LMFDB - Embedded newform 165.4.c.b.34.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 $ x^14 + 66x^12 + 1705x^10 + 22060x^8 + 151880x^6 + 537860x^4 + 825344x^2 + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.5
Root			$-3.20690i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20690i q^{2} +3.00000i q^{3} +3.12958 q^{4} +(4.62093 + 10.1807i) q^{5} +6.62071 q^{6} +1.50972i q^{7} -24.5619i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.20690i q^{2} +3.00000i q^{3} +3.12958 q^{4} +(4.62093 + 10.1807i) q^{5} +6.62071 q^{6} +1.50972i q^{7} -24.5619i q^{8} -9.00000 q^{9} +(22.4678 - 10.1979i) q^{10} +11.0000 q^{11} +9.38875i q^{12} +68.3212i q^{13} +3.33181 q^{14} +(-30.5421 + 13.8628i) q^{15} -29.1690 q^{16} +113.151i q^{17} +19.8621i q^{18} +72.3208 q^{19} +(14.4616 + 31.8614i) q^{20} -4.52917 q^{21} -24.2759i q^{22} -144.617i q^{23} +73.6857 q^{24} +(-82.2939 + 94.0888i) q^{25} +150.778 q^{26} -27.0000i q^{27} +4.72480i q^{28} +133.492 q^{29} +(30.5938 + 67.4035i) q^{30} +177.784 q^{31} -132.122i q^{32} +33.0000i q^{33} +249.713 q^{34} +(-15.3700 + 6.97633i) q^{35} -28.1663 q^{36} +39.8169i q^{37} -159.605i q^{38} -204.964 q^{39} +(250.058 - 113.499i) q^{40} -366.404 q^{41} +9.99542i q^{42} +427.219i q^{43} +34.4254 q^{44} +(-41.5884 - 91.6264i) q^{45} -319.156 q^{46} -340.290i q^{47} -87.5071i q^{48} +340.721 q^{49} +(207.645 + 181.615i) q^{50} -339.453 q^{51} +213.817i q^{52} -659.877i q^{53} -59.5863 q^{54} +(50.8303 + 111.988i) q^{55} +37.0816 q^{56} +216.963i q^{57} -294.603i q^{58} +525.541 q^{59} +(-95.5842 + 43.3848i) q^{60} -462.358 q^{61} -392.353i q^{62} -13.5875i q^{63} -524.933 q^{64} +(-695.559 + 315.708i) q^{65} +72.8278 q^{66} +514.730i q^{67} +354.115i q^{68} +433.852 q^{69} +(15.3961 + 33.9202i) q^{70} -848.333 q^{71} +221.057i q^{72} -987.550i q^{73} +87.8721 q^{74} +(-282.267 - 246.882i) q^{75} +226.334 q^{76} +16.6069i q^{77} +452.335i q^{78} -442.561 q^{79} +(-134.788 - 296.962i) q^{80} +81.0000 q^{81} +808.617i q^{82} -603.960i q^{83} -14.1744 q^{84} +(-1151.96 + 522.863i) q^{85} +942.831 q^{86} +400.475i q^{87} -270.181i q^{88} -1001.29 q^{89} +(-202.211 + 91.7815i) q^{90} -103.146 q^{91} -452.592i q^{92} +533.353i q^{93} -750.987 q^{94} +(334.190 + 736.278i) q^{95} +396.366 q^{96} -468.418i q^{97} -751.937i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.20690i		−	0.780258i	−0.920760	−	0.390129i	$-0.872430\pi$
$2$		−	2.20690i		−	0.780258i	0.920760	−	0.390129i	$-0.127570\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	3.12958			0.391198
$5$	4.62093	+	10.1807i	0.413309	+	0.910591i
$5$	4.62093	+	10.1807i	0.413309	+	0.910591i
$6$	6.62071			0.450482
$7$			1.50972i			0.0815173i	0.999169	+	0.0407587i	$0.0129775\pi$
$7$			1.50972i			0.0815173i	−0.999169	+	0.0407587i	$0.987023\pi$
$8$		−	24.5619i		−	1.08549i
$9$	−9.00000			−0.333333
$10$	22.4678	−	10.1979i	0.710495	−	0.322487i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$			9.38875i			0.225858i
$13$			68.3212i			1.45761i	0.684723	+	0.728804i	$0.259923\pi$
$13$			68.3212i			1.45761i	−0.684723	+	0.728804i	$0.740077\pi$
$14$	3.33181			0.0636045
$15$	−30.5421	+	13.8628i	−0.525730	+	0.238624i
$16$	−29.1690			−0.455766
$17$			113.151i			1.61430i	0.590345	+	0.807151i	$0.298992\pi$
$17$			113.151i			1.61430i	−0.590345	+	0.807151i	$0.701008\pi$
$18$			19.8621i			0.260086i
$19$	72.3208			0.873239			0.436619	−	0.899646i	$-0.356176\pi$
$19$	72.3208			0.873239			0.436619	+	0.899646i	$0.356176\pi$
$20$	14.4616	+	31.8614i	0.161686	+	0.356221i
$21$	−4.52917			−0.0470640
$22$		−	24.2759i		−	0.235257i
$23$		−	144.617i		−	1.31108i	−0.755162	−	0.655539i	$-0.772442\pi$
$23$		−	144.617i		−	1.31108i	0.755162	−	0.655539i	$-0.227558\pi$
$24$	73.6857			0.626710
$25$	−82.2939	+	94.0888i	−0.658351	+	0.752711i
$26$	150.778			1.13731
$27$		−	27.0000i		−	0.192450i
$28$			4.72480i			0.0318894i
$29$	133.492			0.854785			0.427393	−	0.904066i	$-0.359432\pi$
$29$	133.492			0.854785			0.427393	+	0.904066i	$0.359432\pi$
$30$	30.5938	+	67.4035i	0.186188	+	0.410205i
$31$	177.784			1.03003			0.515016	−	0.857180i	$-0.327786\pi$
$31$	177.784			1.03003			0.515016	+	0.857180i	$0.327786\pi$
$32$		−	132.122i		−	0.729878i
$33$			33.0000i			0.174078i
$34$	249.713			1.25957
$35$	−15.3700	+	6.97633i	−0.0742289	+	0.0336918i
$36$	−28.1663			−0.130399
$37$			39.8169i			0.176915i	0.996080	+	0.0884576i	$0.0281938\pi$
$37$			39.8169i			0.176915i	−0.996080	+	0.0884576i	$0.971806\pi$
$38$		−	159.605i		−	0.681351i
$39$	−204.964			−0.841550
$40$	250.058	−	113.499i	0.988440	−	0.448644i
$41$	−366.404			−1.39568			−0.697838	−	0.716256i	$-0.745854\pi$
$41$	−366.404			−1.39568			−0.697838	+	0.716256i	$0.745854\pi$
$42$			9.99542i			0.0367221i
$43$			427.219i			1.51512i	0.652763	+	0.757562i	$0.273610\pi$
$43$			427.219i			1.51512i	−0.652763	+	0.757562i	$0.726390\pi$
$44$	34.4254			0.117951
$45$	−41.5884	−	91.6264i	−0.137770	−	0.303530i
$46$	−319.156			−1.02298
$47$		−	340.290i		−	1.05609i	−0.849215	−	0.528047i	$-0.822924\pi$
$47$		−	340.290i		−	1.05609i	0.849215	−	0.528047i	$-0.177076\pi$
$48$		−	87.5071i		−	0.263137i
$49$	340.721			0.993355
$50$	207.645	+	181.615i	0.587308	+	0.513684i
$51$	−339.453			−0.932018
$52$			213.817i			0.570213i
$53$		−	659.877i		−	1.71021i	−0.518455	−	0.855105i	$-0.673493\pi$
$53$		−	659.877i		−	1.71021i	0.518455	−	0.855105i	$-0.326507\pi$
$54$	−59.5863			−0.150161
$55$	50.8303	+	111.988i	0.124617	+	0.274553i
$56$	37.0816			0.0884865
$57$			216.963i			0.504165i
$58$		−	294.603i		−	0.666953i
$59$	525.541			1.15965			0.579827	−	0.814740i	$-0.303120\pi$
$59$	525.541			1.15965			0.579827	+	0.814740i	$0.303120\pi$
$60$	−95.5842	+	43.3848i	−0.205665	+	0.0933493i
$61$	−462.358			−0.970473			−0.485237	−	0.874383i	$-0.661267\pi$
$61$	−462.358			−0.970473			−0.485237	+	0.874383i	$0.661267\pi$
$62$		−	392.353i		−	0.803691i
$63$		−	13.5875i		−	0.0271724i
$64$	−524.933			−1.02526
$65$	−695.559	+	315.708i	−1.32728	+	0.602442i
$66$	72.8278			0.135825
$67$			514.730i			0.938571i	0.883047	+	0.469285i	$0.155488\pi$
$67$			514.730i			0.938571i	−0.883047	+	0.469285i	$0.844512\pi$
$68$			354.115i			0.631512i
$69$	433.852			0.756951
$70$	15.3961	+	33.9202i	0.0262883	+	0.0579177i
$71$	−848.333			−1.41801			−0.709004	−	0.705204i	$-0.750855\pi$
$71$	−848.333			−1.41801			−0.709004	+	0.705204i	$0.750855\pi$
$72$			221.057i			0.361831i
$73$		−	987.550i		−	1.58334i	−0.610947	−	0.791671i	$-0.709211\pi$
$73$		−	987.550i		−	1.58334i	0.610947	−	0.791671i	$-0.290789\pi$
$74$	87.8721			0.138039
$75$	−282.267	−	246.882i	−0.434578	−	0.380099i
$76$	226.334			0.341609
$77$			16.6069i			0.0245784i
$78$			452.335i			0.656626i
$79$	−442.561			−0.630279			−0.315139	−	0.949045i	$-0.602051\pi$
$79$	−442.561			−0.630279			−0.315139	+	0.949045i	$0.602051\pi$
