LMFDB - Embedded newform 384.4.k.b.287.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(95,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("384.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.k (of order $4$, degree $2$, not 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:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.20
Character	$\chi$	$=$	384.287
Dual form			384.4.k.b.95.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.81196 + 1.96089i) q^{3} +(6.30133 - 6.30133i) q^{5} +24.6728 q^{7} +(19.3098 + 18.8714i) q^{9} +O(q^{10})$	\(q+(4.81196 + 1.96089i) q^{3} +(6.30133 - 6.30133i) q^{5} +24.6728 q^{7} +(19.3098 + 18.8714i) q^{9} +(-40.4669 - 40.4669i) q^{11} +(47.3131 - 47.3131i) q^{13} +(42.6779 - 17.9655i) q^{15} -41.7727i q^{17} +(-10.6193 - 10.6193i) q^{19} +(118.725 + 48.3807i) q^{21} +53.4222i q^{23} +45.5866i q^{25} +(55.9134 + 128.673i) q^{27} +(-105.268 - 105.268i) q^{29} -3.14755i q^{31} +(-115.374 - 274.076i) q^{33} +(155.472 - 155.472i) q^{35} +(-42.1756 - 42.1756i) q^{37} +(320.444 - 134.893i) q^{39} -152.486 q^{41} +(-221.247 + 221.247i) q^{43} +(240.593 - 2.76270i) q^{45} +381.086 q^{47} +265.749 q^{49} +(81.9116 - 201.008i) q^{51} +(294.048 - 294.048i) q^{53} -509.990 q^{55} +(-30.2765 - 71.9231i) q^{57} +(445.445 + 445.445i) q^{59} +(-21.8473 + 21.8473i) q^{61} +(476.429 + 465.611i) q^{63} -596.270i q^{65} +(572.215 + 572.215i) q^{67} +(-104.755 + 257.065i) q^{69} +612.406i q^{71} -331.477i q^{73} +(-89.3901 + 219.361i) q^{75} +(-998.433 - 998.433i) q^{77} +427.462i q^{79} +(16.7398 + 728.808i) q^{81} +(-245.236 + 245.236i) q^{83} +(-263.224 - 263.224i) q^{85} +(-300.128 - 712.967i) q^{87} +188.997 q^{89} +(1167.35 - 1167.35i) q^{91} +(6.17200 - 15.1459i) q^{93} -133.832 q^{95} +1474.45 q^{97} +(-17.7419 - 1545.08i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) $ 44 * q + 2 * q^3 - 8 * q^7	$ 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.81196	+	1.96089i	0.926061	+	0.377373i
$3$	4.81196	+	1.96089i	0.926061	+	0.377373i
$4$		0			0
$5$	6.30133	−	6.30133i	0.563608	−	0.563608i	−0.366723	−	0.930330i	$-0.619520\pi$
$5$	6.30133	−	6.30133i	0.563608	−	0.563608i	0.930330	+	0.366723i	$0.119520\pi$
$6$		0			0
$7$	24.6728			1.33221			0.666104	−	0.745859i	$-0.267961\pi$
$7$	24.6728			1.33221			0.666104	+	0.745859i	$0.267961\pi$
$8$		0			0
$9$	19.3098	+	18.8714i	0.715179	+	0.698941i
$10$		0			0
$11$	−40.4669	−	40.4669i	−1.10920	−	1.10920i	−0.993255	−	0.115946i	$-0.963010\pi$
$11$	−40.4669	−	40.4669i	−1.10920	−	1.10920i	−0.115946	−	0.993255i	$-0.536990\pi$
$12$		0			0
$13$	47.3131	−	47.3131i	1.00941	−	1.00941i	0.00945153	−	0.999955i	$-0.496991\pi$
$13$	47.3131	−	47.3131i	1.00941	−	1.00941i	0.999955	−	0.00945153i	$-0.00300856\pi$
$14$		0			0
$15$	42.6779	−	17.9655i	0.734626	−	0.309245i
$16$		0			0
$17$		−	41.7727i		−	0.595963i	−0.954572	−	0.297982i	$-0.903687\pi$
$17$		−	41.7727i		−	0.595963i	0.954572	−	0.297982i	$-0.0963134\pi$
$18$		0			0
$19$	−10.6193	−	10.6193i	−0.128223	−	0.128223i	0.640083	−	0.768306i	$-0.278900\pi$
$19$	−10.6193	−	10.6193i	−0.128223	−	0.128223i	−0.768306	+	0.640083i	$0.778900\pi$
$20$		0			0
$21$	118.725	+	48.3807i	1.23371	+	0.502739i
$22$		0			0
$23$			53.4222i			0.484317i	0.970237	+	0.242158i	$0.0778554\pi$
$23$			53.4222i			0.484317i	−0.970237	+	0.242158i	$0.922145\pi$
$24$		0			0
$25$			45.5866i			0.364692i
$26$		0			0
$27$	55.9134	+	128.673i	0.398538	+	0.917152i
$28$		0			0
$29$	−105.268	−	105.268i	−0.674064	−	0.674064i	0.284586	−	0.958650i	$-0.408144\pi$
$29$	−105.268	−	105.268i	−0.674064	−	0.674064i	−0.958650	+	0.284586i	$0.908144\pi$
$30$		0			0
$31$		−	3.14755i		−	0.0182361i	−0.999958	−	0.00911803i	$-0.997098\pi$
$31$		−	3.14755i		−	0.0182361i	0.999958	−	0.00911803i	$-0.00290240\pi$
$32$		0			0
$33$	−115.374	−	274.076i	−0.608606	−	1.44577i
$34$		0			0
$35$	155.472	−	155.472i	0.750843	−	0.750843i
$36$		0			0
$37$	−42.1756	−	42.1756i	−0.187395	−	0.187395i	0.607174	−	0.794569i	$-0.292303\pi$
$37$	−42.1756	−	42.1756i	−0.187395	−	0.187395i	−0.794569	+	0.607174i	$0.792303\pi$
$38$		0			0
$39$	320.444	−	134.893i	1.31570	−	0.553850i
$40$		0			0
$41$	−152.486			−0.580836			−0.290418	−	0.956900i	$-0.593794\pi$
$41$	−152.486			−0.580836			−0.290418	+	0.956900i	$0.593794\pi$
$42$		0			0
$43$	−221.247	+	221.247i	−0.784647	+	0.784647i	−0.980611	−	0.195964i	$-0.937216\pi$
$43$	−221.247	+	221.247i	−0.784647	+	0.784647i	0.195964	+	0.980611i	$0.437216\pi$
$44$		0			0
$45$	240.593	−	2.76270i	0.797009	−	0.00915197i
$46$		0			0
$47$	381.086			1.18270			0.591352	−	0.806414i	$-0.298594\pi$
$47$	381.086			1.18270			0.591352	+	0.806414i	$0.298594\pi$
$48$		0			0
$49$	265.749			0.774779
$50$		0			0
$51$	81.9116	−	201.008i	0.224900	−	0.551898i
$52$		0			0
$53$	294.048	−	294.048i	0.762088	−	0.762088i	−0.214612	−	0.976699i	$-0.568849\pi$
$53$	294.048	−	294.048i	0.762088	−	0.762088i	0.976699	+	0.214612i	$0.0688486\pi$
$54$		0			0
$55$	−509.990			−1.25031
$56$		0			0
$57$	−30.2765	−	71.9231i	−0.0703547	−	0.167131i
$58$		0			0
$59$	445.445	+	445.445i	0.982916	+	0.982916i	0.999857	−	0.0169404i	$-0.00539256\pi$
$59$	445.445	+	445.445i	0.982916	+	0.982916i	−0.0169404	+	0.999857i	$0.505393\pi$
$60$		0			0
$61$	−21.8473	+	21.8473i	−0.0458568	+	0.0458568i	−0.729663	−	0.683807i	$-0.760323\pi$
$61$	−21.8473	+	21.8473i	−0.0458568	+	0.0458568i	0.683807	+	0.729663i	$0.260323\pi$
$62$		0			0
$63$	476.429	+	465.611i	0.952768	+	0.931135i
$64$		0			0
$65$		−	596.270i		−	1.13782i
$66$		0			0
$67$	572.215	+	572.215i	1.04339	+	1.04339i	0.999015	+	0.0443759i	$0.0141299\pi$
$67$	572.215	+	572.215i	1.04339	+	1.04339i	0.0443759	+	0.999015i	$0.485870\pi$
$68$		0			0
$69$	−104.755	+	257.065i	−0.182768	+	0.448507i
$70$		0			0
$71$			612.406i			1.02365i	0.859089	+	0.511825i	$0.171031\pi$
$71$			612.406i			1.02365i	−0.859089	+	0.511825i	$0.828969\pi$
$72$		0			0
$73$		−	331.477i		−	0.531458i	−0.964048	−	0.265729i	$-0.914387\pi$
$73$		−	331.477i		−	0.531458i	0.964048	−	0.265729i	$-0.0856126\pi$
$74$		0			0
$75$	−89.3901	+	219.361i	−0.137625	+	0.337728i
$76$		0			0
$77$	−998.433	−	998.433i	−1.47769	−	1.47769i
$78$		0			0
$79$			427.462i			0.608775i	0.952548	+	0.304388i	$0.0984518\pi$
$79$			427.462i			0.608775i	−0.952548	+	0.304388i	$0.901548\pi$
$80$		0			0
$81$	16.7398	+	728.808i	0.0229628	+	0.999736i
