LMFDB - Embedded newform 192.4.k.a.47.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,4,Mod(47,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.3283667211$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	192.47
Dual form			192.4.k.a.143.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.71261 + 4.43190i) q^{3} +(3.17566 + 3.17566i) q^{5} +32.3513 q^{7} +(-12.2835 + 24.0440i) q^{9} +(16.0965 - 16.0965i) q^{11} +(-18.2871 - 18.2871i) q^{13} +(-5.45988 + 22.6886i) q^{15} +38.5606i q^{17} +(56.2887 - 56.2887i) q^{19} +(87.7565 + 143.378i) q^{21} +197.652i q^{23} -104.830i q^{25} +(-139.881 + 10.7831i) q^{27} +(-57.3016 + 57.3016i) q^{29} +148.290i q^{31} +(115.002 + 27.6746i) q^{33} +(102.737 + 102.737i) q^{35} +(-72.5852 + 72.5852i) q^{37} +(31.4408 - 130.652i) q^{39} -73.1133 q^{41} +(-226.984 - 226.984i) q^{43} +(-115.364 + 37.3476i) q^{45} +412.986 q^{47} +703.607 q^{49} +(-170.897 + 104.600i) q^{51} +(-94.8845 - 94.8845i) q^{53} +102.234 q^{55} +(402.155 + 96.7764i) q^{57} +(-344.070 + 344.070i) q^{59} +(-153.024 - 153.024i) q^{61} +(-397.386 + 777.856i) q^{63} -116.147i q^{65} +(603.490 - 603.490i) q^{67} +(-875.976 + 536.154i) q^{69} -711.320i q^{71} -687.773i q^{73} +(464.598 - 284.364i) q^{75} +(520.744 - 520.744i) q^{77} -162.513i q^{79} +(-427.233 - 590.689i) q^{81} +(-748.288 - 748.288i) q^{83} +(-122.455 + 122.455i) q^{85} +(-409.392 - 98.5180i) q^{87} -927.910 q^{89} +(-591.611 - 591.611i) q^{91} +(-657.206 + 402.253i) q^{93} +357.508 q^{95} -208.855 q^{97} +(189.304 + 584.747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	2.71261	+	4.43190i	0.522042	+	0.852920i
$3$	2.71261	+	4.43190i	0.522042	+	0.852920i
$4$		0			0
$5$	3.17566	+	3.17566i	0.284040	+	0.284040i	0.834718	−	0.550678i	$-0.185631\pi$
$5$	3.17566	+	3.17566i	0.284040	+	0.284040i	−0.550678	+	0.834718i	$0.685631\pi$
$6$		0			0
$7$	32.3513			1.74681			0.873403	−	0.486998i	$-0.161908\pi$
$7$	32.3513			1.74681			0.873403	+	0.486998i	$0.161908\pi$
$8$		0			0
$9$	−12.2835	+	24.0440i	−0.454943	+	0.890520i
$10$		0			0
$11$	16.0965	−	16.0965i	0.441208	−	0.441208i	−0.451210	−	0.892418i	$-0.649007\pi$
$11$	16.0965	−	16.0965i	0.441208	−	0.441208i	0.892418	+	0.451210i	$0.149007\pi$
$12$		0			0
$13$	−18.2871	−	18.2871i	−0.390148	−	0.390148i	0.484592	−	0.874740i	$-0.338968\pi$
$13$	−18.2871	−	18.2871i	−0.390148	−	0.390148i	−0.874740	+	0.484592i	$0.838968\pi$
$14$		0			0
$15$	−5.45988	+	22.6886i	−0.0939823	+	0.390544i
$16$		0			0
$17$			38.5606i			0.550136i	0.961425	+	0.275068i	$0.0887003\pi$
$17$			38.5606i			0.550136i	−0.961425	+	0.275068i	$0.911300\pi$
$18$		0			0
$19$	56.2887	−	56.2887i	0.679658	−	0.679658i	−0.280264	−	0.959923i	$-0.590422\pi$
$19$	56.2887	−	56.2887i	0.679658	−	0.679658i	0.959923	+	0.280264i	$0.0904222\pi$
$20$		0			0
$21$	87.7565	+	143.378i	0.911907	+	1.48988i
$22$		0			0
$23$			197.652i			1.79189i	0.444169	+	0.895943i	$0.353499\pi$
$23$			197.652i			1.79189i	−0.444169	+	0.895943i	$0.646501\pi$
$24$		0			0
$25$		−	104.830i		−	0.838643i
$26$		0			0
$27$	−139.881	+	10.7831i	−0.997042	+	0.0768593i
$28$		0			0
$29$	−57.3016	+	57.3016i	−0.366919	+	0.366919i	−0.866352	−	0.499433i	$-0.833542\pi$
$29$	−57.3016	+	57.3016i	−0.366919	+	0.366919i	0.499433	+	0.866352i	$0.333542\pi$
$30$		0			0
$31$			148.290i			0.859151i	0.903031	+	0.429575i	$0.141337\pi$
$31$			148.290i			0.859151i	−0.903031	+	0.429575i	$0.858663\pi$
$32$		0			0
$33$	115.002	+	27.6746i	0.606644	+	0.145986i
$34$		0			0
$35$	102.737	+	102.737i	0.496162	+	0.496162i
$36$		0			0
$37$	−72.5852	+	72.5852i	−0.322512	+	0.322512i	−0.849730	−	0.527218i	$-0.823235\pi$
$37$	−72.5852	+	72.5852i	−0.322512	+	0.322512i	0.527218	+	0.849730i	$0.323235\pi$
$38$		0			0
$39$	31.4408	−	130.652i	0.129091	−	0.536439i
$40$		0			0
$41$	−73.1133			−0.278497			−0.139249	−	0.990257i	$-0.544469\pi$
$41$	−73.1133			−0.278497			−0.139249	+	0.990257i	$0.544469\pi$
$42$		0			0
$43$	−226.984	−	226.984i	−0.804993	−	0.804993i	0.178878	−	0.983871i	$-0.442753\pi$
$43$	−226.984	−	226.984i	−0.804993	−	0.804993i	−0.983871	+	0.178878i	$0.942753\pi$
$44$		0			0
$45$	−115.364	+	37.3476i	−0.382165	+	0.123721i
$46$		0			0
$47$	412.986			1.28171			0.640853	−	0.767663i	$-0.278581\pi$
$47$	412.986			1.28171			0.640853	+	0.767663i	$0.278581\pi$
$48$		0			0
$49$	703.607			2.05133
$50$		0			0
$51$	−170.897	+	104.600i	−0.469222	+	0.287194i
$52$		0			0
$53$	−94.8845	−	94.8845i	−0.245913	−	0.245913i	0.573378	−	0.819291i	$-0.305633\pi$
$53$	−94.8845	−	94.8845i	−0.245913	−	0.245913i	−0.819291	+	0.573378i	$0.805633\pi$
$54$		0			0
$55$	102.234			0.250641
$56$		0			0
$57$	402.155	+	96.7764i	0.934504	+	0.224883i
$58$		0			0
$59$	−344.070	+	344.070i	−0.759222	+	0.759222i	−0.976181	−	0.216959i	$-0.930386\pi$
$59$	−344.070	+	344.070i	−0.759222	+	0.759222i	0.216959	+	0.976181i	$0.430386\pi$
$60$		0			0
$61$	−153.024	−	153.024i	−0.321193	−	0.321193i	0.528032	−	0.849225i	$-0.322930\pi$
$61$	−153.024	−	153.024i	−0.321193	−	0.321193i	−0.849225	+	0.528032i	$0.822930\pi$
$62$		0			0
$63$	−397.386	+	777.856i	−0.794698	+	1.55557i
$64$		0			0
$65$		−	116.147i		−	0.221635i
$66$		0			0
$67$	603.490	−	603.490i	1.10042	−	1.10042i	0.106058	−	0.994360i	$-0.466177\pi$
$67$	603.490	−	603.490i	1.10042	−	1.10042i	0.994360	−	0.106058i	$-0.0338228\pi$
$68$		0			0
$69$	−875.976	+	536.154i	−1.52833	+	0.935441i
$70$		0			0
$71$		−	711.320i		−	1.18899i	−0.804100	−	0.594494i	$-0.797353\pi$
$71$		−	711.320i		−	1.18899i	0.804100	−	0.594494i	$-0.202647\pi$
$72$		0			0
$73$		−	687.773i		−	1.10271i	−0.834271	−	0.551355i	$-0.814111\pi$
$73$		−	687.773i		−	1.10271i	0.834271	−	0.551355i	$-0.185889\pi$
$74$		0			0
$75$	464.598	−	284.364i	0.715295	−	0.437807i
$76$		0			0
$77$	520.744	−	520.744i	0.770704	−	0.770704i
$78$		0			0
$79$		−	162.513i		−	0.231445i	−0.993282	−	0.115723i	$-0.963082\pi$
$79$		−	162.513i		−	0.231445i	0.993282	−	0.115723i	$-0.0369184\pi$
$80$		0			0
$81$	−427.233	−	590.689i	−0.586053	−	0.810273i
$82$		0			0
$83$	−748.288	−	748.288i	−0.989582	−	0.989582i	0.0103646	−	0.999946i	$-0.496701\pi$
$83$	−748.288	−	748.288i	−0.989582	−	0.989582i	−0.999946	+	0.0103646i	$0.996701\pi$
$84$		0			0
$85$	−122.455	+	122.455i	−0.156260	+	0.156260i
$86$		0			0
