LMFDB - Embedded newform 354.3.b.a.119.6

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			119.6
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.48935 + 2.60419i) q^{3} -2.00000 q^{4} +4.30678i q^{5} +(3.68289 + 2.10626i) q^{6} -7.55737 q^{7} +2.82843i q^{8} +(-4.56365 - 7.75713i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.48935 + 2.60419i) q^{3} -2.00000 q^{4} +4.30678i q^{5} +(3.68289 + 2.10626i) q^{6} -7.55737 q^{7} +2.82843i q^{8} +(-4.56365 - 7.75713i) q^{9} +6.09070 q^{10} -1.44085i q^{11} +(2.97871 - 5.20839i) q^{12} +1.74263 q^{13} +10.6877i q^{14} +(-11.2157 - 6.41431i) q^{15} +4.00000 q^{16} -8.57199i q^{17} +(-10.9702 + 6.45398i) q^{18} +8.46524 q^{19} -8.61355i q^{20} +(11.2556 - 19.6809i) q^{21} -2.03768 q^{22} -38.3298i q^{23} +(-7.36577 - 4.21253i) q^{24} +6.45168 q^{25} -2.46445i q^{26} +(26.9980 - 0.331514i) q^{27} +15.1147 q^{28} -41.9595i q^{29} +(-9.07121 + 15.8614i) q^{30} -28.6905 q^{31} -5.65685i q^{32} +(3.75226 + 2.14594i) q^{33} -12.1226 q^{34} -32.5479i q^{35} +(9.12730 + 15.5143i) q^{36} +13.6139 q^{37} -11.9717i q^{38} +(-2.59539 + 4.53814i) q^{39} -12.1814 q^{40} +32.2812i q^{41} +(-27.8329 - 15.9178i) q^{42} -82.1173 q^{43} +2.88171i q^{44} +(33.4082 - 19.6546i) q^{45} -54.2065 q^{46} +18.5419i q^{47} +(-5.95742 + 10.4168i) q^{48} +8.11387 q^{49} -9.12406i q^{50} +(22.3231 + 12.7667i) q^{51} -3.48525 q^{52} -84.8533i q^{53} +(-0.468832 - 38.1809i) q^{54} +6.20544 q^{55} -21.3755i q^{56} +(-12.6077 + 22.0451i) q^{57} -59.3397 q^{58} -7.68115i q^{59} +(22.4314 + 12.8286i) q^{60} -14.2449 q^{61} +40.5745i q^{62} +(34.4892 + 58.6235i) q^{63} -8.00000 q^{64} +7.50510i q^{65} +(3.03482 - 5.30650i) q^{66} -35.0574 q^{67} +17.1440i q^{68} +(99.8181 + 57.0866i) q^{69} -46.0297 q^{70} +24.2338i q^{71} +(21.9405 - 12.9080i) q^{72} +10.7104 q^{73} -19.2530i q^{74} +(-9.60884 + 16.8014i) q^{75} -16.9305 q^{76} +10.8891i q^{77} +(6.41790 + 3.67043i) q^{78} +5.01487 q^{79} +17.2271i q^{80} +(-39.3462 + 70.8017i) q^{81} +45.6526 q^{82} -51.3325i q^{83} +(-22.5112 + 39.3617i) q^{84} +36.9176 q^{85} +116.131i q^{86} +(109.271 + 62.4926i) q^{87} +4.07535 q^{88} +62.4362i q^{89} +(-27.7958 - 47.2464i) q^{90} -13.1697 q^{91} +76.6595i q^{92} +(42.7303 - 74.7157i) q^{93} +26.2222 q^{94} +36.4579i q^{95} +(14.7315 + 8.42506i) q^{96} +22.0158 q^{97} -11.4747i q^{98} +(-11.1769 + 6.57556i) 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
$3$	−1.48935	+	2.60419i	−0.496451	+	0.868065i
$3$	−1.48935	+	2.60419i	−0.496451	+	0.868065i
$4$	−2.00000			−0.500000
$5$			4.30678i			0.861355i	0.902506	+	0.430678i	$0.141725\pi$
$5$			4.30678i			0.861355i	−0.902506	+	0.430678i	$0.858275\pi$
$6$	3.68289	+	2.10626i	0.613814	+	0.351044i
$7$	−7.55737			−1.07962			−0.539812	−	0.841785i	$-0.681505\pi$
$7$	−7.55737			−1.07962			−0.539812	+	0.841785i	$0.681505\pi$
$8$			2.82843i			0.353553i
$9$	−4.56365	−	7.75713i	−0.507072	−	0.861904i
$10$	6.09070			0.609070
$11$		−	1.44085i		−	0.130987i	−0.997853	−	0.0654934i	$-0.979138\pi$
$11$		−	1.44085i		−	0.130987i	0.997853	−	0.0654934i	$-0.0208621\pi$
$12$	2.97871	−	5.20839i	0.248226	−	0.434032i
$13$	1.74263			0.134048			0.0670241	−	0.997751i	$-0.478650\pi$
$13$	1.74263			0.134048			0.0670241	+	0.997751i	$0.478650\pi$
$14$			10.6877i			0.763410i
$15$	−11.2157	−	6.41431i	−0.747712	−	0.427621i
$16$	4.00000			0.250000
$17$		−	8.57199i		−	0.504235i	−0.967697	−	0.252117i	$-0.918873\pi$
$17$		−	8.57199i		−	0.504235i	0.967697	−	0.252117i	$-0.0811269\pi$
$18$	−10.9702	+	6.45398i	−0.609458	+	0.358554i
$19$	8.46524			0.445539			0.222769	−	0.974871i	$-0.428490\pi$
$19$	8.46524			0.445539			0.222769	+	0.974871i	$0.428490\pi$
$20$		−	8.61355i		−	0.430678i
$21$	11.2556	−	19.6809i	0.535981	−	0.937184i
$22$	−2.03768			−0.0926216
$23$		−	38.3298i		−	1.66651i	−0.552888	−	0.833256i	$-0.686474\pi$
$23$		−	38.3298i		−	1.66651i	0.552888	−	0.833256i	$-0.313526\pi$
$24$	−7.36577	−	4.21253i	−0.306907	−	0.175522i
$25$	6.45168			0.258067
$26$		−	2.46445i		−	0.0947864i
$27$	26.9980	−	0.331514i	0.999925	−	0.0122783i
$28$	15.1147			0.539812
$29$		−	41.9595i		−	1.44688i	−0.690388	−	0.723440i	$-0.742560\pi$
$29$		−	41.9595i		−	1.44688i	0.690388	−	0.723440i	$-0.257440\pi$
$30$	−9.07121	+	15.8614i	−0.302374	+	0.528712i
$31$	−28.6905			−0.925501			−0.462750	−	0.886489i	$-0.653137\pi$
$31$	−28.6905			−0.925501			−0.462750	+	0.886489i	$0.653137\pi$
$32$		−	5.65685i		−	0.176777i
$33$	3.75226	+	2.14594i	0.113705	+	0.0650286i
$34$	−12.1226			−0.356548
$35$		−	32.5479i		−	0.929940i
$36$	9.12730	+	15.5143i	0.253536	+	0.430952i
$37$	13.6139			0.367944			0.183972	−	0.982931i	$-0.441104\pi$
$37$	13.6139			0.367944			0.183972	+	0.982931i	$0.441104\pi$
$38$		−	11.9717i		−	0.315044i
$39$	−2.59539	+	4.53814i	−0.0665484	+	0.116363i
$40$	−12.1814			−0.304535
$41$			32.2812i			0.787347i	0.919250	+	0.393674i	$0.128796\pi$
$41$			32.2812i			0.787347i	−0.919250	+	0.393674i	$0.871204\pi$
$42$	−27.8329	−	15.9178i	−0.662689	−	0.378996i
$43$	−82.1173			−1.90970			−0.954852	−	0.297082i	$-0.903987\pi$
$43$	−82.1173			−1.90970			−0.954852	+	0.297082i	$0.903987\pi$
$44$			2.88171i			0.0654934i
$45$	33.4082	−	19.6546i	0.742405	−	0.436769i
$46$	−54.2065			−1.17840
$47$			18.5419i			0.394509i	0.980352	+	0.197254i	$0.0632025\pi$
$47$			18.5419i			0.394509i	−0.980352	+	0.197254i	$0.936798\pi$
$48$	−5.95742	+	10.4168i	−0.124113	+	0.217016i
$49$	8.11387			0.165589
$50$		−	9.12406i		−	0.182481i
$51$	22.3231	+	12.7667i	0.437708	+	0.250328i
$52$	−3.48525			−0.0670241
$53$		−	84.8533i		−	1.60101i	−0.599329	−	0.800503i	$-0.704566\pi$
$53$		−	84.8533i		−	1.60101i	0.599329	−	0.800503i	$-0.295434\pi$
$54$	−0.468832	−	38.1809i	−0.00868207	−	0.707053i
$55$	6.20544			0.112826
$56$		−	21.3755i		−	0.381705i
$57$	−12.6077	+	22.0451i	−0.221188	+	0.386757i
$58$	−59.3397			−1.02310
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	22.4314	+	12.8286i	0.373856	+	0.213810i
$61$	−14.2449			−0.233523			−0.116762	−	0.993160i	$-0.537251\pi$
$61$	−14.2449			−0.233523			−0.116762	+	0.993160i	$0.537251\pi$
$62$			40.5745i			0.654428i
$63$	34.4892	+	58.6235i	0.547448	+	0.930532i
$64$	−8.00000			−0.125000
$65$			7.50510i			0.115463i
$66$	3.03482	−	5.30650i	0.0459821	−	0.0804016i
$67$	−35.0574			−0.523244			−0.261622	−	0.965170i	$-0.584257\pi$
$67$	−35.0574			−0.523244			−0.261622	+	0.965170i	$0.584257\pi$
$68$			17.1440i			0.252117i
$69$	99.8181	+	57.0866i	1.44664	+	0.827342i
$70$	−46.0297			−0.657567
$71$			24.2338i			0.341321i	0.985330	+	0.170660i	$0.0545901\pi$
$71$			24.2338i			0.341321i	−0.985330	+	0.170660i	$0.945410\pi$
$72$	21.9405	−	12.9080i	0.304729	−	0.179277i
$73$	10.7104			0.146717			0.0733586	−	0.997306i	$-0.476628\pi$
$73$	10.7104			0.146717			0.0733586	+	0.997306i	$0.476628\pi$
$74$		−	19.2530i		−	0.260176i
$75$	−9.60884	+	16.8014i	−0.128118	+	0.224019i
$76$	−16.9305			−0.222769
$77$			10.8891i			0.141417i
$78$	6.41790	+	3.67043i	0.0822807	+	0.0470568i
$79$	5.01487			0.0634794			0.0317397	−	0.999496i	$-0.489895\pi$
$79$	5.01487			0.0634794			0.0317397	+	0.999496i	$0.489895\pi$
$80$			17.2271i			0.215339i
