LMFDB - Embedded newform 363.3.b.j.122.1

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 21x^{4} + 111x^{2} + 47 $ x^6 + 21x^4 + 111x^2 + 47
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.1
Root			$-3.50091i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.j.122.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.50091i q^{2} +(-1.38788 - 2.65966i) q^{3} -8.25635 q^{4} +7.89925i q^{5} +(-9.31122 + 4.85883i) q^{6} +1.81458 q^{7} +14.9011i q^{8} +(-5.14758 + 7.38257i) q^{9} +O(q^{10})$	\(q-3.50091i q^{2} +(-1.38788 - 2.65966i) q^{3} -8.25635 q^{4} +7.89925i q^{5} +(-9.31122 + 4.85883i) q^{6} +1.81458 q^{7} +14.9011i q^{8} +(-5.14758 + 7.38257i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +0.0709275 q^{13} -6.35268i q^{14} +(21.0093 - 10.9632i) q^{15} +19.1419 q^{16} +3.66036i q^{17} +(25.8457 + 18.0212i) q^{18} +26.3273 q^{19} -65.2190i q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(39.6318 - 20.6809i) q^{24} -37.3982 q^{25} -0.248311i q^{26} +(26.7794 + 3.44471i) q^{27} -14.9818 q^{28} +30.2099i q^{29} +(-38.3812 - 73.5517i) q^{30} +42.2382 q^{31} -7.40958i q^{32} +12.8146 q^{34} +14.3338i q^{35} +(42.5002 - 60.9531i) q^{36} +3.70009 q^{37} -92.1693i q^{38} +(-0.0984388 - 0.188643i) q^{39} -117.707 q^{40} +71.0750i q^{41} +(-16.8960 + 8.81675i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} -23.9545 q^{46} +27.3581i q^{47} +(-26.5666 - 50.9108i) q^{48} -45.7073 q^{49} +130.928i q^{50} +(9.73532 - 5.08014i) q^{51} -0.585602 q^{52} -21.7252i q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(-36.5391 - 70.0216i) q^{57} +105.762 q^{58} +79.8011i q^{59} +(-173.460 + 90.5160i) q^{60} +79.1672 q^{61} -147.872i q^{62} +(-9.34072 + 13.3963i) q^{63} +50.6272 q^{64} +0.560274i q^{65} -101.689 q^{67} -30.2212i q^{68} +(-18.1983 + 9.49636i) q^{69} +50.1814 q^{70} +46.4092i q^{71} +(-110.008 - 76.7045i) q^{72} +115.500 q^{73} -12.9537i q^{74} +(51.9042 + 99.4665i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +62.8887 q^{79} +151.206i q^{80} +(-28.0047 - 76.0048i) q^{81} +248.827 q^{82} -84.5001i q^{83} +(20.7929 + 39.8465i) q^{84} -28.9141 q^{85} +48.5230i q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(-142.354 + 204.162i) q^{90} +0.128704 q^{91} +56.4929i q^{92} +(-58.6215 - 112.339i) q^{93} +95.7782 q^{94} +207.966i q^{95} +(-19.7070 + 10.2836i) q^{96} -96.2668 q^{97} +160.017i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 18 q^{4} - 10 q^{6} - 22 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 - 18 * q^4 - 10 * q^6 - 22 * q^9	$ 6 q + 4 q^{3} - 18 q^{4} - 10 q^{6} - 22 q^{9} + 18 q^{10} + 14 q^{12} - 42 q^{13} + 28 q^{15} + 30 q^{16} + 94 q^{18} + 84 q^{19} - 28 q^{21} + 48 q^{24} - 108 q^{25} - 38 q^{27} + 132 q^{28} - 148 q^{30} + 66 q^{34} + 46 q^{36} - 42 q^{37} - 82 q^{39} - 294 q^{40} - 206 q^{42} - 156 q^{43} - 118 q^{45} - 60 q^{46} - 88 q^{48} + 138 q^{49} + 182 q^{51} + 114 q^{52} + 140 q^{54} - 24 q^{57} - 54 q^{58} - 562 q^{60} + 264 q^{61} - 122 q^{63} + 294 q^{64} + 24 q^{67} + 152 q^{69} + 336 q^{70} - 306 q^{72} + 72 q^{73} + 62 q^{75} - 408 q^{76} - 194 q^{78} - 250 q^{81} + 798 q^{82} + 328 q^{84} + 330 q^{85} + 462 q^{87} - 230 q^{90} + 300 q^{91} - 266 q^{93} + 120 q^{94} - 386 q^{96} + 126 q^{97}+O(q^{100}) $ 6 * q + 4 * q^3 - 18 * q^4 - 10 * q^6 - 22 * q^9 + 18 * q^10 + 14 * q^12 - 42 * q^13 + 28 * q^15 + 30 * q^16 + 94 * q^18 + 84 * q^19 - 28 * q^21 + 48 * q^24 - 108 * q^25 - 38 * q^27 + 132 * q^28 - 148 * q^30 + 66 * q^34 + 46 * q^36 - 42 * q^37 - 82 * q^39 - 294 * q^40 - 206 * q^42 - 156 * q^43 - 118 * q^45 - 60 * q^46 - 88 * q^48 + 138 * q^49 + 182 * q^51 + 114 * q^52 + 140 * q^54 - 24 * q^57 - 54 * q^58 - 562 * q^60 + 264 * q^61 - 122 * q^63 + 294 * q^64 + 24 * q^67 + 152 * q^69 + 336 * q^70 - 306 * q^72 + 72 * q^73 + 62 * q^75 - 408 * q^76 - 194 * q^78 - 250 * q^81 + 798 * q^82 + 328 * q^84 + 330 * q^85 + 462 * q^87 - 230 * q^90 + 300 * q^91 - 266 * q^93 + 120 * q^94 - 386 * q^96 + 126 * 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 $

$2$		−	3.50091i		−	1.75045i	−0.483713	−	0.875227i	$-0.660712\pi$
$2$		−	3.50091i		−	1.75045i	0.483713	−	0.875227i	$-0.339288\pi$
$3$	−1.38788	−	2.65966i	−0.462626	−	0.886553i
$3$	−1.38788	−	2.65966i	−0.462626	−	0.886553i
$4$	−8.25635			−2.06409
$5$			7.89925i			1.57985i	0.613203	+	0.789925i	$0.289881\pi$
$5$			7.89925i			1.57985i	−0.613203	+	0.789925i	$0.710119\pi$
$6$	−9.31122	+	4.85883i	−1.55187	+	0.809806i
$7$	1.81458			0.259226			0.129613	−	0.991565i	$-0.458626\pi$
$7$	1.81458			0.259226			0.129613	+	0.991565i	$0.458626\pi$
$8$			14.9011i			1.86263i
$9$	−5.14758	+	7.38257i	−0.571954	+	0.820286i
$10$	27.6545			2.76545
$11$		0			0
$11$		0			0
$12$	11.4588	+	21.9591i	0.954901	+	1.82992i
$13$	0.0709275			0.00545596			0.00272798	−	0.999996i	$-0.499132\pi$
$13$	0.0709275			0.00545596			0.00272798	+	0.999996i	$0.499132\pi$
$14$		−	6.35268i		−	0.453763i
$15$	21.0093	−	10.9632i	1.40062	−	0.730880i
$16$	19.1419			1.19637
$17$			3.66036i			0.215315i	0.994188	+	0.107658i	$0.0343351\pi$
$17$			3.66036i			0.215315i	−0.994188	+	0.107658i	$0.965665\pi$
$18$	25.8457	+	18.0212i	1.43587	+	1.00118i
$19$	26.3273			1.38565			0.692823	−	0.721108i	$-0.256367\pi$
$19$	26.3273			1.38565			0.692823	+	0.721108i	$0.256367\pi$
$20$		−	65.2190i		−	3.26095i
$21$	−2.51842	−	4.82617i	−0.119925	−	0.229818i
$22$		0			0
$23$		−	6.84236i		−	0.297494i	−0.988875	−	0.148747i	$-0.952476\pi$
$23$		−	6.84236i		−	0.297494i	0.988875	−	0.148747i	$-0.0475240\pi$
$24$	39.6318	−	20.6809i	1.65132	−	0.861703i
$25$	−37.3982			−1.49593
$26$		−	0.248311i		−	0.00955041i
$27$	26.7794	+	3.44471i	0.991828	+	0.127582i
$28$	−14.9818			−0.535065
$29$			30.2099i			1.04172i	0.853642	+	0.520860i	$0.174389\pi$
$29$			30.2099i			1.04172i	−0.853642	+	0.520860i	$0.825611\pi$
$30$	−38.3812	−	73.5517i	−1.27937	−	2.45172i
$31$	42.2382			1.36252			0.681261	−	0.732041i	$-0.261432\pi$
$31$	42.2382			1.36252			0.681261	+	0.732041i	$0.261432\pi$
$32$		−	7.40958i		−	0.231549i
$33$		0			0
$34$	12.8146			0.376899
$35$			14.3338i			0.409538i
$36$	42.5002	−	60.9531i	1.18056	−	1.69314i
$37$	3.70009			0.100002			0.0500012	−	0.998749i	$-0.484077\pi$
$37$	3.70009			0.100002			0.0500012	+	0.998749i	$0.484077\pi$
$38$		−	92.1693i		−	2.42551i
$39$	−0.0984388	−	0.188643i	−0.00252407	−	0.00483700i
$40$	−117.707			−2.94268
$41$			71.0750i			1.73354i	0.498711	+	0.866769i	$0.333807\pi$
$41$			71.0750i			1.73354i	−0.498711	+	0.866769i	$0.666193\pi$
$42$	−16.8960	+	8.81675i	−0.402285	+	0.209923i
$43$	−13.8601			−0.322329			−0.161164	−	0.986928i	$-0.551525\pi$
$43$	−13.8601			−0.322329			−0.161164	+	0.986928i	$0.551525\pi$
$44$		0			0
$45$	−58.3168	−	40.6621i	−1.29593	−	0.903602i
$46$	−23.9545			−0.520749
$47$			27.3581i			0.582088i	0.956710	+	0.291044i	$0.0940026\pi$
$47$			27.3581i			0.582088i	−0.956710	+	0.291044i	$0.905997\pi$
$48$	−26.5666	−	50.9108i	−0.553470	−	1.06064i
$49$	−45.7073			−0.932802
$50$			130.928i			2.61855i
$51$	9.73532	−	5.08014i	0.190889	−	0.0996105i
$52$	−0.585602			−0.0112616
$53$		−	21.7252i		−	0.409909i	−0.978772	−	0.204954i	$-0.934295\pi$
$53$		−	21.7252i		−	0.409909i	0.978772	−	0.204954i	$-0.0657046\pi$
$54$	12.0596	−	93.7520i	0.223326	−	1.73615i
$55$		0			0
$56$			27.0392i			0.482843i
$57$	−36.5391	−	70.0216i	−0.641036	−	1.22845i
$58$	105.762			1.82348
