LMFDB - Embedded newform 354.3.b.a.119.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.3
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-2.71554 - 1.27509i) q^{3} -2.00000 q^{4} +1.78565i q^{5} +(-1.80326 + 3.84035i) q^{6} -11.5483 q^{7} +2.82843i q^{8} +(5.74827 + 6.92513i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-2.71554 - 1.27509i) q^{3} -2.00000 q^{4} +1.78565i q^{5} +(-1.80326 + 3.84035i) q^{6} -11.5483 q^{7} +2.82843i q^{8} +(5.74827 + 6.92513i) q^{9} +2.52529 q^{10} -0.745177i q^{11} +(5.43107 + 2.55019i) q^{12} +12.9189 q^{13} +16.3318i q^{14} +(2.27687 - 4.84899i) q^{15} +4.00000 q^{16} -1.91970i q^{17} +(9.79361 - 8.12928i) q^{18} +4.83266 q^{19} -3.57130i q^{20} +(31.3599 + 14.7252i) q^{21} -1.05384 q^{22} -10.0353i q^{23} +(3.60651 - 7.68069i) q^{24} +21.8115 q^{25} -18.2701i q^{26} +(-6.77944 - 26.1350i) q^{27} +23.0967 q^{28} +41.9127i q^{29} +(-6.85751 - 3.21998i) q^{30} +16.8592 q^{31} -5.65685i q^{32} +(-0.950171 + 2.02355i) q^{33} -2.71486 q^{34} -20.6213i q^{35} +(-11.4965 - 13.8503i) q^{36} -6.17780 q^{37} -6.83442i q^{38} +(-35.0817 - 16.4728i) q^{39} -5.05057 q^{40} -8.01580i q^{41} +(20.8246 - 44.3496i) q^{42} +51.0816 q^{43} +1.49035i q^{44} +(-12.3658 + 10.2644i) q^{45} -14.1921 q^{46} +6.89940i q^{47} +(-10.8621 - 5.10038i) q^{48} +84.3640 q^{49} -30.8461i q^{50} +(-2.44780 + 5.21301i) q^{51} -25.8378 q^{52} -14.4394i q^{53} +(-36.9605 + 9.58757i) q^{54} +1.33062 q^{55} -32.6636i q^{56} +(-13.1233 - 6.16210i) q^{57} +59.2736 q^{58} +7.68115i q^{59} +(-4.55374 + 9.69798i) q^{60} +96.4359 q^{61} -23.8425i q^{62} +(-66.3829 - 79.9737i) q^{63} -8.00000 q^{64} +23.0686i q^{65} +(2.86174 + 1.34374i) q^{66} +23.1913 q^{67} +3.83940i q^{68} +(-12.7960 + 27.2513i) q^{69} -29.1629 q^{70} +106.769i q^{71} +(-19.5872 + 16.2586i) q^{72} +4.06160 q^{73} +8.73673i q^{74} +(-59.2298 - 27.8117i) q^{75} -9.66533 q^{76} +8.60555i q^{77} +(-23.2961 + 49.6130i) q^{78} -65.0254 q^{79} +7.14259i q^{80} +(-14.9148 + 79.6150i) q^{81} -11.3361 q^{82} +73.8578i q^{83} +(-62.7198 - 29.4504i) q^{84} +3.42790 q^{85} -72.2403i q^{86} +(53.4427 - 113.816i) q^{87} +2.10768 q^{88} +111.229i q^{89} +(14.5160 + 17.4879i) q^{90} -149.192 q^{91} +20.0707i q^{92} +(-45.7817 - 21.4971i) q^{93} +9.75723 q^{94} +8.62944i q^{95} +(-7.21302 + 15.3614i) q^{96} -61.7717 q^{97} -119.309i q^{98} +(5.16044 - 4.28348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.71554	−	1.27509i	−0.905179	−	0.425031i
$3$	−2.71554	−	1.27509i	−0.905179	−	0.425031i
$4$	−2.00000			−0.500000
$5$			1.78565i			0.357130i	0.983928	+	0.178565i	$0.0571454\pi$
$5$			1.78565i			0.357130i	−0.983928	+	0.178565i	$0.942855\pi$
$6$	−1.80326	+	3.84035i	−0.300543	+	0.640058i
$7$	−11.5483			−1.64976			−0.824881	−	0.565307i	$-0.808758\pi$
$7$	−11.5483			−1.64976			−0.824881	+	0.565307i	$0.808758\pi$
$8$			2.82843i			0.353553i
$9$	5.74827	+	6.92513i	0.638696	+	0.769459i
$10$	2.52529			0.252529
$11$		−	0.745177i		−	0.0677433i	−0.999426	−	0.0338717i	$-0.989216\pi$
$11$		−	0.745177i		−	0.0677433i	0.999426	−	0.0338717i	$-0.0107837\pi$
$12$	5.43107	+	2.55019i	0.452589	+	0.212516i
$13$	12.9189			0.993761			0.496880	−	0.867819i	$-0.334479\pi$
$13$	12.9189			0.993761			0.496880	+	0.867819i	$0.334479\pi$
$14$			16.3318i			1.16656i
$15$	2.27687	−	4.84899i	0.151791	−	0.323266i
$16$	4.00000			0.250000
$17$		−	1.91970i		−	0.112923i	−0.998405	−	0.0564617i	$-0.982018\pi$
$17$		−	1.91970i		−	0.112923i	0.998405	−	0.0564617i	$-0.0179819\pi$
$18$	9.79361	−	8.12928i	0.544090	−	0.451627i
$19$	4.83266			0.254351			0.127175	−	0.991880i	$-0.459409\pi$
$19$	4.83266			0.254351			0.127175	+	0.991880i	$0.459409\pi$
$20$		−	3.57130i		−	0.178565i
$21$	31.3599	+	14.7252i	1.49333	+	0.701201i
$22$	−1.05384			−0.0479018
$23$		−	10.0353i		−	0.436319i	−0.975913	−	0.218160i	$-0.929995\pi$
$23$		−	10.0353i		−	0.436319i	0.975913	−	0.218160i	$-0.0700053\pi$
$24$	3.60651	−	7.68069i	0.150271	−	0.320029i
$25$	21.8115			0.872458
$26$		−	18.2701i		−	0.702695i
$27$	−6.77944	−	26.1350i	−0.251090	−	0.967964i
$28$	23.0967			0.824881
$29$			41.9127i			1.44527i	0.691231	+	0.722633i	$0.257069\pi$
$29$			41.9127i			1.44527i	−0.691231	+	0.722633i	$0.742931\pi$
$30$	−6.85751	−	3.21998i	−0.228584	−	0.107333i
$31$	16.8592			0.543845			0.271923	−	0.962319i	$-0.412341\pi$
$31$	16.8592			0.543845			0.271923	+	0.962319i	$0.412341\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−0.950171	+	2.02355i	−0.0287930	+	0.0613198i
$34$	−2.71486			−0.0798489
$35$		−	20.6213i		−	0.589179i
$36$	−11.4965	−	13.8503i	−0.319348	−	0.384729i
$37$	−6.17780			−0.166968			−0.0834838	−	0.996509i	$-0.526605\pi$
$37$	−6.17780			−0.166968			−0.0834838	+	0.996509i	$0.526605\pi$
$38$		−	6.83442i		−	0.179853i
$39$	−35.0817	−	16.4728i	−0.899531	−	0.422380i
$40$	−5.05057			−0.126264
$41$		−	8.01580i		−	0.195507i	−0.995211	−	0.0977537i	$-0.968834\pi$
$41$		−	8.01580i		−	0.195507i	0.995211	−	0.0977537i	$-0.0311657\pi$
$42$	20.8246	−	44.3496i	0.495824	−	1.05594i
$43$	51.0816			1.18794			0.593972	−	0.804486i	$-0.297559\pi$
$43$	51.0816			1.18794			0.593972	+	0.804486i	$0.297559\pi$
$44$			1.49035i			0.0338717i
$45$	−12.3658	+	10.2644i	−0.274796	+	0.228097i
$46$	−14.1921			−0.308524
$47$			6.89940i			0.146796i	0.997303	+	0.0733979i	$0.0233843\pi$
$47$			6.89940i			0.146796i	−0.997303	+	0.0733979i	$0.976616\pi$
$48$	−10.8621	−	5.10038i	−0.226295	−	0.106258i
$49$	84.3640			1.72171
$50$		−	30.8461i		−	0.616921i
$51$	−2.44780	+	5.21301i	−0.0479960	+	0.102216i
$52$	−25.8378			−0.496880
$53$		−	14.4394i		−	0.272441i	−0.990679	−	0.136220i	$-0.956504\pi$
$53$		−	14.4394i		−	0.272441i	0.990679	−	0.136220i	$-0.0434955\pi$
$54$	−36.9605	+	9.58757i	−0.684454	+	0.177548i
$55$	1.33062			0.0241931
$56$		−	32.6636i		−	0.583279i
$57$	−13.1233	−	6.16210i	−0.230233	−	0.108107i
$58$	59.2736			1.02196
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−4.55374	+	9.69798i	−0.0758957	+	0.161633i
$61$	96.4359			1.58092			0.790458	−	0.612516i	$-0.209842\pi$
$61$	96.4359			1.58092			0.790458	+	0.612516i	$0.209842\pi$
$62$		−	23.8425i		−	0.384556i
$63$	−66.3829	−	79.9737i	−1.05370	−	1.26942i
$64$	−8.00000			−0.125000
$65$			23.0686i			0.354901i
$66$	2.86174	+	1.34374i	0.0433597	+	0.0203598i
$67$	23.1913			0.346138			0.173069	−	0.984910i	$-0.444632\pi$
$67$	23.1913			0.346138			0.173069	+	0.984910i	$0.444632\pi$
$68$			3.83940i			0.0564617i
$69$	−12.7960	+	27.2513i	−0.185449	+	0.394947i
$70$	−29.1629			−0.416612
$71$			106.769i			1.50378i	0.659287	+	0.751891i	$0.270858\pi$
$71$			106.769i			1.50378i	−0.659287	+	0.751891i	$0.729142\pi$
$72$	−19.5872	+	16.2586i	−0.272045	+	0.225813i
$73$	4.06160			0.0556384			0.0278192	−	0.999613i	$-0.491144\pi$
$73$	4.06160			0.0556384			0.0278192	+	0.999613i	$0.491144\pi$
$74$			8.73673i			0.118064i
$75$	−59.2298	−	27.8117i	−0.789731	−	0.370822i
$76$	−9.66533			−0.127175
$77$			8.60555i			0.111760i
$78$	−23.2961	+	49.6130i	−0.298668	+	0.636065i
$79$	−65.0254			−0.823106			−0.411553	−	0.911386i	$-0.635014\pi$
$79$	−65.0254			−0.823106			−0.411553	+	0.911386i	$0.635014\pi$
$80$			7.14259i			0.0892824i
