LMFDB - Embedded newform 354.3.b.a.119.13

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			119.13
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(1.10775 - 2.78799i) q^{3} -2.00000 q^{4} +5.86001i q^{5} +(-3.94282 - 1.56659i) q^{6} -9.12163 q^{7} +2.82843i q^{8} +(-6.54579 - 6.17678i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(1.10775 - 2.78799i) q^{3} -2.00000 q^{4} +5.86001i q^{5} +(-3.94282 - 1.56659i) q^{6} -9.12163 q^{7} +2.82843i q^{8} +(-6.54579 - 6.17678i) q^{9} +8.28731 q^{10} +1.47425i q^{11} +(-2.21549 + 5.57598i) q^{12} +3.43626 q^{13} +12.8999i q^{14} +(16.3377 + 6.49141i) q^{15} +4.00000 q^{16} +28.5484i q^{17} +(-8.73528 + 9.25715i) q^{18} -14.2614 q^{19} -11.7200i q^{20} +(-10.1045 + 25.4310i) q^{21} +2.08490 q^{22} +34.5558i q^{23} +(7.88563 + 3.13318i) q^{24} -9.33975 q^{25} -4.85961i q^{26} +(-24.4719 + 11.4073i) q^{27} +18.2433 q^{28} -18.1901i q^{29} +(9.18024 - 23.1050i) q^{30} -12.1587 q^{31} -5.65685i q^{32} +(4.11019 + 1.63309i) q^{33} +40.3735 q^{34} -53.4529i q^{35} +(13.0916 + 12.3536i) q^{36} -17.4723 q^{37} +20.1687i q^{38} +(3.80651 - 9.58027i) q^{39} -16.5746 q^{40} +76.6237i q^{41} +(35.9649 + 14.2899i) q^{42} +3.75414 q^{43} -2.94850i q^{44} +(36.1960 - 38.3584i) q^{45} +48.8692 q^{46} -89.9492i q^{47} +(4.43099 - 11.1520i) q^{48} +34.2041 q^{49} +13.2084i q^{50} +(79.5926 + 31.6243i) q^{51} -6.87252 q^{52} +6.97955i q^{53} +(16.1324 + 34.6085i) q^{54} -8.63911 q^{55} -25.7999i q^{56} +(-15.7980 + 39.7607i) q^{57} -25.7246 q^{58} -7.68115i q^{59} +(-32.6753 - 12.9828i) q^{60} -65.0390 q^{61} +17.1951i q^{62} +(59.7083 + 56.3423i) q^{63} -8.00000 q^{64} +20.1365i q^{65} +(2.30954 - 5.81269i) q^{66} -40.3529 q^{67} -57.0967i q^{68} +(96.3412 + 38.2790i) q^{69} -75.5938 q^{70} -105.305i q^{71} +(17.4706 - 18.5143i) q^{72} -68.0124 q^{73} +24.7095i q^{74} +(-10.3461 + 26.0391i) q^{75} +28.5228 q^{76} -13.4475i q^{77} +(-13.5485 - 5.38322i) q^{78} -31.7025 q^{79} +23.4401i q^{80} +(4.69486 + 80.8638i) q^{81} +108.362 q^{82} +93.6366i q^{83} +(20.2089 - 50.8620i) q^{84} -167.294 q^{85} -5.30916i q^{86} +(-50.7138 - 20.1500i) q^{87} -4.16980 q^{88} -27.7537i q^{89} +(-54.2470 - 51.1889i) q^{90} -31.3443 q^{91} -69.1115i q^{92} +(-13.4688 + 33.8985i) q^{93} -127.207 q^{94} -83.5721i q^{95} +(-15.7713 - 6.26636i) q^{96} +121.425 q^{97} -48.3719i q^{98} +(9.10610 - 9.65012i) 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
$3$	1.10775	−	2.78799i	0.369249	−	0.929331i
$3$	1.10775	−	2.78799i	0.369249	−	0.929331i
$4$	−2.00000			−0.500000
$5$			5.86001i			1.17200i	0.810310	+	0.586001i	$0.199299\pi$
$5$			5.86001i			1.17200i	−0.810310	+	0.586001i	$0.800701\pi$
$6$	−3.94282	−	1.56659i	−0.657136	−	0.261098i
$7$	−9.12163			−1.30309			−0.651545	−	0.758610i	$-0.725879\pi$
$7$	−9.12163			−1.30309			−0.651545	+	0.758610i	$0.725879\pi$
$8$			2.82843i			0.353553i
$9$	−6.54579	−	6.17678i	−0.727311	−	0.686309i
$10$	8.28731			0.828731
$11$			1.47425i			0.134023i	0.997752	+	0.0670113i	$0.0213463\pi$
$11$			1.47425i			0.134023i	−0.997752	+	0.0670113i	$0.978654\pi$
$12$	−2.21549	+	5.57598i	−0.184624	+	0.464665i
$13$	3.43626			0.264328			0.132164	−	0.991228i	$-0.457807\pi$
$13$	3.43626			0.264328			0.132164	+	0.991228i	$0.457807\pi$
$14$			12.8999i			0.921424i
$15$	16.3377	+	6.49141i	1.08918	+	0.432761i
$16$	4.00000			0.250000
$17$			28.5484i			1.67932i	0.543116	+	0.839658i	$0.317244\pi$
$17$			28.5484i			1.67932i	−0.543116	+	0.839658i	$0.682756\pi$
$18$	−8.73528	+	9.25715i	−0.485293	+	0.514286i
$19$	−14.2614			−0.750601			−0.375301	−	0.926903i	$-0.622460\pi$
$19$	−14.2614			−0.750601			−0.375301	+	0.926903i	$0.622460\pi$
$20$		−	11.7200i		−	0.586001i
$21$	−10.1045	+	25.4310i	−0.481164	+	1.21100i
$22$	2.08490			0.0947682
$23$			34.5558i			1.50242i	0.660061	+	0.751212i	$0.270531\pi$
$23$			34.5558i			1.50242i	−0.660061	+	0.751212i	$0.729469\pi$
$24$	7.88563	+	3.13318i	0.328568	+	0.130549i
$25$	−9.33975			−0.373590
$26$		−	4.85961i		−	0.186908i
$27$	−24.4719	+	11.4073i	−0.906366	+	0.422493i
$28$	18.2433			0.651545
$29$		−	18.1901i		−	0.627244i	−0.949548	−	0.313622i	$-0.898458\pi$
$29$		−	18.1901i		−	0.627244i	0.949548	−	0.313622i	$-0.101542\pi$
$30$	9.18024	−	23.1050i	0.306008	−	0.770165i
$31$	−12.1587			−0.392217			−0.196109	−	0.980582i	$-0.562831\pi$
$31$	−12.1587			−0.392217			−0.196109	+	0.980582i	$0.562831\pi$
$32$		−	5.65685i		−	0.176777i
$33$	4.11019	+	1.63309i	0.124551	+	0.0494877i
$34$	40.3735			1.18746
$35$		−	53.4529i		−	1.52722i
$36$	13.0916	+	12.3536i	0.363655	+	0.343154i
$37$	−17.4723			−0.472223			−0.236112	−	0.971726i	$-0.575873\pi$
$37$	−17.4723			−0.472223			−0.236112	+	0.971726i	$0.575873\pi$
$38$			20.1687i			0.530755i
$39$	3.80651	−	9.58027i	0.0976028	−	0.245648i
$40$	−16.5746			−0.414365
$41$			76.6237i			1.86887i	0.356133	+	0.934435i	$0.384095\pi$
$41$			76.6237i			1.86887i	−0.356133	+	0.934435i	$0.615905\pi$
$42$	35.9649	+	14.2899i	0.856307	+	0.340235i
$43$	3.75414			0.0873056			0.0436528	−	0.999047i	$-0.486100\pi$
$43$	3.75414			0.0873056			0.0436528	+	0.999047i	$0.486100\pi$
$44$		−	2.94850i		−	0.0670113i
$45$	36.1960	−	38.3584i	0.804355	−	0.852410i
$46$	48.8692			1.06237
$47$		−	89.9492i		−	1.91381i	−0.290396	−	0.956907i	$-0.593787\pi$
$47$		−	89.9492i		−	1.91381i	0.290396	−	0.956907i	$-0.406213\pi$
$48$	4.43099	−	11.1520i	0.0923122	−	0.232333i
$49$	34.2041			0.698043
$50$			13.2084i			0.264168i
$51$	79.5926	+	31.6243i	1.56064	+	0.620085i
$52$	−6.87252			−0.132164
$53$			6.97955i			0.131690i	0.997830	+	0.0658448i	$0.0209742\pi$
$53$			6.97955i			0.131690i	−0.997830	+	0.0658448i	$0.979026\pi$
$54$	16.1324	+	34.6085i	0.298748	+	0.640898i
$55$	−8.63911			−0.157075
$56$		−	25.7999i		−	0.460712i
$57$	−15.7980	+	39.7607i	−0.277159	+	0.697556i
$58$	−25.7246			−0.443528
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−32.6753	−	12.9828i	−0.544589	−	0.216380i
$61$	−65.0390			−1.06621			−0.533106	−	0.846048i	$-0.678975\pi$
$61$	−65.0390			−1.06621			−0.533106	+	0.846048i	$0.678975\pi$
$62$			17.1951i			0.277340i
$63$	59.7083	+	56.3423i	0.947751	+	0.894322i
$64$	−8.00000			−0.125000
$65$			20.1365i			0.309793i
$66$	2.30954	−	5.81269i	0.0349931	−	0.0880710i
$67$	−40.3529			−0.602282			−0.301141	−	0.953580i	$-0.597367\pi$
$67$	−40.3529			−0.602282			−0.301141	+	0.953580i	$0.597367\pi$
$68$		−	57.0967i		−	0.839658i
$69$	96.3412	+	38.2790i	1.39625	+	0.554769i
$70$	−75.5938			−1.07991
$71$		−	105.305i		−	1.48316i	−0.670863	−	0.741582i	$-0.734076\pi$
$71$		−	105.305i		−	1.48316i	0.670863	−	0.741582i	$-0.265924\pi$
$72$	17.4706	−	18.5143i	0.242647	−	0.257143i
$73$	−68.0124			−0.931677			−0.465838	−	0.884870i	$-0.654247\pi$
$73$	−68.0124			−0.931677			−0.465838	+	0.884870i	$0.654247\pi$
$74$			24.7095i			0.333912i
$75$	−10.3461	+	26.0391i	−0.137948	+	0.347189i
$76$	28.5228			0.375301
$77$		−	13.4475i		−	0.174643i
$78$	−13.5485	−	5.38322i	−0.173699	−	0.0690156i
$79$	−31.7025			−0.401297			−0.200649	−	0.979663i	$-0.564305\pi$
$79$	−31.7025			−0.401297			−0.200649	+	0.979663i	$0.564305\pi$
$80$			23.4401i			0.293001i
