LMFDB - Embedded newform 351.4.l.a.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,4,Mod(127,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("351.127");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	351.l (of order $6$, degree $2$, not 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:	$20.7096704120$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	351.127
Dual form			351.4.l.a.199.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.97372i q^{2} -7.79044 q^{4} +(-9.30367 + 5.37147i) q^{5} +(14.5854 - 8.42091i) q^{7} -0.832741i q^{8} +(21.3447 + 36.9702i) q^{10} -13.1991i q^{11} +(-35.4813 + 30.6281i) q^{13} +(-33.4623 - 57.9585i) q^{14} -65.6326 q^{16} +(-49.0702 + 84.9920i) q^{17} +(-56.0776 - 32.3764i) q^{19} +(72.4796 - 41.8461i) q^{20} -52.4495 q^{22} +(-49.2889 + 85.3709i) q^{23} +(-4.79452 + 8.30436i) q^{25} +(121.707 + 140.993i) q^{26} +(-113.627 + 65.6026i) q^{28} +304.130 q^{29} +(-86.6932 + 50.0523i) q^{31} +254.143i q^{32} +(337.734 + 194.991i) q^{34} +(-90.4654 + 156.691i) q^{35} +(197.075 - 113.781i) q^{37} +(-128.655 + 222.837i) q^{38} +(4.47305 + 7.74755i) q^{40} +(41.8147 + 24.1417i) q^{41} +(85.5052 + 148.099i) q^{43} +102.827i q^{44} +(339.240 + 195.860i) q^{46} +(-23.5689 - 13.6075i) q^{47} +(-29.6765 + 51.4011i) q^{49} +(32.9992 + 19.0521i) q^{50} +(276.415 - 238.606i) q^{52} -611.664 q^{53} +(70.8986 + 122.800i) q^{55} +(-7.01244 - 12.1459i) q^{56} -1208.53i q^{58} +819.677i q^{59} +(-18.3327 - 31.7531i) q^{61} +(198.894 + 344.494i) q^{62} +484.834 q^{64} +(165.588 - 475.540i) q^{65} +(-93.3172 - 53.8767i) q^{67} +(382.278 - 662.125i) q^{68} +(622.645 + 359.484i) q^{70} +(93.2300 + 53.8263i) q^{71} -553.128i q^{73} +(-452.136 - 783.122i) q^{74} +(436.869 + 252.226i) q^{76} +(-111.148 - 192.515i) q^{77} +(-395.090 + 684.315i) q^{79} +(610.624 - 352.544i) q^{80} +(95.9325 - 166.160i) q^{82} +(-14.9734 - 8.64491i) q^{83} -1054.32i q^{85} +(588.505 - 339.774i) q^{86} -10.9914 q^{88} +(43.2247 - 24.9558i) q^{89} +(-259.594 + 745.509i) q^{91} +(383.982 - 665.077i) q^{92} +(-54.0725 + 93.6563i) q^{94} +695.636 q^{95} +(-1209.65 + 698.390i) q^{97} +(204.254 + 117.926i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 306 q^{4} - 3 q^{7} - 10 q^{10} - 13 q^{13} - 126 q^{14} + 1102 q^{16} + 138 q^{17} - 96 q^{19} + 387 q^{20} + 62 q^{22} + 327 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} + 402 q^{29} + 180 q^{31}+ \cdots + 6339 q^{98}+O(q^{100}) $ 80 * q - 306 * q^4 - 3 * q^7 - 10 * q^10 - 13 * q^13 - 126 * q^14 + 1102 * q^16 + 138 * q^17 - 96 * q^19 + 387 * q^20 + 62 * q^22 + 327 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 + 402 * q^29 + 180 * q^31 + 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 - 381 * q^41 - 83 * q^43 - 6 * q^46 - 372 * q^47 + 1613 * q^49 + 708 * q^50 + 402 * q^52 + 2568 * q^53 - 127 * q^55 + 2298 * q^56 - 419 * q^61 - 135 * q^62 - 3178 * q^64 - 363 * q^65 + 879 * q^67 - 1950 * q^68 - 1005 * q^70 + 2598 * q^71 - 471 * q^74 + 1485 * q^76 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 - 1194 * q^83 + 2910 * q^86 - 1562 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 + 539 * q^94 - 10584 * q^95 + 789 * q^97 + 6339 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	3.97372i		−	1.40492i	−0.711722	−	0.702461i	$-0.752085\pi$
$2$		−	3.97372i		−	1.40492i	0.711722	−	0.702461i	$-0.247915\pi$
$3$		0			0
$3$		0			0
$4$	−7.79044			−0.973805
$5$	−9.30367	+	5.37147i	−0.832145	+	0.480439i	−0.854587	−	0.519309i	$-0.826189\pi$
$5$	−9.30367	+	5.37147i	−0.832145	+	0.480439i	0.0224414	+	0.999748i	$0.492856\pi$
$6$		0			0
$7$	14.5854	−	8.42091i	0.787540	−	0.454687i	−0.0515557	−	0.998670i	$-0.516418\pi$
$7$	14.5854	−	8.42091i	0.787540	−	0.454687i	0.839096	+	0.543984i	$0.183085\pi$
$8$		−	0.832741i		−	0.0368023i
$9$		0			0
$10$	21.3447	+	36.9702i	0.674980	+	1.16910i
$11$		−	13.1991i		−	0.361789i	−0.983503	−	0.180894i	$-0.942101\pi$
$11$		−	13.1991i		−	0.361789i	0.983503	−	0.180894i	$-0.0578992\pi$
$12$		0			0
$13$	−35.4813	+	30.6281i	−0.756979	+	0.653439i
$13$	−35.4813	+	30.6281i	−0.756979	+	0.653439i
$14$	−33.4623	−	57.9585i	−0.638799	−	1.10643i
$15$		0			0
$16$	−65.6326			−1.02551
$17$	−49.0702	+	84.9920i	−0.700074	+	1.21256i	0.268366	+	0.963317i	$0.413516\pi$
$17$	−49.0702	+	84.9920i	−0.700074	+	1.21256i	−0.968440	+	0.249247i	$0.919817\pi$
$18$		0			0
$19$	−56.0776	−	32.3764i	−0.677110	−	0.390929i	0.121655	−	0.992572i	$-0.461180\pi$
$19$	−56.0776	−	32.3764i	−0.677110	−	0.390929i	−0.798765	+	0.601643i	$0.794513\pi$
$20$	72.4796	−	41.8461i	0.810347	−	0.467854i
$21$		0			0
$22$	−52.4495			−0.508285
$23$	−49.2889	+	85.3709i	−0.446846	+	0.773959i	−0.998179	−	0.0603258i	$-0.980786\pi$
$23$	−49.2889	+	85.3709i	−0.446846	+	0.773959i	0.551333	+	0.834285i	$0.314119\pi$
$24$		0			0
$25$	−4.79452	+	8.30436i	−0.0383562	+	0.0664349i
$26$	121.707	+	140.993i	0.918030	+	1.06350i
$27$		0			0
$28$	−113.627	+	65.6026i	−0.766910	+	0.442776i
$29$	304.130			1.94743			0.973717	−	0.227762i	$-0.0731407\pi$
$29$	304.130			1.94743			0.973717	+	0.227762i	$0.0731407\pi$
$30$		0			0
$31$	−86.6932	+	50.0523i	−0.502276	+	0.289989i	−0.729653	−	0.683818i	$-0.760318\pi$
$31$	−86.6932	+	50.0523i	−0.502276	+	0.289989i	0.227377	+	0.973807i	$0.426985\pi$
$32$			254.143i			1.40396i
$33$		0			0
$34$	337.734	+	194.991i	1.70356	+	0.983550i
$35$	−90.4654	+	156.691i	−0.436899	+	0.756731i
$36$		0			0
$37$	197.075	−	113.781i	0.875648	−	0.505556i	0.00642714	−	0.999979i	$-0.497954\pi$
$37$	197.075	−	113.781i	0.875648	−	0.505556i	0.869221	+	0.494424i	$0.164621\pi$
$38$	−128.655	+	222.837i	−0.549225	+	0.951286i
$39$		0			0
$40$	4.47305	+	7.74755i	0.0176813	+	0.0306249i
$41$	41.8147	+	24.1417i	0.159277	+	0.0919587i	0.577520	−	0.816377i	$-0.304021\pi$
$41$	41.8147	+	24.1417i	0.159277	+	0.0919587i	−0.418243	+	0.908335i	$0.637354\pi$
$42$		0			0
$43$	85.5052	+	148.099i	0.303242	+	0.525231i	0.976868	−	0.213841i	$-0.0685974\pi$
$43$	85.5052	+	148.099i	0.303242	+	0.525231i	−0.673626	+	0.739072i	$0.735264\pi$
$44$			102.827i			0.352312i
$45$		0			0
$46$	339.240	+	195.860i	1.08735	+	0.627783i
$47$	−23.5689	−	13.6075i	−0.0731465	−	0.0422311i	0.462981	−	0.886368i	$-0.346780\pi$
$47$	−23.5689	−	13.6075i	−0.0731465	−	0.0422311i	−0.536127	+	0.844137i	$0.680113\pi$
$48$		0			0
$49$	−29.6765	+	51.4011i	−0.0865203	+	0.149858i
$50$	32.9992	+	19.0521i	0.0933358	+	0.0538874i
$51$		0			0
$52$	276.415	−	238.606i	0.737150	−	0.636322i
$53$	−611.664			−1.58525			−0.792627	−	0.609707i	$-0.791287\pi$
$53$	−611.664			−1.58525			−0.792627	+	0.609707i	$0.791287\pi$
$54$		0			0
$55$	70.8986	+	122.800i	0.173818	+	0.301061i
$56$	−7.01244	−	12.1459i	−0.0167335	−	0.0289833i
$57$		0			0
$58$		−	1208.53i		−	2.73599i
$59$			819.677i			1.80869i	0.426800	+	0.904346i	$0.359641\pi$
$59$			819.677i			1.80869i	−0.426800	+	0.904346i	$0.640359\pi$
$60$		0			0
$61$	−18.3327	−	31.7531i	−0.0384796	−	0.0666486i	0.846144	−	0.532954i	$-0.178918\pi$
$61$	−18.3327	−	31.7531i	−0.0384796	−	0.0666486i	−0.884624	+	0.466305i	$0.845585\pi$
$62$	198.894	+	344.494i	0.407412	+	0.705658i
$63$		0			0
$64$	484.834			0.946941
$65$	165.588	−	475.540i	0.315979	−	0.907439i
$66$		0			0
$67$	−93.3172	−	53.8767i	−0.170157	−	0.0982401i	0.412503	−	0.910956i	$-0.364655\pi$
