LMFDB - Embedded newform 384.2.k.a.95.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,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, 2, names="a")

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

chi := DirichletCharacter("384.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.4
Root			$1.27715 - 0.607364i$ of defining polynomial
Character	$\chi$	$=$	384.95
Dual form			384.2.k.a.287.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0835731 - 1.73003i) q^{3} +(-0.431733 - 0.431733i) q^{5} +3.10278 q^{7} +(-2.98603 - 0.289169i) q^{9} +O(q^{10})$	\(q+(0.0835731 - 1.73003i) q^{3} +(-0.431733 - 0.431733i) q^{5} +3.10278 q^{7} +(-2.98603 - 0.289169i) q^{9} +(2.98603 - 2.98603i) q^{11} +(-2.10278 - 2.10278i) q^{13} +(-0.782994 + 0.710831i) q^{15} +2.42945i q^{17} +(-0.710831 + 0.710831i) q^{19} +(0.259309 - 5.36790i) q^{21} -5.97206i q^{23} -4.62721i q^{25} +(-0.749823 + 5.14177i) q^{27} +(-2.86119 + 2.86119i) q^{29} -0.524438i q^{31} +(-4.91638 - 5.41549i) q^{33} +(-1.33957 - 1.33957i) q^{35} +(-1.52444 + 1.52444i) q^{37} +(-3.81361 + 3.46214i) q^{39} +1.81568 q^{41} +(0.710831 + 0.710831i) q^{43} +(1.16432 + 1.41401i) q^{45} +7.53805 q^{47} +2.62721 q^{49} +(4.20304 + 0.203037i) q^{51} +(8.83325 + 8.83325i) q^{53} -2.57834 q^{55} +(1.17036 + 1.28917i) q^{57} +(-0.0804722 + 0.0804722i) q^{59} +(5.72999 + 5.72999i) q^{61} +(-9.26498 - 0.897225i) q^{63} +1.81568i q^{65} +(-0.391944 + 0.391944i) q^{67} +(-10.3319 - 0.499104i) q^{69} +5.01985i q^{71} +13.4600i q^{73} +(-8.00523 - 0.386711i) q^{75} +(9.26498 - 9.26498i) q^{77} -3.47556i q^{79} +(8.83276 + 1.72693i) q^{81} +(4.55202 + 4.55202i) q^{83} +(1.04888 - 1.04888i) q^{85} +(4.71083 + 5.18907i) q^{87} +12.5579 q^{89} +(-6.52444 - 6.52444i) q^{91} +(-0.907295 - 0.0438289i) q^{93} +0.613779 q^{95} -8.67609 q^{97} +(-9.77985 + 8.05292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 8 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 + 8 * q^7	$ 12 q - 2 q^{3} + 8 q^{7} + 4 q^{13} - 12 q^{19} + 8 q^{21} + 10 q^{27} - 4 q^{33} + 4 q^{37} - 20 q^{39} + 12 q^{43} + 12 q^{45} - 20 q^{49} + 24 q^{51} - 24 q^{55} - 12 q^{61} + 28 q^{67} - 4 q^{69} - 34 q^{75} - 4 q^{81} - 32 q^{85} + 60 q^{87} - 56 q^{91} - 28 q^{93} - 8 q^{97} - 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 8 * q^7 + 4 * q^13 - 12 * q^19 + 8 * q^21 + 10 * q^27 - 4 * q^33 + 4 * q^37 - 20 * q^39 + 12 * q^43 + 12 * q^45 - 20 * q^49 + 24 * q^51 - 24 * q^55 - 12 * q^61 + 28 * q^67 - 4 * q^69 - 34 * q^75 - 4 * q^81 - 32 * q^85 + 60 * q^87 - 56 * q^91 - 28 * q^93 - 8 * q^97 - 52 * 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
$3$	0.0835731	−	1.73003i	0.0482510	−	0.998835i
$3$	0.0835731	−	1.73003i	0.0482510	−	0.998835i
$4$		0			0
$5$	−0.431733	−	0.431733i	−0.193077	−	0.193077i	0.603947	−	0.797024i	$-0.293594\pi$
$5$	−0.431733	−	0.431733i	−0.193077	−	0.193077i	−0.797024	+	0.603947i	$0.793594\pi$
$6$		0			0
$7$	3.10278			1.17274			0.586369	−	0.810044i	$-0.300557\pi$
$7$	3.10278			1.17274			0.586369	+	0.810044i	$0.300557\pi$
$8$		0			0
$9$	−2.98603	−	0.289169i	−0.995344	−	0.0963895i
$10$		0			0
$11$	2.98603	−	2.98603i	0.900322	−	0.900322i	−0.0951415	−	0.995464i	$-0.530330\pi$
$11$	2.98603	−	2.98603i	0.900322	−	0.900322i	0.995464	+	0.0951415i	$0.0303304\pi$
$12$		0			0
$13$	−2.10278	−	2.10278i	−0.583205	−	0.583205i	0.352578	−	0.935783i	$-0.385305\pi$
$13$	−2.10278	−	2.10278i	−0.583205	−	0.583205i	−0.935783	+	0.352578i	$0.885305\pi$
$14$		0			0
$15$	−0.782994	+	0.710831i	−0.202168	+	0.183536i
$16$		0			0
$17$			2.42945i			0.589229i	0.955616	+	0.294615i	$0.0951913\pi$
$17$			2.42945i			0.589229i	−0.955616	+	0.294615i	$0.904809\pi$
$18$		0			0
$19$	−0.710831	+	0.710831i	−0.163076	+	0.163076i	−0.783928	−	0.620852i	$-0.786787\pi$
$19$	−0.710831	+	0.710831i	−0.163076	+	0.163076i	0.620852	+	0.783928i	$0.286787\pi$
$20$		0			0
$21$	0.259309	−	5.36790i	0.0565858	−	1.17137i
$22$		0			0
$23$		−	5.97206i		−	1.24526i	−0.782516	−	0.622631i	$-0.786064\pi$
$23$		−	5.97206i		−	1.24526i	0.782516	−	0.622631i	$-0.213936\pi$
$24$		0			0
$25$		−	4.62721i		−	0.925443i
$26$		0			0
$27$	−0.749823	+	5.14177i	−0.144304	+	0.989533i
$28$		0			0
$29$	−2.86119	+	2.86119i	−0.531309	+	0.531309i	−0.920962	−	0.389653i	$-0.872595\pi$
$29$	−2.86119	+	2.86119i	−0.531309	+	0.531309i	0.389653	+	0.920962i	$0.372595\pi$
$30$		0			0
$31$		−	0.524438i		−	0.0941918i	−0.998890	−	0.0470959i	$-0.985003\pi$
$31$		−	0.524438i		−	0.0941918i	0.998890	−	0.0470959i	$-0.0149966\pi$
$32$		0			0
$33$	−4.91638	−	5.41549i	−0.855832	−	0.942715i
$34$		0			0
$35$	−1.33957	−	1.33957i	−0.226429	−	0.226429i
$36$		0			0
$37$	−1.52444	+	1.52444i	−0.250616	+	0.250616i	−0.821223	−	0.570607i	$-0.806708\pi$
$37$	−1.52444	+	1.52444i	−0.250616	+	0.250616i	0.570607	+	0.821223i	$0.306708\pi$
$38$		0			0
$39$	−3.81361	+	3.46214i	−0.610666	+	0.554385i
$40$		0			0
$41$	1.81568			0.283561			0.141780	−	0.989898i	$-0.454717\pi$
$41$	1.81568			0.283561			0.141780	+	0.989898i	$0.454717\pi$
$42$		0			0
$43$	0.710831	+	0.710831i	0.108401	+	0.108401i	0.759227	−	0.650826i	$-0.225577\pi$
$43$	0.710831	+	0.710831i	0.108401	+	0.108401i	−0.650826	+	0.759227i	$0.725577\pi$
$44$		0			0
$45$	1.16432	+	1.41401i	0.173567	+	0.210788i
$46$		0			0
$47$	7.53805			1.09954			0.549769	−	0.835317i	$-0.314716\pi$
$47$	7.53805			1.09954			0.549769	+	0.835317i	$0.314716\pi$
$48$		0			0
$49$	2.62721			0.375316
$50$		0			0
$51$	4.20304	+	0.203037i	0.588543	+	0.0284309i
$52$		0			0
$53$	8.83325	+	8.83325i	1.21334	+	1.21334i	0.969921	+	0.243419i	$0.0782690\pi$
$53$	8.83325	+	8.83325i	1.21334	+	1.21334i	0.243419	+	0.969921i	$0.421731\pi$
$54$		0			0
$55$	−2.57834			−0.347663
$56$		0			0
$57$	1.17036	+	1.28917i	0.155017	+	0.170755i
$58$		0			0
$59$	−0.0804722	+	0.0804722i	−0.0104766	+	0.0104766i	−0.712326	−	0.701849i	$-0.752358\pi$
$59$	−0.0804722	+	0.0804722i	−0.0104766	+	0.0104766i	0.701849	+	0.712326i	$0.252358\pi$
$60$		0			0
$61$	5.72999	+	5.72999i	0.733650	+	0.733650i	0.971341	−	0.237691i	$-0.0763906\pi$
$61$	5.72999	+	5.72999i	0.733650	+	0.733650i	−0.237691	+	0.971341i	$0.576391\pi$
$62$		0			0
$63$	−9.26498	−	0.897225i	−1.16728	−	0.113040i
$64$		0			0
$65$			1.81568i			0.225207i
$66$		0			0
$67$	−0.391944	+	0.391944i	−0.0478835	+	0.0478835i	−0.730643	−	0.682760i	$-0.760780\pi$
$67$	−0.391944	+	0.391944i	−0.0478835	+	0.0478835i	0.682760	+	0.730643i	$0.260780\pi$
$68$		0			0
$69$	−10.3319	−	0.499104i	−1.24381	−	0.0600850i
$70$		0			0
