LMFDB - Embedded newform 360.6.k.b.181.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,6,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	360.k (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:	$57.7381751327$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.10
Root			$3.18502 - 2.41984i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.6.k.b.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.765181 + 5.60486i) q^{2} +(-30.8290 - 8.57748i) q^{4} +25.0000i q^{5} -9.19080 q^{7} +(71.6654 - 166.229i) q^{8} +O(q^{10})$	\(q+(-0.765181 + 5.60486i) q^{2} +(-30.8290 - 8.57748i) q^{4} +25.0000i q^{5} -9.19080 q^{7} +(71.6654 - 166.229i) q^{8} +(-140.122 - 19.1295i) q^{10} +160.480i q^{11} +368.546i q^{13} +(7.03263 - 51.5132i) q^{14} +(876.854 + 528.870i) q^{16} +1261.09 q^{17} -2486.75i q^{19} +(214.437 - 770.725i) q^{20} +(-899.467 - 122.796i) q^{22} +422.882 q^{23} -625.000 q^{25} +(-2065.65 - 282.005i) q^{26} +(283.343 + 78.8339i) q^{28} +5666.05i q^{29} +9387.13 q^{31} +(-3635.20 + 4509.96i) q^{32} +(-964.961 + 7068.23i) q^{34} -229.770i q^{35} -3566.43i q^{37} +(13937.9 + 1902.81i) q^{38} +(4155.72 + 1791.63i) q^{40} +5949.95 q^{41} +10658.5i q^{43} +(1376.51 - 4947.43i) q^{44} +(-323.581 + 2370.20i) q^{46} -9243.94 q^{47} -16722.5 q^{49} +(478.238 - 3503.04i) q^{50} +(3161.20 - 11361.9i) q^{52} -8976.82i q^{53} -4011.99 q^{55} +(-658.662 + 1527.78i) q^{56} +(-31757.4 - 4335.55i) q^{58} +27435.6i q^{59} +50515.3i q^{61} +(-7182.86 + 52613.6i) q^{62} +(-22496.2 - 23825.7i) q^{64} -9213.66 q^{65} -5964.39i q^{67} +(-38878.1 - 10817.0i) q^{68} +(1287.83 + 175.816i) q^{70} -67286.3 q^{71} +85768.5 q^{73} +(19989.3 + 2728.96i) q^{74} +(-21330.0 + 76663.9i) q^{76} -1474.94i q^{77} +56567.2 q^{79} +(-13221.7 + 21921.3i) q^{80} +(-4552.79 + 33348.6i) q^{82} +30208.1i q^{83} +31527.2i q^{85} +(-59739.7 - 8155.72i) q^{86} +(26676.4 + 11500.8i) q^{88} -113965. q^{89} -3387.24i q^{91} +(-13037.0 - 3627.26i) q^{92} +(7073.29 - 51811.0i) q^{94} +62168.7 q^{95} -138806. q^{97} +(12795.8 - 93727.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.765181	+	5.60486i	−0.135266	+	0.990809i
$2$	−0.765181	+	5.60486i	−0.135266	+	0.990809i
$3$		0			0
$3$		0			0
$4$	−30.8290	−	8.57748i	−0.963406	−	0.268046i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$		0			0
$7$	−9.19080			−0.0708938			−0.0354469	−	0.999372i	$-0.511285\pi$
$7$	−9.19080			−0.0708938			−0.0354469	+	0.999372i	$0.511285\pi$
$8$	71.6654	−	166.229i	0.395899	−	0.918294i
$9$		0			0
$10$	−140.122	−	19.1295i	−0.443103	−	0.0604929i
$11$			160.480i			0.399888i	0.979807	+	0.199944i	$0.0640760\pi$
$11$			160.480i			0.399888i	−0.979807	+	0.199944i	$0.935924\pi$
$12$		0			0
$13$			368.546i			0.604831i	0.953176	+	0.302415i	$0.0977929\pi$
$13$			368.546i			0.604831i	−0.953176	+	0.302415i	$0.902207\pi$
$14$	7.03263	−	51.5132i	0.00958954	−	0.0702423i
$15$		0			0
$16$	876.854	+	528.870i	0.856303	+	0.516475i
$17$	1261.09			1.05833			0.529167	−	0.848517i	$-0.322504\pi$
$17$	1261.09			1.05833			0.529167	+	0.848517i	$0.322504\pi$
$18$		0			0
$19$		−	2486.75i		−	1.58033i	−0.612894	−	0.790165i	$-0.709995\pi$
$19$		−	2486.75i		−	1.58033i	0.612894	−	0.790165i	$-0.290005\pi$
$20$	214.437	−	770.725i	0.119874	−	0.430848i
$21$		0			0
$22$	−899.467	−	122.796i	−0.396213	−	0.0540914i
$23$	422.882			0.166686			0.0833431	−	0.996521i	$-0.473440\pi$
$23$	422.882			0.166686			0.0833431	+	0.996521i	$0.473440\pi$
$24$		0			0
$25$	−625.000			−0.200000
$26$	−2065.65	−	282.005i	−0.599272	−	0.0818132i
$27$		0			0
$28$	283.343	+	78.8339i	0.0682995	+	0.0190028i
$29$			5666.05i			1.25108i	0.780192	+	0.625540i	$0.215121\pi$
$29$			5666.05i			1.25108i	−0.780192	+	0.625540i	$0.784879\pi$
$30$		0			0
$31$	9387.13			1.75440			0.877200	−	0.480125i	$-0.159409\pi$
$31$	9387.13			1.75440			0.877200	+	0.480125i	$0.159409\pi$
$32$	−3635.20	+	4509.96i	−0.627557	+	0.778571i
$33$		0			0
$34$	−964.961	+	7068.23i	−0.143157	+	1.04861i
$35$		−	229.770i		−	0.0317047i
$36$		0			0
$37$		−	3566.43i		−	0.428281i	−0.976803	−	0.214141i	$-0.931305\pi$
$37$		−	3566.43i		−	0.428281i	0.976803	−	0.214141i	$-0.0686951\pi$
$38$	13937.9	+	1902.81i	1.56581	+	0.213765i
$39$		0			0
$40$	4155.72	+	1791.63i	0.410674	+	0.177051i
$41$	5949.95			0.552782			0.276391	−	0.961045i	$-0.410862\pi$
$41$	5949.95			0.552782			0.276391	+	0.961045i	$0.410862\pi$
$42$		0			0
$43$			10658.5i			0.879077i	0.898224	+	0.439538i	$0.144858\pi$
$43$			10658.5i			0.879077i	−0.898224	+	0.439538i	$0.855142\pi$
$44$	1376.51	−	4947.43i	0.107188	−	0.385255i
$45$		0			0
$46$	−323.581	+	2370.20i	−0.0225470	+	0.165154i
$47$	−9243.94			−0.610397			−0.305198	−	0.952289i	$-0.598723\pi$
$47$	−9243.94			−0.610397			−0.305198	+	0.952289i	$0.598723\pi$
$48$		0			0
$49$	−16722.5			−0.994974
$50$	478.238	−	3503.04i	0.0270533	−	0.198162i
$51$		0			0
$52$	3161.20	−	11361.9i	0.162122	−	0.582697i
$53$		−	8976.82i		−	0.438968i	−0.975616	−	0.219484i	$-0.929563\pi$
$53$		−	8976.82i		−	0.438968i	0.975616	−	0.219484i	$-0.0704374\pi$
$54$		0			0
$55$	−4011.99			−0.178835
$56$	−658.662	+	1527.78i	−0.0280668	+	0.0651014i
$57$		0			0
$58$	−31757.4	−	4335.55i	−1.23958	−	0.169229i
$59$			27435.6i			1.02609i	0.858363	+	0.513044i	$0.171482\pi$
$59$			27435.6i			1.02609i	−0.858363	+	0.513044i	$0.828518\pi$
$60$		0			0
$61$			50515.3i			1.73819i	0.494642	+	0.869097i	$0.335299\pi$
$61$			50515.3i			1.73819i	−0.494642	+	0.869097i	$0.664701\pi$
$62$	−7182.86	+	52613.6i	−0.237311	+	1.73828i
$63$		0			0
$64$	−22496.2	−	23825.7i	−0.686528	−	0.727103i
$65$	−9213.66			−0.270488
$66$		0			0
$67$		−	5964.39i		−	0.162323i	−0.996701	−	0.0811613i	$-0.974137\pi$
$67$		−	5964.39i		−	0.162323i	0.996701	−	0.0811613i	$-0.0258629\pi$
$68$	−38878.1	−	10817.0i	−1.01961	−	0.283683i
$69$		0			0
$70$	1287.83	+	175.816i	0.0314133	+	0.00428857i
$71$	−67286.3			−1.58409			−0.792046	−	0.610461i	$-0.790984\pi$
$71$	−67286.3			−1.58409			−0.792046	+	0.610461i	$0.790984\pi$
$72$		0			0
$73$	85768.5			1.88374			0.941869	−	0.335979i	$-0.109067\pi$
$73$	85768.5			1.88374			0.941869	+	0.335979i	$0.109067\pi$
$74$	19989.3	+	2728.96i	0.424345	+	0.0579320i
$75$		0			0
$76$	−21330.0	+	76663.9i	−0.423601	+	1.52250i
$77$		−	1474.94i		−	0.0283496i
$78$		0			0
$79$	56567.2			1.01976			0.509879	−	0.860246i	$-0.329690\pi$
$79$	56567.2			1.01976			0.509879	+	0.860246i	$0.329690\pi$
$80$	−13221.7	+	21921.3i	−0.230974	+	0.382950i
$81$		0			0
$82$	−4552.79	+	33348.6i	−0.0747727	+	0.547701i
$83$			30208.1i			0.481314i	0.970610	+	0.240657i	$0.0773628\pi$
$83$			30208.1i			0.481314i	−0.970610	+	0.240657i	$0.922637\pi$
$84$		0			0
$85$			31527.2i			0.473302i
