LMFDB - Embedded newform 99.6.f.b.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	99.f (of order $5$ , degree $4$ , 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:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096$ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{4}\cdot 11^{2}$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.5
Root			$-8.59311 - 6.24326i$ of defining polynomial
Character	$\chi$	$=$	99.91
Dual form			99.6.f.b.37.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.78409 - 5.65548i) q^{2} +(18.7192 - 57.6117i) q^{4} +(-48.1408 - 34.9763i) q^{5} +(9.43666 - 29.0431i) q^{7} +(-84.9654 - 261.497i) q^{8} -572.540 q^{10} +(70.0591 - 395.149i) q^{11} +(-460.773 + 334.771i) q^{13} +(-90.7964 - 279.443i) q^{14} +(-572.028 - 415.603i) q^{16} +(-1619.20 - 1176.42i) q^{17} +(497.601 + 1531.46i) q^{19} +(-2916.20 + 2118.74i) q^{20} +(-1689.41 - 3472.09i) q^{22} +1214.78 q^{23} +(128.514 + 395.526i) q^{25} +(-1693.41 + 5211.78i) q^{26} +(-1496.57 - 1087.32i) q^{28} +(2348.47 - 7227.84i) q^{29} +(5873.48 - 4267.33i) q^{31} +1995.37 q^{32} -19257.3 q^{34} +(-1470.11 + 1068.10i) q^{35} +(-406.300 + 1250.46i) q^{37} +(12534.5 + 9106.84i) q^{38} +(-5055.89 + 15560.4i) q^{40} +(-1804.73 - 5554.40i) q^{41} +6357.22 q^{43} +(-21453.7 - 11433.1i) q^{44} +(9455.97 - 6870.16i) q^{46} +(9346.16 + 28764.5i) q^{47} +(12842.7 + 9330.77i) q^{49} +(3237.26 + 2352.01i) q^{50} +(10661.4 + 32812.6i) q^{52} +(5785.79 - 4203.62i) q^{53} +(-17193.6 + 16572.4i) q^{55} -8396.45 q^{56} +(-22596.2 - 69543.9i) q^{58} +(6852.76 - 21090.6i) q^{59} +(-20223.1 - 14693.0i) q^{61} +(21585.9 - 66434.7i) q^{62} +(33837.0 - 24584.1i) q^{64} +33891.1 q^{65} +15543.8 q^{67} +(-98085.7 + 71263.5i) q^{68} +(-5402.87 + 16628.3i) q^{70} +(-52283.6 - 37986.3i) q^{71} +(13634.4 - 41962.5i) q^{73} +(3909.28 + 12031.5i) q^{74} +97544.6 q^{76} +(-10815.2 - 5763.62i) q^{77} +(14114.3 - 10254.6i) q^{79} +(13001.6 + 40014.9i) q^{80} +(-45461.0 - 33029.3i) q^{82} +(96187.9 + 69884.6i) q^{83} +(36802.9 + 113268. i) q^{85} +(49485.2 - 35953.1i) q^{86} +(-109283. + 15253.8i) q^{88} +6612.00 q^{89} +(5374.62 + 16541.4i) q^{91} +(22739.7 - 69985.6i) q^{92} +(235428. + 171049. i) q^{94} +(29609.9 - 91129.9i) q^{95} +(-103201. + 74979.8i) q^{97} +152739. q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 6 q^{2} + 8 q^{4} + 11 q^{5} - 139 q^{7} + 76 q^{8} - 424 q^{10} - 2289 q^{11} - 847 q^{13} - 2022 q^{14} - 7148 q^{16} - 2482 q^{17} + 2958 q^{19} - 8037 q^{20} + 7441 q^{22} - 8140 q^{23} - 13120 q^{25}+ \cdots + 2296174 q^{98}+O(q^{100})$ 20 * q - 6 * q^2 + 8 * q^4 + 11 * q^5 - 139 * q^7 + 76 * q^8 - 424 * q^10 - 2289 * q^11 - 847 * q^13 - 2022 * q^14 - 7148 * q^16 - 2482 * q^17 + 2958 * q^19 - 8037 * q^20 + 7441 * q^22 - 8140 * q^23 - 13120 * q^25 + 13508 * q^26 + 27819 * q^28 + 20210 * q^29 + 5540 * q^31 + 4626 * q^32 + 16540 * q^34 + 34101 * q^35 - 25173 * q^37 + 55878 * q^38 + 22689 * q^40 - 54349 * q^41 - 21688 * q^43 - 24587 * q^44 + 44155 * q^46 + 48387 * q^47 - 78880 * q^49 - 19956 * q^50 + 109051 * q^52 + 74382 * q^53 - 47630 * q^55 - 168894 * q^56 + 1501 * q^58 + 108412 * q^59 + 16737 * q^61 - 132685 * q^62 - 157030 * q^64 + 134194 * q^65 + 20178 * q^67 - 387013 * q^68 - 411988 * q^70 - 143157 * q^71 + 164980 * q^73 - 286114 * q^74 + 46868 * q^76 + 367461 * q^77 + 369613 * q^79 + 107448 * q^80 - 184129 * q^82 - 267741 * q^83 + 379937 * q^85 + 290531 * q^86 - 740846 * q^88 - 205492 * q^89 + 394559 * q^91 + 483181 * q^92 + 561327 * q^94 - 267881 * q^95 - 300567 * q^97 + 2296174 * q^98

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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

)

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

$2$	7.78409	−	5.65548i	1.37605	−	0.999756i	0.378809	−	0.925475i	$-0.376334\pi$
$2$	7.78409	−	5.65548i	1.37605	−	0.999756i	0.997237	−	0.0742813i	$-0.0236663\pi$
$3$		0			0
$3$		0			0
$4$	18.7192	−	57.6117i	0.584974	−	1.80037i
$5$	−48.1408	−	34.9763i	−0.861169	−	0.625676i	0.0670339	−	0.997751i	$-0.478646\pi$
$5$	−48.1408	−	34.9763i	−0.861169	−	0.625676i	−0.928203	+	0.372075i	$0.878646\pi$
$6$		0			0
$7$	9.43666	−	29.0431i	0.0727903	−	0.224025i	−0.908042	−	0.418879i	$-0.862423\pi$
$7$	9.43666	−	29.0431i	0.0727903	−	0.224025i	0.980832	+	0.194854i	$0.0624232\pi$
$8$	−84.9654	−	261.497i	−0.469372	−	1.44458i
$9$		0			0
$10$	−572.540			−1.81053
$11$	70.0591	−	395.149i	0.174575	−	0.984644i
$11$	70.0591	−	395.149i	0.174575	−	0.984644i
$12$		0			0
$13$	−460.773	+	334.771i	−0.756186	+	0.549401i	−0.897738	−	0.440529i	$-0.854791\pi$
$13$	−460.773	+	334.771i	−0.756186	+	0.549401i	0.141552	+	0.989931i	$0.454791\pi$
$14$	−90.7964	−	279.443i	−0.123808	−	0.381042i
$15$		0			0
$16$	−572.028	−	415.603i	−0.558621	−	0.405862i
$17$	−1619.20	−	1176.42i	−1.35887	−	0.987280i	−0.998516	−	0.0544664i	$-0.982654\pi$
$17$	−1619.20	−	1176.42i	−1.35887	−	0.987280i	−0.360359	−	0.932814i	$-0.617346\pi$
$18$		0			0
$19$	497.601	+	1531.46i	0.316226	+	0.973243i	0.975247	+	0.221118i	$0.0709707\pi$
$19$	497.601	+	1531.46i	0.316226	+	0.973243i	−0.659021	+	0.752124i	$0.729029\pi$
$20$	−2916.20	+	2118.74i	−1.63021	+	1.18441i
$21$		0			0
$22$	−1689.41	−	3472.09i	−0.744180	−	1.52945i
$23$	1214.78			0.478827			0.239413	−	0.970918i	$-0.423045\pi$
$23$	1214.78			0.478827			0.239413	+	0.970918i	$0.423045\pi$
$24$		0			0
$25$	128.514	+	395.526i	0.0411246	+	0.126568i
$26$	−1693.41	+	5211.78i	−0.491280	+	1.51200i
$27$		0			0
$28$	−1496.57	−	1087.32i	−0.360747	−	0.262098i
$29$	2348.47	−	7227.84i	0.518549	−	1.59593i	−0.258182	−	0.966096i	$-0.583123\pi$
$29$	2348.47	−	7227.84i	0.518549	−	1.59593i	0.776731	−	0.629833i	$-0.216877\pi$
$30$		0			0
$31$	5873.48	−	4267.33i	1.09772	−	0.797540i	0.117034	−	0.993128i	$-0.462662\pi$
$31$	5873.48	−	4267.33i	1.09772	−	0.797540i	0.980686	+	0.195588i	$0.0626615\pi$
$32$	1995.37			0.344468
$33$		0			0
$34$	−19257.3			−2.85691
$35$	−1470.11	+	1068.10i	−0.202852	+	0.147381i
$36$		0			0
$37$	−406.300	+	1250.46i	−0.0487913	+	0.150164i	−0.972484	−	0.232970i	$-0.925155\pi$
$37$	−406.300	+	1250.46i	−0.0487913	+	0.150164i	0.923693	+	0.383135i	$0.125155\pi$
$38$	12534.5	+	9106.84i	1.40815	+	1.02308i
$39$		0			0
$40$	−5055.89	+	15560.4i	−0.499629	+	1.53770i
$41$	−1804.73	−	5554.40i	−0.167669	−	0.516033i	0.831554	−	0.555444i	$-0.187452\pi$
$41$	−1804.73	−	5554.40i	−0.167669	−	0.516033i	−0.999223	+	0.0394114i	$0.987452\pi$
$42$		0			0
$43$	6357.22			0.524320			0.262160	−	0.965024i	$-0.415565\pi$
$43$	6357.22			0.524320			0.262160	+	0.965024i	$0.415565\pi$
$44$	−21453.7	−	11433.1i	−1.67060	−	0.890291i
$45$		0			0
$46$	9455.97	−	6870.16i	0.658888	−	0.478710i
$47$	9346.16	+	28764.5i	0.617147	+	1.89938i	0.359516	+	0.933139i	$0.382942\pi$
$47$	9346.16	+	28764.5i	0.617147	+	1.89938i	0.257631	+	0.966243i	$0.417058\pi$
$48$		0			0
$49$	12842.7	+	9330.77i	0.764128	+	0.555172i
$50$	3237.26	+	2352.01i	0.183127	+	0.133050i
$51$		0			0
$52$	10661.4	+	32812.6i	0.546774	+	1.68280i
$53$	5785.79	−	4203.62i	0.282926	−	0.205558i	−0.437267	−	0.899332i	$-0.644053\pi$
$53$	5785.79	−	4203.62i	0.282926	−	0.205558i	0.720193	+	0.693774i	$0.244053\pi$
$54$		0			0
$55$	−17193.6	+	16572.4i	−0.766407	+	0.738717i
$56$	−8396.45			−0.357788
$57$		0			0
$58$	−22596.2	−	69543.9i	−0.881993	−	2.71450i
$59$	6852.76	−	21090.6i	0.256292	−	0.788787i	−0.737280	−	0.675587i	$-0.763890\pi$
$59$	6852.76	−	21090.6i	0.256292	−	0.788787i	0.993572	−	0.113199i	$-0.0361099\pi$