$71$			5.01985i			0.595747i	0.954605	+	0.297873i	$0.0962774\pi$
$71$			5.01985i			0.595747i	−0.954605	+	0.297873i	$0.903723\pi$
$72$		0			0
$73$			13.4600i			1.57537i	0.616078	+	0.787686i	$0.288721\pi$
$73$			13.4600i			1.57537i	−0.616078	+	0.787686i	$0.711279\pi$
$74$		0			0
$75$	−8.00523	−	0.386711i	−0.924365	−	0.0446535i
$76$		0			0
$77$	9.26498	−	9.26498i	1.05584	−	1.05584i
$78$		0			0
$79$		−	3.47556i		−	0.391031i	−0.980701	−	0.195516i	$-0.937362\pi$
$79$		−	3.47556i		−	0.391031i	0.980701	−	0.195516i	$-0.0626380\pi$
$80$		0			0
$81$	8.83276	+	1.72693i	0.981418	+	0.191881i
$82$		0			0
$83$	4.55202	+	4.55202i	0.499649	+	0.499649i	0.911329	−	0.411680i	$-0.135058\pi$
$83$	4.55202	+	4.55202i	0.499649	+	0.499649i	−0.411680	+	0.911329i	$0.635058\pi$
$84$		0			0
$85$	1.04888	−	1.04888i	0.113767	−	0.113767i
$86$		0			0
$87$	4.71083	+	5.18907i	0.505054	+	0.556326i
$88$		0			0
$89$	12.5579			1.33114			0.665568	−	0.746338i	$-0.268190\pi$
$89$	12.5579			1.33114			0.665568	+	0.746338i	$0.268190\pi$
$90$		0			0
$91$	−6.52444	−	6.52444i	−0.683947	−	0.683947i
$92$		0			0
$93$	−0.907295	−	0.0438289i	−0.0940821	−	0.00454485i
$94$		0			0
$95$	0.613779			0.0629724
$96$		0			0
$97$	−8.67609			−0.880923			−0.440462	−	0.897771i	$-0.645185\pi$
$97$	−8.67609			−0.880923			−0.440462	+	0.897771i	$0.645185\pi$
$98$		0			0
$99$	−9.77985	+	8.05292i	−0.982912	+	0.809348i
$100$		0			0
$101$	−0.182046	−	0.182046i	−0.0181142	−	0.0181142i	0.697992	−	0.716106i	$-0.254077\pi$
$101$	−0.182046	−	0.182046i	−0.0181142	−	0.0181142i	−0.716106	+	0.697992i	$0.754077\pi$
$102$		0			0
$103$	−6.35720			−0.626394			−0.313197	−	0.949688i	$-0.601400\pi$
$103$	−6.35720			−0.626394			−0.313197	+	0.949688i	$0.601400\pi$
$104$		0			0
$105$	−2.42945	+	2.20555i	−0.237090	+	0.215240i
$106$		0			0
$107$	1.64646	−	1.64646i	0.159169	−	0.159169i	−0.623029	−	0.782199i	$-0.714098\pi$
$107$	1.64646	−	1.64646i	0.159169	−	0.159169i	0.782199	+	0.623029i	$0.214098\pi$
$108$		0			0
$109$	−6.57331	−	6.57331i	−0.629609	−	0.629609i	0.318360	−	0.947970i	$-0.396868\pi$
$109$	−6.57331	−	6.57331i	−0.629609	−	0.629609i	−0.947970	+	0.318360i	$0.896868\pi$
$110$		0			0
$111$	2.50993	+	2.76473i	0.238232	+	0.262417i
$112$		0			0
$113$			8.31277i			0.782000i	0.920391	+	0.391000i	$0.127871\pi$
$113$			8.31277i			0.782000i	−0.920391	+	0.391000i	$0.872129\pi$
$114$		0			0
$115$	−2.57834	+	2.57834i	−0.240431	+	0.240431i
$116$		0			0
$117$	5.67090	+	6.88701i	0.524274	+	0.636704i
$118$		0			0
$119$			7.53805i			0.691012i
$120$		0			0
$121$		−	6.83276i		−	0.621160i
$122$		0			0
$123$	0.151742	−	3.14118i	0.0136821	−	0.283231i
$124$		0			0
$125$	−4.15639	+	4.15639i	−0.371759	+	0.371759i
$126$		0			0
$127$			15.7789i			1.40015i	0.714070	+	0.700074i	$0.246850\pi$
$127$			15.7789i			1.40015i	−0.714070	+	0.700074i	$0.753150\pi$
$128$		0			0
$129$	1.28917	−	1.17036i	0.113505	−	0.103044i
$130$		0			0
$131$	0.0804722	+	0.0804722i	0.00703089	+	0.00703089i	0.710613	−	0.703583i	$-0.248417\pi$
$131$	0.0804722	+	0.0804722i	0.00703089	+	0.00703089i	−0.703583	+	0.710613i	$0.748417\pi$
$132$		0			0
$133$	−2.20555	+	2.20555i	−0.191245	+	0.191245i
$134$		0			0
$135$	2.54359	−	1.89615i	0.218918	−	0.163194i
$136$		0			0
$137$	−13.2604			−1.13291			−0.566457	−	0.824091i	$-0.691686\pi$
$137$	−13.2604			−1.13291			−0.566457	+	0.824091i	$0.691686\pi$
$138$		0			0
$139$	8.39194	+	8.39194i	0.711795	+	0.711795i	0.966911	−	0.255115i	$-0.0821134\pi$
$139$	8.39194	+	8.39194i	0.711795	+	0.711795i	−0.255115	+	0.966911i	$0.582113\pi$
$140$		0			0
$141$	0.629978	−	13.0411i	0.0530537	−	1.09826i
$142$		0			0
$143$	−12.5579			−1.05014
$144$		0			0
$145$	2.47054			0.205167
$146$		0			0
$147$	0.219564	−	4.54517i	0.0181094	−	0.374879i
$148$		0			0
$149$	−5.79002	−	5.79002i	−0.474337	−	0.474337i	0.428978	−	0.903315i	$-0.358874\pi$
$149$	−5.79002	−	5.79002i	−0.474337	−	0.474337i	−0.903315	+	0.428978i	$0.858874\pi$
$150$		0			0
$151$	−9.94610			−0.809402			−0.404701	−	0.914449i	$-0.632624\pi$
$151$	−9.94610			−0.809402			−0.404701	+	0.914449i	$0.632624\pi$
$152$		0			0
$153$	0.702522	−	7.25443i	0.0567955	−	0.586486i
$154$		0			0
$155$	−0.226417	+	0.226417i	−0.0181863	+	0.0181863i
$156$		0			0
$157$	9.15165	+	9.15165i	0.730381	+	0.730381i	0.970695	−	0.240314i	$-0.0772504\pi$
$157$	9.15165	+	9.15165i	0.730381	+	0.730381i	−0.240314	+	0.970695i	$0.577250\pi$
$158$		0			0
$159$	16.0200	−	14.5436i	1.27047	−	1.15338i
$160$		0			0
$161$		−	18.5300i		−	1.46037i
$162$		0			0
$163$	15.7003	−	15.7003i	1.22974	−	1.22974i	0.265678	−	0.964062i	$-0.414404\pi$
$163$	15.7003	−	15.7003i	1.22974	−	1.22974i	0.964062	−	0.265678i	$-0.0855959\pi$
$164$		0			0
$165$	−0.215480	+	4.46061i	−0.0167751	+	0.347258i
$166$		0			0
$167$		−	19.1437i		−	1.48139i	−0.671843	−	0.740694i	$-0.734497\pi$
$167$		−	19.1437i		−	1.48139i	0.671843	−	0.740694i	$-0.265503\pi$
$168$		0			0
$169$		−	4.15667i		−	0.319744i
$170$		0			0
$171$	2.32811	−	1.91701i	0.178035	−	0.146598i
$172$		0			0
$173$	−13.3281	+	13.3281i	−1.01331	+	1.01331i	−0.0134040	+	0.999910i	$0.504267\pi$
$173$	−13.3281	+	13.3281i	−1.01331	+	1.01331i	−0.999910	+	0.0134040i	$0.995733\pi$
$174$		0			0
$175$		−	14.3572i		−	1.08530i
$176$		0			0
$177$	0.132494	+	0.145945i	0.00995889	+	0.0109699i
$178$		0			0
$179$	−9.18451	−	9.18451i	−0.686483	−	0.686483i	0.274970	−	0.961453i	$-0.411332\pi$
$179$	−9.18451	−	9.18451i	−0.686483	−	0.686483i	−0.961453	+	0.274970i	$0.911332\pi$
$180$		0			0
$181$	16.5139	−	16.5139i	1.22747	−	1.22747i	0.262548	−	0.964919i	$-0.415437\pi$
$181$	16.5139	−	16.5139i	1.22747	−	1.22747i	0.964919	−	0.262548i	$-0.0845627\pi$
$182$		0			0
$183$	10.3919	−	9.43420i	0.768195	−	0.697396i
$184$		0			0
$185$	1.31630			0.0967764
$186$		0			0
$187$	7.25443	+	7.25443i	0.530496	+	0.530496i
$188$		0			0
$189$	−2.32653	+	15.9537i	−0.169230	+	1.16046i
$190$		0			0
$191$	3.17852			0.229989			0.114995	−	0.993366i	$-0.463315\pi$
$191$	3.17852			0.229989			0.114995	+	0.993366i	$0.463315\pi$
$192$		0			0
$193$	−11.4600			−0.824907			−0.412454	−	0.910979i	$-0.635328\pi$
$193$	−11.4600			−0.824907			−0.412454	+	0.910979i	$0.635328\pi$
$194$		0			0
$195$	3.14118	+	0.151742i	0.224944	+	0.0108664i
$196$		0			0
$197$	−14.8053	−	14.8053i	−1.05483	−	1.05483i	−0.998407	−	0.0564281i	$-0.982029\pi$
$197$	−14.8053	−	14.8053i	−1.05483	−	1.05483i	−0.0564281	−	0.998407i	$-0.517971\pi$
$198$		0			0
$199$	24.4550			1.73357			0.866783	−	0.498686i	$-0.166184\pi$
$199$	24.4550			1.73357			0.866783	+	0.498686i	$0.166184\pi$
$200$		0			0