$82$		0			0
$83$	−245.236	+	245.236i	−0.324314	+	0.324314i	−0.850420	−	0.526105i	$-0.823652\pi$
$83$	−245.236	+	245.236i	−0.324314	+	0.324314i	0.526105	+	0.850420i	$0.323652\pi$
$84$		0			0
$85$	−263.224	−	263.224i	−0.335889	−	0.335889i
$86$		0			0
$87$	−300.128	−	712.967i	−0.369851	−	0.878599i
$88$		0			0
$89$	188.997			0.225097			0.112548	−	0.993646i	$-0.464099\pi$
$89$	188.997			0.225097			0.112548	+	0.993646i	$0.464099\pi$
$90$		0			0
$91$	1167.35	−	1167.35i	1.34474	−	1.34474i
$92$		0			0
$93$	6.17200	−	15.1459i	0.00688179	−	0.0168877i
$94$		0			0
$95$	−133.832			−0.144535
$96$		0			0
$97$	1474.45			1.54338			0.771689	−	0.636001i	$-0.219412\pi$
$97$	1474.45			1.54338			0.771689	+	0.636001i	$0.219412\pi$
$98$		0			0
$99$	−17.7419	−	1545.08i	−0.0180114	−	1.56854i
$100$		0			0
$101$	223.136	−	223.136i	0.219830	−	0.219830i	−0.588597	−	0.808427i	$-0.700319\pi$
$101$	223.136	−	223.136i	0.219830	−	0.219830i	0.808427	+	0.588597i	$0.200319\pi$
$102$		0			0
$103$	−217.914			−0.208463			−0.104232	−	0.994553i	$-0.533238\pi$
$103$	−217.914			−0.208463			−0.104232	+	0.994553i	$0.533238\pi$
$104$		0			0
$105$	1052.99	−	443.260i	0.978675	−	0.411979i
$106$		0			0
$107$	−335.407	−	335.407i	−0.303038	−	0.303038i	0.539163	−	0.842201i	$-0.318740\pi$
$107$	−335.407	−	335.407i	−0.303038	−	0.303038i	−0.842201	+	0.539163i	$0.818740\pi$
$108$		0			0
$109$	−1032.70	+	1032.70i	−0.907477	+	0.907477i	−0.996068	−	0.0885914i	$-0.971763\pi$
$109$	−1032.70	+	1032.70i	−0.907477	+	0.907477i	0.0885914	+	0.996068i	$0.471763\pi$
$110$		0			0
$111$	−120.245	−	285.649i	−0.102822	−	0.244257i
$112$		0			0
$113$		−	1010.24i		−	0.841020i	−0.907288	−	0.420510i	$-0.861851\pi$
$113$		−	1010.24i		−	0.841020i	0.907288	−	0.420510i	$-0.138149\pi$
$114$		0			0
$115$	336.630	+	336.630i	0.272965	+	0.272965i
$116$		0			0
$117$	1806.47	−	20.7435i	1.42742	−	0.0163909i
$118$		0			0
$119$		−	1030.65i		−	0.793947i
$120$		0			0
$121$			1944.14i			1.46066i
$122$		0			0
$123$	−733.755	−	299.008i	−0.537890	−	0.219192i
$124$		0			0
$125$	1074.92	+	1074.92i	0.769151	+	0.769151i
$126$		0			0
$127$		−	1504.32i		−	1.05108i	−0.850769	−	0.525540i	$-0.823863\pi$
$127$		−	1504.32i		−	1.05108i	0.850769	−	0.525540i	$-0.176137\pi$
$128$		0			0
$129$	−1498.47	+	630.790i	−1.02274	+	0.430527i
$130$		0			0
$131$	−1515.05	+	1515.05i	−1.01046	+	1.01046i	−0.0105196	+	0.999945i	$0.503349\pi$
$131$	−1515.05	+	1515.05i	−1.01046	+	1.01046i	−0.999945	+	0.0105196i	$0.996651\pi$
$132$		0			0
$133$	−262.009	−	262.009i	−0.170820	−	0.170820i
$134$		0			0
$135$	1163.14	+	458.481i	0.741533	+	0.292294i
$136$		0			0
$137$	−2462.36			−1.53557			−0.767787	−	0.640706i	$-0.778642\pi$
$137$	−2462.36			−1.53557			−0.767787	+	0.640706i	$0.778642\pi$
$138$		0			0
$139$	−782.125	+	782.125i	−0.477259	+	0.477259i	−0.904254	−	0.426995i	$-0.859572\pi$
$139$	−782.125	+	782.125i	−0.477259	+	0.477259i	0.426995	+	0.904254i	$0.359572\pi$
$140$		0			0
$141$	1833.77	+	747.266i	1.09526	+	0.446320i
$142$		0			0
$143$	−3829.23			−2.23927
$144$		0			0
$145$	−1326.66			−0.759816
$146$		0			0
$147$	1278.77	+	521.104i	0.717493	+	0.292381i
$148$		0			0
$149$	−2532.54	+	2532.54i	−1.39244	+	1.39244i	−0.572616	+	0.819824i	$0.694071\pi$
$149$	−2532.54	+	2532.54i	−1.39244	+	1.39244i	−0.819824	+	0.572616i	$0.805929\pi$
$150$		0			0
$151$	571.667			0.308090			0.154045	−	0.988064i	$-0.450770\pi$
$151$	571.667			0.308090			0.154045	+	0.988064i	$0.450770\pi$
$152$		0			0
$153$	788.310	−	806.624i	0.416543	−	0.426220i
$154$		0			0
$155$	−19.8338	−	19.8338i	−0.0102780	−	0.0102780i
$156$		0			0
$157$	1664.95	−	1664.95i	0.846353	−	0.846353i	−0.143323	−	0.989676i	$-0.545779\pi$
$157$	1664.95	−	1664.95i	0.846353	−	0.846353i	0.989676	+	0.143323i	$0.0457788\pi$
$158$		0			0
$159$	1991.54	−	838.352i	0.993331	−	0.418149i
$160$		0			0
$161$			1318.08i			0.645211i
$162$		0			0
$163$	−1893.19	−	1893.19i	−0.909731	−	0.909731i	0.0865194	−	0.996250i	$-0.472426\pi$
$163$	−1893.19	−	1893.19i	−0.909731	−	0.909731i	−0.996250	+	0.0865194i	$0.972426\pi$
$164$		0			0
$165$	−2454.05	−	1000.03i	−1.15786	−	0.471833i
$166$		0			0
$167$			2441.42i			1.13127i	0.824655	+	0.565636i	$0.191369\pi$
$167$			2441.42i			1.13127i	−0.824655	+	0.565636i	$0.808631\pi$
$168$		0			0
$169$		−	2280.06i		−	1.03780i
$170$		0			0
$171$	−4.65585	−	405.460i	−0.00208212	−	0.181323i
$172$		0			0
$173$	−856.168	−	856.168i	−0.376262	−	0.376262i	0.493490	−	0.869751i	$-0.335721\pi$
$173$	−856.168	−	856.168i	−0.376262	−	0.376262i	−0.869751	+	0.493490i	$0.835721\pi$
$174$		0			0
$175$			1124.75i			0.485846i
$176$		0			0
$177$	1270.00	+	3016.93i	0.539315	+	1.28117i
$178$		0			0
$179$	−2706.69	+	2706.69i	−1.13021	+	1.13021i	−0.140068	+	0.990142i	$0.544732\pi$
$179$	−2706.69	+	2706.69i	−1.13021	+	1.13021i	−0.990142	+	0.140068i	$0.955268\pi$
$180$		0			0
$181$	155.849	+	155.849i	0.0640008	+	0.0640008i	0.738383	−	0.674382i	$-0.235590\pi$
$181$	155.849	+	155.849i	0.0640008	+	0.0640008i	−0.674382	+	0.738383i	$0.735590\pi$
$182$		0			0
$183$	−147.969	+	62.2882i	−0.0597713	+	0.0251611i
$184$		0			0
$185$	−531.524			−0.211235
$186$		0			0
$187$	−1690.41	+	1690.41i	−0.661043	+	0.661043i
$188$		0			0
$189$	1379.54	+	3174.72i	0.530936	+	1.22184i
$190$		0			0
$191$	−1193.27			−0.452054			−0.226027	−	0.974121i	$-0.572574\pi$
$191$	−1193.27			−0.452054			−0.226027	+	0.974121i	$0.572574\pi$
$192$		0			0
$193$	−5048.50			−1.88290			−0.941448	−	0.337158i	$-0.890534\pi$
$193$	−5048.50			−1.88290			−0.941448	+	0.337158i	$0.890534\pi$
$194$		0			0
$195$	1169.22	−	2869.23i	0.429382	−	1.05369i
$196$		0			0
$197$	544.245	−	544.245i	0.196832	−	0.196832i	−0.601809	−	0.798640i	$-0.705553\pi$
$197$	544.245	−	544.245i	0.196832	−	0.196832i	0.798640	+	0.601809i	$0.205553\pi$
$198$		0			0
$199$	609.004			0.216941			0.108470	−	0.994100i	$-0.465405\pi$
$199$	609.004			0.216941			0.108470	+	0.994100i	$0.465405\pi$
$200$		0			0
$201$	1631.42	+	3875.52i	0.572496	+	1.35999i
$202$		0			0
$203$	−2597.27	−	2597.27i	−0.897994	−	0.897994i
$204$		0			0
$205$	−960.863	+	960.863i	−0.327364	+	0.327364i
$206$		0			0
$207$	−1008.15	+	1031.57i	−0.338509	+	0.346373i
$208$		0			0
$209$			859.463i			0.284451i
$210$		0			0
$211$	407.803	+	407.803i	0.133053	+	0.133053i	0.770497	−	0.637444i	$-0.220008\pi$
