LMFDB - Embedded newform 384.4.k.a.95.9

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			95.9
Character	$\chi$	$=$	384.95
Dual form			384.4.k.a.287.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96089 + 4.81196i) q^{3} +(-6.30133 - 6.30133i) q^{5} -24.6728 q^{7} +(-19.3098 - 18.8714i) q^{9} +O(q^{10})$	\(q+(-1.96089 + 4.81196i) q^{3} +(-6.30133 - 6.30133i) q^{5} -24.6728 q^{7} +(-19.3098 - 18.8714i) q^{9} +(-40.4669 + 40.4669i) q^{11} +(47.3131 + 47.3131i) q^{13} +(42.6779 - 17.9655i) q^{15} -41.7727i q^{17} +(10.6193 - 10.6193i) q^{19} +(48.3807 - 118.725i) q^{21} -53.4222i q^{23} -45.5866i q^{25} +(128.673 - 55.9134i) q^{27} +(105.268 - 105.268i) q^{29} -3.14755i q^{31} +(-115.374 - 274.076i) q^{33} +(155.472 + 155.472i) q^{35} +(-42.1756 + 42.1756i) q^{37} +(-320.444 + 134.893i) q^{39} +152.486 q^{41} +(221.247 + 221.247i) q^{43} +(2.76270 + 240.593i) q^{45} +381.086 q^{47} +265.749 q^{49} +(201.008 + 81.9116i) q^{51} +(-294.048 - 294.048i) q^{53} +509.990 q^{55} +(30.2765 + 71.9231i) q^{57} +(445.445 - 445.445i) q^{59} +(-21.8473 - 21.8473i) q^{61} +(476.429 + 465.611i) q^{63} -596.270i q^{65} +(-572.215 + 572.215i) q^{67} +(257.065 + 104.755i) q^{69} -612.406i q^{71} +331.477i q^{73} +(219.361 + 89.3901i) q^{75} +(998.433 - 998.433i) q^{77} +427.462i q^{79} +(16.7398 + 728.808i) q^{81} +(-245.236 - 245.236i) q^{83} +(-263.224 + 263.224i) q^{85} +(300.128 + 712.967i) q^{87} -188.997 q^{89} +(-1167.35 - 1167.35i) q^{91} +(15.1459 + 6.17200i) q^{93} -133.832 q^{95} +1474.45 q^{97} +(1545.08 - 17.7419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.96089	+	4.81196i	−0.377373	+	0.926061i
$3$	−1.96089	+	4.81196i	−0.377373	+	0.926061i
$4$		0			0
$5$	−6.30133	−	6.30133i	−0.563608	−	0.563608i	0.366723	−	0.930330i	$-0.380480\pi$
$5$	−6.30133	−	6.30133i	−0.563608	−	0.563608i	−0.930330	+	0.366723i	$0.880480\pi$
$6$		0			0
$7$	−24.6728			−1.33221			−0.666104	−	0.745859i	$-0.732039\pi$
$7$	−24.6728			−1.33221			−0.666104	+	0.745859i	$0.732039\pi$
$8$		0			0
$9$	−19.3098	−	18.8714i	−0.715179	−	0.698941i
$10$		0			0
$11$	−40.4669	+	40.4669i	−1.10920	+	1.10920i	−0.115946	+	0.993255i	$0.536990\pi$
$11$	−40.4669	+	40.4669i	−1.10920	+	1.10920i	−0.993255	+	0.115946i	$0.963010\pi$
$12$		0			0
$13$	47.3131	+	47.3131i	1.00941	+	1.00941i	0.999955	+	0.00945153i	$0.00300856\pi$
$13$	47.3131	+	47.3131i	1.00941	+	1.00941i	0.00945153	+	0.999955i	$0.496991\pi$
$14$		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	$-0.721100\pi$
$19$	10.6193	−	10.6193i	0.128223	−	0.128223i	0.768306	+	0.640083i	$0.221100\pi$
$20$		0			0
$21$	48.3807	−	118.725i	0.502739	−	1.23371i
$22$		0			0
$23$		−	53.4222i		−	0.484317i	−0.970237	−	0.242158i	$-0.922145\pi$
$23$		−	53.4222i		−	0.484317i	0.970237	−	0.242158i	$-0.0778554\pi$
$24$		0			0
$25$		−	45.5866i		−	0.364692i
$26$		0			0
$27$	128.673	−	55.9134i	0.917152	−	0.398538i
$28$		0			0
$29$	105.268	−	105.268i	0.674064	−	0.674064i	−0.284586	−	0.958650i	$-0.591856\pi$
$29$	105.268	−	105.268i	0.674064	−	0.674064i	0.958650	+	0.284586i	$0.0918562\pi$
$30$		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	−0.794569	−	0.607174i	$-0.792303\pi$
$37$	−42.1756	+	42.1756i	−0.187395	+	0.187395i	0.607174	+	0.794569i	$0.292303\pi$
$38$		0			0
$39$	−320.444	+	134.893i	−1.31570	+	0.553850i
$40$		0			0
$41$	152.486			0.580836			0.290418	−	0.956900i	$-0.406206\pi$
$41$	152.486			0.580836			0.290418	+	0.956900i	$0.406206\pi$
$42$		0			0
$43$	221.247	+	221.247i	0.784647	+	0.784647i	0.980611	−	0.195964i	$-0.0627836\pi$
$43$	221.247	+	221.247i	0.784647	+	0.784647i	−0.195964	+	0.980611i	$0.562784\pi$
$44$		0			0
$45$	2.76270	+	240.593i	0.00915197	+	0.797009i
$46$		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
$51$	201.008	+	81.9116i	0.551898	+	0.224900i
$52$		0			0
$53$	−294.048	−	294.048i	−0.762088	−	0.762088i	0.214612	−	0.976699i	$-0.431151\pi$
$53$	−294.048	−	294.048i	−0.762088	−	0.762088i	−0.976699	+	0.214612i	$0.931151\pi$
$54$		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	−0.0169404	−	0.999857i	$-0.505393\pi$
$59$	445.445	−	445.445i	0.982916	−	0.982916i	0.999857	+	0.0169404i	$0.00539256\pi$
