LMFDB - Embedded newform 180.4.k.e.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,4,Mod(127,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("180.127");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	180.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6203438010$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.6
Root			$1.13579 - 1.64620i$ of defining polynomial
Character	$\chi$	$=$	180.127
Dual form			180.4.k.e.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.78199 + 0.510409i) q^{2} +(7.47897 + 2.83991i) q^{4} +(-10.9349 + 2.32970i) q^{5} +(-14.4440 + 14.4440i) q^{7} +(19.3569 + 11.7179i) q^{8} +O(q^{10})$	\(q+(2.78199 + 0.510409i) q^{2} +(7.47897 + 2.83991i) q^{4} +(-10.9349 + 2.32970i) q^{5} +(-14.4440 + 14.4440i) q^{7} +(19.3569 + 11.7179i) q^{8} +(-31.6100 + 0.899920i) q^{10} +47.0607i q^{11} +(-8.79525 + 8.79525i) q^{13} +(-47.5554 + 32.8107i) q^{14} +(47.8698 + 42.4791i) q^{16} +(26.4898 + 26.4898i) q^{17} -49.8054 q^{19} +(-88.3980 - 13.6304i) q^{20} +(-24.0202 + 130.922i) q^{22} +(41.2762 + 41.2762i) q^{23} +(114.145 - 50.9501i) q^{25} +(-28.9575 + 19.9791i) q^{26} +(-149.046 + 67.0065i) q^{28} -247.406i q^{29} +62.3240i q^{31} +(111.492 + 142.610i) q^{32} +(60.1738 + 87.2150i) q^{34} +(124.294 - 191.594i) q^{35} +(-73.2182 - 73.2182i) q^{37} +(-138.558 - 25.4211i) q^{38} +(-238.966 - 83.0389i) q^{40} -118.624 q^{41} +(245.335 + 245.335i) q^{43} +(-133.648 + 351.965i) q^{44} +(93.7624 + 135.898i) q^{46} +(-125.525 + 125.525i) q^{47} -74.2578i q^{49} +(343.556 - 83.4822i) q^{50} +(-90.7571 + 40.8017i) q^{52} +(326.574 - 326.574i) q^{53} +(-109.637 - 514.605i) q^{55} +(-448.845 + 110.337i) q^{56} +(126.278 - 688.282i) q^{58} +365.123 q^{59} -268.160 q^{61} +(-31.8107 + 173.385i) q^{62} +(237.380 + 453.646i) q^{64} +(75.6851 - 116.666i) q^{65} +(-112.617 + 112.617i) q^{67} +(122.888 + 273.345i) q^{68} +(443.576 - 469.573i) q^{70} -559.873i q^{71} +(215.825 - 215.825i) q^{73} +(-166.321 - 241.064i) q^{74} +(-372.493 - 141.443i) q^{76} +(-679.744 - 679.744i) q^{77} +1172.36 q^{79} +(-622.417 - 352.984i) q^{80} +(-330.012 - 60.5470i) q^{82} +(592.561 + 592.561i) q^{83} +(-351.377 - 227.951i) q^{85} +(557.299 + 807.742i) q^{86} +(-551.454 + 910.949i) q^{88} +552.071i q^{89} -254.077i q^{91} +(191.483 + 425.924i) q^{92} +(-413.277 + 285.139i) q^{94} +(544.618 - 116.032i) q^{95} +(460.651 + 460.651i) q^{97} +(37.9019 - 206.585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 12 * q^8	$ 12 q + 6 q^{2} + 12 q^{8} - 110 q^{10} + 116 q^{13} + 312 q^{16} + 332 q^{17} - 140 q^{20} + 360 q^{22} + 340 q^{25} + 164 q^{26} - 880 q^{28} + 376 q^{32} + 508 q^{37} - 1600 q^{38} + 1420 q^{40} + 656 q^{41} - 1432 q^{46} + 1570 q^{50} - 932 q^{52} + 644 q^{53} - 2048 q^{56} + 1576 q^{58} - 896 q^{61} - 2440 q^{62} + 2740 q^{65} + 844 q^{68} - 3040 q^{70} + 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 1840 q^{80} - 1352 q^{82} + 500 q^{85} + 2552 q^{86} - 2400 q^{88} + 1840 q^{92} - 4772 q^{97} - 1698 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 12 * q^8 - 110 * q^10 + 116 * q^13 + 312 * q^16 + 332 * q^17 - 140 * q^20 + 360 * q^22 + 340 * q^25 + 164 * q^26 - 880 * q^28 + 376 * q^32 + 508 * q^37 - 1600 * q^38 + 1420 * q^40 + 656 * q^41 - 1432 * q^46 + 1570 * q^50 - 932 * q^52 + 644 * q^53 - 2048 * q^56 + 1576 * q^58 - 896 * q^61 - 2440 * q^62 + 2740 * q^65 + 844 * q^68 - 3040 * q^70 + 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 1840 * q^80 - 1352 * q^82 + 500 * q^85 + 2552 * q^86 - 2400 * q^88 + 1840 * q^92 - 4772 * q^97 - 1698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	2.78199	+	0.510409i	0.983583	+	0.180457i
$2$	2.78199	+	0.510409i	0.983583	+	0.180457i
$3$		0			0
$3$		0			0
$4$	7.47897	+	2.83991i	0.934871	+	0.354989i
$5$	−10.9349	+	2.32970i	−0.978049	+	0.208375i
$5$	−10.9349	+	2.32970i	−0.978049	+	0.208375i
$6$		0			0
$7$	−14.4440	+	14.4440i	−0.779902	+	0.779902i	−0.979814	−	0.199912i	$-0.935934\pi$
$7$	−14.4440	+	14.4440i	−0.779902	+	0.779902i	0.199912	+	0.979814i	$0.435934\pi$
$8$	19.3569	+	11.7179i	0.855463	+	0.517864i
$9$		0			0
$10$	−31.6100	+	0.899920i	−0.999595	+	0.0284580i
$11$			47.0607i			1.28994i	0.764209	+	0.644969i	$0.223130\pi$
$11$			47.0607i			1.28994i	−0.764209	+	0.644969i	$0.776870\pi$
$12$		0			0
$13$	−8.79525	+	8.79525i	−0.187643	+	0.187643i	−0.794676	−	0.607033i	$-0.792360\pi$
$13$	−8.79525	+	8.79525i	−0.187643	+	0.187643i	0.607033	+	0.794676i	$0.292360\pi$
$14$	−47.5554	+	32.8107i	−0.907837	+	0.626360i
$15$		0			0
$16$	47.8698	+	42.4791i	0.747966	+	0.663737i
$17$	26.4898	+	26.4898i	0.377925	+	0.377925i	0.870353	−	0.492428i	$-0.163891\pi$
$17$	26.4898	+	26.4898i	0.377925	+	0.377925i	−0.492428	+	0.870353i	$0.663891\pi$
$18$		0			0
$19$	−49.8054			−0.601376			−0.300688	−	0.953723i	$-0.597216\pi$
$19$	−49.8054			−0.601376			−0.300688	+	0.953723i	$0.597216\pi$
$20$	−88.3980	−	13.6304i	−0.988320	−	0.152393i
$21$		0			0
$22$	−24.0202	+	130.922i	−0.232778	+	1.26876i
$23$	41.2762	+	41.2762i	0.374204	+	0.374204i	0.869006	−	0.494802i	$-0.164759\pi$
$23$	41.2762	+	41.2762i	0.374204	+	0.374204i	−0.494802	+	0.869006i	$0.664759\pi$
$24$		0			0
$25$	114.145	−	50.9501i	0.913160	−	0.407601i
$26$	−28.9575	+	19.9791i	−0.218424	+	0.150701i
$27$		0			0
$28$	−149.046	+	67.0065i	−1.00596	+	0.452251i
$29$		−	247.406i		−	1.58421i	−0.610382	−	0.792107i	$-0.708984\pi$
$29$		−	247.406i		−	1.58421i	0.610382	−	0.792107i	$-0.291016\pi$
$30$		0			0
$31$			62.3240i			0.361088i	0.983567	+	0.180544i	$0.0577858\pi$
$31$			62.3240i			0.361088i	−0.983567	+	0.180544i	$0.942214\pi$
$32$	111.492	+	142.610i	0.615911	+	0.787816i
$33$		0			0
$34$	60.1738	+	87.2150i	0.303521	+	0.439919i
$35$	124.294	−	191.594i	0.600271	−	0.925294i
$36$		0			0
$37$	−73.2182	−	73.2182i	−0.325324	−	0.325324i	0.525481	−	0.850805i	$-0.323885\pi$
$37$	−73.2182	−	73.2182i	−0.325324	−	0.325324i	−0.850805	+	0.525481i	$0.823885\pi$
$38$	−138.558	−	25.4211i	−0.591503	−	0.108522i
$39$		0			0
$40$	−238.966	−	83.0389i	−0.944594	−	0.328240i
$41$	−118.624			−0.451854			−0.225927	−	0.974144i	$-0.572541\pi$
$41$	−118.624			−0.451854			−0.225927	+	0.974144i	$0.572541\pi$
$42$		0			0
$43$	245.335	+	245.335i	0.870076	+	0.870076i	0.992480	−	0.122404i	$-0.0390605\pi$
$43$	245.335	+	245.335i	0.870076	+	0.870076i	−0.122404	+	0.992480i	$0.539060\pi$
$44$	−133.648	+	351.965i	−0.457913	+	1.20593i
$45$		0			0
$46$	93.7624	+	135.898i	0.300533	+	0.435588i
$47$	−125.525	+	125.525i	−0.389567	+	0.389567i	−0.874533	−	0.484966i	$-0.838832\pi$
$47$	−125.525	+	125.525i	−0.389567	+	0.389567i	0.484966	+	0.874533i	$0.338832\pi$
$48$		0			0
$49$		−	74.2578i		−	0.216495i
$50$	343.556	−	83.4822i	0.971723	−	0.236123i
$51$		0			0
$52$	−90.7571	+	40.8017i	−0.242033	+	0.108811i
$53$	326.574	−	326.574i	0.846385	−	0.846385i	−0.143295	−	0.989680i	$-0.545770\pi$
$53$	326.574	−	326.574i	0.846385	−	0.846385i	0.989680	+	0.143295i	$0.0457699\pi$
$54$		0			0
$55$	−109.637	−	514.605i	−0.268790	−	1.26162i
$56$	−448.845	+	110.337i	−1.07106	+	0.263294i
$57$		0			0
$58$	126.278	−	688.282i	0.285882	−	1.55821i
$59$	365.123			0.805677			0.402839	−	0.915271i	$-0.368024\pi$
$59$	365.123			0.805677			0.402839	+	0.915271i	$0.368024\pi$
$60$		0			0
$61$	−268.160			−0.562858			−0.281429	−	0.959582i	$-0.590808\pi$
$61$	−268.160			−0.562858			−0.281429	+	0.959582i	$0.590808\pi$
$62$	−31.8107	+	173.385i	−0.0651608	+	0.355160i
$63$		0			0
$64$	237.380	+	453.646i	0.463633	+	0.886027i
$65$	75.6851	−	116.666i	0.144424	−	0.222624i
