LMFDB - Embedded newform 363.3.b.l.122.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
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			122.3
Root			$-2.00420i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.l.122.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00420i q^{2} +(2.80061 - 1.07544i) q^{3} -0.0168066 q^{4} -5.48438i q^{5} +(-2.15539 - 5.61298i) q^{6} -5.59084 q^{7} -7.98311i q^{8} +(6.68687 - 6.02376i) q^{9} +O(q^{10})$	\(q-2.00420i q^{2} +(2.80061 - 1.07544i) q^{3} -0.0168066 q^{4} -5.48438i q^{5} +(-2.15539 - 5.61298i) q^{6} -5.59084 q^{7} -7.98311i q^{8} +(6.68687 - 6.02376i) q^{9} -10.9918 q^{10} +(-0.0470687 + 0.0180744i) q^{12} +9.71679 q^{13} +11.2051i q^{14} +(-5.89810 - 15.3596i) q^{15} -16.0669 q^{16} +17.8716i q^{17} +(-12.0728 - 13.4018i) q^{18} -18.6589 q^{19} +0.0921737i q^{20} +(-15.6578 + 6.01259i) q^{21} +12.3649i q^{23} +(-8.58532 - 22.3576i) q^{24} -5.07844 q^{25} -19.4744i q^{26} +(12.2492 - 24.0615i) q^{27} +0.0939629 q^{28} +2.47732i q^{29} +(-30.7837 + 11.8210i) q^{30} +49.2308 q^{31} +0.268903i q^{32} +35.8182 q^{34} +30.6623i q^{35} +(-0.112383 + 0.101239i) q^{36} -39.3307 q^{37} +37.3961i q^{38} +(27.2130 - 10.4498i) q^{39} -43.7824 q^{40} -56.5236i q^{41} +(12.0504 + 31.3813i) q^{42} +43.9060 q^{43} +(-33.0366 - 36.6734i) q^{45} +24.7816 q^{46} -57.7840i q^{47} +(-44.9973 + 17.2790i) q^{48} -17.7425 q^{49} +10.1782i q^{50} +(19.2197 + 50.0514i) q^{51} -0.163306 q^{52} +43.1158i q^{53} +(-48.2241 - 24.5498i) q^{54} +44.6323i q^{56} +(-52.2564 + 20.0665i) q^{57} +4.96505 q^{58} +90.0311i q^{59} +(0.0991269 + 0.258143i) q^{60} +30.8695 q^{61} -98.6683i q^{62} +(-37.3852 + 33.6779i) q^{63} -63.7288 q^{64} -53.2906i q^{65} +34.0775 q^{67} -0.300360i q^{68} +(13.2976 + 34.6292i) q^{69} +61.4533 q^{70} +37.5962i q^{71} +(-48.0883 - 53.3820i) q^{72} +12.1261 q^{73} +78.8265i q^{74} +(-14.2228 + 5.46154i) q^{75} +0.313592 q^{76} +(-20.9434 - 54.5402i) q^{78} +63.1447 q^{79} +88.1173i q^{80} +(8.42858 - 80.5603i) q^{81} -113.284 q^{82} -9.70147i q^{83} +(0.263154 - 0.101051i) q^{84} +98.0146 q^{85} -87.9962i q^{86} +(2.66420 + 6.93803i) q^{87} +34.1289i q^{89} +(-73.5007 + 66.2119i) q^{90} -54.3250 q^{91} -0.207811i q^{92} +(137.877 - 52.9446i) q^{93} -115.811 q^{94} +102.333i q^{95} +(0.289188 + 0.753095i) q^{96} -37.8227 q^{97} +35.5595i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.00420i		−	1.00210i	−0.865419	−	0.501049i	$-0.832948\pi$
$2$		−	2.00420i		−	1.00210i	0.865419	−	0.501049i	$-0.167052\pi$
$3$	2.80061	−	1.07544i	0.933538	−	0.358479i
$3$	2.80061	−	1.07544i	0.933538	−	0.358479i
$4$	−0.0168066			−0.00420164
$5$		−	5.48438i		−	1.09688i	−0.836191	−	0.548438i	$-0.815223\pi$
$5$		−	5.48438i		−	1.09688i	0.836191	−	0.548438i	$-0.184777\pi$
$6$	−2.15539	−	5.61298i	−0.359231	−	0.935497i
$7$	−5.59084			−0.798691			−0.399346	−	0.916800i	$-0.630763\pi$
$7$	−5.59084			−0.798691			−0.399346	+	0.916800i	$0.630763\pi$
$8$		−	7.98311i		−	0.997888i
$9$	6.68687	−	6.02376i	0.742986	−	0.669307i
$10$	−10.9918			−1.09918
$11$		0			0
$11$		0			0
$12$	−0.0470687	+	0.0180744i	−0.00392239	+	0.00150620i
$13$	9.71679			0.747446			0.373723	−	0.927540i	$-0.378081\pi$
$13$	9.71679			0.747446			0.373723	+	0.927540i	$0.378081\pi$
$14$			11.2051i			0.800368i
$15$	−5.89810	−	15.3596i	−0.393207	−	1.02398i
$16$	−16.0669			−1.00418
$17$			17.8716i			1.05127i	0.850710	+	0.525635i	$0.176172\pi$
$17$			17.8716i			1.05127i	−0.850710	+	0.525635i	$0.823828\pi$
$18$	−12.0728	−	13.4018i	−0.670712	−	0.744545i
$19$	−18.6589			−0.982047			−0.491024	−	0.871146i	$-0.663377\pi$
$19$	−18.6589			−0.982047			−0.491024	+	0.871146i	$0.663377\pi$
$20$			0.0921737i			0.00460868i
$21$	−15.6578	+	6.01259i	−0.745609	+	0.286314i
$22$		0			0
$23$			12.3649i			0.537603i	0.963196	+	0.268801i	$0.0866275\pi$
$23$			12.3649i			0.537603i	−0.963196	+	0.268801i	$0.913372\pi$
$24$	−8.58532	−	22.3576i	−0.357722	−	0.931566i
$25$	−5.07844			−0.203138
$26$		−	19.4744i		−	0.749014i
$27$	12.2492	−	24.0615i	0.453673	−	0.891168i
$28$	0.0939629			0.00335582
$29$			2.47732i			0.0854250i	0.999087	+	0.0427125i	$0.0135999\pi$
$29$			2.47732i			0.0854250i	−0.999087	+	0.0427125i	$0.986400\pi$
$30$	−30.7837	+	11.8210i	−1.02612	+	0.394032i
$31$	49.2308			1.58809			0.794046	−	0.607858i	$-0.207971\pi$
$31$	49.2308			1.58809			0.794046	+	0.607858i	$0.207971\pi$
$32$			0.268903i			0.00840323i
$33$		0			0
$34$	35.8182			1.05348
$35$			30.6623i			0.876066i
$36$	−0.112383	+	0.101239i	−0.00312176	+	0.00281219i
$37$	−39.3307			−1.06299			−0.531496	−	0.847061i	$-0.678370\pi$
$37$	−39.3307			−1.06299			−0.531496	+	0.847061i	$0.678370\pi$
$38$			37.3961i			0.984108i
$39$	27.2130	−	10.4498i	0.697769	−	0.267943i
$40$	−43.7824			−1.09456
$41$		−	56.5236i		−	1.37862i	−0.724465	−	0.689312i	$-0.757913\pi$
$41$		−	56.5236i		−	1.37862i	0.724465	−	0.689312i	$-0.242087\pi$
$42$	12.0504	+	31.3813i	0.286915	+	0.747174i
$43$	43.9060			1.02107			0.510534	−	0.859857i	$-0.329448\pi$
$43$	43.9060			1.02107			0.510534	+	0.859857i	$0.329448\pi$
$44$		0			0
$45$	−33.0366	−	36.6734i	−0.734147	−	0.814964i
$46$	24.7816			0.538731
$47$		−	57.7840i		−	1.22945i	−0.788743	−	0.614723i	$-0.789268\pi$
$47$		−	57.7840i		−	1.22945i	0.788743	−	0.614723i	$-0.210732\pi$
$48$	−44.9973	+	17.2790i	−0.937444	+	0.359979i
$49$	−17.7425			−0.362092
$50$			10.1782i			0.203564i
$51$	19.2197	+	50.0514i	0.376858	+	0.981400i
$52$	−0.163306			−0.00314050
$53$			43.1158i			0.813506i	0.913538	+	0.406753i	$0.133339\pi$
$53$			43.1158i			0.813506i	−0.913538	+	0.406753i	$0.866661\pi$
$54$	−48.2241	−	24.5498i	−0.893038	−	0.454625i
$55$		0			0
$56$			44.6323i			0.797005i
$57$	−52.2564	+	20.0665i	−0.916778	+	0.352043i
$58$	4.96505			0.0856042
$59$			90.0311i			1.52595i	0.646427	+	0.762976i	$0.276262\pi$
$59$			90.0311i			1.52595i	−0.646427	+	0.762976i	$0.723738\pi$
$60$	0.0991269	+	0.258143i	0.00165211	+	0.00430238i
$61$	30.8695			0.506058			0.253029	−	0.967459i	$-0.418573\pi$
$61$	30.8695			0.506058			0.253029	+	0.967459i	$0.418573\pi$
$62$		−	98.6683i		−	1.59142i
$63$	−37.3852	+	33.6779i	−0.593417	+	0.534570i
$64$	−63.7288			−0.995763
$65$		−	53.2906i		−	0.819855i
$66$		0			0
$67$	34.0775			0.508620			0.254310	−	0.967123i	$-0.418152\pi$
$67$	34.0775			0.508620			0.254310	+	0.967123i	$0.418152\pi$
$68$		−	0.300360i		−	0.00441706i
$69$	13.2976	+	34.6292i	0.192719	+	0.501872i
$70$	61.4533			0.877904
$71$			37.5962i			0.529524i	0.964314	+	0.264762i	$0.0852934\pi$
$71$			37.5962i			0.529524i	−0.964314	+	0.264762i	$0.914707\pi$
$72$	−48.0883	−	53.3820i	−0.667893	−	0.741417i
$73$	12.1261			0.166111			0.0830554	−	0.996545i	$-0.473532\pi$
$73$	12.1261			0.166111			0.0830554	+	0.996545i	$0.473532\pi$
$74$			78.8265i			1.06522i
$75$	−14.2228	+	5.46154i	−0.189637	+	0.0728205i
$76$	0.313592			0.00412621
$77$		0			0
$78$	−20.9434	−	54.5402i	−0.268506	−	0.699233i
$79$	63.1447			0.799300			0.399650	−	0.916668i	$-0.369132\pi$
$79$	63.1447			0.799300			0.399650	+	0.916668i	$0.369132\pi$
$80$			88.1173i			1.10147i