$67$	−93.3172	−	53.8767i	−0.170157	−	0.0982401i	−0.582660	+	0.812716i	$0.697988\pi$
$68$	382.278	−	662.125i	0.681736	−	1.18080i
$69$		0			0
$70$	622.645	+	359.484i	1.06315	+	0.613808i
$71$	93.2300	+	53.8263i	0.155836	+	0.0899720i	0.575890	−	0.817527i	$-0.304656\pi$
$71$	93.2300	+	53.8263i	0.155836	+	0.0899720i	−0.420054	+	0.907499i	$0.637989\pi$
$72$		0			0
$73$		−	553.128i		−	0.886832i	−0.896316	−	0.443416i	$-0.853766\pi$
$73$		−	553.128i		−	0.886832i	0.896316	−	0.443416i	$-0.146234\pi$
$74$	−452.136	−	783.122i	−0.710266	−	1.23022i
$75$		0			0
$76$	436.869	+	252.226i	0.659373	+	0.380689i
$77$	−111.148	−	192.515i	−0.164500	−	0.284923i
$78$		0			0
$79$	−395.090	+	684.315i	−0.562672	+	0.974576i	0.434591	+	0.900628i	$0.356893\pi$
$79$	−395.090	+	684.315i	−0.562672	+	0.974576i	−0.997262	+	0.0739476i	$0.976440\pi$
$80$	610.624	−	352.544i	0.853373	−	0.492695i
$81$		0			0
$82$	95.9325	−	166.160i	0.129195	−	0.223772i
$83$	−14.9734	−	8.64491i	−0.0198018	−	0.0114326i	0.490066	−	0.871685i	$-0.336973\pi$
$83$	−14.9734	−	8.64491i	−0.0198018	−	0.0114326i	−0.509868	+	0.860253i	$0.670306\pi$
$84$		0			0
$85$		−	1054.32i		−	1.34537i
$86$	588.505	−	339.774i	0.737909	−	0.426032i
$87$		0			0
$88$	−10.9914			−0.0133147
$89$	43.2247	−	24.9558i	0.0514810	−	0.0297226i	−0.474039	−	0.880504i	$-0.657204\pi$
$89$	43.2247	−	24.9558i	0.0514810	−	0.0297226i	0.525520	+	0.850782i	$0.323871\pi$
$90$		0			0
$91$	−259.594	+	745.509i	−0.299042	+	0.858798i
$92$	383.982	−	665.077i	0.435140	−	0.753685i
$93$		0			0
$94$	−54.0725	+	93.6563i	−0.0593314	+	0.102765i
$95$	695.636			0.751272
$96$		0			0
$97$	−1209.65	+	698.390i	−1.26620	+	0.731039i	−0.974266	−	0.225401i	$-0.927631\pi$
$97$	−1209.65	+	698.390i	−1.26620	+	0.731039i	−0.291930	+	0.956440i	$0.594298\pi$
$98$	204.254	+	117.926i	0.210538	+	0.121554i
$99$		0			0
$100$	37.3514	−	64.6946i	0.0373514	−	0.0646946i
$101$	−1707.30			−1.68200			−0.841001	−	0.541033i	$-0.818033\pi$
$101$	−1707.30			−1.68200			−0.841001	+	0.541033i	$0.818033\pi$
$102$		0			0
$103$	237.262	+	410.949i	0.226972	+	0.393127i	0.956909	−	0.290387i	$-0.0937842\pi$
$103$	237.262	+	410.949i	0.226972	+	0.393127i	−0.729937	+	0.683514i	$0.760451\pi$
$104$	25.5053	+	29.5467i	0.0240481	+	0.0278586i
$105$		0			0
$106$			2430.58i			2.22716i
$107$	675.268	+	1169.60i	0.610099	+	1.05672i	0.991223	+	0.132199i	$0.0422038\pi$
$107$	675.268	+	1169.60i	0.610099	+	1.05672i	−0.381124	+	0.924524i	$0.624463\pi$
$108$		0			0
$109$		−	1212.35i		−	1.06534i	−0.846324	−	0.532669i	$-0.821189\pi$
$109$		−	1212.35i		−	1.06534i	0.846324	−	0.532669i	$-0.178811\pi$
$110$	487.972	−	281.731i	0.422967	−	0.244200i
$111$		0			0
$112$	−957.281	+	552.686i	−0.807630	+	0.466285i
$113$	469.480			0.390840			0.195420	−	0.980720i	$-0.437393\pi$
$113$	469.480			0.390840			0.195420	+	0.980720i	$0.437393\pi$
$114$		0			0
$115$		−	1059.02i		−	0.858729i
$116$	−2369.31			−1.89642
$117$		0			0
$118$	3257.17			2.54107
$119$			1652.86i			1.27326i
$120$		0			0
$121$	1156.78			0.869109
$122$	−126.178	+	72.8488i	−0.0936361	+	0.0540608i
$123$		0			0
$124$	675.378	−	389.929i	0.489119	−	0.282393i
$125$		−	1445.88i		−	1.03459i
$126$		0			0
$127$	−226.697	−	392.651i	−0.158395	−	0.274347i	0.775895	−	0.630862i	$-0.217298\pi$
$127$	−226.697	−	392.651i	−0.158395	−	0.274347i	−0.934290	+	0.356514i	$0.883965\pi$
$128$			106.554i			0.0735794i
$129$		0			0
$130$	−1889.66	−	658.000i	−1.27488	−	0.443926i
$131$	−817.565	−	1416.06i	−0.545274	−	0.944443i	−0.998590	−	0.0530927i	$-0.983092\pi$
$131$	−817.565	−	1416.06i	−0.545274	−	0.944443i	0.453315	−	0.891350i	$-0.350241\pi$
$132$		0			0
$133$	−1090.56			−0.711002
$134$	−214.091	+	370.816i	−0.138020	+	0.239057i
$135$		0			0
$136$	70.7764	+	40.8628i	0.0446252	+	0.0257644i
$137$	800.149	−	461.966i	0.498988	−	0.288091i	−0.229308	−	0.973354i	$-0.573646\pi$
$137$	800.149	−	461.966i	0.498988	−	0.288091i	0.728295	+	0.685263i	$0.240313\pi$
$138$		0			0
$139$	−543.317			−0.331536			−0.165768	−	0.986165i	$-0.553010\pi$
$139$	−543.317			−0.331536			−0.165768	+	0.986165i	$0.553010\pi$
$140$	704.765	−	1220.69i	0.425454	−	0.736908i
$141$		0			0
$142$	213.891	−	370.470i	0.126404	−	0.218937i
$143$	404.263	+	468.321i	0.236407	+	0.273867i
$144$		0			0
$145$	−2829.53	+	1633.63i	−1.62055	+	0.935624i
$146$	−2197.98			−1.24593
$147$		0			0
$148$	−1535.30	+	886.408i	−0.852710	+	0.492313i
$149$			1227.49i			0.674898i	0.941344	+	0.337449i	$0.109564\pi$
$149$			1227.49i			0.674898i	−0.941344	+	0.337449i	$0.890436\pi$
$150$		0			0
$151$	−2856.94	−	1649.45i	−1.53970	−	0.888945i	−0.998856	−	0.0478207i	$-0.984772\pi$
$151$	−2856.94	−	1649.45i	−1.53970	−	0.888945i	−0.540842	−	0.841124i	$-0.681894\pi$
$152$	−26.9612	+	46.6981i	−0.0143871	+	0.0249192i
$153$		0			0
$154$	−764.999	+	441.672i	−0.400295	+	0.231110i
$155$	537.710	−	931.340i	0.278644	−	0.482626i
$156$		0			0
$157$	765.027	+	1325.07i	0.388891	+	0.673578i	0.992301	−	0.123853i	$-0.0395251\pi$
$157$	765.027	+	1325.07i	0.388891	+	0.673578i	−0.603410	+	0.797431i	$0.706192\pi$
$158$	2719.28	+	1569.97i	1.36920	+	0.790509i
$159$		0			0
$160$	−1365.13	−	2364.47i	−0.674516	−	1.16830i
$161$			1660.23i			0.812699i
$162$		0			0
$163$	−659.353	−	380.678i	−0.316838	−	0.182926i	0.333145	−	0.942876i	$-0.391890\pi$
$163$	−659.353	−	380.678i	−0.316838	−	0.182926i	−0.649982	+	0.759950i	$0.725224\pi$
$164$	−325.755	−	188.075i	−0.155105	−	0.0895498i
$165$		0			0
$166$	−34.3524	+	59.5002i	−0.0160618	+	0.0278199i
$167$	−2885.17	−	1665.76i	−1.33689	−	0.771857i	−0.350549	−	0.936544i	$-0.614005\pi$
$167$	−2885.17	−	1665.76i	−1.33689	−	0.771857i	−0.986346	+	0.164688i	$0.947338\pi$
$168$		0			0
$169$	320.841	−	2173.45i	0.146036	−	0.989279i
$170$	−4189.56			−1.89014
$171$		0			0
$172$	−666.123	−	1153.76i	−0.295299	−	0.511473i
$173$	−381.934	−	661.529i	−0.167849	−	0.290723i	0.769814	−	0.638268i	$-0.220349\pi$
$173$	−381.934	−	661.529i	−0.167849	−	0.290723i	−0.937663	+	0.347545i	$0.887016\pi$
$174$		0			0
$175$			161.497i			0.0697602i
$176$			866.290i			0.371018i
$177$		0			0
$178$	−99.1672	−	171.763i	−0.0417579	−	0.0723267i
$179$	−624.714	−	1082.04i	−0.260857	−	0.451817i	0.705613	−	0.708597i	$-0.250672\pi$
$179$	−624.714	−	1082.04i	−0.260857	−	0.451817i	−0.966470	+	0.256780i	$0.917338\pi$
$180$		0			0
$181$	−1721.72			−0.707040			−0.353520	−	0.935427i	$-0.615015\pi$
$181$	−1721.72			−0.707040			−0.353520	+	0.935427i	$0.615015\pi$
$182$	2962.44	+	1031.55i	1.20654	+	0.420131i
$183$		0			0
$184$	71.0919	+	41.0449i	0.0284835	+	0.0164450i
$185$	−1222.35	+	2117.17i	−0.485778	+	0.841392i
$186$		0			0
$187$	1121.82	+	647.682i	0.438692	+	0.253279i
$188$	183.612	+	106.009i	0.0712304	+	0.0411249i
$189$		0			0
$190$		−	2764.26i		−	1.05548i
$191$	−2482.13	−	4299.18i	−0.940318	−	1.62868i	−0.764866	−	0.644190i	$-0.777195\pi$
$191$	−2482.13	−	4299.18i	−0.940318	−	1.62868i	−0.175452	−	0.984488i	$-0.556139\pi$
$192$		0			0
$193$	−2614.21	−	1509.31i	−0.974999	−	0.562916i	−0.0742425	−	0.997240i	$-0.523654\pi$
$193$	−2614.21	−	1509.31i	−0.974999	−	0.562916i	−0.900757	+	0.434324i	$0.856987\pi$
$194$	2775.21	+	4806.80i	1.02705	+	1.77891i
$195$		0			0
$196$	231.193	−	400.437i	0.0842538	−	0.145932i
$197$	−480.686	+	277.524i	−0.173845	+	0.100369i	−0.584398	−	0.811467i	$-0.698669\pi$