$81$	−39.3462	+	70.8017i	−0.485756	+	0.874095i
$82$	45.6526			0.556739
$83$		−	51.3325i		−	0.618464i	−0.950987	−	0.309232i	$-0.899928\pi$
$83$		−	51.3325i		−	0.618464i	0.950987	−	0.309232i	$-0.100072\pi$
$84$	−22.5112	+	39.3617i	−0.267990	+	0.468592i
$85$	36.9176			0.434325
$86$			116.131i			1.35036i
$87$	109.271	+	62.4926i	1.25598	+	0.718305i
$88$	4.07535			0.0463108
$89$			62.4362i			0.701531i	0.936463	+	0.350765i	$0.114079\pi$
$89$			62.4362i			0.701531i	−0.936463	+	0.350765i	$0.885921\pi$
$90$	−27.7958	−	47.2464i	−0.308843	−	0.524960i
$91$	−13.1697			−0.144722
$92$			76.6595i			0.833256i
$93$	42.7303	−	74.7157i	0.459466	−	0.803394i
$94$	26.2222			0.278960
$95$			36.4579i			0.383767i
$96$	14.7315	+	8.42506i	0.153454	+	0.0877610i
$97$	22.0158			0.226967			0.113483	−	0.993540i	$-0.463799\pi$
$97$	22.0158			0.226967			0.113483	+	0.993540i	$0.463799\pi$
$98$		−	11.4747i		−	0.117089i
$99$	−11.1769	+	6.57556i	−0.112898	+	0.0664198i
$100$	−12.9034			−0.129034
$101$		−	73.2361i		−	0.725110i	−0.931962	−	0.362555i	$-0.881905\pi$
$101$		−	73.2361i		−	0.725110i	0.931962	−	0.362555i	$-0.118095\pi$
$102$	18.0549	−	31.5697i	0.177009	−	0.309506i
$103$	−164.838			−1.60037			−0.800185	−	0.599753i	$-0.795266\pi$
$103$	−164.838			−1.60037			−0.800185	+	0.599753i	$0.795266\pi$
$104$			4.92889i			0.0473932i
$105$	84.7611	+	48.4754i	0.807248	+	0.461670i
$106$	−120.001			−1.13208
$107$		−	172.413i		−	1.61133i	−0.592370	−	0.805666i	$-0.701808\pi$
$107$		−	172.413i		−	1.61133i	0.592370	−	0.805666i	$-0.298192\pi$
$108$	−53.9959	+	0.663029i	−0.499962	+	0.00613915i
$109$	58.9137			0.540493			0.270247	−	0.962791i	$-0.412895\pi$
$109$	58.9137			0.540493			0.270247	+	0.962791i	$0.412895\pi$
$110$		−	8.77581i		−	0.0797801i
$111$	−20.2760	+	35.4533i	−0.182666	+	0.319400i
$112$	−30.2295			−0.269906
$113$		−	43.3610i		−	0.383725i	−0.981422	−	0.191863i	$-0.938547\pi$
$113$		−	43.3610i		−	0.383725i	0.981422	−	0.191863i	$-0.0614528\pi$
$114$	31.1765	+	17.8300i	0.273478	+	0.156404i
$115$	165.078			1.43546
$116$			83.9190i			0.723440i
$117$	−7.95274	−	13.5178i	−0.0679721	−	0.115537i
$118$	−10.8628			−0.0920575
$119$			64.7817i			0.544384i
$120$	18.1424	−	31.7227i	0.151187	−	0.264356i
$121$	118.924			0.982842
$122$			20.1454i			0.165126i
$123$	−84.0666	−	48.0782i	−0.683468	−	0.390880i
$124$	57.3810			0.462750
$125$			135.455i			1.08364i
$126$	82.9062	−	48.7751i	0.657986	−	0.387104i
$127$	105.200			0.828346			0.414173	−	0.910198i	$-0.364071\pi$
$127$	105.200			0.828346			0.414173	+	0.910198i	$0.364071\pi$
$128$			11.3137i			0.0883883i
$129$	122.302	−	213.849i	0.948075	−	1.65775i
$130$	10.6138			0.0816448
$131$			114.760i			0.876027i	0.898968	+	0.438014i	$0.144318\pi$
$131$			114.760i			0.876027i	−0.898968	+	0.438014i	$0.855682\pi$
$132$	−7.50453	−	4.29188i	−0.0568525	−	0.0325143i
$133$	−63.9750			−0.481015
$134$			49.5786i			0.369990i
$135$	1.42776	+	116.274i	0.0105760	+	0.861290i
$136$	24.2452			0.178274
$137$		−	97.4172i		−	0.711074i	−0.934662	−	0.355537i	$-0.884298\pi$
$137$		−	97.4172i		−	0.711074i	0.934662	−	0.355537i	$-0.115702\pi$
$138$	80.7326	−	141.164i	0.585019	−	1.02293i
$139$	−193.546			−1.39242			−0.696210	−	0.717838i	$-0.745132\pi$
$139$	−193.546			−1.39242			−0.696210	+	0.717838i	$0.745132\pi$
$140$			65.0958i			0.464970i
$141$	−48.2867	−	27.6155i	−0.342459	−	0.195854i
$142$	34.2718			0.241350
$143$		−	2.51087i		−	0.0175585i
$144$	−18.2546	−	31.0285i	−0.126768	−	0.215476i
$145$	180.710			1.24628
$146$		−	15.1467i		−	0.103745i
$147$	−12.0844	+	21.1301i	−0.0822069	+	0.143742i
$148$	−27.2279			−0.183972
$149$			77.4438i			0.519757i	0.965641	+	0.259878i	$0.0836825\pi$
$149$			77.4438i			0.519757i	−0.965641	+	0.259878i	$0.916318\pi$
$150$	23.7608	+	13.5889i	0.158405	+	0.0905930i
$151$	−12.5262			−0.0829550			−0.0414775	−	0.999139i	$-0.513206\pi$
$151$	−12.5262			−0.0829550			−0.0414775	+	0.999139i	$0.513206\pi$
$152$			23.9433i			0.157522i
$153$	−66.4940	+	39.1196i	−0.434602	+	0.255683i
$154$	15.3995			0.0999966
$155$		−	123.564i		−	0.797185i
$156$	5.19078	−	9.07628i	0.0332742	−	0.0581813i
$157$	146.987			0.936223			0.468112	−	0.883669i	$-0.344935\pi$
$157$	146.987			0.936223			0.468112	+	0.883669i	$0.344935\pi$
$158$		−	7.09210i		−	0.0448867i
$159$	220.974	+	126.377i	1.38978	+	0.794821i
$160$	24.3628			0.152268
$161$			289.672i			1.79921i
$162$	100.129	+	55.6439i	0.618078	+	0.343481i
$163$	−246.129			−1.51000			−0.754998	−	0.655727i	$-0.772362\pi$
$163$	−246.129			−1.51000			−0.754998	+	0.655727i	$0.772362\pi$
$164$		−	64.5625i		−	0.393674i
$165$	−9.24209	+	16.1602i	−0.0560127	+	0.0979404i
$166$	−72.5951			−0.437320
$167$			25.5764i			0.153152i	0.997064	+	0.0765760i	$0.0243988\pi$
$167$			25.5764i			0.153152i	−0.997064	+	0.0765760i	$0.975601\pi$
$168$	55.6659	+	31.8356i	0.331345	+	0.189498i
$169$	−165.963			−0.982031
$170$		−	52.2094i		−	0.307114i
$171$	−38.6324	−	65.6660i	−0.225920	−	0.384012i
$172$	164.235			0.954852
$173$			174.407i			1.00813i	0.863665	+	0.504066i	$0.168163\pi$
$173$			174.407i			1.00813i	−0.863665	+	0.504066i	$0.831837\pi$
$174$	88.3778	−	154.532i	0.507918	−	0.888115i
$175$	−48.7578			−0.278616
$176$		−	5.76342i		−	0.0327467i
$177$	20.0032	+	11.4399i	0.113012	+	0.0646325i
$178$	88.2982			0.496057
$179$		−	129.907i		−	0.725735i	−0.931841	−	0.362867i	$-0.881798\pi$
$179$		−	129.907i		−	0.725735i	0.931841	−	0.362867i	$-0.118202\pi$
$180$	−66.8165	+	39.3092i	−0.371203	+	0.218385i
$181$	120.878			0.667836			0.333918	−	0.942602i	$-0.391629\pi$
$181$	120.878			0.667836			0.333918	+	0.942602i	$0.391629\pi$
$182$			18.6247i			0.102334i
$183$	21.2157	−	37.0965i	0.115933	−	0.202713i
$184$	108.413			0.589201
$185$			58.6322i			0.316931i
$186$	−105.664	−	60.4298i	−0.568086	−	0.324892i
$187$	−12.3510			−0.0660481
$188$		−	37.0838i		−	0.197254i
$189$	−204.034	+	2.50538i	−1.07954	+	0.0132560i
$190$	51.5592			0.271364
$191$		−	224.044i		−	1.17301i	−0.809947	−	0.586504i	$-0.800504\pi$
$191$		−	224.044i		−	1.17301i	0.809947	−	0.586504i	$-0.199496\pi$
$192$	11.9148	−	20.8335i	0.0620564	−	0.108508i
$193$	−280.113			−1.45136			−0.725682	−	0.688030i	$-0.758476\pi$
$193$	−280.113			−1.45136			−0.725682	+	0.688030i	$0.758476\pi$
$194$		−	31.1350i		−	0.160490i
$195$	−19.5447	−	11.1778i	−0.100229	−	0.0573218i
$196$	−16.2277			−0.0827946
$197$		−	192.055i		−	0.974900i	−0.873151	−	0.487450i	$-0.837927\pi$
$197$		−	192.055i		−	0.974900i	0.873151	−	0.487450i	$-0.162073\pi$
$198$	9.29924	+	15.8065i	0.0469659	+	0.0798309i
$199$	−198.814			−0.999065			−0.499533	−	0.866295i	$-0.666495\pi$
$199$	−198.814			−0.999065			−0.499533	+	0.866295i	$0.666495\pi$
$200$			18.2481i			0.0912406i
$201$	52.2128	−	91.2962i	0.259765	−	0.454210i
$202$	−103.571			−0.512730
$203$			317.104i			1.56209i
$204$	−44.6462	−	25.5334i	−0.218854	−	0.125164i
$205$	−139.028			−0.678186
$206$			233.116i			1.13163i
$207$	−297.329	+	174.924i	−1.43637	+	0.845042i
$208$	6.97051			0.0335121
$209$		−	12.1972i		−	0.0583597i
$210$	68.5545	−	119.870i	0.326450	−	0.570811i
$211$	−181.328			−0.859376			−0.429688	−	0.902977i	$-0.641376\pi$
$211$	−181.328			−0.859376			−0.429688	+	0.902977i	$0.641376\pi$
