LMFDB - Embedded newform 1470.2.d.f.1469.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.4
Root			$1.01575 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.f.1469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(1.41421 + 1.73205i) q^{10} +0.213422i q^{11} +(-0.707107 + 1.58114i) q^{12} -6.70141 q^{13} +(-3.73861 + 1.01132i) q^{15} +1.00000 q^{16} +3.16228i q^{17} +(-2.00000 - 2.23607i) q^{18} +4.89433i q^{19} +(1.41421 + 1.73205i) q^{20} +0.213422i q^{22} -6.47723 q^{23} +(-0.707107 + 1.58114i) q^{24} +(-1.00000 + 4.89898i) q^{25} -6.70141 q^{26} +(4.94975 - 1.58114i) q^{27} -2.02265i q^{29} +(-3.73861 + 1.01132i) q^{30} +0.301824i q^{31} +1.00000 q^{32} +(-0.337449 - 0.150912i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +7.13505i q^{37} +4.89433i q^{38} +(4.73861 - 10.5959i) q^{39} +(1.41421 + 1.73205i) q^{40} +6.70141 q^{41} -2.02265i q^{43} +0.213422i q^{44} +(1.04456 - 6.62638i) q^{45} -6.47723 q^{46} +7.75478i q^{47} +(-0.707107 + 1.58114i) q^{48} +(-1.00000 + 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -6.70141 q^{52} +5.00000 q^{53} +(4.94975 - 1.58114i) q^{54} +(-0.369657 + 0.301824i) q^{55} +(-7.73861 - 3.46081i) q^{57} -2.02265i q^{58} -4.91754 q^{59} +(-3.73861 + 1.01132i) q^{60} +3.46410i q^{61} +0.301824i q^{62} +1.00000 q^{64} +(-9.47723 - 11.6072i) q^{65} +(-0.337449 - 0.150912i) q^{66} -5.32582i q^{67} +3.16228i q^{68} +(4.58009 - 10.2414i) q^{69} +2.02265i q^{71} +(-2.00000 - 2.23607i) q^{72} +11.9886 q^{73} +7.13505i q^{74} +(-7.03886 - 5.04524i) q^{75} +4.89433i q^{76} +(4.73861 - 10.5959i) q^{78} +0.522774 q^{79} +(1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +6.70141 q^{82} -16.7169i q^{83} +(-5.47723 + 4.47214i) q^{85} -2.02265i q^{86} +(3.19808 + 1.43023i) q^{87} +0.213422i q^{88} -10.5744 q^{89} +(1.04456 - 6.62638i) q^{90} -6.47723 q^{92} +(-0.477226 - 0.213422i) q^{93} +7.75478i q^{94} +(-8.47723 + 6.92163i) q^{95} +(-0.707107 + 1.58114i) q^{96} +3.50333 q^{97} +(0.477226 - 0.426844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 16 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9} - 8 q^{15} + 8 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} - 8 q^{30} + 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} - 8 q^{50} - 40 q^{51} + 40 q^{53} - 40 q^{57} - 8 q^{60} + 8 q^{64} - 32 q^{65} - 16 q^{72} + 16 q^{78} + 48 q^{79} - 8 q^{81} - 8 q^{92} + 40 q^{93} - 24 q^{95} - 40 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 16 * q^9 - 8 * q^15 + 8 * q^16 - 16 * q^18 - 8 * q^23 - 8 * q^25 - 8 * q^30 + 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 - 8 * q^50 - 40 * q^51 + 40 * q^53 - 40 * q^57 - 8 * q^60 + 8 * q^64 - 32 * q^65 - 16 * q^72 + 16 * q^78 + 48 * q^79 - 8 * q^81 - 8 * q^92 + 40 * q^93 - 24 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	+	1.58114i	−0.408248	+	0.912871i
$3$	−0.707107	+	1.58114i	−0.408248	+	0.912871i
$4$	1.00000			0.500000
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$6$	−0.707107	+	1.58114i	−0.288675	+	0.645497i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−2.00000	−	2.23607i	−0.666667	−	0.745356i
$10$	1.41421	+	1.73205i	0.447214	+	0.547723i
$11$			0.213422i			0.0643491i	0.999482	+	0.0321745i	$0.0102432\pi$
$11$			0.213422i			0.0643491i	−0.999482	+	0.0321745i	$0.989757\pi$
$12$	−0.707107	+	1.58114i	−0.204124	+	0.456435i
$13$	−6.70141			−1.85864			−0.929318	−	0.369279i	$-0.879605\pi$
$13$	−6.70141			−1.85864			−0.929318	+	0.369279i	$0.879605\pi$
$14$		0			0
$15$	−3.73861	+	1.01132i	−0.965306	+	0.261123i
$16$	1.00000			0.250000
$17$			3.16228i			0.766965i	0.923548	+	0.383482i	$0.125275\pi$
$17$			3.16228i			0.766965i	−0.923548	+	0.383482i	$0.874725\pi$
$18$	−2.00000	−	2.23607i	−0.471405	−	0.527046i
$19$			4.89433i			1.12284i	0.827532	+	0.561418i	$0.189744\pi$
$19$			4.89433i			1.12284i	−0.827532	+	0.561418i	$0.810256\pi$
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$		0			0
$22$			0.213422i			0.0455017i
$23$	−6.47723			−1.35059			−0.675297	−	0.737545i	$-0.735985\pi$
$23$	−6.47723			−1.35059			−0.675297	+	0.737545i	$0.735985\pi$
$24$	−0.707107	+	1.58114i	−0.144338	+	0.322749i
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$	−6.70141			−1.31425
$27$	4.94975	−	1.58114i	0.952579	−	0.304290i
$28$		0			0
$29$		−	2.02265i		−	0.375596i	−0.982208	−	0.187798i	$-0.939865\pi$
$29$		−	2.02265i		−	0.375596i	0.982208	−	0.187798i	$-0.0601350\pi$
$30$	−3.73861	+	1.01132i	−0.682574	+	0.184641i
$31$			0.301824i			0.0542092i	0.999633	+	0.0271046i	$0.00862872\pi$
$31$			0.301824i			0.0542092i	−0.999633	+	0.0271046i	$0.991371\pi$
$32$	1.00000			0.176777
$33$	−0.337449	−	0.150912i	−0.0587424	−	0.0262704i
$34$			3.16228i			0.542326i
$35$		0			0
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$			7.13505i			1.17299i	0.809951	+	0.586497i	$0.199494\pi$
$37$			7.13505i			1.17299i	−0.809951	+	0.586497i	$0.800506\pi$
$38$			4.89433i			0.793965i
$39$	4.73861	−	10.5959i	0.758785	−	1.69670i
$40$	1.41421	+	1.73205i	0.223607	+	0.273861i
$41$	6.70141			1.04658			0.523292	−	0.852153i	$-0.324704\pi$
$41$	6.70141			1.04658			0.523292	+	0.852153i	$0.324704\pi$
$42$		0			0
$43$		−	2.02265i		−	0.308451i	−0.988036	−	0.154225i	$-0.950712\pi$
$43$		−	2.02265i		−	0.308451i	0.988036	−	0.154225i	$-0.0492882\pi$
$44$			0.213422i			0.0321745i
$45$	1.04456	−	6.62638i	0.155713	−	0.987802i
$46$	−6.47723			−0.955015
$47$			7.75478i			1.13115i	0.824696	+	0.565576i	$0.191346\pi$
$47$			7.75478i			1.13115i	−0.824696	+	0.565576i	$0.808654\pi$
$48$	−0.707107	+	1.58114i	−0.102062	+	0.228218i
$49$		0			0
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	−5.00000	−	2.23607i	−0.700140	−	0.313112i
$52$	−6.70141			−0.929318
$53$	5.00000			0.686803			0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000			0.686803			0.343401	+	0.939189i	$0.388421\pi$
$54$	4.94975	−	1.58114i	0.673575	−	0.215166i
$55$	−0.369657	+	0.301824i	−0.0498446	+	0.0406979i
$56$		0			0
$57$	−7.73861	−	3.46081i	−1.02500	−	0.458396i
$58$		−	2.02265i		−	0.265586i
$59$	−4.91754			−0.640209			−0.320105	−	0.947382i	$-0.603718\pi$
$59$	−4.91754			−0.640209			−0.320105	+	0.947382i	$0.603718\pi$
$60$	−3.73861	+	1.01132i	−0.482653	+	0.130561i
$61$			3.46410i			0.443533i	0.975100	+	0.221766i	$0.0711822\pi$
$61$			3.46410i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$62$			0.301824i			0.0383317i
$63$		0			0
$64$	1.00000			0.125000
$65$	−9.47723	−	11.6072i	−1.17551	−	1.43969i
$66$	−0.337449	−	0.150912i	−0.0415372	−	0.0185760i
$67$		−	5.32582i		−	0.650653i	−0.945602	−	0.325326i	$-0.894526\pi$
$67$		−	5.32582i		−	0.650653i	0.945602	−	0.325326i	$-0.105474\pi$
$68$			3.16228i			0.383482i
$69$	4.58009	−	10.2414i	0.551378	−	1.23292i
$70$		0			0
$71$			2.02265i			0.240044i	0.992771	+	0.120022i	$0.0382965\pi$
$71$			2.02265i			0.240044i	−0.992771	+	0.120022i	$0.961703\pi$
$72$	−2.00000	−	2.23607i	−0.235702	−	0.263523i
$73$	11.9886			1.40316			0.701580	−	0.712591i	$-0.252478\pi$
$73$	11.9886			1.40316			0.701580	+	0.712591i	$0.252478\pi$
$74$			7.13505i			0.829432i
$75$	−7.03886	−	5.04524i	−0.812778	−	0.582574i
$76$			4.89433i			0.561418i
$77$		0			0
$78$	4.73861	−	10.5959i	0.536542	−	1.19974i
