LMFDB - Embedded newform 380.3.b.a.191.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.20
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30085 + 1.51914i) q^{2} -4.10739i q^{3} +(-0.615584 - 3.95235i) q^{4} -2.23607 q^{5} +(6.23970 + 5.34309i) q^{6} -8.55175i q^{7} +(6.80496 + 4.20625i) q^{8} -7.87063 q^{9} +O(q^{10})$	\(q+(-1.30085 + 1.51914i) q^{2} -4.10739i q^{3} +(-0.615584 - 3.95235i) q^{4} -2.23607 q^{5} +(6.23970 + 5.34309i) q^{6} -8.55175i q^{7} +(6.80496 + 4.20625i) q^{8} -7.87063 q^{9} +(2.90879 - 3.39690i) q^{10} -17.2986i q^{11} +(-16.2338 + 2.52844i) q^{12} -15.8301 q^{13} +(12.9913 + 11.1245i) q^{14} +9.18440i q^{15} +(-15.2421 + 4.86600i) q^{16} +32.2290 q^{17} +(10.2385 - 11.9566i) q^{18} +4.35890i q^{19} +(1.37649 + 8.83772i) q^{20} -35.1254 q^{21} +(26.2791 + 22.5029i) q^{22} +9.79902i q^{23} +(17.2767 - 27.9506i) q^{24} +5.00000 q^{25} +(20.5925 - 24.0481i) q^{26} -4.63878i q^{27} +(-33.7995 + 5.26432i) q^{28} -31.9344 q^{29} +(-13.9524 - 11.9475i) q^{30} +34.5468i q^{31} +(12.4355 - 29.4849i) q^{32} -71.0522 q^{33} +(-41.9251 + 48.9604i) q^{34} +19.1223i q^{35} +(4.84503 + 31.1075i) q^{36} +7.02156 q^{37} +(-6.62179 - 5.67027i) q^{38} +65.0202i q^{39} +(-15.2164 - 9.40546i) q^{40} -58.5883 q^{41} +(45.6928 - 53.3604i) q^{42} +9.58498i q^{43} +(-68.3703 + 10.6488i) q^{44} +17.5993 q^{45} +(-14.8861 - 12.7470i) q^{46} -4.12010i q^{47} +(19.9866 + 62.6053i) q^{48} -24.1325 q^{49} +(-6.50424 + 7.59571i) q^{50} -132.377i q^{51} +(9.74473 + 62.5659i) q^{52} -47.2057 q^{53} +(7.04696 + 6.03435i) q^{54} +38.6809i q^{55} +(35.9708 - 58.1943i) q^{56} +17.9037 q^{57} +(41.5419 - 48.5130i) q^{58} -10.7555i q^{59} +(36.2999 - 5.65377i) q^{60} -28.6033 q^{61} +(-52.4814 - 44.9401i) q^{62} +67.3077i q^{63} +(28.6149 + 57.2467i) q^{64} +35.3971 q^{65} +(92.4282 - 107.938i) q^{66} +63.0364i q^{67} +(-19.8397 - 127.380i) q^{68} +40.2484 q^{69} +(-29.0495 - 24.8752i) q^{70} -104.831i q^{71} +(-53.5593 - 33.1058i) q^{72} +132.285 q^{73} +(-9.13399 + 10.6667i) q^{74} -20.5369i q^{75} +(17.2279 - 2.68327i) q^{76} -147.934 q^{77} +(-98.7749 - 84.5815i) q^{78} -74.1167i q^{79} +(34.0824 - 10.8807i) q^{80} -89.8889 q^{81} +(76.2145 - 89.0039i) q^{82} +51.1044i q^{83} +(21.6226 + 138.828i) q^{84} -72.0663 q^{85} +(-14.5609 - 12.4686i) q^{86} +131.167i q^{87} +(72.7624 - 117.717i) q^{88} -71.7165 q^{89} +(-22.8940 + 26.7358i) q^{90} +135.375i q^{91} +(38.7291 - 6.03212i) q^{92} +141.897 q^{93} +(6.25902 + 5.35963i) q^{94} -9.74679i q^{95} +(-121.106 - 51.0776i) q^{96} +130.713 q^{97} +(31.3927 - 36.6607i) q^{98} +136.151i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.30085	+	1.51914i	−0.650424	+	0.759571i
$2$	−1.30085	+	1.51914i	−0.650424	+	0.759571i
$3$		−	4.10739i		−	1.36913i	−0.728952	−	0.684564i	$-0.759992\pi$
$3$		−	4.10739i		−	1.36913i	0.728952	−	0.684564i	$-0.240008\pi$
$4$	−0.615584	−	3.95235i	−0.153896	−	0.988087i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	6.23970	+	5.34309i	1.03995	+	0.890515i
$7$		−	8.55175i		−	1.22168i	−0.791754	−	0.610840i	$-0.790832\pi$
$7$		−	8.55175i		−	1.22168i	0.791754	−	0.610840i	$-0.209168\pi$
$8$	6.80496	+	4.20625i	0.850620	+	0.525781i
$9$	−7.87063			−0.874514
$10$	2.90879	−	3.39690i	0.290879	−	0.339690i
$11$		−	17.2986i		−	1.57260i	−0.617842	−	0.786302i	$-0.711993\pi$
$11$		−	17.2986i		−	1.57260i	0.617842	−	0.786302i	$-0.288007\pi$
$12$	−16.2338	+	2.52844i	−1.35282	+	0.210703i
$13$	−15.8301			−1.21770			−0.608849	−	0.793286i	$-0.708368\pi$
$13$	−15.8301			−1.21770			−0.608849	+	0.793286i	$0.708368\pi$
$14$	12.9913	+	11.1245i	0.927952	+	0.794610i
$15$			9.18440i			0.612293i
$16$	−15.2421	+	4.86600i	−0.952632	+	0.304125i
$17$	32.2290			1.89582			0.947912	−	0.318532i	$-0.103190\pi$
$17$	32.2290			1.89582			0.947912	+	0.318532i	$0.103190\pi$
$18$	10.2385	−	11.9566i	0.568805	−	0.664255i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	1.37649	+	8.83772i	0.0688244	+	0.441886i
$21$	−35.1254			−1.67264
$22$	26.2791	+	22.5029i	1.19450	+	1.02286i
$23$			9.79902i			0.426044i	0.977047	+	0.213022i	$0.0683306\pi$
$23$			9.79902i			0.426044i	−0.977047	+	0.213022i	$0.931669\pi$
$24$	17.2767	−	27.9506i	0.719862	−	1.16461i
$25$	5.00000			0.200000
$26$	20.5925	−	24.0481i	0.792020	−	0.924927i
$27$		−	4.63878i		−	0.171807i
$28$	−33.7995	+	5.26432i	−1.20713	+	0.188011i
$29$	−31.9344			−1.10119			−0.550594	−	0.834773i	$-0.685599\pi$
$29$	−31.9344			−1.10119			−0.550594	+	0.834773i	$0.685599\pi$
$30$	−13.9524	−	11.9475i	−0.465080	−	0.398250i
$31$			34.5468i			1.11441i	0.830374	+	0.557206i	$0.188127\pi$
$31$			34.5468i			1.11441i	−0.830374	+	0.557206i	$0.811873\pi$
$32$	12.4355	−	29.4849i	0.388611	−	0.921402i
$33$	−71.0522			−2.15310
$34$	−41.9251	+	48.9604i	−1.23309	+	1.44001i
$35$			19.1223i			0.546351i
$36$	4.84503	+	31.1075i	0.134584	+	0.864096i
$37$	7.02156			0.189772			0.0948859	−	0.995488i	$-0.469751\pi$
$37$	7.02156			0.189772			0.0948859	+	0.995488i	$0.469751\pi$
$38$	−6.62179	−	5.67027i	−0.174258	−	0.149218i
$39$			65.0202i			1.66718i
$40$	−15.2164	−	9.40546i	−0.380409	−	0.235136i
$41$	−58.5883			−1.42898			−0.714491	−	0.699645i	$-0.753342\pi$
$41$	−58.5883			−1.42898			−0.714491	+	0.699645i	$0.753342\pi$
$42$	45.6928	−	53.3604i	1.08792	−	1.27049i
$43$			9.58498i			0.222906i	0.993770	+	0.111453i	$0.0355505\pi$
$43$			9.58498i			0.222906i	−0.993770	+	0.111453i	$0.964449\pi$
$44$	−68.3703	+	10.6488i	−1.55387	+	0.242017i
$45$	17.5993			0.391095
$46$	−14.8861	−	12.7470i	−0.323611	−	0.277110i
$47$		−	4.12010i		−	0.0876618i	−0.999039	−	0.0438309i	$-0.986044\pi$
$47$		−	4.12010i		−	0.0876618i	0.999039	−	0.0438309i	$-0.0139563\pi$
$48$	19.9866	+	62.6053i	0.416387	+	1.30428i
$49$	−24.1325			−0.492500
$50$	−6.50424	+	7.59571i	−0.130085	+	0.151914i
$51$		−	132.377i		−	2.59563i
$52$	9.74473	+	62.5659i	0.187399	+	1.20319i
$53$	−47.2057			−0.890674			−0.445337	−	0.895363i	$-0.646916\pi$
$53$	−47.2057			−0.890674			−0.445337	+	0.895363i	$0.646916\pi$
$54$	7.04696	+	6.03435i	0.130499	+	0.111747i
$55$			38.6809i			0.703290i
$56$	35.9708	−	58.1943i	0.642336	−	1.03918i
$57$	17.9037			0.314100
$58$	41.5419	−	48.5130i	0.716240	−	0.836430i
$59$		−	10.7555i		−	0.182297i	−0.995837	−	0.0911484i	$-0.970946\pi$
$59$		−	10.7555i		−	0.182297i	0.995837	−	0.0911484i	$-0.0290538\pi$
$60$	36.2999	−	5.65377i	0.604999	−	0.0942294i
$61$	−28.6033			−0.468907			−0.234453	−	0.972127i	$-0.575330\pi$
$61$	−28.6033			−0.468907			−0.234453	+	0.972127i	$0.575330\pi$
$62$	−52.4814	−	44.9401i	−0.846475	−	0.724841i
$63$			67.3077i			1.06838i
$64$	28.6149	+	57.2467i	0.447108	+	0.894480i
$65$	35.3971			0.544571
$66$	92.4282	−	107.938i	1.40043	−	1.63543i
$67$			63.0364i			0.940841i	0.882442	+	0.470421i	$0.155898\pi$
$67$			63.0364i			0.940841i	−0.882442	+	0.470421i	$0.844102\pi$
$68$	−19.8397	−	127.380i	−0.291760	−	1.87324i
$69$	40.2484			0.583309
$70$	−29.0495	−	24.8752i	−0.414993	−	0.355360i
$71$		−	104.831i		−	1.47649i	−0.674533	−	0.738244i	$-0.735655\pi$
$71$		−	104.831i		−	1.47649i	0.674533	−	0.738244i	$-0.264345\pi$
$72$	−53.5593	−	33.1058i	−0.743879	−	0.459803i
$73$	132.285			1.81213			0.906064	−	0.423141i	$-0.139072\pi$
$73$	132.285			1.81213			0.906064	+	0.423141i	$0.139072\pi$
$74$	−9.13399	+	10.6667i	−0.123432	+	0.144145i
$75$		−	20.5369i		−	0.273826i
$76$	17.2279	−	2.68327i	0.226683	−	0.0353062i
$77$	−147.934			−1.92122
$78$	−98.7749	−	84.5815i	−1.26634	−	1.08438i
$79$		−	74.1167i		−	0.938185i	−0.883149	−	0.469093i	$-0.844581\pi$
$79$		−	74.1167i		−	0.938185i	0.883149	−	0.469093i	$-0.155419\pi$
