LMFDB - Embedded newform 384.4.k.a.287.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.19
Character	$\chi$	$=$	384.287
Dual form			384.4.k.a.95.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.43190 - 2.71261i) q^{3} +(3.17566 - 3.17566i) q^{5} +32.3513 q^{7} +(12.2835 - 24.0440i) q^{9} +O(q^{10})$	\(q+(4.43190 - 2.71261i) q^{3} +(3.17566 - 3.17566i) q^{5} +32.3513 q^{7} +(12.2835 - 24.0440i) q^{9} +(16.0965 + 16.0965i) q^{11} +(18.2871 - 18.2871i) q^{13} +(5.45988 - 22.6886i) q^{15} +38.5606i q^{17} +(-56.2887 - 56.2887i) q^{19} +(143.378 - 87.7565i) q^{21} +197.652i q^{23} +104.830i q^{25} +(-10.7831 - 139.881i) q^{27} +(-57.3016 - 57.3016i) q^{29} -148.290i q^{31} +(115.002 + 27.6746i) q^{33} +(102.737 - 102.737i) q^{35} +(72.5852 + 72.5852i) q^{37} +(31.4408 - 130.652i) q^{39} +73.1133 q^{41} +(226.984 - 226.984i) q^{43} +(-37.3476 - 115.364i) q^{45} -412.986 q^{47} +703.607 q^{49} +(104.600 + 170.897i) q^{51} +(-94.8845 + 94.8845i) q^{53} +102.234 q^{55} +(-402.155 - 96.7764i) q^{57} +(-344.070 - 344.070i) q^{59} +(153.024 - 153.024i) q^{61} +(397.386 - 777.856i) q^{63} -116.147i q^{65} +(-603.490 - 603.490i) q^{67} +(536.154 + 875.976i) q^{69} -711.320i q^{71} +687.773i q^{73} +(284.364 + 464.598i) q^{75} +(520.744 + 520.744i) q^{77} +162.513i q^{79} +(-427.233 - 590.689i) q^{81} +(-748.288 + 748.288i) q^{83} +(122.455 + 122.455i) q^{85} +(-409.392 - 98.5180i) q^{87} +927.910 q^{89} +(591.611 - 591.611i) q^{91} +(-402.253 - 657.206i) q^{93} -357.508 q^{95} -208.855 q^{97} +(584.747 - 189.304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} + 8 q^{7}+O(q^{10}) $ 44 * q - 2 * q^3 + 8 * q^7	$ 44 q - 2 q^{3} + 8 q^{7} + 4 q^{13} + 20 q^{19} + 56 q^{21} - 134 q^{27} - 4 q^{33} + 4 q^{37} - 596 q^{39} - 436 q^{43} + 252 q^{45} + 972 q^{49} - 648 q^{51} - 280 q^{55} + 916 q^{61} - 1636 q^{67} - 52 q^{69} + 1454 q^{75} - 4 q^{81} - 736 q^{85} - 1284 q^{87} + 424 q^{91} + 2084 q^{93} - 8 q^{97} + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 + 8 * q^7 + 4 * q^13 + 20 * q^19 + 56 * q^21 - 134 * q^27 - 4 * q^33 + 4 * q^37 - 596 * q^39 - 436 * q^43 + 252 * q^45 + 972 * q^49 - 648 * q^51 - 280 * q^55 + 916 * q^61 - 1636 * q^67 - 52 * q^69 + 1454 * q^75 - 4 * q^81 - 736 * q^85 - 1284 * q^87 + 424 * q^91 + 2084 * q^93 - 8 * q^97 + 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.43190	−	2.71261i	0.852920	−	0.522042i
$3$	4.43190	−	2.71261i	0.852920	−	0.522042i
$4$		0			0
$5$	3.17566	−	3.17566i	0.284040	−	0.284040i	−0.550678	−	0.834718i	$-0.685631\pi$
$5$	3.17566	−	3.17566i	0.284040	−	0.284040i	0.834718	+	0.550678i	$0.185631\pi$
$6$		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	0.892418	−	0.451210i	$-0.149007\pi$
$11$	16.0965	+	16.0965i	0.441208	+	0.441208i	−0.451210	+	0.892418i	$0.649007\pi$
$12$		0			0
$13$	18.2871	−	18.2871i	0.390148	−	0.390148i	−0.484592	−	0.874740i	$-0.661032\pi$
$13$	18.2871	−	18.2871i	0.390148	−	0.390148i	0.874740	+	0.484592i	$0.161032\pi$
$14$		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	$-0.409578\pi$
$19$	−56.2887	−	56.2887i	−0.679658	−	0.679658i	−0.959923	+	0.280264i	$0.909578\pi$
$20$		0			0
$21$	143.378	−	87.7565i	1.48988	−	0.911907i
$22$		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
$27$	−10.7831	−	139.881i	−0.0768593	−	0.997042i
$28$		0			0
$29$	−57.3016	−	57.3016i	−0.366919	−	0.366919i	0.499433	−	0.866352i	$-0.333542\pi$
$29$	−57.3016	−	57.3016i	−0.366919	−	0.366919i	−0.866352	+	0.499433i	$0.833542\pi$
$30$		0			0
$31$		−	148.290i		−	0.859151i	−0.903031	−	0.429575i	$-0.858663\pi$
$31$		−	148.290i		−	0.859151i	0.903031	−	0.429575i	$-0.141337\pi$
$32$		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	$-0.176765\pi$
$37$	72.5852	+	72.5852i	0.322512	+	0.322512i	−0.527218	+	0.849730i	$0.676765\pi$
$38$		0			0
$39$	31.4408	−	130.652i	0.129091	−	0.536439i
$40$		0			0
$41$	73.1133			0.278497			0.139249	−	0.990257i	$-0.455531\pi$
$41$	73.1133			0.278497			0.139249	+	0.990257i	$0.455531\pi$
$42$		0			0
$43$	226.984	−	226.984i	0.804993	−	0.804993i	−0.178878	−	0.983871i	$-0.557247\pi$
$43$	226.984	−	226.984i	0.804993	−	0.804993i	0.983871	+	0.178878i	$0.0572468\pi$
$44$		0			0
$45$	−37.3476	−	115.364i	−0.123721	−	0.382165i
$46$		0			0
$47$	−412.986			−1.28171			−0.640853	−	0.767663i	$-0.721419\pi$
$47$	−412.986			−1.28171			−0.640853	+	0.767663i	$0.721419\pi$