$60$		0			0
$61$	−20223.1	−	14693.0i	−0.695863	−	0.505574i	0.182719	−	0.983165i	$-0.441510\pi$
$61$	−20223.1	−	14693.0i	−0.695863	−	0.505574i	−0.878582	+	0.477591i	$0.841510\pi$
$62$	21585.9	−	66434.7i	0.713168	−	2.19490i
$63$		0			0
$64$	33837.0	−	24584.1i	1.03262	−	0.750246i
$65$	33891.1			0.994951
$66$		0			0
$67$	15543.8			0.423028			0.211514	−	0.977375i	$-0.432161\pi$
$67$	15543.8			0.423028			0.211514	+	0.977375i	$0.432161\pi$
$68$	−98085.7	+	71263.5i	−2.57237	+	1.86894i
$69$		0			0
$70$	−5402.87	+	16628.3i	−0.131789	+	0.405605i
$71$	−52283.6	−	37986.3i	−1.23089	−	0.894295i	−0.233935	−	0.972252i	$-0.575160\pi$
$71$	−52283.6	−	37986.3i	−1.23089	−	0.894295i	−0.996957	+	0.0779570i	$0.975160\pi$
$72$		0			0
$73$	13634.4	−	41962.5i	0.299454	−	0.921625i	−0.682235	−	0.731133i	$-0.738992\pi$
$73$	13634.4	−	41962.5i	0.299454	−	0.921625i	0.981689	−	0.190492i	$-0.0610082\pi$
$74$	3909.28	+	12031.5i	0.0829885	+	0.255412i
$75$		0			0
$76$	97544.6			1.93718
$77$	−10815.2	−	5763.62i	−0.207878	−	0.110782i
$78$		0			0
$79$	14114.3	−	10254.6i	0.254444	−	0.184864i	−0.453250	−	0.891383i	$-0.649736\pi$
$79$	14114.3	−	10254.6i	0.254444	−	0.184864i	0.707694	+	0.706519i	$0.249736\pi$
$80$	13001.6	+	40014.9i	0.227129	+	0.699031i
$81$		0			0
$82$	−45461.0	−	33029.3i	−0.746628	−	0.542457i
$83$	96187.9	+	69884.6i	1.53259	+	1.11349i	0.954779	+	0.297316i	$0.0960916\pi$
$83$	96187.9	+	69884.6i	1.53259	+	1.11349i	0.577808	+	0.816173i	$0.303908\pi$
$84$		0			0
$85$	36802.9	+	113268.i	0.552503	+	1.70043i
$86$	49485.2	−	35953.1i	0.721488	−	0.524192i
$87$		0			0
$88$	−109283.	+	15253.8i	−1.50434	+	0.209976i
$89$	6612.00			0.0884826			0.0442413	−	0.999021i	$-0.485913\pi$
$89$	6612.00			0.0884826			0.0442413	+	0.999021i	$0.485913\pi$
$90$		0			0
$91$	5374.62	+	16541.4i	0.0680369	+	0.209396i
$92$	22739.7	−	69985.6i	0.280101	−	0.862063i
$93$		0			0
$94$	235428.	+	171049.i	2.74814	+	1.99664i
$95$	29609.9	−	91129.9i	0.336611	−	1.03598i
$96$		0			0
$97$	−103201.	+	74979.8i	−1.11366	+	0.809124i	−0.983237	−	0.182334i	$-0.941635\pi$
$97$	−103201.	+	74979.8i	−1.11366	+	0.809124i	−0.130427	+	0.991458i	$0.541635\pi$
$98$	152739.			1.60651
$99$		0			0
$100$	25192.6			0.251926
$101$	−60612.2	+	44037.4i	−0.591231	+	0.429554i	−0.842755	−	0.538297i	$-0.819068\pi$
$101$	−60612.2	+	44037.4i	−0.591231	+	0.429554i	0.251525	+	0.967851i	$0.419068\pi$
$102$		0			0
$103$	16296.0	−	50153.8i	0.151352	−	0.465812i	−0.846421	−	0.532514i	$-0.821247\pi$
$103$	16296.0	−	50153.8i	0.151352	−	0.465812i	0.997773	+	0.0667013i	$0.0212475\pi$
$104$	126691.	+	92046.6i	1.14859	+	0.834496i
$105$		0			0
$106$	21263.6	−	65442.7i	0.183812	−	0.565714i
$107$	38090.9	+	117232.i	0.321634	+	0.989888i	0.972937	+	0.231070i	$0.0742228\pi$
$107$	38090.9	+	117232.i	0.321634	+	0.989888i	−0.651303	+	0.758818i	$0.725777\pi$
$108$		0			0
$109$	−134499.			−1.08431			−0.542153	−	0.840280i	$-0.682391\pi$
$109$	−134499.			−1.08431			−0.542153	+	0.840280i	$0.682391\pi$
$110$	−40111.7	+	226239.i	−0.316074	+	1.78273i
$111$		0			0
$112$	−17468.4	+	12691.5i	−0.131586	+	0.0956025i
$113$	−10405.9	−	32026.0i	−0.0766623	−	0.235942i	0.905380	−	0.424602i	$-0.139586\pi$
$113$	−10405.9	−	32026.0i	−0.0766623	−	0.235942i	−0.982043	+	0.188659i	$0.939586\pi$
$114$		0			0
$115$	−58480.5	−	42488.6i	−0.412351	−	0.299590i
$116$	−372447.	−	270598.i	−2.56992	−	1.86715i
$117$		0			0
$118$	−65935.0	−	202927.i	−0.435924	−	1.34164i
$119$	−49446.7	+	35925.2i	−0.320089	+	0.232558i
$120$		0			0
$121$	−151234.	−	55367.6i	−0.939047	−	0.343789i
$122$	−240514.			−1.46299
$123$		0			0
$124$	−135902.	−	418262.i	−0.793726	−	2.44284i
$125$	−49815.7	+	153317.i	−0.285162	+	0.877637i
$126$		0			0
$127$	189823.	+	137914.i	1.04433	+	0.758752i	0.971127	−	0.238565i	$-0.0766770\pi$
$127$	189823.	+	137914.i	1.04433	+	0.758752i	0.0732059	+	0.997317i	$0.476677\pi$
$128$	104625.	−	322002.i	0.564430	−	1.73714i
$129$		0			0
$130$	263811.	−	191670.i	1.36910	−	0.994709i
$131$	−204823.			−1.04280			−0.521399	−	0.853313i	$-0.674590\pi$
$131$	−204823.			−1.04280			−0.521399	+	0.853313i	$0.674590\pi$
$132$		0			0
$133$	49173.9			0.241049
$134$	120994.	−	87907.4i	0.582106	−	0.422925i
$135$		0			0
$136$	−170054.	+	523371.i	−0.788386	+	2.42640i
$137$	−39015.1	−	28346.1i	−0.177595	−	0.129030i	0.495436	−	0.868644i	$-0.335008\pi$
$137$	−39015.1	−	28346.1i	−0.177595	−	0.129030i	−0.673032	+	0.739614i	$0.735008\pi$
$138$		0			0
$139$	36205.7	−	111430.i	0.158942	−	0.489174i	−0.839597	−	0.543210i	$-0.817209\pi$
$139$	36205.7	−	111430.i	0.158942	−	0.489174i	0.998539	+	0.0540363i	$0.0172087\pi$
$140$	34015.6	+	104689.i	0.146676	+	0.451421i
$141$		0			0
$142$	−621811.			−2.58784
$143$	100003.	+	205528.i	0.408953	+	0.840486i
$144$		0			0
$145$	−365861.	+	265813.i	−1.44509	+	1.04992i
$146$	−131186.	−	403749.i	−0.509337	−	1.56758i
$147$		0			0
$148$	64435.6	+	46815.2i	0.241809	+	0.175684i
$149$	167138.	+	121433.i	0.616751	+	0.448096i	0.851785	−	0.523891i	$-0.175520\pi$
$149$	167138.	+	121433.i	0.616751	+	0.448096i	−0.235034	+	0.971987i	$0.575520\pi$
$150$		0			0
$151$	31098.2	+	95710.5i	0.110992	+	0.341600i	0.991090	−	0.133193i	$-0.0425231\pi$
$151$	31098.2	+	95710.5i	0.110992	+	0.341600i	−0.880098	+	0.474793i	$0.842523\pi$
$152$	358192.	−	260242.i	1.25750	−	0.913625i
$153$		0			0
$154$	−116783.	+	16300.6i	−0.396804	+	0.0553862i
$155$	−432010.			−1.44432
$156$		0			0
$157$	24801.2	+	76330.2i	0.0803014	+	0.247142i	0.983145	−	0.182826i	$-0.0585246\pi$
$157$	24801.2	+	76330.2i	0.0803014	+	0.247142i	−0.902844	+	0.429969i	$0.858525\pi$
$158$	51872.2	−	159646.i	0.165307	−	0.508763i
$159$		0			0
$160$	−96058.8	−	69790.8i	−0.296645	−	0.215525i
$161$	11463.5	−	35281.0i	0.0348539	−	0.107269i
$162$		0			0
$163$	15438.1	−	11216.4i	0.0455118	−	0.0330663i	−0.564797	−	0.825230i	$-0.691045\pi$
$163$	15438.1	−	11216.4i	0.0455118	−	0.0330663i	0.610309	+	0.792164i	$0.291045\pi$
$164$	−353781.			−1.02713
$165$		0			0
$166$	1.14397e6			3.22213
$167$	−354930.	+	257871.i	−0.984807	+	0.715504i	−0.958778	−	0.284157i	$-0.908286\pi$
$167$	−354930.	+	257871.i	−0.984807	+	0.715504i	−0.0260291	+	0.999661i	$0.508286\pi$
$168$		0			0
$169$	−14495.8	+	44613.4i	−0.0390413	+	0.120157i
$170$	927060.	+	673548.i	2.46029	+	1.78750i
$171$		0			0
$172$	119002.	−	366250.i	0.306713	−	0.943967i
$173$	−125314.	−	385677.i	−0.318335	−	0.979734i	−0.974360	−	0.224995i	$-0.927763\pi$
$173$	−125314.	−	385677.i	−0.318335	−	0.979734i	0.656025	−	0.754739i	$-0.272237\pi$
$174$		0			0
$175$	12700.0			0.0313480
$176$	−204301.	+	196919.i	−0.497151	+	0.479189i
$177$		0			0
$178$	51468.4	−	37394.0i	0.121756	−	0.0884610i
$179$	−112272.	−	345539.i	−0.261903	−	0.806054i	−0.992391	−	0.123128i	$-0.960707\pi$
$179$	−112272.	−	345539.i	−0.261903	−	0.806054i	0.730488	−	0.682926i	$-0.239293\pi$
$180$		0			0
$181$	506552.	+	368031.i	1.14928	+	0.835004i	0.988386	−	0.151967i	$-0.0485609\pi$
$181$	506552.	+	368031.i	1.14928	+	0.835004i	0.160898	+	0.986971i	$0.448561\pi$
$182$	135386.	+	98363.6i	0.302967	+	0.220118i
$183$		0			0
$184$	−103214.	−	317661.i	−0.224748	−	0.691703i
$185$	63296.2	−	45987.4i	0.135972	−	0.0987891i
$186$		0			0
$187$	−578302.	+	557408.i	−1.20935	+	1.16565i
$188$	1.83212e6			3.78060
$189$		0			0
$190$	−284897.	−	876822.i	−0.572537	−	1.76209i
$191$	−151049.	+	464881.i	−0.299595	+	0.922059i	0.682044	+	0.731311i	$0.261091\pi$
$191$	−151049.	+	464881.i	−0.299595	+	0.922059i	−0.981639	+	0.190748i	$0.938909\pi$
