LMFDB - Embedded newform 538.3.c.a.187.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$538 = 2 \cdot 269$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	538.c (of order $4$ , degree $2$ , 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:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.5
Character	$\chi$	$=$	538.187
Dual form			538.3.c.a.351.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-2.64193 - 2.64193i) q^{3} +2.00000i q^{4} -4.20274 q^{5} -5.28386i q^{6} +(-7.77918 + 7.77918i) q^{7} +(-2.00000 + 2.00000i) q^{8} +4.95961i q^{9} +(-4.20274 - 4.20274i) q^{10} -15.6994i q^{11} +(5.28386 - 5.28386i) q^{12} +1.21471i q^{13} -15.5584 q^{14} +(11.1034 + 11.1034i) q^{15} -4.00000 q^{16} +(20.3774 + 20.3774i) q^{17} +(-4.95961 + 4.95961i) q^{18} +(8.76306 - 8.76306i) q^{19} -8.40548i q^{20} +41.1041 q^{21} +(15.6994 - 15.6994i) q^{22} +16.0177 q^{23} +10.5677 q^{24} -7.33697 q^{25} +(-1.21471 + 1.21471i) q^{26} +(-10.6744 + 10.6744i) q^{27} +(-15.5584 - 15.5584i) q^{28} +(2.23825 - 2.23825i) q^{29} +22.2067i q^{30} +(26.4098 - 26.4098i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-41.4767 + 41.4767i) q^{33} +40.7548i q^{34} +(32.6939 - 32.6939i) q^{35} -9.91922 q^{36} +60.3191 q^{37} +17.5261 q^{38} +(3.20918 - 3.20918i) q^{39} +(8.40548 - 8.40548i) q^{40} -34.5733 q^{41} +(41.1041 + 41.1041i) q^{42} +12.6497i q^{43} +31.3988 q^{44} -20.8439i q^{45} +(16.0177 + 16.0177i) q^{46} +59.4417 q^{47} +(10.5677 + 10.5677i) q^{48} -72.0312i q^{49} +(-7.33697 - 7.33697i) q^{50} -107.671i q^{51} -2.42942 q^{52} +43.5333 q^{53} -21.3489 q^{54} +65.9805i q^{55} -31.1167i q^{56} -46.3028 q^{57} +4.47651 q^{58} +(63.7548 - 63.7548i) q^{59} +(-22.2067 + 22.2067i) q^{60} +22.1208 q^{61} +52.8197 q^{62} +(-38.5817 - 38.5817i) q^{63} -8.00000i q^{64} -5.10510i q^{65} -82.9535 q^{66} -108.610 q^{67} +(-40.7548 + 40.7548i) q^{68} +(-42.3177 - 42.3177i) q^{69} +65.3877 q^{70} +(8.33321 - 8.33321i) q^{71} +(-9.91922 - 9.91922i) q^{72} -45.3971i q^{73} +(60.3191 + 60.3191i) q^{74} +(19.3838 + 19.3838i) q^{75} +(17.5261 + 17.5261i) q^{76} +(122.128 + 122.128i) q^{77} +6.41835 q^{78} +115.012i q^{79} +16.8110 q^{80} +101.039 q^{81} +(-34.5733 - 34.5733i) q^{82} +(-17.6073 + 17.6073i) q^{83} +82.2082i q^{84} +(-85.6408 - 85.6408i) q^{85} +(-12.6497 + 12.6497i) q^{86} -11.8266 q^{87} +(31.3988 + 31.3988i) q^{88} +168.396i q^{89} +(20.8439 - 20.8439i) q^{90} +(-9.44943 - 9.44943i) q^{91} +32.0354i q^{92} -139.546 q^{93} +(59.4417 + 59.4417i) q^{94} +(-36.8289 + 36.8289i) q^{95} +21.1355i q^{96} +45.2003i q^{97} +(72.0312 - 72.0312i) q^{98} +77.8629 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$44 q + 44 q^{2} + 2 q^{3} + 4 q^{7} - 88 q^{8} - 4 q^{12} + 8 q^{14} + 38 q^{15} - 176 q^{16} - 120 q^{18} + 18 q^{19} - 16 q^{21} + 68 q^{23} - 8 q^{24} + 196 q^{25} + 16 q^{26} - 22 q^{27} + 8 q^{28}+ \cdots - 188 q^{99}+O(q^{100})$ 44 * q + 44 * q^2 + 2 * q^3 + 4 * q^7 - 88 * q^8 - 4 * q^12 + 8 * q^14 + 38 * q^15 - 176 * q^16 - 120 * q^18 + 18 * q^19 - 16 * q^21 + 68 * q^23 - 8 * q^24 + 196 * q^25 + 16 * q^26 - 22 * q^27 + 8 * q^28 + 18 * q^29 + 88 * q^31 - 176 * q^32 + 96 * q^33 + 10 * q^35 - 240 * q^36 + 180 * q^37 + 36 * q^38 - 54 * q^39 + 144 * q^41 - 16 * q^42 + 68 * q^46 - 156 * q^47 - 8 * q^48 + 196 * q^50 + 32 * q^52 - 188 * q^53 - 44 * q^54 - 88 * q^57 + 36 * q^58 - 98 * q^59 - 76 * q^60 - 244 * q^61 + 176 * q^62 - 10 * q^63 + 192 * q^66 + 220 * q^67 - 70 * q^69 + 20 * q^70 + 156 * q^71 - 240 * q^72 + 180 * q^74 - 102 * q^75 + 36 * q^76 - 28 * q^77 - 108 * q^78 + 392 * q^81 + 144 * q^82 - 250 * q^83 - 342 * q^85 - 44 * q^86 - 60 * q^87 - 192 * q^90 + 66 * q^91 - 536 * q^93 - 156 * q^94 - 472 * q^95 + 404 * q^98 - 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$ .

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−2.64193	−	2.64193i	−0.880644	−	0.880644i	0.112956	−	0.993600i	$-0.463968\pi$
$3$	−2.64193	−	2.64193i	−0.880644	−	0.880644i	−0.993600	+	0.112956i	$0.963968\pi$
$4$			2.00000i			0.500000i
$5$	−4.20274			−0.840548			−0.420274	−	0.907397i	$-0.638066\pi$
$5$	−4.20274			−0.840548			−0.420274	+	0.907397i	$0.638066\pi$
$6$		−	5.28386i		−	0.880644i
$7$	−7.77918	+	7.77918i	−1.11131	+	1.11131i	−0.118338	+	0.992973i	$0.537757\pi$
$7$	−7.77918	+	7.77918i	−1.11131	+	1.11131i	−0.992973	+	0.118338i	$0.962243\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$			4.95961i			0.551068i
$10$	−4.20274	−	4.20274i	−0.420274	−	0.420274i
$11$		−	15.6994i		−	1.42722i	−0.700544	−	0.713609i	$-0.747059\pi$
$11$		−	15.6994i		−	1.42722i	0.700544	−	0.713609i	$-0.252941\pi$
$12$	5.28386	−	5.28386i	0.440322	−	0.440322i
$13$			1.21471i			0.0934391i	0.998908	+	0.0467195i	$0.0148767\pi$
$13$			1.21471i			0.0934391i	−0.998908	+	0.0467195i	$0.985123\pi$
$14$	−15.5584			−1.11131
$15$	11.1034	+	11.1034i	0.740224	+	0.740224i
$16$	−4.00000			−0.250000
$17$	20.3774	+	20.3774i	1.19867	+	1.19867i	0.974565	+	0.224104i	$0.0719456\pi$
$17$	20.3774	+	20.3774i	1.19867	+	1.19867i	0.224104	+	0.974565i	$0.428054\pi$
$18$	−4.95961	+	4.95961i	−0.275534	+	0.275534i
$19$	8.76306	−	8.76306i	0.461214	−	0.461214i	−0.437839	−	0.899053i	$-0.644256\pi$
$19$	8.76306	−	8.76306i	0.461214	−	0.461214i	0.899053	+	0.437839i	$0.144256\pi$
$20$		−	8.40548i		−	0.420274i
$21$	41.1041			1.95734
$22$	15.6994	−	15.6994i	0.713609	−	0.713609i
$23$	16.0177			0.696423			0.348211	−	0.937416i	$-0.386789\pi$
$23$	16.0177			0.696423			0.348211	+	0.937416i	$0.386789\pi$
$24$	10.5677			0.440322
$25$	−7.33697			−0.293479
$26$	−1.21471	+	1.21471i	−0.0467195	+	0.0467195i
$27$	−10.6744	+	10.6744i	−0.395350	+	0.395350i
$28$	−15.5584	−	15.5584i	−0.555656	−	0.555656i
$29$	2.23825	−	2.23825i	0.0771812	−	0.0771812i	−0.667462	−	0.744644i	$-0.732619\pi$
$29$	2.23825	−	2.23825i	0.0771812	−	0.0771812i	0.744644	+	0.667462i	$0.232619\pi$
$30$			22.2067i			0.740224i
$31$	26.4098	−	26.4098i	0.851930	−	0.851930i	−0.138441	−	0.990371i	$-0.544209\pi$
$31$	26.4098	−	26.4098i	0.851930	−	0.851930i	0.990371	+	0.138441i	$0.0442091\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−41.4767	+	41.4767i	−1.25687	+	1.25687i
$34$			40.7548i			1.19867i
$35$	32.6939	−	32.6939i	0.934110	−	0.934110i
$36$	−9.91922			−0.275534
$37$	60.3191			1.63025			0.815123	−	0.579288i	$-0.196669\pi$
$37$	60.3191			1.63025			0.815123	+	0.579288i	$0.196669\pi$
$38$	17.5261			0.461214
$39$	3.20918	−	3.20918i	0.0822866	−	0.0822866i
$40$	8.40548	−	8.40548i	0.210137	−	0.210137i
$41$	−34.5733			−0.843251			−0.421625	−	0.906770i	$-0.638540\pi$
$41$	−34.5733			−0.843251			−0.421625	+	0.906770i	$0.638540\pi$
$42$	41.1041	+	41.1041i	0.978669	+	0.978669i
$43$			12.6497i			0.294178i	0.989123	+	0.147089i	$0.0469904\pi$
$43$			12.6497i			0.294178i	−0.989123	+	0.147089i	$0.953010\pi$
$44$	31.3988			0.713609
$45$		−	20.8439i		−	0.463199i
$46$	16.0177	+	16.0177i	0.348211	+	0.348211i
$47$	59.4417			1.26472			0.632359	−	0.774676i	$-0.282087\pi$
$47$	59.4417			1.26472			0.632359	+	0.774676i	$0.282087\pi$
$48$	10.5677	+	10.5677i	0.220161	+	0.220161i
$49$		−	72.0312i		−	1.47002i
$50$	−7.33697	−	7.33697i	−0.146739	−	0.146739i
$51$		−	107.671i		−	2.11120i
$52$	−2.42942			−0.0467195
$53$	43.5333			0.821383			0.410692	−	0.911774i	$-0.365287\pi$
$53$	43.5333			0.821383			0.410692	+	0.911774i	$0.365287\pi$
$54$	−21.3489			−0.395350
$55$			65.9805i			1.19965i
$56$		−	31.1167i		−	0.555656i
$57$	−46.3028			−0.812330
$58$	4.47651			0.0771812
$59$	63.7548	−	63.7548i	1.08059	−	1.08059i	0.0841356	−	0.996454i	$-0.473187\pi$
$59$	63.7548	−	63.7548i	1.08059	−	1.08059i	0.996454	−	0.0841356i	$-0.0268129\pi$