$66$		0			0
$67$	−112.617	+	112.617i	−0.205349	+	0.205349i	−0.802287	−	0.596938i	$-0.796384\pi$
$67$	−112.617	+	112.617i	−0.205349	+	0.205349i	0.596938	+	0.802287i	$0.296384\pi$
$68$	122.888	+	273.345i	0.219152	+	0.487469i
$69$		0			0
$70$	443.576	−	469.573i	0.757392	−	0.801781i
$71$		−	559.873i		−	0.935841i	−0.883771	−	0.467921i	$-0.845003\pi$
$71$		−	559.873i		−	0.935841i	0.883771	−	0.467921i	$-0.154997\pi$
$72$		0			0
$73$	215.825	−	215.825i	0.346033	−	0.346033i	−0.512597	−	0.858629i	$-0.671316\pi$
$73$	215.825	−	215.825i	0.346033	−	0.346033i	0.858629	+	0.512597i	$0.171316\pi$
$74$	−166.321	−	241.064i	−0.261276	−	0.378690i
$75$		0			0
$76$	−372.493	−	141.443i	−0.562209	−	0.213482i
$77$	−679.744	−	679.744i	−1.00603	−	1.00603i
$78$		0			0
$79$	1172.36			1.66963			0.834816	−	0.550528i	$-0.185574\pi$
$79$	1172.36			1.66963			0.834816	+	0.550528i	$0.185574\pi$
$80$	−622.417	−	352.984i	−0.869854	−	0.493310i
$81$		0			0
$82$	−330.012	−	60.5470i	−0.444436	−	0.0815402i
$83$	592.561	+	592.561i	0.783639	+	0.783639i	0.980443	−	0.196804i	$-0.0630562\pi$
$83$	592.561	+	592.561i	0.783639	+	0.783639i	−0.196804	+	0.980443i	$0.563056\pi$
$84$		0			0
$85$	−351.377	−	227.951i	−0.448379	−	0.290879i
$86$	557.299	+	807.742i	0.698781	+	1.01280i
$87$		0			0
$88$	−551.454	+	910.949i	−0.668013	+	1.10349i
$89$			552.071i			0.657522i	0.944413	+	0.328761i	$0.106631\pi$
$89$			552.071i			0.657522i	−0.944413	+	0.328761i	$0.893369\pi$
$90$		0			0
$91$		−	254.077i		−	0.292687i
$92$	191.483	+	425.924i	0.216994	+	0.482670i
$93$		0			0
$94$	−413.277	+	285.139i	−0.453471	+	0.312871i
$95$	544.618	−	116.032i	0.588175	−	0.125311i
$96$		0			0
$97$	460.651	+	460.651i	0.482186	+	0.482186i	0.905829	−	0.423643i	$-0.139249\pi$
$97$	460.651	+	460.651i	0.482186	+	0.482186i	−0.423643	+	0.905829i	$0.639249\pi$
$98$	37.9019	−	206.585i	0.0390680	−	0.212941i
$99$		0			0
$100$	998.380	−	56.8929i	0.998380	−	0.0568929i
$101$	5.97644			0.00588790			0.00294395	−	0.999996i	$-0.499063\pi$
$101$	5.97644			0.00588790			0.00294395	+	0.999996i	$0.499063\pi$
$102$		0			0
$103$	−137.824	−	137.824i	−0.131847	−	0.131847i	0.638104	−	0.769951i	$-0.279719\pi$
$103$	−137.824	−	137.824i	−0.131847	−	0.131847i	−0.769951	+	0.638104i	$0.779719\pi$
$104$	−273.311	+	67.1867i	−0.257696	+	0.0633481i
$105$		0			0
$106$	1075.21	−	741.840i	0.985225	−	0.679754i
$107$	−723.943	+	723.943i	−0.654077	+	0.654077i	−0.953972	−	0.299895i	$-0.903048\pi$
$107$	−723.943	+	723.943i	−0.654077	+	0.654077i	0.299895	+	0.953972i	$0.403048\pi$
$108$		0			0
$109$		−	896.758i		−	0.788017i	−0.919107	−	0.394009i	$-0.871088\pi$
$109$		−	896.758i		−	0.788017i	0.919107	−	0.394009i	$-0.128912\pi$
$110$	−42.3508	−	1487.59i	−0.0367090	−	1.28942i
$111$		0			0
$112$	−1305.00	+	77.8631i	−1.10099	+	0.0656908i
$113$	525.727	−	525.727i	0.437665	−	0.437665i	−0.453560	−	0.891226i	$-0.649846\pi$
$113$	525.727	−	525.727i	0.437665	−	0.437665i	0.891226	+	0.453560i	$0.149846\pi$
$114$		0			0
$115$	−547.513	−	355.191i	−0.443964	−	0.288015i
$116$	702.611	−	1850.34i	0.562378	−	1.48103i
$117$		0			0
$118$	1015.77	+	186.362i	0.792450	+	0.145390i
$119$	−765.237			−0.589488
$120$		0			0
$121$	−883.705			−0.663941
$122$	−746.019	−	136.871i	−0.553618	−	0.101572i
$123$		0			0
$124$	−176.995	+	466.119i	−0.128182	+	0.337571i
$125$	−1129.47	+	823.059i	−0.808182	+	0.588933i
$126$		0			0
$127$	−75.4237	+	75.4237i	−0.0526990	+	0.0526990i	−0.732965	−	0.680266i	$-0.761864\pi$
$127$	−75.4237	+	75.4237i	−0.0526990	+	0.0526990i	0.680266	+	0.732965i	$0.261864\pi$
$128$	428.844	+	1383.20i	0.296132	+	0.955147i
$129$		0			0
$130$	270.103	−	285.933i	0.182227	−	0.192907i
$131$		−	1374.47i		−	0.916701i	−0.888771	−	0.458351i	$-0.848440\pi$
$131$		−	1374.47i		−	0.916701i	0.888771	−	0.458351i	$-0.151560\pi$
$132$		0			0
$133$	719.389	−	719.389i	0.469014	−	0.469014i
$134$	−370.782	+	255.820i	−0.239035	+	0.164922i
$135$		0			0
$136$	202.355	+	823.166i	0.127587	+	0.519014i
$137$	2002.37	+	2002.37i	1.24871	+	1.24871i	0.956289	+	0.292424i	$0.0944618\pi$
$137$	2002.37	+	2002.37i	1.24871	+	1.24871i	0.292424	+	0.956289i	$0.405538\pi$
$138$		0			0
$139$	−2575.00			−1.57129			−0.785643	−	0.618679i	$-0.787668\pi$
$139$	−2575.00			−1.57129			−0.785643	+	0.618679i	$0.787668\pi$
$140$	1473.70	−	1079.94i	0.889645	−	0.651941i
$141$		0			0
$142$	285.764	−	1557.56i	0.168879	−	0.920477i
$143$	−413.910	−	413.910i	−0.242048	−	0.242048i
$144$		0			0
$145$	576.382	+	2705.37i	0.330110	+	1.54944i
$146$	710.582	−	490.264i	0.402796	−	0.277908i
$147$		0			0
$148$	−339.663	−	755.529i	−0.188650	−	0.419623i
$149$			1322.91i			0.727364i	0.931523	+	0.363682i	$0.118481\pi$
$149$			1322.91i			0.727364i	−0.931523	+	0.363682i	$0.881519\pi$
$150$		0			0
$151$			57.2419i			0.0308495i	0.999881	+	0.0154248i	$0.00491005\pi$
$151$			57.2419i			0.0308495i	−0.999881	+	0.0154248i	$0.995090\pi$
$152$	−964.079	−	583.616i	−0.514455	−	0.311431i
$153$		0			0
$154$	−1544.09	−	2237.99i	−0.807966	−	1.17105i
$155$	−145.196	−	681.508i	−0.0752415	−	0.353162i
$156$		0			0
$157$	1622.22	+	1622.22i	0.824634	+	0.824634i	0.986769	−	0.162134i	$-0.0518378\pi$
$157$	1622.22	+	1622.22i	0.824634	+	0.824634i	−0.162134	+	0.986769i	$0.551838\pi$
$158$	3261.50	+	598.384i	1.64222	+	0.301297i
$159$		0			0
$160$	−1551.39	−	1299.69i	−0.766552	−	0.642182i
$161$	−1192.39			−0.583685
$162$		0			0
$163$	1696.16	+	1696.16i	0.815052	+	0.815052i	0.985386	−	0.170334i	$-0.0544847\pi$
$163$	1696.16	+	1696.16i	0.815052	+	0.815052i	−0.170334	+	0.985386i	$0.554485\pi$
$164$	−887.188	−	336.882i	−0.422425	−	0.160403i
$165$		0			0
$166$	1346.05	+	1950.95i	0.629361	+	0.912187i
$167$	−2015.29	+	2015.29i	−0.933819	+	0.933819i	−0.997942	−	0.0641235i	$-0.979575\pi$
$167$	−2015.29	+	2015.29i	−0.933819	+	0.933819i	0.0641235	+	0.997942i	$0.479575\pi$
$168$		0			0
$169$			2042.29i			0.929580i
$170$	−861.180	−	813.503i	−0.388526	−	0.367017i
$171$		0			0
$172$	1138.12	+	2531.58i	0.504542	+	1.12228i
$173$	−317.896	+	317.896i	−0.139706	+	0.139706i	−0.773501	−	0.633795i	$-0.781496\pi$
$173$	−317.896	+	317.896i	−0.139706	+	0.139706i	0.633795	+	0.773501i	$0.281496\pi$
$174$		0			0
$175$	−912.786	+	2384.63i	−0.394287	+	1.03006i
$176$	−1999.10	+	2252.79i	−0.856179	+	0.964830i
$177$		0			0
$178$	−281.782	+	1535.86i	−0.118654	+	0.646727i
$179$	−3518.04			−1.46900			−0.734499	−	0.678610i	$-0.762583\pi$
$179$	−3518.04			−1.46900			−0.734499	+	0.678610i	$0.762583\pi$
$180$		0			0
$181$	−4769.86			−1.95879			−0.979395	−	0.201955i	$-0.935271\pi$
$181$	−4769.86			−1.95879			−0.979395	+	0.201955i	$0.935271\pi$
$182$	129.683	−	706.840i	0.0528174	−	0.287882i
$183$		0			0
$184$	315.308	+	1282.65i	0.126331	+	0.513904i
$185$	971.212	+	630.059i	0.385972	+	0.250394i
$186$		0			0
$187$	−1246.63	+	1246.63i	−0.487499	+	0.487499i
$188$	−1295.27	+	582.316i	−0.502486	+	0.225903i
$189$		0			0
$190$	1574.35	−	44.8209i	0.601132	−	0.0171139i
$191$			1728.42i			0.654787i	0.944888	+	0.327393i	$0.106170\pi$
$191$			1728.42i			0.654787i	−0.944888	+	0.327393i	$0.893830\pi$
$192$		0			0
$193$	1439.32	−	1439.32i	0.536813	−	0.536813i	−0.385779	−	0.922591i	$-0.626067\pi$
$193$	1439.32	−	1439.32i	0.536813	−	0.536813i	0.922591	+	0.385779i	$0.126067\pi$
$194$	1046.41	+	1516.65i	0.387256	+	0.561283i
$195$		0			0
$196$	210.885	−	555.372i	0.0768533	−	0.202395i
$197$	658.673	+	658.673i	0.238216	+	0.238216i	0.816111	−	0.577895i	$-0.196126\pi$
$197$	658.673	+	658.673i	0.238216	+	0.238216i	−0.577895	+	0.816111i	$0.696126\pi$
$198$		0			0