$87$	−409.392	−	98.5180i	−0.504499	−	0.121405i
$88$		0			0
$89$	−927.910			−1.10515			−0.552575	−	0.833463i	$-0.686355\pi$
$89$	−927.910			−1.10515			−0.552575	+	0.833463i	$0.686355\pi$
$90$		0			0
$91$	−591.611	−	591.611i	−0.681513	−	0.681513i
$92$		0			0
$93$	−657.206	+	402.253i	−0.732786	+	0.448513i
$94$		0			0
$95$	357.508			0.386100
$96$		0			0
$97$	−208.855			−0.218618			−0.109309	−	0.994008i	$-0.534864\pi$
$97$	−208.855			−0.218618			−0.109309	+	0.994008i	$0.534864\pi$
$98$		0			0
$99$	189.304	+	584.747i	0.192180	+	0.593629i
$100$		0			0
$101$	−0.578244	−	0.578244i	−0.000569677	−	0.000569677i	0.706822	−	0.707392i	$-0.250128\pi$
$101$	−0.578244	−	0.578244i	−0.000569677	−	0.000569677i	−0.707392	+	0.706822i	$0.750128\pi$
$102$		0			0
$103$	1063.26			1.01715			0.508574	−	0.861018i	$-0.330173\pi$
$103$	1063.26			1.01715			0.508574	+	0.861018i	$0.330173\pi$
$104$		0			0
$105$	−176.634	+	734.004i	−0.164169	+	0.682205i
$106$		0			0
$107$	528.504	−	528.504i	0.477499	−	0.477499i	−0.426832	−	0.904331i	$-0.640370\pi$
$107$	528.504	−	528.504i	0.477499	−	0.477499i	0.904331	+	0.426832i	$0.140370\pi$
$108$		0			0
$109$	−522.214	−	522.214i	−0.458890	−	0.458890i	0.439401	−	0.898291i	$-0.355191\pi$
$109$	−522.214	−	522.214i	−0.458890	−	0.458890i	−0.898291	+	0.439401i	$0.855191\pi$
$110$		0			0
$111$	−518.586	−	124.795i	−0.443441	−	0.106712i
$112$		0			0
$113$			152.618i			0.127054i	0.997980	+	0.0635269i	$0.0202349\pi$
$113$			152.618i			0.127054i	−0.997980	+	0.0635269i	$0.979765\pi$
$114$		0			0
$115$	−627.677	+	627.677i	−0.508967	+	0.508967i
$116$		0			0
$117$	664.324	−	215.067i	0.524930	−	0.169939i
$118$		0			0
$119$			1247.48i			0.960980i
$120$		0			0
$121$			812.804i			0.610671i
$122$		0			0
$123$	−198.328	−	324.031i	−0.145387	−	0.237536i
$124$		0			0
$125$	729.863	−	729.863i	0.522248	−	0.522248i
$126$		0			0
$127$		−	399.802i		−	0.279344i	−0.990198	−	0.139672i	$-0.955395\pi$
$127$		−	399.802i		−	0.279344i	0.990198	−	0.139672i	$-0.0446048\pi$
$128$		0			0
$129$	390.250	−	1621.69i	0.266354	−	1.10683i
$130$		0			0
$131$	−1339.67	−	1339.67i	−0.893492	−	0.893492i	0.101358	−	0.994850i	$-0.467681\pi$
$131$	−1339.67	−	1339.67i	−0.893492	−	0.893492i	−0.994850	+	0.101358i	$0.967681\pi$
$132$		0			0
$133$	1821.01	−	1821.01i	1.18723	−	1.18723i
$134$		0			0
$135$	−478.459	−	409.972i	−0.305031	−	0.261369i
$136$		0			0
$137$	1598.46			0.996828			0.498414	−	0.866939i	$-0.333916\pi$
$137$	1598.46			0.996828			0.498414	+	0.866939i	$0.333916\pi$
$138$		0			0
$139$	1670.63	+	1670.63i	1.01943	+	1.01943i	0.999807	+	0.0196259i	$0.00624752\pi$
$139$	1670.63	+	1670.63i	1.01943	+	1.01943i	0.0196259	+	0.999807i	$0.493752\pi$
$140$		0			0
$141$	1120.27	+	1830.31i	0.669105	+	1.09319i
$142$		0			0
$143$	−588.717			−0.344273
$144$		0			0
$145$	−363.941			−0.208439
$146$		0			0
$147$	1908.61	+	3118.31i	1.07088	+	1.74962i
$148$		0			0
$149$	142.214	+	142.214i	0.0781919	+	0.0781919i	0.745121	−	0.666929i	$-0.232392\pi$
$149$	142.214	+	142.214i	0.0781919	+	0.0781919i	−0.666929	+	0.745121i	$0.732392\pi$
$150$		0			0
$151$	−1880.73			−1.01359			−0.506794	−	0.862067i	$-0.669169\pi$
$151$	−1880.73			−1.01359			−0.506794	+	0.862067i	$0.669169\pi$
$152$		0			0
$153$	−927.152	−	473.657i	−0.489907	−	0.250281i
$154$		0			0
$155$	−470.919	+	470.919i	−0.244033	+	0.244033i
$156$		0			0
$157$	1585.52	+	1585.52i	0.805976	+	0.805976i	0.984022	−	0.178046i	$-0.0569777\pi$
$157$	1585.52	+	1585.52i	0.805976	+	0.805976i	−0.178046	+	0.984022i	$0.556978\pi$
$158$		0			0
$159$	163.134	−	677.903i	0.0813670	−	0.338121i
$160$		0			0
$161$			6394.31i			3.13008i
$162$		0			0
$163$	721.338	−	721.338i	0.346623	−	0.346623i	−0.512227	−	0.858850i	$-0.671179\pi$
$163$	721.338	−	721.338i	0.346623	−	0.346623i	0.858850	+	0.512227i	$0.171179\pi$
$164$		0			0
$165$	277.322	+	453.092i	0.130845	+	0.213777i
$166$		0			0
$167$			2199.31i			1.01909i	0.860445	+	0.509544i	$0.170186\pi$
$167$			2199.31i			1.01909i	−0.860445	+	0.509544i	$0.829814\pi$
$168$		0			0
$169$		−	1528.17i		−	0.695569i
$170$		0			0
$171$	661.987	+	2044.83i	0.296044	+	0.914456i
$172$		0			0
$173$	450.646	−	450.646i	0.198046	−	0.198046i	−0.601116	−	0.799162i	$-0.705277\pi$
$173$	450.646	−	450.646i	0.198046	−	0.198046i	0.799162	+	0.601116i	$0.205277\pi$
$174$		0			0
$175$		−	3391.40i		−	1.46495i
$176$		0			0
$177$	−2458.21	−	591.555i	−1.04390	−	0.251209i
$178$		0			0
$179$	1160.45	+	1160.45i	0.484559	+	0.484559i	0.906584	−	0.422025i	$-0.138681\pi$
$179$	1160.45	+	1160.45i	0.484559	+	0.484559i	−0.422025	+	0.906584i	$0.638681\pi$
$180$		0			0
$181$	−125.614	+	125.614i	−0.0515847	+	0.0515847i	−0.732429	−	0.680844i	$-0.761613\pi$
$181$	−125.614	+	125.614i	−0.0515847	+	0.0515847i	0.680844	+	0.732429i	$0.261613\pi$
$182$		0			0
$183$	263.093	−	1093.29i	0.106275	−	0.441628i
$184$		0			0
$185$	−461.012			−0.183212
$186$		0			0
$187$	620.691	+	620.691i	0.242724	+	0.242724i
$188$		0			0
$189$	−4525.34	+	348.846i	−1.74164	+	0.134258i
$190$		0			0
$191$	3729.92			1.41302			0.706512	−	0.707702i	$-0.250268\pi$
$191$	3729.92			1.41302			0.706512	+	0.707702i	$0.250268\pi$
$192$		0			0
$193$	−3286.88			−1.22588			−0.612941	−	0.790129i	$-0.710014\pi$
$193$	−3286.88			−1.22588			−0.612941	+	0.790129i	$0.710014\pi$
$194$		0			0
$195$	514.753	−	315.062i	0.189037	−	0.115703i
$196$		0			0
$197$	−1961.53	−	1961.53i	−0.709406	−	0.709406i	0.257004	−	0.966410i	$-0.417264\pi$
$197$	−1961.53	−	1961.53i	−0.709406	−	0.709406i	−0.966410	+	0.257004i	$0.917264\pi$
$198$		0			0
$199$	202.789			0.0722380			0.0361190	−	0.999347i	$-0.488500\pi$
$199$	202.789			0.0722380			0.0361190	+	0.999347i	$0.488500\pi$
$200$		0			0
$201$	4311.64	+	1037.57i	1.51303	+	0.364103i
$202$		0			0
$203$	−1853.78	+	1853.78i	−0.640936	+	0.640936i
$204$		0			0
$205$	−232.183	−	232.183i	−0.0791043	−	0.0791043i
$206$		0			0
$207$	−4752.36	−	2427.86i	−1.59571	−	0.815207i
$208$		0			0
$209$		−	1812.10i		−	0.599741i
$210$		0			0
$211$	−2022.16	+	2022.16i	−0.659770	+	0.659770i	−0.955325	−	0.295556i	$-0.904495\pi$
$211$	−2022.16	+	2022.16i	−0.659770	+	0.659770i	0.295556	+	0.955325i	$0.404495\pi$
$212$		0			0
$213$	3152.50	−	1929.53i	1.01411	−	0.620702i
$214$		0			0
$215$		−	1441.65i		−	0.457300i
$216$		0			0
$217$			4797.37i			1.50077i
$218$		0			0