$80$	34.0824	−	10.8807i	0.426030	−	0.136009i
$81$	−89.8889			−1.10974
$82$	76.2145	−	89.0039i	0.929445	−	1.08541i
$83$			51.1044i			0.615715i	0.951432	+	0.307858i	$0.0996121\pi$
$83$			51.1044i			0.615715i	−0.951432	+	0.307858i	$0.900388\pi$
$84$	21.6226	+	138.828i	0.257412	+	1.65271i
$85$	−72.0663			−0.847838
$86$	−14.5609	−	12.4686i	−0.169313	−	0.144984i
$87$			131.167i			1.50767i
$88$	72.7624	−	117.717i	0.826845	−	1.33769i
$89$	−71.7165			−0.805803			−0.402901	−	0.915243i	$-0.631998\pi$
$89$	−71.7165			−0.805803			−0.402901	+	0.915243i	$0.631998\pi$
$90$	−22.8940	+	26.7358i	−0.254377	+	0.297064i
$91$			135.375i			1.48764i
$92$	38.7291	−	6.03212i	0.420969	−	0.0655665i
$93$	141.897			1.52577
$94$	6.25902	+	5.35963i	0.0665854	+	0.0570174i
$95$		−	9.74679i		−	0.102598i
$96$	−121.106	−	51.0776i	−1.26152	−	0.532058i
$97$	130.713			1.34756			0.673780	−	0.738932i	$-0.264670\pi$
$97$	130.713			1.34756			0.673780	+	0.738932i	$0.264670\pi$
$98$	31.3927	−	36.6607i	0.320334	−	0.374089i
$99$			136.151i			1.37526i
$100$	−3.07792	−	19.7617i	−0.0307792	−	0.197617i
$101$	85.2316			0.843877			0.421939	−	0.906624i	$-0.361350\pi$
$101$	85.2316			0.843877			0.421939	+	0.906624i	$0.361350\pi$
$102$	201.099	+	172.203i	1.97156	+	1.68826i
$103$		−	112.339i		−	1.09067i	−0.838219	−	0.545335i	$-0.816403\pi$
$103$		−	112.339i		−	1.09067i	0.838219	−	0.545335i	$-0.183597\pi$
$104$	−107.723	−	66.5852i	−1.03580	−	0.640242i
$105$	78.5427			0.748026
$106$	61.4075	−	71.7122i	0.579316	−	0.676530i
$107$			58.5087i			0.546811i	0.961899	+	0.273405i	$0.0881500\pi$
$107$			58.5087i			0.546811i	−0.961899	+	0.273405i	$0.911850\pi$
$108$	−18.3341	+	2.85556i	−0.169760	+	0.0264403i
$109$	−79.1388			−0.726044			−0.363022	−	0.931781i	$-0.618255\pi$
$109$	−79.1388			−0.726044			−0.363022	+	0.931781i	$0.618255\pi$
$110$	−58.7618	−	50.3181i	−0.534198	−	0.457437i
$111$		−	28.8403i		−	0.259822i
$112$	41.6129	+	130.347i	0.371543	+	1.16381i
$113$	68.4029			0.605335			0.302668	−	0.953096i	$-0.402123\pi$
$113$	68.4029			0.605335			0.302668	+	0.953096i	$0.402123\pi$
$114$	−23.2900	+	27.1982i	−0.204298	+	0.238581i
$115$		−	21.9113i		−	0.190533i
$116$	19.6583	+	126.216i	0.169468	+	1.08807i
$117$	124.593			1.06489
$118$	16.3392	+	13.9913i	0.138467	+	0.118570i
$119$		−	275.615i		−	2.31609i
$120$	−38.6319	+	62.4994i	−0.321932	+	0.520829i
$121$	−178.243			−1.47308
$122$	37.2086	−	43.4525i	0.304988	−	0.356168i
$123$			240.645i			1.95646i
$124$	136.541	−	21.2664i	1.10114	−	0.171503i
$125$	−11.1803			−0.0894427
$126$	−102.250	−	87.5571i	−0.811507	−	0.694898i
$127$			135.567i			1.06746i	0.845656	+	0.533728i	$0.179210\pi$
$127$			135.567i			1.06746i	−0.845656	+	0.533728i	$0.820790\pi$
$128$	−124.190	−	30.9992i	−0.970231	−	0.242181i
$129$	39.3692			0.305188
$130$	−46.0463	+	53.7732i	−0.354202	+	0.413640i
$131$		−	177.469i		−	1.35472i	−0.735651	−	0.677361i	$-0.763124\pi$
$131$		−	177.469i		−	1.35472i	0.735651	−	0.677361i	$-0.236876\pi$
$132$	43.7386	+	280.823i	0.331353	+	2.12745i
$133$	37.2762			0.280272
$134$	−95.7612	−	82.0008i	−0.714636	−	0.611946i
$135$			10.3726i			0.0768342i
$136$	219.317	+	135.563i	1.61263	+	0.996789i
$137$	192.634			1.40609			0.703044	−	0.711147i	$-0.251824\pi$
$137$	192.634			1.40609			0.703044	+	0.711147i	$0.251824\pi$
$138$	−52.3570	+	61.1430i	−0.379399	+	0.443065i
$139$			96.5468i			0.694581i	0.937758	+	0.347291i	$0.112898\pi$
$139$			96.5468i			0.694581i	−0.937758	+	0.347291i	$0.887102\pi$
$140$	75.5780	−	11.7714i	0.539843	−	0.0840813i
$141$	−16.9229			−0.120020
$142$	159.253	+	136.369i	1.12150	+	0.960344i
$143$			273.839i			1.91496i
$144$	119.965	−	38.2985i	0.833090	−	0.265962i
$145$	71.4076			0.492466
$146$	−172.083	+	200.960i	−1.17865	+	1.37644i
$147$			99.1215i			0.674296i
$148$	−4.32236	−	27.7516i	−0.0292051	−	0.187511i
$149$	126.703			0.850355			0.425177	−	0.905110i	$-0.360212\pi$
$149$	126.703			0.850355			0.425177	+	0.905110i	$0.360212\pi$
$150$	31.1985	+	26.7154i	0.207990	+	0.178103i
$151$			208.179i			1.37867i	0.724444	+	0.689334i	$0.242097\pi$
$151$			208.179i			1.37867i	−0.724444	+	0.689334i	$0.757903\pi$
$152$	−18.3346	+	29.6621i	−0.120622	+	0.195146i
$153$	−253.663			−1.65793
$154$	192.439	−	224.732i	1.24961	−	1.45930i
$155$		−	77.2489i		−	0.498380i
$156$	256.982	−	40.0254i	1.64732	−	0.256573i
$157$	−248.103			−1.58027			−0.790135	−	0.612932i	$-0.789990\pi$
$157$	−248.103			−1.58027			−0.790135	+	0.612932i	$0.789990\pi$
$158$	112.594	+	96.4146i	0.712618	+	0.610219i
$159$			193.892i			1.21945i
$160$	−27.8067	+	65.9302i	−0.173792	+	0.412064i
$161$	83.7988			0.520489
$162$	116.932	−	136.554i	0.721802	−	0.842926i
$163$		−	240.012i		−	1.47247i	−0.676728	−	0.736233i	$-0.736603\pi$
$163$		−	240.012i		−	1.47247i	0.676728	−	0.736233i	$-0.263397\pi$
$164$	36.0660	+	231.561i	0.219915	+	1.41196i
$165$	158.878			0.962894
$166$	−77.6348	−	66.4791i	−0.467680	−	0.400476i
$167$		−	255.579i		−	1.53041i	−0.643785	−	0.765207i	$-0.722637\pi$
$167$		−	255.579i		−	1.53041i	0.643785	−	0.765207i	$-0.277363\pi$
$168$	−239.027	−	147.746i	−1.42278	−	0.879440i
$169$	81.5910			0.482787
$170$	93.7473	−	109.479i	0.551455	−	0.643993i
$171$		−	34.3073i		−	0.200627i
$172$	37.8832	−	5.90036i	0.220251	−	0.0343044i
$173$	−11.8248			−0.0683514			−0.0341757	−	0.999416i	$-0.510881\pi$
$173$	−11.8248			−0.0683514			−0.0341757	+	0.999416i	$0.510881\pi$
$174$	−199.261	−	170.629i	−1.14518	−	0.980624i
$175$		−	42.7588i		−	0.244336i
$176$	84.1753	+	263.668i	0.478269	+	1.49811i
$177$	−44.1771			−0.249588
$178$	93.2923	−	108.947i	0.524114	−	0.612064i
$179$		−	312.732i		−	1.74711i	−0.486727	−	0.873554i	$-0.661809\pi$
$179$		−	312.732i		−	1.74711i	0.486727	−	0.873554i	$-0.338191\pi$
$180$	−10.8338	−	69.5584i	−0.0601879	−	0.386435i
$181$	−35.0022			−0.193382			−0.0966911	−	0.995314i	$-0.530826\pi$
$181$	−35.0022			−0.193382			−0.0966911	+	0.995314i	$0.530826\pi$
$182$	−205.654	−	176.102i	−1.12996	−	0.967594i
$183$			117.485i			0.641994i
$184$	−41.2171	+	66.6819i	−0.224006	+	0.362402i
$185$	−15.7007			−0.0848685
$186$	−184.586	+	215.562i	−0.992400	+	1.15893i
$187$		−	557.518i		−	2.98138i
$188$	−16.2841	+	2.53627i	−0.0866175	+	0.0134908i
$189$	−39.6697			−0.209892
$190$	14.8068	+	12.6791i	0.0779303	+	0.0667321i
$191$		−	94.0943i		−	0.492641i	−0.969188	−	0.246320i	$-0.920778\pi$
$191$		−	94.0943i		−	0.492641i	0.969188	−	0.246320i	$-0.0792215\pi$
$192$	235.134	−	117.533i	1.22466	−	0.612149i
$193$	−187.124			−0.969554			−0.484777	−	0.874638i	$-0.661099\pi$
$193$	−187.124			−0.969554			−0.484777	+	0.874638i	$0.661099\pi$
$194$	−170.038	+	198.572i	−0.876485	+	1.02357i
$195$		−	145.390i		−	0.745588i
$196$	14.8556	+	95.3800i	0.0757937	+	0.486633i
$197$	117.006			0.593938			0.296969	−	0.954887i	$-0.404024\pi$
$197$	117.006			0.593938			0.296969	+	0.954887i	$0.404024\pi$
$198$	−206.833	−	177.112i	−1.04461	−	0.894505i
$199$		−	126.055i		−	0.633440i	−0.948519	−	0.316720i	$-0.897418\pi$
$199$		−	126.055i		−	0.633440i	0.948519	−	0.316720i	$-0.102582\pi$
$200$	34.0248	+	21.0312i	0.170124	+	0.105156i
$201$	258.915			1.28813
$202$	−110.873	+	129.479i	−0.548878	+	0.640985i
$203$			273.096i			1.34530i
$204$	−523.200	+	81.4892i	−2.56471	+	0.399457i
$205$	131.007			0.639060
$206$	170.659	+	146.136i	0.828440	+	0.709398i
$207$		−	77.1244i		−	0.372582i
$208$	241.284	−	77.0292i	1.16002	−	0.370333i
$209$	75.4030			0.360780
$210$	−102.172	+	119.317i	−0.486534	+	0.568179i
$211$		−	188.920i		−	0.895356i	−0.894195	−	0.447678i	$-0.852251\pi$
$211$		−	188.920i		−	0.895356i	0.894195	−	0.447678i	$-0.147749\pi$