$201$	0.645320	+	0.710831i	0.0455173	+	0.0501382i
$202$		0			0
$203$	−8.87762	+	8.87762i	−0.623087	+	0.623087i
$204$		0			0
$205$	−0.783887	−	0.783887i	−0.0547491	−	0.0547491i
$206$		0			0
$207$	−1.72693	+	17.8328i	−0.120030	+	1.23946i
$208$		0			0
$209$			4.24513i			0.293642i
$210$		0			0
$211$	−6.18639	+	6.18639i	−0.425889	+	0.425889i	−0.887225	−	0.461336i	$-0.847370\pi$
$211$	−6.18639	+	6.18639i	−0.425889	+	0.425889i	0.461336	+	0.887225i	$0.347370\pi$
$212$		0			0
$213$	8.68451	+	0.419525i	0.595053	+	0.0287454i
$214$		0			0
$215$		−	0.613779i		−	0.0418594i
$216$		0			0
$217$		−	1.62721i		−	0.110462i
$218$		0			0
$219$	23.2862	+	1.12489i	1.57354	+	0.0760132i
$220$		0			0
$221$	5.10860	−	5.10860i	0.343641	−	0.343641i
$222$		0			0
$223$		−	8.18996i		−	0.548441i	−0.961667	−	0.274220i	$-0.911580\pi$
$223$		−	8.18996i		−	0.548441i	0.961667	−	0.274220i	$-0.0884197\pi$
$224$		0			0
$225$	−1.33804	+	13.8170i	−0.0892030	+	0.921133i
$226$		0			0
$227$	9.91030	+	9.91030i	0.657770	+	0.657770i	0.954852	−	0.297082i	$-0.0960135\pi$
$227$	9.91030	+	9.91030i	0.657770	+	0.657770i	−0.297082	+	0.954852i	$0.596014\pi$
$228$		0			0
$229$	−7.15165	+	7.15165i	−0.472594	+	0.472594i	−0.902753	−	0.430159i	$-0.858458\pi$
$229$	−7.15165	+	7.15165i	−0.472594	+	0.472594i	0.430159	+	0.902753i	$0.358458\pi$
$230$		0			0
$231$	−15.2544	−	16.8030i	−1.00367	−	1.10556i
$232$		0			0
$233$	−19.6431			−1.28686			−0.643432	−	0.765503i	$-0.722490\pi$
$233$	−19.6431			−1.28686			−0.643432	+	0.765503i	$0.722490\pi$
$234$		0			0
$235$	−3.25443	−	3.25443i	−0.212295	−	0.212295i
$236$		0			0
$237$	−6.01284	−	0.290464i	−0.390576	−	0.0188676i
$238$		0			0
$239$	−9.44247			−0.610782			−0.305391	−	0.952227i	$-0.598787\pi$
$239$	−9.44247			−0.610782			−0.305391	+	0.952227i	$0.598787\pi$
$240$		0			0
$241$	16.6167			1.07037			0.535186	−	0.844734i	$-0.320241\pi$
$241$	16.6167			1.07037			0.535186	+	0.844734i	$0.320241\pi$
$242$		0			0
$243$	3.72583	−	15.1366i	0.239012	−	0.971017i
$244$		0			0
$245$	−1.13425	−	1.13425i	−0.0724649	−	0.0724649i
$246$		0			0
$247$	2.98944			0.190213
$248$		0			0
$249$	8.25557	−	7.49472i	0.523176	−	0.474958i
$250$		0			0
$251$	2.03382	−	2.03382i	0.128374	−	0.128374i	−0.640001	−	0.768374i	$-0.721066\pi$
$251$	2.03382	−	2.03382i	0.128374	−	0.128374i	0.768374	+	0.640001i	$0.221066\pi$
$252$		0			0
$253$	−17.8328	−	17.8328i	−1.12114	−	1.12114i
$254$		0			0
$255$	−1.72693	−	1.90225i	−0.108145	−	0.119123i
$256$		0			0
$257$		−	15.0761i		−	0.940421i	−0.882554	−	0.470211i	$-0.844178\pi$
$257$		−	15.0761i		−	0.940421i	0.882554	−	0.470211i	$-0.155822\pi$
$258$		0			0
$259$	−4.72999	+	4.72999i	−0.293907	+	0.293907i
$260$		0			0
$261$	9.37096	−	7.71623i	0.580048	−	0.477623i
$262$		0			0
$263$			29.8138i			1.83840i	0.393796	+	0.919198i	$0.371162\pi$
$263$			29.8138i			1.83840i	−0.393796	+	0.919198i	$0.628838\pi$
$264$		0			0
$265$		−	7.62721i		−	0.468536i
$266$		0			0
$267$	1.04950	−	21.7256i	0.0642285	−	1.32958i
$268$		0			0
$269$	16.3713	−	16.3713i	0.998176	−	0.998176i	−0.00182258	−	0.999998i	$-0.500580\pi$
$269$	16.3713	−	16.3713i	0.998176	−	0.998176i	0.999998	+	0.00182258i	$0.000580145\pi$
$270$		0			0
$271$			13.3466i			0.810751i	0.914150	+	0.405375i	$0.132859\pi$
$271$			13.3466i			0.810751i	−0.914150	+	0.405375i	$0.867141\pi$
$272$		0			0
$273$	−11.8328	+	10.7422i	−0.716151	+	0.650149i
$274$		0			0
$275$	−13.8170	−	13.8170i	−0.833197	−	0.833197i
$276$		0			0
$277$	−10.6811	+	10.6811i	−0.641766	+	0.641766i	−0.950989	−	0.309224i	$-0.899931\pi$
$277$	−10.6811	+	10.6811i	−0.641766	+	0.641766i	0.309224	+	0.950989i	$0.399931\pi$
$278$		0			0
$279$	−0.151651	+	1.56599i	−0.00907911	+	0.0937533i
$280$		0			0
$281$	−17.5943			−1.04959			−0.524794	−	0.851229i	$-0.675858\pi$
$281$	−17.5943			−1.04959			−0.524794	+	0.851229i	$0.675858\pi$
$282$		0			0
$283$	−17.1758	−	17.1758i	−1.02100	−	1.02100i	−0.999775	−	0.0212224i	$-0.993244\pi$
$283$	−17.1758	−	17.1758i	−1.02100	−	1.02100i	−0.0212224	−	0.999775i	$-0.506756\pi$
$284$		0			0
$285$	0.0512954	−	1.06186i	0.00303848	−	0.0628990i
$286$		0			0
$287$	5.63363			0.332543
$288$		0			0
$289$	11.0978			0.652809
$290$		0			0
$291$	−0.725088	+	15.0099i	−0.0425054	+	0.879897i
$292$		0			0
$293$	3.72465	+	3.72465i	0.217597	+	0.217597i	0.807485	−	0.589888i	$-0.200828\pi$
$293$	3.72465	+	3.72465i	0.217597	+	0.217597i	−0.589888	+	0.807485i	$0.700828\pi$
$294$		0			0
$295$	0.0694851			0.00404558
$296$		0			0
$297$	13.1145	+	17.5925i	0.760979	+	1.02082i
$298$		0			0
$299$	−12.5579	+	12.5579i	−0.726242	+	0.726242i
$300$		0			0
$301$	2.20555	+	2.20555i	0.127126	+	0.127126i
$302$		0			0
$303$	−0.330160	+	0.299731i	−0.0189672	+	0.0172191i
$304$		0			0
$305$		−	4.94765i		−	0.283302i
$306$		0			0
$307$	−13.4408	+	13.4408i	−0.767108	+	0.767108i	−0.977596	−	0.210488i	$-0.932495\pi$
$307$	−13.4408	+	13.4408i	−0.767108	+	0.767108i	0.210488	+	0.977596i	$0.432495\pi$
$308$		0			0
$309$	−0.531291	+	10.9982i	−0.0302241	+	0.625664i
$310$		0			0
$311$			13.8320i			0.784341i	0.919893	+	0.392170i	$0.128276\pi$
$311$			13.8320i			0.784341i	−0.919893	+	0.392170i	$0.871724\pi$
$312$		0			0
$313$			3.94056i			0.222734i	0.993779	+	0.111367i	$0.0355229\pi$
$313$			3.94056i			0.222734i	−0.993779	+	0.111367i	$0.964477\pi$
$314$		0			0
$315$	3.61264	+	4.38736i	0.203549	+	0.247200i
$316$		0			0
$317$	−8.92199	+	8.92199i	−0.501109	+	0.501109i	−0.911782	−	0.410673i	$-0.865294\pi$
$317$	−8.92199	+	8.92199i	−0.501109	+	0.501109i	0.410673	+	0.911782i	$0.365294\pi$
$318$		0			0
$319$			17.0872i			0.956699i
$320$		0			0
$321$	−2.71083	−	2.98603i	−0.151304	−	0.166664i
$322$		0			0
$323$	−1.72693	−	1.72693i	−0.0960891	−	0.0960891i
$324$		0			0
$325$	−9.72999	+	9.72999i	−0.539723	+	0.539723i
$326$		0			0
$327$	−11.9214	+	10.8227i	−0.659255	+	0.598497i
$328$		0			0
$329$	23.3889			1.28947
$330$		0			0
$331$	9.44082	+	9.44082i	0.518914	+	0.518914i	0.917243	−	0.398328i	$-0.130410\pi$
$331$	9.44082	+	9.44082i	0.518914	+	0.518914i	−0.398328	+	0.917243i	$0.630410\pi$
$332$		0			0
$333$	4.99284	−	4.11120i	0.273606	−	0.225292i
$334$		0			0
$335$	0.338430			0.0184904
$336$		0			0
$337$	5.94056			0.323603			0.161801	−	0.986823i	$-0.448270\pi$
$337$	5.94056			0.323603			0.161801	+	0.986823i	$0.448270\pi$
$338$		0			0
$339$	14.3814	+	0.694724i	0.781089	+	0.0377322i
$340$		0			0
$341$	−1.56599	−	1.56599i	−0.0848030	−	0.0848030i
$342$		0			0
$343$	−13.5678			−0.732591
$344$		0			0
$345$	4.24513	+	4.67609i	0.228550	+	0.251752i
$346$		0			0
