LMFDB - Embedded newform 324.5.d.e.163.15

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			163.15
Character	$\chi$	$=$	324.163
Dual form			324.5.d.e.163.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +O(q^{10})$	\(q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +(-81.9341 + 167.841i) q^{10} -73.6273i q^{11} -31.1848 q^{13} +(217.645 + 106.246i) q^{14} +(-62.2781 + 248.309i) q^{16} -53.8013 q^{17} -54.9619i q^{19} +(459.544 + 589.035i) q^{20} +(-264.658 - 129.197i) q^{22} -281.589i q^{23} +1555.25 q^{25} +(-54.7210 + 112.096i) q^{26} +(763.818 - 595.904i) q^{28} +447.195 q^{29} +277.802i q^{31} +(783.282 + 659.580i) q^{32} +(-94.4072 + 193.392i) q^{34} -2827.19i q^{35} +1016.51 q^{37} +(-197.564 - 96.4437i) q^{38} +(2923.70 - 618.259i) q^{40} -1892.32 q^{41} -769.338i q^{43} +(-928.811 + 724.625i) q^{44} +(-1012.19 - 494.115i) q^{46} -2742.20i q^{47} -1265.09 q^{49} +(2729.05 - 5590.44i) q^{50} +(306.914 + 393.397i) q^{52} +4647.69 q^{53} +3437.89i q^{55} +(-801.714 - 3791.25i) q^{56} +(784.709 - 1607.47i) q^{58} -303.446i q^{59} +956.348 q^{61} +(998.577 + 487.469i) q^{62} +(3745.36 - 1658.17i) q^{64} +1456.11 q^{65} +6940.86i q^{67} +(529.502 + 678.706i) q^{68} +(-10162.5 - 4960.97i) q^{70} +5971.60i q^{71} -4339.17 q^{73} +(1783.71 - 3653.92i) q^{74} +(-693.346 + 540.924i) q^{76} +4458.01 q^{77} +3803.76i q^{79} +(2907.96 - 11594.3i) q^{80} +(-3320.52 + 6802.05i) q^{82} +3153.07i q^{83} +2512.15 q^{85} +(-2765.44 - 1349.99i) q^{86} +(974.892 + 4610.20i) q^{88} +7132.44 q^{89} -1888.18i q^{91} +(-3552.26 + 2771.34i) q^{92} +(-9857.00 - 4811.83i) q^{94} +2566.34i q^{95} -1960.81 q^{97} +(-2219.91 + 4547.46i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.75474	−	3.59457i	0.438684	−	0.898641i
$2$	1.75474	−	3.59457i	0.438684	−	0.898641i
$3$		0			0
$3$		0			0
$4$	−9.84180	−	12.6150i	−0.615112	−	0.788440i
$5$	−46.6931			−1.86772			−0.933862	−	0.357633i	$-0.883584\pi$
$5$	−46.6931			−1.86772			−0.933862	+	0.357633i	$0.883584\pi$
$6$		0			0
$7$			60.5483i			1.23568i	0.786304	+	0.617839i	$0.211992\pi$
$7$			60.5483i			1.23568i	−0.786304	+	0.617839i	$0.788008\pi$
$8$	−62.6153	+	13.2409i	−0.978364	+	0.206889i
$9$		0			0
$10$	−81.9341	+	167.841i	−0.819341	+	1.67841i
$11$		−	73.6273i		−	0.608490i	−0.952594	−	0.304245i	$-0.901596\pi$
$11$		−	73.6273i		−	0.608490i	0.952594	−	0.304245i	$-0.0984042\pi$
$12$		0			0
$13$	−31.1848			−0.184525			−0.0922626	−	0.995735i	$-0.529410\pi$
$13$	−31.1848			−0.184525			−0.0922626	+	0.995735i	$0.529410\pi$
$14$	217.645	+	106.246i	1.11043	+	0.542073i
$15$		0			0
$16$	−62.2781	+	248.309i	−0.243274	+	0.969958i
$17$	−53.8013			−0.186164			−0.0930819	−	0.995658i	$-0.529672\pi$
$17$	−53.8013			−0.186164			−0.0930819	+	0.995658i	$0.529672\pi$
$18$		0			0
$19$		−	54.9619i		−	0.152249i	−0.997098	−	0.0761245i	$-0.975745\pi$
$19$		−	54.9619i		−	0.152249i	0.997098	−	0.0761245i	$-0.0242546\pi$
$20$	459.544	+	589.035i	1.14886	+	1.47259i
$21$		0			0
$22$	−264.658	−	129.197i	−0.546814	−	0.266935i
$23$		−	281.589i		−	0.532305i	−0.963931	−	0.266152i	$-0.914248\pi$
$23$		−	281.589i		−	0.532305i	0.963931	−	0.266152i	$-0.0857525\pi$
$24$		0			0
$25$	1555.25			2.48840
$26$	−54.7210	+	112.096i	−0.0809483	+	0.165822i
$27$		0			0
$28$	763.818	−	595.904i	0.974258	−	0.760081i
$29$	447.195			0.531742			0.265871	−	0.964009i	$-0.414341\pi$
$29$	447.195			0.531742			0.265871	+	0.964009i	$0.414341\pi$
$30$		0			0
$31$			277.802i			0.289076i	0.989499	+	0.144538i	$0.0461696\pi$
$31$			277.802i			0.289076i	−0.989499	+	0.144538i	$0.953830\pi$
$32$	783.282	+	659.580i	0.764923	+	0.644121i
$33$		0			0
$34$	−94.4072	+	193.392i	−0.0816671	+	0.167294i
$35$		−	2827.19i		−	2.30791i
$36$		0			0
$37$	1016.51			0.742522			0.371261	−	0.928528i	$-0.378925\pi$
$37$	1016.51			0.742522			0.371261	+	0.928528i	$0.378925\pi$
$38$	−197.564	−	96.4437i	−0.136817	−	0.0667892i
$39$		0			0
$40$	2923.70	−	618.259i	1.82732	−	0.386412i
$41$	−1892.32			−1.12571			−0.562854	−	0.826556i	$-0.690297\pi$
$41$	−1892.32			−1.12571			−0.562854	+	0.826556i	$0.690297\pi$
$42$		0			0
$43$		−	769.338i		−	0.416083i	−0.978120	−	0.208042i	$-0.933291\pi$
$43$		−	769.338i		−	0.416083i	0.978120	−	0.208042i	$-0.0667090\pi$
$44$	−928.811	+	724.625i	−0.479758	+	0.374290i
$45$		0			0
$46$	−1012.19	−	494.115i	−0.478351	−	0.233514i
$47$		−	2742.20i		−	1.24137i	−0.784058	−	0.620687i	$-0.786854\pi$
$47$		−	2742.20i		−	1.24137i	0.784058	−	0.620687i	$-0.213146\pi$
$48$		0			0
$49$	−1265.09			−0.526902
$50$	2729.05	−	5590.44i	1.09162	−	2.23617i
$51$		0			0
$52$	306.914	+	393.397i	0.113504	+	0.145487i
$53$	4647.69			1.65457			0.827286	−	0.561780i	$-0.189883\pi$
$53$	4647.69			1.65457			0.827286	+	0.561780i	$0.189883\pi$
$54$		0			0
$55$			3437.89i			1.13649i
$56$	−801.714	−	3791.25i	−0.255649	−	1.20894i
$57$		0			0
$58$	784.709	−	1607.47i	0.233267	−	0.477845i
$59$		−	303.446i		−	0.0871722i	−0.999050	−	0.0435861i	$-0.986122\pi$
$59$		−	303.446i		−	0.0871722i	0.999050	−	0.0435861i	$-0.0138783\pi$
$60$		0			0
$61$	956.348			0.257014			0.128507	−	0.991709i	$-0.458982\pi$
$61$	956.348			0.257014			0.128507	+	0.991709i	$0.458982\pi$
$62$	998.577	+	487.469i	0.259776	+	0.126813i
$63$		0			0
$64$	3745.36	−	1658.17i	0.914394	−	0.404826i
$65$	1456.11			0.344642
$66$		0			0
$67$			6940.86i			1.54619i	0.634289	+	0.773096i	$0.281293\pi$
$67$			6940.86i			1.54619i	−0.634289	+	0.773096i	$0.718707\pi$
$68$	529.502	+	678.706i	0.114512	+	0.146779i
$69$		0			0
$70$	−10162.5	−	4960.97i	−2.07398	−	1.01244i
$71$			5971.60i			1.18461i	0.805715	+	0.592303i	$0.201781\pi$
$71$			5971.60i			1.18461i	−0.805715	+	0.592303i	$0.798219\pi$
$72$		0			0
$73$	−4339.17			−0.814257			−0.407128	−	0.913371i	$-0.633470\pi$
$73$	−4339.17			−0.814257			−0.407128	+	0.913371i	$0.633470\pi$
$74$	1783.71	−	3653.92i	0.325733	−	0.667261i
$75$		0			0
$76$	−693.346	+	540.924i	−0.120039	+	0.0936502i
$77$	4458.01			0.751898
$78$		0			0
$79$			3803.76i			0.609479i	0.952436	+	0.304740i	$0.0985694\pi$
$79$			3803.76i			0.609479i	−0.952436	+	0.304740i	$0.901431\pi$
$80$	2907.96	−	11594.3i	0.454369	−	1.81161i
$81$		0			0
$82$	−3320.52	+	6802.05i	−0.493831	+	1.01161i
$83$			3153.07i			0.457696i	0.973462	+	0.228848i	$0.0734958\pi$
$83$			3153.07i			0.457696i	−0.973462	+	0.228848i	$0.926504\pi$
$84$		0			0
$85$	2512.15			0.347703
$86$	−2765.44	−	1349.99i	−0.373910	−	0.182529i