$81$	−14.9148	+	79.6150i	−0.184134	+	0.982901i
$82$	−11.3361			−0.138245
$83$			73.8578i			0.889852i	0.895567	+	0.444926i	$0.146770\pi$
$83$			73.8578i			0.889852i	−0.895567	+	0.444926i	$0.853230\pi$
$84$	−62.7198	−	29.4504i	−0.746665	−	0.350600i
$85$	3.42790			0.0403283
$86$		−	72.2403i		−	0.840003i
$87$	53.4427	−	113.816i	0.614284	−	1.30822i
$88$	2.10768			0.0239509
$89$			111.229i			1.24976i	0.780720	+	0.624881i	$0.214853\pi$
$89$			111.229i			1.24976i	−0.780720	+	0.624881i	$0.785147\pi$
$90$	14.5160	+	17.4879i	0.161289	+	0.194310i
$91$	−149.192			−1.63947
$92$			20.0707i			0.218160i
$93$	−45.7817	−	21.4971i	−0.492277	−	0.231151i
$94$	9.75723			0.103800
$95$			8.62944i			0.0908362i
$96$	−7.21302	+	15.3614i	−0.0751357	+	0.160014i
$97$	−61.7717			−0.636821			−0.318411	−	0.947953i	$-0.603149\pi$
$97$	−61.7717			−0.636821			−0.318411	+	0.947953i	$0.603149\pi$
$98$		−	119.309i		−	1.21744i
$99$	5.16044	−	4.28348i	0.0521257	−	0.0432674i
$100$	−43.6229			−0.436229
$101$			119.029i			1.17851i	0.807949	+	0.589253i	$0.200578\pi$
$101$			119.029i			1.17851i	−0.807949	+	0.589253i	$0.799422\pi$
$102$	7.37231	+	3.46171i	0.0722775	+	0.0339383i
$103$	68.9854			0.669761			0.334880	−	0.942261i	$-0.391304\pi$
$103$	68.9854			0.669761			0.334880	+	0.942261i	$0.391304\pi$
$104$			36.5401i			0.351348i
$105$	−26.2940	+	55.9978i	−0.250420	+	0.533312i
$106$	−20.4203			−0.192645
$107$			196.248i			1.83409i	0.398785	+	0.917044i	$0.369432\pi$
$107$			196.248i			1.83409i	−0.398785	+	0.917044i	$0.630568\pi$
$108$	13.5589	+	52.2700i	0.125545	+	0.483982i
$109$	−10.9642			−0.100589			−0.0502945	−	0.998734i	$-0.516016\pi$
$109$	−10.9642			−0.100589			−0.0502945	+	0.998734i	$0.516016\pi$
$110$		−	1.88179i		−	0.0171071i
$111$	16.7760	+	7.87728i	0.151136	+	0.0709665i
$112$	−46.1933			−0.412440
$113$		−	97.4996i		−	0.862829i	−0.902154	−	0.431414i	$-0.858015\pi$
$113$		−	97.4996i		−	0.862829i	0.902154	−	0.431414i	$-0.141985\pi$
$114$	−8.71453	+	18.5591i	−0.0764432	+	0.162799i
$115$	17.9196			0.155822
$116$		−	83.8255i		−	0.722633i
$117$	74.2613	+	89.4650i	0.634712	+	0.764658i
$118$	10.8628			0.0920575
$119$			22.1693i			0.186297i
$120$	13.7150	+	6.43996i	0.114292	+	0.0536663i
$121$	120.445			0.995411
$122$		−	136.381i		−	1.11788i
$123$	−10.2209	+	21.7672i	−0.0830968	+	0.176969i
$124$	−33.7184			−0.271923
$125$			83.5888i			0.668710i
$126$	−113.100	+	93.8796i	−0.897618	+	0.745076i
$127$	104.772			0.824974			0.412487	−	0.910964i	$-0.364660\pi$
$127$	104.772			0.824974			0.412487	+	0.910964i	$0.364660\pi$
$128$			11.3137i			0.0883883i
$129$	−138.714	−	65.1339i	−1.07530	−	0.504914i
$130$	32.6239			0.250953
$131$		−	228.152i		−	1.74162i	−0.491622	−	0.870809i	$-0.663596\pi$
$131$		−	228.152i		−	1.74162i	0.491622	−	0.870809i	$-0.336404\pi$
$132$	1.90034	−	4.04711i	0.0143965	−	0.0306599i
$133$	−55.8092			−0.419618
$134$		−	32.7974i		−	0.244757i
$135$	46.6679	−	12.1057i	0.345688	−	0.0896717i
$136$	5.42973			0.0399244
$137$		−	205.483i		−	1.49988i	−0.661508	−	0.749938i	$-0.730083\pi$
$137$		−	205.483i		−	1.49988i	0.661508	−	0.749938i	$-0.269917\pi$
$138$	38.5392	+	18.0963i	0.279269	+	0.131132i
$139$	120.727			0.868537			0.434269	−	0.900783i	$-0.357007\pi$
$139$	120.727			0.868537			0.434269	+	0.900783i	$0.357007\pi$
$140$			41.2425i			0.294589i
$141$	8.79739	−	18.7356i	0.0623928	−	0.132876i
$142$	150.994			1.06334
$143$		−	9.62686i		−	0.0673207i
$144$	22.9931	+	27.7005i	0.159674	+	0.192365i
$145$	−74.8414			−0.516148
$146$		−	5.74397i		−	0.0393423i
$147$	−229.093	−	107.572i	−1.55846	−	0.731783i
$148$	12.3556			0.0834838
$149$			69.4512i			0.466116i	0.972463	+	0.233058i	$0.0748731\pi$
$149$			69.4512i			0.466116i	−0.972463	+	0.233058i	$0.925127\pi$
$150$	−39.3316	+	83.7636i	−0.262211	+	0.558424i
$151$	−6.07246			−0.0402150			−0.0201075	−	0.999798i	$-0.506401\pi$
$151$	−6.07246			−0.0402150			−0.0201075	+	0.999798i	$0.506401\pi$
$152$			13.6688i			0.0899266i
$153$	13.2942	−	11.0349i	0.0868899	−	0.0721238i
$154$	12.1701			0.0790265
$155$			30.1046i			0.194223i
$156$	70.1634	+	32.9456i	0.449766	+	0.211190i
$157$	30.0174			0.191194			0.0955969	−	0.995420i	$-0.469524\pi$
$157$	30.0174			0.191194			0.0955969	+	0.995420i	$0.469524\pi$
$158$			91.9598i			0.582024i
$159$	−18.4116	+	39.2106i	−0.115796	+	0.246608i
$160$	10.1011			0.0631322
$161$			115.891i			0.719822i
$162$	112.593	+	21.0927i	0.695016	+	0.130202i
$163$	−147.568			−0.905323			−0.452662	−	0.891682i	$-0.649525\pi$
$163$	−147.568			−0.905323			−0.452662	+	0.891682i	$0.649525\pi$
$164$			16.0316i			0.0977537i
$165$	−3.61335	−	1.69667i	−0.0218991	−	0.0102828i
$166$	104.451			0.629221
$167$			200.912i			1.20307i	0.798848	+	0.601533i	$0.205443\pi$
$167$			200.912i			1.20307i	−0.798848	+	0.601533i	$0.794557\pi$
$168$	−41.6492	+	88.6992i	−0.247912	+	0.527972i
$169$	−2.10221			−0.0124391
$170$		−	4.84779i		−	0.0285164i
$171$	27.7795	+	33.4668i	0.162453	+	0.195712i
$172$	−102.163			−0.593972
$173$		−	118.952i		−	0.687586i	−0.939046	−	0.343793i	$-0.888288\pi$
$173$		−	118.952i		−	0.687586i	0.939046	−	0.343793i	$-0.111712\pi$
$174$	−160.959	−	75.5794i	−0.925055	−	0.434364i
$175$	−251.886			−1.43935
$176$		−	2.98071i		−	0.0169358i
$177$	9.79419	−	20.8584i	0.0553344	−	0.117844i
$178$	157.301			0.883716
$179$		−	211.922i		−	1.18392i	−0.805966	−	0.591961i	$-0.798354\pi$
$179$		−	211.922i		−	1.18392i	0.805966	−	0.591961i	$-0.201646\pi$
$180$	24.7317	−	20.5288i	0.137398	−	0.114049i
$181$	−212.957			−1.17656			−0.588280	−	0.808657i	$-0.700195\pi$
$181$	−212.957			−1.17656			−0.588280	+	0.808657i	$0.700195\pi$
$182$			210.989i			1.15928i
$183$	−261.875	−	122.965i	−1.43101	−	0.671939i
$184$	28.3842			0.154262
$185$		−	11.0314i		−	0.0596291i
$186$	−30.4014	+	64.7452i	−0.163449	+	0.348092i
$187$	−1.43051			−0.00764981
$188$		−	13.7988i		−	0.0733979i
$189$	78.2912	+	301.816i	0.414239	+	1.59691i
$190$	12.2039			0.0642309
$191$		−	130.635i		−	0.683951i	−0.939709	−	0.341976i	$-0.888904\pi$
$191$		−	130.635i		−	0.683951i	0.939709	−	0.341976i	$-0.111096\pi$
$192$	21.7243	+	10.2008i	0.113147	+	0.0531289i
$193$	189.980			0.984353			0.492176	−	0.870495i	$-0.336201\pi$
$193$	189.980			0.984353			0.492176	+	0.870495i	$0.336201\pi$
$194$			87.3583i			0.450301i
$195$	29.4146	−	62.6436i	0.150844	−	0.321249i
$196$	−168.728			−0.860857
$197$		−	53.6459i		−	0.272314i	−0.990687	−	0.136157i	$-0.956525\pi$
$197$		−	53.6459i		−	0.272314i	0.990687	−	0.136157i	$-0.0434752\pi$
$198$	−6.05775	−	7.29797i	−0.0305947	−	0.0368584i
$199$	320.253			1.60931			0.804656	−	0.593741i	$-0.202350\pi$
$199$	320.253			1.60931			0.804656	+	0.593741i	$0.202350\pi$
$200$			61.6921i			0.308461i
$201$	−62.9767	−	29.5711i	−0.313317	−	0.147120i
$202$	168.332			0.833329
$203$		−	484.022i		−	2.38435i
$204$	4.89559	−	10.4260i	0.0239980	−	0.0511079i
$205$	14.3134			0.0698214
$206$		−	97.5601i		−	0.473593i
$207$	69.4960	−	57.6858i	0.335729	−	0.278675i
$208$	51.6756			0.248440
$209$		−	3.60119i		−	0.0172306i
$210$	79.1928	+	37.1854i	0.377109	+	0.177073i
$211$	−393.290			−1.86394			−0.931968	−	0.362541i	$-0.881909\pi$
$211$	−393.290			−1.86394			−0.931968	+	0.362541i	$0.881909\pi$