$212$			169.707i			0.800503i
$213$	−63.1095	−	36.0927i	−0.296289	−	0.169449i
$214$	−243.828			−1.13938
$215$		−	353.661i		−	1.64493i
$216$	0.937664	+	76.3618i	0.00434104	+	0.353527i
$217$	216.825			0.999193
$218$		−	83.3166i		−	0.382186i
$219$	−15.9515	+	27.8918i	−0.0728379	+	0.127360i
$220$	−12.4109			−0.0564131
$221$		−	14.9378i		−	0.0675918i
$222$	50.1386	+	28.6746i	0.225850	+	0.129165i
$223$	−218.828			−0.981292			−0.490646	−	0.871359i	$-0.663239\pi$
$223$	−218.828			−0.981292			−0.490646	+	0.871359i	$0.663239\pi$
$224$			42.7510i			0.190852i
$225$	−29.4432	−	50.0465i	−0.130859	−	0.222429i
$226$	−61.3217			−0.271335
$227$			127.826i			0.563109i	0.959545	+	0.281555i	$0.0908501\pi$
$227$			127.826i			0.563109i	−0.959545	+	0.281555i	$0.909150\pi$
$228$	25.2155	−	44.0903i	0.110594	−	0.193378i
$229$	177.398			0.774665			0.387333	−	0.921940i	$-0.373397\pi$
$229$	177.398			0.774665			0.387333	+	0.921940i	$0.373397\pi$
$230$		−	233.455i		−	1.01502i
$231$	−28.3573	−	16.2177i	−0.122759	−	0.0702064i
$232$	118.679			0.511549
$233$		−	385.121i		−	1.65288i	−0.563026	−	0.826439i	$-0.690363\pi$
$233$		−	385.121i		−	1.65288i	0.563026	−	0.826439i	$-0.309637\pi$
$234$	−19.1170	+	11.2469i	−0.0816967	+	0.0480636i
$235$	−79.8559			−0.339812
$236$			15.3623i			0.0650945i
$237$	−7.46892	+	13.0597i	−0.0315144	+	0.0551042i
$238$	91.6152			0.384938
$239$			217.107i			0.908397i	0.890901	+	0.454198i	$0.150074\pi$
$239$			217.107i			0.908397i	−0.890901	+	0.454198i	$0.849926\pi$
$240$	−44.8627	−	25.6573i	−0.186928	−	0.106905i
$241$	−317.112			−1.31582			−0.657910	−	0.753097i	$-0.728559\pi$
$241$	−317.112			−1.31582			−0.657910	+	0.753097i	$0.728559\pi$
$242$		−	168.184i		−	0.694975i
$243$	−125.781	−	207.914i	−0.517617	−	0.855613i
$244$	28.4898			0.116762
$245$			34.9446i			0.142631i
$246$	−67.9928	+	118.888i	−0.276394	+	0.483285i
$247$	14.7518			0.0597237
$248$		−	81.1490i		−	0.327214i
$249$	133.680	+	76.4523i	0.536867	+	0.307037i
$250$	191.563			0.766251
$251$			143.873i			0.573201i	0.958050	+	0.286601i	$0.0925253\pi$
$251$			143.873i			0.573201i	−0.958050	+	0.286601i	$0.907475\pi$
$252$	−68.9784	−	117.247i	−0.273724	−	0.465266i
$253$	−55.2276			−0.218291
$254$		−	148.775i		−	0.585729i
$255$	−54.9834	+	96.1407i	−0.215621	+	0.377022i
$256$	16.0000			0.0625000
$257$		−	16.4196i		−	0.0638893i	−0.999490	−	0.0319447i	$-0.989830\pi$
$257$		−	16.4196i		−	0.0638893i	0.999490	−	0.0319447i	$-0.0101700\pi$
$258$	−302.429	−	172.961i	−1.17220	−	0.670390i
$259$	−102.886			−0.397242
$260$		−	15.0102i		−	0.0577316i
$261$	−325.485	+	191.489i	−1.24707	+	0.733672i
$262$	162.295			0.619445
$263$			92.1036i			0.350204i	0.984550	+	0.175102i	$0.0560255\pi$
$263$			92.1036i			0.350204i	−0.984550	+	0.175102i	$0.943974\pi$
$264$	−6.06964	+	10.6130i	−0.0229911	+	0.0402008i
$265$	365.444			1.37903
$266$			90.4743i			0.340129i
$267$	−162.596	−	92.9896i	−0.608974	−	0.348276i
$268$	70.1148			0.261622
$269$		−	311.229i		−	1.15698i	−0.815688	−	0.578492i	$-0.803641\pi$
$269$		−	311.229i		−	1.15698i	0.815688	−	0.578492i	$-0.196359\pi$
$270$	164.437	−	2.01915i	0.609024	−	0.00747835i
$271$	431.054			1.59061			0.795303	−	0.606212i	$-0.207312\pi$
$271$	431.054			1.59061			0.795303	+	0.606212i	$0.207312\pi$
$272$		−	34.2880i		−	0.126059i
$273$	19.6143	−	34.2964i	0.0718473	−	0.125628i
$274$	−137.769			−0.502806
$275$		−	9.29594i		−	0.0338034i
$276$	−199.636	−	114.173i	−0.723320	−	0.413671i
$277$	−185.215			−0.668647			−0.334324	−	0.942458i	$-0.608508\pi$
$277$	−185.215			−0.668647			−0.334324	+	0.942458i	$0.608508\pi$
$278$			273.716i			0.984590i
$279$	130.933	+	222.556i	0.469296	+	0.797692i
$280$	92.0594			0.328784
$281$			340.216i			1.21073i	0.795947	+	0.605367i	$0.206973\pi$
$281$			340.216i			1.21073i	−0.795947	+	0.605367i	$0.793027\pi$
$282$	−39.0542	+	68.2878i	−0.138490	+	0.242155i
$283$	423.667			1.49706			0.748529	−	0.663102i	$-0.230761\pi$
$283$	423.667			1.49706			0.748529	+	0.663102i	$0.230761\pi$
$284$		−	48.4676i		−	0.170660i
$285$	−94.9434	−	54.2987i	−0.333135	−	0.190522i
$286$	−3.55091			−0.0124158
$287$		−	243.961i		−	0.850039i
$288$	−43.8810	+	25.8159i	−0.152364	+	0.0896386i
$289$	215.521			0.745747
$290$		−	255.563i		−	0.881251i
$291$	−32.7893	+	57.3333i	−0.112678	+	0.197022i
$292$	−21.4207			−0.0733586
$293$		−	449.203i		−	1.53312i	−0.642175	−	0.766558i	$-0.721968\pi$
$293$		−	449.203i		−	1.53312i	0.642175	−	0.766558i	$-0.278032\pi$
$294$	29.8825	+	17.0900i	0.101641	+	0.0581291i
$295$	33.0810			0.112139
$296$			38.5060i			0.130088i
$297$	−0.477664	−	38.9001i	−0.00160830	−	0.130977i
$298$	109.522			0.367524
$299$		−	66.7945i		−	0.223393i
$300$	19.2177	−	33.6029i	0.0640589	−	0.112010i
$301$	620.591			2.06176
$302$			17.7147i			0.0586580i
$303$	190.721	+	109.074i	0.629442	+	0.359982i
$304$	33.8610			0.111385
$305$		−	61.3497i		−	0.201146i
$306$	55.3234	+	94.0368i	0.180795	+	0.307310i
$307$	−572.633			−1.86525			−0.932626	−	0.360843i	$-0.882489\pi$
$307$	−572.633			−1.86525			−0.932626	+	0.360843i	$0.882489\pi$
$308$		−	21.7781i		−	0.0707083i
$309$	245.502	−	429.271i	0.794506	−	1.38923i
$310$	−174.745			−0.563695
$311$		−	429.652i		−	1.38152i	−0.723086	−	0.690758i	$-0.757277\pi$
$311$		−	429.652i		−	1.38152i	0.723086	−	0.690758i	$-0.242723\pi$
$312$	−12.8358	−	7.34087i	−0.0411404	−	0.0235284i
$313$	−12.6944			−0.0405573			−0.0202787	−	0.999794i	$-0.506455\pi$
$313$	−12.6944			−0.0405573			−0.0202787	+	0.999794i	$0.506455\pi$
$314$		−	207.871i		−	0.662010i
$315$	−252.478	+	148.537i	−0.801519	+	0.471547i
$316$	−10.0297			−0.0317397
$317$		−	243.873i		−	0.769316i	−0.923059	−	0.384658i	$-0.874319\pi$
$317$		−	243.873i		−	0.769316i	0.923059	−	0.384658i	$-0.125681\pi$
$318$	178.723	−	312.505i	0.562024	−	0.982720i
$319$	−60.4575			−0.189522
$320$		−	34.4542i		−	0.107669i
$321$	448.996	+	256.783i	1.39874	+	0.799948i
$322$	409.658			1.27223
$323$		−	72.5639i		−	0.224656i
$324$	78.6924	−	141.603i	0.242878	−	0.437047i
$325$	11.2429			0.0345935
$326$			348.079i			1.06773i
$327$	−87.7434	+	153.423i	−0.268328	+	0.469183i
$328$	−91.3051			−0.278369
$329$		−	140.128i		−	0.425921i
$330$	22.8539	+	13.0703i	0.0692543	+	0.0396069i
$331$	51.0402			0.154200			0.0770999	−	0.997023i	$-0.475434\pi$
$331$	51.0402			0.154200			0.0770999	+	0.997023i	$0.475434\pi$
$332$			102.665i			0.309232i
$333$	−62.1293	−	105.605i	−0.186574	−	0.317133i
$334$	36.1705			0.108295
$335$		−	150.984i		−	0.450699i
$336$	45.0224	−	78.7234i	0.133995	−	0.234296i
$337$	124.288			0.368808			0.184404	−	0.982851i	$-0.440965\pi$
$337$	124.288			0.368808			0.184404	+	0.982851i	$0.440965\pi$
$338$			234.707i			0.694401i
$339$	112.920	+	64.5798i	0.333098	+	0.190501i
$340$	−73.8353			−0.217163
$341$			41.3389i			0.121228i
$342$	−92.8657	+	54.6345i	−0.271537	+	0.159750i
$343$	308.992			0.900850
$344$		−	232.263i		−	0.675182i
$345$	−245.859	+	429.894i	−0.712635	+	1.24607i
$346$	246.648			0.712857
$347$			326.948i			0.942214i	0.882076	+	0.471107i	$0.156145\pi$
$347$			326.948i			0.942214i	−0.882076	+	0.471107i	$0.843855\pi$
$348$	−218.541	−	124.985i	−0.627992	−	0.359153i
