LMFDB - Embedded newform 252.4.e.a.71.16

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			71.16
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.968530 + 2.65743i) q^{2} +(-6.12390 - 5.14761i) q^{4} -12.6551i q^{5} -7.00000i q^{7} +(19.6106 - 11.2882i) q^{8} +O(q^{10})$	\(q+(-0.968530 + 2.65743i) q^{2} +(-6.12390 - 5.14761i) q^{4} -12.6551i q^{5} -7.00000i q^{7} +(19.6106 - 11.2882i) q^{8} +(33.6300 + 12.2568i) q^{10} -54.6738 q^{11} +20.4142 q^{13} +(18.6020 + 6.77971i) q^{14} +(11.0043 + 63.0469i) q^{16} +134.981i q^{17} -9.73506i q^{19} +(-65.1434 + 77.4984i) q^{20} +(52.9532 - 145.292i) q^{22} -161.089 q^{23} -35.1511 q^{25} +(-19.7718 + 54.2495i) q^{26} +(-36.0333 + 42.8673i) q^{28} +216.995i q^{29} +240.670i q^{31} +(-178.201 - 31.8197i) q^{32} +(-358.702 - 130.733i) q^{34} -88.5856 q^{35} +72.2696 q^{37} +(25.8703 + 9.42870i) q^{38} +(-142.853 - 248.174i) q^{40} -284.443i q^{41} -402.495i q^{43} +(334.816 + 281.439i) q^{44} +(156.020 - 428.084i) q^{46} -286.218 q^{47} -49.0000 q^{49} +(34.0449 - 93.4116i) q^{50} +(-125.015 - 105.084i) q^{52} +236.625i q^{53} +691.901i q^{55} +(-79.0176 - 137.274i) q^{56} +(-576.650 - 210.166i) q^{58} +445.000 q^{59} -230.853 q^{61} +(-639.563 - 233.096i) q^{62} +(257.152 - 442.738i) q^{64} -258.344i q^{65} +697.530i q^{67} +(694.828 - 826.608i) q^{68} +(85.7978 - 235.410i) q^{70} -786.567 q^{71} -400.494 q^{73} +(-69.9953 + 192.052i) q^{74} +(-50.1123 + 59.6165i) q^{76} +382.716i q^{77} +119.537i q^{79} +(797.863 - 139.260i) q^{80} +(755.887 + 275.491i) q^{82} -1304.02 q^{83} +1708.19 q^{85} +(1069.60 + 389.828i) q^{86} +(-1072.19 + 617.170i) q^{88} +557.553i q^{89} -142.900i q^{91} +(986.494 + 829.225i) q^{92} +(277.211 - 760.605i) q^{94} -123.198 q^{95} +149.617 q^{97} +(47.4580 - 130.214i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.968530	+	2.65743i	−0.342427	+	0.939544i
$2$	−0.968530	+	2.65743i	−0.342427	+	0.939544i
$3$		0			0
$3$		0			0
$4$	−6.12390	−	5.14761i	−0.765487	−	0.643451i
$5$		−	12.6551i		−	1.13190i	−0.824438	−	0.565952i	$-0.808509\pi$
$5$		−	12.6551i		−	1.13190i	0.824438	−	0.565952i	$-0.191491\pi$
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$	19.6106	−	11.2882i	0.866674	−	0.498874i
$9$		0			0
$10$	33.6300	+	12.2568i	1.06347	+	0.387595i
$11$	−54.6738			−1.49861			−0.749307	−	0.662223i	$-0.769613\pi$
$11$	−54.6738			−1.49861			−0.749307	+	0.662223i	$0.769613\pi$
$12$		0			0
$13$	20.4142			0.435530			0.217765	−	0.976001i	$-0.430123\pi$
$13$	20.4142			0.435530			0.217765	+	0.976001i	$0.430123\pi$
$14$	18.6020	+	6.77971i	0.355114	+	0.129425i
$15$		0			0
$16$	11.0043	+	63.0469i	0.171941	+	0.985107i
$17$			134.981i			1.92574i	0.269959	+	0.962872i	$0.412990\pi$
$17$			134.981i			1.92574i	−0.269959	+	0.962872i	$0.587010\pi$
$18$		0			0
$19$		−	9.73506i		−	0.117546i	−0.998271	−	0.0587731i	$-0.981281\pi$
$19$		−	9.73506i		−	0.117546i	0.998271	−	0.0587731i	$-0.0187188\pi$
$20$	−65.1434	+	77.4984i	−0.728325	+	0.866459i
$21$		0			0
$22$	52.9532	−	145.292i	0.513166	−	1.40801i
$23$	−161.089			−1.46041			−0.730205	−	0.683228i	$-0.760576\pi$
$23$	−161.089			−1.46041			−0.730205	+	0.683228i	$0.760576\pi$
$24$		0			0
$25$	−35.1511			−0.281208
$26$	−19.7718	+	54.2495i	−0.149137	+	0.409200i
$27$		0			0
$28$	−36.0333	+	42.8673i	−0.243202	+	0.289327i
$29$			216.995i			1.38948i	0.719260	+	0.694742i	$0.244481\pi$
$29$			216.995i			1.38948i	−0.719260	+	0.694742i	$0.755519\pi$
$30$		0			0
$31$			240.670i			1.39437i	0.716890	+	0.697186i	$0.245565\pi$
$31$			240.670i			1.39437i	−0.716890	+	0.697186i	$0.754435\pi$
$32$	−178.201	−	31.8197i	−0.984429	−	0.175781i
$33$		0			0
$34$	−358.702	−	130.733i	−1.80932	−	0.659427i
$35$	−88.5856			−0.427820
$36$		0			0
$37$	72.2696			0.321109			0.160555	−	0.987027i	$-0.448672\pi$
$37$	72.2696			0.321109			0.160555	+	0.987027i	$0.448672\pi$
$38$	25.8703	+	9.42870i	0.110440	+	0.0402510i
$39$		0			0
$40$	−142.853	−	248.174i	−0.564678	−	0.980993i
$41$		−	284.443i		−	1.08347i	−0.840548	−	0.541737i	$-0.817767\pi$
$41$		−	284.443i		−	1.08347i	0.840548	−	0.541737i	$-0.182233\pi$
$42$		0			0
$43$		−	402.495i		−	1.42744i	−0.700431	−	0.713720i	$-0.747009\pi$
$43$		−	402.495i		−	1.42744i	0.700431	−	0.713720i	$-0.252991\pi$
$44$	334.816	+	281.439i	1.14717	+	0.964285i
$45$		0			0
$46$	156.020	−	428.084i	0.500084	−	1.37212i
$47$	−286.218			−0.888280			−0.444140	−	0.895957i	$-0.646491\pi$
$47$	−286.218			−0.888280			−0.444140	+	0.895957i	$0.646491\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	34.0449	−	93.4116i	0.0962934	−	0.264208i
$51$		0			0
$52$	−125.015	−	105.084i	−0.333393	−	0.280242i
$53$			236.625i			0.613262i	0.951828	+	0.306631i	$0.0992018\pi$
$53$			236.625i			0.613262i	−0.951828	+	0.306631i	$0.900798\pi$
$54$		0			0
$55$			691.901i			1.69629i
$56$	−79.0176	−	137.274i	−0.188557	−	0.327572i
$57$		0			0
$58$	−576.650	−	210.166i	−1.30548	−	0.475797i
$59$	445.000			0.981934			0.490967	−	0.871178i	$-0.336644\pi$
$59$	445.000			0.981934			0.490967	+	0.871178i	$0.336644\pi$
$60$		0			0
$61$	−230.853			−0.484553			−0.242276	−	0.970207i	$-0.577894\pi$
$61$	−230.853			−0.484553			−0.242276	+	0.970207i	$0.577894\pi$
$62$	−639.563	−	233.096i	−1.31007	−	0.477471i
$63$		0			0
$64$	257.152	−	442.738i	0.502249	−	0.864723i
$65$		−	258.344i		−	0.492978i
$66$		0			0
$67$			697.530i			1.27189i	0.771733	+	0.635947i	$0.219390\pi$
$67$			697.530i			1.27189i	−0.771733	+	0.635947i	$0.780610\pi$
$68$	694.828	−	826.608i	1.23912	−	1.47413i
$69$		0			0
$70$	85.7978	−	235.410i	0.146497	−	0.401956i
$71$	−786.567			−1.31477			−0.657383	−	0.753557i	$-0.728336\pi$
$71$	−786.567			−1.31477			−0.657383	+	0.753557i	$0.728336\pi$
$72$		0			0
$73$	−400.494			−0.642113			−0.321056	−	0.947060i	$-0.604038\pi$
$73$	−400.494			−0.642113			−0.321056	+	0.947060i	$0.604038\pi$
$74$	−69.9953	+	192.052i	−0.109957	+	0.301697i
$75$		0			0
$76$	−50.1123	+	59.6165i	−0.0756352	+	0.0899801i
$77$			382.716i			0.566423i
$78$		0			0
$79$			119.537i			0.170240i	0.996371	+	0.0851202i	$0.0271274\pi$
$79$			119.537i			0.170240i	−0.996371	+	0.0851202i	$0.972873\pi$
$80$	797.863	−	139.260i	1.11505	−	0.194621i
$81$		0			0
$82$	755.887	+	275.491i	1.01797	+	0.371011i
$83$	−1304.02			−1.72451			−0.862255	−	0.506474i	$-0.830949\pi$
$83$	−1304.02			−1.72451			−0.862255	+	0.506474i	$0.830949\pi$
$84$		0			0
