LMFDB - Embedded newform 1110.2.d.j.889.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(889,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, 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("1110.889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.57815240704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 $ x^8 - 2x^7 + 2x^6 + 89x^4 - 170x^3 + 162x^2 - 72x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			889.7
Root			$2.20793 + 2.20793i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.j.889.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.353624 + 2.20793i) q^{5} -1.00000 q^{6} -3.94848i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.353624 + 2.20793i) q^{5} -1.00000 q^{6} -3.94848i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.20793 - 0.353624i) q^{10} +1.94848 q^{11} -1.00000i q^{12} -2.85431i q^{13} +3.94848 q^{14} +(-2.20793 - 0.353624i) q^{15} +1.00000 q^{16} -7.07158i q^{17} -1.00000i q^{18} -1.74990 q^{19} +(0.353624 - 2.20793i) q^{20} +3.94848 q^{21} +1.94848i q^{22} -4.68466i q^{23} +1.00000 q^{24} +(-4.74990 - 1.56155i) q^{25} +2.85431 q^{26} -1.00000i q^{27} +3.94848i q^{28} +1.32168 q^{29} +(0.353624 - 2.20793i) q^{30} -6.50867 q^{31} +1.00000i q^{32} +1.94848i q^{33} +7.07158 q^{34} +(8.71796 + 1.39628i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -1.74990i q^{38} +2.85431 q^{39} +(2.20793 + 0.353624i) q^{40} +12.6331 q^{41} +3.94848i q^{42} -1.09417i q^{43} -1.94848 q^{44} +(0.353624 - 2.20793i) q^{45} +4.68466 q^{46} -6.70725i q^{47} +1.00000i q^{48} -8.59048 q^{49} +(1.56155 - 4.74990i) q^{50} +7.07158 q^{51} +2.85431i q^{52} +6.94712i q^{53} +1.00000 q^{54} +(-0.689029 + 4.30210i) q^{55} -3.94848 q^{56} -1.74990i q^{57} +1.32168i q^{58} -2.70725 q^{59} +(2.20793 + 0.353624i) q^{60} +3.28252 q^{61} -6.50867i q^{62} +3.94848i q^{63} -1.00000 q^{64} +(6.30210 + 1.00935i) q^{65} -1.94848 q^{66} -1.33192i q^{67} +7.07158i q^{68} +4.68466 q^{69} +(-1.39628 + 8.71796i) q^{70} -15.3302 q^{71} +1.00000i q^{72} +5.08182i q^{73} +1.00000 q^{74} +(1.56155 - 4.74990i) q^{75} +1.74990 q^{76} -7.69353i q^{77} +2.85431i q^{78} +13.1418 q^{79} +(-0.353624 + 2.20793i) q^{80} +1.00000 q^{81} +12.6331i q^{82} +9.62816i q^{83} -3.94848 q^{84} +(15.6136 + 2.50068i) q^{85} +1.09417 q^{86} +1.32168i q^{87} -1.94848i q^{88} -2.02259 q^{89} +(2.20793 + 0.353624i) q^{90} -11.2702 q^{91} +4.68466i q^{92} -6.50867i q^{93} +6.70725 q^{94} +(0.618807 - 3.86366i) q^{95} -1.00000 q^{96} +1.13334i q^{97} -8.59048i q^{98} -1.94848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} - 2 q^{10} - 10 q^{11} + 6 q^{14} - 2 q^{15} + 8 q^{16} + 24 q^{19} + 2 q^{20} + 6 q^{21} + 8 q^{24} + 8 q^{26} - 10 q^{29} + 2 q^{30} - 38 q^{31} - 2 q^{34} + 12 q^{35} + 8 q^{36} + 8 q^{39} + 2 q^{40} + 26 q^{41} + 10 q^{44} + 2 q^{45} - 12 q^{46} - 30 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{54} + 30 q^{55} - 6 q^{56} - 20 q^{59} + 2 q^{60} - 6 q^{61} - 8 q^{64} + 24 q^{65} + 10 q^{66} - 12 q^{69} + 26 q^{70} - 12 q^{71} + 8 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 2 q^{80} + 8 q^{81} - 6 q^{84} + 44 q^{85} - 2 q^{86} - 64 q^{89} + 2 q^{90} - 44 q^{91} + 52 q^{94} - 8 q^{96} + 10 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 - 2 * q^10 - 10 * q^11 + 6 * q^14 - 2 * q^15 + 8 * q^16 + 24 * q^19 + 2 * q^20 + 6 * q^21 + 8 * q^24 + 8 * q^26 - 10 * q^29 + 2 * q^30 - 38 * q^31 - 2 * q^34 + 12 * q^35 + 8 * q^36 + 8 * q^39 + 2 * q^40 + 26 * q^41 + 10 * q^44 + 2 * q^45 - 12 * q^46 - 30 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^54 + 30 * q^55 - 6 * q^56 - 20 * q^59 + 2 * q^60 - 6 * q^61 - 8 * q^64 + 24 * q^65 + 10 * q^66 - 12 * q^69 + 26 * q^70 - 12 * q^71 + 8 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 2 * q^80 + 8 * q^81 - 6 * q^84 + 44 * q^85 - 2 * q^86 - 64 * q^89 + 2 * q^90 - 44 * q^91 + 52 * q^94 - 8 * q^96 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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
$5$	−0.353624	+	2.20793i	−0.158145	+	0.987416i
$5$	−0.353624	+	2.20793i	−0.158145	+	0.987416i
$6$	−1.00000			−0.408248
$7$		−	3.94848i		−	1.49238i	−0.665730	−	0.746192i	$-0.731880\pi$
$7$		−	3.94848i		−	1.49238i	0.665730	−	0.746192i	$-0.268120\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−2.20793	−	0.353624i	−0.698208	−	0.111826i
$11$	1.94848			0.587488			0.293744	−	0.955884i	$-0.405099\pi$
$11$	1.94848			0.587488			0.293744	+	0.955884i	$0.405099\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	2.85431i		−	0.791642i	−0.918328	−	0.395821i	$-0.870460\pi$
$13$		−	2.85431i		−	0.791642i	0.918328	−	0.395821i	$-0.129540\pi$
$14$	3.94848			1.05528
$15$	−2.20793	−	0.353624i	−0.570085	−	0.0913053i
$16$	1.00000			0.250000
$17$		−	7.07158i		−	1.71511i	−0.514391	−	0.857556i	$-0.671982\pi$
$17$		−	7.07158i		−	1.71511i	0.514391	−	0.857556i	$-0.328018\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.74990			−0.401455			−0.200727	−	0.979647i	$-0.564331\pi$
$19$	−1.74990			−0.401455			−0.200727	+	0.979647i	$0.564331\pi$
$20$	0.353624	−	2.20793i	0.0790727	−	0.493708i
$21$	3.94848			0.861629
$22$			1.94848i			0.415417i
$23$		−	4.68466i		−	0.976819i	−0.872615	−	0.488409i	$-0.837577\pi$
$23$		−	4.68466i		−	0.976819i	0.872615	−	0.488409i	$-0.162423\pi$
$24$	1.00000			0.204124
$25$	−4.74990	−	1.56155i	−0.949980	−	0.312311i
$26$	2.85431			0.559775
$27$		−	1.00000i		−	0.192450i
$28$			3.94848i			0.746192i
$29$	1.32168			0.245431			0.122715	−	0.992442i	$-0.460840\pi$
$29$	1.32168			0.245431			0.122715	+	0.992442i	$0.460840\pi$
$30$	0.353624	−	2.20793i	0.0645626	−	0.403111i
$31$	−6.50867			−1.16899			−0.584496	−	0.811397i	$-0.698708\pi$
$31$	−6.50867			−1.16899			−0.584496	+	0.811397i	$0.698708\pi$
$32$			1.00000i			0.176777i
$33$			1.94848i			0.339187i
$34$	7.07158			1.21277
$35$	8.71796	+	1.39628i	1.47360	+	0.236014i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	1.74990i		−	0.283871i
$39$	2.85431			0.457055
$40$	2.20793	+	0.353624i	0.349104	+	0.0559128i
$41$	12.6331			1.97296			0.986482	−	0.163868i	$-0.0523971\pi$
$41$	12.6331			1.97296			0.986482	+	0.163868i	$0.0523971\pi$
$42$			3.94848i			0.609264i
$43$		−	1.09417i		−	0.166860i	−0.996514	−	0.0834300i	$-0.973413\pi$
$43$		−	1.09417i		−	0.166860i	0.996514	−	0.0834300i	$-0.0265875\pi$
$44$	−1.94848			−0.293744
$45$	0.353624	−	2.20793i	0.0527151	−	0.329139i
$46$	4.68466			0.690715
$47$		−	6.70725i		−	0.978353i	−0.872185	−	0.489176i	$-0.837297\pi$
$47$		−	6.70725i		−	0.978353i	0.872185	−	0.489176i	$-0.162703\pi$
$48$			1.00000i			0.144338i
$49$	−8.59048			−1.22721
$50$	1.56155	−	4.74990i	0.220837	−	0.671737i
$51$	7.07158			0.990220
$52$			2.85431i			0.395821i
$53$			6.94712i			0.954260i	0.878833	+	0.477130i	$0.158323\pi$
$53$			6.94712i			0.954260i	−0.878833	+	0.477130i	$0.841677\pi$
$54$	1.00000			0.136083
$55$	−0.689029	+	4.30210i	−0.0929086	+	0.580095i
$56$	−3.94848			−0.527638
$57$		−	1.74990i		−	0.231780i
$58$			1.32168i			0.173546i
$59$	−2.70725			−0.352454			−0.176227	−	0.984350i	$-0.556389\pi$
$59$	−2.70725			−0.352454			−0.176227	+	0.984350i	$0.556389\pi$