$48$		0			0
$49$	703.607			2.05133
$50$		0			0
$51$	104.600	+	170.897i	0.287194	+	0.469222i
$52$		0			0
$53$	−94.8845	+	94.8845i	−0.245913	+	0.245913i	−0.819291	−	0.573378i	$-0.805633\pi$
$53$	−94.8845	+	94.8845i	−0.245913	+	0.245913i	0.573378	+	0.819291i	$0.305633\pi$
$54$		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	0.216959	−	0.976181i	$-0.430386\pi$
$59$	−344.070	−	344.070i	−0.759222	−	0.759222i	−0.976181	+	0.216959i	$0.930386\pi$
$60$		0			0
$61$	153.024	−	153.024i	0.321193	−	0.321193i	−0.528032	−	0.849225i	$-0.677070\pi$
$61$	153.024	−	153.024i	0.321193	−	0.321193i	0.849225	+	0.528032i	$0.177070\pi$
$62$		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	−0.994360	−	0.106058i	$-0.966177\pi$
$67$	−603.490	−	603.490i	−1.10042	−	1.10042i	−0.106058	−	0.994360i	$-0.533823\pi$
$68$		0			0
$69$	536.154	+	875.976i	0.935441	+	1.52833i
$70$		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	$0.185889\pi$
$73$			687.773i			1.10271i	−0.834271	+	0.551355i	$0.814111\pi$
$74$		0			0
$75$	284.364	+	464.598i	0.437807	+	0.715295i
$76$		0			0
$77$	520.744	+	520.744i	0.770704	+	0.770704i
$78$		0			0
$79$			162.513i			0.231445i	0.993282	+	0.115723i	$0.0369184\pi$
$79$			162.513i			0.231445i	−0.993282	+	0.115723i	$0.963082\pi$
$80$		0			0
$81$	−427.233	−	590.689i	−0.586053	−	0.810273i
$82$		0			0
$83$	−748.288	+	748.288i	−0.989582	+	0.989582i	−0.999946	−	0.0103646i	$-0.996701\pi$
$83$	−748.288	+	748.288i	−0.989582	+	0.989582i	0.0103646	+	0.999946i	$0.496701\pi$
$84$		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	$-0.313645\pi$
$89$	927.910			1.10515			0.552575	+	0.833463i	$0.313645\pi$
$90$		0			0
$91$	591.611	−	591.611i	0.681513	−	0.681513i
$92$		0			0
$93$	−402.253	−	657.206i	−0.448513	−	0.732786i
$94$		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
$99$	584.747	−	189.304i	0.593629	−	0.192180i
$100$		0			0
$101$	−0.578244	+	0.578244i	−0.000569677	+	0.000569677i	−0.707392	−	0.706822i	$-0.750128\pi$
$101$	−0.578244	+	0.578244i	−0.000569677	+	0.000569677i	0.706822	+	0.707392i	$0.250128\pi$
$102$		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	0.904331	−	0.426832i	$-0.140370\pi$
$107$	528.504	+	528.504i	0.477499	+	0.477499i	−0.426832	+	0.904331i	$0.640370\pi$
$108$		0			0
$109$	522.214	−	522.214i	0.458890	−	0.458890i	−0.439401	−	0.898291i	$-0.644809\pi$
$109$	522.214	−	522.214i	0.458890	−	0.458890i	0.898291	+	0.439401i	$0.144809\pi$
$110$		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
$117$	−215.067	−	664.324i	−0.169939	−	0.524930i
$118$		0			0
$119$			1247.48i			0.960980i
$120$		0			0
$121$		−	812.804i		−	0.610671i
$122$		0			0
$123$	324.031	−	198.328i	0.237536	−	0.145387i
$124$		0			0
$125$	729.863	+	729.863i	0.522248	+	0.522248i
$126$		0			0
$127$			399.802i			0.279344i	0.990198	+	0.139672i	$0.0446048\pi$
$127$			399.802i			0.279344i	−0.990198	+	0.139672i	$0.955395\pi$
$128$		0			0
$129$	390.250	−	1621.69i	0.266354	−	1.10683i
$130$		0			0
$131$	−1339.67	+	1339.67i	−0.893492	+	0.893492i	−0.994850	−	0.101358i	$-0.967681\pi$
$131$	−1339.67	+	1339.67i	−0.893492	+	0.893492i	0.101358	+	0.994850i	$0.467681\pi$
$132$		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	$-0.666084\pi$
$137$	−1598.46			−0.996828			−0.498414	+	0.866939i	$0.666084\pi$
$138$		0			0
$139$	−1670.63	+	1670.63i	−1.01943	+	1.01943i	−0.0196259	+	0.999807i	$0.506248\pi$
$139$	−1670.63	+	1670.63i	−1.01943	+	1.01943i	−0.999807	+	0.0196259i	$0.993752\pi$
$140$		0			0
$141$	−1830.31	+	1120.27i	−1.09319	+	0.669105i
$142$		0			0
$143$	588.717			0.344273
$144$		0			0
$145$	−363.941			−0.208439
$146$		0			0
$147$	3118.31	−	1908.61i	1.74962	−	1.07088i
$148$		0			0
$149$	142.214	−	142.214i	0.0781919	−	0.0781919i	−0.666929	−	0.745121i	$-0.732392\pi$
$149$	142.214	−	142.214i	0.0781919	−	0.0781919i	0.745121	+	0.666929i	$0.232392\pi$
$150$		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	$-0.943022\pi$
$157$	−1585.52	+	1585.52i	−0.805976	+	0.805976i	0.178046	+	0.984022i	$0.443022\pi$
$158$		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	$-0.328821\pi$
$163$	−721.338	−	721.338i	−0.346623	−	0.346623i	−0.858850	+	0.512227i	$0.828821\pi$
$164$		0			0
$165$	453.092	−	277.322i	0.213777	−	0.130845i
$166$		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
$171$	−2044.83	+	661.987i	−0.914456	+	0.296044i
$172$		0			0
