LMFDB - Embedded newform 1000.2.d.c.501.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.15
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.572751 - 1.29304i) q^{2} +0.207209i q^{3} +(-1.34391 + 1.48118i) q^{4} +(0.267929 - 0.118679i) q^{6} -2.73181 q^{7} +(2.68496 + 0.889389i) q^{8} +2.95706 q^{9} +O(q^{10})$	\(q+(-0.572751 - 1.29304i) q^{2} +0.207209i q^{3} +(-1.34391 + 1.48118i) q^{4} +(0.267929 - 0.118679i) q^{6} -2.73181 q^{7} +(2.68496 + 0.889389i) q^{8} +2.95706 q^{9} -0.871377i q^{11} +(-0.306913 - 0.278470i) q^{12} +1.98325i q^{13} +(1.56464 + 3.53234i) q^{14} +(-0.387793 - 3.98116i) q^{16} -2.93520 q^{17} +(-1.69366 - 3.82361i) q^{18} +0.905406i q^{19} -0.566054i q^{21} +(-1.12673 + 0.499082i) q^{22} -6.50896 q^{23} +(-0.184289 + 0.556346i) q^{24} +(2.56442 - 1.13591i) q^{26} +1.23435i q^{27} +(3.67131 - 4.04630i) q^{28} +7.71622i q^{29} -4.14455 q^{31} +(-4.92569 + 2.78164i) q^{32} +0.180557 q^{33} +(1.68114 + 3.79533i) q^{34} +(-3.97404 + 4.37995i) q^{36} -0.436790i q^{37} +(1.17073 - 0.518572i) q^{38} -0.410946 q^{39} +5.84841 q^{41} +(-0.731931 + 0.324208i) q^{42} +3.55191i q^{43} +(1.29067 + 1.17106i) q^{44} +(3.72801 + 8.41636i) q^{46} +4.69617 q^{47} +(0.824930 - 0.0803540i) q^{48} +0.462766 q^{49} -0.608198i q^{51} +(-2.93755 - 2.66531i) q^{52} +9.68555i q^{53} +(1.59607 - 0.706977i) q^{54} +(-7.33478 - 2.42964i) q^{56} -0.187608 q^{57} +(9.97739 - 4.41947i) q^{58} +12.8197i q^{59} +12.7406i q^{61} +(2.37379 + 5.35907i) q^{62} -8.07813 q^{63} +(6.41797 + 4.77594i) q^{64} +(-0.103414 - 0.233467i) q^{66} -10.2605i q^{67} +(3.94465 - 4.34756i) q^{68} -1.34871i q^{69} -12.9184 q^{71} +(7.93959 + 2.62998i) q^{72} -9.76540 q^{73} +(-0.564788 + 0.250172i) q^{74} +(-1.34107 - 1.21679i) q^{76} +2.38043i q^{77} +(0.235369 + 0.531370i) q^{78} +3.02177 q^{79} +8.61542 q^{81} +(-3.34968 - 7.56223i) q^{82} +9.88164i q^{83} +(0.838428 + 0.760727i) q^{84} +(4.59276 - 2.03436i) q^{86} -1.59887 q^{87} +(0.774993 - 2.33961i) q^{88} -8.04615 q^{89} -5.41785i q^{91} +(8.74748 - 9.64095i) q^{92} -0.858786i q^{93} +(-2.68973 - 6.07234i) q^{94} +(-0.576380 - 1.02065i) q^{96} +12.1937 q^{97} +(-0.265050 - 0.598376i) q^{98} -2.57672i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.572751	−	1.29304i	−0.404996	−	0.914319i
$2$	−0.572751	−	1.29304i	−0.404996	−	0.914319i
$3$			0.207209i			0.119632i	0.998209	+	0.0598160i	$0.0190514\pi$
$3$			0.207209i			0.119632i	−0.998209	+	0.0598160i	$0.980949\pi$
$4$	−1.34391	+	1.48118i	−0.671957	+	0.740590i
$5$		0			0
$5$		0			0
$6$	0.267929	−	0.118679i	0.109382	−	0.0484504i
$7$	−2.73181			−1.03253			−0.516263	−	0.856430i	$-0.672677\pi$
$7$	−2.73181			−1.03253			−0.516263	+	0.856430i	$0.672677\pi$
