LMFDB - Embedded newform 240.4.v.c.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,4,Mod(17,240)]

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

lf = mfeigenbasis(mf)

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")

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

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			113.1
Root			$1.18766 - 1.18766i$ of defining polynomial
Character	$\chi$	$=$	240.113
Dual form			240.4.v.c.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.11173 + 0.932827i) q^{3} +(-2.48157 + 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(25.2597 - 9.53673i) q^{9} +O(q^{10})$	\(q+(-5.11173 + 0.932827i) q^{3} +(-2.48157 + 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(25.2597 - 9.53673i) q^{9} +28.7164i q^{11} +(14.1789 + 14.1789i) q^{13} +(2.51595 - 58.0402i) q^{15} +(-18.5587 - 18.5587i) q^{17} +49.0735i q^{19} +(-55.8211 + 80.7421i) q^{21} +(-37.7738 + 37.7738i) q^{23} +(-112.684 - 54.1055i) q^{25} +(-120.225 + 72.3121i) q^{27} -125.854 q^{29} -247.367 q^{31} +(-26.7874 - 146.791i) q^{33} +(112.471 + 178.768i) q^{35} +(-127.463 + 127.463i) q^{37} +(-85.7053 - 59.2524i) q^{39} +390.328i q^{41} +(39.3993 + 39.3993i) q^{43} +(41.2806 + 299.033i) q^{45} +(124.560 + 124.560i) q^{47} -13.8625i q^{49} +(112.179 + 77.5549i) q^{51} +(160.441 - 160.441i) q^{53} +(-313.051 - 71.2618i) q^{55} +(-45.7770 - 250.850i) q^{57} -729.423 q^{59} +2.00000 q^{61} +(210.024 - 464.804i) q^{63} +(-189.757 + 119.385i) q^{65} +(329.987 - 329.987i) q^{67} +(157.853 - 228.326i) q^{69} +171.760i q^{71} +(-279.927 - 279.927i) q^{73} +(626.480 + 171.458i) q^{75} +(383.589 + 383.589i) q^{77} +48.0189i q^{79} +(547.102 - 481.789i) q^{81} +(144.451 - 144.451i) q^{83} +(248.371 - 156.262i) q^{85} +(643.334 - 117.400i) q^{87} -1417.21 q^{89} +378.799 q^{91} +(1264.48 - 230.751i) q^{93} +(-534.972 - 121.779i) q^{95} +(908.111 - 908.111i) q^{97} +(273.861 + 725.367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 16 q^{7}+O(q^{10}) $ 8 * q + 6 * q^3 + 16 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

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
$3$	−5.11173	+	0.932827i	−0.983754	+	0.179523i
$3$	−5.11173	+	0.932827i	−0.983754	+	0.179523i
$4$		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	$0.128757\pi$
$11$			28.7164i			0.787121i	−0.919299	+	0.393560i	$0.871243\pi$
$12$		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
$15$	2.51595	−	58.0402i	0.0433078	−	0.999062i
$16$		0			0
$17$	−18.5587	−	18.5587i	−0.264773	−	0.264773i	0.562217	−	0.826990i	$-0.309949\pi$
$17$	−18.5587	−	18.5587i	−0.264773	−	0.264773i	−0.826990	+	0.562217i	$0.809949\pi$
$18$		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	−0.857288	−	0.514837i	$-0.827852\pi$
$23$	−37.7738	+	37.7738i	−0.342451	+	0.342451i	0.514837	+	0.857288i	$0.327852\pi$
$24$		0			0
$25$	−112.684	−	54.1055i	−0.901469	−	0.432844i
$26$		0			0
$27$	−120.225	+	72.3121i	−0.856935	+	0.515425i
$28$		0			0
$29$	−125.854			−0.805882			−0.402941	−	0.915226i	$-0.632012\pi$
$29$	−125.854			−0.805882			−0.402941	+	0.915226i	$0.632012\pi$
$30$		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
$33$	−26.7874	−	146.791i	−0.141306	−	0.774333i
$34$		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	$0.266789\pi$
$41$			390.328i			1.48680i	−0.668845	+	0.743402i	$0.733211\pi$
$42$		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
$45$	41.2806	+	299.033i	0.136750	+	0.990606i
$46$		0			0
$47$	124.560	+	124.560i	0.386575	+	0.386575i	0.873464	−	0.486889i	$-0.161868\pi$
$47$	124.560	+	124.560i	0.386575	+	0.386575i	−0.486889	+	0.873464i	$0.661868\pi$
$48$		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	−0.467943	−	0.883759i	$-0.655005\pi$