$60$	2.20793	+	0.353624i	0.285042	+	0.0456526i
$61$	3.28252			0.420284			0.210142	−	0.977671i	$-0.432607\pi$
$61$	3.28252			0.420284			0.210142	+	0.977671i	$0.432607\pi$
$62$		−	6.50867i		−	0.826602i
$63$			3.94848i			0.497462i
$64$	−1.00000			−0.125000
$65$	6.30210	+	1.00935i	0.781680	+	0.125195i
$66$	−1.94848			−0.239841
$67$		−	1.33192i		−	0.162719i	−0.996685	−	0.0813597i	$-0.974074\pi$
$67$		−	1.33192i		−	0.162719i	0.996685	−	0.0813597i	$-0.0259262\pi$
$68$			7.07158i			0.857556i
$69$	4.68466			0.563967
$70$	−1.39628	+	8.71796i	−0.166887	+	1.04200i
$71$	−15.3302			−1.81935			−0.909677	−	0.415316i	$-0.863671\pi$
$71$	−15.3302			−1.81935			−0.909677	+	0.415316i	$0.863671\pi$
$72$			1.00000i			0.117851i
$73$			5.08182i			0.594782i	0.954756	+	0.297391i	$0.0961164\pi$
$73$			5.08182i			0.594782i	−0.954756	+	0.297391i	$0.903884\pi$
$74$	1.00000			0.116248
$75$	1.56155	−	4.74990i	0.180313	−	0.548471i
$76$	1.74990			0.200727
$77$		−	7.69353i		−	0.876759i
$78$			2.85431i			0.323186i
$79$	13.1418			1.47857			0.739284	−	0.673393i	$-0.235164\pi$
$79$	13.1418			1.47857			0.739284	+	0.673393i	$0.235164\pi$
$80$	−0.353624	+	2.20793i	−0.0395364	+	0.246854i
$81$	1.00000			0.111111
$82$			12.6331i			1.39510i
$83$			9.62816i			1.05683i	0.848987	+	0.528414i	$0.177213\pi$
$83$			9.62816i			1.05683i	−0.848987	+	0.528414i	$0.822787\pi$
$84$	−3.94848			−0.430814
$85$	15.6136	+	2.50068i	1.69353	+	0.271237i
$86$	1.09417			0.117988
$87$			1.32168i			0.141699i
$88$		−	1.94848i		−	0.207709i
$89$	−2.02259			−0.214394			−0.107197	−	0.994238i	$-0.534188\pi$
$89$	−2.02259			−0.214394			−0.107197	+	0.994238i	$0.534188\pi$
$90$	2.20793	+	0.353624i	0.232736	+	0.0372752i
$91$	−11.2702			−1.18143
$92$			4.68466i			0.488409i
$93$		−	6.50867i		−	0.674918i
$94$	6.70725			0.691800
$95$	0.618807	−	3.86366i	0.0634882	−	0.396403i
$96$	−1.00000			−0.102062
$97$			1.13334i			0.115073i	0.998343	+	0.0575365i	$0.0183245\pi$
$97$			1.13334i			0.115073i	−0.998343	+	0.0575365i	$0.981675\pi$
$98$		−	8.59048i		−	0.867770i
$99$	−1.94848			−0.195829
$100$	4.74990	+	1.56155i	0.474990	+	0.156155i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$			7.07158i			0.700191i
$103$		−	1.93612i		−	0.190772i	−0.995440	−	0.0953858i	$-0.969592\pi$
$103$		−	1.93612i		−	0.190772i	0.995440	−	0.0953858i	$-0.0304085\pi$
$104$	−2.85431			−0.279888
$105$	−1.39628	+	8.71796i	−0.136263	+	0.850786i
$106$	−6.94712			−0.674764
$107$			1.39191i			0.134561i	0.997734	+	0.0672803i	$0.0214322\pi$
$107$			1.39191i			0.134561i	−0.997734	+	0.0672803i	$0.978568\pi$
$108$			1.00000i			0.0962250i
$109$	−3.28039			−0.314205			−0.157102	−	0.987582i	$-0.550215\pi$
$109$	−3.28039			−0.314205			−0.157102	+	0.987582i	$0.550215\pi$
$110$	−4.30210	−	0.689029i	−0.410189	−	0.0656963i
$111$	1.00000			0.0949158
$112$		−	3.94848i		−	0.373096i
$113$		−	7.52873i		−	0.708244i	−0.935199	−	0.354122i	$-0.884780\pi$
$113$		−	7.52873i		−	0.708244i	0.935199	−	0.354122i	$-0.115220\pi$
$114$	1.74990			0.163893
$115$	10.3434	+	1.65661i	0.964526	+	0.154479i
$116$	−1.32168			−0.122715
$117$			2.85431i			0.263881i
$118$		−	2.70725i		−	0.249222i
$119$	−27.9220			−2.55961
$120$	−0.353624	+	2.20793i	−0.0322813	+	0.201555i
$121$	−7.20343			−0.654857
$122$			3.28252i			0.297186i
$123$			12.6331i			1.13909i
$124$	6.50867			0.584496
$125$	5.12748	−	9.93524i	0.458615	−	0.888635i
$126$	−3.94848			−0.351758
$127$		−	13.1457i		−	1.16649i	−0.812296	−	0.583246i	$-0.801782\pi$
$127$		−	13.1457i		−	1.16649i	0.812296	−	0.583246i	$-0.198218\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.09417			0.0963366
$130$	−1.00935	+	6.30210i	−0.0885259	+	0.552731i
$131$	21.6821			1.89438			0.947188	−	0.320678i	$-0.103911\pi$
$131$	21.6821			1.89438			0.947188	+	0.320678i	$0.103911\pi$
$132$		−	1.94848i		−	0.169593i
$133$			6.90944i			0.599125i
$134$	1.33192			0.115060
$135$	2.20793	+	0.353624i	0.190028	+	0.0304351i
$136$	−7.07158			−0.606383
$137$		−	18.2098i		−	1.55577i	−0.628409	−	0.777883i	$-0.716294\pi$
$137$		−	18.2098i		−	1.55577i	0.628409	−	0.777883i	$-0.283706\pi$
$138$			4.68466i			0.398785i
$139$	−6.11151			−0.518372			−0.259186	−	0.965827i	$-0.583454\pi$
$139$	−6.11151			−0.518372			−0.259186	+	0.965827i	$0.583454\pi$
$140$	−8.71796	−	1.39628i	−0.736802	−	0.118007i
$141$	6.70725			0.564852
$142$		−	15.3302i		−	1.28648i
$143$		−	5.56155i		−	0.465080i
$144$	−1.00000			−0.0833333
$145$	−0.467379	+	2.91818i	−0.0388137	+	0.242342i
$146$	−5.08182			−0.420574
$147$		−	8.59048i		−	0.708531i
$148$			1.00000i			0.0821995i
$149$	20.5199			1.68105			0.840526	−	0.541771i	$-0.182246\pi$
$149$	20.5199			1.68105			0.840526	+	0.541771i	$0.182246\pi$
$150$	4.74990	+	1.56155i	0.387828	+	0.127500i
$151$	−10.2688			−0.835663			−0.417832	−	0.908525i	$-0.637210\pi$
$151$	−10.2688			−0.835663			−0.417832	+	0.908525i	$0.637210\pi$
$152$			1.74990i			0.141936i
$153$			7.07158i			0.571704i
$154$	7.69353			0.619962
$155$	2.30162	−	14.3707i	0.184871	−	1.15428i
$156$	−2.85431			−0.228527
$157$			5.73754i			0.457906i	0.973438	+	0.228953i	$0.0735302\pi$
$157$			5.73754i			0.457906i	−0.973438	+	0.228953i	$0.926470\pi$
$158$			13.1418i			1.04551i
$159$	−6.94712			−0.550942
$160$	−2.20793	−	0.353624i	−0.174552	−	0.0279564i
$161$	−18.4973			−1.45779
$162$			1.00000i			0.0785674i
$163$		−	15.8641i		−	1.24258i	−0.783583	−	0.621288i	$-0.786610\pi$
$163$		−	15.8641i		−	1.24258i	0.783583	−	0.621288i	$-0.213390\pi$
$164$	−12.6331			−0.986482
$165$	−4.30210	−	0.689029i	−0.334918	−	0.0536408i
$166$	−9.62816			−0.747290
$167$		−	19.1671i		−	1.48320i	−0.670844	−	0.741598i	$-0.734068\pi$
$167$		−	19.1671i		−	1.48320i	0.670844	−	0.741598i	$-0.265932\pi$
$168$		−	3.94848i		−	0.304632i
$169$	4.85294			0.373303
$170$	−2.50068	+	15.6136i	−0.191793	+	1.19751i
$171$	1.74990			0.133818
$172$			1.09417i			0.0834300i
$173$			16.1555i			1.22828i	0.789196	+	0.614141i	$0.210497\pi$
$173$			16.1555i			1.22828i	−0.789196	+	0.614141i	$0.789503\pi$
$174$	−1.32168			−0.100197
$175$	−6.16576	+	18.7549i	−0.466088	+	1.41774i
$176$	1.94848			0.146872
$177$		−	2.70725i		−	0.203489i
$178$		−	2.02259i		−	0.151599i
$179$	7.12583			0.532610			0.266305	−	0.963889i	$-0.414197\pi$
$179$	7.12583			0.532610			0.266305	+	0.963889i	$0.414197\pi$
$180$	−0.353624	+	2.20793i	−0.0263576	+	0.164569i
$181$	−22.5795			−1.67832			−0.839160	−	0.543884i	$-0.816953\pi$
$181$	−22.5795			−1.67832			−0.839160	+	0.543884i	$0.816953\pi$
$182$		−	11.2702i		−	0.835400i
$183$			3.28252i			0.242651i
$184$	−4.68466			−0.345358
$185$	2.20793	+	0.353624i	0.162330	+	0.0259989i
$186$	6.50867			0.477239
$187$		−	13.7788i		−	1.00761i
$188$			6.70725i			0.489176i
$189$	−3.94848			−0.287210
$190$	3.86366	+	0.618807i	0.280299	+	0.0448929i
$191$	−17.6758			−1.27898			−0.639488	−	0.768801i	$-0.720853\pi$
$191$	−17.6758			−1.27898			−0.639488	+	0.768801i	$0.720853\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			4.62291i			0.332764i	0.986061	+	0.166382i	$0.0532085\pi$
$193$			4.62291i			0.332764i	−0.986061	+	0.166382i	$0.946792\pi$
$194$	−1.13334			−0.0813688
$195$	−1.00935	+	6.30210i	−0.0722811	+	0.451303i