$8$	2.68496	+	0.889389i	0.949275	+	0.314446i
$9$	2.95706			0.985688
$10$		0			0
$11$		−	0.871377i		−	0.262730i	−0.991334	−	0.131365i	$-0.958064\pi$
$11$		−	0.871377i		−	0.262730i	0.991334	−	0.131365i	$-0.0419360\pi$
$12$	−0.306913	−	0.278470i	−0.0885982	−	0.0803875i
$13$			1.98325i			0.550054i	0.961437	+	0.275027i	$0.0886867\pi$
$13$			1.98325i			0.550054i	−0.961437	+	0.275027i	$0.911313\pi$
$14$	1.56464	+	3.53234i	0.418169	+	0.944057i
$15$		0			0
$16$	−0.387793	−	3.98116i	−0.0969483	−	0.995289i
$17$	−2.93520			−0.711890			−0.355945	−	0.934507i	$-0.615841\pi$
$17$	−2.93520			−0.711890			−0.355945	+	0.934507i	$0.615841\pi$
$18$	−1.69366	−	3.82361i	−0.399200	−	0.901233i
$19$			0.905406i			0.207714i	0.994592	+	0.103857i	$0.0331185\pi$
$19$			0.905406i			0.207714i	−0.994592	+	0.103857i	$0.966882\pi$
$20$		0			0
$21$		−	0.566054i		−	0.123523i
$22$	−1.12673	+	0.499082i	−0.240219	+	0.106405i
$23$	−6.50896			−1.35721			−0.678606	−	0.734502i	$-0.737416\pi$
$23$	−6.50896			−1.35721			−0.678606	+	0.734502i	$0.737416\pi$
$24$	−0.184289	+	0.556346i	−0.0376178	+	0.113564i
$25$		0			0
$26$	2.56442	−	1.13591i	0.502924	−	0.222769i
$27$			1.23435i			0.237552i
$28$	3.67131	−	4.04630i	0.693813	−	0.764679i
$29$			7.71622i			1.43287i	0.697656	+	0.716433i	$0.254227\pi$
$29$			7.71622i			1.43287i	−0.697656	+	0.716433i	$0.745773\pi$
$30$		0			0
$31$	−4.14455			−0.744383			−0.372191	−	0.928156i	$-0.621394\pi$
$31$	−4.14455			−0.744383			−0.372191	+	0.928156i	$0.621394\pi$
$32$	−4.92569	+	2.78164i	−0.870748	+	0.491730i
$33$	0.180557			0.0314309
$34$	1.68114	+	3.79533i	0.288313	+	0.650895i
$35$		0			0
$36$	−3.97404	+	4.37995i	−0.662340	+	0.729991i
$37$		−	0.436790i		−	0.0718078i	−0.999355	−	0.0359039i	$-0.988569\pi$
$37$		−	0.436790i		−	0.0718078i	0.999355	−	0.0359039i	$-0.0114310\pi$
$38$	1.17073	−	0.518572i	0.189917	−	0.0841234i
$39$	−0.410946			−0.0658040
$40$		0			0
$41$	5.84841			0.913368			0.456684	−	0.889629i	$-0.349037\pi$
$41$	5.84841			0.913368			0.456684	+	0.889629i	$0.349037\pi$
$42$	−0.731931	+	0.324208i	−0.112939	+	0.0500263i
$43$			3.55191i			0.541661i	0.962627	+	0.270830i	$0.0872983\pi$
$43$			3.55191i			0.541661i	−0.962627	+	0.270830i	$0.912702\pi$
$44$	1.29067	+	1.17106i	0.194575	+	0.176543i
$45$		0			0
$46$	3.72801	+	8.41636i	0.549665	+	1.24092i
$47$	4.69617			0.685006			0.342503	−	0.939517i	$-0.388725\pi$
$47$	4.69617			0.685006			0.342503	+	0.939517i	$0.388725\pi$
$48$	0.824930	−	0.0803540i	0.119068	−	0.0115981i
$49$	0.462766			0.0661095
$50$		0			0
$51$		−	0.608198i		−	0.0851648i
$52$	−2.93755	−	2.66531i	−0.407364	−	0.369612i
$53$			9.68555i			1.33041i	0.746660	+	0.665206i	$0.231656\pi$
$53$			9.68555i			1.33041i	−0.746660	+	0.665206i	$0.768344\pi$