$192$		0			0
$193$	109220.	+	79352.8i	0.211061	+	0.153345i	0.688294	−	0.725432i	$-0.258360\pi$
$193$	109220.	+	79352.8i	0.211061	+	0.153345i	−0.477233	+	0.878777i	$0.658360\pi$
$194$	−379279.	+	1.16730e6i	−0.723526	+	2.22678i
$195$		0			0
$196$	777966.	−	565225.i	1.44651	−	1.05095i
$197$	176847.			0.324662			0.162331	−	0.986736i	$-0.448099\pi$
$197$	176847.			0.324662			0.162331	+	0.986736i	$0.448099\pi$
$198$		0			0
$199$	433048.			0.775181			0.387591	−	0.921832i	$-0.373307\pi$
$199$	433048.			0.775181			0.387591	+	0.921832i	$0.373307\pi$
$200$	92509.5	−	67212.1i	0.163535	−	0.118815i
$201$		0			0
$202$	−222759.	+	685582.i	−0.384111	+	1.18217i
$203$	−187757.	−	136413.i	−0.319783	−	0.232336i
$204$		0			0
$205$	−107391.	+	330516.i	−0.178478	+	0.549298i
$206$	−156794.	−	482564.i	−0.257432	−	0.792294i
$207$		0			0
$208$	402707.			0.645403
$209$	640016.	−	89333.8i	1.01350	−	0.141465i
$210$		0			0
$211$	108834.	−	79072.6i	0.168290	−	0.122270i	−0.500452	−	0.865764i	$-0.666833\pi$
$211$	108834.	−	79072.6i	0.168290	−	0.122270i	0.668742	+	0.743494i	$0.266833\pi$
$212$	−133872.	−	412017.i	−0.204575	−	0.629616i
$213$		0			0
$214$	959505.	+	697121.i	1.43223	+	1.04058i
$215$	−306042.	−	222352.i	−0.451528	−	0.328054i
$216$		0			0
$217$	−68510.4	−	210853.i	−0.0987659	−	0.303970i
$218$	−1.04695e6	+	760654.i	−1.49206	+	1.08404i
$219$		0			0
$220$	632913.	+	1.30077e6i	0.881632	+	1.81194i
$221$	1.13992e6			1.56998
$222$		0			0
$223$	−235726.	−	725489.i	−0.317428	−	0.976942i	−0.974744	−	0.223327i	$-0.928308\pi$
$223$	−235726.	−	725489.i	−0.317428	−	0.976942i	0.657316	−	0.753615i	$-0.271692\pi$
$224$	18829.6	−	57951.7i	0.0250739	−	0.0771695i
$225$		0			0
$226$	−262122.	−	190443.i	−0.341376	−	0.248024i
$227$	33519.6	−	103163.i	0.0431752	−	0.132880i	−0.927145	−	0.374702i	$-0.877745\pi$
$227$	33519.6	−	103163.i	0.0431752	−	0.132880i	0.970321	+	0.241822i	$0.0777451\pi$
$228$		0			0
$229$	423208.	−	307479.i	0.533292	−	0.387459i	−0.288296	−	0.957541i	$-0.593089\pi$
$229$	423208.	−	307479.i	0.533292	−	0.387459i	0.821588	+	0.570082i	$0.193089\pi$
$230$	−695511.			−0.866931
$231$		0			0
$232$	−2.08959e6			−2.54884
$233$	177464.	−	128935.i	0.214152	−	0.155590i	−0.475539	−	0.879695i	$-0.657747\pi$
$233$	177464.	−	128935.i	0.214152	−	0.155590i	0.689690	+	0.724105i	$0.257747\pi$
$234$		0			0
$235$	556146.	−	1.71164e6i	0.656930	−	2.02182i
$236$	−1.08679e6	−	789598.i	−1.27018	−	0.922840i
$237$		0			0
$238$	−181724.	+	559290.i	−0.207955	+	0.640021i
$239$	−149117.	−	458935.i	−0.168862	−	0.519704i	0.830438	−	0.557111i	$-0.188090\pi$
$239$	−149117.	−	458935.i	−0.168862	−	0.519704i	−0.999300	+	0.0374068i	$0.988090\pi$
$240$		0			0
$241$	−472230.			−0.523734			−0.261867	−	0.965104i	$-0.584338\pi$
$241$	−472230.			−0.523734			−0.261867	+	0.965104i	$0.584338\pi$
$242$	−1.49035e6	+	424316.i	−1.63588	+	0.465748i
$243$		0			0
$244$	−1.22505e6	+	890048.i	−1.31728	+	0.957060i
$245$	−291902.	−	898381.i	−0.310686	−	0.956193i
$246$		0			0
$247$	−741969.	−	539072.i	−0.773827	−	0.562218i
$248$	−1.61494e6	−	1.17332e6i	−1.66735	−	1.21140i
$249$		0			0
$250$	479310.	+	1.47516e6i	0.485028	+	1.49276i
$251$	296517.	−	215432.i	0.297074	−	0.215837i	−0.429256	−	0.903183i	$-0.641224\pi$
$251$	296517.	−	215432.i	0.297074	−	0.215837i	0.726330	+	0.687346i	$0.241224\pi$
$252$		0			0
$253$	85106.5	−	480020.i	0.0835914	−	0.471474i
$254$	2.25757e6			2.19562
$255$		0			0
$256$	−593079.	−	1.82531e6i	−0.565604	−	1.74075i
$257$	−520203.	+	1.60102e6i	−0.491292	+	1.51204i	0.331363	+	0.943503i	$0.392491\pi$
$257$	−520203.	+	1.60102e6i	−0.491292	+	1.51204i	−0.822656	+	0.568540i	$0.807509\pi$
$258$		0			0
$259$	32483.1	+	23600.4i	0.0300890	+	0.0218610i
$260$	634413.	−	1.95252e6i	0.582021	−	1.79128i
$261$		0			0
$262$	−1.59436e6	+	1.15837e6i	−1.43494	+	1.04254i
$263$	1.52341e6			1.35808			0.679042	−	0.734100i	$-0.262396\pi$
$263$	1.52341e6			1.35808			0.679042	+	0.734100i	$0.262396\pi$
$264$		0			0
$265$	−425560.			−0.372259
$266$	382774.	−	278102.i	0.331695	−	0.240990i
$267$		0			0
$268$	290966.	−	895502.i	0.247460	−	0.761605i
$269$	−55575.7	−	40378.1i	−0.0468278	−	0.0340224i	0.564125	−	0.825689i	$-0.309214\pi$
$269$	−55575.7	−	40378.1i	−0.0468278	−	0.0340224i	−0.610953	+	0.791667i	$0.709214\pi$
$270$		0			0
$271$	367114.	−	1.12986e6i	0.303653	−	0.934549i	−0.676523	−	0.736422i	$-0.736514\pi$
$271$	367114.	−	1.12986e6i	0.303653	−	0.934549i	0.980176	−	0.198128i	$-0.0634860\pi$
$272$	437306.	+	1.34589e6i	0.358396	+	1.10303i
$273$		0			0
$274$	−464008.			−0.373378
$275$	165295.	−	23072.1i	0.131804	−	0.0183973i
$276$		0			0
$277$	1.22085e6	−	887001.i	0.956012	−	0.694583i	0.00379098	−	0.999993i	$-0.498793\pi$
$277$	1.22085e6	−	887001.i	0.956012	−	0.694583i	0.952221	+	0.305409i	$0.0987933\pi$
$278$	−348359.	−	1.07214e6i	−0.270343	−	0.832030i
$279$		0			0
$280$	404212.	+	293677.i	0.308116	+	0.223859i
$281$	1.13878e6	+	827375.i	0.860351	+	0.625081i	0.927980	−	0.372629i	$-0.121544\pi$
$281$	1.13878e6	+	827375.i	0.860351	+	0.625081i	−0.0676296	+	0.997710i	$0.521544\pi$
$282$		0			0
$283$	99556.9	+	306405.i	0.0738933	+	0.227420i	0.981181	−	0.193090i	$-0.0618510\pi$
$283$	99556.9	+	306405.i	0.0738933	+	0.227420i	−0.907288	+	0.420510i	$0.861851\pi$
$284$	−3.16716e6	+	2.30108e6i	−2.33010	+	1.69292i
$285$		0			0
$286$	1.94079e6	+	1.03428e6i	1.40302	+	0.747694i
$287$	−178347.			−0.127809
$288$		0			0
$289$	799097.	+	2.45937e6i	0.562801	+	1.73212i
$290$	−1.34459e6	+	4.13823e6i	−0.938849	+	2.88948i
$291$		0			0
$292$	−2.16230e6	−	1.57101e6i	−1.48409	−	1.07825i
$293$	437404.	−	1.34619e6i	0.297656	−	0.916090i	−0.684661	−	0.728862i	$-0.740050\pi$
$293$	437404.	−	1.34619e6i	0.297656	−	0.916090i	0.982317	−	0.187228i	$-0.0599503\pi$
$294$		0			0
$295$	−1.06757e6	+	775636.i	−0.714236	+	0.518923i
$296$	361513.			0.239825
$297$		0			0
$298$	1.98778e6			1.29666
$299$	−559739.	+	406674.i	−0.362082	+	0.263068i
$300$		0			0
$301$	59990.9	−	184633.i	0.0381654	−	0.117461i
$302$	783360.	+	569144.i	0.494247	+	0.359091i
$303$		0			0
$304$	351836.	−	1.08284e6i	0.218352	−	0.672018i
$305$	459652.	+	1.41466e6i	0.282930	+	0.870769i
$306$		0			0
$307$	637505.			0.386045			0.193022	−	0.981194i	$-0.438171\pi$
$307$	637505.			0.386045			0.193022	+	0.981194i	$0.438171\pi$
$308$	−534504.	+	515192.i	−0.321051	+	0.309451i
$309$		0			0
$310$	−3.36281e6	+	2.44322e6i	−1.98746	+	1.44397i
$311$	345172.	+	1.06233e6i	0.202364	+	0.622814i	0.999811	+	0.0194245i	$0.00618340\pi$
$311$	345172.	+	1.06233e6i	0.202364	+	0.622814i	−0.797447	+	0.603389i	$0.793817\pi$
$312$		0			0
$313$	2.41362e6	+	1.75360e6i	1.39254	+	1.01174i	0.995581	+	0.0939055i	$0.0299352\pi$
$313$	2.41362e6	+	1.75360e6i	1.39254	+	1.01174i	0.396961	+	0.917836i	$0.370065\pi$
$314$	624738.	+	453899.i	0.357581	+	0.259798i
$315$		0			0
$316$	−326579.	−	1.00511e6i	−0.183980	−	0.566232i
$317$	1.58238e6	−	1.14966e6i	0.884426	−	0.642573i	−0.0499930	−	0.998750i	$-0.515920\pi$
$317$	1.58238e6	−	1.14966e6i	0.884426	−	0.642573i	0.934419	+	0.356177i	$0.115920\pi$
$318$		0			0
$319$	−2.69154e6	−	1.43437e6i	−1.48090	−	0.789196i
$320$	−2.48880e6			−1.35867
$321$		0			0
$322$	−110298.	−	339462.i	−0.0592826	−	0.182453i
$323$	995922.	−	3.06513e6i	0.531152	−	1.63472i
$324$		0			0
$325$	−191627.	−	139225.i	−0.100635	−	0.0731154i
$326$	56737.3	−	174619.i	0.0295682	−	0.0910014i
$327$		0			0
$328$	−1.29912e6	+	943863.i	−0.666750	+	0.484422i
$329$	923606.			0.470432
