LMFDB - Embedded newform 99.4.f.b.82.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,4,Mod(37,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.37"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	99.f (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121$ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.2
Root			$2.51217 - 1.82520i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.4.f.b.64.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45957 + 4.49208i) q^{2} +(-11.5763 + 8.41069i) q^{4} +(-1.86000 + 5.72450i) q^{5} +(-8.05785 + 5.85437i) q^{7} +(-24.1083 - 17.5157i) q^{8} -28.4297 q^{10} +(-8.30870 + 35.5242i) q^{11} +(-27.8826 - 85.8139i) q^{13} +(-38.0593 - 27.6517i) q^{14} +(8.12031 - 24.9917i) q^{16} +(-13.8539 + 42.6379i) q^{17} +(110.890 + 80.5660i) q^{19} +(-26.6150 - 81.9125i) q^{20} +(-171.704 + 14.5265i) q^{22} +71.4719 q^{23} +(71.8169 + 52.1780i) q^{25} +(344.786 - 250.502i) q^{26} +(44.0409 - 135.544i) q^{28} +(-119.601 + 86.8950i) q^{29} +(2.38514 + 7.34071i) q^{31} -114.279 q^{32} -211.753 q^{34} +(-18.5257 - 57.0163i) q^{35} +(-8.18776 + 5.94875i) q^{37} +(-200.058 + 615.716i) q^{38} +(145.110 - 105.429i) q^{40} +(305.780 + 222.162i) q^{41} +276.048 q^{43} +(-202.598 - 481.121i) q^{44} +(104.318 + 321.057i) q^{46} +(-191.854 - 139.390i) q^{47} +(-75.3376 + 231.865i) q^{49} +(-129.566 + 398.764i) q^{50} +(1044.53 + 758.897i) q^{52} +(68.6297 + 211.221i) q^{53} +(-187.904 - 113.638i) q^{55} +296.805 q^{56} +(-564.905 - 410.427i) q^{58} +(136.832 - 99.4144i) q^{59} +(70.1651 - 215.946i) q^{61} +(-29.4938 + 21.4285i) q^{62} +(-231.761 - 713.286i) q^{64} +543.103 q^{65} -362.669 q^{67} +(-198.237 - 610.110i) q^{68} +(229.082 - 166.438i) q^{70} +(219.919 - 676.841i) q^{71} +(845.463 - 614.265i) q^{73} +(-38.6729 - 28.0975i) q^{74} -1961.31 q^{76} +(-141.021 - 334.890i) q^{77} +(15.6957 + 48.3063i) q^{79} +(127.961 + 92.9694i) q^{80} +(-551.665 + 1697.85i) q^{82} +(378.188 - 1163.94i) q^{83} +(-218.312 - 158.613i) q^{85} +(402.911 + 1240.03i) q^{86} +(822.541 - 710.895i) q^{88} -964.845 q^{89} +(727.060 + 528.240i) q^{91} +(-827.381 + 601.128i) q^{92} +(346.128 - 1065.27i) q^{94} +(-667.455 + 484.934i) q^{95} +(78.8462 + 242.664i) q^{97} -1151.52 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8} + 8 q^{10} + 87 q^{11} + 171 q^{13} - 12 q^{14} + 44 q^{16} - 36 q^{17} + 324 q^{19} + 87 q^{20} - 521 q^{22} + 84 q^{23} + 263 q^{25} + 774 q^{26}+ \cdots - 5550 q^{98}+O(q^{100})$ 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8 + 8 * q^10 + 87 * q^11 + 171 * q^13 - 12 * q^14 + 44 * q^16 - 36 * q^17 + 324 * q^19 + 87 * q^20 - 521 * q^22 + 84 * q^23 + 263 * q^25 + 774 * q^26 + 387 * q^28 - 393 * q^29 + 15 * q^31 - 102 * q^32 - 712 * q^34 - 1002 * q^35 - 747 * q^37 + 36 * q^38 + 41 * q^40 - 159 * q^41 - 644 * q^43 - 219 * q^44 + 753 * q^46 + 351 * q^47 - 1967 * q^49 - 330 * q^50 + 2871 * q^52 + 531 * q^53 - 716 * q^55 - 1470 * q^56 - 1205 * q^58 + 1002 * q^59 + 1449 * q^61 - 99 * q^62 - 1118 * q^64 + 954 * q^65 - 518 * q^67 - 873 * q^68 + 26 * q^70 - 429 * q^71 + 2547 * q^73 - 468 * q^74 - 2276 * q^76 + 2697 * q^77 + 2805 * q^79 + 1620 * q^80 - 1631 * q^82 + 2553 * q^83 - 197 * q^85 + 1713 * q^86 + 2866 * q^88 - 1788 * q^89 + 2885 * q^91 - 423 * q^92 + 1159 * q^94 - 3009 * q^95 + 9 * q^97 - 5550 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$ .

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.45957	+	4.49208i	0.516034	+	1.58819i	0.781392	+	0.624040i	$0.214510\pi$
$2$	1.45957	+	4.49208i	0.516034	+	1.58819i	−0.265358	+	0.964150i	$0.585490\pi$
$3$		0			0
$3$		0			0
$4$	−11.5763	+	8.41069i	−1.44704	+	1.05134i
$5$	−1.86000	+	5.72450i	−0.166364	+	0.512014i	−0.999134	−	0.0416038i	$-0.986753\pi$
$5$	−1.86000	+	5.72450i	−0.166364	+	0.512014i	0.832771	+	0.553618i	$0.186753\pi$
$6$		0			0
$7$	−8.05785	+	5.85437i	−0.435083	+	0.316106i	−0.783678	−	0.621167i	$-0.786659\pi$
$7$	−8.05785	+	5.85437i	−0.435083	+	0.316106i	0.348595	+	0.937273i	$0.386659\pi$
$8$	−24.1083	−	17.5157i	−1.06545	−	0.774094i
$9$		0			0
$10$	−28.4297			−0.899026
$11$	−8.30870	+	35.5242i	−0.227743	+	0.973721i
$11$	−8.30870	+	35.5242i	−0.227743	+	0.973721i
$12$		0			0
$13$	−27.8826	−	85.8139i	−0.594865	−	1.83081i	−0.555396	−	0.831586i	$-0.687433\pi$
$13$	−27.8826	−	85.8139i	−0.594865	−	1.83081i	−0.0394690	−	0.999221i	$-0.512567\pi$
$14$	−38.0593	−	27.6517i	−0.726555	−	0.527873i
$15$		0			0
$16$	8.12031	−	24.9917i	0.126880	−	0.390496i
$17$	−13.8539	+	42.6379i	−0.197651	+	0.608306i	0.802285	+	0.596941i	$0.203618\pi$
$17$	−13.8539	+	42.6379i	−0.197651	+	0.608306i	−0.999935	+	0.0113645i	$0.996382\pi$
$18$		0			0
$19$	110.890	+	80.5660i	1.33894	+	0.972795i	0.999482	+	0.0321734i	$0.0102429\pi$
$19$	110.890	+	80.5660i	1.33894	+	0.972795i	0.339456	+	0.940622i	$0.389757\pi$
$20$	−26.6150	−	81.9125i	−0.297564	−	0.915809i
$21$		0			0
$22$	−171.704	+	14.5265i	−1.66398	+	0.140775i
$23$	71.4719			0.647953			0.323977	−	0.946065i	$-0.394980\pi$
$23$	71.4719			0.647953			0.323977	+	0.946065i	$0.394980\pi$
$24$		0			0
$25$	71.8169	+	52.1780i	0.574535	+	0.417424i
$26$	344.786	−	250.502i	2.60070	−	1.88952i
$27$		0			0
$28$	44.0409	−	135.544i	0.297248	−	0.914837i
$29$	−119.601	+	86.8950i	−0.765838	+	0.556414i	−0.900695	−	0.434451i	$-0.856942\pi$
$29$	−119.601	+	86.8950i	−0.765838	+	0.556414i	0.134857	+	0.990865i	$0.456942\pi$
$30$		0			0
$31$	2.38514	+	7.34071i	0.0138188	+	0.0425300i	0.957728	−	0.287675i	$-0.0928822\pi$
$31$	2.38514	+	7.34071i	0.0138188	+	0.0425300i	−0.943909	+	0.330205i	$0.892882\pi$
$32$	−114.279			−0.631310
$33$		0			0
$34$	−211.753			−1.06810
$35$	−18.5257	−	57.0163i	−0.0894690	−	0.275357i
$36$		0			0
$37$	−8.18776	+	5.94875i	−0.0363800	+	0.0264316i	−0.605827	−	0.795597i	$-0.707158\pi$
$37$	−8.18776	+	5.94875i	−0.0363800	+	0.0264316i	0.569447	+	0.822028i	$0.307158\pi$
$38$	−200.058	+	615.716i	−0.854046	+	2.62848i
$39$		0			0
$40$	145.110	−	105.429i	0.573599	−	0.416744i
$41$	305.780	+	222.162i	1.16475	+	0.846242i	0.990371	−	0.138436i	$-0.0442075\pi$
$41$	305.780	+	222.162i	1.16475	+	0.846242i	0.174381	+	0.984678i	$0.444207\pi$
$42$		0			0
$43$	276.048			0.979000			0.489500	−	0.872003i	$-0.337179\pi$
$43$	276.048			0.979000			0.489500	+	0.872003i	$0.337179\pi$
$44$	−202.598	−	481.121i	−0.694156	−	1.64845i
$45$		0			0
$46$	104.318	+	321.057i	0.334366	+	1.02907i
$47$	−191.854	−	139.390i	−0.595421	−	0.432599i	0.248830	−	0.968547i	$-0.419954\pi$
$47$	−191.854	−	139.390i	−0.595421	−	0.432599i	−0.844251	+	0.535949i	$0.819954\pi$
$48$		0			0
$49$	−75.3376	+	231.865i	−0.219643	+	0.675992i
$50$	−129.566	+	398.764i	−0.366469	+	1.12788i
$51$		0			0
$52$	1044.53	+	758.897i	2.78559	+	2.02385i
$53$	68.6297	+	211.221i	0.177868	+	0.547422i	0.999753	−	0.0222318i	$-0.00707718\pi$
$53$	68.6297	+	211.221i	0.177868	+	0.547422i	−0.821885	+	0.569654i	$0.807077\pi$
$54$		0			0
$55$	−187.904	−	113.638i	−0.460671	−	0.278599i
$56$	296.805			0.708254
$57$		0			0
$58$	−564.905	−	410.427i	−1.27889	−	0.929168i
$59$	136.832	−	99.4144i	0.301933	−	0.219367i	−0.426494	−	0.904490i	$-0.640252\pi$
