1.45405i
$874$			4.74644i			0.160551i
$875$	8.25693			0.279135
$876$	0.973863			0.0329038
$877$			25.7006i			0.867849i	0.900949	+	0.433925i	$0.142872\pi$
$877$			25.7006i			0.867849i	−0.900949	+	0.433925i	$0.857128\pi$
$878$			3.10327i			0.104730i
$879$		−	0.760887i		−	0.0256641i
$880$	−9.92933			−0.334718
$881$			34.8945i			1.17563i	0.808997	+	0.587813i	$0.200011\pi$
$881$			34.8945i			1.17563i	−0.808997	+	0.587813i	$0.799989\pi$
$882$	3.09365			0.104169
$883$	−44.8367			−1.50887			−0.754437	−	0.656373i	$-0.772090\pi$
$883$	−44.8367			−1.50887			−0.754437	+	0.656373i	$0.772090\pi$
$884$	20.6993	+	4.23274i	0.696193	+	0.142362i
$885$	0.730430			0.0245531
$886$	10.5044			0.352903
$887$			12.5888i			0.422689i	0.977412	+	0.211345i	$0.0677842\pi$
$887$			12.5888i			0.422689i	−0.977412	+	0.211345i	$0.932216\pi$
$888$	0.419196			0.0140673
$889$			15.3691i			0.515464i
$890$			9.93820i			0.333129i
$891$			8.92863i			0.299120i
$892$	13.5210			0.452715
$893$	7.72805			0.258609
$894$			0.507102i			0.0169600i
$895$			41.2474i			1.37875i
$896$		−	22.6514i		−	0.756731i
$897$	1.88715			0.0630101
$898$		−	8.67179i		−	0.289382i
$899$	−6.70492			−0.223622
$900$	33.6102			1.12034
$901$	47.5153	+	9.71627i	1.58296	+	0.323696i
$902$	2.46257			0.0819944
$903$	0.987785			0.0328714
$904$			2.36427i			0.0786345i
$905$	−30.2683			−1.00615
$906$			0.822710i			0.0273327i
$907$		−	3.23283i		−	0.107344i	−0.998559	−	0.0536722i	$-0.982907\pi$
$907$		−	3.23283i		−	0.107344i	0.998559	−	0.0536722i	$-0.0170926\pi$
$908$		−	12.4502i		−	0.413175i
$909$	−38.9433			−1.29167
$910$	8.40183			0.278518
$911$			38.6527i			1.28062i	0.768116	+	0.640310i	$0.221194\pi$
$911$			38.6527i			1.28062i	−0.768116	+	0.640310i	$0.778806\pi$
$912$			0.396909i			0.0131430i
$913$		−	10.2104i		−	0.337914i
$914$	−12.7015			−0.420129
$915$			2.48339i			0.0820984i
$916$	4.17735			0.138024
$917$	32.8615			1.08518
$918$	0.185252	−	0.905935i	0.00611423	−	0.0299003i
$919$	−55.5566			−1.83264			−0.916321	−	0.400443i	$-0.868856\pi$
$919$	−55.5566			−1.83264			−0.916321	+	0.400443i	$0.868856\pi$
$920$	−40.4482			−1.33354
$921$			1.72697i			0.0569055i
$922$	12.2535			0.403548
$923$			40.7177i			1.34024i
$924$		−	0.346114i		−	0.0113863i
$925$			18.0449i			0.593312i
$926$	−4.08459			−0.134228
$927$	−6.62427			−0.217569
$928$			23.2616i			0.763599i
$929$		−	0.121044i		−	0.00397132i	−0.999998	−	0.00198566i	$-0.999368\pi$
$929$		−	0.121044i		−	0.00397132i	0.999998	−	0.00198566i	$-0.000632056\pi$
$930$			0.160778i			0.00527213i
$931$	−3.68905			−0.120904
$932$			17.9218i			0.587049i
$933$	1.49242			0.0488597
$934$	−5.11215			−0.167275
$935$	−13.4947	−	2.75950i	−0.441325	−	0.0902452i
$936$	13.5052			0.441433
$937$	−37.8307			−1.23588			−0.617938	−	0.786227i	$-0.712032\pi$
