LMFDB - Embedded newform 363.3.b.l.122.8

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 $ x^8 + 29x^6 + 282x^4 + 1061*x^2 + 1331
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.8
Root			$3.58727i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.l.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.58727i q^{2} +(-2.74329 + 1.21424i) q^{3} -8.86854 q^{4} +2.08639i q^{5} +(-4.35581 - 9.84093i) q^{6} -8.86303 q^{7} -17.4648i q^{8} +(6.05125 - 6.66201i) q^{9} +O(q^{10})$	\(q+3.58727i q^{2} +(-2.74329 + 1.21424i) q^{3} -8.86854 q^{4} +2.08639i q^{5} +(-4.35581 - 9.84093i) q^{6} -8.86303 q^{7} -17.4648i q^{8} +(6.05125 - 6.66201i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +1.64480 q^{13} -31.7941i q^{14} +(-2.53338 - 5.72358i) q^{15} +27.1769 q^{16} +12.4235i q^{17} +(23.8985 + 21.7075i) q^{18} -10.5657 q^{19} -18.5033i q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(21.2064 + 47.9109i) q^{24} +20.6470 q^{25} +5.90037i q^{26} +(-8.51105 + 25.6235i) q^{27} +78.6021 q^{28} +11.6087i q^{29} +(20.5320 - 9.08793i) q^{30} -23.3883 q^{31} +27.6317i q^{32} -44.5665 q^{34} -18.4918i q^{35} +(-53.6658 + 59.0823i) q^{36} +7.24593 q^{37} -37.9019i q^{38} +(-4.51217 + 1.99719i) q^{39} +36.4384 q^{40} +38.8768i q^{41} +(38.6056 + 87.2204i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +72.9572 q^{46} -45.3086i q^{47} +(-74.5539 + 32.9992i) q^{48} +29.5532 q^{49} +74.0663i q^{50} +(-15.0851 - 34.0812i) q^{51} -14.5870 q^{52} -40.3160i q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(28.9847 - 12.8292i) q^{57} -41.6435 q^{58} -113.181i q^{59} +(22.4674 + 50.7598i) q^{60} -77.5161 q^{61} -83.9001i q^{62} +(-53.6324 + 59.0456i) q^{63} +9.58504 q^{64} +3.43171i q^{65} +62.9082 q^{67} -110.178i q^{68} +(24.6949 + 55.7924i) q^{69} +66.3350 q^{70} +10.2125i q^{71} +(-116.351 - 105.684i) q^{72} +74.6222 q^{73} +25.9931i q^{74} +(-56.6405 + 25.0703i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} -86.3123 q^{79} +56.7016i q^{80} +(-7.76472 - 80.6270i) q^{81} -139.462 q^{82} +11.8083i q^{83} +(-215.628 + 95.4417i) q^{84} -25.9203 q^{85} +56.8381i q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(-45.2904 + 49.8616i) q^{90} -14.5779 q^{91} +180.366i q^{92} +(64.1607 - 28.3989i) q^{93} +162.534 q^{94} -22.0441i q^{95} +(-33.5514 - 75.8016i) q^{96} -77.1678 q^{97} +106.016i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * 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 $

$2$			3.58727i			1.79364i	0.442398	+	0.896819i	$0.354128\pi$
$2$			3.58727i			1.79364i	−0.442398	+	0.896819i	$0.645872\pi$
$3$	−2.74329	+	1.21424i	−0.914429	+	0.404746i
$3$	−2.74329	+	1.21424i	−0.914429	+	0.404746i
$4$	−8.86854			−2.21714
$5$			2.08639i			0.417279i	0.977993	+	0.208639i	$0.0669035\pi$
$5$			2.08639i			0.417279i	−0.977993	+	0.208639i	$0.933097\pi$
$6$	−4.35581	−	9.84093i	−0.725968	−	1.64015i
$7$	−8.86303			−1.26615			−0.633073	−	0.774092i	$-0.718207\pi$
$7$	−8.86303			−1.26615			−0.633073	+	0.774092i	$0.718207\pi$
$8$		−	17.4648i		−	2.18310i
$9$	6.05125	−	6.66201i	0.672361	−	0.740223i
$10$	−7.48447			−0.748447
$11$		0			0
$11$		0			0
$12$	24.3290	−	10.7685i	2.02741	−	0.897377i
$13$	1.64480			0.126523			0.0632617	−	0.997997i	$-0.479850\pi$
$13$	1.64480			0.126523			0.0632617	+	0.997997i	$0.479850\pi$
$14$		−	31.7941i		−	2.27101i
$15$	−2.53338	−	5.72358i	−0.168892	−	0.381572i
$16$	27.1769			1.69855
$17$			12.4235i			0.730794i	0.930852	+	0.365397i	$0.119067\pi$
$17$			12.4235i			0.730794i	−0.930852	+	0.365397i	$0.880933\pi$
$18$	23.8985	+	21.7075i	1.32769	+	1.20597i
$19$	−10.5657			−0.556088			−0.278044	−	0.960568i	$-0.589686\pi$
$19$	−10.5657			−0.556088			−0.278044	+	0.960568i	$0.589686\pi$
$20$		−	18.5033i		−	0.925163i
$21$	24.3138	−	10.7618i	1.15780	−	0.512468i
$22$		0			0
$23$		−	20.3378i		−	0.884251i	−0.896953	−	0.442126i	$-0.854225\pi$
$23$		−	20.3378i		−	0.884251i	0.896953	−	0.442126i	$-0.145775\pi$
$24$	21.2064	+	47.9109i	0.883601	+	1.99629i
$25$	20.6470			0.825878
$26$			5.90037i			0.226937i
$27$	−8.51105	+	25.6235i	−0.315224	+	0.949017i
$28$	78.6021			2.80722
$29$			11.6087i			0.400299i	0.979765	+	0.200149i	$0.0641428\pi$
$29$			11.6087i			0.400299i	−0.979765	+	0.200149i	$0.935857\pi$
$30$	20.5320	−	9.08793i	0.684402	−	0.302931i
$31$	−23.3883			−0.754460			−0.377230	−	0.926120i	$-0.623123\pi$
$31$	−23.3883			−0.754460			−0.377230	+	0.926120i	$0.623123\pi$
$32$			27.6317i			0.863489i
$33$		0			0
$34$	−44.5665			−1.31078
$35$		−	18.4918i		−	0.528336i
$36$	−53.6658	+	59.0823i	−1.49072	+	1.64117i
$37$	7.24593			0.195836			0.0979179	−	0.995194i	$-0.468782\pi$
$37$	7.24593			0.195836			0.0979179	+	0.995194i	$0.468782\pi$
$38$		−	37.9019i		−	0.997420i
$39$	−4.51217	+	1.99719i	−0.115697	+	0.0512099i
$40$	36.4384			0.910961
$41$			38.8768i			0.948215i	0.880467	+	0.474108i	$0.157229\pi$
$41$			38.8768i			0.948215i	−0.880467	+	0.474108i	$0.842771\pi$
$42$	38.6056	+	87.2204i	0.919181	+	2.07668i
$43$	15.8444			0.368474			0.184237	−	0.982882i	$-0.441019\pi$
$43$	15.8444			0.368474			0.184237	+	0.982882i	$0.441019\pi$
$44$		0			0
$45$	13.8996	+	12.6253i	0.308879	+	0.280562i
$46$	72.9572			1.58603
$47$		−	45.3086i		−	0.964013i	−0.876168	−	0.482006i	$-0.839908\pi$
$47$		−	45.3086i		−	0.964013i	0.876168	−	0.482006i	$-0.160092\pi$
$48$	−74.5539	+	32.9992i	−1.55321	+	0.687483i
$49$	29.5532			0.603127
$50$			74.0663i			1.48133i
$51$	−15.0851	−	34.0812i	−0.295786	−	0.668259i
$52$	−14.5870			−0.280520
$53$		−	40.3160i		−	0.760680i	−0.924847	−	0.380340i	$-0.875807\pi$
$53$		−	40.3160i		−	0.760680i	0.924847	−	0.380340i	$-0.124193\pi$
$54$	−91.9184	−	30.5315i	−1.70219	−	0.565398i
$55$		0			0
$56$			154.791i			2.76412i
$57$	28.9847	−	12.8292i	0.508503	−	0.225074i
$58$	−41.6435			−0.717991
$59$		−	113.181i		−	1.91833i	−0.282847	−	0.959165i	$-0.591279\pi$
$59$		−	113.181i		−	1.91833i	0.282847	−	0.959165i	$-0.408721\pi$
$60$	22.4674	+	50.7598i	0.374456	+	0.845996i
$61$	−77.5161			−1.27076			−0.635378	−	0.772202i	$-0.719156\pi$
$61$	−77.5161			−1.27076			−0.635378	+	0.772202i	$0.719156\pi$
$62$		−	83.9001i		−	1.35323i
$63$	−53.6324	+	59.0456i	−0.851308	+	0.937231i
$64$	9.58504			0.149766
$65$			3.43171i			0.0527956i
$66$		0			0
$67$	62.9082			0.938929			0.469464	−	0.882951i	$-0.344447\pi$
$67$	62.9082			0.938929			0.469464	+	0.882951i	$0.344447\pi$
$68$		−	110.178i		−	1.62027i
$69$	24.6949	+	55.7924i	0.357897	+	0.808585i
$70$	66.3350			0.947643
$71$			10.2125i			0.143839i	0.997410	+	0.0719193i	$0.0229124\pi$
$71$			10.2125i			0.143839i	−0.997410	+	0.0719193i	$0.977088\pi$
$72$	−116.351	−	105.684i	−1.61598	−	1.46783i
$73$	74.6222			1.02222			0.511111	−	0.859515i	$-0.329234\pi$
$73$	74.6222			1.02222			0.511111	+	0.859515i	$0.329234\pi$
$74$			25.9931i			0.351258i
$75$	−56.6405	+	25.0703i	−0.755207	+	0.334271i
$76$	93.7020			1.23292
$77$		0			0
$78$	−7.16445	−	16.1864i	−0.0918519	−	0.207518i
$79$	−86.3123			−1.09256			−0.546280	−	0.837602i	$-0.683957\pi$