$85$	1708.19			2.17976
$86$	1069.60	+	389.828i	1.34114	+	0.488794i
$87$		0			0
$88$	−1072.19	+	617.170i	−1.29881	+	0.747620i
$89$			557.553i			0.664051i	0.943270	+	0.332025i	$0.107732\pi$
$89$			557.553i			0.664051i	−0.943270	+	0.332025i	$0.892268\pi$
$90$		0			0
$91$		−	142.900i		−	0.164615i
$92$	986.494	+	829.225i	1.11793	+	0.939703i
$93$		0			0
$94$	277.211	−	760.605i	0.304171	−	0.834579i
$95$	−123.198			−0.133051
$96$		0			0
$97$	149.617			0.156611			0.0783055	−	0.996929i	$-0.475049\pi$
$97$	149.617			0.156611			0.0783055	+	0.996929i	$0.475049\pi$
$98$	47.4580	−	130.214i	0.0489182	−	0.134221i
$99$		0			0
$100$	215.261	+	180.944i	0.215261	+	0.180944i
$101$			500.841i			0.493421i	0.969089	+	0.246711i	$0.0793497\pi$
$101$			500.841i			0.493421i	−0.969089	+	0.246711i	$0.920650\pi$
$102$		0			0
$103$			779.386i			0.745584i	0.927915	+	0.372792i	$0.121600\pi$
$103$			779.386i			0.745584i	−0.927915	+	0.372792i	$0.878400\pi$
$104$	400.335	−	230.441i	0.377463	−	0.217275i
$105$		0			0
$106$	−628.814	−	229.178i	−0.576187	−	0.209998i
$107$	977.734			0.883375			0.441688	−	0.897169i	$-0.354380\pi$
$107$	977.734			0.883375			0.441688	+	0.897169i	$0.354380\pi$
$108$		0			0
$109$	−237.461			−0.208667			−0.104333	−	0.994542i	$-0.533271\pi$
$109$	−237.461			−0.208667			−0.104333	+	0.994542i	$0.533271\pi$
$110$	−1838.68	−	670.127i	−1.59374	−	0.580855i
$111$		0			0
$112$	441.328	−	77.0298i	0.372336	−	0.0649878i
$113$		−	1614.68i		−	1.34422i	−0.740453	−	0.672109i	$-0.765389\pi$
$113$		−	1614.68i		−	1.34422i	0.740453	−	0.672109i	$-0.234611\pi$
$114$		0			0
$115$			2038.60i			1.65305i
$116$	1117.01	−	1328.86i	0.894064	−	1.06363i
$117$		0			0
$118$	−430.996	+	1182.56i	−0.336241	+	0.922571i
$119$	944.865			0.727863
$120$		0			0
$121$	1658.22			1.24584
$122$	223.588	−	613.477i	0.165924	−	0.455259i
$123$		0			0
$124$	1238.87	−	1473.84i	0.897210	−	1.06737i
$125$		−	1137.05i		−	0.813604i
$126$		0			0
$127$			218.111i			0.152395i	0.997093	+	0.0761976i	$0.0242780\pi$
$127$			218.111i			0.152395i	−0.997093	+	0.0761976i	$0.975722\pi$
$128$	927.488	+	1112.17i	0.640462	+	0.767990i
$129$		0			0
$130$	686.531	+	250.214i	0.463175	+	0.168809i
$131$	711.211			0.474342			0.237171	−	0.971468i	$-0.423780\pi$
$131$	711.211			0.474342			0.237171	+	0.971468i	$0.423780\pi$
$132$		0			0
$133$	−68.1454			−0.0444283
$134$	−1853.64	−	675.579i	−1.19500	−	0.435531i
$135$		0			0
$136$	1523.69	+	2647.05i	0.960704	+	1.66899i
$137$			1593.43i			0.993695i	0.867838	+	0.496848i	$0.165509\pi$
$137$			1593.43i			0.993695i	−0.867838	+	0.496848i	$0.834491\pi$
$138$		0			0
$139$			539.813i			0.329398i	0.986344	+	0.164699i	$0.0526653\pi$
$139$			539.813i			0.329398i	−0.986344	+	0.164699i	$0.947335\pi$
$140$	542.489	+	456.004i	0.327491	+	0.275281i
$141$		0			0
$142$	761.814	−	2090.25i	0.450211	−	1.23528i
$143$	−1116.12			−0.652691
$144$		0			0
$145$	2746.09			1.57276
$146$	387.890	−	1064.28i	0.219877	−	0.603293i
$147$		0			0
$148$	−442.572	−	372.016i	−0.245805	−	0.206618i
$149$		−	979.850i		−	0.538741i	−0.963037	−	0.269371i	$-0.913184\pi$
$149$		−	979.850i		−	0.538741i	0.963037	−	0.269371i	$-0.0868156\pi$
$150$		0			0
$151$			168.456i			0.0907865i	0.998969	+	0.0453932i	$0.0144541\pi$
$151$			168.456i			0.0907865i	−0.998969	+	0.0453932i	$0.985546\pi$
$152$	−109.892	−	190.910i	−0.0586407	−	0.101874i
$153$		0			0
$154$	−1017.04	−	370.672i	−0.532179	−	0.193959i
$155$	3045.69			1.57830
$156$		0			0
$157$	−3816.10			−1.93986			−0.969929	−	0.243389i	$-0.921741\pi$
$157$	−3816.10			−1.93986			−0.969929	+	0.243389i	$0.921741\pi$
$158$	−317.662	−	115.775i	−0.159948	−	0.0582949i
$159$		0			0
$160$	−402.681	+	2255.14i	−0.198967	+	1.11428i
$161$			1127.62i			0.551983i
$162$		0			0
$163$		−	1209.54i		−	0.581219i	−0.956842	−	0.290610i	$-0.906142\pi$
$163$		−	1209.54i		−	0.581219i	0.956842	−	0.290610i	$-0.0938581\pi$
$164$	−1464.20	+	1741.90i	−0.697163	+	0.829386i
$165$		0			0
$166$	1262.98	−	3465.33i	0.590519	−	1.62025i
$167$	−1486.01			−0.688570			−0.344285	−	0.938865i	$-0.611879\pi$
$167$	−1486.01			−0.688570			−0.344285	+	0.938865i	$0.611879\pi$
$168$		0			0
$169$	−1780.26			−0.810314
$170$	−1654.44	+	4539.41i	−0.746409	+	2.04798i
$171$		0			0
$172$	−2071.89	+	2464.84i	−0.918487	+	1.09269i
$173$		−	3971.30i		−	1.74527i	−0.488371	−	0.872636i	$-0.662409\pi$
$173$		−	3971.30i		−	1.74527i	0.488371	−	0.872636i	$-0.337591\pi$
$174$		0			0
$175$			246.057i			0.106287i
$176$	−601.644	−	3447.01i	−0.257674	−	1.47630i
$177$		0			0
$178$	−1481.66	−	540.007i	−0.623905	−	0.227389i
$179$	1135.53			0.474154			0.237077	−	0.971491i	$-0.423811\pi$
$179$	1135.53			0.474154			0.237077	+	0.971491i	$0.423811\pi$
$180$		0			0
$181$	71.1317			0.0292109			0.0146055	−	0.999893i	$-0.495351\pi$
$181$	71.1317			0.0292109			0.0146055	+	0.999893i	$0.495351\pi$
$182$	379.746	+	138.403i	0.154663	+	0.0563686i
$183$		0			0
$184$	−3159.06	+	1818.41i	−1.26570	+	0.728561i
$185$		−	914.578i		−	0.363465i
$186$		0			0
$187$		−	7379.90i		−	2.88595i
$188$	1752.77	+	1473.34i	0.679967	+	0.571565i
$189$		0			0
$190$	119.321	−	327.390i	0.0455603	−	0.125007i
$191$	1042.58			0.394964			0.197482	−	0.980307i	$-0.436724\pi$
$191$	1042.58			0.394964			0.197482	+	0.980307i	$0.436724\pi$
$192$		0			0
$193$	−2859.76			−1.06658			−0.533290	−	0.845933i	$-0.679045\pi$
$193$	−2859.76			−1.06658			−0.533290	+	0.845933i	$0.679045\pi$
$194$	−144.908	+	397.596i	−0.0536279	+	0.147143i
$195$		0			0
$196$	300.071	+	252.233i	0.109355	+	0.0919216i
$197$			3286.10i			1.18845i	0.804299	+	0.594225i	$0.202541\pi$
$197$			3286.10i			1.18845i	−0.804299	+	0.594225i	$0.797459\pi$
$198$		0			0
$199$		−	2542.88i		−	0.905829i	−0.891554	−	0.452915i	$-0.850384\pi$
$199$		−	2542.88i		−	0.905829i	0.891554	−	0.452915i	$-0.149616\pi$
$200$	−689.333	+	396.793i	−0.243716	+	0.140288i
$201$		0			0
$202$	−1330.95	−	485.080i	−0.463591	−	0.168961i
$203$	1518.97			0.525175
$204$		0			0
$205$	−3599.64			−1.22639
$206$	−2071.17	−	754.859i	−0.700509	−	0.255308i
$207$		0			0
$208$	224.643	+	1287.05i	0.0748857	+	0.429044i
$209$			532.252i			0.176156i
$210$		0			0
$211$		−	3587.17i		−	1.17038i	−0.810895	−	0.585191i	$-0.801019\pi$
$211$		−	3587.17i		−	1.17038i	0.810895	−	0.585191i	$-0.198981\pi$
$212$	1218.05	−	1449.07i	0.394604	−	0.469445i
$213$		0			0
$214$	−946.965	+	2598.26i	−0.302492	+	0.829970i
