LMFDB - Embedded newform 187.2.d.a.67.6

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			67.6
Root			$-1.19202i$ of defining polynomial
Character	$\chi$	$=$	187.67
Dual form			187.2.d.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19202 q^{2} +1.00943i q^{3} -0.579089 q^{4} -1.48581i q^{5} -1.20326i q^{6} -1.55528i q^{7} +3.07432 q^{8} +1.98105 q^{9} +O(q^{10})$	\(q-1.19202 q^{2} +1.00943i q^{3} -0.579089 q^{4} -1.48581i q^{5} -1.20326i q^{6} -1.55528i q^{7} +3.07432 q^{8} +1.98105 q^{9} +1.77111i q^{10} +1.00000i q^{11} -0.584550i q^{12} +5.20473 q^{13} +1.85393i q^{14} +1.49982 q^{15} -2.50648 q^{16} +(-0.323199 + 4.11042i) q^{17} -2.36145 q^{18} +1.53461 q^{19} +0.860414i q^{20} +1.56995 q^{21} -1.19202i q^{22} -7.99905i q^{23} +3.10332i q^{24} +2.79238 q^{25} -6.20414 q^{26} +5.02802i q^{27} +0.900647i q^{28} -4.55225i q^{29} -1.78781 q^{30} -7.72377i q^{31} -3.16088 q^{32} -1.00943 q^{33} +(0.385259 - 4.89970i) q^{34} -2.31085 q^{35} -1.14721 q^{36} +1.39347i q^{37} -1.82929 q^{38} +5.25381i q^{39} -4.56785i q^{40} +11.1724i q^{41} -1.87141 q^{42} +1.20057 q^{43} -0.579089i q^{44} -2.94346i q^{45} +9.53503i q^{46} -11.1483 q^{47} -2.53011i q^{48} +4.58110 q^{49} -3.32857 q^{50} +(-4.14918 - 0.326246i) q^{51} -3.01400 q^{52} -12.9537 q^{53} -5.99350i q^{54} +1.48581 q^{55} -4.78144i q^{56} +1.54908i q^{57} +5.42637i q^{58} +4.12341 q^{59} -0.868528 q^{60} +9.41605i q^{61} +9.20688i q^{62} -3.08109i q^{63} +8.78078 q^{64} -7.73321i q^{65} +1.20326 q^{66} +1.55409 q^{67} +(0.187161 - 2.38030i) q^{68} +8.07449 q^{69} +2.75457 q^{70} -2.92316i q^{71} +6.09039 q^{72} -4.29526i q^{73} -1.66104i q^{74} +2.81872i q^{75} -0.888676 q^{76} +1.55528 q^{77} -6.26264i q^{78} +12.6164i q^{79} +3.72414i q^{80} +0.867713 q^{81} -13.3178i q^{82} -2.31447 q^{83} -0.909140 q^{84} +(6.10728 + 0.480210i) q^{85} -1.43110 q^{86} +4.59518 q^{87} +3.07432i q^{88} -3.22974 q^{89} +3.50866i q^{90} -8.09481i q^{91} +4.63217i q^{92} +7.79661 q^{93} +13.2890 q^{94} -2.28013i q^{95} -3.19069i q^{96} -12.7015i q^{97} -5.46076 q^{98} +1.98105i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.19202			−0.842885			−0.421443	−	0.906855i	$-0.638476\pi$
$2$	−1.19202			−0.842885			−0.421443	+	0.906855i	$0.638476\pi$
$3$			1.00943i			0.582795i	0.956602	+	0.291397i	$0.0941202\pi$
$3$			1.00943i			0.582795i	−0.956602	+	0.291397i	$0.905880\pi$
$4$	−0.579089			−0.289545
$5$		−	1.48581i		−	0.664472i	−0.943196	−	0.332236i	$-0.892197\pi$
$5$		−	1.48581i		−	0.664472i	0.943196	−	0.332236i	$-0.107803\pi$
$6$		−	1.20326i		−	0.491229i
$7$		−	1.55528i		−	0.587841i	−0.955830	−	0.293921i	$-0.905040\pi$
$7$		−	1.55528i		−	0.587841i	0.955830	−	0.293921i	$-0.0949601\pi$
$8$	3.07432			1.08694
$9$	1.98105			0.660350
$10$			1.77111i			0.560074i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$		−	0.584550i		−	0.168745i
$13$	5.20473			1.44353			0.721766	−	0.692137i	$-0.243331\pi$
$13$	5.20473			1.44353			0.721766	+	0.692137i	$0.243331\pi$
$14$			1.85393i			0.495482i
$15$	1.49982			0.387251
$16$	−2.50648			−0.626619
$17$	−0.323199	+	4.11042i	−0.0783872	+	0.996923i
$17$	−0.323199	+	4.11042i	−0.0783872	+	0.996923i
$18$	−2.36145			−0.556599
$19$	1.53461			0.352064			0.176032	−	0.984384i	$-0.443674\pi$
$19$	1.53461			0.352064			0.176032	+	0.984384i	$0.443674\pi$
$20$			0.860414i			0.192394i
$21$	1.56995			0.342591
$22$		−	1.19202i		−	0.254139i
$23$		−	7.99905i		−	1.66792i	−0.551827	−	0.833959i	$-0.686069\pi$
$23$		−	7.99905i		−	1.66792i	0.551827	−	0.833959i	$-0.313931\pi$
$24$			3.10332i			0.633462i
$25$	2.79238			0.558477
$26$	−6.20414			−1.21673
$27$			5.02802i			0.967644i
$28$			0.900647i			0.170206i
$29$		−	4.55225i		−	0.845332i	−0.906286	−	0.422666i	$-0.861094\pi$
$29$		−	4.55225i		−	0.845332i	0.906286	−	0.422666i	$-0.138906\pi$
$30$	−1.78781			−0.326408
$31$		−	7.72377i		−	1.38723i	−0.720346	−	0.693615i	$-0.756017\pi$
$31$		−	7.72377i		−	1.38723i	0.720346	−	0.693615i	$-0.243983\pi$
$32$	−3.16088			−0.558770
$33$	−1.00943			−0.175719
$34$	0.385259	−	4.89970i	0.0660714	−	0.840292i
$35$	−2.31085			−0.390604
$36$	−1.14721			−0.191201
$37$			1.39347i			0.229085i	0.993418	+	0.114542i	$0.0365402\pi$
$37$			1.39347i			0.229085i	−0.993418	+	0.114542i	$0.963460\pi$
$38$	−1.82929			−0.296749
$39$			5.25381i			0.841283i
$40$		−	4.56785i		−	0.722240i
$41$			11.1724i			1.74484i	0.488757	+	0.872420i	$0.337450\pi$
$41$			11.1724i			1.74484i	−0.488757	+	0.872420i	$0.662550\pi$
$42$	−1.87141			−0.288765
$43$	1.20057			0.183085			0.0915426	−	0.995801i	$-0.470820\pi$
$43$	1.20057			0.183085			0.0915426	+	0.995801i	$0.470820\pi$
$44$		−	0.579089i		−	0.0873010i
$45$		−	2.94346i		−	0.438784i
$46$			9.53503i			1.40586i
$47$	−11.1483			−1.62615			−0.813074	−	0.582160i	$-0.802208\pi$
$47$	−11.1483			−1.62615			−0.813074	+	0.582160i	$0.802208\pi$
$48$		−	2.53011i		−	0.365190i
$49$	4.58110			0.654443
$50$	−3.32857			−0.470732
$51$	−4.14918	−	0.326246i	−0.581002	−	0.0456836i
$52$	−3.01400			−0.417967
$53$	−12.9537			−1.77933			−0.889666	−	0.456611i	$-0.849063\pi$
$53$	−12.9537			−1.77933			−0.889666	+	0.456611i	$0.849063\pi$
$54$		−	5.99350i		−	0.815612i
$55$	1.48581			0.200346
$56$		−	4.78144i		−	0.638947i
$57$			1.54908i			0.205181i
$58$			5.42637i			0.712517i
$59$	4.12341			0.536822			0.268411	−	0.963305i	$-0.413502\pi$
$59$	4.12341			0.536822			0.268411	+	0.963305i	$0.413502\pi$
$60$	−0.868528			−0.112126
$61$			9.41605i			1.20560i	0.797892	+	0.602801i	$0.205949\pi$
$61$			9.41605i			1.20560i	−0.797892	+	0.602801i	$0.794051\pi$
$62$			9.20688i			1.16928i
$63$		−	3.08109i		−	0.388181i
$64$	8.78078			1.09760
$65$		−	7.73321i		−	0.959187i
$66$	1.20326			0.148111
$67$	1.55409			0.189863			0.0949313	−	0.995484i	$-0.469737\pi$
$67$	1.55409			0.189863			0.0949313	+	0.995484i	$0.469737\pi$
$68$	0.187161	−	2.38030i	0.0226966	−	0.288654i
$69$	8.07449			0.972054
$70$	2.75457			0.329234
$71$		−	2.92316i		−	0.346915i	−0.984841	−	0.173457i	$-0.944506\pi$
$71$		−	2.92316i		−	0.346915i	0.984841	−	0.173457i	$-0.0554939\pi$
$72$	6.09039			0.717760
$73$		−	4.29526i		−	0.502722i	−0.967893	−	0.251361i	$-0.919122\pi$
$73$		−	4.29526i		−	0.502722i	0.967893	−	0.251361i	$-0.0808782\pi$
$74$		−	1.66104i		−	0.193092i
$75$			2.81872i			0.325477i
$76$	−0.888676			−0.101938
$77$	1.55528			0.177241
$78$		−	6.26264i		−	0.709105i
$79$			12.6164i			1.41945i	0.704477	+	0.709726i	$0.251181\pi$