$219$	3048.14	−	1865.66i	0.940522	−	0.575661i
$220$		0			0
$221$	705.160	−	705.160i	0.214634	−	0.214634i
$222$		0			0
$223$			1803.88i			0.541688i	0.962623	+	0.270844i	$0.0873028\pi$
$223$			1803.88i			0.541688i	−0.962623	+	0.270844i	$0.912697\pi$
$224$		0			0
$225$	2520.55	+	1287.68i	0.746828	+	0.381535i
$226$		0			0
$227$	−1811.19	−	1811.19i	−0.529573	−	0.529573i	0.390872	−	0.920445i	$-0.372174\pi$
$227$	−1811.19	−	1811.19i	−0.529573	−	0.529573i	−0.920445	+	0.390872i	$0.872174\pi$
$228$		0			0
$229$	−1529.22	+	1529.22i	−0.441281	+	0.441281i	−0.892442	−	0.451161i	$-0.851010\pi$
$229$	−1529.22	+	1529.22i	−0.441281	+	0.441281i	0.451161	+	0.892442i	$0.351010\pi$
$230$		0			0
$231$	3720.46	+	895.308i	1.05969	+	0.255008i
$232$		0			0
$233$	−3502.19			−0.984703			−0.492352	−	0.870396i	$-0.663863\pi$
$233$	−3502.19			−0.984703			−0.492352	+	0.870396i	$0.663863\pi$
$234$		0			0
$235$	1311.50	+	1311.50i	0.364056	+	0.364056i
$236$		0			0
$237$	720.243	−	440.836i	0.197404	−	0.120824i
$238$		0			0
$239$	1874.23			0.507254			0.253627	−	0.967302i	$-0.418376\pi$
$239$	1874.23			0.507254			0.253627	+	0.967302i	$0.418376\pi$
$240$		0			0
$241$	−627.829			−0.167809			−0.0839046	−	0.996474i	$-0.526739\pi$
$241$	−627.829			−0.167809			−0.0839046	+	0.996474i	$0.526739\pi$
$242$		0			0
$243$	1458.96	−	3495.76i	0.385153	−	0.922853i
$244$		0			0
$245$	2234.42	+	2234.42i	0.582660	+	0.582660i
$246$		0			0
$247$	−2058.71			−0.530335
$248$		0			0
$249$	1286.52	−	5346.15i	0.327430	−	1.36064i
$250$		0			0
$251$	1278.26	−	1278.26i	0.321446	−	0.321446i	−0.527876	−	0.849322i	$-0.677011\pi$
$251$	1278.26	−	1278.26i	0.321446	−	0.321446i	0.849322	+	0.527876i	$0.177011\pi$
$252$		0			0
$253$	3181.52	+	3181.52i	0.790594	+	0.790594i
$254$		0			0
$255$	−874.883	−	210.536i	−0.214852	−	0.0517030i
$256$		0			0
$257$		−	4587.43i		−	1.11345i	−0.830698	−	0.556724i	$-0.812058\pi$
$257$		−	4587.43i		−	1.11345i	0.830698	−	0.556724i	$-0.187942\pi$
$258$		0			0
$259$	−2348.22	+	2348.22i	−0.563365	+	0.563365i
$260$		0			0
$261$	−673.900	−	2081.63i	−0.159821	−	0.493676i
$262$		0			0
$263$		−	1063.89i		−	0.249438i	−0.992192	−	0.124719i	$-0.960197\pi$
$263$		−	1063.89i		−	0.249438i	0.992192	−	0.124719i	$-0.0398029\pi$
$264$		0			0
$265$		−	602.642i		−	0.139698i
$266$		0			0
$267$	−2517.06	−	4112.40i	−0.576935	−	0.942603i
$268$		0			0
$269$	5167.40	−	5167.40i	1.17123	−	1.17123i	0.189318	−	0.981916i	$-0.439372\pi$
$269$	5167.40	−	5167.40i	1.17123	−	1.17123i	0.981916	−	0.189318i	$-0.0606276\pi$
$270$		0			0
$271$			6888.32i			1.54404i	0.635597	+	0.772021i	$0.280754\pi$
$271$			6888.32i			1.54404i	−0.635597	+	0.772021i	$0.719246\pi$
$272$		0			0
$273$	1017.15	−	4226.77i	0.225497	−	0.937054i
$274$		0			0
$275$	−1687.40	−	1687.40i	−0.370016	−	0.370016i
$276$		0			0
$277$	−2142.76	+	2142.76i	−0.464786	+	0.464786i	−0.900221	−	0.435434i	$-0.856595\pi$
$277$	−2142.76	+	2142.76i	−0.464786	+	0.464786i	0.435434	+	0.900221i	$0.356595\pi$
$278$		0			0
$279$	−3565.49	−	1821.52i	−0.765091	−	0.390865i
$280$		0			0
$281$	−7913.97			−1.68010			−0.840049	−	0.542510i	$-0.817474\pi$
$281$	−7913.97			−1.68010			−0.840049	+	0.542510i	$0.817474\pi$
$282$		0			0
$283$	−3967.83	−	3967.83i	−0.833438	−	0.833438i	0.154548	−	0.987985i	$-0.450608\pi$
$283$	−3967.83	−	3967.83i	−0.833438	−	0.833438i	−0.987985	+	0.154548i	$0.950608\pi$
$284$		0			0
$285$	969.780	+	1584.44i	0.201561	+	0.329312i
$286$		0			0
$287$	−2365.31			−0.486481
$288$		0			0
$289$	3426.08			0.697351
$290$		0			0
$291$	−566.541	−	925.622i	−0.114128	−	0.186464i
$292$		0			0
$293$	−5006.37	−	5006.37i	−0.998209	−	0.998209i	0.00178897	−	0.999998i	$-0.499431\pi$
$293$	−5006.37	−	5006.37i	−0.998209	−	0.998209i	−0.999998	+	0.00178897i	$0.999431\pi$
$294$		0			0
$295$	−2185.30			−0.431299
$296$		0			0
$297$	−2078.03	+	2425.17i	−0.405992	+	0.473814i
$298$		0			0
$299$	3614.49	−	3614.49i	0.699101	−	0.699101i
$300$		0			0
$301$	−7343.22	−	7343.22i	−1.40617	−	1.40617i
$302$		0			0
$303$	0.994167	−	4.13127i	0.000188493	−	0.000783284i
$304$		0			0
$305$		−	971.908i		−	0.182463i
$306$		0			0
$307$	1435.75	−	1435.75i	0.266914	−	0.266914i	−0.560942	−	0.827855i	$-0.689561\pi$
$307$	1435.75	−	1435.75i	0.266914	−	0.266914i	0.827855	+	0.560942i	$0.189561\pi$
$308$		0			0
$309$	2884.22	+	4712.27i	0.530995	+	0.867546i
$310$		0			0
$311$			3502.88i			0.638681i	0.947640	+	0.319341i	$0.103461\pi$
$311$			3502.88i			0.638681i	−0.947640	+	0.319341i	$0.896539\pi$
$312$		0			0
$313$		−	751.490i		−	0.135708i	−0.997695	−	0.0678542i	$-0.978385\pi$
$313$		−	751.490i		−	0.135708i	0.997695	−	0.0678542i	$-0.0216153\pi$
$314$		0			0
$315$	−3732.17	+	1208.24i	−0.667569	+	0.216117i
$316$		0			0
$317$	−6924.49	+	6924.49i	−1.22687	+	1.22687i	−0.261729	+	0.965141i	$0.584293\pi$
$317$	−6924.49	+	6924.49i	−1.22687	+	1.22687i	−0.965141	+	0.261729i	$0.915707\pi$
$318$		0			0
$319$			1844.71i			0.323775i
$320$		0			0
$321$	3775.90	+	908.650i	0.656543	+	0.157994i
$322$		0			0
$323$	2170.52	+	2170.52i	0.373904	+	0.373904i
$324$		0			0
$325$	−1917.04	+	1917.04i	−0.327195	+	0.327195i
$326$		0			0
$327$	897.836	−	3730.97i	0.151836	−	0.630957i
$328$		0			0
$329$	13360.6			2.23889
$330$		0			0
$331$	−3203.80	−	3203.80i	−0.532014	−	0.532014i	0.389157	−	0.921171i	$-0.372766\pi$
$331$	−3203.80	−	3203.80i	−0.532014	−	0.532014i	−0.921171	+	0.389157i	$0.872766\pi$
$332$		0			0
$333$	−853.644	−	2636.84i	−0.140479	−	0.433928i
$334$		0			0
$335$	3832.96			0.625125
$336$		0			0
$337$	2592.71			0.419091			0.209546	−	0.977799i	$-0.432802\pi$
$337$	2592.71			0.419091			0.209546	+	0.977799i	$0.432802\pi$
$338$		0			0
$339$	−676.387	+	413.993i	−0.108367	+	0.0663274i
$340$		0			0
$341$	2386.95	+	2386.95i	0.379064	+	0.379064i
$342$		0			0
$343$	11666.1			1.83647
$344$		0			0
$345$	−4484.45	−	1079.16i	−0.699810	−	0.168406i
$346$		0			0
$347$	−6043.76	+	6043.76i	−0.935003	+	0.935003i	−0.998013	−	0.0630095i	$-0.979930\pi$
$347$	−6043.76	+	6043.76i	−0.935003	+	0.935003i	0.0630095	+	0.998013i	$0.479930\pi$
$348$		0			0
$349$	−1836.04	−	1836.04i	−0.281607	−	0.281607i	0.552143	−	0.833750i	$-0.313810\pi$
$349$	−1836.04	−	1836.04i	−0.281607	−	0.281607i	−0.833750	+	0.552143i	$0.813810\pi$
$350$		0			0
$351$	2755.21	+	2360.83i	0.418980	+	0.359007i