$199$	−658.733			−0.234655			−0.117327	−	0.993093i	$-0.537433\pi$
$199$	−658.733			−0.234655			−0.117327	+	0.993093i	$0.537433\pi$
$200$	2806.53	+	351.307i	0.992256	+	0.124206i
$201$		0			0
$202$	16.6264	+	3.05043i	0.00579124	+	0.00106251i
$203$	3573.53	+	3573.53i	1.23553	+	1.23553i
$204$		0			0
$205$	1297.15	−	276.359i	0.441935	−	0.0941549i
$206$	−313.080	−	453.773i	−0.105890	−	0.153475i
$207$		0			0
$208$	−794.642	+	47.4125i	−0.264897	+	0.0158051i
$209$		−	2343.87i		−	0.775738i
$210$		0			0
$211$		−	5821.53i		−	1.89939i	−0.313182	−	0.949693i	$-0.601395\pi$
$211$		−	5821.53i		−	1.89939i	0.313182	−	0.949693i	$-0.398605\pi$
$212$	3369.88	−	1515.00i	1.09172	−	0.490803i
$213$		0			0
$214$	−2383.51	+	1644.50i	−0.761371	+	0.525306i
$215$	−3254.28	−	2111.16i	−1.03228	−	0.669675i
$216$		0			0
$217$	−900.208	−	900.208i	−0.281613	−	0.281613i
$218$	457.714	−	2494.77i	0.142203	−	0.775080i
$219$		0			0
$220$	641.457	−	4160.07i	0.196578	−	1.27487i
$221$	−465.969			−0.141830
$222$		0			0
$223$	2315.57	+	2315.57i	0.695347	+	0.695347i	0.963403	−	0.268056i	$-0.0863814\pi$
$223$	2315.57	+	2315.57i	0.695347	+	0.695347i	−0.268056	+	0.963403i	$0.586381\pi$
$224$	−3670.24	−	449.469i	−1.09477	−	0.134069i
$225$		0			0
$226$	1730.90	−	1194.23i	0.509460	−	0.351501i
$227$	2970.19	−	2970.19i	0.868450	−	0.868450i	−0.123851	−	0.992301i	$-0.539524\pi$
$227$	2970.19	−	2970.19i	0.868450	−	0.868450i	0.992301	+	0.123851i	$0.0395243\pi$
$228$		0			0
$229$		−	4981.25i		−	1.43742i	−0.695308	−	0.718712i	$-0.744732\pi$
$229$		−	4981.25i		−	1.43742i	0.695308	−	0.718712i	$-0.255268\pi$
$230$	−1341.89	−	1267.59i	−0.384701	−	0.363403i
$231$		0			0
$232$	2899.09	−	4789.02i	0.820408	−	1.35524i
$233$	−1649.04	+	1649.04i	−0.463659	+	0.463659i	−0.899853	−	0.436194i	$-0.856326\pi$
$233$	−1649.04	+	1649.04i	−0.463659	+	0.463659i	0.436194	+	0.899853i	$0.356326\pi$
$234$		0			0
$235$	1080.17	−	1665.04i	0.299840	−	0.462191i
$236$	2730.74	+	1036.92i	0.753204	+	0.286006i
$237$		0			0
$238$	−2128.88	−	390.584i	−0.579811	−	0.106377i
$239$	3574.98			0.967558			0.483779	−	0.875190i	$-0.339264\pi$
$239$	3574.98			0.967558			0.483779	+	0.875190i	$0.339264\pi$
$240$		0			0
$241$	5135.22			1.37257			0.686283	−	0.727334i	$-0.259241\pi$
$241$	5135.22			1.37257			0.686283	+	0.727334i	$0.259241\pi$
$242$	−2458.46	−	451.051i	−0.653041	−	0.119813i
$243$		0			0
$244$	−2005.56	−	761.549i	−0.526200	−	0.199808i
$245$	172.998	+	812.003i	0.0451121	+	0.211743i
$246$		0			0
$247$	438.051	−	438.051i	0.112844	−	0.112844i
$248$	−730.309	+	1206.40i	−0.186995	+	0.308897i
$249$		0			0
$250$	−3562.27	+	1713.25i	−0.901191	+	0.433423i
$251$		−	6648.06i		−	1.67180i	−0.548882	−	0.835900i	$-0.684946\pi$
$251$		−	6648.06i		−	1.67180i	0.548882	−	0.835900i	$-0.315054\pi$
$252$		0			0
$253$	−1942.49	+	1942.49i	−0.482700	+	0.482700i
$254$	−248.325	+	171.331i	−0.0613437	+	0.0423239i
$255$		0			0
$256$	487.044	+	4066.94i	0.118907	+	0.992905i
$257$	448.260	+	448.260i	0.108800	+	0.108800i	0.759411	−	0.650611i	$-0.225487\pi$
$257$	448.260	+	448.260i	0.108800	+	0.108800i	−0.650611	+	0.759411i	$0.725487\pi$
$258$		0			0
$259$	2115.13			0.507442
$260$	897.366	−	657.600i	0.214047	−	0.156856i
$261$		0			0
$262$	701.541	−	3823.76i	0.165425	−	0.901652i
$263$	145.529	+	145.529i	0.0341205	+	0.0341205i	0.723961	−	0.689841i	$-0.242319\pi$
$263$	145.529	+	145.529i	0.0341205	+	0.0341205i	−0.689841	+	0.723961i	$0.742319\pi$
$264$		0			0
$265$	−2810.24	+	4331.88i	−0.651441	+	1.00417i
$266$	2368.52	−	1634.15i	0.545951	−	0.376678i
$267$		0			0
$268$	−1162.09	+	522.439i	−0.264872	+	0.119078i
$269$		−	2764.90i		−	0.626687i	−0.949640	−	0.313344i	$-0.898551\pi$
$269$		−	2764.90i		−	0.626687i	0.949640	−	0.313344i	$-0.101449\pi$
$270$		0			0
$271$		−	6372.29i		−	1.42837i	−0.699955	−	0.714187i	$-0.746797\pi$
$271$		−	6372.29i		−	1.42837i	0.699955	−	0.714187i	$-0.253203\pi$
$272$	142.798	+	2393.33i	0.0318324	+	0.533517i
$273$		0			0
$274$	4548.54	+	6592.59i	1.00287	+	1.45355i
$275$	2397.75	+	5371.74i	0.525780	+	1.17792i
$276$		0			0
$277$	−387.343	−	387.343i	−0.0840187	−	0.0840187i	0.663848	−	0.747867i	$-0.268922\pi$
$277$	−387.343	−	387.343i	−0.0840187	−	0.0840187i	−0.747867	+	0.663848i	$0.768922\pi$
$278$	−7163.64	−	1314.30i	−1.54549	−	0.283549i
$279$		0			0
$280$	4651.03	−	2252.20i	0.992687	−	0.480696i
$281$	−5284.49			−1.12187			−0.560936	−	0.827859i	$-0.689559\pi$
$281$	−5284.49			−1.12187			−0.560936	+	0.827859i	$0.689559\pi$
$282$		0			0
$283$	−341.577	−	341.577i	−0.0717479	−	0.0717479i	0.670322	−	0.742070i	$-0.266156\pi$
$283$	−341.577	−	341.577i	−0.0717479	−	0.0717479i	−0.742070	+	0.670322i	$0.766156\pi$
$284$	1589.99	−	4187.27i	0.332213	−	0.874890i
$285$		0			0
$286$	−940.232	−	1362.76i	−0.194395	−	0.281754i
$287$	1713.41	−	1713.41i	0.352402	−	0.352402i
$288$		0			0
$289$		−	3509.58i		−	0.714346i
$290$	222.646	+	7820.51i	0.0450835	+	1.58357i
$291$		0			0
$292$	2227.07	−	1001.22i	0.446333	−	0.200658i
$293$	6655.74	−	6655.74i	1.32707	−	1.32707i	0.419161	−	0.907912i	$-0.362324\pi$
$293$	6655.74	−	6655.74i	1.32707	−	1.32707i	0.907912	−	0.419161i	$-0.137676\pi$
$294$		0			0
$295$	−3992.59	+	850.626i	−0.787992	+	0.167883i
$296$	−559.312	−	2275.24i	−0.109829	−	0.446777i
$297$		0			0
$298$	−675.227	+	3680.33i	−0.131258	+	0.715423i
$299$	−726.069			−0.140434
$300$		0			0
$301$	−7087.24			−1.35715
$302$	−29.2168	+	159.247i	−0.00556701	+	0.0303431i
$303$		0			0
$304$	−2384.18	−	2115.69i	−0.449809	−	0.399155i
$305$	2932.31	−	624.732i	0.550503	−	0.117285i
$306$		0			0
$307$	−535.672	+	535.672i	−0.0995844	+	0.0995844i	−0.755144	−	0.655559i	$-0.772433\pi$
$307$	−535.672	+	535.672i	−0.0995844	+	0.0995844i	0.655559	+	0.755144i	$0.272433\pi$
$308$	−3153.37	−	7014.19i	−0.583376	−	1.29763i
$309$		0			0
$310$	−56.0867	−	1970.06i	−0.0102758	−	0.360942i
$311$			3579.61i			0.652672i	0.945254	+	0.326336i	$0.105814\pi$
$311$			3579.61i			0.652672i	−0.945254	+	0.326336i	$0.894186\pi$
$312$		0			0
$313$	6740.52	−	6740.52i	1.21724	−	1.21724i	0.248648	−	0.968594i	$-0.420014\pi$
$313$	6740.52	−	6740.52i	1.21724	−	1.21724i	0.968594	−	0.248648i	$-0.0799861\pi$
$314$	3685.02	+	5341.01i	0.662285	+	0.959907i
$315$		0			0
$316$	8768.05	+	3329.40i	1.56089	+	0.592701i
$317$	−4163.19	−	4163.19i	−0.737628	−	0.737628i	0.234490	−	0.972118i	$-0.424658\pi$
$317$	−4163.19	−	4163.19i	−0.737628	−	0.737628i	−0.972118	+	0.234490i	$0.924658\pi$
$318$		0			0
$319$	11643.1			2.04354
$320$	−3652.59	−	4407.56i	−0.638081	−	0.769969i
$321$		0			0
$322$	−3317.21	−	608.605i	−0.574102	−	0.105330i
$323$	−1319.33	−	1319.33i	−0.227275	−	0.227275i
$324$		0			0
$325$	−555.815	+	1452.05i	−0.0948648	+	0.247832i
$326$	3852.97	+	5584.44i	0.654590	+	0.948753i
$327$		0			0
$328$	−2296.20	−	1390.03i	−0.386544	−	0.233999i
$329$		−	3626.15i		−	0.607648i
$330$		0			0
$331$			8821.65i			1.46490i	0.680821	+	0.732450i	$0.261623\pi$
$331$			8821.65i			1.46490i	−0.680821	+	0.732450i	$0.738377\pi$
$332$	2748.93	+	6114.57i	0.454418	+	1.01078i
$333$		0			0
$334$	−6635.14	+	4577.90i	−1.08700	+	0.749974i
$335$	969.099	−	1493.83i	0.158052	−	0.243631i
$336$		0			0
$337$	3165.30	+	3165.30i	0.511647	+	0.511647i	0.915031	−	0.403384i	$-0.132166\pi$
$337$	3165.30	+	3165.30i	0.511647	+	0.511647i	−0.403384	+	0.915031i	$0.632166\pi$
$338$	−1042.40	+	5681.63i	−0.167749	+	0.914319i
$339$		0			0
$340$	−1980.58	−	2702.71i	−0.315917	−	0.431103i
$341$	−2933.01			−0.465781
$342$		0			0
$343$	−3881.71	−	3881.71i	−0.611057	−	0.611057i
$344$	1874.11	+	7623.75i	0.293736	+	1.19490i
$345$		0			0