$54$	1.59607	−	0.706977i	0.217198	−	0.0962074i
$55$		0			0
$56$	−7.33478	−	2.42964i	−0.980151	−	0.324674i
$57$	−0.187608			−0.0248493
$58$	9.97739	−	4.41947i	1.31010	−	0.580305i
$59$			12.8197i			1.66899i	0.551016	+	0.834495i	$0.314240\pi$
$59$			12.8197i			1.66899i	−0.551016	+	0.834495i	$0.685760\pi$
$60$		0			0
$61$			12.7406i			1.63126i	0.578573	+	0.815630i	$0.303610\pi$
$61$			12.7406i			1.63126i	−0.578573	+	0.815630i	$0.696390\pi$
$62$	2.37379	+	5.35907i	0.301472	+	0.680603i
$63$	−8.07813			−1.01775
$64$	6.41797	+	4.77594i	0.802247	+	0.596993i
$65$		0			0
$66$	−0.103414	−	0.233467i	−0.0127294	−	0.0287379i
$67$		−	10.2605i		−	1.25352i	−0.779212	−	0.626760i	$-0.784381\pi$
$67$		−	10.2605i		−	1.25352i	0.779212	−	0.626760i	$-0.215619\pi$
$68$	3.94465	−	4.34756i	0.478360	−	0.527219i
$69$		−	1.34871i		−	0.162366i
$70$		0			0
$71$	−12.9184			−1.53314			−0.766569	−	0.642162i	$-0.778038\pi$
$71$	−12.9184			−1.53314			−0.766569	+	0.642162i	$0.778038\pi$
$72$	7.93959	+	2.62998i	0.935689	+	0.309946i
$73$	−9.76540			−1.14295			−0.571477	−	0.820618i	$-0.693629\pi$
$73$	−9.76540			−1.14295			−0.571477	+	0.820618i	$0.693629\pi$
$74$	−0.564788	+	0.250172i	−0.0656552	+	0.0290819i
$75$		0			0
$76$	−1.34107	−	1.21679i	−0.153831	−	0.139575i
$77$			2.38043i			0.271276i
$78$	0.235369	+	0.531370i	0.0266503	+	0.0601658i
$79$	3.02177			0.339976			0.169988	−	0.985446i	$-0.445627\pi$
$79$	3.02177			0.339976			0.169988	+	0.985446i	$0.445627\pi$
$80$		0			0
$81$	8.61542			0.957269
$82$	−3.34968	−	7.56223i	−0.369910	−	0.835109i
$83$			9.88164i			1.08465i	0.840169	+	0.542325i	$0.182456\pi$
$83$			9.88164i			1.08465i	−0.840169	+	0.542325i	$0.817544\pi$
$84$	0.838428	+	0.760727i	0.0914800	+	0.0830021i
$85$		0			0
$86$	4.59276	−	2.03436i	0.495250	−	0.219370i
$87$	−1.59887			−0.171417
$88$	0.774993	−	2.33961i	0.0826146	−	0.249403i
$89$	−8.04615			−0.852891			−0.426445	−	0.904513i	$-0.640234\pi$
$89$	−8.04615			−0.852891			−0.426445	+	0.904513i	$0.640234\pi$
$90$		0			0
$91$		−	5.41785i		−	0.567945i
$92$	8.74748	−	9.64095i	0.911988	−	1.00514i
$93$		−	0.858786i		−	0.0890519i
$94$	−2.68973	−	6.07234i	−0.277425	−	0.626314i
$95$		0			0
$96$	−0.576380	−	1.02065i	−0.0588266	−	0.104169i
$97$	12.1937			1.23808			0.619041	−	0.785359i	$-0.287522\pi$
$97$	12.1937			1.23808			0.619041	+	0.785359i	$0.287522\pi$
$98$	−0.265050	−	0.598376i	−0.0267741	−	0.0604451i
$99$		−	2.57672i		−	0.258970i
$100$		0			0
$101$		−	5.51432i		−	0.548696i	−0.961631	−	0.274348i	$-0.911538\pi$
$101$		−	5.51432i		−	0.548696i	0.961631	−	0.274348i	$-0.0884619\pi$
$102$	−0.786426	+	0.348346i	−0.0778678	+	0.0344914i
$103$	4.98581			0.491266			0.245633	−	0.969363i	$-0.421004\pi$
$103$	4.98581			0.491266			0.245633	+	0.969363i	$0.421004\pi$