$330$		0			0
$331$	−340808.			−0.170978			−0.0854888	−	0.996339i	$-0.527245\pi$
$331$	−340808.			−0.170978			−0.0854888	+	0.996339i	$0.527245\pi$
$332$	5.82672e6	−	4.23336e6i	2.90121	−	2.10785i
$333$		0			0
$334$	−1.30442e6	+	4.01459e6i	−0.639810	+	1.96913i
$335$	−748289.	−	543664.i	−0.364299	−	0.264678i
$336$		0			0
$337$	1.24336e6	−	3.82667e6i	0.596380	−	1.83547i	0.0486436	−	0.998816i	$-0.484510\pi$
$337$	1.24336e6	−	3.82667e6i	0.596380	−	1.83547i	0.547736	−	0.836651i	$-0.315490\pi$
$338$	139473.	+	429255.i	0.0664049	+	0.204373i
$339$		0			0
$340$	7.21446e6			3.38459
$341$	−1.27474e6	−	2.61987e6i	−0.593658	−	1.22009i
$342$		0			0
$343$	807412.	−	586619.i	0.370561	−	0.269228i
$344$	−540143.	−	1.66239e6i	−0.246101	−	0.757420i
$345$		0			0
$346$	−3.15664e6	−	2.29343e6i	−1.41754	−	1.02990i
$347$	−3.21125e6	−	2.33311e6i	−1.43170	−	1.04019i	−0.989698	−	0.143173i	$-0.954269\pi$
$347$	−3.21125e6	−	2.33311e6i	−1.43170	−	1.04019i	−0.441999	−	0.897015i	$-0.645731\pi$
$348$		0			0
$349$	−590291.	−	1.81673e6i	−0.259420	−	0.798412i	−0.992927	−	0.118730i	$-0.962118\pi$
$349$	−590291.	−	1.81673e6i	−0.259420	−	0.798412i	0.733507	−	0.679682i	$-0.237882\pi$
$350$	98858.3	−	71824.8i	0.0431363	−	0.0313404i
$351$		0			0
$352$	139794.	−	788469.i	0.0601356	−	0.339178i
$353$	−4.22138e6			−1.80309			−0.901545	−	0.432686i	$-0.857566\pi$
$353$	−4.22138e6			−1.80309			−0.901545	+	0.432686i	$0.857566\pi$
$354$		0			0
$355$	1.18835e6	+	3.65738e6i	0.500467	+	1.54028i
$356$	123771.	−	380928.i	0.0517600	−	0.159301i
$357$		0			0
$358$	−2.82812e6	−	2.05475e6i	−1.16625	−	0.847329i
$359$	−473019.	+	1.45580e6i	−0.193706	+	0.596165i	0.806284	+	0.591529i	$0.201476\pi$
$359$	−473019.	+	1.45580e6i	−0.193706	+	0.596165i	−0.999989	+	0.00463543i	$0.998524\pi$
$360$		0			0
$361$	−94551.5	+	68695.7i	−0.0381857	+	0.0277435i
$362$	6.02444e6			2.41627
$363$		0			0
$364$	1.05359e6			0.416789
$365$	−2.12407e6	+	1.54323e6i	−0.834519	+	0.606313i
$366$		0			0
$367$	−474852.	+	1.46144e6i	−0.184032	+	0.566392i	−0.999930	−	0.0118031i	$-0.996243\pi$
$367$	−474852.	+	1.46144e6i	−0.184032	+	0.566392i	0.815898	+	0.578195i	$0.196243\pi$
$368$	−694889.	−	504866.i	−0.267483	−	0.194338i
$369$		0			0
$370$	232623.	−	715940.i	0.0883382	−	0.271877i
$371$	−67487.5	−	207705.i	−0.0254559	−	0.0783452i
$372$		0			0
$373$	1.42900e6			0.531816			0.265908	−	0.963998i	$-0.414328\pi$
$373$	1.42900e6			0.531816			0.265908	+	0.963998i	$0.414328\pi$
$374$	−1.34915e6	+	7.60949e6i	−0.498747	+	2.81304i
$375$		0			0
$376$	6.72772e6	−	4.88798e6i	2.45413	−	1.78303i
$377$	1.33756e6	+	4.11660e6i	0.484686	+	1.49171i
$378$		0			0
$379$	−2.31879e6	−	1.68470e6i	−0.829208	−	0.602455i	0.0901273	−	0.995930i	$-0.471273\pi$
$379$	−2.31879e6	−	1.68470e6i	−0.829208	−	0.602455i	−0.919335	+	0.393476i	$0.871273\pi$
$380$	−4.69587e6	−	3.41175e6i	−1.66824	−	1.21204i
$381$		0			0
$382$	1.45334e6	+	4.47293e6i	0.509577	+	1.56832i
$383$	2.30326e6	−	1.67341e6i	0.802316	−	0.582917i	−0.109277	−	0.994011i	$-0.534853\pi$
$383$	2.30326e6	−	1.67341e6i	0.802316	−	0.582917i	0.911593	+	0.411095i	$0.134853\pi$
$384$		0			0
$385$	319063.	+	655742.i	0.109704	+	0.225466i
$386$	1.29895e6			0.443737
$387$		0			0
$388$	2.38788e6	+	7.34914e6i	0.805254	+	2.47832i
$389$	−1.45681e6	+	4.48361e6i	−0.488124	+	1.50229i	0.339281	+	0.940685i	$0.389816\pi$
$389$	−1.45681e6	+	4.48361e6i	−0.488124	+	1.50229i	−0.827405	+	0.561606i	$0.810184\pi$
$390$		0			0
$391$	−1.96698e6	−	1.42909e6i	−0.650665	−	0.472736i
$392$	1.34878e6	−	4.15111e6i	0.443328	−	1.36442i
$393$		0			0
$394$	1.37659e6	−	1.00015e6i	0.446750	−	0.324583i
$395$	−1.03814e6			−0.334784
$396$		0			0
$397$	3.61747e6			1.15194			0.575968	−	0.817472i	$-0.304625\pi$
$397$	3.61747e6			1.15194			0.575968	+	0.817472i	$0.304625\pi$
$398$	3.37089e6	−	2.44909e6i	1.06669	−	0.774992i
$399$		0			0
$400$	90868.0	−	279663.i	0.0283963	−	0.0873947i
$401$	−2.81971e6	−	2.04864e6i	−0.875677	−	0.636217i	0.0564269	−	0.998407i	$-0.482029\pi$
$401$	−2.81971e6	−	2.04864e6i	−0.875677	−	0.636217i	−0.932104	+	0.362190i	$0.882029\pi$
$402$		0			0
$403$	−1.27776e6	+	3.93255e6i	−0.391911	+	1.20618i
$404$	1.40246e6	+	4.31632e6i	0.427500	+	1.31571i
$405$		0			0
$406$	−2.23300e6			−0.672316
$407$	465654.	+	248155.i	0.139340	+	0.0742570i
$408$		0			0
$409$	−2.68736e6	+	1.95248e6i	−0.794361	+	0.577137i	−0.909254	−	0.416241i	$-0.863347\pi$
$409$	−2.68736e6	+	1.95248e6i	−0.794361	+	0.577137i	0.114893	+	0.993378i	$0.463347\pi$
$410$	1.03328e6	+	3.18012e6i	0.303570	+	0.934294i
$411$		0			0
$412$	−2.58440e6	−	1.87768e6i	−0.750096	−	0.544976i
$413$	−547869.	−	398050.i	−0.158053	−	0.114832i
$414$		0			0
$415$	−2.18625e6	−	6.72860e6i	−0.623133	−	1.91780i
$416$	−919413.	+	667993.i	−0.260482	+	0.189251i
$417$		0			0
$418$	4.47672e6	−	4.31498e6i	1.25320	−	1.20792i
$419$	5.09570e6			1.41798			0.708988	−	0.705221i	$-0.249152\pi$
$419$	5.09570e6			1.41798			0.708988	+	0.705221i	$0.249152\pi$
$420$		0			0
$421$	988417.	+	3.04204e6i	0.271791	+	0.836487i	0.990051	+	0.140711i	$0.0449390\pi$
$421$	988417.	+	3.04204e6i	0.271791	+	0.836487i	−0.718260	+	0.695775i	$0.755061\pi$
$422$	399982.	−	1.23102e6i	0.109335	−	0.336498i
$423$		0			0
$424$	−1.59082e6	−	1.15580e6i	−0.429741	−	0.312225i
$425$	257215.	−	791625.i	0.0690754	−	0.212592i
$426$		0			0
$427$	−617567.	+	448689.i	−0.163913	+	0.119090i
$428$	7.46696e6			1.97031
$429$		0			0
$430$	−3.63976e6			−0.949297
$431$	−1.32555e6	+	963072.i	−0.343720	+	0.249727i	−0.746230	−	0.665689i	$-0.768138\pi$
$431$	−1.32555e6	+	963072.i	−0.343720	+	0.249727i	0.402510	+	0.915416i	$0.368138\pi$
$432$		0			0
$433$	−69567.6	+	214107.i	−0.0178315	+	0.0548796i	−0.959576	−	0.281449i	$-0.909185\pi$
$433$	−69567.6	+	214107.i	−0.0178315	+	0.0548796i	0.941745	+	0.336328i	$0.109185\pi$
$434$	−1.72577e6	−	1.25384e6i	−0.439803	−	0.319535i
$435$		0			0
$436$	−2.51770e6	+	7.74870e6i	−0.634291	+	1.95215i
$437$	604476.	+	1.86039e6i	0.151417	+	0.466015i
$438$		0			0
$439$	119483.			0.0295899			0.0147950	−	0.999891i	$-0.495290\pi$
$439$	119483.			0.0295899			0.0147950	+	0.999891i	$0.495290\pi$
$440$	5.79448e6	+	3.08798e6i	1.42686	+	0.760401i
$441$		0			0
$442$	8.87323e6	−	6.44678e6i	2.16036	−	1.56959i
$443$	287495.	+	884819.i	0.0696019	+	0.214213i	0.979807	−	0.199945i	$-0.0640763\pi$
$443$	287495.	+	884819.i	0.0696019	+	0.214213i	−0.910205	+	0.414157i	$0.864076\pi$
$444$		0			0
$445$	−318307.	−	231264.i	−0.0761984	−	0.0553614i
$446$	−5.93789e6	−	4.31413e6i	−1.41350	−	1.02697i
$447$		0			0
$448$	−394687.	−	1.21472e6i	−0.0929091	−	0.285945i
$449$	−5.50754e6	+	4.00146e6i	−1.28926	+	0.936705i	−0.999790	−	0.0204816i	$-0.993480\pi$
$449$	−5.50754e6	+	4.00146e6i	−1.28926	+	0.936705i	−0.289473	+	0.957186i	$0.593480\pi$
$450$		0			0
$451$	−2.32125e6	+	324002.i	−0.537379	+	0.0750078i
$452$	−2.03986e6			−0.469628
$453$		0			0
$454$	−322515.	−	992599.i	−0.0734362	−	0.226013i
$455$	319818.	−	984300.i	0.0724228	−	0.222894i
$456$		0			0
$457$	6.73792e6	+	4.89539e6i	1.50916	+	1.09647i	0.966548	+	0.256487i	$0.0825651\pi$
$457$	6.73792e6	+	4.89539e6i	1.50916	+	1.09647i	0.542613	+	0.839983i	$0.317435\pi$
$458$	1.55535e6	−	4.78689e6i	0.346470	−	1.06632i
$459$		0			0
$460$	−3.54255e6	+	2.57381e6i	−0.780586	+	0.567129i
$461$	164594.			0.0360713			0.0180356	−	0.999837i	$-0.494259\pi$
$461$	164594.			0.0360713			0.0180356	+	0.999837i	$0.494259\pi$
$462$		0			0
$463$	−243247.			−0.0527345			−0.0263672	−	0.999652i	$-0.508394\pi$
