LMFDB - Embedded newform 25.4.d.a.6.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.6
Character	$\chi$	$=$	25.6
Dual form			25.4.d.a.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906232 + 2.78910i) q^{2} +(5.49244 - 3.99049i) q^{3} +(-0.485661 + 0.352853i) q^{4} +(-10.1222 + 4.74784i) q^{5} +(16.1073 + 11.7026i) q^{6} -23.0864 q^{7} +(17.5561 + 12.7553i) q^{8} +(5.89942 - 18.1565i) q^{9} +O(q^{10})$	\(q+(0.906232 + 2.78910i) q^{2} +(5.49244 - 3.99049i) q^{3} +(-0.485661 + 0.352853i) q^{4} +(-10.1222 + 4.74784i) q^{5} +(16.1073 + 11.7026i) q^{6} -23.0864 q^{7} +(17.5561 + 12.7553i) q^{8} +(5.89942 - 18.1565i) q^{9} +(-22.4152 - 23.9290i) q^{10} +(-10.1957 - 31.3790i) q^{11} +(-1.25941 + 3.87605i) q^{12} +(6.98730 - 21.5047i) q^{13} +(-20.9216 - 64.3901i) q^{14} +(-36.6491 + 66.4696i) q^{15} +(-21.1498 + 65.0923i) q^{16} +(103.416 + 75.1358i) q^{17} +55.9866 q^{18} +(-64.4944 - 46.8579i) q^{19} +(3.24065 - 5.87748i) q^{20} +(-126.801 + 92.1260i) q^{21} +(78.2794 - 56.8733i) q^{22} +(3.36642 + 10.3608i) q^{23} +147.326 q^{24} +(79.9161 - 96.1167i) q^{25} +66.3107 q^{26} +(16.5927 + 51.0670i) q^{27} +(11.2122 - 8.14611i) q^{28} +(3.28945 - 2.38992i) q^{29} +(-218.603 - 41.9810i) q^{30} +(-44.1789 - 32.0979i) q^{31} -27.1110 q^{32} +(-181.217 - 131.662i) q^{33} +(-115.842 + 356.526i) q^{34} +(233.684 - 109.610i) q^{35} +(3.54148 + 10.8996i) q^{36} +(-80.2988 + 247.134i) q^{37} +(72.2443 - 222.345i) q^{38} +(-47.4370 - 145.996i) q^{39} +(-238.266 - 45.7571i) q^{40} +(33.2460 - 102.321i) q^{41} +(-371.859 - 270.171i) q^{42} +124.154 q^{43} +(16.0238 + 11.6420i) q^{44} +(26.4895 + 211.793i) q^{45} +(-25.8465 + 18.7786i) q^{46} +(368.812 - 267.958i) q^{47} +(143.586 + 441.914i) q^{48} +189.981 q^{49} +(340.501 + 135.789i) q^{50} +867.832 q^{51} +(4.19455 + 12.9095i) q^{52} +(-559.680 + 406.631i) q^{53} +(-127.394 + 92.5571i) q^{54} +(252.184 + 269.216i) q^{55} +(-405.307 - 294.473i) q^{56} -541.218 q^{57} +(9.64673 + 7.00876i) q^{58} +(130.566 - 401.842i) q^{59} +(-5.65497 - 45.2135i) q^{60} +(-125.372 - 385.857i) q^{61} +(49.4877 - 152.307i) q^{62} +(-136.196 + 419.169i) q^{63} +(144.629 + 445.123i) q^{64} +(31.3743 + 250.848i) q^{65} +(202.992 - 624.746i) q^{66} +(-484.733 - 352.179i) q^{67} -76.7368 q^{68} +(59.8345 + 43.4723i) q^{69} +(517.486 + 552.434i) q^{70} +(-734.084 + 533.343i) q^{71} +(335.162 - 243.510i) q^{72} +(-218.714 - 673.134i) q^{73} -762.051 q^{74} +(55.3812 - 846.820i) q^{75} +47.8564 q^{76} +(235.381 + 724.427i) q^{77} +(364.208 - 264.612i) q^{78} +(69.9257 - 50.8040i) q^{79} +(-94.9665 - 759.290i) q^{80} +(711.928 + 517.246i) q^{81} +315.511 q^{82} +(-40.4126 - 29.3615i) q^{83} +(29.0751 - 89.4840i) q^{84} +(-1403.52 - 269.536i) q^{85} +(112.512 + 346.278i) q^{86} +(8.53012 - 26.2530i) q^{87} +(221.251 - 680.941i) q^{88} +(202.969 + 624.673i) q^{89} +(-566.705 + 265.815i) q^{90} +(-161.311 + 496.465i) q^{91} +(-5.29078 - 3.84398i) q^{92} -370.736 q^{93} +(1081.59 + 785.820i) q^{94} +(875.296 + 168.094i) q^{95} +(-148.905 + 108.186i) q^{96} +(43.2567 - 31.4278i) q^{97} +(172.167 + 529.875i) q^{98} -629.882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.906232	+	2.78910i	0.320401	+	0.986094i	0.973474	+	0.228799i	$0.0734797\pi$
$2$	0.906232	+	2.78910i	0.320401	+	0.986094i	−0.653072	+	0.757296i	$0.726520\pi$
$3$	5.49244	−	3.99049i	1.05702	−	0.767970i	0.0834857	−	0.996509i	$-0.473395\pi$
$3$	5.49244	−	3.99049i	1.05702	−	0.767970i	0.973535	+	0.228539i	$0.0733947\pi$
$4$	−0.485661	+	0.352853i	−0.0607076	+	0.0441067i
$5$	−10.1222	+	4.74784i	−0.905353	+	0.424660i
$5$	−10.1222	+	4.74784i	−0.905353	+	0.424660i
$6$	16.1073	+	11.7026i	1.09596	+	0.796263i
$7$	−23.0864			−1.24655			−0.623274	−	0.782004i	$-0.714198\pi$
$7$	−23.0864			−1.24655			−0.623274	+	0.782004i	$0.714198\pi$
$8$	17.5561	+	12.7553i	0.775878	+	0.563708i
$9$	5.89942	−	18.1565i	0.218497	−	0.672464i
$10$	−22.4152	−	23.9290i	−0.708831	−	0.756702i
$11$	−10.1957	−	31.3790i	−0.279464	−	0.860102i	−0.988004	−	0.154431i	$-0.950646\pi$
$11$	−10.1957	−	31.3790i	−0.279464	−	0.860102i	0.708539	−	0.705671i	$-0.249354\pi$
$12$	−1.25941	+	3.87605i	−0.0302966	+	0.0932433i
$13$	6.98730	−	21.5047i	0.149071	−	0.458794i	−0.848441	−	0.529290i	$-0.822458\pi$
$13$	6.98730	−	21.5047i	0.149071	−	0.458794i	0.997512	+	0.0704960i	$0.0224582\pi$
$14$	−20.9216	−	64.3901i	−0.399396	−	1.22921i
$15$	−36.6491	+	66.4696i	−0.630851	+	1.14416i
$16$	−21.1498	+	65.0923i	−0.330465	+	1.01707i
$17$	103.416	+	75.1358i	1.47541	+	1.07195i	0.979000	+	0.203858i	$0.0653481\pi$
$17$	103.416	+	75.1358i	1.47541	+	1.07195i	0.496408	+	0.868089i	$0.334652\pi$
$18$	55.9866			0.733120
$19$	−64.4944	−	46.8579i	−0.778738	−	0.565786i	0.125862	−	0.992048i	$-0.459830\pi$
$19$	−64.4944	−	46.8579i	−0.778738	−	0.565786i	−0.904600	+	0.426261i	$0.859830\pi$
$20$	3.24065	−	5.87748i	0.0362315	−	0.0657122i
$21$	−126.801	+	92.1260i	−1.31763	+	0.957312i
$22$	78.2794	−	56.8733i	0.758601	−	0.551156i
$23$	3.36642	+	10.3608i	0.0305195	+	0.0939293i	0.965156	−	0.261675i	$-0.0842750\pi$
$23$	3.36642	+	10.3608i	0.0305195	+	0.0939293i	−0.934636	+	0.355605i	$0.884275\pi$
$24$	147.326			1.25303
$25$	79.9161	−	96.1167i	0.639328	−	0.768934i
$26$	66.3107			0.500177
$27$	16.5927	+	51.0670i	0.118269	+	0.363994i
$28$	11.2122	−	8.14611i	0.0756750	−	0.0549811i
$29$	3.28945	−	2.38992i	0.0210633	−	0.0153034i	−0.577204	−	0.816600i	$-0.695856\pi$
$29$	3.28945	−	2.38992i	0.0210633	−	0.0153034i	0.598267	+	0.801297i	$0.295856\pi$
$30$	−218.603	−	41.9810i	−1.33037	−	0.255488i
$31$	−44.1789	−	32.0979i	−0.255960	−	0.185966i	0.452404	−	0.891813i	$-0.350567\pi$
$31$	−44.1789	−	32.0979i	−0.255960	−	0.185966i	−0.708364	+	0.705847i	$0.750567\pi$
$32$	−27.1110			−0.149768
$33$	−181.217	−	131.662i	−0.955932	−	0.694525i
$34$	−115.842	+	356.526i	−0.584318	+	1.79835i
$35$	233.684	−	109.610i	1.12857	−	0.529358i
$36$	3.54148	+	10.8996i	0.0163957	+	0.0504609i
$37$	−80.2988	+	247.134i	−0.356785	+	1.09807i	0.598182	+	0.801360i	$0.295890\pi$
$37$	−80.2988	+	247.134i	−0.356785	+	1.09807i	−0.954967	+	0.296711i	$0.904110\pi$
$38$	72.2443	−	222.345i	0.308410	−	0.949188i
$39$	−47.4370	−	145.996i	−0.194769	−	0.599438i
$40$	−238.266	−	45.7571i	−0.941827	−	0.180871i
$41$	33.2460	−	102.321i	0.126638	−	0.389751i	−0.867558	−	0.497336i	$-0.834312\pi$
$41$	33.2460	−	102.321i	0.126638	−	0.389751i	0.994196	+	0.107585i	$0.0343117\pi$
$42$	−371.859	−	270.171i	−1.36617	−	0.992580i
$43$	124.154			0.440310			0.220155	−	0.975465i	$-0.429344\pi$
$43$	124.154			0.440310			0.220155	+	0.975465i	$0.429344\pi$
$44$	16.0238	+	11.6420i	0.0549019	+	0.0398885i
$45$	26.4895	+	211.793i	0.0877516	+	0.701605i
$46$	−25.8465	+	18.7786i	−0.0828446	+	0.0601901i
$47$	368.812	−	267.958i	1.14461	−	0.831609i	0.156857	−	0.987621i	$-0.449864\pi$
$47$	368.812	−	267.958i	1.14461	−	0.831609i	0.987755	+	0.156012i	$0.0498638\pi$
$48$	143.586	+	441.914i	0.431769	+	1.32885i
$49$	189.981			0.553881
$50$	340.501	+	135.789i	0.963083	+	0.384071i
$51$	867.832			2.38276
$52$	4.19455	+	12.9095i	0.0111861	+	0.0344274i
$53$	−559.680	+	406.631i	−1.45053	+	1.05387i	−0.464819	+	0.885406i	$0.653881\pi$
$53$	−559.680	+	406.631i	−1.45053	+	1.05387i	−0.985708	+	0.168463i	$0.946119\pi$
$54$	−127.394	+	92.5571i	−0.321039	+	0.233249i
$55$	252.184	+	269.216i	0.618264	+	0.660019i
$56$	−405.307	−	294.473i	−0.967168	−	0.702689i
$57$	−541.218			−1.25765
$58$	9.64673	+	7.00876i	0.0218393	+	0.0158672i
$59$	130.566	−	401.842i	0.288107	−	0.886701i	−0.697344	−	0.716737i	$-0.745635\pi$
$59$	130.566	−	401.842i	0.288107	−	0.886701i	0.985450	−	0.169964i	$-0.0543652\pi$
$60$	−5.65497	−	45.2135i	−0.0121676	−	0.0972839i
$61$	−125.372	−	385.857i	−0.263152	−	0.809900i	−0.992113	−	0.125344i	$-0.959996\pi$
$61$	−125.372	−	385.857i	−0.263152	−	0.809900i	0.728961	−	0.684555i	$-0.240004\pi$
$62$	49.4877	−	152.307i	0.101370	−	0.311985i
$63$	−136.196	+	419.169i	−0.272367	+	0.838259i
$64$	144.629	+	445.123i	0.282479	+	0.869382i
$65$	31.3743	+	250.848i	0.0598693	+	0.478676i
$66$	202.992	−	624.746i	0.378585	−	1.16517i
$67$	−484.733	−	352.179i	−0.883873	−	0.642172i	0.0504000	−	0.998729i	$-0.483950\pi$
$67$	−484.733	−	352.179i	−0.883873	−	0.642172i	−0.934273	+	0.356558i	$0.883950\pi$
$68$	−76.7368			−0.136849
$69$	59.8345	+	43.4723i	0.104395	+	0.0758471i
$70$	517.486	+	552.434i	0.883591	+	0.943265i
$71$	−734.084	+	533.343i	−1.22704	+	0.891496i	−0.996665	−	0.0816063i	$-0.973995\pi$
$71$	−734.084	+	533.343i	−1.22704	+	0.891496i	−0.230374	+	0.973102i	$0.573995\pi$
$72$	335.162	−	243.510i	0.548601	−	0.398582i
$73$	−218.714	−	673.134i	−0.350666	−	1.07924i	−0.958480	−	0.285159i	$-0.907954\pi$
$73$	−218.714	−	673.134i	−0.350666	−	1.07924i	0.607815	−	0.794079i	$-0.292046\pi$
$74$	−762.051			−1.19712
$75$	55.3812	−	846.820i	0.0852650	−	1.30376i
$76$	47.8564			0.0722303
$77$	235.381	+	724.427i	0.348365	+	1.07216i
$78$	364.208	−	264.612i	0.528698	−	0.384121i
