LMFDB - Embedded newform 240.4.v.c.113.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,4,Mod(17,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.17"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	240.v (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.1604584014$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.2
Root			$-1.18766 + 1.18766i$ of defining polynomial
Character	$\chi$	$=$	240.113
Dual form			240.4.v.c.17.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.932827 - 5.11173i) q^{3} +(2.48157 - 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(-25.2597 - 9.53673i) q^{9} -28.7164i q^{11} +(14.1789 + 14.1789i) q^{13} +(-53.4105 - 22.8543i) q^{15} +(18.5587 + 18.5587i) q^{17} +49.0735i q^{19} +(-55.8211 - 80.7421i) q^{21} +(37.7738 - 37.7738i) q^{23} +(-112.684 - 54.1055i) q^{25} +(-72.3121 + 120.225i) q^{27} +125.854 q^{29} -247.367 q^{31} +(-146.791 - 26.7874i) q^{33} +(-112.471 - 178.768i) q^{35} +(-127.463 + 127.463i) q^{37} +(85.7053 - 59.2524i) q^{39} -390.328i q^{41} +(39.3993 + 39.3993i) q^{43} +(-166.648 + 251.701i) q^{45} +(-124.560 - 124.560i) q^{47} -13.8625i q^{49} +(112.179 - 77.5549i) q^{51} +(-160.441 + 160.441i) q^{53} +(-313.051 - 71.2618i) q^{55} +(250.850 + 45.7770i) q^{57} +729.423 q^{59} +2.00000 q^{61} +(-464.804 + 210.024i) q^{63} +(189.757 - 119.385i) q^{65} +(329.987 - 329.987i) q^{67} +(-157.853 - 228.326i) q^{69} -171.760i q^{71} +(-279.927 - 279.927i) q^{73} +(-381.687 + 525.538i) q^{75} +(-383.589 - 383.589i) q^{77} +48.0189i q^{79} +(547.102 + 481.789i) q^{81} +(-144.451 + 144.451i) q^{83} +(248.371 - 156.262i) q^{85} +(117.400 - 643.334i) q^{87} +1417.21 q^{89} +378.799 q^{91} +(-230.751 + 1264.48i) q^{93} +(534.972 + 121.779i) q^{95} +(908.111 - 908.111i) q^{97} +(-273.861 + 725.367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 16 q^{7} + 68 q^{13} - 90 q^{15} - 492 q^{21} - 220 q^{25} - 702 q^{27} - 616 q^{31} - 240 q^{33} - 1156 q^{37} - 548 q^{43} + 180 q^{45} + 852 q^{51} - 460 q^{55} + 684 q^{57} + 16 q^{61}+ \cdots + 1904 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 + 16 * q^7 + 68 * q^13 - 90 * q^15 - 492 * q^21 - 220 * q^25 - 702 * q^27 - 616 * q^31 - 240 * q^33 - 1156 * q^37 - 548 * q^43 + 180 * q^45 + 852 * q^51 - 460 * q^55 + 684 * q^57 + 16 * q^61 - 1428 * q^63 - 404 * q^67 - 2512 * q^73 + 2910 * q^75 + 288 * q^81 + 4940 * q^85 + 1680 * q^87 + 1304 * q^91 + 3408 * q^93 + 1904 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.932827	−	5.11173i	0.179523	−	0.983754i
$3$	0.932827	−	5.11173i	0.179523	−	0.983754i
$4$		0			0
$5$	2.48157	−	10.9015i	0.221958	−	0.975056i
$5$	2.48157	−	10.9015i	0.221958	−	0.975056i
$6$		0			0
$7$	13.3578	−	13.3578i	0.721254	−	0.721254i	−0.247606	−	0.968861i	$-0.579644\pi$
$7$	13.3578	−	13.3578i	0.721254	−	0.721254i	0.968861	+	0.247606i	$0.0796440\pi$
$8$		0			0
$9$	−25.2597	−	9.53673i	−0.935543	−	0.353212i
$10$		0			0
$11$		−	28.7164i		−	0.787121i	−0.919299	−	0.393560i	$-0.871243\pi$
$11$		−	28.7164i		−	0.787121i	0.919299	−	0.393560i	$-0.128757\pi$
$12$		0			0
$13$	14.1789	+	14.1789i	0.302502	+	0.302502i	0.841992	−	0.539490i	$-0.181383\pi$
$13$	14.1789	+	14.1789i	0.302502	+	0.302502i	−0.539490	+	0.841992i	$0.681383\pi$
$14$		0			0
$15$	−53.4105	−	22.8543i	−0.919369	−	0.393397i
$16$		0			0
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	0.826990	−	0.562217i	$-0.190051\pi$
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	−0.562217	+	0.826990i	$0.690051\pi$
$18$		0			0
$19$			49.0735i			0.592538i	0.955105	+	0.296269i	$0.0957425\pi$
$19$			49.0735i			0.592538i	−0.955105	+	0.296269i	$0.904258\pi$
$20$		0			0
$21$	−55.8211	−	80.7421i	−0.580055	−	0.839018i
$22$		0			0
$23$	37.7738	−	37.7738i	0.342451	−	0.342451i	−0.514837	−	0.857288i	$-0.672148\pi$
$23$	37.7738	−	37.7738i	0.342451	−	0.342451i	0.857288	+	0.514837i	$0.172148\pi$
$24$		0			0
$25$	−112.684	−	54.1055i	−0.901469	−	0.432844i
$26$		0			0
$27$	−72.3121	+	120.225i	−0.515425	+	0.856935i
$28$		0			0
$29$	125.854			0.805882			0.402941	−	0.915226i	$-0.367988\pi$
$29$	125.854			0.805882			0.402941	+	0.915226i	$0.367988\pi$
$30$		0			0
$31$	−247.367			−1.43318			−0.716588	−	0.697496i	$-0.754297\pi$
$31$	−247.367			−1.43318			−0.716588	+	0.697496i	$0.754297\pi$
$32$		0			0
$33$	−146.791	−	26.7874i	−0.774333	−	0.141306i
$34$		0			0
$35$	−112.471	−	178.768i	−0.543175	−	0.863352i
$36$		0			0
$37$	−127.463	+	127.463i	−0.566347	+	0.566347i	−0.931103	−	0.364756i	$-0.881152\pi$
$37$	−127.463	+	127.463i	−0.566347	+	0.566347i	0.364756	+	0.931103i	$0.381152\pi$
$38$		0			0
$39$	85.7053	−	59.2524i	0.351893	−	0.243281i
$40$		0			0
$41$		−	390.328i		−	1.48680i	−0.668845	−	0.743402i	$-0.733211\pi$
$41$		−	390.328i		−	1.48680i	0.668845	−	0.743402i	$-0.266789\pi$
$42$		0			0
$43$	39.3993	+	39.3993i	0.139729	+	0.139729i	0.773511	−	0.633783i	$-0.218499\pi$
$43$	39.3993	+	39.3993i	0.139729	+	0.139729i	−0.633783	+	0.773511i	$0.718499\pi$
$44$		0			0
$45$	−166.648	+	251.701i	−0.552053	+	0.833809i
$46$		0			0
$47$	−124.560	−	124.560i	−0.386575	−	0.386575i	0.486889	−	0.873464i	$-0.338132\pi$
$47$	−124.560	−	124.560i	−0.386575	−	0.386575i	−0.873464	+	0.486889i	$0.838132\pi$
$48$		0			0
$49$		−	13.8625i		−	0.0404155i
$50$		0			0
$51$	112.179	−	77.5549i	0.308004	−	0.212938i
$52$		0			0
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	−0.883759	−	0.467943i	$-0.844995\pi$
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	0.467943	+	0.883759i	$0.344995\pi$
$54$		0			0
$55$	−313.051	−	71.2618i	−0.767487	−	0.174708i
$56$		0			0
$57$	250.850	+	45.7770i	0.582912	+	0.106374i
$58$		0			0
$59$	729.423			1.60954			0.804769	−	0.593588i	$-0.202289\pi$
$59$	729.423			1.60954			0.804769	+	0.593588i	$0.202289\pi$
$60$		0			0
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$		0			0
$63$	−464.804	+	210.024i	−0.929520	+	0.420009i
$64$		0			0
$65$	189.757	−	119.385i	0.362099	−	0.227813i
$66$		0			0
$67$	329.987	−	329.987i	0.601706	−	0.601706i	−0.339059	−	0.940765i	$-0.610109\pi$
$67$	329.987	−	329.987i	0.601706	−	0.601706i	0.940765	+	0.339059i	$0.110109\pi$
$68$		0			0
$69$	−157.853	−	228.326i	−0.275410	−	0.398365i
$70$		0			0
$71$		−	171.760i		−	0.287100i	−0.989643	−	0.143550i	$-0.954148\pi$
$71$		−	171.760i		−	0.287100i	0.989643	−	0.143550i	$-0.0458518\pi$
$72$		0			0
$73$	−279.927	−	279.927i	−0.448807	−	0.448807i	0.446151	−	0.894958i	$-0.352795\pi$
$73$	−279.927	−	279.927i	−0.448807	−	0.448807i	−0.894958	+	0.446151i	$0.852795\pi$
$74$		0			0