$86$	−59739.7	−	8155.72i	−0.870997	−	0.118909i
$87$		0			0
$88$	26676.4	+	11500.8i	0.367215	+	0.158315i
$89$	−113965.			−1.52509			−0.762544	−	0.646936i	$-0.776050\pi$
$89$	−113965.			−1.52509			−0.762544	+	0.646936i	$0.776050\pi$
$90$		0			0
$91$		−	3387.24i		−	0.0428787i
$92$	−13037.0	−	3627.26i	−0.160586	−	0.0446796i
$93$		0			0
$94$	7073.29	−	51811.0i	0.0825661	−	0.604787i
$95$	62168.7			0.706745
$96$		0			0
$97$	−138806.			−1.49788			−0.748942	−	0.662635i	$-0.769438\pi$
$97$	−138806.			−1.49788			−0.748942	+	0.662635i	$0.769438\pi$
$98$	12795.8	−	93727.5i	0.134586	−	0.985830i
$99$		0			0
$100$	19268.1	+	5360.92i	0.192681	+	0.0536092i
$101$			128473.i			1.25317i	0.779354	+	0.626584i	$0.215547\pi$
$101$			128473.i			1.25317i	−0.779354	+	0.626584i	$0.784453\pi$
$102$		0			0
$103$	−117231.			−1.08880			−0.544401	−	0.838825i	$-0.683243\pi$
$103$	−117231.			−1.08880			−0.544401	+	0.838825i	$0.683243\pi$
$104$	61263.1	+	26412.0i	0.555412	+	0.239452i
$105$		0			0
$106$	50313.9	+	6868.90i	0.434934	+	0.0593776i
$107$		−	17654.6i		−	0.149073i	−0.997218	−	0.0745366i	$-0.976252\pi$
$107$		−	17654.6i		−	0.149073i	0.997218	−	0.0745366i	$-0.0237477\pi$
$108$		0			0
$109$			75398.4i			0.607849i	0.952696	+	0.303925i	$0.0982971\pi$
$109$			75398.4i			0.607849i	−0.952696	+	0.303925i	$0.901703\pi$
$110$	3069.90	−	22486.7i	0.0241904	−	0.177192i
$111$		0			0
$112$	−8058.99	−	4860.74i	−0.0607066	−	0.0366149i
$113$	−69211.7			−0.509898			−0.254949	−	0.966954i	$-0.582059\pi$
$113$	−69211.7			−0.509898			−0.254949	+	0.966954i	$0.582059\pi$
$114$		0			0
$115$			10572.0i			0.0745443i
$116$	48600.4	−	174678.i	0.335347	−	1.20530i
$117$		0			0
$118$	−153773.	−	20993.2i	−1.01666	−	0.138795i
$119$	−11590.4			−0.0750294
$120$		0			0
$121$	135297.			0.840089
$122$	−283131.	−	38653.4i	−1.72222	−	0.235119i
$123$		0			0
$124$	−289396.	−	80517.9i	−1.69020	−	0.470260i
$125$		−	15625.0i		−	0.0894427i
$126$		0			0
$127$	−118525.			−0.652078			−0.326039	−	0.945356i	$-0.605714\pi$
$127$	−118525.			−0.652078			−0.326039	+	0.945356i	$0.605714\pi$
$128$	150754.	−	107857.i	0.813285	−	0.581866i
$129$		0			0
$130$	7050.12	−	51641.3i	0.0365880	−	0.268002i
$131$			83761.8i			0.426450i	0.977003	+	0.213225i	$0.0683967\pi$
$131$			83761.8i			0.426450i	−0.977003	+	0.213225i	$0.931603\pi$
$132$		0			0
$133$			22855.2i			0.112036i
$134$	33429.6	+	4563.84i	0.160831	+	0.0219568i
$135$		0			0
$136$	90376.3	−	209629.i	0.418994	−	0.971863i
$137$	−174055.			−0.792291			−0.396145	−	0.918188i	$-0.629652\pi$
$137$	−174055.			−0.792291			−0.396145	+	0.918188i	$0.629652\pi$
$138$		0			0
$139$		−	310792.i		−	1.36437i	−0.731179	−	0.682186i	$-0.761029\pi$
$139$		−	310792.i		−	1.36437i	0.731179	−	0.682186i	$-0.238971\pi$
$140$	−1970.85	+	7083.58i	−0.00849832	+	0.0305445i
$141$		0			0
$142$	51486.2	−	377130.i	0.214274	−	1.56953i
$143$	−59144.2			−0.241865
$144$		0			0
$145$	−141651.			−0.559500
$146$	−65628.5	+	480721.i	−0.254806	+	1.86643i
$147$		0			0
$148$	−30590.9	+	109949.i	−0.114799	+	0.412609i
$149$		−	293656.i		−	1.08361i	−0.840504	−	0.541805i	$-0.817741\pi$
$149$		−	293656.i		−	1.08361i	0.840504	−	0.541805i	$-0.182259\pi$
$150$		0			0
$151$	26058.5			0.0930052			0.0465026	−	0.998918i	$-0.485192\pi$
$151$	26058.5			0.0930052			0.0465026	+	0.998918i	$0.485192\pi$
$152$	−413370.	−	178214.i	−1.45121	−	0.625651i
$153$		0			0
$154$	8266.82	+	1128.60i	0.0280890	+	0.00383474i
$155$			234678.i			0.784592i
$156$		0			0
$157$			427448.i			1.38399i	0.721900	+	0.691997i	$0.243269\pi$
$157$			427448.i			1.38399i	−0.721900	+	0.691997i	$0.756731\pi$
$158$	−43284.2	+	317051.i	−0.137939	+	1.01039i
$159$		0			0
$160$	−112749.	−	90879.9i	−0.348188	−	0.280652i
$161$	−3886.62			−0.0118170
$162$		0			0
$163$			547292.i			1.61343i	0.590941	+	0.806715i	$0.298757\pi$
$163$			547292.i			1.61343i	−0.590941	+	0.806715i	$0.701243\pi$
$164$	−183431.	−	51035.5i	−0.532553	−	0.148171i
$165$		0			0
$166$	−169312.	−	23114.7i	−0.476890	−	0.0651055i
$167$	203146.			0.563659			0.281829	−	0.959465i	$-0.409059\pi$
$167$	203146.			0.563659			0.281829	+	0.959465i	$0.409059\pi$
$168$		0			0
$169$	235467.			0.634180
$170$	−176706.	−	24124.0i	−0.468952	−	0.0640217i
$171$		0			0
$172$	91423.4	−	328592.i	0.235633	−	0.846908i
$173$			94689.2i			0.240539i	0.992741	+	0.120269i	$0.0383759\pi$
$173$			94689.2i			0.240539i	−0.992741	+	0.120269i	$0.961624\pi$
$174$		0			0
$175$	5744.25			0.0141788
$176$	−84872.9	+	140717.i	−0.206532	+	0.342425i
$177$		0			0
$178$	87203.6	−	638756.i	0.206293	−	1.51107i
$179$			290099.i			0.676727i	0.941016	+	0.338363i	$0.109873\pi$
$179$			290099.i			0.676727i	−0.941016	+	0.338363i	$0.890127\pi$
$180$		0			0
$181$		−	63999.0i		−	0.145203i	−0.997361	−	0.0726017i	$-0.976870\pi$
$181$		−	63999.0i		−	0.145203i	0.997361	−	0.0726017i	$-0.0231302\pi$
$182$	18985.0	+	2591.85i	0.0424847	+	0.00580005i
$183$		0			0
$184$	30306.0	−	70295.2i	0.0659909	−	0.153067i
$185$	89160.7			0.191533
$186$		0			0
$187$			202379.i			0.423216i
$188$	284981.	+	79289.6i	0.588060	+	0.163615i
$189$		0			0
$190$	−47570.3	+	348447.i	−0.0955987	+	0.700249i
$191$	391768.			0.777044			0.388522	−	0.921439i	$-0.372986\pi$
$191$	391768.			0.777044			0.388522	+	0.921439i	$0.372986\pi$
$192$		0			0
$193$	−641122.			−1.23893			−0.619466	−	0.785024i	$-0.712651\pi$
$193$	−641122.			−1.23893			−0.619466	+	0.785024i	$0.712651\pi$
$194$	106212.	−	777988.i	0.202613	−	1.48412i
$195$		0			0
$196$	515539.	+	143437.i	0.958564	+	0.266699i
$197$			312130.i			0.573019i	0.958077	+	0.286510i	$0.0924951\pi$
$197$			312130.i			0.573019i	−0.958077	+	0.286510i	$0.907505\pi$
$198$		0			0
$199$	171473.			0.306946			0.153473	−	0.988153i	$-0.450954\pi$
$199$	171473.			0.306946			0.153473	+	0.988153i	$0.450954\pi$
$200$	−44790.8	+	103893.i	−0.0791798	+	0.183659i
$201$		0			0
$202$	−720075.	−	98305.3i	−1.24165	−	0.169511i
$203$		−	52075.5i		−	0.0886938i
$204$		0			0
$205$			148749.i			0.247211i
$206$	89702.8	−	657063.i	0.147278	−	1.07879i
$207$		0			0
$208$	−194913.	+	323161.i	−0.312380	+	0.517918i
$209$	399073.			0.631955
$210$		0			0
$211$			679022.i			1.04997i	0.851111	+	0.524986i	$0.175930\pi$
$211$			679022.i			1.04997i	−0.851111	+	0.524986i	$0.824070\pi$
$212$	−76998.5	+	276746.i	−0.117664	+	0.422905i
$213$		0			0
$214$	98951.8	+	13509.0i	0.147703	+	0.0201646i
$215$	−266464.			−0.393135
$216$		0			0
$217$	−86275.3			−0.124376
$218$	−422598.	−	57693.5i	−0.602263	−	0.0822215i
$219$		0			0
$220$	123686.	+	34412.8i	0.172291	+	0.0479361i
$221$			464769.i			0.640113i
$222$		0			0
$223$	976043.			1.31434			0.657169	−	0.753743i	$-0.271754\pi$
$223$	976043.			1.31434			0.657169	+	0.753743i	$0.271754\pi$
