LMFDB - Embedded newform 384.3.i.c.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(161,384)]

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([0, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("384.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.i (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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.4
Root			$-1.28499 - 1.53258i$ of defining polynomial
Character	$\chi$	$=$	384.161
Dual form			384.3.i.c.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06336 - 2.17774i) q^{3} +(3.17955 + 3.17955i) q^{5} +6.03979i q^{7} +(-0.485128 + 8.98692i) q^{9} +O(q^{10})$	\(q+(-2.06336 - 2.17774i) q^{3} +(3.17955 + 3.17955i) q^{5} +6.03979i q^{7} +(-0.485128 + 8.98692i) q^{9} +(-13.0097 - 13.0097i) q^{11} +(-6.39520 - 6.39520i) q^{13} +(0.363700 - 13.4848i) q^{15} +4.39848i q^{17} +(-3.21075 - 3.21075i) q^{19} +(13.1531 - 12.4622i) q^{21} -34.0396 q^{23} -4.78097i q^{25} +(20.5722 - 17.4867i) q^{27} +(-27.9597 + 27.9597i) q^{29} +7.90993 q^{31} +(-1.48814 + 55.1754i) q^{33} +(-19.2038 + 19.2038i) q^{35} +(-20.0443 + 20.0443i) q^{37} +(-0.731530 + 27.1227i) q^{39} -45.1067 q^{41} +(-36.0095 + 36.0095i) q^{43} +(-30.1168 + 27.0318i) q^{45} +5.08935i q^{47} +12.5209 q^{49} +(9.57876 - 9.07563i) q^{51} +(-20.7687 - 20.7687i) q^{53} -82.7299i q^{55} +(-0.367268 + 13.6171i) q^{57} +(-39.0656 - 39.0656i) q^{59} +(49.8322 + 49.8322i) q^{61} +(-54.2791 - 2.93007i) q^{63} -40.6677i q^{65} +(44.9162 + 44.9162i) q^{67} +(70.2358 + 74.1295i) q^{69} -46.6947 q^{71} -97.3523i q^{73} +(-10.4117 + 9.86483i) q^{75} +(78.5758 - 78.5758i) q^{77} +40.1637 q^{79} +(-80.5293 - 8.71960i) q^{81} +(-35.5451 + 35.5451i) q^{83} +(-13.9852 + 13.9852i) q^{85} +(118.580 + 3.19823i) q^{87} +69.6795 q^{89} +(38.6257 - 38.6257i) q^{91} +(-16.3210 - 17.2258i) q^{93} -20.4174i q^{95} +61.0939 q^{97} +(123.228 - 110.606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3}+O(q^{10}) $ 20 * q - 6 * q^3	$ 20 q - 6 q^{3} - 92 q^{13} + 116 q^{15} - 52 q^{19} - 48 q^{21} + 18 q^{27} + 80 q^{31} + 60 q^{33} + 116 q^{37} + 172 q^{43} - 60 q^{45} - 364 q^{49} + 128 q^{51} + 244 q^{61} - 296 q^{63} + 356 q^{67} + 20 q^{69} - 146 q^{75} - 384 q^{79} - 188 q^{81} - 48 q^{85} + 136 q^{91} + 132 q^{93} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 - 92 * q^13 + 116 * q^15 - 52 * q^19 - 48 * q^21 + 18 * q^27 + 80 * q^31 + 60 * q^33 + 116 * q^37 + 172 * q^43 - 60 * q^45 - 364 * q^49 + 128 * q^51 + 244 * q^61 - 296 * q^63 + 356 * q^67 + 20 * q^69 - 146 * q^75 - 384 * q^79 - 188 * q^81 - 48 * q^85 + 136 * q^91 + 132 * q^93 + 472 * q^97 - 452 * 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
$3$	−2.06336	−	2.17774i	−0.687785	−	0.725914i
$3$	−2.06336	−	2.17774i	−0.687785	−	0.725914i
$4$		0			0
$5$	3.17955	+	3.17955i	0.635909	+	0.635909i	0.949544	−	0.313634i	$-0.101547\pi$
$5$	3.17955	+	3.17955i	0.635909	+	0.635909i	−0.313634	+	0.949544i	$0.601547\pi$
$6$		0			0
$7$			6.03979i			0.862827i	0.902154	+	0.431414i	$0.141985\pi$
$7$			6.03979i			0.862827i	−0.902154	+	0.431414i	$0.858015\pi$
$8$		0			0
$9$	−0.485128	+	8.98692i	−0.0539031	+	0.998546i
$10$		0			0
$11$	−13.0097	−	13.0097i	−1.18270	−	1.18270i	−0.979042	−	0.203657i	$-0.934717\pi$
$11$	−13.0097	−	13.0097i	−1.18270	−	1.18270i	−0.203657	−	0.979042i	$-0.565283\pi$
$12$		0			0
$13$	−6.39520	−	6.39520i	−0.491939	−	0.491939i	0.416978	−	0.908917i	$-0.363089\pi$
$13$	−6.39520	−	6.39520i	−0.491939	−	0.491939i	−0.908917	+	0.416978i	$0.863089\pi$
$14$		0			0
$15$	0.363700	−	13.4848i	0.0242466	−	0.898985i
$16$		0			0
$17$			4.39848i			0.258734i	0.991597	+	0.129367i	$0.0412945\pi$
$17$			4.39848i			0.258734i	−0.991597	+	0.129367i	$0.958705\pi$
$18$		0			0
$19$	−3.21075	−	3.21075i	−0.168987	−	0.168987i	0.617547	−	0.786534i	$-0.288126\pi$
$19$	−3.21075	−	3.21075i	−0.168987	−	0.168987i	−0.786534	+	0.617547i	$0.788126\pi$
$20$		0			0
$21$	13.1531	−	12.4622i	0.626339	−	0.593440i
$22$		0			0
$23$	−34.0396			−1.47998			−0.739992	−	0.672616i	$-0.765171\pi$
$23$	−34.0396			−1.47998			−0.739992	+	0.672616i	$0.765171\pi$
$24$		0			0
$25$		−	4.78097i		−	0.191239i
$26$		0			0
$27$	20.5722	−	17.4867i	0.761933	−	0.647656i
$28$		0			0
$29$	−27.9597	+	27.9597i	−0.964128	+	0.964128i	−0.999378	−	0.0352510i	$-0.988777\pi$
$29$	−27.9597	+	27.9597i	−0.964128	+	0.964128i	0.0352510	+	0.999378i	$0.488777\pi$
$30$		0			0
$31$	7.90993			0.255159			0.127580	−	0.991828i	$-0.459279\pi$
$31$	7.90993			0.255159			0.127580	+	0.991828i	$0.459279\pi$
$32$		0			0
$33$	−1.48814	+	55.1754i	−0.0450952	+	1.67198i
$34$		0			0
$35$	−19.2038	+	19.2038i	−0.548680	+	0.548680i
$36$		0			0
$37$	−20.0443	+	20.0443i	−0.541736	+	0.541736i	−0.924038	−	0.382301i	$-0.875132\pi$
$37$	−20.0443	+	20.0443i	−0.541736	+	0.541736i	0.382301	+	0.924038i	$0.375132\pi$
$38$		0			0
$39$	−0.731530	+	27.1227i	−0.0187572	+	0.695453i
$40$		0			0
$41$	−45.1067			−1.10016			−0.550081	−	0.835111i	$-0.685403\pi$
$41$	−45.1067			−1.10016			−0.550081	+	0.835111i	$0.685403\pi$
$42$		0			0
$43$	−36.0095	+	36.0095i	−0.837431	+	0.837431i	−0.988520	−	0.151089i	$-0.951722\pi$
$43$	−36.0095	+	36.0095i	−0.837431	+	0.837431i	0.151089	+	0.988520i	$0.451722\pi$
$44$		0			0
$45$	−30.1168	+	27.0318i	−0.669262	+	0.600707i
$46$		0			0
$47$			5.08935i			0.108284i	0.998533	+	0.0541421i	$0.0172424\pi$
$47$			5.08935i			0.108284i	−0.998533	+	0.0541421i	$0.982758\pi$
$48$		0			0
$49$	12.5209			0.255529
$50$		0			0
$51$	9.57876	−	9.07563i	0.187819	−	0.177953i
$52$		0			0
$53$	−20.7687	−	20.7687i	−0.391863	−	0.391863i	0.483488	−	0.875351i	$-0.339370\pi$
$53$	−20.7687	−	20.7687i	−0.391863	−	0.391863i	−0.875351	+	0.483488i	$0.839370\pi$
$54$		0			0
$55$		−	82.7299i		−	1.50418i
$56$		0			0
$57$	−0.367268	+	13.6171i	−0.00644331	+	0.238896i
$58$		0			0
$59$	−39.0656	−	39.0656i	−0.662129	−	0.662129i	0.293753	−	0.955881i	$-0.405096\pi$
$59$	−39.0656	−	39.0656i	−0.662129	−	0.662129i	−0.955881	+	0.293753i	$0.905096\pi$
$60$		0			0
$61$	49.8322	+	49.8322i	0.816921	+	0.816921i	0.985661	−	0.168739i	$-0.0539696\pi$
$61$	49.8322	+	49.8322i	0.816921	+	0.816921i	−0.168739	+	0.985661i	$0.553970\pi$
$62$		0			0
$63$	−54.2791	−	2.93007i	−0.861573	−	0.0465090i
$64$		0			0
$65$		−	40.6677i		−	0.625657i
$66$		0			0
$67$	44.9162	+	44.9162i	0.670390	+	0.670390i	0.957806	−	0.287416i	$-0.0927961\pi$
$67$	44.9162	+	44.9162i	0.670390	+	0.670390i	−0.287416	+	0.957806i	$0.592796\pi$
$68$		0			0
$69$	70.2358	+	74.1295i	1.01791	+	1.07434i