$79$	−86.3123			−1.09256			−0.546280	+	0.837602i	$0.683957\pi$
$80$			56.7016i			0.708770i
$81$	−7.76472	−	80.6270i	−0.0958608	−	0.995395i
$82$	−139.462			−1.70075
$83$			11.8083i			0.142269i	0.997467	+	0.0711343i	$0.0226619\pi$
$83$			11.8083i			0.142269i	−0.997467	+	0.0711343i	$0.977338\pi$
$84$	−215.628	+	95.4417i	−2.56700	+	1.13621i
$85$	−25.9203			−0.304945
$86$			56.8381i			0.660908i
$87$	−14.0957	−	31.8459i	−0.162019	−	0.366045i
$88$		0			0
$89$		−	74.5782i		−	0.837957i	−0.907996	−	0.418979i	$-0.862388\pi$
$89$		−	74.5782i		−	0.837957i	0.907996	−	0.418979i	$-0.137612\pi$
$90$	−45.2904	+	49.8616i	−0.503227	+	0.554018i
$91$	−14.5779			−0.160197
$92$			180.366i			1.96050i
$93$	64.1607	−	28.3989i	0.689900	−	0.305365i
$94$	162.534			1.72909
$95$		−	22.0441i		−	0.232044i
$96$	−33.5514	−	75.8016i	−0.349494	−	0.789600i
$97$	−77.1678			−0.795544			−0.397772	−	0.917484i	$-0.630217\pi$
$97$	−77.1678			−0.795544			−0.397772	+	0.917484i	$0.630217\pi$
$98$			106.016i			1.08179i
$99$		0			0
$100$	−183.108			−1.83108
$101$			12.7954i			0.126687i	0.997992	+	0.0633436i	$0.0201764\pi$
$101$			12.7954i			0.126687i	−0.997992	+	0.0633436i	$0.979824\pi$
$102$	122.259	−	54.1143i	1.19861	−	0.530533i
$103$	70.5641			0.685088			0.342544	−	0.939502i	$-0.388711\pi$
$103$	70.5641			0.685088			0.342544	+	0.939502i	$0.388711\pi$
$104$		−	28.7262i		−	0.276213i
$105$	22.4534	+	50.7282i	0.213842	+	0.483126i
$106$	144.625			1.36438
$107$		−	184.220i		−	1.72168i	−0.508873	−	0.860842i	$-0.669938\pi$
$107$		−	184.220i		−	1.72168i	0.508873	−	0.860842i	$-0.330062\pi$
$108$	75.4806	−	227.243i	0.698895	−	2.10410i
$109$	58.5394			0.537058			0.268529	−	0.963272i	$-0.413462\pi$
$109$	58.5394			0.537058			0.268529	+	0.963272i	$0.413462\pi$
$110$		0			0
$111$	−19.8777	+	8.79828i	−0.179078	+	0.0792638i
$112$	−240.869			−2.15062
$113$		−	151.997i		−	1.34511i	−0.740048	−	0.672555i	$-0.765197\pi$
$113$		−	151.997i		−	1.34511i	0.740048	−	0.672555i	$-0.234803\pi$
$114$	46.0220	+	103.976i	0.403702	+	0.912070i
$115$	42.4326			0.368979
$116$		−	102.952i		−	0.887517i
$117$	9.95313	−	10.9577i	0.0850695	−	0.0936556i
$118$	406.013			3.44079
$119$		−	110.110i		−	0.925292i
$120$	−99.9611	+	44.2449i	−0.833009	+	0.368708i
$121$		0			0
$122$		−	278.071i		−	2.27927i
$123$	−47.2057	−	106.650i	−0.383786	−	0.867076i
$124$	207.420			1.67274
$125$			95.2375i			0.761900i
$126$	−211.813	−	192.394i	−1.68105	−	1.52694i
$127$	14.2743			0.112396			0.0561979	−	0.998420i	$-0.482102\pi$
$127$	14.2743			0.112396			0.0561979	+	0.998420i	$0.482102\pi$
$128$			144.911i			1.13212i
$129$	−43.4657	+	19.2388i	−0.336943	+	0.149138i
$130$	−12.3105			−0.0946961
$131$		−	153.686i		−	1.17318i	−0.809885	−	0.586589i	$-0.800471\pi$
$131$		−	153.686i		−	1.17318i	0.809885	−	0.586589i	$-0.199529\pi$
$132$		0			0
$133$	93.6438			0.704088
$134$			225.669i			1.68410i
$135$	−53.4606	−	17.7574i	−0.396005	−	0.131536i
$136$	216.974			1.59540
$137$			80.6411i			0.588621i	0.955710	+	0.294311i	$0.0950900\pi$
$137$			80.6411i			0.588621i	−0.955710	+	0.294311i	$0.904910\pi$
$138$	−200.143	+	88.5874i	−1.45031	+	0.641938i
$139$	−211.941			−1.52476			−0.762379	−	0.647130i	$-0.775969\pi$
$139$	−211.941			−1.52476			−0.762379	+	0.647130i	$0.775969\pi$
$140$			163.995i			1.17139i
$141$	55.0154	+	124.295i	0.390180	+	0.881521i
$142$	−36.6352			−0.257994
$143$		0			0
$144$	164.454	−	181.052i	1.14204	−	1.25731i
$145$	−24.2202			−0.167036
$146$			267.690i			1.83350i
$147$	−81.0730	+	35.8847i	−0.551517	+	0.244113i
$148$	−64.2608			−0.434194
$149$		−	226.330i		−	1.51899i	−0.650513	−	0.759495i	$-0.725446\pi$
$149$		−	226.330i		−	1.51899i	0.650513	−	0.759495i	$-0.274554\pi$
$150$	−89.9342	−	203.185i	−0.599561	−	1.35457i
$151$	−272.729			−1.80615			−0.903076	−	0.429481i	$-0.858696\pi$
$151$	−272.729			−1.80615			−0.903076	+	0.429481i	$0.858696\pi$
$152$			184.527i			1.21399i
$153$	82.7654	+	75.1777i	0.540951	+	0.491357i
$154$		0			0
$155$		−	48.7971i		−	0.314820i
$156$	40.0164	−	17.7121i	0.256515	−	0.113539i
$157$	6.05930			0.0385943			0.0192971	−	0.999814i	$-0.493857\pi$
$157$	6.05930			0.0385943			0.0192971	+	0.999814i	$0.493857\pi$
$158$		−	309.626i		−	1.95966i
$159$	48.9533	+	110.598i	0.307882	+	0.695588i
$160$	−57.6505			−0.360316
$161$			180.254i			1.11959i
$162$	289.231	−	27.8542i	1.78538	−	0.171939i
$163$	161.927			0.993416			0.496708	−	0.867918i	$-0.334542\pi$
$163$	161.927			0.993416			0.496708	+	0.867918i	$0.334542\pi$
$164$		−	344.781i		−	2.10232i
$165$		0			0
$166$	−42.3596			−0.255178
$167$			159.209i			0.953347i	0.879081	+	0.476673i	$0.158158\pi$
$167$			159.209i			0.953347i	−0.879081	+	0.476673i	$0.841842\pi$
$168$	−187.953	−	424.636i	−1.11877	−	2.52759i
$169$	−166.295			−0.983992
$170$		−	92.9832i		−	0.546960i
$171$	−63.9355	+	70.3886i	−0.373892	+	0.411629i
$172$	−140.516			−0.816956
$173$		−	38.4198i		−	0.222080i	−0.993816	−	0.111040i	$-0.964582\pi$
$173$		−	38.4198i		−	0.222080i	0.993816	−	0.111040i	$-0.0354181\pi$
$174$	114.240	−	50.5651i	0.656552	−	0.290604i
$175$	−182.995			−1.04568
$176$		0			0
$177$	137.429	+	310.489i	0.776437	+	1.75418i
$178$	267.532			1.50299
$179$			136.154i			0.760635i	0.924856	+	0.380317i	$0.124185\pi$
$179$			136.154i			0.760635i	−0.924856	+	0.380317i	$0.875815\pi$
$180$	−123.269	−	111.968i	−0.684827	−	0.622044i
$181$	−130.340			−0.720110			−0.360055	−	0.932931i	$-0.617242\pi$
$181$	−130.340			−0.720110			−0.360055	+	0.932931i	$0.617242\pi$
$182$		−	52.2951i		−	0.287336i
$183$	212.649	−	94.1230i	1.16202	−	0.514333i
$184$	−355.195			−1.93041
$185$			15.1179i			0.0817181i
$186$	101.875	+	230.162i	0.547713	+	1.23743i
$187$		0			0
$188$			401.821i			2.13735i
$189$	75.4337	−	227.101i	0.399120	−	1.20159i
$190$	79.0784			0.416202
$191$			315.580i			1.65225i	0.563486	+	0.826125i	$0.309460\pi$
$191$			315.580i			1.65225i	−0.563486	+	0.826125i	$0.690540\pi$
$192$	−26.2945	+	11.6385i	−0.136951	+	0.0606173i
$193$	−146.410			−0.758601			−0.379300	−	0.925274i	$-0.623835\pi$
$193$	−146.410			−0.758601			−0.379300	+	0.925274i	$0.623835\pi$
$194$		−	276.822i		−	1.42692i
$195$	−4.16691	−	9.41417i	−0.0213688	−	0.0482778i
$196$	−262.094			−1.33721
$197$			229.459i			1.16476i	0.812915	+	0.582382i	$0.197879\pi$
$197$			229.459i			1.16476i	−0.812915	+	0.582382i	$0.802121\pi$
$198$		0			0
$199$	−389.358			−1.95657			−0.978287	−	0.207253i	$-0.933548\pi$
$199$	−389.358			−1.95657			−0.978287	+	0.207253i	$0.933548\pi$
$200$		−	360.595i		−	1.80297i
$201$	−172.575	+	76.3856i	−0.858584	+	0.380028i
$202$	−45.9006			−0.227231
$203$		−	102.888i		−	0.506837i
$204$	133.783	+	302.251i	0.655797	+	1.48162i
$205$	−81.1124			−0.395670
$206$			253.133i			1.22880i
$207$	−135.490	−	123.069i	−0.654543	−	0.594536i
$208$	44.7006			0.214907
$209$		0			0
$210$	−181.976	+	80.5465i	−0.866553	+	0.383555i
$211$	−203.989			−0.966774			−0.483387	−	0.875407i	$-0.660594\pi$
$211$	−203.989			−0.966774			−0.483387	+	0.875407i	$0.660594\pi$
$212$			357.544i			1.68653i