$212$			28.8787i			0.136220i
$213$	136.140	−	289.934i	0.639155	−	1.36119i
$214$	277.536			1.29690
$215$			91.2137i			0.424250i
$216$	73.9210	−	19.1751i	0.342227	−	0.0887738i
$217$	−194.696			−0.897215
$218$			15.5057i			0.0711272i
$219$	−11.0294	−	5.17893i	−0.0503627	−	0.0236481i
$220$	−2.66125			−0.0120966
$221$		−	24.8004i		−	0.112219i
$222$	11.1402	−	23.7249i	0.0501809	−	0.106869i
$223$	274.501			1.23095			0.615474	−	0.788157i	$-0.288965\pi$
$223$	274.501			1.23095			0.615474	+	0.788157i	$0.288965\pi$
$224$			65.3272i			0.291639i
$225$	125.378	+	151.047i	0.557236	+	0.671321i
$226$	−137.885			−0.610112
$227$		−	442.703i		−	1.95023i	−0.221693	−	0.975117i	$-0.571158\pi$
$227$		−	442.703i		−	1.95023i	0.221693	−	0.975117i	$-0.428842\pi$
$228$	26.2465	+	12.3242i	0.115116	+	0.0540535i
$229$	−7.55300			−0.0329825			−0.0164913	−	0.999864i	$-0.505250\pi$
$229$	−7.55300			−0.0329825			−0.0164913	+	0.999864i	$0.505250\pi$
$230$		−	25.3421i		−	0.110183i
$231$	10.9729	−	23.3687i	0.0475017	−	0.101163i
$232$	−118.547			−0.510979
$233$		−	136.009i		−	0.583730i	−0.956459	−	0.291865i	$-0.905724\pi$
$233$		−	136.009i		−	0.583730i	0.956459	−	0.291865i	$-0.0942759\pi$
$234$	126.523	−	105.021i	0.540695	−	0.448809i
$235$	−12.3199			−0.0524251
$236$		−	15.3623i		−	0.0650945i
$237$	176.579	+	82.9135i	0.745058	+	0.349846i
$238$	31.3521			0.131732
$239$		−	27.9745i		−	0.117048i	−0.998286	−	0.0585240i	$-0.981361\pi$
$239$		−	27.9745i		−	0.117048i	0.998286	−	0.0585240i	$-0.0186394\pi$
$240$	9.10748	−	19.3960i	0.0379478	−	0.0808165i
$241$	409.989			1.70120			0.850599	−	0.525816i	$-0.176240\pi$
$241$	409.989			1.70120			0.850599	+	0.525816i	$0.176240\pi$
$242$		−	170.335i		−	0.703862i
$243$	142.018	−	197.180i	0.584438	−	0.811439i
$244$	−192.872			−0.790458
$245$			150.644i			0.614875i
$246$	30.7835	+	14.4545i	0.125136	+	0.0587583i
$247$	62.4327			0.252764
$248$			47.6850i			0.192278i
$249$	94.1756	−	200.563i	0.378215	−	0.805475i
$250$	118.212			0.472850
$251$			500.885i			1.99556i	0.0666089	+	0.997779i	$0.478782\pi$
$251$			500.885i			1.99556i	−0.0666089	+	0.997779i	$0.521218\pi$
$252$	132.766	+	159.947i	0.526849	+	0.634712i
$253$	−7.47810			−0.0295577
$254$		−	148.169i		−	0.583344i
$255$	−9.30860	−	4.37090i	−0.0365043	−	0.0171408i
$256$	16.0000			0.0625000
$257$			294.631i			1.14642i	0.819407	+	0.573211i	$0.194303\pi$
$257$			294.631i			1.14642i	−0.819407	+	0.573211i	$0.805697\pi$
$258$	−92.1132	+	196.171i	−0.357028	+	0.760353i
$259$	71.3433			0.275457
$260$		−	46.1372i		−	0.177451i
$261$	−290.251	+	240.926i	−1.11207	+	0.923087i
$262$	−322.656			−1.23151
$263$		−	156.170i		−	0.593801i	−0.954908	−	0.296900i	$-0.904047\pi$
$263$		−	156.170i		−	0.593801i	0.954908	−	0.296900i	$-0.0959529\pi$
$264$	−5.72347	−	2.68749i	−0.0216798	−	0.0101799i
$265$	25.7836			0.0972967
$266$			78.9261i			0.296715i
$267$	141.827	−	302.046i	0.531188	−	1.13126i
$268$	−46.3826			−0.173069
$269$		−	116.851i		−	0.434390i	−0.976128	−	0.217195i	$-0.930309\pi$
$269$		−	116.851i		−	0.434390i	0.976128	−	0.217195i	$-0.0696907\pi$
$270$	−17.1200	−	65.9984i	−0.0634075	−	0.244439i
$271$	−426.656			−1.57438			−0.787188	−	0.616713i	$-0.788464\pi$
$271$	−426.656			−1.57438			−0.787188	+	0.616713i	$0.788464\pi$
$272$		−	7.67879i		−	0.0282308i
$273$	405.135	+	190.233i	1.48401	+	0.696826i
$274$	−290.597			−1.06057
$275$		−	16.2534i		−	0.0591032i
$276$	25.5920	−	54.5026i	0.0927247	−	0.197473i
$277$	20.5199			0.0740791			0.0370396	−	0.999314i	$-0.488207\pi$
$277$	20.5199			0.0740791			0.0370396	+	0.999314i	$0.488207\pi$
$278$		−	170.733i		−	0.614148i
$279$	96.9112	+	116.752i	0.347352	+	0.418466i
$280$	58.3257			0.208306
$281$			362.113i			1.28866i	0.764748	+	0.644330i	$0.222863\pi$
$281$			362.113i			1.28866i	−0.764748	+	0.644330i	$0.777137\pi$
$282$	−26.4961	−	12.4414i	−0.0939578	−	0.0441184i
$283$	305.735			1.08034			0.540168	−	0.841557i	$-0.318361\pi$
$283$	305.735			1.08034			0.540168	+	0.841557i	$0.318361\pi$
$284$		−	213.537i		−	0.751891i
$285$	11.0033	−	23.4335i	0.0386082	−	0.0822230i
$286$	−13.6144			−0.0476029
$287$			92.5691i			0.322540i
$288$	39.1744	−	32.5171i	0.136022	−	0.112907i
$289$	285.315			0.987248
$290$			105.842i			0.364971i
$291$	167.743	+	78.7647i	0.576437	+	0.270669i
$292$	−8.12320			−0.0278192
$293$		−	342.369i		−	1.16850i	−0.811575	−	0.584248i	$-0.801390\pi$
$293$		−	342.369i		−	1.16850i	0.811575	−	0.584248i	$-0.198610\pi$
$294$	−152.130	+	323.987i	−0.517448	+	1.10200i
$295$	−13.7158			−0.0464943
$296$		−	17.4735i		−	0.0590320i
$297$	−19.4752	+	5.05188i	−0.0655731	+	0.0170097i
$298$	98.2189			0.329594
$299$		−	129.645i		−	0.433597i
$300$	118.460	+	55.6233i	0.394865	+	0.185411i
$301$	−589.907			−1.95982
$302$			8.58776i			0.0284363i
$303$	151.773	−	323.228i	0.500902	−	1.06676i
$304$	19.3307			0.0635877
$305$			172.201i			0.564592i
$306$	−15.6058	−	18.8008i	−0.0509992	−	0.0614404i
$307$	86.2033			0.280792			0.140396	−	0.990095i	$-0.455162\pi$
$307$	86.2033			0.280792			0.140396	+	0.990095i	$0.455162\pi$
$308$		−	17.2111i		−	0.0558802i
$309$	−187.332	−	87.9629i	−0.606253	−	0.284669i
$310$	42.5743			0.137336
$311$			412.943i			1.32779i	0.747826	+	0.663895i	$0.231098\pi$
$311$			412.943i			1.32779i	−0.747826	+	0.663895i	$0.768902\pi$
$312$	46.5921	−	99.2261i	0.149334	−	0.318032i
$313$	−219.728			−0.702006			−0.351003	−	0.936374i	$-0.614159\pi$
$313$	−219.728			−0.702006			−0.351003	+	0.936374i	$0.614159\pi$
$314$		−	42.4510i		−	0.135194i
$315$	142.805	−	118.537i	0.453349	−	0.376306i
$316$	130.051			0.411553
$317$			226.936i			0.715887i	0.933743	+	0.357943i	$0.116522\pi$
$317$			226.936i			0.715887i	−0.933743	+	0.357943i	$0.883478\pi$
$318$	55.4522	+	26.0379i	0.174378	+	0.0818801i
$319$	31.2324			0.0979072
$320$		−	14.2852i		−	0.0446412i
$321$	250.234	−	532.917i	0.779546	−	1.66018i
$322$	163.895			0.508991
$323$		−	9.27725i		−	0.0287221i
$324$	29.8296	−	159.230i	0.0920668	−	0.491451i
$325$	281.780			0.867015
$326$			208.692i			0.640160i
$327$	29.7737	+	13.9804i	0.0910511	+	0.0427535i
$328$	22.6721			0.0691223
$329$		−	79.6766i		−	0.242178i
$330$	−2.39945	+	5.11005i	−0.00727107	+	0.0154850i
$331$	204.510			0.617855			0.308927	−	0.951086i	$-0.400030\pi$
$331$	204.510			0.617855			0.308927	+	0.951086i	$0.400030\pi$
$332$		−	147.716i		−	0.444926i
$333$	−35.5117	−	42.7821i	−0.106642	−	0.128475i
$334$	284.133			0.850696
$335$			41.4115i			0.123616i
$336$	125.440	+	58.9009i	0.373332	+	0.175300i
$337$	−247.241			−0.733653			−0.366826	−	0.930289i	$-0.619556\pi$
$337$	−247.241			−0.733653			−0.366826	+	0.930289i	$0.619556\pi$
$338$			2.97297i			0.00879578i
$339$	−124.321	+	264.764i	−0.366729	+	0.781014i
$340$	−6.85581			−0.0201641
$341$		−	12.5631i		−	0.0368419i
$342$	47.3292	−	39.2861i	0.138390	−	0.114872i
$343$	−408.395			−1.19066
$344$			144.481i			0.420002i
$345$	−48.6613	−	22.8492i	−0.141047	−	0.0662294i
$346$	−168.224			−0.486197
$347$		−	505.806i		−	1.45766i	−0.684697	−	0.728828i	$-0.740066\pi$
$347$		−	505.806i		−	1.45766i	0.684697	−	0.728828i	$-0.259934\pi$
$348$	−106.885	+	227.631i	−0.307142	+	0.654112i
$349$	509.307			1.45933			0.729667	−	0.683803i	$-0.239675\pi$