$173$	450.646	+	450.646i	0.198046	+	0.198046i	0.799162	−	0.601116i	$-0.205277\pi$
$173$	450.646	+	450.646i	0.198046	+	0.198046i	−0.601116	+	0.799162i	$0.705277\pi$
$174$		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	−0.422025	−	0.906584i	$-0.638681\pi$
$179$	1160.45	−	1160.45i	0.484559	−	0.484559i	0.906584	+	0.422025i	$0.138681\pi$
$180$		0			0
$181$	125.614	+	125.614i	0.0515847	+	0.0515847i	0.732429	−	0.680844i	$-0.238387\pi$
$181$	125.614	+	125.614i	0.0515847	+	0.0515847i	−0.680844	+	0.732429i	$0.738387\pi$
$182$		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
$189$	−348.846	−	4525.34i	−0.134258	−	1.74164i
$190$		0			0
$191$	−3729.92			−1.41302			−0.706512	−	0.707702i	$-0.749732\pi$
$191$	−3729.92			−1.41302			−0.706512	+	0.707702i	$0.749732\pi$
$192$		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
$195$	−315.062	−	514.753i	−0.115703	−	0.189037i
$196$		0			0
$197$	−1961.53	+	1961.53i	−0.709406	+	0.709406i	−0.966410	−	0.257004i	$-0.917264\pi$
$197$	−1961.53	+	1961.53i	−0.709406	+	0.709406i	0.257004	+	0.966410i	$0.417264\pi$
$198$		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	$-0.0955048\pi$
$211$	2022.16	+	2022.16i	0.659770	+	0.659770i	−0.295556	+	0.955325i	$0.595505\pi$
$212$		0			0
$213$	−1929.53	−	3152.50i	−0.620702	−	1.01411i
$214$		0			0
$215$		−	1441.65i		−	0.457300i
$216$		0			0
$217$		−	4797.37i		−	1.50077i
$218$		0			0
$219$	1865.66	+	3048.14i	0.575661	+	0.940522i
$220$		0			0
$221$	705.160	+	705.160i	0.214634	+	0.214634i
$222$		0			0
$223$		−	1803.88i		−	0.541688i	−0.962623	−	0.270844i	$-0.912697\pi$
$223$		−	1803.88i		−	0.541688i	0.962623	−	0.270844i	$-0.0873028\pi$
$224$		0			0
$225$	2520.55	+	1287.68i	0.746828	+	0.381535i
$226$		0			0
$227$	−1811.19	+	1811.19i	−0.529573	+	0.529573i	−0.920445	−	0.390872i	$-0.872174\pi$
$227$	−1811.19	+	1811.19i	−0.529573	+	0.529573i	0.390872	+	0.920445i	$0.372174\pi$
$228$		0			0
$229$	1529.22	+	1529.22i	0.441281	+	0.441281i	0.892442	−	0.451161i	$-0.148990\pi$
$229$	1529.22	+	1529.22i	0.441281	+	0.441281i	−0.451161	+	0.892442i	$0.648990\pi$
$230$		0			0
$231$	3720.46	+	895.308i	1.05969	+	0.255008i
$232$		0			0
$233$	3502.19			0.984703			0.492352	−	0.870396i	$-0.336137\pi$
$233$	3502.19			0.984703			0.492352	+	0.870396i	$0.336137\pi$
$234$		0			0
$235$	−1311.50	+	1311.50i	−0.364056	+	0.364056i
$236$		0			0
$237$	440.836	+	720.243i	0.120824	+	0.197404i
$238$		0			0
$239$	−1874.23			−0.507254			−0.253627	−	0.967302i	$-0.581624\pi$
$239$	−1874.23			−0.507254			−0.253627	+	0.967302i	$0.581624\pi$
$240$		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
$243$	−3495.76	−	1458.96i	−0.922853	−	0.385153i
$244$		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	0.849322	−	0.527876i	$-0.177011\pi$
$251$	1278.26	+	1278.26i	0.321446	+	0.321446i	−0.527876	+	0.849322i	$0.677011\pi$
$252$		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
$261$	−2081.63	+	673.900i	−0.493676	+	0.159821i
$262$		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
$267$	4112.40	−	2517.06i	0.942603	−	0.576935i
$268$		0			0
$269$	5167.40	+	5167.40i	1.17123	+	1.17123i	0.981916	+	0.189318i	$0.0606276\pi$
$269$	5167.40	+	5167.40i	1.17123	+	1.17123i	0.189318	+	0.981916i	$0.439372\pi$
$270$		0			0
$271$		−	6888.32i		−	1.54404i	−0.635597	−	0.772021i	$-0.719246\pi$
$271$		−	6888.32i		−	1.54404i	0.635597	−	0.772021i	$-0.280754\pi$
$272$		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	$-0.143405\pi$
$277$	2142.76	+	2142.76i	0.464786	+	0.464786i	−0.435434	+	0.900221i	$0.643405\pi$
$278$		0			0
$279$	−3565.49	−	1821.52i	−0.765091	−	0.390865i
$280$		0			0
$281$	7913.97			1.68010			0.840049	−	0.542510i	$-0.182526\pi$
$281$	7913.97			1.68010			0.840049	+	0.542510i	$0.182526\pi$
$282$		0			0
$283$	3967.83	−	3967.83i	0.833438	−	0.833438i	−0.154548	−	0.987985i	$-0.549392\pi$
$283$	3967.83	−	3967.83i	0.833438	−	0.833438i	0.987985	+	0.154548i	$0.0493920\pi$
$284$		0			0
$285$	−1584.44	+	969.780i	−0.329312	+	0.201561i
$286$		0			0
$287$	2365.31			0.486481
$288$		0			0
$289$	3426.08			0.697351
$290$		0			0
$291$	−925.622	+	566.541i	−0.186464	+	0.114128i
$292$		0			0
$293$	−5006.37	+	5006.37i	−0.998209	+	0.998209i	−0.999998	−	0.00178897i	$-0.999431\pi$
$293$	−5006.37	+	5006.37i	−0.998209	+	0.998209i	0.00178897	+	0.999998i	$0.499431\pi$
$294$		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	$-0.310439\pi$
