LMFDB - Embedded newform 912.3.be.j.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$1.60382 - 2.77790i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-1.60382 - 2.77790i) q^{5} +13.4491 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-1.60382 - 2.77790i) q^{5} +13.4491 q^{7} +(1.50000 - 2.59808i) q^{9} +3.80276 q^{11} +(10.8671 + 6.27412i) q^{13} +(-4.81146 - 2.77790i) q^{15} +(14.4766 + 25.0742i) q^{17} +(-11.3779 + 15.2166i) q^{19} +(20.1737 - 11.6473i) q^{21} +(-14.1475 + 24.5042i) q^{23} +(7.35552 - 12.7401i) q^{25} -5.19615i q^{27} +(23.9335 + 13.8180i) q^{29} -40.4552i q^{31} +(5.70414 - 3.29329i) q^{33} +(-21.5700 - 37.3604i) q^{35} -27.0114i q^{37} +21.7342 q^{39} +(-54.3074 + 31.3544i) q^{41} +(-16.4814 - 28.5467i) q^{43} -9.62293 q^{45} +(-39.9582 + 69.2096i) q^{47} +131.879 q^{49} +(43.4298 + 25.0742i) q^{51} +(14.5718 + 8.41305i) q^{53} +(-6.09895 - 10.5637i) q^{55} +(-3.88887 + 32.6784i) q^{57} +(72.4502 - 41.8292i) q^{59} +(35.8592 - 62.1099i) q^{61} +(20.1737 - 34.9419i) q^{63} -40.2503i q^{65} +(-81.8710 - 47.2682i) q^{67} +49.0085i q^{69} +(46.5560 - 26.8791i) q^{71} +(51.3925 + 89.0144i) q^{73} -25.4803i q^{75} +51.1439 q^{77} +(-67.8435 + 39.1695i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.94648 q^{83} +(46.4357 - 80.4291i) q^{85} +47.8669 q^{87} +(-22.6612 - 13.0834i) q^{89} +(146.153 + 84.3816i) q^{91} +(-35.0353 - 60.6829i) q^{93} +(60.5182 + 7.20193i) q^{95} +(132.495 - 76.4962i) q^{97} +(5.70414 - 9.87986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−1.60382	−	2.77790i	−0.320764	−	0.555580i	0.659882	−	0.751370i	$-0.270606\pi$
$5$	−1.60382	−	2.77790i	−0.320764	−	0.555580i	−0.980646	+	0.195790i	$0.937273\pi$
$6$		0			0
$7$	13.4491			1.92131			0.960653	−	0.277752i	$-0.0895892\pi$
$7$	13.4491			1.92131			0.960653	+	0.277752i	$0.0895892\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	3.80276			0.345705			0.172853	−	0.984948i	$-0.444702\pi$
$11$	3.80276			0.345705			0.172853	+	0.984948i	$0.444702\pi$
$12$		0			0
$13$	10.8671	+	6.27412i	0.835931	+	0.482625i	0.855879	−	0.517176i	$-0.173017\pi$
$13$	10.8671	+	6.27412i	0.835931	+	0.482625i	−0.0199482	+	0.999801i	$0.506350\pi$
$14$		0			0
$15$	−4.81146	−	2.77790i	−0.320764	−	0.185193i
$16$		0			0
$17$	14.4766	+	25.0742i	0.851565	+	1.47495i	0.879796	+	0.475352i	$0.157679\pi$
$17$	14.4766	+	25.0742i	0.851565	+	1.47495i	−0.0282314	+	0.999601i	$0.508988\pi$
$18$		0			0
$19$	−11.3779	+	15.2166i	−0.598835	+	0.800872i
$19$	−11.3779	+	15.2166i	−0.598835	+	0.800872i
$20$		0			0
$21$	20.1737	−	11.6473i	0.960653	−	0.554633i
$22$		0			0
$23$	−14.1475	+	24.5042i	−0.615110	+	1.06540i	0.375255	+	0.926922i	$0.377555\pi$
$23$	−14.1475	+	24.5042i	−0.615110	+	1.06540i	−0.990365	+	0.138480i	$0.955778\pi$
$24$		0			0
$25$	7.35552	−	12.7401i	0.294221	−	0.509605i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	23.9335	+	13.8180i	0.825292	+	0.476482i	0.852238	−	0.523154i	$-0.175245\pi$
$29$	23.9335	+	13.8180i	0.825292	+	0.476482i	−0.0269460	+	0.999637i	$0.508578\pi$
$30$		0			0
$31$		−	40.4552i		−	1.30501i	−0.757785	−	0.652504i	$-0.773719\pi$
$31$		−	40.4552i		−	1.30501i	0.757785	−	0.652504i	$-0.226281\pi$
$32$		0			0
$33$	5.70414	−	3.29329i	0.172853	−	0.0997966i
$34$		0			0
$35$	−21.5700	−	37.3604i	−0.616286	−	1.06744i
$36$		0			0
$37$		−	27.0114i		−	0.730039i	−0.931000	−	0.365019i	$-0.881062\pi$
$37$		−	27.0114i		−	0.730039i	0.931000	−	0.365019i	$-0.118938\pi$
$38$		0			0
$39$	21.7342			0.557287
$40$		0			0
$41$	−54.3074	+	31.3544i	−1.32457	+	0.764741i	−0.984454	−	0.175642i	$-0.943800\pi$
$41$	−54.3074	+	31.3544i	−1.32457	+	0.764741i	−0.340116	+	0.940383i	$0.610466\pi$
$42$		0			0
$43$	−16.4814	−	28.5467i	−0.383289	−	0.663877i	0.608241	−	0.793753i	$-0.291875\pi$
$43$	−16.4814	−	28.5467i	−0.383289	−	0.663877i	−0.991530	+	0.129876i	$0.958542\pi$
$44$		0			0
$45$	−9.62293			−0.213843
$46$		0			0
$47$	−39.9582	+	69.2096i	−0.850174	+	1.47255i	0.0308762	+	0.999523i	$0.490170\pi$
$47$	−39.9582	+	69.2096i	−0.850174	+	1.47255i	−0.881051	+	0.473022i	$0.843163\pi$
$48$		0			0
$49$	131.879			2.69142
$50$		0			0
$51$	43.4298	+	25.0742i	0.851565	+	0.491651i
$52$		0			0
$53$	14.5718	+	8.41305i	0.274940	+	0.158737i	0.631131	−	0.775677i	$-0.282591\pi$
$53$	14.5718	+	8.41305i	0.274940	+	0.158737i	−0.356190	+	0.934413i	$0.615925\pi$
$54$		0			0
$55$	−6.09895	−	10.5637i	−0.110890	−	0.192067i
$56$		0			0
$57$	−3.88887	+	32.6784i	−0.0682258	+	0.573305i
$58$		0			0
$59$	72.4502	−	41.8292i	1.22797	−	0.708969i	0.261365	−	0.965240i	$-0.415827\pi$
$59$	72.4502	−	41.8292i	1.22797	−	0.708969i	0.966605	+	0.256271i	$0.0824940\pi$
$60$		0			0
$61$	35.8592	−	62.1099i	0.587856	−	1.01820i	−0.406657	−	0.913581i	$-0.633306\pi$
$61$	35.8592	−	62.1099i	0.587856	−	1.01820i	0.994513	−	0.104615i	$-0.0333610\pi$
$62$		0			0
$63$	20.1737	−	34.9419i	0.320218	−	0.554633i
$64$		0			0
$65$		−	40.2503i		−	0.619235i
$66$		0			0
$67$	−81.8710	−	47.2682i	−1.22195	−	0.705496i	−0.256620	−	0.966512i	$-0.582609\pi$
$67$	−81.8710	−	47.2682i	−1.22195	−	0.705496i	−0.965334	+	0.261016i	$0.915942\pi$
$68$		0			0
$69$			49.0085i			0.710268i
$70$		0			0
$71$	46.5560	−	26.8791i	0.655719	−	0.378579i	−0.134925	−	0.990856i	$-0.543079\pi$
$71$	46.5560	−	26.8791i	0.655719	−	0.378579i	0.790644	+	0.612276i	$0.209746\pi$
$72$		0			0
$73$	51.3925	+	89.0144i	0.704007	+	1.21938i	0.967049	+	0.254591i	$0.0819409\pi$
$73$	51.3925	+	89.0144i	0.704007	+	1.21938i	−0.263042	+	0.964784i	$0.584726\pi$
$74$		0			0
$75$		−	25.4803i		−	0.339737i
$76$		0			0
$77$	51.1439			0.664206
$78$		0			0
$79$	−67.8435	+	39.1695i	−0.858778	+	0.495816i	−0.863603	−	0.504173i	$-0.831798\pi$
$79$	−67.8435	+	39.1695i	−0.858778	+	0.495816i	0.00482474	+	0.999988i	$0.498464\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.94648			−0.0595961			−0.0297981	−	0.999556i	$-0.509486\pi$
$83$	−4.94648			−0.0595961			−0.0297981	+	0.999556i	$0.509486\pi$
$84$		0			0
$85$	46.4357	−	80.4291i	0.546303	−	0.946224i
$86$		0			0
$87$	47.8669			0.550195
$88$		0			0
$89$	−22.6612	−	13.0834i	−0.254620	−	0.147005i	0.367258	−	0.930119i	$-0.380297\pi$
$89$	−22.6612	−	13.0834i	−0.254620	−	0.147005i	−0.621878	+	0.783114i	$0.713630\pi$