$212$	29.0591	+	186.573i	0.137071	+	0.880064i
$213$	−430.580			−2.02150
$214$	−88.8831	−	76.1110i	−0.415341	−	0.355659i
$215$		−	21.4327i		−	0.0996868i
$216$	19.5119	−	31.5667i	0.0903326	−	0.146142i
$217$	295.435			1.36145
$218$	102.948	−	120.223i	0.472237	−	0.551482i
$219$		−	543.347i		−	2.48104i
$220$	152.881	−	23.8114i	0.694912	−	0.108233i
$221$	−510.187			−2.30854
$222$	43.8124	+	37.5168i	0.197353	+	0.168995i
$223$		−	13.2572i		−	0.0594492i	−0.999558	−	0.0297246i	$-0.990537\pi$
$223$		−	13.2572i		−	0.0594492i	0.999558	−	0.0297246i	$-0.00946303\pi$
$224$	−252.147	−	106.346i	−1.12566	−	0.474757i
$225$	−39.3531			−0.174903
$226$	−88.9818	+	103.914i	−0.393725	+	0.459795i
$227$		−	330.240i		−	1.45480i	−0.686213	−	0.727400i	$-0.740728\pi$
$227$		−	330.240i		−	1.45480i	0.686213	−	0.727400i	$-0.259272\pi$
$228$	−11.0212	−	70.7616i	−0.0483387	−	0.310358i
$229$	−154.700			−0.675546			−0.337773	−	0.941228i	$-0.609674\pi$
$229$	−154.700			−0.675546			−0.337773	+	0.941228i	$0.609674\pi$
$230$	33.2863	+	28.5033i	0.144723	+	0.123927i
$231$			607.621i			2.63039i
$232$	−217.313	−	134.324i	−0.936692	−	0.578984i
$233$	−334.942			−1.43752			−0.718760	−	0.695258i	$-0.755290\pi$
$233$	−334.942			−1.43752			−0.718760	+	0.695258i	$0.755290\pi$
$234$	−162.076	+	189.274i	−0.692633	+	0.808862i
$235$			9.21283i			0.0392035i
$236$	−42.5095	+	6.62092i	−0.180125	+	0.0280547i
$237$	−304.426			−1.28450
$238$	418.698	+	358.533i	1.75923	+	1.50644i
$239$			5.12926i			0.0214613i	0.999942	+	0.0107307i	$0.00341575\pi$
$239$			5.12926i			0.0214613i	−0.999942	+	0.0107307i	$0.996584\pi$
$240$	−44.6913	−	139.990i	−0.186214	−	0.583290i
$241$	−92.3840			−0.383336			−0.191668	−	0.981460i	$-0.561390\pi$
$241$	−92.3840			−0.383336			−0.191668	+	0.981460i	$0.561390\pi$
$242$	231.867	−	270.776i	0.958129	−	1.11891i
$243$			327.459i			1.34757i
$244$	17.6077	+	113.050i	0.0721629	+	0.463321i
$245$	53.9619			0.220253
$246$	−365.573	−	313.042i	−1.48607	−	1.27253i
$247$		−	69.0017i		−	0.279359i
$248$	−145.312	+	235.089i	−0.585937	+	0.947941i
$249$	209.905			0.842994
$250$	14.5439	−	16.9845i	0.0581757	−	0.0679381i
$251$			54.8825i			0.218655i	0.994006	+	0.109328i	$0.0348698\pi$
$251$			54.8825i			0.218655i	−0.994006	+	0.109328i	$0.965130\pi$
$252$	266.023	−	41.4335i	1.05565	−	0.164419i
$253$	169.510			0.669999
$254$	−205.946	−	176.352i	−0.810809	−	0.694300i
$255$			296.004i			1.16080i
$256$	208.644	−	148.336i	0.815016	−	0.579439i
$257$	50.9563			0.198274			0.0991368	−	0.995074i	$-0.468392\pi$
$257$	50.9563			0.198274			0.0991368	+	0.995074i	$0.468392\pi$
$258$	−51.2134	+	59.8074i	−0.198502	+	0.231812i
$259$		−	60.0466i		−	0.231840i
$260$	−21.7899	−	139.902i	−0.0838073	−	0.538083i
$261$	251.344			0.963004
$262$	269.600	+	230.860i	1.02901	+	0.881144i
$263$		−	412.962i		−	1.57020i	−0.619370	−	0.785099i	$-0.712612\pi$
$263$		−	412.962i		−	1.57020i	0.619370	−	0.785099i	$-0.287388\pi$
$264$	−483.507	−	298.863i	−1.83147	−	1.13206i
$265$	105.555			0.398322
$266$	−48.4907	+	56.6279i	−0.182296	+	0.212887i
$267$			294.567i			1.10325i
$268$	249.142	−	38.8042i	0.929633	−	0.144792i
$269$	159.174			0.591726			0.295863	−	0.955230i	$-0.404393\pi$
$269$	159.174			0.591726			0.295863	+	0.955230i	$0.404393\pi$
$270$	−15.7575	−	13.4932i	−0.0583610	−	0.0499749i
$271$			153.048i			0.564752i	0.959304	+	0.282376i	$0.0911226\pi$
$271$			153.048i			0.564752i	−0.959304	+	0.282376i	$0.908877\pi$
$272$	−491.238	+	156.827i	−1.80602	+	0.576568i
$273$	556.037			2.03676
$274$	−250.588	+	292.638i	−0.914554	+	1.06802i
$275$		−	86.4932i		−	0.314521i
$276$	−24.7762	−	159.076i	−0.0897690	−	0.576361i
$277$	364.029			1.31418			0.657092	−	0.753810i	$-0.271786\pi$
$277$	364.029			1.31418			0.657092	+	0.753810i	$0.271786\pi$
$278$	−146.668	−	125.593i	−0.527584	−	0.451773i
$279$		−	271.905i		−	0.974569i
$280$	−80.4332	+	130.126i	−0.287261	+	0.464737i
$281$	−309.295			−1.10070			−0.550348	−	0.834936i	$-0.685505\pi$
$281$	−309.295			−1.10070			−0.550348	+	0.834936i	$0.685505\pi$
$282$	22.0141	−	25.7082i	0.0780641	−	0.0911639i
$283$		−	85.2798i		−	0.301342i	−0.988584	−	0.150671i	$-0.951857\pi$
$283$		−	85.2798i		−	0.301342i	0.988584	−	0.150671i	$-0.0481434\pi$
$284$	−414.327	+	64.5321i	−1.45890	+	0.227226i
$285$	−40.0339			−0.140470
$286$	−416.000	−	356.223i	−1.45454	−	1.24553i
$287$			501.032i			1.74576i
$288$	−97.8755	+	232.064i	−0.339845	+	0.805779i
$289$	749.710			2.59415
$290$	−92.8905	+	108.478i	−0.320312	+	0.374063i
$291$		−	536.890i		−	1.84498i
$292$	−81.4327	−	522.838i	−0.278879	−	1.79054i
$293$	105.393			0.359702			0.179851	−	0.983694i	$-0.442438\pi$
$293$	105.393			0.359702			0.179851	+	0.983694i	$0.442438\pi$
$294$	−150.580	−	128.942i	−0.512175	−	0.438578i
$295$			24.0501i			0.0815256i
$296$	47.7814	+	29.5344i	0.161424	+	0.0997784i
$297$	−80.2445			−0.270184
$298$	−164.821	+	192.480i	−0.553091	+	0.645905i
$299$		−	155.119i		−	0.518793i
$300$	−81.1691	+	12.6422i	−0.270564	+	0.0421407i
$301$	81.9684			0.272320
$302$	−316.253	−	270.809i	−1.04720	−	0.896719i
$303$		−	350.079i		−	1.15538i
$304$	−21.2104	−	66.4388i	−0.0697711	−	0.218549i
$305$	63.9590			0.209701
$306$	329.977	−	385.349i	1.07836	−	1.25931i
$307$			302.784i			0.986266i	0.869954	+	0.493133i	$0.164148\pi$
$307$			302.784i			0.986266i	−0.869954	+	0.493133i	$0.835852\pi$
$308$	91.0656	+	584.686i	0.295668	+	1.89833i
$309$	−461.419			−1.49327
$310$	117.352	+	100.489i	0.378555	+	0.324159i
$311$			75.6298i			0.243183i	0.992580	+	0.121591i	$0.0387997\pi$
$311$			75.6298i			0.243183i	−0.992580	+	0.121591i	$0.961200\pi$
$312$	−273.491	+	442.460i	−0.876574	+	1.41814i
$313$	−90.5396			−0.289264			−0.144632	−	0.989486i	$-0.546200\pi$
$313$	−90.5396			−0.289264			−0.144632	+	0.989486i	$0.546200\pi$
$314$	322.744	−	376.903i	1.02785	−	1.20033i
$315$		−	150.504i		−	0.477792i
$316$	−292.935	+	45.6250i	−0.927009	+	0.144383i
$317$	201.518			0.635705			0.317852	−	0.948140i	$-0.397038\pi$
$317$	201.518			0.635705			0.317852	+	0.948140i	$0.397038\pi$
$318$	−294.550	−	252.224i	−0.926257	−	0.793159i
$319$			552.423i			1.73173i
$320$	−63.9850	−	128.008i	−0.199953	−	0.400024i
$321$	240.318			0.748654
$322$	−109.010	+	127.302i	−0.338539	+	0.395349i
$323$			140.483i			0.434932i
$324$	55.3342	+	355.272i	0.170784	+	1.09652i
$325$	−79.1503			−0.243539
$326$	364.612	+	312.219i	1.11844	+	0.957728i
$327$			325.054i			0.994048i
$328$	−398.691	−	246.437i	−1.21552	−	0.751332i
$329$	−35.2341			−0.107095
$330$	−206.676	+	241.358i	−0.626290	+	0.731387i
$331$			578.963i			1.74913i	0.484907	+	0.874566i	$0.338854\pi$
$331$			578.963i			1.74913i	−0.484907	+	0.874566i	$0.661146\pi$
$332$	201.982	−	31.4590i	0.608380	−	0.0947561i
$333$	−55.2641			−0.165958
$334$	388.261	+	332.470i	1.16246	+	0.995418i
$335$		−	140.954i		−	0.420757i
$336$	535.385	−	170.920i	1.59341	−	0.508691i
$337$	592.466			1.75806			0.879030	−	0.476767i	$-0.158191\pi$
$337$	592.466			1.75806			0.879030	+	0.476767i	$0.158191\pi$
$338$	−106.138	+	123.948i	−0.314016	+	0.366711i
$339$		−	280.957i		−	0.828782i
$340$	44.3628	+	284.831i	0.130479	+	0.837738i
$341$	597.612			1.75253
$342$	52.1176	+	44.6286i	0.152391	+	0.130493i
$343$		−	212.661i		−	0.620002i
$344$	−40.3168	+	65.2254i	−0.117200	+	0.189609i
$345$	−89.9981			−0.260864
$346$	15.3823	−	17.9635i	0.0444574	−	0.0519178i
$347$		−	299.965i		−	0.864451i	−0.901765	−	0.432226i	$-0.857728\pi$
$347$		−	299.965i		−	0.864451i	0.901765	−	0.432226i	$-0.142272\pi$
$348$	518.418	−	80.7444i	1.48971	−	0.232024i
