LMFDB - Embedded newform 690.2.d.c.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(139,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.4
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	690.139
Dual form			690.2.d.c.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} -3.35026 q^{11} -1.00000i q^{12} -4.96239i q^{13} +2.96239 q^{14} +(-1.48119 - 1.67513i) q^{15} +1.00000 q^{16} -1.35026i q^{17} -1.00000i q^{18} +4.96239 q^{19} +(1.67513 - 1.48119i) q^{20} +2.96239 q^{21} -3.35026i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(0.612127 - 4.96239i) q^{25} +4.96239 q^{26} -1.00000i q^{27} +2.96239i q^{28} -7.73813 q^{29} +(1.67513 - 1.48119i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -3.35026i q^{33} +1.35026 q^{34} +(4.38787 + 4.96239i) q^{35} +1.00000 q^{36} +7.61213i q^{37} +4.96239i q^{38} +4.96239 q^{39} +(1.48119 + 1.67513i) q^{40} +4.70052 q^{41} +2.96239i q^{42} -10.3127i q^{43} +3.35026 q^{44} +(1.67513 - 1.48119i) q^{45} +1.00000 q^{46} -3.22425i q^{47} +1.00000i q^{48} -1.77575 q^{49} +(4.96239 + 0.612127i) q^{50} +1.35026 q^{51} +4.96239i q^{52} -6.96239i q^{53} +1.00000 q^{54} +(5.61213 - 4.96239i) q^{55} -2.96239 q^{56} +4.96239i q^{57} -7.73813i q^{58} -1.22425 q^{59} +(1.48119 + 1.67513i) q^{60} -11.0884 q^{61} -4.00000i q^{62} +2.96239i q^{63} -1.00000 q^{64} +(7.35026 + 8.31265i) q^{65} +3.35026 q^{66} +7.61213i q^{67} +1.35026i q^{68} +1.00000 q^{69} +(-4.96239 + 4.38787i) q^{70} -2.18664 q^{71} +1.00000i q^{72} -9.92478i q^{73} -7.61213 q^{74} +(4.96239 + 0.612127i) q^{75} -4.96239 q^{76} +9.92478i q^{77} +4.96239i q^{78} +4.12601 q^{79} +(-1.67513 + 1.48119i) q^{80} +1.00000 q^{81} +4.70052i q^{82} -6.38787i q^{83} -2.96239 q^{84} +(2.00000 + 2.26187i) q^{85} +10.3127 q^{86} -7.73813i q^{87} +3.35026i q^{88} -9.92478 q^{89} +(1.48119 + 1.67513i) q^{90} -14.7005 q^{91} +1.00000i q^{92} -4.00000i q^{93} +3.22425 q^{94} +(-8.31265 + 7.35026i) q^{95} -1.00000 q^{96} -12.8872i q^{97} -1.77575i q^{98} +3.35026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 4 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} - 4 q^{21} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 28 q^{29} - 24 q^{31} - 12 q^{34} + 28 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{46} - 14 q^{49} + 8 q^{50} - 12 q^{51} + 6 q^{54} + 32 q^{55} + 4 q^{56} - 4 q^{59} - 2 q^{60} - 28 q^{61} - 6 q^{64} + 24 q^{65} + 6 q^{69} - 8 q^{70} + 12 q^{71} - 44 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{79} + 6 q^{81} + 4 q^{84} + 12 q^{85} + 20 q^{86} - 16 q^{89} - 2 q^{90} - 48 q^{91} + 16 q^{94} - 8 q^{95} - 6 q^{96}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 4 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 - 4 * q^21 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 28 * q^29 - 24 * q^31 - 12 * q^34 + 28 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^46 - 14 * q^49 + 8 * q^50 - 12 * q^51 + 6 * q^54 + 32 * q^55 + 4 * q^56 - 4 * q^59 - 2 * q^60 - 28 * q^61 - 6 * q^64 + 24 * q^65 + 6 * q^69 - 8 * q^70 + 12 * q^71 - 44 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^79 + 6 * q^81 + 4 * q^84 + 12 * q^85 + 20 * q^86 - 16 * q^89 - 2 * q^90 - 48 * q^91 + 16 * q^94 - 8 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$	−1.00000			−0.408248
$7$		−	2.96239i		−	1.11968i	−0.828602	−	0.559839i	$-0.810863\pi$
$7$		−	2.96239i		−	1.11968i	0.828602	−	0.559839i	$-0.189137\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−1.48119	−	1.67513i	−0.468395	−	0.529723i
$11$	−3.35026			−1.01014			−0.505071	−	0.863078i	$-0.668534\pi$
$11$	−3.35026			−1.01014			−0.505071	+	0.863078i	$0.668534\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	4.96239i		−	1.37632i	−0.725559	−	0.688159i	$-0.758419\pi$
$13$		−	4.96239i		−	1.37632i	0.725559	−	0.688159i	$-0.241581\pi$
$14$	2.96239			0.791732
$15$	−1.48119	−	1.67513i	−0.382443	−	0.432517i
$16$	1.00000			0.250000
$17$		−	1.35026i		−	0.327487i	−0.986503	−	0.163743i	$-0.947643\pi$
$17$		−	1.35026i		−	0.327487i	0.986503	−	0.163743i	$-0.0523569\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.96239			1.13845			0.569225	−	0.822182i	$-0.307243\pi$
$19$	4.96239			1.13845			0.569225	+	0.822182i	$0.307243\pi$
$20$	1.67513	−	1.48119i	0.374571	−	0.331205i
$21$	2.96239			0.646446
$22$		−	3.35026i		−	0.714278i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.00000			0.204124
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$	4.96239			0.973204
$27$		−	1.00000i		−	0.192450i
$28$			2.96239i			0.559839i
$29$	−7.73813			−1.43694			−0.718468	−	0.695560i	$-0.755156\pi$
$29$	−7.73813			−1.43694			−0.718468	+	0.695560i	$0.755156\pi$
$30$	1.67513	−	1.48119i	0.305836	−	0.270428i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			1.00000i			0.176777i
$33$		−	3.35026i		−	0.583206i
$34$	1.35026			0.231568
$35$	4.38787	+	4.96239i	0.741686	+	0.838797i
$36$	1.00000			0.166667
$37$			7.61213i			1.25143i	0.780053	+	0.625713i	$0.215192\pi$
$37$			7.61213i			1.25143i	−0.780053	+	0.625713i	$0.784808\pi$
$38$			4.96239i			0.805006i
$39$	4.96239			0.794618
$40$	1.48119	+	1.67513i	0.234197	+	0.264861i
$41$	4.70052			0.734098			0.367049	−	0.930202i	$-0.380368\pi$
$41$	4.70052			0.734098			0.367049	+	0.930202i	$0.380368\pi$
$42$			2.96239i			0.457106i
$43$		−	10.3127i		−	1.57266i	−0.617804	−	0.786332i	$-0.711977\pi$
$43$		−	10.3127i		−	1.57266i	0.617804	−	0.786332i	$-0.288023\pi$
$44$	3.35026			0.505071
$45$	1.67513	−	1.48119i	0.249714	−	0.220803i
$46$	1.00000			0.147442
$47$		−	3.22425i		−	0.470306i	−0.971958	−	0.235153i	$-0.924441\pi$
$47$		−	3.22425i		−	0.470306i	0.971958	−	0.235153i	$-0.0755591\pi$
$48$			1.00000i			0.144338i
$49$	−1.77575			−0.253678
$50$	4.96239	+	0.612127i	0.701788	+	0.0865678i
$51$	1.35026			0.189074
$52$			4.96239i			0.688159i
$53$		−	6.96239i		−	0.956358i	−0.878263	−	0.478179i	$-0.841297\pi$
$53$		−	6.96239i		−	0.956358i	0.878263	−	0.478179i	$-0.158703\pi$
$54$	1.00000			0.136083
$55$	5.61213	−	4.96239i	0.756739	−	0.669128i
$56$	−2.96239			−0.395866
$57$			4.96239i			0.657284i
$58$		−	7.73813i		−	1.01607i
$59$	−1.22425			−0.159384			−0.0796921	−	0.996820i	$-0.525394\pi$
$59$	−1.22425			−0.159384			−0.0796921	+	0.996820i	$0.525394\pi$
$60$	1.48119	+	1.67513i	0.191221	+	0.216258i
$61$	−11.0884			−1.41972			−0.709862	−	0.704341i	$-0.751243\pi$
$61$	−11.0884			−1.41972			−0.709862	+	0.704341i	$0.751243\pi$
$62$		−	4.00000i		−	0.508001i
$63$			2.96239i			0.373226i
$64$	−1.00000			−0.125000
$65$	7.35026	+	8.31265i	0.911688	+	1.03106i
$66$	3.35026			0.412389
$67$			7.61213i			0.929969i	0.885319	+	0.464985i	$0.153940\pi$
$67$			7.61213i			0.929969i	−0.885319	+	0.464985i	$0.846060\pi$
$68$			1.35026i			0.163743i
$69$	1.00000			0.120386
$70$	−4.96239	+	4.38787i	−0.593119	+	0.524451i
$71$	−2.18664			−0.259507			−0.129753	−	0.991546i	$-0.541419\pi$
$71$	−2.18664			−0.259507			−0.129753	+	0.991546i	$0.541419\pi$
$72$			1.00000i			0.117851i
