LMFDB - Embedded newform 160.4.n.c.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 48x^{6} + 628x^{4} + 1556x^{2} + 400 $ x^8 + 48x^6 + 628x^4 + 1556*x^2 + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$1.68152i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.4.n.c.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.13008 + 6.13008i) q^{3} +(3.85931 - 10.4931i) q^{5} +(-24.7564 + 24.7564i) q^{7} +48.1559i q^{9} +39.8969i q^{11} +(3.91401 - 3.91401i) q^{13} +(87.9816 - 40.6659i) q^{15} +(42.3071 + 42.3071i) q^{17} +61.0166 q^{19} -303.518 q^{21} +(41.1255 + 41.1255i) q^{23} +(-95.2115 - 80.9924i) q^{25} +(-129.687 + 129.687i) q^{27} -57.2951i q^{29} -228.768i q^{31} +(-244.571 + 244.571i) q^{33} +(164.230 + 355.315i) q^{35} +(231.478 + 231.478i) q^{37} +47.9864 q^{39} +78.1643 q^{41} +(-147.056 - 147.056i) q^{43} +(505.306 + 185.848i) q^{45} +(34.7589 - 34.7589i) q^{47} -882.762i q^{49} +518.692i q^{51} +(132.875 - 132.875i) q^{53} +(418.643 + 153.974i) q^{55} +(374.037 + 374.037i) q^{57} -275.683 q^{59} -322.195 q^{61} +(-1192.17 - 1192.17i) q^{63} +(-25.9648 - 56.1755i) q^{65} +(89.6397 - 89.6397i) q^{67} +504.206i q^{69} -292.232i q^{71} +(299.669 - 299.669i) q^{73} +(-87.1638 - 1080.14i) q^{75} +(-987.704 - 987.704i) q^{77} +227.280 q^{79} -289.778 q^{81} +(287.663 + 287.663i) q^{83} +(607.210 - 280.658i) q^{85} +(351.224 - 351.224i) q^{87} -471.695i q^{89} +193.794i q^{91} +(1402.37 - 1402.37i) q^{93} +(235.482 - 640.255i) q^{95} +(1200.49 + 1200.49i) q^{97} -1921.27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 6 q^{5} - 70 q^{7} + 144 q^{13} + 134 q^{15} - 100 q^{17} - 176 q^{19} - 516 q^{21} + 198 q^{23} - 172 q^{25} + 288 q^{27} + 172 q^{33} - 170 q^{35} + 492 q^{37} - 756 q^{39} - 28 q^{41}+ \cdots - 8412 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 6 * q^5 - 70 * q^7 + 144 * q^13 + 134 * q^15 - 100 * q^17 - 176 * q^19 - 516 * q^21 + 198 * q^23 - 172 * q^25 + 288 * q^27 + 172 * q^33 - 170 * q^35 + 492 * q^37 - 756 * q^39 - 28 * q^41 - 654 * q^43 + 10 * q^45 + 690 * q^47 + 580 * q^53 + 2392 * q^55 - 248 * q^57 - 1808 * q^59 - 1068 * q^61 - 3106 * q^63 + 2200 * q^65 + 1878 * q^67 + 1952 * q^73 + 2178 * q^75 + 340 * q^77 + 1808 * q^79 - 7844 * q^81 + 506 * q^83 + 184 * q^85 - 784 * q^87 + 3708 * q^93 + 5800 * q^95 + 5576 * q^97 - 8412 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	6.13008	+	6.13008i	1.17974	+	1.17974i	0.979811	+	0.199924i	$0.0640694\pi$
$3$	6.13008	+	6.13008i	1.17974	+	1.17974i	0.199924	+	0.979811i	$0.435931\pi$
$4$		0			0
$5$	3.85931	−	10.4931i	0.345187	−	0.938534i
$5$	3.85931	−	10.4931i	0.345187	−	0.938534i
$6$		0			0
$7$	−24.7564	+	24.7564i	−1.33672	+	1.33672i	−0.437506	+	0.899215i	$0.644138\pi$
$7$	−24.7564	+	24.7564i	−1.33672	+	1.33672i	−0.899215	+	0.437506i	$0.855862\pi$
$8$		0			0
$9$			48.1559i			1.78355i
$10$		0			0
$11$			39.8969i			1.09358i	0.837270	+	0.546789i	$0.184150\pi$
$11$			39.8969i			1.09358i	−0.837270	+	0.546789i	$0.815850\pi$
$12$		0			0
$13$	3.91401	−	3.91401i	0.0835038	−	0.0835038i	−0.664121	−	0.747625i	$-0.731194\pi$
$13$	3.91401	−	3.91401i	0.0835038	−	0.0835038i	0.747625	+	0.664121i	$0.231194\pi$
$14$		0			0
$15$	87.9816	−	40.6659i	1.51445	−	0.699992i
$16$		0			0
$17$	42.3071	+	42.3071i	0.603587	+	0.603587i	0.941263	−	0.337675i	$-0.109641\pi$
$17$	42.3071	+	42.3071i	0.603587	+	0.603587i	−0.337675	+	0.941263i	$0.609641\pi$
$18$		0			0
$19$	61.0166			0.736745			0.368373	−	0.929678i	$-0.379915\pi$
$19$	61.0166			0.736745			0.368373	+	0.929678i	$0.379915\pi$
$20$		0			0
$21$	−303.518			−3.15396
$22$		0			0
$23$	41.1255	+	41.1255i	0.372837	+	0.372837i	0.868510	−	0.495672i	$-0.165078\pi$
$23$	41.1255	+	41.1255i	0.372837	+	0.372837i	−0.495672	+	0.868510i	$0.665078\pi$
$24$		0			0
$25$	−95.2115	−	80.9924i	−0.761692	−	0.647940i
$26$		0			0
$27$	−129.687	+	129.687i	−0.924382	+	0.924382i
$28$		0			0
$29$		−	57.2951i		−	0.366877i	−0.983031	−	0.183439i	$-0.941277\pi$
$29$		−	57.2951i		−	0.366877i	0.983031	−	0.183439i	$-0.0587228\pi$
$30$		0			0
$31$		−	228.768i		−	1.32542i	−0.748878	−	0.662708i	$-0.769407\pi$
$31$		−	228.768i		−	1.32542i	0.748878	−	0.662708i	$-0.230593\pi$
$32$		0			0
$33$	−244.571	+	244.571i	−1.29013	+	1.29013i
$34$		0			0
$35$	164.230	+	355.315i	0.793140	+	1.71598i
$36$		0			0
$37$	231.478	+	231.478i	1.02851	+	1.02851i	0.999582	+	0.0289245i	$0.00920823\pi$
$37$	231.478	+	231.478i	1.02851	+	1.02851i	0.0289245	+	0.999582i	$0.490792\pi$
$38$		0			0
$39$	47.9864			0.197025
$40$		0			0
$41$	78.1643			0.297737			0.148868	−	0.988857i	$-0.452437\pi$
$41$	78.1643			0.297737			0.148868	+	0.988857i	$0.452437\pi$
$42$		0			0
$43$	−147.056	−	147.056i	−0.521531	−	0.521531i	0.396503	−	0.918034i	$-0.370224\pi$
$43$	−147.056	−	147.056i	−0.521531	−	0.521531i	−0.918034	+	0.396503i	$0.870224\pi$
$44$		0			0
$45$	505.306	+	185.848i	1.67392	+	0.615659i
$46$		0			0
$47$	34.7589	−	34.7589i	0.107875	−	0.107875i	−0.651109	−	0.758984i	$-0.725696\pi$
$47$	34.7589	−	34.7589i	0.107875	−	0.107875i	0.758984	+	0.651109i	$0.225696\pi$
$48$		0			0
$49$		−	882.762i		−	2.57365i
$50$		0			0
$51$			518.692i			1.42415i
$52$		0			0
$53$	132.875	−	132.875i	0.344374	−	0.344374i	−0.513635	−	0.858009i	$-0.671701\pi$
$53$	132.875	−	132.875i	0.344374	−	0.344374i	0.858009	+	0.513635i	$0.171701\pi$
$54$		0			0
$55$	418.643	+	153.974i	1.02636	+	0.377489i
$56$		0			0
$57$	374.037	+	374.037i	0.869165	+	0.869165i
$58$		0			0
$59$	−275.683			−0.608320			−0.304160	−	0.952621i	$-0.598376\pi$
$59$	−275.683			−0.608320			−0.304160	+	0.952621i	$0.598376\pi$
$60$		0			0
$61$	−322.195			−0.676276			−0.338138	−	0.941097i	$-0.609797\pi$
$61$	−322.195			−0.676276			−0.338138	+	0.941097i	$0.609797\pi$
$62$		0			0
$63$	−1192.17	−	1192.17i	−2.38411	−	2.38411i
$64$		0			0
$65$	−25.9648	−	56.1755i	−0.0495467	−	0.107196i
$66$		0			0
$67$	89.6397	−	89.6397i	0.163451	−	0.163451i	−0.620643	−	0.784094i	$-0.713128\pi$
$67$	89.6397	−	89.6397i	0.163451	−	0.163451i	0.784094	+	0.620643i	$0.213128\pi$
$68$		0			0
$69$			504.206i			0.879699i
$70$		0			0
$71$		−	292.232i		−	0.488472i	−0.969716	−	0.244236i	$-0.921463\pi$
$71$		−	292.232i		−	0.488472i	0.969716	−	0.244236i	$-0.0785372\pi$
$72$		0			0
$73$	299.669	−	299.669i	0.480461	−	0.480461i	−0.424818	−	0.905279i	$-0.639662\pi$