$224$	33410.4	−	41450.2i	0.0444899	−	0.0551959i
$225$		0			0
$226$	52959.5	−	387922.i	0.0689720	−	0.505212i
$227$			243426.i			0.313547i	0.987635	+	0.156773i	$0.0501092\pi$
$227$			243426.i			0.313547i	−0.987635	+	0.156773i	$0.949891\pi$
$228$		0			0
$229$			1.33345e6i			1.68030i	0.542354	+	0.840150i	$0.317533\pi$
$229$			1.33345e6i			1.68030i	−0.542354	+	0.840150i	$0.682467\pi$
$230$	−59254.9	−	8089.54i	−0.0738592	−	0.0100833i
$231$		0			0
$232$	941861.	+	406059.i	1.14886	+	0.495301i
$233$	1.01947e6			1.23023			0.615114	−	0.788438i	$-0.289110\pi$
$233$	1.01947e6			1.23023			0.615114	+	0.788438i	$0.289110\pi$
$234$		0			0
$235$		−	231098.i		−	0.272978i
$236$	235328.	−	845812.i	0.275039	−	0.988539i
$237$		0			0
$238$	8868.77	−	64962.7i	0.0101489	−	0.0743398i
$239$	975796.			1.10501			0.552503	−	0.833511i	$-0.313673\pi$
$239$	975796.			1.10501			0.552503	+	0.833511i	$0.313673\pi$
$240$		0			0
$241$	359018.			0.398175			0.199087	−	0.979982i	$-0.436202\pi$
$241$	359018.			0.398175			0.199087	+	0.979982i	$0.436202\pi$
$242$	−103527.	+	758323.i	−0.113636	+	0.832368i
$243$		0			0
$244$	433294.	−	1.55734e6i	0.465916	−	1.67459i
$245$		−	418063.i		−	0.444966i
$246$		0			0
$247$	916482.			0.955832
$248$	672732.	−	1.56041e6i	0.694565	−	1.61106i
$249$		0			0
$250$	87576.0	+	11956.0i	0.0886207	+	0.0120986i
$251$			208180.i			0.208572i	0.994547	+	0.104286i	$0.0332557\pi$
$251$			208180.i			0.208572i	−0.994547	+	0.104286i	$0.966744\pi$
$252$		0			0
$253$			67864.0i			0.0666558i
$254$	90692.8	−	664314.i	0.0882041	−	0.646084i
$255$		0			0
$256$	489169.	+	927483.i	0.466508	+	0.884517i
$257$	−1.82101e6			−1.71981			−0.859904	−	0.510456i	$-0.829477\pi$
$257$	−1.82101e6			−1.71981			−0.859904	+	0.510456i	$0.829477\pi$
$258$		0			0
$259$			32778.3i			0.0303625i
$260$	284048.	+	79029.9i	0.260590	+	0.0725034i
$261$		0			0
$262$	−469474.	−	64093.0i	−0.422531	−	0.0576843i
$263$	1.74901e6			1.55921			0.779603	−	0.626274i	$-0.215421\pi$
$263$	1.74901e6			1.55921			0.779603	+	0.626274i	$0.215421\pi$
$264$		0			0
$265$	224421.			0.196313
$266$	−128100.	−	17488.4i	−0.111006	−	0.0151546i
$267$		0			0
$268$	−51159.4	+	183876.i	−0.0435099	+	0.156383i
$269$		−	1.48042e6i		−	1.24740i	−0.781665	−	0.623699i	$-0.785629\pi$
$269$		−	1.48042e6i		−	1.24740i	0.781665	−	0.623699i	$-0.214371\pi$
$270$		0			0
$271$	1.04418e6			0.863680			0.431840	−	0.901950i	$-0.357864\pi$
$271$	1.04418e6			0.863680			0.431840	+	0.901950i	$0.357864\pi$
$272$	1.10579e6	+	666951.i	0.906255	+	0.546603i
$273$		0			0
$274$	133183.	−	975553.i	0.107170	−	0.785009i
$275$		−	100300.i		−	0.0799776i
$276$		0			0
$277$			22792.5i			0.0178481i	0.999960	+	0.00892407i	$0.00284066\pi$
$277$			22792.5i			0.0178481i	−0.999960	+	0.00892407i	$0.997159\pi$
$278$	1.74195e6	+	237812.i	1.35183	+	0.184553i
$279$		0			0
$280$	−38194.4	−	16466.6i	−0.0291142	−	0.0125518i
$281$	−181092.			−0.136815			−0.0684074	−	0.997657i	$-0.521792\pi$
$281$	−181092.			−0.136815			−0.0684074	+	0.997657i	$0.521792\pi$
$282$		0			0
$283$			1.00940e6i			0.749200i	0.927187	+	0.374600i	$0.122220\pi$
$283$			1.00940e6i			0.749200i	−0.927187	+	0.374600i	$0.877780\pi$
$284$	2.07437e6	+	577146.i	1.52612	+	0.424610i
$285$		0			0
$286$	45256.1	−	331495.i	0.0327161	−	0.239642i
$287$	−54684.8			−0.0391888
$288$		0			0
$289$	170486.			0.120073
$290$	108389.	−	793935.i	0.0756815	−	0.554358i
$291$		0			0
$292$	−2.64416e6	−	735677.i	−1.81481	−	0.504929i
$293$			2.25558e6i			1.53493i	0.641090	+	0.767465i	$0.278482\pi$
$293$			2.25558e6i			1.53493i	−0.641090	+	0.767465i	$0.721518\pi$
$294$		0			0
$295$	−685890.			−0.458880
$296$	−592844.	−	255589.i	−0.393288	−	0.169556i
$297$		0			0
$298$	1.64590e6	+	224700.i	1.07365	+	0.146576i
$299$			155852.i			0.100817i
$300$		0			0
$301$		−	97960.6i		−	0.0623211i
$302$	−19939.5	+	146054.i	−0.0125805	+	0.0921504i
$303$		0			0
$304$	1.31517e6	−	2.18051e6i	0.816200	−	1.35324i
$305$	−1.26288e6			−0.777344
$306$		0			0
$307$			2.42181e6i			1.46654i	0.679938	+	0.733270i	$0.262007\pi$
$307$			2.42181e6i			1.46654i	−0.679938	+	0.733270i	$0.737993\pi$
$308$	−12651.2	+	45470.8i	−0.00759900	+	0.0273122i
$309$		0			0
$310$	−1.31534e6	−	179572.i	−0.777381	−	0.106129i
$311$	1.04918e6			0.615107			0.307554	−	0.951531i	$-0.400490\pi$
$311$	1.04918e6			0.615107			0.307554	+	0.951531i	$0.400490\pi$
$312$		0			0
$313$	919355.			0.530423			0.265212	−	0.964190i	$-0.414558\pi$
$313$	919355.			0.530423			0.265212	+	0.964190i	$0.414558\pi$
$314$	−2.39579e6	−	327075.i	−1.37127	−	0.187208i
$315$		0			0
$316$	−1.74391e6	−	485204.i	−0.982441	−	0.273342i
$317$			761677.i			0.425719i	0.977083	+	0.212859i	$0.0682776\pi$
$317$			761677.i			0.425719i	−0.977083	+	0.212859i	$0.931722\pi$
$318$		0			0
$319$	−909285.			−0.500292
$320$	595643.	−	562404.i	0.325170	−	0.307025i
$321$		0			0
$322$	2973.97	−	21784.0i	0.00159844	−	0.0117084i
$323$		−	3.13601e6i		−	1.67252i
$324$		0			0
$325$		−	230341.i		−	0.120966i
$326$	−3.06750e6	−	418778.i	−1.59860	−	0.218243i
$327$		0			0
$328$	426405.	−	989054.i	0.218846	−	0.507616i
$329$	84959.2			0.0432734
$330$		0			0
$331$		−	1.27292e6i		−	0.638605i	−0.947653	−	0.319302i	$-0.896551\pi$
$331$		−	1.27292e6i		−	0.638605i	0.947653	−	0.319302i	$-0.103449\pi$
$332$	259109.	−	931285.i	0.129014	−	0.463700i
$333$		0			0
$334$	−155443.	+	1.13860e6i	−0.0762440	+	0.558478i
$335$	149110.			0.0725928
$336$		0			0
$337$	1.61635e6			0.775286			0.387643	−	0.921810i	$-0.373289\pi$
$337$	1.61635e6			0.775286			0.387643	+	0.921810i	$0.373289\pi$
$338$	−180175.	+	1.31976e6i	−0.0857832	+	0.628351i
$339$		0			0
$340$	270424.	−	971952.i	0.126867	−	0.455982i
$341$			1.50644e6i			0.701564i
$342$		0			0
$343$	308163.			0.141431
$344$	1.77176e6	+	763848.i	0.807251	+	0.348026i
$345$		0			0
$346$	−530720.	−	72454.4i	−0.238328	−	0.0325368i
$347$			349978.i			0.156033i	0.996952	+	0.0780167i	$0.0248587\pi$
$347$			349978.i			0.156033i	−0.996952	+	0.0780167i	$0.975141\pi$
$348$		0			0
$349$		−	2.38580e6i		−	1.04850i	−0.851563	−	0.524252i	$-0.824345\pi$
$349$		−	2.38580e6i		−	1.04850i	0.851563	−	0.524252i	$-0.175655\pi$
$350$	−4395.40	+	32195.7i	−0.00191791	+	0.0140485i
$351$		0			0
$352$	−723758.	−	583375.i	−0.311341	−	0.250952i
$353$	−3.84764e6			−1.64345			−0.821727	−	0.569882i	$-0.806989\pi$
$353$	−3.84764e6			−1.64345			−0.821727	+	0.569882i	$0.806989\pi$
$354$		0			0
$355$		−	1.68216e6i		−	0.708428i
$356$	3.51342e6	+	977529.i	1.46928	+	0.408794i
$357$		0			0
$358$	−1.62596e6	−	221978.i	−0.670507	−	0.0915383i
$359$	2.69844e6			1.10503			0.552517	−	0.833501i	$-0.313667\pi$
$359$	2.69844e6			1.10503			0.552517	+	0.833501i	$0.313667\pi$
$360$		0			0