$197$	−480.686	+	277.524i	−0.173845	+	0.100369i	0.410553	+	0.911837i	$0.365336\pi$
$198$		0			0
$199$	−2047.37	+	3546.14i	−0.729316	+	1.26321i	0.227856	+	0.973695i	$0.426828\pi$
$199$	−2047.37	+	3546.14i	−0.729316	+	1.26321i	−0.957173	+	0.289518i	$0.906505\pi$
$200$	6.91538	+	3.99260i	0.00244496	+	0.00141160i
$201$		0			0
$202$			6784.31i			2.36308i
$203$	4435.88	−	2561.05i	1.53368	−	0.885472i
$204$		0			0
$205$	−518.707			−0.176722
$206$	1633.00	−	942.811i	0.552312	−	0.318877i
$207$		0			0
$208$	2328.73	−	2010.20i	0.776289	−	0.670107i
$209$	−427.339	+	740.174i	−0.141434	+	0.244971i
$210$		0			0
$211$	−1251.29	+	2167.29i	−0.408257	+	0.707122i	−0.994695	−	0.102873i	$-0.967197\pi$
$211$	−1251.29	+	2167.29i	−0.408257	+	0.707122i	0.586438	+	0.809994i	$0.300530\pi$
$212$	4765.13			1.54373
$213$		0			0
$214$	4647.66	−	2683.33i	1.48461	−	0.857142i
$215$	−1591.02	−	918.578i	−0.504684	−	0.291379i
$216$		0			0
$217$	−842.972	+	1460.07i	−0.263708	+	0.456756i
$218$	−4817.53			−1.49672
$219$		0			0
$220$	−552.331	−	956.665i	−0.169264	−	0.293174i
$221$	−862.071	−	4518.55i	−0.262394	−	1.37534i
$222$		0			0
$223$			5961.87i			1.79030i	0.445768	+	0.895149i	$0.352931\pi$
$223$			5961.87i			1.79030i	−0.445768	+	0.895149i	$0.647069\pi$
$224$	2140.12	+	3706.80i	0.638361	+	1.10567i
$225$		0			0
$226$		−	1865.58i		−	0.549100i
$227$	−73.8361	+	42.6293i	−0.0215889	+	0.0124643i	−0.510756	−	0.859726i	$-0.670634\pi$
$227$	−73.8361	+	42.6293i	−0.0215889	+	0.0124643i	0.489167	+	0.872190i	$0.337301\pi$
$228$		0			0
$229$	5514.11	−	3183.57i	1.59119	−	0.918674i	0.598087	−	0.801431i	$-0.295928\pi$
$229$	5514.11	−	3183.57i	1.59119	−	0.918674i	0.993103	−	0.117243i	$-0.0374056\pi$
$230$	−4208.23			−1.20645
$231$		0			0
$232$		−	253.262i		−	0.0716701i
$233$	−1809.23			−0.508698			−0.254349	−	0.967112i	$-0.581861\pi$
$233$	−1809.23			−0.508698			−0.254349	+	0.967112i	$0.581861\pi$
$234$		0			0
$235$	292.370			0.0811580
$236$		−	6385.64i		−	1.76131i
$237$		0			0
$238$	6568.01			1.78883
$239$	2866.58	−	1655.02i	0.775832	−	0.447927i	−0.0591193	−	0.998251i	$-0.518829\pi$
$239$	2866.58	−	1655.02i	0.775832	−	0.447927i	0.834951	+	0.550324i	$0.185496\pi$
$240$		0			0
$241$	1026.51	−	592.657i	0.274371	−	0.158408i	−0.356501	−	0.934295i	$-0.616030\pi$
$241$	1026.51	−	592.657i	0.274371	−	0.158408i	0.630873	+	0.775887i	$0.282697\pi$
$242$		−	4596.73i		−	1.22103i
$243$		0			0
$244$	142.819	+	247.370i	0.0374716	+	0.0649027i
$245$		−	637.625i		−	0.166271i
$246$		0			0
$247$	2981.33	−	568.793i	0.768007	−	0.146524i
$248$	41.6806	+	72.1930i	0.0106723	+	0.0184849i
$249$		0			0
$250$	−5745.53			−1.45352
$251$	197.379	−	341.871i	0.0496353	−	0.0859708i	−0.840140	−	0.542369i	$-0.817527\pi$
$251$	197.379	−	341.871i	0.0496353	−	0.0859708i	0.889776	+	0.456398i	$0.150861\pi$
$252$		0			0
$253$	1126.82	+	650.569i	0.280010	+	0.161664i
$254$	−1560.28	+	900.830i	−0.385437	+	0.222532i
$255$		0			0
$256$	4302.09			1.05031
$257$	3333.35	−	5773.53i	0.809061	−	1.40133i	−0.104454	−	0.994530i	$-0.533309\pi$
$257$	3333.35	−	5773.53i	0.809061	−	1.40133i	0.913515	−	0.406805i	$-0.133357\pi$
$258$		0			0
$259$	1916.29	−	3319.11i	0.459739	−	0.796291i
$260$	−1290.00	+	3704.67i	−0.307702	+	0.883668i
$261$		0			0
$262$	−5627.04	+	3248.77i	−1.32687	+	0.766068i
$263$	4100.57			0.961415			0.480708	−	0.876881i	$-0.340380\pi$
$263$	4100.57			0.961415			0.480708	+	0.876881i	$0.340380\pi$
$264$		0			0
$265$	5690.72	−	3285.54i	1.31916	−	0.761619i
$266$			4333.56i			0.998901i
$267$		0			0
$268$	726.982	+	419.723i	0.165700	+	0.0956667i
$269$	−1263.72	+	2188.83i	−0.286433	+	0.496116i	−0.972956	−	0.230992i	$-0.925803\pi$
$269$	−1263.72	+	2188.83i	−0.286433	+	0.496116i	0.686523	+	0.727108i	$0.259136\pi$
$270$		0			0
$271$	−292.278	+	168.747i	−0.0655152	+	0.0378252i	−0.532400	−	0.846493i	$-0.678710\pi$
$271$	−292.278	+	168.747i	−0.0655152	+	0.0378252i	0.466885	+	0.884318i	$0.345376\pi$
$272$	3220.60	−	5578.25i	0.717933	−	1.24350i
$273$		0			0
$274$	−1835.72	−	3179.57i	−0.404745	−	0.701039i
$275$	109.610	+	63.2833i	0.0240354	+	0.0138768i
$276$		0			0
$277$	3626.92	+	6282.01i	0.786716	+	1.36263i	0.927968	+	0.372659i	$0.121554\pi$
$277$	3626.92	+	6282.01i	0.786716	+	1.36263i	−0.141252	+	0.989974i	$0.545113\pi$
$278$			2158.99i			0.465783i
$279$		0			0
$280$	130.483	+	75.3343i	0.0278494	+	0.0160789i
$281$	544.880	+	314.587i	0.115676	+	0.0667853i	0.556721	−	0.830699i	$-0.312059\pi$
$281$	544.880	+	314.587i	0.115676	+	0.0667853i	−0.441046	+	0.897485i	$0.645392\pi$
$282$		0			0
$283$	−2742.57	+	4750.27i	−0.576074	+	0.997789i	0.419850	+	0.907593i	$0.362083\pi$
$283$	−2742.57	+	4750.27i	−0.576074	+	0.997789i	−0.995924	+	0.0901957i	$0.971251\pi$
$284$	−726.302	−	419.331i	−0.151754	−	0.0876152i
$285$		0			0
$286$	1860.97	−	1606.43i	0.384761	−	0.332133i
$287$	813.182			0.167250
$288$		0			0
$289$	−2359.26	−	4086.36i	−0.480208	−	0.831745i
$290$	6491.58	+	11243.7i	1.31448	+	2.27674i
$291$		0			0
$292$			4309.11i			0.863602i
$293$			7738.23i			1.54291i	0.636285	+	0.771454i	$0.280470\pi$
$293$			7738.23i			1.54291i	−0.636285	+	0.771454i	$0.719530\pi$
$294$		0			0
$295$	−4402.87	−	7626.00i	−0.868967	−	1.50509i
$296$	−94.7505	−	164.113i	−0.0186056	−	0.0322259i
$297$		0			0
$298$	4877.70			0.948179
$299$	−865.914	−	4538.69i	−0.167482	−	0.877858i
$300$		0			0
$301$	2494.26	+	1440.06i	0.477631	+	0.275761i
$302$	−6554.47	+	11352.7i	−1.24890	+	2.16315i
$303$		0			0
$304$	3680.52	+	2124.95i	0.694382	+	0.400902i
$305$	341.122	+	196.947i	0.0640412	+	0.0369742i
$306$		0			0
$307$			7239.21i			1.34581i	0.739729	+	0.672904i	$0.234953\pi$
$307$			7239.21i			1.34581i	−0.739729	+	0.672904i	$0.765047\pi$
$308$	865.895	+	1499.77i	0.160191	+	0.277460i
$309$		0			0
$310$	−3700.88	−	2136.71i	−0.678052	−	0.391473i
$311$	−3437.27	−	5953.53i	−0.626719	−	1.08551i	−0.988206	−	0.153132i	$-0.951064\pi$
$311$	−3437.27	−	5953.53i	−0.626719	−	1.08551i	0.361486	−	0.932377i	$-0.382269\pi$
$312$		0			0
$313$	5164.67	−	8945.48i	0.932667	−	1.61543i	0.153924	−	0.988083i	$-0.450809\pi$
$313$	5164.67	−	8945.48i	0.932667	−	1.61543i	0.778743	−	0.627343i	$-0.215858\pi$
$314$	5265.44	−	3040.00i	0.946325	−	0.546361i
$315$		0			0
$316$	3077.92	−	5331.12i	0.547932	−	0.949046i
$317$	2643.50	+	1526.23i	0.468372	+	0.270415i	0.715558	−	0.698553i	$-0.246173\pi$
$317$	2643.50	+	1526.23i	0.468372	+	0.270415i	−0.247186	+	0.968968i	$0.579506\pi$
$318$		0			0
$319$		−	4014.24i		−	0.704560i
$320$	−4510.73	+	2604.27i	−0.787993	+	0.454948i
$321$		0			0
$322$	6597.29			1.14178
$323$	5503.48	−	3177.43i	0.948054	−	0.547359i
$324$		0			0
$325$	−84.2308	−	441.496i	−0.0143763	−	0.0753532i
$326$	−1512.71	+	2620.08i	−0.256997	+	0.445132i
$327$		0			0
$328$	20.1038	−	34.8208i	0.00338429	−	0.00586177i
$329$	−458.351			−0.0768077
$330$		0			0
$331$	269.692	−	155.707i	0.0447843	−	0.0258562i	−0.477441	−	0.878664i	$-0.658435\pi$
$331$	269.692	−	155.707i	0.0447843	−	0.0258562i	0.522225	+	0.852808i	$0.325102\pi$
$332$	116.650	+	67.3476i	0.0192831	+	0.0111331i
$333$		0			0
$334$	−6619.24	+	11464.9i	−1.08440	+	1.87823i
$335$	1157.59			0.188794
$336$		0			0
$337$	−4866.45	−	8428.95i	−0.786625	−	1.36247i	−0.928023	−	0.372522i	$-0.878493\pi$
$337$	−4866.45	−	8428.95i	−0.786625	−	1.36247i	0.141398	−	0.989953i	$-0.454840\pi$