$87$		0			0
$88$	974.892	+	4610.20i	0.125890	+	0.595325i
$89$	7132.44			0.900447			0.450224	−	0.892916i	$-0.351344\pi$
$89$	7132.44			0.900447			0.450224	+	0.892916i	$0.351344\pi$
$90$		0			0
$91$		−	1888.18i		−	0.228014i
$92$	−3552.26	+	2771.34i	−0.419690	+	0.327427i
$93$		0			0
$94$	−9857.00	−	4811.83i	−1.11555	−	0.544571i
$95$			2566.34i			0.284359i
$96$		0			0
$97$	−1960.81			−0.208397			−0.104199	−	0.994557i	$-0.533228\pi$
$97$	−1960.81			−0.208397			−0.104199	+	0.994557i	$0.533228\pi$
$98$	−2219.91	+	4547.46i	−0.231144	+	0.473496i
$99$		0			0
$100$	−15306.4	−	19619.5i	−1.53064	−	1.96195i
$101$	7699.91			0.754820			0.377410	−	0.926046i	$-0.376815\pi$
$101$	7699.91			0.754820			0.377410	+	0.926046i	$0.376815\pi$
$102$		0			0
$103$		−	3689.52i		−	0.347772i	−0.984766	−	0.173886i	$-0.944367\pi$
$103$		−	3689.52i		−	0.347772i	0.984766	−	0.173886i	$-0.0556325\pi$
$104$	1952.64	−	412.914i	0.180533	−	0.0381763i
$105$		0			0
$106$	8155.48	−	16706.4i	0.725835	−	1.48687i
$107$		−	13741.5i		−	1.20024i	−0.799911	−	0.600118i	$-0.795120\pi$
$107$		−	13741.5i		−	1.20024i	0.799911	−	0.600118i	$-0.204880\pi$
$108$		0			0
$109$	18709.9			1.57478			0.787388	−	0.616458i	$-0.211433\pi$
$109$	18709.9			1.57478			0.787388	+	0.616458i	$0.211433\pi$
$110$	12357.7	+	6032.59i	1.02130	+	0.498561i
$111$		0			0
$112$	−15034.7	−	3770.83i	−1.19856	−	0.300608i
$113$	10001.0			0.783225			0.391613	−	0.920130i	$-0.371917\pi$
$113$	10001.0			0.783225			0.391613	+	0.920130i	$0.371917\pi$
$114$		0			0
$115$			13148.3i			0.994199i
$116$	−4401.20	−	5641.38i	−0.327081	−	0.419246i
$117$		0			0
$118$	−1090.76	−	532.469i	−0.0783366	−	0.0382411i
$119$		−	3257.58i		−	0.230039i
$120$		0			0
$121$	9220.02			0.629740
$122$	1678.14	−	3437.66i	0.112748	−	0.230963i
$123$		0			0
$124$	3504.48	−	2734.07i	0.227919	−	0.177814i
$125$	−43436.1			−2.77991
$126$		0			0
$127$			18883.8i			1.17080i	0.810745	+	0.585400i	$0.199063\pi$
$127$			18883.8i			1.17080i	−0.810745	+	0.585400i	$0.800937\pi$
$128$	611.727	−	16372.6i	0.0373369	−	0.999303i
$129$		0			0
$130$	2555.10	−	5234.09i	0.151189	−	0.309710i
$131$		−	29676.9i		−	1.72932i	−0.502358	−	0.864660i	$-0.667534\pi$
$131$		−	29676.9i		−	1.72932i	0.502358	−	0.864660i	$-0.332466\pi$
$132$		0			0
$133$	3327.85			0.188131
$134$	24949.4	+	12179.4i	1.38947	+	0.678290i
$135$		0			0
$136$	3368.79	−	712.379i	0.182136	−	0.0385153i
$137$	−16665.6			−0.887931			−0.443965	−	0.896044i	$-0.646429\pi$
$137$	−16665.6			−0.887931			−0.443965	+	0.896044i	$0.646429\pi$
$138$		0			0
$139$		−	4094.51i		−	0.211920i	−0.994370	−	0.105960i	$-0.966208\pi$
$139$		−	4094.51i		−	0.211920i	0.994370	−	0.105960i	$-0.0337915\pi$
$140$	−35665.1	+	27824.6i	−1.81965	+	1.41962i
$141$		0			0
$142$	21465.3	+	10478.6i	1.06454	+	0.519668i
$143$			2296.05i			0.112282i
$144$		0			0
$145$	−20880.9			−0.993147
$146$	−7614.11	+	15597.4i	−0.357202	+	0.731725i
$147$		0			0
$148$	−10004.3	−	12823.3i	−0.456735	−	0.585434i
$149$	5869.18			0.264365			0.132183	−	0.991225i	$-0.457801\pi$
$149$	5869.18			0.264365			0.132183	+	0.991225i	$0.457801\pi$
$150$		0			0
$151$			33169.5i			1.45474i	0.686246	+	0.727369i	$0.259257\pi$
$151$			33169.5i			1.45474i	−0.686246	+	0.727369i	$0.740743\pi$
$152$	727.745	+	3441.46i	0.0314987	+	0.148955i
$153$		0			0
$154$	7822.63	−	16024.6i	0.329846	−	0.675687i
$155$		−	12971.4i		−	0.539914i
$156$		0			0
$157$	22178.5			0.899772			0.449886	−	0.893086i	$-0.351465\pi$
$157$	22178.5			0.899772			0.449886	+	0.893086i	$0.351465\pi$
$158$	13672.9	+	6674.60i	0.547703	+	0.267369i
$159$		0			0
$160$	−36573.9	−	30797.8i	−1.42867	−	1.20304i
$161$	17049.7			0.657758
$162$		0			0
$163$			31303.8i			1.17821i	0.808057	+	0.589104i	$0.200519\pi$
$163$			31303.8i			1.17821i	−0.808057	+	0.589104i	$0.799481\pi$
$164$	18623.8	+	23871.6i	0.692437	+	0.887553i
$165$		0			0
$166$	11333.9	+	5532.80i	0.411304	+	0.200784i
$167$			26040.4i			0.933717i	0.884332	+	0.466858i	$0.154614\pi$
$167$			26040.4i			0.933717i	−0.884332	+	0.466858i	$0.845386\pi$
$168$		0			0
$169$	−27588.5			−0.965950
$170$	4408.17	−	9030.10i	0.152532	−	0.312460i
$171$		0			0
$172$	−9705.23	+	7571.67i	−0.328057	+	0.255938i
$173$	−15660.8			−0.523264			−0.261632	−	0.965168i	$-0.584261\pi$
$173$	−15660.8			−0.523264			−0.261632	+	0.965168i	$0.584261\pi$
$174$		0			0
$175$			94167.5i			3.07486i
$176$	18282.3	+	4585.37i	0.590210	+	0.148030i
$177$		0			0
$178$	12515.6	−	25638.0i	0.395012	−	0.809179i
$179$			36836.7i			1.14967i	0.818268	+	0.574837i	$0.194935\pi$
$179$			36836.7i			1.14967i	−0.818268	+	0.574837i	$0.805065\pi$
$180$		0			0
$181$	56961.0			1.73868			0.869342	−	0.494211i	$-0.164543\pi$
$181$	56961.0			1.73868			0.869342	+	0.494211i	$0.164543\pi$
$182$	−6787.20	−	3313.26i	−0.204903	−	0.100026i
$183$		0			0
$184$	3728.50	+	17631.8i	0.110128	+	0.520788i
$185$	−47464.2			−1.38683
$186$		0			0
$187$			3961.25i			0.113279i
$188$	−34592.9	+	26988.1i	−0.978749	+	0.763584i
$189$		0			0
$190$	9224.88	+	4503.26i	0.255537	+	0.124744i
$191$			39071.7i			1.07102i	0.844530	+	0.535508i	$0.179880\pi$
$191$			39071.7i			1.07102i	−0.844530	+	0.535508i	$0.820120\pi$
$192$		0			0
$193$	4051.93			0.108780			0.0543898	−	0.998520i	$-0.482679\pi$
$193$	4051.93			0.108780			0.0543898	+	0.998520i	$0.482679\pi$
$194$	−3440.71	+	7048.26i	−0.0914206	+	0.187274i
$195$		0			0
$196$	12450.8	+	15959.2i	0.324104	+	0.415431i
$197$	44869.6			1.15617			0.578083	−	0.815978i	$-0.303801\pi$
$197$	44869.6			1.15617			0.578083	+	0.815978i	$0.303801\pi$
$198$		0			0
$199$		−	56256.7i		−	1.42059i	−0.703905	−	0.710294i	$-0.748562\pi$
$199$		−	56256.7i		−	1.42059i	0.703905	−	0.710294i	$-0.251438\pi$
$200$	−97382.3	+	20592.9i	−2.43456	+	0.514822i
$201$		0			0
$202$	13511.3	−	27677.8i	0.331127	−	0.678312i
$203$			27076.9i			0.657062i
$204$		0			0
$205$	88358.1			2.10251
$206$	−13262.2	−	6474.13i	−0.312523	−	0.152562i
$207$		0			0
$208$	1942.13	−	7743.46i	0.0448902	−	0.178982i
$209$	−4046.70			−0.0926420
$210$		0			0
$211$		−	73103.9i		−	1.64201i	−0.570921	−	0.821005i	$-0.693414\pi$
$211$		−	73103.9i		−	1.64201i	0.570921	−	0.821005i	$-0.306586\pi$
$212$	−45741.7	−	58630.8i	−1.01775	−	1.30453i
$213$		0			0
$214$	−49394.7	−	24112.7i	−1.07858	−	0.526525i
$215$			35922.8i			0.777129i
$216$		0			0
$217$	−16820.4			−0.357205
$218$	32831.0	−	67254.0i	0.690829	−	1.41516i
$219$		0			0
$220$	43369.1	−	33835.0i	0.896055	−	0.699070i