$73$	299.669	−	299.669i	0.480461	−	0.480461i	0.905279	+	0.424818i	$0.139662\pi$
$74$		0			0
$75$	−87.1638	−	1080.14i	−0.134197	−	1.66299i
$76$		0			0
$77$	−987.704	−	987.704i	−1.46181	−	1.46181i
$78$		0			0
$79$	227.280			0.323684			0.161842	−	0.986817i	$-0.448257\pi$
$79$	227.280			0.323684			0.161842	+	0.986817i	$0.448257\pi$
$80$		0			0
$81$	−289.778			−0.397501
$82$		0			0
$83$	287.663	+	287.663i	0.380423	+	0.380423i	0.871255	−	0.490831i	$-0.163307\pi$
$83$	287.663	+	287.663i	0.380423	+	0.380423i	−0.490831	+	0.871255i	$0.663307\pi$
$84$		0			0
$85$	607.210	−	280.658i	0.774838	−	0.358137i
$86$		0			0
$87$	351.224	−	351.224i	0.432818	−	0.432818i
$88$		0			0
$89$		−	471.695i		−	0.561793i	−0.959738	−	0.280897i	$-0.909368\pi$
$89$		−	471.695i		−	0.561793i	0.959738	−	0.280897i	$-0.0906318\pi$
$90$		0			0
$91$			193.794i			0.223243i
$92$		0			0
$93$	1402.37	−	1402.37i	1.56364	−	1.56364i
$94$		0			0
$95$	235.482	−	640.255i	0.254315	−	0.691461i
$96$		0			0
$97$	1200.49	+	1200.49i	1.25661	+	1.25661i	0.952700	+	0.303914i	$0.0982934\pi$
$97$	1200.49	+	1200.49i	1.25661	+	1.25661i	0.303914	+	0.952700i	$0.401707\pi$
$98$		0			0
$99$	−1921.27			−1.95045
$100$		0			0
$101$	−767.393			−0.756025			−0.378012	−	0.925801i	$-0.623392\pi$
$101$	−767.393			−0.756025			−0.378012	+	0.925801i	$0.623392\pi$
$102$		0			0
$103$	931.505	+	931.505i	0.891106	+	0.891106i	0.994627	−	0.103522i	$-0.0330111\pi$
$103$	931.505	+	931.505i	0.891106	+	0.891106i	−0.103522	+	0.994627i	$0.533011\pi$
$104$		0			0
$105$	−1171.37	+	3184.85i	−1.08870	+	2.96009i
$106$		0			0
$107$	647.000	−	647.000i	0.584559	−	0.584559i	−0.351593	−	0.936153i	$-0.614360\pi$
$107$	647.000	−	647.000i	0.584559	−	0.584559i	0.936153	+	0.351593i	$0.114360\pi$
$108$		0			0
$109$			764.489i			0.671787i	0.941900	+	0.335893i	$0.109038\pi$
$109$			764.489i			0.671787i	−0.941900	+	0.335893i	$0.890962\pi$
$110$		0			0
$111$			2837.96i			2.42673i
$112$		0			0
$113$	1621.22	−	1621.22i	1.34966	−	1.34966i	0.463631	−	0.886029i	$-0.346546\pi$
$113$	1621.22	−	1621.22i	1.34966	−	1.34966i	0.886029	−	0.463631i	$-0.153454\pi$
$114$		0			0
$115$	590.251	−	272.819i	0.478619	−	0.221222i
$116$		0			0
$117$	188.482	+	188.482i	0.148933	+	0.148933i
$118$		0			0
$119$	−2094.75			−1.61366
$120$		0			0
$121$	−260.761			−0.195914
$122$		0			0
$123$	479.153	+	479.153i	0.351250	+	0.351250i
$124$		0			0
$125$	−1217.31	+	686.491i	−0.871039	+	0.491213i
$126$		0			0
$127$	−677.560	+	677.560i	−0.473415	+	0.473415i	−0.903018	−	0.429603i	$-0.858654\pi$
$127$	−677.560	+	677.560i	−0.473415	+	0.473415i	0.429603	+	0.903018i	$0.358654\pi$
$128$		0			0
$129$		−	1802.93i		−	1.23054i
$130$		0			0
$131$			2455.55i			1.63773i	0.573987	+	0.818864i	$0.305396\pi$
$131$			2455.55i			1.63773i	−0.573987	+	0.818864i	$0.694604\pi$
$132$		0			0
$133$	−1510.55	+	1510.55i	−0.984824	+	0.984824i
$134$		0			0
$135$	860.321	+	1861.33i	0.548479	+	1.18665i
$136$		0			0
$137$	−1862.77	−	1862.77i	−1.16166	−	1.16166i	−0.984113	−	0.177545i	$-0.943185\pi$
$137$	−1862.77	−	1862.77i	−1.16166	−	1.16166i	−0.177545	−	0.984113i	$-0.556815\pi$
$138$		0			0
$139$	1502.67			0.916942			0.458471	−	0.888709i	$-0.348397\pi$
$139$	1502.67			0.916942			0.458471	+	0.888709i	$0.348397\pi$
$140$		0			0
$141$	426.150			0.254527
$142$		0			0
$143$	156.157	+	156.157i	0.0913180	+	0.0913180i
$144$		0			0
$145$	−601.205	−	221.120i	−0.344327	−	0.126641i
$146$		0			0
$147$	5411.40	−	5411.40i	3.03623	−	3.03623i
$148$		0			0
$149$			685.429i			0.376863i	0.982086	+	0.188431i	$0.0603403\pi$
$149$			685.429i			0.376863i	−0.982086	+	0.188431i	$0.939660\pi$
$150$		0			0
$151$		−	978.613i		−	0.527407i	−0.964604	−	0.263703i	$-0.915056\pi$
$151$		−	978.613i		−	0.527407i	0.964604	−	0.263703i	$-0.0849440\pi$
$152$		0			0
$153$	−2037.34	+	2037.34i	−1.07653	+	1.07653i
$154$		0			0
$155$	−2400.49	−	882.886i	−1.24395	−	0.457517i
$156$		0			0
$157$	−42.4528	−	42.4528i	−0.0215803	−	0.0215803i	0.696234	−	0.717815i	$-0.254857\pi$
$157$	−42.4528	−	42.4528i	−0.0215803	−	0.0215803i	−0.717815	+	0.696234i	$0.754857\pi$
$158$		0			0
$159$	1629.07			0.812540
$160$		0			0
$161$	−2036.24			−0.996760
$162$		0			0
$163$	−2229.20	−	2229.20i	−1.07119	−	1.07119i	−0.997264	−	0.0739278i	$-0.976447\pi$
$163$	−2229.20	−	2229.20i	−1.07119	−	1.07119i	−0.0739278	−	0.997264i	$-0.523553\pi$
$164$		0			0
$165$	1622.44	+	3510.19i	0.765496	+	1.65617i
$166$		0			0
$167$	−2342.39	+	2342.39i	−1.08539	+	1.08539i	−0.0893888	+	0.995997i	$0.528491\pi$
$167$	−2342.39	+	2342.39i	−1.08539	+	1.08539i	−0.995997	+	0.0893888i	$0.971509\pi$
$168$		0			0
$169$			2166.36i			0.986054i
$170$		0			0
$171$			2938.31i			1.31402i
$172$		0			0
$173$	985.302	−	985.302i	0.433012	−	0.433012i	−0.456640	−	0.889652i	$-0.650947\pi$
$173$	985.302	−	985.302i	0.433012	−	0.433012i	0.889652	+	0.456640i	$0.150947\pi$
$174$		0			0
$175$	4362.18	−	352.012i	1.88428	−	0.152055i
$176$		0			0
$177$	−1689.96	−	1689.96i	−0.717656	−	0.717656i
$178$		0			0
$179$	−2439.33			−1.01857			−0.509285	−	0.860598i	$-0.670090\pi$
$179$	−2439.33			−1.01857			−0.509285	+	0.860598i	$0.670090\pi$
$180$		0			0
$181$	−2622.89			−1.07712			−0.538558	−	0.842588i	$-0.681031\pi$
$181$	−2622.89			−1.07712			−0.538558	+	0.842588i	$0.681031\pi$
$182$		0			0
$183$	−1975.08	−	1975.08i	−0.797827	−	0.797827i
$184$		0			0
$185$	3322.27	−	1535.58i	1.32031	−	0.610261i
$186$		0			0
$187$	−1687.92	+	1687.92i	−0.660070	+	0.660070i
$188$		0			0
$189$		−	6421.18i		−	2.47128i
$190$		0			0
$191$			2884.40i			1.09271i	0.837554	+	0.546355i	$0.183985\pi$
$191$			2884.40i			1.09271i	−0.837554	+	0.546355i	$0.816015\pi$
$192$		0			0
$193$	1447.81	−	1447.81i	0.539978	−	0.539978i	−0.383545	−	0.923522i	$-0.625297\pi$
$193$	1447.81	−	1447.81i	0.539978	−	0.539978i	0.923522	+	0.383545i	$0.125297\pi$
$194$		0			0
$195$	185.194	−	503.527i	0.0680104	−	0.184914i
$196$		0			0
$197$	2564.35	+	2564.35i	0.927423	+	0.927423i	0.997539	−	0.0701154i	$-0.0223367\pi$
$197$	2564.35	+	2564.35i	0.927423	+	0.927423i	−0.0701154	+	0.997539i	$0.522337\pi$
$198$		0			0
$199$	1720.17			0.612761			0.306380	−	0.951909i	$-0.400882\pi$
$199$	1720.17			0.612761			0.306380	+	0.951909i	$0.400882\pi$
$200$		0			0
$201$	1099.00			0.385658
$202$		0			0