$79$			12.6164i			1.41945i	−0.704477	+	0.709726i	$0.748819\pi$
$80$			3.72414i			0.416371i
$81$	0.867713			0.0964125
$82$		−	13.3178i		−	1.47070i
$83$	−2.31447			−0.254046			−0.127023	−	0.991900i	$-0.540542\pi$
$83$	−2.31447			−0.254046			−0.127023	+	0.991900i	$0.540542\pi$
$84$	−0.909140			−0.0991953
$85$	6.10728	+	0.480210i	0.662428	+	0.0520861i
$86$	−1.43110			−0.154320
$87$	4.59518			0.492655
$88$			3.07432i			0.327724i
$89$	−3.22974			−0.342352			−0.171176	−	0.985240i	$-0.554757\pi$
$89$	−3.22974			−0.342352			−0.171176	+	0.985240i	$0.554757\pi$
$90$			3.50866i			0.369845i
$91$		−	8.09481i		−	0.848567i
$92$			4.63217i			0.482937i
$93$	7.79661			0.808471
$94$	13.2890			1.37066
$95$		−	2.28013i		−	0.233937i
$96$		−	3.19069i		−	0.325648i
$97$		−	12.7015i		−	1.28964i	−0.764334	−	0.644821i	$-0.776932\pi$
$97$		−	12.7015i		−	1.28964i	0.764334	−	0.644821i	$-0.223068\pi$
$98$	−5.46076			−0.551620
$99$			1.98105i			0.199103i
$100$	−1.61704			−0.161704
$101$	5.79591			0.576714			0.288357	−	0.957523i	$-0.406891\pi$
$101$	5.79591			0.576714			0.288357	+	0.957523i	$0.406891\pi$
$102$	4.94591	+	0.388892i	0.489718	+	0.0385061i
$103$	−2.74178			−0.270155			−0.135078	−	0.990835i	$-0.543128\pi$
$103$	−2.74178			−0.270155			−0.135078	+	0.990835i	$0.543128\pi$
$104$	16.0010			1.56903
$105$		−	2.33264i		−	0.227642i
$106$	15.4411			1.49977
$107$			2.37019i			0.229135i	0.993415	+	0.114567i	$0.0365482\pi$
$107$			2.37019i			0.229135i	−0.993415	+	0.114567i	$0.963452\pi$
$108$		−	2.91167i		−	0.280176i
$109$			2.72065i			0.260591i	0.991475	+	0.130296i	$0.0415926\pi$
$109$			2.72065i			0.260591i	−0.991475	+	0.130296i	$0.958407\pi$
$110$	−1.77111			−0.168869
$111$	−1.40661			−0.133510
$112$			3.89828i			0.368352i
$113$			17.2409i			1.62188i	0.585127	+	0.810942i	$0.301045\pi$
$113$			17.2409i			1.62188i	−0.585127	+	0.810942i	$0.698955\pi$
$114$		−	1.84654i		−	0.172944i
$115$	−11.8850			−1.10829
$116$			2.63616i			0.244761i
$117$	10.3108			0.953236
$118$	−4.91518			−0.452479
$119$	6.39286	+	0.502665i	0.586032	+	0.0460792i
$120$	4.61092			0.420918
$121$	−1.00000			−0.0909091
$122$		−	11.2241i		−	1.01618i
$123$	−11.2778			−1.01688
$124$			4.47275i			0.401665i
$125$		−	11.5780i		−	1.03556i
$126$			3.67272i			0.327192i
$127$	−21.1729			−1.87879			−0.939394	−	0.342840i	$-0.888611\pi$
$127$	−21.1729			−1.87879			−0.939394	+	0.342840i	$0.888611\pi$
$128$	−4.14511			−0.366379
$129$			1.21189i			0.106701i
$130$			9.21814i			0.808484i
$131$		−	1.54993i		−	0.135418i	−0.997705	−	0.0677091i	$-0.978431\pi$
$131$		−	1.54993i		−	0.135418i	0.997705	−	0.0677091i	$-0.0215690\pi$
$132$	0.584550			0.0508786
$133$		−	2.38675i		−	0.206957i
$134$	−1.85251			−0.160032
$135$	7.47066			0.642972
$136$	−0.993618	+	12.6368i	−0.0852020	+	1.08359i
$137$	−15.3777			−1.31381			−0.656903	−	0.753975i	$-0.728134\pi$
$137$	−15.3777			−1.31381			−0.656903	+	0.753975i	$0.728134\pi$
$138$	−9.62494			−0.819330
$139$		−	6.40429i		−	0.543204i	−0.962410	−	0.271602i	$-0.912447\pi$
$139$		−	6.40429i		−	0.543204i	0.962410	−	0.271602i	$-0.0875535\pi$
$140$	1.33819			0.113097
$141$		−	11.2534i		−	0.947711i
$142$			3.48446i			0.292409i
$143$			5.20473i			0.435241i
$144$	−4.96546			−0.413788
$145$	−6.76376			−0.561700
$146$			5.12004i			0.423737i
$147$			4.62430i			0.381406i
$148$		−	0.806943i		−	0.0663303i
$149$	19.5406			1.60083			0.800414	−	0.599447i	$-0.204613\pi$
$149$	19.5406			1.60083			0.800414	+	0.599447i	$0.204613\pi$
$150$		−	3.35996i		−	0.274340i
$151$	−14.1014			−1.14756			−0.573779	−	0.819010i	$-0.694523\pi$
$151$	−14.1014			−1.14756			−0.573779	+	0.819010i	$0.694523\pi$
$152$	4.71789			0.382671
$153$	−0.640273	+	8.14295i	−0.0517630	+	0.658318i
$154$	−1.85393			−0.149394
$155$	−11.4760			−0.921776
$156$		−	3.04242i		−	0.243589i
$157$	−8.32334			−0.664275			−0.332138	−	0.943231i	$-0.607770\pi$
$157$	−8.32334			−0.664275			−0.332138	+	0.943231i	$0.607770\pi$
$158$		−	15.0390i		−	1.19644i
$159$		−	13.0759i		−	1.03699i
$160$			4.69645i			0.371287i
$161$	−12.4408			−0.980471
$162$	−1.03433			−0.0812647
$163$			12.9657i			1.01555i	0.861490	+	0.507774i	$0.169532\pi$
$163$			12.9657i			1.01555i	−0.861490	+	0.507774i	$0.830468\pi$
$164$		−	6.46983i		−	0.505209i
$165$			1.49982i			0.116761i
$166$	2.75889			0.214131
$167$			7.23940i			0.560202i	0.959971	+	0.280101i	$0.0903679\pi$
$167$			7.23940i			0.560202i	−0.959971	+	0.280101i	$0.909632\pi$
$168$	4.82653			0.372375
$169$	14.0892			1.08378
$170$	−7.28000	−	0.572420i	−0.558350	−	0.0439026i
$171$	3.04014			0.232485
$172$	−0.695237			−0.0530114
$173$			10.5099i			0.799053i	0.916722	+	0.399526i	$0.130825\pi$
$173$			10.5099i			0.799053i	−0.916722	+	0.399526i	$0.869175\pi$
$174$	−5.47754			−0.415252
$175$		−	4.34294i		−	0.328295i
$176$		−	2.50648i		−	0.188933i
$177$			4.16229i			0.312857i
$178$	3.84992			0.288564
$179$	−3.26506			−0.244042			−0.122021	−	0.992528i	$-0.538938\pi$
$179$	−3.26506			−0.244042			−0.122021	+	0.992528i	$0.538938\pi$
$180$			1.70452i			0.127048i
$181$		−	9.14852i		−	0.680004i	−0.940425	−	0.340002i	$-0.889572\pi$
$181$		−	9.14852i		−	0.680004i	0.940425	−	0.340002i	$-0.110428\pi$
$182$			9.64918i			0.715245i
$183$	−9.50485			−0.702619
$184$		−	24.5917i		−	1.81292i
$185$	2.07042			0.152221
$186$	−9.29371			−0.681448
$187$	−4.11042	−	0.323199i	−0.300584	−	0.0236346i
$188$	6.45587			0.470843
$189$	7.81999			0.568821
$190$			2.71796i			0.197182i
$191$	−8.51453			−0.616090			−0.308045	−	0.951372i	$-0.599675\pi$
$191$	−8.51453			−0.616090			−0.308045	+	0.951372i	$0.599675\pi$
$192$			8.86359i			0.639675i
$193$		−	14.0800i		−	1.01350i	−0.862092	−	0.506752i	$-0.830846\pi$
$193$		−	14.0800i		−	1.01350i	0.862092	−	0.506752i	$-0.169154\pi$
$194$			15.1404i			1.08702i
$195$	7.80614			0.559009
$196$	−2.65287			−0.189490
$197$		−	22.7981i		−	1.62430i	−0.583452	−	0.812148i	$-0.698298\pi$
$197$		−	22.7981i		−	1.62430i	0.583452	−	0.812148i	$-0.301702\pi$
$198$		−	2.36145i		−	0.167821i
$199$			14.6341i			1.03738i	0.854962	+	0.518691i	$0.173581\pi$
$199$			14.6341i			1.03738i	−0.854962	+	0.518691i	$0.826419\pi$
$200$	8.58469			0.607029
$201$			1.56875i			0.110651i
$202$	−6.90883			−0.486104
$203$	−7.08003			−0.496921
$204$	2.40275	+	0.188926i	0.168226	+	0.0132275i
$205$	16.6001			1.15940
$206$	3.26825			0.227710
$207$		−	15.8465i		−	1.10141i
$208$	−13.0455			−0.904544
$209$			1.53461i			0.106151i
$210$			2.78055i			0.191876i
$211$			9.06204i			0.623857i	0.950106	+	0.311928i	$0.100975\pi$