$81$	8.42858	−	80.5603i	0.104056	−	0.994571i
$82$	−113.284			−1.38152
$83$		−	9.70147i		−	0.116885i	−0.998291	−	0.0584426i	$-0.981387\pi$
$83$		−	9.70147i		−	0.116885i	0.998291	−	0.0584426i	$-0.0186135\pi$
$84$	0.263154	−	0.101051i	0.00313278	−	0.00120299i
$85$	98.0146			1.15311
$86$		−	87.9962i		−	1.02321i
$87$	2.66420	+	6.93803i	0.0306230	+	0.0797474i
$88$		0			0
$89$			34.1289i			0.383471i	0.981447	+	0.191735i	$0.0614115\pi$
$89$			34.1289i			0.383471i	−0.981447	+	0.191735i	$0.938588\pi$
$90$	−73.5007	+	66.2119i	−0.816674	+	0.735688i
$91$	−54.3250			−0.596978
$92$		−	0.207811i		−	0.00225881i
$93$	137.877	−	52.9446i	1.48254	−	0.569297i
$94$	−115.811			−1.23203
$95$			102.333i			1.07718i
$96$	0.289188	+	0.753095i	0.00301238	+	0.00784473i
$97$	−37.8227			−0.389925			−0.194962	−	0.980811i	$-0.562458\pi$
$97$	−37.8227			−0.389925			−0.194962	+	0.980811i	$0.562458\pi$
$98$			35.5595i			0.362852i
$99$		0			0
$100$	0.0853512			0.000853512
$101$		−	46.9047i		−	0.464403i	−0.972668	−	0.232202i	$-0.925407\pi$
$101$		−	46.9047i		−	0.464403i	0.972668	−	0.232202i	$-0.0745929\pi$
$102$	100.313	−	38.5202i	0.983460	−	0.377649i
$103$	104.797			1.01744			0.508722	−	0.860931i	$-0.330118\pi$
$103$	104.797			1.01744			0.508722	+	0.860931i	$0.330118\pi$
$104$		−	77.5702i		−	0.745867i
$105$	32.9753	+	85.8733i	0.314051	+	0.817841i
$106$	86.4126			0.815213
$107$		−	46.6302i		−	0.435796i	−0.975972	−	0.217898i	$-0.930080\pi$
$107$		−	46.6302i		−	0.435796i	0.975972	−	0.217898i	$-0.0699200\pi$
$108$	−0.205867	+	0.404392i	−0.00190617	+	0.00374437i
$109$	168.413			1.54507			0.772537	−	0.634969i	$-0.218987\pi$
$109$	168.413			1.54507			0.772537	+	0.634969i	$0.218987\pi$
$110$		0			0
$111$	−110.150	+	42.2977i	−0.992344	+	0.381060i
$112$	89.8277			0.802033
$113$		−	46.3202i		−	0.409913i	−0.978771	−	0.204957i	$-0.934295\pi$
$113$		−	46.3202i		−	0.409913i	0.978771	−	0.204957i	$-0.0657053\pi$
$114$	40.2171	+	104.732i	0.352782	+	0.918702i
$115$	67.8136			0.589684
$116$		−	0.0416353i		−	0.000358925i
$117$	64.9750	−	58.5317i	0.555342	−	0.500271i
$118$	180.440			1.52915
$119$		−	99.9172i		−	0.839640i
$120$	−122.618	+	47.0852i	−1.02181	+	0.392376i
$121$		0			0
$122$		−	61.8686i		−	0.507120i
$123$	−60.7875	−	158.301i	−0.494207	−	1.28700i
$124$	−0.827402			−0.00667260
$125$		−	109.257i		−	0.874059i
$126$	67.4971	+	74.9274i	0.535692	+	0.594662i
$127$	68.2888			0.537707			0.268854	−	0.963181i	$-0.413355\pi$
$127$	68.2888			0.537707			0.268854	+	0.963181i	$0.413355\pi$
$128$			128.801i			1.00626i
$129$	122.964	−	47.2180i	0.953206	−	0.366031i
$130$	−106.805			−0.821576
$131$			162.272i			1.23872i	0.785109	+	0.619358i	$0.212607\pi$
$131$			162.272i			1.23872i	−0.785109	+	0.619358i	$0.787393\pi$
$132$		0			0
$133$	104.319			0.784353
$134$		−	68.2981i		−	0.509687i
$135$	−131.963	−	67.1792i	−0.977501	−	0.497624i
$136$	142.671			1.04905
$137$			52.8671i			0.385891i	0.981209	+	0.192946i	$0.0618041\pi$
$137$			52.8671i			0.385891i	−0.981209	+	0.192946i	$0.938196\pi$
$138$	69.4037	−	26.6510i	0.502926	−	0.193124i
$139$	86.5357			0.622559			0.311279	−	0.950318i	$-0.399242\pi$
$139$	86.5357			0.622559			0.311279	+	0.950318i	$0.399242\pi$
$140$		−	0.515328i		−	0.00368092i
$141$	−62.1430	−	161.831i	−0.440730	−	1.14773i
$142$	75.3502			0.530635
$143$		0			0
$144$	−107.438	+	96.7835i	−0.746095	+	0.672107i
$145$	13.5866			0.0937006
$146$		−	24.3031i		−	0.166459i
$147$	−49.6899	+	19.0809i	−0.338027	+	0.129802i
$148$	0.661015			0.00446631
$149$		−	64.4499i		−	0.432550i	−0.976332	−	0.216275i	$-0.930609\pi$
$149$		−	64.4499i		−	0.432550i	0.976332	−	0.216275i	$-0.0693908\pi$
$150$	10.9460	+	28.5052i	0.0729734	+	0.190035i
$151$	−44.6348			−0.295595			−0.147797	−	0.989018i	$-0.547218\pi$
$151$	−44.6348			−0.295595			−0.147797	+	0.989018i	$0.547218\pi$
$152$			148.956i			0.979973i
$153$	107.654	+	119.505i	0.703622	+	0.781079i
$154$		0			0
$155$		−	270.001i		−	1.74194i
$156$	−0.457357	+	0.175625i	−0.00293178	+	0.00112580i
$157$	−141.066			−0.898510			−0.449255	−	0.893404i	$-0.648311\pi$
$157$	−141.066			−0.898510			−0.449255	+	0.893404i	$0.648311\pi$
$158$		−	126.554i		−	0.800978i
$159$	46.3683	+	120.751i	0.291625	+	0.759439i
$160$	1.47477			0.00921731
$161$		−	69.1300i		−	0.429379i
$162$	−161.459	−	16.8925i	−0.996659	−	0.104275i
$163$	120.965			0.742114			0.371057	−	0.928610i	$-0.378995\pi$
$163$	120.965			0.742114			0.371057	+	0.928610i	$0.378995\pi$
$164$			0.949967i			0.00579248i
$165$		0			0
$166$	−19.4437			−0.117130
$167$			107.432i			0.643304i	0.946858	+	0.321652i	$0.104238\pi$
$167$			107.432i			0.643304i	−0.946858	+	0.321652i	$0.895762\pi$
$168$	47.9992	+	124.998i	0.285709	+	0.744034i
$169$	−74.5839			−0.441325
$170$		−	196.441i		−	1.15553i
$171$	−124.770	+	112.397i	−0.729647	+	0.657291i
$172$	−0.737909			−0.00429017
$173$			328.814i			1.90066i	0.311246	+	0.950329i	$0.399254\pi$
$173$			328.814i			1.90066i	−0.311246	+	0.950329i	$0.600746\pi$
$174$	13.9052	−	5.33959i	0.0799148	−	0.0306873i
$175$	28.3928			0.162244
$176$		0			0
$177$	96.8227	+	252.142i	0.547021	+	1.42453i
$178$	68.4011			0.384276
$179$			48.2985i			0.269824i	0.990858	+	0.134912i	$0.0430752\pi$
$179$			48.2985i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$180$	0.555232	+	0.616354i	0.00308462	+	0.00342419i
$181$	0.0665674			0.000367776			0.000183888	−	1.00000i	$-0.499941\pi$
$181$	0.0665674			0.000367776			0.000183888		1.00000i	$0.499941\pi$
$182$			108.878i			0.598231i
$183$	86.4536	−	33.1982i	0.472424	−	0.181411i
$184$	98.7100			0.536467
$185$			215.705i			1.16597i
$186$	−106.111	−	276.332i	−0.570492	−	1.48566i
$187$		0			0
$188$			0.971151i			0.00516570i
$189$	−68.4832	+	134.524i	−0.362345	+	0.711768i
$190$	205.095			1.07944
$191$			197.414i			1.03358i	0.856112	+	0.516790i	$0.172873\pi$
$191$			197.414i			1.03358i	−0.856112	+	0.516790i	$0.827127\pi$
$192$	−178.480	+	68.5363i	−0.929583	+	0.356960i
$193$	−1.52366			−0.00789462			−0.00394731	−	0.999992i	$-0.501256\pi$
$193$	−1.52366			−0.00789462			−0.00394731	+	0.999992i	$0.501256\pi$
$194$			75.8042i			0.390743i
$195$	−57.3106	−	149.246i	−0.293901	−	0.765366i
$196$	0.298191			0.00152138
$197$		−	215.460i		−	1.09370i	−0.837229	−	0.546852i	$-0.815826\pi$
$197$		−	215.460i		−	1.09370i	0.837229	−	0.546852i	$-0.184174\pi$
$198$		0			0
$199$	−106.663			−0.535993			−0.267997	−	0.963420i	$-0.586362\pi$
$199$	−106.663			−0.535993			−0.267997	+	0.963420i	$0.586362\pi$
$200$			40.5417i			0.202709i
$201$	95.4380	−	36.6482i	0.474816	−	0.182329i
$202$	−94.0063			−0.465378
$203$		−	13.8503i		−	0.0682282i
$204$	−0.323018	−	0.841193i	−0.00158342	−	0.00412349i
$205$	−309.997			−1.51218
$206$		−	210.033i		−	1.01958i
$207$	74.4830	+	82.6823i	0.359821	+	0.399431i
$208$	−156.119			−0.750573
$209$		0			0
$210$	172.107	−	66.0891i	0.819557	−	0.314710i
$211$	−214.825			−1.01813			−0.509065	−	0.860728i	$-0.670009\pi$
$211$	−214.825			−1.01813			−0.509065	+	0.860728i	$0.670009\pi$
$212$		−	0.724629i		−	0.00341806i
$213$	40.4323	+	105.292i	0.189823	+	0.494331i
$214$	−93.4561			−0.436711