$59$	136.832	−	99.4144i	0.301933	−	0.219367i	0.728427	+	0.685123i	$0.240252\pi$
$60$		0			0
$61$	70.1651	−	215.946i	0.147274	−	0.453263i	−0.850022	−	0.526747i	$-0.823412\pi$
$61$	70.1651	−	215.946i	0.147274	−	0.453263i	0.997296	+	0.0734835i	$0.0234116\pi$
$62$	−29.4938	+	21.4285i	−0.0604147	+	0.0438939i
$63$		0			0
$64$	−231.761	−	713.286i	−0.452658	−	1.39314i
$65$	543.103			1.03636
$66$		0			0
$67$	−362.669			−0.661300			−0.330650	−	0.943753i	$-0.607268\pi$
$67$	−362.669			−0.661300			−0.330650	+	0.943753i	$0.607268\pi$
$68$	−198.237	−	610.110i	−0.353526	−	1.08804i
$69$		0			0
$70$	229.082	−	166.438i	0.391151	−	0.284188i
$71$	219.919	−	676.841i	0.367600	−	1.13136i	−0.580737	−	0.814091i	$-0.697236\pi$
$71$	219.919	−	676.841i	0.367600	−	1.13136i	0.948337	−	0.317265i	$-0.102764\pi$
$72$		0			0
$73$	845.463	−	614.265i	1.35553	−	0.984853i	0.356820	−	0.934173i	$-0.383861\pi$
$73$	845.463	−	614.265i	1.35553	−	0.984853i	0.998715	−	0.0506801i	$-0.0161389\pi$
$74$	−38.6729	−	28.0975i	−0.0607517	−	0.0441387i
$75$		0			0
$76$	−1961.31			−2.96023
$77$	−141.021	−	334.890i	−0.208713	−	0.495640i
$78$		0			0
$79$	15.6957	+	48.3063i	0.0223532	+	0.0687959i	0.961611	−	0.274417i	$-0.0884848\pi$
$79$	15.6957	+	48.3063i	0.0223532	+	0.0687959i	−0.939258	+	0.343213i	$0.888485\pi$
$80$	127.961	+	92.9694i	0.178831	+	0.129929i
$81$		0			0
$82$	−551.665	+	1697.85i	−0.742942	+	2.28654i
$83$	378.188	−	1163.94i	0.500139	−	1.53927i	−0.308653	−	0.951175i	$-0.599878\pi$
$83$	378.188	−	1163.94i	0.500139	−	1.53927i	0.808792	−	0.588095i	$-0.200122\pi$
$84$		0			0
$85$	−218.312	−	158.613i	−0.278580	−	0.202400i
$86$	402.911	+	1240.03i	0.505197	+	1.55484i
$87$		0			0
$88$	822.541	−	710.895i	0.996399	−	0.861156i
$89$	−964.845			−1.14914			−0.574569	−	0.818456i	$-0.694830\pi$
$89$	−964.845			−1.14914			−0.574569	+	0.818456i	$0.694830\pi$
$90$		0			0
$91$	727.060	+	528.240i	0.837545	+	0.608512i
$92$	−827.381	+	601.128i	−0.937614	+	0.681216i
$93$		0			0
$94$	346.128	−	1065.27i	0.379791	−	1.16888i
$95$	−667.455	+	484.934i	−0.720836	+	0.523718i
$96$		0			0
$97$	78.8462	+	242.664i	0.0825321	+	0.254008i	0.983804	−	0.179245i	$-0.0573656\pi$
$97$	78.8462	+	242.664i	0.0825321	+	0.254008i	−0.901272	+	0.433253i	$0.857366\pi$
$98$	−1151.52			−1.18695
$99$		0			0
$100$	−1270.23			−1.27023
$101$	−41.9267	−	129.037i	−0.0413055	−	0.127125i	0.928277	−	0.371889i	$-0.121290\pi$
$101$	−41.9267	−	129.037i	−0.0413055	−	0.127125i	−0.969583	+	0.244763i	$0.921290\pi$
$102$		0			0
$103$	557.554	−	405.087i	0.533373	−	0.387518i	−0.288245	−	0.957557i	$-0.593072\pi$
$103$	557.554	−	405.087i	0.533373	−	0.387518i	0.821618	+	0.570039i	$0.193072\pi$
$104$	−830.890	+	2557.21i	−0.783418	+	2.41111i
$105$		0			0
$106$	−848.650	+	616.581i	−0.777625	+	0.564977i
$107$	784.130	+	569.704i	0.708455	+	0.514723i	0.882675	−	0.469984i	$-0.155740\pi$
$107$	784.130	+	569.704i	0.708455	+	0.514723i	−0.174220	+	0.984707i	$0.555740\pi$
$108$		0			0
$109$	−235.888			−0.207284			−0.103642	−	0.994615i	$-0.533050\pi$
$109$	−235.888			−0.207284			−0.103642	+	0.994615i	$0.533050\pi$
$110$	236.214	−	1009.94i	0.204746	−	0.875400i
$111$		0			0
$112$	80.8787	+	248.919i	0.0682350	+	0.210006i
$113$	416.768	+	302.800i	0.346958	+	0.252080i	0.747592	−	0.664159i	$-0.231210\pi$
$113$	416.768	+	302.800i	0.346958	+	0.252080i	−0.400634	+	0.916238i	$0.631210\pi$
$114$		0			0
$115$	−132.938	+	409.141i	−0.107796	+	0.331761i
$116$	653.689	−	2011.85i	0.523220	−	1.61031i
$117$		0			0
$118$	646.293	+	469.559i	0.504204	+	0.366326i
$119$	−137.985	−	424.675i	−0.106295	−	0.327142i
$120$		0			0
$121$	−1192.93	−	590.319i	−0.896267	−	0.443515i
$122$	1072.46			0.795867
$123$		0			0
$124$	−89.3515	−	64.9177i	−0.0647097	−	0.0470144i
$125$	−1040.97	+	756.306i	−0.744854	+	0.541168i
$126$		0			0
$127$	319.132	−	982.188i	0.222980	−	0.686261i	−0.775511	−	0.631334i	$-0.782508\pi$
$127$	319.132	−	982.188i	0.222980	−	0.686261i	0.998490	−	0.0549264i	$-0.0174924\pi$
$128$	2126.24	−	1544.80i	1.46824	−	1.06674i
$129$		0			0
$130$	792.694	+	2439.66i	0.534799	+	1.64594i
$131$	−1366.16			−0.911157			−0.455578	−	0.890196i	$-0.650568\pi$
$131$	−1366.16			−0.911157			−0.455578	+	0.890196i	$0.650568\pi$
$132$		0			0
$133$	−1365.19			−0.890056
$134$	−529.339	−	1629.14i	−0.341253	−	1.05027i
$135$		0			0
$136$	1080.83	−	785.267i	0.681472	−	0.495118i
$137$	−467.210	+	1437.92i	−0.291361	+	0.896716i	0.693059	+	0.720881i	$0.256263\pi$
$137$	−467.210	+	1437.92i	−0.291361	+	0.896716i	−0.984420	+	0.175835i	$0.943737\pi$
$138$		0			0
$139$	848.109	−	616.187i	0.517523	−	0.376002i	−0.298147	−	0.954520i	$-0.596369\pi$
$139$	848.109	−	616.187i	0.517523	−	0.376002i	0.815670	+	0.578518i	$0.196369\pi$
$140$	694.005	+	504.224i	0.418958	+	0.304391i
$141$		0			0
$142$	3361.41			1.98650
$143$	3280.13	−	277.505i	1.91817	−	0.162280i
$144$		0			0
$145$	−274.973	−	846.279i	−0.157484	−	0.484687i
$146$	3993.34	+	2901.33i	2.26364	+	1.64463i
$147$		0			0
$148$	44.7510	−	137.729i	0.0248548	−	0.0764952i
$149$	119.658	−	368.270i	0.0657905	−	0.202482i	−0.912757	−	0.408502i	$-0.866051\pi$
$149$	119.658	−	368.270i	0.0657905	−	0.202482i	0.978548	+	0.206020i	$0.0660512\pi$
$150$		0			0
$151$	−549.139	−	398.973i	−0.295949	−	0.215019i	0.429895	−	0.902879i	$-0.358551\pi$
$151$	−549.139	−	398.973i	−0.295949	−	0.215019i	−0.725844	+	0.687859i	$0.758551\pi$
$152$	−1262.19	−	3884.63i	−0.673535	−	2.07293i
$153$		0			0
$154$	1298.53	−	1122.27i	0.679468	−	0.587243i
$155$	−46.4582			−0.0240749
$156$		0			0
$157$	2919.99	+	2121.50i	1.48434	+	1.07843i	0.976127	+	0.217200i	$0.0696925\pi$
$157$	2919.99	+	2121.50i	1.48434	+	1.07843i	0.508210	+	0.861233i	$0.330308\pi$
$158$	−194.087	+	141.012i	−0.0977260	+	0.0710021i
$159$		0			0
$160$	212.560	−	654.192i	0.105027	−	0.323240i
$161$	−575.910	+	418.423i	−0.281913	+	0.204822i
$162$		0			0
$163$	284.219	+	874.736i	0.136575	+	0.420335i	0.995832	−	0.0912099i	$-0.0290734\pi$
$163$	284.219	+	874.736i	0.136575	+	0.420335i	−0.859257	+	0.511545i	$0.829073\pi$
$164$	−5408.35			−2.57513
$165$		0			0
$166$	5780.52			2.70274
$167$	713.424	+	2195.69i	0.330577	+	1.01741i	0.968860	+	0.247610i	$0.0796453\pi$
$167$	713.424	+	2195.69i	0.330577	+	1.01741i	−0.638282	+	0.769802i	$0.720355\pi$
$168$		0			0
$169$	−4809.17	+	3494.07i	−2.18897	+	1.59038i
$170$	393.861	−	1212.18i	0.177693	−	0.546883i
$171$		0			0
$172$	−3195.62	+	2321.76i	−1.41665	+	1.02926i
$173$	−370.871	−	269.454i	−0.162987	−	0.118417i	0.503302	−	0.864111i	$-0.332118\pi$
$173$	−370.871	−	269.454i	−0.162987	−	0.118417i	−0.666289	+	0.745693i	$0.732118\pi$
$174$		0			0
$175$	−884.159			−0.381921
$176$	820.342	+	496.116i	0.351338	+	0.212478i
$177$		0			0
$178$	−1408.25	−	4334.16i	−0.592995	−	1.82505i
$179$	−2880.70	−	2092.95i	−1.20287	−	0.873935i	−0.208304	−	0.978064i	$-0.566794\pi$
$179$	−2880.70	−	2092.95i	−1.20287	−	0.873935i	−0.994564	+	0.104129i	$0.966794\pi$
$180$		0			0
$181$	248.804	−	765.741i	0.102174	−	0.314459i	−0.886883	−	0.461994i	$-0.847134\pi$
$181$	248.804	−	765.741i	0.102174	−	0.314459i	0.989057	+	0.147535i	$0.0471340\pi$
$182$	−1311.71	+	4037.01i	−0.534231	+	1.64419i
$183$		0			0
$184$	−1723.07	−	1251.88i	−0.690360	−	0.501576i