$221$	1677.78			0.0343519
$222$		0			0
$223$		−	75906.6i		−	1.52641i	−0.646159	−	0.763203i	$-0.723626\pi$
$223$		−	75906.6i		−	1.52641i	0.646159	−	0.763203i	$-0.276374\pi$
$224$	−39936.4	+	47426.3i	−0.795927	+	0.945200i
$225$		0			0
$226$	17549.1	−	35949.3i	0.343589	−	0.703839i
$227$			41237.3i			0.800273i	0.916456	+	0.400136i	$0.131037\pi$
$227$			41237.3i			0.800273i	−0.916456	+	0.400136i	$0.868963\pi$
$228$		0			0
$229$	27584.3			0.526005			0.263003	−	0.964795i	$-0.415287\pi$
$229$	27584.3			0.526005			0.263003	+	0.964795i	$0.415287\pi$
$230$	47262.4	+	23071.8i	0.893428	+	0.436139i
$231$		0			0
$232$	−28001.2	+	5921.26i	−0.520237	+	0.110012i
$233$	−49430.2			−0.910502			−0.455251	−	0.890363i	$-0.650450\pi$
$233$	−49430.2			−0.910502			−0.455251	+	0.890363i	$0.650450\pi$
$234$		0			0
$235$			128042.i			2.31855i
$236$	−3827.99	+	2986.46i	−0.0687300	+	0.0536207i
$237$		0			0
$238$	−11709.6	−	5716.19i	−0.206722	−	0.100914i
$239$			112055.i			1.96172i	0.194717	+	0.980859i	$0.437621\pi$
$239$			112055.i			1.96172i	−0.194717	+	0.980859i	$0.562379\pi$
$240$		0			0
$241$	41096.6			0.707573			0.353787	−	0.935326i	$-0.384894\pi$
$241$	41096.6			0.707573			0.353787	+	0.935326i	$0.384894\pi$
$242$	16178.7	−	33142.0i	0.276257	−	0.565910i
$243$		0			0
$244$	−9412.18	−	12064.4i	−0.158092	−	0.202640i
$245$	59071.1			0.984109
$246$		0			0
$247$			1713.97i			0.0280938i
$248$	−3678.35	−	17394.7i	−0.0598067	−	0.282822i
$249$		0			0
$250$	−76219.0	+	156134.i	−1.21950	+	2.49814i
$251$		−	50848.1i		−	0.807099i	−0.914958	−	0.403550i	$-0.867776\pi$
$251$		−	50848.1i		−	0.807099i	0.914958	−	0.403550i	$-0.132224\pi$
$252$		0			0
$253$	−20732.7			−0.323902
$254$	67879.2	+	33136.2i	1.05213	+	0.513612i
$255$		0			0
$256$	−57778.9	−	30928.5i	−0.881636	−	0.471931i
$257$	−12810.0			−0.193948			−0.0969738	−	0.995287i	$-0.530916\pi$
$257$	−12810.0			−0.193948			−0.0969738	+	0.995287i	$0.530916\pi$
$258$		0			0
$259$			61548.1i			0.917519i
$260$	−14330.8	−	18368.9i	−0.211994	−	0.271730i
$261$		0			0
$262$	−106675.	−	52075.1i	−1.55404	−	0.758625i
$263$		−	31691.3i		−	0.458172i	−0.973406	−	0.229086i	$-0.926426\pi$
$263$		−	31691.3i		−	0.458172i	0.973406	−	0.229086i	$-0.0735737\pi$
$264$		0			0
$265$	−217015.			−3.09029
$266$	5839.50	−	11962.2i	0.0825301	−	0.169062i
$267$		0			0
$268$	87559.1	−	68310.5i	1.21908	−	0.951082i
$269$	54892.9			0.758598			0.379299	−	0.925274i	$-0.376165\pi$
$269$	54892.9			0.758598			0.379299	+	0.925274i	$0.376165\pi$
$270$		0			0
$271$		−	106332.i		−	1.44785i	−0.689877	−	0.723927i	$-0.742335\pi$
$271$		−	106332.i		−	1.44785i	0.689877	−	0.723927i	$-0.257665\pi$
$272$	3350.65	−	13359.4i	0.0452888	−	0.180571i
$273$		0			0
$274$	−29243.7	+	59905.5i	−0.389521	+	0.797931i
$275$		−	114509.i		−	1.51416i
$276$		0			0
$277$	−50333.1			−0.655986			−0.327993	−	0.944680i	$-0.606372\pi$
$277$	−50333.1			−0.655986			−0.327993	+	0.944680i	$0.606372\pi$
$278$	−14718.0	−	7184.78i	−0.190440	−	0.0929660i
$279$		0			0
$280$	37434.5	+	177025.i	0.477481	+	2.25797i
$281$	6096.41			0.0772078			0.0386039	−	0.999255i	$-0.487709\pi$
$281$	6096.41			0.0772078			0.0386039	+	0.999255i	$0.487709\pi$
$282$		0			0
$283$			51378.2i			0.641513i	0.947162	+	0.320757i	$0.103937\pi$
$283$			51378.2i			0.641513i	−0.947162	+	0.320757i	$0.896063\pi$
$284$	75331.9	−	58771.3i	0.933990	−	0.728666i
$285$		0			0
$286$	8253.30	+	4028.96i	0.100901	+	0.0492562i
$287$		−	114576.i		−	1.39101i
$288$		0			0
$289$	−80626.4			−0.965343
$290$	−36640.5	+	75057.8i	−0.435678	+	0.892483i
$291$		0			0
$292$	42705.3	+	54738.8i	0.500859	+	0.641992i
$293$	−91281.3			−1.06328			−0.531639	−	0.846971i	$-0.678424\pi$
$293$	−91281.3			−1.06328			−0.531639	+	0.846971i	$0.678424\pi$
$294$		0			0
$295$			14168.9i			0.162814i
$296$	−63649.3	+	13459.6i	−0.726457	+	0.153620i
$297$		0			0
$298$	10298.9	−	21097.1i	0.115973	−	0.237570i
$299$			8781.29i			0.0982236i
$300$		0			0
$301$	46582.1			0.514145
$302$	119230.	+	58203.8i	1.30729	+	0.638171i
$303$		0			0
$304$	13647.5	+	3422.92i	0.147675	+	0.0370382i
$305$	−44654.9			−0.480031
$306$		0			0
$307$		−	108180.i		−	1.14781i	−0.818923	−	0.573904i	$-0.805428\pi$
$307$		−	108180.i		−	1.14781i	0.818923	−	0.573904i	$-0.194572\pi$
$308$	−43874.8	−	56237.9i	−0.462502	−	0.592826i
$309$		0			0
$310$	−46626.7	−	22761.5i	−0.485189	−	0.236852i
$311$		−	100082.i		−	1.03475i	−0.855760	−	0.517373i	$-0.826910\pi$
$311$		−	100082.i		−	1.03475i	0.855760	−	0.517373i	$-0.173090\pi$
$312$		0			0
$313$	−151791.			−1.54937			−0.774687	−	0.632345i	$-0.782093\pi$
$313$	−151791.			−1.54937			−0.774687	+	0.632345i	$0.782093\pi$
$314$	38917.4	−	79722.0i	0.394716	−	0.808572i
$315$		0			0
$316$	47984.5	−	37435.8i	0.480537	−	0.374898i
$317$	−112404.			−1.11857			−0.559285	−	0.828976i	$-0.688924\pi$
$317$	−112404.			−1.11857			−0.559285	+	0.828976i	$0.688924\pi$
$318$		0			0
$319$		−	32925.7i		−	0.323560i
$320$	−174882.	+	77425.0i	−1.70784	+	0.756103i
$321$		0			0
$322$	29917.8	−	61286.4i	0.288548	−	0.591088i
$323$			2957.02i			0.0283433i
$324$		0			0
$325$	−48500.0			−0.459172
$326$	112524.	+	54929.9i	1.05879	+	0.516861i
$327$		0			0
$328$	118488.	−	25056.0i	1.10135	−	0.232897i
$329$	166035.			1.53394
$330$		0			0
$331$		−	114926.i		−	1.04897i	−0.851420	−	0.524484i	$-0.824258\pi$
$331$		−	114926.i		−	1.04897i	0.851420	−	0.524484i	$-0.175742\pi$
$332$	39776.0	−	31031.8i	0.360865	−	0.281534i
$333$		0			0
$334$	93604.0	+	45694.1i	0.839076	+	0.409607i
$335$		−	324090.i		−	2.88786i
$336$		0			0
$337$	123292.			1.08562			0.542808	−	0.839857i	$-0.317361\pi$
$337$	123292.			1.08562			0.542808	+	0.839857i	$0.317361\pi$
$338$	−48410.6	+	99168.7i	−0.423747	+	0.868043i
$339$		0			0
$340$	−24724.1	−	31690.9i	−0.213876	−	0.274143i
$341$	20453.8			0.175900
$342$		0			0
$343$			68777.2i			0.584597i
$344$	10186.7	+	48172.4i	0.0860831	+	0.407081i
$345$		0			0
$346$	−27480.5	+	56293.6i	−0.229548	+	0.470227i
$347$		−	95659.4i		−	0.794454i	−0.917720	−	0.397227i	$-0.869973\pi$
$347$		−	95659.4i		−	0.794454i	0.917720	−	0.397227i	$-0.130027\pi$
$348$		0			0
$349$	43087.1			0.353750			0.176875	−	0.984233i	$-0.443401\pi$
$349$	43087.1			0.353750			0.176875	+	0.984233i	$0.443401\pi$
$350$	338491.	+	165239.i	2.76319	+	1.34889i
$351$		0			0
$352$	48563.1	−	57670.9i	0.391941	−	0.465448i
$353$	112874.			0.905825			0.452912	−	0.891555i	$-0.350385\pi$