$347$	−4.09918	+	4.09918i	−0.220056	+	0.220056i	−0.808522	−	0.588466i	$-0.799732\pi$
$347$	−4.09918	+	4.09918i	−0.220056	+	0.220056i	0.588466	+	0.808522i	$0.299732\pi$
$348$		0			0
$349$	8.10278	+	8.10278i	0.433732	+	0.433732i	0.889896	−	0.456164i	$-0.150777\pi$
$349$	8.10278	+	8.10278i	0.433732	+	0.433732i	−0.456164	+	0.889896i	$0.650777\pi$
$350$		0			0
$351$	12.3887	−	9.23527i	0.661259	−	0.492942i
$352$		0			0
$353$			29.2465i			1.55664i	0.627870	+	0.778318i	$0.283927\pi$
$353$			29.2465i			1.55664i	−0.627870	+	0.778318i	$0.716073\pi$
$354$		0			0
$355$	2.16724	−	2.16724i	0.115025	−	0.115025i
$356$		0			0
$357$	13.0411	+	0.629978i	0.690207	+	0.0333420i
$358$		0			0
$359$		−	21.3235i		−	1.12541i	−0.826657	−	0.562706i	$-0.809760\pi$
$359$		−	21.3235i		−	1.12541i	0.826657	−	0.562706i	$-0.190240\pi$
$360$		0			0
$361$			17.9894i			0.946812i
$362$		0			0
$363$	−11.8209	−	0.571035i	−0.620437	−	0.0299716i
$364$		0			0
$365$	5.81112	−	5.81112i	0.304168	−	0.304168i
$366$		0			0
$367$		−	32.8277i		−	1.71359i	−0.515654	−	0.856797i	$-0.672451\pi$
$367$		−	32.8277i		−	1.71359i	0.515654	−	0.856797i	$-0.327549\pi$
$368$		0			0
$369$	−5.42166	−	0.525036i	−0.282240	−	0.0273323i
$370$		0			0
$371$	27.4076	+	27.4076i	1.42293	+	1.42293i
$372$		0			0
$373$	−1.35720	+	1.35720i	−0.0702732	+	0.0702732i	−0.741370	−	0.671097i	$-0.765824\pi$
$373$	−1.35720	+	1.35720i	−0.0702732	+	0.0702732i	0.671097	+	0.741370i	$0.265824\pi$
$374$		0			0
$375$	6.84333	+	7.53805i	0.353388	+	0.389263i
$376$		0			0
$377$	12.0329			0.619724
$378$		0			0
$379$	−17.3869	−	17.3869i	−0.893106	−	0.893106i	0.101708	−	0.994814i	$-0.467569\pi$
$379$	−17.3869	−	17.3869i	−0.893106	−	0.893106i	−0.994814	+	0.101708i	$0.967569\pi$
$380$		0			0
$381$	27.2980	+	1.31869i	1.39852	+	0.0675585i
$382$		0			0
$383$	−32.9757			−1.68498			−0.842491	−	0.538711i	$-0.818912\pi$
$383$	−32.9757			−1.68498			−0.842491	+	0.538711i	$0.818912\pi$
$384$		0			0
$385$	−8.00000			−0.407718
$386$		0			0
$387$	−1.91701	−	2.32811i	−0.0974473	−	0.118345i
$388$		0			0
$389$	3.97434	+	3.97434i	0.201507	+	0.201507i	0.800645	−	0.599138i	$-0.204490\pi$
$389$	3.97434	+	3.97434i	0.201507	+	0.201507i	−0.599138	+	0.800645i	$0.704490\pi$
$390$		0			0
$391$	14.5089			0.733744
$392$		0			0
$393$	0.145945	−	0.132494i	0.00736195	−	0.00668346i
$394$		0			0
$395$	−1.50052	+	1.50052i	−0.0754991	+	0.0754991i
$396$		0			0
$397$	15.9355	+	15.9355i	0.799782	+	0.799782i	0.983061	−	0.183279i	$-0.0586712\pi$
$397$	15.9355	+	15.9355i	0.799782	+	0.799782i	−0.183279	+	0.983061i	$0.558671\pi$
$398$		0			0
$399$	3.63135	+	4.00000i	0.181795	+	0.200250i
$400$		0			0
$401$		−	29.7716i		−	1.48672i	−0.668891	−	0.743361i	$-0.733231\pi$
$401$		−	29.7716i		−	1.48672i	0.668891	−	0.743361i	$-0.266769\pi$
$402$		0			0
$403$	−1.10278	+	1.10278i	−0.0549331	+	0.0549331i
$404$		0			0
$405$	−3.06782	−	4.55897i	−0.152441	−	0.226537i
$406$		0			0
$407$			9.10404i			0.451270i
$408$		0			0
$409$			15.6655i			0.774610i	0.921952	+	0.387305i	$0.126594\pi$
$409$			15.6655i			0.774610i	−0.921952	+	0.387305i	$0.873406\pi$
$410$		0			0
$411$	−1.10821	+	22.9410i	−0.0546642	+	1.13159i
$412$		0			0
$413$	−0.249687	+	0.249687i	−0.0122863	+	0.0122863i
$414$		0			0
$415$		−	3.93051i		−	0.192941i
$416$		0			0
$417$	15.2197	−	13.8170i	0.745311	−	0.676621i
$418$		0			0
$419$	−14.1554	−	14.1554i	−0.691538	−	0.691538i	0.271032	−	0.962570i	$-0.412635\pi$
$419$	−14.1554	−	14.1554i	−0.691538	−	0.691538i	−0.962570	+	0.271032i	$0.912635\pi$
$420$		0			0
$421$	7.35720	−	7.35720i	0.358568	−	0.358568i	−0.504717	−	0.863285i	$-0.668403\pi$
$421$	7.35720	−	7.35720i	0.358568	−	0.358568i	0.863285	+	0.504717i	$0.168403\pi$
$422$		0			0
$423$	−22.5089	−	2.17977i	−1.09442	−	0.105984i
$424$		0			0
$425$	11.2416			0.545298
$426$		0			0
$427$	17.7789	+	17.7789i	0.860380	+	0.860380i
$428$		0			0
$429$	−1.04950	+	21.7256i	−0.0506705	+	1.04892i
$430$		0			0
$431$	20.7097			0.997553			0.498776	−	0.866731i	$-0.333783\pi$
$431$	20.7097			0.997553			0.498776	+	0.866731i	$0.333783\pi$
$432$		0			0
$433$	−23.4005			−1.12456			−0.562279	−	0.826948i	$-0.690075\pi$
$433$	−23.4005			−1.12456			−0.562279	+	0.826948i	$0.690075\pi$
$434$		0			0
$435$	0.206471	−	4.27411i	0.00989951	−	0.204928i
$436$		0			0
$437$	4.24513	+	4.24513i	0.203072	+	0.203072i
$438$		0			0
$439$	−20.2594			−0.966931			−0.483465	−	0.875363i	$-0.660622\pi$
$439$	−20.2594			−0.966931			−0.483465	+	0.875363i	$0.660622\pi$
$440$		0			0
$441$	−7.84494	−	0.759707i	−0.373569	−	0.0361765i
$442$		0			0
$443$	−4.05264	+	4.05264i	−0.192547	+	0.192547i	−0.796796	−	0.604249i	$-0.793473\pi$
$443$	−4.05264	+	4.05264i	−0.192547	+	0.192547i	0.604249	+	0.796796i	$0.293473\pi$
$444$		0			0
$445$	−5.42166	−	5.42166i	−0.257011	−	0.257011i
$446$		0			0
$447$	−10.5008	+	9.53303i	−0.496671	+	0.450897i
$448$		0			0
$449$			5.38394i			0.254084i	0.991897	+	0.127042i	$0.0405483\pi$
$449$			5.38394i			0.254084i	−0.991897	+	0.127042i	$0.959452\pi$
$450$		0			0
$451$	5.42166	−	5.42166i	0.255296	−	0.255296i
$452$		0			0
$453$	−0.831227	+	17.2071i	−0.0390544	+	0.808459i
$454$		0			0
$455$			5.63363i			0.264109i
$456$		0			0
$457$		−	28.0766i		−	1.31337i	−0.754165	−	0.656685i	$-0.771958\pi$
$457$		−	28.0766i		−	1.31337i	0.754165	−	0.656685i	$-0.228042\pi$
$458$		0			0
$459$	−12.4917	−	1.82166i	−0.583062	−	0.0850279i
$460$		0			0
$461$	−22.7962	+	22.7962i	−1.06172	+	1.06172i	−0.0637594	+	0.997965i	$0.520309\pi$
$461$	−22.7962	+	22.7962i	−1.06172	+	1.06172i	−0.997965	+	0.0637594i	$0.979691\pi$
$462$		0			0
$463$		−	0.740035i		−	0.0343923i	−0.999852	−	0.0171962i	$-0.994526\pi$
$463$		−	0.740035i		−	0.0343923i	0.999852	−	0.0171962i	$-0.00547398\pi$
$464$		0			0
$465$	0.372787	+	0.410632i	0.0172876	+	0.0190426i
$466$		0			0
$467$	9.73282	+	9.73282i	0.450381	+	0.450381i	0.895481	−	0.445100i	$-0.146832\pi$
$467$	9.73282	+	9.73282i	0.450381	+	0.450381i	−0.445100	+	0.895481i	$0.646832\pi$
$468$		0			0
$469$	−1.21611	+	1.21611i	−0.0561549	+	0.0561549i
$470$		0			0
$471$	16.5975	−	15.0678i	0.764772	−	0.694289i
$472$		0			0
$473$	4.24513			0.195191
$474$		0			0
$475$	3.28917	+	3.28917i	0.150917	+	0.150917i
$476$		0			0
$477$	−23.8221	−	28.9307i	−1.09074	−	1.32464i
$478$		0			0
$479$	28.2478			1.29067			0.645337	−	0.763898i	$-0.276717\pi$
$479$	28.2478			1.29067			0.645337	+	0.763898i	$0.276717\pi$
$480$		0			0
$481$	6.41110			0.292321
$482$		0			0
$483$	−32.0575	−	1.54861i	−1.45866	−	0.0704641i
$484$		0			0
$485$	3.74576	+	3.74576i	0.170086	+	0.170086i
$486$		0			0