$73$		−	9.92478i		−	1.16161i	−0.814044	−	0.580804i	$-0.802738\pi$
$73$		−	9.92478i		−	1.16161i	0.814044	−	0.580804i	$-0.197262\pi$
$74$	−7.61213			−0.884892
$75$	4.96239	+	0.612127i	0.573007	+	0.0706823i
$76$	−4.96239			−0.569225
$77$			9.92478i			1.13103i
$78$			4.96239i			0.561880i
$79$	4.12601			0.464212			0.232106	−	0.972690i	$-0.425438\pi$
$79$	4.12601			0.464212			0.232106	+	0.972690i	$0.425438\pi$
$80$	−1.67513	+	1.48119i	−0.187285	+	0.165603i
$81$	1.00000			0.111111
$82$			4.70052i			0.519086i
$83$		−	6.38787i		−	0.701160i	−0.936533	−	0.350580i	$-0.885984\pi$
$83$		−	6.38787i		−	0.701160i	0.936533	−	0.350580i	$-0.114016\pi$
$84$	−2.96239			−0.323223
$85$	2.00000	+	2.26187i	0.216930	+	0.245334i
$86$	10.3127			1.11204
$87$		−	7.73813i		−	0.829615i
$88$			3.35026i			0.357139i
$89$	−9.92478			−1.05202			−0.526012	−	0.850477i	$-0.676313\pi$
$89$	−9.92478			−1.05202			−0.526012	+	0.850477i	$0.676313\pi$
$90$	1.48119	+	1.67513i	0.156132	+	0.176574i
$91$	−14.7005			−1.54103
$92$			1.00000i			0.104257i
$93$		−	4.00000i		−	0.414781i
$94$	3.22425			0.332556
$95$	−8.31265	+	7.35026i	−0.852860	+	0.754121i
$96$	−1.00000			−0.102062
$97$		−	12.8872i		−	1.30849i	−0.756281	−	0.654247i	$-0.772986\pi$
$97$		−	12.8872i		−	1.30849i	0.756281	−	0.654247i	$-0.227014\pi$
$98$		−	1.77575i		−	0.179377i
$99$	3.35026			0.336714
$100$	−0.612127	+	4.96239i	−0.0612127	+	0.496239i
$101$	4.26187			0.424071			0.212036	−	0.977262i	$-0.431991\pi$
$101$	4.26187			0.424071			0.212036	+	0.977262i	$0.431991\pi$
$102$			1.35026i			0.133696i
$103$		−	0.261865i		−	0.0258023i	−0.999917	−	0.0129012i	$-0.995893\pi$
$103$		−	0.261865i		−	0.0258023i	0.999917	−	0.0129012i	$-0.00410668\pi$
$104$	−4.96239			−0.486602
$105$	−4.96239	+	4.38787i	−0.484280	+	0.428213i
$106$	6.96239			0.676247
$107$			9.08840i			0.878608i	0.898338	+	0.439304i	$0.144775\pi$
$107$			9.08840i			0.878608i	−0.898338	+	0.439304i	$0.855225\pi$
$108$			1.00000i			0.0962250i
$109$	−18.9380			−1.81393			−0.906963	−	0.421210i	$-0.861606\pi$
$109$	−18.9380			−1.81393			−0.906963	+	0.421210i	$0.861606\pi$
$110$	4.96239	+	5.61213i	0.473145	+	0.535095i
$111$	−7.61213			−0.722511
$112$		−	2.96239i		−	0.279919i
$113$		−	6.64974i		−	0.625555i	−0.949826	−	0.312777i	$-0.898741\pi$
$113$		−	6.64974i		−	0.625555i	0.949826	−	0.312777i	$-0.101259\pi$
$114$	−4.96239			−0.464770
$115$	1.48119	+	1.67513i	0.138122	+	0.156207i
$116$	7.73813			0.718468
$117$			4.96239i			0.458773i
$118$		−	1.22425i		−	0.112702i
$119$	−4.00000			−0.366679
$120$	−1.67513	+	1.48119i	−0.152918	+	0.135214i
$121$	0.224254			0.0203867
$122$		−	11.0884i		−	1.00390i
$123$			4.70052i			0.423832i
$124$	4.00000			0.359211
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$	−2.96239			−0.263911
$127$		−	0.186642i		−	0.0165618i	−0.999966	−	0.00828091i	$-0.997364\pi$
$127$		−	0.186642i		−	0.0165618i	0.999966	−	0.00828091i	$-0.00263593\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	10.3127			0.907978
$130$	−8.31265	+	7.35026i	−0.729068	+	0.644661i
$131$	7.92478			0.692391			0.346196	−	0.938162i	$-0.387473\pi$
$131$	7.92478			0.692391			0.346196	+	0.938162i	$0.387473\pi$
$132$			3.35026i			0.291603i
$133$		−	14.7005i		−	1.27470i
$134$	−7.61213			−0.657588
$135$	1.48119	+	1.67513i	0.127481	+	0.144172i
$136$	−1.35026			−0.115784
$137$		−	9.19982i		−	0.785993i	−0.919540	−	0.392997i	$-0.871438\pi$
$137$		−	9.19982i		−	0.785993i	0.919540	−	0.392997i	$-0.128562\pi$
$138$			1.00000i			0.0851257i
$139$	−8.62530			−0.731588			−0.365794	−	0.930696i	$-0.619203\pi$
$139$	−8.62530			−0.731588			−0.365794	+	0.930696i	$0.619203\pi$
$140$	−4.38787	−	4.96239i	−0.370843	−	0.419398i
$141$	3.22425			0.271531
$142$		−	2.18664i		−	0.183499i
$143$			16.6253i			1.39028i
$144$	−1.00000			−0.0833333
$145$	12.9624	−	11.4617i	1.07647	−	0.951841i
$146$	9.92478			0.821380
$147$		−	1.77575i		−	0.146461i
$148$		−	7.61213i		−	0.625713i
$149$	−4.64974			−0.380921			−0.190461	−	0.981695i	$-0.560998\pi$
$149$	−4.64974			−0.380921			−0.190461	+	0.981695i	$0.560998\pi$
$150$	−0.612127	+	4.96239i	−0.0499799	+	0.405177i
$151$	10.7005			0.870796			0.435398	−	0.900238i	$-0.356608\pi$
$151$	10.7005			0.870796			0.435398	+	0.900238i	$0.356608\pi$
$152$		−	4.96239i		−	0.402503i
$153$			1.35026i			0.109162i
$154$	−9.92478			−0.799761
$155$	6.70052	−	5.92478i	0.538199	−	0.475890i
$156$	−4.96239			−0.397309
$157$			17.0132i			1.35780i	0.734231	+	0.678900i	$0.237543\pi$
$157$			17.0132i			1.35780i	−0.734231	+	0.678900i	$0.762457\pi$
$158$			4.12601i			0.328248i
$159$	6.96239			0.552153
$160$	−1.48119	−	1.67513i	−0.117099	−	0.132431i
$161$	−2.96239			−0.233469
$162$			1.00000i			0.0785674i
$163$			12.6253i			0.988890i	0.869209	+	0.494445i	$0.164629\pi$
$163$			12.6253i			0.988890i	−0.869209	+	0.494445i	$0.835371\pi$
$164$	−4.70052			−0.367049
$165$	4.96239	+	5.61213i	0.386321	+	0.436903i
$166$	6.38787			0.495795
$167$			24.6253i			1.90556i	0.303657	+	0.952781i	$0.401792\pi$
$167$			24.6253i			1.90556i	−0.303657	+	0.952781i	$0.598208\pi$
$168$		−	2.96239i		−	0.228553i
$169$	−11.6253			−0.894254
$170$	−2.26187	+	2.00000i	−0.173477	+	0.153393i
$171$	−4.96239			−0.379483
$172$			10.3127i			0.786332i
$173$		−	4.44851i		−	0.338214i	−0.985598	−	0.169107i	$-0.945912\pi$
$173$		−	4.44851i		−	0.338214i	0.985598	−	0.169107i	$-0.0540883\pi$
$174$	7.73813			0.586626
$175$	−14.7005	−	1.81336i	−1.11126	−	0.137077i
$176$	−3.35026			−0.252535
$177$		−	1.22425i		−	0.0920205i
$178$		−	9.92478i		−	0.743894i
$179$	13.8496			1.03516			0.517582	−	0.855634i	$-0.326832\pi$
$179$	13.8496			1.03516			0.517582	+	0.855634i	$0.326832\pi$
$180$	−1.67513	+	1.48119i	−0.124857	+	0.110402i
$181$	−22.6859			−1.68623			−0.843116	−	0.537732i	$-0.819281\pi$
$181$	−22.6859			−1.68623			−0.843116	+	0.537732i	$0.819281\pi$
$182$		−	14.7005i		−	1.08968i
$183$		−	11.0884i		−	0.819678i
$184$	−1.00000			−0.0737210
$185$	−11.2750	−	12.7513i	−0.828957	−	0.937495i
$186$	4.00000			0.293294
$187$			4.52373i			0.330808i
$188$			3.22425i			0.235153i
$189$	−2.96239			−0.215482
$190$	−7.35026	−	8.31265i	−0.533244	−	0.603063i
$191$	−19.3258			−1.39837			−0.699184	−	0.714942i	$-0.746453\pi$
$191$	−19.3258			−1.39837			−0.699184	+	0.714942i	$0.746453\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	5.92478i		−	0.426475i	−0.977000	−	0.213237i	$-0.931599\pi$
$193$		−	5.92478i		−	0.426475i	0.977000	−	0.213237i	$-0.0684008\pi$
$194$	12.8872			0.925245
$195$	−8.31265	+	7.35026i	−0.595281	+	0.526363i
$196$	1.77575			0.126839
$197$		−	8.07522i		−	0.575336i	−0.957730	−	0.287668i	$-0.907120\pi$
$197$		−	8.07522i		−	0.575336i	0.957730	−	0.287668i	$-0.0928799\pi$
$198$			3.35026i			0.238093i
$199$	−15.9756			−1.13248			−0.566239	−	0.824241i	$-0.691602\pi$
$199$	−15.9756			−1.13248			−0.566239	+	0.824241i	$0.691602\pi$
$200$	−4.96239	−	0.612127i	−0.350894	−	0.0432839i
$201$	−7.61213			−0.536918
$202$			4.26187i			0.299864i
$203$			22.9234i			1.60890i
$204$	−1.35026			−0.0945372
