LMFDB - Embedded newform 363.3.b.g.122.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.3
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.g.122.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-2.00000 - 2.23607i) q^{3} +3.00000 q^{4} -6.61803i q^{5} +(2.23607 - 2.00000i) q^{6} +8.85410 q^{7} +7.00000i q^{8} +(-1.00000 + 8.94427i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-2.00000 - 2.23607i) q^{3} +3.00000 q^{4} -6.61803i q^{5} +(2.23607 - 2.00000i) q^{6} +8.85410 q^{7} +7.00000i q^{8} +(-1.00000 + 8.94427i) q^{9} +6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +13.2361 q^{13} +8.85410i q^{14} +(-14.7984 + 13.2361i) q^{15} +5.00000 q^{16} -6.00000i q^{17} +(-8.94427 - 1.00000i) q^{18} -9.12461 q^{19} -19.8541i q^{20} +(-17.7082 - 19.7984i) q^{21} -17.5279i q^{23} +(15.6525 - 14.0000i) q^{24} -18.7984 q^{25} +13.2361i q^{26} +(22.0000 - 15.6525i) q^{27} +26.5623 q^{28} -26.3951i q^{29} +(-13.2361 - 14.7984i) q^{30} -6.20163 q^{31} +33.0000i q^{32} +6.00000 q^{34} -58.5967i q^{35} +(-3.00000 + 26.8328i) q^{36} -19.5967 q^{37} -9.12461i q^{38} +(-26.4721 - 29.5967i) q^{39} +46.3262 q^{40} -5.59675i q^{41} +(19.7984 - 17.7082i) q^{42} +26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +17.5279 q^{46} -17.7082i q^{47} +(-10.0000 - 11.1803i) q^{48} +29.3951 q^{49} -18.7984i q^{50} +(-13.4164 + 12.0000i) q^{51} +39.7082 q^{52} +22.2705i q^{53} +(15.6525 + 22.0000i) q^{54} +61.9787i q^{56} +(18.2492 + 20.4033i) q^{57} +26.3951 q^{58} +21.9098i q^{59} +(-44.3951 + 39.7082i) q^{60} +93.3738 q^{61} -6.20163i q^{62} +(-8.85410 + 79.1935i) q^{63} -13.0000 q^{64} -87.5967i q^{65} -76.7902 q^{67} -18.0000i q^{68} +(-39.1935 + 35.0557i) q^{69} +58.5967 q^{70} -65.8197i q^{71} +(-62.6099 - 7.00000i) q^{72} -15.0213 q^{73} -19.5967i q^{74} +(37.5967 + 42.0344i) q^{75} -27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} -118.061 q^{79} -33.0902i q^{80} +(-79.0000 - 17.8885i) q^{81} +5.59675 q^{82} +111.185i q^{83} +(-53.1246 - 59.3951i) q^{84} -39.7082 q^{85} +26.2918i q^{86} +(-59.0213 + 52.7902i) q^{87} -97.6656i q^{89} +(-6.61803 + 59.1935i) q^{90} +117.193 q^{91} -52.5836i q^{92} +(12.4033 + 13.8673i) q^{93} +17.7082 q^{94} +60.3870i q^{95} +(73.7902 - 66.0000i) q^{96} -121.185 q^{97} +29.3951i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9	$ 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9} + 22 q^{10} - 24 q^{12} + 44 q^{13} - 10 q^{15} + 20 q^{16} + 44 q^{19} - 44 q^{21} - 26 q^{25} + 88 q^{27} + 66 q^{28} - 44 q^{30} - 74 q^{31} + 24 q^{34} - 12 q^{36} + 20 q^{37} - 88 q^{39} + 154 q^{40} + 30 q^{42} + 132 q^{43} + 40 q^{45} + 88 q^{46} - 40 q^{48} - 30 q^{49} + 132 q^{52} - 88 q^{57} - 42 q^{58} - 30 q^{60} + 132 q^{61} - 22 q^{63} - 52 q^{64} - 12 q^{67} + 40 q^{69} + 136 q^{70} - 154 q^{73} + 52 q^{75} + 132 q^{76} + 20 q^{78} - 110 q^{79} - 316 q^{81} - 76 q^{82} - 132 q^{84} - 132 q^{85} - 330 q^{87} - 22 q^{90} + 272 q^{91} + 148 q^{93} + 44 q^{94} - 42 q^{97}+O(q^{100}) $ 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9 + 22 * q^10 - 24 * q^12 + 44 * q^13 - 10 * q^15 + 20 * q^16 + 44 * q^19 - 44 * q^21 - 26 * q^25 + 88 * q^27 + 66 * q^28 - 44 * q^30 - 74 * q^31 + 24 * q^34 - 12 * q^36 + 20 * q^37 - 88 * q^39 + 154 * q^40 + 30 * q^42 + 132 * q^43 + 40 * q^45 + 88 * q^46 - 40 * q^48 - 30 * q^49 + 132 * q^52 - 88 * q^57 - 42 * q^58 - 30 * q^60 + 132 * q^61 - 22 * q^63 - 52 * q^64 - 12 * q^67 + 40 * q^69 + 136 * q^70 - 154 * q^73 + 52 * q^75 + 132 * q^76 + 20 * q^78 - 110 * q^79 - 316 * q^81 - 76 * q^82 - 132 * q^84 - 132 * q^85 - 330 * q^87 - 22 * q^90 + 272 * q^91 + 148 * q^93 + 44 * q^94 - 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.500000i	0.968246	+	0.250000i	$0.0804306\pi$
$2$			1.00000i			0.500000i	−0.968246	+	0.250000i	$0.919569\pi$
$3$	−2.00000	−	2.23607i	−0.666667	−	0.745356i
$3$	−2.00000	−	2.23607i	−0.666667	−	0.745356i
$4$	3.00000			0.750000
$5$		−	6.61803i		−	1.32361i	−0.749677	−	0.661803i	$-0.769791\pi$
$5$		−	6.61803i		−	1.32361i	0.749677	−	0.661803i	$-0.230209\pi$
$6$	2.23607	−	2.00000i	0.372678	−	0.333333i
$7$	8.85410			1.26487			0.632436	−	0.774613i	$-0.282055\pi$
$7$	8.85410			1.26487			0.632436	+	0.774613i	$0.282055\pi$
$8$			7.00000i			0.875000i
$9$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$10$	6.61803			0.661803
$11$		0			0
$11$		0			0
$12$	−6.00000	−	6.70820i	−0.500000	−	0.559017i
$13$	13.2361			1.01816			0.509080	−	0.860719i	$-0.329986\pi$
$13$	13.2361			1.01816			0.509080	+	0.860719i	$0.329986\pi$
$14$			8.85410i			0.632436i
$15$	−14.7984	+	13.2361i	−0.986558	+	0.882405i
$16$	5.00000			0.312500
$17$		−	6.00000i		−	0.352941i	−0.984306	−	0.176471i	$-0.943532\pi$
$17$		−	6.00000i		−	0.352941i	0.984306	−	0.176471i	$-0.0564680\pi$
$18$	−8.94427	−	1.00000i	−0.496904	−	0.0555556i
$19$	−9.12461			−0.480243			−0.240121	−	0.970743i	$-0.577187\pi$
$19$	−9.12461			−0.480243			−0.240121	+	0.970743i	$0.577187\pi$
$20$		−	19.8541i		−	0.992705i
$21$	−17.7082	−	19.7984i	−0.843248	−	0.942780i
$22$		0			0
$23$		−	17.5279i		−	0.762081i	−0.924558	−	0.381041i	$-0.875566\pi$
$23$		−	17.5279i		−	0.762081i	0.924558	−	0.381041i	$-0.124434\pi$
$24$	15.6525	−	14.0000i	0.652186	−	0.583333i
$25$	−18.7984			−0.751935
$26$			13.2361i			0.509080i
$27$	22.0000	−	15.6525i	0.814815	−	0.579721i
$28$	26.5623			0.948654
$29$		−	26.3951i		−	0.910177i	−0.890446	−	0.455088i	$-0.849608\pi$
$29$		−	26.3951i		−	0.910177i	0.890446	−	0.455088i	$-0.150392\pi$
$30$	−13.2361	−	14.7984i	−0.441202	−	0.493279i
$31$	−6.20163			−0.200052			−0.100026	−	0.994985i	$-0.531893\pi$
$31$	−6.20163			−0.200052			−0.100026	+	0.994985i	$0.531893\pi$
$32$			33.0000i			1.03125i
$33$		0			0
$34$	6.00000			0.176471
$35$		−	58.5967i		−	1.67419i
$36$	−3.00000	+	26.8328i	−0.0833333	+	0.745356i
$37$	−19.5967			−0.529642			−0.264821	−	0.964298i	$-0.585313\pi$
$37$	−19.5967			−0.529642			−0.264821	+	0.964298i	$0.585313\pi$
$38$		−	9.12461i		−	0.240121i
$39$	−26.4721	−	29.5967i	−0.678773	−	0.758891i
$40$	46.3262			1.15816
$41$		−	5.59675i		−	0.136506i	−0.997668	−	0.0682530i	$-0.978257\pi$
$41$		−	5.59675i		−	0.136506i	0.997668	−	0.0682530i	$-0.0217425\pi$
$42$	19.7984	−	17.7082i	0.471390	−	0.421624i
$43$	26.2918			0.611437			0.305719	−	0.952122i	$-0.401103\pi$
$43$	26.2918			0.611437			0.305719	+	0.952122i	$0.401103\pi$
$44$		0			0
$45$	59.1935	+	6.61803i	1.31541	+	0.147067i
$46$	17.5279			0.381041
$47$		−	17.7082i		−	0.376770i	−0.982095	−	0.188385i	$-0.939675\pi$
$47$		−	17.7082i		−	0.376770i	0.982095	−	0.188385i	$-0.0603253\pi$
$48$	−10.0000	−	11.1803i	−0.208333	−	0.232924i
$49$	29.3951			0.599900
$50$		−	18.7984i		−	0.375967i
$51$	−13.4164	+	12.0000i	−0.263067	+	0.235294i
$52$	39.7082			0.763619
$53$			22.2705i			0.420198i	0.977680	+	0.210099i	$0.0673787\pi$
$53$			22.2705i			0.420198i	−0.977680	+	0.210099i	$0.932621\pi$
$54$	15.6525	+	22.0000i	0.289861	+	0.407407i
$55$		0			0
$56$			61.9787i			1.10676i
$57$	18.2492	+	20.4033i	0.320162	+	0.357952i
$58$	26.3951			0.455088
$59$			21.9098i			0.371353i	0.982611	+	0.185677i	$0.0594477\pi$
$59$			21.9098i			0.371353i	−0.982611	+	0.185677i	$0.940552\pi$
$60$	−44.3951	+	39.7082i	−0.739919	+	0.661803i
$61$	93.3738			1.53072			0.765359	−	0.643603i	$-0.222561\pi$
$61$	93.3738			1.53072			0.765359	+	0.643603i	$0.222561\pi$