$487$	−19.7094			−0.893117			−0.446559	−	0.894754i	$-0.647351\pi$
$487$	−19.7094			−0.893117			−0.446559	+	0.894754i	$0.647351\pi$
$488$		0			0
$489$	−25.8499	−	28.4741i	−1.16897	−	1.28764i
$490$		0			0
$491$	29.4414	−	29.4414i	1.32867	−	1.32867i	0.422143	−	0.906529i	$-0.361278\pi$
$491$	29.4414	−	29.4414i	1.32867	−	1.32867i	0.906529	−	0.422143i	$-0.138722\pi$
$492$		0			0
$493$	−6.95112	−	6.95112i	−0.313063	−	0.313063i
$494$		0			0
$495$	7.69899	+	0.745574i	0.346044	+	0.0335111i
$496$		0			0
$497$			15.5755i			0.698656i
$498$		0			0
$499$	4.43026	−	4.43026i	0.198326	−	0.198326i	−0.600956	−	0.799282i	$-0.705213\pi$
$499$	4.43026	−	4.43026i	0.198326	−	0.198326i	0.799282	+	0.600956i	$0.205213\pi$
$500$		0			0
$501$	−33.1193	−	1.59990i	−1.47966	−	0.0714784i
$502$		0			0
$503$		−	27.6805i		−	1.23421i	−0.786879	−	0.617107i	$-0.788304\pi$
$503$		−	27.6805i		−	1.23421i	0.786879	−	0.617107i	$-0.211696\pi$
$504$		0			0
$505$			0.157190i			0.00699488i
$506$		0			0
$507$	−7.19119	−	0.347386i	−0.319372	−	0.0154280i
$508$		0			0
$509$	17.3235	−	17.3235i	0.767851	−	0.767851i	−0.209877	−	0.977728i	$-0.567306\pi$
$509$	17.3235	−	17.3235i	0.767851	−	0.767851i	0.977728	+	0.209877i	$0.0673063\pi$
$510$		0			0
$511$			41.7633i			1.84750i
$512$		0			0
$513$	−3.12193	−	4.18793i	−0.137837	−	0.184902i
$514$		0			0
$515$	2.74461	+	2.74461i	0.120942	+	0.120942i
$516$		0			0
$517$	22.5089	−	22.5089i	0.989938	−	0.989938i
$518$		0			0
$519$	21.9441	+	24.1719i	0.963240	+	1.06103i
$520$		0			0
$521$	10.1284			0.443735			0.221868	−	0.975077i	$-0.428785\pi$
$521$	10.1284			0.443735			0.221868	+	0.975077i	$0.428785\pi$
$522$		0			0
$523$	1.45641	+	1.45641i	0.0636842	+	0.0636842i	0.738232	−	0.674547i	$-0.235661\pi$
$523$	1.45641	+	1.45641i	0.0636842	+	0.0636842i	−0.674547	+	0.738232i	$0.735661\pi$
$524$		0			0
$525$	−24.8384	−	1.19988i	−1.08404	−	0.0523669i
$526$		0			0
$527$	1.27410			0.0555006
$528$		0			0
$529$	−12.6655			−0.550675
$530$		0			0
$531$	0.263563	−	0.217023i	0.0114376	−	0.00941798i
$532$		0			0
$533$	−3.81796	−	3.81796i	−0.165374	−	0.165374i
$534$		0			0
$535$	−1.42166			−0.0614638
$536$		0			0
$537$	−16.6571	+	15.1219i	−0.718806	+	0.652560i
$538$		0			0
$539$	7.84494	−	7.84494i	0.337905	−	0.337905i
$540$		0			0
$541$	−5.18996	−	5.18996i	−0.223134	−	0.223134i	0.586683	−	0.809817i	$-0.300434\pi$
$541$	−5.18996	−	5.18996i	−0.223134	−	0.223134i	−0.809817	+	0.586683i	$0.800434\pi$
$542$		0			0
$543$	−27.1894	−	29.9497i	−1.16681	−	1.28526i
$544$		0			0
$545$			5.67583i			0.243126i
$546$		0			0
$547$	12.6413	−	12.6413i	0.540505	−	0.540505i	−0.383172	−	0.923677i	$-0.625168\pi$
$547$	12.6413	−	12.6413i	0.540505	−	0.540505i	0.923677	+	0.383172i	$0.125168\pi$
$548$		0			0
$549$	−15.4530	−	18.7669i	−0.659518	−	0.800950i
$550$		0			0
$551$		−	4.06764i		−	0.173287i
$552$		0			0
$553$		−	10.7839i		−	0.458578i
$554$		0			0
$555$	0.110007	−	2.27724i	0.00466955	−	0.0966636i
$556$		0			0
$557$	6.90317	−	6.90317i	0.292497	−	0.292497i	−0.545569	−	0.838066i	$-0.683686\pi$
$557$	6.90317	−	6.90317i	0.292497	−	0.292497i	0.838066	+	0.545569i	$0.183686\pi$
$558$		0			0
$559$		−	2.98944i		−	0.126440i
$560$		0			0
$561$	13.1567	−	11.9441i	0.555475	−	0.504281i
$562$		0			0
$563$	−18.3840	−	18.3840i	−0.774794	−	0.774794i	0.204146	−	0.978940i	$-0.434558\pi$
$563$	−18.3840	−	18.3840i	−0.774794	−	0.774794i	−0.978940	+	0.204146i	$0.934558\pi$
$564$		0			0
$565$	3.58890	−	3.58890i	0.150986	−	0.150986i
$566$		0			0
$567$	27.4061	+	5.35828i	1.15095	+	0.225027i
$568$		0			0
$569$	−43.5570			−1.82601			−0.913003	−	0.407953i	$-0.866243\pi$
$569$	−43.5570			−1.82601			−0.913003	+	0.407953i	$0.866243\pi$
$570$		0			0
$571$	7.00859	+	7.00859i	0.293301	+	0.293301i	0.838383	−	0.545082i	$-0.183502\pi$
$571$	7.00859	+	7.00859i	0.293301	+	0.293301i	−0.545082	+	0.838383i	$0.683502\pi$
$572$		0			0
$573$	0.265638	−	5.49894i	0.0110972	−	0.229721i
$574$		0			0
$575$	−27.6340			−1.15242
$576$		0			0
$577$	28.4494			1.18436			0.592182	−	0.805804i	$-0.298267\pi$
$577$	28.4494			1.18436			0.592182	+	0.805804i	$0.298267\pi$
$578$		0			0
$579$	−0.957746	+	19.8261i	−0.0398026	+	0.823946i
$580$		0			0
$581$	14.1239	+	14.1239i	0.585958	+	0.585958i
$582$		0			0
$583$	52.7527			2.18479
$584$		0			0
$585$	0.525036	−	5.42166i	0.0217076	−	0.224158i
$586$		0			0
$587$	19.9011	−	19.9011i	0.821405	−	0.821405i	−0.164904	−	0.986310i	$-0.552732\pi$
$587$	19.9011	−	19.9011i	0.821405	−	0.821405i	0.986310	+	0.164904i	$0.0527315\pi$
$588$		0			0
$589$	0.372787	+	0.372787i	0.0153604	+	0.0153604i
$590$		0			0
$591$	−26.8510	+	24.3764i	−1.10450	+	1.00271i
$592$		0			0
$593$			20.4344i			0.839140i	0.907723	+	0.419570i	$0.137819\pi$
$593$			20.4344i			0.839140i	−0.907723	+	0.419570i	$0.862181\pi$
$594$		0			0
$595$	3.25443	−	3.25443i	0.133418	−	0.133418i
$596$		0			0
$597$	2.04378	−	42.3079i	0.0836462	−	1.73155i
$598$		0			0
$599$		−	32.6704i		−	1.33488i	−0.744665	−	0.667438i	$-0.767391\pi$
$599$		−	32.6704i		−	1.33488i	0.744665	−	0.667438i	$-0.232609\pi$
$600$		0			0
$601$			6.73553i			0.274748i	0.990519	+	0.137374i	$0.0438662\pi$
$601$			6.73553i			0.274748i	−0.990519	+	0.137374i	$0.956134\pi$
$602$		0			0
$603$	1.28369	−	1.05702i	0.0522760	−	0.0430451i
$604$		0			0
$605$	−2.94993	+	2.94993i	−0.119932	+	0.119932i
$606$		0			0
$607$		−	21.2388i		−	0.862058i	−0.902338	−	0.431029i	$-0.858151\pi$
$607$		−	21.2388i		−	0.862058i	0.902338	−	0.431029i	$-0.141849\pi$
$608$		0			0
$609$	14.6167	+	16.1005i	0.592297	+	0.652426i
$610$		0			0
$611$	−15.8508	−	15.8508i	−0.641256	−	0.641256i
$612$		0			0
$613$	9.62219	−	9.62219i	0.388637	−	0.388637i	−0.485564	−	0.874201i	$-0.661386\pi$
$613$	9.62219	−	9.62219i	0.388637	−	0.388637i	0.874201	+	0.485564i	$0.161386\pi$
$614$		0			0
$615$	−1.42166	+	1.29064i	−0.0573270	+	0.0520436i
$616$		0			0
$617$	3.74576			0.150798			0.0753992	−	0.997153i	$-0.475977\pi$
$617$	3.74576			0.150798			0.0753992	+	0.997153i	$0.475977\pi$
$618$		0			0
$619$	−13.0680	−	13.0680i	−0.525249	−	0.525249i	0.393903	−	0.919152i	$-0.371124\pi$
$619$	−13.0680	−	13.0680i	−0.525249	−	0.525249i	−0.919152	+	0.393903i	$0.871124\pi$
$620$		0			0
$621$	30.7070	+	4.47799i	1.23223	+	0.179696i
$622$		0			0
$623$	38.9643			1.56107
$624$		0			0
$625$	−19.5472			−0.781887
$626$		0			0
$627$	7.34422	+	0.354779i	0.293300	+	0.0141685i
$628$		0			0
$629$	−3.70355	−	3.70355i	−0.147670	−	0.147670i
$630$		0			0
$631$	7.51388			0.299123			0.149561	−	0.988752i	$-0.452214\pi$
$631$	7.51388			0.299123			0.149561	+	0.988752i	$0.452214\pi$