$90$		0			0
$91$	146.153	+	84.3816i	1.60608	+	0.927270i
$92$		0			0
$93$	−35.0353	−	60.6829i	−0.376723	−	0.652504i
$94$		0			0
$95$	60.5182	+	7.20193i	0.637033	+	0.0758098i
$96$		0			0
$97$	132.495	−	76.4962i	1.36593	−	0.788621i	0.375526	−	0.926812i	$-0.377462\pi$
$97$	132.495	−	76.4962i	1.36593	−	0.788621i	0.990406	+	0.138191i	$0.0441288\pi$
$98$		0			0
$99$	5.70414	−	9.87986i	0.0576176	−	0.0997966i
$100$		0			0
$101$	−32.3369	+	56.0091i	−0.320167	+	0.554546i	−0.980522	−	0.196408i	$-0.937072\pi$
$101$	−32.3369	+	56.0091i	−0.320167	+	0.554546i	0.660355	+	0.750953i	$0.270406\pi$
$102$		0			0
$103$		−	18.6301i		−	0.180874i	−0.995902	−	0.0904372i	$-0.971174\pi$
$103$		−	18.6301i		−	0.180874i	0.995902	−	0.0904372i	$-0.0288264\pi$
$104$		0			0
$105$	−64.7100	−	37.3604i	−0.616286	−	0.355813i
$106$		0			0
$107$		−	136.749i		−	1.27803i	−0.769196	−	0.639013i	$-0.779343\pi$
$107$		−	136.749i		−	1.27803i	0.769196	−	0.639013i	$-0.220657\pi$
$108$		0			0
$109$	−39.3264	+	22.7051i	−0.360792	+	0.208303i	−0.669428	−	0.742877i	$-0.733461\pi$
$109$	−39.3264	+	22.7051i	−0.360792	+	0.208303i	0.308636	+	0.951180i	$0.400128\pi$
$110$		0			0
$111$	−23.3926	−	40.5171i	−0.210744	−	0.365019i
$112$		0			0
$113$		−	73.5630i		−	0.651000i	−0.945542	−	0.325500i	$-0.894467\pi$
$113$		−	73.5630i		−	0.651000i	0.945542	−	0.325500i	$-0.105533\pi$
$114$		0			0
$115$	90.7604			0.789221
$116$		0			0
$117$	32.6013	−	18.8224i	0.278644	−	0.160875i
$118$		0			0
$119$	194.698	+	337.226i	1.63612	+	2.83384i
$120$		0			0
$121$	−106.539			−0.880488
$122$		0			0
$123$	−54.3074	+	94.0631i	−0.441523	+	0.764741i
$124$		0			0
$125$	−127.379			−1.01903
$126$		0			0
$127$	−11.5879	−	6.69027i	−0.0912432	−	0.0526793i	0.453684	−	0.891163i	$-0.350109\pi$
$127$	−11.5879	−	6.69027i	−0.0912432	−	0.0526793i	−0.544927	+	0.838483i	$0.683443\pi$
$128$		0			0
$129$	−49.4443	−	28.5467i	−0.383289	−	0.221292i
$130$		0			0
$131$	−62.6392	−	108.494i	−0.478162	−	0.828201i	0.521525	−	0.853236i	$-0.325364\pi$
$131$	−62.6392	−	108.494i	−0.478162	−	0.828201i	−0.999687	+	0.0250353i	$0.992030\pi$
$132$		0			0
$133$	−153.023	+	204.650i	−1.15055	+	1.53872i
$134$		0			0
$135$	−14.4344	+	8.33370i	−0.106921	+	0.0617311i
$136$		0			0
$137$	109.699	−	190.005i	0.800726	−	1.38690i	−0.118413	−	0.992964i	$-0.537781\pi$
$137$	109.699	−	190.005i	0.800726	−	1.38690i	0.919139	−	0.393933i	$-0.128886\pi$
$138$		0			0
$139$	26.7725	−	46.3714i	0.192608	−	0.333607i	−0.753506	−	0.657441i	$-0.771639\pi$
$139$	26.7725	−	46.3714i	0.192608	−	0.333607i	0.946114	+	0.323834i	$0.104972\pi$
$140$		0			0
$141$			138.419i			0.981697i
$142$		0			0
$143$	41.3250	+	23.8590i	0.288986	+	0.166846i
$144$		0			0
$145$		−	88.6464i		−	0.611354i
$146$		0			0
$147$	197.819	−	114.211i	1.34571	−	0.776945i
$148$		0			0
$149$	−2.24602	−	3.89022i	−0.0150739	−	0.0261088i	0.858390	−	0.512998i	$-0.171465\pi$
$149$	−2.24602	−	3.89022i	−0.0150739	−	0.0261088i	−0.873464	+	0.486889i	$0.838132\pi$
$150$		0			0
$151$			166.976i			1.10580i	0.833247	+	0.552900i	$0.186479\pi$
$151$			166.976i			1.10580i	−0.833247	+	0.552900i	$0.813521\pi$
$152$		0			0
$153$	86.8596			0.567710
$154$		0			0
$155$	−112.381	+	64.8830i	−0.725036	+	0.418600i
$156$		0			0
$157$	−59.3282	−	102.760i	−0.377887	−	0.654519i	0.612868	−	0.790185i	$-0.290016\pi$
$157$	−59.3282	−	102.760i	−0.377887	−	0.654519i	−0.990755	+	0.135666i	$0.956683\pi$
$158$		0			0
$159$	29.1437			0.183293
$160$		0			0
$161$	−190.272	+	329.561i	−1.18181	+	2.04696i
$162$		0			0
$163$	−253.644			−1.55610			−0.778050	−	0.628202i	$-0.783791\pi$
$163$	−253.644			−1.55610			−0.778050	+	0.628202i	$0.783791\pi$
$164$		0			0
$165$	−18.2968	−	10.5637i	−0.110890	−	0.0640223i
$166$		0			0
$167$	−44.8688	−	25.9050i	−0.268676	−	0.155120i	0.359610	−	0.933103i	$-0.382910\pi$
$167$	−44.8688	−	25.9050i	−0.268676	−	0.155120i	−0.628286	+	0.777983i	$0.716243\pi$
$168$		0			0
$169$	−5.77076	−	9.99524i	−0.0341465	−	0.0591434i
$170$		0			0
$171$	22.4670	+	52.3854i	0.131386	+	0.306348i
$172$		0			0
$173$	−66.0037	+	38.1073i	−0.381524	+	0.220273i	−0.678481	−	0.734618i	$-0.737362\pi$
$173$	−66.0037	+	38.1073i	−0.381524	+	0.220273i	0.296957	+	0.954891i	$0.404028\pi$
$174$		0			0
$175$	98.9254	−	171.344i	0.565288	−	0.979107i
$176$		0			0
$177$	72.4502	−	125.487i	0.409323	−	0.708969i
$178$		0			0
$179$		−	228.631i		−	1.27727i	−0.769512	−	0.638633i	$-0.779500\pi$
$179$		−	228.631i		−	1.27727i	0.769512	−	0.638633i	$-0.220500\pi$
$180$		0			0
$181$	215.923	+	124.663i	1.19294	+	0.688746i	0.958973	−	0.283498i	$-0.0914948\pi$
$181$	215.923	+	124.663i	1.19294	+	0.688746i	0.233970	+	0.972244i	$0.424828\pi$
$182$		0			0
$183$		−	124.220i		−	0.678797i
$184$		0			0
$185$	−75.0350	+	43.3215i	−0.405595	+	0.234170i
$186$		0			0
$187$	55.0510	+	95.3512i	0.294391	+	0.509899i
$188$		0			0
$189$		−	69.8838i		−	0.369755i
$190$		0			0
$191$	−167.431			−0.876602			−0.438301	−	0.898828i	$-0.644420\pi$
$191$	−167.431			−0.876602			−0.438301	+	0.898828i	$0.644420\pi$
$192$		0			0
$193$	162.065	−	93.5684i	0.839717	−	0.484811i	−0.0174513	−	0.999848i	$-0.505555\pi$
$193$	162.065	−	93.5684i	0.839717	−	0.484811i	0.857168	+	0.515037i	$0.172222\pi$
$194$		0			0
$195$	−34.8578	−	60.3754i	−0.178758	−	0.309618i
$196$		0			0
$197$	−255.184			−1.29535			−0.647674	−	0.761918i	$-0.724258\pi$
$197$	−255.184			−1.29535			−0.647674	+	0.761918i	$0.724258\pi$
$198$		0			0
$199$	−75.9172	+	131.492i	−0.381493	+	0.660766i	−0.991276	−	0.131803i	$-0.957923\pi$
$199$	−75.9172	+	131.492i	−0.381493	+	0.660766i	0.609783	+	0.792569i	$0.291257\pi$
$200$		0			0
$201$	−163.742			−0.814637
$202$		0			0
$203$	321.885	+	185.840i	1.58564	+	0.915469i
$204$		0			0
$205$	174.199	+	100.574i	0.849750	+	0.490603i
$206$		0			0
$207$	42.4426	+	73.5127i	0.205037	+	0.355134i
$208$		0			0
$209$	−43.2673	+	57.8650i	−0.207021	+	0.276866i
$210$		0			0
$211$	146.990	−	84.8648i	0.696636	−	0.402203i	−0.109458	−	0.993991i	$-0.534911\pi$
$211$	146.990	−	84.8648i	0.696636	−	0.402203i	0.806093	+	0.591789i	$0.201578\pi$
$212$		0			0
$213$	46.5560	−	80.6374i	0.218573	−	0.378579i
$214$		0			0
$215$	−52.8666	+	91.5676i	−0.245891	+	0.425896i
$216$		0			0
$217$		−	544.088i		−	2.50732i
$218$		0			0