$349$	−204.300			−0.585386			−0.292693	−	0.956206i	$-0.594551\pi$
$349$	−204.300			−0.585386			−0.292693	+	0.956206i	$0.594551\pi$
$350$	64.9566	+	55.6227i	0.185590	+	0.158922i
$351$			73.4321i			0.209208i
$352$	−510.048	−	215.118i	−1.44900	−	0.611130i
$353$	−562.400			−1.59320			−0.796601	−	0.604506i	$-0.793371\pi$
$353$	−562.400			−1.59320			−0.796601	+	0.604506i	$0.793371\pi$
$354$	57.4677	−	67.1112i	0.162338	−	0.189580i
$355$			234.409i			0.660306i
$356$	44.1475	+	283.448i	0.124010	+	0.796203i
$357$	−1132.06			−3.17102
$358$	475.085	+	406.818i	1.32705	+	1.13636i
$359$			154.369i			0.429997i	0.976614	+	0.214998i	$0.0689746\pi$
$359$			154.369i			0.429997i	−0.976614	+	0.214998i	$0.931025\pi$
$360$	119.762	+	74.0268i	0.332673	+	0.205630i
$361$	−19.0000			−0.0526316
$362$	45.5325	−	53.1733i	0.125781	−	0.146887i
$363$			732.113i			2.01684i
$364$	535.048	−	83.3346i	1.46991	−	0.228941i
$365$	−295.799			−0.810408
$366$	−178.476	−	152.830i	−0.487640	−	0.417569i
$367$			45.3220i			0.123493i	0.998092	+	0.0617466i	$0.0196671\pi$
$367$			45.3220i			0.123493i	−0.998092	+	0.0617466i	$0.980333\pi$
$368$	−47.6821	−	149.358i	−0.129571	−	0.405863i
$369$	461.126			1.24966
$370$	20.4242	−	23.8516i	0.0552006	−	0.0644637i
$371$			403.692i			1.08812i
$372$	−87.3495	−	560.826i	−0.234810	−	1.50760i
$373$	−617.732			−1.65612			−0.828059	−	0.560641i	$-0.810555\pi$
$373$	−617.732			−1.65612			−0.828059	+	0.560641i	$0.810555\pi$
$374$	846.949	+	725.247i	2.26457	+	1.93916i
$375$			45.9220i			0.122459i
$376$	17.3302	−	28.0371i	0.0460909	−	0.0745669i
$377$	505.524			1.34091
$378$	51.6043	−	60.2639i	0.136519	−	0.159428i
$379$		−	206.852i		−	0.545784i	−0.962045	−	0.272892i	$-0.912020\pi$
$379$		−	206.852i		−	0.545784i	0.962045	−	0.272892i	$-0.0879802\pi$
$380$	−38.5227	+	5.99997i	−0.101376	+	0.0157894i
$381$	556.826			1.46149
$382$	142.943	+	122.403i	0.374195	+	0.320425i
$383$		−	178.107i		−	0.465032i	−0.972593	−	0.232516i	$-0.925304\pi$
$383$		−	178.107i		−	0.465032i	0.972593	−	0.232516i	$-0.0746958\pi$
$384$	−127.326	+	510.095i	−0.331577	+	1.32837i
$385$	330.790			0.859194
$386$	243.420	−	284.268i	0.630622	−	0.736445i
$387$		−	75.4398i		−	0.194935i
$388$	−80.4650	−	516.624i	−0.207384	−	1.33151i
$389$	−426.409			−1.09617			−0.548084	−	0.836423i	$-0.684643\pi$
$389$	−426.409			−1.09617			−0.548084	+	0.836423i	$0.684643\pi$
$390$	220.867	+	189.130i	0.566327	+	0.484948i
$391$			315.813i			0.807705i
$392$	−164.221	−	101.507i	−0.418930	−	0.258947i
$393$	−728.932			−1.85479
$394$	−152.207	+	177.748i	−0.386312	+	0.451138i
$395$			165.730i			0.419569i
$396$	538.117	−	83.8124i	1.35888	−	0.211648i
$397$	−639.706			−1.61135			−0.805675	−	0.592357i	$-0.798197\pi$
$397$	−639.706			−1.61135			−0.805675	+	0.592357i	$0.798197\pi$
$398$	191.495	+	163.978i	0.481143	+	0.412005i
$399$		−	153.108i		−	0.383729i
$400$	−76.2106	+	24.3300i	−0.190526	+	0.0608251i
$401$	−587.043			−1.46395			−0.731973	−	0.681333i	$-0.761400\pi$
$401$	−587.043			−1.46395			−0.731973	+	0.681333i	$0.761400\pi$
$402$	−336.809	+	393.328i	−0.837833	+	0.978429i
$403$		−	546.878i		−	1.35702i
$404$	−52.4672	−	336.865i	−0.129869	−	0.833824i
$405$	200.998			0.496290
$406$	−414.871	−	355.256i	−1.02185	−	0.875015i
$407$		−	121.463i		−	0.298436i
$408$	556.811	−	900.820i	1.36473	−	2.20789i
$409$	−165.516			−0.404685			−0.202342	−	0.979315i	$-0.564855\pi$
$409$	−165.516			−0.404685			−0.202342	+	0.979315i	$0.564855\pi$
$410$	−170.421	+	199.019i	−0.415660	+	0.485412i
$411$		−	791.222i		−	1.92512i
$412$	−444.002	+	69.1540i	−1.07768	+	0.167850i
$413$	−91.9785			−0.222708
$414$	117.163	+	100.327i	0.283002	+	0.242336i
$415$		−	114.273i		−	0.275356i
$416$	−196.855	+	466.747i	−0.473210	+	1.12199i
$417$	396.555			0.950972
$418$	−98.0880	+	114.548i	−0.234660	+	0.274038i
$419$		−	612.808i		−	1.46255i	−0.682083	−	0.731275i	$-0.738926\pi$
$419$		−	612.808i		−	1.46255i	0.682083	−	0.731275i	$-0.261074\pi$
$420$	−48.3496	−	310.428i	−0.115118	−	0.739114i
$421$	−234.767			−0.557641			−0.278820	−	0.960343i	$-0.589943\pi$
$421$	−234.767			−0.557641			−0.278820	+	0.960343i	$0.589943\pi$
$422$	286.997	+	245.757i	0.680087	+	0.582362i
$423$			32.4278i			0.0766615i
$424$	−321.233	−	198.559i	−0.757625	−	0.468300i
$425$	161.145			0.379165
$426$	560.120	−	654.112i	1.31484	−	1.53548i
$427$			244.608i			0.572854i
$428$	231.247	−	36.0170i	0.540296	−	0.0841519i
$429$	1124.76			2.62182
$430$	32.5593	+	27.8807i	0.0757192	+	0.0648387i
$431$		−	336.696i		−	0.781198i	−0.920561	−	0.390599i	$-0.872268\pi$
$431$		−	336.696i		−	0.781198i	0.920561	−	0.390599i	$-0.127732\pi$
$432$	22.5723	+	70.7048i	0.0522507	+	0.163668i
$433$	29.8962			0.0690444			0.0345222	−	0.999404i	$-0.489009\pi$
$433$	29.8962			0.0690444			0.0345222	+	0.999404i	$0.489009\pi$
$434$	−384.317	+	448.808i	−0.885523	+	1.03412i
$435$		−	293.299i		−	0.674250i
$436$	48.7166	+	312.784i	0.111735	+	0.717395i
$437$	−42.7129			−0.0977412
$438$	825.421	+	706.812i	1.88452	+	1.61373i
$439$		−	175.373i		−	0.399483i	−0.979849	−	0.199742i	$-0.935990\pi$
$439$		−	175.373i		−	0.399483i	0.979849	−	0.199742i	$-0.0640103\pi$
$440$	−162.702	+	263.222i	−0.369776	+	0.598232i
$441$	189.938			0.430698
$442$	663.677	−	775.047i	1.50153	−	1.75350i
$443$			33.7175i			0.0761117i	0.999276	+	0.0380558i	$0.0121165\pi$
$443$			33.7175i			0.0761117i	−0.999276	+	0.0380558i	$0.987884\pi$
$444$	−113.987	+	17.7536i	−0.256727	+	0.0399856i
$445$	160.363			0.360366
$446$	20.1395	+	17.2456i	0.0451559	+	0.0386672i
$447$		−	520.418i		−	1.16424i
$448$	489.560	−	244.708i	1.09277	−	0.546223i
$449$	18.0477			0.0401952			0.0200976	−	0.999798i	$-0.493602\pi$
$449$	18.0477			0.0401952			0.0200976	+	0.999798i	$0.493602\pi$
$450$	51.1925	−	59.7830i	0.113761	−	0.132851i
$451$			1013.50i			2.24722i
$452$	−42.1077	−	270.352i	−0.0931586	−	0.598124i
$453$	855.071			1.88757
$454$	501.681	+	429.592i	1.10502	+	0.946238i
$455$		−	302.707i		−	0.665291i
$456$	121.834	+	75.3073i	0.267179	+	0.165148i
$457$	74.2957			0.162573			0.0812864	−	0.996691i	$-0.474097\pi$
$457$	74.2957			0.162573			0.0812864	+	0.996691i	$0.474097\pi$
$458$	201.242	−	235.011i	0.439392	−	0.513125i
$459$		−	149.503i		−	0.325715i
$460$	−86.6010	+	13.4882i	−0.188263	+	0.0293222i
$461$	818.673			1.77586			0.887932	−	0.459975i	$-0.152142\pi$
$461$	818.673			1.77586			0.887932	+	0.459975i	$0.152142\pi$
$462$	−923.062	−	790.423i	−1.99797	−	1.71087i
$463$			741.844i			1.60225i	0.598494	+	0.801127i	$0.295766\pi$
$463$			741.844i			1.60225i	−0.598494	+	0.801127i	$0.704234\pi$
$464$	486.748	−	155.393i	1.04903	−	0.334899i
$465$	−317.291			−0.682347
$466$	435.709	−	508.825i	0.934998	−	1.09190i
$467$		−	469.156i		−	1.00462i	−0.864688	−	0.502309i	$-0.832484\pi$
$467$		−	469.156i		−	1.00462i	0.864688	−	0.502309i	$-0.167516\pi$
$468$	−76.6972	−	492.433i	−0.163883	−	1.05221i
$469$	539.072			1.14941
$470$	−13.9956	−	11.9845i	−0.0297779	−	0.0254989i
$471$			1019.05i			2.16359i
$472$	45.2404	−	73.1908i	0.0958482	−	0.155065i
$473$	165.807			0.350544
$474$	396.012	−	462.466i	0.835468	−	0.975666i
$475$			21.7945i			0.0458831i
$476$	−1089.32	+	169.664i	−2.28850	+	0.356437i
$477$	371.539			0.778907
$478$	−7.79208	−	6.67240i	−0.0163014	−	0.0139590i
$479$			495.526i			1.03450i	0.855834	+	0.517250i	$0.173044\pi$
$479$			495.526i			1.03450i	−0.855834	+	0.517250i	$0.826956\pi$
$480$	270.801	+	114.213i	0.564168	+	0.237944i
$481$	−111.152			−0.231085
$482$	120.178	−	140.344i	0.249331	−	0.291171i
$483$		−	344.194i		−	0.712617i
$484$	109.724	+	704.478i	0.226702	+	1.45553i
$485$	−292.284			−0.602647