$196$	8.59048			0.613606
$197$		−	0.0617522i		−	0.00439966i	−0.999998	−	0.00219983i	$-0.999300\pi$
$197$		−	0.0617522i		−	0.00439966i	0.999998	−	0.00219983i	$-0.000700229\pi$
$198$		−	1.94848i		−	0.138472i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−1.56155	+	4.74990i	−0.110418	+	0.335869i
$201$	1.33192			0.0939460
$202$			2.00000i			0.140720i
$203$		−	5.21864i		−	0.366277i
$204$	−7.07158			−0.495110
$205$	−4.46738	+	27.8931i	−0.312015	+	1.94814i
$206$	1.93612			0.134896
$207$			4.68466i			0.325606i
$208$		−	2.85431i		−	0.197910i
$209$	−3.40964			−0.235850
$210$	−8.71796	−	1.39628i	−0.601596	−	0.0963522i
$211$	4.28388			0.294915			0.147457	−	0.989068i	$-0.452891\pi$
$211$	4.28388			0.294915			0.147457	+	0.989068i	$0.452891\pi$
$212$		−	6.94712i		−	0.477130i
$213$		−	15.3302i		−	1.05040i
$214$	−1.39191			−0.0951487
$215$	2.41586	+	0.386926i	0.164760	+	0.0263881i
$216$	−1.00000			−0.0680414
$217$			25.6993i			1.74459i
$218$		−	3.28039i		−	0.222176i
$219$	−5.08182			−0.343397
$220$	0.689029	−	4.30210i	0.0464543	−	0.290048i
$221$	−20.1845			−1.35775
$222$			1.00000i			0.0671156i
$223$			9.67968i			0.648199i	0.946023	+	0.324100i	$0.105061\pi$
$223$			9.67968i			0.648199i	−0.946023	+	0.324100i	$0.894939\pi$
$224$	3.94848			0.263819
$225$	4.74990	+	1.56155i	0.316660	+	0.104104i
$226$	7.52873			0.500804
$227$		−	24.8429i		−	1.64888i	−0.565948	−	0.824441i	$-0.691490\pi$
$227$		−	24.8429i		−	1.64888i	0.565948	−	0.824441i	$-0.308510\pi$
$228$			1.74990i			0.115890i
$229$	−5.29275			−0.349755			−0.174877	−	0.984590i	$-0.555953\pi$
$229$	−5.29275			−0.349755			−0.174877	+	0.984590i	$0.555953\pi$
$230$	−1.65661	+	10.3434i	−0.109233	+	0.682023i
$231$	7.69353			0.506197
$232$		−	1.32168i		−	0.0867728i
$233$			17.7665i			1.16392i	0.813217	+	0.581960i	$0.197714\pi$
$233$			17.7665i			1.16392i	−0.813217	+	0.581960i	$0.802286\pi$
$234$	−2.85431			−0.186592
$235$	14.8091	+	2.37184i	0.966041	+	0.154722i
$236$	2.70725			0.176227
$237$			13.1418i			0.853652i
$238$		−	27.9220i		−	1.80991i
$239$	16.6970			1.08004			0.540020	−	0.841652i	$-0.318417\pi$
$239$	16.6970			1.08004			0.540020	+	0.841652i	$0.318417\pi$
$240$	−2.20793	−	0.353624i	−0.142521	−	0.0228263i
$241$	8.85042			0.570105			0.285053	−	0.958512i	$-0.407989\pi$
$241$	8.85042			0.570105			0.285053	+	0.958512i	$0.407989\pi$
$242$		−	7.20343i		−	0.463054i
$243$			1.00000i			0.0641500i
$244$	−3.28252			−0.210142
$245$	3.03780	−	18.9672i	0.194078	−	1.21177i
$246$	−12.6331			−0.805459
$247$			4.99475i			0.317808i
$248$			6.50867i			0.413301i
$249$	−9.62816			−0.610160
$250$	9.93524	+	5.12748i	0.628360	+	0.324290i
$251$	2.19107			0.138299			0.0691496	−	0.997606i	$-0.477971\pi$
$251$	2.19107			0.138299			0.0691496	+	0.997606i	$0.477971\pi$
$252$		−	3.94848i		−	0.248731i
$253$		−	9.12796i		−	0.573870i
$254$	13.1457			0.824834
$255$	−2.50068	+	15.6136i	−0.156599	+	0.977759i
$256$	1.00000			0.0625000
$257$			25.3742i			1.58280i	0.611300	+	0.791399i	$0.290647\pi$
$257$			25.3742i			1.58280i	−0.611300	+	0.791399i	$0.709353\pi$
$258$			1.09417i			0.0681203i
$259$	−3.94848			−0.245347
$260$	−6.30210	−	1.00935i	−0.390840	−	0.0625973i
$261$	−1.32168			−0.0818102
$262$			21.6821i			1.33953i
$263$		−	6.34175i		−	0.391049i	−0.980699	−	0.195524i	$-0.937359\pi$
$263$		−	6.34175i		−	0.391049i	0.980699	−	0.195524i	$-0.0626409\pi$
$264$	1.94848			0.119921
$265$	−15.3387	−	2.45667i	−0.942251	−	0.150912i
$266$	−6.90944			−0.423645
$267$		−	2.02259i		−	0.123780i
$268$			1.33192i			0.0813597i
$269$	−14.2875			−0.871124			−0.435562	−	0.900159i	$-0.643450\pi$
$269$	−14.2875			−0.871124			−0.435562	+	0.900159i	$0.643450\pi$
$270$	−0.353624	+	2.20793i	−0.0215209	+	0.134370i
$271$	−14.0606			−0.854120			−0.427060	−	0.904223i	$-0.640451\pi$
$271$	−14.0606			−0.854120			−0.427060	+	0.904223i	$0.640451\pi$
$272$		−	7.07158i		−	0.428778i
$273$		−	11.2702i		−	0.682101i
$274$	18.2098			1.10009
$275$	−9.25508	−	3.04265i	−0.558102	−	0.183479i
$276$	−4.68466			−0.281983
$277$		−	2.85431i		−	0.171499i	−0.996317	−	0.0857493i	$-0.972672\pi$
$277$		−	2.85431i		−	0.171499i	0.996317	−	0.0857493i	$-0.0273284\pi$
$278$		−	6.11151i		−	0.366544i
$279$	6.50867			0.389664
$280$	1.39628	−	8.71796i	0.0834435	−	0.520998i
$281$	−4.58338			−0.273421			−0.136711	−	0.990611i	$-0.543653\pi$
$281$	−4.58338			−0.273421			−0.136711	+	0.990611i	$0.543653\pi$
$282$			6.70725i			0.399411i
$283$		−	6.55417i		−	0.389605i	−0.980842	−	0.194803i	$-0.937593\pi$
$283$		−	6.55417i		−	0.389605i	0.980842	−	0.194803i	$-0.0624066\pi$
$284$	15.3302			0.909677
$285$	3.86366	+	0.618807i	0.228863	+	0.0366549i
$286$	5.56155			0.328862
$287$		−	49.8817i		−	2.94442i
$288$		−	1.00000i		−	0.0589256i
$289$	−33.0073			−1.94161
$290$	−2.91818	−	0.467379i	−0.171362	−	0.0274454i
$291$	−1.13334			−0.0664374
$292$		−	5.08182i		−	0.297391i
$293$		−	26.6133i		−	1.55476i	−0.629029	−	0.777382i	$-0.716547\pi$
$293$		−	26.6133i		−	1.55476i	0.629029	−	0.777382i	$-0.283453\pi$
$294$	8.59048			0.501007
$295$	0.957347	−	5.97741i	0.0557389	−	0.348018i
$296$	−1.00000			−0.0581238
$297$		−	1.94848i		−	0.113062i
$298$			20.5199i			1.18868i
$299$	−13.3714			−0.773291
$300$	−1.56155	+	4.74990i	−0.0901563	+	0.274236i
$301$	−4.32032			−0.249019
$302$		−	10.2688i		−	0.590903i
$303$			2.00000i			0.114897i
$304$	−1.74990			−0.100364
$305$	−1.16078	+	7.24757i	−0.0664659	+	0.414995i
$306$	−7.07158			−0.404256
$307$		−	4.68679i		−	0.267489i	−0.991016	−	0.133744i	$-0.957300\pi$
$307$		−	4.68679i		−	0.267489i	0.991016	−	0.133744i	$-0.0427001\pi$
$308$			7.69353i			0.438379i
$309$	1.93612			0.110142
$310$	14.3707	+	2.30162i	0.816200	+	0.130723i
$311$	10.8480			0.615132			0.307566	−	0.951527i	$-0.400486\pi$
$311$	10.8480			0.615132			0.307566	+	0.951527i	$0.400486\pi$
$312$		−	2.85431i		−	0.161593i
$313$			26.2197i			1.48203i	0.671490	+	0.741013i	$0.265655\pi$
$313$			26.2197i			1.48203i	−0.671490	+	0.741013i	$0.734345\pi$
$314$	−5.73754			−0.323788
$315$	−8.71796	−	1.39628i	−0.491201	−	0.0786713i
$316$	−13.1418			−0.739284
$317$			25.1922i			1.41493i	0.706747	+	0.707466i	$0.250162\pi$
$317$			25.1922i			1.41493i	−0.706747	+	0.707466i	$0.749838\pi$
$318$		−	6.94712i		−	0.389575i
$319$	2.57527			0.144188
$320$	0.353624	−	2.20793i	0.0197682	−	0.123427i
$321$	−1.39191			−0.0776886
$322$		−	18.4973i		−	1.03081i
$323$			12.3746i			0.688539i
$324$	−1.00000			−0.0555556
$325$	−4.45715	+	13.5577i	−0.247238	+	0.752044i
$326$	15.8641			0.878633
$327$		−	3.28039i		−	0.181406i
$328$		−	12.6331i		−	0.697548i
$329$	−26.4834			−1.46008
$330$	0.689029	−	4.30210i	0.0379298	−	0.236823i
$331$	6.45502			0.354800			0.177400	−	0.984139i	$-0.443231\pi$
$331$	6.45502			0.354800			0.177400	+	0.984139i	$0.443231\pi$
$332$		−	9.62816i		−	0.528414i
$333$			1.00000i			0.0547997i
$334$	19.1671			1.04878
$335$	2.94077	+	0.470997i	0.160672	+	0.0257333i
$336$	3.94848			0.215407
$337$		−	22.3149i		−	1.21557i	−0.794101	−	0.607786i	$-0.792058\pi$
$337$		−	22.3149i		−	1.21557i	0.794101	−	0.607786i	$-0.207942\pi$
$338$			4.85294i			0.263965i
$339$	7.52873			0.408905
$340$	−15.6136	−	2.50068i	−0.846764	−	0.135618i