$215$	−5093.60			−1.61573
$216$		0			0
$217$	1684.69			0.527023
$218$	229.988	−	631.037i	0.0714531	−	0.196052i
$219$		0			0
$220$	3561.63	−	4237.13i	1.09148	−	1.29849i
$221$			2755.53i			0.838719i
$222$		0			0
$223$		−	4638.93i		−	1.39303i	−0.717542	−	0.696515i	$-0.754733\pi$
$223$		−	4638.93i		−	1.39303i	0.717542	−	0.696515i	$-0.245267\pi$
$224$	−222.738	+	1247.41i	−0.0664389	+	0.372079i
$225$		0			0
$226$	4290.91	+	1563.87i	1.26295	+	0.460297i
$227$	−1111.26			−0.324920			−0.162460	−	0.986715i	$-0.551943\pi$
$227$	−1111.26			−0.324920			−0.162460	+	0.986715i	$0.551943\pi$
$228$		0			0
$229$	−1778.98			−0.513354			−0.256677	−	0.966497i	$-0.582628\pi$
$229$	−1778.98			−0.513354			−0.256677	+	0.966497i	$0.582628\pi$
$230$	−5417.44	−	1974.44i	−1.55311	−	0.566048i
$231$		0			0
$232$	2449.49	+	4255.41i	0.693177	+	1.20423i
$233$			3753.80i			1.05545i	0.849416	+	0.527724i	$0.176955\pi$
$233$			3753.80i			1.05545i	−0.849416	+	0.527724i	$0.823045\pi$
$234$		0			0
$235$			3622.11i			1.00545i
$236$	−2725.14	−	2290.69i	−0.751658	−	0.631827i
$237$		0			0
$238$	−915.131	+	2510.92i	−0.249240	+	0.683859i
$239$	−3976.89			−1.07633			−0.538167	−	0.842838i	$-0.680883\pi$
$239$	−3976.89			−1.07633			−0.538167	+	0.842838i	$0.680883\pi$
$240$		0			0
$241$	−3970.27			−1.06119			−0.530596	−	0.847625i	$-0.678032\pi$
$241$	−3970.27			−1.06119			−0.530596	+	0.847625i	$0.678032\pi$
$242$	−1606.04	+	4406.61i	−0.426611	+	1.17053i
$243$		0			0
$244$	1413.72	+	1188.34i	0.370919	+	0.311786i
$245$			620.099i			0.161701i
$246$		0			0
$247$		−	198.734i		−	0.0511949i
$248$	2716.73	+	4719.68i	0.695616	+	1.20847i
$249$		0			0
$250$	3021.62	+	1101.26i	0.764417	+	0.278600i
$251$	3587.05			0.902043			0.451021	−	0.892513i	$-0.351060\pi$
$251$	3587.05			0.902043			0.451021	+	0.892513i	$0.351060\pi$
$252$		0			0
$253$	8807.35			2.18859
$254$	−579.614	−	211.247i	−0.143182	−	0.0521842i
$255$		0			0
$256$	−3853.81	+	1387.57i	−0.940872	+	0.338762i
$257$		−	3810.98i		−	0.924989i	−0.886622	−	0.462495i	$-0.846954\pi$
$257$		−	3810.98i		−	0.924989i	0.886622	−	0.462495i	$-0.153046\pi$
$258$		0			0
$259$		−	505.887i		−	0.121368i
$260$	−1329.85	+	1582.07i	−0.317208	+	0.377369i
$261$		0			0
$262$	−688.829	+	1889.99i	−0.162428	+	0.445665i
$263$	7696.70			1.80456			0.902279	−	0.431152i	$-0.141893\pi$
$263$	7696.70			1.80456			0.902279	+	0.431152i	$0.141893\pi$
$264$		0			0
$265$	2994.51			0.694155
$266$	66.0009	−	181.092i	0.0152134	−	0.0417423i
$267$		0			0
$268$	3590.61	−	4271.60i	0.818401	−	0.973618i
$269$		−	4740.67i		−	1.07451i	−0.843419	−	0.537256i	$-0.819461\pi$
$269$		−	4740.67i		−	1.07451i	0.843419	−	0.537256i	$-0.180539\pi$
$270$		0			0
$271$			600.724i			0.134655i	0.997731	+	0.0673273i	$0.0214472\pi$
$271$			600.724i			0.134655i	−0.997731	+	0.0673273i	$0.978553\pi$
$272$	−8510.11	+	1485.36i	−1.89706	+	0.331115i
$273$		0			0
$274$	−4234.44	−	1543.29i	−0.933621	−	0.340268i
$275$	1921.84			0.421423
$276$		0			0
$277$	5664.46			1.22868			0.614340	−	0.789041i	$-0.289422\pi$
$277$	5664.46			1.22868			0.614340	+	0.789041i	$0.289422\pi$
$278$	−1434.52	−	522.825i	−0.309484	−	0.112795i
$279$		0			0
$280$	−1737.22	+	999.974i	−0.370780	+	0.213428i
$281$		−	3388.03i		−	0.719263i	−0.933094	−	0.359632i	$-0.882902\pi$
$281$		−	3388.03i		−	0.719263i	0.933094	−	0.359632i	$-0.117098\pi$
$282$		0			0
$283$			1247.72i			0.262082i	0.991377	+	0.131041i	$0.0418319\pi$
$283$			1247.72i			0.262082i	−0.991377	+	0.131041i	$0.958168\pi$
$284$	4816.86	+	4048.94i	1.00644	+	0.845987i
$285$		0			0
$286$	1081.00	−	2966.02i	0.223499	−	0.613233i
$287$	−1991.10			−0.409515
$288$		0			0
$289$	−13306.8			−2.70849
$290$	−2659.67	+	7297.56i	−0.538557	+	1.47768i
$291$		0			0
$292$	2452.58	+	2061.58i	0.491529	+	0.413168i
$293$			2038.06i			0.406365i	0.979141	+	0.203183i	$0.0651285\pi$
$293$			2038.06i			0.406365i	−0.979141	+	0.203183i	$0.934871\pi$
$294$		0			0
$295$		−	5631.52i		−	1.11146i
$296$	1417.25	−	815.796i	0.278297	−	0.160193i
$297$		0			0
$298$	2603.89	+	949.014i	0.506171	+	0.184480i
$299$	−3288.51			−0.636052
$300$		0			0
$301$	−2817.46			−0.539521
$302$	−447.661	−	163.155i	−0.0852979	−	0.0310878i
$303$		0			0
$304$	613.765	−	107.127i	0.115796	−	0.0202111i
$305$			2921.47i			0.548468i
$306$		0			0
$307$			8630.77i			1.60451i	0.596983	+	0.802254i	$0.296366\pi$
$307$			8630.77i			1.60451i	−0.596983	+	0.802254i	$0.703634\pi$
$308$	1970.07	−	2343.72i	0.364465	−	0.433590i
$309$		0			0
$310$	−2949.85	+	8093.72i	−0.540452	+	1.48288i
$311$	4047.39			0.737963			0.368982	−	0.929437i	$-0.379707\pi$
$311$	4047.39			0.737963			0.368982	+	0.929437i	$0.379707\pi$
$312$		0			0
$313$	3682.50			0.665007			0.332503	−	0.943102i	$-0.392107\pi$
$313$	3682.50			0.665007			0.332503	+	0.943102i	$0.392107\pi$
$314$	3696.00	−	10141.0i	0.664260	−	1.82258i
$315$		0			0
$316$	615.331	−	732.034i	0.109541	−	0.130317i
$317$			6404.69i			1.13477i	0.823451	+	0.567387i	$0.192046\pi$
$317$			6404.69i			1.13477i	−0.823451	+	0.567387i	$0.807954\pi$
$318$		0			0
$319$		−	11863.9i		−	2.08230i
$320$	−5602.89	−	3254.27i	−0.978784	−	0.568498i
$321$		0			0
$322$	−2996.59	−	1092.14i	−0.518613	−	0.189014i
$323$	1314.05			0.226364
$324$		0			0
$325$	−717.582			−0.122475
$326$	3214.28	+	1171.48i	0.546081	+	0.199025i
$327$		0			0
$328$	−3210.85	−	5578.09i	−0.540518	−	0.939020i
$329$			2003.53i			0.335738i
$330$		0			0
$331$			9148.17i			1.51912i	0.650437	+	0.759560i	$0.274586\pi$
$331$			9148.17i			1.51912i	−0.650437	+	0.759560i	$0.725414\pi$
$332$	7985.66	+	6712.56i	1.32009	+	1.10964i
$333$		0			0
$334$	1439.25	−	3948.98i	0.235785	−	0.646942i
$335$	8827.30			1.43966
$336$		0			0
$337$	3499.07			0.565597			0.282799	−	0.959179i	$-0.408737\pi$
$337$	3499.07			0.565597			0.282799	+	0.959179i	$0.408737\pi$
$338$	1724.23	−	4730.92i	0.277473	−	0.761326i
$339$		0			0
$340$	−10460.8	−	8793.11i	−1.66858	−	1.40257i
$341$		−	13158.3i		−	2.08963i
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−4543.46	−	7893.17i	−0.712113	−	1.23713i
$345$		0			0
$346$	10553.5	+	3846.32i	1.63976	+	0.597629i
$347$	2078.62			0.321574			0.160787	−	0.986989i	$-0.448597\pi$
$347$	2078.62			0.321574			0.160787	+	0.986989i	$0.448597\pi$
$348$		0			0
$349$	440.842			0.0676153			0.0338076	−	0.999428i	$-0.489237\pi$
$349$	440.842			0.0676153			0.0338076	+	0.999428i	$0.489237\pi$
