LMFDB - Embedded newform 252.4.e.a.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.614971 - 2.76076i) q^{2} +(-7.24362 - 3.39558i) q^{4} +2.97985i q^{5} +7.00000i q^{7} +(-13.8290 + 17.9097i) q^{8} +O(q^{10})$	\(q+(0.614971 - 2.76076i) q^{2} +(-7.24362 - 3.39558i) q^{4} +2.97985i q^{5} +7.00000i q^{7} +(-13.8290 + 17.9097i) q^{8} +(8.22665 + 1.83252i) q^{10} -14.5861 q^{11} +27.9716 q^{13} +(19.3253 + 4.30480i) q^{14} +(40.9401 + 49.1926i) q^{16} +47.0690i q^{17} +148.649i q^{19} +(10.1183 - 21.5849i) q^{20} +(-8.97001 + 40.2687i) q^{22} +85.1221 q^{23} +116.121 q^{25} +(17.2017 - 77.2228i) q^{26} +(23.7690 - 50.7053i) q^{28} -197.212i q^{29} +213.574i q^{31} +(160.986 - 82.7739i) q^{32} +(129.946 + 28.9461i) q^{34} -20.8589 q^{35} -3.00048 q^{37} +(410.385 + 91.4149i) q^{38} +(-53.3683 - 41.2083i) q^{40} -4.26768i q^{41} +261.825i q^{43} +(105.656 + 49.5281i) q^{44} +(52.3476 - 235.002i) q^{46} -96.0780 q^{47} -49.0000 q^{49} +(71.4108 - 320.581i) q^{50} +(-202.615 - 94.9796i) q^{52} +131.677i q^{53} -43.4643i q^{55} +(-125.368 - 96.8030i) q^{56} +(-544.455 - 121.280i) q^{58} +294.327 q^{59} +134.782 q^{61} +(589.628 + 131.342i) q^{62} +(-129.517 - 495.348i) q^{64} +83.3510i q^{65} +148.648i q^{67} +(159.827 - 340.950i) q^{68} +(-12.8276 + 57.5866i) q^{70} -796.550 q^{71} -163.335 q^{73} +(-1.84521 + 8.28361i) q^{74} +(504.750 - 1076.76i) q^{76} -102.102i q^{77} +1347.64i q^{79} +(-146.586 + 121.995i) q^{80} +(-11.7821 - 2.62450i) q^{82} -534.740 q^{83} -140.259 q^{85} +(722.836 + 161.015i) q^{86} +(201.711 - 261.233i) q^{88} -398.405i q^{89} +195.801i q^{91} +(-616.592 - 289.039i) q^{92} +(-59.0852 + 265.249i) q^{94} -442.952 q^{95} +1711.36 q^{97} +(-30.1336 + 135.277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4}+O(q^{10}) $ 36 * q - 24 * q^4	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.614971	−	2.76076i	0.217425	−	0.976077i
$2$	0.614971	−	2.76076i	0.217425	−	0.976077i
$3$		0			0
$3$		0			0
$4$	−7.24362	−	3.39558i	−0.905453	−	0.424447i
$5$			2.97985i			0.266526i	0.991081	+	0.133263i	$0.0425454\pi$
$5$			2.97985i			0.266526i	−0.991081	+	0.133263i	$0.957455\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	−13.8290	+	17.9097i	−0.611161	+	0.791506i
$9$		0			0
$10$	8.22665	+	1.83252i	0.260150	+	0.0579494i
$11$	−14.5861			−0.399806			−0.199903	−	0.979816i	$-0.564063\pi$
$11$	−14.5861			−0.399806			−0.199903	+	0.979816i	$0.564063\pi$
$12$		0			0
$13$	27.9716			0.596763			0.298381	−	0.954447i	$-0.403553\pi$
$13$	27.9716			0.596763			0.298381	+	0.954447i	$0.403553\pi$
$14$	19.3253	+	4.30480i	0.368922	+	0.0821790i
$15$		0			0
$16$	40.9401	+	49.1926i	0.639689	+	0.768634i
$17$			47.0690i			0.671525i	0.941947	+	0.335762i	$0.108994\pi$
$17$			47.0690i			0.671525i	−0.941947	+	0.335762i	$0.891006\pi$
$18$		0			0
$19$			148.649i			1.79487i	0.441151	+	0.897433i	$0.354570\pi$
$19$			148.649i			1.79487i	−0.441151	+	0.897433i	$0.645430\pi$
$20$	10.1183	−	21.5849i	0.113126	−	0.241326i
$21$		0			0
$22$	−8.97001	+	40.2687i	−0.0869279	+	0.390241i
$23$	85.1221			0.771704			0.385852	−	0.922561i	$-0.373908\pi$
$23$	85.1221			0.771704			0.385852	+	0.922561i	$0.373908\pi$
$24$		0			0
$25$	116.121			0.928964
$26$	17.2017	−	77.2228i	0.129751	−	0.582486i
$27$		0			0
$28$	23.7690	−	50.7053i	0.160426	−	0.342229i
$29$		−	197.212i		−	1.26280i	−0.775455	−	0.631402i	$-0.782480\pi$
$29$		−	197.212i		−	1.26280i	0.775455	−	0.631402i	$-0.217520\pi$
$30$		0			0
$31$			213.574i			1.23739i	0.785631	+	0.618695i	$0.212338\pi$
$31$			213.574i			1.23739i	−0.785631	+	0.618695i	$0.787662\pi$
$32$	160.986	−	82.7739i	0.889330	−	0.457265i
$33$		0			0
$34$	129.946	+	28.9461i	0.655460	+	0.146006i
$35$	−20.8589			−0.100737
$36$		0			0
$37$	−3.00048			−0.0133318			−0.00666589	−	0.999978i	$-0.502122\pi$
$37$	−3.00048			−0.0133318			−0.00666589	+	0.999978i	$0.502122\pi$
$38$	410.385	+	91.4149i	1.75193	+	0.390249i
$39$		0			0
$40$	−53.3683	−	41.2083i	−0.210957	−	0.162890i
$41$		−	4.26768i		−	0.0162561i	−0.999967	−	0.00812805i	$-0.997413\pi$
$41$		−	4.26768i		−	0.0162561i	0.999967	−	0.00812805i	$-0.00258727\pi$
$42$		0			0
$43$			261.825i			0.928556i	0.885689	+	0.464278i	$0.153686\pi$
$43$			261.825i			0.928556i	−0.885689	+	0.464278i	$0.846314\pi$
$44$	105.656	+	49.5281i	0.362005	+	0.169697i
$45$		0			0
$46$	52.3476	−	235.002i	0.167788	−	0.753242i
$47$	−96.0780			−0.298179			−0.149090	−	0.988824i	$-0.547634\pi$
$47$	−96.0780			−0.298179			−0.149090	+	0.988824i	$0.547634\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	71.4108	−	320.581i	0.201980	−	0.906740i
$51$		0			0
$52$	−202.615	−	94.9796i	−0.540340	−	0.253294i
$53$			131.677i			0.341268i	0.985334	+	0.170634i	$0.0545816\pi$
$53$			131.677i			0.341268i	−0.985334	+	0.170634i	$0.945418\pi$
$54$		0			0
$55$		−	43.4643i		−	0.106559i
$56$	−125.368	−	96.8030i	−0.299161	−	0.230997i
$57$		0			0
$58$	−544.455	−	121.280i	−1.23259	−	0.274565i
$59$	294.327			0.649460			0.324730	−	0.945807i	$-0.394727\pi$
$59$	294.327			0.649460			0.324730	+	0.945807i	$0.394727\pi$
$60$		0			0
$61$	134.782			0.282904			0.141452	−	0.989945i	$-0.454823\pi$
$61$	134.782			0.282904			0.141452	+	0.989945i	$0.454823\pi$
$62$	589.628	+	131.342i	1.20779	+	0.269040i
$63$		0			0
$64$	−129.517	−	495.348i	−0.252963	−	0.967476i
$65$			83.3510i			0.159053i
$66$		0			0
$67$			148.648i			0.271049i	0.990774	+	0.135525i	$0.0432720\pi$
$67$			148.648i			0.271049i	−0.990774	+	0.135525i	$0.956728\pi$
$68$	159.827	−	340.950i	0.285027	−	0.608034i
$69$		0			0
$70$	−12.8276	+	57.5866i	−0.0219028	+	0.0983273i
$71$	−796.550			−1.33145			−0.665726	−	0.746197i	$-0.731878\pi$
$71$	−796.550			−1.33145			−0.665726	+	0.746197i	$0.731878\pi$
$72$		0			0
$73$	−163.335			−0.261875			−0.130938	−	0.991391i	$-0.541799\pi$
$73$	−163.335			−0.261875			−0.130938	+	0.991391i	$0.541799\pi$
$74$	−1.84521	+	8.28361i	−0.00289866	+	0.0130128i
$75$		0			0
$76$	504.750	−	1076.76i	0.761826	−	1.62517i
$77$		−	102.102i		−	0.151112i
$78$		0			0
$79$			1347.64i			1.91925i	0.281275	+	0.959627i	$0.409243\pi$
$79$			1347.64i			1.91925i	−0.281275	+	0.959627i	$0.590757\pi$
$80$	−146.586	+	121.995i	−0.204861	+	0.170494i
$81$		0			0
$82$	−11.7821	−	2.62450i	−0.0158672	−	0.00353448i
$83$	−534.740			−0.707173			−0.353586	−	0.935402i	$-0.615038\pi$
$83$	−534.740			−0.707173			−0.353586	+	0.935402i	$0.615038\pi$
$84$		0			0