$352$		0			0
$353$			7004.62i			1.05614i	0.849200	+	0.528071i	$0.177085\pi$
$353$			7004.62i			1.05614i	−0.849200	+	0.528071i	$0.822915\pi$
$354$		0			0
$355$	2258.91	−	2258.91i	0.337720	−	0.337720i
$356$		0			0
$357$	−5528.72	+	3383.94i	−0.819639	+	0.501673i
$358$		0			0
$359$		−	3792.90i		−	0.557609i	−0.960348	−	0.278805i	$-0.910062\pi$
$359$		−	3792.90i		−	0.557609i	0.960348	−	0.278805i	$-0.0899382\pi$
$360$		0			0
$361$			522.169i			0.0761291i
$362$		0			0
$363$	−3602.26	+	2204.82i	−0.520854	+	0.318796i
$364$		0			0
$365$	2184.14	−	2184.14i	0.313213	−	0.313213i
$366$		0			0
$367$			4167.61i			0.592773i	0.955068	+	0.296386i	$0.0957816\pi$
$367$			4167.61i			0.592773i	−0.955068	+	0.296386i	$0.904218\pi$
$368$		0			0
$369$	898.086	−	1757.94i	0.126700	−	0.248007i
$370$		0			0
$371$	−3069.64	−	3069.64i	−0.429562	−	0.429562i
$372$		0			0
$373$	−5292.64	+	5292.64i	−0.734698	+	0.734698i	−0.971547	−	0.236848i	$-0.923886\pi$
$373$	−5292.64	+	5292.64i	−0.734698	+	0.734698i	0.236848	+	0.971547i	$0.423886\pi$
$374$		0			0
$375$	5214.52	+	1254.85i	0.718071	+	0.172800i
$376$		0			0
$377$	2095.76			0.286305
$378$		0			0
$379$	4863.55	+	4863.55i	0.659165	+	0.659165i	0.955183	−	0.296017i	$-0.0956586\pi$
$379$	4863.55	+	4863.55i	0.659165	+	0.659165i	−0.296017	+	0.955183i	$0.595659\pi$
$380$		0			0
$381$	1771.88	−	1084.51i	0.238258	−	0.145829i
$382$		0			0
$383$	−6729.11			−0.897759			−0.448879	−	0.893592i	$-0.648177\pi$
$383$	−6729.11			−0.897759			−0.448879	+	0.893592i	$0.648177\pi$
$384$		0			0
$385$	3307.41			0.437821
$386$		0			0
$387$	8245.76	−	2669.46i	1.08309	−	0.350636i
$388$		0			0
$389$	1689.70	+	1689.70i	0.220234	+	0.220234i	0.808597	−	0.588363i	$-0.200227\pi$
$389$	1689.70	+	1689.70i	0.220234	+	0.220234i	−0.588363	+	0.808597i	$0.700227\pi$
$390$		0			0
$391$	−7621.59			−0.985781
$392$		0			0
$393$	2303.28	−	9571.28i	0.295636	−	1.22852i
$394$		0			0
$395$	516.087	−	516.087i	0.0657397	−	0.0657397i
$396$		0			0
$397$	8515.47	+	8515.47i	1.07652	+	1.07652i	0.996819	+	0.0797039i	$0.0253975\pi$
$397$	8515.47	+	8515.47i	1.07652	+	1.07652i	0.0797039	+	0.996819i	$0.474603\pi$
$398$		0			0
$399$	13010.2	+	3130.84i	1.63240	+	0.392828i
$400$		0			0
$401$		−	4257.88i		−	0.530246i	−0.964215	−	0.265123i	$-0.914588\pi$
$401$		−	4257.88i		−	0.530246i	0.964215	−	0.265123i	$-0.0854125\pi$
$402$		0			0
$403$	2711.79	−	2711.79i	0.335196	−	0.335196i
$404$		0			0
$405$	519.081	−	3232.57i	0.0636873	−	0.396612i
$406$		0			0
$407$			2336.74i			0.284589i
$408$		0			0
$409$		−	5141.14i		−	0.621548i	−0.950484	−	0.310774i	$-0.899412\pi$
$409$		−	5141.14i		−	0.621548i	0.950484	−	0.310774i	$-0.100588\pi$
$410$		0			0
$411$	4335.99	+	7084.20i	0.520386	+	0.850214i
$412$		0			0
$413$	−11131.1	+	11131.1i	−1.32621	+	1.32621i
$414$		0			0
$415$		−	4752.62i		−	0.562161i
$416$		0			0
$417$	−2872.30	+	11935.9i	−0.337307	+	1.40168i
$418$		0			0
$419$	9514.69	+	9514.69i	1.10936	+	1.10936i	0.993234	+	0.116129i	$0.0370487\pi$
$419$	9514.69	+	9514.69i	1.10936	+	1.10936i	0.116129	+	0.993234i	$0.462951\pi$
$420$		0			0
$421$	−942.451	+	942.451i	−0.109103	+	0.109103i	−0.759551	−	0.650448i	$-0.774581\pi$
$421$	−942.451	+	942.451i	−0.109103	+	0.109103i	0.650448	+	0.759551i	$0.274581\pi$
$422$		0			0
$423$	−5072.90	+	9929.86i	−0.583104	+	1.14139i
$424$		0			0
$425$	4042.32			0.461367
$426$		0			0
$427$	−4950.54	−	4950.54i	−0.561062	−	0.561062i
$428$		0			0
$429$	−1596.96	−	2609.13i	−0.179725	−	0.293637i
$430$		0			0
$431$	−106.218			−0.0118709			−0.00593543	−	0.999982i	$-0.501889\pi$
$431$	−106.218			−0.0118709			−0.00593543	+	0.999982i	$0.501889\pi$
$432$		0			0
$433$	4043.15			0.448733			0.224367	−	0.974505i	$-0.427969\pi$
$433$	4043.15			0.448733			0.224367	+	0.974505i	$0.427969\pi$
$434$		0			0
$435$	−987.231	−	1612.95i	−0.108814	−	0.177782i
$436$		0			0
$437$	11125.6	+	11125.6i	1.21787	+	1.21787i
$438$		0			0
$439$	2283.39			0.248246			0.124123	−	0.992267i	$-0.460388\pi$
$439$	2283.39			0.248246			0.124123	+	0.992267i	$0.460388\pi$
$440$		0			0
$441$	−8642.73	+	16917.6i	−0.933239	+	1.82675i
$442$		0			0
$443$	3308.60	−	3308.60i	0.354845	−	0.354845i	−0.507064	−	0.861909i	$-0.669269\pi$
$443$	3308.60	−	3308.60i	0.354845	−	0.354845i	0.861909	+	0.507064i	$0.169269\pi$
$444$		0			0
$445$	−2946.73	−	2946.73i	−0.313906	−	0.313906i
$446$		0			0
$447$	−244.506	+	1016.05i	−0.0258719	+	0.107511i
$448$		0			0
$449$			5247.10i			0.551506i	0.961229	+	0.275753i	$0.0889272\pi$
$449$			5247.10i			0.551506i	−0.961229	+	0.275753i	$0.911073\pi$
$450$		0			0
$451$	−1176.87	+	1176.87i	−0.122875	+	0.122875i
$452$		0			0
$453$	−5101.69	−	8335.21i	−0.529136	−	0.864509i
$454$		0			0
$455$		−	3757.51i		−	0.387154i
$456$		0			0
$457$		−	682.527i		−	0.0698627i	−0.999390	−	0.0349314i	$-0.988879\pi$
$457$		−	682.527i		−	0.0698627i	0.999390	−	0.0349314i	$-0.0111213\pi$
$458$		0			0
$459$	−415.801	−	5393.89i	−0.0422831	−	0.548508i
$460$		0			0
$461$	5158.76	−	5158.76i	0.521187	−	0.521187i	−0.396743	−	0.917930i	$-0.629859\pi$
$461$	5158.76	−	5158.76i	0.521187	−	0.521187i	0.917930	+	0.396743i	$0.129859\pi$
$462$		0			0
$463$		−	4260.25i		−	0.427625i	−0.976875	−	0.213813i	$-0.931412\pi$
$463$		−	4260.25i		−	0.427625i	0.976875	−	0.213813i	$-0.0685882\pi$
$464$		0			0
$465$	−3364.49	−	809.645i	−0.335536	−	0.0807449i
$466$		0			0
$467$	−501.947	−	501.947i	−0.0497374	−	0.0497374i	0.681801	−	0.731538i	$-0.261197\pi$
$467$	−501.947	−	501.947i	−0.0497374	−	0.0497374i	−0.731538	+	0.681801i	$0.761197\pi$
$468$		0			0
$469$	19523.7	−	19523.7i	1.92222	−	1.92222i
$470$		0			0
$471$	−2725.96	+	11327.8i	−0.266679	+	1.10819i
$472$		0			0
$473$	−7307.30			−0.710338
$474$		0			0
$475$	−5900.76	−	5900.76i	−0.569991	−	0.569991i
$476$		0			0
$477$	3446.92	−	1115.90i	0.330867	−	0.107114i
$478$		0			0
$479$	−15980.7			−1.52438			−0.762190	−	0.647353i	$-0.775876\pi$
$479$	−15980.7			−1.52438			−0.762190	+	0.647353i	$0.775876\pi$
$480$		0			0
$481$	2654.74			0.251655
$482$		0			0
$483$	−28339.0	+	17345.3i	−2.66970	+	1.63403i
$484$		0			0
$485$	−663.251	−	663.251i	−0.0620963	−	0.0620963i
$486$		0			0
$487$	−1901.65			−0.176945			−0.0884723	−	0.996079i	$-0.528198\pi$
$487$	−1901.65			−0.176945			−0.0884723	+	0.996079i	$0.528198\pi$