$219$	154.177	+	89.0144i	0.704007	+	0.406459i
$220$		0			0
$221$			363.312i			1.64394i
$222$		0			0
$223$	−165.300	+	95.4359i	−0.741255	+	0.427964i	−0.822525	−	0.568728i	$-0.807436\pi$
$223$	−165.300	+	95.4359i	−0.741255	+	0.427964i	0.0812706	+	0.996692i	$0.474102\pi$
$224$		0			0
$225$	−22.0665	−	38.2204i	−0.0980735	−	0.169868i
$226$		0			0
$227$		−	88.8250i		−	0.391299i	−0.980674	−	0.195650i	$-0.937318\pi$
$227$		−	88.8250i		−	0.391299i	0.980674	−	0.195650i	$-0.0626816\pi$
$228$		0			0
$229$	127.409			0.556370			0.278185	−	0.960528i	$-0.410267\pi$
$229$	127.409			0.556370			0.278185	+	0.960528i	$0.410267\pi$
$230$		0			0
$231$	76.7158	−	44.2919i	0.332103	−	0.191740i
$232$		0			0
$233$	−22.6993	−	39.3164i	−0.0974221	−	0.168740i	0.813195	−	0.581992i	$-0.197726\pi$
$233$	−22.6993	−	39.3164i	−0.0974221	−	0.168740i	−0.910617	+	0.413252i	$0.864393\pi$
$234$		0			0
$235$	256.343			1.09082
$236$		0			0
$237$	−67.8435	+	117.508i	−0.286259	+	0.495816i
$238$		0			0
$239$	−114.325			−0.478349			−0.239175	−	0.970977i	$-0.576877\pi$
$239$	−114.325			−0.478349			−0.239175	+	0.970977i	$0.576877\pi$
$240$		0			0
$241$	193.424	+	111.673i	0.802589	+	0.463375i	0.844376	−	0.535752i	$-0.179972\pi$
$241$	193.424	+	111.673i	0.802589	+	0.463375i	−0.0417867	+	0.999127i	$0.513305\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−211.511	−	366.348i	−0.863310	−	1.49530i
$246$		0			0
$247$	−219.115	+	93.9738i	−0.887106	+	0.380461i
$248$		0			0
$249$	−7.41972	+	4.28378i	−0.0297981	+	0.0172039i
$250$		0			0
$251$	−102.125	+	176.885i	−0.406872	+	0.704722i	−0.994537	−	0.104381i	$-0.966714\pi$
$251$	−102.125	+	176.885i	−0.406872	+	0.704722i	0.587666	+	0.809104i	$0.300047\pi$
$252$		0			0
$253$	−53.7997	+	93.1838i	−0.212647	+	0.368315i
$254$		0			0
$255$		−	160.858i		−	0.630816i
$256$		0			0
$257$	103.115	+	59.5334i	0.401225	+	0.231647i	0.687012	−	0.726646i	$-0.258922\pi$
$257$	103.115	+	59.5334i	0.401225	+	0.231647i	−0.285787	+	0.958293i	$0.592255\pi$
$258$		0			0
$259$		−	363.280i		−	1.40263i
$260$		0			0
$261$	71.8004	−	41.4540i	0.275097	−	0.158827i
$262$		0			0
$263$	43.0529	+	74.5698i	0.163699	+	0.283535i	0.936193	−	0.351487i	$-0.114324\pi$
$263$	43.0529	+	74.5698i	0.163699	+	0.283535i	−0.772493	+	0.635023i	$0.780991\pi$
$264$		0			0
$265$		−	53.9721i		−	0.203668i
$266$		0			0
$267$	−45.3224			−0.169747
$268$		0			0
$269$	−98.9214	+	57.1123i	−0.367737	+	0.212313i	−0.672470	−	0.740125i	$-0.734766\pi$
$269$	−98.9214	+	57.1123i	−0.367737	+	0.212313i	0.304732	+	0.952438i	$0.401433\pi$
$270$		0			0
$271$	−33.9996	−	58.8891i	−0.125460	−	0.217303i	0.796453	−	0.604701i	$-0.206707\pi$
$271$	−33.9996	−	58.8891i	−0.125460	−	0.217303i	−0.921913	+	0.387398i	$0.873374\pi$
$272$		0			0
$273$	292.306			1.07072
$274$		0			0
$275$	27.9713	−	48.4476i	0.101714	−	0.176173i
$276$		0			0
$277$	90.3153			0.326048			0.163024	−	0.986622i	$-0.447875\pi$
$277$	90.3153			0.326048			0.163024	+	0.986622i	$0.447875\pi$
$278$		0			0
$279$	−105.106	−	60.6829i	−0.376723	−	0.217501i
$280$		0			0
$281$	283.344	+	163.589i	1.00834	+	0.582166i	0.910705	−	0.413056i	$-0.135539\pi$
$281$	283.344	+	163.589i	1.00834	+	0.582166i	0.0976354	+	0.995222i	$0.468872\pi$
$282$		0			0
$283$	−115.912	−	200.766i	−0.409584	−	0.709420i	0.585259	−	0.810846i	$-0.300993\pi$
$283$	−115.912	−	200.766i	−0.409584	−	0.709420i	−0.994843	+	0.101426i	$0.967659\pi$
$284$		0			0
$285$	97.0143	−	41.6074i	0.340401	−	0.145991i
$286$		0			0
$287$	−730.388	+	421.690i	−2.54490	+	1.46930i
$288$		0			0
$289$	−274.644	+	475.697i	−0.950324	+	1.64601i
$290$		0			0
$291$	132.495	−	229.489i	0.455310	−	0.788621i
$292$		0			0
$293$		−	72.3530i		−	0.246939i	−0.992348	−	0.123469i	$-0.960598\pi$
$293$		−	72.3530i		−	0.246939i	0.992348	−	0.123469i	$-0.0394021\pi$
$294$		0			0
$295$	−232.394	−	134.173i	−0.787778	−	0.454824i
$296$		0			0
$297$		−	19.7597i		−	0.0665310i
$298$		0			0
$299$	−307.485	+	177.527i	−1.02838	+	0.593735i
$300$		0			0
$301$	−221.661	−	383.929i	−0.736416	−	1.27551i
$302$		0			0
$303$			112.018i			0.369697i
$304$		0			0
$305$	−230.047			−0.754252
$306$		0			0
$307$	−224.904	+	129.848i	−0.732586	+	0.422959i	−0.819367	−	0.573269i	$-0.805675\pi$
$307$	−224.904	+	129.848i	−0.732586	+	0.422959i	0.0867815	+	0.996227i	$0.472342\pi$
$308$		0			0
$309$	−16.1341	−	27.9451i	−0.0522139	−	0.0904372i
$310$		0			0
$311$	−379.983			−1.22181			−0.610905	−	0.791704i	$-0.709194\pi$
$311$	−379.983			−1.22181			−0.610905	+	0.791704i	$0.709194\pi$
$312$		0			0
$313$	−228.173	+	395.207i	−0.728986	+	1.26264i	0.228326	+	0.973585i	$0.426675\pi$
$313$	−228.173	+	395.207i	−0.728986	+	1.26264i	−0.957312	+	0.289056i	$0.906659\pi$
$314$		0			0
$315$	−129.420			−0.410857
$316$		0			0
$317$	19.5569	+	11.2912i	0.0616937	+	0.0356189i	0.530530	−	0.847666i	$-0.321993\pi$
$317$	19.5569	+	11.2912i	0.0616937	+	0.0356189i	−0.468836	+	0.883285i	$0.655326\pi$
$318$		0			0
$319$	91.0132	+	52.5465i	0.285308	+	0.164723i
$320$		0			0
$321$	−118.428	−	205.123i	−0.368934	−	0.639013i
$322$		0			0
$323$	−546.256	−	65.0069i	−1.69120	−	0.201260i
$324$		0			0
$325$	159.866	−	92.2988i	0.491896	−	0.283996i
$326$		0			0
$327$	−39.3264	+	68.1152i	−0.120264	+	0.208303i
$328$		0			0
$329$	−537.403	+	930.810i	−1.63345	+	2.82921i
$330$		0			0
$331$			186.891i			0.564627i	0.959322	+	0.282313i	$0.0911018\pi$
$331$			186.891i			0.564627i	−0.959322	+	0.282313i	$0.908898\pi$
$332$		0			0
$333$	−70.1777	−	40.5171i	−0.210744	−	0.121673i
$334$		0			0
$335$			303.239i			0.905191i
$336$		0			0
$337$	−243.566	+	140.623i	−0.722747	+	0.417278i	−0.815763	−	0.578386i	$-0.803683\pi$
$337$	−243.566	+	140.623i	−0.722747	+	0.417278i	0.0930158	+	0.995665i	$0.470349\pi$
$338$		0			0
$339$	−63.7074	−	110.345i	−0.187928	−	0.325500i
$340$		0			0
$341$		−	153.842i		−	0.451148i
$342$		0			0
$343$	1114.66			3.24973
$344$		0			0
$345$	136.141	−	78.6009i	0.394611	−	0.227829i
$346$		0			0
$347$	−280.511	−	485.859i	−0.808388	−	1.40017i	−0.913980	−	0.405759i	$-0.867007\pi$
$347$	−280.511	−	485.859i	−0.808388	−	1.40017i	0.105592	−	0.994410i	$-0.466326\pi$
$348$		0			0
$349$	−492.624			−1.41153			−0.705765	−	0.708446i	$-0.749397\pi$
$349$	−492.624			−1.41153			−0.705765	+	0.708446i	$0.749397\pi$