$215$		−	240.797i		−	1.11999i
$216$	−192.086	−	97.7865i	−0.889286	−	0.452715i
$217$	−275.242			−1.26840
$218$		−	337.533i		−	1.54832i
$219$	33.9605	−	13.0408i	0.155071	−	0.0595472i
$220$		0			0
$221$			173.654i			0.785767i
$222$	84.7729	+	220.763i	0.381860	+	0.994426i
$223$	44.7688			0.200757			0.100379	−	0.994949i	$-0.467995\pi$
$223$	44.7688			0.200757			0.100379	+	0.994949i	$0.467995\pi$
$224$		−	1.50340i		−	0.00671159i
$225$	−33.9589	+	30.5913i	−0.150928	+	0.135961i
$226$	−92.8348			−0.410773
$227$		−	224.504i		−	0.989004i	−0.869177	−	0.494502i	$-0.835351\pi$
$227$		−	224.504i		−	0.989004i	0.869177	−	0.494502i	$-0.164649\pi$
$228$	0.878250	−	0.337248i	0.00385197	−	0.00147916i
$229$	−104.101			−0.454589			−0.227294	−	0.973826i	$-0.572988\pi$
$229$	−104.101			−0.454589			−0.227294	+	0.973826i	$0.572988\pi$
$230$		−	135.912i		−	0.590921i
$231$		0			0
$232$	19.7767			0.0852446
$233$		−	61.5290i		−	0.264073i	−0.991245	−	0.132036i	$-0.957848\pi$
$233$		−	61.5290i		−	0.264073i	0.991245	−	0.132036i	$-0.0421516\pi$
$234$	−117.309	−	130.223i	−0.501320	−	0.556507i
$235$	−316.909			−1.34855
$236$		−	1.51311i		−	0.00641150i
$237$	176.844	−	67.9081i	0.746177	−	0.286532i
$238$	−200.254			−0.841402
$239$			149.260i			0.624520i	0.949997	+	0.312260i	$0.101086\pi$
$239$			149.260i			0.624520i	−0.949997	+	0.312260i	$0.898914\pi$
$240$	94.7645	+	246.782i	0.394852	+	1.02826i
$241$	−358.881			−1.48913			−0.744567	−	0.667548i	$-0.767344\pi$
$241$	−358.881			−1.48913			−0.744567	+	0.667548i	$0.767344\pi$
$242$		0			0
$243$	−63.0323	−	234.683i	−0.259392	−	0.965772i
$244$	−0.518811			−0.00212627
$245$			97.3067i			0.397170i
$246$	−317.266	+	121.830i	−1.28970	+	0.495244i
$247$	−181.305			−0.734027
$248$		−	393.015i		−	1.58474i
$249$	−10.4333	−	27.1701i	−0.0419008	−	0.109117i
$250$	−218.973			−0.875894
$251$			357.022i			1.42240i	0.702990	+	0.711199i	$0.251848\pi$
$251$			357.022i			1.42240i	−0.702990	+	0.711199i	$0.748152\pi$
$252$	0.628318	−	0.566010i	0.00249332	−	0.00224607i
$253$		0			0
$254$		−	136.864i		−	0.538836i
$255$	274.501	−	105.408i	1.07647	−	0.413366i
$256$	3.22681			0.0126047
$257$		−	66.0935i		−	0.257173i	−0.991698	−	0.128586i	$-0.958956\pi$
$257$		−	66.0935i		−	0.257173i	0.991698	−	0.128586i	$-0.0410440\pi$
$258$	−94.6343	−	246.443i	−0.366800	−	0.955207i
$259$	219.892			0.849003
$260$			0.895632i			0.00344474i
$261$	14.9228	+	16.5656i	0.0571755	+	0.0634696i
$262$	325.224			1.24131
$263$		−	85.4194i		−	0.324789i	−0.986726	−	0.162394i	$-0.948078\pi$
$263$		−	85.4194i		−	0.324789i	0.986726	−	0.162394i	$-0.0519216\pi$
$264$		0			0
$265$	236.464			0.892315
$266$		−	209.076i		−	0.785999i
$267$	36.7035	+	95.5819i	0.137466	+	0.357985i
$268$	−0.572726			−0.00213704
$269$			161.784i			0.601427i	0.953715	+	0.300713i	$0.0972248\pi$
$269$			161.784i			0.601427i	−0.953715	+	0.300713i	$0.902775\pi$
$270$	−134.640	+	264.479i	−0.498668	+	0.979553i
$271$	259.994			0.959386			0.479693	−	0.877436i	$-0.340748\pi$
$271$	259.994			0.959386			0.479693	+	0.877436i	$0.340748\pi$
$272$		−	287.142i		−	1.05567i
$273$	−152.143	+	58.4231i	−0.557302	+	0.214004i
$274$	105.956			0.386701
$275$		0			0
$276$	−0.223487	−	0.581998i	−0.000809737	−	0.00210869i
$277$	86.7920			0.313329			0.156664	−	0.987652i	$-0.449926\pi$
$277$	86.7920			0.313329			0.156664	+	0.987652i	$0.449926\pi$
$278$		−	173.435i		−	0.623865i
$279$	329.200	−	296.555i	1.17993	−	1.06292i
$280$	244.780			0.874216
$281$			484.715i			1.72496i	0.506087	+	0.862482i	$0.331091\pi$
$281$			484.715i			1.72496i	−0.506087	+	0.862482i	$0.668909\pi$
$282$	−324.340	+	124.547i	−1.15014	+	0.441655i
$283$	−432.072			−1.52676			−0.763379	−	0.645951i	$-0.776461\pi$
$283$	−432.072			−1.52676			−0.763379	+	0.645951i	$0.776461\pi$
$284$		−	0.631864i		−	0.00222487i
$285$	110.052	+	286.594i	0.386148	+	1.00559i
$286$		0			0
$287$			316.014i			1.10109i
$288$	1.61981	+	1.79812i	0.00562434	+	0.00624348i
$289$	−30.3935			−0.105168
$290$		−	27.2302i		−	0.0938973i
$291$	−105.927	+	40.6759i	−0.364010	+	0.139780i
$292$	−0.203798			−0.000697939
$293$		−	5.52957i		−	0.0188723i	−0.999955	−	0.00943613i	$-0.996996\pi$
$293$		−	5.52957i		−	0.0188723i	0.999955	−	0.00943613i	$-0.00300366\pi$
$294$	38.2419	+	99.5884i	0.130075	+	0.338736i
$295$	493.765			1.67378
$296$			313.981i			1.06075i
$297$		0			0
$298$	−129.170			−0.433458
$299$			120.147i			0.401829i
$300$	0.239036	−	0.0917898i	0.000796786	−	0.000305966i
$301$	−245.471			−0.815519
$302$			89.4569i			0.296215i
$303$	−50.4430	−	131.362i	−0.166479	−	0.433538i
$304$	299.791			0.986156
$305$		−	169.300i		−	0.555083i
$306$	239.512	−	215.760i	0.782718	−	0.705099i
$307$	−219.257			−0.714191			−0.357095	−	0.934068i	$-0.616233\pi$
$307$	−219.257			−0.714191			−0.357095	+	0.934068i	$0.616233\pi$
$308$		0			0
$309$	293.495	−	112.702i	0.949823	−	0.364732i
$310$	−541.135			−1.74560
$311$			142.150i			0.457075i	0.973535	+	0.228537i	$0.0733943\pi$
$311$			142.150i			0.457075i	−0.973535	+	0.228537i	$0.926606\pi$
$312$	−83.4218	−	217.244i	−0.267377	−	0.696295i
$313$	94.2857			0.301232			0.150616	−	0.988592i	$-0.451874\pi$
$313$	94.2857			0.301232			0.150616	+	0.988592i	$0.451874\pi$
$314$			282.724i			0.900396i
$315$	184.702	+	205.035i	0.586357	+	0.650905i
$316$	−1.06125			−0.00335838
$317$		−	501.215i		−	1.58112i	−0.612385	−	0.790560i	$-0.709790\pi$
$317$		−	501.215i		−	1.58112i	0.612385	−	0.790560i	$-0.290210\pi$
$318$	242.008	−	92.9312i	0.761032	−	0.292237i
$319$		0			0
$320$			349.513i			1.09223i
$321$	−50.1478	−	130.593i	−0.156224	−	0.406832i
$322$	−138.550			−0.430280
$323$		−	333.464i		−	1.03240i
$324$	−0.141655	+	1.35394i	−0.000437208	+	0.00417883i
$325$	−49.3462			−0.151834
$326$		−	242.437i		−	0.743672i
$327$	471.660	−	181.118i	1.44239	−	0.553876i
$328$	−451.234			−1.37571
$329$			323.061i			0.981948i
$330$		0			0
$331$	−653.489			−1.97429			−0.987143	−	0.159839i	$-0.948903\pi$
$331$	−653.489			−1.97429			−0.987143	+	0.159839i	$0.948903\pi$
$332$			0.163048i			0.000491110i
$333$	−263.000	+	236.919i	−0.789789	+	0.711468i
$334$	215.314			0.644654
$335$		−	186.894i		−	0.557893i
$336$	251.573	−	96.6040i	0.748728	−	0.287512i
$337$	−659.365			−1.95657			−0.978287	−	0.207256i	$-0.933547\pi$
$337$	−659.365			−1.95657			−0.978287	+	0.207256i	$0.933547\pi$
$338$			149.481i			0.442251i
$339$	−49.8144	−	129.725i	−0.146945	−	0.382669i
$340$	−1.64729			−0.00484497
$341$		0			0
$342$	225.265	+	250.063i	0.658670	+	0.731179i
$343$	373.147			1.08789
$344$		−	350.506i		−	1.01891i
$345$	189.920	−	72.9292i	0.550492	−	0.211389i
$346$	659.008			1.90465
$347$			277.880i			0.800806i	0.916339	+	0.400403i	$0.131130\pi$
$347$			277.880i			0.800806i	−0.916339	+	0.400403i	$0.868870\pi$
$348$	−0.0447761	−	0.116604i	−0.000128667	−	0.000335070i
$349$	252.775			0.724284			0.362142	−	0.932123i	$-0.382046\pi$
$349$	252.775			0.724284			0.362142	+	0.932123i	$0.382046\pi$
$350$		−	56.9047i		−	0.162585i
$351$	119.023	−	233.801i	0.339096	−	0.666100i
$352$		0			0
$353$		−	560.803i		−	1.58868i	−0.607476	−	0.794338i	$-0.707818\pi$