$62$		−	6.20163i		−	0.100026i
$63$	−8.85410	+	79.1935i	−0.140541	+	1.25704i
$64$	−13.0000			−0.203125
$65$		−	87.5967i		−	1.34764i
$66$		0			0
$67$	−76.7902			−1.14612			−0.573062	−	0.819512i	$-0.694244\pi$
$67$	−76.7902			−1.14612			−0.573062	+	0.819512i	$0.694244\pi$
$68$		−	18.0000i		−	0.264706i
$69$	−39.1935	+	35.0557i	−0.568022	+	0.508054i
$70$	58.5967			0.837096
$71$		−	65.8197i		−	0.927037i	−0.886087	−	0.463519i	$-0.846587\pi$
$71$		−	65.8197i		−	0.927037i	0.886087	−	0.463519i	$-0.153413\pi$
$72$	−62.6099	−	7.00000i	−0.869582	−	0.0972222i
$73$	−15.0213			−0.205771			−0.102886	−	0.994693i	$-0.532808\pi$
$73$	−15.0213			−0.205771			−0.102886	+	0.994693i	$0.532808\pi$
$74$		−	19.5967i		−	0.264821i
$75$	37.5967	+	42.0344i	0.501290	+	0.560459i
$76$	−27.3738			−0.360182
$77$		0			0
$78$	29.5967	−	26.4721i	0.379445	−	0.339386i
$79$	−118.061			−1.49444			−0.747220	−	0.664577i	$-0.768612\pi$
$79$	−118.061			−1.49444			−0.747220	+	0.664577i	$0.768612\pi$
$80$		−	33.0902i		−	0.413627i
$81$	−79.0000	−	17.8885i	−0.975309	−	0.220846i
$82$	5.59675			0.0682530
$83$			111.185i			1.33958i	0.742549	+	0.669791i	$0.233616\pi$
$83$			111.185i			1.33958i	−0.742549	+	0.669791i	$0.766384\pi$
$84$	−53.1246	−	59.3951i	−0.632436	−	0.707085i
$85$	−39.7082			−0.467155
$86$			26.2918i			0.305719i
$87$	−59.0213	+	52.7902i	−0.678406	+	0.606784i
$88$		0			0
$89$		−	97.6656i		−	1.09737i	−0.836030	−	0.548683i	$-0.815129\pi$
$89$		−	97.6656i		−	1.09737i	0.836030	−	0.548683i	$-0.184871\pi$
$90$	−6.61803	+	59.1935i	−0.0735337	+	0.657706i
$91$	117.193			1.28784
$92$		−	52.5836i		−	0.571561i
$93$	12.4033	+	13.8673i	0.133368	+	0.149110i
$94$	17.7082			0.188385
$95$			60.3870i			0.635653i
$96$	73.7902	−	66.0000i	0.768648	−	0.687500i
$97$	−121.185			−1.24933			−0.624667	−	0.780891i	$-0.714765\pi$
$97$	−121.185			−1.24933			−0.624667	+	0.780891i	$0.714765\pi$
$98$			29.3951i			0.299950i
$99$		0			0
$100$	−56.3951			−0.563951
$101$			185.589i			1.83751i	0.394827	+	0.918756i	$0.370805\pi$
$101$			185.589i			1.83751i	−0.394827	+	0.918756i	$0.629195\pi$
$102$	−12.0000	−	13.4164i	−0.117647	−	0.131533i
$103$	172.589			1.67562			0.837809	−	0.545964i	$-0.183836\pi$
$103$	172.589			1.67562			0.837809	+	0.545964i	$0.183836\pi$
$104$			92.6525i			0.890889i
$105$	−131.026	+	117.193i	−1.24787	+	1.11613i
$106$	−22.2705			−0.210099
$107$			65.7821i			0.614786i	0.951583	+	0.307393i	$0.0994566\pi$
$107$			65.7821i			0.614786i	−0.951583	+	0.307393i	$0.900543\pi$
$108$	66.0000	−	46.9574i	0.611111	−	0.434791i
$109$	107.331			0.984690			0.492345	−	0.870400i	$-0.336140\pi$
$109$	107.331			0.984690			0.492345	+	0.870400i	$0.336140\pi$
$110$		0			0
$111$	39.1935	+	43.8197i	0.353095	+	0.394772i
$112$	44.2705			0.395272
$113$		−	31.6656i		−	0.280227i	−0.990135	−	0.140113i	$-0.955253\pi$
$113$		−	31.6656i		−	0.280227i	0.990135	−	0.140113i	$-0.0447467\pi$
$114$	−20.4033	+	18.2492i	−0.178976	+	0.160081i
$115$	−116.000			−1.00870
$116$		−	79.1854i		−	0.682632i
$117$	−13.2361	+	118.387i	−0.113129	+	1.01185i
$118$	−21.9098			−0.185677
$119$		−	53.1246i		−	0.446425i
$120$	−92.6525	−	103.589i	−0.772104	−	0.863238i
$121$		0			0
$122$			93.3738i			0.765359i
$123$	−12.5147	+	11.1935i	−0.101746	+	0.0910040i
$124$	−18.6049			−0.150039
$125$		−	41.0426i		−	0.328341i
$126$	−79.1935	−	8.85410i	−0.628520	−	0.0702707i
$127$	−101.416			−0.798554			−0.399277	−	0.916830i	$-0.630739\pi$
$127$	−101.416			−0.798554			−0.399277	+	0.916830i	$0.630739\pi$
$128$			119.000i			0.929688i
$129$	−52.5836	−	58.7902i	−0.407625	−	0.455738i
$130$	87.5967			0.673821
$131$			130.992i			0.999938i	0.866043	+	0.499969i	$0.166655\pi$
$131$			130.992i			0.999938i	−0.866043	+	0.499969i	$0.833345\pi$
$132$		0			0
$133$	−80.7902			−0.607445
$134$		−	76.7902i		−	0.573062i
$135$	−103.589	−	145.597i	−0.767323	−	1.07849i
$136$	42.0000			0.308824
$137$			208.748i			1.52371i	0.647750	+	0.761853i	$0.275710\pi$
$137$			208.748i			1.52371i	−0.647750	+	0.761853i	$0.724290\pi$
$138$	−35.0557	−	39.1935i	−0.254027	−	0.284011i
$139$	81.5805			0.586910			0.293455	−	0.955973i	$-0.405195\pi$
$139$	81.5805			0.586910			0.293455	+	0.955973i	$0.405195\pi$
$140$		−	175.790i		−	1.25564i
$141$	−39.5967	+	35.4164i	−0.280828	+	0.251180i
$142$	65.8197			0.463519
$143$		0			0
$144$	−5.00000	+	44.7214i	−0.0347222	+	0.310565i
$145$	−174.684			−1.20472
$146$		−	15.0213i		−	0.102886i
$147$	−58.7902	−	65.7295i	−0.399934	−	0.447139i
$148$	−58.7902			−0.397231
$149$		−	6.99187i		−	0.0469253i	−0.999725	−	0.0234626i	$-0.992531\pi$
$149$		−	6.99187i		−	0.0469253i	0.999725	−	0.0234626i	$-0.00746908\pi$
$150$	−42.0344	+	37.5967i	−0.280230	+	0.250645i
$151$	55.4508			0.367224			0.183612	−	0.982999i	$-0.441221\pi$
$151$	55.4508			0.367224			0.183612	+	0.982999i	$0.441221\pi$
$152$		−	63.8723i		−	0.420212i
$153$	53.6656	+	6.00000i	0.350756	+	0.0392157i
$154$		0			0
$155$			41.0426i			0.264791i
$156$	−79.4164	−	88.7902i	−0.509080	−	0.569168i
$157$	42.0000			0.267516			0.133758	−	0.991014i	$-0.457296\pi$
$157$	42.0000			0.267516			0.133758	+	0.991014i	$0.457296\pi$
$158$		−	118.061i		−	0.747220i
$159$	49.7984	−	44.5410i	0.313197	−	0.280132i
$160$	218.395			1.36497
$161$		−	155.193i		−	0.963935i
$162$	17.8885	−	79.0000i	0.110423	−	0.487654i
$163$	−158.790			−0.974173			−0.487087	−	0.873354i	$-0.661940\pi$
$163$	−158.790			−0.974173			−0.487087	+	0.873354i	$0.661940\pi$
$164$		−	16.7902i		−	0.102380i
$165$		0			0
$166$	−111.185			−0.669791
$167$			285.177i			1.70765i	0.520562	+	0.853824i	$0.325723\pi$
$167$			285.177i			1.70765i	−0.520562	+	0.853824i	$0.674277\pi$
$168$	138.589	−	123.957i	0.824932	−	0.737842i
$169$	6.19350			0.0366479
$170$		−	39.7082i		−	0.233578i
$171$	9.12461	−	81.6130i	0.0533603	−	0.477269i
$172$	78.8754			0.458578
$173$			59.7984i			0.345655i	0.984952	+	0.172828i	$0.0552904\pi$
$173$			59.7984i			0.345655i	−0.984952	+	0.172828i	$0.944710\pi$
$174$	−52.7902	−	59.0213i	−0.303392	−	0.339203i
$175$	−166.443			−0.951101
$176$		0			0
$177$	48.9919	−	43.8197i	0.276790	−	0.247569i
$178$	97.6656			0.548683
$179$			263.838i			1.47395i	0.675918	+	0.736977i	$0.263748\pi$
$179$			263.838i			1.47395i	−0.675918	+	0.736977i	$0.736252\pi$
$180$	177.580	+	19.8541i	0.986558	+	0.110301i
$181$	225.967			1.24844			0.624220	−	0.781249i	$-0.285417\pi$
$181$	225.967			1.24844			0.624220	+	0.781249i	$0.285417\pi$
$182$			117.193i			0.643920i
$183$	−186.748	−	208.790i	−1.02048	−	1.14093i
$184$	122.695			0.666821
$185$			129.692i			0.701038i
$186$	−13.8673	+	12.4033i	−0.0745551	+	0.0666842i
$187$		0			0
$188$		−	53.1246i		−	0.282578i
$189$	194.790	−	138.589i	1.03064	−	0.733273i
$190$	−60.3870			−0.317826
$191$			60.0851i			0.314582i	0.987552	+	0.157291i	$0.0502760\pi$
$191$			60.0851i			0.314582i	−0.987552	+	0.157291i	$0.949724\pi$
$192$	26.0000	+	29.0689i	0.135417	+	0.151400i
$193$	−35.6869			−0.184906			−0.0924532	−	0.995717i	$-0.529471\pi$
$193$	−35.6869			−0.184906			−0.0924532	+	0.995717i	$0.529471\pi$
$194$		−	121.185i		−	0.624667i
$195$	−195.872	+	175.193i	−1.00447	+	0.898428i
$196$	88.1854			0.449925
$197$		−	145.605i		−	0.739111i	−0.929209	−	0.369556i	$-0.879510\pi$
$197$		−	145.605i		−	0.739111i	0.929209	−	0.369556i	$-0.120490\pi$
$198$		0			0
$199$	241.185			1.21199			0.605993	−	0.795470i	$-0.292776\pi$
$199$	241.185			1.21199			0.605993	+	0.795470i	$0.292776\pi$