$346$	−1046.64	+	722.128i	−0.162624	+	0.112202i
$347$	−856.765	+	856.765i	−0.132546	+	0.132546i	−0.770267	−	0.637721i	$-0.779877\pi$
$347$	−856.765	+	856.765i	−0.132546	+	0.132546i	0.637721	+	0.770267i	$0.279877\pi$
$348$		0			0
$349$		−	3731.17i		−	0.572278i	−0.958188	−	0.286139i	$-0.907628\pi$
$349$		−	3731.17i		−	0.572278i	0.958188	−	0.286139i	$-0.0923720\pi$
$350$	−3756.50	+	6168.14i	−0.573696	+	0.942002i
$351$		0			0
$352$	−6711.31	+	5246.88i	−1.01623	+	0.794487i
$353$	1774.39	−	1774.39i	0.267539	−	0.267539i	−0.560569	−	0.828108i	$-0.689417\pi$
$353$	1774.39	−	1774.39i	0.267539	−	0.267539i	0.828108	+	0.560569i	$0.189417\pi$
$354$		0			0
$355$	1304.34	+	6122.17i	0.195005	+	0.915298i
$356$	−1567.83	+	4128.92i	−0.233413	+	0.614698i
$357$		0			0
$358$	−9787.16	−	1795.64i	−1.44488	−	0.265091i
$359$	10477.6			1.54036			0.770178	−	0.637829i	$-0.220168\pi$
$359$	10477.6			1.54036			0.770178	+	0.637829i	$0.220168\pi$
$360$		0			0
$361$	−4378.42			−0.638347
$362$	−13269.7	−	2434.58i	−1.92663	−	0.353477i
$363$		0			0
$364$	721.555	−	1900.23i	0.103901	−	0.273624i
$365$	−1857.22	+	2862.83i	−0.266333	+	0.410541i
$366$		0			0
$367$	−5250.87	+	5250.87i	−0.746848	+	0.746848i	−0.973886	−	0.227038i	$-0.927096\pi$
$367$	−5250.87	+	5250.87i	−0.746848	+	0.746848i	0.227038	+	0.973886i	$0.427096\pi$
$368$	222.507	+	3729.27i	0.0315190	+	0.528265i
$369$		0			0
$370$	2380.32	+	2248.53i	0.334451	+	0.315935i
$371$			9434.06i			1.32019i
$372$		0			0
$373$	3349.09	−	3349.09i	0.464904	−	0.464904i	−0.435355	−	0.900259i	$-0.643377\pi$
$373$	3349.09	−	3349.09i	0.464904	−	0.464904i	0.900259	+	0.435355i	$0.143377\pi$
$374$	−4104.40	+	2831.82i	−0.567469	+	0.391523i
$375$		0			0
$376$	−3900.66	+	958.879i	−0.535003	+	0.131517i
$377$	2176.00	+	2176.00i	0.297267	+	0.297267i
$378$		0			0
$379$	1701.61			0.230622			0.115311	−	0.993329i	$-0.463213\pi$
$379$	1701.61			0.230622			0.115311	+	0.993329i	$0.463213\pi$
$380$	4402.70	+	678.870i	0.594352	+	0.0916454i
$381$		0			0
$382$	−882.202	+	4808.46i	−0.118161	+	0.644037i
$383$	−5674.07	−	5674.07i	−0.757001	−	0.757001i	0.218775	−	0.975775i	$-0.429794\pi$
$383$	−5674.07	−	5674.07i	−0.757001	−	0.757001i	−0.975775	+	0.218775i	$0.929794\pi$
$384$		0			0
$385$	9016.54	+	5849.35i	1.19357	+	0.774312i
$386$	4738.83	−	3269.55i	0.624871	−	0.431128i
$387$		0			0
$388$	2136.99	+	4753.40i	0.279611	+	0.621951i
$389$		−	2301.42i		−	0.299965i	−0.988689	−	0.149983i	$-0.952078\pi$
$389$		−	2301.42i		−	0.299965i	0.988689	−	0.149983i	$-0.0479218\pi$
$390$		0			0
$391$			2186.80i			0.282842i
$392$	870.148	−	1437.40i	0.112115	−	0.185203i
$393$		0			0
$394$	1496.23	+	2168.62i	0.191317	+	0.277293i
$395$	−12819.7	+	2731.25i	−1.63298	+	0.347909i
$396$		0			0
$397$	−7499.18	−	7499.18i	−0.948043	−	0.948043i	0.0506721	−	0.998715i	$-0.483864\pi$
$397$	−7499.18	−	7499.18i	−0.948043	−	0.948043i	−0.998715	+	0.0506721i	$0.983864\pi$
$398$	−1832.59	−	336.223i	−0.230803	−	0.0423451i
$399$		0			0
$400$	7628.42	+	2409.81i	0.953553	+	0.301226i
$401$	9495.99			1.18256			0.591280	−	0.806466i	$-0.298623\pi$
$401$	9495.99			1.18256			0.591280	+	0.806466i	$0.298623\pi$
$402$		0			0
$403$	−548.155	−	548.155i	−0.0677557	−	0.0677557i
$404$	44.6976	+	16.9725i	0.00550442	+	0.00209014i
$405$		0			0
$406$	8117.58	+	11765.5i	0.992288	+	1.43821i
$407$	3445.70	−	3445.70i	0.419648	−	0.419648i
$408$		0			0
$409$			10456.4i			1.26415i	0.774909	+	0.632073i	$0.217796\pi$
$409$			10456.4i			1.26415i	−0.774909	+	0.632073i	$0.782204\pi$
$410$	3749.71	−	106.753i	0.451671	−	0.0128589i
$411$		0			0
$412$	−639.375	−	1422.19i	−0.0764557	−	0.170064i
$413$	−5273.83	+	5273.83i	−0.628349	+	0.628349i
$414$		0			0
$415$	−7860.10	−	5099.12i	−0.929728	−	0.603147i
$416$	−2234.89	−	273.691i	−0.263400	−	0.0322568i
$417$		0			0
$418$	1196.33	−	6520.64i	0.139987	−	0.763002i
$419$	8542.91			0.996058			0.498029	−	0.867160i	$-0.334057\pi$
$419$	8542.91			0.996058			0.498029	+	0.867160i	$0.334057\pi$
$420$		0			0
$421$	−3112.71			−0.360342			−0.180171	−	0.983635i	$-0.557665\pi$
$421$	−3112.71			−0.360342			−0.180171	+	0.983635i	$0.557665\pi$
$422$	2971.36	−	16195.4i	0.342757	−	1.86820i
$423$		0			0
$424$	10148.2	−	2494.69i	1.16236	−	0.285738i
$425$	4373.34	+	1674.02i	0.499148	+	0.191063i
$426$		0			0
$427$	3873.30	−	3873.30i	0.438974	−	0.438974i
$428$	−7470.28	+	3358.41i	−0.843667	+	0.379287i
$429$		0			0
$430$	−7975.82	−	7534.26i	−0.894484	−	0.844963i
$431$		−	1474.93i		−	0.164837i	−0.996598	−	0.0824187i	$-0.973736\pi$
$431$		−	1474.93i		−	0.164837i	0.996598	−	0.0824187i	$-0.0262645\pi$
$432$		0			0
$433$	−6196.57	+	6196.57i	−0.687733	+	0.687733i	−0.961730	−	0.273998i	$-0.911654\pi$
$433$	−6196.57	+	6196.57i	−0.687733	+	0.687733i	0.273998	+	0.961730i	$0.411654\pi$
$434$	−2044.90	−	2963.85i	−0.226171	−	0.327809i
$435$		0			0
$436$	2546.71	−	6706.82i	0.279737	−	0.736694i
$437$	−2055.78	−	2055.78i	−0.225037	−	0.225037i
$438$		0			0
$439$	−4661.49			−0.506790			−0.253395	−	0.967363i	$-0.581547\pi$
$439$	−4661.49			−0.506790			−0.253395	+	0.967363i	$0.581547\pi$
$440$	3907.87	−	11245.9i	0.423410	−	1.21847i
$441$		0			0
$442$	−1296.32	−	237.835i	−0.139502	−	0.0255942i
$443$	−5250.61	−	5250.61i	−0.563124	−	0.563124i	0.367069	−	0.930194i	$-0.380361\pi$
$443$	−5250.61	−	5250.61i	−0.563124	−	0.563124i	−0.930194	+	0.367069i	$0.880361\pi$
$444$		0			0
$445$	−1286.16	−	6036.85i	−0.137011	−	0.643088i
$446$	5260.02	+	7623.80i	0.558451	+	0.809411i
$447$		0			0
$448$	−9981.17	−	3123.74i	−1.05260	−	0.329427i
$449$			2992.06i			0.314485i	0.987560	+	0.157243i	$0.0502605\pi$
$449$			2992.06i			0.314485i	−0.987560	+	0.157243i	$0.949740\pi$
$450$		0			0
$451$		−	5582.54i		−	0.582864i
$452$	5424.91	−	2438.88i	0.564527	−	0.253794i
$453$		0			0
$454$	9779.05	−	6747.03i	1.01091	−	0.697475i
$455$	591.923	+	2778.31i	0.0609885	+	0.286262i
$456$		0			0
$457$	13147.8	+	13147.8i	1.34579	+	1.34579i	0.890175	+	0.455619i	$0.150582\pi$
$457$	13147.8	+	13147.8i	1.34579	+	1.34579i	0.455619	+	0.890175i	$0.349418\pi$
$458$	2542.47	−	13857.8i	0.259393	−	1.41383i
$459$		0			0
$460$	−3086.12	−	4211.35i	−0.312807	−	0.426859i
$461$	−3239.67			−0.327302			−0.163651	−	0.986518i	$-0.552327\pi$
$461$	−3239.67			−0.327302			−0.163651	+	0.986518i	$0.552327\pi$
$462$		0			0
$463$	−1552.82	−	1552.82i	−0.155865	−	0.155865i	0.624867	−	0.780732i	$-0.285153\pi$
$463$	−1552.82	−	1552.82i	−0.155865	−	0.155865i	−0.780732	+	0.624867i	$0.785153\pi$
$464$	10509.6	−	11843.3i	1.05150	−	1.18494i
$465$		0			0
$466$	−5429.32	+	3745.94i	−0.539717	+	0.372377i
$467$	−6322.16	+	6322.16i	−0.626456	+	0.626456i	−0.947174	−	0.320719i	$-0.896076\pi$
$467$	−6322.16	+	6322.16i	−0.626456	+	0.626456i	0.320719	+	0.947174i	$0.396076\pi$
$468$		0			0
$469$		−	3253.29i		−	0.320305i
$470$	3854.86	−	4080.79i	0.378323	−	0.400495i
$471$		0			0
$472$	7067.65	+	4278.49i	0.689227	+	0.417232i
$473$	−11545.6	+	11545.6i	−1.12234	+	1.12234i
$474$		0			0
$475$	−5685.04	+	2537.59i	−0.549152	+	0.245121i
$476$	−5723.18	−	2173.20i	−0.551095	−	0.209262i
$477$		0			0
$478$	9945.57	+	1824.70i	0.951673	+	0.174602i
$479$	−7141.64			−0.681232			−0.340616	−	0.940203i	$-0.610636\pi$
$479$	−7141.64			−0.681232			−0.340616	+	0.940203i	$0.610636\pi$
$480$		0			0
$481$	1287.94			0.122090
$482$	14286.1	+	2621.06i	1.35003	+	0.247689i
$483$		0			0
$484$	−6609.20	−	2509.64i	−0.620699	−	0.235691i
$485$	−6110.36	−	3964.00i	−0.572076	−	0.371126i
$486$		0			0
$487$	3827.76	−	3827.76i	0.356165	−	0.356165i	−0.506232	−	0.862397i	$-0.668962\pi$