$213$	−12.4005	−	28.0159i	−0.0582181	−	0.131530i
$214$	660.848			3.08808
$215$			33.0576i			0.153756i
$216$	447.509	+	148.644i	2.07180	+	0.688166i
$217$	207.291			0.955257
$218$			209.997i			0.963288i
$219$	−204.710	+	90.6091i	−0.934750	+	0.413740i
$220$		0			0
$221$			20.4342i			0.0924626i
$222$	−31.5618	−	71.3066i	−0.142170	−	0.321201i
$223$	−16.5198			−0.0740799			−0.0370399	−	0.999314i	$-0.511793\pi$
$223$	−16.5198			−0.0740799			−0.0370399	+	0.999314i	$0.511793\pi$
$224$		−	244.900i		−	1.09330i
$225$	124.940	−	137.550i	0.555289	−	0.611334i
$226$	545.256			2.41264
$227$			112.858i			0.497173i	0.968610	+	0.248587i	$0.0799661\pi$
$227$			112.858i			0.497173i	−0.968610	+	0.248587i	$0.920034\pi$
$228$	−257.052	+	113.777i	−1.12742	+	0.499020i
$229$	−368.618			−1.60969			−0.804843	−	0.593487i	$-0.797751\pi$
$229$	−368.618			−1.60969			−0.804843	+	0.593487i	$0.797751\pi$
$230$			152.217i			0.661815i
$231$		0			0
$232$	202.743			0.873892
$233$			174.540i			0.749100i	0.927207	+	0.374550i	$0.122203\pi$
$233$			174.540i			0.749100i	−0.927207	+	0.374550i	$0.877797\pi$
$234$	39.3083	+	35.7046i	0.167984	+	0.152584i
$235$	94.5316			0.402262
$236$			1003.75i			4.25320i
$237$	236.779	−	104.804i	0.999069	−	0.442210i
$238$	394.994			1.65964
$239$		−	345.353i		−	1.44499i	−0.691375	−	0.722496i	$-0.742995\pi$
$239$		−	345.353i		−	1.44499i	0.691375	−	0.722496i	$-0.257005\pi$
$240$	−68.8493	−	155.549i	−0.286872	−	0.648120i
$241$	261.447			1.08484			0.542421	−	0.840107i	$-0.317508\pi$
$241$	261.447			1.08484			0.542421	+	0.840107i	$0.317508\pi$
$242$		0			0
$243$	119.201	+	211.755i	0.490540	+	0.871419i
$244$	687.454			2.81744
$245$			61.6597i			0.251672i
$246$	382.584	−	169.340i	1.55522	−	0.688374i
$247$	−17.3785			−0.0703581
$248$			408.471i			1.64706i
$249$	−14.3381	−	32.3935i	−0.0575826	−	0.130095i
$250$	−341.643			−1.36657
$251$			198.345i			0.790220i	0.918634	+	0.395110i	$0.129294\pi$
$251$			198.345i			0.790220i	−0.918634	+	0.395110i	$0.870706\pi$
$252$	475.641	−	523.648i	1.88746	−	2.07797i
$253$		0			0
$254$			51.2057i			0.201597i
$255$	71.1068	−	31.4734i	0.278850	−	0.123425i
$256$	−481.495			−1.88084
$257$			1.86519i			0.00725755i	0.999993	+	0.00362878i	$0.00115508\pi$
$257$			1.86519i			0.00725755i	−0.999993	+	0.00362878i	$0.998845\pi$
$258$	−69.0150	−	155.923i	−0.267500	−	0.604354i
$259$	−64.2208			−0.247957
$260$		−	30.4343i		−	0.117055i
$261$	77.3370	+	70.2469i	0.296310	+	0.269145i
$262$	551.315			2.10425
$263$		−	27.0901i		−	0.103004i	−0.998673	−	0.0515020i	$-0.983599\pi$
$263$		−	27.0901i		−	0.103004i	0.998673	−	0.0515020i	$-0.0164009\pi$
$264$		0			0
$265$	84.1151			0.317416
$266$			335.926i			1.26288i
$267$	90.5557	+	204.589i	0.339160	+	0.766252i
$268$	−557.904			−2.08173
$269$		−	142.848i		−	0.531033i	−0.964106	−	0.265516i	$-0.914458\pi$
$269$		−	142.848i		−	0.531033i	0.964106	−	0.265516i	$-0.0855425\pi$
$270$	63.7007	−	191.778i	0.235929	−	0.710289i
$271$	105.327			0.388661			0.194331	−	0.980936i	$-0.437746\pi$
$271$	105.327			0.388661			0.194331	+	0.980936i	$0.437746\pi$
$272$			337.631i			1.24129i
$273$	39.9915	−	17.7011i	0.146489	−	0.0648392i
$274$	−289.282			−1.05577
$275$		0			0
$276$	−219.008	−	494.797i	−0.793507	−	1.79274i
$277$	−244.920			−0.884186			−0.442093	−	0.896969i	$-0.645764\pi$
$277$	−244.920			−0.884186			−0.442093	+	0.896969i	$0.645764\pi$
$278$		−	760.292i		−	2.73486i
$279$	−141.528	+	155.813i	−0.507270	+	0.558469i
$280$	−322.955			−1.15341
$281$		−	65.1115i		−	0.231713i	−0.993266	−	0.115857i	$-0.963039\pi$
$281$		−	65.1115i		−	0.231713i	0.993266	−	0.115857i	$-0.0369613\pi$
$282$	−445.879	+	197.356i	−1.58113	+	0.699842i
$283$	157.576			0.556805			0.278403	−	0.960464i	$-0.410195\pi$
$283$	157.576			0.556805			0.278403	+	0.960464i	$0.410195\pi$
$284$		−	90.5703i		−	0.318910i
$285$	26.7668	+	60.4734i	0.0939187	+	0.212187i
$286$		0			0
$287$		−	344.566i		−	1.20058i
$288$	184.082	+	167.206i	0.639175	+	0.580577i
$289$	134.657			0.465940
$290$		−	86.8847i		−	0.299602i
$291$	211.693	−	93.7001i	0.727469	−	0.321993i
$292$	−661.790			−2.26640
$293$		−	184.009i		−	0.628018i	−0.949420	−	0.314009i	$-0.898328\pi$
$293$		−	184.009i		−	0.628018i	0.949420	−	0.314009i	$-0.101672\pi$
$294$	−128.728	−	290.831i	−0.437851	−	0.989221i
$295$	236.141			0.800478
$296$		−	126.549i		−	0.427529i
$297$		0			0
$298$	811.906			2.72452
$299$		−	33.4517i		−	0.111879i
$300$	502.319	−	222.337i	1.67440	−	0.741124i
$301$	−140.429			−0.466542
$302$		−	978.353i		−	3.23958i
$303$	−15.5367	−	35.1015i	−0.0512761	−	0.115846i
$304$	−287.142			−0.944544
$305$		−	161.729i		−	0.530259i
$306$	−269.683	+	296.902i	−0.881317	+	0.970269i
$307$	−386.672			−1.25952			−0.629759	−	0.776790i	$-0.716846\pi$
$307$	−386.672			−1.25952			−0.629759	+	0.776790i	$0.716846\pi$
$308$		0			0
$309$	−193.578	+	85.6816i	−0.626465	+	0.277287i
$310$	175.049			0.564673
$311$		−	92.2420i		−	0.296598i	−0.988943	−	0.148299i	$-0.952620\pi$
$311$		−	92.2420i		−	0.296598i	0.988943	−	0.148299i	$-0.0473798\pi$
$312$	34.8804	+	78.8042i	0.111796	+	0.252577i
$313$	−74.3978			−0.237693			−0.118846	−	0.992913i	$-0.537920\pi$
$313$	−74.3978			−0.237693			−0.118846	+	0.992913i	$0.537920\pi$
$314$			21.7364i			0.0692242i
$315$	−123.192	−	111.898i	−0.391087	−	0.355233i
$316$	765.464			2.42236
$317$		−	523.779i		−	1.65230i	−0.563450	−	0.826150i	$-0.690526\pi$
$317$		−	523.779i		−	1.65230i	0.563450	−	0.826150i	$-0.309474\pi$
$318$	−396.747	+	175.609i	−1.24763	+	0.552229i
$319$		0			0
$320$			19.9982i			0.0624943i
$321$	223.687	+	505.369i	0.696845	+	1.57436i
$322$	−646.622			−2.00814
$323$		−	131.262i		−	0.406385i
$324$	68.8617	+	715.044i	0.212536	+	2.20692i
$325$	33.9602			0.104493
$326$			580.876i			1.78183i
$327$	−160.590	+	71.0807i	−0.491102	+	0.217372i
$328$	678.976			2.07005
$329$			401.571i			1.22058i
$330$		0			0
$331$	251.706			0.760441			0.380221	−	0.924896i	$-0.375848\pi$
$331$	251.706			0.760441			0.380221	+	0.924896i	$0.375848\pi$
$332$		−	104.722i		−	0.315429i
$333$	43.8469	−	48.2724i	0.131672	−	0.144962i
$334$	−571.126			−1.70996
$335$			131.251i			0.391795i
$336$	660.773	−	292.473i	1.96659	−	0.870454i
$337$	49.6503			0.147330			0.0736651	−	0.997283i	$-0.476530\pi$
$337$	49.6503			0.147330			0.0736651	+	0.997283i	$0.476530\pi$
$338$		−	596.544i		−	1.76492i
$339$	184.561	+	416.972i	0.544428	+	1.23001i
$340$	229.875			0.676104
$341$		0			0
$342$	−252.503	−	229.354i	−0.738313	−	0.670626i
$343$	172.357			0.502499
$344$		−	276.719i		−	0.804415i
$345$	−116.405	+	51.5233i	−0.337405	+	0.149343i
$346$	137.822			0.398330
$347$		−	459.779i		−	1.32501i	−0.749057	−	0.662505i	$-0.769493\pi$
$347$		−	459.779i		−	1.32501i	0.749057	−	0.662505i	$-0.230507\pi$
$348$	125.008	+	282.427i	0.359219	+	0.811571i
$349$	393.749			1.12822			0.564111	−	0.825699i	$-0.309219\pi$
$349$	393.749			1.12822			0.564111	+	0.825699i	$0.309219\pi$
$350$		−	656.452i		−	1.87558i
$351$	−13.9990	+	42.1456i	−0.0398833	+	0.120073i
$352$		0			0