$350$		0			0
$351$	32.6013	−	56.4671i	0.0928812	−	0.160875i
$352$		0			0
$353$	−83.3367			−0.236081			−0.118041	−	0.993009i	$-0.537661\pi$
$353$	−83.3367			−0.236081			−0.118041	+	0.993009i	$0.537661\pi$
$354$		0			0
$355$	−149.335	−	86.2187i	−0.420662	−	0.242869i
$356$		0			0
$357$	584.093	+	337.226i	1.63612	+	0.944612i
$358$		0			0
$359$	36.5567	+	63.3181i	0.101829	+	0.176374i	0.912438	−	0.409214i	$-0.134197\pi$
$359$	36.5567	+	63.3181i	0.101829	+	0.176374i	−0.810609	+	0.585588i	$0.800864\pi$
$360$		0			0
$361$	−102.088	−	346.264i	−0.282792	−	0.959181i
$362$		0			0
$363$	−159.809	+	92.2655i	−0.440244	+	0.254175i
$364$		0			0
$365$	164.849	−	285.526i	0.451640	−	0.782264i
$366$		0			0
$367$	−159.837	+	276.846i	−0.435523	+	0.754348i	−0.997338	−	0.0729149i	$-0.976770\pi$
$367$	−159.837	+	276.846i	−0.435523	+	0.754348i	0.561815	+	0.827263i	$0.310103\pi$
$368$		0			0
$369$			188.126i			0.509827i
$370$		0			0
$371$	195.979	+	113.148i	0.528244	+	0.304982i
$372$		0			0
$373$			61.6757i			0.165350i	0.996577	+	0.0826752i	$0.0263464\pi$
$373$			61.6757i			0.165350i	−0.996577	+	0.0826752i	$0.973654\pi$
$374$		0			0
$375$	−191.068	+	110.313i	−0.509515	+	0.294169i
$376$		0			0
$377$	173.392	+	300.323i	0.459925	+	0.796613i
$378$		0			0
$379$		−	482.980i		−	1.27435i	−0.770718	−	0.637177i	$-0.780102\pi$
$379$		−	482.980i		−	1.27435i	0.770718	−	0.637177i	$-0.219898\pi$
$380$		0			0
$381$	−23.1758			−0.0608288
$382$		0			0
$383$	−503.570	+	290.736i	−1.31480	+	0.759103i	−0.982888	−	0.184206i	$-0.941029\pi$
$383$	−503.570	+	290.736i	−1.31480	+	0.759103i	−0.331917	+	0.943309i	$0.607695\pi$
$384$		0			0
$385$	−82.0256	−	142.072i	−0.213053	−	0.369019i
$386$		0			0
$387$	−98.8887			−0.255526
$388$		0			0
$389$	24.2668	−	42.0314i	0.0623826	−	0.108050i	−0.833147	−	0.553051i	$-0.813463\pi$
$389$	24.2668	−	42.0314i	0.0623826	−	0.108050i	0.895530	+	0.445001i	$0.146797\pi$
$390$		0			0
$391$	−819.233			−2.09522
$392$		0			0
$393$	−187.918	−	108.494i	−0.478162	−	0.276067i
$394$		0			0
$395$	217.618	+	125.642i	0.550931	+	0.318080i
$396$		0			0
$397$	22.3761	+	38.7566i	0.0563630	+	0.0976236i	0.892830	−	0.450393i	$-0.148716\pi$
$397$	22.3761	+	38.7566i	0.0563630	+	0.0976236i	−0.836467	+	0.548017i	$0.815383\pi$
$398$		0			0
$399$	−52.3020	+	439.496i	−0.131083	+	1.10149i
$400$		0			0
$401$	−432.355	+	249.620i	−1.07819	+	0.622494i	−0.930408	−	0.366526i	$-0.880547\pi$
$401$	−432.355	+	249.620i	−1.07819	+	0.622494i	−0.147783	+	0.989020i	$0.547214\pi$
$402$		0			0
$403$	253.821	−	439.631i	0.629829	−	1.09090i
$404$		0			0
$405$	−14.4344	+	25.0011i	−0.0356405	+	0.0617311i
$406$		0			0
$407$		−	102.718i		−	0.252378i
$408$		0			0
$409$	−78.1774	−	45.1358i	−0.191143	−	0.110356i	0.401375	−	0.915914i	$-0.368533\pi$
$409$	−78.1774	−	45.1358i	−0.191143	−	0.110356i	−0.592517	+	0.805558i	$0.701866\pi$
$410$		0			0
$411$		−	380.010i		−	0.924598i
$412$		0			0
$413$	974.393	−	562.566i	2.35931	−	1.36215i
$414$		0			0
$415$	7.93327	+	13.7408i	0.0191163	+	0.0331104i
$416$		0			0
$417$		−	92.7428i		−	0.222405i
$418$		0			0
$419$	−259.036			−0.618225			−0.309113	−	0.951025i	$-0.600032\pi$
$419$	−259.036			−0.618225			−0.309113	+	0.951025i	$0.600032\pi$
$420$		0			0
$421$	354.525	−	204.685i	0.842102	−	0.486188i	−0.0158764	−	0.999874i	$-0.505054\pi$
$421$	354.525	−	204.685i	0.842102	−	0.486188i	0.857978	+	0.513686i	$0.171720\pi$
$422$		0			0
$423$	119.875	+	207.629i	0.283391	+	0.490848i
$424$		0			0
$425$	425.931			1.00219
$426$		0			0
$427$	482.275	−	835.325i	1.12945	−	1.95627i
$428$		0			0
$429$	82.6499			0.192657
$430$		0			0
$431$	455.378	+	262.913i	1.05656	+	0.610006i	0.924479	−	0.381233i	$-0.124500\pi$
$431$	455.378	+	262.913i	1.05656	+	0.610006i	0.132082	+	0.991239i	$0.457834\pi$
$432$		0			0
$433$	352.115	+	203.294i	0.813200	+	0.469501i	0.848066	−	0.529891i	$-0.177767\pi$
$433$	352.115	+	203.294i	0.813200	+	0.469501i	−0.0348661	+	0.999392i	$0.511100\pi$
$434$		0			0
$435$	−76.7700	−	132.970i	−0.176483	−	0.305677i
$436$		0			0
$437$	−211.902	−	494.083i	−0.484901	−	1.13062i
$438$		0			0
$439$	277.213	−	160.049i	0.631465	−	0.364576i	−0.149854	−	0.988708i	$-0.547881\pi$
$439$	277.213	−	160.049i	0.631465	−	0.364576i	0.781319	+	0.624132i	$0.214547\pi$
$440$		0			0
$441$	197.819	−	342.633i	0.448569	−	0.776945i
$442$		0			0
$443$	52.8765	−	91.5849i	0.119360	−	0.206738i	−0.800154	−	0.599794i	$-0.795249\pi$
$443$	52.8765	−	91.5849i	0.119360	−	0.206738i	0.919514	+	0.393057i	$0.128582\pi$
$444$		0			0
$445$			83.9340i			0.188616i
$446$		0			0
$447$	−6.73805	−	3.89022i	−0.0150739	−	0.00870295i
$448$		0			0
$449$			101.405i			0.225846i	0.993604	+	0.112923i	$0.0360213\pi$
$449$			101.405i			0.225846i	−0.993604	+	0.112923i	$0.963979\pi$
$450$		0			0
$451$	−206.518	+	119.233i	−0.457911	+	0.264375i
$452$		0			0
$453$	144.605	+	250.464i	0.319217	+	0.552900i
$454$		0			0
$455$		−	541.332i		−	1.18974i
$456$		0			0
$457$	−225.233			−0.492850			−0.246425	−	0.969162i	$-0.579256\pi$
$457$	−225.233			−0.492850			−0.246425	+	0.969162i	$0.579256\pi$
$458$		0			0
$459$	130.289	−	75.2226i	0.283855	−	0.163884i
$460$		0			0
$461$	306.397	+	530.695i	0.664635	+	1.15118i	0.979384	+	0.202007i	$0.0647463\pi$
$461$	306.397	+	530.695i	0.664635	+	1.15118i	−0.314749	+	0.949175i	$0.601920\pi$
$462$		0			0
$463$	425.105			0.918153			0.459077	−	0.888397i	$-0.348180\pi$
$463$	425.105			0.918153			0.459077	+	0.888397i	$0.348180\pi$
$464$		0			0
$465$	−112.381	+	194.649i	−0.241679	+	0.418600i
$466$		0			0
$467$	680.895			1.45802			0.729010	−	0.684504i	$-0.239981\pi$
$467$	680.895			1.45802			0.729010	+	0.684504i	$0.239981\pi$
$468$		0			0
$469$	−1101.09	−	635.717i	−2.34775	−	1.35547i
$470$		0			0
$471$	−177.985	−	102.760i	−0.377887	−	0.218173i
$472$		0			0
$473$	−62.6750	−	108.556i	−0.132505	−	0.229506i
$474$		0			0
$475$	110.171	+	256.881i	0.231939	+	0.540803i
$476$		0			0
$477$	43.7155	−	25.2391i	0.0916467	−	0.0529123i
$478$		0			0
$479$	353.532	−	612.335i	0.738062	−	1.27836i	−0.215304	−	0.976547i	$-0.569074\pi$
$479$	353.532	−	612.335i	0.738062	−	1.27836i	0.953367	−	0.301814i	$-0.0975923\pi$
$480$		0			0
$481$	169.473	−	293.536i	0.352335	−	0.610262i
$482$		0			0
$483$			659.122i			1.36464i