$488$		0			0
$489$	5153.61	+	1240.19i	0.476593	+	0.114690i
$490$		0			0
$491$	−5271.77	+	5271.77i	−0.484545	+	0.484545i	−0.906580	−	0.422035i	$-0.861316\pi$
$491$	−5271.77	+	5271.77i	−0.484545	+	0.484545i	0.422035	+	0.906580i	$0.361316\pi$
$492$		0			0
$493$	−2209.58	−	2209.58i	−0.201855	−	0.201855i
$494$		0			0
$495$	−1255.79	+	2458.13i	−0.114028	+	0.223201i
$496$		0			0
$497$		−	23012.1i		−	2.07693i
$498$		0			0
$499$	−29.4722	+	29.4722i	−0.00264400	+	0.00264400i	−0.708428	−	0.705784i	$-0.750595\pi$
$499$	−29.4722	+	29.4722i	−0.00264400	+	0.00264400i	0.705784	+	0.708428i	$0.250595\pi$
$500$		0			0
$501$	−9747.11	+	5965.87i	−0.869200	+	0.532007i
$502$		0			0
$503$		−	11304.7i		−	1.00209i	−0.865421	−	0.501045i	$-0.832949\pi$
$503$		−	11304.7i		−	1.00209i	0.865421	−	0.501045i	$-0.167051\pi$
$504$		0			0
$505$		−	3.67261i		−	0.000323622i
$506$		0			0
$507$	6772.68	−	4145.32i	0.593264	−	0.363117i
$508$		0			0
$509$	2527.57	−	2527.57i	0.220103	−	0.220103i	−0.588439	−	0.808542i	$-0.700257\pi$
$509$	2527.57	−	2527.57i	0.220103	−	0.220103i	0.808542	+	0.588439i	$0.200257\pi$
$510$		0			0
$511$		−	22250.4i		−	1.92622i
$512$		0			0
$513$	−7266.76	+	8480.69i	−0.625410	+	0.729886i
$514$		0			0
$515$	3376.56	+	3376.56i	0.288911	+	0.288911i
$516$		0			0
$517$	6647.64	−	6647.64i	0.565499	−	0.565499i
$518$		0			0
$519$	3219.65	+	774.790i	0.272306	+	0.0655289i
$520$		0			0
$521$	55.5878			0.00467437			0.00233719	−	0.999997i	$-0.499256\pi$
$521$	55.5878			0.00467437			0.00233719	+	0.999997i	$0.499256\pi$
$522$		0			0
$523$	14970.9	+	14970.9i	1.25169	+	1.25169i	0.954963	+	0.296723i	$0.0958940\pi$
$523$	14970.9	+	14970.9i	1.25169	+	1.25169i	0.296723	+	0.954963i	$0.404106\pi$
$524$		0			0
$525$	15030.3	−	9199.55i	1.24948	−	0.764764i
$526$		0			0
$527$	−5718.14			−0.472650
$528$		0			0
$529$	−26899.5			−2.21086
$530$		0			0
$531$	−4046.46	−	12499.2i	−0.330700	−	1.02151i
$532$		0			0
$533$	1337.03	+	1337.03i	0.108655	+	0.108655i
$534$		0			0
$535$	3356.70			0.271258
$536$		0			0
$537$	−1995.15	+	8290.85i	−0.160329	+	0.666250i
$538$		0			0
$539$	11325.6	−	11325.6i	0.905063	−	0.905063i
$540$		0			0
$541$	1527.27	+	1527.27i	0.121372	+	0.121372i	0.765184	−	0.643812i	$-0.222648\pi$
$541$	1527.27	+	1527.27i	0.121372	+	0.121372i	−0.643812	+	0.765184i	$0.722648\pi$
$542$		0			0
$543$	−897.452	−	215.967i	−0.0709270	−	0.0170682i
$544$		0			0
$545$		−	3316.75i		−	0.260686i
$546$		0			0
$547$	8402.23	−	8402.23i	0.656770	−	0.656770i	−0.297844	−	0.954615i	$-0.596268\pi$
$547$	8402.23	−	8402.23i	0.656770	−	0.656770i	0.954615	+	0.297844i	$0.0962676\pi$
$548$		0			0
$549$	5559.00	−	1799.66i	0.432154	−	0.139904i
$550$		0			0
$551$			6450.86i			0.498759i
$552$		0			0
$553$		−	5257.52i		−	0.404290i
$554$		0			0
$555$	−1250.55	−	2043.16i	−0.0956446	−	0.156265i
$556$		0			0
$557$	−11345.5	+	11345.5i	−0.863060	+	0.863060i	−0.991692	−	0.128633i	$-0.958941\pi$
$557$	−11345.5	+	11345.5i	−0.863060	+	0.863060i	0.128633	+	0.991692i	$0.458941\pi$
$558$		0			0
$559$			8301.74i			0.628133i
$560$		0			0
$561$	−1067.15	+	4434.53i	−0.0803119	+	0.333736i
$562$		0			0
$563$	6452.36	+	6452.36i	0.483010	+	0.483010i	0.906092	−	0.423082i	$-0.139052\pi$
$563$	6452.36	+	6452.36i	0.483010	+	0.483010i	−0.423082	+	0.906092i	$0.639052\pi$
$564$		0			0
$565$	−484.662	+	484.662i	−0.0360883	+	0.0360883i
$566$		0			0
$567$	−13821.5	−	19109.5i	−1.02372	−	1.41539i
$568$		0			0
$569$	−8010.89			−0.590218			−0.295109	−	0.955464i	$-0.595356\pi$
$569$	−8010.89			−0.590218			−0.295109	+	0.955464i	$0.595356\pi$
$570$		0			0
$571$	13548.1	+	13548.1i	0.992946	+	0.992946i	0.999975	−	0.00702892i	$-0.00223739\pi$
$571$	13548.1	+	13548.1i	0.992946	+	0.992946i	−0.00702892	+	0.999975i	$0.502237\pi$
$572$		0			0
$573$	10117.8	+	16530.6i	0.737658	+	1.20519i
$574$		0			0
$575$	20720.0			1.50275
$576$		0			0
$577$	3085.97			0.222652			0.111326	−	0.993784i	$-0.464490\pi$
$577$	3085.97			0.222652			0.111326	+	0.993784i	$0.464490\pi$
$578$		0			0
$579$	−8916.04	−	14567.1i	−0.639962	−	1.04558i
$580$		0			0
$581$	−24208.1	−	24208.1i	−1.72861	−	1.72861i
$582$		0			0
$583$	−3054.62			−0.216997
$584$		0			0
$585$	2792.65	+	1426.69i	0.197371	+	0.100831i
$586$		0			0
$587$	7599.07	−	7599.07i	0.534323	−	0.534323i	−0.387533	−	0.921856i	$-0.626673\pi$
$587$	7599.07	−	7599.07i	0.534323	−	0.534323i	0.921856	+	0.387533i	$0.126673\pi$
$588$		0			0
$589$	8347.05	+	8347.05i	0.583929	+	0.583929i
$590$		0			0
$591$	3372.43	−	14014.1i	0.234726	−	0.975406i
$592$		0			0
$593$		−	13043.4i		−	0.903253i	−0.892207	−	0.451627i	$-0.850844\pi$
$593$		−	13043.4i		−	0.903253i	0.892207	−	0.451627i	$-0.149156\pi$
$594$		0			0
$595$	−3961.59	+	3961.59i	−0.272957	+	0.272957i
$596$		0			0
$597$	550.089	+	898.742i	0.0377113	+	0.0616132i
$598$		0			0
$599$		−	12441.1i		−	0.848630i	−0.905515	−	0.424315i	$-0.860515\pi$
$599$		−	12441.1i		−	0.848630i	0.905515	−	0.424315i	$-0.139485\pi$
$600$		0			0
$601$		−	556.990i		−	0.0378038i	−0.999821	−	0.0189019i	$-0.993983\pi$
$601$		−	556.990i		−	0.0378038i	0.999821	−	0.0189019i	$-0.00601702\pi$
$602$		0			0
$603$	7097.39	+	21923.3i	0.479317	+	1.48057i
$604$		0			0
$605$	−2581.19	+	2581.19i	−0.173455	+	0.173455i
$606$		0			0
$607$		−	10080.8i		−	0.674080i	−0.941490	−	0.337040i	$-0.890574\pi$
$607$		−	10080.8i		−	0.674080i	0.941490	−	0.337040i	$-0.109426\pi$
$608$		0			0
$609$	−13244.4	−	3187.18i	−0.881262	−	0.212071i
$610$		0			0
$611$	−7552.31	−	7552.31i	−0.500055	−	0.500055i
$612$		0			0
$613$	−13360.3	+	13360.3i	−0.880290	+	0.880290i	−0.993564	−	0.113274i	$-0.963866\pi$
$613$	−13360.3	+	13360.3i	−0.880290	+	0.880290i	0.113274	+	0.993564i	$0.463866\pi$
$614$		0			0
$615$	399.190	−	1658.84i	0.0261738	−	0.108765i
$616$		0			0
$617$	28317.5			1.84768			0.923840	−	0.382779i	$-0.125033\pi$
$617$	28317.5			1.84768			0.923840	+	0.382779i	$0.125033\pi$
$618$		0			0
$619$	−5399.53	−	5399.53i	−0.350606	−	0.350606i	0.509729	−	0.860335i	$-0.329746\pi$
$619$	−5399.53	−	5399.53i	−0.350606	−	0.350606i	−0.860335	+	0.509729i	$0.829746\pi$
$620$		0			0
$621$	−2131.30	−	27647.8i	−0.137723	−	1.78659i
$622$		0			0
$623$	−30019.1			−1.93048
$624$		0			0
$625$	−8468.19			−0.541964
$626$		0			0
$627$	8031.06	−	4915.54i	0.511531	−	0.313090i
$628$		0			0