$185$	−18.8244	−	57.9355i	−0.00748106	−	0.0230243i
$186$		0			0
$187$	−1399.57	−	846.413i	−0.547307	−	0.330994i
$188$	3393.33			1.31640
$189$		0			0
$190$	−3152.56	−	2290.47i	−1.20374	−	0.874568i
$191$	−1836.35	+	1334.19i	−0.695674	+	0.505437i	−0.878520	−	0.477705i	$-0.841469\pi$
$191$	−1836.35	+	1334.19i	−0.695674	+	0.505437i	0.182847	+	0.983141i	$0.441469\pi$
$192$		0			0
$193$	−1477.59	+	4547.55i	−0.551083	+	1.69606i	0.154986	+	0.987917i	$0.450467\pi$
$193$	−1477.59	+	4547.55i	−0.551083	+	1.69606i	−0.706069	+	0.708143i	$0.749533\pi$
$194$	−974.983	+	708.367i	−0.360823	+	0.262153i
$195$		0			0
$196$	−1078.01	−	3317.79i	−0.392862	−	1.20911i
$197$	2009.15			0.726630			0.363315	−	0.931666i	$-0.381645\pi$
$197$	2009.15			0.726630			0.363315	+	0.931666i	$0.381645\pi$
$198$		0			0
$199$	3250.22			1.15780			0.578900	−	0.815398i	$-0.303482\pi$
$199$	3250.22			1.15780			0.578900	+	0.815398i	$0.303482\pi$
$200$	−817.450	−	2515.85i	−0.289012	−	0.889488i
$201$		0			0
$202$	518.450	−	376.676i	0.180584	−	0.131202i
$203$	455.009	−	1400.37i	0.157317	−	0.484172i
$204$		0			0
$205$	−1840.52	+	1337.22i	−0.627061	+	0.455586i
$206$	2633.47	+	1913.33i	0.890691	+	0.647125i
$207$		0			0
$208$	−2371.05			−0.790399
$209$	−3783.39	+	3269.86i	−1.25216	+	1.08221i
$210$		0			0
$211$	−95.3371	−	293.417i	−0.0311056	−	0.0957331i	0.934298	−	0.356492i	$-0.116027\pi$
$211$	−95.3371	−	293.417i	−0.0311056	−	0.0957331i	−0.965404	+	0.260759i	$0.916027\pi$
$212$	−2570.99	−	1867.93i	−0.832907	−	0.605143i
$213$		0			0
$214$	−1414.67	+	4353.89i	−0.451890	+	1.39078i
$215$	−513.450	+	1580.24i	−0.162870	+	0.501262i
$216$		0			0
$217$	−62.1943	−	45.1868i	−0.0194563	−	0.0141359i
$218$	−344.294	−	1059.63i	−0.106966	−	0.329207i
$219$		0			0
$220$	3131.01	−	264.888i	0.959511	−	0.0811762i
$221$	4045.20			1.23127
$222$		0			0
$223$	−3744.98	−	2720.89i	−1.12458	−	0.817058i	−0.139687	−	0.990196i	$-0.544610\pi$
$223$	−3744.98	−	2720.89i	−1.12458	−	0.817058i	−0.984898	+	0.173137i	$0.944610\pi$
$224$	920.846	−	669.033i	0.274672	−	0.199561i
$225$		0			0
$226$	−751.901	+	2314.11i	−0.221308	+	0.681117i
$227$	2093.34	−	1520.90i	0.612070	−	0.444695i	−0.238073	−	0.971247i	$-0.576516\pi$
$227$	2093.34	−	1520.90i	0.612070	−	0.444695i	0.850142	+	0.526553i	$0.176516\pi$
$228$		0			0
$229$	675.764	+	2079.79i	0.195003	+	0.600158i	0.999977	+	0.00684712i	$0.00217952\pi$
$229$	675.764	+	2079.79i	0.195003	+	0.600158i	−0.804973	+	0.593311i	$0.797820\pi$
$230$	−2031.92			−0.582526
$231$		0			0
$232$	4405.41			1.24668
$233$	−2059.58	−	6338.75i	−0.579090	−	1.78225i	−0.621810	−	0.783168i	$-0.713603\pi$
$233$	−2059.58	−	6338.75i	−0.579090	−	1.78225i	0.0427208	−	0.999087i	$-0.486397\pi$
$234$		0			0
$235$	1154.79	−	839.002i	0.320553	−	0.232895i
$236$	−747.869	+	2301.71i	−0.206280	+	0.634866i
$237$		0			0
$238$	1706.28	−	1239.68i	0.464712	−	0.337633i
$239$	1800.04	+	1307.80i	0.487174	+	0.353953i	0.804097	−	0.594499i	$-0.202650\pi$
$239$	1800.04	+	1307.80i	0.487174	+	0.353953i	−0.316922	+	0.948451i	$0.602650\pi$
$240$		0			0
$241$	745.650			0.199301			0.0996505	−	0.995023i	$-0.468228\pi$
$241$	745.650			0.199301			0.0996505	+	0.995023i	$0.468228\pi$
$242$	910.600	−	6220.35i	0.241883	−	1.65231i
$243$		0			0
$244$	1004.00	+	3090.00i	0.263420	+	0.810724i
$245$	−1187.18	−	862.539i	−0.309577	−	0.224921i
$246$		0			0
$247$	3821.79	−	11762.3i	0.984513	−	3.03002i
$248$	71.0761	−	218.750i	0.0181989	−	0.0560106i
$249$		0			0
$250$	−4916.74	−	3572.22i	−1.24385	−	0.903709i
$251$	546.697	+	1682.56i	0.137479	+	0.423116i	0.995967	−	0.0897164i	$-0.0285961\pi$
$251$	546.697	+	1682.56i	0.137479	+	0.423116i	−0.858489	+	0.512833i	$0.828596\pi$
$252$		0			0
$253$	−593.839	+	2538.98i	−0.147566	+	0.630926i
$254$	4877.86			1.20498
$255$		0			0
$256$	5188.69	+	3769.81i	1.26677	+	0.920363i
$257$	−1942.61	+	1411.39i	−0.471505	+	0.342569i	−0.798028	−	0.602621i	$-0.794123\pi$
$257$	−1942.61	+	1411.39i	−0.471505	+	0.342569i	0.326522	+	0.945189i	$0.394123\pi$
$258$		0			0
$259$	31.1495	−	95.8683i	0.00747311	−	0.0229999i
$260$	−6287.13	+	4567.87i	−1.49966	+	1.08957i
$261$		0			0
$262$	−1993.99	−	6136.88i	−0.470188	−	1.44709i
$263$	5999.10			1.40654			0.703270	−	0.710923i	$-0.251722\pi$
$263$	5999.10			1.40654			0.703270	+	0.710923i	$0.251722\pi$
$264$		0			0
$265$	−1336.78			−0.309879
$266$	−1992.59	−	6132.57i	−0.459299	−	1.41358i
$267$		0			0
$268$	4198.37	−	3050.30i	0.956927	−	0.695248i
$269$	−241.484	+	743.212i	−0.0547344	+	0.168455i	−0.974687	−	0.223575i	$-0.928227\pi$
$269$	−241.484	+	743.212i	−0.0547344	+	0.168455i	0.919952	+	0.392030i	$0.128227\pi$
$270$		0			0
$271$	−363.969	+	264.439i	−0.0815851	+	0.0592751i	−0.627830	−	0.778350i	$-0.716057\pi$
$271$	−363.969	+	264.439i	−0.0815851	+	0.0592751i	0.546245	+	0.837625i	$0.316057\pi$
$272$	953.097	+	692.465i	0.212463	+	0.154364i
$273$		0			0
$274$	−7141.19			−1.57451
$275$	−2450.28	+	2117.70i	−0.537301	+	0.464372i
$276$		0			0
$277$	−1303.43	−	4011.55i	−0.282728	−	0.870147i	−0.987070	−	0.160287i	$-0.948758\pi$
$277$	−1303.43	−	4011.55i	−0.282728	−	0.870147i	0.704342	−	0.709860i	$-0.251242\pi$
$278$	4005.83	+	2910.41i	0.864223	+	0.627895i
$279$		0			0
$280$	−552.058	+	1699.06i	−0.117828	+	0.362636i
$281$	945.957	−	2911.36i	0.200822	−	0.618068i	−0.799037	−	0.601282i	$-0.794657\pi$
$281$	945.957	−	2911.36i	0.200822	−	0.618068i	0.999859	−	0.0167855i	$-0.00534323\pi$
$282$		0			0
$283$	4714.18	+	3425.05i	0.990208	+	0.719428i	0.959967	−	0.280115i	$-0.0903725\pi$
$283$	4714.18	+	3425.05i	0.990208	+	0.719428i	0.0302411	+	0.999543i	$0.490372\pi$
$284$	3146.85	+	9685.00i	0.657504	+	2.02359i
$285$		0			0
$286$	6034.14	+	14329.6i	1.24757	+	2.96268i
$287$	−3764.55			−0.774267
$288$		0			0
$289$	2348.64	+	1706.39i	0.478047	+	0.347321i
$290$	3400.21	−	2470.40i	0.688508	−	0.500230i
$291$		0			0
$292$	−4620.96	+	14221.9i	−0.926100	+	2.85024i
$293$	−370.485	+	269.173i	−0.0738703	+	0.0536699i	−0.624108	−	0.781338i	$-0.714537\pi$
$293$	−370.485	+	269.173i	−0.0738703	+	0.0536699i	0.550237	+	0.835008i	$0.314537\pi$
$294$		0			0
$295$	314.589	+	968.206i	0.0620885	+	0.191089i
$296$	301.590			0.0592215
$297$		0			0
$298$	1828.95			0.355531
$299$	−1992.82	−	6133.28i	−0.385445	−	1.18628i
$300$		0			0
$301$	−2224.36	+	1616.09i	−0.425946	+	0.309468i
$302$	990.713	−	3049.10i	0.188772	−	0.580980i
$303$		0			0
$304$	2913.94	−	2117.10i	0.549757	−	0.399422i
$305$	1105.67	+	803.320i	0.207576	+	0.150813i
$306$		0			0
$307$	3941.62			0.732769			0.366385	−	0.930463i	$-0.380595\pi$
$307$	3941.62			0.732769			0.366385	+	0.930463i	$0.380595\pi$
$308$	4449.17	+	2690.71i	0.823100	+	0.497784i
$309$		0			0
$310$	−67.8088	−	208.694i	−0.0124235	−	0.0382356i
$311$	2220.01	+	1612.93i	0.404776	+	0.294087i	0.771483	−	0.636249i	$-0.219515\pi$
$311$	2220.01	+	1612.93i	0.404776	+	0.294087i	−0.366708	+	0.930336i	$0.619515\pi$
$312$		0			0
$313$	−607.584	+	1869.95i	−0.109721	+	0.337687i	−0.990809	−	0.135265i	$-0.956811\pi$
$313$	−607.584	+	1869.95i	−0.109721	+	0.337687i	0.881088	+	0.472952i	$0.156811\pi$
$314$	−5268.02	+	16213.3i	−0.946789	+	2.91392i
$315$		0			0
$316$	−587.987	−	427.197i	−0.104674	−	0.0760498i
