LMFDB - Embedded newform 324.5.d.e.163.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.9
Character	$\chi$	$=$	324.163
Dual form			324.5.d.e.163.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +O(q^{10})$	\(q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +(14.8544 + 41.5509i) q^{10} -219.387i q^{11} -37.0701 q^{13} +(44.8790 - 16.0441i) q^{14} +(50.2175 - 251.026i) q^{16} -284.021 q^{17} -45.4901i q^{19} +(136.502 - 111.899i) q^{20} +(-826.332 + 295.412i) q^{22} +201.286i q^{23} -503.304 q^{25} +(49.9160 + 139.626i) q^{26} +(-120.862 - 147.435i) q^{28} +1228.31 q^{29} +1514.77i q^{31} +(-1013.12 + 148.868i) q^{32} +(382.443 + 1069.78i) q^{34} -131.443i q^{35} -1521.29 q^{37} +(-171.340 + 61.2538i) q^{38} +(-605.277 - 363.464i) q^{40} +2633.95 q^{41} -39.9593i q^{43} +(2225.36 + 2714.63i) q^{44} +(758.153 - 271.038i) q^{46} +2884.86i q^{47} +2259.03 q^{49} +(677.714 + 1895.72i) q^{50} +(458.694 - 376.021i) q^{52} -1415.13 q^{53} +2420.19i q^{55} +(-392.576 + 653.757i) q^{56} +(-1653.95 - 4626.47i) q^{58} +2832.86i q^{59} -5257.27 q^{61} +(5705.44 - 2039.68i) q^{62} +(1924.92 + 3615.51i) q^{64} +408.941 q^{65} -930.592i q^{67} +(3514.39 - 2880.97i) q^{68} +(-495.087 + 176.992i) q^{70} +1162.75i q^{71} -2162.87 q^{73} +(2048.47 + 5730.02i) q^{74} +(461.430 + 562.881i) q^{76} +2614.04 q^{77} +7485.40i q^{79} +(-553.978 + 2769.22i) q^{80} +(-3546.69 - 9920.88i) q^{82} +1116.31i q^{83} +3133.20 q^{85} +(-150.508 + 53.8064i) q^{86} +(7228.27 - 12037.3i) q^{88} +6739.71 q^{89} -441.696i q^{91} +(-2041.75 - 2490.66i) q^{92} +(10865.9 - 3884.55i) q^{94} +501.828i q^{95} +12046.6 q^{97} +(-3041.85 - 8508.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8} + 14 q^{10} + 2 q^{13} + 252 q^{14} + q^{16} + 28 q^{17} - 140 q^{20} + 33 q^{22} + 1752 q^{25} - 548 q^{26} - 258 q^{28} + 526 q^{29} - 121 q^{32} - 385 q^{34} - 4 q^{37} + 1395 q^{38} + 2276 q^{40} - 2762 q^{41} - 3357 q^{44} + 1788 q^{46} - 3428 q^{49} + 6375 q^{50} - 1438 q^{52} + 5044 q^{53} - 7506 q^{56} + 4064 q^{58} + 2 q^{61} + 9162 q^{62} + 4513 q^{64} - 2014 q^{65} - 11405 q^{68} - 3666 q^{70} - 1708 q^{73} + 14620 q^{74} - 1581 q^{76} - 3942 q^{77} - 22760 q^{80} - 4243 q^{82} + 1252 q^{85} + 22113 q^{86} - 1995 q^{88} - 6524 q^{89} - 30294 q^{92} - 7524 q^{94} - 5638 q^{97} + 46469 q^{98}+O(q^{100}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8 + 14 * q^10 + 2 * q^13 + 252 * q^14 + q^16 + 28 * q^17 - 140 * q^20 + 33 * q^22 + 1752 * q^25 - 548 * q^26 - 258 * q^28 + 526 * q^29 - 121 * q^32 - 385 * q^34 - 4 * q^37 + 1395 * q^38 + 2276 * q^40 - 2762 * q^41 - 3357 * q^44 + 1788 * q^46 - 3428 * q^49 + 6375 * q^50 - 1438 * q^52 + 5044 * q^53 - 7506 * q^56 + 4064 * q^58 + 2 * q^61 + 9162 * q^62 + 4513 * q^64 - 2014 * q^65 - 11405 * q^68 - 3666 * q^70 - 1708 * q^73 + 14620 * q^74 - 1581 * q^76 - 3942 * q^77 - 22760 * q^80 - 4243 * q^82 + 1252 * q^85 + 22113 * q^86 - 1995 * q^88 - 6524 * q^89 - 30294 * q^92 - 7524 * q^94 - 5638 * q^97 + 46469 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34653	−	3.76654i	−0.336633	−	0.941636i
$2$	−1.34653	−	3.76654i	−0.336633	−	0.941636i
$3$		0			0
$3$		0			0
$4$	−12.3737	+	10.1435i	−0.773357	+	0.633971i
$5$	−11.0316			−0.441263			−0.220632	−	0.975357i	$-0.570812\pi$
$5$	−11.0316			−0.441263			−0.220632	+	0.975357i	$0.570812\pi$
$6$		0			0
$7$			11.9152i			0.243167i	0.992581	+	0.121583i	$0.0387972\pi$
$7$			11.9152i			0.243167i	−0.992581	+	0.121583i	$0.961203\pi$
$8$	54.8676	+	32.9476i	0.857307	+	0.514806i
$9$		0			0
$10$	14.8544	+	41.5509i	0.148544	+	0.415509i
$11$		−	219.387i		−	1.81312i	−0.422080	−	0.906559i	$-0.638700\pi$
$11$		−	219.387i		−	1.81312i	0.422080	−	0.906559i	$-0.361300\pi$
$12$		0			0
$13$	−37.0701			−0.219349			−0.109675	−	0.993968i	$-0.534981\pi$
$13$	−37.0701			−0.219349			−0.109675	+	0.993968i	$0.534981\pi$
$14$	44.8790	−	16.0441i	0.228975	−	0.0818579i
$15$		0			0
$16$	50.2175	−	251.026i	0.196162	−	0.980571i
$17$	−284.021			−0.982771			−0.491386	−	0.870942i	$-0.663509\pi$
$17$	−284.021			−0.982771			−0.491386	+	0.870942i	$0.663509\pi$
$18$		0			0
$19$		−	45.4901i		−	0.126011i	−0.998013	−	0.0630057i	$-0.979931\pi$
$19$		−	45.4901i		−	0.126011i	0.998013	−	0.0630057i	$-0.0200686\pi$
$20$	136.502	−	111.899i	0.341254	−	0.279748i
$21$		0			0
$22$	−826.332	+	295.412i	−1.70730	+	0.610354i
$23$			201.286i			0.380503i	0.981735	+	0.190252i	$0.0609304\pi$
$23$			201.286i			0.380503i	−0.981735	+	0.190252i	$0.939070\pi$
$24$		0			0
$25$	−503.304			−0.805287
$26$	49.9160	+	139.626i	0.0738402	+	0.206547i
$27$		0			0
$28$	−120.862	−	147.435i	−0.154161	−	0.188055i
$29$	1228.31			1.46053			0.730265	−	0.683164i	$-0.239397\pi$
$29$	1228.31			1.46053			0.730265	+	0.683164i	$0.239397\pi$
$30$		0			0
$31$			1514.77i			1.57624i	0.615520	+	0.788121i	$0.288946\pi$
$31$			1514.77i			1.57624i	−0.615520	+	0.788121i	$0.711054\pi$
$32$	−1013.12	+	148.868i	−0.989376	+	0.145379i
$33$		0			0
$34$	382.443	+	1069.78i	0.330833	+	0.925413i
$35$		−	131.443i		−	0.107301i
$36$		0			0
$37$	−1521.29			−1.11124			−0.555622	−	0.831435i	$-0.687520\pi$
$37$	−1521.29			−1.11124			−0.555622	+	0.831435i	$0.687520\pi$
$38$	−171.340	+	61.2538i	−0.118657	+	0.0424195i
$39$		0			0
$40$	−605.277	−	363.464i	−0.378298	−	0.227165i
$41$	2633.95			1.56689			0.783447	−	0.621459i	$-0.213460\pi$
$41$	2633.95			1.56689			0.783447	+	0.621459i	$0.213460\pi$
$42$		0			0
$43$		−	39.9593i		−	0.0216113i	−0.999942	−	0.0108056i	$-0.996560\pi$
$43$		−	39.9593i		−	0.0216113i	0.999942	−	0.0108056i	$-0.00343961\pi$
$44$	2225.36	+	2714.63i	1.14946	+	1.40219i
$45$		0			0
$46$	758.153	−	271.038i	0.358295	−	0.128090i
$47$			2884.86i			1.30596i	0.757377	+	0.652978i	$0.226481\pi$
$47$			2884.86i			1.30596i	−0.757377	+	0.652978i	$0.773519\pi$
$48$		0			0
$49$	2259.03			0.940870
$50$	677.714	+	1895.72i	0.271086	+	0.758287i
$51$		0			0
$52$	458.694	−	376.021i	0.169635	−	0.139061i
$53$	−1415.13			−0.503783			−0.251892	−	0.967755i	$-0.581053\pi$
$53$	−1415.13			−0.503783			−0.251892	+	0.967755i	$0.581053\pi$
$54$		0			0
$55$			2420.19i			0.800062i
$56$	−392.576	+	653.757i	−0.125184	+	0.208469i
$57$		0			0
$58$	−1653.95	−	4626.47i	−0.491662	−	1.37529i
$59$			2832.86i			0.813808i	0.913471	+	0.406904i	$0.133392\pi$
$59$			2832.86i			0.813808i	−0.913471	+	0.406904i	$0.866608\pi$
$60$		0			0
$61$	−5257.27			−1.41287			−0.706433	−	0.707780i	$-0.749697\pi$
$61$	−5257.27			−1.41287			−0.706433	+	0.707780i	$0.749697\pi$
$62$	5705.44	−	2039.68i	1.48425	−	0.530614i
$63$		0			0
$64$	1924.92	+	3615.51i	0.469950	+	0.882693i
$65$	408.941			0.0967909
$66$		0			0
$67$		−	930.592i		−	0.207305i	−0.994614	−	0.103653i	$-0.966947\pi$
$67$		−	930.592i		−	0.207305i	0.994614	−	0.103653i	$-0.0330530\pi$