$205$	−7.87399	+	6.96239i	−0.549943	+	0.486274i
$206$	0.261865			0.0182450
$207$			1.00000i			0.0695048i
$208$		−	4.96239i		−	0.344080i
$209$	−16.6253			−1.15000
$210$	−4.38787	−	4.96239i	−0.302792	−	0.342437i
$211$	21.7743			1.49901			0.749503	−	0.662000i	$-0.230292\pi$
$211$	21.7743			1.49901			0.749503	+	0.662000i	$0.230292\pi$
$212$			6.96239i			0.478179i
$213$		−	2.18664i		−	0.149826i
$214$	−9.08840			−0.621270
$215$	15.2750	+	17.2750i	1.04175	+	1.17815i
$216$	−1.00000			−0.0680414
$217$			11.8496i			0.804400i
$218$		−	18.9380i		−	1.28264i
$219$	9.92478			0.670654
$220$	−5.61213	+	4.96239i	−0.378370	+	0.334564i
$221$	−6.70052			−0.450726
$222$		−	7.61213i		−	0.510893i
$223$		−	3.81336i		−	0.255361i	−0.991815	−	0.127681i	$-0.959247\pi$
$223$		−	3.81336i		−	0.255361i	0.991815	−	0.127681i	$-0.0407533\pi$
$224$	2.96239			0.197933
$225$	−0.612127	+	4.96239i	−0.0408085	+	0.330826i
$226$	6.64974			0.442334
$227$			16.9380i			1.12421i	0.827065	+	0.562106i	$0.190009\pi$
$227$			16.9380i			1.12421i	−0.827065	+	0.562106i	$0.809991\pi$
$228$		−	4.96239i		−	0.328642i
$229$	26.9380			1.78011			0.890055	−	0.455853i	$-0.150666\pi$
$229$	26.9380			1.78011			0.890055	+	0.455853i	$0.150666\pi$
$230$	−1.67513	+	1.48119i	−0.110455	+	0.0976671i
$231$	−9.92478			−0.653002
$232$			7.73813i			0.508033i
$233$		−	27.4010i		−	1.79510i	−0.440910	−	0.897551i	$-0.645344\pi$
$233$		−	27.4010i		−	1.79510i	0.440910	−	0.897551i	$-0.354656\pi$
$234$	−4.96239			−0.324401
$235$	4.77575	+	5.40105i	0.311535	+	0.352325i
$236$	1.22425			0.0796921
$237$			4.12601i			0.268013i
$238$		−	4.00000i		−	0.259281i
$239$	−7.48612			−0.484237			−0.242118	−	0.970247i	$-0.577842\pi$
$239$	−7.48612			−0.484237			−0.242118	+	0.970247i	$0.577842\pi$
$240$	−1.48119	−	1.67513i	−0.0956107	−	0.108129i
$241$	−13.0738			−0.842158			−0.421079	−	0.907024i	$-0.638348\pi$
$241$	−13.0738			−0.842158			−0.421079	+	0.907024i	$0.638348\pi$
$242$			0.224254i			0.0144156i
$243$			1.00000i			0.0641500i
$244$	11.0884			0.709862
$245$	2.97461	−	2.63023i	0.190041	−	0.168039i
$246$	−4.70052			−0.299694
$247$		−	24.6253i		−	1.56687i
$248$			4.00000i			0.254000i
$249$	6.38787			0.404815
$250$	−9.21933	+	6.32487i	−0.583082	+	0.400020i
$251$	−5.02302			−0.317050			−0.158525	−	0.987355i	$-0.550674\pi$
$251$	−5.02302			−0.317050			−0.158525	+	0.987355i	$0.550674\pi$
$252$		−	2.96239i		−	0.186613i
$253$			3.35026i			0.210629i
$254$	0.186642			0.0117110
$255$	−2.26187	+	2.00000i	−0.141643	+	0.125245i
$256$	1.00000			0.0625000
$257$		−	19.4010i		−	1.21020i	−0.796148	−	0.605102i	$-0.793132\pi$
$257$		−	19.4010i		−	1.21020i	0.796148	−	0.605102i	$-0.206868\pi$
$258$			10.3127i			0.642038i
$259$	22.5501			1.40119
$260$	−7.35026	−	8.31265i	−0.455844	−	0.515529i
$261$	7.73813			0.478979
$262$			7.92478i			0.489594i
$263$			15.4763i			0.954308i	0.878820	+	0.477154i	$0.158332\pi$
$263$			15.4763i			0.954308i	−0.878820	+	0.477154i	$0.841668\pi$
$264$	−3.35026			−0.206194
$265$	10.3127	+	11.6629i	0.633501	+	0.716447i
$266$	14.7005			0.901347
$267$		−	9.92478i		−	0.607387i
$268$		−	7.61213i		−	0.464985i
$269$	20.2130			1.23241			0.616204	−	0.787587i	$-0.288670\pi$
$269$	20.2130			1.23241			0.616204	+	0.787587i	$0.288670\pi$
$270$	−1.67513	+	1.48119i	−0.101945	+	0.0901426i
$271$	30.3996			1.84665			0.923323	−	0.384024i	$-0.125462\pi$
$271$	30.3996			1.84665			0.923323	+	0.384024i	$0.125462\pi$
$272$		−	1.35026i		−	0.0818716i
$273$		−	14.7005i		−	0.889716i
$274$	9.19982			0.555781
$275$	−2.05079	+	16.6253i	−0.123667	+	1.00254i
$276$	−1.00000			−0.0601929
$277$		−	20.8119i		−	1.25047i	−0.780437	−	0.625234i	$-0.785003\pi$
$277$		−	20.8119i		−	1.25047i	0.780437	−	0.625234i	$-0.214997\pi$
$278$		−	8.62530i		−	0.517311i
$279$	4.00000			0.239474
$280$	4.96239	−	4.38787i	0.296559	−	0.262226i
$281$	19.8496			1.18413			0.592063	−	0.805892i	$-0.298314\pi$
$281$	19.8496			1.18413			0.592063	+	0.805892i	$0.298314\pi$
$282$			3.22425i			0.192002i
$283$			12.3879i			0.736383i	0.929750	+	0.368191i	$0.120023\pi$
$283$			12.3879i			0.736383i	−0.929750	+	0.368191i	$0.879977\pi$
$284$	2.18664			0.129753
$285$	−7.35026	−	8.31265i	−0.435392	−	0.492399i
$286$	−16.6253			−0.983075
$287$		−	13.9248i		−	0.821954i
$288$		−	1.00000i		−	0.0589256i
$289$	15.1768			0.892753
$290$	11.4617	+	12.9624i	0.673053	+	0.761178i
$291$	12.8872			0.755459
$292$			9.92478i			0.580804i
$293$			9.03761i			0.527983i	0.964525	+	0.263991i	$0.0850391\pi$
$293$			9.03761i			0.527983i	−0.964525	+	0.263991i	$0.914961\pi$
$294$	1.77575			0.103564
$295$	2.05079	−	1.81336i	0.119401	−	0.105578i
$296$	7.61213			0.442446
$297$			3.35026i			0.194402i
$298$		−	4.64974i		−	0.269352i
$299$	−4.96239			−0.286982
$300$	−4.96239	−	0.612127i	−0.286504	−	0.0353412i
$301$	−30.5501			−1.76088
$302$			10.7005i			0.615746i
$303$			4.26187i			0.244838i
$304$	4.96239			0.284613
$305$	18.5745	−	16.4241i	1.06357	−	0.940440i
$306$	−1.35026			−0.0771893
$307$			30.5501i			1.74359i	0.489875	+	0.871793i	$0.337042\pi$
$307$			30.5501i			1.74359i	−0.489875	+	0.871793i	$0.662958\pi$
$308$		−	9.92478i		−	0.565517i
$309$	0.261865			0.0148970
$310$	5.92478	+	6.70052i	0.336505	+	0.380564i
$311$	14.4387			0.818741			0.409371	−	0.912368i	$-0.365748\pi$
$311$	14.4387			0.818741			0.409371	+	0.912368i	$0.365748\pi$
$312$		−	4.96239i		−	0.280940i
$313$			27.9610i			1.58045i	0.612818	+	0.790224i	$0.290036\pi$
$313$			27.9610i			1.58045i	−0.612818	+	0.790224i	$0.709964\pi$
$314$	−17.0132			−0.960109
$315$	−4.38787	−	4.96239i	−0.247229	−	0.279599i
$316$	−4.12601			−0.232106
$317$		−	1.47627i		−	0.0829156i	−0.999140	−	0.0414578i	$-0.986800\pi$
$317$		−	1.47627i		−	0.0829156i	0.999140	−	0.0414578i	$-0.0132002\pi$
$318$			6.96239i			0.390431i
$319$	25.9248			1.45151
$320$	1.67513	−	1.48119i	0.0936427	−	0.0828013i
$321$	−9.08840			−0.507265
$322$		−	2.96239i		−	0.165087i
$323$		−	6.70052i		−	0.372827i
$324$	−1.00000			−0.0555556
$325$	−24.6253	−	3.03761i	−1.36597	−	0.168496i
$326$	−12.6253			−0.699251
$327$		−	18.9380i		−	1.04727i
$328$		−	4.70052i		−	0.259543i
$329$	−9.55149			−0.526591
$330$	−5.61213	+	4.96239i	−0.308937	+	0.273171i
$331$	23.1754			1.27383			0.636917	−	0.770932i	$-0.280209\pi$
$331$	23.1754			1.27383			0.636917	+	0.770932i	$0.280209\pi$
$332$			6.38787i			0.350580i
$333$		−	7.61213i		−	0.417142i
$334$	−24.6253			−1.34744
$335$	−11.2750	−	12.7513i	−0.616021	−	0.696678i
$336$	2.96239			0.161612
$337$			21.0376i			1.14599i	0.819558	+	0.572996i	$0.194219\pi$
$337$			21.0376i			1.14599i	−0.819558	+	0.572996i	$0.805781\pi$
$338$		−	11.6253i		−	0.632333i
$339$	6.64974			0.361164
$340$	−2.00000	−	2.26187i	−0.108465	−	0.122667i
$341$	13.4010			0.725707
$342$		−	4.96239i		−	0.268335i
$343$		−	15.4763i		−	0.835640i
$344$	−10.3127			−0.556021
$345$	−1.67513	+	1.48119i	−0.0901860	+	0.0797448i
$346$	4.44851			0.239153
$347$		−	3.37470i		−	0.181163i	−0.995889	−	0.0905817i	$-0.971127\pi$