$317$	−1972.03	−	6069.28i	−0.349401	−	1.07535i	−0.959185	−	0.282778i	$-0.908744\pi$
$317$	−1972.03	−	6069.28i	−0.349401	−	1.07535i	0.609784	−	0.792568i	$-0.291256\pi$
$318$		0			0
$319$	−2093.15	−	4970.70i	−0.367378	−	0.872432i
$320$	4514.28			0.788612
$321$		0			0
$322$	−2720.17	−	1976.32i	−0.470773	−	0.342037i
$323$	−4971.41	+	3611.94i	−0.856399	+	0.622210i
$324$		0			0
$325$	2475.16	−	7617.74i	0.422452	−	1.30017i
$326$	−3514.55	+	2553.47i	−0.597094	+	0.433814i
$327$		0			0
$328$	−3480.52	−	10711.9i	−0.585913	−	1.80326i
$329$	2361.97			0.395805
$330$		0			0
$331$	3351.60			0.556557			0.278279	−	0.960500i	$-0.410236\pi$
$331$	3351.60			0.556557			0.278279	+	0.960500i	$0.410236\pi$
$332$	5411.54	+	16655.0i	0.894569	+	2.75320i
$333$		0			0
$334$	−8821.95	+	6409.52i	−1.44526	+	1.05004i
$335$	674.565	−	2076.10i	0.110016	−	0.338595i
$336$		0			0
$337$	2127.64	−	1545.82i	0.343916	−	0.249870i	−0.402396	−	0.915466i	$-0.631823\pi$
$337$	2127.64	−	1545.82i	0.343916	−	0.249870i	0.746312	+	0.665596i	$0.231823\pi$
$338$	−22714.9	−	16503.4i	−3.65541	−	2.65581i
$339$		0			0
$340$	3861.29			0.615906
$341$	−280.590	+	23.7383i	−0.0445595	+	0.00376981i
$342$		0			0
$343$	−1806.06	−	5558.48i	−0.284309	−	0.875014i
$344$	−6655.07	−	4835.19i	−1.04307	−	0.757837i
$345$		0			0
$346$	669.097	−	2059.27i	0.103962	−	0.319962i
$347$	2710.55	−	8342.20i	0.419336	−	1.29058i	−0.488978	−	0.872296i	$-0.662630\pi$
$347$	2710.55	−	8342.20i	0.419336	−	1.29058i	0.908314	−	0.418288i	$-0.137370\pi$
$348$		0			0
$349$	5365.95	+	3898.59i	0.823017	+	0.597957i	0.917575	−	0.397563i	$-0.130144\pi$
$349$	5365.95	+	3898.59i	0.823017	+	0.597957i	−0.0945581	+	0.995519i	$0.530144\pi$
$350$	−1290.49	−	3971.71i	−0.197084	−	0.606563i
$351$		0			0
$352$	949.513	−	4059.68i	0.143776	−	0.614720i
$353$	−722.467			−0.108932			−0.0544661	−	0.998516i	$-0.517346\pi$
$353$	−722.467			−0.108932			−0.0544661	+	0.998516i	$0.517346\pi$
$354$		0			0
$355$	3465.52	+	2517.85i	0.518115	+	0.376433i
$356$	11169.4	−	8115.01i	1.66285	−	1.20813i
$357$		0			0
$358$	5197.13	−	15995.1i	0.767254	−	2.36136i
$359$	6597.95	−	4793.69i	0.969990	−	0.704739i	0.0145406	−	0.999894i	$-0.495371\pi$
$359$	6597.95	−	4793.69i	0.969990	−	0.704739i	0.955449	+	0.295155i	$0.0953714\pi$
$360$		0			0
$361$	3686.08	+	11344.6i	0.537407	+	1.65397i
$362$	3802.92			0.552146
$363$		0			0
$364$	−12859.5			−1.85171
$365$	1943.79	+	5982.39i	0.278748	+	0.857897i
$366$		0			0
$367$	−9647.07	+	7009.00i	−1.37213	+	0.996913i	−0.374566	+	0.927200i	$0.622208\pi$
$367$	−9647.07	+	7009.00i	−1.37213	+	0.996913i	−0.997567	+	0.0697126i	$0.977792\pi$
$368$	580.374	−	1786.21i	0.0822122	−	0.253023i
$369$		0			0
$370$	232.775	−	169.121i	0.0327065	−	0.0237627i
$371$	−1789.57	−	1300.20i	−0.250431	−	0.181949i
$372$		0			0
$373$	−5520.95			−0.766391			−0.383195	−	0.923667i	$-0.625176\pi$
$373$	−5520.95			−0.766391			−0.383195	+	0.923667i	$0.625176\pi$
$374$	1759.39	−	7522.36i	0.243252	−	1.04003i
$375$		0			0
$376$	2183.76	+	6720.93i	0.299518	+	0.921823i
$377$	10791.6	+	7840.54i	1.47426	+	1.07111i
$378$		0			0
$379$	2086.95	−	6422.98i	0.282848	−	0.870518i	−0.704187	−	0.710015i	$-0.748688\pi$
$379$	2086.95	−	6422.98i	0.282848	−	0.870518i	0.987035	−	0.160503i	$-0.0513117\pi$
$380$	3648.04	−	11227.5i	0.492475	−	1.51568i
$381$		0			0
$382$	−8673.55	−	6301.70i	−1.16172	−	0.844040i
$383$	1642.23	+	5054.26i	0.219097	+	0.674310i	0.998837	+	0.0482074i	$0.0153509\pi$
$383$	1642.23	+	5054.26i	0.219097	+	0.674310i	−0.779741	+	0.626102i	$0.784649\pi$
$384$		0			0
$385$	2179.38	−	184.379i	0.288497	−	0.0244073i
$386$	−22584.6			−2.97804
$387$		0			0
$388$	−2953.72	−	2146.00i	−0.386475	−	0.280790i
$389$	−92.0601	+	66.8856i	−0.0119991	+	0.00871783i	−0.593769	−	0.804636i	$-0.702361\pi$
$389$	−92.0601	+	66.8856i	−0.0119991	+	0.00871783i	0.581770	+	0.813354i	$0.302361\pi$
$390$		0			0
$391$	−990.163	+	3047.41i	−0.128068	+	0.394154i
$392$	5877.55	−	4270.29i	0.757299	−	0.550210i
$393$		0			0
$394$	2932.49	+	9025.27i	0.374966	+	1.15403i
$395$	−305.723			−0.0389433
$396$		0			0
$397$	−4034.28			−0.510012			−0.255006	−	0.966940i	$-0.582077\pi$
$397$	−4034.28			−0.510012			−0.255006	+	0.966940i	$0.582077\pi$
$398$	4743.91	+	14600.3i	0.597465	+	1.83881i
$399$		0			0
$400$	1887.20	−	1371.13i	0.235899	−	0.171391i
$401$	−3098.74	+	9536.93i	−0.385894	+	1.18766i	0.549936	+	0.835207i	$0.314652\pi$
$401$	−3098.74	+	9536.93i	−0.385894	+	1.18766i	−0.935830	+	0.352452i	$0.885348\pi$
$402$		0			0
$403$	563.430	−	409.356i	0.0696438	−	0.0505992i
$404$	1570.65	+	1141.14i	0.193422	+	0.140529i
$405$		0			0
$406$	6954.71			0.850139
$407$	−143.295	−	340.290i	−0.0174517	−	0.0414436i
$408$		0			0
$409$	91.0554	+	280.240i	0.0110083	+	0.0338801i	0.956410	−	0.292028i	$-0.0943300\pi$
$409$	91.0554	+	280.240i	0.0110083	+	0.0338801i	−0.945401	+	0.325908i	$0.894330\pi$
$410$	−8693.24	−	6316.01i	−1.04714	−	0.760794i
$411$		0			0
$412$	−3047.36	+	9378.82i	−0.364400	+	1.12151i
$413$	−520.564	+	1602.13i	−0.0620225	+	0.190886i
$414$		0			0
$415$	5959.56	+	4329.87i	0.704924	+	0.512157i
$416$	3186.41	+	9806.75i	0.375544	+	1.15581i
$417$		0			0
$418$	−20210.6	−	12222.7i	−2.36491	−	1.43022i
$419$	1094.76			0.127643			0.0638215	−	0.997961i	$-0.479671\pi$
$419$	1094.76			0.127643			0.0638215	+	0.997961i	$0.479671\pi$
$420$		0			0
$421$	−10574.2	−	7682.63i	−1.22412	−	0.889379i	−0.227689	−	0.973734i	$-0.573117\pi$
$421$	−10574.2	−	7682.63i	−1.22412	−	0.889379i	−0.996436	+	0.0843554i	$0.973117\pi$
$422$	1178.90	−	856.524i	0.135991	−	0.0988031i
$423$		0			0
$424$	2045.14	−	6294.28i	0.234247	−	0.720937i
$425$	−3219.70	+	2339.25i	−0.367479	+	0.266989i
$426$		0			0
$427$	698.848	+	2150.83i	0.0792029	+	0.243761i
$428$	−13868.9			−1.56631
$429$		0			0
$430$	−7847.97			−0.880146
$431$	455.301	+	1401.27i	0.0508842	+	0.156605i	0.973270	−	0.229665i	$-0.0737631\pi$
$431$	455.301	+	1401.27i	0.0508842	+	0.156605i	−0.922386	+	0.386271i	$0.873763\pi$
$432$		0			0
$433$	3285.04	−	2386.72i	0.364594	−	0.264893i	−0.390372	−	0.920657i	$-0.627654\pi$
$433$	3285.04	−	2386.72i	0.364594	−	0.264893i	0.754966	+	0.655764i	$0.227654\pi$
$434$	112.206	−	345.335i	0.0124103	−	0.0381949i
$435$		0			0
$436$	2730.72	−	1983.98i	0.299949	−	0.217926i
$437$	7925.49	+	5758.21i	0.867569	+	0.630326i
$438$		0			0
$439$	11732.1			1.27550			0.637749	−	0.770244i	$-0.279866\pi$
$439$	11732.1			1.27550			0.637749	+	0.770244i	$0.279866\pi$
$440$	2539.59	+	6030.90i	0.275160	+	0.653436i
$441$		0			0
$442$	5904.24	+	18171.4i	0.635375	+	1.95548i
$443$	−738.883	−	536.830i	−0.0792447	−	0.0575747i	0.547458	−	0.836833i	$-0.315596\pi$
$443$	−738.883	−	536.830i	−0.0792447	−	0.0575747i	−0.626702	+	0.779259i	$0.715596\pi$
$444$		0			0
$445$	1794.61	−	5523.25i	0.191175	−	0.588376i
$446$	6756.40	−	20794.1i	0.717320	−	2.20768i
$447$		0			0
$448$	6043.33	+	4390.74i	0.637323	+	0.463042i
$449$	−4495.39	−	13835.4i	−0.472495	−	1.45419i	−0.849306	−	0.527901i	$-0.822979\pi$
$449$	−4495.39	−	13835.4i	−0.472495	−	1.45419i	0.376810	−	0.926290i	$-0.377021\pi$
$450$		0			0
$451$	−10432.8	+	9016.71i	−1.08927	+	0.941419i
$452$	−7371.40			−0.767083
$453$		0			0
$454$	9887.37	+	7183.59i	1.02211	+	0.742605i