$79$	0.522774			0.0588167			0.0294084	−	0.999567i	$-0.490638\pi$
$79$	0.522774			0.0588167			0.0294084	+	0.999567i	$0.490638\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$82$	6.70141			0.740047
$83$		−	16.7169i		−	1.83491i	−0.397835	−	0.917457i	$-0.630238\pi$
$83$		−	16.7169i		−	1.83491i	0.397835	−	0.917457i	$-0.369762\pi$
$84$		0			0
$85$	−5.47723	+	4.47214i	−0.594089	+	0.485071i
$86$		−	2.02265i		−	0.218108i
$87$	3.19808	+	1.43023i	0.342871	+	0.153336i
$88$			0.213422i			0.0227508i
$89$	−10.5744			−1.12088			−0.560442	−	0.828194i	$-0.689369\pi$
$89$	−10.5744			−1.12088			−0.560442	+	0.828194i	$0.689369\pi$
$90$	1.04456	−	6.62638i	0.110106	−	0.698482i
$91$		0			0
$92$	−6.47723			−0.675297
$93$	−0.477226	−	0.213422i	−0.0494860	−	0.0221308i
$94$			7.75478i			0.799845i
$95$	−8.47723	+	6.92163i	−0.869745	+	0.710144i
$96$	−0.707107	+	1.58114i	−0.0721688	+	0.161374i
$97$	3.50333			0.355709			0.177854	−	0.984057i	$-0.443084\pi$
$97$	3.50333			0.355709			0.177854	+	0.984057i	$0.443084\pi$
$98$		0			0
$99$	0.477226	−	0.426844i	0.0479630	−	0.0428994i
$100$	−1.00000	+	4.89898i	−0.100000	+	0.489898i
$101$	−11.3137			−1.12576			−0.562878	−	0.826540i	$-0.690306\pi$
$101$	−11.3137			−1.12576			−0.562878	+	0.826540i	$0.690306\pi$
$102$	−5.00000	−	2.23607i	−0.495074	−	0.221404i
$103$	−10.5744			−1.04193			−0.520963	−	0.853579i	$-0.674427\pi$
$103$	−10.5744			−1.04193			−0.520963	+	0.853579i	$0.674427\pi$
$104$	−6.70141			−0.657127
$105$		0			0
$106$	5.00000			0.485643
$107$	5.47723			0.529503			0.264752	−	0.964317i	$-0.414710\pi$
$107$	5.47723			0.529503			0.264752	+	0.964317i	$0.414710\pi$
$108$	4.94975	−	1.58114i	0.476290	−	0.152145i
$109$	12.4317			1.19074			0.595369	−	0.803452i	$-0.297006\pi$
$109$	12.4317			1.19074			0.595369	+	0.803452i	$0.297006\pi$
$110$	−0.369657	+	0.301824i	−0.0352454	+	0.0287778i
$111$	−11.2815	−	5.04524i	−1.07079	−	0.478873i
$112$		0			0
$113$	6.52277			0.613611			0.306806	−	0.951772i	$-0.400740\pi$
$113$	6.52277			0.613611			0.306806	+	0.951772i	$0.400740\pi$
$114$	−7.73861	−	3.46081i	−0.724787	−	0.324135i
$115$	−9.16018	−	11.2189i	−0.854191	−	1.04617i
$116$		−	2.02265i		−	0.187798i
$117$	13.4028	+	14.9848i	1.23909	+	1.38535i
$118$	−4.91754			−0.452696
$119$		0			0
$120$	−3.73861	+	1.01132i	−0.341287	+	0.0923207i
$121$	10.9545			0.995859
$122$			3.46410i			0.313625i
$123$	−4.73861	+	10.5959i	−0.427266	+	0.955397i
$124$			0.301824i			0.0271046i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$		0			0
$127$			13.6298i			1.20945i	0.796434	+	0.604726i	$0.206717\pi$
$127$			13.6298i			1.20945i	−0.796434	+	0.604726i	$0.793283\pi$
$128$	1.00000			0.0883883
$129$	3.19808	+	1.43023i	0.281576	+	0.125924i
$130$	−9.47723	−	11.6072i	−0.831208	−	1.01802i
$131$	6.02651			0.526539			0.263269	−	0.964722i	$-0.415199\pi$
$131$	6.02651			0.526539			0.263269	+	0.964722i	$0.415199\pi$
$132$	−0.337449	−	0.150912i	−0.0293712	−	0.0131352i
$133$		0			0
$134$		−	5.32582i		−	0.460081i
$135$	9.73861	+	6.33715i	0.838166	+	0.545415i
$136$			3.16228i			0.271163i
$137$	7.47723			0.638822			0.319411	−	0.947616i	$-0.396515\pi$
$137$	7.47723			0.638822			0.319411	+	0.947616i	$0.396515\pi$
$138$	4.58009	−	10.2414i	0.389883	−	0.871805i
$139$			7.53185i			0.638843i	0.947613	+	0.319422i	$0.103489\pi$
$139$			7.53185i			0.638843i	−0.947613	+	0.319422i	$0.896511\pi$
$140$		0			0
$141$	−12.2614	−	5.48346i	−1.03260	−	0.461791i
$142$			2.02265i			0.169737i
$143$		−	1.43023i		−	0.119602i
$144$	−2.00000	−	2.23607i	−0.166667	−	0.186339i
$145$	3.50333	−	2.86045i	0.290935	−	0.237548i
$146$	11.9886			0.992184
$147$		0			0
$148$			7.13505i			0.586497i
$149$		−	2.44949i		−	0.200670i	−0.994954	−	0.100335i	$-0.968009\pi$
$149$		−	2.44949i		−	0.200670i	0.994954	−	0.100335i	$-0.0319915\pi$
$150$	−7.03886	−	5.04524i	−0.574721	−	0.411942i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$			4.89433i			0.396982i
$153$	7.07107	−	6.32456i	0.571662	−	0.511310i
$154$		0			0
$155$	−0.522774	+	0.426844i	−0.0419903	+	0.0342849i
$156$	4.73861	−	10.5959i	0.379393	−	0.848348i
$157$	8.79052			0.701560			0.350780	−	0.936458i	$-0.385916\pi$
$157$	8.79052			0.701560			0.350780	+	0.936458i	$0.385916\pi$
$158$	0.522774			0.0415897
$159$	−3.53553	+	7.90569i	−0.280386	+	0.626962i
$160$	1.41421	+	1.73205i	0.111803	+	0.136931i
$161$		0			0
$162$	−1.00000	+	8.94427i	−0.0785674	+	0.702728i
$163$			14.6969i			1.15115i	0.817748	+	0.575577i	$0.195222\pi$
$163$			14.6969i			1.15115i	−0.817748	+	0.575577i	$0.804778\pi$
$164$	6.70141			0.523292
$165$	−0.215838	−	0.797901i	−0.0168030	−	0.0621165i
$166$		−	16.7169i		−	1.29748i
$167$			14.6830i			1.13620i	0.822958	+	0.568102i	$0.192322\pi$
$167$			14.6830i			1.13620i	−0.822958	+	0.568102i	$0.807678\pi$
$168$		0			0
$169$	31.9089			2.45453
$170$	−5.47723	+	4.47214i	−0.420084	+	0.342997i
$171$	10.9441	−	9.78866i	0.836913	−	0.748557i
$172$		−	2.02265i		−	0.154225i
$173$		−	11.5207i		−	0.875903i	−0.898999	−	0.437952i	$-0.855704\pi$
$173$		−	11.5207i		−	0.875903i	0.898999	−	0.437952i	$-0.144296\pi$
$174$	3.19808	+	1.43023i	0.242446	+	0.108425i
$175$		0			0
$176$			0.213422i			0.0160873i
$177$	3.47723	−	7.77531i	0.261364	−	0.584428i
$178$	−10.5744			−0.792584
$179$		−	14.9104i		−	1.11445i	−0.830361	−	0.557226i	$-0.811866\pi$
$179$		−	14.9104i		−	1.11445i	0.830361	−	0.557226i	$-0.188134\pi$
$180$	1.04456	−	6.62638i	0.0778566	−	0.493901i
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$		0			0
$183$	−5.47723	−	2.44949i	−0.404888	−	0.181071i
$184$	−6.47723			−0.477507
$185$	−12.3583	+	10.0905i	−0.908598	+	0.741867i
$186$	−0.477226	−	0.213422i	−0.0349919	−	0.0156488i
$187$	−0.674899			−0.0493535
$188$			7.75478i			0.565576i
$189$		0			0
$190$	−8.47723	+	6.92163i	−0.615003	+	0.502148i
$191$			1.59580i			0.115468i	0.998332	+	0.0577341i	$0.0183876\pi$
$191$			1.59580i			0.115468i	−0.998332	+	0.0577341i	$0.981612\pi$
$192$	−0.707107	+	1.58114i	−0.0510310	+	0.114109i
$193$		−	7.34847i		−	0.528954i	−0.964392	−	0.264477i	$-0.914801\pi$
$193$		−	7.34847i		−	0.528954i	0.964392	−	0.264477i	$-0.0851994\pi$
$194$	3.50333			0.251524
$195$	25.0540	−	6.77729i	1.79415	−	0.485332i
$196$		0			0
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$	0.477226	−	0.426844i	0.0339149	−	0.0303344i
$199$			22.4378i			1.59057i	0.606235	+	0.795286i	$0.292679\pi$
$199$			22.4378i			1.59057i	−0.606235	+	0.795286i	$0.707321\pi$
$200$	−1.00000	+	4.89898i	−0.0707107	+	0.346410i
$201$	8.42087	+	3.76593i	0.593962	+	0.265628i
$202$	−11.3137			−0.796030
$203$		0			0
$204$	−5.00000	−	2.23607i	−0.350070	−	0.156556i
$205$	9.47723	+	11.6072i	0.661918	+	0.810681i
$206$	−10.5744			−0.736753
$207$	12.9545	+	14.4835i	0.900397	+	1.00667i
$208$	−6.70141			−0.464659
$209$	−1.04456			−0.0722535
$210$		0			0
$211$	13.5228			0.930946			0.465473	−	0.885062i	$-0.345884\pi$
$211$	13.5228			0.930946			0.465473	+	0.885062i	$0.345884\pi$
$212$	5.00000			0.343401
$213$	−3.19808	−	1.43023i	−0.219129	−	0.0979975i
$214$	5.47723			0.374415
$215$	3.50333	−	2.86045i	0.238925	−	0.195081i
$216$	4.94975	−	1.58114i	0.336788	−	0.107583i
$217$		0			0
$218$	12.4317			0.841979
$219$	−8.47723	+	18.9557i	−0.572838	+	1.28090i