$211$			9.06204i			0.623857i	−0.950106	+	0.311928i	$0.899025\pi$
$212$	7.50137			0.515196
$213$	2.95072			0.202180
$214$		−	2.82531i		−	0.193134i
$215$		−	1.78381i		−	0.121655i
$216$			15.4578i			1.05177i
$217$	−12.0126			−0.815471
$218$		−	3.24307i		−	0.219648i
$219$	4.33577			0.292984
$220$	−0.860414			−0.0580091
$221$	−1.68216	+	21.3936i	−0.113154	+	1.43909i
$222$	1.67671			0.112533
$223$	14.6207			0.979073			0.489537	−	0.871983i	$-0.337166\pi$
$223$	14.6207			0.979073			0.489537	+	0.871983i	$0.337166\pi$
$224$			4.91606i			0.328468i
$225$	5.53185			0.368790
$226$		−	20.5514i		−	1.36706i
$227$			9.72377i			0.645389i	0.946503	+	0.322695i	$0.104589\pi$
$227$			9.72377i			0.645389i	−0.946503	+	0.322695i	$0.895411\pi$
$228$		−	0.897057i		−	0.0594090i
$229$	−4.99339			−0.329973			−0.164986	−	0.986296i	$-0.552758\pi$
$229$	−4.99339			−0.329973			−0.164986	+	0.986296i	$0.552758\pi$
$230$	14.1672			0.934157
$231$			1.56995i			0.103295i
$232$		−	13.9951i		−	0.918823i
$233$		−	7.94542i		−	0.520522i	−0.965538	−	0.260261i	$-0.916191\pi$
$233$		−	7.94542i		−	0.520522i	0.965538	−	0.260261i	$-0.0838085\pi$
$234$	−12.2907			−0.803469
$235$			16.5642i			1.08053i
$236$	−2.38782			−0.155434
$237$	−12.7353			−0.827250
$238$	−7.62041	−	0.599186i	−0.493958	−	0.0388395i
$239$	5.35599			0.346450			0.173225	−	0.984882i	$-0.444581\pi$
$239$	5.35599			0.346450			0.173225	+	0.984882i	$0.444581\pi$
$240$	−3.75926			−0.242659
$241$		−	16.4981i		−	1.06274i	−0.847140	−	0.531370i	$-0.821678\pi$
$241$		−	16.4981i		−	1.06274i	0.847140	−	0.531370i	$-0.178322\pi$
$242$	1.19202			0.0766259
$243$			15.9600i			1.02383i
$244$		−	5.45274i		−	0.349076i
$245$		−	6.80662i		−	0.434859i
$246$	13.4433			0.857116
$247$	7.98722			0.508215
$248$		−	23.7454i		−	1.50783i
$249$		−	2.33629i		−	0.148057i
$250$			13.8012i			0.872862i
$251$	21.5448			1.35990			0.679948	−	0.733260i	$-0.262002\pi$
$251$	21.5448			1.35990			0.679948	+	0.733260i	$0.262002\pi$
$252$			1.78423i			0.112396i
$253$	7.99905			0.502896
$254$	25.2385			1.58360
$255$	−0.484739	+	6.16488i	−0.0303555	+	0.386059i
$256$	−12.6205			−0.788783
$257$	−8.58874			−0.535751			−0.267875	−	0.963454i	$-0.586322\pi$
$257$	−8.58874			−0.535751			−0.267875	+	0.963454i	$0.586322\pi$
$258$		−	1.44460i		−	0.0899368i
$259$	2.16724			0.134666
$260$			4.47822i			0.277727i
$261$		−	9.01824i		−	0.558215i
$262$			1.84755i			0.114142i
$263$	−4.24354			−0.261668			−0.130834	−	0.991404i	$-0.541765\pi$
$263$	−4.24354			−0.261668			−0.130834	+	0.991404i	$0.541765\pi$
$264$	−3.10332			−0.190996
$265$			19.2467i			1.18232i
$266$			2.84505i			0.174441i
$267$		−	3.26020i		−	0.199521i
$268$	−0.899959			−0.0549737
$269$			17.1444i			1.04531i	0.852544	+	0.522655i	$0.175059\pi$
$269$			17.1444i			1.04531i	−0.852544	+	0.522655i	$0.824941\pi$
$270$	−8.90518			−0.541952
$271$	−14.5170			−0.881847			−0.440923	−	0.897545i	$-0.645349\pi$
$271$	−14.5170			−0.881847			−0.440923	+	0.897545i	$0.645349\pi$
$272$	0.810090	−	10.3027i	0.0491189	−	0.624691i
$273$	8.17115			0.494540
$274$	18.3305			1.10739
$275$			2.79238i			0.168387i
$276$	−4.67585			−0.281453
$277$			4.42600i			0.265933i	0.991121	+	0.132966i	$0.0424502\pi$
$277$			4.42600i			0.265933i	−0.991121	+	0.132966i	$0.957550\pi$
$278$			7.63403i			0.457859i
$279$		−	15.3012i		−	0.916058i
$280$	−7.10429			−0.424562
$281$	−7.87555			−0.469816			−0.234908	−	0.972018i	$-0.575479\pi$
$281$	−7.87555			−0.469816			−0.234908	+	0.972018i	$0.575479\pi$
$282$			13.4143i			0.798812i
$283$			15.0477i			0.894494i	0.894411	+	0.447247i	$0.147595\pi$
$283$			15.0477i			0.894494i	−0.894411	+	0.447247i	$0.852405\pi$
$284$			1.69277i			0.100447i
$285$	2.30163			0.136337
$286$		−	6.20414i		−	0.366858i
$287$	17.3763			1.02569
$288$	−6.26186			−0.368984
$289$	−16.7911	−	2.65696i	−0.987711	−	0.156292i
$290$	8.06253			0.473448
$291$	12.8213			0.751597
$292$			2.48734i			0.145561i
$293$	20.2281			1.18174			0.590868	−	0.806768i	$-0.298785\pi$
$293$	20.2281			1.18174			0.590868	+	0.806768i	$0.298785\pi$
$294$		−	5.51226i		−	0.321481i
$295$		−	6.12658i		−	0.356703i
$296$			4.28398i			0.249001i
$297$	−5.02802			−0.291755
$298$	−23.2928			−1.34931
$299$		−	41.6329i		−	2.40769i
$300$		−	1.63229i		−	0.0942402i
$301$		−	1.86722i		−	0.107625i
$302$	16.8092			0.967260
$303$			5.85056i			0.336106i
$304$	−3.84646			−0.220610
$305$	13.9904			0.801089
$306$	0.763218	−	9.70655i	0.0436303	−	0.554887i
$307$	−22.8646			−1.30495			−0.652477	−	0.757809i	$-0.726270\pi$
$307$	−22.8646			−1.30495			−0.652477	+	0.757809i	$0.726270\pi$
$308$	−0.900647			−0.0513191
$309$		−	2.76763i		−	0.157445i
$310$	13.6796			0.776951
$311$		−	20.3213i		−	1.15232i	−0.817338	−	0.576159i	$-0.804551\pi$
$311$		−	20.3213i		−	1.15232i	0.817338	−	0.576159i	$-0.195449\pi$
$312$			16.1519i			0.914422i
$313$		−	4.16633i		−	0.235495i	−0.993044	−	0.117747i	$-0.962433\pi$
$313$		−	4.16633i		−	0.235495i	0.993044	−	0.117747i	$-0.0375673\pi$
$314$	9.92159			0.559908
$315$	−4.57790			−0.257936
$316$		−	7.30601i		−	0.410995i
$317$			3.22793i			0.181299i	0.995883	+	0.0906494i	$0.0288943\pi$
$317$			3.22793i			0.181299i	−0.995883	+	0.0906494i	$0.971106\pi$
$318$			15.5867i			0.874060i
$319$	4.55225			0.254877
$320$		−	13.0465i		−	0.729324i
$321$	−2.39254			−0.133539
$322$	14.8296			0.826424
$323$	−0.495984	+	6.30789i	−0.0275973	+	0.350980i
$324$	−0.502483			−0.0279157
$325$	14.5336			0.806178
$326$		−	15.4553i		−	0.855990i
$327$	−2.74631			−0.151871
$328$			34.3477i			1.89653i
$329$			17.3388i			0.955917i
$330$		−	1.78781i		−	0.0984158i
$331$	12.1256			0.666484			0.333242	−	0.942841i	$-0.391857\pi$
$331$	12.1256			0.666484			0.333242	+	0.942841i	$0.391857\pi$
$332$	1.34028			0.0735576
$333$			2.76053i			0.151276i
$334$		−	8.62951i		−	0.472186i
$335$		−	2.30908i		−	0.126158i
$336$	−3.93504			−0.214674
$337$		−	1.19676i		−	0.0651917i	−0.999469	−	0.0325959i	$-0.989623\pi$
$337$		−	1.19676i		−	0.0651917i	0.999469	−	0.0325959i	$-0.0103774\pi$
$338$	−16.7946			−0.913504
$339$	−17.4034			−0.945225
$340$	−3.53666	−	0.278085i	−0.191802	−	0.0150813i
$341$	7.72377			0.418266
$342$	−3.62391			−0.195958
$343$		−	18.0119i		−	0.972549i
$344$	3.69094			0.199002
$345$		−	11.9971i		−	0.645903i
$346$		−	12.5280i		−	0.673510i
$347$		−	25.3234i		−	1.35943i	−0.733476	−	0.679715i	$-0.762103\pi$
$347$		−	25.3234i		−	1.35943i	0.733476	−	0.679715i	$-0.237897\pi$
$348$	−2.66102			−0.142646