$70$		0			0
$71$	−46.6947			−0.657672			−0.328836	−	0.944387i	$-0.606656\pi$
$71$	−46.6947			−0.657672			−0.328836	+	0.944387i	$0.606656\pi$
$72$		0			0
$73$		−	97.3523i		−	1.33359i	−0.745240	−	0.666797i	$-0.767665\pi$
$73$		−	97.3523i		−	1.33359i	0.745240	−	0.666797i	$-0.232335\pi$
$74$		0			0
$75$	−10.4117	+	9.86483i	−0.138823	+	0.131531i
$76$		0			0
$77$	78.5758	−	78.5758i	1.02047	−	1.02047i
$78$		0			0
$79$	40.1637			0.508402			0.254201	−	0.967151i	$-0.418188\pi$
$79$	40.1637			0.508402			0.254201	+	0.967151i	$0.418188\pi$
$80$		0			0
$81$	−80.5293	−	8.71960i	−0.994189	−	0.107649i
$82$		0			0
$83$	−35.5451	+	35.5451i	−0.428254	+	0.428254i	−0.888033	−	0.459779i	$-0.847929\pi$
$83$	−35.5451	+	35.5451i	−0.428254	+	0.428254i	0.459779	+	0.888033i	$0.347929\pi$
$84$		0			0
$85$	−13.9852	+	13.9852i	−0.164531	+	0.164531i
$86$		0			0
$87$	118.580	+	3.19823i	1.36299	+	0.0367613i
$88$		0			0
$89$	69.6795			0.782916			0.391458	−	0.920196i	$-0.371971\pi$
$89$	69.6795			0.782916			0.391458	+	0.920196i	$0.371971\pi$
$90$		0			0
$91$	38.6257	−	38.6257i	0.424458	−	0.424458i
$92$		0			0
$93$	−16.3210	−	17.2258i	−0.175495	−	0.185224i
$94$		0			0
$95$		−	20.4174i		−	0.214920i
$96$		0			0
$97$	61.0939			0.629834			0.314917	−	0.949119i	$-0.398023\pi$
$97$	61.0939			0.629834			0.314917	+	0.949119i	$0.398023\pi$
$98$		0			0
$99$	123.228	−	110.606i	1.24473	−	1.11723i
$100$		0			0
$101$	−104.036	−	104.036i	−1.03006	−	1.03006i	−0.999534	−	0.0305280i	$-0.990281\pi$
$101$	−104.036	−	104.036i	−1.03006	−	1.03006i	−0.0305280	−	0.999534i	$-0.509719\pi$
$102$		0			0
$103$			57.2961i			0.556272i	0.960542	+	0.278136i	$0.0897167\pi$
$103$			57.2961i			0.556272i	−0.960542	+	0.278136i	$0.910283\pi$
$104$		0			0
$105$	81.4452	+	2.19667i	0.775668	+	0.0209207i
$106$		0			0
$107$	92.4468	+	92.4468i	0.863989	+	0.863989i	0.991799	−	0.127810i	$-0.0407947\pi$
$107$	92.4468	+	92.4468i	0.863989	+	0.863989i	−0.127810	+	0.991799i	$0.540795\pi$
$108$		0			0
$109$	−75.3749	−	75.3749i	−0.691513	−	0.691513i	0.271052	−	0.962565i	$-0.412629\pi$
$109$	−75.3749	−	75.3749i	−0.691513	−	0.691513i	−0.962565	+	0.271052i	$0.912629\pi$
$110$		0			0
$111$	85.0096	+	2.29281i	0.765853	+	0.0206559i
$112$		0			0
$113$		−	112.254i		−	0.993401i	−0.867922	−	0.496701i	$-0.834545\pi$
$113$		−	112.254i		−	0.993401i	0.867922	−	0.496701i	$-0.165455\pi$
$114$		0			0
$115$	−108.231	−	108.231i	−0.941135	−	0.941135i
$116$		0			0
$117$	60.5756	−	54.3707i	0.517740	−	0.464706i
$118$		0			0
$119$	−26.5659			−0.223243
$120$		0			0
$121$			217.504i			1.79756i
$122$		0			0
$123$	93.0711	+	98.2307i	0.756676	+	0.798624i
$124$		0			0
$125$	94.6900	−	94.6900i	0.757520	−	0.757520i
$126$		0			0
$127$	−93.6335			−0.737272			−0.368636	−	0.929574i	$-0.620175\pi$
$127$	−93.6335			−0.737272			−0.368636	+	0.929574i	$0.620175\pi$
$128$		0			0
$129$	152.720	+	4.11903i	1.18388	+	0.0319305i
$130$		0			0
$131$	−81.5208	+	81.5208i	−0.622296	+	0.622296i	−0.946118	−	0.323822i	$-0.895032\pi$
$131$	−81.5208	+	81.5208i	−0.622296	+	0.622296i	0.323822	+	0.946118i	$0.395032\pi$
$132$		0			0
$133$	19.3922	−	19.3922i	0.145806	−	0.145806i
$134$		0			0
$135$	121.010	+	9.81037i	0.896371	+	0.0726694i
$136$		0			0
$137$	−24.5510			−0.179205			−0.0896023	−	0.995978i	$-0.528560\pi$
$137$	−24.5510			−0.179205			−0.0896023	+	0.995978i	$0.528560\pi$
$138$		0			0
$139$	3.06917	−	3.06917i	0.0220804	−	0.0220804i	−0.695980	−	0.718061i	$-0.745030\pi$
$139$	3.06917	−	3.06917i	0.0220804	−	0.0220804i	0.718061	+	0.695980i	$0.245030\pi$
$140$		0			0
$141$	11.0833	−	10.5011i	0.0786050	−	0.0744762i
$142$		0			0
$143$			166.399i			1.16363i
$144$		0			0
$145$	−177.798			−1.22620
$146$		0			0
$147$	−25.8351	−	27.2674i	−0.175749	−	0.185492i
$148$		0			0
$149$	−5.86344	−	5.86344i	−0.0393519	−	0.0393519i	0.687157	−	0.726509i	$-0.258858\pi$
$149$	−5.86344	−	5.86344i	−0.0393519	−	0.0393519i	−0.726509	+	0.687157i	$0.758858\pi$
$150$		0			0
$151$			179.561i			1.18914i	0.804043	+	0.594571i	$0.202678\pi$
$151$			179.561i			1.18914i	−0.804043	+	0.594571i	$0.797322\pi$
$152$		0			0
$153$	−39.5288	−	2.13382i	−0.258358	−	0.0139466i
$154$		0			0
$155$	25.1500	+	25.1500i	0.162258	+	0.162258i
$156$		0			0
$157$	14.8689	+	14.8689i	0.0947067	+	0.0947067i	0.752873	−	0.658166i	$-0.228668\pi$
$157$	14.8689	+	14.8689i	0.0947067	+	0.0947067i	−0.658166	+	0.752873i	$0.728668\pi$
$158$		0			0
$159$	−2.37568	+	88.0822i	−0.0149414	+	0.553976i
$160$		0			0
$161$		−	205.592i		−	1.27697i
$162$		0			0
$163$	66.1190	+	66.1190i	0.405638	+	0.405638i	0.880214	−	0.474577i	$-0.157399\pi$
$163$	66.1190	+	66.1190i	0.405638	+	0.405638i	−0.474577	+	0.880214i	$0.657399\pi$
$164$		0			0
$165$	−180.164	+	170.701i	−1.09191	+	1.03455i
$166$		0			0
$167$	158.709			0.950353			0.475176	−	0.879891i	$-0.342384\pi$
$167$	158.709			0.950353			0.475176	+	0.879891i	$0.342384\pi$
$168$		0			0
$169$		−	87.2028i		−	0.515993i
$170$		0			0
$171$	30.4123	−	27.2971i	0.177850	−	0.159632i
$172$		0			0
$173$	−76.9955	+	76.9955i	−0.445061	+	0.445061i	−0.893709	−	0.448648i	$-0.851906\pi$
$173$	−76.9955	+	76.9955i	−0.445061	+	0.445061i	0.448648	+	0.893709i	$0.351906\pi$
$174$		0			0
$175$	28.8760			0.165006
$176$		0			0
$177$	−4.46861	+	165.681i	−0.0252464	+	0.936051i
$178$		0			0
$179$	101.360	−	101.360i	0.566257	−	0.566257i	−0.364821	−	0.931078i	$-0.618870\pi$
$179$	101.360	−	101.360i	0.566257	−	0.566257i	0.931078	+	0.364821i	$0.118870\pi$
$180$		0			0
$181$	212.373	−	212.373i	1.17333	−	1.17333i	0.191920	−	0.981411i	$-0.438529\pi$
$181$	212.373	−	212.373i	1.17333	−	1.17333i	0.981411	−	0.191920i	$-0.0614714\pi$
$182$		0			0
$183$	5.70017	−	211.343i	0.0311485	−	1.15488i
$184$		0			0
$185$	−127.463			−0.688991
$186$		0			0
$187$	57.2229	−	57.2229i	0.306005	−	0.306005i
$188$		0			0
$189$	105.616	+	124.252i	0.558815	+	0.657416i
$190$		0			0
$191$			36.3314i			0.190217i	0.995467	+	0.0951083i	$0.0303197\pi$
$191$			36.3314i			0.190217i	−0.995467	+	0.0951083i	$0.969680\pi$
$192$		0			0
$193$	47.1090			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$193$	47.1090			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$194$		0			0
$195$	−88.5638	+	83.9119i	−0.454173	+	0.430317i
$196$		0			0
$197$	32.2783	+	32.2783i	0.163849	+	0.163849i	0.784269	−	0.620420i	$-0.213038\pi$
$197$	32.2783	+	32.2783i	0.163849	+	0.163849i	−0.620420	+	0.784269i	$0.713038\pi$
$198$		0			0
$199$		−	118.181i		−	0.593874i	−0.954897	−	0.296937i	$-0.904035\pi$
$199$		−	118.181i		−	0.593874i	0.954897	−	0.296937i	$-0.0959651\pi$