$463$	−243247.			−0.0527345			−0.0263672	+	0.999652i	$0.508394\pi$
$464$	−4.34730e6	+	3.15850e6i	−0.937399	+	0.681060i
$465$		0			0
$466$	652208.	−	2.00729e6i	0.139130	−	0.428199i
$467$	2.64014e6	+	1.91818e6i	0.560190	+	0.407002i	0.831529	−	0.555482i	$-0.187466\pi$
$467$	2.64014e6	+	1.91818e6i	0.560190	+	0.407002i	−0.271338	+	0.962484i	$0.587466\pi$
$468$		0			0
$469$	146681.	−	451438.i	0.0307923	−	0.0947690i
$470$	−5.35105e6	−	1.64688e7i	−1.11736	−	3.43889i
$471$		0			0
$472$	−6.09738e6			−1.25976
$473$	445381.	−	2.51205e6i	0.0915333	−	0.516268i
$474$		0			0
$475$	−541783.	+	393629.i	−0.110177	+	0.0800484i
$476$	1.14411e6	+	3.52120e6i	0.231446	+	0.712317i
$477$		0			0
$478$	−3.75624e6	−	2.72906e6i	−0.751940	−	0.546316i
$479$	−1.20525e6	−	875663.i	−0.240014	−	0.174381i	0.461275	−	0.887257i	$-0.347392\pi$
$479$	−1.20525e6	−	875663.i	−0.240014	−	0.174381i	−0.701290	+	0.712876i	$0.747392\pi$
$480$		0			0
$481$	−231407.	−	712197.i	−0.0456051	−	0.140358i
$482$	−3.67588e6	+	2.67068e6i	−0.720682	+	0.523606i
$483$		0			0
$484$	−6.02080e6	+	7.67643e6i	−1.16826	+	1.48952i
$485$	7.59069e6			1.46530
$486$		0			0
$487$	−1.55402e6	−	4.78278e6i	−0.296916	−	0.913815i	−0.982571	−	0.185888i	$-0.940484\pi$
$487$	−1.55402e6	−	4.78278e6i	−0.296916	−	0.913815i	0.685654	−	0.727927i	$-0.259516\pi$
$488$	−2.12389e6	+	6.53667e6i	−0.403723	+	1.24253i
$489$		0			0
$490$	−7.35296e6	−	5.34224e6i	−1.38348	−	1.00516i
$491$	1.37605e6	−	4.23504e6i	0.257590	−	0.792781i	−0.735718	−	0.677288i	$-0.763155\pi$
$491$	1.37605e6	−	4.23504e6i	0.257590	−	0.792781i	0.993308	−	0.115493i	$-0.0368449\pi$
$492$		0			0
$493$	−1.23056e7	+	8.94057e6i	−2.28027	+	1.65671i
$494$	−8.82427e6			−1.62690
$495$		0			0
$496$	−5.13331e6			−0.936900
$497$	−1.59662e6	+	1.16001e6i	−0.289942	+	0.210655i
$498$		0			0
$499$	−2.40259e6	+	7.39441e6i	−0.431945	+	1.32939i	0.464241	+	0.885709i	$0.346327\pi$
$499$	−2.40259e6	+	7.39441e6i	−0.431945	+	1.32939i	−0.896185	+	0.443680i	$0.853673\pi$
$500$	7.90034e6	+	5.73993e6i	1.41326	+	1.02679i
$501$		0			0
$502$	1.08974e6	−	3.35389e6i	0.193004	−	0.594004i
$503$	996062.	+	3.06556e6i	0.175536	+	0.540244i	0.999658	−	0.0261687i	$-0.00833070\pi$
$503$	996062.	+	3.06556e6i	0.175536	+	0.540244i	−0.824122	+	0.566413i	$0.808331\pi$
$504$		0			0
$505$	4.45819e6			0.777911
$506$	−2.05226e6	−	4.21783e6i	−0.356333	−	0.732341i
$507$		0			0
$508$	1.14988e7	−	8.35436e6i	1.97694	−	1.43633i
$509$	−383192.	−	1.17934e6i	−0.0655575	−	0.201765i	0.912912	−	0.408156i	$-0.133828\pi$
$509$	−383192.	−	1.17934e6i	−0.0655575	−	0.201765i	−0.978470	+	0.206391i	$0.933828\pi$
$510$		0			0
$511$	−1.09006e6	−	791972.i	−0.184670	−	0.134171i
$512$	−6.17441e6	−	4.48597e6i	−1.04093	−	0.756278i
$513$		0			0
$514$	5.00522e6	+	1.54045e7i	0.835633	+	2.57181i
$515$	−2.53870e6	+	1.84447e6i	−0.421787	+	0.306446i
$516$		0			0
$517$	1.20211e7	−	1.67791e6i	1.97795	−	0.276084i
$518$	386323.			0.0632596
$519$		0			0
$520$	−2.87957e6	−	8.86240e6i	−0.467002	−	1.43728i
$521$	1.39277e6	−	4.28651e6i	0.224795	−	0.691846i	−0.773518	−	0.633775i	$-0.781505\pi$
$521$	1.39277e6	−	4.28651e6i	0.224795	−	0.691846i	0.998312	−	0.0580720i	$-0.0184953\pi$
$522$		0			0
$523$	−1.83670e6	−	1.33444e6i	−0.293620	−	0.213327i	0.431216	−	0.902249i	$-0.358085\pi$
$523$	−1.83670e6	−	1.33444e6i	−0.293620	−	0.213327i	−0.724836	+	0.688921i	$0.758085\pi$
$524$	−3.83412e6	+	1.18002e7i	−0.610010	+	1.87742i
$525$		0			0
$526$	1.18583e7	−	8.61559e6i	1.86879	−	1.35775i
$527$	−1.45305e7			−2.27906
$528$		0			0
$529$	−4.96065e6			−0.770725
$530$	−3.31260e6	+	2.40674e6i	−0.512246	+	0.372169i
$531$		0			0
$532$	920495.	−	2.83299e6i	0.141008	−	0.433977i
$533$	2.69103e6	+	1.95514e6i	0.410298	+	0.298099i
$534$		0			0
$535$	2.26661e6	−	6.97592e6i	0.342368	−	1.05370i
$536$	−1.32068e6	−	4.06464e6i	−0.198557	−	0.611097i
$537$		0			0
$538$	−660963.			−0.0984514
$539$	4.58679e6	−	4.42107e6i	0.680044	−	0.655475i
$540$		0			0
$541$	594522.	−	431945.i	0.0873322	−	0.0634506i	−0.543262	−	0.839563i	$-0.682811\pi$
$541$	594522.	−	431945.i	0.0873322	−	0.0634506i	0.630595	+	0.776112i	$0.282811\pi$
$542$	−3.53225e6	−	1.08712e7i	−0.516480	−	1.58956i
$543$		0			0
$544$	−3.23091e6	−	2.34740e6i	−0.468089	−	0.340086i
$545$	6.47488e6	+	4.70427e6i	0.933771	+	0.678424i
$546$		0			0
$547$	−3.11865e6	−	9.59822e6i	−0.445655	−	1.37158i	−0.881764	−	0.471690i	$-0.843644\pi$
$547$	−3.11865e6	−	9.59822e6i	−0.445655	−	1.37158i	0.436110	−	0.899894i	$-0.356356\pi$
$548$	−2.36340e6	+	1.71711e6i	−0.336191	+	0.244257i
$549$		0			0
$550$	1.15619e6	−	1.11442e6i	0.162976	−	0.157088i
$551$	1.22377e7			1.71721
$552$		0			0
$553$	−164634.	−	506692.i	−0.0228932	−	0.0704582i
$554$	4.48681e6	−	1.38090e7i	0.621103	−	1.91156i
$555$		0			0
$556$	−5.74190e6	−	4.17174e6i	−0.787715	−	0.572308i
$557$	529373.	−	1.62924e6i	0.0722976	−	0.222509i	−0.908378	−	0.418150i	$-0.862679\pi$
$557$	529373.	−	1.62924e6i	0.0722976	−	0.222509i	0.980676	+	0.195641i	$0.0626787\pi$
$558$		0			0
$559$	−2.92924e6	+	2.12821e6i	−0.396483	+	0.288062i
$560$	1.28485e6			0.173134
$561$		0			0
$562$	1.35436e7			1.80881
$563$	−3.57065e6	+	2.59423e6i	−0.474763	+	0.344935i	−0.799294	−	0.600940i	$-0.794793\pi$
$563$	−3.57065e6	+	2.59423e6i	−0.474763	+	0.344935i	0.324532	+	0.945875i	$0.394793\pi$
$564$		0			0
$565$	−619204.	+	1.90571e6i	−0.0816042	+	0.251152i
$566$	2.50782e6	+	1.82204e6i	0.329045	+	0.239065i
$567$		0			0
$568$	−5.49098e6	+	1.68995e7i	−0.714133	+	2.19788i
$569$	1.31326e6	+	4.04181e6i	0.170048	+	0.523354i	0.999373	−	0.0354130i	$-0.0112747\pi$
$569$	1.31326e6	+	4.04181e6i	0.170048	+	0.523354i	−0.829325	+	0.558767i	$0.811275\pi$
$570$		0			0
$571$	2.86179e6			0.367322			0.183661	−	0.982990i	$-0.441205\pi$
$571$	2.86179e6			0.367322			0.183661	+	0.982990i	$0.441205\pi$
$572$	1.37128e7	−	1.91404e6i	1.75241	−	0.244603i
$573$		0			0
$574$	−1.38827e6	+	1.00864e6i	−0.175871	+	0.127778i
$575$	156117.	+	480478.i	0.0196916	+	0.0606044i
$576$		0			0
$577$	7.56221e6	+	5.49427e6i	0.945604	+	0.687022i	0.949763	−	0.312970i	$-0.101324\pi$
$577$	7.56221e6	+	5.49427e6i	0.945604	+	0.687022i	−0.00415903	+	0.999991i	$0.501324\pi$
$578$	2.01291e7	+	1.46247e7i	2.50614	+	1.82082i
$579$		0			0
$580$	8.46534e6	+	2.60536e7i	1.04490	+	3.21587i
$581$	2.93735e6	−	2.13411e6i	0.361007	−	0.262287i
$582$		0			0
$583$	−1.25571e6	−	2.58075e6i	−0.153009	−	0.314467i
$584$	−1.21315e7			−1.47191
$585$		0			0
$586$	−4.20856e6	−	1.29526e7i	−0.506278	−	1.55816i
$587$	81580.3	−	251078.i	0.00977214	−	0.0300756i	−0.946052	−	0.324016i	$-0.894967\pi$
$587$	81580.3	−	251078.i	0.00977214	−	0.0300756i	0.955824	+	0.293941i	$0.0949668\pi$
$588$		0			0
$589$	9.45790e6	+	6.87156e6i	1.12333	+	0.816145i
$590$	−3.92348e6	+	1.20752e7i	−0.464025	+	1.42812i
$591$		0			0
$592$	752110.	−	546440.i	0.0882017	−	0.0640823i
$593$	1.46405e6			0.170969			0.0854846	−	0.996339i	$-0.472756\pi$
$593$	1.46405e6			0.170969			0.0854846	+	0.996339i	$0.472756\pi$
$594$		0			0
$595$	3.63694e6			0.421156
$596$	1.01246e7	−	7.35598e6i	1.16752	−	0.848253i
$597$		0			0
$598$	−2.05712e6	+	6.33117e6i	−0.235238	+	0.723988i
$599$	1.04245e6	+	757382.i	0.118710	+	0.0862478i	0.645556	−	0.763713i	$-0.276626\pi$
$599$	1.04245e6	+	757382.i	0.118710	+	0.0862478i	−0.526846	+	0.849961i	$0.676626\pi$
$600$		0			0
$601$	−3.84287e6	+	1.18271e7i	−0.433980	+	1.33565i	0.460148	+	0.887842i	$0.347796\pi$
$601$	−3.84287e6	+	1.18271e7i	−0.433980	+	1.33565i	−0.894128	+	0.447811i	$0.852204\pi$