$486$	−497.457	−	425.975i	−1.02357	−	0.876492i
$487$			206.341i			0.423698i	0.977302	+	0.211849i	$0.0679485\pi$
$487$			206.341i			0.423698i	−0.977302	+	0.211849i	$0.932051\pi$
$488$	−194.644	−	120.313i	−0.398861	−	0.246542i
$489$	−985.822			−2.01600
$490$	−70.1963	+	81.9758i	−0.143258	+	0.167297i
$491$			371.192i			0.755991i	0.925807	+	0.377996i	$0.123387\pi$
$491$			371.192i			0.755991i	−0.925807	+	0.377996i	$0.876613\pi$
$492$	951.111	−	148.137i	1.93315	−	0.301091i
$493$	−1029.22			−2.08766
$494$	104.823	+	89.7607i	0.212193	+	0.181702i
$495$		−	304.443i		−	0.615037i
$496$	−168.105	−	526.566i	−0.338921	−	1.06162i
$497$	−896.486			−1.80380
$498$	−273.055	+	318.876i	−0.548304	+	0.640314i
$499$			341.223i			0.683813i	0.939734	+	0.341907i	$0.111073\pi$
$499$			341.223i			0.683813i	−0.939734	+	0.341907i	$0.888927\pi$
$500$	6.88244	+	44.1886i	0.0137649	+	0.0883772i
$501$	−1049.76			−2.09533
$502$	−83.3742	−	71.3938i	−0.166084	−	0.142219i
$503$		−	573.405i		−	1.13997i	−0.821655	−	0.569985i	$-0.806949\pi$
$503$		−	573.405i		−	1.13997i	0.821655	−	0.569985i	$-0.193051\pi$
$504$	−283.113	+	458.026i	−0.561732	+	0.908781i
$505$	−190.584			−0.377393
$506$	−220.507	+	257.509i	−0.435784	+	0.508912i
$507$		−	335.126i		−	0.660997i
$508$	535.808	−	83.4529i	1.05474	−	0.164277i
$509$	−134.154			−0.263565			−0.131782	−	0.991279i	$-0.542070\pi$
$509$	−134.154			−0.263565			−0.131782	+	0.991279i	$0.542070\pi$
$510$	−449.672	−	385.057i	−0.881710	−	0.755013i
$511$		−	1131.27i		−	2.21384i
$512$	−46.0704	+	509.923i	−0.0899812	+	0.995943i
$513$	20.2200			0.0394151
$514$	−66.2865	+	77.4099i	−0.128962	+	0.150603i
$515$			251.197i			0.487762i
$516$	−24.2351	−	155.601i	−0.0469672	−	0.301552i
$517$	−71.2722			−0.137857
$518$	91.2194	+	78.1116i	0.176099	+	0.150795i
$519$			48.5690i			0.0935819i
$520$	240.876	+	148.889i	0.463223	+	0.286325i
$521$	45.7024			0.0877205			0.0438603	−	0.999038i	$-0.486034\pi$
$521$	45.7024			0.0877205			0.0438603	+	0.999038i	$0.486034\pi$
$522$	−326.961	+	381.827i	−0.626361	+	0.731470i
$523$		−	695.267i		−	1.32938i	−0.747118	−	0.664691i	$-0.768563\pi$
$523$		−	695.267i		−	1.32938i	0.747118	−	0.664691i	$-0.231437\pi$
$524$	−701.417	+	109.247i	−1.33858	+	0.208486i
$525$	−175.627			−0.334527
$526$	627.348	+	537.201i	1.19268	+	1.02130i
$527$			1113.41i			2.11273i
$528$	1082.99	−	345.740i	2.05111	−	0.654811i
$529$	432.979			0.818486
$530$	−137.311	+	160.353i	−0.259078	+	0.302553i
$531$			84.6526i			0.159421i
$532$	−22.9466	−	147.329i	−0.0431328	−	0.276934i
$533$	927.456			1.74007
$534$	−447.489	−	383.187i	−0.837995	−	0.717579i
$535$		−	130.829i		−	0.244541i
$536$	−265.147	+	428.960i	−0.494677	+	0.800298i
$537$	−1284.51			−2.39202
$538$	−207.062	+	241.809i	−0.384873	+	0.449458i
$539$			417.459i			0.774507i
$540$	40.9962	−	6.38522i	0.0759189	−	0.0118245i
$541$	854.031			1.57861			0.789307	−	0.613998i	$-0.210440\pi$
$541$	854.031			1.57861			0.789307	+	0.613998i	$0.210440\pi$
$542$	−232.501	−	199.092i	−0.428969	−	0.367329i
$543$			143.767i			0.264765i
$544$	400.785	−	950.268i	0.736737	−	1.74682i
$545$	176.960			0.324697
$546$	−723.320	+	844.699i	−1.32476	+	1.54707i
$547$			730.236i			1.33498i	0.744617	+	0.667492i	$0.232632\pi$
$547$			730.236i			1.33498i	−0.744617	+	0.667492i	$0.767368\pi$
$548$	−118.582	−	761.357i	−0.216391	−	1.38934i
$549$	225.126			0.410066
$550$	131.395	+	112.515i	0.238901	+	0.204572i
$551$		−	139.199i		−	0.252630i
$552$	273.888	+	169.295i	0.496175	+	0.306693i
$553$	−633.827			−1.14616
$554$	−473.547	+	553.012i	−0.854778	+	0.998216i
$555$			64.4888i			0.116196i
$556$	381.587	−	59.4327i	0.686307	−	0.106893i
$557$	644.497			1.15709			0.578543	−	0.815652i	$-0.303621\pi$
$557$	644.497			1.15709			0.578543	+	0.815652i	$0.303621\pi$
$558$	413.062	+	353.707i	0.740254	+	0.633883i
$559$		−	151.731i		−	0.271433i
$560$	−93.0492	−	291.464i	−0.166159	−	0.520472i
$561$	−2289.94			−4.08189
$562$	402.347	−	469.864i	0.715919	−	0.836056i
$563$		−	236.145i		−	0.419440i	−0.977761	−	0.209720i	$-0.932745\pi$
$563$		−	236.145i		−	0.419440i	0.977761	−	0.209720i	$-0.0672553\pi$
$564$	10.4174	+	66.8850i	0.0184706	+	0.118591i
$565$	−152.953			−0.270714
$566$	129.552	+	110.936i	0.228891	+	0.196000i
$567$			768.708i			1.35575i
$568$	440.944	−	713.369i	0.776310	−	1.25593i
$569$	511.234			0.898477			0.449239	−	0.893412i	$-0.351695\pi$
$569$	511.234			0.898477			0.449239	+	0.893412i	$0.351695\pi$
$570$	52.0780	−	60.8171i	0.0913649	−	0.106697i
$571$		−	285.885i		−	0.500674i	−0.968159	−	0.250337i	$-0.919459\pi$
$571$		−	285.885i		−	0.500674i	0.968159	−	0.250337i	$-0.0805414\pi$
$572$	1082.31	−	168.571i	1.89214	−	0.294704i
$573$	−386.482			−0.674488
$574$	−761.139	−	651.767i	−1.32603	−	1.13548i
$575$			48.9951i			0.0852088i
$576$	−225.217	−	450.567i	−0.391003	−	0.782235i
$577$	396.251			0.686744			0.343372	−	0.939200i	$-0.388431\pi$
$577$	396.251			0.686744			0.343372	+	0.939200i	$0.388431\pi$
$578$	−975.259	+	1138.92i	−1.68730	+	1.97044i
$579$			768.590i			1.32744i
$580$	−43.9574	−	282.228i	−0.0757886	−	0.486599i
$581$	437.032			0.752207
$582$	815.612	+	698.412i	1.40139	+	1.20002i
$583$			816.595i			1.40068i
$584$	900.196	+	556.425i	1.54143	+	0.952783i
$585$	−278.597			−0.476235
$586$	−137.100	+	160.106i	−0.233959	+	0.273219i
$587$			204.563i			0.348488i	0.984702	+	0.174244i	$0.0557482\pi$
$587$			204.563i			0.348488i	−0.984702	+	0.174244i	$0.944252\pi$
$588$	391.763	−	61.0176i	0.666263	−	0.103771i
$589$	−150.586			−0.255664
$590$	−36.5355	−	31.2855i	−0.0619245	−	0.0530263i
$591$		−	480.588i		−	0.813177i
$592$	−107.023	+	34.1669i	−0.180783	+	0.0577144i
$593$	−212.039			−0.357569			−0.178785	−	0.983888i	$-0.557217\pi$
$593$	−212.039			−0.357569			−0.178785	+	0.983888i	$0.557217\pi$
$594$	104.386	−	121.903i	0.175734	−	0.205224i
$595$			616.293i			1.03579i
$596$	−77.9962	−	500.774i	−0.130866	−	0.840224i
$597$	−517.755			−0.867261
$598$	235.648	+	201.786i	0.394060	+	0.337436i
$599$			662.916i			1.10671i	0.832947	+	0.553353i	$0.186652\pi$
$599$			662.916i			1.10671i	−0.832947	+	0.553353i	$0.813348\pi$
$600$	86.3835	−	139.753i	0.143972	−	0.232922i
$601$	831.567			1.38364			0.691820	−	0.722070i	$-0.256809\pi$
$601$	831.567			1.38364			0.691820	+	0.722070i	$0.256809\pi$
$602$	−106.628	+	124.522i	−0.177124	+	0.206846i
$603$		−	496.136i		−	0.822779i
$604$	822.795	−	128.152i	1.36224	−	0.212171i
$605$	398.563			0.658783
$606$	531.820	+	455.400i	0.877591	+	0.751485i
$607$		−	734.539i		−	1.21011i	−0.796182	−	0.605057i	$-0.793150\pi$
$607$		−	734.539i		−	1.21011i	0.796182	−	0.605057i	$-0.206850\pi$
$608$	128.522	+	54.2052i	0.211384	+	0.0891534i
$609$	1121.71			1.84189
$610$	−83.2009	+	97.1627i	−0.136395	+	0.159283i
$611$			65.2215i			0.106746i
$612$	156.151	+	1002.56i	0.255148	+	1.63817i
$613$	−206.027			−0.336097			−0.168048	−	0.985779i	$-0.553746\pi$
$613$	−206.027			−0.336097			−0.168048	+	0.985779i	$0.553746\pi$
$614$	−459.971	−	393.876i	−0.749139	−	0.641491i
$615$		−	538.098i		−	0.874956i
$616$	−1006.68	−	622.246i	−1.63423	−	1.01014i
$617$	−634.031			−1.02760			−0.513801	−	0.857909i	$-0.671763\pi$
$617$	−634.031			−1.02760			−0.513801	+	0.857909i	$0.671763\pi$
$618$	600.237	−	700.961i	0.971257	−	1.13424i
$619$			152.766i			0.246796i	0.992357	+	0.123398i	$0.0393791\pi$
$619$			152.766i			0.246796i	−0.992357	+	0.123398i	$0.960621\pi$
$620$	−305.315	+	47.5532i	−0.492443	+	0.0766987i
$621$	45.4555			0.0731972
$622$	−114.892	−	98.3830i	−0.184714	−	0.158172i
$623$			613.301i			0.984432i
$624$	−316.389	−	991.045i	−0.507033	−	1.58821i