$353$	112874.			0.905825			0.452912	+	0.891555i	$0.350385\pi$
$354$		0			0
$355$		−	278833.i		−	2.21252i
$356$	−70196.1	−	89976.0i	−0.553876	−	0.709948i
$357$		0			0
$358$	132412.	+	64638.8i	1.03315	+	0.504344i
$359$			223134.i			1.73132i	0.500632	+	0.865660i	$0.333101\pi$
$359$			223134.i			1.73132i	−0.500632	+	0.865660i	$0.666899\pi$
$360$		0			0
$361$	127300.			0.976820
$362$	99951.6	−	204750.i	0.762733	−	1.56245i
$363$		0			0
$364$	−23819.5	+	18583.1i	−0.179775	+	0.140254i
$365$	202610.			1.52081
$366$		0			0
$367$		−	106530.i		−	0.790933i	−0.918481	−	0.395466i	$-0.870583\pi$
$367$		−	106530.i		−	0.790933i	0.918481	−	0.395466i	$-0.129417\pi$
$368$	69921.2	+	17536.9i	0.516313	+	0.129496i
$369$		0			0
$370$	−83287.1	+	170613.i	−0.608379	+	1.24626i
$371$			281410.i			2.04452i
$372$		0			0
$373$	142881.			1.02697			0.513484	−	0.858099i	$-0.328355\pi$
$373$	142881.			1.02697			0.513484	+	0.858099i	$0.328355\pi$
$374$	14239.0	+	6950.95i	0.101797	+	0.0496936i
$375$		0			0
$376$	36309.2	+	171703.i	0.256827	+	1.21452i
$377$	−13945.7			−0.0981197
$378$		0			0
$379$		−	95242.7i		−	0.663061i	−0.943445	−	0.331530i	$-0.892435\pi$
$379$		−	95242.7i		−	0.663061i	0.943445	−	0.331530i	$-0.107565\pi$
$380$	32374.5	−	25257.4i	0.224200	−	0.174913i
$381$		0			0
$382$	140446.	+	68560.6i	0.962459	+	0.469838i
$383$			54154.9i			0.369182i	0.982815	+	0.184591i	$0.0590960\pi$
$383$			54154.9i			0.369182i	−0.982815	+	0.184591i	$0.940904\pi$
$384$		0			0
$385$	−208158.			−1.40434
$386$	7110.07	−	14564.9i	0.0477199	−	0.0977538i
$387$		0			0
$388$	19297.9	+	24735.7i	0.128188	+	0.164309i
$389$	−13026.5			−0.0860850			−0.0430425	−	0.999073i	$-0.513705\pi$
$389$	−13026.5			−0.0860850			−0.0430425	+	0.999073i	$0.513705\pi$
$390$		0			0
$391$			15149.9i			0.0990959i
$392$	79214.2	−	16751.0i	0.515503	−	0.109010i
$393$		0			0
$394$	78734.4	−	161287.i	0.507191	−	1.03898i
$395$		−	177609.i		−	1.13834i
$396$		0			0
$397$	54407.2			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$397$	54407.2			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$398$	−202218.	−	98715.7i	−1.27660	−	0.623190i
$399$		0			0
$400$	−96857.9	+	386182.i	−0.605362	+	2.41364i
$401$	−50422.4			−0.313570			−0.156785	−	0.987633i	$-0.550113\pi$
$401$	−50422.4			−0.313570			−0.156785	+	0.987633i	$0.550113\pi$
$402$		0			0
$403$		−	8663.19i		−	0.0533418i
$404$	−75781.0	−	97134.7i	−0.464299	−	0.595130i
$405$		0			0
$406$	97329.6	+	47512.8i	0.590463	+	0.288243i
$407$		−	74843.1i		−	0.451817i
$408$		0			0
$409$	40833.8			0.244103			0.122052	−	0.992524i	$-0.461053\pi$
$409$	40833.8			0.244103			0.122052	+	0.992524i	$0.461053\pi$
$410$	155045.	−	317609.i	0.922340	−	1.88941i
$411$		0			0
$412$	−46543.4	+	36311.5i	−0.274198	+	0.213919i
$413$	18373.2			0.107717
$414$		0			0
$415$		−	147226.i		−	0.854850i
$416$	−24426.4	−	20568.8i	−0.141148	−	0.118857i
$417$		0			0
$418$	−7100.89	+	14546.1i	−0.0406406	+	0.0832519i
$419$			33332.6i			0.189864i	0.995484	+	0.0949318i	$0.0302633\pi$
$419$			33332.6i			0.189864i	−0.995484	+	0.0949318i	$0.969737\pi$
$420$		0			0
$421$	8360.62			0.0471709			0.0235855	−	0.999722i	$-0.492492\pi$
$421$	8360.62			0.0471709			0.0235855	+	0.999722i	$0.492492\pi$
$422$	−262777.	−	128278.i	−1.47558	−	0.720324i
$423$		0			0
$424$	−291017.	+	61539.7i	−1.61877	+	0.342313i
$425$	−83674.4			−0.463249
$426$		0			0
$427$			57905.2i			0.317586i
$428$	−173350.	+	135241.i	−0.946314	+	0.738280i
$429$		0			0
$430$	129127.	+	63035.1i	0.698360	+	0.340914i
$431$		−	88445.3i		−	0.476124i	−0.971250	−	0.238062i	$-0.923488\pi$
$431$		−	88445.3i		−	0.476124i	0.971250	−	0.238062i	$-0.0765122\pi$
$432$		0			0
$433$	119092.			0.635195			0.317598	−	0.948226i	$-0.397124\pi$
$433$	119092.			0.635195			0.317598	+	0.948226i	$0.397124\pi$
$434$	−29515.4	+	60462.1i	−0.156700	+	0.320999i
$435$		0			0
$436$	−184139.	−	236026.i	−0.968664	−	1.24162i
$437$	−15476.7			−0.0810429
$438$		0			0
$439$			119492.i			0.620028i	0.950732	+	0.310014i	$0.100334\pi$
$439$			119492.i			0.620028i	−0.950732	+	0.310014i	$0.899666\pi$
$440$	−45520.7	−	215264.i	−0.235128	−	1.11190i
$441$		0			0
$442$	2944.07	−	6030.90i	0.0150696	−	0.0308700i
$443$			203706.i			1.03800i	0.854776	+	0.518998i	$0.173695\pi$
$443$			203706.i			1.03800i	−0.854776	+	0.518998i	$0.826305\pi$
$444$		0			0
$445$	−333036.			−1.68179
$446$	−272851.	−	133196.i	−1.37169	−	0.669610i
$447$		0			0
$448$	100399.	+	226775.i	0.500235	+	1.12990i
$449$	−77156.2			−0.382717			−0.191359	−	0.981520i	$-0.561289\pi$
$449$	−77156.2			−0.382717			−0.191359	+	0.981520i	$0.561289\pi$
$450$		0			0
$451$			139326.i			0.684982i
$452$	−98427.8	−	126163.i	−0.481771	−	0.617526i
$453$		0			0
$454$	148230.	+	72360.5i	0.719158	+	0.351067i
$455$			88165.1i			0.425867i
$456$		0			0
$457$	280840.			1.34471			0.672353	−	0.740231i	$-0.265284\pi$
$457$	280840.			1.34471			0.672353	+	0.740231i	$0.265284\pi$
$458$	48403.1	−	99153.4i	0.230750	−	0.472690i
$459$		0			0
$460$	165866.	−	129403.i	0.783866	−	0.611544i
$461$	401621.			1.88980			0.944898	−	0.327365i	$-0.106161\pi$
$461$	401621.			1.88980			0.944898	+	0.327365i	$0.106161\pi$
$462$		0			0
$463$		−	59820.5i		−	0.279054i	−0.990218	−	0.139527i	$-0.955442\pi$
$463$		−	59820.5i		−	0.279054i	0.990218	−	0.139527i	$-0.0445582\pi$
$464$	−27850.5	+	111043.i	−0.129359	+	0.515767i
$465$		0			0
$466$	−86737.1	+	177680.i	−0.399423	+	0.818215i
$467$			208473.i			0.955909i	0.878385	+	0.477955i	$0.158622\pi$
$467$			208473.i			0.955909i	−0.878385	+	0.477955i	$0.841378\pi$
$468$		0			0
$469$	−420257.			−1.91060
$470$	460254.	+	224679.i	2.08354	+	1.01711i
$471$		0			0
$472$	4017.91	+	19000.4i	0.0180350	+	0.0852862i
$473$	−56644.3			−0.253183
$474$		0			0
$475$		−	85479.3i		−	0.378856i
$476$	−41094.5	+	32060.4i	−0.181372	+	0.141500i
$477$		0			0
$478$	402790.	+	196628.i	1.76288	+	0.860575i
$479$		−	160119.i		−	0.697864i	−0.937148	−	0.348932i	$-0.886544\pi$
$479$		−	160119.i		−	0.697864i	0.937148	−	0.348932i	$-0.113456\pi$
$480$		0			0
$481$	−31699.7			−0.137014
$482$	72113.7	−	147724.i	0.310401	−	0.635855i
$483$		0			0
$484$	−90741.6	−	116311.i	−0.387361	−	0.496512i
$485$	91556.4			0.389229
$486$		0			0
$487$		−	371960.i		−	1.56834i	−0.620549	−	0.784168i	$-0.713090\pi$
$487$		−	371960.i		−	1.56834i	0.620549	−	0.784168i	$-0.286910\pi$
$488$	−59882.0	+	12662.9i	−0.251453	+	0.0531734i
$489$		0			0
$490$	103654.	−	212335.i	0.431713	−	0.884361i