$79$	69.9257	−	50.8040i	0.0995856	−	0.0723532i	−0.536878	−	0.843660i	$-0.680397\pi$
$79$	69.9257	−	50.8040i	0.0995856	−	0.0723532i	0.636464	+	0.771307i	$0.280397\pi$
$80$	−94.9665	−	759.290i	−0.132720	−	1.06114i
$81$	711.928	+	517.246i	0.976582	+	0.709528i
$82$	315.511			0.424906
$83$	−40.4126	−	29.3615i	−0.0534441	−	0.0388294i	0.560742	−	0.827990i	$-0.310516\pi$
$83$	−40.4126	−	29.3615i	−0.0534441	−	0.0388294i	−0.614187	+	0.789161i	$0.710516\pi$
$84$	29.0751	−	89.4840i	0.0377662	−	0.116232i
$85$	−1403.52	−	269.536i	−1.79098	−	0.343944i
$86$	112.512	+	346.278i	0.141076	+	0.434187i
$87$	8.53012	−	26.2530i	0.0105118	−	0.0323519i
$88$	221.251	−	680.941i	0.268017	−	0.824870i
$89$	202.969	+	624.673i	0.241737	+	0.743991i	0.996156	+	0.0875977i	$0.0279190\pi$
$89$	202.969	+	624.673i	0.241737	+	0.743991i	−0.754418	+	0.656394i	$0.772081\pi$
$90$	−566.705	+	265.815i	−0.663732	+	0.311326i
$91$	−161.311	+	496.465i	−0.185825	+	0.571909i
$92$	−5.29078	−	3.84398i	−0.00599567	−	0.00435611i
$93$	−370.736			−0.413372
$94$	1081.59	+	785.820i	1.18678	+	0.862247i
$95$	875.296	+	168.094i	0.945300	+	0.181538i
$96$	−148.905	+	108.186i	−0.158308	+	0.115018i
$97$	43.2567	−	31.4278i	0.0452789	−	0.0328970i	−0.564916	−	0.825149i	$-0.691091\pi$
$97$	43.2567	−	31.4278i	0.0452789	−	0.0328970i	0.610195	+	0.792252i	$0.291091\pi$
$98$	172.167	+	529.875i	0.177464	+	0.546178i
$99$	−629.882			−0.639450
$100$	−4.89700	+	74.8788i	−0.00489700	+	0.0748788i
$101$	−97.8634			−0.0964136			−0.0482068	−	0.998837i	$-0.515351\pi$
$101$	−97.8634			−0.0964136			−0.0482068	+	0.998837i	$0.515351\pi$
$102$	786.457	+	2420.47i	0.763440	+	2.34963i
$103$	1108.95	−	805.697i	1.06085	−	0.770754i	0.0866060	−	0.996243i	$-0.472398\pi$
$103$	1108.95	−	805.697i	1.06085	−	0.770754i	0.974246	+	0.225489i	$0.0723979\pi$
$104$	396.968	−	288.414i	0.374287	−	0.271936i
$105$	846.096	−	1534.54i	0.786386	−	1.42625i
$106$	−1641.33	−	1192.50i	−1.50397	−	1.09269i
$107$	−157.443			−0.142249			−0.0711244	−	0.997467i	$-0.522659\pi$
$107$	−157.443			−0.142249			−0.0711244	+	0.997467i	$0.522659\pi$
$108$	−26.0776	−	18.9465i	−0.0232344	−	0.0168808i
$109$	248.352	−	764.348i	0.218236	−	0.671663i	−0.780672	−	0.624942i	$-0.785123\pi$
$109$	248.352	−	764.348i	0.218236	−	0.671663i	0.998908	−	0.0467211i	$-0.0148772\pi$
$110$	−522.331	+	947.338i	−0.452748	+	0.821138i
$111$	545.151	+	1677.80i	0.466157	+	1.43468i
$112$	488.272	−	1502.75i	0.411941	−	1.26782i
$113$	−206.016	+	634.054i	−0.171508	+	0.527847i	−0.999457	−	0.0329564i	$-0.989508\pi$
$113$	−206.016	+	634.054i	−0.171508	+	0.527847i	0.827949	+	0.560804i	$0.189508\pi$
$114$	−490.469	−	1509.51i	−0.402953	−	1.24016i
$115$	−83.2668	−	88.8903i	−0.0675189	−	0.0720788i
$116$	−0.754264	+	2.32139i	−0.000603721	+	0.00185806i
$117$	−349.230	−	253.730i	−0.275951	−	0.200490i
$118$	1239.10			0.966681
$119$	−2387.49	−	1734.61i	−1.83917	−	1.33623i
$120$	−1491.25	+	699.478i	−1.13443	+	0.532111i
$121$	196.112	−	142.483i	0.147342	−	0.107050i
$122$	962.575	−	699.351i	0.714323	−	0.518986i
$123$	−225.708	−	694.658i	−0.165459	−	0.509229i
$124$	32.7818			0.0237411
$125$	−352.576	+	1352.34i	−0.252283	+	0.967654i
$126$	−1292.53			−0.913869
$127$	123.294	+	379.461i	0.0861465	+	0.265132i	0.984845	−	0.173435i	$-0.0554865\pi$
$127$	123.294	+	379.461i	0.0861465	+	0.265132i	−0.898699	+	0.438566i	$0.855486\pi$
$128$	−1285.89	+	934.254i	−0.887951	+	0.645134i
$129$	681.909	−	495.436i	0.465417	−	0.338145i
$130$	−671.208	+	314.833i	−0.452837	+	0.212405i
$131$	−80.7018	−	58.6333i	−0.0538241	−	0.0391055i	0.560548	−	0.828122i	$-0.310591\pi$
$131$	−80.7018	−	58.6333i	−0.0538241	−	0.0391055i	−0.614372	+	0.789017i	$0.710591\pi$
$132$	134.467			0.0886656
$133$	1488.94	+	1081.78i	0.970734	+	0.705280i
$134$	542.980	−	1671.12i	0.350047	−	1.07734i
$135$	−410.411	−	438.129i	−0.261649	−	0.279319i
$136$	857.198	+	2638.18i	0.540471	+	1.66340i
$137$	−888.714	+	2735.18i	−0.554219	+	1.70571i	0.143780	+	0.989610i	$0.454074\pi$
$137$	−888.714	+	2735.18i	−0.554219	+	1.70571i	−0.697998	+	0.716099i	$0.745926\pi$
$138$	−67.0245	+	206.280i	−0.0413442	+	0.127244i
$139$	331.520	+	1020.32i	0.202296	+	0.622604i	0.999814	+	0.0193081i	$0.00614633\pi$
$139$	331.520	+	1020.32i	0.202296	+	0.622604i	−0.797517	+	0.603296i	$0.793854\pi$
$140$	−74.8148	+	135.690i	−0.0451643	+	0.0819134i
$141$	956.396	−	2943.48i	0.571227	−	1.75806i
$142$	−2152.80	−	1564.10i	−1.27224	−	0.924339i
$143$	−746.036			−0.436270
$144$	1057.08	+	768.013i	0.611736	+	0.444452i
$145$	−21.9493	+	39.8089i	−0.0125710	+	0.0227997i
$146$	1679.23	−	1220.03i	0.951876	−	0.691579i
$147$	1043.46	−	758.118i	0.585463	−	0.425364i
$148$	−48.2042	−	148.357i	−0.0267727	−	0.0823979i
$149$	1542.11			0.847884			0.423942	−	0.905689i	$-0.360646\pi$
$149$	1542.11			0.847884			0.423942	+	0.905689i	$0.360646\pi$
$150$	2412.05	−	612.952i	1.31295	−	0.333649i
$151$	269.554			0.145271			0.0726357	−	0.997359i	$-0.476859\pi$
$151$	269.554			0.145271			0.0726357	+	0.997359i	$0.476859\pi$
$152$	−534.586	−	1645.29i	−0.285267	−	0.877962i
$153$	1974.30	−	1434.41i	1.04322	−	0.757943i
$154$	−1807.19	+	1313.00i	−0.945632	+	0.687042i
$155$	599.581	+	115.145i	0.310707	+	0.0596689i
$156$	74.5535	+	54.1663i	0.0382632	+	0.0277998i
$157$	−746.763			−0.379606			−0.189803	−	0.981822i	$-0.560785\pi$
$157$	−746.763			−0.379606			−0.189803	+	0.981822i	$0.560785\pi$
$158$	205.066	+	148.989i	0.103254	+	0.0750187i
$159$	−1451.35	+	4466.79i	−0.723896	+	2.22792i
$160$	274.421	−	128.718i	0.135593	−	0.0636005i
$161$	−77.7185	−	239.193i	−0.0380440	−	0.117087i
$162$	−797.477	+	2454.38i	−0.386763	+	1.19034i
$163$	−95.3713	+	293.523i	−0.0458285	+	0.141046i	−0.971352	−	0.237643i	$-0.923625\pi$
$163$	−95.3713	+	293.523i	−0.0458285	+	0.141046i	0.925524	+	0.378689i	$0.123625\pi$
$164$	19.9579	+	61.4241i	0.00950275	+	0.0292465i
$165$	2459.41	+	472.312i	1.16039	+	0.222845i
$166$	45.2688	−	139.323i	0.0211659	−	0.0651419i
$167$	1076.45	+	782.086i	0.498791	+	0.362393i	0.808555	−	0.588421i	$-0.200250\pi$
$167$	1076.45	+	782.086i	0.498791	+	0.362393i	−0.309764	+	0.950813i	$0.600250\pi$
$168$	−3401.22			−1.56196
$169$	1363.78	+	990.845i	0.620747	+	0.450999i
$170$	−520.154	−	4158.82i	−0.234671	−	1.87627i
$171$	−1231.26	+	894.560i	−0.550623	+	0.400051i
$172$	−60.2968	+	43.8082i	−0.0267302	+	0.0194206i
$173$	−181.390	−	558.261i	−0.0797157	−	0.245340i	0.903254	−	0.429106i	$-0.141171\pi$
$173$	−181.390	−	558.261i	−0.0797157	−	0.245340i	−0.982970	+	0.183766i	$0.941171\pi$
$174$	80.9525			0.0352701
$175$	−1844.97	+	2218.99i	−0.796953	+	0.958512i
$176$	2258.17			0.967135
$177$	−886.419	−	2728.12i	−0.376426	−	1.15852i
$178$	−1558.34	+	1132.20i	−0.656193	+	0.476752i
$179$	−318.972	+	231.747i	−0.133191	+	0.0967686i	−0.652386	−	0.757887i	$-0.726232\pi$
$179$	−318.972	+	231.747i	−0.133191	+	0.0967686i	0.519195	+	0.854656i	$0.326232\pi$
$180$	−87.5968	−	93.5126i	−0.0362726	−	0.0387223i
$181$	−1828.34	−	1328.37i	−0.750826	−	0.545507i	0.145257	−	0.989394i	$-0.453599\pi$
$181$	−1828.34	−	1328.37i	−0.750826	−	0.545507i	−0.896083	+	0.443887i	$0.853599\pi$
$182$	−1530.88			−0.623495
$183$	−2228.36	−	1619.00i	−0.900136	−	0.653987i
$184$	−73.0532	+	224.835i	−0.0292693	+	0.0900817i
$185$	−360.557	−	2882.78i	−0.143290	−	1.14565i
$186$	−335.973	−	1034.02i	−0.132445	−	0.407623i
$187$	1303.30	−	4011.13i	0.509660	−	1.56857i
$188$	−84.5679	+	260.273i	−0.0328072	+	0.100970i
$189$	−383.065	−	1178.95i	−0.147428	−	0.453736i
$190$	324.391	+	2593.62i	0.123862	+	0.990319i
$191$	−179.253	+	551.684i	−0.0679073	+	0.208997i	−0.979252	−	0.202647i	$-0.935045\pi$
$191$	−179.253	+	551.684i	−0.0679073	+	0.208997i	0.911344	+	0.411645i	$0.135045\pi$
$192$	2570.63	+	1867.67i	0.966246	+	0.702019i
$193$	−484.411			−0.180667			−0.0903333	−	0.995912i	$-0.528793\pi$
$193$	−484.411			−0.180667			−0.0903333	+	0.995912i	$0.528793\pi$
$194$	126.856	+	92.1661i	0.0469470	+	0.0341090i
$195$	1173.33	+	1252.57i	0.430892	+	0.459992i
$196$	−92.2664	+	67.0355i	−0.0336248	+	0.0244298i
$197$	718.404	−	521.951i	0.259818	−	0.188769i	−0.450249	−	0.892903i	$-0.648665\pi$
$197$	718.404	−	521.951i	0.259818	−	0.188769i	0.710067	+	0.704134i	$0.248665\pi$
$198$	−570.820	−	1756.80i	−0.204881	−	0.630558i
$199$	2561.69			0.912530			0.456265	−	0.889844i	$-0.349187\pi$
$199$	2561.69			0.912530			0.456265	+	0.889844i	$0.349187\pi$
$200$	2629.01	−	668.085i	0.929495	−	0.236204i
$201$	−4067.73			−1.42744
$202$	−88.6870	−	272.950i	−0.0308911	−	0.0950729i
$203$	−75.9414	+	55.1747i	−0.0262564	+	0.0190764i
$204$	−421.472	+	306.218i	−0.144652	+	0.105096i
$205$	149.281	+	1193.55i	0.0508596	+	0.406641i
$206$	3252.13	+	2362.81i	1.09993	+	0.799149i
$207$	207.976			0.0698325
$208$	1252.01	+	909.639i	0.417362	+	0.303231i
$209$	−812.792	+	2501.52i	−0.269005	+	0.827911i
$210$	5046.74	+	969.190i	1.65837	+	0.318478i
$211$	−1834.57	−	5646.23i	−0.598565	−	1.84219i	−0.536116	−	0.844144i	$-0.680109\pi$