$53$	160.441	−	160.441i	0.415816	−	0.415816i	0.883759	+	0.467943i	$0.155005\pi$
$54$		0			0
$55$	−313.051	−	71.2618i	−0.767487	−	0.174708i
$56$		0			0
$57$	−45.7770	−	250.850i	−0.106374	−	0.582912i
$58$		0			0
$59$	−729.423			−1.60954			−0.804769	−	0.593588i	$-0.797711\pi$
$59$	−729.423			−1.60954			−0.804769	+	0.593588i	$0.797711\pi$
$60$		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
$63$	210.024	−	464.804i	0.420009	−	0.929520i
$64$		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	$0.0458518\pi$
$71$			171.760i			0.287100i	−0.989643	+	0.143550i	$0.954148\pi$
$72$		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
$75$	626.480	+	171.458i	0.964529	+	0.263978i
$76$		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	−0.605111	−	0.796141i	$-0.706871\pi$
$83$	144.451	−	144.451i	0.191031	−	0.191031i	0.796141	+	0.605111i	$0.206871\pi$
$84$		0			0
$85$	248.371	−	156.262i	0.316937	−	0.199400i
$86$		0			0
$87$	643.334	−	117.400i	0.792789	−	0.144674i
$88$		0			0
$89$	−1417.21			−1.68790			−0.843952	−	0.536419i	$-0.819777\pi$
$89$	−1417.21			−1.68790			−0.843952	+	0.536419i	$0.819777\pi$
$90$		0			0
$91$	378.799			0.436361
$92$		0			0
$93$	1264.48	−	230.751i	1.40989	−	0.257288i
$94$		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	$0.0531926\pi$
$101$			337.668i			0.332665i	−0.986070	+	0.166333i	$0.946807\pi$
$102$		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
$105$	−741.683	−	808.899i	−0.689342	−	0.751814i
$106$		0			0
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	0.384481	−	0.923133i	$-0.374380\pi$
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	−0.923133	+	0.384481i	$0.874380\pi$
$108$		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	−0.810922	−	0.585154i	$-0.801034\pi$
$113$	−271.193	+	271.193i	−0.225767	+	0.225767i	0.585154	+	0.810922i	$0.301034\pi$
$114$		0			0
$115$	−318.051	−	505.527i	−0.257899	−	0.409919i
$116$		0			0
$117$	493.375	+	222.934i	0.389851	+	0.176156i
$118$		0			0
$119$	−495.806			−0.381937
$120$		0			0
$121$	506.367			0.380441
$122$		0			0
$123$	−364.108	−	1995.25i	−0.266915	−	1.46265i
$124$		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	$0.229460\pi$
$131$			1979.28i			1.32008i	−0.751231	+	0.660039i	$0.770540\pi$
$132$		0			0
$133$	655.514	+	655.514i	0.427371	+	0.427371i
$134$		0			0
$135$	−489.962	−	1490.07i	−0.312364	−	0.949962i
$136$		0			0
$137$	−507.451	−	507.451i	−0.316456	−	0.316456i	0.530948	−	0.847404i	$-0.321836\pi$
$137$	−507.451	−	507.451i	−0.316456	−	0.316456i	−0.847404	+	0.530948i	$0.821836\pi$
$138$		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
$147$	12.9313	+	70.8616i	0.00725550	+	0.0397590i
$148$		0			0
$149$	−363.356			−0.199780			−0.0998902	−	0.994998i	$-0.531849\pi$
$149$	−363.356			−0.199780			−0.0998902	+	0.994998i	$0.531849\pi$
$150$		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
$153$	−645.774	−	291.797i	−0.341227	−	0.154185i
$154$		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
$165$	1666.71	+	72.2492i	0.786382	+	0.0340884i
$166$		0			0
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.814724	+	0.579848i	$0.196888\pi$
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.579848	+	0.814724i	$0.303112\pi$
$168$		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	−0.984375	−	0.176086i	$-0.943656\pi$
$173$	−1839.23	+	1839.23i	−0.808288	+	0.808288i	0.176086	+	0.984375i	$0.443656\pi$
$174$		0			0
$175$	−2227.94	+	782.476i	−0.962379	+	0.337998i
$176$		0			0
$177$	3728.61	−	680.425i	1.58339	−	0.288948i
$178$		0			0
$179$	−821.582			−0.343061			−0.171530	−	0.985179i	$-0.554871\pi$
$179$	−821.582			−0.343061			−0.171530	+	0.985179i	$0.554871\pi$
$180$		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
$183$	−10.2235	+	1.86565i	−0.00412973	+	0.000753623i