$211$	407.803	+	407.803i	0.133053	+	0.133053i	−0.637444	+	0.770497i	$0.720008\pi$
$212$		0			0
$213$	−1200.86	+	2946.87i	−0.386298	+	0.947964i
$214$		0			0
$215$			2788.30i			0.884466i
$216$		0			0
$217$		−	77.6591i		−	0.0242942i
$218$		0			0
$219$	649.989	−	1595.05i	0.200558	−	0.492163i
$220$		0			0
$221$	−1976.40	−	1976.40i	−0.601569	−	0.601569i
$222$		0			0
$223$		−	2957.32i		−	0.888057i	−0.896013	−	0.444028i	$-0.853549\pi$
$223$		−	2957.32i		−	0.888057i	0.896013	−	0.444028i	$-0.146451\pi$
$224$		0			0
$225$	−860.283	+	880.269i	−0.254899	+	0.260821i
$226$		0			0
$227$	254.883	−	254.883i	0.0745250	−	0.0745250i	−0.668862	−	0.743387i	$-0.733218\pi$
$227$	254.883	−	254.883i	0.0745250	−	0.0745250i	0.743387	+	0.668862i	$0.233218\pi$
$228$		0			0
$229$	−349.739	−	349.739i	−0.100923	−	0.100923i	0.654842	−	0.755765i	$-0.272735\pi$
$229$	−349.739	−	349.739i	−0.100923	−	0.100923i	−0.755765	+	0.654842i	$0.772735\pi$
$230$		0			0
$231$	−2846.60	−	6762.23i	−0.810790	−	1.92607i
$232$		0			0
$233$	1869.42			0.525621			0.262810	−	0.964847i	$-0.415351\pi$
$233$	1869.42			0.525621			0.262810	+	0.964847i	$0.415351\pi$
$234$		0			0
$235$	2401.35	−	2401.35i	0.666581	−	0.666581i
$236$		0			0
$237$	−838.205	+	2056.93i	−0.229735	+	0.563763i
$238$		0			0
$239$	2120.63			0.573943			0.286972	−	0.957939i	$-0.407351\pi$
$239$	2120.63			0.573943			0.286972	+	0.957939i	$0.407351\pi$
$240$		0			0
$241$	3096.26			0.827584			0.413792	−	0.910372i	$-0.364204\pi$
$241$	3096.26			0.827584			0.413792	+	0.910372i	$0.364204\pi$
$242$		0			0
$243$	−1348.56	+	3539.82i	−0.356009	+	0.934483i
$244$		0			0
$245$	1674.57	−	1674.57i	0.436671	−	0.436671i
$246$		0			0
$247$	−1004.87			−0.258859
$248$		0			0
$249$	−1660.94	+	699.183i	−0.422723	+	0.177948i
$250$		0			0
$251$	2393.97	+	2393.97i	0.602017	+	0.602017i	0.940847	−	0.338830i	$-0.110031\pi$
$251$	2393.97	+	2393.97i	0.602017	+	0.602017i	−0.338830	+	0.940847i	$0.610031\pi$
$252$		0			0
$253$	2161.83	−	2161.83i	0.537205	−	0.537205i
$254$		0			0
$255$	−750.468	−	1782.77i	−0.184299	−	0.437810i
$256$		0			0
$257$		−	3582.50i		−	0.869535i	−0.900543	−	0.434768i	$-0.856831\pi$
$257$		−	3582.50i		−	0.869535i	0.900543	−	0.434768i	$-0.143169\pi$
$258$		0			0
$259$	−1040.59	−	1040.59i	−0.249649	−	0.249649i
$260$		0			0
$261$	−46.1530	−	4019.28i	−0.0109456	−	0.953208i
$262$		0			0
$263$			2196.24i			0.514928i	0.966288	+	0.257464i	$0.0828869\pi$
$263$			2196.24i			0.514928i	−0.966288	+	0.257464i	$0.917113\pi$
$264$		0			0
$265$		−	3705.79i		−	0.859037i
$266$		0			0
$267$	909.443	+	370.601i	0.208453	+	0.0849454i
$268$		0			0
$269$	−64.1764	−	64.1764i	−0.0145461	−	0.0145461i	0.699796	−	0.714342i	$-0.253274\pi$
$269$	−64.1764	−	64.1764i	−0.0145461	−	0.0145461i	−0.714342	+	0.699796i	$0.753274\pi$
$270$		0			0
$271$			3627.40i			0.813095i	0.913630	+	0.406548i	$0.133268\pi$
$271$			3627.40i			0.813095i	−0.913630	+	0.406548i	$0.866732\pi$
$272$		0			0
$273$	7906.27	−	3328.19i	1.75278	−	0.737843i
$274$		0			0
$275$	1844.75	−	1844.75i	0.404518	−	0.404518i
$276$		0			0
$277$	3476.10	+	3476.10i	0.754001	+	0.754001i	0.975223	−	0.221222i	$-0.0710046\pi$
$277$	3476.10	+	3476.10i	0.754001	+	0.754001i	−0.221222	+	0.975223i	$0.571005\pi$
$278$		0			0
$279$	59.3988	−	60.7788i	0.0127459	−	0.0130420i
$280$		0			0
$281$	−5597.90			−1.18841			−0.594204	−	0.804314i	$-0.702533\pi$
$281$	−5597.90			−1.18841			−0.594204	+	0.804314i	$0.702533\pi$
$282$		0			0
$283$	−236.800	+	236.800i	−0.0497395	+	0.0497395i	−0.731539	−	0.681800i	$-0.761198\pi$
$283$	−236.800	+	236.800i	−0.0497395	+	0.0497395i	0.681800	+	0.731539i	$0.261198\pi$
$284$		0			0
$285$	−643.993	−	262.429i	−0.133849	−	0.0545437i
$286$		0			0
$287$	−3762.26			−0.773795
$288$		0			0
$289$	3168.04			0.644828
$290$		0			0
$291$	7094.98	+	2891.23i	1.42926	+	0.582429i
$292$		0			0
$293$	3077.11	−	3077.11i	0.613537	−	0.613537i	−0.330329	−	0.943866i	$-0.607160\pi$
$293$	3077.11	−	3077.11i	0.613537	−	0.613537i	0.943866	+	0.330329i	$0.107160\pi$
$294$		0			0
$295$	5613.79			1.10796
$296$		0			0
$297$	2944.35	−	7469.63i	0.575247	−	1.45937i
$298$		0			0
$299$	2527.57	+	2527.57i	0.488873	+	0.488873i
$300$		0			0
$301$	−5458.79	+	5458.79i	−1.04531	+	1.04531i
$302$		0			0
$303$	1511.26	−	636.175i	0.286534	−	0.120618i
$304$		0			0
$305$			275.334i			0.0516905i
$306$		0			0
$307$	−1749.92	−	1749.92i	−0.325321	−	0.325321i	0.525483	−	0.850804i	$-0.323885\pi$
$307$	−1749.92	−	1749.92i	−0.325321	−	0.325321i	−0.850804	+	0.525483i	$0.823885\pi$
$308$		0			0
$309$	−1048.59	−	427.305i	−0.193050	−	0.0786685i
$310$		0			0
$311$		−	7073.49i		−	1.28971i	−0.764304	−	0.644856i	$-0.776917\pi$
$311$		−	7073.49i		−	1.28971i	0.764304	−	0.644856i	$-0.223083\pi$
$312$		0			0
$313$			9046.73i			1.63371i	0.576843	+	0.816855i	$0.304284\pi$
$313$			9046.73i			1.63371i	−0.576843	+	0.816855i	$0.695716\pi$
$314$		0			0
$315$	5936.10	−	68.1636i	1.06178	−	0.0121923i
$316$		0			0
$317$	−4477.40	−	4477.40i	−0.793300	−	0.793300i	0.188729	−	0.982029i	$-0.439563\pi$
$317$	−4477.40	−	4477.40i	−0.793300	−	0.793300i	−0.982029	+	0.188729i	$0.939563\pi$
$318$		0			0
$319$			8519.77i			1.49535i
$320$		0			0
$321$	−956.269	−	2271.66i	−0.166273	−	0.394990i
$322$		0			0
$323$	−443.599	+	443.599i	−0.0764164	+	0.0764164i
$324$		0			0
$325$	2156.84	+	2156.84i	0.368123	+	0.368123i
$326$		0			0
$327$	−6994.33	+	2944.31i	−1.18284	+	0.497922i
$328$		0			0
$329$	9402.47			1.57561
$330$		0			0
$331$	−1060.84	+	1060.84i	−0.176160	+	0.176160i	−0.789680	−	0.613519i	$-0.789753\pi$
$331$	−1060.84	+	1060.84i	−0.176160	+	0.176160i	0.613519	+	0.789680i	$0.289753\pi$
$332$		0			0
$333$	−18.4911	−	1610.32i	−0.00304296	−	0.264999i
$334$		0			0
$335$	7211.43			1.17613
$336$		0			0
$337$	−127.151			−0.0205529			−0.0102765	−	0.999947i	$-0.503271\pi$
$337$	−127.151			−0.0205529			−0.0102765	+	0.999947i	$0.503271\pi$
$338$		0			0
$339$	1980.96	−	4861.22i	0.317378	−	0.778836i
$340$		0			0
$341$	−127.372	+	127.372i	−0.0202275	+	0.0202275i
$342$		0			0
$343$	−1906.00			−0.300041
$344$		0			0
$345$	959.756	+	2279.95i	0.149773	+	0.355792i
$346$		0			0
$347$	−2671.89	−	2671.89i	−0.413357	−	0.413357i	0.469549	−	0.882906i	$-0.344416\pi$
$347$	−2671.89	−	2671.89i	−0.413357	−	0.413357i	−0.882906	+	0.469549i	$0.844416\pi$
$348$		0			0
$349$	7144.55	−	7144.55i	1.09581	−	1.09581i	0.100920	−	0.994895i	$-0.467821\pi$