$347$		−	3.37470i		−	0.181163i	0.995889	−	0.0905817i	$-0.0288726\pi$
$348$			7.73813i			0.414808i
$349$	4.44851			0.238123			0.119062	−	0.992887i	$-0.462011\pi$
$349$	4.44851			0.238123			0.119062	+	0.992887i	$0.462011\pi$
$350$	1.81336	−	14.7005i	0.0969280	−	0.785776i
$351$	−4.96239			−0.264873
$352$		−	3.35026i		−	0.178570i
$353$		−	35.4010i		−	1.88421i	−0.335321	−	0.942104i	$-0.608845\pi$
$353$		−	35.4010i		−	1.88421i	0.335321	−	0.942104i	$-0.391155\pi$
$354$	1.22425			0.0650684
$355$	3.66291	−	3.23884i	0.194407	−	0.171900i
$356$	9.92478			0.526012
$357$		−	4.00000i		−	0.211702i
$358$			13.8496i			0.731972i
$359$	34.5501			1.82348			0.911742	−	0.410764i	$-0.134738\pi$
$359$	34.5501			1.82348			0.911742	+	0.410764i	$0.134738\pi$
$360$	−1.48119	−	1.67513i	−0.0780658	−	0.0882871i
$361$	5.62530			0.296068
$362$		−	22.6859i		−	1.19235i
$363$			0.224254i			0.0117703i
$364$	14.7005			0.770517
$365$	14.7005	+	16.6253i	0.769461	+	0.870208i
$366$	11.0884			0.579600
$367$		−	22.8119i		−	1.19077i	−0.803439	−	0.595387i	$-0.796999\pi$
$367$		−	22.8119i		−	1.19077i	0.803439	−	0.595387i	$-0.203001\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	−4.70052			−0.244699
$370$	12.7513	−	11.2750i	0.662909	−	0.586161i
$371$	−20.6253			−1.07081
$372$			4.00000i			0.207390i
$373$			10.8364i			0.561087i	0.959841	+	0.280543i	$0.0905146\pi$
$373$			10.8364i			0.561087i	−0.959841	+	0.280543i	$0.909485\pi$
$374$	−4.52373			−0.233917
$375$	−9.21933	+	6.32487i	−0.476084	+	0.326615i
$376$	−3.22425			−0.166278
$377$			38.3996i			1.97768i
$378$		−	2.96239i		−	0.152369i
$379$	32.4387			1.66626			0.833131	−	0.553076i	$-0.186546\pi$
$379$	32.4387			1.66626			0.833131	+	0.553076i	$0.186546\pi$
$380$	8.31265	−	7.35026i	0.426430	−	0.377060i
$381$	0.186642			0.00956198
$382$		−	19.3258i		−	0.988795i
$383$		−	32.9986i		−	1.68615i	−0.537797	−	0.843074i	$-0.680743\pi$
$383$		−	32.9986i		−	1.68615i	0.537797	−	0.843074i	$-0.319257\pi$
$384$	1.00000			0.0510310
$385$	−14.7005	−	16.6253i	−0.749208	−	0.847304i
$386$	5.92478			0.301563
$387$			10.3127i			0.524221i
$388$			12.8872i			0.654247i
$389$	−29.1246			−1.47668			−0.738338	−	0.674431i	$-0.764389\pi$
$389$	−29.1246			−1.47668			−0.738338	+	0.674431i	$0.764389\pi$
$390$	−7.35026	−	8.31265i	−0.372195	−	0.420927i
$391$	−1.35026			−0.0682857
$392$			1.77575i			0.0896887i
$393$			7.92478i			0.399752i
$394$	8.07522			0.406824
$395$	−6.91160	+	6.11142i	−0.347761	+	0.307499i
$396$	−3.35026			−0.168357
$397$		−	13.7381i		−	0.689497i	−0.938695	−	0.344749i	$-0.887964\pi$
$397$		−	13.7381i		−	0.689497i	0.938695	−	0.344749i	$-0.112036\pi$
$398$		−	15.9756i		−	0.800783i
$399$	14.7005			0.735947
$400$	0.612127	−	4.96239i	0.0306063	−	0.248119i
$401$	−1.44992			−0.0724057			−0.0362028	−	0.999344i	$-0.511526\pi$
$401$	−1.44992			−0.0724057			−0.0362028	+	0.999344i	$0.511526\pi$
$402$		−	7.61213i		−	0.379658i
$403$			19.8496i			0.988777i
$404$	−4.26187			−0.212036
$405$	−1.67513	+	1.48119i	−0.0832379	+	0.0736011i
$406$	−22.9234			−1.13767
$407$		−	25.5026i		−	1.26412i
$408$		−	1.35026i		−	0.0668479i
$409$	17.8496			0.882604			0.441302	−	0.897359i	$-0.354517\pi$
$409$	17.8496			0.882604			0.441302	+	0.897359i	$0.354517\pi$
$410$	−6.96239	−	7.87399i	−0.343848	−	0.388869i
$411$	9.19982			0.453793
$412$			0.261865i			0.0129012i
$413$			3.62672i			0.178459i
$414$	−1.00000			−0.0491473
$415$	9.46168	+	10.7005i	0.464456	+	0.525268i
$416$	4.96239			0.243301
$417$		−	8.62530i		−	0.422383i
$418$		−	16.6253i		−	0.813170i
$419$	−17.9003			−0.874489			−0.437244	−	0.899343i	$-0.644046\pi$
$419$	−17.9003			−0.874489			−0.437244	+	0.899343i	$0.644046\pi$
$420$	4.96239	−	4.38787i	0.242140	−	0.214106i
$421$	7.61213			0.370992			0.185496	−	0.982645i	$-0.440611\pi$
$421$	7.61213			0.370992			0.185496	+	0.982645i	$0.440611\pi$
$422$			21.7743i			1.05996i
$423$			3.22425i			0.156769i
$424$	−6.96239			−0.338123
$425$	−6.70052	−	0.826531i	−0.325023	−	0.0400927i
$426$	2.18664			0.105943
$427$			32.8481i			1.58963i
$428$		−	9.08840i		−	0.439304i
$429$	−16.6253			−0.802677
$430$	−17.2750	+	15.2750i	−0.833076	+	0.736628i
$431$	−22.9525			−1.10558			−0.552792	−	0.833319i	$-0.686438\pi$
$431$	−22.9525			−1.10558			−0.552792	+	0.833319i	$0.686438\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			33.7645i			1.62262i	0.584618	+	0.811309i	$0.301244\pi$
$433$			33.7645i			1.62262i	−0.584618	+	0.811309i	$0.698756\pi$
$434$	−11.8496			−0.568797
$435$	11.4617	+	12.9624i	0.549546	+	0.621499i
$436$	18.9380			0.906963
$437$		−	4.96239i		−	0.237383i
$438$			9.92478i			0.474224i
$439$	23.4763			1.12046			0.560231	−	0.828337i	$-0.310713\pi$
$439$	23.4763			1.12046			0.560231	+	0.828337i	$0.310713\pi$
$440$	−4.96239	−	5.61213i	−0.236573	−	0.267548i
$441$	1.77575			0.0845593
$442$		−	6.70052i		−	0.318711i
$443$		−	30.5501i		−	1.45148i	−0.687970	−	0.725739i	$-0.741498\pi$
$443$		−	30.5501i		−	1.45148i	0.687970	−	0.725739i	$-0.258502\pi$
$444$	7.61213			0.361256
$445$	16.6253	−	14.7005i	0.788115	−	0.696872i
$446$	3.81336			0.180568
$447$		−	4.64974i		−	0.219925i
$448$			2.96239i			0.139960i
$449$	−32.7005			−1.54323			−0.771617	−	0.636088i	$-0.780552\pi$
$449$	−32.7005			−1.54323			−0.771617	+	0.636088i	$0.780552\pi$
$450$	−4.96239	−	0.612127i	−0.233929	−	0.0288559i
$451$	−15.7480			−0.741544
$452$			6.64974i			0.312777i
$453$			10.7005i			0.502754i
$454$	−16.9380			−0.794937
$455$	24.6253	−	21.7743i	1.15445	−	1.02080i
$456$	4.96239			0.232385
$457$		−	5.81336i		−	0.271937i	−0.990713	−	0.135969i	$-0.956585\pi$
$457$		−	5.81336i		−	0.271937i	0.990713	−	0.135969i	$-0.0434147\pi$
$458$			26.9380i			1.25873i
$459$	−1.35026			−0.0630248
$460$	−1.48119	−	1.67513i	−0.0690610	−	0.0781034i
$461$	−23.9902			−1.11733			−0.558666	−	0.829392i	$-0.688687\pi$
$461$	−23.9902			−1.11733			−0.558666	+	0.829392i	$0.688687\pi$
$462$		−	9.92478i		−	0.461742i
$463$		−	35.3620i		−	1.64341i	−0.569911	−	0.821706i	$-0.693022\pi$
$463$		−	35.3620i		−	1.64341i	0.569911	−	0.821706i	$-0.306978\pi$
$464$	−7.73813			−0.359234
$465$	5.92478	+	6.70052i	0.274755	+	0.310729i
$466$	27.4010			1.26933
$467$			1.98541i			0.0918739i	0.998944	+	0.0459369i	$0.0146273\pi$
$467$			1.98541i			0.0918739i	−0.998944	+	0.0459369i	$0.985373\pi$
$468$		−	4.96239i		−	0.229386i
$469$	22.5501			1.04127
$470$	−5.40105	+	4.77575i	−0.249132	+	0.220289i
$471$	−17.0132			−0.783926
$472$			1.22425i			0.0563508i
$473$			34.5501i			1.58861i
$474$	−4.12601			−0.189514
$475$	3.03761	−	24.6253i	0.139375	−	1.12989i
$476$	4.00000			0.183340
$477$			6.96239i			0.318786i
$478$		−	7.48612i		−	0.342407i
$479$	−11.0738			−0.505975			−0.252988	−	0.967470i	$-0.581413\pi$
$479$	−11.0738			−0.505975			−0.252988	+	0.967470i	$0.581413\pi$
$480$	1.67513	−	1.48119i	0.0764589	−	0.0676070i
$481$	37.7743			1.72236
$482$		−	13.0738i		−	0.595496i
$483$		−	2.96239i		−	0.134793i
$484$	−0.224254			−0.0101934
$485$	19.0884	+	21.5877i	0.866759	+	0.980246i
$486$	−1.00000			−0.0453609