$602$	−577213.	−	1.77648e6i	−0.0649149	−	0.199788i
$603$		0			0
$604$	6.09618e6			0.679932
$605$	5.34399e6	+	7.95507e6i	0.593577	+	0.883599i
$606$		0			0
$607$	−1.14217e7	+	8.29837e6i	−1.25823	+	0.914157i	−0.998669	−	0.0515694i	$-0.983578\pi$
$607$	−1.14217e7	+	8.29837e6i	−1.25823	+	0.914157i	−0.259560	+	0.965727i	$0.583578\pi$
$608$	992898.	+	3.05583e6i	0.108930	+	0.335251i
$609$		0			0
$610$	1.15786e7	+	8.41231e6i	1.25988	+	0.915358i
$611$	−1.39360e7	−	1.01251e7i	−1.51020	−	1.09723i
$612$		0			0
$613$	−5.18824e6	−	1.59678e7i	−0.557659	−	1.71630i	−0.688815	−	0.724937i	$-0.741869\pi$
$613$	−5.18824e6	−	1.59678e7i	−0.557659	−	1.71630i	0.131156	−	0.991362i	$-0.458131\pi$
$614$	4.96240e6	−	3.60539e6i	0.531215	−	0.385950i
$615$		0			0
$616$	−588248.	+	3.31785e6i	−0.0624610	+	0.352294i
$617$	1.49155e6			0.157734			0.0788670	−	0.996885i	$-0.474870\pi$
$617$	1.49155e6			0.157734			0.0788670	+	0.996885i	$0.474870\pi$
$618$		0			0
$619$	2.45026e6	+	7.54111e6i	0.257031	+	0.791059i	0.993423	+	0.114504i	$0.0365278\pi$
$619$	2.45026e6	+	7.54111e6i	0.257031	+	0.791059i	−0.736392	+	0.676555i	$0.763472\pi$
$620$	−8.08687e6	+	2.48888e7i	−0.844892	+	2.60031i
$621$		0			0
$622$	8.69482e6	+	6.31716e6i	0.901125	+	0.654705i
$623$	62395.2	−	192033.i	0.00644067	−	0.0198223i
$624$		0			0
$625$	8.81205e6	−	6.40233e6i	0.902354	−	0.655599i
$626$	2.87053e7			2.92770
$627$		0			0
$628$	4.86177e6			0.491921
$629$	2.12895e6	−	1.54677e6i	0.214555	−	0.155884i
$630$		0			0
$631$	3.59807e6	−	1.10737e7i	0.359747	−	1.10719i	−0.593459	−	0.804864i	$-0.702238\pi$
$631$	3.59807e6	−	1.10737e7i	0.359747	−	1.10719i	0.953206	−	0.302322i	$-0.0977619\pi$
$632$	−3.88078e6	−	2.81955e6i	−0.386479	−	0.280794i
$633$		0			0
$634$	5.81547e6	−	1.78982e7i	0.574594	−	1.76842i
$635$	−4.31448e6	−	1.32786e7i	−0.424614	−	1.30683i
$636$		0			0
$637$	−9.04124e6			−0.882835
$638$	−2.90633e7	+	4.05667e6i	−2.82679	+	0.394565i
$639$		0			0
$640$	−1.62992e7	+	1.18421e7i	−1.57295	+	1.14282i
$641$	1.70566e6	+	5.24949e6i	0.163964	+	0.504628i	0.998958	−	0.0456295i	$-0.0145294\pi$
$641$	1.70566e6	+	5.24949e6i	0.163964	+	0.504628i	−0.834995	+	0.550258i	$0.814529\pi$
$642$		0			0
$643$	4.00037e6	+	2.90644e6i	0.381569	+	0.277226i	0.761992	−	0.647587i	$-0.224222\pi$
$643$	4.00037e6	+	2.90644e6i	0.381569	+	0.277226i	−0.380423	+	0.924813i	$0.624222\pi$
$644$	−1.81801e6	−	1.32086e6i	−0.172735	−	0.125500i
$645$		0			0
$646$	−9.58243e6	−	2.94917e7i	−0.903430	−	2.78047i
$647$	−5.86897e6	+	4.26406e6i	−0.551190	+	0.400463i	−0.828224	−	0.560397i	$-0.810649\pi$
$647$	−5.86897e6	+	4.26406e6i	−0.551190	+	0.400463i	0.277034	+	0.960860i	$0.410649\pi$
$648$		0			0
$649$	−7.85384e6	−	4.18545e6i	−0.731932	−	0.390060i
$650$	−2.27903e6			−0.211576
$651$		0			0
$652$	−357209.	−	1.09938e6i	−0.0329081	−	0.101281i
$653$	6.04957e6	−	1.86186e7i	0.555189	−	1.70870i	−0.140253	−	0.990116i	$-0.544792\pi$
$653$	6.04957e6	−	1.86186e7i	0.555189	−	1.70870i	0.695443	−	0.718582i	$-0.255208\pi$
$654$		0			0
$655$	9.86034e6	+	7.16396e6i	0.898025	+	0.652454i
$656$	−1.27606e6	+	3.92732e6i	−0.115774	+	0.356317i
$657$		0			0
$658$	7.18943e6	−	5.22343e6i	0.647336	−	0.470317i
$659$	−4.24342e6			−0.380630			−0.190315	−	0.981723i	$-0.560951\pi$
$659$	−4.24342e6			−0.380630			−0.190315	+	0.981723i	$0.560951\pi$
$660$		0			0
$661$	1.86117e7			1.65685			0.828424	−	0.560101i	$-0.189238\pi$
$661$	1.86117e7			1.65685			0.828424	+	0.560101i	$0.189238\pi$
$662$	−2.65288e6	+	1.92743e6i	−0.235273	+	0.170936i
$663$		0			0
$664$	1.01019e7	−	3.10906e7i	0.889169	−	2.73658i
$665$	−2.36727e6	−	1.71992e6i	−0.207584	−	0.150819i
$666$		0			0
$667$	2.85287e6	−	8.78025e6i	0.248295	−	0.764174i
$668$	8.21242e6	+	2.52752e7i	0.712082	+	2.19156i
$669$		0			0
$670$	−8.89943e6			−0.765906
$671$	−7.22272e6	+	6.96177e6i	−0.619291	+	0.596916i
$672$		0			0
$673$	−1.23020e7	+	8.93791e6i	−1.04698	+	0.760674i	−0.971635	−	0.236484i	$-0.924005\pi$
$673$	−1.23020e7	+	8.93791e6i	−1.04698	+	0.760674i	−0.0753420	+	0.997158i	$0.524005\pi$
$674$	−1.19632e7	−	3.68190e7i	−1.01437	−	3.12192i
$675$		0			0
$676$	2.29890e6	+	1.67025e6i	0.193488	+	0.140577i
$677$	−6.61522e6	−	4.80624e6i	−0.554719	−	0.403027i	0.274803	−	0.961500i	$-0.411387\pi$
$677$	−6.61522e6	−	4.80624e6i	−0.554719	−	0.403027i	−0.829522	+	0.558474i	$0.811387\pi$
$678$		0			0
$679$	1.20377e6	+	3.70483e6i	0.100200	+	0.308385i
$680$	2.64921e7	−	1.92477e7i	2.19707	−	1.59627i
$681$		0			0
$682$	−2.47393e7	−	1.31840e7i	−2.03670	−	1.08539i
$683$	−7.72453e6			−0.633608			−0.316804	−	0.948491i	$-0.602610\pi$
$683$	−7.72453e6			−0.633608			−0.316804	+	0.948491i	$0.602610\pi$
$684$		0			0
$685$	886774.	+	2.72921e6i	0.0722082	+	0.222234i
$686$	2.96736e6	−	9.13259e6i	0.240746	−	0.740941i
$687$		0			0
$688$	−3.63651e6	−	2.64208e6i	−0.292896	−	0.212801i
$689$	−1.25868e6	+	3.87383e6i	−0.101011	+	0.310880i
$690$		0			0
$691$	−1.62835e7	+	1.18307e7i	−1.29734	+	0.942573i	−0.999926	−	0.0121760i	$-0.996124\pi$
$691$	−1.62835e7	+	1.18307e7i	−1.29734	+	0.942573i	−0.297414	+	0.954749i	$0.596124\pi$
$692$	−2.45653e7			−1.95010
$693$		0			0
$694$	−3.81916e7			−3.01002
$695$	−5.64037e6	+	4.09797e6i	−0.442940	+	0.321815i
$696$		0			0
$697$	−3.61208e6	+	1.11168e7i	−0.281627	+	0.866760i
$698$	−1.48694e7	−	1.08032e7i	−1.15519	−	0.839295i
$699$		0			0
$700$	237734.	−	731671.i	0.0183378	−	0.0564379i
$701$	2.29781e6	+	7.07193e6i	0.176611	+	0.543554i	0.999703	−	0.0243541i	$-0.00775291\pi$
$701$	2.29781e6	+	7.07193e6i	0.176611	+	0.543554i	−0.823092	+	0.567908i	$0.807753\pi$
$702$		0			0
$703$	−2.11721e6			−0.161575
$704$	−7.34377e6	−	1.50930e7i	−0.558454	−	1.14774i
$705$		0			0
$706$	−3.28596e7	+	2.38739e7i	−2.48113	+	1.80265i
$707$	707003.	+	2.17593e6i	0.0531952	+	0.163718i
$708$		0			0
$709$	5.35574e6	+	3.89117e6i	0.400132	+	0.290713i	0.769595	−	0.638533i	$-0.220458\pi$
$709$	5.35574e6	+	3.89117e6i	0.400132	+	0.290713i	−0.369463	+	0.929246i	$0.620458\pi$
$710$	2.99345e7	+	2.17487e7i	2.22857	+	1.61915i
$711$		0			0
$712$	−561791.	−	1.72901e6i	−0.0415312	−	0.127820i
$713$	7.13500e6	−	5.18388e6i	0.525618	−	0.381884i
$714$		0			0
$715$	2.37438e6	−	1.33920e7i	0.173694	−	0.979673i
$716$	−2.20087e7			−1.60440
$717$		0			0
$718$	4.55123e6	+	1.40072e7i	0.329471	+	1.01401i
$719$	−5.35083e6	+	1.64682e7i	−0.386010	+	1.18802i	0.549735	+	0.835339i	$0.314729\pi$
$719$	−5.35083e6	+	1.64682e7i	−0.386010	+	1.18802i	−0.935745	+	0.352678i	$0.885271\pi$
$720$		0			0
$721$	−1.30284e6	−	946569.i	−0.0933369	−	0.0678132i
$722$	−347491.	+	1.06947e6i	−0.0248085	+	0.0763528i
$723$		0			0
$724$	3.06851e7	−	2.22941e7i	2.17561	−	1.58068i
$725$	3.16061e6			0.223319
$726$		0			0
$727$	1.02515e7			0.719366			0.359683	−	0.933075i	$-0.382885\pi$
$727$	1.02515e7			0.719366			0.359683	+	0.933075i	$0.382885\pi$
$728$	3.86886e6	−	2.81089e6i	0.270554	−	0.196569i
$729$		0			0
$730$	−7.80627e6	+	2.40252e7i	−0.542171	+	1.66863i
$731$	−1.02936e7	−	7.47876e6i	−0.712484	−	0.517650i
$732$		0			0
$733$	−885952.	+	2.72668e6i	−0.0609046	+	0.187445i	−0.976880	−	0.213790i	$-0.931419\pi$
$733$	−885952.	+	2.72668e6i	−0.0609046	+	0.187445i	0.915975	+	0.401235i	$0.131419\pi$
$734$	4.56887e6	+	1.40615e7i	0.313018	+	0.963369i
$735$		0			0
$736$	2.42394e6			0.164940
$737$	1.08898e6	−	6.14210e6i	0.0738503	−	0.416532i
$738$		0			0
$739$	−304632.	+	221328.i	−0.0205194	+	0.0149082i	−0.597998	−	0.801498i	$-0.704037\pi$
$739$	−304632.	+	221328.i	−0.0205194	+	0.0149082i	0.577478	+	0.816406i	$0.304037\pi$