$338$	−8636.66	−	1274.93i	−1.38986	−	0.205169i
$339$		0			0
$340$			8213.59i			1.31013i
$341$	660.645	+	1144.27i	0.104915	+	0.181718i
$342$		0			0
$343$			6776.36i			1.06673i
$344$	123.328	−	71.2037i	0.0193297	−	0.0111600i
$345$		0			0
$346$	−2628.73	+	1517.70i	−0.408444	+	0.235815i
$347$	2113.33			0.326944			0.163472	−	0.986548i	$-0.447731\pi$
$347$	2113.33			0.326944			0.163472	+	0.986548i	$0.447731\pi$
$348$		0			0
$349$			2324.82i			0.356575i	0.983978	+	0.178287i	$0.0570557\pi$
$349$			2324.82i			0.356575i	−0.983978	+	0.178287i	$0.942944\pi$
$350$	641.744			0.0980076
$351$		0			0
$352$	3354.46			0.507936
$353$			4808.41i			0.725002i	0.931983	+	0.362501i	$0.118077\pi$
$353$			4808.41i			0.725002i	−0.931983	+	0.362501i	$0.881923\pi$
$354$		0			0
$355$	−1156.51			−0.172904
$356$	−336.739	+	194.416i	−0.0501324	+	0.0289440i
$357$		0			0
$358$	−4299.71	+	2482.44i	−0.634768	+	0.366483i
$359$			7076.66i			1.04037i	0.854055	+	0.520184i	$0.174136\pi$
$359$			7076.66i			1.04037i	−0.854055	+	0.520184i	$0.825864\pi$
$360$		0			0
$361$	−1333.03	−	2308.88i	−0.194348	−	0.336621i
$362$			6841.62i			0.993336i
$363$		0			0
$364$	2022.35	−	5807.84i	0.291209	−	0.836301i
$365$	2971.11	+	5146.12i	0.426069	+	0.737973i
$366$		0			0
$367$	−10259.0			−1.45917			−0.729587	−	0.683889i	$-0.760287\pi$
$367$	−10259.0			−1.45917			−0.729587	+	0.683889i	$0.760287\pi$
$368$	3234.96	−	5603.11i	0.458244	−	0.793702i
$369$		0			0
$370$	8413.04	+	4857.27i	1.18209	+	0.682480i
$371$	−8921.39	+	5150.77i	−1.24845	+	0.720794i
$372$		0			0
$373$	742.285			0.103040			0.0515202	−	0.998672i	$-0.483593\pi$
$373$	742.285			0.103040			0.0515202	+	0.998672i	$0.483593\pi$
$374$	2573.70	−	4457.79i	0.355837	−	0.616328i
$375$		0			0
$376$	−11.3316	+	19.6268i	−0.00155420	+	0.00269196i
$377$	−10790.9	+	9314.93i	−1.47417	+	1.27253i
$378$		0			0
$379$	−1383.08	+	798.523i	−0.187452	+	0.108225i	−0.590789	−	0.806826i	$-0.701183\pi$
$379$	−1383.08	+	798.523i	−0.187452	+	0.108225i	0.403337	+	0.915051i	$0.367850\pi$
$380$	−5419.31			−0.731592
$381$		0			0
$382$	−17083.7	+	9863.29i	−2.28816	+	1.32107i
$383$		−	11882.3i		−	1.58527i	−0.609696	−	0.792635i	$-0.708708\pi$
$383$		−	11882.3i		−	1.58527i	0.609696	−	0.792635i	$-0.291292\pi$
$384$		0			0
$385$	2068.18	+	1194.06i	0.273777	+	0.158065i
$386$	−5997.59	+	10388.1i	−0.790853	+	1.36980i
$387$		0			0
$388$	9423.68	−	5440.77i	1.23303	−	0.711889i
$389$	−21.4339	+	37.1246i	−0.00279368	+	0.00483879i	−0.867419	−	0.497579i	$-0.834223\pi$
$389$	−21.4339	+	37.1246i	−0.00279368	+	0.00483879i	0.864625	+	0.502417i	$0.167556\pi$
$390$		0			0
$391$	−4837.23	−	8378.33i	−0.625650	−	1.08366i
$392$	42.8038	+	24.7128i	0.00551510	+	0.00318415i
$393$		0			0
$394$	1102.80	+	1910.11i	0.141011	+	0.244239i
$395$		−	8488.86i		−	1.08132i
$396$		0			0
$397$	6201.11	+	3580.21i	0.783941	+	0.452609i	0.837825	−	0.545938i	$-0.183827\pi$
$397$	6201.11	+	3580.21i	0.783941	+	0.452609i	−0.0538839	+	0.998547i	$0.517160\pi$
$398$	14091.4	+	8135.65i	1.77471	+	1.02463i
$399$		0			0
$400$	314.677	−	545.036i	0.0393346	−	0.0681295i
$401$	−10742.7	−	6202.29i	−1.33782	−	0.772388i	−0.351332	−	0.936251i	$-0.614271\pi$
$401$	−10742.7	−	6202.29i	−1.33782	−	0.772388i	−0.986483	+	0.163863i	$0.947605\pi$
$402$		0			0
$403$	1542.98	−	4431.17i	0.190722	−	0.547722i
$404$	13300.6			1.63794
$405$		0			0
$406$	−10176.9	−	17626.9i	−1.24402	−	2.15470i
$407$	−1501.81	−	2601.22i	−0.182904	−	0.316800i
$408$		0			0
$409$			7232.55i			0.874393i	0.899366	+	0.437197i	$0.144029\pi$
$409$			7232.55i			0.874393i	−0.899366	+	0.437197i	$0.855971\pi$
$410$			2061.20i			0.248281i
$411$		0			0
$412$	−1848.37	−	3201.47i	−0.221026	−	0.382828i
$413$	6902.43	+	11955.4i	0.822388	+	1.42442i
$414$		0			0
$415$	185.744			0.0219706
$416$	−7783.93	−	9017.33i	−0.917400	−	1.06277i
$417$		0			0
$418$	2941.24	+	1698.13i	0.344165	+	0.198704i
$419$	−2835.58	+	4911.38i	−0.330614	+	0.572641i	−0.982632	−	0.185563i	$-0.940589\pi$
$419$	−2835.58	+	4911.38i	−0.330614	+	0.572641i	0.652018	+	0.758203i	$0.273923\pi$
$420$		0			0
$421$	5489.27	+	3169.23i	0.635465	+	0.366886i	0.782865	−	0.622191i	$-0.213757\pi$
$421$	5489.27	+	3169.23i	0.635465	+	0.366886i	−0.147401	+	0.989077i	$0.547091\pi$
$422$	8612.22	+	4972.27i	0.993451	+	0.573569i
$423$		0			0
$424$			509.358i			0.0583410i
$425$	−470.536	−	814.992i	−0.0537044	−	0.0930187i
$426$		0			0
$427$	−534.780	−	308.755i	−0.0606085	−	0.0349923i
$428$	−5260.63	−	9111.69i	−0.594118	−	1.02904i
$429$		0			0
$430$	−3650.17	+	6322.28i	−0.409365	+	0.709041i
$431$	6644.54	−	3836.23i	0.742590	−	0.428734i	−0.0804203	−	0.996761i	$-0.525626\pi$
$431$	6644.54	−	3836.23i	0.742590	−	0.428734i	0.823010	+	0.568027i	$0.192293\pi$
$432$		0			0
$433$	8922.12	−	15453.6i	0.990230	−	1.71513i	0.374352	−	0.927287i	$-0.377865\pi$
$433$	8922.12	−	15453.6i	0.990230	−	1.71513i	0.615878	−	0.787842i	$-0.288802\pi$
$434$	5801.91	+	3349.74i	0.641707	+	0.370489i
$435$		0			0
$436$			9444.72i			1.03743i
$437$	5528.01	−	3191.60i	0.605127	−	0.349370i
$438$		0			0
$439$	−9700.37			−1.05461			−0.527304	−	0.849676i	$-0.676797\pi$
$439$	−9700.37			−1.05461			−0.527304	+	0.849676i	$0.676797\pi$
$440$	102.261	−	59.0402i	0.0110797	−	0.00639689i
$441$		0			0
$442$	−17955.4	+	3425.63i	−1.93225	+	0.368644i
$443$	653.632	−	1132.12i	0.0701016	−	0.121420i	−0.828844	−	0.559480i	$-0.811001\pi$
$443$	653.632	−	1132.12i	0.0701016	−	0.121420i	0.898946	+	0.438060i	$0.144334\pi$
$444$		0			0
$445$	−268.099	+	464.360i	−0.0285598	+	0.0494670i
$446$	23690.8			2.51523
$447$		0			0
$448$	7071.52	−	4082.74i	0.745754	−	0.430561i
$449$	874.196	+	504.717i	0.0918839	+	0.0530492i	0.545238	−	0.838281i	$-0.316439\pi$
$449$	874.196	+	504.717i	0.0918839	+	0.0530492i	−0.453354	+	0.891331i	$0.649773\pi$
$450$		0			0
$451$	318.649	−	551.916i	0.0332696	−	0.0576247i
$452$	−3657.45			−0.380602
$453$		0			0
$454$	169.397	+	293.404i	0.0175114	+	0.0303307i
$455$	−1589.31	−	8330.37i	−0.163754	−	0.858316i
$456$		0			0
$457$			958.840i			0.0981459i	0.998795	+	0.0490729i	$0.0156267\pi$
$457$			958.840i			0.0981459i	−0.998795	+	0.0490729i	$0.984373\pi$
$458$	−12650.6	−	21911.5i	−1.29067	−	2.23550i
$459$		0			0
$460$			8250.20i			0.836234i
$461$	1114.50	−	643.458i	0.112598	−	0.0650083i	−0.442644	−	0.896698i	$-0.645959\pi$
$461$	1114.50	−	643.458i	0.112598	−	0.0650083i	0.555241	+	0.831689i	$0.312626\pi$
$462$		0			0
$463$	13747.3	−	7937.03i	1.37990	−	0.796685i	0.387752	−	0.921764i	$-0.373252\pi$
$463$	13747.3	−	7937.03i	1.37990	−	0.796685i	0.992147	+	0.125078i	$0.0399182\pi$
$464$	−19960.9			−1.99711
$465$		0			0
$466$			7189.38i			0.714681i
$467$	−14009.8			−1.38822			−0.694108	−	0.719871i	$-0.744201\pi$
$467$	−14009.8			−1.38822			−0.694108	+	0.719871i	$0.744201\pi$
$468$		0			0
$469$	−1814.76			−0.178674
$470$		−	1161.80i		−	0.114021i
$471$		0			0
$472$	682.579			0.0665641
$473$	1954.78	−	1128.59i	0.190023	−	0.109710i
$474$		0			0
$475$	537.731	−	310.459i	0.0519427	−	0.0299891i
$476$		−	12876.5i		−	1.23990i
$477$		0			0
$478$	−6576.59	−	11391.0i	−0.629302	−	1.08998i
$479$			6339.79i			0.604744i	0.953190	+	0.302372i	$0.0977785\pi$
$479$			6339.79i			0.604744i	−0.953190	+	0.302372i	$0.902222\pi$
$480$		0			0
$481$	−3507.57	+	10073.2i	−0.332498	+	0.954878i
$482$	−2355.05	−	4079.07i	−0.222551	−	0.385470i