$59$			79.8011i			1.35256i	0.736644	+	0.676281i	$0.236409\pi$
$59$			79.8011i			1.35256i	−0.736644	+	0.676281i	$0.763591\pi$
$60$	−173.460	+	90.5160i	−2.89100	+	1.50860i
$61$	79.1672			1.29782			0.648912	−	0.760864i	$-0.275224\pi$
$61$	79.1672			1.29782			0.648912	+	0.760864i	$0.275224\pi$
$62$		−	147.872i		−	2.38503i
$63$	−9.34072	+	13.3963i	−0.148265	+	0.212639i
$64$	50.6272			0.791050
$65$			0.560274i			0.00861961i
$66$		0			0
$67$	−101.689			−1.51775			−0.758874	−	0.651238i	$-0.774250\pi$
$67$	−101.689			−1.51775			−0.758874	+	0.651238i	$0.774250\pi$
$68$		−	30.2212i		−	0.444430i
$69$	−18.1983	+	9.49636i	−0.263744	+	0.137628i
$70$	50.1814			0.716878
$71$			46.4092i			0.653651i	0.945085	+	0.326826i	$0.105979\pi$
$71$			46.4092i			0.653651i	−0.945085	+	0.326826i	$0.894021\pi$
$72$	−110.008	−	76.7045i	−1.52789	−	1.06534i
$73$	115.500			1.58219			0.791094	−	0.611695i	$-0.209512\pi$
$73$	115.500			1.58219			0.791094	+	0.611695i	$0.209512\pi$
$74$		−	12.9537i		−	0.175050i
$75$	51.9042	+	99.4665i	0.692056	+	1.32622i
$76$	−217.367			−2.86009
$77$		0			0
$78$	−0.660422	+	0.344625i	−0.00846695	+	0.00441827i
$79$	62.8887			0.796060			0.398030	−	0.917372i	$-0.369694\pi$
$79$	62.8887			0.796060			0.398030	+	0.917372i	$0.369694\pi$
$80$			151.206i			1.89008i
$81$	−28.0047	−	76.0048i	−0.345738	−	0.938331i
$82$	248.827			3.03448
$83$		−	84.5001i		−	1.01807i	−0.860745	−	0.509037i	$-0.830002\pi$
$83$		−	84.5001i		−	1.01807i	0.860745	−	0.509037i	$-0.169998\pi$
$84$	20.7929	+	39.8465i	0.247535	+	0.474364i
$85$	−28.9141			−0.340166
$86$			48.5230i			0.564221i
$87$	80.3481	−	41.9277i	0.923541	−	0.481927i
$88$		0			0
$89$			45.3523i			0.509577i	0.966997	+	0.254788i	$0.0820058\pi$
$89$			45.3523i			0.509577i	−0.966997	+	0.254788i	$0.917994\pi$
$90$	−142.354	+	204.162i	−1.58171	+	2.26846i
$91$	0.128704			0.00141433
$92$			56.4929i			0.614053i
$93$	−58.6215	−	112.339i	−0.630338	−	1.20795i
$94$	95.7782			1.01892
$95$			207.966i			2.18911i
$96$	−19.7070	+	10.2836i	−0.205281	+	0.107121i
$97$	−96.2668			−0.992441			−0.496220	−	0.868197i	$-0.665279\pi$
$97$	−96.2668			−0.992441			−0.496220	+	0.868197i	$0.665279\pi$
$98$			160.017i			1.63283i
$99$		0			0
$100$	308.772			3.08772
$101$		−	55.6956i		−	0.551441i	−0.961238	−	0.275721i	$-0.911083\pi$
$101$		−	55.6956i		−	0.551441i	0.961238	−	0.275721i	$-0.0889165\pi$
$102$	−17.7851	−	34.0824i	−0.174364	−	0.334142i
$103$	130.478			1.26678			0.633390	−	0.773833i	$-0.281663\pi$
$103$	130.478			1.26678			0.633390	+	0.773833i	$0.281663\pi$
$104$			1.05690i			0.0101625i
$105$	38.1232	−	19.8936i	0.363078	−	0.189463i
$106$	−76.0578			−0.717526
$107$		−	58.1396i		−	0.543361i	−0.962388	−	0.271680i	$-0.912421\pi$
$107$		−	58.1396i		−	0.543361i	0.962388	−	0.271680i	$-0.0875794\pi$
$108$	−221.100	−	28.4407i	−2.04722	−	0.263340i
$109$	49.0112			0.449644			0.224822	−	0.974400i	$-0.427820\pi$
$109$	49.0112			0.449644			0.224822	+	0.974400i	$0.427820\pi$
$110$		0			0
$111$	−5.13528	−	9.84099i	−0.0462638	−	0.0886575i
$112$	34.7345			0.310129
$113$		−	52.2060i		−	0.462000i	−0.972954	−	0.231000i	$-0.925800\pi$
$113$		−	52.2060i		−	0.462000i	0.972954	−	0.231000i	$-0.0741997\pi$
$114$	−245.139	+	127.920i	−2.15034	+	1.12210i
$115$	54.0495			0.469996
$116$		−	249.423i		−	2.15020i
$117$	−0.365105	+	0.523627i	−0.00312056	+	0.00447545i
$118$	279.376			2.36760
$119$			6.64203i			0.0558154i
$120$	163.363	+	313.061i	1.36136	+	2.60884i
$121$		0			0
$122$		−	277.157i		−	2.27178i
$123$	189.035	−	98.6435i	1.53687	−	0.801980i
$124$	−348.733			−2.81236
$125$		−	97.9365i		−	0.783492i
$126$	46.8991	+	32.7010i	0.372215	+	0.259532i
$127$	−58.4724			−0.460412			−0.230206	−	0.973142i	$-0.573940\pi$
$127$	−58.4724			−0.460412			−0.230206	+	0.973142i	$0.573940\pi$
$128$		−	206.879i		−	1.61624i
$129$	19.2362	+	36.8632i	0.149118	+	0.285762i
$130$	1.96147			0.0150882
$131$			147.683i			1.12735i	0.825997	+	0.563675i	$0.190613\pi$
$131$			147.683i			1.12735i	−0.825997	+	0.563675i	$0.809387\pi$
$132$		0			0
$133$	47.7730			0.359196
$134$			356.004i			2.65675i
$135$	−27.2107	+	211.537i	−0.201560	+	1.56694i
$136$	−54.5433			−0.401054
$137$			165.454i			1.20769i	0.797101	+	0.603846i	$0.206366\pi$
$137$			165.454i			1.20769i	−0.797101	+	0.603846i	$0.793634\pi$
$138$	33.2459	+	63.7107i	0.240912	+	0.461672i
$139$	−52.0963			−0.374794			−0.187397	−	0.982284i	$-0.560005\pi$
$139$	−52.0963			−0.374794			−0.187397	+	0.982284i	$0.560005\pi$
$140$		−	118.345i		−	0.845323i
$141$	72.7633	−	37.9698i	0.516052	−	0.269289i
$142$	162.474			1.14419
$143$		0			0
$144$	−98.5343	+	141.316i	−0.684266	+	0.981362i
$145$	−238.636			−1.64576
$146$		−	404.354i		−	2.76955i
$147$	63.4362	+	121.566i	0.431539	+	0.826979i
$148$	−30.5492			−0.206414
$149$			30.5445i			0.204997i	0.994733	+	0.102498i	$0.0326836\pi$
$149$			30.5445i			0.204997i	−0.994733	+	0.102498i	$0.967316\pi$
$150$	348.223	−	181.712i	2.32149	−	1.21141i
$151$	−165.277			−1.09455			−0.547274	−	0.836954i	$-0.684334\pi$
$151$	−165.277			−1.09455			−0.547274	+	0.836954i	$0.684334\pi$
$152$			392.304i			2.58095i
$153$	−27.0229	−	18.8420i	−0.176620	−	0.123150i
$154$		0			0
$155$			333.650i			2.15258i
$156$	0.812745	+	1.55750i	0.00520990	+	0.00998399i
$157$	−211.125			−1.34474			−0.672372	−	0.740213i	$-0.734725\pi$
$157$	−211.125			−1.34474			−0.672372	+	0.740213i	$0.734725\pi$
$158$		−	220.168i		−	1.39347i
$159$	−57.7816	+	30.1519i	−0.363406	+	0.189635i
$160$	58.5301			0.365813
$161$		−	12.4160i		−	0.0771181i
$162$	−266.086	+	98.0420i	−1.64250	+	0.605197i
$163$	−87.4133			−0.536278			−0.268139	−	0.963380i	$-0.586409\pi$
$163$	−87.4133			−0.536278			−0.268139	+	0.963380i	$0.586409\pi$
$164$		−	586.820i		−	3.57817i
$165$		0			0
$166$	−295.827			−1.78209
$167$			41.3661i			0.247701i	0.992301	+	0.123851i	$0.0395244\pi$
$167$			41.3661i			0.247701i	−0.992301	+	0.123851i	$0.960476\pi$
$168$	71.9151	−	37.5271i	0.428066	−	0.223376i
$169$	−168.995			−0.999970
$170$			101.226i			0.595445i
$171$	−135.522	+	194.363i	−0.792526	+	1.13663i
$172$	114.434			0.665314
$173$			206.834i			1.19557i	0.801656	+	0.597786i	$0.203953\pi$
$173$			206.834i			1.19557i	−0.801656	+	0.597786i	$0.796047\pi$
$174$	−146.785	−	281.291i	−0.843591	−	1.61662i
$175$	−67.8621			−0.387784
$176$		0			0
$177$	212.244	−	110.754i	1.19912	−	0.625730i
$178$	158.774			0.891990
$179$			138.292i			0.772580i	0.922377	+	0.386290i	$0.126244\pi$
$179$			138.292i			0.772580i	−0.922377	+	0.386290i	$0.873756\pi$
$180$	481.484	+	335.720i	2.67491	+	1.86511i
$181$	−61.9311			−0.342161			−0.171080	−	0.985257i	$-0.554726\pi$
$181$	−61.9311			−0.342161			−0.171080	+	0.985257i	$0.554726\pi$
$182$		−	0.450580i		−	0.00247571i
$183$	−109.875	−	210.558i	−0.600407	−	1.15059i
$184$	101.958			0.554122
$185$			29.2280i			0.157989i
$186$	−393.289	+	205.228i	−2.11446	+	1.10338i
$187$		0			0
$188$		−	225.878i		−	1.20148i
$189$	48.5933	+	6.25071i	0.257108	+	0.0330726i
$190$	728.069			3.83194
$191$		−	24.2902i		−	0.127174i	−0.997976	−	0.0635869i	$-0.979746\pi$
$191$		−	24.2902i		−	0.127174i	0.997976	−	0.0635869i	$-0.0202540\pi$
$192$	−70.2644	−	134.651i	−0.365960	−	0.701308i
$193$	201.813			1.04566			0.522831	−	0.852436i	$-0.324876\pi$
$193$	201.813			1.04566			0.522831	+	0.852436i	$0.324876\pi$
$194$			337.021i			1.73722i
$195$	1.49014	−	0.777593i	0.00764174	−	0.00398766i
$196$	377.375			1.92538
$197$			64.9088i			0.329486i	0.986337	+	0.164743i	$0.0526795\pi$