$104$	−1.76388	+	5.32493i	−0.172962	+	0.522152i
$105$		0			0
$106$	12.5238	−	5.54740i	1.21642	−	0.538811i
$107$			12.4436i			1.20297i	0.798883	+	0.601486i	$0.205425\pi$
$107$			12.4436i			1.20297i	−0.798883	+	0.601486i	$0.794575\pi$
$108$	−1.82830	−	1.65887i	−0.175928	−	0.159624i
$109$			4.64042i			0.444472i	0.974993	+	0.222236i	$0.0713355\pi$
$109$			4.64042i			0.444472i	−0.974993	+	0.222236i	$0.928664\pi$
$110$		0			0
$111$	0.0905066			0.00859051
$112$	1.05938	+	10.8758i	0.100102	+	1.02766i
$113$	−17.0652			−1.60536			−0.802680	−	0.596410i	$-0.796593\pi$
$113$	−17.0652			−1.60536			−0.802680	+	0.596410i	$0.796593\pi$
$114$	0.107452	+	0.242585i	0.0100638	+	0.0227201i
$115$		0			0
$116$	−11.4291	−	10.3699i	−1.06117	−	0.962824i
$117$			5.86459i			0.542181i
$118$	16.5765	−	7.34252i	1.52599	−	0.675934i
$119$	8.01840			0.735045
$120$		0			0
$121$	10.2407			0.930973
$122$	16.4741	−	7.29716i	1.49149	−	0.660654i
$123$			1.21184i			0.109268i
$124$	5.56991	−	6.13883i	0.500193	−	0.551283i
$125$		0			0
$126$	4.62675	+	10.4454i	0.412184	+	0.930546i
$127$	3.92450			0.348243			0.174121	−	0.984724i	$-0.444291\pi$
$127$	3.92450			0.348243			0.174121	+	0.984724i	$0.444291\pi$
$128$	2.49959	−	11.0341i	0.220935	−	0.975289i
$129$	−0.735986			−0.0647999
$130$		0			0
$131$		−	16.8728i		−	1.47419i	−0.675792	−	0.737093i	$-0.736198\pi$
$131$		−	16.8728i		−	1.47419i	0.675792	−	0.737093i	$-0.263802\pi$
$132$	−0.242653	+	0.267437i	−0.0211202	+	0.0232774i
$133$		−	2.47339i		−	0.214470i
$134$	−13.2673	+	5.87671i	−1.14612	+	0.507671i
$135$		0			0
$136$	−7.88088	−	2.61053i	−0.675780	−	0.223851i
$137$	−6.81761			−0.582468			−0.291234	−	0.956652i	$-0.594066\pi$
$137$	−6.81761			−0.582468			−0.291234	+	0.956652i	$0.594066\pi$
$138$	−1.74394	+	0.772476i	−0.148454	+	0.0657575i
$139$		−	13.4616i		−	1.14180i	−0.821021	−	0.570898i	$-0.806595\pi$
$139$		−	13.4616i		−	1.14180i	0.821021	−	0.570898i	$-0.193405\pi$
$140$		0			0
$141$			0.973086i			0.0819486i
$142$	7.39905	+	16.7041i	0.620914	+	1.40178i
$143$	1.72816			0.144516
$144$	−1.14673	−	11.7725i	−0.0955607	−	0.981045i
$145$		0			0
$146$	5.59314	+	12.6271i	0.462891	+	1.04502i
$147$			0.0958892i			0.00790880i
$148$	0.646965	+	0.587008i	0.0531802	+	0.0482518i
$149$		−	19.6182i		−	1.60719i	−0.595179	−	0.803593i	$-0.702919\pi$
$149$		−	19.6182i		−	1.60719i	0.595179	−	0.803593i	$-0.297081\pi$
$150$		0			0
$151$	−21.8652			−1.77937			−0.889684	−	0.456577i	$-0.849075\pi$
$151$	−21.8652			−1.77937			−0.889684	+	0.456577i	$0.849075\pi$
$152$	−0.805258	+	2.43097i	−0.0653150	+	0.197178i
$153$	−8.67957			−0.701702
$154$	3.07800	−	1.36340i	0.248032	−	0.109866i
$155$		0			0
$156$	0.552275	−	0.608685i	0.0442174	−	0.0487338i