$60$		0			0
$61$	−21.8473	−	21.8473i	−0.0458568	−	0.0458568i	0.683807	−	0.729663i	$-0.260323\pi$
$61$	−21.8473	−	21.8473i	−0.0458568	−	0.0458568i	−0.729663	+	0.683807i	$0.760323\pi$
$62$		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	−0.0443759	+	0.999015i	$0.514130\pi$
$67$	−572.215	+	572.215i	−1.04339	+	1.04339i	−0.999015	+	0.0443759i	$0.985870\pi$
$68$		0			0
$69$	257.065	+	104.755i	0.448507	+	0.182768i
$70$		0			0
$71$		−	612.406i		−	1.02365i	−0.859089	−	0.511825i	$-0.828969\pi$
$71$		−	612.406i		−	1.02365i	0.859089	−	0.511825i	$-0.171031\pi$
$72$		0			0
$73$			331.477i			0.531458i	0.964048	+	0.265729i	$0.0856126\pi$
$73$			331.477i			0.531458i	−0.964048	+	0.265729i	$0.914387\pi$
$74$		0			0
$75$	219.361	+	89.3901i	0.337728	+	0.137625i
$76$		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	0.526105	−	0.850420i	$-0.323652\pi$
$83$	−245.236	−	245.236i	−0.324314	−	0.324314i	−0.850420	+	0.526105i	$0.823652\pi$
$84$		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	$-0.535901\pi$
$89$	−188.997			−0.225097			−0.112548	+	0.993646i	$0.535901\pi$
$90$		0			0
$91$	−1167.35	−	1167.35i	−1.34474	−	1.34474i
$92$		0			0
$93$	15.1459	+	6.17200i	0.0168877	+	0.00688179i
$94$		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
$99$	1545.08	−	17.7419i	1.56854	−	0.0180114i
$100$		0			0
$101$	−223.136	−	223.136i	−0.219830	−	0.219830i	0.588597	−	0.808427i	$-0.299681\pi$
$101$	−223.136	−	223.136i	−0.219830	−	0.219830i	−0.808427	+	0.588597i	$0.799681\pi$
$102$		0			0
$103$	217.914			0.208463			0.104232	−	0.994553i	$-0.466762\pi$
$103$	217.914			0.208463			0.104232	+	0.994553i	$0.466762\pi$
$104$		0			0
$105$	−1052.99	+	443.260i	−0.978675	+	0.411979i
$106$		0			0
$107$	−335.407	+	335.407i	−0.303038	+	0.303038i	−0.842201	−	0.539163i	$-0.818740\pi$
$107$	−335.407	+	335.407i	−0.303038	+	0.303038i	0.539163	+	0.842201i	$0.318740\pi$
$108$		0			0
$109$	−1032.70	−	1032.70i	−0.907477	−	0.907477i	0.0885914	−	0.996068i	$-0.471763\pi$
$109$	−1032.70	−	1032.70i	−0.907477	−	0.907477i	−0.996068	+	0.0885914i	$0.971763\pi$
$110$		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
$117$	−20.7435	−	1806.47i	−0.0163909	−	1.42742i
$118$		0			0
$119$			1030.65i			0.793947i
$120$		0			0
$121$		−	1944.14i		−	1.46066i
$122$		0			0
$123$	−299.008	+	733.755i	−0.219192	+	0.537890i
$124$		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	−0.999945	−	0.0105196i	$-0.996651\pi$
$131$	−1515.05	−	1515.05i	−1.01046	−	1.01046i	−0.0105196	−	0.999945i	$-0.503349\pi$
$132$		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	$-0.221358\pi$
$137$	2462.36			1.53557			0.767787	+	0.640706i	$0.221358\pi$
$138$		0			0
$139$	782.125	+	782.125i	0.477259	+	0.477259i	0.904254	−	0.426995i	$-0.140428\pi$
$139$	782.125	+	782.125i	0.477259	+	0.477259i	−0.426995	+	0.904254i	$0.640428\pi$
$140$		0			0
$141$	−747.266	+	1833.77i	−0.446320	+	1.09526i
$142$		0			0
$143$	−3829.23			−2.23927
$144$		0			0
$145$	−1326.66			−0.759816
$146$		0			0
$147$	−521.104	+	1278.77i	−0.292381	+	0.717493i
$148$		0			0
$149$	2532.54	+	2532.54i	1.39244	+	1.39244i	0.819824	+	0.572616i	$0.194071\pi$
$149$	2532.54	+	2532.54i	1.39244	+	1.39244i	0.572616	+	0.819824i	$0.305929\pi$
$150$		0			0
$151$	−571.667			−0.308090			−0.154045	−	0.988064i	$-0.549230\pi$
$151$	−571.667			−0.308090			−0.154045	+	0.988064i	$0.549230\pi$
$152$		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	0.989676	−	0.143323i	$-0.0457788\pi$
$157$	1664.95	+	1664.95i	0.846353	+	0.846353i	−0.143323	+	0.989676i	$0.545779\pi$
$158$		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	$-0.527574\pi$
$163$	1893.19	−	1893.19i	0.909731	−	0.909731i	0.996250	+	0.0865194i	$0.0275744\pi$
$164$		0			0
$165$	−1000.03	+	2454.05i	−0.471833	+	1.15786i
$166$		0			0
$167$		−	2441.42i		−	1.13127i	−0.824655	−	0.565636i	$-0.808631\pi$
$167$		−	2441.42i		−	1.13127i	0.824655	−	0.565636i	$-0.191369\pi$
$168$		0			0
$169$			2280.06i			1.03780i
$170$		0			0
$171$	−405.460	+	4.65585i	−0.181323	+	0.00208212i
$172$		0			0
$173$	856.168	−	856.168i	0.376262	−	0.376262i	−0.493490	−	0.869751i	$-0.664279\pi$
