LMFDB - Embedded newform 144.5.q.c.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not 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:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 $ x^8 - 3x^7 + 6x^6 + 121x^5 + 1104x^4 - 1647x^3 + 6529x^2 + 85254*x + 440076
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Root			$-3.05006 - 3.25531i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.5.q.c.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.89427 - 1.37550i) q^{3} +(27.4152 - 15.8282i) q^{5} +(-37.6830 + 65.2688i) q^{7} +(77.2160 - 24.4682i) q^{9} +O(q^{10})$	\(q+(8.89427 - 1.37550i) q^{3} +(27.4152 - 15.8282i) q^{5} +(-37.6830 + 65.2688i) q^{7} +(77.2160 - 24.4682i) q^{9} +(123.267 + 71.1682i) q^{11} +(96.3079 + 166.810i) q^{13} +(222.067 - 178.490i) q^{15} -325.855i q^{17} -314.164 q^{19} +(-245.385 + 632.352i) q^{21} +(443.852 - 256.258i) q^{23} +(188.564 - 326.602i) q^{25} +(653.124 - 323.837i) q^{27} +(-136.614 - 78.8739i) q^{29} +(-183.725 - 318.221i) q^{31} +(1194.26 + 463.435i) q^{33} +2385.82i q^{35} +1737.04 q^{37} +(1086.04 + 1351.18i) q^{39} +(-342.317 + 197.637i) q^{41} +(360.381 - 624.198i) q^{43} +(1729.61 - 1892.99i) q^{45} +(-2153.71 - 1243.45i) q^{47} +(-1639.52 - 2839.72i) q^{49} +(-448.215 - 2898.24i) q^{51} +3986.04i q^{53} +4505.86 q^{55} +(-2794.26 + 432.133i) q^{57} +(2136.75 - 1233.65i) q^{59} +(-1240.49 + 2148.59i) q^{61} +(-1312.72 + 5961.83i) q^{63} +(5280.61 + 3048.76i) q^{65} +(-3298.19 - 5712.64i) q^{67} +(3595.26 - 2889.75i) q^{69} +5828.07i q^{71} -8790.44 q^{73} +(1227.90 - 3164.26i) q^{75} +(-9290.13 + 5363.66i) q^{77} +(-1934.52 + 3350.69i) q^{79} +(5363.62 - 3778.67i) q^{81} +(-10422.5 - 6017.43i) q^{83} +(-5157.70 - 8933.39i) q^{85} +(-1323.57 - 513.613i) q^{87} -7637.03i q^{89} -14516.7 q^{91} +(-2071.81 - 2577.63i) q^{93} +(-8612.88 + 4972.65i) q^{95} +(1455.75 - 2521.44i) q^{97} +(11259.5 + 2479.20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	$ 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) $ 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	8.89427	−	1.37550i	0.988252	−	0.152834i
$3$	8.89427	−	1.37550i	0.988252	−	0.152834i
$4$		0			0
$5$	27.4152	−	15.8282i	1.09661	−	0.633128i	0.161281	−	0.986908i	$-0.448437\pi$
$5$	27.4152	−	15.8282i	1.09661	−	0.633128i	0.935329	+	0.353780i	$0.115104\pi$
$6$		0			0
$7$	−37.6830	+	65.2688i	−0.769041	+	1.33202i	0.169043	+	0.985609i	$0.445932\pi$
$7$	−37.6830	+	65.2688i	−0.769041	+	1.33202i	−0.938084	+	0.346409i	$0.887401\pi$
$8$		0			0
$9$	77.2160	−	24.4682i	0.953284	−	0.302076i
$10$		0			0
$11$	123.267	+	71.1682i	1.01873	+	0.588167i	0.913737	−	0.406306i	$-0.133183\pi$
$11$	123.267	+	71.1682i	1.01873	+	0.588167i	0.104997	+	0.994473i	$0.466517\pi$
$12$		0			0
$13$	96.3079	+	166.810i	0.569870	+	0.987043i	0.996578	+	0.0826539i	$0.0263396\pi$
$13$	96.3079	+	166.810i	0.569870	+	0.987043i	−0.426709	+	0.904389i	$0.640327\pi$
$14$		0			0
$15$	222.067	−	178.490i	0.986964	−	0.793289i
$16$		0			0
$17$		−	325.855i		−	1.12753i	−0.825937	−	0.563763i	$-0.809353\pi$
$17$		−	325.855i		−	1.12753i	0.825937	−	0.563763i	$-0.190647\pi$
$18$		0			0
$19$	−314.164			−0.870260			−0.435130	−	0.900368i	$-0.643298\pi$
$19$	−314.164			−0.870260			−0.435130	+	0.900368i	$0.643298\pi$
$20$		0			0
$21$	−245.385	+	632.352i	−0.556429	+	1.43390i
$22$		0			0
$23$	443.852	−	256.258i	0.839040	−	0.484420i	−0.0178977	−	0.999840i	$-0.505697\pi$
$23$	443.852	−	256.258i	0.839040	−	0.484420i	0.856938	+	0.515420i	$0.172364\pi$
$24$		0			0
$25$	188.564	−	326.602i	0.301702	−	0.522564i
$26$		0			0
$27$	653.124	−	323.837i	0.895917	−	0.444221i
$28$		0			0
$29$	−136.614	−	78.8739i	−0.162442	−	0.0937859i	0.416575	−	0.909101i	$-0.363230\pi$
$29$	−136.614	−	78.8739i	−0.162442	−	0.0937859i	−0.579017	+	0.815315i	$0.696564\pi$
$30$		0			0
$31$	−183.725	−	318.221i	−0.191181	−	0.331135i	0.754461	−	0.656345i	$-0.227898\pi$
$31$	−183.725	−	318.221i	−0.191181	−	0.331135i	−0.945642	+	0.325210i	$0.894565\pi$
$32$		0			0
$33$	1194.26	+	463.435i	1.09666	+	0.425560i
$34$		0			0
$35$			2385.82i			1.94760i
$36$		0			0
$37$	1737.04			1.26884			0.634419	−	0.772989i	$-0.281239\pi$
$37$	1737.04			1.26884			0.634419	+	0.772989i	$0.281239\pi$
$38$		0			0
$39$	1086.04	+	1351.18i	0.714028	+	0.888352i
$40$		0			0
$41$	−342.317	+	197.637i	−0.203639	+	0.117571i	−0.598352	−	0.801234i	$-0.704177\pi$
$41$	−342.317	+	197.637i	−0.203639	+	0.117571i	0.394713	+	0.918805i	$0.370844\pi$
$42$		0			0
$43$	360.381	−	624.198i	0.194906	−	0.337587i	−0.751964	−	0.659204i	$-0.770893\pi$
$43$	360.381	−	624.198i	0.194906	−	0.337587i	0.946870	+	0.321618i	$0.104227\pi$
$44$		0			0
$45$	1729.61	−	1892.99i	0.854127	−	0.934811i
$46$		0			0
$47$	−2153.71	−	1243.45i	−0.974971	−	0.562900i	−0.0742227	−	0.997242i	$-0.523648\pi$
$47$	−2153.71	−	1243.45i	−0.974971	−	0.562900i	−0.900748	+	0.434342i	$0.856981\pi$
$48$		0			0
$49$	−1639.52	−	2839.72i	−0.682847	−	1.18273i
$50$		0			0
$51$	−448.215	−	2898.24i	−0.172324	−	1.11428i
$52$		0			0
$53$			3986.04i			1.41902i	0.704694	+	0.709512i	$0.251084\pi$
$53$			3986.04i			1.41902i	−0.704694	+	0.709512i	$0.748916\pi$
$54$		0			0
$55$	4505.86			1.48954
$56$		0			0
$57$	−2794.26	+	432.133i	−0.860036	+	0.133005i
$58$		0			0
$59$	2136.75	−	1233.65i	0.613831	−	0.354396i	−0.160632	−	0.987014i	$-0.551353\pi$
$59$	2136.75	−	1233.65i	0.613831	−	0.354396i	0.774463	+	0.632619i	$0.218020\pi$
$60$		0			0
$61$	−1240.49	+	2148.59i	−0.333375	+	0.577422i	−0.983171	−	0.182686i	$-0.941521\pi$
$61$	−1240.49	+	2148.59i	−0.333375	+	0.577422i	0.649796	+	0.760108i	$0.274854\pi$
$62$		0			0
$63$	−1312.72	+	5961.83i	−0.330743	+	1.50210i
$64$		0			0
$65$	5280.61	+	3048.76i	1.24985	+	0.721601i
$66$		0			0
$67$	−3298.19	−	5712.64i	−0.734728	−	1.27259i	−0.954843	−	0.297112i	$-0.903977\pi$
$67$	−3298.19	−	5712.64i	−0.734728	−	1.27259i	0.220115	−	0.975474i	$-0.429357\pi$
$68$		0			0
$69$	3595.26	−	2889.75i	0.755147	−	0.606963i
$70$		0			0
$71$			5828.07i			1.15613i	0.815990	+	0.578066i	$0.196193\pi$
$71$			5828.07i			1.15613i	−0.815990	+	0.578066i	$0.803807\pi$
$72$		0			0
$73$	−8790.44			−1.64955			−0.824774	−	0.565463i	$-0.808697\pi$
$73$	−8790.44			−1.64955			−0.824774	+	0.565463i	$0.808697\pi$
$74$		0			0
$75$	1227.90	−	3164.26i	0.218293	−	0.562535i
$76$		0			0
$77$	−9290.13	+	5363.66i	−1.56690	+	0.904648i
$78$		0			0
$79$	−1934.52	+	3350.69i	−0.309970	+	0.536883i	−0.978355	−	0.206932i	$-0.933652\pi$
$79$	−1934.52	+	3350.69i	−0.309970	+	0.536883i	0.668386	+	0.743815i	$0.266986\pi$
$80$		0			0
$81$	5363.62	−	3778.67i	0.817500	−	0.575929i
$82$		0			0