$220$	−0.369657	+	0.301824i	−0.0249223	+	0.0203490i
$221$		−	21.1917i		−	1.42551i
$222$	−11.2815	−	5.04524i	−0.757165	−	0.338614i
$223$	−6.39617			−0.428319			−0.214160	−	0.976799i	$-0.568701\pi$
$223$	−6.39617			−0.428319			−0.214160	+	0.976799i	$0.568701\pi$
$224$		0			0
$225$	12.9545	−	7.56189i	0.863630	−	0.504126i
$226$	6.52277			0.433889
$227$		−	10.3923i		−	0.689761i	−0.938647	−	0.344881i	$-0.887919\pi$
$227$		−	10.3923i		−	0.689761i	0.938647	−	0.344881i	$-0.112081\pi$
$228$	−7.73861	−	3.46081i	−0.512502	−	0.229198i
$229$		−	7.23003i		−	0.477774i	−0.971047	−	0.238887i	$-0.923218\pi$
$229$		−	7.23003i		−	0.477774i	0.971047	−	0.238887i	$-0.0767825\pi$
$230$	−9.16018	−	11.2189i	−0.604004	−	0.739751i
$231$		0			0
$232$		−	2.02265i		−	0.132793i
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$	13.4028	+	14.9848i	0.876170	+	0.979588i
$235$	−13.4317	+	10.9669i	−0.876186	+	0.715403i
$236$	−4.91754			−0.320105
$237$	−0.369657	+	0.826579i	−0.0240118	+	0.0536921i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−3.73861	+	1.01132i	−0.241326	+	0.0652806i
$241$		−	3.98886i		−	0.256945i	−0.991713	−	0.128472i	$-0.958993\pi$
$241$		−	3.98886i		−	0.256945i	0.991713	−	0.128472i	$-0.0410074\pi$
$242$	10.9545			0.704179
$243$	−13.4350	−	7.90569i	−0.861858	−	0.507151i
$244$			3.46410i			0.221766i
$245$		0			0
$246$	−4.73861	+	10.5959i	−0.302123	+	0.675567i
$247$		−	32.7989i		−	2.08694i
$248$			0.301824i			0.0191658i
$249$	26.4317	+	11.8206i	1.67504	+	0.749100i
$250$	−9.89949	+	5.19615i	−0.626099	+	0.328634i
$251$	−16.6009			−1.04784			−0.523920	−	0.851768i	$-0.675531\pi$
$251$	−16.6009			−1.04784			−0.523920	+	0.851768i	$0.675531\pi$
$252$		0			0
$253$		−	1.38238i		−	0.0869095i
$254$			13.6298i			0.855212i
$255$	−3.19808	−	11.8225i	−0.200272	−	0.740356i
$256$	1.00000			0.0625000
$257$		−	23.6451i		−	1.47494i	−0.675381	−	0.737469i	$-0.736021\pi$
$257$		−	23.6451i		−	1.47494i	0.675381	−	0.737469i	$-0.263979\pi$
$258$	3.19808	+	1.43023i	0.199104	+	0.0890420i
$259$		0			0
$260$	−9.47723	−	11.6072i	−0.587753	−	0.719847i
$261$	−4.52277	+	4.04529i	−0.279953	+	0.250397i
$262$	6.02651			0.372319
$263$	−2.00000			−0.123325			−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000			−0.123325			−0.0616626	+	0.998097i	$0.519640\pi$
$264$	−0.337449	−	0.150912i	−0.0207686	−	0.00928799i
$265$	7.07107	+	8.66025i	0.434372	+	0.531995i
$266$		0			0
$267$	7.47723	−	16.7196i	0.457599	−	1.02322i
$268$		−	5.32582i		−	0.325326i
$269$	28.8948			1.76174			0.880872	−	0.473354i	$-0.156957\pi$
$269$	28.8948			1.76174			0.880872	+	0.473354i	$0.156957\pi$
$270$	9.73861	+	6.33715i	0.592673	+	0.385666i
$271$			6.32456i			0.384189i	0.981376	+	0.192095i	$0.0615281\pi$
$271$			6.32456i			0.384189i	−0.981376	+	0.192095i	$0.938472\pi$
$272$			3.16228i			0.191741i
$273$		0			0
$274$	7.47723			0.451716
$275$	−1.04555	−	0.213422i	−0.0630490	−	0.0128698i
$276$	4.58009	−	10.2414i	0.275689	−	0.616459i
$277$			9.79796i			0.588702i	0.955697	+	0.294351i	$0.0951035\pi$
$277$			9.79796i			0.588702i	−0.955697	+	0.294351i	$0.904896\pi$
$278$			7.53185i			0.451730i
$279$	0.674899	−	0.603648i	0.0404051	−	0.0361395i
$280$		0			0
$281$			11.6072i			0.692427i	0.938156	+	0.346213i	$0.112533\pi$
$281$			11.6072i			0.692427i	−0.938156	+	0.346213i	$0.887467\pi$
$282$	−12.2614	−	5.48346i	−0.730155	−	0.326535i
$283$	−24.7165			−1.46925			−0.734623	−	0.678476i	$-0.762641\pi$
$283$	−24.7165			−1.46925			−0.734623	+	0.678476i	$0.762641\pi$
$284$			2.02265i			0.120022i
$285$	−4.94975	−	18.2980i	−0.293198	−	1.08388i
$286$		−	1.43023i		−	0.0845711i
$287$		0			0
$288$	−2.00000	−	2.23607i	−0.117851	−	0.131762i
$289$	7.00000			0.411765
$290$	3.50333	−	2.86045i	0.205722	−	0.167972i
$291$	−2.47723	+	5.53924i	−0.145218	+	0.324716i
$292$	11.9886			0.701580
$293$		−	4.59250i		−	0.268297i	−0.990961	−	0.134148i	$-0.957170\pi$
$293$		−	4.59250i		−	0.268297i	0.990961	−	0.134148i	$-0.0428299\pi$
$294$		0			0
$295$	−6.95445	−	8.51743i	−0.404904	−	0.495904i
$296$			7.13505i			0.414716i
$297$	0.337449	+	1.05638i	0.0195808	+	0.0612976i
$298$		−	2.44949i		−	0.141895i
$299$	43.4065			2.51027
$300$	−7.03886	−	5.04524i	−0.406389	−	0.291287i
$301$		0			0
$302$	−2.00000			−0.115087
$303$	8.00000	−	17.8885i	0.459588	−	1.02767i
$304$			4.89433i			0.280709i
$305$	−6.00000	+	4.89898i	−0.343559	+	0.280515i
$306$	7.07107	−	6.32456i	0.404226	−	0.361551i
$307$	−3.50333			−0.199945			−0.0999727	−	0.994990i	$-0.531876\pi$
$307$	−3.50333			−0.199945			−0.0999727	+	0.994990i	$0.531876\pi$
$308$		0			0
$309$	7.47723	−	16.7196i	0.425365	−	0.951144i
$310$	−0.522774	+	0.426844i	−0.0296916	+	0.0242431i
$311$	28.8948			1.63847			0.819236	−	0.573457i	$-0.194398\pi$
$311$	28.8948			1.63847			0.819236	+	0.573457i	$0.194398\pi$
$312$	4.73861	−	10.5959i	0.268271	−	0.599872i
$313$	23.2379			1.31348			0.656742	−	0.754115i	$-0.271934\pi$
$313$	23.2379			1.31348			0.656742	+	0.754115i	$0.271934\pi$
$314$	8.79052			0.496078
$315$		0			0
$316$	0.522774			0.0294084
$317$	33.9089			1.90451			0.952257	−	0.305298i	$-0.0987561\pi$
$317$	33.9089			1.90451			0.952257	+	0.305298i	$0.0987561\pi$
$318$	−3.53553	+	7.90569i	−0.198263	+	0.443329i
$319$	0.431677			0.0241693
$320$	1.41421	+	1.73205i	0.0790569	+	0.0968246i
$321$	−3.87298	+	8.66025i	−0.216169	+	0.483368i
$322$		0			0
$323$	−15.4772			−0.861176
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$	6.70141	−	32.8301i	0.371727	−	1.82108i
$326$			14.6969i			0.813988i
$327$	−8.79052	+	19.6562i	−0.486117	+	1.08699i
$328$	6.70141			0.370023
$329$		0			0
$330$	−0.215838	−	0.797901i	−0.0118815	−	0.0439230i
$331$	−11.4317			−0.628342			−0.314171	−	0.949366i	$-0.601726\pi$
$331$	−11.4317			−0.628342			−0.314171	+	0.949366i	$0.601726\pi$
$332$		−	16.7169i		−	0.917457i
$333$	15.9545	−	14.2701i	0.874299	−	0.781996i
$334$			14.6830i			0.803417i
$335$	9.22460	−	7.53185i	0.503994	−	0.411509i
$336$		0			0
$337$			17.1464i			0.934025i	0.884251	+	0.467013i	$0.154670\pi$
$337$			17.1464i			0.934025i	−0.884251	+	0.467013i	$0.845330\pi$
$338$	31.9089			1.73562
$339$	−4.61230	+	10.3134i	−0.250506	+	0.560148i
$340$	−5.47723	+	4.47214i	−0.297044	+	0.242536i
$341$	−0.0644158			−0.00348831
$342$	10.9441	−	9.78866i	0.591787	−	0.529310i
$343$		0			0
$344$		−	2.02265i		−	0.109054i
$345$	24.2158	−	6.55057i	1.30374	−	0.352671i
$346$		−	11.5207i		−	0.619357i
$347$	−6.52277			−0.350161			−0.175080	−	0.984554i	$-0.556019\pi$
$347$	−6.52277			−0.350161			−0.175080	+	0.984554i	$0.556019\pi$
$348$	3.19808	+	1.43023i	0.171435	+	0.0766682i
$349$			32.5282i			1.74120i	0.491994	+	0.870599i	$0.336268\pi$
$349$			32.5282i			1.74120i	−0.491994	+	0.870599i	$0.663732\pi$
$350$		0			0
$351$	−33.1703	+	10.5959i	−1.77050	+	0.565565i
$352$			0.213422i			0.0113754i
$353$		−	13.2528i		−	0.705373i	−0.935742	−	0.352687i	$-0.885268\pi$
$353$		−	13.2528i		−	0.705373i	0.935742	−	0.352687i	$-0.114732\pi$
$354$	3.47723	−	7.77531i	0.184812	−	0.413253i
$355$	−3.50333	+	2.86045i	−0.185937	+	0.151817i
$356$	−10.5744			−0.560442
$357$		0			0
$358$		−	14.9104i		−	0.788037i
$359$		−	6.49478i		−	0.342781i	−0.985203	−	0.171391i	$-0.945174\pi$
$359$		−	6.49478i		−	0.342781i	0.985203	−	0.171391i	$-0.0548261\pi$