$203$	1418.42	+	1418.42i	0.490413	+	0.490413i
$204$		0			0
$205$	301.660	−	820.188i	0.102775	−	0.279436i
$206$		0			0
$207$	−1980.43	+	1980.43i	−0.664974	+	0.664974i
$208$		0			0
$209$			2434.37i			0.805689i
$210$		0			0
$211$		−	3499.42i		−	1.14175i	−0.821036	−	0.570877i	$-0.806603\pi$
$211$		−	3499.42i		−	1.14175i	0.821036	−	0.570877i	$-0.193397\pi$
$212$		0			0
$213$	1791.41	−	1791.41i	0.576268	−	0.576268i
$214$		0			0
$215$	−2110.61	+	975.543i	−0.669500	+	0.309449i
$216$		0			0
$217$	5663.48	+	5663.48i	1.77171	+	1.77171i
$218$		0			0
$219$	3674.00			1.13363
$220$		0			0
$221$	331.181			0.100804
$222$		0			0
$223$	−2444.27	−	2444.27i	−0.733992	−	0.733992i	0.237416	−	0.971408i	$-0.423699\pi$
$223$	−2444.27	−	2444.27i	−0.733992	−	0.733992i	−0.971408	+	0.237416i	$0.923699\pi$
$224$		0			0
$225$	3900.26	−	4584.99i	1.15563	−	1.35852i
$226$		0			0
$227$	−3143.97	+	3143.97i	−0.919263	+	0.919263i	−0.996976	−	0.0777126i	$-0.975238\pi$
$227$	−3143.97	+	3143.97i	−0.919263	+	0.919263i	0.0777126	+	0.996976i	$0.475238\pi$
$228$		0			0
$229$		−	1166.60i		−	0.336643i	−0.985732	−	0.168322i	$-0.946165\pi$
$229$		−	1166.60i		−	0.336643i	0.985732	−	0.168322i	$-0.0538348\pi$
$230$		0			0
$231$		−	12109.4i		−	3.44910i
$232$		0			0
$233$	336.170	−	336.170i	0.0945202	−	0.0945202i	−0.658266	−	0.752786i	$-0.728710\pi$
$233$	336.170	−	336.170i	0.0945202	−	0.0945202i	0.752786	+	0.658266i	$0.228710\pi$
$234$		0			0
$235$	−230.584	−	498.875i	−0.0640071	−	0.138481i
$236$		0			0
$237$	1393.25	+	1393.25i	0.381861	+	0.381861i
$238$		0			0
$239$	−3032.96			−0.820861			−0.410431	−	0.911892i	$-0.634622\pi$
$239$	−3032.96			−0.820861			−0.410431	+	0.911892i	$0.634622\pi$
$240$		0			0
$241$	267.807			0.0715808			0.0357904	−	0.999359i	$-0.488605\pi$
$241$	267.807			0.0715808			0.0357904	+	0.999359i	$0.488605\pi$
$242$		0			0
$243$	1725.19	+	1725.19i	0.455436	+	0.455436i
$244$		0			0
$245$	−9262.93	−	3406.85i	−2.41546	−	0.888391i
$246$		0			0
$247$	238.819	−	238.819i	0.0615211	−	0.0615211i
$248$		0			0
$249$			3526.80i			0.897597i
$250$		0			0
$251$		−	3968.98i		−	0.998086i	−0.866577	−	0.499043i	$-0.833685\pi$
$251$		−	3968.98i		−	0.998086i	0.866577	−	0.499043i	$-0.166315\pi$
$252$		0			0
$253$	−1640.78	+	1640.78i	−0.407727	+	0.407727i
$254$		0			0
$255$	5442.70	+	2001.79i	1.33661	+	0.491597i
$256$		0			0
$257$	−2966.28	−	2966.28i	−0.719967	−	0.719967i	0.248631	−	0.968598i	$-0.420019\pi$
$257$	−2966.28	−	2966.28i	−0.719967	−	0.719967i	−0.968598	+	0.248631i	$0.920019\pi$
$258$		0			0
$259$	−11461.1			−2.74965
$260$		0			0
$261$	2759.10			0.654344
$262$		0			0
$263$	−2935.29	−	2935.29i	−0.688205	−	0.688205i	0.273630	−	0.961835i	$-0.411776\pi$
$263$	−2935.29	−	2935.29i	−0.688205	−	0.688205i	−0.961835	+	0.273630i	$0.911776\pi$
$264$		0			0
$265$	−881.470	−	1907.08i	−0.204333	−	0.442080i
$266$		0			0
$267$	2891.53	−	2891.53i	0.662767	−	0.662767i
$268$		0			0
$269$		−	7502.76i		−	1.70056i	−0.526328	−	0.850282i	$-0.676432\pi$
$269$		−	7502.76i		−	1.70056i	0.526328	−	0.850282i	$-0.323568\pi$
$270$		0			0
$271$		−	5879.39i		−	1.31789i	−0.752192	−	0.658944i	$-0.771004\pi$
$271$		−	5879.39i		−	1.31789i	0.752192	−	0.658944i	$-0.228996\pi$
$272$		0			0
$273$	−1187.97	+	1187.97i	−0.263367	+	0.263367i
$274$		0			0
$275$	3231.35	−	3798.64i	0.708573	−	0.832970i
$276$		0			0
$277$	3793.74	+	3793.74i	0.822901	+	0.822901i	0.986523	−	0.163622i	$-0.0523176\pi$
$277$	3793.74	+	3793.74i	0.822901	+	0.822901i	−0.163622	+	0.986523i	$0.552318\pi$
$278$		0			0
$279$	11016.5			2.36395
$280$		0			0
$281$	−7248.81			−1.53889			−0.769445	−	0.638713i	$-0.779467\pi$
$281$	−7248.81			−1.53889			−0.769445	+	0.638713i	$0.779467\pi$
$282$		0			0
$283$	6178.38	+	6178.38i	1.29776	+	1.29776i	0.929867	+	0.367895i	$0.119922\pi$
$283$	6178.38	+	6178.38i	1.29776	+	1.29776i	0.367895	+	0.929867i	$0.380078\pi$
$284$		0			0
$285$	5368.34	−	2481.29i	1.11576	−	0.515716i
$286$		0			0
$287$	−1935.07	+	1935.07i	−0.397991	+	0.397991i
$288$		0			0
$289$		−	1333.22i		−	0.271365i
$290$		0			0
$291$			14718.2i			2.96494i
$292$		0			0
$293$	−4934.53	+	4934.53i	−0.983886	+	0.983886i	−0.999872	−	0.0159864i	$-0.994911\pi$
$293$	−4934.53	+	4934.53i	−0.983886	+	0.983886i	0.0159864	+	0.999872i	$0.494911\pi$
$294$		0			0
$295$	−1063.95	+	2892.78i	−0.209984	+	0.570929i
$296$		0			0
$297$	−5174.11	−	5174.11i	−1.01088	−	1.01088i
$298$		0			0
$299$	321.931			0.0622667
$300$		0			0
$301$	7281.17			1.39428
$302$		0			0
$303$	−4704.19	−	4704.19i	−0.891909	−	0.891909i
$304$		0			0
$305$	−1243.45	+	3380.83i	−0.233442	+	0.634708i
$306$		0			0
$307$	−504.108	+	504.108i	−0.0937165	+	0.0937165i	−0.752411	−	0.658694i	$-0.771109\pi$
$307$	−504.108	+	504.108i	−0.0937165	+	0.0937165i	0.658694	+	0.752411i	$0.271109\pi$
$308$		0			0
$309$			11420.4i			2.10254i
$310$		0			0
$311$		−	692.275i		−	0.126223i	−0.998006	−	0.0631115i	$-0.979898\pi$
$311$		−	692.275i		−	0.126223i	0.998006	−	0.0631115i	$-0.0201024\pi$
$312$		0			0
$313$	−294.306	+	294.306i	−0.0531474	+	0.0531474i	−0.733181	−	0.680034i	$-0.761965\pi$
$313$	−294.306	+	294.306i	−0.0531474	+	0.0531474i	0.680034	+	0.733181i	$0.261965\pi$
$314$		0			0
$315$	−17110.5	+	7908.62i	−3.06053	+	1.41460i
$316$		0			0
$317$	−373.771	−	373.771i	−0.0662242	−	0.0662242i	0.673219	−	0.739443i	$-0.264911\pi$
$317$	−373.771	−	373.771i	−0.0662242	−	0.0662242i	−0.739443	+	0.673219i	$0.764911\pi$
$318$		0			0
$319$	2285.90			0.401209
$320$		0			0
$321$	7932.33			1.37925
$322$		0			0
$323$	2581.44	+	2581.44i	0.444690	+	0.444690i
$324$		0			0
$325$	−689.663	+	55.6533i	−0.117710	+	0.00949874i
$326$		0			0
$327$	−4686.38	+	4686.38i	−0.792530	+	0.792530i
$328$		0			0
$329$			1721.01i			0.288397i
$330$		0			0
$331$		−	2858.98i		−	0.474755i	−0.971418	−	0.237377i	$-0.923712\pi$
$331$		−	2858.98i		−	0.474755i	0.971418	−	0.237377i	$-0.0762878\pi$
$332$		0			0
$333$	−11147.0	+	11147.0i	−1.83439	+	1.83439i
$334$		0			0
$335$	−594.653	−	1286.55i	−0.0969832	−	0.209826i
$336$		0			0
$337$	−3231.30	−	3231.30i	−0.522314	−	0.522314i	0.395955	−	0.918270i	$-0.370413\pi$
$337$	−3231.30	−	3231.30i	−0.522314	−	0.522314i	−0.918270	+	0.395955i	$0.870413\pi$
$338$		0			0
$339$	19876.4			3.18448
$340$		0			0
$341$	9127.12			1.44945
$342$		0			0
$343$	13362.6	+	13362.6i	2.10353	+	2.10353i
$344$		0			0