$349$	25.8802			1.38534			0.692669	−	0.721256i	$-0.256435\pi$
$349$	25.8802			1.38534			0.692669	+	0.721256i	$0.256435\pi$
$350$			5.17687i			0.276715i
$351$			26.1695i			1.39682i
$352$		−	3.16088i		−	0.168476i
$353$	−11.7596			−0.625899			−0.312949	−	0.949770i	$-0.601317\pi$
$353$	−11.7596			−0.625899			−0.312949	+	0.949770i	$0.601317\pi$
$354$		−	4.96153i		−	0.263703i
$355$	−4.34324			−0.230515
$356$	1.87031			0.0991263
$357$	−0.507405	+	6.45314i	−0.0268547	+	0.341537i
$358$	3.89202			0.205699
$359$	−9.76052			−0.515140			−0.257570	−	0.966260i	$-0.582922\pi$
$359$	−9.76052			−0.515140			−0.257570	+	0.966260i	$0.582922\pi$
$360$		−	9.04914i		−	0.476931i
$361$	−16.6450			−0.876051
$362$			10.9052i			0.573165i
$363$		−	1.00943i		−	0.0529813i
$364$			4.68762i			0.245698i
$365$	−6.38192			−0.334045
$366$	11.3300			0.592227
$367$			12.5357i			0.654356i	0.944963	+	0.327178i	$0.106098\pi$
$367$			12.5357i			0.654356i	−0.944963	+	0.327178i	$0.893902\pi$
$368$			20.0494i			1.04515i
$369$			22.1331i			1.15221i
$370$	−2.46799			−0.128304
$371$			20.1467i			1.04596i
$372$	−4.51493			−0.234088
$373$	−5.24536			−0.271595			−0.135797	−	0.990737i	$-0.543360\pi$
$373$	−5.24536			−0.271595			−0.135797	+	0.990737i	$0.543360\pi$
$374$	4.89970	+	0.385259i	0.253357	+	0.0199213i
$375$	11.6871			0.603522
$376$	−34.2735			−1.76752
$377$		−	23.6932i		−	1.22026i
$378$	−9.32158			−0.479450
$379$		−	4.03879i		−	0.207458i	−0.994606	−	0.103729i	$-0.966922\pi$
$379$		−	4.03879i		−	0.207458i	0.994606	−	0.103729i	$-0.0330775\pi$
$380$			1.32040i			0.0677351i
$381$		−	21.3725i		−	1.09495i
$382$	10.1495			0.519293
$383$	−10.9018			−0.557055			−0.278527	−	0.960428i	$-0.589846\pi$
$383$	−10.9018			−0.557055			−0.278527	+	0.960428i	$0.589846\pi$
$384$		−	4.18420i		−	0.213524i
$385$		−	2.31085i		−	0.117772i
$386$			16.7837i			0.854267i
$387$	2.37839			0.120900
$388$			7.35531i			0.373409i
$389$	−16.0965			−0.816125			−0.408062	−	0.912954i	$-0.633795\pi$
$389$	−16.0965			−0.816125			−0.408062	+	0.912954i	$0.633795\pi$
$390$	−9.30507			−0.471180
$391$	32.8795	+	2.58528i	1.66279	+	0.130743i
$392$	14.0838			0.711339
$393$	1.56455			0.0789210
$394$			27.1758i			1.36909i
$395$	18.7455			0.943187
$396$		−	1.14721i		−	0.0576492i
$397$			32.2222i			1.61719i	0.588368	+	0.808594i	$0.299771\pi$
$397$			32.2222i			1.61719i	−0.588368	+	0.808594i	$0.700229\pi$
$398$		−	17.4441i		−	0.874394i
$399$	2.40926			0.120614
$400$	−6.99904			−0.349952
$401$			19.9882i			0.998165i	0.866554	+	0.499083i	$0.166330\pi$
$401$			19.9882i			0.998165i	−0.866554	+	0.499083i	$0.833670\pi$
$402$		−	1.86998i		−	0.0932661i
$403$		−	40.2001i		−	2.00251i
$404$	−3.35635			−0.166985
$405$		−	1.28925i		−	0.0640635i
$406$	8.43953			0.418847
$407$	−1.39347			−0.0690717
$408$	−12.7559	−	1.00299i	−0.631513	−	0.0496553i
$409$	5.71130			0.282405			0.141203	−	0.989981i	$-0.454903\pi$
$409$	5.71130			0.282405			0.141203	+	0.989981i	$0.454903\pi$
$410$	−19.7876			−0.977239
$411$		−	15.5227i		−	0.765679i
$412$	1.58773			0.0782220
$413$		−	6.41306i		−	0.315566i
$414$			18.8894i			0.928362i
$415$			3.43885i			0.168806i
$416$	−16.4515			−0.806602
$417$	6.46468			0.316577
$418$		−	1.82929i		−	0.0894733i
$419$		−	13.5437i		−	0.661652i	−0.943692	−	0.330826i	$-0.892673\pi$
$419$		−	13.5437i		−	0.661652i	0.943692	−	0.330826i	$-0.107327\pi$
$420$			1.35081i			0.0659126i
$421$	−7.19379			−0.350604			−0.175302	−	0.984515i	$-0.556090\pi$
$421$	−7.19379			−0.350604			−0.175302	+	0.984515i	$0.556090\pi$
$422$		−	10.8021i		−	0.525839i
$423$	−22.0854			−1.07383
$424$	−39.8240			−1.93402
$425$	−0.902494	+	11.4779i	−0.0437774	+	0.556758i
$426$	−3.51732			−0.170415
$427$	14.6446			0.708702
$428$		−	1.37255i		−	0.0663448i
$429$	−5.25381			−0.253656
$430$			2.12634i			0.102541i
$431$			5.18207i			0.249612i	0.992181	+	0.124806i	$0.0398308\pi$
$431$			5.18207i			0.249612i	−0.992181	+	0.124806i	$0.960169\pi$
$432$		−	12.6026i		−	0.606344i
$433$	2.13944			0.102815			0.0514074	−	0.998678i	$-0.483629\pi$
$433$	2.13944			0.102815			0.0514074	+	0.998678i	$0.483629\pi$
$434$	14.3193			0.687348
$435$		−	6.82754i		−	0.327356i
$436$		−	1.57550i		−	0.0754528i
$437$		−	12.2754i		−	0.587213i
$438$	−5.16832			−0.246952
$439$			29.6223i			1.41380i	0.707315	+	0.706898i	$0.249906\pi$
$439$			29.6223i			1.41380i	−0.707315	+	0.706898i	$0.750094\pi$
$440$	4.56785			0.217764
$441$	9.07539			0.432161
$442$	2.00517	−	25.5016i	0.0953761	−	1.21299i
$443$	−24.7620			−1.17648			−0.588239	−	0.808687i	$-0.700178\pi$
$443$	−24.7620			−1.17648			−0.588239	+	0.808687i	$0.700178\pi$
$444$	0.814553			0.0386570
$445$			4.79877i			0.227484i
$446$	−17.4281			−0.825246
$447$			19.7249i			0.932954i
$448$		−	13.6566i		−	0.645213i
$449$			15.9985i			0.755016i	0.926006	+	0.377508i	$0.123219\pi$
$449$			15.9985i			0.755016i	−0.926006	+	0.377508i	$0.876781\pi$
$450$	−6.59407			−0.310848
$451$	−11.1724			−0.526089
$452$		−	9.98400i		−	0.469608i
$453$		−	14.2344i		−	0.668791i
$454$		−	11.5909i		−	0.543989i
$455$	−12.0273			−0.563849
$456$			4.76238i			0.223019i
$457$	−8.25616			−0.386207			−0.193103	−	0.981178i	$-0.561855\pi$
$457$	−8.25616			−0.386207			−0.193103	+	0.981178i	$0.561855\pi$
$458$	5.95222			0.278129
$459$	−20.6673	−	1.62505i	−0.964666	−	0.0758508i
$460$	6.88250			0.320898
$461$	−11.6964			−0.544755			−0.272377	−	0.962190i	$-0.587810\pi$
$461$	−11.6964			−0.544755			−0.272377	+	0.962190i	$0.587810\pi$
$462$		−	1.87141i		−	0.0870658i
$463$	27.5274			1.27931			0.639653	−	0.768663i	$-0.279078\pi$
$463$	27.5274			1.27931			0.639653	+	0.768663i	$0.279078\pi$
$464$			11.4101i			0.529701i
$465$		−	11.5842i		−	0.537206i
$466$			9.47109i			0.438740i
$467$	16.6329			0.769679			0.384840	−	0.922983i	$-0.374257\pi$
$467$	16.6329			0.769679			0.384840	+	0.922983i	$0.374257\pi$
$468$	−5.97089			−0.276004
$469$		−	2.41705i		−	0.111609i
$470$		−	19.7449i		−	0.910763i
$471$		−	8.40183i		−	0.387136i
$472$	12.6767			0.583492
$473$			1.20057i			0.0552023i
$474$	15.1808			0.697277
$475$	4.28522			0.196619
$476$	−3.70204	−	0.291088i	−0.169683	−	0.0133420i
$477$	−25.6620			−1.17498
$478$	−6.38445			−0.292018
$479$			16.6491i			0.760716i	0.924839	+	0.380358i	$0.124199\pi$
$479$			16.6491i			0.760716i	−0.924839	+	0.380358i	$0.875801\pi$
$480$	−4.74074			−0.216384
$481$			7.25263i			0.330691i
$482$			19.6661i			0.895767i
$483$		−	12.5581i		−	0.571413i
$484$	0.579089			0.0263222
$485$	−18.8720			−0.856932