$75$	−381.687	+	525.538i	−0.587646	+	0.809118i
$76$		0			0
$77$	−383.589	−	383.589i	−0.567714	−	0.567714i
$78$		0			0
$79$			48.0189i			0.0683866i	0.999415	+	0.0341933i	$0.0108862\pi$
$79$			48.0189i			0.0683866i	−0.999415	+	0.0341933i	$0.989114\pi$
$80$		0			0
$81$	547.102	+	481.789i	0.750483	+	0.660890i
$82$		0			0
$83$	−144.451	+	144.451i	−0.191031	+	0.191031i	−0.796141	−	0.605111i	$-0.793129\pi$
$83$	−144.451	+	144.451i	−0.191031	+	0.191031i	0.605111	+	0.796141i	$0.293129\pi$
$84$		0			0
$85$	248.371	−	156.262i	0.316937	−	0.199400i
$86$		0			0
$87$	117.400	−	643.334i	0.144674	−	0.792789i
$88$		0			0
$89$	1417.21			1.68790			0.843952	−	0.536419i	$-0.180223\pi$
$89$	1417.21			1.68790			0.843952	+	0.536419i	$0.180223\pi$
$90$		0			0
$91$	378.799			0.436361
$92$		0			0
$93$	−230.751	+	1264.48i	−0.257288	+	1.40989i
$94$		0			0
$95$	534.972	+	121.779i	0.577758	+	0.131519i
$96$		0			0
$97$	908.111	−	908.111i	0.950564	−	0.950564i	−0.0482702	−	0.998834i	$-0.515371\pi$
$97$	908.111	−	908.111i	0.950564	−	0.950564i	0.998834	+	0.0482702i	$0.0153708\pi$
$98$		0			0
$99$	−273.861	+	725.367i	−0.278020	+	0.736385i
$100$		0			0
$101$		−	337.668i		−	0.332665i	−0.986070	−	0.166333i	$-0.946807\pi$
$101$		−	337.668i		−	0.332665i	0.986070	−	0.166333i	$-0.0531926\pi$
$102$		0			0
$103$	933.505	+	933.505i	0.893019	+	0.893019i	0.994806	−	0.101787i	$-0.0324561\pi$
$103$	933.505	+	933.505i	0.893019	+	0.893019i	−0.101787	+	0.994806i	$0.532456\pi$
$104$		0			0
$105$	−1018.73	+	408.164i	−0.946838	+	0.379359i
$106$		0			0
$107$	596.188	+	596.188i	0.538651	+	0.538651i	0.923133	−	0.384481i	$-0.125620\pi$
$107$	596.188	+	596.188i	0.538651	+	0.538651i	−0.384481	+	0.923133i	$0.625620\pi$
$108$		0			0
$109$			2074.60i			1.82303i	0.411264	+	0.911516i	$0.365087\pi$
$109$			2074.60i			1.82303i	−0.411264	+	0.911516i	$0.634913\pi$
$110$		0			0
$111$	532.657	+	770.460i	0.455474	+	0.658818i
$112$		0			0
$113$	271.193	−	271.193i	0.225767	−	0.225767i	−0.585154	−	0.810922i	$-0.698966\pi$
$113$	271.193	−	271.193i	0.225767	−	0.225767i	0.810922	+	0.585154i	$0.198966\pi$
$114$		0			0
$115$	−318.051	−	505.527i	−0.257899	−	0.409919i
$116$		0			0
$117$	−222.934	−	493.375i	−0.176156	−	0.389851i
$118$		0			0
$119$	495.806			0.381937
$120$		0			0
$121$	506.367			0.380441
$122$		0			0
$123$	−1995.25	−	364.108i	−1.46265	−	0.266915i
$124$		0			0
$125$	−869.461	+	1094.15i	−0.622135	+	0.782910i
$126$		0			0
$127$	−105.588	+	105.588i	−0.0737747	+	0.0737747i	−0.743031	−	0.669257i	$-0.766613\pi$
$127$	−105.588	+	105.588i	−0.0737747	+	0.0737747i	0.669257	+	0.743031i	$0.266613\pi$
$128$		0			0
$129$	238.151	−	164.646i	0.162543	−	0.112374i
$130$		0			0
$131$		−	1979.28i		−	1.32008i	−0.751231	−	0.660039i	$-0.770540\pi$
$131$		−	1979.28i		−	1.32008i	0.751231	−	0.660039i	$-0.229460\pi$
$132$		0			0
$133$	655.514	+	655.514i	0.427371	+	0.427371i
$134$		0			0
$135$	1131.18	+	1086.65i	0.721157	+	0.692772i
$136$		0			0
$137$	507.451	+	507.451i	0.316456	+	0.316456i	0.847404	−	0.530948i	$-0.178164\pi$
$137$	507.451	+	507.451i	0.316456	+	0.316456i	−0.530948	+	0.847404i	$0.678164\pi$
$138$		0			0
$139$			68.4333i			0.0417585i	0.999782	+	0.0208793i	$0.00664656\pi$
$139$			68.4333i			0.0417585i	−0.999782	+	0.0208793i	$0.993353\pi$
$140$		0			0
$141$	−752.913	+	520.527i	−0.449693	+	0.310895i
$142$		0			0
$143$	407.167	−	407.167i	0.238105	−	0.238105i
$144$		0			0
$145$	312.316	−	1372.00i	0.178872	−	0.785780i
$146$		0			0
$147$	−70.8616	−	12.9313i	−0.0397590	−	0.00725550i
$148$		0			0
$149$	363.356			0.199780			0.0998902	−	0.994998i	$-0.468151\pi$
$149$	363.356			0.199780			0.0998902	+	0.994998i	$0.468151\pi$
$150$		0			0
$151$	2083.14			1.12267			0.561337	−	0.827588i	$-0.310287\pi$
$151$	2083.14			1.12267			0.561337	+	0.827588i	$0.310287\pi$
$152$		0			0
$153$	−291.797	−	645.774i	−0.154185	−	0.341227i
$154$		0			0
$155$	−613.859	+	2696.66i	−0.318105	+	1.39743i
$156$		0			0
$157$	−1208.52	+	1208.52i	−0.614333	+	0.614333i	−0.944072	−	0.329739i	$-0.893039\pi$
$157$	−1208.52	+	1208.52i	−0.614333	+	0.614333i	0.329739	+	0.944072i	$0.393039\pi$
$158$		0			0
$159$	670.468	+	969.795i	0.334412	+	0.483709i
$160$		0			0
$161$		−	1009.15i		−	0.493989i
$162$		0			0
$163$	−626.062	−	626.062i	−0.300840	−	0.300840i	0.540502	−	0.841343i	$-0.318234\pi$
$163$	−626.062	−	626.062i	−0.300840	−	0.300840i	−0.841343	+	0.540502i	$0.818234\pi$
$164$		0			0
$165$	−656.294	+	1533.76i	−0.309651	+	0.723654i
$166$		0			0
$167$	−3009.65	−	3009.65i	−1.39457	−	1.39457i	−0.814724	−	0.579848i	$-0.803112\pi$
$167$	−3009.65	−	3009.65i	−1.39457	−	1.39457i	−0.579848	−	0.814724i	$-0.696888\pi$
$168$		0			0
$169$		−	1794.92i		−	0.816985i
$170$		0			0
$171$	468.000	−	1239.58i	0.209292	−	0.554345i
$172$		0			0
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	−0.176086	−	0.984375i	$-0.556344\pi$
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	0.984375	+	0.176086i	$0.0563438\pi$
$174$		0			0
$175$	−2227.94	+	782.476i	−0.962379	+	0.337998i
$176$		0			0
$177$	680.425	−	3728.61i	0.288948	−	1.58339i
$178$		0			0
$179$	821.582			0.343061			0.171530	−	0.985179i	$-0.445129\pi$
$179$	821.582			0.343061			0.171530	+	0.985179i	$0.445129\pi$
$180$		0			0
$181$	2314.20			0.950350			0.475175	−	0.879891i	$-0.342385\pi$
$181$	2314.20			0.950350			0.475175	+	0.879891i	$0.342385\pi$
$182$		0			0
$183$	1.86565	−	10.2235i	0.000753623	−	0.00412973i
$184$		0			0
$185$	1073.23	+	1705.84i	0.426515	+	0.677925i
$186$		0			0
$187$	532.938	−	532.938i	0.208408	−	0.208408i
$188$		0			0
$189$	640.007	+	2571.87i	0.246316	+	0.989820i
$190$		0			0
$191$		−	931.167i		−	0.352758i	−0.984322	−	0.176379i	$-0.943562\pi$
$191$		−	931.167i		−	0.352758i	0.984322	−	0.176379i	$-0.0564385\pi$
$192$		0			0
$193$	−2623.28	−	2623.28i	−0.978382	−	0.978382i	0.0213891	−	0.999771i	$-0.493191\pi$
$193$	−2623.28	−	2623.28i	−0.978382	−	0.978382i	−0.999771	+	0.0213891i	$0.993191\pi$
$194$		0			0
$195$	−433.254	−	1081.35i	−0.159107	−	0.397114i
$196$		0			0
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.996210	−	0.0869796i	$-0.972279\pi$
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.0869796	−	0.996210i	$-0.527721\pi$
$198$		0			0
$199$		−	109.458i		−	0.0389912i	−0.999810	−	0.0194956i	$-0.993794\pi$
$199$		−	109.458i		−	0.0389912i	0.999810	−	0.0194956i	$-0.00620603\pi$
$200$		0			0
$201$	−1378.98	−	1994.63i	−0.483911	−	0.699951i
$202$		0			0
$203$	1681.14	−	1681.14i	0.581246	−	0.581246i
$204$		0			0
$205$	−4255.14	−	968.625i	−1.44972	−	0.330008i