$85$	−140.259			−0.178979
$86$	722.836	+	161.015i	0.906342	+	0.201891i
$87$		0			0
$88$	201.711	−	261.233i	0.244346	−	0.316449i
$89$		−	398.405i		−	0.474504i	−0.971448	−	0.237252i	$-0.923753\pi$
$89$		−	398.405i		−	0.474504i	0.971448	−	0.237252i	$-0.0762466\pi$
$90$		0			0
$91$			195.801i			0.225555i
$92$	−616.592	−	289.039i	−0.698741	−	0.327548i
$93$		0			0
$94$	−59.0852	+	265.249i	−0.0648316	+	0.291046i
$95$	−442.952			−0.478378
$96$		0			0
$97$	1711.36			1.79137			0.895684	−	0.444691i	$-0.146686\pi$
$97$	1711.36			1.79137			0.895684	+	0.444691i	$0.146686\pi$
$98$	−30.1336	+	135.277i	−0.0310607	+	0.139440i
$99$		0			0
$100$	−841.133	−	394.296i	−0.841133	−	0.394296i
$101$			1871.61i			1.84388i	0.387333	+	0.921940i	$0.373396\pi$
$101$			1871.61i			1.84388i	−0.387333	+	0.921940i	$0.626604\pi$
$102$		0			0
$103$		−	11.8187i		−	0.0113061i	−0.999984	−	0.00565306i	$-0.998201\pi$
$103$		−	11.8187i		−	0.0113061i	0.999984	−	0.00565306i	$-0.00179944\pi$
$104$	−386.819	+	500.963i	−0.364718	+	0.472341i
$105$		0			0
$106$	363.529	+	80.9775i	0.333104	+	0.0742003i
$107$	−1350.29			−1.21998			−0.609990	−	0.792409i	$-0.708827\pi$
$107$	−1350.29			−1.21998			−0.609990	+	0.792409i	$0.708827\pi$
$108$		0			0
$109$	−571.162			−0.501903			−0.250951	−	0.968000i	$-0.580743\pi$
$109$	−571.162			−0.501903			−0.250951	+	0.968000i	$0.580743\pi$
$110$	−119.994	−	26.7293i	−0.104009	−	0.0231685i
$111$		0			0
$112$	−344.348	+	286.581i	−0.290516	+	0.241780i
$113$		−	967.624i		−	0.805544i	−0.915300	−	0.402772i	$-0.868047\pi$
$113$		−	967.624i		−	0.805544i	0.915300	−	0.402772i	$-0.131953\pi$
$114$		0			0
$115$			253.651i			0.205679i
$116$	−669.649	+	1428.53i	−0.535994	+	1.14341i
$117$		0			0
$118$	181.003	−	812.567i	0.141209	−	0.633923i
$119$	−329.483			−0.253812
$120$		0			0
$121$	−1118.25			−0.840155
$122$	82.8873	−	372.102i	0.0615104	−	0.276136i
$123$		0			0
$124$	725.209	−	1547.05i	0.525207	−	1.12040i
$125$			718.502i			0.514118i
$126$		0			0
$127$			208.578i			0.145734i	0.997342	+	0.0728672i	$0.0232149\pi$
$127$			208.578i			0.145734i	−0.997342	+	0.0728672i	$0.976785\pi$
$128$	−1447.19	+	52.9421i	−0.999332	+	0.0365583i
$129$		0			0
$130$	230.112	+	51.2584i	0.155248	+	0.0345820i
$131$	−1680.47			−1.12079			−0.560393	−	0.828227i	$-0.689350\pi$
$131$	−1680.47			−1.12079			−0.560393	+	0.828227i	$0.689350\pi$
$132$		0			0
$133$	−1040.54			−0.678396
$134$	410.383	+	91.4145i	0.264565	+	0.0589329i
$135$		0			0
$136$	−842.994	−	650.918i	−0.531516	−	0.410410i
$137$			1504.86i			0.938460i	0.883076	+	0.469230i	$0.155469\pi$
$137$			1504.86i			0.938460i	−0.883076	+	0.469230i	$0.844531\pi$
$138$		0			0
$139$		−	1613.01i		−	0.984273i	−0.870518	−	0.492136i	$-0.836216\pi$
$139$		−	1613.01i		−	0.984273i	0.870518	−	0.492136i	$-0.163784\pi$
$140$	151.094	+	70.8281i	0.0912128	+	0.0427576i
$141$		0			0
$142$	−489.855	+	2199.08i	−0.289491	+	1.29960i
$143$	−407.995			−0.238589
$144$		0			0
$145$	587.661			0.336570
$146$	−100.446	+	450.929i	−0.0569382	+	0.255610i
$147$		0			0
$148$	21.7343	+	10.1884i	0.0120713	+	0.00565864i
$149$		−	50.6741i		−	0.0278616i	−0.999903	−	0.0139308i	$-0.995566\pi$
$149$		−	50.6741i		−	0.0278616i	0.999903	−	0.0139308i	$-0.00443446\pi$
$150$		0			0
$151$			99.3618i			0.0535493i	0.999641	+	0.0267747i	$0.00852366\pi$
$151$			99.3618i			0.0535493i	−0.999641	+	0.0267747i	$0.991476\pi$
$152$	−2662.27	−	2055.67i	−1.42065	−	1.09695i
$153$		0			0
$154$	−281.881	−	62.7901i	−0.147497	−	0.0328556i
$155$	−636.419			−0.329796
$156$		0			0
$157$	2638.39			1.34119			0.670593	−	0.741825i	$-0.266040\pi$
$157$	2638.39			1.34119			0.670593	+	0.741825i	$0.266040\pi$
$158$	3720.51	+	828.758i	1.87334	+	0.417294i
$159$		0			0
$160$	246.654	+	479.714i	0.121873	+	0.237029i
$161$			595.855i			0.291677i
$162$		0			0
$163$		−	2611.58i		−	1.25494i	−0.778642	−	0.627468i	$-0.784091\pi$
$163$		−	2611.58i		−	1.25494i	0.778642	−	0.627468i	$-0.215909\pi$
$164$	−14.4912	+	30.9135i	−0.00689986	+	0.0147191i
$165$		0			0
$166$	−328.850	+	1476.29i	−0.153757	+	0.690255i
$167$	3438.19			1.59314			0.796572	−	0.604544i	$-0.206645\pi$
$167$	3438.19			1.59314			0.796572	+	0.604544i	$0.206645\pi$
$168$		0			0
$169$	−1414.59			−0.643874
$170$	−86.2549	+	387.221i	−0.0389144	+	0.174697i
$171$		0			0
$172$	889.047	−	1896.56i	0.394123	−	0.840764i
$173$		−	3976.76i		−	1.74767i	−0.486219	−	0.873837i	$-0.661624\pi$
$173$		−	3976.76i		−	1.74767i	0.486219	−	0.873837i	$-0.338376\pi$
$174$		0			0
$175$			812.844i			0.351115i
$176$	−597.155	−	717.526i	−0.255751	−	0.307304i
$177$		0			0
$178$	−1099.90	−	245.007i	−0.463152	−	0.103169i
$179$	3605.92			1.50569			0.752846	−	0.658197i	$-0.228681\pi$
$179$	3605.92			1.50569			0.752846	+	0.658197i	$0.228681\pi$
$180$		0			0
$181$	−1160.80			−0.476693			−0.238346	−	0.971180i	$-0.576605\pi$
$181$	−1160.80			−0.476693			−0.238346	+	0.971180i	$0.576605\pi$
$182$	540.560	+	120.412i	0.220159	+	0.0490413i
$183$		0			0
$184$	−1177.15	+	1524.51i	−0.471635	+	0.610808i
$185$		−	8.94097i		−	0.00355326i
$186$		0			0
$187$		−	686.552i		−	0.268480i
$188$	695.953	+	326.241i	0.269987	+	0.126561i
$189$		0			0
$190$	−272.403	+	1222.88i	−0.104011	+	0.466934i
$191$	4106.76			1.55578			0.777891	−	0.628399i	$-0.216290\pi$
$191$	4106.76			1.55578			0.777891	+	0.628399i	$0.216290\pi$
$192$		0			0
$193$	−2388.95			−0.890987			−0.445494	−	0.895285i	$-0.646972\pi$
$193$	−2388.95			−0.890987			−0.445494	+	0.895285i	$0.646972\pi$
$194$	1052.44	−	4724.67i	0.389488	−	1.74851i
$195$		0			0
$196$	354.937	+	166.383i	0.129350	+	0.0606353i
$197$		−	3236.10i		−	1.17037i	−0.810901	−	0.585184i	$-0.801022\pi$
$197$		−	3236.10i		−	1.17037i	0.810901	−	0.585184i	$-0.198978\pi$
$198$		0			0
$199$		−	3509.90i		−	1.25030i	−0.780503	−	0.625152i	$-0.785037\pi$
$199$		−	3509.90i		−	1.25030i	0.780503	−	0.625152i	$-0.214963\pi$
$200$	−1605.83	+	2079.69i	−0.567747	+	0.735281i
$201$		0			0
$202$	5167.06	+	1150.98i	1.79977	+	0.400906i
$203$	1380.48			0.477295
$204$		0			0
$205$	12.7170			0.00433267
$206$	−32.6286	−	7.26816i	−0.0110357	−	0.00245824i
$207$		0			0
$208$	1145.16	+	1375.99i	0.381743	+	0.458692i
$209$		−	2168.21i		−	0.717598i
$210$		0			0
$211$		−	485.243i		−	0.158320i	−0.996862	−	0.0791599i	$-0.974776\pi$
$211$		−	485.243i		−	0.158320i	0.996862	−	0.0791599i	$-0.0252238\pi$
$212$	447.119	−	953.818i	0.144850	−	0.309002i
$213$		0			0