$349$	509.307			1.45933			0.729667	+	0.683803i	$0.239675\pi$
$350$			356.221i			1.01777i
$351$	−87.5828	−	337.636i	−0.249524	−	0.961925i
$352$	−4.21536			−0.0119754
$353$			219.659i			0.622263i	0.950367	+	0.311131i	$0.100708\pi$
$353$			219.659i			0.622263i	−0.950367	+	0.311131i	$0.899292\pi$
$354$	−29.4983	−	13.8511i	−0.0833284	−	0.0391273i
$355$	−190.651			−0.537045
$356$		−	222.458i		−	0.624881i
$357$	28.2680	−	60.2015i	0.0791820	−	0.168632i
$358$	−299.703			−0.837160
$359$			546.736i			1.52294i	0.648200	+	0.761470i	$0.275522\pi$
$359$			546.736i			1.52294i	−0.648200	+	0.761470i	$0.724478\pi$
$360$	−29.0321	−	34.9759i	−0.0806446	−	0.0971552i
$361$	−337.645			−0.935306
$362$			301.167i			0.831954i
$363$	−327.072	−	153.578i	−0.901025	−	0.423081i
$364$	298.383			0.819734
$365$			7.25259i			0.0198701i
$366$	−173.899	+	370.347i	−0.475133	+	1.01188i
$367$	−521.911			−1.42210			−0.711051	−	0.703141i	$-0.751780\pi$
$367$	−521.911			−1.42210			−0.711051	+	0.703141i	$0.751780\pi$
$368$		−	40.1413i		−	0.109080i
$369$	55.5104	−	46.0770i	0.150435	−	0.124870i
$370$	−15.6007			−0.0421641
$371$			166.751i			0.449462i
$372$	91.5635	+	42.9941i	0.246138	+	0.115576i
$373$	−343.013			−0.919605			−0.459803	−	0.888021i	$-0.652080\pi$
$373$	−343.013			−0.919605			−0.459803	+	0.888021i	$0.652080\pi$
$374$			2.02305i			0.00540923i
$375$	106.584	−	226.988i	0.284223	−	0.605302i
$376$	−19.5145			−0.0519001
$377$			541.466i			1.43625i
$378$	426.832	−	110.720i	1.12919	−	0.292911i
$379$	−18.7321			−0.0494251			−0.0247125	−	0.999695i	$-0.507867\pi$
$379$	−18.7321			−0.0494251			−0.0247125	+	0.999695i	$0.507867\pi$
$380$		−	17.2589i		−	0.0454181i
$381$	−284.511	−	133.594i	−0.746748	−	0.350640i
$382$	−184.745			−0.483627
$383$			204.540i			0.534047i	0.963690	+	0.267023i	$0.0860401\pi$
$383$			204.540i			0.534047i	−0.963690	+	0.267023i	$0.913960\pi$
$384$	14.4260	−	30.7228i	0.0375678	−	0.0800072i
$385$	−15.3665			−0.0399129
$386$		−	268.672i		−	0.696043i
$387$	293.631	+	353.747i	0.758736	+	0.914074i
$388$	123.543			0.318411
$389$		−	301.791i		−	0.775813i	−0.921699	−	0.387906i	$-0.873198\pi$
$389$		−	301.791i		−	0.775813i	0.921699	−	0.387906i	$-0.126802\pi$
$390$	−88.5914	−	41.5986i	−0.227157	−	0.106663i
$391$	−19.2648			−0.0492706
$392$			238.617i			0.608718i
$393$	−290.915	+	619.555i	−0.740242	+	1.57647i
$394$	−75.8668			−0.192555
$395$		−	116.112i		−	0.293956i
$396$	−10.3209	+	8.56695i	−0.0260628	+	0.0216337i
$397$	−117.202			−0.295220			−0.147610	−	0.989046i	$-0.547158\pi$
$397$	−117.202			−0.295220			−0.147610	+	0.989046i	$0.547158\pi$
$398$		−	452.906i		−	1.13796i
$399$	151.552	+	71.1620i	0.379829	+	0.178351i
$400$	87.2458			0.218115
$401$			475.194i			1.18502i	0.805562	+	0.592512i	$0.201864\pi$
$401$			475.194i			1.18502i	−0.805562	+	0.592512i	$0.798136\pi$
$402$	−41.8198	+	89.0626i	−0.104029	+	0.221549i
$403$	217.802			0.540452
$404$		−	238.058i		−	0.589253i
$405$	−142.164	−	26.6326i	−0.351023	−	0.0657595i
$406$	−684.511			−1.68599
$407$			4.60355i			0.0113109i
$408$	−14.7446	−	6.92341i	−0.0361388	−	0.0169691i
$409$	388.836			0.950700			0.475350	−	0.879797i	$-0.342321\pi$
$409$	388.836			0.950700			0.475350	+	0.879797i	$0.342321\pi$
$410$		−	20.2422i		−	0.0493712i
$411$	−262.010	+	557.996i	−0.637495	+	1.35766i
$412$	−137.971			−0.334880
$413$		−	88.7044i		−	0.214781i
$414$	−81.5801	−	98.2822i	−0.197053	−	0.237397i
$415$	−131.884			−0.317793
$416$		−	73.0803i		−	0.175674i
$417$	−327.838	−	153.938i	−0.786181	−	0.369156i
$418$	−5.09285			−0.0121838
$419$		−	693.013i		−	1.65397i	−0.562225	−	0.826984i	$-0.690055\pi$
$419$		−	693.013i		−	1.65397i	0.562225	−	0.826984i	$-0.309945\pi$
$420$	52.5881	−	111.996i	0.125210	−	0.266656i
$421$	−221.118			−0.525222			−0.262611	−	0.964902i	$-0.584584\pi$
$421$	−221.118			−0.525222			−0.262611	+	0.964902i	$0.584584\pi$
$422$			556.197i			1.31800i
$423$	−47.7792	+	39.6596i	−0.112953	+	0.0937579i
$424$	40.8407			0.0963224
$425$		−	41.8714i		−	0.0985210i
$426$	−410.028	−	192.531i	−0.962508	−	0.451951i
$427$	−1113.67			−2.60814
$428$		−	392.495i		−	0.917044i
$429$	−12.2752	+	26.1421i	−0.0286134	+	0.0609372i
$430$	128.996			0.299990
$431$			325.753i			0.755806i	0.925845	+	0.377903i	$0.123355\pi$
$431$			325.753i			0.755806i	−0.925845	+	0.377903i	$0.876645\pi$
$432$	−27.1177	−	104.540i	−0.0627725	−	0.241991i
$433$	−1.20391			−0.00278039			−0.00139020	−	0.999999i	$-0.500443\pi$
$433$	−1.20391			−0.00278039			−0.00139020	+	0.999999i	$0.500443\pi$
$434$			275.341i			0.634427i
$435$	203.234	+	95.4299i	0.467206	+	0.219379i
$436$	21.9284			0.0502945
$437$		−	48.4974i		−	0.110978i
$438$	−7.32411	+	15.5980i	−0.0167217	+	0.0356118i
$439$	419.342			0.955220			0.477610	−	0.878572i	$-0.341503\pi$
$439$	419.342			0.955220			0.477610	+	0.878572i	$0.341503\pi$
$440$			3.76357i			0.00855357i
$441$	484.947	+	584.231i	1.09965	+	1.32479i
$442$	−35.0730			−0.0793507
$443$			644.630i			1.45515i	0.686030	+	0.727573i	$0.259352\pi$
$443$			644.630i			1.45515i	−0.686030	+	0.727573i	$0.740648\pi$
$444$	−33.5521	−	15.7546i	−0.0755678	−	0.0354833i
$445$	−198.616			−0.446327
$446$		−	388.204i		−	0.870412i
$447$	88.5569	−	188.597i	0.198114	−	0.421918i
$448$	92.3867			0.206220
$449$			239.766i			0.534001i	0.963696	+	0.267000i	$0.0860325\pi$
$449$			239.766i			0.534001i	−0.963696	+	0.267000i	$0.913967\pi$
$450$	213.613	−	177.311i	0.474695	−	0.394025i
$451$	−5.97319			−0.0132443
$452$			194.999i			0.431414i
$453$	16.4900	+	7.74296i	0.0364017	+	0.0170926i
$454$	−626.076			−1.37902
$455$		−	266.404i		−	0.585503i
$456$	17.4291	−	37.1182i	0.0382216	−	0.0813996i
$457$	−328.108			−0.717960			−0.358980	−	0.933345i	$-0.616875\pi$
$457$	−328.108			−0.717960			−0.358980	+	0.933345i	$0.616875\pi$
$458$			10.6815i			0.0233222i
$459$	−50.1713	+	13.0145i	−0.109306	+	0.0283540i
$460$	−35.8392			−0.0779112
$461$		−	74.2008i		−	0.160956i	−0.996756	−	0.0804781i	$-0.974355\pi$
$461$		−	74.2008i		−	0.160956i	0.996756	−	0.0804781i	$-0.0256447\pi$
$462$	−33.0483	−	15.5180i	−0.0715331	−	0.0335888i
$463$	412.622			0.891193			0.445596	−	0.895234i	$-0.352992\pi$
$463$	412.622			0.891193			0.445596	+	0.895234i	$0.352992\pi$
$464$			167.651i			0.361317i
$465$	38.3862	−	81.7501i	0.0825509	−	0.175807i
$466$	−192.346			−0.412760
$467$		−	842.237i		−	1.80350i	−0.432253	−	0.901752i	$-0.642281\pi$
$467$		−	842.237i		−	1.80350i	0.432253	−	0.901752i	$-0.357719\pi$
$468$	−148.523	−	178.930i	−0.317356	−	0.382329i
$469$	−267.821			−0.571046
$470$			17.4230i			0.0370701i
$471$	−81.5134	−	38.2751i	−0.173065	−	0.0812634i
$472$	−21.7256			−0.0460287
$473$		−	38.0648i		−	0.0804753i
$474$	117.257	−	249.720i	0.247378	−	0.526836i
$475$	105.407			0.221910
$476$		−	44.3386i		−	0.0931484i
$477$	99.9944	−	83.0013i	0.209632	−	0.174007i
$478$	−39.5619			−0.0827654
$479$			506.383i			1.05717i	0.848882	+	0.528583i	$0.177277\pi$
$479$			506.383i			1.05717i	−0.848882	+	0.528583i	$0.822723\pi$
$480$	−27.4300	−	12.8799i	−0.0571459	−	0.0268332i
$481$	−79.8104			−0.165926
$482$		−	579.811i		−	1.20293i
$483$	147.772	−	314.707i	0.305947	−	0.651568i
$484$	−240.889			−0.497705