$83$	−10422.5	−	6017.43i	−1.51292	−	0.873483i	−0.999886	−	0.0151136i	$-0.995189\pi$
$83$	−10422.5	−	6017.43i	−1.51292	−	0.873483i	−0.513032	−	0.858370i	$-0.671478\pi$
$84$		0			0
$85$	−5157.70	−	8933.39i	−0.713868	−	1.23646i
$86$		0			0
$87$	−1323.57	−	513.613i	−0.174867	−	0.0678575i
$88$		0			0
$89$		−	7637.03i		−	0.964150i	−0.876130	−	0.482075i	$-0.839883\pi$
$89$		−	7637.03i		−	0.964150i	0.876130	−	0.482075i	$-0.160117\pi$
$90$		0			0
$91$	−14516.7			−1.75301
$92$		0			0
$93$	−2071.81	−	2577.63i	−0.239543	−	0.298026i
$94$		0			0
$95$	−8612.88	+	4972.65i	−0.954336	+	0.550986i
$96$		0			0
$97$	1455.75	−	2521.44i	0.154719	−	0.267981i	−0.778238	−	0.627970i	$-0.783886\pi$
$97$	1455.75	−	2521.44i	0.154719	−	0.267981i	0.932957	+	0.359989i	$0.117219\pi$
$98$		0			0
$99$	11259.5	+	2479.20i	1.14881	+	0.252954i
$100$		0			0
$101$	−9442.90	−	5451.86i	−0.925683	−	0.534444i	−0.0402396	−	0.999190i	$-0.512812\pi$
$101$	−9442.90	−	5451.86i	−0.925683	−	0.534444i	−0.885444	+	0.464746i	$0.846145\pi$
$102$		0			0
$103$	−3638.56	−	6302.16i	−0.342969	−	0.594039i	0.642014	−	0.766693i	$-0.278099\pi$
$103$	−3638.56	−	6302.16i	−0.342969	−	0.594039i	−0.984983	+	0.172654i	$0.944766\pi$
$104$		0			0
$105$	3281.70	+	21220.1i	0.297660	+	1.92472i
$106$		0			0
$107$			5525.48i			0.482617i	0.970449	+	0.241308i	$0.0775765\pi$
$107$			5525.48i			0.482617i	−0.970449	+	0.241308i	$0.922424\pi$
$108$		0			0
$109$	7186.35			0.604861			0.302431	−	0.953171i	$-0.402202\pi$
$109$	7186.35			0.604861			0.302431	+	0.953171i	$0.402202\pi$
$110$		0			0
$111$	15449.7	−	2389.30i	1.25393	−	0.193921i
$112$		0			0
$113$	−10742.0	+	6201.93i	−0.841260	+	0.485702i	−0.857692	−	0.514163i	$-0.828103\pi$
$113$	−10742.0	+	6201.93i	−0.841260	+	0.485702i	0.0164323	+	0.999865i	$0.494769\pi$
$114$		0			0
$115$	8112.21	−	14050.8i	0.613400	−	1.06244i
$116$		0			0
$117$	11518.1	+	10523.9i	0.841410	+	0.768788i
$118$		0			0
$119$	21268.2	+	12279.2i	1.50188	+	0.867113i
$120$		0			0
$121$	2809.31	+	4865.88i	0.191880	+	0.332346i
$122$		0			0
$123$	−2772.81	+	2228.69i	−0.183278	+	0.147313i
$124$		0			0
$125$			7846.74i			0.502191i
$126$		0			0
$127$	−9013.28			−0.558824			−0.279412	−	0.960171i	$-0.590140\pi$
$127$	−9013.28			−0.558824			−0.279412	+	0.960171i	$0.590140\pi$
$128$		0			0
$129$	2346.74	−	6047.49i	0.141021	−	0.363409i
$130$		0			0
$131$	−309.401	+	178.633i	−0.0180293	+	0.0104092i	−0.508988	−	0.860774i	$-0.669980\pi$
$131$	−309.401	+	178.633i	−0.0180293	+	0.0104092i	0.490958	+	0.871183i	$0.336647\pi$
$132$		0			0
$133$	11838.6	−	20505.1i	0.669265	−	1.15920i
$134$		0			0
$135$	12779.8	−	19215.9i	0.701222	−	1.05437i
$136$		0			0
$137$	12811.2	+	7396.54i	0.682571	+	0.394083i	0.800823	−	0.598901i	$-0.204396\pi$
$137$	12811.2	+	7396.54i	0.682571	+	0.394083i	−0.118252	+	0.992984i	$0.537729\pi$
$138$		0			0
$139$	1079.62	+	1869.95i	0.0558779	+	0.0967834i	0.892611	−	0.450827i	$-0.148871\pi$
$139$	1079.62	+	1869.95i	0.0558779	+	0.0967834i	−0.836733	+	0.547611i	$0.815538\pi$
$140$		0			0
$141$	−20866.0	−	8097.10i	−1.04955	−	0.407278i
$142$		0			0
$143$			27416.2i			1.34071i
$144$		0			0
$145$	−4993.73			−0.237514
$146$		0			0
$147$	−18488.3	−	23002.1i	−0.855585	−	1.06447i
$148$		0			0
$149$	24982.1	−	14423.4i	1.12527	−	0.649675i	0.182529	−	0.983201i	$-0.441572\pi$
$149$	24982.1	−	14423.4i	1.12527	−	0.649675i	0.942741	+	0.333526i	$0.108238\pi$
$150$		0			0
$151$	−4752.65	+	8231.82i	−0.208440	+	0.361029i	−0.951223	−	0.308503i	$-0.900172\pi$
$151$	−4752.65	+	8231.82i	−0.208440	+	0.361029i	0.742783	+	0.669532i	$0.233505\pi$
$152$		0			0
$153$	−7973.08	−	25161.2i	−0.340599	−	1.07485i
$154$		0			0
$155$	−10073.7	−	5816.07i	−0.419302	−	0.242084i
$156$		0			0
$157$	4937.68	+	8552.31i	0.200320	+	0.346964i	0.948631	−	0.316383i	$-0.102469\pi$
$157$	4937.68	+	8552.31i	0.200320	+	0.346964i	−0.748312	+	0.663347i	$0.769135\pi$
$158$		0			0
$159$	5482.81	+	35452.9i	0.216875	+	1.40235i
$160$		0			0
$161$			38626.3i			1.49015i
$162$		0			0
$163$	22464.8			0.845525			0.422763	−	0.906240i	$-0.361060\pi$
$163$	22464.8			0.845525			0.422763	+	0.906240i	$0.361060\pi$
$164$		0			0
$165$	40076.3	−	6197.82i	1.47204	−	0.227652i
$166$		0			0
$167$	14694.7	−	8484.01i	0.526901	−	0.304206i	−0.212853	−	0.977084i	$-0.568275\pi$
$167$	14694.7	−	8484.01i	0.526901	−	0.304206i	0.739753	+	0.672878i	$0.234942\pi$
$168$		0			0
$169$	−4269.94	+	7395.76i	−0.149503	+	0.258946i
$170$		0			0
$171$	−24258.5	+	7687.02i	−0.829605	+	0.262885i
$172$		0			0
$173$	−32441.8	−	18730.3i	−1.08396	−	0.625825i	−0.151998	−	0.988381i	$-0.548571\pi$
$173$	−32441.8	−	18730.3i	−1.08396	−	0.625825i	−0.931962	+	0.362556i	$0.881904\pi$
$174$		0			0
$175$	14211.3	+	24614.7i	0.464043	+	0.803745i
$176$		0			0
$177$	17307.9	−	13911.5i	0.552456	−	0.444046i
$178$		0			0
$179$		−	44760.9i		−	1.39699i	−0.715615	−	0.698495i	$-0.753853\pi$
$179$		−	44760.9i		−	1.39699i	0.715615	−	0.698495i	$-0.246147\pi$
$180$		0			0
$181$	−29208.0			−0.891548			−0.445774	−	0.895146i	$-0.647071\pi$
$181$	−29208.0			−0.891548			−0.445774	+	0.895146i	$0.647071\pi$
$182$		0			0
$183$	−8077.84	+	20816.4i	−0.241209	+	0.621590i
$184$		0			0
$185$	47621.4	−	27494.2i	1.39142	−	0.803337i
$186$		0			0
$187$	23190.5	−	40167.1i	0.663173	−	1.14865i
$188$		0			0
$189$	−3475.15	+	54831.8i	−0.0972859	+	1.53500i
$190$		0			0
$191$	−25988.4	−	15004.4i	−0.712383	−	0.411294i	0.0995598	−	0.995032i	$-0.468257\pi$
$191$	−25988.4	−	15004.4i	−0.712383	−	0.411294i	−0.811943	+	0.583737i	$0.801590\pi$
$192$		0			0
$193$	8615.87	+	14923.1i	0.231305	+	0.400632i	0.958192	−	0.286125i	$-0.0923672\pi$
$193$	8615.87	+	14923.1i	0.231305	+	0.400632i	−0.726888	+	0.686756i	$0.759034\pi$
$194$		0			0
$195$	51160.8	+	19853.0i	1.34545	+	0.522104i
$196$		0			0
$197$			67892.1i			1.74939i	0.484673	+	0.874695i	$0.338938\pi$
$197$			67892.1i			1.74939i	−0.484673	+	0.874695i	$0.661062\pi$
$198$		0			0
$199$	26996.5			0.681713			0.340857	−	0.940115i	$-0.389283\pi$
$199$	26996.5			0.681713			0.340857	+	0.940115i	$0.389283\pi$
$200$		0			0
$201$	−37192.8	−	46273.0i	−0.920590	−	1.14534i
$202$		0			0
$203$	10296.0	−	5944.41i	0.249849	−	0.144250i
$204$		0			0
$205$	−6256.47	+	10836.5i	−0.148875	+	0.257859i
$206$		0			0
$207$	28002.3	−	30647.5i	0.653512	−	0.715244i
$208$		0			0
$209$	−38726.0	−	22358.5i	−0.886564	−	0.511858i
$210$		0			0
$211$	11819.5	+	20472.1i	0.265482	+	0.459829i	0.967690	−	0.252143i	$-0.0811354\pi$
$211$	11819.5	+	20472.1i	0.265482	+	0.459829i	−0.702207	+	0.711972i	$0.747802\pi$
$212$		0			0
$213$	8016.52	+	51836.4i	0.176696	+	1.14255i
$214$		0			0
$215$		−	22816.7i		−	0.493601i
$216$		0			0
$217$	27693.2			0.588103
$218$		0			0