$214$	−830.392	+	3727.84i	−0.265254	+	1.19079i
$215$	−780.198			−0.247484
$216$		0			0
$217$	−1495.02			−0.467690
$218$	−351.248	+	1576.84i	−0.109126	+	0.489896i
$219$		0			0
$220$	−147.586	+	314.839i	−0.0452285	+	0.0964837i
$221$			1316.59i			0.400741i
$222$		0			0
$223$			96.8412i			0.0290806i	0.999894	+	0.0145403i	$0.00462848\pi$
$223$			96.8412i			0.0290806i	−0.999894	+	0.0145403i	$0.995372\pi$
$224$	579.417	+	1126.90i	0.172830	+	0.336135i
$225$		0			0
$226$	−2671.38	−	595.061i	−0.786273	−	0.175145i
$227$	3635.58			1.06300			0.531502	−	0.847057i	$-0.321628\pi$
$227$	3635.58			1.06300			0.531502	+	0.847057i	$0.321628\pi$
$228$		0			0
$229$	4587.11			1.32369			0.661845	−	0.749641i	$-0.269774\pi$
$229$	4587.11			1.32369			0.661845	+	0.749641i	$0.269774\pi$
$230$	700.270	+	155.988i	0.200758	+	0.0447197i
$231$		0			0
$232$	3532.01	+	2727.24i	0.999518	+	0.771778i
$233$			4490.81i			1.26267i	0.775509	+	0.631336i	$0.217493\pi$
$233$			4490.81i			1.26267i	−0.775509	+	0.631336i	$0.782507\pi$
$234$		0			0
$235$		−	286.298i		−	0.0794724i
$236$	−2131.99	−	999.411i	−0.588055	−	0.275661i
$237$		0			0
$238$	−202.623	+	909.625i	−0.0551852	+	0.247741i
$239$	3218.42			0.871057			0.435528	−	0.900175i	$-0.356562\pi$
$239$	3218.42			0.871057			0.435528	+	0.900175i	$0.356562\pi$
$240$		0			0
$241$	2254.22			0.602520			0.301260	−	0.953542i	$-0.402593\pi$
$241$	2254.22			0.602520			0.301260	+	0.953542i	$0.402593\pi$
$242$	−687.689	+	3087.21i	−0.182671	+	0.820056i
$243$		0			0
$244$	−976.313	−	457.665i	−0.256156	−	0.120078i
$245$		−	146.013i		−	0.0380751i
$246$		0			0
$247$			4157.95i			1.07111i
$248$	−3825.06	−	2953.52i	−0.979402	−	0.756245i
$249$		0			0
$250$	1983.61	+	441.858i	0.501819	+	0.111782i
$251$	−3998.17			−1.00543			−0.502714	−	0.864453i	$-0.667665\pi$
$251$	−3998.17			−1.00543			−0.502714	+	0.864453i	$0.667665\pi$
$252$		0			0
$253$	−1241.60			−0.308532
$254$	575.834	+	128.269i	0.142248	+	0.0316863i
$255$		0			0
$256$	−743.817	+	4027.90i	−0.181596	+	0.983373i
$257$		−	3387.39i		−	0.822177i	−0.911595	−	0.411088i	$-0.865149\pi$
$257$		−	3387.39i		−	0.822177i	0.911595	−	0.411088i	$-0.134851\pi$
$258$		0			0
$259$		−	21.0033i		−	0.00503894i
$260$	283.025	−	603.763i	0.0675094	−	0.144015i
$261$		0			0
$262$	−1033.44	+	4639.37i	−0.243687	+	1.09397i
$263$	3331.72			0.781151			0.390575	−	0.920571i	$-0.372276\pi$
$263$	3331.72			0.781151			0.390575	+	0.920571i	$0.372276\pi$
$264$		0			0
$265$	−392.377			−0.0909567
$266$	−639.905	+	2872.70i	−0.147500	+	0.662166i
$267$		0			0
$268$	504.748	−	1076.75i	0.115046	−	0.245422i
$269$			5844.63i			1.32473i	0.749180	+	0.662367i	$0.230448\pi$
$269$			5844.63i			1.32473i	−0.749180	+	0.662367i	$0.769552\pi$
$270$		0			0
$271$		−	6710.76i		−	1.50424i	−0.659025	−	0.752121i	$-0.729031\pi$
$271$		−	6710.76i		−	1.50424i	0.659025	−	0.752121i	$-0.270969\pi$
$272$	−2315.45	+	1927.01i	−0.516157	+	0.429567i
$273$		0			0
$274$	4154.57	+	925.447i	0.916009	+	0.204045i
$275$	−1693.74			−0.371405
$276$		0			0
$277$	−4400.29			−0.954469			−0.477235	−	0.878776i	$-0.658361\pi$
$277$	−4400.29			−0.954469			−0.477235	+	0.878776i	$0.658361\pi$
$278$	−4453.14	−	991.956i	−0.960726	−	0.214006i
$279$		0			0
$280$	288.458	−	373.578i	0.0615667	−	0.0797341i
$281$		−	4749.75i		−	1.00835i	−0.863601	−	0.504175i	$-0.831797\pi$
$281$		−	4749.75i		−	1.00835i	0.863601	−	0.504175i	$-0.168203\pi$
$282$		0			0
$283$		−	1497.32i		−	0.314510i	−0.987558	−	0.157255i	$-0.949735\pi$
$283$		−	1497.32i		−	0.314510i	0.987558	−	0.157255i	$-0.0502645\pi$
$284$	5769.90	+	2704.75i	1.20557	+	0.565131i
$285$		0			0
$286$	−250.905	+	1126.38i	−0.0518753	+	0.232881i
$287$	29.8738			0.00614423
$288$		0			0
$289$	2697.51			0.549055
$290$	361.395	−	1622.39i	0.0731787	−	0.328518i
$291$		0			0
$292$	1183.14	+	554.616i	0.237116	+	0.111152i
$293$		−	3651.08i		−	0.727982i	−0.931403	−	0.363991i	$-0.881414\pi$
$293$		−	3651.08i		−	0.727982i	0.931403	−	0.363991i	$-0.118586\pi$
$294$		0			0
$295$			877.050i			0.173098i
$296$	41.4936	−	53.7378i	0.00814786	−	0.0105522i
$297$		0			0
$298$	−139.899	−	31.1631i	−0.0271951	−	0.00605781i
$299$	2381.00			0.460524
$300$		0			0
$301$	−1832.77			−0.350961
$302$	274.314	+	61.1046i	0.0522683	+	0.0116430i
$303$		0			0
$304$	−7312.43	+	6085.71i	−1.37959	+	1.14816i
$305$			401.631i			0.0754011i
$306$		0			0
$307$		−	210.827i		−	0.0391940i	−0.999808	−	0.0195970i	$-0.993762\pi$
$307$		−	210.827i		−	0.0391940i	0.999808	−	0.0195970i	$-0.00623832\pi$
$308$	−346.697	+	739.592i	−0.0641393	+	0.136825i
$309$		0			0
$310$	−391.379	+	1757.00i	−0.0717060	+	0.321907i
$311$	724.581			0.132113			0.0660566	−	0.997816i	$-0.478958\pi$
$311$	724.581			0.132113			0.0660566	+	0.997816i	$0.478958\pi$
$312$		0			0
$313$	8805.01			1.59006			0.795030	−	0.606571i	$-0.207455\pi$
$313$	8805.01			1.59006			0.795030	+	0.606571i	$0.207455\pi$
$314$	1622.53	−	7283.96i	0.291608	−	1.30910i
$315$		0			0
$316$	4576.01	−	9761.78i	0.814622	−	1.73779i
$317$			6348.48i			1.12481i	0.826860	+	0.562407i	$0.190125\pi$
$317$			6348.48i			1.12481i	−0.826860	+	0.562407i	$0.809875\pi$
$318$		0			0
$319$			2876.55i			0.504877i
$320$	1476.06	−	385.942i	0.257857	−	0.0674213i
$321$		0			0
$322$	1645.01	+	366.433i	0.284699	+	0.0634178i
$323$	−6996.77			−1.20530
$324$		0			0
$325$	3248.07			0.554371
$326$	−7209.95	−	1606.05i	−1.22491	−	0.272855i
$327$		0			0
$328$	76.4331	+	59.0178i	0.0128668	+	0.00993510i
$329$		−	672.546i		−	0.112701i
$330$		0			0
$331$		−	5556.10i		−	0.922631i	−0.887236	−	0.461315i	$-0.847378\pi$
$331$		−	5556.10i		−	0.922631i	0.887236	−	0.461315i	$-0.152622\pi$
$332$	3873.45	+	1815.75i	0.640312	+	0.300158i
$333$		0			0
$334$	2114.39	−	9492.02i	0.346390	−	1.55503i
$335$	−442.950			−0.0722416
$336$		0			0
$337$	−3816.67			−0.616936			−0.308468	−	0.951235i	$-0.599816\pi$
$337$	−3816.67			−0.616936			−0.308468	+	0.951235i	$0.599816\pi$
$338$	−869.933	+	3905.35i	−0.139994	+	0.628471i
$339$		0			0
$340$	1015.98	+	476.259i	0.162057	+	0.0759670i
$341$		−	3115.21i		−	0.494716i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	−4689.21	−	3620.78i	−0.734958	−	0.567498i
$345$		0			0
$346$	−10978.9	−	2445.59i	−1.70586	−	0.379988i
$347$	−12314.6			−1.90514			−0.952571	−	0.304317i	$-0.901572\pi$
$347$	−12314.6			−1.90514			−0.952571	+	0.304317i	$0.901572\pi$
$348$		0			0
$349$	−8216.49			−1.26023			−0.630113	−	0.776503i	$-0.716991\pi$