$349$	166.626			0.477439			0.238720	−	0.971089i	$-0.423272\pi$
$349$	166.626			0.477439			0.238720	+	0.971089i	$0.423272\pi$
$350$			68.9539i			0.197011i
$351$	47.0474	−	0.577706i	0.134038	−	0.00164589i
$352$	−8.15070			−0.0231554
$353$		−	334.717i		−	0.948207i	−0.880469	−	0.474104i	$-0.842772\pi$
$353$		−	334.717i		−	0.948207i	0.880469	−	0.474104i	$-0.157228\pi$
$354$	16.1785	−	28.2888i	0.0457020	−	0.0799118i
$355$	−104.370			−0.293999
$356$		−	124.872i		−	0.350765i
$357$	−168.704	−	96.4829i	−0.472561	−	0.270260i
$358$	−183.716			−0.513172
$359$			428.484i			1.19355i	0.802409	+	0.596774i	$0.203551\pi$
$359$			428.484i			1.19355i	−0.802409	+	0.596774i	$0.796449\pi$
$360$	55.5917	+	94.4927i	0.154421	+	0.262480i
$361$	−289.340			−0.801495
$362$		−	170.948i		−	0.472232i
$363$	−177.120	+	309.701i	−0.487933	+	0.853171i
$364$	26.3394			0.0723609
$365$			46.1271i			0.126376i
$366$	−52.4624	−	30.0036i	−0.143340	−	0.0819769i
$367$	72.4790			0.197490			0.0987452	−	0.995113i	$-0.468517\pi$
$367$	72.4790			0.197490			0.0987452	+	0.995113i	$0.468517\pi$
$368$		−	153.319i		−	0.416628i
$369$	250.410	−	147.320i	0.678617	−	0.399242i
$370$	82.9185			0.224104
$371$			641.268i			1.72849i
$372$	−85.4607	+	149.431i	−0.229733	+	0.401697i
$373$	−184.577			−0.494844			−0.247422	−	0.968908i	$-0.579583\pi$
$373$	−184.577			−0.494844			−0.247422	+	0.968908i	$0.579583\pi$
$374$			17.4669i			0.0467030i
$375$	−352.752	−	201.741i	−0.940672	−	0.537976i
$376$	−52.4444			−0.139480
$377$		−	73.1198i		−	0.193952i
$378$	3.54314	+	288.547i	0.00937338	+	0.763352i
$379$	350.819			0.925644			0.462822	−	0.886451i	$-0.346837\pi$
$379$	350.819			0.925644			0.462822	+	0.886451i	$0.346837\pi$
$380$		−	72.9158i		−	0.191884i
$381$	−156.680	+	273.961i	−0.411234	+	0.719058i
$382$	−316.847			−0.829442
$383$			509.957i			1.33148i	0.746183	+	0.665741i	$0.231884\pi$
$383$			509.957i			1.33148i	−0.746183	+	0.665741i	$0.768116\pi$
$384$	−29.4631	−	16.8501i	−0.0767268	−	0.0438805i
$385$	−46.8968			−0.121810
$386$			396.140i			1.02627i
$387$	374.755	+	636.995i	0.968358	+	1.64598i
$388$	−44.0316			−0.113483
$389$		−	326.339i		−	0.838918i	−0.907774	−	0.419459i	$-0.862220\pi$
$389$		−	326.339i		−	0.838918i	0.907774	−	0.419459i	$-0.137780\pi$
$390$	−15.8077	+	27.6404i	−0.0405326	+	0.0708729i
$391$	−328.562			−0.840313
$392$			22.9495i			0.0585446i
$393$	−298.856	−	170.918i	−0.760448	−	0.434905i
$394$	−271.607			−0.689359
$395$			21.5979i			0.0546783i
$396$	22.3538	−	13.1511i	0.0564490	−	0.0332099i
$397$	−612.557			−1.54296			−0.771482	−	0.636251i	$-0.780484\pi$
$397$	−612.557			−1.54296			−0.771482	+	0.636251i	$0.780484\pi$
$398$			281.165i			0.706446i
$399$	95.2814	−	166.603i	0.238800	−	0.417552i
$400$	25.8067			0.0645168
$401$			699.110i			1.74342i	0.490025	+	0.871708i	$0.336988\pi$
$401$			699.110i			1.74342i	−0.490025	+	0.871708i	$0.663012\pi$
$402$	−129.112	−	73.8401i	−0.321175	−	0.183682i
$403$	−49.9969			−0.124062
$404$			146.472i			0.362555i
$405$	−304.927	−	169.455i	−0.752906	−	0.418408i
$406$	448.452			1.10456
$407$		−	19.6157i		−	0.0481959i
$408$	−36.1097	+	63.1393i	−0.0885043	+	0.154753i
$409$	614.945			1.50353			0.751767	−	0.659429i	$-0.229202\pi$
$409$	614.945			1.50353			0.751767	+	0.659429i	$0.229202\pi$
$410$			196.615i			0.479550i
$411$	253.693	+	145.089i	0.617259	+	0.353014i
$412$	329.676			0.800185
$413$			58.0493i			0.140555i
$414$	247.379	+	420.487i	0.597535	+	1.01567i
$415$	221.078			0.532717
$416$		−	9.85779i		−	0.0236966i
$417$	288.259	−	504.033i	0.691269	−	1.20871i
$418$	−17.2494			−0.0412666
$419$		−	102.324i		−	0.244211i	−0.992517	−	0.122105i	$-0.961035\pi$
$419$		−	102.324i		−	0.244211i	0.992517	−	0.122105i	$-0.0389646\pi$
$420$	−169.522	−	96.9507i	−0.403624	−	0.230835i
$421$	−41.8359			−0.0993728			−0.0496864	−	0.998765i	$-0.515822\pi$
$421$	−41.8359			−0.0993728			−0.0496864	+	0.998765i	$0.515822\pi$
$422$			256.437i			0.607671i
$423$	143.832	−	84.6188i	0.340029	−	0.200044i
$424$	240.001			0.566041
$425$		−	55.3037i		−	0.130126i
$426$	−51.0428	+	89.2503i	−0.119819	+	0.209508i
$427$	107.654			0.252117
$428$			344.825i			0.805666i
$429$	6.53880	+	3.73958i	0.0152420	+	0.00871696i
$430$	−500.152			−1.16314
$431$		−	135.042i		−	0.313322i	−0.987652	−	0.156661i	$-0.949927\pi$
$431$		−	135.042i		−	0.313322i	0.987652	−	0.156661i	$-0.0500730\pi$
$432$	107.992	−	1.32606i	0.249981	−	0.00306958i
$433$	90.1298			0.208152			0.104076	−	0.994569i	$-0.466811\pi$
$433$	90.1298			0.208152			0.104076	+	0.994569i	$0.466811\pi$
$434$		−	306.637i		−	0.706536i
$435$	−269.141	+	470.604i	−0.618716	+	1.08185i
$436$	−117.827			−0.270247
$437$		−	324.471i		−	0.742496i
$438$	39.4450	+	22.5588i	0.0900571	+	0.0515042i
$439$	721.675			1.64391			0.821953	−	0.569555i	$-0.192884\pi$
$439$	721.675			1.64391			0.821953	+	0.569555i	$0.192884\pi$
$440$			17.5516i			0.0398901i
$441$	−37.0289	−	62.9403i	−0.0839657	−	0.142722i
$442$	−21.1252			−0.0477946
$443$			568.366i			1.28299i	0.767126	+	0.641496i	$0.221686\pi$
$443$			568.366i			1.28299i	−0.767126	+	0.641496i	$0.778314\pi$
$444$	40.5520	−	70.9067i	0.0913332	−	0.159700i
$445$	−268.899			−0.604267
$446$			309.470i			0.693878i
$447$	−201.679	−	115.341i	−0.451182	−	0.258034i
$448$	60.4590			0.134953
$449$			637.032i			1.41878i	0.704816	+	0.709390i	$0.251029\pi$
$449$			637.032i			1.41878i	−0.704816	+	0.709390i	$0.748971\pi$
$450$	−70.7765	+	41.6390i	−0.157281	+	0.0925311i
$451$	46.5126			0.103132
$452$			86.7219i			0.191863i
$453$	18.6559	−	32.6207i	0.0411831	−	0.0720103i
$454$	180.773			0.398179
$455$		−	56.7189i		−	0.124657i
$456$	−62.3530	−	35.6601i	−0.136739	−	0.0782019i
$457$	464.295			1.01596			0.507982	−	0.861368i	$-0.330392\pi$
$457$	464.295			1.01596			0.507982	+	0.861368i	$0.330392\pi$
$458$		−	250.879i		−	0.547771i
$459$	−2.84174	−	231.426i	−0.00619115	−	0.504197i
$460$	−330.155			−0.717729
$461$			226.153i			0.490570i	0.969451	+	0.245285i	$0.0788816\pi$
$461$			226.153i			0.490570i	−0.969451	+	0.245285i	$0.921118\pi$
$462$	−22.9353	+	40.1032i	−0.0496434	+	0.0868035i
$463$	518.157			1.11913			0.559565	−	0.828787i	$-0.310968\pi$
$463$	518.157			1.11913			0.559565	+	0.828787i	$0.310968\pi$
$464$		−	167.838i		−	0.361720i
$465$	321.784	+	184.030i	0.692008	+	0.395763i
$466$	−544.643			−1.16876
$467$		−	76.6230i		−	0.164075i	−0.996629	−	0.0820374i	$-0.973857\pi$
$467$		−	76.6230i		−	0.164075i	0.996629	−	0.0820374i	$-0.0261427\pi$
$468$	15.9055	+	27.0356i	0.0339861	+	0.0577683i
$469$	264.942			0.564908
$470$			112.933i			0.240283i
$471$	−218.916	+	382.783i	−0.464789	+	0.812702i
$472$	21.7256			0.0460287
$473$			118.319i			0.250146i
$474$	18.4692	+	10.5626i	0.0389646	+	0.0222841i
$475$	54.6150			0.114979
$476$		−	129.563i		−	0.272192i
$477$	−658.218	+	387.241i	−1.37991	+	0.811826i
$478$	307.035			0.642333
$479$		−	533.564i		−	1.11391i	−0.830542	−	0.556956i	$-0.811969\pi$
$479$		−	533.564i		−	1.11391i	0.830542	−	0.556956i	$-0.188031\pi$
$480$	−36.2848	+	63.4455i	−0.0755934	+	0.132178i
$481$	23.7240			0.0493223
$482$			448.465i			0.930425i
$483$	−754.363	−	431.425i	−1.56183	−	0.893219i
$484$	−237.848			−0.491421
$485$			94.8170i			0.195499i