$307$	−1435.75	−	1435.75i	−0.266914	−	0.266914i	−0.827855	+	0.560942i	$0.810439\pi$
$308$		0			0
$309$	4712.27	−	2884.22i	0.867546	−	0.530995i
$310$		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	$0.0216153\pi$
$313$			751.490i			0.135708i	−0.997695	+	0.0678542i	$0.978385\pi$
$314$		0			0
$315$	−1208.24	−	3732.17i	−0.216117	−	0.667569i
$316$		0			0
$317$	−6924.49	−	6924.49i	−1.22687	−	1.22687i	−0.965141	−	0.261729i	$-0.915707\pi$
$317$	−6924.49	−	6924.49i	−1.22687	−	1.22687i	−0.261729	−	0.965141i	$-0.584293\pi$
$318$		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	$-0.627234\pi$
$331$	3203.80	−	3203.80i	0.532014	−	0.532014i	0.921171	+	0.389157i	$0.127234\pi$
$332$		0			0
$333$	2636.84	−	853.644i	0.433928	−	0.140479i
$334$		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
$339$	413.993	+	676.387i	0.0663274	+	0.108367i
$340$		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	0.0630095	−	0.998013i	$-0.479930\pi$
$347$	−6043.76	−	6043.76i	−0.935003	−	0.935003i	−0.998013	+	0.0630095i	$0.979930\pi$
$348$		0			0
$349$	1836.04	−	1836.04i	0.281607	−	0.281607i	−0.552143	−	0.833750i	$-0.686190\pi$
$349$	1836.04	−	1836.04i	0.281607	−	0.281607i	0.833750	+	0.552143i	$0.186190\pi$
$350$		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
$357$	3383.94	+	5528.72i	0.501673	+	0.819639i
$358$		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
$363$	−2204.82	−	3602.26i	−0.318796	−	0.520854i
$364$		0			0
$365$	2184.14	+	2184.14i	0.313213	+	0.313213i
$366$		0			0
$367$		−	4167.61i		−	0.592773i	−0.955068	−	0.296386i	$-0.904218\pi$
$367$		−	4167.61i		−	0.592773i	0.955068	−	0.296386i	$-0.0957816\pi$
$368$		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	$-0.0761144\pi$
$373$	5292.64	+	5292.64i	0.734698	+	0.734698i	−0.236848	+	0.971547i	$0.576114\pi$
$374$		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	$-0.904341\pi$
$379$	−4863.55	+	4863.55i	−0.659165	+	0.659165i	0.296017	+	0.955183i	$0.404341\pi$
$380$		0			0
$381$	1084.51	+	1771.88i	0.145829	+	0.238258i
$382$		0			0
$383$	6729.11			0.897759			0.448879	−	0.893592i	$-0.351823\pi$
$383$	6729.11			0.897759			0.448879	+	0.893592i	$0.351823\pi$
$384$		0			0
$385$	3307.41			0.437821
$386$		0			0
$387$	−2669.46	−	8245.76i	−0.350636	−	1.08309i
$388$		0			0
$389$	1689.70	−	1689.70i	0.220234	−	0.220234i	−0.588363	−	0.808597i	$-0.700227\pi$
$389$	1689.70	−	1689.70i	0.220234	−	0.220234i	0.808597	+	0.588363i	$0.200227\pi$
$390$		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	−0.0797039	+	0.996819i	$0.525397\pi$
$397$	−8515.47	+	8515.47i	−1.07652	+	1.07652i	−0.996819	+	0.0797039i	$0.974603\pi$
$398$		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
$405$	−3232.57	−	519.081i	−0.396612	−	0.0636873i
$406$		0			0
$407$			2336.74i			0.284589i
$408$		0			0
$409$			5141.14i			0.621548i	0.950484	+	0.310774i	$0.100588\pi$
$409$			5141.14i			0.621548i	−0.950484	+	0.310774i	$0.899412\pi$
$410$		0			0
$411$	−7084.20	+	4335.99i	−0.850214	+	0.520386i
$412$		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	0.116129	−	0.993234i	$-0.462951\pi$
$419$	9514.69	−	9514.69i	1.10936	−	1.10936i	0.993234	−	0.116129i	$-0.0370487\pi$
$420$		0			0
$421$	942.451	+	942.451i	0.109103	+	0.109103i	0.759551	−	0.650448i	$-0.225419\pi$
$421$	942.451	+	942.451i	0.109103	+	0.109103i	−0.650448	+	0.759551i	$0.725419\pi$
$422$		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
$429$	2609.13	−	1596.96i	0.293637	−	0.179725i
$430$		0			0
$431$	106.218			0.0118709			0.00593543	−	0.999982i	$-0.498111\pi$
$431$	106.218			0.0118709			0.00593543	+	0.999982i	$0.498111\pi$
$432$		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
$435$	−1612.95	+	987.231i	−0.177782	+	0.108814i
$436$		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	0.861909	−	0.507064i	$-0.169269\pi$
$443$	3308.60	+	3308.60i	0.354845	+	0.354845i	−0.507064	+	0.861909i	$0.669269\pi$
$444$		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
$453$	−8335.21	+	5101.69i	−0.864509	+	0.529136i
$454$		0			0
$455$		−	3757.51i		−	0.387154i
$456$		0			0
$457$			682.527i			0.0698627i	0.999390	+	0.0349314i	$0.0111213\pi$
$457$			682.527i			0.0698627i	−0.999390	+	0.0349314i	$0.988879\pi$
$458$		0			0
$459$	5393.89	−	415.801i	0.548508	−	0.0422831i
$460$		0			0