$349$	−8216.49			−1.26023			−0.630113	+	0.776503i	$0.716991\pi$
$350$	2244.07	+	499.875i	0.342716	+	0.0763413i
$351$		0			0
$352$	−2348.15	+	1207.35i	−0.355560	+	0.182817i
$353$			9603.40i			1.44798i	0.689810	+	0.723990i	$0.257694\pi$
$353$			9603.40i			1.44798i	−0.689810	+	0.723990i	$0.742306\pi$
$354$		0			0
$355$		−	2373.60i		−	0.354866i
$356$	−1352.81	+	2885.89i	−0.201402	+	0.429640i
$357$		0			0
$358$	2217.53	−	9955.08i	0.327375	−	1.46967i
$359$	7618.71			1.12006			0.560028	−	0.828474i	$-0.310790\pi$
$359$	7618.71			1.12006			0.560028	+	0.828474i	$0.310790\pi$
$360$		0			0
$361$	−15237.6			−2.22154
$362$	−713.856	+	3204.68i	−0.103645	+	0.465289i
$363$		0			0
$364$	664.857	−	1418.31i	0.0957363	−	0.204229i
$365$		−	486.713i		−	0.0697965i
$366$		0			0
$367$			7619.79i			1.08379i	0.840447	+	0.541894i	$0.182292\pi$
$367$			7619.79i			1.08379i	−0.840447	+	0.541894i	$0.817708\pi$
$368$	3484.91	+	4187.37i	0.493650	+	0.593158i
$369$		0			0
$370$	−24.6839	−	5.49844i	−0.00346825	−	0.000772568i
$371$	−921.739			−0.128987
$372$		0			0
$373$	−102.877			−0.0142809			−0.00714045	−	0.999975i	$-0.502273\pi$
$373$	−102.877			−0.0142809			−0.00714045	+	0.999975i	$0.502273\pi$
$374$	−1895.41	−	422.210i	−0.262057	−	0.0583742i
$375$		0			0
$376$	1328.66	−	1720.73i	0.182236	−	0.236011i
$377$		−	5516.33i		−	0.753595i
$378$		0			0
$379$		−	10008.1i		−	1.35641i	−0.734871	−	0.678207i	$-0.762757\pi$
$379$		−	10008.1i		−	1.35641i	0.734871	−	0.678207i	$-0.237243\pi$
$380$	3208.57	+	1504.08i	0.433148	+	0.203046i
$381$		0			0
$382$	2525.54	−	11337.8i	0.338266	−	1.51856i
$383$	−6622.81			−0.883576			−0.441788	−	0.897119i	$-0.645656\pi$
$383$	−6622.81			−0.883576			−0.441788	+	0.897119i	$0.645656\pi$
$384$		0			0
$385$	304.250			0.0402753
$386$	−1469.14	+	6595.33i	−0.193723	+	0.869672i
$387$		0			0
$388$	−12396.5	−	5811.07i	−1.62200	−	0.760341i
$389$		−	10793.4i		−	1.40681i	−0.710791	−	0.703403i	$-0.751663\pi$
$389$		−	10793.4i		−	1.40681i	0.710791	−	0.703403i	$-0.248337\pi$
$390$		0			0
$391$			4006.62i			0.518218i
$392$	677.621	−	877.577i	0.0873088	−	0.113072i
$393$		0			0
$394$	−8934.10	−	1990.11i	−1.14237	−	0.254467i
$395$	−4015.75			−0.511530
$396$		0			0
$397$	4491.35			0.567795			0.283897	−	0.958855i	$-0.408373\pi$
$397$	4491.35			0.567795			0.283897	+	0.958855i	$0.408373\pi$
$398$	−9690.01	−	2158.49i	−1.22039	−	0.271847i
$399$		0			0
$400$	4753.98	+	5712.27i	0.594248	+	0.714033i
$401$			14004.7i			1.74404i	0.489467	+	0.872022i	$0.337191\pi$
$401$			14004.7i			1.74404i	−0.489467	+	0.872022i	$0.662809\pi$
$402$		0			0
$403$			5974.01i			0.738428i
$404$	6355.19	−	13557.2i	0.782630	−	1.66955i
$405$		0			0
$406$	848.957	−	3811.19i	0.103776	−	0.465877i
$407$	43.7652			0.00533012
$408$		0			0
$409$	14406.8			1.74173			0.870867	−	0.491519i	$-0.163558\pi$
$409$	14406.8			1.74173			0.870867	+	0.491519i	$0.163558\pi$
$410$	7.82061	−	35.1087i	0.000942030	−	0.00422902i
$411$		0			0
$412$	−40.1313	+	85.6102i	−0.00479886	+	0.0102372i
$413$			2060.29i			0.245473i
$414$		0			0
$415$		−	1593.44i		−	0.188480i
$416$	4503.03	−	2315.31i	0.530719	−	0.272879i
$417$		0			0
$418$	−5985.90	−	1333.38i	−0.700431	−	0.156024i
$419$	−13240.1			−1.54372			−0.771862	−	0.635790i	$-0.780674\pi$
$419$	−13240.1			−1.54372			−0.771862	+	0.635790i	$0.780674\pi$
$420$		0			0
$421$	4321.30			0.500255			0.250128	−	0.968213i	$-0.419527\pi$
$421$	4321.30			0.500255			0.250128	+	0.968213i	$0.419527\pi$
$422$	−1339.64	−	298.410i	−0.154532	−	0.0344227i
$423$		0			0
$424$	−2358.30	−	1820.96i	−0.270116	−	0.208570i
$425$			5465.68i			0.623822i
$426$		0			0
$427$			943.477i			0.106928i
$428$	9781.02	+	4585.03i	1.10463	+	0.517817i
$429$		0			0
$430$	−479.799	+	2153.94i	−0.0538092	+	0.241564i
$431$	1296.30			0.144874			0.0724371	−	0.997373i	$-0.476922\pi$
$431$	1296.30			0.144874			0.0724371	+	0.997373i	$0.476922\pi$
$432$		0			0
$433$	−10543.7			−1.17020			−0.585101	−	0.810961i	$-0.698945\pi$
$433$	−10543.7			−1.17020			−0.585101	+	0.810961i	$0.698945\pi$
$434$	−919.395	+	4127.40i	−0.101687	+	0.456501i
$435$		0			0
$436$	4137.28	+	1939.43i	0.454449	+	0.213031i
$437$			12653.3i			1.38510i
$438$		0			0
$439$			13198.6i			1.43493i	0.696595	+	0.717465i	$0.254698\pi$
$439$			13198.6i			1.43493i	−0.696595	+	0.717465i	$0.745302\pi$
$440$	778.433	+	601.067i	0.0843417	+	0.0651245i
$441$		0			0
$442$	3634.80	+	809.668i	0.391154	+	0.0871311i
$443$	2362.08			0.253331			0.126666	−	0.991945i	$-0.459573\pi$
$443$	2362.08			0.253331			0.126666	+	0.991945i	$0.459573\pi$
$444$		0			0
$445$	1187.19			0.126467
$446$	267.355	+	59.5545i	0.0283849	+	0.00632284i
$447$		0			0
$448$	3467.43	−	906.621i	0.365671	−	0.0956112i
$449$		−	12464.5i		−	1.31010i	−0.755583	−	0.655052i	$-0.772647\pi$
$449$		−	12464.5i		−	1.31010i	0.755583	−	0.655052i	$-0.227353\pi$
$450$		0			0
$451$			62.2487i			0.00649928i
$452$	−3285.64	+	7009.11i	−0.341911	+	0.729382i
$453$		0			0
$454$	2235.78	−	10037.0i	0.231124	−	1.03757i
$455$	−583.457			−0.0601162
$456$		0			0
$457$	14842.4			1.51925			0.759627	−	0.650359i	$-0.225381\pi$
$457$	14842.4			1.51925			0.759627	+	0.650359i	$0.225381\pi$
$458$	2820.94	−	12663.9i	0.287803	−	1.29202i
$459$		0			0
$460$	861.291	−	1837.35i	0.0872998	−	0.186232i
$461$		−	9687.52i		−	0.978727i	−0.872080	−	0.489363i	$-0.837229\pi$
$461$		−	9687.52i		−	0.978727i	0.872080	−	0.489363i	$-0.162771\pi$
$462$		0			0
$463$			15024.8i			1.50812i	0.656803	+	0.754062i	$0.271908\pi$
$463$			15024.8i			1.50812i	−0.656803	+	0.754062i	$0.728092\pi$
$464$	9701.36	−	8073.88i	0.970635	−	0.807802i
$465$		0			0
$466$	12398.1	+	2761.72i	1.23246	+	0.274537i
$467$	−10567.3			−1.04710			−0.523549	−	0.851995i	$-0.675392\pi$
$467$	−10567.3			−1.04710			−0.523549	+	0.851995i	$0.675392\pi$
$468$		0			0
$469$	−1040.54			−0.102447
$470$	−790.400	−	176.065i	−0.0775712	−	0.0172793i
$471$		0			0
$472$	−4070.25	+	5271.32i	−0.396925	+	0.514051i
$473$		−	3819.00i		−	0.371242i
$474$		0			0
$475$			17261.2i			1.66737i
$476$	2386.65	+	1118.79i	0.229815	+	0.107730i
$477$		0			0
$478$	1979.24	−	8885.31i	0.189390	−	0.850219i
$479$	18844.8			1.79758			0.898788	−	0.438384i	$-0.144449\pi$
$479$	18844.8			1.79758			0.898788	+	0.438384i	$0.144449\pi$
$480$		0			0
$481$	−83.9281			−0.00795590
$482$	1386.28	−	6223.38i	0.131003	−	0.588106i
$483$		0			0
$484$	8100.15	+	3797.09i	0.760721	+	0.356602i