$353$		−	560.803i		−	1.58868i	0.607476	−	0.794338i	$-0.292182\pi$
$354$	505.343	−	194.052i	1.42752	−	0.548169i
$355$	206.192			0.580823
$356$		−	0.573590i		−	0.00161121i
$357$	−107.455	−	279.829i	−0.300993	−	0.783836i
$358$	96.7998			0.270390
$359$			296.063i			0.824689i	0.911028	+	0.412345i	$0.135290\pi$
$359$			296.063i			0.824689i	−0.911028	+	0.412345i	$0.864710\pi$
$360$	−292.767	+	263.735i	−0.813243	+	0.732597i
$361$	−12.8456			−0.0355834
$362$		−	0.133414i		−	0.000368547i
$363$		0			0
$364$	0.913018			0.00250829
$365$		−	66.5041i		−	0.182203i
$366$	−66.5357	−	173.270i	−0.181792	−	0.473415i
$367$	84.8579			0.231220			0.115610	−	0.993295i	$-0.463118\pi$
$367$	84.8579			0.231220			0.115610	+	0.993295i	$0.463118\pi$
$368$		−	198.666i		−	0.539852i
$369$	−340.485	−	377.966i	−0.922722	−	1.02430i
$370$	432.315			1.16842
$371$		−	241.054i		−	0.649740i
$372$	−2.31723	+	0.889818i	−0.00622912	+	0.00239198i
$373$	−316.098			−0.847447			−0.423724	−	0.905792i	$-0.639277\pi$
$373$	−316.098			−0.847447			−0.423724	+	0.905792i	$0.639277\pi$
$374$		0			0
$375$	−117.499	−	305.988i	−0.313332	−	0.815968i
$376$	−461.296			−1.22685
$377$			24.0716i			0.0638505i
$378$	269.613	+	137.254i	0.713262	+	0.363105i
$379$	−108.737			−0.286905			−0.143453	−	0.989657i	$-0.545820\pi$
$379$	−108.737			−0.286905			−0.143453	+	0.989657i	$0.545820\pi$
$380$		−	1.71986i		−	0.00452594i
$381$	191.251	−	73.4403i	0.501970	−	0.192757i
$382$	395.656			1.03575
$383$			442.014i			1.15408i	0.816715	+	0.577041i	$0.195793\pi$
$383$			442.014i			1.15408i	−0.816715	+	0.577041i	$0.804207\pi$
$384$	138.517	+	360.721i	0.360721	+	0.939378i
$385$		0			0
$386$			3.05372i			0.00791119i
$387$	293.594	−	264.479i	0.758640	−	0.683408i
$388$	0.635670			0.00163833
$389$			509.597i			1.31002i	0.755621	+	0.655009i	$0.227335\pi$
$389$			509.597i			1.31002i	−0.755621	+	0.655009i	$0.772665\pi$
$390$	−299.119	+	114.862i	−0.766972	+	0.294517i
$391$	−220.980			−0.565165
$392$			141.640i			0.361327i
$393$	174.513	+	454.460i	0.444053	+	1.15639i
$394$	−431.824			−1.09600
$395$		−	346.310i		−	0.876734i
$396$		0			0
$397$	13.0481			0.0328668			0.0164334	−	0.999865i	$-0.494769\pi$
$397$	13.0481			0.0328668			0.0164334	+	0.999865i	$0.494769\pi$
$398$			213.773i			0.537118i
$399$	292.157	−	112.188i	0.732223	−	0.281174i
$400$	81.5950			0.203988
$401$			549.606i			1.37059i	0.728267	+	0.685294i	$0.240326\pi$
$401$			549.606i			1.37059i	−0.728267	+	0.685294i	$0.759674\pi$
$402$	−73.4502	−	191.277i	−0.182712	−	0.475812i
$403$	478.366			1.18701
$404$			0.788308i			0.00195126i
$405$	−441.823	−	46.2255i	−1.09092	−	0.114137i
$406$	−27.7588			−0.0683714
$407$		0			0
$408$	399.566	−	153.433i	0.979327	−	0.376062i
$409$	−618.166			−1.51141			−0.755704	−	0.654913i	$-0.772705\pi$
$409$	−618.166			−1.51141			−0.755704	+	0.654913i	$0.772705\pi$
$410$			621.295i			1.51535i
$411$	56.8552	+	148.060i	0.138334	+	0.360244i
$412$	−1.76128			−0.00427494
$413$		−	503.350i		−	1.21876i
$414$	165.712	−	149.279i	0.400270	−	0.360576i
$415$	−53.2066			−0.128209
$416$			2.61288i			0.00628096i
$417$	242.353	−	93.0636i	0.581182	−	0.223174i
$418$		0			0
$419$			440.342i			1.05094i	0.850814	+	0.525468i	$0.176110\pi$
$419$			440.342i			1.05094i	−0.850814	+	0.525468i	$0.823890\pi$
$420$	−0.554203	−	1.44324i	−0.00131953	−	0.00343627i
$421$	574.230			1.36397			0.681983	−	0.731368i	$-0.261118\pi$
$421$	574.230			1.36397			0.681983	+	0.731368i	$0.261118\pi$
$422$			430.552i			1.02027i
$423$	−348.077	−	386.394i	−0.822877	−	0.913462i
$424$	344.198			0.811788
$425$		−	90.7598i		−	0.213552i
$426$	211.027	−	81.0344i	0.495368	−	0.190222i
$427$	−172.587			−0.404184
$428$			0.783693i			0.00183106i
$429$		0			0
$430$	−482.605			−1.12234
$431$			661.481i			1.53476i	0.641193	+	0.767380i	$0.278440\pi$
$431$			661.481i			1.53476i	−0.641193	+	0.767380i	$0.721560\pi$
$432$	−196.807	+	386.595i	−0.455572	+	0.894897i
$433$	212.781			0.491412			0.245706	−	0.969344i	$-0.420980\pi$
$433$	212.781			0.491412			0.245706	+	0.969344i	$0.420980\pi$
$434$			551.639i			1.27106i
$435$	38.0508	−	14.6115i	0.0874731	−	0.0335897i
$436$	−2.83045			−0.00649185
$437$		−	230.715i		−	0.527951i
$438$	−26.1364	−	68.0635i	−0.0596722	−	0.155396i
$439$	103.815			0.236482			0.118241	−	0.992985i	$-0.462275\pi$
$439$	103.815			0.236482			0.118241	+	0.992985i	$0.462275\pi$
$440$		0			0
$441$	−118.642	+	106.877i	−0.269029	+	0.242351i
$442$	348.038			0.787416
$443$		−	276.769i		−	0.624760i	−0.949957	−	0.312380i	$-0.898874\pi$
$443$		−	276.769i		−	0.624760i	0.949957	−	0.312380i	$-0.101126\pi$
$444$	1.85125	−	0.710879i	0.00416947	−	0.00160108i
$445$	187.176			0.420620
$446$		−	89.7255i		−	0.201178i
$447$	−69.3118	−	180.499i	−0.155060	−	0.403802i
$448$	356.298			0.795308
$449$		−	497.877i		−	1.10886i	−0.832231	−	0.554428i	$-0.812937\pi$
$449$		−	497.877i		−	1.10886i	0.832231	−	0.554428i	$-0.187063\pi$
$450$	61.3111	+	68.0603i	0.136247	+	0.151245i
$451$		0			0
$452$			0.778483i			0.00172231i
$453$	−125.005	+	48.0018i	−0.275949	+	0.105964i
$454$	−449.950			−0.991079
$455$			297.939i			0.654812i
$456$	160.193	+	417.168i	0.351300	+	0.914842i
$457$	−811.116			−1.77487			−0.887435	−	0.460932i	$-0.847515\pi$
$457$	−811.116			−1.77487			−0.887435	+	0.460932i	$0.847515\pi$
$458$			208.638i			0.455543i
$459$	430.018	+	218.912i	0.936858	+	0.476933i
$460$	−1.13971			−0.00247764
$461$		−	790.057i		−	1.71379i	−0.515492	−	0.856894i	$-0.672391\pi$
$461$		−	790.057i		−	1.71379i	0.515492	−	0.856894i	$-0.327609\pi$
$462$		0			0
$463$	540.381			1.16713			0.583565	−	0.812067i	$-0.301658\pi$
$463$	540.381			1.16713			0.583565	+	0.812067i	$0.301658\pi$
$464$		−	39.8030i		−	0.0857824i
$465$	−290.369	−	756.168i	−0.624449	−	1.62617i
$466$	−123.316			−0.264627
$467$		−	277.866i		−	0.595003i	−0.954721	−	0.297501i	$-0.903847\pi$
$467$		−	277.866i		−	0.595003i	0.954721	−	0.297501i	$-0.0961533\pi$
$468$	−1.09201	+	0.983716i	−0.00233335	+	0.00210196i
$469$	−190.522			−0.406230
$470$			635.149i			1.35138i
$471$	−395.072	+	151.708i	−0.838793	+	0.322097i
$472$	718.728			1.52273
$473$		0			0
$474$	−136.101	−	354.430i	−0.287133	−	0.747743i
$475$	94.7581			0.199491
$476$			1.67927i			0.00352787i
$477$	259.719	+	288.310i	0.544485	+	0.604423i
$478$	299.147			0.625831
$479$			470.226i			0.981683i	0.871249	+	0.490841i	$0.163311\pi$
$479$			470.226i			0.981683i	−0.871249	+	0.490841i	$0.836689\pi$
$480$	4.13026	−	1.58602i	0.00860470	−	0.00330421i
$481$	−382.168			−0.794529
$482$			719.269i			1.49226i
$483$	−74.3449	−	193.606i	−0.153923	−	0.400841i
$484$		0			0
$485$			207.434i			0.427699i
$486$	−470.350	+	126.329i	−0.967799	+	0.259936i
$487$	254.199			0.521969			0.260984	−	0.965343i	$-0.415953\pi$
$487$	254.199			0.521969			0.260984	+	0.965343i	$0.415953\pi$
$488$		−	246.435i		−	0.504989i
$489$	338.775	−	130.090i	0.692792	−	0.266032i
$490$	195.022			0.398004
$491$			123.123i			0.250760i	0.992109	+	0.125380i	$0.0400151\pi$
$491$			123.123i			0.250760i	−0.992109	+	0.125380i	$0.959985\pi$
$492$	1.02163	+	2.66049i	0.00207648	+	0.00540750i
$493$	−44.2737			−0.0898047