$184$		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	$0.0564385\pi$
$191$			931.167i			0.352758i	−0.984322	+	0.176379i	$0.943562\pi$
$192$		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
$195$	858.621	−	787.274i	0.315319	−	0.289117i
$196$		0			0
$197$	2995.05	+	2995.05i	1.08319	+	1.08319i	0.996210	+	0.0869796i	$0.0277215\pi$
$197$	2995.05	+	2995.05i	1.08319	+	1.08319i	0.0869796	+	0.996210i	$0.472279\pi$
$198$		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
$207$	−593.915	+	1314.39i	−0.199420	+	0.441336i
$208$		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
$213$	−160.222	−	877.989i	−0.0515409	−	0.282436i
$214$		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
$225$	−3362.34	−	292.053i	−0.996249	−	0.0865343i
$226$		0			0
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	0.472362	−	0.881404i	$-0.343401\pi$
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	−0.881404	+	0.472362i	$0.843401\pi$
$228$		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	−0.371515	−	0.928427i	$-0.621162\pi$
$233$	1980.71	−	1980.71i	0.556912	−	0.556912i	0.928427	+	0.371515i	$0.121162\pi$
$234$		0			0
$235$	−1667.00	+	1048.79i	−0.462736	+	0.291129i
$236$		0			0
$237$	−44.7933	−	245.460i	−0.0122769	−	0.0672756i
$238$		0			0
$239$	−2976.20			−0.805500			−0.402750	−	0.915310i	$-0.631946\pi$
$239$	−2976.20			−0.805500			−0.402750	+	0.915310i	$0.631946\pi$
$240$		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
$243$	−2347.21	+	2973.13i	−0.619645	+	0.784882i
$244$		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	$-0.937885\pi$
$251$		−	1542.14i		−	0.387805i	0.981021	−	0.193902i	$-0.0621145\pi$
$252$		0			0
$253$	−1084.73	−	1084.73i	−0.269550	−	0.269550i
$254$		0			0
$255$	−1123.84	+	1030.46i	−0.275991	+	0.253057i
$256$		0			0
$257$	428.853	+	428.853i	0.104090	+	0.104090i	0.757234	−	0.653144i	$-0.226550\pi$
$257$	428.853	+	428.853i	0.104090	+	0.104090i	−0.653144	+	0.757234i	$0.726550\pi$
$258$		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	$-0.413120\pi$
$263$	5256.99	−	5256.99i	1.23255	−	1.23255i	0.962982	−	0.269565i	$-0.0868798\pi$
$264$		0			0
$265$	1350.89	+	2147.18i	0.313150	+	0.497738i
$266$		0			0
$267$	7244.38	−	1322.01i	1.66048	−	0.303017i
$268$		0			0
$269$	1930.34			0.437528			0.218764	−	0.975778i	$-0.429797\pi$
$269$	1930.34			0.437528			0.218764	+	0.975778i	$0.429797\pi$
$270$		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
$273$	−1936.32	+	353.353i	−0.429272	+	0.0783367i
$274$		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	$0.138909\pi$
$281$			3981.96i			0.845351i	−0.906281	+	0.422676i	$0.861091\pi$
$282$		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
$285$	2848.24	+	123.467i	0.591982	+	0.0256615i
$286$		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	−0.0951570	−	0.995462i	$-0.530335\pi$
$293$	4515.35	−	4515.35i	0.900305	−	0.900305i	0.995462	+	0.0951570i	$0.0303353\pi$
$294$		0			0
$295$	1810.11	−	7951.77i	0.357250	−	1.56939i
$296$		0			0
$297$	−2076.54	−	3452.42i	−0.405701	−	0.674511i
$298$		0			0
$299$	−1071.18			−0.207184
$300$		0			0
$301$	1052.58			0.201560
$302$		0			0
$303$	−314.986	−	1726.07i	−0.0597210	−	0.327261i
$304$		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	$-0.880866\pi$
$311$		−	4010.21i		−	0.731184i	0.930775	−	0.365592i	$-0.119134\pi$
$312$		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
$315$	4545.85	+	3443.01i	0.813110	+	0.615847i
$316$		0			0
$317$	−3112.10	−	3112.10i	−0.551397	−	0.551397i	0.375447	−	0.926844i	$-0.377489\pi$
$317$	−3112.10	−	3112.10i	−0.551397	−	0.551397i	−0.926844	+	0.375447i	$0.877489\pi$
$318$		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
$327$	−1935.24	−	10604.8i	−0.327275	−	1.79342i