$625$	25.0000			0.0400000
$626$	117.778	−	137.543i	0.188144	−	0.219716i
$627$		−	309.709i		−	0.493954i
$628$	152.728	+	980.588i	0.243197	+	1.56145i
$629$	226.298			0.359774
$630$	228.638	+	195.784i	0.362917	+	0.310768i
$631$			1083.57i			1.71723i	0.512621	+	0.858615i	$0.328675\pi$
$631$			1083.57i			1.71723i	−0.512621	+	0.858615i	$0.671325\pi$
$632$	311.753	−	504.361i	0.493280	−	0.798039i
$633$	−775.968			−1.22586
$634$	−262.145	+	306.135i	−0.413478	+	0.482863i
$635$		−	303.137i		−	0.477381i
$636$	766.329	−	119.357i	1.20492	−	0.187668i
$637$	382.019			0.599716
$638$	−839.208	−	718.618i	−1.31537	−	1.12636i
$639$			825.083i			1.29121i
$640$	277.696	+	69.3162i	0.433901	+	0.108307i
$641$	566.330			0.883510			0.441755	−	0.897136i	$-0.354356\pi$
$641$	566.330			0.883510			0.441755	+	0.897136i	$0.354356\pi$
$642$	−312.617	+	365.077i	−0.486943	+	0.568656i
$643$		−	1015.89i		−	1.57992i	−0.613159	−	0.789960i	$-0.710102\pi$
$643$		−	1015.89i		−	1.57992i	0.613159	−	0.789960i	$-0.289898\pi$
$644$	−51.5852	−	331.202i	−0.0801012	−	0.514289i
$645$	−88.0322			−0.136484
$646$	−213.414	−	182.747i	−0.330362	−	0.282890i
$647$		−	12.7553i		−	0.0197145i	−0.999951	−	0.00985724i	$-0.996862\pi$
$647$		−	12.7553i		−	0.0197145i	0.999951	−	0.00985724i	$-0.00313771\pi$
$648$	−611.690	−	378.095i	−0.943966	−	0.583480i
$649$	−186.056			−0.286681
$650$	102.963	−	120.241i	0.158404	−	0.184985i
$651$		−	1213.47i		−	1.86401i
$652$	−948.611	+	147.748i	−1.45493	+	0.226607i
$653$	849.551			1.30100			0.650498	−	0.759508i	$-0.274560\pi$
$653$	849.551			1.30100			0.650498	+	0.759508i	$0.274560\pi$
$654$	−493.803	−	422.846i	−0.755050	−	0.646553i
$655$			396.832i			0.605850i
$656$	893.009	−	285.091i	1.36129	−	0.434590i
$657$	−1041.17			−1.58473
$658$	45.8343	−	53.5256i	0.0696569	−	0.0813459i
$659$		−	217.500i		−	0.330046i	−0.986290	−	0.165023i	$-0.947230\pi$
$659$		−	217.500i		−	0.330046i	0.986290	−	0.165023i	$-0.0527699\pi$
$660$	−97.8025	−	627.940i	−0.148186	−	0.951423i
$661$	441.440			0.667837			0.333918	−	0.942602i	$-0.391629\pi$
$661$	441.440			0.667837			0.333918	+	0.942602i	$0.391629\pi$
$662$	−879.526	−	753.143i	−1.32859	−	1.13768i
$663$			2095.54i			3.16069i
$664$	−214.958	+	347.763i	−0.323732	+	0.523740i
$665$	−83.3522			−0.125342
$666$	71.8902	−	83.9539i	0.107943	−	0.126057i
$667$		−	312.926i		−	0.469155i
$668$	−1010.14	+	157.330i	−1.51218	+	0.235525i
$669$	−54.4524			−0.0813937
$670$	214.129	+	183.359i	0.319595	+	0.273671i
$671$			494.798i			0.737405i
$672$	−436.803	+	1035.67i	−0.650004	+	1.54117i
$673$	724.701			1.07682			0.538411	−	0.842683i	$-0.319025\pi$
$673$	724.701			1.07682			0.538411	+	0.842683i	$0.319025\pi$
$674$	−770.709	+	900.040i	−1.14349	+	1.33537i
$675$		−	23.1939i		−	0.0343613i
$676$	−50.2261	−	322.476i	−0.0742989	−	0.477035i
$677$	403.934			0.596653			0.298327	−	0.954464i	$-0.403571\pi$
$677$	403.934			0.596653			0.298327	+	0.954464i	$0.403571\pi$
$678$	426.814	+	365.483i	0.629518	+	0.539060i
$679$		−	1117.83i		−	1.64628i
$680$	−490.408	−	303.129i	−0.721188	−	0.445777i
$681$	−1356.42			−1.99181
$682$	−777.403	+	907.858i	−1.13989	+	1.33117i
$683$			891.638i			1.30547i	0.757585	+	0.652736i	$0.226379\pi$
$683$			891.638i			1.30547i	−0.757585	+	0.652736i	$0.773621\pi$
$684$	−135.594	+	21.1190i	−0.198237	+	0.0308757i
$685$	−430.743			−0.628821
$686$	323.062	+	276.640i	0.470936	+	0.403265i
$687$			635.413i			0.924910i
$688$	−46.6405	−	146.095i	−0.0677915	−	0.212348i
$689$	747.270			1.08457
$690$	117.074	−	136.720i	0.169672	−	0.198145i
$691$		−	449.009i		−	0.649796i	−0.945749	−	0.324898i	$-0.894670\pi$
$691$		−	449.009i		−	0.649796i	0.945749	−	0.324898i	$-0.105330\pi$
$692$	7.27915	+	46.7357i	0.0105190	+	0.0675372i
$693$	1164.33			1.68013
$694$	455.689	+	390.209i	0.656612	+	0.562260i
$695$		−	215.885i		−	0.310626i
$696$	−551.722	+	892.587i	−0.792703	+	1.28245i
$697$	−1888.24			−2.70910
$698$	265.763	−	310.360i	0.380750	−	0.444642i
$699$			1375.74i			1.96815i
$700$	−168.998	+	26.3216i	−0.241425	+	0.0376023i
$701$	1019.24			1.45398			0.726988	−	0.686650i	$-0.240920\pi$
$701$	1019.24			1.45398			0.726988	+	0.686650i	$0.240920\pi$
$702$	−111.554	−	95.5241i	−0.158909	−	0.136074i
$703$			30.6063i			0.0435366i
$704$	990.290	−	495.000i	1.40666	−	0.703124i
$705$	37.8407			0.0536747
$706$	731.597	−	854.365i	1.03626	−	1.21015i
$707$		−	728.880i		−	1.03095i
$708$	27.1947	+	174.603i	0.0384106	+	0.246615i
$709$	−698.661			−0.985417			−0.492708	−	0.870194i	$-0.663993\pi$
$709$	−698.661			−0.985417			−0.492708	+	0.870194i	$0.663993\pi$
$710$	−356.100	−	304.930i	−0.501549	−	0.429479i
$711$			583.344i			0.820456i
$712$	−488.028	−	301.657i	−0.685432	−	0.423676i
$713$	−338.524			−0.474789
$714$	1472.63	−	1719.75i	2.06251	−	2.40862i
$715$		−	612.322i		−	0.856394i
$716$	−1236.03	+	192.513i	−1.72629	+	0.268873i
$717$	21.0679			0.0293834
$718$	−234.508	−	200.810i	−0.326613	−	0.279680i
$719$		−	848.462i		−	1.18006i	−0.807382	−	0.590029i	$-0.799116\pi$
$719$		−	848.462i		−	1.18006i	0.807382	−	0.590029i	$-0.200884\pi$
$720$	−268.250	+	85.6380i	−0.372569	+	0.118942i
$721$	−960.695			−1.33245
$722$	24.7161	−	28.8637i	0.0342329	−	0.0399774i
$723$			379.457i			0.524836i
$724$	21.5468	+	138.341i	0.0297607	+	0.191078i
$725$	−159.672			−0.220238
$726$	−1112.18	−	952.368i	−1.53193	−	1.31180i
$727$			398.224i			0.547764i	0.961763	+	0.273882i	$0.0883078\pi$
$727$			398.224i			0.547764i	−0.961763	+	0.273882i	$0.911692\pi$
$728$	−569.420	+	921.220i	−0.782171	+	1.26541i
$729$	536.002			0.735257
$730$	384.790	−	449.361i	0.527109	−	0.615563i
$731$			308.914i			0.422592i
$732$	464.341	−	72.3218i	0.634346	−	0.0988003i
$733$	116.789			0.159330			0.0796650	−	0.996822i	$-0.474615\pi$
$733$	116.789			0.159330			0.0796650	+	0.996822i	$0.474615\pi$
$734$	−68.8505	−	58.9571i	−0.0938018	−	0.0803230i
$735$		−	221.642i		−	0.301554i
$736$	288.923	+	121.856i	0.392558	+	0.165565i
$737$	1090.44			1.47957
$738$	−599.856	+	700.516i	−0.812813	+	0.949209i
$739$		−	34.6399i		−	0.0468741i	−0.999725	−	0.0234370i	$-0.992539\pi$
$739$		−	34.6399i		−	0.0468741i	0.999725	−	0.0234370i	$-0.00746092\pi$
$740$	9.66509	+	62.0546i	0.0130609	+	0.0838575i
$741$	−283.416			−0.382478
$742$	−613.265	−	525.142i	−0.826503	−	0.707739i
$743$		−	624.797i		−	0.840911i	−0.907313	−	0.420456i	$-0.861870\pi$
$743$		−	624.797i		−	0.840911i	0.907313	−	0.420456i	$-0.138130\pi$
$744$	965.603	+	596.854i	1.29785	+	0.802223i
$745$	−283.316			−0.380290
$746$	803.576	−	938.422i	1.07718	−	1.25794i
$747$		−	402.223i		−	0.538452i
$748$	−2203.51	+	343.199i	−2.94586	+	0.458823i
$749$	500.352			0.668027
$750$	−69.7620	−	59.7376i	−0.0930160	−	0.0796501i
$751$		−	425.557i		−	0.566654i	−0.959023	−	0.283327i	$-0.908562\pi$
$751$		−	425.557i		−	0.566654i	0.959023	−	0.283327i	$-0.0914381\pi$
$752$	20.0484	+	62.7991i	0.0266602	+	0.0835094i
$753$	225.423			0.299367
$754$	−657.611	+	767.963i	−0.872163	+	1.01852i
$755$		−	465.502i		−	0.616559i
$756$	24.4200	+	156.788i	0.0323016	+	0.207392i
$757$	−145.392			−0.192063			−0.0960316	−	0.995378i	$-0.530615\pi$
$757$	−145.392			−0.192063			−0.0960316	+	0.995378i	$0.530615\pi$
$758$	314.238	+	269.083i	0.414562	+	0.354991i
$759$		−	696.242i		−	0.917315i
$760$	40.9974	−	66.3265i	0.0539440	−	0.0872718i
$761$	−1158.73			−1.52264			−0.761321	−	0.648375i	$-0.775449\pi$
$761$	−1158.73			−1.52264			−0.761321	+	0.648375i	$0.775449\pi$
$762$	−724.347	+	845.898i	−0.950586	+	1.11010i
$763$			676.776i			0.886993i
$764$	−371.894	+	57.9230i	−0.486772	+	0.0758154i
$765$	567.207			0.741447