$487$		−	17.4372i		−	0.790157i	−0.918647	−	0.395078i	$-0.870717\pi$
$487$		−	17.4372i		−	0.790157i	0.918647	−	0.395078i	$-0.129283\pi$
$488$			11.0884i			0.501948i
$489$	−12.6253			−0.570936
$490$	2.63023	+	2.97461i	0.118821	+	0.134379i
$491$	14.8773			0.671404			0.335702	−	0.941968i	$-0.391027\pi$
$491$	14.8773			0.671404			0.335702	+	0.941968i	$0.391027\pi$
$492$		−	4.70052i		−	0.211916i
$493$			10.4485i			0.470577i
$494$	24.6253			1.10794
$495$	−5.61213	+	4.96239i	−0.252246	+	0.223043i
$496$	−4.00000			−0.179605
$497$			6.47768i			0.290564i
$498$			6.38787i			0.286247i
$499$	16.1016			0.720805			0.360403	−	0.932797i	$-0.382639\pi$
$499$	16.1016			0.720805			0.360403	+	0.932797i	$0.382639\pi$
$500$	−6.32487	−	9.21933i	−0.282857	−	0.412301i
$501$	−24.6253			−1.10018
$502$		−	5.02302i		−	0.224188i
$503$			38.8021i			1.73010i	0.501686	+	0.865050i	$0.332713\pi$
$503$			38.8021i			1.73010i	−0.501686	+	0.865050i	$0.667287\pi$
$504$	2.96239			0.131955
$505$	−7.13918	+	6.31265i	−0.317689	+	0.280909i
$506$	−3.35026			−0.148937
$507$		−	11.6253i		−	0.516298i
$508$			0.186642i			0.00828091i
$509$	−23.4372			−1.03884			−0.519419	−	0.854520i	$-0.673852\pi$
$509$	−23.4372			−1.03884			−0.519419	+	0.854520i	$0.673852\pi$
$510$	−2.00000	−	2.26187i	−0.0885615	−	0.100157i
$511$	−29.4010			−1.30063
$512$			1.00000i			0.0441942i
$513$		−	4.96239i		−	0.219095i
$514$	19.4010			0.855743
$515$	0.387873	+	0.438658i	0.0170917	+	0.0193296i
$516$	−10.3127			−0.453989
$517$			10.8021i			0.475076i
$518$			22.5501i			0.990794i
$519$	4.44851			0.195268
$520$	8.31265	−	7.35026i	0.364534	−	0.322330i
$521$	21.1490			0.926556			0.463278	−	0.886213i	$-0.346673\pi$
$521$	21.1490			0.926556			0.463278	+	0.886213i	$0.346673\pi$
$522$			7.73813i			0.338689i
$523$			11.7626i			0.514341i	0.966366	+	0.257171i	$0.0827903\pi$
$523$			11.7626i			0.514341i	−0.966366	+	0.257171i	$0.917210\pi$
$524$	−7.92478			−0.346196
$525$	1.81336	−	14.7005i	0.0791414	−	0.641583i
$526$	−15.4763			−0.674797
$527$			5.40105i			0.235273i
$528$		−	3.35026i		−	0.145801i
$529$	−1.00000			−0.0434783
$530$	−11.6629	+	10.3127i	−0.506605	+	0.447953i
$531$	1.22425			0.0531281
$532$			14.7005i			0.637349i
$533$		−	23.3258i		−	1.01035i
$534$	9.92478			0.429487
$535$	−13.4617	−	15.2243i	−0.581999	−	0.658202i
$536$	7.61213			0.328794
$537$			13.8496i			0.597652i
$538$			20.2130i			0.871444i
$539$	5.94921			0.256251
$540$	−1.48119	−	1.67513i	−0.0637405	−	0.0720862i
$541$	−21.1754			−0.910401			−0.455200	−	0.890389i	$-0.650432\pi$
$541$	−21.1754			−0.910401			−0.455200	+	0.890389i	$0.650432\pi$
$542$			30.3996i			1.30578i
$543$		−	22.6859i		−	0.973547i
$544$	1.35026			0.0578920
$545$	31.7235	−	28.0508i	1.35889	−	1.20156i
$546$	14.7005			0.629124
$547$		−	5.29948i		−	0.226589i	−0.993561	−	0.113295i	$-0.963860\pi$
$547$		−	5.29948i		−	0.226589i	0.993561	−	0.113295i	$-0.0361404\pi$
$548$			9.19982i			0.392997i
$549$	11.0884			0.473241
$550$	−16.6253	−	2.05079i	−0.708905	−	0.0874458i
$551$	−38.3996			−1.63588
$552$		−	1.00000i		−	0.0425628i
$553$		−	12.2228i		−	0.519768i
$554$	20.8119			0.884215
$555$	12.7513	−	11.2750i	0.541263	−	0.478599i
$556$	8.62530			0.365794
$557$			7.99015i			0.338554i	0.985569	+	0.169277i	$0.0541432\pi$
$557$			7.99015i			0.338554i	−0.985569	+	0.169277i	$0.945857\pi$
$558$			4.00000i			0.169334i
$559$	−51.1754			−2.16449
$560$	4.38787	+	4.96239i	0.185421	+	0.209699i
$561$	−4.52373			−0.190992
$562$			19.8496i			0.837303i
$563$			15.1636i			0.639070i	0.947574	+	0.319535i	$0.103527\pi$
$563$			15.1636i			0.639070i	−0.947574	+	0.319535i	$0.896473\pi$
$564$	−3.22425			−0.135766
$565$	9.84955	+	11.1392i	0.414374	+	0.468629i
$566$	−12.3879			−0.520701
$567$		−	2.96239i		−	0.124409i
$568$			2.18664i			0.0917495i
$569$	25.5223			1.06995			0.534976	−	0.844868i	$-0.320321\pi$
$569$	25.5223			1.06995			0.534976	+	0.844868i	$0.320321\pi$
$570$	8.31265	−	7.35026i	0.348179	−	0.307869i
$571$	6.76590			0.283144			0.141572	−	0.989928i	$-0.454784\pi$
$571$	6.76590			0.283144			0.141572	+	0.989928i	$0.454784\pi$
$572$		−	16.6253i		−	0.695139i
$573$		−	19.3258i		−	0.807348i
$574$	13.9248			0.581209
$575$	−4.96239	−	0.612127i	−0.206946	−	0.0255275i
$576$	1.00000			0.0416667
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$			15.1768i			0.631271i
$579$	5.92478			0.246225
$580$	−12.9624	+	11.4617i	−0.538234	+	0.475920i
$581$	−18.9234			−0.785073
$582$			12.8872i			0.534190i
$583$			23.3258i			0.966057i
$584$	−9.92478			−0.410690
$585$	−7.35026	−	8.31265i	−0.303896	−	0.343686i
$586$	−9.03761			−0.373340
$587$			12.8773i			0.531504i	0.964041	+	0.265752i	$0.0856202\pi$
$587$			12.8773i			0.531504i	−0.964041	+	0.265752i	$0.914380\pi$
$588$			1.77575i			0.0732305i
$589$	−19.8496			−0.817887
$590$	1.81336	+	2.05079i	0.0746548	+	0.0844295i
$591$	8.07522			0.332170
$592$			7.61213i			0.312856i
$593$			16.2981i			0.669281i	0.942346	+	0.334641i	$0.108615\pi$
$593$			16.2981i			0.669281i	−0.942346	+	0.334641i	$0.891385\pi$
$594$	−3.35026			−0.137463
$595$	6.70052	−	5.92478i	0.274695	−	0.242892i
$596$	4.64974			0.190461
$597$		−	15.9756i		−	0.653836i
$598$		−	4.96239i		−	0.202927i
$599$	−9.91493			−0.405113			−0.202556	−	0.979271i	$-0.564925\pi$
$599$	−9.91493			−0.405113			−0.202556	+	0.979271i	$0.564925\pi$
$600$	0.612127	−	4.96239i	0.0249900	−	0.202589i
$601$	−7.40105			−0.301895			−0.150948	−	0.988542i	$-0.548232\pi$
$601$	−7.40105			−0.301895			−0.150948	+	0.988542i	$0.548232\pi$
$602$		−	30.5501i		−	1.24513i
$603$		−	7.61213i		−	0.309990i
$604$	−10.7005			−0.435398
$605$	−0.375654	+	0.332163i	−0.0152725	+	0.0135044i
$606$	−4.26187			−0.173126
$607$			13.9610i			0.566658i	0.959023	+	0.283329i	$0.0914389\pi$
$607$			13.9610i			0.566658i	−0.959023	+	0.283329i	$0.908561\pi$
$608$			4.96239i			0.201251i
$609$	−22.9234			−0.928902
$610$	16.4241	+	18.5745i	0.664991	+	0.752060i
$611$	−16.0000			−0.647291
$612$		−	1.35026i		−	0.0545811i
$613$		−	41.3865i		−	1.67158i	−0.549047	−	0.835792i	$-0.685009\pi$
$613$		−	41.3865i		−	1.67158i	0.549047	−	0.835792i	$-0.314991\pi$
$614$	−30.5501			−1.23290
$615$	−6.96239	−	7.87399i	−0.280751	−	0.317510i
$616$	9.92478			0.399881
$617$		−	29.3014i		−	1.17963i	−0.807539	−	0.589815i	$-0.799201\pi$
$617$		−	29.3014i		−	1.17963i	0.807539	−	0.589815i	$-0.200799\pi$
$618$			0.261865i			0.0105338i
$619$	19.0376			0.765186			0.382593	−	0.923917i	$-0.375031\pi$
$619$	19.0376			0.765186			0.382593	+	0.923917i	$0.375031\pi$
$620$	−6.70052	+	5.92478i	−0.269099	+	0.237945i
$621$	−1.00000			−0.0401286
$622$			14.4387i			0.578937i
$623$			29.4010i			1.17793i
$624$	4.96239			0.198655
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−27.9610			−1.11755
$627$		−	16.6253i		−	0.663951i
$628$		−	17.0132i		−	0.678900i
$629$	10.2784			0.409825
$630$	4.96239	−	4.38787i	0.197706	−	0.174817i
$631$	12.4993			0.497589			0.248794	−	0.968556i	$-0.419966\pi$
$631$	12.4993			0.497589			0.248794	+	0.968556i	$0.419966\pi$