$211$	−1834.57	−	5646.23i	−0.598565	−	1.84219i	−0.0624487	−	0.998048i	$-0.519891\pi$
$212$	128.333	−	394.970i	0.0415754	−	0.127956i
$213$	−1903.61	+	5858.71i	−0.612363	+	1.88466i
$214$	−142.680	−	439.124i	−0.0455767	−	0.140271i
$215$	−1256.71	+	589.464i	−0.398636	+	0.186982i
$216$	−360.070	+	1108.18i	−0.113424	+	0.349084i
$217$	1019.93	+	741.024i	0.319067	+	0.231815i
$218$	2356.90			0.732246
$219$	−3887.41	−	2824.37i	−1.19948	−	0.871476i
$220$	−217.470	−	41.7635i	−0.0666446	−	0.0127986i
$221$	2338.37	−	1698.92i	0.711745	−	0.517113i
$222$	−4185.52	+	3040.96i	−1.26538	+	0.919350i
$223$	1254.79	+	3861.86i	0.376803	+	1.15968i	0.942254	+	0.334899i	$0.108702\pi$
$223$	1254.79	+	3861.86i	0.376803	+	1.15968i	−0.565451	+	0.824782i	$0.691298\pi$
$224$	625.894			0.186693
$225$	−1273.69	−	2018.03i	−0.377389	−	0.597935i
$226$	−1955.13			−0.575458
$227$	−104.511	−	321.653i	−0.0305580	−	0.0940479i	0.934614	−	0.355663i	$-0.115745\pi$
$227$	−104.511	−	321.653i	−0.0305580	−	0.0940479i	−0.965172	+	0.261615i	$0.915745\pi$
$228$	262.848	−	190.971i	0.0763489	−	0.0554708i
$229$	3014.84	−	2190.41i	0.869983	−	0.632079i	−0.0605996	−	0.998162i	$-0.519301\pi$
$229$	3014.84	−	2190.41i	0.869983	−	0.632079i	0.930582	+	0.366083i	$0.119301\pi$
$230$	172.464	−	312.794i	0.0494433	−	0.0896741i
$231$	4183.64	+	3039.59i	1.19161	+	0.865759i
$232$	88.2340			0.0249692
$233$	−539.192	−	391.746i	−0.151604	−	0.110147i	0.509398	−	0.860531i	$-0.329868\pi$
$233$	−539.192	−	391.746i	−0.151604	−	0.110147i	−0.661001	+	0.750385i	$0.729868\pi$
$234$	391.195	−	1203.97i	0.109287	−	0.336351i
$235$	−2460.95	+	4463.37i	−0.683127	+	1.23897i
$236$	78.3803	+	241.230i	0.0216192	+	0.0665370i
$237$	181.330	−	558.076i	0.0496989	−	0.152958i
$238$	2674.38	−	8230.90i	0.728380	−	2.24172i
$239$	−104.814	−	322.586i	−0.0283677	−	0.0873068i	0.935870	−	0.352345i	$-0.114616\pi$
$239$	−104.814	−	322.586i	−0.0283677	−	0.0873068i	−0.964238	+	0.265038i	$0.914616\pi$
$240$	−3551.54	−	3791.39i	−0.955212	−	1.01972i
$241$	−1482.91	+	4563.93i	−0.396360	+	1.21987i	0.531538	+	0.847034i	$0.321614\pi$
$241$	−1482.91	+	4563.93i	−0.396360	+	1.21987i	−0.927898	+	0.372835i	$0.878386\pi$
$242$	575.122	+	417.851i	0.152770	+	0.110994i
$243$	4524.52			1.19444
$244$	197.039	+	143.157i	0.0516974	+	0.0375603i
$245$	−1923.02	+	901.999i	−0.501458	+	0.235211i
$246$	1732.92	−	1259.04i	0.449135	−	0.326316i
$247$	−1458.31	+	1059.52i	−0.375667	+	0.272938i
$248$	−366.193	−	1127.03i	−0.0937633	−	0.288574i
$249$	−339.130			−0.0863113
$250$	−4091.31	+	242.163i	−1.03503	+	0.0612629i
$251$	5089.00			1.27974			0.639870	−	0.768483i	$-0.278988\pi$
$251$	5089.00			1.27974			0.639870	+	0.768483i	$0.278988\pi$
$252$	−81.7600	−	251.631i	−0.0204381	−	0.0629019i
$253$	290.788	−	211.270i	0.0722597	−	0.0524997i
$254$	−946.620	+	687.759i	−0.233843	+	0.169897i
$255$	−8784.33	+	4120.33i	−2.15724	+	1.01186i
$256$	−741.880	−	539.007i	−0.181123	−	0.131594i
$257$	196.116			0.0476007			0.0238003	−	0.999717i	$-0.492423\pi$
$257$	196.116			0.0476007			0.0238003	+	0.999717i	$0.492423\pi$
$258$	1999.79	+	1452.93i	0.482563	+	0.350603i
$259$	1853.81	−	5705.44i	0.444749	−	1.36880i
$260$	−103.750	−	110.757i	−0.0247473	−	0.0264186i
$261$	−23.9869	−	73.8241i	−0.00568871	−	0.0175080i
$262$	90.3993	−	278.221i	0.0213164	−	0.0656051i
$263$	1766.86	−	5437.83i	0.414255	−	1.27495i	−0.498660	−	0.866798i	$-0.666174\pi$
$263$	1766.86	−	5437.83i	0.414255	−	1.27495i	0.912915	−	0.408149i	$-0.133826\pi$
$264$	−1502.08	−	4622.93i	−0.350177	−	1.07773i
$265$	3734.55	−	6773.25i	0.865703	−	1.57010i
$266$	−1667.86	+	5133.14i	−0.384448	+	1.18321i
$267$	3607.55	+	2621.04i	0.826885	+	0.600767i
$268$	359.683			0.0819819
$269$	1561.66	+	1134.61i	0.353963	+	0.257169i	0.750530	−	0.660837i	$-0.229798\pi$
$269$	1561.66	+	1134.61i	0.353963	+	0.257169i	−0.396567	+	0.918006i	$0.629798\pi$
$270$	850.055	−	1541.72i	0.191603	−	0.347505i
$271$	−2609.72	+	1896.08i	−0.584980	+	0.425013i	−0.840516	−	0.541787i	$-0.817748\pi$
$271$	−2609.72	+	1896.08i	−0.584980	+	0.425013i	0.255536	+	0.966799i	$0.417748\pi$
$272$	−7077.98	+	5142.45i	−1.57781	+	1.14635i
$273$	1095.15	+	3370.52i	0.242789	+	0.747227i
$274$	−8434.06			−1.85956
$275$	−3830.84	−	1527.71i	−0.840031	−	0.334998i
$276$	−44.3987			−0.00968292
$277$	−1076.72	−	3313.79i	−0.233551	−	0.718795i	−0.997310	−	0.0732945i	$-0.976649\pi$
$277$	−1076.72	−	3313.79i	−0.233551	−	0.718795i	0.763760	−	0.645501i	$-0.223351\pi$
$278$	−2545.32	+	1849.28i	−0.549130	+	0.398967i
$279$	−843.416	+	612.778i	−0.180982	+	0.131491i
$280$	5500.69	+	1056.37i	1.17403	+	0.225464i
$281$	−5479.65	−	3981.20i	−1.16330	−	0.845190i	−0.173112	−	0.984902i	$-0.555382\pi$
$281$	−5479.65	−	3981.20i	−1.16330	−	0.845190i	−0.990192	+	0.139712i	$0.955382\pi$
$282$	9076.37			1.91663
$283$	−5888.07	−	4277.94i	−1.23678	−	0.898576i	−0.239403	−	0.970920i	$-0.576952\pi$
$283$	−5888.07	−	4277.94i	−1.23678	−	0.898576i	−0.997380	+	0.0723447i	$0.976952\pi$
$284$	168.324	−	518.048i	0.0351697	−	0.108241i
$285$	5478.29	−	2569.61i	1.13862	−	0.534073i
$286$	−676.081	−	2080.76i	−0.139782	−	0.430203i
$287$	−767.530	+	2362.21i	−0.157860	+	0.485844i
$288$	−159.939	+	492.241i	−0.0327239	+	0.100714i
$289$	3531.19	+	10867.9i	0.718743	+	2.21206i
$290$	−130.922	−	25.1426i	−0.0265104	−	0.00509112i
$291$	112.172	−	345.231i	0.0225968	−	0.0695457i
$292$	343.739	+	249.741i	0.0688897	+	0.0500513i
$293$	7447.74			1.48499			0.742494	−	0.669853i	$-0.233643\pi$
$293$	7447.74			1.48499			0.742494	+	0.669853i	$0.233643\pi$
$294$	3060.08	+	2223.28i	0.607032	+	0.441035i
$295$	586.268	+	4687.42i	0.115708	+	0.925125i
$296$	−4562.00	+	3314.48i	−0.895813	+	0.650846i
$297$	1433.26	−	1041.32i	0.280020	−	0.203447i
$298$	1397.51	+	4301.10i	0.271663	+	0.836093i
$299$	246.328			0.0476438
$300$	271.907	+	430.809i	0.0523285	+	0.0829092i
$301$	−2866.27			−0.548867
$302$	244.278	+	751.812i	0.0465452	+	0.143251i
$303$	−537.509	+	390.523i	−0.101911	+	0.0740428i
$304$	4414.13	−	3207.05i	0.832789	−	0.605057i
$305$	3101.02	+	3310.45i	0.582177	+	0.621495i
$306$	5789.88	+	4206.59i	1.08165	+	0.785866i
$307$	10393.1			1.93214			0.966068	−	0.258290i	$-0.0831589\pi$
$307$	10393.1			1.93214			0.966068	+	0.258290i	$0.0831589\pi$
$308$	−369.932	−	268.771i	−0.0684378	−	0.0497230i
$309$	2875.70	−	8850.48i	0.529426	−	1.62941i
$310$	222.209	+	1776.64i	0.0407117	+	0.325504i
$311$	−554.724	−	1707.26i	−0.101143	−	0.311286i	0.887663	−	0.460494i	$-0.152328\pi$
$311$	−554.724	−	1707.26i	−0.101143	−	0.311286i	−0.988806	+	0.149208i	$0.952328\pi$
$312$	1029.41	−	3168.19i	0.186791	−	0.574883i
$313$	−1045.63	+	3218.13i	−0.188826	+	0.581148i	−0.999993	−	0.00366673i	$-0.998833\pi$
$313$	−1045.63	+	3218.13i	−0.188826	+	0.581148i	0.811167	+	0.584815i	$0.198833\pi$
$314$	−676.740	−	2082.79i	−0.121626	−	0.374327i
$315$	−611.547	−	4889.53i	−0.109387	−	0.874583i
$316$	−16.0338	+	49.3471i	−0.00285435	+	0.00878478i
$317$	−116.264	−	84.4709i	−0.0205995	−	0.0149664i	0.577438	−	0.816435i	$-0.304053\pi$
$317$	−116.264	−	84.4709i	−0.0205995	−	0.0149664i	−0.598037	+	0.801468i	$0.704053\pi$
$318$	−13773.6			−2.42888
$319$	−108.531	−	78.8527i	−0.0190489	−	0.0138398i
$320$	−3577.34	−	3818.93i	−0.624935	−	0.667140i
$321$	−864.748	+	628.276i	−0.150360	+	0.109243i
$322$	596.701	−	433.529i	0.103270	−	0.0750299i
$323$	−3149.02	−	9691.67i	−0.542464	−	1.66953i
$324$	−528.268			−0.0905809
$325$	−1508.56	−	2390.17i	−0.257477	−	0.407946i
$326$	−905.091			−0.153768
$327$	−1686.07	−	5189.18i	−0.285137	−	0.877560i
$328$	1888.80	−	1372.29i	0.317961	−	0.231013i
$329$	−8514.54	+	6186.17i	−1.42681	+	1.03664i
$330$	911.474	+	7287.56i	0.152045	+	1.21566i
$331$	3825.63	+	2779.48i	0.635273	+	0.461553i	0.858223	−	0.513277i	$-0.171569\pi$
$331$	3825.63	+	2779.48i	0.635273	+	0.461553i	−0.222950	+	0.974830i	$0.571569\pi$
$332$	29.9871			0.00495710
$333$	4013.39	+	2915.90i	0.660457	+	0.479850i
$334$	−1205.80	+	3711.07i	−0.197540	+	0.607966i
$335$	6578.63	+	1263.38i	1.07292	+	0.206047i
$336$	−3314.89	−	10202.2i	−0.538221	−	1.65647i
$337$	−669.211	+	2059.62i	−0.108173	+	0.332922i	−0.990462	−	0.137786i	$-0.956001\pi$
$337$	−669.211	+	2059.62i	−0.108173	+	0.332922i	0.882289	+	0.470708i	$0.156001\pi$
$338$	−1527.66	+	4701.65i	−0.245839	+	0.756616i
$339$	1398.65	+	4304.61i	0.224084	+	0.689658i
$340$	776.742	−	364.334i	0.123896	−	0.0581141i
$341$	−556.766	+	1713.55i	−0.0884181	+	0.272123i
$342$	−3610.82	−	2623.41i	−0.570909	−	0.414789i
$343$	3532.65			0.556109
$344$	2179.66	+	1583.62i	0.341627	+	0.248206i
$345$	−812.054	−	155.949i	−0.126723	−	0.0243363i
$346$	1392.66	−	1011.83i	0.216387	−	0.157214i
$347$	−4639.89	+	3371.08i	−0.717817	+	0.521525i	−0.885686	−	0.464285i	$-0.846311\pi$
$347$	−4639.89	+	3371.08i	−0.717817	+	0.521525i	0.167869	+	0.985809i	$0.446311\pi$
$348$	5.12072	+	15.7600i	0.000788791	+	0.00242765i
$349$	−8077.21			−1.23886			−0.619431	−	0.785051i	$-0.712637\pi$
$349$	−8077.21			−1.23886			−0.619431	+	0.785051i	$0.712637\pi$