$766$	270.570	+	231.691i	0.353225	+	0.302468i
$767$			170.260i			0.221982i
$768$	−609.275	−	856.982i	−0.793327	−	1.11586i
$769$	−23.3322			−0.0303410			−0.0151705	−	0.999885i	$-0.504829\pi$
$769$	−23.3322			−0.0303410			−0.0151705	+	0.999885i	$0.504829\pi$
$770$	−430.308	+	502.517i	−0.558841	+	0.652619i
$771$		−	209.297i		−	0.271462i
$772$	115.190	+	739.579i	0.149210	+	0.958004i
$773$	814.780			1.05405			0.527024	−	0.849850i	$-0.323308\pi$
$773$	814.780			1.05405			0.527024	+	0.849850i	$0.323308\pi$
$774$	114.604	+	98.1358i	0.148067	+	0.126790i
$775$			172.734i			0.222882i
$776$	889.498	+	549.812i	1.14626	+	0.708521i
$777$	−246.635			−0.317419
$778$	554.694	−	647.776i	0.712975	−	0.832618i
$779$		−	255.380i		−	0.327831i
$780$	−574.630	+	89.4995i	−0.736705	+	0.114743i
$781$	−1813.43			−2.32193
$782$	−479.764	−	410.825i	−0.613509	−	0.525351i
$783$			148.137i			0.189191i
$784$	367.830	−	117.429i	0.469171	−	0.149782i
$785$	554.774			0.706719
$786$	948.230	−	1107.35i	1.20640	−	1.40884i
$787$		−	839.432i		−	1.06662i	−0.845919	−	0.533312i	$-0.820947\pi$
$787$		−	839.432i		−	1.06662i	0.845919	−	0.533312i	$-0.179053\pi$
$788$	−72.0268	−	462.447i	−0.0914046	−	0.586862i
$789$	−1696.20			−2.14980
$790$	−251.767	−	215.590i	−0.318693	−	0.272898i
$791$		−	584.964i		−	0.739525i
$792$	−572.686	+	926.503i	−0.723088	+	1.16983i
$793$	452.792			0.570987
$794$	832.161	−	971.805i	1.04806	−	1.22394i
$795$		−	433.556i		−	0.545354i
$796$	−498.212	+	77.5972i	−0.625894	+	0.0974839i
$797$	1337.61			1.67831			0.839153	−	0.543896i	$-0.183051\pi$
$797$	1337.61			1.67831			0.839153	+	0.543896i	$0.183051\pi$
$798$	232.593	+	199.170i	0.291469	+	0.249587i
$799$		−	132.787i		−	0.166191i
$800$	62.1777	−	147.424i	0.0777221	−	0.184280i
$801$	564.453			0.704686
$802$	763.654	−	891.801i	0.952187	−	1.11197i
$803$		−	2288.36i		−	2.84976i
$804$	−159.384	−	1023.32i	−0.198239	−	1.27279i
$805$	−187.380			−0.232770
$806$	830.785	+	711.405i	1.03075	+	0.882637i
$807$		−	653.791i		−	0.810150i
$808$	579.998	+	358.505i	0.717819	+	0.443695i
$809$	1258.72			1.55589			0.777945	−	0.628332i	$-0.216262\pi$
$809$	1258.72			1.55589			0.777945	+	0.628332i	$0.216262\pi$
$810$	−261.468	+	305.344i	−0.322799	+	0.376968i
$811$		−	525.545i		−	0.648021i	−0.946054	−	0.324010i	$-0.894969\pi$
$811$		−	525.545i		−	0.648021i	0.946054	−	0.324010i	$-0.105031\pi$
$812$	1079.37	−	168.113i	1.32927	−	0.207036i
$813$	628.626			0.773218
$814$	184.520	+	158.006i	0.226683	+	0.194110i
$815$			536.683i			0.658507i
$816$	644.147	+	2017.71i	0.789396	+	2.47268i
$817$	−41.7799			−0.0511382
$818$	215.312	−	251.443i	0.263217	−	0.307387i
$819$		−	1065.48i		−	1.30096i
$820$	−80.6460	−	517.787i	−0.0983488	−	0.631447i
$821$	−1499.42			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$821$	−1499.42			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$822$	1201.98	+	1029.26i	1.46226	+	1.25214i
$823$			1049.06i			1.27467i	0.770586	+	0.637336i	$0.219964\pi$
$823$			1049.06i			1.27467i	−0.770586	+	0.637336i	$0.780036\pi$
$824$	472.525	−	764.462i	0.573453	−	0.927745i
$825$	−355.261			−0.430619
$826$	119.650	−	139.728i	0.144855	−	0.169163i
$827$		−	451.107i		−	0.545474i	−0.962089	−	0.272737i	$-0.912071\pi$
$827$		−	451.107i		−	0.545474i	0.962089	−	0.272737i	$-0.0879289\pi$
$828$	−304.822	+	47.4765i	−0.368143	+	0.0573388i
$829$	1094.98			1.32084			0.660420	−	0.750896i	$-0.270378\pi$
$829$	1094.98			1.32084			0.660420	+	0.750896i	$0.270378\pi$
$830$	173.597	+	148.652i	0.209153	+	0.179099i
$831$		−	1495.21i		−	1.79929i
$832$	−452.976	−	906.219i	−0.544443	−	1.08921i
$833$	−777.766			−0.933693
$834$	−515.858	+	602.423i	−0.618535	+	0.722330i
$835$			571.492i			0.684422i
$836$	−46.4169	−	298.019i	−0.0555226	−	0.356482i
$837$	160.255			0.191463
$838$	930.943	+	797.171i	1.11091	+	0.951278i
$839$		−	136.146i		−	0.162271i	−0.996703	−	0.0811357i	$-0.974145\pi$
$839$		−	136.146i		−	0.162271i	0.996703	−	0.0811357i	$-0.0258547\pi$
$840$	534.480	+	330.370i	0.636285	+	0.393298i
$841$	178.809			0.212615
$842$	305.396	−	356.644i	0.362703	−	0.423568i
$843$			1270.40i			1.50699i
$844$	−746.678	+	116.296i	−0.884690	+	0.137792i
$845$	−182.443			−0.215909
$846$	−49.2624	−	42.1837i	−0.0582298	−	0.0498625i
$847$			1524.29i			1.79963i
$848$	719.515	−	229.703i	0.848485	−	0.270876i
$849$	−350.277			−0.412576
$850$	−209.625	+	244.802i	−0.246618	+	0.288003i
$851$			68.8044i			0.0808512i
$852$	265.058	+	1701.80i	0.311101	+	1.99742i
$853$	765.324			0.897214			0.448607	−	0.893729i	$-0.351920\pi$
$853$	765.324			0.897214			0.448607	+	0.893729i	$0.351920\pi$
$854$	−371.595	−	318.199i	−0.435123	−	0.372598i
$855$			76.7134i			0.0897232i
$856$	−246.102	+	398.150i	−0.287503	+	0.465128i
$857$	840.307			0.980521			0.490261	−	0.871576i	$-0.336902\pi$
$857$	840.307			0.980521			0.490261	+	0.871576i	$0.336902\pi$
$858$	−1463.14	+	1708.67i	−1.70530	+	1.99146i
$859$		−	882.727i		−	1.02762i	−0.857904	−	0.513811i	$-0.828233\pi$
$859$		−	882.727i		−	1.02762i	0.857904	−	0.513811i	$-0.171767\pi$
$860$	−84.7093	+	13.1936i	−0.0984992	+	0.0153414i
$861$	2057.93			2.39017
$862$	511.489	+	437.991i	0.593375	+	0.508110i
$863$			766.394i			0.888057i	0.896013	+	0.444029i	$0.146451\pi$
$863$			766.394i			0.888057i	−0.896013	+	0.444029i	$0.853549\pi$
$864$	−136.774	−	57.6857i	−0.158303	−	0.0667658i
$865$	26.4410			0.0305677
$866$	−38.8905	+	45.4166i	−0.0449082	+	0.0524441i
$867$		−	3079.35i		−	3.55173i
$868$	−181.865	−	1167.66i	−0.209522	−	1.34523i
$869$	−1282.12			−1.47539
$870$	445.562	+	381.537i	0.512140	+	0.438549i
$871$		−	997.870i		−	1.14566i
$872$	−538.537	−	332.878i	−0.617588	−	0.381740i
$873$	−1028.79			−1.17846
$874$	55.5631	−	64.8870i	0.0635733	−	0.0742414i
$875$			95.6115i			0.109270i
$876$	−2147.50	+	334.476i	−2.45148	+	0.381822i
$877$	−599.534			−0.683619			−0.341810	−	0.939769i	$-0.611040\pi$
$877$	−599.534			−0.683619			−0.341810	+	0.939769i	$0.611040\pi$
$878$	266.417	+	228.134i	0.303436	+	0.259834i
$879$		−	432.888i		−	0.492478i
$880$	−188.222	−	589.579i	−0.213888	−	0.669976i
$881$	1225.60			1.39114			0.695572	−	0.718456i	$-0.255151\pi$
$881$	1225.60			1.39114			0.695572	+	0.718456i	$0.255151\pi$
$882$	−247.080	+	288.542i	−0.280136	+	0.327146i
$883$		−	354.586i		−	0.401569i	−0.979635	−	0.200785i	$-0.935651\pi$
$883$		−	354.586i		−	0.401569i	0.979635	−	0.200785i	$-0.0643491\pi$
$884$	314.063	+	2016.44i	0.355275	+	2.28104i
$885$	98.7829			0.111619
$886$	−51.2216	−	43.8613i	−0.0578122	−	0.0495049i
$887$			662.363i			0.746745i	0.927682	+	0.373373i	$0.121799\pi$
$887$			662.363i			0.746745i	−0.927682	+	0.373373i	$0.878201\pi$
$888$	121.309	−	196.257i	0.136610	−	0.221010i
$889$	1159.34			1.30409
$890$	−208.608	+	243.614i	−0.234391	+	0.273724i
$891$			1554.96i			1.74518i
$892$	−52.3970	+	8.16091i	−0.0587410	+	0.00914900i
$893$	17.9591			0.0201110
$894$	790.588	+	676.985i	0.884327	+	0.757253i
$895$			699.291i			0.781330i
$896$	−265.097	+	1062.04i	−0.295867	+	1.18531i
$897$	−637.134			−0.710294
$898$	−23.4773	+	27.4170i	−0.0261440	+	0.0305311i
$899$		−	1103.23i		−	1.22718i
$900$	24.2252	+	155.537i	0.0269168	+	0.172819i
$901$	−1521.39			−1.68856
$902$	−1539.65	−	1318.41i	−1.70692	−	1.46165i
$903$		−	336.676i		−	0.372841i
$904$	465.479	+	287.719i	0.514910	+	0.318274i
$905$	78.2673			0.0864831
$906$	−1112.32	+	1298.97i	−1.22772	+	1.43375i
$907$			852.877i			0.940327i	0.882579	+	0.470164i	$0.155805\pi$
$907$			852.877i			0.940327i	−0.882579	+	0.470164i	$0.844195\pi$
$908$	−1305.22	+	203.290i	−1.43747	+	0.223888i
$909$	−670.826			−0.737983
$910$	459.855	+	393.776i	0.505336	+	0.432721i