$494$			363.370i			0.735567i
$495$		0			0
$496$	−790.989			−1.59474
$497$		−	210.194i		−	0.422926i
$498$	−54.4542	+	20.9104i	−0.109346	+	0.0419888i
$499$	65.3282			0.130918			0.0654591	−	0.997855i	$-0.479149\pi$
$499$	65.3282			0.130918			0.0654591	+	0.997855i	$0.479149\pi$
$500$			1.83624i			0.00367249i
$501$	115.536	+	300.875i	0.230611	+	0.600549i
$502$	715.543			1.42538
$503$			425.899i			0.846718i	0.905962	+	0.423359i	$0.139149\pi$
$503$			425.899i			0.846718i	−0.905962	+	0.423359i	$0.860851\pi$
$504$	268.854	+	298.450i	0.533441	+	0.592163i
$505$	−257.243			−0.509393
$506$		0			0
$507$	−208.881	+	80.2103i	−0.411994	+	0.158206i
$508$	−1.14770			−0.00225925
$509$			69.8611i			0.137252i	0.997642	+	0.0686258i	$0.0218614\pi$
$509$			69.8611i			0.137252i	−0.997642	+	0.0686258i	$0.978139\pi$
$510$	−211.259	−	550.154i	−0.414234	−	1.07873i
$511$	−67.7951			−0.132671
$512$			508.736i			0.993625i
$513$	−228.556	+	448.962i	−0.445529	+	0.875169i
$514$	−132.464			−0.257713
$515$		−	574.746i		−	1.11601i
$516$	−2.06660	+	0.793574i	−0.00400503	+	0.00153793i
$517$		0			0
$518$		−	440.706i		−	0.850785i
$519$	353.618	+	920.881i	0.681346	+	1.77434i
$520$	−425.424			−0.818124
$521$			100.640i			0.193168i	0.995325	+	0.0965839i	$0.0307916\pi$
$521$			100.640i			0.193168i	−0.995325	+	0.0965839i	$0.969208\pi$
$522$	33.2006	−	29.9083i	0.0636028	−	0.0572955i
$523$	851.945			1.62896			0.814479	−	0.580193i	$-0.197023\pi$
$523$	851.945			1.62896			0.814479	+	0.580193i	$0.197023\pi$
$524$		−	2.72723i		−	0.00520464i
$525$	79.5171	−	30.5346i	0.151461	−	0.0581611i
$526$	−171.197			−0.325470
$527$			879.833i			1.66951i
$528$		0			0
$529$	376.110			0.710983
$530$		−	473.920i		−	0.894188i
$531$	542.326	+	602.027i	1.02133	+	1.13376i
$532$	−1.75324			−0.00329557
$533$		−	549.228i		−	1.03045i
$534$	191.565	−	73.5610i	0.358736	−	0.137755i
$535$	−255.738			−0.478014
$536$		−	272.044i		−	0.507546i
$537$	51.9420	+	135.265i	0.0967262	+	0.251891i
$538$	324.247			0.602689
$539$		0			0
$540$	2.21784	+	1.12905i	0.00410711	+	0.00209084i
$541$	−731.425			−1.35199			−0.675994	−	0.736907i	$-0.736285\pi$
$541$	−731.425			−1.35199			−0.675994	+	0.736907i	$0.736285\pi$
$542$		−	521.078i		−	0.961399i
$543$	0.186430	−	0.0715890i	0.000343332	−	0.000131840i
$544$	−4.80573			−0.00883406
$545$		−	923.642i		−	1.69476i
$546$	117.091	+	304.925i	0.214453	+	0.558472i
$547$	123.279			0.225373			0.112686	−	0.993631i	$-0.464054\pi$
$547$	123.279			0.225373			0.112686	+	0.993631i	$0.464054\pi$
$548$		−	0.888514i		−	0.00162138i
$549$	206.421	−	185.951i	0.375994	−	0.338708i
$550$		0			0
$551$		−	46.2241i		−	0.0838913i
$552$	276.449	−	106.156i	0.500813	−	0.192312i
$553$	−353.032			−0.638394
$554$		−	173.948i		−	0.313986i
$555$	231.977	+	604.105i	0.417976	+	1.08848i
$556$	−1.45437			−0.00261577
$557$		−	201.775i		−	0.362253i	−0.983460	−	0.181127i	$-0.942026\pi$
$557$		−	201.775i		−	0.362253i	0.983460	−	0.181127i	$-0.0579744\pi$
$558$	−594.355	−	659.783i	−1.06515	−	1.18241i
$559$	426.625			0.763193
$560$		−	492.649i		−	0.879731i
$561$		0			0
$562$	971.465			1.72858
$563$		−	484.108i		−	0.859871i	−0.902860	−	0.429936i	$-0.858536\pi$
$563$		−	484.108i		−	0.859871i	0.902860	−	0.429936i	$-0.141464\pi$
$564$	1.04441	+	2.71982i	0.00185179	+	0.00482237i
$565$	−254.037			−0.449624
$566$			865.958i			1.52996i
$567$	−47.1228	+	450.400i	−0.0831090	+	0.794356i
$568$	300.135			0.528406
$569$		−	467.419i		−	0.821474i	−0.911754	−	0.410737i	$-0.865271\pi$
$569$		−	467.419i		−	0.821474i	0.911754	−	0.410737i	$-0.134729\pi$
$570$	574.391	−	220.566i	1.00770	−	0.386958i
$571$	−656.796			−1.15026			−0.575128	−	0.818064i	$-0.695048\pi$
$571$	−656.796			−1.15026			−0.575128	+	0.818064i	$0.695048\pi$
$572$		0			0
$573$	212.306	+	552.879i	0.370516	+	0.964885i
$574$	633.355			1.10341
$575$		−	62.7942i		−	0.109207i
$576$	−426.147	+	383.887i	−0.739838	+	0.666471i
$577$	−873.454			−1.51378			−0.756892	−	0.653540i	$-0.773283\pi$
$577$	−873.454			−1.51378			−0.756892	+	0.653540i	$0.773283\pi$
$578$			60.9146i			0.105389i
$579$	−4.26719	+	1.63860i	−0.00736993	+	0.00283005i
$580$	−0.228344			−0.000393697
$581$			54.2394i			0.0933552i
$582$	81.5225	+	212.298i	0.140073	+	0.364774i
$583$		0			0
$584$		−	96.8039i		−	0.165760i
$585$	−321.010	−	356.348i	−0.548735	−	0.609141i
$586$	−11.0824			−0.0189119
$587$		−	790.603i		−	1.34685i	−0.739254	−	0.673427i	$-0.764822\pi$
$587$		−	790.603i		−	1.34685i	0.739254	−	0.673427i	$-0.235178\pi$
$588$	0.835117	−	0.320685i	0.00142027	−	0.000545383i
$589$	−918.593			−1.55958
$590$		−	989.603i		−	1.67729i
$591$	−231.713	−	603.419i	−0.392069	−	1.02101i
$592$	631.924			1.06744
$593$			928.634i			1.56599i	0.622026	+	0.782997i	$0.286310\pi$
$593$			928.634i			1.56599i	−0.622026	+	0.782997i	$0.713690\pi$
$594$		0			0
$595$	−547.984			−0.920981
$596$			1.08318i			0.00181742i
$597$	−298.721	+	114.709i	−0.500370	+	0.192142i
$598$	240.798			0.402672
$599$		−	917.368i		−	1.53150i	−0.643139	−	0.765749i	$-0.722368\pi$
$599$		−	917.368i		−	1.53150i	0.643139	−	0.765749i	$-0.277632\pi$
$600$	43.6000	+	113.542i	0.0726667	+	0.189236i
$601$	−955.662			−1.59012			−0.795060	−	0.606530i	$-0.792561\pi$
$601$	−955.662			−1.59012			−0.795060	+	0.606530i	$0.792561\pi$
$602$			491.973i			0.817230i
$603$	227.872	−	205.275i	0.377897	−	0.340423i
$604$	0.750158			0.00124198
$605$		0			0
$606$	−263.275	+	101.098i	−0.434448	+	0.166828i
$607$	781.619			1.28768			0.643838	−	0.765162i	$-0.277341\pi$
$607$	781.619			1.28768			0.643838	+	0.765162i	$0.277341\pi$
$608$		−	5.01744i		−	0.00825237i
$609$	−14.8951	−	38.7894i	−0.0244584	−	0.0636936i
$610$	−339.311			−0.556248
$611$		−	561.475i		−	0.918944i
$612$	−1.80930	−	2.00847i	−0.00295637	−	0.00328181i
$613$	−85.9782			−0.140258			−0.0701290	−	0.997538i	$-0.522341\pi$
$613$	−85.9782			−0.140258			−0.0701290	+	0.997538i	$0.522341\pi$
$614$			439.433i			0.715690i
$615$	−868.181	+	333.382i	−1.41168	+	0.542084i
$616$		0			0
$617$			7.47837i			0.0121205i	0.999982	+	0.00606027i	$0.00192905\pi$
$617$			7.47837i			0.0121205i	−0.999982	+	0.00606027i	$0.998071\pi$
$618$	−225.878	−	588.223i	−0.365498	−	0.951817i
$619$	325.144			0.525273			0.262636	−	0.964895i	$-0.415408\pi$
$619$	325.144			0.525273			0.262636	+	0.964895i	$0.415408\pi$
$620$			4.53779i			0.00731901i
$621$	297.518	+	151.459i	0.479094	+	0.243896i
$622$	284.897			0.458034
$623$		−	190.809i		−	0.306275i
$624$	−437.229	+	167.896i	−0.700688	+	0.269064i
$625$	−726.170			−1.16187
$626$		−	188.967i		−	0.301864i
$627$		0			0
$628$	2.37084			0.00377522
$629$		−	702.902i		−	1.11749i
$630$	410.931	−	370.180i	0.652271	−	0.587587i
$631$	−685.538			−1.08643			−0.543216	−	0.839593i	$-0.682793\pi$
$631$	−685.538			−1.08643			−0.543216	+	0.839593i	$0.682793\pi$
$632$		−	504.091i		−	0.797612i
$633$	−601.643	+	231.031i	−0.950463	+	0.364978i
$634$	−1004.53			−1.58444
$635$		−	374.522i		−	0.589798i
$636$	−0.779292	−	2.02941i	−0.00122530	−	0.00319089i
$637$	−172.400			−0.270644
$638$		0			0
$639$	226.471	+	251.401i	0.354414	+	0.393429i