$485$			5099.60i			0.477446i
$486$		0			0
$487$			9562.33i			0.889755i	0.895591	+	0.444878i	$0.146753\pi$
$487$			9562.33i			0.889755i	−0.895591	+	0.444878i	$0.853247\pi$
$488$	−1863.91	+	2413.92i	−0.172900	+	0.223920i
$489$		0			0
$490$	−403.106	−	89.7935i	−0.0371642	−	0.00827848i
$491$	−10643.7			−0.978298			−0.489149	−	0.872200i	$-0.662693\pi$
$491$	−10643.7			−0.978298			−0.489149	+	0.872200i	$0.662693\pi$
$492$		0			0
$493$	9282.58			0.848005
$494$	11479.1	+	2557.02i	1.04548	+	0.232886i
$495$		0			0
$496$	−10506.3	+	8743.76i	−0.951100	+	0.791545i
$497$		−	5575.85i		−	0.503241i
$498$		0			0
$499$			7550.79i			0.677394i	0.940895	+	0.338697i	$0.109986\pi$
$499$			7550.79i			0.677394i	−0.940895	+	0.338697i	$0.890014\pi$
$500$	2439.73	−	5204.56i	0.218216	−	0.465510i
$501$		0			0
$502$	−2458.76	+	11038.0i	−0.218605	+	0.981374i
$503$	1090.04			0.0966255			0.0483127	−	0.998832i	$-0.484616\pi$
$503$	1090.04			0.0966255			0.0483127	+	0.998832i	$0.484616\pi$
$504$		0			0
$505$	−5577.10			−0.491441
$506$	−763.546	+	3427.75i	−0.0670825	+	0.301151i
$507$		0			0
$508$	708.242	−	1510.86i	0.0618566	−	0.131956i
$509$			7957.32i			0.692931i	0.938063	+	0.346465i	$0.112618\pi$
$509$			7957.32i			0.692931i	−0.938063	+	0.346465i	$0.887382\pi$
$510$		0			0
$511$		−	1143.34i		−	0.0989795i
$512$	10662.6	+	4530.54i	0.920364	+	0.391062i
$513$		0			0
$514$	−9351.77	−	2083.15i	−0.802508	−	0.178762i
$515$	35.2179			0.00301337
$516$		0			0
$517$	1401.40			0.119214
$518$	−57.9853	−	12.9165i	−0.00491839	−	0.00109559i
$519$		0			0
$520$	−1492.79	−	1152.66i	−0.125891	−	0.0972068i
$521$			6770.45i			0.569326i	0.958628	+	0.284663i	$0.0918816\pi$
$521$			6770.45i			0.569326i	−0.958628	+	0.284663i	$0.908118\pi$
$522$		0			0
$523$		−	9837.70i		−	0.822510i	−0.911520	−	0.411255i	$-0.865091\pi$
$523$		−	9837.70i		−	0.822510i	0.911520	−	0.411255i	$-0.134909\pi$
$524$	12172.7	+	5706.15i	1.01482	+	0.475714i
$525$		0			0
$526$	2048.91	−	9198.09i	0.169842	−	0.762463i
$527$	−10052.7			−0.830938
$528$		0			0
$529$	−4921.23			−0.404474
$530$	−241.301	+	1083.26i	−0.0197763	+	0.0887808i
$531$		0			0
$532$	7537.31	+	3533.25i	0.614255	+	0.287943i
$533$		−	119.374i		−	0.00970103i
$534$		0			0
$535$		−	4023.67i		−	0.325156i
$536$	−2662.25	−	2055.66i	−0.214537	−	0.165655i
$537$		0			0
$538$	16135.6	+	3594.28i	1.29304	+	0.288030i
$539$	714.717			0.0571151
$540$		0			0
$541$	11900.7			0.945749			0.472874	−	0.881130i	$-0.343216\pi$
$541$	11900.7			0.945749			0.472874	+	0.881130i	$0.343216\pi$
$542$	−18526.8	−	4126.92i	−1.46826	−	0.327060i
$543$		0			0
$544$	3896.09	+	7577.46i	0.307065	+	0.597207i
$545$		−	1701.98i		−	0.133770i
$546$		0			0
$547$			4883.36i			0.381714i	0.981618	+	0.190857i	$0.0611267\pi$
$547$			4883.36i			0.381714i	−0.981618	+	0.190857i	$0.938873\pi$
$548$	5109.88	−	10900.7i	0.398327	−	0.849731i
$549$		0			0
$550$	−1041.60	+	4676.02i	−0.0807529	+	0.362520i
$551$	29315.4			2.26657
$552$		0			0
$553$	−9433.46			−0.725410
$554$	−2706.05	+	12148.2i	−0.207526	+	0.931636i
$555$		0			0
$556$	−5477.11	+	11684.0i	−0.417772	+	0.891212i
$557$			1481.08i			0.112667i	0.998412	+	0.0563334i	$0.0179410\pi$
$557$			1481.08i			0.112667i	−0.998412	+	0.0563334i	$0.982059\pi$
$558$		0			0
$559$			7323.65i			0.554128i
$560$	−853.967	−	1026.10i	−0.0644405	−	0.0774300i
$561$		0			0
$562$	−13112.9	−	2920.96i	−0.984228	−	0.219241i
$563$	−20443.6			−1.53037			−0.765183	−	0.643813i	$-0.777351\pi$
$563$	−20443.6			−1.53037			−0.765183	+	0.643813i	$0.777351\pi$
$564$		0			0
$565$	2883.37			0.214698
$566$	−4133.74	−	920.808i	−0.306986	−	0.0683824i
$567$		0			0
$568$	11015.5	−	14266.0i	0.813732	−	1.05385i
$569$		−	17488.2i		−	1.28848i	−0.764824	−	0.644240i	$-0.777174\pi$
$569$		−	17488.2i		−	1.28848i	0.764824	−	0.644240i	$-0.222826\pi$
$570$		0			0
$571$		−	6945.88i		−	0.509065i	−0.967064	−	0.254532i	$-0.918078\pi$
$571$		−	6945.88i		−	0.509065i	0.967064	−	0.254532i	$-0.0819215\pi$
$572$	2955.36	+	1385.38i	0.216031	+	0.101269i
$573$		0			0
$574$	18.3715	−	82.4744i	0.00133591	−	0.00599724i
$575$	9884.42			0.716885
$576$		0			0
$577$	24227.0			1.74797			0.873987	−	0.485949i	$-0.161526\pi$
$577$	24227.0			1.74797			0.873987	+	0.485949i	$0.161526\pi$
$578$	1658.89	−	7447.17i	0.119378	−	0.535920i
$579$		0			0
$580$	−4256.80	−	1995.45i	−0.304748	−	0.142856i
$581$		−	3743.18i		−	0.267286i
$582$		0			0
$583$		−	1920.65i		−	0.136441i
$584$	2258.76	−	2925.28i	0.160048	−	0.207276i
$585$		0			0
$586$	−10079.8	−	2245.31i	−0.710566	−	0.158281i
$587$	15665.7			1.10152			0.550760	−	0.834663i	$-0.314338\pi$
$587$	15665.7			1.10152			0.550760	+	0.834663i	$0.314338\pi$
$588$		0			0
$589$	−31747.7			−2.22095
$590$	2421.33	+	539.360i	0.168957	+	0.0376358i
$591$		0			0
$592$	−122.840	−	147.601i	−0.00852819	−	0.0102473i
$593$		−	3668.32i		−	0.254030i	−0.991901	−	0.127015i	$-0.959460\pi$
$593$		−	3668.32i		−	0.254030i	0.991901	−	0.127015i	$-0.0405397\pi$
$594$		0			0
$595$		−	981.810i		−	0.0676475i
$596$	−172.068	+	367.064i	−0.0118258	+	0.0252274i
$597$		0			0
$598$	1464.24	−	6573.37i	0.100129	−	0.449507i
$599$	11412.5			0.778469			0.389235	−	0.921139i	$-0.372740\pi$
$599$	11412.5			0.778469			0.389235	+	0.921139i	$0.372740\pi$
$600$		0			0
$601$	−10557.7			−0.716566			−0.358283	−	0.933613i	$-0.616638\pi$
$601$	−10557.7			−0.716566			−0.358283	+	0.933613i	$0.616638\pi$
$602$	−1127.10	+	5059.85i	−0.0763078	+	0.342565i
$603$		0			0
$604$	337.391	−	719.739i	0.0227289	−	0.0484864i
$605$		−	3332.20i		−	0.223923i
$606$		0			0
$607$			6370.55i			0.425985i	0.977054	+	0.212992i	$0.0683209\pi$
$607$			6370.55i			0.425985i	−0.977054	+	0.212992i	$0.931679\pi$
$608$	12304.3	+	23930.4i	0.820730	+	1.59623i
$609$		0			0
$610$	1108.81	+	246.992i	0.0735973	+	0.0163941i
$611$	−2687.45			−0.177942
$612$		0			0
$613$	−11921.8			−0.785506			−0.392753	−	0.919644i	$-0.628477\pi$
$613$	−11921.8			−0.785506			−0.392753	+	0.919644i	$0.628477\pi$
$614$	−582.045	−	129.653i	−0.0382564	−	0.00852176i
$615$		0			0
$616$	1828.63	+	1411.98i	0.119606	+	0.0923541i
$617$			10885.0i			0.710233i	0.934822	+	0.355117i	$0.115559\pi$
$617$			10885.0i			0.710233i	−0.934822	+	0.355117i	$0.884441\pi$
$618$		0			0
$619$		−	22866.9i		−	1.48481i	−0.669949	−	0.742407i	$-0.733684\pi$
$619$		−	22866.9i		−	1.48481i	0.669949	−	0.742407i	$-0.266316\pi$
$620$	4609.98	+	2161.01i	0.298615	+	0.139981i
$621$		0			0