$350$	−7860.94	−	3134.89i	−1.20053	−	0.478762i
$351$	1214.12			0.184629
$352$	276.414	+	850.714i	0.0418549	+	0.128816i
$353$	−3016.92	+	2191.92i	−0.454885	+	0.330493i	−0.791521	−	0.611142i	$-0.790711\pi$
$353$	−3016.92	+	2191.92i	−0.454885	+	0.330493i	0.336637	+	0.941635i	$0.390711\pi$
$354$	6805.68	−	4944.61i	1.02180	−	0.742382i
$355$	4898.28	−	8883.90i	0.732321	−	1.32819i
$356$	−318.992	−	231.761i	−0.0474903	−	0.0345037i
$357$	−20035.1			−2.97023
$358$	−935.428	−	679.628i	−0.138097	−	0.100334i
$359$	−2778.12	+	8550.19i	−0.408423	+	1.25700i	0.509580	+	0.860423i	$0.329801\pi$
$359$	−2778.12	+	8550.19i	−0.408423	+	1.25700i	−0.918003	+	0.396573i	$0.870199\pi$
$360$	−2236.42	+	4056.14i	−0.327416	+	0.593826i
$361$	−155.686	−	479.152i	−0.0226981	−	0.0698575i
$362$	2048.04	−	6303.22i	0.297355	−	0.915166i
$363$	508.552	−	1565.16i	0.0735319	−	0.226308i
$364$	−96.8369	−	298.033i	−0.0139440	−	0.0429154i
$365$	5409.79	+	5775.14i	0.775785	+	0.828178i
$366$	2496.13	−	7682.29i	0.356488	−	1.09716i
$367$	−2587.97	−	1880.27i	−0.368096	−	0.267437i	0.388325	−	0.921522i	$-0.373054\pi$
$367$	−2587.97	−	1880.27i	−0.368096	−	0.267437i	−0.756421	+	0.654085i	$0.773054\pi$
$368$	−745.607			−0.105618
$369$	−1661.66	−	1207.26i	−0.234424	−	0.170319i
$370$	7713.59	−	3618.09i	1.08381	−	0.508367i
$371$	12921.0	−	9387.64i	1.80815	−	1.31370i
$372$	180.052	−	130.816i	0.0250948	−	0.0182325i
$373$	1508.05	+	4641.29i	0.209340	+	0.644282i	0.999507	+	0.0313905i	$0.00999356\pi$
$373$	1508.05	+	4641.29i	0.209340	+	0.644282i	−0.790167	+	0.612891i	$0.790006\pi$
$374$	12368.5			1.71006
$375$	3459.99	+	8834.58i	0.476461	+	1.21658i
$376$	9892.77			1.35686
$377$	−28.4102	−	87.4376i	−0.00388117	−	0.0119450i
$378$	2941.06	−	2136.81i	0.400190	−	0.290755i
$379$	−1685.85	+	1224.84i	−0.228486	+	0.166005i	−0.696138	−	0.717908i	$-0.745100\pi$
$379$	−1685.85	+	1224.84i	−0.228486	+	0.166005i	0.467652	+	0.883912i	$0.345100\pi$
$380$	−484.410	+	227.214i	−0.0653940	+	0.0306733i
$381$	2191.42	+	1592.16i	0.294672	+	0.214092i
$382$	−1701.14			−0.227849
$383$	−6355.68	−	4617.67i	−0.847938	−	0.616063i	0.0766388	−	0.997059i	$-0.475581\pi$
$383$	−6355.68	−	4617.67i	−0.847938	−	0.616063i	−0.924577	+	0.380996i	$0.875581\pi$
$384$	−3334.54	+	10262.7i	−0.443138	+	1.36384i
$385$	−5822.03	−	6215.22i	−0.770696	−	0.822745i
$386$	−438.989	−	1351.07i	−0.0578858	−	0.178154i
$387$	732.437	−	2254.21i	0.0962064	−	0.296093i
$388$	−9.91868	+	30.5266i	−0.00129780	+	0.00399420i
$389$	−1411.80	−	4345.07i	−0.184013	−	0.566333i	0.815917	−	0.578169i	$-0.196232\pi$
$389$	−1411.80	−	4345.07i	−0.184013	−	0.566333i	−0.999930	+	0.0118357i	$0.996232\pi$
$390$	−2430.23	+	4407.65i	−0.315537	+	0.572282i
$391$	−430.325	+	1324.41i	−0.0556585	+	0.171299i
$392$	3335.33	+	2423.26i	0.429744	+	0.312227i
$393$	−677.226			−0.0869250
$394$	2106.81	+	1530.69i	0.269390	+	0.195723i
$395$	−466.590	+	846.242i	−0.0594346	+	0.107795i
$396$	305.909	−	222.256i	0.0388195	−	0.0282040i
$397$	−11428.8	+	8303.49i	−1.44482	+	1.04972i	−0.457814	+	0.889048i	$0.651367\pi$
$397$	−11428.8	+	8303.49i	−1.44482	+	1.04972i	−0.987007	+	0.160676i	$0.948633\pi$
$398$	2321.49	+	7144.80i	0.292376	+	0.899841i
$399$	12494.8			1.56772
$400$	4566.25	+	7234.77i	0.570782	+	0.904346i
$401$	−8967.23			−1.11671			−0.558357	−	0.829601i	$-0.688568\pi$
$401$	−8967.23			−1.11671			−0.558357	+	0.829601i	$0.688568\pi$
$402$	−3686.31	−	11345.3i	−0.457354	−	1.40759i
$403$	−998.946	+	725.777i	−0.123477	+	0.0897110i
$404$	47.5285	−	34.5315i	0.00585304	−	0.00425249i
$405$	−9662.05	−	1855.53i	−1.18546	−	0.227659i
$406$	−222.708	−	161.807i	−0.0272237	−	0.0197792i
$407$	8573.53			1.04416
$408$	15235.8	+	11069.4i	1.84873	+	1.34318i
$409$	3544.85	−	10909.9i	0.428561	−	1.31898i	−0.470982	−	0.882143i	$-0.656100\pi$
$409$	3544.85	−	10909.9i	0.428561	−	1.31898i	0.899543	−	0.436832i	$-0.143900\pi$
$410$	−3193.65	+	1497.99i	−0.384690	+	0.180441i
$411$	6033.50	+	18569.2i	0.724114	+	2.22859i
$412$	−254.279	+	782.591i	−0.0304064	+	0.0935813i
$413$	−3014.31	+	9277.08i	−0.359139	+	1.10532i
$414$	188.474	+	580.065i	0.0223744	+	0.0688614i
$415$	548.466	+	105.329i	0.0648750	+	0.0124588i
$416$	−189.432	+	583.013i	−0.0223262	+	0.0687128i
$417$	5892.41	+	4281.09i	0.691973	+	0.502748i
$418$	−7713.55			−0.902588
$419$	−12212.5	−	8872.89i	−1.42391	−	1.03453i	−0.991110	−	0.133043i	$-0.957525\pi$
$419$	−12212.5	−	8872.89i	−1.42391	−	1.03453i	−0.432801	−	0.901489i	$-0.642475\pi$
$420$	130.553	+	1043.82i	0.0151674	+	0.121269i
$421$	6550.68	−	4759.35i	0.758339	−	0.550966i	−0.140061	−	0.990143i	$-0.544730\pi$
$421$	6550.68	−	4759.35i	0.758339	−	0.550966i	0.898400	+	0.439177i	$0.144730\pi$
$422$	14085.3	−	10233.6i	1.62479	−	1.18048i
$423$	−2689.41	−	8277.15i	−0.309134	−	0.951415i
$424$	−15012.5			−1.71951
$425$	15486.4	−	3935.41i	1.76753	−	0.449165i
$426$	−18065.6			−2.05465
$427$	2894.40	+	8908.03i	0.328032	+	1.00958i
$428$	76.4641	−	55.5544i	0.00863559	−	0.00627412i
$429$	−4097.56	+	2977.05i	−0.461147	+	0.335043i
$430$	−2782.94	−	2970.89i	−0.312105	−	0.333183i
$431$	−8532.88	−	6199.50i	−0.953629	−	0.692852i	−0.00196669	−	0.999998i	$-0.500626\pi$
$431$	−8532.88	−	6199.50i	−0.953629	−	0.692852i	−0.951662	+	0.307146i	$0.900626\pi$
$432$	−3675.00			−0.409290
$433$	−9807.46	−	7125.54i	−1.08849	−	0.790835i	−0.109347	−	0.994004i	$-0.534876\pi$
$433$	−9807.46	−	7125.54i	−1.08849	−	0.790835i	−0.979144	+	0.203169i	$0.934876\pi$
$434$	−1142.49	+	3516.23i	−0.126362	+	0.388904i
$435$	38.3019	+	306.237i	0.00422169	+	0.0337539i
$436$	149.088	+	458.846i	0.0163762	+	0.0504007i
$437$	268.369	−	825.956i	0.0293772	−	0.0904138i
$438$	4354.54	−	13401.9i	0.475041	−	1.46203i
$439$	−4264.20	−	13123.9i	−0.463598	−	1.42681i	−0.860738	−	0.509049i	$-0.829997\pi$
$439$	−4264.20	−	13123.9i	−0.463598	−	1.42681i	0.397140	−	0.917758i	$-0.370003\pi$
$440$	993.460	+	7943.06i	0.107639	+	0.860615i
$441$	1120.78	−	3449.40i	0.121021	−	0.372465i
$442$	6857.56	+	4982.31i	0.737966	+	0.536164i
$443$	4540.71			0.486988			0.243494	−	0.969902i	$-0.421706\pi$
$443$	4540.71			0.486988			0.243494	+	0.969902i	$0.421706\pi$
$444$	−856.777	−	622.485i	−0.0915785	−	0.0665356i
$445$	−5020.33	−	5359.38i	−0.534801	−	0.570919i
$446$	−9633.95	+	6999.47i	−1.02283	+	0.743127i
$447$	8469.95	−	6153.78i	0.896230	−	0.651150i
$448$	−3338.97	−	10276.3i	−0.352124	−	1.08373i
$449$	17013.4			1.78822			0.894110	−	0.447848i	$-0.147809\pi$
$449$	17013.4			1.78822			0.894110	+	0.447848i	$0.147809\pi$
$450$	4474.23	−	5381.24i	0.468704	−	0.563721i
$451$	−3549.68			−0.370617
$452$	−123.674	−	380.629i	−0.0128697	−	0.0396090i
$453$	1480.51	−	1075.65i	0.153555	−	0.111564i
$454$	802.410	−	582.985i	0.0829493	−	0.0602662i
$455$	−724.319	−	5791.18i	−0.0746299	−	0.596692i
$456$	−9501.67	−	6903.37i	−0.975782	−	0.708947i
$457$	260.393			0.0266535			0.0133268	−	0.999911i	$-0.495758\pi$
$457$	260.393			0.0266535			0.0133268	+	0.999911i	$0.495758\pi$
$458$	8841.40	+	6423.65i	0.902034	+	0.655366i
$459$	−2121.02	+	6527.82i	−0.215688	+	0.663818i
$460$	71.8047	+	13.7896i	0.00727807	+	0.00139770i
$461$	3313.69	+	10198.5i	0.334781	+	1.03035i	0.966830	+	0.255421i	$0.0822139\pi$
$461$	3313.69	+	10198.5i	0.334781	+	1.03035i	−0.632049	+	0.774928i	$0.717786\pi$
$462$	−4686.36	+	14423.1i	−0.471925	+	1.45243i
$463$	−4017.07	+	12363.3i	−0.403216	+	1.24097i	0.519159	+	0.854678i	$0.326245\pi$
$463$	−4017.07	+	12363.3i	−0.403216	+	1.24097i	−0.922375	+	0.386295i	$0.873755\pi$
$464$	85.9946	+	264.664i	0.00860387	+	0.0264800i
$465$	3752.65	−	1760.20i	0.374247	−	0.175542i
$466$	603.984	−	1858.87i	0.0600408	−	0.184787i
$467$	−6068.69	−	4409.16i	−0.601340	−	0.436899i	0.245014	−	0.969519i	$-0.421207\pi$
$467$	−6068.69	−	4409.16i	−0.601340	−	0.436899i	−0.846354	+	0.532621i	$0.821207\pi$
$468$	259.137			0.0255953
$469$	11190.7	+	8130.54i	1.10179	+	0.800497i
$470$	−14679.0	−	2818.99i	−1.44062	−	0.276660i
$471$	−4101.55	+	2979.95i	−0.401251	+	0.291526i
$472$	7417.84	−	5389.37i	0.723376	−	0.525564i
$473$	−1265.83	−	3895.83i	−0.123051	−	0.378712i
$474$	1720.85			0.166754
$475$	−9657.97	+	2454.29i	−0.932922	+	0.237075i
$476$	1771.58			0.170588
$477$	4081.23	+	12560.7i	0.391754	+	1.20569i
$478$	804.736	−	584.675i	0.0770037	−	0.0559464i
$479$	2637.83	−	1916.49i	0.251619	−	0.182812i	−0.454825	−	0.890581i	$-0.650298\pi$
$479$	2637.83	−	1916.49i	0.251619	−	0.182812i	0.706444	+	0.707769i	$0.250298\pi$
$480$	993.593	−	1802.05i	0.0944814	−	0.171359i
$481$	4753.48	+	3453.60i	0.450603	+	0.327382i
$482$	−14073.1			−1.32990
$483$	−1381.36	−	1003.62i	−0.130133	−	0.0945470i
$484$	−44.9680	+	138.397i	−0.00422314	+	0.0129975i
$485$	−288.637	+	523.493i	−0.0270233	+	0.0490115i
$486$	4100.27	+	12619.3i	0.382700	+	1.17783i
$487$	−2679.05	+	8245.28i	−0.249280	+	0.767206i	0.745623	+	0.666368i	$0.232152\pi$
$487$	−2679.05	+	8245.28i	−0.249280	+	0.767206i	−0.994903	+	0.100837i	$0.967848\pi$
$488$	2720.65	−	8373.30i	0.252373	−	0.776724i