$632$		0			0
$633$	10.1857	+	11.2197i	0.404843	+	0.445942i
$634$		0			0
$635$	6.81226	−	6.81226i	0.270336	−	0.270336i
$636$		0			0
$637$	−5.52444	−	5.52444i	−0.218886	−	0.218886i
$638$		0			0
$639$	1.45158	−	14.9894i	0.0574238	−	0.592973i
$640$		0			0
$641$			27.7227i			1.09498i	0.836811	+	0.547491i	$0.184417\pi$
$641$			27.7227i			1.09498i	−0.836811	+	0.547491i	$0.815583\pi$
$642$		0			0
$643$	19.7003	−	19.7003i	0.776903	−	0.776903i	−0.202400	−	0.979303i	$-0.564874\pi$
$643$	19.7003	−	19.7003i	0.776903	−	0.776903i	0.979303	+	0.202400i	$0.0648742\pi$
$644$		0			0
$645$	−1.06186	−	0.0512954i	−0.0418106	−	0.00201976i
$646$		0			0
$647$			5.29520i			0.208176i	0.994568	+	0.104088i	$0.0331923\pi$
$647$			5.29520i			0.208176i	−0.994568	+	0.104088i	$0.966808\pi$
$648$		0			0
$649$			0.480585i			0.0188646i
$650$		0			0
$651$	−2.81513	−	0.135991i	−0.110334	−	0.00532992i
$652$		0			0
$653$	−29.7039	+	29.7039i	−1.16240	+	1.16240i	−0.178457	+	0.983948i	$0.557110\pi$
$653$	−29.7039	+	29.7039i	−1.16240	+	1.16240i	−0.983948	+	0.178457i	$0.942890\pi$
$654$		0			0
$655$		−	0.0694851i		−	0.00271501i
$656$		0			0
$657$	3.89220	−	40.1919i	0.151849	−	1.56804i
$658$		0			0
$659$	1.03268	+	1.03268i	0.0402276	+	0.0402276i	0.726934	−	0.686707i	$-0.240944\pi$
$659$	1.03268	+	1.03268i	0.0402276	+	0.0402276i	−0.686707	+	0.726934i	$0.740944\pi$
$660$		0			0
$661$	−29.8277	+	29.8277i	−1.16016	+	1.16016i	−0.175725	+	0.984439i	$0.556227\pi$
$661$	−29.8277	+	29.8277i	−1.16016	+	1.16016i	−0.984439	+	0.175725i	$0.943773\pi$
$662$		0			0
$663$	−8.41110	−	9.26498i	−0.326660	−	0.359822i
$664$		0			0
$665$	1.90442			0.0738502
$666$		0			0
$667$	17.0872	+	17.0872i	0.661619	+	0.661619i
$668$		0			0
$669$	−14.1689	−	0.684461i	−0.547802	−	0.0264628i
$670$		0			0
$671$	34.2198			1.32104
$672$		0			0
$673$	−0.891685			−0.0343719			−0.0171860	−	0.999852i	$-0.505471\pi$
$673$	−0.891685			−0.0343719			−0.0171860	+	0.999852i	$0.505471\pi$
$674$		0			0
$675$	23.7920	+	3.46959i	0.915756	+	0.133545i
$676$		0			0
$677$	8.13073	+	8.13073i	0.312489	+	0.312489i	0.845873	−	0.533384i	$-0.179080\pi$
$677$	8.13073	+	8.13073i	0.312489	+	0.312489i	−0.533384	+	0.845873i	$0.679080\pi$
$678$		0			0
$679$	−26.9200			−1.03309
$680$		0			0
$681$	17.9734	−	16.3169i	0.688742	−	0.625266i
$682$		0			0
$683$	−14.5917	+	14.5917i	−0.558337	+	0.558337i	−0.928834	−	0.370497i	$-0.879187\pi$
$683$	−14.5917	+	14.5917i	−0.558337	+	0.558337i	0.370497	+	0.928834i	$0.379187\pi$
$684$		0			0
$685$	5.72496	+	5.72496i	0.218740	+	0.218740i
$686$		0			0
$687$	11.7749	+	12.9703i	0.449241	+	0.494847i
$688$		0			0
$689$		−	37.1487i		−	1.41525i
$690$		0			0
$691$	−11.2197	+	11.2197i	−0.426817	+	0.426817i	−0.887543	−	0.460726i	$-0.847589\pi$
$691$	−11.2197	+	11.2197i	−0.426817	+	0.426817i	0.460726	+	0.887543i	$0.347589\pi$
$692$		0			0
$693$	−30.3447	+	24.9864i	−1.15270	+	0.949154i
$694$		0			0
$695$		−	7.24616i		−	0.274863i
$696$		0			0
$697$			4.41110i			0.167082i
$698$		0			0
$699$	−1.64164	+	33.9833i	−0.0620924	+	1.28536i
$700$		0			0
$701$	14.7166	−	14.7166i	0.555837	−	0.555837i	−0.372282	−	0.928120i	$-0.621425\pi$
$701$	14.7166	−	14.7166i	0.555837	−	0.555837i	0.928120	+	0.372282i	$0.121425\pi$
$702$		0			0
$703$		−	2.16724i		−	0.0817389i
$704$		0			0
$705$	−5.90225	+	5.35828i	−0.222292	+	0.201805i
$706$		0			0
$707$	−0.564847	−	0.564847i	−0.0212433	−	0.0212433i
$708$		0			0
$709$	23.2978	−	23.2978i	0.874966	−	0.874966i	−0.118043	−	0.993009i	$-0.537662\pi$
$709$	23.2978	−	23.2978i	0.874966	−	0.874966i	0.993009	+	0.118043i	$0.0376620\pi$
$710$		0			0
$711$	−1.00502	+	10.3781i	−0.0376913	+	0.389211i
$712$		0			0
$713$	−3.13198			−0.117293
$714$		0			0
$715$	5.42166	+	5.42166i	0.202759	+	0.202759i
$716$		0			0
$717$	−0.789136	+	16.3358i	−0.0294708	+	0.610071i
$718$		0			0
$719$	−27.3421			−1.01969			−0.509844	−	0.860267i	$-0.670297\pi$
$719$	−27.3421			−1.01969			−0.509844	+	0.860267i	$0.670297\pi$
$720$		0			0
$721$	−19.7250			−0.734596
$722$		0			0
$723$	1.38871	−	28.7474i	0.0516465	−	1.06913i
$724$		0			0
$725$	13.2393	+	13.2393i	0.491696	+	0.491696i
$726$		0			0
$727$	−24.1517			−0.895735			−0.447868	−	0.894100i	$-0.647816\pi$
$727$	−24.1517			−0.895735			−0.447868	+	0.894100i	$0.647816\pi$
$728$		0			0
$729$	−25.8755	−	7.71083i	−0.958353	−	0.285586i
$730$		0			0
$731$	−1.72693	+	1.72693i	−0.0638729	+	0.0638729i
$732$		0			0
$733$	6.00502	+	6.00502i	0.221801	+	0.221801i	0.809256	−	0.587456i	$-0.199870\pi$
$733$	6.00502	+	6.00502i	0.221801	+	0.221801i	−0.587456	+	0.809256i	$0.699870\pi$
$734$		0			0
$735$	−2.05709	+	1.86751i	−0.0758770	+	0.0688840i
$736$		0			0
$737$			2.34071i			0.0862212i
$738$		0			0
$739$	−10.9008	+	10.9008i	−0.400992	+	0.400992i	−0.878583	−	0.477590i	$-0.841510\pi$
$739$	−10.9008	+	10.9008i	−0.400992	+	0.400992i	0.477590	+	0.878583i	$0.341510\pi$
$740$		0			0
$741$	0.249837	−	5.17183i	0.00917798	−	0.189992i
$742$		0			0
$743$			1.29064i			0.0473490i	0.999720	+	0.0236745i	$0.00753652\pi$
$743$			1.29064i			0.0473490i	−0.999720	+	0.0236745i	$0.992463\pi$
$744$		0			0
$745$			4.99948i			0.183167i
$746$		0			0
$747$	−12.2762	−	14.9088i	−0.449162	−	0.545483i
$748$		0			0
$749$	5.10860	−	5.10860i	0.186664	−	0.186664i
$750$		0			0
$751$		−	1.46552i		−	0.0534774i	−0.999642	−	0.0267387i	$-0.991488\pi$
$751$		−	1.46552i		−	0.0534774i	0.999642	−	0.0267387i	$-0.00851221\pi$
$752$		0			0
$753$	−3.34861	−	3.68855i	−0.122030	−	0.134418i
$754$		0			0
$755$	4.29406	+	4.29406i	0.156277	+	0.156277i
$756$		0			0
$757$	−4.71943	+	4.71943i	−0.171530	+	0.171530i	−0.787651	−	0.616121i	$-0.788703\pi$
$757$	−4.71943	+	4.71943i	−0.171530	+	0.171530i	0.616121	+	0.787651i	$0.288703\pi$
$758$		0			0
$759$	−32.3416	+	29.3609i	−1.17393	+	1.06573i
$760$		0			0
$761$	29.1578			1.05697			0.528485	−	0.848943i	$-0.322760\pi$
$761$	29.1578			1.05697			0.528485	+	0.848943i	$0.322760\pi$
$762$		0			0
$763$	−20.3955	−	20.3955i	−0.738367	−	0.738367i
$764$		0			0
$765$	−3.43528	+	2.82867i	−0.124203	+	0.102271i
$766$		0			0
$767$	0.338430			0.0122200
$768$		0			0
$769$	20.8122			0.750505			0.375253	−	0.926923i	$-0.377556\pi$
$769$	20.8122			0.750505			0.375253	+	0.926923i	$0.377556\pi$
$770$		0			0
$771$	−26.0822	−	1.25996i	−0.939326	−	0.0453762i
$772$		0			0
$773$	26.6607	+	26.6607i	0.958918	+	0.958918i	0.999189	−	0.0402703i	$-0.0128219\pi$
$773$	26.6607	+	26.6607i	0.958918	+	0.958918i	−0.0402703	+	0.999189i	$0.512822\pi$
$774$		0			0
$775$	−2.42669			−0.0871691
$776$		0			0