$68$	3514.39	−	2880.97i	0.760033	−	0.623048i
$69$		0			0
$70$	−495.087	+	176.992i	−0.101038	+	0.0361209i
$71$			1162.75i			0.230659i	0.993327	+	0.115329i	$0.0367923\pi$
$71$			1162.75i			0.230659i	−0.993327	+	0.115329i	$0.963208\pi$
$72$		0			0
$73$	−2162.87			−0.405867			−0.202934	−	0.979192i	$-0.565048\pi$
$73$	−2162.87			−0.405867			−0.202934	+	0.979192i	$0.565048\pi$
$74$	2048.47	+	5730.02i	0.374081	+	1.04639i
$75$		0			0
$76$	461.430	+	562.881i	0.0798875	+	0.0974518i
$77$	2614.04			0.440890
$78$		0			0
$79$			7485.40i			1.19939i	0.800229	+	0.599695i	$0.204711\pi$
$79$			7485.40i			1.19939i	−0.800229	+	0.599695i	$0.795289\pi$
$80$	−553.978	+	2769.22i	−0.0865591	+	0.432690i
$81$		0			0
$82$	−3546.69	−	9920.88i	−0.527467	−	1.47544i
$83$			1116.31i			0.162043i	0.996712	+	0.0810215i	$0.0258182\pi$
$83$			1116.31i			0.162043i	−0.996712	+	0.0810215i	$0.974182\pi$
$84$		0			0
$85$	3133.20			0.433661
$86$	−150.508	+	53.8064i	−0.0203500	+	0.00727506i
$87$		0			0
$88$	7228.27	−	12037.3i	0.933403	−	1.55440i
$89$	6739.71			0.850866			0.425433	−	0.904990i	$-0.360122\pi$
$89$	6739.71			0.850866			0.425433	+	0.904990i	$0.360122\pi$
$90$		0			0
$91$		−	441.696i		−	0.0533385i
$92$	−2041.75	−	2490.66i	−0.241228	−	0.294265i
$93$		0			0
$94$	10865.9	−	3884.55i	1.22974	−	0.439627i
$95$			501.828i			0.0556042i
$96$		0			0
$97$	12046.6			1.28032			0.640161	−	0.768240i	$-0.278867\pi$
$97$	12046.6			1.28032			0.640161	+	0.768240i	$0.278867\pi$
$98$	−3041.85	−	8508.73i	−0.316727	−	0.885957i
$99$		0			0
$100$	6227.74	−	5105.28i	0.622774	−	0.510528i
$101$	9555.20			0.936692			0.468346	−	0.883545i	$-0.344850\pi$
$101$	9555.20			0.936692			0.468346	+	0.883545i	$0.344850\pi$
$102$		0			0
$103$			11503.4i			1.08431i	0.840279	+	0.542154i	$0.182391\pi$
$103$			11503.4i			1.08431i	−0.840279	+	0.542154i	$0.817609\pi$
$104$	−2033.95	−	1221.37i	−0.188050	−	0.112922i
$105$		0			0
$106$	1905.51	+	5330.14i	0.169590	+	0.474380i
$107$			6602.72i			0.576707i	0.957524	+	0.288353i	$0.0931078\pi$
$107$			6602.72i			0.576707i	−0.957524	+	0.288353i	$0.906892\pi$
$108$		0			0
$109$	12045.3			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$109$	12045.3			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$110$	9115.74	−	3258.86i	0.753367	−	0.269327i
$111$		0			0
$112$	2991.02	+	598.350i	0.238442	+	0.0477001i
$113$	−3730.69			−0.292168			−0.146084	−	0.989272i	$-0.546667\pi$
$113$	−3730.69			−0.292168			−0.146084	+	0.989272i	$0.546667\pi$
$114$		0			0
$115$		−	2220.50i		−	0.167902i
$116$	−15198.7	+	12459.4i	−1.12951	+	0.925933i
$117$		0			0
$118$	10670.1	−	3814.54i	0.766311	−	0.273954i
$119$		−	3384.16i		−	0.238977i
$120$		0			0
$121$	−33489.7			−2.28739
$122$	7079.08	+	19801.7i	0.475617	+	1.33041i
$123$		0			0
$124$	−15365.1	−	18743.3i	−0.999291	−	1.21900i
$125$	12447.0			0.796607
$126$		0			0
$127$			26549.7i			1.64608i	0.567980	+	0.823042i	$0.307725\pi$
$127$			26549.7i			1.64608i	−0.567980	+	0.823042i	$0.692275\pi$
$128$	11026.0	−	12118.7i	0.672975	−	0.739665i
$129$		0			0
$130$	−550.652	−	1540.30i	−0.0325830	−	0.0911418i
$131$		−	1319.64i		−	0.0768978i	−0.999261	−	0.0384489i	$-0.987758\pi$
$131$		−	1319.64i		−	0.0768978i	0.999261	−	0.0384489i	$-0.0122417\pi$
$132$		0			0
$133$	542.022			0.0306418
$134$	−3505.12	+	1253.07i	−0.195206	+	0.0697856i
$135$		0			0
$136$	−15583.6	−	9357.79i	−0.842537	−	0.505936i
$137$	−25812.9			−1.37530			−0.687648	−	0.726044i	$-0.741357\pi$
$137$	−25812.9			−1.37530			−0.687648	+	0.726044i	$0.741357\pi$
$138$		0			0
$139$			13138.0i			0.679985i	0.940428	+	0.339993i	$0.110425\pi$
$139$			13138.0i			0.679985i	−0.940428	+	0.339993i	$0.889575\pi$
$140$	1333.30	+	1626.44i	0.0680254	+	0.0829816i
$141$		0			0
$142$	4379.55	−	1565.68i	0.217197	−	0.0776472i
$143$			8132.70i			0.397706i
$144$		0			0
$145$	−13550.2			−0.644478
$146$	2912.37	+	8146.54i	0.136628	+	0.382179i
$147$		0			0
$148$	18824.0	−	15431.3i	0.859388	−	0.704496i
$149$	−25936.4			−1.16826			−0.584128	−	0.811662i	$-0.698563\pi$
$149$	−25936.4			−1.16826			−0.584128	+	0.811662i	$0.698563\pi$
$150$		0			0
$151$			28395.5i			1.24536i	0.782475	+	0.622681i	$0.213957\pi$
$151$			28395.5i			1.24536i	−0.782475	+	0.622681i	$0.786043\pi$
$152$	1498.79	−	2495.93i	0.0648714	−	0.108030i
$153$		0			0
$154$	−3519.88	−	9845.88i	−0.148418	−	0.415158i
$155$		−	16710.3i		−	0.695538i
$156$		0			0
$157$	−5520.37			−0.223959			−0.111980	−	0.993711i	$-0.535719\pi$
$157$	−5520.37			−0.223959			−0.111980	+	0.993711i	$0.535719\pi$
$158$	28194.1	−	10079.3i	1.12939	−	0.403754i
$159$		0			0
$160$	11176.3	−	1642.25i	0.436575	−	0.0641504i
$161$	−2398.36			−0.0925257
$162$		0			0
$163$		−	407.281i		−	0.0153292i	−0.999971	−	0.00766459i	$-0.997560\pi$
$163$		−	407.281i		−	0.0153292i	0.999971	−	0.00766459i	$-0.00243974\pi$
$164$	−32591.7	+	26717.5i	−1.21177	+	0.993365i
$165$		0			0
$166$	4204.65	−	1503.15i	0.152586	−	0.0545490i
$167$		−	23742.9i		−	0.851334i	−0.904880	−	0.425667i	$-0.860040\pi$
$167$		−	23742.9i		−	0.851334i	0.904880	−	0.425667i	$-0.139960\pi$
$168$		0			0
$169$	−27186.8			−0.951886
$170$	−4218.95	−	11801.3i	−0.145984	−	0.408351i
$171$		0			0
$172$	405.328	+	494.444i	0.0137009	+	0.0167132i
$173$	2826.49			0.0944400			0.0472200	−	0.998885i	$-0.484964\pi$
$173$	2826.49			0.0944400			0.0472200	+	0.998885i	$0.484964\pi$
$174$		0			0
$175$		−	5996.96i		−	0.195819i
$176$	−55072.0	−	11017.1i	−1.77789	−	0.355665i
$177$		0			0
$178$	−9075.23	−	25385.4i	−0.286429	−	0.801206i
$179$		−	45743.4i		−	1.42765i	−0.700323	−	0.713826i	$-0.746961\pi$
$179$		−	45743.4i		−	1.42765i	0.700323	−	0.713826i	$-0.253039\pi$
$180$		0			0
$181$	−24226.2			−0.739483			−0.369742	−	0.929135i	$-0.620554\pi$
$181$	−24226.2			−0.739483			−0.369742	+	0.929135i	$0.620554\pi$
$182$	−1663.67	+	594.757i	−0.0502255	+	0.0179555i
$183$		0			0
$184$	−6631.89	+	11044.1i	−0.195885	+	0.326208i
$185$	16782.3			0.490351
$186$		0			0
$187$			62310.5i			1.78188i
$188$	−29262.6	−	35696.4i	−0.827938	−	1.00997i
$189$		0			0
$190$	1890.16	−	675.726i	0.0523589	−	0.0187182i
$191$			22522.0i			0.617362i	0.951166	+	0.308681i	$0.0998875\pi$
$191$			22522.0i			0.617362i	−0.951166	+	0.308681i	$0.900112\pi$
$192$		0			0
$193$	18288.7			0.490985			0.245493	−	0.969398i	$-0.421050\pi$
$193$	18288.7			0.490985			0.245493	+	0.969398i	$0.421050\pi$
$194$	−16221.1	−	45373.9i	−0.430998	−	1.20560i
$195$		0			0
$196$	−27952.6	+	22914.5i	−0.727628	+	0.596484i
$197$	−36300.2			−0.935356			−0.467678	−	0.883899i	$-0.654909\pi$
$197$	−36300.2			−0.935356			−0.467678	+	0.883899i	$0.654909\pi$
$198$		0			0
$199$			47336.5i			1.19533i	0.801744	+	0.597667i	$0.203906\pi$
$199$			47336.5i			1.19533i	−0.801744	+	0.597667i	$0.796094\pi$
$200$	−27615.1	−	16582.6i	−0.690378	−	0.414566i