$455$	−4376.24	+	3179.52i	−0.450904	+	0.327601i
$456$		0			0
$457$	559.410	−	1721.69i	0.0572606	−	0.176230i	−0.918335	−	0.395803i	$-0.870466\pi$
$457$	559.410	−	1721.69i	0.0572606	−	0.176230i	0.975596	+	0.219573i	$0.0704663\pi$
$458$	−8356.25	+	6071.17i	−0.852537	+	0.619404i
$459$		0			0
$460$	−1902.22	−	5854.44i	−0.192808	−	0.593401i
$461$	−15271.1			−1.54284			−0.771419	−	0.636328i	$-0.780453\pi$
$461$	−15271.1			−1.54284			−0.771419	+	0.636328i	$0.780453\pi$
$462$		0			0
$463$	−12919.4			−1.29679			−0.648397	−	0.761302i	$-0.724560\pi$
$463$	−12919.4			−1.29679			−0.648397	+	0.761302i	$0.724560\pi$
$464$	1200.46	+	3694.65i	0.120108	+	0.369654i
$465$		0			0
$466$	25468.1	−	18503.6i	2.53173	−	1.83941i
$467$	1120.49	−	3448.51i	0.111028	−	0.341709i	−0.880070	−	0.474844i	$-0.842504\pi$
$467$	1120.49	−	3448.51i	0.111028	−	0.341709i	0.991098	+	0.133135i	$0.0425045\pi$
$468$		0			0
$469$	2922.33	−	2123.20i	0.287720	−	0.209041i
$470$	5454.35	+	3962.82i	0.535299	+	0.388917i
$471$		0			0
$472$	−5040.11			−0.491504
$473$	−2293.60	+	9806.38i	−0.222960	+	0.953273i
$474$		0			0
$475$	3759.97	+	11572.0i	0.363199	+	1.11781i
$476$	5169.17	+	3755.62i	0.497749	+	0.361636i
$477$		0			0
$478$	−3247.48	+	9994.73i	−0.310746	+	0.956377i
$479$	−2325.95	+	7158.52i	−0.221869	+	0.682842i	0.776726	+	0.629839i	$0.216879\pi$
$479$	−2325.95	+	7158.52i	−0.221869	+	0.682842i	−0.998594	+	0.0530027i	$0.983121\pi$
$480$		0			0
$481$	738.782	+	536.756i	0.0700323	+	0.0508815i
$482$	1088.32	+	3349.52i	0.102846	+	0.316528i
$483$		0			0
$484$	18774.7	−	3199.65i	1.76322	−	0.300493i
$485$	−1535.78			−0.143786
$486$		0			0
$487$	8956.17	+	6507.04i	0.833353	+	0.605466i	0.920506	−	0.390729i	$-0.127777\pi$
$487$	8956.17	+	6507.04i	0.833353	+	0.605466i	−0.0871530	+	0.996195i	$0.527777\pi$
$488$	−5474.02	+	3977.11i	−0.507781	+	0.368925i
$489$		0			0
$490$	2141.82	−	6591.85i	0.197465	−	0.607734i
$491$	12589.0	−	9146.43i	1.15709	−	0.840678i	0.167686	−	0.985840i	$-0.446371\pi$
$491$	12589.0	−	9146.43i	1.15709	−	0.840678i	0.989408	+	0.145163i	$0.0463706\pi$
$492$		0			0
$493$	−2048.08	−	6303.35i	−0.187102	−	0.575839i
$494$	58415.2			5.32029
$495$		0			0
$496$	202.825			0.0183611
$497$	2190.40	+	6741.37i	0.197692	+	0.608434i
$498$		0			0
$499$	6505.61	−	4726.61i	0.583630	−	0.424032i	−0.256401	−	0.966570i	$-0.582537\pi$
$499$	6505.61	−	4726.61i	0.583630	−	0.424032i	0.840031	+	0.542539i	$0.182537\pi$
$500$	5689.50	−	17510.5i	0.508884	−	1.56618i
$501$		0			0
$502$	−6760.25	+	4911.61i	−0.601045	+	0.436685i
$503$	2493.19	+	1811.41i	0.221005	+	0.160570i	0.692779	−	0.721150i	$-0.256386\pi$
$503$	2493.19	+	1811.41i	0.221005	+	0.160570i	−0.471774	+	0.881720i	$0.656386\pi$
$504$		0			0
$505$	816.656			0.0719618
$506$	−12272.0	+	1038.23i	−1.07818	+	0.0912157i
$507$		0			0
$508$	4566.50	+	14054.2i	0.398830	+	1.22747i
$509$	−9792.05	−	7114.34i	−0.852701	−	0.619524i	0.0731882	−	0.997318i	$-0.476683\pi$
$509$	−9792.05	−	7114.34i	−0.852701	−	0.619524i	−0.925890	+	0.377794i	$0.876683\pi$
$510$		0			0
$511$	−3216.48	+	9899.31i	−0.278452	+	0.856986i
$512$	−2863.84	+	8813.98i	−0.247197	+	0.760794i
$513$		0			0
$514$	−9175.45	−	6666.36i	−0.787377	−	0.572063i
$515$	1281.87	+	3945.18i	0.109681	+	0.337563i
$516$		0			0
$517$	6545.77	−	5657.30i	0.556833	−	0.481253i
$518$	476.113			0.0403846
$519$		0			0
$520$	−13093.3	−	9512.85i	−1.10419	−	0.802242i
$521$	−723.094	+	525.359i	−0.0608048	+	0.0441773i	−0.617772	−	0.786357i	$-0.711965\pi$
$521$	−723.094	+	525.359i	−0.0608048	+	0.0441773i	0.556968	+	0.830534i	$0.311965\pi$
$522$		0			0
$523$	1461.97	−	4499.48i	0.122232	−	0.376193i	−0.871154	−	0.491009i	$-0.836628\pi$
$523$	1461.97	−	4499.48i	0.122232	−	0.376193i	0.993387	+	0.114817i	$0.0366281\pi$
$524$	15815.0	−	11490.3i	1.31848	−	0.957932i
$525$		0			0
$526$	8756.07	+	26948.4i	0.725823	+	2.23385i
$527$	−346.035			−0.0286025
$528$		0			0
$529$	−7058.77			−0.580157
$530$	−1951.12	−	6004.94i	−0.159908	−	0.492147i
$531$		0			0
$532$	15803.9	−	11482.2i	1.28795	−	0.935748i
$533$	10538.7	−	32434.7i	0.856435	−	2.63584i
$534$		0			0
$535$	−4719.75	+	3429.10i	−0.381406	+	0.277108i
$536$	8743.35	+	6352.42i	0.704581	+	0.511908i
$537$		0			0
$538$	−3691.03			−0.295783
$539$	−7610.86	−	4602.80i	−0.608205	−	0.367823i
$540$		0			0
$541$	−5944.61	−	18295.6i	−0.472419	−	1.45396i	−0.849407	−	0.527739i	$-0.823040\pi$
$541$	−5944.61	−	18295.6i	−0.472419	−	1.45396i	0.376987	−	0.926219i	$-0.376960\pi$
$542$	−1719.12	−	1249.01i	−0.136241	−	0.0989847i
$543$		0			0
$544$	1583.21	−	4872.63i	0.124779	−	0.384030i
$545$	438.753	−	1350.34i	0.0344846	−	0.106133i
$546$		0			0
$547$	−1572.62	−	1142.57i	−0.122925	−	0.0893105i	0.524624	−	0.851334i	$-0.324206\pi$
$547$	−1572.62	−	1142.57i	−0.122925	−	0.0893105i	−0.647549	+	0.762024i	$0.724206\pi$
$548$	−6685.36	−	20575.4i	−0.521139	−	1.60390i
$549$		0			0
$550$	−13089.2	−	7915.95i	−1.01478	−	0.613704i
$551$	−20263.3			−1.56669
$552$		0			0
$553$	−409.276	−	297.356i	−0.0314723	−	0.0228660i
$554$	16117.8	−	11710.2i	1.23606	−	0.898052i
$555$		0			0
$556$	−4635.42	+	14266.4i	−0.353571	+	1.08818i
$557$	−11344.0	+	8241.91i	−0.862947	+	0.626967i	−0.928685	−	0.370869i	$-0.879060\pi$
$557$	−11344.0	+	8241.91i	−0.862947	+	0.626967i	0.0657384	+	0.997837i	$0.479060\pi$
$558$		0			0
$559$	−7696.95	−	23688.8i	−0.582373	−	1.79236i
$560$	−1575.37			−0.118878
$561$		0			0
$562$	14458.7			1.08524
$563$	−2766.65	−	8514.86i	−0.207105	−	0.637404i	−0.999620	−	0.0275520i	$-0.991229\pi$
$563$	−2766.65	−	8514.86i	−0.207105	−	0.637404i	0.792515	−	0.609852i	$-0.208771\pi$
$564$		0			0
$565$	−2508.57	+	1822.58i	−0.186790	+	0.135711i
$566$	−8504.95	+	26175.6i	−0.631607	+	1.94389i
$567$		0			0
$568$	−17157.3	+	12465.5i	−1.26743	+	0.920845i
$569$	14526.8	+	10554.4i	1.07029	+	0.777612i	0.975965	−	0.217929i	$-0.0699301\pi$
$569$	14526.8	+	10554.4i	1.07029	+	0.777612i	0.0943269	+	0.995541i	$0.469930\pi$
$570$		0			0
$571$	−10089.5			−0.739464			−0.369732	−	0.929138i	$-0.620551\pi$
$571$	−10089.5			−0.739464			−0.369732	+	0.929138i	$0.620551\pi$
$572$	−35637.9	+	30800.7i	−2.60506	+	2.25147i
$573$		0			0
$574$	−5494.61	−	16910.7i	−0.399548	−	1.22968i
$575$	5132.89	+	3729.26i	0.372272	+	0.270471i
$576$		0			0
$577$	−6570.03	+	20220.5i	−0.474027	+	1.45891i	0.373238	+	0.927736i	$0.378248\pi$
$577$	−6570.03	+	20220.5i	−0.474027	+	1.45891i	−0.847265	+	0.531170i	$0.821752\pi$
$578$	−4237.24	+	13040.9i	−0.304924	+	0.938459i
$579$		0			0
$580$	10301.0	+	7484.08i	0.737455	+	0.535793i
$581$	3766.77	+	11592.9i	0.268971	+	0.827807i
$582$		0			0
$583$	−8073.66	+	683.044i	−0.573545	+	0.0485228i
$584$	−31142.0			−2.20662
$585$		0			0
$586$	−1749.90	−	1271.37i	−0.123358	−	0.0896245i
$587$	6016.43	−	4371.19i	0.423040	−	0.307357i	−0.355820	−	0.934555i	$-0.615798\pi$
$587$	6016.43	−	4371.19i	0.423040	−	0.307357i	0.778860	+	0.627198i	$0.215798\pi$
$588$		0			0
$589$	−326.924	+	1006.17i	−0.0228704	+	0.0703879i
$590$	−3890.10	+	2826.32i	−0.271445	+	0.197217i
$591$		0			0
$592$	82.1826	+	252.932i	0.00570555	+	0.0175599i
$593$	−1727.95			−0.119660			−0.0598301	−	0.998209i	$-0.519056\pi$
$593$	−1727.95			−0.119660			−0.0598301	+	0.998209i	$0.519056\pi$