$60$	−22.2067	+	22.2067i	−0.370112	+	0.370112i
$61$	22.1208			0.362637			0.181318	−	0.983424i	$-0.441964\pi$
$61$	22.1208			0.362637			0.181318	+	0.983424i	$0.441964\pi$
$62$	52.8197			0.851930
$63$	−38.5817	−	38.5817i	−0.612408	−	0.612408i
$64$		−	8.00000i		−	0.125000i
$65$		−	5.10510i		−	0.0785400i
$66$	−82.9535			−1.25687
$67$	−108.610			−1.62104			−0.810520	−	0.585710i	$-0.800816\pi$
$67$	−108.610			−1.62104			−0.810520	+	0.585710i	$0.800816\pi$
$68$	−40.7548	+	40.7548i	−0.599335	+	0.599335i
$69$	−42.3177	−	42.3177i	−0.613300	−	0.613300i
$70$	65.3877			0.934110
$71$	8.33321	−	8.33321i	0.117369	−	0.117369i	−0.645983	−	0.763352i	$-0.723552\pi$
$71$	8.33321	−	8.33321i	0.117369	−	0.117369i	0.763352	+	0.645983i	$0.223552\pi$
$72$	−9.91922	−	9.91922i	−0.137767	−	0.137767i
$73$		−	45.3971i		−	0.621879i	−0.950430	−	0.310939i	$-0.899356\pi$
$73$		−	45.3971i		−	0.621879i	0.950430	−	0.310939i	$-0.100644\pi$
$74$	60.3191	+	60.3191i	0.815123	+	0.815123i
$75$	19.3838	+	19.3838i	0.258450	+	0.258450i
$76$	17.5261	+	17.5261i	0.230607	+	0.230607i
$77$	122.128	+	122.128i	1.58608	+	1.58608i
$78$	6.41835			0.0822866
$79$			115.012i			1.45585i	0.685656	+	0.727926i	$0.259515\pi$
$79$			115.012i			1.45585i	−0.685656	+	0.727926i	$0.740485\pi$
$80$	16.8110			0.210137
$81$	101.039			1.24739
$82$	−34.5733	−	34.5733i	−0.421625	−	0.421625i
$83$	−17.6073	+	17.6073i	−0.212136	+	0.212136i	−0.805174	−	0.593038i	$-0.797928\pi$
$83$	−17.6073	+	17.6073i	−0.212136	+	0.212136i	0.593038	+	0.805174i	$0.297928\pi$
$84$			82.2082i			0.978669i
$85$	−85.6408	−	85.6408i	−1.00754	−	1.00754i
$86$	−12.6497	+	12.6497i	−0.147089	+	0.147089i
$87$	−11.8266			−0.135938
$88$	31.3988	+	31.3988i	0.356804	+	0.356804i
$89$			168.396i			1.89209i	0.324033	+	0.946046i	$0.394961\pi$
$89$			168.396i			1.89209i	−0.324033	+	0.946046i	$0.605039\pi$
$90$	20.8439	−	20.8439i	0.231599	−	0.231599i
$91$	−9.44943	−	9.44943i	−0.103840	−	0.103840i
$92$			32.0354i			0.348211i
$93$	−139.546			−1.50049
$94$	59.4417	+	59.4417i	0.632359	+	0.632359i
$95$	−36.8289	+	36.8289i	−0.387672	+	0.387672i
$96$			21.1355i			0.220161i
$97$			45.2003i			0.465982i	0.972479	+	0.232991i	$0.0748513\pi$
$97$			45.2003i			0.465982i	−0.972479	+	0.232991i	$0.925149\pi$
$98$	72.0312	−	72.0312i	0.735012	−	0.735012i
$99$	77.8629			0.786493
$100$		−	14.6739i		−	0.146739i
$101$	−104.348	−	104.348i	−1.03315	−	1.03315i	−0.999431	−	0.0337191i	$-0.989265\pi$
$101$	−104.348	−	104.348i	−1.03315	−	1.03315i	−0.0337191	−	0.999431i	$-0.510735\pi$
$102$	107.671	−	107.671i	1.05560	−	1.05560i
$103$		−	42.0822i		−	0.408565i	−0.978912	−	0.204283i	$-0.934514\pi$
$103$		−	42.0822i		−	0.408565i	0.978912	−	0.204283i	$-0.0654861\pi$
$104$	−2.42942	−	2.42942i	−0.0233598	−	0.0233598i
$105$	−172.750			−1.64524
$106$	43.5333	+	43.5333i	0.410692	+	0.410692i
$107$	92.8106	−	92.8106i	0.867389	−	0.867389i	−0.124794	−	0.992183i	$-0.539827\pi$
$107$	92.8106	−	92.8106i	0.867389	−	0.867389i	0.992183	+	0.124794i	$0.0398269\pi$
$108$	−21.3489	−	21.3489i	−0.197675	−	0.197675i
$109$	−7.74003	+	7.74003i	−0.0710094	+	0.0710094i	−0.741720	−	0.670710i	$-0.765989\pi$
$109$	−7.74003	+	7.74003i	−0.0710094	+	0.0710094i	0.670710	+	0.741720i	$0.265989\pi$
$110$	−65.9805	+	65.9805i	−0.599823	+	0.599823i
$111$	−159.359	−	159.359i	−1.43567	−	1.43567i
$112$	31.1167	−	31.1167i	0.277828	−	0.277828i
$113$	−52.3685	+	52.3685i	−0.463438	+	0.463438i	−0.899781	−	0.436343i	$-0.856274\pi$
$113$	−52.3685	+	52.3685i	−0.463438	+	0.463438i	0.436343	+	0.899781i	$0.356274\pi$
$114$	−46.3028	−	46.3028i	−0.406165	−	0.406165i
$115$	−67.3183			−0.585377
$116$	4.47651	+	4.47651i	0.0385906	+	0.0385906i
$117$	−6.02448			−0.0514913
$118$	127.510			1.08059
$119$	−317.039			−2.66419
$120$	−44.4134			−0.370112
$121$	−125.471			−1.03695
$122$	22.1208	+	22.1208i	0.181318	+	0.181318i
$123$	91.3403	+	91.3403i	0.742604	+	0.742604i
$124$	52.8197	+	52.8197i	0.425965	+	0.425965i
$125$	135.904			1.08723
$126$		−	77.1634i		−	0.612408i
$127$		−	135.667i		−	1.06825i	−0.845406	−	0.534124i	$-0.820642\pi$
$127$		−	135.667i		−	1.06825i	0.845406	−	0.534124i	$-0.179358\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	33.4196	−	33.4196i	0.259066	−	0.259066i
$130$	5.10510	−	5.10510i	0.0392700	−	0.0392700i
$131$	203.219			1.55129			0.775645	−	0.631169i	$-0.217425\pi$
$131$	203.219			1.55129			0.775645	+	0.631169i	$0.217425\pi$
$132$	−82.9535	−	82.9535i	−0.628435	−	0.628435i
$133$			136.339i			1.02510i
$134$	−108.610	−	108.610i	−0.810520	−	0.810520i
$135$	44.8619	−	44.8619i	0.332310	−	0.332310i
$136$	−81.5095			−0.599335
$137$	−164.074	+	164.074i	−1.19762	+	1.19762i	−0.222744	+	0.974877i	$0.571501\pi$
$137$	−164.074	+	164.074i	−1.19762	+	1.19762i	−0.974877	+	0.222744i	$0.928499\pi$
$138$		−	84.6355i		−	0.613300i
$139$	76.8463	+	76.8463i	0.552851	+	0.552851i	0.927263	−	0.374411i	$-0.122155\pi$
$139$	76.8463	+	76.8463i	0.552851	+	0.552851i	−0.374411	+	0.927263i	$0.622155\pi$
$140$	65.3877	+	65.3877i	0.467055	+	0.467055i
$141$	−157.041	−	157.041i	−1.11377	−	1.11377i
$142$	16.6664			0.117369
$143$	19.0702			0.133358
$144$		−	19.8384i		−	0.137767i
$145$	−9.40680	+	9.40680i	−0.0648745	+	0.0648745i
$146$	45.3971	−	45.3971i	0.310939	−	0.310939i
$147$	−190.302	+	190.302i	−1.29457	+	1.29457i
$148$			120.638i			0.815123i
$149$			57.3202i			0.384700i	0.981326	+	0.192350i	$0.0616108\pi$
$149$			57.3202i			0.384700i	−0.981326	+	0.192350i	$0.938389\pi$
$150$			38.7676i			0.258450i
$151$		−	80.7973i		−	0.535082i	−0.963547	−	0.267541i	$-0.913789\pi$
$151$		−	80.7973i		−	0.535082i	0.963547	−	0.267541i	$-0.0862110\pi$
$152$			35.0522i			0.230607i
$153$	−101.064	+	101.064i	−0.660548	+	0.660548i
$154$			244.257i			1.58608i
$155$	−110.994	+	110.994i	−0.716088	+	0.716088i
$156$	6.41835	+	6.41835i	0.0411433	+	0.0411433i
$157$	−2.73260	−	2.73260i	−0.0174051	−	0.0174051i	0.698351	−	0.715756i	$-0.253918\pi$
$157$	−2.73260	−	2.73260i	−0.0174051	−	0.0174051i	−0.715756	+	0.698351i	$0.753918\pi$
$158$	−115.012	+	115.012i	−0.727926	+	0.727926i
$159$	−115.012	−	115.012i	−0.723346	−	0.723346i
$160$	16.8110	+	16.8110i	0.105069	+	0.105069i
$161$	−124.605	+	124.605i	−0.773942	+	0.773942i
$162$	101.039	+	101.039i	0.623696	+	0.623696i
$163$	124.364	−	124.364i	0.762969	−	0.762969i	−0.213889	−	0.976858i	$-0.568613\pi$
$163$	124.364	−	124.364i	0.762969	−	0.762969i	0.976858	+	0.213889i	$0.0686131\pi$
$164$		−	69.1466i		−	0.421625i
$165$	174.316	−	174.316i	1.05646	−	1.05646i
$166$	−35.2146			−0.212136
$167$	63.3114	+	63.3114i	0.379110	+	0.379110i	0.870781	−	0.491671i	$-0.163614\pi$
$167$	63.3114	+	63.3114i	0.379110	+	0.379110i	−0.491671	+	0.870781i	$0.663614\pi$
$168$	−82.2082	+	82.2082i	−0.489335	+	0.489335i
$169$	167.524			0.991269
$170$		−	171.282i		−	1.00754i
$171$	43.4614	+	43.4614i	0.254160	+	0.254160i
$172$	−25.2993			−0.147089
$173$	260.069			1.50329			0.751645	−	0.659568i	$-0.229261\pi$
$173$	260.069			1.50329			0.751645	+	0.659568i	$0.229261\pi$
$174$	−11.8266	−	11.8266i	−0.0679692	−	0.0679692i
$175$	57.0756	−	57.0756i	0.326146	−	0.326146i
$176$			62.7976i			0.356804i
$177$	−336.872			−1.90323
$178$	−168.396	+	168.396i	−0.946046	+	0.946046i
$179$	−1.26822	−	1.26822i	−0.00708502	−	0.00708502i	0.703555	−	0.710640i	$-0.251595\pi$
$179$	−1.26822	−	1.26822i	−0.00708502	−	0.00708502i	−0.710640	+	0.703555i	$0.751595\pi$
$180$	41.6879			0.231599
$181$	80.4184	−	80.4184i	0.444301	−	0.444301i	−0.449154	−	0.893455i	$-0.648274\pi$
$181$	80.4184	−	80.4184i	0.444301	−	0.444301i	0.893455	+	0.449154i	$0.148274\pi$
$182$		−	18.8989i		−	0.103840i
$183$	−58.4418	−	58.4418i	−0.319354	−	0.319354i
$184$	−32.0354	+	32.0354i	−0.174106	+	0.174106i