$486$		−	19.0246i		−	0.862973i
$487$		−	22.2517i		−	1.00832i	−0.863610	−	0.504160i	$-0.831802\pi$
$487$		−	22.2517i		−	1.00832i	0.863610	−	0.504160i	$-0.168198\pi$
$488$			28.9480i			1.31041i
$489$	−13.0879			−0.591856
$490$			8.11363i			0.366536i
$491$	32.6279			1.47248			0.736238	−	0.676723i	$-0.236600\pi$
$491$	32.6279			1.47248			0.736238	+	0.676723i	$0.236600\pi$
$492$	6.53085			0.294433
$493$	18.7117	+	1.47128i	0.842731	+	0.0662632i
$494$	−9.52093			−0.428367
$495$	2.94346			0.132298
$496$			19.3594i			0.869265i
$497$	−4.54633			−0.203931
$498$			2.78491i			0.124795i
$499$		−	22.2958i		−	0.998095i	−0.866575	−	0.499048i	$-0.833683\pi$
$499$		−	22.2958i		−	0.998095i	0.866575	−	0.499048i	$-0.166317\pi$
$500$			6.70468i			0.299842i
$501$	−7.30767			−0.326483
$502$	−25.6818			−1.14624
$503$			4.28526i			0.191070i	0.995426	+	0.0955351i	$0.0304562\pi$
$503$			4.28526i			0.191070i	−0.995426	+	0.0955351i	$0.969544\pi$
$504$		−	9.47227i		−	0.421929i
$505$		−	8.61159i		−	0.383211i
$506$	−9.53503			−0.423884
$507$			14.2220i			0.631623i
$508$	12.2610			0.543993
$509$	36.2422			1.60641			0.803203	−	0.595706i	$-0.203128\pi$
$509$	36.2422			1.60641			0.803203	+	0.595706i	$0.203128\pi$
$510$	0.577818	−	7.34865i	0.0255862	−	0.325404i
$511$	−6.68034			−0.295521
$512$	23.3341			1.03123
$513$			7.71605i			0.340672i
$514$	10.2379			0.451576
$515$			4.07375i			0.179511i
$516$		−	0.701794i		−	0.0308947i
$517$		−	11.1483i		−	0.490302i
$518$	−2.58339			−0.113508
$519$	−10.6090			−0.465684
$520$		−	23.7744i		−	1.04258i
$521$		−	19.9090i		−	0.872230i	−0.899891	−	0.436115i	$-0.856354\pi$
$521$		−	19.9090i		−	0.872230i	0.899891	−	0.436115i	$-0.143646\pi$
$522$			10.7499i			0.470511i
$523$	34.5902			1.51252			0.756262	−	0.654269i	$-0.227024\pi$
$523$	34.5902			1.51252			0.756262	+	0.654269i	$0.227024\pi$
$524$			0.897549i			0.0392096i
$525$	4.38390			0.191329
$526$	5.05839			0.220556
$527$	31.7479	+	2.49631i	1.38296	+	0.108741i
$528$	2.53011			0.110109
$529$	−40.9848			−1.78195
$530$		−	22.9425i		−	0.996558i
$531$	8.16868			0.354490
$532$			1.38214i			0.0599234i
$533$			58.1494i			2.51873i
$534$			3.88622i			0.168173i
$535$	3.52164			0.152254
$536$	4.77779			0.206369
$537$		−	3.29585i		−	0.142226i
$538$		−	20.4364i		−	0.881077i
$539$			4.58110i			0.197322i
$540$	−4.32618			−0.186169
$541$			20.3416i			0.874556i	0.899326	+	0.437278i	$0.144057\pi$
$541$			20.3416i			0.874556i	−0.899326	+	0.437278i	$0.855943\pi$
$542$	17.3046			0.743296
$543$	9.23479			0.396303
$544$	1.02159	−	12.9925i	0.0438004	−	0.557051i
$545$	4.04236			0.173156
$546$	−9.74017			−0.416841
$547$			35.9241i			1.53600i	0.640449	+	0.768001i	$0.278748\pi$
$547$			35.9241i			1.53600i	−0.640449	+	0.768001i	$0.721252\pi$
$548$	8.90507			0.380406
$549$			18.6537i			0.796119i
$550$		−	3.32857i		−	0.141931i
$551$		−	6.98593i		−	0.297611i
$552$	24.8236			1.05656
$553$	19.6220			0.834413
$554$		−	5.27588i		−	0.224151i
$555$			2.08995i			0.0887134i
$556$			3.70865i			0.157282i
$557$	7.62266			0.322982			0.161491	−	0.986874i	$-0.448370\pi$
$557$	7.62266			0.322982			0.161491	+	0.986874i	$0.448370\pi$
$558$			18.2393i			0.772131i
$559$	6.24864			0.264289
$560$	5.79208			0.244760
$561$	0.326246	−	4.14918i	0.0137741	−	0.175179i
$562$	9.38781			0.396001
$563$	32.6469			1.37590			0.687952	−	0.725756i	$-0.258510\pi$
$563$	32.6469			1.37590			0.687952	+	0.725756i	$0.258510\pi$
$564$			6.51675i			0.274405i
$565$	25.6166			1.07770
$566$		−	17.9372i		−	0.753955i
$567$		−	1.34954i		−	0.0566752i
$568$		−	8.98673i		−	0.377075i
$569$	−12.8485			−0.538638			−0.269319	−	0.963051i	$-0.586799\pi$
$569$	−12.8485			−0.538638			−0.269319	+	0.963051i	$0.586799\pi$
$570$	−2.74359			−0.114916
$571$			31.9196i			1.33579i	0.744255	+	0.667896i	$0.232805\pi$
$571$			31.9196i			1.33579i	−0.744255	+	0.667896i	$0.767195\pi$
$572$		−	3.01400i		−	0.126022i
$573$		−	8.59482i		−	0.359054i
$574$	−20.7128			−0.864538
$575$		−	22.3364i		−	0.931493i
$576$	17.3952			0.724799
$577$	26.1890			1.09026			0.545131	−	0.838351i	$-0.316480\pi$
$577$	26.1890			1.09026			0.545131	+	0.838351i	$0.316480\pi$
$578$	20.0153	+	3.16715i	0.832527	+	0.131736i
$579$	14.2128			0.590665
$580$	3.91682			0.162637
$581$			3.59965i			0.149339i
$582$	−15.2832			−0.633510
$583$		−	12.9537i		−	0.536489i
$584$		−	13.2050i		−	0.546428i
$585$		−	15.3199i		−	0.633399i
$586$	−24.1122			−0.996068
$587$	43.1448			1.78078			0.890388	−	0.455202i	$-0.150433\pi$
$587$	43.1448			1.78078			0.890388	+	0.455202i	$0.150433\pi$
$588$		−	2.67788i		−	0.110434i
$589$		−	11.8530i		−	0.488393i
$590$			7.30300i			0.300660i
$591$	23.0131			0.946631
$592$		−	3.49270i		−	0.143549i
$593$	−37.9167			−1.55705			−0.778527	−	0.627611i	$-0.784033\pi$
$593$	−37.9167			−1.55705			−0.778527	+	0.627611i	$0.784033\pi$
$594$	5.99350			0.245916
$595$	0.746862	−	9.49854i	0.0306184	−	0.389402i
$596$	−11.3158			−0.463511
$597$	−14.7721			−0.604581
$598$			49.6272i			2.02941i
$599$	−11.4536			−0.467982			−0.233991	−	0.972239i	$-0.575179\pi$
$599$	−11.4536			−0.467982			−0.233991	+	0.972239i	$0.575179\pi$
$600$			8.66565i			0.353774i
$601$		−	30.2055i		−	1.23211i	−0.787703	−	0.616055i	$-0.788730\pi$
$601$		−	30.2055i		−	1.23211i	0.787703	−	0.616055i	$-0.211270\pi$
$602$			2.22577i			0.0907155i
$603$	3.07874			0.125376
$604$	8.16599			0.332269
$605$			1.48581i			0.0604066i
$606$		−	6.97398i		−	0.283299i
$607$		−	9.79597i		−	0.397606i	−0.980039	−	0.198803i	$-0.936295\pi$
$607$		−	9.79597i		−	0.397606i	0.980039	−	0.198803i	$-0.0637054\pi$
$608$	−4.85072			−0.196723
$609$		−	7.14680i		−	0.289603i
$610$	−16.6769			−0.675226
$611$	−58.0239			−2.34740
$612$	0.370775	−	4.71549i	0.0149877	−	0.190613i
$613$	−47.5860			−1.92198			−0.960990	−	0.276582i	$-0.910798\pi$
$613$	−47.5860			−1.92198			−0.960990	+	0.276582i	$0.910798\pi$
$614$	27.2551			1.09993
$615$			16.7566i			0.675691i
$616$	4.78144			0.192650
$617$		−	21.1929i		−	0.853193i	−0.904442	−	0.426596i	$-0.859713\pi$
$617$		−	21.1929i		−	0.853193i	0.904442	−	0.426596i	$-0.140287\pi$
$618$			3.29907i			0.132708i
$619$		−	18.5125i		−	0.744081i	−0.928216	−	0.372041i	$-0.878658\pi$
$619$		−	18.5125i		−	0.744081i	0.928216	−	0.372041i	$-0.121342\pi$
$620$	6.64564			0.266895
$621$	40.2194			1.61395
$622$			24.2234i			0.971271i
$623$			5.02316i			0.201249i
$624$		−	13.1685i		−	0.527164i
$625$	−3.24069			−0.129627
$626$			4.96635i			0.198495i
$627$	−1.54908			−0.0618644