$80$	−134.788	−	296.962i	−0.188372	−	0.415016i
$81$	81.0000			0.111111
$82$			808.617i			1.08899i
$83$		−	603.960i		−	0.798713i	−0.916796	−	0.399357i	$-0.869234\pi$
$83$		−	603.960i		−	0.798713i	0.916796	−	0.399357i	$-0.130766\pi$
$84$	−14.1744			−0.0184114
$85$	−1151.96	+	522.863i	−1.46997	+	0.667205i
$86$	942.831			1.18219
$87$			400.475i			0.493511i
$88$		−	270.181i		−	0.327288i
$89$	−1001.29			−1.19254			−0.596270	−	0.802784i	$-0.703351\pi$
$89$	−1001.29			−1.19254			−0.596270	+	0.802784i	$0.703351\pi$
$90$	−202.211	+	91.7815i	−0.236832	+	0.107496i
$91$	−103.146			−0.118820
$92$		−	452.592i		−	0.512891i
$93$			533.353i			0.594690i
$94$	−750.987			−0.824025
$95$	334.190	+	736.278i	0.360917	+	0.795163i
$96$	396.366			0.421395
$97$		−	468.418i		−	0.490315i	−0.969483	−	0.245158i	$-0.921160\pi$
$97$		−	468.418i		−	0.490315i	0.969483	−	0.245158i	$-0.0788397\pi$
$98$		−	751.937i		−	0.775073i
$99$	−99.0000			−0.100504
$100$	−257.546	+	294.459i	−0.257546	+	0.294459i
$101$	1577.43			1.55406			0.777031	−	0.629462i	$-0.216725\pi$
$101$	1577.43			1.55406			0.777031	+	0.629462i	$0.216725\pi$
$102$			749.139i			0.727214i
$103$		−	776.371i		−	0.742700i	−0.928493	−	0.371350i	$-0.878895\pi$
$103$		−	776.371i		−	0.742700i	0.928493	−	0.371350i	$-0.121105\pi$
$104$	1678.10			1.58222
$105$	−20.9290	−	46.1101i	−0.0194520	−	0.0428561i
$106$	−1456.28			−1.33440
$107$		−	409.524i		−	0.370002i	−0.982738	−	0.185001i	$-0.940771\pi$
$107$		−	409.524i		−	0.370002i	0.982738	−	0.185001i	$-0.0592288\pi$
$108$		−	84.4988i		−	0.0752861i
$109$	−374.126			−0.328760			−0.164380	−	0.986397i	$-0.552562\pi$
$109$	−374.126			−0.328760			−0.164380	+	0.986397i	$0.552562\pi$
$110$	247.146	−	112.177i	0.214222	−	0.0972336i
$111$	−119.451			−0.102142
$112$		−	44.0371i		−	0.0371528i
$113$		−	1477.62i		−	1.23012i	−0.788482	−	0.615058i	$-0.789133\pi$
$113$		−	1477.62i		−	1.23012i	0.788482	−	0.615058i	$-0.210867\pi$
$114$	478.815			0.393378
$115$	1472.31	−	668.267i	1.19386	−	0.541880i
$116$	417.773			0.334390
$117$		−	614.891i		−	0.485869i
$118$		−	1159.82i		−	0.904828i
$119$	−170.826			−0.131594
$120$	340.497	+	750.173i	0.259025	+	0.570676i
$121$	121.000			0.0909091
$122$			1020.38i			0.757219i
$123$		−	1099.21i		−	0.805793i
$124$	556.391			0.402947
$125$	−1338.17	−	403.033i	−0.957514	−	0.288387i
$126$	−29.9863			−0.0212015
$127$			566.909i			0.396103i	0.980192	+	0.198051i	$0.0634613\pi$
$127$			566.909i			0.396103i	−0.980192	+	0.198051i	$0.936539\pi$
$128$			101.498i			0.0700880i
$129$	−1281.66			−0.874758
$130$	696.736	+	1535.03i	0.470060	+	1.03562i
$131$	328.369			0.219006			0.109503	−	0.993986i	$-0.465074\pi$
$131$	328.369			0.219006			0.109503	+	0.993986i	$0.465074\pi$
$132$			103.276i			0.0680988i
$133$			109.184i			0.0711841i
$134$	1135.96			0.732327
$135$	274.879	−	124.765i	0.175243	−	0.0795414i
$136$	2779.20			1.75231
$137$		−	635.136i		−	0.396082i	−0.980194	−	0.198041i	$-0.936542\pi$
$137$		−	635.136i		−	0.396082i	0.980194	−	0.198041i	$-0.0634580\pi$
$138$		−	957.468i		−	0.590617i
$139$	573.459			0.349929			0.174965	−	0.984575i	$-0.444019\pi$
$139$	573.459			0.349929			0.174965	+	0.984575i	$0.444019\pi$
$140$	−48.1019	+	21.8330i	−0.0290382	+	0.0131802i
$141$	1020.87			0.609736
$142$			1872.19i			1.10641i
$143$			751.533i			0.439485i
$144$	262.521			0.151922
$145$	616.856	+	1359.04i	0.353290	+	0.778360i
$146$	−2179.43			−1.23542
$147$			1022.16i			0.573514i
$148$			124.610i			0.0692089i
$149$	844.518			0.464333			0.232167	−	0.972676i	$-0.425419\pi$
$149$	844.518			0.464333			0.232167	+	0.972676i	$0.425419\pi$
$150$	−544.844	+	622.935i	−0.296575	+	0.339083i
$151$	25.5488			0.0137691			0.00688455	−	0.999976i	$-0.497809\pi$
$151$	25.5488			0.0137691			0.00688455	+	0.999976i	$0.497809\pi$
$152$		−	1776.34i		−	0.947895i
$153$		−	1018.36i		−	0.538101i
$154$	36.6499			0.0191775
$155$	821.530	+	1809.97i	0.425722	+	0.937938i
$156$	−641.451			−0.329213
$157$		−	964.739i		−	0.490411i	−0.969471	−	0.245206i	$-0.921145\pi$
$157$		−	964.739i		−	0.490411i	0.969471	−	0.245206i	$-0.0788555\pi$
$158$			976.689i			0.491780i
$159$	1979.63			0.987390
$160$	1345.10	−	610.527i	0.664620	−	0.301665i
$161$	218.332			0.106876
$162$		−	178.759i		−	0.0866953i
$163$		−	1619.81i		−	0.778363i	−0.921161	−	0.389182i	$-0.872758\pi$
$163$		−	1619.81i		−	0.778363i	0.921161	−	0.389182i	$-0.127242\pi$
$164$	−1146.69			−0.545985
$165$	−335.964	+	152.491i	−0.158514	+	0.0719479i
$166$	−1332.88			−0.623202
$167$			2814.68i			1.30423i	0.758119	+	0.652116i	$0.226119\pi$
$167$			2814.68i			1.30423i	−0.758119	+	0.652116i	$0.773881\pi$
$168$			111.245i			0.0510877i
$169$	−2470.79			−1.12462
$170$	1153.91	+	2542.26i	0.520592	+	1.14695i
$171$	−650.888			−0.291080
$172$			1337.02i			0.592714i
$173$			3386.43i			1.48824i	0.668047	+	0.744119i	$0.267130\pi$
$173$			3386.43i			1.48824i	−0.668047	+	0.744119i	$0.732870\pi$
$174$	883.809			0.385065
$175$	−142.048	−	124.241i	−0.0613590	−	0.0536670i
$176$	−320.859			−0.137419
$177$			1576.62i			0.669526i
$178$			2209.74i			0.930489i
$179$	−2759.40			−1.15222			−0.576110	−	0.817372i	$-0.695430\pi$
$179$	−2759.40			−1.15222			−0.576110	+	0.817372i	$0.695430\pi$
$180$	−130.154	−	286.753i	−0.0538952	−	0.118740i
$181$	2520.55			1.03509			0.517544	−	0.855657i	$-0.326847\pi$
$181$	2520.55			1.03509			0.517544	+	0.855657i	$0.326847\pi$
$182$			227.633i			0.0927104i
$183$		−	1387.07i		−	0.560303i
$184$	−3552.07			−1.42317
$185$	−405.365	+	183.992i	−0.161097	+	0.0731207i
$186$	1177.06			0.464011
$187$			1244.66i			0.486730i
$188$		−	1064.97i		−	0.413142i
$189$	40.7625			0.0156880
$190$	1624.89	−	737.524i	0.620432	−	0.281609i
$191$	3747.78			1.41979			0.709894	−	0.704308i	$-0.248743\pi$
$191$	3747.78			1.41979			0.709894	+	0.704308i	$0.248743\pi$
$192$		−	1574.80i		−	0.591933i
$193$		−	2544.51i		−	0.949004i	−0.880254	−	0.474502i	$-0.842628\pi$
$193$		−	2544.51i		−	0.949004i	0.880254	−	0.474502i	$-0.157372\pi$
$194$	−1033.75			−0.382572
$195$	−947.124	−	2086.68i	−0.347820	−	0.766308i
$196$	1066.31			0.388599
$197$		−	2239.70i		−	0.810011i	−0.914314	−	0.405005i	$-0.867270\pi$
$197$		−	2239.70i		−	0.810011i	0.914314	−	0.405005i	$-0.132730\pi$
$198$			218.483i			0.0784188i
$199$	−1074.20			−0.382654			−0.191327	−	0.981526i	$-0.561279\pi$
$199$	−1074.20			−0.382654			−0.191327	+	0.981526i	$0.561279\pi$
$200$	2311.00	+	2021.30i	0.817062	+	0.714636i
$201$	−1544.19			−0.541884
$202$		−	3481.24i		−	1.21257i
$203$			201.535i			0.0696798i
$204$	−1062.35			−0.364603
$205$	−1693.13	−	3730.25i	−0.576845	−	1.27089i
$206$	−1713.38			−0.579498
$207$			1301.56i			0.437026i
$208$		−	1992.86i		−	0.664328i
$209$	795.529			0.263291
$210$	−101.761	+	46.1882i	−0.0334388	+	0.0151776i
$211$	4873.15			1.58996			0.794980	−	0.606636i	$-0.207482\pi$