$350$	−653.881	−	238.314i	−0.0998612	−	0.0363955i
$351$		0			0
$352$	9742.90	+	1739.70i	1.47528	+	0.263428i
$353$		−	9178.79i		−	1.38396i	−0.721917	−	0.691980i	$-0.756739\pi$
$353$		−	9178.79i		−	1.38396i	0.721917	−	0.691980i	$-0.243261\pi$
$354$		0			0
$355$			9954.07i			1.48819i
$356$	2870.07	−	3414.40i	0.427284	−	0.508323i
$357$		0			0
$358$	−1099.80	+	3017.59i	−0.162363	+	0.445488i
$359$	−4145.03			−0.609377			−0.304689	−	0.952452i	$-0.598552\pi$
$359$	−4145.03			−0.609377			−0.304689	+	0.952452i	$0.598552\pi$
$360$		0			0
$361$	6764.23			0.986183
$362$	−68.8932	+	189.028i	−0.0100026	+	0.0274450i
$363$		0			0
$364$	−735.591	+	875.103i	−0.105922	+	0.126011i
$365$			5068.28i			0.726811i
$366$		0			0
$367$			8939.78i			1.27153i	0.771882	+	0.635766i	$0.219316\pi$
$367$			8939.78i			1.27153i	−0.771882	+	0.635766i	$0.780684\pi$
$368$	−1772.67	−	10156.2i	−0.251105	−	1.43866i
$369$		0			0
$370$	2430.43	+	885.796i	0.341492	+	0.124460i
$371$	1656.37			0.231791
$372$		0			0
$373$	−3045.70			−0.422789			−0.211394	−	0.977401i	$-0.567800\pi$
$373$	−3045.70			−0.422789			−0.211394	+	0.977401i	$0.567800\pi$
$374$	19611.6	+	7147.66i	2.71148	+	0.988227i
$375$		0			0
$376$	−5612.91	+	3230.90i	−0.769850	+	0.443140i
$377$			4429.79i			0.605161i
$378$		0			0
$379$			2484.79i			0.336768i	0.985721	+	0.168384i	$0.0538549\pi$
$379$			2484.79i			0.336768i	−0.985721	+	0.168384i	$0.946145\pi$
$380$	754.452	+	634.175i	0.101849	+	0.0856118i
$381$		0			0
$382$	−1009.77	+	2770.57i	−0.135246	+	0.371086i
$383$	−11581.0			−1.54506			−0.772532	−	0.634976i	$-0.781010\pi$
$383$	−11581.0			−1.54506			−0.772532	+	0.634976i	$0.781010\pi$
$384$		0			0
$385$	4843.31			0.641137
$386$	2769.76	−	7599.62i	0.365226	−	1.00210i
$387$		0			0
$388$	−916.237	−	770.168i	−0.119884	−	0.100772i
$389$			1830.00i			0.238521i	0.992863	+	0.119260i	$0.0380523\pi$
$389$			1830.00i			0.238521i	−0.992863	+	0.119260i	$0.961948\pi$
$390$		0			0
$391$		−	21744.0i		−	2.81238i
$392$	−960.920	+	553.123i	−0.123811	+	0.0712677i
$393$		0			0
$394$	−8732.58	−	3182.68i	−1.11660	−	0.406958i
$395$	1512.75			0.192696
$396$		0			0
$397$	588.740			0.0744283			0.0372141	−	0.999307i	$-0.488152\pi$
$397$	588.740			0.0744283			0.0372141	+	0.999307i	$0.488152\pi$
$398$	6757.53	+	2462.86i	0.851067	+	0.310181i
$399$		0			0
$400$	−386.811	−	2216.16i	−0.0483514	−	0.277020i
$401$		−	9109.24i		−	1.13440i	−0.823580	−	0.567199i	$-0.808027\pi$
$401$		−	9109.24i		−	1.13440i	0.823580	−	0.567199i	$-0.191973\pi$
$402$		0			0
$403$			4913.08i			0.607291i
$404$	2578.13	−	3067.10i	0.317492	−	0.377708i
$405$		0			0
$406$	−1471.17	+	4036.55i	−0.179834	+	0.493425i
$407$	−3951.25			−0.481219
$408$		0			0
$409$	−13261.3			−1.60324			−0.801622	−	0.597831i	$-0.796029\pi$
$409$	−13261.3			−1.60324			−0.801622	+	0.597831i	$0.796029\pi$
$410$	3486.36	−	9565.81i	0.419949	−	1.15225i
$411$		0			0
$412$	4011.97	−	4772.88i	0.479747	−	0.570735i
$413$		−	3115.00i		−	0.371136i
$414$		0			0
$415$			16502.4i			1.95198i
$416$	−3637.83	−	649.575i	−0.428748	−	0.0765578i
$417$		0			0
$418$	−1414.42	−	515.503i	−0.165507	−	0.0603207i
$419$	−11493.5			−1.34008			−0.670039	−	0.742326i	$-0.733722\pi$
$419$	−11493.5			−1.34008			−0.670039	+	0.742326i	$0.733722\pi$
$420$		0			0
$421$	3591.89			0.415815			0.207907	−	0.978149i	$-0.433335\pi$
$421$	3591.89			0.415815			0.207907	+	0.978149i	$0.433335\pi$
$422$	9532.65	+	3474.28i	1.09963	+	0.400771i
$423$		0			0
$424$	2671.08	+	4640.35i	0.305941	+	0.531499i
$425$		−	4744.72i		−	0.541535i
$426$		0			0
$427$			1615.97i			0.183144i
$428$	−5987.55	−	5032.99i	−0.676213	−	0.568409i
$429$		0			0
$430$	4933.31	−	13535.9i	0.553268	−	1.51805i
$431$	−11259.5			−1.25835			−0.629176	−	0.777263i	$-0.716608\pi$
$431$	−11259.5			−1.25835			−0.629176	+	0.777263i	$0.716608\pi$
$432$		0			0
$433$	14951.7			1.65943			0.829717	−	0.558184i	$-0.188502\pi$
$433$	14951.7			1.65943			0.829717	+	0.558184i	$0.188502\pi$
$434$	−1631.67	+	4476.94i	−0.180467	+	0.495162i
$435$		0			0
$436$	1454.19	+	1222.36i	0.159732	+	0.134267i
$437$			1568.21i			0.171666i
$438$		0			0
$439$		−	11017.3i		−	1.19778i	−0.800831	−	0.598891i	$-0.795608\pi$
$439$		−	11017.3i		−	1.19778i	0.800831	−	0.598891i	$-0.204392\pi$
$440$	7810.34	+	13568.6i	0.846234	+	1.47013i
$441$		0			0
$442$	−7322.63	−	2668.81i	−0.788014	−	0.287200i
$443$	14953.2			1.60372			0.801860	−	0.597511i	$-0.203844\pi$
$443$	14953.2			1.60372			0.801860	+	0.597511i	$0.203844\pi$
$444$		0			0
$445$	7055.88			0.751642
$446$	12327.6	+	4492.94i	1.30881	+	0.477011i
$447$		0			0
$448$	−3099.17	−	1800.06i	−0.326835	−	0.189832i
$449$			9385.12i			0.986439i	0.869905	+	0.493219i	$0.164180\pi$
$449$			9385.12i			0.986439i	−0.869905	+	0.493219i	$0.835820\pi$
$450$		0			0
$451$			15551.5i			1.62371i
$452$	−8311.75	+	9888.15i	−0.864938	+	1.02898i
$453$		0			0
$454$	1076.29	−	2953.10i	0.111262	−	0.305277i
$455$	−1808.41			−0.186328
$456$		0			0
$457$	−7640.65			−0.782089			−0.391044	−	0.920372i	$-0.627886\pi$
$457$	−7640.65			−0.782089			−0.391044	+	0.920372i	$0.627886\pi$
$458$	1722.99	−	4727.51i	0.175786	−	0.482319i
$459$		0			0
$460$	10493.9	−	12484.2i	1.06365	−	1.26539i
$461$			8794.02i			0.888456i	0.895914	+	0.444228i	$0.146522\pi$
$461$			8794.02i			0.888456i	−0.895914	+	0.444228i	$0.853478\pi$
$462$		0			0
$463$			16696.9i			1.67596i	0.545700	+	0.837981i	$0.316264\pi$
$463$			16696.9i			1.67596i	−0.545700	+	0.837981i	$0.683736\pi$
$464$	−13680.9	+	2387.87i	−1.36879	+	0.238910i
$465$		0			0
$466$	−9975.47	−	3635.67i	−0.991641	−	0.361414i
$467$	9385.67			0.930015			0.465008	−	0.885307i	$-0.346052\pi$
$467$	9385.67			0.930015			0.465008	+	0.885307i	$0.346052\pi$
$468$		0			0
$469$	4882.71			0.480731
$470$	−9625.52	−	3508.12i	−0.944664	−	0.344293i
$471$		0			0
$472$	8726.73	−	5023.27i	0.851017	−	0.489861i
$473$			22005.9i			2.13918i
$474$		0			0
$475$			342.198i			0.0330550i
$476$	−5786.26	−	4863.80i	−0.557170	−	0.468344i
$477$		0			0
$478$	3851.74	−	10568.3i	0.368566	−	1.01126i
$479$	−9831.94			−0.937856			−0.468928	−	0.883236i	$-0.655360\pi$
$479$	−9831.94			−0.937856			−0.468928	+	0.883236i	$0.655360\pi$
$480$		0			0
$481$	1475.33			0.139853
$482$	3845.33	−	10550.7i	0.363381	−	0.997038i
$483$		0			0
$484$	−10154.8	−	8535.86i	−0.953678	−	0.801640i
$485$		−	1893.41i		−	0.177269i
$486$		0			0
