LMFDB - Embedded newform 363.3.b.g.122.2

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

$q$-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	$-0.919569\pi$
$2$		−	1.00000i		−	0.500000i	0.968246	−	0.250000i	$-0.0804306\pi$
$3$	−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	$0.230209\pi$
$5$			6.61803i			1.32361i	−0.749677	+	0.661803i	$0.769791\pi$
$6$	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	$0.0564680\pi$
$17$			6.00000i			0.352941i	−0.984306	+	0.176471i	$0.943532\pi$
$18$	−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	$0.124434\pi$
$23$			17.5279i			0.762081i	−0.924558	+	0.381041i	$0.875566\pi$
$24$	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	$0.150392\pi$
$29$			26.3951i			0.910177i	−0.890446	+	0.455088i	$0.849608\pi$
$30$	−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	$0.0217425\pi$
$41$			5.59675i			0.136506i	−0.997668	+	0.0682530i	$0.978257\pi$
$42$	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	$0.0603253\pi$
$47$			17.7082i			0.376770i	−0.982095	+	0.188385i	$0.939675\pi$
$48$	−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	$-0.932621\pi$
$53$		−	22.2705i		−	0.420198i	0.977680	−	0.210099i	$-0.0673787\pi$
$54$	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	$-0.940552\pi$
$59$		−	21.9098i		−	0.371353i	0.982611	−	0.185677i	$-0.0594477\pi$
$60$	−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	$0.153413\pi$
$71$			65.8197i			0.927037i	−0.886087	+	0.463519i	$0.846587\pi$
$72$	−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	$-0.766384\pi$
$83$		−	111.185i		−	1.33958i	0.742549	−	0.669791i	$-0.233616\pi$
$84$	−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	$0.184871\pi$
$89$			97.6656i			1.09737i	−0.836030	+	0.548683i	$0.815129\pi$
$90$	−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	$-0.629195\pi$
$101$		−	185.589i		−	1.83751i	0.394827	−	0.918756i	$-0.370805\pi$
$102$	−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	$-0.900543\pi$
$107$		−	65.7821i		−	0.614786i	0.951583	−	0.307393i	$-0.0994566\pi$
$108$	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	$0.0447467\pi$
$113$			31.6656i			0.280227i	−0.990135	+	0.140113i	$0.955253\pi$
$114$	−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	$-0.833345\pi$
$131$		−	130.992i		−	0.999938i	0.866043	−	0.499969i	$-0.166655\pi$
$132$		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	$-0.724290\pi$
$137$		−	208.748i		−	1.52371i	0.647750	−	0.761853i	$-0.275710\pi$
$138$	−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	$0.00746908\pi$
$149$			6.99187i			0.0469253i	−0.999725	+	0.0234626i	$0.992531\pi$
$150$	−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	$-0.674277\pi$
$167$		−	285.177i		−	1.70765i	0.520562	−	0.853824i	$-0.325723\pi$
$168$	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	$-0.944710\pi$
$173$		−	59.7984i		−	0.345655i	0.984952	−	0.172828i	$-0.0552904\pi$
$174$	−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	$-0.736252\pi$
$179$		−	263.838i		−	1.47395i	0.675918	−	0.736977i	$-0.263748\pi$
$180$	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	$-0.949724\pi$
$191$		−	60.0851i		−	0.314582i	0.987552	−	0.157291i	$-0.0502760\pi$
$192$	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	$0.120490\pi$
$197$			145.605i			0.739111i	−0.929209	+	0.369556i	$0.879510\pi$
$198$		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	$-0.728914\pi$
$227$		−	341.572i		−	1.50472i	0.658750	−	0.752362i	$-0.271086\pi$
$228$	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	$0.326365\pi$
$233$			398.371i			1.70975i	−0.518838	+	0.854873i	$0.673635\pi$
$234$	−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	$-0.890500\pi$
$239$		−	161.210i		−	0.674518i	0.941412	−	0.337259i	$-0.109500\pi$
$240$	−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	$-0.968975\pi$
$251$		−	48.8510i		−	0.194625i	0.995254	−	0.0973127i	$-0.0310247\pi$
$252$	−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	$-0.898826\pi$
$257$		−	160.636i		−	0.625044i	0.949911	−	0.312522i	$-0.101174\pi$
$258$	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	$-0.913982\pi$
$263$		−	140.420i		−	0.533914i	0.963708	−	0.266957i	$-0.0860183\pi$
$264$		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	$0.279266\pi$
$269$			413.745i			1.53808i	−0.639198	+	0.769042i	$0.720734\pi$
$270$	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	$0.248216\pi$