$484$		0			0
$485$	−424.998	−	245.373i	−0.876284	−	0.505923i
$486$		0			0
$487$			366.314i			0.752185i	0.926582	+	0.376093i	$0.122733\pi$
$487$			366.314i			0.752185i	−0.926582	+	0.376093i	$0.877267\pi$
$488$		0			0
$489$	−380.467	+	219.662i	−0.778050	+	0.449207i
$490$		0			0
$491$	294.938	+	510.848i	0.600689	+	1.04042i	0.992717	+	0.120471i	$0.0384403\pi$
$491$	294.938	+	510.848i	0.600689	+	1.04042i	−0.392028	+	0.919953i	$0.628226\pi$
$492$		0			0
$493$			800.150i			1.62302i
$494$		0			0
$495$	−36.5937			−0.0739266
$496$		0			0
$497$	626.139	−	361.501i	1.25984	−	0.727367i
$498$		0			0
$499$	406.594	+	704.241i	0.814818	+	1.41131i	0.909459	+	0.415794i	$0.136496\pi$
$499$	406.594	+	704.241i	0.814818	+	1.41131i	−0.0946412	+	0.995511i	$0.530170\pi$
$500$		0			0
$501$	−89.7377			−0.179117
$502$		0			0
$503$	149.241	−	258.493i	0.296701	−	0.513902i	−0.678678	−	0.734436i	$-0.737447\pi$
$503$	149.241	−	258.493i	0.296701	−	0.513902i	0.975379	+	0.220534i	$0.0707801\pi$
$504$		0			0
$505$	207.450			0.410793
$506$		0			0
$507$	−17.3123	−	9.99524i	−0.0341465	−	0.0197145i
$508$		0			0
$509$	177.042	+	102.215i	0.347823	+	0.200816i	0.663726	−	0.747976i	$-0.268974\pi$
$509$	177.042	+	102.215i	0.347823	+	0.200816i	−0.315903	+	0.948791i	$0.602307\pi$
$510$		0			0
$511$	691.185	+	1197.17i	1.35261	+	2.34279i
$512$		0			0
$513$	79.0676	+	59.1212i	0.154128	+	0.115246i
$514$		0			0
$515$	−51.7524	+	29.8793i	−0.100490	+	0.0580180i
$516$		0			0
$517$	−151.951	+	263.188i	−0.293910	+	0.509067i
$518$		0			0
$519$	−66.0037	+	114.322i	−0.127175	+	0.220273i
$520$		0			0
$521$		−	484.380i		−	0.929712i	−0.885386	−	0.464856i	$-0.846106\pi$
$521$		−	484.380i		−	0.929712i	0.885386	−	0.464856i	$-0.153894\pi$
$522$		0			0
$523$	−658.312	−	380.077i	−1.25872	−	0.726724i	−0.285896	−	0.958261i	$-0.592291\pi$
$523$	−658.312	−	380.077i	−1.25872	−	0.726724i	−0.972826	+	0.231537i	$0.925625\pi$
$524$		0			0
$525$		−	342.688i		−	0.652738i
$526$		0			0
$527$	1014.38	−	585.654i	1.92482	−	1.11130i
$528$		0			0
$529$	−135.805	−	235.222i	−0.256721	−	0.444654i
$530$		0			0
$531$		−	250.975i		−	0.472646i
$532$		0			0
$533$	−786.885			−1.47633
$534$		0			0
$535$	−379.874	+	219.320i	−0.710045	+	0.409945i
$536$		0			0
$537$	−198.000	−	342.946i	−0.368715	−	0.638633i
$538$		0			0
$539$	501.506			0.930437
$540$		0			0
$541$	−72.1653	+	124.994i	−0.133392	+	0.231042i	−0.924982	−	0.380011i	$-0.875920\pi$
$541$	−72.1653	+	124.994i	−0.133392	+	0.231042i	0.791590	+	0.611053i	$0.209254\pi$
$542$		0			0
$543$	431.845			0.795295
$544$		0			0
$545$	126.145	+	72.8298i	0.231458	+	0.133633i
$546$		0			0
$547$	741.808	+	428.283i	1.35614	+	0.782968i	0.989101	−	0.147238i	$-0.0470383\pi$
$547$	741.808	+	428.283i	1.35614	+	0.782968i	0.367039	+	0.930206i	$0.380372\pi$
$548$		0			0
$549$	−107.578	−	186.330i	−0.195952	−	0.339399i
$550$		0			0
$551$	−482.574	+	206.966i	−0.875816	+	0.375619i
$552$		0			0
$553$	−912.436	+	526.795i	−1.64998	+	0.952614i
$554$		0			0
$555$	−75.0350	+	129.964i	−0.135198	+	0.234170i
$556$		0			0
$557$	−11.0025	+	19.0569i	−0.0197532	+	0.0342135i	−0.875733	−	0.482796i	$-0.839621\pi$
$557$	−11.0025	+	19.0569i	−0.0197532	+	0.0342135i	0.855980	+	0.517009i	$0.172955\pi$
$558$		0			0
$559$		−	413.626i		−	0.739940i
$560$		0			0
$561$	165.153	+	95.3512i	0.294391	+	0.169966i
$562$		0			0
$563$		−	939.181i		−	1.66817i	−0.551634	−	0.834086i	$-0.685995\pi$
$563$		−	939.181i		−	1.66817i	0.551634	−	0.834086i	$-0.314005\pi$
$564$		0			0
$565$	−204.351	+	117.982i	−0.361683	+	0.208818i
$566$		0			0
$567$	−60.5211	−	104.826i	−0.106739	−	0.184878i
$568$		0			0
$569$		−	201.604i		−	0.354313i	−0.984183	−	0.177157i	$-0.943310\pi$
$569$		−	201.604i		−	0.354313i	0.984183	−	0.177157i	$-0.0566899\pi$
$570$		0			0
$571$	−282.557			−0.494846			−0.247423	−	0.968908i	$-0.579584\pi$
$571$	−282.557			−0.494846			−0.247423	+	0.968908i	$0.579584\pi$
$572$		0			0
$573$	−251.147	+	145.000i	−0.438301	+	0.253053i
$574$		0			0
$575$	208.125	+	360.483i	0.361956	+	0.626926i
$576$		0			0
$577$	519.599			0.900518			0.450259	−	0.892898i	$-0.351332\pi$
$577$	519.599			0.900518			0.450259	+	0.892898i	$0.351332\pi$
$578$		0			0
$579$	162.065	−	280.705i	0.279906	−	0.484811i
$580$		0			0
$581$	−66.5259			−0.114502
$582$		0			0
$583$	55.4132	+	31.9928i	0.0950483	+	0.0548762i
$584$		0			0
$585$	−104.573	−	60.3754i	−0.178758	−	0.103206i
$586$		0			0
$587$	373.198	+	646.397i	0.635771	+	1.10119i	0.986351	+	0.164655i	$0.0526510\pi$
$587$	373.198	+	646.397i	0.635771	+	1.10119i	−0.350580	+	0.936533i	$0.614016\pi$
$588$		0			0
$589$	615.590	+	460.295i	1.04514	+	0.781485i
$590$		0			0
$591$	−382.775	+	220.995i	−0.647674	+	0.373935i
$592$		0			0
$593$	173.133	−	299.876i	0.291962	−	0.505693i	−0.682312	−	0.731061i	$-0.739025\pi$
$593$	173.133	−	299.876i	0.291962	−	0.505693i	0.974274	+	0.225369i	$0.0723587\pi$
$594$		0			0
$595$	624.521	−	1081.70i	1.04961	−	1.81799i
$596$		0			0
$597$			262.985i			0.440510i
$598$		0			0
$599$	51.7364	+	29.8700i	0.0863712	+	0.0498664i	0.542564	−	0.840015i	$-0.317454\pi$
$599$	51.7364	+	29.8700i	0.0863712	+	0.0498664i	−0.456192	+	0.889881i	$0.650787\pi$
$600$		0			0
$601$		−	884.543i		−	1.47179i	−0.677098	−	0.735893i	$-0.736763\pi$
$601$		−	884.543i		−	1.47179i	0.677098	−	0.735893i	$-0.263237\pi$
$602$		0			0
$603$	−245.613	+	141.805i	−0.407318	+	0.235165i
$604$		0			0
$605$	170.870	+	295.955i	0.282429	+	0.489181i
$606$		0			0
$607$			351.505i			0.579085i	0.957165	+	0.289543i	$0.0935032\pi$
$607$			351.505i			0.579085i	−0.957165	+	0.289543i	$0.906497\pi$
$608$		0			0
$609$	643.769			1.05709
$610$		0			0
$611$	−868.459	+	501.405i	−1.42137	+	0.820631i
$612$		0			0
$613$	−440.780	−	763.453i	−0.719053	−	1.24544i	−0.961375	−	0.275241i	$-0.911242\pi$
$613$	−440.780	−	763.453i	−0.719053	−	1.24544i	0.242322	−	0.970196i	$-0.422091\pi$
$614$		0			0
$615$	348.397			0.566500
$616$		0			0
$617$	41.3979	−	71.7033i	0.0670955	−	0.116213i	−0.830526	−	0.556980i	$-0.811960\pi$
$617$	41.3979	−	71.7033i	0.0670955	−	0.116213i	0.897622	+	0.440767i	$0.145293\pi$
$618$		0			0
$619$	857.297			1.38497			0.692485	−	0.721432i	$-0.256516\pi$
$619$	857.297			1.38497			0.692485	+	0.721432i	$0.256516\pi$