$219$	−78184.5	+	12091.3i	−1.63017	+	0.252106i
$220$		0			0
$221$	54355.9	−	31382.4i	1.11292	−	0.642543i
$222$		0			0
$223$	−28978.0	+	50191.3i	−0.582718	+	1.00930i	0.412438	+	0.910986i	$0.364677\pi$
$223$	−28978.0	+	50191.3i	−0.582718	+	1.00930i	−0.995156	+	0.0983112i	$0.968656\pi$
$224$		0			0
$225$	6568.78	−	29832.7i	0.129754	−	0.589289i
$226$		0			0
$227$	−8712.47	−	5030.15i	−0.169079	−	0.0976178i	0.413073	−	0.910698i	$-0.364456\pi$
$227$	−8712.47	−	5030.15i	−0.169079	−	0.0976178i	−0.582151	+	0.813080i	$0.697789\pi$
$228$		0			0
$229$	−28899.8	−	50056.0i	−0.551093	−	0.954520i	−0.998196	−	0.0600381i	$-0.980878\pi$
$229$	−28899.8	−	50056.0i	−0.551093	−	0.954520i	0.447104	−	0.894482i	$-0.352456\pi$
$230$		0			0
$231$	−75251.2	+	60484.4i	−1.41023	+	1.13349i
$232$		0			0
$233$		−	68323.8i		−	1.25852i	−0.777195	−	0.629260i	$-0.783358\pi$
$233$		−	68323.8i		−	1.25852i	0.777195	−	0.629260i	$-0.216642\pi$
$234$		0			0
$235$	−78726.0			−1.42555
$236$		0			0
$237$	−12597.3	+	32462.9i	−0.224274	+	0.577950i
$238$		0			0
$239$	30122.2	−	17391.1i	0.527340	−	0.304460i	−0.212592	−	0.977141i	$-0.568191\pi$
$239$	30122.2	−	17391.1i	0.527340	−	0.304460i	0.739933	+	0.672681i	$0.234857\pi$
$240$		0			0
$241$	−45982.8	+	79644.5i	−0.791701	+	1.37127i	0.133213	+	0.991087i	$0.457471\pi$
$241$	−45982.8	+	79644.5i	−0.791701	+	1.37127i	−0.924913	+	0.380178i	$0.875863\pi$
$242$		0			0
$243$	42507.9	−	40986.2i	0.719874	−	0.694104i
$244$		0			0
$245$	−89895.4	−	51901.2i	−1.49763	−	0.864659i
$246$		0			0
$247$	−30256.5	−	52405.7i	−0.495935	−	0.858984i
$248$		0			0
$249$	−100977.	−	39184.4i	−1.62864	−	0.631997i
$250$		0			0
$251$			69806.6i			1.10802i	0.832509	+	0.554012i	$0.186904\pi$
$251$			69806.6i			1.10802i	−0.832509	+	0.554012i	$0.813096\pi$
$252$		0			0
$253$	72949.7			1.13968
$254$		0			0
$255$	−58161.9	−	72361.6i	−0.894454	−	1.11283i
$256$		0			0
$257$	15210.4	−	8781.70i	0.230289	−	0.132957i	−0.380416	−	0.924815i	$-0.624219\pi$
$257$	15210.4	−	8781.70i	0.230289	−	0.132957i	0.610705	+	0.791858i	$0.290886\pi$
$258$		0			0
$259$	−65456.8	+	113375.i	−0.975788	+	1.69011i
$260$		0			0
$261$	−12478.7	−	2747.64i	−0.183184	−	0.0403347i
$262$		0			0
$263$	−26492.4	−	15295.4i	−0.383009	−	0.221131i	0.296117	−	0.955152i	$-0.404308\pi$
$263$	−26492.4	−	15295.4i	−0.383009	−	0.221131i	−0.679127	+	0.734021i	$0.737641\pi$
$264$		0			0
$265$	63091.8	+	109278.i	0.898423	+	1.55611i
$266$		0			0
$267$	−10504.8	−	67925.8i	−0.147355	−	0.952823i
$268$		0			0
$269$		−	59574.8i		−	0.823299i	−0.911342	−	0.411650i	$-0.864953\pi$
$269$		−	59574.8i		−	0.823299i	0.911342	−	0.411650i	$-0.135047\pi$
$270$		0			0
$271$	94290.1			1.28389			0.641945	−	0.766751i	$-0.278128\pi$
$271$	94290.1			1.28389			0.641945	+	0.766751i	$0.278128\pi$
$272$		0			0
$273$	−129115.	+	19967.7i	−1.73242	+	0.267919i
$274$		0			0
$275$	46487.4	−	26839.5i	0.614709	−	0.354902i
$276$		0			0
$277$	49687.7	−	86061.7i	0.647574	−	1.12163i	−0.336126	−	0.941817i	$-0.609117\pi$
$277$	49687.7	−	86061.7i	0.647574	−	1.12163i	0.983700	−	0.179815i	$-0.0575499\pi$
$278$		0			0
$279$	−21972.8	−	20076.3i	−0.282278	−	0.257914i
$280$		0			0
$281$	68740.8	+	39687.5i	0.870567	+	0.502622i	0.867536	−	0.497374i	$-0.165702\pi$
$281$	68740.8	+	39687.5i	0.870567	+	0.502622i	0.00303013	+	0.999995i	$0.499035\pi$
$282$		0			0
$283$	33460.0	+	57954.4i	0.417785	+	0.723625i	0.995716	−	0.0924607i	$-0.0294732\pi$
$283$	33460.0	+	57954.4i	0.417785	+	0.723625i	−0.577931	+	0.816085i	$0.696140\pi$
$284$		0			0
$285$	−69765.4	+	56075.1i	−0.858915	+	0.690368i
$286$		0			0
$287$		−	29790.2i		−	0.361667i
$288$		0			0
$289$	−22660.4			−0.271314
$290$		0			0
$291$	9479.60	−	24428.7i	0.111945	−	0.288479i
$292$		0			0
$293$	−48467.1	+	27982.5i	−0.564562	+	0.325950i	−0.754974	−	0.655754i	$-0.772351\pi$
$293$	−48467.1	+	27982.5i	−0.564562	+	0.325950i	0.190413	+	0.981704i	$0.439017\pi$
$294$		0			0
$295$	39053.0	−	67641.7i	0.448756	−	0.777268i
$296$		0			0
$297$	103555.	+	6563.17i	1.17398	+	0.0744048i
$298$		0			0
$299$	85493.0	+	49359.4i	0.956287	+	0.552112i
$300$		0			0
$301$	27160.4	+	47043.3i	0.299781	+	0.519236i
$302$		0			0
$303$	−91486.7	−	35501.6i	−0.996489	−	0.386689i
$304$		0			0
$305$			78538.8i			0.844276i
$306$		0			0
$307$	−8707.80			−0.0923914			−0.0461957	−	0.998932i	$-0.514710\pi$
$307$	−8707.80			−0.0923914			−0.0461957	+	0.998932i	$0.514710\pi$
$308$		0			0
$309$	−41030.9	−	51048.3i	−0.429729	−	0.534643i
$310$		0			0
$311$	48339.3	−	27908.7i	0.499781	−	0.288549i	−0.228842	−	0.973464i	$-0.573494\pi$
$311$	48339.3	−	27908.7i	0.499781	−	0.288549i	0.728623	+	0.684915i	$0.240161\pi$
$312$		0			0
$313$	−29519.7	+	51129.6i	−0.301316	+	0.521895i	−0.976434	−	0.215815i	$-0.930759\pi$
$313$	−29519.7	+	51129.6i	−0.301316	+	0.521895i	0.675118	+	0.737710i	$0.264093\pi$
$314$		0			0
$315$	58376.6	+	184223.i	0.588325	+	1.85662i
$316$		0			0
$317$	−26277.2	−	15171.2i	−0.261494	−	0.150973i	0.363522	−	0.931586i	$-0.381574\pi$
$317$	−26277.2	−	15171.2i	−0.261494	−	0.150973i	−0.625016	+	0.780612i	$0.714907\pi$
$318$		0			0
$319$	−11226.6	−	19445.1i	−0.110323	−	0.191086i
$320$		0			0
$321$	7600.31	+	49145.1i	0.0737601	+	0.476947i
$322$		0			0
$323$			102372.i			0.981240i
$324$		0			0
$325$	72640.8			0.687724
$326$		0			0
$327$	63917.4	−	9884.85i	0.597755	−	0.0924432i
$328$		0			0
$329$	162316.	−	93713.5i	1.49958	−	0.865785i
$330$		0			0
$331$	63460.5	−	109917.i	0.579225	−	1.00325i	−0.416343	−	0.909207i	$-0.636689\pi$
$331$	63460.5	−	109917.i	0.579225	−	1.00325i	0.995568	−	0.0940397i	$-0.0299781\pi$
$332$		0			0
$333$	134127.	−	42502.2i	1.20956	−	0.383286i
$334$		0			0
$335$	−180842.	−	104409.i	−1.61142	−	0.930353i
$336$		0			0
$337$	−89198.2	−	154496.i	−0.785410	−	1.36037i	−0.928754	−	0.370697i	$-0.879119\pi$
$337$	−89198.2	−	154496.i	−0.785410	−	1.36037i	0.143344	−	0.989673i	$-0.454214\pi$
$338$		0			0
$339$	−87011.9	+	69937.3i	−0.757145	+	0.608569i
$340$		0			0
$341$		−	52301.4i		−	0.449785i
$342$		0			0
$343$	66173.6			0.562466
$344$		0			0
$345$	52825.3	−	136130.i	0.443817	−	1.14371i
$346$		0			0
$347$	97741.3	−	56431.0i	0.811744	−	0.468661i	−0.0358168	−	0.999358i	$-0.511403\pi$
$347$	97741.3	−	56431.0i	0.811744	−	0.468661i	0.847561	+	0.530697i	$0.178070\pi$
$348$		0			0
$349$	36754.1	−	63660.0i	0.301756	−	0.522656i	−0.674778	−	0.738021i	$-0.735761\pi$
$349$	36754.1	−	63660.0i	0.301756	−	0.522656i	0.976534	+	0.215365i	$0.0690940\pi$
$350$		0			0
$351$	116920.	+	77759.6i	0.949021	+	0.631160i
$352$		0			0
$353$	183043.	+	105680.i	1.46894	+	0.848091i	0.999394	−	0.0348180i	$-0.0110851\pi$
$353$	183043.	+	105680.i	1.46894	+	0.848091i	0.469544	+	0.882909i	$0.344418\pi$