$200$		−	131.589i		−	0.657943i
$201$	153.580	+	171.708i	0.764082	+	0.854270i
$202$	−185.589			−0.918756
$203$		−	233.705i		−	1.15126i
$204$	−40.2492	+	36.0000i	−0.197300	+	0.176471i
$205$	−37.0395			−0.180680
$206$			172.589i			0.837809i
$207$	156.774	+	17.5279i	0.757362	+	0.0846757i
$208$	66.1803			0.318175
$209$		0			0
$210$	−117.193	−	131.026i	−0.558064	−	0.623935i
$211$	−42.7376			−0.202548			−0.101274	−	0.994859i	$-0.532292\pi$
$211$	−42.7376			−0.202548			−0.101274	+	0.994859i	$0.532292\pi$
$212$			66.8115i			0.315149i
$213$	−147.177	+	131.639i	−0.690973	+	0.618025i
$214$	−65.7821			−0.307393
$215$		−	174.000i		−	0.809302i
$216$	109.567	+	154.000i	0.507256	+	0.712963i
$217$	−54.9098			−0.253041
$218$			107.331i			0.492345i
$219$	30.0426	+	33.5886i	0.137181	+	0.153373i
$220$		0			0
$221$		−	79.4164i		−	0.359350i
$222$	−43.8197	+	39.1935i	−0.197386	+	0.176547i
$223$	−165.992			−0.744358			−0.372179	−	0.928161i	$-0.621389\pi$
$223$	−165.992			−0.744358			−0.372179	+	0.928161i	$0.621389\pi$
$224$			292.185i			1.30440i
$225$	18.7984	−	168.138i	0.0835483	−	0.747279i
$226$	31.6656			0.140113
$227$			341.572i			1.50472i	0.658750	+	0.752362i	$0.271086\pi$
$227$			341.572i			1.50472i	−0.658750	+	0.752362i	$0.728914\pi$
$228$	54.7477	+	61.2098i	0.240121	+	0.268464i
$229$	246.774			1.07762			0.538808	−	0.842429i	$-0.318875\pi$
$229$	246.774			1.07762			0.538808	+	0.842429i	$0.318875\pi$
$230$		−	116.000i		−	0.504348i
$231$		0			0
$232$	184.766			0.796405
$233$		−	398.371i		−	1.70975i	−0.518838	−	0.854873i	$-0.673635\pi$
$233$		−	398.371i		−	1.70975i	0.518838	−	0.854873i	$-0.326365\pi$
$234$	−118.387	−	13.2361i	−0.505927	−	0.0565644i
$235$	−117.193			−0.498696
$236$			65.7295i			0.278515i
$237$	236.122	+	263.992i	0.996293	+	1.11389i
$238$	53.1246			0.223213
$239$			161.210i			0.674518i	0.941412	+	0.337259i	$0.109500\pi$
$239$			161.210i			0.674518i	−0.941412	+	0.337259i	$0.890500\pi$
$240$	−73.9919	+	66.1803i	−0.308299	+	0.275751i
$241$	159.644			0.662425			0.331212	−	0.943556i	$-0.392542\pi$
$241$	159.644			0.662425			0.331212	+	0.943556i	$0.392542\pi$
$242$		0			0
$243$	118.000	+	212.426i	0.485597	+	0.874183i
$244$	280.122			1.14804
$245$		−	194.538i		−	0.794032i
$246$	−11.1935	−	12.5147i	−0.0455020	−	0.0508728i
$247$	−120.774			−0.488963
$248$		−	43.4114i		−	0.175046i
$249$	248.618	−	222.371i	0.998466	−	0.893055i
$250$	41.0426			0.164170
$251$			48.8510i			0.194625i	0.995254	+	0.0973127i	$0.0310247\pi$
$251$			48.8510i			0.194625i	−0.995254	+	0.0973127i	$0.968975\pi$
$252$	−26.5623	+	237.580i	−0.105406	+	0.942780i
$253$		0			0
$254$		−	101.416i		−	0.399277i
$255$	79.4164	+	88.7902i	0.311437	+	0.348197i
$256$	−171.000			−0.667969
$257$			160.636i			0.625044i	0.949911	+	0.312522i	$0.101174\pi$
$257$			160.636i			0.625044i	−0.949911	+	0.312522i	$0.898826\pi$
$258$	58.7902	−	52.5836i	0.227869	−	0.203812i
$259$	−173.512			−0.669929
$260$		−	262.790i		−	1.01073i
$261$	236.085	+	26.3951i	0.904541	+	0.101131i
$262$	−130.992			−0.499969
$263$			140.420i			0.533914i	0.963708	+	0.266957i	$0.0860183\pi$
$263$			140.420i			0.533914i	−0.963708	+	0.266957i	$0.913982\pi$
$264$		0			0
$265$	147.387			0.556177
$266$		−	80.7902i		−	0.303723i
$267$	−218.387	+	195.331i	−0.817929	+	0.731578i
$268$	−230.371			−0.859592
$269$		−	413.745i		−	1.53808i	−0.639198	−	0.769042i	$-0.720734\pi$
$269$		−	413.745i		−	1.53808i	0.639198	−	0.769042i	$-0.279266\pi$
$270$	145.597	−	103.589i	0.539247	−	0.383662i
$271$	−57.7771			−0.213200			−0.106600	−	0.994302i	$-0.533996\pi$
$271$	−57.7771			−0.213200			−0.106600	+	0.994302i	$0.533996\pi$
$272$		−	30.0000i		−	0.110294i
$273$	−234.387	−	262.053i	−0.858560	−	0.959900i
$274$	−208.748			−0.761853
$275$		0			0
$276$	−117.580	+	105.167i	−0.426016	+	0.381041i
$277$	329.135			1.18821			0.594106	−	0.804387i	$-0.297506\pi$
$277$	329.135			1.18821			0.594106	+	0.804387i	$0.297506\pi$
$278$			81.5805i			0.293455i
$279$	6.20163	−	55.4690i	0.0222281	−	0.198814i
$280$	410.177			1.46492
$281$		−	395.161i		−	1.40627i	−0.711058	−	0.703133i	$-0.751784\pi$
$281$		−	395.161i		−	1.40627i	0.711058	−	0.703133i	$-0.248216\pi$
$282$	−35.4164	−	39.5967i	−0.125590	−	0.140414i
$283$	−287.082			−1.01442			−0.507212	−	0.861821i	$-0.669324\pi$
$283$	−287.082			−1.01442			−0.507212	+	0.861821i	$0.669324\pi$
$284$		−	197.459i		−	0.695278i
$285$	135.029	−	120.774i	0.473787	−	0.423768i
$286$		0			0
$287$		−	49.5542i		−	0.172663i
$288$	−295.161	−	33.0000i	−1.02486	−	0.114583i
$289$	253.000			0.875433
$290$		−	174.684i		−	0.602358i
$291$	242.371	+	270.979i	0.832889	+	0.931198i
$292$	−45.0639			−0.154328
$293$		−	71.7659i		−	0.244935i	−0.992473	−	0.122467i	$-0.960919\pi$
$293$		−	71.7659i		−	0.244935i	0.992473	−	0.122467i	$-0.0390807\pi$
$294$	65.7295	−	58.7902i	0.223570	−	0.199967i
$295$	145.000			0.491525
$296$		−	137.177i		−	0.463437i
$297$		0			0
$298$	6.99187			0.0234626
$299$		−	232.000i		−	0.775920i
$300$	112.790	+	126.103i	0.375967	+	0.420344i
$301$	232.790			0.773390
$302$			55.4508i			0.183612i
$303$	414.989	−	371.177i	1.36960	−	1.22501i
$304$	−45.6231			−0.150076
$305$		−	617.951i		−	2.02607i
$306$	−6.00000	+	53.6656i	−0.0196078	+	0.175378i
$307$	−116.961			−0.380979			−0.190489	−	0.981689i	$-0.561008\pi$
$307$	−116.961			−0.380979			−0.190489	+	0.981689i	$0.561008\pi$
$308$		0			0
$309$	−345.177	−	385.920i	−1.11708	−	1.24893i
$310$	−41.0426			−0.132395
$311$		−	183.141i		−	0.588877i	−0.955670	−	0.294439i	$-0.904867\pi$
$311$		−	183.141i		−	0.588877i	0.955670	−	0.294439i	$-0.0951327\pi$
$312$	207.177	−	185.305i	0.664030	−	0.593926i
$313$	−74.7821			−0.238920			−0.119460	−	0.992839i	$-0.538116\pi$
$313$	−74.7821			−0.238920			−0.119460	+	0.992839i	$0.538116\pi$
$314$			42.0000i			0.133758i
$315$	524.105	+	58.5967i	1.66383	+	0.186021i
$316$	−354.182			−1.12083
$317$			17.6718i			0.0557471i	0.999611	+	0.0278736i	$0.00887358\pi$
$317$			17.6718i			0.0557471i	−0.999611	+	0.0278736i	$0.991126\pi$
$318$	44.5410	+	49.7984i	0.140066	+	0.156599i
$319$		0			0
$320$			86.0344i			0.268858i
$321$	147.093	−	131.564i	0.458235	−	0.409857i
$322$	155.193			0.481967
$323$			54.7477i			0.169497i
$324$	−237.000	−	53.6656i	−0.731481	−	0.165635i
$325$	−248.817			−0.765589
$326$		−	158.790i		−	0.487087i
$327$	−214.663	−	240.000i	−0.656460	−	0.733945i
$328$	39.1772			0.119443
$329$		−	156.790i		−	0.476566i
$330$		0			0
$331$	−395.580			−1.19511			−0.597554	−	0.801829i	$-0.703860\pi$
$331$	−395.580			−1.19511			−0.597554	+	0.801829i	$0.703860\pi$
$332$			333.556i			1.00469i
$333$	19.5967	−	175.279i	0.0588491	−	0.526362i
$334$	−285.177			−0.853824
$335$			508.200i			1.51702i
$336$	−88.5410	−	98.9919i	−0.263515	−	0.294619i
$337$	−500.302			−1.48458			−0.742288	−	0.670081i	$-0.766259\pi$
$337$	−500.302			−1.48458			−0.742288	+	0.670081i	$0.766259\pi$
$338$			6.19350i			0.0183240i
$339$	−70.8065	+	63.3313i	−0.208869	+	0.186818i
$340$	−119.125			−0.350367
$341$		0			0
$342$	81.6130	+	9.12461i	0.238635	+	0.0266802i
$343$	−173.584			−0.506075
$344$			184.043i			0.535007i
$345$	232.000	+	259.384i	0.672464	+	0.751837i
$346$	−59.7984			−0.172828
$347$			616.976i			1.77803i	0.457880	+	0.889014i	$0.348609\pi$
$347$			616.976i			1.77803i	−0.457880	+	0.889014i	$0.651391\pi$
$348$	−177.064	+	158.371i	−0.508804	+	0.455088i