$211$	4873.15			1.58996			0.794980	+	0.606636i	$0.207482\pi$
$212$		−	2065.14i		−	0.669031i
$213$		−	2545.00i		−	0.818688i
$214$	−903.779			−0.288697
$215$	−4349.40	+	1974.15i	−1.37966	+	0.626215i
$216$	−663.171			−0.208903
$217$			268.405i			0.0839655i
$218$			825.660i			0.256517i
$219$	2962.65			0.914143
$220$	159.078	+	350.476i	0.0487501	+	0.107405i
$221$	−7730.61			−2.35302
$222$			263.616i			0.0796971i
$223$			1941.68i			0.583069i	0.956560	+	0.291534i	$0.0941658\pi$
$223$			1941.68i			0.583069i	−0.956560	+	0.291534i	$0.905834\pi$
$224$	199.468			0.0594977
$225$	740.645	−	846.800i	0.219450	−	0.250904i
$226$	−3260.97			−0.959807
$227$		−	1347.48i		−	0.393987i	−0.980405	−	0.196994i	$-0.936882\pi$
$227$		−	1347.48i		−	0.393987i	0.980405	−	0.196994i	$-0.0631179\pi$
$228$			679.003i			0.197228i
$229$	818.085			0.236072			0.118036	−	0.993009i	$-0.462340\pi$
$229$	818.085			0.236072			0.118036	+	0.993009i	$0.462340\pi$
$230$	−1474.80	−	3249.24i	−0.422806	−	0.931514i
$231$	−49.8208			−0.0141903
$232$		−	3278.81i		−	0.927863i
$233$			217.090i			0.0610389i	0.999534	+	0.0305195i	$0.00971615\pi$
$233$			217.090i			0.0610389i	−0.999534	+	0.0305195i	$0.990284\pi$
$234$	−1357.00			−0.379103
$235$	3464.40	−	1572.46i	0.961670	−	0.436493i
$236$	1644.72			0.453654
$237$		−	1327.68i		−	0.363891i
$238$			376.997i			0.102677i
$239$	−3964.48			−1.07297			−0.536487	−	0.843909i	$-0.680249\pi$
$239$	−3964.48			−1.07297			−0.536487	+	0.843909i	$0.680249\pi$
$240$	890.885	−	404.364i	0.239610	−	0.108757i
$241$	3973.08			1.06194			0.530972	−	0.847390i	$-0.321827\pi$
$241$	3973.08			1.06194			0.530972	+	0.847390i	$0.321827\pi$
$242$		−	267.035i		−	0.0709325i
$243$			243.000i			0.0641500i
$244$	−1446.99			−0.379647
$245$	1574.45	+	3468.78i	0.410563	+	0.904540i
$246$	−2425.85			−0.628726
$247$			4941.05i			1.27284i
$248$		−	4366.72i		−	1.11809i
$249$	1811.88			0.461137
$250$	−889.453	+	2953.20i	−0.225016	+	0.747108i
$251$	−4308.81			−1.08355			−0.541773	−	0.840525i	$-0.682247\pi$
$251$	−4308.81			−1.08355			−0.541773	+	0.840525i	$0.682247\pi$
$252$		−	42.5232i		−	0.0106298i
$253$		−	1590.79i		−	0.395305i
$254$	1251.11			0.309062
$255$	−1568.59	−	3455.87i	−0.385211	−	0.848687i
$256$	−3975.46			−0.970572
$257$			6343.46i			1.53967i	0.638245	+	0.769833i	$0.279661\pi$
$257$			6343.46i			1.53967i	−0.638245	+	0.769833i	$0.720339\pi$
$258$			2828.49i			0.682536i
$259$	−60.1125			−0.0144217
$260$	−2176.81	+	988.035i	−0.519231	+	0.235674i
$261$	−1201.42			−0.284928
$262$		−	724.679i		−	0.170881i
$263$			4404.34i			1.03264i	0.856397	+	0.516318i	$0.172698\pi$
$263$			4404.34i			1.03264i	−0.856397	+	0.516318i	$0.827302\pi$
$264$	810.543			0.188960
$265$	6718.02	−	3049.25i	1.55730	−	0.706845i
$266$	240.959			0.0555419
$267$		−	3003.86i		−	0.688514i
$268$			1610.89i			0.367167i
$269$	4817.34			1.09189			0.545945	−	0.837821i	$-0.316171\pi$
$269$	4817.34			1.09189			0.545945	+	0.837821i	$0.316171\pi$
$270$	−275.345	−	606.632i	−0.0620627	−	0.136735i
$271$	−2171.29			−0.486702			−0.243351	−	0.969938i	$-0.578247\pi$
$271$	−2171.29			−0.486702			−0.243351	+	0.969938i	$0.578247\pi$
$272$		−	3300.50i		−	0.735744i
$273$		−	309.438i		−	0.0686009i
$274$	−1401.68			−0.309046
$275$	−905.233	+	1034.98i	−0.198500	+	0.226951i
$276$	1357.78			0.296118
$277$		−	1351.39i		−	0.293131i	−0.989201	−	0.146565i	$-0.953178\pi$
$277$		−	1351.39i		−	0.293131i	0.989201	−	0.146565i	$-0.0468219\pi$
$278$		−	1265.57i		−	0.273035i
$279$	−1600.06			−0.343344
$280$	171.352	+	377.518i	0.0365723	+	0.0805750i
$281$	−3118.19			−0.661978			−0.330989	−	0.943635i	$-0.607382\pi$
$281$	−3118.19			−0.661978			−0.330989	+	0.943635i	$0.607382\pi$
$282$		−	2252.96i		−	0.475751i
$283$		−	4164.03i		−	0.874651i	−0.899303	−	0.437325i	$-0.855926\pi$
$283$		−	4164.03i		−	0.874651i	0.899303	−	0.437325i	$-0.144074\pi$
$284$	−2654.93			−0.554722
$285$	−2208.83	+	1002.57i	−0.459088	+	0.208376i
$286$	1658.56			0.342912
$287$		−	553.168i		−	0.113772i
$288$			1189.10i			0.243293i
$289$	−7890.13			−1.60597
$290$	2999.27	−	1361.34i	0.607321	−	0.275658i
$291$	1405.25			0.283084
$292$		−	3090.62i		−	0.619401i
$293$			1431.01i			0.285326i	0.989771	+	0.142663i	$0.0455665\pi$
$293$			1431.01i			0.285326i	−0.989771	+	0.142663i	$0.954433\pi$
$294$	2255.81			0.447488
$295$	2428.49	+	5350.38i	0.479295	+	1.05597i
$296$	977.980			0.192040
$297$		−	297.000i		−	0.0580259i
$298$		−	1863.77i		−	0.362299i
$299$	9880.43			1.91104
$300$	−883.377	−	772.637i	−0.170006	−	0.148694i
$301$	−644.982			−0.123509
$302$		−	56.3837i		−	0.0107434i
$303$			4732.29i			0.897238i
$304$	−2109.53			−0.397993
$305$	−2136.53	−	4707.13i	−0.401105	−	0.883704i
$306$	−2247.42			−0.419857
$307$			8616.73i			1.60190i	0.598733	+	0.800949i	$0.295671\pi$
$307$			8616.73i			1.60190i	−0.598733	+	0.800949i	$0.704329\pi$
$308$			51.9728i			0.00961502i
$309$	2329.11			0.428798
$310$	3994.43	−	1813.04i	0.731833	−	0.332173i
$311$	6469.81			1.17964			0.589822	−	0.807534i	$-0.299198\pi$
$311$	6469.81			1.17964			0.589822	+	0.807534i	$0.299198\pi$
$312$			5034.30i			0.913497i
$313$			3751.51i			0.677470i	0.940882	+	0.338735i	$0.109999\pi$
$313$			3751.51i			0.677470i	−0.940882	+	0.338735i	$0.890001\pi$
$314$	−2129.09			−0.382647
$315$	138.330	−	62.7869i	0.0247430	−	0.0112306i
$316$	−1385.03			−0.246564
$317$			4014.08i			0.711208i	0.934637	+	0.355604i	$0.115725\pi$
$317$			4014.08i			0.711208i	−0.934637	+	0.355604i	$0.884275\pi$
$318$		−	4368.85i		−	0.770419i
$319$	1468.41			0.257727
$320$	−2425.68	−	5344.19i	−0.423749	−	0.933591i
$321$	1228.57			0.213620
$322$		−	481.837i		−	0.0833904i
$323$			8183.17i			1.40967i
$324$	253.496			0.0434665
$325$	−6428.26	−	5622.42i	−1.09716	−	0.959618i
$326$	−3574.76			−0.607324
$327$		−	1122.38i		−	0.189809i
$328$			8999.58i			1.51500i
$329$	513.743			0.0860899
$330$	336.532	+	741.439i	0.0561379	+	0.123681i
$331$	7277.84			1.20854			0.604269	−	0.796780i	$-0.293465\pi$
$331$	7277.84			1.20854			0.604269	+	0.796780i	$0.293465\pi$
$332$		−	1890.14i		−	0.312455i
$333$		−	358.352i		−	0.0589718i
$334$	6211.73			1.01764
$335$	−5240.32	+	2378.53i	−0.854654	+	0.387920i
$336$	132.111			0.0214502
$337$			839.290i			0.135665i	0.997697	+	0.0678324i	$0.0216083\pi$
$337$			839.290i			0.135665i	−0.997697	+	0.0678324i	$0.978392\pi$
$338$			5452.79i			0.877493i
$339$	4432.87			0.710208
$340$	−3605.15	+	1636.34i	−0.575049	+	0.261009i
$341$	1955.63			0.310566
$342$			1436.44i			0.227117i
$343$			1032.23i			0.162493i
$344$	10493.3			1.64466
$345$	2004.80	+	4416.92i	0.312855	+	0.689273i
$346$	7473.51			1.16121
$347$			2255.56i			0.348948i	0.984662	+	0.174474i	$0.0558224\pi$
$347$			2255.56i			0.348948i	−0.984662	+	0.174474i	$0.944178\pi$
$348$			1253.32i			0.193060i
$349$	−10347.5			−1.58708			−0.793540	−	0.608518i	$-0.791764\pi$