$640$	706.393			1.10374
$641$		−	273.299i		−	0.426364i	−0.977013	−	0.213182i	$-0.931617\pi$
$641$		−	273.299i		−	0.426364i	0.977013	−	0.213182i	$-0.0683826\pi$
$642$	−261.734	+	100.506i	−0.407686	+	0.156551i
$643$	184.624			0.287129			0.143564	−	0.989641i	$-0.454144\pi$
$643$	184.624			0.287129			0.143564	+	0.989641i	$0.454144\pi$
$644$			1.16184i			0.00180410i
$645$	−258.962	−	674.379i	−0.401491	−	1.04555i
$646$	−668.328			−1.03456
$647$		−	360.098i		−	0.556565i	−0.960499	−	0.278283i	$-0.910235\pi$
$647$		−	360.098i		−	0.556565i	0.960499	−	0.278283i	$-0.0897652\pi$
$648$	−643.121	−	67.2862i	−0.992471	−	0.103837i
$649$		0			0
$650$			98.8995i			0.152153i
$651$	−770.846	+	296.005i	−1.18410	+	0.454693i
$652$	−2.03300			−0.00311810
$653$		−	1030.37i		−	1.57789i	−0.614461	−	0.788947i	$-0.710626\pi$
$653$		−	1030.37i		−	1.57789i	0.614461	−	0.788947i	$-0.289374\pi$
$654$	−362.995	−	945.300i	−0.555039	−	1.44541i
$655$	889.960			1.35872
$656$			908.161i			1.38439i
$657$	81.0857	−	73.0447i	0.123418	−	0.111179i
$658$	647.478			0.984009
$659$		−	1071.63i		−	1.62614i	−0.582166	−	0.813070i	$-0.697795\pi$
$659$		−	1071.63i		−	1.62614i	0.582166	−	0.813070i	$-0.302205\pi$
$660$		0			0
$661$	441.357			0.667712			0.333856	−	0.942624i	$-0.391650\pi$
$661$	441.357			0.667712			0.333856	+	0.942624i	$0.391650\pi$
$662$			1309.72i			1.97843i
$663$	186.754	+	486.339i	0.281681	+	0.733543i
$664$	−77.4479			−0.116638
$665$		−	572.125i		−	0.860338i
$666$	474.832	+	527.103i	0.712961	+	0.791446i
$667$	−30.6318			−0.0459247
$668$		−	1.80556i		−	0.00270293i
$669$	125.380	−	48.1460i	0.187414	−	0.0719671i
$670$	−374.573			−0.559064
$671$		0			0
$672$	−1.61681	−	4.21043i	−0.00240596	−	0.00626552i
$673$	370.702			0.550820			0.275410	−	0.961327i	$-0.411186\pi$
$673$	370.702			0.550820			0.275410	+	0.961327i	$0.411186\pi$
$674$			1321.50i			1.96068i
$675$	−62.2068	+	122.195i	−0.0921582	+	0.181030i
$676$	1.25350			0.00185429
$677$		−	75.2277i		−	0.111119i	−0.998455	−	0.0555596i	$-0.982306\pi$
$677$		−	75.2277i		−	0.111119i	0.998455	−	0.0555596i	$-0.0176943\pi$
$678$	−259.994	+	99.8379i	−0.383472	+	0.147253i
$679$	211.461			0.311430
$680$		−	782.461i		−	1.15068i
$681$	−241.440	−	628.749i	−0.354537	−	0.923272i
$682$		0			0
$683$		−	987.234i		−	1.44544i	−0.691142	−	0.722719i	$-0.742892\pi$
$683$		−	987.234i		−	1.44544i	0.691142	−	0.722719i	$-0.257108\pi$
$684$	2.09695	−	1.88900i	0.00306572	−	0.00276170i
$685$	289.943			0.423275
$686$		−	747.860i		−	1.09017i
$687$	−291.546	+	111.954i	−0.424376	+	0.162960i
$688$	−705.434			−1.02534
$689$			418.947i			0.608051i
$690$	−146.165	−	380.637i	−0.211833	−	0.551647i
$691$	1026.80			1.48597			0.742983	−	0.669311i	$-0.233411\pi$
$691$	1026.80			1.48597			0.742983	+	0.669311i	$0.233411\pi$
$692$		−	5.52624i		−	0.00798589i
$693$		0			0
$694$	556.925			0.802486
$695$		−	474.595i		−	0.682870i
$696$	55.3870	−	21.2686i	0.0795790	−	0.0305584i
$697$	1010.17			1.44931
$698$		−	506.611i		−	0.725804i
$699$	−66.1705	−	172.319i	−0.0946645	−	0.246522i
$700$	−0.477185			−0.000681693
$701$			186.947i			0.266687i	0.991070	+	0.133343i	$0.0425713\pi$
$701$			186.947i			0.266687i	−0.991070	+	0.133343i	$0.957429\pi$
$702$	−468.583	−	238.545i	−0.667498	−	0.339808i
$703$	733.868			1.04391
$704$		0			0
$705$	−887.541	+	340.816i	−1.25892	+	0.483427i
$706$	−1123.96			−1.59201
$707$			262.237i			0.370915i
$708$	−1.62726	−	4.23765i	−0.00229839	−	0.00598538i
$709$	−713.675			−1.00659			−0.503297	−	0.864114i	$-0.667880\pi$
$709$	−713.675			−1.00659			−0.503297	+	0.864114i	$0.667880\pi$
$710$		−	413.249i		−	0.582042i
$711$	422.241	−	380.369i	0.593869	−	0.534977i
$712$	272.455			0.382661
$713$			608.733i			0.853762i
$714$	−560.833	+	215.360i	−0.785481	+	0.301625i
$715$		0			0
$716$		−	0.811733i		−	0.00113370i
$717$	160.520	+	418.020i	0.223877	+	0.583013i
$718$	593.369			0.826420
$719$			498.723i			0.693634i	0.937933	+	0.346817i	$0.112738\pi$
$719$			498.723i			0.693634i	−0.937933	+	0.346817i	$0.887262\pi$
$720$	530.797	+	589.229i	0.737219	+	0.818374i
$721$	−585.902			−0.812624
$722$			25.7452i			0.0356581i
$723$	−1005.09	+	385.954i	−1.39016	+	0.533823i
$724$	−0.00111877			−1.54526e−6
$725$		−	12.5809i		−	0.0173530i
$726$		0			0
$727$	427.838			0.588498			0.294249	−	0.955729i	$-0.404930\pi$
$727$	427.838			0.588498			0.294249	+	0.955729i	$0.404930\pi$
$728$			433.683i			0.595718i
$729$	−428.915	−	589.468i	−0.588361	−	0.808598i
$730$	−133.287			−0.182585
$731$			784.669i			1.07342i
$732$	−1.45299	+	0.557948i	−0.00198496	+	0.000762224i
$733$	−957.424			−1.30617			−0.653086	−	0.757284i	$-0.726526\pi$
$733$	−957.424			−1.30617			−0.653086	+	0.757284i	$0.726526\pi$
$734$		−	170.072i		−	0.231706i
$735$	104.647	+	272.518i	0.142377	+	0.370773i
$736$	−3.32495			−0.00451760
$737$		0			0
$738$	−757.518	+	682.398i	−1.02645	+	0.924659i
$739$	1134.98			1.53584			0.767918	−	0.640549i	$-0.221293\pi$
$739$	1134.98			1.53584			0.767918	+	0.640549i	$0.221293\pi$
$740$		−	3.62526i		−	0.00489900i
$741$	−507.764	+	194.982i	−0.685242	+	0.263133i
$742$	−483.119			−0.651104
$743$			866.886i			1.16674i	0.812207	+	0.583369i	$0.198266\pi$
$743$			866.886i			1.16674i	−0.812207	+	0.583369i	$0.801734\pi$
$744$	−422.663	−	1100.68i	−0.568095	−	1.47941i
$745$	−353.468			−0.474454
$746$			633.522i			0.849226i
$747$	−58.4393	−	64.8725i	−0.0782321	−	0.0868441i
$748$		0			0
$749$			260.702i			0.348067i
$750$	−613.260	+	235.492i	−0.817680	+	0.313989i
$751$	−1157.47			−1.54124			−0.770618	−	0.637297i	$-0.780053\pi$
$751$	−1157.47			−1.54124			−0.770618	+	0.637297i	$0.780053\pi$
$752$			928.412i			1.23459i
$753$	383.954	+	999.881i	0.509900	+	1.32786i
$754$	48.2443			0.0639845
$755$			244.794i			0.324231i
$756$	1.15097	−	2.26089i	0.00152244	−	0.00299060i
$757$	−410.295			−0.542001			−0.271001	−	0.962579i	$-0.587355\pi$
$757$	−410.295			−0.542001			−0.271001	+	0.962579i	$0.587355\pi$
$758$			217.931i			0.287508i
$759$		0			0
$760$	816.931			1.07491
$761$		−	253.490i		−	0.333101i	−0.986033	−	0.166550i	$-0.946737\pi$
$761$		−	253.490i		−	0.333101i	0.986033	−	0.166550i	$-0.0532629\pi$
$762$	−147.189	−	383.304i	−0.193161	−	0.503024i
$763$	−941.571			−1.23404
$764$		−	3.31785i		−	0.00434273i
$765$	655.411	−	590.417i	0.856747	−	0.771786i
$766$	885.883			1.15650
$767$			874.814i			1.14057i
$768$	9.03703	−	3.47022i	0.0117670	−	0.00451852i
$769$	788.887			1.02586			0.512931	−	0.858430i	$-0.328560\pi$
$769$	788.887			1.02586			0.512931	+	0.858430i	$0.328560\pi$
$770$		0			0
$771$	−71.0793	−	185.102i	−0.0921910	−	0.240081i
$772$	0.0256075			3.31704e−5
$773$		−	343.352i		−	0.444182i	−0.975026	−	0.222091i	$-0.928712\pi$
$773$		−	343.352i		−	0.444182i	0.975026	−	0.222091i	$-0.0712881\pi$
$774$	−530.068	−	588.419i	−0.684843	−	0.760232i
$775$	−250.016			−0.322601
$776$			301.943i			0.389101i
$777$	615.832	−	236.480i	0.792576	−	0.304349i
$778$	1021.33			1.31277
$779$			1054.67i			1.35387i
$780$	0.963195	+	2.50832i	0.00123487	+	0.00321580i
$781$		0			0
$782$			442.887i			0.566351i
$783$	59.6082	+	30.3452i	0.0761280	+	0.0387550i