$197$			64.9088i			0.329486i	−0.986337	+	0.164743i	$0.947320\pi$
$198$		0			0
$199$	136.263			0.684741			0.342370	−	0.939565i	$-0.388770\pi$
$199$	136.263			0.684741			0.342370	+	0.939565i	$0.388770\pi$
$200$		−	557.273i		−	2.78637i
$201$	141.132	+	270.458i	0.702150	+	1.34556i
$202$	−194.985			−0.965273
$203$			54.8183i			0.270041i
$204$	−80.3781	+	41.9434i	−0.394011	+	0.205605i
$205$	−561.440			−2.73873
$206$		−	456.792i		−	2.21744i
$207$	50.5142	+	35.2216i	0.244030	+	0.170153i
$208$	1.35768			0.00652733
$209$		0			0
$210$	−69.6458	−	133.466i	−0.331647	−	0.635550i
$211$	−1.24195			−0.00588601			−0.00294300	−	0.999996i	$-0.500937\pi$
$211$	−1.24195			−0.00588601			−0.00294300	+	0.999996i	$0.500937\pi$
$212$			179.370i			0.846087i
$213$	123.433	−	64.4104i	0.579497	−	0.302396i
$214$	−203.541			−0.951128
$215$		−	109.485i		−	0.509231i
$216$	−51.3299	+	399.041i	−0.237638	+	1.84741i
$217$	76.6446			0.353201
$218$		−	171.584i		−	0.787080i
$219$	−160.300	−	307.190i	−0.731962	−	1.40269i
$220$		0			0
$221$			0.259620i			0.00117475i
$222$	−34.4524	+	17.9781i	−0.155191	+	0.0809826i
$223$	124.259			0.557216			0.278608	−	0.960405i	$-0.410127\pi$
$223$	124.259			0.557216			0.278608	+	0.960405i	$0.410127\pi$
$224$		−	13.4453i		−	0.0600236i
$225$	192.510	−	276.095i	0.855602	−	1.22709i
$226$	−182.768			−0.808709
$227$			47.7075i			0.210165i	0.994464	+	0.105083i	$0.0335107\pi$
$227$			47.7075i			0.210165i	−0.994464	+	0.105083i	$0.966489\pi$
$228$	301.679	+	578.122i	1.32315	+	2.53562i
$229$	−73.2074			−0.319683			−0.159841	−	0.987143i	$-0.551098\pi$
$229$	−73.2074			−0.319683			−0.159841	+	0.987143i	$0.551098\pi$
$230$		−	189.222i		−	0.822706i
$231$		0			0
$232$	−450.160			−1.94034
$233$		−	185.396i		−	0.795689i	−0.917453	−	0.397844i	$-0.869758\pi$
$233$		−	185.396i		−	0.795689i	0.917453	−	0.397844i	$-0.130242\pi$
$234$	1.83317	+	1.27820i	0.00783406	+	0.00546239i
$235$	−216.109			−0.919612
$236$		−	658.866i		−	2.79180i
$237$	−87.2819	−	167.263i	−0.368278	−	0.705750i
$238$	23.2531			0.0977022
$239$		−	350.968i		−	1.46848i	−0.678887	−	0.734242i	$-0.737538\pi$
$239$		−	350.968i		−	1.46848i	0.678887	−	0.734242i	$-0.262462\pi$
$240$	402.158	−	209.856i	1.67566	−	0.874400i
$241$	−175.508			−0.728248			−0.364124	−	0.931351i	$-0.618631\pi$
$241$	−175.508			−0.728248			−0.364124	+	0.931351i	$0.618631\pi$
$242$		0			0
$243$	−163.280	+	179.969i	−0.671934	+	0.740611i
$244$	−653.632			−2.67882
$245$		−	361.053i		−	1.47369i
$246$	−345.342	−	661.795i	−1.40383	−	2.69022i
$247$	1.86733			0.00756003
$248$			629.394i			2.53788i
$249$	−224.742	+	117.276i	−0.902577	+	0.470988i
$250$	−342.867			−1.37147
$251$		−	139.009i		−	0.553821i	−0.960896	−	0.276911i	$-0.910689\pi$
$251$		−	139.009i		−	0.553821i	0.960896	−	0.276911i	$-0.0893106\pi$
$252$	77.1202	−	110.604i	0.306032	−	0.438906i
$253$		0			0
$254$			204.706i			0.805930i
$255$	40.1293	+	76.9017i	0.157370	+	0.301575i
$256$	−521.756			−2.03811
$257$		−	427.373i		−	1.66293i	−0.555578	−	0.831465i	$-0.687503\pi$
$257$		−	427.373i		−	1.66293i	0.555578	−	0.831465i	$-0.312497\pi$
$258$	129.055	−	67.3441i	0.500212	−	0.261023i
$259$	6.71412			0.0259233
$260$		−	4.62582i		−	0.0177916i
$261$	−223.027	−	155.508i	−0.854509	−	0.595816i
$262$	517.024			1.97337
$263$			201.638i			0.766686i	0.923606	+	0.383343i	$0.125227\pi$
$263$			201.638i			0.766686i	−0.923606	+	0.383343i	$0.874773\pi$
$264$		0			0
$265$	171.613			0.647595
$266$		−	167.249i		−	0.628755i
$267$	120.622	−	62.9435i	0.451767	−	0.235744i
$268$	839.580			3.13276
$269$			343.050i			1.27528i	0.770334	+	0.637640i	$0.220089\pi$
$269$			343.050i			1.27528i	−0.770334	+	0.637640i	$0.779911\pi$
$270$	740.571	+	95.2619i	2.74286	+	0.352822i
$271$	407.587			1.50401			0.752005	−	0.659157i	$-0.229087\pi$
$271$	407.587			1.50401			0.752005	+	0.659157i	$0.229087\pi$
$272$			70.0661i			0.257596i
$273$	−0.178625	−	0.342308i	−0.000654305	−	0.00125388i
$274$	579.239			2.11401
$275$		0			0
$276$	150.252	−	78.4053i	0.544391	−	0.284077i
$277$	496.996			1.79421			0.897104	−	0.441819i	$-0.145667\pi$
$277$	496.996			1.79421			0.897104	+	0.441819i	$0.145667\pi$
$278$			182.384i			0.656059i
$279$	−217.425	+	311.826i	−0.779299	+	1.11766i
$280$	−213.590			−0.762820
$281$		−	387.006i		−	1.37725i	−0.725119	−	0.688623i	$-0.758215\pi$
$281$		−	387.006i		−	1.37725i	0.725119	−	0.688623i	$-0.241785\pi$
$282$	−132.929	−	254.738i	−0.471378	−	0.903325i
$283$	221.755			0.783587			0.391793	−	0.920053i	$-0.371855\pi$
$283$	221.755			0.783587			0.391793	+	0.920053i	$0.371855\pi$
$284$		−	383.171i		−	1.34919i
$285$	553.118	−	288.631i	1.94077	−	1.01274i
$286$		0			0
$287$			128.971i			0.449378i
$288$	54.7017	+	38.1414i	0.189937	+	0.132436i
$289$	275.602			0.953639
$290$			835.441i			2.88083i
$291$	133.607	+	256.037i	0.459129	+	0.879852i
$292$	−953.606			−3.26577
$293$		−	442.759i		−	1.51112i	−0.655078	−	0.755561i	$-0.727364\pi$
$293$		−	442.759i		−	1.51112i	0.655078	−	0.755561i	$-0.272636\pi$
$294$	425.591	−	222.084i	1.44759	−	0.755388i
$295$	−630.369			−2.13684
$296$			55.1353i			0.186268i
$297$		0			0
$298$	106.933			0.358837
$299$		−	0.485311i		−	0.00162312i
$300$	−428.539	−	821.230i	−1.42846	−	2.73743i
$301$	−25.1503			−0.0835560
$302$			578.618i			1.91595i
$303$	−148.131	+	77.2987i	−0.488882	+	0.255111i
$304$	503.953			1.65774
$305$			625.362i			2.05037i
$306$	−65.9642	+	94.6046i	−0.215569	+	0.309165i
$307$	−324.906			−1.05832			−0.529162	−	0.848521i	$-0.677494\pi$
$307$	−324.906			−1.05832			−0.529162	+	0.848521i	$0.677494\pi$
$308$		0			0
$309$	−181.088	−	347.028i	−0.586046	−	1.12307i
$310$	1168.08			3.76799
$311$		−	117.004i		−	0.376218i	−0.982148	−	0.188109i	$-0.939764\pi$
$311$		−	117.004i		−	0.376218i	0.982148	−	0.188109i	$-0.0602359\pi$
$312$	2.81098	−	1.46684i	0.00900956	−	0.00470142i
$313$	−146.076			−0.466695			−0.233348	−	0.972393i	$-0.574968\pi$
$313$	−146.076			−0.466695			−0.233348	+	0.972393i	$0.574968\pi$
$314$			739.129i			2.35391i
$315$	−105.821	−	73.7847i	−0.335939	−	0.234237i
$316$	−519.231			−1.64314
$317$		−	67.5628i		−	0.213132i	−0.994306	−	0.106566i	$-0.966014\pi$
$317$		−	67.5628i		−	0.213132i	0.994306	−	0.106566i	$-0.0339855\pi$
$318$	105.559	+	202.288i	0.331946	+	0.636125i
$319$		0			0
$320$			399.917i			1.24974i
$321$	−154.632	+	80.6907i	−0.481718	+	0.251373i
$322$	−43.4673			−0.134992
$323$			96.3673i			0.298351i
$324$	231.217	+	627.522i	0.713632	+	1.93680i
$325$	−2.65256			−0.00816173
$326$			306.026i			0.938730i
$327$	−68.0216	−	130.353i	−0.208017	−	0.398633i
$328$	−1059.09			−3.22894
$329$			49.6436i			0.150892i
$330$		0			0
$331$	303.465			0.916814			0.458407	−	0.888742i	$-0.348420\pi$
$331$	303.465			0.916814			0.458407	+	0.888742i	$0.348420\pi$
$332$			697.662i			2.10139i
$333$	−19.0465	+	27.3162i	−0.0571968	+	0.0820306i
$334$	144.819			0.433589
$335$		−	803.268i		−	2.39781i
$336$	−48.2072	−	92.3819i	−0.143474	−	0.274946i
$337$	555.438			1.64819			0.824093	−	0.566455i	$-0.191686\pi$
$337$	555.438			1.64819			0.824093	+	0.566455i	$0.191686\pi$
$338$			591.636i			1.75040i
$339$	−138.850	+	72.4556i	−0.409588	+	0.213733i
$340$	238.725			0.702132
$341$		0			0
$342$	680.447	+	474.449i	1.98961	+	1.38728i
$343$	−171.854			−0.501033
$344$		−	206.531i		−	0.600380i
$345$	−75.0142	−	143.753i	−0.217432	−	0.416676i
$346$	724.106			2.09279
$347$			387.970i			1.11807i	0.829144	+	0.559034i	$0.188828\pi$