$173$	856.168	−	856.168i	0.376262	−	0.376262i	0.869751	+	0.493490i	$0.164279\pi$
$174$		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	−0.990142	−	0.140068i	$-0.955268\pi$
$179$	−2706.69	−	2706.69i	−1.13021	−	1.13021i	−0.140068	−	0.990142i	$-0.544732\pi$
$180$		0			0
$181$	155.849	−	155.849i	0.0640008	−	0.0640008i	−0.674382	−	0.738383i	$-0.735590\pi$
$181$	155.849	−	155.849i	0.0640008	−	0.0640008i	0.738383	+	0.674382i	$0.235590\pi$
$182$		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
$189$	−3174.72	+	1379.54i	−1.22184	+	0.530936i
$190$		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
$195$	2869.23	+	1169.22i	1.05369	+	0.429382i
$196$		0			0
$197$	−544.245	−	544.245i	−0.196832	−	0.196832i	0.601809	−	0.798640i	$-0.294447\pi$
$197$	−544.245	−	544.245i	−0.196832	−	0.196832i	−0.798640	+	0.601809i	$0.794447\pi$
$198$		0			0
$199$	−609.004			−0.216941			−0.108470	−	0.994100i	$-0.534595\pi$
$199$	−609.004			−0.216941			−0.108470	+	0.994100i	$0.534595\pi$
$200$		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	$-0.779992\pi$
$211$	−407.803	+	407.803i	−0.133053	+	0.133053i	0.637444	+	0.770497i	$0.279992\pi$
$212$		0			0
$213$	2946.87	+	1200.86i	0.947964	+	0.386298i
$214$		0			0
$215$		−	2788.30i		−	0.884466i
$216$		0			0
$217$			77.6591i			0.0242942i
$218$		0			0
$219$	−1595.05	−	649.989i	−0.492163	−	0.200558i
$220$		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	0.743387	−	0.668862i	$-0.233218\pi$
$227$	254.883	+	254.883i	0.0745250	+	0.0745250i	−0.668862	+	0.743387i	$0.733218\pi$
$228$		0			0
$229$	−349.739	+	349.739i	−0.100923	+	0.100923i	−0.755765	−	0.654842i	$-0.772735\pi$
$229$	−349.739	+	349.739i	−0.100923	+	0.100923i	0.654842	+	0.755765i	$0.272735\pi$
$230$		0			0
$231$	2846.60	+	6762.23i	0.810790	+	1.92607i
$232$		0			0
$233$	−1869.42			−0.525621			−0.262810	−	0.964847i	$-0.584649\pi$
$233$	−1869.42			−0.525621			−0.262810	+	0.964847i	$0.584649\pi$
$234$		0			0
$235$	−2401.35	−	2401.35i	−0.666581	−	0.666581i
$236$		0			0
$237$	−2056.93	−	838.205i	−0.563763	−	0.229735i
$238$		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
$243$	−3539.82	−	1348.56i	−0.934483	−	0.356009i
$244$		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	−0.338830	−	0.940847i	$-0.610031\pi$
$251$	2393.97	−	2393.97i	0.602017	−	0.602017i	0.940847	+	0.338830i	$0.110031\pi$
$252$		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
$261$	−4019.28	+	46.1530i	−0.953208	+	0.0109456i
$262$		0			0
$263$		−	2196.24i		−	0.514928i	−0.966288	−	0.257464i	$-0.917113\pi$
$263$		−	2196.24i		−	0.514928i	0.966288	−	0.257464i	$-0.0828869\pi$
$264$		0			0
$265$			3705.79i			0.859037i
$266$		0			0
$267$	370.601	−	909.443i	0.0849454	−	0.208453i
$268$		0			0
$269$	64.1764	−	64.1764i	0.0145461	−	0.0145461i	−0.699796	−	0.714342i	$-0.746726\pi$
$269$	64.1764	−	64.1764i	0.0145461	−	0.0145461i	0.714342	+	0.699796i	$0.246726\pi$
$270$		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	−0.221222	−	0.975223i	$-0.571005\pi$
$277$	3476.10	−	3476.10i	0.754001	−	0.754001i	0.975223	+	0.221222i	$0.0710046\pi$
$278$		0			0
$279$	−59.3988	+	60.7788i	−0.0127459	+	0.0130420i
$280$		0			0
$281$	5597.90			1.18841			0.594204	−	0.804314i	$-0.297467\pi$
$281$	5597.90			1.18841			0.594204	+	0.804314i	$0.297467\pi$
$282$		0			0
$283$	236.800	+	236.800i	0.0497395	+	0.0497395i	0.731539	−	0.681800i	$-0.238802\pi$
$283$	236.800	+	236.800i	0.0497395	+	0.0497395i	−0.681800	+	0.731539i	$0.738802\pi$
$284$		0			0
$285$	262.429	−	643.993i	0.0545437	−	0.133849i
$286$		0			0
$287$	−3762.26			−0.773795
$288$		0			0
$289$	3168.04			0.644828
$290$		0			0
$291$	−2891.23	+	7094.98i	−0.582429	+	1.42926i
$292$		0			0
$293$	−3077.11	−	3077.11i	−0.613537	−	0.613537i	0.330329	−	0.943866i	$-0.392840\pi$
$293$	−3077.11	−	3077.11i	−0.613537	−	0.613537i	−0.943866	+	0.330329i	$0.892840\pi$
$294$		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	$-0.676115\pi$
$307$	1749.92	−	1749.92i	0.325321	−	0.325321i	0.850804	+	0.525483i	$0.176115\pi$
$308$		0			0
$309$	−427.305	+	1048.59i	−0.0786685	+	0.193050i
$310$		0			0
$311$			7073.49i			1.28971i	0.764304	+	0.644856i	$0.223083\pi$