$620$		0			0
$621$	127.328	+	73.5127i	0.205037	+	0.118378i
$622$		0			0
$623$	−304.773	−	175.961i	−0.489203	−	0.282441i
$624$		0			0
$625$	20.4049	+	35.3423i	0.0326478	+	0.0565477i
$626$		0			0
$627$	−14.7884	+	124.268i	−0.0235860	+	0.198195i
$628$		0			0
$629$	677.290	−	391.034i	1.07677	−	0.621675i
$630$		0			0
$631$	20.4080	−	35.3476i	0.0323423	−	0.0560184i	−0.849401	−	0.527748i	$-0.823037\pi$
$631$	20.4080	−	35.3476i	0.0323423	−	0.0560184i	0.881743	+	0.471729i	$0.156370\pi$
$632$		0			0
$633$	146.990	−	254.594i	0.232212	−	0.402203i
$634$		0			0
$635$			42.9200i			0.0675906i
$636$		0			0
$637$	1433.15	+	827.428i	2.24984	+	1.29894i
$638$		0			0
$639$		−	161.275i		−	0.252386i
$640$		0			0
$641$	−437.570	+	252.631i	−0.682636	+	0.394120i	−0.800848	−	0.598868i	$-0.795617\pi$
$641$	−437.570	+	252.631i	−0.682636	+	0.394120i	0.118211	+	0.992988i	$0.462284\pi$
$642$		0			0
$643$	−32.5113	−	56.3112i	−0.0505619	−	0.0875758i	0.839637	−	0.543148i	$-0.182768\pi$
$643$	−32.5113	−	56.3112i	−0.0505619	−	0.0875758i	−0.890199	+	0.455573i	$0.849435\pi$
$644$		0			0
$645$			183.135i			0.283931i
$646$		0			0
$647$	−992.146			−1.53346			−0.766728	−	0.641973i	$-0.778116\pi$
$647$	−992.146			−1.53346			−0.766728	+	0.641973i	$0.778116\pi$
$648$		0			0
$649$	275.511	−	159.066i	0.424516	−	0.245094i
$650$		0			0
$651$	−471.194	−	816.132i	−0.723801	−	1.25366i
$652$		0			0
$653$	−522.408			−0.800012			−0.400006	−	0.916512i	$-0.630992\pi$
$653$	−522.408			−0.800012			−0.400006	+	0.916512i	$0.630992\pi$
$654$		0			0
$655$	−200.924	+	348.011i	−0.306755	+	0.531314i
$656$		0			0
$657$	308.355			0.469338
$658$		0			0
$659$	375.653	+	216.883i	0.570035	+	0.329110i	0.757163	−	0.653226i	$-0.226585\pi$
$659$	375.653	+	216.883i	0.570035	+	0.329110i	−0.187128	+	0.982335i	$0.559918\pi$
$660$		0			0
$661$	698.382	+	403.211i	1.05655	+	0.610002i	0.924477	−	0.381238i	$-0.124502\pi$
$661$	698.382	+	403.211i	1.05655	+	0.610002i	0.132077	+	0.991239i	$0.457835\pi$
$662$		0			0
$663$	314.637	+	544.968i	0.474566	+	0.821972i
$664$		0			0
$665$	813.918	+	96.8598i	1.22394	+	0.145654i
$666$		0			0
$667$	−677.199	+	390.981i	−1.01529	+	0.586178i
$668$		0			0
$669$	−165.300	+	286.308i	−0.247085	+	0.427964i
$670$		0			0
$671$	136.364	−	236.189i	0.203225	−	0.351996i
$672$		0			0
$673$			632.426i			0.939711i	0.882743	+	0.469856i	$0.155694\pi$
$673$			632.426i			0.939711i	−0.882743	+	0.469856i	$0.844306\pi$
$674$		0			0
$675$	−66.1996	−	38.2204i	−0.0980735	−	0.0566228i
$676$		0			0
$677$		−	40.9163i		−	0.0604377i	−0.999543	−	0.0302188i	$-0.990380\pi$
$677$		−	40.9163i		−	0.0604377i	0.999543	−	0.0302188i	$-0.00962042\pi$
$678$		0			0
$679$	1781.95	−	1028.81i	2.62437	−	1.51518i
$680$		0			0
$681$	−76.9247	−	133.237i	−0.112958	−	0.195650i
$682$		0			0
$683$			311.925i			0.456698i	0.973579	+	0.228349i	$0.0733327\pi$
$683$			311.925i			0.456698i	−0.973579	+	0.228349i	$0.926667\pi$
$684$		0			0
$685$	−703.753			−1.02738
$686$		0			0
$687$	191.113	−	110.339i	0.278185	−	0.160610i
$688$		0			0
$689$	105.569	+	182.851i	0.153221	+	0.265386i
$690$		0			0
$691$	365.025			0.528256			0.264128	−	0.964488i	$-0.414916\pi$
$691$	365.025			0.528256			0.264128	+	0.964488i	$0.414916\pi$
$692$		0			0
$693$	76.7158	−	132.876i	0.110701	−	0.191740i
$694$		0			0
$695$	−171.753			−0.247127
$696$		0			0
$697$	−1572.37	−	907.810i	−2.25591	−	1.30245i
$698$		0			0
$699$	−68.0980	−	39.3164i	−0.0974221	−	0.0562467i
$700$		0			0
$701$	421.057	+	729.292i	0.600652	+	1.04036i	0.992722	+	0.120425i	$0.0384256\pi$
$701$	421.057	+	729.292i	0.600652	+	1.04036i	−0.392071	+	0.919935i	$0.628241\pi$
$702$		0			0
$703$	411.021	+	307.333i	0.584668	+	0.437173i
$704$		0			0
$705$	384.515	−	222.000i	0.545411	−	0.314893i
$706$		0			0
$707$	−434.903	+	753.275i	−0.615139	+	1.06545i
$708$		0			0
$709$	−186.737	+	323.438i	−0.263381	+	0.456189i	−0.967138	−	0.254252i	$-0.918171\pi$
$709$	−186.737	+	323.438i	−0.263381	+	0.456189i	0.703757	+	0.710440i	$0.251504\pi$
$710$		0			0
$711$			235.017i			0.330544i
$712$		0			0
$713$	991.325	+	572.342i	1.39036	+	0.802723i
$714$		0			0
$715$		−	153.062i		−	0.214073i
$716$		0			0
$717$	−171.488	+	99.0087i	−0.239175	+	0.138087i
$718$		0			0
$719$	104.659	+	181.275i	0.145562	+	0.252121i	0.929583	−	0.368614i	$-0.120168\pi$
$719$	104.659	+	181.275i	0.145562	+	0.252121i	−0.784020	+	0.620735i	$0.786834\pi$
$720$		0			0
$721$		−	250.558i		−	0.347515i
$722$		0			0
$723$	386.848			0.535059
$724$		0			0
$725$	352.086	−	203.277i	0.485636	−	0.280382i
$726$		0			0
$727$	−414.076	−	717.201i	−0.569568	−	0.986521i	−0.996609	−	0.0822887i	$-0.973777\pi$
$727$	−414.076	−	717.201i	−0.569568	−	0.986521i	0.427040	−	0.904233i	$-0.359556\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	477.190	−	826.518i	0.652791	−	1.13067i
$732$		0			0
$733$	609.404			0.831383			0.415692	−	0.909506i	$-0.363540\pi$
$733$	609.404			0.831383			0.415692	+	0.909506i	$0.363540\pi$
$734$		0			0
$735$	−634.533	−	366.348i	−0.863310	−	0.498432i
$736$		0			0
$737$	−311.336	−	179.750i	−0.422436	−	0.243894i
$738$		0			0
$739$	−545.399	−	944.660i	−0.738024	−	1.27829i	−0.953384	−	0.301760i	$-0.902426\pi$
$739$	−545.399	−	944.660i	−0.738024	−	1.27829i	0.215360	−	0.976535i	$-0.430907\pi$
$740$		0			0
$741$	−247.289	+	330.720i	−0.333723	+	0.446316i
$742$		0			0
$743$	349.717	−	201.909i	0.470682	−	0.271749i	−0.245843	−	0.969310i	$-0.579065\pi$
$743$	349.717	−	201.909i	0.470682	−	0.271749i	0.716525	+	0.697561i	$0.245731\pi$
$744$		0			0
$745$	−7.20442	+	12.4784i	−0.00967037	+	0.0167496i
$746$		0			0
$747$	−7.41972	+	12.8513i	−0.00993269	+	0.0172039i
$748$		0			0
$749$		−	1839.15i		−	2.45548i
$750$		0			0
$751$	253.904	+	146.591i	0.338088	+	0.195195i	0.659426	−	0.751769i	$-0.270799\pi$
$751$	253.904	+	146.591i	0.338088	+	0.195195i	−0.321338	+	0.946964i	$0.604133\pi$
$752$		0			0
$753$			353.771i			0.469815i
$754$		0			0
$755$	463.842	−	267.800i	0.614361	−	0.354701i
$756$		0			0
$757$	429.921	+	744.645i	0.567928	+	0.983679i	0.996771	+	0.0803005i	$0.0255880\pi$
$757$	429.921	+	744.645i	0.567928	+	0.983679i	−0.428843	+	0.903379i	$0.641079\pi$
$758$		0			0
$759$			186.368i			0.245544i
$760$		0			0
$761$	−362.129			−0.475860			−0.237930	−	0.971282i	$-0.576469\pi$