$354$		0			0
$355$	92247.8	+	159778.i	0.731980	+	1.26783i
$356$		0			0
$357$	206055.	+	79959.9i	1.61676	+	0.627388i
$358$		0			0
$359$		−	36755.1i		−	0.285186i	−0.989781	−	0.142593i	$-0.954456\pi$
$359$		−	36755.1i		−	0.285186i	0.989781	−	0.142593i	$-0.0455440\pi$
$360$		0			0
$361$	−31622.1			−0.242648
$362$		0			0
$363$	31679.8	+	39414.2i	0.240419	+	0.299116i
$364$		0			0
$365$	−240992.	+	139137.i	−1.80891	+	1.04437i
$366$		0			0
$367$	−73577.0	+	127439.i	−0.546273	+	0.946173i	0.452252	+	0.891890i	$0.350621\pi$
$367$	−73577.0	+	127439.i	−0.546273	+	0.946173i	−0.998526	+	0.0542832i	$0.982713\pi$
$368$		0			0
$369$	−21596.5	+	23636.6i	−0.158610	+	0.173593i
$370$		0			0
$371$	−260164.	−	150206.i	−1.89016	−	1.09129i
$372$		0			0
$373$	21799.0	+	37757.1i	0.156682	+	0.271382i	0.933670	−	0.358134i	$-0.116587\pi$
$373$	21799.0	+	37757.1i	0.156682	+	0.271382i	−0.776988	+	0.629515i	$0.783253\pi$
$374$		0			0
$375$	10793.2	+	69791.0i	0.0767518	+	0.496292i
$376$		0			0
$377$		−	30384.7i		−	0.213783i
$378$		0			0
$379$	169833.			1.18234			0.591170	−	0.806547i	$-0.298666\pi$
$379$	169833.			1.18234			0.591170	+	0.806547i	$0.298666\pi$
$380$		0			0
$381$	−80166.5	+	12397.8i	−0.552259	+	0.0854072i
$382$		0			0
$383$	106228.	−	61330.5i	0.724169	−	0.418099i	−0.0921163	−	0.995748i	$-0.529363\pi$
$383$	106228.	−	61330.5i	0.724169	−	0.418099i	0.816285	+	0.577649i	$0.196030\pi$
$384$		0			0
$385$	−169794.	+	294092.i	−1.14552	+	1.98409i
$386$		0			0
$387$	12554.2	−	57015.9i	0.0838235	−	0.380692i
$388$		0			0
$389$	−50495.3	−	29153.5i	−0.333696	−	0.192660i	0.323785	−	0.946131i	$-0.395045\pi$
$389$	−50495.3	−	29153.5i	−0.333696	−	0.192660i	−0.657481	+	0.753471i	$0.728378\pi$
$390$		0			0
$391$	−83503.0	−	144631.i	−0.546196	−	0.946039i
$392$		0			0
$393$	−2506.19	+	2014.39i	−0.0162266	+	0.0130424i
$394$		0			0
$395$			122480.i			0.785002i
$396$		0			0
$397$	−134572.			−0.853834			−0.426917	−	0.904291i	$-0.640400\pi$
$397$	−134572.			−0.853834			−0.426917	+	0.904291i	$0.640400\pi$
$398$		0			0
$399$	77091.1	−	198662.i	0.484238	−	1.24787i
$400$		0			0
$401$	185654.	−	107187.i	1.15456	−	0.666584i	0.204563	−	0.978853i	$-0.434423\pi$
$401$	185654.	−	107187.i	1.15456	−	0.666584i	0.949994	+	0.312269i	$0.101089\pi$
$402$		0			0
$403$	35388.3	−	61294.4i	0.217896	−	0.377408i
$404$		0			0
$405$	87235.3	−	188490.i	0.531842	−	1.14915i
$406$		0			0
$407$	214119.	+	123622.i	1.29261	+	0.746288i
$408$		0			0
$409$	24369.5	+	42209.2i	0.145680	+	0.252325i	0.929626	−	0.368503i	$-0.120130\pi$
$409$	24369.5	+	42209.2i	0.145680	+	0.252325i	−0.783946	+	0.620828i	$0.786796\pi$
$410$		0			0
$411$	124120.	+	48165.0i	0.734782	+	0.285133i
$412$		0			0
$413$			185951.i			1.09018i
$414$		0			0
$415$	−380980.			−2.21211
$416$		0			0
$417$	12174.5	+	15146.8i	0.0700132	+	0.0871063i
$418$		0			0
$419$	59650.3	−	34439.1i	0.339770	−	0.196166i	−0.320400	−	0.947282i	$-0.603817\pi$
$419$	59650.3	−	34439.1i	0.339770	−	0.196166i	0.660170	+	0.751116i	$0.270484\pi$
$420$		0			0
$421$	157677.	−	273105.i	0.889620	−	1.54087i	0.0492953	−	0.998784i	$-0.484302\pi$
$421$	157677.	−	273105.i	0.889620	−	1.54087i	0.840325	−	0.542083i	$-0.182364\pi$
$422$		0			0
$423$	−196726.	−	43316.5i	−1.09946	−	0.242087i
$424$		0			0
$425$	−106425.	−	61444.5i	−0.589204	−	0.340177i
$426$		0			0
$427$	−93490.6	−	161930.i	−0.512758	−	0.888122i
$428$		0			0
$429$	37711.1	+	243847.i	0.204906	+	1.32496i
$430$		0			0
$431$			151597.i			0.816088i	0.912962	+	0.408044i	$0.133789\pi$
$431$			151597.i			0.816088i	−0.912962	+	0.408044i	$0.866211\pi$
$432$		0			0
$433$	−237835.			−1.26853			−0.634265	−	0.773116i	$-0.718697\pi$
$433$	−237835.			−1.26853			−0.634265	+	0.773116i	$0.718697\pi$
$434$		0			0
$435$	−44415.6	+	6868.89i	−0.234724	+	0.0363001i
$436$		0			0
$437$	−139442.	+	80507.1i	−0.730183	+	0.421571i
$438$		0			0
$439$	32350.4	−	56032.6i	0.167861	−	0.290745i	−0.769806	−	0.638278i	$-0.779647\pi$
$439$	32350.4	−	56032.6i	0.167861	−	0.290745i	0.937668	+	0.347533i	$0.112981\pi$
$440$		0			0
$441$	−196080.	−	179156.i	−1.00822	−	0.921201i
$442$		0			0
$443$	4469.49	+	2580.46i	0.0227746	+	0.0131489i	0.511344	−	0.859376i	$-0.329148\pi$
$443$	4469.49	+	2580.46i	0.0227746	+	0.0131489i	−0.488569	+	0.872525i	$0.662481\pi$
$444$		0			0
$445$	−120880.	−	209371.i	−0.610430	−	1.05730i
$446$		0			0
$447$	202358.	−	162649.i	1.01276	−	0.814021i
$448$		0			0
$449$			165679.i			0.821816i	0.911677	+	0.410908i	$0.134788\pi$
$449$			165679.i			0.821816i	−0.911677	+	0.410908i	$0.865212\pi$
$450$		0			0
$451$	−56261.8			−0.276605
$452$		0			0
$453$	−30948.4	+	79753.3i	−0.150814	+	0.388644i
$454$		0			0
$455$	−397979.	+	229773.i	−1.92237	+	1.10988i
$456$		0			0
$457$	204489.	−	354185.i	0.979121	−	1.69589i	0.313519	−	0.949582i	$-0.398492\pi$
$457$	204489.	−	354185.i	0.979121	−	1.69589i	0.665603	−	0.746306i	$-0.268174\pi$
$458$		0			0
$459$	−105524.	−	212824.i	−0.500871	−	1.01017i
$460$		0			0
$461$	−75485.9	−	43581.8i	−0.355193	−	0.205071i	0.311777	−	0.950155i	$-0.399076\pi$
$461$	−75485.9	−	43581.8i	−0.355193	−	0.205071i	−0.666970	+	0.745085i	$0.732409\pi$
$462$		0			0
$463$	8403.24	+	14554.8i	0.0391999	+	0.0678962i	0.884960	−	0.465668i	$-0.154186\pi$
$463$	8403.24	+	14554.8i	0.0391999	+	0.0678962i	−0.845760	+	0.533564i	$0.820852\pi$
$464$		0			0
$465$	−97598.4	−	37873.2i	−0.451374	−	0.175157i
$466$		0			0
$467$			394500.i			1.80889i	0.426585	+	0.904447i	$0.359716\pi$
$467$			394500.i			1.80889i	−0.426585	+	0.904447i	$0.640284\pi$
$468$		0			0
$469$	497143.			2.26014
$470$		0			0
$471$	55680.8	+	69274.8i	0.250994	+	0.312272i
$472$		0			0
$473$	88846.0	−	51295.3i	0.397114	−	0.229274i
$474$		0			0
$475$	−59240.0	+	102607.i	−0.262559	+	0.454766i
$476$		0			0
$477$	97531.1	+	307786.i	0.428653	+	1.35273i
$478$		0			0
$479$	90406.6	+	52196.3i	0.394030	+	0.227493i	0.683905	−	0.729571i	$-0.260280\pi$
$479$	90406.6	+	52196.3i	0.394030	+	0.227493i	−0.289875	+	0.957065i	$0.593614\pi$
$480$		0			0
$481$	167291.	+	289756.i	0.723072	+	1.25240i
$482$		0			0
$483$	53130.6	+	343553.i	0.227746	+	1.47265i
$484$		0			0
$485$		−	92167.7i		−	0.391828i
$486$		0			0
$487$	−106236.			−0.447936			−0.223968	−	0.974597i	$-0.571901\pi$
$487$	−106236.			−0.447936			−0.223968	+	0.974597i	$0.571901\pi$
$488$		0			0
$489$	199808.	−	30900.3i	0.835592	−	0.129225i
$490$		0			0
$491$	−78832.6	+	45514.0i	−0.326997	+	0.188792i	−0.654507	−	0.756056i	$-0.727124\pi$
$491$	−78832.6	+	45514.0i	−0.326997	+	0.188792i	0.327510	+	0.944848i	$0.393790\pi$
$492$		0			0
$493$	−25701.5	+	44516.2i	−0.105746	+	0.183157i
$494$		0			0
$495$	347924.	−	110250.i	1.41995	−	0.449955i