$201$		0			0
$202$	−12866.4	−	35990.1i	−0.315321	−	0.882023i
$203$			14635.5i			0.355152i
$204$		0			0
$205$	−29056.6			−0.691412
$206$	43328.2	−	15489.7i	1.02102	−	0.365014i
$207$		0			0
$208$	−1861.57	+	9305.56i	−0.0430280	+	0.215088i
$209$	−9979.95			−0.228473
$210$		0			0
$211$			46490.2i			1.04423i	0.852875	+	0.522115i	$0.174857\pi$
$211$			46490.2i			1.04423i	−0.852875	+	0.522115i	$0.825143\pi$
$212$	17510.4	−	14354.4i	0.389604	−	0.319384i
$213$		0			0
$214$	24869.4	−	8890.76i	0.543048	−	0.194138i
$215$			440.814i			0.00953626i
$216$		0			0
$217$	−18048.7			−0.383290
$218$	−16219.3	−	45369.1i	−0.341287	−	0.954656i
$219$		0			0
$220$	−24549.3	−	29946.7i	−0.507216	−	0.618734i
$221$	10528.7			0.215570
$222$		0			0
$223$		−	82597.9i		−	1.66096i	−0.557048	−	0.830480i	$-0.688066\pi$
$223$		−	82597.9i		−	1.66096i	0.557048	−	0.830480i	$-0.311934\pi$
$224$	−1773.79	−	12071.5i	−0.0353514	−	0.240583i
$225$		0			0
$226$	5023.49	+	14051.8i	0.0983533	+	0.275116i
$227$		−	29701.6i		−	0.576405i	−0.957569	−	0.288203i	$-0.906942\pi$
$227$		−	29701.6i		−	0.576405i	0.957569	−	0.288203i	$-0.0930577\pi$
$228$		0			0
$229$	45335.9			0.864512			0.432256	−	0.901751i	$-0.357718\pi$
$229$	45335.9			0.864512			0.432256	+	0.901751i	$0.357718\pi$
$230$	−8363.63	+	2989.98i	−0.158103	+	0.0565213i
$231$		0			0
$232$	67394.2	+	40469.7i	1.25212	+	0.751889i
$233$	−50931.3			−0.938151			−0.469075	−	0.883158i	$-0.655413\pi$
$233$	−50931.3			−0.938151			−0.469075	+	0.883158i	$0.655413\pi$
$234$		0			0
$235$		−	31824.5i		−	0.576270i
$236$	−28735.3	−	35053.1i	−0.515930	−	0.629364i
$237$		0			0
$238$	−12746.6	+	4556.87i	−0.225030	+	0.0804475i
$239$		−	36888.3i		−	0.645792i	−0.946434	−	0.322896i	$-0.895344\pi$
$239$		−	36888.3i		−	0.645792i	0.946434	−	0.322896i	$-0.104656\pi$
$240$		0			0
$241$	8387.27			0.144407			0.0722033	−	0.997390i	$-0.476997\pi$
$241$	8387.27			0.144407			0.0722033	+	0.997390i	$0.476997\pi$
$242$	45094.9	+	126141.i	0.770011	+	2.15389i
$243$		0			0
$244$	65052.0	−	53327.3i	1.09265	−	0.895715i
$245$	−24920.7			−0.415171
$246$		0			0
$247$			1686.32i			0.0276405i
$248$	−49907.9	+	83111.8i	−0.811458	+	1.35132i
$249$		0			0
$250$	−16760.2	−	46882.1i	−0.268164	−	0.750114i
$251$		−	1475.47i		−	0.0234198i	−0.999931	−	0.0117099i	$-0.996273\pi$
$251$		−	1475.47i		−	0.0234198i	0.999931	−	0.0117099i	$-0.00372746\pi$
$252$		0			0
$253$	44159.6			0.689897
$254$	100001.	−	35750.0i	1.55001	−	0.554126i
$255$		0			0
$256$	−60492.4	−	25211.8i	−0.923041	−	0.384702i
$257$	−34673.1			−0.524960			−0.262480	−	0.964937i	$-0.584540\pi$
$257$	−34673.1			−0.524960			−0.262480	+	0.964937i	$0.584540\pi$
$258$		0			0
$259$		−	18126.5i		−	0.270218i
$260$	−5060.12	+	4148.11i	−0.0748539	+	0.0613626i
$261$		0			0
$262$	−4970.49	+	1776.94i	−0.0724097	+	0.0258863i
$263$			19032.4i			0.275158i	0.990491	+	0.137579i	$0.0439321\pi$
$263$			19032.4i			0.275158i	−0.990491	+	0.137579i	$0.956068\pi$
$264$		0			0
$265$	15611.1			0.222301
$266$	−729.850	−	2041.55i	−0.0103150	−	0.0288534i
$267$		0			0
$268$	9439.50	+	11514.9i	0.131425	+	0.160321i
$269$	−58724.1			−0.811544			−0.405772	−	0.913974i	$-0.632997\pi$
$269$	−58724.1			−0.811544			−0.405772	+	0.913974i	$0.632997\pi$
$270$		0			0
$271$		−	31474.1i		−	0.428563i	−0.976772	−	0.214281i	$-0.931259\pi$
$271$		−	31474.1i		−	0.428563i	0.976772	−	0.214281i	$-0.0687409\pi$
$272$	−14262.8	+	71296.7i	−0.192782	+	0.963677i
$273$		0			0
$274$	34757.9	+	97225.5i	0.462969	+	1.29503i
$275$			110418.i			1.46008i
$276$		0			0
$277$	66531.5			0.867098			0.433549	−	0.901130i	$-0.357261\pi$
$277$	66531.5			0.867098			0.433549	+	0.901130i	$0.357261\pi$
$278$	49484.8	−	17690.7i	0.640299	−	0.228905i
$279$		0			0
$280$	4330.73	−	7211.98i	0.0552389	−	0.0919895i
$281$	123720.			1.56685			0.783424	−	0.621488i	$-0.213471\pi$
$281$	123720.			1.56685			0.783424	+	0.621488i	$0.213471\pi$
$282$		0			0
$283$			54735.0i			0.683427i	0.939804	+	0.341713i	$0.111007\pi$
$283$			54735.0i			0.683427i	−0.939804	+	0.341713i	$0.888993\pi$
$284$	−11794.4	−	14387.5i	−0.146231	−	0.178382i
$285$		0			0
$286$	30632.2	−	10950.9i	0.374495	−	0.133881i
$287$			31383.9i			0.381016i
$288$		0			0
$289$	−2853.15			−0.0341609
$290$	18245.7	+	51037.2i	0.216952	+	0.606864i
$291$		0			0
$292$	26762.7	−	21939.1i	0.313880	−	0.257308i
$293$	88617.9			1.03225			0.516127	−	0.856512i	$-0.327373\pi$
$293$	88617.9			1.03225			0.516127	+	0.856512i	$0.327373\pi$
$294$		0			0
$295$		−	31251.0i		−	0.359103i
$296$	−83469.8	−	50122.9i	−0.952677	−	0.572075i
$297$		0			0
$298$	34924.2	+	97690.7i	0.393273	+	1.10007i
$299$		−	7461.69i		−	0.0834632i
$300$		0			0
$301$	476.121			0.00525514
$302$	106953.	−	38235.4i	1.17268	−	0.419230i
$303$		0			0
$304$	−11419.2	−	2284.40i	−0.123563	−	0.0247186i
$305$	57996.0			0.623446
$306$		0			0
$307$		−	123447.i		−	1.30980i	−0.755716	−	0.654900i	$-0.772711\pi$
$307$		−	123447.i		−	1.30980i	0.755716	−	0.654900i	$-0.227289\pi$
$308$	−32345.3	+	26515.6i	−0.340965	+	0.279511i
$309$		0			0
$310$	−62940.1	+	22500.9i	−0.654943	+	0.234141i
$311$		−	60543.1i		−	0.625956i	−0.949760	−	0.312978i	$-0.898673\pi$
$311$		−	60543.1i		−	0.625956i	0.949760	−	0.312978i	$-0.101327\pi$
$312$		0			0
$313$	−52386.2			−0.534722			−0.267361	−	0.963596i	$-0.586152\pi$
$313$	−52386.2			−0.534722			−0.267361	+	0.963596i	$0.586152\pi$
$314$	7433.35	+	20792.7i	0.0753920	+	0.210888i
$315$		0			0
$316$	−75928.4	−	92622.1i	−0.760378	−	0.927557i
$317$	25997.4			0.258708			0.129354	−	0.991598i	$-0.458710\pi$
$317$	25997.4			0.258708			0.129354	+	0.991598i	$0.458710\pi$
$318$		0			0
$319$		−	269474.i		−	2.64811i
$320$	−21234.9	−	39884.8i	−0.207372	−	0.389500i
$321$		0			0
$322$	3229.46	+	9033.52i	0.0311472	+	0.0871255i
$323$			12920.1i			0.123840i
$324$		0			0
$325$	18657.5			0.176639
$326$	−1534.04	+	548.416i	−0.0144345	+	0.00516030i
$327$		0			0
$328$	144518.	+	86782.1i	1.34331	+	0.806645i
$329$	−34373.6			−0.317565
$330$		0			0
$331$			43231.1i			0.394584i	0.980345	+	0.197292i	$0.0632148\pi$
$331$			43231.1i			0.394584i	−0.980345	+	0.197292i	$0.936785\pi$
$332$	−11323.4	−	13812.9i	−0.102731	−	0.125317i
$333$		0			0
$334$	−89428.5	+	31970.5i	−0.801647	+	0.286587i
$335$			10265.9i			0.0914761i
$336$		0			0
$337$	11852.8			0.104366			0.0521831	−	0.998638i	$-0.483382\pi$
$337$	11852.8			0.104366			0.0521831	+	0.998638i	$0.483382\pi$
$338$	36607.9	+	102400.i	0.320436	+	0.896330i
$339$		0			0
$340$	−38769.3	+	31781.7i	−0.335375	+	0.274928i
$341$	332321.			2.85791
$342$		0			0
$343$			55525.0i			0.471955i
$344$	1316.56	−	2192.47i	0.0111256	−	0.0185275i
$345$		0			0
$346$	−3805.96	−	10646.1i	−0.0317916	−	0.0889281i
$347$			29124.4i			0.241879i	0.992660	+	0.120940i	$0.0385907\pi$
$347$			29124.4i			0.241879i	−0.992660	+	0.120940i	$0.961409\pi$