$489$	647.478	+	1992.73i	0.0598773	+	0.184283i
$490$	−4258.46	−	4546.06i	−0.392608	−	0.419122i
$491$	−730.668	+	2248.76i	−0.0671580	+	0.206691i	−0.979004	−	0.203842i	$-0.934657\pi$
$491$	−730.668	+	2248.76i	−0.0671580	+	0.206691i	0.911846	+	0.410533i	$0.134657\pi$
$492$	354.730	+	257.727i	0.0325050	+	0.0236163i
$493$	519.749			0.0474813
$494$	−4276.67	−	3107.18i	−0.389507	−	0.282993i
$495$	6375.77	−	2990.58i	0.578928	−	0.271549i
$496$	3023.70	−	2196.85i	0.273726	−	0.198874i
$497$	16947.3	−	12313.0i	1.52956	−	1.11129i
$498$	−307.331	−	945.867i	−0.0276543	−	0.0851111i
$499$	−8407.18			−0.754223			−0.377111	−	0.926168i	$-0.623083\pi$
$499$	−8407.18			−0.754223			−0.377111	+	0.926168i	$0.623083\pi$
$500$	−305.944	−	781.185i	−0.0273645	−	0.0698713i
$501$	9033.24			0.805539
$502$	4611.81	+	14193.7i	0.410030	+	1.26194i
$503$	11463.0	−	8328.32i	1.01612	−	0.738254i	0.0506352	−	0.998717i	$-0.483875\pi$
$503$	11463.0	−	8328.32i	1.01612	−	0.738254i	0.965484	+	0.260464i	$0.0838754\pi$
$504$	−7737.68	+	5621.75i	−0.683857	+	0.496851i
$505$	990.589	−	464.640i	0.0872884	−	0.0409430i
$506$	852.774	+	619.576i	0.0749218	+	0.0544339i
$507$	11444.4			1.00250
$508$	−193.773	−	140.785i	−0.0169238	−	0.0122959i
$509$	5208.73	−	16030.8i	0.453581	−	1.39598i	−0.419212	−	0.907888i	$-0.637694\pi$
$509$	5208.73	−	16030.8i	0.453581	−	1.39598i	0.872793	−	0.488090i	$-0.162306\pi$
$510$	−19452.6	−	20766.4i	−1.68897	−	1.80304i
$511$	5049.32	+	15540.2i	0.437121	+	1.34532i
$512$	−3098.30	+	9535.59i	−0.267435	+	0.823081i
$513$	1322.76	−	4071.03i	0.113843	−	0.350371i
$514$	177.727	+	546.986i	0.0152513	+	0.0469387i
$515$	−7399.61	+	13420.5i	−0.633137	+	1.14831i
$516$	−156.360	+	481.228i	−0.0133399	+	0.0410560i
$517$	−12168.5	−	8840.95i	−1.03515	−	0.752078i
$518$	17593.0			1.49226
$519$	−3224.01	−	2342.38i	−0.272675	−	0.198110i
$520$	−2648.83	+	4804.11i	−0.223382	+	0.405142i
$521$	−7388.51	+	5368.07i	−0.621298	+	0.451400i	−0.853375	−	0.521298i	$-0.825448\pi$
$521$	−7388.51	+	5368.07i	−0.621298	+	0.451400i	0.232076	+	0.972698i	$0.425448\pi$
$522$	184.165	−	133.804i	0.0154419	−	0.0112192i
$523$	4037.14	+	12425.0i	0.337537	+	1.03883i	0.965459	+	0.260555i	$0.0839056\pi$
$523$	4037.14	+	12425.0i	0.337537	+	1.03883i	−0.627922	+	0.778276i	$0.716094\pi$
$524$	59.8827			0.00499235
$525$	−1278.55	+	19550.0i	−0.106287	+	1.62520i
$526$	16767.8			1.38995
$527$	−2157.09	−	6638.84i	−0.178300	−	0.548752i
$528$	12402.8	−	9011.20i	1.02228	−	0.742731i
$529$	9747.30	−	7081.83i	0.801126	−	0.582052i
$530$	22275.6	+	4277.87i	1.82564	+	0.350601i
$531$	−6525.79	−	4741.27i	−0.533325	−	0.387483i
$532$	−1104.83			−0.0900385
$533$	−1968.07	−	1429.89i	−0.159938	−	0.116202i
$534$	−4041.05	+	12437.1i	−0.327478	+	1.00787i
$535$	1593.67	−	747.515i	0.128785	−	0.0604073i
$536$	−4017.89	−	12365.8i	−0.323780	−	0.996493i
$537$	−827.152	+	2545.71i	−0.0664698	+	0.204573i
$538$	−1749.32	+	5383.84i	−0.140183	+	0.431439i
$539$	−1936.98	−	5961.41i	−0.154790	−	0.476394i
$540$	353.916	+	67.9670i	0.0282039	+	0.00541636i
$541$	4049.31	−	12462.5i	0.321799	−	0.990396i	−0.651066	−	0.759021i	$-0.725678\pi$
$541$	4049.31	−	12462.5i	0.321799	−	0.990396i	0.972865	−	0.231374i	$-0.0743222\pi$
$542$	−7653.35	−	5560.49i	−0.606531	−	0.440670i
$543$	−15342.9			−1.21257
$544$	−2803.69	−	2037.00i	−0.220969	−	0.160544i
$545$	1115.15	+	8915.98i	0.0876470	+	0.700768i
$546$	−8408.24	+	6108.94i	−0.659047	+	0.478825i
$547$	−13874.1	+	10080.1i	−1.08448	+	0.787923i	−0.978459	−	0.206441i	$-0.933812\pi$
$547$	−13874.1	+	10080.1i	−1.08448	+	0.787923i	−0.106024	+	0.994364i	$0.533812\pi$
$548$	−533.504	−	1641.96i	−0.0415879	−	0.127994i
$549$	−7745.45			−0.602127
$550$	789.304	−	12069.0i	0.0611928	−	0.935684i
$551$	−324.138			−0.0250612
$552$	495.960	+	1526.41i	0.0382418	+	0.117696i
$553$	−1614.33	+	1172.88i	−0.124138	+	0.0901916i
$554$	8266.72	−	6006.12i	0.633970	−	0.460606i
$555$	−13484.0	−	14394.7i	−1.03129	−	1.10094i
$556$	−521.028	−	378.549i	−0.0397419	−	0.0288742i
$557$	−2642.14			−0.200990			−0.100495	−	0.994938i	$-0.532043\pi$
$557$	−2642.14			−0.200990			−0.100495	+	0.994938i	$0.532043\pi$
$558$	−2473.43	−	1797.05i	−0.187650	−	0.136335i
$559$	867.502	−	2669.90i	0.0656376	−	0.202012i
$560$	2192.43	+	17529.3i	0.165441	+	1.32276i
$561$	−8848.12	−	27231.7i	−0.665896	−	2.04942i
$562$	6138.11	−	18891.2i	0.460713	−	1.41793i
$563$	−6044.68	+	18603.6i	−0.452491	+	1.39263i	0.421564	+	0.906799i	$0.361481\pi$
$563$	−6044.68	+	18603.6i	−0.452491	+	1.39263i	−0.874055	+	0.485827i	$0.838519\pi$
$564$	574.134	+	1767.00i	0.0428642	+	0.131922i
$565$	−925.053	−	7396.12i	−0.0688801	−	0.550721i
$566$	6595.61	−	20299.2i	0.489813	−	1.50749i
$567$	−16435.8	−	11941.3i	−1.21736	−	0.884461i
$568$	−19690.6			−1.45458
$569$	4013.66	+	2916.09i	0.295714	+	0.214849i	0.725742	−	0.687967i	$-0.241496\pi$
$569$	4013.66	+	2916.09i	0.295714	+	0.214849i	−0.430028	+	0.902815i	$0.641496\pi$
$570$	12131.5	+	12950.8i	0.891461	+	0.951666i
$571$	−8114.55	+	5895.57i	−0.594717	+	0.432087i	−0.844000	−	0.536344i	$-0.819805\pi$
$571$	−8114.55	+	5895.57i	−0.594717	+	0.432087i	0.249283	+	0.968431i	$0.419805\pi$
$572$	362.321	−	263.241i	0.0264849	−	0.0192424i
$573$	1216.95	+	3745.40i	0.0887242	+	0.273065i
$574$	−7284.00			−0.529666
$575$	1264.88	+	504.424i	0.0917374	+	0.0365842i
$576$	8935.13			0.646349
$577$	6944.95	+	21374.3i	0.501078	+	1.54216i	0.807266	+	0.590188i	$0.200946\pi$
$577$	6944.95	+	21374.3i	0.501078	+	1.54216i	−0.306188	+	0.951971i	$0.599054\pi$
$578$	−27111.5	+	19697.6i	−1.95102	+	1.41750i
$579$	−2660.60	+	1933.04i	−0.190968	+	0.138747i
$580$	−3.38679	−	27.0786i	−0.000242463	−	0.00193858i
$581$	932.981	+	677.850i	0.0666206	+	0.0484027i
$582$	1064.54			0.0758186
$583$	18466.0	+	13416.3i	1.31181	+	0.953082i
$584$	4746.22	−	14607.4i	0.336301	−	1.03503i
$585$	4739.63	+	910.211i	0.334974	+	0.0643292i
$586$	6749.38	+	20772.5i	0.475792	+	1.46434i
$587$	6336.07	−	19500.4i	0.445515	−	1.37115i	−0.436403	−	0.899751i	$-0.643748\pi$
$587$	6336.07	−	19500.4i	0.445515	−	1.37115i	0.881918	−	0.471403i	$-0.156252\pi$
$588$	−239.263	+	736.377i	−0.0167807	+	0.0516457i
$589$	1345.25	+	4140.26i	0.0941090	+	0.289638i
$590$	−12542.4	+	5883.04i	−0.875187	+	0.410510i
$591$	1862.95	−	5733.57i	0.129664	−	0.399065i
$592$	−14388.2	−	10453.7i	−0.998907	−	0.725749i
$593$	−373.656			−0.0258756			−0.0129378	−	0.999916i	$-0.504118\pi$
$593$	−373.656			−0.0258756			−0.0129378	+	0.999916i	$0.504118\pi$
$594$	4203.21	+	3053.81i	0.290336	+	0.210942i
$595$	32402.2	+	6222.61i	2.23254	+	0.428743i
$596$	−748.944	+	544.139i	−0.0514730	+	0.0373973i
$597$	14069.9	−	10222.4i	0.964563	−	0.700796i
$598$	223.230	+	687.031i	0.0152651	+	0.0469813i
$599$	−2173.18			−0.148236			−0.0741182	−	0.997249i	$-0.523614\pi$
$599$	−2173.18			−0.148236			−0.0741182	+	0.997249i	$0.523614\pi$
$600$	11773.7	−	14160.5i	0.801098	−	0.963497i
$601$	14405.7			0.977739			0.488869	−	0.872357i	$-0.337409\pi$
$601$	14405.7			0.977739			0.488869	+	0.872357i	$0.337409\pi$
$602$	−2597.51	−	7994.30i	−0.175858	−	0.541235i
$603$	−9253.99	+	6723.42i	−0.624961	+	0.454061i
$604$	−130.912	+	95.1131i	−0.00881909	+	0.00640744i
$605$	−1308.58	+	2373.35i	−0.0879364	+	0.159488i
$606$	−1576.31	−	1145.26i	−0.105666	−	0.0767706i
$607$	−5142.91			−0.343895			−0.171948	−	0.985106i	$-0.555006\pi$
$607$	−5142.91			−0.343895			−0.171948	+	0.985106i	$0.555006\pi$
$608$	1748.50	+	1270.36i	0.116630	+	0.0847369i
$609$	−196.930	+	606.087i	−0.0131034	+	0.0403282i
$610$	−6422.92	+	11649.1i	−0.426322	+	0.773210i
$611$	−3185.35	−	9803.49i	−0.210909	−	0.649111i
$612$	−452.703	+	1393.28i	−0.0299010	+	0.0920258i
$613$	7778.26	−	23939.0i	0.512497	−	1.57730i	−0.275293	−	0.961360i	$-0.588775\pi$
$613$	7778.26	−	23939.0i	0.512497	−	1.57730i	0.787790	−	0.615944i	$-0.211225\pi$
$614$	9418.56	+	28987.3i	0.619059	+	1.90527i
$615$	5582.78	+	5959.81i	0.366048	+	0.390769i
$616$	−5107.89	+	15720.5i	−0.334095	+	1.02824i
$617$	15687.9	+	11397.9i	1.02362	+	0.743701i	0.967021	−	0.254697i	$-0.0819756\pi$
$617$	15687.9	+	11397.9i	1.02362	+	0.743701i	0.0565950	+	0.998397i	$0.481976\pi$
$618$	27290.9			1.77638
$619$	4465.49	+	3244.37i	0.289957	+	0.210666i	0.723249	−	0.690588i	$-0.242648\pi$
$619$	4465.49	+	3244.37i	0.289957	+	0.210666i	−0.433292	+	0.901254i	$0.642648\pi$
$620$	−331.823	+	155.643i	−0.0214941	+	0.0100819i
$621$	−473.236	+	343.826i	−0.0305802	+	0.0222178i
$622$	4259.01	−	3094.35i	0.274551	−	0.199473i
$623$	−4685.81	−	14421.4i	−0.301337	−	0.927421i
$624$	10506.5			0.674033
$625$	−2851.85	−	15362.5i	−0.182518	−	0.983202i
$626$	−9923.25			−0.633567
$627$	5518.07	+	16982.9i	0.351468	+	1.08171i
$628$	362.674	−	263.498i	0.0230450	−	0.0167432i
$629$	−26872.8	+	19524.2i	−1.70348	+	1.23765i
$630$	13083.2	−	6136.71i	0.827374	−	0.388083i
$631$	−5841.61	−	4244.18i	−0.368544	−	0.267763i	0.388063	−	0.921633i	$-0.373144\pi$
$631$	−5841.61	−	4244.18i	−0.368544	−	0.267763i	−0.756607	+	0.653870i	$0.773144\pi$