$594$		0			0
$595$	2687.70			0.185185
$596$	1712.20	+	5269.62i	0.117675	+	0.362168i
$597$		0			0
$598$	24642.5	−	17903.8i	1.68513	−	1.22432i
$599$	−854.645	+	2630.33i	−0.0582969	+	0.179419i	−0.975965	−	0.217929i	$-0.930070\pi$
$599$	−854.645	+	2630.33i	−0.0582969	+	0.179419i	0.917668	+	0.397349i	$0.130070\pi$
$600$		0			0
$601$	9978.89	−	7250.09i	0.677283	−	0.492075i	−0.195172	−	0.980769i	$-0.562527\pi$
$601$	9978.89	−	7250.09i	0.677283	−	0.492075i	0.872455	+	0.488694i	$0.162527\pi$
$602$	−10506.2	−	7633.20i	−0.711297	−	0.516787i
$603$		0			0
$604$	9712.64			0.654307
$605$	5598.13	−	5730.93i	0.376192	−	0.385117i
$606$		0			0
$607$	2570.13	+	7910.05i	0.171859	+	0.528928i	0.999476	−	0.0323655i	$-0.0103041\pi$
$607$	2570.13	+	7910.05i	0.171859	+	0.528928i	−0.827617	+	0.561293i	$0.810304\pi$
$608$	−12672.4	−	9207.03i	−0.845285	−	0.614136i
$609$		0			0
$610$	−1994.77	+	6139.28i	−0.132403	+	0.407495i
$611$	−6612.21	+	20350.3i	−0.437809	+	1.34744i
$612$		0			0
$613$	1049.66	+	762.620i	0.0691602	+	0.0502478i	0.621828	−	0.783154i	$-0.286390\pi$
$613$	1049.66	+	762.620i	0.0691602	+	0.0502478i	−0.552668	+	0.833402i	$0.686390\pi$
$614$	5753.05	+	17706.1i	0.378134	+	1.16378i
$615$		0			0
$616$	−2466.06	+	10543.7i	−0.161300	+	0.689642i
$617$	13415.2			0.875328			0.437664	−	0.899139i	$-0.355806\pi$
$617$	13415.2			0.875328			0.437664	+	0.899139i	$0.355806\pi$
$618$		0			0
$619$	−11943.5	−	8677.44i	−0.775523	−	0.563450i	0.128109	−	0.991760i	$-0.459109\pi$
$619$	−11943.5	−	8677.44i	−0.775523	−	0.563450i	−0.903632	+	0.428310i	$0.859109\pi$
$620$	537.815	−	390.745i	0.0348374	−	0.0253108i
$621$		0			0
$622$	−4005.17	+	12326.6i	−0.258188	+	0.794620i
$623$	7774.57	−	5648.56i	0.499971	−	0.363250i
$624$		0			0
$625$	1035.68	+	3187.49i	0.0662835	+	0.204000i
$626$	−9286.78			−0.592930
$627$		0			0
$628$	−51646.0			−3.28169
$629$	−140.210	−	431.522i	−0.00888797	−	0.0273544i
$630$		0			0
$631$	−20996.8	+	15255.1i	−1.32467	+	0.962432i	−0.324813	+	0.945778i	$0.605301\pi$
$631$	−20996.8	+	15255.1i	−1.32467	+	0.962432i	−0.999861	+	0.0166535i	$0.994699\pi$
$632$	467.723	−	1439.50i	0.0294384	−	0.0906019i
$633$		0			0
$634$	24385.4	−	17717.0i	1.52755	−	1.10983i
$635$	5028.95	+	3653.74i	0.314280	+	0.228338i
$636$		0			0
$637$	21997.9			1.36827
$638$	19273.7	−	16657.6i	1.19601	−	1.03367i
$639$		0			0
$640$	4888.41	+	15045.0i	0.301924	+	0.929226i
$641$	−16063.7	−	11671.0i	−0.989827	−	0.719152i	−0.0299440	−	0.999552i	$-0.509533\pi$
$641$	−16063.7	−	11671.0i	−0.989827	−	0.719152i	−0.959883	+	0.280400i	$0.909533\pi$
$642$		0			0
$643$	−4581.91	+	14101.7i	−0.281015	+	0.864877i	0.706549	+	0.707664i	$0.250251\pi$
$643$	−4581.91	+	14101.7i	−0.281015	+	0.864877i	−0.987565	+	0.157213i	$0.949749\pi$
$644$	3147.69	−	9687.59i	0.192603	−	0.592771i
$645$		0			0
$646$	−23481.2	−	17060.1i	−1.43012	−	1.03904i
$647$	−9349.60	−	28775.1i	−0.568115	−	1.74848i	−0.658509	−	0.752573i	$-0.728812\pi$
$647$	−9349.60	−	28775.1i	−0.568115	−	1.74848i	0.0903934	−	0.995906i	$-0.471188\pi$
$648$		0			0
$649$	2394.71	+	5686.85i	0.144839	+	0.343958i
$650$	37832.2			2.28292
$651$		0			0
$652$	−10647.3	−	7735.74i	−0.639543	−	0.464655i
$653$	−7520.52	+	5463.98i	−0.450690	+	0.327446i	−0.789868	−	0.613277i	$-0.789851\pi$
$653$	−7520.52	+	5463.98i	−0.450690	+	0.327446i	0.339178	+	0.940722i	$0.389851\pi$
$654$		0			0
$655$	2541.05	−	7820.55i	0.151583	−	0.466525i
$656$	8035.26	−	5837.96i	0.478238	−	0.347460i
$657$		0			0
$658$	3447.45	+	10610.2i	0.204249	+	0.628613i
$659$	−15034.4			−0.888705			−0.444353	−	0.895852i	$-0.646566\pi$
$659$	−15034.4			−0.888705			−0.444353	+	0.895852i	$0.646566\pi$
$660$		0			0
$661$	18459.0			1.08619			0.543095	−	0.839671i	$-0.317252\pi$
$661$	18459.0			1.08619			0.543095	+	0.839671i	$0.317252\pi$
$662$	4891.88	+	15055.6i	0.287203	+	0.883919i
$663$		0			0
$664$	−29504.8	+	21436.5i	−1.72441	+	1.25286i
$665$	2539.26	−	7815.05i	0.148073	−	0.455721i
$666$		0			0
$667$	−8548.09	+	6210.55i	−0.496227	+	0.360530i
$668$	−26726.1	−	19417.7i	−1.54800	−	1.12469i
$669$		0			0
$670$	10310.6			0.594525
$671$	7088.32	+	4286.79i	0.407811	+	0.246631i
$672$		0			0
$673$	−4568.65	−	14060.8i	−0.261677	−	0.805358i	−0.992440	−	0.122727i	$-0.960836\pi$
$673$	−4568.65	−	14060.8i	−0.261677	−	0.805358i	0.730764	−	0.682630i	$-0.239164\pi$
$674$	10049.4	+	7301.29i	0.574313	+	0.417263i
$675$		0			0
$676$	26285.0	−	80896.9i	1.49550	−	4.60269i
$677$	9528.48	−	29325.6i	0.540929	−	1.66481i	−0.189547	−	0.981872i	$-0.560702\pi$
$677$	9528.48	−	29325.6i	0.540929	−	1.66481i	0.730476	−	0.682938i	$-0.239298\pi$
$678$		0			0
$679$	−2055.97	−	1493.75i	−0.116202	−	0.0844255i
$680$	2484.92	+	7647.79i	0.140136	+	0.431293i
$681$		0			0
$682$	−516.174	−	1225.78i	−0.0289814	−	0.0688236i
$683$	−7599.08			−0.425726			−0.212863	−	0.977082i	$-0.568279\pi$
$683$	−7599.08			−0.425726			−0.212863	+	0.977082i	$0.568279\pi$
$684$		0			0
$685$	−7362.37	−	5349.08i	−0.410660	−	0.298362i
$686$	22333.1	−	16225.9i	1.24297	−	0.903074i
$687$		0			0
$688$	2241.60	−	6898.93i	0.124215	−	0.382296i
$689$	16212.1	−	11778.8i	0.896417	−	0.651285i
$690$		0			0
$691$	−795.657	−	2448.78i	−0.0438035	−	0.134813i	0.926763	−	0.375647i	$-0.122579\pi$
$691$	−795.657	−	2448.78i	−0.0438035	−	0.134813i	−0.970567	+	0.240833i	$0.922579\pi$
$692$	6559.61			0.360345
$693$		0			0
$694$	41430.1			2.26609
$695$	1949.88	+	6001.11i	0.106422	+	0.327532i
$696$		0			0
$697$	−13708.8	+	9960.01i	−0.744988	+	0.541266i
$698$	−9680.84	+	29794.5i	−0.524964	+	1.61567i
$699$		0			0
$700$	10235.3	−	7436.38i	0.552655	−	0.401527i
$701$	15435.4	+	11214.5i	0.831652	+	0.604231i	0.920026	−	0.391857i	$-0.128167\pi$
$701$	15435.4	+	11214.5i	0.831652	+	0.604231i	−0.0883741	+	0.996087i	$0.528167\pi$
$702$		0			0
$703$	−1387.20			−0.0744231
$704$	27264.5	−	2306.62i	1.45962	−	0.123486i
$705$		0			0
$706$	−1054.49	−	3245.38i	−0.0562127	−	0.173005i
$707$	1093.27	+	794.307i	0.0581565	+	0.0422531i
$708$		0			0
$709$	4345.14	−	13373.0i	0.230162	−	0.708367i	−0.767564	−	0.640972i	$-0.778531\pi$
$709$	4345.14	−	13373.0i	0.230162	−	0.708367i	0.997726	−	0.0673949i	$-0.0214687\pi$
$710$	−6252.23	+	19242.4i	−0.330482	+	1.01712i
$711$		0			0
$712$	23260.8	+	16900.0i	1.22435	+	0.889541i
$713$	170.470	+	524.654i	0.00895395	+	0.0275574i
$714$		0			0
$715$	−4512.48	+	19293.3i	−0.236024	+	1.00913i
$716$	50951.0			2.65940
$717$		0			0
$718$	31163.8	+	22641.8i	1.61981	+	1.17686i
$719$	−9313.93	+	6766.96i	−0.483103	+	0.350995i	−0.802526	−	0.596618i	$-0.796511\pi$
$719$	−9313.93	+	6766.96i	−0.483103	+	0.350995i	0.319423	+	0.947612i	$0.396511\pi$
$720$		0			0
$721$	−2121.16	+	6528.25i	−0.109565	+	0.337205i
$722$	−45580.7	+	33116.3i	−2.34950	+	1.70701i
$723$		0			0
$724$	3560.17	+	10957.1i	0.182752	+	0.562454i
$725$	−13123.4			−0.672261
$726$		0			0
$727$	23297.3			1.18851			0.594257	−	0.804275i	$-0.297446\pi$
$727$	23297.3			1.18851			0.594257	+	0.804275i	$0.297446\pi$
$728$	−8275.70	−	25470.0i	−0.421316	−	1.29668i
$729$		0			0
$730$	−24036.3	+	17463.4i	−1.21866	+	0.885408i
$731$	−3824.34	+	11770.1i	−0.193500	+	0.595531i
$732$		0			0