$740$	−1.46456e6	−	4.50745e6i	−0.0983167	−	0.302588i
$741$		0			0
$742$	−1.70000e6	−	1.23512e6i	−0.113355	−	0.0823569i
$743$	1.37323e7	+	9.97708e6i	0.912579	+	0.663028i	0.941666	−	0.336549i	$-0.109260\pi$
$743$	1.37323e7	+	9.97708e6i	0.912579	+	0.663028i	−0.0290867	+	0.999577i	$0.509260\pi$
$744$		0			0
$745$	−3.79888e6	−	1.16918e7i	−0.250764	−	0.771772i
$746$	1.11235e7	−	8.08169e6i	0.731803	−	0.531686i
$747$		0			0
$748$	2.12879e7	+	4.37511e7i	1.39116	+	2.85914i
$749$	3.76422e6			0.245172
$750$		0			0
$751$	−8.33469e6	−	2.56515e7i	−0.539250	−	1.65964i	−0.734283	−	0.678843i	$-0.762482\pi$
$751$	−8.33469e6	−	2.56515e7i	−0.539250	−	1.65964i	0.195034	−	0.980797i	$-0.437518\pi$
$752$	6.60834e6	−	2.03384e7i	0.426136	−	1.31151i
$753$		0			0
$754$	3.36930e7	+	2.44794e7i	2.15830	+	1.56810i
$755$	1.85051e6	−	5.69528e6i	0.118147	−	0.363620i
$756$		0			0
$757$	9.92063e6	−	7.20776e6i	0.629216	−	0.457152i	−0.226913	−	0.973915i	$-0.572863\pi$
$757$	9.92063e6	−	7.20776e6i	0.629216	−	0.457152i	0.856128	+	0.516763i	$0.172863\pi$
$758$	−2.75775e7			−1.74334
$759$		0			0
$760$	−2.63460e7			−1.65455
$761$	−1.38569e7	+	1.00676e7i	−0.867371	+	0.630182i	−0.929880	−	0.367862i	$-0.880090\pi$
$761$	−1.38569e7	+	1.00676e7i	−0.867371	+	0.630182i	0.0625089	+	0.998044i	$0.480090\pi$
$762$		0			0
$763$	−1.26922e6	+	3.90625e6i	−0.0789269	+	0.242912i
$764$	2.39551e7	+	1.74044e7i	1.48479	+	1.07876i
$765$		0			0
$766$	8.46482e6	−	2.60520e7i	0.521250	−	1.60424i
$767$	3.90297e6	+	1.20121e7i	0.239556	+	0.737277i
$768$		0			0
$769$	−1.67008e7			−1.01841			−0.509203	−	0.860647i	$-0.670060\pi$
$769$	−1.67008e7			−1.01841			−0.509203	+	0.860647i	$0.670060\pi$
$770$	6.19214e6	+	3.29990e6i	0.376369	+	0.200574i
$771$		0			0
$772$	6.61615e6	−	4.80691e6i	0.399542	−	0.290284i
$773$	4.41732e6	+	1.35951e7i	0.265895	+	0.818341i	0.991486	+	0.130215i	$0.0415666\pi$
$773$	4.41732e6	+	1.35951e7i	0.265895	+	0.818341i	−0.725591	+	0.688127i	$0.758433\pi$
$774$		0			0
$775$	2.44267e6	+	1.77470e6i	0.146087	+	0.106138i
$776$	2.83755e7	+	2.06160e7i	1.69157	+	1.22899i
$777$		0			0
$778$	1.40170e7	+	4.31398e7i	0.830244	+	2.55523i
$779$	7.60829e6	−	5.52775e6i	0.449204	−	0.326366i
$780$		0			0
$781$	−1.86732e7	+	1.79985e7i	−1.09545	+	1.05587i
$782$	−2.33934e7			−1.36797
$783$		0			0
$784$	−3.46849e6	−	1.06749e7i	−0.201535	−	0.620261i
$785$	1.47580e6	−	4.54205e6i	0.0854779	−	0.263074i
$786$		0			0
$787$	−2.27948e7	−	1.65614e7i	−1.31190	−	0.953148i	−0.999995	−	0.00303342i	$-0.999034\pi$
$787$	−2.27948e7	−	1.65614e7i	−1.31190	−	0.953148i	−0.311901	−	0.950115i	$-0.600966\pi$
$788$	3.31042e6	−	1.01884e7i	0.189919	−	0.584510i
$789$		0			0
$790$	−8.08101e6	+	5.87120e6i	−0.460678	+	0.334702i
$791$	−1.02833e6			−0.0584374
$792$		0			0
$793$	1.42371e7			0.803965
$794$	2.81587e7	−	2.04585e7i	1.58512	−	1.15165i
$795$		0			0
$796$	8.10630e6	−	2.49486e7i	0.453461	−	1.39561i
$797$	6.56832e6	+	4.77217e6i	0.366276	+	0.266115i	0.755665	−	0.654958i	$-0.227314\pi$
$797$	6.56832e6	+	4.77217e6i	0.366276	+	0.266115i	−0.389389	+	0.921073i	$0.627314\pi$
$798$		0			0
$799$	1.87058e7	−	5.75706e7i	1.03660	−	3.19032i
$800$	256434.	+	789222.i	0.0141661	+	0.0435988i
$801$		0			0
$802$	−3.35350e7			−1.84103
$803$	−1.56262e7	−	8.32749e6i	−0.855195	−	0.455749i
$804$		0			0
$805$	−1.78586e6	+	1.29750e6i	−0.0971309	+	0.0705698i
$806$	1.22942e7	+	3.78377e7i	0.666596	+	2.05157i
$807$		0			0
$808$	1.66656e7	+	1.21082e7i	0.898031	+	0.652458i
$809$	1.43065e7	+	1.03943e7i	0.768534	+	0.558372i	0.901516	−	0.432746i	$-0.142455\pi$
$809$	1.43065e7	+	1.03943e7i	0.768534	+	0.558372i	−0.132982	+	0.991118i	$0.542455\pi$
$810$		0			0
$811$	3.19470e6	+	9.83229e6i	0.170561	+	0.524931i	0.999403	−	0.0345508i	$-0.0110001\pi$
$811$	3.19470e6	+	9.83229e6i	0.170561	+	0.524931i	−0.828842	+	0.559482i	$0.811000\pi$
$812$	−1.13737e7	+	8.26345e6i	−0.605355	+	0.439816i
$813$		0			0
$814$	5.02813e6	−	701830.i	0.265978	−	0.0371254i
$815$	−1.13551e6			−0.0598821
$816$		0			0
$817$	3.16336e6	+	9.73582e6i	0.165803	+	0.510290i
$818$	−9.87646e6	+	3.03966e7i	−0.516081	+	1.58833i
$819$		0			0
$820$	1.70313e7	+	1.23740e7i	0.884532	+	0.642650i
$821$	4.38222e6	−	1.34871e7i	0.226901	−	0.698330i	−0.771192	−	0.636603i	$-0.780339\pi$
$821$	4.38222e6	−	1.34871e7i	0.226901	−	0.698330i	0.998093	−	0.0617272i	$-0.0196609\pi$
$822$		0			0
$823$	−6.66919e6	+	4.84545e6i	−0.343221	+	0.249364i	−0.746019	−	0.665924i	$-0.768037\pi$
$823$	−6.66919e6	+	4.84545e6i	−0.343221	+	0.249364i	0.402799	+	0.915289i	$0.368037\pi$
$824$	−1.44996e7			−0.743942
$825$		0			0
$826$	−6.51583e6			−0.332292
$827$	−375203.	+	272601.i	−0.0190767	+	0.0138600i	−0.597283	−	0.802031i	$-0.703753\pi$
$827$	−375203.	+	272601.i	−0.0190767	+	0.0138600i	0.578206	+	0.815891i	$0.303753\pi$
$828$		0			0
$829$	1.05752e7	−	3.25472e7i	0.534445	−	1.64485i	−0.210401	−	0.977615i	$-0.567477\pi$
$829$	1.05752e7	−	3.25472e7i	0.534445	−	1.64485i	0.744846	−	0.667237i	$-0.232523\pi$
$830$	−5.50714e7	−	4.00117e7i	−2.77480	−	2.01601i
$831$		0			0
$832$	−7.36117e6	+	2.26553e7i	−0.368670	+	1.13465i
$833$	−9.81805e6	−	3.02168e7i	−0.490244	−	1.50882i
$834$		0			0
$835$	2.61060e7			1.29576
$836$	6.83389e6	−	3.85446e7i	0.338183	−	1.90743i
$837$		0			0
$838$	3.96654e7	−	2.88186e7i	1.95120	−	1.41763i
$839$	2.19708e6	+	6.76193e6i	0.107756	+	0.331639i	0.990367	−	0.138464i	$-0.0442166\pi$
$839$	2.19708e6	+	6.76193e6i	0.107756	+	0.331639i	−0.882611	+	0.470103i	$0.844217\pi$
$840$		0			0
$841$	−3.01325e7	−	2.18926e7i	−1.46908	−	1.06735i
$842$	2.48981e7	+	1.80895e7i	1.21028	+	0.879320i
$843$		0			0
$844$	−2.51822e6	−	7.75029e6i	−0.121685	−	0.374508i
$845$	2.25825e6	−	1.64072e6i	0.108800	−	0.0790481i
$846$		0			0
$847$	−3.03519e6	+	3.86982e6i	−0.145371	+	0.185346i
$848$	−5.05667e6			−0.241476
$849$		0			0
$850$	−2.47483e6	−	7.61676e6i	−0.117489	−	0.361595i
$851$	−493565.	+	1.51904e6i	−0.0233626	+	0.0719026i
$852$		0			0
$853$	1.00383e7	+	7.29328e6i	0.472378	+	0.343203i	0.798367	−	0.602171i	$-0.205697\pi$
$853$	1.00383e7	+	7.29328e6i	0.472378	+	0.343203i	−0.325989	+	0.945373i	$0.605697\pi$
$854$	−2.26965e6	+	6.98527e6i	−0.106491	+	0.327747i
$855$		0			0
$856$	2.74193e7	−	1.99213e7i	1.27900	−	0.929251i
$857$	9.60549e6			0.446753			0.223376	−	0.974732i	$-0.428292\pi$
$857$	9.60549e6			0.446753			0.223376	+	0.974732i	$0.428292\pi$
$858$		0			0
$859$	1.35157e7			0.624964			0.312482	−	0.949924i	$-0.398840\pi$
$859$	1.35157e7			0.624964			0.312482	+	0.949924i	$0.398840\pi$
$860$	−1.85389e7	+	1.34693e7i	−0.854749	+	0.621012i
$861$		0			0
$862$	−4.87161e6	+	1.49933e7i	−0.223308	+	0.687272i
$863$	2.75417e7	+	2.00102e7i	1.25882	+	0.914588i	0.998699	−	0.0509875i	$-0.0162369\pi$
$863$	2.75417e7	+	2.00102e7i	1.25882	+	0.914588i	0.260123	+	0.965575i	$0.416237\pi$
$864$		0			0
$865$	−7.45685e6	+	2.29498e7i	−0.338856	+	1.04289i
$866$	669356.	+	2.06007e6i	0.0303293	+	0.0933440i
$867$		0			0
$868$	−1.34301e7			−0.605033
$869$	−3.06327e6	−	6.29568e6i	−0.137606	−	0.282809i
$870$		0			0
$871$	−7.16215e6	+	5.20361e6i	−0.319888	+	0.232412i
$872$	1.14277e7	+	3.51710e7i	0.508943	+	1.56636i
$873$		0			0
$874$	1.52267e7	+	1.10628e7i	0.674258	+	0.489877i
$875$	3.98270e6	+	2.89360e6i	0.175856	+	0.127767i
$876$		0			0
$877$	−1.19668e6	−	3.68301e6i	−0.0525387	−	0.161698i	0.921344	−	0.388747i	$-0.127092\pi$
$877$	−1.19668e6	−	3.68301e6i	−0.0525387	−	0.161698i	−0.973883	+	0.227050i	$0.927092\pi$
$878$	930065.	−	675732.i	0.0407171	−	0.0295827i