$81$	4.69486	+	80.8638i	0.0579612	+	0.998319i
$82$	108.362			1.32149
$83$			93.6366i			1.12815i	0.825723	+	0.564076i	$0.190768\pi$
$83$			93.6366i			1.12815i	−0.825723	+	0.564076i	$0.809232\pi$
$84$	20.2089	−	50.8620i	0.240582	−	0.605501i
$85$	−167.294			−1.96816
$86$		−	5.30916i		−	0.0617344i
$87$	−50.7138	−	20.1500i	−0.582917	−	0.231609i
$88$	−4.16980			−0.0473841
$89$		−	27.7537i		−	0.311839i	−0.987770	−	0.155920i	$-0.950166\pi$
$89$		−	27.7537i		−	0.311839i	0.987770	−	0.155920i	$-0.0498340\pi$
$90$	−54.2470	−	51.1889i	−0.602745	−	0.568765i
$91$	−31.3443			−0.344443
$92$		−	69.1115i		−	0.751212i
$93$	−13.4688	+	33.8985i	−0.144826	+	0.364500i
$94$	−127.207			−1.35327
$95$		−	83.5721i		−	0.879706i
$96$	−15.7713	−	6.26636i	−0.164284	−	0.0652746i
$97$	121.425			1.25181			0.625904	−	0.779900i	$-0.284730\pi$
$97$	121.425			1.25181			0.625904	+	0.779900i	$0.284730\pi$
$98$		−	48.3719i		−	0.493591i
$99$	9.10610	−	9.65012i	0.0919808	−	0.0974760i
$100$	18.6795			0.186795
$101$			65.3909i			0.647435i	0.946154	+	0.323717i	$0.104933\pi$
$101$			65.3909i			0.647435i	−0.946154	+	0.323717i	$0.895067\pi$
$102$	44.7236	−	112.561i	0.438466	−	1.10354i
$103$	−110.812			−1.07585			−0.537924	−	0.842993i	$-0.680791\pi$
$103$	−110.812			−1.07585			−0.537924	+	0.842993i	$0.680791\pi$
$104$			9.71922i			0.0934540i
$105$	−149.026	−	59.2122i	−1.41930	−	0.563926i
$106$	9.87057			0.0931186
$107$		−	99.7097i		−	0.931866i	−0.884820	−	0.465933i	$-0.845719\pi$
$107$		−	99.7097i		−	0.931866i	0.884820	−	0.465933i	$-0.154281\pi$
$108$	48.9438	−	22.8146i	0.453183	−	0.211247i
$109$	44.8327			0.411309			0.205654	−	0.978625i	$-0.434068\pi$
$109$	44.8327			0.411309			0.205654	+	0.978625i	$0.434068\pi$
$110$			12.2175i			0.111069i
$111$	−19.3548	+	48.7125i	−0.174368	+	0.438852i
$112$	−36.4865			−0.325772
$113$			110.164i			0.974899i	0.873151	+	0.487449i	$0.162073\pi$
$113$			110.164i			0.974899i	−0.873151	+	0.487449i	$0.837927\pi$
$114$	56.2301	+	22.3418i	0.493247	+	0.195981i
$115$	−202.497			−1.76085
$116$			36.3801i			0.313622i
$117$	−22.4931	−	21.2250i	−0.192248	−	0.181410i
$118$	−10.8628			−0.0920575
$119$		−	260.408i		−	2.18830i
$120$	−18.3605	+	46.2099i	−0.153004	+	0.385083i
$121$	118.827			0.982038
$122$			91.9790i			0.753926i
$123$	213.626	+	84.8796i	1.73680	+	0.690078i
$124$	24.3175			0.196109
$125$			91.7693i			0.734154i
$126$	79.6800	−	84.4403i	0.632381	−	0.670161i
$127$	152.224			1.19862			0.599308	−	0.800518i	$-0.295442\pi$
$127$	152.224			1.19862			0.599308	+	0.800518i	$0.295442\pi$
$128$			11.3137i			0.0883883i
$129$	4.15864	−	10.4665i	0.0322375	−	0.0811358i
$130$	28.4774			0.219057
$131$		−	1.82224i		−	0.0139102i	−0.999976	−	0.00695510i	$-0.997786\pi$
$131$		−	1.82224i		−	0.0139102i	0.999976	−	0.00695510i	$-0.00221389\pi$
$132$	−8.22038	−	3.26619i	−0.0622756	−	0.0247438i
$133$	130.087			0.978101
$134$			57.0676i			0.425878i
$135$	−66.8470	−	143.406i	−0.495163	−	1.06226i
$136$	−80.7470			−0.593728
$137$		−	55.6275i		−	0.406040i	−0.979175	−	0.203020i	$-0.934924\pi$
$137$		−	55.6275i		−	0.406040i	0.979175	−	0.203020i	$-0.0650757\pi$
$138$	54.1347	−	136.247i	0.392281	−	0.987297i
$139$	−186.244			−1.33989			−0.669943	−	0.742412i	$-0.733682\pi$
$139$	−186.244			−1.33989			−0.669943	+	0.742412i	$0.733682\pi$
$140$			106.906i			0.763612i
$141$	−250.778	−	99.6409i	−1.77856	−	0.706673i
$142$	−148.923			−1.04875
$143$			5.06590i			0.0354259i
$144$	−26.1832	−	24.7071i	−0.181828	−	0.171577i
$145$	106.594			0.735131
$146$			96.1840i			0.658795i
$147$	37.8895	−	95.3608i	0.257752	−	0.648713i
$148$	34.9445			0.236112
$149$			95.5822i			0.641492i	0.947165	+	0.320746i	$0.103934\pi$
$149$			95.5822i			0.641492i	−0.947165	+	0.320746i	$0.896066\pi$
$150$	36.8249	+	14.6316i	0.245499	+	0.0975438i
$151$	−50.3733			−0.333598			−0.166799	−	0.985991i	$-0.553343\pi$
$151$	−50.3733			−0.333598			−0.166799	+	0.985991i	$0.553343\pi$
$152$		−	40.3374i		−	0.265378i
$153$	176.337	−	186.872i	1.15253	−	1.22138i
$154$	−19.0177			−0.123492
$155$		−	71.2504i		−	0.459680i
$156$	−7.61302	+	19.1605i	−0.0488014	+	0.122824i
$157$	−228.156			−1.45322			−0.726610	−	0.687050i	$-0.758905\pi$
$157$	−228.156			−1.45322			−0.726610	+	0.687050i	$0.758905\pi$
$158$			44.8341i			0.283760i
$159$	19.4589	+	7.73157i	0.122383	+	0.0486262i
$160$	33.1492			0.207183
$161$		−	315.205i		−	1.95779i
$162$	114.359	−	6.63953i	0.705918	−	0.0409848i
$163$	221.956			1.36170			0.680848	−	0.732425i	$-0.261611\pi$
$163$	221.956			1.36170			0.680848	+	0.732425i	$0.261611\pi$
$164$		−	153.247i		−	0.934435i
$165$	−9.56995	+	24.0858i	−0.0579997	+	0.145974i
$166$	132.422			0.797724
$167$		−	44.3646i		−	0.265657i	−0.991139	−	0.132828i	$-0.957594\pi$
$167$		−	44.3646i		−	0.265657i	0.991139	−	0.132828i	$-0.0424059\pi$
$168$	−71.9298	−	28.5797i	−0.428154	−	0.170117i
$169$	−157.192			−0.930131
$170$			236.589i			1.39170i
$171$	93.3523	+	88.0896i	0.545920	+	0.515144i
$172$	−7.50828			−0.0436528
$173$		−	291.492i		−	1.68492i	−0.538757	−	0.842461i	$-0.681106\pi$
$173$		−	291.492i		−	1.68492i	0.538757	−	0.842461i	$-0.318894\pi$
$174$	−28.4964	+	71.7201i	−0.163772	+	0.412184i
$175$	85.1937			0.486821
$176$			5.89699i			0.0335056i
$177$	−21.4150	−	8.50876i	−0.120989	−	0.0480721i
$178$	−39.2496			−0.220503
$179$			190.344i			1.06337i	0.846941	+	0.531687i	$0.178442\pi$
$179$			190.344i			1.06337i	−0.846941	+	0.531687i	$0.821558\pi$
$180$	−72.3920	+	76.7169i	−0.402178	+	0.426205i
$181$	−193.609			−1.06966			−0.534832	−	0.844958i	$-0.679625\pi$
$181$	−193.609			−1.06966			−0.534832	+	0.844958i	$0.679625\pi$
$182$			44.3275i			0.243558i
$183$	−72.0467	+	181.328i	−0.393698	+	0.990864i
$184$	−97.7385			−0.531187
$185$		−	102.388i		−	0.553447i
$186$	47.9397	+	19.0478i	0.257740	+	0.102407i
$187$	−42.0874			−0.225066
$188$			179.898i			0.956907i
$189$	223.223	−	104.053i	1.18108	−	0.550547i
$190$	−118.189			−0.622046
$191$			320.439i			1.67769i	0.544369	+	0.838846i	$0.316769\pi$
$191$			320.439i			1.67769i	−0.544369	+	0.838846i	$0.683231\pi$
$192$	−8.86197	+	22.3039i	−0.0461561	+	0.116166i
$193$	149.827			0.776304			0.388152	−	0.921595i	$-0.373114\pi$
$193$	149.827			0.776304			0.388152	+	0.921595i	$0.373114\pi$
$194$		−	171.721i		−	0.885162i
$195$	56.1405	+	22.3062i	0.287900	+	0.114391i
$196$	−68.4082			−0.349021
$197$			215.279i			1.09279i	0.837529	+	0.546393i	$0.184000\pi$
$197$			215.279i			1.09279i	−0.837529	+	0.546393i	$0.816000\pi$
$198$	−13.6473	−	12.8780i	−0.0689259	−	0.0650402i
$199$	136.185			0.684344			0.342172	−	0.939637i	$-0.388837\pi$
$199$	136.185			0.684344			0.342172	+	0.939637i	$0.388837\pi$
$200$		−	26.4168i		−	0.132084i
$201$	−44.7008	+	112.504i	−0.222392	+	0.559719i
$202$	92.4767			0.457805
$203$			165.923i			0.817355i
$204$	−159.185	−	63.2487i	−0.780319	−	0.310043i
$205$	−449.016			−2.19032
$206$			156.712i			0.760740i
$207$	213.443	−	226.195i	1.03113	−	1.09273i
$208$	13.7450			0.0660820
$209$		−	21.0249i		−	0.100597i
$210$	−83.7387	+	210.755i	−0.398756	+	1.00359i
$211$	357.473			1.69419			0.847093	−	0.531444i	$-0.178351\pi$
$211$	357.473			1.69419			0.847093	+	0.531444i	$0.178351\pi$