$349$	310.200			0.888826			0.444413	−	0.895822i	$-0.353412\pi$
$349$	310.200			0.888826			0.444413	+	0.895822i	$0.353412\pi$
$350$		−	166.443i		−	0.475551i
$351$	291.193	−	207.177i	0.829611	−	0.590249i
$352$		0			0
$353$			308.577i			0.874157i	0.899423	+	0.437078i	$0.143987\pi$
$353$			308.577i			0.874157i	−0.899423	+	0.437078i	$0.856013\pi$
$354$	43.8197	+	48.9919i	0.123784	+	0.138395i
$355$	−435.597			−1.22703
$356$		−	292.997i		−	0.823025i
$357$	−118.790	+	106.249i	−0.332746	+	0.297617i
$358$	−263.838			−0.736977
$359$			136.790i			0.381031i	0.981684	+	0.190516i	$0.0610160\pi$
$359$			136.790i			0.381031i	−0.981684	+	0.190516i	$0.938984\pi$
$360$	−46.3262	+	414.354i	−0.128684	+	1.15098i
$361$	−277.741			−0.769367
$362$			225.967i			0.624220i
$363$		0			0
$364$	351.580			0.965880
$365$			99.4114i			0.272360i
$366$	208.790	−	186.748i	0.570465	−	0.510240i
$367$	−126.024			−0.343391			−0.171695	−	0.985150i	$-0.554924\pi$
$367$	−126.024			−0.343391			−0.171695	+	0.985150i	$0.554924\pi$
$368$		−	87.6393i		−	0.238150i
$369$	50.0588	+	5.59675i	0.135661	+	0.0151673i
$370$	−129.692			−0.350519
$371$			197.185i			0.531497i
$372$	37.2098	+	41.6018i	0.100026	+	0.111833i
$373$	−347.528			−0.931710			−0.465855	−	0.884861i	$-0.654253\pi$
$373$	−347.528			−0.931710			−0.465855	+	0.884861i	$0.654253\pi$
$374$		0			0
$375$	−91.7740	+	82.0851i	−0.244731	+	0.218894i
$376$	123.957			0.329674
$377$		−	349.368i		−	0.926705i
$378$	138.589	+	194.790i	0.366637	+	0.515318i
$379$	−474.354			−1.25159			−0.625797	−	0.779986i	$-0.715226\pi$
$379$	−474.354			−1.25159			−0.625797	+	0.779986i	$0.715226\pi$
$380$			181.161i			0.476739i
$381$	202.833	+	226.774i	0.532370	+	0.595207i
$382$	−60.0851			−0.157291
$383$		−	292.456i		−	0.763592i	−0.924247	−	0.381796i	$-0.875306\pi$
$383$		−	292.456i		−	0.763592i	0.924247	−	0.381796i	$-0.124694\pi$
$384$	266.092	−	238.000i	0.692948	−	0.619792i
$385$		0			0
$386$		−	35.6869i		−	0.0924532i
$387$	−26.2918	+	235.161i	−0.0679375	+	0.607651i
$388$	−363.556			−0.937000
$389$			78.5511i			0.201931i	0.994890	+	0.100965i	$0.0321931\pi$
$389$			78.5511i			0.201931i	−0.994890	+	0.100965i	$0.967807\pi$
$390$	−175.193	−	195.872i	−0.449214	−	0.502237i
$391$	−105.167			−0.268970
$392$			205.766i			0.524913i
$393$	292.907	−	261.984i	0.745310	−	0.666625i
$394$	145.605			0.369556
$395$			781.330i			1.97805i
$396$		0			0
$397$	166.741			0.420004			0.210002	−	0.977701i	$-0.432653\pi$
$397$	166.741			0.420004			0.210002	+	0.977701i	$0.432653\pi$
$398$			241.185i			0.605993i
$399$	161.580	+	180.652i	0.404964	+	0.452763i
$400$	−93.9919			−0.234980
$401$		−	196.918i		−	0.491067i	−0.969388	−	0.245534i	$-0.921037\pi$
$401$		−	196.918i		−	0.491067i	0.969388	−	0.245534i	$-0.0789632\pi$
$402$	−171.708	+	153.580i	−0.427135	+	0.382041i
$403$	−82.0851			−0.203685
$404$			556.766i			1.37813i
$405$	−118.387	+	522.825i	−0.292314	+	1.29093i
$406$	233.705			0.575628
$407$		0			0
$408$	−84.0000	−	93.9149i	−0.205882	−	0.230183i
$409$	−720.825			−1.76241			−0.881204	−	0.472737i	$-0.843266\pi$
$409$	−720.825			−1.76241			−0.881204	+	0.472737i	$0.843266\pi$
$410$		−	37.0395i		−	0.0903402i
$411$	466.774	−	417.495i	1.13570	−	1.01580i
$412$	517.766			1.25671
$413$			193.992i			0.469714i
$414$	−17.5279	+	156.774i	−0.0423378	+	0.378681i
$415$	735.829			1.77308
$416$			436.790i			1.04998i
$417$	−163.161	−	182.420i	−0.391273	−	0.437457i
$418$		0			0
$419$		−	267.408i		−	0.638206i	−0.947720	−	0.319103i	$-0.896618\pi$
$419$		−	267.408i		−	0.638206i	0.947720	−	0.319103i	$-0.103382\pi$
$420$	−393.079	+	351.580i	−0.935902	+	0.837096i
$421$	685.967			1.62938			0.814688	−	0.579899i	$-0.196908\pi$
$421$	685.967			1.62938			0.814688	+	0.579899i	$0.196908\pi$
$422$		−	42.7376i		−	0.101274i
$423$	158.387	+	17.7082i	0.374437	+	0.0418634i
$424$	−155.894			−0.367674
$425$			112.790i			0.265389i
$426$	−131.639	−	147.177i	−0.309012	−	0.345486i
$427$	826.741			1.93616
$428$			197.346i			0.461090i
$429$		0			0
$430$	174.000			0.404651
$431$			552.387i			1.28164i	0.767691	+	0.640820i	$0.221406\pi$
$431$			552.387i			1.28164i	−0.767691	+	0.640820i	$0.778594\pi$
$432$	110.000	−	78.2624i	0.254630	−	0.181163i
$433$	−284.621			−0.657324			−0.328662	−	0.944448i	$-0.606598\pi$
$433$	−284.621			−0.657324			−0.328662	+	0.944448i	$0.606598\pi$
$434$		−	54.9098i		−	0.126520i
$435$	349.368	+	390.605i	0.803144	+	0.897942i
$436$	321.994			0.738518
$437$			159.935i			0.365984i
$438$	−33.5886	+	30.0426i	−0.0766863	+	0.0685903i
$439$	−532.058			−1.21198			−0.605988	−	0.795474i	$-0.707222\pi$
$439$	−532.058			−1.21198			−0.605988	+	0.795474i	$0.707222\pi$
$440$		0			0
$441$	−29.3951	+	262.918i	−0.0666556	+	0.596186i
$442$	79.4164			0.179675
$443$			120.297i			0.271550i	0.990740	+	0.135775i	$0.0433525\pi$
$443$			120.297i			0.271550i	−0.990740	+	0.135775i	$0.956648\pi$
$444$	117.580	+	131.459i	0.264821	+	0.296079i
$445$	−646.354			−1.45248
$446$		−	165.992i		−	0.372179i
$447$	−15.6343	+	13.9837i	−0.0349761	+	0.0312835i
$448$	−115.103			−0.256927
$449$			68.6687i			0.152937i	0.997072	+	0.0764685i	$0.0243645\pi$
$449$			68.6687i			0.152937i	−0.997072	+	0.0764685i	$0.975636\pi$
$450$	168.138	+	18.7984i	0.373639	+	0.0417742i
$451$		0			0
$452$		−	94.9969i		−	0.210170i
$453$	−110.902	−	123.992i	−0.244816	−	0.273713i
$454$	−341.572			−0.752362
$455$		−	775.591i		−	1.70459i
$456$	−142.823	+	127.745i	−0.313208	+	0.280142i
$457$	−695.507			−1.52190			−0.760949	−	0.648812i	$-0.775266\pi$
$457$	−695.507			−1.52190			−0.760949	+	0.648812i	$0.775266\pi$
$458$			246.774i			0.538808i
$459$	−93.9149	−	132.000i	−0.204608	−	0.287582i
$460$	−348.000			−0.756522
$461$		−	824.322i		−	1.78812i	−0.447950	−	0.894059i	$-0.647846\pi$
$461$		−	824.322i		−	1.78812i	0.447950	−	0.894059i	$-0.352154\pi$
$462$		0			0
$463$	−158.137			−0.341548			−0.170774	−	0.985310i	$-0.554627\pi$
$463$	−158.137			−0.341548			−0.170774	+	0.985310i	$0.554627\pi$
$464$		−	131.976i		−	0.284430i
$465$	91.7740	−	82.0851i	0.197363	−	0.176527i
$466$	398.371			0.854873
$467$			763.310i			1.63450i	0.576286	+	0.817248i	$0.304502\pi$
$467$			763.310i			1.63450i	−0.576286	+	0.817248i	$0.695498\pi$
$468$	−39.7082	+	355.161i	−0.0848466	+	0.758891i
$469$	−679.909			−1.44970
$470$		−	117.193i		−	0.249348i
$471$	−84.0000	−	93.9149i	−0.178344	−	0.199395i
$472$	−153.369			−0.324934
$473$		0			0
$474$	−263.992	+	236.122i	−0.556945	+	0.498147i
$475$	171.528			0.361111
$476$		−	159.374i		−	0.334819i
$477$	−199.193	−	22.2705i	−0.417596	−	0.0466887i
$478$	−161.210			−0.337259
$479$		−	74.8228i		−	0.156206i	−0.996945	−	0.0781031i	$-0.975114\pi$
$479$		−	74.8228i		−	0.156206i	0.996945	−	0.0781031i	$-0.0248863\pi$
$480$	−436.790	−	488.346i	−0.909980	−	1.01739i
$481$	−259.384			−0.539260
$482$			159.644i			0.331212i
$483$	−347.023	+	310.387i	−0.718475	+	0.642623i
$484$		0			0
$485$			802.009i			1.65363i
$486$	−212.426	+	118.000i	−0.437091	+	0.242798i
$487$	302.976			0.622127			0.311063	−	0.950389i	$-0.399315\pi$
$487$	302.976			0.622127			0.311063	+	0.950389i	$0.399315\pi$
$488$			653.617i			1.33938i
$489$	317.580	+	355.066i	0.649449	+	0.726106i
$490$	194.538			0.397016
$491$		−	798.774i		−	1.62683i	−0.581683	−	0.813415i	$-0.697606\pi$
$491$		−	798.774i		−	1.62683i	0.581683	−	0.813415i	$-0.302394\pi$
$492$	−37.5441	+	33.5805i	−0.0763092	+	0.0682530i
$493$	−158.371			−0.321239