$487$			2622.06i			0.243977i	0.992531	+	0.121989i	$0.0389272\pi$
$487$			2622.06i			0.243977i	−0.992531	+	0.121989i	$0.961073\pi$
$488$	−4527.17	+	2605.92i	−0.419950	+	0.241731i
$489$		0			0
$490$	−1647.87	−	600.585i	−0.151925	−	0.0553707i
$491$	−5883.02			−0.540727			−0.270363	−	0.962758i	$-0.587144\pi$
$491$	−5883.02			−0.540727			−0.270363	+	0.962758i	$0.587144\pi$
$492$		0			0
$493$	−29290.2			−2.67579
$494$	528.122	+	192.480i	0.0480998	+	0.0175305i
$495$		0			0
$496$	−15173.5	+	2648.39i	−1.37361	+	0.239750i
$497$			5505.97i			0.496935i
$498$		0			0
$499$			1441.12i			0.129285i	0.997908	+	0.0646426i	$0.0205907\pi$
$499$			1441.12i			0.129285i	−0.997908	+	0.0646426i	$0.979409\pi$
$500$	−5853.07	+	6963.15i	−0.523514	+	0.622803i
$501$		0			0
$502$	−3474.17	+	9532.35i	−0.308884	+	0.847509i
$503$	−8788.30			−0.779028			−0.389514	−	0.921021i	$-0.627357\pi$
$503$	−8788.30			−0.779028			−0.389514	+	0.921021i	$0.627357\pi$
$504$		0			0
$505$	6338.18			0.558506
$506$	−8530.19	+	23405.0i	−0.749433	+	2.05628i
$507$		0			0
$508$	1122.75	−	1335.69i	0.0980588	−	0.116657i
$509$			10472.3i			0.911941i	0.889995	+	0.455970i	$0.150708\pi$
$509$			10472.3i			0.911941i	−0.889995	+	0.455970i	$0.849292\pi$
$510$		0			0
$511$			2803.46i			0.242696i
$512$	45.1682	−	11585.1i	0.00389877	−	0.999992i
$513$		0			0
$514$	10127.4	+	3691.05i	0.869068	+	0.316741i
$515$	9863.19			0.843930
$516$		0			0
$517$	15648.6			1.33119
$518$	1344.36	+	489.967i	0.114031	+	0.0415597i
$519$		0			0
$520$	−2916.24	−	5066.28i	−0.245934	−	0.427252i
$521$		−	9614.56i		−	0.808487i	−0.914651	−	0.404243i	$-0.867535\pi$
$521$		−	9614.56i		−	0.808487i	0.914651	−	0.404243i	$-0.132465\pi$
$522$		0			0
$523$			14841.7i			1.24088i	0.784252	+	0.620442i	$0.213047\pi$
$523$			14841.7i			1.24088i	−0.784252	+	0.620442i	$0.786953\pi$
$524$	−4355.38	−	3661.03i	−0.363103	−	0.305216i
$525$		0			0
$526$	−7454.49	+	20453.5i	−0.617930	+	1.69546i
$527$	−32485.8			−2.68520
$528$		0			0
$529$	13782.8			1.13280
$530$	−2900.27	+	7957.70i	−0.237697	+	0.652189i
$531$		0			0
$532$	417.316	+	350.786i	0.0340093	+	0.0285874i
$533$		−	5806.68i		−	0.471886i
$534$		0			0
$535$		−	12373.3i		−	0.999897i
$536$	7873.88	+	13679.0i	0.634515	+	1.10232i
$537$		0			0
$538$	12598.0	+	4591.48i	1.00955	+	0.367942i
$539$	2679.01			0.214088
$540$		0			0
$541$	13197.9			1.04884			0.524418	−	0.851461i	$-0.324283\pi$
$541$	13197.9			1.04884			0.524418	+	0.851461i	$0.324283\pi$
$542$	−1596.38	−	581.819i	−0.126514	−	0.0461094i
$543$		0			0
$544$	4295.05	−	24053.7i	0.338509	−	1.89576i
$545$			3005.09i			0.236191i
$546$		0			0
$547$		−	9310.59i		−	0.727774i	−0.931443	−	0.363887i	$-0.881449\pi$
$547$		−	9310.59i		−	0.727774i	0.931443	−	0.363887i	$-0.118551\pi$
$548$	8202.37	−	9758.03i	0.639394	−	0.760661i
$549$		0			0
$550$	−1861.36	+	5107.16i	−0.144307	+	0.395946i
$551$	2112.46			0.163328
$552$		0			0
$553$	836.760			0.0643448
$554$	−5486.20	+	15052.9i	−0.420734	+	1.15440i
$555$		0			0
$556$	2778.75	−	3305.76i	0.211952	−	0.252150i
$557$		−	4384.04i		−	0.333496i	−0.986000	−	0.166748i	$-0.946673\pi$
$557$		−	4384.04i		−	0.333496i	0.986000	−	0.166748i	$-0.0533267\pi$
$558$		0			0
$559$		−	8216.62i		−	0.621693i
$560$	−974.818	−	5585.04i	−0.0735600	−	0.421448i
$561$		0			0
$562$	9003.47	+	3281.41i	0.675780	+	0.246295i
$563$	−11361.4			−0.850494			−0.425247	−	0.905077i	$-0.639813\pi$
$563$	−11361.4			−0.850494			−0.425247	+	0.905077i	$0.639813\pi$
$564$		0			0
$565$	−20433.9			−1.52153
$566$	−3315.73	−	1208.45i	−0.246238	−	0.0897440i
$567$		0			0
$568$	−15425.1	+	8878.95i	−1.13947	+	0.655902i
$569$		−	21724.4i		−	1.60058i	−0.599610	−	0.800292i	$-0.704678\pi$
$569$		−	21724.4i		−	1.60058i	0.599610	−	0.800292i	$-0.295322\pi$
$570$		0			0
$571$		−	10763.6i		−	0.788864i	−0.918925	−	0.394432i	$-0.870941\pi$
$571$		−	10763.6i		−	0.788864i	0.918925	−	0.394432i	$-0.129059\pi$
$572$	6835.02	+	5745.36i	0.499627	+	0.419975i
$573$		0			0
$574$	1928.44	−	5291.21i	0.140229	−	0.384758i
$575$	5662.46			0.410680
$576$		0			0
$577$	5730.04			0.413422			0.206711	−	0.978402i	$-0.433724\pi$
$577$	5730.04			0.413422			0.206711	+	0.978402i	$0.433724\pi$
$578$	12888.0	−	35361.9i	0.927460	−	2.54475i
$579$		0			0
$580$	−16816.8	−	14135.8i	−1.20393	−	1.01200i
$581$			9128.11i			0.651804i
$582$		0			0
$583$		−	12937.2i		−	0.919044i
$584$	−7853.92	+	4520.87i	−0.556503	+	0.320333i
$585$		0			0
$586$	−5416.02	−	1973.93i	−0.381798	−	0.139150i
$587$	24254.9			1.70546			0.852731	−	0.522350i	$-0.174944\pi$
$587$	24254.9			1.70546			0.852731	+	0.522350i	$0.174944\pi$
$588$		0			0
$589$	2342.93			0.163903
$590$	14965.4	+	5454.29i	1.04426	+	0.380593i
$591$		0			0
$592$	795.273	+	4556.37i	0.0552120	+	0.316327i
$593$			20835.8i			1.44287i	0.692480	+	0.721437i	$0.256518\pi$
$593$			20835.8i			1.44287i	−0.692480	+	0.721437i	$0.743482\pi$
$594$		0			0
$595$		−	11957.3i		−	0.823871i
$596$	−5043.88	+	6000.50i	−0.346654	+	0.412399i
$597$		0			0
$598$	3185.03	−	8739.00i	0.217802	−	0.597599i
$599$	−831.154			−0.0566946			−0.0283473	−	0.999598i	$-0.509024\pi$
$599$	−831.154			−0.0566946			−0.0283473	+	0.999598i	$0.509024\pi$
$600$		0			0
$601$	−18473.9			−1.25385			−0.626925	−	0.779079i	$-0.715687\pi$
$601$	−18473.9			−1.25385			−0.626925	+	0.779079i	$0.715687\pi$
$602$	2728.80	−	7487.22i	0.184747	−	0.506904i
$603$		0			0
$604$	867.146	−	1031.61i	0.0584167	−	0.0694959i
$605$		−	20984.9i		−	1.41018i
$606$		0			0
$607$			6159.06i			0.411843i	0.978569	+	0.205921i	$0.0660191\pi$
$607$			6159.06i			0.411843i	−0.978569	+	0.205921i	$0.933981\pi$
$608$	−309.767	+	1734.80i	−0.0206624	+	0.115716i
$609$		0			0
$610$	−7763.60	−	2829.53i	−0.515310	−	0.187810i
$611$	−5842.92			−0.386873
$612$		0			0
$613$	−27005.1			−1.77932			−0.889661	−	0.456622i	$-0.849059\pi$
$613$	−27005.1			−1.77932			−0.889661	+	0.456622i	$0.849059\pi$
$614$	−22935.7	−	8359.16i	−1.50751	−	0.549427i
$615$		0			0
$616$	4320.19	+	7505.30i	0.282574	+	0.490904i
$617$			5795.62i			0.378157i	0.981962	+	0.189079i	$0.0605501\pi$
$617$			5795.62i			0.378157i	−0.981962	+	0.189079i	$0.939450\pi$
$618$		0			0
$619$			5231.26i			0.339680i	0.985472	+	0.169840i	$0.0543251\pi$
$619$			5231.26i			0.339680i	−0.985472	+	0.169840i	$0.945675\pi$
$620$	−18651.5	−	15678.0i	−1.20817	−	1.01556i
$621$		0			0
$622$	−3920.02	+	10755.7i	−0.252699	+	0.693349i
$623$	3902.87			0.250988