$212$		−	13.9591i		−	0.0658448i
$213$	−293.588	−	116.651i	−1.37835	−	0.547656i
$214$	−141.011			−0.658929
$215$			21.9993i			0.102322i
$216$	−32.2648	−	69.2169i	−0.149374	−	0.320449i
$217$	110.908			0.511094
$218$		−	63.4029i		−	0.290839i
$219$	−75.3405	+	189.618i	−0.344021	+	0.865835i
$220$	17.2782			0.0785374
$221$			98.0996i			0.443890i
$222$	68.8899	+	27.3719i	0.310315	+	0.123297i
$223$	249.319			1.11802			0.559011	−	0.829160i	$-0.311181\pi$
$223$	249.319			1.11802			0.559011	+	0.829160i	$0.311181\pi$
$224$			51.5997i			0.230356i
$225$	61.1361	+	57.6896i	0.271716	+	0.256398i
$226$	155.795			0.689358
$227$		−	48.0024i		−	0.211464i	−0.994395	−	0.105732i	$-0.966281\pi$
$227$		−	48.0024i		−	0.211464i	0.994395	−	0.105732i	$-0.0337186\pi$
$228$	31.5961	−	79.5214i	0.138579	−	0.348778i
$229$	82.3570			0.359637			0.179819	−	0.983700i	$-0.442449\pi$
$229$	82.3570			0.359637			0.179819	+	0.983700i	$0.442449\pi$
$230$			286.374i			1.24511i
$231$	−37.4916	−	14.8965i	−0.162301	−	0.0644869i
$232$	51.4493			0.221764
$233$			157.587i			0.676337i	0.941086	+	0.338169i	$0.109807\pi$
$233$			157.587i			0.676337i	−0.941086	+	0.338169i	$0.890193\pi$
$234$	−30.0167	+	31.8100i	−0.128277	+	0.135940i
$235$	527.104			2.24299
$236$			15.3623i			0.0650945i
$237$	−35.1183	+	88.3863i	−0.148179	+	0.372938i
$238$	−368.272			−1.54736
$239$		−	97.4320i		−	0.407665i	−0.979006	−	0.203833i	$-0.934660\pi$
$239$		−	97.4320i		−	0.407665i	0.979006	−	0.203833i	$-0.0653398\pi$
$240$	65.3507	+	25.9656i	0.272294	+	0.108190i
$241$	257.798			1.06970			0.534850	−	0.844947i	$-0.320368\pi$
$241$	257.798			1.06970			0.534850	+	0.844947i	$0.320368\pi$
$242$		−	168.046i		−	0.694406i
$243$	230.648	+	76.4874i	0.949170	+	0.314763i
$244$	130.078			0.533106
$245$			200.436i			0.818108i
$246$	120.038	−	302.113i	0.487959	−	1.22810i
$247$	−49.0060			−0.198405
$248$		−	34.3901i		−	0.138670i
$249$	261.058	+	103.726i	1.04843	+	0.416569i
$250$	129.781			0.519125
$251$			194.437i			0.774648i	0.921944	+	0.387324i	$0.126600\pi$
$251$			194.437i			0.774648i	−0.921944	+	0.387324i	$0.873400\pi$
$252$	−119.417	−	112.685i	−0.473875	−	0.447161i
$253$	−50.9438			−0.201359
$254$		−	215.278i		−	0.847550i
$255$	−185.319	+	466.414i	−0.726742	+	1.82907i
$256$	16.0000			0.0625000
$257$			288.036i			1.12076i	0.828235	+	0.560381i	$0.189345\pi$
$257$			288.036i			1.12076i	−0.828235	+	0.560381i	$0.810655\pi$
$258$	−14.8019	−	5.88120i	−0.0573716	−	0.0227954i
$259$	159.376			0.615349
$260$		−	40.2731i		−	0.154896i
$261$	−112.356	+	119.068i	−0.430483	+	0.456201i
$262$	−2.57703			−0.00983599
$263$		−	216.045i		−	0.821462i	−0.911757	−	0.410731i	$-0.865274\pi$
$263$		−	216.045i		−	0.821462i	0.911757	−	0.410731i	$-0.134726\pi$
$264$	−4.61908	+	11.6254i	−0.0174965	+	0.0440355i
$265$	−40.9002			−0.154341
$266$		−	183.971i		−	0.691622i
$267$	−77.3770	−	30.7440i	−0.289802	−	0.115146i
$268$	80.7058			0.301141
$269$		−	429.157i		−	1.59538i	−0.603068	−	0.797690i	$-0.706055\pi$
$269$		−	429.157i		−	1.59538i	0.603068	−	0.797690i	$-0.293945\pi$
$270$	−202.806	+	94.5360i	−0.751134	+	0.350133i
$271$	−145.962			−0.538606			−0.269303	−	0.963056i	$-0.586793\pi$
$271$	−145.962			−0.538606			−0.269303	+	0.963056i	$0.586793\pi$
$272$			114.193i			0.419829i
$273$	−34.7216	+	87.3877i	−0.127185	+	0.320101i
$274$	−78.6692			−0.287114
$275$		−	13.7691i		−	0.0500695i
$276$	−192.682	−	76.5581i	−0.698125	−	0.277384i
$277$	440.680			1.59090			0.795451	−	0.606018i	$-0.207234\pi$
$277$	440.680			1.59090			0.795451	+	0.606018i	$0.207234\pi$
$278$			263.389i			0.947443i
$279$	79.5886	+	75.1018i	0.285264	+	0.269182i
$280$	151.188			0.539955
$281$			360.009i			1.28117i	0.767887	+	0.640585i	$0.221308\pi$
$281$			360.009i			1.28117i	−0.767887	+	0.640585i	$0.778692\pi$
$282$	−140.914	+	354.653i	−0.499693	+	1.25764i
$283$	349.931			1.23651			0.618254	−	0.785979i	$-0.287840\pi$
$283$	349.931			1.23651			0.618254	+	0.785979i	$0.287840\pi$
$284$			210.609i			0.741582i
$285$	−232.998	−	92.5767i	−0.817538	−	0.324831i
$286$	7.16427			0.0250499
$287$		−	698.933i		−	2.43531i
$288$	−34.9411	+	37.0286i	−0.121323	+	0.128572i
$289$	−526.009			−1.82010
$290$		−	150.747i		−	0.519816i
$291$	134.509	−	338.533i	0.462229	−	1.16334i
$292$	136.025			0.465838
$293$			112.271i			0.383176i	0.981475	+	0.191588i	$0.0613638\pi$
$293$			112.271i			0.383176i	−0.981475	+	0.191588i	$0.938636\pi$
$294$	−134.860	−	53.5838i	−0.458709	−	0.182258i
$295$	45.0116			0.152582
$296$		−	49.4190i		−	0.166956i
$297$	−16.8172	−	36.0776i	−0.0566236	−	0.121473i
$298$	135.174			0.453603
$299$			118.743i			0.397133i
$300$	20.6922	−	52.0783i	0.0689739	−	0.173594i
$301$	−34.2439			−0.113767
$302$			71.2385i			0.235889i
$303$	182.309	+	72.4366i	0.601681	+	0.239065i
$304$	−57.0457			−0.187650
$305$		−	381.129i		−	1.24960i
$306$	−264.276	−	249.378i	−0.863649	−	0.814961i
$307$	306.152			0.997237			0.498618	−	0.866822i	$-0.333841\pi$
$307$	306.152			0.997237			0.498618	+	0.866822i	$0.333841\pi$
$308$			26.8951i			0.0873217i
$309$	−122.752	+	308.944i	−0.397256	+	0.999819i
$310$	−100.763			−0.325043
$311$		−	48.8450i		−	0.157058i	−0.996912	−	0.0785290i	$-0.974978\pi$
$311$		−	48.8450i		−	0.157058i	0.996912	−	0.0785290i	$-0.0250223\pi$
$312$	27.0971	+	10.7664i	0.0868497	+	0.0345078i
$313$	−230.948			−0.737852			−0.368926	−	0.929459i	$-0.620274\pi$
$313$	−230.948			−0.737852			−0.368926	+	0.929459i	$0.620274\pi$
$314$			322.661i			1.02758i
$315$	−330.166	+	349.891i	−1.04815	+	1.11077i
$316$	63.4050			0.200649
$317$		−	577.951i		−	1.82319i	−0.411091	−	0.911594i	$-0.634852\pi$
$317$		−	577.951i		−	1.82319i	0.411091	−	0.911594i	$-0.365148\pi$
$318$	10.9341	−	27.5191i	0.0343839	−	0.0865379i
$319$	26.8167			0.0840648
$320$		−	46.8801i		−	0.146500i
$321$	−277.990	−	110.453i	−0.866012	−	0.344091i
$322$	−445.767			−1.38437
$323$		−	407.140i		−	1.26050i
$324$	−9.38971	−	161.728i	−0.0289806	−	0.499159i
$325$	−32.0938			−0.0987503
$326$		−	313.894i		−	0.962864i
$327$	49.6632	−	124.993i	0.151875	−	0.382242i
$328$	−216.725			−0.660746
$329$			820.483i			2.49387i
$330$	34.0624	+	13.5339i	0.103219	+	0.0410120i
$331$	−551.705			−1.66678			−0.833391	−	0.552684i	$-0.813604\pi$
$331$	−551.705			−1.66678			−0.833391	+	0.552684i	$0.813604\pi$
$332$		−	187.273i		−	0.564076i
$333$	114.370	+	107.922i	0.343453	+	0.324091i
$334$	−62.7411			−0.187848
$335$		−	236.468i		−	0.705876i
$336$	−40.4178	+	101.724i	−0.120291	+	0.302750i
$337$	221.571			0.657482			0.328741	−	0.944420i	$-0.393376\pi$
$337$	221.571			0.657482			0.328741	+	0.944420i	$0.393376\pi$
$338$			222.303i			0.657702i
$339$	307.135	+	122.033i	0.906003	+	0.359980i
$340$	334.587			0.984081
$341$		−	17.9250i		−	0.0525660i
$342$	124.578	−	132.020i	0.364262	−	0.386024i
$343$	134.963			0.393477
$344$			10.6183i			0.0308672i
$345$	−224.316	+	564.561i	−0.650190	+	1.63641i
$346$	−412.231			−1.19142
$347$			111.195i			0.320446i	0.987081	+	0.160223i	$0.0512213\pi$
$347$			111.195i			0.320446i	−0.987081	+	0.160223i	$0.948779\pi$
$348$	101.428	+	40.3000i	0.291458	+	0.115805i
$349$	−661.311			−1.89488			−0.947438	−	0.319941i	$-0.896337\pi$