$461$	5158.76	+	5158.76i	0.521187	+	0.521187i	0.917930	−	0.396743i	$-0.129859\pi$
$461$	5158.76	+	5158.76i	0.521187	+	0.521187i	−0.396743	+	0.917930i	$0.629859\pi$
$462$		0			0
$463$			4260.25i			0.427625i	0.976875	+	0.213813i	$0.0685882\pi$
$463$			4260.25i			0.427625i	−0.976875	+	0.213813i	$0.931412\pi$
$464$		0			0
$465$	−3364.49	−	809.645i	−0.335536	−	0.0807449i
$466$		0			0
$467$	−501.947	+	501.947i	−0.0497374	+	0.0497374i	−0.731538	−	0.681801i	$-0.761197\pi$
$467$	−501.947	+	501.947i	−0.0497374	+	0.0497374i	0.681801	+	0.731538i	$0.261197\pi$
$468$		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
$477$	1115.90	+	3446.92i	0.107114	+	0.330867i
$478$		0			0
$479$	15980.7			1.52438			0.762190	−	0.647353i	$-0.224124\pi$
$479$	15980.7			1.52438			0.762190	+	0.647353i	$0.224124\pi$
$480$		0			0
$481$	2654.74			0.251655
$482$		0			0
$483$	17345.3	+	28339.0i	1.63403	+	2.66970i
$484$		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	0.422035	−	0.906580i	$-0.361316\pi$
$491$	−5271.77	−	5271.77i	−0.484545	−	0.484545i	−0.906580	+	0.422035i	$0.861316\pi$
$492$		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	$-0.249405\pi$
$499$	29.4722	+	29.4722i	0.00264400	+	0.00264400i	−0.705784	+	0.708428i	$0.749405\pi$
$500$		0			0
$501$	5965.87	+	9747.11i	0.532007	+	0.869200i
$502$		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
$507$	4145.32	+	6772.68i	0.363117	+	0.593264i
$508$		0			0
$509$	2527.57	+	2527.57i	0.220103	+	0.220103i	0.808542	−	0.588439i	$-0.200257\pi$
$509$	2527.57	+	2527.57i	0.220103	+	0.220103i	−0.588439	+	0.808542i	$0.700257\pi$
$510$		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	$-0.500744\pi$
$521$	−55.5878			−0.00467437			−0.00233719	+	0.999997i	$0.500744\pi$
$522$		0			0
$523$	−14970.9	+	14970.9i	−1.25169	+	1.25169i	−0.296723	+	0.954963i	$0.595894\pi$
$523$	−14970.9	+	14970.9i	−1.25169	+	1.25169i	−0.954963	+	0.296723i	$0.904106\pi$
$524$		0			0
$525$	9199.55	+	15030.3i	0.764764	+	1.24948i
$526$		0			0
$527$	5718.14			0.472650
$528$		0			0
$529$	−26899.5			−2.21086
$530$		0			0
$531$	−12499.2	+	4046.46i	−1.02151	+	0.330700i
$532$		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	$-0.777352\pi$
$541$	−1527.27	+	1527.27i	−0.121372	+	0.121372i	0.643812	+	0.765184i	$0.277352\pi$
$542$		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	$-0.403732\pi$
$547$	−8402.23	−	8402.23i	−0.656770	−	0.656770i	−0.954615	+	0.297844i	$0.903732\pi$
$548$		0			0
$549$	−1799.66	−	5559.00i	−0.139904	−	0.432154i
$550$		0			0
$551$			6450.86i			0.498759i
$552$		0			0
$553$			5257.52i			0.404290i
$554$		0			0
$555$	2043.16	−	1250.55i	0.156265	−	0.0956446i
$556$		0			0
$557$	−11345.5	−	11345.5i	−0.863060	−	0.863060i	0.128633	−	0.991692i	$-0.458941\pi$
$557$	−11345.5	−	11345.5i	−0.863060	−	0.863060i	−0.991692	+	0.128633i	$0.958941\pi$
$558$		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	−0.423082	−	0.906092i	$-0.639052\pi$
$563$	6452.36	−	6452.36i	0.483010	−	0.483010i	0.906092	+	0.423082i	$0.139052\pi$
$564$		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	$-0.404644\pi$
$569$	8010.89			0.590218			0.295109	+	0.955464i	$0.404644\pi$
$570$		0			0
$571$	−13548.1	+	13548.1i	−0.992946	+	0.992946i	−0.999975	−	0.00702892i	$-0.997763\pi$
$571$	−13548.1	+	13548.1i	−0.992946	+	0.992946i	0.00702892	+	0.999975i	$0.497763\pi$
$572$		0			0
$573$	−16530.6	+	10117.8i	−1.20519	+	0.737658i
$574$		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
$579$	−14567.1	+	8916.04i	−1.04558	+	0.639962i
$580$		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	0.921856	−	0.387533i	$-0.126673\pi$
$587$	7599.07	+	7599.07i	0.534323	+	0.534323i	−0.387533	+	0.921856i	$0.626673\pi$
$588$		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
$597$	898.742	−	550.089i	0.0616132	−	0.0377113i
$598$		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	$0.00601702\pi$
$601$			556.990i			0.0378038i	−0.999821	+	0.0189019i	$0.993983\pi$
$602$		0			0
$603$	−21923.3	+	7097.39i	−1.48057	+	0.479317i
$604$		0			0
$605$	−2581.19	−	2581.19i	−0.173455	−	0.173455i
$606$		0			0
$607$			10080.8i			0.674080i	0.941490	+	0.337040i	$0.109426\pi$
$607$			10080.8i			0.674080i	−0.941490	+	0.337040i	$0.890574\pi$
$608$		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	$-0.0361339\pi$
$613$	13360.3	+	13360.3i	0.880290	+	0.880290i	−0.113274	+	0.993564i	$0.536134\pi$
$614$		0			0