$349$	−10347.5			−1.58708			−0.793540	+	0.608518i	$0.791764\pi$
$350$	−274.188	+	313.486i	−0.0418741	+	0.0478758i
$351$	1844.67			0.280517
$352$		−	1453.34i		−	0.220066i
$353$		−	2178.70i		−	0.328500i	−0.986419	−	0.164250i	$-0.947480\pi$
$353$		−	2178.70i		−	0.328500i	0.986419	−	0.164250i	$-0.0525204\pi$
$354$	3479.45			0.522403
$355$	−3920.09	−	8636.64i	−0.586076	−	1.29123i
$356$	−3133.61			−0.466520
$357$		−	512.479i		−	0.0759756i
$358$			6089.72i			0.899028i
$359$	6432.48			0.945665			0.472832	−	0.881152i	$-0.343232\pi$
$359$	6432.48			0.945665			0.472832	+	0.881152i	$0.343232\pi$
$360$	−2250.52	+	1021.49i	−0.329480	+	0.149548i
$361$	−1628.70			−0.237454
$362$		−	5562.60i		−	0.807635i
$363$			363.000i			0.0524864i
$364$	−322.804			−0.0464823
$365$	10054.0	−	4563.41i	1.44178	−	0.654410i
$366$	−3061.14			−0.437181
$367$		−	7654.12i		−	1.08867i	−0.838868	−	0.544335i	$-0.816782\pi$
$367$		−	7654.12i		−	1.08867i	0.838868	−	0.544335i	$-0.183218\pi$
$368$			4218.34i			0.597544i
$369$	3297.64			0.465225
$370$	406.051	+	894.601i	0.0570530	+	0.125697i
$371$	996.231			0.139412
$372$			1669.17i			0.232641i
$373$		−	361.440i		−	0.0501734i	−0.999685	−	0.0250867i	$-0.992014\pi$
$373$		−	361.440i		−	0.0501734i	0.999685	−	0.0250867i	$-0.00798618\pi$
$374$	2746.84			0.379775
$375$	1209.10	−	4014.50i	0.166500	−	0.552821i
$376$	−8358.17			−1.14638
$377$			9120.31i			1.24594i
$378$		−	89.9588i		−	0.0122407i
$379$	8972.22			1.21602			0.608010	−	0.793929i	$-0.291968\pi$
$379$	8972.22			1.21602			0.608010	+	0.793929i	$0.291968\pi$
$380$	1045.88	+	2304.24i	0.141190	+	0.311066i
$381$	−1700.73			−0.228690
$382$		−	8270.98i		−	1.10780i
$383$		−	8031.77i		−	1.07155i	−0.844360	−	0.535776i	$-0.820019\pi$
$383$		−	8031.77i		−	1.07155i	0.844360	−	0.535776i	$-0.179981\pi$
$384$	−304.495			−0.0404653
$385$	−169.071	+	76.7396i	−0.0223809	+	0.0101585i
$386$	−5615.48			−0.740468
$387$		−	3844.97i		−	0.505041i
$388$		−	1465.95i		−	0.191810i
$389$	1091.68			0.142289			0.0711443	−	0.997466i	$-0.477335\pi$
$389$	1091.68			0.142289			0.0711443	+	0.997466i	$0.477335\pi$
$390$	−4605.09	+	2090.21i	−0.597917	+	0.271389i
$391$	16363.6			2.11647
$392$		−	8368.75i		−	1.07828i
$393$			985.108i			0.126443i
$394$	−4942.80			−0.632017
$395$	−2045.05	−	4505.59i	−0.260500	−	0.573926i
$396$	−309.829			−0.0393169
$397$			545.504i			0.0689623i	0.999405	+	0.0344812i	$0.0109779\pi$
$397$			545.504i			0.0689623i	−0.999405	+	0.0344812i	$0.989022\pi$
$398$			2370.66i			0.298569i
$399$	−327.553			−0.0410981
$400$	2400.43	−	2744.48i	0.300054	−	0.343060i
$401$	6886.67			0.857616			0.428808	−	0.903396i	$-0.358934\pi$
$401$	6886.67			0.857616			0.428808	+	0.903396i	$0.358934\pi$
$402$			3407.87i			0.422809i
$403$			12146.4i			1.50138i
$404$	4936.70			0.607946
$405$	374.296	+	824.638i	0.0459232	+	0.101177i
$406$	444.768			0.0543682
$407$			437.986i			0.0533420i
$408$			8337.61i			1.01170i
$409$	−9815.16			−1.18662			−0.593311	−	0.804973i	$-0.702180\pi$
$409$	−9815.16			−1.18662			−0.593311	+	0.804973i	$0.702180\pi$
$410$	−8232.30	+	3736.57i	−0.991621	+	0.450088i
$411$	1905.41			0.228678
$412$		−	2429.72i		−	0.290543i
$413$			793.420i			0.0945318i
$414$	2872.40			0.340993
$415$	6148.74	−	2790.86i	0.727301	−	0.330115i
$416$	9026.74			1.06388
$417$			1720.38i			0.202032i
$418$		−	1755.65i		−	0.205435i
$419$	2666.80			0.310935			0.155467	−	0.987841i	$-0.450312\pi$
$419$	2666.80			0.310935			0.155467	+	0.987841i	$0.450312\pi$
$420$	−65.4990	−	144.306i	−0.00760958	−	0.0167652i
$421$	−8269.30			−0.957295			−0.478647	−	0.878007i	$-0.658873\pi$
$421$	−8269.30			−0.957295			−0.478647	+	0.878007i	$0.658873\pi$
$422$		−	10754.6i		−	1.24058i
$423$			3062.61i			0.352031i
$424$	−16207.8			−1.85642
$425$	−10646.2	−	9311.63i	−1.21510	−	1.06278i
$426$	−5616.56			−0.638787
$427$		−	698.032i		−	0.0791104i
$428$		−	1281.64i		−	0.144744i
$429$	−2254.60			−0.253737
$430$	4356.76	+	9598.70i	0.488609	+	1.07649i
$431$	11805.7			1.31940			0.659698	−	0.751531i	$-0.270684\pi$
$431$	11805.7			1.31940			0.659698	+	0.751531i	$0.270684\pi$
$432$			787.564i			0.0877122i
$433$			12938.9i			1.43604i	0.696023	+	0.718020i	$0.254951\pi$
$433$			12938.9i			1.43604i	−0.696023	+	0.718020i	$0.745049\pi$
$434$	592.343			0.0655147
$435$	−4077.12	+	1850.57i	−0.449386	+	0.203972i
$436$	−1170.86			−0.128610
$437$		−	10458.8i		−	1.14488i
$438$		−	6538.28i		−	0.713267i
$439$	474.875			0.0516277			0.0258138	−	0.999667i	$-0.491782\pi$
$439$	474.875			0.0516277			0.0258138	+	0.999667i	$0.491782\pi$
$440$	2750.63	−	1248.49i	0.298026	−	0.135271i
$441$	−3066.49			−0.331118
$442$			17060.7i			1.83596i
$443$		−	3691.55i		−	0.395916i	−0.980210	−	0.197958i	$-0.936569\pi$
$443$		−	3691.55i		−	0.395916i	0.980210	−	0.197958i	$-0.0634310\pi$
$444$	−373.831			−0.0399578
$445$	−4626.88	−	10193.8i	−0.492888	−	1.08592i
$446$	4285.09			0.454944
$447$			2533.56i			0.268083i
$448$		−	792.502i		−	0.0835763i
$449$	−15741.4			−1.65453			−0.827266	−	0.561811i	$-0.810105\pi$
$449$	−15741.4			−1.65453			−0.827266	+	0.561811i	$0.810105\pi$
$450$	−1868.80	−	1634.53i	−0.195769	−	0.171228i
$451$	−4030.44			−0.420812
$452$		−	4624.35i		−	0.481219i
$453$			76.6465i			0.00794959i
$454$	−2973.75			−0.307412
$455$	−476.631	−	1050.10i	−0.0491095	−	0.108197i
$456$	5329.01			0.547267
$457$		−	3995.03i		−	0.408927i	−0.978874	−	0.204463i	$-0.934455\pi$
$457$		−	3995.03i		−	0.408927i	0.978874	−	0.204463i	$-0.0655450\pi$
$458$		−	1805.43i		−	0.184197i
$459$	3055.07			0.310673
$460$	4607.71	−	2091.40i	0.467034	−	0.211982i
$461$	−11467.6			−1.15856			−0.579281	−	0.815128i	$-0.696667\pi$
$461$	−11467.6			−1.15856			−0.579281	+	0.815128i	$0.696667\pi$
$462$			109.950i			0.0110721i
$463$		−	14675.0i		−	1.47301i	−0.676430	−	0.736507i	$-0.736474\pi$
$463$		−	14675.0i		−	1.47301i	0.676430	−	0.736507i	$-0.263526\pi$
$464$	−3893.82			−0.389582
$465$	−5429.91	+	2464.59i	−0.541519	+	0.245791i
$466$	479.097			0.0476261
$467$		−	1509.15i		−	0.149540i	−0.997201	−	0.0747700i	$-0.976178\pi$
$467$		−	1509.15i		−	0.149540i	0.997201	−	0.0747700i	$-0.0238223\pi$
$468$		−	1924.35i		−	0.190071i
$469$	−777.098			−0.0765097
$470$	−3470.26	−	7645.58i	−0.340577	−	0.750350i
$471$	2894.22			0.283139
$472$		−	12908.3i		−	1.25880i
$473$			4699.41i			0.456827i
$474$	−2930.07			−0.283929
$475$	−5951.57	+	6804.58i	−0.574898	+	0.657296i
$476$	−534.616			−0.0514791
$477$			5938.90i			0.570070i
$478$			8749.22i			0.837196i
$479$	2021.17			0.192797			0.0963986	−	0.995343i	$-0.469268\pi$
$479$	2021.17			0.192797			0.0963986	+	0.995343i	$0.469268\pi$
$480$	1831.58	+	4035.29i	0.174166	+	0.383719i
$481$	−2720.34			−0.257873
$482$		−	8768.19i		−	0.828589i
$483$			654.995i			0.0617046i
$484$	378.680			0.0355635
$485$	4768.83	−	2164.53i	0.446477	−	0.202652i
$486$	536.277			0.0500535