$491$			66814.9i			0.277147i	0.990352	+	0.138574i	$0.0442517\pi$
$491$			66814.9i			0.277147i	−0.990352	+	0.138574i	$0.955748\pi$
$492$		0			0
$493$	−24059.7			−0.0989911
$494$	6160.99	+	3007.57i	0.0252462	+	0.0123243i
$495$		0			0
$496$	−68980.8	−	17301.0i	−0.280391	−	0.0703246i
$497$	−361570.			−1.46379
$498$		0			0
$499$		−	332728.i		−	1.33625i	−0.744048	−	0.668127i	$-0.767096\pi$
$499$		−	332728.i		−	1.33625i	0.744048	−	0.668127i	$-0.232904\pi$
$500$	427490.	+	547948.i	1.70996	+	2.19179i
$501$		0			0
$502$	−182777.	−	89225.0i	−0.725293	−	0.354062i
$503$			12673.0i			0.0500892i	0.999686	+	0.0250446i	$0.00797278\pi$
$503$			12673.0i			0.0500892i	−0.999686	+	0.0250446i	$0.992027\pi$
$504$		0			0
$505$	−359533.			−1.40980
$506$	−36380.4	+	74524.9i	−0.142091	+	0.291072i
$507$		0			0
$508$	238220.	−	185851.i	0.923105	−	0.720174i
$509$	38905.4			0.150167			0.0750834	−	0.997177i	$-0.476078\pi$
$509$	38905.4			0.150167			0.0750834	+	0.997177i	$0.476078\pi$
$510$		0			0
$511$		−	262729.i		−	1.00616i
$512$	−212561.	+	153419.i	−0.810856	+	0.585245i
$513$		0			0
$514$	−22478.3	+	46046.5i	−0.0850817	+	0.174289i
$515$			172275.i			0.649543i
$516$		0			0
$517$	−201900.			−0.755364
$518$	221239.	+	108001.i	0.824521	+	0.402501i
$519$		0			0
$520$	−91175.0	+	19280.3i	−0.337186	+	0.0713027i
$521$	−28001.3			−0.103158			−0.0515790	−	0.998669i	$-0.516425\pi$
$521$	−28001.3			−0.103158			−0.0515790	+	0.998669i	$0.516425\pi$
$522$		0			0
$523$			306435.i			1.12030i	0.828391	+	0.560151i	$0.189257\pi$
$523$			306435.i			1.12030i	−0.828391	+	0.560151i	$0.810743\pi$
$524$	−374375.	+	292074.i	−1.36346	+	1.06373i
$525$		0			0
$526$	−113916.	−	55609.9i	−0.411732	−	0.200993i
$527$		−	14946.1i		−	0.0538155i
$528$		0			0
$529$	200548.			0.716652
$530$	−380805.	+	780076.i	−1.35566	+	2.77706i
$531$		0			0
$532$	−32752.0	−	41980.9i	−0.115722	−	0.148330i
$533$	59011.4			0.207722
$534$		0			0
$535$			641634.i			2.24171i
$536$	−91903.2	−	434604.i	−0.319890	−	1.51274i
$537$		0			0
$538$	96322.6	−	197316.i	0.332785	−	0.681707i
$539$			93145.3i			0.320615i
$540$		0			0
$541$	387269.			1.32318			0.661590	−	0.749866i	$-0.269882\pi$
$541$	387269.			1.32318			0.661590	+	0.749866i	$0.269882\pi$
$542$	−382217.	−	186584.i	−1.30110	−	0.635151i
$543$		0			0
$544$	−42141.6	−	35486.3i	−0.142401	−	0.119912i
$545$	−873624.			−2.94125
$546$		0			0
$547$			254245.i			0.849724i	0.905258	+	0.424862i	$0.139677\pi$
$547$			254245.i			0.849724i	−0.905258	+	0.424862i	$0.860323\pi$
$548$	164019.	+	210237.i	0.546177	+	0.700080i
$549$		0			0
$550$	−411609.	−	200933.i	−1.36069	−	0.664240i
$551$		−	24578.7i		−	0.0809571i
$552$		0			0
$553$	−230311.			−0.753120
$554$	−88321.4	+	180926.i	−0.287771	+	0.589496i
$555$		0			0
$556$	−51652.3	+	40297.3i	−0.167086	+	0.130355i
$557$	154243.			0.497159			0.248580	−	0.968611i	$-0.420036\pi$
$557$	154243.			0.497159			0.248580	+	0.968611i	$0.420036\pi$
$558$		0			0
$559$			23991.6i			0.0767779i
$560$	702016.	+	176072.i	2.23857	+	0.561454i
$561$		0			0
$562$	10697.6	−	21913.9i	0.0338699	−	0.0693822i
$563$			217837.i			0.687251i	0.939107	+	0.343626i	$0.111655\pi$
$563$			217837.i			0.687251i	−0.939107	+	0.343626i	$0.888345\pi$
$564$		0			0
$565$	−466978.			−1.46285
$566$	184682.	+	90155.2i	0.576490	+	0.281422i
$567$		0			0
$568$	−79069.4	−	373914.i	−0.245082	−	1.15898i
$569$	−224329.			−0.692886			−0.346443	−	0.938071i	$-0.612611\pi$
$569$	−224329.			−0.692886			−0.346443	+	0.938071i	$0.612611\pi$
$570$		0			0
$571$		−	262311.i		−	0.804535i	−0.915522	−	0.402268i	$-0.868222\pi$
$571$		−	262311.i		−	0.804535i	0.915522	−	0.402268i	$-0.131778\pi$
$572$	28964.7	−	22597.2i	0.0885274	−	0.0690659i
$573$		0			0
$574$	−411852.	−	201052.i	−1.25002	−	0.610216i
$575$		−	437941.i		−	1.32458i
$576$		0			0
$577$	450994.			1.35462			0.677312	−	0.735696i	$-0.263145\pi$
$577$	450994.			1.35462			0.677312	+	0.735696i	$0.263145\pi$
$578$	−141478.	+	289817.i	−0.423481	+	0.867497i
$579$		0			0
$580$	205506.	+	263413.i	0.610897	+	0.783036i
$581$	−190913.			−0.565565
$582$		0			0
$583$		−	342197.i		−	1.00679i
$584$	271699.	−	57454.6i	0.796640	−	0.168461i
$585$		0			0
$586$	−160175.	+	328117.i	−0.466443	+	0.955505i
$587$		−	355346.i		−	1.03128i	−0.856807	−	0.515638i	$-0.827555\pi$
$587$		−	355346.i		−	1.03128i	0.856807	−	0.515638i	$-0.172445\pi$
$588$		0			0
$589$	15268.5			0.0440115
$590$	50930.9	+	24862.6i	0.146311	+	0.0714238i
$591$		0			0
$592$	−63306.5	+	252409.i	−0.180636	+	0.720215i
$593$	−89819.5			−0.255424			−0.127712	−	0.991811i	$-0.540763\pi$
$593$	−89819.5			−0.255424			−0.127712	+	0.991811i	$0.540763\pi$
$594$		0			0
$595$			152106.i			0.429649i
$596$	−57763.2	−	74039.9i	−0.162614	−	0.208436i
$597$		0			0
$598$	31564.9	+	15408.9i	0.0882678	+	0.0430892i
$599$			413022.i			1.15112i	0.817761	+	0.575558i	$0.195215\pi$
$599$			413022.i			1.15112i	−0.817761	+	0.575558i	$0.804785\pi$
$600$		0			0
$601$	258635.			0.716041			0.358020	−	0.933714i	$-0.383452\pi$
$601$	258635.			0.716041			0.358020	+	0.933714i	$0.383452\pi$
$602$	81739.3	−	167442.i	0.225548	−	0.462032i
$603$		0			0
$604$	418434.	−	326447.i	1.14697	−	0.894828i
$605$	−430512.			−1.17618
$606$		0			0
$607$			308801.i			0.838111i	0.907961	+	0.419055i	$0.137639\pi$
$607$			308801.i			0.838111i	−0.907961	+	0.419055i	$0.862361\pi$
$608$	36251.8	−	43050.6i	0.0980668	−	0.116459i
$609$		0			0
$610$	−78357.6	+	160515.i	−0.210582	+	0.431376i
$611$			85514.7i			0.229065i
$612$		0			0
$613$	−464349.			−1.23573			−0.617865	−	0.786284i	$-0.712002\pi$
$613$	−464349.			−1.23573			−0.617865	+	0.786284i	$0.712002\pi$
$614$	−388859.	−	189827.i	−1.03147	−	0.503525i
$615$		0			0
$616$	−279139.	+	59028.0i	−0.735631	+	0.155560i
$617$	507377.			1.33278			0.666392	−	0.745601i	$-0.267838\pi$
$617$	507377.			1.33278			0.666392	+	0.745601i	$0.267838\pi$
$618$		0			0
$619$		−	282768.i		−	0.737986i	−0.929432	−	0.368993i	$-0.879703\pi$
$619$		−	282768.i		−	0.737986i	0.929432	−	0.368993i	$-0.120297\pi$
$620$	−163635.	+	127662.i	−0.425690	+	0.332108i
$621$		0			0
$622$	−359750.	−	175617.i	−0.929865	−	0.453927i
$623$			431857.i			1.11266i
$624$		0			0
$625$	1.05614e6			2.70372
$626$	−266353.	+	545621.i	−0.679686	+	1.39233i
$627$		0			0
$628$	−218276.	−	279782.i	−0.553461	−	0.709416i
$629$	−54689.8			−0.138231
$630$		0			0
$631$			403620.i			1.01371i	0.862031	+	0.506855i	$0.169192\pi$