$341$	−12.6820			−0.686769
$342$			1.74990i			0.0946238i
$343$			6.28000i			0.339088i
$344$	−1.09417			−0.0589939
$345$	−1.65661	+	10.3434i	−0.0891887	+	0.556870i
$346$	−16.1555			−0.868527
$347$			1.82039i			0.0977238i	0.998806	+	0.0488619i	$0.0155594\pi$
$347$			1.82039i			0.0977238i	−0.998806	+	0.0488619i	$0.984441\pi$
$348$		−	1.32168i		−	0.0708497i
$349$	−28.6443			−1.53330			−0.766648	−	0.642068i	$-0.778077\pi$
$349$	−28.6443			−1.53330			−0.766648	+	0.642068i	$0.778077\pi$
$350$	−18.7549	−	6.16576i	−1.00249	−	0.329574i
$351$	−2.85431			−0.152352
$352$			1.94848i			0.103854i
$353$			25.6924i			1.36747i	0.729732	+	0.683733i	$0.239645\pi$
$353$			25.6924i			1.36747i	−0.729732	+	0.683733i	$0.760355\pi$
$354$	2.70725			0.143889
$355$	5.42111	−	33.8479i	0.287723	−	1.79646i
$356$	2.02259			0.107197
$357$		−	27.9220i		−	1.47779i
$358$			7.12583i			0.376612i
$359$	−8.62467			−0.455193			−0.227596	−	0.973756i	$-0.573087\pi$
$359$	−8.62467			−0.455193			−0.227596	+	0.973756i	$0.573087\pi$
$360$	−2.20793	−	0.353624i	−0.116368	−	0.0186376i
$361$	−15.9378			−0.838834
$362$		−	22.5795i		−	1.18675i
$363$		−	7.20343i		−	0.378082i
$364$	11.2702			0.590717
$365$	−11.2203	−	1.79705i	−0.587297	−	0.0940620i
$366$	−3.28252			−0.171580
$367$		−	10.9890i		−	0.573621i	−0.957987	−	0.286811i	$-0.907405\pi$
$367$		−	10.9890i		−	0.573621i	0.957987	−	0.286811i	$-0.0925951\pi$
$368$		−	4.68466i		−	0.244205i
$369$	−12.6331			−0.657655
$370$	−0.353624	+	2.20793i	−0.0183840	+	0.114785i
$371$	27.4305			1.42412
$372$			6.50867i			0.337459i
$373$		−	20.8052i		−	1.07725i	−0.842544	−	0.538627i	$-0.818943\pi$
$373$		−	20.8052i		−	1.07725i	0.842544	−	0.538627i	$-0.181057\pi$
$374$	13.7788			0.712486
$375$	9.93524	+	5.12748i	0.513054	+	0.264782i
$376$	−6.70725			−0.345900
$377$		−	3.77249i		−	0.194293i
$378$		−	3.94848i		−	0.203088i
$379$	36.0136			1.84990			0.924948	−	0.380093i	$-0.124108\pi$
$379$	36.0136			1.84990			0.924948	+	0.380093i	$0.124108\pi$
$380$	−0.618807	+	3.86366i	−0.0317441	+	0.198201i
$381$	13.1457			0.673474
$382$		−	17.6758i		−	0.904372i
$383$		−	13.6441i		−	0.697183i	−0.937275	−	0.348591i	$-0.886660\pi$
$383$		−	13.6441i		−	0.697183i	0.937275	−	0.348591i	$-0.113340\pi$
$384$	1.00000			0.0510310
$385$	16.9868	+	2.72061i	0.865726	+	0.138655i
$386$	−4.62291			−0.235300
$387$			1.09417i			0.0556200i
$388$		−	1.13334i		−	0.0575365i
$389$	33.5661			1.70187			0.850935	−	0.525271i	$-0.176036\pi$
$389$	33.5661			1.70187			0.850935	+	0.525271i	$0.176036\pi$
$390$	−6.30210	−	1.00935i	−0.319119	−	0.0511104i
$391$	−33.1280			−1.67535
$392$			8.59048i			0.433885i
$393$			21.6821i			1.09372i
$394$	0.0617522			0.00311103
$395$	−4.64726	+	29.0162i	−0.233829	+	1.45996i
$396$	1.94848			0.0979147
$397$			30.4472i			1.52810i	0.645155	+	0.764052i	$0.276793\pi$
$397$			30.4472i			1.52810i	−0.645155	+	0.764052i	$0.723207\pi$
$398$			8.00000i			0.401004i
$399$	−6.90944			−0.345905
$400$	−4.74990	−	1.56155i	−0.237495	−	0.0780776i
$401$	35.3263			1.76411			0.882055	−	0.471147i	$-0.156160\pi$
$401$	35.3263			1.76411			0.882055	+	0.471147i	$0.156160\pi$
$402$			1.33192i			0.0664299i
$403$			18.5777i			0.925423i
$404$	−2.00000			−0.0995037
$405$	−0.353624	+	2.20793i	−0.0175717	+	0.109713i
$406$	5.21864			0.258997
$407$		−	1.94848i		−	0.0965825i
$408$		−	7.07158i		−	0.350096i
$409$	−9.54169			−0.471806			−0.235903	−	0.971777i	$-0.575805\pi$
$409$	−9.54169			−0.471806			−0.235903	+	0.971777i	$0.575805\pi$
$410$	−27.8931	−	4.46738i	−1.37754	−	0.220628i
$411$	18.2098			0.898222
$412$			1.93612i			0.0953858i
$413$			10.6895i			0.525996i
$414$	−4.68466			−0.230238
$415$	−21.2583	−	3.40475i	−1.04353	−	0.167132i
$416$	2.85431			0.139944
$417$		−	6.11151i		−	0.299282i
$418$		−	3.40964i		−	0.166771i
$419$	−22.9149			−1.11947			−0.559733	−	0.828673i	$-0.689096\pi$
$419$	−22.9149			−1.11947			−0.559733	+	0.828673i	$0.689096\pi$
$420$	1.39628	−	8.71796i	0.0681313	−	0.425393i
$421$	22.0197			1.07317			0.536586	−	0.843845i	$-0.319714\pi$
$421$	22.0197			1.07317			0.536586	+	0.843845i	$0.319714\pi$
$422$			4.28388i			0.208536i
$423$			6.70725i			0.326118i
$424$	6.94712			0.337382
$425$	−11.0427	+	33.5893i	−0.535647	+	1.62932i
$426$	15.3302			0.742748
$427$		−	12.9610i		−	0.627225i
$428$		−	1.39191i		−	0.0672803i
$429$	5.56155			0.268514
$430$	−0.386926	+	2.41586i	−0.0186592	+	0.116503i
$431$	32.1957			1.55081			0.775405	−	0.631464i	$-0.217546\pi$
$431$	32.1957			1.55081			0.775405	+	0.631464i	$0.217546\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	7.27016i		−	0.349382i	−0.984623	−	0.174691i	$-0.944107\pi$
$433$		−	7.27016i		−	0.349382i	0.984623	−	0.174691i	$-0.0558926\pi$
$434$	−25.6993			−1.23361
$435$	−2.91818	−	0.467379i	−0.139916	−	0.0224091i
$436$	3.28039			0.157102
$437$			8.19769i			0.392148i
$438$		−	5.08182i		−	0.242819i
$439$	26.9647			1.28695			0.643476	−	0.765466i	$-0.277491\pi$
$439$	26.9647			1.28695			0.643476	+	0.765466i	$0.277491\pi$
$440$	4.30210	+	0.689029i	0.205095	+	0.0328482i
$441$	8.59048			0.409071
$442$		−	20.1845i		−	0.960077i
$443$			26.1806i			1.24388i	0.783066	+	0.621938i	$0.213655\pi$
$443$			26.1806i			1.24388i	−0.783066	+	0.621938i	$0.786345\pi$
$444$	−1.00000			−0.0474579
$445$	0.715236	−	4.46573i	0.0339054	−	0.211696i
$446$	−9.67968			−0.458346
$447$			20.5199i			0.970556i
$448$			3.94848i			0.186548i
$449$	41.8892			1.97687			0.988436	−	0.151636i	$-0.0484543\pi$
$449$	41.8892			1.97687			0.988436	+	0.151636i	$0.0484543\pi$
$450$	−1.56155	+	4.74990i	−0.0736123	+	0.223912i
$451$	24.6154			1.15909
$452$			7.52873i			0.354122i
$453$		−	10.2688i		−	0.482470i
$454$	24.8429			1.16594
$455$	3.98540	−	24.8837i	0.186838	−	1.16657i
$456$	−1.74990			−0.0819466
$457$			29.9082i			1.39904i	0.714611	+	0.699522i	$0.246604\pi$
$457$			29.9082i			1.39904i	−0.714611	+	0.699522i	$0.753396\pi$
$458$		−	5.29275i		−	0.247314i
$459$	−7.07158			−0.330073
$460$	−10.3434	−	1.65661i	−0.482263	−	0.0772397i
$461$	−2.90583			−0.135338			−0.0676689	−	0.997708i	$-0.521556\pi$
$461$	−2.90583			−0.135338			−0.0676689	+	0.997708i	$0.521556\pi$
$462$			7.69353i			0.357935i
$463$			37.2750i			1.73232i	0.499770	+	0.866158i	$0.333418\pi$
$463$			37.2750i			1.73232i	−0.499770	+	0.866158i	$0.666582\pi$
$464$	1.32168			0.0613576
$465$	14.3707	+	2.30162i	0.666424	+	0.106735i
$466$	−17.7665			−0.823016
$467$			38.3240i			1.77342i	0.462323	+	0.886712i	$0.347016\pi$
$467$			38.3240i			1.77342i	−0.462323	+	0.886712i	$0.652984\pi$
$468$		−	2.85431i		−	0.131940i
$469$	−5.25904			−0.242840
$470$	−2.37184	+	14.8091i	−0.109405	+	0.683094i
$471$	−5.73754			−0.264372
$472$			2.70725i			0.124611i
$473$		−	2.13197i		−	0.0980283i
$474$	−13.1418			−0.603623
$475$	8.31185	+	2.73256i	0.381374	+	0.125379i
$476$	27.9220			1.27980
$477$		−	6.94712i		−	0.318087i
$478$			16.6970i			0.763704i
$479$	−34.6874			−1.58491			−0.792453	−	0.609932i	$-0.791197\pi$
$479$	−34.6874			−1.58491			−0.792453	+	0.609932i	$0.791197\pi$
$480$	0.353624	−	2.20793i	0.0161406	−	0.100778i
$481$	−2.85431			−0.130145
$482$			8.85042i			0.403125i
$483$		−	18.4973i		−	0.841655i
$484$	7.20343			0.327429