$311$			7073.49i			1.28971i	−0.764304	+	0.644856i	$0.776917\pi$
$312$		0			0
$313$		−	9046.73i		−	1.63371i	−0.576843	−	0.816855i	$-0.695716\pi$
$313$		−	9046.73i		−	1.63371i	0.576843	−	0.816855i	$-0.304284\pi$
$314$		0			0
$315$	−68.1636	−	5936.10i	−0.0121923	−	1.06178i
$316$		0			0
$317$	4477.40	−	4477.40i	0.793300	−	0.793300i	−0.188729	−	0.982029i	$-0.560437\pi$
$317$	4477.40	−	4477.40i	0.793300	−	0.793300i	0.982029	+	0.188729i	$0.0604369\pi$
$318$		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	$-0.210247\pi$
$331$	1060.84	+	1060.84i	0.176160	+	0.176160i	−0.613519	+	0.789680i	$0.710247\pi$
$332$		0			0
$333$	1610.32	−	18.4911i	0.264999	−	0.00304296i
$334$		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
$339$	4861.22	+	1980.96i	0.778836	+	0.317378i
$340$		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	−0.882906	−	0.469549i	$-0.844416\pi$
$347$	−2671.89	+	2671.89i	−0.413357	+	0.413357i	0.469549	+	0.882906i	$0.344416\pi$
$348$		0			0
$349$	7144.55	+	7144.55i	1.09581	+	1.09581i	0.994895	+	0.100920i	$0.0321785\pi$
$349$	7144.55	+	7144.55i	1.09581	+	1.09581i	0.100920	+	0.994895i	$0.467821\pi$
$350$		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
$357$	−4959.45	−	2020.99i	−0.735244	−	0.299614i
$358$		0			0
$359$		−	750.165i		−	0.110285i	−0.998479	−	0.0551423i	$-0.982439\pi$
$359$		−	750.165i		−	0.110285i	0.998479	−	0.0551423i	$-0.0175613\pi$
$360$		0			0
$361$			6633.46i			0.967118i
$362$		0			0
$363$	9355.09	+	3812.23i	1.35266	+	0.551213i
$364$		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	−0.724776	−	0.688985i	$-0.758057\pi$
$373$	−257.833	+	257.833i	−0.0357911	+	0.0357911i	0.688985	+	0.724776i	$0.258057\pi$
$374$		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	$-0.133971\pi$
$379$	3719.90	+	3719.90i	0.504164	+	0.504164i	−0.408565	+	0.912729i	$0.633971\pi$
$380$		0			0
$381$	7238.74	+	2949.81i	0.973364	+	0.396649i
$382$		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
$387$	−97.0015	−	8447.48i	−0.0127412	−	1.10959i
$388$		0			0
$389$	5797.69	+	5797.69i	0.755667	+	0.755667i	0.975531	−	0.219864i	$-0.0705613\pi$
$389$	5797.69	+	5797.69i	0.755667	+	0.755667i	−0.219864	+	0.975531i	$0.570561\pi$
$390$		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	0.743060	−	0.669225i	$-0.233374\pi$
$397$	584.046	+	584.046i	0.0738348	+	0.0738348i	−0.669225	+	0.743060i	$0.733374\pi$
$398$		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
$405$	4486.97	−	4697.94i	0.550517	−	0.576401i
$406$		0			0
$407$		−	3413.43i		−	0.415718i
$408$		0			0
$409$		−	2543.09i		−	0.307451i	−0.988114	−	0.153726i	$-0.950873\pi$
$409$		−	2543.09i		−	0.307451i	0.988114	−	0.153726i	$-0.0491272\pi$
$410$		0			0
$411$	−4828.41	+	11848.8i	−0.579484	+	1.42204i
$412$		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	0.464263	−	0.885697i	$-0.346319\pi$
$419$	−3614.52	−	3614.52i	−0.421434	−	0.421434i	−0.885697	+	0.464263i	$0.846319\pi$
$420$		0			0
$421$	−10063.8	+	10063.8i	−1.16504	+	1.16504i	−0.181683	+	0.983357i	$0.558155\pi$
$421$	−10063.8	+	10063.8i	−1.16504	+	1.16504i	−0.983357	+	0.181683i	$0.941845\pi$
$422$		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
$429$	7508.68	−	18426.1i	0.845041	−	2.07370i
$430$		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
$435$	2601.44	−	6383.84i	0.286734	−	0.703636i
$436$		0			0
$437$	−567.308	−	567.308i	−0.0621007	−	0.0621007i
$438$		0			0
$439$	2550.46			0.277282			0.138641	−	0.990343i	$-0.455727\pi$
$439$	2550.46			0.277282			0.138641	+	0.990343i	$0.455727\pi$
$440$		0			0
$441$	−5131.57	−	5015.06i	−0.554106	−	0.541525i
$442$		0			0
$443$	6114.74	−	6114.74i	0.655801	−	0.655801i	−0.298582	−	0.954384i	$-0.596514\pi$
$443$	6114.74	−	6114.74i	0.655801	−	0.655801i	0.954384	+	0.298582i	$0.0965138\pi$
$444$		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
$453$	1120.97	−	2750.84i	0.116265	−	0.285310i
$454$		0			0
$455$			14711.7i			1.51581i
$456$		0			0
$457$			1301.43i			0.133213i	0.997779	+	0.0666063i	$0.0212172\pi$
$457$			1301.43i			0.133213i	−0.997779	+	0.0666063i	$0.978783\pi$
$458$		0			0