$347$			387.970i			1.11807i	−0.829144	+	0.559034i	$0.811172\pi$
$348$	−663.381	+	346.169i	−1.90627	+	0.994740i
$349$	−452.035			−1.29523			−0.647615	−	0.761968i	$-0.724233\pi$
$349$	−452.035			−1.29523			−0.647615	+	0.761968i	$0.724233\pi$
$350$			237.579i			0.678797i
$351$	1.89939	+	0.244325i	0.00541138	+	0.000696082i
$352$		0			0
$353$		−	304.454i		−	0.862476i	−0.902238	−	0.431238i	$-0.858077\pi$
$353$		−	304.454i		−	0.862476i	0.902238	−	0.431238i	$-0.141923\pi$
$354$	−387.740	−	743.046i	−1.09531	−	2.09900i
$355$	−366.598			−1.03267
$356$		−	374.444i		−	1.05181i
$357$	17.6655	−	9.21833i	0.0494833	−	0.0258216i
$358$	484.147			1.35236
$359$			303.114i			0.844329i	0.906519	+	0.422164i	$0.138730\pi$
$359$			303.114i			0.844329i	−0.906519	+	0.422164i	$0.861270\pi$
$360$	605.908	−	868.983i	1.68308	−	2.41384i
$361$	332.125			0.920015
$362$			216.815i			0.598936i
$363$		0			0
$364$	−1.06262			−0.00291929
$365$			912.362i			2.49962i
$366$	−737.144	+	384.660i	−2.01405	+	1.05098i
$367$	−419.963			−1.14431			−0.572157	−	0.820144i	$-0.693893\pi$
$367$	−419.963			−1.14431			−0.572157	+	0.820144i	$0.693893\pi$
$368$		−	130.975i		−	0.355911i
$369$	−524.716	−	365.865i	−1.42200	−	0.991503i
$370$	102.324			0.276552
$371$		−	39.4221i		−	0.106259i
$372$	483.999	+	927.511i	1.30107	+	2.49331i
$373$	198.795			0.532963			0.266482	−	0.963840i	$-0.414139\pi$
$373$	198.795			0.532963			0.266482	+	0.963840i	$0.414139\pi$
$374$		0			0
$375$	−260.478	+	135.924i	−0.694608	+	0.362464i
$376$	−407.665			−1.08422
$377$			2.14271i			0.00568359i
$378$	21.8832	−	170.121i	0.0578920	−	0.450055i
$379$	72.4096			0.191054			0.0955271	−	0.995427i	$-0.469546\pi$
$379$	72.4096			0.191054			0.0955271	+	0.995427i	$0.469546\pi$
$380$		−	1717.04i		−	4.51852i
$381$	81.1525	+	155.517i	0.212999	+	0.408180i
$382$	−85.0377			−0.222612
$383$		−	524.906i		−	1.37051i	−0.728303	−	0.685256i	$-0.759691\pi$
$383$		−	524.906i		−	1.37051i	0.728303	−	0.685256i	$-0.240309\pi$
$384$	−550.229	+	287.123i	−1.43289	+	0.747717i
$385$		0			0
$386$		−	706.528i		−	1.83038i
$387$	71.3462	−	102.323i	0.184357	−	0.264402i
$388$	794.812			2.04848
$389$			372.921i			0.958665i	0.877633	+	0.479332i	$0.159121\pi$
$389$			372.921i			0.958665i	−0.877633	+	0.479332i	$0.840879\pi$
$390$	−2.72228	−	5.21684i	−0.00698020	−	0.0133765i
$391$	25.0455			0.0640550
$392$		−	681.087i		−	1.73747i
$393$	392.786	−	204.966i	0.999456	−	0.521542i
$394$	227.240			0.576750
$395$			496.774i			1.25766i
$396$		0			0
$397$	−184.584			−0.464947			−0.232474	−	0.972603i	$-0.574682\pi$
$397$	−184.584			−0.464947			−0.232474	+	0.972603i	$0.574682\pi$
$398$		−	477.045i		−	1.19861i
$399$	−66.3031	−	127.060i	−0.166173	−	0.318446i
$400$	−715.871			−1.78968
$401$			90.7909i			0.226411i	0.993572	+	0.113206i	$0.0361119\pi$
$401$			90.7909i			0.226411i	−0.993572	+	0.113206i	$0.963888\pi$
$402$	946.850	−	494.090i	2.35535	−	1.22908i
$403$	2.99585			0.00743387
$404$			459.842i			1.13822i
$405$	600.381	−	221.217i	1.48242	−	0.546214i
$406$	191.914			0.472694
$407$		0			0
$408$	75.6995	+	145.067i	0.185538	+	0.355555i
$409$	−549.923			−1.34456			−0.672278	−	0.740299i	$-0.734684\pi$
$409$	−549.923			−1.34456			−0.672278	+	0.740299i	$0.734684\pi$
$410$			1965.55i			4.79402i
$411$	440.051	−	229.630i	1.07068	−	0.558710i
$412$	−1077.27			−2.61474
$413$			144.806i			0.350619i
$414$	123.308	−	176.845i	0.297844	−	0.427163i
$415$	667.488			1.60840
$416$		−	0.525543i		−	0.00126332i
$417$	72.3034	+	138.558i	0.173389	+	0.332275i
$418$		0			0
$419$		−	298.402i		−	0.712176i	−0.934452	−	0.356088i	$-0.884110\pi$
$419$		−	298.402i		−	0.712176i	0.934452	−	0.356088i	$-0.115890\pi$
$420$	−314.758	+	164.249i	−0.749424	+	0.391068i
$421$	−122.600			−0.291212			−0.145606	−	0.989343i	$-0.546513\pi$
$421$	−122.600			−0.291212			−0.145606	+	0.989343i	$0.546513\pi$
$422$			4.34794i			0.0103032i
$423$	−201.973	−	140.828i	−0.477478	−	0.332927i
$424$	323.728			0.763510
$425$		−	136.891i		−	0.322096i
$426$	−225.495	−	432.127i	−0.529330	−	1.01438i
$427$	143.655			0.336430
$428$			480.021i			1.12154i
$429$		0			0
$430$	−383.296			−0.891385
$431$		−	591.029i		−	1.37130i	−0.727933	−	0.685649i	$-0.759519\pi$
$431$		−	591.029i		−	1.37130i	0.727933	−	0.685649i	$-0.240481\pi$
$432$	512.607	+	65.9382i	1.18659	+	0.152635i
$433$	642.334			1.48345			0.741725	−	0.670704i	$-0.234008\pi$
$433$	642.334			1.48345			0.741725	+	0.670704i	$0.234008\pi$
$434$		−	268.326i		−	0.618262i
$435$	331.197	+	634.690i	0.761373	+	1.45906i
$436$	−404.653			−0.928103
$437$		−	180.141i		−	0.412221i
$438$	−1075.44	+	561.194i	−2.45535	+	1.28126i
$439$	−476.217			−1.08478			−0.542388	−	0.840128i	$-0.682480\pi$
$439$	−476.217			−1.08478			−0.542388	+	0.840128i	$0.682480\pi$
$440$		0			0
$441$	235.282	−	337.437i	0.533520	−	0.765164i
$442$	0.908906			0.00205635
$443$		−	107.721i		−	0.243164i	−0.992581	−	0.121582i	$-0.961203\pi$
$443$		−	107.721i		−	0.243164i	0.992581	−	0.121582i	$-0.0387967\pi$
$444$	42.3986	+	81.2506i	0.0954924	+	0.182997i
$445$	−358.250			−0.805055
$446$		−	435.020i		−	0.975381i
$447$	81.2379	−	42.3920i	0.181740	−	0.0948368i
$448$	91.8672			0.205061
$449$			224.475i			0.499945i	0.968253	+	0.249972i	$0.0804216\pi$
$449$			224.475i			0.499945i	−0.968253	+	0.249972i	$0.919578\pi$
$450$	−966.582	−	673.961i	−2.14796	−	1.49769i
$451$		0			0
$452$			431.031i			0.953608i
$453$	229.384	+	439.580i	0.506366	+	0.970375i
$454$	167.019			0.367884
$455$			1.01666i			0.00223443i
$456$	1043.40	−	544.471i	2.28815	−	1.19402i
$457$	−71.2882			−0.155992			−0.0779958	−	0.996954i	$-0.524852\pi$
$457$	−71.2882			−0.155992			−0.0779958	+	0.996954i	$0.524852\pi$
$458$			256.292i			0.559590i
$459$	−12.6089	+	98.0221i	−0.0274704	+	0.213556i
$460$	−446.251			−0.970112
$461$		−	876.537i		−	1.90138i	−0.310141	−	0.950691i	$-0.600376\pi$
$461$		−	876.537i		−	1.90138i	0.310141	−	0.950691i	$-0.399624\pi$
$462$		0			0
$463$	−824.691			−1.78119			−0.890595	−	0.454797i	$-0.849712\pi$
$463$	−824.691			−1.78119			−0.890595	+	0.454797i	$0.849712\pi$
$464$			578.273i			1.24628i
$465$	887.395	−	463.066i	1.90838	−	0.995840i
$466$	−649.052			−1.39282
$467$			321.061i			0.687496i	0.939062	+	0.343748i	$0.111697\pi$
$467$			321.061i			0.687496i	−0.939062	+	0.343748i	$0.888303\pi$
$468$	3.01444	−	4.32325i	0.00644110	−	0.00923771i
$469$	−184.523			−0.393440
$470$			756.576i			1.60974i
$471$	293.016	+	561.521i	0.622114	+	1.19219i
$472$	−1189.12			−2.51933
$473$		0			0
$474$	−585.571	+	305.566i	−1.23538	+	0.644654i
$475$	−984.593			−2.07283
$476$		−	54.8389i		−	0.115208i
$477$	160.388	+	111.832i	0.336242	+	0.234449i
$478$	−1228.71			−2.57051
$479$			433.218i			0.904422i	0.891911	+	0.452211i	$0.149365\pi$
$479$			433.218i			0.904422i	−0.891911	+	0.452211i	$0.850635\pi$
$480$	−81.2327	−	155.670i	−0.169235	−	0.324313i
$481$	0.262438			0.000545610
$482$			614.436i			1.27476i
$483$	−33.0224	+	17.2319i	−0.0683694	+	0.0356769i
$484$		0			0
$485$		−	760.436i		−	1.56791i
$486$	630.053	+	571.627i	1.29641	+	1.17619i
$487$	−352.557			−0.723936			−0.361968	−	0.932191i	$-0.617895\pi$
$487$	−352.557			−0.723936			−0.361968	+	0.932191i	$0.617895\pi$
$488$			1179.68i			2.41737i
$489$	121.319	+	232.490i	0.248096	+	0.475439i
$490$	−1264.01			−2.57962
$491$		−	446.385i		−	0.909134i	−0.890713	−	0.454567i	$-0.849794\pi$
$491$		−	446.385i		−	0.909134i	0.890713	−	0.454567i	$-0.150206\pi$