$361$	−3.70781e6			−1.49744
$362$	358706.	+	48970.9i	0.143869	+	0.0196411i
$363$		0			0
$364$	−29053.9	+	104425.i	−0.0114935	+	0.0413096i
$365$			2.14421e6i			0.842434i
$366$		0			0
$367$	1.14096e6			0.442186			0.221093	−	0.975253i	$-0.429038\pi$
$367$	1.14096e6			0.442186			0.221093	+	0.975253i	$0.429038\pi$
$368$	370806.	+	223650.i	0.142734	+	0.0860892i
$369$		0			0
$370$	−68224.1	+	499734.i	−0.0259080	+	0.189773i
$371$			82504.2i			0.0311201i
$372$		0			0
$373$			461958.i			0.171922i	0.996299	+	0.0859608i	$0.0273960\pi$
$373$			461958.i			0.171922i	−0.996299	+	0.0859608i	$0.972604\pi$
$374$	−1.13431e6	−	154857.i	−0.419326	−	0.0572468i
$375$		0			0
$376$	−662470.	+	1.53661e6i	−0.241655	+	0.560524i
$377$	−2.08820e6			−0.756691
$378$		0			0
$379$		−	4.36174e6i		−	1.55977i	−0.625920	−	0.779887i	$-0.715277\pi$
$379$		−	4.36174e6i		−	1.55977i	0.625920	−	0.779887i	$-0.284723\pi$
$380$	−1.91660e6	−	533250.i	−0.680882	−	0.189440i
$381$		0			0
$382$	−299774.	+	2.19581e6i	−0.105108	+	0.769903i
$383$	417638.			0.145480			0.0727400	−	0.997351i	$-0.476826\pi$
$383$	417638.			0.145480			0.0727400	+	0.997351i	$0.476826\pi$
$384$		0			0
$385$	36873.4			0.0126783
$386$	490574.	−	3.59340e6i	0.167586	−	1.22754i
$387$		0			0
$388$	4.27924e6	+	1.19060e6i	1.44307	+	0.401502i
$389$		−	1.92396e6i		−	0.644647i	−0.946630	−	0.322323i	$-0.895536\pi$
$389$		−	1.92396e6i		−	0.644647i	0.946630	−	0.322323i	$-0.104464\pi$
$390$		0			0
$391$	533291.			0.176410
$392$	−1.19843e6	+	2.77977e6i	−0.393909	+	0.913679i
$393$		0			0
$394$	−1.74944e6	−	238836.i	−0.567753	−	0.0775102i
$395$			1.41418e6i			0.456049i
$396$		0			0
$397$			2.95436e6i			0.940778i	0.882459	+	0.470389i	$0.155886\pi$
$397$			2.95436e6i			0.940778i	−0.882459	+	0.470389i	$0.844114\pi$
$398$	−131208.	+	961080.i	−0.0415194	+	0.304125i
$399$		0			0
$400$	−548034.	−	330544.i	−0.171261	−	0.103295i
$401$	1.57105e6			0.487898			0.243949	−	0.969788i	$-0.421557\pi$
$401$	1.57105e6			0.487898			0.243949	+	0.969788i	$0.421557\pi$
$402$		0			0
$403$			3.45959e6i			1.06112i
$404$	1.10198e6	−	3.96070e6i	0.335907	−	1.20731i
$405$		0			0
$406$	291876.	+	39847.2i	0.0878787	+	0.0119973i
$407$	572339.			0.171265
$408$		0			0
$409$	−5.18294e6			−1.53203			−0.766016	−	0.642821i	$-0.777764\pi$
$409$	−5.18294e6			−1.53203			−0.766016	+	0.642821i	$0.777764\pi$
$410$	−833716.	−	113820.i	−0.244939	−	0.0334394i
$411$		0			0
$412$	3.61411e6	+	1.00554e6i	1.04896	+	0.291849i
$413$		−	252155.i		−	0.0727432i
$414$		0			0
$415$	−755202.			−0.215250
$416$	−1.66213e6	−	1.33974e6i	−0.470903	−	0.379565i
$417$		0			0
$418$	−305363.	+	2.23675e6i	−0.0854822	+	0.626147i
$419$		−	4.81218e6i		−	1.33908i	−0.742776	−	0.669540i	$-0.766491\pi$
$419$		−	4.81218e6i		−	1.33908i	0.742776	−	0.669540i	$-0.233509\pi$
$420$		0			0
$421$		−	4.66983e6i		−	1.28409i	−0.766667	−	0.642045i	$-0.778086\pi$
$421$		−	4.66983e6i		−	1.28409i	0.766667	−	0.642045i	$-0.221914\pi$
$422$	−3.80583e6	−	519575.i	−1.04032	−	0.142026i
$423$		0			0
$424$	−1.49221e6	−	643327.i	−0.403102	−	0.173787i
$425$	−788180.			−0.211667
$426$		0			0
$427$		−	464276.i		−	0.123227i
$428$	−151432.	+	544275.i	−0.0399585	+	0.143618i
$429$		0			0
$430$	203893.	−	1.49349e6i	0.0531779	−	0.389522i
$431$	3.07756e6			0.798020			0.399010	−	0.916947i	$-0.369354\pi$
$431$	3.07756e6			0.798020			0.399010	+	0.916947i	$0.369354\pi$
$432$		0			0
$433$	−2.60694e6			−0.668206			−0.334103	−	0.942537i	$-0.608433\pi$
$433$	−2.60694e6			−0.668206			−0.334103	+	0.942537i	$0.608433\pi$
$434$	66016.3	−	483561.i	0.0168239	−	0.123233i
$435$		0			0
$436$	646728.	−	2.32446e6i	0.162932	−	0.585606i
$437$		−	1.05160e6i		−	0.263419i
$438$		0			0
$439$	7.17040e6			1.77575			0.887876	−	0.460083i	$-0.152180\pi$
$439$	7.17040e6			1.77575			0.887876	+	0.460083i	$0.152180\pi$
$440$	−287521.	+	666910.i	−0.0708007	+	0.164223i
$441$		0			0
$442$	−2.60497e6	−	355633.i	−0.634230	−	0.0865857i
$443$			5.08067e6i			1.23002i	0.788520	+	0.615009i	$0.210848\pi$
$443$			5.08067e6i			1.23002i	−0.788520	+	0.615009i	$0.789152\pi$
$444$		0			0
$445$		−	2.84912e6i		−	0.682041i
$446$	−746850.	+	5.47059e6i	−0.177786	+	1.30226i
$447$		0			0
$448$	206758.	+	218978.i	0.0486706	+	0.0515471i
$449$	−3.18246e6			−0.744984			−0.372492	−	0.928035i	$-0.621497\pi$
$449$	−3.18246e6			−0.744984			−0.372492	+	0.928035i	$0.621497\pi$
$450$		0			0
$451$			954846.i			0.221051i
$452$	2.13373e6	+	593662.i	0.491239	+	0.136676i
$453$		0			0
$454$	−1.36437e6	−	186265.i	−0.310665	−	0.0424123i
$455$	84680.9			0.0191760
$456$		0			0
$457$	−1.54454e6			−0.345946			−0.172973	−	0.984927i	$-0.555337\pi$
$457$	−1.54454e6			−0.345946			−0.172973	+	0.984927i	$0.555337\pi$
$458$	−7.47378e6	−	1.02033e6i	−1.66486	−	0.227288i
$459$		0			0
$460$	90681.5	−	325926.i	0.0199813	−	0.0718164i
$461$		−	888536.i		−	0.194725i	−0.995249	−	0.0973627i	$-0.968959\pi$
$461$		−	888536.i		−	0.194725i	0.995249	−	0.0973627i	$-0.0310407\pi$
$462$		0			0
$463$	3.53164e6			0.765640			0.382820	−	0.923823i	$-0.374953\pi$
$463$	3.53164e6			0.765640			0.382820	+	0.923823i	$0.374953\pi$
$464$	−2.99660e6	+	4.96829e6i	−0.646151	+	1.07130i
$465$		0			0
$466$	−780081.	+	5.71400e6i	−0.166408	+	1.21892i
$467$		−	7.13335e6i		−	1.51357i	−0.653666	−	0.756783i	$-0.726770\pi$
$467$		−	7.13335e6i		−	1.51357i	0.653666	−	0.756783i	$-0.273230\pi$
$468$		0			0
$469$			54817.5i			0.0115077i
$470$	1.29528e6	+	176832.i	0.270469	+	0.0369247i
$471$		0			0
$472$	4.56059e6	+	1.96618e6i	0.942250	+	0.406227i
$473$	−1.71048e6			−0.351532
$474$		0			0
$475$			1.55422e6i			0.316066i
$476$	357321.	+	99416.5i	0.0722838	+	0.0201113i
$477$		0			0
$478$	−746661.	+	5.46920e6i	−0.149470	+	1.09485i
$479$	−5.02213e6			−1.00011			−0.500057	−	0.865992i	$-0.666688\pi$
$479$	−5.02213e6			−1.00011			−0.500057	+	0.865992i	$0.666688\pi$
$480$		0			0
$481$	1.31439e6			0.259038
$482$	−274714.	+	2.01225e6i	−0.0538596	+	0.394515i
$483$		0			0
$484$	−4.17108e6	−	1.16051e6i	−0.809347	−	0.225183i
$485$		−	3.47015e6i		−	0.669874i
$486$		0			0
$487$	−9.04360e6			−1.72790			−0.863951	−	0.503576i	$-0.832017\pi$
$487$	−9.04360e6			−1.72790			−0.863951	+	0.503576i	$0.832017\pi$
$488$	8.39710e6	+	3.62020e6i	1.59617	+	0.688149i
$489$		0			0
$490$	2.34319e6	+	319894.i	0.440876	+	0.0601889i
$491$			1.91922e6i			0.359270i	0.983733	+	0.179635i	$0.0574916\pi$
$491$			1.91922e6i			0.359270i	−0.983733	+	0.179635i	$0.942508\pi$
$492$		0			0
$493$			7.14538e6i			1.32406i
$494$	−701275.	+	5.13675e6i	−0.129292	+	0.947047i
$495$		0			0
$496$	8.23114e6	+	4.96457e6i	1.50230	+	0.906103i
$497$	618415.			0.112302
$498$		0			0
$499$			1.22004e6i			0.219342i	0.993968	+	0.109671i	$0.0349797\pi$