$360$	1.04456	−	6.62638i	0.0550529	−	0.349241i
$361$	−4.95445			−0.260761
$362$		−	3.16228i		−	0.166206i
$363$	−7.74597	+	17.3205i	−0.406558	+	0.909091i
$364$		0			0
$365$	16.9545	+	20.7649i	0.887437	+	1.08688i
$366$	−5.47723	−	2.44949i	−0.286299	−	0.128037i
$367$	−8.11562			−0.423632			−0.211816	−	0.977310i	$-0.567938\pi$
$367$	−8.11562			−0.423632			−0.211816	+	0.977310i	$0.567938\pi$
$368$	−6.47723			−0.337649
$369$	−13.4028	−	14.9848i	−0.697723	−	0.780078i
$370$	−12.3583	+	10.0905i	−0.642476	+	0.524579i
$371$		0			0
$372$	−0.477226	−	0.213422i	−0.0247430	−	0.0110654i
$373$			3.61845i			0.187356i	0.995603	+	0.0936781i	$0.0298624\pi$
$373$			3.61845i			0.187356i	−0.995603	+	0.0936781i	$0.970138\pi$
$374$	−0.674899			−0.0348982
$375$	−1.21584	−	19.3267i	−0.0627856	−	0.998027i
$376$			7.75478i			0.399922i
$377$			13.5546i			0.698097i
$378$		0			0
$379$	−9.52277			−0.489152			−0.244576	−	0.969630i	$-0.578649\pi$
$379$	−9.52277			−0.489152			−0.244576	+	0.969630i	$0.578649\pi$
$380$	−8.47723	+	6.92163i	−0.434872	+	0.355072i
$381$	−21.5507	−	9.63774i	−1.10407	−	0.493757i
$382$			1.59580i			0.0816484i
$383$		−	0.826579i		−	0.0422362i	−0.999777	−	0.0211181i	$-0.993277\pi$
$383$		−	0.826579i		−	0.0422362i	0.999777	−	0.0211181i	$-0.00672260\pi$
$384$	−0.707107	+	1.58114i	−0.0360844	+	0.0806872i
$385$		0			0
$386$		−	7.34847i		−	0.374027i
$387$	−4.52277	+	4.04529i	−0.229906	+	0.205634i
$388$	3.50333			0.177854
$389$		−	7.34847i		−	0.372582i	−0.982495	−	0.186291i	$-0.940353\pi$
$389$		−	7.34847i		−	0.372582i	0.982495	−	0.186291i	$-0.0596468\pi$
$390$	25.0540	−	6.77729i	1.26866	−	0.343181i
$391$		−	20.4828i		−	1.03586i
$392$		0			0
$393$	−4.26139	+	9.52875i	−0.214959	+	0.480662i
$394$	9.00000			0.453413
$395$	0.739315	+	0.905472i	0.0371990	+	0.0455592i
$396$	0.477226	−	0.426844i	0.0239815	−	0.0214497i
$397$	−30.3734			−1.52440			−0.762198	−	0.647344i	$-0.775880\pi$
$397$	−30.3734			−1.52440			−0.762198	+	0.647344i	$0.775880\pi$
$398$			22.4378i			1.12470i
$399$		0			0
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$			30.3494i			1.51558i	0.652500	+	0.757789i	$0.273720\pi$
$401$			30.3494i			1.51558i	−0.652500	+	0.757789i	$0.726280\pi$
$402$	8.42087	+	3.76593i	0.419995	+	0.187827i
$403$		−	2.02265i		−	0.100755i
$404$	−11.3137			−0.562878
$405$	−16.9061	+	10.9171i	−0.840073	+	0.542473i
$406$		0			0
$407$	−1.52277			−0.0754811
$408$	−5.00000	−	2.23607i	−0.247537	−	0.110702i
$409$			22.4378i			1.10948i	0.832025	+	0.554738i	$0.187182\pi$
$409$			22.4378i			1.10948i	−0.832025	+	0.554738i	$0.812818\pi$
$410$	9.47723	+	11.6072i	0.468047	+	0.573238i
$411$	−5.28720	+	11.8225i	−0.260798	+	0.583162i
$412$	−10.5744			−0.520963
$413$		0			0
$414$	12.9545	+	14.4835i	0.636677	+	0.711826i
$415$	28.9545	−	23.6412i	1.42132	−	1.16050i
$416$	−6.70141			−0.328564
$417$	−11.9089	−	5.32582i	−0.583181	−	0.260807i
$418$	−1.04456			−0.0510909
$419$	16.6009			0.811007			0.405504	−	0.914093i	$-0.367096\pi$
$419$	16.6009			0.811007			0.405504	+	0.914093i	$0.367096\pi$
$420$		0			0
$421$	−2.95445			−0.143991			−0.0719956	−	0.997405i	$-0.522937\pi$
$421$	−2.95445			−0.143991			−0.0719956	+	0.997405i	$0.522937\pi$
$422$	13.5228			0.658278
$423$	17.3402	−	15.5096i	0.843110	−	0.754101i
$424$	5.00000			0.242821
$425$	−15.4919	−	3.16228i	−0.751469	−	0.153393i
$426$	−3.19808	−	1.43023i	−0.154948	−	0.0692947i
$427$		0			0
$428$	5.47723			0.264752
$429$	2.26139	+	1.01132i	0.109181	+	0.0488271i
$430$	3.50333	−	2.86045i	0.168945	−	0.137943i
$431$			37.0576i			1.78500i	0.451045	+	0.892501i	$0.351051\pi$
$431$			37.0576i			1.78500i	−0.451045	+	0.892501i	$0.648949\pi$
$432$	4.94975	−	1.58114i	0.238145	−	0.0760726i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	2.04555	+	7.56189i	0.0980766	+	0.362565i
$436$	12.4317			0.595369
$437$		−	31.7017i		−	1.51650i
$438$	−8.47723	+	18.9557i	−0.405058	+	0.905736i
$439$			22.7396i			1.08530i	0.839958	+	0.542651i	$0.182579\pi$
$439$			22.7396i			1.08530i	−0.839958	+	0.542651i	$0.817421\pi$
$440$	−0.369657	+	0.301824i	−0.0176227	+	0.0143889i
$441$		0			0
$442$		−	21.1917i		−	1.00799i
$443$	−36.9545			−1.75576			−0.877879	−	0.478882i	$-0.841042\pi$
$443$	−36.9545			−1.75576			−0.877879	+	0.478882i	$0.841042\pi$
$444$	−11.2815	−	5.04524i	−0.535396	−	0.239437i
$445$	−14.9545	−	18.3154i	−0.708909	−	0.868233i
$446$	−6.39617			−0.302867
$447$	3.87298	+	1.73205i	0.183186	+	0.0819232i
$448$		0			0
$449$		−	3.51660i		−	0.165959i	−0.996551	−	0.0829793i	$-0.973556\pi$
$449$		−	3.51660i		−	0.165959i	0.996551	−	0.0829793i	$-0.0264435\pi$
$450$	12.9545	−	7.56189i	0.610679	−	0.356471i
$451$			1.43023i			0.0673468i
$452$	6.52277			0.306806
$453$	1.41421	−	3.16228i	0.0664455	−	0.148577i
$454$		−	10.3923i		−	0.487735i
$455$		0			0
$456$	−7.73861	−	3.46081i	−0.362394	−	0.162067i
$457$			37.9113i			1.77342i	0.462330	+	0.886708i	$0.347014\pi$
$457$			37.9113i			1.77342i	−0.462330	+	0.886708i	$0.652986\pi$
$458$		−	7.23003i		−	0.337837i
$459$	5.00000	+	15.6525i	0.233380	+	0.730595i
$460$	−9.16018	−	11.2189i	−0.427096	−	0.523083i
$461$	16.2957			0.758965			0.379482	−	0.925199i	$-0.376102\pi$
$461$	16.2957			0.758965			0.379482	+	0.925199i	$0.376102\pi$
$462$		0			0
$463$			17.6751i			0.821433i	0.911763	+	0.410716i	$0.134721\pi$
$463$			17.6751i			0.821433i	−0.911763	+	0.410716i	$0.865279\pi$
$464$		−	2.02265i		−	0.0938990i
$465$	−0.305242	−	1.12840i	−0.0141552	−	0.0523284i
$466$	−4.00000			−0.185296
$467$		−	34.3392i		−	1.58903i	−0.607246	−	0.794514i	$-0.707726\pi$
$467$		−	34.3392i		−	1.58903i	0.607246	−	0.794514i	$-0.292274\pi$
$468$	13.4028	+	14.9848i	0.619546	+	0.692673i
$469$		0			0
$470$	−13.4317	+	10.9669i	−0.619557	+	0.505866i
$471$	−6.21584	+	13.8990i	−0.286411	+	0.640434i
$472$	−4.91754			−0.226348
$473$	0.431677			0.0198485
$474$	−0.369657	+	0.826579i	−0.0169789	+	0.0379660i
$475$	−23.9772	−	4.89433i	−1.10015	−	0.224567i
$476$		0			0
$477$	−10.0000	−	11.1803i	−0.457869	−	0.511913i
$478$		0			0
$479$	11.3781			0.519880			0.259940	−	0.965625i	$-0.416297\pi$
$479$	11.3781			0.519880			0.259940	+	0.965625i	$0.416297\pi$
$480$	−3.73861	+	1.01132i	−0.170644	+	0.0461604i
$481$		−	47.8149i		−	2.18017i
$482$		−	3.98886i		−	0.181687i
$483$		0			0
$484$	10.9545			0.497930
$485$	4.95445	+	6.06794i	0.224970	+	0.275531i
$486$	−13.4350	−	7.90569i	−0.609425	−	0.358610i
$487$		−	36.6308i		−	1.65990i	−0.557839	−	0.829949i	$-0.688369\pi$
$487$		−	36.6308i		−	1.65990i	0.557839	−	0.829949i	$-0.311631\pi$
$488$			3.46410i			0.156813i
$489$	−23.2379	−	10.3923i	−1.05085	−	0.469956i
$490$		0			0
$491$		−	4.04529i		−	0.182561i	−0.995825	−	0.0912807i	$-0.970904\pi$
$491$		−	4.04529i		−	0.182561i	0.995825	−	0.0912807i	$-0.0290961\pi$
$492$	−4.73861	+	10.5959i	−0.213633	+	0.477698i
$493$	6.39617			0.288069
$494$		−	32.7989i		−	1.47569i
$495$	1.41421	+	0.222931i	0.0635642	+	0.0100200i
$496$			0.301824i			0.0135523i
$497$		0			0
$498$	26.4317	+	11.8206i	1.18443	+	0.529694i
$499$	−41.9089			−1.87610			−0.938050	−	0.346500i	$-0.887370\pi$
$499$	−41.9089			−1.87610			−0.938050	+	0.346500i	$0.887370\pi$
$500$	−9.89949	+	5.19615i	−0.442719	+	0.232379i
$501$	−23.2158	−	10.3824i	−1.03721	−	0.463853i