$628$	4.81996			0.192337
$629$	−5.72774	−	0.450367i	−0.228380	−	0.0179573i
$630$	5.45695			0.217410
$631$	−0.137527			−0.00547485			−0.00273743	−	0.999996i	$-0.500871\pi$
$631$	−0.137527			−0.00547485			−0.00273743	+	0.999996i	$0.500871\pi$
$632$			38.7868i			1.54286i
$633$	−9.14750			−0.363580
$634$		−	3.84776i		−	0.152814i
$635$			31.4587i			1.24840i
$636$			7.57211i			0.300254i
$637$	23.8434			0.944709
$638$	−5.42637			−0.214832
$639$		−	5.79092i		−	0.229085i
$640$			6.15882i			0.243449i
$641$		−	15.1282i		−	0.597528i	−0.954327	−	0.298764i	$-0.903426\pi$
$641$		−	15.1282i		−	0.597528i	0.954327	−	0.298764i	$-0.0965744\pi$
$642$	2.85195			0.112558
$643$		−	29.0892i		−	1.14717i	−0.819147	−	0.573583i	$-0.805553\pi$
$643$		−	29.0892i		−	1.14717i	0.819147	−	0.573583i	$-0.194447\pi$
$644$	7.20432			0.283890
$645$	1.80064			0.0708999
$646$	0.591222	−	7.51913i	0.0232613	−	0.295836i
$647$	24.5069			0.963466			0.481733	−	0.876318i	$-0.340007\pi$
$647$	24.5069			0.963466			0.481733	+	0.876318i	$0.340007\pi$
$648$	2.66763			0.104794
$649$			4.12341i			0.161858i
$650$	−17.3243			−0.679516
$651$		−	12.1259i		−	0.475252i
$652$		−	7.50827i		−	0.294047i
$653$		−	45.6670i		−	1.78709i	−0.448977	−	0.893543i	$-0.648212\pi$
$653$		−	45.6670i		−	1.78709i	0.448977	−	0.893543i	$-0.351788\pi$
$654$	3.27365			0.128010
$655$	−2.30290			−0.0899816
$656$		−	28.0034i		−	1.09335i
$657$		−	8.50913i		−	0.331973i
$658$		−	20.6681i		−	0.805728i
$659$	−29.4534			−1.14734			−0.573670	−	0.819086i	$-0.694481\pi$
$659$	−29.4534			−1.14734			−0.573670	+	0.819086i	$0.694481\pi$
$660$		−	0.868528i		−	0.0338074i
$661$	46.8843			1.82359			0.911794	−	0.410649i	$-0.134698\pi$
$661$	46.8843			1.82359			0.911794	+	0.410649i	$0.134698\pi$
$662$	−14.4540			−0.561769
$663$	−21.5954	−	1.69802i	−0.838694	−	0.0659458i
$664$	−7.11542			−0.276132
$665$	−3.54625			−0.137518
$666$		−	3.29061i		−	0.127509i
$667$	−36.4137			−1.40994
$668$		−	4.19226i		−	0.162204i
$669$			14.7586i			0.570599i
$670$			2.75247i			0.106337i
$671$	−9.41605			−0.363503
$672$	−4.96242			−0.191429
$673$			41.9285i			1.61622i	0.589029	+	0.808112i	$0.299510\pi$
$673$			41.9285i			1.61622i	−0.589029	+	0.808112i	$0.700490\pi$
$674$			1.42656i			0.0549492i
$675$			14.0402i			0.540406i
$676$	−8.15889			−0.313804
$677$			3.14033i			0.120693i	0.998177	+	0.0603464i	$0.0192205\pi$
$677$			3.14033i			0.120693i	−0.998177	+	0.0603464i	$0.980779\pi$
$678$	20.7452			0.796716
$679$	−19.7544			−0.758105
$680$	18.7758	+	1.47632i	0.720018	+	0.0566144i
$681$	−9.81547			−0.376130
$682$	−9.20688			−0.352550
$683$			8.21587i			0.314372i	0.987569	+	0.157186i	$0.0502421\pi$
$683$			8.21587i			0.314372i	−0.987569	+	0.157186i	$0.949758\pi$
$684$	−1.76051			−0.0673149
$685$			22.8483i			0.872988i
$686$			21.4705i			0.819747i
$687$		−	5.04048i		−	0.192306i
$688$	−3.00920			−0.114725
$689$	−67.4207			−2.56852
$690$			14.3008i			0.544422i
$691$			33.4934i			1.27415i	0.770803	+	0.637074i	$0.219855\pi$
$691$			33.4934i			1.27415i	−0.770803	+	0.637074i	$0.780145\pi$
$692$		−	6.08617i		−	0.231362i
$693$	3.08109			0.117041
$694$			30.1860i			1.14584i
$695$	−9.51552			−0.360944
$696$	14.1271			0.535485
$697$	−45.9234	−	3.61091i	−1.73947	−	0.136773i
$698$	−30.8497			−1.16768
$699$	8.02034			0.303357
$700$			2.51495i			0.0950562i
$701$	−24.2817			−0.917107			−0.458553	−	0.888667i	$-0.651632\pi$
$701$	−24.2817			−0.917107			−0.458553	+	0.888667i	$0.651632\pi$
$702$		−	31.1945i		−	1.17736i
$703$			2.13843i			0.0806525i
$704$			8.78078i			0.330938i
$705$	−16.7204			−0.629728
$706$	14.0176			0.527561
$707$		−	9.01426i		−	0.339016i
$708$		−	2.41034i		−	0.0905861i
$709$		−	19.4170i		−	0.729221i	−0.931160	−	0.364611i	$-0.881202\pi$
$709$		−	19.4170i		−	0.729221i	0.931160	−	0.364611i	$-0.118798\pi$
$710$	5.17723			0.194298
$711$			24.9937i			0.937336i
$712$	−9.92929			−0.372116
$713$	−61.7828			−2.31379
$714$	0.604837	−	7.69227i	0.0226354	−	0.287876i
$715$	7.73321			0.289206
$716$	1.89076			0.0706611
$717$			5.40650i			0.201909i
$718$	11.6347			0.434204
$719$		−	6.24400i		−	0.232862i	−0.993199	−	0.116431i	$-0.962855\pi$
$719$		−	6.24400i		−	0.232862i	0.993199	−	0.116431i	$-0.0371454\pi$
$720$			7.37770i			0.274951i
$721$			4.26423i			0.158808i
$722$	19.8411			0.738410
$723$	16.6537			0.619359
$724$			5.29781i			0.196892i
$725$		−	12.7116i		−	0.472098i
$726$			1.20326i			0.0446572i
$727$	−36.0153			−1.33573			−0.667866	−	0.744281i	$-0.732792\pi$
$727$	−36.0153			−1.33573			−0.667866	+	0.744281i	$0.732792\pi$
$728$		−	24.8861i		−	0.922340i
$729$	−13.5073			−0.500272
$730$	7.60738			0.281562
$731$	−0.388023	+	4.93485i	−0.0143515	+	0.182522i
$732$	5.50416			0.203440
$733$	−11.2325			−0.414883			−0.207442	−	0.978247i	$-0.566514\pi$
$733$	−11.2325			−0.414883			−0.207442	+	0.978247i	$0.566514\pi$
$734$		−	14.9427i		−	0.551547i
$735$	6.87081			0.253434
$736$			25.2841i			0.931983i
$737$			1.55409i			0.0572457i
$738$		−	26.3831i		−	0.971177i
$739$	−10.8530			−0.399233			−0.199616	−	0.979874i	$-0.563970\pi$
$739$	−10.8530			−0.399233			−0.199616	+	0.979874i	$0.563970\pi$
$740$	−1.19896			−0.0440747
$741$			8.06255i			0.296185i
$742$		−	24.0153i		−	0.881628i
$743$		−	43.2634i		−	1.58718i	−0.608453	−	0.793590i	$-0.708210\pi$
$743$		−	43.2634i		−	1.58718i	0.608453	−	0.793590i	$-0.291790\pi$
$744$	23.9693			0.878757
$745$		−	29.0335i		−	1.06371i
$746$	6.25257			0.228923
$747$	−4.58508			−0.167759
$748$	2.38030	+	0.187161i	0.0870324	+	0.00684328i
$749$	3.68631			0.134695
$750$	−13.9313			−0.508699
$751$			53.0594i			1.93616i	0.250634	+	0.968082i	$0.419361\pi$
$751$			53.0594i			1.93616i	−0.250634	+	0.968082i	$0.580639\pi$
$752$	27.9430			1.01898
$753$			21.7480i			0.792541i
$754$			28.2428i			1.02854i
$755$			20.9520i			0.762521i
$756$	−4.52847			−0.164699
$757$	−20.9143			−0.760144			−0.380072	−	0.924957i	$-0.624101\pi$
$757$	−20.9143			−0.760144			−0.380072	+	0.924957i	$0.624101\pi$
$758$			4.81431i			0.174864i
$759$			8.07449i			0.293085i
$760$		−	7.00987i		−	0.254275i
$761$	−0.935912			−0.0339268			−0.0169634	−	0.999856i	$-0.505400\pi$
$761$	−0.935912			−0.0339268			−0.0169634	+	0.999856i	$0.505400\pi$
$762$			25.4765i			0.922915i
$763$	4.23138			0.153186
$764$	4.93067			0.178386
$765$	12.0988	+	0.951321i	0.437434	+	0.0343951i
$766$	12.9951			0.469533
$767$	21.4612			0.774919
$768$		−	12.7395i		−	0.459698i
$769$	−7.39918			−0.266821			−0.133411	−	0.991061i	$-0.542593\pi$