$353$			16.9433i			0.0479980i	0.999712	+	0.0239990i	$0.00763985\pi$
$353$			16.9433i			0.0479980i	−0.999712	+	0.0239990i	$0.992360\pi$
$354$	−1113.81	+	492.997i	−3.14636	+	1.39265i
$355$	−21.3074			−0.0600208
$356$			661.400i			1.85786i
$357$	133.699	+	302.063i	0.374508	+	0.846114i
$358$	−488.421			−1.36430
$359$		−	75.8881i		−	0.211387i	−0.994399	−	0.105694i	$-0.966294\pi$
$359$		−	75.8881i		−	0.211387i	0.994399	−	0.105694i	$-0.0337063\pi$
$360$	220.498	−	242.753i	0.612495	−	0.674314i
$361$	−249.367			−0.690767
$362$		−	467.565i		−	1.29162i
$363$		0			0
$364$	129.285			0.355179
$365$			155.691i			0.426552i
$366$	337.645	+	762.830i	0.922527	+	2.08423i
$367$	619.307			1.68749			0.843743	−	0.536748i	$-0.180347\pi$
$367$	619.307			1.68749			0.843743	+	0.536748i	$0.180347\pi$
$368$		−	552.717i		−	1.50195i
$369$	258.998	+	235.253i	0.701891	+	0.637543i
$370$	−54.2319			−0.146573
$371$			357.322i			0.963132i
$372$	−569.012	+	251.857i	−1.52960	+	0.677035i
$373$	365.674			0.980359			0.490179	−	0.871622i	$-0.336931\pi$
$373$	365.674			0.980359			0.490179	+	0.871622i	$0.336931\pi$
$374$		0			0
$375$	−115.641	−	261.264i	−0.308376	−	0.696704i
$376$	−791.305			−2.10454
$377$			19.0940i			0.0506472i
$378$	814.675	+	270.601i	2.15523	+	0.715877i
$379$	−409.884			−1.08149			−0.540744	−	0.841187i	$-0.681857\pi$
$379$	−409.884			−1.08149			−0.540744	+	0.841187i	$0.681857\pi$
$380$			195.499i			0.514472i
$381$	−39.1584	+	17.3324i	−0.102778	+	0.0454918i
$382$	−1132.07			−2.96354
$383$		−	52.9616i		−	0.138281i	−0.997607	−	0.0691404i	$-0.977974\pi$
$383$		−	52.9616i		−	0.138281i	0.997607	−	0.0691404i	$-0.0220257\pi$
$384$	−175.956	−	397.532i	−0.458219	−	1.03524i
$385$		0			0
$386$		−	525.213i		−	1.36065i
$387$	95.8783	−	105.555i	0.247748	−	0.272753i
$388$	684.366			1.76383
$389$		−	90.6661i		−	0.233075i	−0.993186	−	0.116537i	$-0.962821\pi$
$389$		−	90.6661i		−	0.233075i	0.993186	−	0.116537i	$-0.0371795\pi$
$390$	33.7712	−	14.9479i	0.0865929	−	0.0383279i
$391$	252.666			0.646205
$392$		−	516.141i		−	1.31669i
$393$	186.612	+	421.606i	0.474839	+	1.07279i
$394$	−823.131			−2.08916
$395$		−	180.081i		−	0.455902i
$396$		0			0
$397$	−335.768			−0.845763			−0.422882	−	0.906185i	$-0.638981\pi$
$397$	−335.768			−0.845763			−0.422882	+	0.906185i	$0.638981\pi$
$398$		−	1396.74i		−	3.50939i
$399$	−256.892	+	113.706i	−0.643839	+	0.284977i
$400$	561.119			1.40280
$401$			18.9212i			0.0471849i	0.999722	+	0.0235925i	$0.00751041\pi$
$401$			18.9212i			0.0471849i	−0.999722	+	0.0235925i	$0.992490\pi$
$402$	−274.016	−	619.075i	−0.681632	−	1.53999i
$403$	−38.4691			−0.0954569
$404$		−	113.477i		−	0.280883i
$405$	168.220	−	16.2003i	0.415357	−	0.0400007i
$406$	369.087			0.909082
$407$		0			0
$408$	−595.221	+	263.458i	−1.45888	+	0.645730i
$409$	119.263			0.291596			0.145798	−	0.989314i	$-0.453425\pi$
$409$	119.263			0.291596			0.145798	+	0.989314i	$0.453425\pi$
$410$		−	290.972i		−	0.709689i
$411$	−97.9175	−	221.222i	−0.238242	−	0.538252i
$412$	−625.800			−1.51893
$413$			1003.13i			2.42889i
$414$	441.482	−	486.042i	1.06638	−	1.17401i
$415$	−24.6367			−0.0593657
$416$			45.4487i			0.109252i
$417$	581.416	−	257.347i	1.39428	−	0.617140i
$418$		0			0
$419$			412.874i			0.985381i	0.870205	+	0.492690i	$0.163986\pi$
$419$			412.874i			0.985381i	−0.870205	+	0.492690i	$0.836014\pi$
$420$	−199.129	−	449.885i	−0.474117	−	1.07116i
$421$	604.942			1.43692			0.718458	−	0.695570i	$-0.244848\pi$
$421$	604.942			1.43692			0.718458	+	0.695570i	$0.244848\pi$
$422$		−	731.766i		−	1.73404i
$423$	−301.846	−	274.174i	−0.713585	−	0.648165i
$424$	−704.111			−1.66064
$425$			256.507i			0.603547i
$426$	100.501	−	44.4839i	0.235918	−	0.104422i
$427$	687.027			1.60896
$428$			1633.76i			3.81721i
$429$		0			0
$430$	−118.587			−0.275783
$431$		−	443.420i		−	1.02882i	−0.857545	−	0.514409i	$-0.828011\pi$
$431$		−	443.420i		−	1.02882i	0.857545	−	0.514409i	$-0.171989\pi$
$432$	−231.304	+	696.365i	−0.535425	+	1.61196i
$433$	218.980			0.505727			0.252864	−	0.967502i	$-0.418628\pi$
$433$	218.980			0.505727			0.252864	+	0.967502i	$0.418628\pi$
$434$			743.609i			1.71338i
$435$	66.4431	−	29.4092i	0.152743	−	0.0676072i
$436$	−519.159			−1.19073
$437$			214.882i			0.491721i
$438$	−325.040	−	734.352i	−0.742100	−	1.67660i
$439$	−171.641			−0.390982			−0.195491	−	0.980705i	$-0.562630\pi$
$439$	−171.641			−0.390982			−0.195491	+	0.980705i	$0.562630\pi$
$440$		0			0
$441$	178.834	−	196.884i	0.405519	−	0.446449i
$442$	−73.3032			−0.165844
$443$		−	592.539i		−	1.33756i	−0.743461	−	0.668780i	$-0.766817\pi$
$443$		−	592.539i		−	1.33756i	0.743461	−	0.668780i	$-0.233183\pi$
$444$	176.286	−	78.0279i	0.397040	−	0.175739i
$445$	155.599			0.349662
$446$		−	59.2611i		−	0.132872i
$447$	274.818	+	620.887i	0.614805	+	1.38901i
$448$	−84.9525			−0.189626
$449$			436.128i			0.971331i	0.874145	+	0.485665i	$0.161423\pi$
$449$			436.128i			0.971331i	−0.874145	+	0.485665i	$0.838577\pi$
$450$	493.430	+	448.194i	1.09651	+	0.995986i
$451$		0			0
$452$			1347.99i			2.98229i
$453$	748.174	−	331.158i	1.65160	−	0.731033i
$454$	−404.854			−0.891749
$455$		−	30.4153i		−	0.0668469i
$456$	−224.060	−	506.211i	−0.491360	−	1.11011i
$457$	−238.541			−0.521973			−0.260986	−	0.965343i	$-0.584048\pi$
$457$	−238.541			−0.521973			−0.260986	+	0.965343i	$0.584048\pi$
$458$		−	1322.34i		−	2.88719i
$459$	−318.333	−	105.737i	−0.693536	−	0.230364i
$460$	−376.315			−0.818077
$461$		−	711.175i		−	1.54268i	−0.636424	−	0.771339i	$-0.719587\pi$
$461$		−	711.175i		−	1.54268i	0.636424	−	0.771339i	$-0.280413\pi$
$462$		0			0
$463$	−461.487			−0.996732			−0.498366	−	0.866967i	$-0.666066\pi$
$463$	−461.487			−0.996732			−0.498366	+	0.866967i	$0.666066\pi$
$464$			315.487i			0.679929i
$465$	59.2513	+	133.865i	0.127422	+	0.287881i
$466$	−626.124			−1.34361
$467$			48.3844i			0.103607i	0.998657	+	0.0518035i	$0.0164969\pi$
$467$			48.3844i			0.103607i	−0.998657	+	0.0518035i	$0.983503\pi$
$468$	−88.2697	+	97.1789i	−0.188611	+	0.207647i
$469$	−557.557			−1.18882
$470$			339.111i			0.721512i
$471$	−16.6224	+	7.35744i	−0.0352917	+	0.0156209i
$472$	−1976.69			−4.18790
$473$		0			0
$474$	375.960	+	849.393i	0.793164	+	1.79197i
$475$	−218.149			−0.459261
$476$			976.513i			2.05150i
$477$	−268.586	−	243.962i	−0.563073	−	0.511452i
$478$	1238.88			2.59179
$479$			171.425i			0.357880i	0.983860	+	0.178940i	$0.0572668\pi$
$479$			171.425i			0.357880i	−0.983860	+	0.178940i	$0.942733\pi$
$480$	158.152	−	70.0015i	0.329483	−	0.145836i
$481$	11.9181			0.0247778
$482$			937.883i			1.94581i
$483$	−218.872	−	494.489i	−0.453150	−	1.02379i
$484$		0			0
$485$		−	161.002i		−	0.331964i
$486$	−759.622	+	427.608i	−1.56301	+	0.879851i
$487$	−495.498			−1.01745			−0.508725	−	0.860929i	$-0.669883\pi$
$487$	−495.498			−1.01745			−0.508725	+	0.860929i	$0.669883\pi$
$488$			1353.80i			2.77418i
$489$	−444.212	+	196.618i	−0.908409	+	0.402081i
$490$	−221.190			−0.451408
$491$		−	330.249i		−	0.672604i	−0.941754	−	0.336302i	$-0.890824\pi$
$491$		−	330.249i		−	0.672604i	0.941754	−	0.336302i	$-0.109176\pi$