$937$	−37.8307			−1.23588			−0.617938	+	0.786227i	$0.712032\pi$
$938$			5.31241i			0.173456i
$939$	−1.80453			−0.0588888
$940$			31.4086i			1.02443i
$941$			38.3847i			1.25131i	0.780102	+	0.625653i	$0.215167\pi$
$941$			38.3847i			1.25131i	−0.780102	+	0.625653i	$0.784833\pi$
$942$			0.224080i			0.00730093i
$943$	−44.1861			−1.43890
$944$	7.29439			0.237412
$945$			3.79945i			0.123596i
$946$			2.18628i			0.0710819i
$947$			25.7810i			0.837768i	0.908040	+	0.418884i	$0.137579\pi$
$947$			25.7810i			0.837768i	−0.908040	+	0.418884i	$0.862421\pi$
$948$	−1.70217			−0.0552838
$949$			16.8448i			0.546805i
$950$	3.87891			0.125848
$951$	−0.768692			−0.0249265
$952$	2.82670	−	13.8234i	0.0916139	−	0.448018i
$953$	23.3685			0.756979			0.378490	−	0.925606i	$-0.376444\pi$
$953$	23.3685			0.756979			0.378490	+	0.925606i	$0.376444\pi$
$954$	14.7852			0.478688
$955$			57.0375i			1.84569i
$956$	−3.45111			−0.111617
$957$			0.464550i			0.0150168i
$958$			3.95412i			0.127752i
$959$		−	11.8789i		−	0.383589i
$960$	−1.21146			−0.0390996
$961$	29.3465			0.946662
$962$			3.45805i			0.111492i
$963$		−	25.5636i		−	0.823777i
$964$		−	45.9550i		−	1.48011i
$965$	69.2497			2.22923
$966$		−	0.601051i		−	0.0193385i
$967$	2.00843			0.0645867			0.0322933	−	0.999478i	$-0.489719\pi$
$967$	2.00843			0.0645867			0.0322933	+	0.999478i	$0.489719\pi$
$968$	1.60626			0.0516270
$969$	−0.110306	+	0.539430i	−0.00354355	+	0.0173290i
$970$	−20.1513			−0.647021
$971$	−28.1844			−0.904479			−0.452240	−	0.891896i	$-0.649375\pi$
$971$	−28.1844			−0.904479			−0.452240	+	0.891896i	$0.649375\pi$
$972$			4.37099i			0.140199i
$973$	−2.98892			−0.0958204
$974$		−	1.27499i		−	0.0408534i
$975$		−	1.54223i		−	0.0493907i
$976$			24.8002i			0.793836i
$977$	21.6336			0.692119			0.346060	−	0.938213i	$-0.387519\pi$
$977$	21.6336			0.692119			0.346060	+	0.938213i	$0.387519\pi$
$978$	−0.930901			−0.0297669
$979$			7.08143i			0.226323i
$980$		−	14.9932i		−	0.478939i
$981$			40.3632i			1.28870i
$982$	3.62101			0.115551
$983$		−	8.38196i		−	0.267343i	−0.991026	−	0.133671i	$-0.957323\pi$
$983$		−	8.38196i		−	0.267343i	0.991026	−	0.133671i	$-0.0426767\pi$
$984$	0.838862			0.0267419
$985$	−50.5574			−1.61089
$986$	−1.80942	+	8.84858i	−0.0576237	+	0.281796i
$987$	−0.978618			−0.0311498
$988$	−7.68056			−0.244351
$989$		−	39.2286i		−	1.24740i
$990$	−4.19911			−0.133457
$991$			3.74342i			0.118914i	0.998231	+	0.0594569i	$0.0189369\pi$
$991$			3.74342i			0.118914i	−0.998231	+	0.0594569i	$0.981063\pi$
$992$			5.73651i			0.182134i
$993$			2.78673i			0.0884343i
$994$	12.9684			0.411334
$995$	68.6531			2.17645
$996$		−	1.65879i		−	0.0525607i
$997$			6.81952i			0.215976i	0.994152	+	0.107988i	$0.0344409\pi$