$185$	−253.506			−1.37030
$186$	−139.546	−	139.546i	−0.750247	−	0.750247i
$187$	319.912	−	319.912i	1.71076	−	1.71076i
$188$			118.883i			0.632359i
$189$		−	166.077i		−	0.878713i
$190$	−73.6578			−0.387672
$191$		−	358.860i		−	1.87885i	−0.342756	−	0.939424i	$-0.611361\pi$
$191$		−	358.860i		−	1.87885i	0.342756	−	0.939424i	$-0.388639\pi$
$192$	−21.1355	+	21.1355i	−0.110080	+	0.110080i
$193$	−30.4979	+	30.4979i	−0.158020	+	0.158020i	−0.781689	−	0.623669i	$-0.785642\pi$
$193$	−30.4979	+	30.4979i	−0.158020	+	0.158020i	0.623669	+	0.781689i	$0.285642\pi$
$194$	−45.2003	+	45.2003i	−0.232991	+	0.232991i
$195$	−13.4873	+	13.4873i	−0.0691658	+	0.0691658i
$196$	144.062			0.735012
$197$	−67.9508	+	67.9508i	−0.344928	+	0.344928i	−0.858216	−	0.513288i	$-0.828427\pi$
$197$	−67.9508	+	67.9508i	−0.344928	+	0.344928i	0.513288	+	0.858216i	$0.328427\pi$
$198$	77.8629	+	77.8629i	0.393247	+	0.393247i
$199$			91.9764i			0.462193i	0.972931	+	0.231097i	$0.0742313\pi$
$199$			91.9764i			0.462193i	−0.972931	+	0.231097i	$0.925769\pi$
$200$	14.6739	−	14.6739i	0.0733697	−	0.0733697i
$201$	286.940	+	286.940i	1.42756	+	1.42756i
$202$		−	208.696i		−	1.03315i
$203$			34.8236i			0.171545i
$204$	215.343			1.05560
$205$	145.303			0.708793
$206$	42.0822	−	42.0822i	0.204283	−	0.204283i
$207$			79.4416i			0.383776i
$208$		−	4.85883i		−	0.0233598i
$209$	−137.575	−	137.575i	−0.658252	−	0.658252i
$210$	−172.750	−	172.750i	−0.822619	−	0.822619i
$211$		−	281.631i		−	1.33474i	−0.744725	−	0.667372i	$-0.767419\pi$
$211$		−	281.631i		−	1.33474i	0.744725	−	0.667372i	$-0.232581\pi$
$212$			87.0666i			0.410692i
$213$	−44.0316			−0.206721
$214$	185.621			0.867389
$215$		−	53.1633i		−	0.247271i
$216$		−	42.6978i		−	0.197675i
$217$			410.893i			1.89352i
$218$	−15.4801			−0.0710094
$219$	−119.936	+	119.936i	−0.547654	+	0.547654i
$220$	−131.961			−0.599823
$221$	−24.7526	+	24.7526i	−0.112003	+	0.112003i
$222$		−	318.718i		−	1.43567i
$223$	204.071	−	204.071i	0.915115	−	0.915115i	−0.0815541	−	0.996669i	$-0.525988\pi$
$223$	204.071	−	204.071i	0.915115	−	0.915115i	0.996669	+	0.0815541i	$0.0259883\pi$
$224$	62.2334			0.277828
$225$		−	36.3885i		−	0.161727i
$226$	−104.737			−0.463438
$227$	−178.918	+	178.918i	−0.788184	+	0.788184i	−0.981196	−	0.193012i	$-0.938174\pi$
$227$	−178.918	+	178.918i	−0.788184	+	0.788184i	0.193012	+	0.981196i	$0.438174\pi$
$228$		−	92.6057i		−	0.406165i
$229$	−13.0595	−	13.0595i	−0.0570283	−	0.0570283i	0.678017	−	0.735046i	$-0.262839\pi$
$229$	−13.0595	−	13.0595i	−0.0570283	−	0.0570283i	−0.735046	+	0.678017i	$0.762839\pi$
$230$	−67.3183	−	67.3183i	−0.292688	−	0.292688i
$231$		−	645.310i		−	2.79355i
$232$			8.95302i			0.0385906i
$233$		−	50.7731i		−	0.217910i	−0.994047	−	0.108955i	$-0.965250\pi$
$233$		−	50.7731i		−	0.217910i	0.994047	−	0.108955i	$-0.0347505\pi$
$234$	−6.02448	−	6.02448i	−0.0257456	−	0.0257456i
$235$	−249.818			−1.06306
$236$	127.510	+	127.510i	0.540295	+	0.540295i
$237$	303.855	−	303.855i	1.28209	−	1.28209i
$238$	−317.039	−	317.039i	−1.33209	−	1.33209i
$239$	−306.969			−1.28439			−0.642195	−	0.766541i	$-0.721976\pi$
$239$	−306.969			−1.28439			−0.642195	+	0.766541i	$0.721976\pi$
$240$	−44.4134	−	44.4134i	−0.185056	−	0.185056i
$241$	257.200	−	257.200i	1.06722	−	1.06722i	0.0696504	−	0.997571i	$-0.477812\pi$
$241$	257.200	−	257.200i	1.06722	−	1.06722i	0.997571	−	0.0696504i	$-0.0221884\pi$
$242$	−125.471	−	125.471i	−0.518475	−	0.518475i
$243$	−170.868	−	170.868i	−0.703159	−	0.703159i
$244$			44.2417i			0.181318i
$245$			302.729i			1.23563i
$246$			182.681i			0.742604i
$247$	10.6446	+	10.6446i	0.0430954	+	0.0430954i
$248$			105.639i			0.425965i
$249$	93.0345			0.373632
$250$	135.904	+	135.904i	0.543616	+	0.543616i
$251$	180.395	+	180.395i	0.718707	+	0.718707i	0.968340	−	0.249634i	$-0.0803102\pi$
$251$	180.395	+	180.395i	0.718707	+	0.718707i	−0.249634	+	0.968340i	$0.580310\pi$
$252$	77.1634	−	77.1634i	0.306204	−	0.306204i
$253$		−	251.469i		−	0.993947i
$254$	135.667	−	135.667i	0.534124	−	0.534124i
$255$			452.514i			1.77457i
$256$	16.0000			0.0625000
$257$	227.649	+	227.649i	0.885794	+	0.885794i	0.994116	−	0.108322i	$-0.0345476\pi$
$257$	227.649	+	227.649i	0.885794	+	0.885794i	−0.108322	+	0.994116i	$0.534548\pi$
$258$	66.8391			0.259066
$259$	−469.233	+	469.233i	−1.81171	+	1.81171i
$260$	10.2102			0.0392700
$261$	11.1009	+	11.1009i	0.0425321	+	0.0425321i
$262$	203.219	+	203.219i	0.775645	+	0.775645i
$263$	289.446			1.10055			0.550277	−	0.834982i	$-0.314522\pi$
$263$	289.446			1.10055			0.550277	+	0.834982i	$0.314522\pi$
$264$		−	165.907i		−	0.628435i
$265$	−182.959			−0.690412
$266$	−136.339	+	136.339i	−0.512552	+	0.512552i
$267$	444.891	−	444.891i	1.66626	−	1.66626i
$268$		−	217.219i		−	0.810520i
$269$	131.967	+	234.405i	0.490582	+	0.871395i
$269$	131.967	+	234.405i	0.490582	+	0.871395i
$270$	89.7238			0.332310
$271$	−99.5676	−	99.5676i	−0.367408	−	0.367408i	0.499123	−	0.866531i	$-0.333656\pi$
$271$	−99.5676	−	99.5676i	−0.367408	−	0.367408i	−0.866531	+	0.499123i	$0.833656\pi$
$272$	−81.5095	−	81.5095i	−0.299667	−	0.299667i
$273$			49.9295i			0.182892i
$274$	−328.148			−1.19762
$275$			115.186i			0.418858i
$276$	84.6355	−	84.6355i	0.306650	−	0.306650i
$277$	−86.2116	+	86.2116i	−0.311233	+	0.311233i	−0.845387	−	0.534154i	$-0.820630\pi$
$277$	−86.2116	+	86.2116i	−0.311233	+	0.311233i	0.534154	+	0.845387i	$0.320630\pi$
$278$			153.693i			0.552851i
$279$	130.982	+	130.982i	0.469471	+	0.469471i
$280$			130.775i			0.467055i
$281$	−263.133	+	263.133i	−0.936415	+	0.936415i	−0.998096	−	0.0616810i	$-0.980354\pi$
$281$	−263.133	+	263.133i	−0.936415	+	0.936415i	0.0616810	+	0.998096i	$0.480354\pi$
$282$		−	314.082i		−	1.11377i
$283$	339.372			1.19919			0.599597	−	0.800302i	$-0.295328\pi$
$283$	339.372			1.19919			0.599597	+	0.800302i	$0.295328\pi$
$284$	16.6664	+	16.6664i	0.0586846	+	0.0586846i
$285$	194.599			0.682803
$286$	19.0702	+	19.0702i	0.0666790	+	0.0666790i
$287$	268.952	−	268.952i	0.937114	−	0.937114i
$288$	19.8384	−	19.8384i	0.0688835	−	0.0688835i
$289$			541.475i			1.87362i
$290$	−18.8136			−0.0648745
$291$	119.416	−	119.416i	0.410365	−	0.410365i
$292$	90.7943			0.310939
$293$	−295.679			−1.00914			−0.504572	−	0.863370i	$-0.668350\pi$
$293$	−295.679			−1.00914			−0.504572	+	0.863370i	$0.668350\pi$
$294$	−380.603			−1.29457
$295$	−267.945	+	267.945i	−0.908288	+	0.908288i
$296$	−120.638	+	120.638i	−0.407562	+	0.407562i
$297$	167.582	+	167.582i	0.564250	+	0.564250i
$298$	−57.3202	+	57.3202i	−0.192350	+	0.192350i
$299$			19.4569i			0.0650731i
$300$	−38.7676	+	38.7676i	−0.129225	+	0.129225i
$301$	−98.4040	−	98.4040i	−0.326924	−	0.326924i
$302$	80.7973	−	80.7973i	0.267541	−	0.267541i
$303$			551.362i			1.81968i
$304$	−35.0522	+	35.0522i	−0.115303	+	0.115303i
$305$	−92.9682			−0.304814
$306$	−202.128			−0.660548
$307$	239.609			0.780487			0.390243	−	0.920712i	$-0.372391\pi$
$307$	239.609			0.780487			0.390243	+	0.920712i	$0.372391\pi$
$308$	−244.257	+	244.257i	−0.793041	+	0.793041i
$309$	−111.178	+	111.178i	−0.359800	+	0.359800i
$310$	−221.987			−0.716088
$311$	−163.604	−	163.604i	−0.526059	−	0.526059i	0.393336	−	0.919395i	$-0.371321\pi$
$311$	−163.604	−	163.604i	−0.526059	−	0.526059i	−0.919395	+	0.393336i	$0.871321\pi$
$312$			12.8367i			0.0411433i
$313$	224.705			0.717908			0.358954	−	0.933355i	$-0.383134\pi$
$313$	224.705			0.717908			0.358954	+	0.933355i	$0.383134\pi$
$314$		−	5.46519i		−	0.0174051i
$315$	162.149	+	162.149i	0.514758	+	0.514758i
$316$	−230.025			−0.727926
$317$	−278.202	−	278.202i	−0.877608	−	0.877608i	0.115679	−	0.993287i	$-0.463096\pi$