$485$	−2.50233	−	0.400775i	−0.113625	−	0.0181983i
$486$	−1.00000			−0.0453609
$487$		−	13.9575i		−	0.632477i	−0.948680	−	0.316238i	$-0.897580\pi$
$487$		−	13.9575i		−	0.632477i	0.948680	−	0.316238i	$-0.102420\pi$
$488$		−	3.28252i		−	0.148593i
$489$	15.8641			0.717401
$490$	18.9672	+	3.03780i	0.856850	+	0.137234i
$491$	−6.54245			−0.295257			−0.147628	−	0.989043i	$-0.547164\pi$
$491$	−6.54245			−0.295257			−0.147628	+	0.989043i	$0.547164\pi$
$492$		−	12.6331i		−	0.569546i
$493$		−	9.34640i		−	0.420941i
$494$	−4.99475			−0.224724
$495$	0.689029	−	4.30210i	0.0309695	−	0.193365i
$496$	−6.50867			−0.292248
$497$			60.5308i			2.71518i
$498$		−	9.62816i		−	0.431448i
$499$	35.0668			1.56981			0.784903	−	0.619619i	$-0.212713\pi$
$499$	35.0668			1.56981			0.784903	+	0.619619i	$0.212713\pi$
$500$	−5.12748	+	9.93524i	−0.229308	+	0.444317i
$501$	19.1671			0.856324
$502$			2.19107i			0.0977923i
$503$			11.7637i			0.524520i	0.964997	+	0.262260i	$0.0844677\pi$
$503$			11.7637i			0.524520i	−0.964997	+	0.262260i	$0.915532\pi$
$504$	3.94848			0.175879
$505$	−0.707248	+	4.41586i	−0.0314721	+	0.196503i
$506$	9.12796			0.405787
$507$			4.85294i			0.215527i
$508$			13.1457i			0.583246i
$509$	−9.43532			−0.418213			−0.209107	−	0.977893i	$-0.567056\pi$
$509$	−9.43532			−0.418213			−0.209107	+	0.977893i	$0.567056\pi$
$510$	−15.6136	−	2.50068i	−0.691380	−	0.110732i
$511$	20.0654			0.887643
$512$			1.00000i			0.0441942i
$513$			1.74990i			0.0772600i
$514$	−25.3742			−1.11921
$515$	4.27482	+	0.684658i	0.188371	+	0.0301697i
$516$	−1.09417			−0.0481683
$517$		−	13.0689i		−	0.574771i
$518$		−	3.94848i		−	0.173486i
$519$	−16.1555			−0.709149
$520$	1.00935	−	6.30210i	0.0442629	−	0.276365i
$521$	30.8998			1.35375			0.676873	−	0.736100i	$-0.263335\pi$
$521$	30.8998			1.35375			0.676873	+	0.736100i	$0.263335\pi$
$522$		−	1.32168i		−	0.0578485i
$523$			25.3748i			1.10956i	0.831997	+	0.554781i	$0.187198\pi$
$523$			25.3748i			1.10956i	−0.831997	+	0.554781i	$0.812802\pi$
$524$	−21.6821			−0.947188
$525$	−18.7549	−	6.16576i	−0.818530	−	0.269096i
$526$	6.34175			0.276513
$527$			46.0266i			2.00495i
$528$			1.94848i			0.0847967i
$529$	1.05398			0.0458250
$530$	2.45667	−	15.3387i	0.106711	−	0.666272i
$531$	2.70725			0.117485
$532$		−	6.90944i		−	0.299562i
$533$		−	36.0588i		−	1.56188i
$534$	2.02259			0.0875260
$535$	−3.07323	−	0.492211i	−0.132867	−	0.0212801i
$536$	−1.33192			−0.0575300
$537$			7.12583i			0.307502i
$538$		−	14.2875i		−	0.615978i
$539$	−16.7384			−0.720973
$540$	−2.20793	−	0.353624i	−0.0950141	−	0.0152175i
$541$	29.6782			1.27597			0.637984	−	0.770050i	$-0.279769\pi$
$541$	29.6782			1.27597			0.637984	+	0.770050i	$0.279769\pi$
$542$		−	14.0606i		−	0.603954i
$543$		−	22.5795i		−	0.968979i
$544$	7.07158			0.303192
$545$	1.16003	−	7.24288i	0.0496900	−	0.310251i
$546$	11.2702			0.482318
$547$		−	7.59048i		−	0.324546i	−0.986746	−	0.162273i	$-0.948118\pi$
$547$		−	7.59048i		−	0.324546i	0.986746	−	0.162273i	$-0.0518825\pi$
$548$			18.2098i			0.777883i
$549$	−3.28252			−0.140095
$550$	3.04265	−	9.25508i	0.129739	−	0.394638i
$551$	−2.31282			−0.0985292
$552$		−	4.68466i		−	0.199392i
$553$		−	51.8901i		−	2.20659i
$554$	2.85431			0.121268
$555$	−0.353624	+	2.20793i	−0.0150105	+	0.0937214i
$556$	6.11151			0.259186
$557$		−	9.72731i		−	0.412159i	−0.978535	−	0.206080i	$-0.933929\pi$
$557$		−	9.72731i		−	0.412159i	0.978535	−	0.206080i	$-0.0660706\pi$
$558$			6.50867i			0.275534i
$559$	−3.12311			−0.132093
$560$	8.71796	+	1.39628i	0.368401	+	0.0590034i
$561$	13.7788			0.581743
$562$		−	4.58338i		−	0.193338i
$563$		−	30.1836i		−	1.27209i	−0.771654	−	0.636043i	$-0.780570\pi$
$563$		−	30.1836i		−	1.27209i	0.771654	−	0.636043i	$-0.219430\pi$
$564$	−6.70725			−0.282426
$565$	16.6229	+	2.66234i	0.699331	+	0.112005i
$566$	6.55417			0.275493
$567$		−	3.94848i		−	0.165821i
$568$			15.3302i			0.643239i
$569$	11.2437			0.471360			0.235680	−	0.971831i	$-0.424268\pi$
$569$	11.2437			0.471360			0.235680	+	0.971831i	$0.424268\pi$
$570$	−0.618807	+	3.86366i	−0.0259190	+	0.161831i
$571$	−33.7936			−1.41422			−0.707110	−	0.707104i	$-0.750001\pi$
$571$	−33.7936			−1.41422			−0.707110	+	0.707104i	$0.750001\pi$
$572$			5.56155i			0.232540i
$573$		−	17.6758i		−	0.738417i
$574$	49.8817			2.08202
$575$	−7.31534	+	22.2517i	−0.305071	+	0.927958i
$576$	1.00000			0.0416667
$577$		−	8.37942i		−	0.348840i	−0.984671	−	0.174420i	$-0.944195\pi$
$577$		−	8.37942i		−	0.348840i	0.984671	−	0.174420i	$-0.0558050\pi$
$578$		−	33.0073i		−	1.37292i
$579$	−4.62291			−0.192121
$580$	0.467379	−	2.91818i	0.0194069	−	0.121171i
$581$	38.0166			1.57719
$582$		−	1.13334i		−	0.0469783i
$583$			13.5363i			0.560617i
$584$	5.08182			0.210287
$585$	−6.30210	−	1.00935i	−0.260560	−	0.0417315i
$586$	26.6133			1.09938
$587$		−	13.6113i		−	0.561799i	−0.959737	−	0.280900i	$-0.909367\pi$
$587$		−	13.6113i		−	0.561799i	0.959737	−	0.280900i	$-0.0906328\pi$
$588$			8.59048i			0.354266i
$589$	11.3895			0.469297
$590$	5.97741	+	0.957347i	0.246086	+	0.0394134i
$591$	0.0617522			0.00254015
$592$		−	1.00000i		−	0.0410997i
$593$			14.4577i			0.593708i	0.954923	+	0.296854i	$0.0959375\pi$
$593$			14.4577i			0.593708i	−0.954923	+	0.296854i	$0.904062\pi$
$594$	1.94848			0.0799471
$595$	9.87389	−	61.6498i	0.404790	−	2.52740i
$596$	−20.5199			−0.840526
$597$			8.00000i			0.327418i
$598$		−	13.3714i		−	0.546799i
$599$	−12.3927			−0.506351			−0.253175	−	0.967420i	$-0.581475\pi$
$599$	−12.3927			−0.506351			−0.253175	+	0.967420i	$0.581475\pi$
$600$	−4.74990	−	1.56155i	−0.193914	−	0.0637501i
$601$	7.15320			0.291785			0.145893	−	0.989300i	$-0.453395\pi$
$601$	7.15320			0.291785			0.145893	+	0.989300i	$0.453395\pi$
$602$		−	4.32032i		−	0.176083i
$603$			1.33192i			0.0542398i
$604$	10.2688			0.417832
$605$	2.54731	−	15.9047i	0.103563	−	0.646616i
$606$	−2.00000			−0.0812444
$607$		−	44.8818i		−	1.82170i	−0.412742	−	0.910848i	$-0.635429\pi$
$607$		−	44.8818i		−	1.82170i	0.412742	−	0.910848i	$-0.364571\pi$
$608$		−	1.74990i		−	0.0709678i
$609$	5.21864			0.211470
$610$	−7.24757	−	1.16078i	−0.293446	−	0.0469985i
$611$	−19.1445			−0.774505
$612$		−	7.07158i		−	0.285852i
$613$			18.4084i			0.743506i	0.928332	+	0.371753i	$0.121243\pi$
$613$			18.4084i			0.743506i	−0.928332	+	0.371753i	$0.878757\pi$
$614$	4.68679			0.189143
$615$	−27.8931	−	4.46738i	−1.12476	−	0.180142i
$616$	−7.69353			−0.309981
$617$			8.41858i			0.338919i	0.985537	+	0.169460i	$0.0542023\pi$
$617$			8.41858i			0.338919i	−0.985537	+	0.169460i	$0.945798\pi$
$618$			1.93612i			0.0778822i
$619$	−32.4298			−1.30346			−0.651731	−	0.758450i	$-0.725957\pi$
$619$	−32.4298			−1.30346			−0.651731	+	0.758450i	$0.725957\pi$
$620$	−2.30162	+	14.3707i	−0.0924353	+	0.577140i
$621$	−4.68466			−0.187989
$622$			10.8480i			0.434964i
$623$			7.98615i			0.319958i
$624$	2.85431			0.114264
$625$	20.1231	+	14.8344i	0.804924	+	0.593378i
$626$	−26.2197			−1.04795
$627$		−	3.40964i		−	0.136168i
$628$		−	5.73754i		−	0.228953i
$629$	−7.07158			−0.281963
$630$	1.39628	−	8.71796i	0.0556290	−	0.347332i
$631$	−9.59437			−0.381946			−0.190973	−	0.981595i	$-0.561164\pi$