$328$		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
$333$	−2004.10	+	4435.26i	−0.329801	+	0.729883i
$334$		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
$345$	2097.36	+	2287.44i	0.327299	+	0.356960i
$346$		0			0
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.948592	−	0.316503i	$-0.897491\pi$
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.316503	−	0.948592i	$-0.602509\pi$
$348$		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	−0.0433491	−	0.999060i	$-0.513803\pi$
$353$	6338.53	−	6338.53i	0.955711	−	0.955711i	0.999060	+	0.0433491i	$0.0138028\pi$
$354$		0			0
$355$	−1872.43	−	426.233i	−0.279939	−	0.0637242i
$356$		0			0
$357$	2534.43	−	462.501i	0.375732	−	0.0685663i
$358$		0			0
$359$	8827.47			1.29776			0.648880	−	0.760890i	$-0.275238\pi$
$359$	8827.47			1.29776			0.648880	+	0.760890i	$0.275238\pi$
$360$		0			0
$361$	4450.80			0.648899
$362$		0			0
$363$	−2588.42	+	472.353i	−0.374261	+	0.0682978i
$364$		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
$375$	−3423.80	+	6404.06i	−0.471478	+	0.881878i
$376$		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	−0.584880	−	0.811120i	$-0.698858\pi$
$383$	1695.77	−	1695.77i	0.226240	−	0.226240i	0.811120	+	0.584880i	$0.198858\pi$
$384$		0			0
$385$	−5133.58	+	3229.77i	−0.679562	+	0.427544i
$386$		0			0
$387$	1370.95	+	619.472i	0.180076	+	0.0813683i
$388$		0			0
$389$	−12362.2			−1.61128			−0.805640	−	0.592405i	$-0.798178\pi$
$389$	−12362.2			−1.61128			−0.805640	+	0.592405i	$0.798178\pi$
$390$		0			0
$391$	1402.06			0.181343
$392$		0			0
$393$	−1846.32	−	10117.5i	−0.236984	−	1.29863i
$394$		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	$-0.954631\pi$
$401$		−	2281.30i		−	0.284096i	0.989860	−	0.142048i	$-0.0453688\pi$
$402$		0			0
$403$	−3507.40	−	3507.40i	−0.433538	−	0.433538i
$404$		0			0
$405$	3894.53	+	7159.80i	0.477829	+	0.878453i
$406$		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
$417$	−63.8364	−	349.813i	−0.00749660	−	0.0410801i
$418$		0			0
$419$	2142.28			0.249779			0.124889	−	0.992171i	$-0.460142\pi$
$419$	2142.28			0.249779			0.124889	+	0.992171i	$0.460142\pi$
$420$		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
$423$	4334.26	+	1958.46i	0.498200	+	0.225115i
$424$		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	$0.340935\pi$
$431$			15707.3i			1.75543i	−0.479179	+	0.877717i	$0.659065\pi$
$432$		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
$435$	−316.644	+	7304.62i	−0.0349009	+	0.805126i
$436$		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	−0.594115	−	0.804380i	$-0.702498\pi$
$443$	1960.53	−	1960.53i	0.210265	−	0.210265i	0.804380	+	0.594115i	$0.202498\pi$
$444$		0			0
$445$	3516.89	−	15449.6i	0.374644	−	1.64580i
$446$		0			0
$447$	1857.38	−	338.948i	0.196535	−	0.0358651i
$448$		0			0
$449$	17849.2			1.87607			0.938036	−	0.346537i	$-0.112643\pi$
$449$	17849.2			1.87607			0.938036	+	0.346537i	$0.112643\pi$
$450$		0			0
$451$	−11208.8			−1.17029
$452$		0			0
$453$	−10648.5	+	1943.21i	−1.10443	+	0.201545i
$454$		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	$-0.852505\pi$
$461$		−	8848.20i		−	0.893930i	0.894552	−	0.446965i	$-0.147495\pi$
$462$		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
$465$	−622.365	+	14357.3i	−0.0620677	+	1.43183i
$466$		0			0
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	0.776618	−	0.629971i	$-0.216933\pi$
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	−0.629971	+	0.776618i	$0.716933\pi$
$468$		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
$477$	2522.60	−	5582.76i	0.242143	−	0.535885i
$478$		0			0
$479$	5039.60			0.480720			0.240360	−	0.970684i	$-0.422734\pi$
$479$	5039.60			0.480720			0.240360	+	0.970684i	$0.422734\pi$
$480$		0			0