$496$		0			0
$497$	−380391.	−	219619.i	−1.53999	−	0.889113i
$498$		0			0
$499$	−69176.0	−	119816.i	−0.277814	−	0.481188i	0.693027	−	0.720912i	$-0.256277\pi$
$499$	−69176.0	−	119816.i	−0.277814	−	0.481188i	−0.970841	+	0.239723i	$0.922943\pi$
$500$		0			0
$501$	119029.	−	95671.7i	0.474218	−	0.381161i
$502$		0			0
$503$		−	63792.4i		−	0.252135i	−0.992022	−	0.126067i	$-0.959764\pi$
$503$		−	63792.4i		−	0.252135i	0.992022	−	0.126067i	$-0.0402356\pi$
$504$		0			0
$505$	−345172.			−1.35348
$506$		0			0
$507$	−27805.1	+	71653.2i	−0.108171	+	0.278753i
$508$		0			0
$509$	−423634.	+	244585.i	−1.63514	+	0.944049i	−0.652668	+	0.757644i	$0.726350\pi$
$509$	−423634.	+	244585.i	−1.63514	+	0.944049i	−0.982473	+	0.186405i	$0.940316\pi$
$510$		0			0
$511$	331250.	−	573742.i	1.26857	−	2.19723i
$512$		0			0
$513$	−205188.	+	101738.i	−0.779681	+	0.386588i
$514$		0			0
$515$	−199504.	−	115184.i	−0.752206	−	0.434286i
$516$		0			0
$517$	−176987.	−	306551.i	−0.662158	−	1.14689i
$518$		0			0
$519$	−314310.	−	121969.i	−1.16687	−	0.452807i
$520$		0			0
$521$			339386.i			1.25031i	0.780500	+	0.625156i	$0.214965\pi$
$521$			339386.i			1.25031i	−0.780500	+	0.625156i	$0.785035\pi$
$522$		0			0
$523$	−379243.			−1.38648			−0.693242	−	0.720705i	$-0.743818\pi$
$523$	−379243.			−1.38648			−0.693242	+	0.720705i	$0.743818\pi$
$524$		0			0
$525$	160257.	+	199382.i	0.581430	+	0.723382i
$526$		0			0
$527$	−103694.	+	59867.6i	−0.373363	+	0.215561i
$528$		0			0
$529$	−8583.94	+	14867.8i	−0.0306744	+	0.0531295i
$530$		0			0
$531$	134806.	−	147540.i	0.478101	−	0.523264i
$532$		0			0
$533$	−65935.7	−	38068.0i	−0.232095	−	0.134000i
$534$		0			0
$535$	87458.4	+	151482.i	0.305558	+	0.529242i
$536$		0			0
$537$	−61568.8	−	398116.i	−0.213507	−	1.38058i
$538$		0			0
$539$		−	466725.i		−	1.60651i
$540$		0			0
$541$	−494913.			−1.69096			−0.845481	−	0.534005i	$-0.820686\pi$
$541$	−494913.			−1.69096			−0.845481	+	0.534005i	$0.820686\pi$
$542$		0			0
$543$	−259784.	+	40175.7i	−0.881074	+	0.136259i
$544$		0			0
$545$	197016.	−	113747.i	0.663297	−	0.382955i
$546$		0			0
$547$	−93045.4	+	161159.i	−0.310971	+	0.538618i	−0.978573	−	0.205901i	$-0.933988\pi$
$547$	−93045.4	+	161159.i	−0.310971	+	0.538618i	0.667602	+	0.744519i	$0.267321\pi$
$548$		0			0
$549$	−43213.4	+	196258.i	−0.143375	+	0.651152i
$550$		0			0
$551$	42919.1	+	24779.3i	0.141367	+	0.0816181i
$552$		0			0
$553$	−145797.	−	252528.i	−0.476759	−	0.825770i
$554$		0			0
$555$	385739.	−	310044.i	1.25230	−	1.00656i
$556$		0			0
$557$			119662.i			0.385698i	0.981228	+	0.192849i	$0.0617728\pi$
$557$			119662.i			0.385698i	−0.981228	+	0.192849i	$0.938227\pi$
$558$		0			0
$559$	138830.			0.444283
$560$		0			0
$561$	151012.	−	389156.i	0.479830	−	1.23651i
$562$		0			0
$563$	−22885.5	+	13213.0i	−0.0722012	+	0.0416854i	−0.535666	−	0.844430i	$-0.679939\pi$
$563$	−22885.5	+	13213.0i	−0.0722012	+	0.0416854i	0.463465	+	0.886115i	$0.346606\pi$
$564$		0			0
$565$	−196331.	+	340055.i	−0.615023	+	1.06525i
$566$		0			0
$567$	44512.4	+	492469.i	0.138457	+	1.53184i
$568$		0			0
$569$	453562.	+	261864.i	1.40092	+	0.808820i	0.994487	−	0.104862i	$-0.0334402\pi$
$569$	453562.	+	261864.i	1.40092	+	0.808820i	0.406430	+	0.913682i	$0.366774\pi$
$570$		0			0
$571$	−161586.	−	279875.i	−0.495600	−	0.858405i	0.504387	−	0.863478i	$-0.331719\pi$
$571$	−161586.	−	279875.i	−0.495600	−	0.858405i	−0.999987	+	0.00507280i	$0.998385\pi$
$572$		0			0
$573$	−251787.	−	97706.3i	−0.766873	−	0.297586i
$574$		0			0
$575$		−	193284.i		−	0.584603i
$576$		0			0
$577$	350692.			1.05335			0.526676	−	0.850066i	$-0.323438\pi$
$577$	350692.			1.05335			0.526676	+	0.850066i	$0.323438\pi$
$578$		0			0
$579$	97158.7	+	120879.i	0.289817	+	0.360574i
$580$		0			0
$581$	785501.	−	453509.i	2.32699	−	1.34349i
$582$		0			0
$583$	−283679.	+	491346.i	−0.834622	+	1.44561i
$584$		0			0
$585$	482345.	+	106206.i	1.40944	+	0.310340i
$586$		0			0
$587$	415397.	+	239829.i	1.20555	+	0.696027i	0.961785	−	0.273806i	$-0.0882827\pi$
$587$	415397.	+	239829.i	1.20555	+	0.696027i	0.243769	+	0.969833i	$0.421616\pi$
$588$		0			0
$589$	57719.7	+	99973.4i	0.166377	+	0.288173i
$590$		0			0
$591$	93385.8	+	603850.i	0.267366	+	1.72884i
$592$		0			0
$593$			177843.i			0.505740i	0.967500	+	0.252870i	$0.0813745\pi$
$593$			177843.i			0.505740i	−0.967500	+	0.252870i	$0.918625\pi$
$594$		0			0
$595$	777430.			2.19597
$596$		0			0
$597$	240114.	−	37133.8i	0.673704	−	0.104189i
$598$		0			0
$599$	−16977.8	+	9802.11i	−0.0473180	+	0.0273191i	−0.523472	−	0.852043i	$-0.675364\pi$
$599$	−16977.8	+	9802.11i	−0.0473180	+	0.0273191i	0.476154	+	0.879362i	$0.342030\pi$
$600$		0			0
$601$	−197404.	+	341913.i	−0.546520	+	0.946600i	0.451990	+	0.892023i	$0.350714\pi$
$601$	−197404.	+	341913.i	−0.546520	+	0.946600i	−0.998510	+	0.0545772i	$0.982619\pi$
$602$		0			0
$603$	−394451.	−	360406.i	−1.08482	−	0.991191i
$604$		0			0
$605$	154036.	+	88932.8i	0.420835	+	0.242969i
$606$		0			0
$607$	351729.	+	609212.i	0.954620	+	1.65345i	0.735235	+	0.677813i	$0.237072\pi$
$607$	351729.	+	609212.i	0.954620	+	1.65345i	0.219386	+	0.975638i	$0.429595\pi$
$608$		0			0
$609$	83399.0	−	67033.4i	0.224867	−	0.180741i
$610$		0			0
$611$		−	479015.i		−	1.28312i
$612$		0			0
$613$	96392.2			0.256520			0.128260	−	0.991741i	$-0.459061\pi$
$613$	96392.2			0.256520			0.128260	+	0.991741i	$0.459061\pi$
$614$		0			0
$615$	−40741.0	+	104989.i	−0.107716	+	0.277583i
$616$		0			0
$617$	−439772.	+	253903.i	−1.15520	+	0.666956i	−0.950149	−	0.311796i	$-0.899070\pi$
$617$	−439772.	+	253903.i	−1.15520	+	0.666956i	−0.205052	+	0.978751i	$0.565736\pi$
$618$		0			0
$619$	−43453.6	+	75263.9i	−0.113408	+	0.196429i	−0.917142	−	0.398560i	$-0.869510\pi$
$619$	−43453.6	+	75263.9i	−0.113408	+	0.196429i	0.803734	+	0.594989i	$0.202843\pi$
$620$		0			0
$621$	206904.	−	311104.i	0.536521	−	0.806720i
$622$		0			0
$623$	498460.	+	287786.i	1.28426	+	0.741470i
$624$		0			0
$625$	242052.	+	419247.i	0.619654	+	1.07327i
$626$		0			0
$627$	−375193.	−	145594.i	−0.954377	−	0.370348i
$628$		0			0
$629$		−	566023.i		−	1.43065i
$630$		0			0
$631$	571591.			1.43558			0.717788	−	0.696261i	$-0.245154\pi$
$631$	571591.			1.43558			0.717788	+	0.696261i	$0.245154\pi$
$632$		0			0
$633$	133286.	+	165826.i	0.332641	+	0.413852i
$634$		0			0
$635$	−247101.	+	142664.i	−0.612812	+	0.353807i
$636$		0			0
$637$	315797.	−	546976.i	0.778267	−	1.34800i
$638$		0			0
$639$	142602.	+	450020.i	0.349240	+	1.10212i
$640$		0			0
$641$	332304.	+	191856.i	0.808759	+	0.466937i	0.846525	−	0.532350i	$-0.178691\pi$
$641$	332304.	+	191856.i	0.808759	+	0.466937i	−0.0377659	+	0.999287i	$0.512024\pi$
$642$		0			0