$492$	418.646	+	945.833i	0.850906	+	1.92242i
$493$	−144.220			−0.292536
$494$		−	62.3413i		−	0.126197i
$495$		0			0
$496$	−635.619			−1.28149
$497$		−	90.5140i		−	0.182121i
$498$	116.205	−	51.4346i	0.233342	−	0.103282i
$499$	109.801			0.220042			0.110021	−	0.993929i	$-0.464908\pi$
$499$	109.801			0.220042			0.110021	+	0.993929i	$0.464908\pi$
$500$		−	844.618i		−	1.68924i
$501$	−193.318	−	436.756i	−0.385863	−	0.871768i
$502$	−711.519			−1.41737
$503$			571.702i			1.13658i	0.822827	+	0.568292i	$0.192396\pi$
$503$			571.702i			1.13658i	−0.822827	+	0.568292i	$0.807604\pi$
$504$	1031.22	+	936.679i	2.04607	+	1.85849i
$505$	−26.6963			−0.0528639
$506$		0			0
$507$	456.194	−	201.921i	0.899791	−	0.398267i
$508$	−126.592			−0.249197
$509$			540.924i			1.06272i	0.847146	+	0.531360i	$0.178319\pi$
$509$			540.924i			1.06272i	−0.847146	+	0.531360i	$0.821681\pi$
$510$	112.904	+	255.080i	0.221380	+	0.500156i
$511$	−661.379			−1.29428
$512$		−	1147.61i		−	2.24143i
$513$	89.9250	−	270.729i	0.175292	−	0.527737i
$514$	−6.69095			−0.0130174
$515$			147.224i			0.285873i
$516$	385.477	−	170.620i	0.747049	−	0.330660i
$517$		0			0
$518$		−	230.378i		−	0.444745i
$519$	46.6507	+	105.396i	0.0898858	+	0.203076i
$520$	59.9341			0.115258
$521$		−	337.888i		−	0.648537i	−0.945965	−	0.324269i	$-0.894882\pi$
$521$		−	337.888i		−	0.648537i	0.945965	−	0.324269i	$-0.105118\pi$
$522$	−251.995	+	277.429i	−0.482749	+	0.531474i
$523$	−307.433			−0.587827			−0.293913	−	0.955832i	$-0.594958\pi$
$523$	−307.433			−0.587827			−0.293913	+	0.955832i	$0.594958\pi$
$524$			1362.97i			2.60109i
$525$	502.007	−	222.199i	0.956203	−	0.423236i
$526$	97.1795			0.184752
$527$		−	290.564i		−	0.551355i
$528$		0			0
$529$	115.375			0.218100
$530$			301.744i			0.569329i
$531$	−754.016	−	684.889i	−1.41999	−	1.28981i
$532$	−830.484			−1.56106
$533$			63.9448i			0.119971i
$534$	−733.918	+	324.848i	−1.37438	+	0.608330i
$535$	384.356			0.718422
$536$		−	1098.68i		−	2.04978i
$537$	−165.323	−	373.509i	−0.307864	−	0.695547i
$538$	512.434			0.952480
$539$		0			0
$540$	474.118	+	157.482i	0.877996	+	0.291634i
$541$	82.7018			0.152868			0.0764342	−	0.997075i	$-0.475646\pi$
$541$	82.7018			0.152868			0.0764342	+	0.997075i	$0.475646\pi$
$542$			377.838i			0.697118i
$543$	357.560	−	158.264i	0.658490	−	0.291462i
$544$	−343.282			−0.631033
$545$			122.136i			0.224103i
$546$	63.4987	+	143.461i	0.116298	+	0.262748i
$547$	396.695			0.725220			0.362610	−	0.931941i	$-0.381886\pi$
$547$	396.695			0.725220			0.362610	+	0.931941i	$0.381886\pi$
$548$		−	715.169i		−	1.30505i
$549$	−469.069	+	516.413i	−0.854407	+	0.940642i
$550$		0			0
$551$		−	122.653i		−	0.222601i
$552$	974.402	−	431.291i	1.76522	−	0.781325i
$553$	764.988			1.38334
$554$		−	878.594i		−	1.58591i
$555$	−18.3567	−	41.4726i	−0.0330751	−	0.0747254i
$556$	1879.61			3.38060
$557$		−	383.089i		−	0.687771i	−0.939012	−	0.343886i	$-0.888257\pi$
$557$		−	383.089i		−	0.687771i	0.939012	−	0.343886i	$-0.111743\pi$
$558$	−558.943	−	507.701i	−1.00169	−	0.909858i
$559$	26.0609			0.0466206
$560$		−	502.548i		−	0.897407i
$561$		0			0
$562$	233.573			0.415610
$563$			144.837i			0.257259i	0.991693	+	0.128629i	$0.0410577\pi$
$563$			144.837i			0.257259i	−0.991693	+	0.128629i	$0.958942\pi$
$564$	−487.907	−	1102.31i	−0.865083	−	1.95445i
$565$	317.126			0.561285
$566$			565.268i			0.998707i
$567$	68.8189	+	714.599i	0.121374	+	1.26032i
$568$	178.360			0.314014
$569$			923.151i			1.62241i	0.584763	+	0.811204i	$0.301188\pi$
$569$			923.151i			1.62241i	−0.584763	+	0.811204i	$0.698812\pi$
$570$	−216.935	+	96.0200i	−0.380587	+	0.168456i
$571$	−421.725			−0.738573			−0.369287	−	0.929316i	$-0.620398\pi$
$571$	−421.725			−0.738573			−0.369287	+	0.929316i	$0.620398\pi$
$572$		0			0
$573$	−383.189	−	865.726i	−0.668742	−	1.51087i
$574$	1236.05			2.15340
$575$		−	419.913i		−	0.730284i
$576$	58.0015	−	63.8556i	0.100697	−	0.110860i
$577$	460.408			0.797934			0.398967	−	0.916965i	$-0.369369\pi$
$577$	460.408			0.797934			0.398967	+	0.916965i	$0.369369\pi$
$578$			483.051i			0.835728i
$579$	401.644	−	177.776i	0.693686	−	0.307041i
$580$	214.798			0.370342
$581$		−	104.657i		−	0.180133i
$582$	336.128	+	759.403i	0.577539	+	1.30482i
$583$		0			0
$584$		−	1303.26i		−	2.23161i
$585$	22.8621	+	20.7661i	0.0390805	+	0.0354977i
$586$	660.091			1.12644
$587$		−	42.4644i		−	0.0723413i	−0.999346	−	0.0361707i	$-0.988484\pi$
$587$		−	42.4644i		−	0.0723413i	0.999346	−	0.0361707i	$-0.0115160\pi$
$588$	718.999	−	318.245i	1.22279	−	0.541232i
$589$	247.112			0.419546
$590$			847.103i			1.43577i
$591$	−278.617	−	629.471i	−0.471434	−	1.06509i
$592$	196.921			0.332638
$593$			106.267i			0.179203i	0.995978	+	0.0896015i	$0.0285593\pi$
$593$			106.267i			0.179203i	−0.995978	+	0.0896015i	$0.971441\pi$
$594$		0			0
$595$	229.732			0.386105
$596$			2007.21i			3.36781i
$597$	1068.12	−	472.774i	1.78915	−	0.791916i
$598$	120.000			0.200670
$599$		−	728.012i		−	1.21538i	−0.794174	−	0.607690i	$-0.792096\pi$
$599$		−	728.012i		−	1.21538i	0.794174	−	0.607690i	$-0.207904\pi$
$600$	437.848	+	989.215i	0.729747	+	1.64869i
$601$	118.594			0.197327			0.0986635	−	0.995121i	$-0.468543\pi$
$601$	118.594			0.197327			0.0986635	+	0.995121i	$0.468543\pi$
$602$		−	503.758i		−	0.836807i
$603$	380.674	−	419.095i	0.631299	−	0.695017i
$604$	2418.71			4.00448
$605$		0			0
$606$	125.919	−	55.7343i	0.207787	−	0.0919708i
$607$	−713.203			−1.17496			−0.587482	−	0.809237i	$-0.699881\pi$
$607$	−713.203			−1.17496			−0.587482	+	0.809237i	$0.699881\pi$
$608$		−	291.947i		−	0.480176i
$609$	124.930	+	282.251i	0.205140	+	0.463466i
$610$	580.167			0.951093
$611$		−	74.5238i		−	0.121970i
$612$	−734.009	−	666.716i	−1.19936	−	1.08941i
$613$	−687.465			−1.12148			−0.560739	−	0.827993i	$-0.689483\pi$
$613$	−687.465			−1.12148			−0.560739	+	0.827993i	$0.689483\pi$
$614$		−	1387.10i		−	2.25912i
$615$	222.515	−	98.4898i	0.361812	−	0.160146i
$616$		0			0
$617$		−	762.156i		−	1.23526i	−0.786468	−	0.617631i	$-0.788093\pi$
$617$		−	762.156i		−	1.23526i	0.786468	−	0.617631i	$-0.211907\pi$
$618$	−307.363	−	694.416i	−0.497352	−	1.12365i
$619$	−530.698			−0.857348			−0.428674	−	0.903459i	$-0.641019\pi$
$619$	−530.698			−0.857348			−0.428674	+	0.903459i	$0.641019\pi$
$620$			432.759i			0.697999i
$621$	521.124	+	173.096i	0.839170	+	0.278737i
$622$	330.897			0.531989
$623$			660.988i			1.06098i
$624$	−122.627	+	54.2772i	−0.196517	+	0.0869827i
$625$	317.471			0.507954
$626$		−	266.885i		−	0.426334i
$627$		0			0
$628$	−53.7372			−0.0855688
$629$			90.0197i			0.143116i
$630$	401.410	−	441.925i	0.637159	−	0.701468i
$631$	676.449			1.07203			0.536013	−	0.844210i	$-0.319930\pi$
$631$	676.449			1.07203			0.536013	+	0.844210i	$0.319930\pi$
$632$			1507.43i			2.38517i
$633$	559.602	−	247.692i	0.884047	−	0.391298i
$634$	1878.94			2.96363
$635$			29.7817i			0.0469004i
$636$	−434.144	−	980.847i	−0.682617	−	1.54221i
$637$	48.6093			0.0763097
$638$		0			0
$639$	68.0360	+	61.7987i	0.106473	+	0.0967115i