$733$	10078.1	−	7322.20i	0.507837	−	0.368965i	−0.304165	−	0.952619i	$-0.598377\pi$
$733$	10078.1	−	7322.20i	0.507837	−	0.368965i	0.812003	+	0.583654i	$0.198377\pi$
$734$	−45565.5	−	33105.3i	−2.29136	−	1.66477i
$735$		0			0
$736$	−8167.76			−0.409059
$737$	3013.31	−	12883.5i	0.150606	−	0.643922i
$738$		0			0
$739$	6903.68	+	21247.4i	0.343648	+	1.05764i	0.962303	+	0.271978i	$0.0876778\pi$
$739$	6903.68	+	21247.4i	0.343648	+	1.05764i	−0.618655	+	0.785663i	$0.712322\pi$
$740$	705.194	+	512.354i	0.0350317	+	0.0254520i
$741$		0			0
$742$	3228.61	−	9936.63i	0.159738	−	0.491624i
$743$	−10596.5	+	32612.5i	−0.523212	+	1.61028i	0.244614	+	0.969621i	$0.421339\pi$
$743$	−10596.5	+	32612.5i	−0.523212	+	1.61028i	−0.767825	+	0.640659i	$0.778661\pi$
$744$		0			0
$745$	1885.60	+	1369.97i	0.0927287	+	0.0673714i
$746$	−8058.18	−	24800.5i	−0.395484	−	1.21717i
$747$		0			0
$748$	23320.7	−	1972.97i	1.13996	−	0.0964425i
$749$	−9653.65			−0.470944
$750$		0			0
$751$	15565.4	+	11308.9i	0.756312	+	0.549493i	0.897777	−	0.440450i	$-0.145181\pi$
$751$	15565.4	+	11308.9i	0.756312	+	0.549493i	−0.141465	+	0.989943i	$0.545181\pi$
$752$	−5041.52	+	3662.88i	−0.244475	+	0.177622i
$753$		0			0
$754$	−19469.3	+	59920.4i	−0.940360	+	2.89413i
$755$	3305.31	−	2401.45i	0.159328	−	0.115759i
$756$		0			0
$757$	−4457.45	−	13718.6i	−0.214014	−	0.658668i	−0.999222	−	0.0394359i	$-0.987444\pi$
$757$	−4457.45	−	13718.6i	−0.214014	−	0.658668i	0.785208	−	0.619232i	$-0.212556\pi$
$758$	31898.6			1.52851
$759$		0			0
$760$	24585.2			1.17342
$761$	7973.32	+	24539.4i	0.379806	+	1.16892i	0.940178	+	0.340683i	$0.110658\pi$
$761$	7973.32	+	24539.4i	0.379806	+	1.16892i	−0.560372	+	0.828241i	$0.689342\pi$
$762$		0			0
$763$	1900.75	−	1380.98i	0.0901859	−	0.0655239i
$764$	10036.8	−	30890.0i	0.475284	−	1.46277i
$765$		0			0
$766$	−20307.2	+	14754.1i	−0.957871	+	0.695934i
$767$	−12346.4	−	8970.17i	−0.581228	−	0.422287i
$768$		0			0
$769$	−1832.44			−0.0859291			−0.0429646	−	0.999077i	$-0.513680\pi$
$769$	−1832.44			−0.0859291			−0.0429646	+	0.999077i	$0.513680\pi$
$770$	4009.19	+	9520.83i	0.187638	+	0.445593i
$771$		0			0
$772$	−21143.0	−	65071.4i	−0.985689	−	3.03364i
$773$	30476.8	+	22142.7i	1.41808	+	1.03030i	0.992085	+	0.125570i	$0.0400760\pi$
$773$	30476.8	+	22142.7i	1.41808	+	1.03030i	0.425995	+	0.904725i	$0.359924\pi$
$774$		0			0
$775$	−211.730	+	651.638i	−0.00981364	+	0.0302033i
$776$	2349.58	−	7231.27i	0.108692	−	0.334520i
$777$		0			0
$778$	−434.823	−	315.918i	−0.0200375	−	0.0145581i
$779$	16009.1	+	49271.0i	0.736311	+	2.26613i
$780$		0			0
$781$	22217.0	+	13436.1i	1.01791	+	0.615598i
$782$	−15134.4			−0.692079
$783$		0			0
$784$	5182.95	+	3765.63i	0.236104	+	0.171539i
$785$	−17575.7	+	12769.5i	−0.799113	+	0.580590i
$786$		0			0
$787$	9808.52	−	30187.5i	0.444264	−	1.36730i	−0.439024	−	0.898475i	$-0.644676\pi$
$787$	9808.52	−	30187.5i	0.444264	−	1.36730i	0.883289	−	0.468830i	$-0.155324\pi$
$788$	−23258.6	+	16898.3i	−1.05146	+	0.763932i
$789$		0			0
$790$	−446.223	−	1373.33i	−0.0200961	−	0.0618493i
$791$	−5130.96			−0.230639
$792$		0			0
$793$	−20487.6			−0.917446
$794$	−5888.29	−	18122.3i	−0.263184	−	0.809996i
$795$		0			0
$796$	−37625.6	+	27336.6i	−1.67538	+	1.21724i
$797$	9351.45	−	28780.8i	0.415615	−	1.27913i	−0.496084	−	0.868275i	$-0.665229\pi$
$797$	9351.45	−	28780.8i	0.415615	−	1.27913i	0.911699	−	0.410858i	$-0.134771\pi$
$798$		0			0
$799$	8601.22	−	6249.15i	0.380838	−	0.276695i
$800$	−8207.19	−	5962.87i	−0.362710	−	0.263524i
$801$		0			0
$802$	−47363.4			−2.08536
$803$	14796.5	+	35138.1i	0.650260	+	1.54421i
$804$		0			0
$805$	−1324.07	−	4075.06i	−0.0579717	−	0.178419i
$806$	2661.22	+	1933.49i	0.116300	+	0.0844967i
$807$		0			0
$808$	−1249.40	+	3845.25i	−0.0543980	+	0.167420i
$809$	2434.74	−	7493.36i	0.105811	−	0.325652i	−0.884109	−	0.467281i	$-0.845234\pi$
$809$	2434.74	−	7493.36i	0.105811	−	0.325652i	0.989920	+	0.141628i	$0.0452338\pi$
$810$		0			0
$811$	−33536.1	−	24365.4i	−1.45205	−	1.05498i	−0.985347	−	0.170564i	$-0.945441\pi$
$811$	−33536.1	−	24365.4i	−1.45205	−	1.05498i	−0.466704	−	0.884413i	$-0.654559\pi$
$812$	6510.78	+	20038.1i	0.281384	+	0.866010i
$813$		0			0
$814$	1319.46	−	1140.37i	0.0568146	−	0.0491030i
$815$	−5536.07			−0.237939
$816$		0			0
$817$	30610.9	+	22240.1i	1.31082	+	0.952366i
$818$	−1125.96	+	818.056i	−0.0481274	+	0.0349666i
$819$		0			0
$820$	10059.5	−	30960.1i	0.428408	−	1.31850i
$821$	−14844.6	+	10785.2i	−0.631034	+	0.458473i	−0.856758	−	0.515718i	$-0.827525\pi$
$821$	−14844.6	+	10785.2i	−0.631034	+	0.458473i	0.225724	+	0.974191i	$0.427525\pi$
$822$		0			0
$823$	−8201.31	−	25241.0i	−0.347363	−	1.06907i	−0.960307	−	0.278946i	$-0.910015\pi$
$823$	−8201.31	−	25241.0i	−0.347363	−	1.06907i	0.612944	−	0.790126i	$-0.289985\pi$
$824$	−20537.1			−0.868256
$825$		0			0
$826$	−7956.70			−0.335168
$827$	2363.74	+	7274.85i	0.0993898	+	0.305890i	0.988373	−	0.152050i	$-0.0485874\pi$
$827$	2363.74	+	7274.85i	0.0993898	+	0.305890i	−0.888983	+	0.457940i	$0.848587\pi$
$828$		0			0
$829$	23147.8	−	16817.9i	0.969791	−	0.704595i	0.0143874	−	0.999896i	$-0.495420\pi$
$829$	23147.8	−	16817.9i	0.969791	−	0.704595i	0.955404	+	0.295302i	$0.0954202\pi$
$830$	−10751.8	+	33090.6i	−0.449638	+	1.38384i
$831$		0			0
$832$	−54747.7	+	39776.6i	−2.28129	+	1.65746i
$833$	−8842.52	−	6424.46i	−0.367797	−	0.267220i
$834$		0			0
$835$	−13896.2			−0.575926
$836$	16295.9	−	69673.8i	0.674171	−	2.88244i
$837$		0			0
$838$	1597.87	+	4917.74i	0.0658682	+	0.202721i
$839$	10416.9	+	7568.35i	0.428644	+	0.311428i	0.781107	−	0.624398i	$-0.214656\pi$
$839$	10416.9	+	7568.35i	0.428644	+	0.311428i	−0.352462	+	0.935826i	$0.614656\pi$
$840$		0			0
$841$	−783.022	+	2409.89i	−0.0321055	+	0.0988107i
$842$	19077.2	−	58713.6i	0.780812	−	2.40309i
$843$		0			0
$844$	3571.49	+	2594.84i	0.145659	+	0.105827i
$845$	−11056.7	−	34029.0i	−0.450133	−	1.38537i
$846$		0			0
$847$	13068.4	−	2227.16i	0.530148	−	0.0903495i
$848$	5836.07			0.236334
$849$		0			0
$850$	−15207.5	−	11048.9i	−0.613661	−	0.445851i
$851$	−585.195	+	425.169i	−0.0235725	+	0.0171264i
$852$		0			0
$853$	−196.513	+	604.804i	−0.00788800	+	0.0242768i	−0.954923	−	0.296853i	$-0.904063\pi$
$853$	−196.513	+	604.804i	−0.00788800	+	0.0242768i	0.947035	+	0.321130i	$0.104063\pi$
$854$	−8641.70	+	6278.56i	−0.346268	+	0.251578i
$855$		0			0
$856$	−8925.29	−	27469.2i	−0.356379	−	1.09682i
$857$	7820.86			0.311733			0.155867	−	0.987778i	$-0.450183\pi$
$857$	7820.86			0.311733			0.155867	+	0.987778i	$0.450183\pi$
$858$		0			0
$859$	119.816			0.00475910			0.00237955	−	0.999997i	$-0.499243\pi$
$859$	119.816			0.00475910			0.00237955	+	0.999997i	$0.499243\pi$
$860$	−7347.02	−	22611.8i	−0.291315	−	0.896577i
$861$		0			0
$862$	−5630.09	+	4090.50i	−0.222461	+	0.161628i
$863$	9940.00	−	30592.2i	0.392076	−	1.20669i	−0.539139	−	0.842217i	$-0.681250\pi$
$863$	9940.00	−	30592.2i	0.392076	−	1.20669i	0.931215	−	0.364469i	$-0.118750\pi$
$864$		0			0
$865$	2232.31	−	1621.87i	0.0877465	−	0.0637515i
$866$	15516.1	+	11273.1i	0.608843	+	0.442351i
$867$		0			0
$868$	1100.03			0.0430156
$869$	−1846.45	+	156.213i	−0.0720788	+	0.00609799i
$870$		0			0
$871$	10112.2	+	31122.0i	0.393384	+	1.21071i