$487$			5048.84i			0.469784i	0.972021	+	0.234892i	$0.0754737\pi$
$487$			5048.84i			0.469784i	−0.972021	+	0.234892i	$0.924526\pi$
$488$			11356.4i			1.05344i
$489$	4859.42			0.449388
$490$	7655.26	−	3474.65i	0.705774	−	0.320345i
$491$	−18950.5			−1.74180			−0.870899	−	0.491462i	$-0.836463\pi$
$491$	−18950.5			−1.74180			−0.870899	+	0.491462i	$0.836463\pi$
$492$		−	3440.08i		−	0.315225i
$493$			15104.7i			1.37988i
$494$	10904.4			0.993143
$495$	−457.473	−	1007.89i	−0.0415391	−	0.0915178i
$496$	−5185.79			−0.469454
$497$		−	1280.75i		−	0.115592i
$498$		−	3998.64i		−	0.359806i
$499$	−8942.71			−0.802266			−0.401133	−	0.916020i	$-0.631383\pi$
$499$	−8942.71			−0.802266			−0.401133	+	0.916020i	$0.631383\pi$
$500$	−4187.91	−	1261.32i	−0.374578	−	0.112816i
$501$	−8444.05			−0.752999
$502$			9509.13i			0.845445i
$503$		−	6281.34i		−	0.556801i	−0.960465	−	0.278401i	$-0.910196\pi$
$503$		−	6281.34i		−	0.556801i	0.960465	−	0.278401i	$-0.0898043\pi$
$504$	−333.735			−0.0294955
$505$	7289.21	+	16059.4i	0.642308	+	1.41511i
$506$	−3510.72			−0.308439
$507$		−	7412.37i		−	0.649300i
$508$			1774.19i			0.154955i
$509$	3877.32			0.337641			0.168820	−	0.985647i	$-0.446004\pi$
$509$	3877.32			0.337641			0.168820	+	0.985647i	$0.446004\pi$
$510$	−7626.77	+	3461.72i	−0.662194	+	0.300564i
$511$	1490.93			0.129070
$512$			9585.44i			0.827384i
$513$		−	1952.66i		−	0.168055i
$514$	13999.4			1.20134
$515$	7904.02	−	3587.56i	0.676296	−	0.306965i
$516$	−4011.06			−0.342203
$517$		−	3743.19i		−	0.318424i
$518$			132.662i			0.0112526i
$519$	−10159.3			−0.859235
$520$	7754.39	+	17084.2i	0.653947	+	1.44076i
$521$	−19738.2			−1.65978			−0.829892	−	0.557923i	$-0.811598\pi$
$521$	−19738.2			−1.65978			−0.829892	+	0.557923i	$0.811598\pi$
$522$			2651.43i			0.222318i
$523$		−	21804.4i		−	1.82302i	−0.411274	−	0.911512i	$-0.634916\pi$
$523$		−	21804.4i		−	1.82302i	0.411274	−	0.911512i	$-0.365084\pi$
$524$	1027.66			0.0856747
$525$	372.723	−	426.144i	0.0309847	−	0.0354256i
$526$	9719.95			0.805722
$527$			20116.5i			1.66278i
$528$		−	962.578i		−	0.0793387i
$529$	−8747.15			−0.718924
$530$	−6729.40	−	14826.0i	−0.551521	−	1.21510i
$531$	−4729.87			−0.386551
$532$			341.702i			0.0278471i
$533$		−	25033.2i		−	2.03435i
$534$	−6629.22			−0.537218
$535$	4169.25	−	1892.38i	0.336920	−	0.152925i
$536$	12642.7			1.01881
$537$		−	8278.20i		−	0.665234i
$538$		−	10631.4i		−	0.851956i
$539$	3747.93			0.299508
$540$	860.258	−	390.463i	0.0685548	−	0.0311164i
$541$	6332.36			0.503234			0.251617	−	0.967827i	$-0.419038\pi$
$541$	6332.36			0.503234			0.251617	+	0.967827i	$0.419038\pi$
$542$			4791.81i			0.379753i
$543$			7561.64i			0.597608i
$544$	14949.7			1.17824
$545$	−1728.81	−	3808.87i	−0.135879	−	0.299365i
$546$	−682.900			−0.0535264
$547$		−	1049.90i		−	0.0820669i	−0.999158	−	0.0410334i	$-0.986935\pi$
$547$		−	1049.90i		−	0.0820669i	0.999158	−	0.0410334i	$-0.0130650\pi$
$548$		−	1987.71i		−	0.154947i
$549$	4161.22			0.323491
$550$	2284.09	+	1997.76i	0.177080	+	0.154881i
$551$	9654.23			0.746432
$552$		−	10656.2i		−	0.821665i
$553$		−	668.144i		−	0.0513786i
$554$	−2982.39			−0.228718
$555$	−551.975	−	1216.09i	−0.0422162	−	0.0930096i
$556$	1794.69			0.136892
$557$			7763.68i			0.590588i	0.955406	+	0.295294i	$0.0954176\pi$
$557$			7763.68i			0.590588i	−0.955406	+	0.295294i	$0.904582\pi$
$558$			3531.17i			0.267897i
$559$	−29188.2			−2.20846
$560$	448.329	−	203.493i	0.0338310	−	0.0153556i
$561$	−3733.98			−0.281014
$562$			6881.55i			0.516514i
$563$			5779.52i			0.432642i	0.976322	+	0.216321i	$0.0694058\pi$
$563$			5779.52i			0.432642i	−0.976322	+	0.216321i	$0.930594\pi$
$564$	3194.90			0.238528
$565$	15043.3	−	6828.00i	1.12013	−	0.508418i
$566$	−9189.61			−0.682453
$567$			122.287i			0.00905748i
$568$			20836.7i			1.53924i
$569$	−7128.46			−0.525203			−0.262601	−	0.964904i	$-0.584580\pi$
$569$	−7128.46			−0.525203			−0.262601	+	0.964904i	$0.584580\pi$
$570$	2212.57	+	4874.68i	0.162587	+	0.358207i
$571$	−13775.0			−1.00957			−0.504784	−	0.863245i	$-0.668428\pi$
$571$	−13775.0			−1.00957			−0.504784	+	0.863245i	$0.668428\pi$
$572$			2351.99i			0.171926i
$573$			11243.3i			0.819715i
$574$	−1220.79			−0.0887712
$575$	13606.9	+	11901.1i	0.986862	+	0.863150i
$576$	4724.39			0.341753
$577$		−	14483.4i		−	1.04498i	−0.852646	−	0.522488i	$-0.825004\pi$
$577$		−	14483.4i		−	1.04498i	0.852646	−	0.522488i	$-0.174996\pi$
$578$			17412.7i			1.25307i
$579$	7633.53			0.547908
$580$	1930.50	+	4253.23i	0.138207	+	0.304493i
$581$	911.811			0.0651090
$582$		−	3101.25i		−	0.220878i
$583$		−	7258.65i		−	0.515648i
$584$	−24256.1			−1.71871
$585$	6260.03	−	2841.37i	0.442428	−	0.200814i
$586$	3158.10			0.222628
$587$			18694.1i			1.31446i	0.753691	+	0.657228i	$0.228271\pi$
$587$			18694.1i			1.31446i	−0.753691	+	0.657228i	$0.771729\pi$
$588$			3198.94i			0.224357i
$589$	12857.5			0.899464
$590$	11807.8	−	5359.44i	0.823928	−	0.373974i
$591$	6719.10			0.467660
$592$		−	1161.42i		−	0.0806320i
$593$		−	15320.9i		−	1.06097i	−0.847694	−	0.530486i	$-0.822010\pi$
$593$		−	15320.9i		−	1.06097i	0.847694	−	0.530486i	$-0.177990\pi$
$594$	−655.450			−0.0452751
$595$	−789.378	−	1739.14i	−0.0543888	−	0.119828i
$596$	2642.99			0.181646
$597$		−	3222.61i		−	0.220926i
$598$		−	21805.1i		−	1.49110i
$599$	−14142.5			−0.964684			−0.482342	−	0.875983i	$-0.660214\pi$
$599$	−14142.5			−0.964684			−0.482342	+	0.875983i	$0.660214\pi$
$600$	−6063.89	+	6933.00i	−0.412595	+	0.471731i
$601$	−15024.9			−1.01977			−0.509883	−	0.860244i	$-0.670311\pi$
$601$	−15024.9			−1.01977			−0.509883	+	0.860244i	$0.670311\pi$
$602$			1423.41i			0.0963687i
$603$		−	4632.57i		−	0.312857i
$604$	79.9572			0.00538644
$605$	559.133	+	1231.87i	0.0375735	+	0.0827810i
$606$	10443.7			0.700077
$607$			8612.72i			0.575913i	0.957643	+	0.287957i	$0.0929759\pi$
$607$			8612.72i			0.575913i	−0.957643	+	0.287957i	$0.907024\pi$
$608$		−	9555.18i		−	0.637358i
$609$	−604.606			−0.0402297
$610$	−10388.2	+	4715.10i	−0.689517	+	0.312965i
$611$	23249.0			1.53937
$612$		−	3187.04i		−	0.210504i
$613$		−	1215.02i		−	0.0800558i	−0.999199	−	0.0400279i	$-0.987255\pi$
$613$		−	1215.02i		−	0.0800558i	0.999199	−	0.0400279i	$-0.0127447\pi$
$614$	19016.3			1.24989
$615$	11190.8	−	5079.39i	0.733748	−	0.333042i
$616$	407.898			0.0266797
$617$			17602.6i			1.14855i	0.818662	+	0.574275i	$0.194716\pi$
$617$			17602.6i			1.14855i	−0.818662	+	0.574275i	$0.805284\pi$
$618$		−	5140.13i		−	0.334573i
$619$	2312.91			0.150184			0.0750920	−	0.997177i	$-0.476075\pi$
$619$	2312.91			0.150184			0.0750920	+	0.997177i	$0.476075\pi$
$620$	2571.05	+	5664.46i	0.166542	+	0.366920i
$621$	−3904.67			−0.252317
$622$		−	14278.2i		−	0.920426i
$623$		−	1511.66i		−	0.0972127i
$624$	5978.59			0.383550
$625$	−2080.42	−	15485.9i	−0.133147	−	0.991096i
$626$	8279.22			0.528601