$349$	7144.55	−	7144.55i	1.09581	−	1.09581i	0.994895	−	0.100920i	$-0.0321785\pi$
$350$		0			0
$351$	8733.34	+	3442.47i	1.32807	+	0.523492i
$352$		0			0
$353$		−	4391.32i		−	0.662114i	−0.943611	−	0.331057i	$-0.892595\pi$
$353$		−	4391.32i		−	0.662114i	0.943611	−	0.331057i	$-0.107405\pi$
$354$		0			0
$355$	3858.97	+	3858.97i	0.576938	+	0.576938i
$356$		0			0
$357$	2020.99	−	4959.45i	0.299614	−	0.735244i
$358$		0			0
$359$			750.165i			0.110285i	0.998479	+	0.0551423i	$0.0175613\pi$
$359$			750.165i			0.110285i	−0.998479	+	0.0551423i	$0.982439\pi$
$360$		0			0
$361$		−	6633.46i		−	0.967118i
$362$		0			0
$363$	−3812.23	+	9355.09i	−0.551213	+	1.35266i
$364$		0			0
$365$	−2088.74	−	2088.74i	−0.299534	−	0.299534i
$366$		0			0
$367$		−	8873.45i		−	1.26210i	−0.775743	−	0.631049i	$-0.782625\pi$
$367$		−	8873.45i		−	1.26210i	0.775743	−	0.631049i	$-0.217375\pi$
$368$		0			0
$369$	−2944.48	−	2877.62i	−0.415402	−	0.405970i
$370$		0			0
$371$	7255.01	−	7255.01i	1.01526	−	1.01526i
$372$		0			0
$373$	−257.833	−	257.833i	−0.0357911	−	0.0357911i	0.688985	−	0.724776i	$-0.258057\pi$
$373$	−257.833	−	257.833i	−0.0357911	−	0.0357911i	−0.724776	+	0.688985i	$0.758057\pi$
$374$		0			0
$375$	3064.68	+	7280.28i	0.422024	+	1.00254i
$376$		0			0
$377$	−9961.15			−1.36081
$378$		0			0
$379$	−3719.90	+	3719.90i	−0.504164	+	0.504164i	−0.912729	−	0.408565i	$-0.866029\pi$
$379$	−3719.90	+	3719.90i	−0.504164	+	0.504164i	0.408565	+	0.912729i	$0.366029\pi$
$380$		0			0
$381$	2949.81	−	7238.74i	0.396649	−	0.973364i
$382$		0			0
$383$	9336.03			1.24556			0.622779	−	0.782398i	$-0.286004\pi$
$383$	9336.03			1.24556			0.622779	+	0.782398i	$0.286004\pi$
$384$		0			0
$385$	−12582.9			−1.66567
$386$		0			0
$387$	−8447.48	+	97.0015i	−1.10959	+	0.0127412i
$388$		0			0
$389$	−5797.69	+	5797.69i	−0.755667	+	0.755667i	−0.975531	−	0.219864i	$-0.929439\pi$
$389$	−5797.69	+	5797.69i	−0.755667	+	0.755667i	0.219864	+	0.975531i	$0.429439\pi$
$390$		0			0
$391$	2231.59			0.288635
$392$		0			0
$393$	−10261.2	+	4319.52i	−1.31707	+	0.554430i
$394$		0			0
$395$	2693.58	+	2693.58i	0.343110	+	0.343110i
$396$		0			0
$397$	584.046	−	584.046i	0.0738348	−	0.0738348i	−0.669225	−	0.743060i	$-0.733374\pi$
$397$	584.046	−	584.046i	0.0738348	−	0.0738348i	0.743060	+	0.669225i	$0.233374\pi$
$398$		0			0
$399$	−747.007	−	1774.55i	−0.0937271	−	0.222653i
$400$		0			0
$401$			1656.54i			0.206293i	0.994666	+	0.103147i	$0.0328911\pi$
$401$			1656.54i			0.206293i	−0.994666	+	0.103147i	$0.967109\pi$
$402$		0			0
$403$	−148.921	−	148.921i	−0.0184076	−	0.0184076i
$404$		0			0
$405$	4697.94	+	4486.97i	0.576401	+	0.550517i
$406$		0			0
$407$			3413.43i			0.415718i
$408$		0			0
$409$			2543.09i			0.307451i	0.988114	+	0.153726i	$0.0491272\pi$
$409$			2543.09i			0.307451i	−0.988114	+	0.153726i	$0.950873\pi$
$410$		0			0
$411$	−11848.8	−	4828.41i	−1.42204	−	0.579484i
$412$		0			0
$413$	10990.4	+	10990.4i	1.30945	+	1.30945i
$414$		0			0
$415$			3090.62i			0.365572i
$416$		0			0
$417$	−5297.21	+	2229.89i	−0.622076	+	0.261866i
$418$		0			0
$419$	−3614.52	+	3614.52i	−0.421434	+	0.421434i	−0.885697	−	0.464263i	$-0.846319\pi$
$419$	−3614.52	+	3614.52i	−0.421434	+	0.421434i	0.464263	+	0.885697i	$0.346319\pi$
$420$		0			0
$421$	−10063.8	−	10063.8i	−1.16504	−	1.16504i	−0.983357	−	0.181683i	$-0.941845\pi$
$421$	−10063.8	−	10063.8i	−1.16504	−	1.16504i	−0.181683	−	0.983357i	$-0.558155\pi$
$422$		0			0
$423$	7358.71	+	7191.63i	0.845845	+	0.826640i
$424$		0			0
$425$	1904.27			0.217343
$426$		0			0
$427$	−539.036	+	539.036i	−0.0610908	+	0.0610908i
$428$		0			0
$429$	−18426.1	−	7508.68i	−2.07370	−	0.845041i
$430$		0			0
$431$	3495.35			0.390639			0.195319	−	0.980740i	$-0.437426\pi$
$431$	3495.35			0.390639			0.195319	+	0.980740i	$0.437426\pi$
$432$		0			0
$433$	16071.3			1.78369			0.891843	−	0.452345i	$-0.149413\pi$
$433$	16071.3			1.78369			0.891843	+	0.452345i	$0.149413\pi$
$434$		0			0
$435$	−6383.84	−	2601.44i	−0.703636	−	0.286734i
$436$		0			0
$437$	567.308	−	567.308i	0.0621007	−	0.0621007i
$438$		0			0
$439$	−2550.46			−0.277282			−0.138641	−	0.990343i	$-0.544273\pi$
$439$	−2550.46			−0.277282			−0.138641	+	0.990343i	$0.544273\pi$
$440$		0			0
$441$	5131.57	+	5015.06i	0.554106	+	0.541525i
$442$		0			0
$443$	6114.74	+	6114.74i	0.655801	+	0.655801i	0.954384	−	0.298582i	$-0.0965138\pi$
$443$	6114.74	+	6114.74i	0.655801	+	0.655801i	−0.298582	+	0.954384i	$0.596514\pi$
$444$		0			0
$445$	1190.93	−	1190.93i	0.126866	−	0.126866i
$446$		0			0
$447$	−17152.5	+	7220.44i	−1.81495	+	0.764016i
$448$		0			0
$449$		−	7434.00i		−	0.781364i	−0.920526	−	0.390682i	$-0.872239\pi$
$449$		−	7434.00i		−	0.781364i	0.920526	−	0.390682i	$-0.127761\pi$
$450$		0			0
$451$	6170.62	+	6170.62i	0.644265	+	0.644265i
$452$		0			0
$453$	2750.84	+	1120.97i	0.285310	+	0.116265i
$454$		0			0
$455$		−	14711.7i		−	1.51581i
$456$		0			0
$457$		−	1301.43i		−	0.133213i	−0.997779	−	0.0666063i	$-0.978783\pi$
$457$		−	1301.43i		−	0.133213i	0.997779	−	0.0666063i	$-0.0212172\pi$
$458$		0			0
$459$	5375.01	−	2335.65i	0.546589	−	0.237514i
$460$		0			0
$461$	11243.0	+	11243.0i	1.13587	+	1.13587i	0.989183	+	0.146689i	$0.0468616\pi$
$461$	11243.0	+	11243.0i	1.13587	+	1.13587i	0.146689	+	0.989183i	$0.453138\pi$
$462$		0			0
$463$		−	7824.20i		−	0.785359i	−0.919675	−	0.392679i	$-0.871548\pi$
$463$		−	7824.20i		−	0.785359i	0.919675	−	0.392679i	$-0.128452\pi$
$464$		0			0
$465$	−56.5474	−	134.331i	−0.00563941	−	0.0133967i
$466$		0			0
$467$	7493.61	−	7493.61i	0.742533	−	0.742533i	−0.230532	−	0.973065i	$-0.574047\pi$
$467$	7493.61	−	7493.61i	0.742533	−	0.742533i	0.973065	+	0.230532i	$0.0740465\pi$
$468$		0			0
$469$	14118.2	+	14118.2i	1.39001	+	1.39001i
$470$		0			0
$471$	11276.4	−	4746.88i	1.10317	−	0.464384i
$472$		0			0
$473$	17906.3			1.74066
$474$		0			0
$475$	484.099	−	484.099i	0.0467621	−	0.0467621i
$476$		0			0
$477$	11227.1	−	128.920i	1.07768	−	0.0123749i
$478$		0			0
$479$	−13051.7			−1.24499			−0.622493	−	0.782626i	$-0.713880\pi$
$479$	−13051.7			−1.24499			−0.622493	+	0.782626i	$0.713880\pi$
$480$		0			0
$481$	−3990.91			−0.378316
$482$		0			0
$483$	−2584.60	+	6342.53i	−0.243485	+	0.597505i
$484$		0			0
$485$	9290.98	−	9290.98i	0.869859	−	0.869859i
$486$		0			0
$487$	−7486.49			−0.696602			−0.348301	−	0.937383i	$-0.613241\pi$