$487$	3827.76	−	3827.76i	0.356165	−	0.356165i	0.862397	+	0.506232i	$0.168962\pi$
$488$	−5190.75	−	3142.28i	−0.481504	−	0.291484i
$489$		0			0
$490$	66.8261	+	2347.29i	0.00616101	+	0.216407i
$491$		−	14943.2i		−	1.37348i	−0.726904	−	0.686739i	$-0.759041\pi$
$491$		−	14943.2i		−	1.37348i	0.726904	−	0.686739i	$-0.240959\pi$
$492$		0			0
$493$	6553.74	−	6553.74i	0.598713	−	0.598713i
$494$	1442.24	−	995.069i	0.131355	−	0.0906281i
$495$		0			0
$496$	−2647.47	+	2983.44i	−0.239667	+	0.270082i
$497$	8086.80	+	8086.80i	0.729865	+	0.729865i
$498$		0			0
$499$	2324.51			0.208535			0.104268	−	0.994549i	$-0.466750\pi$
$499$	2324.51			0.208535			0.104268	+	0.994549i	$0.466750\pi$
$500$	−10784.7	+	2948.04i	−0.964610	+	0.263681i
$501$		0			0
$502$	3393.23	−	18494.8i	0.301688	−	1.64435i
$503$	4791.06	+	4791.06i	0.424697	+	0.424697i	0.886817	−	0.462120i	$-0.152911\pi$
$503$	4791.06	+	4791.06i	0.424697	+	0.424697i	−0.462120	+	0.886817i	$0.652911\pi$
$504$		0			0
$505$	−65.3519	+	13.9233i	−0.00575865	+	0.00122689i
$506$	−6395.44	+	4412.52i	−0.561882	+	0.387669i
$507$		0			0
$508$	−778.287	+	349.895i	−0.0679742	+	0.0305592i
$509$			3391.52i			0.295337i	0.989037	+	0.147668i	$0.0471768\pi$
$509$			3391.52i			0.295337i	−0.989037	+	0.147668i	$0.952823\pi$
$510$		0			0
$511$			6234.74i			0.539743i
$512$	−720.851	+	11562.8i	−0.0622215	+	0.998062i
$513$		0			0
$514$	1018.26	+	1475.85i	0.0873804	+	0.126648i
$515$	1828.19	+	1186.01i	0.156426	+	0.101479i
$516$		0			0
$517$	−5907.27	−	5907.27i	−0.502517	−	0.502517i
$518$	5884.27	+	1079.58i	0.499112	+	0.0915714i
$519$		0			0
$520$	2832.11	−	1371.41i	0.238839	−	0.115655i
$521$	10835.4			0.911146			0.455573	−	0.890198i	$-0.349434\pi$
$521$	10835.4			0.911146			0.455573	+	0.890198i	$0.349434\pi$
$522$		0			0
$523$	1210.80	+	1210.80i	0.101233	+	0.101233i	0.755909	−	0.654676i	$-0.227195\pi$
$523$	1210.80	+	1210.80i	0.101233	+	0.101233i	−0.654676	+	0.755909i	$0.727195\pi$
$524$	3903.36	−	10279.6i	0.325418	−	0.856997i
$525$		0			0
$526$	330.581	+	479.139i	0.0274030	+	0.0397176i
$527$	−1650.95	+	1650.95i	−0.136464	+	0.136464i
$528$		0			0
$529$		−	8759.55i		−	0.719943i
$530$	−10029.1	+	10616.9i	−0.821955	+	0.870128i
$531$		0			0
$532$	7423.28	−	3337.29i	0.604963	−	0.271973i
$533$	1043.33	−	1043.33i	0.0847874	−	0.0847874i
$534$		0			0
$535$	6229.69	−	9602.83i	0.503426	−	0.776012i
$536$	−3499.57	+	860.282i	−0.282012	+	0.0693256i
$537$		0			0
$538$	1411.23	−	7691.93i	0.113090	−	0.616399i
$539$	3494.62			0.279265
$540$		0			0
$541$	−7014.81			−0.557468			−0.278734	−	0.960368i	$-0.589915\pi$
$541$	−7014.81			−0.557468			−0.278734	+	0.960368i	$0.589915\pi$
$542$	3252.47	−	17727.7i	0.257760	−	1.40492i
$543$		0			0
$544$	−824.311	+	6731.10i	−0.0649670	+	0.530503i
$545$	2089.18	+	9805.98i	0.164203	+	0.770719i
$546$		0			0
$547$	10104.9	−	10104.9i	0.789860	−	0.789860i	−0.191611	−	0.981471i	$-0.561371\pi$
$547$	10104.9	−	10104.9i	0.789860	−	0.789860i	0.981471	+	0.191611i	$0.0613711\pi$
$548$	9289.09	+	20662.2i	0.724106	+	1.61066i
$549$		0			0
$550$	3928.73	+	16168.0i	0.304585	+	1.25346i
$551$			12322.2i			0.952708i
$552$		0			0
$553$	−16933.6	+	16933.6i	−1.30215	+	1.30215i
$554$	−879.882	−	1275.29i	−0.0674776	−	0.0978011i
$555$		0			0
$556$	−19258.4	−	7312.77i	−1.46895	−	0.557789i
$557$	−1950.22	−	1950.22i	−0.148355	−	0.148355i	0.629028	−	0.777383i	$-0.283453\pi$
$557$	−1950.22	−	1950.22i	−0.148355	−	0.148355i	−0.777383	+	0.629028i	$0.783453\pi$
$558$		0			0
$559$	−4315.57			−0.326528
$560$	14088.7	−	3891.68i	1.06313	−	0.293667i
$561$		0			0
$562$	−14701.4	−	2697.25i	−1.10346	−	0.202450i
$563$	−4425.60	−	4425.60i	−0.331291	−	0.331291i	0.521786	−	0.853077i	$-0.325266\pi$
$563$	−4425.60	−	4425.60i	−0.331291	−	0.331291i	−0.853077	+	0.521786i	$0.825266\pi$
$564$		0			0
$565$	−4523.99	+	6973.56i	−0.336860	+	0.519257i
$566$	−775.921	−	1124.61i	−0.0576226	−	0.0835174i
$567$		0			0
$568$	6560.56	−	10837.4i	0.484639	−	0.800577i
$569$			14666.9i			1.08061i	0.841469	+	0.540305i	$0.181691\pi$
$569$			14666.9i			1.08061i	−0.841469	+	0.540305i	$0.818309\pi$
$570$		0			0
$571$		−	664.054i		−	0.0486686i	−0.999704	−	0.0243343i	$-0.992253\pi$
$571$		−	664.054i		−	0.0486686i	0.999704	−	0.0243343i	$-0.00774662\pi$
$572$	−1920.15	−	4271.09i	−0.140359	−	0.312208i
$573$		0			0
$574$	5641.23	−	3892.15i	0.410210	−	0.283023i
$575$	6814.50	+	2608.45i	0.494234	+	0.189182i
$576$		0			0
$577$	583.058	+	583.058i	0.0420676	+	0.0420676i	0.727828	−	0.685760i	$-0.240530\pi$
$577$	583.058	+	583.058i	0.0420676	+	0.0420676i	−0.685760	+	0.727828i	$0.740530\pi$
$578$	1791.32	−	9763.63i	0.128909	−	0.702619i
$579$		0			0
$580$	−3372.26	+	21870.2i	−0.241423	+	1.56571i
$581$	−17117.9			−1.22232
$582$		0			0
$583$	15368.8	+	15368.8i	1.09178	+	1.09178i
$584$	6706.72	−	1648.68i	0.475216	−	0.116820i
$585$		0			0
$586$	21913.4	−	15119.1i	1.54477	−	1.06581i
$587$	6911.99	−	6911.99i	0.486011	−	0.486011i	−0.421034	−	0.907045i	$-0.638333\pi$
$587$	6911.99	−	6911.99i	0.486011	−	0.486011i	0.907045	+	0.421034i	$0.138333\pi$
$588$		0			0
$589$		−	3104.07i		−	0.217150i
$590$	−11541.5	+	328.582i	−0.805351	+	0.0229279i
$591$		0			0
$592$	−394.697	−	6615.19i	−0.0274019	−	0.459261i
$593$	11384.8	−	11384.8i	0.788396	−	0.788396i	−0.192835	−	0.981231i	$-0.561768\pi$
$593$	11384.8	−	11384.8i	0.788396	−	0.788396i	0.981231	+	0.192835i	$0.0617682\pi$
$594$		0			0
$595$	8367.80	−	1782.77i	0.576549	−	0.122834i
$596$	−3756.95	+	9894.02i	−0.258206	+	0.679991i
$597$		0			0
$598$	−2019.92	−	370.592i	−0.138128	−	0.0253422i
$599$	−25321.6			−1.72723			−0.863616	−	0.504151i	$-0.831806\pi$
$599$	−25321.6			−1.72723			−0.863616	+	0.504151i	$0.831806\pi$
$600$		0			0
$601$	27777.8			1.88533			0.942663	−	0.333746i	$-0.108313\pi$
$601$	27777.8			1.88533			0.942663	+	0.333746i	$0.108313\pi$
$602$	−19716.6	−	3617.39i	−1.33487	−	0.244907i
$603$		0			0
$604$	−162.562	+	428.110i	−0.0109512	+	0.0288403i
$605$	9663.25	−	2058.77i	0.649367	−	0.138348i
$606$		0			0
$607$	−19575.7	+	19575.7i	−1.30898	+	1.30898i	−0.386833	+	0.922150i	$0.626431\pi$
$607$	−19575.7	+	19575.7i	−1.30898	+	1.30898i	−0.922150	+	0.386833i	$0.873569\pi$
$608$	−5552.89	−	7102.74i	−0.370394	−	0.473773i
$609$		0			0
$610$	8476.53	−	241.323i	0.562630	−	0.0160178i
$611$		−	2208.04i		−	0.146199i
$612$		0			0
$613$	−12841.3	+	12841.3i	−0.846091	+	0.846091i	−0.989643	−	0.143552i	$-0.954147\pi$
$613$	−12841.3	+	12841.3i	−0.846091	+	0.846091i	0.143552	+	0.989643i	$0.454147\pi$
$614$	−1763.65	+	1216.82i	−0.115920	+	0.0799788i
$615$		0			0
$616$	−5192.55	−	21122.9i	−0.339633	−	1.38160i
$617$	−15254.6	−	15254.6i	−0.995346	−	0.995346i	0.00464336	−	0.999989i	$-0.498522\pi$
$617$	−15254.6	−	15254.6i	−0.995346	−	0.995346i	−0.999989	+	0.00464336i	$0.998522\pi$
$618$		0			0
$619$	−13042.3			−0.846874			−0.423437	−	0.905926i	$-0.639176\pi$
$619$	−13042.3			−0.846874			−0.423437	+	0.905926i	$0.639176\pi$
$620$	849.504	−	5509.32i	0.0550273	−	0.356870i
$621$		0			0
$622$	−1827.07	+	9958.45i	−0.117779	+	0.641957i
$623$	−7974.11	−	7974.11i	−0.512803	−	0.512803i
$624$		0			0
$625$	10433.2	−	11631.4i	0.667723	−	0.744410i
$626$	22192.5	−	15311.7i	1.41692	−	0.977599i
$627$		0			0
$628$	7525.59	+	16739.5i	0.478191	+	1.06366i
$629$		−	3879.07i		−	0.245896i
$630$		0			0
$631$		−	6843.39i		−	0.431745i	−0.976422	−	0.215872i	$-0.930740\pi$
$631$		−	6843.39i		−	0.431745i	0.976422	−	0.215872i	$-0.0692595\pi$
$632$	22693.3	+	13737.7i	1.42831	+	0.864644i
$633$		0			0
$634$	−9457.04	−	13706.9i	−0.592409	−	0.858629i
$635$	649.038	−	1000.47i	0.0405611	−	0.0625233i