$345$	5290.69	+	1945.89i	0.825627	+	0.303661i
$346$		0			0
$347$	−409.696	+	409.696i	−0.0633822	+	0.0633822i	−0.738087	−	0.674705i	$-0.764271\pi$
$347$	−409.696	+	409.696i	−0.0633822	+	0.0633822i	0.674705	+	0.738087i	$0.264271\pi$
$348$		0			0
$349$			11074.0i			1.69851i	0.527985	+	0.849254i	$0.322948\pi$
$349$			11074.0i			1.69851i	−0.527985	+	0.849254i	$0.677052\pi$
$350$		0			0
$351$			1015.19i			0.154379i
$352$		0			0
$353$	6319.28	−	6319.28i	0.952808	−	0.952808i	−0.0461279	−	0.998936i	$-0.514688\pi$
$353$	6319.28	−	6319.28i	0.952808	−	0.952808i	0.998936	+	0.0461279i	$0.0146882\pi$
$354$		0			0
$355$	−3066.43	−	1127.81i	−0.458448	−	0.168614i
$356$		0			0
$357$	−12841.0	−	12841.0i	−1.90369	−	1.90369i
$358$		0			0
$359$	4184.62			0.615197			0.307599	−	0.951516i	$-0.400475\pi$
$359$	4184.62			0.615197			0.307599	+	0.951516i	$0.400475\pi$
$360$		0			0
$361$	−3135.98			−0.457206
$362$		0			0
$363$	−1598.49	−	1598.49i	−0.231126	−	0.231126i
$364$		0			0
$365$	−1987.95	−	4300.98i	−0.285080	−	0.616778i
$366$		0			0
$367$	9312.80	−	9312.80i	1.32459	−	1.32459i	0.414573	−	0.910016i	$-0.363931\pi$
$367$	9312.80	−	9312.80i	1.32459	−	1.32459i	0.910016	−	0.414573i	$-0.136069\pi$
$368$		0			0
$369$			3764.07i			0.531028i
$370$		0			0
$371$			6579.03i			0.920664i
$372$		0			0
$373$	8975.91	−	8975.91i	1.24599	−	1.24599i	0.288516	−	0.957475i	$-0.406838\pi$
$373$	8975.91	−	8975.91i	1.24599	−	1.24599i	0.957475	−	0.288516i	$-0.0931620\pi$
$374$		0			0
$375$	−11670.5	−	3253.99i	−1.60710	−	0.448094i
$376$		0			0
$377$	−224.253	−	224.253i	−0.0306356	−	0.0306356i
$378$		0			0
$379$	−6461.55			−0.875745			−0.437873	−	0.899037i	$-0.644268\pi$
$379$	−6461.55			−0.875745			−0.437873	+	0.899037i	$0.644268\pi$
$380$		0			0
$381$	−8307.00			−1.11701
$382$		0			0
$383$	1950.41	+	1950.41i	0.260212	+	0.260212i	0.825140	−	0.564928i	$-0.191096\pi$
$383$	1950.41	+	1950.41i	0.260212	+	0.260212i	−0.564928	+	0.825140i	$0.691096\pi$
$384$		0			0
$385$	−14176.0	+	6552.25i	−1.87656	+	0.867360i
$386$		0			0
$387$	7081.61	−	7081.61i	0.930177	−	0.930177i
$388$		0			0
$389$		−	2200.34i		−	0.286791i	−0.989665	−	0.143395i	$-0.954198\pi$
$389$		−	2200.34i		−	0.286791i	0.989665	−	0.143395i	$-0.0458021\pi$
$390$		0			0
$391$			3479.80i			0.450080i
$392$		0			0
$393$	−15052.7	+	15052.7i	−1.93209	+	1.93209i
$394$		0			0
$395$	877.145	−	2384.88i	0.111731	−	0.303788i
$396$		0			0
$397$	−8376.96	−	8376.96i	−1.05901	−	1.05901i	−0.998146	−	0.0608650i	$-0.980614\pi$
$397$	−8376.96	−	8376.96i	−1.05901	−	1.05901i	−0.0608650	−	0.998146i	$-0.519386\pi$
$398$		0			0
$399$	−18519.6			−2.32366
$400$		0			0
$401$	290.707			0.0362025			0.0181013	−	0.999836i	$-0.494238\pi$
$401$	290.707			0.0362025			0.0181013	+	0.999836i	$0.494238\pi$
$402$		0			0
$403$	−895.398	−	895.398i	−0.110677	−	0.110677i
$404$		0			0
$405$	−1118.34	+	3040.68i	−0.137212	+	0.373068i
$406$		0			0
$407$	−9235.24	+	9235.24i	−1.12475	+	1.12475i
$408$		0			0
$409$		−	8428.73i		−	1.01901i	−0.860469	−	0.509503i	$-0.829829\pi$
$409$		−	8428.73i		−	1.01901i	0.860469	−	0.509503i	$-0.170171\pi$
$410$		0			0
$411$		−	22837.9i		−	2.74090i
$412$		0			0
$413$	6824.93	−	6824.93i	0.813154	−	0.813154i
$414$		0			0
$415$	4128.67	−	1908.30i	0.488357	−	0.225723i
$416$		0			0
$417$	9211.50	+	9211.50i	1.08175	+	1.08175i
$418$		0			0
$419$	−1668.89			−0.194584			−0.0972921	−	0.995256i	$-0.531018\pi$
$419$	−1668.89			−0.194584			−0.0972921	+	0.995256i	$0.531018\pi$
$420$		0			0
$421$	6288.66			0.728006			0.364003	−	0.931398i	$-0.381410\pi$
$421$	6288.66			0.728006			0.364003	+	0.931398i	$0.381410\pi$
$422$		0			0
$423$	1673.84	+	1673.84i	0.192400	+	0.192400i
$424$		0			0
$425$	−601.565	−	7454.68i	−0.0686593	−	0.850835i
$426$		0			0
$427$	7976.40	−	7976.40i	0.903993	−	0.903993i
$428$		0			0
$429$			1914.51i			0.215462i
$430$		0			0
$431$		−	8216.05i		−	0.918221i	−0.888379	−	0.459111i	$-0.848168\pi$
$431$		−	8216.05i		−	0.918221i	0.888379	−	0.459111i	$-0.151832\pi$
$432$		0			0
$433$	2360.26	−	2360.26i	0.261956	−	0.261956i	−0.563893	−	0.825848i	$-0.690697\pi$
$433$	2360.26	−	2360.26i	0.261956	−	0.261956i	0.825848	+	0.563893i	$0.190697\pi$
$434$		0			0
$435$	−2329.96	−	5040.92i	−0.256811	−	0.555617i
$436$		0			0
$437$	2509.34	+	2509.34i	0.274686	+	0.274686i
$438$		0			0
$439$	5099.36			0.554395			0.277197	−	0.960813i	$-0.410594\pi$
$439$	5099.36			0.554395			0.277197	+	0.960813i	$0.410594\pi$
$440$		0			0
$441$	42510.2			4.59023
$442$		0			0
$443$	10295.8	+	10295.8i	1.10422	+	1.10422i	0.993896	+	0.110321i	$0.0351877\pi$
$443$	10295.8	+	10295.8i	1.10422	+	1.10422i	0.110321	+	0.993896i	$0.464812\pi$
$444$		0			0
$445$	−4949.56	−	1820.42i	−0.527262	−	0.193924i
$446$		0			0
$447$	−4201.74	+	4201.74i	−0.444598	+	0.444598i
$448$		0			0
$449$			15903.5i			1.67157i	0.549059	+	0.835783i	$0.314986\pi$
$449$			15903.5i			1.67157i	−0.549059	+	0.835783i	$0.685014\pi$
$450$		0			0
$451$			3118.51i			0.325598i
$452$		0			0
$453$	5998.98	−	5998.98i	0.622200	−	0.622200i
$454$		0			0
$455$	2033.50	+	747.909i	0.209521	+	0.0770605i
$456$		0			0
$457$	318.354	+	318.354i	0.0325864	+	0.0325864i	0.723212	−	0.690626i	$-0.242665\pi$
$457$	318.354	+	318.354i	0.0325864	+	0.0325864i	−0.690626	+	0.723212i	$0.742665\pi$
$458$		0			0
$459$	−10973.4			−1.11589
$460$		0			0
$461$	2740.90			0.276912			0.138456	−	0.990369i	$-0.455786\pi$
$461$	2740.90			0.276912			0.138456	+	0.990369i	$0.455786\pi$
$462$		0			0
$463$	6535.16	+	6535.16i	0.655971	+	0.655971i	0.954424	−	0.298453i	$-0.0964707\pi$
$463$	6535.16	+	6535.16i	0.655971	+	0.655971i	−0.298453	+	0.954424i	$0.596471\pi$
$464$		0			0
$465$	−9303.04	−	20127.4i	−0.927781	−	2.00728i
$466$		0			0
$467$	−1340.80	+	1340.80i	−0.132858	+	0.132858i	−0.770409	−	0.637551i	$-0.779948\pi$
$467$	−1340.80	+	1340.80i	−0.132858	+	0.132858i	0.637551	+	0.770409i	$0.279948\pi$
$468$		0			0
$469$			4438.32i			0.436977i
$470$		0			0
$471$		−	520.479i		−	0.0509180i
$472$		0			0
$473$	5867.08	−	5867.08i	0.570335	−	0.570335i
$474$		0			0
$475$	−5809.48	−	4941.88i	−0.561173	−	0.477367i
$476$		0			0
$477$	6398.72	+	6398.72i	0.614208	+	0.614208i
$478$		0			0
$479$	1242.74			0.118544			0.0592718	−	0.998242i	$-0.481122\pi$
$479$	1242.74			0.118544			0.0592718	+	0.998242i	$0.481122\pi$
$480$		0			0