$640$	−302.341			−0.472408
$641$			785.884i			1.22603i	0.790072	+	0.613014i	$0.210043\pi$
$641$			785.884i			1.22603i	−0.790072	+	0.613014i	$0.789957\pi$
$642$	−1812.90	+	802.427i	−2.82383	+	1.24989i
$643$	−849.706			−1.32147			−0.660736	−	0.750619i	$-0.729756\pi$
$643$	−849.706			−1.32147			−0.660736	+	0.750619i	$0.729756\pi$
$644$		−	1598.59i		−	2.48229i
$645$	−40.1398	−	90.6865i	−0.0622323	−	0.140599i
$646$	470.875			0.728908
$647$			1169.38i			1.80738i	0.428184	+	0.903692i	$0.359154\pi$
$647$			1169.38i			1.80738i	−0.428184	+	0.903692i	$0.640846\pi$
$648$	−1408.13	+	135.609i	−2.17305	+	0.209274i
$649$		0			0
$650$			121.825i			0.187423i
$651$	−568.658	+	251.700i	−0.873515	+	0.386636i
$652$	−1436.05			−2.20254
$653$		−	535.533i		−	0.820111i	−0.912060	−	0.410056i	$-0.865509\pi$
$653$		−	535.533i		−	0.820111i	0.912060	−	0.410056i	$-0.134491\pi$
$654$	−254.986	−	576.082i	−0.389887	−	0.880859i
$655$	320.650			0.489542
$656$			1056.55i			1.61059i
$657$	451.558	−	497.134i	0.687303	−	0.756673i
$658$	−1440.55			−2.18928
$659$		−	138.756i		−	0.210555i	−0.994443	−	0.105278i	$-0.966427\pi$
$659$		−	138.756i		−	0.210555i	0.994443	−	0.105278i	$-0.0335731\pi$
$660$		0			0
$661$	27.1690			0.0411029			0.0205515	−	0.999789i	$-0.493458\pi$
$661$	27.1690			0.0411029			0.0205515	+	0.999789i	$0.493458\pi$
$662$			902.939i			1.36396i
$663$	−24.8120	−	56.0570i	−0.0374239	−	0.0845505i
$664$	206.229			0.310586
$665$			195.378i			0.293801i
$666$	173.166	+	157.291i	0.260010	+	0.236173i
$667$	236.094			0.353965
$668$		−	1411.95i		−	2.11370i
$669$	45.3186	−	20.0590i	0.0677408	−	0.0299835i
$670$	−470.835			−0.702738
$671$		0			0
$672$	297.367	+	671.831i	0.442511	+	0.999749i
$673$	657.485			0.976946			0.488473	−	0.872579i	$-0.337554\pi$
$673$	657.485			0.976946			0.488473	+	0.872579i	$0.337554\pi$
$674$			178.109i			0.264257i
$675$	−175.727	+	529.047i	−0.260337	+	0.783773i
$676$	1474.79			2.18164
$677$		−	611.265i		−	0.902902i	−0.892296	−	0.451451i	$-0.850907\pi$
$677$		−	611.265i		−	0.902902i	0.892296	−	0.451451i	$-0.149093\pi$
$678$	−1495.79	+	662.071i	−2.20619	+	0.976506i
$679$	683.940			1.00728
$680$			452.693i			0.665725i
$681$	−137.037	−	309.603i	−0.201229	−	0.454630i
$682$		0			0
$683$			990.520i			1.45025i	0.688618	+	0.725124i	$0.258218\pi$
$683$			990.520i			1.45025i	−0.688618	+	0.725124i	$0.741782\pi$
$684$	567.015	−	624.244i	0.828969	−	0.912637i
$685$	−168.249			−0.245619
$686$			618.293i			0.901302i
$687$	1011.23	−	447.590i	1.47194	−	0.651514i
$688$	430.600			0.625872
$689$		−	66.3120i		−	0.0962439i
$690$	−184.828	−	417.576i	−0.267867	−	0.605183i
$691$	573.077			0.829345			0.414672	−	0.909971i	$-0.363896\pi$
$691$	573.077			0.829345			0.414672	+	0.909971i	$0.363896\pi$
$692$			340.727i			0.492380i
$693$		0			0
$694$	1649.35			2.37659
$695$		−	442.193i		−	0.636249i
$696$	−556.182	+	246.178i	−0.799112	+	0.353704i
$697$	−482.986			−0.692950
$698$			1412.49i			2.02362i
$699$	−211.933	−	478.814i	−0.303195	−	0.684999i
$700$	1622.89			2.31842
$701$		−	819.026i		−	1.16837i	−0.811621	−	0.584184i	$-0.801415\pi$
$701$		−	819.026i		−	1.16837i	0.811621	−	0.584184i	$-0.198585\pi$
$702$	−151.188	−	50.2183i	−0.215367	−	0.0715361i
$703$	−76.5580			−0.108902
$704$		0			0
$705$	−259.327	+	114.784i	−0.367840	+	0.162814i
$706$	−60.7802			−0.0860910
$707$		−	113.406i		−	0.160405i
$708$	−1218.80	−	2753.59i	−1.72146	−	3.88925i
$709$	179.842			0.253656			0.126828	−	0.991925i	$-0.459520\pi$
$709$	179.842			0.253656			0.126828	+	0.991925i	$0.459520\pi$
$710$		−	76.4354i		−	0.107656i
$711$	−522.297	+	575.013i	−0.734596	+	0.808739i
$712$	−1302.49			−1.82934
$713$			475.665i			0.667132i
$714$	−1083.58	+	479.617i	−1.51762	+	0.671732i
$715$		0			0
$716$		−	1207.48i		−	1.68643i
$717$	419.341	+	947.403i	0.584855	+	1.32134i
$718$	272.231			0.379152
$719$			666.337i			0.926755i	0.886161	+	0.463378i	$0.153363\pi$
$719$			666.337i			0.926755i	−0.886161	+	0.463378i	$0.846637\pi$
$720$	377.747	+	343.116i	0.524648	+	0.476550i
$721$	−625.411			−0.867422
$722$		−	894.547i		−	1.23898i
$723$	−717.225	+	317.459i	−0.992012	+	0.439086i
$724$	1155.92			1.59658
$725$			239.684i			0.330598i
$726$		0			0
$727$	162.429			0.223424			0.111712	−	0.993741i	$-0.464367\pi$
$727$	162.429			0.223424			0.111712	+	0.993741i	$0.464367\pi$
$728$			254.601i			0.349726i
$729$	−584.124	−	436.165i	−0.801267	−	0.598306i
$730$	−558.508			−0.765079
$731$			196.842i			0.269278i
$732$	−1885.88	+	834.733i	−2.57635	+	1.14035i
$733$	−1169.88			−1.59602			−0.798008	−	0.602646i	$-0.794113\pi$
$733$	−1169.88			−1.59602			−0.798008	+	0.602646i	$0.794113\pi$
$734$			2221.62i			3.02674i
$735$	−74.8695	−	169.150i	−0.101863	−	0.230136i
$736$	561.967			0.763542
$737$		0			0
$738$	−843.919	+	929.096i	−1.14352	+	1.25894i
$739$	242.377			0.327979			0.163990	−	0.986462i	$-0.447564\pi$
$739$	242.377			0.327979			0.163990	+	0.986462i	$0.447564\pi$
$740$		−	134.073i		−	0.181180i
$741$	47.6741	−	21.1016i	0.0643375	−	0.0284772i
$742$	−1281.81			−1.72751
$743$			823.655i			1.10855i	0.832333	+	0.554277i	$0.187005\pi$
$743$			823.655i			1.10855i	−0.832333	+	0.554277i	$0.812995\pi$
$744$	−495.981	−	1120.55i	−0.666641	−	1.50612i
$745$	472.213			0.633842
$746$			1311.77i			1.75841i
$747$	78.6669	+	71.4549i	0.105310	+	0.0956559i
$748$		0			0
$749$			1632.75i			2.17990i
$750$	937.226	−	414.836i	1.24963	−	0.553115i
$751$	−6.13817			−0.00817333			−0.00408666	−	0.999992i	$-0.501301\pi$
$751$	−6.13817			−0.00817333			−0.00408666	+	0.999992i	$0.501301\pi$
$752$		−	1231.35i		−	1.63743i
$753$	−240.838	−	544.118i	−0.319839	−	0.722600i
$754$	−68.4954			−0.0908427
$755$		−	569.020i		−	0.753669i
$756$	−668.987	+	2014.06i	−0.884903	+	2.66410i
$757$	−1102.27			−1.45610			−0.728052	−	0.685522i	$-0.759574\pi$
$757$	−1102.27			−1.45610			−0.728052	+	0.685522i	$0.759574\pi$
$758$		−	1470.37i		−	1.93980i
$759$		0			0
$760$	−384.996			−0.506574
$761$		−	1200.28i		−	1.57724i	−0.614882	−	0.788619i	$-0.710796\pi$
$761$		−	1200.28i		−	1.57724i	0.614882	−	0.788619i	$-0.289204\pi$
$762$	−62.1759	−	140.472i	−0.0815957	−	0.184346i
$763$	−518.836			−0.679995
$764$		−	2798.73i		−	3.66326i
$765$	−156.850	+	172.681i	−0.205033	+	0.225727i
$766$	189.988			0.248026
$767$		−	186.161i		−	0.242714i
$768$	1320.88	−	584.649i	1.71989	−	0.761262i
$769$	1038.16			1.35001			0.675007	−	0.737811i	$-0.264141\pi$
$769$	1038.16			1.35001			0.675007	+	0.737811i	$0.264141\pi$
$770$		0			0
$771$	−2.26479	−	5.11676i	−0.00293747	−	0.00663652i
$772$	1298.44			1.68192
$773$			586.211i			0.758359i	0.925323	+	0.379179i	$0.123794\pi$
$773$			586.211i			0.758359i	−0.925323	+	0.379179i	$0.876206\pi$
$774$	378.656	+	343.942i	0.489220	+	0.444369i
$775$	−482.896			−0.623092
$776$			1347.72i			1.73675i
$777$	176.176	−	77.9794i	0.226739	−	0.100360i
$778$	325.244			0.418052
$779$		−	410.760i		−	0.527291i
$780$	36.9545	+	83.4899i	0.0473775	+	0.107038i
$781$		0			0
$782$			906.383i			1.15906i