$348$		0			0
$349$	119977.			0.985023			0.492512	−	0.870306i	$-0.336079\pi$
$349$	119977.			0.985023			0.492512	+	0.870306i	$0.336079\pi$
$350$	−22587.8	+	8075.08i	−0.184390	+	0.0659191i
$351$		0			0
$352$	32659.8	+	222266.i	0.263589	+	1.79385i
$353$	−154758.			−1.24195			−0.620975	−	0.783831i	$-0.713263\pi$
$353$	−154758.			−1.24195			−0.620975	+	0.783831i	$0.713263\pi$
$354$		0			0
$355$		−	12827.0i		−	0.101781i
$356$	−83395.3	+	68364.5i	−0.658023	+	0.539424i
$357$		0			0
$358$	−172294.	+	61594.9i	−1.34433	+	0.480594i
$359$			66839.6i			0.518615i	0.965795	+	0.259307i	$0.0834942\pi$
$359$			66839.6i			0.518615i	−0.965795	+	0.259307i	$0.916506\pi$
$360$		0			0
$361$	128252.			0.984121
$362$	32621.3	+	91249.1i	0.248934	+	0.696324i
$363$		0			0
$364$	4480.36	+	5465.42i	0.0338151	+	0.0412497i
$365$	23859.8			0.179094
$366$		0			0
$367$		−	94571.4i		−	0.702147i	−0.936348	−	0.351073i	$-0.885817\pi$
$367$		−	94571.4i		−	0.702147i	0.936348	−	0.351073i	$-0.114183\pi$
$368$	50528.1	+	10108.1i	0.373110	+	0.0746403i
$369$		0			0
$370$	−22597.8	−	63211.2i	−0.165068	−	0.461732i
$371$		−	16861.5i		−	0.122503i
$372$		0			0
$373$	−181061.			−1.30139			−0.650694	−	0.759340i	$-0.725522\pi$
$373$	−181061.			−1.30139			−0.650694	+	0.759340i	$0.725522\pi$
$374$	234695.	−	83903.0i	1.67788	−	0.599839i
$375$		0			0
$376$	−95049.0	+	158285.i	−0.672313	+	1.11960i
$377$	−45533.4			−0.320366
$378$		0			0
$379$			51191.3i			0.356384i	0.983996	+	0.178192i	$0.0570248\pi$
$379$			51191.3i			0.356384i	−0.983996	+	0.178192i	$0.942975\pi$
$380$	−5090.31	−	6209.47i	−0.0352514	−	0.0430019i
$381$		0			0
$382$	84830.0	−	30326.5i	0.581330	−	0.207824i
$383$		−	152568.i		−	1.04008i	−0.854143	−	0.520039i	$-0.825917\pi$
$383$		−	152568.i		−	1.04008i	0.854143	−	0.520039i	$-0.174083\pi$
$384$		0			0
$385$	−28836.9			−0.194548
$386$	−24626.3	−	68885.2i	−0.165282	−	0.462329i
$387$		0			0
$388$	−149061.	+	122195.i	−0.990147	+	0.811687i
$389$	−67896.8			−0.448694			−0.224347	−	0.974509i	$-0.572025\pi$
$389$	−67896.8			−0.448694			−0.224347	+	0.974509i	$0.572025\pi$
$390$		0			0
$391$		−	57169.5i		−	0.373947i
$392$	123948.	+	74429.5i	0.806614	+	0.484365i
$393$		0			0
$394$	48879.4	+	136726.i	0.314871	+	0.880765i
$395$		−	82575.7i		−	0.529247i
$396$		0			0
$397$	−126087.			−0.799998			−0.399999	−	0.916516i	$-0.630990\pi$
$397$	−126087.			−0.799998			−0.399999	+	0.916516i	$0.630990\pi$
$398$	178295.	−	63740.0i	1.12557	−	0.402389i
$399$		0			0
$400$	−25274.7	+	126343.i	−0.157967	+	0.789641i
$401$	−70890.8			−0.440860			−0.220430	−	0.975403i	$-0.570746\pi$
$401$	−70890.8			−0.440860			−0.220430	+	0.975403i	$0.570746\pi$
$402$		0			0
$403$		−	56152.6i		−	0.345748i
$404$	−118233.	+	96923.5i	−0.724398	+	0.593836i
$405$		0			0
$406$	55125.1	−	19707.1i	0.334424	−	0.119556i
$407$			333752.i			2.01482i
$408$		0			0
$409$	43544.2			0.260306			0.130153	−	0.991494i	$-0.458453\pi$
$409$	43544.2			0.260306			0.130153	+	0.991494i	$0.458453\pi$
$410$	39125.6	+	109443.i	0.232752	+	0.651059i
$411$		0			0
$412$	−116685.	−	142340.i	−0.687420	−	0.838557i
$413$	−33754.1			−0.197891
$414$		0			0
$415$		−	12314.7i		−	0.0715036i
$416$	37556.5	−	5518.55i	0.217019	−	0.0318888i
$417$		0			0
$418$	13438.3	+	37589.9i	0.0769116	+	0.215139i
$419$			210600.i			1.19958i	0.800156	+	0.599792i	$0.204750\pi$
$419$			210600.i			1.19958i	−0.800156	+	0.599792i	$0.795250\pi$
$420$		0			0
$421$	84126.0			0.474642			0.237321	−	0.971431i	$-0.423731\pi$
$421$	84126.0			0.474642			0.237321	+	0.971431i	$0.423731\pi$
$422$	175107.	−	62600.4i	0.983285	−	0.351522i
$423$		0			0
$424$	−77644.7	−	46625.0i	−0.431897	−	0.259350i
$425$	142949.			0.791413
$426$		0			0
$427$		−	62641.3i		−	0.343562i
$428$	−66974.9	−	81700.1i	−0.365615	−	0.446000i
$429$		0			0
$430$	1660.34	−	593.569i	0.00897969	−	0.00321022i
$431$			150083.i			0.807933i	0.914774	+	0.403967i	$0.132369\pi$
$431$			150083.i			0.807933i	−0.914774	+	0.403967i	$0.867631\pi$
$432$		0			0
$433$	71221.5			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	71221.5			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	24303.2	+	67981.3i	0.129028	+	0.360919i
$435$		0			0
$436$	−149045.	+	122182.i	−0.784050	+	0.642736i
$437$	9156.53			0.0479477
$438$		0			0
$439$		−	109245.i		−	0.566858i	−0.958993	−	0.283429i	$-0.908528\pi$
$439$		−	109245.i		−	0.566858i	0.958993	−	0.283429i	$-0.0914720\pi$
$440$	−79739.3	+	132790.i	−0.411876	+	0.685899i
$441$		0			0
$442$	−14177.2	−	39656.7i	−0.0725680	−	0.202989i
$443$		−	230658.i		−	1.17533i	−0.809103	−	0.587666i	$-0.800047\pi$
$443$		−	230658.i		−	1.17533i	0.809103	−	0.587666i	$-0.199953\pi$
$444$		0			0
$445$	−74349.7			−0.375456
$446$	−311109.	+	111221.i	−1.56402	+	0.559133i
$447$		0			0
$448$	−43079.4	+	22935.7i	−0.214642	+	0.114276i
$449$	9751.64			0.0483710			0.0241855	−	0.999707i	$-0.492301\pi$
$449$	9751.64			0.0483710			0.0241855	+	0.999707i	$0.492301\pi$
$450$		0			0
$451$		−	577854.i		−	2.84096i
$452$	46162.5	−	37842.4i	0.225950	−	0.185226i
$453$		0			0
$454$	−111872.	+	39994.1i	−0.542764	+	0.194037i
$455$			4872.61i			0.0235363i
$456$		0			0
$457$	66139.1			0.316684			0.158342	−	0.987384i	$-0.449385\pi$
$457$	66139.1			0.316684			0.158342	+	0.987384i	$0.449385\pi$
$458$	−61046.1	−	170760.i	−0.291023	−	0.814056i
$459$		0			0
$460$	22523.8	+	27475.9i	0.106445	+	0.129848i
$461$	173989.			0.818692			0.409346	−	0.912379i	$-0.365757\pi$
$461$	173989.			0.818692			0.409346	+	0.912379i	$0.365757\pi$
$462$		0			0
$463$			173993.i			0.811650i	0.913951	+	0.405825i	$0.133016\pi$
$463$			173993.i			0.811650i	−0.913951	+	0.405825i	$0.866984\pi$
$464$	61682.4	−	308337.i	0.286500	−	1.43215i
$465$		0			0
$466$	68580.5	+	191835.i	0.315812	+	0.883397i
$467$			172090.i			0.789080i	0.918879	+	0.394540i	$0.129096\pi$
$467$			172090.i			0.789080i	−0.918879	+	0.394540i	$0.870904\pi$
$468$		0			0
$469$	11088.2			0.0504097
$470$	−119868.	+	42852.7i	−0.542637	+	0.193991i
$471$		0			0
$472$	−93336.0	+	155433.i	−0.418953	+	0.697683i
$473$	−8766.55			−0.0391838
$474$		0			0
$475$			22895.4i			0.101475i
$476$	34327.3	+	41874.6i	0.151505	+	0.184815i
$477$		0			0
$478$	−138941.	+	49671.2i	−0.608101	+	0.217395i
$479$		−	218398.i		−	0.951869i	−0.879481	−	0.475935i	$-0.842110\pi$
$479$		−	218398.i		−	0.951869i	0.879481	−	0.475935i	$-0.157890\pi$
$480$		0			0
$481$	56394.4			0.243751
$482$	−11293.7	−	31591.0i	−0.0486119	−	0.135978i
$483$		0			0
$484$	414392.	−	339704.i	1.76897	−	1.45014i
$485$	−132893.			−0.564959
$486$		0			0
$487$			392112.i			1.65330i	0.562716	+	0.826650i	$0.309757\pi$
$487$			392112.i			1.65330i	−0.562716	+	0.826650i	$0.690243\pi$
$488$	−288454.	−	173214.i	−1.21126	−	0.727351i
$489$		0			0