$200$		0			0
$201$	5.13784	−	190.494i	0.0255614	−	0.947731i
$202$		0			0
$203$	−168.871	−	168.871i	−0.831875	−	0.831875i
$204$		0			0
$205$	−143.419	−	143.419i	−0.699604	−	0.699604i
$206$		0			0
$207$	16.5136	−	305.911i	0.0797756	−	1.47783i
$208$		0			0
$209$			83.5416i			0.399721i
$210$		0			0
$211$	63.8884	+	63.8884i	0.302789	+	0.302789i	0.842104	−	0.539315i	$-0.181317\pi$
$211$	63.8884	+	63.8884i	0.302789	+	0.302789i	−0.539315	+	0.842104i	$0.681317\pi$
$212$		0			0
$213$	96.3478	+	101.689i	0.452337	+	0.477413i
$214$		0			0
$215$	−228.988			−1.06506
$216$		0			0
$217$			47.7743i			0.220158i
$218$		0			0
$219$	−212.008	+	200.872i	−0.968075	+	0.917226i
$220$		0			0
$221$	28.1292	−	28.1292i	0.127281	−	0.127281i
$222$		0			0
$223$	42.8886			0.192326			0.0961628	−	0.995366i	$-0.469343\pi$
$223$	42.8886			0.192326			0.0961628	+	0.995366i	$0.469343\pi$
$224$		0			0
$225$	42.9661	+	2.31938i	0.190961	+	0.0103084i
$226$		0			0
$227$	23.0035	−	23.0035i	0.101337	−	0.101337i	−0.654621	−	0.755958i	$-0.727172\pi$
$227$	23.0035	−	23.0035i	0.101337	−	0.101337i	0.755958	+	0.654621i	$0.227172\pi$
$228$		0			0
$229$	−241.282	+	241.282i	−1.05363	+	1.05363i	−0.0551571	+	0.998478i	$0.517566\pi$
$229$	−241.282	+	241.282i	−1.05363	+	1.05363i	−0.998478	+	0.0551571i	$0.982434\pi$
$230$		0			0
$231$	−333.248	−	8.98807i	−1.44263	−	0.0389094i
$232$		0			0
$233$	240.310			1.03137			0.515687	−	0.856777i	$-0.327537\pi$
$233$	240.310			1.03137			0.515687	+	0.856777i	$0.327537\pi$
$234$		0			0
$235$	−16.1818	+	16.1818i	−0.0688589	+	0.0688589i
$236$		0			0
$237$	−82.8721	−	87.4663i	−0.349671	−	0.369056i
$238$		0			0
$239$		−	218.171i		−	0.912851i	−0.889762	−	0.456425i	$-0.849130\pi$
$239$		−	218.171i		−	0.912851i	0.889762	−	0.456425i	$-0.150870\pi$
$240$		0			0
$241$	−88.9611			−0.369133			−0.184567	−	0.982820i	$-0.559088\pi$
$241$	−88.9611			−0.369133			−0.184567	+	0.982820i	$0.559088\pi$
$242$		0			0
$243$	147.172	+	193.364i	0.605644	+	0.795736i
$244$		0			0
$245$	39.8109	+	39.8109i	0.162493	+	0.162493i
$246$		0			0
$247$			41.0667i			0.166262i
$248$		0			0
$249$	150.750	+	4.06591i	0.605423	+	0.0163289i
$250$		0			0
$251$	−169.225	−	169.225i	−0.674205	−	0.674205i	0.284478	−	0.958683i	$-0.408180\pi$
$251$	−169.225	−	169.225i	−0.674205	−	0.674205i	−0.958683	+	0.284478i	$0.908180\pi$
$252$		0			0
$253$	442.845	+	442.845i	1.75038	+	1.75038i
$254$		0			0
$255$	59.3125	+	1.59973i	0.232598	+	0.00627343i
$256$		0			0
$257$			393.109i			1.52961i	0.644262	+	0.764804i	$0.277164\pi$
$257$			393.109i			1.52961i	−0.644262	+	0.764804i	$0.722836\pi$
$258$		0			0
$259$	−121.063	−	121.063i	−0.467425	−	0.467425i
$260$		0			0
$261$	−237.707	−	264.835i	−0.910756	−	1.01470i
$262$		0			0
$263$	−179.865			−0.683897			−0.341948	−	0.939719i	$-0.611087\pi$
$263$	−179.865			−0.683897			−0.341948	+	0.939719i	$0.611087\pi$
$264$		0			0
$265$		−	132.070i		−	0.498378i
$266$		0			0
$267$	−143.774	−	151.744i	−0.538478	−	0.568330i
$268$		0			0
$269$	−290.530	+	290.530i	−1.08004	+	1.08004i	−0.0835324	+	0.996505i	$0.526620\pi$
$269$	−290.530	+	290.530i	−1.08004	+	1.08004i	−0.996505	+	0.0835324i	$0.973380\pi$
$270$		0			0
$271$	−496.550			−1.83229			−0.916144	−	0.400849i	$-0.868715\pi$
$271$	−496.550			−1.83229			−0.916144	+	0.400849i	$0.868715\pi$
$272$		0			0
$273$	−163.815	−	4.41829i	−0.600056	−	0.0161842i
$274$		0			0
$275$	−62.1989	+	62.1989i	−0.226178	+	0.226178i
$276$		0			0
$277$	93.0101	−	93.0101i	0.335776	−	0.335776i	−0.518999	−	0.854775i	$-0.673695\pi$
$277$	93.0101	−	93.0101i	0.335776	−	0.335776i	0.854775	+	0.518999i	$0.173695\pi$
$278$		0			0
$279$	−3.83733	+	71.0859i	−0.0137539	+	0.254788i
$280$		0			0
$281$	−300.875			−1.07073			−0.535365	−	0.844621i	$-0.679826\pi$
$281$	−300.875			−1.07073			−0.535365	+	0.844621i	$0.679826\pi$
$282$		0			0
$283$	101.469	−	101.469i	0.358549	−	0.358549i	−0.504729	−	0.863278i	$-0.668408\pi$
$283$	101.469	−	101.469i	0.358549	−	0.358549i	0.863278	+	0.504729i	$0.168408\pi$
$284$		0			0
$285$	−44.4639	+	42.1284i	−0.156014	+	0.147819i
$286$		0			0
$287$		−	272.435i		−	0.949250i
$288$		0			0
$289$	269.653			0.933057
$290$		0			0
$291$	−126.058	−	133.047i	−0.433190	−	0.457205i
$292$		0			0
$293$	321.104	+	321.104i	1.09592	+	1.09592i	0.994883	+	0.101037i	$0.0322160\pi$
$293$	321.104	+	321.104i	1.09592	+	1.09592i	0.101037	+	0.994883i	$0.467784\pi$
$294$		0			0
$295$		−	248.422i		−	0.842107i
$296$		0			0
$297$	−495.135	−	40.1409i	−1.66712	−	0.135155i
$298$		0			0
$299$	217.690	+	217.690i	0.728061	+	0.728061i
$300$		0			0
$301$	−217.490	−	217.490i	−0.722558	−	0.722558i
$302$		0			0
$303$	−11.9004	+	441.228i	−0.0392753	+	1.45620i
$304$		0			0
$305$			316.888i			1.03898i
$306$		0			0
$307$	94.2282	+	94.2282i	0.306932	+	0.306932i	0.843718	−	0.536786i	$-0.180362\pi$
$307$	94.2282	+	94.2282i	0.306932	+	0.306932i	−0.536786	+	0.843718i	$0.680362\pi$
$308$		0			0
$309$	124.776	−	118.222i	0.403806	−	0.382596i
$310$		0			0
$311$	245.712			0.790070			0.395035	−	0.918666i	$-0.370732\pi$
$311$	245.712			0.790070			0.395035	+	0.918666i	$0.370732\pi$
$312$		0			0
$313$			353.841i			1.13048i	0.824925	+	0.565242i	$0.191217\pi$
$313$			353.841i			1.13048i	−0.824925	+	0.565242i	$0.808783\pi$
$314$		0			0
$315$	−163.267	−	181.899i	−0.518307	−	0.577458i
$316$		0			0
$317$	−234.024	+	234.024i	−0.738245	+	0.738245i	−0.972238	−	0.233994i	$-0.924821\pi$
$317$	−234.024	+	234.024i	−0.738245	+	0.738245i	0.233994	+	0.972238i	$0.424821\pi$
$318$		0			0
$319$	727.494			2.28055
$320$		0			0
$321$	10.5747	−	392.076i	0.0329431	−	1.22142i
$322$		0			0
$323$	14.1224	−	14.1224i	0.0437226	−	0.0437226i
$324$		0			0
$325$	−30.5752	+	30.5752i	−0.0940777	+	0.0940777i
$326$		0			0
$327$	−8.62193	+	319.673i	−0.0263668	+	0.977592i
$328$		0			0
$329$	−30.7386			−0.0934305
$330$		0			0
$331$	−32.5392	+	32.5392i	−0.0983058	+	0.0983058i	−0.754549	−	0.656243i	$-0.772144\pi$
$331$	−32.5392	+	32.5392i	−0.0983058	+	0.0983058i	0.656243	+	0.754549i	$0.272144\pi$
$332$		0			0
$333$	−170.412	−	189.860i	−0.511748	−	0.570150i
$334$		0			0
$335$			285.626i			0.852615i
$336$		0			0
$337$	−185.573			−0.550660			−0.275330	−	0.961350i	$-0.588787\pi$
$337$	−185.573			−0.550660			−0.275330	+	0.961350i	$0.588787\pi$
$338$		0			0
$339$	−244.461	+	231.621i	−0.721124	+	0.683247i
$340$		0			0
$341$	−102.906	−	102.906i	−0.301776	−	0.301776i
$342$		0			0
$343$			371.574i			1.08330i
$344$		0			0
$345$	−12.3802	+	459.016i	−0.0358846	+	1.33048i
$346$		0			0