$643$	−405119.	−	701687.i	−0.979853	−	1.69716i	−0.662888	−	0.748718i	$-0.730670\pi$
$643$	−405119.	−	701687.i	−0.979853	−	1.69716i	−0.316965	−	0.948437i	$-0.602664\pi$
$644$		0			0
$645$	−31384.5	−	202938.i	−0.0754389	−	0.487802i
$646$		0			0
$647$		−	687173.i		−	1.64156i	−0.571243	−	0.820781i	$-0.693539\pi$
$647$		−	687173.i		−	1.64156i	0.571243	−	0.820781i	$-0.306461\pi$
$648$		0			0
$649$	351187.			0.833775
$650$		0			0
$651$	246311.	−	38092.1i	0.581194	−	0.0898820i
$652$		0			0
$653$	−189470.	+	109391.i	−0.444339	+	0.256539i	−0.705437	−	0.708773i	$-0.749249\pi$
$653$	−189470.	+	109391.i	−0.444339	+	0.256539i	0.261097	+	0.965312i	$0.415916\pi$
$654$		0			0
$655$	−5654.87	+	9794.52i	−0.0131807	+	0.0228297i
$656$		0			0
$657$	−678762.	+	215086.i	−1.57249	+	0.498289i
$658$		0			0
$659$	−71298.2	−	41164.1i	−0.164175	−	0.0947867i	0.415661	−	0.909520i	$-0.363550\pi$
$659$	−71298.2	−	41164.1i	−0.164175	−	0.0947867i	−0.579836	+	0.814733i	$0.696884\pi$
$660$		0			0
$661$	−205017.	−	355100.i	−0.469231	−	0.812732i	0.530150	−	0.847904i	$-0.322136\pi$
$661$	−205017.	−	355100.i	−0.469231	−	0.812732i	−0.999381	+	0.0351716i	$0.988802\pi$
$662$		0			0
$663$	440290.	−	353890.i	1.00164	−	0.805085i
$664$		0			0
$665$		−	749537.i		−	1.69492i
$666$		0			0
$667$	−80848.4			−0.181727
$668$		0			0
$669$	−188700.	+	486274.i	−0.421617	+	1.08650i
$670$		0			0
$671$	−305822.	+	176566.i	−0.679241	+	0.392160i
$672$		0			0
$673$	−265864.	+	460490.i	−0.586989	+	1.01669i	0.407636	+	0.913145i	$0.366353\pi$
$673$	−265864.	+	460490.i	−0.586989	+	1.01669i	−0.994624	+	0.103549i	$0.966980\pi$
$674$		0			0
$675$	17389.5	−	274376.i	0.0381662	−	0.602196i
$676$		0			0
$677$	149580.	+	86360.3i	0.326361	+	0.188424i	0.654224	−	0.756301i	$-0.272995\pi$
$677$	149580.	+	86360.3i	0.326361	+	0.188424i	−0.327864	+	0.944725i	$0.606329\pi$
$678$		0			0
$679$	109714.	+	190030.i	0.237970	+	0.412177i
$680$		0			0
$681$	−84410.0	−	32755.4i	−0.182012	−	0.0706300i
$682$		0			0
$683$			452646.i			0.970324i	0.874424	+	0.485162i	$0.161239\pi$
$683$			452646.i			0.970324i	−0.874424	+	0.485162i	$0.838761\pi$
$684$		0			0
$685$	468296.			0.998019
$686$		0			0
$687$	−325895.	−	405460.i	−0.690501	−	0.859081i
$688$		0			0
$689$	−664912.	+	383887.i	−1.40064	+	0.808658i
$690$		0			0
$691$	117795.	−	204027.i	0.246701	−	0.427298i	−0.715908	−	0.698195i	$-0.753987\pi$
$691$	117795.	−	204027.i	0.246701	−	0.427298i	0.962608	+	0.270897i	$0.0873203\pi$
$692$		0			0
$693$	−586107.	+	641473.i	−1.22042	+	1.33571i
$694$		0			0
$695$	59196.0	+	34176.8i	0.122553	+	0.0707558i
$696$		0			0
$697$	64400.9	+	111546.i	0.132564	+	0.229608i
$698$		0			0
$699$	−93979.6	−	607690.i	−0.192344	−	1.24373i
$700$		0			0
$701$			41298.8i			0.0840430i	0.999117	+	0.0420215i	$0.0133798\pi$
$701$			41298.8i			0.0840430i	−0.999117	+	0.0420215i	$0.986620\pi$
$702$		0			0
$703$	−545715.			−1.10422
$704$		0			0
$705$	−700210.	+	108288.i	−1.40880	+	0.217872i
$706$		0			0
$707$	711673.	−	410885.i	1.42378	−	0.822018i
$708$		0			0
$709$	−32914.9	+	57010.2i	−0.0654786	+	0.113412i	−0.896906	−	0.442221i	$-0.854191\pi$
$709$	−32914.9	+	57010.2i	−0.0654786	+	0.113412i	0.831428	+	0.555633i	$0.187524\pi$
$710$		0			0
$711$	−67390.6	+	306061.i	−0.133309	+	0.605437i
$712$		0			0
$713$	−163093.	−	94162.0i	−0.320817	−	0.185224i
$714$		0			0
$715$	433950.	+	751623.i	0.848843	+	1.47024i
$716$		0			0
$717$	243993.	−	196114.i	0.474613	−	0.381479i
$718$		0			0
$719$			551850.i			1.06749i	0.845646	+	0.533745i	$0.179216\pi$
$719$			551850.i			1.06749i	−0.845646	+	0.533745i	$0.820784\pi$
$720$		0			0
$721$	548447.			1.05503
$722$		0			0
$723$	−299432.	+	771629.i	−0.572824	+	1.47615i
$724$		0			0
$725$	−51520.8	+	29745.6i	−0.0980182	+	0.0565908i
$726$		0			0
$727$	69946.0	−	121150.i	0.132341	−	0.229221i	−0.792238	−	0.610213i	$-0.791084\pi$
$727$	69946.0	−	121150.i	0.132341	−	0.229221i	0.924579	+	0.380992i	$0.124417\pi$
$728$		0			0
$729$	321700.	−	423012.i	0.605335	−	0.795971i
$730$		0			0
$731$	−203398.	−	117432.i	−0.380638	−	0.219761i
$732$		0			0
$733$	348037.	+	602817.i	0.647764	+	1.12196i	0.983656	+	0.180060i	$0.0576291\pi$
$733$	348037.	+	602817.i	0.647764	+	1.12196i	−0.335891	+	0.941901i	$0.609038\pi$
$734$		0			0
$735$	−870944.	−	337971.i	−1.61219	−	0.625612i
$736$		0			0
$737$		−	938905.i		−	1.72857i
$738$		0			0
$739$	−360220.			−0.659598			−0.329799	−	0.944051i	$-0.606981\pi$
$739$	−360220.			−0.659598			−0.329799	+	0.944051i	$0.606981\pi$
$740$		0			0
$741$	−341193.	−	424493.i	−0.621390	−	0.773097i
$742$		0			0
$743$	−55134.1	+	31831.7i	−0.0998718	+	0.0576610i	−0.549104	−	0.835754i	$-0.685031\pi$
$743$	−55134.1	+	31831.7i	−0.0998718	+	0.0576610i	0.449232	+	0.893415i	$0.351698\pi$
$744$		0			0
$745$	456594.	−	790844.i	0.822655	−	1.42488i
$746$		0			0
$747$	−952018.	−	209622.i	−1.70610	−	0.375661i
$748$		0			0
$749$	−360641.	−	208216.i	−0.642854	−	0.371152i
$750$		0			0
$751$	−369552.	−	640082.i	−0.655232	−	1.13490i	−0.981836	−	0.189734i	$-0.939237\pi$
$751$	−369552.	−	640082.i	−0.655232	−	1.13490i	0.326603	−	0.945162i	$-0.394096\pi$
$752$		0			0
$753$	96019.2	+	620878.i	0.169343	+	1.09501i
$754$		0			0
$755$			300903.i			0.527877i
$756$		0			0
$757$	−315416.			−0.550416			−0.275208	−	0.961385i	$-0.588747\pi$
$757$	−315416.			−0.550416			−0.275208	+	0.961385i	$0.588747\pi$
$758$		0			0
$759$	648834.	−	100343.i	1.12629	−	0.174181i
$760$		0			0
$761$	814012.	−	469970.i	1.40560	−	0.811523i	0.410640	−	0.911798i	$-0.365305\pi$
$761$	814012.	−	469970.i	1.40560	−	0.811523i	0.994960	+	0.100274i	$0.0319721\pi$
$762$		0			0
$763$	−270803.	+	469045.i	−0.465163	+	0.805685i
$764$		0			0
$765$	−616841.	−	563601.i	−1.05402	−	0.963051i
$766$		0			0
$767$	411571.	+	237621.i	0.699607	+	0.403919i
$768$		0			0
$769$	−173503.	−	300517.i	−0.293397	−	0.508178i	0.681214	−	0.732085i	$-0.261452\pi$
$769$	−173503.	−	300517.i	−0.293397	−	0.508178i	−0.974611	+	0.223906i	$0.928119\pi$
$770$		0			0
$771$	123206.	−	99028.7i	0.207263	−	0.166591i
$772$		0			0
$773$		−	4630.27i		−	0.00774903i	−0.999992	−	0.00387451i	$-0.998767\pi$
$773$		−	4630.27i		−	0.00774903i	0.999992	−	0.00387451i	$-0.00123330\pi$
$774$		0			0
$775$	−138576.			−0.230719
$776$		0			0
$777$	−426243.	+	1.09842e6i	−0.706018	+	1.81939i
$778$		0			0
$779$	107544.	−	62090.3i	0.177219	−	0.102317i
$780$		0			0
$781$	−414773.	+	718407.i	−0.679999	+	1.17779i
$782$		0			0
$783$	−114768.	−	7273.80i	−0.187196	−	0.0118642i
$784$		0			0
$785$	270735.	+	156309.i	0.439345	+	0.253656i
$786$		0			0
$787$	251477.	+	435571.i	0.406021	+	0.703250i	0.994440	−	0.105307i	$-0.0335825\pi$