$481$	1812.01			0.171768
$482$		0			0
$483$	−12482.3	−	12482.3i	−1.17591	−	1.17591i
$484$		0			0
$485$	17230.0	−	7963.85i	1.61314	−	0.745607i
$486$		0			0
$487$	−3634.13	+	3634.13i	−0.338148	+	0.338148i	−0.855670	−	0.517522i	$-0.826855\pi$
$487$	−3634.13	+	3634.13i	−0.338148	+	0.338148i	0.517522	+	0.855670i	$0.326855\pi$
$488$		0			0
$489$		−	27330.3i		−	2.52744i
$490$		0			0
$491$		−	8273.21i		−	0.760417i	−0.924901	−	0.380209i	$-0.875852\pi$
$491$		−	8273.21i		−	0.760417i	0.924901	−	0.380209i	$-0.124148\pi$
$492$		0			0
$493$	2423.99	−	2423.99i	0.221442	−	0.221442i
$494$		0			0
$495$	−7414.77	+	20160.1i	−0.673271	+	1.83057i
$496$		0			0
$497$	7234.62	+	7234.62i	0.652952	+	0.652952i
$498$		0			0
$499$	−9939.45			−0.891685			−0.445843	−	0.895111i	$-0.647096\pi$
$499$	−9939.45			−0.891685			−0.445843	+	0.895111i	$0.647096\pi$
$500$		0			0
$501$	−28718.1			−2.56094
$502$		0			0
$503$	−9659.72	−	9659.72i	−0.856274	−	0.856274i	0.134623	−	0.990897i	$-0.457018\pi$
$503$	−9659.72	−	9659.72i	−0.856274	−	0.856274i	−0.990897	+	0.134623i	$0.957018\pi$
$504$		0			0
$505$	−2961.61	+	8052.36i	−0.260970	+	0.709555i
$506$		0			0
$507$	−13280.0	+	13280.0i	−1.16328	+	1.16328i
$508$		0			0
$509$			14929.3i			1.30006i	0.759910	+	0.650029i	$0.225243\pi$
$509$			14929.3i			1.30006i	−0.759910	+	0.650029i	$0.774757\pi$
$510$		0			0
$511$			14837.5i			1.28448i
$512$		0			0
$513$	−7913.07	+	7913.07i	−0.681034	+	0.681034i
$514$		0			0
$515$	13369.4	−	6179.43i	1.14393	−	0.528735i
$516$		0			0
$517$	1386.77	+	1386.77i	0.117969	+	0.117969i
$518$		0			0
$519$	12080.0			1.02168
$520$		0			0
$521$	−23080.6			−1.94084			−0.970420	−	0.241424i	$-0.922385\pi$
$521$	−23080.6			−1.94084			−0.970420	+	0.241424i	$0.922385\pi$
$522$		0			0
$523$	−6732.75	−	6732.75i	−0.562911	−	0.562911i	0.367222	−	0.930133i	$-0.380309\pi$
$523$	−6732.75	−	6732.75i	−0.562911	−	0.562911i	−0.930133	+	0.367222i	$0.880309\pi$
$524$		0			0
$525$	28898.4	+	24582.7i	2.40234	+	2.04357i
$526$		0			0
$527$	9678.51	−	9678.51i	0.800005	−	0.800005i
$528$		0			0
$529$		−	8784.38i		−	0.721984i
$530$		0			0
$531$		−	13275.7i		−	1.08497i
$532$		0			0
$533$	305.935	−	305.935i	0.0248622	−	0.0248622i
$534$		0			0
$535$	−4292.08	−	9286.03i	−0.346846	−	0.750411i
$536$		0			0
$537$	−14953.3	−	14953.3i	−1.20164	−	1.20164i
$538$		0			0
$539$	35219.4			2.81449
$540$		0			0
$541$	4028.80			0.320170			0.160085	−	0.987103i	$-0.448823\pi$
$541$	4028.80			0.320170			0.160085	+	0.987103i	$0.448823\pi$
$542$		0			0
$543$	−16078.6	−	16078.6i	−1.27071	−	1.27071i
$544$		0			0
$545$	8021.88	+	2950.40i	0.630495	+	0.231892i
$546$		0			0
$547$	−7081.68	+	7081.68i	−0.553548	+	0.553548i	−0.927463	−	0.373915i	$-0.878015\pi$
$547$	−7081.68	+	7081.68i	−0.553548	+	0.553548i	0.373915	+	0.927463i	$0.378015\pi$
$548$		0			0
$549$		−	15515.6i		−	1.20617i
$550$		0			0
$551$		−	3495.95i		−	0.270295i
$552$		0			0
$553$	−5626.65	+	5626.65i	−0.432675	+	0.432675i
$554$		0			0
$555$	29779.0	+	10952.6i	2.27757	+	0.837676i
$556$		0			0
$557$	−727.875	−	727.875i	−0.0553700	−	0.0553700i	0.678880	−	0.734250i	$-0.262466\pi$
$557$	−727.875	−	727.875i	−0.0553700	−	0.0553700i	−0.734250	+	0.678880i	$0.762466\pi$
$558$		0			0
$559$	−1151.16			−0.0870997
$560$		0			0
$561$	−20694.2			−1.55742
$562$		0			0
$563$	−4652.44	−	4652.44i	−0.348272	−	0.348272i	0.511194	−	0.859466i	$-0.329203\pi$
$563$	−4652.44	−	4652.44i	−0.348272	−	0.348272i	−0.859466	+	0.511194i	$0.829203\pi$
$564$		0			0
$565$	−10754.9	−	23268.4i	−0.800816	−	1.73259i
$566$		0			0
$567$	7173.88	−	7173.88i	0.531348	−	0.531348i
$568$		0			0
$569$		−	3230.44i		−	0.238009i	−0.992894	−	0.119004i	$-0.962030\pi$
$569$		−	3230.44i		−	0.238009i	0.992894	−	0.119004i	$-0.0379703\pi$
$570$		0			0
$571$		−	6786.07i		−	0.497353i	−0.968587	−	0.248676i	$-0.920004\pi$
$571$		−	6786.07i		−	0.497353i	0.968587	−	0.248676i	$-0.0799955\pi$
$572$		0			0
$573$	−17681.6	+	17681.6i	−1.28911	+	1.28911i
$574$		0			0
$575$	−584.764	−	7246.48i	−0.0424111	−	0.525563i
$576$		0			0
$577$	7363.77	+	7363.77i	0.531296	+	0.531296i	0.920958	−	0.389662i	$-0.127408\pi$
$577$	7363.77	+	7363.77i	0.531296	+	0.531296i	−0.389662	+	0.920958i	$0.627408\pi$
$578$		0			0
$579$	17750.4			1.27406
$580$		0			0
$581$	−14243.0			−1.01704
$582$		0			0
$583$	5301.30	+	5301.30i	0.376600	+	0.376600i
$584$		0			0
$585$	2705.18	−	1250.36i	0.191189	−	0.0883691i
$586$		0			0
$587$	−7380.21	+	7380.21i	−0.518933	+	0.518933i	−0.917249	−	0.398315i	$-0.869595\pi$
$587$	−7380.21	+	7380.21i	−0.518933	+	0.518933i	0.398315	+	0.917249i	$0.369595\pi$
$588$		0			0
$589$		−	13958.6i		−	0.976495i
$590$		0			0
$591$			31439.4i			2.18823i
$592$		0			0
$593$	−13227.6	+	13227.6i	−0.916009	+	0.916009i	−0.996736	−	0.0807272i	$-0.974276\pi$
$593$	−13227.6	+	13227.6i	−0.916009	+	0.916009i	0.0807272	+	0.996736i	$0.474276\pi$
$594$		0			0
$595$	−8084.27	+	21980.4i	−0.557013	+	1.51447i
$596$		0			0
$597$	10544.8	+	10544.8i	0.722895	+	0.722895i
$598$		0			0
$599$	−10522.3			−0.717746			−0.358873	−	0.933386i	$-0.616839\pi$
$599$	−10522.3			−0.717746			−0.358873	+	0.933386i	$0.616839\pi$
$600$		0			0
$601$	17165.8			1.16507			0.582534	−	0.812806i	$-0.302061\pi$
$601$	17165.8			1.16507			0.582534	+	0.812806i	$0.302061\pi$
$602$		0			0
$603$	4316.67	+	4316.67i	0.291523	+	0.291523i
$604$		0			0
$605$	−1006.36	+	2736.20i	−0.0676269	+	0.183872i
$606$		0			0
$607$	−1210.76	+	1210.76i	−0.0809609	+	0.0809609i	−0.746428	−	0.665467i	$-0.768233\pi$
$607$	−1210.76	+	1210.76i	−0.0809609	+	0.0809609i	0.665467	+	0.746428i	$0.268233\pi$
$608$		0			0
$609$			17390.1i			1.15711i
$610$		0			0
$611$		−	272.093i		−	0.0180159i
$612$		0			0
$613$	−1106.73	+	1106.73i	−0.0729209	+	0.0729209i	−0.742627	−	0.669706i	$-0.766420\pi$
$613$	−1106.73	+	1106.73i	−0.0729209	+	0.0729209i	0.669706	+	0.742627i	$0.266420\pi$
$614$		0			0
$615$	6877.02	−	3178.62i	0.450908	−	0.208413i
$616$		0			0
$617$	8893.45	+	8893.45i	0.580286	+	0.580286i	0.934982	−	0.354696i	$-0.115415\pi$
$617$	8893.45	+	8893.45i	0.580286	+	0.580286i	−0.354696	+	0.934982i	$0.615415\pi$
$618$		0			0
$619$	−22972.1			−1.49164			−0.745822	−	0.666145i	$-0.767943\pi$
$619$	−22972.1			−1.49164			−0.745822	+	0.666145i	$0.767943\pi$
$620$		0			0
$621$	−10666.9			−0.689288
$622$		0			0