$494$		−	120.774i		−	0.244482i
$495$		0			0
$496$	−31.0081			−0.0625164
$497$		−	582.774i		−	1.17258i
$498$	222.371	+	248.618i	0.446528	+	0.499233i
$499$	584.741			1.17183			0.585913	−	0.810374i	$-0.300736\pi$
$499$	584.741			1.17183			0.585913	+	0.810374i	$0.300736\pi$
$500$		−	123.128i		−	0.246255i
$501$	637.676	−	570.354i	1.27281	−	1.13843i
$502$	−48.8510			−0.0973127
$503$		−	553.935i		−	1.10126i	−0.834749	−	0.550631i	$-0.814387\pi$
$503$		−	553.935i		−	1.10126i	0.834749	−	0.550631i	$-0.185613\pi$
$504$	−554.354	−	61.9787i	−1.09991	−	0.122974i
$505$	1228.23			2.43214
$506$		0			0
$507$	−12.3870	−	13.8491i	−0.0244319	−	0.0273157i
$508$	−304.249			−0.598916
$509$		−	85.8897i		−	0.168742i	−0.996434	−	0.0843711i	$-0.973112\pi$
$509$		−	85.8897i		−	0.168742i	0.996434	−	0.0843711i	$-0.0268881\pi$
$510$	−88.7902	+	79.4164i	−0.174099	+	0.155718i
$511$	−133.000			−0.260274
$512$			305.000i			0.595703i
$513$	−200.741	+	142.823i	−0.391309	+	0.278407i
$514$	−160.636			−0.312522
$515$		−	1142.20i		−	2.21786i
$516$	−157.751	−	176.371i	−0.305719	−	0.341804i
$517$		0			0
$518$		−	173.512i		−	0.334964i
$519$	133.713	−	119.597i	0.257636	−	0.230437i
$520$	613.177			1.17919
$521$		−	733.611i		−	1.40808i	−0.710159	−	0.704041i	$-0.751377\pi$
$521$		−	733.611i		−	1.40808i	0.710159	−	0.704041i	$-0.248623\pi$
$522$	−26.3951	+	236.085i	−0.0505654	+	0.452270i
$523$	301.003			0.575532			0.287766	−	0.957701i	$-0.407088\pi$
$523$	301.003			0.575532			0.287766	+	0.957701i	$0.407088\pi$
$524$			392.976i			0.749953i
$525$	332.885	+	372.177i	0.634068	+	0.708909i
$526$	−140.420			−0.266957
$527$			37.2098i			0.0706067i
$528$		0			0
$529$	221.774			0.419232
$530$			147.387i			0.278089i
$531$	−195.967	−	21.9098i	−0.369054	−	0.0412615i
$532$	−242.371			−0.455584
$533$		−	74.0789i		−	0.138985i
$534$	−195.331	−	218.387i	−0.365789	−	0.408964i
$535$	435.348			0.813735
$536$		−	537.532i		−	1.00286i
$537$	589.959	−	527.676i	1.09862	−	0.982636i
$538$	413.745			0.769042
$539$		0			0
$540$	−310.766	−	436.790i	−0.575492	−	0.808871i
$541$	381.826			0.705778			0.352889	−	0.935665i	$-0.385199\pi$
$541$	381.826			0.705778			0.352889	+	0.935665i	$0.385199\pi$
$542$		−	57.7771i		−	0.106600i
$543$	−451.935	−	505.279i	−0.832293	−	0.930532i
$544$	198.000			0.363971
$545$		−	710.322i		−	1.30334i
$546$	262.053	−	234.387i	0.479950	−	0.429280i
$547$	186.026			0.340085			0.170042	−	0.985437i	$-0.445610\pi$
$547$	186.026			0.340085			0.170042	+	0.985437i	$0.445610\pi$
$548$			626.243i			1.14278i
$549$	−93.3738	+	835.161i	−0.170080	+	1.52124i
$550$		0			0
$551$			240.845i			0.437106i
$552$	−245.390	−	274.354i	−0.444547	−	0.497019i
$553$	−1045.32			−1.89027
$554$			329.135i			0.594106i
$555$	290.000	−	259.384i	0.522523	−	0.467358i
$556$	244.741			0.440182
$557$			436.605i			0.783851i	0.919997	+	0.391925i	$0.128191\pi$
$557$			436.605i			0.783851i	−0.919997	+	0.391925i	$0.871809\pi$
$558$	55.4690	+	6.20163i	0.0994069	+	0.0111140i
$559$	348.000			0.622540
$560$		−	292.984i		−	0.523185i
$561$		0			0
$562$	395.161			0.703133
$563$		−	247.646i		−	0.439868i	−0.975515	−	0.219934i	$-0.929416\pi$
$563$		−	247.646i		−	0.439868i	0.975515	−	0.219934i	$-0.0705842\pi$
$564$	−118.790	+	106.249i	−0.210621	+	0.188385i
$565$	−209.564			−0.370910
$566$		−	287.082i		−	0.507212i
$567$	−699.474	−	158.387i	−1.23364	−	0.279342i
$568$	460.738			0.811158
$569$		−	277.613i		−	0.487896i	−0.969788	−	0.243948i	$-0.921557\pi$
$569$		−	277.613i		−	0.487896i	0.969788	−	0.243948i	$-0.0784427\pi$
$570$	120.774	+	135.029i	0.211884	+	0.236894i
$571$	−1010.88			−1.77037			−0.885187	−	0.465236i	$-0.845969\pi$
$571$	−1010.88			−1.77037			−0.885187	+	0.465236i	$0.845969\pi$
$572$		0			0
$573$	134.354	−	120.170i	0.234476	−	0.209721i
$574$	49.5542			0.0863313
$575$			329.495i			0.573035i
$576$	13.0000	−	116.276i	0.0225694	−	0.201867i
$577$	260.185			0.450928			0.225464	−	0.974252i	$-0.427610\pi$
$577$	260.185			0.450928			0.225464	+	0.974252i	$0.427610\pi$
$578$			253.000i			0.437716i
$579$	71.3738	+	79.7984i	0.123271	+	0.137821i
$580$	−524.051			−0.903537
$581$			984.447i			1.69440i
$582$	−270.979	+	242.371i	−0.465599	+	0.416445i
$583$		0			0
$584$		−	105.149i		−	0.180050i
$585$	783.489	+	87.5967i	1.33930	+	0.149738i
$586$	71.7659			0.122467
$587$			1007.26i			1.71594i	0.513698	+	0.857971i	$0.328275\pi$
$587$			1007.26i			1.71594i	−0.513698	+	0.857971i	$0.671725\pi$
$588$	−176.371	−	197.188i	−0.299950	−	0.335355i
$589$	56.5874			0.0960737
$590$			145.000i			0.245763i
$591$	−325.582	+	291.210i	−0.550901	+	0.492741i
$592$	−97.9837			−0.165513
$593$		−	13.9837i		−	0.0235813i	−0.999930	−	0.0117907i	$-0.996247\pi$
$593$		−	13.9837i		−	0.0235813i	0.999930	−	0.0117907i	$-0.00375317\pi$
$594$		0			0
$595$	−351.580			−0.590892
$596$		−	20.9756i		−	0.0351940i
$597$	−482.371	−	539.307i	−0.807991	−	0.903362i
$598$	232.000			0.387960
$599$		−	173.368i		−	0.289428i	−0.989473	−	0.144714i	$-0.953774\pi$
$599$		−	173.368i		−	0.289428i	0.989473	−	0.144714i	$-0.0462263\pi$
$600$	−294.241	+	263.177i	−0.490402	+	0.438629i
$601$	785.130			1.30637			0.653186	−	0.757197i	$-0.273432\pi$
$601$	785.130			1.30637			0.653186	+	0.757197i	$0.273432\pi$
$602$			232.790i			0.386695i
$603$	76.7902	−	686.833i	0.127347	−	1.13903i
$604$	166.353			0.275418
$605$		0			0
$606$	371.177	+	414.989i	0.612504	+	0.684800i
$607$	−13.3437			−0.0219830			−0.0109915	−	0.999940i	$-0.503499\pi$
$607$	−13.3437			−0.0219830			−0.0109915	+	0.999940i	$0.503499\pi$
$608$		−	301.112i		−	0.495250i
$609$	−522.580	+	467.410i	−0.858096	+	0.767504i
$610$	617.951			1.01303
$611$		−	234.387i		−	0.383612i
$612$	160.997	+	18.0000i	0.263067	+	0.0294118i
$613$	624.079			1.01807			0.509037	−	0.860745i	$-0.330002\pi$
$613$	624.079			1.01807			0.509037	+	0.860745i	$0.330002\pi$
$614$		−	116.961i		−	0.190489i
$615$	74.0789	+	82.8228i	0.120454	+	0.134671i
$616$		0			0
$617$		−	1103.25i		−	1.78808i	−0.447986	−	0.894041i	$-0.647859\pi$
$617$		−	1103.25i		−	1.78808i	0.447986	−	0.894041i	$-0.352141\pi$
$618$	385.920	−	345.177i	0.624466	−	0.558539i
$619$	−183.210			−0.295977			−0.147988	−	0.988989i	$-0.547280\pi$
$619$	−183.210			−0.295977			−0.147988	+	0.988989i	$0.547280\pi$
$620$			123.128i			0.198593i
$621$	−274.354	−	385.613i	−0.441795	−	0.620955i
$622$	183.141			0.294439
$623$		−	864.741i		−	1.38803i
$624$	−132.361	−	147.984i	−0.212116	−	0.237153i
$625$	−741.580			−1.18653
$626$		−	74.7821i		−	0.119460i
$627$		0			0
$628$	126.000			0.200637
$629$			117.580i			0.186932i
$630$	−58.5967	+	524.105i	−0.0930107	+	0.831913i
$631$	278.831			0.441887			0.220944	−	0.975287i	$-0.429086\pi$
$631$	278.831			0.441887			0.220944	+	0.975287i	$0.429086\pi$
$632$		−	826.425i		−	1.30763i
$633$	85.4752	+	95.5642i	0.135032	+	0.150970i
$634$	−17.6718			−0.0278736
$635$			671.177i			1.05697i
$636$	149.395	−	133.623i	0.234898	−	0.210099i
$637$	389.076			0.610794
$638$		0			0
$639$	588.709	+	65.8197i	0.921297	+	0.103004i
$640$	787.546			1.23054
$641$			686.328i			1.07071i	0.844626	+	0.535357i	$0.179823\pi$
$641$			686.328i			1.07071i	−0.844626	+	0.535357i	$0.820177\pi$
$642$	131.564	+	147.093i	0.204929	+	0.229117i
$643$	−135.161			−0.210204			−0.105102	−	0.994461i	$-0.533517\pi$
$643$	−135.161			−0.210204			−0.105102	+	0.994461i	$0.533517\pi$
$644$		−	465.580i		−	0.722951i
$645$	−389.076	+	348.000i	−0.603218	+	0.539535i