$485$		−	110.302i		−	0.227428i
$486$	−278.854	−	200.844i	−0.573774	−	0.413260i
$487$	−577.614			−1.18607			−0.593033	−	0.805178i	$-0.702070\pi$
$487$	−577.614			−1.18607			−0.593033	+	0.805178i	$0.702070\pi$
$488$			272.762i			0.558938i
$489$	400.725	+	188.163i	0.819479	+	0.384791i
$490$	213.043			0.434782
$491$			426.796i			0.869239i	0.900614	+	0.434619i	$0.143117\pi$
$491$			426.796i			0.869239i	−0.900614	+	0.434619i	$0.856883\pi$
$492$	20.4418	−	43.5344i	0.0415484	−	0.0884845i
$493$	80.4598			0.163204
$494$		−	88.2931i		−	0.178731i
$495$	7.64878	+	9.21474i	0.0154521	+	0.0186156i
$496$	67.4368			0.135961
$497$		−	1233.00i		−	2.48088i
$498$	−283.639	−	133.184i	−0.569557	−	0.267439i
$499$	139.417			0.279392			0.139696	−	0.990194i	$-0.455387\pi$
$499$	139.417			0.279392			0.139696	+	0.990194i	$0.455387\pi$
$500$		−	167.178i		−	0.334355i
$501$	256.182	−	545.584i	0.511341	−	1.08899i
$502$	708.359			1.41107
$503$			609.140i			1.21101i	0.795840	+	0.605507i	$0.207030\pi$
$503$			609.140i			1.21101i	−0.795840	+	0.605507i	$0.792970\pi$
$504$	226.200	−	187.759i	0.448809	−	0.372538i
$505$	−212.544			−0.420879
$506$			10.5756i			0.0209005i
$507$	5.70863	+	2.68052i	0.0112596	+	0.00528702i
$508$	−209.543			−0.412487
$509$			153.641i			0.301849i	0.988545	+	0.150925i	$0.0482250\pi$
$509$			153.641i			0.301849i	−0.988545	+	0.150925i	$0.951775\pi$
$510$	−6.18139	+	13.1643i	−0.0121204	+	0.0258124i
$511$	−46.9047			−0.0917901
$512$		−	22.6274i		−	0.0441942i
$513$	−32.7627	−	126.302i	−0.0638650	−	0.246202i
$514$	416.671			0.810643
$515$			123.184i			0.239191i
$516$	277.428	+	130.268i	0.537651	+	0.252457i
$517$	5.14127			0.00994443
$518$		−	100.895i		−	0.194777i
$519$	−151.675	+	323.019i	−0.292246	+	0.622388i
$520$	−65.2478			−0.125477
$521$		−	282.101i		−	0.541461i	−0.962655	−	0.270731i	$-0.912735\pi$
$521$		−	282.101i		−	0.541461i	0.962655	−	0.270731i	$-0.0872653\pi$
$522$	340.720	+	410.477i	0.652721	+	0.786355i
$523$	629.761			1.20413			0.602066	−	0.798446i	$-0.294344\pi$
$523$	629.761			1.20413			0.602066	+	0.798446i	$0.294344\pi$
$524$			456.304i			0.870809i
$525$	684.005	+	321.178i	1.30287	+	0.611768i
$526$	−220.857			−0.419881
$527$		−	32.3646i		−	0.0614128i
$528$	−3.80068	+	8.09421i	−0.00719826	+	0.0153300i
$529$	428.292			0.809626
$530$		−	36.4635i		−	0.0687991i
$531$	−53.1929	+	44.1533i	−0.100175	+	0.0831512i
$532$	111.618			0.209809
$533$		−	103.555i		−	0.194288i
$534$	−427.158	−	200.574i	−0.799920	−	0.375607i
$535$	−350.429			−0.655007
$536$			65.5948i			0.122378i
$537$	−270.221	+	575.482i	−0.503204	+	1.07166i
$538$	−165.252			−0.307160
$539$		−	62.8661i		−	0.116635i
$540$	−93.3359	+	24.2114i	−0.172844	+	0.0448359i
$541$	−953.437			−1.76236			−0.881180	−	0.472780i	$-0.843250\pi$
$541$	−953.437			−1.76236			−0.881180	+	0.472780i	$0.843250\pi$
$542$			603.383i			1.11325i
$543$	578.293	+	271.541i	1.06500	+	0.500075i
$544$	−10.8595			−0.0199622
$545$		−	19.5782i		−	0.0359233i
$546$	269.031	−	572.948i	0.492730	−	1.04936i
$547$	−822.432			−1.50353			−0.751766	−	0.659429i	$-0.770798\pi$
$547$	−822.432			−1.50353			−0.751766	+	0.659429i	$0.770798\pi$
$548$			410.966i			0.749938i
$549$	554.339	+	667.831i	1.00973	+	1.21645i
$550$	−22.9858			−0.0417923
$551$			202.550i			0.367605i
$552$	−77.0784	−	36.1926i	−0.139635	−	0.0655662i
$553$	750.935			1.35793
$554$		−	29.0196i		−	0.0523819i
$555$	−14.0661	+	29.9561i	−0.0253442	+	0.0539750i
$556$	−241.453			−0.434269
$557$		−	798.431i		−	1.43345i	−0.697356	−	0.716725i	$-0.745640\pi$
$557$		−	798.431i		−	1.43345i	0.697356	−	0.716725i	$-0.254360\pi$
$558$	165.112	−	137.053i	0.295900	−	0.245615i
$559$	659.918			1.18053
$560$		−	82.4850i		−	0.147295i
$561$	3.88461	+	1.82404i	0.00692444	+	0.00325141i
$562$	512.105			0.911220
$563$			180.641i			0.320855i	0.987048	+	0.160427i	$0.0512873\pi$
$563$			180.641i			0.320855i	−0.987048	+	0.160427i	$0.948713\pi$
$564$	−17.5948	+	37.4711i	−0.0311964	+	0.0664382i
$565$	174.100			0.308142
$566$		−	432.375i		−	0.763914i
$567$	172.241	−	919.420i	0.303777	−	1.62155i
$568$	−301.987			−0.531668
$569$			1.80268i			0.00316815i	0.999999	+	0.00158408i	$0.000504227\pi$
$569$			1.80268i			0.00316815i	−0.999999	+	0.00158408i	$0.999496\pi$
$570$	−33.1400	−	15.5611i	−0.0581404	−	0.0273001i
$571$	738.401			1.29317			0.646586	−	0.762841i	$-0.276196\pi$
$571$	738.401			1.29317			0.646586	+	0.762841i	$0.276196\pi$
$572$			19.2537i			0.0336603i
$573$	−166.572	+	354.743i	−0.290701	+	0.619098i
$574$	130.913			0.228071
$575$		−	218.885i		−	0.380670i
$576$	−45.9861	−	55.4010i	−0.0798371	−	0.0961823i
$577$	395.540			0.685511			0.342756	−	0.939425i	$-0.388640\pi$
$577$	395.540			0.685511			0.342756	+	0.939425i	$0.388640\pi$
$578$		−	403.496i		−	0.698090i
$579$	−515.898	−	242.243i	−0.891015	−	0.418381i
$580$	149.683			0.258074
$581$		−	852.934i		−	1.46804i
$582$	111.390	−	237.225i	0.191392	−	0.407603i
$583$	−10.7599			−0.0184560
$584$			11.4879i			0.0196711i
$585$	−159.753	+	132.604i	−0.273082	+	0.226674i
$586$	−484.183			−0.826251
$587$			533.936i			0.909601i	0.890593	+	0.454800i	$0.150289\pi$
$587$			533.936i			0.909601i	−0.890593	+	0.454800i	$0.849711\pi$
$588$	458.187	+	215.144i	0.779229	+	0.365891i
$589$	81.4748			0.138327
$590$			19.3971i			0.0328764i
$591$	−68.4036	+	145.677i	−0.115742	+	0.246493i
$592$	−24.7112			−0.0417419
$593$		−	355.410i		−	0.599343i	−0.954043	−	0.299671i	$-0.903123\pi$
$593$		−	355.410i		−	0.599343i	0.954043	−	0.299671i	$-0.0968770\pi$
$594$	7.14443	+	27.5421i	0.0120277	+	0.0463672i
$595$	−39.5866			−0.0665321
$596$		−	138.902i		−	0.233058i
$597$	−869.659	−	408.353i	−1.45671	−	0.684008i
$598$	−183.346			−0.306599
$599$			413.169i			0.689765i	0.938646	+	0.344882i	$0.112081\pi$
$599$			413.169i			0.689765i	−0.938646	+	0.344882i	$0.887919\pi$
$600$	78.6633	−	167.527i	0.131105	−	0.279212i
$601$	658.900			1.09634			0.548170	−	0.836367i	$-0.315325\pi$
$601$	658.900			1.09634			0.548170	+	0.836367i	$0.315325\pi$
$602$			834.255i			1.38581i
$603$	133.310	+	160.603i	0.221077	+	0.266339i
$604$	12.1449			0.0201075
$605$			215.072i			0.355491i
$606$	−457.113	−	214.640i	−0.754312	−	0.354191i
$607$	960.745			1.58278			0.791388	−	0.611314i	$-0.209359\pi$
$607$	960.745			1.58278			0.791388	+	0.611314i	$0.209359\pi$
$608$		−	27.3377i		−	0.0449633i
$609$	−617.174	+	1314.38i	−1.01342	+	2.15826i
$610$	243.528			0.399227
$611$			89.1326i			0.145880i
$612$	−26.5883	+	22.0699i	−0.0434449	+	0.0360619i
$613$	429.573			0.700772			0.350386	−	0.936605i	$-0.386050\pi$
$613$	429.573			0.700772			0.350386	+	0.936605i	$0.386050\pi$
$614$		−	121.910i		−	0.198550i
$615$	−38.8685	−	18.2509i	−0.0632009	−	0.0296763i
$616$	−24.3402			−0.0395133
$617$			672.416i			1.08981i	0.838496	+	0.544907i	$0.183435\pi$
$617$			672.416i			1.08981i	−0.838496	+	0.544907i	$0.816565\pi$
$618$	−124.398	+	264.928i	−0.201292	+	0.428686i
$619$	417.284			0.674126			0.337063	−	0.941482i	$-0.390567\pi$
$619$	417.284			0.674126			0.337063	+	0.941482i	$0.390567\pi$
$620$		−	60.2092i		−	0.0971116i
$621$	−262.274	+	68.0339i	−0.422341	+	0.109555i
$622$	583.989			0.938890
$623$		−	1284.51i		−	2.06181i