$783$	−297.454	−	98.8020i	−0.379890	−	0.126184i
$784$	803.164			1.02444
$785$			12.6421i			0.0161046i
$786$	−1512.41	+	669.427i	−1.92419	+	0.851689i
$787$	−373.464			−0.474541			−0.237271	−	0.971444i	$-0.576253\pi$
$787$	−373.464			−0.474541			−0.237271	+	0.971444i	$0.576253\pi$
$788$		−	2034.96i		−	2.58244i
$789$	32.8938	+	74.3158i	0.0416905	+	0.0941899i
$790$	646.002			0.817724
$791$			1347.16i			1.70311i
$792$		0			0
$793$	−127.499			−0.160780
$794$		−	1204.49i		−	1.51699i
$795$	−230.752	+	102.136i	−0.290254	+	0.128473i
$796$	3453.04			4.33799
$797$			836.809i			1.04995i	0.851118	+	0.524974i	$0.175925\pi$
$797$			836.809i			1.04995i	−0.851118	+	0.524974i	$0.824075\pi$
$798$	−407.894	−	921.541i	−0.511145	−	1.15481i
$799$	562.891			0.704495
$800$			570.510i			0.713137i
$801$	−496.841	−	451.291i	−0.620275	−	0.563410i
$802$	−67.8754			−0.0846326
$803$		0			0
$804$	1530.49	−	677.429i	1.90360	−	0.842573i
$805$	−376.081			−0.467182
$806$		−	137.999i		−	0.171215i
$807$	173.451	+	391.873i	0.214933	+	0.485592i
$808$	223.469			0.276571
$809$		−	518.833i		−	0.641326i	−0.947193	−	0.320663i	$-0.896094\pi$
$809$		−	518.833i		−	0.641326i	0.947193	−	0.320663i	$-0.103906\pi$
$810$	58.1148	+	603.450i	0.0717467	+	0.745000i
$811$	−782.670			−0.965068			−0.482534	−	0.875877i	$-0.660284\pi$
$811$	−782.670			−0.965068			−0.482534	+	0.875877i	$0.660284\pi$
$812$			912.466i			1.12373i
$813$	−288.943	+	127.892i	−0.355403	+	0.157309i
$814$		0			0
$815$			337.843i			0.414531i
$816$	−409.965	−	926.220i	−0.502408	−	1.13507i
$817$	−167.406			−0.204904
$818$			427.828i			0.523017i
$819$	−88.2148	+	97.1184i	−0.107710	+	0.118582i
$820$	719.348			0.877254
$821$		−	551.621i		−	0.671889i	−0.941882	−	0.335944i	$-0.890945\pi$
$821$		−	551.621i		−	0.671889i	0.941882	−	0.335944i	$-0.109055\pi$
$822$	793.583	−	351.257i	0.965429	−	0.427320i
$823$	−46.1726			−0.0561028			−0.0280514	−	0.999606i	$-0.508930\pi$
$823$	−46.1726			−0.0561028			−0.0280514	+	0.999606i	$0.508930\pi$
$824$		−	1232.39i		−	1.49562i
$825$		0			0
$826$	−3598.50			−4.35654
$827$			596.211i			0.720932i	0.932772	+	0.360466i	$0.117382\pi$
$827$			596.211i			0.720932i	−0.932772	+	0.360466i	$0.882618\pi$
$828$	1201.60	+	1091.44i	1.45121	+	1.31817i
$829$	−1387.07			−1.67319			−0.836593	−	0.547825i	$-0.815456\pi$
$829$	−1387.07			−1.67319			−0.836593	+	0.547825i	$0.815456\pi$
$830$		−	88.3788i		−	0.106480i
$831$	671.885	−	297.391i	0.808526	−	0.357871i
$832$	15.7655			0.0189489
$833$			367.154i			0.440761i
$834$	923.176	+	2085.70i	1.10693	+	2.50084i
$835$	−332.172			−0.397811
$836$		0			0
$837$	199.059	−	599.288i	0.237824	−	0.715995i
$838$	−1481.09			−1.76742
$839$			1665.00i			1.98451i	0.124217	+	0.992255i	$0.460358\pi$
$839$			1665.00i			1.98451i	−0.124217	+	0.992255i	$0.539642\pi$
$840$	885.958	−	392.144i	1.05471	−	0.466838i
$841$	706.239			0.839761
$842$			2170.09i			2.57731i
$843$	79.0609	+	178.620i	0.0937851	+	0.211886i
$844$	1809.09			2.14347
$845$		−	346.956i		−	0.410599i
$846$	983.537	−	1082.81i	1.16257	−	1.27991i
$847$		0			0
$848$		−	1095.66i		−	1.29206i
$849$	−432.276	+	191.335i	−0.509159	+	0.225365i
$850$	−920.163			−1.08254
$851$		−	147.366i		−	0.173168i
$852$	109.974	+	248.460i	0.129077	+	0.291620i
$853$	812.549			0.952578			0.476289	−	0.879289i	$-0.341982\pi$
$853$	812.549			0.952578			0.476289	+	0.879289i	$0.341982\pi$
$854$			2464.55i			2.88589i
$855$	−146.858	−	133.395i	−0.171764	−	0.156017i
$856$	−3217.37			−3.75861
$857$			551.421i			0.643431i	0.946836	+	0.321716i	$0.104260\pi$
$857$			551.421i			0.643431i	−0.946836	+	0.321716i	$0.895740\pi$
$858$		0			0
$859$	−1196.04			−1.39236			−0.696180	−	0.717868i	$-0.745118\pi$
$859$	−1196.04			−1.39236			−0.696180	+	0.717868i	$0.745118\pi$
$860$		−	293.173i		−	0.340898i
$861$	418.386	+	945.245i	0.485930	+	1.09784i
$862$	1590.67			1.84533
$863$			716.382i			0.830106i	0.909797	+	0.415053i	$0.136237\pi$
$863$			716.382i			0.830106i	−0.909797	+	0.415053i	$0.863763\pi$
$864$	−708.019	−	235.175i	−0.819466	−	0.272193i
$865$	80.1588			0.0926691
$866$			785.541i			0.907091i
$867$	−369.402	+	163.505i	−0.426070	+	0.188588i
$868$	−1838.37			−2.11793
$869$		0			0
$870$	105.499	+	238.350i	0.121263	+	0.273965i
$871$	103.472			0.118797
$872$		−	1022.38i		−	1.17245i
$873$	−466.962	+	514.093i	−0.534893	+	0.588880i
$874$	−770.841			−0.881970
$875$		−	844.093i		−	0.964677i
$876$	1815.48	−	803.571i	2.07247	−	0.917318i
$877$	−991.635			−1.13071			−0.565357	−	0.824847i	$-0.691261\pi$
$877$	−991.635			−1.13071			−0.565357	+	0.824847i	$0.691261\pi$
$878$		−	615.724i		−	0.701280i
$879$	223.431	+	504.790i	0.254188	+	0.574278i
$880$		0			0
$881$			1256.55i			1.42628i	0.701021	+	0.713140i	$0.252728\pi$
$881$			1256.55i			1.42628i	−0.701021	+	0.713140i	$0.747272\pi$
$882$	706.276	+	641.527i	0.800767	+	0.727354i
$883$	278.326			0.315205			0.157603	−	0.987503i	$-0.449624\pi$
$883$	278.326			0.315205			0.157603	+	0.987503i	$0.449624\pi$
$884$		−	181.222i		−	0.205002i
$885$	−647.803	+	286.732i	−0.731981	+	0.323990i
$886$	2125.60			2.39910
$887$			1174.00i			1.32357i	0.749695	+	0.661784i	$0.230200\pi$
$887$			1174.00i			1.32357i	−0.749695	+	0.661784i	$0.769800\pi$
$888$	153.660	+	347.159i	0.173041	+	0.390945i
$889$	−126.513			−0.142310
$890$			558.178i			0.627166i
$891$		0			0
$892$	146.507			0.164245
$893$			478.716i			0.536076i
$894$	−2227.29	+	985.848i	−2.49138	+	1.10274i
$895$	−284.070			−0.317397
$896$		−	1284.35i		−	1.43342i
$897$	40.6183	+	91.7676i	0.0452824	+	0.102305i
$898$	−1564.51			−1.74222
$899$		−	271.506i		−	0.302009i
$900$	−1108.03	+	1219.87i	−1.23115	+	1.35541i
$901$	500.866			0.555900
$902$		0			0
$903$	385.237	−	170.514i	0.426619	−	0.188831i
$904$	−2654.60			−2.93651
$905$		−	271.940i		−	0.300487i
$906$	1187.95	+	2683.90i	1.31121	+	2.96237i
$907$	145.616			0.160547			0.0802736	−	0.996773i	$-0.474421\pi$
$907$	145.616			0.160547			0.0802736	+	0.996773i	$0.474421\pi$
$908$		−	1000.89i		−	1.10230i
$909$	85.2431	+	77.4282i	0.0937768	+	0.0851796i
$910$	109.108			0.119899
$911$		−	1076.70i		−	1.18189i	−0.806713	−	0.590943i	$-0.798756\pi$
$911$		−	1076.70i		−	1.18189i	0.806713	−	0.590943i	$-0.201244\pi$
$912$	787.712	−	348.658i	0.863719	−	0.382301i
$913$		0			0
$914$		−	855.714i		−	0.936230i
$915$	196.378	+	443.669i	0.214620	+	0.484884i
$916$	3269.11			3.56889
$917$			1362.13i			1.48541i
$918$	379.308	−	1141.95i	0.413189	−	1.24395i
$919$	−316.112			−0.343974			−0.171987	−	0.985099i	$-0.555019\pi$
$919$	−316.112			−0.343974			−0.171987	+	0.985099i	$0.555019\pi$
$920$		−	741.077i		−	0.805518i
$921$	1060.75	−	469.512i	1.15174	−	0.509785i
$922$	2551.18			2.76701
$923$			16.7976i			0.0181990i
$924$		0			0
$925$	149.606			0.161737
$926$		−	1655.48i		−	1.78778i
$927$	427.001	−	470.098i	0.460627	−	0.507118i
$928$	−320.767			−0.345654
$929$		−	1118.65i		−	1.20414i	−0.798442	−	0.602072i	$-0.794342\pi$
$929$		−	1118.65i		−	1.20414i	0.798442	−	0.602072i	$-0.205658\pi$
$930$	−480.209	+	212.551i	−0.516353	+	0.228549i