$622$	445.596	−	2000.40i	0.0287247	−	0.128953i
$623$	2788.83			0.179345
$624$		0			0
$625$	12374.0			0.791938
$626$	5414.83	−	24308.5i	0.345719	−	1.55202i
$627$		0			0
$628$	−19111.5	−	8958.85i	−1.21438	−	0.569263i
$629$		−	141.230i		−	0.00895261i
$630$		0			0
$631$		−	627.472i		−	0.0395868i	−0.999804	−	0.0197934i	$-0.993699\pi$
$631$		−	627.472i		−	0.0395868i	0.999804	−	0.0197934i	$-0.00630085\pi$
$632$	−24135.8	−	18636.5i	−1.51910	−	1.17297i
$633$		0			0
$634$	17526.6	+	3904.13i	1.09791	+	0.244563i
$635$	−621.530			−0.0388420
$636$		0			0
$637$	−1370.61			−0.0852518
$638$	7941.46	+	1768.99i	0.492799	+	0.109773i
$639$		0			0
$640$	−157.759	−	4312.39i	−0.00974373	−	0.266347i
$641$		−	12854.0i		−	0.792047i	−0.918240	−	0.396024i	$-0.870390\pi$
$641$		−	12854.0i		−	0.792047i	0.918240	−	0.396024i	$-0.129610\pi$
$642$		0			0
$643$		−	31056.4i		−	1.90473i	−0.304956	−	0.952366i	$-0.598642\pi$
$643$		−	31056.4i		−	1.90473i	0.304956	−	0.952366i	$-0.401358\pi$
$644$	2023.27	−	4316.15i	0.123801	−	0.264099i
$645$		0			0
$646$	−4302.81	+	19316.4i	−0.262062	+	1.17646i
$647$	9340.79			0.567580			0.283790	−	0.958886i	$-0.408408\pi$
$647$	9340.79			0.567580			0.283790	+	0.958886i	$0.408408\pi$
$648$		0			0
$649$	−4293.07			−0.259658
$650$	1997.47	−	8967.16i	0.120534	−	0.541109i
$651$		0			0
$652$	−8867.82	+	18917.3i	−0.532654	+	1.13629i
$653$		−	4651.62i		−	0.278763i	−0.990239	−	0.139381i	$-0.955489\pi$
$653$		−	4651.62i		−	0.278763i	0.990239	−	0.139381i	$-0.0445114\pi$
$654$		0			0
$655$		−	5007.53i		−	0.298718i
$656$	209.938	−	174.719i	0.0124950	−	0.0103988i
$657$		0			0
$658$	−1856.74	−	413.597i	−0.110005	−	0.0245041i
$659$	30458.7			1.80046			0.900231	−	0.435413i	$-0.143398\pi$
$659$	30458.7			1.80046			0.900231	+	0.435413i	$0.143398\pi$
$660$		0			0
$661$	22311.1			1.31286			0.656431	−	0.754386i	$-0.272065\pi$
$661$	22311.1			1.31286			0.656431	+	0.754386i	$0.272065\pi$
$662$	−15339.1	−	3416.84i	−0.900559	−	0.200603i
$663$		0			0
$664$	7394.92	−	9577.05i	0.432197	−	0.559732i
$665$		−	3100.66i		−	0.180810i
$666$		0			0
$667$		−	16787.1i		−	0.974511i
$668$	−24904.9	−	11674.6i	−1.44252	−	0.676206i
$669$		0			0
$670$	−272.401	+	1222.88i	−0.0157071	+	0.0705133i
$671$	−1965.95			−0.113107
$672$		0			0
$673$	−12390.1			−0.709661			−0.354831	−	0.934931i	$-0.615461\pi$
$673$	−12390.1			−0.709661			−0.354831	+	0.934931i	$0.615461\pi$
$674$	−2347.14	+	10536.9i	−0.134137	+	0.602177i
$675$		0			0
$676$	10246.8	+	4803.36i	0.582998	+	0.273291i
$677$			32115.6i			1.82319i	0.411084	+	0.911597i	$0.365150\pi$
$677$			32115.6i			1.82319i	−0.411084	+	0.911597i	$0.634850\pi$
$678$		0			0
$679$			11979.5i			0.677074i
$680$	1939.64	−	2511.99i	0.109385	−	0.141663i
$681$		0			0
$682$	−8600.36	−	1915.77i	−0.482881	−	0.107564i
$683$	−22387.2			−1.25421			−0.627104	−	0.778936i	$-0.715760\pi$
$683$	−22387.2			−1.25421			−0.627104	+	0.778936i	$0.715760\pi$
$684$		0			0
$685$	−4484.26			−0.250124
$686$	−946.942	−	210.935i	−0.0527032	−	0.0117399i
$687$		0			0
$688$	−12879.8	+	10719.1i	−0.713720	+	0.593987i
$689$			3683.21i			0.203656i
$690$		0			0
$691$		−	18455.0i		−	1.01601i	−0.861354	−	0.508005i	$-0.830383\pi$
$691$		−	18455.0i		−	1.01601i	0.861354	−	0.508005i	$-0.169617\pi$
$692$	−13503.4	+	28806.1i	−0.741795	+	1.58244i
$693$		0			0
$694$	−7573.14	+	33997.8i	−0.414226	+	1.85957i
$695$	4806.53			0.262334
$696$		0			0
$697$	200.876			0.0109164
$698$	−5052.91	+	22683.8i	−0.274005	+	1.23008i
$699$		0			0
$700$	2760.07	−	5887.93i	0.149030	−	0.317918i
$701$		−	19758.3i		−	1.06457i	−0.846566	−	0.532283i	$-0.821334\pi$
$701$		−	19758.3i		−	1.06457i	0.846566	−	0.532283i	$-0.178666\pi$
$702$		0			0
$703$		−	446.019i		−	0.0239287i
$704$	1889.15	+	7225.17i	0.101136	+	0.386803i
$705$		0			0
$706$	26512.7	+	5905.81i	1.41334	+	0.314827i
$707$	−13101.2			−0.696921
$708$		0			0
$709$	−5354.63			−0.283635			−0.141818	−	0.989893i	$-0.545295\pi$
$709$	−5354.63			−0.283635			−0.141818	+	0.989893i	$0.545295\pi$
$710$	−6552.94	−	1459.69i	−0.346376	−	0.0771568i
$711$		0			0
$712$	7135.32	+	5509.54i	0.375572	+	0.289998i
$713$			18179.9i			0.954899i
$714$		0			0
$715$		−	1215.76i		−	0.0635902i
$716$	−26119.9	−	12244.2i	−1.36333	−	0.639087i
$717$		0			0
$718$	4685.29	−	21033.5i	0.243528	−	1.09326i
$719$	−6327.40			−0.328195			−0.164097	−	0.986444i	$-0.552471\pi$
$719$	−6327.40			−0.328195			−0.164097	+	0.986444i	$0.552471\pi$
$720$		0			0
$721$	82.7309			0.00427331
$722$	−9370.67	+	42067.3i	−0.483019	+	2.16840i
$723$		0			0
$724$	8408.37	+	3941.58i	0.431622	+	0.202331i
$725$		−	22900.4i		−	1.17310i
$726$		0			0
$727$		−	17148.8i		−	0.874846i	−0.899256	−	0.437423i	$-0.855891\pi$
$727$		−	17148.8i		−	0.874846i	0.899256	−	0.437423i	$-0.144109\pi$
$728$	−3506.74	−	2707.73i	−0.178528	−	0.137851i
$729$		0			0
$730$	−1343.70	−	299.314i	−0.0681267	−	0.0151755i
$731$	−12323.8			−0.623548
$732$		0			0
$733$	−14960.0			−0.753832			−0.376916	−	0.926247i	$-0.623016\pi$
$733$	−14960.0			−0.753832			−0.376916	+	0.926247i	$0.623016\pi$
$734$	21036.4	+	4685.95i	1.05786	+	0.235643i
$735$		0			0
$736$	13703.5	−	7045.89i	0.686299	−	0.352873i
$737$		−	2168.20i		−	0.108367i
$738$		0			0
$739$		−	11540.8i		−	0.574470i	−0.957860	−	0.287235i	$-0.907264\pi$
$739$		−	11540.8i		−	0.574470i	0.957860	−	0.287235i	$-0.0927361\pi$
$740$	−30.3598	+	64.7650i	−0.00150817	+	0.00321731i
$741$		0			0
$742$	−566.843	+	2544.70i	−0.0280451	+	0.125902i
$743$	−22310.2			−1.10159			−0.550795	−	0.834640i	$-0.685675\pi$
$743$	−22310.2			−1.10159			−0.550795	+	0.834640i	$0.685675\pi$
$744$		0			0
$745$	151.001			0.00742583
$746$	−63.2665	+	284.019i	−0.00310503	+	0.0139393i
$747$		0			0
$748$	−2331.24	+	4973.12i	−0.113955	+	0.243096i
$749$		−	9452.06i		−	0.461109i
$750$		0			0
$751$		−	21276.7i		−	1.03382i	−0.856040	−	0.516909i	$-0.827083\pi$
$751$		−	21276.7i		−	1.03382i	0.856040	−	0.516909i	$-0.172917\pi$
$752$	−3933.44	−	4726.33i	−0.190742	−	0.229191i
$753$		0			0
$754$	−15229.3	−	3392.38i	−0.735567	−	0.163850i
$755$	−296.083			−0.0142723
$756$		0			0
$757$	−18995.8			−0.912042			−0.456021	−	0.889969i	$-0.650726\pi$
$757$	−18995.8			−0.912042			−0.456021	+	0.889969i	$0.650726\pi$
$758$	−27629.9	−	6154.68i	−1.32396	−	0.294918i
$759$		0			0
$760$	6125.58	−	7933.15i	0.292366	−	0.378639i
$761$			24525.2i			1.16825i	0.811664	+	0.584124i	$0.198562\pi$
$761$			24525.2i			1.16825i	−0.811664	+	0.584124i	$0.801438\pi$