$349$	−661.311			−1.89488			−0.947438	+	0.319941i	$0.896337\pi$
$350$		−	120.482i		−	0.344235i
$351$	−84.0918	+	39.1985i	−0.239578	+	0.111677i
$352$	8.33960			0.0236921
$353$			75.7721i			0.214652i	0.994224	+	0.107326i	$0.0342288\pi$
$353$			75.7721i			0.214652i	−0.994224	+	0.107326i	$0.965771\pi$
$354$	−12.0332	+	30.2853i	−0.0339921	+	0.0855518i
$355$	617.086			1.73827
$356$			55.5073i			0.155920i
$357$	−726.014	−	288.466i	−2.03365	−	0.808027i
$358$	269.187			0.751920
$359$			268.049i			0.746656i	0.927699	+	0.373328i	$0.121783\pi$
$359$			268.049i			0.746656i	−0.927699	+	0.373328i	$0.878217\pi$
$360$	108.494	+	102.378i	0.301372	+	0.284383i
$361$	−157.612			−0.436598
$362$			273.805i			0.756367i
$363$	131.630	−	331.288i	0.362616	−	0.912638i
$364$	62.6886			0.172221
$365$		−	398.553i		−	1.09193i
$366$	256.437	+	101.889i	0.700647	+	0.278386i
$367$	−141.800			−0.386377			−0.193188	−	0.981162i	$-0.561883\pi$
$367$	−141.800			−0.386377			−0.193188	+	0.981162i	$0.561883\pi$
$368$			138.223i			0.375606i
$369$	473.287	−	501.563i	1.28262	−	1.35925i
$370$	−144.798			−0.391346
$371$		−	63.6648i		−	0.171603i
$372$	26.9376	−	67.7969i	0.0724129	−	0.182250i
$373$	699.710			1.87590			0.937949	−	0.346774i	$-0.112723\pi$
$373$	699.710			1.87590			0.937949	+	0.346774i	$0.112723\pi$
$374$			59.5205i			0.159146i
$375$	255.852	+	101.657i	0.682272	+	0.271086i
$376$	254.415			0.676635
$377$		−	62.5058i		−	0.165798i
$378$	−147.154	−	315.686i	−0.389295	−	0.835147i
$379$	102.781			0.271189			0.135594	−	0.990764i	$-0.456706\pi$
$379$	102.781			0.271189			0.135594	+	0.990764i	$0.456706\pi$
$380$			167.144i			0.439853i
$381$	168.626	−	424.400i	0.442588	−	1.11391i
$382$	453.169			1.18631
$383$			220.510i			0.575743i	0.957669	+	0.287872i	$0.0929476\pi$
$383$			220.510i			0.575743i	−0.957669	+	0.287872i	$0.907052\pi$
$384$	31.5425	+	12.5327i	0.0821420	+	0.0326373i
$385$	78.8028			0.204682
$386$		−	211.887i		−	0.548930i
$387$	−24.5738	−	23.1885i	−0.0634983	−	0.0599186i
$388$	−242.851			−0.625904
$389$			453.559i			1.16596i	0.812486	+	0.582980i	$0.198114\pi$
$389$			453.559i			1.16596i	−0.812486	+	0.582980i	$0.801886\pi$
$390$	31.5457	−	79.3947i	0.0808864	−	0.203576i
$391$	−986.510			−2.52304
$392$			96.7438i			0.246795i
$393$	−5.08038	−	2.01857i	−0.0129272	−	0.00513632i
$394$	304.451			0.772717
$395$		−	185.777i		−	0.470322i
$396$	−18.2122	+	19.3002i	−0.0459904	+	0.0487380i
$397$	118.483			0.298445			0.149222	−	0.988804i	$-0.452323\pi$
$397$	118.483			0.298445			0.149222	+	0.988804i	$0.452323\pi$
$398$		−	192.594i		−	0.483904i
$399$	144.104	−	362.682i	0.361163	−	0.908979i
$400$	−37.3590			−0.0933975
$401$		−	544.939i		−	1.35895i	−0.733698	−	0.679475i	$-0.762207\pi$
$401$		−	544.939i		−	1.35895i	0.733698	−	0.679475i	$-0.237793\pi$
$402$	159.104	+	63.2165i	0.395781	+	0.157255i
$403$	−41.7806			−0.103674
$404$		−	130.782i		−	0.323717i
$405$	−473.863	+	27.5119i	−1.17003	+	0.0679307i
$406$	234.651			0.577957
$407$		−	25.7584i		−	0.0632886i
$408$	−89.4472	+	225.122i	−0.219233	+	0.551769i
$409$	−102.472			−0.250542			−0.125271	−	0.992123i	$-0.539980\pi$
$409$	−102.472			−0.250542			−0.125271	+	0.992123i	$0.539980\pi$
$410$			635.004i			1.54879i
$411$	−155.089	−	61.6212i	−0.377346	−	0.149930i
$412$	221.625			0.537924
$413$			70.0646i			0.169648i
$414$	−319.888	−	301.854i	−0.772676	−	0.729117i
$415$	−548.712			−1.32220
$416$		−	19.4384i		−	0.0467270i
$417$	−206.311	+	519.247i	−0.494752	+	1.24520i
$418$	−29.7337			−0.0711331
$419$			96.9216i			0.231316i	0.993289	+	0.115658i	$0.0368977\pi$
$419$			96.9216i			0.231316i	−0.993289	+	0.115658i	$0.963102\pi$
$420$	298.052	+	118.424i	0.709648	+	0.281963i
$421$	−110.783			−0.263143			−0.131571	−	0.991307i	$-0.542002\pi$
$421$	−110.783			−0.263143			−0.131571	+	0.991307i	$0.542002\pi$
$422$		−	505.544i		−	1.19797i
$423$	−555.596	+	588.789i	−1.31347	+	1.39194i
$424$	−19.7411			−0.0465593
$425$		−	266.635i		−	0.627375i
$426$	−164.969	+	415.197i	−0.387252	+	0.974640i
$427$	593.261			1.38937
$428$			199.419i			0.465933i
$429$	14.1237	+	5.61174i	0.0329224	+	0.0130810i
$430$	31.1117			0.0723529
$431$		−	607.229i		−	1.40888i	−0.709762	−	0.704442i	$-0.751197\pi$
$431$		−	607.229i		−	1.40888i	0.709762	−	0.704442i	$-0.248803\pi$
$432$	−97.8875	+	45.6293i	−0.226592	+	0.105623i
$433$	−59.6603			−0.137784			−0.0688918	−	0.997624i	$-0.521946\pi$
$433$	−59.6603			−0.137784			−0.0688918	+	0.997624i	$0.521946\pi$
$434$		−	156.847i		−	0.361398i
$435$	118.079	−	297.183i	0.271446	−	0.683180i
$436$	−89.6653			−0.205654
$437$		−	492.814i		−	1.12772i
$438$	268.160	+	106.548i	0.612238	+	0.243259i
$439$	−626.921			−1.42806			−0.714032	−	0.700113i	$-0.753133\pi$
$439$	−626.921			−1.42806			−0.714032	+	0.700113i	$0.753133\pi$
$440$		−	24.4351i		−	0.0555343i
$441$	−223.893	−	211.271i	−0.507694	−	0.479073i
$442$	138.734			0.313877
$443$		−	468.294i		−	1.05710i	−0.848903	−	0.528548i	$-0.822737\pi$
$443$		−	468.294i		−	1.05710i	0.848903	−	0.528548i	$-0.177263\pi$
$444$	38.7097	−	97.4251i	0.0871840	−	0.219426i
$445$	162.637			0.365476
$446$		−	352.590i		−	0.790561i
$447$	266.483	+	105.881i	0.596158	+	0.236870i
$448$	72.9730			0.162886
$449$			368.675i			0.821102i	0.911838	+	0.410551i	$0.134664\pi$
$449$			368.675i			0.821102i	−0.911838	+	0.410551i	$0.865336\pi$
$450$	81.5854	−	86.4595i	0.181301	−	0.192132i
$451$	−112.962			−0.250471
$452$		−	220.327i		−	0.487449i
$453$	−55.8008	+	140.440i	−0.123181	+	0.310023i
$454$	−67.8857			−0.149528
$455$		−	183.678i		−	0.403688i
$456$	−112.460	−	44.6836i	−0.246623	−	0.0979904i
$457$	−400.226			−0.875768			−0.437884	−	0.899031i	$-0.644272\pi$
$457$	−400.226			−0.875768			−0.437884	+	0.899031i	$0.644272\pi$
$458$		−	116.470i		−	0.254302i
$459$	−325.660	−	698.632i	−0.709499	−	1.52207i
$460$	404.994			0.880423
$461$			126.850i			0.275162i	0.990490	+	0.137581i	$0.0439328\pi$
$461$			126.850i			0.275162i	−0.990490	+	0.137581i	$0.956067\pi$
$462$	−21.0668	+	53.0212i	−0.0455991	+	0.114764i
$463$	135.294			0.292213			0.146106	−	0.989269i	$-0.453326\pi$
$463$	135.294			0.292213			0.146106	+	0.989269i	$0.453326\pi$
$464$		−	72.7603i		−	0.156811i
$465$	−198.645	−	78.9274i	−0.427194	−	0.169736i
$466$	222.861			0.478243
$467$		−	684.277i		−	1.46526i	−0.680626	−	0.732631i	$-0.738292\pi$
$467$		−	684.277i		−	1.46526i	0.680626	−	0.732631i	$-0.261708\pi$
$468$	44.9861	+	42.4500i	0.0961242	+	0.0907052i
$469$	368.084			0.784828
$470$		−	745.437i		−	1.58604i
$471$	−252.739	+	636.096i	−0.536600	+	1.35052i
$472$	21.7256			0.0460287
$473$			5.53453i			0.0117009i
$474$	124.997	+	49.6648i	0.263707	+	0.104778i
$475$	133.198			0.280417
$476$			520.815i			1.09415i
$477$	43.1111	−	45.6867i	0.0903797	−	0.0957792i
$478$	−137.790			−0.288263
$479$			823.062i			1.71829i	0.511730	+	0.859146i	$0.329005\pi$
$479$			823.062i			1.71829i	−0.511730	+	0.859146i	$0.670995\pi$
$480$	36.7210	−	92.4198i	0.0765020	−	0.192541i
$481$	−60.0393			−0.124822
$482$		−	364.581i		−	0.756392i
$483$	−878.789	−	349.167i	−1.81944	−	0.722913i
$484$	−237.653			−0.491019
$485$			711.555i			1.46712i