$624$	−140.327	−	65.8912i	−0.224883	−	0.105595i
$625$	396.026			0.633642
$626$			310.742i			0.496393i
$627$	−4.59185	+	9.77916i	−0.00732353	+	0.0155967i
$628$	−60.0348			−0.0955969
$629$			11.8595i			0.0188546i
$630$	−167.636	−	201.957i	−0.266089	−	0.320566i
$631$	−450.425			−0.713827			−0.356914	−	0.934137i	$-0.616171\pi$
$631$	−450.425			−0.713827			−0.356914	+	0.934137i	$0.616171\pi$
$632$		−	183.920i		−	0.291012i
$633$	1067.99	+	501.482i	1.68719	+	0.792231i
$634$	320.936			0.506208
$635$			187.085i			0.294622i
$636$	36.8231	−	78.4212i	0.0578980	−	0.123304i
$637$	1089.89			1.71097
$638$		−	44.1693i		−	0.0692308i
$639$	−739.386	+	613.734i	−1.15710	+	0.960461i
$640$	−20.2023			−0.0315661
$641$		−	115.281i		−	0.179845i	−0.995949	−	0.0899224i	$-0.971338\pi$
$641$		−	115.281i		−	0.179845i	0.995949	−	0.0899224i	$-0.0286619\pi$
$642$	−753.659	−	353.884i	−1.17392	−	0.551222i
$643$	−527.375			−0.820179			−0.410090	−	0.912045i	$-0.634503\pi$
$643$	−527.375			−0.820179			−0.410090	+	0.912045i	$0.634503\pi$
$644$		−	231.783i		−	0.359911i
$645$	116.306	−	247.694i	0.180320	−	0.384022i
$646$	−13.1200			−0.0203096
$647$			728.113i			1.12537i	0.826672	+	0.562684i	$0.190231\pi$
$647$			728.113i			1.12537i	−0.826672	+	0.562684i	$0.809769\pi$
$648$	−225.185	−	42.1855i	−0.347508	−	0.0651010i
$649$	5.72381			0.00881943
$650$		−	398.497i		−	0.613072i
$651$	528.703	+	248.255i	0.812140	+	0.381344i
$652$	295.135			0.452662
$653$			550.967i			0.843748i	0.906654	+	0.421874i	$0.138628\pi$
$653$			550.967i			0.843748i	−0.906654	+	0.421874i	$0.861372\pi$
$654$	19.7713	−	42.1064i	0.0302313	−	0.0643828i
$655$	407.399			0.621983
$656$		−	32.0632i		−	0.0488768i
$657$	23.3472	+	28.1271i	0.0355360	+	0.0428114i
$658$	−112.680			−0.171246
$659$		−	1004.05i		−	1.52360i	−0.647814	−	0.761798i	$-0.724317\pi$
$659$		−	1004.05i		−	1.52360i	0.647814	−	0.761798i	$-0.275683\pi$
$660$	7.22671	+	3.39334i	0.0109496	+	0.00514142i
$661$	1148.58			1.73764			0.868820	−	0.495128i	$-0.164879\pi$
$661$	1148.58			1.73764			0.868820	+	0.495128i	$0.164879\pi$
$662$		−	289.221i		−	0.436889i
$663$	−31.6228	+	67.3463i	−0.0476965	+	0.101578i
$664$	−208.901			−0.314610
$665$		−	99.6556i		−	0.149858i
$666$	−60.5030	+	50.2211i	−0.0908453	+	0.0754070i
$667$	420.609			0.630597
$668$		−	401.824i		−	0.601533i
$669$	−745.418	−	350.015i	−1.11423	−	0.523192i
$670$	58.5646			0.0874099
$671$		−	71.8618i		−	0.107097i
$672$	83.2984	−	177.398i	0.123956	−	0.263986i
$673$	919.426			1.36616			0.683080	−	0.730343i	$-0.260640\pi$
$673$	919.426			1.36616			0.683080	+	0.730343i	$0.260640\pi$
$674$			349.651i			0.518771i
$675$	−147.869	−	570.043i	−0.219066	−	0.844508i
$676$	4.20442			0.00621956
$677$			460.569i			0.680308i	0.940370	+	0.340154i	$0.110479\pi$
$677$			460.569i			0.680308i	−0.940370	+	0.340154i	$0.889521\pi$
$678$	374.432	+	175.817i	0.552260	+	0.259317i
$679$	713.360			1.05060
$680$			9.69558i			0.0142582i
$681$	−564.488	+	1202.18i	−0.828910	+	1.76531i
$682$	−17.7669			−0.0260511
$683$		−	652.668i		−	0.955590i	−0.878471	−	0.477795i	$-0.841436\pi$
$683$		−	652.668i		−	0.955590i	0.878471	−	0.477795i	$-0.158564\pi$
$684$	−55.5589	−	66.9336i	−0.0812265	−	0.0978562i
$685$	366.920			0.535650
$686$			577.558i			0.841921i
$687$	20.5104	+	9.63078i	0.0298551	+	0.0140186i
$688$	204.326			0.296986
$689$		−	186.541i		−	0.270741i
$690$	−32.3136	+	68.8174i	−0.0468313	+	0.0997354i
$691$	−563.046			−0.814828			−0.407414	−	0.913243i	$-0.633569\pi$
$691$	−563.046			−0.814828			−0.407414	+	0.913243i	$0.633569\pi$
$692$			237.905i			0.343793i
$693$	−59.5945	+	49.4670i	−0.0859950	+	0.0713809i
$694$	−715.318			−1.03072
$695$			215.575i			0.310180i
$696$	321.919	+	151.159i	0.462527	+	0.217182i
$697$	−15.3879			−0.0220773
$698$		−	720.269i		−	1.03190i
$699$	−173.425	+	369.338i	−0.248104	+	0.528380i
$700$	503.772			0.719674
$701$		−	806.290i		−	1.15020i	−0.818083	−	0.575100i	$-0.804963\pi$
$701$		−	806.290i		−	1.15020i	0.818083	−	0.575100i	$-0.195037\pi$
$702$	−477.489	+	123.861i	−0.680183	+	0.176440i
$703$	−29.8552			−0.0424683
$704$			5.96141i			0.00846792i
$705$	33.4551	+	15.7090i	0.0474541	+	0.0222823i
$706$	310.644			0.440006
$707$		−	1374.59i		−	1.94425i
$708$	−19.5884	+	41.7169i	−0.0276672	+	0.0589221i
$709$	−1111.39			−1.56755			−0.783776	−	0.621044i	$-0.786709\pi$
$709$	−1111.39			−1.56755			−0.783776	+	0.621044i	$0.786709\pi$
$710$			269.621i			0.379748i
$711$	−373.783	−	450.309i	−0.525715	−	0.633346i
$712$	−314.603			−0.441858
$713$		−	169.188i		−	0.237290i
$714$	−85.1378	−	39.9769i	−0.119241	−	0.0559901i
$715$	17.1902			0.0240422
$716$			423.844i			0.591961i
$717$	−35.6701	+	75.9656i	−0.0497491	+	0.105949i
$718$	773.201			1.07688
$719$			1117.80i			1.55466i	0.629095	+	0.777328i	$0.283426\pi$
$719$			1117.80i			1.55466i	−0.629095	+	0.777328i	$0.716574\pi$
$720$	−49.4634	+	41.0575i	−0.0686991	+	0.0570244i
$721$	−796.666			−1.10495
$722$			477.503i			0.661361i
$723$	−1113.34	−	522.774i	−1.53989	−	0.723062i
$724$	425.915			0.588280
$725$			914.178i			1.26094i
$726$	−217.193	+	462.550i	−0.299163	+	0.637121i
$727$	933.966			1.28468			0.642342	−	0.766418i	$-0.277963\pi$
$727$	933.966			1.28468			0.642342	+	0.766418i	$0.277963\pi$
$728$		−	421.978i		−	0.579640i
$729$	−637.079	+	354.361i	−0.873907	+	0.486092i
$730$	10.2567			0.0140503
$731$		−	98.0612i		−	0.134147i
$732$	523.750	+	245.930i	0.715506	+	0.335970i
$733$	−491.852			−0.671012			−0.335506	−	0.942038i	$-0.608907\pi$
$733$	−491.852			−0.671012			−0.335506	+	0.942038i	$0.608907\pi$
$734$			738.094i			1.00558i
$735$	192.086	−	409.080i	0.261341	−	0.556572i
$736$	−56.7684			−0.0771310
$737$		−	17.2816i		−	0.0234486i
$738$	−65.1627	−	78.5036i	−0.0882963	−	0.106373i
$739$	−1264.81			−1.71152			−0.855758	−	0.517377i	$-0.826909\pi$
$739$	−1264.81			−1.71152			−0.855758	+	0.517377i	$0.826909\pi$
$740$			22.0628i			0.0298145i
$741$	−169.538	−	79.6075i	−0.228796	−	0.107433i
$742$	235.821			0.317818
$743$		−	215.306i		−	0.289779i	−0.989448	−	0.144890i	$-0.953717\pi$
$743$		−	215.306i		−	0.289779i	0.989448	−	0.144890i	$-0.0462827\pi$
$744$	60.8029	−	129.490i	0.0817243	−	0.174046i
$745$	−124.015			−0.166464
$746$			485.093i			0.650259i
$747$	−511.474	+	424.554i	−0.684705	+	0.568346i
$748$	2.86103			0.00382490
$749$		−	2266.33i		−	3.02581i
$750$	−321.010	−	150.732i	−0.428013	−	0.200976i
$751$	−164.755			−0.219381			−0.109691	−	0.993966i	$-0.534986\pi$
$751$	−164.755			−0.219381			−0.109691	+	0.993966i	$0.534986\pi$
$752$			27.5976i			0.0366989i
$753$	638.676	−	1360.17i	0.848175	−	1.80634i
$754$	765.749			1.01558
$755$		−	10.8433i		−	0.0143620i
$756$	−156.582	−	603.632i	−0.207120	−	0.798455i
$757$	−1079.49			−1.42601			−0.713004	−	0.701160i	$-0.752666\pi$
$757$	−1079.49			−1.42601			−0.713004	+	0.701160i	$0.752666\pi$
$758$			26.4912i			0.0349488i
$759$	20.3070	+	9.53528i	0.0267550	+	0.0125630i
$760$	−24.4077			−0.0321154
$761$		−	814.605i		−	1.07044i	−0.844713	−	0.535220i	$-0.820229\pi$
$761$		−	814.605i		−	1.07044i	0.844713	−	0.535220i	$-0.179771\pi$
$762$	−188.930	+	402.360i	−0.247940	+	0.528031i
$763$	126.618			0.165948
$764$			261.269i			0.341976i