$762$		0			0
$763$		−	3998.13i		−	0.189701i
$764$	−29747.8	−	13944.8i	−1.40869	−	0.660348i
$765$		0			0
$766$	−4072.84	+	18284.0i	−0.192112	+	0.862438i
$767$	8232.79			0.387573
$768$		0			0
$769$	12318.1			0.577636			0.288818	−	0.957384i	$-0.406738\pi$
$769$	12318.1			0.577636			0.288818	+	0.957384i	$0.406738\pi$
$770$	187.105	−	839.961i	0.00875687	−	0.0393118i
$771$		0			0
$772$	17304.7	+	8111.88i	0.806747	+	0.378177i
$773$			29609.2i			1.37771i	0.724901	+	0.688853i	$0.241886\pi$
$773$			29609.2i			1.37771i	−0.724901	+	0.688853i	$0.758114\pi$
$774$		0			0
$775$			24800.4i			1.14949i
$776$	−23666.5	+	30650.1i	−1.09482	+	1.41788i
$777$		0			0
$778$	−29798.0	−	6637.64i	−1.37315	−	0.305875i
$779$	634.387			0.0291775
$780$		0			0
$781$	11618.5			0.532322
$782$	11061.3	+	2463.95i	0.505821	+	0.112674i
$783$		0			0
$784$	−2006.06	−	2410.44i	−0.0913841	−	0.109805i
$785$			7861.99i			0.357461i
$786$		0			0
$787$		−	23458.7i		−	1.06253i	−0.847206	−	0.531265i	$-0.821717\pi$
$787$		−	23458.7i		−	1.06253i	0.847206	−	0.531265i	$-0.178283\pi$
$788$	−10988.4	+	23441.1i	−0.496759	+	1.05971i
$789$		0			0
$790$	−2469.57	+	11086.5i	−0.111220	+	0.499293i
$791$	6773.37			0.304467
$792$		0			0
$793$	3770.08			0.168826
$794$	2762.05	−	12399.6i	0.123453	−	0.554211i
$795$		0			0
$796$	−11918.2	+	25424.4i	−0.530688	+	1.13209i
$797$			11962.9i			0.531680i	0.964017	+	0.265840i	$0.0856492\pi$
$797$			11962.9i			0.531680i	−0.964017	+	0.265840i	$0.914351\pi$
$798$		0			0
$799$		−	4522.30i		−	0.200235i
$800$	18693.8	−	9611.74i	0.826156	−	0.424783i
$801$		0			0
$802$	38663.7	+	8612.49i	1.70232	+	0.379199i
$803$	2382.41			0.104699
$804$		0			0
$805$	−1775.56			−0.0777393
$806$	16492.8	+	3673.84i	0.720763	+	0.160553i
$807$		0			0
$808$	−33520.0	−	25882.5i	−1.45944	−	1.12691i
$809$			3777.90i			0.164183i	0.996625	+	0.0820914i	$0.0261600\pi$
$809$			3777.90i			0.164183i	−0.996625	+	0.0820914i	$0.973840\pi$
$810$		0			0
$811$		−	133.384i		−	0.00577527i	−0.999996	−	0.00288763i	$-0.999081\pi$
$811$		−	133.384i		−	0.00577527i	0.999996	−	0.00288763i	$-0.000919164\pi$
$812$	−9999.70	−	4687.54i	−0.432168	−	0.202587i
$813$		0			0
$814$	26.9143	−	120.825i	0.00115890	−	0.00520261i
$815$	7782.10			0.334473
$816$		0			0
$817$	−38920.0			−1.66663
$818$	8859.75	−	39773.7i	0.378697	−	1.70007i
$819$		0			0
$820$	−92.1174	−	43.1817i	−0.00392302	−	0.00183899i
$821$		−	19162.7i		−	0.814595i	−0.913296	−	0.407298i	$-0.866471\pi$
$821$		−	19162.7i		−	0.814595i	0.913296	−	0.407298i	$-0.133529\pi$
$822$		0			0
$823$		−	7574.02i		−	0.320794i	−0.987053	−	0.160397i	$-0.948722\pi$
$823$		−	7574.02i		−	0.320794i	0.987053	−	0.160397i	$-0.0512775\pi$
$824$	211.670	+	163.441i	0.00894887	+	0.00690987i
$825$		0			0
$826$	5687.97	+	1267.02i	0.239600	+	0.0533719i
$827$	−34129.2			−1.43505			−0.717527	−	0.696531i	$-0.754726\pi$
$827$	−34129.2			−1.43505			−0.717527	+	0.696531i	$0.754726\pi$
$828$		0			0
$829$	34706.3			1.45404			0.727021	−	0.686615i	$-0.240904\pi$
$829$	34706.3			1.45404			0.727021	+	0.686615i	$0.240904\pi$
$830$	−4399.12	−	979.922i	−0.183971	−	0.0409802i
$831$		0			0
$832$	−3622.80	−	13855.6i	−0.150959	−	0.577353i
$833$		−	2306.38i		−	0.0959321i
$834$		0			0
$835$			10245.3i			0.424614i
$836$	−7362.32	+	15705.7i	−0.304583	+	0.649751i
$837$		0			0
$838$	−8142.27	+	36552.7i	−0.335644	+	1.50679i
$839$	39467.7			1.62405			0.812025	−	0.583623i	$-0.198365\pi$
$839$	39467.7			1.62405			0.812025	+	0.583623i	$0.198365\pi$
$840$		0			0
$841$	−14503.5			−0.594676
$842$	2657.48	−	11930.1i	0.108768	−	0.488287i
$843$		0			0
$844$	−1647.68	+	3514.91i	−0.0671984	+	0.143351i
$845$		−	4215.27i		−	0.171609i
$846$		0			0
$847$		−	7827.73i		−	0.317549i
$848$	−6477.53	+	5390.87i	−0.262310	+	0.218306i
$849$		0			0
$850$	15089.4	+	3361.24i	0.608899	+	0.135635i
$851$	−255.407			−0.0102882
$852$		0			0
$853$	15904.1			0.638389			0.319194	−	0.947689i	$-0.396588\pi$
$853$	15904.1			0.638389			0.319194	+	0.947689i	$0.396588\pi$
$854$	2604.72	+	580.211i	0.104370	+	0.0232487i
$855$		0			0
$856$	18673.2	−	24183.4i	0.745605	−	0.965621i
$857$		−	21592.9i		−	0.860677i	−0.902668	−	0.430338i	$-0.858394\pi$
$857$		−	21592.9i		−	0.860677i	0.902668	−	0.430338i	$-0.141606\pi$
$858$		0			0
$859$			9787.59i			0.388764i	0.980926	+	0.194382i	$0.0622701\pi$
$859$			9787.59i			0.388764i	−0.980926	+	0.194382i	$0.937730\pi$
$860$	5651.46	+	2649.22i	0.224085	+	0.105044i
$861$		0			0
$862$	797.189	−	3578.79i	0.0314993	−	0.141408i
$863$	−15577.8			−0.614455			−0.307227	−	0.951636i	$-0.599401\pi$
$863$	−15577.8			−0.614455			−0.307227	+	0.951636i	$0.599401\pi$
$864$		0			0
$865$	11850.1			0.465800
$866$	−6484.06	+	29108.6i	−0.254431	+	1.14221i
$867$		0			0
$868$	10829.4	+	5076.46i	0.423471	+	0.198510i
$869$		−	19656.7i		−	0.767329i
$870$		0			0
$871$			4157.93i			0.161752i
$872$	7898.60	−	10229.4i	0.306744	−	0.397259i
$873$		0			0
$874$	34932.8	+	7781.43i	1.35197	+	0.301157i
$875$	−5029.52			−0.194318
$876$		0			0
$877$	9974.67			0.384060			0.192030	−	0.981389i	$-0.438493\pi$
$877$	9974.67			0.384060			0.192030	+	0.981389i	$0.438493\pi$
$878$	36438.2	+	8116.75i	1.40060	+	0.311990i
$879$		0			0
$880$	2138.12	−	1779.43i	0.0819045	−	0.0681643i
$881$			8716.38i			0.333328i	0.986014	+	0.166664i	$0.0532996\pi$
$881$			8716.38i			0.333328i	−0.986014	+	0.166664i	$0.946700\pi$
$882$		0			0
$883$			31703.2i			1.20826i	0.796884	+	0.604132i	$0.206480\pi$
$883$			31703.2i			1.20826i	−0.796884	+	0.604132i	$0.793520\pi$
$884$	4470.60	−	9536.91i	0.170093	−	0.362852i
$885$		0			0
$886$	1452.61	−	6521.13i	0.0550805	−	0.247271i
$887$	46045.2			1.74301			0.871503	−	0.490390i	$-0.163146\pi$
$887$	46045.2			1.74301			0.871503	+	0.490390i	$0.163146\pi$
$888$		0			0
$889$	−1460.04			−0.0550825
$890$	730.085	−	3277.54i	0.0274972	−	0.123442i
$891$		0			0
$892$	328.832	−	701.481i	0.0123432	−	0.0263311i
$893$		−	14281.9i		−	0.535192i
$894$		0			0
$895$			10745.1i			0.401305i
$896$	−370.595	−	10130.3i	−0.0138177	−	0.377712i
$897$		0			0
$898$	−34411.6	−	7665.32i	−1.27876	−	0.284850i
$899$	42119.4			1.56258
$900$		0			0
$901$	−6197.91			−0.229170
$902$	171.854	+	38.2812i	0.00634380	+	0.00141311i
$903$		0			0
$904$	17329.9	+	13381.3i	0.637593	+	0.492317i
$905$		−	3459.00i		−	0.127051i
$906$		0			0
$907$		−	30436.7i		−	1.11426i	−0.830425	−	0.557131i	$-0.811902\pi$