$486$	−294.035	+	177.881i	−0.605009	+	0.366010i
$487$	489.185			1.00449			0.502243	−	0.864726i	$-0.332508\pi$
$487$	489.185			1.00449			0.502243	+	0.864726i	$0.332508\pi$
$488$		−	40.2907i		−	0.0825629i
$489$	366.574	−	640.969i	0.749639	−	1.31077i
$490$	49.4191			0.100855
$491$		−	606.586i		−	1.23541i	−0.786411	−	0.617704i	$-0.788063\pi$
$491$		−	606.586i		−	1.23541i	0.786411	−	0.617704i	$-0.211937\pi$
$492$	168.133	+	96.1564i	0.341734	+	0.195440i
$493$	−359.676			−0.729567
$494$		−	20.8621i		−	0.0422310i
$495$	−28.3194	−	48.1364i	−0.0572110	−	0.0972453i
$496$	−114.762			−0.231375
$497$		−	183.144i		−	0.368499i
$498$	108.120	−	189.052i	0.217108	−	0.379622i
$499$	−369.127			−0.739733			−0.369867	−	0.929085i	$-0.620597\pi$
$499$	−369.127			−0.739733			−0.369867	+	0.929085i	$0.620597\pi$
$500$		−	270.911i		−	0.541821i
$501$	−66.6059	−	38.0923i	−0.132946	−	0.0760326i
$502$	203.468			0.405314
$503$		−	400.802i		−	0.796823i	−0.917207	−	0.398412i	$-0.869562\pi$
$503$		−	400.802i		−	0.796823i	0.917207	−	0.398412i	$-0.130438\pi$
$504$	−165.812	+	97.5502i	−0.328993	+	0.193552i
$505$	315.411			0.624577
$506$			78.1036i			0.154355i
$507$	247.178	−	432.200i	0.487531	−	0.852466i
$508$	−210.400			−0.414173
$509$			299.978i			0.589347i	0.955598	+	0.294674i	$0.0952110\pi$
$509$			299.978i			0.589347i	−0.955598	+	0.294674i	$0.904789\pi$
$510$	135.963	+	77.7583i	0.266595	+	0.152467i
$511$	−80.9421			−0.158399
$512$		−	22.6274i		−	0.0441942i
$513$	228.544	−	2.80635i	0.445505	−	0.00547046i
$514$	−23.2208			−0.0451766
$515$		−	709.921i		−	1.37849i
$516$	−244.603	+	427.699i	−0.474038	+	0.828873i
$517$	26.7162			0.0516754
$518$			145.502i			0.280892i
$519$	−454.189	−	259.753i	−0.875123	−	0.500488i
$520$	−21.2276			−0.0408224
$521$		−	708.930i		−	1.36071i	−0.732883	−	0.680355i	$-0.761826\pi$
$521$		−	708.930i		−	1.36071i	0.732883	−	0.680355i	$-0.238174\pi$
$522$	270.806	+	460.306i	0.518785	+	0.881812i
$523$	416.470			0.796310			0.398155	−	0.917318i	$-0.369651\pi$
$523$	416.470			0.796310			0.398155	+	0.917318i	$0.369651\pi$
$524$		−	229.519i		−	0.438014i
$525$	72.6176	−	126.975i	0.138319	−	0.241856i
$526$	130.254			0.247632
$527$			245.935i			0.466669i
$528$	15.0091	+	8.58377i	0.0284262	+	0.0162571i
$529$	−940.171			−1.77726
$530$		−	516.816i		−	0.975125i
$531$	−59.5837	+	35.0541i	−0.112210	+	0.0660152i
$532$	127.950			0.240507
$533$			56.2542i			0.105542i
$534$	−131.507	+	229.946i	−0.246268	+	0.430610i
$535$	742.542			1.38793
$536$		−	99.1572i		−	0.184995i
$537$	338.302	+	193.477i	0.629985	+	0.360292i
$538$	−440.144			−0.818112
$539$		−	11.6909i		−	0.0216900i
$540$	−2.85552	−	232.548i	−0.00528799	−	0.430645i
$541$	684.135			1.26457			0.632287	−	0.774734i	$-0.282116\pi$
$541$	684.135			1.26457			0.632287	+	0.774734i	$0.282116\pi$
$542$		−	609.603i		−	1.12473i
$543$	−180.031	+	314.791i	−0.331548	+	0.579725i
$544$	−48.4905			−0.0891369
$545$			253.728i			0.465557i
$546$	−48.5024	−	27.7388i	−0.0888323	−	0.0508037i
$547$	−585.998			−1.07130			−0.535648	−	0.844442i	$-0.679932\pi$
$547$	−585.998			−1.07130			−0.535648	+	0.844442i	$0.679932\pi$
$548$			194.834i			0.355537i
$549$	65.0088	+	110.500i	0.118413	+	0.201275i
$550$	−13.1464			−0.0239026
$551$		−	355.197i		−	0.644641i
$552$	−161.465	+	282.328i	−0.292510	+	0.511464i
$553$	−37.8993			−0.0685339
$554$			261.934i			0.472805i
$555$	−152.690	−	87.3241i	−0.275116	−	0.157341i
$556$	387.093			0.696210
$557$			994.178i			1.78488i	0.451167	+	0.892440i	$0.351008\pi$
$557$			994.178i			1.78488i	−0.451167	+	0.892440i	$0.648992\pi$
$558$	314.742	−	185.168i	0.564054	−	0.331842i
$559$	−143.100			−0.255992
$560$		−	130.192i		−	0.232485i
$561$	18.3950	−	32.1644i	0.0327896	−	0.0573340i
$562$	481.138			0.856118
$563$		−	365.647i		−	0.649462i	−0.945806	−	0.324731i	$-0.894726\pi$
$563$		−	365.647i		−	0.649462i	0.945806	−	0.324731i	$-0.105274\pi$
$564$	96.5735	+	55.2309i	0.171230	+	0.0979272i
$565$	186.746			0.330524
$566$		−	599.156i		−	1.05858i
$567$	297.354	−	535.075i	0.524434	−	0.943694i
$568$	−68.5435			−0.120675
$569$			546.268i			0.960049i	0.877255	+	0.480024i	$0.159372\pi$
$569$			546.268i			0.960049i	−0.877255	+	0.480024i	$0.840628\pi$
$570$	−76.7900	+	134.270i	−0.134719	+	0.235562i
$571$	485.449			0.850173			0.425086	−	0.905153i	$-0.360244\pi$
$571$	485.449			0.850173			0.425086	+	0.905153i	$0.360244\pi$
$572$			5.02174i			0.00877927i
$573$	583.455	+	333.681i	1.01825	+	0.582341i
$574$	−345.013			−0.601069
$575$		−	247.291i		−	0.430072i
$576$	36.5092	+	62.0571i	0.0633840	+	0.107738i
$577$	415.829			0.720673			0.360337	−	0.932822i	$-0.382662\pi$
$577$	415.829			0.720673			0.360337	+	0.932822i	$0.382662\pi$
$578$		−	304.793i		−	0.527323i
$579$	417.188	−	729.470i	0.720532	−	1.25988i
$580$	−361.420			−0.623139
$581$			387.939i			0.667709i
$582$	81.0816	+	46.3710i	0.139315	+	0.0796753i
$583$	−122.261			−0.209711
$584$			30.2935i			0.0518724i
$585$	58.2181	−	34.2507i	0.0995181	−	0.0585481i
$586$	−635.269			−1.08408
$587$			746.799i			1.27223i	0.771594	+	0.636115i	$0.219460\pi$
$587$			746.799i			1.27223i	−0.771594	+	0.636115i	$0.780540\pi$
$588$	24.1688	−	42.2602i	0.0411035	−	0.0718710i
$589$	−242.872			−0.412347
$590$		−	46.7836i		−	0.0792942i
$591$	500.149	+	286.038i	0.846277	+	0.483991i
$592$	54.4558			0.0919861
$593$			375.211i			0.632733i	0.948637	+	0.316366i	$0.102463\pi$
$593$			375.211i			0.632733i	−0.948637	+	0.316366i	$0.897537\pi$
$594$	−55.0131	+	0.675519i	−0.0926147	+	0.00113724i
$595$	−279.000			−0.468908
$596$		−	154.888i		−	0.259878i
$597$	296.104	−	517.750i	0.495987	−	0.867253i
$598$	−94.4617			−0.157963
$599$		−	642.551i		−	1.07271i	−0.843993	−	0.536353i	$-0.819801\pi$
$599$		−	642.551i		−	1.07271i	0.843993	−	0.536353i	$-0.180199\pi$
$600$	−47.5216	−	27.1779i	−0.0792027	−	0.0452965i
$601$	107.097			0.178199			0.0890993	−	0.996023i	$-0.471601\pi$
$601$	107.097			0.178199			0.0890993	+	0.996023i	$0.471601\pi$
$602$		−	877.648i		−	1.45789i
$603$	159.990	+	271.945i	0.265323	+	0.450986i
$604$	25.0524			0.0414775
$605$			512.179i			0.846576i
$606$	154.255	−	269.720i	0.254545	−	0.445083i
$607$	−782.020			−1.28834			−0.644168	−	0.764884i	$-0.722796\pi$
$607$	−782.020			−1.28834			−0.644168	+	0.764884i	$0.722796\pi$
$608$		−	47.8866i		−	0.0787609i
$609$	−825.799	−	472.279i	−1.35599	−	0.775500i
$610$	−86.7615			−0.142232
$611$			32.3116i			0.0528832i
$612$	132.988	−	78.2391i	0.217301	−	0.127842i
$613$	−463.459			−0.756051			−0.378025	−	0.925795i	$-0.623397\pi$
$613$	−463.459			−0.756051			−0.378025	+	0.925795i	$0.623397\pi$
$614$			809.825i			1.31893i
$615$	207.062	−	362.056i	0.336686	−	0.588709i
$616$	−30.7990			−0.0499983
$617$			47.3205i			0.0766945i	0.999264	+	0.0383472i	$0.0122093\pi$
$617$			47.3205i			0.0766945i	−0.999264	+	0.0383472i	$0.987791\pi$
$618$	−607.080	−	347.193i	−0.982331	−	0.561801i
$619$	−186.924			−0.301978			−0.150989	−	0.988535i	$-0.548246\pi$
$619$	−186.924			−0.301978			−0.150989	+	0.988535i	$0.548246\pi$
$620$			247.127i			0.398592i
$621$	−12.7069	−	1034.83i	−0.0204619	−	1.66639i
$622$	−607.619			−0.976879
$623$		−	471.854i		−	0.757390i