$631$			403620.i			1.01371i	−0.862031	+	0.506855i	$0.830808\pi$
$632$	−50365.2	−	238174.i	−0.126095	−	0.596293i
$633$		0			0
$634$	−197239.	+	404043.i	−0.490699	+	1.00519i
$635$		−	881745.i		−	2.18673i
$636$		0			0
$637$	39451.6			0.0972267
$638$	−118354.	−	57776.0i	−0.290764	−	0.141940i
$639$		0			0
$640$	−28563.4	+	764487.i	−0.0697350	+	1.86642i
$641$	362055.			0.881168			0.440584	−	0.897711i	$-0.354771\pi$
$641$	362055.			0.881168			0.440584	+	0.897711i	$0.354771\pi$
$642$		0			0
$643$			400278.i			0.968144i	0.875028	+	0.484072i	$0.160843\pi$
$643$			400278.i			0.968144i	−0.875028	+	0.484072i	$0.839157\pi$
$644$	−167800.	−	215083.i	−0.404595	−	0.518602i
$645$		0			0
$646$	10629.2	+	5188.80i	0.0254704	+	0.0124337i
$647$			98990.1i			0.236474i	0.992985	+	0.118237i	$0.0377242\pi$
$647$			98990.1i			0.236474i	−0.992985	+	0.118237i	$0.962276\pi$
$648$		0			0
$649$	−22341.9			−0.0530434
$650$	−85104.7	+	174336.i	−0.201431	+	0.412630i
$651$		0			0
$652$	394898.	−	308086.i	0.928945	−	0.724730i
$653$	538330.			1.26247			0.631237	−	0.775590i	$-0.282547\pi$
$653$	538330.			1.26247			0.631237	+	0.775590i	$0.282547\pi$
$654$		0			0
$655$			1.38570e6i			3.22989i
$656$	117850.	−	469879.i	0.273856	−	1.09189i
$657$		0			0
$658$	291348.	−	596824.i	0.672915	−	1.37846i
$659$		−	145745.i		−	0.335601i	−0.985821	−	0.167801i	$-0.946334\pi$
$659$		−	145745.i		−	0.335601i	0.985821	−	0.167801i	$-0.0536665\pi$
$660$		0			0
$661$	−252352.			−0.577568			−0.288784	−	0.957394i	$-0.593251\pi$
$661$	−252352.			−0.577568			−0.288784	+	0.957394i	$0.593251\pi$
$662$	−413109.	−	201665.i	−0.942646	−	0.460166i
$663$		0			0
$664$	−41749.4	−	197430.i	−0.0946923	−	0.447793i
$665$	−155388.			−0.351377
$666$		0			0
$667$		−	125925.i		−	0.283049i
$668$	328501.	−	256285.i	0.736179	−	0.574341i
$669$		0			0
$670$	−1.16496e6	−	568693.i	−2.59515	−	1.26686i
$671$		−	70413.3i		−	0.156390i
$672$		0			0
$673$	654664.			1.44540			0.722701	−	0.691161i	$-0.242901\pi$
$673$	654664.			1.44540			0.722701	+	0.691161i	$0.242901\pi$
$674$	216346.	−	443182.i	0.476243	−	0.975580i
$675$		0			0
$676$	271520.	+	348030.i	0.594168	+	0.761594i
$677$	213512.			0.465849			0.232924	−	0.972495i	$-0.425171\pi$
$677$	213512.			0.465849			0.232924	+	0.972495i	$0.425171\pi$
$678$		0			0
$679$		−	118724.i		−	0.257512i
$680$	−157299.	+	33263.2i	−0.340180	+	0.0719359i
$681$		0			0
$682$	35891.1	−	73522.5i	0.0771645	−	0.158071i
$683$			885039.i			1.89724i	0.316425	+	0.948618i	$0.397517\pi$
$683$			885039.i			1.89724i	−0.316425	+	0.948618i	$0.602483\pi$
$684$		0			0
$685$	778168.			1.65841
$686$	247224.	+	120686.i	0.525343	+	0.256453i
$687$		0			0
$688$	191034.	+	47912.9i	0.403583	+	0.101222i
$689$	−144937.			−0.305310
$690$		0			0
$691$			441853.i			0.925384i	0.886519	+	0.462692i	$0.153116\pi$
$691$			441853.i			0.925384i	−0.886519	+	0.462692i	$0.846884\pi$
$692$	154130.	+	197561.i	0.321866	+	0.412562i
$693$		0			0
$694$	−343854.	−	167857.i	−0.713929	−	0.348514i
$695$			191185.i			0.395808i
$696$		0			0
$697$	101809.			0.209566
$698$	75606.6	−	154879.i	0.155185	−	0.317894i
$699$		0			0
$700$	1.18793e6	−	926777.i	2.42434	−	1.89138i
$701$	−340679.			−0.693281			−0.346640	−	0.937998i	$-0.612678\pi$
$701$	−340679.			−0.693281			−0.346640	+	0.937998i	$0.612678\pi$
$702$		0			0
$703$		−	55869.5i		−	0.113048i
$704$	−122086.	−	275760.i	−0.246333	−	0.556399i
$705$		0			0
$706$	198064.	−	405733.i	0.397371	−	0.814011i
$707$			466216.i			0.932715i
$708$		0			0
$709$	−585440.			−1.16464			−0.582318	−	0.812961i	$-0.697854\pi$
$709$	−585440.			−1.16464			−0.582318	+	0.812961i	$0.697854\pi$
$710$	−1.00228e6	−	489278.i	−1.98826	−	0.970597i
$711$		0			0
$712$	−446600.	+	94440.0i	−0.880966	+	0.186293i
$713$	78226.1			0.153877
$714$		0			0
$715$		−	107210.i		−	0.209711i
$716$	464697.	−	362540.i	0.906449	−	0.707179i
$717$		0			0
$718$	802071.	+	391542.i	1.55584	+	0.759503i
$719$			306988.i			0.593832i	0.954904	+	0.296916i	$0.0959581\pi$
$719$			306988.i			0.593832i	−0.954904	+	0.296916i	$0.904042\pi$
$720$		0			0
$721$	223394.			0.429735
$722$	223378.	−	457589.i	0.428516	−	0.877811i
$723$		0			0
$724$	−560599.	−	718565.i	−1.06949	−	1.37085i
$725$	695498.			1.32318
$726$		0			0
$727$		−	564049.i		−	1.06721i	−0.845735	−	0.533603i	$-0.820838\pi$
$727$		−	564049.i		−	1.06721i	0.845735	−	0.533603i	$-0.179162\pi$
$728$	25001.2	+	118229.i	0.0471736	+	0.223081i
$729$		0			0
$730$	355526.	−	728293.i	0.667154	−	1.36666i
$731$			41391.4i			0.0774597i
$732$		0			0
$733$	581920.			1.08307			0.541533	−	0.840679i	$-0.317844\pi$
$733$	581920.			1.08307			0.541533	+	0.840679i	$0.317844\pi$
$734$	−382929.	−	186932.i	−0.710765	−	0.346970i
$735$		0			0
$736$	185731.	−	220564.i	0.342869	−	0.407173i
$737$	511037.			0.940843
$738$		0			0
$739$			193774.i			0.354818i	0.984137	+	0.177409i	$0.0567715\pi$
$739$			193774.i			0.354818i	−0.984137	+	0.177409i	$0.943228\pi$
$740$	467133.	+	598762.i	0.853054	+	1.09343i
$741$		0			0
$742$	1.01155e6	+	493800.i	1.83729	+	0.896899i
$743$			88312.5i			0.159972i	0.996796	+	0.0799861i	$0.0254876\pi$
$743$			88312.5i			0.159972i	−0.996796	+	0.0799861i	$0.974512\pi$
$744$		0			0
$745$	−274050.			−0.493762
$746$	250719.	−	513595.i	0.450514	−	0.922875i
$747$		0			0
$748$	49971.3	−	38985.8i	0.0893135	−	0.0696792i
$749$	832024.			1.48311
$750$		0			0
$751$		−	547536.i		−	0.970806i	−0.874290	−	0.485403i	$-0.838673\pi$
$751$		−	547536.i		−	0.970806i	0.874290	−	0.485403i	$-0.161327\pi$
$752$	680912.	+	170779.i	1.20408	+	0.301994i
$753$		0			0
$754$	−24471.0	+	50128.6i	−0.0430436	+	0.0881744i
$755$		−	1.54879e6i		−	2.71705i
$756$		0			0
$757$	−45164.0			−0.0788135			−0.0394068	−	0.999223i	$-0.512547\pi$
$757$	−45164.0			−0.0788135			−0.0394068	+	0.999223i	$0.512547\pi$
$758$	−342356.	−	167126.i	−0.595854	−	0.290874i
$759$		0			0
$760$	−33980.7	−	160692.i	−0.0588308	−	0.278207i
$761$	200370.			0.345989			0.172995	−	0.984923i	$-0.444656\pi$
$761$	200370.			0.345989			0.172995	+	0.984923i	$0.444656\pi$
$762$		0			0
$763$			1.13285e6i			1.94592i
$764$	492891.	−	384536.i	0.844432	−	0.658795i
$765$		0			0
$766$	194663.	+	95027.7i	0.331762	+	0.161954i
$767$			9462.90i			0.0160855i
$768$		0			0
$769$	425668.			0.719810			0.359905	−	0.932989i	$-0.382809\pi$
$769$	425668.			0.719810			0.359905	+	0.932989i	$0.382809\pi$
$770$	−365263.	+	748238.i	−0.616061	+	1.26200i
$771$		0			0