$632$		−	4.12601i		−	0.164124i
$633$			21.7743i			0.865452i
$634$	1.47627			0.0586302
$635$	0.276454	+	0.312650i	0.0109707	+	0.0124072i
$636$	−6.96239			−0.276077
$637$			8.81194i			0.349142i
$638$			25.9248i			1.02637i
$639$	2.18664			0.0865022
$640$	1.48119	+	1.67513i	0.0585493	+	0.0662154i
$641$	−34.0263			−1.34396			−0.671980	−	0.740569i	$-0.734556\pi$
$641$	−34.0263			−1.34396			−0.671980	+	0.740569i	$0.734556\pi$
$642$		−	9.08840i		−	0.358690i
$643$		−	7.34041i		−	0.289478i	−0.989470	−	0.144739i	$-0.953766\pi$
$643$		−	7.34041i		−	0.289478i	0.989470	−	0.144739i	$-0.0462342\pi$
$644$	2.96239			0.116734
$645$	−17.2750	+	15.2750i	−0.680204	+	0.601454i
$646$	6.70052			0.263629
$647$			14.9525i			0.587845i	0.955829	+	0.293922i	$0.0949608\pi$
$647$			14.9525i			0.587845i	−0.955829	+	0.293922i	$0.905039\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	4.10157			0.161001
$650$	3.03761	−	24.6253i	0.119145	−	0.965884i
$651$	−11.8496			−0.464421
$652$		−	12.6253i		−	0.494445i
$653$			20.4485i			0.800212i	0.916469	+	0.400106i	$0.131027\pi$
$653$			20.4485i			0.800212i	−0.916469	+	0.400106i	$0.868973\pi$
$654$	18.9380			0.740532
$655$	−13.2750	+	11.7381i	−0.518699	+	0.458647i
$656$	4.70052			0.183525
$657$			9.92478i			0.387202i
$658$		−	9.55149i		−	0.372356i
$659$	−38.4241			−1.49679			−0.748395	−	0.663254i	$-0.769175\pi$
$659$	−38.4241			−1.49679			−0.748395	+	0.663254i	$0.769175\pi$
$660$	−4.96239	−	5.61213i	−0.193161	−	0.218452i
$661$	−39.3112			−1.52903			−0.764515	−	0.644606i	$-0.777021\pi$
$661$	−39.3112			−1.52903			−0.764515	+	0.644606i	$0.777021\pi$
$662$			23.1754i			0.900737i
$663$		−	6.70052i		−	0.260227i
$664$	−6.38787			−0.247898
$665$	21.7743	+	24.6253i	0.844372	+	0.954928i
$666$	7.61213			0.294964
$667$			7.73813i			0.299622i
$668$		−	24.6253i		−	0.952781i
$669$	3.81336			0.147433
$670$	12.7513	−	11.2750i	0.492626	−	0.435593i
$671$	37.1490			1.43412
$672$			2.96239i			0.114277i
$673$			25.5515i			0.984938i	0.870330	+	0.492469i	$0.163905\pi$
$673$			25.5515i			0.984938i	−0.870330	+	0.492469i	$0.836095\pi$
$674$	−21.0376			−0.810339
$675$	−4.96239	−	0.612127i	−0.191002	−	0.0235608i
$676$	11.6253			0.447127
$677$		−	36.2130i		−	1.39178i	−0.718149	−	0.695889i	$-0.755010\pi$
$677$		−	36.2130i		−	1.39178i	0.718149	−	0.695889i	$-0.244990\pi$
$678$			6.64974i			0.255382i
$679$	−38.1768			−1.46509
$680$	2.26187	−	2.00000i	0.0867386	−	0.0766965i
$681$	−16.9380			−0.649064
$682$			13.4010i			0.513153i
$683$		−	15.4763i		−	0.592183i	−0.955160	−	0.296092i	$-0.904317\pi$
$683$		−	15.4763i		−	0.592183i	0.955160	−	0.296092i	$-0.0956833\pi$
$684$	4.96239			0.189742
$685$	13.6267	+	15.4109i	0.520650	+	0.588820i
$686$	15.4763			0.590887
$687$			26.9380i			1.02775i
$688$		−	10.3127i		−	0.393166i
$689$	−34.5501			−1.31625
$690$	−1.48119	−	1.67513i	−0.0563881	−	0.0637711i
$691$	−37.6531			−1.43239			−0.716195	−	0.697900i	$-0.754118\pi$
$691$	−37.6531			−1.43239			−0.716195	+	0.697900i	$0.754118\pi$
$692$			4.44851i			0.169107i
$693$		−	9.92478i		−	0.377011i
$694$	3.37470			0.128102
$695$	14.4485	−	12.7757i	0.548063	−	0.484612i
$696$	−7.73813			−0.293313
$697$		−	6.34694i		−	0.240407i
$698$			4.44851i			0.168378i
$699$	27.4010			1.03640
$700$	14.7005	+	1.81336i	0.555628	+	0.0685385i
$701$	28.3488			1.07072			0.535361	−	0.844624i	$-0.320176\pi$
$701$	28.3488			1.07072			0.535361	+	0.844624i	$0.320176\pi$
$702$		−	4.96239i		−	0.187293i
$703$			37.7743i			1.42469i
$704$	3.35026			0.126268
$705$	−5.40105	+	4.77575i	−0.203415	+	0.179865i
$706$	35.4010			1.33234
$707$		−	12.6253i		−	0.474823i
$708$			1.22425i			0.0460103i
$709$	43.5633			1.63605			0.818026	−	0.575181i	$-0.195068\pi$
$709$	43.5633			1.63605			0.818026	+	0.575181i	$0.195068\pi$
$710$	3.23884	+	3.66291i	0.121552	+	0.137467i
$711$	−4.12601			−0.154737
$712$			9.92478i			0.371947i
$713$			4.00000i			0.149801i
$714$	4.00000			0.149696
$715$	−24.6253	−	27.8496i	−0.920934	−	1.04151i
$716$	−13.8496			−0.517582
$717$		−	7.48612i		−	0.279574i
$718$			34.5501i			1.28940i
$719$	−32.3634			−1.20695			−0.603476	−	0.797381i	$-0.706218\pi$
$719$	−32.3634			−1.20695			−0.603476	+	0.797381i	$0.706218\pi$
$720$	1.67513	−	1.48119i	0.0624284	−	0.0552009i
$721$	−0.775746			−0.0288903
$722$			5.62530i			0.209352i
$723$		−	13.0738i		−	0.486220i
$724$	22.6859			0.843116
$725$	−4.73672	+	38.3996i	−0.175917	+	1.42613i
$726$	−0.224254			−0.00832284
$727$			6.96239i			0.258221i	0.991630	+	0.129110i	$0.0412121\pi$
$727$			6.96239i			0.258221i	−0.991630	+	0.129110i	$0.958788\pi$
$728$			14.7005i			0.544838i
$729$	−1.00000			−0.0370370
$730$	−16.6253	+	14.7005i	−0.615330	+	0.544091i
$731$	−13.9248			−0.515026
$732$			11.0884i			0.409839i
$733$			9.68735i			0.357810i	0.983866	+	0.178905i	$0.0572555\pi$
$733$			9.68735i			0.357810i	−0.983866	+	0.178905i	$0.942744\pi$
$734$	22.8119			0.842004
$735$	2.63023	+	2.97461i	0.0970173	+	0.109720i
$736$	1.00000			0.0368605
$737$		−	25.5026i		−	0.939401i
$738$		−	4.70052i		−	0.173029i
$739$	42.9234			1.57896			0.789481	−	0.613775i	$-0.210350\pi$
$739$	42.9234			1.57896			0.789481	+	0.613775i	$0.210350\pi$
$740$	11.2750	+	12.7513i	0.414479	+	0.468747i
$741$	24.6253			0.904633
$742$		−	20.6253i		−	0.757179i
$743$		−	16.9986i		−	0.623618i	−0.950145	−	0.311809i	$-0.899065\pi$
$743$		−	16.9986i		−	0.623618i	0.950145	−	0.311809i	$-0.100935\pi$
$744$	−4.00000			−0.146647
$745$	7.78892	−	6.88717i	0.285364	−	0.252326i
$746$	−10.8364			−0.396748
$747$			6.38787i			0.233720i
$748$		−	4.52373i		−	0.165404i
$749$	26.9234			0.983758
$750$	−6.32487	−	9.21933i	−0.230952	−	0.336642i
$751$	−17.9003			−0.653193			−0.326596	−	0.945164i	$-0.605902\pi$
$751$	−17.9003			−0.653193			−0.326596	+	0.945164i	$0.605902\pi$
$752$		−	3.22425i		−	0.117576i
$753$		−	5.02302i		−	0.183049i
$754$	−38.3996			−1.39843
$755$	−17.9248	+	15.8496i	−0.652349	+	0.576824i
$756$	2.96239			0.107741
$757$		−	12.3879i		−	0.450245i	−0.974330	−	0.225122i	$-0.927722\pi$
$757$		−	12.3879i		−	0.450245i	0.974330	−	0.225122i	$-0.0722782\pi$
$758$			32.4387i			1.17823i
$759$	−3.35026			−0.121607
$760$	7.35026	+	8.31265i	0.266622	+	0.301532i
$761$	38.5764			1.39839			0.699197	−	0.714929i	$-0.253541\pi$
$761$	38.5764			1.39839			0.699197	+	0.714929i	$0.253541\pi$
$762$			0.186642i			0.00676134i
$763$			56.1016i			2.03101i
$764$	19.3258			0.699184
$765$	−2.00000	−	2.26187i	−0.0723102	−	0.0817779i
$766$	32.9986			1.19229
$767$			6.07522i			0.219364i
$768$			1.00000i			0.0360844i
$769$	−34.2228			−1.23411			−0.617054	−	0.786921i	$-0.711674\pi$
$769$	−34.2228			−1.23411			−0.617054	+	0.786921i	$0.711674\pi$
$770$	16.6253	−	14.7005i	0.599134	−	0.529770i
$771$	19.4010			0.698712
$772$			5.92478i			0.213237i
$773$		−	13.5613i		−	0.487768i	−0.969804	−	0.243884i	$-0.921578\pi$
$773$		−	13.5613i		−	0.487768i	0.969804	−	0.243884i	$-0.0784215\pi$
$774$	−10.3127			−0.370681
$775$	−2.44851	+	19.8496i	−0.0879530	+	0.713017i
$776$	−12.8872			−0.462622