$157$		−	5.34144i		−	0.426293i	−0.977020	−	0.213147i	$-0.931629\pi$
$157$		−	5.34144i		−	0.426293i	0.977020	−	0.213147i	$-0.0683712\pi$
$158$	−1.73072	−	3.90727i	−0.137689	−	0.310846i
$159$	−2.00693			−0.159160
$160$		0			0
$161$	17.7812			1.40136
$162$	−4.93449	−	11.1401i	−0.387690	−	0.875249i
$163$			17.4676i			1.36817i	0.729401	+	0.684086i	$0.239799\pi$
$163$			17.4676i			1.36817i	−0.729401	+	0.684086i	$0.760201\pi$
$164$	−7.85975	+	8.66255i	−0.613744	+	0.676431i
$165$		0			0
$166$	12.7774	−	5.65971i	0.991716	−	0.439279i
$167$	11.5956			0.897293			0.448647	−	0.893709i	$-0.351906\pi$
$167$	11.5956			0.897293			0.448647	+	0.893709i	$0.351906\pi$
$168$	0.503442	−	1.51983i	0.0388414	−	0.117257i
$169$	9.06673			0.697441
$170$		0			0
$171$			2.67734i			0.204742i
$172$	−5.26102	−	4.77346i	−0.401149	−	0.363973i
$173$			9.07537i			0.689988i	0.938605	+	0.344994i	$0.112119\pi$
$173$			9.07537i			0.689988i	−0.938605	+	0.344994i	$0.887881\pi$
$174$	0.915752	+	2.06740i	0.0694230	+	0.156729i
$175$		0			0
$176$	−3.46909	+	0.337914i	−0.261493	+	0.0254712i
$177$	−2.65636			−0.199664
$178$	4.60844	+	10.4040i	0.345417	+	0.779814i
$179$		−	10.0236i		−	0.749200i	−0.927186	−	0.374600i	$-0.877780\pi$
$179$		−	10.0236i		−	0.749200i	0.927186	−	0.374600i	$-0.122220\pi$
$180$		0			0
$181$			14.2992i			1.06285i	0.847106	+	0.531424i	$0.178343\pi$
$181$			14.2992i			1.06285i	−0.847106	+	0.531424i	$0.821657\pi$
$182$	−7.00550	+	3.10307i	−0.519282	+	0.230015i
$183$	−2.63995			−0.195151
$184$	−17.4763	−	5.78900i	−1.28837	−	0.426771i
$185$		0			0
$186$	−1.11045	+	0.491870i	−0.0814218	+	0.0360657i
$187$			2.55767i			0.187035i
$188$	−6.31124	+	6.95587i	−0.460294	+	0.507309i
$189$		−	3.37202i		−	0.245278i
$190$		0			0
$191$	−13.4414			−0.972588			−0.486294	−	0.873795i	$-0.661652\pi$
$191$	−13.4414			−0.972588			−0.486294	+	0.873795i	$0.661652\pi$
$192$	−0.989616	+	1.32986i	−0.0714194	+	0.0959743i
$193$	20.0219			1.44121			0.720606	−	0.693345i	$-0.243864\pi$
$193$	20.0219			1.44121			0.720606	+	0.693345i	$0.243864\pi$
$194$	−6.98394	−	15.7669i	−0.501418	−	1.13200i
$195$		0			0
$196$	−0.621918	+	0.685441i	−0.0444227	+	0.0489601i
$197$		−	13.4963i		−	0.961568i	−0.876839	−	0.480784i	$-0.840352\pi$
$197$		−	13.4963i		−	0.961568i	0.876839	−	0.480784i	$-0.159648\pi$
$198$	−3.33180	+	1.47582i	−0.236781	+	0.104882i
$199$	−14.1065			−0.999981			−0.499990	−	0.866031i	$-0.666663\pi$
$199$	−14.1065			−0.999981			−0.499990	+	0.866031i	$0.666663\pi$
$200$		0			0
$201$	2.12607			0.149961
$202$	−7.13025	+	3.15833i	−0.501683	+	0.222219i
$203$		−	21.0792i		−	1.47947i
$204$	0.900852	+	0.817366i	0.0630722	+	0.0572271i
$205$		0			0
$206$	−2.85562	−	6.44686i	−0.198961	−	0.449174i
$207$	−19.2474			−1.33779