$772$	−39878.3	−	51115.2i	−0.0669117	−	0.0857661i
$773$	−199528.			−0.333922			−0.166961	−	0.985964i	$-0.553395\pi$
$773$	−199528.			−0.333922			−0.166961	+	0.985964i	$0.553395\pi$
$774$		0			0
$775$			432051.i			0.719335i
$776$	122777.	−	25962.9i	0.203889	−	0.0431152i
$777$		0			0
$778$	−22858.0	+	46824.5i	−0.0377641	+	0.0773595i
$779$			104005.i			0.171388i
$780$		0			0
$781$	439673.			0.720821
$782$	54457.2	+	26584.1i	0.0890517	+	0.0434718i
$783$		0			0
$784$	78787.6	−	314134.i	0.128182	−	0.511073i
$785$	−1.03558e6			−1.68053
$786$		0			0
$787$			1.03914e6i			1.67774i	0.544329	+	0.838872i	$0.316784\pi$
$787$			1.03914e6i			1.67774i	−0.544329	+	0.838872i	$0.683216\pi$
$788$	−441598.	−	566032.i	−0.711171	−	0.911566i
$789$		0			0
$790$	−638428.	−	311658.i	−1.02296	−	0.499371i
$791$			605543.i			0.967815i
$792$		0			0
$793$	−29823.5			−0.0474255
$794$	95470.4	−	195570.i	0.151435	−	0.310214i
$795$		0			0
$796$	−709680.	+	553667.i	−1.12005	+	0.873821i
$797$	−25153.9			−0.0395994			−0.0197997	−	0.999804i	$-0.506303\pi$
$797$	−25153.9			−0.0395994			−0.0197997	+	0.999804i	$0.506303\pi$
$798$		0			0
$799$			147534.i			0.231099i
$800$	1.21820e6	+	1.02581e6i	1.90343	+	1.60283i
$801$		0			0
$802$	−88478.1	+	181247.i	−0.137558	+	0.281787i
$803$			319482.i			0.495467i
$804$		0			0
$805$	−796106.			−1.22851
$806$	−31140.4	−	15201.6i	−0.0479351	−	0.0234002i
$807$		0			0
$808$	−482133.	+	101954.i	−0.738489	+	0.156164i
$809$	−975055.			−1.48981			−0.744907	−	0.667168i	$-0.767506\pi$
$809$	−975055.			−1.48981			−0.744907	+	0.667168i	$0.767506\pi$
$810$		0			0
$811$			240015.i			0.364919i	0.983213	+	0.182460i	$0.0584059\pi$
$811$			240015.i			0.364919i	−0.983213	+	0.182460i	$0.941594\pi$
$812$	341576.	−	266485.i	0.518054	−	0.404167i
$813$		0			0
$814$	−269028.	−	131330.i	−0.406022	−	0.198205i
$815$		−	1.46167e6i		−	2.20057i
$816$		0			0
$817$	−42284.3			−0.0633483
$818$	71652.7	−	146780.i	0.107084	−	0.219361i
$819$		0			0
$820$	−869603.	−	1.11464e6i	−1.29328	−	1.65770i
$821$	813612.			1.20707			0.603533	−	0.797338i	$-0.293759\pi$
$821$	813612.			1.20707			0.603533	+	0.797338i	$0.293759\pi$
$822$		0			0
$823$			27847.9i			0.0411143i	0.999789	+	0.0205572i	$0.00654401\pi$
$823$			27847.9i			0.0411143i	−0.999789	+	0.0205572i	$0.993456\pi$
$824$	48852.6	+	231020.i	0.0719504	+	0.340248i
$825$		0			0
$826$	32240.1	−	66043.5i	0.0472537	−	0.0967988i
$827$		−	1.05969e6i		−	1.54941i	−0.632323	−	0.774705i	$-0.717898\pi$
$827$		−	1.05969e6i		−	1.54941i	0.632323	−	0.774705i	$-0.282102\pi$
$828$		0			0
$829$	−904280.			−1.31581			−0.657906	−	0.753100i	$-0.728558\pi$
$829$	−904280.			−1.31581			−0.657906	+	0.753100i	$0.728558\pi$
$830$	−529215.	−	258344.i	−0.768203	−	0.375009i
$831$		0			0
$832$	−116798.	+	51709.5i	−0.168729	+	0.0747006i
$833$	68063.7			0.0980902
$834$		0			0
$835$		−	1.21591e6i		−	1.74393i
$836$	39826.7	+	51049.2i	0.0569852	+	0.0730426i
$837$		0			0
$838$	119816.	+	58490.0i	0.170619	+	0.0832902i
$839$		−	356605.i		−	0.506598i	−0.967388	−	0.253299i	$-0.918484\pi$
$839$		−	356605.i		−	0.506598i	0.967388	−	0.253299i	$-0.0815157\pi$
$840$		0			0
$841$	−507298.			−0.717251
$842$	14670.7	−	30052.8i	0.0206931	−	0.0423897i
$843$		0			0
$844$	−922208.	+	719474.i	−1.29463	+	1.01002i
$845$	1.28819e6			1.80413
$846$		0			0
$847$			558256.i			0.778156i
$848$	−289450.	+	1.15407e6i	−0.402514	+	1.60487i
$849$		0			0
$850$	−146827.	+	300773.i	−0.203220	+	0.416295i
$851$		−	286239.i		−	0.395248i
$852$		0			0
$853$	−187933.			−0.258288			−0.129144	−	0.991626i	$-0.541223\pi$
$853$	−187933.			−0.258288			−0.129144	+	0.991626i	$0.541223\pi$
$854$	208144.	+	101608.i	0.285396	+	0.139320i
$855$		0			0
$856$	181950.	+	860429.i	0.248316	+	1.17427i
$857$	−849660.			−1.15687			−0.578434	−	0.815729i	$-0.696336\pi$
$857$	−849660.			−1.15687			−0.578434	+	0.815729i	$0.696336\pi$
$858$		0			0
$859$			1.20764e6i			1.63663i	0.574769	+	0.818315i	$0.305092\pi$
$859$			1.20764e6i			1.63663i	−0.574769	+	0.818315i	$0.694908\pi$
$860$	453167.	−	353545.i	0.612719	−	0.478022i
$861$		0			0
$862$	−317923.	−	155198.i	−0.427865	−	0.208868i
$863$			77194.2i			0.103648i	0.998656	+	0.0518242i	$0.0165036\pi$
$863$			77194.2i			0.103648i	−0.998656	+	0.0518242i	$0.983496\pi$
$864$		0			0
$865$	731250.			0.977313
$866$	208975.	−	428085.i	0.278650	−	0.570813i
$867$		0			0
$868$	165543.	+	212190.i	0.219721	+	0.281635i
$869$	280060.			0.370862
$870$		0			0
$871$		−	216449.i		−	0.285311i
$872$	−1.17153e6	+	247736.i	−1.54070	+	0.325804i
$873$		0			0
$874$	−27157.5	+	55631.9i	−0.0355522	+	0.0728285i
$875$		−	2.62998e6i		−	3.43508i
$876$		0			0
$877$	142910.			0.185808			0.0929040	−	0.995675i	$-0.470385\pi$
$877$	142910.			0.185808			0.0929040	+	0.995675i	$0.470385\pi$
$878$	429523.	+	209678.i	0.557183	+	0.271996i
$879$		0			0
$880$	−853659.	−	214105.i	−1.10235	−	0.276479i
$881$	305226.			0.393250			0.196625	−	0.980479i	$-0.437002\pi$
$881$	305226.			0.393250			0.196625	+	0.980479i	$0.437002\pi$
$882$		0			0
$883$		−	902045.i		−	1.15693i	−0.815707	−	0.578465i	$-0.803652\pi$
$883$		−	902045.i		−	1.15693i	0.815707	−	0.578465i	$-0.196348\pi$
$884$	−16512.4	−	21165.3i	−0.0211303	−	0.0270844i
$885$		0			0
$886$	732233.	+	357450.i	0.932785	+	0.455352i
$887$			920608.i			1.17011i	0.810993	+	0.585056i	$0.198927\pi$
$887$			920608.i			1.17011i	−0.810993	+	0.585056i	$0.801073\pi$
$888$		0			0
$889$	−1.14338e6			−1.44673
$890$	−584391.	+	1.19712e6i	−0.737774	+	1.51132i
$891$		0			0
$892$	−957564.	+	747057.i	−1.20348	+	0.938911i
$893$	−150716.			−0.188998
$894$		0			0
$895$		−	1.72002e6i		−	2.14728i
$896$	991331.	+	37039.0i	1.23482	+	0.0461364i
$897$		0			0
$898$	−135389.	+	277343.i	−0.167892	+	0.343926i
$899$			124232.i			0.153714i
$900$		0			0
$901$	−250052.			−0.308022
$902$	500817.	+	244481.i	0.615553	+	0.300491i
$903$		0			0
$904$	−626216.	+	132422.i	−0.766280	+	0.162041i
$905$	−2.65969e6			−3.24738
$906$		0			0
$907$		−	492993.i		−	0.599275i	−0.954053	−	0.299638i	$-0.903134\pi$
$907$		−	492993.i		−	0.599275i	0.954053	−	0.299638i	$-0.0968658\pi$
$908$	520209.	−	405849.i	0.630967	−	0.492258i
$909$		0			0
$910$	316915.	+	154707.i	0.382702	+	0.186821i
$911$			240916.i			0.290288i	0.989411	+	0.145144i	$0.0463646\pi$
$911$			240916.i			0.290288i	−0.989411	+	0.145144i	$0.953635\pi$
$912$		0			0
$913$	232152.			0.278503
$914$	492801.	−	1.00950e6i	0.589901	−	1.20841i