$765$	19.7045	+	23.7387i	0.0257575	+	0.0310310i
$766$	289.263			0.377628
$767$			99.2319i			0.129377i
$768$	−43.4486	−	20.4015i	−0.0565737	−	0.0265645i
$769$	21.7364			0.0282658			0.0141329	−	0.999900i	$-0.495501\pi$
$769$	21.7364			0.0282658			0.0141329	+	0.999900i	$0.495501\pi$
$770$			21.7315i			0.0282227i
$771$	375.682	−	800.080i	0.487266	−	1.03772i
$772$	−379.960			−0.492176
$773$			35.3364i			0.0457133i	0.999739	+	0.0228567i	$0.00727613\pi$
$773$			35.3364i			0.0457133i	−0.999739	+	0.0228567i	$0.992724\pi$
$774$	500.273	−	415.257i	0.646348	−	0.536507i
$775$	367.724			0.474482
$776$		−	174.717i		−	0.225150i
$777$	−193.735	−	90.9695i	−0.249338	−	0.117078i
$778$	−426.797			−0.548582
$779$		−	38.7377i		−	0.0497274i
$780$	−58.8293	+	125.287i	−0.0754221	+	0.160625i
$781$	79.5615			0.101871
$782$			27.2446i			0.0348396i
$783$	1095.39	−	284.145i	1.39897	−	0.362892i
$784$	337.456			0.430428
$785$			53.6006i			0.0682810i
$786$	876.183	+	411.416i	1.11474	+	0.523430i
$787$	240.928			0.306135			0.153067	−	0.988216i	$-0.451085\pi$
$787$	240.928			0.306135			0.153067	+	0.988216i	$0.451085\pi$
$788$			107.292i			0.136157i
$789$	−199.131	+	424.084i	−0.252384	+	0.537496i
$790$	−164.208			−0.207858
$791$			1125.96i			1.42346i
$792$	12.1155	+	14.5959i	0.0152973	+	0.0184292i
$793$	1245.85			1.57105
$794$			165.749i			0.208752i
$795$	−70.0163	−	32.8765i	−0.0880709	−	0.0413541i
$796$	−640.506			−0.804656
$797$		−	315.047i		−	0.395291i	−0.980274	−	0.197645i	$-0.936671\pi$
$797$		−	315.047i		−	0.395291i	0.980274	−	0.197645i	$-0.0633294\pi$
$798$	100.638	−	214.327i	0.126113	−	0.268580i
$799$	13.2448			0.0165767
$800$		−	123.384i		−	0.154230i
$801$	−770.274	+	639.373i	−0.961641	+	0.798219i
$802$	672.026			0.837938
$803$		−	3.02661i		−	0.00376913i
$804$	125.953	+	59.1421i	0.156659	+	0.0735599i
$805$	−206.941			−0.257070
$806$		−	308.019i		−	0.382157i
$807$	−148.996	+	317.313i	−0.184629	+	0.393200i
$808$	−336.665			−0.416665
$809$		−	1018.98i		−	1.25956i	−0.776773	−	0.629780i	$-0.783145\pi$
$809$		−	1018.98i		−	1.25956i	0.776773	−	0.629780i	$-0.216855\pi$
$810$	−37.6642	+	201.051i	−0.0464990	+	0.248211i
$811$	−572.354			−0.705738			−0.352869	−	0.935673i	$-0.614794\pi$
$811$	−572.354			−0.705738			−0.352869	+	0.935673i	$0.614794\pi$
$812$			968.045i			1.19217i
$813$	1158.60	+	544.027i	1.42509	+	0.669159i
$814$	6.51041			0.00799804
$815$		−	263.504i		−	0.323318i
$816$	−9.79118	+	20.8520i	−0.0119990	+	0.0255540i
$817$	246.860			0.302154
$818$		−	549.897i		−	0.672246i
$819$	−857.594	−	1033.17i	−1.04712	−	1.26150i
$820$	−28.6268			−0.0349107
$821$		−	175.620i		−	0.213910i	−0.994264	−	0.106955i	$-0.965890\pi$
$821$		−	175.620i		−	0.213910i	0.994264	−	0.106955i	$-0.0341101\pi$
$822$	789.126	+	370.538i	0.960007	+	0.450777i
$823$	493.146			0.599205			0.299603	−	0.954064i	$-0.403146\pi$
$823$	493.146			0.599205			0.299603	+	0.954064i	$0.403146\pi$
$824$			195.120i			0.236796i
$825$	−20.7246	+	44.1367i	−0.0251207	+	0.0534990i
$826$	−125.447			−0.151873
$827$		−	676.616i		−	0.818158i	−0.912499	−	0.409079i	$-0.865850\pi$
$827$		−	676.616i		−	0.818158i	0.912499	−	0.409079i	$-0.134150\pi$
$828$	−138.992	+	115.372i	−0.167865	+	0.139338i
$829$	−368.388			−0.444376			−0.222188	−	0.975004i	$-0.571320\pi$
$829$	−368.388			−0.444376			−0.222188	+	0.975004i	$0.571320\pi$
$830$			186.512i			0.224713i
$831$	−55.7226	−	26.1648i	−0.0670549	−	0.0314860i
$832$	−103.351			−0.124220
$833$		−	161.953i		−	0.194422i
$834$	−217.701	+	463.632i	−0.261032	+	0.555914i
$835$	−358.758			−0.429651
$836$			7.20238i			0.00861528i
$837$	−114.296	−	440.615i	−0.136554	−	0.526422i
$838$	−980.068			−1.16953
$839$		−	37.7331i		−	0.0449739i	−0.999747	−	0.0224869i	$-0.992842\pi$
$839$		−	37.7331i		−	0.0449739i	0.999747	−	0.0224869i	$-0.00715842\pi$
$840$	−158.386	−	74.3708i	−0.188554	−	0.0885367i
$841$	−915.678			−1.08880
$842$			312.709i			0.371388i
$843$	461.729	−	983.331i	0.547721	−	1.16647i
$844$	786.581			0.931968
$845$		−	3.75381i		−	0.00444238i
$846$	56.0872	+	67.5700i	0.0662969	+	0.0798700i
$847$	−1390.94			−1.64219
$848$		−	57.7574i		−	0.0681102i
$849$	−830.235	−	389.841i	−0.977898	−	0.459177i
$850$	−59.2151			−0.0696648
$851$			61.9963i			0.0728512i
$852$	−272.280	+	579.868i	−0.319578	+	0.680596i
$853$	493.290			0.578300			0.289150	−	0.957284i	$-0.406627\pi$
$853$	493.290			0.578300			0.289150	+	0.957284i	$0.406627\pi$
$854$			1574.97i			1.84423i
$855$	−59.7600	+	49.6043i	−0.0698947	+	0.0580167i
$856$	−555.072			−0.648448
$857$		−	595.688i		−	0.695086i	−0.937664	−	0.347543i	$-0.887016\pi$
$857$		−	595.688i		−	0.695086i	0.937664	−	0.347543i	$-0.112984\pi$
$858$	36.9705	+	17.3597i	0.0430891	+	0.0202327i
$859$	240.833			0.280364			0.140182	−	0.990126i	$-0.455231\pi$
$859$	240.833			0.280364			0.140182	+	0.990126i	$0.455231\pi$
$860$		−	182.427i		−	0.212125i
$861$	118.034	−	251.375i	0.137090	−	0.291957i
$862$	460.684			0.534436
$863$			347.730i			0.402932i	0.979496	+	0.201466i	$0.0645706\pi$
$863$			347.730i			0.402932i	−0.979496	+	0.201466i	$0.935429\pi$
$864$	−147.842	+	38.3503i	−0.171113	+	0.0443869i
$865$	212.407			0.245557
$866$			1.70259i			0.00196603i
$867$	−774.782	−	363.803i	−0.893636	−	0.419612i
$868$	389.391			0.448607
$869$			48.4554i			0.0557600i
$870$	134.958	−	287.417i	0.155124	−	0.330364i
$871$	299.606			0.343979
$872$		−	31.0115i		−	0.0355636i
$873$	−355.080	−	427.777i	−0.406736	−	0.490008i
$874$	−68.5857			−0.0784733
$875$		−	965.311i		−	1.10321i
$876$	22.0588	+	10.3579i	0.0251813	+	0.0118240i
$877$	−395.722			−0.451222			−0.225611	−	0.974217i	$-0.572438\pi$
$877$	−395.722			−0.451222			−0.225611	+	0.974217i	$0.572438\pi$
$878$		−	593.039i		−	0.675443i
$879$	−436.553	+	929.716i	−0.496648	+	1.05770i
$880$	5.32249			0.00604829
$881$		−	1164.13i		−	1.32137i	−0.750664	−	0.660684i	$-0.770266\pi$
$881$		−	1164.13i		−	1.32137i	0.750664	−	0.660684i	$-0.229734\pi$
$882$	826.228	−	685.818i	0.936767	−	0.777572i
$883$	62.8922			0.0712256			0.0356128	−	0.999366i	$-0.488662\pi$
$883$	62.8922			0.0712256			0.0356128	+	0.999366i	$0.488662\pi$
$884$			49.6007i			0.0561094i
$885$	37.2458	+	17.4890i	0.0420857	+	0.0197615i
$886$	911.644			1.02894
$887$			376.556i			0.424527i	0.977212	+	0.212264i	$0.0680835\pi$
$887$			376.556i			0.424527i	−0.977212	+	0.212264i	$0.931916\pi$
$888$	−22.2803	+	47.4498i	−0.0250904	+	0.0534345i
$889$	−1209.94			−1.36101
$890$			280.885i			0.315601i
$891$	59.3272	+	11.1142i	0.0665850	+	0.0124738i
$892$	−549.003			−0.615474
$893$			33.3425i			0.0373376i
$894$	−266.717	−	125.238i	−0.298341	−	0.140088i
$895$	378.418			0.422814
$896$		−	130.654i		−	0.145820i
$897$	−165.310	+	352.057i	−0.184292	+	0.392483i
$898$	339.081			0.377596
$899$			706.615i			0.786001i
$900$	−250.756	−	302.094i	−0.278618	−	0.335660i
$901$	−27.7192			−0.0307649
$902$			8.44736i			0.00936515i
$903$	1601.91	+	752.187i	1.77399	+	0.832987i
$904$	275.771			0.305056
$905$		−	380.267i		−	0.420184i
$906$	10.9502	−	23.3204i	0.0120863	−	0.0257399i
$907$	−23.9537			−0.0264099			−0.0132049	−	0.999913i	$-0.504203\pi$
$907$	−23.9537			−0.0264099			−0.0132049	+	0.999913i	$0.504203\pi$
$908$			885.406i			0.975117i