$784$	285.068			0.363607
$785$			773.660i			0.985554i
$786$	910.828	−	349.758i	1.15881	−	0.444985i
$787$	193.445			0.245800			0.122900	−	0.992419i	$-0.460781\pi$
$787$	193.445			0.245800			0.122900	+	0.992419i	$0.460781\pi$
$788$			3.62114i			0.00459535i
$789$	−91.8631	−	239.227i	−0.116430	−	0.303202i
$790$	−694.073			−0.878574
$791$			258.969i			0.327394i
$792$		0			0
$793$	299.953			0.378251
$794$		−	26.1510i		−	0.0329358i
$795$	662.243	−	254.301i	0.833010	−	0.319876i
$796$	1.79263			0.00225205
$797$			531.926i			0.667411i	0.942677	+	0.333705i	$0.108299\pi$
$797$			531.926i			0.667411i	−0.942677	+	0.333705i	$0.891701\pi$
$798$	−224.848	−	585.540i	−0.281764	−	0.733760i
$799$	1032.69			1.29248
$800$		−	1.36561i		−	0.00170701i
$801$	205.584	+	228.216i	0.256660	+	0.284913i
$802$	1101.52			1.37346
$803$		0			0
$804$	−1.60399	+	0.615931i	−0.00199501	+	0.000766083i
$805$	−379.135			−0.470975
$806$		−	958.740i		−	1.18950i
$807$	173.988	+	453.094i	0.215599	+	0.561455i
$808$	−374.445			−0.463423
$809$			290.427i			0.358995i	0.983758	+	0.179497i	$0.0574471\pi$
$809$			290.427i			0.358995i	−0.983758	+	0.179497i	$0.942553\pi$
$810$	−92.6451	+	885.501i	−0.114377	+	1.09321i
$811$	−384.552			−0.474170			−0.237085	−	0.971489i	$-0.576192\pi$
$811$	−384.552			−0.474170			−0.237085	+	0.971489i	$0.576192\pi$
$812$			0.232776i			0.000286671i
$813$	728.142	−	279.607i	0.895623	−	0.343919i
$814$		0			0
$815$		−	663.416i		−	0.814008i
$816$	−308.803	−	804.173i	−0.378435	−	0.985506i
$817$	−819.237			−1.00274
$818$			1238.93i			1.51458i
$819$	−363.265	+	327.241i	−0.443547	+	0.399562i
$820$	5.20998			0.00635364
$821$		−	621.724i		−	0.757277i	−0.925545	−	0.378638i	$-0.876392\pi$
$821$		−	621.724i		−	0.757277i	0.925545	−	0.378638i	$-0.123608\pi$
$822$	296.742	−	113.949i	0.361000	−	0.138624i
$823$	−286.383			−0.347974			−0.173987	−	0.984748i	$-0.555665\pi$
$823$	−286.383			−0.347974			−0.173987	+	0.984748i	$0.555665\pi$
$824$		−	836.604i		−	1.01530i
$825$		0			0
$826$	−1008.81			−1.22132
$827$			417.508i			0.504847i	0.967617	+	0.252423i	$0.0812276\pi$
$827$			417.508i			0.504847i	−0.967617	+	0.252423i	$0.918772\pi$
$828$	−1.25180	−	1.38961i	−0.00151184	−	0.00167827i
$829$	370.857			0.447355			0.223677	−	0.974663i	$-0.428194\pi$
$829$	370.857			0.447355			0.223677	+	0.974663i	$0.428194\pi$
$830$			106.636i			0.128478i
$831$	243.071	−	93.3393i	0.292504	−	0.112322i
$832$	−619.240			−0.744279
$833$		−	317.087i		−	0.380656i
$834$	−186.518	−	485.723i	−0.223642	−	0.582402i
$835$	589.197			0.705625
$836$		0			0
$837$	603.038	−	1184.57i	0.720475	−	1.41526i
$838$	882.532			1.05314
$839$			865.855i			1.03201i	0.856586	+	0.516004i	$0.172581\pi$
$839$			865.855i			1.03201i	−0.856586	+	0.516004i	$0.827419\pi$
$840$	685.535	−	263.246i	0.816113	−	0.313388i
$841$	834.863			0.992703
$842$		−	1150.87i		−	1.36683i
$843$	521.280	+	1357.50i	0.618363	+	1.61032i
$844$	3.61048			0.00427782
$845$			409.047i			0.484079i
$846$	−774.410	+	697.615i	−0.915379	+	0.824604i
$847$		0			0
$848$		−	692.739i		−	0.816910i
$849$	−1210.07	+	464.666i	−1.42529	+	0.547310i
$850$	−181.901			−0.214001
$851$		−	486.319i		−	0.571468i
$852$	−0.679529	−	1.76961i	−0.000797569	−	0.00207700i
$853$	1346.86			1.57897			0.789483	−	0.613772i	$-0.210349\pi$
$853$	1346.86			1.57897			0.789483	+	0.613772i	$0.210349\pi$
$854$			345.897i			0.405032i
$855$	616.427	+	684.285i	0.720967	+	0.800333i
$856$	−372.254			−0.434876
$857$			770.599i			0.899182i	0.893235	+	0.449591i	$0.148430\pi$
$857$			770.599i			0.899182i	−0.893235	+	0.449591i	$0.851570\pi$
$858$		0			0
$859$	−549.532			−0.639735			−0.319867	−	0.947462i	$-0.603638\pi$
$859$	−549.532			−0.639735			−0.319867	+	0.947462i	$0.603638\pi$
$860$			4.04697i			0.00470578i
$861$	339.853	+	885.034i	0.394719	+	1.02791i
$862$	1325.74			1.53798
$863$			1095.93i			1.26990i	0.772552	+	0.634952i	$0.218980\pi$
$863$			1095.93i			1.26990i	−0.772552	+	0.634952i	$0.781020\pi$
$864$	6.47023	+	3.29385i	0.00748869	+	0.00381232i
$865$	1803.34			2.08479
$866$		−	426.456i		−	0.492443i
$867$	−85.1205	+	32.6863i	−0.0981782	+	0.0377004i
$868$	4.62587			0.00532935
$869$		0			0
$870$	−29.2843	−	76.2613i	−0.0336602	−	0.0876567i
$871$	331.124			0.380166
$872$		−	1344.46i		−	1.54181i
$873$	−252.916	+	227.835i	−0.289709	+	0.260979i
$874$	−462.398			−0.529059
$875$			610.841i			0.698104i
$876$	−0.570760	+	0.219172i	−0.000651552	+	0.000250196i
$877$	1443.15			1.64556			0.822778	−	0.568363i	$-0.192423\pi$
$877$	1443.15			1.64556			0.822778	+	0.568363i	$0.192423\pi$
$878$		−	208.066i		−	0.236978i
$879$	−5.94670	−	15.4862i	−0.00676531	−	0.0176180i
$880$		0			0
$881$			162.080i			0.183973i	0.995760	+	0.0919866i	$0.0293217\pi$
$881$			162.080i			0.183973i	−0.995760	+	0.0919866i	$0.970678\pi$
$882$	214.202	+	237.782i	0.242859	+	0.269594i
$883$	−87.1163			−0.0986595			−0.0493297	−	0.998783i	$-0.515709\pi$
$883$	−87.1163			−0.0986595			−0.0493297	+	0.998783i	$0.515709\pi$
$884$		−	2.91854i		−	0.00330151i
$885$	1382.85	−	531.013i	1.56254	−	0.600015i
$886$	−554.699			−0.626071
$887$			816.228i			0.920212i	0.887864	+	0.460106i	$0.152189\pi$
$887$			816.228i			0.920212i	−0.887864	+	0.460106i	$0.847811\pi$
$888$	337.667	+	879.340i	0.380255	+	0.990248i
$889$	−381.792			−0.429462
$890$		−	375.137i		−	0.421503i
$891$		0			0
$892$	−0.752410			−0.000843509
$893$			1078.19i			1.20737i
$894$	−361.756	+	138.915i	−0.404649	+	0.155385i
$895$	264.888			0.295964
$896$		−	720.105i		−	0.803688i
$897$	129.210	+	336.485i	0.144047	+	0.375122i
$898$	−997.843			−1.11118
$899$			121.961i			0.135663i
$900$	0.570733	−	0.514135i	0.000634148	−	0.000571262i
$901$	−770.548			−0.855214
$902$		0			0
$903$	−687.470	+	263.989i	−0.761318	+	0.292346i
$904$	−369.779			−0.409047
$905$		−	0.365081i		−	0.000403404i
$906$	96.2052	+	250.534i	0.106187	+	0.276528i
$907$	558.559			0.615832			0.307916	−	0.951414i	$-0.400368\pi$
$907$	558.559			0.615832			0.307916	+	0.951414i	$0.400368\pi$
$908$			3.77314i			0.00415544i
$909$	−282.543	−	313.646i	−0.310828	−	0.345045i
$910$	597.129			0.656186
$911$		−	1627.04i		−	1.78600i	−0.450058	−	0.892999i	$-0.648597\pi$
$911$		−	1627.04i		−	1.78600i	0.450058	−	0.892999i	$-0.351403\pi$
$912$	839.600	−	322.407i	0.920614	−	0.353516i
$913$		0			0
$914$			1625.64i			1.77860i
$915$	−182.072	−	474.144i	−0.198985	−	0.518191i
$916$	1.74958			0.00191002
$917$		−	907.235i		−	0.989351i
$918$	438.743	−	861.840i	0.477934	−	0.938824i
$919$	−57.5879			−0.0626637			−0.0313319	−	0.999509i	$-0.509975\pi$
$919$	−57.5879			−0.0626637			−0.0313319	+	0.999509i	$0.509975\pi$
$920$		−	541.363i		−	0.588438i
$921$	−614.053	+	235.796i	−0.666724	+	0.256022i
$922$	−1583.43			−1.71739
$923$			365.315i			0.395791i
$924$		0			0
$925$	199.739			0.215934
$926$		−	1083.03i		−	1.16958i
$927$	700.763	−	631.271i	0.755947	−	0.680983i
$928$	−0.666161			−0.000717846
$929$		−	21.5006i		−	0.0231438i	−0.999933	−	0.0115719i	$-0.996316\pi$
$929$		−	21.5006i		−	0.0231438i	0.999933	−	0.0115719i	$-0.00368353\pi$
$930$	−1515.51	+	581.956i	−1.62958	+	0.625759i