$483$		0			0
$484$	−9011.85			−0.846342
$485$	7502.77	−	12995.2i	0.702440	−	1.21666i
$486$		0			0
$487$	17214.5	+	9938.82i	1.60178	+	0.924786i	0.991132	+	0.132882i	$0.0424231\pi$
$487$	17214.5	+	9938.82i	1.60178	+	0.924786i	0.610645	+	0.791904i	$0.290910\pi$
$488$	−26.4421	+	15.2664i	−0.00245282	+	0.00141614i
$489$		0			0
$490$	−2533.74			−0.233598
$491$	−7865.62	+	13623.7i	−0.722954	+	1.25219i	0.236856	+	0.971545i	$0.423883\pi$
$491$	−7865.62	+	13623.7i	−0.722954	+	1.25219i	−0.959811	+	0.280649i	$0.909450\pi$
$492$		0			0
$493$	−14923.7	+	25848.7i	−1.36335	+	2.36139i
$494$	−2260.22	−	11847.0i	−0.205855	−	1.07899i
$495$		0			0
$496$	5689.90	−	3285.06i	0.515088	−	0.297386i
$497$	1813.07			0.163636
$498$		0			0
$499$	5543.66	−	3200.63i	0.497331	−	0.287134i	−0.230280	−	0.973125i	$-0.573964\pi$
$499$	5543.66	−	3200.63i	0.497331	−	0.287134i	0.727611	+	0.685990i	$0.240631\pi$
$500$			11264.1i			1.00749i
$501$		0			0
$502$	−1358.50	−	784.329i	−0.120782	−	0.0697337i
$503$	7906.80	−	13695.0i	0.700889	−	1.21397i	−0.267266	−	0.963623i	$-0.586120\pi$
$503$	7906.80	−	13695.0i	0.700889	−	1.21397i	0.968155	−	0.250352i	$-0.0805464\pi$
$504$		0			0
$505$	15884.1	−	9170.69i	1.39967	−	0.808100i
$506$	2585.18	−	4477.66i	0.227125	−	0.393392i
$507$		0			0
$508$	1766.07	+	3058.92i	0.154245	+	0.267161i
$509$	12705.4	+	7335.46i	1.10640	+	0.638779i	0.937894	−	0.346922i	$-0.112773\pi$
$509$	12705.4	+	7335.46i	1.10640	+	0.638779i	0.168504	+	0.985701i	$0.446106\pi$
$510$		0			0
$511$	−4657.84	−	8067.62i	−0.403231	−	0.698416i
$512$		−	16242.9i		−	1.40203i
$513$		0			0
$514$	−22942.4	−	13245.8i	−1.96877	−	1.13667i
$515$	−4414.81	−	2548.89i	−0.377747	−	0.218092i
$516$		0			0
$517$	−179.607	+	311.089i	−0.0152787	+	0.0264636i
$518$	−13189.2	−	7614.79i	−1.11873	−	0.645897i
$519$		0			0
$520$	−396.002	−	137.892i	−0.0333958	−	0.0116288i
$521$	−4671.22			−0.392802			−0.196401	−	0.980524i	$-0.562925\pi$
$521$	−4671.22			−0.392802			−0.196401	+	0.980524i	$0.562925\pi$
$522$		0			0
$523$	2987.41	+	5174.35i	0.249771	+	0.432617i	0.963462	−	0.267844i	$-0.0863112\pi$
$523$	2987.41	+	5174.35i	0.249771	+	0.432617i	−0.713691	+	0.700461i	$0.752978\pi$
$524$	6369.19	+	11031.8i	0.530991	+	0.919703i
$525$		0			0
$526$		−	16294.5i		−	1.35071i
$527$		−	9824.30i		−	0.812056i
$528$		0			0
$529$	1224.70	+	2121.25i	0.100658	+	0.174344i
$530$	−13055.8	−	22613.3i	−1.07001	−	1.85332i
$531$		0			0
$532$	8495.91			0.692377
$533$	−2223.05	+	424.125i	−0.180659	+	0.0344670i
$534$		0			0
$535$	−12564.9	−	7254.37i	−1.01538	−	0.586231i
$536$	−44.8653	+	77.7091i	−0.00361546	+	0.00626216i
$537$		0			0
$538$	8697.78	+	5021.67i	0.697004	+	0.402415i
$539$	678.448	+	391.702i	0.0542168	+	0.0313021i
$540$		0			0
$541$			744.548i			0.0591694i	0.999562	+	0.0295847i	$0.00941847\pi$
$541$			744.548i			0.0591694i	−0.999562	+	0.0295847i	$0.990582\pi$
$542$	670.552	+	1161.43i	0.0531415	+	0.0920437i
$543$		0			0
$544$	−21600.2	−	12470.9i	−1.70239	−	0.982875i
$545$	6512.10	+	11279.3i	0.511830	+	0.886516i
$546$		0			0
$547$	11128.6	−	19275.3i	0.869882	−	1.50668i	0.00776623	−	0.999970i	$-0.497528\pi$
$547$	11128.6	−	19275.3i	0.869882	−	1.50668i	0.862116	−	0.506711i	$-0.169139\pi$
$548$	−6233.51	+	3598.92i	−0.485917	+	0.280544i
$549$		0			0
$550$	251.470	−	435.559i	0.0194959	−	0.0337678i
$551$	−17054.9	−	9846.65i	−1.31863	−	0.761309i
$552$		0			0
$553$			13308.1i			1.02336i
$554$	24962.9	−	14412.3i	1.91439	−	1.10527i
$555$		0			0
$556$	4232.68			0.322852
$557$	2730.61	−	1576.52i	0.207719	−	0.119927i	−0.392532	−	0.919739i	$-0.628401\pi$
$557$	2730.61	−	1576.52i	0.207719	−	0.119927i	0.600251	+	0.799812i	$0.295067\pi$
$558$		0			0
$559$	−7569.84	−	2635.89i	−0.572755	−	0.199439i
$560$	5937.48	−	10284.0i	0.448043	−	0.776034i
$561$		0			0
$562$	1250.08	−	2165.20i	0.0938281	−	0.162515i
$563$	−3181.58			−0.238166			−0.119083	−	0.992884i	$-0.537995\pi$
$563$	−3181.58			−0.238166			−0.119083	+	0.992884i	$0.537995\pi$
$564$		0			0
$565$	−4367.89	+	2521.80i	−0.325236	+	0.187775i
$566$	18876.2	+	10898.2i	1.40182	+	0.809339i
$567$		0			0
$568$	44.8234	−	77.6364i	0.00331118	−	0.00573513i
$569$	7985.60			0.588355			0.294177	−	0.955751i	$-0.404954\pi$
$569$	7985.60			0.588355			0.294177	+	0.955751i	$0.404954\pi$
$570$		0			0
$571$	−742.326	−	1285.75i	−0.0544052	−	0.0942326i	0.837540	−	0.546376i	$-0.183993\pi$
$571$	−742.326	−	1285.75i	−0.0544052	−	0.0942326i	−0.891945	+	0.452143i	$0.850660\pi$
$572$	−3149.39	−	3648.42i	−0.230214	−	0.266693i
$573$		0			0
$574$		−	3231.36i		−	0.234972i
$575$	−472.634	−	818.626i	−0.0342786	−	0.0593723i
$576$		0			0
$577$		−	2749.63i		−	0.198386i	−0.995068	−	0.0991930i	$-0.968374\pi$
$577$		−	2749.63i		−	0.198386i	0.995068	−	0.0991930i	$-0.0316261\pi$
$578$	−16238.1	+	9375.05i	−1.16854	+	0.674655i
$579$		0			0
$580$	22043.3	−	12726.7i	1.57810	−	0.911115i
$581$	−291.192			−0.0207929
$582$		0			0
$583$			8073.41i			0.573527i
$584$	−460.613			−0.0326375
$585$		0			0
$586$	30749.5			2.16767
$587$			23260.7i			1.63555i	0.575536	+	0.817777i	$0.304794\pi$
$587$			23260.7i			1.63555i	−0.575536	+	0.817777i	$0.695206\pi$
$588$		0			0
$589$	6482.06			0.453461
$590$	−30303.6	+	17495.8i	−2.11454	+	1.22083i
$591$		0			0
$592$	−12934.6	+	7467.77i	−0.897985	+	0.518452i
$593$			16160.4i			1.11910i	0.828796	+	0.559551i	$0.189027\pi$
$593$			16160.4i			1.11910i	−0.828796	+	0.559551i	$0.810973\pi$
$594$		0			0
$595$	−8878.31	−	15377.7i	−0.611723	−	1.05954i
$596$		−	9562.68i		−	0.657219i
$597$		0			0
$598$	−18035.5	+	3440.90i	−1.23332	+	0.235299i
$599$	10780.2	+	18671.9i	0.735340	+	1.27365i	0.954574	+	0.297974i	$0.0963107\pi$
$599$	10780.2	+	18671.9i	0.735340	+	1.27365i	−0.219234	+	0.975672i	$0.570356\pi$
$600$		0			0
$601$	−2699.28			−0.183205			−0.0916024	−	0.995796i	$-0.529199\pi$
$601$	−2699.28			−0.183205			−0.0916024	+	0.995796i	$0.529199\pi$
$602$	5722.41	−	9911.51i	0.387422	−	0.671035i
$603$		0			0
$604$	22256.8	+	12850.0i	1.49937	+	0.865659i
$605$	−10762.3	+	6213.64i	−0.723225	+	0.417554i
$606$		0			0
$607$	−9180.67			−0.613891			−0.306945	−	0.951727i	$-0.599307\pi$
$607$	−9180.67			−0.613891			−0.306945	+	0.951727i	$0.599307\pi$
$608$	8228.26	−	14251.8i	0.548848	−	0.950633i
$609$		0			0
$610$	782.611	−	1355.52i	0.0519459	−	0.0899729i
$611$	1253.03	−	239.059i	0.0829658	−	0.0158286i
$612$		0			0
$613$	−15016.1	+	8669.55i	−0.989388	+	0.571223i	−0.905091	−	0.425218i	$-0.860198\pi$
$613$	−15016.1	+	8669.55i	−0.989388	+	0.571223i	−0.0842964	+	0.996441i	$0.526864\pi$
$614$	28766.6			1.89076
$615$		0			0
$616$	−160.315	+	92.5579i	−0.0104858	+	0.00605400i
$617$			24030.4i			1.56796i	0.620789	+	0.783978i	$0.286812\pi$
$617$			24030.4i			1.56796i	−0.620789	+	0.783978i	$0.713188\pi$
$618$		0			0
$619$	−4252.29	−	2455.06i	−0.276113	−	0.159414i	0.355550	−	0.934657i	$-0.384294\pi$
$619$	−4252.29	−	2455.06i	−0.276113	−	0.159414i	−0.631662	+	0.775244i	$0.717627\pi$
$620$	−4188.99	+	7255.55i	−0.271345	+	0.469984i
$621$		0			0
$622$	−23657.6	+	13658.7i	−1.52506	+	0.880492i
$623$	420.301	−	727.982i	0.0270289	−	0.0468154i
$624$		0			0
$625$	7167.21	+	12414.0i	0.458701	+	0.794494i
$626$	−35546.8	−	20523.0i	−2.26955	−	1.31032i
$627$		0			0
$628$	−5959.90	−	10322.8i	−0.378703	−	0.655934i
$629$			22333.1i			1.41571i
$630$		0			0