$624$	−10.3816	+	18.1526i	−0.0166371	+	0.0290906i
$625$	−422.084			−0.675334
$626$			17.9527i			0.0286784i
$627$	31.7638	+	18.1659i	0.0506600	+	0.0289728i
$628$	−293.974			−0.468112
$629$		−	116.699i		−	0.185530i
$630$	210.063	+	357.058i	0.333434	+	0.566759i
$631$	1227.59			1.94546			0.972731	−	0.231934i	$-0.0745054\pi$
$631$	1227.59			1.94546			0.972731	+	0.231934i	$0.0745054\pi$
$632$			14.1842i			0.0224434i
$633$	270.062	−	472.214i	0.426638	−	0.745994i
$634$	−344.889			−0.543989
$635$			453.073i			0.713500i
$636$	−441.949	−	252.753i	−0.694888	−	0.397411i
$637$	14.1394			0.0221969
$638$			85.4999i			0.134012i
$639$	187.985	−	110.595i	0.294186	−	0.173074i
$640$	−48.7256			−0.0761338
$641$			221.674i			0.345825i	0.984937	+	0.172912i	$0.0553178\pi$
$641$			221.674i			0.345825i	−0.984937	+	0.172912i	$0.944682\pi$
$642$	363.146	−	634.976i	0.565649	−	0.989059i
$643$	−998.147			−1.55233			−0.776164	−	0.630531i	$-0.782837\pi$
$643$	−998.147			−1.55233			−0.776164	+	0.630531i	$0.782837\pi$
$644$		−	579.345i		−	0.899603i
$645$	921.001	+	526.726i	1.42791	+	0.816629i
$646$	−102.621			−0.158856
$647$		−	658.871i		−	1.01835i	−0.860664	−	0.509174i	$-0.829951\pi$
$647$		−	658.871i		−	1.01835i	0.860664	−	0.509174i	$-0.170049\pi$
$648$	−200.257	−	111.288i	−0.309039	−	0.171741i
$649$	−11.0674			−0.0170530
$650$		−	15.8998i		−	0.0244613i
$651$	−322.929	+	564.654i	−0.496051	+	0.867364i
$652$	492.259			0.754998
$653$		−	228.454i		−	0.349853i	−0.984581	−	0.174927i	$-0.944031\pi$
$653$		−	228.454i		−	0.349853i	0.984581	−	0.174927i	$-0.0559688\pi$
$654$	216.973	+	124.088i	0.331762	+	0.189737i
$655$	−494.244			−0.754571
$656$			129.125i			0.196837i
$657$	−48.8783	−	83.0816i	−0.0743962	−	0.126456i
$658$	−198.171			−0.301172
$659$			885.023i			1.34298i	0.741015	+	0.671489i	$0.234345\pi$
$659$			885.023i			1.34298i	−0.741015	+	0.671489i	$0.765655\pi$
$660$	18.4842	−	32.3203i	0.0280063	−	0.0489702i
$661$	−1058.11			−1.60078			−0.800388	−	0.599482i	$-0.795373\pi$
$661$	−1058.11			−1.60078			−0.800388	+	0.599482i	$0.795373\pi$
$662$		−	72.1817i		−	0.109036i
$663$	38.9009	+	22.2476i	0.0586740	+	0.0335560i
$664$	145.190			0.218660
$665$		−	275.526i		−	0.414325i
$666$	−149.348	+	87.8641i	−0.224247	+	0.131928i
$667$	−1608.30			−2.41124
$668$		−	51.1528i		−	0.0765760i
$669$	325.912	−	569.871i	0.487164	−	0.851825i
$670$	−213.524			−0.318693
$671$			20.5249i			0.0305885i
$672$	−111.332	−	63.6713i	−0.165672	−	0.0947489i
$673$	−469.585			−0.697748			−0.348874	−	0.937170i	$-0.613436\pi$
$673$	−469.585			−0.697748			−0.348874	+	0.937170i	$0.613436\pi$
$674$		−	175.770i		−	0.260787i
$675$	174.182	−	2.13882i	0.258048	−	0.00316863i
$676$	331.927			0.491016
$677$			443.218i			0.654679i	0.944907	+	0.327340i	$0.106152\pi$
$677$			443.218i			0.654679i	−0.944907	+	0.327340i	$0.893848\pi$
$678$	91.3297	−	159.693i	0.134705	−	0.235536i
$679$	−166.381			−0.245039
$680$			104.419i			0.153557i
$681$	−332.883	−	190.378i	−0.488815	−	0.279556i
$682$	58.4620			0.0857214
$683$		−	1328.21i		−	1.94468i	−0.233579	−	0.972338i	$-0.575044\pi$
$683$		−	1328.21i		−	1.94468i	0.233579	−	0.972338i	$-0.424956\pi$
$684$	77.2648	+	131.332i	0.112960	+	0.192006i
$685$	419.554			0.612488
$686$		−	436.980i		−	0.636997i
$687$	−264.209	+	461.980i	−0.384583	+	0.672459i
$688$	−328.469			−0.477426
$689$		−	147.868i		−	0.214612i
$690$	607.962	+	347.697i	0.881105	+	0.503909i
$691$	48.5779			0.0703008			0.0351504	−	0.999382i	$-0.488809\pi$
$691$	48.5779			0.0703008			0.0351504	+	0.999382i	$0.488809\pi$
$692$		−	348.814i		−	0.504066i
$693$	84.4680	−	49.6939i	0.121887	−	0.0717084i
$694$	462.375			0.666246
$695$		−	833.561i		−	1.19937i
$696$	−176.756	+	309.064i	−0.253959	+	0.444058i
$697$	276.714			0.397008
$698$		−	235.645i		−	0.337600i
$699$	1002.93	+	573.581i	1.43481	+	0.820574i
$700$	97.5155			0.139308
$701$			61.1899i			0.0872895i	0.999047	+	0.0436447i	$0.0138970\pi$
$701$			61.1899i			0.0872895i	−0.999047	+	0.0436447i	$0.986103\pi$
$702$	−0.816999	−	66.5350i	−0.00116382	−	0.0947793i
$703$	115.245			0.163934
$704$			11.5268i			0.0163733i
$705$	118.934	−	207.960i	0.168700	−	0.294979i
$706$	−473.362			−0.670484
$707$			553.472i			0.782846i
$708$	−40.0064	−	22.8799i	−0.0565062	−	0.0323162i
$709$	−74.1032			−0.104518			−0.0522590	−	0.998634i	$-0.516642\pi$
$709$	−74.1032			−0.104518			−0.0522590	+	0.998634i	$0.516642\pi$
$710$			147.601i			0.207888i
$711$	−22.8861	−	38.9010i	−0.0321886	−	0.0547131i
$712$	−176.596			−0.248029
$713$			1099.70i			1.54236i
$714$	−136.447	+	238.584i	−0.191103	+	0.334151i
$715$	10.8138			0.0151241
$716$			259.813i			0.362867i
$717$	−565.388	−	323.349i	−0.788547	−	0.450975i
$718$	605.968			0.843966
$719$			723.283i			1.00596i	0.864299	+	0.502978i	$0.167762\pi$
$719$			723.283i			1.00596i	−0.864299	+	0.502978i	$0.832238\pi$
$720$	133.633	−	78.6185i	0.185601	−	0.109192i
$721$	1245.74			1.72780
$722$			409.188i			0.566743i
$723$	472.293	−	825.822i	0.653240	−	1.14222i
$724$	−241.757			−0.333918
$725$		−	270.709i		−	0.373392i
$726$	437.983	+	250.485i	0.603283	+	0.345021i
$727$	−516.229			−0.710081			−0.355041	−	0.934851i	$-0.615533\pi$
$727$	−516.229			−0.710081			−0.355041	+	0.934851i	$0.615533\pi$
$728$		−	37.2495i		−	0.0511669i
$729$	728.780	−	17.9004i	0.999698	−	0.0245548i
$730$	65.2336			0.0893610
$731$			703.908i			0.962939i
$732$	−42.4314	+	74.1930i	−0.0579665	+	0.101357i
$733$	168.340			0.229658			0.114829	−	0.993385i	$-0.463368\pi$
$733$	168.340			0.229658			0.114829	+	0.993385i	$0.463368\pi$
$734$		−	102.501i		−	0.139647i
$735$	−91.0025	−	52.0449i	−0.123813	−	0.0708094i
$736$	−216.826			−0.294600
$737$			50.5126i			0.0685381i
$738$	−208.342	−	354.133i	−0.282307	−	0.479855i
$739$	−1035.35			−1.40101			−0.700505	−	0.713647i	$-0.747042\pi$
$739$	−1035.35			−1.40101			−0.700505	+	0.713647i	$0.747042\pi$
$740$		−	117.264i		−	0.158465i
$741$	−21.9706	+	38.4164i	−0.0296499	+	0.0518440i
$742$	906.890			1.22222
$743$		−	380.032i		−	0.511483i	−0.966745	−	0.255742i	$-0.917680\pi$
$743$		−	380.032i		−	0.511483i	0.966745	−	0.255742i	$-0.0823196\pi$
$744$	211.328	+	120.860i	0.284043	+	0.162446i
$745$	−333.533			−0.447695
$746$			261.031i			0.349908i
$747$	−398.193	+	234.264i	−0.533056	+	0.313606i
$748$	24.7020			0.0330240
$749$			1302.99i			1.73963i
$750$	−285.305	+	498.867i	−0.380406	+	0.665155i
$751$	−338.055			−0.450140			−0.225070	−	0.974343i	$-0.572261\pi$
$751$	−338.055			−0.450140			−0.225070	+	0.974343i	$0.572261\pi$
$752$			74.1676i			0.0986272i
$753$	−374.674	−	214.279i	−0.497576	−	0.284566i
$754$	−103.407			−0.137145
$755$		−	53.9475i		−	0.0714537i
$756$	408.067	−	5.01075i	0.539772	−	0.00662798i
$757$	1085.38			1.43379			0.716893	−	0.697184i	$-0.245564\pi$
$757$	1085.38			1.43379			0.716893	+	0.697184i	$0.245564\pi$
$758$		−	496.133i		−	0.654529i
$759$	82.2535	−	143.823i	0.108371	−	0.189491i
$760$	−103.118			−0.135682
$761$			79.0684i			0.103901i	0.998650	+	0.0519503i	$0.0165437\pi$
$761$			79.0684i			0.103901i	−0.998650	+	0.0519503i	$0.983456\pi$
$762$	387.440	+	221.579i	0.508451	+	0.290786i
$763$	−445.233			−0.583530
$764$			448.089i			0.586504i