$206$		0			0
$207$	−1314.39	+	593.915i	−0.441336	+	0.199420i
$208$		0			0
$209$	1409.21			0.466399
$210$		0			0
$211$	−2714.94			−0.885801			−0.442901	−	0.896571i	$-0.646051\pi$
$211$	−2714.94			−0.885801			−0.442901	+	0.896571i	$0.646051\pi$
$212$		0			0
$213$	−877.989	−	160.222i	−0.282436	−	0.0515409i
$214$		0			0
$215$	527.281	−	331.737i	0.167257	−	0.105229i
$216$		0			0
$217$	−3304.29	+	3304.29i	−1.03368	+	1.03368i
$218$		0			0
$219$	−1692.03	+	1169.79i	−0.522087	+	0.360945i
$220$		0			0
$221$			526.283i			0.160188i
$222$		0			0
$223$	−2830.49	−	2830.49i	−0.849971	−	0.849971i	0.140158	−	0.990129i	$-0.455239\pi$
$223$	−2830.49	−	2830.49i	−0.849971	−	0.849971i	−0.990129	+	0.140158i	$0.955239\pi$
$224$		0			0
$225$	2330.36	+	2441.32i	0.690478	+	0.723354i
$226$		0			0
$227$	1398.96	+	1398.96i	0.409042	+	0.409042i	0.881404	−	0.472362i	$-0.156599\pi$
$227$	1398.96	+	1398.96i	0.409042	+	0.409042i	−0.472362	+	0.881404i	$0.656599\pi$
$228$		0			0
$229$			3930.38i			1.13418i	0.823656	+	0.567089i	$0.191931\pi$
$229$			3930.38i			1.13418i	−0.823656	+	0.567089i	$0.808069\pi$
$230$		0			0
$231$	−2318.63	+	1602.98i	−0.660408	+	0.456573i
$232$		0			0
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	−0.928427	−	0.371515i	$-0.878838\pi$
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	0.371515	+	0.928427i	$0.378838\pi$
$234$		0			0
$235$	−1667.00	+	1048.79i	−0.462736	+	0.291129i
$236$		0			0
$237$	245.460	+	44.7933i	0.0672756	+	0.0122769i
$238$		0			0
$239$	2976.20			0.805500			0.402750	−	0.915310i	$-0.368054\pi$
$239$	2976.20			0.805500			0.402750	+	0.915310i	$0.368054\pi$
$240$		0			0
$241$	1835.45			0.490587			0.245294	−	0.969449i	$-0.421116\pi$
$241$	1835.45			0.490587			0.245294	+	0.969449i	$0.421116\pi$
$242$		0			0
$243$	2973.13	−	2347.21i	0.784882	−	0.619645i
$244$		0			0
$245$	−151.122	−	34.4008i	−0.0394074	−	0.00897057i
$246$		0			0
$247$	−695.808	+	695.808i	−0.179244	+	0.179244i
$248$		0			0
$249$	603.648	+	873.143i	0.153633	+	0.222222i
$250$		0			0
$251$			1542.14i			0.387805i	0.981021	+	0.193902i	$0.0621145\pi$
$251$			1542.14i			0.387805i	−0.981021	+	0.193902i	$0.937885\pi$
$252$		0			0
$253$	−1084.73	−	1084.73i	−0.269550	−	0.269550i
$254$		0			0
$255$	−567.082	−	1415.37i	−0.139263	−	0.347584i
$256$		0			0
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	0.653144	−	0.757234i	$-0.273450\pi$
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	−0.757234	+	0.653144i	$0.773450\pi$
$258$		0			0
$259$			3405.26i			0.816960i
$260$		0			0
$261$	−3179.04	−	1200.24i	−0.753937	−	0.284647i
$262$		0			0
$263$	−5256.99	+	5256.99i	−1.23255	+	1.23255i	−0.269565	+	0.962982i	$0.586880\pi$
$263$	−5256.99	+	5256.99i	−1.23255	+	1.23255i	−0.962982	+	0.269565i	$0.913120\pi$
$264$		0			0
$265$	1350.89	+	2147.18i	0.313150	+	0.497738i
$266$		0			0
$267$	1322.01	−	7244.38i	0.303017	−	1.66048i
$268$		0			0
$269$	−1930.34			−0.437528			−0.218764	−	0.975778i	$-0.570203\pi$
$269$	−1930.34			−0.437528			−0.218764	+	0.975778i	$0.570203\pi$
$270$		0			0
$271$	3261.67			0.731116			0.365558	−	0.930789i	$-0.380878\pi$
$271$	3261.67			0.731116			0.365558	+	0.930789i	$0.380878\pi$
$272$		0			0
$273$	353.353	−	1936.32i	0.0783367	−	0.429272i
$274$		0			0
$275$	−1553.72	+	3235.87i	−0.340700	+	0.709565i
$276$		0			0
$277$	4865.57	−	4865.57i	1.05539	−	1.05539i	0.0570194	−	0.998373i	$-0.481840\pi$
$277$	4865.57	−	4865.57i	1.05539	−	1.05539i	0.998373	−	0.0570194i	$-0.0181597\pi$
$278$		0			0
$279$	6248.41	+	2359.07i	1.34080	+	0.506215i
$280$		0			0
$281$		−	3981.96i		−	0.845351i	−0.906281	−	0.422676i	$-0.861091\pi$
$281$		−	3981.96i		−	0.845351i	0.906281	−	0.422676i	$-0.138909\pi$
$282$		0			0
$283$	4092.66	+	4092.66i	0.859658	+	0.859658i	0.991298	−	0.131640i	$-0.0420242\pi$
$283$	4092.66	+	4092.66i	0.859658	+	0.859658i	−0.131640	+	0.991298i	$0.542024\pi$
$284$		0			0
$285$	1121.54	−	2621.04i	0.233103	−	0.544761i
$286$		0			0
$287$	−5213.93	−	5213.93i	−1.07236	−	1.07236i
$288$		0			0
$289$		−	4224.15i		−	0.859791i
$290$		0			0
$291$	−3794.91	−	5489.13i	−0.764473	−	1.10577i
$292$		0			0
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	−0.995462	−	0.0951570i	$-0.969665\pi$
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	0.0951570	+	0.995462i	$0.469665\pi$
$294$		0			0
$295$	1810.11	−	7951.77i	0.357250	−	1.56939i
$296$		0			0
$297$	3452.42	+	2076.54i	0.674511	+	0.405701i
$298$		0			0
$299$	1071.18			0.207184
$300$		0			0
$301$	1052.58			0.201560
$302$		0			0
$303$	−1726.07	−	314.986i	−0.327261	−	0.0597210i
$304$		0			0
$305$	4.96314	−	21.8029i	0.000931766	−	0.00409322i
$306$		0			0
$307$	−1831.07	+	1831.07i	−0.340406	+	0.340406i	−0.856520	−	0.516114i	$-0.827378\pi$
$307$	−1831.07	+	1831.07i	−0.340406	+	0.340406i	0.516114	+	0.856520i	$0.327378\pi$
$308$		0			0
$309$	5642.63	−	3901.03i	1.03883	−	0.718194i
$310$		0			0
$311$			4010.21i			0.731184i	0.930775	+	0.365592i	$0.119134\pi$
$311$			4010.21i			0.731184i	−0.930775	+	0.365592i	$0.880866\pi$
$312$		0			0
$313$	6072.69	+	6072.69i	1.09664	+	1.09664i	0.994801	+	0.101841i	$0.0324733\pi$
$313$	6072.69	+	6072.69i	1.09664	+	1.09664i	0.101841	+	0.994801i	$0.467527\pi$
$314$		0			0
$315$	1136.13	+	5588.23i	0.203218	+	0.999559i
$316$		0			0
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	0.926844	−	0.375447i	$-0.122511\pi$
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	−0.375447	+	0.926844i	$0.622511\pi$
$318$		0			0
$319$		−	3614.09i		−	0.634326i
$320$		0			0
$321$	3603.70	−	2491.42i	0.626600	−	0.433200i
$322$		0			0
$323$	−910.737	+	910.737i	−0.156888	+	0.156888i
$324$		0			0
$325$	−830.574	−	2364.89i	−0.141760	−	0.403632i
$326$		0			0
$327$	10604.8	+	1935.24i	1.79342	+	0.327275i
$328$		0			0
$329$	−3327.71			−0.557637
$330$		0			0
$331$	9589.47			1.59240			0.796201	−	0.605033i	$-0.206840\pi$
$331$	9589.47			1.59240			0.796201	+	0.605033i	$0.206840\pi$
$332$		0			0
$333$	4435.26	−	2004.10i	0.729883	−	0.329801i
$334$		0			0
$335$	−2778.45	−	4416.22i	−0.453144	−	0.720251i
$336$		0			0
$337$	−2561.34	+	2561.34i	−0.414021	+	0.414021i	−0.883137	−	0.469115i	$-0.844573\pi$
$337$	−2561.34	+	2561.34i	−0.414021	+	0.414021i	0.469115	+	0.883137i	$0.344573\pi$
$338$		0			0
$339$	−1133.29	−	1639.24i	−0.181569	−	0.262630i
$340$		0			0
$341$			7103.50i			1.12808i
$342$		0			0
$343$	4396.56	+	4396.56i	0.692104	+	0.692104i
$344$		0			0
$345$	−2880.81	+	1154.22i	−0.449558	+	0.180120i
$346$		0			0
$347$	8177.44	+	8177.44i	1.26509	+	1.26509i	0.948592	+	0.316503i	$0.102509\pi$