$631$	−5594.69	−	3230.10i	−0.352965	−	0.203785i	0.313025	−	0.949745i	$-0.398658\pi$
$631$	−5594.69	−	3230.10i	−0.352965	−	0.203785i	−0.665991	+	0.745960i	$0.731991\pi$
$632$	569.858	+	329.007i	0.0358666	+	0.0207076i
$633$		0			0
$634$	6064.80	−	10504.5i	0.379911	−	0.658026i
$635$	4218.23	+	2435.39i	0.263615	+	0.152198i
$636$		0			0
$637$	−521.360	−	2732.71i	−0.0324286	−	0.169975i
$638$	−15951.5			−0.989851
$639$		0			0
$640$	−572.354	−	991.346i	−0.0353504	−	0.0612287i
$641$	−2364.30	−	4095.09i	−0.145685	−	0.252334i	0.783943	−	0.620833i	$-0.213205\pi$
$641$	−2364.30	−	4095.09i	−0.145685	−	0.252334i	−0.929628	+	0.368498i	$0.879872\pi$
$642$		0			0
$643$			4789.29i			0.293734i	0.989156	+	0.146867i	$0.0469190\pi$
$643$			4789.29i			0.293734i	−0.989156	+	0.146867i	$0.953081\pi$
$644$		−	12933.9i		−	0.791410i
$645$		0			0
$646$	−12626.2	−	21869.3i	−0.768997	−	1.33194i
$647$	11606.9	+	20103.8i	0.705278	+	1.22158i	0.966591	+	0.256323i	$0.0825110\pi$
$647$	11606.9	+	20103.8i	0.705278	+	1.22158i	−0.261313	+	0.965254i	$0.584156\pi$
$648$		0			0
$649$	10819.0			0.654365
$650$	−1754.38	+	334.709i	−0.105865	+	0.0201975i
$651$		0			0
$652$	5136.65	+	2965.65i	0.308538	+	0.178134i
$653$	3728.90	−	6458.65i	0.223466	−	0.387054i	−0.732392	−	0.680883i	$-0.761596\pi$
$653$	3728.90	−	6458.65i	0.223466	−	0.387054i	0.955858	+	0.293829i	$0.0949296\pi$
$654$		0			0
$655$	15212.7	+	8783.05i	0.907495	+	0.523942i
$656$	−2744.41	−	1584.48i	−0.163340	−	0.0943045i
$657$		0			0
$658$			1821.36i			0.107909i
$659$	−3138.19	−	5435.50i	−0.185503	−	0.321300i	0.758243	−	0.651972i	$-0.226058\pi$
$659$	−3138.19	−	5435.50i	−0.185503	−	0.321300i	−0.943746	+	0.330672i	$0.892725\pi$
$660$		0			0
$661$	19166.5	+	11065.8i	1.12782	+	0.651149i	0.943387	−	0.331695i	$-0.107620\pi$
$661$	19166.5	+	11065.8i	1.12782	+	0.651149i	0.184437	+	0.982844i	$0.440954\pi$
$662$	−618.734	−	1071.68i	−0.0363260	−	0.0629184i
$663$		0			0
$664$	−7.19897	+	12.4690i	−0.000420745	+	0.000728751i
$665$	10146.2	−	5857.89i	0.591657	−	0.341593i
$666$		0			0
$667$	−14990.3	+	25963.9i	−0.870202	+	1.50723i
$668$	22476.8	+	12977.0i	1.30187	+	0.751638i
$669$		0			0
$670$		−	4599.93i		−	0.265240i
$671$	−419.112	+	241.974i	−0.0241127	+	0.0139215i
$672$		0			0
$673$	3435.45			0.196771			0.0983855	−	0.995148i	$-0.468632\pi$
$673$	3435.45			0.196771			0.0983855	+	0.995148i	$0.468632\pi$
$674$	−33494.3	+	19337.9i	−1.91417	+	1.10515i
$675$		0			0
$676$	−2499.49	+	16932.1i	−0.142210	+	0.963365i
$677$	−9949.28	+	17232.7i	−0.564818	+	0.978294i	0.432248	+	0.901755i	$0.357720\pi$
$677$	−9949.28	+	17232.7i	−0.564818	+	0.978294i	−0.997067	+	0.0765395i	$0.975613\pi$
$678$		0			0
$679$	−11762.2	+	20372.7i	−0.664787	+	1.15145i
$680$	−877.973			−0.0495128
$681$		0			0
$682$	4547.01	−	2625.22i	0.255299	−	0.147397i
$683$	24354.1	+	14060.9i	1.36440	+	0.787736i	0.990206	−	0.139615i	$-0.0445865\pi$
$683$	24354.1	+	14060.9i	1.36440	+	0.787736i	0.374193	+	0.927351i	$0.377920\pi$
$684$		0			0
$685$	−4962.88	+	8595.96i	−0.276820	+	0.479467i
$686$	26927.3			1.49867
$687$		0			0
$688$	−5611.93	−	9720.15i	−0.310978	−	0.538630i
$689$	21702.6	−	18734.1i	1.20001	−	1.03587i
$690$		0			0
$691$		−	9235.73i		−	0.508457i	−0.967144	−	0.254229i	$-0.918178\pi$
$691$		−	9235.73i		−	0.508457i	0.967144	−	0.254229i	$-0.0818215\pi$
$692$	2975.43	+	5153.60i	0.163452	+	0.283108i
$693$		0			0
$694$		−	8397.78i		−	0.459330i
$695$	5054.84	−	2918.41i	0.275886	−	0.159283i
$696$		0			0
$697$	−4103.71	+	2369.28i	−0.223012	+	0.128756i
$698$	9238.17			0.500960
$699$		0			0
$700$		−	1258.13i		−	0.0679328i
$701$	−6671.95			−0.359481			−0.179741	−	0.983714i	$-0.557526\pi$
$701$	−6671.95			−0.359481			−0.179741	+	0.983714i	$0.557526\pi$
$702$		0			0
$703$	−14735.4			−0.790547
$704$		−	6399.37i		−	0.342593i
$705$		0			0
$706$	19107.3			1.01857
$707$	−24901.7	+	14377.0i	−1.32464	+	0.764784i
$708$		0			0
$709$	25327.2	−	14622.7i	1.34158	−	0.774564i	0.354545	−	0.935039i	$-0.384636\pi$
$709$	25327.2	−	14622.7i	1.34158	−	0.774564i	0.987040	+	0.160475i	$0.0513025\pi$
$710$			4595.63i			0.242917i
$711$		0			0
$712$	−20.7817	−	35.9950i	−0.00109386	−	0.00189462i
$713$		−	9868.10i		−	0.518322i
$714$		0			0
$715$	−6276.70	−	2185.61i	−0.328301	−	0.114318i
$716$	4866.80	+	8429.54i	0.254023	+	0.439982i
$717$		0			0
$718$	28120.6			1.46163
$719$	−1136.47	+	1968.42i	−0.0589473	+	0.102100i	−0.893993	−	0.448081i	$-0.852108\pi$
$719$	−1136.47	+	1968.42i	−0.0589473	+	0.102100i	0.835046	+	0.550180i	$0.185441\pi$
$720$		0			0
$721$	6921.14	+	3995.92i	0.357499	+	0.206402i
$722$	−9174.85	+	5297.10i	−0.472926	+	0.273044i
$723$		0			0
$724$	13412.9			0.688519
$725$	−1458.16	+	2525.61i	−0.0746961	+	0.129377i
$726$		0			0
$727$	−11663.3	+	20201.4i	−0.595004	+	1.03058i	0.398542	+	0.917150i	$0.369516\pi$
$727$	−11663.3	+	20201.4i	−0.595004	+	1.03058i	−0.993546	+	0.113428i	$0.963817\pi$
$728$	620.816	+	216.174i	0.0316057	+	0.0110054i
$729$		0			0
$730$	20449.2	−	11806.4i	1.03679	−	0.598594i
$731$	−16783.0			−0.849169
$732$		0			0
$733$	−15695.3	+	9061.68i	−0.790885	+	0.456618i	−0.840274	−	0.542162i	$-0.817606\pi$
$733$	−15695.3	+	9061.68i	−0.790885	+	0.456618i	0.0493889	+	0.998780i	$0.484273\pi$
$734$			40766.5i			2.05002i
$735$		0			0
$736$	−21696.5	−	12526.5i	−1.08661	−	0.627352i
$737$	−711.124	+	1231.70i	−0.0355422	+	0.0615608i
$738$		0			0
$739$	−4511.88	+	2604.94i	−0.224590	+	0.129667i	−0.608074	−	0.793880i	$-0.708058\pi$
$739$	−4511.88	+	2604.94i	−0.224590	+	0.129667i	0.383484	+	0.923548i	$0.374724\pi$
$740$	9522.63	−	16493.7i	0.473053	−	0.819351i
$741$		0			0
$742$	20467.7	+	35451.1i	1.01266	+	1.75398i
$743$	−24499.2	−	14144.6i	−1.20968	−	0.698407i	−0.246988	−	0.969019i	$-0.579441\pi$
$743$	−24499.2	−	14144.6i	−1.20968	−	0.698407i	−0.962689	+	0.270612i	$0.912774\pi$
$744$		0			0
$745$	−6593.43	−	11420.2i	−0.324248	−	0.561613i
$746$		−	2949.63i		−	0.144764i
$747$		0			0
$748$	−8739.45	−	5045.72i	−0.427200	−	0.246644i
$749$	19698.2	+	11372.7i	0.960956	+	0.554808i
$750$		0			0
$751$	442.421	−	766.295i	0.0214969	−	0.0372337i	−0.855077	−	0.518501i	$-0.826490\pi$
$751$	442.421	−	766.295i	0.0214969	−	0.0372337i	0.876574	+	0.481268i	$0.159823\pi$
$752$	1546.89	+	893.098i	0.0750124	+	0.0433084i
$753$		0			0
$754$	37014.9	+	42880.1i	1.78780	+	2.07109i
$755$	35440.0			1.70834
$756$		0			0
$757$	11514.6	+	19943.9i	0.552847	+	0.957559i	0.998068	+	0.0621380i	$0.0197919\pi$
$757$	11514.6	+	19943.9i	0.552847	+	0.957559i	−0.445221	+	0.895421i	$0.646875\pi$
$758$	3173.11	+	5495.98i	0.152048	+	0.263355i
$759$		0			0
$760$		−	579.285i		−	0.0276485i
$761$		−	9076.63i		−	0.432362i	−0.976353	−	0.216181i	$-0.930640\pi$
$761$		−	9076.63i		−	0.432362i	0.976353	−	0.216181i	$-0.0693602\pi$
$762$		0			0
$763$	−10209.1	−	17682.6i	−0.484395	−	0.838997i
$764$	19336.9	+	33492.5i	0.915686	+	1.58601i
$765$		0			0
$766$	−47217.0			−2.22718
$767$	−25105.1	−	29083.2i	−1.18187	−	1.36914i
$768$		0			0
$769$	−13198.7	−	7620.25i	−0.618928	−	0.357338i	0.157523	−	0.987515i	$-0.449649\pi$
$769$	−13198.7	−	7620.25i	−0.618928	−	0.357338i	−0.776452	+	0.630177i	$0.782982\pi$
$770$	4744.86	−	8218.35i	0.222069	−	0.384635i
$771$		0			0
$772$	20365.8	+	11758.2i	0.949459	+	0.548170i
$773$	−7248.35	−	4184.84i	−0.337264	−	0.194719i	0.321797	−	0.946809i	$-0.395713\pi$