$317$	−278.202	−	278.202i	−0.877608	−	0.877608i	−0.993287	+	0.115679i	$0.963096\pi$
$318$		−	230.024i		−	0.723346i
$319$	−35.1392	−	35.1392i	−0.110154	−	0.110154i
$320$			33.6219i			0.105069i
$321$	−490.399			−1.52772
$322$	−249.209			−0.773942
$323$	357.136			1.10569
$324$			202.078i			0.623696i
$325$		−	8.91228i		−	0.0274224i
$326$	248.728			0.762969
$327$	40.8972			0.125068
$328$	69.1466	−	69.1466i	0.210813	−	0.210813i
$329$	−462.408	+	462.408i	−1.40549	+	1.40549i
$330$	348.632			1.05646
$331$	108.806			0.328718			0.164359	−	0.986401i	$-0.447444\pi$
$331$	108.806			0.328718			0.164359	+	0.986401i	$0.447444\pi$
$332$	−35.2146	−	35.2146i	−0.106068	−	0.106068i
$333$			299.159i			0.898376i
$334$			126.623i			0.379110i
$335$	456.459			1.36256
$336$	−164.416			−0.489335
$337$	290.704	−	290.704i	0.862625	−	0.862625i	−0.129018	−	0.991642i	$-0.541182\pi$
$337$	290.704	−	290.704i	0.862625	−	0.862625i	0.991642	+	0.129018i	$0.0411824\pi$
$338$	167.524	+	167.524i	0.495635	+	0.495635i
$339$	276.708			0.816248
$340$	171.282	−	171.282i	0.503770	−	0.503770i
$341$	−414.618	−	414.618i	−1.21589	−	1.21589i
$342$			86.9227i			0.254160i
$343$	179.164	+	179.164i	0.522344	+	0.522344i
$344$	−25.2993	−	25.2993i	−0.0735446	−	0.0735446i
$345$	177.850	+	177.850i	0.515509	+	0.515509i
$346$	260.069	+	260.069i	0.751645	+	0.751645i
$347$	−143.691			−0.414095			−0.207048	−	0.978331i	$-0.566386\pi$
$347$	−143.691			−0.414095			−0.207048	+	0.978331i	$0.566386\pi$
$348$		−	23.6533i		−	0.0679692i
$349$	300.144			0.860012			0.430006	−	0.902826i	$-0.358512\pi$
$349$	300.144			0.860012			0.430006	+	0.902826i	$0.358512\pi$
$350$	114.151			0.326146
$351$	−12.9663	−	12.9663i	−0.0369411	−	0.0369411i
$352$	−62.7976	+	62.7976i	−0.178402	+	0.178402i
$353$		−	541.225i		−	1.53322i	−0.642115	−	0.766608i	$-0.721943\pi$
$353$		−	541.225i		−	1.53322i	0.642115	−	0.766608i	$-0.278057\pi$
$354$	−336.872	−	336.872i	−0.951615	−	0.951615i
$355$	−35.0223	+	35.0223i	−0.0986545	+	0.0986545i
$356$	−336.792			−0.946046
$357$	837.594	+	837.594i	2.34620	+	2.34620i
$358$		−	2.53644i		−	0.00708502i
$359$	−48.0321	+	48.0321i	−0.133794	+	0.133794i	−0.770832	−	0.637038i	$-0.780159\pi$
$359$	−48.0321	+	48.0321i	−0.133794	+	0.133794i	0.637038	+	0.770832i	$0.280159\pi$
$360$	41.6879	+	41.6879i	0.115800	+	0.115800i
$361$			207.417i			0.574564i
$362$	160.837			0.444301
$363$	331.486	+	331.486i	0.913184	+	0.913184i
$364$	18.8989	−	18.8989i	0.0519200	−	0.0519200i
$365$			190.792i			0.522719i
$366$		−	116.884i		−	0.319354i
$367$	−15.3631	+	15.3631i	−0.0418613	+	0.0418613i	−0.727728	−	0.685866i	$-0.759423\pi$
$367$	−15.3631	+	15.3631i	−0.0418613	+	0.0418613i	0.685866	+	0.727728i	$0.259423\pi$
$368$	−64.0709			−0.174106
$369$		−	171.470i		−	0.464688i
$370$	−253.506	−	253.506i	−0.685150	−	0.685150i
$371$	−338.653	+	338.653i	−0.912812	+	0.912812i
$372$		−	279.092i		−	0.750247i
$373$	86.2389	+	86.2389i	0.231203	+	0.231203i	0.813195	−	0.581991i	$-0.197726\pi$
$373$	86.2389	+	86.2389i	0.231203	+	0.231203i	−0.581991	+	0.813195i	$0.697726\pi$
$374$	639.825			1.71076
$375$	−359.049	−	359.049i	−0.957464	−	0.957464i
$376$	−118.883	+	118.883i	−0.316179	+	0.316179i
$377$	2.71883	+	2.71883i	0.00721174	+	0.00721174i
$378$	166.077	−	166.077i	0.439356	−	0.439356i
$379$	326.883	−	326.883i	0.862489	−	0.862489i	−0.129137	−	0.991627i	$-0.541221\pi$
$379$	326.883	−	326.883i	0.862489	−	0.862489i	0.991627	+	0.129137i	$0.0412208\pi$
$380$	−73.6578	−	73.6578i	−0.193836	−	0.193836i
$381$	−358.424	+	358.424i	−0.940746	+	0.940746i
$382$	358.860	−	358.860i	0.939424	−	0.939424i
$383$	167.177	+	167.177i	0.436493	+	0.436493i	0.890830	−	0.454337i	$-0.150124\pi$
$383$	167.177	+	167.177i	0.436493	+	0.436493i	−0.454337	+	0.890830i	$0.650124\pi$
$384$	−42.2709			−0.110080
$385$	−513.274	−	513.274i	−1.33318	−	1.33318i
$386$	−60.9959			−0.158020
$387$	−62.7374			−0.162112
$388$	−90.4006			−0.232991
$389$	−156.002			−0.401033			−0.200516	−	0.979690i	$-0.564262\pi$
$389$	−156.002			−0.401033			−0.200516	+	0.979690i	$0.564262\pi$
$390$	−26.9747			−0.0691658
$391$	326.399	+	326.399i	0.834781	+	0.834781i
$392$	144.062	+	144.062i	0.367506	+	0.367506i
$393$	−536.891	−	536.891i	−1.36613	−	1.36613i
$394$	−135.902			−0.344928
$395$		−	483.367i		−	1.22371i
$396$			155.726i			0.393247i
$397$	−190.062	+	190.062i	−0.478746	+	0.478746i	−0.904730	−	0.425985i	$-0.859928\pi$
$397$	−190.062	+	190.062i	−0.478746	+	0.478746i	0.425985	+	0.904730i	$0.359928\pi$
$398$	−91.9764	+	91.9764i	−0.231097	+	0.231097i
$399$	360.198	−	360.198i	0.902752	−	0.902752i
$400$	29.3479			0.0733697
$401$	439.773	+	439.773i	1.09669	+	1.09669i	0.994795	+	0.101896i	$0.0324910\pi$
$401$	439.773	+	439.773i	1.09669	+	1.09669i	0.101896	+	0.994795i	$0.467509\pi$
$402$			573.879i			1.42756i
$403$	32.0802	+	32.0802i	0.0796036	+	0.0796036i
$404$	208.696	−	208.696i	0.516575	−	0.516575i
$405$	−424.640			−1.04849
$406$	−34.8236	+	34.8236i	−0.0857723	+	0.0857723i
$407$		−	946.973i		−	2.32672i
$408$	215.343	+	215.343i	0.527800	+	0.527800i
$409$	163.157	+	163.157i	0.398916	+	0.398916i	0.877851	−	0.478935i	$-0.158977\pi$
$409$	163.157	+	163.157i	0.398916	+	0.398916i	−0.478935	+	0.877851i	$0.658977\pi$
$410$	145.303	+	145.303i	0.354396	+	0.354396i
$411$	866.945			2.10936
$412$	84.1644			0.204283
$413$			991.920i			2.40174i
$414$	−79.4416	+	79.4416i	−0.191888	+	0.191888i
$415$	73.9988	−	73.9988i	0.178310	−	0.178310i
$416$	4.85883	−	4.85883i	0.0116799	−	0.0116799i
$417$		−	406.046i		−	0.973730i
$418$		−	275.150i		−	0.658252i
$419$		−	157.994i		−	0.377075i	−0.982066	−	0.188538i	$-0.939625\pi$
$419$		−	157.994i		−	0.377075i	0.982066	−	0.188538i	$-0.0603747\pi$
$420$		−	345.500i		−	0.822619i
$421$		−	94.7762i		−	0.225122i	−0.993645	−	0.112561i	$-0.964095\pi$
$421$		−	94.7762i		−	0.225122i	0.993645	−	0.112561i	$-0.0359053\pi$
$422$	281.631	−	281.631i	0.667372	−	0.667372i
$423$			294.808i			0.696945i
$424$	−87.0666	+	87.0666i	−0.205346	+	0.205346i
$425$	−149.508	−	149.508i	−0.351784	−	0.351784i
$426$	−44.0316	−	44.0316i	−0.103360	−	0.103360i
$427$	−172.082	+	172.082i	−0.403002	+	0.403002i
$428$	185.621	+	185.621i	0.433695	+	0.433695i
$429$	−50.3821	−	50.3821i	−0.117441	−	0.117441i
$430$	53.1633	−	53.1633i	0.123636	−	0.123636i
$431$	−432.658	−	432.658i	−1.00385	−	1.00385i	−0.999993	−	0.00385457i	$-0.998773\pi$
$431$	−432.658	−	432.658i	−1.00385	−	1.00385i	−0.00385457	−	0.999993i	$-0.501227\pi$
$432$	42.6978	−	42.6978i	0.0988374	−	0.0988374i
$433$		−	174.247i		−	0.402417i	−0.979548	−	0.201209i	$-0.935513\pi$
$433$		−	174.247i		−	0.402417i	0.979548	−	0.201209i	$-0.0644869\pi$
$434$	−410.893	+	410.893i	−0.946759	+	0.946759i
$435$	49.7043			0.114263
$436$	−15.4801	−	15.4801i	−0.0355047	−	0.0355047i
$437$	140.364	−	140.364i	0.321200	−	0.321200i
$438$	−239.872			−0.547654
$439$		−	57.0370i		−	0.129925i	−0.997888	−	0.0649625i	$-0.979307\pi$
$439$		−	57.0370i		−	0.129925i	0.997888	−	0.0649625i	$-0.0206928\pi$
$440$	−131.961	−	131.961i	−0.299911	−	0.299911i
$441$	357.247			0.810083
$442$	−49.5051			−0.112003
$443$	−344.142	−	344.142i	−0.776844	−	0.776844i	0.202449	−	0.979293i	$-0.435110\pi$
$443$	−344.142	−	344.142i	−0.776844	−	0.776844i	−0.979293	+	0.202449i	$0.935110\pi$
$444$	318.718	−	318.718i	0.717833	−	0.717833i
$445$		−	707.725i		−	1.59039i
$446$	408.141			0.915115
$447$	151.436	−	151.436i	0.338783	−	0.338783i
$448$	62.2334	+	62.2334i	0.138914	+	0.138914i
$449$	56.1655			0.125090			0.0625451	−	0.998042i	$-0.480078\pi$
$449$	56.1655			0.125090			0.0625451	+	0.998042i	$0.480078\pi$
$450$	36.3885	−	36.3885i	0.0808634	−	0.0808634i
$451$			542.780i			1.20350i
$452$	−104.737	−	104.737i	−0.231719	−	0.231719i