$347$	51.9585	+	51.9585i	0.149736	+	0.149736i	0.778000	−	0.628264i	$-0.216234\pi$
$347$	51.9585	+	51.9585i	0.149736	+	0.149736i	−0.628264	+	0.778000i	$0.716234\pi$
$348$		0			0
$349$	−378.719	−	378.719i	−1.08515	−	1.08515i	−0.996020	−	0.0891344i	$-0.971590\pi$
$349$	−378.719	−	378.719i	−1.08515	−	1.08515i	−0.0891344	−	0.996020i	$-0.528410\pi$
$350$		0			0
$351$	−243.394	−	19.7322i	−0.693431	−	0.0562170i
$352$		0			0
$353$			326.435i			0.924744i	0.886686	+	0.462372i	$0.153002\pi$
$353$			326.435i			0.924744i	−0.886686	+	0.462372i	$0.846998\pi$
$354$		0			0
$355$	−148.468	−	148.468i	−0.418220	−	0.418220i
$356$		0			0
$357$	54.8149	+	57.8537i	0.153543	+	0.162055i
$358$		0			0
$359$	254.927			0.710103			0.355051	−	0.934847i	$-0.384463\pi$
$359$	254.927			0.710103			0.355051	+	0.934847i	$0.384463\pi$
$360$		0			0
$361$		−	340.382i		−	0.942887i
$362$		0			0
$363$	473.668	−	448.789i	1.30487	−	1.23633i
$364$		0			0
$365$	309.536	−	309.536i	0.848045	−	0.848045i
$366$		0			0
$367$	124.247			0.338548			0.169274	−	0.985569i	$-0.445858\pi$
$367$	124.247			0.338548			0.169274	+	0.985569i	$0.445858\pi$
$368$		0			0
$369$	21.8825	−	405.370i	0.0593021	−	1.09856i
$370$		0			0
$371$	125.439	−	125.439i	0.338110	−	0.338110i
$372$		0			0
$373$	201.674	−	201.674i	0.540680	−	0.540680i	−0.383048	−	0.923728i	$-0.625126\pi$
$373$	201.674	−	201.674i	0.540680	−	0.540680i	0.923728	+	0.383048i	$0.125126\pi$
$374$		0			0
$375$	−401.589	−	10.8313i	−1.07091	−	0.0288835i
$376$		0			0
$377$	357.616			0.948583
$378$		0			0
$379$	−227.541	+	227.541i	−0.600372	+	0.600372i	−0.940411	−	0.340040i	$-0.889560\pi$
$379$	−227.541	+	227.541i	−0.600372	+	0.600372i	0.340040	+	0.940411i	$0.389560\pi$
$380$		0			0
$381$	193.199	+	203.910i	0.507084	+	0.535196i
$382$		0			0
$383$		−	128.933i		−	0.336641i	−0.985732	−	0.168320i	$-0.946166\pi$
$383$		−	128.933i		−	0.336641i	0.985732	−	0.168320i	$-0.0538343\pi$
$384$		0			0
$385$	499.671			1.29785
$386$		0			0
$387$	−306.145	−	341.084i	−0.791073	−	0.881353i
$388$		0			0
$389$	−107.474	−	107.474i	−0.276283	−	0.276283i	0.555340	−	0.831623i	$-0.312588\pi$
$389$	−107.474	−	107.474i	−0.276283	−	0.276283i	−0.831623	+	0.555340i	$0.812588\pi$
$390$		0			0
$391$		−	149.723i		−	0.382922i
$392$		0			0
$393$	345.738	+	9.32494i	0.879739	+	0.0237276i
$394$		0			0
$395$	127.702	+	127.702i	0.323297	+	0.323297i
$396$		0			0
$397$	259.306	+	259.306i	0.653163	+	0.653163i	0.953753	−	0.300591i	$-0.0971837\pi$
$397$	259.306	+	259.306i	0.653163	+	0.653163i	−0.300591	+	0.953753i	$0.597184\pi$
$398$		0			0
$399$	−82.2444	−	2.21822i	−0.206126	−	0.00555946i
$400$		0			0
$401$		−	335.810i		−	0.837431i	−0.908117	−	0.418716i	$-0.862480\pi$
$401$		−	335.810i		−	0.837431i	0.908117	−	0.418716i	$-0.137520\pi$
$402$		0			0
$403$	−50.5856	−	50.5856i	−0.125523	−	0.125523i
$404$		0			0
$405$	−228.322	−	283.771i	−0.563759	−	0.700669i
$406$		0			0
$407$	521.539			1.28142
$408$		0			0
$409$		−	66.3618i		−	0.162254i	−0.996704	−	0.0811269i	$-0.974148\pi$
$409$		−	66.3618i		−	0.162254i	0.996704	−	0.0811269i	$-0.0258519\pi$
$410$		0			0
$411$	50.6575	+	53.4658i	0.123254	+	0.130087i
$412$		0			0
$413$	235.948	−	235.948i	0.571303	−	0.571303i
$414$		0			0
$415$	−226.035			−0.544662
$416$		0			0
$417$	−13.0167	−	0.351074i	−0.0312150	−	0.000841904i
$418$		0			0
$419$	371.566	−	371.566i	0.886792	−	0.886792i	−0.107422	−	0.994214i	$-0.534260\pi$
$419$	371.566	−	371.566i	0.886792	−	0.886792i	0.994214	+	0.107422i	$0.0342596\pi$
$420$		0			0
$421$	−487.629	+	487.629i	−1.15826	+	1.15826i	−0.173416	+	0.984849i	$0.555481\pi$
$421$	−487.629	+	487.629i	−1.15826	+	1.15826i	−0.984849	+	0.173416i	$0.944519\pi$
$422$		0			0
$423$	−45.7376	−	2.46899i	−0.108127	−	0.00583685i
$424$		0			0
$425$	21.0290			0.0494800
$426$		0			0
$427$	−300.976	+	300.976i	−0.704862	+	0.704862i
$428$		0			0
$429$	362.375	−	343.341i	0.844696	−	0.800328i
$430$		0			0
$431$		−	505.901i		−	1.17378i	−0.809665	−	0.586892i	$-0.800351\pi$
$431$		−	505.901i		−	1.17378i	0.809665	−	0.586892i	$-0.199649\pi$
$432$		0			0
$433$	−758.226			−1.75110			−0.875550	−	0.483128i	$-0.839500\pi$
$433$	−758.226			−1.75110			−0.875550	+	0.483128i	$0.839500\pi$
$434$		0			0
$435$	366.861	+	387.199i	0.843359	+	0.890113i
$436$		0			0
$437$	109.293	+	109.293i	0.250097	+	0.250097i
$438$		0			0
$439$		−	145.760i		−	0.332026i	−0.986124	−	0.166013i	$-0.946911\pi$
$439$		−	145.760i		−	0.332026i	0.986124	−	0.166013i	$-0.0530895\pi$
$440$		0			0
$441$	−6.07425	+	112.525i	−0.0137738	+	0.255158i
$442$		0			0
$443$	607.046	+	607.046i	1.37031	+	1.37031i	0.859983	+	0.510323i	$0.170474\pi$
$443$	607.046	+	607.046i	1.37031	+	1.37031i	0.510323	+	0.859983i	$0.329526\pi$
$444$		0			0
$445$	221.549	+	221.549i	0.497864	+	0.497864i
$446$		0			0
$447$	−0.670702	+	24.8674i	−0.00150045	+	0.0556318i
$448$		0			0
$449$		−	190.654i		−	0.424620i	−0.977202	−	0.212310i	$-0.931901\pi$
$449$		−	190.654i		−	0.424620i	0.977202	−	0.212310i	$-0.0680986\pi$
$450$		0			0
$451$	586.824	+	586.824i	1.30116	+	1.30116i
$452$		0			0
$453$	391.037	−	370.497i	0.863216	−	0.817875i
$454$		0			0
$455$	245.624			0.539834
$456$		0			0
$457$		−	128.091i		−	0.280287i	−0.990131	−	0.140143i	$-0.955244\pi$
$457$		−	128.091i		−	0.280287i	0.990131	−	0.140143i	$-0.0447563\pi$
$458$		0			0
$459$	76.9150	+	90.4863i	0.167571	+	0.197138i
$460$		0			0
$461$	74.2060	−	74.2060i	0.160968	−	0.160968i	−0.622028	−	0.782995i	$-0.713691\pi$
$461$	74.2060	−	74.2060i	0.160968	−	0.160968i	0.782995	+	0.622028i	$0.213691\pi$
$462$		0			0
$463$	−620.192			−1.33951			−0.669753	−	0.742584i	$-0.733600\pi$
$463$	−620.192			−1.33951			−0.669753	+	0.742584i	$0.733600\pi$
$464$		0			0
$465$	2.87684	−	106.664i	0.00618675	−	0.229384i
$466$		0			0
$467$	331.708	−	331.708i	0.710296	−	0.710296i	−0.256301	−	0.966597i	$-0.582504\pi$
$467$	331.708	−	331.708i	0.710296	−	0.710296i	0.966597	+	0.256301i	$0.0825038\pi$
$468$		0			0
$469$	−271.284	+	271.284i	−0.578431	+	0.578431i
$470$		0			0
$471$	1.70082	−	63.0607i	0.00361108	−	0.133887i
$472$		0			0
$473$	936.946			1.98086
$474$		0			0
$475$	−15.3505	+	15.3505i	−0.0323168	+	0.0323168i
$476$		0			0
$477$	196.722	−	176.571i	0.412415	−	0.370170i
$478$		0			0
$479$			867.941i			1.81198i	0.423294	+	0.905992i	$0.360874\pi$
$479$			867.941i			1.81198i	−0.423294	+	0.905992i	$0.639126\pi$
$480$		0			0
$481$	256.374			0.533002
$482$		0			0
$483$	−447.727	+	424.210i	−0.926970	+	0.878281i
$484$		0			0
$485$	194.251	+	194.251i	0.400517	+	0.400517i
$486$		0			0