$481$	−3614.58			−0.342642
$482$		0			0
$483$	−941.362	−	5158.51i	−0.0886821	−	0.485963i
$484$		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	$-0.780084\pi$
$491$		−	13865.7i		−	1.27444i	0.770681	−	0.637221i	$-0.219916\pi$
$492$		0			0
$493$	2335.69	+	2335.69i	0.213375	+	0.213375i
$494$		0			0
$495$	−8587.17	+	1185.43i	−0.779726	+	0.107639i
$496$		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	−0.964106	−	0.265517i	$-0.914457\pi$
$503$	−7880.86	+	7880.86i	−0.698589	+	0.698589i	0.265517	+	0.964106i	$0.414457\pi$
$504$		0			0
$505$	−3681.07	−	837.946i	−0.324368	−	0.0738379i
$506$		0			0
$507$	1674.35	+	9175.14i	0.146667	+	0.803713i
$508$		0			0
$509$	−1788.46			−0.155741			−0.0778704	−	0.996963i	$-0.524812\pi$
$509$	−1788.46			−0.155741			−0.0778704	+	0.996963i	$0.524812\pi$
$510$		0			0
$511$	−7478.42			−0.647408
$512$		0			0
$513$	−3548.60	−	5899.84i	−0.305409	−	0.507766i
$514$		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	$0.278444\pi$
$521$			18251.6i			1.53478i	−0.641183	+	0.767388i	$0.721556\pi$
$522$		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
$525$	10658.7	−	6078.09i	0.886066	−	0.505276i
$526$		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
$537$	4199.71	−	766.393i	0.337488	−	0.0615872i
$538$		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
$543$	−11829.6	+	2158.75i	−0.934911	+	0.170609i
$544$		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
$555$	7077.31	+	7718.69i	0.541288	+	0.590343i
$556$		0			0
$557$	8716.96	+	8716.96i	0.663105	+	0.663105i	0.956111	−	0.293006i	$-0.0946555\pi$
$557$	8716.96	+	8716.96i	0.663105	+	0.663105i	−0.293006	+	0.956111i	$0.594656\pi$
$558$		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	−0.993077	−	0.117462i	$-0.962524\pi$
$563$	−11697.0	+	11697.0i	−0.875615	+	0.875615i	0.117462	+	0.993077i	$0.462524\pi$
$564$		0			0
$565$	−2283.42	−	3629.39i	−0.170025	−	0.270247i
$566$		0			0
$567$	872.435	−	13743.7i	0.0646188	−	1.01796i
$568$		0			0
$569$	11517.5			0.848576			0.424288	−	0.905527i	$-0.360524\pi$
$569$	11517.5			0.848576			0.424288	+	0.905527i	$0.360524\pi$
$570$		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
$573$	−868.617	−	4759.88i	−0.0633281	−	0.347027i
$574$		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
$585$	−3654.65	+	4825.28i	−0.258293	+	0.341027i
$586$		0			0
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	0.340767	−	0.940148i	$-0.389313\pi$
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	−0.940148	+	0.340767i	$0.889313\pi$
$588$		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	−0.847691	−	0.530491i	$-0.822008\pi$
$593$	−4580.53	+	4580.53i	−0.317200	+	0.317200i	0.530491	+	0.847691i	$0.322008\pi$
$594$		0			0
$595$	1230.38	−	5405.01i	0.0847740	−	0.372410i
$596$		0			0
$597$	102.105	+	559.518i	0.00699979	+	0.0383577i
$598$		0			0
$599$	10195.8			0.695477			0.347738	−	0.937592i	$-0.386950\pi$
$599$	10195.8			0.695477			0.347738	+	0.937592i	$0.386950\pi$
$600$		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
$603$	5188.36	−	11482.4i	0.350392	−	0.775452i
$604$		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
$615$	22654.7	+	982.047i	1.48541	+	0.0643902i
$616$		0			0
$617$	−17118.9	−	17118.9i	−1.11698	−	1.11698i	−0.992182	−	0.124803i	$-0.960170\pi$
$617$	−17118.9	−	17118.9i	−1.11698	−	1.11698i	−0.124803	−	0.992182i	$-0.539830\pi$
$618$		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
$627$	7203.53	−	1314.55i	0.458822	−	0.0837291i
$628$		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
$633$	13878.0	−	2532.57i	0.871410	−	0.159021i
$634$		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	$-0.875402\pi$
$641$		−	12383.2i		−	0.763035i	0.924362	−	0.381518i	$-0.124598\pi$
$642$		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