$761$	−362.129			−0.475860			−0.237930	+	0.971282i	$0.576469\pi$
$762$		0			0
$763$	−528.906	+	305.364i	−0.693192	+	0.400215i
$764$		0			0
$765$	−139.307	−	241.287i	−0.182101	−	0.315408i
$766$		0			0
$767$	1049.77			1.36866
$768$		0			0
$769$	487.791	−	844.879i	0.634318	−	1.09867i	−0.352341	−	0.935872i	$-0.614614\pi$
$769$	487.791	−	844.879i	0.634318	−	1.09867i	0.986659	−	0.162800i	$-0.0520525\pi$
$770$		0			0
$771$	206.230			0.267483
$772$		0			0
$773$	−911.939	−	526.508i	−1.17974	−	0.681123i	−0.223785	−	0.974639i	$-0.571841\pi$
$773$	−911.939	−	526.508i	−1.17974	−	0.681123i	−0.955954	+	0.293516i	$0.905175\pi$
$774$		0			0
$775$	−515.405	−	297.569i	−0.665038	−	0.383960i
$776$		0			0
$777$	−314.610	−	544.921i	−0.404904	−	0.701314i
$778$		0			0
$779$	140.796	−	1183.12i	0.180740	−	1.51877i
$780$		0			0
$781$	177.041	−	102.215i	0.226686	−	0.130877i
$782$		0			0
$783$	71.8004	−	124.362i	0.0916991	−	0.158827i
$784$		0			0
$785$	−190.304	+	329.616i	−0.242425	+	0.419893i
$786$		0			0
$787$			913.563i			1.16082i	0.814325	+	0.580408i	$0.197107\pi$
$787$			913.563i			1.16082i	−0.814325	+	0.580408i	$0.802893\pi$
$788$		0			0
$789$	129.159	+	74.5698i	0.163699	+	0.0945118i
$790$		0			0
$791$		−	989.359i		−	1.25077i
$792$		0			0
$793$	779.371	−	449.970i	0.982813	−	0.567427i
$794$		0			0
$795$	−46.7412	−	80.9581i	−0.0587940	−	0.101834i
$796$		0			0
$797$		−	816.039i		−	1.02389i	−0.859019	−	0.511944i	$-0.828925\pi$
$797$		−	816.039i		−	1.02389i	0.859019	−	0.511944i	$-0.171075\pi$
$798$		0			0
$799$	−2313.83			−2.89591
$800$		0			0
$801$	−67.9835	+	39.2503i	−0.0848733	+	0.0490016i
$802$		0			0
$803$	195.433	+	338.500i	0.243379	+	0.421545i
$804$		0			0
$805$	1220.65			1.51634
$806$		0			0
$807$	−98.9214	+	171.337i	−0.122579	+	0.212313i
$808$		0			0
$809$	276.891			0.342263			0.171131	−	0.985248i	$-0.445258\pi$
$809$	276.891			0.342263			0.171131	+	0.985248i	$0.445258\pi$
$810$		0			0
$811$	−336.585	−	194.327i	−0.415025	−	0.239615i	0.277922	−	0.960604i	$-0.410354\pi$
$811$	−336.585	−	194.327i	−0.415025	−	0.239615i	−0.692946	+	0.720989i	$0.743688\pi$
$812$		0			0
$813$	−101.999	−	58.8891i	−0.125460	−	0.0724343i
$814$		0			0
$815$	406.800	+	704.599i	0.499141	+	0.864538i
$816$		0			0
$817$	621.907	+	74.0096i	0.761208	+	0.0905871i
$818$		0			0
$819$	438.459	−	253.145i	0.535360	−	0.309090i
$820$		0			0
$821$	−87.0636	+	150.799i	−0.106046	+	0.183677i	−0.914165	−	0.405342i	$-0.867152\pi$
$821$	−87.0636	+	150.799i	−0.106046	+	0.183677i	0.808119	+	0.589019i	$0.200486\pi$
$822$		0			0
$823$	−380.531	+	659.098i	−0.462370	+	0.800849i	−0.999079	−	0.0429193i	$-0.986334\pi$
$823$	−380.531	+	659.098i	−0.462370	+	0.800849i	0.536708	+	0.843768i	$0.319668\pi$
$824$		0			0
$825$		−	96.8953i		−	0.117449i
$826$		0			0
$827$	−873.488	−	504.308i	−1.05621	−	0.609804i	−0.131830	−	0.991272i	$-0.542085\pi$
$827$	−873.488	−	504.308i	−1.05621	−	0.609804i	−0.924382	+	0.381468i	$0.875419\pi$
$828$		0			0
$829$			620.664i			0.748690i	0.927290	+	0.374345i	$0.122132\pi$
$829$			620.664i			0.748690i	−0.927290	+	0.374345i	$0.877868\pi$
$830$		0			0
$831$	135.473	−	78.2153i	0.163024	−	0.0941219i
$832$		0			0
$833$	1909.16	+	3306.77i	2.29191	+	3.96971i
$834$		0			0
$835$			166.188i			0.199028i
$836$		0			0
$837$	−210.212			−0.251149
$838$		0			0
$839$	170.995	−	98.7241i	0.203808	−	0.117669i	−0.394622	−	0.918843i	$-0.629125\pi$
$839$	170.995	−	98.7241i	0.203808	−	0.117669i	0.598431	+	0.801175i	$0.295791\pi$
$840$		0			0
$841$	−38.6262	−	66.9025i	−0.0459289	−	0.0795512i
$842$		0			0
$843$	566.688			0.672227
$844$		0			0
$845$	−18.5105	+	32.0612i	−0.0219059	+	0.0379422i
$846$		0			0
$847$	−1432.86			−1.69169
$848$		0			0
$849$	−347.737	−	200.766i	−0.409584	−	0.236473i
$850$		0			0
$851$	661.895	+	382.145i	0.777785	+	0.449054i
$852$		0			0
$853$	−377.151	−	653.245i	−0.442147	−	0.765821i	0.555702	−	0.831382i	$-0.312450\pi$
$853$	−377.151	−	653.245i	−0.442147	−	0.765821i	−0.997849	+	0.0655608i	$0.979116\pi$
$854$		0			0
$855$	109.488	−	146.428i	0.128057	−	0.171261i
$856$		0			0
$857$	706.597	−	407.954i	0.824500	−	0.476025i	−0.0274656	−	0.999623i	$-0.508744\pi$
$857$	706.597	−	407.954i	0.824500	−	0.476025i	0.851966	+	0.523597i	$0.175410\pi$
$858$		0			0
$859$	−570.974	+	988.956i	−0.664696	+	1.15129i	0.314671	+	0.949201i	$0.398106\pi$
$859$	−570.974	+	988.956i	−0.664696	+	1.15129i	−0.979368	+	0.202087i	$0.935228\pi$
$860$		0			0
$861$	−730.388	+	1265.07i	−0.848302	+	1.46930i
$862$		0			0
$863$			390.979i			0.453047i	0.974006	+	0.226523i	$0.0727360\pi$
$863$			390.979i			0.453047i	−0.974006	+	0.226523i	$0.927264\pi$
$864$		0			0
$865$	211.716	+	122.234i	0.244759	+	0.141311i
$866$		0			0
$867$			951.394i			1.09734i
$868$		0			0
$869$	−257.992	+	148.952i	−0.296884	+	0.171406i
$870$		0			0
$871$	−593.133	−	1027.34i	−0.680980	−	1.17949i
$872$		0			0
$873$		−	458.977i		−	0.525747i
$874$		0			0
$875$	−1713.14			−1.95787
$876$		0			0
$877$	−174.496	+	100.745i	−0.198969	+	0.114875i	−0.596175	−	0.802855i	$-0.703313\pi$
$877$	−174.496	+	100.745i	−0.198969	+	0.114875i	0.397205	+	0.917730i	$0.369980\pi$
$878$		0			0
$879$	−62.6596	−	108.530i	−0.0712850	−	0.123469i
$880$		0			0
$881$	−373.067			−0.423458			−0.211729	−	0.977328i	$-0.567909\pi$
$881$	−373.067			−0.423458			−0.211729	+	0.977328i	$0.567909\pi$
$882$		0			0
$883$	−388.328	+	672.603i	−0.439782	+	0.761725i	−0.997672	−	0.0681898i	$-0.978278\pi$
$883$	−388.328	+	672.603i	−0.439782	+	0.761725i	0.557890	+	0.829915i	$0.311611\pi$
$884$		0			0
$885$	−464.789			−0.525185
$886$		0			0
$887$	−1076.08	−	621.274i	−1.21317	−	0.700422i	−0.249719	−	0.968318i	$-0.580338\pi$
$887$	−1076.08	−	621.274i	−1.21317	−	0.700422i	−0.963448	+	0.267897i	$0.913671\pi$
$888$		0			0
$889$	−155.847	−	89.9784i	−0.175306	−	0.101213i
$890$		0			0
$891$	−17.1124	−	29.6396i	−0.0192059	−	0.0332655i
$892$		0			0
$893$	−598.494	−	1395.49i	−0.670206	−	1.56269i
$894$		0			0
$895$	−635.113	+	366.683i	−0.709623	+	0.409701i
$896$		0			0
$897$	−307.485	+	532.580i	−0.342793	+	0.593735i
$898$		0			0
$899$	559.010	−	968.234i	0.621813	−	1.07701i
$900$		0			0
$901$			487.169i			0.540698i
$902$		0			0
$903$	−664.984	−	383.929i	−0.736416	−	0.425170i