$773$	−7248.35	−	4184.84i	−0.337264	−	0.194719i	−0.659061	+	0.752089i	$0.729046\pi$
$774$		0			0
$775$		−	959.908i		−	0.0444915i
$776$	581.578	+	1007.32i	0.0269039	+	0.0465990i
$777$		0			0
$778$	147.523	+	85.1722i	0.00679813	+	0.00392490i
$779$	−1563.25	−	2707.62i	−0.0718987	−	0.124532i
$780$		0			0
$781$	710.459	−	1230.55i	0.0325509	−	0.0563797i
$782$	−33293.1	+	19221.8i	−1.52245	+	0.878990i
$783$		0			0
$784$	1947.74	−	3373.59i	0.0887273	−	0.153680i
$785$	−14235.1	−	8218.65i	−0.647227	−	0.373677i
$786$		0			0
$787$		−	837.374i		−	0.0379278i	−0.999820	−	0.0189639i	$-0.993963\pi$
$787$		−	837.374i		−	0.0379278i	0.999820	−	0.0189639i	$-0.00603676\pi$
$788$	3744.75	−	2162.03i	0.169291	−	0.0977402i
$789$		0			0
$790$	−33732.3			−1.51917
$791$	6847.58	−	3953.45i	0.307803	−	0.177710i
$792$		0			0
$793$	1623.00	+	565.146i	0.0726790	+	0.0253076i
$794$	14226.8	−	24641.5i	0.635880	−	1.10138i
$795$		0			0
$796$	15949.9	−	27626.0i	0.710211	−	1.23012i
$797$	38951.1			1.73114			0.865570	−	0.500788i	$-0.166956\pi$
$797$	38951.1			1.73114			0.865570	+	0.500788i	$0.166956\pi$
$798$		0			0
$799$	2313.06	−	1335.45i	0.102416	−	0.0591299i
$800$	−2110.50	−	1218.50i	−0.0932717	−	0.0538505i
$801$		0			0
$802$	−24646.2	+	42688.4i	−1.08514	+	1.87953i
$803$	−7300.79			−0.320846
$804$		0			0
$805$	−8917.89	−	15446.2i	−0.390452	−	0.676284i
$806$	−17608.2	−	6131.35i	−0.769507	−	0.267950i
$807$		0			0
$808$			1421.74i			0.0619016i
$809$	−11894.2	−	20601.3i	−0.516906	−	0.895308i	−0.999807	−	0.0196331i	$-0.993750\pi$
$809$	−11894.2	−	20601.3i	−0.516906	−	0.895308i	0.482901	−	0.875675i	$-0.339583\pi$
$810$		0			0
$811$		−	35866.7i		−	1.55296i	−0.630143	−	0.776479i	$-0.717004\pi$
$811$		−	35866.7i		−	1.55296i	0.630143	−	0.776479i	$-0.282996\pi$
$812$	−34557.4	+	19951.7i	−1.49351	+	0.862277i
$813$		0			0
$814$	−10336.5	+	5967.78i	−0.445079	+	0.256966i
$815$	8179.20			0.351540
$816$		0			0
$817$		−	11073.4i		−	0.474186i
$818$	28740.1			1.22845
$819$		0			0
$820$	4040.95			0.172093
$821$			218.313i			0.00928035i	0.999989	+	0.00464017i	$0.00147702\pi$
$821$			218.313i			0.00928035i	−0.999989	+	0.00464017i	$0.998523\pi$
$822$		0			0
$823$	16796.3			0.711399			0.355700	−	0.934600i	$-0.384243\pi$
$823$	16796.3			0.711399			0.355700	+	0.934600i	$0.384243\pi$
$824$	342.214	−	197.578i	0.0144680	−	0.00835308i
$825$		0			0
$826$	47507.2	−	27428.3i	2.00120	−	1.15539i
$827$		−	5954.17i		−	0.250359i	−0.992134	−	0.125180i	$-0.960049\pi$
$827$		−	5954.17i		−	0.250359i	0.992134	−	0.125180i	$-0.0399507\pi$
$828$		0			0
$829$	−10443.7	−	18089.0i	−0.437544	−	0.757848i	0.559956	−	0.828523i	$-0.310818\pi$
$829$	−10443.7	−	18089.0i	−0.437544	−	0.757848i	−0.997499	+	0.0706747i	$0.977485\pi$
$830$		−	738.093i		−	0.0308670i
$831$		0			0
$832$	−17202.5	+	14849.5i	−0.716815	+	0.618768i
$833$	−2912.46	−	5044.52i	−0.121141	−	0.209823i
$834$		0			0
$835$	35790.3			1.48332
$836$	3329.16	−	5766.28i	0.137729	−	0.238554i
$837$		0			0
$838$	19516.4	+	11267.8i	0.804515	+	0.464487i
$839$	30794.2	−	17779.0i	1.26714	−	0.731586i	0.292697	−	0.956205i	$-0.405447\pi$
$839$	30794.2	−	17779.0i	1.26714	−	0.731586i	0.974447	+	0.224619i	$0.0721138\pi$
$840$		0			0
$841$	68106.2			2.79250
$842$	12593.6	−	21812.8i	0.515446	−	0.892778i
$843$		0			0
$844$	9748.08	−	16884.2i	0.397563	−	0.688599i
$845$	8689.62	+	21944.4i	0.353766	+	0.893385i
$846$		0			0
$847$	16872.2	−	9741.18i	0.684458	−	0.395172i
$848$	40145.1			1.62569
$849$		0			0
$850$	−3238.55	+	1869.78i	−0.130684	+	0.0754504i
$851$			22432.7i			0.903622i
$852$		0			0
$853$	4359.17	+	2516.77i	0.174977	+	0.101023i	0.584930	−	0.811084i	$-0.301122\pi$
$853$	4359.17	+	2516.77i	0.174977	+	0.101023i	−0.409954	+	0.912106i	$0.634455\pi$
$854$	−1226.91	+	2125.06i	−0.0491615	+	0.0851501i
$855$		0			0
$856$	973.973	−	562.324i	0.0388899	−	0.0224531i
$857$	−21165.7	+	36660.1i	−0.843649	+	1.46124i	0.0431411	+	0.999069i	$0.486263\pi$
$857$	−21165.7	+	36660.1i	−0.843649	+	1.46124i	−0.886790	+	0.462173i	$0.847070\pi$
$858$		0			0
$859$	5920.82	+	10255.2i	0.235176	+	0.407336i	0.959324	−	0.282308i	$-0.0911002\pi$
$859$	5920.82	+	10255.2i	0.235176	+	0.407336i	−0.724148	+	0.689644i	$0.757767\pi$
$860$	12394.8	+	7156.13i	0.491463	+	0.283746i
$861$		0			0
$862$	−15244.1	−	26403.5i	−0.602338	−	1.04328i
$863$			3264.28i			0.128757i	0.997926	+	0.0643785i	$0.0205065\pi$
$863$			3264.28i			0.128757i	−0.997926	+	0.0643785i	$0.979494\pi$
$864$		0			0
$865$	7106.78	+	4103.10i	0.279350	+	0.161283i
$866$	−61408.1	−	35454.0i	−2.40962	−	1.39120i
$867$		0			0
$868$	6567.12	−	11374.6i	0.256800	−	0.444791i
$869$	9032.34	+	5214.82i	0.352591	+	0.203568i
$870$		0			0
$871$	4961.15	−	946.513i	0.192999	−	0.0368213i
$872$	−1009.57			−0.0392069
$873$		0			0
$874$	−12682.5	−	21966.8i	−0.490838	−	0.850156i
$875$	−12175.7	−	21088.9i	−0.470414	−	0.814781i
$876$		0			0
$877$		−	17140.5i		−	0.659968i	−0.943987	−	0.329984i	$-0.892957\pi$
$877$		−	17140.5i		−	0.659968i	0.943987	−	0.329984i	$-0.107043\pi$
$878$			38546.5i			1.48164i
$879$		0			0
$880$	−4653.26	−	8059.68i	−0.178251	−	0.308741i
$881$	−16988.8	−	29425.4i	−0.649678	−	1.12527i	−0.983200	−	0.182533i	$-0.941571\pi$
$881$	−16988.8	−	29425.4i	−0.649678	−	1.12527i	0.333522	−	0.942742i	$-0.391763\pi$
$882$		0			0
$883$	−8053.03			−0.306915			−0.153458	−	0.988155i	$-0.549041\pi$
$883$	−8053.03			−0.306915			−0.153458	+	0.988155i	$0.549041\pi$
$884$	6715.91	+	35201.5i	0.255521	+	1.33931i
$885$		0			0
$886$	−4498.74	−	2597.35i	−0.170585	−	0.0984873i
$887$	16356.1	−	28329.7i	0.619149	−	1.07240i	−0.370492	−	0.928836i	$-0.620811\pi$
$887$	16356.1	−	28329.7i	0.619149	−	1.07240i	0.989641	−	0.143563i	$-0.0458558\pi$
$888$		0			0
$889$	−6612.96	−	3817.99i	−0.249484	−	0.144040i
$890$	1845.24	+	1065.35i	0.0694972	+	0.0401242i
$891$		0			0
$892$		−	46445.6i		−	1.74340i
$893$	881.127	+	1526.16i	0.0330188	+	0.0571902i
$894$		0			0
$895$	11624.3	+	6711.27i	0.434141	+	0.250652i
$896$	897.285	+	1554.14i	0.0334555	+	0.0579467i
$897$		0			0
$898$	2005.60	−	3473.81i	0.0745299	−	0.129090i
$899$	−26366.0	+	15222.4i	−0.978149	+	0.564735i
$900$		0			0
$901$	30014.4	−	51986.5i	1.10980	−	1.92222i
$902$	−2193.16	−	1266.22i	−0.0809581	−	0.0467412i
$903$		0			0
$904$		−	390.955i		−	0.0143838i
$905$	16018.3	−	9248.16i	0.588360	−	0.339690i
$906$		0			0
$907$	36380.8			1.33187			0.665935	−	0.746010i	$-0.268033\pi$
$907$	36380.8			1.33187			0.665935	+	0.746010i	$0.268033\pi$
$908$	575.216	−	332.101i	0.0210234	−	0.0121378i
$909$		0			0
$910$	−33102.5	+	6315.46i	−1.20587	+	0.230061i
$911$	−2145.59	+	3716.27i	−0.0780314	+	0.135154i	−0.902400	−	0.430898i	$-0.858197\pi$
$911$	−2145.59	+	3716.27i	−0.0780314	+	0.135154i	0.824369	+	0.566053i	$0.191530\pi$
$912$		0			0
$913$	−114.105	+	197.636i	−0.00413617	+	0.00716406i
$914$	3810.16			0.137887
$915$		0			0
$916$	−42957.3	+	24801.4i	−1.54951	+	0.894609i
$917$	−23849.1	−	13769.3i	−0.858851	−	0.495858i
$918$		0			0
$919$	−1282.45	+	2221.27i	−0.0460329	+	0.0797313i	−0.888124	−	0.459604i	$-0.847991\pi$
$919$	−1282.45	+	2221.27i	−0.0460329	+	0.0797313i	0.842091	+	0.539336i	$0.181325\pi$
$920$	−881.887			−0.0316032
$921$		0			0
$922$	−2556.92	−	4428.72i	−0.0913316	−	0.158191i
$923$	−4956.52	+	945.628i	−0.176756	+	0.0337224i
$924$		0			0