$645$	2385.87	−	2187.62i	0.145649	−	0.133546i
$646$		0			0
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	0.776014	−	0.630716i	$-0.217239\pi$
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	−0.630716	+	0.776014i	$0.717239\pi$
$648$		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	−0.999993	−	0.00379136i	$-0.998793\pi$
$653$	−16623.3	+	16623.3i	−0.996201	+	0.996201i	0.00379136	+	0.999993i	$0.498793\pi$
$654$		0			0
$655$	−21577.0	−	4911.71i	−1.28715	−	0.293002i
$656$		0			0
$657$	−9740.43	−	4401.27i	−0.578403	−	0.261354i
$658$		0			0
$659$	−20089.8			−1.18754			−0.593768	−	0.804636i	$-0.702360\pi$
$659$	−20089.8			−1.18754			−0.593768	+	0.804636i	$0.702360\pi$
$660$		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
$663$	490.931	+	2690.22i	0.0287574	+	0.157586i
$664$		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
$675$	17459.8	−	1643.58i	0.995599	−	0.0937207i
$676$		0			0
$677$	−14662.4	−	14662.4i	−0.832380	−	0.832380i	0.155462	−	0.987842i	$-0.450313\pi$
$677$	−14662.4	−	14662.4i	−0.832380	−	0.832380i	−0.987842	+	0.155462i	$0.950313\pi$
$678$		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	−0.0996976	−	0.995018i	$-0.531788\pi$
$683$	15981.2	−	15981.2i	0.895320	−	0.895320i	0.995018	+	0.0996976i	$0.0317875\pi$
$684$		0			0
$685$	6791.23	−	4272.68i	0.378803	−	0.238322i
$686$		0			0
$687$	−3666.36	−	20091.1i	−0.203611	−	1.11575i
$688$		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
$693$	13347.5	+	6031.14i	0.731645	+	0.330598i
$694$		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	$-0.939695\pi$
$701$		−	6990.49i		−	0.376643i	0.982107	−	0.188322i	$-0.0603048\pi$
$702$		0			0
$703$	−6255.06	−	6255.06i	−0.335582	−	0.335582i
$704$		0			0
$705$	7542.91	−	6916.13i	0.402954	−	0.369470i
$706$		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
$717$	15213.6	−	2776.28i	0.792414	−	0.144605i
$718$		0			0
$719$	20143.8			1.04484			0.522418	−	0.852690i	$-0.325030\pi$
$719$	20143.8			1.04484			0.522418	+	0.852690i	$0.325030\pi$
$720$		0			0
$721$	24939.2			1.28819
$722$		0			0
$723$	−9382.32	+	1712.15i	−0.482617	+	0.0880715i
$724$		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
$735$	−804.585	−	34.8775i	−0.0403776	−	0.00175031i
$736$		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	−0.559977	−	0.828508i	$-0.689190\pi$
$743$	5438.49	−	5438.49i	0.268531	−	0.268531i	0.828508	+	0.559977i	$0.189190\pi$
$744$		0			0
$745$	901.693	−	3961.11i	0.0443429	−	0.194797i
$746$		0			0
$747$	2271.20	−	5026.38i	0.111243	−	0.246192i
$748$		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
$753$	1438.55	+	7883.01i	0.0696197	+	0.381505i
$754$		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	$0.221148\pi$
$761$			26879.5i			1.28040i	−0.768210	+	0.640198i	$0.778852\pi$
$762$		0			0
$763$	27712.1	+	27712.1i	1.31487	+	1.31487i
$764$		0			0
$765$	4783.54	−	6315.77i	0.226078	−	0.298493i
$766$		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	−0.115263	−	0.993335i	$-0.536771\pi$
$773$	18871.2	−	18871.2i	0.878072	−	0.878072i	0.993335	+	0.115263i	$0.0367711\pi$
$774$		0			0
$775$	27874.2	+	13383.9i	1.29196	+	0.620341i
$776$		0			0
$777$	−3176.52	−	17406.8i	−0.146663	−	0.803688i
$778$		0			0
$779$	−19154.7			−0.880988
$780$		0			0
$781$	−4932.32			−0.225982
$782$		0			0
$783$	15130.8	−	9100.79i	0.690588	−	0.415371i
$784$		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
$795$	−8908.37	−	9715.69i	−0.397418	−	0.433434i
$796$		0			0
$797$	17463.9	+	17463.9i	0.776163	+	0.776163i	0.979176	−	0.203013i	$-0.0650735\pi$
$797$	17463.9	+	17463.9i	0.776163	+	0.776163i	−0.203013	+	0.979176i	$0.565073\pi$
$798$		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
$807$	−9867.40	+	1800.68i	−0.430420	+	0.0785462i