$627$			2386.59i			0.152011i
$628$		−	3019.23i		−	0.191848i
$629$	−4505.32			−0.285595
$630$	−138.565	−	305.282i	−0.00876277	−	0.0193059i
$631$	22763.2			1.43612			0.718059	−	0.695982i	$-0.245031\pi$
$631$	22763.2			1.43612			0.718059	+	0.695982i	$0.245031\pi$
$632$			10870.1i			0.684163i
$633$			14619.4i			0.917963i
$634$	8858.67			0.554926
$635$	−5771.54	+	2619.65i	−0.360687	+	0.163713i
$636$	6195.43			0.386265
$637$			23278.5i			1.44792i
$638$		−	3240.63i		−	0.201094i
$639$	7635.00			0.472670
$640$	−1033.32	+	469.017i	−0.0638215	+	0.0289680i
$641$	−519.128			−0.0319880			−0.0159940	−	0.999872i	$-0.505091\pi$
$641$	−519.128			−0.0319880			−0.0159940	+	0.999872i	$0.505091\pi$
$642$		−	2711.34i		−	0.166679i
$643$		−	12006.6i		−	0.736382i	−0.929750	−	0.368191i	$-0.879977\pi$
$643$		−	12006.6i		−	0.736382i	0.929750	−	0.368191i	$-0.120023\pi$
$644$	683.288			0.0418095
$645$	−5922.46	−	13048.2i	−0.361545	−	0.796546i
$646$	18059.5			1.09991
$647$			9014.17i			0.547734i	0.961768	+	0.273867i	$0.0883028\pi$
$647$			9014.17i			0.547734i	−0.961768	+	0.273867i	$0.911697\pi$
$648$		−	1989.51i		−	0.120610i
$649$	5780.95			0.349649
$650$	−12408.1	+	14186.5i	−0.748749	+	0.856065i
$651$	−805.215			−0.0484775
$652$		−	5069.33i		−	0.304494i
$653$		−	26556.4i		−	1.59148i	−0.605641	−	0.795738i	$-0.707083\pi$
$653$		−	26556.4i		−	1.59148i	0.605641	−	0.795738i	$-0.292917\pi$
$654$	−2476.98			−0.148100
$655$	1517.37	+	3343.04i	0.0905171	+	0.199425i
$656$	10687.6			0.636101
$657$			8887.95i			0.527781i
$658$		−	1133.78i		−	0.0671723i
$659$	8015.80			0.473826			0.236913	−	0.971531i	$-0.423864\pi$
$659$	8015.80			0.473826			0.236913	+	0.971531i	$0.423864\pi$
$660$	−1051.43	+	477.233i	−0.0620102	+	0.0281459i
$661$	2593.17			0.152591			0.0762953	−	0.997085i	$-0.475691\pi$
$661$	2593.17			0.152591			0.0762953	+	0.997085i	$0.475691\pi$
$662$		−	16061.5i		−	0.942971i
$663$		−	23191.8i		−	1.35852i
$664$	−14834.4			−0.866998
$665$	−1111.57	+	504.534i	−0.0648196	+	0.0294210i
$666$	−790.849			−0.0460132
$667$		−	19305.2i		−	1.12069i
$668$			8808.79i			0.510213i
$669$	−5825.03			−0.336635
$670$	5249.19	+	11564.9i	0.302677	+	0.666850i
$671$	−5085.94			−0.292609
$672$			598.403i			0.0343510i
$673$			17727.8i			1.01539i	0.861537	+	0.507694i	$0.169502\pi$
$673$			17727.8i			1.01539i	−0.861537	+	0.507694i	$0.830498\pi$
$674$	1852.23			0.105853
$675$	2540.40	+	2221.94i	0.144859	+	0.126700i
$676$	−7732.55			−0.439949
$677$			3681.04i			0.208972i	0.994526	+	0.104486i	$0.0333197\pi$
$677$			3681.04i			0.208972i	−0.994526	+	0.104486i	$0.966680\pi$
$678$		−	9782.90i		−	0.554145i
$679$	707.180			0.0399692
$680$	12842.5	+	28294.3i	0.724247	+	1.59564i
$681$	4042.43			0.227469
$682$		−	4315.88i		−	0.242322i
$683$			7829.21i			0.438619i	0.975655	+	0.219309i	$0.0703804\pi$
$683$			7829.21i			0.438619i	−0.975655	+	0.219309i	$0.929620\pi$
$684$	−2037.01			−0.113870
$685$	6466.14	−	2934.92i	0.360669	−	0.163704i
$686$	2278.03			0.126786
$687$			2454.26i			0.136296i
$688$		−	12461.6i		−	0.690542i
$689$	45083.6			2.49281
$690$	9747.71	−	4424.40i	0.537810	−	0.244107i
$691$	4983.99			0.274385			0.137192	−	0.990544i	$-0.456192\pi$
$691$	4983.99			0.274385			0.137192	+	0.990544i	$0.456192\pi$
$692$			10598.1i			0.582196i
$693$		−	149.462i		−	0.00819280i
$694$	4977.80			0.272269
$695$	2649.92	+	5838.23i	0.144629	+	0.318643i
$696$	9836.43			0.535702
$697$		−	41458.9i		−	2.25304i
$698$			22836.0i			1.23833i
$699$	−651.271			−0.0352408
$700$	−444.551	−	388.822i	−0.0240035	−	0.0209944i
$701$	1748.60			0.0942135			0.0471068	−	0.998890i	$-0.485000\pi$
$701$	1748.60			0.0942135			0.0471068	+	0.998890i	$0.485000\pi$
$702$		−	4071.01i		−	0.218875i
$703$			2879.59i			0.154489i
$704$	−5774.26			−0.309127
$705$	4717.38	+	10393.2i	0.252009	+	0.555220i
$706$	−4808.18			−0.256315
$707$			2381.48i			0.126683i
$708$			4934.17i			0.261917i
$709$	−22959.1			−1.21614			−0.608072	−	0.793882i	$-0.708057\pi$
$709$	−22959.1			−1.21614			−0.608072	+	0.793882i	$0.708057\pi$
$710$	−19060.2	+	8651.26i	−1.00749	+	0.457290i
$711$	3983.05			0.210093
$712$			24593.5i			1.29449i
$713$		−	25710.7i		−	1.35045i
$714$	−1130.99			−0.0592805
$715$	−7651.15	+	3472.79i	−0.400191	+	0.181643i
$716$	−8635.78			−0.450746
$717$		−	11893.4i		−	0.619482i
$718$		−	14195.9i		−	0.737862i
$719$	−23344.8			−1.21087			−0.605435	−	0.795895i	$-0.707001\pi$
$719$	−23344.8			−1.21087			−0.605435	+	0.795895i	$0.707001\pi$
$720$	1213.09	+	2672.65i	0.0627907	+	0.138339i
$721$	1172.10			0.0605429
$722$			3594.37i			0.185275i
$723$			11919.2i			0.613113i
$724$	7888.27			0.404924
$725$	−10985.6	+	12560.1i	−0.562749	+	0.643406i
$726$	801.105			0.0409529
$727$			16238.3i			0.828400i	0.910186	+	0.414200i	$0.135939\pi$
$727$			16238.3i			0.828400i	−0.910186	+	0.414200i	$0.864061\pi$
$728$			2533.46i			0.128979i
$729$	−729.000			−0.0370370
$730$	−10071.0	−	22188.1i	−0.510608	−	1.12496i
$731$	−48340.3			−2.44587
$732$		−	4340.97i		−	0.219189i
$733$			36830.4i			1.85588i	0.372729	+	0.927940i	$0.378422\pi$
$733$			36830.4i			1.85588i	−0.372729	+	0.927940i	$0.621578\pi$
$734$	−16891.9			−0.849442
$735$	−10406.3	+	4723.35i	−0.522236	+	0.237038i
$736$	−19107.1			−0.956926
$737$			5662.03i			0.282990i
$738$		−	7277.56i		−	0.362995i
$739$	−33393.1			−1.66223			−0.831114	−	0.556102i	$-0.812296\pi$
$739$	−33393.1			−1.66223			−0.831114	+	0.556102i	$0.812296\pi$
$740$	−1268.62	+	575.817i	−0.0630210	+	0.0286047i
$741$	−14823.1			−0.734874
$742$		−	2198.58i		−	0.108777i
$743$			17151.0i			0.846850i	0.905931	+	0.423425i	$0.139172\pi$
$743$			17151.0i			0.846850i	−0.905931	+	0.423425i	$0.860828\pi$
$744$	13100.2			0.645531
$745$	3902.46	+	8597.80i	0.191913	+	0.422818i
$746$	−797.663			−0.0391482
$747$			5435.64i			0.266238i
$748$			3895.27i			0.190408i
$749$	618.267			0.0301615
$750$	−8859.61	−	2668.36i	−0.431343	−	0.129913i
$751$	23603.0			1.14685			0.573425	−	0.819258i	$-0.305614\pi$
$751$	23603.0			1.14685			0.573425	+	0.819258i	$0.305614\pi$
$752$			9925.93i			0.481332i
$753$		−	12926.4i		−	0.625585i
$754$	20127.6			0.972155
$755$	118.059	+	260.105i	0.00569089	+	0.0125380i
$756$	127.570			0.00613712
$757$			40304.2i			1.93511i	0.252655	+	0.967556i	$0.418696\pi$
$757$			40304.2i			1.93511i	−0.252655	+	0.967556i	$0.581304\pi$
$758$		−	19800.8i		−	0.948809i
$759$	4772.37			0.228229
$760$	18084.4	−	8208.34i	0.863144	−	0.391773i
$761$	−12908.2			−0.614876			−0.307438	−	0.951568i	$-0.599472\pi$
$761$	−12908.2			−0.614876			−0.307438	+	0.951568i	$0.599472\pi$
$762$			3753.34i			0.178437i
$763$		−	564.826i		−	0.0267996i
$764$	11729.0			0.555419
$765$	10367.6	−	4705.77i	0.489989	−	0.222402i
$766$	−17725.3			−0.836087
$767$			35905.6i			1.69032i
$768$		−	11926.4i		−	0.560360i
$769$	−4151.97			−0.194700			−0.0973498	−	0.995250i	$-0.531037\pi$