$502$	−16.6009			−0.740935
$503$		−	22.4378i		−	1.00045i	−0.865895	−	0.500225i	$-0.833251\pi$
$503$		−	22.4378i		−	1.00045i	0.865895	−	0.500225i	$-0.166749\pi$
$504$		0			0
$505$	−16.0000	−	19.5959i	−0.711991	−	0.872007i
$506$		−	1.38238i		−	0.0614543i
$507$	−22.5630	+	50.4524i	−1.00206	+	2.24067i
$508$			13.6298i			0.604726i
$509$	9.22460			0.408873			0.204437	−	0.978880i	$-0.434464\pi$
$509$	9.22460			0.408873			0.204437	+	0.978880i	$0.434464\pi$
$510$	−3.19808	−	11.8225i	−0.141614	−	0.523511i
$511$		0			0
$512$	1.00000			0.0441942
$513$	7.73861	+	24.2257i	0.341668	+	1.06959i
$514$		−	23.6451i		−	1.04294i
$515$	−14.9545	−	18.3154i	−0.658972	−	0.807072i
$516$	3.19808	+	1.43023i	0.140788	+	0.0629622i
$517$	−1.65504			−0.0727885
$518$		0			0
$519$	18.2158	+	8.14637i	0.799587	+	0.357586i
$520$	−9.47723	−	11.6072i	−0.415604	−	0.509009i
$521$	−18.6256			−0.816002			−0.408001	−	0.912981i	$-0.633774\pi$
$521$	−18.6256			−0.816002			−0.408001	+	0.912981i	$0.633774\pi$
$522$	−4.52277	+	4.04529i	−0.197956	+	0.177058i
$523$	−14.0777			−0.615576			−0.307788	−	0.951455i	$-0.599589\pi$
$523$	−14.0777			−0.615576			−0.307788	+	0.951455i	$0.599589\pi$
$524$	6.02651			0.263269
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	−0.954451			−0.0415765
$528$	−0.337449	−	0.150912i	−0.0146856	−	0.00656760i
$529$	18.9545			0.824107
$530$	7.07107	+	8.66025i	0.307148	+	0.376177i
$531$	9.83508	+	10.9960i	0.426806	+	0.477184i
$532$		0			0
$533$	−44.9089			−1.94522
$534$	7.47723	−	16.7196i	0.323571	−	0.723527i
$535$	7.74597	+	9.48683i	0.334887	+	0.410152i
$536$		−	5.32582i		−	0.230041i
$537$	23.5753	+	10.5432i	1.01735	+	0.454973i
$538$	28.8948			1.24574
$539$		0			0
$540$	9.73861	+	6.33715i	0.419083	+	0.272707i
$541$	19.4772			0.837391			0.418696	−	0.908127i	$-0.362487\pi$
$541$	19.4772			0.837391			0.418696	+	0.908127i	$0.362487\pi$
$542$			6.32456i			0.271663i
$543$	5.00000	+	2.23607i	0.214571	+	0.0959589i
$544$			3.16228i			0.135582i
$545$	17.5810	+	21.5323i	0.753089	+	0.922342i
$546$		0			0
$547$		−	23.2144i		−	0.992575i	−0.868158	−	0.496287i	$-0.834696\pi$
$547$		−	23.2144i		−	0.992575i	0.868158	−	0.496287i	$-0.165304\pi$
$548$	7.47723			0.319411
$549$	7.74597	−	6.92820i	0.330590	−	0.295689i
$550$	−1.04555	−	0.213422i	−0.0445824	−	0.00910033i
$551$	9.89949			0.421733
$552$	4.58009	−	10.2414i	0.194942	−	0.435903i
$553$		0			0
$554$			9.79796i			0.416275i
$555$	−7.21584	−	26.6752i	−0.306295	−	1.13230i
$556$			7.53185i			0.319422i
$557$	−37.8634			−1.60432			−0.802161	−	0.597108i	$-0.796316\pi$
$557$	−37.8634			−1.60432			−0.802161	+	0.597108i	$0.796316\pi$
$558$	0.674899	−	0.603648i	0.0285707	−	0.0255545i
$559$			13.5546i			0.573298i
$560$		0			0
$561$	0.477226	−	1.06711i	0.0201485	−	0.0450534i
$562$			11.6072i			0.489619i
$563$		−	10.3923i		−	0.437983i	−0.975727	−	0.218992i	$-0.929723\pi$
$563$		−	10.3923i		−	0.437983i	0.975727	−	0.218992i	$-0.0702768\pi$
$564$	−12.2614	−	5.48346i	−0.516298	−	0.230895i
$565$	9.22460	+	11.2978i	0.388082	+	0.475301i
$566$	−24.7165			−1.03891
$567$		0			0
$568$			2.02265i			0.0848683i
$569$		−	12.0340i		−	0.504493i	−0.967663	−	0.252246i	$-0.918831\pi$
$569$		−	12.0340i		−	0.504493i	0.967663	−	0.252246i	$-0.0811693\pi$
$570$	−4.94975	−	18.2980i	−0.207322	−	0.766419i
$571$	−6.95445			−0.291035			−0.145517	−	0.989356i	$-0.546485\pi$
$571$	−6.95445			−0.291035			−0.145517	+	0.989356i	$0.546485\pi$
$572$		−	1.43023i		−	0.0598008i
$573$	−2.52319	−	1.12840i	−0.105408	−	0.0471397i
$574$		0			0
$575$	6.47723	−	31.7318i	0.270119	−	1.32331i
$576$	−2.00000	−	2.23607i	−0.0833333	−	0.0931695i
$577$	−14.8170			−0.616841			−0.308421	−	0.951250i	$-0.599800\pi$
$577$	−14.8170			−0.616841			−0.308421	+	0.951250i	$0.599800\pi$
$578$	7.00000			0.291162
$579$	11.6190	+	5.19615i	0.482867	+	0.215945i
$580$	3.50333	−	2.86045i	0.145468	−	0.118774i
$581$		0			0
$582$	−2.47723	+	5.53924i	−0.102684	+	0.229609i
$583$			1.06711i			0.0441951i
$584$	11.9886			0.496092
$585$	−7.00000	+	44.4061i	−0.289414	+	1.83597i
$586$		−	4.59250i		−	0.189715i
$587$		−	27.4110i		−	1.13137i	−0.824621	−	0.565686i	$-0.808611\pi$
$587$		−	27.4110i		−	1.13137i	0.824621	−	0.565686i	$-0.191389\pi$
$588$		0			0
$589$	−1.47723			−0.0608680
$590$	−6.95445	−	8.51743i	−0.286310	−	0.350657i
$591$	−6.36396	+	14.2302i	−0.261778	+	0.585354i
$592$			7.13505i			0.293249i
$593$			36.2942i			1.49042i	0.666828	+	0.745212i	$0.267652\pi$
$593$			36.2942i			1.49042i	−0.666828	+	0.745212i	$0.732348\pi$
$594$	0.337449	+	1.05638i	0.0138457	+	0.0433440i
$595$		0			0
$596$		−	2.44949i		−	0.100335i
$597$	−35.4772	−	15.8659i	−1.45199	−	0.649348i
$598$	43.4065			1.77503
$599$			5.75267i			0.235048i	0.993070	+	0.117524i	$0.0374956\pi$
$599$			5.75267i			0.235048i	−0.993070	+	0.117524i	$0.962504\pi$
$600$	−7.03886	−	5.04524i	−0.287360	−	0.205971i
$601$		−	16.7169i		−	0.681895i	−0.940082	−	0.340947i	$-0.889252\pi$
$601$		−	16.7169i		−	0.681895i	0.940082	−	0.340947i	$-0.110748\pi$
$602$		0			0
$603$	−11.9089	+	10.6516i	−0.484968	+	0.433769i
$604$	−2.00000			−0.0813788
$605$	15.4919	+	18.9737i	0.629837	+	0.771389i
$606$	8.00000	−	17.8885i	0.324978	−	0.726672i
$607$	26.4360			1.07300			0.536502	−	0.843899i	$-0.319745\pi$
$607$	26.4360			1.07300			0.536502	+	0.843899i	$0.319745\pi$
$608$			4.89433i			0.198491i
$609$		0			0
$610$	−6.00000	+	4.89898i	−0.242933	+	0.198354i
$611$		−	51.9680i		−	2.10240i
$612$	7.07107	−	6.32456i	0.285831	−	0.255655i
$613$			25.4504i			1.02793i	0.857810	+	0.513967i	$0.171825\pi$
$613$			25.4504i			1.02793i	−0.857810	+	0.513967i	$0.828175\pi$
$614$	−3.50333			−0.141383
$615$	−25.0540	+	6.77729i	−1.01027	+	0.273287i
$616$		0			0
$617$	25.4772			1.02567			0.512837	−	0.858486i	$-0.328594\pi$
$617$	25.4772			1.02567			0.512837	+	0.858486i	$0.328594\pi$
$618$	7.47723	−	16.7196i	0.300778	−	0.672560i
$619$			26.7284i			1.07431i	0.843484	+	0.537154i	$0.180500\pi$
$619$			26.7284i			1.07431i	−0.843484	+	0.537154i	$0.819500\pi$
$620$	−0.522774	+	0.426844i	−0.0209951	+	0.0171424i
$621$	−32.0606	+	10.2414i	−1.28655	+	0.410973i
$622$	28.8948			1.15857
$623$		0			0
$624$	4.73861	−	10.5959i	0.189696	−	0.424174i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	23.2379			0.928773
$627$	0.738613	−	1.65159i	0.0294974	−	0.0659581i
$628$	8.79052			0.350780
$629$	−22.5630			−0.899646
$630$		0			0
$631$	−7.47723			−0.297664			−0.148832	−	0.988863i	$-0.547551\pi$
$631$	−7.47723			−0.297664			−0.148832	+	0.988863i	$0.547551\pi$
$632$	0.522774			0.0207949
$633$	−9.56205	+	21.3814i	−0.380057	+	0.849834i
$634$	33.9089			1.34669
$635$	−23.6076	+	19.2755i	−0.936837	+	0.764924i
$636$	−3.53553	+	7.90569i	−0.140193	+	0.313481i
$637$		0			0
$638$	0.431677			0.0170902
$639$	4.52277	−	4.04529i	0.178918	−	0.160029i
$640$	1.41421	+	1.73205i	0.0559017	+	0.0684653i
$641$			6.28136i			0.248099i	0.992276	+	0.124049i	$0.0395881\pi$
$641$			6.28136i			0.248099i	−0.992276	+	0.124049i	$0.960412\pi$
$642$	−3.87298	+	8.66025i	−0.152854	+	0.341793i
$643$	20.4095			0.804871			0.402436	−	0.915448i	$-0.368164\pi$
$643$	20.4095			0.804871			0.402436	+	0.915448i	$0.368164\pi$
$644$		0			0
$645$	2.04555	+	7.56189i	0.0805434	+	0.297749i