$879$		0			0
$880$	1.67227e7	−	2.33417e6i	0.727948	−	0.101607i
$881$	−2.91447e7			−1.26509			−0.632543	−	0.774525i	$-0.717989\pi$
$881$	−2.91447e7			−1.26509			−0.632543	+	0.774525i	$0.717989\pi$
$882$		0			0
$883$	1.18195e7	+	3.63765e7i	0.510147	+	1.57007i	0.791941	+	0.610597i	$0.209070\pi$
$883$	1.18195e7	+	3.63765e7i	0.510147	+	1.57007i	−0.281794	+	0.959475i	$0.590930\pi$
$884$	2.13383e7	−	6.56726e7i	0.918395	−	2.82653i
$885$		0			0
$886$	7.24196e6	+	5.26159e6i	0.309936	+	0.225182i
$887$	7.81116e6	−	2.40403e7i	0.333354	−	1.02596i	−0.634172	−	0.773192i	$-0.718659\pi$
$887$	7.81116e6	−	2.40403e7i	0.333354	−	1.02596i	0.967527	−	0.252768i	$-0.0813409\pi$
$888$		0			0
$889$	5.79674e6	−	4.21158e6i	0.245997	−	0.178727i
$890$	−3.78564e6			−0.160200
$891$		0			0
$892$	−4.62092e7			−1.94454
$893$	−3.94010e7	+	2.86265e7i	−1.65340	+	1.20127i
$894$		0			0
$895$	−6.68080e6	+	2.05614e7i	−0.278786	+	0.858015i
$896$	−8.36462e6	−	6.07725e6i	−0.348078	−	0.252893i
$897$		0			0
$898$	−2.02410e7	+	6.22955e7i	−0.837610	+	2.57790i
$899$	−1.70499e7	−	5.24743e7i	−0.703596	−	2.16545i
$900$		0			0
$901$	−1.43136e7			−0.587404
$902$	−1.62365e7	+	1.56498e7i	−0.664469	+	0.640463i
$903$		0			0
$904$	−7.49054e6	+	5.44219e6i	−0.304854	+	0.221489i
$905$	−1.15134e7	−	3.54346e7i	−0.467286	−	1.43816i
$906$		0			0
$907$	3.43290e7	+	2.49415e7i	1.38562	+	1.00671i	0.996330	+	0.0855944i	$0.0272789\pi$
$907$	3.43290e7	+	2.49415e7i	1.38562	+	1.00671i	0.389288	+	0.921116i	$0.372721\pi$
$908$	−5.31593e6	−	3.86225e6i	−0.213976	−	0.155462i
$909$		0			0
$910$	−3.07719e6	−	9.47061e6i	−0.123183	−	0.379118i
$911$	−3.70665e6	+	2.69304e6i	−0.147974	+	0.107509i	−0.659309	−	0.751872i	$-0.729151\pi$
$911$	−3.70665e6	+	2.69304e6i	−0.147974	+	0.107509i	0.511335	+	0.859381i	$0.329151\pi$
$912$		0			0
$913$	3.43537e7	−	3.31125e7i	1.36394	−	1.31466i
$914$	8.01344e7			3.17288
$915$		0			0
$916$	−9.79226e6	−	3.01375e7i	−0.385606	−	1.18677i
$917$	−1.93284e6	+	5.94868e6i	−0.0759056	+	0.233613i
$918$		0			0
$919$	−1.49737e7	−	1.08790e7i	−0.584843	−	0.424913i	0.255624	−	0.966776i	$-0.417719\pi$
$919$	−1.49737e7	−	1.08790e7i	−0.584843	−	0.424913i	−0.840467	+	0.541863i	$0.817719\pi$
$920$	−6.14180e6	+	1.89025e7i	−0.239236	+	0.736292i
$921$		0			0
$922$	1.28121e6	−	930857.i	0.0496357	−	0.0360625i
$923$	3.68076e7			1.42211
$924$		0			0
$925$	−546806.			−0.0210126
$926$	−1.89346e6	+	1.37568e6i	−0.0725651	+	0.0527216i
$927$		0			0
$928$	4.68607e6	−	1.44222e7i	0.178623	−	0.549746i
$929$	3.39555e7	+	2.46701e7i	1.29084	+	0.937847i	0.999822	−	0.0188716i	$-0.00600739\pi$
$929$	3.39555e7	+	2.46701e7i	1.29084	+	0.937847i	0.291014	+	0.956719i	$0.406007\pi$
$930$		0			0
$931$	−7.89914e6	+	2.43111e7i	−0.298680	+	0.919242i
$932$	−4.10620e6	−	1.26376e7i	−0.154846	−	0.476567i
$933$		0			0
$934$	3.13993e7			1.17775
$935$	4.73360e7	−	6.60719e6i	1.77077	−	0.247166i
$936$		0			0
$937$	−6.05508e6	+	4.39927e6i	−0.225305	+	0.163694i	−0.694711	−	0.719289i	$-0.744468\pi$
$937$	−6.05508e6	+	4.39927e6i	−0.225305	+	0.163694i	0.469406	+	0.882982i	$0.344468\pi$
$938$	−1.41132e6	−	4.34359e6i	−0.0523742	−	0.161191i
$939$		0			0
$940$	−8.81999e7	−	6.40810e7i	−3.25573	−	2.36543i
$941$	−3.34949e7	−	2.43355e7i	−1.23312	−	0.895912i	−0.235998	−	0.971754i	$-0.575836\pi$
$941$	−3.34949e7	−	2.43355e7i	−1.23312	−	0.895912i	−0.997120	+	0.0758412i	$0.975836\pi$
$942$		0			0
$943$	−2.19236e6	−	6.74738e6i	−0.0802845	−	0.247090i
$944$	−1.26853e7	+	9.21641e6i	−0.463309	+	0.336614i
$945$		0			0
$946$	−1.07399e7	−	2.20729e7i	−0.390188	−	0.801920i
$947$	4.38933e7			1.59046			0.795231	−	0.606307i	$-0.207350\pi$
$947$	4.38933e7			1.59046			0.795231	+	0.606307i	$0.207350\pi$
$948$		0			0
$949$	7.76545e6	+	2.38996e7i	0.279899	+	0.861440i
$950$	−1.99114e6	+	6.12809e6i	−0.0715800	+	0.220301i
$951$		0			0
$952$	1.35956e7	+	9.87776e6i	0.486189	+	0.353237i
$953$	−872998.	+	2.68681e6i	−0.0311373	+	0.0958308i	−0.965417	−	0.260709i	$-0.916044\pi$
$953$	−872998.	+	2.68681e6i	−0.0311373	+	0.0958308i	0.934280	+	0.356540i	$0.116044\pi$
$954$		0			0
$955$	2.35315e7	−	1.70966e7i	0.834912	−	0.606599i
$956$	−2.92314e7			−1.03444
$957$		0			0
$958$	−1.43340e7			−0.504609
$959$	−1.19143e6	+	865625.i	−0.0418333	+	0.0303937i
$960$		0			0
$961$	7.44076e6	−	2.29003e7i	0.259901	−	0.799894i
$962$	−5.82910e6	−	4.23509e6i	−0.203079	−	0.147545i
$963$		0			0
$964$	−8.83975e6	+	2.72059e7i	−0.306371	+	0.942912i
$965$	−2.48245e6	−	7.64021e6i	−0.0858150	−	0.264111i
$966$		0			0
$967$	−1.10642e7			−0.380499			−0.190249	−	0.981736i	$-0.560930\pi$
$967$	−1.10642e7			−0.380499			−0.190249	+	0.981736i	$0.560930\pi$
$968$	−1.62875e6	+	4.42516e7i	−0.0558682	+	1.51789i
$969$		0			0
$970$	5.90867e7	−	4.29290e7i	2.01632	−	1.46494i
$971$	4.55825e6	+	1.40289e7i	0.155149	+	0.477501i	0.998176	−	0.0603711i	$-0.0192284\pi$
$971$	4.55825e6	+	1.40289e7i	0.155149	+	0.477501i	−0.843027	+	0.537872i	$0.819228\pi$
$972$		0			0
$973$	−2.89459e6	−	2.10305e6i	−0.0980179	−	0.0712142i
$974$	−3.91456e7	−	2.84409e7i	−1.32216	−	0.960608i
$975$		0			0
$976$	5.46176e6	+	1.68096e7i	0.183530	+	0.564848i
$977$	−1.50923e7	+	1.09652e7i	−0.505848	+	0.367520i	−0.811246	−	0.584705i	$-0.801210\pi$
$977$	−1.50923e7	+	1.09652e7i	−0.505848	+	0.367520i	0.305398	+	0.952225i	$0.401210\pi$
$978$		0			0
$979$	463231.	−	2.61272e6i	0.0154469	−	0.0871238i
$980$	−5.72214e7			−1.90324
$981$		0			0
$982$	−1.32399e7	−	4.07481e7i	−0.438132	−	1.34843i
$983$	−4.42126e6	+	1.36072e7i	−0.145936	+	0.449144i	−0.997130	−	0.0757064i	$-0.975879\pi$
$983$	−4.42126e6	+	1.36072e7i	−0.145936	+	0.449144i	0.851194	+	0.524851i	$0.175879\pi$
$984$		0			0
$985$	−8.51354e6	−	6.18545e6i	−0.279589	−	0.203133i
$986$	−4.52251e7	+	1.39188e8i	−1.48145	+	4.55943i
$987$		0			0
$988$	−4.49459e7	+	3.26551e7i	−1.46487	+	1.06429i
$989$	7.72263e6			0.251058
$990$		0			0
$991$	3.51472e7			1.13686			0.568429	−	0.822732i	$-0.307551\pi$
$991$	3.51472e7			1.13686			0.568429	+	0.822732i	$0.307551\pi$
$992$	1.17198e7	−	8.51492e6i	0.378129	−	0.274727i
$993$		0			0
$994$	−5.86782e6	+	1.80593e7i	−0.188370	+	0.579742i
$995$	−2.08473e7	−	1.51464e7i	−0.667562	−	0.485012i
$996$		0			0
$997$	4.13366e6	−	1.27221e7i	0.131703	−	0.405341i	−0.863359	−	0.504589i	$-0.831644\pi$
$997$	4.13366e6	−	1.27221e7i	0.131703	−	0.405341i	0.995063	+	0.0992486i	$0.0316439\pi$
$998$	2.31169e7	+	7.11466e7i	0.734689	+	2.26114i
$999$		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	99.6.f.b.91.5		20
3.2	odd	2		33.6.e.b.25.1	yes	20
11.2	odd	10		1089.6.a.bi.1.10		10
11.4	even	5	inner	99.6.f.b.37.5		20
11.9	even	5		1089.6.a.bk.1.1		10
33.2	even	10		363.6.a.t.1.1		10
33.20	odd	10		363.6.a.r.1.10		10
33.26	odd	10		33.6.e.b.4.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.4.1	✓	20	33.26	odd	10
33.6.e.b.25.1	yes	20	3.2	odd	2
99.6.f.b.37.5		20	11.4	even	5	inner
99.6.f.b.91.5		20	1.1	even	1	trivial
363.6.a.r.1.10		10	33.20	odd	10
363.6.a.t.1.1		10	33.2	even	10
1089.6.a.bi.1.10		10	11.2	odd	10
1089.6.a.bk.1.1		10	11.9	even	5

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

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Newspace parameters

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Embedding invariants

$q$ -expansion

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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	99.6.f.b.91.5

Level	$99$
Weight	$6$
Character	99.91
Analytic conductor	$15.878$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$