$499$			1.22004e6i			0.219342i	−0.993968	+	0.109671i	$0.965020\pi$
$500$	−134023.	+	481703.i	−0.0239748	+	0.0861697i
$501$		0			0
$502$	−1.16682e6	−	159296.i	−0.206655	−	0.0282127i
$503$	−7.08742e6			−1.24902			−0.624508	−	0.781018i	$-0.714700\pi$
$503$	−7.08742e6			−1.24902			−0.624508	+	0.781018i	$0.714700\pi$
$504$		0			0
$505$	−3.21183e6			−0.560434
$506$	−380368.	−	51928.3i	−0.0660432	−	0.00901628i
$507$		0			0
$508$	3.65399e6	+	1.01664e6i	0.628215	+	0.174787i
$509$			5.58984e6i			0.956324i	0.878272	+	0.478162i	$0.158697\pi$
$509$			5.58984e6i			0.956324i	−0.878272	+	0.478162i	$0.841303\pi$
$510$		0			0
$511$	−788281.			−0.133545
$512$	−5.57272e6	+	2.03203e6i	−0.939490	+	0.342575i
$513$		0			0
$514$	1.39340e6	−	1.02065e7i	0.232632	−	1.70400i
$515$		−	2.93077e6i		−	0.486927i
$516$		0			0
$517$		−	1.48346e6i		−	0.244090i
$518$	−183718.	−	25081.4i	−0.0300834	−	0.00410702i
$519$		0			0
$520$	−660300.	+	1.53158e6i	−0.107086	+	0.248388i
$521$	−8.47810e6			−1.36837			−0.684186	−	0.729308i	$-0.739842\pi$
$521$	−8.47810e6			−1.36837			−0.684186	+	0.729308i	$0.739842\pi$
$522$		0			0
$523$		−	6.21299e6i		−	0.993223i	−0.867973	−	0.496611i	$-0.834577\pi$
$523$		−	6.21299e6i		−	0.993223i	0.867973	−	0.496611i	$-0.165423\pi$
$524$	718465.	−	2.58229e6i	0.114308	−	0.410844i
$525$		0			0
$526$	−1.33831e6	+	9.80298e6i	−0.210908	+	1.54488i
$527$	1.18380e7			1.85674
$528$		0			0
$529$	−6.25751e6			−0.972216
$530$	−171722.	+	1.25785e6i	−0.0265545	+	0.194508i
$531$		0			0
$532$	196040.	−	704603.i	0.0300307	−	0.107936i
$533$			2.19283e6i			0.334339i
$534$		0			0
$535$	441366.			0.0666675
$536$	−991454.	−	427440.i	−0.149060	−	0.0642633i
$537$		0			0
$538$	8.29757e6	+	1.13279e6i	1.23593	+	0.168731i
$539$		−	2.68363e6i		−	0.397878i
$540$		0			0
$541$			7.13892e6i			1.04867i	0.851512	+	0.524335i	$0.175686\pi$
$541$			7.13892e6i			1.04867i	−0.851512	+	0.524335i	$0.824314\pi$
$542$	−798989.	+	5.85250e6i	−0.116827	+	0.855742i
$543$		0			0
$544$	−4.58430e6	+	5.68746e6i	−0.664165	+	0.823989i
$545$	−1.88496e6			−0.271838
$546$		0			0
$547$		−	7.31142e6i		−	1.04480i	−0.852700	−	0.522400i	$-0.825037\pi$
$547$		−	7.31142e6i		−	1.04480i	0.852700	−	0.522400i	$-0.174963\pi$
$548$	5.36593e6	+	1.49295e6i	0.763298	+	0.212370i
$549$		0			0
$550$	562167.	+	76747.6i	0.0792426	+	0.0108183i
$551$	1.40900e7			1.97712
$552$		0			0
$553$	−519898.			−0.0722945
$554$	−127749.	−	17440.4i	−0.0176841	−	0.00241425i
$555$		0			0
$556$	−2.66581e6	+	9.58140e6i	−0.365715	+	1.31444i
$557$		−	1.92783e6i		−	0.263288i	−0.991297	−	0.131644i	$-0.957974\pi$
$557$		−	1.92783e6i		−	0.263288i	0.991297	−	0.131644i	$-0.0420256\pi$
$558$		0			0
$559$	−3.92817e6			−0.531692
$560$	121518.	−	201475.i	0.0163747	−	0.0271488i
$561$		0			0
$562$	138568.	−	1.01499e6i	0.0185064	−	0.135557i
$563$			1.29516e7i			1.72208i	0.508539	+	0.861039i	$0.330186\pi$
$563$			1.29516e7i			1.72208i	−0.508539	+	0.861039i	$0.669814\pi$
$564$		0			0
$565$		−	1.73029e6i		−	0.228033i
$566$	−5.65756e6	−	772375.i	−0.742314	−	0.101341i
$567$		0			0
$568$	−4.82210e6	+	1.11849e7i	−0.627141	+	1.45466i
$569$	−7.26039e6			−0.940112			−0.470056	−	0.882637i	$-0.655766\pi$
$569$	−7.26039e6			−0.940112			−0.470056	+	0.882637i	$0.655766\pi$
$570$		0			0
$571$		−	1.83619e6i		−	0.235682i	−0.993032	−	0.117841i	$-0.962403\pi$
$571$		−	1.83619e6i		−	0.235682i	0.993032	−	0.117841i	$-0.0375973\pi$
$572$	1.82336e6	+	507308.i	0.233014	+	0.0648309i
$573$		0			0
$574$	41843.8	−	306501.i	0.00530092	−	0.0388286i
$575$	−264301.			−0.0333372
$576$		0			0
$577$	2.04937e6			0.256260			0.128130	−	0.991757i	$-0.459102\pi$
$577$	2.04937e6			0.256260			0.128130	+	0.991757i	$0.459102\pi$
$578$	−130453.	+	955550.i	−0.0162418	+	0.118969i
$579$		0			0
$580$	4.36696e6	+	1.21501e6i	0.539026	+	0.149972i
$581$		−	277637.i		−	0.0341222i
$582$		0			0
$583$	1.44060e6			0.175538
$584$	6.14663e6	−	1.42572e7i	0.745770	−	1.72983i
$585$		0			0
$586$	−1.26422e7	−	1.72593e6i	−1.52082	−	0.207624i
$587$			2.38716e6i			0.285947i	0.989726	+	0.142974i	$0.0456664\pi$
$587$			2.38716e6i			0.285947i	−0.989726	+	0.142974i	$0.954334\pi$
$588$		0			0
$589$		−	2.33434e7i		−	2.77253i
$590$	524830.	−	3.84432e6i	0.0620710	−	0.454663i
$591$		0			0
$592$	1.88618e6	−	3.12724e6i	0.221196	−	0.366738i
$593$	−1.01237e7			−1.18223			−0.591116	−	0.806587i	$-0.701312\pi$
$593$	−1.01237e7			−1.18223			−0.591116	+	0.806587i	$0.701312\pi$
$594$		0			0
$595$		−	289760.i		−	0.0335542i
$596$	−2.51883e6	+	9.05311e6i	−0.290457	+	1.04396i
$597$		0			0
$598$	−873527.	−	119255.i	−0.0998903	−	0.0136371i
$599$	−3.96697e6			−0.451743			−0.225872	−	0.974157i	$-0.572523\pi$
$599$	−3.96697e6			−0.451743			−0.225872	+	0.974157i	$0.572523\pi$
$600$		0			0
$601$	5.94578e6			0.671464			0.335732	−	0.941958i	$-0.391016\pi$
$601$	5.94578e6			0.671464			0.335732	+	0.941958i	$0.391016\pi$
$602$	549056.	+	74957.6i	0.0617483	+	0.00842994i
$603$		0			0
$604$	−803358.	−	223516.i	−0.0896018	−	0.0249297i
$605$			3.38243e6i			0.375699i
$606$		0			0
$607$	−900508.			−0.0992010			−0.0496005	−	0.998769i	$-0.515795\pi$
$607$	−900508.			−0.0992010			−0.0496005	+	0.998769i	$0.515795\pi$
$608$	1.12151e7	+	9.03981e6i	1.23040	+	0.991746i
$609$		0			0
$610$	966334.	−	7.07828e6i	0.105148	−	0.770200i
$611$		−	3.40682e6i		−	0.369187i
$612$		0			0
$613$		−	4.07379e6i		−	0.437872i	−0.975739	−	0.218936i	$-0.929741\pi$
$613$		−	4.07379e6i		−	0.437872i	0.975739	−	0.218936i	$-0.0702586\pi$
$614$	−1.35739e7	−	1.85312e6i	−1.45306	−	0.198373i
$615$		0			0
$616$	−245177.	−	105702.i	−0.0260333	−	0.0112236i
$617$	−3.83021e6			−0.405051			−0.202525	−	0.979277i	$-0.564915\pi$
$617$	−3.83021e6			−0.405051			−0.202525	+	0.979277i	$0.564915\pi$
$618$		0			0
$619$		−	9.65601e6i		−	1.01291i	−0.862266	−	0.506455i	$-0.830955\pi$
$619$		−	9.65601e6i		−	1.01291i	0.862266	−	0.506455i	$-0.169045\pi$
$620$	2.01295e6	−	7.23490e6i	0.210307	−	0.755881i
$621$		0			0
$622$	−802816.	+	5.88053e6i	−0.0832032	+	0.609454i
$623$	1.04743e6			0.108119
$624$		0			0
$625$	390625.			0.0400000
$626$	−703473.	+	5.15286e6i	−0.0717483	+	0.525548i
$627$		0			0
$628$	3.66643e6	−	1.31778e7i	0.370974	−	1.33335i
$629$		−	4.49758e6i		−	0.453265i
$630$		0			0
$631$	8.80367e6			0.880218			0.440109	−	0.897944i	$-0.354940\pi$
$631$	8.80367e6			0.880218			0.440109	+	0.897944i	$0.354940\pi$
$632$	4.05391e6	−	9.40311e6i	0.403721	−	0.936437i
$633$		0			0
$634$	−4.26910e6	−	582821.i	−0.421806	−	0.0575854i
$635$		−	2.96312e6i		−	0.291618i
$636$		0			0
$637$		−	6.16303e6i		−	0.601791i
$638$	695768.	−	5.09642e6i	0.0676726	−	0.495694i
$639$		0			0
$640$	2.69642e6	+	3.76884e6i	0.260218	+	0.363712i
$641$	8.42581e6			0.809966			0.404983	−	0.914324i	$-0.367278\pi$