$631$	−9.59437			−0.381946			−0.190973	+	0.981595i	$0.561164\pi$
$632$		−	13.1418i		−	0.522753i
$633$			4.28388i			0.170269i
$634$	−25.1922			−1.00051
$635$	29.0248	+	4.64863i	1.15181	+	0.184475i
$636$	6.94712			0.275471
$637$			24.5199i			0.971512i
$638$			2.57527i			0.101956i
$639$	15.3302			0.606452
$640$	2.20793	+	0.353624i	0.0872761	+	0.0139782i
$641$	5.48861			0.216787			0.108393	−	0.994108i	$-0.465429\pi$
$641$	5.48861			0.216787			0.108393	+	0.994108i	$0.465429\pi$
$642$		−	1.39191i		−	0.0549342i
$643$		−	8.95257i		−	0.353055i	−0.984296	−	0.176527i	$-0.943514\pi$
$643$		−	8.95257i		−	0.353055i	0.984296	−	0.176527i	$-0.0564864\pi$
$644$	18.4973			0.728895
$645$	−0.386926	+	2.41586i	−0.0152352	+	0.0951243i
$646$	−12.3746			−0.486871
$647$		−	1.50369i		−	0.0591161i	−0.999563	−	0.0295581i	$-0.990590\pi$
$647$		−	1.50369i		−	0.0591161i	0.999563	−	0.0295581i	$-0.00940999\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−5.27501			−0.207062
$650$	−13.5577	−	4.45715i	−0.531775	−	0.174824i
$651$	−25.6993			−1.00724
$652$			15.8641i			0.621288i
$653$			13.4624i			0.526824i	0.964683	+	0.263412i	$0.0848479\pi$
$653$			13.4624i			0.526824i	−0.964683	+	0.263412i	$0.915152\pi$
$654$	3.28039			0.128274
$655$	−7.66732	+	47.8726i	−0.299587	+	1.87054i
$656$	12.6331			0.493241
$657$		−	5.08182i		−	0.198261i
$658$		−	26.4834i		−	1.03243i
$659$	34.1933			1.33198			0.665990	−	0.745961i	$-0.268009\pi$
$659$	34.1933			1.33198			0.665990	+	0.745961i	$0.268009\pi$
$660$	4.30210	+	0.689029i	0.167459	+	0.0268204i
$661$	9.22525			0.358821			0.179410	−	0.983774i	$-0.442581\pi$
$661$	9.22525			0.358821			0.179410	+	0.983774i	$0.442581\pi$
$662$			6.45502i			0.250882i
$663$		−	20.1845i		−	0.783899i
$664$	9.62816			0.373645
$665$	−15.2556	−	2.44334i	−0.591585	−	0.0947488i
$666$	−1.00000			−0.0387492
$667$		−	6.19164i		−	0.239741i
$668$			19.1671i			0.741598i
$669$	−9.67968			−0.374238
$670$	−0.470997	+	2.94077i	−0.0181962	+	0.113612i
$671$	6.39592			0.246912
$672$			3.94848i			0.152316i
$673$			24.8553i			0.958100i	0.877788	+	0.479050i	$0.159019\pi$
$673$			24.8553i			0.958100i	−0.877788	+	0.479050i	$0.840981\pi$
$674$	22.3149			0.859539
$675$	−1.56155	+	4.74990i	−0.0601042	+	0.182824i
$676$	−4.85294			−0.186652
$677$			40.6422i			1.56201i	0.624527	+	0.781003i	$0.285292\pi$
$677$			40.6422i			1.56201i	−0.624527	+	0.781003i	$0.714708\pi$
$678$			7.52873i			0.289139i
$679$	4.47496			0.171733
$680$	2.50068	−	15.6136i	0.0958967	−	0.598753i
$681$	24.8429			0.951982
$682$		−	12.6820i		−	0.485619i
$683$			9.24336i			0.353687i	0.984239	+	0.176844i	$0.0565887\pi$
$683$			9.24336i			0.353687i	−0.984239	+	0.176844i	$0.943411\pi$
$684$	−1.74990			−0.0669091
$685$	40.2059	+	6.43941i	1.53619	+	0.246037i
$686$	−6.28000			−0.239771
$687$		−	5.29275i		−	0.201931i
$688$		−	1.09417i		−	0.0417150i
$689$	19.8292			0.755432
$690$	−10.3434	−	1.65661i	−0.393766	−	0.0630660i
$691$	−19.0605			−0.725094			−0.362547	−	0.931965i	$-0.618093\pi$
$691$	−19.0605			−0.725094			−0.362547	+	0.931965i	$0.618093\pi$
$692$		−	16.1555i		−	0.614141i
$693$			7.69353i			0.292253i
$694$	−1.82039			−0.0691012
$695$	2.16118	−	13.4938i	0.0819781	−	0.511848i
$696$	1.32168			0.0500983
$697$		−	89.3363i		−	3.38385i
$698$		−	28.6443i		−	1.08420i
$699$	−17.7665			−0.671990
$700$	6.16576	−	18.7549i	0.233044	−	0.708868i
$701$	25.0173			0.944892			0.472446	−	0.881360i	$-0.343371\pi$
$701$	25.0173			0.944892			0.472446	+	0.881360i	$0.343371\pi$
$702$		−	2.85431i		−	0.107729i
$703$			1.74990i			0.0659987i
$704$	−1.94848			−0.0734361
$705$	−2.37184	+	14.8091i	−0.0893288	+	0.557744i
$706$	−25.6924			−0.966945
$707$		−	7.89696i		−	0.296996i
$708$			2.70725i			0.101745i
$709$	−25.3151			−0.950727			−0.475364	−	0.879789i	$-0.657684\pi$
$709$	−25.3151			−0.950727			−0.475364	+	0.879789i	$0.657684\pi$
$710$	33.8479	+	5.42111i	1.27029	+	0.203451i
$711$	−13.1418			−0.492856
$712$			2.02259i			0.0757997i
$713$			30.4909i			1.14189i
$714$	27.9220			1.04495
$715$	12.2795	+	1.96670i	0.459228	+	0.0735503i
$716$	−7.12583			−0.266305
$717$			16.6970i			0.623562i
$718$		−	8.62467i		−	0.321870i
$719$	39.2193			1.46263			0.731317	−	0.682038i	$-0.238906\pi$
$719$	39.2193			1.46263			0.731317	+	0.682038i	$0.238906\pi$
$720$	0.353624	−	2.20793i	0.0131788	−	0.0822847i
$721$	−7.64473			−0.284705
$722$		−	15.9378i		−	0.593145i
$723$			8.85042i			0.329151i
$724$	22.5795			0.839160
$725$	−6.27787	−	2.06388i	−0.233154	−	0.0766506i
$726$	7.20343			0.267344
$727$		−	21.5896i		−	0.800714i	−0.916359	−	0.400357i	$-0.868886\pi$
$727$		−	21.5896i		−	0.800714i	0.916359	−	0.400357i	$-0.131114\pi$
$728$			11.2702i			0.417700i
$729$	−1.00000			−0.0370370
$730$	1.79705	−	11.2203i	0.0665119	−	0.415281i
$731$	−7.73754			−0.286183
$732$		−	3.28252i		−	0.121325i
$733$		−	47.7530i		−	1.76380i	−0.471441	−	0.881898i	$-0.656266\pi$
$733$		−	47.7530i		−	1.76380i	0.471441	−	0.881898i	$-0.343734\pi$
$734$	10.9890			0.405612
$735$	18.9672	+	3.03780i	0.699615	+	0.112051i
$736$	4.68466			0.172679
$737$		−	2.59521i		−	0.0955957i
$738$		−	12.6331i		−	0.465032i
$739$	3.09690			0.113921			0.0569606	−	0.998376i	$-0.481859\pi$
$739$	3.09690			0.113921			0.0569606	+	0.998376i	$0.481859\pi$
$740$	−2.20793	−	0.353624i	−0.0811651	−	0.0129995i
$741$	−4.99475			−0.183487
$742$			27.4305i			1.00701i
$743$		−	41.6355i		−	1.52746i	−0.645538	−	0.763728i	$-0.723367\pi$
$743$		−	41.6355i		−	1.52746i	0.645538	−	0.763728i	$-0.276633\pi$
$744$	−6.50867			−0.238619
$745$	−7.25631	+	45.3064i	−0.265851	+	1.65990i
$746$	20.8052			0.761734
$747$		−	9.62816i		−	0.352276i
$748$			13.7788i			0.503804i
$749$	5.49591			0.200816
$750$	−5.12748	+	9.93524i	−0.187229	+	0.362784i
$751$	−5.58511			−0.203803			−0.101902	−	0.994794i	$-0.532493\pi$
$751$	−5.58511			−0.203803			−0.101902	+	0.994794i	$0.532493\pi$
$752$		−	6.70725i		−	0.244588i
$753$			2.19107i			0.0798471i
$754$	3.77249			0.137386
$755$	3.63129	−	22.6728i	0.132156	−	0.825147i
$756$	3.94848			0.143605
$757$			31.7409i			1.15364i	0.816870	+	0.576821i	$0.195707\pi$
$757$			31.7409i			1.15364i	−0.816870	+	0.576821i	$0.804293\pi$
$758$			36.0136i			1.30807i
$759$	9.12796			0.331324
$760$	−3.86366	−	0.618807i	−0.140150	−	0.0224465i
$761$	19.8602			0.719933			0.359967	−	0.932965i	$-0.382788\pi$
$761$	19.8602			0.719933			0.359967	+	0.932965i	$0.382788\pi$
$762$			13.1457i			0.476218i
$763$			12.9526i			0.468914i
$764$	17.6758			0.639488
$765$	−15.6136	−	2.50068i	−0.564509	−	0.0904123i
$766$	13.6441			0.492983
$767$			7.72731i			0.279017i
$768$			1.00000i			0.0360844i
$769$	−11.7902			−0.425166			−0.212583	−	0.977143i	$-0.568188\pi$
$769$	−11.7902			−0.425166			−0.212583	+	0.977143i	$0.568188\pi$
$770$	−2.72061	+	16.9868i	−0.0980442	+	0.612160i
$771$	−25.3742			−0.913828
$772$		−	4.62291i		−	0.166382i
$773$		−	9.69778i		−	0.348805i	−0.984674	−	0.174402i	$-0.944201\pi$
$773$		−	9.69778i		−	0.348805i	0.984674	−	0.174402i	$-0.0557994\pi$
$774$	−1.09417			−0.0393293
$775$	30.9155	+	10.1636i	1.11052	+	0.365088i
$776$	1.13334			0.0406844
$777$		−	3.94848i		−	0.141651i
$778$			33.5661i			1.20340i
$779$	−22.1067			−0.792056