$453$	−213.461	+	213.461i	−0.471216	+	0.471216i
$454$	−357.836			−0.788184
$455$	39.7135	+	39.7135i	0.0872824	+	0.0872824i
$456$	92.6057	−	92.6057i	0.203083	−	0.203083i
$457$		−	838.647i		−	1.83511i	−0.397603	−	0.917557i	$-0.630158\pi$
$457$		−	838.647i		−	1.83511i	0.397603	−	0.917557i	$-0.369842\pi$
$458$		−	26.1190i		−	0.0570283i
$459$	−435.034			−0.947787
$460$		−	134.637i		−	0.292688i
$461$	−301.956	+	301.956i	−0.655003	+	0.655003i	−0.954193	−	0.299190i	$-0.903283\pi$
$461$	−301.956	+	301.956i	−0.655003	+	0.655003i	0.299190	+	0.954193i	$0.403283\pi$
$462$	645.310	−	645.310i	1.39677	−	1.39677i
$463$	−78.4692	+	78.4692i	−0.169480	+	0.169480i	−0.786751	−	0.617271i	$-0.788238\pi$
$463$	−78.4692	+	78.4692i	−0.169480	+	0.169480i	0.617271	+	0.786751i	$0.288238\pi$
$464$	−8.95302	+	8.95302i	−0.0192953	+	0.0192953i
$465$	586.475			1.26124
$466$	50.7731	−	50.7731i	0.108955	−	0.108955i
$467$	538.949	+	538.949i	1.15407	+	1.15407i	0.985730	+	0.168337i	$0.0538396\pi$
$467$	538.949	+	538.949i	1.15407	+	1.15407i	0.168337	+	0.985730i	$0.446160\pi$
$468$		−	12.0490i		−	0.0257456i
$469$	844.894	−	844.894i	1.80148	−	1.80148i
$470$	−249.818	−	249.818i	−0.531528	−	0.531528i
$471$			14.4387i			0.0306553i
$472$			255.019i			0.540295i
$473$	198.592			0.419857
$474$	607.709			1.28209
$475$	−64.2944	+	64.2944i	−0.135357	+	0.135357i
$476$		−	634.077i		−	1.33209i
$477$			215.908i			0.452638i
$478$	−306.969	−	306.969i	−0.642195	−	0.642195i
$479$	560.930	+	560.930i	1.17104	+	1.17104i	0.981961	+	0.189084i	$0.0605518\pi$
$479$	560.930	+	560.930i	1.17104	+	1.17104i	0.189084	+	0.981961i	$0.439448\pi$
$480$		−	88.8268i		−	0.185056i
$481$			73.2701i			0.152329i
$482$	514.401			1.06722
$483$	658.394			1.36314
$484$		−	250.942i		−	0.518475i
$485$		−	189.965i		−	0.391681i
$486$		−	341.735i		−	0.703159i
$487$	805.074			1.65313			0.826565	−	0.562842i	$-0.190292\pi$
$487$	805.074			1.65313			0.826565	+	0.562842i	$0.190292\pi$
$488$	−44.2417	+	44.2417i	−0.0906592	+	0.0906592i
$489$	−657.122			−1.34381
$490$	−302.729	+	302.729i	−0.617813	+	0.617813i
$491$		−	146.377i		−	0.298119i	−0.988828	−	0.149060i	$-0.952375\pi$
$491$		−	146.377i		−	0.298119i	0.988828	−	0.149060i	$-0.0476246\pi$
$492$	−182.681	+	182.681i	−0.371302	+	0.371302i
$493$	91.2195			0.185029
$494$			21.2891i			0.0430954i
$495$	−327.237			−0.661086
$496$	−105.639	+	105.639i	−0.212982	+	0.212982i
$497$			129.651i			0.260867i
$498$	93.0345	+	93.0345i	0.186816	+	0.186816i
$499$	431.944	+	431.944i	0.865620	+	0.865620i	0.991984	−	0.126364i	$-0.0403308\pi$
$499$	431.944	+	431.944i	0.865620	+	0.865620i	−0.126364	+	0.991984i	$0.540331\pi$
$500$			271.808i			0.543616i
$501$		−	334.529i		−	0.667722i
$502$			360.791i			0.718707i
$503$	630.830	+	630.830i	1.25413	+	1.25413i	0.953849	+	0.300285i	$0.0970819\pi$
$503$	630.830	+	630.830i	1.25413	+	1.25413i	0.300285	+	0.953849i	$0.402918\pi$
$504$	154.327			0.306204
$505$	438.548	+	438.548i	0.868413	+	0.868413i
$506$	251.469	−	251.469i	0.496973	−	0.496973i
$507$	−442.588	−	442.588i	−0.872955	−	0.872955i
$508$	271.335			0.534124
$509$	119.843	+	119.843i	0.235448	+	0.235448i	0.814962	−	0.579514i	$-0.196758\pi$
$509$	119.843	+	119.843i	0.235448	+	0.235448i	−0.579514	+	0.814962i	$0.696758\pi$
$510$	−452.514	+	452.514i	−0.887283	+	0.887283i
$511$	353.152	+	353.152i	0.691101	+	0.691101i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$			187.082i			0.364681i
$514$			455.298i			0.885794i
$515$			176.861i			0.343419i
$516$	66.8391	+	66.8391i	0.129533	+	0.129533i
$517$		−	933.199i		−	1.80503i
$518$	−938.466			−1.81171
$519$	−687.085	−	687.085i	−1.32386	−	1.32386i
$520$	10.2102	+	10.2102i	0.0196350	+	0.0196350i
$521$	89.9902	−	89.9902i	0.172726	−	0.172726i	−0.615450	−	0.788176i	$-0.711026\pi$
$521$	89.9902	−	89.9902i	0.172726	−	0.172726i	0.788176	+	0.615450i	$0.211026\pi$
$522$			22.2017i			0.0425321i
$523$	−265.015	+	265.015i	−0.506720	+	0.506720i	−0.913518	−	0.406798i	$-0.866645\pi$
$523$	−265.015	+	265.015i	−0.506720	+	0.506720i	0.406798	+	0.913518i	$0.366645\pi$
$524$			406.438i			0.775645i
$525$	−301.580			−0.574438
$526$	289.446	+	289.446i	0.550277	+	0.550277i
$527$	1076.33			2.04236
$528$	165.907	−	165.907i	0.314218	−	0.314218i
$529$	−272.433			−0.514995
$530$	−182.959	−	182.959i	−0.345206	−	0.345206i
$531$	316.199	+	316.199i	0.595478	+	0.595478i
$532$	−272.678			−0.512552
$533$		−	41.9964i		−	0.0787926i
$534$	889.782			1.66626
$535$	−390.059	+	390.059i	−0.729082	+	0.729082i
$536$	217.219	−	217.219i	0.405260	−	0.405260i
$537$			6.70110i			0.0124788i
$538$	−102.439	+	366.372i	−0.190406	+	0.680989i
$539$	−1130.85			−2.09805
$540$	89.7238	+	89.7238i	0.166155	+	0.166155i
$541$	53.8416	+	53.8416i	0.0995223	+	0.0995223i	0.755115	−	0.655593i	$-0.227581\pi$
$541$	53.8416	+	53.8416i	0.0995223	+	0.0995223i	−0.655593	+	0.755115i	$0.727581\pi$
$542$		−	199.135i		−	0.367408i
$543$	−424.920			−0.782542
$544$		−	163.019i		−	0.299667i
$545$	32.5293	−	32.5293i	0.0596868	−	0.0596868i
$546$	−49.9295	+	49.9295i	−0.0914460	+	0.0914460i
$547$		−	714.572i		−	1.30635i	−0.757208	−	0.653174i	$-0.773437\pi$
$547$		−	714.572i		−	1.30635i	0.757208	−	0.653174i	$-0.226563\pi$
$548$	−328.148	−	328.148i	−0.598811	−	0.598811i
$549$			109.711i			0.199837i
$550$	−115.186	+	115.186i	−0.209429	+	0.209429i
$551$		−	39.2279i		−	0.0711941i
$552$	169.271			0.306650
$553$	−894.701	−	894.701i	−1.61790	−	1.61790i
$554$	−172.423			−0.311233
$555$	669.744	+	669.744i	1.20675	+	1.20675i
$556$	−153.693	+	153.693i	−0.276426	+	0.276426i
$557$	−327.709	+	327.709i	−0.588346	+	0.588346i	−0.937183	−	0.348837i	$-0.886577\pi$
$557$	−327.709	+	327.709i	−0.588346	+	0.588346i	0.348837	+	0.937183i	$0.386577\pi$
$558$			261.965i			0.469471i
$559$	−15.3657			−0.0274878
$560$	−130.775	+	130.775i	−0.233528	+	0.233528i
$561$	−1690.37			−3.01314
$562$	−526.265			−0.936415
$563$	−976.122			−1.73379			−0.866893	−	0.498494i	$-0.833887\pi$
$563$	−976.122			−1.73379			−0.866893	+	0.498494i	$0.833887\pi$
$564$	314.082	−	314.082i	0.556883	−	0.556883i
$565$	220.091	−	220.091i	0.389542	−	0.389542i
$566$	339.372	+	339.372i	0.599597	+	0.599597i
$567$	−785.999	+	785.999i	−1.38624	+	1.38624i
$568$			33.3329i			0.0586846i
$569$	3.78604	−	3.78604i	0.00665384	−	0.00665384i	−0.703772	−	0.710426i	$-0.748502\pi$
$569$	3.78604	−	3.78604i	0.00665384	−	0.00665384i	0.710426	+	0.703772i	$0.248502\pi$
$570$	194.599	+	194.599i	0.341401	+	0.341401i
$571$	−351.098	+	351.098i	−0.614883	+	0.614883i	−0.944214	−	0.329331i	$-0.893177\pi$
$571$	−351.098	+	351.098i	−0.614883	+	0.614883i	0.329331	+	0.944214i	$0.393177\pi$
$572$			38.1404i			0.0666790i
$573$	−948.084	+	948.084i	−1.65460	+	1.65460i
$574$	537.903			0.937114
$575$	−117.522			−0.204385
$576$	39.6769			0.0688835
$577$	335.104	−	335.104i	0.580769	−	0.580769i	−0.354346	−	0.935115i	$-0.615296\pi$
$577$	335.104	−	335.104i	0.580769	−	0.580769i	0.935115	+	0.354346i	$0.115296\pi$
$578$	−541.475	+	541.475i	−0.936808	+	0.936808i
$579$	161.147			0.278319
$580$	−18.8136	−	18.8136i	−0.0324373	−	0.0324373i
$581$		−	273.940i		−	0.471498i
$582$	238.832			0.410365
$583$		−	683.447i		−	1.17229i
$584$	90.7943	+	90.7943i	0.155470	+	0.155470i
$585$	25.3193			0.0432809
$586$	−295.679	−	295.679i	−0.504572	−	0.504572i
$587$			769.243i			1.31047i	0.755427	+	0.655233i	$0.227429\pi$
$587$			769.243i			1.31047i	−0.755427	+	0.655233i	$0.772571\pi$
$588$	−380.603	−	380.603i	−0.647284	−	0.647284i
$589$		−	462.862i		−	0.785844i
$590$	−535.890			−0.908288
$591$	359.043			0.607517
$592$	−241.276			−0.407562
$593$			71.0043i			0.119737i	0.998206	+	0.0598687i	$0.0190682\pi$