$492$	−1560.74	+	814.435i	−3.17224	+	1.65536i
$493$	−110.579			−0.224298
$494$		−	6.53734i		−	0.0132335i
$495$		0			0
$496$	808.517			1.63007
$497$			84.2134i			0.169443i
$498$	410.572	+	786.799i	0.824442	+	1.57992i
$499$	89.7694			0.179899			0.0899493	−	0.995946i	$-0.471329\pi$
$499$	89.7694			0.179899			0.0899493	+	0.995946i	$0.471329\pi$
$500$			808.598i			1.61720i
$501$	110.020	−	57.4111i	0.219600	−	0.114593i
$502$	−486.658			−0.969438
$503$		−	976.022i		−	1.94040i	−0.242303	−	0.970201i	$-0.577903\pi$
$503$		−	976.022i		−	1.94040i	0.242303	−	0.970201i	$-0.422097\pi$
$504$	−199.619	−	139.187i	−0.396069	−	0.276164i
$505$	439.954			0.871195
$506$		0			0
$507$	234.545	+	449.469i	0.462612	+	0.886527i
$508$	482.768			0.950331
$509$		−	321.665i		−	0.631955i	−0.948767	−	0.315977i	$-0.897668\pi$
$509$		−	321.665i		−	0.631955i	0.948767	−	0.315977i	$-0.102332\pi$
$510$	269.226	−	140.489i	0.527894	−	0.275468i
$511$	209.584			0.410144
$512$			999.103i			1.95137i
$513$	705.027	+	90.6899i	1.37432	+	0.176783i
$514$	−1496.19			−2.91088
$515$			1030.68i			2.00132i
$516$	−158.821	−	304.356i	−0.307792	−	0.589836i
$517$		0			0
$518$		−	23.5055i		−	0.0453774i
$519$	550.108	−	287.060i	1.05994	−	0.553103i
$520$	−8.34869			−0.0160552
$521$			306.382i			0.588066i	0.955795	+	0.294033i	$0.0949975\pi$
$521$			306.382i			0.588066i	−0.955795	+	0.294033i	$0.905002\pi$
$522$	−544.419	+	780.796i	−1.04295	+	1.49578i
$523$	671.607			1.28414			0.642072	−	0.766645i	$-0.278075\pi$
$523$	671.607			1.28414			0.642072	+	0.766645i	$0.278075\pi$
$524$		−	1219.32i		−	2.32695i
$525$	94.1844	+	180.490i	0.179399	+	0.343791i
$526$	705.917			1.34205
$527$			154.607i			0.293372i
$528$		0			0
$529$	482.182			0.911497
$530$		−	600.800i		−	1.13358i
$531$	−589.137	−	410.783i	−1.10949	−	0.773603i
$532$	−394.430			−0.741411
$533$			5.04117i			0.00945811i
$534$	−220.359	−	422.286i	−0.412658	−	0.790797i
$535$	459.259			0.858429
$536$		−	1515.28i		−	2.82701i
$537$	367.809	−	191.932i	0.684933	−	0.357416i
$538$	1200.99			2.23232
$539$		0			0
$540$	224.661	−	1746.52i	0.416038	−	3.23430i
$541$	−184.101			−0.340298			−0.170149	−	0.985418i	$-0.554425\pi$
$541$	−184.101			−0.340298			−0.170149	+	0.985418i	$0.554425\pi$
$542$		−	1426.92i		−	2.63270i
$543$	85.9528	+	164.716i	0.158292	+	0.303344i
$544$	27.1217			0.0498561
$545$			387.152i			0.710370i
$546$	−1.19839	+	0.625350i	−0.00219485	+	0.00114533i
$547$	607.119			1.10991			0.554954	−	0.831881i	$-0.312736\pi$
$547$	607.119			1.10991			0.554954	+	0.831881i	$0.312736\pi$
$548$		−	1366.04i		−	2.49278i
$549$	−407.520	+	584.458i	−0.742295	+	1.06459i
$550$		0			0
$551$			795.344i			1.44346i
$552$	−141.506	−	271.175i	−0.256351	−	0.491259i
$553$	114.117			0.206359
$554$		−	1739.94i		−	3.14068i
$555$	77.7365	−	40.5649i	0.140066	−	0.0730899i
$556$	430.125			0.773606
$557$			406.124i			0.729127i	0.931178	+	0.364564i	$0.118782\pi$
$557$			406.124i			0.729127i	−0.931178	+	0.364564i	$0.881218\pi$
$558$	1091.67	+	761.183i	1.95641	+	1.36413i
$559$	−0.983064			−0.00175861
$560$			274.376i			0.489958i
$561$		0			0
$562$	−1354.87			−2.41081
$563$			322.277i			0.572429i	0.958166	+	0.286214i	$0.0923969\pi$
$563$			322.277i			0.572429i	−0.958166	+	0.286214i	$0.907603\pi$
$564$	−600.759	+	313.491i	−1.06518	+	0.555836i
$565$	412.388			0.729891
$566$		−	776.344i		−	1.37163i
$567$	−50.8169	−	137.917i	−0.0896242	−	0.243240i
$568$	−691.547			−1.21751
$569$			436.015i			0.766284i	0.923690	+	0.383142i	$0.125158\pi$
$569$			436.015i			0.766284i	−0.923690	+	0.383142i	$0.874842\pi$
$570$	−1010.47	−	1936.42i	−1.77276	−	3.39722i
$571$	155.637			0.272569			0.136284	−	0.990670i	$-0.456484\pi$
$571$	155.637			0.272569			0.136284	+	0.990670i	$0.456484\pi$
$572$		0			0
$573$	−64.6036	+	33.7118i	−0.112746	+	0.0588339i
$574$	451.517			0.786615
$575$			255.892i			0.445029i
$576$	−260.608	+	373.759i	−0.452444	+	0.648887i
$577$	838.269			1.45281			0.726403	−	0.687269i	$-0.241191\pi$
$577$	838.269			1.45281			0.726403	+	0.687269i	$0.241191\pi$
$578$		−	964.856i		−	1.66930i
$579$	−280.092	−	536.753i	−0.483751	−	0.927035i
$580$	1970.26			3.39700
$581$		−	153.332i		−	0.263911i
$582$	896.361	−	467.744i	1.54014	−	0.803684i
$583$		0			0
$584$			1721.07i			2.94704i
$585$	−4.13627	−	2.88406i	−0.00707054	−	0.00493002i
$586$	−1550.06			−2.64515
$587$			610.233i			1.03958i	0.854294	+	0.519790i	$0.173990\pi$
$587$			610.233i			1.03958i	−0.854294	+	0.519790i	$0.826010\pi$
$588$	−523.751	−	1003.69i	−0.890733	−	1.70696i
$589$	1112.02			1.88797
$590$			2206.86i			3.74045i
$591$	172.635	−	90.0855i	0.292107	−	0.152429i
$592$	70.8266			0.119640
$593$		−	626.517i		−	1.05652i	−0.849083	−	0.528260i	$-0.822845\pi$
$593$		−	626.517i		−	1.05652i	0.849083	−	0.528260i	$-0.177155\pi$
$594$		0			0
$595$	−52.4671			−0.0881799
$596$		−	252.186i		−	0.423130i
$597$	−189.117	−	362.414i	−0.316779	−	0.607059i
$598$	−1.69903			−0.00284119
$599$		−	1146.62i		−	1.91423i	−0.289710	−	0.957115i	$-0.593559\pi$
$599$		−	1146.62i		−	1.91423i	0.289710	−	0.957115i	$-0.406441\pi$
$600$	−1482.16	+	773.427i	−2.47026	+	1.28905i
$601$	611.591			1.01762			0.508811	−	0.860878i	$-0.330085\pi$
$601$	611.591			1.01762			0.508811	+	0.860878i	$0.330085\pi$
$602$			88.0490i			0.146261i
$603$	523.453	−	750.727i	0.868082	−	1.24499i
$604$	1364.58			2.25924
$605$		0			0
$606$	270.616	+	518.594i	0.446560	+	0.855766i
$607$	−111.551			−0.183774			−0.0918870	−	0.995769i	$-0.529290\pi$
$607$	−111.551			−0.183774			−0.0918870	+	0.995769i	$0.529290\pi$
$608$		−	195.074i		−	0.320845i
$609$	145.798	−	76.0812i	0.239406	−	0.124928i
$610$	2189.33			3.58907
$611$			1.94044i			0.00317585i
$612$	223.110	+	155.566i	0.364559	+	0.254193i
$613$	−724.023			−1.18111			−0.590557	−	0.806996i	$-0.701092\pi$
$613$	−724.023			−1.18111			−0.590557	+	0.806996i	$0.701092\pi$
$614$			1137.46i			1.85255i
$615$	779.210	+	1493.24i	1.26701	+	2.42803i
$616$		0			0
$617$		−	305.723i		−	0.495499i	−0.968824	−	0.247749i	$-0.920309\pi$
$617$		−	305.723i		−	0.495499i	0.968824	−	0.247749i	$-0.0796910\pi$
$618$	−1214.91	+	633.972i	−1.96588	+	1.02585i
$619$	991.029			1.60102			0.800508	−	0.599321i	$-0.204563\pi$
$619$	991.029			1.60102			0.800508	+	0.599321i	$0.204563\pi$
$620$		−	2754.73i		−	4.44311i
$621$	23.5700	−	183.234i	0.0379548	−	0.295063i
$622$	−409.620			−0.658553
$623$			82.2955i			0.132096i
$624$	−1.88430	−	3.61098i	−0.00301971	−	0.00578682i
$625$	−161.330			−0.258127
$626$			511.397i			0.816928i
$627$		0			0
$628$	1743.12			2.77567
$629$			13.5437i			0.0215321i
$630$	−258.313	+	370.468i	−0.410021	+	0.588045i
$631$	−540.450			−0.856498			−0.428249	−	0.903661i	$-0.640869\pi$
$631$	−540.450			−0.856498			−0.428249	+	0.903661i	$0.640869\pi$
$632$			937.109i			1.48277i
$633$	1.72367	+	3.30316i	0.00272302	+	0.00521826i
$634$	−236.531			−0.373077
$635$		−	461.888i		−	0.727383i
$636$	477.065	−	248.944i	0.750101	−	0.391422i
$637$	−3.24190			−0.00508933
$638$		0			0
$639$	−342.619	−	238.895i	−0.536181	−	0.373858i
$640$	1634.19			2.55343
$641$			284.824i			0.444342i	0.975008	+	0.222171i	$0.0713144\pi$
$641$			284.824i			0.444342i	−0.975008	+	0.222171i	$0.928686\pi$
$642$	282.491	+	541.351i	0.440017	+	0.843225i
$643$	162.316			0.252436			0.126218	−	0.992003i	$-0.459716\pi$
$643$	162.316			0.252436			0.126218	+	0.992003i	$0.459716\pi$
$644$			102.511i			0.159179i