$777$	7.78774	+	8.57834i	0.279384	+	0.307746i
$778$		0			0
$779$	−1.29064	+	1.29064i	−0.0462419	+	0.0462419i
$780$		0			0
$781$	14.9894	+	14.9894i	0.536364	+	0.536364i
$782$		0			0
$783$	−12.5662	−	16.8569i	−0.449078	−	0.602418i
$784$		0			0
$785$		−	7.90214i		−	0.282040i
$786$		0			0
$787$	−32.7875	+	32.7875i	−1.16875	+	1.16875i	−0.186243	+	0.982504i	$0.559631\pi$
$787$	−32.7875	+	32.7875i	−1.16875	+	1.16875i	−0.982504	+	0.186243i	$0.940369\pi$
$788$		0			0
$789$	51.5788	+	2.49163i	1.83625	+	0.0887044i
$790$		0			0
$791$			25.7927i			0.917082i
$792$		0			0
$793$		−	24.0978i		−	0.855736i
$794$		0			0
$795$	−13.1953	−	0.637430i	−0.467990	−	0.0226073i
$796$		0			0
$797$	11.2627	−	11.2627i	0.398945	−	0.398945i	−0.478916	−	0.877861i	$-0.658970\pi$
$797$	11.2627	−	11.2627i	0.398945	−	0.398945i	0.877861	+	0.478916i	$0.158970\pi$
$798$		0			0
$799$			18.3133i			0.647880i
$800$		0			0
$801$	−37.4983	−	3.63135i	−1.32494	−	0.128307i
$802$		0			0
$803$	40.1919	+	40.1919i	1.41834	+	1.41834i
$804$		0			0
$805$	−8.00000	+	8.00000i	−0.281963	+	0.281963i
$806$		0			0
$807$	−26.9547	−	29.6911i	−0.948850	−	1.04518i
$808$		0			0
$809$	48.5934			1.70845			0.854227	−	0.519900i	$-0.174031\pi$
$809$	48.5934			1.70845			0.854227	+	0.519900i	$0.174031\pi$
$810$		0			0
$811$	19.2197	+	19.2197i	0.674894	+	0.674894i	0.958840	−	0.283946i	$-0.0916436\pi$
$811$	19.2197	+	19.2197i	0.674894	+	0.674894i	−0.283946	+	0.958840i	$0.591644\pi$
$812$		0			0
$813$	23.0901	+	1.11542i	0.809806	+	0.0391195i
$814$		0			0
$815$	−13.5567			−0.474869
$816$		0			0
$817$	−1.01056			−0.0353551
$818$		0			0
$819$	17.5955	+	21.3688i	0.614837	+	0.746688i
$820$		0			0
$821$	−33.7881	−	33.7881i	−1.17921	−	1.17921i	−0.979945	−	0.199268i	$-0.936143\pi$
$821$	−33.7881	−	33.7881i	−1.17921	−	1.17921i	−0.199268	−	0.979945i	$-0.563857\pi$
$822$		0			0
$823$	4.37833			0.152619			0.0763094	−	0.997084i	$-0.475686\pi$
$823$	4.37833			0.152619			0.0763094	+	0.997084i	$0.475686\pi$
$824$		0			0
$825$	−25.0586	+	22.7491i	−0.872429	+	0.792024i
$826$		0			0
$827$	−14.2044	+	14.2044i	−0.493934	+	0.493934i	−0.909543	−	0.415609i	$-0.863568\pi$
$827$	−14.2044	+	14.2044i	−0.493934	+	0.493934i	0.415609	+	0.909543i	$0.363568\pi$
$828$		0			0
$829$	−14.8483	−	14.8483i	−0.515704	−	0.515704i	0.400564	−	0.916269i	$-0.368814\pi$
$829$	−14.8483	−	14.8483i	−0.515704	−	0.515704i	−0.916269	+	0.400564i	$0.868814\pi$
$830$		0			0
$831$	17.5860	+	19.3713i	0.610053	+	0.671984i
$832$		0			0
$833$			6.38269i			0.221147i
$834$		0			0
$835$	−8.26499	+	8.26499i	−0.286022	+	0.286022i
$836$		0			0
$837$	2.69654	+	0.393236i	0.0932060	+	0.0135922i
$838$		0			0
$839$			3.11543i			0.107557i	0.998553	+	0.0537784i	$0.0171265\pi$
$839$			3.11543i			0.107557i	−0.998553	+	0.0537784i	$0.982874\pi$
$840$		0			0
$841$			12.6272i			0.435421i
$842$		0			0
$843$	−1.47041	+	30.4387i	−0.0506436	+	1.04837i
$844$		0			0
$845$	−1.79457	+	1.79457i	−0.0617352	+	0.0617352i
$846$		0			0
$847$		−	21.2005i		−	0.728459i
$848$		0			0
$849$	−31.1502	+	28.2793i	−1.06907	+	0.970544i
$850$		0			0
$851$	9.10404	+	9.10404i	0.312082	+	0.312082i
$852$		0			0
$853$	−35.4550	+	35.4550i	−1.21395	+	1.21395i	−0.244240	+	0.969715i	$0.578538\pi$
$853$	−35.4550	+	35.4550i	−1.21395	+	1.21395i	−0.969715	+	0.244240i	$0.921462\pi$
$854$		0			0
$855$	−1.83276	−	0.177486i	−0.0626792	−	0.00606988i
$856$		0			0
$857$	14.0817			0.481021			0.240511	−	0.970646i	$-0.422685\pi$
$857$	14.0817			0.481021			0.240511	+	0.970646i	$0.422685\pi$
$858$		0			0
$859$	−30.9547	−	30.9547i	−1.05616	−	1.05616i	−0.998326	−	0.0578344i	$-0.981580\pi$
$859$	−30.9547	−	30.9547i	−1.05616	−	1.05616i	−0.0578344	−	0.998326i	$-0.518420\pi$
$860$		0			0
$861$	0.470820	−	9.74637i	0.0160455	−	0.332155i
$862$		0			0
$863$	14.4458			0.491740			0.245870	−	0.969303i	$-0.420926\pi$
$863$	14.4458			0.491740			0.245870	+	0.969303i	$0.420926\pi$
$864$		0			0
$865$	11.5083			0.391295
$866$		0			0
$867$	0.927474	−	19.1995i	0.0314987	−	0.652049i
$868$		0			0
$869$	−10.3781	−	10.3781i	−0.352054	−	0.352054i
$870$		0			0
$871$	1.64834			0.0558518
$872$		0			0
$873$	25.9071	+	2.50885i	0.876822	+	0.0849118i
$874$		0			0
$875$	−12.8963	+	12.8963i	−0.435976	+	0.435976i
$876$		0			0
$877$	−11.3672	−	11.3672i	−0.383845	−	0.383845i	0.488641	−	0.872485i	$-0.337493\pi$
$877$	−11.3672	−	11.3672i	−0.383845	−	0.383845i	−0.872485	+	0.488641i	$0.837493\pi$
$878$		0			0
$879$	6.75506	−	6.13249i	0.227842	−	0.206844i
$880$		0			0
$881$			10.2172i			0.344226i	0.985077	+	0.172113i	$0.0550594\pi$
$881$			10.2172i			0.344226i	−0.985077	+	0.172113i	$0.944941\pi$
$882$		0			0
$883$	0.230246	−	0.230246i	0.00774840	−	0.00774840i	−0.703222	−	0.710970i	$-0.748256\pi$
$883$	0.230246	−	0.230246i	0.00774840	−	0.00774840i	0.710970	+	0.703222i	$0.248256\pi$
$884$		0			0
$885$	0.00580708	−	0.120211i	0.000195203	−	0.00404087i
$886$		0			0
$887$			34.2664i			1.15055i	0.817959	+	0.575276i	$0.195105\pi$
$887$			34.2664i			1.15055i	−0.817959	+	0.575276i	$0.804895\pi$
$888$		0			0
$889$			48.9583i			1.64201i
$890$		0			0
$891$	31.5316	−	21.2182i	1.05635	−	0.710837i
$892$		0			0
$893$	−5.35828	+	5.35828i	−0.179308	+	0.179308i
$894$		0			0
$895$			7.93051i			0.265088i
$896$		0			0
$897$	20.6761	+	22.7751i	0.690355	+	0.760438i
$898$		0			0
$899$	1.50052	+	1.50052i	0.0500450	+	0.0500450i
$900$		0			0
$901$	−21.4600	+	21.4600i	−0.714935	+	0.714935i
$902$		0			0
$903$	4.00000	−	3.63135i	0.133112	−	0.120844i
$904$		0			0
$905$	−14.2592			−0.473991
$906$		0			0
$907$	−26.5436	−	26.5436i	−0.881366	−	0.881366i	0.112308	−	0.993673i	$-0.464176\pi$
$907$	−26.5436	−	26.5436i	−0.881366	−	0.881366i	−0.993673	+	0.112308i	$0.964176\pi$
$908$		0			0
$909$	0.490953	+	0.596236i	0.0162839	+	0.0197759i
$910$		0			0
$911$	−24.1636			−0.800576			−0.400288	−	0.916389i	$-0.631090\pi$
$911$	−24.1636			−0.800576			−0.400288	+	0.916389i	$0.631090\pi$
$912$		0			0
$913$	27.1849			0.899690
$914$		0			0
$915$	−8.55960	−	0.413491i	−0.282972	−	0.0136696i
$916$		0			0
$917$	0.249687	+	0.249687i	0.00824540	+	0.00824540i
$918$		0			0
$919$	25.8272			0.851961			0.425981	−	0.904732i	$-0.359929\pi$
$919$	25.8272			0.851961			0.425981	+	0.904732i	$0.359929\pi$
$920$		0			0
$921$	22.1298	+	24.3764i	0.729201	+	0.803228i
$922$		0			0
$923$	10.5556	−	10.5556i	0.347443	−	0.347443i
$924$		0			0
$925$	7.05390	+	7.05390i	0.231931	+	0.231931i
$926$		0			0
$927$	18.9828	+	1.83830i	0.623477	+	0.0603778i
$928$		0			0
$929$		−	29.6272i		−	0.972036i	−0.873949	−	0.486018i	$-0.838449\pi$