$624$		0			0
$625$	−18783.3			−1.20213
$626$	−3566.61	+	9785.99i	−0.227716	+	0.624803i
$627$		0			0
$628$	23369.4	+	19643.8i	1.48494	+	1.24820i
$629$			9755.01i			0.618374i
$630$		0			0
$631$		−	23803.5i		−	1.50175i	−0.660446	−	0.750873i	$-0.729633\pi$
$631$		−	23803.5i		−	1.50175i	0.660446	−	0.750873i	$-0.270367\pi$
$632$	1349.36	+	2344.20i	0.0849285	+	0.147543i
$633$		0			0
$634$	−17020.0	−	6203.14i	−1.06617	−	0.388577i
$635$	2760.21			0.172497
$636$		0			0
$637$	−1000.30			−0.0622186
$638$	31527.6	+	11490.6i	1.95641	+	0.713036i
$639$		0			0
$640$	14074.6	−	11737.4i	0.869292	−	0.724942i
$641$		−	8168.04i		−	0.503305i	−0.967818	−	0.251652i	$-0.919026\pi$
$641$		−	8168.04i		−	0.503305i	0.967818	−	0.251652i	$-0.0809740\pi$
$642$		0			0
$643$			17627.8i			1.08114i	0.841299	+	0.540570i	$0.181791\pi$
$643$			17627.8i			1.08114i	−0.841299	+	0.540570i	$0.818209\pi$
$644$	5804.57	−	6905.46i	0.355174	−	0.422536i
$645$		0			0
$646$	−1272.69	+	3491.99i	−0.0775131	+	0.212679i
$647$	−28417.7			−1.72676			−0.863380	−	0.504554i	$-0.831657\pi$
$647$	−28417.7			−1.72676			−0.863380	+	0.504554i	$0.831657\pi$
$648$		0			0
$649$	−24329.8			−1.47154
$650$	695.000	−	1906.93i	0.0419387	−	0.115070i
$651$		0			0
$652$	−6226.25	+	7407.12i	−0.373986	+	0.444916i
$653$		−	9922.03i		−	0.594608i	−0.954783	−	0.297304i	$-0.903913\pi$
$653$		−	9922.03i		−	0.594608i	0.954783	−	0.297304i	$-0.0960875\pi$
$654$		0			0
$655$		−	9000.43i		−	0.536910i
$656$	17933.2	−	3130.08i	1.06734	−	0.186294i
$657$		0			0
$658$	−5324.24	−	1940.48i	−0.315441	−	0.114966i
$659$	31590.6			1.86737			0.933685	−	0.358096i	$-0.116574\pi$
$659$	31590.6			1.86737			0.933685	+	0.358096i	$0.116574\pi$
$660$		0			0
$661$	−23653.3			−1.39184			−0.695922	−	0.718118i	$-0.745004\pi$
$661$	−23653.3			−1.39184			−0.695922	+	0.718118i	$0.745004\pi$
$662$	−24310.6	−	8860.28i	−1.42728	−	0.520188i
$663$		0			0
$664$	−25572.5	+	14720.0i	−1.49459	+	0.860313i
$665$			862.386i			0.0502886i
$666$		0			0
$667$		−	34955.6i		−	2.02922i
$668$	9100.19	+	7649.41i	0.527091	+	0.443061i
$669$		0			0
$670$	−8549.51	+	23458.0i	−0.492980	+	1.35263i
$671$	12621.6			0.726158
$672$		0			0
$673$	27532.0			1.57694			0.788471	−	0.615072i	$-0.210873\pi$
$673$	27532.0			1.57694			0.788471	+	0.615072i	$0.210873\pi$
$674$	−3388.95	+	9298.54i	−0.193676	+	0.531404i
$675$		0			0
$676$	10902.1	+	9164.08i	0.620285	+	0.521397i
$677$			968.353i			0.0549732i	0.999622	+	0.0274866i	$0.00875035\pi$
$677$			968.353i			0.0549732i	−0.999622	+	0.0274866i	$0.991250\pi$
$678$		0			0
$679$		−	1047.32i		−	0.0591934i
$680$	33498.7	−	19282.5i	1.88914	−	1.08743i
$681$		0			0
$682$	34967.3	+	12744.2i	1.96330	+	0.715545i
$683$	7733.59			0.433261			0.216631	−	0.976254i	$-0.430493\pi$
$683$	7733.59			0.433261			0.216631	+	0.976254i	$0.430493\pi$
$684$		0			0
$685$	20165.0			1.12477
$686$	−911.499	−	332.206i	−0.0507306	−	0.0184893i
$687$		0			0
$688$	25376.0	−	4429.16i	1.40618	−	0.245436i
$689$			4830.51i			0.267094i
$690$		0			0
$691$		−	2771.04i		−	0.152554i	−0.997087	−	0.0762772i	$-0.975697\pi$
$691$		−	2771.04i		−	0.152554i	0.997087	−	0.0762772i	$-0.0243034\pi$
$692$	−20442.7	+	24319.8i	−1.12300	+	1.33598i
$693$		0			0
$694$	−2013.21	+	5523.80i	−0.110116	+	0.302133i
$695$	6831.38			0.372847
$696$		0			0
$697$	38394.3			2.08650
$698$	−426.969	+	1171.51i	−0.0231533	+	0.0635275i
$699$		0			0
$700$	1266.61	−	1506.83i	0.0683904	−	0.0813612i
$701$			17578.8i			0.947136i	0.880757	+	0.473568i	$0.157034\pi$
$701$			17578.8i			0.947136i	−0.880757	+	0.473568i	$0.842966\pi$
$702$		0			0
$703$		−	703.549i		−	0.0377452i
$704$	−14059.4	+	24206.2i	−0.752678	+	1.29589i
$705$		0			0
$706$	24392.0	+	8889.94i	1.30029	+	0.473905i
$707$	3505.89			0.186496
$708$		0			0
$709$	25369.8			1.34384			0.671921	−	0.740623i	$-0.265469\pi$
$709$	25369.8			1.34384			0.671921	+	0.740623i	$0.265469\pi$
$710$	−26452.3	−	9640.82i	−1.39822	−	0.509596i
$711$		0			0
$712$	6293.79	+	10934.0i	0.331278	+	0.575516i
$713$		−	38769.3i		−	2.03636i
$714$		0			0
$715$			14124.6i			0.738785i
$716$	−6953.87	−	5845.26i	−0.362959	−	0.305095i
$717$		0			0
$718$	4014.59	−	11015.1i	0.208667	−	0.572537i
$719$	17275.9			0.896079			0.448039	−	0.894014i	$-0.352122\pi$
$719$	17275.9			0.896079			0.448039	+	0.894014i	$0.352122\pi$
$720$		0			0
$721$	5455.70			0.281804
$722$	−6551.36	+	17975.5i	−0.337696	+	0.926563i
$723$		0			0
$724$	−435.603	−	366.158i	−0.0223606	−	0.0187958i
$725$		−	7627.61i		−	0.390734i
$726$		0			0
$727$			33464.3i			1.70718i	0.520942	+	0.853592i	$0.325581\pi$
$727$			33464.3i			1.70718i	−0.520942	+	0.853592i	$0.674419\pi$
$728$	−1613.08	−	2802.35i	−0.0821221	−	0.142667i
$729$		0			0
$730$	−13468.6	−	4908.78i	−0.682871	−	0.248880i
$731$	54329.1			2.74888
$732$		0			0
$733$	234.049			0.0117937			0.00589686	−	0.999983i	$-0.498123\pi$
$733$	234.049			0.0117937			0.00589686	+	0.999983i	$0.498123\pi$
$734$	−23756.9	−	8658.44i	−1.19466	−	0.435407i
$735$		0			0
$736$	28706.2	+	5125.82i	1.43767	+	0.256712i
$737$		−	38136.6i		−	1.90608i
$738$		0			0
$739$			6761.49i			0.336570i	0.985738	+	0.168285i	$0.0538229\pi$
$739$			6761.49i			0.336570i	−0.985738	+	0.168285i	$0.946177\pi$
$740$	−4707.89	+	5600.78i	−0.233872	+	0.278228i
$741$		0			0
$742$	−1604.25	+	4401.70i	−0.0793717	+	0.217778i
$743$	−3237.46			−0.159853			−0.0799266	−	0.996801i	$-0.525469\pi$
$743$	−3237.46			−0.159853			−0.0799266	+	0.996801i	$0.525469\pi$
$744$		0			0
$745$	−12400.1			−0.609804
$746$	2949.85	−	8093.73i	0.144774	−	0.397229i
$747$		0			0
$748$	−37988.9	+	45193.8i	−1.85697	+	2.20916i
$749$		−	6844.14i		−	0.333884i
$750$		0			0
$751$		−	3412.67i		−	0.165819i	−0.996557	−	0.0829096i	$-0.973579\pi$
$751$		−	3412.67i		−	0.165819i	0.996557	−	0.0829096i	$-0.0264213\pi$
$752$	−3149.62	−	18045.1i	−0.152732	−	0.875051i
$753$		0			0
$754$	−11771.9	−	4290.39i	−0.568576	−	0.207224i
$755$	2131.82			0.102762
$756$		0			0
$757$	6746.45			0.323915			0.161958	−	0.986798i	$-0.448219\pi$
$757$	6746.45			0.323915			0.161958	+	0.986798i	$0.448219\pi$
$758$	−6603.16	−	2406.59i	−0.316408	−	0.115319i
$759$		0			0
$760$	−2415.99	+	1390.69i	−0.115312	+	0.0663757i
$761$			3036.45i			0.144640i	0.997381	+	0.0723202i	$0.0230403\pi$
$761$			3036.45i			0.144640i	−0.997381	+	0.0723202i	$0.976960\pi$
$762$		0			0
$763$			1662.23i			0.0788686i