$490$	33556.4	+	93864.8i	0.139760	+	0.390940i
$491$			209717.i			0.869903i	0.900454	+	0.434951i	$0.143234\pi$
$491$			209717.i			0.869903i	−0.900454	+	0.434951i	$0.856766\pi$
$492$		0			0
$493$	−348864.			−1.43537
$494$	6351.60	−	2270.68i	0.0260273	−	0.00930470i
$495$		0			0
$496$	380247.	+	76067.9i	1.54562	+	0.309199i
$497$	−13854.4			−0.0560885
$498$		0			0
$499$		−	135886.i		−	0.545725i	−0.962053	−	0.272862i	$-0.912030\pi$
$499$		−	135886.i		−	0.545725i	0.962053	−	0.272862i	$-0.0879704\pi$
$500$	−154015.	+	126256.i	−0.616061	+	0.505025i
$501$		0			0
$502$	−5557.42	+	1986.76i	−0.0220529	+	0.00788385i
$503$		−	232332.i		−	0.918275i	−0.888365	−	0.459137i	$-0.848159\pi$
$503$		−	232332.i		−	0.918275i	0.888365	−	0.459137i	$-0.151841\pi$
$504$		0			0
$505$	−105409.			−0.413328
$506$	−59462.2	−	166329.i	−0.232242	−	0.649632i
$507$		0			0
$508$	−269308.	−	328518.i	−1.04357	−	1.27301i
$509$	145319.			0.560901			0.280451	−	0.959868i	$-0.409516\pi$
$509$	145319.			0.560901			0.280451	+	0.959868i	$0.409516\pi$
$510$		0			0
$511$		−	25770.9i		−	0.0986935i
$512$	−13506.6	+	261796.i	−0.0515234	+	0.998672i
$513$		0			0
$514$	46688.3	+	130598.i	0.176719	+	0.494321i
$515$		−	126901.i		−	0.478465i
$516$		0			0
$517$	632900.			2.36785
$518$	−68274.1	+	24407.8i	−0.254447	+	0.0909641i
$519$		0			0
$520$	22437.7	+	13473.6i	0.0829795	+	0.0498285i
$521$	−443088.			−1.63235			−0.816177	−	0.577803i	$-0.803910\pi$
$521$	−443088.			−1.63235			−0.816177	+	0.577803i	$0.803910\pi$
$522$		0			0
$523$		−	73202.4i		−	0.267622i	−0.991007	−	0.133811i	$-0.957278\pi$
$523$		−	73202.4i		−	0.267622i	0.991007	−	0.133811i	$-0.0427215\pi$
$524$	13385.8	+	16328.9i	0.0487509	+	0.0594694i
$525$		0			0
$526$	71686.3	−	25627.7i	0.259098	−	0.0926271i
$527$		−	430226.i		−	1.54909i
$528$		0			0
$529$	239325.			0.855217
$530$	−21020.8	−	58799.9i	−0.0748338	−	0.209327i
$531$		0			0
$532$	−6706.83	+	5498.02i	−0.0236970	+	0.0194260i
$533$	−97640.6			−0.343697
$534$		0			0
$535$		−	72838.4i		−	0.254480i
$536$	30660.7	−	51059.4i	0.106722	−	0.177724i
$537$		0			0
$538$	79073.8	+	221187.i	0.273192	+	0.764179i
$539$		−	495602.i		−	1.70591i
$540$		0			0
$541$	438165.			1.49707			0.748536	−	0.663094i	$-0.230757\pi$
$541$	438165.			1.49707			0.748536	+	0.663094i	$0.230757\pi$
$542$	−118548.	+	42380.8i	−0.403550	+	0.144268i
$543$		0			0
$544$	287748.	−	42281.7i	0.972330	−	0.142874i
$545$	−132878.			−0.447364
$546$		0			0
$547$		−	312024.i		−	1.04283i	−0.853303	−	0.521416i	$-0.825404\pi$
$547$		−	312024.i		−	1.04283i	0.853303	−	0.521416i	$-0.174596\pi$
$548$	319402.	−	261834.i	1.06359	−	0.871898i
$549$		0			0
$550$	415896.	−	148682.i	1.37486	−	0.491510i
$551$		−	55875.7i		−	0.184043i
$552$		0			0
$553$	−89189.8			−0.291652
$554$	−89586.7	−	250594.i	−0.291893	−	0.816490i
$555$		0			0
$556$	−133266.	−	162566.i	−0.431091	−	0.525871i
$557$	−312549.			−1.00741			−0.503707	−	0.863874i	$-0.668031\pi$
$557$	−312549.			−1.00741			−0.503707	+	0.863874i	$0.668031\pi$
$558$		0			0
$559$			1481.29i			0.00474042i
$560$	−32995.7	−	6600.75i	−0.105216	−	0.0210483i
$561$		0			0
$562$	−166593.	−	465996.i	−0.527452	−	1.47540i
$563$		−	86349.2i		−	0.272422i	−0.990680	−	0.136211i	$-0.956508\pi$
$563$		−	86349.2i		−	0.272422i	0.990680	−	0.136211i	$-0.0434925\pi$
$564$		0			0
$565$	41155.5			0.128923
$566$	206162.	−	73702.3i	0.643539	−	0.230064i
$567$		0			0
$568$	−38309.8	+	63797.4i	−0.118744	+	0.197745i
$569$	−554958.			−1.71410			−0.857049	−	0.515235i	$-0.827705\pi$
$569$	−554958.			−1.71410			−0.857049	+	0.515235i	$0.827705\pi$
$570$		0			0
$571$			303511.i			0.930898i	0.885075	+	0.465449i	$0.154107\pi$
$571$			303511.i			0.930898i	−0.885075	+	0.465449i	$0.845893\pi$
$572$	−82494.3	−	100632.i	−0.252134	−	0.307569i
$573$		0			0
$574$	118209.	−	42259.4i	0.358779	−	0.128263i
$575$		−	101308.i		−	0.306414i
$576$		0			0
$577$	−500884.			−1.50448			−0.752238	−	0.658892i	$-0.771026\pi$
$577$	−500884.			−1.50448			−0.752238	+	0.658892i	$0.771026\pi$
$578$	3841.86	+	10746.5i	0.0114997	+	0.0321671i
$579$		0			0
$580$	167666.	−	137446.i	0.498412	−	0.408580i
$581$	−13301.1			−0.0394035
$582$		0			0
$583$			310461.i			0.913418i
$584$	−118671.	−	71261.2i	−0.347953	−	0.208943i
$585$		0			0
$586$	−119327.	−	333783.i	−0.347490	−	0.972007i
$587$			575710.i			1.67081i	0.549633	+	0.835406i	$0.314767\pi$
$587$			575710.i			1.67081i	−0.549633	+	0.835406i	$0.685233\pi$
$588$		0			0
$589$	68907.0			0.198624
$590$	−117708.	+	42080.4i	−0.338145	+	0.120886i
$591$		0			0
$592$	−76395.5	+	381885.i	−0.217984	+	1.08965i
$593$	138143.			0.392843			0.196421	−	0.980520i	$-0.437068\pi$
$593$	138143.			0.392843			0.196421	+	0.980520i	$0.437068\pi$
$594$		0			0
$595$			37332.6i			0.105452i
$596$	320930.	−	263087.i	0.903478	−	0.740640i
$597$		0			0
$598$	−28104.8	+	10047.4i	−0.0785919	+	0.0280964i
$599$		−	191294.i		−	0.533147i	−0.963815	−	0.266574i	$-0.914108\pi$
$599$		−	191294.i		−	0.533147i	0.963815	−	0.266574i	$-0.0858916\pi$
$600$		0			0
$601$	−406240.			−1.12469			−0.562346	−	0.826902i	$-0.690101\pi$
$601$	−406240.			−1.12469			−0.562346	+	0.826902i	$0.690101\pi$
$602$	−641.112	−	1793.33i	−0.00176905	−	0.00494843i
$603$		0			0
$604$	−288031.	−	351358.i	−0.789524	−	0.963110i
$605$	369445.			1.00934
$606$		0			0
$607$		−	68666.5i		−	0.186366i	−0.995649	−	0.0931831i	$-0.970296\pi$
$607$		−	68666.5i		−	0.186366i	0.995649	−	0.0931831i	$-0.0297042\pi$
$608$	6772.03	+	46087.0i	0.0183194	+	0.124673i
$609$		0			0
$610$	−78093.4	−	218445.i	−0.209872	−	0.587059i
$611$		−	106942.i		−	0.286461i
$612$		0			0
$613$	−572114.			−1.52252			−0.761258	−	0.648450i	$-0.775418\pi$
$613$	−572114.			−1.52252			−0.761258	+	0.648450i	$0.775418\pi$
$614$	−464970.	+	166225.i	−1.23335	+	0.440921i
$615$		0			0
$616$	143426.	+	86126.1i	0.377978	+	0.226973i
$617$	−20380.8			−0.0535367			−0.0267684	−	0.999642i	$-0.508522\pi$
$617$	−20380.8			−0.0535367			−0.0267684	+	0.999642i	$0.508522\pi$
$618$		0			0
$619$			448721.i			1.17110i	0.810635	+	0.585552i	$0.199122\pi$
$619$			448721.i			1.17110i	−0.810635	+	0.585552i	$0.800878\pi$
$620$	169501.	+	206768.i	0.440951	+	0.537899i
$621$		0			0
$622$	−228038.	+	81523.2i	−0.589423	+	0.210717i
$623$			80304.8i			0.206902i
$624$		0			0
$625$	177255.			0.453773
$626$	70539.6	+	197315.i	0.180005	+	0.503514i
$627$		0			0
$628$	68307.5	−	55996.1i	0.173200	−	0.141984i
$629$	432079.			1.09210
$630$		0			0
$631$			402529.i			1.01097i	0.862835	+	0.505486i	$0.168687\pi$
$631$			402529.i			1.01097i	−0.862835	+	0.505486i	$0.831313\pi$
$632$	−246625.	+	410706.i	−0.617453	+	1.02825i
$633$		0			0
$634$	−35006.2	−	97920.2i	−0.0870897	−	0.243609i
$635$		−	292885.i		−	0.726357i
$636$		0			0
$637$	−83742.3			−0.206379
$638$	−1.01499e6	+	362856.i	−2.49356	+	0.891441i