$907$		−	30436.7i		−	1.11426i	0.830425	−	0.557131i	$-0.188098\pi$
$908$	−26334.8	−	12344.9i	−0.962500	−	0.451189i
$909$		0			0
$910$	−358.809	+	1610.79i	−0.0130708	+	0.0586781i
$911$	33110.9			1.20419			0.602093	−	0.798426i	$-0.294334\pi$
$911$	33110.9			1.20419			0.602093	+	0.798426i	$0.294334\pi$
$912$		0			0
$913$	7799.76			0.282732
$914$	9127.66	−	40976.4i	0.330324	−	1.48291i
$915$		0			0
$916$	−33227.3	−	15575.9i	−1.19854	−	0.561836i
$917$		−	11763.3i		−	0.423617i
$918$		0			0
$919$			36489.9i			1.30978i	0.755723	+	0.654891i	$0.227285\pi$
$919$			36489.9i			1.30978i	−0.755723	+	0.654891i	$0.772715\pi$
$920$	−4542.82	−	3507.74i	−0.162796	−	0.125703i
$921$		0			0
$922$	−26745.0	−	5957.55i	−0.955312	−	0.212800i
$923$	−22280.7			−0.794561
$924$		0			0
$925$	−348.417			−0.0123847
$926$	41479.9	+	9239.82i	1.47205	+	0.327904i
$927$		0			0
$928$	−16324.0	−	31748.4i	−0.577437	−	1.12305i
$929$			1922.94i			0.0679113i	0.999423	+	0.0339556i	$0.0108105\pi$
$929$			1922.94i			0.0679113i	−0.999423	+	0.0339556i	$0.989190\pi$
$930$		0			0
$931$		−	7283.81i		−	0.256409i
$932$	15248.9	−	32529.7i	0.535938	−	1.14329i
$933$		0			0
$934$	−6498.57	+	29173.7i	−0.227665	+	1.02205i
$935$	2045.82			0.0715567
$936$		0			0
$937$	820.948			0.0286224			0.0143112	−	0.999898i	$-0.495444\pi$
$937$	820.948			0.0286224			0.0143112	+	0.999898i	$0.495444\pi$
$938$	−639.902	+	2872.68i	−0.0222745	+	0.0999962i
$939$		0			0
$940$	−972.147	+	2073.83i	−0.0337318	+	0.0719585i
$941$		−	2949.16i		−	0.102168i	−0.998694	−	0.0510839i	$-0.983732\pi$
$941$		−	2949.16i		−	0.102168i	0.998694	−	0.0510839i	$-0.0162676\pi$
$942$		0			0
$943$		−	363.274i		−	0.0125449i
$944$	12049.8	+	14478.7i	0.415452	+	0.499197i
$945$		0			0
$946$	−10543.3	−	2348.57i	−0.362361	−	0.0807174i
$947$	−14834.6			−0.509038			−0.254519	−	0.967068i	$-0.581917\pi$
$947$	−14834.6			−0.509038			−0.254519	+	0.967068i	$0.581917\pi$
$948$		0			0
$949$	−4568.73			−0.156277
$950$	47654.1	+	10615.1i	1.62748	+	0.362527i
$951$		0			0
$952$	4556.43	−	5900.96i	0.155120	−	0.200894i
$953$			23219.2i			0.789237i	0.918845	+	0.394619i	$0.129123\pi$
$953$			23219.2i			0.789237i	−0.918845	+	0.394619i	$0.870877\pi$
$954$		0			0
$955$			12237.5i			0.414656i
$956$	−23313.0	−	10928.4i	−0.788701	−	0.369718i
$957$		0			0
$958$	11589.0	−	52025.9i	0.390838	−	1.75457i
$959$	−10534.0			−0.354705
$960$		0			0
$961$	−15823.0			−0.531135
$962$	−51.6133	+	231.705i	−0.00172981	+	0.00776558i
$963$		0			0
$964$	−16328.7	−	7654.39i	−0.545553	−	0.255738i
$965$		−	7118.71i		−	0.237471i
$966$		0			0
$967$			8504.08i			0.282805i	0.989952	+	0.141403i	$0.0451613\pi$
$967$			8504.08i			0.282805i	−0.989952	+	0.141403i	$0.954839\pi$
$968$	15464.2	−	20027.5i	0.513470	−	0.664988i
$969$		0			0
$970$	14078.8	+	3136.11i	0.466024	+	0.103809i
$971$	−23347.8			−0.771645			−0.385822	−	0.922573i	$-0.626082\pi$
$971$	−23347.8			−0.771645			−0.385822	+	0.922573i	$0.626082\pi$
$972$		0			0
$973$	11291.1			0.372020
$974$	26399.3	+	5880.56i	0.868470	+	0.193455i
$975$		0			0
$976$	5518.01	+	6630.30i	0.180970	+	0.217449i
$977$		−	38899.9i		−	1.27382i	−0.770940	−	0.636908i	$-0.780213\pi$
$977$		−	38899.9i		−	1.27382i	0.770940	−	0.636908i	$-0.219787\pi$
$978$		0			0
$979$			5811.16i			0.189709i
$980$	−495.797	+	1057.66i	−0.0161609	+	0.0344752i
$981$		0			0
$982$	−6545.58	+	29384.8i	−0.212707	+	0.954894i
$983$	−9378.14			−0.304289			−0.152145	−	0.988358i	$-0.548618\pi$
$983$	−9378.14			−0.304289			−0.152145	+	0.988358i	$0.548618\pi$
$984$		0			0
$985$	9643.08			0.311933
$986$	5708.52	−	25627.0i	0.184377	−	0.827718i
$987$		0			0
$988$	14118.6	−	30118.6i	0.454629	−	0.969839i
$989$			22287.1i			0.716570i
$990$		0			0
$991$			30417.6i			0.975023i	0.873117	+	0.487511i	$0.162095\pi$
$991$			30417.6i			0.975023i	−0.873117	+	0.487511i	$0.837905\pi$
$992$	17678.4	+	34382.5i	0.565816	+	1.10045i
$993$		0			0
$994$	−15393.6	−	3428.99i	−0.491202	−	0.109417i
$995$	10459.0			0.333238
$996$		0			0
$997$	−42253.4			−1.34221			−0.671103	−	0.741364i	$-0.734179\pi$
$997$	−42253.4			−1.34221			−0.671103	+	0.741364i	$0.734179\pi$
$998$	20845.9	+	4643.52i	0.661189	+	0.147282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.19	yes	36
3.2	odd	2	inner	252.4.e.a.71.18	yes	36
4.3	odd	2	inner	252.4.e.a.71.17	✓	36
12.11	even	2	inner	252.4.e.a.71.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.17	✓	36	4.3	odd	2	inner
252.4.e.a.71.18	yes	36	3.2	odd	2	inner
252.4.e.a.71.19	yes	36	1.1	even	1	trivial
252.4.e.a.71.20	yes	36	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.614971 - 2.76076i) q^{2} +(-7.24362 - 3.39558i) q^{4} +2.97985i q^{5} +7.00000i q^{7} +(-13.8290 + 17.9097i) q^{8} +O(q^{10})\)	\(q+(0.614971 - 2.76076i) q^{2} +(-7.24362 - 3.39558i) q^{4} +2.97985i q^{5} +7.00000i q^{7} +(-13.8290 + 17.9097i) q^{8} +(8.22665 + 1.83252i) q^{10} -14.5861 q^{11} +27.9716 q^{13} +(19.3253 + 4.30480i) q^{14} +(40.9401 + 49.1926i) q^{16} +47.0690i q^{17} +148.649i q^{19} +(10.1183 - 21.5849i) q^{20} +(-8.97001 + 40.2687i) q^{22} +85.1221 q^{23} +116.121 q^{25} +(17.2017 - 77.2228i) q^{26} +(23.7690 - 50.7053i) q^{28} -197.212i q^{29} +213.574i q^{31} +(160.986 - 82.7739i) q^{32} +(129.946 + 28.9461i) q^{34} -20.8589 q^{35} -3.00048 q^{37} +(410.385 + 91.4149i) q^{38} +(-53.3683 - 41.2083i) q^{40} -4.26768i q^{41} +261.825i q^{43} +(105.656 + 49.5281i) q^{44} +(52.3476 - 235.002i) q^{46} -96.0780 q^{47} -49.0000 q^{49} +(71.4108 - 320.581i) q^{50} +(-202.615 - 94.9796i) q^{52} +131.677i q^{53} -43.4643i q^{55} +(-125.368 - 96.8030i) q^{56} +(-544.455 - 121.280i) q^{58} +294.327 q^{59} +134.782 q^{61} +(589.628 + 131.342i) q^{62} +(-129.517 - 495.348i) q^{64} +83.3510i q^{65} +148.648i q^{67} +(159.827 - 340.950i) q^{68} +(-12.8276 + 57.5866i) q^{70} -796.550 q^{71} -163.335 q^{73} +(-1.84521 + 8.28361i) q^{74} +(504.750 - 1076.76i) q^{76} -102.102i q^{77} +1347.64i q^{79} +(-146.586 + 121.995i) q^{80} +(-11.7821 - 2.62450i) q^{82} -534.740 q^{83} -140.259 q^{85} +(722.836 + 161.015i) q^{86} +(201.711 - 261.233i) q^{88} -398.405i q^{89} +195.801i q^{91} +(-616.592 - 289.039i) q^{92} +(-59.0852 + 265.249i) q^{94} -442.952 q^{95} +1711.36 q^{97} +(-30.1336 + 135.277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 36 * q - 24 * q^4	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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