$646$	−15.4772			−0.608943
$647$			23.8680i			0.938348i	0.883106	+	0.469174i	$0.155448\pi$
$647$			23.8680i			0.938348i	−0.883106	+	0.469174i	$0.844552\pi$
$648$	−1.00000	+	8.94427i	−0.0392837	+	0.351364i
$649$		−	1.04951i		−	0.0411969i
$650$	6.70141	−	32.8301i	0.262851	−	1.28770i
$651$		0			0
$652$			14.6969i			0.575577i
$653$	−25.8634			−1.01211			−0.506056	−	0.862501i	$-0.668897\pi$
$653$	−25.8634			−1.01211			−0.506056	+	0.862501i	$0.668897\pi$
$654$	−8.79052	+	19.6562i	−0.343737	+	0.768619i
$655$	8.52277	+	10.4382i	0.333012	+	0.407855i
$656$	6.70141			0.261646
$657$	−23.9772	−	26.8073i	−0.935440	−	1.04585i
$658$		0			0
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	−0.215838	−	0.797901i	−0.00840150	−	0.0310583i
$661$		−	13.2528i		−	0.515473i	−0.966215	−	0.257736i	$-0.917023\pi$
$661$		−	13.2528i		−	0.515473i	0.966215	−	0.257736i	$-0.0829766\pi$
$662$	−11.4317			−0.444305
$663$	33.5071	+	14.9848i	1.30131	+	0.581962i
$664$		−	16.7169i		−	0.648740i
$665$		0			0
$666$	15.9545	−	14.2701i	0.618222	−	0.552955i
$667$			13.1011i			0.507278i
$668$			14.6830i			0.568102i
$669$	4.52277	−	10.1132i	0.174861	−	0.391000i
$670$	9.22460	−	7.53185i	0.356377	−	0.290981i
$671$	−0.739315			−0.0285409
$672$		0			0
$673$			48.4514i			1.86766i	0.357713	+	0.933832i	$0.383557\pi$
$673$			48.4514i			1.86766i	−0.357713	+	0.933832i	$0.616443\pi$
$674$			17.1464i			0.660456i
$675$	2.79622	+	25.8299i	0.107627	+	0.994191i
$676$	31.9089			1.22727
$677$		−	32.9090i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$677$		−	32.9090i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$678$	−4.61230	+	10.3134i	−0.177134	+	0.396084i
$679$		0			0
$680$	−5.47723	+	4.47214i	−0.210042	+	0.171499i
$681$	16.4317	+	7.34847i	0.629663	+	0.281594i
$682$	−0.0644158			−0.00246661
$683$	2.95445			0.113049			0.0565245	−	0.998401i	$-0.481998\pi$
$683$	2.95445			0.113049			0.0565245	+	0.998401i	$0.481998\pi$
$684$	10.9441	−	9.78866i	0.418456	−	0.374279i
$685$	10.5744	+	12.9509i	0.404027	+	0.494830i
$686$		0			0
$687$	11.4317	+	5.11240i	0.436146	+	0.195050i
$688$		−	2.02265i		−	0.0771127i
$689$	−33.5071			−1.27652
$690$	24.2158	−	6.55057i	0.921881	−	0.249376i
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$		−	11.5207i		−	0.437952i
$693$		0			0
$694$	−6.52277			−0.247601
$695$	−13.0455	+	10.6516i	−0.494846	+	0.404040i
$696$	3.19808	+	1.43023i	0.121223	+	0.0542126i
$697$			21.1917i			0.802694i
$698$			32.5282i			1.23121i
$699$	2.82843	−	6.32456i	0.106981	−	0.239217i
$700$		0			0
$701$			7.03320i			0.265640i	0.991140	+	0.132820i	$0.0424033\pi$
$701$			7.03320i			0.265640i	−0.991140	+	0.132820i	$0.957597\pi$
$702$	−33.1703	+	10.5959i	−1.25193	+	0.399915i
$703$	−34.9213			−1.31708
$704$			0.213422i			0.00804364i
$705$	−7.84259	−	28.9921i	−0.295369	−	1.09191i
$706$		−	13.2528i		−	0.498774i
$707$		0			0
$708$	3.47723	−	7.77531i	0.130682	−	0.292214i
$709$	10.4317			0.391770			0.195885	−	0.980627i	$-0.437242\pi$
$709$	10.4317			0.391770			0.195885	+	0.980627i	$0.437242\pi$
$710$	−3.50333	+	2.86045i	−0.131477	+	0.107351i
$711$	−1.04555	−	1.16896i	−0.0392111	−	0.0438394i
$712$	−10.5744			−0.396292
$713$		−	1.95498i		−	0.0732146i
$714$		0			0
$715$	2.47723	−	2.02265i	0.0926430	−	0.0756427i
$716$		−	14.9104i		−	0.557226i
$717$		0			0
$718$		−	6.49478i		−	0.242383i
$719$	−47.2795			−1.76323			−0.881614	−	0.471970i	$-0.843543\pi$
$719$	−47.2795			−1.76323			−0.881614	+	0.471970i	$0.843543\pi$
$720$	1.04456	−	6.62638i	0.0389283	−	0.246951i
$721$		0			0
$722$	−4.95445			−0.184386
$723$	6.30694	+	2.82055i	0.234557	+	0.104897i
$724$		−	3.16228i		−	0.117525i
$725$	9.90890	+	2.02265i	0.368007	+	0.0751192i
$726$	−7.74597	+	17.3205i	−0.287480	+	0.642824i
$727$	23.6076			0.875556			0.437778	−	0.899083i	$-0.355766\pi$
$727$	23.6076			0.875556			0.437778	+	0.899083i	$0.355766\pi$
$728$		0			0
$729$	22.0000	−	15.6525i	0.814815	−	0.579721i
$730$	16.9545	+	20.7649i	0.627512	+	0.768543i
$731$	6.39617			0.236571
$732$	−5.47723	−	2.44949i	−0.202444	−	0.0905357i
$733$	36.3355			1.34208			0.671041	−	0.741420i	$-0.265848\pi$
$733$	36.3355			1.34208			0.671041	+	0.741420i	$0.265848\pi$
$734$	−8.11562			−0.299553
$735$		0			0
$736$	−6.47723			−0.238754
$737$	1.13665			0.0418689
$738$	−13.4028	−	14.9848i	−0.493365	−	0.551598i
$739$	−4.47723			−0.164697			−0.0823487	−	0.996604i	$-0.526242\pi$
$739$	−4.47723			−0.164697			−0.0823487	+	0.996604i	$0.526242\pi$
$740$	−12.3583	+	10.0905i	−0.454299	+	0.370933i
$741$	51.8596	+	23.1923i	1.90511	+	0.851991i
$742$		0			0
$743$	−19.4317			−0.712879			−0.356440	−	0.934318i	$-0.616009\pi$
$743$	−19.4317			−0.712879			−0.356440	+	0.934318i	$0.616009\pi$
$744$	−0.477226	−	0.213422i	−0.0174959	−	0.00782442i
$745$	4.24264	−	3.46410i	0.155438	−	0.126915i
$746$			3.61845i			0.132481i
$747$	−37.3800	+	33.4337i	−1.36766	+	1.22328i
$748$	−0.674899			−0.0246767
$749$		0			0
$750$	−1.21584	−	19.3267i	−0.0443961	−	0.705712i
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$			7.75478i			0.282788i
$753$	11.7386	−	26.2483i	0.427779	−	0.956543i
$754$			13.5546i			0.493629i
$755$	−2.82843	−	3.46410i	−0.102937	−	0.126072i
$756$		0			0
$757$		−	30.2476i		−	1.09937i	−0.835373	−	0.549683i	$-0.814748\pi$
$757$		−	30.2476i		−	1.09937i	0.835373	−	0.549683i	$-0.185252\pi$
$758$	−9.52277			−0.345883
$759$	2.18574	+	0.977491i	0.0793372	+	0.0354807i
$760$	−8.47723	+	6.92163i	−0.307501	+	0.251074i
$761$	9.52984			0.345456			0.172728	−	0.984970i	$-0.444742\pi$
$761$	9.52984			0.345456			0.172728	+	0.984970i	$0.444742\pi$
$762$	−21.5507	−	9.63774i	−0.780698	−	0.349139i
$763$		0			0
$764$			1.59580i			0.0577341i
$765$	20.9545	+	3.30318i	0.757610	+	0.119427i
$766$		−	0.826579i		−	0.0298655i
$767$	32.9545			1.18992
$768$	−0.707107	+	1.58114i	−0.0255155	+	0.0570544i
$769$		−	28.8412i		−	1.04004i	−0.854154	−	0.520020i	$-0.825924\pi$
$769$		−	28.8412i		−	1.04004i	0.854154	−	0.520020i	$-0.174076\pi$
$770$		0			0
$771$	37.3861	+	16.7196i	1.34643	+	0.602141i
$772$		−	7.34847i		−	0.264477i
$773$			28.8412i			1.03735i	0.854973	+	0.518673i	$0.173574\pi$
$773$			28.8412i			1.03735i	−0.854973	+	0.518673i	$0.826426\pi$
$774$	−4.52277	+	4.04529i	−0.162568	+	0.145405i
$775$	−1.47863	−	0.301824i	−0.0531139	−	0.0108418i
$776$	3.50333			0.125762
$777$		0			0
$778$		−	7.34847i		−	0.263455i
$779$			32.7989i			1.17514i
$780$	25.0540	−	6.77729i	0.897076	−	0.242666i
$781$	−0.431677			−0.0154466
$782$		−	20.4828i		−	0.732463i
$783$	−3.19808	−	10.0116i	−0.114290	−	0.357785i
$784$		0			0
$785$	12.4317	+	15.2256i	0.443706	+	0.543426i
$786$	−4.26139	+	9.52875i	−0.151999	+	0.339879i
$787$	34.6804			1.23622			0.618112	−	0.786090i	$-0.287898\pi$
$787$	34.6804			1.23622			0.618112	+	0.786090i	$0.287898\pi$
$788$	9.00000			0.320612
$789$	1.41421	−	3.16228i	0.0503473	−	0.112580i
$790$	0.739315	+	0.905472i	0.0263036	+	0.0322152i
$791$		0			0
$792$	0.477226	−	0.426844i	0.0169575	−	0.0151672i
$793$		−	23.2144i		−	0.824366i
$794$	−30.3734			−1.07791
$795$	−18.6931	+	5.05662i	−0.662975	+	0.179340i
$796$			22.4378i			0.795286i
$797$			28.9201i			1.02440i	0.858865	+	0.512201i	$0.171170\pi$
$797$			28.9201i			1.02440i	−0.858865	+	0.512201i	$0.828830\pi$
$798$		0			0