$931$	331.056			0.355591
$932$			1.03409i			0.00110954i
$933$	152.873	+	398.108i	0.163852	+	0.426696i
$934$	−556.899			−0.596251
$935$		0			0
$936$	−467.264	−	518.702i	−0.499214	−	0.554169i
$937$	228.958			0.244352			0.122176	−	0.992508i	$-0.461013\pi$
$937$	228.958			0.244352			0.122176	+	0.992508i	$0.461013\pi$
$938$			381.844i			0.407083i
$939$	264.058	−	101.398i	0.281212	−	0.107985i
$940$	5.32616			0.00566613
$941$			863.164i			0.917284i	0.888621	+	0.458642i	$0.151664\pi$
$941$			863.164i			0.917284i	−0.888621	+	0.458642i	$0.848336\pi$
$942$	304.052	+	791.801i	0.322773	+	0.840553i
$943$	698.906			0.741152
$944$		−	1446.53i		−	1.53234i
$945$	737.782	+	375.588i	0.780722	+	0.397448i
$946$		0			0
$947$			1155.70i			1.22038i	0.792253	+	0.610192i	$0.208908\pi$
$947$			1155.70i			1.22038i	−0.792253	+	0.610192i	$0.791092\pi$
$948$	−2.97214	+	1.14130i	−0.00313517	+	0.00120391i
$949$	117.827			0.124159
$950$		−	189.914i		−	0.199909i
$951$	−539.025	−	1403.71i	−0.566798	−	1.47603i
$952$	−797.649			−0.837867
$953$		−	1797.11i		−	1.88574i	−0.333163	−	0.942869i	$-0.608116\pi$
$953$		−	1797.11i		−	1.88574i	0.333163	−	0.942869i	$-0.391884\pi$
$954$	577.830	−	520.529i	0.605692	−	0.545628i
$955$	1082.69			1.13371
$956$		−	2.50855i		−	0.00262401i
$957$		0			0
$958$	942.426			0.983743
$959$		−	295.571i		−	0.308208i
$960$	375.879	+	978.852i	0.391541	+	1.01964i
$961$	1462.68			1.52204
$962$			765.941i			0.796196i
$963$	−280.889	−	311.810i	−0.291681	−	0.323790i
$964$	6.03156			0.00625681
$965$			8.35634i			0.00865942i
$966$	−388.025	+	149.002i	−0.401682	+	0.154246i
$967$	1767.36			1.82767			0.913835	−	0.406085i	$-0.133106\pi$
$967$	1767.36			1.82767			0.913835	+	0.406085i	$0.133106\pi$
$968$		0			0
$969$	−358.619	−	933.904i	−0.370092	−	0.963781i
$970$	415.739			0.428597
$971$			508.729i			0.523922i	0.965078	+	0.261961i	$0.0843692\pi$
$971$			508.729i			0.523922i	−0.965078	+	0.261961i	$0.915631\pi$
$972$	1.05936	+	3.94421i	0.00108987	+	0.00405783i
$973$	−483.807			−0.497233
$974$		−	509.465i		−	0.523064i
$975$	−138.200	+	53.0687i	−0.141743	+	0.0544294i
$976$	−495.979			−0.508175
$977$		−	1414.51i		−	1.44781i	−0.689902	−	0.723903i	$-0.742346\pi$
$977$		−	1414.51i		−	1.44781i	0.689902	−	0.723903i	$-0.257654\pi$
$978$	−260.726	−	678.972i	−0.266590	−	0.694246i
$979$		0			0
$980$		−	1.63539i		−	0.00166877i
$981$	1126.16	−	1014.48i	1.14797	−	1.03413i
$982$	246.764			0.251287
$983$			1.12205i			0.00114145i	1.00000		0.000570727i	$0.000181668\pi$
$983$			1.12205i			0.00114145i	−1.00000		0.000570727i	$0.999818\pi$
$984$	−1263.73	+	485.273i	−1.28428	+	0.493164i
$985$	−1181.66			−1.19966
$986$			88.7332i			0.0899931i
$987$	347.432	+	904.769i	0.352008	+	0.916686i
$988$	3.04711			0.00308412
$989$			542.891i			0.548929i
$990$		0			0
$991$	−1431.64			−1.44464			−0.722320	−	0.691559i	$-0.756924\pi$
$991$	−1431.64			−1.44464			−0.722320	+	0.691559i	$0.756924\pi$
$992$			13.2383i			0.0133451i
$993$	−1830.17	+	702.785i	−1.84307	+	0.707740i
$994$	−421.271			−0.423814
$995$			584.979i			0.587918i
$996$	0.175348	+	0.456636i	0.000176052	+	0.000458470i
$997$	1166.36			1.16987			0.584937	−	0.811079i	$-0.301119\pi$
$997$	1166.36			1.16987			0.584937	+	0.811079i	$0.301119\pi$
$998$		−	130.931i		−	0.131193i
$999$	−481.769	+	946.358i	−0.482251	+	0.947305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.l.122.3		8
3.2	odd	2	inner	363.3.b.l.122.6		8
11.2	odd	10		363.3.h.o.323.3		16
11.3	even	5		363.3.h.j.251.2		16
11.4	even	5		363.3.h.j.269.3		16
11.5	even	5		363.3.h.n.245.3		16
11.6	odd	10		363.3.h.o.245.2		16
11.7	odd	10		33.3.h.b.5.2	✓	16
11.8	odd	10		33.3.h.b.20.3	yes	16
11.9	even	5		363.3.h.n.323.2		16
11.10	odd	2		363.3.b.m.122.6		8
33.2	even	10		363.3.h.o.323.2		16
33.5	odd	10		363.3.h.n.245.2		16
33.8	even	10		33.3.h.b.20.2	yes	16
33.14	odd	10		363.3.h.j.251.3		16
33.17	even	10		363.3.h.o.245.3		16
33.20	odd	10		363.3.h.n.323.3		16
33.26	odd	10		363.3.h.j.269.2		16
33.29	even	10		33.3.h.b.5.3	yes	16
33.32	even	2		363.3.b.m.122.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.2	✓	16	11.7	odd	10
33.3.h.b.5.3	yes	16	33.29	even	10
33.3.h.b.20.2	yes	16	33.8	even	10
33.3.h.b.20.3	yes	16	11.8	odd	10
363.3.b.l.122.3		8	1.1	even	1	trivial
363.3.b.l.122.6		8	3.2	odd	2	inner
363.3.b.m.122.3		8	33.32	even	2
363.3.b.m.122.6		8	11.10	odd	2
363.3.h.j.251.2		16	11.3	even	5
363.3.h.j.251.3		16	33.14	odd	10
363.3.h.j.269.2		16	33.26	odd	10
363.3.h.j.269.3		16	11.4	even	5
363.3.h.n.245.2		16	33.5	odd	10
363.3.h.n.245.3		16	11.5	even	5
363.3.h.n.323.2		16	11.9	even	5
363.3.h.n.323.3		16	33.20	odd	10
363.3.h.o.245.2		16	11.6	odd	10
363.3.h.o.245.3		16	33.17	even	10
363.3.h.o.323.2		16	33.2	even	10
363.3.h.o.323.3		16	11.2	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)

\(f(q)\)	\(=\)	\(q-2.00420i q^{2} +(2.80061 - 1.07544i) q^{3} -0.0168066 q^{4} -5.48438i q^{5} +(-2.15539 - 5.61298i) q^{6} -5.59084 q^{7} -7.98311i q^{8} +(6.68687 - 6.02376i) q^{9} +O(q^{10})\)	\(q-2.00420i q^{2} +(2.80061 - 1.07544i) q^{3} -0.0168066 q^{4} -5.48438i q^{5} +(-2.15539 - 5.61298i) q^{6} -5.59084 q^{7} -7.98311i q^{8} +(6.68687 - 6.02376i) q^{9} -10.9918 q^{10} +(-0.0470687 + 0.0180744i) q^{12} +9.71679 q^{13} +11.2051i q^{14} +(-5.89810 - 15.3596i) q^{15} -16.0669 q^{16} +17.8716i q^{17} +(-12.0728 - 13.4018i) q^{18} -18.6589 q^{19} +0.0921737i q^{20} +(-15.6578 + 6.01259i) q^{21} +12.3649i q^{23} +(-8.58532 - 22.3576i) q^{24} -5.07844 q^{25} -19.4744i q^{26} +(12.2492 - 24.0615i) q^{27} +0.0939629 q^{28} +2.47732i q^{29} +(-30.7837 + 11.8210i) q^{30} +49.2308 q^{31} +0.268903i q^{32} +35.8182 q^{34} +30.6623i q^{35} +(-0.112383 + 0.101239i) q^{36} -39.3307 q^{37} +37.3961i q^{38} +(27.2130 - 10.4498i) q^{39} -43.7824 q^{40} -56.5236i q^{41} +(12.0504 + 31.3813i) q^{42} +43.9060 q^{43} +(-33.0366 - 36.6734i) q^{45} +24.7816 q^{46} -57.7840i q^{47} +(-44.9973 + 17.2790i) q^{48} -17.7425 q^{49} +10.1782i q^{50} +(19.2197 + 50.0514i) q^{51} -0.163306 q^{52} +43.1158i q^{53} +(-48.2241 - 24.5498i) q^{54} +44.6323i q^{56} +(-52.2564 + 20.0665i) q^{57} +4.96505 q^{58} +90.0311i q^{59} +(0.0991269 + 0.258143i) q^{60} +30.8695 q^{61} -98.6683i q^{62} +(-37.3852 + 33.6779i) q^{63} -63.7288 q^{64} -53.2906i q^{65} +34.0775 q^{67} -0.300360i q^{68} +(13.2976 + 34.6292i) q^{69} +61.4533 q^{70} +37.5962i q^{71} +(-48.0883 - 53.3820i) q^{72} +12.1261 q^{73} +78.8265i q^{74} +(-14.2228 + 5.46154i) q^{75} +0.313592 q^{76} +(-20.9434 - 54.5402i) q^{78} +63.1447 q^{79} +88.1173i q^{80} +(8.42858 - 80.5603i) q^{81} -113.284 q^{82} -9.70147i q^{83} +(0.263154 - 0.101051i) q^{84} +98.0146 q^{85} -87.9962i q^{86} +(2.66420 + 6.93803i) q^{87} +34.1289i q^{89} +(-73.5007 + 66.2119i) q^{90} -54.3250 q^{91} -0.207811i q^{92} +(137.877 - 52.9446i) q^{93} -115.811 q^{94} +102.333i q^{95} +(0.289188 + 0.753095i) q^{96} -37.8227 q^{97} +35.5595i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) \) 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

L-functions

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