$615$	399.190	−	1658.84i	0.0261738	−	0.108765i
$616$		0			0
$617$	−28317.5			−1.84768			−0.923840	−	0.382779i	$-0.874967\pi$
$617$	−28317.5			−1.84768			−0.923840	+	0.382779i	$0.874967\pi$
$618$		0			0
$619$	5399.53	−	5399.53i	0.350606	−	0.350606i	−0.509729	−	0.860335i	$-0.670254\pi$
$619$	5399.53	−	5399.53i	0.350606	−	0.350606i	0.860335	+	0.509729i	$0.170254\pi$
$620$		0			0
$621$	27647.8	−	2131.30i	1.78659	−	0.137723i
$622$		0			0
$623$	30019.1			1.93048
$624$		0			0
$625$	−8468.19			−0.541964
$626$		0			0
$627$	−4915.54	−	8031.06i	−0.313090	−	0.511531i
$628$		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	$-0.0681122\pi$
$643$	12470.6	+	12470.6i	0.764842	+	0.764842i	−0.212352	+	0.977193i	$0.568112\pi$
$644$		0			0
$645$	−3910.63	−	6389.24i	−0.238730	−	0.390040i
$646$		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
$651$	−13013.4	−	21261.5i	−0.783465	−	1.28004i
$652$		0			0
$653$	4674.02	+	4674.02i	0.280105	+	0.280105i	0.833151	−	0.553046i	$-0.186535\pi$
$653$	4674.02	+	4674.02i	0.280105	+	0.280105i	−0.553046	+	0.833151i	$0.686535\pi$
$654$		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	0.279146	−	0.960249i	$-0.409949\pi$
$659$	20967.1	−	20967.1i	1.23939	−	1.23939i	0.960249	−	0.279146i	$-0.0900512\pi$
$660$		0			0
$661$	−17021.5	−	17021.5i	−1.00160	−	1.00160i	−0.999999	−	0.00160195i	$-0.999490\pi$
$661$	−17021.5	−	17021.5i	−1.00160	−	1.00160i	−0.00160195	−	0.999999i	$-0.500510\pi$
$662$		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
$669$	−4893.22	−	7994.60i	−0.282784	−	0.462016i
$670$		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
$675$	14663.8	−	1130.39i	0.836162	−	0.0644575i
$676$		0			0
$677$	7945.30	−	7945.30i	0.451053	−	0.451053i	−0.444651	−	0.895704i	$-0.646672\pi$
$677$	7945.30	−	7945.30i	0.451053	−	0.451053i	0.895704	+	0.444651i	$0.146672\pi$
$678$		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	0.167714	−	0.985836i	$-0.446361\pi$
$683$	−14603.2	−	14603.2i	−0.818121	−	0.818121i	−0.985836	+	0.167714i	$0.946361\pi$
$684$		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	$-0.175510\pi$
$691$	5956.77	+	5956.77i	0.327940	+	0.327940i	−0.523863	+	0.851803i	$0.675510\pi$
$692$		0			0
$693$	18917.3	−	6124.25i	1.03695	−	0.335701i
$694$		0			0
$695$			10610.7i			0.579119i
$696$		0			0
$697$			2819.29i			0.153211i
$698$		0			0
$699$	15521.3	−	9500.07i	0.839872	−	0.514057i
$700$		0			0
$701$	−19922.3	−	19922.3i	−1.07340	−	1.07340i	−0.997084	−	0.0763183i	$-0.975683\pi$
$701$	−19922.3	−	19922.3i	−1.07340	−	1.07340i	−0.0763183	−	0.997084i	$-0.524317\pi$
$702$		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	$-0.173687\pi$
$709$	6339.66	+	6339.66i	0.335812	+	0.335812i	−0.518976	+	0.854789i	$0.673687\pi$
$710$		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
$717$	−8306.39	+	5084.06i	−0.432647	+	0.264808i
$718$		0			0
$719$	−23861.1			−1.23765			−0.618824	−	0.785530i	$-0.712390\pi$
$719$	−23861.1			−1.23765			−0.618824	+	0.785530i	$0.712390\pi$
$720$		0			0
$721$	34397.9			1.77676
$722$		0			0
$723$	−2782.47	+	1703.06i	−0.143128	+	0.0876035i
$724$		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	$-0.889053\pi$
$733$	−11874.1	+	11874.1i	−0.598334	+	0.598334i	0.341535	+	0.939869i	$0.389053\pi$
$734$		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	−0.961372	−	0.275253i	$-0.911238\pi$
$739$	−24843.0	−	24843.0i	−1.23662	−	1.23662i	−0.275253	−	0.961372i	$-0.588762\pi$
$740$		0			0
$741$	−9124.00	+	5584.49i	−0.452333	+	0.276857i
$742$		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
$747$	8800.30	+	27183.4i	0.431039	+	1.33145i
$748$		0			0
$749$	17097.8	+	17097.8i	0.834098	+	0.834098i
$750$		0			0
$751$		−	34126.2i		−	1.65817i	−0.559124	−	0.829084i	$-0.688862\pi$
$751$		−	34126.2i		−	1.65817i	0.559124	−	0.829084i	$-0.311138\pi$
$752$		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	$-0.169819\pi$
$757$	7341.39	+	7341.39i	0.352480	+	0.352480i	−0.508551	+	0.861032i	$0.669819\pi$
$758$		0			0
$759$	−5469.94	+	22730.4i	−0.261589	+	1.08704i
$760$		0			0
$761$	18960.2			0.903162			0.451581	−	0.892230i	$-0.350860\pi$
$761$	18960.2			0.903162			0.451581	+	0.892230i	$0.350860\pi$
$762$		0			0
$763$	16894.3	−	16894.3i	0.801592	−	0.801592i
$764$		0			0
$765$	4448.50	−	1440.15i	0.210243	−	0.0680635i
$766$		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