$632$	1875.64			0.118052
$633$	−32607.5	−	23690.7i	−2.04744	−	1.48756i
$634$	130.235	−	400.822i	0.00815820	−	0.0251083i
$635$	−3049.62	−	3255.58i	−0.190584	−	0.203455i
$636$	−871.260	−	2681.46i	−0.0543203	−	0.167181i
$637$	1327.45	−	4085.48i	0.0825677	−	0.254117i
$638$	121.573	−	374.163i	0.00754408	−	0.0232183i
$639$	5353.00	+	16474.8i	0.331395	+	1.01993i
$640$	8580.29	−	15561.9i	0.529947	−	0.961151i
$641$	−3909.89	+	12033.4i	−0.240923	+	0.741483i	0.755358	+	0.655313i	$0.227463\pi$
$641$	−3909.89	+	12033.4i	−0.240923	+	0.741483i	−0.996280	+	0.0861709i	$0.972537\pi$
$642$	−2535.98	−	1842.50i	−0.155899	−	0.113267i
$643$	−2621.20			−0.160762			−0.0803810	−	0.996764i	$-0.525614\pi$
$643$	−2621.20			−0.160762			−0.0803810	+	0.996764i	$0.525614\pi$
$644$	122.145	+	88.7435i	0.00747389	+	0.00543010i
$645$	−4550.14	+	8252.47i	−0.277770	+	0.503784i
$646$	24177.3	−	17565.8i	1.47251	−	1.06984i
$647$	−18737.8	+	13613.8i	−1.13858	+	0.827225i	−0.986920	−	0.161209i	$-0.948461\pi$
$647$	−18737.8	+	13613.8i	−1.13858	+	0.827225i	−0.151657	+	0.988433i	$0.548461\pi$
$648$	5901.08	+	18161.7i	0.357741	+	1.10101i
$649$	−13940.6			−0.843169
$650$	5299.29	−	6373.57i	0.319778	−	0.384603i
$651$	8558.96			0.515287
$652$	−57.2523	−	176.205i	−0.00343892	−	0.0105839i
$653$	−2605.80	+	1893.23i	−0.156161	+	0.113457i	−0.663122	−	0.748512i	$-0.730769\pi$
$653$	−2605.80	+	1893.23i	−0.156161	+	0.113457i	0.506961	+	0.861969i	$0.330769\pi$
$654$	12945.1	−	9405.20i	0.773999	−	0.562343i
$655$	1095.26	+	210.336i	0.0653363	+	0.0125474i
$656$	5957.14	+	4328.12i	0.354554	+	0.257599i
$657$	−13512.1			−0.802368
$658$	−24970.0	−	18141.7i	−1.47938	−	1.07483i
$659$	−3369.76	+	10371.1i	−0.199192	+	0.613048i	0.800711	+	0.599051i	$0.204456\pi$
$659$	−3369.76	+	10371.1i	−0.199192	+	0.613048i	−0.999902	+	0.0139970i	$0.995544\pi$
$660$	−1361.10	+	638.428i	−0.0802737	+	0.0376527i
$661$	−7834.53	−	24112.2i	−0.461010	−	1.41884i	−0.863932	−	0.503609i	$-0.832005\pi$
$661$	−7834.53	−	24112.2i	−0.461010	−	1.41884i	0.402921	−	0.915235i	$-0.367995\pi$
$662$	−4285.33	+	13188.9i	−0.251592	+	0.774321i
$663$	6063.80	−	18662.5i	0.355201	−	1.09320i
$664$	−334.975	−	1030.95i	−0.0195776	−	0.0602537i
$665$	−20207.4	−	3880.69i	−1.17836	−	0.226296i
$666$	−4495.65	+	13836.2i	−0.261566	+	0.805018i
$667$	35.8352	+	26.0358i	0.00208027	+	0.00151141i
$668$	−798.751			−0.0462644
$669$	22302.6	+	16203.8i	1.28889	+	0.936433i
$670$	2438.08	+	19493.3i	0.140584	+	1.12402i
$671$	−10829.5	+	7868.12i	−0.623055	+	0.452676i
$672$	3437.68	−	2497.62i	0.197339	−	0.143375i
$673$	5668.36	+	17445.4i	0.324664	+	0.999215i	0.971592	+	0.236663i	$0.0760537\pi$
$673$	5668.36	+	17445.4i	0.324664	+	0.999215i	−0.646927	+	0.762552i	$0.723946\pi$
$674$	−6350.94			−0.362951
$675$	6234.41	+	2486.24i	0.355500	+	0.141771i
$676$	−1011.96			−0.0575762
$677$	−2357.65	−	7256.09i	−0.133843	−	0.411926i	0.861565	−	0.507647i	$-0.169484\pi$
$677$	−2357.65	−	7256.09i	−0.133843	−	0.411926i	−0.995408	+	0.0957206i	$0.969484\pi$
$678$	−10738.5	+	7801.95i	−0.608271	+	0.441935i
$679$	−998.641	+	725.555i	−0.0564423	+	0.0410077i
$680$	−21202.4	−	22634.3i	−1.19570	−	1.27645i
$681$	−1857.58	−	1349.61i	−0.104526	−	0.0759429i
$682$	−5283.81			−0.296668
$683$	11840.9	+	8602.91i	0.663366	+	0.481963i	0.867798	−	0.496917i	$-0.165535\pi$
$683$	11840.9	+	8602.91i	0.663366	+	0.481963i	−0.204432	+	0.978881i	$0.565535\pi$
$684$	282.325	−	868.907i	0.0157821	−	0.0485723i
$685$	−3990.49	−	31905.4i	−0.222582	−	1.77962i
$686$	3201.40	+	9852.91i	0.178178	+	0.548376i
$687$	7818.01	−	24061.4i	0.434171	−	1.33624i
$688$	−2625.83	+	8081.48i	−0.145507	+	0.447825i
$689$	4833.83	+	14877.0i	0.267277	+	0.822595i
$690$	−300.953	−	2406.22i	−0.0166045	−	0.132758i
$691$	2186.27	−	6728.66i	0.120361	−	0.370434i	−0.872666	−	0.488318i	$-0.837611\pi$
$691$	2186.27	−	6728.66i	0.120361	−	0.370434i	0.993027	+	0.117883i	$0.0376108\pi$
$692$	285.078	+	207.122i	0.0156605	+	0.0113780i
$693$	14541.7			0.797105
$694$	−13607.1	−	9886.13i	−0.744262	−	0.540738i
$695$	−8199.99	−	8753.78i	−0.447545	−	0.477770i
$696$	484.620	−	352.097i	0.0263929	−	0.0191756i
$697$	11126.1	−	8083.58i	0.604635	−	0.439293i
$698$	−7319.82	−	22528.1i	−0.396933	−	1.22163i
$699$	−4524.74			−0.244838
$700$	113.054	−	1728.68i	0.00610435	−	0.0933400i
$701$	12304.1			0.662937			0.331468	−	0.943466i	$-0.392456\pi$
$701$	12304.1			0.662937			0.331468	+	0.943466i	$0.392456\pi$
$702$	1100.27	+	3386.29i	0.0591554	+	0.182062i
$703$	16759.0	−	12176.1i	0.899116	−	0.653246i
$704$	12492.9	−	9076.65i	0.668814	−	0.485922i
$705$	4294.40	+	34335.2i	0.229413	+	1.83424i
$706$	−8847.49	−	6428.08i	−0.471643	−	0.342669i
$707$	2259.31			0.120184
$708$	1393.12	+	1012.16i	0.0739503	+	0.0537281i
$709$	2825.10	−	8694.77i	0.149646	−	0.460562i	−0.847933	−	0.530103i	$-0.822153\pi$
$709$	2825.10	−	8694.77i	0.149646	−	0.460562i	0.997579	+	0.0695404i	$0.0221533\pi$
$710$	29217.0	+	5610.91i	1.54436	+	0.296583i
$711$	−509.904	−	1569.32i	−0.0268958	−	0.0827767i
$712$	−4404.53	+	13555.7i	−0.231835	+	0.713516i
$713$	183.834	−	565.783i	0.00965588	−	0.0297177i
$714$	−18156.5	−	55879.8i	−0.951664	−	2.92892i
$715$	7551.49	−	3542.06i	0.394979	−	0.185266i
$716$	73.1398	−	225.101i	0.00381754	−	0.0117492i
$717$	−1862.96	−	1353.52i	−0.0970343	−	0.0704995i
$718$	−26364.9			−1.37038
$719$	−2907.80	−	2112.64i	−0.150824	−	0.109580i	0.509814	−	0.860285i	$-0.329714\pi$
$719$	−2907.80	−	2112.64i	−0.150824	−	0.109580i	−0.660638	+	0.750704i	$0.729714\pi$
$720$	−14346.3	−	2755.11i	−0.742578	−	0.142607i
$721$	−25601.6	+	18600.6i	−1.32240	+	0.960781i
$722$	1195.31	−	868.447i	0.0616136	−	0.0447649i
$723$	10067.5	+	30984.7i	0.517863	+	1.59382i
$724$	1356.67			0.0696413
$725$	33.1681	−	507.164i	0.00169908	−	0.0259801i
$726$	4826.26			0.246721
$727$	−5718.08	−	17598.5i	−0.291708	−	0.897786i	−0.984307	−	0.176463i	$-0.943534\pi$
$727$	−5718.08	−	17598.5i	−0.291708	−	0.897786i	0.692599	−	0.721323i	$-0.256466\pi$
$728$	−9164.55	+	6658.43i	−0.466567	+	0.338981i
$729$	5628.61	−	4089.43i	0.285963	−	0.207764i
$730$	−11204.9	+	20322.0i	−0.568099	+	1.03035i
$731$	12839.5	+	9328.42i	0.649637	+	0.471989i
$732$	1653.50			0.0834904
$733$	28255.0	+	20528.5i	1.42377	+	1.03443i	0.991135	+	0.132858i	$0.0424156\pi$
$733$	28255.0	+	20528.5i	1.42377	+	1.03443i	0.432634	+	0.901570i	$0.357584\pi$
$734$	2898.96	−	8922.07i	0.145780	−	0.448664i
$735$	−6962.64	+	12628.0i	−0.349416	+	0.633727i
$736$	−91.2669	−	280.891i	−0.00457085	−	0.0140676i
$737$	−6108.85	+	18801.1i	−0.305322	+	0.939685i
$738$	1861.33	−	5728.58i	0.0928408	−	0.285734i
$739$	−6001.98	−	18472.2i	−0.298764	−	0.919500i	−0.981931	−	0.189238i	$-0.939398\pi$
$739$	−6001.98	−	18472.2i	−0.298764	−	0.919500i	0.683168	−	0.730262i	$-0.260602\pi$
$740$	1192.31	+	1272.83i	0.0592298	+	0.0632299i
$741$	−3781.65	+	11638.7i	−0.187480	+	0.577003i
$742$	37892.4	+	27530.5i	1.87476	+	1.36210i
$743$	39704.0			1.96043			0.980214	−	0.197943i	$-0.0634260\pi$
$743$	39704.0			1.96043			0.980214	+	0.197943i	$0.0634260\pi$
$744$	−6508.69	−	4728.84i	−0.320726	−	0.233021i
$745$	−15609.5	+	7321.70i	−0.767634	+	0.360062i
$746$	−11578.4	+	8412.18i	−0.568250	+	0.412857i
$747$	−771.514	+	560.537i	−0.0377888	+	0.0274551i
$748$	782.382	+	2407.92i	0.0382443	+	0.117704i
$749$	3634.80			0.177320
$750$	−21504.9	+	17656.4i	−1.04700	+	0.859628i
$751$	−18656.7			−0.906515			−0.453258	−	0.891380i	$-0.649738\pi$
$751$	−18656.7			−0.906515			−0.453258	+	0.891380i	$0.649738\pi$
$752$	9641.69	+	29674.1i	0.467548	+	1.43897i
$753$	27951.0	−	20307.6i	1.35271	−	0.982802i
$754$	218.126	−	158.478i	0.0105354	−	0.00765440i
$755$	−2728.47	+	1279.80i	−0.131522	+	0.0616909i
$756$	602.037	+	437.405i	0.0289628	+	0.0210427i
$757$	34418.7			1.65253			0.826267	−	0.563279i	$-0.190460\pi$
$757$	34418.7			1.65253			0.826267	+	0.563279i	$0.190460\pi$
$758$	−4943.96	−	3592.00i	−0.236903	−	0.172120i
$759$	754.066	−	2320.78i	0.0360617	−	0.110987i
$760$	13222.7	+	14115.7i	0.631103	+	0.673724i
$761$	2868.97	+	8829.77i	0.136662	+	0.420603i	0.995845	−	0.0910659i	$-0.0290274\pi$
$761$	2868.97	+	8829.77i	0.136662	+	0.420603i	−0.859183	+	0.511669i	$0.829027\pi$
$762$	−2454.75	+	7554.95i	−0.116701	+	0.359169i
$763$	−5733.54	+	17646.0i	−0.272042	+	0.837259i
$764$	−107.607	−	331.182i	−0.00509568	−	0.0156829i
$765$	−13173.8	+	23893.0i	−0.622614	+	1.12922i
$766$	7119.41	−	21911.3i	0.335816	−	1.03353i
$767$	−7729.18	−	5615.58i	−0.363865	−	0.264363i
$768$	−6225.64			−0.292511
$769$	−7267.60	−	5280.22i	−0.340802	−	0.247607i	0.404198	−	0.914671i	$-0.367551\pi$
$769$	−7267.60	−	5280.22i	−0.340802	−	0.247607i	−0.745000	+	0.667064i	$0.767551\pi$
$770$	12058.7	−	21870.6i	0.564372	−	1.02359i
$771$	1077.15	−	782.599i	0.0503149	−	0.0365559i
$772$	235.260	−	170.926i	0.0109678	−	0.00796861i
$773$	−12651.6	−	38937.5i	−0.588674	−	1.81175i	−0.583985	−	0.811764i	$-0.698507\pi$