$487$		−	815.778i		−	1.67511i	−0.546354	−	0.837554i	$-0.683985\pi$
$487$		−	815.778i		−	1.67511i	0.546354	−	0.837554i	$-0.316015\pi$
$488$		0			0
$489$	7.56317	−	280.417i	0.0154666	−	0.573450i
$490$		0			0
$491$	−337.746	−	337.746i	−0.687874	−	0.687874i	0.273888	−	0.961762i	$-0.411690\pi$
$491$	−337.746	−	337.746i	−0.687874	−	0.687874i	−0.961762	+	0.273888i	$0.911690\pi$
$492$		0			0
$493$	−122.980	−	122.980i	−0.249453	−	0.249453i
$494$		0			0
$495$	743.486	+	40.1345i	1.50199	+	0.0810799i
$496$		0			0
$497$		−	282.026i		−	0.567457i
$498$		0			0
$499$	−515.289	−	515.289i	−1.03264	−	1.03264i	−0.999449	−	0.0331940i	$-0.989432\pi$
$499$	−515.289	−	515.289i	−1.03264	−	1.03264i	−0.0331940	−	0.999449i	$-0.510568\pi$
$500$		0			0
$501$	−327.473	−	345.627i	−0.653639	−	0.689875i
$502$		0			0
$503$	196.781			0.391215			0.195607	−	0.980682i	$-0.437332\pi$
$503$	196.781			0.391215			0.195607	+	0.980682i	$0.437332\pi$
$504$		0			0
$505$		−	661.576i		−	1.31005i
$506$		0			0
$507$	−189.905	+	179.930i	−0.374567	+	0.354892i
$508$		0			0
$509$	−29.3054	+	29.3054i	−0.0575744	+	0.0575744i	−0.735308	−	0.677733i	$-0.762962\pi$
$509$	−29.3054	+	29.3054i	−0.0575744	+	0.0575744i	0.677733	+	0.735308i	$0.262962\pi$
$510$		0			0
$511$	587.988			1.15066
$512$		0			0
$513$	−122.197	−	9.90664i	−0.238202	−	0.0193112i
$514$		0			0
$515$	−182.175	+	182.175i	−0.353739	+	0.353739i
$516$		0			0
$517$	66.2109	−	66.2109i	0.128068	−	0.128068i
$518$		0			0
$519$	326.546	+	8.80731i	0.629182	+	0.0169698i
$520$		0			0
$521$	−770.641			−1.47916			−0.739578	−	0.673071i	$-0.764975\pi$
$521$	−770.641			−1.47916			−0.739578	+	0.673071i	$0.764975\pi$
$522$		0			0
$523$	258.725	−	258.725i	0.494694	−	0.494694i	−0.415087	−	0.909782i	$-0.636249\pi$
$523$	258.725	−	258.725i	0.494694	−	0.494694i	0.909782	+	0.415087i	$0.136249\pi$
$524$		0			0
$525$	−59.5815	−	62.8846i	−0.113489	−	0.119780i
$526$		0			0
$527$			34.7917i			0.0660183i
$528$		0			0
$529$	629.695			1.19035
$530$		0			0
$531$	370.031	−	332.127i	0.696857	−	0.625475i
$532$		0			0
$533$	288.466	+	288.466i	0.541212	+	0.541212i
$534$		0			0
$535$			587.878i			1.09884i
$536$		0			0
$537$	−429.878	−	11.5943i	−0.800517	−	0.0215909i
$538$		0			0
$539$	−162.894	−	162.894i	−0.302214	−	0.302214i
$540$		0			0
$541$	122.667	+	122.667i	0.226742	+	0.226742i	0.811330	−	0.584588i	$-0.198744\pi$
$541$	122.667	+	122.667i	0.226742	+	0.226742i	−0.584588	+	0.811330i	$0.698744\pi$
$542$		0			0
$543$	−900.694	−	24.2927i	−1.65874	−	0.0447380i
$544$		0			0
$545$		−	479.316i		−	0.879479i
$546$		0			0
$547$	334.075	+	334.075i	0.610740	+	0.610740i	0.943139	−	0.332399i	$-0.107858\pi$
$547$	334.075	+	334.075i	0.610740	+	0.610740i	−0.332399	+	0.943139i	$0.607858\pi$
$548$		0			0
$549$	−472.013	+	423.663i	−0.859768	+	0.771699i
$550$		0			0
$551$	179.543			0.325849
$552$		0			0
$553$			242.581i			0.438663i
$554$		0			0
$555$	263.002	+	277.582i	0.473878	+	0.500148i
$556$		0			0
$557$	−159.480	+	159.480i	−0.286320	+	0.286320i	−0.835623	−	0.549303i	$-0.814893\pi$
$557$	−159.480	+	159.480i	−0.286320	+	0.286320i	0.549303	+	0.835623i	$0.314893\pi$
$558$		0			0
$559$	460.576			0.823929
$560$		0			0
$561$	−242.688	−	6.54557i	−0.432599	−	0.0116677i
$562$		0			0
$563$	−341.226	+	341.226i	−0.606086	+	0.606086i	−0.941921	−	0.335835i	$-0.890982\pi$
$563$	−341.226	+	341.226i	−0.606086	+	0.606086i	0.335835	+	0.941921i	$0.390982\pi$
$564$		0			0
$565$	356.918	−	356.918i	0.631713	−	0.631713i
$566$		0			0
$567$	52.6646	−	486.380i	0.0928828	−	0.857813i
$568$		0			0
$569$	−882.975			−1.55180			−0.775901	−	0.630855i	$-0.782704\pi$
$569$	−882.975			−1.55180			−0.775901	+	0.630855i	$0.782704\pi$
$570$		0			0
$571$	370.112	−	370.112i	0.648181	−	0.648181i	−0.304372	−	0.952553i	$-0.598447\pi$
$571$	370.112	−	370.112i	0.648181	−	0.648181i	0.952553	+	0.304372i	$0.0984466\pi$
$572$		0			0
$573$	79.1204	−	74.9645i	0.138081	−	0.130828i
$574$		0			0
$575$			162.742i			0.283030i
$576$		0			0
$577$	−698.607			−1.21076			−0.605378	−	0.795938i	$-0.706978\pi$
$577$	−698.607			−1.21076			−0.605378	+	0.795938i	$0.706978\pi$
$578$		0			0
$579$	−97.2025	−	102.591i	−0.167880	−	0.177187i
$580$		0			0
$581$	−214.685	−	214.685i	−0.369509	−	0.369509i
$582$		0			0
$583$			540.389i			0.926911i
$584$		0			0
$585$	365.477	+	19.7290i	0.624747	+	0.0337248i
$586$		0			0
$587$	196.072	+	196.072i	0.334024	+	0.334024i	0.854112	−	0.520088i	$-0.174101\pi$
$587$	196.072	+	196.072i	0.334024	+	0.334024i	−0.520088	+	0.854112i	$0.674101\pi$
$588$		0			0
$589$	−25.3968	−	25.3968i	−0.0431185	−	0.0431185i
$590$		0			0
$591$	3.69222	−	136.895i	0.00624742	−	0.231633i
$592$		0			0
$593$			774.011i			1.30525i	0.757683	+	0.652623i	$0.226331\pi$
$593$			774.011i			1.30525i	−0.757683	+	0.652623i	$0.773669\pi$
$594$		0			0
$595$	−84.4675	−	84.4675i	−0.141962	−	0.141962i
$596$		0			0
$597$	−257.368	+	243.849i	−0.431102	+	0.408458i
$598$		0			0
$599$	−783.533			−1.30807			−0.654034	−	0.756465i	$-0.726925\pi$
$599$	−783.533			−1.30807			−0.654034	+	0.756465i	$0.726925\pi$
$600$		0			0
$601$			797.210i			1.32647i	0.748410	+	0.663236i	$0.230818\pi$
$601$			797.210i			1.32647i	−0.748410	+	0.663236i	$0.769182\pi$
$602$		0			0
$603$	−425.448	+	381.868i	−0.705552	+	0.633280i
$604$		0			0
$605$	−691.565	+	691.565i	−1.14308	+	1.14308i
$606$		0			0
$607$	−433.576			−0.714293			−0.357146	−	0.934048i	$-0.616250\pi$
$607$	−433.576			−0.714293			−0.357146	+	0.934048i	$0.616250\pi$
$608$		0			0
$609$	−19.3167	+	716.197i	−0.0317186	+	1.17602i
$610$		0			0
$611$	32.5475	−	32.5475i	0.0532692	−	0.0532692i
$612$		0			0
$613$	493.642	−	493.642i	0.805289	−	0.805289i	−0.178628	−	0.983917i	$-0.557166\pi$
$613$	493.642	−	493.642i	0.805289	−	0.805289i	0.983917	+	0.178628i	$0.0571658\pi$
$614$		0			0
$615$	−16.4053	+	608.253i	−0.0266752	+	0.989029i
$616$		0			0
$617$	685.069			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$617$	685.069			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$618$		0			0
$619$	−379.995	+	379.995i	−0.613885	+	0.613885i	−0.943956	−	0.330071i	$-0.892927\pi$
$619$	−379.995	+	379.995i	−0.613885	+	0.613885i	0.330071	+	0.943956i	$0.392927\pi$
$620$		0			0
$621$	−700.269	+	595.241i	−1.12765	+	0.958520i
$622$		0			0
$623$			420.850i			0.675521i
$624$		0			0
$625$	482.618			0.772189
$626$		0			0
$627$	181.932	−	172.376i	0.290163	−	0.274922i
$628$		0			0
$629$	−88.1642	−	88.1642i	−0.140166	−	0.140166i
$630$		0			0
$631$		−	489.285i		−	0.775412i	−0.921783	−	0.387706i	$-0.873268\pi$