$347$	8177.44	+	8177.44i	1.26509	+	1.26509i	0.316503	+	0.948592i	$0.397491\pi$
$348$		0			0
$349$		−	2766.04i		−	0.424249i	−0.977243	−	0.212124i	$-0.931962\pi$
$349$		−	2766.04i		−	0.424249i	0.977243	−	0.212124i	$-0.0680382\pi$
$350$		0			0
$351$	−2729.96	+	679.347i	−0.415141	+	0.103307i
$352$		0			0
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	−0.999060	−	0.0433491i	$-0.986197\pi$
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	0.0433491	+	0.999060i	$0.486197\pi$
$354$		0			0
$355$	−1872.43	−	426.233i	−0.279939	−	0.0637242i
$356$		0			0
$357$	462.501	−	2534.43i	0.0685663	−	0.375732i
$358$		0			0
$359$	−8827.47			−1.29776			−0.648880	−	0.760890i	$-0.724762\pi$
$359$	−8827.47			−1.29776			−0.648880	+	0.760890i	$0.724762\pi$
$360$		0			0
$361$	4450.80			0.648899
$362$		0			0
$363$	472.353	−	2588.42i	0.0682978	−	0.374261i
$364$		0			0
$365$	−3746.27	+	2356.95i	−0.537229	+	0.337996i
$366$		0			0
$367$	−6191.27	+	6191.27i	−0.880605	+	0.880605i	−0.993596	−	0.112991i	$-0.963957\pi$
$367$	−6191.27	+	6191.27i	−0.880605	+	0.880605i	0.112991	+	0.993596i	$0.463957\pi$
$368$		0			0
$369$	−3722.45	+	9859.55i	−0.525157	+	1.39097i
$370$		0			0
$371$			4286.28i			0.599818i
$372$		0			0
$373$	3584.46	+	3584.46i	0.497577	+	0.497577i	0.910683	−	0.413106i	$-0.135556\pi$
$373$	3584.46	+	3584.46i	0.497577	+	0.497577i	−0.413106	+	0.910683i	$0.635556\pi$
$374$		0			0
$375$	4781.95	+	5465.10i	0.658503	+	0.752578i
$376$		0			0
$377$	1784.48	+	1784.48i	0.243781	+	0.243781i
$378$		0			0
$379$		−	7110.48i		−	0.963695i	−0.876255	−	0.481848i	$-0.839966\pi$
$379$		−	7110.48i		−	0.963695i	0.876255	−	0.481848i	$-0.160034\pi$
$380$		0			0
$381$	441.241	+	638.231i	0.0593319	+	0.0858203i
$382$		0			0
$383$	−1695.77	+	1695.77i	−0.226240	+	0.226240i	−0.811120	−	0.584880i	$-0.801142\pi$
$383$	−1695.77	+	1695.77i	−0.226240	+	0.226240i	0.584880	+	0.811120i	$0.301142\pi$
$384$		0			0
$385$	−5133.58	+	3229.77i	−0.679562	+	0.427544i
$386$		0			0
$387$	−619.472	−	1370.95i	−0.0813683	−	0.180076i
$388$		0			0
$389$	12362.2			1.61128			0.805640	−	0.592405i	$-0.201822\pi$
$389$	12362.2			1.61128			0.805640	+	0.592405i	$0.201822\pi$
$390$		0			0
$391$	1402.06			0.181343
$392$		0			0
$393$	−10117.5	−	1846.32i	−1.29863	−	0.236984i
$394$		0			0
$395$	523.476	+	119.162i	0.0666808	+	0.0151790i
$396$		0			0
$397$	−1340.12	+	1340.12i	−0.169417	+	0.169417i	−0.786723	−	0.617306i	$-0.788224\pi$
$397$	−1340.12	+	1340.12i	−0.169417	+	0.169417i	0.617306	+	0.786723i	$0.288224\pi$
$398$		0			0
$399$	3962.30	−	2739.33i	0.497150	−	0.343705i
$400$		0			0
$401$			2281.30i			0.284096i	0.989860	+	0.142048i	$0.0453688\pi$
$401$			2281.30i			0.284096i	−0.989860	+	0.142048i	$0.954631\pi$
$402$		0			0
$403$	−3507.40	−	3507.40i	−0.433538	−	0.433538i
$404$		0			0
$405$	6609.87	−	4768.61i	0.810981	−	0.585072i
$406$		0			0
$407$	3660.29	+	3660.29i	0.445783	+	0.445783i
$408$		0			0
$409$		−	4614.82i		−	0.557917i	−0.960303	−	0.278959i	$-0.910011\pi$
$409$		−	4614.82i		−	0.557917i	0.960303	−	0.278959i	$-0.0899892\pi$
$410$		0			0
$411$	3067.32	−	2120.59i	0.368126	−	0.254504i
$412$		0			0
$413$	9743.49	−	9743.49i	1.16089	−	1.16089i
$414$		0			0
$415$	1216.26	+	1933.19i	0.143865	+	0.228667i
$416$		0			0
$417$	349.813	+	63.8364i	0.0410801	+	0.00749660i
$418$		0			0
$419$	−2142.28			−0.249779			−0.124889	−	0.992171i	$-0.539858\pi$
$419$	−2142.28			−0.249779			−0.124889	+	0.992171i	$0.539858\pi$
$420$		0			0
$421$	−8889.30			−1.02907			−0.514534	−	0.857470i	$-0.672035\pi$
$421$	−8889.30			−1.02907			−0.514534	+	0.857470i	$0.672035\pi$
$422$		0			0
$423$	1958.46	+	4334.26i	0.225115	+	0.498200i
$424$		0			0
$425$	−1087.13	−	3095.38i	−0.124079	−	0.353289i
$426$		0			0
$427$	26.7156	−	26.7156i	0.00302778	−	0.00302778i
$428$		0			0
$429$	−1701.52	−	2461.15i	−0.191492	−	0.276982i
$430$		0			0
$431$		−	15707.3i		−	1.75543i	−0.479179	−	0.877717i	$-0.659065\pi$
$431$		−	15707.3i		−	1.75543i	0.479179	−	0.877717i	$-0.340935\pi$
$432$		0			0
$433$	5430.81	+	5430.81i	0.602744	+	0.602744i	0.941040	−	0.338296i	$-0.109851\pi$
$433$	5430.81	+	5430.81i	0.602744	+	0.602744i	−0.338296	+	0.941040i	$0.609851\pi$
$434$		0			0
$435$	−6721.94	−	2876.31i	−0.740902	−	0.317031i
$436$		0			0
$437$	1853.69	+	1853.69i	0.202915	+	0.202915i
$438$		0			0
$439$			8221.92i			0.893874i	0.894565	+	0.446937i	$0.147485\pi$
$439$			8221.92i			0.893874i	−0.894565	+	0.446937i	$0.852515\pi$
$440$		0			0
$441$	−132.203	+	350.163i	−0.0142753	+	0.0378105i
$442$		0			0
$443$	−1960.53	+	1960.53i	−0.210265	+	0.210265i	−0.804380	−	0.594115i	$-0.797502\pi$
$443$	−1960.53	+	1960.53i	−0.210265	+	0.210265i	0.594115	+	0.804380i	$0.297502\pi$
$444$		0			0
$445$	3516.89	−	15449.6i	0.374644	−	1.64580i
$446$		0			0
$447$	338.948	−	1857.38i	0.0358651	−	0.196535i
$448$		0			0
$449$	−17849.2			−1.87607			−0.938036	−	0.346537i	$-0.887357\pi$
$449$	−17849.2			−1.87607			−0.938036	+	0.346537i	$0.887357\pi$
$450$		0			0
$451$	−11208.8			−1.17029
$452$		0			0
$453$	1943.21	−	10648.5i	0.201545	−	1.10443i
$454$		0			0
$455$	940.015	−	4129.46i	0.0968540	−	0.425477i
$456$		0			0
$457$	−6346.80	+	6346.80i	−0.649652	+	0.649652i	−0.952909	−	0.303257i	$-0.901926\pi$
$457$	−6346.80	+	6346.80i	−0.649652	+	0.649652i	0.303257	+	0.952909i	$0.401926\pi$
$458$		0			0
$459$	−3573.22	+	889.192i	−0.363363	+	0.0904225i
$460$		0			0
$461$			8848.20i			0.893930i	0.894552	+	0.446965i	$0.147495\pi$
$461$			8848.20i			0.893930i	−0.894552	+	0.446965i	$0.852505\pi$
$462$		0			0
$463$	−1329.43	−	1329.43i	−0.133443	−	0.133443i	0.637230	−	0.770673i	$-0.280080\pi$
$463$	−1329.43	−	1329.43i	−0.133443	−	0.133443i	−0.770673	+	0.637230i	$0.780080\pi$
$464$		0			0
$465$	13212.0	+	5653.40i	1.31762	+	0.563807i
$466$		0			0
$467$	−1479.96	−	1479.96i	−0.146647	−	0.146647i	0.629971	−	0.776618i	$-0.283067\pi$
$467$	−1479.96	−	1479.96i	−0.146647	−	0.146647i	−0.776618	+	0.629971i	$0.783067\pi$
$468$		0			0
$469$		−	8815.81i		−	0.867966i
$470$		0			0
$471$	5050.29	+	7304.96i	0.494066	+	0.714639i
$472$		0			0
$473$	1131.41	−	1131.41i	0.109983	−	0.109983i
$474$		0			0
$475$	2655.14	−	5529.77i	0.256476	−	0.534155i
$476$		0			0
$477$	5582.76	−	2522.60i	0.535885	−	0.242143i
$478$		0			0
$479$	−5039.60			−0.480720			−0.240360	−	0.970684i	$-0.577266\pi$
$479$	−5039.60			−0.480720			−0.240360	+	0.970684i	$0.577266\pi$
$480$		0			0
$481$	−3614.58			−0.342642
$482$		0			0
$483$	−5158.51	−	941.362i	−0.485963	−	0.0886821i
$484$		0			0
$485$	−7646.20	−	12153.3i	−0.715868	−	1.13784i