$929$		−	29.6272i		−	0.972036i	0.873949	−	0.486018i	$-0.161551\pi$
$930$		0			0
$931$	−1.86751	+	1.86751i	−0.0612050	+	0.0612050i
$932$		0			0
$933$	23.9298	+	1.15598i	0.783427	+	0.0378452i
$934$		0			0
$935$		−	6.26395i		−	0.204853i
$936$		0			0
$937$		−	33.4005i		−	1.09115i	−0.838063	−	0.545574i	$-0.816312\pi$
$937$		−	33.4005i		−	1.09115i	0.838063	−	0.545574i	$-0.183688\pi$
$938$		0			0
$939$	6.81730	+	0.329325i	0.222474	+	0.0107471i
$940$		0			0
$941$	15.6688	−	15.6688i	0.510788	−	0.510788i	−0.403980	−	0.914768i	$-0.632374\pi$
$941$	15.6688	−	15.6688i	0.510788	−	0.510788i	0.914768	+	0.403980i	$0.132374\pi$
$942$		0			0
$943$		−	10.8433i		−	0.353107i
$944$		0			0
$945$	7.89220	−	5.88332i	0.256733	−	0.191384i
$946$		0			0
$947$	−21.4040	−	21.4040i	−0.695536	−	0.695536i	0.267908	−	0.963444i	$-0.413668\pi$
$947$	−21.4040	−	21.4040i	−0.695536	−	0.695536i	−0.963444	+	0.267908i	$0.913668\pi$
$948$		0			0
$949$	28.3033	−	28.3033i	0.918764	−	0.918764i
$950$		0			0
$951$	14.6897	+	16.1810i	0.476346	+	0.524704i
$952$		0			0
$953$	−30.7403			−0.995777			−0.497888	−	0.867241i	$-0.665891\pi$
$953$	−30.7403			−0.995777			−0.497888	+	0.867241i	$0.665891\pi$
$954$		0			0
$955$	−1.37227	−	1.37227i	−0.0444056	−	0.0444056i
$956$		0			0
$957$	29.5614	+	1.42803i	0.955585	+	0.0461616i
$958$		0			0
$959$	−41.1441			−1.32861
$960$		0			0
$961$	30.7250			0.991128
$962$		0			0
$963$	−5.39249	+	4.44028i	−0.173770	+	0.143086i
$964$		0			0
$965$	4.94765	+	4.94765i	0.159271	+	0.159271i
$966$		0			0
$967$	15.8172			0.508646			0.254323	−	0.967119i	$-0.418147\pi$
$967$	15.8172			0.508646			0.254323	+	0.967119i	$0.418147\pi$
$968$		0			0
$969$	−3.13198	+	2.84333i	−0.100614	+	0.0913408i
$970$		0			0
$971$	−13.8170	+	13.8170i	−0.443409	+	0.443409i	−0.893156	−	0.449747i	$-0.851514\pi$
$971$	−13.8170	+	13.8170i	−0.443409	+	0.443409i	0.449747	+	0.893156i	$0.351514\pi$
$972$		0			0
$973$	26.0383	+	26.0383i	0.834750	+	0.834750i
$974$		0			0
$975$	16.0200	+	17.6464i	0.513052	+	0.565136i
$976$		0			0
$977$			16.1005i			0.515101i	0.966265	+	0.257550i	$0.0829154\pi$
$977$			16.1005i			0.515101i	−0.966265	+	0.257550i	$0.917085\pi$
$978$		0			0
$979$	37.4983	−	37.4983i	1.19845	−	1.19845i
$980$		0			0
$981$	17.7273	+	21.5289i	0.565990	+	0.687365i
$982$		0			0
$983$			37.0765i			1.18256i	0.806468	+	0.591278i	$0.201376\pi$
$983$			37.0765i			1.18256i	−0.806468	+	0.591278i	$0.798624\pi$
$984$		0			0
$985$			12.7839i			0.407329i
$986$		0			0
$987$	1.95468	−	40.4635i	0.0622182	−	1.28797i
$988$		0			0
$989$	4.24513	−	4.24513i	0.134987	−	0.134987i
$990$		0			0
$991$		−	40.7089i		−	1.29316i	−0.762846	−	0.646580i	$-0.776199\pi$
$991$		−	40.7089i		−	1.29316i	0.762846	−	0.646580i	$-0.223801\pi$
$992$		0			0
$993$	17.1219	−	15.5439i	0.543348	−	0.493272i
$994$		0			0
$995$	−10.5580	−	10.5580i	−0.334712	−	0.334712i
$996$		0			0
$997$	−9.52444	+	9.52444i	−0.301642	+	0.301642i	−0.841656	−	0.540014i	$-0.818419\pi$
$997$	−9.52444	+	9.52444i	−0.301642	+	0.301642i	0.540014	+	0.841656i	$0.318419\pi$
$998$		0			0
$999$	−6.69525	−	8.98136i	−0.211828	−	0.284158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.k.a.95.4		12
3.2	odd	2	inner	384.2.k.a.95.6		12
4.3	odd	2		384.2.k.b.95.3		12
8.3	odd	2		48.2.k.a.35.5	yes	12
8.5	even	2		192.2.k.a.47.3		12
12.11	even	2		384.2.k.b.95.1		12
16.3	odd	4		192.2.k.a.143.1		12
16.5	even	4		384.2.k.b.287.1		12
16.11	odd	4	inner	384.2.k.a.287.6		12
16.13	even	4		48.2.k.a.11.2	✓	12
24.5	odd	2		192.2.k.a.47.1		12
24.11	even	2		48.2.k.a.35.2	yes	12
48.5	odd	4		384.2.k.b.287.3		12
48.11	even	4	inner	384.2.k.a.287.4		12
48.29	odd	4		48.2.k.a.11.5	yes	12
48.35	even	4		192.2.k.a.143.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.2	✓	12	16.13	even	4
48.2.k.a.11.5	yes	12	48.29	odd	4
48.2.k.a.35.2	yes	12	24.11	even	2
48.2.k.a.35.5	yes	12	8.3	odd	2
192.2.k.a.47.1		12	24.5	odd	2
192.2.k.a.47.3		12	8.5	even	2
192.2.k.a.143.1		12	16.3	odd	4
192.2.k.a.143.3		12	48.35	even	4
384.2.k.a.95.4		12	1.1	even	1	trivial
384.2.k.a.95.6		12	3.2	odd	2	inner
384.2.k.a.287.4		12	48.11	even	4	inner
384.2.k.a.287.6		12	16.11	odd	4	inner
384.2.k.b.95.1		12	12.11	even	2
384.2.k.b.95.3		12	4.3	odd	2
384.2.k.b.287.1		12	16.5	even	4
384.2.k.b.287.3		12	48.5	odd	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0835731 - 1.73003i) q^{3} +(-0.431733 - 0.431733i) q^{5} +3.10278 q^{7} +(-2.98603 - 0.289169i) q^{9} +O(q^{10})\)	\(q+(0.0835731 - 1.73003i) q^{3} +(-0.431733 - 0.431733i) q^{5} +3.10278 q^{7} +(-2.98603 - 0.289169i) q^{9} +(2.98603 - 2.98603i) q^{11} +(-2.10278 - 2.10278i) q^{13} +(-0.782994 + 0.710831i) q^{15} +2.42945i q^{17} +(-0.710831 + 0.710831i) q^{19} +(0.259309 - 5.36790i) q^{21} -5.97206i q^{23} -4.62721i q^{25} +(-0.749823 + 5.14177i) q^{27} +(-2.86119 + 2.86119i) q^{29} -0.524438i q^{31} +(-4.91638 - 5.41549i) q^{33} +(-1.33957 - 1.33957i) q^{35} +(-1.52444 + 1.52444i) q^{37} +(-3.81361 + 3.46214i) q^{39} +1.81568 q^{41} +(0.710831 + 0.710831i) q^{43} +(1.16432 + 1.41401i) q^{45} +7.53805 q^{47} +2.62721 q^{49} +(4.20304 + 0.203037i) q^{51} +(8.83325 + 8.83325i) q^{53} -2.57834 q^{55} +(1.17036 + 1.28917i) q^{57} +(-0.0804722 + 0.0804722i) q^{59} +(5.72999 + 5.72999i) q^{61} +(-9.26498 - 0.897225i) q^{63} +1.81568i q^{65} +(-0.391944 + 0.391944i) q^{67} +(-10.3319 - 0.499104i) q^{69} +5.01985i q^{71} +13.4600i q^{73} +(-8.00523 - 0.386711i) q^{75} +(9.26498 - 9.26498i) q^{77} -3.47556i q^{79} +(8.83276 + 1.72693i) q^{81} +(4.55202 + 4.55202i) q^{83} +(1.04888 - 1.04888i) q^{85} +(4.71083 + 5.18907i) q^{87} +12.5579 q^{89} +(-6.52444 - 6.52444i) q^{91} +(-0.907295 - 0.0438289i) q^{93} +0.613779 q^{95} -8.67609 q^{97} +(-9.77985 + 8.05292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 8 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 + 8 * q^7	\( 12 q - 2 q^{3} + 8 q^{7} + 4 q^{13} - 12 q^{19} + 8 q^{21} + 10 q^{27} - 4 q^{33} + 4 q^{37} - 20 q^{39} + 12 q^{43} + 12 q^{45} - 20 q^{49} + 24 q^{51} - 24 q^{55} - 12 q^{61} + 28 q^{67} - 4 q^{69} - 34 q^{75} - 4 q^{81} - 32 q^{85} + 60 q^{87} - 56 q^{91} - 28 q^{93} - 8 q^{97} - 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 8 * q^7 + 4 * q^13 - 12 * q^19 + 8 * q^21 + 10 * q^27 - 4 * q^33 + 4 * q^37 - 20 * q^39 + 12 * q^43 + 12 * q^45 - 20 * q^49 + 24 * q^51 - 24 * q^55 - 12 * q^61 + 28 * q^67 - 4 * q^69 - 34 * q^75 - 4 * q^81 - 32 * q^85 + 60 * q^87 - 56 * q^91 - 28 * q^93 - 8 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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