$281$			395.161i			1.40627i	−0.711058	+	0.703133i	$0.751784\pi$
$282$	−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	$0.0390807\pi$
$293$			71.7659i			0.244935i	−0.992473	+	0.122467i	$0.960919\pi$
$294$	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	$0.0951327\pi$
$311$			183.141i			0.588877i	−0.955670	+	0.294439i	$0.904867\pi$
$312$	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	$-0.991126\pi$
$317$		−	17.6718i		−	0.0557471i	0.999611	−	0.0278736i	$-0.00887358\pi$
$318$	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	$-0.651391\pi$
$347$		−	616.976i		−	1.77803i	0.457880	−	0.889014i	$-0.348609\pi$
$348$	−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	$-0.856013\pi$
$353$		−	308.577i		−	0.874157i	0.899423	−	0.437078i	$-0.143987\pi$
$354$	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	$-0.938984\pi$
$359$		−	136.790i		−	0.381031i	0.981684	−	0.190516i	$-0.0610160\pi$
$360$	−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	$0.124694\pi$
$383$			292.456i			0.763592i	−0.924247	+	0.381796i	$0.875306\pi$
$384$	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	$-0.967807\pi$
$389$		−	78.5511i		−	0.201931i	0.994890	−	0.100965i	$-0.0321931\pi$
$390$	−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	$0.0789632\pi$
$401$			196.918i			0.491067i	−0.969388	+	0.245534i	$0.921037\pi$
$402$	−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	$0.103382\pi$
$419$			267.408i			0.638206i	−0.947720	+	0.319103i	$0.896618\pi$
$420$	−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	$-0.778594\pi$
$431$		−	552.387i		−	1.28164i	0.767691	−	0.640820i	$-0.221406\pi$
$432$	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	$-0.956648\pi$
$443$		−	120.297i		−	0.271550i	0.990740	−	0.135775i	$-0.0433525\pi$
$444$	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	$-0.975636\pi$
$449$		−	68.6687i		−	0.152937i	0.997072	−	0.0764685i	$-0.0243645\pi$
$450$	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	$0.352154\pi$
$461$			824.322i			1.78812i	−0.447950	+	0.894059i	$0.647846\pi$
$462$		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	$-0.695498\pi$
$467$		−	763.310i		−	1.63450i	0.576286	−	0.817248i	$-0.304502\pi$
$468$	−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	$0.0248863\pi$
$479$			74.8228i			0.156206i	−0.996945	+	0.0781031i	$0.975114\pi$
$480$	−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	$0.302394\pi$
$491$			798.774i			1.62683i	−0.581683	+	0.813415i	$0.697606\pi$
$492$	−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	$0.185613\pi$
$503$			553.935i			1.10126i	−0.834749	+	0.550631i	$0.814387\pi$
$504$	−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	$0.0268881\pi$
$509$			85.8897i			0.168742i	−0.996434	+	0.0843711i	$0.973112\pi$
$510$	−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	$0.248623\pi$
$521$			733.611i			1.40808i	−0.710159	+	0.704041i	$0.751377\pi$
$522$	−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	$-0.871809\pi$
$557$		−	436.605i		−	0.783851i	0.919997	−	0.391925i	$-0.128191\pi$
$558$	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	$0.0705842\pi$
$563$			247.646i			0.439868i	−0.975515	+	0.219934i	$0.929416\pi$
$564$	−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	$0.0784427\pi$
$569$			277.613i			0.487896i	−0.969788	+	0.243948i	$0.921557\pi$
$570$	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	$-0.671725\pi$
$587$		−	1007.26i		−	1.71594i	0.513698	−	0.857971i	$-0.328275\pi$
$588$	−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	$0.00375317\pi$
$593$			13.9837i			0.0235813i	−0.999930	+	0.0117907i	$0.996247\pi$
$594$		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	$0.0462263\pi$
$599$			173.368i			0.289428i	−0.989473	+	0.144714i	$0.953774\pi$
$600$	−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	$0.352141\pi$
$617$			1103.25i			1.78808i	−0.447986	+	0.894041i	$0.647859\pi$
$618$	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	$-0.820177\pi$
$641$		−	686.328i		−	1.07071i	0.844626	−	0.535357i	$-0.179823\pi$
$642$	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	$0.0226152\pi$
$647$			91.8584i			0.141976i	−0.997477	+	0.0709879i	$0.977385\pi$
$648$	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	$-0.793423\pi$
$653$		−	789.313i		−	1.20875i	0.796700	−	0.604374i	$-0.206577\pi$