$771$	−12443.9	−	20331.0i	−0.581267	−	0.949681i
$772$		0			0
$773$	18559.5	−	18559.5i	0.863568	−	0.863568i	−0.128183	−	0.991751i	$-0.540914\pi$
$773$	18559.5	−	18559.5i	0.863568	−	0.863568i	0.991751	+	0.128183i	$0.0409145\pi$
$774$		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	$-0.178707\pi$
$787$	6934.87	+	6934.87i	0.314106	+	0.314106i	−0.532392	+	0.846498i	$0.678707\pi$
$788$		0			0
$789$	−2885.92	−	4715.05i	−0.130217	−	0.212751i
$790$		0			0
$791$			4937.38i			0.221938i
$792$		0			0
$793$		−	5596.74i		−	0.250626i
$794$		0			0
$795$	1634.73	+	2670.85i	0.0729284	+	0.119151i
$796$		0			0
$797$	1033.71	+	1033.71i	0.0459424	+	0.0459424i	0.729705	−	0.683762i	$-0.239658\pi$
$797$	1033.71	+	1033.71i	0.0459424	+	0.0459424i	−0.683762	+	0.729705i	$0.739658\pi$
$798$		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	$-0.711510\pi$
$809$	−28378.6			−1.23330			−0.616649	+	0.787239i	$0.711510\pi$
$810$		0			0
$811$	−18955.2	+	18955.2i	−0.820723	+	0.820723i	−0.986212	−	0.165489i	$-0.947080\pi$
$811$	−18955.2	+	18955.2i	−0.820723	+	0.820723i	0.165489	+	0.986212i	$0.447080\pi$
$812$		0			0
$813$	−18685.3	−	30528.3i	−0.806056	−	1.31694i
$814$		0			0
$815$	−4581.45			−0.196909
$816$		0			0
$817$	−25553.2			−1.09424
$818$		0			0
$819$	−6957.69	−	21491.8i	−0.296851	−	0.916951i
$820$		0			0
$821$	26166.4	−	26166.4i	1.11232	−	1.11232i	0.119482	−	0.992836i	$-0.461877\pi$
$821$	26166.4	−	26166.4i	1.11232	−	1.11232i	0.992836	−	0.119482i	$-0.0381233\pi$
$822$		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	−0.869745	−	0.493501i	$-0.835717\pi$
$827$	−32421.5	−	32421.5i	−1.36325	−	1.36325i	−0.493501	−	0.869745i	$-0.664283\pi$
$828$		0			0
$829$	−508.732	+	508.732i	−0.0213136	+	0.0213136i	−0.717683	−	0.696370i	$-0.754797\pi$
$829$	−508.732	+	508.732i	−0.0213136	+	0.0213136i	0.696370	+	0.717683i	$0.254797\pi$
$830$		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
$837$	−20743.0	+	1599.02i	−0.856609	+	0.0660338i
$838$		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
$843$	35073.9	−	21467.5i	1.43299	−	0.877083i
$844$		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	0.924826	+	0.380390i	$0.124210\pi$
$853$	32516.7	+	32516.7i	1.30522	+	1.30522i	0.380390	+	0.924826i	$0.375790\pi$
$854$		0			0
$855$	−4391.43	+	8595.93i	−0.175654	+	0.343830i
$856$		0			0
$857$	17192.8			0.685292			0.342646	−	0.939465i	$-0.388677\pi$
$857$	17192.8			0.685292			0.342646	+	0.939465i	$0.388677\pi$
$858$		0			0
$859$	28319.0	−	28319.0i	1.12483	−	1.12483i	0.133827	−	0.991005i	$-0.457273\pi$
$859$	28319.0	−	28319.0i	1.12483	−	1.12483i	0.991005	−	0.133827i	$-0.0427266\pi$
$860$		0			0
$861$	10482.8	−	6416.17i	0.414929	−	0.253963i
$862$		0			0
$863$	25432.8			1.00318			0.501589	−	0.865106i	$-0.332749\pi$
$863$	25432.8			1.00318			0.501589	+	0.865106i	$0.332749\pi$
$864$		0			0
$865$	2862.20			0.112506
$866$		0			0
$867$	15184.1	−	9293.64i	0.594784	−	0.364047i
$868$		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	0.410231	−	0.911982i	$-0.365448\pi$
$877$	34340.0	−	34340.0i	1.32221	−	1.32221i	0.911982	−	0.410231i	$-0.134552\pi$
$878$		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	0.999920	+	0.0126765i	$0.00403517\pi$
$883$	26569.1	+	26569.1i	1.01260	+	1.01260i	0.0126765	+	0.999920i	$0.495965\pi$
$884$		0			0
$885$	−9685.03	+	5927.87i	−0.367863	+	0.225156i
$886$		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
$891$	2631.08	−	16385.0i	0.0989274	−	0.616070i
$892$		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	$-0.931155\pi$
$907$	−20817.3	+	20817.3i	−0.762101	+	0.762101i	0.214601	+	0.976702i	$0.431155\pi$
$908$		0			0
$909$	6.80048	+	21.0062i	0.000248138	+	0.000766480i
$910$		0			0
$911$	−9545.92			−0.347168			−0.173584	−	0.984819i	$-0.555535\pi$
$911$	−9545.92			−0.347168			−0.173584	+	0.984819i	$0.555535\pi$
$912$		0			0
$913$	−24089.7			−0.873222
$914$		0			0
$915$	−2636.41	−	4307.40i	−0.0952536	−	0.155626i
$916$		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
$933$	9501.94	+	15524.4i	0.333419	+	0.544744i
$934$		0			0
$935$			3942.21i			0.137887i
$936$		0			0
$937$			9723.86i			0.339023i	0.985528	+	0.169512i	$0.0542190\pi$
$937$			9723.86i			0.339023i	−0.985528	+	0.169512i	$0.945781\pi$
$938$		0			0
$939$	2038.50	+	3330.53i	0.0708455	+	0.115748i
$940$		0			0
$941$	−24237.0	−	24237.0i	−0.839644	−	0.839644i	0.149168	−	0.988812i	$-0.452340\pi$