$631$		−	489.285i		−	0.775412i	0.921783	−	0.387706i	$-0.126732\pi$
$632$		0			0
$633$	7.30802	−	270.957i	0.0115451	−	0.428052i
$634$		0			0
$635$	−297.712	−	297.712i	−0.468838	−	0.468838i
$636$		0			0
$637$	−80.0739	−	80.0739i	−0.125705	−	0.125705i
$638$		0			0
$639$	22.6529	−	419.641i	0.0354505	−	0.656716i
$640$		0			0
$641$			492.158i			0.767797i	0.923375	+	0.383898i	$0.125419\pi$
$641$			492.158i			0.767797i	−0.923375	+	0.383898i	$0.874581\pi$
$642$		0			0
$643$	−169.985	−	169.985i	−0.264362	−	0.264362i	0.562462	−	0.826823i	$-0.309854\pi$
$643$	−169.985	−	169.985i	−0.264362	−	0.264362i	−0.826823	+	0.562462i	$0.809854\pi$
$644$		0			0
$645$	472.483	+	498.677i	0.732532	+	0.773142i
$646$		0			0
$647$	−1003.50			−1.55101			−0.775503	−	0.631343i	$-0.782504\pi$
$647$	−1003.50			−1.55101			−0.775503	+	0.631343i	$0.782504\pi$
$648$		0			0
$649$			1016.46i			1.56620i
$650$		0			0
$651$	104.040	−	98.5754i	0.159816	−	0.151422i
$652$		0			0
$653$	407.090	−	407.090i	0.623415	−	0.623415i	−0.322988	−	0.946403i	$-0.604687\pi$
$653$	407.090	−	407.090i	0.623415	−	0.623415i	0.946403	+	0.322988i	$0.104687\pi$
$654$		0			0
$655$	−518.398			−0.791448
$656$		0			0
$657$	874.897	+	47.2283i	1.33165	+	0.0718848i
$658$		0			0
$659$	−635.355	+	635.355i	−0.964119	+	0.964119i	−0.999378	−	0.0352587i	$-0.988774\pi$
$659$	−635.355	+	635.355i	−0.964119	+	0.964119i	0.0352587	+	0.999378i	$0.488774\pi$
$660$		0			0
$661$	196.325	−	196.325i	0.297013	−	0.297013i	−0.542830	−	0.839843i	$-0.682647\pi$
$661$	196.325	−	196.325i	0.297013	−	0.297013i	0.839843	+	0.542830i	$0.182647\pi$
$662$		0			0
$663$	−119.299	−	3.21762i	−0.179937	−	0.00485312i
$664$		0			0
$665$	123.317			0.185439
$666$		0			0
$667$	951.737	−	951.737i	1.42689	−	1.42689i
$668$		0			0
$669$	−88.4944	−	93.4003i	−0.132279	−	0.139612i
$670$		0			0
$671$		−	1296.60i		−	1.93234i
$672$		0			0
$673$	−489.653			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$673$	−489.653			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$674$		0			0
$675$	−83.6034	−	98.3549i	−0.123857	−	0.145711i
$676$		0			0
$677$	−832.940	−	832.940i	−1.23034	−	1.23034i	−0.963833	−	0.266507i	$-0.914131\pi$
$677$	−832.940	−	832.940i	−1.23034	−	1.23034i	−0.266507	−	0.963833i	$-0.585869\pi$
$678$		0			0
$679$			368.994i			0.543438i
$680$		0			0
$681$	−97.5600	−	2.63131i	−0.143260	−	0.00386388i
$682$		0			0
$683$	−773.804	−	773.804i	−1.13295	−	1.13295i	−0.989684	−	0.143264i	$-0.954240\pi$
$683$	−773.804	−	773.804i	−1.13295	−	1.13295i	−0.143264	−	0.989684i	$-0.545760\pi$
$684$		0			0
$685$	−78.0611	−	78.0611i	−0.113958	−	0.113958i
$686$		0			0
$687$	1023.30	+	27.5996i	1.48952	+	0.0401741i
$688$		0			0
$689$			265.640i			0.385545i
$690$		0			0
$691$	−840.306	−	840.306i	−1.21607	−	1.21607i	−0.968996	−	0.247077i	$-0.920530\pi$
$691$	−840.306	−	840.306i	−1.21607	−	1.21607i	−0.247077	−	0.968996i	$-0.579470\pi$
$692$		0			0
$693$	668.035	+	744.274i	0.963975	+	1.07399i
$694$		0			0
$695$	19.5171			0.0280822
$696$		0			0
$697$		−	198.401i		−	0.284650i
$698$		0			0
$699$	−495.845	−	523.334i	−0.709364	−	0.748689i
$700$		0			0
$701$	529.432	−	529.432i	0.755253	−	0.755253i	−0.220201	−	0.975454i	$-0.570671\pi$
$701$	529.432	−	529.432i	0.755253	−	0.755253i	0.975454	+	0.220201i	$0.0706715\pi$
$702$		0			0
$703$	128.714			0.183092
$704$		0			0
$705$	68.6288	+	1.85100i	0.0973458	+	0.00262553i
$706$		0			0
$707$	628.357	−	628.357i	0.888765	−	0.888765i
$708$		0			0
$709$	56.2182	−	56.2182i	0.0792923	−	0.0792923i	−0.666348	−	0.745641i	$-0.732144\pi$
$709$	56.2182	−	56.2182i	0.0792923	−	0.0792923i	0.745641	+	0.666348i	$0.232144\pi$
$710$		0			0
$711$	−19.4845	+	360.948i	−0.0274044	+	0.507663i
$712$		0			0
$713$	−269.251			−0.377631
$714$		0			0
$715$	−529.074	+	529.074i	−0.739964	+	0.739964i
$716$		0			0
$717$	−475.121	+	450.165i	−0.662651	+	0.627845i
$718$		0			0
$719$		−	966.944i		−	1.34485i	−0.740167	−	0.672423i	$-0.765254\pi$
$719$		−	966.944i		−	1.34485i	0.740167	−	0.672423i	$-0.234746\pi$
$720$		0			0
$721$	−346.056			−0.479967
$722$		0			0
$723$	183.558	+	193.734i	0.253884	+	0.267959i
$724$		0			0
$725$	133.674	+	133.674i	0.184378	+	0.184378i
$726$		0			0
$727$			1338.18i			1.84069i	0.391110	+	0.920344i	$0.372091\pi$
$727$			1338.18i			1.84069i	−0.391110	+	0.920344i	$0.627909\pi$
$728$		0			0
$729$	117.429	−	719.480i	0.161083	−	0.986941i
$730$		0			0
$731$	−158.387	−	158.387i	−0.216672	−	0.216672i
$732$		0			0
$733$	−757.046	−	757.046i	−1.03280	−	1.03280i	−0.999443	−	0.0333615i	$-0.989379\pi$
$733$	−757.046	−	757.046i	−1.03280	−	1.03280i	−0.0333615	−	0.999443i	$-0.510621\pi$
$734$		0			0
$735$	4.55386	−	168.842i	0.00619573	−	0.229717i
$736$		0			0
$737$		−	1168.69i		−	1.58574i
$738$		0			0
$739$	495.335	+	495.335i	0.670278	+	0.670278i	0.957780	−	0.287502i	$-0.0928249\pi$
$739$	495.335	+	495.335i	0.670278	+	0.670278i	−0.287502	+	0.957780i	$0.592825\pi$
$740$		0			0
$741$	89.4328	−	84.7353i	0.120692	−	0.114353i
$742$		0			0
$743$	−1421.01			−1.91253			−0.956266	−	0.292500i	$-0.905513\pi$
$743$	−1421.01			−1.91253			−0.956266	+	0.292500i	$0.905513\pi$
$744$		0			0
$745$		−	37.2861i		−	0.0500485i
$746$		0			0
$747$	−302.197	−	336.685i	−0.404547	−	0.450716i
$748$		0			0
$749$	−558.359	+	558.359i	−0.745473	+	0.745473i
$750$		0			0
$751$	143.509			0.191090			0.0955452	−	0.995425i	$-0.469541\pi$
$751$	143.509			0.191090			0.0955452	+	0.995425i	$0.469541\pi$
$752$		0			0
$753$	−19.3572	+	717.702i	−0.0257068	+	0.953123i
$754$		0			0
$755$	−570.921	+	570.921i	−0.756187	+	0.756187i
$756$		0			0
$757$	−651.883	+	651.883i	−0.861140	+	0.861140i	−0.991471	−	0.130331i	$-0.958396\pi$
$757$	−651.883	+	651.883i	−0.861140	+	0.861140i	0.130331	+	0.991471i	$0.458396\pi$
$758$		0			0
$759$	50.6558	−	1878.15i	0.0667402	−	2.47450i
$760$		0			0
$761$	−434.623			−0.571122			−0.285561	−	0.958361i	$-0.592180\pi$
$761$	−434.623			−0.571122			−0.285561	+	0.958361i	$0.592180\pi$
$762$		0			0
$763$	455.249	−	455.249i	0.596656	−	0.596656i
$764$		0			0
$765$	−118.899	−	132.468i	−0.155423	−	0.173161i
$766$		0			0
$767$			499.665i			0.651453i
$768$		0			0
$769$	17.1894			0.0223529			0.0111764	−	0.999938i	$-0.496442\pi$
$769$	17.1894			0.0223529			0.0111764	+	0.999938i	$0.496442\pi$
$770$		0			0
$771$	856.091	−	811.125i	1.11036	−	1.05204i
$772$		0			0
$773$	553.125	+	553.125i	0.715557	+	0.715557i	0.967692	−	0.252135i	$-0.0811328\pi$
$773$	553.125	+	553.125i	0.715557	+	0.715557i	−0.252135	+	0.967692i	$0.581133\pi$
$774$		0			0