$486$	108.170	−	326.186i	0.222571	−	0.671165i
$487$	592.347			1.21632			0.608159	−	0.793815i	$-0.291908\pi$
$487$	592.347			1.21632			0.608159	+	0.793815i	$0.291908\pi$
$488$		−	183.958i		−	0.376963i
$489$	245.871	−	618.813i	0.502805	−	1.26547i
$490$	283.460			0.578490
$491$			161.871i			0.329677i	0.986321	+	0.164838i	$0.0527103\pi$
$491$			161.871i			0.329677i	−0.986321	+	0.164838i	$0.947290\pi$
$492$	−427.252	−	169.759i	−0.868399	−	0.345039i
$493$	519.297			1.05334
$494$			69.3049i			0.140293i
$495$	56.5498	+	53.3619i	0.114242	+	0.107802i
$496$	−48.6350			−0.0980543
$497$			960.549i			1.93269i
$498$	146.690	−	369.192i	0.294559	−	0.741349i
$499$	459.838			0.921518			0.460759	−	0.887525i	$-0.347577\pi$
$499$	459.838			0.921518			0.460759	+	0.887525i	$0.347577\pi$
$500$		−	183.539i		−	0.367077i
$501$	−123.688	−	49.1448i	−0.246883	−	0.0980934i
$502$	274.975			0.547759
$503$			974.237i			1.93685i	0.249298	+	0.968427i	$0.419800\pi$
$503$			974.237i			1.93685i	−0.249298	+	0.968427i	$0.580200\pi$
$504$	−159.360	+	168.881i	−0.316190	+	0.335081i
$505$	−383.192			−0.758795
$506$			72.0454i			0.142382i
$507$	−174.129	+	438.250i	−0.343450	+	0.864399i
$508$	−304.449			−0.599308
$509$		−	377.335i		−	0.741325i	−0.928768	−	0.370663i	$-0.879131\pi$
$509$		−	377.335i		−	0.741325i	0.928768	−	0.370663i	$-0.120869\pi$
$510$	659.608	+	262.081i	1.29335	+	0.513884i
$511$	620.384			1.21406
$512$		−	22.6274i		−	0.0441942i
$513$	349.004	−	162.685i	0.680319	−	0.317124i
$514$	407.344			0.792498
$515$		−	649.362i		−	1.26090i
$516$	−8.31727	+	20.9330i	−0.0161187	+	0.0405679i
$517$	132.607			0.256494
$518$		−	225.391i		−	0.435118i
$519$	−812.676	−	322.899i	−1.56585	−	0.622156i
$520$	−56.9547			−0.109528
$521$		−	162.150i		−	0.311229i	−0.987818	−	0.155614i	$-0.950264\pi$
$521$		−	162.150i		−	0.311229i	0.987818	−	0.155614i	$-0.0497357\pi$
$522$	168.388	+	158.895i	0.322583	+	0.304397i
$523$	208.802			0.399238			0.199619	−	0.979874i	$-0.436030\pi$
$523$	208.802			0.399238			0.199619	+	0.979874i	$0.436030\pi$
$524$			3.64447i			0.00695510i
$525$	94.3731	−	237.519i	0.179758	−	0.452418i
$526$	−305.533			−0.580861
$527$		−	347.112i		−	0.658657i
$528$	16.4408	+	6.53237i	0.0311378	+	0.0123719i
$529$	−665.101			−1.25728
$530$			57.8417i			0.109135i
$531$	−47.4447	+	50.2792i	−0.0893498	+	0.0946878i
$532$	−260.175			−0.489050
$533$			263.299i			0.493995i
$534$	−43.4786	+	109.428i	−0.0814207	+	0.204921i
$535$	584.300			1.09215
$536$		−	114.135i		−	0.212939i
$537$	530.678	+	210.853i	0.988227	+	0.392650i
$538$	−606.920			−1.12810
$539$			50.4253i			0.0935535i
$540$	133.694	+	286.811i	0.247582	+	0.531132i
$541$	352.865			0.652246			0.326123	−	0.945327i	$-0.394258\pi$
$541$	352.865			0.652246			0.326123	+	0.945327i	$0.394258\pi$
$542$			206.422i			0.380852i
$543$	−214.470	+	539.781i	−0.394972	+	0.994072i
$544$	161.494			0.296864
$545$			262.720i			0.482055i
$546$	123.585	+	49.1037i	0.226346	+	0.0899335i
$547$	−770.600			−1.40878			−0.704388	−	0.709815i	$-0.748778\pi$
$547$	−770.600			−1.40878			−0.704388	+	0.709815i	$0.748778\pi$
$548$			111.255i			0.203020i
$549$	425.732	+	401.731i	0.775468	+	0.731751i
$550$	−19.4725			−0.0354045
$551$			259.416i			0.470810i
$552$	−108.269	+	272.494i	−0.196140	+	0.493649i
$553$	289.178			0.522926
$554$		−	623.215i		−	1.12494i
$555$	−285.456	−	113.420i	−0.514335	−	0.204360i
$556$	372.489			0.669943
$557$		−	876.693i		−	1.57395i	−0.616982	−	0.786977i	$-0.711645\pi$
$557$		−	876.693i		−	1.57395i	0.616982	−	0.786977i	$-0.288355\pi$
$558$	106.210	−	112.555i	0.190341	−	0.201712i
$559$	12.9002			0.0230773
$560$		−	213.811i		−	0.381806i
$561$	−46.6221	+	117.339i	−0.0831054	+	0.209161i
$562$	509.130			0.905924
$563$			554.277i			0.984507i	0.870452	+	0.492253i	$0.163827\pi$
$563$			554.277i			0.984507i	−0.870452	+	0.492253i	$0.836173\pi$
$564$	501.555	+	199.282i	0.889282	+	0.353337i
$565$	−645.560			−1.14258
$566$		−	494.878i		−	0.874343i
$567$	−42.8247	−	737.610i	−0.0755286	−	1.30090i
$568$	297.846			0.524377
$569$			809.715i			1.42305i	0.702661	+	0.711525i	$0.251995\pi$
$569$			809.715i			1.42305i	−0.702661	+	0.711525i	$0.748005\pi$
$570$	−130.923	+	329.509i	−0.229690	+	0.578087i
$571$	−558.346			−0.977838			−0.488919	−	0.872329i	$-0.662609\pi$
$571$	−558.346			−0.977838			−0.488919	+	0.872329i	$0.662609\pi$
$572$		−	10.1318i		−	0.0177129i
$573$	893.381	+	354.965i	1.55913	+	0.619486i
$574$	−988.440			−1.72202
$575$		−	322.742i		−	0.561291i
$576$	52.3664	+	49.4142i	0.0909138	+	0.0857886i
$577$	−554.180			−0.960451			−0.480225	−	0.877145i	$-0.659445\pi$
$577$	−554.180			−0.960451			−0.480225	+	0.877145i	$0.659445\pi$
$578$			743.889i			1.28700i
$579$	165.970	−	417.715i	0.286649	−	0.721443i
$580$	−213.188			−0.367566
$581$		−	854.119i		−	1.47008i
$582$	−478.758	−	190.224i	−0.822608	−	0.326845i
$583$	−10.2896			−0.0176494
$584$		−	192.368i		−	0.329397i
$585$	124.379	−	131.810i	0.212614	−	0.225316i
$586$	158.775			0.270946
$587$			97.9007i			0.166781i	0.996517	+	0.0833907i	$0.0265750\pi$
$587$			97.9007i			0.166781i	−0.996517	+	0.0833907i	$0.973425\pi$
$588$	−75.7790	+	190.722i	−0.128876	+	0.324356i
$589$	173.401			0.294399
$590$		−	63.6560i		−	0.107892i
$591$	600.196	+	238.475i	1.01556	+	0.403510i
$592$	−69.8891			−0.118056
$593$			572.655i			0.965691i	0.875706	+	0.482845i	$0.160397\pi$
$593$			572.655i			0.965691i	−0.875706	+	0.482845i	$0.839603\pi$
$594$	−51.0215	+	23.7831i	−0.0858947	+	0.0400389i
$595$	1525.99			2.56469
$596$		−	191.164i		−	0.320746i
$597$	150.858	−	379.681i	0.252693	−	0.635982i
$598$	167.928			0.280815
$599$			398.358i			0.665038i	0.943097	+	0.332519i	$0.107899\pi$
$599$			398.358i			0.665038i	−0.943097	+	0.332519i	$0.892101\pi$
$600$	−73.6498	−	29.2631i	−0.122750	−	0.0487719i
$601$	522.651			0.869636			0.434818	−	0.900518i	$-0.356813\pi$
$601$	522.651			0.869636			0.434818	+	0.900518i	$0.356813\pi$
$602$			48.4282i			0.0804454i
$603$	264.142	+	249.251i	0.438046	+	0.413351i
$604$	100.747			0.166799
$605$			696.325i			1.15095i
$606$	102.441	−	257.824i	0.169044	−	0.425453i
$607$	−926.833			−1.52691			−0.763454	−	0.645863i	$-0.776498\pi$
$607$	−926.833			−1.52691			−0.763454	+	0.645863i	$0.776498\pi$
$608$			80.6748i			0.132689i
$609$	462.592	+	183.801i	0.759593	+	0.301807i
$610$	−538.998			−0.883603
$611$		−	309.089i		−	0.505874i
$612$	−352.674	+	373.743i	−0.576264	+	0.610692i
$613$	−19.2421			−0.0313900			−0.0156950	−	0.999877i	$-0.504996\pi$
$613$	−19.2421			−0.0313900			−0.0156950	+	0.999877i	$0.504996\pi$
$614$		−	432.964i		−	0.705153i
$615$	−497.396	+	1251.85i	−0.808774	+	2.03553i
$616$	38.0354			0.0617458
$617$			661.828i			1.07266i	0.844010	+	0.536328i	$0.180189\pi$
$617$			661.828i			1.07266i	−0.844010	+	0.536328i	$0.819811\pi$
$618$	436.913	+	173.598i	0.706979	+	0.280902i
$619$	−558.769			−0.902696			−0.451348	−	0.892348i	$-0.649057\pi$
$619$	−558.769			−0.902696			−0.451348	+	0.892348i	$0.649057\pi$
$620$			142.501i			0.229840i
$621$	−394.189	−	845.645i	−0.634764	−	1.36175i
$622$	−69.0773			−0.111057
$623$			253.159i			0.406354i