$787$	251477.	+	435571.i	0.406021	+	0.703250i	−0.588418	+	0.808557i	$0.700249\pi$
$788$		0			0
$789$	−256669.	−	99600.9i	−0.412306	−	0.159996i
$790$		0			0
$791$		−	934828.i		−	1.49410i
$792$		0			0
$793$	−477875.			−0.759921
$794$		0			0
$795$	711468.	+	885166.i	1.12570	+	1.40052i
$796$		0			0
$797$	210541.	−	121556.i	0.331451	−	0.191363i	−0.325034	−	0.945702i	$-0.605376\pi$
$797$	210541.	−	121556.i	0.331451	−	0.191363i	0.656485	+	0.754339i	$0.272042\pi$
$798$		0			0
$799$	−405183.	+	701797.i	−0.634684	+	1.09930i
$800$		0			0
$801$	−186864.	−	589701.i	−0.291247	−	0.919108i
$802$		0			0
$803$	−1.08357e6	−	625599.i	−1.68045	−	0.970209i
$804$		0			0
$805$	611385.	+	1.05895e6i	0.943459	+	1.63412i
$806$		0			0
$807$	−81945.3	−	529874.i	−0.125828	−	0.813627i
$808$		0			0
$809$		−	600348.i		−	0.917289i	−0.888620	−	0.458644i	$-0.848335\pi$
$809$		−	600348.i		−	0.917289i	0.888620	−	0.458644i	$-0.151665\pi$
$810$		0			0
$811$	168852.			0.256722			0.128361	−	0.991727i	$-0.459028\pi$
$811$	168852.			0.256722			0.128361	+	0.991727i	$0.459028\pi$
$812$		0			0
$813$	838642.	−	129696.i	1.26881	−	0.196222i
$814$		0			0
$815$	615877.	−	355577.i	0.927211	−	0.535326i
$816$		0			0
$817$	−113219.	+	196100.i	−0.169619	+	0.293788i
$818$		0			0
$819$	−1.12092e6	+	355197.i	−1.67112	+	0.529543i
$820$		0			0
$821$	445541.	+	257233.i	0.660999	+	0.381628i	0.792658	−	0.609667i	$-0.208697\pi$
$821$	445541.	+	257233.i	0.660999	+	0.381628i	−0.131658	+	0.991295i	$0.542030\pi$
$822$		0			0
$823$	602121.	+	1.04290e6i	0.888963	+	1.53973i	0.841103	+	0.540875i	$0.181907\pi$
$823$	602121.	+	1.04290e6i	0.888963	+	1.53973i	0.0478604	+	0.998854i	$0.484760\pi$
$824$		0			0
$825$	376553.	−	302661.i	0.553246	−	0.444681i
$826$		0			0
$827$		−	682316.i		−	0.997641i	−0.866705	−	0.498821i	$-0.833767\pi$
$827$		−	682316.i		−	0.997641i	0.866705	−	0.498821i	$-0.166233\pi$
$828$		0			0
$829$	−1.14603e6			−1.66758			−0.833791	−	0.552081i	$-0.813834\pi$
$829$	−1.14603e6			−1.66758			−0.833791	+	0.552081i	$0.813834\pi$
$830$		0			0
$831$	323558.	−	833801.i	0.468544	−	1.20743i
$832$		0			0
$833$	−925338.	+	534244.i	−1.33355	+	0.769927i
$834$		0			0
$835$	268573.	−	465182.i	0.385203	−	0.667191i
$836$		0			0
$837$	−223047.	−	148340.i	−0.318379	−	0.211743i
$838$		0			0
$839$	−284696.	−	164370.i	−0.404444	−	0.233506i	0.283956	−	0.958837i	$-0.408353\pi$
$839$	−284696.	−	164370.i	−0.404444	−	0.233506i	−0.688400	+	0.725332i	$0.741686\pi$
$840$		0			0
$841$	−341198.	−	590973.i	−0.482408	−	0.835556i
$842$		0			0
$843$	665989.	+	258438.i	0.937157	+	0.363665i
$844$		0			0
$845$			270342.i			0.378617i
$846$		0			0
$847$	−423453.			−0.590254
$848$		0			0
$849$	377318.	+	469437.i	0.523471	+	0.651272i
$850$		0			0
$851$	770989.	−	445131.i	1.06461	−	0.614651i
$852$		0			0
$853$	−188763.	+	326948.i	−0.259430	+	0.449346i	−0.966089	−	0.258208i	$-0.916868\pi$
$853$	−188763.	+	326948.i	−0.259430	+	0.449346i	0.706660	+	0.707554i	$0.250201\pi$
$854$		0			0
$855$	−543380.	+	594709.i	−0.743313	+	0.813528i
$856$		0			0
$857$	372750.	+	215207.i	0.507524	+	0.293019i	0.731815	−	0.681503i	$-0.238673\pi$
$857$	372750.	+	215207.i	0.507524	+	0.293019i	−0.224291	+	0.974522i	$0.572007\pi$
$858$		0			0
$859$	−84365.9	−	146126.i	−0.114335	−	0.198035i	0.803178	−	0.595738i	$-0.203141\pi$
$859$	−84365.9	−	146126.i	−0.114335	−	0.198035i	−0.917514	+	0.397704i	$0.869807\pi$
$860$		0			0
$861$	−40976.5	−	264962.i	−0.0552749	−	0.357418i
$862$		0			0
$863$			641651.i			0.861543i	0.902461	+	0.430772i	$0.141759\pi$
$863$			641651.i			0.861543i	−0.902461	+	0.430772i	$0.858241\pi$
$864$		0			0
$865$	−1.18587e6			−1.58491
$866$		0			0
$867$	−201548.	+	31169.5i	−0.268127	+	0.0414660i
$868$		0			0
$869$	−476925.	+	275353.i	−0.631554	+	0.364628i
$870$		0			0
$871$	635284.	−	1.10034e6i	0.837398	−	1.45042i
$872$		0			0
$873$	50712.3	−	230315.i	0.0665403	−	0.302199i
$874$		0			0
$875$	−512148.	−	295689.i	−0.668928	−	0.386206i
$876$		0			0
$877$	559865.	+	969715.i	0.727921	+	1.26080i	0.957760	+	0.287568i	$0.0928468\pi$
$877$	559865.	+	969715.i	0.727921	+	1.26080i	−0.229839	+	0.973229i	$0.573820\pi$
$878$		0			0
$879$	−392589.	+	315550.i	−0.508113	+	0.408405i
$880$		0			0
$881$		−	293548.i		−	0.378205i	−0.981957	−	0.189103i	$-0.939442\pi$
$881$		−	293548.i		−	0.378205i	0.981957	−	0.189103i	$-0.0605579\pi$
$882$		0			0
$883$	1.07664e6			1.38085			0.690426	−	0.723403i	$-0.257423\pi$
$883$	1.07664e6			1.38085			0.690426	+	0.723403i	$0.257423\pi$
$884$		0			0
$885$	254306.	−	655341.i	0.324691	−	0.836721i
$886$		0			0
$887$	−1.09244e6	+	630719.i	−1.38851	+	0.801657i	−0.993148	−	0.116867i	$-0.962715\pi$
$887$	−1.09244e6	+	630719.i	−1.38851	+	0.801657i	−0.395364	+	0.918525i	$0.629381\pi$
$888$		0			0
$889$	339647.	−	588286.i	0.429759	−	0.744364i
$890$		0			0
$891$	930077.	−	84066.2i	1.17156	−	0.105893i
$892$		0			0
$893$	676618.	+	390645.i	0.848478	+	0.489869i
$894$		0			0
$895$	−708485.	−	1.22713e6i	−0.884473	−	1.53195i
$896$		0			0
$897$	828292.	+	321420.i	1.02943	+	0.399473i
$898$		0			0
$899$			57964.4i			0.0717203i
$900$		0			0
$901$	1.29887e6			1.59999
$902$		0			0
$903$	306280.	+	381056.i	0.375616	+	0.467319i
$904$		0			0
$905$	−800745.	+	462310.i	−0.977680	+	0.564464i
$906$		0			0
$907$	−106701.	+	184812.i	−0.129705	+	0.224655i	−0.923562	−	0.383449i	$-0.874736\pi$
$907$	−106701.	+	184812.i	−0.129705	+	0.224655i	0.793857	+	0.608104i	$0.208070\pi$
$908$		0			0
$909$	−862540.	−	189920.i	−1.04388	−	0.229849i
$910$		0			0
$911$	735102.	+	424411.i	0.885749	+	0.511388i	0.872550	−	0.488525i	$-0.162465\pi$
$911$	735102.	+	424411.i	0.885749	+	0.511388i	0.0131995	+	0.999913i	$0.495798\pi$
$912$		0			0
$913$	−856498.	−	1.48350e6i	−1.02751	−	1.77970i
$914$		0			0
$915$	108030.	+	698545.i	0.129034	+	0.834357i
$916$		0			0
$917$		−	26925.7i		−	0.0320205i
$918$		0			0
$919$	650728.			0.770493			0.385246	−	0.922814i	$-0.374116\pi$
$919$	650728.			0.770493			0.385246	+	0.922814i	$0.374116\pi$
$920$		0			0
$921$	−77449.5	+	11977.6i	−0.0913060	+	0.0141205i
$922$		0			0
$923$	−972181.	+	561289.i	−1.14115	+	0.658845i
$924$		0			0
$925$	327543.	−	567321.i	0.382811	−	0.663049i
$926$		0			0
$927$	−435157.	−	397599.i	−0.506392	−	0.462685i
$928$		0			0
$929$	236742.	+	136683.i	0.274312	+	0.158374i	0.630846	−	0.775908i	$-0.282708\pi$
$929$	236742.	+	136683.i	0.274312	+	0.158374i	−0.356534	+	0.934282i	$0.616041\pi$
$930$		0			0
$931$	515076.	+	892138.i	0.594254	+	1.02928i
$932$		0			0
$933$	391554.	−	314718.i	0.449809	−	0.361542i
$934$		0			0
$935$		−	1.46826e6i		−	1.67949i
$936$		0			0
$937$	1.19093e6			1.35646			0.678232	−	0.734848i	$-0.262746\pi$