$487$	−7486.49			−0.696602			−0.348301	+	0.937383i	$0.613241\pi$
$488$		0			0
$489$	−5397.62	−	12822.3i	−0.499159	−	1.18577i
$490$		0			0
$491$	−6345.55	−	6345.55i	−0.583239	−	0.583239i	0.352553	−	0.935792i	$-0.385314\pi$
$491$	−6345.55	−	6345.55i	−0.583239	−	0.583239i	−0.935792	+	0.352553i	$0.885314\pi$
$492$		0			0
$493$	−4397.35	+	4397.35i	−0.401717	+	0.401717i
$494$		0			0
$495$	−9847.82	−	9624.23i	−0.894196	−	0.873893i
$496$		0			0
$497$			15109.8i			1.36372i
$498$		0			0
$499$	−7412.65	−	7412.65i	−0.665001	−	0.665001i	0.291553	−	0.956555i	$-0.405828\pi$
$499$	−7412.65	−	7412.65i	−0.665001	−	0.665001i	−0.956555	+	0.291553i	$0.905828\pi$
$500$		0			0
$501$	−4787.34	+	11748.0i	−0.426911	+	1.04763i
$502$		0			0
$503$		−	3879.66i		−	0.343908i	−0.985105	−	0.171954i	$-0.944992\pi$
$503$		−	3879.66i		−	0.343908i	0.985105	−	0.171954i	$-0.0550080\pi$
$504$		0			0
$505$		−	2812.10i		−	0.247796i
$506$		0			0
$507$	4470.93	−	10971.5i	0.391639	−	0.961071i
$508$		0			0
$509$	4843.90	+	4843.90i	0.421811	+	0.421811i	0.885827	−	0.464016i	$-0.153592\pi$
$509$	4843.90	+	4843.90i	0.421811	+	0.421811i	−0.464016	+	0.885827i	$0.653592\pi$
$510$		0			0
$511$		−	8178.48i		−	0.708013i
$512$		0			0
$513$	772.657	−	1960.18i	0.0664983	−	0.168702i
$514$		0			0
$515$	−1373.15	+	1373.15i	−0.117492	+	0.117492i
$516$		0			0
$517$	−15421.3	−	15421.3i	−1.31186	−	1.31186i
$518$		0			0
$519$	−2440.99	−	5798.69i	−0.206450	−	0.490432i
$520$		0			0
$521$	1803.41			0.151649			0.0758244	−	0.997121i	$-0.475841\pi$
$521$	1803.41			0.151649			0.0758244	+	0.997121i	$0.475841\pi$
$522$		0			0
$523$	15074.6	−	15074.6i	1.26036	−	1.26036i	0.309440	−	0.950919i	$-0.399859\pi$
$523$	15074.6	−	15074.6i	1.26036	−	1.26036i	0.950919	−	0.309440i	$-0.100141\pi$
$524$		0			0
$525$	−2205.51	+	5412.25i	−0.183345	+	0.449924i
$526$		0			0
$527$	−131.482			−0.0108680
$528$		0			0
$529$	9313.07			0.765437
$530$		0			0
$531$	195.297	+	17007.7i	0.0159608	+	1.38996i
$532$		0			0
$533$	−7214.57	+	7214.57i	−0.586300	+	0.586300i
$534$		0			0
$535$	−4227.02			−0.341589
$536$		0			0
$537$	−18332.0	+	7716.96i	−1.47315	+	0.620133i
$538$		0			0
$539$	−10754.0	−	10754.0i	−0.859386	−	0.859386i
$540$		0			0
$541$	−13914.7	+	13914.7i	−1.10580	+	1.10580i	−0.112106	+	0.993696i	$0.535760\pi$
$541$	−13914.7	+	13914.7i	−1.10580	+	1.10580i	−0.993696	+	0.112106i	$0.964240\pi$
$542$		0			0
$543$	444.335	+	1055.54i	0.0351165	+	0.0834208i
$544$		0			0
$545$			13014.8i			1.02292i
$546$		0			0
$547$	2457.00	+	2457.00i	0.192054	+	0.192054i	0.796583	−	0.604529i	$-0.206639\pi$
$547$	2457.00	+	2457.00i	0.192054	+	0.192054i	−0.604529	+	0.796583i	$0.706639\pi$
$548$		0			0
$549$	−834.158	+	9.57855i	−0.0648470	+	0.000744631i
$550$		0			0
$551$			2235.76i			0.172862i
$552$		0			0
$553$			10546.7i			0.811015i
$554$		0			0
$555$	−2557.67	−	1042.26i	−0.195616	−	0.0797143i
$556$		0			0
$557$	−13996.0	−	13996.0i	−1.06468	−	1.06468i	−0.997758	−	0.0669265i	$-0.978681\pi$
$557$	−13996.0	−	13996.0i	−1.06468	−	1.06468i	−0.0669265	−	0.997758i	$-0.521319\pi$
$558$		0			0
$559$			20935.7i			1.58406i
$560$		0			0
$561$	−11448.9	+	4819.48i	−0.861627	+	0.362707i
$562$		0			0
$563$	−10933.7	+	10933.7i	−0.818474	+	0.818474i	−0.985887	−	0.167413i	$-0.946459\pi$
$563$	−10933.7	+	10933.7i	−0.818474	+	0.818474i	0.167413	+	0.985887i	$0.446459\pi$
$564$		0			0
$565$	−6365.84	−	6365.84i	−0.474005	−	0.474005i
$566$		0			0
$567$	413.020	+	17981.8i	0.0305912	+	1.33186i
$568$		0			0
$569$	4515.04			0.332654			0.166327	−	0.986071i	$-0.446809\pi$
$569$	4515.04			0.332654			0.166327	+	0.986071i	$0.446809\pi$
$570$		0			0
$571$	−6425.75	+	6425.75i	−0.470945	+	0.470945i	−0.902220	−	0.431276i	$-0.858064\pi$
$571$	−6425.75	+	6425.75i	−0.470945	+	0.470945i	0.431276	+	0.902220i	$0.358064\pi$
$572$		0			0
$573$	−5741.98	−	2339.88i	−0.418629	−	0.170593i
$574$		0			0
$575$	−2435.33			−0.176627
$576$		0			0
$577$	962.109			0.0694161			0.0347081	−	0.999397i	$-0.488950\pi$
$577$	962.109			0.0694161			0.0347081	+	0.999397i	$0.488950\pi$
$578$		0			0
$579$	−24293.2	−	9899.54i	−1.74368	−	0.710554i
$580$		0			0
$581$	−6050.66	+	6050.66i	−0.432054	+	0.432054i
$582$		0			0
$583$	−23798.4			−1.69062
$584$		0			0
$585$	11252.5	−	11513.9i	0.795269	−	0.813745i
$586$		0			0
$587$	3139.23	+	3139.23i	0.220732	+	0.220732i	0.808807	−	0.588074i	$-0.200114\pi$
$587$	3139.23	+	3139.23i	0.220732	+	0.220732i	−0.588074	+	0.808807i	$0.700114\pi$
$588$		0			0
$589$	−33.4250	+	33.4250i	−0.00233829	+	0.00233829i
$590$		0			0
$591$	3686.09	−	1551.68i	0.256557	−	0.107999i
$592$		0			0
$593$			28278.3i			1.95827i	0.203219	+	0.979133i	$0.434860\pi$
$593$			28278.3i			1.95827i	−0.203219	+	0.979133i	$0.565140\pi$
$594$		0			0
$595$	−6494.47	−	6494.47i	−0.447475	−	0.447475i
$596$		0			0
$597$	2930.50	+	1194.19i	0.200900	+	0.0818675i
$598$		0			0
$599$			10012.2i			0.682950i	0.939891	+	0.341475i	$0.110927\pi$
$599$			10012.2i			0.682950i	−0.939891	+	0.341475i	$0.889073\pi$
$600$		0			0
$601$			10154.9i			0.689229i	0.938744	+	0.344614i	$0.111990\pi$
$601$			10154.9i			0.689229i	−0.938744	+	0.344614i	$0.888010\pi$
$602$		0			0
$603$	250.877	+	21847.9i	0.0169428	+	1.47548i
$604$		0			0
$605$	12250.6	+	12250.6i	0.823238	+	0.823238i
$606$		0			0
$607$		−	25322.5i		−	1.69326i	−0.532183	−	0.846629i	$-0.678628\pi$
$607$		−	25322.5i		−	1.69326i	0.532183	−	0.846629i	$-0.321372\pi$
$608$		0			0
$609$	−7405.00	−	17590.9i	−0.492719	−	1.17048i
$610$		0			0
$611$	18030.3	−	18030.3i	1.19383	−	1.19383i
$612$		0			0
$613$	−13323.5	−	13323.5i	−0.877863	−	0.877863i	0.115451	−	0.993313i	$-0.463169\pi$
$613$	−13323.5	−	13323.5i	−0.877863	−	0.877863i	−0.993313	+	0.115451i	$0.963169\pi$
$614$		0			0
$615$	−6507.77	+	2739.49i	−0.426697	+	0.179621i
$616$		0			0
$617$	−2727.73			−0.177981			−0.0889906	−	0.996032i	$-0.528364\pi$
$617$	−2727.73			−0.177981			−0.0889906	+	0.996032i	$0.528364\pi$
$618$		0			0
$619$	9506.19	−	9506.19i	0.617263	−	0.617263i	−0.327565	−	0.944829i	$-0.606228\pi$
$619$	9506.19	−	9506.19i	0.617263	−	0.617263i	0.944829	+	0.327565i	$0.106228\pi$
$620$		0			0
$621$	−6873.98	+	2987.01i	−0.444192	+	0.193019i
$622$		0			0
$623$	4663.08			0.299876
$624$		0			0
$625$	7848.55			0.502307
$626$		0			0
$627$	−1685.31	+	4135.70i	−0.107344	+	0.263419i
$628$		0			0