$646$	−54.7477			−0.0847487
$647$		−	91.8584i		−	0.141976i	−0.997477	−	0.0709879i	$-0.977385\pi$
$647$		−	91.8584i		−	0.141976i	0.997477	−	0.0709879i	$-0.0226152\pi$
$648$	125.220	−	553.000i	0.193240	−	0.853395i
$649$		0			0
$650$		−	248.817i		−	0.382795i
$651$	109.820	+	122.782i	0.168694	+	0.188605i
$652$	−476.371			−0.730630
$653$			789.313i			1.20875i	0.796700	+	0.604374i	$0.206577\pi$
$653$			789.313i			1.20875i	−0.796700	+	0.604374i	$0.793423\pi$
$654$	240.000	−	214.663i	0.366972	−	0.328230i
$655$	866.909			1.32352
$656$		−	27.9837i		−	0.0426581i
$657$	15.0213	−	134.354i	0.0228634	−	0.204497i
$658$	156.790			0.238283
$659$			4.76585i			0.00723194i	0.999993	+	0.00361597i	$0.00115100\pi$
$659$			4.76585i			0.00723194i	−0.999993	+	0.00361597i	$0.998849\pi$
$660$		0			0
$661$	−1267.85			−1.91808			−0.959042	−	0.283264i	$-0.908583\pi$
$661$	−1267.85			−1.91808			−0.959042	+	0.283264i	$0.908583\pi$
$662$		−	395.580i		−	0.597554i
$663$	−177.580	+	158.833i	−0.267844	+	0.239567i
$664$	−778.298			−1.17213
$665$			534.673i			0.804019i
$666$	175.279	+	19.5967i	0.263181	+	0.0294245i
$667$	−462.650			−0.693628
$668$			855.532i			1.28074i
$669$	331.984	+	371.169i	0.496239	+	0.554812i
$670$	−508.200			−0.758508
$671$		0			0
$672$	653.346	−	584.371i	0.972242	−	0.869599i
$673$	183.447			0.272581			0.136290	−	0.990669i	$-0.456482\pi$
$673$	183.447			0.272581			0.136290	+	0.990669i	$0.456482\pi$
$674$		−	500.302i		−	0.742288i
$675$	−413.564	+	294.241i	−0.612688	+	0.435913i
$676$	18.5805			0.0274859
$677$			152.137i			0.224722i	0.993667	+	0.112361i	$0.0358413\pi$
$677$			152.137i			0.224722i	−0.993667	+	0.112361i	$0.964159\pi$
$678$	−63.3313	−	70.8065i	−0.0934089	−	0.104434i
$679$	−1072.99			−1.58025
$680$		−	277.957i		−	0.408761i
$681$	763.779	−	683.145i	1.12156	−	1.00315i
$682$		0			0
$683$		−	778.746i		−	1.14019i	−0.821580	−	0.570093i	$-0.806907\pi$
$683$		−	778.746i		−	1.14019i	0.821580	−	0.570093i	$-0.193093\pi$
$684$	27.3738	−	244.839i	0.0400202	−	0.357952i
$685$	1381.50			2.01679
$686$		−	173.584i		−	0.253037i
$687$	−493.548	−	551.803i	−0.718410	−	0.803207i
$688$	131.459			0.191074
$689$			294.774i			0.427829i
$690$	−259.384	+	232.000i	−0.375919	+	0.336232i
$691$	−452.807			−0.655292			−0.327646	−	0.944801i	$-0.606255\pi$
$691$	−452.807			−0.655292			−0.327646	+	0.944801i	$0.606255\pi$
$692$			179.395i			0.259242i
$693$		0			0
$694$	−616.976			−0.889014
$695$		−	539.902i		−	0.776838i
$696$	−369.532	−	413.149i	−0.530936	−	0.593605i
$697$	−33.5805			−0.0481786
$698$			310.200i			0.444413i
$699$	−890.784	+	796.741i	−1.27437	+	1.13983i
$700$	−499.328			−0.713326
$701$		−	53.1610i		−	0.0758359i	−0.999281	−	0.0379180i	$-0.987927\pi$
$701$		−	53.1610i		−	0.0758359i	0.999281	−	0.0379180i	$-0.0120726\pi$
$702$	207.177	+	291.193i	0.295124	+	0.414806i
$703$	178.813			0.254357
$704$		0			0
$705$	234.387	+	262.053i	0.332464	+	0.371706i
$706$	−308.577			−0.437078
$707$			1643.22i			2.32422i
$708$	146.976	−	131.459i	0.207593	−	0.185677i
$709$	1080.66			1.52420			0.762102	−	0.647457i	$-0.224168\pi$
$709$	1080.66			1.52420			0.762102	+	0.647457i	$0.224168\pi$
$710$		−	435.597i		−	0.613517i
$711$	118.061	−	1055.97i	0.166049	−	1.48519i
$712$	683.659			0.960196
$713$			108.701i			0.152456i
$714$	−106.249	−	118.790i	−0.148808	−	0.166373i
$715$		0			0
$716$			791.514i			1.10547i
$717$	360.476	−	322.420i	0.502756	−	0.449679i
$718$	−136.790			−0.190516
$719$		−	908.348i		−	1.26335i	−0.775234	−	0.631675i	$-0.782368\pi$
$719$		−	908.348i		−	1.26335i	0.775234	−	0.631675i	$-0.217632\pi$
$720$	295.967	+	33.0902i	0.411066	+	0.0459586i
$721$	1528.12			2.11944
$722$		−	277.741i		−	0.384683i
$723$	−319.289	−	356.976i	−0.441616	−	0.493742i
$724$	677.902			0.936329
$725$			496.185i			0.684394i
$726$		0			0
$727$	−64.4195			−0.0886101			−0.0443050	−	0.999018i	$-0.514107\pi$
$727$	−64.4195			−0.0886101			−0.0443050	+	0.999018i	$0.514107\pi$
$728$			820.354i			1.12686i
$729$	239.000	−	688.709i	0.327846	−	0.944731i
$730$	−99.4114			−0.136180
$731$		−	157.751i		−	0.215801i
$732$	−560.243	−	626.371i	−0.765359	−	0.855698i
$733$	1060.08			1.44622			0.723108	−	0.690735i	$-0.242713\pi$
$733$	1060.08			1.44622			0.723108	+	0.690735i	$0.242713\pi$
$734$		−	126.024i		−	0.171695i
$735$	−435.000	+	389.076i	−0.591837	+	0.529355i
$736$	578.420			0.785896
$737$		0			0
$738$	−5.59675	+	50.0588i	−0.00758367	+	0.0678304i
$739$	−159.915			−0.216394			−0.108197	−	0.994129i	$-0.534508\pi$
$739$	−159.915			−0.216394			−0.108197	+	0.994129i	$0.534508\pi$
$740$			389.076i			0.525778i
$741$	241.548	+	270.059i	0.325976	+	0.364452i
$742$	−197.185			−0.265748
$743$		−	63.1447i		−	0.0849862i	−0.999097	−	0.0424931i	$-0.986470\pi$
$743$		−	63.1447i		−	0.0849862i	0.999097	−	0.0424931i	$-0.0135300\pi$
$744$	−97.0708	+	86.8228i	−0.130472	+	0.116697i
$745$	−46.2724			−0.0621106
$746$		−	347.528i		−	0.465855i
$747$	−994.472	−	111.185i	−1.33129	−	0.148843i
$748$		0			0
$749$			582.442i			0.777626i
$750$	−82.0851	−	91.7740i	−0.109447	−	0.122365i
$751$	164.322			0.218804			0.109402	−	0.993998i	$-0.465106\pi$
$751$	164.322			0.218804			0.109402	+	0.993998i	$0.465106\pi$
$752$		−	88.5410i		−	0.117741i
$753$	109.234	−	97.7020i	0.145065	−	0.129750i
$754$	349.368			0.463352
$755$		−	366.976i		−	0.486060i
$756$	584.371	−	415.766i	0.772977	−	0.549955i
$757$	−906.273			−1.19719			−0.598595	−	0.801052i	$-0.704274\pi$
$757$	−906.273			−1.19719			−0.598595	+	0.801052i	$0.704274\pi$
$758$		−	474.354i		−	0.625797i
$759$		0			0
$760$	−422.709			−0.556196
$761$			229.259i			0.301260i	0.988590	+	0.150630i	$0.0481301\pi$
$761$			229.259i			0.301260i	−0.988590	+	0.150630i	$0.951870\pi$
$762$	−226.774	+	202.833i	−0.297604	+	0.266185i
$763$	950.322			1.24551
$764$			180.255i			0.235936i
$765$	39.7082	−	355.161i	0.0519061	−	0.464263i
$766$	292.456			0.381796
$767$			290.000i			0.378096i
$768$	342.000	+	382.368i	0.445312	+	0.497875i
$769$	−541.254			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$769$	−541.254			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$770$		0			0
$771$	359.193	−	321.272i	0.465880	−	0.416696i
$772$	−107.061			−0.138680
$773$		−	748.920i		−	0.968848i	−0.874833	−	0.484424i	$-0.839029\pi$
$773$		−	748.920i		−	0.968848i	0.874833	−	0.484424i	$-0.160971\pi$
$774$	−235.161	−	26.2918i	−0.303826	−	0.0339687i
$775$	116.580			0.150426
$776$		−	848.298i		−	1.09317i
$777$	347.023	+	387.984i	0.446619	+	0.499336i
$778$	−78.5511			−0.100965
$779$			51.0682i			0.0655560i
$780$	−587.617	+	525.580i	−0.753355	+	0.673821i
$781$		0			0
$782$		−	105.167i		−	0.134485i
$783$	−413.149	−	580.693i	−0.527649	−	0.741625i
$784$	146.976			0.187469
$785$		−	277.957i		−	0.354086i
$786$	261.984	+	292.907i	0.333313	+	0.372655i
$787$	−246.255			−0.312904			−0.156452	−	0.987686i	$-0.550006\pi$
$787$	−246.255			−0.312904			−0.156452	+	0.987686i	$0.550006\pi$
$788$		−	436.815i		−	0.554333i
$789$	313.988	−	280.839i	0.397956	−	0.355943i
$790$	−781.330			−0.989025
$791$		−	280.371i		−	0.354451i
$792$		0			0
$793$	1235.90			1.55852
$794$			166.741i			0.210002i
$795$	−294.774	−	329.567i	−0.370785	−	0.414550i
$796$	723.556			0.908990
$797$		−	1004.34i		−	1.26015i	−0.776536	−	0.630073i	$-0.783025\pi$
$797$		−	1004.34i		−	1.26015i	0.776536	−	0.630073i	$-0.216975\pi$
$798$	−180.652	+	161.580i	−0.226382	+	0.202482i