$780$	1.00935	−	6.30210i	0.0361405	−	0.225651i
$781$	−29.8705			−1.06885
$782$		−	33.1280i		−	1.18465i
$783$		−	1.32168i		−	0.0472331i
$784$	−8.59048			−0.306803
$785$	−12.6681	−	2.02893i	−0.452143	−	0.0724157i
$786$	−21.6821			−0.773376
$787$			26.5199i			0.945331i	0.881242	+	0.472666i	$0.156708\pi$
$787$			26.5199i			0.945331i	−0.881242	+	0.472666i	$0.843292\pi$
$788$			0.0617522i			0.00219983i
$789$	6.34175			0.225772
$790$	−29.0162	−	4.64726i	−1.03235	−	0.165342i
$791$	−29.7270			−1.05697
$792$			1.94848i			0.0692362i
$793$		−	9.36932i		−	0.332714i
$794$	−30.4472			−1.08053
$795$	2.45667	−	15.3387i	0.0871290	−	0.544009i
$796$	−8.00000			−0.283552
$797$			18.4131i			0.652227i	0.945331	+	0.326113i	$0.105739\pi$
$797$			18.4131i			0.652227i	−0.945331	+	0.326113i	$0.894261\pi$
$798$		−	6.90944i		−	0.244592i
$799$	−47.4309			−1.67798
$800$	1.56155	−	4.74990i	0.0552092	−	0.167934i
$801$	2.02259			0.0714647
$802$			35.3263i			1.24741i
$803$			9.90181i			0.349427i
$804$	−1.33192			−0.0469730
$805$	6.54108	−	40.8407i	0.230543	−	1.43944i
$806$	−18.5777			−0.654373
$807$		−	14.2875i		−	0.502944i
$808$		−	2.00000i		−	0.0703598i
$809$	−14.4367			−0.507567			−0.253783	−	0.967261i	$-0.581675\pi$
$809$	−14.4367			−0.507567			−0.253783	+	0.967261i	$0.581675\pi$
$810$	−2.20793	−	0.353624i	−0.0775787	−	0.0124251i
$811$	−43.7939			−1.53781			−0.768906	−	0.639362i	$-0.779199\pi$
$811$	−43.7939			−1.53781			−0.768906	+	0.639362i	$0.779199\pi$
$812$			5.21864i			0.183138i
$813$		−	14.0606i		−	0.493126i
$814$	1.94848			0.0682941
$815$	35.0269	+	5.60994i	1.22694	+	0.196508i
$816$	7.07158			0.247555
$817$			1.91469i			0.0669867i
$818$		−	9.54169i		−	0.333617i
$819$	11.2702			0.393811
$820$	4.46738	−	27.8931i	0.156008	−	0.974068i
$821$	39.4260			1.37598			0.687989	−	0.725721i	$-0.258494\pi$
$821$	39.4260			1.37598			0.687989	+	0.725721i	$0.258494\pi$
$822$			18.2098i			0.635139i
$823$			11.8469i			0.412958i	0.978451	+	0.206479i	$0.0662005\pi$
$823$			11.8469i			0.412958i	−0.978451	+	0.206479i	$0.933800\pi$
$824$	−1.93612			−0.0674480
$825$	3.04265	−	9.25508i	0.105932	−	0.322221i
$826$	−10.6895			−0.371936
$827$			42.5470i			1.47951i	0.672879	+	0.739753i	$0.265058\pi$
$827$			42.5470i			1.47951i	−0.672879	+	0.739753i	$0.734942\pi$
$828$		−	4.68466i		−	0.162803i
$829$	−51.4709			−1.78766			−0.893830	−	0.448407i	$-0.851992\pi$
$829$	−51.4709			−1.78766			−0.893830	+	0.448407i	$0.851992\pi$
$830$	3.40475	−	21.2583i	0.118180	−	0.737886i
$831$	2.85431			0.0990147
$832$			2.85431i			0.0989552i
$833$			60.7483i			2.10481i
$834$	6.11151			0.211624
$835$	42.3196	+	6.77795i	1.46453	+	0.234561i
$836$	3.40964			0.117925
$837$			6.50867i			0.224973i
$838$		−	22.9149i		−	0.791582i
$839$	−50.8426			−1.75528			−0.877641	−	0.479318i	$-0.840884\pi$
$839$	−50.8426			−1.75528			−0.877641	+	0.479318i	$0.840884\pi$
$840$	8.71796	+	1.39628i	0.300798	+	0.0481761i
$841$	−27.2532			−0.939764
$842$			22.0197i			0.758848i
$843$		−	4.58338i		−	0.157860i
$844$	−4.28388			−0.147457
$845$	−1.71612	+	10.7150i	−0.0590362	+	0.368606i
$846$	−6.70725			−0.230600
$847$			28.4426i			0.977299i
$848$			6.94712i			0.238565i
$849$	6.55417			0.224939
$850$	−33.5893	−	11.0427i	−1.15210	−	0.378760i
$851$	−4.68466			−0.160588
$852$			15.3302i			0.525202i
$853$			29.5725i			1.01254i	0.862374	+	0.506271i	$0.168977\pi$
$853$			29.5725i			1.01254i	−0.862374	+	0.506271i	$0.831023\pi$
$854$	12.9610			0.443515
$855$	−0.618807	+	3.86366i	−0.0211627	+	0.132134i
$856$	1.39191			0.0475744
$857$		−	10.2526i		−	0.350221i	−0.984549	−	0.175110i	$-0.943972\pi$
$857$		−	10.2526i		−	0.350221i	0.984549	−	0.175110i	$-0.0560282\pi$
$858$			5.56155i			0.189868i
$859$	38.6190			1.31766			0.658832	−	0.752290i	$-0.271051\pi$
$859$	38.6190			1.31766			0.658832	+	0.752290i	$0.271051\pi$
$860$	−2.41586	−	0.386926i	−0.0823801	−	0.0131941i
$861$	49.8817			1.69996
$862$			32.1957i			1.09659i
$863$			32.1703i			1.09509i	0.836776	+	0.547546i	$0.184438\pi$
$863$			32.1703i			1.09509i	−0.836776	+	0.547546i	$0.815562\pi$
$864$	1.00000			0.0340207
$865$	−35.6703	−	5.71298i	−1.21283	−	0.194247i
$866$	7.27016			0.247050
$867$		−	33.0073i		−	1.12099i
$868$		−	25.6993i		−	0.872293i
$869$	25.6065			0.868642
$870$	0.467379	−	2.91818i	0.0158456	−	0.0989357i
$871$	−3.80169			−0.128815
$872$			3.28039i			0.111088i
$873$		−	1.13334i		−	0.0383576i
$874$	−8.19769			−0.277291
$875$	−39.2291	−	20.2457i	−1.32619	−	0.684431i
$876$	5.08182			0.171699
$877$		−	51.6586i		−	1.74439i	−0.489160	−	0.872194i	$-0.662696\pi$
$877$		−	51.6586i		−	1.74439i	0.489160	−	0.872194i	$-0.337304\pi$
$878$			26.9647i			0.910013i
$879$	26.6133			0.897643
$880$	−0.689029	+	4.30210i	−0.0232272	+	0.145024i
$881$	19.1695			0.645837			0.322919	−	0.946427i	$-0.395336\pi$
$881$	19.1695			0.645837			0.322919	+	0.946427i	$0.395336\pi$
$882$			8.59048i			0.289257i
$883$		−	48.1632i		−	1.62082i	−0.585864	−	0.810410i	$-0.699245\pi$
$883$		−	48.1632i		−	1.62082i	0.585864	−	0.810410i	$-0.300755\pi$
$884$	20.1845			0.678877
$885$	5.97741	+	0.957347i	0.200928	+	0.0321809i
$886$	−26.1806			−0.879553
$887$		−	4.46894i		−	0.150052i	−0.997182	−	0.0750262i	$-0.976096\pi$
$887$		−	4.46894i		−	0.150052i	0.997182	−	0.0750262i	$-0.0239040\pi$
$888$		−	1.00000i		−	0.0335578i
$889$	−51.9055			−1.74085
$890$	4.46573	+	0.715236i	0.149692	+	0.0239748i
$891$	1.94848			0.0652765
$892$		−	9.67968i		−	0.324100i
$893$			11.7370i			0.392764i
$894$	−20.5199			−0.686287
$895$	−2.51986	+	15.7333i	−0.0842298	+	0.525907i
$896$	−3.94848			−0.131909
$897$		−	13.3714i		−	0.446460i
$898$			41.8892i			1.39786i
$899$	−8.60240			−0.286906
$900$	−4.74990	−	1.56155i	−0.158330	−	0.0520518i
$901$	49.1271			1.63666
$902$			24.6154i			0.819603i
$903$		−	4.32032i		−	0.143771i
$904$	−7.52873			−0.250402
$905$	7.98465	−	49.8539i	0.265419	−	1.65720i
$906$	10.2688			0.341158
$907$			32.1767i			1.06841i	0.845355	+	0.534205i	$0.179389\pi$
$907$			32.1767i			1.06841i	−0.845355	+	0.534205i	$0.820611\pi$
$908$			24.8429i			0.824441i
$909$	−2.00000			−0.0663358
$910$	24.8837	+	3.98540i	0.824887	+	0.132115i
$911$	18.2462			0.604524			0.302262	−	0.953225i	$-0.402258\pi$
$911$	18.2462			0.604524			0.302262	+	0.953225i	$0.402258\pi$
$912$		−	1.74990i		−	0.0579450i
$913$			18.7603i			0.620874i
$914$	−29.9082			−0.989274
$915$	−7.24757	−	1.16078i	−0.239597	−	0.0383741i
$916$	5.29275			0.174877
$917$		−	85.6114i		−	2.82714i
$918$		−	7.07158i		−	0.233397i
$919$	−7.13908			−0.235497			−0.117748	−	0.993043i	$-0.537568\pi$
$919$	−7.13908			−0.235497			−0.117748	+	0.993043i	$0.537568\pi$
$920$	1.65661	−	10.3434i	0.0546167	−	0.341012i
$921$	4.68679			0.154435
$922$		−	2.90583i		−	0.0956983i
$923$			43.7569i			1.44028i
$924$	−7.69353			−0.253098
$925$	−1.56155	+	4.74990i	−0.0513435	+	0.156176i
$926$	−37.2750			−1.22493
$927$			1.93612i			0.0635905i
$928$			1.32168i			0.0433864i
$929$	−5.25780			−0.172503			−0.0862515	−	0.996273i	$-0.527489\pi$
$929$	−5.25780			−0.172503			−0.0862515	+	0.996273i	$0.527489\pi$
$930$	−2.30162	+	14.3707i	−0.0754731	+	0.471233i
$931$	15.0325			0.492670
$932$		−	17.7665i		−	0.581960i