$624$	15.2260	−	38.3211i	0.0244007	−	0.0614120i
$625$	−771.263			−1.23402
$626$			326.609i			0.521740i
$627$	−58.6172	−	23.2902i	−0.0934883	−	0.0371455i
$628$	456.311			0.726610
$629$		−	498.804i		−	0.793012i
$630$	494.821	+	466.926i	0.785431	+	0.741152i
$631$	−812.363			−1.28742			−0.643711	−	0.765269i	$-0.722606\pi$
$631$	−812.363			−1.28742			−0.643711	+	0.765269i	$0.722606\pi$
$632$		−	89.6682i		−	0.141880i
$633$	395.990	−	996.633i	0.625576	−	1.57446i
$634$	−817.346			−1.28919
$635$			892.036i			1.40478i
$636$	−38.9178	−	15.4631i	−0.0611916	−	0.0243131i
$637$	117.534			0.184512
$638$		−	37.9245i		−	0.0594428i
$639$	−650.443	+	689.302i	−1.01791	+	1.07872i
$640$	−66.2985			−0.103591
$641$			507.120i			0.791139i	0.918436	+	0.395569i	$0.129453\pi$
$641$			507.120i			0.791139i	−0.918436	+	0.395569i	$0.870547\pi$
$642$	−156.204	+	393.137i	−0.243309	+	0.612363i
$643$	−719.491			−1.11896			−0.559480	−	0.828844i	$-0.688999\pi$
$643$	−719.491			−1.11896			−0.559480	+	0.828844i	$0.688999\pi$
$644$			630.410i			0.978897i
$645$	61.3339	+	24.3697i	0.0950913	+	0.0377824i
$646$	−575.783			−0.891305
$647$			703.918i			1.08797i	0.839094	+	0.543986i	$0.183085\pi$
$647$			703.918i			1.08797i	−0.839094	+	0.543986i	$0.816915\pi$
$648$	−228.717	+	13.2791i	−0.352959	+	0.0204924i
$649$	11.3239			0.0174482
$650$			45.3875i			0.0698270i
$651$	122.857	−	309.209i	0.188721	−	0.474976i
$652$	−443.913			−0.680848
$653$			1125.85i			1.72412i	0.506802	+	0.862062i	$0.330827\pi$
$653$			1125.85i			1.72412i	−0.506802	+	0.862062i	$0.669173\pi$
$654$	−176.767	−	70.2344i	−0.270286	−	0.107392i
$655$	10.6783			0.0163028
$656$			306.495i			0.467218i
$657$	445.195	+	420.097i	0.677618	+	0.639418i
$658$	1160.34			1.76343
$659$			724.827i			1.09989i	0.835201	+	0.549945i	$0.185351\pi$
$659$			724.827i			1.09989i	−0.835201	+	0.549945i	$0.814649\pi$
$660$	19.1399	−	48.1715i	0.0289998	−	0.0729872i
$661$	131.667			0.199194			0.0995969	−	0.995028i	$-0.468245\pi$
$661$	131.667			0.199194			0.0995969	+	0.995028i	$0.468245\pi$
$662$			780.228i			1.17859i
$663$	273.501	+	108.670i	0.412520	+	0.163906i
$664$	−264.844			−0.398862
$665$			762.314i			1.14634i
$666$	152.625	−	161.743i	0.229167	−	0.242858i
$667$	628.572			0.942386
$668$			88.7293i			0.132828i
$669$	276.182	−	695.099i	0.412829	−	1.03901i
$670$	−334.417			−0.499130
$671$		−	95.8836i		−	0.142897i
$672$	143.860	+	57.1594i	0.214077	+	0.0850587i
$673$	379.049			0.563223			0.281611	−	0.959529i	$-0.409131\pi$
$673$	379.049			0.563223			0.281611	+	0.959529i	$0.409131\pi$
$674$		−	313.349i		−	0.464910i
$675$	228.561	−	106.542i	0.338609	−	0.157839i
$676$	314.384			0.465065
$677$		−	119.387i		−	0.176347i	−0.996105	−	0.0881735i	$-0.971897\pi$
$677$		−	119.387i		−	0.176347i	0.996105	−	0.0881735i	$-0.0281030\pi$
$678$	172.581	−	434.355i	0.254544	−	0.640641i
$679$	−1107.60			−1.63122
$680$		−	473.178i		−	0.695850i
$681$	−133.830	−	53.1745i	−0.196520	−	0.0780830i
$682$	−25.3498			−0.0371698
$683$			655.524i			0.959772i	0.877331	+	0.479886i	$0.159322\pi$
$683$			655.524i			0.959772i	−0.877331	+	0.479886i	$0.840678\pi$
$684$	−186.705	−	176.179i	−0.272960	−	0.257572i
$685$	325.978			0.475880
$686$		−	190.866i		−	0.278230i
$687$	91.2307	−	229.611i	0.132796	−	0.334222i
$688$	15.0166			0.0218264
$689$			23.9836i			0.0348092i
$690$	798.409	+	317.230i	1.15711	+	0.459754i
$691$	−68.0969			−0.0985483			−0.0492742	−	0.998785i	$-0.515691\pi$
$691$	−68.0969			−0.0985483			−0.0492742	+	0.998785i	$0.515691\pi$
$692$			582.983i			0.842461i
$693$	−83.0625	+	88.0248i	−0.119859	+	0.127020i
$694$	157.253			0.226589
$695$		−	1091.39i		−	1.57035i
$696$	56.9928	−	143.440i	0.0818862	−	0.206092i
$697$	−2187.48			−3.13842
$698$			935.236i			1.33988i
$699$	439.350	+	174.566i	0.628541	+	0.249737i
$700$	−170.387			−0.243411
$701$			614.362i			0.876408i	0.898876	+	0.438204i	$0.144385\pi$
$701$			614.362i			0.876408i	−0.898876	+	0.438204i	$0.855615\pi$
$702$	55.4351	+	118.924i	0.0789674	+	0.169407i
$703$	249.179			0.354451
$704$		−	11.7940i		−	0.0167528i
$705$	583.897	−	1469.56i	0.828223	−	2.08448i
$706$	107.158			0.151782
$707$		−	596.471i		−	0.843665i
$708$	42.8299	+	17.0175i	0.0604943	+	0.0240361i
$709$	−635.282			−0.896026			−0.448013	−	0.894027i	$-0.647868\pi$
$709$	−635.282			−0.896026			−0.448013	+	0.894027i	$0.647868\pi$
$710$		−	872.692i		−	1.22914i
$711$	207.518	+	195.819i	0.291868	+	0.275414i
$712$	78.4992			0.110252
$713$		−	420.155i		−	0.589277i
$714$	−407.952	+	1026.74i	−0.571361	+	1.43801i
$715$	−29.6863			−0.0415192
$716$		−	380.688i		−	0.531687i
$717$	−271.640	−	107.930i	−0.378856	−	0.150530i
$718$	379.079			0.527965
$719$			549.236i			0.763889i	0.924185	+	0.381944i	$0.124745\pi$
$719$			549.236i			0.763889i	−0.924185	+	0.381944i	$0.875255\pi$
$720$	144.784	−	153.434i	0.201089	−	0.213102i
$721$	1010.79			1.40193
$722$			222.897i			0.308721i
$723$	285.575	−	718.738i	0.394986	−	0.994105i
$724$	387.219			0.534832
$725$			169.891i			0.234332i
$726$	−468.511	−	186.153i	−0.645332	−	0.256409i
$727$	152.671			0.210002			0.105001	−	0.994472i	$-0.466515\pi$
$727$	152.671			0.210002			0.105001	+	0.994472i	$0.466515\pi$
$728$		−	88.6551i		−	0.121779i
$729$	468.746	−	558.317i	0.642999	−	0.765867i
$730$	−563.640			−0.772109
$731$			107.175i			0.146614i
$732$	144.093	−	362.656i	0.196849	−	0.495432i
$733$	−447.647			−0.610706			−0.305353	−	0.952239i	$-0.598774\pi$
$733$	−447.647			−0.610706			−0.305353	+	0.952239i	$0.598774\pi$
$734$			200.536i			0.273209i
$735$	558.815	+	222.033i	0.760293	+	0.302086i
$736$	195.477			0.265594
$737$		−	59.4902i		−	0.0807194i
$738$	−709.317	−	669.330i	−0.961134	−	0.906951i
$739$	−339.860			−0.459891			−0.229946	−	0.973203i	$-0.573855\pi$
$739$	−339.860			−0.459891			−0.229946	+	0.973203i	$0.573855\pi$
$740$			204.775i			0.276724i
$741$	−54.2862	+	136.628i	−0.0732607	+	0.184384i
$742$	−90.0357			−0.121342
$743$		−	712.179i		−	0.958518i	−0.877673	−	0.479259i	$-0.840905\pi$
$743$		−	712.179i		−	0.958518i	0.877673	−	0.479259i	$-0.159095\pi$
$744$	−95.8793	−	38.0955i	−0.128870	−	0.0512037i
$745$	−560.113			−0.751830
$746$		−	989.539i		−	1.32646i
$747$	578.373	−	612.926i	0.774261	−	0.820517i
$748$	84.1747			0.112533
$749$			909.515i			1.21431i
$750$	143.765	−	361.829i	0.191686	−	0.482439i
$751$	−945.130			−1.25850			−0.629248	−	0.777205i	$-0.716637\pi$
$751$	−945.130			−1.25850			−0.629248	+	0.777205i	$0.716637\pi$
$752$		−	359.797i		−	0.478453i
$753$	542.087	+	215.386i	0.719904	+	0.286038i
$754$	−88.3966			−0.117237
$755$		−	295.188i		−	0.390977i
$756$	−446.447	+	208.107i	−0.590538	+	0.275273i
$757$	−115.161			−0.152128			−0.0760640	−	0.997103i	$-0.524235\pi$
$757$	−115.161			−0.152128			−0.0760640	+	0.997103i	$0.524235\pi$
$758$		−	145.354i		−	0.191759i
$759$	−56.4328	+	142.031i	−0.0743515	+	0.187129i
$760$	236.378			0.311023
$761$		−	1338.58i		−	1.75897i	−0.475926	−	0.879486i	$-0.657887\pi$
$761$		−	1338.58i		−	1.75897i	0.475926	−	0.879486i	$-0.342113\pi$
$762$	−600.192	−	238.473i	−0.787654	−	0.312957i
$763$	−408.947			−0.535972
$764$		−	640.878i		−	0.838846i
$765$	1095.07	+	1033.34i	1.43146	+	1.35077i