$941$	−24237.0	−	24237.0i	−0.839644	−	0.839644i	−0.988812	+	0.149168i	$0.952340\pi$
$942$		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	−0.995897	−	0.0904976i	$-0.971154\pi$
$947$	−26385.5	+	26385.5i	−0.905399	+	0.905399i	0.0904976	+	0.995897i	$0.471154\pi$
$948$		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	$-0.564982\pi$
$953$	−11928.6			−0.405464			−0.202732	+	0.979234i	$0.564982\pi$
$954$		0			0
$955$	−11845.0	+	11845.0i	−0.401355	+	0.401355i
$956$		0			0
$957$	−5003.99	−	8175.59i	−0.169024	−	0.276154i
$958$		0			0
$959$	−51712.2			−1.74126
$960$		0			0
$961$	7801.07			0.261860
$962$		0			0
$963$	19199.2	−	6215.51i	0.642458	−	0.207988i
$964$		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	0.835697	−	0.549191i	$-0.185064\pi$
$971$	8668.87	+	8668.87i	0.286506	+	0.286506i	−0.549191	+	0.835697i	$0.685064\pi$
$972$		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
$981$	−6141.54	−	18970.7i	−0.199882	−	0.617420i
$982$		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
$987$	−59213.0	+	36242.2i	−1.90960	+	1.16880i
$988$		0			0
$989$	44863.9	+	44863.9i	1.44246	+	1.44246i
$990$		0			0
$991$		−	1498.28i		−	0.0480268i	−0.999712	−	0.0240134i	$-0.992356\pi$
$991$		−	1498.28i		−	0.0480268i	0.999712	−	0.0240134i	$-0.00764444\pi$
$992$		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	−0.834484	−	0.551033i	$-0.814234\pi$
$997$	−43616.9	−	43616.9i	−1.38552	−	1.38552i	−0.551033	−	0.834484i	$-0.685766\pi$
$998$		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	384.4.k.a.287.19		44
3.2	odd	2	inner	384.4.k.a.287.7		44
4.3	odd	2		384.4.k.b.287.4		44
8.3	odd	2		48.4.k.a.11.22	yes	44
8.5	even	2		192.4.k.a.143.4		44
12.11	even	2		384.4.k.b.287.16		44
16.3	odd	4	inner	384.4.k.a.95.7		44
16.5	even	4		48.4.k.a.35.1	yes	44
16.11	odd	4		192.4.k.a.47.16		44
16.13	even	4		384.4.k.b.95.16		44
24.5	odd	2		192.4.k.a.143.16		44
24.11	even	2		48.4.k.a.11.1	✓	44
48.5	odd	4		48.4.k.a.35.22	yes	44
48.11	even	4		192.4.k.a.47.4		44
48.29	odd	4		384.4.k.b.95.4		44
48.35	even	4	inner	384.4.k.a.95.19		44

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.43190 - 2.71261i) q^{3} +(3.17566 - 3.17566i) q^{5} +32.3513 q^{7} +(12.2835 - 24.0440i) q^{9} +O(q^{10})\)	\(q+(4.43190 - 2.71261i) q^{3} +(3.17566 - 3.17566i) q^{5} +32.3513 q^{7} +(12.2835 - 24.0440i) q^{9} +(16.0965 + 16.0965i) q^{11} +(18.2871 - 18.2871i) q^{13} +(5.45988 - 22.6886i) q^{15} +38.5606i q^{17} +(-56.2887 - 56.2887i) q^{19} +(143.378 - 87.7565i) q^{21} +197.652i q^{23} +104.830i q^{25} +(-10.7831 - 139.881i) q^{27} +(-57.3016 - 57.3016i) q^{29} -148.290i q^{31} +(115.002 + 27.6746i) q^{33} +(102.737 - 102.737i) q^{35} +(72.5852 + 72.5852i) q^{37} +(31.4408 - 130.652i) q^{39} +73.1133 q^{41} +(226.984 - 226.984i) q^{43} +(-37.3476 - 115.364i) q^{45} -412.986 q^{47} +703.607 q^{49} +(104.600 + 170.897i) q^{51} +(-94.8845 + 94.8845i) q^{53} +102.234 q^{55} +(-402.155 - 96.7764i) q^{57} +(-344.070 - 344.070i) q^{59} +(153.024 - 153.024i) q^{61} +(397.386 - 777.856i) q^{63} -116.147i q^{65} +(-603.490 - 603.490i) q^{67} +(536.154 + 875.976i) q^{69} -711.320i q^{71} +687.773i q^{73} +(284.364 + 464.598i) q^{75} +(520.744 + 520.744i) q^{77} +162.513i q^{79} +(-427.233 - 590.689i) q^{81} +(-748.288 + 748.288i) q^{83} +(122.455 + 122.455i) q^{85} +(-409.392 - 98.5180i) q^{87} +927.910 q^{89} +(591.611 - 591.611i) q^{91} +(-402.253 - 657.206i) q^{93} -357.508 q^{95} -208.855 q^{97} +(584.747 - 189.304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} + 8 q^{7}+O(q^{10}) \) 44 * q - 2 * q^3 + 8 * q^7	\( 44 q - 2 q^{3} + 8 q^{7} + 4 q^{13} + 20 q^{19} + 56 q^{21} - 134 q^{27} - 4 q^{33} + 4 q^{37} - 596 q^{39} - 436 q^{43} + 252 q^{45} + 972 q^{49} - 648 q^{51} - 280 q^{55} + 916 q^{61} - 1636 q^{67} - 52 q^{69} + 1454 q^{75} - 4 q^{81} - 736 q^{85} - 1284 q^{87} + 424 q^{91} + 2084 q^{93} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 + 8 * q^7 + 4 * q^13 + 20 * q^19 + 56 * q^21 - 134 * q^27 - 4 * q^33 + 4 * q^37 - 596 * q^39 - 436 * q^43 + 252 * q^45 + 972 * q^49 - 648 * q^51 - 280 * q^55 + 916 * q^61 - 1636 * q^67 - 52 * q^69 + 1454 * q^75 - 4 * q^81 - 736 * q^85 - 1284 * q^87 + 424 * q^91 + 2084 * q^93 - 8 * q^97 + 1196 * q^99

Introduction

L-functions

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