$915$		0			0
$916$	−271479.	−	347976.i	−0.323552	−	0.414724i
$917$	1.79688e6			2.13688
$918$		0			0
$919$			155183.i			0.183744i	0.995771	+	0.0918719i	$0.0292850\pi$
$919$			155183.i			0.183744i	−0.995771	+	0.0918719i	$0.970715\pi$
$920$	−174095.	−	823284.i	−0.205689	−	0.972689i
$921$		0			0
$922$	704740.	−	1.44365e6i	0.829024	−	1.69825i
$923$		−	186223.i		−	0.218590i
$924$		0			0
$925$	1.58093e6			1.84769
$926$	−215029.	−	104969.i	−0.250769	−	0.122417i
$927$		0			0
$928$	350279.	+	294961.i	0.406742	+	0.342506i
$929$	704709.			0.816541			0.408271	−	0.912861i	$-0.366132\pi$
$929$	704709.			0.816541			0.408271	+	0.912861i	$0.366132\pi$
$930$		0			0
$931$			69531.9i			0.0802204i
$932$	486482.	+	623564.i	0.560061	+	0.717876i
$933$		0			0
$934$	749371.	+	365816.i	0.859019	+	0.419342i
$935$		−	184963.i		−	0.211574i
$936$		0			0
$937$	−237273.			−0.270252			−0.135126	−	0.990828i	$-0.543144\pi$
$937$	−237273.			−0.270252			−0.135126	+	0.990828i	$0.543144\pi$
$938$	−737440.	+	1.51064e6i	−0.838149	+	1.71694i
$939$		0			0
$940$	1.61525e6	−	1.26016e6i	1.82803	−	1.42617i
$941$	−114952.			−0.129819			−0.0649096	−	0.997891i	$-0.520676\pi$
$941$	−114952.			−0.129819			−0.0649096	+	0.997891i	$0.520676\pi$
$942$		0			0
$943$			532856.i			0.599220i
$944$	75348.5	+	18898.1i	0.0845534	+	0.0212067i
$945$		0			0
$946$	−99395.8	+	203612.i	−0.111067	+	0.227520i
$947$			1.02806e6i			1.14635i	0.819432	+	0.573177i	$0.194289\pi$
$947$			1.02806e6i			1.14635i	−0.819432	+	0.573177i	$0.805711\pi$
$948$		0			0
$949$	135316.			0.150251
$950$	−307261.	−	149994.i	−0.340455	−	0.166198i
$951$		0			0
$952$	43133.3	+	203974.i	0.0475925	+	0.225062i
$953$	−837599.			−0.922253			−0.461127	−	0.887334i	$-0.652555\pi$
$953$	−837599.			−0.922253			−0.461127	+	0.887334i	$0.652555\pi$
$954$		0			0
$955$		−	1.82438e6i		−	2.00036i
$956$	1.41358e6	−	1.10283e6i	1.54670	−	1.20668i
$957$		0			0
$958$	−575557.	−	280966.i	−0.627130	−	0.306142i
$959$		−	1.00907e6i		−	1.09720i
$960$		0			0
$961$	846347.			0.916435
$962$	−55624.7	+	113947.i	−0.0601059	+	0.123126i
$963$		0			0
$964$	−404464.	−	518435.i	−0.435237	−	0.557879i
$965$	−189197.			−0.203170
$966$		0			0
$967$			106803.i			0.114217i	0.998368	+	0.0571087i	$0.0181881\pi$
$967$			106803.i			0.114217i	−0.998368	+	0.0571087i	$0.981812\pi$
$968$	−577315.	+	122081.i	−0.616115	+	0.130286i
$969$		0			0
$970$	160657.	−	329105.i	0.170749	−	0.349777i
$971$			689120.i			0.730897i	0.930832	+	0.365448i	$0.119084\pi$
$971$			689120.i			0.730897i	−0.930832	+	0.365448i	$0.880916\pi$
$972$		0			0
$973$	247915.			0.261865
$974$	−1.33704e6	−	652693.i	−1.40937	−	0.688004i
$975$		0			0
$976$	−59559.6	+	237470.i	−0.0625247	+	0.249292i
$977$	587467.			0.615453			0.307726	−	0.951475i	$-0.400432\pi$
$977$	587467.			0.615453			0.307726	+	0.951475i	$0.400432\pi$
$978$		0			0
$979$		−	525143.i		−	0.547913i
$980$	−581366.	−	745184.i	−0.605337	−	0.775910i
$981$		0			0
$982$	240170.	+	117243.i	0.249056	+	0.121580i
$983$			390947.i			0.404586i	0.979325	+	0.202293i	$0.0648393\pi$
$983$			390947.i			0.404586i	−0.979325	+	0.202293i	$0.935161\pi$
$984$		0			0
$985$	−2.09510e6			−2.15940
$986$	−42218.4	+	86484.1i	−0.0434258	+	0.0889575i
$987$		0			0
$988$	21621.8	−	16868.6i	0.0221502	−	0.0172808i
$989$	−216637.			−0.221483
$990$		0			0
$991$			462949.i			0.471396i	0.971826	+	0.235698i	$0.0757376\pi$
$991$			462949.i			0.471396i	−0.971826	+	0.235698i	$0.924262\pi$
$992$	−183233.	+	217597.i	−0.186200	+	0.221121i
$993$		0			0
$994$	−634460.	+	1.29969e6i	−0.642143	+	1.31542i
$995$			2.62680e6i			2.65327i
$996$		0			0
$997$	773284.			0.777944			0.388972	−	0.921249i	$-0.372830\pi$
$997$	773284.			0.777944			0.388972	+	0.921249i	$0.372830\pi$
$998$	−1.19601e6	−	583851.i	−1.20081	−	0.586193i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.e.163.15		22
3.2	odd	2		324.5.d.f.163.8		22
4.3	odd	2	inner	324.5.d.e.163.16		22
9.2	odd	6		36.5.f.a.31.22	yes	44
9.4	even	3		108.5.f.a.19.16		44
9.5	odd	6		36.5.f.a.7.7	✓	44
9.7	even	3		108.5.f.a.91.1		44
12.11	even	2		324.5.d.f.163.7		22
36.7	odd	6		108.5.f.a.91.16		44
36.11	even	6		36.5.f.a.31.7	yes	44
36.23	even	6		36.5.f.a.7.22	yes	44
36.31	odd	6		108.5.f.a.19.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.7	✓	44	9.5	odd	6
36.5.f.a.7.22	yes	44	36.23	even	6
36.5.f.a.31.7	yes	44	36.11	even	6
36.5.f.a.31.22	yes	44	9.2	odd	6
108.5.f.a.19.1		44	36.31	odd	6
108.5.f.a.19.16		44	9.4	even	3
108.5.f.a.91.1		44	9.7	even	3
108.5.f.a.91.16		44	36.7	odd	6
324.5.d.e.163.15		22	1.1	even	1	trivial
324.5.d.e.163.16		22	4.3	odd	2	inner
324.5.d.f.163.7		22	12.11	even	2
324.5.d.f.163.8		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)

\(f(q)\)	\(=\)	\(q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +O(q^{10})\)	\(q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +(-81.9341 + 167.841i) q^{10} -73.6273i q^{11} -31.1848 q^{13} +(217.645 + 106.246i) q^{14} +(-62.2781 + 248.309i) q^{16} -53.8013 q^{17} -54.9619i q^{19} +(459.544 + 589.035i) q^{20} +(-264.658 - 129.197i) q^{22} -281.589i q^{23} +1555.25 q^{25} +(-54.7210 + 112.096i) q^{26} +(763.818 - 595.904i) q^{28} +447.195 q^{29} +277.802i q^{31} +(783.282 + 659.580i) q^{32} +(-94.4072 + 193.392i) q^{34} -2827.19i q^{35} +1016.51 q^{37} +(-197.564 - 96.4437i) q^{38} +(2923.70 - 618.259i) q^{40} -1892.32 q^{41} -769.338i q^{43} +(-928.811 + 724.625i) q^{44} +(-1012.19 - 494.115i) q^{46} -2742.20i q^{47} -1265.09 q^{49} +(2729.05 - 5590.44i) q^{50} +(306.914 + 393.397i) q^{52} +4647.69 q^{53} +3437.89i q^{55} +(-801.714 - 3791.25i) q^{56} +(784.709 - 1607.47i) q^{58} -303.446i q^{59} +956.348 q^{61} +(998.577 + 487.469i) q^{62} +(3745.36 - 1658.17i) q^{64} +1456.11 q^{65} +6940.86i q^{67} +(529.502 + 678.706i) q^{68} +(-10162.5 - 4960.97i) q^{70} +5971.60i q^{71} -4339.17 q^{73} +(1783.71 - 3653.92i) q^{74} +(-693.346 + 540.924i) q^{76} +4458.01 q^{77} +3803.76i q^{79} +(2907.96 - 11594.3i) q^{80} +(-3320.52 + 6802.05i) q^{82} +3153.07i q^{83} +2512.15 q^{85} +(-2765.44 - 1349.99i) q^{86} +(974.892 + 4610.20i) q^{88} +7132.44 q^{89} -1888.18i q^{91} +(-3552.26 + 2771.34i) q^{92} +(-9857.00 - 4811.83i) q^{94} +2566.34i q^{95} -1960.81 q^{97} +(-2219.91 + 4547.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) \) 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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