$775$		−	37.8171i		−	0.0487963i
$776$		0			0
$777$	−13.8481	+	513.440i	−0.0178225	+	0.660798i
$778$		0			0
$779$	144.826	+	144.826i	0.185913	+	0.185913i
$780$		0			0
$781$	607.484	+	607.484i	0.777828	+	0.777828i
$782$		0			0
$783$	−86.2686	+	1064.12i	−0.110177	+	1.35902i
$784$		0			0
$785$			94.5530i			0.120450i
$786$		0			0
$787$	274.851	+	274.851i	0.349239	+	0.349239i	0.859826	−	0.510587i	$-0.170572\pi$
$787$	274.851	+	274.851i	0.349239	+	0.349239i	−0.510587	+	0.859826i	$0.670572\pi$
$788$		0			0
$789$	371.125	+	391.699i	0.470374	+	0.496450i
$790$		0			0
$791$	677.993			0.857134
$792$		0			0
$793$		−	637.374i		−	0.803750i
$794$		0			0
$795$	−287.615	+	272.508i	−0.361780	+	0.342777i
$796$		0			0
$797$	165.770	−	165.770i	0.207993	−	0.207993i	−0.595421	−	0.803414i	$-0.703015\pi$
$797$	165.770	−	165.770i	0.207993	−	0.207993i	0.803414	+	0.595421i	$0.203015\pi$
$798$		0			0
$799$	−22.3854			−0.0280168
$800$		0			0
$801$	−33.8035	+	626.204i	−0.0422016	+	0.781778i
$802$		0			0
$803$	−1266.52	+	1266.52i	−1.57724	+	1.57724i
$804$		0			0
$805$	653.690	−	653.690i	0.812037	−	0.812037i
$806$		0			0
$807$	1232.17	+	33.2329i	1.52685	+	0.0411808i
$808$		0			0
$809$	−184.708			−0.228316			−0.114158	−	0.993463i	$-0.536417\pi$
$809$	−184.708			−0.228316			−0.114158	+	0.993463i	$0.536417\pi$
$810$		0			0
$811$	−585.531	+	585.531i	−0.721986	+	0.721986i	−0.969010	−	0.247023i	$-0.920548\pi$
$811$	−585.531	+	585.531i	−0.721986	+	0.721986i	0.247023	+	0.969010i	$0.420548\pi$
$812$		0			0
$813$	1024.56	+	1081.36i	1.26022	+	1.33008i
$814$		0			0
$815$			420.457i			0.515898i
$816$		0			0
$817$	231.235			0.283029
$818$		0			0
$819$	328.387	+	365.864i	0.400961	+	0.446720i
$820$		0			0
$821$	−659.299	−	659.299i	−0.803044	−	0.803044i	0.180526	−	0.983570i	$-0.442220\pi$
$821$	−659.299	−	659.299i	−0.803044	−	0.803044i	−0.983570	+	0.180526i	$0.942220\pi$
$822$		0			0
$823$		−	1397.61i		−	1.69819i	−0.528237	−	0.849097i	$-0.677147\pi$
$823$		−	1397.61i		−	1.69819i	0.528237	−	0.849097i	$-0.322853\pi$
$824$		0			0
$825$	263.792	+	7.11476i	0.319748	+	0.00862395i
$826$		0			0
$827$	−78.1971	−	78.1971i	−0.0945551	−	0.0945551i	0.658247	−	0.752802i	$-0.271298\pi$
$827$	−78.1971	−	78.1971i	−0.0945551	−	0.0945551i	−0.752802	+	0.658247i	$0.771298\pi$
$828$		0			0
$829$	30.4254	+	30.4254i	0.0367014	+	0.0367014i	0.725219	−	0.688518i	$-0.241738\pi$
$829$	30.4254	+	30.4254i	0.0367014	+	0.0367014i	−0.688518	+	0.725219i	$0.741738\pi$
$830$		0			0
$831$	−394.465	−	10.6392i	−0.474687	−	0.0128028i
$832$		0			0
$833$			55.0731i			0.0661141i
$834$		0			0
$835$	504.622	+	504.622i	0.604338	+	0.604338i
$836$		0			0
$837$	162.725	−	138.319i	0.194414	−	0.165255i
$838$		0			0
$839$	694.526			0.827802			0.413901	−	0.910322i	$-0.364166\pi$
$839$	694.526			0.827802			0.413901	+	0.910322i	$0.364166\pi$
$840$		0			0
$841$		−	722.489i		−	0.859084i
$842$		0			0
$843$	620.812	+	655.228i	0.736432	+	0.777258i
$844$		0			0
$845$	277.265	−	277.265i	0.328125	−	0.328125i
$846$		0			0
$847$	−1313.68			−1.55098
$848$		0			0
$849$	−430.341	−	11.6068i	−0.506880	−	0.0136711i
$850$		0			0
$851$	682.298	−	682.298i	0.801761	−	0.801761i
$852$		0			0
$853$	−727.489	+	727.489i	−0.852860	+	0.852860i	−0.990484	−	0.137625i	$-0.956053\pi$
$853$	−727.489	+	727.489i	−0.852860	+	0.852860i	0.137625	+	0.990484i	$0.456053\pi$
$854$		0			0
$855$	183.490	+	9.90506i	0.214608	+	0.0115849i
$856$		0			0
$857$	−1275.44			−1.48826			−0.744128	−	0.668037i	$-0.767135\pi$
$857$	−1275.44			−1.48826			−0.744128	+	0.668037i	$0.767135\pi$
$858$		0			0
$859$	2.20191	−	2.20191i	0.00256334	−	0.00256334i	−0.705824	−	0.708387i	$-0.749423\pi$
$859$	2.20191	−	2.20191i	0.00256334	−	0.00256334i	0.708387	+	0.705824i	$0.249423\pi$
$860$		0			0
$861$	−593.293	+	562.130i	−0.689074	+	0.652880i
$862$		0			0
$863$			1311.55i			1.51976i	0.650063	+	0.759880i	$0.274742\pi$
$863$			1311.55i			1.51976i	−0.650063	+	0.759880i	$0.725258\pi$
$864$		0			0
$865$	−489.622			−0.566037
$866$		0			0
$867$	−556.391	−	587.236i	−0.641743	−	0.677319i
$868$		0			0
$869$	−522.518	−	522.518i	−0.601287	−	0.601287i
$870$		0			0
$871$		−	574.496i		−	0.659582i
$872$		0			0
$873$	−29.6383	+	549.046i	−0.0339500	+	0.628918i
$874$		0			0
$875$	571.908	+	571.908i	0.653609	+	0.653609i
$876$		0			0
$877$	449.158	+	449.158i	0.512152	+	0.512152i	0.915185	−	0.403033i	$-0.132044\pi$
$877$	449.158	+	449.158i	0.512152	+	0.512152i	−0.403033	+	0.915185i	$0.632044\pi$
$878$		0			0
$879$	36.7303	−	1361.84i	0.0417864	−	1.54930i
$880$		0			0
$881$		−	982.786i		−	1.11553i	−0.829998	−	0.557767i	$-0.811658\pi$
$881$		−	982.786i		−	1.11553i	0.829998	−	0.557767i	$-0.188342\pi$
$882$		0			0
$883$	233.961	+	233.961i	0.264962	+	0.264962i	0.827066	−	0.562104i	$-0.190008\pi$
$883$	233.961	+	233.961i	0.264962	+	0.264962i	−0.562104	+	0.827066i	$0.690008\pi$
$884$		0			0
$885$	−540.999	+	512.582i	−0.611298	+	0.579189i
$886$		0			0
$887$	−1421.57			−1.60267			−0.801334	−	0.598217i	$-0.795876\pi$
$887$	−1421.57			−1.60267			−0.801334	+	0.598217i	$0.795876\pi$
$888$		0			0
$889$		−	565.527i		−	0.636138i
$890$		0			0
$891$	934.222	+	1161.10i	1.04851	+	1.30314i
$892$		0			0
$893$	16.3406	−	16.3406i	0.0182986	−	0.0182986i
$894$		0			0
$895$	644.558			0.720176
$896$		0			0
$897$	24.9010	−	923.246i	0.0277603	−	1.02926i
$898$		0			0
$899$	−221.159	+	221.159i	−0.246006	+	0.246006i
$900$		0			0
$901$	91.3508	−	91.3508i	0.101388	−	0.101388i
$902$		0			0
$903$	−24.8781	+	922.396i	−0.0275505	+	1.02148i
$904$		0			0
$905$	1350.50			1.49226
$906$		0			0
$907$	−358.736	+	358.736i	−0.395519	+	0.395519i	−0.876649	−	0.481130i	$-0.840226\pi$
$907$	−358.736	+	358.736i	−0.395519	+	0.395519i	0.481130	+	0.876649i	$0.340226\pi$
$908$		0			0
$909$	985.436	−	884.494i	1.08409	−	0.973041i
$910$		0			0
$911$			353.455i			0.387986i	0.981003	+	0.193993i	$0.0621439\pi$
$911$			353.455i			0.387986i	−0.981003	+	0.193993i	$0.937856\pi$
$912$		0			0
$913$	924.862			1.01299
$914$		0			0
$915$	690.100	−	653.852i	0.754207	−	0.714592i
$916$		0			0
$917$	−492.368	−	492.368i	−0.536934	−	0.536934i
$918$		0			0
$919$			1519.58i			1.65351i	0.562560	+	0.826757i	$0.309817\pi$
$919$			1519.58i			1.65351i	−0.562560	+	0.826757i	$0.690183\pi$
$920$		0			0
$921$	10.7785	−	399.631i	0.0117030	−	0.433910i
$922$		0			0
$923$	298.622	+	298.622i	0.323534	+	0.323534i
$924$		0			0
$925$	95.8309	+	95.8309i	0.103601	+	0.103601i
$926$		0			0
$927$	−514.915	−	27.7959i	−0.555464	−	0.0299848i
$928$		0			0