$799$	−24.5228			−0.867553
$800$	−1.00000	+	4.89898i	−0.0353553	+	0.173205i
$801$	21.1488	+	23.6451i	0.747256	+	0.835457i
$802$			30.3494i			1.07168i
$803$			2.55863i			0.0902921i
$804$	8.42087	+	3.76593i	0.296981	+	0.132814i
$805$		0			0
$806$		−	2.02265i		−	0.0712447i
$807$	−20.4317	+	45.6866i	−0.719229	+	1.60825i
$808$	−11.3137			−0.398015
$809$		−	40.1474i		−	1.41151i	−0.708458	−	0.705753i	$-0.750609\pi$
$809$		−	40.1474i		−	1.41151i	0.708458	−	0.705753i	$-0.249391\pi$
$810$	−16.9061	+	10.9171i	−0.594021	+	0.383586i
$811$		−	6.70527i		−	0.235454i	−0.993046	−	0.117727i	$-0.962439\pi$
$811$		−	6.70527i		−	0.235454i	0.993046	−	0.117727i	$-0.0375608\pi$
$812$		0			0
$813$	−10.0000	−	4.47214i	−0.350715	−	0.156845i
$814$	−1.52277			−0.0533732
$815$	−25.4558	+	20.7846i	−0.891679	+	0.728053i
$816$	−5.00000	−	2.23607i	−0.175035	−	0.0782780i
$817$	9.89949			0.346339
$818$			22.4378i			0.784518i
$819$		0			0
$820$	9.47723	+	11.6072i	0.330959	+	0.405340i
$821$		−	50.9009i		−	1.77645i	−0.459406	−	0.888226i	$-0.651938\pi$
$821$		−	50.9009i		−	1.77645i	0.459406	−	0.888226i	$-0.348062\pi$
$822$	−5.28720	+	11.8225i	−0.184412	+	0.412358i
$823$		−	32.5855i		−	1.13586i	−0.823077	−	0.567929i	$-0.807745\pi$
$823$		−	32.5855i		−	1.13586i	0.823077	−	0.567929i	$-0.192255\pi$
$824$	−10.5744			−0.368376
$825$	1.07676	−	1.50225i	0.0374881	−	0.0523015i
$826$		0			0
$827$	39.9089			1.38777			0.693884	−	0.720087i	$-0.255898\pi$
$827$	39.9089			1.38777			0.693884	+	0.720087i	$0.255898\pi$
$828$	12.9545	+	14.4835i	0.450198	+	0.503337i
$829$			18.8296i			0.653980i	0.945028	+	0.326990i	$0.106034\pi$
$829$			18.8296i			0.653980i	−0.945028	+	0.326990i	$0.893966\pi$
$830$	28.9545	−	23.6412i	1.00502	−	0.820598i
$831$	−15.4919	−	6.92820i	−0.537409	−	0.240337i
$832$	−6.70141			−0.232330
$833$		0			0
$834$	−11.9089	−	5.32582i	−0.412372	−	0.184418i
$835$	−25.4317	+	20.7649i	−0.880099	+	0.718598i
$836$	−1.04456			−0.0361267
$837$	0.477226	+	1.49395i	0.0164953	+	0.0516385i
$838$	16.6009			0.573469
$839$	37.3156			1.28828			0.644139	−	0.764908i	$-0.277216\pi$
$839$	37.3156			1.28828			0.644139	+	0.764908i	$0.277216\pi$
$840$		0			0
$841$	24.9089			0.858928
$842$	−2.95445			−0.101817
$843$	−18.3526	−	8.20752i	−0.632096	−	0.282682i
$844$	13.5228			0.465473
$845$	45.1260	+	55.2678i	1.55238	+	1.90127i
$846$	17.3402	−	15.5096i	0.596169	−	0.533230i
$847$		0			0
$848$	5.00000			0.171701
$849$	17.4772	−	39.0803i	0.599817	−	1.34123i
$850$	−15.4919	−	3.16228i	−0.531369	−	0.108465i
$851$		−	46.2153i		−	1.58424i
$852$	−3.19808	−	1.43023i	−0.109565	−	0.0489988i
$853$	−53.9165			−1.84607			−0.923033	−	0.384720i	$-0.874298\pi$
$853$	−53.9165			−1.84607			−0.923033	+	0.384720i	$0.874298\pi$
$854$		0			0
$855$	32.4317	+	5.11240i	1.10914	+	0.174840i
$856$	5.47723			0.187208
$857$		−	40.3619i		−	1.37874i	−0.724411	−	0.689369i	$-0.757888\pi$
$857$		−	40.3619i		−	1.37874i	0.724411	−	0.689369i	$-0.242112\pi$
$858$	2.26139	+	1.01132i	0.0772025	+	0.0345260i
$859$		−	17.9242i		−	0.611564i	−0.952102	−	0.305782i	$-0.901082\pi$
$859$		−	17.9242i		−	0.611564i	0.952102	−	0.305782i	$-0.0989179\pi$
$860$	3.50333	−	2.86045i	0.119462	−	0.0975407i
$861$		0			0
$862$			37.0576i			1.26219i
$863$	−15.5228			−0.528401			−0.264201	−	0.964468i	$-0.585108\pi$
$863$	−15.5228			−0.528401			−0.264201	+	0.964468i	$0.585108\pi$
$864$	4.94975	−	1.58114i	0.168394	−	0.0537914i
$865$	19.9545	−	16.2927i	0.678472	−	0.553970i
$866$		0			0
$867$	−4.94975	+	11.0680i	−0.168102	+	0.375888i
$868$		0			0
$869$			0.111571i			0.00378480i
$870$	2.04555	+	7.56189i	0.0693506	+	0.256372i
$871$			35.6905i			1.20933i
$872$	12.4317			0.420990
$873$	−7.00665	−	7.83368i	−0.237139	−	0.265130i
$874$		−	31.7017i		−	1.07232i
$875$		0			0
$876$	−8.47723	+	18.9557i	−0.286419	+	0.640452i
$877$		−	42.2816i		−	1.42775i	−0.700274	−	0.713874i	$-0.746939\pi$
$877$		−	42.2816i		−	1.42775i	0.700274	−	0.713874i	$-0.253061\pi$
$878$			22.7396i			0.767424i
$879$	7.26139	+	3.24739i	0.244921	+	0.109532i
$880$	−0.369657	+	0.301824i	−0.0124611	+	0.0101745i
$881$	−26.5004			−0.892821			−0.446411	−	0.894828i	$-0.647298\pi$
$881$	−26.5004			−0.892821			−0.446411	+	0.894828i	$0.647298\pi$
$882$		0			0
$883$		−	29.2823i		−	0.985428i	−0.870191	−	0.492714i	$-0.836005\pi$
$883$		−	29.2823i		−	0.985428i	0.870191	−	0.492714i	$-0.163995\pi$
$884$		−	21.1917i		−	0.712755i
$885$	18.3848	−	4.97322i	0.617997	−	0.167173i
$886$	−36.9545			−1.24151
$887$			3.46410i			0.116313i	0.998307	+	0.0581566i	$0.0185223\pi$
$887$			3.46410i			0.116313i	−0.998307	+	0.0581566i	$0.981478\pi$
$888$	−11.2815	−	5.04524i	−0.378582	−	0.169307i
$889$		0			0
$890$	−14.9545	−	18.3154i	−0.501274	−	0.613933i
$891$	−1.90890	−	0.213422i	−0.0639506	−	0.00714990i
$892$	−6.39617			−0.214160
$893$	−37.9545			−1.27010
$894$	3.87298	+	1.73205i	0.129532	+	0.0579284i
$895$	25.8255	−	21.0864i	0.863251	−	0.704842i
$896$		0			0
$897$	−30.6931	+	68.6318i	−1.02481	+	2.29155i
$898$		−	3.51660i		−	0.117350i
$899$	0.610483			0.0203608
$900$	12.9545	−	7.56189i	0.431815	−	0.252063i
$901$			15.8114i			0.526754i
$902$			1.43023i			0.0476213i
$903$		0			0
$904$	6.52277			0.216944
$905$	5.47723	−	4.47214i	0.182069	−	0.148659i
$906$	1.41421	−	3.16228i	0.0469841	−	0.105060i
$907$			9.79796i			0.325336i	0.986681	+	0.162668i	$0.0520099\pi$
$907$			9.79796i			0.325336i	−0.986681	+	0.162668i	$0.947990\pi$
$908$		−	10.3923i		−	0.344881i
$909$	22.6274	+	25.2982i	0.750504	+	0.839089i
$910$		0			0
$911$		−	15.1238i		−	0.501073i	−0.968107	−	0.250537i	$-0.919393\pi$
$911$		−	15.1238i		−	0.501073i	0.968107	−	0.250537i	$-0.0806071\pi$
$912$	−7.73861	−	3.46081i	−0.256251	−	0.114599i
$913$	3.56774			0.118075
$914$			37.9113i			1.25399i
$915$	−3.50333	−	12.9509i	−0.115816	−	0.428145i
$916$		−	7.23003i		−	0.238887i
$917$		0			0
$918$	5.00000	+	15.6525i	0.165025	+	0.516609i
$919$	−32.4317			−1.06982			−0.534911	−	0.844908i	$-0.679655\pi$
$919$	−32.4317			−1.06982			−0.534911	+	0.844908i	$0.679655\pi$
$920$	−9.16018	−	11.2189i	−0.302002	−	0.369876i
$921$	2.47723	−	5.53924i	0.0816274	−	0.182524i
$922$	16.2957			0.536669
$923$		−	13.5546i		−	0.446155i
$924$		0			0
$925$	−34.9545	−	7.13505i	−1.14930	−	0.234599i
$926$			17.6751i			0.580841i
$927$	21.1488	+	23.6451i	0.694617	+	0.776606i
$928$		−	2.02265i		−	0.0663966i
$929$	−23.6720			−0.776652			−0.388326	−	0.921522i	$-0.626947\pi$
$929$	−23.6720			−0.776652			−0.388326	+	0.921522i	$0.626947\pi$
$930$	−0.305242	−	1.12840i	−0.0100093	−	0.0370018i
$931$		0			0
$932$	−4.00000			−0.131024
$933$	−20.4317	+	45.6866i	−0.668903	+	1.49571i
$934$		−	34.3392i		−	1.12361i
$935$	−0.954451	−	1.16896i	−0.0312139	−	0.0382291i
$936$	13.4028	+	14.9848i	0.438085	+	0.489794i
$937$	−22.6918			−0.741310			−0.370655	−	0.928771i	$-0.620867\pi$
$937$	−22.6918			−0.741310			−0.370655	+	0.928771i	$0.620867\pi$
$938$		0			0
$939$	−16.4317	+	36.7423i	−0.536228	+	1.19904i
$940$	−13.4317	+	10.9669i	−0.438093	+	0.357701i
$941$	4.98196			0.162407			0.0812036	−	0.996698i	$-0.474124\pi$
$941$	4.98196			0.162407			0.0812036	+	0.996698i	$0.474124\pi$
$942$	−6.21584	+	13.8990i	−0.202523	+	0.452855i
$943$	−43.4065			−1.41351
$944$	−4.91754			−0.160052