$641$	8.42581e6			0.809966			0.404983	+	0.914324i	$0.367278\pi$
$642$		0			0
$643$			559011.i			0.0533204i	0.999645	+	0.0266602i	$0.00848720\pi$
$643$			559011.i			0.0533204i	−0.999645	+	0.0266602i	$0.991513\pi$
$644$	119821.	+	33337.4i	0.0113846	+	0.00316751i
$645$		0			0
$646$	1.75769e7	+	2.39961e6i	1.65715	+	0.226235i
$647$	1.60950e7			1.51158			0.755790	−	0.654814i	$-0.227253\pi$
$647$	1.60950e7			1.51158			0.755790	+	0.654814i	$0.227253\pi$
$648$		0			0
$649$	−4.40286e6			−0.410320
$650$	1.29103e6	+	176253.i	0.119854	+	0.0163626i
$651$		0			0
$652$	4.69438e6	−	1.68725e7i	0.432473	−	1.55439i
$653$		−	2.03856e7i		−	1.87085i	−0.353520	−	0.935427i	$-0.615015\pi$
$653$		−	2.03856e7i		−	1.87085i	0.353520	−	0.935427i	$-0.384985\pi$
$654$		0			0
$655$	−2.09405e6			−0.190714
$656$	5.21723e6	+	3.14675e6i	0.473348	+	0.285498i
$657$		0			0
$658$	−65009.2	+	476185.i	−0.00585343	+	0.0428757i
$659$		−	6.70475e6i		−	0.601408i	−0.953718	−	0.300704i	$-0.902778\pi$
$659$		−	6.70475e6i		−	0.601408i	0.953718	−	0.300704i	$-0.0972216\pi$
$660$		0			0
$661$			5.17558e6i			0.460739i	0.973103	+	0.230370i	$0.0739935\pi$
$661$			5.17558e6i			0.460739i	−0.973103	+	0.230370i	$0.926006\pi$
$662$	7.13456e6	+	974017.i	0.632736	+	0.0863817i
$663$		0			0
$664$	5.02146e6	+	2.16487e6i	0.441987	+	0.190552i
$665$	−571380.			−0.0501038
$666$		0			0
$667$			2.39607e6i			0.208538i
$668$	−6.26278e6	−	1.74248e6i	−0.543032	−	0.151087i
$669$		0			0
$670$	−114096.	+	835739.i	−0.00981936	+	0.0719257i
$671$	−8.10668e6			−0.695083
$672$		0			0
$673$	−2.31161e6			−0.196733			−0.0983664	−	0.995150i	$-0.531362\pi$
$673$	−2.31161e6			−0.196733			−0.0983664	+	0.995150i	$0.531362\pi$
$674$	−1.23680e6	+	9.05945e6i	−0.104870	+	0.768160i
$675$		0			0
$676$	−7.25920e6	−	2.01971e6i	−0.610973	−	0.169989i
$677$		−	1.01425e7i		−	0.850496i	−0.905077	−	0.425248i	$-0.860187\pi$
$677$		−	1.01425e7i		−	0.850496i	0.905077	−	0.425248i	$-0.139813\pi$
$678$		0			0
$679$	1.27574e6			0.106191
$680$	5.24073e6	+	2.25941e6i	0.434630	+	0.187380i
$681$		0			0
$682$	−8.44342e6	−	1.15270e6i	−0.695116	−	0.0948979i
$683$		−	5.34488e6i		−	0.438416i	−0.975678	−	0.219208i	$-0.929653\pi$
$683$		−	5.34488e6i		−	0.438416i	0.975678	−	0.219208i	$-0.0703473\pi$
$684$		0			0
$685$		−	4.35137e6i		−	0.354323i
$686$	−235801.	+	1.72721e6i	−0.0191309	+	0.140131i
$687$		0			0
$688$	−5.63698e6	+	9.34599e6i	−0.454021	+	0.752756i
$689$	3.30837e6			0.265501
$690$		0			0
$691$		−	5.80594e6i		−	0.462570i	−0.972886	−	0.231285i	$-0.925707\pi$
$691$		−	5.80594e6i		−	0.462570i	0.972886	−	0.231285i	$-0.0742930\pi$
$692$	812195.	−	2.91917e6i	0.0644755	−	0.231737i
$693$		0			0
$694$	−1.96158e6	−	267797.i	−0.154599	−	0.0211060i
$695$	7.76980e6			0.610166
$696$		0			0
$697$	7.50341e6			0.585028
$698$	1.33721e7	+	1.82557e6i	1.03887	+	0.141827i
$699$		0			0
$700$	−177090.	−	49271.2i	−0.0136599	−	0.00380056i
$701$		−	6.84282e6i		−	0.525945i	−0.964803	−	0.262972i	$-0.915297\pi$
$701$		−	6.84282e6i		−	0.525945i	0.964803	−	0.262972i	$-0.0847028\pi$
$702$		0			0
$703$	−8.86881e6			−0.676826
$704$	3.82355e6	−	3.61018e6i	0.290760	−	0.274534i
$705$		0			0
$706$	2.94414e6	−	2.15655e7i	0.222304	−	1.62835i
$707$		−	1.18077e6i		−	0.0888418i
$708$		0			0
$709$			1.09625e7i			0.819019i	0.912306	+	0.409509i	$0.134300\pi$
$709$			1.09625e7i			0.819019i	−0.912306	+	0.409509i	$0.865700\pi$
$710$	9.42826e6	+	1.28716e6i	0.701917	+	0.0958264i
$711$		0			0
$712$	−8.16732e6	+	1.89442e7i	−0.603781	+	1.40048i
$713$	3.96965e6			0.292434
$714$		0			0
$715$		−	1.47861e6i		−	0.108165i
$716$	2.48831e6	−	8.94345e6i	0.181394	−	0.651963i
$717$		0			0
$718$	−2.06479e6	+	1.51244e7i	−0.149474	+	1.09488i
$719$	−4.16072e6			−0.300156			−0.150078	−	0.988674i	$-0.547952\pi$
$719$	−4.16072e6			−0.300156			−0.150078	+	0.988674i	$0.547952\pi$
$720$		0			0
$721$	1.07744e6			0.0771893
$722$	2.83715e6	−	2.07818e7i	0.202553	−	1.48368i
$723$		0			0
$724$	−548950.	+	1.97303e6i	−0.0389212	+	0.139890i
$725$		−	3.54128e6i		−	0.250216i
$726$		0			0
$727$	2.27412e7			1.59580			0.797899	−	0.602791i	$-0.205945\pi$
$727$	2.27412e7			1.59580			0.797899	+	0.602791i	$0.205945\pi$
$728$	−563057.	−	242748.i	−0.0393753	−	0.0169756i
$729$		0			0
$730$	−1.20180e7	−	1.64071e6i	−0.834691	−	0.113953i
$731$			1.34414e7i			0.930358i
$732$		0			0
$733$			2.60697e7i			1.79216i	0.443898	+	0.896078i	$0.353595\pi$
$733$			2.60697e7i			1.79216i	−0.443898	+	0.896078i	$0.646405\pi$
$734$	−873041.	+	6.39492e6i	−0.0598129	+	0.438122i
$735$		0			0
$736$	−1.53726e6	+	1.90718e6i	−0.104605	+	0.129777i
$737$	957163.			0.0649109
$738$		0			0
$739$			467568.i			0.0314944i	0.999876	+	0.0157472i	$0.00501270\pi$
$739$			467568.i			0.0314944i	−0.999876	+	0.0157472i	$0.994987\pi$
$740$	−2.74873e6	−	764774.i	−0.184524	−	0.0513397i
$741$		0			0
$742$	−462425.	−	63130.7i	−0.0308341	−	0.00420950i
$743$	−1.98379e6			−0.131833			−0.0659165	−	0.997825i	$-0.520997\pi$
$743$	−1.98379e6			−0.131833			−0.0659165	+	0.997825i	$0.520997\pi$
$744$		0			0
$745$	7.34140e6			0.484605
$746$	−2.58921e6	−	353482.i	−0.170341	−	0.0232552i
$747$		0			0
$748$	1.73590e6	−	6.23914e6i	0.113441	−	0.407728i
$749$			162260.i			0.0105684i
$750$		0			0
$751$	1.55338e7			1.00503			0.502515	−	0.864568i	$-0.332408\pi$
$751$	1.55338e7			1.00503			0.502515	+	0.864568i	$0.332408\pi$
$752$	−8.10558e6	−	4.88884e6i	−0.522684	−	0.315254i
$753$		0			0
$754$	1.59785e6	−	1.17041e7i	0.102355	−	0.749737i
$755$			651463.i			0.0415932i
$756$		0			0
$757$			2.40224e6i			0.152362i	0.997094	+	0.0761811i	$0.0242727\pi$
$757$			2.40224e6i			0.152362i	−0.997094	+	0.0761811i	$0.975727\pi$
$758$	2.44470e7	+	3.33752e6i	1.54544	+	0.210985i
$759$		0			0
$760$	4.45534e6	−	1.03342e7i	0.279800	−	0.649000i
$761$	2.53929e7			1.58946			0.794732	−	0.606960i	$-0.207611\pi$
$761$	2.53929e7			1.58946			0.794732	+	0.606960i	$0.207611\pi$
$762$		0			0
$763$		−	692972.i		−	0.0430928i
$764$	−1.20778e7	−	3.36038e6i	−0.748609	−	0.208284i
$765$		0			0
$766$	−319569.	+	2.34081e6i	−0.0196785	+	0.144143i
$767$	−1.01113e7			−0.620609
$768$		0			0
$769$	−1.96036e6			−0.119542			−0.0597709	−	0.998212i	$-0.519037\pi$
$769$	−1.96036e6			−0.119542			−0.0597709	+	0.998212i	$0.519037\pi$
$770$	−28214.9	+	206671.i	−0.00171495	+	0.0125618i
$771$		0			0
$772$	1.97651e7	+	5.49921e6i	1.19359	+	0.332091i
$773$			3.14540e7i			1.89334i	0.322211	+	0.946668i	$0.395574\pi$
$773$			3.14540e7i			1.89334i	−0.322211	+	0.946668i	$0.604426\pi$
$774$		0			0
$775$	−5.86696e6			−0.350880
$776$	−9.94757e6	+	2.30736e7i	−0.593011	+	1.37550i
$777$		0			0
$778$	1.07835e7	+	1.47218e6i	0.638722	+	0.0871990i
$779$		−	1.47960e7i		−	0.873577i