$764$	−6384.63	−	5366.77i	−0.302340	−	0.254140i
$765$		0			0
$766$	11216.5	−	30775.6i	0.529072	−	1.45166i
$767$	9084.34			0.427662
$768$		0			0
$769$	−34980.1			−1.64033			−0.820166	−	0.572126i	$-0.806119\pi$
$769$	−34980.1			−1.64033			−0.820166	+	0.572126i	$0.806119\pi$
$770$	−4690.89	+	12870.8i	−0.219543	+	0.602377i
$771$		0			0
$772$	17512.9	+	14720.9i	0.816453	+	0.686292i
$773$		−	30696.6i		−	1.42830i	−0.699991	−	0.714152i	$-0.746812\pi$
$773$		−	30696.6i		−	1.42830i	0.699991	−	0.714152i	$-0.253188\pi$
$774$		0			0
$775$		−	8459.79i		−	0.392109i
$776$	2934.07	−	1688.91i	0.135731	−	0.0781292i
$777$		0			0
$778$	−4863.09	−	1772.41i	−0.224101	−	0.0816760i
$779$	−2769.07			−0.127358
$780$		0			0
$781$	43004.6			1.97033
$782$	57783.1	+	21059.7i	2.64235	+	0.963034i
$783$		0			0
$784$	−539.208	−	3089.30i	−0.0245631	−	0.140730i
$785$			48293.0i			2.19573i
$786$		0			0
$787$		−	3052.05i		−	0.138239i	−0.997608	−	0.0691194i	$-0.977981\pi$
$787$		−	3052.05i		−	0.138239i	0.997608	−	0.0691194i	$-0.0220189\pi$
$788$	16915.5	−	20123.7i	0.764709	−	0.909743i
$789$		0			0
$790$	−1465.15	+	4020.04i	−0.0659843	+	0.181046i
$791$	−11302.8			−0.508066
$792$		0			0
$793$	−4712.69			−0.211037
$794$	−570.213	+	1564.54i	−0.0254863	+	0.0699287i
$795$		0			0
$796$	−13089.8	+	15572.3i	−0.582857	+	0.693401i
$797$		−	1234.09i		−	0.0548478i	−0.999624	−	0.0274239i	$-0.991270\pi$
$797$		−	1234.09i		−	0.0548478i	0.999624	−	0.0274239i	$-0.00873040\pi$
$798$		0			0
$799$		−	38633.9i		−	1.71060i
$800$	6263.94	+	1118.50i	0.276830	+	0.0494311i
$801$		0			0
$802$	24207.2	+	8822.58i	1.06582	+	0.388449i
$803$	21896.5			0.962279
$804$		0			0
$805$	14270.2			0.624792
$806$	−13056.2	−	4758.47i	−0.570577	−	0.207953i
$807$		0			0
$808$	5653.61	+	9821.80i	0.246155	+	0.427636i
$809$			3433.48i			0.149215i	0.997213	+	0.0746074i	$0.0237704\pi$
$809$			3433.48i			0.149215i	−0.997213	+	0.0746074i	$0.976230\pi$
$810$		0			0
$811$		−	6937.93i		−	0.300399i	−0.988656	−	0.150199i	$-0.952008\pi$
$811$		−	6937.93i		−	0.300399i	0.988656	−	0.150199i	$-0.0479916\pi$
$812$	−9302.00	−	7819.05i	−0.402015	−	0.337925i
$813$		0			0
$814$	3826.91	−	10500.2i	0.164783	−	0.452127i
$815$	−15306.9			−0.657885
$816$		0			0
$817$	−3918.31			−0.167790
$818$	12843.9	−	35240.9i	0.548994	−	1.50632i
$819$		0			0
$820$	22043.9	+	18529.6i	0.938786	+	0.789122i
$821$			13149.1i			0.558961i	0.960151	+	0.279480i	$0.0901622\pi$
$821$			13149.1i			0.558961i	−0.960151	+	0.279480i	$0.909838\pi$
$822$		0			0
$823$			954.970i			0.0404474i	0.999795	+	0.0202237i	$0.00643784\pi$
$823$			954.970i			0.0404474i	−0.999795	+	0.0202237i	$0.993562\pi$
$824$	8797.89	+	15284.2i	0.371953	+	0.646179i
$825$		0			0
$826$	8277.91	+	3016.97i	0.348699	+	0.127087i
$827$	43123.8			1.81325			0.906627	−	0.421933i	$-0.138648\pi$
$827$	43123.8			1.81325			0.906627	+	0.421933i	$0.138648\pi$
$828$		0			0
$829$	−31968.7			−1.33935			−0.669674	−	0.742655i	$-0.733566\pi$
$829$	−31968.7			−1.33935			−0.669674	+	0.742655i	$0.733566\pi$
$830$	−43854.1	−	15983.1i	−1.83397	−	0.668411i
$831$		0			0
$832$	5249.55	−	9038.16i	0.218745	−	0.376613i
$833$		−	6614.06i		−	0.275106i
$834$		0			0
$835$			18805.6i			0.779395i
$836$	2739.83	−	3259.46i	0.113348	−	0.134845i
$837$		0			0
$838$	11131.8	−	30543.1i	0.458879	−	1.25906i
$839$	−42957.3			−1.76764			−0.883820	−	0.467828i	$-0.845037\pi$
$839$	−42957.3			−1.76764			−0.883820	+	0.467828i	$0.845037\pi$
$840$		0			0
$841$	−22697.9			−0.930663
$842$	−3478.85	+	9545.21i	−0.142386	+	0.390676i
$843$		0			0
$844$	−18465.3	+	21967.4i	−0.753084	+	0.895913i
$845$			22529.3i			0.917198i
$846$		0			0
$847$		−	11607.5i		−	0.470885i
$848$	−14918.4	+	2603.88i	−0.604129	+	0.105445i
$849$		0			0
$850$	12608.8	+	4595.40i	0.508797	+	0.185436i
$851$	−11641.9			−0.468951
$852$		0			0
$853$	21646.3			0.868881			0.434440	−	0.900701i	$-0.356946\pi$
$853$	21646.3			0.868881			0.434440	+	0.900701i	$0.356946\pi$
$854$	−4294.34	−	1565.12i	−0.172072	−	0.0627134i
$855$		0			0
$856$	19174.0	−	11036.9i	0.765599	−	0.440693i
$857$		−	356.948i		−	0.0142277i	−0.999975	−	0.00711383i	$-0.997736\pi$
$857$		−	356.948i		−	0.0142277i	0.999975	−	0.00711383i	$-0.00226442\pi$
$858$		0			0
$859$		−	1149.84i		−	0.0456717i	−0.999739	−	0.0228358i	$-0.992730\pi$
$859$		−	1149.84i		−	0.0456717i	0.999739	−	0.0228358i	$-0.00726951\pi$
$860$	31192.7	+	26219.9i	1.23682	+	1.03964i
$861$		0			0
$862$	10905.1	−	29921.3i	0.430894	−	1.18228i
$863$	2969.14			0.117116			0.0585578	−	0.998284i	$-0.481350\pi$
$863$	2969.14			0.117116			0.0585578	+	0.998284i	$0.481350\pi$
$864$		0			0
$865$	−50257.1			−1.97548
$866$	−14481.2	+	39733.3i	−0.568236	+	1.55911i
$867$		0			0
$868$	−10316.9	−	8672.11i	−0.403429	−	0.339114i
$869$		−	6535.55i		−	0.255125i
$870$		0			0
$871$			14239.5i			0.553948i
$872$	−4656.76	+	2680.52i	−0.180846	+	0.104098i
$873$		0			0
$874$	−4167.42	−	1518.86i	−0.161287	−	0.0587830i
$875$	−7959.32			−0.307513
$876$		0			0
$877$	5168.95			0.199023			0.0995114	−	0.995036i	$-0.468272\pi$
$877$	5168.95			0.199023			0.0995114	+	0.995036i	$0.468272\pi$
$878$	29277.7	+	10670.6i	1.12537	+	0.410153i
$879$		0			0
$880$	−43622.2	+	7613.85i	−1.67103	+	0.291662i
$881$			23562.0i			0.901047i	0.892764	+	0.450524i	$0.148763\pi$
$881$			23562.0i			0.901047i	−0.892764	+	0.450524i	$0.851237\pi$
$882$		0			0
$883$		−	2688.60i		−	0.102467i	−0.998687	−	0.0512337i	$-0.983685\pi$
$883$		−	2688.60i		−	0.102467i	0.998687	−	0.0512337i	$-0.0163153\pi$
$884$	14184.4	−	16874.6i	0.539675	−	0.642029i
$885$		0			0
$886$	−14482.6	+	39737.1i	−0.549158	+	1.50677i
$887$	14185.3			0.536976			0.268488	−	0.963283i	$-0.413476\pi$
$887$	14185.3			0.536976			0.268488	+	0.963283i	$0.413476\pi$
$888$		0			0
$889$	1526.77			0.0576000
$890$	−6833.84	+	18750.5i	−0.257383	+	0.706201i
$891$		0			0
$892$	−23879.4	+	28408.3i	−0.896347	+	1.06635i
$893$			2786.35i			0.104414i
$894$		0			0
$895$		−	14370.2i		−	0.536697i
$896$	7785.18	−	6492.41i	0.290273	−	0.242072i
$897$		0			0
$898$	−24940.3	−	9089.77i	−0.926803	−	0.337783i
$899$	−52224.2			−1.93746
$900$		0			0
$901$	−31939.8			−1.18099
$902$	−41327.2	−	15062.1i	−1.52555	−	0.556003i
$903$		0			0
$904$	−18226.9	−	31664.9i	−0.670595	−	1.16500i
$905$		−	900.177i		−	0.0330640i
$906$		0			0
$907$		−	20699.4i		−	0.757786i	−0.925441	−	0.378893i	$-0.876305\pi$