$872$	5686.88	+	4131.76i	0.220851	+	0.160458i
$873$		0			0
$874$	−14298.6	+	44006.4i	−0.553382	+	1.70313i
$875$	3960.25	−	12188.4i	0.153007	−	0.470906i
$876$		0			0
$877$	−6320.86	−	4592.37i	−0.243375	−	0.176822i	0.459410	−	0.888224i	$-0.348061\pi$
$877$	−6320.86	−	4592.37i	−0.243375	−	0.176822i	−0.702786	+	0.711402i	$0.748061\pi$
$878$	17123.8	+	52701.6i	0.658201	+	2.02573i
$879$		0			0
$880$	−4365.85	+	3773.26i	−0.167242	+	0.144542i
$881$	11759.7			0.449709			0.224855	−	0.974392i	$-0.427809\pi$
$881$	11759.7			0.449709			0.224855	+	0.974392i	$0.427809\pi$
$882$		0			0
$883$	7639.22	+	5550.22i	0.291144	+	0.211529i	0.723764	−	0.690048i	$-0.242411\pi$
$883$	7639.22	+	5550.22i	0.291144	+	0.211529i	−0.432619	+	0.901577i	$0.642411\pi$
$884$	−46828.5	+	34022.9i	−1.78169	+	1.29447i
$885$		0			0
$886$	1333.04	−	4102.66i	0.0505465	−	0.155566i
$887$	30976.4	−	22505.6i	1.17259	−	0.851934i	0.181270	−	0.983433i	$-0.441979\pi$
$887$	30976.4	−	22505.6i	1.17259	−	0.851934i	0.991316	+	0.131499i	$0.0419791\pi$
$888$		0			0
$889$	3178.57	+	9782.64i	0.119917	+	0.369066i
$890$	27430.2			1.03311
$891$		0			0
$892$	66237.6			2.48632
$893$	−10044.5	−	30913.8i	−0.376402	−	1.15845i
$894$		0			0
$895$	17339.2	−	12597.6i	0.647581	−	0.470495i
$896$	−8089.05	+	24895.5i	−0.301603	+	0.928239i
$897$		0			0
$898$	55588.3	−	40387.3i	2.06571	−	1.50083i
$899$	−923.135	−	670.697i	−0.0342473	−	0.0248821i
$900$		0			0
$901$	−9956.78			−0.368156
$902$	−55731.1	−	33704.4i	−2.05725	−	1.24416i
$903$		0			0
$904$	−4743.83	−	14600.0i	−0.174533	−	0.537156i
$905$	3920.70	+	2848.56i	0.144010	+	0.104629i
$906$		0			0
$907$	12422.6	−	38232.9i	0.454782	−	1.39967i	−0.416610	−	0.909085i	$-0.636782\pi$
$907$	12422.6	−	38232.9i	0.454782	−	1.39967i	0.871391	−	0.490588i	$-0.163218\pi$
$908$	−11441.3	+	35212.8i	−0.418166	+	1.28698i
$909$		0			0
$910$	−20670.1	−	15017.7i	−0.752974	−	0.547068i
$911$	−6470.55	−	19914.3i	−0.235323	−	0.724249i	−0.997078	−	0.0763845i	$-0.975662\pi$
$911$	−6470.55	−	19914.3i	−0.235323	−	0.724249i	0.761756	−	0.647864i	$-0.224338\pi$
$912$		0			0
$913$	38205.9	+	23105.7i	1.38492	+	0.837553i
$914$	8550.45			0.309435
$915$		0			0
$916$	−25315.3	−	18392.6i	−0.913145	−	0.663439i
$917$	11008.3	−	7997.98i	0.396429	−	0.288022i
$918$		0			0
$919$	−14412.6	+	44357.6i	−0.517333	+	1.59219i	0.261663	+	0.965159i	$0.415729\pi$
$919$	−14412.6	+	44357.6i	−0.517333	+	1.59219i	−0.778996	+	0.627029i	$0.784271\pi$
$920$	10371.3	−	7535.20i	0.371665	−	0.270031i
$921$		0			0
$922$	−22289.2	−	68599.2i	−0.796157	−	2.45032i
$923$	−64214.3			−2.28997
$924$		0			0
$925$	−898.413			−0.0319348
$926$	−18856.7	−	58035.0i	−0.669190	−	2.05956i
$927$		0			0
$928$	13667.9	−	9930.31i	0.483481	−	0.351270i
$929$	−15712.4	+	48357.8i	−0.554906	+	1.70782i	0.141286	+	0.989969i	$0.454876\pi$
$929$	−15712.4	+	48357.8i	−0.554906	+	1.70782i	−0.696192	+	0.717856i	$0.745124\pi$
$930$		0			0
$931$	−27034.6	+	19641.8i	−0.951690	+	0.691443i
$932$	77155.7	+	56056.9i	2.71171	+	1.97018i
$933$		0			0
$934$	17126.4			0.599993
$935$	7448.48	−	6437.48i	0.260525	−	0.225164i
$936$		0			0
$937$	5230.89	+	16099.0i	0.182375	+	0.561293i	0.999893	−	0.0146096i	$-0.00465055\pi$
$937$	5230.89	+	16099.0i	0.182375	+	0.561293i	−0.817518	+	0.575903i	$0.804651\pi$
$938$	13802.9	+	10028.4i	0.480470	+	0.349082i
$939$		0			0
$940$	−6311.60	+	19425.1i	−0.219002	+	0.674018i
$941$	6371.09	−	19608.2i	0.220714	−	0.679287i	−0.777985	−	0.628283i	$-0.783758\pi$
$941$	6371.09	−	19608.2i	0.220714	−	0.679287i	0.998698	−	0.0510038i	$-0.0162421\pi$
$942$		0			0
$943$	21854.7	+	15878.4i	0.754705	+	0.548325i
$944$	−1373.42	−	4226.95i	−0.0473528	−	0.145737i
$945$		0			0
$946$	−47398.7	+	4010.01i	−1.62903	+	0.137819i
$947$	46642.8			1.60052			0.800258	−	0.599656i	$-0.204696\pi$
$947$	46642.8			1.60052			0.800258	+	0.599656i	$0.204696\pi$
$948$		0			0
$949$	−76286.2	−	55425.2i	−2.60944	−	1.89587i
$950$	−46494.4	+	33780.2i	−1.58787	+	1.15366i
$951$		0			0
$952$	−4111.90	+	12655.1i	−0.139987	+	0.430835i
$953$	−12290.8	+	8929.79i	−0.417773	+	0.303530i	−0.776741	−	0.629820i	$-0.783129\pi$
$953$	−12290.8	+	8929.79i	−0.417773	+	0.303530i	0.358968	+	0.933350i	$0.383129\pi$
$954$		0			0
$955$	−4221.93	−	12993.8i	−0.143056	−	0.440281i
$956$	−31837.3			−1.07708
$957$		0			0
$958$	−35551.5			−1.19897
$959$	−4653.43	−	14321.8i	−0.156691	−	0.482247i
$960$		0			0
$961$	24053.2	−	17475.7i	0.807399	−	0.586610i
$962$	−1332.85	+	4102.10i	−0.0446704	+	0.137481i
$963$		0			0
$964$	−8631.88	+	6271.43i	−0.288396	+	0.209532i
$965$	−23284.1	−	16916.9i	−0.776727	−	0.564325i
$966$		0			0
$967$	−31663.0			−1.05296			−0.526481	−	0.850187i	$-0.676489\pi$
$967$	−31663.0			−1.05296			−0.526481	+	0.850187i	$0.676489\pi$
$968$	18419.7	+	35126.7i	0.611603	+	1.16634i
$969$		0			0
$970$	−2241.57	−	6898.85i	−0.0741985	−	0.228359i
$971$	−18374.8	−	13350.1i	−0.607287	−	0.441220i	0.241171	−	0.970483i	$-0.422469\pi$
$971$	−18374.8	−	13350.1i	−0.607287	−	0.441220i	−0.848458	+	0.529263i	$0.822469\pi$
$972$		0			0
$973$	−3226.55	+	9930.29i	−0.106309	+	0.327184i
$974$	−16158.0	+	49729.3i	−0.531557	+	1.63596i
$975$		0			0
$976$	−4827.11	−	3507.10i	−0.158311	−	0.115020i
$977$	−17034.6	−	52427.1i	−0.557815	−	1.71678i	−0.688390	−	0.725340i	$-0.741682\pi$
$977$	−17034.6	−	52427.1i	−0.557815	−	1.71678i	0.130575	−	0.991438i	$-0.458318\pi$
$978$		0			0
$979$	8016.61	−	34275.3i	0.261708	−	1.11894i
$980$	20997.8			0.684437
$981$		0			0
$982$	59461.0	+	43200.9i	1.93226	+	1.40387i
$983$	41726.4	−	30316.0i	1.35388	−	0.983653i	0.355075	−	0.934838i	$-0.384455\pi$
$983$	41726.4	−	30316.0i	1.35388	−	0.983653i	0.998808	−	0.0488155i	$-0.0155446\pi$
$984$		0			0
$985$	−3737.03	+	11501.4i	−0.120885	+	0.372045i
$986$	25325.9	−	18400.3i	0.817991	−	0.594306i
$987$		0			0
$988$	54686.4	+	168308.i	1.76094	+	5.41961i
$989$	19729.7			0.634346
$990$		0			0
$991$	8219.68			0.263478			0.131739	−	0.991284i	$-0.457944\pi$
$991$	8219.68			0.263478			0.131739	+	0.991284i	$0.457944\pi$
$992$	−272.572	−	838.891i	−0.00872397	−	0.0268496i
$993$		0			0
$994$	−27085.7	+	19678.9i	−0.864293	+	0.627946i
$995$	−6045.42	+	18605.9i	−0.192616	+	0.592811i
$996$		0			0
$997$	22916.4	−	16649.7i	0.727952	−	0.528888i	−0.160963	−	0.986960i	$-0.551460\pi$
$997$	22916.4	−	16649.7i	0.727952	−	0.528888i	0.888915	+	0.458072i	$0.151460\pi$
$998$	30727.7	+	22325.0i	0.974616	+	0.708100i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.b.82.2		8
3.2	odd	2		33.4.e.b.16.1	✓	8
11.3	even	5		1089.4.a.bg.1.4		4
11.8	odd	10		1089.4.a.z.1.1		4
11.9	even	5	inner	99.4.f.b.64.2		8
33.8	even	10		363.4.a.t.1.4		4
33.14	odd	10		363.4.a.p.1.1		4
33.20	odd	10		33.4.e.b.31.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.16.1	✓	8	3.2	odd	2
33.4.e.b.31.1	yes	8	33.20	odd	10
99.4.f.b.64.2		8	11.9	even	5	inner
99.4.f.b.82.2		8	1.1	even	1	trivial
363.4.a.p.1.1		4	33.14	odd	10
363.4.a.t.1.4		4	33.8	even	10
1089.4.a.z.1.1		4	11.8	odd	10
1089.4.a.bg.1.4		4	11.3	even	5

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	99.4.f.b.82.2

Level	$99$
Weight	$4$
Character	99.82
Analytic conductor	$5.841$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$