$766$	311.848			0.407112
$767$		−	26.3944i		−	0.0344126i
$768$	17.7239	−	44.6079i	0.0230781	−	0.0580832i
$769$	900.995			1.17164			0.585822	−	0.810440i	$-0.300772\pi$
$769$	900.995			1.17164			0.585822	+	0.810440i	$0.300772\pi$
$770$		−	111.444i		−	0.144732i
$771$	803.041	+	319.071i	1.04156	+	0.413840i
$772$	−299.653			−0.388152
$773$			651.171i			0.842394i	0.906969	+	0.421197i	$0.138390\pi$
$773$			651.171i			0.842394i	−0.906969	+	0.421197i	$0.861610\pi$
$774$	−32.7935	+	34.7527i	−0.0423688	+	0.0449001i
$775$	113.560			0.146529
$776$			343.443i			0.442581i
$777$	176.548	−	444.338i	0.227217	−	0.571863i
$778$	641.429			0.824459
$779$		−	1092.76i		−	1.40278i
$780$	−112.281	−	44.6124i	−0.143950	−	0.0571953i
$781$	155.245			0.198777
$782$			1395.14i			1.78406i
$783$	207.500	+	445.145i	0.265006	+	0.568512i
$784$	136.816			0.174511
$785$		−	1336.99i		−	1.70318i
$786$	−2.85470	+	7.18474i	−0.00363193	+	0.00914089i
$787$	−124.482			−0.158173			−0.0790864	−	0.996868i	$-0.525200\pi$
$787$	−124.482			−0.158173			−0.0790864	+	0.996868i	$0.525200\pi$
$788$		−	430.558i		−	0.546393i
$789$	−602.330	−	239.323i	−0.763410	−	0.303324i
$790$	−262.728			−0.332568
$791$		−	1004.87i		−	1.27038i
$792$	27.2947	+	25.7559i	0.0344630	+	0.0325201i
$793$	−223.491			−0.281830
$794$		−	167.560i		−	0.211032i
$795$	−45.3071	+	114.030i	−0.0569901	+	0.143433i
$796$	−272.369			−0.342172
$797$			127.953i			0.160543i	0.996773	+	0.0802714i	$0.0255787\pi$
$797$			127.953i			0.160543i	−0.996773	+	0.0802714i	$0.974421\pi$
$798$	−512.911	−	203.794i	−0.642745	−	0.255380i
$799$	2567.90			3.21390
$800$			52.8336i			0.0660420i
$801$	−171.428	+	181.670i	−0.214018	+	0.226804i
$802$	−770.661			−0.960923
$803$		−	100.267i		−	0.124866i
$804$	89.4016	−	225.007i	0.111196	−	0.279860i
$805$	1847.10			2.29454
$806$			59.0867i			0.0733086i
$807$	−1196.49	−	475.397i	−1.48264	−	0.589092i
$808$	−184.953			−0.228903
$809$		−	199.093i		−	0.246098i	−0.992401	−	0.123049i	$-0.960733\pi$
$809$		−	199.093i		−	0.246098i	0.992401	−	0.123049i	$-0.0392672\pi$
$810$	38.9077	+	670.144i	0.0480342	+	0.827338i
$811$	1434.93			1.76933			0.884666	−	0.466226i	$-0.154386\pi$
$811$	1434.93			1.76933			0.884666	+	0.466226i	$0.154386\pi$
$812$		−	331.846i		−	0.408677i
$813$	−161.689	+	406.941i	−0.198880	+	0.500543i
$814$	−36.4279			−0.0447518
$815$			1300.67i			1.59591i
$816$	318.370	+	126.497i	0.390160	+	0.155021i
$817$	−53.5394			−0.0655317
$818$			144.917i			0.177160i
$819$	205.173	+	193.607i	0.250517	+	0.236394i
$820$	898.032			1.09516
$821$		−	204.428i		−	0.248999i	−0.992220	−	0.124500i	$-0.960267\pi$
$821$		−	204.428i		−	0.248999i	0.992220	−	0.124500i	$-0.0397326\pi$
$822$	−87.1455	+	219.329i	−0.106016	+	0.266824i
$823$	680.399			0.826730			0.413365	−	0.910565i	$-0.364353\pi$
$823$	680.399			0.826730			0.413365	+	0.910565i	$0.364353\pi$
$824$		−	313.425i		−	0.380370i
$825$	−38.3882	−	15.2527i	−0.0465311	−	0.0184881i
$826$	99.0862			0.119959
$827$		−	397.160i		−	0.480242i	−0.970743	−	0.240121i	$-0.922813\pi$
$827$		−	397.160i		−	0.480242i	0.970743	−	0.240121i	$-0.0771872\pi$
$828$	−426.887	+	452.390i	−0.515563	+	0.546365i
$829$	746.956			0.901033			0.450516	−	0.892768i	$-0.351240\pi$
$829$	746.956			0.901033			0.450516	+	0.892768i	$0.351240\pi$
$830$			775.996i			0.934935i
$831$	488.161	−	1228.61i	0.587439	−	1.47847i
$832$	−27.4901			−0.0330410
$833$			976.471i			1.17223i
$834$	734.327	+	291.768i	0.880488	+	0.349842i
$835$	259.977			0.311350
$836$			42.0497i			0.0502987i
$837$	297.547	−	138.699i	0.355493	−	0.165709i
$838$	137.068			0.163565
$839$		−	1127.81i		−	1.34423i	−0.740448	−	0.672113i	$-0.765387\pi$
$839$		−	1127.81i		−	1.34423i	0.740448	−	0.672113i	$-0.234613\pi$
$840$	167.477	−	421.510i	0.199378	−	0.501797i
$841$	510.121			0.606565
$842$			156.671i			0.186070i
$843$	1003.70	+	398.799i	1.19063	+	0.473071i
$844$	−714.947			−0.847093
$845$		−	921.148i		−	1.09012i
$846$	832.673	+	785.732i	0.984248	+	0.928761i
$847$	−1083.89			−1.27968
$848$			27.9182i			0.0329224i
$849$	387.635	−	975.606i	0.456579	−	1.14912i
$850$	−377.078			−0.443621
$851$		−	603.768i		−	0.709480i
$852$	587.177	+	233.302i	0.689174	+	0.273828i
$853$	753.312			0.883133			0.441566	−	0.897229i	$-0.354423\pi$
$853$	753.312			0.883133			0.441566	+	0.897229i	$0.354423\pi$
$854$		−	838.998i		−	0.982433i
$855$	−516.206	+	547.046i	−0.603750	+	0.639820i
$856$	282.022			0.329464
$857$			1266.55i			1.47789i	0.673768	+	0.738943i	$0.264675\pi$
$857$			1266.55i			1.47789i	−0.673768	+	0.738943i	$0.735325\pi$
$858$	7.93619	−	19.9739i	0.00924964	−	0.0232796i
$859$	−1387.04			−1.61472			−0.807359	−	0.590061i	$-0.799104\pi$
$859$	−1387.04			−1.61472			−0.807359	+	0.590061i	$0.799104\pi$
$860$		−	43.9986i		−	0.0511612i
$861$	−1948.62	−	774.241i	−2.26320	−	0.899234i
$862$	−858.751			−0.996231
$863$		−	1367.09i		−	1.58412i	−0.610445	−	0.792059i	$-0.709009\pi$
$863$		−	1367.09i		−	1.58412i	0.610445	−	0.792059i	$-0.290991\pi$
$864$	64.5295	+	138.434i	0.0746870	+	0.160224i
$865$	1708.14			1.97473
$866$			84.3724i			0.0974278i
$867$	−582.684	+	1466.51i	−0.672070	+	1.69147i
$868$	−221.815			−0.255547
$869$		−	46.7373i		−	0.0537829i
$870$	−420.281	−	166.989i	−0.483081	−	0.191942i
$871$	−138.663			−0.159200
$872$			126.806i			0.145420i
$873$	−794.826	−	750.018i	−0.910453	−	0.859127i
$874$	−696.945			−0.797420
$875$		−	837.085i		−	0.956669i
$876$	150.681	−	379.236i	0.172010	−	0.432918i
$877$	−944.692			−1.07719			−0.538593	−	0.842566i	$-0.681044\pi$
$877$	−944.692			−1.07719			−0.538593	+	0.842566i	$0.681044\pi$
$878$			886.600i			1.00979i
$879$	313.010	+	124.367i	0.356097	+	0.141487i
$880$	−34.5564			−0.0392687
$881$			429.229i			0.487206i	0.969875	+	0.243603i	$0.0783295\pi$
$881$			429.229i			0.487206i	−0.969875	+	0.243603i	$0.921671\pi$
$882$	−298.782	+	316.633i	−0.338756	+	0.358994i
$883$	−1082.26			−1.22566			−0.612829	−	0.790215i	$-0.709969\pi$
$883$	−1082.26			−1.22566			−0.612829	+	0.790215i	$0.709969\pi$
$884$		−	196.199i		−	0.221945i
$885$	49.8615	−	125.492i	0.0563406	−	0.141799i
$886$	−662.267			−0.747480
$887$		−	1230.27i		−	1.38701i	−0.720454	−	0.693503i	$-0.756067\pi$
$887$		−	1230.27i		−	1.38701i	0.720454	−	0.693503i	$-0.243933\pi$
$888$	−137.780	−	54.7438i	−0.155157	−	0.0616484i
$889$	−1388.53			−1.56191
$890$		−	230.003i		−	0.258431i
$891$	−119.213	+	6.92138i	−0.133797	+	0.00776811i
$892$	−498.638			−0.559011
$893$			1282.80i			1.43651i
$894$	149.738	−	376.863i	0.167492	−	0.421547i
$895$	−1115.42			−1.24628
$896$		−	103.199i		−	0.115178i
$897$	331.054	+	131.537i	0.369068	+	0.146641i
$898$	521.385			0.580607
$899$			221.168i			0.246016i
$900$	−122.272	−	115.379i	−0.135858	−	0.128199i
$901$	−199.255			−0.221148
$902$			159.753i			0.177110i
$903$	−37.9335	+	95.4716i	−0.0420084	+	0.105727i
$904$	−311.590			−0.344679
$905$		−	1134.55i		−	1.25365i
$906$	198.612	+	78.9143i	0.219219	+	0.0871018i
$907$	509.761			0.562029			0.281015	−	0.959703i	$-0.409329\pi$
$907$	509.761			0.562029			0.281015	+	0.959703i	$0.409329\pi$
$908$			96.0049i			0.105732i
$909$	403.905	−	428.035i	0.444340	−	0.470886i