$459$	−2335.65	−	5375.01i	−0.237514	−	0.546589i
$460$		0			0
$461$	−11243.0	+	11243.0i	−1.13587	+	1.13587i	−0.146689	+	0.989183i	$0.546862\pi$
$461$	−11243.0	+	11243.0i	−1.13587	+	1.13587i	−0.989183	+	0.146689i	$0.953138\pi$
$462$		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	0.973065	−	0.230532i	$-0.0740465\pi$
$467$	7493.61	+	7493.61i	0.742533	+	0.742533i	−0.230532	+	0.973065i	$0.574047\pi$
$468$		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
$477$	128.920	+	11227.1i	0.0123749	+	1.07768i
$478$		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
$483$	−6342.53	−	2584.60i	−0.597505	−	0.243485i
$484$		0			0
$485$	−9290.98	−	9290.98i	−0.869859	−	0.869859i
$486$		0			0
$487$	7486.49			0.696602			0.348301	−	0.937383i	$-0.386759\pi$
$487$	7486.49			0.696602			0.348301	+	0.937383i	$0.386759\pi$
$488$		0			0
$489$	5397.62	+	12822.3i	0.499159	+	1.18577i
$490$		0			0
$491$	−6345.55	+	6345.55i	−0.583239	+	0.583239i	−0.935792	−	0.352553i	$-0.885314\pi$
$491$	−6345.55	+	6345.55i	−0.583239	+	0.583239i	0.352553	+	0.935792i	$0.385314\pi$
$492$		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	$-0.594172\pi$
$499$	7412.65	−	7412.65i	0.665001	−	0.665001i	0.956555	+	0.291553i	$0.0941721\pi$
$500$		0			0
$501$	11748.0	+	4787.34i	1.04763	+	0.426911i
$502$		0			0
$503$			3879.66i			0.343908i	0.985105	+	0.171954i	$0.0550080\pi$
$503$			3879.66i			0.343908i	−0.985105	+	0.171954i	$0.944992\pi$
$504$		0			0
$505$			2812.10i			0.247796i
$506$		0			0
$507$	−10971.5	−	4470.93i	−0.961071	−	0.391639i
$508$		0			0
$509$	−4843.90	+	4843.90i	−0.421811	+	0.421811i	−0.885827	−	0.464016i	$-0.846408\pi$
$509$	−4843.90	+	4843.90i	−0.421811	+	0.421811i	0.464016	+	0.885827i	$0.346408\pi$
$510$		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	$-0.524159\pi$
$521$	−1803.41			−0.151649			−0.0758244	+	0.997121i	$0.524159\pi$
$522$		0			0
$523$	−15074.6	−	15074.6i	−1.26036	−	1.26036i	−0.950919	−	0.309440i	$-0.899859\pi$
$523$	−15074.6	−	15074.6i	−1.26036	−	1.26036i	−0.309440	−	0.950919i	$-0.600141\pi$
$524$		0			0
$525$	−5412.25	−	2205.51i	−0.449924	−	0.183345i
$526$		0			0
$527$	−131.482			−0.0108680
$528$		0			0
$529$	9313.07			0.765437
$530$		0			0
$531$	−17007.7	+	195.297i	−1.38996	+	0.0159608i
$532$		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	−0.993696	−	0.112106i	$-0.964240\pi$
$541$	−13914.7	−	13914.7i	−1.10580	−	1.10580i	−0.112106	−	0.993696i	$-0.535760\pi$
$542$		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	$-0.793361\pi$
$547$	−2457.00	+	2457.00i	−0.192054	+	0.192054i	0.604529	+	0.796583i	$0.293361\pi$
$548$		0			0
$549$	9.57855	+	834.158i	0.000744631	+	0.0648470i
$550$		0			0
$551$		−	2235.76i		−	0.172862i
$552$		0			0
$553$		−	10546.7i		−	0.811015i
$554$		0			0
$555$	−1042.26	+	2557.67i	−0.0797143	+	0.195616i
$556$		0			0
$557$	13996.0	−	13996.0i	1.06468	−	1.06468i	0.0669265	−	0.997758i	$-0.478681\pi$
$557$	13996.0	−	13996.0i	1.06468	−	1.06468i	0.997758	−	0.0669265i	$-0.0213193\pi$
$558$		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	0.167413	−	0.985887i	$-0.446459\pi$
$563$	−10933.7	−	10933.7i	−0.818474	−	0.818474i	−0.985887	+	0.167413i	$0.946459\pi$
$564$		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	$-0.553191\pi$
$569$	−4515.04			−0.332654			−0.166327	+	0.986071i	$0.553191\pi$
$570$		0			0
$571$	6425.75	+	6425.75i	0.470945	+	0.470945i	0.902220	−	0.431276i	$-0.141936\pi$
$571$	6425.75	+	6425.75i	0.470945	+	0.470945i	−0.431276	+	0.902220i	$0.641936\pi$
$572$		0			0
$573$	2339.88	−	5741.98i	0.170593	−	0.418629i
$574$		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
$579$	9899.54	−	24293.2i	0.710554	−	1.74368i
$580$		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	−0.588074	−	0.808807i	$-0.700114\pi$
$587$	3139.23	−	3139.23i	0.220732	−	0.220732i	0.808807	+	0.588074i	$0.200114\pi$
$588$		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
$597$	1194.19	−	2930.50i	0.0818675	−	0.200900i
$598$		0			0
$599$		−	10012.2i		−	0.682950i	−0.939891	−	0.341475i	$-0.889073\pi$
$599$		−	10012.2i		−	0.682950i	0.939891	−	0.341475i	$-0.110927\pi$
$600$		0			0