$629$	−2798.92	−	2798.92i	−0.177425	−	0.177425i
$630$		0			0
$631$	6123.81			0.386347			0.193174	−	0.981165i	$-0.438122\pi$
$631$	6123.81			0.386347			0.193174	+	0.981165i	$0.438122\pi$
$632$		0			0
$633$	−14447.4	−	3476.68i	−0.907158	−	0.218303i
$634$		0			0
$635$	1269.63	−	1269.63i	0.0793447	−	0.0793447i
$636$		0			0
$637$	−12866.9	−	12866.9i	−0.800323	−	0.800323i
$638$		0			0
$639$	17103.0	+	8737.47i	1.05882	+	0.540922i
$640$		0			0
$641$			20240.4i			1.24719i	0.781748	+	0.623594i	$0.214328\pi$
$641$			20240.4i			1.24719i	−0.781748	+	0.623594i	$0.785672\pi$
$642$		0			0
$643$	−12470.6	+	12470.6i	−0.764842	+	0.764842i	−0.977193	−	0.212352i	$-0.931888\pi$
$643$	−12470.6	+	12470.6i	−0.764842	+	0.764842i	0.212352	+	0.977193i	$0.431888\pi$
$644$		0			0
$645$	6389.24	−	3910.63i	0.390040	−	0.238730i
$646$		0			0
$647$			7081.47i			0.430296i	0.976581	+	0.215148i	$0.0690234\pi$
$647$			7081.47i			0.430296i	−0.976581	+	0.215148i	$0.930977\pi$
$648$		0			0
$649$			11076.7i			0.669949i
$650$		0			0
$651$	−21261.5	+	13013.4i	−1.28004	+	0.783465i
$652$		0			0
$653$	4674.02	−	4674.02i	0.280105	−	0.280105i	−0.553046	−	0.833151i	$-0.686535\pi$
$653$	4674.02	−	4674.02i	0.280105	−	0.280105i	0.833151	+	0.553046i	$0.186535\pi$
$654$		0			0
$655$		−	8508.67i		−	0.507575i
$656$		0			0
$657$	16536.9	+	8448.24i	0.981985	+	0.501670i
$658$		0			0
$659$	20967.1	+	20967.1i	1.23939	+	1.23939i	0.960249	+	0.279146i	$0.0900512\pi$
$659$	20967.1	+	20967.1i	1.23939	+	1.23939i	0.279146	+	0.960249i	$0.409949\pi$
$660$		0			0
$661$	17021.5	−	17021.5i	1.00160	−	1.00160i	0.00160195	−	0.999999i	$-0.499490\pi$
$661$	17021.5	−	17021.5i	1.00160	−	1.00160i	0.999999	−	0.00160195i	$-0.000509918\pi$
$662$		0			0
$663$	5038.02	+	1212.37i	0.295114	+	0.0710176i
$664$		0			0
$665$	11565.8			0.674442
$666$		0			0
$667$	−11325.8	−	11325.8i	−0.657477	−	0.657477i
$668$		0			0
$669$	−7994.60	+	4893.22i	−0.462016	+	0.282784i
$670$		0			0
$671$	−4926.32			−0.283426
$672$		0			0
$673$	5131.88			0.293937			0.146969	−	0.989141i	$-0.453048\pi$
$673$	5131.88			0.293937			0.146969	+	0.989141i	$0.453048\pi$
$674$		0			0
$675$	1130.39	+	14663.8i	0.0644575	+	0.836162i
$676$		0			0
$677$	7945.30	+	7945.30i	0.451053	+	0.451053i	0.895704	−	0.444651i	$-0.146672\pi$
$677$	7945.30	+	7945.30i	0.451053	+	0.451053i	−0.444651	+	0.895704i	$0.646672\pi$
$678$		0			0
$679$	−6756.72			−0.381884
$680$		0			0
$681$	3113.96	−	12940.1i	0.175224	−	0.728143i
$682$		0			0
$683$	−14603.2	+	14603.2i	−0.818121	+	0.818121i	−0.985836	−	0.167714i	$-0.946361\pi$
$683$	−14603.2	+	14603.2i	−0.818121	+	0.818121i	0.167714	+	0.985836i	$0.446361\pi$
$684$		0			0
$685$	5076.16	+	5076.16i	0.283139	+	0.283139i
$686$		0			0
$687$	−10925.5	−	2629.16i	−0.606745	−	0.146010i
$688$		0			0
$689$			3470.32i			0.191885i
$690$		0			0
$691$	−5956.77	+	5956.77i	−0.327940	+	0.327940i	−0.851803	−	0.523863i	$-0.824490\pi$
$691$	−5956.77	+	5956.77i	−0.327940	+	0.327940i	0.523863	+	0.851803i	$0.324490\pi$
$692$		0			0
$693$	6124.25	+	18917.3i	0.335701	+	1.03695i
$694$		0			0
$695$			10610.7i			0.579119i
$696$		0			0
$697$		−	2819.29i		−	0.153211i
$698$		0			0
$699$	−9500.07	−	15521.3i	−0.514057	−	0.839872i
$700$		0			0
$701$	−19922.3	+	19922.3i	−1.07340	+	1.07340i	−0.0763183	+	0.997084i	$0.524317\pi$
$701$	−19922.3	+	19922.3i	−1.07340	+	1.07340i	−0.997084	+	0.0763183i	$0.975683\pi$
$702$		0			0
$703$			8171.45i			0.438395i
$704$		0			0
$705$	−2254.85	+	9370.06i	−0.120458	+	0.500563i
$706$		0			0
$707$	−18.7069	−	18.7069i	−0.000995115	−	0.000995115i
$708$		0			0
$709$	−6339.66	+	6339.66i	−0.335812	+	0.335812i	−0.854789	−	0.518976i	$-0.826313\pi$
$709$	−6339.66	+	6339.66i	−0.335812	+	0.335812i	0.518976	+	0.854789i	$0.326313\pi$
$710$		0			0
$711$	3907.48	+	1996.23i	0.206107	+	0.105295i
$712$		0			0
$713$	−29309.9			−1.53950
$714$		0			0
$715$	−1869.57	−	1869.57i	−0.0977871	−	0.0977871i
$716$		0			0
$717$	5084.06	+	8306.39i	0.264808	+	0.432647i
$718$		0			0
$719$	23861.1			1.23765			0.618824	−	0.785530i	$-0.287610\pi$
$719$	23861.1			1.23765			0.618824	+	0.785530i	$0.287610\pi$
$720$		0			0
$721$	34397.9			1.77676
$722$		0			0
$723$	−1703.06	−	2782.47i	−0.0876035	−	0.143128i
$724$		0			0
$725$	6006.95	+	6006.95i	0.307714	+	0.307714i
$726$		0			0
$727$	−13991.5			−0.713776			−0.356888	−	0.934147i	$-0.616162\pi$
$727$	−13991.5			−0.713776			−0.356888	+	0.934147i	$0.616162\pi$
$728$		0			0
$729$	19450.5	−	3016.70i	0.988185	−	0.153264i
$730$		0			0
$731$	8752.62	−	8752.62i	0.442856	−	0.442856i
$732$		0			0
$733$	11874.1	+	11874.1i	0.598334	+	0.598334i	0.939869	−	0.341535i	$-0.110947\pi$
$733$	11874.1	+	11874.1i	0.598334	+	0.598334i	−0.341535	+	0.939869i	$0.610947\pi$
$734$		0			0
$735$	−3841.60	+	15963.8i	−0.192789	+	0.801135i
$736$		0			0
$737$		−	19428.2i		−	0.971026i
$738$		0			0
$739$	24843.0	−	24843.0i	1.23662	−	1.23662i	0.275253	−	0.961372i	$-0.411238\pi$
$739$	24843.0	−	24843.0i	1.23662	−	1.23662i	0.961372	−	0.275253i	$-0.0887615\pi$
$740$		0			0
$741$	−5584.49	−	9124.00i	−0.276857	−	0.452333i
$742$		0			0
$743$			12479.8i			0.616204i	0.951353	+	0.308102i	$0.0996939\pi$
$743$			12479.8i			0.616204i	−0.951353	+	0.308102i	$0.900306\pi$
$744$		0			0
$745$			903.245i			0.0444192i
$746$		0			0
$747$	27183.4	−	8800.30i	1.33145	−	0.431039i
$748$		0			0
$749$	17097.8	−	17097.8i	0.834098	−	0.834098i
$750$		0			0
$751$			34126.2i			1.65817i	0.559124	+	0.829084i	$0.311138\pi$
$751$			34126.2i			1.65817i	−0.559124	+	0.829084i	$0.688862\pi$
$752$		0			0
$753$	9132.53	+	2197.69i	0.441976	+	0.106359i
$754$		0			0
$755$	−5972.57	−	5972.57i	−0.287899	−	0.287899i
$756$		0			0
$757$	−7341.39	+	7341.39i	−0.352480	+	0.352480i	−0.861032	−	0.508551i	$-0.830181\pi$
$757$	−7341.39	+	7341.39i	−0.352480	+	0.352480i	0.508551	+	0.861032i	$0.330181\pi$
$758$		0			0
$759$	−5469.94	+	22730.4i	−0.261589	+	1.08704i
$760$		0			0
$761$	−18960.2			−0.903162			−0.451581	−	0.892230i	$-0.649140\pi$
$761$	−18960.2			−0.903162			−0.451581	+	0.892230i	$0.649140\pi$
$762$		0			0
$763$	−16894.3	−	16894.3i	−0.801592	−	0.801592i
$764$		0			0
$765$	−1440.15	−	4448.50i	−0.0680635	−	0.210243i
$766$		0			0
$767$	12584.1			0.592418
$768$		0			0
$769$	12020.7			0.563692			0.281846	−	0.959460i	$-0.409053\pi$