$623$	11677.5	+	11677.5i	0.750961	+	0.750961i
$624$		0			0
$625$	2505.45	+	15422.8i	0.160349	+	0.987060i
$626$		0			0
$627$	−14922.9	+	14922.9i	−0.950500	+	0.950500i
$628$		0			0
$629$			19586.3i			1.24159i
$630$		0			0
$631$		−	11679.3i		−	0.736841i	−0.929659	−	0.368421i	$-0.879899\pi$
$631$		−	11679.3i		−	0.736841i	0.929659	−	0.368421i	$-0.120101\pi$
$632$		0			0
$633$	21451.7	−	21451.7i	1.34697	−	1.34697i
$634$		0			0
$635$	4494.81	+	9724.64i	0.280899	+	0.607733i
$636$		0			0
$637$	−3455.13	−	3455.13i	−0.214910	−	0.214910i
$638$		0			0
$639$	14072.7			0.871215
$640$		0			0
$641$	−8323.58			−0.512889			−0.256444	−	0.966559i	$-0.582551\pi$
$641$	−8323.58			−0.512889			−0.256444	+	0.966559i	$0.582551\pi$
$642$		0			0
$643$	−6727.94	−	6727.94i	−0.412634	−	0.412634i	0.470021	−	0.882655i	$-0.344246\pi$
$643$	−6727.94	−	6727.94i	−0.412634	−	0.412634i	−0.882655	+	0.470021i	$0.844246\pi$
$644$		0			0
$645$	−18918.4	−	6958.07i	−1.15490	−	0.424766i
$646$		0			0
$647$	13449.0	−	13449.0i	0.817212	−	0.817212i	−0.168491	−	0.985703i	$-0.553889\pi$
$647$	13449.0	−	13449.0i	0.817212	−	0.817212i	0.985703	+	0.168491i	$0.0538894\pi$
$648$		0			0
$649$		−	10998.9i		−	0.665245i
$650$		0			0
$651$			69435.2i			4.18030i
$652$		0			0
$653$	−15365.4	+	15365.4i	−0.920819	+	0.920819i	−0.997087	−	0.0762684i	$-0.975699\pi$
$653$	−15365.4	+	15365.4i	−0.920819	+	0.920819i	0.0762684	+	0.997087i	$0.475699\pi$
$654$		0			0
$655$	25766.4	+	9476.73i	1.53706	+	0.565323i
$656$		0			0
$657$	14430.8	+	14430.8i	0.856926	+	0.856926i
$658$		0			0
$659$	−21082.3			−1.24621			−0.623103	−	0.782140i	$-0.714128\pi$
$659$	−21082.3			−1.24621			−0.623103	+	0.782140i	$0.714128\pi$
$660$		0			0
$661$	7301.23			0.429629			0.214815	−	0.976655i	$-0.431085\pi$
$661$	7301.23			0.429629			0.214815	+	0.976655i	$0.431085\pi$
$662$		0			0
$663$	2030.16	+	2030.16i	0.118922	+	0.118922i
$664$		0			0
$665$	10020.7	+	21680.1i	0.584342	+	1.26424i
$666$		0			0
$667$	2356.29	−	2356.29i	0.136786	−	0.136786i
$668$		0			0
$669$		−	29967.1i		−	1.73183i
$670$		0			0
$671$		−	12854.6i		−	0.739561i
$672$		0			0
$673$	10993.3	−	10993.3i	0.629660	−	0.629660i	−0.318322	−	0.947983i	$-0.603119\pi$
$673$	10993.3	−	10993.3i	0.629660	−	0.629660i	0.947983	+	0.318322i	$0.103119\pi$
$674$		0			0
$675$	22851.4	−	1844.02i	1.30304	−	0.105150i
$676$		0			0
$677$	5657.33	+	5657.33i	0.321165	+	0.321165i	0.849214	−	0.528049i	$-0.177076\pi$
$677$	5657.33	+	5657.33i	0.321165	+	0.321165i	−0.528049	+	0.849214i	$0.677076\pi$
$678$		0			0
$679$	−59439.8			−3.35948
$680$		0			0
$681$	−38545.6			−2.16897
$682$		0			0
$683$	−5770.21	−	5770.21i	−0.323266	−	0.323266i	0.526752	−	0.850019i	$-0.323409\pi$
$683$	−5770.21	−	5770.21i	−0.323266	−	0.323266i	−0.850019	+	0.526752i	$0.823409\pi$
$684$		0			0
$685$	−26735.3	+	12357.3i	−1.49124	+	0.689266i
$686$		0			0
$687$	7151.38	−	7151.38i	0.397150	−	0.397150i
$688$		0			0
$689$		−	1040.15i		−	0.0575130i
$690$		0			0
$691$		−	3134.83i		−	0.172583i	−0.996270	−	0.0862913i	$-0.972498\pi$
$691$		−	3134.83i		−	0.172583i	0.996270	−	0.0862913i	$-0.0275016\pi$
$692$		0			0
$693$	47563.8	−	47563.8i	2.60721	−	2.60721i
$694$		0			0
$695$	5799.27	−	15767.7i	0.316516	−	0.860581i
$696$		0			0
$697$	3306.90	+	3306.90i	0.179710	+	0.179710i
$698$		0			0
$699$	4121.49			0.223018
$700$		0			0
$701$	34125.7			1.83867			0.919336	−	0.393474i	$-0.128727\pi$
$701$	34125.7			1.83867			0.919336	+	0.393474i	$0.128727\pi$
$702$		0			0
$703$	14124.0	+	14124.0i	0.757747	+	0.757747i
$704$		0			0
$705$	1644.64	−	4471.65i	0.0878594	−	0.238882i
$706$		0			0
$707$	18997.9	−	18997.9i	1.01059	−	1.01059i
$708$		0			0
$709$		−	12711.1i		−	0.673309i	−0.941628	−	0.336655i	$-0.890704\pi$
$709$		−	12711.1i		−	0.673309i	0.941628	−	0.336655i	$-0.109296\pi$
$710$		0			0
$711$			10944.9i			0.577306i
$712$		0			0
$713$	9408.19	−	9408.19i	0.494165	−	0.494165i
$714$		0			0
$715$	2241.23	−	1035.91i	0.117227	−	0.0541832i
$716$		0			0
$717$	−18592.3	−	18592.3i	−0.968399	−	0.968399i
$718$		0			0
$719$	12602.2			0.653661			0.326830	−	0.945083i	$-0.394019\pi$
$719$	12602.2			0.653661			0.326830	+	0.945083i	$0.394019\pi$
$720$		0			0
$721$	−46121.5			−2.38232
$722$		0			0
$723$	1641.68	+	1641.68i	0.0844464	+	0.0844464i
$724$		0			0
$725$	−4640.47	+	5455.15i	−0.237714	+	0.279447i
$726$		0			0
$727$	18428.4	−	18428.4i	0.940125	−	0.940125i	−0.0581809	−	0.998306i	$-0.518530\pi$
$727$	18428.4	−	18428.4i	0.940125	−	0.940125i	0.998306	+	0.0581809i	$0.0185300\pi$
$728$		0			0
$729$			28975.1i			1.47209i
$730$		0			0
$731$		−	12443.0i		−	0.629579i
$732$		0			0
$733$	−21332.0	+	21332.0i	−1.07492	+	1.07492i	−0.0779625	+	0.996956i	$0.524841\pi$
$733$	−21332.0	+	21332.0i	−1.07492	+	1.07492i	−0.996956	+	0.0779625i	$0.975159\pi$
$734$		0			0
$735$	−35898.3	−	77666.8i	−1.80153	−	3.89767i
$736$		0			0
$737$	3576.34	+	3576.34i	0.178747	+	0.178747i
$738$		0			0
$739$	8156.48			0.406009			0.203005	−	0.979178i	$-0.434929\pi$
$739$	8156.48			0.406009			0.203005	+	0.979178i	$0.434929\pi$
$740$		0			0
$741$	2927.96			0.145157
$742$		0			0
$743$	−11951.4	−	11951.4i	−0.590115	−	0.590115i	0.347548	−	0.937662i	$-0.387015\pi$
$743$	−11951.4	−	11951.4i	−0.590115	−	0.590115i	−0.937662	+	0.347548i	$0.887015\pi$
$744$		0			0
$745$	7192.29	+	2645.28i	0.353698	+	0.130088i
$746$		0			0
$747$	−13852.7	+	13852.7i	−0.678504	+	0.678504i
$748$		0			0
$749$			32034.8i			1.56279i
$750$		0			0
$751$		−	24042.3i		−	1.16820i	−0.811683	−	0.584098i	$-0.801449\pi$
$751$		−	24042.3i		−	1.16820i	0.811683	−	0.584098i	$-0.198551\pi$
$752$		0			0
$753$	24330.2	−	24330.2i	1.17748	−	1.17748i
$754$		0			0
$755$	−10268.7	−	3776.77i	−0.494989	−	0.182054i
$756$		0			0
$757$	19323.8	+	19323.8i	0.927787	+	0.927787i	0.997563	−	0.0697761i	$-0.0222285\pi$
$757$	19323.8	+	19323.8i	0.927787	+	0.927787i	−0.0697761	+	0.997563i	$0.522228\pi$
$758$		0			0
$759$	−20116.2			−0.962020
$760$		0			0
$761$	18554.7			0.883848			0.441924	−	0.897052i	$-0.354296\pi$
$761$	18554.7			0.883848			0.441924	+	0.897052i	$0.354296\pi$
$762$		0			0
$763$	−18926.0	−	18926.0i	−0.897992	−	0.897992i
$764$		0			0
$765$	13515.3	+	29240.7i	0.638754	+	1.38196i
$766$		0			0
$767$	−1079.02	+	1079.02i	−0.0507970	+	0.0507970i
$768$		0			0
$769$		−	12128.1i		−	0.568728i	−0.958716	−	0.284364i	$-0.908218\pi$