$208$	7.89562	−	0.769089i	0.547463	−	0.0533267i
$209$	0.788950			0.0545728
$210$		0			0
$211$			13.1355i			0.904288i	0.891945	+	0.452144i	$0.149341\pi$
$211$			13.1355i			0.904288i	−0.891945	+	0.452144i	$0.850659\pi$
$212$	−14.3460	−	13.0165i	−0.985290	−	0.893979i
$213$		−	2.67681i		−	0.183412i
$214$	16.0901	−	7.12710i	1.09990	−	0.487199i
$215$		0			0
$216$	−1.09782	+	3.31419i	−0.0746973	+	0.225502i
$217$	11.3221			0.768594
$218$	6.00026	−	2.65780i	0.406389	−	0.180009i
$219$		−	2.02347i		−	0.136734i
$220$		0			0
$221$		−	5.82122i		−	0.391578i
$222$	−0.0518377	−	0.117029i	−0.00347912	−	0.00785446i
$223$	0.718852			0.0481379			0.0240689	−	0.999710i	$-0.492338\pi$
$223$	0.718852			0.0481379			0.0240689	+	0.999710i	$0.492338\pi$
$224$	13.4560	−	7.59891i	0.899070	−	0.507724i
$225$		0			0
$226$	9.77411	+	22.0660i	0.650164	+	1.46781i
$227$		−	12.0713i		−	0.801198i	−0.916254	−	0.400599i	$-0.868802\pi$
$227$		−	12.0713i		−	0.801198i	0.916254	−	0.400599i	$-0.131198\pi$
$228$	0.252129	−	0.277881i	0.0166976	−	0.0184031i
$229$		−	10.3408i		−	0.683342i	−0.939820	−	0.341671i	$-0.889007\pi$
$229$		−	10.3408i		−	0.683342i	0.939820	−	0.341671i	$-0.110993\pi$
$230$		0			0
$231$	−0.493246			−0.0324532
$232$	−6.86272	+	20.7177i	−0.450560	+	1.36018i
$233$	4.03296			0.264208			0.132104	−	0.991236i	$-0.457827\pi$
$233$	4.03296			0.264208			0.132104	+	0.991236i	$0.457827\pi$
$234$	7.58316	−	3.35895i	0.495727	−	0.219581i
$235$		0			0
$236$	−18.9884	−	17.2286i	−1.23604	−	1.12149i
$237$			0.626136i			0.0406719i
$238$	−4.59254	−	10.3681i	−0.297690	−	0.672065i
$239$	−11.7267			−0.758540			−0.379270	−	0.925286i	$-0.623825\pi$
$239$	−11.7267			−0.758540			−0.379270	+	0.925286i	$0.623825\pi$
$240$		0			0
$241$	12.7697			0.822569			0.411284	−	0.911507i	$-0.365080\pi$
$241$	12.7697			0.822569			0.411284	+	0.911507i	$0.365080\pi$
$242$	−5.86537	−	13.2417i	−0.377040	−	0.851206i
$243$			5.48825i			0.352072i
$244$	−18.8711	−	17.1222i	−1.20810	−	1.09614i
$245$		0			0
$246$	1.56696	−	0.694082i	0.0999057	−	0.0442531i
$247$	−1.79564			−0.114254
$248$	−11.1279	−	3.68612i	−0.706624	−	0.234069i
$249$	−2.04756			−0.129759
$250$		0			0
$251$		−	22.8026i		−	1.43929i	−0.694344	−	0.719644i	$-0.744305\pi$
$251$		−	22.8026i		−	1.43929i	0.694344	−	0.719644i	$-0.255695\pi$
$252$	10.8563	−	11.9652i	0.683883	−	0.753735i
$253$			5.67176i			0.356581i
$254$	−2.24776	−	5.07454i	−0.141037	−	0.318405i
$255$		0			0
$256$	−15.6992	+	3.08773i	−0.981202	+	0.192983i
$257$	−22.6835			−1.41496			−0.707478	−	0.706736i	$-0.750167\pi$
$257$	−22.6835			−1.41496			−0.707478	+	0.706736i	$0.750167\pi$
$258$	0.421536	+	0.951660i	0.0262437	+	0.0592478i
$259$			1.19323i			0.0741435i
$260$		0			0
$261$			22.8174i			1.41236i