$925$			2182.11i			0.0775648i
$926$	−31539.5	−	54628.1i	−1.11928	−	1.93865i
$927$		0			0
$928$			77292.7i			2.73411i
$929$	−6908.90	+	3988.86i	−0.243998	+	0.140872i	−0.617013	−	0.786953i	$-0.711657\pi$
$929$	−6908.90	+	3988.86i	−0.243998	+	0.140872i	0.373015	+	0.927825i	$0.378324\pi$
$930$		0			0
$931$	3328.37	−	1921.63i	0.117167	−	0.0676467i
$932$	14094.7			0.495373
$933$		0			0
$934$			55671.1i			1.95034i
$935$	−13916.0			−0.486741
$936$		0			0
$937$	−22558.1			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$937$	−22558.1			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$938$			7211.36i			0.251023i
$939$		0			0
$940$	−2277.69			−0.0790320
$941$	−4724.10	+	2727.46i	−0.163657	+	0.0944874i	−0.579592	−	0.814907i	$-0.696788\pi$
$941$	−4724.10	+	2727.46i	−0.163657	+	0.0944874i	0.415935	+	0.909395i	$0.363455\pi$
$942$		0			0
$943$	−4122.00	+	2379.84i	−0.142345	+	0.0821827i
$944$		−	53797.5i		−	1.85483i
$945$		0			0
$946$	−4484.71	−	7767.74i	−0.154134	−	0.266967i
$947$		−	3424.86i		−	0.117522i	−0.998272	−	0.0587609i	$-0.981285\pi$
$947$		−	3424.86i		−	0.117522i	0.998272	−	0.0587609i	$-0.0187149\pi$
$948$		0			0
$949$	16941.3	+	19625.7i	0.579491	+	0.671314i
$950$	−1233.68	−	2136.79i	−0.0421324	−	0.0729754i
$951$		0			0
$952$	1376.41			0.0468588
$953$	−16363.6	+	28342.7i	−0.556212	+	0.963388i	0.441596	+	0.897214i	$0.354413\pi$
$953$	−16363.6	+	28342.7i	−0.556212	+	0.963388i	−0.997808	+	0.0661741i	$0.978921\pi$
$954$		0			0
$955$	46185.8	+	26665.4i	1.56496	+	0.903531i
$956$	−22331.9	+	12893.3i	−0.755509	+	0.436193i
$957$		0			0
$958$	25192.5			0.849618
$959$	7780.35	−	13476.0i	0.261982	−	0.453766i
$960$		0			0
$961$	−9885.03	+	17121.4i	−0.331813	+	0.574716i
$962$	40027.9	+	13938.1i	1.34153	+	0.467134i
$963$		0			0
$964$	−7996.98	+	4617.06i	−0.267184	+	0.154259i
$965$	32429.0			1.08179
$966$		0			0
$967$	−49213.4	+	28413.4i	−1.63660	+	0.944893i	−0.654612	+	0.755965i	$0.727168\pi$
$967$	−49213.4	+	28413.4i	−1.63660	+	0.944893i	−0.981991	+	0.188928i	$0.939499\pi$
$968$		−	963.302i		−	0.0319852i
$969$		0			0
$970$	−51639.2	−	29813.9i	−1.70931	−	0.986873i
$971$	−20615.6	+	35707.3i	−0.681346	+	1.18013i	0.293224	+	0.956044i	$0.405272\pi$
$971$	−20615.6	+	35707.3i	−0.681346	+	1.18013i	−0.974570	+	0.224083i	$0.928061\pi$
$972$		0			0
$973$	−7924.52	+	4575.23i	−0.261098	+	0.150745i
$974$	39494.1	−	68405.7i	1.29925	−	2.25037i
$975$		0			0
$976$	1203.22	+	2084.04i	0.0394612	+	0.0683488i
$977$	−21854.4	−	12617.7i	−0.715644	−	0.413177i	0.0975031	−	0.995235i	$-0.468914\pi$
$977$	−21854.4	−	12617.7i	−0.715644	−	0.413177i	−0.813147	+	0.582058i	$0.802248\pi$
$978$		0			0
$979$	−329.394	−	570.526i	−0.0107533	−	0.0186252i
$980$			4967.38i			0.161915i
$981$		0			0
$982$	54136.6	+	31255.8i	1.75923	+	1.01569i
$983$	−11991.4	−	6923.25i	−0.389081	−	0.224636i	0.292681	−	0.956210i	$-0.405453\pi$
$983$	−11991.4	−	6923.25i	−0.389081	−	0.224636i	−0.681762	+	0.731574i	$0.738786\pi$
$984$		0			0
$985$	2981.43	−	5163.99i	0.0964428	−	0.167044i
$986$	102715.	+	59302.7i	3.31757	+	1.91540i
$987$		0			0
$988$	−23225.9	+	4431.15i	−0.747888	+	0.142686i
$989$	−16857.8			−0.542010
$990$		0			0
$991$	−2076.06	−	3595.85i	−0.0665473	−	0.115263i	0.830832	−	0.556523i	$-0.187865\pi$
$991$	−2076.06	−	3595.85i	−0.0665473	−	0.115263i	−0.897379	+	0.441260i	$0.854532\pi$
$992$	−12720.5	−	22032.5i	−0.407132	−	0.705174i
$993$		0			0
$994$		−	7204.62i		−	0.229896i
$995$		−	43989.5i		−	1.40157i
$996$		0			0
$997$	18813.1	+	32585.3i	0.597610	+	1.03509i	0.993173	+	0.116652i	$0.0372162\pi$
$997$	18813.1	+	32585.3i	0.597610	+	1.03509i	−0.395563	+	0.918439i	$0.629450\pi$
$998$	−12718.4	−	22028.9i	−0.403401	−	0.698711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.4.l.a.127.8		80
3.2	odd	2		117.4.l.a.88.33	yes	80
9.4	even	3		351.4.r.a.10.33		80
9.5	odd	6		117.4.r.a.49.8	yes	80
13.4	even	6		351.4.r.a.316.33		80
39.17	odd	6		117.4.r.a.43.8	yes	80
117.4	even	6	inner	351.4.l.a.199.33		80
117.95	odd	6		117.4.l.a.4.8	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.8	✓	80	117.95	odd	6
117.4.l.a.88.33	yes	80	3.2	odd	2
117.4.r.a.43.8	yes	80	39.17	odd	6
117.4.r.a.49.8	yes	80	9.5	odd	6
351.4.l.a.127.8		80	1.1	even	1	trivial
351.4.l.a.199.33		80	117.4	even	6	inner
351.4.r.a.10.33		80	9.4	even	3
351.4.r.a.316.33		80	13.4	even	6

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	351.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.97372i q^{2} -7.79044 q^{4} +(-9.30367 + 5.37147i) q^{5} +(14.5854 - 8.42091i) q^{7} -0.832741i q^{8} +(21.3447 + 36.9702i) q^{10} -13.1991i q^{11} +(-35.4813 + 30.6281i) q^{13} +(-33.4623 - 57.9585i) q^{14} -65.6326 q^{16} +(-49.0702 + 84.9920i) q^{17} +(-56.0776 - 32.3764i) q^{19} +(72.4796 - 41.8461i) q^{20} -52.4495 q^{22} +(-49.2889 + 85.3709i) q^{23} +(-4.79452 + 8.30436i) q^{25} +(121.707 + 140.993i) q^{26} +(-113.627 + 65.6026i) q^{28} +304.130 q^{29} +(-86.6932 + 50.0523i) q^{31} +254.143i q^{32} +(337.734 + 194.991i) q^{34} +(-90.4654 + 156.691i) q^{35} +(197.075 - 113.781i) q^{37} +(-128.655 + 222.837i) q^{38} +(4.47305 + 7.74755i) q^{40} +(41.8147 + 24.1417i) q^{41} +(85.5052 + 148.099i) q^{43} +102.827i q^{44} +(339.240 + 195.860i) q^{46} +(-23.5689 - 13.6075i) q^{47} +(-29.6765 + 51.4011i) q^{49} +(32.9992 + 19.0521i) q^{50} +(276.415 - 238.606i) q^{52} -611.664 q^{53} +(70.8986 + 122.800i) q^{55} +(-7.01244 - 12.1459i) q^{56} -1208.53i q^{58} +819.677i q^{59} +(-18.3327 - 31.7531i) q^{61} +(198.894 + 344.494i) q^{62} +484.834 q^{64} +(165.588 - 475.540i) q^{65} +(-93.3172 - 53.8767i) q^{67} +(382.278 - 662.125i) q^{68} +(622.645 + 359.484i) q^{70} +(93.2300 + 53.8263i) q^{71} -553.128i q^{73} +(-452.136 - 783.122i) q^{74} +(436.869 + 252.226i) q^{76} +(-111.148 - 192.515i) q^{77} +(-395.090 + 684.315i) q^{79} +(610.624 - 352.544i) q^{80} +(95.9325 - 166.160i) q^{82} +(-14.9734 - 8.64491i) q^{83} -1054.32i q^{85} +(588.505 - 339.774i) q^{86} -10.9914 q^{88} +(43.2247 - 24.9558i) q^{89} +(-259.594 + 745.509i) q^{91} +(383.982 - 665.077i) q^{92} +(-54.0725 + 93.6563i) q^{94} +695.636 q^{95} +(-1209.65 + 698.390i) q^{97} +(204.254 + 117.926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 306 q^{4} - 3 q^{7} - 10 q^{10} - 13 q^{13} - 126 q^{14} + 1102 q^{16} + 138 q^{17} - 96 q^{19} + 387 q^{20} + 62 q^{22} + 327 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} + 402 q^{29} + 180 q^{31}+ \cdots + 6339 q^{98}+O(q^{100}) \) 80 * q - 306 * q^4 - 3 * q^7 - 10 * q^10 - 13 * q^13 - 126 * q^14 + 1102 * q^16 + 138 * q^17 - 96 * q^19 + 387 * q^20 + 62 * q^22 + 327 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 + 402 * q^29 + 180 * q^31 + 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 - 381 * q^41 - 83 * q^43 - 6 * q^46 - 372 * q^47 + 1613 * q^49 + 708 * q^50 + 402 * q^52 + 2568 * q^53 - 127 * q^55 + 2298 * q^56 - 419 * q^61 - 135 * q^62 - 3178 * q^64 - 363 * q^65 + 879 * q^67 - 1950 * q^68 - 1005 * q^70 + 2598 * q^71 - 471 * q^74 + 1485 * q^76 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 - 1194 * q^83 + 2910 * q^86 - 1562 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 + 539 * q^94 - 10584 * q^95 + 789 * q^97 + 6339 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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