$769$	−4151.97			−0.194700			−0.0973498	+	0.995250i	$0.531037\pi$
$770$	169.357	+	373.122i	0.00792622	+	0.0174628i
$771$	−19030.4			−0.888927
$772$		−	7963.26i		−	0.371249i
$773$		−	34207.0i		−	1.59164i	−0.605531	−	0.795822i	$-0.707039\pi$
$773$		−	34207.0i		−	1.59164i	0.605531	−	0.795822i	$-0.292961\pi$
$774$	−8485.48			−0.394062
$775$	−14630.6	+	16727.5i	−0.678123	+	0.775317i
$776$	−11505.2			−0.532234
$777$		−	180.338i		−	0.00832635i
$778$		−	2409.22i		−	0.111022i
$779$	−26498.6			−1.21876
$780$	−2964.10	−	6530.43i	−0.136067	−	0.299778i
$781$	−9331.66			−0.427546
$782$		−	36112.8i		−	1.65140i
$783$		−	3604.27i		−	0.164504i
$784$	−9938.49			−0.452737
$785$	9821.74	−	4458.00i	0.446564	−	0.202691i
$786$	2174.04			0.0986582
$787$		−	7957.51i		−	0.360425i	−0.983628	−	0.180213i	$-0.942321\pi$
$787$		−	7957.51i		−	0.360425i	0.983628	−	0.180213i	$-0.0576785\pi$
$788$		−	7009.34i		−	0.316875i
$789$	−13213.0			−0.596193
$790$	−9943.39	+	4513.21i	−0.447810	+	0.203257i
$791$	2230.80			0.100276
$792$			2431.63i			0.109096i
$793$		−	31588.9i		−	1.41457i
$794$	1203.87			0.0538084
$795$	9147.75	+	20154.1i	0.408097	+	0.899108i
$796$	−3361.81			−0.149694
$797$		−	23524.5i		−	1.04552i	−0.852479	−	0.522762i	$-0.824902\pi$
$797$		−	23524.5i		−	1.04552i	0.852479	−	0.522762i	$-0.175098\pi$
$798$			722.877i			0.0320671i
$799$	38504.1			1.70485
$800$	12431.2	+	10872.8i	0.549387	+	0.480516i
$801$	9011.57			0.397513
$802$		−	15198.2i		−	0.669162i
$803$		−	10863.1i		−	0.477396i
$804$	−4832.67			−0.211984
$805$	1008.90	+	2222.77i	0.0441726	+	0.0973199i
$806$	26806.0			1.17147
$807$			14452.0i			0.630404i
$808$		−	38744.7i		−	1.68692i
$809$	11428.3			0.496659			0.248329	−	0.968676i	$-0.420118\pi$
$809$	11428.3			0.496659			0.248329	+	0.968676i	$0.420118\pi$
$810$	1819.89	−	826.034i	0.0789439	−	0.0358319i
$811$	−16762.6			−0.725789			−0.362895	−	0.931830i	$-0.618211\pi$
$811$	−16762.6			−0.725789			−0.362895	+	0.931830i	$0.618211\pi$
$812$			630.722i			0.0272586i
$813$		−	6513.86i		−	0.280997i
$814$	966.593			0.0416205
$815$	16490.8	−	7485.03i	0.708770	−	0.321704i
$816$	9901.51			0.424782
$817$			30896.9i			1.32307i
$818$			21661.1i			0.925871i
$819$	928.314			0.0396068
$820$	−5298.79	−	11674.1i	−0.225661	−	0.497169i
$821$	4391.15			0.186665			0.0933326	−	0.995635i	$-0.470248\pi$
$821$	4391.15			0.186665			0.0933326	+	0.995635i	$0.470248\pi$
$822$		−	4205.05i		−	0.178428i
$823$		−	28052.8i		−	1.18816i	−0.804404	−	0.594082i	$-0.797515\pi$
$823$		−	28052.8i		−	1.18816i	0.804404	−	0.594082i	$-0.202485\pi$
$824$	−19069.2			−0.806196
$825$	−3104.93	−	2715.70i	−0.131030	−	0.114604i
$826$	1751.00			0.0737592
$827$		−	5791.95i		−	0.243538i	−0.992558	−	0.121769i	$-0.961143\pi$
$827$		−	5791.95i		−	0.243538i	0.992558	−	0.121769i	$-0.0388567\pi$
$828$			4073.33i			0.170964i
$829$	37447.0			1.56886			0.784432	−	0.620215i	$-0.212955\pi$
$829$	37447.0			1.56886			0.784432	+	0.620215i	$0.212955\pi$
$830$	−6159.15	−	13569.7i	−0.257575	−	0.567482i
$831$	4054.17			0.169239
$832$		−	35864.0i		−	1.49443i
$833$			38552.9i			1.60357i
$834$	3796.71			0.157637
$835$	−28655.5	+	13006.5i	−1.18762	+	0.539051i
$836$	2489.68			0.102999
$837$		−	4800.18i		−	0.198230i
$838$		−	5885.37i		−	0.242609i
$839$	−6001.17			−0.246941			−0.123470	−	0.992348i	$-0.539402\pi$
$839$	−6001.17			−0.246941			−0.123470	+	0.992348i	$0.539402\pi$
$840$	−1132.55	+	514.055i	−0.0465200	+	0.0211150i
$841$	−6568.98			−0.269342
$842$			18249.5i			0.746936i
$843$		−	9354.58i		−	0.382193i
$844$	15250.9			0.621989
$845$	−11417.4	−	25154.4i	−0.464815	−	1.02407i
$846$	6758.88			0.274675
$847$			182.676i			0.00741066i
$848$			19248.0i			0.779455i
$849$	12492.1			0.504980
$850$	−20549.9	+	23495.2i	−0.829240	+	0.948093i
$851$	5758.22			0.231950
$852$		−	7964.79i		−	0.320269i
$853$		−	1272.58i		−	0.0510812i	−0.999674	−	0.0255406i	$-0.991869\pi$
$853$		−	1272.58i		−	0.0510812i	0.999674	−	0.0255406i	$-0.00813070\pi$
$854$	−1540.49			−0.0617265
$855$	−3007.71	−	6626.50i	−0.120306	−	0.265054i
$856$	−10058.7			−0.401634
$857$		−	21932.2i		−	0.874201i	−0.899413	−	0.437100i	$-0.856005\pi$
$857$		−	21932.2i		−	0.874201i	0.899413	−	0.437100i	$-0.143995\pi$
$858$			4975.68i			0.197980i
$859$	23911.6			0.949770			0.474885	−	0.880048i	$-0.342490\pi$
$859$	23911.6			0.949770			0.474885	+	0.880048i	$0.342490\pi$
$860$	−13611.8	+	6178.28i	−0.539720	+	0.244974i
$861$	1659.50			0.0656861
$862$		−	26054.0i		−	1.02947i
$863$			12447.1i			0.490967i	0.969401	+	0.245484i	$0.0789468\pi$
$863$			12447.1i			0.490967i	−0.969401	+	0.245484i	$0.921053\pi$
$864$	−3567.29			−0.140465
$865$	−34476.2	+	15648.5i	−1.35518	+	0.615102i
$866$	28554.9			1.12048
$867$		−	23670.4i		−	0.927207i
$868$			839.996i			0.0328471i
$869$	−4868.17			−0.190036
$870$	4084.02	+	8997.81i	0.159151	+	0.350637i
$871$	−35167.0			−1.36807
$872$			9189.25i			0.356866i
$873$			4215.76i			0.163438i
$874$	−23081.6			−0.893304
$875$	608.467	−	2020.26i	0.0235085	−	0.0780540i
$876$	9271.87			0.357611
$877$		−	29036.8i		−	1.11802i	−0.829160	−	0.559011i	$-0.811181\pi$
$877$		−	29036.8i		−	1.11802i	0.829160	−	0.559011i	$-0.188819\pi$
$878$		−	1048.00i		−	0.0402829i
$879$	−4293.03			−0.164733
$880$	−1482.67	−	3266.58i	−0.0567963	−	0.125132i
$881$	40243.9			1.53899			0.769495	−	0.638652i	$-0.220508\pi$
$881$	40243.9			1.53899			0.769495	+	0.638652i	$0.220508\pi$
$882$			6767.43i			0.258358i
$883$		−	40042.9i		−	1.52610i	−0.646337	−	0.763052i	$-0.723700\pi$
$883$		−	40042.9i		−	1.52610i	0.646337	−	0.763052i	$-0.276300\pi$
$884$	−24193.6			−0.920496
$885$	−16051.1	+	7285.47i	−0.609664	+	0.276721i
$886$	−8146.89			−0.308917
$887$		−	21075.4i		−	0.797793i	−0.916996	−	0.398896i	$-0.869393\pi$
$887$		−	21075.4i		−	0.797793i	0.916996	−	0.398896i	$-0.130607\pi$
$888$			2933.94i			0.110875i
$889$	−855.875			−0.0322892
$890$	−22496.7	+	10211.1i	−0.847294	+	0.384579i
$891$	891.000			0.0335013
$892$			6076.64i			0.228095i
$893$		−	24610.1i		−	0.922222i
$894$	5591.31			0.209174
$895$	−12751.0	−	28092.7i	−0.476223	−	1.04920i
$896$	−153.234			−0.00571339
$897$			29641.3i			1.10334i
$898$			34739.8i			1.29096i
$899$	23732.7			0.880457
$900$	2317.91	−	2650.13i	0.0858486	−	0.0981530i
$901$	74665.7			2.76079
$902$			8894.79i			0.328342i
$903$		−	1934.95i		−	0.0713079i
$904$	−36293.2			−1.33528
$905$	11647.3	+	25661.0i	0.427811	+	0.942541i
$906$	169.151			0.00620273
$907$			31049.7i			1.13670i	0.822786	+	0.568351i	$0.192419\pi$
$907$			31049.7i			1.13670i	−0.822786	+	0.568351i	$0.807581\pi$
$908$		−	4217.04i		−	0.154127i
$909$	−14196.9			−0.518021
$910$	−2317.47	+	1051.88i	−0.0844212	+	0.0383180i
$911$	−17625.2			−0.640996			−0.320498	−	0.947249i	$-0.603850\pi$
$911$	−17625.2			−0.640996			−0.320498	+	0.947249i	$0.603850\pi$
$912$		−	6328.58i		−	0.229781i