$636$		0			0
$637$	653.116	+	653.116i	0.0406239	+	0.0406239i
$638$	32391.0	+	5942.74i	2.00999	+	0.368770i
$639$		0			0
$640$	−7911.82	−	14126.1i	−0.488660	−	0.872475i
$641$	2449.97			0.150964			0.0754820	−	0.997147i	$-0.475950\pi$
$641$	2449.97			0.150964			0.0754820	+	0.997147i	$0.475950\pi$
$642$		0			0
$643$	−22279.7	−	22279.7i	−1.36645	−	1.36645i	−0.865448	−	0.500999i	$-0.832966\pi$
$643$	−22279.7	−	22279.7i	−1.36645	−	1.36645i	−0.500999	−	0.865448i	$-0.667034\pi$
$644$	−8917.82	−	3386.27i	−0.545670	−	0.207201i
$645$		0			0
$646$	−2996.98	−	4343.78i	−0.182530	−	0.264557i
$647$	−5040.77	+	5040.77i	−0.306295	+	0.306295i	−0.843471	−	0.537175i	$-0.819491\pi$
$647$	−5040.77	+	5040.77i	−0.306295	+	0.306295i	0.537175	+	0.843471i	$0.319491\pi$
$648$		0			0
$649$			17182.9i			1.03927i
$650$	−2287.41	+	3755.91i	−0.138030	+	0.226644i
$651$		0			0
$652$	7868.58	+	17502.5i	0.472634	+	1.05130i
$653$	4532.72	−	4532.72i	0.271637	−	0.271637i	−0.558122	−	0.829759i	$-0.688478\pi$
$653$	4532.72	−	4532.72i	0.271637	−	0.271637i	0.829759	+	0.558122i	$0.188478\pi$
$654$		0			0
$655$	3202.10	+	15029.7i	0.191017	+	0.896579i
$656$	−5678.53	−	5039.06i	−0.337972	−	0.299912i
$657$		0			0
$658$	1850.82	−	10087.9i	0.109654	−	0.597672i
$659$	−12951.7			−0.765595			−0.382797	−	0.923832i	$-0.625039\pi$
$659$	−12951.7			−0.765595			−0.382797	+	0.923832i	$0.625039\pi$
$660$		0			0
$661$	6827.08			0.401729			0.200864	−	0.979619i	$-0.435625\pi$
$661$	6827.08			0.401729			0.200864	+	0.979619i	$0.435625\pi$
$662$	−4502.65	+	24541.8i	−0.264351	+	1.44085i
$663$		0			0
$664$	4526.56	+	18413.8i	0.264555	+	1.07619i
$665$	−6190.50	+	9542.42i	−0.360988	+	0.556450i
$666$		0			0
$667$	10212.0	−	10212.0i	0.592819	−	0.592819i
$668$	−20795.5	+	9349.04i	−1.20449	+	0.541505i
$669$		0			0
$670$	3458.49	−	3661.18i	0.199422	−	0.211110i
$671$		−	12619.8i		−	0.726052i
$672$		0			0
$673$	9731.89	−	9731.89i	0.557410	−	0.557410i	−0.371159	−	0.928569i	$-0.621040\pi$
$673$	9731.89	−	9731.89i	0.557410	−	0.557410i	0.928569	+	0.371159i	$0.121040\pi$
$674$	7190.25	+	10421.5i	0.410917	+	0.595578i
$675$		0			0
$676$	−5799.91	+	15274.2i	−0.329990	+	0.869037i
$677$	7885.88	+	7885.88i	0.447679	+	0.447679i	0.894582	−	0.446903i	$-0.147473\pi$
$677$	7885.88	+	7885.88i	0.447679	+	0.447679i	−0.446903	+	0.894582i	$0.647473\pi$
$678$		0			0
$679$	−13307.3			−0.752115
$680$	−4130.46	−	8529.83i	−0.232935	−	0.481035i
$681$		0			0
$682$	−8159.61	−	1497.03i	−0.458134	−	0.0840534i
$683$	15861.8	+	15861.8i	0.888629	+	0.888629i	0.994391	−	0.105763i	$-0.0337284\pi$
$683$	15861.8	+	15861.8i	0.888629	+	0.888629i	−0.105763	+	0.994391i	$0.533728\pi$
$684$		0			0
$685$	−26560.6	−	17230.8i	−1.48150	−	0.961102i
$686$	−8817.63	−	12780.1i	−0.490756	−	0.711295i
$687$		0			0
$688$	1322.53	+	22165.8i	0.0732861	+	1.22829i
$689$			5744.60i			0.317637i
$690$		0			0
$691$			30100.7i			1.65714i	0.559883	+	0.828572i	$0.310846\pi$
$691$			30100.7i			1.65714i	−0.559883	+	0.828572i	$0.689154\pi$
$692$	−3280.33	+	1474.74i	−0.180201	+	0.0810132i
$693$		0			0
$694$	−2820.81	+	1946.21i	−0.154289	+	0.106451i
$695$	28157.5	−	5998.98i	1.53680	−	0.327416i
$696$		0			0
$697$	−3142.34	−	3142.34i	−0.170767	−	0.170767i
$698$	1904.43	−	10380.1i	0.103272	−	0.562883i
$699$		0			0
$700$	−13598.8	+	15242.4i	−0.734268	+	0.823010i
$701$	20267.4			1.09199			0.545997	−	0.837787i	$-0.316151\pi$
$701$	20267.4			1.09199			0.545997	+	0.837787i	$0.316151\pi$
$702$		0			0
$703$	3646.66	+	3646.66i	0.195642	+	0.195642i
$704$	−21348.9	+	11171.3i	−1.14292	+	0.598058i
$705$		0			0
$706$	5842.01	−	4030.68i	0.311426	−	0.214868i
$707$	−86.3236	+	86.3236i	−0.00459199	+	0.00459199i
$708$		0			0
$709$			18499.1i			0.979900i	0.871750	+	0.489950i	$0.162985\pi$
$709$			18499.1i			0.979900i	−0.871750	+	0.489950i	$0.837015\pi$
$710$	503.841	+	17697.6i	0.0266321	+	0.935462i
$711$		0			0
$712$	−6469.13	+	10686.4i	−0.340507	+	0.562485i
$713$	−2572.50	+	2572.50i	−0.135120	+	0.135120i
$714$		0			0
$715$	5490.36	+	3561.79i	0.287172	+	0.186298i
$716$	−26311.3	−	9990.91i	−1.37332	−	0.521478i
$717$		0			0
$718$	29148.7	+	5347.87i	1.51507	+	0.277968i
$719$	25990.9			1.34812			0.674060	−	0.738676i	$-0.264549\pi$
$719$	25990.9			1.34812			0.674060	+	0.738676i	$0.264549\pi$
$720$		0			0
$721$	3981.47			0.205656
$722$	−12180.7	−	2234.79i	−0.627867	−	0.115194i
$723$		0			0
$724$	−35673.6	−	13546.0i	−1.83122	−	0.695348i
$725$	−12605.4	−	28240.2i	−0.645727	−	1.44664i
$726$		0			0
$727$	23543.5	−	23543.5i	1.20107	−	1.20107i	0.227232	−	0.973841i	$-0.427033\pi$
$727$	23543.5	−	23543.5i	1.20107	−	1.20107i	0.973841	−	0.227232i	$-0.0729675\pi$
$728$	2977.26	−	4918.15i	0.151572	−	0.250383i
$729$		0			0
$730$	−6627.99	+	7016.44i	−0.336045	+	0.355740i
$731$			12997.8i			0.657646i
$732$		0			0
$733$	16546.7	−	16546.7i	0.833789	−	0.833789i	−0.154244	−	0.988033i	$-0.549294\pi$
$733$	16546.7	−	16546.7i	0.833789	−	0.833789i	0.988033	+	0.154244i	$0.0492942\pi$
$734$	−17288.0	+	11927.8i	−0.869361	+	0.599813i
$735$		0			0
$736$	−1284.44	+	10488.4i	−0.0643274	+	0.525280i
$737$	−5299.85	−	5299.85i	−0.264888	−	0.264888i
$738$		0			0
$739$	−8124.95			−0.404440			−0.202220	−	0.979340i	$-0.564816\pi$
$739$	−8124.95			−0.404440			−0.202220	+	0.979340i	$0.564816\pi$
$740$	5474.35	+	7470.34i	0.271947	+	0.371102i
$741$		0			0
$742$	−4815.23	+	26245.5i	−0.238238	+	1.29852i
$743$	5222.62	+	5222.62i	0.257873	+	0.257873i	0.824188	−	0.566316i	$-0.191632\pi$
$743$	5222.62	+	5222.62i	0.257873	+	0.257873i	−0.566316	+	0.824188i	$0.691632\pi$
$744$		0			0
$745$	−3081.99	−	14465.9i	−0.151564	−	0.711398i
$746$	11026.5	−	7607.73i	0.541167	−	0.373376i
$747$		0			0
$748$	−12863.8	+	5783.17i	−0.628806	+	0.282692i
$749$		−	20913.3i		−	1.02023i
$750$		0			0
$751$		−	27086.9i		−	1.31613i	−0.752961	−	0.658066i	$-0.771375\pi$
$751$		−	27086.9i		−	1.31613i	0.752961	−	0.658066i	$-0.228625\pi$
$752$	−11341.0	+	676.664i	−0.549953	+	0.0328130i
$753$		0			0
$754$	4942.97	+	7164.27i	0.238743	+	0.346031i
$755$	−133.356	−	625.936i	−0.00642826	−	0.0301724i
$756$		0			0
$757$	−11094.6	−	11094.6i	−0.532684	−	0.532684i	0.388686	−	0.921370i	$-0.372929\pi$
$757$	−11094.6	−	11094.6i	−0.532684	−	0.532684i	−0.921370	+	0.388686i	$0.872929\pi$
$758$	4733.87	+	868.517i	0.226836	+	0.0416174i
$759$		0			0
$760$	11901.8	+	4135.79i	0.568056	+	0.197396i
$761$	8006.53			0.381388			0.190694	−	0.981649i	$-0.438926\pi$
$761$	8006.53			0.381388			0.190694	+	0.981649i	$0.438926\pi$
$762$		0			0
$763$	12952.8	+	12952.8i	0.614576	+	0.614576i
$764$	−4908.56	+	12926.8i	−0.232442	+	0.612141i
$765$		0			0
$766$	−12889.1	−	18681.3i	−0.607967	−	0.881179i
$767$	−3211.35	+	3211.35i	−0.151180	+	0.151180i
$768$		0			0
$769$		−	5515.54i		−	0.258642i	−0.991603	−	0.129321i	$-0.958720\pi$
$769$		−	5515.54i		−	0.258642i	0.991603	−	0.129321i	$-0.0412797\pi$
$770$	22098.4	+	20875.0i	1.03425	+	0.976989i
$771$		0			0
$772$	14852.2	−	6677.11i	0.692413	−	0.311288i
$773$	−7904.07	+	7904.07i	−0.367774	+	0.367774i	−0.866665	−	0.498891i	$-0.833741\pi$
$773$	−7904.07	+	7904.07i	−0.367774	+	0.367774i	0.498891	+	0.866665i	$0.333741\pi$
$774$		0			0
$775$	3175.42	+	7113.98i	0.147180	+	0.329731i
$776$	3518.90	+	14314.7i	0.162785	+	0.662199i
$777$		0			0
$778$	1174.66	−	6402.52i	0.0541308	−	0.295041i
$779$	5908.13			0.271734
$780$		0			0
$781$	26348.0			1.20718
$782$	−1116.16	+	6083.65i	−0.0510407	+	0.278198i
$783$		0			0
$784$	3154.41	−	3554.71i	0.143696	−	0.161931i
$785$	−21518.2	−	13959.6i	−0.978366	−	0.634700i
$786$		0			0