$910$	−259.760			−0.285451
$911$			437.916i			0.480698i	0.970687	+	0.240349i	$0.0772619\pi$
$911$			437.916i			0.480698i	−0.970687	+	0.240349i	$0.922738\pi$
$912$	−63.1922	+	159.043i	−0.0692896	+	0.174389i
$913$	−138.044			−0.151198
$914$			566.005i			0.619262i
$915$	−1062.58	−	422.195i	−1.16130	−	0.461415i
$916$	−164.714			−0.179819
$917$			16.6218i			0.0181262i
$918$	−988.015	+	460.553i	−1.07627	+	0.501692i
$919$	−206.806			−0.225034			−0.112517	−	0.993650i	$-0.535891\pi$
$919$	−206.806			−0.225034			−0.112517	+	0.993650i	$0.535891\pi$
$920$		−	572.749i		−	0.622553i
$921$	339.139	−	853.548i	0.368229	−	0.926763i
$922$	179.393			0.194569
$923$		−	361.854i		−	0.392041i
$924$	74.9833	+	29.7929i	0.0811507	+	0.0322434i
$925$	163.187			0.176418
$926$		−	191.335i		−	0.206626i
$927$	725.355	+	684.463i	0.782476	+	0.738364i
$928$	−102.899			−0.110882
$929$		−	80.0844i		−	0.0862050i	−0.999071	−	0.0431025i	$-0.986276\pi$
$929$		−	80.0844i		−	0.0862050i	0.999071	−	0.0431025i	$-0.0137242\pi$
$930$	−111.620	+	280.927i	−0.120022	+	0.302072i
$931$	−487.799			−0.523952
$932$		−	315.173i		−	0.338169i
$933$	−136.179	−	54.1079i	−0.145959	−	0.0579935i
$934$	−967.715			−1.03610
$935$		−	246.632i		−	0.263778i
$936$	60.0334	−	63.6200i	0.0641383	−	0.0679701i
$937$	689.289			0.735634			0.367817	−	0.929898i	$-0.380105\pi$
$937$	689.289			0.735634			0.367817	+	0.929898i	$0.380105\pi$
$938$		−	520.550i		−	0.554957i
$939$	−255.831	+	643.880i	−0.272451	+	0.685708i
$940$	−1054.21			−1.12150
$941$		−	1465.80i		−	1.55770i	−0.627208	−	0.778852i	$-0.715803\pi$
$941$		−	1465.80i		−	1.55770i	0.627208	−	0.778852i	$-0.284197\pi$
$942$	899.575	+	357.426i	0.954963	+	0.379433i
$943$	−2647.79			−2.80784
$944$		−	30.7246i		−	0.0325472i
$945$	609.754	+	1308.09i	0.645242	+	1.38422i
$946$	7.82701			0.00827380
$947$		−	1235.79i		−	1.30496i	−0.757808	−	0.652478i	$-0.773730\pi$
$947$		−	1235.79i		−	1.30496i	0.757808	−	0.652478i	$-0.226270\pi$
$948$	70.2367	−	176.773i	0.0740893	−	0.186469i
$949$	−233.708			−0.246268
$950$		−	188.371i		−	0.198285i
$951$	−1611.32	−	640.223i	−1.69434	−	0.673210i
$952$	736.544			0.773680
$953$			621.805i			0.652472i	0.945288	+	0.326236i	$0.105780\pi$
$953$			621.805i			0.652472i	−0.945288	+	0.326236i	$0.894220\pi$
$954$	−64.6107	−	60.9683i	−0.0677261	−	0.0639081i
$955$	−1877.78			−1.96626
$956$			194.864i			0.203833i
$957$	29.7061	−	74.7646i	0.0310408	−	0.0781240i
$958$	1163.99			1.21502
$959$			507.414i			0.529107i
$960$	−130.701	−	51.9313i	−0.136147	−	0.0540951i
$961$	−813.165			−0.846166
$962$			84.9084i			0.0882623i
$963$	−615.884	+	652.679i	−0.639548	+	0.677756i
$964$	−515.596			−0.534850
$965$			877.986i			0.909830i
$966$	−493.797	+	1242.79i	−0.511177	+	1.28654i
$967$	445.212			0.460406			0.230203	−	0.973143i	$-0.426061\pi$
$967$	445.212			0.460406			0.230203	+	0.973143i	$0.426061\pi$
$968$			336.092i			0.347203i
$969$	−1135.10	−	451.008i	−1.17142	−	0.465437i
$970$	1006.29			1.03741
$971$		−	778.821i		−	0.802081i	−0.916060	−	0.401041i	$-0.868649\pi$
$971$		−	778.821i		−	0.802081i	0.916060	−	0.401041i	$-0.131351\pi$
$972$	−461.297	−	152.975i	−0.474585	−	0.157382i
$973$	1698.85			1.74599
$974$		−	837.705i		−	0.860067i
$975$	−35.5518	+	89.4773i	−0.0364634	+	0.0917716i
$976$	−260.156			−0.266553
$977$		−	1097.06i		−	1.12289i	−0.827514	−	0.561445i	$-0.810246\pi$
$977$		−	1097.06i		−	1.12289i	0.827514	−	0.561445i	$-0.189754\pi$
$978$	−875.133	−	347.715i	−0.894819	−	0.355537i
$979$	40.9158			0.0417935
$980$		−	400.873i		−	0.409054i
$981$	−293.465	−	276.921i	−0.299149	−	0.282285i
$982$	228.921			0.233117
$983$			1642.72i			1.67112i	0.549396	+	0.835562i	$0.314858\pi$
$983$			1642.72i			1.67112i	−0.549396	+	0.835562i	$0.685142\pi$
$984$	−240.076	+	604.226i	−0.243980	+	0.614051i
$985$	−1261.54			−1.28075
$986$		−	734.396i		−	0.744824i
$987$	2287.50	+	908.888i	2.31763	+	0.920859i
$988$	98.0120			0.0992024
$989$			129.727i			0.131170i
$990$	75.4651	−	79.9736i	0.0762273	−	0.0807814i
$991$	516.307			0.520996			0.260498	−	0.965474i	$-0.416113\pi$
$991$	516.307			0.520996			0.260498	+	0.965474i	$0.416113\pi$
$992$			68.7802i			0.0693349i
$993$	−611.149	+	1538.15i	−0.615457	+	1.54899i
$994$	1358.42			1.36662
$995$			798.043i			0.802053i
$996$	−522.116	−	207.451i	−0.524213	−	0.208284i
$997$	−199.897			−0.200498			−0.100249	−	0.994962i	$-0.531964\pi$
$997$	−199.897			−0.200498			−0.100249	+	0.994962i	$0.531964\pi$
$998$		−	650.309i		−	0.651612i
$999$	427.579	−	199.312i	0.428007	−	0.199511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.13	✓	40
3.2	odd	2	inner	354.3.b.a.119.33	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.13	✓	40	1.1	even	1	trivial
354.3.b.a.119.33	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.10775 - 2.78799i) q^{3} -2.00000 q^{4} +5.86001i q^{5} +(-3.94282 - 1.56659i) q^{6} -9.12163 q^{7} +2.82843i q^{8} +(-6.54579 - 6.17678i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(1.10775 - 2.78799i) q^{3} -2.00000 q^{4} +5.86001i q^{5} +(-3.94282 - 1.56659i) q^{6} -9.12163 q^{7} +2.82843i q^{8} +(-6.54579 - 6.17678i) q^{9} +8.28731 q^{10} +1.47425i q^{11} +(-2.21549 + 5.57598i) q^{12} +3.43626 q^{13} +12.8999i q^{14} +(16.3377 + 6.49141i) q^{15} +4.00000 q^{16} +28.5484i q^{17} +(-8.73528 + 9.25715i) q^{18} -14.2614 q^{19} -11.7200i q^{20} +(-10.1045 + 25.4310i) q^{21} +2.08490 q^{22} +34.5558i q^{23} +(7.88563 + 3.13318i) q^{24} -9.33975 q^{25} -4.85961i q^{26} +(-24.4719 + 11.4073i) q^{27} +18.2433 q^{28} -18.1901i q^{29} +(9.18024 - 23.1050i) q^{30} -12.1587 q^{31} -5.65685i q^{32} +(4.11019 + 1.63309i) q^{33} +40.3735 q^{34} -53.4529i q^{35} +(13.0916 + 12.3536i) q^{36} -17.4723 q^{37} +20.1687i q^{38} +(3.80651 - 9.58027i) q^{39} -16.5746 q^{40} +76.6237i q^{41} +(35.9649 + 14.2899i) q^{42} +3.75414 q^{43} -2.94850i q^{44} +(36.1960 - 38.3584i) q^{45} +48.8692 q^{46} -89.9492i q^{47} +(4.43099 - 11.1520i) q^{48} +34.2041 q^{49} +13.2084i q^{50} +(79.5926 + 31.6243i) q^{51} -6.87252 q^{52} +6.97955i q^{53} +(16.1324 + 34.6085i) q^{54} -8.63911 q^{55} -25.7999i q^{56} +(-15.7980 + 39.7607i) q^{57} -25.7246 q^{58} -7.68115i q^{59} +(-32.6753 - 12.9828i) q^{60} -65.0390 q^{61} +17.1951i q^{62} +(59.7083 + 56.3423i) q^{63} -8.00000 q^{64} +20.1365i q^{65} +(2.30954 - 5.81269i) q^{66} -40.3529 q^{67} -57.0967i q^{68} +(96.3412 + 38.2790i) q^{69} -75.5938 q^{70} -105.305i q^{71} +(17.4706 - 18.5143i) q^{72} -68.0124 q^{73} +24.7095i q^{74} +(-10.3461 + 26.0391i) q^{75} +28.5228 q^{76} -13.4475i q^{77} +(-13.5485 - 5.38322i) q^{78} -31.7025 q^{79} +23.4401i q^{80} +(4.69486 + 80.8638i) q^{81} +108.362 q^{82} +93.6366i q^{83} +(20.2089 - 50.8620i) q^{84} -167.294 q^{85} -5.30916i q^{86} +(-50.7138 - 20.1500i) q^{87} -4.16980 q^{88} -27.7537i q^{89} +(-54.2470 - 51.1889i) q^{90} -31.3443 q^{91} -69.1115i q^{92} +(-13.4688 + 33.8985i) q^{93} -127.207 q^{94} -83.5721i q^{95} +(-15.7713 - 6.26636i) q^{96} +121.425 q^{97} -48.3719i q^{98} +(9.10610 - 9.65012i) 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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