$937$	1.19093e6			1.35646			0.678232	+	0.734848i	$0.262746\pi$
$938$		0			0
$939$	−192227.	+	495364.i	−0.218013	+	0.561815i
$940$		0			0
$941$	1.21799e6	−	703208.i	1.37551	−	0.794153i	0.383898	−	0.923375i	$-0.374581\pi$
$941$	1.21799e6	−	703208.i	1.37551	−	0.794153i	0.991616	+	0.129222i	$0.0412480\pi$
$942$		0			0
$943$	−101292.	+	175443.i	−0.113907	+	0.197293i
$944$		0			0
$945$	772616.	+	1.55823e6i	0.865168	+	1.74489i
$946$		0			0
$947$	1.13971e6	+	658009.i	1.27085	+	0.733723i	0.975147	−	0.221558i	$-0.0711144\pi$
$947$	1.13971e6	+	658009.i	1.27085	+	0.733723i	0.295698	+	0.955281i	$0.404448\pi$
$948$		0			0
$949$	−846589.	−	1.46634e6i	−0.940027	−	1.62817i
$950$		0			0
$951$	−254585.	−	98792.0i	−0.281495	−	0.109235i
$952$		0			0
$953$			1.09774e6i			1.20868i	0.796725	+	0.604342i	$0.206564\pi$
$953$			1.09774e6i			1.20868i	−0.796725	+	0.604342i	$0.793436\pi$
$954$		0			0
$955$	−949973.			−1.04161
$956$		0			0
$957$	−126599.	−	157508.i	−0.138232	−	0.171980i
$958$		0			0
$959$	−965527.	+	557447.i	−1.04985	+	0.606131i
$960$		0			0
$961$	394251.	−	682863.i	0.426900	−	0.739412i
$962$		0			0
$963$	135198.	+	426655.i	0.145787	+	0.460070i
$964$		0			0
$965$	472412.	+	272747.i	0.507302	+	0.292891i
$966$		0			0
$967$	−24500.4	−	42436.0i	−0.0262012	−	0.0453817i	0.852628	−	0.522519i	$-0.175008\pi$
$967$	−24500.4	−	42436.0i	−0.0262012	−	0.0453817i	−0.878829	+	0.477137i	$0.841674\pi$
$968$		0			0
$969$	140813.	+	910522.i	0.149967	+	0.969713i
$970$		0			0
$971$			1.83854e6i			1.95000i	0.222198	+	0.975001i	$0.428677\pi$
$971$			1.83854e6i			1.95000i	−0.222198	+	0.975001i	$0.571323\pi$
$972$		0			0
$973$	−162733.			−0.171890
$974$		0			0
$975$	646087.	−	99917.7i	0.679644	−	0.105107i
$976$		0			0
$977$	−549300.	+	317138.i	−0.575467	+	0.332246i	−0.759330	−	0.650706i	$-0.774473\pi$
$977$	−549300.	+	317138.i	−0.575467	+	0.332246i	0.183863	+	0.982952i	$0.441140\pi$
$978$		0			0
$979$	543513.	−	941393.i	0.567081	−	0.982213i
$980$		0			0
$981$	554901.	−	175837.i	0.576604	−	0.182714i
$982$		0			0
$983$	791690.	+	457082.i	0.819310	+	0.473029i	0.850178	−	0.526495i	$-0.176494\pi$
$983$	791690.	+	457082.i	0.819310	+	0.473029i	−0.0308686	+	0.999523i	$0.509827\pi$
$984$		0			0
$985$	1.07461e6	+	1.86128e6i	1.10759	+	1.91840i
$986$		0			0
$987$	1.31478e6	−	1.05678e6i	1.34965	−	1.08480i
$988$		0			0
$989$		−	369402.i		−	0.377665i
$990$		0			0
$991$	119.608			0.000121790			6.08950e−5	−	1.00000i	$-0.499981\pi$
$991$	119.608			0.000121790			6.08950e−5		1.00000i	$0.499981\pi$
$992$		0			0
$993$	413244.	−	1.06492e6i	0.419090	−	1.07999i
$994$		0			0
$995$	740117.	−	427306.i	0.747574	−	0.431612i
$996$		0			0
$997$	−569592.	+	986562.i	−0.573025	+	0.992508i	0.423228	+	0.906023i	$0.360897\pi$
$997$	−569592.	+	986562.i	−0.573025	+	0.992508i	−0.996253	+	0.0864852i	$0.972436\pi$
$998$		0			0
$999$	1.13450e6	−	562518.i	1.13677	−	0.563645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.q.c.65.4		8
3.2	odd	2		432.5.q.c.305.1		8
4.3	odd	2		36.5.g.a.29.1	yes	8
9.2	odd	6		1296.5.e.g.161.2		8
9.4	even	3		432.5.q.c.17.1		8
9.5	odd	6	inner	144.5.q.c.113.4		8
9.7	even	3		1296.5.e.g.161.7		8
12.11	even	2		108.5.g.a.89.1		8
36.7	odd	6		324.5.c.a.161.7		8
36.11	even	6		324.5.c.a.161.2		8
36.23	even	6		36.5.g.a.5.1	✓	8
36.31	odd	6		108.5.g.a.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.1	✓	8	36.23	even	6
36.5.g.a.29.1	yes	8	4.3	odd	2
108.5.g.a.17.1		8	36.31	odd	6
108.5.g.a.89.1		8	12.11	even	2
144.5.q.c.65.4		8	1.1	even	1	trivial
144.5.q.c.113.4		8	9.5	odd	6	inner
324.5.c.a.161.2		8	36.11	even	6
324.5.c.a.161.7		8	36.7	odd	6
432.5.q.c.17.1		8	9.4	even	3
432.5.q.c.305.1		8	3.2	odd	2
1296.5.e.g.161.2		8	9.2	odd	6
1296.5.e.g.161.7		8	9.7	even	3

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.89427 - 1.37550i) q^{3} +(27.4152 - 15.8282i) q^{5} +(-37.6830 + 65.2688i) q^{7} +(77.2160 - 24.4682i) q^{9} +O(q^{10})\)	\(q+(8.89427 - 1.37550i) q^{3} +(27.4152 - 15.8282i) q^{5} +(-37.6830 + 65.2688i) q^{7} +(77.2160 - 24.4682i) q^{9} +(123.267 + 71.1682i) q^{11} +(96.3079 + 166.810i) q^{13} +(222.067 - 178.490i) q^{15} -325.855i q^{17} -314.164 q^{19} +(-245.385 + 632.352i) q^{21} +(443.852 - 256.258i) q^{23} +(188.564 - 326.602i) q^{25} +(653.124 - 323.837i) q^{27} +(-136.614 - 78.8739i) q^{29} +(-183.725 - 318.221i) q^{31} +(1194.26 + 463.435i) q^{33} +2385.82i q^{35} +1737.04 q^{37} +(1086.04 + 1351.18i) q^{39} +(-342.317 + 197.637i) q^{41} +(360.381 - 624.198i) q^{43} +(1729.61 - 1892.99i) q^{45} +(-2153.71 - 1243.45i) q^{47} +(-1639.52 - 2839.72i) q^{49} +(-448.215 - 2898.24i) q^{51} +3986.04i q^{53} +4505.86 q^{55} +(-2794.26 + 432.133i) q^{57} +(2136.75 - 1233.65i) q^{59} +(-1240.49 + 2148.59i) q^{61} +(-1312.72 + 5961.83i) q^{63} +(5280.61 + 3048.76i) q^{65} +(-3298.19 - 5712.64i) q^{67} +(3595.26 - 2889.75i) q^{69} +5828.07i q^{71} -8790.44 q^{73} +(1227.90 - 3164.26i) q^{75} +(-9290.13 + 5363.66i) q^{77} +(-1934.52 + 3350.69i) q^{79} +(5363.62 - 3778.67i) q^{81} +(-10422.5 - 6017.43i) q^{83} +(-5157.70 - 8933.39i) q^{85} +(-1323.57 - 513.613i) q^{87} -7637.03i q^{89} -14516.7 q^{91} +(-2071.81 - 2577.63i) q^{93} +(-8612.88 + 4972.65i) q^{95} +(1455.75 - 2521.44i) q^{97} +(11259.5 + 2479.20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9}+O(q^{10}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9	\( 8 q + 9 q^{3} - 9 q^{5} - 13 q^{7} + 21 q^{9} + 18 q^{11} - 5 q^{13} - 225 q^{15} - 562 q^{19} - 1167 q^{21} + 1719 q^{23} + 353 q^{25} - 648 q^{27} + 2115 q^{29} - 187 q^{31} + 3258 q^{33} + 16 q^{37} + 8265 q^{39} - 7920 q^{41} + 68 q^{43} + 5679 q^{45} - 13689 q^{47} - 327 q^{49} - 10449 q^{51} + 1818 q^{55} - 21861 q^{57} + 20052 q^{59} - 1937 q^{61} - 5559 q^{63} + 25965 q^{65} - 154 q^{67} + 21645 q^{69} - 7802 q^{73} + 30297 q^{75} - 25641 q^{77} + 2195 q^{79} + 19701 q^{81} - 37017 q^{83} - 3042 q^{85} - 22455 q^{87} - 15830 q^{91} - 36489 q^{93} + 37116 q^{95} + 7282 q^{97} + 10035 q^{99}+O(q^{100}) \) 8 * q + 9 * q^3 - 9 * q^5 - 13 * q^7 + 21 * q^9 + 18 * q^11 - 5 * q^13 - 225 * q^15 - 562 * q^19 - 1167 * q^21 + 1719 * q^23 + 353 * q^25 - 648 * q^27 + 2115 * q^29 - 187 * q^31 + 3258 * q^33 + 16 * q^37 + 8265 * q^39 - 7920 * q^41 + 68 * q^43 + 5679 * q^45 - 13689 * q^47 - 327 * q^49 - 10449 * q^51 + 1818 * q^55 - 21861 * q^57 + 20052 * q^59 - 1937 * q^61 - 5559 * q^63 + 25965 * q^65 - 154 * q^67 + 21645 * q^69 - 7802 * q^73 + 30297 * q^75 - 25641 * q^77 + 2195 * q^79 + 19701 * q^81 - 37017 * q^83 - 3042 * q^85 - 22455 * q^87 - 15830 * q^91 - 36489 * q^93 + 37116 * q^95 + 7282 * q^97 + 10035 * q^99

Introduction

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