$765$	−168.479	−	286.375i	−0.220234	−	0.374346i
$766$	721.189			0.941500
$767$		−	13.3854i		−	0.0174516i
$768$	−23.8297	+	41.6671i	−0.0310282	+	0.0542540i
$769$	−1391.93			−1.81005			−0.905027	−	0.425354i	$-0.860150\pi$
$769$	−1391.93			−1.81005			−0.905027	+	0.425354i	$0.860150\pi$
$770$			66.3221i			0.0861326i
$771$	42.7597	+	24.4545i	0.0554601	+	0.0317179i
$772$	560.227			0.725682
$773$		−	790.660i		−	1.02285i	−0.859329	−	0.511423i	$-0.829118\pi$
$773$		−	790.660i		−	1.02285i	0.859329	−	0.511423i	$-0.170882\pi$
$774$	900.846	−	529.983i	1.16388	−	0.684732i
$775$	−185.102			−0.238841
$776$			62.2700i			0.0802449i
$777$	153.233	−	267.934i	0.197211	−	0.344832i
$778$	−461.513			−0.593204
$779$			273.268i			0.350794i
$780$	39.0895	+	22.3555i	0.0501147	+	0.0286609i
$781$	34.9174			0.0447085
$782$			464.657i			0.594191i
$783$	−13.9102	−	1132.82i	−0.0177652	−	1.44677i
$784$	32.4555			0.0413973
$785$			633.040i			0.806421i
$786$	−241.714	+	422.646i	−0.307524	+	0.537718i
$787$	−704.151			−0.894728			−0.447364	−	0.894352i	$-0.647637\pi$
$787$	−704.151			−0.894728			−0.447364	+	0.894352i	$0.647637\pi$
$788$			384.111i			0.487450i
$789$	−239.856	−	137.175i	−0.304000	−	0.173859i
$790$	30.5441			0.0386634
$791$			327.695i			0.414279i
$792$	−18.5985	−	31.6130i	−0.0234829	−	0.0399155i
$793$	−24.8236			−0.0313034
$794$			866.286i			1.09104i
$795$	−544.276	+	951.687i	−0.684623	+	1.19709i
$796$	397.628			0.499533
$797$		−	121.809i		−	0.152834i	−0.997076	−	0.0764172i	$-0.975652\pi$
$797$		−	121.809i		−	0.152834i	0.997076	−	0.0764172i	$-0.0243481\pi$
$798$	−235.613	−	134.748i	−0.295254	−	0.168857i
$799$	158.941			0.198925
$800$		−	36.4962i		−	0.0456203i
$801$	484.326	−	284.937i	0.604652	−	0.355727i
$802$	988.691			1.23278
$803$		−	15.4321i		−	0.0192180i
$804$	−104.426	+	182.592i	−0.129883	+	0.227105i
$805$	−1247.55			−1.54976
$806$			70.7063i			0.0877249i
$807$	810.500	+	463.530i	1.00434	+	0.574387i
$808$	207.143			0.256365
$809$			785.610i			0.971088i	0.874212	+	0.485544i	$0.161379\pi$
$809$			785.610i			0.971088i	−0.874212	+	0.485544i	$0.838621\pi$
$810$	−239.646	+	431.232i	−0.295859	+	0.532385i
$811$	1166.21			1.43799			0.718995	−	0.695015i	$-0.244602\pi$
$811$	1166.21			1.43799			0.718995	+	0.695015i	$0.244602\pi$
$812$		−	634.207i		−	0.781043i
$813$	−641.992	+	1122.55i	−0.789658	+	1.38075i
$814$	−27.7408			−0.0340796
$815$		−	1060.02i		−	1.30064i
$816$	89.2925	+	51.0669i	0.109427	+	0.0625820i
$817$	−695.142			−0.850848
$818$		−	869.664i		−	1.06316i
$819$	60.1018	+	102.159i	0.0733844	+	0.124736i
$820$	278.056			0.339093
$821$			811.650i			0.988612i	0.869288	+	0.494306i	$0.164578\pi$
$821$			811.650i			0.988612i	−0.869288	+	0.494306i	$0.835422\pi$
$822$	205.186	−	358.776i	0.249618	−	0.436468i
$823$	−315.707			−0.383605			−0.191803	−	0.981434i	$-0.561433\pi$
$823$	−315.707			−0.383605			−0.191803	+	0.981434i	$0.561433\pi$
$824$		−	466.233i		−	0.565817i
$825$	24.2084	+	13.8449i	0.0293435	+	0.0167817i
$826$	82.0941			0.0993875
$827$		−	415.828i		−	0.502815i	−0.967881	−	0.251408i	$-0.919107\pi$
$827$		−	415.828i		−	0.502815i	0.967881	−	0.251408i	$-0.0808934\pi$
$828$	594.658	−	349.847i	0.718186	−	0.422521i
$829$	659.837			0.795944			0.397972	−	0.917398i	$-0.369714\pi$
$829$	659.837			0.795944			0.397972	+	0.917398i	$0.369714\pi$
$830$		−	312.651i		−	0.376688i
$831$	275.851	−	482.336i	0.331951	−	0.580429i
$832$	−13.9410			−0.0167560
$833$		−	69.5520i		−	0.0834958i
$834$	−712.810	−	407.660i	−0.854688	−	0.488801i
$835$	−110.152			−0.131918
$836$			24.3944i			0.0291799i
$837$	−774.586	+	9.51132i	−0.925431	+	0.0113636i
$838$	−144.708			−0.172683
$839$		−	571.520i		−	0.681192i	−0.940210	−	0.340596i	$-0.889371\pi$
$839$		−	571.520i		−	0.681192i	0.940210	−	0.340596i	$-0.110629\pi$
$840$	−137.109	+	239.740i	−0.163225	+	0.285405i
$841$	−919.600			−1.09346
$842$			59.1650i			0.0702672i
$843$	−885.988	−	506.702i	−1.05099	−	0.601070i
$844$	362.657			0.429688
$845$		−	714.767i		−	0.845878i
$846$	−119.669	−	203.409i	−0.141453	−	0.240436i
$847$	−898.752			−1.06110
$848$		−	339.413i		−	0.400251i
$849$	−630.990	+	1103.31i	−0.743216	+	1.29954i
$850$	−78.2113			−0.0920133
$851$		−	521.819i		−	0.613184i
$852$	126.219	+	72.1854i	0.148144	+	0.0847246i
$853$	−371.630			−0.435674			−0.217837	−	0.975985i	$-0.569900\pi$
$853$	−371.630			−0.435674			−0.217837	+	0.975985i	$0.569900\pi$
$854$		−	152.246i		−	0.178274i
$855$	282.809	−	166.381i	0.330770	−	0.194598i
$856$	487.656			0.569692
$857$			953.985i			1.11317i	0.830791	+	0.556584i	$0.187888\pi$
$857$			953.985i			1.11317i	−0.830791	+	0.556584i	$0.812112\pi$
$858$	5.28856	−	9.24726i	0.00616382	−	0.0107777i
$859$	1557.09			1.81268			0.906338	−	0.422554i	$-0.138866\pi$
$859$	1557.09			1.81268			0.906338	+	0.422554i	$0.138866\pi$
$860$			707.321i			0.822467i
$861$	635.323	+	363.345i	0.737889	+	0.422003i
$862$	−190.978			−0.221552
$863$		−	958.744i		−	1.11094i	−0.831535	−	0.555472i	$-0.812538\pi$
$863$		−	958.744i		−	1.11094i	0.831535	−	0.555472i	$-0.187462\pi$
$864$	−1.87533	−	152.724i	−0.00217052	−	0.176763i
$865$	−751.131			−0.868359
$866$		−	127.463i		−	0.147186i
$867$	−320.987	+	561.258i	−0.370227	+	0.647357i
$868$	−433.650			−0.499597
$869$		−	7.22570i		−	0.00831496i
$870$	665.535	+	380.623i	0.764983	+	0.437498i
$871$	−61.0919			−0.0701400
$872$			166.633i			0.191093i
$873$	−100.472	−	170.779i	−0.115089	−	0.195623i
$874$	−458.871			−0.525024
$875$		−	1023.69i		−	1.16993i
$876$	31.9030	−	55.7837i	0.0364190	−	0.0636800i
$877$	−1252.02			−1.42762			−0.713810	−	0.700339i	$-0.753032\pi$
$877$	−1252.02			−1.42762			−0.713810	+	0.700339i	$0.753032\pi$
$878$		−	1020.60i		−	1.16242i
$879$	1169.81	+	669.022i	1.33084	+	0.761117i
$880$	24.8218			0.0282065
$881$			66.0494i			0.0749710i	0.999297	+	0.0374855i	$0.0119348\pi$
$881$			66.0494i			0.0749710i	−0.999297	+	0.0374855i	$0.988065\pi$
$882$	−89.0111	+	52.3667i	−0.100920	+	0.0593727i
$883$	433.485			0.490923			0.245462	−	0.969406i	$-0.421060\pi$
$883$	433.485			0.490923			0.245462	+	0.969406i	$0.421060\pi$
$884$			29.8756i			0.0337959i
$885$	−49.2693	+	86.1493i	−0.0556715	+	0.0973438i
$886$	803.790			0.907212
$887$			481.753i			0.543126i	0.962421	+	0.271563i	$0.0875405\pi$
$887$			481.753i			0.543126i	−0.962421	+	0.271563i	$0.912459\pi$
$888$	−100.277	−	57.3491i	−0.112925	−	0.0645824i
$889$	−795.035			−0.894303
$890$			380.280i			0.427281i
$891$	102.015	+	56.6921i	0.114495	+	0.0636275i
$892$	437.656			0.490646
$893$			156.962i			0.175769i
$894$	−163.117	+	285.217i	−0.182458	+	0.319034i
$895$	559.478			0.625115
$896$		−	85.5019i		−	0.0954262i
$897$	173.946	+	99.4806i	0.193919	+	0.110904i
$898$	900.899			1.00323
$899$			1203.84i			1.33909i
$900$	58.8864	+	100.093i	0.0654294	+	0.111215i
$901$	−727.362			−0.807282
$902$		−	65.7787i		−	0.0729254i
$903$	−924.279	+	1616.14i	−1.02357	+	1.78974i
$904$	122.643			0.135667
$905$			520.596i			0.575244i
$906$	−46.1326	−	26.3835i	−0.0509189	−	0.0291208i
$907$	1163.50			1.28280			0.641399	−	0.767208i	$-0.278354\pi$
$907$	1163.50			1.28280			0.641399	+	0.767208i	$0.278354\pi$
$908$		−	255.652i		−	0.281555i