$808$		0			0
$809$	−24097.9			−1.04727			−0.523633	−	0.851944i	$-0.675424\pi$
$809$	−24097.9			−1.04727			−0.523633	+	0.851944i	$0.675424\pi$
$810$		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
$813$	−16672.8	+	3042.57i	−0.719238	+	0.131252i
$814$		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	$-0.797728\pi$
$821$		−	27925.3i		−	1.18709i	0.804802	−	0.593544i	$-0.202272\pi$
$822$		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
$825$	−4923.67	+	17990.3i	−0.207782	+	0.759200i
$826$		0			0
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	0.980768	−	0.195178i	$-0.0625285\pi$
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	−0.195178	+	0.980768i	$0.562529\pi$
$828$		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
$837$	29739.6	−	17887.6i	1.22814	−	0.738695i
$838$		0			0
$839$	−30903.4			−1.27164			−0.635820	−	0.771838i	$-0.719338\pi$
$839$	−30903.4			−1.27164			−0.635820	+	0.771838i	$0.719338\pi$
$840$		0			0
$841$	−8549.68			−0.350555
$842$		0			0
$843$	−3714.48	−	20354.7i	−0.151760	−	0.831618i
$844$		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
$855$	−14674.6	+	2025.78i	−0.586971	+	0.0810295i
$856$		0			0
$857$	−13852.9	−	13852.9i	−0.552167	−	0.552167i	0.374899	−	0.927066i	$-0.377677\pi$
$857$	−13852.9	−	13852.9i	−0.552167	−	0.552167i	−0.927066	+	0.374899i	$0.877677\pi$
$858$		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	−0.567481	−	0.823386i	$-0.692082\pi$
$863$	6487.75	−	6487.75i	0.255905	−	0.255905i	0.823386	+	0.567481i	$0.192082\pi$
$864$		0			0
$865$	−15486.1	−	24614.4i	−0.608720	−	0.967533i
$866$		0			0
$867$	3940.40	+	21592.8i	0.154352	+	0.845823i
$868$		0			0
$869$	−1378.93			−0.0538285
$870$		0			0
$871$	9357.71			0.364034
$872$		0			0
$873$	14278.2	−	31599.0i	0.553543	−	1.22504i
$874$		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	$0.218993\pi$
$881$			33209.0i			1.26996i	−0.772527	+	0.634982i	$0.781007\pi$
$882$		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
$885$	−1835.19	+	42335.9i	−0.0697055	+	1.60803i
$886$		0			0
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	0.0873406	−	0.996179i	$-0.472163\pi$
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	−0.996179	+	0.0873406i	$0.972163\pi$
$888$		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
$897$	5475.59	−	999.226i	0.203818	−	0.0371942i
$898$		0			0
$899$	31132.2			1.15497
$900$		0			0
$901$	−5955.13			−0.220193
$902$		0			0
$903$	−5380.49	+	981.871i	−0.198285	+	0.0361845i
$904$		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	$0.207929\pi$
$911$			33422.1i			1.21550i	−0.794127	+	0.607752i	$0.792071\pi$
$912$		0			0
$913$	4148.12	+	4148.12i	0.150364	+	0.150364i
$914$		0			0
$915$	5.03191	−	116.080i	0.000181803	−	0.00419399i
$916$		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
$927$	32482.6	+	14677.4i	1.15088	+	0.520033i
$928$		0			0
$929$	5721.21			0.202053			0.101026	−	0.994884i	$-0.467787\pi$
$929$	5721.21			0.202053			0.101026	+	0.994884i	$0.467787\pi$
$930$		0			0
$931$	680.282			0.0239477
$932$		0			0
$933$	3740.83	+	20499.1i	0.131264	+	0.719305i
$934$		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	$-0.946678\pi$
$941$		−	9625.77i		−	0.333466i	0.986002	−	0.166733i	$-0.0533217\pi$
$942$		0			0
$943$	−14744.1	−	14744.1i	−0.509157	−	0.509157i
$944$		0			0
$945$	−26448.9	−	13359.3i	−0.910459	−	0.459870i
$946$		0			0
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	0.744400	−	0.667734i	$-0.232736\pi$
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	−0.667734	+	0.744400i	$0.732736\pi$
$948$		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	−0.588798	−	0.808281i	$-0.700398\pi$
$953$	6457.14	−	6457.14i	0.219483	−	0.219483i	0.808281	+	0.588798i	$0.200398\pi$