$645$	−291.192	+	151.951i	−0.451460	+	0.235584i
$646$	337.373			0.522249
$647$		−	278.296i		−	0.430133i	−0.976599	−	0.215067i	$-0.931003\pi$
$647$		−	278.296i		−	0.430133i	0.976599	−	0.215067i	$-0.0689969\pi$
$648$	1132.55	−	417.300i	1.74777	−	0.643982i
$649$		0			0
$650$			9.28637i			0.0142867i
$651$	−106.373	−	203.849i	−0.163400	−	0.313132i
$652$	721.715			1.10692
$653$			597.644i			0.915228i	0.889151	+	0.457614i	$0.151296\pi$
$653$			597.644i			0.915228i	−0.889151	+	0.457614i	$0.848704\pi$
$654$	−456.354	+	238.137i	−0.697789	+	0.364124i
$655$	−1166.58			−1.78104
$656$			1360.51i			2.07394i
$657$	−594.545	+	852.685i	−0.904939	+	1.29785i
$658$	173.797			0.264130
$659$		−	187.267i		−	0.284169i	−0.989855	−	0.142085i	$-0.954620\pi$
$659$		−	187.267i		−	0.284169i	0.989855	−	0.142085i	$-0.0453805\pi$
$660$		0			0
$661$	218.982			0.331289			0.165645	−	0.986186i	$-0.447030\pi$
$661$	218.982			0.331289			0.165645	+	0.986186i	$0.447030\pi$
$662$		−	1062.40i		−	1.60484i
$663$	0.690502	−	0.360322i	0.00104148	−	0.000543471i
$664$	1259.14			1.89630
$665$			377.371i			0.567475i
$666$	95.6314	+	66.6801i	0.143591	+	0.100120i
$667$	206.707			0.309905
$668$		−	341.533i		−	0.511277i
$669$	−172.457	−	330.487i	−0.257783	−	0.494002i
$670$	−2812.17			−4.19726
$671$		0			0
$672$	−35.7599	+	18.6604i	−0.0532141	+	0.0277685i
$673$	614.140			0.912541			0.456271	−	0.889841i	$-0.349185\pi$
$673$	614.140			0.912541			0.456271	+	0.889841i	$0.349185\pi$
$674$		−	1944.54i		−	2.88507i
$675$	−1001.50	−	128.826i	−1.48370	−	0.190853i
$676$	1395.28			2.06402
$677$		−	815.420i		−	1.20446i	−0.798322	−	0.602230i	$-0.794279\pi$
$677$		−	815.420i		−	1.20446i	0.798322	−	0.602230i	$-0.205721\pi$
$678$	253.660	+	486.102i	0.374130	+	0.716964i
$679$	−174.684			−0.257267
$680$		−	430.851i		−	0.633605i
$681$	126.886	−	66.2122i	0.186323	−	0.0972279i
$682$		0			0
$683$		−	95.9038i		−	0.140416i	−0.997532	−	0.0702078i	$-0.977634\pi$
$683$		−	95.9038i		−	0.140416i	0.997532	−	0.0702078i	$-0.0223662\pi$
$684$	1118.92	−	1604.73i	1.63584	−	2.34609i
$685$	−1306.96			−1.90797
$686$			601.645i			0.877034i
$687$	101.603	+	194.707i	0.147894	+	0.283416i
$688$	−265.309			−0.385623
$689$		−	1.54091i		−	0.00223645i
$690$	−503.267	+	262.618i	−0.729372	+	0.380605i
$691$	296.210			0.428669			0.214335	−	0.976760i	$-0.431242\pi$
$691$	296.210			0.428669			0.214335	+	0.976760i	$0.431242\pi$
$692$		−	1707.69i		−	2.46776i
$693$		0			0
$694$	1358.25			1.95713
$695$		−	411.522i		−	0.592118i
$696$	624.767	+	1197.27i	0.897654	+	1.72022i
$697$	−260.160			−0.373257
$698$			1582.53i			2.26724i
$699$	−493.089	+	257.307i	−0.705421	+	0.368107i
$700$	560.293			0.800419
$701$		−	744.172i		−	1.06159i	−0.847501	−	0.530793i	$-0.821894\pi$
$701$		−	744.172i		−	1.06159i	0.847501	−	0.530793i	$-0.178106\pi$
$702$	0.855358	−	6.64960i	0.00121846	−	0.00947236i
$703$	97.4133			0.138568
$704$		0			0
$705$	299.933	+	574.776i	0.425436	+	0.815285i
$706$	−1065.87			−1.50972
$707$		−	101.064i		−	0.142948i
$708$	−1752.36	+	914.426i	−2.47508	+	1.29156i
$709$	−787.672			−1.11096			−0.555481	−	0.831529i	$-0.687466\pi$
$709$	−787.672			−1.11096			−0.555481	+	0.831529i	$0.687466\pi$
$710$			1283.43i			1.80764i
$711$	−323.725	+	464.281i	−0.455310	+	0.652997i
$712$	−675.798			−0.949155
$713$		−	289.009i		−	0.405342i
$714$	−32.2725	−	61.8454i	−0.0451996	−	0.0866182i
$715$		0			0
$716$		−	1141.78i		−	1.59467i
$717$	−933.455	+	487.101i	−1.30189	+	0.679360i
$718$	1061.17			1.47796
$719$		−	488.774i		−	0.679796i	−0.940462	−	0.339898i	$-0.889607\pi$
$719$		−	488.774i		−	0.679796i	0.940462	−	0.339898i	$-0.110393\pi$
$720$	−1116.29	−	778.348i	−1.55041	−	1.08104i
$721$	236.764			0.328382
$722$		−	1162.74i		−	1.61044i
$723$	243.583	+	466.791i	0.336906	+	0.645630i
$724$	511.324			0.706249
$725$		−	1129.80i		−	1.55834i
$726$		0			0
$727$	270.772			0.372452			0.186226	−	0.982507i	$-0.440374\pi$
$727$	270.772			0.372452			0.186226	+	0.982507i	$0.440374\pi$
$728$			1.91782i			0.00263437i
$729$	705.268	+	184.494i	0.967446	+	0.253079i
$730$	3194.09			4.37547
$731$		−	50.7331i		−	0.0694023i
$732$	907.162	+	1738.44i	1.23929	+	2.37492i
$733$	−406.257			−0.554238			−0.277119	−	0.960836i	$-0.589380\pi$
$733$	−406.257			−0.554238			−0.277119	+	0.960836i	$0.589380\pi$
$734$			1470.25i			2.00307i
$735$	−960.280	+	501.098i	−1.30650	+	0.681767i
$736$	−50.6990			−0.0688845
$737$		0			0
$738$	−1280.86	+	1836.98i	−1.73558	+	2.48914i
$739$	929.057			1.25718			0.628591	−	0.777736i	$-0.283632\pi$
$739$	929.057			1.25718			0.628591	+	0.777736i	$0.283632\pi$
$740$		−	241.316i		−	0.326103i
$741$	−2.59162	−	4.96646i	−0.00349747	−	0.00670237i
$742$	−138.013			−0.186001
$743$			725.561i			0.976529i	0.872696	+	0.488265i	$0.162370\pi$
$743$			725.561i			0.976529i	−0.872696	+	0.488265i	$0.837630\pi$
$744$	1673.97	−	873.522i	2.24996	−	1.17409i
$745$	−241.279			−0.323864
$746$		−	695.964i		−	0.932927i
$747$	623.828	+	434.972i	0.835111	+	0.582291i
$748$		0			0
$749$		−	105.499i		−	0.140853i
$750$	475.857	+	911.909i	0.634476	+	1.21588i
$751$	1100.10			1.46485			0.732425	−	0.680847i	$-0.238388\pi$
$751$	1100.10			1.46485			0.732425	+	0.680847i	$0.238388\pi$
$752$			523.685i			0.696390i
$753$	−369.717	+	192.928i	−0.490992	+	0.256212i
$754$	7.50144			0.00994886
$755$		−	1305.56i		−	1.72922i
$756$	−401.203	−	51.6080i	−0.530692	−	0.0682646i
$757$	−1261.28			−1.66616			−0.833078	−	0.553155i	$-0.813424\pi$
$757$	−1261.28			−1.66616			−0.833078	+	0.553155i	$0.813424\pi$
$758$		−	253.499i		−	0.334431i
$759$		0			0
$760$	−3098.91			−4.07752
$761$			116.639i			0.153270i	0.997059	+	0.0766352i	$0.0244177\pi$
$761$			116.639i			0.153270i	−0.997059	+	0.0766352i	$0.975582\pi$
$762$	544.449	−	284.107i	0.714500	−	0.372844i
$763$	88.9348			0.116559
$764$			200.548i			0.262498i
$765$	148.838	−	213.461i	0.194559	−	0.279033i
$766$	−1837.65			−2.39902
$767$			5.66009i			0.00737952i
$768$	724.135	+	1387.69i	0.942884	+	1.80689i
$769$	−1252.94			−1.62930			−0.814652	−	0.579949i	$-0.803072\pi$
$769$	−1252.94			−1.62930			−0.814652	+	0.579949i	$0.803072\pi$
$770$		0			0
$771$	−1136.67	+	593.142i	−1.47428	+	0.769315i
$772$	−1666.24			−2.15834
$773$			1168.27i			1.51134i	0.654953	+	0.755670i	$0.272689\pi$
$773$			1168.27i			1.51134i	−0.654953	+	0.755670i	$0.727311\pi$
$774$	−358.225	−	249.776i	−0.462823	−	0.322708i
$775$	−1579.63			−2.03823
$776$		−	1434.48i		−	1.84855i
$777$	−9.31839	−	17.8573i	−0.0119928	−	0.0229823i
$778$	1305.56			1.67810
$779$			1871.21i			2.40207i
$780$	−12.3031	+	6.42008i	−0.0157732	+	0.00823087i
$781$		0			0
$782$		−	87.6820i		−	0.112125i
$783$	−104.064	+	809.002i	−0.132905	+	1.03321i
$784$	−874.922			−1.11597
$785$		−	1667.73i		−	2.12450i
$786$	−717.566	−	1375.11i	−0.912934	−	1.74950i
$787$	−1106.83			−1.40639			−0.703195	−	0.710997i	$-0.748244\pi$
$787$	−1106.83			−1.40639			−0.703195	+	0.710997i	$0.748244\pi$
$788$		−	535.909i		−	0.680088i
$789$	536.289	−	279.850i	0.679708	−	0.354689i
$790$	1739.16			2.20147
$791$		−	94.7321i		−	0.119762i
$792$		0			0
$793$	5.61513			0.00708088
$794$			646.212i			0.813869i
$795$	−238.177	−	456.431i	−0.299594	−	0.574127i
$796$	−1125.04			−1.41336
$797$		−	64.9469i		−	0.0814892i	−0.999170	−	0.0407446i	$-0.987027\pi$
$797$		−	64.9469i		−	0.0814892i	0.999170	−	0.0407446i	$-0.0129730\pi$
$798$	−444.825	+	232.121i	−0.557425	+	0.290879i
$799$	−100.141			−0.125332
$800$			277.105i			0.346381i