$593$			71.0043i			0.119737i	−0.998206	+	0.0598687i	$0.980932\pi$
$594$			335.164i			0.564250i
$595$	1332.43			2.23938
$596$	−114.640			−0.192350
$597$	242.995	−	242.995i	0.407028	−	0.407028i
$598$	−19.4569	+	19.4569i	−0.0325366	+	0.0325366i
$599$	−1076.73			−1.79755			−0.898776	−	0.438408i	$-0.855542\pi$
$599$	−1076.73			−1.79755			−0.898776	+	0.438408i	$0.855542\pi$
$600$	−77.5351			−0.129225
$601$	−175.605	−	175.605i	−0.292188	−	0.292188i	0.545756	−	0.837944i	$-0.316242\pi$
$601$	−175.605	−	175.605i	−0.292188	−	0.292188i	−0.837944	+	0.545756i	$0.816242\pi$
$602$		−	196.808i		−	0.326924i
$603$		−	538.662i		−	0.893303i
$604$	161.595			0.267541
$605$	527.322			0.871607
$606$	−551.362	+	551.362i	−0.909838	+	0.909838i
$607$	259.740	+	259.740i	0.427908	+	0.427908i	0.887915	−	0.460007i	$-0.152153\pi$
$607$	259.740	+	259.740i	0.427908	+	0.427908i	−0.460007	+	0.887915i	$0.652153\pi$
$608$	−70.1045			−0.115303
$609$	92.0015	−	92.0015i	0.151070	−	0.151070i
$610$	−92.9682	−	92.9682i	−0.152407	−	0.152407i
$611$			72.2044i			0.118174i
$612$	−202.128	−	202.128i	−0.330274	−	0.330274i
$613$	−379.063	−	379.063i	−0.618374	−	0.618374i	0.326740	−	0.945114i	$-0.394050\pi$
$613$	−379.063	−	379.063i	−0.618374	−	0.618374i	−0.945114	+	0.326740i	$0.894050\pi$
$614$	239.609	+	239.609i	0.390243	+	0.390243i
$615$	−383.879	−	383.879i	−0.624194	−	0.624194i
$616$	−488.514			−0.793041
$617$		−	1216.75i		−	1.97204i	−0.166617	−	0.986022i	$-0.553284\pi$
$617$		−	1216.75i		−	1.97204i	0.166617	−	0.986022i	$-0.446716\pi$
$618$	−222.357			−0.359800
$619$	−279.546			−0.451609			−0.225804	−	0.974173i	$-0.572501\pi$
$619$	−279.546			−0.451609			−0.225804	+	0.974173i	$0.572501\pi$
$620$	−221.987	−	221.987i	−0.358044	−	0.358044i
$621$	−170.980	+	170.980i	−0.275330	+	0.275330i
$622$		−	327.209i		−	0.526059i
$623$	−1309.98	−	1309.98i	−2.10270	−	2.10270i
$624$	−12.8367	+	12.8367i	−0.0205716	+	0.0205716i
$625$	−387.745			−0.620391
$626$	224.705	+	224.705i	0.358954	+	0.358954i
$627$			726.926i			1.15937i
$628$	5.46519	−	5.46519i	0.00870253	−	0.00870253i
$629$	1229.15	+	1229.15i	1.95413	+	1.95413i
$630$			324.298i			0.514758i
$631$	−316.272			−0.501223			−0.250611	−	0.968088i	$-0.580632\pi$
$631$	−316.272			−0.501223			−0.250611	+	0.968088i	$0.580632\pi$
$632$	−230.025	−	230.025i	−0.363963	−	0.363963i
$633$	−744.050	+	744.050i	−1.17543	+	1.17543i
$634$		−	556.403i		−	0.877608i
$635$			570.175i			0.897913i
$636$	230.024	−	230.024i	0.361673	−	0.361673i
$637$	87.4969			0.137358
$638$		−	70.2785i		−	0.110154i
$639$	41.3295	+	41.3295i	0.0646784	+	0.0646784i
$640$	−33.6219	+	33.6219i	−0.0525343	+	0.0525343i
$641$			1028.78i			1.60496i	0.596682	+	0.802478i	$0.296486\pi$
$641$			1028.78i			1.60496i	−0.596682	+	0.802478i	$0.703514\pi$
$642$	−490.399	−	490.399i	−0.763861	−	0.763861i
$643$	−509.410			−0.792239			−0.396119	−	0.918199i	$-0.629643\pi$
$643$	−509.410			−0.792239			−0.396119	+	0.918199i	$0.629643\pi$
$644$	−249.209	−	249.209i	−0.386971	−	0.386971i
$645$	−140.454	+	140.454i	−0.217758	+	0.217758i
$646$	357.136	+	357.136i	0.552843	+	0.552843i
$647$	−471.689	+	471.689i	−0.729040	+	0.729040i	−0.970429	−	0.241388i	$-0.922397\pi$
$647$	−471.689	+	471.689i	−0.729040	+	0.729040i	0.241388	+	0.970429i	$0.422397\pi$
$648$	−202.078	+	202.078i	−0.311848	+	0.311848i
$649$	−1000.91	−	1000.91i	−1.54224	−	1.54224i
$650$	8.91228	−	8.91228i	0.0137112	−	0.0137112i
$651$	1085.55	−	1085.55i	1.66752	−	1.66752i
$652$	248.728	+	248.728i	0.381485	+	0.381485i
$653$	790.921			1.21121			0.605606	−	0.795765i	$-0.292931\pi$
$653$	790.921			1.21121			0.605606	+	0.795765i	$0.292931\pi$
$654$	40.8972	+	40.8972i	0.0625340	+	0.0625340i
$655$	−854.077			−1.30393
$656$	138.293			0.210813
$657$	225.152			0.342697
$658$	−924.816			−1.40549
$659$	−435.242			−0.660458			−0.330229	−	0.943901i	$-0.607126\pi$
$659$	−435.242			−0.660458			−0.330229	+	0.943901i	$0.607126\pi$
$660$	348.632	+	348.632i	0.528230	+	0.528230i
$661$	−78.4982	−	78.4982i	−0.118757	−	0.118757i	0.645231	−	0.763988i	$-0.276761\pi$
$661$	−78.4982	−	78.4982i	−0.118757	−	0.118757i	−0.763988	+	0.645231i	$0.776761\pi$
$662$	108.806	+	108.806i	0.164359	+	0.164359i
$663$	130.789			0.197269
$664$		−	70.4291i		−	0.106068i
$665$		−	572.997i		−	0.861649i
$666$	−299.159	+	299.159i	−0.449188	+	0.449188i
$667$	35.8517	−	35.8517i	0.0537507	−	0.0537507i
$668$	−126.623	+	126.623i	−0.189555	+	0.189555i
$669$	−1078.28			−1.61178
$670$	456.459	+	456.459i	0.681281	+	0.681281i
$671$		−	347.284i		−	0.517562i
$672$	−164.416	−	164.416i	−0.244667	−	0.244667i
$673$	−769.203	+	769.203i	−1.14295	+	1.14295i	−0.155038	+	0.987909i	$0.549550\pi$
$673$	−769.203	+	769.203i	−1.14295	+	1.14295i	−0.987909	+	0.155038i	$0.950450\pi$
$674$	581.409			0.862625
$675$	78.3181	−	78.3181i	0.116027	−	0.116027i
$676$			335.049i			0.495635i
$677$	494.417	+	494.417i	0.730305	+	0.730305i	0.970680	−	0.240375i	$-0.0772704\pi$
$677$	494.417	+	494.417i	0.730305	+	0.730305i	−0.240375	+	0.970680i	$0.577270\pi$
$678$	276.708	+	276.708i	0.408124	+	0.408124i
$679$	−351.621	−	351.621i	−0.517851	−	0.517851i
$680$	342.563			0.503770
$681$	945.378			1.38822
$682$		−	829.237i		−	1.21589i
$683$	−516.786	+	516.786i	−0.756642	+	0.756642i	−0.975710	−	0.219068i	$-0.929698\pi$
$683$	−516.786	+	516.786i	−0.756642	+	0.756642i	0.219068	+	0.975710i	$0.429698\pi$
$684$	−86.9227	+	86.9227i	−0.127080	+	0.127080i
$685$	689.561	−	689.561i	1.00666	−	1.00666i
$686$			358.328i			0.522344i
$687$			69.0045i			0.100443i
$688$		−	50.5987i		−	0.0735446i
$689$			52.8803i			0.0767493i
$690$			355.701i			0.515509i
$691$	−142.498	+	142.498i	−0.206221	+	0.206221i	−0.802659	−	0.596438i	$-0.796582\pi$
$691$	−142.498	+	142.498i	−0.206221	+	0.206221i	0.596438	+	0.802659i	$0.296582\pi$
$692$			520.138i			0.751645i
$693$	−605.709	+	605.709i	−0.874039	+	0.874039i
$694$	−143.691	−	143.691i	−0.207048	−	0.207048i
$695$	−322.965	−	322.965i	−0.464698	−	0.464698i
$696$	23.6533	−	23.6533i	0.0339846	−	0.0339846i
$697$	−704.513	−	704.513i	−1.01078	−	1.01078i
$698$	300.144	+	300.144i	0.430006	+	0.430006i
$699$	−134.139	+	134.139i	−0.191901	+	0.191901i
$700$	114.151	+	114.151i	0.163073	+	0.163073i
$701$	467.417	−	467.417i	0.666786	−	0.666786i	−0.290185	−	0.956971i	$-0.593717\pi$
$701$	467.417	−	467.417i	0.666786	−	0.666786i	0.956971	+	0.290185i	$0.0937167\pi$
$702$		−	25.9327i		−	0.0369411i
$703$	528.580	−	528.580i	0.751892	−	0.751892i
$704$	−125.595			−0.178402
$705$	660.003	+	660.003i	0.936174	+	0.936174i
$706$	541.225	−	541.225i	0.766608	−	0.766608i
$707$	1623.49			2.29630
$708$		−	673.743i		−	0.951615i
$709$	367.429	+	367.429i	0.518236	+	0.518236i	0.917037	−	0.398801i	$-0.130574\pi$
$709$	367.429	+	367.429i	0.518236	+	0.518236i	−0.398801	+	0.917037i	$0.630574\pi$
$710$	−70.0447			−0.0986545
$711$	−570.416			−0.802273
$712$	−336.792	−	336.792i	−0.473023	−	0.473023i
$713$	423.025	−	423.025i	0.593303	−	0.593303i
$714$			1675.19i			2.34620i
$715$	−80.1470			−0.112094
$716$	2.53644	−	2.53644i	0.00354251	−	0.00354251i
$717$	810.992	+	810.992i	1.13109	+	1.13109i
$718$	−96.0643			−0.133794
$719$	621.212	−	621.212i	0.863995	−	0.863995i	−0.127805	−	0.991799i	$-0.540793\pi$
$719$	621.212	−	621.212i	0.863995	−	0.863995i	0.991799	+	0.127805i	$0.0407931\pi$
$720$			83.3758i			0.115800i
$721$	327.365	+	327.365i	0.454043	+	0.454043i
$722$	−207.417	+	207.417i	−0.287282	+	0.287282i
$723$	−1359.01			−1.87968
$724$	160.837	+	160.837i	0.222150	+	0.222150i
$725$	−16.4220	+	16.4220i	−0.0226511	+	0.0226511i
$726$			662.972i			0.913184i
$727$		−	378.499i		−	0.520632i	−0.965523	−	0.260316i	$-0.916173\pi$