$913$		−	6643.56i		−	0.240821i
$914$	−8816.64			−0.319068
$915$	14121.4	−	6409.58i	0.510207	−	0.231578i
$916$	2560.27			0.0923511
$917$			495.747i			0.0178528i
$918$		−	6742.25i		−	0.242405i
$919$	51856.3			1.86135			0.930675	−	0.365848i	$-0.119221\pi$
$919$	51856.3			1.86135			0.930675	+	0.365848i	$0.119221\pi$
$920$	−16413.9	−	36162.7i	−0.588207	−	1.29592i
$921$	−25850.2			−0.924856
$922$			25307.8i			0.903977i
$923$		−	57959.2i		−	2.06690i
$924$	−155.918			−0.00555123
$925$	−3746.33	−	3276.69i	−0.133166	−	0.116472i
$926$	−32386.3			−1.14933
$927$			6987.34i			0.247567i
$928$		−	17637.2i		−	0.623889i
$929$	24369.1			0.860628			0.430314	−	0.902679i	$-0.358403\pi$
$929$	24369.1			0.860628			0.430314	+	0.902679i	$0.358403\pi$
$930$	5439.11	+	11983.3i	0.191780	+	0.422524i
$931$	24641.2			0.867436
$932$			679.403i			0.0238783i
$933$			19409.4i			0.681067i
$934$	−3330.55			−0.116680
$935$	−12671.5	+	5751.49i	−0.443212	+	0.201170i
$936$	−15102.9			−0.527408
$937$			31621.9i			1.10250i	0.834341	+	0.551249i	$0.185849\pi$
$937$			31621.9i			1.10250i	−0.834341	+	0.551249i	$0.814151\pi$
$938$			1714.98i			0.0596973i
$939$	−11254.5			−0.391137
$940$	10842.1	−	4921.14i	0.376203	−	0.170755i
$941$	−8576.25			−0.297107			−0.148554	−	0.988904i	$-0.547462\pi$
$941$	−8576.25			−0.297107			−0.148554	+	0.988904i	$0.547462\pi$
$942$		−	6387.26i		−	0.220921i
$943$			52988.3i			1.82984i
$944$	−15329.5			−0.528531
$945$	188.361	+	414.991i	0.00648400	+	0.0142854i
$946$	10371.1			0.356443
$947$			24802.7i			0.851087i	0.904938	+	0.425544i	$0.139917\pi$
$947$			24802.7i			0.851087i	−0.904938	+	0.425544i	$0.860083\pi$
$948$		−	4155.10i		−	0.142354i
$949$	67470.6			2.30789
$950$	15017.0	+	13134.5i	0.512860	+	0.448569i
$951$	−12042.2			−0.410616
$952$			4195.82i			0.142844i
$953$			34824.6i			1.18371i	0.806043	+	0.591857i	$0.201605\pi$
$953$			34824.6i			1.18371i	−0.806043	+	0.591857i	$0.798395\pi$
$954$	13106.6			0.444801
$955$	17318.2	+	38155.1i	0.586812	+	1.29285i
$956$	−12407.2			−0.419745
$957$			4405.22i			0.148799i
$958$		−	4460.53i		−	0.150431i
$959$	958.878			0.0322876
$960$	16032.6	−	7277.04i	0.539009	−	0.244651i
$961$	1816.26			0.0609669
$962$			6003.53i			0.201207i
$963$			3685.71i			0.123334i
$964$	12434.1			0.415430
$965$	25904.9	−	11758.0i	0.864155	−	0.392232i
$966$	1445.51			0.0481455
$967$		−	11980.0i		−	0.398399i	−0.979959	−	0.199199i	$-0.936166\pi$
$967$		−	11980.0i		−	0.398399i	0.979959	−	0.199199i	$-0.0638341\pi$
$968$		−	2971.99i		−	0.0986812i
$969$	−24549.5			−0.813874
$970$	−4776.90	−	10524.3i	−0.158121	−	0.348367i
$971$	−32808.5			−1.08432			−0.542161	−	0.840275i	$-0.682394\pi$
$971$	−32808.5			−1.08432			−0.542161	+	0.840275i	$0.682394\pi$
$972$			760.489i			0.0250954i
$973$			865.764i			0.0285253i
$974$	11142.3			0.366553
$975$	16867.3	−	19284.8i	0.554036	−	0.633444i
$976$	13486.5			0.442309
$977$		−	46876.8i		−	1.53503i	−0.641032	−	0.767514i	$-0.721493\pi$
$977$		−	46876.8i		−	1.53503i	0.641032	−	0.767514i	$-0.278507\pi$
$978$		−	10724.3i		−	0.350638i
$979$	−11014.1			−0.359564
$980$	4927.37	+	10855.8i	0.160611	+	0.353854i
$981$	3367.14			0.109587
$982$			41821.8i			1.35905i
$983$			9569.95i			0.310513i	0.987874	+	0.155256i	$0.0496204\pi$
$983$			9569.95i			0.310513i	−0.987874	+	0.155256i	$0.950380\pi$
$984$	−26998.7			−0.874683
$985$	22801.8	−	10349.5i	0.737588	−	0.334785i
$986$	33334.6			1.07666
$987$			1541.23i			0.0497041i
$988$			15463.4i			0.497932i
$989$	61783.3			1.98645
$990$	−2224.32	+	1009.60i	−0.0714075	+	0.0324112i
$991$	1528.89			0.0490077			0.0245039	−	0.999700i	$-0.492199\pi$
$991$	1528.89			0.0490077			0.0245039	+	0.999700i	$0.492199\pi$
$992$		−	23489.2i		−	0.751798i
$993$			21833.5i			0.697750i
$994$	−2826.48			−0.0901917
$995$	−4963.82	−	10936.1i	−0.158154	−	0.348441i
$996$	5670.43			0.180396
$997$			46090.7i			1.46410i	0.681251	+	0.732050i	$0.261436\pi$
$997$			46090.7i			1.46410i	−0.681251	+	0.732050i	$0.738564\pi$
$998$			19735.7i			0.625974i
$999$	1075.06			0.0340474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.5	✓	14
3.2	odd	2		495.4.c.d.199.10		14
5.2	odd	4		825.4.a.ba.1.6		7
5.3	odd	4		825.4.a.bd.1.2		7
5.4	even	2	inner	165.4.c.b.34.10	yes	14
15.2	even	4		2475.4.a.bs.1.2		7
15.8	even	4		2475.4.a.bo.1.6		7
15.14	odd	2		495.4.c.d.199.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.5	✓	14	1.1	even	1	trivial
165.4.c.b.34.10	yes	14	5.4	even	2	inner
495.4.c.d.199.5		14	15.14	odd	2
495.4.c.d.199.10		14	3.2	odd	2
825.4.a.ba.1.6		7	5.2	odd	4
825.4.a.bd.1.2		7	5.3	odd	4
2475.4.a.bo.1.6		7	15.8	even	4
2475.4.a.bs.1.2		7	15.2	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.20690i q^{2} +3.00000i q^{3} +3.12958 q^{4} +(4.62093 + 10.1807i) q^{5} +6.62071 q^{6} +1.50972i q^{7} -24.5619i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.20690i q^{2} +3.00000i q^{3} +3.12958 q^{4} +(4.62093 + 10.1807i) q^{5} +6.62071 q^{6} +1.50972i q^{7} -24.5619i q^{8} -9.00000 q^{9} +(22.4678 - 10.1979i) q^{10} +11.0000 q^{11} +9.38875i q^{12} +68.3212i q^{13} +3.33181 q^{14} +(-30.5421 + 13.8628i) q^{15} -29.1690 q^{16} +113.151i q^{17} +19.8621i q^{18} +72.3208 q^{19} +(14.4616 + 31.8614i) q^{20} -4.52917 q^{21} -24.2759i q^{22} -144.617i q^{23} +73.6857 q^{24} +(-82.2939 + 94.0888i) q^{25} +150.778 q^{26} -27.0000i q^{27} +4.72480i q^{28} +133.492 q^{29} +(30.5938 + 67.4035i) q^{30} +177.784 q^{31} -132.122i q^{32} +33.0000i q^{33} +249.713 q^{34} +(-15.3700 + 6.97633i) q^{35} -28.1663 q^{36} +39.8169i q^{37} -159.605i q^{38} -204.964 q^{39} +(250.058 - 113.499i) q^{40} -366.404 q^{41} +9.99542i q^{42} +427.219i q^{43} +34.4254 q^{44} +(-41.5884 - 91.6264i) q^{45} -319.156 q^{46} -340.290i q^{47} -87.5071i q^{48} +340.721 q^{49} +(207.645 + 181.615i) q^{50} -339.453 q^{51} +213.817i q^{52} -659.877i q^{53} -59.5863 q^{54} +(50.8303 + 111.988i) q^{55} +37.0816 q^{56} +216.963i q^{57} -294.603i q^{58} +525.541 q^{59} +(-95.5842 + 43.3848i) q^{60} -462.358 q^{61} -392.353i q^{62} -13.5875i q^{63} -524.933 q^{64} +(-695.559 + 315.708i) q^{65} +72.8278 q^{66} +514.730i q^{67} +354.115i q^{68} +433.852 q^{69} +(15.3961 + 33.9202i) q^{70} -848.333 q^{71} +221.057i q^{72} -987.550i q^{73} +87.8721 q^{74} +(-282.267 - 246.882i) q^{75} +226.334 q^{76} +16.6069i q^{77} +452.335i q^{78} -442.561 q^{79} +(-134.788 - 296.962i) q^{80} +81.0000 q^{81} +808.617i q^{82} -603.960i q^{83} -14.1744 q^{84} +(-1151.96 + 522.863i) q^{85} +942.831 q^{86} +400.475i q^{87} -270.181i q^{88} -1001.29 q^{89} +(-202.211 + 91.7815i) q^{90} -103.146 q^{91} -452.592i q^{92} +533.353i q^{93} -750.987 q^{94} +(334.190 + 736.278i) q^{95} +396.366 q^{96} -468.418i q^{97} -751.937i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Introduction

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