$629$	−1761.79	+	1761.79i	−0.111681	+	0.111681i
$630$		0			0
$631$	6939.01			0.437778			0.218889	−	0.975750i	$-0.429757\pi$
$631$	6939.01			0.437778			0.218889	+	0.975750i	$0.429757\pi$
$632$		0			0
$633$	1162.67	+	2761.98i	0.0730049	+	0.173426i
$634$		0			0
$635$	−9479.23	−	9479.23i	−0.592397	−	0.592397i
$636$		0			0
$637$	12573.4	−	12573.4i	0.782067	−	0.782067i
$638$		0			0
$639$	−11557.0	+	11825.5i	−0.715472	+	0.732094i
$640$		0			0
$641$			25374.4i			1.56354i	0.623567	+	0.781770i	$0.285683\pi$
$641$			25374.4i			1.56354i	−0.623567	+	0.781770i	$0.714317\pi$
$642$		0			0
$643$	17483.4	+	17483.4i	1.07228	+	1.07228i	0.997175	+	0.0751092i	$0.0239306\pi$
$643$	17483.4	+	17483.4i	1.07228	+	1.07228i	0.0751092	+	0.997175i	$0.476069\pi$
$644$		0			0
$645$	−5467.54	+	13417.2i	−0.333774	+	0.819070i
$646$		0			0
$647$		−	23409.6i		−	1.42245i	−0.702964	−	0.711225i	$-0.748141\pi$
$647$		−	23409.6i		−	1.42245i	0.702964	−	0.711225i	$-0.251859\pi$
$648$		0			0
$649$		−	36051.6i		−	2.18050i
$650$		0			0
$651$	152.281	−	373.692i	0.00916798	−	0.0224979i
$652$		0			0
$653$	9012.83	+	9012.83i	0.540122	+	0.540122i	0.923565	−	0.383443i	$-0.125262\pi$
$653$	9012.83	+	9012.83i	0.540122	+	0.540122i	−0.383443	+	0.923565i	$0.625262\pi$
$654$		0			0
$655$			19093.7i			1.13901i
$656$		0			0
$657$	6255.44	−	6400.76i	0.371458	−	0.380088i
$658$		0			0
$659$	−358.576	+	358.576i	−0.0211960	+	0.0211960i	−0.717625	−	0.696429i	$-0.754771\pi$
$659$	−358.576	+	358.576i	−0.0211960	+	0.0211960i	0.696429	+	0.717625i	$0.254771\pi$
$660$		0			0
$661$	14598.1	+	14598.1i	0.859004	+	0.859004i	0.991221	−	0.132217i	$-0.0422095\pi$
$661$	14598.1	+	14598.1i	0.859004	+	0.859004i	−0.132217	+	0.991221i	$0.542210\pi$
$662$		0			0
$663$	−5634.84	−	13385.8i	−0.330074	−	0.784106i
$664$		0			0
$665$	−3302.01			−0.192551
$666$		0			0
$667$	5623.67	−	5623.67i	0.326461	−	0.326461i
$668$		0			0
$669$	5798.97	−	14230.5i	0.335129	−	0.822395i
$670$		0			0
$671$	1768.19			0.101729
$672$		0			0
$673$	−26625.5			−1.52502			−0.762509	−	0.646978i	$-0.776033\pi$
$673$	−26625.5			−1.52502			−0.762509	+	0.646978i	$0.776033\pi$
$674$		0			0
$675$	−5865.75	+	2548.90i	−0.334478	+	0.145344i
$676$		0			0
$677$	−5301.22	+	5301.22i	−0.300949	+	0.300949i	−0.841385	−	0.540436i	$-0.818259\pi$
$677$	−5301.22	+	5301.22i	−0.300949	+	0.300949i	0.540436	+	0.841385i	$0.318259\pi$
$678$		0			0
$679$	36378.8			2.05610
$680$		0			0
$681$	1726.28	−	726.688i	0.0971384	−	0.0408910i
$682$		0			0
$683$	4314.17	+	4314.17i	0.241694	+	0.241694i	0.817551	−	0.575857i	$-0.195331\pi$
$683$	4314.17	+	4314.17i	0.241694	+	0.241694i	−0.575857	+	0.817551i	$0.695331\pi$
$684$		0			0
$685$	−15516.1	+	15516.1i	−0.865461	+	0.865461i
$686$		0			0
$687$	−997.129	−	2368.73i	−0.0553753	−	0.131547i
$688$		0			0
$689$		−	27824.7i		−	1.53851i
$690$		0			0
$691$	8509.21	+	8509.21i	0.468460	+	0.468460i	0.901415	−	0.432955i	$-0.142529\pi$
$691$	8509.21	+	8509.21i	0.468460	+	0.468460i	−0.432955	+	0.901415i	$0.642529\pi$
$692$		0			0
$693$	−437.744	−	38121.4i	−0.0239950	−	2.08963i
$694$		0			0
$695$			9856.85i			0.537974i
$696$		0			0
$697$			6369.75i			0.346157i
$698$		0			0
$699$	8995.56	+	3665.72i	0.486757	+	0.198355i
$700$		0			0
$701$	2086.28	+	2086.28i	0.112408	+	0.112408i	0.761073	−	0.648666i	$-0.224673\pi$
$701$	2086.28	+	2086.28i	0.112408	+	0.112408i	−0.648666	+	0.761073i	$0.724673\pi$
$702$		0			0
$703$			895.754i			0.0480569i
$704$		0			0
$705$	16263.9	−	6846.40i	0.868845	−	0.365745i
$706$		0			0
$707$	5505.39	−	5505.39i	0.292859	−	0.292859i
$708$		0			0
$709$	19902.7	+	19902.7i	1.05425	+	1.05425i	0.998442	+	0.0558039i	$0.0177722\pi$
$709$	19902.7	+	19902.7i	1.05425	+	1.05425i	0.0558039	+	0.998442i	$0.482228\pi$
$710$		0			0
$711$	−8066.81	+	8254.22i	−0.425498	+	0.435383i
$712$		0			0
$713$	168.149			0.00883203
$714$		0			0
$715$	−24129.2	+	24129.2i	−1.26207	+	1.26207i
$716$		0			0
$717$	10204.4	+	4158.33i	0.531507	+	0.216591i
$718$		0			0
$719$	−6725.66			−0.348852			−0.174426	−	0.984670i	$-0.555807\pi$
$719$	−6725.66			−0.348852			−0.174426	+	0.984670i	$0.555807\pi$
$720$		0			0
$721$	−5376.57			−0.277717
$722$		0			0
$723$	14899.1	+	6071.42i	0.766393	+	0.312308i
$724$		0			0
$725$	4798.83	−	4798.83i	0.245826	−	0.245826i
$726$		0			0
$727$	14601.8			0.744911			0.372456	−	0.928050i	$-0.378516\pi$
$727$	14601.8			0.744911			0.372456	+	0.928050i	$0.378516\pi$
$728$		0			0
$729$	−13430.4	+	14389.1i	−0.682334	+	0.731040i
$730$		0			0
$731$	9242.08	+	9242.08i	0.467621	+	0.467621i
$732$		0			0
$733$	16119.5	−	16119.5i	0.812259	−	0.812259i	−0.172713	−	0.984972i	$-0.555253\pi$
$733$	16119.5	−	16119.5i	0.812259	−	0.812259i	0.984972	+	0.172713i	$0.0552533\pi$
$734$		0			0
$735$	11341.6	−	4774.32i	0.569173	−	0.239597i
$736$		0			0
$737$		−	46311.5i		−	2.31466i
$738$		0			0
$739$	−26403.6	−	26403.6i	−1.31431	−	1.31431i	−0.918208	−	0.396099i	$-0.870364\pi$
$739$	−26403.6	−	26403.6i	−1.31431	−	1.31431i	−0.396099	−	0.918208i	$-0.629636\pi$
$740$		0			0
$741$	−4835.38	−	1970.43i	−0.239719	−	0.0976864i
$742$		0			0
$743$			24491.2i			1.20928i	0.796499	+	0.604640i	$0.206683\pi$
$743$			24491.2i			1.20928i	−0.796499	+	0.604640i	$0.793317\pi$
$744$		0			0
$745$			31916.7i			1.56958i
$746$		0			0
$747$	−9363.40	+	107.519i	−0.458620	+	0.00526628i
$748$		0			0
$749$	−8275.45	−	8275.45i	−0.403709	−	0.403709i
$750$		0			0
$751$		−	15477.7i		−	0.752050i	−0.926609	−	0.376025i	$-0.877291\pi$
$751$		−	15477.7i		−	0.752050i	0.926609	−	0.376025i	$-0.122709\pi$
$752$		0			0
$753$	6825.38	+	16214.0i	0.330320	+	0.784690i
$754$		0			0
$755$	3602.26	−	3602.26i	0.173642	−	0.173642i
$756$		0			0
$757$	11191.6	+	11191.6i	0.537340	+	0.537340i	0.922747	−	0.385407i	$-0.125939\pi$
$757$	11191.6	+	11191.6i	0.537340	+	0.537340i	−0.385407	+	0.922747i	$0.625939\pi$
$758$		0			0
$759$	14641.7	−	6163.52i	0.700212	−	0.294758i
$760$		0			0
$761$	−10016.9			−0.477153			−0.238576	−	0.971124i	$-0.576681\pi$
$761$	−10016.9			−0.477153			−0.238576	+	0.971124i	$0.576681\pi$
$762$		0			0
$763$	−25479.7	+	25479.7i	−1.20895	+	1.20895i
$764$		0			0
$765$	−115.405	−	10050.2i	−0.00545424	−	0.474988i
$766$		0			0
$767$	42150.8			1.98432
$768$		0			0
$769$	1463.91			0.0686475			0.0343238	−	0.999411i	$-0.489072\pi$
$769$	1463.91			0.0686475			0.0343238	+	0.999411i	$0.489072\pi$
$770$		0			0