$801$	−334.817	−	233.455i	−0.417999	−	0.291454i
$802$	317.851			0.396322
$803$		0			0
$804$	−1165.24	−	2233.00i	−1.44930	−	2.77736i
$805$	98.0773			0.121835
$806$		−	10.4882i		−	0.0130126i
$807$	912.397	−	476.112i	1.13060	−	0.589978i
$808$	829.924			1.02713
$809$		−	642.302i		−	0.793946i	−0.917830	−	0.396973i	$-0.870061\pi$
$809$		−	642.302i		−	0.793946i	0.917830	−	0.396973i	$-0.129939\pi$
$810$	−774.458	−	2101.88i	−0.956121	−	2.59491i
$811$	−91.2449			−0.112509			−0.0562546	−	0.998416i	$-0.517916\pi$
$811$	−91.2449			−0.112509			−0.0562546	+	0.998416i	$0.517916\pi$
$812$		−	452.599i		−	0.557388i
$813$	−565.681	−	1084.04i	−0.695795	−	1.33339i
$814$		0			0
$815$		−	690.500i		−	0.847239i
$816$	186.352	−	97.2433i	0.228373	−	0.119171i
$817$	−364.899			−0.446633
$818$			1925.23i			2.35358i
$819$	−0.662514	+	0.950165i	−0.000808930	+	0.00116015i
$820$	4635.44			5.65297
$821$			905.166i			1.10252i	0.834335	+	0.551258i	$0.185852\pi$
$821$			905.166i			1.10252i	−0.834335	+	0.551258i	$0.814148\pi$
$822$	−803.913	−	1540.58i	−0.977996	−	1.87418i
$823$	625.549			0.760084			0.380042	−	0.924969i	$-0.375910\pi$
$823$	625.549			0.760084			0.380042	+	0.924969i	$0.375910\pi$
$824$			1944.27i			2.35955i
$825$		0			0
$826$	506.951			0.613742
$827$		−	908.489i		−	1.09854i	−0.835647	−	0.549268i	$-0.814907\pi$
$827$		−	908.489i		−	1.09854i	0.835647	−	0.549268i	$-0.185093\pi$
$828$	−417.063	−	290.802i	−0.503699	−	0.351210i
$829$	−586.720			−0.707744			−0.353872	−	0.935294i	$-0.615135\pi$
$829$	−586.720			−0.707744			−0.353872	+	0.935294i	$0.615135\pi$
$830$		−	2336.81i		−	2.81544i
$831$	−689.770	−	1321.84i	−0.830048	−	1.59066i
$832$	3.59086			0.00431594
$833$		−	167.305i		−	0.200847i
$834$	485.080	−	253.127i	0.581631	−	0.303510i
$835$	−326.761			−0.391331
$836$		0			0
$837$	1131.11	+	145.498i	1.35139	+	0.173833i
$838$	−1044.68			−1.24663
$839$			1023.90i			1.22039i	0.792253	+	0.610193i	$0.208908\pi$
$839$			1023.90i			1.22039i	−0.792253	+	0.610193i	$0.791092\pi$
$840$	296.436	+	568.076i	0.352901	+	0.676281i
$841$	−71.6379			−0.0851818
$842$			429.212i			0.509753i
$843$	−1029.31	+	537.118i	−1.22100	+	0.637150i
$844$	10.2539			0.0121492
$845$		−	1334.93i		−	1.57980i
$846$	−493.027	+	707.090i	−0.582774	+	0.835803i
$847$		0			0
$848$		−	415.860i		−	0.490401i
$849$	−307.769	−	589.793i	−0.362508	−	0.694691i
$850$	−479.242			−0.563814
$851$		−	25.3174i		−	0.0297501i
$852$	−1019.10	+	531.794i	−1.19613	+	0.624172i
$853$	394.785			0.462820			0.231410	−	0.972856i	$-0.425666\pi$
$853$	394.785			0.462820			0.231410	+	0.972856i	$0.425666\pi$
$854$		−	502.924i		−	0.588904i
$855$	−1535.32	−	1070.52i	−1.79570	−	1.25207i
$856$	866.342			1.01208
$857$			1.34510i			0.00156955i	1.00000		0.000784774i	$0.000249801\pi$
$857$			1.34510i			0.00156955i	−1.00000		0.000784774i	$0.999750\pi$
$858$		0			0
$859$	847.638			0.986772			0.493386	−	0.869810i	$-0.335759\pi$
$859$	847.638			0.986772			0.493386	+	0.869810i	$0.335759\pi$
$860$			903.943i			1.05110i
$861$	343.020	−	178.997i	0.398398	−	0.207894i
$862$	−2069.14			−2.40039
$863$			465.409i			0.539292i	0.962960	+	0.269646i	$0.0869067\pi$
$863$			465.409i			0.539292i	−0.962960	+	0.269646i	$0.913093\pi$
$864$	25.5239	−	198.424i	0.0295415	−	0.229657i
$865$	−1633.83			−1.88882
$866$		−	2248.75i		−	2.59671i
$867$	−382.502	−	733.007i	−0.441179	−	0.845452i
$868$	−632.804			−0.729037
$869$		0			0
$870$	2221.99	−	1159.49i	2.55401	−	1.33275i
$871$	−7.21256			−0.00828078
$872$			730.319i			0.837521i
$873$	495.541	−	710.696i	0.567630	−	0.814085i
$874$	−630.655			−0.721574
$875$		−	177.714i		−	0.203102i
$876$	1323.49	+	2536.27i	1.51083	+	2.89528i
$877$	520.939			0.594001			0.297001	−	0.954877i	$-0.404014\pi$
$877$	520.939			0.594001			0.297001	+	0.954877i	$0.404014\pi$
$878$			1667.19i			1.89885i
$879$	−1177.59	+	614.496i	−1.33969	+	0.699085i
$880$		0			0
$881$		−	606.759i		−	0.688717i	−0.938838	−	0.344358i	$-0.888096\pi$
$881$		−	606.759i		−	0.688717i	0.938838	−	0.344358i	$-0.111904\pi$
$882$	−1181.34	−	823.701i	−1.33938	−	0.933901i
$883$	−111.764			−0.126574			−0.0632868	−	0.997995i	$-0.520158\pi$
$883$	−111.764			−0.126574			−0.0632868	+	0.997995i	$0.520158\pi$
$884$		−	2.14351i		−	0.00242479i
$885$	874.876	+	1676.57i	0.988561	+	1.89443i
$886$	−377.123			−0.425646
$887$		−	11.3992i		−	0.0128514i	−0.999979	−	0.00642569i	$-0.997955\pi$
$887$		−	11.3992i		−	0.0128514i	0.999979	−	0.00642569i	$-0.00204538\pi$
$888$	146.641	−	76.5211i	0.165136	−	0.0861725i
$889$	−106.103			−0.119351
$890$			1254.20i			1.40921i
$891$		0			0
$892$	−1025.93			−1.15014
$893$			720.265i			0.806567i
$894$	−148.411	−	284.406i	−0.166007	−	0.318128i
$895$	−1092.40			−1.22056
$896$		−	375.400i		−	0.418973i
$897$	−1.29076	+	0.673553i	−0.00143898	+	0.000750896i
$898$	785.867			0.875130
$899$			1276.01i			1.41937i
$900$	−1589.43	+	2279.53i	−1.76604	+	2.53282i
$901$	79.5220			0.0882597
$902$		0			0
$903$	34.9056	+	66.8914i	0.0386552	+	0.0740768i
$904$	777.925			0.860536
$905$		−	489.209i		−	0.540563i
$906$	1538.93	−	803.052i	1.69860	−	0.886371i
$907$	1595.32			1.75890			0.879451	−	0.475989i	$-0.157910\pi$
$907$	1595.32			1.75890			0.879451	+	0.475989i	$0.157910\pi$
$908$		−	393.889i		−	0.433799i
$909$	411.177	+	286.698i	0.452340	+	0.315399i
$910$	3.55925			0.00391126
$911$		−	605.434i		−	0.664581i	−0.943177	−	0.332291i	$-0.892178\pi$
$911$		−	605.434i		−	0.664581i	0.943177	−	0.332291i	$-0.107822\pi$
$912$	−699.425	−	1340.34i	−0.766914	−	1.46967i
$913$		0			0
$914$			249.573i			0.273056i
$915$	1663.25	−	867.927i	1.81776	−	0.948554i
$916$	604.425			0.659853
$917$			267.983i			0.292238i
$918$	343.166	+	44.1425i	0.373819	+	0.0480856i
$919$	−367.560			−0.399956			−0.199978	−	0.979800i	$-0.564087\pi$
$919$	−367.560			−0.399956			−0.199978	+	0.979800i	$0.564087\pi$
$920$			805.395i			0.875430i
$921$	450.930	+	864.139i	0.489609	+	0.938261i
$922$	−3068.67			−3.32828
$923$			3.29169i			0.00356630i
$924$		0			0
$925$	−138.377			−0.149597
$926$			2887.17i			3.11789i
$927$	−671.648	+	963.266i	−0.724540	+	1.03912i
$928$	223.843			0.241210
$929$		−	1671.79i		−	1.79956i	−0.436349	−	0.899778i	$-0.643729\pi$
$929$		−	1671.79i		−	1.79956i	0.436349	−	0.899778i	$-0.356271\pi$
$930$	−1621.15	−	3106.69i	−1.74317	−	3.34053i
$931$	−1203.35			−1.29253
$932$			1530.69i			1.64237i
$933$	−311.191	+	162.387i	−0.333538	+	0.174049i
$934$	1124.00			1.20343
$935$		0			0
$936$	−7.80261	−	5.44046i	−0.00833612	−	0.00581246i
$937$	1000.87			1.06817			0.534085	−	0.845431i	$-0.320656\pi$
$937$	1000.87			1.06817			0.534085	+	0.845431i	$0.320656\pi$
$938$			645.999i			0.688698i
$939$	202.735	+	388.512i	0.215906	+	0.413750i
$940$	1784.27			1.89816
$941$			352.323i			0.374413i	0.982321	+	0.187206i	$0.0599433\pi$
$941$			352.323i			0.374413i	−0.982321	+	0.187206i	$0.940057\pi$
$942$	1965.83	−	1025.82i	2.08687	−	1.08898i
$943$	486.321			0.515717
$944$			1527.54i			1.61816i
$945$	−49.3760	+	383.851i	−0.0522497	+	0.406192i
$946$		0			0
$947$			1536.20i			1.62217i	0.584927	+	0.811086i	$0.301123\pi$
$947$			1536.20i			1.62217i	−0.584927	+	0.811086i	$0.698877\pi$
$948$	720.630	+	1380.98i	0.760158	+	1.45673i
$949$	8.19211			0.00863236
$950$			3446.97i			3.62839i
$951$	−179.694	+	93.7690i	−0.188953	+	0.0986004i
$952$	−98.9733			−0.103964
$953$		−	897.350i		−	0.941606i	−0.882238	−	0.470803i	$-0.843964\pi$