$933$			10.8480i			0.355146i
$934$	−38.3240			−1.25400
$935$	30.4227	+	4.87252i	0.994928	+	0.159349i
$936$	2.85431			0.0932959
$937$			15.7885i			0.515787i	0.966173	+	0.257893i	$0.0830283\pi$
$937$			15.7885i			0.515787i	−0.966173	+	0.257893i	$0.916972\pi$
$938$		−	5.25904i		−	0.171714i
$939$	−26.2197			−0.855649
$940$	−14.8091	−	2.37184i	−0.483020	−	0.0773610i
$941$	−33.2443			−1.08373			−0.541866	−	0.840465i	$-0.682282\pi$
$941$	−33.2443			−1.08373			−0.541866	+	0.840465i	$0.682282\pi$
$942$		−	5.73754i		−	0.186939i
$943$		−	59.1819i		−	1.92723i
$944$	−2.70725			−0.0881134
$945$	1.39628	−	8.71796i	0.0454209	−	0.283595i
$946$	2.13197			0.0693165
$947$			44.3008i			1.43958i	0.694190	+	0.719792i	$0.255763\pi$
$947$			44.3008i			1.43958i	−0.694190	+	0.719792i	$0.744237\pi$
$948$		−	13.1418i		−	0.426826i
$949$	14.5051			0.470854
$950$	−2.73256	+	8.31185i	−0.0886560	+	0.269672i
$951$	−25.1922			−0.816912
$952$			27.9220i			0.904957i
$953$		−	28.1950i		−	0.913326i	−0.889640	−	0.456663i	$-0.849044\pi$
$953$		−	28.1950i		−	0.913326i	0.889640	−	0.456663i	$-0.150956\pi$
$954$	6.94712			0.224921
$955$	6.25058	−	39.0269i	0.202264	−	1.26288i
$956$	−16.6970			−0.540020
$957$			2.57527i			0.0832468i
$958$		−	34.6874i		−	1.12070i
$959$	−71.9009			−2.32180
$960$	2.20793	+	0.353624i	0.0712606	+	0.0114132i
$961$	11.3628			0.366541
$962$		−	2.85431i		−	0.0920265i
$963$		−	1.39191i		−	0.0448536i
$964$	−8.85042			−0.285053
$965$	−10.2070	−	1.63477i	−0.328577	−	0.0526251i
$966$	18.4973			0.595140
$967$		−	33.2039i		−	1.06777i	−0.845558	−	0.533883i	$-0.820732\pi$
$967$		−	33.2039i		−	1.06777i	0.845558	−	0.533883i	$-0.179268\pi$
$968$			7.20343i			0.231527i
$969$	−12.3746			−0.397528
$970$	0.400775	−	2.50233i	0.0128681	−	0.0803449i
$971$	2.03617			0.0653437			0.0326719	−	0.999466i	$-0.489598\pi$
$971$	2.03617			0.0653437			0.0326719	+	0.999466i	$0.489598\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			24.1312i			0.773610i
$974$	13.9575			0.447229
$975$	−13.5577	−	4.45715i	−0.434193	−	0.142743i
$976$	3.28252			0.105071
$977$			56.1770i			1.79726i	0.438707	+	0.898630i	$0.355436\pi$
$977$			56.1770i			1.79726i	−0.438707	+	0.898630i	$0.644564\pi$
$978$			15.8641i			0.507279i
$979$	−3.94097			−0.125954
$980$	−3.03780	+	18.9672i	−0.0970390	+	0.605884i
$981$	3.28039			0.104735
$982$		−	6.54245i		−	0.208778i
$983$		−	33.6894i		−	1.07452i	−0.843415	−	0.537262i	$-0.819459\pi$
$983$		−	33.6894i		−	1.07452i	0.843415	−	0.537262i	$-0.180541\pi$
$984$	12.6331			0.402730
$985$	0.136345	+	0.0218371i	0.00434430	+	0.000695787i
$986$	9.34640			0.297650
$987$		−	26.4834i		−	0.842977i
$988$		−	4.99475i		−	0.158904i
$989$	−5.12583			−0.162992
$990$	4.30210	+	0.689029i	0.136730	+	0.0218988i
$991$	−8.02621			−0.254961			−0.127480	−	0.991841i	$-0.540689\pi$
$991$	−8.02621			−0.254961			−0.127480	+	0.991841i	$0.540689\pi$
$992$		−	6.50867i		−	0.206650i
$993$			6.45502i			0.204844i
$994$	−60.5308			−1.91992
$995$	−2.82899	+	17.6634i	−0.0896850	+	0.559968i
$996$	9.62816			0.305080
$997$		−	10.3089i		−	0.326487i	−0.986586	−	0.163243i	$-0.947804\pi$
$997$		−	10.3089i		−	0.326487i	0.986586	−	0.163243i	$-0.0521956\pi$
$998$			35.0668i			1.11002i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.d.j.889.7	yes	8
3.2	odd	2		3330.2.d.o.1999.2		8
5.2	odd	4		5550.2.a.cl.1.4		4
5.3	odd	4		5550.2.a.cm.1.1		4
5.4	even	2	inner	1110.2.d.j.889.3	✓	8
15.14	odd	2		3330.2.d.o.1999.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.j.889.3	✓	8	5.4	even	2	inner
1110.2.d.j.889.7	yes	8	1.1	even	1	trivial
3330.2.d.o.1999.2		8	3.2	odd	2
3330.2.d.o.1999.6		8	15.14	odd	2
5550.2.a.cl.1.4		4	5.2	odd	4
5550.2.a.cm.1.1		4	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.353624 + 2.20793i) q^{5} -1.00000 q^{6} -3.94848i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.353624 + 2.20793i) q^{5} -1.00000 q^{6} -3.94848i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.20793 - 0.353624i) q^{10} +1.94848 q^{11} -1.00000i q^{12} -2.85431i q^{13} +3.94848 q^{14} +(-2.20793 - 0.353624i) q^{15} +1.00000 q^{16} -7.07158i q^{17} -1.00000i q^{18} -1.74990 q^{19} +(0.353624 - 2.20793i) q^{20} +3.94848 q^{21} +1.94848i q^{22} -4.68466i q^{23} +1.00000 q^{24} +(-4.74990 - 1.56155i) q^{25} +2.85431 q^{26} -1.00000i q^{27} +3.94848i q^{28} +1.32168 q^{29} +(0.353624 - 2.20793i) q^{30} -6.50867 q^{31} +1.00000i q^{32} +1.94848i q^{33} +7.07158 q^{34} +(8.71796 + 1.39628i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -1.74990i q^{38} +2.85431 q^{39} +(2.20793 + 0.353624i) q^{40} +12.6331 q^{41} +3.94848i q^{42} -1.09417i q^{43} -1.94848 q^{44} +(0.353624 - 2.20793i) q^{45} +4.68466 q^{46} -6.70725i q^{47} +1.00000i q^{48} -8.59048 q^{49} +(1.56155 - 4.74990i) q^{50} +7.07158 q^{51} +2.85431i q^{52} +6.94712i q^{53} +1.00000 q^{54} +(-0.689029 + 4.30210i) q^{55} -3.94848 q^{56} -1.74990i q^{57} +1.32168i q^{58} -2.70725 q^{59} +(2.20793 + 0.353624i) q^{60} +3.28252 q^{61} -6.50867i q^{62} +3.94848i q^{63} -1.00000 q^{64} +(6.30210 + 1.00935i) q^{65} -1.94848 q^{66} -1.33192i q^{67} +7.07158i q^{68} +4.68466 q^{69} +(-1.39628 + 8.71796i) q^{70} -15.3302 q^{71} +1.00000i q^{72} +5.08182i q^{73} +1.00000 q^{74} +(1.56155 - 4.74990i) q^{75} +1.74990 q^{76} -7.69353i q^{77} +2.85431i q^{78} +13.1418 q^{79} +(-0.353624 + 2.20793i) q^{80} +1.00000 q^{81} +12.6331i q^{82} +9.62816i q^{83} -3.94848 q^{84} +(15.6136 + 2.50068i) q^{85} +1.09417 q^{86} +1.32168i q^{87} -1.94848i q^{88} -2.02259 q^{89} +(2.20793 + 0.353624i) q^{90} -11.2702 q^{91} +4.68466i q^{92} -6.50867i q^{93} +6.70725 q^{94} +(0.618807 - 3.86366i) q^{95} -1.00000 q^{96} +1.13334i q^{97} -8.59048i q^{98} -1.94848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} - 2 q^{10} - 10 q^{11} + 6 q^{14} - 2 q^{15} + 8 q^{16} + 24 q^{19} + 2 q^{20} + 6 q^{21} + 8 q^{24} + 8 q^{26} - 10 q^{29} + 2 q^{30} - 38 q^{31} - 2 q^{34} + 12 q^{35} + 8 q^{36} + 8 q^{39} + 2 q^{40} + 26 q^{41} + 10 q^{44} + 2 q^{45} - 12 q^{46} - 30 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{54} + 30 q^{55} - 6 q^{56} - 20 q^{59} + 2 q^{60} - 6 q^{61} - 8 q^{64} + 24 q^{65} + 10 q^{66} - 12 q^{69} + 26 q^{70} - 12 q^{71} + 8 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 2 q^{80} + 8 q^{81} - 6 q^{84} + 44 q^{85} - 2 q^{86} - 64 q^{89} + 2 q^{90} - 44 q^{91} + 52 q^{94} - 8 q^{96} + 10 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 - 2 * q^10 - 10 * q^11 + 6 * q^14 - 2 * q^15 + 8 * q^16 + 24 * q^19 + 2 * q^20 + 6 * q^21 + 8 * q^24 + 8 * q^26 - 10 * q^29 + 2 * q^30 - 38 * q^31 - 2 * q^34 + 12 * q^35 + 8 * q^36 + 8 * q^39 + 2 * q^40 + 26 * q^41 + 10 * q^44 + 2 * q^45 - 12 * q^46 - 30 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^54 + 30 * q^55 - 6 * q^56 - 20 * q^59 + 2 * q^60 - 6 * q^61 - 8 * q^64 + 24 * q^65 + 10 * q^66 - 12 * q^69 + 26 * q^70 - 12 * q^71 + 8 * q^74 - 4 * q^75 - 24 * q^76 + 16 * q^79 - 2 * q^80 + 8 * q^81 - 6 * q^84 + 44 * q^85 - 2 * q^86 - 64 * q^89 + 2 * q^90 - 44 * q^91 + 52 * q^94 - 8 * q^96 + 10 * q^99

Introduction

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