$777$			22.5501i			0.808980i
$778$		−	29.1246i		−	1.04417i
$779$	23.3258			0.835734
$780$	8.31265	−	7.35026i	0.297641	−	0.263182i
$781$	7.32582			0.262139
$782$		−	1.35026i		−	0.0482853i
$783$			7.73813i			0.276538i
$784$	−1.77575			−0.0634195
$785$	−25.1998	−	28.4993i	−0.899420	−	1.01718i
$786$	−7.92478			−0.282667
$787$		−	37.0132i		−	1.31938i	−0.751539	−	0.659689i	$-0.770688\pi$
$787$		−	37.0132i		−	1.31938i	0.751539	−	0.659689i	$-0.229312\pi$
$788$			8.07522i			0.287668i
$789$	−15.4763			−0.550970
$790$	−6.11142	−	6.91160i	−0.217435	−	0.245904i
$791$	−19.6991			−0.700420
$792$		−	3.35026i		−	0.119046i
$793$			55.0249i			1.95399i
$794$	13.7381			0.487548
$795$	−11.6629	+	10.3127i	−0.413641	+	0.365752i
$796$	15.9756			0.566239
$797$		−	47.6893i		−	1.68924i	−0.535366	−	0.844620i	$-0.679826\pi$
$797$		−	47.6893i		−	1.68924i	0.535366	−	0.844620i	$-0.320174\pi$
$798$			14.7005i			0.520393i
$799$	−4.35359			−0.154019
$800$	4.96239	+	0.612127i	0.175447	+	0.0216420i
$801$	9.92478			0.350675
$802$		−	1.44992i		−	0.0511985i
$803$			33.2506i			1.17339i
$804$	7.61213			0.268459
$805$	4.96239	−	4.38787i	0.174901	−	0.154652i
$806$	−19.8496			−0.699171
$807$			20.2130i			0.711531i
$808$		−	4.26187i		−	0.149932i
$809$	9.17538			0.322589			0.161295	−	0.986906i	$-0.448433\pi$
$809$	9.17538			0.322589			0.161295	+	0.986906i	$0.448433\pi$
$810$	−1.48119	−	1.67513i	−0.0520439	−	0.0588581i
$811$	−38.5501			−1.35368			−0.676838	−	0.736132i	$-0.736650\pi$
$811$	−38.5501			−1.35368			−0.676838	+	0.736132i	$0.736650\pi$
$812$		−	22.9234i		−	0.804452i
$813$			30.3996i			1.06616i
$814$	25.5026			0.893866
$815$	−18.7005	−	21.1490i	−0.655051	−	0.740818i
$816$	1.35026			0.0472686
$817$		−	51.1754i		−	1.79040i
$818$			17.8496i			0.624095i
$819$	14.7005			0.513678
$820$	7.87399	−	6.96239i	0.274972	−	0.243137i
$821$	43.4372			1.51597			0.757985	−	0.652272i	$-0.226184\pi$
$821$	43.4372			1.51597			0.757985	+	0.652272i	$0.226184\pi$
$822$			9.19982i			0.320880i
$823$		−	3.51247i		−	0.122437i	−0.998124	−	0.0612184i	$-0.980501\pi$
$823$		−	3.51247i		−	0.122437i	0.998124	−	0.0612184i	$-0.0194986\pi$
$824$	−0.261865			−0.00912250
$825$	−16.6253	−	2.05079i	−0.578819	−	0.0713992i
$826$	−3.62672			−0.126190
$827$			9.56325i			0.332547i	0.986080	+	0.166273i	$0.0531734\pi$
$827$			9.56325i			0.332547i	−0.986080	+	0.166273i	$0.946827\pi$
$828$		−	1.00000i		−	0.0347524i
$829$	−30.5764			−1.06196			−0.530982	−	0.847383i	$-0.678177\pi$
$829$	−30.5764			−1.06196			−0.530982	+	0.847383i	$0.678177\pi$
$830$	−10.7005	+	9.46168i	−0.371421	+	0.328420i
$831$	20.8119			0.721958
$832$			4.96239i			0.172040i
$833$			2.39772i			0.0830762i
$834$	8.62530			0.298670
$835$	−36.4749	−	41.2506i	−1.26226	−	1.42754i
$836$	16.6253			0.574998
$837$			4.00000i			0.138260i
$838$		−	17.9003i		−	0.618357i
$839$	−22.1768			−0.765628			−0.382814	−	0.923825i	$-0.625045\pi$
$839$	−22.1768			−0.765628			−0.382814	+	0.923825i	$0.625045\pi$
$840$	4.38787	+	4.96239i	0.151396	+	0.171219i
$841$	30.8787			1.06478
$842$			7.61213i			0.262331i
$843$			19.8496i			0.683655i
$844$	−21.7743			−0.749503
$845$	19.4739	−	17.2193i	0.669923	−	0.592363i
$846$	−3.22425			−0.110852
$847$		−	0.664327i		−	0.0228265i
$848$		−	6.96239i		−	0.239089i
$849$	−12.3879			−0.425151
$850$	0.826531	−	6.70052i	0.0283498	−	0.229826i
$851$	7.61213			0.260940
$852$			2.18664i			0.0749131i
$853$			29.7381i			1.01821i	0.860703	+	0.509107i	$0.170024\pi$
$853$			29.7381i			1.01821i	−0.860703	+	0.509107i	$0.829976\pi$
$854$	−32.8481			−1.12404
$855$	8.31265	−	7.35026i	0.284287	−	0.251374i
$856$	9.08840			0.310635
$857$			22.2520i			0.760114i	0.924963	+	0.380057i	$0.124096\pi$
$857$			22.2520i			0.760114i	−0.924963	+	0.380057i	$0.875904\pi$
$858$		−	16.6253i		−	0.567578i
$859$	−11.0738			−0.377833			−0.188917	−	0.981993i	$-0.560498\pi$
$859$	−11.0738			−0.377833			−0.188917	+	0.981993i	$0.560498\pi$
$860$	−15.2750	−	17.2750i	−0.520875	−	0.589074i
$861$	13.9248			0.474555
$862$		−	22.9525i		−	0.781767i
$863$			22.8218i			0.776863i	0.921478	+	0.388431i	$0.126983\pi$
$863$			22.8218i			0.776863i	−0.921478	+	0.388431i	$0.873017\pi$
$864$	1.00000			0.0340207
$865$	6.58910	+	7.45183i	0.224036	+	0.253370i
$866$	−33.7645			−1.14736
$867$			15.1768i			0.515431i
$868$		−	11.8496i		−	0.402200i
$869$	−13.8232			−0.468920
$870$	−12.9624	+	11.4617i	−0.439466	+	0.388587i
$871$	37.7743			1.27993
$872$			18.9380i			0.641320i
$873$			12.8872i			0.436164i
$874$	4.96239			0.167855
$875$	27.3112	−	18.7367i	0.923288	−	0.633417i
$876$	−9.92478			−0.335327
$877$		−	8.81194i		−	0.297558i	−0.988870	−	0.148779i	$-0.952466\pi$
$877$		−	8.81194i		−	0.297558i	0.988870	−	0.148779i	$-0.0475343\pi$
$878$			23.4763i			0.792286i
$879$	−9.03761			−0.304831
$880$	5.61213	−	4.96239i	0.189185	−	0.167282i
$881$	21.4010			0.721020			0.360510	−	0.932755i	$-0.382603\pi$
$881$	21.4010			0.721020			0.360510	+	0.932755i	$0.382603\pi$
$882$			1.77575i			0.0597925i
$883$		−	6.17679i		−	0.207866i	−0.994584	−	0.103933i	$-0.966857\pi$
$883$		−	6.17679i		−	0.207866i	0.994584	−	0.103933i	$-0.0331427\pi$
$884$	6.70052			0.225363
$885$	1.81336	+	2.05079i	0.0609554	+	0.0689364i
$886$	30.5501			1.02635
$887$		−	35.5975i		−	1.19525i	−0.801776	−	0.597624i	$-0.796111\pi$
$887$		−	35.5975i		−	1.19525i	0.801776	−	0.597624i	$-0.203889\pi$
$888$			7.61213i			0.255446i
$889$	−0.552907			−0.0185439
$890$	14.7005	+	16.6253i	0.492763	+	0.557281i
$891$	−3.35026			−0.112238
$892$			3.81336i			0.127681i
$893$		−	16.0000i		−	0.535420i
$894$	4.64974			0.155511
$895$	−23.1998	+	20.5139i	−0.775484	+	0.685703i
$896$	−2.96239			−0.0989665
$897$		−	4.96239i		−	0.165689i
$898$		−	32.7005i		−	1.09123i
$899$	30.9525			1.03232
$900$	0.612127	−	4.96239i	0.0204042	−	0.165413i
$901$	−9.40105			−0.313194
$902$		−	15.7480i		−	0.524351i
$903$		−	30.5501i		−	1.01664i
$904$	−6.64974			−0.221167
$905$	38.0019	−	33.6023i	1.26323	−	1.11698i
$906$	−10.7005			−0.355501
$907$			5.53690i			0.183850i	0.995766	+	0.0919249i	$0.0293020\pi$
$907$			5.53690i			0.183850i	−0.995766	+	0.0919249i	$0.970698\pi$
$908$		−	16.9380i		−	0.562106i
$909$	−4.26187			−0.141357
$910$	21.7743	+	24.6253i	0.721812	+	0.816321i
$911$	−15.4763			−0.512752			−0.256376	−	0.966577i	$-0.582528\pi$
$911$	−15.4763			−0.512752			−0.256376	+	0.966577i	$0.582528\pi$
$912$			4.96239i			0.164321i
$913$			21.4010i			0.708271i
$914$	5.81336			0.192289
$915$	16.4241	+	18.5745i	0.542963	+	0.614055i
$916$	−26.9380			−0.890055
$917$		−	23.4763i		−	0.775255i
$918$		−	1.35026i		−	0.0445653i
$919$	5.17347			0.170657			0.0853285	−	0.996353i	$-0.472806\pi$
$919$	5.17347			0.170657			0.0853285	+	0.996353i	$0.472806\pi$
$920$	1.67513	−	1.48119i	0.0552274	−	0.0488335i
$921$	−30.5501			−1.00666
$922$		−	23.9902i		−	0.790074i
$923$			10.8510i			0.357164i
$924$	9.92478			0.326501
$925$	37.7743	+	4.65959i	1.24201	+	0.153206i
$926$	35.3620			1.16207
$927$			0.261865i			0.00860078i