$799$	−106.249			−0.132978
$800$		−	620.346i		−	0.775433i
$801$	873.548	+	97.6656i	1.09057	+	0.121930i
$802$	196.918			0.245534
$803$		0			0
$804$	460.741	+	515.125i	0.573062	+	0.640702i
$805$	−1027.08			−1.27587
$806$		−	82.0851i		−	0.101843i
$807$	−925.161	+	827.489i	−1.14642	+	1.02539i
$808$	−1299.12			−1.60782
$809$			1326.34i			1.63948i	0.572737	+	0.819739i	$0.305882\pi$
$809$			1326.34i			1.63948i	−0.572737	+	0.819739i	$0.694118\pi$
$810$	−522.825	−	118.387i	−0.645463	−	0.146157i
$811$	1162.32			1.43320			0.716598	−	0.697486i	$-0.245698\pi$
$811$	1162.32			1.43320			0.716598	+	0.697486i	$0.245698\pi$
$812$		−	701.115i		−	0.863442i
$813$	115.554	+	129.193i	0.142133	+	0.158910i
$814$		0			0
$815$			1050.88i			1.28942i
$816$	−67.0820	+	60.0000i	−0.0822084	+	0.0735294i
$817$	−239.902			−0.293638
$818$		−	720.825i		−	0.881204i
$819$	−117.193	+	1048.21i	−0.143093	+	1.27987i
$820$	−111.118			−0.135510
$821$			948.169i			1.15490i	0.816428	+	0.577448i	$0.195951\pi$
$821$			948.169i			1.15490i	−0.816428	+	0.577448i	$0.804049\pi$
$822$	417.495	+	466.774i	0.507902	+	0.567852i
$823$	1477.83			1.79566			0.897831	−	0.440341i	$-0.145142\pi$
$823$	1477.83			1.79566			0.897831	+	0.440341i	$0.145142\pi$
$824$			1208.12i			1.46617i
$825$		0			0
$826$	−193.992			−0.234857
$827$		−	160.637i		−	0.194241i	−0.995273	−	0.0971206i	$-0.969037\pi$
$827$		−	160.637i		−	0.194241i	0.995273	−	0.0971206i	$-0.0309632\pi$
$828$	470.322	+	52.5836i	0.568022	+	0.0635068i
$829$	217.580			0.262461			0.131231	−	0.991352i	$-0.458107\pi$
$829$	217.580			0.262461			0.131231	+	0.991352i	$0.458107\pi$
$830$			735.829i			0.886540i
$831$	−658.269	−	735.967i	−0.792141	−	0.885641i
$832$	−172.069			−0.206814
$833$		−	176.371i		−	0.211730i
$834$	182.420	−	163.161i	0.218728	−	0.195637i
$835$	1887.31			2.26025
$836$		0			0
$837$	−136.436	+	97.0708i	−0.163006	+	0.115975i
$838$	267.408			0.319103
$839$		−	547.909i		−	0.653050i	−0.945189	−	0.326525i	$-0.894122\pi$
$839$		−	547.909i		−	0.653050i	0.945189	−	0.326525i	$-0.105878\pi$
$840$	−820.354	−	917.184i	−0.976612	−	1.09189i
$841$	144.298			0.171579
$842$			685.967i			0.814688i
$843$	−883.607	+	790.322i	−1.04817	+	0.937511i
$844$	−128.213			−0.151911
$845$		−	40.9888i		−	0.0485074i
$846$	−17.7082	+	158.387i	−0.0209317	+	0.187219i
$847$		0			0
$848$			111.353i			0.131312i
$849$	574.164	+	641.935i	0.676283	+	0.756107i
$850$	−112.790			−0.132694
$851$			343.489i			0.403630i
$852$	−441.532	+	394.918i	−0.518230	+	0.463519i
$853$	−731.447			−0.857499			−0.428749	−	0.903423i	$-0.641046\pi$
$853$	−731.447			−0.857499			−0.428749	+	0.903423i	$0.641046\pi$
$854$			826.741i			0.968081i
$855$	−540.118	−	60.3870i	−0.631717	−	0.0706281i
$856$	−460.475			−0.537938
$857$			333.112i			0.388696i	0.980933	+	0.194348i	$0.0622590\pi$
$857$			333.112i			0.388696i	−0.980933	+	0.194348i	$0.937741\pi$
$858$		0			0
$859$	146.468			0.170510			0.0852551	−	0.996359i	$-0.472829\pi$
$859$	146.468			0.170510			0.0852551	+	0.996359i	$0.472829\pi$
$860$		−	522.000i		−	0.606977i
$861$	−110.807	+	99.1084i	−0.128695	+	0.115108i
$862$	−552.387			−0.640820
$863$			636.486i			0.737527i	0.929523	+	0.368764i	$0.120219\pi$
$863$			636.486i			0.737527i	−0.929523	+	0.368764i	$0.879781\pi$
$864$	516.532	+	726.000i	0.597838	+	0.840278i
$865$	395.748			0.457512
$866$		−	284.621i		−	0.328662i
$867$	−506.000	−	565.725i	−0.583622	−	0.652509i
$868$	−164.729			−0.189781
$869$		0			0
$870$	−390.605	+	349.368i	−0.448971	+	0.401572i
$871$	−1016.40			−1.16694
$872$			751.319i			0.861604i
$873$	121.185	−	1083.91i	0.138815	−	1.24160i
$874$	−159.935			−0.182992
$875$		−	363.395i		−	0.415309i
$876$	90.1277	+	100.766i	0.102886	+	0.115030i
$877$	−1268.86			−1.44682			−0.723409	−	0.690420i	$-0.757426\pi$
$877$	−1268.86			−1.44682			−0.723409	+	0.690420i	$0.757426\pi$
$878$		−	532.058i		−	0.605988i
$879$	−160.473	+	143.532i	−0.182564	+	0.163290i
$880$		0			0
$881$			425.862i			0.483385i	0.970353	+	0.241693i	$0.0777025\pi$
$881$			425.862i			0.483385i	−0.970353	+	0.241693i	$0.922297\pi$
$882$	−262.918	−	29.3951i	−0.298093	−	0.0333278i
$883$	695.193			0.787309			0.393654	−	0.919259i	$-0.371211\pi$
$883$	695.193			0.787309			0.393654	+	0.919259i	$0.371211\pi$
$884$		−	238.249i		−	0.269513i
$885$	−290.000	−	324.230i	−0.327684	−	0.366361i
$886$	−120.297			−0.135775
$887$			426.741i			0.481106i	0.970636	+	0.240553i	$0.0773289\pi$
$887$			426.741i			0.481106i	−0.970636	+	0.240553i	$0.922671\pi$
$888$	−306.738	+	274.354i	−0.345425	+	0.308958i
$889$	−897.951			−1.01007
$890$		−	646.354i		−	0.726241i
$891$		0			0
$892$	−497.976			−0.558269
$893$			161.580i			0.180941i
$894$	−13.9837	−	15.6343i	−0.0156418	−	0.0174880i
$895$	1746.09			1.95094
$896$			1053.64i			1.17594i
$897$	−518.768	+	464.000i	−0.578336	+	0.517280i
$898$	−68.6687			−0.0764685
$899$			163.693i			0.182083i
$900$	56.3951	−	504.413i	0.0626612	−	0.560459i
$901$	133.623			0.148305
$902$		0			0
$903$	−465.580	−	520.535i	−0.515593	−	0.576451i
$904$	221.659			0.245198
$905$		−	1495.46i		−	1.65244i
$906$	123.992	−	110.902i	0.136856	−	0.122408i
$907$	−687.951			−0.758491			−0.379245	−	0.925296i	$-0.623816\pi$
$907$	−687.951			−0.758491			−0.379245	+	0.925296i	$0.623816\pi$
$908$			1024.72i			1.12854i
$909$	−1659.96	−	185.589i	−1.82613	−	0.204168i
$910$	775.591			0.852297
$911$			1710.59i			1.87771i	0.344317	+	0.938854i	$0.388111\pi$
$911$			1710.59i			1.87771i	−0.344317	+	0.938854i	$0.611889\pi$
$912$	91.2461	+	102.016i	0.100051	+	0.111860i
$913$		0			0
$914$		−	695.507i		−	0.760949i
$915$	−1381.78	+	1235.90i	−1.51014	+	1.35071i
$916$	740.322			0.808212
$917$			1159.82i			1.26479i
$918$	132.000	−	93.9149i	0.143791	−	0.102304i
$919$	−386.065			−0.420092			−0.210046	−	0.977691i	$-0.567361\pi$
$919$	−386.065			−0.420092			−0.210046	+	0.977691i	$0.567361\pi$
$920$		−	812.000i		−	0.882609i
$921$	233.921	+	261.532i	0.253986	+	0.283965i
$922$	824.322			0.894059
$923$		−	871.193i		−	0.943872i
$924$		0			0
$925$	368.387			0.398256
$926$		−	158.137i		−	0.170774i
$927$	−172.589	+	1543.68i	−0.186180	+	1.66524i
$928$	871.039			0.938620
$929$			74.6563i			0.0803620i	0.999192	+	0.0401810i	$0.0127935\pi$
$929$			74.6563i			0.0803620i	−0.999192	+	0.0401810i	$0.987207\pi$
$930$	82.0851	+	91.7740i	0.0882636	+	0.0986817i
$931$	−268.219			−0.288098
$932$		−	1195.11i		−	1.28231i
$933$	−409.515	+	366.282i	−0.438923	+	0.392585i
$934$	−763.310			−0.817248
$935$		0			0
$936$	−828.709	−	92.6525i	−0.885373	−	0.0989877i
$937$	568.303			0.606513			0.303257	−	0.952909i	$-0.401926\pi$
$937$	568.303			0.606513			0.303257	+	0.952909i	$0.401926\pi$
$938$		−	679.909i		−	0.724849i
$939$	149.564	+	167.218i	0.159280	+	0.178081i
$940$	−351.580			−0.374022
$941$			199.483i			0.211990i	0.994367	+	0.105995i	$0.0338028\pi$
$941$			199.483i			0.211990i	−0.994367	+	0.105995i	$0.966197\pi$
$942$	93.9149	−	84.0000i	0.0996973	−	0.0891720i
$943$	−98.0990			−0.104029
$944$			109.549i			0.116048i
$945$	−917.184	−	1289.13i	−0.970565	−	1.36416i
$946$		0			0
$947$		−	984.860i		−	1.03998i	−0.854173	−	0.519990i	$-0.825936\pi$
$947$		−	984.860i		−	1.03998i	0.854173	−	0.519990i	$-0.174064\pi$
$948$	708.365	+	791.976i	0.747220	+	0.835417i
$949$	−198.823			−0.209508
$950$			171.528i			0.180556i
$951$	39.5154	−	35.3437i	0.0415515	−	0.0371648i