$909$	−568.102	+	334.224i	−0.624975	+	0.367683i
$910$	−80.2126			−0.0881457
$911$			1108.25i			1.21652i	0.793738	+	0.608260i	$0.208132\pi$
$911$			1108.25i			1.21652i	−0.793738	+	0.608260i	$0.791868\pi$
$912$	−50.4310	+	88.1805i	−0.0552971	+	0.0966892i
$913$	−73.9627			−0.0810106
$914$		−	656.613i		−	0.718395i
$915$	159.766	+	91.3714i	0.174608	+	0.0998594i
$916$	−354.797			−0.387333
$917$		−	867.281i		−	0.945780i
$918$	−327.286	+	4.01882i	−0.356521	+	0.00437780i
$919$	1280.58			1.39344			0.696722	−	0.717341i	$-0.254641\pi$
$919$	1280.58			1.39344			0.696722	+	0.717341i	$0.254641\pi$
$920$			466.910i			0.507511i
$921$	852.853	−	1491.25i	0.926007	−	1.61916i
$922$	319.828			0.346885
$923$			42.2305i			0.0457535i
$924$	56.7145	+	32.4354i	0.0613793	+	0.0351032i
$925$	87.8328			0.0949544
$926$		−	732.785i		−	0.791344i
$927$	752.264	+	1278.67i	0.811504	+	1.37937i
$928$	−237.359			−0.255775
$929$		−	202.697i		−	0.218188i	−0.994031	−	0.109094i	$-0.965205\pi$
$929$		−	202.697i		−	0.218188i	0.994031	−	0.109094i	$-0.0347950\pi$
$930$	260.258	−	455.071i	0.279847	−	0.489323i
$931$	68.6858			0.0737764
$932$			770.242i			0.826439i
$933$	1118.90	+	639.903i	1.19925	+	0.685855i
$934$	−108.361			−0.116018
$935$		−	53.1929i		−	0.0568908i
$936$	38.2341	−	22.4937i	0.0408484	−	0.0240318i
$937$	1323.93			1.41295			0.706474	−	0.707739i	$-0.250285\pi$
$937$	1323.93			1.41295			0.706474	+	0.707739i	$0.250285\pi$
$938$		−	374.684i		−	0.399450i
$939$	18.9065	−	33.0588i	0.0201347	−	0.0352064i
$940$	159.712			0.169906
$941$			1178.03i			1.25189i	0.779866	+	0.625947i	$0.215287\pi$
$941$			1178.03i			1.25189i	−0.779866	+	0.625947i	$0.784713\pi$
$942$	541.336	+	309.594i	0.574667	+	0.328656i
$943$	1237.33			1.31212
$944$		−	30.7246i		−	0.0325472i
$945$	−10.7901	−	878.727i	−0.0114181	−	0.929870i
$946$	167.328			0.176880
$947$			324.850i			0.343030i	0.985181	+	0.171515i	$0.0548662\pi$
$947$			324.850i			0.343030i	−0.985181	+	0.171515i	$0.945134\pi$
$948$	14.9378	−	26.1194i	0.0157572	−	0.0275521i
$949$	18.6641			0.0196672
$950$		−	77.2373i		−	0.0813025i
$951$	635.093	+	363.214i	0.667816	+	0.381928i
$952$	−183.230			−0.192469
$953$			1341.08i			1.40722i	0.710588	+	0.703609i	$0.248429\pi$
$953$			1341.08i			1.40722i	−0.710588	+	0.703609i	$0.751571\pi$
$954$	547.641	+	930.861i	0.574047	+	0.975746i
$955$	964.909			1.01038
$956$		−	434.214i		−	0.454198i
$957$	90.0427	−	157.443i	0.0940885	−	0.164517i
$958$	−754.574			−0.787655
$959$			736.218i			0.767693i
$960$	89.7254	+	51.3145i	0.0934640	+	0.0534526i
$961$	−137.854			−0.143449
$962$		−	33.5508i		−	0.0348761i
$963$	−1337.43	+	786.831i	−1.38881	+	0.817062i
$964$	634.225			0.657910
$965$		−	1206.39i		−	1.25014i
$966$	−610.126	+	1066.83i	−0.631601	+	1.10438i
$967$	1126.33			1.16477			0.582385	−	0.812913i	$-0.302120\pi$
$967$	1126.33			1.16477			0.582385	+	0.812913i	$0.302120\pi$
$968$			336.368i			0.347487i
$969$	188.971	+	108.073i	0.195016	+	0.111531i
$970$	134.092			0.138239
$971$			1336.41i			1.37633i	0.725556	+	0.688163i	$0.241583\pi$
$971$			1336.41i			1.37633i	−0.725556	+	0.688163i	$0.758417\pi$
$972$	251.562	+	415.828i	0.258808	+	0.427806i
$973$	1462.70			1.50329
$974$		−	691.812i		−	0.710280i
$975$	−16.7446	+	29.2786i	−0.0171740	+	0.0300294i
$976$	−56.9797			−0.0583808
$977$		−	1155.39i		−	1.18259i	−0.806456	−	0.591295i	$-0.798617\pi$
$977$		−	1155.39i		−	1.18259i	0.806456	−	0.591295i	$-0.201383\pi$
$978$	−906.466	−	518.414i	−0.926857	−	0.530075i
$979$	89.9615			0.0918912
$980$		−	69.8892i		−	0.0713155i
$981$	−268.862	−	457.002i	−0.274069	−	0.465853i
$982$	−857.841			−0.873566
$983$		−	944.120i		−	0.960448i	−0.877146	−	0.480224i	$-0.840555\pi$
$983$		−	944.120i		−	0.960448i	0.877146	−	0.480224i	$-0.159445\pi$
$984$	135.986	−	237.776i	0.138197	−	0.241643i
$985$	827.140			0.839736
$986$			508.659i			0.515882i
$987$	364.921	+	208.700i	0.369727	+	0.211449i
$988$	−29.5035			−0.0298619
$989$			3147.54i			3.18254i
$990$	−68.0751	+	40.0497i	−0.0687628	+	0.0404543i
$991$	1671.42			1.68660			0.843300	−	0.537443i	$-0.180610\pi$
$991$	1671.42			1.68660			0.843300	+	0.537443i	$0.180610\pi$
$992$			162.298i			0.163607i
$993$	−76.0169	+	132.918i	−0.0765527	+	0.133855i
$994$	−259.004			−0.260568
$995$		−	856.247i		−	0.860550i
$996$	−267.360	−	152.905i	−0.268433	−	0.153519i
$997$	−1563.13			−1.56783			−0.783917	−	0.620866i	$-0.786781\pi$
$997$	−1563.13			−1.56783			−0.783917	+	0.620866i	$0.786781\pi$
$998$			522.024i			0.523071i
$999$	367.549	−	4.51322i	0.367917	−	0.00451774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.6	✓	40
3.2	odd	2	inner	354.3.b.a.119.26	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.6	✓	40	1.1	even	1	trivial
354.3.b.a.119.26	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.48935 + 2.60419i) q^{3} -2.00000 q^{4} +4.30678i q^{5} +(3.68289 + 2.10626i) q^{6} -7.55737 q^{7} +2.82843i q^{8} +(-4.56365 - 7.75713i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.48935 + 2.60419i) q^{3} -2.00000 q^{4} +4.30678i q^{5} +(3.68289 + 2.10626i) q^{6} -7.55737 q^{7} +2.82843i q^{8} +(-4.56365 - 7.75713i) q^{9} +6.09070 q^{10} -1.44085i q^{11} +(2.97871 - 5.20839i) q^{12} +1.74263 q^{13} +10.6877i q^{14} +(-11.2157 - 6.41431i) q^{15} +4.00000 q^{16} -8.57199i q^{17} +(-10.9702 + 6.45398i) q^{18} +8.46524 q^{19} -8.61355i q^{20} +(11.2556 - 19.6809i) q^{21} -2.03768 q^{22} -38.3298i q^{23} +(-7.36577 - 4.21253i) q^{24} +6.45168 q^{25} -2.46445i q^{26} +(26.9980 - 0.331514i) q^{27} +15.1147 q^{28} -41.9595i q^{29} +(-9.07121 + 15.8614i) q^{30} -28.6905 q^{31} -5.65685i q^{32} +(3.75226 + 2.14594i) q^{33} -12.1226 q^{34} -32.5479i q^{35} +(9.12730 + 15.5143i) q^{36} +13.6139 q^{37} -11.9717i q^{38} +(-2.59539 + 4.53814i) q^{39} -12.1814 q^{40} +32.2812i q^{41} +(-27.8329 - 15.9178i) q^{42} -82.1173 q^{43} +2.88171i q^{44} +(33.4082 - 19.6546i) q^{45} -54.2065 q^{46} +18.5419i q^{47} +(-5.95742 + 10.4168i) q^{48} +8.11387 q^{49} -9.12406i q^{50} +(22.3231 + 12.7667i) q^{51} -3.48525 q^{52} -84.8533i q^{53} +(-0.468832 - 38.1809i) q^{54} +6.20544 q^{55} -21.3755i q^{56} +(-12.6077 + 22.0451i) q^{57} -59.3397 q^{58} -7.68115i q^{59} +(22.4314 + 12.8286i) q^{60} -14.2449 q^{61} +40.5745i q^{62} +(34.4892 + 58.6235i) q^{63} -8.00000 q^{64} +7.50510i q^{65} +(3.03482 - 5.30650i) q^{66} -35.0574 q^{67} +17.1440i q^{68} +(99.8181 + 57.0866i) q^{69} -46.0297 q^{70} +24.2338i q^{71} +(21.9405 - 12.9080i) q^{72} +10.7104 q^{73} -19.2530i q^{74} +(-9.60884 + 16.8014i) q^{75} -16.9305 q^{76} +10.8891i q^{77} +(6.41790 + 3.67043i) q^{78} +5.01487 q^{79} +17.2271i q^{80} +(-39.3462 + 70.8017i) q^{81} +45.6526 q^{82} -51.3325i q^{83} +(-22.5112 + 39.3617i) q^{84} +36.9176 q^{85} +116.131i q^{86} +(109.271 + 62.4926i) q^{87} +4.07535 q^{88} +62.4362i q^{89} +(-27.7958 - 47.2464i) q^{90} -13.1697 q^{91} +76.6595i q^{92} +(42.7303 - 74.7157i) q^{93} +26.2222 q^{94} +36.4579i q^{95} +(14.7315 + 8.42506i) q^{96} +22.0158 q^{97} -11.4747i q^{98} +(-11.1769 + 6.57556i) 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

Groups

Database

Properties

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