$601$		−	10154.9i		−	0.689229i	−0.938744	−	0.344614i	$-0.888010\pi$
$601$		−	10154.9i		−	0.689229i	0.938744	−	0.344614i	$-0.111990\pi$
$602$		0			0
$603$	21847.9	−	250.877i	1.47548	−	0.0169428i
$604$		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	−0.993313	−	0.115451i	$-0.963169\pi$
$613$	−13323.5	+	13323.5i	−0.877863	+	0.877863i	0.115451	+	0.993313i	$0.463169\pi$
$614$		0			0
$615$	6507.77	−	2739.49i	0.426697	−	0.179621i
$616$		0			0
$617$	2727.73			0.177981			0.0889906	−	0.996032i	$-0.471636\pi$
$617$	2727.73			0.177981			0.0889906	+	0.996032i	$0.471636\pi$
$618$		0			0
$619$	−9506.19	−	9506.19i	−0.617263	−	0.617263i	0.327565	−	0.944829i	$-0.393772\pi$
$619$	−9506.19	−	9506.19i	−0.617263	−	0.617263i	−0.944829	+	0.327565i	$0.893772\pi$
$620$		0			0
$621$	−2987.01	−	6873.98i	−0.193019	−	0.444192i
$622$		0			0
$623$	4663.08			0.299876
$624$		0			0
$625$	7848.55			0.502307
$626$		0			0
$627$	−4135.70	−	1685.31i	−0.263419	−	0.107344i
$628$		0			0
$629$	1761.79	+	1761.79i	0.111681	+	0.111681i
$630$		0			0
$631$	−6939.01			−0.437778			−0.218889	−	0.975750i	$-0.570243\pi$
$631$	−6939.01			−0.437778			−0.218889	+	0.975750i	$0.570243\pi$
$632$		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	−0.0751092	+	0.997175i	$0.523931\pi$
$643$	−17483.4	+	17483.4i	−1.07228	+	1.07228i	−0.997175	+	0.0751092i	$0.976069\pi$
$644$		0			0
$645$	13417.2	+	5467.54i	0.819070	+	0.333774i
$646$		0			0
$647$			23409.6i			1.42245i	0.702964	+	0.711225i	$0.251859\pi$
$647$			23409.6i			1.42245i	−0.702964	+	0.711225i	$0.748141\pi$
$648$		0			0
$649$			36051.6i			2.18050i
$650$		0			0
$651$	−373.692	−	152.281i	−0.0224979	−	0.00916798i
$652$		0			0
$653$	−9012.83	+	9012.83i	−0.540122	+	0.540122i	−0.923565	−	0.383443i	$-0.874738\pi$
$653$	−9012.83	+	9012.83i	−0.540122	+	0.540122i	0.383443	+	0.923565i	$0.374738\pi$
$654$		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	0.696429	−	0.717625i	$-0.254771\pi$
$659$	−358.576	−	358.576i	−0.0211960	−	0.0211960i	−0.717625	+	0.696429i	$0.754771\pi$
$660$		0			0
$661$	14598.1	−	14598.1i	0.859004	−	0.859004i	−0.132217	−	0.991221i	$-0.542210\pi$
$661$	14598.1	−	14598.1i	0.859004	−	0.859004i	0.991221	+	0.132217i	$0.0422095\pi$
$662$		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
$669$	14230.5	+	5798.97i	0.822395	+	0.335129i
$670$		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
$675$	−2548.90	−	5865.75i	−0.145344	−	0.334478i
$676$		0			0
$677$	5301.22	+	5301.22i	0.300949	+	0.300949i	0.841385	−	0.540436i	$-0.181741\pi$
$677$	5301.22	+	5301.22i	0.300949	+	0.300949i	−0.540436	+	0.841385i	$0.681741\pi$
$678$		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	−0.575857	−	0.817551i	$-0.695331\pi$
$683$	4314.17	−	4314.17i	0.241694	−	0.241694i	0.817551	+	0.575857i	$0.195331\pi$
$684$		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	$-0.857471\pi$
$691$	−8509.21	+	8509.21i	−0.468460	+	0.468460i	0.432955	+	0.901415i	$0.357471\pi$
$692$		0			0
$693$	−38121.4	+	437.744i	−2.08963	+	0.0239950i
$694$		0			0
$695$		−	9856.85i		−	0.537974i
$696$		0			0
$697$		−	6369.75i		−	0.346157i
$698$		0			0
$699$	3665.72	−	8995.56i	0.198355	−	0.486757i
$700$		0			0
$701$	−2086.28	+	2086.28i	−0.112408	+	0.112408i	−0.761073	−	0.648666i	$-0.775327\pi$
$701$	−2086.28	+	2086.28i	−0.112408	+	0.112408i	0.648666	+	0.761073i	$0.275327\pi$
$702$		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	0.0558039	−	0.998442i	$-0.482228\pi$
$709$	19902.7	−	19902.7i	1.05425	−	1.05425i	0.998442	−	0.0558039i	$-0.0177722\pi$
$710$		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
$717$	−4158.33	+	10204.4i	−0.216591	+	0.531507i
$718$		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
$723$	−6071.42	+	14899.1i	−0.312308	+	0.766393i
$724$		0			0
$725$	−4798.83	−	4798.83i	−0.245826	−	0.245826i
$726$		0			0
$727$	−14601.8			−0.744911			−0.372456	−	0.928050i	$-0.621484\pi$
$727$	−14601.8			−0.744911			−0.372456	+	0.928050i	$0.621484\pi$
$728$		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	0.984972	−	0.172713i	$-0.0552533\pi$
$733$	16119.5	+	16119.5i	0.812259	+	0.812259i	−0.172713	+	0.984972i	$0.555253\pi$