$769$	12020.7			0.563692			0.281846	+	0.959460i	$0.409053\pi$
$770$		0			0
$771$	20331.0	−	12443.9i	0.949681	−	0.581267i
$772$		0			0
$773$	18559.5	+	18559.5i	0.863568	+	0.863568i	0.991751	−	0.128183i	$-0.0409145\pi$
$773$	18559.5	+	18559.5i	0.863568	+	0.863568i	−0.128183	+	0.991751i	$0.540914\pi$
$774$		0			0
$775$	15545.3			0.720520
$776$		0			0
$777$	−16776.9	−	4037.27i	−0.774606	−	0.186405i
$778$		0			0
$779$	−4115.45	+	4115.45i	−0.189283	+	0.189283i
$780$		0			0
$781$	−11449.8	−	11449.8i	−0.524590	−	0.524590i
$782$		0			0
$783$	7397.53	−	8633.30i	0.337632	−	0.394034i
$784$		0			0
$785$			10070.1i			0.457858i
$786$		0			0
$787$	−6934.87	+	6934.87i	−0.314106	+	0.314106i	−0.846498	−	0.532392i	$-0.821293\pi$
$787$	−6934.87	+	6934.87i	−0.314106	+	0.314106i	0.532392	+	0.846498i	$0.321293\pi$
$788$		0			0
$789$	4715.05	−	2885.92i	0.212751	−	0.130217i
$790$		0			0
$791$			4937.38i			0.221938i
$792$		0			0
$793$			5596.74i			0.250626i
$794$		0			0
$795$	2670.85	−	1634.73i	0.119151	−	0.0729284i
$796$		0			0
$797$	1033.71	−	1033.71i	0.0459424	−	0.0459424i	−0.683762	−	0.729705i	$-0.739658\pi$
$797$	1033.71	−	1033.71i	0.0459424	−	0.0459424i	0.729705	+	0.683762i	$0.239658\pi$
$798$		0			0
$799$			15925.0i			0.705113i
$800$		0			0
$801$	11398.0	−	22310.7i	0.502780	−	0.984158i
$802$		0			0
$803$	−11070.8	−	11070.8i	−0.486524	−	0.486524i
$804$		0			0
$805$	−20306.2	+	20306.2i	−0.889067	+	0.889067i
$806$		0			0
$807$	36918.5	+	8884.24i	1.61040	+	0.387534i
$808$		0			0
$809$	28378.6			1.23330			0.616649	−	0.787239i	$-0.288490\pi$
$809$	28378.6			1.23330			0.616649	+	0.787239i	$0.288490\pi$
$810$		0			0
$811$	18955.2	+	18955.2i	0.820723	+	0.820723i	0.986212	−	0.165489i	$-0.0529202\pi$
$811$	18955.2	+	18955.2i	0.820723	+	0.820723i	−0.165489	+	0.986212i	$0.552920\pi$
$812$		0			0
$813$	−30528.3	+	18685.3i	−1.31694	+	0.806056i
$814$		0			0
$815$	4581.45			0.196909
$816$		0			0
$817$	−25553.2			−1.09424
$818$		0			0
$819$	21491.8	−	6957.69i	0.916951	−	0.296851i
$820$		0			0
$821$	26166.4	+	26166.4i	1.11232	+	1.11232i	0.992836	+	0.119482i	$0.0381233\pi$
$821$	26166.4	+	26166.4i	1.11232	+	1.11232i	0.119482	+	0.992836i	$0.461877\pi$
$822$		0			0
$823$	22421.9			0.949672			0.474836	−	0.880074i	$-0.342507\pi$
$823$	22421.9			0.949672			0.474836	+	0.880074i	$0.342507\pi$
$824$		0			0
$825$	2901.13	−	12055.7i	0.122430	−	0.508757i
$826$		0			0
$827$	−32421.5	+	32421.5i	−1.36325	+	1.36325i	−0.493501	+	0.869745i	$0.664283\pi$
$827$	−32421.5	+	32421.5i	−1.36325	+	1.36325i	−0.869745	+	0.493501i	$0.835717\pi$
$828$		0			0
$829$	508.732	+	508.732i	0.0213136	+	0.0213136i	0.717683	−	0.696370i	$-0.245203\pi$
$829$	508.732	+	508.732i	0.0213136	+	0.0213136i	−0.696370	+	0.717683i	$0.745203\pi$
$830$		0			0
$831$	−15309.0	−	3684.02i	−0.639063	−	0.153787i
$832$		0			0
$833$			27131.5i			1.12851i
$834$		0			0
$835$	−6984.26	+	6984.26i	−0.289461	+	0.289461i
$836$		0			0
$837$	−1599.02	−	20743.0i	−0.0660338	−	0.856609i
$838$		0			0
$839$		−	28733.8i		−	1.18236i	−0.806539	−	0.591181i	$-0.798662\pi$
$839$		−	28733.8i		−	1.18236i	0.806539	−	0.591181i	$-0.201338\pi$
$840$		0			0
$841$			17822.0i			0.730741i
$842$		0			0
$843$	−21467.5	−	35073.9i	−0.877083	−	1.43299i
$844$		0			0
$845$	4852.94	−	4852.94i	0.197569	−	0.197569i
$846$		0			0
$847$			26295.3i			1.06672i
$848$		0			0
$849$	6821.84	−	28348.2i	0.275765	−	1.14595i
$850$		0			0
$851$	−14346.6	−	14346.6i	−0.577904	−	0.577904i
$852$		0			0
$853$	−32516.7	+	32516.7i	−1.30522	+	1.30522i	−0.380390	+	0.924826i	$0.624210\pi$
$853$	−32516.7	+	32516.7i	−1.30522	+	1.30522i	−0.924826	+	0.380390i	$0.875790\pi$
$854$		0			0
$855$	−4391.43	+	8595.93i	−0.175654	+	0.343830i
$856$		0			0
$857$	−17192.8			−0.685292			−0.342646	−	0.939465i	$-0.611323\pi$
$857$	−17192.8			−0.685292			−0.342646	+	0.939465i	$0.611323\pi$
$858$		0			0
$859$	−28319.0	−	28319.0i	−1.12483	−	1.12483i	−0.991005	−	0.133827i	$-0.957273\pi$
$859$	−28319.0	−	28319.0i	−1.12483	−	1.12483i	−0.133827	−	0.991005i	$-0.542727\pi$
$860$		0			0
$861$	−6416.17	−	10482.8i	−0.253963	−	0.414929i
$862$		0			0
$863$	−25432.8			−1.00318			−0.501589	−	0.865106i	$-0.667251\pi$
$863$	−25432.8			−1.00318			−0.501589	+	0.865106i	$0.667251\pi$
$864$		0			0
$865$	2862.20			0.112506
$866$		0			0
$867$	9293.64	+	15184.1i	0.364047	+	0.594784i
$868$		0			0
$869$	−2615.90	−	2615.90i	−0.102115	−	0.102115i
$870$		0			0
$871$	−22072.1			−0.858652
$872$		0			0
$873$	2565.46	−	5021.71i	0.0994589	−	0.194684i
$874$		0			0
$875$	23612.0	−	23612.0i	0.912266	−	0.912266i
$876$		0			0
$877$	−34340.0	−	34340.0i	−1.32221	−	1.32221i	−0.911982	−	0.410231i	$-0.865448\pi$
$877$	−34340.0	−	34340.0i	−1.32221	−	1.32221i	−0.410231	−	0.911982i	$-0.634552\pi$
$878$		0			0
$879$	8607.39	−	35768.1i	0.330285	−	1.37250i
$880$		0			0
$881$			1486.40i			0.0568423i	0.999596	+	0.0284211i	$0.00904795\pi$
$881$			1486.40i			0.0568423i	−0.999596	+	0.0284211i	$0.990952\pi$
$882$		0			0
$883$	−26569.1	+	26569.1i	−1.01260	+	1.01260i	−0.0126765	+	0.999920i	$0.504035\pi$
$883$	−26569.1	+	26569.1i	−1.01260	+	1.01260i	−0.999920	+	0.0126765i	$0.995965\pi$
$884$		0			0
$885$	−5927.87	−	9685.03i	−0.225156	−	0.367863i
$886$		0			0
$887$		−	24047.1i		−	0.910284i	−0.890419	−	0.455142i	$-0.849588\pi$
$887$		−	24047.1i		−	0.910284i	0.890419	−	0.455142i	$-0.150412\pi$
$888$		0			0
$889$		−	12934.1i		−	0.487959i
$890$		0			0
$891$	−16385.0	−	2631.08i	−0.616070	−	0.0989274i
$892$		0			0
$893$	23246.4	−	23246.4i	0.871123	−	0.871123i
$894$		0			0
$895$			7370.39i			0.275268i
$896$		0			0
$897$	25823.7	+	6214.34i	0.961237	+	0.231316i
$898$		0			0
$899$	−8497.26	−	8497.26i	−0.315238	−	0.315238i
$900$		0			0
$901$	3658.80	−	3658.80i	0.135286	−	0.135286i
$902$		0			0
$903$	12625.1	−	52463.7i	0.465268	−	1.93343i
$904$		0			0
$905$	−797.817			−0.0293042
$906$		0			0
$907$	20817.3	+	20817.3i	0.762101	+	0.762101i	0.976702	−	0.214601i	$-0.0688451\pi$
$907$	20817.3	+	20817.3i	0.762101	+	0.762101i	−0.214601	+	0.976702i	$0.568845\pi$
$908$		0			0
$909$	21.0062	−	6.80048i	0.000766480	−	0.000248138i
$910$		0			0
$911$	9545.92			0.347168			0.173584	−	0.984819i	$-0.444465\pi$
$911$	9545.92			0.347168			0.173584	+	0.984819i	$0.444465\pi$
$912$		0			0
$913$	−24089.7			−0.873222