$931$	−312.249			−0.335391
$932$		−	1547.92i		−	1.66086i
$933$	112.004	+	253.046i	0.120047	+	0.271218i
$934$	−173.568			−0.185833
$935$		0			0
$936$	−191.374	−	173.829i	−0.204459	−	0.185715i
$937$	−1051.22			−1.12189			−0.560947	−	0.827852i	$-0.689563\pi$
$937$	−1051.22			−1.12189			−0.560947	+	0.827852i	$0.689563\pi$
$938$		−	2000.11i		−	2.13231i
$939$	204.094	−	90.3366i	0.217353	−	0.0962051i
$940$	−838.357			−0.891869
$941$			320.555i			0.340654i	0.985388	+	0.170327i	$0.0544824\pi$
$941$			320.555i			0.340654i	−0.985388	+	0.170327i	$0.945518\pi$
$942$	−26.3932	−	59.6292i	−0.0280182	−	0.0633006i
$943$	790.668			0.838461
$944$		−	3075.92i		−	3.25839i
$945$	473.823	+	157.384i	0.501400	+	0.166544i
$946$		0			0
$947$		−	689.980i		−	0.728596i	−0.931283	−	0.364298i	$-0.881309\pi$
$947$		−	689.980i		−	0.728596i	0.931283	−	0.364298i	$-0.118691\pi$
$948$	−2099.89	+	929.456i	−2.21507	+	0.980439i
$949$	122.739			0.129335
$950$		−	782.560i		−	0.823747i
$951$	635.993	+	1436.88i	0.668762	+	1.51091i
$952$	−1923.04			−2.02000
$953$		−	1342.08i		−	1.40827i	−0.710067	−	0.704134i	$-0.751335\pi$
$953$		−	1342.08i		−	1.40827i	0.710067	−	0.704134i	$-0.248665\pi$
$954$	875.160	−	963.491i	0.917359	−	1.00995i
$955$	−658.424			−0.689449
$956$			3062.78i			3.20374i
$957$		0			0
$958$	−614.947			−0.641907
$959$		−	714.724i		−	0.745281i
$960$	−24.2825	−	54.8607i	−0.0252943	−	0.0571466i
$961$	−413.990			−0.430790
$962$			42.7536i			0.0444424i
$963$	−1227.28	−	1114.76i	−1.27443	−	1.15759i
$964$	−2318.65			−2.40524
$965$		−	305.469i		−	0.316548i
$966$	1773.87	−	785.153i	1.83630	−	0.812787i
$967$	−1283.30			−1.32709			−0.663546	−	0.748135i	$-0.730949\pi$
$967$	−1283.30			−1.32709			−0.663546	+	0.748135i	$0.730949\pi$
$968$		0			0
$969$	159.384	+	360.091i	0.164483	+	0.371611i
$970$	577.560			0.595423
$971$		−	850.821i		−	0.876231i	−0.898919	−	0.438116i	$-0.855646\pi$
$971$		−	850.821i		−	0.876231i	0.898919	−	0.438116i	$-0.144354\pi$
$972$	−1057.14	−	1877.96i	−1.08759	−	1.93205i
$973$	1878.44			1.93057
$974$		−	1777.49i		−	1.82494i
$975$	−93.1626	+	41.2358i	−0.0955514	+	0.0422931i
$976$	−2106.64			−2.15845
$977$		−	1212.63i		−	1.24118i	−0.784136	−	0.620589i	$-0.786893\pi$
$977$		−	1212.63i		−	1.24118i	0.784136	−	0.620589i	$-0.213107\pi$
$978$	−705.322	−	1593.51i	−0.721188	−	1.62936i
$979$		0			0
$980$		−	546.831i		−	0.557991i
$981$	354.236	−	389.990i	0.361097	−	0.397543i
$982$	1184.69			1.20641
$983$		−	454.656i		−	0.462519i	−0.972892	−	0.231260i	$-0.925715\pi$
$983$		−	454.656i		−	0.462519i	0.972892	−	0.231260i	$-0.0742846\pi$
$984$	−1862.63	+	824.438i	−1.89291	+	0.837844i
$985$	−478.741			−0.486031
$986$		−	517.357i		−	0.524703i
$987$	−487.603	−	1101.63i	−0.494026	−	1.11614i
$988$	154.122			0.155993
$989$		−	322.239i		−	0.325823i
$990$		0			0
$991$	697.554			0.703889			0.351945	−	0.936021i	$-0.385521\pi$
$991$	697.554			0.703889			0.351945	+	0.936021i	$0.385521\pi$
$992$		−	646.256i		−	0.651468i
$993$	−690.502	+	305.631i	−0.695369	+	0.307786i
$994$	324.699			0.326659
$995$		−	812.355i		−	0.816437i
$996$	127.158	+	287.283i	0.127669	+	0.288437i
$997$	−653.975			−0.655943			−0.327971	−	0.944688i	$-0.606365\pi$
$997$	−653.975			−0.655943			−0.327971	+	0.944688i	$0.606365\pi$
$998$			393.885i			0.394675i
$999$	−61.6705	+	185.666i	−0.0617322	+	0.185852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.l.122.8		8
3.2	odd	2	inner	363.3.b.l.122.1		8
11.2	odd	10		33.3.h.b.26.1	yes	16
11.3	even	5		363.3.h.n.251.4		16
11.4	even	5		363.3.h.n.269.1		16
11.5	even	5		363.3.h.j.245.1		16
11.6	odd	10		33.3.h.b.14.4	yes	16
11.7	odd	10		363.3.h.o.269.4		16
11.8	odd	10		363.3.h.o.251.1		16
11.9	even	5		363.3.h.j.323.4		16
11.10	odd	2		363.3.b.m.122.1		8
33.2	even	10		33.3.h.b.26.4	yes	16
33.5	odd	10		363.3.h.j.245.4		16
33.8	even	10		363.3.h.o.251.4		16
33.14	odd	10		363.3.h.n.251.1		16
33.17	even	10		33.3.h.b.14.1	✓	16
33.20	odd	10		363.3.h.j.323.1		16
33.26	odd	10		363.3.h.n.269.4		16
33.29	even	10		363.3.h.o.269.1		16
33.32	even	2		363.3.b.m.122.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.1	✓	16	33.17	even	10
33.3.h.b.14.4	yes	16	11.6	odd	10
33.3.h.b.26.1	yes	16	11.2	odd	10
33.3.h.b.26.4	yes	16	33.2	even	10
363.3.b.l.122.1		8	3.2	odd	2	inner
363.3.b.l.122.8		8	1.1	even	1	trivial
363.3.b.m.122.1		8	11.10	odd	2
363.3.b.m.122.8		8	33.32	even	2
363.3.h.j.245.1		16	11.5	even	5
363.3.h.j.245.4		16	33.5	odd	10
363.3.h.j.323.1		16	33.20	odd	10
363.3.h.j.323.4		16	11.9	even	5
363.3.h.n.251.1		16	33.14	odd	10
363.3.h.n.251.4		16	11.3	even	5
363.3.h.n.269.1		16	11.4	even	5
363.3.h.n.269.4		16	33.26	odd	10
363.3.h.o.251.1		16	11.8	odd	10
363.3.h.o.251.4		16	33.8	even	10
363.3.h.o.269.1		16	33.29	even	10
363.3.h.o.269.4		16	11.7	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)

\(f(q)\)	\(=\)	\(q+3.58727i q^{2} +(-2.74329 + 1.21424i) q^{3} -8.86854 q^{4} +2.08639i q^{5} +(-4.35581 - 9.84093i) q^{6} -8.86303 q^{7} -17.4648i q^{8} +(6.05125 - 6.66201i) q^{9} +O(q^{10})\)	\(q+3.58727i q^{2} +(-2.74329 + 1.21424i) q^{3} -8.86854 q^{4} +2.08639i q^{5} +(-4.35581 - 9.84093i) q^{6} -8.86303 q^{7} -17.4648i q^{8} +(6.05125 - 6.66201i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +1.64480 q^{13} -31.7941i q^{14} +(-2.53338 - 5.72358i) q^{15} +27.1769 q^{16} +12.4235i q^{17} +(23.8985 + 21.7075i) q^{18} -10.5657 q^{19} -18.5033i q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(21.2064 + 47.9109i) q^{24} +20.6470 q^{25} +5.90037i q^{26} +(-8.51105 + 25.6235i) q^{27} +78.6021 q^{28} +11.6087i q^{29} +(20.5320 - 9.08793i) q^{30} -23.3883 q^{31} +27.6317i q^{32} -44.5665 q^{34} -18.4918i q^{35} +(-53.6658 + 59.0823i) q^{36} +7.24593 q^{37} -37.9019i q^{38} +(-4.51217 + 1.99719i) q^{39} +36.4384 q^{40} +38.8768i q^{41} +(38.6056 + 87.2204i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +72.9572 q^{46} -45.3086i q^{47} +(-74.5539 + 32.9992i) q^{48} +29.5532 q^{49} +74.0663i q^{50} +(-15.0851 - 34.0812i) q^{51} -14.5870 q^{52} -40.3160i q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(28.9847 - 12.8292i) q^{57} -41.6435 q^{58} -113.181i q^{59} +(22.4674 + 50.7598i) q^{60} -77.5161 q^{61} -83.9001i q^{62} +(-53.6324 + 59.0456i) q^{63} +9.58504 q^{64} +3.43171i q^{65} +62.9082 q^{67} -110.178i q^{68} +(24.6949 + 55.7924i) q^{69} +66.3350 q^{70} +10.2125i q^{71} +(-116.351 - 105.684i) q^{72} +74.6222 q^{73} +25.9931i q^{74} +(-56.6405 + 25.0703i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} -86.3123 q^{79} +56.7016i q^{80} +(-7.76472 - 80.6270i) q^{81} -139.462 q^{82} +11.8083i q^{83} +(-215.628 + 95.4417i) q^{84} -25.9203 q^{85} +56.8381i q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(-45.2904 + 49.8616i) q^{90} -14.5779 q^{91} +180.366i q^{92} +(64.1607 - 28.3989i) q^{93} +162.534 q^{94} -22.0441i q^{95} +(-33.5514 - 75.8016i) q^{96} -77.1678 q^{97} +106.016i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * q^97

Introduction

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