$769$		−	12128.1i		−	0.568728i	0.958716	−	0.284364i	$-0.0917824\pi$
$770$		0			0
$771$		−	36367.1i		−	1.69874i
$772$		0			0
$773$	708.645	−	708.645i	0.0329731	−	0.0329731i	−0.690428	−	0.723401i	$-0.742578\pi$
$773$	708.645	−	708.645i	0.0329731	−	0.0329731i	0.723401	+	0.690428i	$0.242578\pi$
$774$		0			0
$775$	−18528.5	+	21781.3i	−0.858790	+	1.00956i
$776$		0			0
$777$	−70257.7	−	70257.7i	−3.24386	−	3.24386i
$778$		0			0
$779$	4769.32			0.219356
$780$		0			0
$781$	11659.1			0.534183
$782$		0			0
$783$	7430.44	+	7430.44i	0.339135	+	0.339135i
$784$		0			0
$785$	−609.302	+	281.624i	−0.0277031	+	0.0128046i
$786$		0			0
$787$	−17551.1	+	17551.1i	−0.794952	+	0.794952i	−0.982295	−	0.187342i	$-0.940013\pi$
$787$	−17551.1	+	17551.1i	−0.794952	+	0.794952i	0.187342	+	0.982295i	$0.440013\pi$
$788$		0			0
$789$		−	35987.2i		−	1.62380i
$790$		0			0
$791$			80271.2i			3.60824i
$792$		0			0
$793$	−1261.07	+	1261.07i	−0.0564716	+	0.0564716i
$794$		0			0
$795$	6287.09	−	17094.1i	0.280478	−	0.762596i
$796$		0			0
$797$	−6146.22	−	6146.22i	−0.273162	−	0.273162i	0.557210	−	0.830372i	$-0.311872\pi$
$797$	−6146.22	−	6146.22i	−0.273162	−	0.273162i	−0.830372	+	0.557210i	$0.811872\pi$
$798$		0			0
$799$	2941.10			0.130223
$800$		0			0
$801$	22714.9			1.00199
$802$		0			0
$803$	11955.9	+	11955.9i	0.525421	+	0.525421i
$804$		0			0
$805$	−7858.49	+	21366.5i	−0.344069	+	0.935493i
$806$		0			0
$807$	45992.6	−	45992.6i	2.00621	−	2.00621i
$808$		0			0
$809$		−	19731.6i		−	0.857512i	−0.903420	−	0.428756i	$-0.858952\pi$
$809$		−	19731.6i		−	0.857512i	0.903420	−	0.428756i	$-0.141048\pi$
$810$		0			0
$811$			14471.4i			0.626584i	0.949657	+	0.313292i	$0.101432\pi$
$811$			14471.4i			0.626584i	−0.949657	+	0.313292i	$0.898568\pi$
$812$		0			0
$813$	36041.2	−	36041.2i	1.55476	−	1.55476i
$814$		0			0
$815$	−31994.4	+	14788.1i	−1.37511	+	0.635588i
$816$		0			0
$817$	−8972.86	−	8972.86i	−0.384236	−	0.384236i
$818$		0			0
$819$	−9332.30			−0.398165
$820$		0			0
$821$	−2871.85			−0.122080			−0.0610402	−	0.998135i	$-0.519442\pi$
$821$	−2871.85			−0.122080			−0.0610402	+	0.998135i	$0.519442\pi$
$822$		0			0
$823$	−18286.4	−	18286.4i	−0.774514	−	0.774514i	0.204378	−	0.978892i	$-0.434483\pi$
$823$	−18286.4	−	18286.4i	−0.774514	−	0.774514i	−0.978892	+	0.204378i	$0.934483\pi$
$824$		0			0
$825$	43094.4	−	3477.56i	1.81861	−	0.146755i
$826$		0			0
$827$	5489.70	−	5489.70i	0.230829	−	0.230829i	−0.582210	−	0.813039i	$-0.697812\pi$
$827$	5489.70	−	5489.70i	0.230829	−	0.230829i	0.813039	+	0.582210i	$0.197812\pi$
$828$		0			0
$829$		−	29539.6i		−	1.23758i	−0.785556	−	0.618790i	$-0.787623\pi$
$829$		−	29539.6i		−	1.23758i	0.785556	−	0.618790i	$-0.212377\pi$
$830$		0			0
$831$			46511.9i			1.94161i
$832$		0			0
$833$	37347.1	−	37347.1i	1.55342	−	1.55342i
$834$		0			0
$835$	15539.0	+	33619.0i	0.644010	+	1.39333i
$836$		0			0
$837$	29668.3	+	29668.3i	1.22519	+	1.22519i
$838$		0			0
$839$	20156.2			0.829402			0.414701	−	0.909958i	$-0.363886\pi$
$839$	20156.2			0.829402			0.414701	+	0.909958i	$0.363886\pi$
$840$		0			0
$841$	21106.3			0.865401
$842$		0			0
$843$	−44435.8	−	44435.8i	−1.81548	−	1.81548i
$844$		0			0
$845$	22731.9	+	8360.66i	0.925445	+	0.340373i
$846$		0			0
$847$	6455.52	−	6455.52i	0.261882	−	0.261882i
$848$		0			0
$849$			75748.0i			3.06203i
$850$		0			0
$851$			19039.3i			0.766931i
$852$		0			0
$853$	−27083.5	+	27083.5i	−1.08713	+	1.08713i	−0.0913059	+	0.995823i	$0.529104\pi$
$853$	−27083.5	+	27083.5i	−1.08713	+	1.08713i	−0.995823	+	0.0913059i	$0.970896\pi$
$854$		0			0
$855$	30832.0	+	11339.8i	1.23325	+	0.453584i
$856$		0			0
$857$	15103.3	+	15103.3i	0.602006	+	0.602006i	0.940844	−	0.338839i	$-0.110034\pi$
$857$	15103.3	+	15103.3i	0.602006	+	0.602006i	−0.338839	+	0.940844i	$0.610034\pi$
$858$		0			0
$859$	4377.87			0.173890			0.0869448	−	0.996213i	$-0.472290\pi$
$859$	4377.87			0.173890			0.0869448	+	0.996213i	$0.472290\pi$
$860$		0			0
$861$	−23724.3			−0.939048
$862$		0			0
$863$	−22079.6	−	22079.6i	−0.870913	−	0.870913i	0.121659	−	0.992572i	$-0.461179\pi$
$863$	−22079.6	−	22079.6i	−0.870913	−	0.870913i	−0.992572	+	0.121659i	$0.961179\pi$
$864$		0			0
$865$	−6536.31	−	14141.5i	−0.256926	−	0.555867i
$866$		0			0
$867$	8172.73	−	8172.73i	0.320139	−	0.320139i
$868$		0			0
$869$			9067.77i			0.353974i
$870$		0			0
$871$		−	701.700i		−	0.0272976i
$872$		0			0
$873$	−57810.7	+	57810.7i	−2.24123	+	2.24123i
$874$		0			0
$875$	13141.3	−	47131.4i	0.507722	−	1.82095i
$876$		0			0
$877$	26079.5	+	26079.5i	1.00415	+	1.00415i	0.999991	+	0.00416334i	$0.00132523\pi$
$877$	26079.5	+	26079.5i	1.00415	+	1.00415i	0.00416334	+	0.999991i	$0.498675\pi$
$878$		0			0
$879$	−60498.2			−2.32145
$880$		0			0
$881$	30018.3			1.14795			0.573975	−	0.818873i	$-0.305401\pi$
$881$	30018.3			1.14795			0.573975	+	0.818873i	$0.305401\pi$
$882$		0			0
$883$	29541.6	+	29541.6i	1.12588	+	1.12588i	0.990840	+	0.135043i	$0.0431173\pi$
$883$	29541.6	+	29541.6i	1.12588	+	1.12588i	0.135043	+	0.990840i	$0.456883\pi$
$884$		0			0
$885$	−24255.0	+	11210.9i	−0.921270	+	0.425819i
$886$		0			0
$887$	−4219.79	+	4219.79i	−0.159737	+	0.159737i	−0.782450	−	0.622713i	$-0.786030\pi$
$887$	−4219.79	+	4219.79i	−0.159737	+	0.159737i	0.622713	+	0.782450i	$0.286030\pi$
$888$		0			0
$889$		−	33547.9i		−	1.26565i
$890$		0			0
$891$		−	11561.3i		−	0.434699i
$892$		0			0
$893$	2120.87	−	2120.87i	0.0794761	−	0.0794761i
$894$		0			0
$895$	−9414.12	+	25596.2i	−0.351597	+	0.955962i
$896$		0			0
$897$	1973.46	+	1973.46i	0.0734582	+	0.0734582i
$898$		0			0
$899$	−13107.3			−0.486265
$900$		0			0
$901$	11243.1			0.415719
$902$		0			0
$903$	44634.2	+	44634.2i	1.64489	+	1.64489i
$904$		0			0
$905$	−10122.6	+	27522.3i	−0.371807	+	1.01091i
$906$		0			0
$907$	25632.3	−	25632.3i	0.938375	−	0.938375i	−0.0598338	−	0.998208i	$-0.519057\pi$
$907$	25632.3	−	25632.3i	0.938375	−	0.938375i	0.998208	+	0.0598338i	$0.0190571\pi$
$908$		0			0
$909$		−	36954.5i		−	1.34841i
$910$		0			0
$911$		−	36817.7i		−	1.33900i	−0.742814	−	0.669498i	$-0.766509\pi$
$911$		−	36817.7i		−	1.33900i	0.742814	−	0.669498i	$-0.233491\pi$
$912$		0			0
$913$	−11476.9	+	11476.9i	−0.416023	+	0.416023i
$914$		0			0
$915$	−28347.2	+	13102.3i	−1.02419	+	0.473388i
$916$		0			0
$917$	−60790.7	−	60790.7i	−2.18919	−	2.18919i