$904$		0			0
$905$		−	799.749i		−	0.883700i
$906$		0			0
$907$	−983.751	+	567.969i	−1.08462	+	0.626206i	−0.932139	−	0.362100i	$-0.882060\pi$
$907$	−983.751	+	567.969i	−1.08462	+	0.626206i	−0.152481	+	0.988306i	$0.548726\pi$
$908$		0			0
$909$	97.0107	+	168.027i	0.106722	+	0.184849i
$910$		0			0
$911$			818.723i			0.898708i	0.893354	+	0.449354i	$0.148346\pi$
$911$			818.723i			0.898708i	−0.893354	+	0.449354i	$0.851654\pi$
$912$		0			0
$913$	−18.8103			−0.0206027
$914$		0			0
$915$	−345.070	+	199.226i	−0.377126	+	0.217734i
$916$		0			0
$917$	−842.444	−	1459.16i	−0.918696	−	1.59123i
$918$		0			0
$919$	617.082			0.671471			0.335736	−	0.941956i	$-0.391015\pi$
$919$	617.082			0.671471			0.335736	+	0.941956i	$0.391015\pi$
$920$		0			0
$921$	−224.904	+	389.545i	−0.244195	+	0.422959i
$922$		0			0
$923$	674.572			0.730847
$924$		0			0
$925$	−344.129	−	198.683i	−0.372031	−	0.214792i
$926$		0			0
$927$	−48.4023	−	27.9451i	−0.0522139	−	0.0301457i
$928$		0			0
$929$	−641.452	−	1111.03i	−0.690476	−	1.19594i	−0.971682	−	0.236292i	$-0.924068\pi$
$929$	−641.452	−	1111.03i	−0.690476	−	1.19594i	0.281206	−	0.959647i	$-0.409266\pi$
$930$		0			0
$931$	−1500.51	+	2006.75i	−1.61172	+	2.15548i
$932$		0			0
$933$	−569.975	+	329.075i	−0.610905	+	0.352706i
$934$		0			0
$935$	176.584	−	305.852i	0.188860	−	0.327115i
$936$		0			0
$937$	−475.178	+	823.033i	−0.507127	+	0.878370i	0.492839	+	0.870121i	$0.335959\pi$
$937$	−475.178	+	823.033i	−0.507127	+	0.878370i	−0.999966	+	0.00824928i	$0.997374\pi$
$938$		0			0
$939$			790.413i			0.841760i
$940$		0			0
$941$	1130.73	+	652.828i	1.20163	+	0.693760i	0.960917	−	0.276837i	$-0.0892863\pi$
$941$	1130.73	+	652.828i	1.20163	+	0.693760i	0.240710	+	0.970597i	$0.422620\pi$
$942$		0			0
$943$		−	1774.35i		−	1.88160i
$944$		0			0
$945$	−194.130	+	112.081i	−0.205429	+	0.118604i
$946$		0			0
$947$	29.8342	+	51.6743i	0.0315039	+	0.0545663i	0.881347	−	0.472469i	$-0.156637\pi$
$947$	29.8342	+	51.6743i	0.0315039	+	0.0545663i	−0.849844	+	0.527035i	$0.823304\pi$
$948$		0			0
$949$			1289.77i			1.35908i
$950$		0			0
$951$	39.1138			0.0411291
$952$		0			0
$953$	−1215.44	+	701.736i	−1.27538	+	0.736344i	−0.975996	−	0.217787i	$-0.930116\pi$
$953$	−1215.44	+	701.736i	−1.27538	+	0.736344i	−0.299389	+	0.954131i	$0.596783\pi$
$954$		0			0
$955$	268.529	+	465.107i	0.281183	+	0.487023i
$956$		0			0
$957$	182.026			0.190205
$958$		0			0
$959$	1475.36	−	2555.40i	1.53844	−	2.66465i
$960$		0			0
$961$	−675.626			−0.703045
$962$		0			0
$963$	−355.284	−	205.123i	−0.368934	−	0.213004i
$964$		0			0
$965$	−519.848	−	300.134i	−0.538702	−	0.311020i
$966$		0			0
$967$	119.084	+	206.260i	0.123148	+	0.213299i	0.921008	−	0.389545i	$-0.127368\pi$
$967$	119.084	+	206.260i	0.123148	+	0.213299i	−0.797859	+	0.602844i	$0.794034\pi$
$968$		0			0
$969$	−875.682	+	375.561i	−0.903697	+	0.387576i
$970$		0			0
$971$	427.235	−	246.664i	0.439995	−	0.254031i	−0.263601	−	0.964632i	$-0.584910\pi$
$971$	427.235	−	246.664i	0.439995	−	0.254031i	0.703595	+	0.710601i	$0.251577\pi$
$972$		0			0
$973$	360.068	−	623.656i	0.370059	−	0.640962i
$974$		0			0
$975$	159.866	−	276.896i	0.163965	−	0.283996i
$976$		0			0
$977$		−	184.075i		−	0.188408i	−0.995553	−	0.0942041i	$-0.969969\pi$
$977$		−	184.075i		−	0.188408i	0.995553	−	0.0942041i	$-0.0300306\pi$
$978$		0			0
$979$	−86.1750	−	49.7532i	−0.0880235	−	0.0508204i
$980$		0			0
$981$			136.230i			0.138869i
$982$		0			0
$983$	1231.25	−	710.865i	1.25255	−	0.723159i	0.280933	−	0.959727i	$-0.409356\pi$
$983$	1231.25	−	710.865i	1.25255	−	0.723159i	0.971615	+	0.236569i	$0.0760229\pi$
$984$		0			0
$985$	409.269	+	708.874i	0.415501	+	0.719669i
$986$		0			0
$987$			1861.62i			1.88614i
$988$		0			0
$989$	932.687			0.943061
$990$		0			0
$991$	313.263	−	180.862i	0.316108	−	0.182505i	−0.333549	−	0.942733i	$-0.608246\pi$
$991$	313.263	−	180.862i	0.316108	−	0.182505i	0.649656	+	0.760228i	$0.274913\pi$
$992$		0			0
$993$	161.853	+	280.337i	0.162994	+	0.282313i
$994$		0			0
$995$	487.030			0.489478
$996$		0			0
$997$	943.768	−	1634.65i	0.946608	−	1.63957i	0.194107	−	0.980980i	$-0.437819\pi$
$997$	943.768	−	1634.65i	0.946608	−	1.63957i	0.752500	−	0.658592i	$-0.228848\pi$
$998$		0			0
$999$	−140.355			−0.140496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.4		20
4.3	odd	2		456.3.w.a.145.4	✓	20
12.11	even	2		1368.3.bv.c.145.7		20
19.8	odd	6	inner	912.3.be.j.673.4		20
76.27	even	6		456.3.w.a.217.4	yes	20
228.179	odd	6		1368.3.bv.c.217.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.4	✓	20	4.3	odd	2
456.3.w.a.217.4	yes	20	76.27	even	6
912.3.be.j.145.4		20	1.1	even	1	trivial
912.3.be.j.673.4		20	19.8	odd	6	inner
1368.3.bv.c.145.7		20	12.11	even	2
1368.3.bv.c.217.7		20	228.179	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-1.60382 - 2.77790i) q^{5} +13.4491 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-1.60382 - 2.77790i) q^{5} +13.4491 q^{7} +(1.50000 - 2.59808i) q^{9} +3.80276 q^{11} +(10.8671 + 6.27412i) q^{13} +(-4.81146 - 2.77790i) q^{15} +(14.4766 + 25.0742i) q^{17} +(-11.3779 + 15.2166i) q^{19} +(20.1737 - 11.6473i) q^{21} +(-14.1475 + 24.5042i) q^{23} +(7.35552 - 12.7401i) q^{25} -5.19615i q^{27} +(23.9335 + 13.8180i) q^{29} -40.4552i q^{31} +(5.70414 - 3.29329i) q^{33} +(-21.5700 - 37.3604i) q^{35} -27.0114i q^{37} +21.7342 q^{39} +(-54.3074 + 31.3544i) q^{41} +(-16.4814 - 28.5467i) q^{43} -9.62293 q^{45} +(-39.9582 + 69.2096i) q^{47} +131.879 q^{49} +(43.4298 + 25.0742i) q^{51} +(14.5718 + 8.41305i) q^{53} +(-6.09895 - 10.5637i) q^{55} +(-3.88887 + 32.6784i) q^{57} +(72.4502 - 41.8292i) q^{59} +(35.8592 - 62.1099i) q^{61} +(20.1737 - 34.9419i) q^{63} -40.2503i q^{65} +(-81.8710 - 47.2682i) q^{67} +49.0085i q^{69} +(46.5560 - 26.8791i) q^{71} +(51.3925 + 89.0144i) q^{73} -25.4803i q^{75} +51.1439 q^{77} +(-67.8435 + 39.1695i) q^{79} +(-4.50000 - 7.79423i) q^{81} -4.94648 q^{83} +(46.4357 - 80.4291i) q^{85} +47.8669 q^{87} +(-22.6612 - 13.0834i) q^{89} +(146.153 + 84.3816i) q^{91} +(-35.0353 - 60.6829i) q^{93} +(60.5182 + 7.20193i) q^{95} +(132.495 - 76.4962i) q^{97} +(5.70414 - 9.87986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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