$945$		0			0
$946$	0.431677			0.0140350
$947$	−32.8634			−1.06792			−0.533958	−	0.845511i	$-0.679296\pi$
$947$	−32.8634			−1.06792			−0.533958	+	0.845511i	$0.679296\pi$
$948$	−0.369657	+	0.826579i	−0.0120059	+	0.0268460i
$949$	−80.3406			−2.60797
$950$	−23.9772	−	4.89433i	−0.777924	−	0.158793i
$951$	−23.9772	+	53.6147i	−0.777514	+	1.73858i
$952$		0			0
$953$	25.0455			0.811305			0.405652	−	0.914027i	$-0.367044\pi$
$953$	25.0455			0.811305			0.405652	+	0.914027i	$0.367044\pi$
$954$	−10.0000	−	11.1803i	−0.323762	−	0.361977i
$955$	−2.76401	+	2.25681i	−0.0894413	+	0.0730285i
$956$		0			0
$957$	−0.305242	+	0.682541i	−0.00986706	+	0.0220634i
$958$	11.3781			0.367611
$959$		0			0
$960$	−3.73861	+	1.01132i	−0.120663	+	0.0326403i
$961$	30.9089			0.997061
$962$		−	47.8149i		−	1.54161i
$963$	−10.9545	−	12.2474i	−0.353002	−	0.394669i
$964$		−	3.98886i		−	0.128472i
$965$	12.7279	−	10.3923i	0.409726	−	0.334540i
$966$		0			0
$967$		−	46.4287i		−	1.49305i	−0.665359	−	0.746524i	$-0.731721\pi$
$967$		−	46.4287i		−	1.49305i	0.665359	−	0.746524i	$-0.268279\pi$
$968$	10.9545			0.352089
$969$	10.9441	−	24.4716i	0.351574	−	0.786142i
$970$	4.95445	+	6.06794i	0.159078	+	0.194830i
$971$	−0.980140			−0.0314542			−0.0157271	−	0.999876i	$-0.505006\pi$
$971$	−0.980140			−0.0314542			−0.0157271	+	0.999876i	$0.505006\pi$
$972$	−13.4350	−	7.90569i	−0.430929	−	0.253575i
$973$		0			0
$974$		−	36.6308i		−	1.17373i
$975$	47.1703	+	33.8102i	1.51066	+	1.08279i
$976$			3.46410i			0.110883i
$977$	−39.9089			−1.27680			−0.638399	−	0.769705i	$-0.720403\pi$
$977$	−39.9089			−1.27680			−0.638399	+	0.769705i	$0.720403\pi$
$978$	−23.2379	−	10.3923i	−0.743066	−	0.332309i
$979$		−	2.25681i		−	0.0721278i
$980$		0			0
$981$	−24.8634	−	27.7981i	−0.793826	−	0.887524i
$982$		−	4.04529i		−	0.129090i
$983$			33.8144i			1.07851i	0.842142	+	0.539257i	$0.181295\pi$
$983$			33.8144i			1.07851i	−0.842142	+	0.539257i	$0.818705\pi$
$984$	−4.73861	+	10.5959i	−0.151061	+	0.337784i
$985$	12.7279	+	15.5885i	0.405545	+	0.496690i
$986$	6.39617			0.203696
$987$		0			0
$988$		−	32.7989i		−	1.04347i
$989$			13.1011i			0.416592i
$990$	1.41421	+	0.222931i	0.0449467	+	0.00708521i
$991$	21.4772			0.682247			0.341123	−	0.940019i	$-0.389193\pi$
$991$	21.4772			0.682247			0.341123	+	0.940019i	$0.389193\pi$
$992$			0.301824i			0.00958292i
$993$	8.08342	−	18.0751i	0.256519	−	0.573595i
$994$		0			0
$995$	−38.8634	+	31.7318i	−1.23205	+	1.00597i
$996$	26.4317	+	11.8206i	0.837520	+	0.374550i
$997$	15.4919			0.490634			0.245317	−	0.969443i	$-0.421108\pi$
$997$	15.4919			0.490634			0.245317	+	0.969443i	$0.421108\pi$
$998$	−41.9089			−1.32660
$999$	11.2815	+	35.3167i	0.356931	+	1.11737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.f.1469.4		8
3.2	odd	2		1470.2.d.e.1469.1		8
5.4	even	2		1470.2.d.e.1469.5		8
7.2	even	3		210.2.t.e.59.2	yes	8
7.3	odd	6		210.2.t.e.89.1	yes	8
7.6	odd	2	inner	1470.2.d.f.1469.5		8
15.14	odd	2	inner	1470.2.d.f.1469.8		8
21.2	odd	6		210.2.t.f.59.4	yes	8
21.17	even	6		210.2.t.f.89.3	yes	8
21.20	even	2		1470.2.d.e.1469.8		8
35.2	odd	12		1050.2.s.i.101.5		16
35.3	even	12		1050.2.s.i.551.6		16
35.9	even	6		210.2.t.f.59.3	yes	8
35.17	even	12		1050.2.s.i.551.3		16
35.23	odd	12		1050.2.s.i.101.4		16
35.24	odd	6		210.2.t.f.89.4	yes	8
35.34	odd	2		1470.2.d.e.1469.4		8
105.2	even	12		1050.2.s.i.101.3		16
105.17	odd	12		1050.2.s.i.551.5		16
105.23	even	12		1050.2.s.i.101.6		16
105.38	odd	12		1050.2.s.i.551.4		16
105.44	odd	6		210.2.t.e.59.1	✓	8
105.59	even	6		210.2.t.e.89.2	yes	8
105.104	even	2	inner	1470.2.d.f.1469.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.1	✓	8	105.44	odd	6
210.2.t.e.59.2	yes	8	7.2	even	3
210.2.t.e.89.1	yes	8	7.3	odd	6
210.2.t.e.89.2	yes	8	105.59	even	6
210.2.t.f.59.3	yes	8	35.9	even	6
210.2.t.f.59.4	yes	8	21.2	odd	6
210.2.t.f.89.3	yes	8	21.17	even	6
210.2.t.f.89.4	yes	8	35.24	odd	6
1050.2.s.i.101.3		16	105.2	even	12
1050.2.s.i.101.4		16	35.23	odd	12
1050.2.s.i.101.5		16	35.2	odd	12
1050.2.s.i.101.6		16	105.23	even	12
1050.2.s.i.551.3		16	35.17	even	12
1050.2.s.i.551.4		16	105.38	odd	12
1050.2.s.i.551.5		16	105.17	odd	12
1050.2.s.i.551.6		16	35.3	even	12
1470.2.d.e.1469.1		8	3.2	odd	2
1470.2.d.e.1469.4		8	35.34	odd	2
1470.2.d.e.1469.5		8	5.4	even	2
1470.2.d.e.1469.8		8	21.20	even	2
1470.2.d.f.1469.1		8	105.104	even	2	inner
1470.2.d.f.1469.4		8	1.1	even	1	trivial
1470.2.d.f.1469.5		8	7.6	odd	2	inner
1470.2.d.f.1469.8		8	15.14	odd	2	inner

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.707107 + 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(1.41421 + 1.73205i) q^{10} +0.213422i q^{11} +(-0.707107 + 1.58114i) q^{12} -6.70141 q^{13} +(-3.73861 + 1.01132i) q^{15} +1.00000 q^{16} +3.16228i q^{17} +(-2.00000 - 2.23607i) q^{18} +4.89433i q^{19} +(1.41421 + 1.73205i) q^{20} +0.213422i q^{22} -6.47723 q^{23} +(-0.707107 + 1.58114i) q^{24} +(-1.00000 + 4.89898i) q^{25} -6.70141 q^{26} +(4.94975 - 1.58114i) q^{27} -2.02265i q^{29} +(-3.73861 + 1.01132i) q^{30} +0.301824i q^{31} +1.00000 q^{32} +(-0.337449 - 0.150912i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +7.13505i q^{37} +4.89433i q^{38} +(4.73861 - 10.5959i) q^{39} +(1.41421 + 1.73205i) q^{40} +6.70141 q^{41} -2.02265i q^{43} +0.213422i q^{44} +(1.04456 - 6.62638i) q^{45} -6.47723 q^{46} +7.75478i q^{47} +(-0.707107 + 1.58114i) q^{48} +(-1.00000 + 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -6.70141 q^{52} +5.00000 q^{53} +(4.94975 - 1.58114i) q^{54} +(-0.369657 + 0.301824i) q^{55} +(-7.73861 - 3.46081i) q^{57} -2.02265i q^{58} -4.91754 q^{59} +(-3.73861 + 1.01132i) q^{60} +3.46410i q^{61} +0.301824i q^{62} +1.00000 q^{64} +(-9.47723 - 11.6072i) q^{65} +(-0.337449 - 0.150912i) q^{66} -5.32582i q^{67} +3.16228i q^{68} +(4.58009 - 10.2414i) q^{69} +2.02265i q^{71} +(-2.00000 - 2.23607i) q^{72} +11.9886 q^{73} +7.13505i q^{74} +(-7.03886 - 5.04524i) q^{75} +4.89433i q^{76} +(4.73861 - 10.5959i) q^{78} +0.522774 q^{79} +(1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +6.70141 q^{82} -16.7169i q^{83} +(-5.47723 + 4.47214i) q^{85} -2.02265i q^{86} +(3.19808 + 1.43023i) q^{87} +0.213422i q^{88} -10.5744 q^{89} +(1.04456 - 6.62638i) q^{90} -6.47723 q^{92} +(-0.477226 - 0.213422i) q^{93} +7.75478i q^{94} +(-8.47723 + 6.92163i) q^{95} +(-0.707107 + 1.58114i) q^{96} +3.50333 q^{97} +(0.477226 - 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 16 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 16 q^{9} - 8 q^{15} + 8 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} - 8 q^{30} + 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} - 8 q^{50} - 40 q^{51} + 40 q^{53} - 40 q^{57} - 8 q^{60} + 8 q^{64} - 32 q^{65} - 16 q^{72} + 16 q^{78} + 48 q^{79} - 8 q^{81} - 8 q^{92} + 40 q^{93} - 24 q^{95} - 40 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 16 * q^9 - 8 * q^15 + 8 * q^16 - 16 * q^18 - 8 * q^23 - 8 * q^25 - 8 * q^30 + 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 - 8 * q^50 - 40 * q^51 + 40 * q^53 - 40 * q^57 - 8 * q^60 + 8 * q^64 - 32 * q^65 - 16 * q^72 + 16 * q^78 + 48 * q^79 - 8 * q^81 - 8 * q^92 + 40 * q^93 - 24 * q^95 - 40 * q^99

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