$918$		0			0
$919$	35594.4			1.27764			0.638820	−	0.769356i	$-0.279423\pi$
$919$	35594.4			1.27764			0.638820	+	0.769356i	$0.279423\pi$
$920$		0			0
$921$	−6180.45			−0.221121
$922$		0			0
$923$	−1143.80	−	1143.80i	−0.0407893	−	0.0407893i
$924$		0			0
$925$	−3291.39	−	40787.3i	−0.116995	−	1.44981i
$926$		0			0
$927$	−44857.4	+	44857.4i	−1.58933	+	1.58933i
$928$		0			0
$929$			8332.43i			0.294271i	0.989116	+	0.147136i	$0.0470054\pi$
$929$			8332.43i			0.294271i	−0.989116	+	0.147136i	$0.952995\pi$
$930$		0			0
$931$		−	53863.1i		−	1.89613i
$932$		0			0
$933$	4243.71	−	4243.71i	0.148910	−	0.148910i
$934$		0			0
$935$	11197.4	+	24225.8i	0.391650	+	0.847346i
$936$		0			0
$937$	12357.6	+	12357.6i	0.430850	+	0.430850i	0.888917	−	0.458068i	$-0.151458\pi$
$937$	12357.6	+	12357.6i	0.430850	+	0.430850i	−0.458068	+	0.888917i	$0.651458\pi$
$938$		0			0
$939$	−3608.24			−0.125400
$940$		0			0
$941$	−27699.9			−0.959609			−0.479805	−	0.877375i	$-0.659292\pi$
$941$	−27699.9			−0.959609			−0.479805	+	0.877375i	$0.659292\pi$
$942$		0			0
$943$	3214.54	+	3214.54i	0.111007	+	0.111007i
$944$		0			0
$945$	−67378.3	−	24781.3i	−2.31938	−	0.853055i
$946$		0			0
$947$	−22168.8	+	22168.8i	−0.760707	+	0.760707i	−0.976450	−	0.215744i	$-0.930782\pi$
$947$	−22168.8	+	22168.8i	−0.760707	+	0.760707i	0.215744	+	0.976450i	$0.430782\pi$
$948$		0			0
$949$		−	2345.81i		−	0.0802406i
$950$		0			0
$951$		−	4582.50i		−	0.156254i
$952$		0			0
$953$	−38765.3	+	38765.3i	−1.31766	+	1.31766i	−0.402040	+	0.915622i	$0.631699\pi$
$953$	−38765.3	+	38765.3i	−1.31766	+	1.31766i	−0.915622	+	0.402040i	$0.868301\pi$
$954$		0			0
$955$	30266.3	+	11131.8i	1.02555	+	0.377189i
$956$		0			0
$957$	14012.7	+	14012.7i	0.473320	+	0.473320i
$958$		0			0
$959$	92231.0			3.10563
$960$		0			0
$961$	−22543.7			−0.756729
$962$		0			0
$963$	31156.8	+	31156.8i	1.04259	+	1.04259i
$964$		0			0
$965$	−9604.51	−	20779.6i	−0.320394	−	0.693180i
$966$		0			0
$967$	−15823.6	+	15823.6i	−0.526217	+	0.526217i	−0.919442	−	0.393225i	$-0.871359\pi$
$967$	−15823.6	+	15823.6i	−0.526217	+	0.526217i	0.393225	+	0.919442i	$0.371359\pi$
$968$		0			0
$969$			31648.8i			1.04923i
$970$		0			0
$971$		−	27275.7i		−	0.901462i	−0.892660	−	0.450731i	$-0.851163\pi$
$971$		−	27275.7i		−	0.901462i	0.892660	−	0.450731i	$-0.148837\pi$
$972$		0			0
$973$	−37200.8	+	37200.8i	−1.22570	+	1.22570i
$974$		0			0
$975$	−4568.85	−	3886.53i	−0.150072	−	0.127660i
$976$		0			0
$977$	−11792.8	−	11792.8i	−0.386167	−	0.386167i	0.487151	−	0.873318i	$-0.338036\pi$
$977$	−11792.8	−	11792.8i	−0.386167	−	0.386167i	−0.873318	+	0.487151i	$0.838036\pi$
$978$		0			0
$979$	18819.2			0.614365
$980$		0			0
$981$	−36814.6			−1.19817
$982$		0			0
$983$	−8795.96	−	8795.96i	−0.285399	−	0.285399i	0.549859	−	0.835258i	$-0.314682\pi$
$983$	−8795.96	−	8795.96i	−0.285399	−	0.285399i	−0.835258	+	0.549859i	$0.814682\pi$
$984$		0			0
$985$	36804.7	−	17011.4i	1.19055	−	0.550284i
$986$		0			0
$987$	−10550.0	+	10550.0i	−0.340232	+	0.340232i
$988$		0			0
$989$		−	12095.5i		−	0.388893i
$990$		0			0
$991$		−	4679.64i		−	0.150004i	−0.997183	−	0.0750019i	$-0.976104\pi$
$991$		−	4679.64i		−	0.150004i	0.997183	−	0.0750019i	$-0.0238963\pi$
$992$		0			0
$993$	17525.8	−	17525.8i	0.560085	−	0.560085i
$994$		0			0
$995$	6638.65	−	18049.9i	0.211517	−	0.575097i
$996$		0			0
$997$	9376.75	+	9376.75i	0.297858	+	0.297858i	0.840174	−	0.542316i	$-0.182453\pi$
$997$	9376.75	+	9376.75i	0.297858	+	0.297858i	−0.542316	+	0.840174i	$0.682453\pi$
$998$		0			0
$999$	−60039.4			−1.90146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.n.c.127.4	yes	8
4.3	odd	2		160.4.n.f.127.1	yes	8
5.3	odd	4		160.4.n.f.63.1	yes	8
8.3	odd	2		320.4.n.f.127.4		8
8.5	even	2		320.4.n.i.127.1		8
20.3	even	4	inner	160.4.n.c.63.4	✓	8
40.3	even	4		320.4.n.i.63.1		8
40.13	odd	4		320.4.n.f.63.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.c.63.4	✓	8	20.3	even	4	inner
160.4.n.c.127.4	yes	8	1.1	even	1	trivial
160.4.n.f.63.1	yes	8	5.3	odd	4
160.4.n.f.127.1	yes	8	4.3	odd	2
320.4.n.f.63.4		8	40.13	odd	4
320.4.n.f.127.4		8	8.3	odd	2
320.4.n.i.63.1		8	40.3	even	4
320.4.n.i.127.1		8	8.5	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.13008 + 6.13008i) q^{3} +(3.85931 - 10.4931i) q^{5} +(-24.7564 + 24.7564i) q^{7} +48.1559i q^{9} +39.8969i q^{11} +(3.91401 - 3.91401i) q^{13} +(87.9816 - 40.6659i) q^{15} +(42.3071 + 42.3071i) q^{17} +61.0166 q^{19} -303.518 q^{21} +(41.1255 + 41.1255i) q^{23} +(-95.2115 - 80.9924i) q^{25} +(-129.687 + 129.687i) q^{27} -57.2951i q^{29} -228.768i q^{31} +(-244.571 + 244.571i) q^{33} +(164.230 + 355.315i) q^{35} +(231.478 + 231.478i) q^{37} +47.9864 q^{39} +78.1643 q^{41} +(-147.056 - 147.056i) q^{43} +(505.306 + 185.848i) q^{45} +(34.7589 - 34.7589i) q^{47} -882.762i q^{49} +518.692i q^{51} +(132.875 - 132.875i) q^{53} +(418.643 + 153.974i) q^{55} +(374.037 + 374.037i) q^{57} -275.683 q^{59} -322.195 q^{61} +(-1192.17 - 1192.17i) q^{63} +(-25.9648 - 56.1755i) q^{65} +(89.6397 - 89.6397i) q^{67} +504.206i q^{69} -292.232i q^{71} +(299.669 - 299.669i) q^{73} +(-87.1638 - 1080.14i) q^{75} +(-987.704 - 987.704i) q^{77} +227.280 q^{79} -289.778 q^{81} +(287.663 + 287.663i) q^{83} +(607.210 - 280.658i) q^{85} +(351.224 - 351.224i) q^{87} -471.695i q^{89} +193.794i q^{91} +(1402.37 - 1402.37i) q^{93} +(235.482 - 640.255i) q^{95} +(1200.49 + 1200.49i) q^{97} -1921.27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 6 q^{5} - 70 q^{7} + 144 q^{13} + 134 q^{15} - 100 q^{17} - 176 q^{19} - 516 q^{21} + 198 q^{23} - 172 q^{25} + 288 q^{27} + 172 q^{33} - 170 q^{35} + 492 q^{37} - 756 q^{39} - 28 q^{41}+ \cdots - 8412 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 6 * q^5 - 70 * q^7 + 144 * q^13 + 134 * q^15 - 100 * q^17 - 176 * q^19 - 516 * q^21 + 198 * q^23 - 172 * q^25 + 288 * q^27 + 172 * q^33 - 170 * q^35 + 492 * q^37 - 756 * q^39 - 28 * q^41 - 654 * q^43 + 10 * q^45 + 690 * q^47 + 580 * q^53 + 2392 * q^55 - 248 * q^57 - 1808 * q^59 - 1068 * q^61 - 3106 * q^63 + 2200 * q^65 + 1878 * q^67 + 1952 * q^73 + 2178 * q^75 + 340 * q^77 + 1808 * q^79 - 7844 * q^81 + 506 * q^83 + 184 * q^85 - 784 * q^87 + 3708 * q^93 + 5800 * q^95 + 5576 * q^97 - 8412 * q^99

Introduction

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