$773$	−12651.6	−	38937.5i	−0.588674	−	1.81175i	−0.00468915	−	0.999989i	$-0.501493\pi$
$774$	6950.96			0.322800
$775$	−6615.75	+	1681.20i	−0.306638	+	0.0779231i
$776$	1160.29			0.0536752
$777$	−12585.6	−	38734.4i	−0.581087	−	1.78840i
$778$	10839.4	−	7875.27i	0.499500	−	0.362908i
$779$	−6938.71	+	5041.27i	−0.319134	+	0.231864i
$780$	−1011.81	−	194.312i	−0.0464471	−	0.00891983i
$781$	24220.2	+	17597.0i	1.10969	+	0.806238i
$782$	−4083.87			−0.186750
$783$	176.627	+	128.327i	0.00806147	+	0.00585700i
$784$	−4018.06	+	12366.3i	−0.183038	+	0.563334i
$785$	7558.85	−	3545.51i	0.343677	−	0.161203i
$786$	−613.724	−	1888.85i	−0.0278509	−	0.0857162i
$787$	−9825.58	+	30240.0i	−0.445037	+	1.36968i	0.437407	+	0.899264i	$0.355897\pi$
$787$	−9825.58	+	30240.0i	−0.445037	+	1.36968i	−0.882443	+	0.470418i	$0.844103\pi$
$788$	−164.729	+	506.983i	−0.00744698	+	0.0229194i
$789$	−11995.3	−	36917.6i	−0.541245	−	1.66578i
$790$	−2783.09	−	534.472i	−0.125339	−	0.0240704i
$791$	4756.18	−	14638.0i	0.213793	−	0.657987i
$792$	−11058.3	−	8034.31i	−0.496135	−	0.360463i
$793$	−9173.74			−0.410806
$794$	−33516.4	−	24351.1i	−1.49805	−	1.08840i
$795$	−6516.83	−	52104.3i	−0.290727	−	2.32447i
$796$	−1244.11	+	903.902i	−0.0553976	+	0.0402487i
$797$	3984.77	−	2895.11i	0.177099	−	0.128670i	−0.495704	−	0.868491i	$-0.665090\pi$
$797$	3984.77	−	2895.11i	0.177099	−	0.128670i	0.672803	+	0.739821i	$0.265090\pi$
$798$	11323.1	+	34849.1i	0.502300	+	1.54592i
$799$	58274.1			2.58021
$800$	−2166.60	+	2605.82i	−0.0957511	+	0.115162i
$801$	12539.3			0.553127
$802$	−8126.39	−	25010.5i	−0.357796	−	1.10118i
$803$	−18892.3	+	13726.1i	−0.830256	+	0.603216i
$804$	1975.54	−	1435.31i	0.0866566	−	0.0629597i
$805$	1922.33	+	2052.15i	0.0841655	+	0.0898496i
$806$	−2929.54	−	2128.43i	−0.128026	−	0.0930160i
$807$	13105.0			0.571645
$808$	−1718.10	−	1248.27i	−0.0748052	−	0.0543491i
$809$	−3212.47	+	9886.98i	−0.139610	+	0.429676i	−0.996279	−	0.0861917i	$-0.972530\pi$
$809$	−3212.47	+	9886.98i	−0.139610	+	0.429676i	0.856669	+	0.515867i	$0.172530\pi$
$810$	−3580.82	−	28629.9i	−0.155330	−	1.24192i
$811$	−5579.09	−	17170.7i	−0.241564	−	0.743458i	−0.996183	−	0.0872941i	$-0.972178\pi$
$811$	−5579.09	−	17170.7i	−0.241564	−	0.743458i	0.754618	−	0.656164i	$-0.227822\pi$
$812$	17.4132	−	53.5924i	0.000752567	−	0.00231616i
$813$	−6767.48	+	20828.2i	−0.291938	+	0.898494i
$814$	7769.60	+	23912.4i	0.334551	+	1.02964i
$815$	−428.235	−	3423.89i	−0.0184054	−	0.147158i
$816$	−18354.5	+	56489.2i	−0.787420	+	2.42343i
$817$	−8007.24	−	5817.60i	−0.342886	−	0.249121i
$818$	33641.3			1.43795
$819$	8062.45	+	5857.71i	0.343986	+	0.249921i
$820$	−493.649	−	526.988i	−0.0210231	−	0.0224429i
$821$	23831.0	−	17314.2i	1.01304	−	0.736018i	0.0481966	−	0.998838i	$-0.484653\pi$
$821$	23831.0	−	17314.2i	1.01304	−	0.736018i	0.964845	+	0.262820i	$0.0846526\pi$
$822$	−46323.6	+	33656.0i	−1.96560	+	1.42809i
$823$	−10379.1	−	31943.7i	−0.439604	−	1.35296i	−0.888294	−	0.459275i	$-0.848109\pi$
$823$	−10379.1	−	31943.7i	−0.439604	−	1.35296i	0.448690	−	0.893687i	$-0.351891\pi$
$824$	29745.6			1.25757
$825$	−27137.0	+	6896.07i	−1.14520	+	0.291019i
$826$	−28606.3			−1.20501
$827$	−5545.46	−	17067.2i	−0.233174	−	0.717634i	−0.997358	−	0.0726371i	$-0.976859\pi$
$827$	−5545.46	−	17067.2i	−0.233174	−	0.717634i	0.764185	−	0.644997i	$-0.223141\pi$
$828$	−101.006	+	73.3850i	−0.00423937	+	0.00308008i
$829$	−10695.1	+	7770.43i	−0.448077	+	0.325547i	−0.788836	−	0.614604i	$-0.789316\pi$
$829$	−10695.1	+	7770.43i	−0.448077	+	0.325547i	0.340759	+	0.940151i	$0.389316\pi$
$830$	203.265	+	1625.18i	0.00850053	+	0.0679647i
$831$	−19137.4	−	13904.2i	−0.798882	−	0.580421i
$832$	10582.8			0.440977
$833$	19647.0	+	14274.4i	0.817200	+	0.593731i
$834$	−6600.47	+	20314.2i	−0.274048	+	0.843432i
$835$	−14609.2	−	2805.59i	−0.605476	−	0.116277i
$836$	−487.927	−	1501.69i	−0.0201858	−	0.0621255i
$837$	906.095	−	2788.67i	0.0374184	−	0.115162i
$838$	13680.0	−	42102.7i	0.563923	−	1.73558i
$839$	10547.9	+	32463.0i	0.434032	+	1.33581i	0.894075	+	0.447917i	$0.147834\pi$
$839$	10547.9	+	32463.0i	0.434032	+	1.33581i	−0.460043	+	0.887897i	$0.652166\pi$
$840$	34427.6	−	16148.4i	1.41413	−	0.663302i
$841$	−7531.51	+	23179.6i	−0.308808	+	0.950412i
$842$	19210.7	+	13957.4i	0.786277	+	0.571264i
$843$	−45983.6			−1.87872
$844$	2883.27	+	2094.82i	0.117590	+	0.0854345i
$845$	−18508.8	−	3554.47i	−0.753516	−	0.144707i
$846$	20648.5	−	15002.0i	0.839138	−	0.609670i
$847$	−4527.51	+	3289.43i	−0.183668	+	0.133443i
$848$	−14631.5	−	45031.0i	−0.592507	−	1.82355i
$849$	−49411.0			−1.99738
$850$	25010.5	+	39626.6i	1.00924	+	1.59904i
$851$	−2830.83			−0.114030
$852$	−1142.76	−	3517.04i	−0.0459510	−	0.141422i
$853$	−8629.78	+	6269.90i	−0.346399	+	0.251673i	−0.747357	−	0.664423i	$-0.768677\pi$
$853$	−8629.78	+	6269.90i	−0.346399	+	0.251673i	0.400958	+	0.916096i	$0.368677\pi$
$854$	−22222.4	+	16145.5i	−0.890438	+	0.646941i
$855$	8215.74	−	14900.7i	0.328623	−	0.596015i
$856$	−2764.09	−	2008.23i	−0.110368	−	0.0801868i
$857$	−36411.5			−1.45133			−0.725667	−	0.688046i	$-0.758469\pi$
$857$	−36411.5			−1.45133			−0.725667	+	0.688046i	$0.758469\pi$
$858$	−12016.6	−	8730.58i	−0.478136	−	0.347386i
$859$	−10022.2	+	30845.3i	−0.398084	+	1.22518i	0.528450	+	0.848965i	$0.322774\pi$
$859$	−10022.2	+	30845.3i	−0.398084	+	1.22518i	−0.926534	+	0.376212i	$0.877226\pi$
$860$	402.340	−	729.713i	0.0159531	−	0.0289337i
$861$	5210.78	+	16037.1i	0.206252	+	0.634778i
$862$	9558.22	−	29417.2i	0.377673	−	1.16236i
$863$	2892.80	−	8903.13i	0.114104	−	0.351178i	−0.877655	−	0.479293i	$-0.840893\pi$
$863$	2892.80	−	8903.13i	0.114104	−	0.351178i	0.991759	+	0.128116i	$0.0408930\pi$
$864$	−449.843	−	1384.47i	−0.0177129	−	0.0545148i
$865$	4486.59	+	4789.59i	0.176357	+	0.188267i
$866$	10986.0	−	33811.3i	0.431084	−	1.32674i
$867$	62763.0	+	45600.0i	2.45853	+	1.78622i
$868$	−756.814			−0.0295944
$869$	−2307.12	−	1676.22i	−0.0900617	−	0.0654337i
$870$	−819.413	+	384.349i	−0.0319319	+	0.0149778i
$871$	−10960.5	+	7963.25i	−0.426385	+	0.309787i
$872$	14109.5	−	10251.2i	0.547946	−	0.398106i
$873$	−315.431	−	970.798i	−0.0122288	−	0.0376363i
$874$	2546.88			0.0985690
$875$	8139.71	−	31220.6i	0.314483	−	1.20623i
$876$	2884.55			0.111256
$877$	5449.81	+	16772.8i	0.209837	+	0.645812i	0.999480	+	0.0322455i	$0.0102659\pi$
$877$	5449.81	+	16772.8i	0.209837	+	0.645812i	−0.789643	+	0.613567i	$0.789734\pi$
$878$	32739.4	−	23786.5i	1.25843	−	0.914302i
$879$	40906.3	−	29720.1i	1.56966	−	1.14043i
$880$	−22857.5	+	10721.4i	−0.875599	+	0.410703i
$881$	34441.7	+	25023.4i	1.31711	+	0.956935i	0.999963	+	0.00855755i	$0.00272398\pi$
$881$	34441.7	+	25023.4i	1.31711	+	0.956935i	0.317144	+	0.948377i	$0.397276\pi$
$882$	10636.4			0.406061
$883$	−477.880	−	347.200i	−0.0182129	−	0.0132324i	0.578642	−	0.815582i	$-0.303583\pi$
$883$	−477.880	−	347.200i	−0.0182129	−	0.0132324i	−0.596854	+	0.802350i	$0.703583\pi$
$884$	−536.183	+	1650.20i	−0.0204002	+	0.0627854i
$885$	21925.1	+	23405.8i	0.832774	+	0.889016i
$886$	4114.94	+	12664.5i	0.156032	+	0.480216i
$887$	1272.22	−	3915.50i	0.0481590	−	0.148218i	−0.924085	−	0.382187i	$-0.875171\pi$
$887$	1272.22	−	3915.50i	0.0481590	−	0.148218i	0.972244	+	0.233968i	$0.0751712\pi$
$888$	−11830.1	+	36409.2i	−0.447062	+	1.37592i
$889$	−2846.42	−	8760.38i	−0.107386	−	0.330499i
$890$	10398.2	−	18859.0i	0.391629	−	0.710287i
$891$	8972.09	−	27613.3i	0.337347	−	1.03825i
$892$	−1972.07	−	1432.80i	−0.0740245	−	0.0537820i
$893$	−36342.2			−1.36187
$894$	24839.2	+	18046.8i	0.929248	+	0.675138i
$895$	2128.39	−	3860.21i	0.0794908	−	0.144170i
$896$	29686.5	−	21568.5i	1.10687	−	0.804190i
$897$	1352.94	−	982.969i	0.0503605	−	0.0365890i
$898$	15418.1	+	47451.9i	0.572948	+	1.76335i
$899$	−222.036			−0.00823727
$900$	1330.65	+	530.654i	0.0492834	+	0.0196539i
$901$	−88432.1			−3.26981
$902$	−3216.84	−	9900.41i	−0.118746	−	0.365463i
$903$	−15742.8	+	11437.8i	−0.580164	+	0.421514i
$904$	−11704.4	+	8503.72i	−0.430621	+	0.312864i
$905$	24813.6	+	4765.27i	0.911417	+	0.175031i
$906$	4341.78	+	3154.49i	0.159212	+	0.115674i
$907$	−16833.1			−0.616244			−0.308122	−	0.951347i	$-0.599700\pi$
$907$	−16833.1			−0.616244			−0.308122	+	0.951347i	$0.599700\pi$
$908$	164.254	+	119.337i	0.00600325	+	0.00436161i
$909$	−577.337	+	1776.86i	−0.0210661	+	0.0648347i
$910$	15495.8	−	7268.35i	0.564483	−	0.264773i
$911$	258.564	+	795.779i	0.00940353	+	0.0289411i	0.955648	−	0.294511i	$-0.0951567\pi$
$911$	258.564	+	795.779i	0.00940353	+	0.0289411i	−0.946245	+	0.323452i	$0.895157\pi$
$912$	11446.6	−	35229.1i	0.415609	−	1.27911i
$913$	−509.301	+	1567.47i	−0.0184615	+	0.0568188i
$914$	235.976	+	726.261i	0.00853983	+	0.0262829i
$915$	30242.5	+	5807.85i	1.09266	+	0.209838i
$916$	−691.296	+	2127.59i	−0.0249357	+	0.0767441i
$917$	1863.11	+	1353.63i	0.0670943	+	0.0487468i
$918$	−20128.9			−0.723694
$919$	20095.6	+	14600.3i	0.721320	+	0.524069i	0.886806	−	0.462143i	$-0.152919\pi$
$919$	20095.6	+	14600.3i	0.721320	+	0.524069i	−0.165486	+	0.986212i	$0.552919\pi$