$734$		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	0.396099	−	0.918208i	$-0.370364\pi$
$739$	26403.6	−	26403.6i	1.31431	−	1.31431i	0.918208	−	0.396099i	$-0.129636\pi$
$740$		0			0
$741$	−1970.43	+	4835.38i	−0.0976864	+	0.239719i
$742$		0			0
$743$		−	24491.2i		−	1.20928i	−0.796499	−	0.604640i	$-0.793317\pi$
$743$		−	24491.2i		−	1.20928i	0.796499	−	0.604640i	$-0.206683\pi$
$744$		0			0
$745$		−	31916.7i		−	1.56958i
$746$		0			0
$747$	107.519	+	9363.40i	0.00526628	+	0.458620i
$748$		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	−0.385407	−	0.922747i	$-0.625939\pi$
$757$	11191.6	−	11191.6i	0.537340	−	0.537340i	0.922747	+	0.385407i	$0.125939\pi$
$758$		0			0
$759$	−14641.7	+	6163.52i	−0.700212	+	0.294758i
$760$		0			0
$761$	10016.9			0.477153			0.238576	−	0.971124i	$-0.423319\pi$
$761$	10016.9			0.477153			0.238576	+	0.971124i	$0.423319\pi$
$762$		0			0
$763$	25479.7	+	25479.7i	1.20895	+	1.20895i
$764$		0			0
$765$	10050.2	−	115.405i	0.474988	−	0.00545424i
$766$		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
$771$	17238.9	+	7024.89i	0.805243	+	0.328139i
$772$		0			0
$773$	−26695.6	−	26695.6i	−1.24214	−	1.24214i	−0.959111	−	0.283030i	$-0.908660\pi$
$773$	−26695.6	−	26695.6i	−1.24214	−	1.24214i	−0.283030	−	0.959111i	$-0.591340\pi$
$774$		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	$-0.595933\pi$
$787$	14529.3	−	14529.3i	0.658087	−	0.658087i	0.954927	+	0.296840i	$0.0959328\pi$
$788$		0			0
$789$	10568.2	+	4306.58i	0.476855	+	0.194320i
$790$		0			0
$791$			24925.5i			1.12041i
$792$		0			0
$793$		−	2067.33i		−	0.0925763i
$794$		0			0
$795$	−17832.1	−	7266.64i	−0.795521	−	0.324177i
$796$		0			0
$797$	18417.2	−	18417.2i	0.818532	−	0.818532i	−0.167363	−	0.985895i	$-0.553525\pi$
$797$	18417.2	−	18417.2i	0.818532	−	0.818532i	0.985895	+	0.167363i	$0.0535253\pi$
$798$		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	$-0.599033\pi$
$809$	−14088.2			−0.612253			−0.306127	+	0.951991i	$0.599033\pi$
$810$		0			0
$811$	−16384.8	−	16384.8i	−0.709429	−	0.709429i	0.256986	−	0.966415i	$-0.417271\pi$
$811$	−16384.8	−	16384.8i	−0.709429	−	0.709429i	−0.966415	+	0.256986i	$0.917271\pi$
$812$		0			0
$813$	−17454.9	−	7112.92i	−0.752976	−	0.306840i
$814$		0			0
$815$	−23859.2			−1.02546
$816$		0			0
$817$	4698.99			0.201220
$818$		0			0
$819$	511.802	+	44570.8i	0.0218361	+	1.90162i
$820$		0			0
$821$	−1002.06	−	1002.06i	−0.0425968	−	0.0425968i	0.685488	−	0.728084i	$-0.259589\pi$
$821$	−1002.06	−	1002.06i	−0.0425968	−	0.0425968i	−0.728084	+	0.685488i	$0.759589\pi$
$822$		0			0
$823$	36539.2			1.54760			0.773802	−	0.633428i	$-0.218353\pi$
$823$	36539.2			1.54760			0.773802	+	0.633428i	$0.218353\pi$
$824$		0			0
$825$	−12494.2	+	5259.50i	−0.527262	+	0.221954i
$826$		0			0
$827$	−1314.92	+	1314.92i	−0.0552892	+	0.0552892i	−0.734211	−	0.678922i	$-0.762448\pi$
$827$	−1314.92	+	1314.92i	−0.0552892	+	0.0552892i	0.678922	+	0.734211i	$0.262448\pi$
$828$		0			0
$829$	−18101.1	−	18101.1i	−0.758357	−	0.758357i	0.217667	−	0.976023i	$-0.430155\pi$
$829$	−18101.1	−	18101.1i	−0.758357	−	0.758357i	−0.976023	+	0.217667i	$0.930155\pi$
$830$		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
$837$	−175.990	−	405.005i	−0.00726777	−	0.0167252i
$838$		0			0
$839$		−	11658.5i		−	0.479734i	−0.970806	−	0.239867i	$-0.922896\pi$
$839$		−	11658.5i		−	0.479734i	0.970806	−	0.239867i	$-0.0771038\pi$
$840$		0			0
$841$			2226.09i			0.0912745i
$842$		0			0
$843$	−10976.8	+	26936.8i	−0.448473	+	1.10054i
$844$		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	−0.853690	−	0.520781i	$-0.825641\pi$
$853$	−8293.73	+	8293.73i	−0.332910	+	0.332910i	0.520781	+	0.853690i	$0.325641\pi$
$854$		0			0
$855$	2584.27	+	2525.60i	0.103369	+	0.101022i
$856$		0			0
$857$	5209.55			0.207649			0.103824	−	0.994596i	$-0.466892\pi$
$857$	5209.55			0.207649			0.103824	+	0.994596i	$0.466892\pi$
$858$		0			0
$859$	−21529.9	−	21529.9i	−0.855168	−	0.855168i	0.135596	−	0.990764i	$-0.456705\pi$
$859$	−21529.9	−	21529.9i	−0.855168	−	0.855168i	−0.990764	+	0.135596i	$0.956705\pi$
$860$		0			0
$861$	7377.37	−	18103.8i	0.292009	−	0.716581i