$952$	371.872			0.390622
$953$		−	762.371i		−	0.799969i	−0.916522	−	0.399985i	$-0.869015\pi$
$953$		−	762.371i		−	0.799969i	0.916522	−	0.399985i	$-0.130985\pi$
$954$	22.2705	−	199.193i	0.0233443	−	0.208798i
$955$	397.646			0.416383
$956$			483.629i			0.505888i
$957$		0			0
$958$	74.8228			0.0781031
$959$			1848.27i			1.92729i
$960$	192.379	−	172.069i	0.200395	−	0.179238i
$961$	−922.540			−0.959979
$962$		−	259.384i		−	0.269630i
$963$	−588.373	−	65.7821i	−0.610979	−	0.0683096i
$964$	478.933			0.496819
$965$			236.177i			0.244743i
$966$	−310.387	−	347.023i	−0.321312	−	0.359237i
$967$	−1466.73			−1.51679			−0.758394	−	0.651797i	$-0.774015\pi$
$967$	−1466.73			−1.51679			−0.758394	+	0.651797i	$0.774015\pi$
$968$		0			0
$969$	122.420	−	109.495i	0.126336	−	0.112998i
$970$	−802.009			−0.826813
$971$		−	1142.56i		−	1.17668i	−0.808613	−	0.588341i	$-0.799781\pi$
$971$		−	1142.56i		−	1.17668i	0.808613	−	0.588341i	$-0.200219\pi$
$972$	354.000	+	637.279i	0.364198	+	0.655637i
$973$	722.322			0.742366
$974$			302.976i			0.311063i
$975$	497.633	+	556.371i	0.510393	+	0.570637i
$976$	466.869			0.478350
$977$			38.6989i			0.0396099i	0.999804	+	0.0198050i	$0.00630453\pi$
$977$			38.6989i			0.0396099i	−0.999804	+	0.0198050i	$0.993695\pi$
$978$	−355.066	+	317.580i	−0.363053	+	0.324724i
$979$		0			0
$980$		−	583.614i		−	0.595524i
$981$	−107.331	+	960.000i	−0.109410	+	0.978593i
$982$	798.774			0.813415
$983$		−	1212.60i		−	1.23357i	−0.787132	−	0.616784i	$-0.788435\pi$
$983$		−	1212.60i		−	1.23357i	0.787132	−	0.616784i	$-0.211565\pi$
$984$	−78.3545	−	87.6030i	−0.0796285	−	0.0890274i
$985$	−963.618			−0.978292
$986$		−	158.371i		−	0.160619i
$987$	−350.594	+	313.580i	−0.355211	+	0.317711i
$988$	−362.322			−0.366723
$989$		−	460.839i		−	0.465965i
$990$		0			0
$991$	−1413.89			−1.42673			−0.713367	−	0.700790i	$-0.752831\pi$
$991$	−1413.89			−1.42673			−0.713367	+	0.700790i	$0.752831\pi$
$992$		−	204.654i		−	0.206304i
$993$	791.161	+	884.545i	0.796738	+	0.890780i
$994$	582.774			0.586292
$995$		−	1596.17i		−	1.60419i
$996$	745.854	−	667.112i	0.748849	−	0.669791i
$997$	−943.007			−0.945844			−0.472922	−	0.881104i	$-0.656801\pi$
$997$	−943.007			−0.945844			−0.472922	+	0.881104i	$0.656801\pi$
$998$			584.741i			0.585913i
$999$	−431.128	+	306.738i	−0.431560	+	0.307045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.g.122.3		4
3.2	odd	2	inner	363.3.b.g.122.2		4
11.2	odd	10		33.3.h.a.26.1	yes	8
11.3	even	5		363.3.h.i.251.2		8
11.4	even	5		363.3.h.i.269.1		8
11.5	even	5		363.3.h.g.245.1		8
11.6	odd	10		33.3.h.a.14.2	yes	8
11.7	odd	10		363.3.h.h.269.2		8
11.8	odd	10		363.3.h.h.251.1		8
11.9	even	5		363.3.h.g.323.2		8
11.10	odd	2		363.3.b.f.122.1		4
33.2	even	10		33.3.h.a.26.2	yes	8
33.5	odd	10		363.3.h.g.245.2		8
33.8	even	10		363.3.h.h.251.2		8
33.14	odd	10		363.3.h.i.251.1		8
33.17	even	10		33.3.h.a.14.1	✓	8
33.20	odd	10		363.3.h.g.323.1		8
33.26	odd	10		363.3.h.i.269.2		8
33.29	even	10		363.3.h.h.269.1		8
33.32	even	2		363.3.b.f.122.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.a.14.1	✓	8	33.17	even	10
33.3.h.a.14.2	yes	8	11.6	odd	10
33.3.h.a.26.1	yes	8	11.2	odd	10
33.3.h.a.26.2	yes	8	33.2	even	10
363.3.b.f.122.1		4	11.10	odd	2
363.3.b.f.122.4		4	33.32	even	2
363.3.b.g.122.2		4	3.2	odd	2	inner
363.3.b.g.122.3		4	1.1	even	1	trivial
363.3.h.g.245.1		8	11.5	even	5
363.3.h.g.245.2		8	33.5	odd	10
363.3.h.g.323.1		8	33.20	odd	10
363.3.h.g.323.2		8	11.9	even	5
363.3.h.h.251.1		8	11.8	odd	10
363.3.h.h.251.2		8	33.8	even	10
363.3.h.h.269.1		8	33.29	even	10
363.3.h.h.269.2		8	11.7	odd	10
363.3.h.i.251.1		8	33.14	odd	10
363.3.h.i.251.2		8	11.3	even	5
363.3.h.i.269.1		8	11.4	even	5
363.3.h.i.269.2		8	33.26	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-2.00000 - 2.23607i) q^{3} +3.00000 q^{4} -6.61803i q^{5} +(2.23607 - 2.00000i) q^{6} +8.85410 q^{7} +7.00000i q^{8} +(-1.00000 + 8.94427i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-2.00000 - 2.23607i) q^{3} +3.00000 q^{4} -6.61803i q^{5} +(2.23607 - 2.00000i) q^{6} +8.85410 q^{7} +7.00000i q^{8} +(-1.00000 + 8.94427i) q^{9} +6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +13.2361 q^{13} +8.85410i q^{14} +(-14.7984 + 13.2361i) q^{15} +5.00000 q^{16} -6.00000i q^{17} +(-8.94427 - 1.00000i) q^{18} -9.12461 q^{19} -19.8541i q^{20} +(-17.7082 - 19.7984i) q^{21} -17.5279i q^{23} +(15.6525 - 14.0000i) q^{24} -18.7984 q^{25} +13.2361i q^{26} +(22.0000 - 15.6525i) q^{27} +26.5623 q^{28} -26.3951i q^{29} +(-13.2361 - 14.7984i) q^{30} -6.20163 q^{31} +33.0000i q^{32} +6.00000 q^{34} -58.5967i q^{35} +(-3.00000 + 26.8328i) q^{36} -19.5967 q^{37} -9.12461i q^{38} +(-26.4721 - 29.5967i) q^{39} +46.3262 q^{40} -5.59675i q^{41} +(19.7984 - 17.7082i) q^{42} +26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +17.5279 q^{46} -17.7082i q^{47} +(-10.0000 - 11.1803i) q^{48} +29.3951 q^{49} -18.7984i q^{50} +(-13.4164 + 12.0000i) q^{51} +39.7082 q^{52} +22.2705i q^{53} +(15.6525 + 22.0000i) q^{54} +61.9787i q^{56} +(18.2492 + 20.4033i) q^{57} +26.3951 q^{58} +21.9098i q^{59} +(-44.3951 + 39.7082i) q^{60} +93.3738 q^{61} -6.20163i q^{62} +(-8.85410 + 79.1935i) q^{63} -13.0000 q^{64} -87.5967i q^{65} -76.7902 q^{67} -18.0000i q^{68} +(-39.1935 + 35.0557i) q^{69} +58.5967 q^{70} -65.8197i q^{71} +(-62.6099 - 7.00000i) q^{72} -15.0213 q^{73} -19.5967i q^{74} +(37.5967 + 42.0344i) q^{75} -27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} -118.061 q^{79} -33.0902i q^{80} +(-79.0000 - 17.8885i) q^{81} +5.59675 q^{82} +111.185i q^{83} +(-53.1246 - 59.3951i) q^{84} -39.7082 q^{85} +26.2918i q^{86} +(-59.0213 + 52.7902i) q^{87} -97.6656i q^{89} +(-6.61803 + 59.1935i) q^{90} +117.193 q^{91} -52.5836i q^{92} +(12.4033 + 13.8673i) q^{93} +17.7082 q^{94} +60.3870i q^{95} +(73.7902 - 66.0000i) q^{96} -121.185 q^{97} +29.3951i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9	\( 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9} + 22 q^{10} - 24 q^{12} + 44 q^{13} - 10 q^{15} + 20 q^{16} + 44 q^{19} - 44 q^{21} - 26 q^{25} + 88 q^{27} + 66 q^{28} - 44 q^{30} - 74 q^{31} + 24 q^{34} - 12 q^{36} + 20 q^{37} - 88 q^{39} + 154 q^{40} + 30 q^{42} + 132 q^{43} + 40 q^{45} + 88 q^{46} - 40 q^{48} - 30 q^{49} + 132 q^{52} - 88 q^{57} - 42 q^{58} - 30 q^{60} + 132 q^{61} - 22 q^{63} - 52 q^{64} - 12 q^{67} + 40 q^{69} + 136 q^{70} - 154 q^{73} + 52 q^{75} + 132 q^{76} + 20 q^{78} - 110 q^{79} - 316 q^{81} - 76 q^{82} - 132 q^{84} - 132 q^{85} - 330 q^{87} - 22 q^{90} + 272 q^{91} + 148 q^{93} + 44 q^{94} - 42 q^{97}+O(q^{100}) \) 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9 + 22 * q^10 - 24 * q^12 + 44 * q^13 - 10 * q^15 + 20 * q^16 + 44 * q^19 - 44 * q^21 - 26 * q^25 + 88 * q^27 + 66 * q^28 - 44 * q^30 - 74 * q^31 + 24 * q^34 - 12 * q^36 + 20 * q^37 - 88 * q^39 + 154 * q^40 + 30 * q^42 + 132 * q^43 + 40 * q^45 + 88 * q^46 - 40 * q^48 - 30 * q^49 + 132 * q^52 - 88 * q^57 - 42 * q^58 - 30 * q^60 + 132 * q^61 - 22 * q^63 - 52 * q^64 - 12 * q^67 + 40 * q^69 + 136 * q^70 - 154 * q^73 + 52 * q^75 + 132 * q^76 + 20 * q^78 - 110 * q^79 - 316 * q^81 - 76 * q^82 - 132 * q^84 - 132 * q^85 - 330 * q^87 - 22 * q^90 + 272 * q^91 + 148 * q^93 + 44 * q^94 - 42 * q^97

Introduction

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Modular forms

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