$911$		−	34.0499i		−	0.0373764i	−0.999825	−	0.0186882i	$-0.994051\pi$
$911$		−	34.0499i		−	0.0373764i	0.999825	−	0.0186882i	$-0.00594899\pi$
$912$	−272.890	+	87.1194i	−0.299221	+	0.0955257i
$913$	884.036			0.968277
$914$	−96.6475	+	112.866i	−0.105741	+	0.123486i
$915$		−	262.704i		−	0.287108i
$916$	95.2309	+	611.429i	0.103964	+	0.667499i
$917$	−1517.67			−1.65504
$918$	227.117	+	194.481i	0.247404	+	0.211853i
$919$			70.0240i			0.0761958i	0.999274	+	0.0380979i	$0.0121299\pi$
$919$			70.0240i			0.0761958i	−0.999274	+	0.0380979i	$0.987870\pi$
$920$	92.1642	−	149.105i	0.100179	−	0.162071i
$921$	1243.65			1.35032
$922$	−1064.97	+	1243.68i	−1.15507	+	1.34889i
$923$			1659.48i			1.79792i
$924$	2401.53	−	374.042i	2.59906	−	0.404807i
$925$	35.1078			0.0379544
$926$	−1126.97	−	965.026i	−1.21703	−	1.04215i
$927$			884.178i			0.953805i
$928$	−397.122	+	941.583i	−0.427933	+	1.01464i
$929$	−603.637			−0.649771			−0.324885	−	0.945753i	$-0.605326\pi$
$929$	−603.637			−0.649771			−0.324885	+	0.945753i	$0.605326\pi$
$930$	412.748	−	482.010i	0.443815	−	0.518291i
$931$		−	105.191i		−	0.112987i
$932$	206.185	+	1323.81i	0.221229	+	1.42039i
$933$	310.641			0.332948
$934$	712.715	+	610.301i	0.763078	+	0.653428i
$935$			1246.65i			1.33331i
$936$	847.847	+	524.067i	0.905819	+	0.559901i
$937$	−429.763			−0.458659			−0.229329	−	0.973349i	$-0.573653\pi$
$937$	−429.763			−0.458659			−0.229329	+	0.973349i	$0.573653\pi$
$938$	−701.251	+	818.926i	−0.747602	+	0.873056i
$939$			371.881i			0.396040i
$940$	36.4123	−	5.67127i	0.0387365	−	0.00603327i
$941$	1509.71			1.60437			0.802184	−	0.597077i	$-0.203671\pi$
$941$	1509.71			1.60437			0.802184	+	0.597077i	$0.203671\pi$
$942$	−1548.09	−	1325.63i	−1.64340	−	1.40725i
$943$		−	574.107i		−	0.608810i
$944$	52.3364	+	163.937i	0.0554411	+	0.173662i
$945$	88.7041			0.0938668
$946$	−215.690	+	251.885i	−0.228002	+	0.266263i
$947$			34.9178i			0.0368720i	0.999830	+	0.0184360i	$0.00586870\pi$
$947$			34.9178i			0.0368720i	−0.999830	+	0.0184360i	$0.994131\pi$
$948$	187.400	+	1203.20i	0.197679	+	1.26919i
$949$	−2094.09			−2.20662
$950$	−33.1089	−	28.3513i	−0.0348515	−	0.0298435i
$951$		−	827.714i		−	0.870362i
$952$	1159.30	−	1875.55i	1.21776	−	1.97011i
$953$	546.041			0.572970			0.286485	−	0.958085i	$-0.407513\pi$
$953$	546.041			0.572970			0.286485	+	0.958085i	$0.407513\pi$
$954$	−483.316	+	564.420i	−0.506620	+	0.591635i
$955$			210.401i			0.220316i
$956$	20.2726	−	3.15749i	0.0212057	−	0.00330282i
$957$	2269.01			2.37096
$958$	−752.774	−	644.604i	−0.785776	−	0.672864i
$959$		−	1647.36i		−	1.71779i
$960$	−525.776	+	262.811i	−0.547684	+	0.273761i
$961$	−232.479			−0.241913
$962$	144.592	−	168.855i	0.150303	−	0.175525i
$963$		−	460.500i		−	0.478193i
$964$	56.8701	+	365.134i	0.0589939	+	0.378769i
$965$	418.422			0.433598
$966$	522.880	+	447.744i	0.541283	+	0.463504i
$967$		−	1508.66i		−	1.56014i	−0.625690	−	0.780072i	$-0.715183\pi$
$967$		−	1508.66i		−	1.56014i	0.625690	−	0.780072i	$-0.284817\pi$
$968$	−1212.94	−	749.734i	−1.25303	−	0.774519i
$969$	577.018			0.595478
$970$	380.217	−	444.020i	0.391976	−	0.457753i
$971$		−	905.996i		−	0.933054i	−0.884507	−	0.466527i	$-0.845505\pi$
$971$		−	905.996i		−	0.933054i	0.884507	−	0.466527i	$-0.154495\pi$
$972$	1294.23	−	201.579i	1.33152	−	0.207386i
$973$	825.645			0.848556
$974$	−313.461	−	268.418i	−0.321829	−	0.275584i
$975$			325.101i			0.333437i
$976$	435.975	−	139.184i	0.446696	−	0.142606i
$977$	574.517			0.588042			0.294021	−	0.955799i	$-0.405006\pi$
$977$	574.517			0.588042			0.294021	+	0.955799i	$0.405006\pi$
$978$	1282.41	−	1497.60i	1.31125	−	1.53129i
$979$			1240.60i			1.26721i
$980$	−33.2181	−	213.276i	−0.0338960	−	0.217629i
$981$	622.872			0.634936
$982$	−563.893	−	482.864i	−0.574229	−	0.491715i
$983$			1341.15i			1.36434i	0.731194	+	0.682170i	$0.238964\pi$
$983$			1341.15i			1.36434i	−0.731194	+	0.682170i	$0.761036\pi$
$984$	−1012.21	+	1637.58i	−1.02867	+	1.66420i
$985$	−261.633			−0.265617
$986$	1338.85	−	1563.52i	1.35786	−	1.58573i
$987$			144.720i			0.146626i
$988$	−272.719	+	42.4763i	−0.276031	+	0.0429922i
$989$	−93.9234			−0.0949680
$990$	462.492	+	396.035i	0.467164	+	0.400035i
$991$			1056.29i			1.06589i	0.846151	+	0.532944i	$0.178914\pi$
$991$			1056.29i			1.06589i	−0.846151	+	0.532944i	$0.821086\pi$
$992$	1018.61	+	429.608i	1.02682	+	0.433072i
$993$	2378.02			2.39479
$994$	1166.19	−	1361.89i	1.17323	−	1.37011i
$995$			281.867i			0.283283i
$996$	−129.214	−	829.620i	−0.129733	−	0.832951i
$997$	315.711			0.316661			0.158331	−	0.987386i	$-0.449389\pi$
$997$	315.711			0.316661			0.158331	+	0.987386i	$0.449389\pi$
$998$	−518.366	−	443.879i	−0.519405	−	0.444769i
$999$		−	32.5714i		−	0.0326040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.20	yes	72
4.3	odd	2	inner	380.3.b.a.191.19	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.19	✓	72	4.3	odd	2	inner
380.3.b.a.191.20	yes	72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30085 + 1.51914i) q^{2} -4.10739i q^{3} +(-0.615584 - 3.95235i) q^{4} -2.23607 q^{5} +(6.23970 + 5.34309i) q^{6} -8.55175i q^{7} +(6.80496 + 4.20625i) q^{8} -7.87063 q^{9} +O(q^{10})\)	\(q+(-1.30085 + 1.51914i) q^{2} -4.10739i q^{3} +(-0.615584 - 3.95235i) q^{4} -2.23607 q^{5} +(6.23970 + 5.34309i) q^{6} -8.55175i q^{7} +(6.80496 + 4.20625i) q^{8} -7.87063 q^{9} +(2.90879 - 3.39690i) q^{10} -17.2986i q^{11} +(-16.2338 + 2.52844i) q^{12} -15.8301 q^{13} +(12.9913 + 11.1245i) q^{14} +9.18440i q^{15} +(-15.2421 + 4.86600i) q^{16} +32.2290 q^{17} +(10.2385 - 11.9566i) q^{18} +4.35890i q^{19} +(1.37649 + 8.83772i) q^{20} -35.1254 q^{21} +(26.2791 + 22.5029i) q^{22} +9.79902i q^{23} +(17.2767 - 27.9506i) q^{24} +5.00000 q^{25} +(20.5925 - 24.0481i) q^{26} -4.63878i q^{27} +(-33.7995 + 5.26432i) q^{28} -31.9344 q^{29} +(-13.9524 - 11.9475i) q^{30} +34.5468i q^{31} +(12.4355 - 29.4849i) q^{32} -71.0522 q^{33} +(-41.9251 + 48.9604i) q^{34} +19.1223i q^{35} +(4.84503 + 31.1075i) q^{36} +7.02156 q^{37} +(-6.62179 - 5.67027i) q^{38} +65.0202i q^{39} +(-15.2164 - 9.40546i) q^{40} -58.5883 q^{41} +(45.6928 - 53.3604i) q^{42} +9.58498i q^{43} +(-68.3703 + 10.6488i) q^{44} +17.5993 q^{45} +(-14.8861 - 12.7470i) q^{46} -4.12010i q^{47} +(19.9866 + 62.6053i) q^{48} -24.1325 q^{49} +(-6.50424 + 7.59571i) q^{50} -132.377i q^{51} +(9.74473 + 62.5659i) q^{52} -47.2057 q^{53} +(7.04696 + 6.03435i) q^{54} +38.6809i q^{55} +(35.9708 - 58.1943i) q^{56} +17.9037 q^{57} +(41.5419 - 48.5130i) q^{58} -10.7555i q^{59} +(36.2999 - 5.65377i) q^{60} -28.6033 q^{61} +(-52.4814 - 44.9401i) q^{62} +67.3077i q^{63} +(28.6149 + 57.2467i) q^{64} +35.3971 q^{65} +(92.4282 - 107.938i) q^{66} +63.0364i q^{67} +(-19.8397 - 127.380i) q^{68} +40.2484 q^{69} +(-29.0495 - 24.8752i) q^{70} -104.831i q^{71} +(-53.5593 - 33.1058i) q^{72} +132.285 q^{73} +(-9.13399 + 10.6667i) q^{74} -20.5369i q^{75} +(17.2279 - 2.68327i) q^{76} -147.934 q^{77} +(-98.7749 - 84.5815i) q^{78} -74.1167i q^{79} +(34.0824 - 10.8807i) q^{80} -89.8889 q^{81} +(76.2145 - 89.0039i) q^{82} +51.1044i q^{83} +(21.6226 + 138.828i) q^{84} -72.0663 q^{85} +(-14.5609 - 12.4686i) q^{86} +131.167i q^{87} +(72.7624 - 117.717i) q^{88} -71.7165 q^{89} +(-22.8940 + 26.7358i) q^{90} +135.375i q^{91} +(38.7291 - 6.03212i) q^{92} +141.897 q^{93} +(6.25902 + 5.35963i) q^{94} -9.74679i q^{95} +(-121.106 - 51.0776i) q^{96} +130.713 q^{97} +(31.3927 - 36.6607i) q^{98} +136.151i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

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