$862$		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
$867$	−6212.17	+	15244.5i	−0.243341	+	0.597150i
$868$		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	0.898536	−	0.438900i	$-0.144632\pi$
$877$	11937.5	+	11937.5i	0.459636	+	0.459636i	−0.438900	+	0.898536i	$0.644632\pi$
$878$		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	$-0.722696\pi$
$883$	3179.05	−	3179.05i	0.121159	−	0.121159i	0.765087	+	0.643927i	$0.222696\pi$
$884$		0			0
$885$	11008.0	−	27013.3i	0.418114	−	1.02604i
$886$		0			0
$887$			24947.8i			0.944380i	0.881497	+	0.472190i	$0.156536\pi$
$887$			24947.8i			0.944380i	−0.881497	+	0.472190i	$0.843464\pi$
$888$		0			0
$889$			37115.9i			1.40026i
$890$		0			0
$891$	−30170.0	−	28815.2i	−1.13438	−	1.08344i
$892$		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	$-0.0818970\pi$
$907$	19465.8	+	19465.8i	0.712626	+	0.712626i	−0.254458	+	0.967084i	$0.581897\pi$
$908$		0			0
$909$	97.8296	+	8519.59i	0.00356964	+	0.310866i
$910$		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
$915$	−1324.90	−	539.900i	−0.0478686	−	0.0195066i
$916$		0			0
$917$	37380.7	+	37380.7i	1.34615	+	1.34615i
$918$		0			0
$919$	37455.2			1.34443			0.672216	−	0.740355i	$-0.265343\pi$
$919$	37455.2			1.34443			0.672216	+	0.740355i	$0.265343\pi$
$920$		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
$933$	−34037.3	−	13870.3i	−1.19435	−	0.486703i
$934$		0			0
$935$		−	21303.7i		−	0.745138i
$936$		0			0
$937$			30708.1i			1.07064i	0.844650	+	0.535320i	$0.179809\pi$
$937$			30708.1i			1.07064i	−0.844650	+	0.535320i	$0.820191\pi$
$938$		0			0
$939$	43532.4	+	17739.6i	1.51292	+	0.616518i
$940$		0			0
$941$	−817.247	+	817.247i	−0.0283119	+	0.0283119i	−0.721121	−	0.692809i	$-0.756373\pi$
$941$	−817.247	+	817.247i	−0.0283119	+	0.0283119i	0.692809	+	0.721121i	$0.256373\pi$
$942$		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	0.323644	−	0.946179i	$-0.395092\pi$
$947$	−18142.1	−	18142.1i	−0.622535	−	0.622535i	−0.946179	+	0.323644i	$0.895092\pi$
$948$		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	$-0.454811\pi$
$953$	8325.23			0.282981			0.141490	+	0.989940i	$0.454811\pi$
$954$		0			0
$955$	7519.21	+	7519.21i	0.254781	+	0.254781i
$956$		0			0
$957$	−40996.8	−	16706.3i	−1.38478	−	0.564304i
$958$		0			0
$959$	−60753.4			−2.04570
$960$		0			0
$961$	29781.1			0.999667
$962$		0			0
$963$	12806.3	−	147.053i	0.428532	−	0.00492078i
$964$		0			0
$965$	31812.2	+	31812.2i	1.06122	+	1.06122i
$966$		0			0
$967$	−8911.71			−0.296361			−0.148181	−	0.988960i	$-0.547342\pi$
$967$	−8911.71			−0.296361			−0.148181	+	0.988960i	$0.547342\pi$
$968$		0			0
$969$	3004.42	−	1264.73i	0.0996037	−	0.0419288i
$970$		0			0
$971$	−24556.5	+	24556.5i	−0.811593	+	0.811593i	−0.984873	−	0.173280i	$-0.944563\pi$
$971$	−24556.5	+	24556.5i	−0.811593	+	0.811593i	0.173280	+	0.984873i	$0.444563\pi$
$972$		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
$981$	452.769	+	39429.9i	0.0147358	+	1.28328i
$982$		0			0
$983$		−	52008.6i		−	1.68751i	−0.536732	−	0.843753i	$-0.680341\pi$
$983$		−	52008.6i		−	1.68751i	0.536732	−	0.843753i	$-0.319659\pi$
$984$		0			0
$985$			6858.94i			0.221872i
$986$		0			0
$987$	18437.2	−	45244.3i	0.594592	−	1.45911i
$988$		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	−0.654041	−	0.756459i	$-0.726927\pi$
$997$	3224.20	−	3224.20i	0.102419	−	0.102419i	0.756459	+	0.654041i	$0.226927\pi$
$998$		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.a.95.9		44
3.2	odd	2	inner	384.4.k.a.95.3		44
4.3	odd	2		384.4.k.b.95.14		44
8.3	odd	2		48.4.k.a.35.20	yes	44
8.5	even	2		192.4.k.a.47.14		44
12.11	even	2		384.4.k.b.95.20		44
16.3	odd	4		192.4.k.a.143.20		44
16.5	even	4		384.4.k.b.287.20		44
16.11	odd	4	inner	384.4.k.a.287.3		44
16.13	even	4		48.4.k.a.11.3	✓	44
24.5	odd	2		192.4.k.a.47.20		44
24.11	even	2		48.4.k.a.35.3	yes	44
48.5	odd	4		384.4.k.b.287.14		44
48.11	even	4	inner	384.4.k.a.287.9		44
48.29	odd	4		48.4.k.a.11.20	yes	44
48.35	even	4		192.4.k.a.143.14		44

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

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)

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