$486$		0			0
$487$	−1292.93	+	1292.93i	−0.120305	+	0.120305i	−0.764696	−	0.644391i	$-0.777111\pi$
$487$	−1292.93	+	1292.93i	−0.120305	+	0.120305i	0.644391	+	0.764696i	$0.277111\pi$
$488$		0			0
$489$	−3784.27	+	2616.26i	−0.349961	+	0.241945i
$490$		0			0
$491$			13865.7i			1.27444i	0.770681	+	0.637221i	$0.219916\pi$
$491$			13865.7i			1.27444i	−0.770681	+	0.637221i	$0.780084\pi$
$492$		0			0
$493$	2335.69	+	2335.69i	0.213375	+	0.213375i
$494$		0			0
$495$	7227.96	+	4785.53i	0.656308	+	0.434532i
$496$		0			0
$497$	−2294.33	−	2294.33i	−0.207072	−	0.207072i
$498$		0			0
$499$		−	10884.3i		−	0.976453i	−0.872717	−	0.488226i	$-0.837644\pi$
$499$		−	10884.3i		−	0.976453i	0.872717	−	0.488226i	$-0.162356\pi$
$500$		0			0
$501$	−18192.0	+	12577.0i	−1.62227	+	1.12156i
$502$		0			0
$503$	7880.86	−	7880.86i	0.698589	−	0.698589i	−0.265517	−	0.964106i	$-0.585543\pi$
$503$	7880.86	−	7880.86i	0.698589	−	0.698589i	0.964106	+	0.265517i	$0.0855427\pi$
$504$		0			0
$505$	−3681.07	−	837.946i	−0.324368	−	0.0738379i
$506$		0			0
$507$	−9175.14	−	1674.35i	−0.803713	−	0.146667i
$508$		0			0
$509$	1788.46			0.155741			0.0778704	−	0.996963i	$-0.475188\pi$
$509$	1788.46			0.155741			0.0778704	+	0.996963i	$0.475188\pi$
$510$		0			0
$511$	−7478.42			−0.647408
$512$		0			0
$513$	−5899.84	−	3548.60i	−0.507766	−	0.305409i
$514$		0			0
$515$	12493.1	−	7860.01i	1.06896	−	0.672531i
$516$		0			0
$517$	−3576.93	+	3576.93i	−0.304281	+	0.304281i
$518$		0			0
$519$	−7685.96	−	11117.3i	−0.650051	−	0.940263i
$520$		0			0
$521$		−	18251.6i		−	1.53478i	−0.641183	−	0.767388i	$-0.721556\pi$
$521$		−	18251.6i		−	1.53478i	0.641183	−	0.767388i	$-0.278444\pi$
$522$		0			0
$523$	2125.69	+	2125.69i	0.177725	+	0.177725i	0.790363	−	0.612639i	$-0.209892\pi$
$523$	2125.69	+	2125.69i	0.177725	+	0.177725i	−0.612639	+	0.790363i	$0.709892\pi$
$524$		0			0
$525$	1921.53	+	12118.5i	0.159738	+	1.00742i
$526$		0			0
$527$	−4590.80	−	4590.80i	−0.379466	−	0.379466i
$528$		0			0
$529$			9313.29i			0.765455i
$530$		0			0
$531$	−18425.0	−	6956.30i	−1.50579	−	0.568508i
$532$		0			0
$533$	5534.42	−	5534.42i	0.449761	−	0.449761i
$534$		0			0
$535$	7978.81	−	5019.84i	0.644774	−	0.405657i
$536$		0			0
$537$	766.393	−	4199.71i	0.0615872	−	0.337488i
$538$		0			0
$539$	−398.082			−0.0318119
$540$		0			0
$541$	−2214.16			−0.175960			−0.0879798	−	0.996122i	$-0.528041\pi$
$541$	−2214.16			−0.175960			−0.0879798	+	0.996122i	$0.528041\pi$
$542$		0			0
$543$	2158.75	−	11829.6i	0.170609	−	0.934911i
$544$		0			0
$545$	22616.2	+	5148.26i	1.77756	+	0.404637i
$546$		0			0
$547$	−12385.1	+	12385.1i	−0.968098	+	0.968098i	−0.999507	−	0.0314090i	$-0.990001\pi$
$547$	−12385.1	+	12385.1i	−0.968098	+	0.968098i	0.0314090	+	0.999507i	$0.490001\pi$
$548$		0			0
$549$	−50.5193	−	19.0735i	−0.00392735	−	0.00148276i
$550$		0			0
$551$			6176.11i			0.477516i
$552$		0			0
$553$	641.427	+	641.427i	0.0493242	+	0.0493242i
$554$		0			0
$555$	9720.96	−	3894.79i	0.743481	−	0.297882i
$556$		0			0
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$558$		0			0
$559$			1117.28i			0.0845363i
$560$		0			0
$561$	−2227.10	−	3221.38i	−0.167608	−	0.242436i
$562$		0			0
$563$	11697.0	−	11697.0i	0.875615	−	0.875615i	−0.117462	−	0.993077i	$-0.537476\pi$
$563$	11697.0	−	11697.0i	0.875615	−	0.875615i	0.993077	+	0.117462i	$0.0374759\pi$
$564$		0			0
$565$	−2283.42	−	3629.39i	−0.170025	−	0.270247i
$566$		0			0
$567$	13743.7	−	872.435i	1.01796	−	0.0646188i
$568$		0			0
$569$	−11517.5			−0.848576			−0.424288	−	0.905527i	$-0.639476\pi$
$569$	−11517.5			−0.848576			−0.424288	+	0.905527i	$0.639476\pi$
$570$		0			0
$571$	11093.9			0.813072			0.406536	−	0.913635i	$-0.366737\pi$
$571$	11093.9			0.813072			0.406536	+	0.913635i	$0.366737\pi$
$572$		0			0
$573$	−4759.88	−	868.617i	−0.347027	−	0.0633281i
$574$		0			0
$575$	−6300.25	+	2212.72i	−0.456937	+	0.160481i
$576$		0			0
$577$	−14119.4	+	14119.4i	−1.01871	+	1.01871i	−0.0188920	+	0.999822i	$0.506014\pi$
$577$	−14119.4	+	14119.4i	−1.01871	+	1.01871i	−0.999822	+	0.0188920i	$0.993986\pi$
$578$		0			0
$579$	−15856.6	+	10962.4i	−1.13813	+	0.786846i
$580$		0			0
$581$			3859.10i			0.275564i
$582$		0			0
$583$	4607.29	+	4607.29i	0.327297	+	0.327297i
$584$		0			0
$585$	−5931.73	+	1205.96i	−0.419226	+	0.0852316i
$586$		0			0
$587$	8524.33	+	8524.33i	0.599381	+	0.599381i	0.940148	−	0.340767i	$-0.110687\pi$
$587$	8524.33	+	8524.33i	0.599381	+	0.599381i	−0.340767	+	0.940148i	$0.610687\pi$
$588$		0			0
$589$		−	12139.2i		−	0.849211i
$590$		0			0
$591$	−18103.8	+	12516.0i	−1.26005	+	0.871135i
$592$		0			0
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	−0.530491	−	0.847691i	$-0.677992\pi$
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	0.847691	+	0.530491i	$0.177992\pi$
$594$		0			0
$595$	1230.38	−	5405.01i	0.0847740	−	0.372410i
$596$		0			0
$597$	−559.518	−	102.105i	−0.0383577	−	0.00699979i
$598$		0			0
$599$	−10195.8			−0.695477			−0.347738	−	0.937592i	$-0.613050\pi$
$599$	−10195.8			−0.695477			−0.347738	+	0.937592i	$0.613050\pi$
$600$		0			0
$601$	18915.8			1.28385			0.641923	−	0.766769i	$-0.278137\pi$
$601$	18915.8			1.28385			0.641923	+	0.766769i	$0.278137\pi$
$602$		0			0
$603$	−11482.4	+	5188.36i	−0.775452	+	0.350392i
$604$		0			0
$605$	1256.59	−	5520.14i	0.0844421	−	0.370952i
$606$		0			0
$607$	−12758.2	+	12758.2i	−0.853113	+	0.853113i	−0.990515	−	0.137402i	$-0.956125\pi$
$607$	−12758.2	+	12758.2i	−0.853113	+	0.853113i	0.137402	+	0.990515i	$0.456125\pi$
$608$		0			0
$609$	−7025.33	−	10161.8i	−0.467456	−	0.676149i
$610$		0			0
$611$		−	3532.26i		−	0.233879i
$612$		0			0
$613$	7340.02	+	7340.02i	0.483622	+	0.483622i	0.906286	−	0.422664i	$-0.138905\pi$
$613$	7340.02	+	7340.02i	0.483622	+	0.483622i	−0.422664	+	0.906286i	$0.638905\pi$
$614$		0			0
$615$	−8920.67	+	20847.6i	−0.584904	+	1.36692i
$616$		0			0
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.992182	+	0.124803i	$0.0398299\pi$
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.124803	+	0.992182i	$0.460170\pi$
$618$		0			0
$619$			3176.16i			0.206237i	0.994669	+	0.103118i	$0.0328820\pi$
$619$			3176.16i			0.206237i	−0.994669	+	0.103118i	$0.967118\pi$
$620$		0			0
$621$	1809.84	+	7272.84i	0.116950	+	0.469966i
$622$		0			0
$623$	18930.8	−	18930.8i	1.21741	−	1.21741i
$624$		0			0
$625$	9770.20	+	12193.6i	0.625293	+	0.780390i
$626$		0			0
$627$	1314.55	−	7203.53i	0.0837291	−	0.458822i
$628$		0			0
$629$	−4731.09			−0.299906
$630$		0			0
$631$	11467.2			0.723459			0.361729	−	0.932283i	$-0.382186\pi$