$639$		0			0
$640$	−121634.	+	133688.i	−0.296959	+	0.326387i
$641$	−353813.			−0.861108			−0.430554	−	0.902565i	$-0.641682\pi$
$641$	−353813.			−0.861108			−0.430554	+	0.902565i	$0.641682\pi$
$642$		0			0
$643$			263141.i			0.636452i	0.948015	+	0.318226i	$0.103087\pi$
$643$			263141.i			0.636452i	−0.948015	+	0.318226i	$0.896913\pi$
$644$	29676.6	−	24327.8i	0.0715554	−	0.0586586i
$645$		0			0
$646$	48664.3	−	17397.4i	0.116613	−	0.0416887i
$647$			265174.i			0.633464i	0.948515	+	0.316732i	$0.102586\pi$
$647$			265174.i			0.633464i	−0.948515	+	0.316732i	$0.897414\pi$
$648$		0			0
$649$	621494.			1.47553
$650$	−25122.9	−	70274.4i	−0.0594625	−	0.166330i
$651$		0			0
$652$	4131.27	+	5039.58i	0.00971825	+	0.0118549i
$653$	5877.92			0.0137847			0.00689235	−	0.999976i	$-0.497806\pi$
$653$	5877.92			0.0137847			0.00689235	+	0.999976i	$0.497806\pi$
$654$		0			0
$655$			14557.7i			0.0339322i
$656$	132270.	−	661190.i	0.307365	−	1.53645i
$657$		0			0
$658$	46285.0	+	129470.i	0.106903	+	0.299031i
$659$		−	554642.i		−	1.27715i	−0.769560	−	0.638575i	$-0.779524\pi$
$659$		−	554642.i		−	1.27715i	0.769560	−	0.638575i	$-0.220476\pi$
$660$		0			0
$661$	−821227.			−1.87958			−0.939789	−	0.341755i	$-0.888979\pi$
$661$	−821227.			−1.87958			−0.939789	+	0.341755i	$0.888979\pi$
$662$	162832.	−	58212.0i	0.371555	−	0.132830i
$663$		0			0
$664$	−36779.8	+	61249.5i	−0.0834206	+	0.138921i
$665$	−5979.36			−0.0135211
$666$		0			0
$667$			247241.i			0.555736i
$668$	240836.	+	293787.i	0.539721	+	0.658385i
$669$		0			0
$670$	38667.0	−	13823.4i	0.0861372	−	0.0307938i
$671$			1.15338e6i			2.56169i
$672$		0			0
$673$	516865.			1.14116			0.570580	−	0.821242i	$-0.306718\pi$
$673$	516865.			1.14116			0.570580	+	0.821242i	$0.306718\pi$
$674$	−15960.1	−	44643.9i	−0.0351330	−	0.0982749i
$675$		0			0
$676$	336402.	−	275770.i	0.736148	−	0.603468i
$677$	690686.			1.50697			0.753483	−	0.657468i	$-0.228372\pi$
$677$	690686.			1.50697			0.753483	+	0.657468i	$0.228372\pi$
$678$		0			0
$679$			143537.i			0.311332i
$680$	171911.	+	103231.i	0.371780	+	0.223251i
$681$		0			0
$682$	−447480.	−	1.25170e6i	−0.962066	−	2.69111i
$683$			764551.i			1.63895i	0.573117	+	0.819474i	$0.305734\pi$
$683$			764551.i			1.63895i	−0.573117	+	0.819474i	$0.694266\pi$
$684$		0			0
$685$	284757.			0.606868
$686$	209138.	−	74766.2i	0.444410	−	0.158875i
$687$		0			0
$688$	−10030.8	−	2006.65i	−0.0211914	−	0.00423931i
$689$	52458.9			0.110505
$690$		0			0
$691$			321130.i			0.672550i	0.941764	+	0.336275i	$0.109167\pi$
$691$			321130.i			0.672550i	−0.941764	+	0.336275i	$0.890833\pi$
$692$	−34974.2	+	28670.6i	−0.0730358	+	0.0598722i
$693$		0			0
$694$	109698.	−	39216.9i	0.227762	−	0.0814244i
$695$		−	144933.i		−	0.300053i
$696$		0			0
$697$	−748096.			−1.53990
$698$	−161552.	−	451898.i	−0.331591	−	0.927534i
$699$		0			0
$700$	60830.3	+	74204.6i	0.124144	+	0.151438i
$701$	621799.			1.26536			0.632680	−	0.774413i	$-0.281955\pi$
$701$	621799.			1.26536			0.632680	+	0.774413i	$0.281955\pi$
$702$		0			0
$703$			69203.8i			0.140029i
$704$	793196.	−	422302.i	1.60043	−	0.852075i
$705$		0			0
$706$	208386.	+	582903.i	0.418081	+	1.16946i
$707$			113852.i			0.227772i
$708$		0			0
$709$	−524870.			−1.04414			−0.522070	−	0.852903i	$-0.674840\pi$
$709$	−524870.			−1.04414			−0.522070	+	0.852903i	$0.674840\pi$
$710$	−48313.4	+	17271.9i	−0.0958409	+	0.0342629i
$711$		0			0
$712$	369792.	+	222057.i	0.729454	+	0.438031i
$713$	−304902.			−0.599765
$714$		0			0
$715$		−	89716.5i		−	0.175493i
$716$	463999.	+	566015.i	0.905089	+	1.10408i
$717$		0			0
$718$	251754.	−	90001.5i	0.488346	−	0.174583i
$719$			348658.i			0.674438i	0.941426	+	0.337219i	$0.109486\pi$
$719$			348658.i			0.674438i	−0.941426	+	0.337219i	$0.890514\pi$
$720$		0			0
$721$	−137065.			−0.263668
$722$	−172695.	−	483066.i	−0.331287	−	0.926684i
$723$		0			0
$724$	299768.	−	245739.i	0.571885	−	0.468811i
$725$	−618211.			−1.17615
$726$		0			0
$727$			604820.i			1.14435i	0.820133	+	0.572173i	$0.193899\pi$
$727$			604820.i			1.14435i	−0.820133	+	0.572173i	$0.806101\pi$
$728$	14552.8	−	24234.8i	0.0274590	−	0.0457275i
$729$		0			0
$730$	−32128.0	−	89869.2i	−0.0602890	−	0.168642i
$731$			11349.3i			0.0212389i
$732$		0			0
$733$	−475610.			−0.885204			−0.442602	−	0.896718i	$-0.645945\pi$
$733$	−475610.			−0.885204			−0.442602	+	0.896718i	$0.645945\pi$
$734$	−356208.	+	127343.i	−0.661167	+	0.236365i
$735$		0			0
$736$	−29965.1	−	203927.i	−0.0553172	−	0.376461i
$737$	−204160.			−0.375868
$738$		0			0
$739$			844449.i			1.54627i	0.634244	+	0.773133i	$0.281312\pi$
$739$			844449.i			1.54627i	−0.634244	+	0.773133i	$0.718688\pi$
$740$	−207659.	+	170231.i	−0.379216	+	0.310868i
$741$		0			0
$742$	−63509.5	+	22704.5i	−0.115354	+	0.0412386i
$743$		−	620323.i		−	1.12367i	−0.827248	−	0.561837i	$-0.810095\pi$
$743$		−	620323.i		−	1.12367i	0.827248	−	0.561837i	$-0.189905\pi$
$744$		0			0
$745$	286120.			0.515508
$746$	243804.	+	681974.i	0.438090	+	1.22543i
$747$		0			0
$748$	−632049.	−	771013.i	−1.12966	−	1.37803i
$749$	−78672.5			−0.140236
$750$		0			0
$751$			730748.i			1.29565i	0.761789	+	0.647825i	$0.224321\pi$
$751$			730748.i			1.29565i	−0.761789	+	0.647825i	$0.775679\pi$
$752$	724175.	+	144870.i	1.28058	+	0.256179i
$753$		0			0
$754$	61312.0	+	171503.i	0.107846	+	0.301669i
$755$		−	313247.i		−	0.549533i
$756$		0			0
$757$	−769023.			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$757$	−769023.			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$758$	192814.	−	68930.6i	0.335584	−	0.119970i
$759$		0			0
$760$	−16534.0	+	27534.1i	−0.0286253	+	0.0476699i
$761$	−275394.			−0.475538			−0.237769	−	0.971322i	$-0.576416\pi$
$761$	−275394.			−0.475538			−0.237769	+	0.971322i	$0.576416\pi$
$762$		0			0
$763$			143522.i			0.246529i
$764$	−228452.	−	278680.i	−0.391389	−	0.477441i
$765$		0			0
$766$	−574654.	+	205437.i	−0.979375	+	0.350124i
$767$		−	105014.i		−	0.178508i
$768$		0			0
$769$	−52842.1			−0.0893568			−0.0446784	−	0.999001i	$-0.514226\pi$
$769$	−52842.1			−0.0893568			−0.0446784	+	0.999001i	$0.514226\pi$
$770$	38829.8	+	108616.i	0.0654914	+	0.183194i
$771$		0			0
$772$	−226299.	+	185512.i	−0.379707	+	0.311270i
$773$	195309.			0.326861			0.163430	−	0.986555i	$-0.447744\pi$
$773$	195309.			0.326861			0.163430	+	0.986555i	$0.447744\pi$
$774$		0			0
$775$		−	762389.i		−	1.26933i
$776$	660966.	+	396905.i	1.09763	+	0.659117i
$777$		0			0
$778$	91425.1	+	255736.i	0.151045	+	0.422506i
$779$		−	119819.i		−	0.197446i
$780$		0			0
$781$	255093.			0.418211
$782$	−215331.	+	76980.4i	−0.352122	+	0.125883i
$783$		0			0
$784$	113443.	−	567076.i	0.184563	−	0.922590i
$785$	60898.4			0.0988250
$786$		0			0
$787$			782238.i			1.26296i	0.775393	+	0.631480i	$0.217552\pi$