$907$		−	20699.4i		−	0.757786i	0.925441	−	0.378893i	$-0.123695\pi$
$908$	6805.24	+	5720.33i	0.248722	+	0.209070i
$909$		0			0
$910$	1751.50	−	4805.72i	0.0638039	−	0.175064i
$911$	−9933.52			−0.361265			−0.180632	−	0.983551i	$-0.557814\pi$
$911$	−9933.52			−0.361265			−0.180632	+	0.983551i	$0.557814\pi$
$912$		0			0
$913$	71295.4			2.58438
$914$	7400.20	−	20304.5i	0.267808	−	0.734807i
$915$		0			0
$916$	10894.3	+	9157.47i	0.392966	+	0.330318i
$917$		−	4978.48i		−	0.179284i
$918$		0			0
$919$		−	25808.6i		−	0.926386i	−0.886258	−	0.463193i	$-0.846704\pi$
$919$		−	25808.6i		−	0.926386i	0.886258	−	0.463193i	$-0.153296\pi$
$920$	23012.2	+	39978.1i	0.824661	+	1.43265i
$921$		0			0
$922$	−23369.5	−	8517.27i	−0.834744	−	0.304231i
$923$	−16057.2			−0.572620
$924$		0			0
$925$	−2540.35			−0.0902987
$926$	−44370.9	−	16171.4i	−1.57464	−	0.573895i
$927$		0			0
$928$	6904.73	−	38668.7i	0.244245	−	1.36785i
$929$		−	13319.7i		−	0.470404i	−0.971946	−	0.235202i	$-0.924425\pi$
$929$		−	13319.7i		−	0.470404i	0.971946	−	0.235202i	$-0.0755752\pi$
$930$		0			0
$931$			477.018i			0.0167923i
$932$	19323.1	−	22987.9i	0.679130	−	0.807932i
$933$		0			0
$934$	−9090.31	+	24941.8i	−0.318462	+	0.873790i
$935$	−93393.3			−3.26662
$936$		0			0
$937$	−29536.0			−1.02977			−0.514887	−	0.857258i	$-0.672166\pi$
$937$	−29536.0			−1.02977			−0.514887	+	0.857258i	$0.672166\pi$
$938$	−4729.05	+	12975.5i	−0.164615	+	0.451668i
$939$		0			0
$940$	18645.2	−	22181.4i	0.646957	−	0.769658i
$941$		−	22509.8i		−	0.779809i	−0.920855	−	0.389904i	$-0.872508\pi$
$941$		−	22509.8i		−	0.779809i	0.920855	−	0.389904i	$-0.127492\pi$
$942$		0			0
$943$			45820.7i			1.58232i
$944$	4896.90	+	28055.9i	0.168835	+	0.967310i
$945$		0			0
$946$	−58479.2	−	21313.4i	−2.00986	−	0.732514i
$947$	11623.6			0.398854			0.199427	−	0.979913i	$-0.436092\pi$
$947$	11623.6			0.398854			0.199427	+	0.979913i	$0.436092\pi$
$948$		0			0
$949$	−8175.77			−0.279659
$950$	−909.367	−	331.429i	−0.0310566	−	0.0113189i
$951$		0			0
$952$	18529.4	−	10665.9i	0.630820	−	0.363112i
$953$		−	14400.8i		−	0.489493i	−0.969587	−	0.244746i	$-0.921295\pi$
$953$		−	14400.8i		−	0.489493i	0.969587	−	0.244746i	$-0.0787047\pi$
$954$		0			0
$955$		−	13193.9i		−	0.447062i
$956$	24354.1	+	20471.5i	0.823920	+	0.692568i
$957$		0			0
$958$	9522.54	−	26127.7i	0.321147	−	0.881157i
$959$	11154.0			0.375581
$960$		0			0
$961$	−28130.8			−0.944273
$962$	−1428.90	+	3920.59i	−0.0478894	+	0.131398i
$963$		0			0
$964$	24313.5	+	20437.4i	0.812330	+	0.682826i
$965$			36190.5i			1.20727i
$966$		0			0
$967$			29295.7i			0.974237i	0.873336	+	0.487118i	$0.161952\pi$
$967$			29295.7i			0.974237i	−0.873336	+	0.487118i	$0.838048\pi$
$968$	32518.7	−	18718.4i	1.07974	−	0.621520i
$969$		0			0
$970$	5031.61	+	1833.83i	0.166552	+	0.0607017i
$971$	44558.1			1.47264			0.736322	−	0.676632i	$-0.236561\pi$
$971$	44558.1			1.47264			0.736322	+	0.676632i	$0.236561\pi$
$972$		0			0
$973$	3778.69			0.124501
$974$	−6967.96	−	2539.55i	−0.229228	−	0.0835445i
$975$		0			0
$976$	−2540.37	−	14554.6i	−0.0833147	−	0.477336i
$977$		−	25091.0i		−	0.821630i	−0.911719	−	0.410815i	$-0.865244\pi$
$977$		−	25091.0i		−	0.821630i	0.911719	−	0.410815i	$-0.134756\pi$
$978$		0			0
$979$		−	30483.5i		−	0.995156i
$980$	3192.03	−	3797.42i	0.104046	−	0.123780i
$981$		0			0
$982$	5697.88	−	15633.7i	0.185160	−	0.508037i
$983$	13047.8			0.423359			0.211679	−	0.977339i	$-0.432107\pi$
$983$	13047.8			0.423359			0.211679	+	0.977339i	$0.432107\pi$
$984$		0			0
$985$	41585.8			1.34521
$986$	28368.4	−	77836.7i	0.916263	−	2.51402i
$987$		0			0
$988$	−1023.00	+	1217.03i	−0.0329414	+	0.0391890i
$989$			64837.6i			2.08465i
$990$		0			0
$991$		−	18841.9i		−	0.603970i	−0.953313	−	0.301985i	$-0.902351\pi$
$991$		−	18841.9i		−	0.603970i	0.953313	−	0.301985i	$-0.0976492\pi$
$992$	7658.04	−	42887.5i	0.245104	−	1.37266i
$993$		0			0
$994$	−14631.7	−	5332.70i	−0.466892	−	0.170164i
$995$	−32180.4			−1.02531
$996$		0			0
$997$	−32804.6			−1.04206			−0.521030	−	0.853539i	$-0.674452\pi$
$997$	−32804.6			−1.04206			−0.521030	+	0.853539i	$0.674452\pi$
$998$	−3829.67	−	1395.77i	−0.121469	−	0.0442707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.16	yes	36
3.2	odd	2	inner	252.4.e.a.71.21	yes	36
4.3	odd	2	inner	252.4.e.a.71.22	yes	36
12.11	even	2	inner	252.4.e.a.71.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.15	✓	36	12.11	even	2	inner
252.4.e.a.71.16	yes	36	1.1	even	1	trivial
252.4.e.a.71.21	yes	36	3.2	odd	2	inner
252.4.e.a.71.22	yes	36	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.968530 + 2.65743i) q^{2} +(-6.12390 - 5.14761i) q^{4} -12.6551i q^{5} -7.00000i q^{7} +(19.6106 - 11.2882i) q^{8} +O(q^{10})\)	\(q+(-0.968530 + 2.65743i) q^{2} +(-6.12390 - 5.14761i) q^{4} -12.6551i q^{5} -7.00000i q^{7} +(19.6106 - 11.2882i) q^{8} +(33.6300 + 12.2568i) q^{10} -54.6738 q^{11} +20.4142 q^{13} +(18.6020 + 6.77971i) q^{14} +(11.0043 + 63.0469i) q^{16} +134.981i q^{17} -9.73506i q^{19} +(-65.1434 + 77.4984i) q^{20} +(52.9532 - 145.292i) q^{22} -161.089 q^{23} -35.1511 q^{25} +(-19.7718 + 54.2495i) q^{26} +(-36.0333 + 42.8673i) q^{28} +216.995i q^{29} +240.670i q^{31} +(-178.201 - 31.8197i) q^{32} +(-358.702 - 130.733i) q^{34} -88.5856 q^{35} +72.2696 q^{37} +(25.8703 + 9.42870i) q^{38} +(-142.853 - 248.174i) q^{40} -284.443i q^{41} -402.495i q^{43} +(334.816 + 281.439i) q^{44} +(156.020 - 428.084i) q^{46} -286.218 q^{47} -49.0000 q^{49} +(34.0449 - 93.4116i) q^{50} +(-125.015 - 105.084i) q^{52} +236.625i q^{53} +691.901i q^{55} +(-79.0176 - 137.274i) q^{56} +(-576.650 - 210.166i) q^{58} +445.000 q^{59} -230.853 q^{61} +(-639.563 - 233.096i) q^{62} +(257.152 - 442.738i) q^{64} -258.344i q^{65} +697.530i q^{67} +(694.828 - 826.608i) q^{68} +(85.7978 - 235.410i) q^{70} -786.567 q^{71} -400.494 q^{73} +(-69.9953 + 192.052i) q^{74} +(-50.1123 + 59.6165i) q^{76} +382.716i q^{77} +119.537i q^{79} +(797.863 - 139.260i) q^{80} +(755.887 + 275.491i) q^{82} -1304.02 q^{83} +1708.19 q^{85} +(1069.60 + 389.828i) q^{86} +(-1072.19 + 617.170i) q^{88} +557.553i q^{89} -142.900i q^{91} +(986.494 + 829.225i) q^{92} +(277.211 - 760.605i) q^{94} -123.198 q^{95} +149.617 q^{97} +(47.4580 - 130.214i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 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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