$654$	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	$-0.998849\pi$
$659$		−	4.76585i		−	0.00723194i	0.999993	−	0.00361597i	$-0.00115100\pi$
$660$		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	$-0.964159\pi$
$677$		−	152.137i		−	0.224722i	0.993667	−	0.112361i	$-0.0358413\pi$
$678$	−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	$0.193093\pi$
$683$			778.746i			1.14019i	−0.821580	+	0.570093i	$0.806907\pi$
$684$	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	$0.0120726\pi$
$701$			53.1610i			0.0758359i	−0.999281	+	0.0379180i	$0.987927\pi$
$702$	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	$0.217632\pi$
$719$			908.348i			1.26335i	−0.775234	+	0.631675i	$0.782368\pi$
$720$	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	$0.0135300\pi$
$743$			63.1447i			0.0849862i	−0.999097	+	0.0424931i	$0.986470\pi$
$744$	−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	$-0.951870\pi$
$761$		−	229.259i		−	0.301260i	0.988590	−	0.150630i	$-0.0481301\pi$
$762$	−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	$0.160971\pi$
$773$			748.920i			0.968848i	−0.874833	+	0.484424i	$0.839029\pi$
$774$	−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	$0.216975\pi$
$797$			1004.34i			1.26015i	−0.776536	+	0.630073i	$0.783025\pi$
$798$	−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	$-0.694118\pi$
$809$		−	1326.34i		−	1.63948i	0.572737	−	0.819739i	$-0.305882\pi$
$810$	−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	$-0.804049\pi$
$821$		−	948.169i		−	1.15490i	0.816428	−	0.577448i	$-0.195951\pi$
$822$	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	$0.0309632\pi$
$827$			160.637i			0.194241i	−0.995273	+	0.0971206i	$0.969037\pi$
$828$	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	$0.105878\pi$
$839$			547.909i			0.653050i	−0.945189	+	0.326525i	$0.894122\pi$
$840$	−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	$-0.937741\pi$
$857$		−	333.112i		−	0.388696i	0.980933	−	0.194348i	$-0.0622590\pi$
$858$		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	$-0.879781\pi$
$863$		−	636.486i		−	0.737527i	0.929523	−	0.368764i	$-0.120219\pi$
$864$	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	$-0.922297\pi$
$881$		−	425.862i		−	0.483385i	0.970353	−	0.241693i	$-0.0777025\pi$
$882$	−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	$-0.922671\pi$
$887$		−	426.741i		−	0.481106i	0.970636	−	0.240553i	$-0.0773289\pi$
$888$	−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	$-0.611889\pi$
$911$		−	1710.59i		−	1.87771i	0.344317	−	0.938854i	$-0.388111\pi$
$912$	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	$-0.987207\pi$
$929$		−	74.6563i		−	0.0803620i	0.999192	−	0.0401810i	$-0.0127935\pi$
$930$	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	$-0.966197\pi$
$941$		−	199.483i		−	0.211990i	0.994367	−	0.105995i	$-0.0338028\pi$
$942$	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	$0.174064\pi$
$947$			984.860i			1.03998i	−0.854173	+	0.519990i	$0.825936\pi$
$948$	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	$0.130985\pi$
$953$			762.371i			0.799969i	−0.916522	+	0.399985i	$0.869015\pi$
$954$	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	$0.200219\pi$
$971$			1142.56i			1.17668i	−0.808613	+	0.588341i	$0.799781\pi$
$972$	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	$-0.993695\pi$
$977$		−	38.6989i		−	0.0396099i	0.999804	−	0.0198050i	$-0.00630453\pi$
$978$	−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	$0.211565\pi$
$983$			1212.60i			1.23357i	−0.787132	+	0.616784i	$0.788435\pi$
$984$	−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.122.2		4
3.2	odd	2	inner	363.3.b.g.122.3		4
11.2	odd	10		33.3.h.a.26.2	yes	8
11.3	even	5		363.3.h.i.251.1		8
11.4	even	5		363.3.h.i.269.2		8
11.5	even	5		363.3.h.g.245.2		8
11.6	odd	10		33.3.h.a.14.1	✓	8
11.7	odd	10		363.3.h.h.269.1		8
11.8	odd	10		363.3.h.h.251.2		8
11.9	even	5		363.3.h.g.323.1		8
11.10	odd	2		363.3.b.f.122.4		4
33.2	even	10		33.3.h.a.26.1	yes	8
33.5	odd	10		363.3.h.g.245.1		8
33.8	even	10		363.3.h.h.251.1		8
33.14	odd	10		363.3.h.i.251.2		8
33.17	even	10		33.3.h.a.14.2	yes	8
33.20	odd	10		363.3.h.g.323.2		8
33.26	odd	10		363.3.h.i.269.1		8
33.29	even	10		363.3.h.h.269.2		8
33.32	even	2		363.3.b.f.122.1		4

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

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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