$787$			782238.i			1.26296i	−0.775393	+	0.631480i	$0.782448\pi$
$788$	449169.	−	368213.i	0.723364	−	0.592989i
$789$		0			0
$790$	−311025.	+	111191.i	−0.498358	+	0.178162i
$791$		−	44451.9i		−	0.0710456i
$792$		0			0
$793$	194887.			0.309911
$794$	169780.	+	474912.i	0.269305	+	0.753307i
$795$		0			0
$796$	−480159.	−	585728.i	−0.757807	−	0.924421i
$797$	1.17343e6			1.84731			0.923655	−	0.383226i	$-0.125187\pi$
$797$	1.17343e6			1.84731			0.923655	+	0.383226i	$0.125187\pi$
$798$		0			0
$799$		−	819359.i		−	1.28346i
$800$	509908.	−	74926.0i	0.796731	−	0.117072i
$801$		0			0
$802$	95456.6	+	267013.i	0.148408	+	0.415130i
$803$			474505.i			0.735885i
$804$		0			0
$805$	26457.7			0.0408282
$806$	−211501.	+	75611.1i	−0.325569	+	0.116390i
$807$		0			0
$808$	524271.	+	314820.i	0.803033	+	0.482214i
$809$	421614.			0.644196			0.322098	−	0.946706i	$-0.395612\pi$
$809$	421614.			0.644196			0.322098	+	0.946706i	$0.395612\pi$
$810$		0			0
$811$			504037.i			0.766339i	0.923678	+	0.383169i	$0.125167\pi$
$811$			504037.i			0.766339i	−0.923678	+	0.383169i	$0.874833\pi$
$812$	−148455.	−	181095.i	−0.225156	−	0.274659i
$813$		0			0
$814$	1.25709e6	−	449407.i	1.89722	−	0.678253i
$815$			4492.95i			0.00676420i
$816$		0			0
$817$	−1817.75			−0.00272327
$818$	−58633.6	−	164011.i	−0.0876275	−	0.245113i
$819$		0			0
$820$	359538.	−	294737.i	0.534709	−	0.438335i
$821$	71554.1			0.106157			0.0530785	−	0.998590i	$-0.483097\pi$
$821$	71554.1			0.106157			0.0530785	+	0.998590i	$0.483097\pi$
$822$		0			0
$823$		−	812709.i		−	1.19987i	−0.800048	−	0.599936i	$-0.795193\pi$
$823$		−	812709.i		−	1.19987i	0.800048	−	0.599936i	$-0.204807\pi$
$824$	−379010.	+	631166.i	−0.558208	+	0.929585i
$825$		0			0
$826$	45450.9	+	127136.i	0.0666166	+	0.186341i
$827$		−	375951.i		−	0.549693i	−0.961488	−	0.274847i	$-0.911373\pi$
$827$		−	375951.i		−	0.549693i	0.961488	−	0.274847i	$-0.0886271\pi$
$828$		0			0
$829$	423699.			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$829$	423699.			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$830$	−46383.9	+	16582.1i	−0.0673304	+	0.0240704i
$831$		0			0
$832$	−71356.8	−	134027.i	−0.103083	−	0.193618i
$833$	−641611.			−0.924660
$834$		0			0
$835$			261921.i			0.375662i
$836$	123489.	−	101232.i	0.176691	−	0.144845i
$837$		0			0
$838$	793234.	−	283579.i	1.12957	−	0.403819i
$839$			1.10840e6i			1.57460i	0.616568	+	0.787302i	$0.288523\pi$
$839$			1.10840e6i			1.57460i	−0.616568	+	0.787302i	$0.711477\pi$
$840$		0			0
$841$	801453.			1.13315
$842$	−113278.	−	316864.i	−0.159780	−	0.446940i
$843$		0			0
$844$	−471575.	−	575256.i	−0.662012	−	0.807563i
$845$	299914.			0.420032
$846$		0			0
$847$		−	399036.i		−	0.556218i
$848$	−71064.1	+	355234.i	−0.0988231	+	0.493995i
$849$		0			0
$850$	−192485.	−	538423.i	−0.266415	−	0.745223i
$851$		−	306215.i		−	0.422832i
$852$		0			0
$853$	−509319.			−0.699989			−0.349995	−	0.936752i	$-0.613817\pi$
$853$	−509319.			−0.699989			−0.349995	+	0.936752i	$0.613817\pi$
$854$	−235941.	+	84348.4i	−0.323510	+	0.115654i
$855$		0			0
$856$	−217543.	+	362276.i	−0.296892	+	0.494415i
$857$	656788.			0.894260			0.447130	−	0.894469i	$-0.352446\pi$
$857$	656788.			0.894260			0.447130	+	0.894469i	$0.352446\pi$
$858$		0			0
$859$		−	1.05866e6i		−	1.43474i	−0.696694	−	0.717368i	$-0.745347\pi$
$859$		−	1.05866e6i		−	1.43474i	0.696694	−	0.717368i	$-0.254653\pi$
$860$	−4471.41	−	5454.50i	−0.00604571	−	0.00737494i
$861$		0			0
$862$	565292.	−	202091.i	0.760779	−	0.271977i
$863$		−	676878.i		−	0.908844i	−0.890787	−	0.454422i	$-0.849846\pi$
$863$		−	676878.i		−	0.908844i	0.890787	−	0.454422i	$-0.150154\pi$
$864$		0			0
$865$	−31180.7			−0.0416729
$866$	−95902.0	−	268259.i	−0.127877	−	0.357700i
$867$		0			0
$868$	223330.	−	183078.i	0.296420	−	0.242994i
$869$	1.64220e6			2.17464
$870$		0			0
$871$			34497.1i			0.0454723i
$872$	660896.	+	396862.i	0.869161	+	0.521924i
$873$		0			0
$874$	−12329.5	−	34488.5i	−0.0161408	−	0.0451493i
$875$			148308.i			0.193708i
$876$		0			0
$877$	1.47583e6			1.91883			0.959415	−	0.281998i	$-0.0909973\pi$
$877$	1.47583e6			1.91883			0.959415	+	0.281998i	$0.0909973\pi$
$878$	−411478.	+	147102.i	−0.533774	+	0.190823i
$879$		0			0
$880$	607531.	+	121536.i	0.784518	+	0.156942i
$881$	−599513.			−0.772408			−0.386204	−	0.922413i	$-0.626214\pi$
$881$	−599513.			−0.772408			−0.386204	+	0.922413i	$0.626214\pi$
$882$		0			0
$883$			729187.i			0.935229i	0.883933	+	0.467614i	$0.154886\pi$
$883$			729187.i			0.935229i	−0.883933	+	0.467614i	$0.845114\pi$
$884$	−130279.	+	106798.i	−0.166713	+	0.136665i
$885$		0			0
$886$	−868783.	+	310588.i	−1.10674	+	0.395655i
$887$			1.45744e6i			1.85244i	0.376981	+	0.926221i	$0.376962\pi$
$887$			1.45744e6i			1.85244i	−0.376981	+	0.926221i	$0.623038\pi$
$888$		0			0
$889$	−316344.			−0.400273
$890$	100114.	+	280041.i	0.126391	+	0.353543i
$891$		0			0
$892$	837834.	+	1.02204e6i	1.05300	+	1.28452i
$893$	131232.			0.164565
$894$		0			0
$895$			504622.i			0.629970i
$896$	144396.	+	131377.i	0.179862	+	0.163645i
$897$		0			0
$898$	−13130.9	−	36730.0i	−0.0162833	−	0.0455479i
$899$			1.86060e6i			2.30215i
$900$		0			0
$901$	401926.			0.495104
$902$	−2.17651e6	+	778098.i	−2.67515	+	0.956360i
$903$		0			0
$904$	−204694.	−	122917.i	−0.250478	−	0.150410i
$905$	267253.			0.326307
$906$		0			0
$907$			3476.53i			0.00422602i	0.999998	+	0.00211301i	$0.000672593\pi$
$907$			3476.53i			0.00422602i	−0.999998	+	0.00211301i	$0.999327\pi$
$908$	301279.	+	367519.i	0.365424	+	0.445767i
$909$		0			0
$910$	18352.9	−	6561.11i	0.0221627	−	0.00792309i
$911$		−	822935.i		−	0.991583i	−0.868442	−	0.495791i	$-0.834878\pi$
$911$		−	822935.i		−	0.991583i	0.868442	−	0.495791i	$-0.165122\pi$
$912$		0			0
$913$	244905.			0.293803
$914$	−89058.3	−	249116.i	−0.106606	−	0.298201i
$915$		0			0
$916$	−560973.	+	459866.i	−0.668577	+	0.548076i
$917$	15723.8			0.0186990
$918$		0			0
$919$		−	873279.i		−	1.03400i	−0.855984	−	0.517002i	$-0.827048\pi$
$919$		−	873279.i		−	1.03400i	0.855984	−	0.517002i	$-0.172952\pi$
$920$	73160.2	−	121834.i	0.0864369	−	0.143944i
$921$		0			0
$922$	−234282.	−	655338.i	−0.275598	−	0.770910i
$923$		−	43103.2i		−	0.0505949i
$924$		0			0
$925$	765673.			0.894870
$926$	655351.	−	234286.i	0.764279	−	0.273228i
$927$		0			0
$928$	−1.24442e6	+	182856.i	−1.44501	+	0.212330i
$929$	−345961.			−0.400863			−0.200431	−	0.979708i	$-0.564234\pi$
$929$	−345961.			−0.400863			−0.200431	+	0.979708i	$0.564234\pi$
$930$		0			0
$931$		−	102763.i		−	0.118560i
$932$	630209.	−	516623.i	0.725526	−	0.594760i
$933$		0			0
$934$	648183.	−	231724.i	0.743026	−	0.265630i
$935$		−	687384.i		−	0.786278i
$936$		0			0
$937$	−1.10958e6			−1.26380			−0.631901	−	0.775049i	$-0.717725\pi$
$937$	−1.10958e6			−1.26380			−0.631901	+	0.775049i	$0.717725\pi$