$631$	11467.2			0.723459			0.361729	+	0.932283i	$0.382186\pi$
$632$		0			0
$633$	−2532.57	+	13878.0i	−0.159021	+	0.871410i
$634$		0			0
$635$	889.036	+	1413.08i	0.0555596	+	0.0883094i
$636$		0			0
$637$	196.556	−	196.556i	0.0122258	−	0.0122258i
$638$		0			0
$639$	−1638.02	+	4338.59i	−0.101407	+	0.268595i
$640$		0			0
$641$			12383.2i			0.763035i	0.924362	+	0.381518i	$0.124598\pi$
$641$			12383.2i			0.763035i	−0.924362	+	0.381518i	$0.875402\pi$
$642$		0			0
$643$	11142.9	+	11142.9i	0.683413	+	0.683413i	0.960768	−	0.277354i	$-0.0894576\pi$
$643$	11142.9	+	11142.9i	0.683413	+	0.683413i	−0.277354	+	0.960768i	$0.589458\pi$
$644$		0			0
$645$	−1203.89	−	3004.78i	−0.0734933	−	0.183431i
$646$		0			0
$647$	−2391.21	−	2391.21i	−0.145299	−	0.145299i	0.630716	−	0.776014i	$-0.282761\pi$
$647$	−2391.21	−	2391.21i	−0.145299	−	0.145299i	−0.776014	+	0.630716i	$0.782761\pi$
$648$		0			0
$649$		−	20946.4i		−	1.26690i
$650$		0			0
$651$	13808.3	+	19973.0i	0.831322	+	1.20246i
$652$		0			0
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	−0.00379136	−	0.999993i	$-0.501207\pi$
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	0.999993	+	0.00379136i	$0.00120683\pi$
$654$		0			0
$655$	−21577.0	−	4911.71i	−1.28715	−	0.293002i
$656$		0			0
$657$	4401.27	+	9740.43i	0.261354	+	0.578403i
$658$		0			0
$659$	20089.8			1.18754			0.593768	−	0.804636i	$-0.297640\pi$
$659$	20089.8			1.18754			0.593768	+	0.804636i	$0.297640\pi$
$660$		0			0
$661$	541.434			0.0318598			0.0159299	−	0.999873i	$-0.494929\pi$
$661$	541.434			0.0318598			0.0159299	+	0.999873i	$0.494929\pi$
$662$		0			0
$663$	2690.22	+	490.931i	0.157586	+	0.0287574i
$664$		0			0
$665$	8772.76	−	5519.36i	0.511569	−	0.321852i
$666$		0			0
$667$	4753.99	−	4753.99i	0.275975	−	0.275975i
$668$		0			0
$669$	−17109.1	+	11828.3i	−0.988751	+	0.683573i
$670$		0			0
$671$		−	57.4328i		−	0.00330428i
$672$		0			0
$673$	−24314.3	−	24314.3i	−1.39264	−	1.39264i	−0.819354	−	0.573288i	$-0.805668\pi$
$673$	−24314.3	−	24314.3i	−1.39264	−	1.39264i	−0.573288	−	0.819354i	$-0.694332\pi$
$674$		0			0
$675$	14653.2	−	9634.87i	0.835558	−	0.549402i
$676$		0			0
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	0.987842	−	0.155462i	$-0.0496867\pi$
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	−0.155462	+	0.987842i	$0.549687\pi$
$678$		0			0
$679$		−	24260.8i		−	1.37120i
$680$		0			0
$681$	8456.13	−	5846.14i	0.475829	−	0.328964i
$682$		0			0
$683$	−15981.2	+	15981.2i	−0.895320	+	0.895320i	−0.995018	−	0.0996976i	$-0.968212\pi$
$683$	−15981.2	+	15981.2i	−0.895320	+	0.895320i	0.0996976	+	0.995018i	$0.468212\pi$
$684$		0			0
$685$	6791.23	−	4272.68i	0.378803	−	0.238322i
$686$		0			0
$687$	20091.1	+	3666.36i	1.11575	+	0.203611i
$688$		0			0
$689$	−4549.75			−0.251570
$690$		0			0
$691$	16714.9			0.920209			0.460105	−	0.887865i	$-0.347812\pi$
$691$	16714.9			0.920209			0.460105	+	0.887865i	$0.347812\pi$
$692$		0			0
$693$	6031.14	+	13347.5i	0.330598	+	0.731645i
$694$		0			0
$695$	746.023	+	169.822i	0.0407169	+	0.00926865i
$696$		0			0
$697$	7243.96	−	7243.96i	0.393665	−	0.393665i
$698$		0			0
$699$	8277.19	+	11972.5i	0.447886	+	0.647842i
$700$		0			0
$701$			6990.49i			0.376643i	0.982107	+	0.188322i	$0.0603048\pi$
$701$			6990.49i			0.376643i	−0.982107	+	0.188322i	$0.939695\pi$
$702$		0			0
$703$	−6255.06	−	6255.06i	−0.335582	−	0.335582i
$704$		0			0
$705$	3806.09	+	9499.58i	0.203327	+	0.507482i
$706$		0			0
$707$	−4510.51	−	4510.51i	−0.239936	−	0.239936i
$708$		0			0
$709$			28175.0i			1.49243i	0.665705	+	0.746215i	$0.268131\pi$
$709$			28175.0i			1.49243i	−0.665705	+	0.746215i	$0.731869\pi$
$710$		0			0
$711$	457.943	−	1212.94i	0.0241550	−	0.0639787i
$712$		0			0
$713$	−9343.99	+	9343.99i	−0.490793	+	0.490793i
$714$		0			0
$715$	−3428.31	−	5449.13i	−0.179317	−	0.285015i
$716$		0			0
$717$	2776.28	−	15213.6i	0.144605	−	0.792414i
$718$		0			0
$719$	−20143.8			−1.04484			−0.522418	−	0.852690i	$-0.674970\pi$
$719$	−20143.8			−1.04484			−0.522418	+	0.852690i	$0.674970\pi$
$720$		0			0
$721$	24939.2			1.28819
$722$		0			0
$723$	1712.15	−	9382.32i	0.0880715	−	0.482617i
$724$		0			0
$725$	−14181.7	−	6809.41i	−0.726477	−	0.348821i
$726$		0			0
$727$	9805.90	−	9805.90i	0.500249	−	0.500249i	−0.411267	−	0.911515i	$-0.634913\pi$
$727$	9805.90	−	9805.90i	0.500249	−	0.500249i	0.911515	+	0.411267i	$0.134913\pi$
$728$		0			0
$729$	−9224.92	−	17387.4i	−0.468674	−	0.883371i
$730$		0			0
$731$			1462.39i			0.0739926i
$732$		0			0
$733$	16533.1	+	16533.1i	0.833100	+	0.833100i	0.987940	−	0.154840i	$-0.0494861\pi$
$733$	16533.1	+	16533.1i	0.833100	+	0.833100i	−0.154840	+	0.987940i	$0.549486\pi$
$734$		0			0
$735$	−316.818	+	740.405i	−0.0158994	+	0.0371568i
$736$		0			0
$737$	−9476.04	−	9476.04i	−0.473615	−	0.473615i
$738$		0			0
$739$		−	15250.1i		−	0.759114i	−0.925168	−	0.379557i	$-0.876076\pi$
$739$		−	15250.1i		−	0.759114i	0.925168	−	0.379557i	$-0.123924\pi$
$740$		0			0
$741$	2907.72	+	4205.85i	0.144153	+	0.208510i
$742$		0			0
$743$	−5438.49	+	5438.49i	−0.268531	+	0.268531i	−0.828508	−	0.559977i	$-0.810810\pi$
$743$	−5438.49	+	5438.49i	−0.268531	+	0.268531i	0.559977	+	0.828508i	$0.310810\pi$
$744$		0			0
$745$	901.693	−	3961.11i	0.0443429	−	0.194797i
$746$		0			0
$747$	5026.38	−	2271.20i	0.246192	−	0.111243i
$748$		0			0
$749$	15927.5			0.777009
$750$		0			0
$751$	−2087.82			−0.101446			−0.0507228	−	0.998713i	$-0.516152\pi$
$751$	−2087.82			−0.101446			−0.0507228	+	0.998713i	$0.516152\pi$
$752$		0			0
$753$	7883.01	+	1438.55i	0.381505	+	0.0696197i
$754$		0			0
$755$	5169.46	−	22709.3i	0.249187	−	1.09467i
$756$		0			0
$757$	−10258.6	+	10258.6i	−0.492546	+	0.492546i	−0.909107	−	0.416562i	$-0.863235\pi$
$757$	−10258.6	+	10258.6i	−0.492546	+	0.492546i	0.416562	+	0.909107i	$0.363235\pi$
$758$		0			0
$759$	−6556.70	+	4532.98i	−0.313561	+	0.216781i
$760$		0			0
$761$		−	26879.5i		−	1.28040i	−0.768210	−	0.640198i	$-0.778852\pi$
$761$		−	26879.5i		−	1.28040i	0.768210	−	0.640198i	$-0.221148\pi$
$762$		0			0
$763$	27712.1	+	27712.1i	1.31487	+	1.31487i
$764$		0			0
$765$	−7763.99	+	1578.48i	−0.366938	+	0.0746012i
$766$		0			0
$767$	10342.4	+	10342.4i	0.486888	+	0.486888i
$768$		0			0
$769$		−	25180.9i		−	1.18082i	−0.807105	−	0.590408i	$-0.798967\pi$
$769$		−	25180.9i		−	1.18082i	0.807105	−	0.590408i	$-0.201033\pi$
$770$		0			0
$771$	−2592.23	+	1792.14i	−0.121085	+	0.0837124i
$772$		0			0
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	−0.993335	−	0.115263i	$-0.963229\pi$