$928$		−	7.73813i		−	0.254017i
$929$	44.3996			1.45670			0.728352	−	0.685203i	$-0.240286\pi$
$929$	44.3996			1.45670			0.728352	+	0.685203i	$0.240286\pi$
$930$	−6.70052	+	5.92478i	−0.219719	+	0.194281i
$931$	−8.81194			−0.288800
$932$			27.4010i			0.897551i
$933$			14.4387i			0.472700i
$934$	−1.98541			−0.0649647
$935$	−6.70052	−	7.57784i	−0.219131	−	0.247822i
$936$	4.96239			0.162201
$937$			3.99015i			0.130353i	0.997874	+	0.0651763i	$0.0207610\pi$
$937$			3.99015i			0.130353i	−0.997874	+	0.0651763i	$0.979239\pi$
$938$			22.5501i			0.736286i
$939$	−27.9610			−0.912472
$940$	−4.77575	−	5.40105i	−0.155768	−	0.176163i
$941$	−2.30280			−0.0750692			−0.0375346	−	0.999295i	$-0.511950\pi$
$941$	−2.30280			−0.0750692			−0.0375346	+	0.999295i	$0.511950\pi$
$942$		−	17.0132i		−	0.554319i
$943$		−	4.70052i		−	0.153070i
$944$	−1.22425			−0.0398461
$945$	4.96239	−	4.38787i	0.161427	−	0.142738i
$946$	−34.5501			−1.12332
$947$		−	24.7269i		−	0.803515i	−0.915746	−	0.401758i	$-0.868399\pi$
$947$		−	24.7269i		−	0.803515i	0.915746	−	0.401758i	$-0.131601\pi$
$948$		−	4.12601i		−	0.134007i
$949$	−49.2506			−1.59874
$950$	24.6253	+	3.03761i	0.798950	+	0.0985531i
$951$	1.47627			0.0478713
$952$			4.00000i			0.129641i
$953$		−	11.6775i		−	0.378271i	−0.981951	−	0.189136i	$-0.939431\pi$
$953$		−	11.6775i		−	0.378271i	0.981951	−	0.189136i	$-0.0605686\pi$
$954$	−6.96239			−0.225416
$955$	32.3733	−	28.6253i	1.04757	−	0.926293i
$956$	7.48612			0.242118
$957$			25.9248i			0.838029i
$958$		−	11.0738i		−	0.357779i
$959$	−27.2534			−0.880059
$960$	1.48119	+	1.67513i	0.0478053	+	0.0540646i
$961$	−15.0000			−0.483871
$962$			37.7743i			1.21789i
$963$		−	9.08840i		−	0.292869i
$964$	13.0738			0.421079
$965$	8.77575	+	9.92478i	0.282501	+	0.319490i
$966$	2.96239			0.0953133
$967$		−	51.2116i		−	1.64685i	−0.567423	−	0.823427i	$-0.692059\pi$
$967$		−	51.2116i		−	1.64685i	0.567423	−	0.823427i	$-0.307941\pi$
$968$		−	0.224254i		−	0.00720779i
$969$	6.70052			0.215252
$970$	−21.5877	+	19.0884i	−0.693139	+	0.612891i
$971$	14.8265			0.475806			0.237903	−	0.971289i	$-0.423540\pi$
$971$	14.8265			0.475806			0.237903	+	0.971289i	$0.423540\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			25.5515i			0.819143i
$974$	17.4372			0.558725
$975$	3.03761	−	24.6253i	0.0972814	−	0.788641i
$976$	−11.0884			−0.354931
$977$			16.6958i			0.534145i	0.963676	+	0.267073i	$0.0860564\pi$
$977$			16.6958i			0.534145i	−0.963676	+	0.267073i	$0.913944\pi$
$978$		−	12.6253i		−	0.403713i
$979$	33.2506			1.06269
$980$	−2.97461	+	2.63023i	−0.0950203	+	0.0840195i
$981$	18.9380			0.604642
$982$			14.8773i			0.474754i
$983$		−	30.0263i		−	0.957692i	−0.877899	−	0.478846i	$-0.841055\pi$
$983$		−	30.0263i		−	0.957692i	0.877899	−	0.478846i	$-0.158945\pi$
$984$	4.70052			0.149847
$985$	11.9610	+	13.5271i	0.381108	+	0.431008i
$986$	−10.4485			−0.332748
$987$		−	9.55149i		−	0.304027i
$988$			24.6253i			0.783435i
$989$	−10.3127			−0.327923
$990$	−4.96239	−	5.61213i	−0.157715	−	0.178365i
$991$	−1.40105			−0.0445057			−0.0222529	−	0.999752i	$-0.507084\pi$
$991$	−1.40105			−0.0445057			−0.0222529	+	0.999752i	$0.507084\pi$
$992$		−	4.00000i		−	0.127000i
$993$			23.1754i			0.735448i
$994$	−6.47768			−0.205460
$995$	26.7612	−	23.6629i	0.848386	−	0.750165i
$996$	−6.38787			−0.202408
$997$		−	13.2144i		−	0.418504i	−0.977862	−	0.209252i	$-0.932897\pi$
$997$		−	13.2144i		−	0.418504i	0.977862	−	0.209252i	$-0.0671030\pi$
$998$			16.1016i			0.509686i
$999$	7.61213			0.240837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.d.c.139.4	yes	6
3.2	odd	2		2070.2.d.e.829.3		6
5.2	odd	4		3450.2.a.bo.1.3		3
5.3	odd	4		3450.2.a.bt.1.1		3
5.4	even	2	inner	690.2.d.c.139.1	✓	6
15.14	odd	2		2070.2.d.e.829.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.1	✓	6	5.4	even	2	inner
690.2.d.c.139.4	yes	6	1.1	even	1	trivial
2070.2.d.e.829.3		6	3.2	odd	2
2070.2.d.e.829.6		6	15.14	odd	2
3450.2.a.bo.1.3		3	5.2	odd	4
3450.2.a.bt.1.1		3	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} -3.35026 q^{11} -1.00000i q^{12} -4.96239i q^{13} +2.96239 q^{14} +(-1.48119 - 1.67513i) q^{15} +1.00000 q^{16} -1.35026i q^{17} -1.00000i q^{18} +4.96239 q^{19} +(1.67513 - 1.48119i) q^{20} +2.96239 q^{21} -3.35026i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(0.612127 - 4.96239i) q^{25} +4.96239 q^{26} -1.00000i q^{27} +2.96239i q^{28} -7.73813 q^{29} +(1.67513 - 1.48119i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -3.35026i q^{33} +1.35026 q^{34} +(4.38787 + 4.96239i) q^{35} +1.00000 q^{36} +7.61213i q^{37} +4.96239i q^{38} +4.96239 q^{39} +(1.48119 + 1.67513i) q^{40} +4.70052 q^{41} +2.96239i q^{42} -10.3127i q^{43} +3.35026 q^{44} +(1.67513 - 1.48119i) q^{45} +1.00000 q^{46} -3.22425i q^{47} +1.00000i q^{48} -1.77575 q^{49} +(4.96239 + 0.612127i) q^{50} +1.35026 q^{51} +4.96239i q^{52} -6.96239i q^{53} +1.00000 q^{54} +(5.61213 - 4.96239i) q^{55} -2.96239 q^{56} +4.96239i q^{57} -7.73813i q^{58} -1.22425 q^{59} +(1.48119 + 1.67513i) q^{60} -11.0884 q^{61} -4.00000i q^{62} +2.96239i q^{63} -1.00000 q^{64} +(7.35026 + 8.31265i) q^{65} +3.35026 q^{66} +7.61213i q^{67} +1.35026i q^{68} +1.00000 q^{69} +(-4.96239 + 4.38787i) q^{70} -2.18664 q^{71} +1.00000i q^{72} -9.92478i q^{73} -7.61213 q^{74} +(4.96239 + 0.612127i) q^{75} -4.96239 q^{76} +9.92478i q^{77} +4.96239i q^{78} +4.12601 q^{79} +(-1.67513 + 1.48119i) q^{80} +1.00000 q^{81} +4.70052i q^{82} -6.38787i q^{83} -2.96239 q^{84} +(2.00000 + 2.26187i) q^{85} +10.3127 q^{86} -7.73813i q^{87} +3.35026i q^{88} -9.92478 q^{89} +(1.48119 + 1.67513i) q^{90} -14.7005 q^{91} +1.00000i q^{92} -4.00000i q^{93} +3.22425 q^{94} +(-8.31265 + 7.35026i) q^{95} -1.00000 q^{96} -12.8872i q^{97} -1.77575i q^{98} +3.35026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 4 q^{14} + 2 q^{15} + 6 q^{16} + 8 q^{19} - 4 q^{21} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 28 q^{29} - 24 q^{31} - 12 q^{34} + 28 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{46} - 14 q^{49} + 8 q^{50} - 12 q^{51} + 6 q^{54} + 32 q^{55} + 4 q^{56} - 4 q^{59} - 2 q^{60} - 28 q^{61} - 6 q^{64} + 24 q^{65} + 6 q^{69} - 8 q^{70} + 12 q^{71} - 44 q^{74} + 8 q^{75} - 8 q^{76} + 8 q^{79} + 6 q^{81} + 4 q^{84} + 12 q^{85} + 20 q^{86} - 16 q^{89} - 2 q^{90} - 48 q^{91} + 16 q^{94} - 8 q^{95} - 6 q^{96}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 4 * q^14 + 2 * q^15 + 6 * q^16 + 8 * q^19 - 4 * q^21 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 28 * q^29 - 24 * q^31 - 12 * q^34 + 28 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^46 - 14 * q^49 + 8 * q^50 - 12 * q^51 + 6 * q^54 + 32 * q^55 + 4 * q^56 - 4 * q^59 - 2 * q^60 - 28 * q^61 - 6 * q^64 + 24 * q^65 + 6 * q^69 - 8 * q^70 + 12 * q^71 - 44 * q^74 + 8 * q^75 - 8 * q^76 + 8 * q^79 + 6 * q^81 + 4 * q^84 + 12 * q^85 + 20 * q^86 - 16 * q^89 - 2 * q^90 - 48 * q^91 + 16 * q^94 - 8 * q^95 - 6 * q^96

Introduction

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