$938$	−14930.6	−	41764.1i	−0.0169696	−	0.0474676i
$939$		0			0
$940$	322813.	+	393788.i	0.365339	+	0.445663i
$941$	−322543.			−0.364257			−0.182129	−	0.983275i	$-0.558299\pi$
$941$	−322543.			−0.364257			−0.182129	+	0.983275i	$0.558299\pi$
$942$		0			0
$943$			530177.i			0.596208i
$944$	711124.	+	142259.i	0.797997	+	0.159638i
$945$		0			0
$946$	11804.4	+	33019.6i	0.0131905	+	0.0368969i
$947$		−	139420.i		−	0.155463i	−0.996974	−	0.0777314i	$-0.975232\pi$
$947$		−	139420.i		−	0.155463i	0.996974	−	0.0777314i	$-0.0247676\pi$
$948$		0			0
$949$	80177.6			0.0890268
$950$	86236.4	−	30829.3i	0.0955528	−	0.0341599i
$951$		0			0
$952$	111500.	−	185681.i	0.123027	−	0.204877i
$953$	−1.68438e6			−1.85462			−0.927308	−	0.374300i	$-0.877883\pi$
$953$	−1.68438e6			−1.85462			−0.927308	+	0.374300i	$0.877883\pi$
$954$		0			0
$955$		−	248453.i		−	0.272419i
$956$	374178.	+	456445.i	0.409413	+	0.499428i
$957$		0			0
$958$	−822605.	+	294079.i	−0.896314	+	0.320430i
$959$		−	307566.i		−	0.334426i
$960$		0			0
$961$	−1.37100e6			−1.48454
$962$	−75936.8	−	212412.i	−0.0820545	−	0.229525i
$963$		0			0
$964$	−103782.	+	85076.6i	−0.111678	+	0.0915495i
$965$	−201753.			−0.216654
$966$		0			0
$967$		−	45357.5i		−	0.0485061i	−0.999706	−	0.0242530i	$-0.992279\pi$
$967$		−	45357.5i		−	0.0485061i	0.999706	−	0.0242530i	$-0.00772074\pi$
$968$	−1.83750e6	−	1.10340e6i	−1.96100	−	1.17756i
$969$		0			0
$970$	178944.	+	500546.i	0.190184	+	0.531986i
$971$		−	1.18319e6i		−	1.25492i	−0.778648	−	0.627461i	$-0.784094\pi$
$971$		−	1.18319e6i		−	1.25492i	0.778648	−	0.627461i	$-0.215906\pi$
$972$		0			0
$973$	−156541.			−0.165350
$974$	1.47691e6	−	527990.i	1.55681	−	0.556555i
$975$		0			0
$976$	−264007.	+	1.31971e6i	−0.277151	+	1.38542i
$977$	−1.12593e6			−1.17957			−0.589783	−	0.807562i	$-0.700787\pi$
$977$	−1.12593e6			−1.17957			−0.589783	+	0.807562i	$0.700787\pi$
$978$		0			0
$979$		−	1.47861e6i		−	1.54272i
$980$	308361.	−	252784.i	0.321076	−	0.263206i
$981$		0			0
$982$	789909.	−	282390.i	0.819132	−	0.292838i
$983$		−	1.35328e6i		−	1.40049i	−0.713904	−	0.700243i	$-0.753075\pi$
$983$		−	1.35328e6i		−	1.40049i	0.713904	−	0.700243i	$-0.246925\pi$
$984$		0			0
$985$	400449.			0.412738
$986$	469756.	+	1.31401e6i	0.483191	+	1.35159i
$987$		0			0
$988$	−17105.3	−	20866.0i	−0.0175233	−	0.0213760i
$989$	8043.24			0.00822316
$990$		0			0
$991$		−	1.02847e6i		−	1.04724i	−0.851953	−	0.523619i	$-0.824582\pi$
$991$		−	1.02847e6i		−	1.04724i	0.851953	−	0.523619i	$-0.175418\pi$
$992$	−225501.	−	1.53464e6i	−0.229153	−	1.55950i
$993$		0			0
$994$	18655.3	+	52183.1i	0.0188812	+	0.0528150i
$995$		−	522196.i		−	0.527457i
$996$		0			0
$997$	1.12806e6			1.13486			0.567430	−	0.823422i	$-0.307938\pi$
$997$	1.12806e6			1.13486			0.567430	+	0.823422i	$0.307938\pi$
$998$	−511821.	+	182975.i	−0.513874	+	0.183709i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.e.163.9		22
3.2	odd	2		324.5.d.f.163.14		22
4.3	odd	2	inner	324.5.d.e.163.10		22
9.2	odd	6		36.5.f.a.31.16	yes	44
9.4	even	3		108.5.f.a.19.21		44
9.5	odd	6		36.5.f.a.7.2	✓	44
9.7	even	3		108.5.f.a.91.7		44
12.11	even	2		324.5.d.f.163.13		22
36.7	odd	6		108.5.f.a.91.21		44
36.11	even	6		36.5.f.a.31.2	yes	44
36.23	even	6		36.5.f.a.7.16	yes	44
36.31	odd	6		108.5.f.a.19.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.2	✓	44	9.5	odd	6
36.5.f.a.7.16	yes	44	36.23	even	6
36.5.f.a.31.2	yes	44	36.11	even	6
36.5.f.a.31.16	yes	44	9.2	odd	6
108.5.f.a.19.7		44	36.31	odd	6
108.5.f.a.19.21		44	9.4	even	3
108.5.f.a.91.7		44	9.7	even	3
108.5.f.a.91.21		44	36.7	odd	6
324.5.d.e.163.9		22	1.1	even	1	trivial
324.5.d.e.163.10		22	4.3	odd	2	inner
324.5.d.f.163.13		22	12.11	even	2
324.5.d.f.163.14		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +O(q^{10})\)	\(q+(-1.34653 - 3.76654i) q^{2} +(-12.3737 + 10.1435i) q^{4} -11.0316 q^{5} +11.9152i q^{7} +(54.8676 + 32.9476i) q^{8} +(14.8544 + 41.5509i) q^{10} -219.387i q^{11} -37.0701 q^{13} +(44.8790 - 16.0441i) q^{14} +(50.2175 - 251.026i) q^{16} -284.021 q^{17} -45.4901i q^{19} +(136.502 - 111.899i) q^{20} +(-826.332 + 295.412i) q^{22} +201.286i q^{23} -503.304 q^{25} +(49.9160 + 139.626i) q^{26} +(-120.862 - 147.435i) q^{28} +1228.31 q^{29} +1514.77i q^{31} +(-1013.12 + 148.868i) q^{32} +(382.443 + 1069.78i) q^{34} -131.443i q^{35} -1521.29 q^{37} +(-171.340 + 61.2538i) q^{38} +(-605.277 - 363.464i) q^{40} +2633.95 q^{41} -39.9593i q^{43} +(2225.36 + 2714.63i) q^{44} +(758.153 - 271.038i) q^{46} +2884.86i q^{47} +2259.03 q^{49} +(677.714 + 1895.72i) q^{50} +(458.694 - 376.021i) q^{52} -1415.13 q^{53} +2420.19i q^{55} +(-392.576 + 653.757i) q^{56} +(-1653.95 - 4626.47i) q^{58} +2832.86i q^{59} -5257.27 q^{61} +(5705.44 - 2039.68i) q^{62} +(1924.92 + 3615.51i) q^{64} +408.941 q^{65} -930.592i q^{67} +(3514.39 - 2880.97i) q^{68} +(-495.087 + 176.992i) q^{70} +1162.75i q^{71} -2162.87 q^{73} +(2048.47 + 5730.02i) q^{74} +(461.430 + 562.881i) q^{76} +2614.04 q^{77} +7485.40i q^{79} +(-553.978 + 2769.22i) q^{80} +(-3546.69 - 9920.88i) q^{82} +1116.31i q^{83} +3133.20 q^{85} +(-150.508 + 53.8064i) q^{86} +(7228.27 - 12037.3i) q^{88} +6739.71 q^{89} -441.696i q^{91} +(-2041.75 - 2490.66i) q^{92} +(10865.9 - 3884.55i) q^{94} +501.828i q^{95} +12046.6 q^{97} +(-3041.85 - 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) \) 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8} + 14 q^{10} + 2 q^{13} + 252 q^{14} + q^{16} + 28 q^{17} - 140 q^{20} + 33 q^{22} + 1752 q^{25} - 548 q^{26} - 258 q^{28} + 526 q^{29} - 121 q^{32} - 385 q^{34} - 4 q^{37} + 1395 q^{38} + 2276 q^{40} - 2762 q^{41} - 3357 q^{44} + 1788 q^{46} - 3428 q^{49} + 6375 q^{50} - 1438 q^{52} + 5044 q^{53} - 7506 q^{56} + 4064 q^{58} + 2 q^{61} + 9162 q^{62} + 4513 q^{64} - 2014 q^{65} - 11405 q^{68} - 3666 q^{70} - 1708 q^{73} + 14620 q^{74} - 1581 q^{76} - 3942 q^{77} - 22760 q^{80} - 4243 q^{82} + 1252 q^{85} + 22113 q^{86} - 1995 q^{88} - 6524 q^{89} - 30294 q^{92} - 7524 q^{94} - 5638 q^{97} + 46469 q^{98}+O(q^{100}) \) 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8 + 14 * q^10 + 2 * q^13 + 252 * q^14 + q^16 + 28 * q^17 - 140 * q^20 + 33 * q^22 + 1752 * q^25 - 548 * q^26 - 258 * q^28 + 526 * q^29 - 121 * q^32 - 385 * q^34 - 4 * q^37 + 1395 * q^38 + 2276 * q^40 - 2762 * q^41 - 3357 * q^44 + 1788 * q^46 - 3428 * q^49 + 6375 * q^50 - 1438 * q^52 + 5044 * q^53 - 7506 * q^56 + 4064 * q^58 + 2 * q^61 + 9162 * q^62 + 4513 * q^64 - 2014 * q^65 - 11405 * q^68 - 3666 * q^70 - 1708 * q^73 + 14620 * q^74 - 1581 * q^76 - 3942 * q^77 - 22760 * q^80 - 4243 * q^82 + 1252 * q^85 + 22113 * q^86 - 1995 * q^88 - 6524 * q^89 - 30294 * q^92 - 7524 * q^94 - 5638 * q^97 + 46469 * q^98

Introduction

L-functions

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