$780$		0			0
$781$		−	1.07981e7i		−	0.633460i
$782$	−408065.	+	2.98902e6i	−0.0238623	+	0.174788i
$783$		0			0
$784$	−1.46632e7	−	8.84404e6i	−0.851999	−	0.513879i
$785$	−1.06862e7			−0.618941
$786$		0			0
$787$		−	2.21797e7i		−	1.27650i	−0.769831	−	0.638248i	$-0.779660\pi$
$787$		−	2.21797e7i		−	1.27650i	0.769831	−	0.638248i	$-0.220340\pi$
$788$	2.67728e6	−	9.62264e6i	0.153596	−	0.552050i
$789$		0			0
$790$	−7.92629e6	−	1.08210e6i	−0.451858	−	0.0616881i
$791$	636111.			0.0361486
$792$		0			0
$793$	−1.86172e7			−1.05131
$794$	−1.65588e7	−	2.26062e6i	−0.932131	−	0.127255i
$795$		0			0
$796$	−5.28633e6	−	1.47080e6i	−0.295714	−	0.0822757i
$797$			2.05722e7i			1.14719i	0.819139	+	0.573595i	$0.194452\pi$
$797$			2.05722e7i			1.14719i	−0.819139	+	0.573595i	$0.805548\pi$
$798$		0			0
$799$	−1.16574e7			−0.646004
$800$	2.27200e6	−	2.81873e6i	0.125511	−	0.155714i
$801$		0			0
$802$	−1.20214e6	+	8.80553e6i	−0.0659962	+	0.483414i
$803$			1.37641e7i			0.753285i
$804$		0			0
$805$		−	97165.6i		−	0.00528473i
$806$	−1.93906e7	−	2.64722e6i	−1.05136	−	0.143533i
$807$		0			0
$808$	2.13560e7	+	9.20708e6i	1.15078	+	0.496128i
$809$	3.45753e7			1.85735			0.928676	−	0.370892i	$-0.120948\pi$
$809$	3.45753e7			1.85735			0.928676	+	0.370892i	$0.120948\pi$
$810$		0			0
$811$			2.43908e7i			1.30219i	0.758997	+	0.651094i	$0.225690\pi$
$811$			2.43908e7i			1.30219i	−0.758997	+	0.651094i	$0.774310\pi$
$812$	−446676.	+	1.60544e6i	−0.0237740	+	0.0854482i
$813$		0			0
$814$	−437944.	+	3.20788e6i	−0.0231663	+	0.169691i
$815$	−1.36823e7			−0.721548
$816$		0			0
$817$	2.65051e7			1.38923
$818$	3.96589e6	−	2.90497e7i	0.207232	−	1.51795i
$819$		0			0
$820$	1.27589e6	−	4.58577e6i	0.0662641	−	0.238165i
$821$		−	5.77124e6i		−	0.298821i	−0.988775	−	0.149410i	$-0.952262\pi$
$821$		−	5.77124e6i		−	0.298821i	0.988775	−	0.149410i	$-0.0477376\pi$
$822$		0			0
$823$	−9.22421e6			−0.474711			−0.237356	−	0.971423i	$-0.576281\pi$
$823$	−9.22421e6			−0.474711			−0.237356	+	0.971423i	$0.576281\pi$
$824$	−8.40139e6	+	1.94872e7i	−0.431055	+	0.999840i
$825$		0			0
$826$	1.41329e6	+	192944.i	0.0720747	+	0.00983970i
$827$		−	1.36273e7i		−	0.692859i	−0.938076	−	0.346430i	$-0.887394\pi$
$827$		−	1.36273e7i		−	0.692859i	0.938076	−	0.346430i	$-0.112606\pi$
$828$		0			0
$829$		−	5.64154e6i		−	0.285109i	−0.989787	−	0.142555i	$-0.954468\pi$
$829$		−	5.64154e6i		−	0.285109i	0.989787	−	0.142555i	$-0.0455317\pi$
$830$	577867.	−	4.23281e6i	0.0291161	−	0.213272i
$831$		0			0
$832$	8.78088e6	−	8.29087e6i	0.439774	−	0.415233i
$833$	−2.10886e7			−1.05302
$834$		0			0
$835$			5.07864e6i			0.252076i
$836$	−1.23030e7	−	3.42304e6i	−0.608829	−	0.169393i
$837$		0			0
$838$	2.69716e7	+	3.68219e6i	1.32677	+	0.181132i
$839$	−1.01209e7			−0.496379			−0.248189	−	0.968712i	$-0.579836\pi$
$839$	−1.01209e7			−0.496379			−0.248189	+	0.968712i	$0.579836\pi$
$840$		0			0
$841$	−1.15929e7			−0.565201
$842$	2.61737e7	+	3.57327e6i	1.27229	+	0.173694i
$843$		0			0
$844$	5.82430e6	−	2.09336e7i	0.281441	−	1.01155i
$845$			5.88667e6i			0.283614i
$846$		0			0
$847$	−1.24349e6			−0.0595572
$848$	4.74757e6	−	7.87136e6i	0.226716	−	0.375890i
$849$		0			0
$850$	603101.	−	4.41764e6i	0.0286314	−	0.209722i
$851$		−	1.50818e6i		−	0.0713886i
$852$		0			0
$853$			8.59170e6i			0.404302i	0.979354	+	0.202151i	$0.0647932\pi$
$853$			8.59170e6i			0.404302i	−0.979354	+	0.202151i	$0.935207\pi$
$854$	2.60220e6	+	355255.i	0.122095	+	0.0166685i
$855$		0			0
$856$	−2.93471e6	−	1.26523e6i	−0.136893	−	0.0590179i
$857$	1.17834e7			0.548049			0.274024	−	0.961723i	$-0.411645\pi$
$857$	1.17834e7			0.548049			0.274024	+	0.961723i	$0.411645\pi$
$858$		0			0
$859$			2.83473e6i			0.131078i	0.997850	+	0.0655389i	$0.0208767\pi$
$859$			2.83473e6i			0.131078i	−0.997850	+	0.0655389i	$0.979123\pi$
$860$	8.21481e6	+	2.28559e6i	0.378749	+	0.105378i
$861$		0			0
$862$	−2.35489e6	+	1.72493e7i	−0.107945	+	0.790685i
$863$	−2.08041e7			−0.950870			−0.475435	−	0.879751i	$-0.657709\pi$
$863$	−2.08041e7			−0.950870			−0.475435	+	0.879751i	$0.657709\pi$
$864$		0			0
$865$	−2.36723e6			−0.107572
$866$	1.99478e6	−	1.46115e7i	0.0903858	−	0.662065i
$867$		0			0
$868$	2.65978e6	+	740024.i	0.119825	+	0.0333385i
$869$			9.07789e6i			0.407789i
$870$		0			0
$871$	2.19815e6			0.0981776
$872$	1.25334e7	+	5.40345e6i	0.558184	+	0.240647i
$873$		0			0
$874$	5.89408e6	+	804665.i	0.260998	+	0.0356317i
$875$			143606.i			0.00634094i
$876$		0			0
$877$			2.82780e7i			1.24151i	0.784006	+	0.620754i	$0.213173\pi$
$877$			2.82780e7i			1.24151i	−0.784006	+	0.620754i	$0.786827\pi$
$878$	−5.48666e6	+	4.01891e7i	−0.240199	+	1.75943i
$879$		0			0
$880$	−3.51793e6	−	2.12182e6i	−0.153137	−	0.0923639i
$881$	1.63898e6			0.0711432			0.0355716	−	0.999367i	$-0.488675\pi$
$881$	1.63898e6			0.0711432			0.0355716	+	0.999367i	$0.488675\pi$
$882$		0			0
$883$			2.72729e7i			1.17714i	0.808445	+	0.588572i	$0.200310\pi$
$883$			2.72729e7i			1.17714i	−0.808445	+	0.588572i	$0.799690\pi$
$884$	3.98655e6	−	1.43284e7i	0.171580	−	0.616689i
$885$		0			0
$886$	−2.84765e7	−	3.88763e6i	−1.21871	−	0.166380i
$887$	3.68277e7			1.57168			0.785842	−	0.618427i	$-0.212230\pi$
$887$	3.68277e7			1.57168			0.785842	+	0.618427i	$0.212230\pi$
$888$		0			0
$889$	1.08934e6			0.0462283
$890$	1.59689e7	+	2.18009e6i	0.675772	+	0.0922571i
$891$		0			0
$892$	−3.00904e7	−	8.37199e6i	−1.26624	−	0.352303i
$893$			2.29873e7i			0.964628i
$894$		0			0
$895$	−7.25247e6			−0.302641
$896$	−1.38555e6	+	991291.i	−0.0576569	+	0.0412507i
$897$		0			0
$898$	2.43516e6	−	1.78373e7i	0.100771	−	0.738137i
$899$			5.31879e7i			2.19490i
$900$		0			0
$901$		−	1.13206e7i		−	0.464575i
$902$	−5.35178e6	−	730631.i	−0.219019	−	0.0299007i
$903$		0			0
$904$	−4.96008e6	+	1.15050e7i	−0.201868	+	0.468236i
$905$	1.59998e6			0.0649370
$906$		0			0
$907$			1.18940e7i			0.480077i	0.970763	+	0.240038i	$0.0771600\pi$
$907$			1.18940e7i			0.480077i	−0.970763	+	0.240038i	$0.922840\pi$
$908$	2.08798e6	−	7.50458e6i	0.0840450	−	0.302073i
$909$		0			0
$910$	−64796.3	+	474625.i	−0.00259386	+	0.0189997i
$911$	3.24936e7			1.29719			0.648593	−	0.761135i	$-0.275358\pi$
$911$	3.24936e7			1.29719			0.648593	+	0.761135i	$0.275358\pi$
$912$		0			0
$913$	−4.84779e6			−0.192472
$914$	1.18185e6	−	8.65692e6i	0.0467948	−	0.342766i
$915$		0			0
$916$	1.14376e7	−	4.11088e7i	0.450398	−	1.61881i
$917$		−	769839.i		−	0.0302327i
$918$		0			0
$919$	6.30861e6			0.246402			0.123201	−	0.992382i	$-0.460684\pi$
$919$	6.30861e6			0.246402			0.123201	+	0.992382i	$0.460684\pi$
$920$	1.75738e6	+	757650.i	0.0684536	+	0.0295120i
$921$		0			0
$922$	4.98012e6	+	679891.i	0.192936	+	0.0263398i
$923$		−	2.47981e7i		−	0.958108i
$924$		0			0