$769$	−7.39918			−0.266821			−0.133411	+	0.991061i	$0.542593\pi$
$770$			2.75457i			0.0992679i
$771$		−	8.66973i		−	0.312233i
$772$			8.15360i			0.293455i
$773$	33.2012			1.19416			0.597082	−	0.802180i	$-0.296327\pi$
$773$	33.2012			1.19416			0.597082	+	0.802180i	$0.296327\pi$
$774$	−2.83509			−0.101905
$775$		−	21.5677i		−	0.774735i
$776$		−	39.0485i		−	1.40176i
$777$			2.18767i			0.0784824i
$778$	19.1873			0.687899
$779$			17.1453i			0.614295i
$780$	−4.52045			−0.161858
$781$	2.92316			0.104599
$782$	−39.1930	−	3.08171i	−1.40154	−	0.110202i
$783$	22.8888			0.817980
$784$	−11.4824			−0.410086
$785$			12.3669i			0.441392i
$786$	−1.86497			−0.0665213
$787$		−	37.9856i		−	1.35404i	−0.735964	−	0.677020i	$-0.763271\pi$
$787$		−	37.9856i		−	1.35404i	0.735964	−	0.677020i	$-0.236729\pi$
$788$			13.2021i			0.470306i
$789$		−	4.28356i		−	0.152499i
$790$	−22.3450			−0.794998
$791$	26.8144			0.953409
$792$			6.09039i			0.216413i
$793$			49.0080i			1.74032i
$794$		−	38.4095i		−	1.36310i
$795$	−19.4282			−0.689049
$796$		−	8.47444i		−	0.300369i
$797$	−35.3094			−1.25072			−0.625362	−	0.780335i	$-0.715049\pi$
$797$	−35.3094			−1.25072			−0.625362	+	0.780335i	$0.715049\pi$
$798$	−2.87188			−0.101664
$799$	3.60312	−	45.8242i	0.127469	−	1.62115i
$800$	−8.82639			−0.312060
$801$	−6.39829			−0.226072
$802$		−	23.8264i		−	0.841338i
$803$	4.29526			0.151576
$804$		−	0.908446i		−	0.0320384i
$805$			18.4846i			0.651496i
$806$			47.9193i			1.68789i
$807$	−17.3060			−0.609202
$808$	17.8185			0.626853
$809$			28.6056i			1.00572i	0.864368	+	0.502859i	$0.167719\pi$
$809$			28.6056i			1.00572i	−0.864368	+	0.502859i	$0.832281\pi$
$810$			1.53681i			0.0539981i
$811$		−	27.4914i		−	0.965355i	−0.875798	−	0.482678i	$-0.839664\pi$
$811$		−	27.4914i		−	0.965355i	0.875798	−	0.482678i	$-0.160336\pi$
$812$	4.09997			0.143881
$813$		−	14.6539i		−	0.513936i
$814$	1.66104			0.0582195
$815$	19.2644			0.674804
$816$	10.3998	+	0.817729i	0.364067	+	0.0286262i
$817$	1.84241			0.0644577
$818$	−6.80798			−0.238035
$819$		−	16.0362i		−	0.560351i
$820$	−9.61291			−0.335697
$821$			10.6722i			0.372463i	0.982506	+	0.186231i	$0.0596274\pi$
$821$			10.6722i			0.372463i	−0.982506	+	0.186231i	$0.940373\pi$
$822$			18.5034i			0.645380i
$823$		−	45.2398i		−	1.57696i	−0.615060	−	0.788480i	$-0.710868\pi$
$823$		−	45.2398i		−	1.57696i	0.615060	−	0.788480i	$-0.289132\pi$
$824$	−8.42911			−0.293642
$825$	−2.81872			−0.0981351
$826$			7.64449i			0.265986i
$827$			27.8351i			0.967920i	0.875090	+	0.483960i	$0.160802\pi$
$827$			27.8351i			0.967920i	−0.875090	+	0.483960i	$0.839198\pi$
$828$			9.17656i			0.318907i
$829$	0.782490			0.0271770			0.0135885	−	0.999908i	$-0.495675\pi$
$829$	0.782490			0.0271770			0.0135885	+	0.999908i	$0.495675\pi$
$830$		−	4.09917i		−	0.142284i
$831$	−4.46774			−0.154984
$832$	45.7016			1.58442
$833$	−1.48061	+	18.8302i	−0.0512999	+	0.652429i
$834$	−7.70602			−0.266838
$835$	10.7563			0.372239
$836$		−	0.888676i		−	0.0307355i
$837$	38.8353			1.34234
$838$			16.1443i			0.557696i
$839$			42.8782i			1.48032i	0.672430	+	0.740160i	$0.265250\pi$
$839$			42.8782i			1.48032i	−0.672430	+	0.740160i	$0.734750\pi$
$840$		−	7.17128i		−	0.247433i
$841$	8.27702			0.285414
$842$	8.57513			0.295519
$843$		−	7.94982i		−	0.273806i
$844$		−	5.24773i		−	0.180634i
$845$		−	20.9338i		−	0.720144i
$846$	26.3262			0.905113
$847$			1.55528i			0.0534401i
$848$	32.4682			1.11496
$849$	−15.1896			−0.521306
$850$	1.07579	−	13.6818i	0.0368993	−	0.469283i
$851$	11.1464			0.382095
$852$	−1.70873			−0.0585402
$853$			6.49549i			0.222401i	0.993798	+	0.111201i	$0.0354696\pi$
$853$			6.49549i			0.222401i	−0.993798	+	0.111201i	$0.964530\pi$
$854$	−17.4567			−0.597355
$855$		−	4.51706i		−	0.154480i
$856$			7.28673i			0.249055i
$857$		−	28.0716i		−	0.958906i	−0.877568	−	0.479453i	$-0.840835\pi$
$857$		−	28.0716i		−	0.958906i	0.877568	−	0.479453i	$-0.159165\pi$
$858$	6.26264			0.213803
$859$	−23.9195			−0.816123			−0.408061	−	0.912955i	$-0.633795\pi$
$859$	−23.9195			−0.816123			−0.408061	+	0.912955i	$0.633795\pi$
$860$			1.03299i			0.0352246i
$861$			17.5401i			0.597766i
$862$		−	6.17713i		−	0.210394i
$863$	21.2949			0.724886			0.362443	−	0.932006i	$-0.381943\pi$
$863$	21.2949			0.724886			0.362443	+	0.932006i	$0.381943\pi$
$864$		−	15.8930i		−	0.540690i
$865$	15.6157			0.530949
$866$	−2.55025			−0.0866610
$867$	2.68202	−	16.9494i	0.0910861	−	0.575633i
$868$	6.95639			0.236115
$869$	−12.6164			−0.427981
$870$			8.13856i			0.275923i
$871$	8.08863			0.274073
$872$			8.36417i			0.283246i
$873$		−	25.1623i		−	0.851615i
$874$			14.6325i			0.494953i
$875$	−18.0070			−0.608747
$876$	−2.51080			−0.0848320
$877$			21.5370i			0.727251i	0.931545	+	0.363626i	$0.118461\pi$
$877$			21.5370i			0.727251i	−0.931545	+	0.363626i	$0.881539\pi$
$878$		−	35.3104i		−	1.19167i
$879$			20.4188i			0.688710i
$880$	−3.72414			−0.125541
$881$		−	10.1340i		−	0.341421i	−0.985321	−	0.170711i	$-0.945394\pi$
$881$		−	10.1340i		−	0.341421i	0.985321	−	0.170711i	$-0.0546064\pi$
$882$	−10.8180			−0.364262
$883$	45.4932			1.53097			0.765484	−	0.643455i	$-0.222500\pi$
$883$	45.4932			1.53097			0.765484	+	0.643455i	$0.222500\pi$
$884$	0.974121	−	12.3888i	0.0327632	−	0.416681i
$885$	6.18436			0.207885
$886$	29.5168			0.991635
$887$			38.8227i			1.30354i	0.758417	+	0.651770i	$0.225973\pi$
$887$			38.8227i			1.30354i	−0.758417	+	0.651770i	$0.774027\pi$
$888$	−4.32438			−0.145117
$889$			32.9298i			1.10443i
$890$		−	5.72023i		−	0.191743i
$891$			0.867713i			0.0290695i
$892$	−8.46668			−0.283485
$893$	−17.1083			−0.572508
$894$		−	23.5124i		−	0.786373i
$895$			4.85124i			0.162159i
$896$			6.44681i			0.215373i
$897$	42.0255			1.40319
$898$		−	19.0705i		−	0.636392i
$899$	−35.1605			−1.17267
$900$	−3.20344			−0.106781
$901$	4.18663	−	53.2453i	0.139477	−	1.77386i
$902$	13.3178			0.443433
$903$	1.88483			0.0627233
$904$			53.0040i			1.76289i
$905$	−13.5929			−0.451844
$906$			16.9677i			0.563714i
$907$		−	24.8445i		−	0.824947i	−0.910970	−	0.412473i	$-0.864665\pi$
$907$		−	24.8445i		−	0.824947i	0.910970	−	0.412473i	$-0.135335\pi$
$908$		−	5.63093i		−	0.186869i
$909$	11.4820			0.380833
$910$	14.3368			0.475260
$911$		−	26.5185i		−	0.878598i	−0.898341	−	0.439299i	$-0.855227\pi$
$911$		−	26.5185i		−	0.878598i	0.898341	−	0.439299i	$-0.144773\pi$
$912$		−	3.88274i		−	0.128570i
$913$		−	2.31447i		−	0.0765977i
$914$	9.84151			0.325528
$915$			14.1224i			0.466871i