$953$		−	897.350i		−	0.941606i	0.882238	−	0.470803i	$-0.156036\pi$
$954$	391.514	−	561.502i	0.410392	−	0.588577i
$955$	191.874			0.200915
$956$			2897.71i			3.03108i
$957$		0			0
$958$	1516.66			1.58315
$959$			300.230i			0.313065i
$960$	1063.64	−	555.036i	1.10796	−	0.578163i
$961$	823.062			0.856465
$962$		−	0.918772i		−	0.000955064i
$963$	429.220	+	299.279i	0.445711	+	0.310777i
$964$	1449.05			1.50317
$965$			1594.17i			1.65199i
$966$	60.3274	+	115.608i	0.0624507	+	0.119677i
$967$	1717.58			1.77620			0.888099	−	0.459652i	$-0.152026\pi$
$967$	1717.58			1.77620			0.888099	+	0.459652i	$0.152026\pi$
$968$		0			0
$969$	256.304	−	133.746i	0.264504	−	0.138025i
$970$	−2662.21			−2.74455
$971$			1498.74i			1.54350i	0.635927	+	0.771749i	$0.280618\pi$
$971$			1498.74i			1.54350i	−0.635927	+	0.771749i	$0.719382\pi$
$972$	1348.09	−	1485.88i	1.38693	−	1.52869i
$973$	−94.5330			−0.0971563
$974$			1234.27i			1.26722i
$975$	3.68143	+	7.05491i	0.00377583	+	0.00723581i
$976$	1515.41			1.55267
$977$			56.4391i			0.0577677i	0.999583	+	0.0288839i	$0.00919530\pi$
$977$			56.4391i			0.0577677i	−0.999583	+	0.0288839i	$0.990805\pi$
$978$	813.925	−	424.727i	0.832234	−	0.434281i
$979$		0			0
$980$			2980.98i			3.04182i
$981$	−252.289	+	361.828i	−0.257175	+	0.368836i
$982$	−1562.75			−1.59140
$983$		−	47.5555i		−	0.0483779i	−0.999707	−	0.0241889i	$-0.992300\pi$
$983$		−	47.5555i		−	0.0483779i	0.999707	−	0.0241889i	$-0.00770033\pi$
$984$	1469.89	+	2816.83i	1.49379	+	2.86263i
$985$	−512.731			−0.520539
$986$			387.127i			0.392624i
$987$	132.035	−	68.8992i	0.133774	−	0.0698067i
$988$	−15.4173			−0.0156046
$989$			94.8360i			0.0958908i
$990$		0			0
$991$	−218.685			−0.220671			−0.110336	−	0.993894i	$-0.535193\pi$
$991$	−218.685			−0.220671			−0.110336	+	0.993894i	$0.535193\pi$
$992$		−	312.967i		−	0.315491i
$993$	−421.173	−	807.115i	−0.424142	−	0.812804i
$994$	294.823			0.296603
$995$			1076.38i			1.08179i
$996$	1855.54	−	968.270i	1.86300	−	0.972159i
$997$	657.652			0.659631			0.329816	−	0.944045i	$-0.393013\pi$
$997$	657.652			0.659631			0.329816	+	0.944045i	$0.393013\pi$
$998$		−	314.274i		−	0.314904i
$999$	99.0861	+	12.7458i	0.0991853	+	0.0127585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.j.122.1	✓	6
3.2	odd	2	inner	363.3.b.j.122.6	yes	6
11.2	odd	10		363.3.h.p.323.6		24
11.3	even	5		363.3.h.q.251.1		24
11.4	even	5		363.3.h.q.269.6		24
11.5	even	5		363.3.h.q.245.6		24
11.6	odd	10		363.3.h.p.245.1		24
11.7	odd	10		363.3.h.p.269.1		24
11.8	odd	10		363.3.h.p.251.6		24
11.9	even	5		363.3.h.q.323.1		24
11.10	odd	2		363.3.b.k.122.6	yes	6
33.2	even	10		363.3.h.p.323.1		24
33.5	odd	10		363.3.h.q.245.1		24
33.8	even	10		363.3.h.p.251.1		24
33.14	odd	10		363.3.h.q.251.6		24
33.17	even	10		363.3.h.p.245.6		24
33.20	odd	10		363.3.h.q.323.6		24
33.26	odd	10		363.3.h.q.269.1		24
33.29	even	10		363.3.h.p.269.6		24
33.32	even	2		363.3.b.k.122.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.1	✓	6	1.1	even	1	trivial
363.3.b.j.122.6	yes	6	3.2	odd	2	inner
363.3.b.k.122.1	yes	6	33.32	even	2
363.3.b.k.122.6	yes	6	11.10	odd	2
363.3.h.p.245.1		24	11.6	odd	10
363.3.h.p.245.6		24	33.17	even	10
363.3.h.p.251.1		24	33.8	even	10
363.3.h.p.251.6		24	11.8	odd	10
363.3.h.p.269.1		24	11.7	odd	10
363.3.h.p.269.6		24	33.29	even	10
363.3.h.p.323.1		24	33.2	even	10
363.3.h.p.323.6		24	11.2	odd	10
363.3.h.q.245.1		24	33.5	odd	10
363.3.h.q.245.6		24	11.5	even	5
363.3.h.q.251.1		24	11.3	even	5
363.3.h.q.251.6		24	33.14	odd	10
363.3.h.q.269.1		24	33.26	odd	10
363.3.h.q.269.6		24	11.4	even	5
363.3.h.q.323.1		24	11.9	even	5
363.3.h.q.323.6		24	33.20	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)

\(f(q)\)	\(=\)	\(q-3.50091i q^{2} +(-1.38788 - 2.65966i) q^{3} -8.25635 q^{4} +7.89925i q^{5} +(-9.31122 + 4.85883i) q^{6} +1.81458 q^{7} +14.9011i q^{8} +(-5.14758 + 7.38257i) q^{9} +O(q^{10})\)	\(q-3.50091i q^{2} +(-1.38788 - 2.65966i) q^{3} -8.25635 q^{4} +7.89925i q^{5} +(-9.31122 + 4.85883i) q^{6} +1.81458 q^{7} +14.9011i q^{8} +(-5.14758 + 7.38257i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +0.0709275 q^{13} -6.35268i q^{14} +(21.0093 - 10.9632i) q^{15} +19.1419 q^{16} +3.66036i q^{17} +(25.8457 + 18.0212i) q^{18} +26.3273 q^{19} -65.2190i q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(39.6318 - 20.6809i) q^{24} -37.3982 q^{25} -0.248311i q^{26} +(26.7794 + 3.44471i) q^{27} -14.9818 q^{28} +30.2099i q^{29} +(-38.3812 - 73.5517i) q^{30} +42.2382 q^{31} -7.40958i q^{32} +12.8146 q^{34} +14.3338i q^{35} +(42.5002 - 60.9531i) q^{36} +3.70009 q^{37} -92.1693i q^{38} +(-0.0984388 - 0.188643i) q^{39} -117.707 q^{40} +71.0750i q^{41} +(-16.8960 + 8.81675i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} -23.9545 q^{46} +27.3581i q^{47} +(-26.5666 - 50.9108i) q^{48} -45.7073 q^{49} +130.928i q^{50} +(9.73532 - 5.08014i) q^{51} -0.585602 q^{52} -21.7252i q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(-36.5391 - 70.0216i) q^{57} +105.762 q^{58} +79.8011i q^{59} +(-173.460 + 90.5160i) q^{60} +79.1672 q^{61} -147.872i q^{62} +(-9.34072 + 13.3963i) q^{63} +50.6272 q^{64} +0.560274i q^{65} -101.689 q^{67} -30.2212i q^{68} +(-18.1983 + 9.49636i) q^{69} +50.1814 q^{70} +46.4092i q^{71} +(-110.008 - 76.7045i) q^{72} +115.500 q^{73} -12.9537i q^{74} +(51.9042 + 99.4665i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +62.8887 q^{79} +151.206i q^{80} +(-28.0047 - 76.0048i) q^{81} +248.827 q^{82} -84.5001i q^{83} +(20.7929 + 39.8465i) q^{84} -28.9141 q^{85} +48.5230i q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(-142.354 + 204.162i) q^{90} +0.128704 q^{91} +56.4929i q^{92} +(-58.6215 - 112.339i) q^{93} +95.7782 q^{94} +207.966i q^{95} +(-19.7070 + 10.2836i) q^{96} -96.2668 q^{97} +160.017i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 18 q^{4} - 10 q^{6} - 22 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 - 18 * q^4 - 10 * q^6 - 22 * q^9	\( 6 q + 4 q^{3} - 18 q^{4} - 10 q^{6} - 22 q^{9} + 18 q^{10} + 14 q^{12} - 42 q^{13} + 28 q^{15} + 30 q^{16} + 94 q^{18} + 84 q^{19} - 28 q^{21} + 48 q^{24} - 108 q^{25} - 38 q^{27} + 132 q^{28} - 148 q^{30} + 66 q^{34} + 46 q^{36} - 42 q^{37} - 82 q^{39} - 294 q^{40} - 206 q^{42} - 156 q^{43} - 118 q^{45} - 60 q^{46} - 88 q^{48} + 138 q^{49} + 182 q^{51} + 114 q^{52} + 140 q^{54} - 24 q^{57} - 54 q^{58} - 562 q^{60} + 264 q^{61} - 122 q^{63} + 294 q^{64} + 24 q^{67} + 152 q^{69} + 336 q^{70} - 306 q^{72} + 72 q^{73} + 62 q^{75} - 408 q^{76} - 194 q^{78} - 250 q^{81} + 798 q^{82} + 328 q^{84} + 330 q^{85} + 462 q^{87} - 230 q^{90} + 300 q^{91} - 266 q^{93} + 120 q^{94} - 386 q^{96} + 126 q^{97}+O(q^{100}) \) 6 * q + 4 * q^3 - 18 * q^4 - 10 * q^6 - 22 * q^9 + 18 * q^10 + 14 * q^12 - 42 * q^13 + 28 * q^15 + 30 * q^16 + 94 * q^18 + 84 * q^19 - 28 * q^21 + 48 * q^24 - 108 * q^25 - 38 * q^27 + 132 * q^28 - 148 * q^30 + 66 * q^34 + 46 * q^36 - 42 * q^37 - 82 * q^39 - 294 * q^40 - 206 * q^42 - 156 * q^43 - 118 * q^45 - 60 * q^46 - 88 * q^48 + 138 * q^49 + 182 * q^51 + 114 * q^52 + 140 * q^54 - 24 * q^57 - 54 * q^58 - 562 * q^60 + 264 * q^61 - 122 * q^63 + 294 * q^64 + 24 * q^67 + 152 * q^69 + 336 * q^70 - 306 * q^72 + 72 * q^73 + 62 * q^75 - 408 * q^76 - 194 * q^78 - 250 * q^81 + 798 * q^82 + 328 * q^84 + 330 * q^85 + 462 * q^87 - 230 * q^90 + 300 * q^91 - 266 * q^93 + 120 * q^94 - 386 * q^96 + 126 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more