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	0.115263	+	0.993335i	$0.463229\pi$
$774$		0			0
$775$	27874.2	+	13383.9i	1.29196	+	0.620341i
$776$		0			0
$777$	17406.8	+	3176.52i	0.803688	+	0.146663i
$778$		0			0
$779$	19154.7			0.880988
$780$		0			0
$781$	−4932.32			−0.225982
$782$		0			0
$783$	−9100.79	+	15130.8i	−0.415371	+	0.690588i
$784$		0			0
$785$	10175.6	+	16173.6i	0.462653	+	0.735365i
$786$		0			0
$787$	−14716.0	+	14716.0i	−0.666542	+	0.666542i	−0.956914	−	0.290372i	$-0.906221\pi$
$787$	−14716.0	+	14716.0i	−0.666542	+	0.666542i	0.290372	+	0.956914i	$0.406221\pi$
$788$		0			0
$789$	21968.5	+	31776.2i	0.991253	+	1.43379i
$790$		0			0
$791$		−	7245.10i		−	0.325672i
$792$		0			0
$793$	28.3578	+	28.3578i	0.00126988	+	0.00126988i
$794$		0			0
$795$	12236.0	−	4902.46i	0.545869	−	0.218708i
$796$		0			0
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	0.203013	−	0.979176i	$-0.434927\pi$
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	−0.979176	+	0.203013i	$0.934927\pi$
$798$		0			0
$799$		−	4623.35i		−	0.204709i
$800$		0			0
$801$	−35798.1	−	13515.5i	−1.57911	−	0.596188i
$802$		0			0
$803$	−8038.49	+	8038.49i	−0.353265	+	0.353265i
$804$		0			0
$805$	−11001.2	−	2504.28i	−0.481667	−	0.109645i
$806$		0			0
$807$	−1800.68	+	9867.40i	−0.0785462	+	0.430420i
$808$		0			0
$809$	24097.9			1.04727			0.523633	−	0.851944i	$-0.324576\pi$
$809$	24097.9			1.04727			0.523633	+	0.851944i	$0.324576\pi$
$810$		0			0
$811$	−25302.7			−1.09556			−0.547780	−	0.836622i	$-0.684527\pi$
$811$	−25302.7			−1.09556			−0.547780	+	0.836622i	$0.684527\pi$
$812$		0			0
$813$	3042.57	−	16672.8i	0.131252	−	0.719238i
$814$		0			0
$815$	−8378.61	+	5271.38i	−0.360110	+	0.226562i
$816$		0			0
$817$	−1933.46	+	1933.46i	−0.0827945	+	0.0827945i
$818$		0			0
$819$	−9568.33	−	3612.50i	−0.408235	−	0.154128i
$820$		0			0
$821$			27925.3i			1.18709i	0.804802	+	0.593544i	$0.202272\pi$
$821$			27925.3i			1.18709i	−0.804802	+	0.593544i	$0.797728\pi$
$822$		0			0
$823$	−997.907	−	997.907i	−0.0422659	−	0.0422659i	0.685658	−	0.727924i	$-0.259515\pi$
$823$	−997.907	−	997.907i	−0.0422659	−	0.0422659i	−0.727924	+	0.685658i	$0.759515\pi$
$824$		0			0
$825$	15091.6	+	10960.7i	0.636874	+	0.462548i
$826$		0			0
$827$	−18683.3	−	18683.3i	−0.785590	−	0.785590i	0.195178	−	0.980768i	$-0.437471\pi$
$827$	−18683.3	−	18683.3i	−0.785590	−	0.785590i	−0.980768	+	0.195178i	$0.937471\pi$
$828$		0			0
$829$			21146.9i			0.885962i	0.896531	+	0.442981i	$0.146079\pi$
$829$			21146.9i			0.885962i	−0.896531	+	0.442981i	$0.853921\pi$
$830$		0			0
$831$	−20332.8	−	29410.2i	−0.848780	−	1.22771i
$832$		0			0
$833$	257.270	−	257.270i	0.0107009	−	0.0107009i
$834$		0			0
$835$	−40278.2	+	25340.9i	−1.66932	+	1.05025i
$836$		0			0
$837$	17887.6	−	29739.6i	0.738695	−	1.22814i
$838$		0			0
$839$	30903.4			1.27164			0.635820	−	0.771838i	$-0.280662\pi$
$839$	30903.4			1.27164			0.635820	+	0.771838i	$0.280662\pi$
$840$		0			0
$841$	−8549.68			−0.350555
$842$		0			0
$843$	−20354.7	−	3714.48i	−0.831618	−	0.151760i
$844$		0			0
$845$	−19567.2	−	4454.21i	−0.796607	−	0.181337i
$846$		0			0
$847$	6763.96	−	6763.96i	0.274395	−	0.274395i
$848$		0			0
$849$	24738.3	−	17102.8i	1.00002	−	0.691364i
$850$		0			0
$851$			9629.53i			0.387892i
$852$		0			0
$853$	181.224	+	181.224i	0.00727432	+	0.00727432i	0.710735	−	0.703460i	$-0.248363\pi$
$853$	181.224	+	181.224i	0.00727432	+	0.00727432i	−0.703460	+	0.710735i	$0.748363\pi$
$854$		0			0
$855$	−12351.8	−	8177.98i	−0.494063	−	0.327112i
$856$		0			0
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	0.927066	−	0.374899i	$-0.122323\pi$
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	−0.374899	+	0.927066i	$0.622323\pi$
$858$		0			0
$859$			8910.47i			0.353925i	0.984218	+	0.176962i	$0.0566271\pi$
$859$			8910.47i			0.353925i	−0.984218	+	0.176962i	$0.943373\pi$
$860$		0			0
$861$	−31515.9	+	21788.5i	−1.24746	+	0.862428i
$862$		0			0
$863$	−6487.75	+	6487.75i	−0.255905	+	0.255905i	−0.823386	−	0.567481i	$-0.807918\pi$
$863$	−6487.75	+	6487.75i	−0.255905	+	0.255905i	0.567481	+	0.823386i	$0.307918\pi$
$864$		0			0
$865$	−15486.1	−	24614.4i	−0.608720	−	0.967533i
$866$		0			0
$867$	−21592.8	−	3940.40i	−0.845823	−	0.154352i
$868$		0			0
$869$	1378.93			0.0538285
$870$		0			0
$871$	9357.71			0.364034
$872$		0			0
$873$	−31599.0	+	14278.2i	−1.22504	+	0.553543i
$874$		0			0
$875$	3001.35	+	26229.5i	0.115959	+	1.01339i
$876$		0			0
$877$	−20231.6	+	20231.6i	−0.778987	+	0.778987i	−0.979659	−	0.200672i	$-0.935688\pi$
$877$	−20231.6	+	20231.6i	−0.778987	+	0.778987i	0.200672	+	0.979659i	$0.435688\pi$
$878$		0			0
$879$	18869.2	+	27293.3i	0.724054	+	1.04730i
$880$		0			0
$881$		−	33209.0i		−	1.26996i	−0.772527	−	0.634982i	$-0.781007\pi$
$881$		−	33209.0i		−	1.26996i	0.772527	−	0.634982i	$-0.218993\pi$
$882$		0			0
$883$	−26984.3	−	26984.3i	−1.02842	−	1.02842i	−0.999584	−	0.0288331i	$-0.990821\pi$
$883$	−26984.3	−	26984.3i	−1.02842	−	1.02842i	−0.0288331	−	0.999584i	$-0.509179\pi$
$884$		0			0
$885$	−38958.8	−	16670.4i	−1.47976	−	0.633187i
$886$		0			0
$887$	24008.9	+	24008.9i	0.908838	+	0.908838i	0.996179	−	0.0873406i	$-0.0278369\pi$
$887$	24008.9	+	24008.9i	0.908838	+	0.908838i	−0.0873406	+	0.996179i	$0.527837\pi$
$888$		0			0
$889$			2820.84i			0.106421i
$890$		0			0
$891$	13835.3	−	15710.8i	0.520200	−	0.590720i
$892$		0			0
$893$	6112.61	−	6112.61i	0.229060	−	0.229060i
$894$		0			0
$895$	2038.81	−	8956.44i	0.0761452	−	0.334504i
$896$		0			0
$897$	999.226	−	5475.59i	0.0371942	−	0.203818i
$898$		0			0
$899$	−31132.2			−1.15497
$900$		0			0
$901$	−5955.13			−0.220193
$902$		0			0
$903$	981.871	−	5380.49i	0.0361845	−	0.198285i
$904$		0			0
$905$	5742.86	−	25228.2i	0.210938	−	0.926645i
$906$		0			0
$907$	23026.7	−	23026.7i	0.842989	−	0.842989i	−0.146258	−	0.989246i	$-0.546723\pi$
$907$	23026.7	−	23026.7i	0.842989	−	0.842989i	0.989246	+	0.146258i	$0.0467229\pi$
$908$		0			0
$909$	−3220.25	+	8529.38i	−0.117501	+	0.311223i
$910$		0			0
$911$		−	33422.1i		−	1.21550i	−0.794127	−	0.607752i	$-0.792071\pi$
$911$		−	33422.1i		−	1.21550i	0.794127	−	0.607752i	$-0.207929\pi$
$912$		0			0
$913$	4148.12	+	4148.12i	0.150364	+	0.150364i
$914$		0			0
$915$	−106.821	−	45.7086i	−0.00385945	−	0.00165145i
$916$		0			0
$917$	−26438.8	−	26438.8i	−0.952112	−	0.952112i
$918$		0			0
$919$			42542.2i			1.52703i	0.645792	+	0.763513i	$0.276527\pi$
$919$			42542.2i			1.52703i	−0.645792	+	0.763513i	$0.723473\pi$
$920$		0			0
$921$	7651.86	+	11068.0i	0.273765	+	0.395986i
$922$		0			0