$787$	−27606.7	+	27606.7i	−1.25041	+	1.25041i	−0.294870	+	0.955537i	$0.595276\pi$
$787$	−27606.7	+	27606.7i	−1.25041	+	1.25041i	−0.955537	+	0.294870i	$0.904724\pi$
$788$	3055.62	+	6796.76i	0.138137	+	0.307265i
$789$		0			0
$790$	−37058.3	+	1055.03i	−1.66896	+	0.0475144i
$791$			15187.2i			0.682673i
$792$		0			0
$793$	2358.53	−	2358.53i	0.105617	−	0.105617i
$794$	−17035.0	−	24690.3i	−0.761398	−	1.10356i
$795$		0			0
$796$	−4926.64	−	1870.74i	−0.219372	−	0.0832998i
$797$	19000.5	+	19000.5i	0.844456	+	0.844456i	0.989435	−	0.144979i	$-0.0463113\pi$
$797$	19000.5	+	19000.5i	0.844456	+	0.844456i	−0.144979	+	0.989435i	$0.546311\pi$
$798$		0			0
$799$	−6650.24			−0.294454
$800$	19992.2	+	10597.7i	0.883540	+	0.468356i
$801$		0			0
$802$	26417.8	+	4846.84i	1.16315	+	0.213401i
$803$	10156.9	+	10156.9i	0.446361	+	0.446361i
$804$		0			0
$805$	13038.7	−	2777.90i	0.570872	−	0.121625i
$806$	−1245.18	−	1804.75i	−0.0544164	−	0.0788704i
$807$		0			0
$808$	115.685	+	70.0315i	0.00503688	+	0.00304913i
$809$		−	33025.1i		−	1.43523i	−0.696440	−	0.717615i	$-0.745234\pi$
$809$		−	33025.1i		−	1.43523i	0.696440	−	0.717615i	$-0.254766\pi$
$810$		0			0
$811$			19125.0i			0.828075i	0.910260	+	0.414037i	$0.135882\pi$
$811$			19125.0i			0.828075i	−0.910260	+	0.414037i	$0.864118\pi$
$812$	16577.8	+	36874.9i	0.716463	+	1.59366i
$813$		0			0
$814$	11344.6	−	7827.19i	0.488487	−	0.337030i
$815$	−22498.9	−	14595.8i	−0.966997	−	0.627325i
$816$		0			0
$817$	−12219.0	−	12219.0i	−0.523243	−	0.523243i
$818$	−5337.04	+	29089.6i	−0.228124	+	1.24339i
$819$		0			0
$820$	10486.2	+	1616.90i	0.446576	+	0.0688594i
$821$	−8022.85			−0.341047			−0.170523	−	0.985354i	$-0.554546\pi$
$821$	−8022.85			−0.341047			−0.170523	+	0.985354i	$0.554546\pi$
$822$		0			0
$823$	−941.682	−	941.682i	−0.0398845	−	0.0398845i	0.686883	−	0.726768i	$-0.258978\pi$
$823$	−941.682	−	941.682i	−0.0398845	−	0.0398845i	−0.726768	+	0.686883i	$0.758978\pi$
$824$	−1052.84	−	4282.87i	−0.0445113	−	0.181069i
$825$		0			0
$826$	−17363.6	+	11980.0i	−0.731424	+	0.504644i
$827$	413.194	−	413.194i	0.0173739	−	0.0173739i	−0.698366	−	0.715740i	$-0.746089\pi$
$827$	413.194	−	413.194i	0.0173739	−	0.0173739i	0.715740	+	0.698366i	$0.246089\pi$
$828$		0			0
$829$			13830.1i			0.579418i	0.957115	+	0.289709i	$0.0935585\pi$
$829$			13830.1i			0.579418i	−0.957115	+	0.289709i	$0.906441\pi$
$830$	−19264.1	−	18197.6i	−0.805623	−	0.761021i
$831$		0			0
$832$	−6077.75	−	1902.11i	−0.253255	−	0.0792595i
$833$	1967.07	−	1967.07i	0.0818188	−	0.0818188i
$834$		0			0
$835$	17342.0	−	26732.0i	0.718736	−	1.10790i
$836$	6656.39	−	17529.8i	0.275378	−	0.725214i
$837$		0			0
$838$	23766.3	+	4360.38i	0.979705	+	0.179745i
$839$	−29230.2			−1.20279			−0.601393	−	0.798954i	$-0.705387\pi$
$839$	−29230.2			−1.20279			−0.601393	+	0.798954i	$0.705387\pi$
$840$		0			0
$841$	−36820.9			−1.50973
$842$	−8659.53	−	1588.75i	−0.354426	−	0.0650262i
$843$		0			0
$844$	16532.6	−	43539.0i	0.674260	−	1.77568i
$845$	−4757.91	−	22332.2i	−0.193701	−	0.909175i
$846$		0			0
$847$	12764.2	−	12764.2i	0.517809	−	0.517809i
$848$	29505.6	−	1760.46i	1.19484	−	0.0712906i
$849$		0			0
$850$	11312.2	+	6889.30i	0.456475	+	0.278001i
$851$		−	6044.34i		−	0.243475i
$852$		0			0
$853$	−20858.3	+	20858.3i	−0.837251	+	0.837251i	−0.988496	−	0.151245i	$-0.951672\pi$
$853$	−20858.3	+	20858.3i	−0.837251	+	0.837251i	0.151245	+	0.988496i	$0.451672\pi$
$854$	12752.5	−	8798.52i	0.510984	−	0.352552i
$855$		0			0
$856$	−22496.4	+	5530.18i	−0.898261	+	0.220815i
$857$	−24905.5	−	24905.5i	−0.992714	−	0.992714i	0.00725972	−	0.999974i	$-0.497689\pi$
$857$	−24905.5	−	24905.5i	−0.992714	−	0.992714i	−0.999974	+	0.00725972i	$0.997689\pi$
$858$		0			0
$859$	26939.2			1.07003			0.535013	−	0.844844i	$-0.320307\pi$
$859$	26939.2			1.07003			0.535013	+	0.844844i	$0.320307\pi$
$860$	−18343.1	−	25031.2i	−0.727320	−	0.992507i
$861$		0			0
$862$	752.818	−	4103.25i	0.0297460	−	0.162131i
$863$	17233.1	+	17233.1i	0.679747	+	0.679747i	0.959943	−	0.280196i	$-0.0903995\pi$
$863$	17233.1	+	17233.1i	0.679747	+	0.679747i	−0.280196	+	0.959943i	$0.590399\pi$
$864$		0			0
$865$	2735.57	−	4216.77i	0.107528	−	0.165751i
$866$	−20401.6	+	14076.0i	−0.800548	+	0.552336i
$867$		0			0
$868$	−4176.12	−	9289.13i	−0.163303	−	0.363241i
$869$			55172.1i			2.15372i
$870$		0			0
$871$		−	1981.00i		−	0.0770649i
$872$	10508.2	−	17358.5i	0.408086	−	0.674119i
$873$		0			0
$874$	−4669.87	−	6768.45i	−0.180733	−	0.261952i
$875$	4425.77	−	28202.3i	0.170992	−	1.08961i
$876$		0			0
$877$	8676.94	+	8676.94i	0.334093	+	0.334093i	0.854138	−	0.520046i	$-0.174085\pi$
$877$	8676.94	+	8676.94i	0.334093	+	0.334093i	−0.520046	+	0.854138i	$0.674085\pi$
$878$	−12968.2	−	2379.26i	−0.498470	−	0.0914536i
$879$		0			0
$880$	16611.7	−	29291.3i	0.636339	−	1.12206i
$881$	9480.93			0.362566			0.181283	−	0.983431i	$-0.441975\pi$
$881$	9480.93			0.362566			0.181283	+	0.983431i	$0.441975\pi$
$882$		0			0
$883$	−27861.7	−	27861.7i	−1.06186	−	1.06186i	−0.997956	−	0.0639013i	$-0.979646\pi$
$883$	−27861.7	−	27861.7i	−1.06186	−	1.06186i	−0.0639013	−	0.997956i	$-0.520354\pi$
$884$	−3484.96	−	1323.31i	−0.132593	−	0.0503480i
$885$		0			0
$886$	−11927.2	−	17287.1i	−0.452260	−	0.655499i
$887$	27498.7	−	27498.7i	1.04094	−	1.04094i	0.0418178	−	0.999125i	$-0.486685\pi$
$887$	27498.7	−	27498.7i	1.04094	−	1.04094i	0.999125	−	0.0418178i	$-0.0133149\pi$
$888$		0			0
$889$		−	2178.84i		−	0.0822001i
$890$	−496.820	−	17450.9i	−0.0187117	−	0.657255i
$891$		0			0
$892$	10742.1	+	23894.1i	0.403219	+	0.896899i
$893$	6251.80	−	6251.80i	0.234276	−	0.234276i
$894$		0			0
$895$	38469.5	−	8195.97i	1.43675	−	0.306102i
$896$	−26173.2	−	13784.7i	−0.975875	−	0.513968i
$897$		0			0
$898$	−1527.17	+	8323.88i	−0.0567510	+	0.309322i
$899$	15419.4			0.572040
$900$		0			0
$901$	17301.8			0.639739
$902$	2849.38	−	15530.6i	0.105182	−	0.573295i
$903$		0			0
$904$	16336.9	−	4016.01i	0.601058	−	0.147755i
$905$	52158.0	−	11112.3i	1.91579	−	0.408162i
$906$		0			0
$907$	−1450.80	+	1450.80i	−0.0531127	+	0.0531127i	−0.733164	−	0.680052i	$-0.761957\pi$
$907$	−1450.80	+	1450.80i	−0.0531127	+	0.0531127i	0.680052	+	0.733164i	$0.261957\pi$
$908$	30649.0	−	13778.9i	1.12018	−	0.503599i
$909$		0			0
$910$	228.649	+	8031.37i	0.00832928	+	0.292568i
$911$		−	20370.8i		−	0.740850i	−0.928862	−	0.370425i	$-0.879212\pi$
$911$		−	20370.8i		−	0.740850i	0.928862	−	0.370425i	$-0.120788\pi$
$912$		0			0
$913$	−27886.3	+	27886.3i	−1.01085	+	1.01085i
$914$	29866.3	+	43287.8i	1.08084	+	1.56656i
$915$		0			0
$916$	14146.3	−	37254.6i	0.510269	−	1.34381i
$917$	19852.8	+	19852.8i	0.714937	+	0.714937i
$918$		0			0
$919$	21825.1			0.783399			0.391699	−	0.920093i	$-0.371887\pi$
$919$	21825.1			0.783399			0.391699	+	0.920093i	$0.371887\pi$
$920$	−6436.06	−	13291.1i	−0.230642	−	0.476300i
$921$		0			0
$922$	−9012.73	−	1653.56i	−0.321929	−	0.0590639i
$923$	4924.22	+	4924.22i	0.175604	+	0.175604i
$924$		0			0
$925$	−12088.0	−	4627.02i	−0.429676	−	0.164471i
$926$	−3527.35	−	5112.49i	−0.125179	−	0.181433i
$927$		0			0
$928$	35282.6	−	27583.8i	1.24807	−	0.975735i
$929$			9339.19i			0.329827i	0.986308	+	0.164913i	$0.0527345\pi$
$929$			9339.19i			0.329827i	−0.986308	+	0.164913i	$0.947266\pi$
$930$		0			0
$931$			3698.44i			0.130195i
$932$	−17016.3	+	7650.01i	−0.598055	+	0.268867i
$933$		0			0
$934$	−20815.1	+	14361.3i	−0.729219	+	0.503123i
$935$	10727.5	−	16536.0i	0.375216	−	0.578381i
$936$		0			0
$937$	431.639	+	431.639i	0.0150491	+	0.0150491i	0.714591	−	0.699542i	$-0.246613\pi$