$916$	2.89162			0.0955419
$917$	−2.41058			−0.0796044
$918$	24.6358	+	1.93709i	0.813103	+	0.0639335i
$919$	−9.88416			−0.326048			−0.163024	−	0.986622i	$-0.552125\pi$
$919$	−9.88416			−0.326048			−0.163024	+	0.986622i	$0.552125\pi$
$920$	−36.5385			−1.20464
$921$		−	23.0802i		−	0.760520i
$922$	13.9423			0.459166
$923$		−	15.2142i		−	0.500782i
$924$		−	0.909140i		−	0.0299085i
$925$			3.89110i			0.127939i
$926$	−32.8132			−1.07831
$927$	−5.43160			−0.178397
$928$			14.3891i			0.472346i
$929$		−	46.5735i		−	1.52803i	−0.645201	−	0.764013i	$-0.723226\pi$
$929$		−	46.5735i		−	1.52803i	0.645201	−	0.764013i	$-0.276774\pi$
$930$			13.8086i			0.452803i
$931$	7.03020			0.230406
$932$			4.60111i			0.150714i
$933$	20.5130			0.671565
$934$	−19.8268			−0.648751
$935$	−0.480210	+	6.10728i	−0.0157046	+	0.199729i
$936$	31.6988			1.03611
$937$	9.23669			0.301750			0.150875	−	0.988553i	$-0.451791\pi$
$937$	9.23669			0.301750			0.150875	+	0.988553i	$0.451791\pi$
$938$			2.88117i			0.0940736i
$939$	4.20562			0.137245
$940$		−	9.59217i		−	0.312862i
$941$			20.1903i			0.658186i	0.944298	+	0.329093i	$0.106743\pi$
$941$			20.1903i			0.658186i	−0.944298	+	0.329093i	$0.893257\pi$
$942$			10.0152i			0.326311i
$943$	89.3688			2.91025
$944$	−10.3352			−0.336383
$945$		−	11.6190i		−	0.377966i
$946$		−	1.43110i		−	0.0465292i
$947$		−	21.1183i		−	0.686253i	−0.939289	−	0.343126i	$-0.888514\pi$
$947$		−	21.1183i		−	0.686253i	0.939289	−	0.343126i	$-0.111486\pi$
$948$	7.37491			0.239526
$949$		−	22.3557i		−	0.725695i
$950$	−5.10806			−0.165727
$951$	−3.25837			−0.105660
$952$	19.6537	+	1.54535i	0.636981	+	0.0500852i
$953$	17.1986			0.557116			0.278558	−	0.960419i	$-0.410144\pi$
$953$	17.1986			0.557116			0.278558	+	0.960419i	$0.410144\pi$
$954$	30.5896			0.990376
$955$			12.6509i			0.409375i
$956$	−3.10160			−0.100313
$957$			4.59518i			0.148541i
$958$		−	19.8460i		−	0.641196i
$959$			23.9167i			0.772309i
$960$	13.1696			0.425046
$961$	−28.6566			−0.924407
$962$		−	8.64527i		−	0.278735i
$963$			4.69546i			0.151309i
$964$			9.55390i			0.307710i
$965$	−20.9202			−0.673445
$966$			14.9695i			0.481636i
$967$	−49.1884			−1.58179			−0.790897	−	0.611950i	$-0.790385\pi$
$967$	−49.1884			−1.58179			−0.790897	+	0.611950i	$0.790385\pi$
$968$	−3.07432			−0.0988125
$969$	−6.36737	−	0.500661i	−0.204550	−	0.0160836i
$970$	22.4957			0.722295
$971$	23.9468			0.768490			0.384245	−	0.923231i	$-0.374462\pi$
$971$	23.9468			0.768490			0.384245	+	0.923231i	$0.374462\pi$
$972$		−	9.24225i		−	0.296445i
$973$	−9.96047			−0.319318
$974$			26.5244i			0.849898i
$975$			14.6706i			0.469837i
$976$		−	23.6011i		−	0.755453i
$977$	−19.6927			−0.630025			−0.315013	−	0.949087i	$-0.602009\pi$
$977$	−19.6927			−0.630025			−0.315013	+	0.949087i	$0.602009\pi$
$978$	15.6011			0.498867
$979$		−	3.22974i		−	0.103223i
$980$			3.94164i			0.125911i
$981$			5.38975i			0.172081i
$982$	−38.8931			−1.24113
$983$			33.6080i			1.07193i	0.844241	+	0.535964i	$0.180052\pi$
$983$			33.6080i			1.07193i	−0.844241	+	0.535964i	$0.819948\pi$
$984$	−34.6716			−1.10529
$985$	−33.8735			−1.07930
$986$	−22.3047	−	1.75380i	−0.710325	−	0.0558522i
$987$	−17.5023			−0.557104
$988$	−4.62532			−0.147151
$989$		−	9.60342i		−	0.305371i
$990$	−3.50866			−0.111512
$991$		−	40.1199i		−	1.27445i	−0.770677	−	0.637226i	$-0.780082\pi$
$991$		−	40.1199i		−	1.27445i	0.770677	−	0.637226i	$-0.219918\pi$
$992$			24.4139i			0.775143i
$993$			12.2400i			0.388423i
$994$	5.41931			0.171890
$995$	21.7434			0.689312
$996$			1.35292i			0.0428690i
$997$			8.44014i			0.267302i	0.991028	+	0.133651i	$0.0426701\pi$
$997$			8.44014i			0.267302i	−0.991028	+	0.133651i	$0.957330\pi$
$998$			26.5770i			0.841280i
$999$	−7.00640			−0.221673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.d.a.67.6	yes	16
3.2	odd	2		1683.2.g.b.1189.12		16
4.3	odd	2		2992.2.b.g.1937.7		16
17.4	even	4		3179.2.a.bb.1.6		8
17.13	even	4		3179.2.a.bc.1.6		8
17.16	even	2	inner	187.2.d.a.67.5	✓	16
51.50	odd	2		1683.2.g.b.1189.11		16
68.67	odd	2		2992.2.b.g.1937.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.5	✓	16	17.16	even	2	inner
187.2.d.a.67.6	yes	16	1.1	even	1	trivial
1683.2.g.b.1189.11		16	51.50	odd	2
1683.2.g.b.1189.12		16	3.2	odd	2
2992.2.b.g.1937.7		16	4.3	odd	2
2992.2.b.g.1937.10		16	68.67	odd	2
3179.2.a.bb.1.6		8	17.4	even	4
3179.2.a.bc.1.6		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)

\(f(q)\)	\(=\)	\(q-1.19202 q^{2} +1.00943i q^{3} -0.579089 q^{4} -1.48581i q^{5} -1.20326i q^{6} -1.55528i q^{7} +3.07432 q^{8} +1.98105 q^{9} +O(q^{10})\)	\(q-1.19202 q^{2} +1.00943i q^{3} -0.579089 q^{4} -1.48581i q^{5} -1.20326i q^{6} -1.55528i q^{7} +3.07432 q^{8} +1.98105 q^{9} +1.77111i q^{10} +1.00000i q^{11} -0.584550i q^{12} +5.20473 q^{13} +1.85393i q^{14} +1.49982 q^{15} -2.50648 q^{16} +(-0.323199 + 4.11042i) q^{17} -2.36145 q^{18} +1.53461 q^{19} +0.860414i q^{20} +1.56995 q^{21} -1.19202i q^{22} -7.99905i q^{23} +3.10332i q^{24} +2.79238 q^{25} -6.20414 q^{26} +5.02802i q^{27} +0.900647i q^{28} -4.55225i q^{29} -1.78781 q^{30} -7.72377i q^{31} -3.16088 q^{32} -1.00943 q^{33} +(0.385259 - 4.89970i) q^{34} -2.31085 q^{35} -1.14721 q^{36} +1.39347i q^{37} -1.82929 q^{38} +5.25381i q^{39} -4.56785i q^{40} +11.1724i q^{41} -1.87141 q^{42} +1.20057 q^{43} -0.579089i q^{44} -2.94346i q^{45} +9.53503i q^{46} -11.1483 q^{47} -2.53011i q^{48} +4.58110 q^{49} -3.32857 q^{50} +(-4.14918 - 0.326246i) q^{51} -3.01400 q^{52} -12.9537 q^{53} -5.99350i q^{54} +1.48581 q^{55} -4.78144i q^{56} +1.54908i q^{57} +5.42637i q^{58} +4.12341 q^{59} -0.868528 q^{60} +9.41605i q^{61} +9.20688i q^{62} -3.08109i q^{63} +8.78078 q^{64} -7.73321i q^{65} +1.20326 q^{66} +1.55409 q^{67} +(0.187161 - 2.38030i) q^{68} +8.07449 q^{69} +2.75457 q^{70} -2.92316i q^{71} +6.09039 q^{72} -4.29526i q^{73} -1.66104i q^{74} +2.81872i q^{75} -0.888676 q^{76} +1.55528 q^{77} -6.26264i q^{78} +12.6164i q^{79} +3.72414i q^{80} +0.867713 q^{81} -13.3178i q^{82} -2.31447 q^{83} -0.909140 q^{84} +(6.10728 + 0.480210i) q^{85} -1.43110 q^{86} +4.59518 q^{87} +3.07432i q^{88} -3.22974 q^{89} +3.50866i q^{90} -8.09481i q^{91} +4.63217i q^{92} +7.79661 q^{93} +13.2890 q^{94} -2.28013i q^{95} -3.19069i q^{96} -12.7015i q^{97} -5.46076 q^{98} +1.98105i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) \) 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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