$925$			2.22902e6i			0.0856563i
$926$	−2.70235e6	+	1.97944e7i	−0.103565	+	0.758603i
$927$		0			0
$928$	−2.55537e7	−	2.05972e7i	−0.974054	−	0.785123i
$929$	9.87673e6			0.375469			0.187734	−	0.982220i	$-0.439886\pi$
$929$	9.87673e6			0.375469			0.187734	+	0.982220i	$0.439886\pi$
$930$		0			0
$931$			4.15847e7i			1.57239i
$932$	−3.14293e7	−	8.74450e6i	−1.18521	−	0.329758i
$933$		0			0
$934$	3.99815e7	+	5.45831e6i	1.49966	+	0.204734i
$935$	−5.05948e6			−0.189268
$936$		0			0
$937$	1.06437e7			0.396046			0.198023	−	0.980197i	$-0.436548\pi$
$937$	1.06437e7			0.396046			0.198023	+	0.980197i	$0.436548\pi$
$938$	−307245.	−	41945.3i	−0.0114019	−	0.00155660i
$939$		0			0
$940$	−1.98224e6	+	7.12453e6i	−0.0731706	+	0.262988i
$941$		−	4.65943e7i		−	1.71537i	−0.514174	−	0.857686i	$-0.671901\pi$
$941$		−	4.65943e7i		−	1.71537i	0.514174	−	0.857686i	$-0.328099\pi$
$942$		0			0
$943$	2.51613e6			0.0921410
$944$	−1.45099e7	+	2.40570e7i	−0.529948	+	0.878641i
$945$		0			0
$946$	1.30883e6	−	9.58701e6i	0.0475505	−	0.348302i
$947$			2.99997e7i			1.08703i	0.839399	+	0.543516i	$0.182907\pi$
$947$			2.99997e7i			1.08703i	−0.839399	+	0.543516i	$0.817093\pi$
$948$		0			0
$949$			3.16097e7i			1.13934i
$950$	−8.71118e6	−	1.18926e6i	−0.313161	−	0.0427531i
$951$		0			0
$952$	−830631.	+	1.92666e6i	−0.0297041	+	0.0688991i
$953$	1.52026e7			0.542233			0.271116	−	0.962547i	$-0.412607\pi$
$953$	1.52026e7			0.542233			0.271116	+	0.962547i	$0.412607\pi$
$954$		0			0
$955$			9.79421e6i			0.347505i
$956$	−3.00828e7	−	8.36987e6i	−1.06457	−	0.296192i
$957$		0			0
$958$	3.84284e6	−	2.81484e7i	0.135282	−	0.990922i
$959$	1.59970e6			0.0561685
$960$		0			0
$961$	5.94891e7			2.07792
$962$	−1.00575e6	+	7.36700e6i	−0.0350390	+	0.256657i
$963$		0			0
$964$	−1.10682e7	−	3.07947e6i	−0.383604	−	0.106729i
$965$		−	1.60280e7i		−	0.554067i
$966$		0			0
$967$	−4.59930e7			−1.58171			−0.790853	−	0.612006i	$-0.790363\pi$
$967$	−4.59930e7			−1.58171			−0.790853	+	0.612006i	$0.790363\pi$
$968$	9.69613e6	−	2.24903e7i	0.332591	−	0.771449i
$969$		0			0
$970$	1.94497e7	+	2.65529e6i	0.663718	+	0.0906114i
$971$		−	3.27040e7i		−	1.11315i	−0.830799	−	0.556573i	$-0.812116\pi$
$971$		−	3.27040e7i		−	1.11315i	0.830799	−	0.556573i	$-0.187884\pi$
$972$		0			0
$973$			2.85643e6i			0.0967255i
$974$	6.92000e6	−	5.06882e7i	0.233727	−	1.71202i
$975$		0			0
$976$	−2.67160e7	+	4.42945e7i	−0.897733	+	1.48842i
$977$	−1.60025e7			−0.536353			−0.268177	−	0.963370i	$-0.586421\pi$
$977$	−1.60025e7			−0.536353			−0.268177	+	0.963370i	$0.586421\pi$
$978$		0			0
$979$		−	1.82890e7i		−	0.609865i
$980$	−3.58593e6	+	1.28885e7i	−0.119271	+	0.428683i
$981$		0			0
$982$	−1.07570e7	−	1.46855e6i	−0.355968	−	0.0485971i
$983$	−5.81035e7			−1.91787			−0.958933	−	0.283634i	$-0.908460\pi$
$983$	−5.81035e7			−1.91787			−0.958933	+	0.283634i	$0.908460\pi$
$984$		0			0
$985$	−7.80324e6			−0.256262
$986$	−4.00489e7	−	5.46751e6i	−1.31189	−	0.179101i
$987$		0			0
$988$	−2.82542e7	−	7.86110e6i	−0.920854	−	0.256207i
$989$			4.50731e6i			0.146530i
$990$		0			0
$991$	−1.47014e7			−0.475527			−0.237764	−	0.971323i	$-0.576414\pi$
$991$	−1.47014e7			−0.475527			−0.237764	+	0.971323i	$0.576414\pi$
$992$	−3.41241e7	+	4.23356e7i	−1.10099	+	1.36593i
$993$		0			0
$994$	−473200.	+	3.46613e6i	−0.0151907	+	0.111270i
$995$			4.28681e6i			0.137270i
$996$		0			0
$997$		−	3.26322e7i		−	1.03970i	−0.854257	−	0.519850i	$-0.825988\pi$
$997$		−	3.26322e7i		−	1.03970i	0.854257	−	0.519850i	$-0.174012\pi$
$998$	−6.83815e6	−	933550.i	−0.217326	−	0.0296696i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.6.k.b.181.10		20
3.2	odd	2		40.6.d.a.21.11	✓	20
8.5	even	2	inner	360.6.k.b.181.9		20
12.11	even	2		160.6.d.a.81.16		20
15.2	even	4		200.6.f.c.149.20		20
15.8	even	4		200.6.f.b.149.1		20
15.14	odd	2		200.6.d.b.101.10		20
24.5	odd	2		40.6.d.a.21.12	yes	20
24.11	even	2		160.6.d.a.81.5		20
60.23	odd	4		800.6.f.c.49.5		20
60.47	odd	4		800.6.f.b.49.16		20
60.59	even	2		800.6.d.c.401.5		20
120.29	odd	2		200.6.d.b.101.9		20
120.53	even	4		200.6.f.c.149.19		20
120.59	even	2		800.6.d.c.401.16		20
120.77	even	4		200.6.f.b.149.2		20
120.83	odd	4		800.6.f.b.49.15		20
120.107	odd	4		800.6.f.c.49.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.11	✓	20	3.2	odd	2
40.6.d.a.21.12	yes	20	24.5	odd	2
160.6.d.a.81.5		20	24.11	even	2
160.6.d.a.81.16		20	12.11	even	2
200.6.d.b.101.9		20	120.29	odd	2
200.6.d.b.101.10		20	15.14	odd	2
200.6.f.b.149.1		20	15.8	even	4
200.6.f.b.149.2		20	120.77	even	4
200.6.f.c.149.19		20	120.53	even	4
200.6.f.c.149.20		20	15.2	even	4
360.6.k.b.181.9		20	8.5	even	2	inner
360.6.k.b.181.10		20	1.1	even	1	trivial
800.6.d.c.401.5		20	60.59	even	2
800.6.d.c.401.16		20	120.59	even	2
800.6.f.b.49.15		20	120.83	odd	4
800.6.f.b.49.16		20	60.47	odd	4
800.6.f.c.49.5		20	60.23	odd	4
800.6.f.c.49.6		20	120.107	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.765181 + 5.60486i) q^{2} +(-30.8290 - 8.57748i) q^{4} +25.0000i q^{5} -9.19080 q^{7} +(71.6654 - 166.229i) q^{8} +O(q^{10})\)	\(q+(-0.765181 + 5.60486i) q^{2} +(-30.8290 - 8.57748i) q^{4} +25.0000i q^{5} -9.19080 q^{7} +(71.6654 - 166.229i) q^{8} +(-140.122 - 19.1295i) q^{10} +160.480i q^{11} +368.546i q^{13} +(7.03263 - 51.5132i) q^{14} +(876.854 + 528.870i) q^{16} +1261.09 q^{17} -2486.75i q^{19} +(214.437 - 770.725i) q^{20} +(-899.467 - 122.796i) q^{22} +422.882 q^{23} -625.000 q^{25} +(-2065.65 - 282.005i) q^{26} +(283.343 + 78.8339i) q^{28} +5666.05i q^{29} +9387.13 q^{31} +(-3635.20 + 4509.96i) q^{32} +(-964.961 + 7068.23i) q^{34} -229.770i q^{35} -3566.43i q^{37} +(13937.9 + 1902.81i) q^{38} +(4155.72 + 1791.63i) q^{40} +5949.95 q^{41} +10658.5i q^{43} +(1376.51 - 4947.43i) q^{44} +(-323.581 + 2370.20i) q^{46} -9243.94 q^{47} -16722.5 q^{49} +(478.238 - 3503.04i) q^{50} +(3161.20 - 11361.9i) q^{52} -8976.82i q^{53} -4011.99 q^{55} +(-658.662 + 1527.78i) q^{56} +(-31757.4 - 4335.55i) q^{58} +27435.6i q^{59} +50515.3i q^{61} +(-7182.86 + 52613.6i) q^{62} +(-22496.2 - 23825.7i) q^{64} -9213.66 q^{65} -5964.39i q^{67} +(-38878.1 - 10817.0i) q^{68} +(1287.83 + 175.816i) q^{70} -67286.3 q^{71} +85768.5 q^{73} +(19989.3 + 2728.96i) q^{74} +(-21330.0 + 76663.9i) q^{76} -1474.94i q^{77} +56567.2 q^{79} +(-13221.7 + 21921.3i) q^{80} +(-4552.79 + 33348.6i) q^{82} +30208.1i q^{83} +31527.2i q^{85} +(-59739.7 - 8155.72i) q^{86} +(26676.4 + 11500.8i) q^{88} -113965. q^{89} -3387.24i q^{91} +(-13037.0 - 3627.26i) q^{92} +(7073.29 - 51811.0i) q^{94} +62168.7 q^{95} -138806. q^{97} +(12795.8 - 93727.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Introduction

L-functions

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