$909$	−824.291	+	684.211i	−0.906811	+	0.752707i
$910$	−376.752			−0.414013
$911$			1206.04i			1.32387i	0.749562	+	0.661934i	$0.230264\pi$
$911$			1206.04i			1.32387i	−0.749562	+	0.661934i	$0.769736\pi$
$912$	−52.4931	−	24.6484i	−0.0575582	−	0.0270268i
$913$	55.0371			0.0602816
$914$			464.014i			0.507674i
$915$	219.572	−	467.617i	0.239969	−	0.511057i
$916$	15.1060			0.0164913
$917$			2634.77i			2.87325i
$918$	18.4052	+	70.9530i	0.0200493	+	0.0772908i
$919$	−1598.15			−1.73901			−0.869503	−	0.493928i	$-0.835561\pi$
$919$	−1598.15			−1.73901			−0.869503	+	0.493928i	$0.835561\pi$
$920$			50.6842i			0.0550915i
$921$	−234.088	−	109.917i	−0.254167	−	0.119346i
$922$	−104.936			−0.113813
$923$			1379.33i			1.49440i
$924$	−21.9458	+	46.7373i	−0.0237508	+	0.0505815i
$925$	−134.747			−0.145672
$926$		−	583.536i		−	0.630168i
$927$	396.546	+	477.733i	0.427774	+	0.515353i
$928$	237.094			0.255490
$929$		−	1452.09i		−	1.56307i	−0.623860	−	0.781536i	$-0.714436\pi$
$929$		−	1452.09i		−	1.56307i	0.623860	−	0.781536i	$-0.285564\pi$
$930$	−115.612	−	54.2863i	−0.124314	−	0.0583723i
$931$	407.703			0.437919
$932$			272.018i			0.291865i
$933$	526.541	−	1121.36i	0.564353	−	1.20189i
$934$	−1191.10			−1.27527
$935$		−	2.55439i		−	0.00273197i
$936$	−253.045	+	210.043i	−0.270347	+	0.224404i
$937$	−1685.43			−1.79875			−0.899374	−	0.437180i	$-0.855977\pi$
$937$	−1685.43			−1.79875			−0.899374	+	0.437180i	$0.855977\pi$
$938$			378.756i			0.403791i
$939$	596.679	+	280.174i	0.635441	+	0.298375i
$940$	24.6398			0.0262126
$941$			1194.87i			1.26979i	0.772598	+	0.634896i	$0.218957\pi$
$941$			1194.87i			1.26979i	−0.772598	+	0.634896i	$0.781043\pi$
$942$	−54.1291	+	115.277i	−0.0574619	+	0.122375i
$943$	−80.4413			−0.0853036
$944$			30.7246i			0.0325472i
$945$	−538.937	+	139.800i	−0.570304	+	0.147937i
$946$	−53.8318			−0.0569046
$947$			1848.34i			1.95178i	0.218262	+	0.975890i	$0.429961\pi$
$947$			1848.34i			1.95178i	−0.218262	+	0.975890i	$0.570039\pi$
$948$	−353.158	−	165.827i	−0.372529	−	0.174923i
$949$	52.4714			0.0552912
$950$		−	149.069i		−	0.156914i
$951$	289.365	−	616.253i	0.304274	−	0.648005i
$952$	−62.7043			−0.0658658
$953$		−	1254.18i		−	1.31603i	−0.753004	−	0.658016i	$-0.771396\pi$
$953$		−	1254.18i		−	1.31603i	0.753004	−	0.658016i	$-0.228604\pi$
$954$	−117.382	−	141.414i	−0.123042	−	0.148232i
$955$	233.268			0.244259
$956$			55.9489i			0.0585240i
$957$	−84.8127	−	39.8243i	−0.0886235	−	0.0416136i
$958$	716.133			0.747529
$959$			2372.99i			2.47444i
$960$	−18.2150	+	38.7919i	−0.0189739	+	0.0404083i
$961$	−676.768			−0.704233
$962$			112.869i			0.117327i
$963$	−1359.04	+	1128.08i	−1.41126	+	1.17143i
$964$	−819.977			−0.850599
$965$			339.238i			0.351542i
$966$	−445.063	−	208.982i	−0.460728	−	0.216337i
$967$	1708.87			1.76718			0.883592	−	0.468258i	$-0.155118\pi$
$967$	1708.87			1.76718			0.883592	+	0.468258i	$0.155118\pi$
$968$			340.669i			0.351931i
$969$	−11.8294	+	25.1927i	−0.0122078	+	0.0259987i
$970$	−155.991			−0.160816
$971$			1740.47i			1.79245i	0.443595	+	0.896227i	$0.353703\pi$
$971$			1740.47i			1.79245i	−0.443595	+	0.896227i	$0.646297\pi$
$972$	−284.037	+	394.359i	−0.292219	+	0.405719i
$973$	−1394.19			−1.43288
$974$			816.869i			0.838675i
$975$	−765.183	−	359.296i	−0.784804	−	0.368509i
$976$	385.744			0.395229
$977$		−	1178.72i		−	1.20647i	−0.797565	−	0.603233i	$-0.793879\pi$
$977$		−	1178.72i		−	1.20647i	0.797565	−	0.603233i	$-0.206121\pi$
$978$	266.102	−	566.711i	0.272088	−	0.579459i
$979$	82.8852			0.0846631
$980$		−	301.289i		−	0.307437i
$981$	−63.0252	−	75.9286i	−0.0642459	−	0.0773992i
$982$	603.581			0.614645
$983$			1796.55i			1.82762i	0.406142	+	0.913810i	$0.366874\pi$
$983$			1796.55i			1.82762i	−0.406142	+	0.913810i	$0.633126\pi$
$984$	−61.5669	−	28.9091i	−0.0625680	−	0.0293791i
$985$	95.7927			0.0972515
$986$		−	113.787i		−	0.115403i
$987$	−101.595	+	216.365i	−0.102933	+	0.219214i
$988$	−124.865			−0.126382
$989$		−	512.621i		−	0.518323i
$990$	13.0316	−	10.8170i	0.0131632	−	0.0109263i
$991$	1554.59			1.56871			0.784354	−	0.620314i	$-0.212995\pi$
$991$	1554.59			1.56871			0.784354	+	0.620314i	$0.212995\pi$
$992$		−	95.3700i		−	0.0961391i
$993$	−555.354	−	260.769i	−0.559269	−	0.262608i
$994$	−1743.72			−1.75425
$995$			571.859i			0.574733i
$996$	−188.351	+	401.127i	−0.189108	+	0.402738i
$997$	299.784			0.300686			0.150343	−	0.988634i	$-0.451962\pi$
$997$	299.784			0.300686			0.150343	+	0.988634i	$0.451962\pi$
$998$		−	197.165i		−	0.197560i
$999$	41.8820	+	161.457i	0.0419239	+	0.161619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.3	✓	40
3.2	odd	2	inner	354.3.b.a.119.23	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.3	✓	40	1.1	even	1	trivial
354.3.b.a.119.23	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.71554 - 1.27509i) q^{3} -2.00000 q^{4} +1.78565i q^{5} +(-1.80326 + 3.84035i) q^{6} -11.5483 q^{7} +2.82843i q^{8} +(5.74827 + 6.92513i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-2.71554 - 1.27509i) q^{3} -2.00000 q^{4} +1.78565i q^{5} +(-1.80326 + 3.84035i) q^{6} -11.5483 q^{7} +2.82843i q^{8} +(5.74827 + 6.92513i) q^{9} +2.52529 q^{10} -0.745177i q^{11} +(5.43107 + 2.55019i) q^{12} +12.9189 q^{13} +16.3318i q^{14} +(2.27687 - 4.84899i) q^{15} +4.00000 q^{16} -1.91970i q^{17} +(9.79361 - 8.12928i) q^{18} +4.83266 q^{19} -3.57130i q^{20} +(31.3599 + 14.7252i) q^{21} -1.05384 q^{22} -10.0353i q^{23} +(3.60651 - 7.68069i) q^{24} +21.8115 q^{25} -18.2701i q^{26} +(-6.77944 - 26.1350i) q^{27} +23.0967 q^{28} +41.9127i q^{29} +(-6.85751 - 3.21998i) q^{30} +16.8592 q^{31} -5.65685i q^{32} +(-0.950171 + 2.02355i) q^{33} -2.71486 q^{34} -20.6213i q^{35} +(-11.4965 - 13.8503i) q^{36} -6.17780 q^{37} -6.83442i q^{38} +(-35.0817 - 16.4728i) q^{39} -5.05057 q^{40} -8.01580i q^{41} +(20.8246 - 44.3496i) q^{42} +51.0816 q^{43} +1.49035i q^{44} +(-12.3658 + 10.2644i) q^{45} -14.1921 q^{46} +6.89940i q^{47} +(-10.8621 - 5.10038i) q^{48} +84.3640 q^{49} -30.8461i q^{50} +(-2.44780 + 5.21301i) q^{51} -25.8378 q^{52} -14.4394i q^{53} +(-36.9605 + 9.58757i) q^{54} +1.33062 q^{55} -32.6636i q^{56} +(-13.1233 - 6.16210i) q^{57} +59.2736 q^{58} +7.68115i q^{59} +(-4.55374 + 9.69798i) q^{60} +96.4359 q^{61} -23.8425i q^{62} +(-66.3829 - 79.9737i) q^{63} -8.00000 q^{64} +23.0686i q^{65} +(2.86174 + 1.34374i) q^{66} +23.1913 q^{67} +3.83940i q^{68} +(-12.7960 + 27.2513i) q^{69} -29.1629 q^{70} +106.769i q^{71} +(-19.5872 + 16.2586i) q^{72} +4.06160 q^{73} +8.73673i q^{74} +(-59.2298 - 27.8117i) q^{75} -9.66533 q^{76} +8.60555i q^{77} +(-23.2961 + 49.6130i) q^{78} -65.0254 q^{79} +7.14259i q^{80} +(-14.9148 + 79.6150i) q^{81} -11.3361 q^{82} +73.8578i q^{83} +(-62.7198 - 29.4504i) q^{84} +3.42790 q^{85} -72.2403i q^{86} +(53.4427 - 113.816i) q^{87} +2.10768 q^{88} +111.229i q^{89} +(14.5160 + 17.4879i) q^{90} -149.192 q^{91} +20.0707i q^{92} +(-45.7817 - 21.4971i) q^{93} +9.75723 q^{94} +8.62944i q^{95} +(-7.21302 + 15.3614i) q^{96} -61.7717 q^{97} -119.309i q^{98} +(5.16044 - 4.28348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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