$954$		0			0
$955$	−10151.1	−	2310.75i	−0.343959	−	0.0782977i
$956$		0			0
$957$	3371.32	+	18474.3i	0.113876	+	0.624021i
$958$		0			0
$959$	−13556.9			−0.456491
$960$		0			0
$961$	31399.6			1.05399
$962$		0			0
$963$	−20745.2	−	9373.84i	−0.694190	−	0.313674i
$964$		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	$0.115641\pi$
$971$			21504.3i			0.710716i	−0.934730	+	0.355358i	$0.884359\pi$
$972$		0			0
$973$	914.119	+	914.119i	0.0301185	+	0.0301185i
$974$		0			0
$975$	6451.71	+	11313.9i	0.211918	+	0.371625i
$976$		0			0
$977$	−8996.19	−	8996.19i	−0.294589	−	0.294589i	0.544301	−	0.838890i	$-0.316795\pi$
$977$	−8996.19	−	8996.19i	−0.294589	−	0.294589i	−0.838890	+	0.544301i	$0.816795\pi$
$978$		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	−0.390509	−	0.920599i	$-0.627701\pi$
$983$	16337.3	−	16337.3i	0.530090	−	0.530090i	0.920599	+	0.390509i	$0.127701\pi$
$984$		0			0
$985$	−40082.8	+	25218.0i	−1.29659	+	0.815748i
$986$		0			0
$987$	−17010.4	+	3104.18i	−0.548578	+	0.100108i
$988$		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
$993$	−49018.8	+	8945.31i	−1.56653	+	0.285872i
$994$		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.113.1		8
3.2	odd	2	inner	240.4.v.c.113.2		8
4.3	odd	2		15.4.e.a.8.2	yes	8
5.2	odd	4	inner	240.4.v.c.17.2		8
12.11	even	2		15.4.e.a.8.3	yes	8
15.2	even	4	inner	240.4.v.c.17.1		8
20.3	even	4		75.4.e.c.32.2		8
20.7	even	4		15.4.e.a.2.3	yes	8
20.19	odd	2		75.4.e.c.68.3		8
60.23	odd	4		75.4.e.c.32.3		8
60.47	odd	4		15.4.e.a.2.2	✓	8
60.59	even	2		75.4.e.c.68.2		8

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

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

\(f(q)\)	\(=\)	\(q+(-5.11173 + 0.932827i) q^{3} +(-2.48157 + 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(25.2597 - 9.53673i) q^{9} +O(q^{10})\)	\(q+(-5.11173 + 0.932827i) q^{3} +(-2.48157 + 10.9015i) q^{5} +(13.3578 - 13.3578i) q^{7} +(25.2597 - 9.53673i) q^{9} +28.7164i q^{11} +(14.1789 + 14.1789i) q^{13} +(2.51595 - 58.0402i) q^{15} +(-18.5587 - 18.5587i) q^{17} +49.0735i q^{19} +(-55.8211 + 80.7421i) q^{21} +(-37.7738 + 37.7738i) q^{23} +(-112.684 - 54.1055i) q^{25} +(-120.225 + 72.3121i) q^{27} -125.854 q^{29} -247.367 q^{31} +(-26.7874 - 146.791i) q^{33} +(112.471 + 178.768i) q^{35} +(-127.463 + 127.463i) q^{37} +(-85.7053 - 59.2524i) q^{39} +390.328i q^{41} +(39.3993 + 39.3993i) q^{43} +(41.2806 + 299.033i) q^{45} +(124.560 + 124.560i) q^{47} -13.8625i q^{49} +(112.179 + 77.5549i) q^{51} +(160.441 - 160.441i) q^{53} +(-313.051 - 71.2618i) q^{55} +(-45.7770 - 250.850i) q^{57} -729.423 q^{59} +2.00000 q^{61} +(210.024 - 464.804i) q^{63} +(-189.757 + 119.385i) q^{65} +(329.987 - 329.987i) q^{67} +(157.853 - 228.326i) q^{69} +171.760i q^{71} +(-279.927 - 279.927i) q^{73} +(626.480 + 171.458i) q^{75} +(383.589 + 383.589i) q^{77} +48.0189i q^{79} +(547.102 - 481.789i) q^{81} +(144.451 - 144.451i) q^{83} +(248.371 - 156.262i) q^{85} +(643.334 - 117.400i) q^{87} -1417.21 q^{89} +378.799 q^{91} +(1264.48 - 230.751i) q^{93} +(-534.972 - 121.779i) q^{95} +(908.111 - 908.111i) q^{97} +(273.861 + 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 16 q^{7}+O(q^{10}) \) 8 * q + 6 * q^3 + 16 * q^7	\( 8 q + 6 q^{3} + 16 q^{7} + 68 q^{13} - 90 q^{15} - 492 q^{21} - 220 q^{25} - 702 q^{27} - 616 q^{31} - 240 q^{33} - 1156 q^{37} - 548 q^{43} + 180 q^{45} + 852 q^{51} - 460 q^{55} + 684 q^{57} + 16 q^{61} - 1428 q^{63} - 404 q^{67} - 2512 q^{73} + 2910 q^{75} + 288 q^{81} + 4940 q^{85} + 1680 q^{87} + 1304 q^{91} + 3408 q^{93} + 1904 q^{97}+O(q^{100}) \) 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

Varieties

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Database

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