$937$	431.639	+	431.639i	0.0150491	+	0.0150491i	−0.699542	+	0.714591i	$0.746613\pi$
$938$	1660.51	−	9050.63i	0.0578012	−	0.315047i
$939$		0			0
$940$	12807.1	−	9385.17i	0.444384	−	0.325649i
$941$	−21225.1			−0.735300			−0.367650	−	0.929964i	$-0.619838\pi$
$941$	−21225.1			−0.735300			−0.367650	+	0.929964i	$0.619838\pi$
$942$		0			0
$943$	−4896.37	−	4896.37i	−0.169086	−	0.169086i
$944$	17478.4	+	15510.1i	0.602619	+	0.534758i
$945$		0			0
$946$	−38012.9	+	26226.9i	−1.30645	+	0.901384i
$947$	−11052.1	+	11052.1i	−0.379244	+	0.379244i	−0.870830	−	0.491585i	$-0.836418\pi$
$947$	−11052.1	+	11052.1i	−0.379244	+	0.379244i	0.491585	+	0.870830i	$0.336418\pi$
$948$		0			0
$949$			3796.47i			0.129861i
$950$	−17110.9	+	4157.87i	−0.584371	+	0.141999i
$951$		0			0
$952$	−14812.6	−	8966.99i	−0.504285	−	0.305275i
$953$	−22553.2	+	22553.2i	−0.766600	+	0.766600i	−0.977506	−	0.210906i	$-0.932359\pi$
$953$	−22553.2	+	22553.2i	−0.766600	+	0.766600i	0.210906	+	0.977506i	$0.432359\pi$
$954$		0			0
$955$	−4026.70	−	18900.2i	−0.136441	−	0.640413i
$956$	26737.2	+	10152.6i	0.904541	+	0.343472i
$957$		0			0
$958$	−19868.0	−	3645.16i	−0.670048	−	0.122933i
$959$	−57844.3			−1.94775
$960$		0			0
$961$	25906.7			0.869616
$962$	3583.05	+	657.379i	0.120086	+	0.0220320i
$963$		0			0
$964$	38406.1	+	14583.6i	1.28317	+	0.487246i
$965$	−12385.7	+	19092.1i	−0.413171	+	0.636887i
$966$		0			0
$967$	−18695.9	+	18695.9i	−0.621739	+	0.621739i	−0.945976	−	0.324237i	$-0.894892\pi$
$967$	−18695.9	+	18695.9i	−0.621739	+	0.621739i	0.324237	+	0.945976i	$0.394892\pi$
$968$	−17105.8	−	10355.2i	−0.567976	−	0.343831i
$969$		0			0
$970$	−14975.7	−	14146.6i	−0.495712	−	0.468268i
$971$			11285.7i			0.372993i	0.982456	+	0.186496i	$0.0597133\pi$
$971$			11285.7i			0.372993i	−0.982456	+	0.186496i	$0.940287\pi$
$972$		0			0
$973$	37193.3	−	37193.3i	1.22545	−	1.22545i
$974$	12602.5	−	8695.07i	0.414590	−	0.286045i
$975$		0			0
$976$	−12836.8	−	11391.2i	−0.420999	−	0.373590i
$977$	−9765.98	−	9765.98i	−0.319797	−	0.319797i	0.528892	−	0.848689i	$-0.322608\pi$
$977$	−9765.98	−	9765.98i	−0.319797	−	0.319797i	−0.848689	+	0.528892i	$0.822608\pi$
$978$		0			0
$979$	−25980.8			−0.848162
$980$	−1012.17	+	6564.25i	−0.0329923	+	0.213966i
$981$		0			0
$982$	7627.15	−	41571.9i	0.247854	−	1.35093i
$983$	−33483.4	−	33483.4i	−1.08642	−	1.08642i	−0.995894	−	0.0905295i	$-0.971144\pi$
$983$	−33483.4	−	33483.4i	−1.08642	−	1.08642i	−0.0905295	−	0.995894i	$-0.528856\pi$
$984$		0			0
$985$	−8737.05	−	5668.03i	−0.282625	−	0.183349i
$986$	21577.5	−	14887.4i	0.696926	−	0.480842i
$987$		0			0
$988$	4520.19	−	2032.14i	0.145553	−	0.0654363i
$989$			20253.0i			0.651171i
$990$		0			0
$991$			35651.6i			1.14280i	0.820673	+	0.571398i	$0.193599\pi$
$991$			35651.6i			1.14280i	−0.820673	+	0.571398i	$0.806401\pi$
$992$	−8888.02	+	6948.62i	−0.284471	+	0.222398i
$993$		0			0
$994$	18369.8	+	26625.0i	0.586173	+	0.849591i
$995$	7203.19	−	1534.65i	0.229504	−	0.0488961i
$996$		0			0
$997$	−19421.9	−	19421.9i	−0.616949	−	0.616949i	0.327799	−	0.944748i	$-0.393693\pi$
$997$	−19421.9	−	19421.9i	−0.616949	−	0.616949i	−0.944748	+	0.327799i	$0.893693\pi$
$998$	6466.76	+	1186.45i	0.205112	+	0.0376316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.4.k.e.127.6		12
3.2	odd	2		20.4.e.b.7.1	yes	12
4.3	odd	2	inner	180.4.k.e.127.3		12
5.3	odd	4	inner	180.4.k.e.163.3		12
12.11	even	2		20.4.e.b.7.4	yes	12
15.2	even	4		100.4.e.e.43.3		12
15.8	even	4		20.4.e.b.3.4	yes	12
15.14	odd	2		100.4.e.e.7.6		12
20.3	even	4	inner	180.4.k.e.163.6		12
24.5	odd	2		320.4.n.k.127.2		12
24.11	even	2		320.4.n.k.127.5		12
60.23	odd	4		20.4.e.b.3.1	✓	12
60.47	odd	4		100.4.e.e.43.6		12
60.59	even	2		100.4.e.e.7.3		12
120.53	even	4		320.4.n.k.63.5		12
120.83	odd	4		320.4.n.k.63.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.1	✓	12	60.23	odd	4
20.4.e.b.3.4	yes	12	15.8	even	4
20.4.e.b.7.1	yes	12	3.2	odd	2
20.4.e.b.7.4	yes	12	12.11	even	2
100.4.e.e.7.3		12	60.59	even	2
100.4.e.e.7.6		12	15.14	odd	2
100.4.e.e.43.3		12	15.2	even	4
100.4.e.e.43.6		12	60.47	odd	4
180.4.k.e.127.3		12	4.3	odd	2	inner
180.4.k.e.127.6		12	1.1	even	1	trivial
180.4.k.e.163.3		12	5.3	odd	4	inner
180.4.k.e.163.6		12	20.3	even	4	inner
320.4.n.k.63.2		12	120.83	odd	4
320.4.n.k.63.5		12	120.53	even	4
320.4.n.k.127.2		12	24.5	odd	2
320.4.n.k.127.5		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.78199 + 0.510409i) q^{2} +(7.47897 + 2.83991i) q^{4} +(-10.9349 + 2.32970i) q^{5} +(-14.4440 + 14.4440i) q^{7} +(19.3569 + 11.7179i) q^{8} +O(q^{10})\)	\(q+(2.78199 + 0.510409i) q^{2} +(7.47897 + 2.83991i) q^{4} +(-10.9349 + 2.32970i) q^{5} +(-14.4440 + 14.4440i) q^{7} +(19.3569 + 11.7179i) q^{8} +(-31.6100 + 0.899920i) q^{10} +47.0607i q^{11} +(-8.79525 + 8.79525i) q^{13} +(-47.5554 + 32.8107i) q^{14} +(47.8698 + 42.4791i) q^{16} +(26.4898 + 26.4898i) q^{17} -49.8054 q^{19} +(-88.3980 - 13.6304i) q^{20} +(-24.0202 + 130.922i) q^{22} +(41.2762 + 41.2762i) q^{23} +(114.145 - 50.9501i) q^{25} +(-28.9575 + 19.9791i) q^{26} +(-149.046 + 67.0065i) q^{28} -247.406i q^{29} +62.3240i q^{31} +(111.492 + 142.610i) q^{32} +(60.1738 + 87.2150i) q^{34} +(124.294 - 191.594i) q^{35} +(-73.2182 - 73.2182i) q^{37} +(-138.558 - 25.4211i) q^{38} +(-238.966 - 83.0389i) q^{40} -118.624 q^{41} +(245.335 + 245.335i) q^{43} +(-133.648 + 351.965i) q^{44} +(93.7624 + 135.898i) q^{46} +(-125.525 + 125.525i) q^{47} -74.2578i q^{49} +(343.556 - 83.4822i) q^{50} +(-90.7571 + 40.8017i) q^{52} +(326.574 - 326.574i) q^{53} +(-109.637 - 514.605i) q^{55} +(-448.845 + 110.337i) q^{56} +(126.278 - 688.282i) q^{58} +365.123 q^{59} -268.160 q^{61} +(-31.8107 + 173.385i) q^{62} +(237.380 + 453.646i) q^{64} +(75.6851 - 116.666i) q^{65} +(-112.617 + 112.617i) q^{67} +(122.888 + 273.345i) q^{68} +(443.576 - 469.573i) q^{70} -559.873i q^{71} +(215.825 - 215.825i) q^{73} +(-166.321 - 241.064i) q^{74} +(-372.493 - 141.443i) q^{76} +(-679.744 - 679.744i) q^{77} +1172.36 q^{79} +(-622.417 - 352.984i) q^{80} +(-330.012 - 60.5470i) q^{82} +(592.561 + 592.561i) q^{83} +(-351.377 - 227.951i) q^{85} +(557.299 + 807.742i) q^{86} +(-551.454 + 910.949i) q^{88} +552.071i q^{89} -254.077i q^{91} +(191.483 + 425.924i) q^{92} +(-413.277 + 285.139i) q^{94} +(544.618 - 116.032i) q^{95} +(460.651 + 460.651i) q^{97} +(37.9019 - 206.585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 12 * q^8	\( 12 q + 6 q^{2} + 12 q^{8} - 110 q^{10} + 116 q^{13} + 312 q^{16} + 332 q^{17} - 140 q^{20} + 360 q^{22} + 340 q^{25} + 164 q^{26} - 880 q^{28} + 376 q^{32} + 508 q^{37} - 1600 q^{38} + 1420 q^{40} + 656 q^{41} - 1432 q^{46} + 1570 q^{50} - 932 q^{52} + 644 q^{53} - 2048 q^{56} + 1576 q^{58} - 896 q^{61} - 2440 q^{62} + 2740 q^{65} + 844 q^{68} - 3040 q^{70} + 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 1840 q^{80} - 1352 q^{82} + 500 q^{85} + 2552 q^{86} - 2400 q^{88} + 1840 q^{92} - 4772 q^{97} - 1698 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 12 * q^8 - 110 * q^10 + 116 * q^13 + 312 * q^16 + 332 * q^17 - 140 * q^20 + 360 * q^22 + 340 * q^25 + 164 * q^26 - 880 * q^28 + 376 * q^32 + 508 * q^37 - 1600 * q^38 + 1420 * q^40 + 656 * q^41 - 1432 * q^46 + 1570 * q^50 - 932 * q^52 + 644 * q^53 - 2048 * q^56 + 1576 * q^58 - 896 * q^61 - 2440 * q^62 + 2740 * q^65 + 844 * q^68 - 3040 * q^70 + 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 1840 * q^80 - 1352 * q^82 + 500 * q^85 + 2552 * q^86 - 2400 * q^88 + 1840 * q^92 - 4772 * q^97 - 1698 * q^98

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