$914$		0			0
$915$	4307.40	−	2636.41i	0.155626	−	0.0952536i
$916$		0			0
$917$	−43340.0	−	43340.0i	−1.56076	−	1.56076i
$918$		0			0
$919$	12290.4			0.441156			0.220578	−	0.975369i	$-0.429206\pi$
$919$	12290.4			0.441156			0.220578	+	0.975369i	$0.429206\pi$
$920$		0			0
$921$	10257.7	+	2468.47i	0.366996	+	0.0883157i
$922$		0			0
$923$	−13008.0	+	13008.0i	−0.463881	+	0.463881i
$924$		0			0
$925$	7609.13	+	7609.13i	0.270472	+	0.270472i
$926$		0			0
$927$	−13060.5	+	25565.1i	−0.462745	+	0.905791i
$928$		0			0
$929$		−	26256.0i		−	0.927268i	−0.886027	−	0.463634i	$-0.846545\pi$
$929$		−	26256.0i		−	0.927268i	0.886027	−	0.463634i	$-0.153455\pi$
$930$		0			0
$931$	39605.1	−	39605.1i	1.39420	−	1.39420i
$932$		0			0
$933$	−15524.4	+	9501.94i	−0.544744	+	0.333419i
$934$		0			0
$935$			3942.21i			0.137887i
$936$		0			0
$937$		−	9723.86i		−	0.339023i	−0.985528	−	0.169512i	$-0.945781\pi$
$937$		−	9723.86i		−	0.339023i	0.985528	−	0.169512i	$-0.0542190\pi$
$938$		0			0
$939$	3330.53	−	2038.50i	0.115748	−	0.0708455i
$940$		0			0
$941$	−24237.0	+	24237.0i	−0.839644	+	0.839644i	−0.988812	−	0.149168i	$-0.952340\pi$
$941$	−24237.0	+	24237.0i	−0.839644	+	0.839644i	0.149168	+	0.988812i	$0.452340\pi$
$942$		0			0
$943$		−	14451.0i		−	0.499035i
$944$		0			0
$945$	−15478.8	−	13263.1i	−0.532830	−	0.456560i
$946$		0			0
$947$	−26385.5	−	26385.5i	−0.905399	−	0.905399i	0.0904976	−	0.995897i	$-0.471154\pi$
$947$	−26385.5	−	26385.5i	−0.905399	−	0.905399i	−0.995897	+	0.0904976i	$0.971154\pi$
$948$		0			0
$949$	−12577.4	+	12577.4i	−0.430220	+	0.430220i
$950$		0			0
$951$	−49472.1	−	11905.2i	−1.68690	−	0.405943i
$952$		0			0
$953$	11928.6			0.405464			0.202732	−	0.979234i	$-0.435018\pi$
$953$	11928.6			0.405464			0.202732	+	0.979234i	$0.435018\pi$
$954$		0			0
$955$	11845.0	+	11845.0i	0.401355	+	0.401355i
$956$		0			0
$957$	−8175.59	+	5003.99i	−0.276154	+	0.169024i
$958$		0			0
$959$	51712.2			1.74126
$960$		0			0
$961$	7801.07			0.261860
$962$		0			0
$963$	6215.51	+	19199.2i	0.207988	+	0.642458i
$964$		0			0
$965$	−10438.0	−	10438.0i	−0.348199	−	0.348199i
$966$		0			0
$967$	−52495.5			−1.74575			−0.872876	−	0.487943i	$-0.837748\pi$
$967$	−52495.5			−1.74575			−0.872876	+	0.487943i	$0.837748\pi$
$968$		0			0
$969$	−3731.75	+	15507.3i	−0.123716	+	0.514104i
$970$		0			0
$971$	8668.87	−	8668.87i	0.286506	−	0.286506i	−0.549191	−	0.835697i	$-0.685064\pi$
$971$	8668.87	−	8668.87i	0.286506	−	0.286506i	0.835697	+	0.549191i	$0.185064\pi$
$972$		0			0
$973$	54047.1	+	54047.1i	1.78075	+	1.78075i
$974$		0			0
$975$	−13696.3	−	3295.95i	−0.449880	−	0.108261i
$976$		0			0
$977$			34992.7i			1.14587i	0.819600	+	0.572936i	$0.194196\pi$
$977$			34992.7i			1.14587i	−0.819600	+	0.572936i	$0.805804\pi$
$978$		0			0
$979$	−14936.1	+	14936.1i	−0.487600	+	0.487600i
$980$		0			0
$981$	18970.7	−	6141.54i	0.617420	−	0.199882i
$982$		0			0
$983$			60755.5i			1.97131i	0.168767	+	0.985656i	$0.446021\pi$
$983$			60755.5i			1.97131i	−0.168767	+	0.985656i	$0.553979\pi$
$984$		0			0
$985$		−	12458.3i		−	0.402999i
$986$		0			0
$987$	36242.2	+	59213.0i	1.16880	+	1.90960i
$988$		0			0
$989$	44863.9	−	44863.9i	1.44246	−	1.44246i
$990$		0			0
$991$			1498.28i			0.0480268i	0.999712	+	0.0240134i	$0.00764444\pi$
$991$			1498.28i			0.0480268i	−0.999712	+	0.0240134i	$0.992356\pi$
$992$		0			0
$993$	5508.25	−	22889.6i	0.176031	−	0.731499i
$994$		0			0
$995$	643.990	+	643.990i	0.0205185	+	0.0205185i
$996$		0			0
$997$	43616.9	−	43616.9i	1.38552	−	1.38552i	0.551033	−	0.834484i	$-0.314234\pi$
$997$	43616.9	−	43616.9i	1.38552	−	1.38552i	0.834484	−	0.551033i	$-0.185766\pi$
$998$		0			0
$999$	9370.60	−	10936.0i	0.296770	−	0.346346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.4.k.a.47.16		44
3.2	odd	2	inner	192.4.k.a.47.4		44
4.3	odd	2		48.4.k.a.35.1	yes	44
8.3	odd	2		384.4.k.b.95.16		44
8.5	even	2		384.4.k.a.95.7		44
12.11	even	2		48.4.k.a.35.22	yes	44
16.3	odd	4		384.4.k.a.287.19		44
16.5	even	4		48.4.k.a.11.22	yes	44
16.11	odd	4	inner	192.4.k.a.143.4		44
16.13	even	4		384.4.k.b.287.4		44
24.5	odd	2		384.4.k.a.95.19		44
24.11	even	2		384.4.k.b.95.4		44
48.5	odd	4		48.4.k.a.11.1	✓	44
48.11	even	4	inner	192.4.k.a.143.16		44
48.29	odd	4		384.4.k.b.287.16		44
48.35	even	4		384.4.k.a.287.7		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.1	✓	44	48.5	odd	4
48.4.k.a.11.22	yes	44	16.5	even	4
48.4.k.a.35.1	yes	44	4.3	odd	2
48.4.k.a.35.22	yes	44	12.11	even	2
192.4.k.a.47.4		44	3.2	odd	2	inner
192.4.k.a.47.16		44	1.1	even	1	trivial
192.4.k.a.143.4		44	16.11	odd	4	inner
192.4.k.a.143.16		44	48.11	even	4	inner
384.4.k.a.95.7		44	8.5	even	2
384.4.k.a.95.19		44	24.5	odd	2
384.4.k.a.287.7		44	48.35	even	4
384.4.k.a.287.19		44	16.3	odd	4
384.4.k.b.95.4		44	24.11	even	2
384.4.k.b.95.16		44	8.3	odd	2
384.4.k.b.287.4		44	16.13	even	4
384.4.k.b.287.16		44	48.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.71261 + 4.43190i) q^{3} +(3.17566 + 3.17566i) q^{5} +32.3513 q^{7} +(-12.2835 + 24.0440i) q^{9} +(16.0965 - 16.0965i) q^{11} +(-18.2871 - 18.2871i) q^{13} +(-5.45988 + 22.6886i) q^{15} +38.5606i q^{17} +(56.2887 - 56.2887i) q^{19} +(87.7565 + 143.378i) q^{21} +197.652i q^{23} -104.830i q^{25} +(-139.881 + 10.7831i) q^{27} +(-57.3016 + 57.3016i) q^{29} +148.290i q^{31} +(115.002 + 27.6746i) q^{33} +(102.737 + 102.737i) q^{35} +(-72.5852 + 72.5852i) q^{37} +(31.4408 - 130.652i) q^{39} -73.1133 q^{41} +(-226.984 - 226.984i) q^{43} +(-115.364 + 37.3476i) q^{45} +412.986 q^{47} +703.607 q^{49} +(-170.897 + 104.600i) q^{51} +(-94.8845 - 94.8845i) q^{53} +102.234 q^{55} +(402.155 + 96.7764i) q^{57} +(-344.070 + 344.070i) q^{59} +(-153.024 - 153.024i) q^{61} +(-397.386 + 777.856i) q^{63} -116.147i q^{65} +(603.490 - 603.490i) q^{67} +(-875.976 + 536.154i) q^{69} -711.320i q^{71} -687.773i q^{73} +(464.598 - 284.364i) q^{75} +(520.744 - 520.744i) q^{77} -162.513i q^{79} +(-427.233 - 590.689i) q^{81} +(-748.288 - 748.288i) q^{83} +(-122.455 + 122.455i) q^{85} +(-409.392 - 98.5180i) q^{87} -927.910 q^{89} +(-591.611 - 591.611i) q^{91} +(-657.206 + 402.253i) q^{93} +357.508 q^{95} -208.855 q^{97} +(189.304 + 584.747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

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