$771$	7024.89	−	17238.9i	0.328139	−	0.805243i
$772$		0			0
$773$	26695.6	−	26695.6i	1.24214	−	1.24214i	0.283030	−	0.959111i	$-0.408660\pi$
$773$	26695.6	−	26695.6i	1.24214	−	1.24214i	0.959111	−	0.283030i	$-0.0913397\pi$
$774$		0			0
$775$	143.486			0.00665055
$776$		0			0
$777$	−2966.80	−	7047.76i	−0.136980	−	0.325402i
$778$		0			0
$779$	1619.30	+	1619.30i	0.0744768	+	0.0744768i
$780$		0			0
$781$	24782.2	−	24782.2i	1.13544	−	1.13544i
$782$		0			0
$783$	7659.27	−	19431.1i	0.349579	−	0.886860i
$784$		0			0
$785$		−	20982.8i		−	0.954022i
$786$		0			0
$787$	−14529.3	−	14529.3i	−0.658087	−	0.658087i	0.296840	−	0.954927i	$-0.404067\pi$
$787$	−14529.3	−	14529.3i	−0.658087	−	0.658087i	−0.954927	+	0.296840i	$0.904067\pi$
$788$		0			0
$789$	−4306.58	+	10568.2i	−0.194320	+	0.476855i
$790$		0			0
$791$		−	24925.5i		−	1.12041i
$792$		0			0
$793$			2067.33i			0.0925763i
$794$		0			0
$795$	7266.64	−	17832.1i	0.324177	−	0.795521i
$796$		0			0
$797$	−18417.2	−	18417.2i	−0.818532	−	0.818532i	0.167363	−	0.985895i	$-0.446475\pi$
$797$	−18417.2	−	18417.2i	−0.818532	−	0.818532i	−0.985895	+	0.167363i	$0.946475\pi$
$798$		0			0
$799$		−	15919.0i		−	0.704848i
$800$		0			0
$801$	3649.49	+	3566.63i	0.160984	+	0.157329i
$802$		0			0
$803$	−13413.8	+	13413.8i	−0.589494	+	0.589494i
$804$		0			0
$805$	8305.63	+	8305.63i	0.363646	+	0.363646i
$806$		0			0
$807$	−182.971	−	434.657i	−0.00798128	−	0.0189599i
$808$		0			0
$809$	14088.2			0.612253			0.306127	−	0.951991i	$-0.400967\pi$
$809$	14088.2			0.612253			0.306127	+	0.951991i	$0.400967\pi$
$810$		0			0
$811$	16384.8	−	16384.8i	0.709429	−	0.709429i	−0.256986	−	0.966415i	$-0.582729\pi$
$811$	16384.8	−	16384.8i	0.709429	−	0.709429i	0.966415	+	0.256986i	$0.0827294\pi$
$812$		0			0
$813$	−7112.92	+	17454.9i	−0.306840	+	0.752976i
$814$		0			0
$815$	−23859.2			−1.02546
$816$		0			0
$817$	4698.99			0.201220
$818$		0			0
$819$	44570.8	−	511.802i	1.90162	−	0.0218361i
$820$		0			0
$821$	1002.06	−	1002.06i	0.0425968	−	0.0425968i	−0.685488	−	0.728084i	$-0.740411\pi$
$821$	1002.06	−	1002.06i	0.0425968	−	0.0425968i	0.728084	+	0.685488i	$0.240411\pi$
$822$		0			0
$823$	−36539.2			−1.54760			−0.773802	−	0.633428i	$-0.781647\pi$
$823$	−36539.2			−1.54760			−0.773802	+	0.633428i	$0.781647\pi$
$824$		0			0
$825$	12494.2	−	5259.50i	0.527262	−	0.221954i
$826$		0			0
$827$	−1314.92	−	1314.92i	−0.0552892	−	0.0552892i	0.678922	−	0.734211i	$-0.262448\pi$
$827$	−1314.92	−	1314.92i	−0.0552892	−	0.0552892i	−0.734211	+	0.678922i	$0.762448\pi$
$828$		0			0
$829$	−18101.1	+	18101.1i	−0.758357	+	0.758357i	−0.976023	−	0.217667i	$-0.930155\pi$
$829$	−18101.1	+	18101.1i	−0.758357	+	0.758357i	0.217667	+	0.976023i	$0.430155\pi$
$830$		0			0
$831$	9910.59	+	23543.1i	0.413712	+	0.982791i
$832$		0			0
$833$		−	11101.1i		−	0.461740i
$834$		0			0
$835$	15384.2	+	15384.2i	0.637594	+	0.637594i
$836$		0			0
$837$	405.005	−	175.990i	0.0167252	−	0.00726777i
$838$		0			0
$839$			11658.5i			0.479734i	0.970806	+	0.239867i	$0.0771038\pi$
$839$			11658.5i			0.479734i	−0.970806	+	0.239867i	$0.922896\pi$
$840$		0			0
$841$		−	2226.09i		−	0.0912745i
$842$		0			0
$843$	−26936.8	−	10976.8i	−1.10054	−	0.448473i
$844$		0			0
$845$	−14367.4	−	14367.4i	−0.584915	−	0.584915i
$846$		0			0
$847$			47967.3i			1.94590i
$848$		0			0
$849$	−1603.81	+	675.133i	−0.0648322	+	0.0272915i
$850$		0			0
$851$	2253.11	−	2253.11i	0.0907587	−	0.0907587i
$852$		0			0
$853$	−8293.73	−	8293.73i	−0.332910	−	0.332910i	0.520781	−	0.853690i	$-0.325641\pi$
$853$	−8293.73	−	8293.73i	−0.332910	−	0.332910i	−0.853690	+	0.520781i	$0.825641\pi$
$854$		0			0
$855$	−2584.27	−	2525.60i	−0.103369	−	0.101022i
$856$		0			0
$857$	−5209.55			−0.207649			−0.103824	−	0.994596i	$-0.533108\pi$
$857$	−5209.55			−0.207649			−0.103824	+	0.994596i	$0.533108\pi$
$858$		0			0
$859$	21529.9	−	21529.9i	0.855168	−	0.855168i	−0.135596	−	0.990764i	$-0.543295\pi$
$859$	21529.9	−	21529.9i	0.855168	−	0.855168i	0.990764	+	0.135596i	$0.0432950\pi$
$860$		0			0
$861$	−18103.8	−	7377.37i	−0.716581	−	0.292009i
$862$		0			0
$863$	31954.7			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$863$	31954.7			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$864$		0			0
$865$	−10790.0			−0.424128
$866$		0			0
$867$	15244.5	+	6212.17i	0.597150	+	0.243341i
$868$		0			0
$869$	17298.0	−	17298.0i	0.675254	−	0.675254i
$870$		0			0
$871$	54146.5			2.10641
$872$		0			0
$873$	28471.4	+	27824.9i	1.10379	+	1.07873i
$874$		0			0
$875$	26521.4	+	26521.4i	1.02467	+	1.02467i
$876$		0			0
$877$	11937.5	−	11937.5i	0.459636	−	0.459636i	−0.438900	−	0.898536i	$-0.644632\pi$
$877$	11937.5	−	11937.5i	0.459636	−	0.459636i	0.898536	+	0.438900i	$0.144632\pi$
$878$		0			0
$879$	20840.8	−	8773.04i	0.799706	−	0.336641i
$880$		0			0
$881$		−	30514.2i		−	1.16691i	−0.812144	−	0.583457i	$-0.801700\pi$
$881$		−	30514.2i		−	1.16691i	0.812144	−	0.583457i	$-0.198300\pi$
$882$		0			0
$883$	−3179.05	−	3179.05i	−0.121159	−	0.121159i	0.643927	−	0.765087i	$-0.277304\pi$
$883$	−3179.05	−	3179.05i	−0.121159	−	0.121159i	−0.765087	+	0.643927i	$0.777304\pi$
$884$		0			0
$885$	27013.3	+	11008.0i	1.02604	+	0.418114i
$886$		0			0
$887$		−	24947.8i		−	0.944380i	−0.881497	−	0.472190i	$-0.843464\pi$
$887$		−	24947.8i		−	0.944380i	0.881497	−	0.472190i	$-0.156536\pi$
$888$		0			0
$889$		−	37115.9i		−	1.40026i
$890$		0			0
$891$	28815.2	−	30170.0i	1.08344	−	1.13438i
$892$		0			0
$893$	−4046.88	−	4046.88i	−0.151650	−	0.151650i
$894$		0			0
$895$			34111.5i			1.27399i
$896$		0			0
$897$	7206.27	+	17118.8i	0.268239	+	0.637214i
$898$		0			0
$899$	−331.338	+	331.338i	−0.0122923	+	0.0122923i
$900$		0			0
$901$	−12283.2	−	12283.2i	−0.454176	−	0.454176i
$902$		0			0
$903$	−36971.5	+	15563.4i	−1.36250	+	0.573551i
$904$		0			0
$905$	1964.11			0.0721427
$906$		0			0
$907$	−19465.8	+	19465.8i	−0.712626	+	0.712626i	−0.967084	−	0.254458i	$-0.918103\pi$
$907$	−19465.8	+	19465.8i	−0.712626	+	0.712626i	0.254458	+	0.967084i	$0.418103\pi$
$908$		0			0
$909$	8519.59	−	97.8296i	0.310866	−	0.00356964i
$910$		0			0
$911$	−4256.52			−0.154802			−0.0774010	−	0.997000i	$-0.524662\pi$
$911$	−4256.52			−0.154802			−0.0774010	+	0.997000i	$0.524662\pi$
$912$		0			0
$913$	19847.8			0.719460
$914$		0			0
$915$	−539.900	+	1324.90i	−0.0195066	+	0.0478686i
$916$		0			0