$997$			6.81952i			0.215976i	−0.994152	+	0.107988i	$0.965559\pi$
$998$		−	0.241853i		−	0.00765572i
$999$	−1.56379			−0.0494761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.d.a.67.9	✓	16
3.2	odd	2		1683.2.g.b.1189.7		16
4.3	odd	2		2992.2.b.g.1937.9		16
17.4	even	4		3179.2.a.bb.1.4		8
17.13	even	4		3179.2.a.bc.1.4		8
17.16	even	2	inner	187.2.d.a.67.10	yes	16
51.50	odd	2		1683.2.g.b.1189.8		16
68.67	odd	2		2992.2.b.g.1937.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.9	✓	16	1.1	even	1	trivial
187.2.d.a.67.10	yes	16	17.16	even	2	inner
1683.2.g.b.1189.7		16	3.2	odd	2
1683.2.g.b.1189.8		16	51.50	odd	2
2992.2.b.g.1937.8		16	68.67	odd	2
2992.2.b.g.1937.9		16	4.3	odd	2
3179.2.a.bb.1.4		8	17.4	even	4
3179.2.a.bc.1.4		8	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.420099 q^{2} -0.0890922i q^{3} -1.82352 q^{4} +3.34068i q^{5} -0.0374276i q^{6} +2.13044i q^{7} -1.60626 q^{8} +2.99206 q^{9} +O(q^{10})\)	\(q+0.420099 q^{2} -0.0890922i q^{3} -1.82352 q^{4} +3.34068i q^{5} -0.0374276i q^{6} +2.13044i q^{7} -1.60626 q^{8} +2.99206 q^{9} +1.40342i q^{10} +1.00000i q^{11} +0.162461i q^{12} -2.81007 q^{13} +0.894998i q^{14} +0.297629 q^{15} +2.97225 q^{16} +(4.03951 + 0.826028i) q^{17} +1.25696 q^{18} -1.49888 q^{19} -6.09179i q^{20} +0.189806 q^{21} +0.420099i q^{22} -7.53789i q^{23} +0.143105i q^{24} -6.16015 q^{25} -1.18051 q^{26} -0.533846i q^{27} -3.88490i q^{28} +5.21426i q^{29} +0.125034 q^{30} +1.28588i q^{31} +4.46115 q^{32} +0.0890922 q^{33} +(1.69700 + 0.347014i) q^{34} -7.11713 q^{35} -5.45608 q^{36} -2.92929i q^{37} -0.629677 q^{38} +0.250355i q^{39} -5.36599i q^{40} -5.86187i q^{41} +0.0797373 q^{42} +5.20419 q^{43} -1.82352i q^{44} +9.99553i q^{45} -3.16666i q^{46} -5.15589 q^{47} -0.264804i q^{48} +2.46121 q^{49} -2.58787 q^{50} +(0.0735927 - 0.359889i) q^{51} +5.12421 q^{52} +11.7626 q^{53} -0.224268i q^{54} -3.34068 q^{55} -3.42204i q^{56} +0.133538i q^{57} +2.19051i q^{58} +2.45417 q^{59} -0.542731 q^{60} +8.34393i q^{61} +0.540198i q^{62} +6.37442i q^{63} -4.07037 q^{64} -9.38754i q^{65} +0.0374276 q^{66} +5.93567 q^{67} +(-7.36612 - 1.50628i) q^{68} -0.671567 q^{69} -2.98990 q^{70} -14.4899i q^{71} -4.80602 q^{72} -5.99444i q^{73} -1.23059i q^{74} +0.548821i q^{75} +2.73323 q^{76} -2.13044 q^{77} +0.105174i q^{78} +10.4774i q^{79} +9.92933i q^{80} +8.92863 q^{81} -2.46257i q^{82} -10.2104 q^{83} -0.346114 q^{84} +(-2.75950 + 13.4947i) q^{85} +2.18628 q^{86} +0.464550 q^{87} -1.60626i q^{88} +7.08143 q^{89} +4.19911i q^{90} -5.98669i q^{91} +13.7455i q^{92} +0.114562 q^{93} -2.16598 q^{94} -5.00727i q^{95} -0.397454i q^{96} +14.3588i q^{97} +1.03395 q^{98} +2.99206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

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