$923$	2435.36	−	2435.36i	0.0868482	−	0.0868482i
$924$		0			0
$925$	21259.5	−	7466.56i	0.755684	−	0.265404i
$926$		0			0
$927$	−14677.4	−	32482.6i	−0.520033	−	1.15088i
$928$		0			0
$929$	−5721.21			−0.202053			−0.101026	−	0.994884i	$-0.532213\pi$
$929$	−5721.21			−0.202053			−0.101026	+	0.994884i	$0.532213\pi$
$930$		0			0
$931$	680.282			0.0239477
$932$		0			0
$933$	20499.1	+	3740.83i	0.719305	+	0.131264i
$934$		0			0
$935$	−4487.28	−	7132.32i	−0.156952	−	0.249467i
$936$		0			0
$937$	1344.01	−	1344.01i	0.0468589	−	0.0468589i	−0.683289	−	0.730148i	$-0.739451\pi$
$937$	1344.01	−	1344.01i	0.0468589	−	0.0468589i	0.730148	+	0.683289i	$0.239451\pi$
$938$		0			0
$939$	36706.8	−	25377.2i	1.27570	−	0.881953i
$940$		0			0
$941$			9625.77i			0.333466i	0.986002	+	0.166733i	$0.0533217\pi$
$941$			9625.77i			0.333466i	−0.986002	+	0.166733i	$0.946678\pi$
$942$		0			0
$943$	−14744.1	−	14744.1i	−0.509157	−	0.509157i
$944$		0			0
$945$	29625.4	−	594.731i	1.01980	−	0.0204726i
$946$		0			0
$947$	−2234.24	−	2234.24i	−0.0766664	−	0.0766664i	0.667734	−	0.744400i	$-0.267264\pi$
$947$	−2234.24	−	2234.24i	−0.0766664	−	0.0766664i	−0.744400	+	0.667734i	$0.767264\pi$
$948$		0			0
$949$		−	7938.11i		−	0.271530i
$950$		0			0
$951$	18811.3	−	13005.2i	0.641427	−	0.443451i
$952$		0			0
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	−0.808281	−	0.588798i	$-0.799602\pi$
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	0.588798	+	0.808281i	$0.299602\pi$
$954$		0			0
$955$	−10151.1	−	2310.75i	−0.343959	−	0.0782977i
$956$		0			0
$957$	−18474.3	−	3371.32i	−0.624021	−	0.113876i
$958$		0			0
$959$	13556.9			0.456491
$960$		0			0
$961$	31399.6			1.05399
$962$		0			0
$963$	−9373.84	−	20745.2i	−0.313674	−	0.694190i
$964$		0			0
$965$	−35107.4	+	22087.7i	−1.17114	+	0.736817i
$966$		0			0
$967$	−13166.9	+	13166.9i	−0.437869	+	0.437869i	−0.891294	−	0.453425i	$-0.850202\pi$
$967$	−13166.9	+	13166.9i	−0.437869	+	0.437869i	0.453425	+	0.891294i	$0.350202\pi$
$968$		0			0
$969$	3805.89	+	5505.01i	0.126174	+	0.182504i
$970$		0			0
$971$		−	21504.3i		−	0.710716i	−0.934730	−	0.355358i	$-0.884359\pi$
$971$		−	21504.3i		−	0.710716i	0.934730	−	0.355358i	$-0.115641\pi$
$972$		0			0
$973$	914.119	+	914.119i	0.0301185	+	0.0301185i
$974$		0			0
$975$	−12863.5	+	2039.65i	−0.422523	+	0.0669959i
$976$		0			0
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	0.838890	−	0.544301i	$-0.183205\pi$
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	−0.544301	+	0.838890i	$0.683205\pi$
$978$		0			0
$979$		−	40697.1i		−	1.32858i
$980$		0			0
$981$	19784.9	−	52403.7i	0.643917	−	1.70553i
$982$		0			0
$983$	−16337.3	+	16337.3i	−0.530090	+	0.530090i	−0.920599	−	0.390509i	$-0.872299\pi$
$983$	−16337.3	+	16337.3i	−0.530090	+	0.530090i	0.390509	+	0.920599i	$0.372299\pi$
$984$		0			0
$985$	−40082.8	+	25218.0i	−1.29659	+	0.815748i
$986$		0			0
$987$	−3104.18	+	17010.4i	−0.100108	+	0.548578i
$988$		0			0
$989$	2976.52			0.0957004
$990$		0			0
$991$	18296.9			0.586500			0.293250	−	0.956036i	$-0.405263\pi$
$991$	18296.9			0.586500			0.293250	+	0.956036i	$0.405263\pi$
$992$		0			0
$993$	8945.31	−	49018.8i	0.285872	−	1.56653i
$994$		0			0
$995$	−1193.25	−	271.627i	−0.0380186	−	0.00865441i
$996$		0			0
$997$	20406.0	−	20406.0i	0.648210	−	0.648210i	−0.304350	−	0.952560i	$-0.598439\pi$
$997$	20406.0	−	20406.0i	0.648210	−	0.648210i	0.952560	+	0.304350i	$0.0984393\pi$
$998$		0			0
$999$	−6107.09	−	24541.4i	−0.193413	−	0.777232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.4.v.c.113.2		8
3.2	odd	2	inner	240.4.v.c.113.1		8
4.3	odd	2		15.4.e.a.8.3	yes	8
5.2	odd	4	inner	240.4.v.c.17.1		8
12.11	even	2		15.4.e.a.8.2	yes	8
15.2	even	4	inner	240.4.v.c.17.2		8
20.3	even	4		75.4.e.c.32.3		8
20.7	even	4		15.4.e.a.2.2	✓	8
20.19	odd	2		75.4.e.c.68.2		8
60.23	odd	4		75.4.e.c.32.2		8
60.47	odd	4		15.4.e.a.2.3	yes	8
60.59	even	2		75.4.e.c.68.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.2	✓	8	20.7	even	4
15.4.e.a.2.3	yes	8	60.47	odd	4
15.4.e.a.8.2	yes	8	12.11	even	2
15.4.e.a.8.3	yes	8	4.3	odd	2
75.4.e.c.32.2		8	60.23	odd	4
75.4.e.c.32.3		8	20.3	even	4
75.4.e.c.68.2		8	20.19	odd	2
75.4.e.c.68.3		8	60.59	even	2
240.4.v.c.17.1		8	5.2	odd	4	inner
240.4.v.c.17.2		8	15.2	even	4	inner
240.4.v.c.113.1		8	3.2	odd	2	inner
240.4.v.c.113.2		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	240.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.932827 - 5.11173i) q^{3} +(2.48157 - 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(-25.2597 - 9.53673i) q^{9} -28.7164i q^{11} +(14.1789 + 14.1789i) q^{13} +(-53.4105 - 22.8543i) q^{15} +(18.5587 + 18.5587i) q^{17} +49.0735i q^{19} +(-55.8211 - 80.7421i) q^{21} +(37.7738 - 37.7738i) q^{23} +(-112.684 - 54.1055i) q^{25} +(-72.3121 + 120.225i) q^{27} +125.854 q^{29} -247.367 q^{31} +(-146.791 - 26.7874i) q^{33} +(-112.471 - 178.768i) q^{35} +(-127.463 + 127.463i) q^{37} +(85.7053 - 59.2524i) q^{39} -390.328i q^{41} +(39.3993 + 39.3993i) q^{43} +(-166.648 + 251.701i) q^{45} +(-124.560 - 124.560i) q^{47} -13.8625i q^{49} +(112.179 - 77.5549i) q^{51} +(-160.441 + 160.441i) q^{53} +(-313.051 - 71.2618i) q^{55} +(250.850 + 45.7770i) q^{57} +729.423 q^{59} +2.00000 q^{61} +(-464.804 + 210.024i) q^{63} +(189.757 - 119.385i) q^{65} +(329.987 - 329.987i) q^{67} +(-157.853 - 228.326i) q^{69} -171.760i q^{71} +(-279.927 - 279.927i) q^{73} +(-381.687 + 525.538i) q^{75} +(-383.589 - 383.589i) q^{77} +48.0189i q^{79} +(547.102 + 481.789i) q^{81} +(-144.451 + 144.451i) q^{83} +(248.371 - 156.262i) q^{85} +(117.400 - 643.334i) q^{87} +1417.21 q^{89} +378.799 q^{91} +(-230.751 + 1264.48i) q^{93} +(534.972 + 121.779i) q^{95} +(908.111 - 908.111i) q^{97} +(-273.861 + 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 16 q^{7} + 68 q^{13} - 90 q^{15} - 492 q^{21} - 220 q^{25} - 702 q^{27} - 616 q^{31} - 240 q^{33} - 1156 q^{37} - 548 q^{43} + 180 q^{45} + 852 q^{51} - 460 q^{55} + 684 q^{57} + 16 q^{61}+ \cdots + 1904 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 + 16 * q^7 + 68 * q^13 - 90 * q^15 - 492 * q^21 - 220 * q^25 - 702 * q^27 - 616 * q^31 - 240 * q^33 - 1156 * q^37 - 548 * q^43 + 180 * q^45 + 852 * q^51 - 460 * q^55 + 684 * q^57 + 16 * q^61 - 1428 * q^63 - 404 * q^67 - 2512 * q^73 + 2910 * q^75 + 288 * q^81 + 4940 * q^85 + 1680 * q^87 + 1304 * q^91 + 3408 * q^93 + 1904 * q^97

Introduction

L-functions

Modular forms

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Database

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