$727$		−	378.499i		−	0.520632i	0.965523	−	0.260316i	$-0.0838267\pi$
$728$	37.7977			0.0519200
$729$		−	6.50783i		−	0.00892707i
$730$	−190.792	+	190.792i	−0.261359	+	0.261359i
$731$	−257.767	+	257.767i	−0.352623	+	0.352623i
$732$	116.884	−	116.884i	0.159677	−	0.159677i
$733$	−199.192	+	199.192i	−0.271748	+	0.271748i	−0.829804	−	0.558055i	$-0.811548\pi$
$733$	−199.192	+	199.192i	−0.271748	+	0.271748i	0.558055	+	0.829804i	$0.311548\pi$
$734$	−30.7262			−0.0418613
$735$	799.788	−	799.788i	1.08815	−	1.08815i
$736$	−64.0709	−	64.0709i	−0.0870528	−	0.0870528i
$737$			1705.11i			2.31358i
$738$	171.470	−	171.470i	0.232344	−	0.232344i
$739$	−626.498	−	626.498i	−0.847764	−	0.847764i	0.142089	−	0.989854i	$-0.454618\pi$
$739$	−626.498	−	626.498i	−0.847764	−	0.847764i	−0.989854	+	0.142089i	$0.954618\pi$
$740$		−	507.011i		−	0.685150i
$741$		−	56.2444i		−	0.0759034i
$742$	−677.307			−0.912812
$743$	214.623			0.288860			0.144430	−	0.989515i	$-0.453865\pi$
$743$	214.623			0.288860			0.144430	+	0.989515i	$0.453865\pi$
$744$	279.092	−	279.092i	0.375123	−	0.375123i
$745$		−	240.902i		−	0.323358i
$746$			172.478i			0.231203i
$747$	−87.3252	−	87.3252i	−0.116901	−	0.116901i
$748$	639.825	+	639.825i	0.855381	+	0.855381i
$749$			1443.98i			1.92788i
$750$		−	718.098i		−	0.957464i
$751$	−1224.27			−1.63019			−0.815093	−	0.579330i	$-0.803314\pi$
$751$	−1224.27			−1.63019			−0.815093	+	0.579330i	$0.803314\pi$
$752$	−237.767			−0.316179
$753$		−	953.185i		−	1.26585i
$754$			5.43765i			0.00721174i
$755$			339.570i			0.449762i
$756$	332.153			0.439356
$757$	614.004	−	614.004i	0.811102	−	0.811102i	−0.173697	−	0.984799i	$-0.555571\pi$
$757$	614.004	−	614.004i	0.811102	−	0.811102i	0.984799	+	0.173697i	$0.0555713\pi$
$758$	653.767			0.862489
$759$	−664.363	+	664.363i	−0.875313	+	0.875313i
$760$		−	147.316i		−	0.193836i
$761$	−882.566	+	882.566i	−1.15975	+	1.15975i	−0.175215	+	0.984530i	$0.556062\pi$
$761$	−882.566	+	882.566i	−1.15975	+	1.15975i	−0.984530	+	0.175215i	$0.943938\pi$
$762$	−716.848			−0.940746
$763$		−	120.422i		−	0.157827i
$764$	717.720			0.939424
$765$	424.745	−	424.745i	0.555222	−	0.555222i
$766$			334.354i			0.436493i
$767$	77.4435	+	77.4435i	0.100969	+	0.100969i
$768$	−42.2709	−	42.2709i	−0.0550402	−	0.0550402i
$769$		−	855.059i		−	1.11191i	−0.831212	−	0.555955i	$-0.812353\pi$
$769$		−	855.059i		−	1.11191i	0.831212	−	0.555955i	$-0.187647\pi$
$770$		−	1026.55i		−	1.33318i
$771$		−	1202.87i		−	1.56014i
$772$	−60.9959	−	60.9959i	−0.0790102	−	0.0790102i
$773$	1194.00			1.54464			0.772318	−	0.635236i	$-0.219097\pi$
$773$	1194.00			1.54464			0.772318	+	0.635236i	$0.219097\pi$
$774$	−62.7374	−	62.7374i	−0.0810561	−	0.0810561i
$775$	−193.768	+	193.768i	−0.250023	+	0.250023i
$776$	−90.4006	−	90.4006i	−0.116496	−	0.116496i
$777$	2479.36			3.19094
$778$	−156.002	−	156.002i	−0.200516	−	0.200516i
$779$	−302.968	+	302.968i	−0.388919	+	0.388919i
$780$	−26.9747	−	26.9747i	−0.0345829	−	0.0345829i
$781$	−130.826	−	130.826i	−0.167511	−	0.167511i
$782$			652.798i			0.834781i
$783$			47.7842i			0.0610271i
$784$			288.125i			0.367506i
$785$	11.4844	+	11.4844i	0.0146298	+	0.0146298i
$786$		−	1073.78i		−	1.36613i
$787$	−381.334			−0.484541			−0.242271	−	0.970209i	$-0.577892\pi$
$787$	−381.334			−0.484541			−0.242271	+	0.970209i	$0.577892\pi$
$788$	−135.902	−	135.902i	−0.172464	−	0.172464i
$789$	−764.695	−	764.695i	−0.969196	−	0.969196i
$790$	483.367	−	483.367i	0.611857	−	0.611857i
$791$		−	814.768i		−	1.03005i
$792$	−155.726	+	155.726i	−0.196623	+	0.196623i
$793$			26.8704i			0.0338845i
$794$	−380.124			−0.478746
$795$	483.366	+	483.366i	0.608007	+	0.608007i
$796$	−183.953			−0.231097
$797$	−654.333	+	654.333i	−0.820994	+	0.820994i	−0.986251	−	0.165256i	$-0.947155\pi$
$797$	−654.333	+	654.333i	−0.820994	+	0.820994i	0.165256	+	0.986251i	$0.447155\pi$
$798$	720.396			0.902752
$799$	1211.27	+	1211.27i	1.51598	+	1.51598i
$800$	29.3479	+	29.3479i	0.0366849	+	0.0366849i
$801$	−835.179			−1.04267
$802$			879.546i			1.09669i
$803$	−712.708			−0.887556
$804$	−573.879	+	573.879i	−0.713780	+	0.713780i
$805$	523.681	−	523.681i	0.650536	−	0.650536i
$806$			64.1605i			0.0796036i
$807$	270.636	−	967.930i	0.335360	−	1.19942i
$808$	417.393			0.516575
$809$	290.607	+	290.607i	0.359217	+	0.359217i	0.863524	−	0.504307i	$-0.168252\pi$
$809$	290.607	+	290.607i	0.359217	+	0.359217i	−0.504307	+	0.863524i	$0.668252\pi$
$810$	−424.640	−	424.640i	−0.524247	−	0.524247i
$811$		−	1290.54i		−	1.59130i	−0.605757	−	0.795650i	$-0.707130\pi$
$811$		−	1290.54i		−	1.59130i	0.605757	−	0.795650i	$-0.292870\pi$
$812$	−69.6471			−0.0857723
$813$			526.101i			0.647111i
$814$	946.973	−	946.973i	1.16336	−	1.16336i
$815$	−522.669	+	522.669i	−0.641312	+	0.641312i
$816$			430.685i			0.527800i
$817$	110.850	+	110.850i	0.135679	+	0.135679i
$818$			326.313i			0.398916i
$819$	46.8655	−	46.8655i	0.0572228	−	0.0572228i
$820$			290.605i			0.354396i
$821$	−553.997			−0.674783			−0.337392	−	0.941364i	$-0.609545\pi$
$821$	−553.997			−0.674783			−0.337392	+	0.941364i	$0.609545\pi$
$822$	866.945	+	866.945i	1.05468	+	1.05468i
$823$	98.6980			0.119925			0.0599623	−	0.998201i	$-0.480902\pi$
$823$	98.6980			0.119925			0.0599623	+	0.998201i	$0.480902\pi$
$824$	84.1644	+	84.1644i	0.102141	+	0.102141i
$825$	304.314	−	304.314i	0.368865	−	0.368865i
$826$	−991.920	+	991.920i	−1.20087	+	1.20087i
$827$			217.735i			0.263283i	0.991297	+	0.131642i	$0.0420248\pi$
$827$			217.735i			0.263283i	−0.991297	+	0.131642i	$0.957975\pi$
$828$	−158.883			−0.191888
$829$	28.3525	−	28.3525i	0.0342009	−	0.0342009i	−0.689800	−	0.724000i	$-0.742301\pi$
$829$	28.3525	−	28.3525i	0.0342009	−	0.0342009i	0.724000	+	0.689800i	$0.242301\pi$
$830$	147.998			0.178310
$831$	455.530			0.548171
$832$	9.71767			0.0116799
$833$	1467.81	−	1467.81i	1.76207	−	1.76207i
$834$	406.046	−	406.046i	0.486865	−	0.486865i
$835$	−266.081	−	266.081i	−0.318660	−	0.318660i
$836$	275.150	−	275.150i	0.329126	−	0.329126i
$837$			563.820i			0.673620i
$838$	157.994	−	157.994i	0.188538	−	0.188538i
$839$	−885.287	−	885.287i	−1.05517	−	1.05517i	−0.998387	−	0.0567830i	$-0.981916\pi$
$839$	−885.287	−	885.287i	−1.05517	−	1.05517i	−0.0567830	−	0.998387i	$-0.518084\pi$
$840$	345.500	−	345.500i	0.411309	−	0.411309i
$841$			830.980i			0.988086i
$842$	94.7762	−	94.7762i	0.112561	−	0.112561i
$843$	1390.36			1.64930
$844$	563.262			0.667372
$845$	−704.062			−0.833209
$846$	−294.808	+	294.808i	−0.348472	+	0.348472i
$847$	976.061	−	976.061i	1.15237	−	1.15237i
$848$	−174.133			−0.205346
$849$	−896.597	−	896.597i	−1.05606	−	1.05606i
$850$		−	299.017i		−	0.351784i
$851$	966.175			1.13534
$852$		−	88.0631i		−	0.103360i
$853$	−575.775	−	575.775i	−0.675001	−	0.675001i	0.283864	−	0.958865i	$-0.408384\pi$
$853$	−575.775	−	575.775i	−0.675001	−	0.675001i	−0.958865	+	0.283864i	$0.908384\pi$
$854$	−344.164			−0.403002
$855$	−182.657	−	182.657i	−0.213634	−	0.213634i
$856$			371.243i			0.433695i
$857$	−492.516	−	492.516i	−0.574698	−	0.574698i	0.358740	−	0.933438i	$-0.383207\pi$
$857$	−492.516	−	492.516i	−0.574698	−	0.574698i	−0.933438	+	0.358740i	$0.883207\pi$
$858$		−	100.764i		−	0.117441i
$859$	−289.429			−0.336937			−0.168469	−	0.985707i	$-0.553882\pi$
$859$	−289.429			−0.336937			−0.168469	+	0.985707i	$0.553882\pi$
$860$	106.327			0.123636
$861$	−1421.10			−1.65053
$862$		−	865.316i		−	1.00385i
$863$		−	672.153i		−	0.778856i	−0.921057	−	0.389428i	$-0.872673\pi$
$863$		−	672.153i		−	0.778856i	0.921057	−	0.389428i	$-0.127327\pi$
$864$	85.3955			0.0988374
$865$	−1093.00			−1.26359
$866$	174.247	−	174.247i	0.201209	−	0.201209i
$867$	1430.54	−	1430.54i	1.64999	−	1.64999i
$868$	−821.787			−0.946759