$262$	−21.8173	+	9.66392i	−1.34788	+	0.597039i
$263$	−15.0066			−0.925346			−0.462673	−	0.886529i	$-0.653110\pi$
$263$	−15.0066			−0.925346			−0.462673	+	0.886529i	$0.653110\pi$
$264$	0.484787	+	0.160585i	0.0298366	+	0.00988334i
$265$		0			0
$266$	−3.19820	+	1.41664i	−0.196094	+	0.0868596i
$267$		−	1.66723i		−	0.102033i
$268$	15.1977	+	13.7892i	0.928345	+	0.842312i
$269$			15.3940i			0.938591i	0.883041	+	0.469295i	$0.155492\pi$
$269$			15.3940i			0.938591i	−0.883041	+	0.469295i	$0.844508\pi$
$270$		0			0
$271$	−15.1636			−0.921121			−0.460561	−	0.887628i	$-0.652352\pi$
$271$	−15.1636			−0.921121			−0.460561	+	0.887628i	$0.652352\pi$
$272$	1.13825	+	11.6855i	0.0690165	+	0.708537i
$273$	1.12262			0.0679443
$274$	3.90479	+	8.81546i	0.235897	+	0.532561i
$275$		0			0
$276$	1.99769	+	1.81255i	0.120247	+	0.109103i
$277$			9.80905i			0.589369i	0.955595	+	0.294684i	$0.0952145\pi$
$277$			9.80905i			0.589369i	−0.955595	+	0.294684i	$0.904785\pi$
$278$	−17.4064	+	7.71012i	−1.04396	+	0.462422i
$279$	−12.2557			−0.733729
$280$		0			0
$281$	3.41960			0.203996			0.101998	−	0.994785i	$-0.467476\pi$
$281$	3.41960			0.203996			0.101998	+	0.994785i	$0.467476\pi$
$282$	1.25824	−	0.557335i	0.0749271	−	0.0331888i
$283$		−	24.5466i		−	1.45914i	−0.683904	−	0.729572i	$-0.739719\pi$
$283$		−	24.5466i		−	1.45914i	0.683904	−	0.729572i	$-0.260281\pi$
$284$	17.3613	−	19.1346i	1.03020	−	1.13543i
$285$		0			0
$286$	−0.989803	−	2.23458i	−0.0585282	−	0.132133i
$287$	−15.9767			−0.943076
$288$	−14.5656	+	8.22550i	−0.858286	+	0.484692i
$289$	−8.38461			−0.493212
$290$		0			0
$291$			2.52664i			0.148114i
$292$	13.1238	−	14.4643i	0.768015	−	0.846460i
$293$		−	22.9522i		−	1.34088i	−0.741962	−	0.670442i	$-0.766104\pi$
$293$		−	22.9522i		−	1.34088i	0.741962	−	0.670442i	$-0.233896\pi$
$294$	0.123989	−	0.0549206i	0.00723117	−	0.00320303i
$295$		0			0
$296$	0.388476	−	1.17276i	0.0225797	−	0.0681654i
$297$	1.07559			0.0624120
$298$	−25.3672	+	11.2363i	−1.46948	+	0.650904i
$299$		−	12.9089i		−	0.746540i
$300$		0			0
$301$		−	9.70312i		−	0.559279i
$302$	12.5233	+	28.2727i	0.720637	+	1.62691i
$303$	1.14261			0.0656415
$304$	3.60456	−	0.351110i	0.206736	−	0.0201375i
$305$		0			0
$306$	4.97123	+	11.2231i	0.284186	+	0.641579i
$307$		−	2.31183i		−	0.131943i	−0.997822	−	0.0659714i	$-0.978985\pi$
$307$		−	2.31183i		−	0.131943i	0.997822	−	0.0659714i	$-0.0210146\pi$
$308$	−3.52585	−	3.19910i	−0.200904	−	0.182285i
$309$			1.03310i			0.0587711i
$310$		0			0
$311$	0.398156			0.0225774			0.0112887	−	0.999936i	$-0.496407\pi$
$311$	0.398156			0.0225774			0.0112887	+	0.999936i	$0.496407\pi$
$312$	−1.10337	−	0.365491i	−0.0624661	−	0.0206918i
$313$	27.7896			1.57076			0.785380	−	0.619013i	$-0.212467\pi$