$920$	−328.023	−	2622.66i	−0.0117550	−	0.0939852i
$921$	57083.5	−	41473.6i	2.04231	−	1.48382i
$922$	−25441.6	+	18484.4i	−0.908757	+	0.660250i
$923$	6340.12	+	19512.9i	0.226097	+	0.695855i
$924$	−3104.36			−0.110526
$925$	17336.6	+	27468.1i	0.616241	+	0.976372i
$926$	−38122.8			−1.35291
$927$	−8086.53	−	24887.8i	−0.286512	−	0.881792i
$928$	−89.1801	+	64.7931i	−0.00315461	+	0.00229196i
$929$	−1642.75	+	1193.53i	−0.0580162	+	0.0421512i	−0.616415	−	0.787421i	$-0.711416\pi$
$929$	−1642.75	+	1193.53i	−0.0580162	+	0.0421512i	0.558399	+	0.829572i	$0.311416\pi$
$930$	8310.13	+	8871.36i	0.293011	+	0.312799i
$931$	−12252.7	−	8902.12i	−0.431328	−	0.313378i
$932$	400.094			0.0140617
$933$	−9859.61	−	7163.42i	−0.345969	−	0.251361i
$934$	6797.93	−	20921.9i	0.238153	−	0.732961i
$935$	5852.05	+	46789.2i	0.204687	+	1.63654i
$936$	−2894.72	−	8909.03i	−0.101086	−	0.311112i
$937$	16731.1	−	51493.0i	0.583331	−	1.79531i	−0.0225425	−	0.999746i	$-0.507176\pi$
$937$	16731.1	−	51493.0i	0.583331	−	1.79531i	0.605873	−	0.795561i	$-0.292824\pi$
$938$	−12535.4	+	38580.1i	−0.436351	+	1.34295i
$939$	7098.83	+	21848.0i	0.246711	+	0.759299i
$940$	−379.726	−	3036.04i	−0.0131758	−	0.105345i
$941$	−12321.8	+	37922.8i	−0.426866	+	1.31376i	0.474330	+	0.880347i	$0.342690\pi$
$941$	−12321.8	+	37922.8i	−0.426866	+	1.31376i	−0.901196	+	0.433411i	$0.857310\pi$
$942$	−12028.3	−	8739.09i	−0.416034	−	0.302266i
$943$	1172.04			0.0404740
$944$	23395.4	+	16997.7i	0.806626	+	0.586048i
$945$	9474.91	+	10114.8i	0.326158	+	0.348185i
$946$	9718.71	−	7061.06i	0.334020	−	0.242679i
$947$	−32529.8	+	23634.3i	−1.11624	+	0.810995i	−0.983635	−	0.180175i	$-0.942334\pi$
$947$	−32529.8	+	23634.3i	−1.11624	+	0.810995i	−0.132604	+	0.991169i	$0.542334\pi$
$948$	108.854	+	335.019i	0.00372935	+	0.0114777i
$949$	−16003.8			−0.547422
$950$	−15597.6	−	24712.8i	−0.532687	−	0.843990i
$951$	−975.655			−0.0332679
$952$	−19789.6	−	60906.1i	−0.673723	−	2.07351i
$953$	−32429.3	+	23561.3i	−1.10230	+	0.800864i	−0.981433	−	0.191805i	$-0.938566\pi$
$953$	−32429.3	+	23561.3i	−1.10230	+	0.800864i	−0.120862	+	0.992669i	$0.538566\pi$
$954$	−31334.5	+	22765.9i	−1.06341	+	0.772613i
$955$	−804.880	−	6435.30i	−0.0272726	−	0.218054i
$956$	164.730	+	119.683i	0.00557295	+	0.00404898i
$957$	−910.764			−0.0307636
$958$	7735.77	+	5620.36i	0.260889	+	0.189547i
$959$	20517.2	−	63145.4i	0.690860	−	2.12625i
$960$	−34887.7	−	6699.93i	−1.17291	−	0.225249i
$961$	−8284.42	−	25496.8i	−0.278085	−	0.855857i
$962$	−5324.67	+	16387.7i	−0.178456	+	0.549230i
$963$	−928.824	+	2858.63i	−0.0310809	+	0.0956572i
$964$	−890.206	−	2739.77i	−0.0297423	−	0.0915375i
$965$	4903.28	−	2299.90i	0.163567	−	0.0767218i
$966$	1547.35	−	4762.26i	0.0515375	−	0.158616i
$967$	−27925.3	−	20289.0i	−0.928664	−	0.674714i	0.0170010	−	0.999855i	$-0.494588\pi$
$967$	−27925.3	−	20289.0i	−0.928664	−	0.674714i	−0.945665	+	0.325141i	$0.894588\pi$
$968$	5260.37			0.174664
$969$	−55970.3	−	40664.8i	−1.85555	−	1.34813i
$970$	−1721.64	−	330.629i	−0.0569883	−	0.0109442i
$971$	23202.4	−	16857.5i	0.766838	−	0.557141i	−0.134162	−	0.990959i	$-0.542834\pi$
$971$	23202.4	−	16857.5i	0.766838	−	0.557141i	0.901000	+	0.433819i	$0.142834\pi$
$972$	−2197.39	+	1596.49i	−0.0725115	+	0.0526827i
$973$	−7653.61	−	23555.4i	−0.252172	−	0.776106i
$974$	−25424.7			−0.836407
$975$	−17823.6	−	7107.94i	−0.585449	−	0.233473i
$976$	27767.9			0.910685
$977$	5681.83	+	17486.9i	0.186057	+	0.572625i	0.999965	−	0.00836916i	$-0.00266402\pi$
$977$	5681.83	+	17486.9i	0.186057	+	0.572625i	−0.813908	+	0.580994i	$0.802664\pi$
$978$	−4971.16	+	3611.76i	−0.162536	+	0.118089i
$979$	17532.2	−	12737.9i	0.572352	−	0.415838i
$980$	615.661	−	1116.61i	0.0200679	−	0.0363967i
$981$	−12412.8	−	9018.41i	−0.403985	−	0.293512i
$982$	−6934.17			−0.225334
$983$	3855.47	+	2801.16i	0.125097	+	0.0908883i	0.648574	−	0.761151i	$-0.275366\pi$
$983$	3855.47	+	2801.16i	0.125097	+	0.0908883i	−0.523477	+	0.852040i	$0.675366\pi$
$984$	4897.99	−	15074.5i	0.158681	−	0.488370i
$985$	−4793.66	+	8694.14i	−0.155065	+	0.281237i
$986$	471.013	+	1449.63i	0.0152131	+	0.0468211i
$987$	−22079.7	+	67954.4i	−0.712062	+	2.19150i
$988$	334.387	−	1029.14i	0.0107675	−	0.0331389i
$989$	417.955	+	1286.33i	0.0134380	+	0.0413580i
$990$	14118.9	+	15072.5i	0.453262	+	0.483873i
$991$	10828.5	−	33326.7i	0.347103	−	1.06827i	−0.613345	−	0.789815i	$-0.710177\pi$
$991$	10828.5	−	33326.7i	0.347103	−	1.06827i	0.960448	−	0.278458i	$-0.0898234\pi$
$992$	1197.73	+	870.204i	0.0383347	+	0.0278518i
$993$	32103.5			1.02596
$994$	49700.3	+	36109.4i	1.58591	+	1.15223i
$995$	−25929.8	+	12162.5i	−0.826162	+	0.387515i
$996$	164.702	−	119.663i	0.00523976	−	0.00380691i
$997$	10665.3	−	7748.82i	0.338791	−	0.246146i	−0.405361	−	0.914157i	$-0.632854\pi$
$997$	10665.3	−	7748.82i	0.338791	−	0.246146i	0.744152	+	0.668011i	$0.232854\pi$
$998$	−7618.86	−	23448.4i	−0.241654	−	0.743735i
$999$	−13952.8			−0.441888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.6.6	✓	28
3.2	odd	2		225.4.h.b.181.2		28
5.2	odd	4		125.4.e.b.99.4		56
5.3	odd	4		125.4.e.b.99.11		56
5.4	even	2		125.4.d.a.26.2		28
25.3	odd	20		125.4.e.b.24.4		56
25.4	even	10		125.4.d.a.101.2		28
25.11	even	5		625.4.a.c.1.11		14
25.14	even	10		625.4.a.d.1.4		14
25.21	even	5	inner	25.4.d.a.21.6	yes	28
25.22	odd	20		125.4.e.b.24.11		56
75.71	odd	10		225.4.h.b.46.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.6.6	✓	28	1.1	even	1	trivial
25.4.d.a.21.6	yes	28	25.21	even	5	inner
125.4.d.a.26.2		28	5.4	even	2
125.4.d.a.101.2		28	25.4	even	10
125.4.e.b.24.4		56	25.3	odd	20
125.4.e.b.24.11		56	25.22	odd	20
125.4.e.b.99.4		56	5.2	odd	4
125.4.e.b.99.11		56	5.3	odd	4
225.4.h.b.46.2		28	75.71	odd	10
225.4.h.b.181.2		28	3.2	odd	2
625.4.a.c.1.11		14	25.11	even	5
625.4.a.d.1.4		14	25.14	even	10

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906232 + 2.78910i) q^{2} +(5.49244 - 3.99049i) q^{3} +(-0.485661 + 0.352853i) q^{4} +(-10.1222 + 4.74784i) q^{5} +(16.1073 + 11.7026i) q^{6} -23.0864 q^{7} +(17.5561 + 12.7553i) q^{8} +(5.89942 - 18.1565i) q^{9} +O(q^{10})\)	\(q+(0.906232 + 2.78910i) q^{2} +(5.49244 - 3.99049i) q^{3} +(-0.485661 + 0.352853i) q^{4} +(-10.1222 + 4.74784i) q^{5} +(16.1073 + 11.7026i) q^{6} -23.0864 q^{7} +(17.5561 + 12.7553i) q^{8} +(5.89942 - 18.1565i) q^{9} +(-22.4152 - 23.9290i) q^{10} +(-10.1957 - 31.3790i) q^{11} +(-1.25941 + 3.87605i) q^{12} +(6.98730 - 21.5047i) q^{13} +(-20.9216 - 64.3901i) q^{14} +(-36.6491 + 66.4696i) q^{15} +(-21.1498 + 65.0923i) q^{16} +(103.416 + 75.1358i) q^{17} +55.9866 q^{18} +(-64.4944 - 46.8579i) q^{19} +(3.24065 - 5.87748i) q^{20} +(-126.801 + 92.1260i) q^{21} +(78.2794 - 56.8733i) q^{22} +(3.36642 + 10.3608i) q^{23} +147.326 q^{24} +(79.9161 - 96.1167i) q^{25} +66.3107 q^{26} +(16.5927 + 51.0670i) q^{27} +(11.2122 - 8.14611i) q^{28} +(3.28945 - 2.38992i) q^{29} +(-218.603 - 41.9810i) q^{30} +(-44.1789 - 32.0979i) q^{31} -27.1110 q^{32} +(-181.217 - 131.662i) q^{33} +(-115.842 + 356.526i) q^{34} +(233.684 - 109.610i) q^{35} +(3.54148 + 10.8996i) q^{36} +(-80.2988 + 247.134i) q^{37} +(72.2443 - 222.345i) q^{38} +(-47.4370 - 145.996i) q^{39} +(-238.266 - 45.7571i) q^{40} +(33.2460 - 102.321i) q^{41} +(-371.859 - 270.171i) q^{42} +124.154 q^{43} +(16.0238 + 11.6420i) q^{44} +(26.4895 + 211.793i) q^{45} +(-25.8465 + 18.7786i) q^{46} +(368.812 - 267.958i) q^{47} +(143.586 + 441.914i) q^{48} +189.981 q^{49} +(340.501 + 135.789i) q^{50} +867.832 q^{51} +(4.19455 + 12.9095i) q^{52} +(-559.680 + 406.631i) q^{53} +(-127.394 + 92.5571i) q^{54} +(252.184 + 269.216i) q^{55} +(-405.307 - 294.473i) q^{56} -541.218 q^{57} +(9.64673 + 7.00876i) q^{58} +(130.566 - 401.842i) q^{59} +(-5.65497 - 45.2135i) q^{60} +(-125.372 - 385.857i) q^{61} +(49.4877 - 152.307i) q^{62} +(-136.196 + 419.169i) q^{63} +(144.629 + 445.123i) q^{64} +(31.3743 + 250.848i) q^{65} +(202.992 - 624.746i) q^{66} +(-484.733 - 352.179i) q^{67} -76.7368 q^{68} +(59.8345 + 43.4723i) q^{69} +(517.486 + 552.434i) q^{70} +(-734.084 + 533.343i) q^{71} +(335.162 - 243.510i) q^{72} +(-218.714 - 673.134i) q^{73} -762.051 q^{74} +(55.3812 - 846.820i) q^{75} +47.8564 q^{76} +(235.381 + 724.427i) q^{77} +(364.208 - 264.612i) q^{78} +(69.9257 - 50.8040i) q^{79} +(-94.9665 - 759.290i) q^{80} +(711.928 + 517.246i) q^{81} +315.511 q^{82} +(-40.4126 - 29.3615i) q^{83} +(29.0751 - 89.4840i) q^{84} +(-1403.52 - 269.536i) q^{85} +(112.512 + 346.278i) q^{86} +(8.53012 - 26.2530i) q^{87} +(221.251 - 680.941i) q^{88} +(202.969 + 624.673i) q^{89} +(-566.705 + 265.815i) q^{90} +(-161.311 + 496.465i) q^{91} +(-5.29078 - 3.84398i) q^{92} -370.736 q^{93} +(1081.59 + 785.820i) q^{94} +(875.296 + 168.094i) q^{95} +(-148.905 + 108.186i) q^{96} +(43.2567 - 31.4278i) q^{97} +(172.167 + 529.875i) q^{98} -629.882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

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