$869$	1805.62			2.07782
$870$	49.7043	+	49.7043i	0.0571313	+	0.0571313i
$871$		−	131.929i		−	0.151469i
$872$		−	30.9601i		−	0.0355047i
$873$	−224.176			−0.256788
$874$	280.729			0.321200
$875$	−1057.22	+	1057.22i	−1.20825	+	1.20825i
$876$	−239.872	−	239.872i	−0.273827	−	0.273827i
$877$	−1179.69			−1.34514			−0.672572	−	0.740031i	$-0.734811\pi$
$877$	−1179.69			−1.34514			−0.672572	+	0.740031i	$0.734811\pi$
$878$	57.0370	−	57.0370i	0.0649625	−	0.0649625i
$879$	781.164	+	781.164i	0.888697	+	0.888697i
$880$		−	263.922i		−	0.299911i
$881$	−777.782	−	777.782i	−0.882840	−	0.882840i	0.110983	−	0.993822i	$-0.464600\pi$
$881$	−777.782	−	777.782i	−0.882840	−	0.882840i	−0.993822	+	0.110983i	$0.964600\pi$
$882$	357.247	+	357.247i	0.405042	+	0.405042i
$883$	4.54482	+	4.54482i	0.00514703	+	0.00514703i	0.709676	−	0.704529i	$-0.248842\pi$
$883$	4.54482	+	4.54482i	0.00514703	+	0.00514703i	−0.704529	+	0.709676i	$0.748842\pi$
$884$	−49.5051	−	49.5051i	−0.0560013	−	0.0560013i
$885$	1415.78			1.59976
$886$		−	688.284i		−	0.776844i
$887$	31.3090			0.0352977			0.0176488	−	0.999844i	$-0.494382\pi$
$887$	31.3090			0.0352977			0.0176488	+	0.999844i	$0.494382\pi$
$888$	637.436			0.717833
$889$	1055.38	+	1055.38i	1.18716	+	1.18716i
$890$	707.725	−	707.725i	0.795197	−	0.795197i
$891$		−	1586.25i		−	1.78030i
$892$	408.141	+	408.141i	0.457557	+	0.457557i
$893$	520.892	−	520.892i	0.583305	−	0.583305i
$894$	302.872			0.338783
$895$	5.33000	+	5.33000i	0.00595530	+	0.00595530i
$896$			124.467i			0.138914i
$897$	51.4037	−	51.4037i	0.0573062	−	0.0573062i
$898$	56.1655	+	56.1655i	0.0625451	+	0.0625451i
$899$		−	118.224i		−	0.131506i
$900$	72.7770			0.0808634
$901$	887.095	+	887.095i	0.984567	+	0.984567i
$902$	−542.780	+	542.780i	−0.601751	+	0.601751i
$903$			519.954i			0.575807i
$904$		−	209.474i		−	0.231719i
$905$	−337.978	+	337.978i	−0.373456	+	0.373456i
$906$	−426.922			−0.471216
$907$			860.206i			0.948408i	0.880415	+	0.474204i	$0.157264\pi$
$907$			860.206i			0.948408i	−0.880415	+	0.474204i	$0.842736\pi$
$908$	−357.836	−	357.836i	−0.394092	−	0.394092i
$909$	517.526	−	517.526i	0.569336	−	0.569336i
$910$			79.4270i			0.0872824i
$911$	−484.640	−	484.640i	−0.531987	−	0.531987i	0.389176	−	0.921163i	$-0.372760\pi$
$911$	−484.640	−	484.640i	−0.531987	−	0.531987i	−0.921163	+	0.389176i	$0.872760\pi$
$912$	185.211			0.203083
$913$	276.424	+	276.424i	0.302764	+	0.302764i
$914$	838.647	−	838.647i	0.917557	−	0.917557i
$915$	245.616	+	245.616i	0.268432	+	0.268432i
$916$	26.1190	−	26.1190i	0.0285142	−	0.0285142i
$917$	−1580.88	+	1580.88i	−1.72397	+	1.72397i
$918$	−435.034	−	435.034i	−0.473893	−	0.473893i
$919$	−1029.09	+	1029.09i	−1.11980	+	1.11980i	−0.128026	+	0.991771i	$0.540864\pi$
$919$	−1029.09	+	1029.09i	−1.11980	+	1.11980i	−0.991771	+	0.128026i	$0.959136\pi$
$920$	134.637	−	134.637i	0.146344	−	0.146344i
$921$	−633.032	−	633.032i	−0.687331	−	0.687331i
$922$	−603.913			−0.655003
$923$	10.1224	+	10.1224i	0.0109669	+	0.0109669i
$924$	1290.62			1.39677
$925$	−442.560			−0.478443
$926$	−156.938			−0.169480
$927$	208.711			0.225147
$928$	−17.9060			−0.0192953
$929$	650.854	+	650.854i	0.700597	+	0.700597i	0.964539	−	0.263942i	$-0.0850227\pi$
$929$	650.854	+	650.854i	0.700597	+	0.700597i	−0.263942	+	0.964539i	$0.585023\pi$
$930$	586.475	+	586.475i	0.630619	+	0.630619i
$931$	−631.214	−	631.214i	−0.677996	−	0.677996i
$932$	101.546			0.108955
$933$			864.463i			0.926542i
$934$			1077.90i			1.15407i
$935$	−1344.51	+	1344.51i	−1.43798	+	1.43798i
$936$	12.0490	−	12.0490i	0.0128728	−	0.0128728i
$937$	−456.155	+	456.155i	−0.486825	+	0.486825i	−0.907303	−	0.420478i	$-0.861862\pi$
$937$	−456.155	+	456.155i	−0.486825	+	0.486825i	0.420478	+	0.907303i	$0.361862\pi$
$938$	1689.79			1.80148
$939$	−593.655	−	593.655i	−0.632221	−	0.632221i
$940$		−	499.636i		−	0.531528i
$941$	355.514	+	355.514i	0.377805	+	0.377805i	0.870310	−	0.492505i	$-0.163919\pi$
$941$	355.514	+	355.514i	0.377805	+	0.377805i	−0.492505	+	0.870310i	$0.663919\pi$
$942$	−14.4387	+	14.4387i	−0.0153277	+	0.0153277i
$943$	−553.785			−0.587259
$944$	−255.019	+	255.019i	−0.270147	+	0.270147i
$945$			697.977i			0.738600i
$946$	198.592	+	198.592i	0.209928	+	0.209928i
$947$	11.0708	+	11.0708i	0.0116904	+	0.0116904i	0.712928	−	0.701237i	$-0.247369\pi$
$947$	11.0708	+	11.0708i	0.0116904	+	0.0116904i	−0.701237	+	0.712928i	$0.747369\pi$
$948$	607.709	+	607.709i	0.641043	+	0.641043i
$949$	55.1443			0.0581078
$950$	−128.589			−0.135357
$951$			1469.98i			1.54572i
$952$	634.077	−	634.077i	0.666047	−	0.666047i
$953$	−435.136	+	435.136i	−0.456596	+	0.456596i	−0.897537	−	0.440940i	$-0.854645\pi$
$953$	−435.136	+	435.136i	−0.456596	+	0.456596i	0.440940	+	0.897537i	$0.354645\pi$
$954$	−215.908	+	215.908i	−0.226319	+	0.226319i
$955$			1508.20i			1.57926i
$956$		−	613.939i		−	0.642195i
$957$			185.671i			0.194014i
$958$			1121.86i			1.17104i
$959$		−	2552.72i		−	2.66186i
$960$	88.8268	−	88.8268i	0.0925280	−	0.0925280i
$961$		−	433.958i		−	0.451569i
$962$	−73.2701	+	73.2701i	−0.0761644	+	0.0761644i
$963$	460.304	+	460.304i	0.477990	+	0.477990i
$964$	514.401	+	514.401i	0.533611	+	0.533611i
$965$	128.175	−	128.175i	0.132824	−	0.132824i
$966$	658.394	+	658.394i	0.681568	+	0.681568i
$967$	−460.220	−	460.220i	−0.475926	−	0.475926i	0.427900	−	0.903826i	$-0.359253\pi$
$967$	−460.220	−	460.220i	−0.475926	−	0.475926i	−0.903826	+	0.427900i	$0.859253\pi$
$968$	250.942	−	250.942i	0.259238	−	0.259238i
$969$	−943.530	−	943.530i	−0.973715	−	0.973715i
$970$	189.965	−	189.965i	0.195840	−	0.195840i
$971$			1541.61i			1.58765i	0.608144	+	0.793827i	$0.291914\pi$
$971$			1541.61i			1.58765i	−0.608144	+	0.793827i	$0.708086\pi$
$972$	341.735	−	341.735i	0.351579	−	0.351579i
$973$	−1195.60			−1.22878
$974$	805.074	+	805.074i	0.826565	+	0.826565i
$975$	−23.5456	+	23.5456i	−0.0241494	+	0.0241494i
$976$	−88.4834			−0.0906592
$977$		−	62.2311i		−	0.0636961i	−0.999493	−	0.0318481i	$-0.989861\pi$
$977$		−	62.2311i		−	0.0636961i	0.999493	−	0.0318481i	$-0.0101393\pi$
$978$	−657.122	−	657.122i	−0.671904	−	0.671904i
$979$	2643.72			2.70043
$980$	−605.457			−0.617813
$981$	−38.3875	−	38.3875i	−0.0391310	−	0.0391310i
$982$	146.377	−	146.377i	0.149060	−	0.149060i
$983$		−	54.3113i		−	0.0552506i	−0.999618	−	0.0276253i	$-0.991205\pi$
$983$		−	54.3113i		−	0.0552506i	0.999618	−	0.0276253i	$-0.00879453\pi$
$984$	−365.361			−0.371302
$985$	285.579	−	285.579i	0.289928	−	0.289928i
$986$	91.2195	+	91.2195i	0.0925147	+	0.0925147i
$987$	2443.30			2.47548
$988$	−21.2891	+	21.2891i	−0.0215477	+	0.0215477i
$989$			202.619i			0.204873i
$990$	−327.237	−	327.237i	−0.330543	−	0.330543i
$991$	881.235	−	881.235i	0.889238	−	0.889238i	−0.105212	−	0.994450i	$-0.533552\pi$
$991$	881.235	−	881.235i	0.889238	−	0.889238i	0.994450	+	0.105212i	$0.0335520\pi$
$992$	−211.279			−0.212982
$993$	−287.457	−	287.457i	−0.289483	−	0.289483i
$994$	−129.651	+	129.651i	−0.130434	+	0.130434i
$995$		−	386.553i		−	0.388495i
$996$			186.069i			0.186816i
$997$	543.463			0.545099			0.272549	−	0.962142i	$-0.412133\pi$
$997$	543.463			0.545099			0.272549	+	0.962142i	$0.412133\pi$
$998$			863.888i			0.865620i
$999$	−643.873	+	643.873i	−0.644517	+	0.644517i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.a.187.5	✓	44
269.82	odd	4	inner	538.3.c.a.351.5	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.a.187.5	✓	44	1.1	even	1	trivial
538.3.c.a.351.5	yes	44	269.82	odd	4	inner

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	538.3.c.a.187.5

Level	$538$
Weight	$3$
Character	538.187
Analytic conductor	$14.659$
Analytic rank	$0$
Dimension	$44$
Inner twists	$2$