$917$	−37380.7	+	37380.7i	−1.34615	+	1.34615i
$918$		0			0
$919$	−37455.2			−1.34443			−0.672216	−	0.740355i	$-0.734657\pi$
$919$	−37455.2			−1.34443			−0.672216	+	0.740355i	$0.734657\pi$
$920$		0			0
$921$	−4989.16	−	11852.0i	−0.178500	−	0.424034i
$922$		0			0
$923$	28974.8	+	28974.8i	1.03328	+	1.03328i
$924$		0			0
$925$	1922.64	−	1922.64i	0.0683416	−	0.0683416i
$926$		0			0
$927$	−4207.89	−	4112.35i	−0.149089	−	0.145704i
$928$		0			0
$929$			51223.8i			1.80904i	0.426429	+	0.904521i	$0.359771\pi$
$929$			51223.8i			1.80904i	−0.426429	+	0.904521i	$0.640229\pi$
$930$		0			0
$931$	−2822.08	−	2822.08i	−0.0993448	−	0.0993448i
$932$		0			0
$933$	13870.3	−	34037.3i	0.486703	−	1.19435i
$934$		0			0
$935$			21303.7i			0.745138i
$936$		0			0
$937$		−	30708.1i		−	1.07064i	−0.844650	−	0.535320i	$-0.820191\pi$
$937$		−	30708.1i		−	1.07064i	0.844650	−	0.535320i	$-0.179809\pi$
$938$		0			0
$939$	−17739.6	+	43532.4i	−0.616518	+	1.51292i
$940$		0			0
$941$	817.247	+	817.247i	0.0283119	+	0.0283119i	0.721121	−	0.692809i	$-0.243627\pi$
$941$	817.247	+	817.247i	0.0283119	+	0.0283119i	−0.692809	+	0.721121i	$0.743627\pi$
$942$		0			0
$943$		−	8146.12i		−	0.281309i
$944$		0			0
$945$	28697.9	+	11312.0i	0.987877	+	0.389397i
$946$		0			0
$947$	−18142.1	+	18142.1i	−0.622535	+	0.622535i	−0.946179	−	0.323644i	$-0.895092\pi$
$947$	−18142.1	+	18142.1i	−0.622535	+	0.622535i	0.323644	+	0.946179i	$0.395092\pi$
$948$		0			0
$949$	−15683.2	−	15683.2i	−0.536457	−	0.536457i
$950$		0			0
$951$	−12765.4	−	30324.8i	−0.435274	−	1.03401i
$952$		0			0
$953$	−8325.23			−0.282981			−0.141490	−	0.989940i	$-0.545189\pi$
$953$	−8325.23			−0.282981			−0.141490	+	0.989940i	$0.545189\pi$
$954$		0			0
$955$	−7519.21	+	7519.21i	−0.254781	+	0.254781i
$956$		0			0
$957$	−16706.3	+	40996.8i	−0.564304	+	1.38478i
$958$		0			0
$959$	−60753.4			−2.04570
$960$		0			0
$961$	29781.1			0.999667
$962$		0			0
$963$	−147.053	−	12806.3i	−0.00492078	−	0.428532i
$964$		0			0
$965$	−31812.2	+	31812.2i	−1.06122	+	1.06122i
$966$		0			0
$967$	8911.71			0.296361			0.148181	−	0.988960i	$-0.452658\pi$
$967$	8911.71			0.296361			0.148181	+	0.988960i	$0.452658\pi$
$968$		0			0
$969$	−3004.42	+	1264.73i	−0.0996037	+	0.0419288i
$970$		0			0
$971$	−24556.5	−	24556.5i	−0.811593	−	0.811593i	0.173280	−	0.984873i	$-0.444563\pi$
$971$	−24556.5	−	24556.5i	−0.811593	−	0.811593i	−0.984873	+	0.173280i	$0.944563\pi$
$972$		0			0
$973$	−19297.2	+	19297.2i	−0.635808	+	0.635808i
$974$		0			0
$975$	6149.30	+	14607.9i	0.201985	+	0.479824i
$976$		0			0
$977$		−	501.936i		−	0.0164364i	−0.999966	−	0.00821819i	$-0.997384\pi$
$977$		−	501.936i		−	0.0164364i	0.999966	−	0.00821819i	$-0.00261596\pi$
$978$		0			0
$979$	−7648.10	−	7648.10i	−0.249678	−	0.249678i
$980$		0			0
$981$	−39429.9	+	452.769i	−1.28328	+	0.0147358i
$982$		0			0
$983$			52008.6i			1.68751i	0.536732	+	0.843753i	$0.319659\pi$
$983$			52008.6i			1.68751i	−0.536732	+	0.843753i	$0.680341\pi$
$984$		0			0
$985$		−	6858.94i		−	0.221872i
$986$		0			0
$987$	45244.3	+	18437.2i	1.45911	+	0.594592i
$988$		0			0
$989$	−11819.5	−	11819.5i	−0.380018	−	0.380018i
$990$		0			0
$991$		−	27605.3i		−	0.884876i	−0.896799	−	0.442438i	$-0.854114\pi$
$991$		−	27605.3i		−	0.884876i	0.896799	−	0.442438i	$-0.145886\pi$
$992$		0			0
$993$	−7184.91	+	3024.53i	−0.229613	+	0.0966571i
$994$		0			0
$995$	3837.54	−	3837.54i	0.122269	−	0.122269i
$996$		0			0
$997$	3224.20	+	3224.20i	0.102419	+	0.102419i	0.756459	−	0.654041i	$-0.226927\pi$
$997$	3224.20	+	3224.20i	0.102419	+	0.102419i	−0.654041	+	0.756459i	$0.726927\pi$
$998$		0			0
$999$	3068.67	−	7785.03i	0.0971856	−	0.246554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.k.b.287.20		44
3.2	odd	2	inner	384.4.k.b.287.14		44
4.3	odd	2		384.4.k.a.287.3		44
8.3	odd	2		192.4.k.a.143.20		44
8.5	even	2		48.4.k.a.11.3	✓	44
12.11	even	2		384.4.k.a.287.9		44
16.3	odd	4	inner	384.4.k.b.95.14		44
16.5	even	4		192.4.k.a.47.14		44
16.11	odd	4		48.4.k.a.35.20	yes	44
16.13	even	4		384.4.k.a.95.9		44
24.5	odd	2		48.4.k.a.11.20	yes	44
24.11	even	2		192.4.k.a.143.14		44
48.5	odd	4		192.4.k.a.47.20		44
48.11	even	4		48.4.k.a.35.3	yes	44
48.29	odd	4		384.4.k.a.95.3		44
48.35	even	4	inner	384.4.k.b.95.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.3	✓	44	8.5	even	2
48.4.k.a.11.20	yes	44	24.5	odd	2
48.4.k.a.35.3	yes	44	48.11	even	4
48.4.k.a.35.20	yes	44	16.11	odd	4
192.4.k.a.47.14		44	16.5	even	4
192.4.k.a.47.20		44	48.5	odd	4
192.4.k.a.143.14		44	24.11	even	2
192.4.k.a.143.20		44	8.3	odd	2
384.4.k.a.95.3		44	48.29	odd	4
384.4.k.a.95.9		44	16.13	even	4
384.4.k.a.287.3		44	4.3	odd	2
384.4.k.a.287.9		44	12.11	even	2
384.4.k.b.95.14		44	16.3	odd	4	inner
384.4.k.b.95.20		44	48.35	even	4	inner
384.4.k.b.287.14		44	3.2	odd	2	inner
384.4.k.b.287.20		44	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.81196 + 1.96089i) q^{3} +(6.30133 - 6.30133i) q^{5} +24.6728 q^{7} +(19.3098 + 18.8714i) q^{9} +O(q^{10})\)	\(q+(4.81196 + 1.96089i) q^{3} +(6.30133 - 6.30133i) q^{5} +24.6728 q^{7} +(19.3098 + 18.8714i) q^{9} +(-40.4669 - 40.4669i) q^{11} +(47.3131 - 47.3131i) q^{13} +(42.6779 - 17.9655i) q^{15} -41.7727i q^{17} +(-10.6193 - 10.6193i) q^{19} +(118.725 + 48.3807i) q^{21} +53.4222i q^{23} +45.5866i q^{25} +(55.9134 + 128.673i) q^{27} +(-105.268 - 105.268i) q^{29} -3.14755i q^{31} +(-115.374 - 274.076i) q^{33} +(155.472 - 155.472i) q^{35} +(-42.1756 - 42.1756i) q^{37} +(320.444 - 134.893i) q^{39} -152.486 q^{41} +(-221.247 + 221.247i) q^{43} +(240.593 - 2.76270i) q^{45} +381.086 q^{47} +265.749 q^{49} +(81.9116 - 201.008i) q^{51} +(294.048 - 294.048i) q^{53} -509.990 q^{55} +(-30.2765 - 71.9231i) q^{57} +(445.445 + 445.445i) q^{59} +(-21.8473 + 21.8473i) q^{61} +(476.429 + 465.611i) q^{63} -596.270i q^{65} +(572.215 + 572.215i) q^{67} +(-104.755 + 257.065i) q^{69} +612.406i q^{71} -331.477i q^{73} +(-89.3901 + 219.361i) q^{75} +(-998.433 - 998.433i) q^{77} +427.462i q^{79} +(16.7398 + 728.808i) q^{81} +(-245.236 + 245.236i) q^{83} +(-263.224 - 263.224i) q^{85} +(-300.128 - 712.967i) q^{87} +188.997 q^{89} +(1167.35 - 1167.35i) q^{91} +(6.17200 - 15.1459i) q^{93} -133.832 q^{95} +1474.45 q^{97} +(-17.7419 - 1545.08i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) \) 44 * q + 2 * q^3 - 8 * q^7	\( 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more