$929$			95.2916i			0.102574i	0.998684	+	0.0512872i	$0.0163324\pi$
$929$			95.2916i			0.102574i	−0.998684	+	0.0512872i	$0.983668\pi$
$930$		0			0
$931$	−40.2015	−	40.2015i	−0.0431810	−	0.0431810i
$932$		0			0
$933$	−506.991	−	535.097i	−0.543398	−	0.573523i
$934$		0			0
$935$	363.886			0.389182
$936$		0			0
$937$			701.772i			0.748956i	0.927236	+	0.374478i	$0.122178\pi$
$937$			701.772i			0.748956i	−0.927236	+	0.374478i	$0.877822\pi$
$938$		0			0
$939$	770.576	−	730.101i	0.820634	−	0.777530i
$940$		0			0
$941$	88.8345	−	88.8345i	0.0944044	−	0.0944044i	−0.658327	−	0.752732i	$-0.728736\pi$
$941$	88.8345	−	88.8345i	0.0944044	−	0.0944044i	0.752732	+	0.658327i	$0.228736\pi$
$942$		0			0
$943$	1535.41			1.62822
$944$		0			0
$945$	−59.2526	+	730.875i	−0.0627012	+	0.773413i
$946$		0			0
$947$	345.769	−	345.769i	0.365120	−	0.365120i	−0.500574	−	0.865694i	$-0.666878\pi$
$947$	345.769	−	345.769i	0.365120	−	0.365120i	0.865694	+	0.500574i	$0.166878\pi$
$948$		0			0
$949$	−622.588	+	622.588i	−0.656046	+	0.656046i
$950$		0			0
$951$	992.517	+	26.7693i	1.04366	+	0.0281486i
$952$		0			0
$953$	1627.75			1.70803			0.854013	−	0.520251i	$-0.174162\pi$
$953$	1627.75			1.70803			0.854013	+	0.520251i	$0.174162\pi$
$954$		0			0
$955$	−115.517	+	115.517i	−0.120961	+	0.120961i
$956$		0			0
$957$	−1501.08	−	1584.30i	−1.56853	−	1.65548i
$958$		0			0
$959$		−	148.283i		−	0.154623i
$960$		0			0
$961$	−898.433			−0.934894
$962$		0			0
$963$	−875.660	+	785.963i	−0.909304	+	0.816161i
$964$		0			0
$965$	149.785	+	149.785i	0.155218	+	0.155218i
$966$		0			0
$967$		−	1444.31i		−	1.49360i	−0.665049	−	0.746799i	$-0.731590\pi$
$967$		−	1444.31i		−	1.49360i	0.665049	−	0.746799i	$-0.268410\pi$
$968$		0			0
$969$	−59.8945	−	1.61542i	−0.0618106	−	0.00166710i
$970$		0			0
$971$	−165.972	−	165.972i	−0.170929	−	0.170929i	0.616458	−	0.787388i	$-0.288567\pi$
$971$	−165.972	−	165.972i	−0.170929	−	0.170929i	−0.787388	+	0.616458i	$0.788567\pi$
$972$		0			0
$973$	18.5371	+	18.5371i	0.0190515	+	0.0190515i
$974$		0			0
$975$	129.673	+	3.49742i	0.132998	+	0.00358710i
$976$		0			0
$977$		−	1708.09i		−	1.74830i	−0.485658	−	0.874149i	$-0.661420\pi$
$977$		−	1708.09i		−	1.74830i	0.485658	−	0.874149i	$-0.338580\pi$
$978$		0			0
$979$	−906.510	−	906.510i	−0.925955	−	0.925955i
$980$		0			0
$981$	713.955	−	640.822i	0.727783	−	0.653233i
$982$		0			0
$983$	285.345			0.290279			0.145140	−	0.989411i	$-0.453637\pi$
$983$	285.345			0.290279			0.145140	+	0.989411i	$0.453637\pi$
$984$		0			0
$985$			205.261i			0.208386i
$986$		0			0
$987$	63.4247	+	66.9408i	0.0642601	+	0.0678225i
$988$		0			0
$989$	1225.75	−	1225.75i	1.23938	−	1.23938i
$990$		0			0
$991$	437.191			0.441162			0.220581	−	0.975369i	$-0.429205\pi$
$991$	437.191			0.441162			0.220581	+	0.975369i	$0.429205\pi$
$992$		0			0
$993$	138.002	+	3.72207i	0.138975	+	0.00374831i
$994$		0			0
$995$	375.762	−	375.762i	0.377650	−	0.377650i
$996$		0			0
$997$	1029.10	−	1029.10i	1.03220	−	1.03220i	0.0327341	−	0.999464i	$-0.489579\pi$
$997$	1029.10	−	1029.10i	1.03220	−	1.03220i	0.999464	−	0.0327341i	$-0.0104215\pi$
$998$		0			0
$999$	−61.8458	+	762.862i	−0.0619077	+	0.763626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.c.161.4		20
3.2	odd	2	inner	384.3.i.c.161.3		20
4.3	odd	2		384.3.i.d.161.7		20
8.3	odd	2		48.3.i.b.29.3	yes	20
8.5	even	2		192.3.i.b.17.7		20
12.11	even	2		384.3.i.d.161.8		20
16.3	odd	4		48.3.i.b.5.8	yes	20
16.5	even	4	inner	384.3.i.c.353.3		20
16.11	odd	4		384.3.i.d.353.8		20
16.13	even	4		192.3.i.b.113.8		20
24.5	odd	2		192.3.i.b.17.8		20
24.11	even	2		48.3.i.b.29.8	yes	20
48.5	odd	4	inner	384.3.i.c.353.4		20
48.11	even	4		384.3.i.d.353.7		20
48.29	odd	4		192.3.i.b.113.7		20
48.35	even	4		48.3.i.b.5.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.3	✓	20	48.35	even	4
48.3.i.b.5.8	yes	20	16.3	odd	4
48.3.i.b.29.3	yes	20	8.3	odd	2
48.3.i.b.29.8	yes	20	24.11	even	2
192.3.i.b.17.7		20	8.5	even	2
192.3.i.b.17.8		20	24.5	odd	2
192.3.i.b.113.7		20	48.29	odd	4
192.3.i.b.113.8		20	16.13	even	4
384.3.i.c.161.3		20	3.2	odd	2	inner
384.3.i.c.161.4		20	1.1	even	1	trivial
384.3.i.c.353.3		20	16.5	even	4	inner
384.3.i.c.353.4		20	48.5	odd	4	inner
384.3.i.d.161.7		20	4.3	odd	2
384.3.i.d.161.8		20	12.11	even	2
384.3.i.d.353.7		20	48.11	even	4
384.3.i.d.353.8		20	16.11	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.06336 - 2.17774i) q^{3} +(3.17955 + 3.17955i) q^{5} +6.03979i q^{7} +(-0.485128 + 8.98692i) q^{9} +O(q^{10})\)	\(q+(-2.06336 - 2.17774i) q^{3} +(3.17955 + 3.17955i) q^{5} +6.03979i q^{7} +(-0.485128 + 8.98692i) q^{9} +(-13.0097 - 13.0097i) q^{11} +(-6.39520 - 6.39520i) q^{13} +(0.363700 - 13.4848i) q^{15} +4.39848i q^{17} +(-3.21075 - 3.21075i) q^{19} +(13.1531 - 12.4622i) q^{21} -34.0396 q^{23} -4.78097i q^{25} +(20.5722 - 17.4867i) q^{27} +(-27.9597 + 27.9597i) q^{29} +7.90993 q^{31} +(-1.48814 + 55.1754i) q^{33} +(-19.2038 + 19.2038i) q^{35} +(-20.0443 + 20.0443i) q^{37} +(-0.731530 + 27.1227i) q^{39} -45.1067 q^{41} +(-36.0095 + 36.0095i) q^{43} +(-30.1168 + 27.0318i) q^{45} +5.08935i q^{47} +12.5209 q^{49} +(9.57876 - 9.07563i) q^{51} +(-20.7687 - 20.7687i) q^{53} -82.7299i q^{55} +(-0.367268 + 13.6171i) q^{57} +(-39.0656 - 39.0656i) q^{59} +(49.8322 + 49.8322i) q^{61} +(-54.2791 - 2.93007i) q^{63} -40.6677i q^{65} +(44.9162 + 44.9162i) q^{67} +(70.2358 + 74.1295i) q^{69} -46.6947 q^{71} -97.3523i q^{73} +(-10.4117 + 9.86483i) q^{75} +(78.5758 - 78.5758i) q^{77} +40.1637 q^{79} +(-80.5293 - 8.71960i) q^{81} +(-35.5451 + 35.5451i) q^{83} +(-13.9852 + 13.9852i) q^{85} +(118.580 + 3.19823i) q^{87} +69.6795 q^{89} +(38.6257 - 38.6257i) q^{91} +(-16.3210 - 17.2258i) q^{93} -20.4174i q^{95} +61.0939 q^{97} +(123.228 - 110.606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3}+O(q^{10}) \) 20 * q - 6 * q^3	\( 20 q - 6 q^{3} - 92 q^{13} + 116 q^{15} - 52 q^{19} - 48 q^{21} + 18 q^{27} + 80 q^{31} + 60 q^{33} + 116 q^{37} + 172 q^{43} - 60 q^{45} - 364 q^{49} + 128 q^{51} + 244 q^{61} - 296 q^{63} + 356 q^{67} + 20 q^{69} - 146 q^{75} - 384 q^{79} - 188 q^{81} - 48 q^{85} + 136 q^{91} + 132 q^{93} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 - 92 * q^13 + 116 * q^15 - 52 * q^19 - 48 * q^21 + 18 * q^27 + 80 * q^31 + 60 * q^33 + 116 * q^37 + 172 * q^43 - 60 * q^45 - 364 * q^49 + 128 * q^51 + 244 * q^61 - 296 * q^63 + 356 * q^67 + 20 * q^69 - 146 * q^75 - 384 * q^79 - 188 * q^81 - 48 * q^85 + 136 * q^91 + 132 * q^93 + 472 * q^97 - 452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more