$313$	27.7896			1.57076			0.785380	+	0.619013i	$0.212467\pi$
$314$	−6.90670	+	3.05931i	−0.389768	+	0.172647i
$315$		0			0
$316$	−4.06100	+	4.47579i	−0.228449	+	0.251783i
$317$			16.7194i			0.939056i	0.882918	+	0.469528i	$0.155576\pi$
$317$			16.7194i			0.939056i	−0.882918	+	0.469528i	$0.844424\pi$
$318$	1.14947	+	2.59504i	0.0644590	+	0.145523i
$319$	6.72374			0.376457
$320$		0			0
$321$	−2.57843			−0.143914
$322$	−10.1842	−	22.9919i	−0.567544	−	1.28129i
$323$		−	2.65755i		−	0.147870i
$324$	−11.5784	+	12.7610i	−0.643244	+	0.708945i
$325$		0			0
$326$	22.5864	−	10.0046i	1.25094	−	0.554104i
$327$	−0.961535			−0.0531730
$328$	15.7027	+	5.20151i	0.867037	+	0.287205i
$329$	−12.8290			−0.707286
$330$		0			0
$331$			12.7840i			0.702673i	0.936249	+	0.351337i	$0.114273\pi$
$331$			12.7840i			0.702673i	−0.936249	+	0.351337i	$0.885727\pi$
$332$	−14.6365	−	13.2801i	−0.803282	−	0.728838i
$333$		−	1.29162i		−	0.0707801i
$334$	−6.64138	−	14.9936i	−0.363400	−	0.820412i
$335$		0			0
$336$	−2.25355	+	0.219512i	−0.122941	+	0.0119753i
$337$	4.73648			0.258012			0.129006	−	0.991644i	$-0.458821\pi$
$337$	4.73648			0.258012			0.129006	+	0.991644i	$0.458821\pi$
$338$	−5.19298	−	11.7237i	−0.282461	−	0.637683i
$339$		−	3.53606i		−	0.192052i
$340$		0			0
$341$			3.61147i			0.195572i
$342$	3.46192	−	1.53345i	0.187199	−	0.0829195i
$343$	17.8585			0.964266
$344$	−3.15903	+	9.53671i	−0.170323	+	0.514185i
$345$		0			0
$346$	11.7348	−	5.19793i	0.630869	−	0.279442i
$347$			25.7080i			1.38008i	0.723773	+	0.690038i	$0.242406\pi$
$347$			25.7080i			1.38008i	−0.723773	+	0.690038i	$0.757594\pi$
$348$	2.14874	−	2.36821i	0.115184	−	0.126949i
$349$			7.18541i			0.384626i	0.981334	+	0.192313i	$0.0615989\pi$
$349$			7.18541i			0.384626i	−0.981334	+	0.192313i	$0.938401\pi$
$350$		0			0
$351$	−2.44803			−0.130666
$352$	2.42386	+	4.29214i	0.129192	+	0.228772i
$353$	5.97661			0.318103			0.159052	−	0.987270i	$-0.449156\pi$
$353$	5.97661			0.318103			0.159052	+	0.987270i	$0.449156\pi$
$354$	1.52143	+	3.43479i	0.0808632	+	0.182557i
$355$		0			0
$356$	10.8133	−	11.9178i	0.573106	−	0.631643i
$357$			1.66148i			0.0879349i
$358$	−12.9610	+	5.74103i	−0.685008	+	0.303423i
$359$	30.7769			1.62434			0.812171	−	0.583420i	$-0.198286\pi$
$359$	30.7769			1.62434			0.812171	+	0.583420i	$0.198286\pi$
$360$		0			0
$361$	18.1802			0.956855
$362$	18.4894	−	8.18985i	0.971782	−	0.430449i
$363$			2.12196i			0.111374i
$364$	8.02481	+	7.28112i	0.420614	+	0.381634i
$365$		0			0
$366$	1.51203	+	3.41357i	0.0790353	+	0.178430i
$367$	22.3956			1.16904			0.584520	−	0.811379i	$-0.301283\pi$
$367$	22.3956			1.16904			0.584520	+	0.811379i	$0.301283\pi$
$368$	2.52413	+	25.9132i	0.131579	+	1.35082i
$369$	17.2941			0.900296
$370$		0			0
$371$		−	26.4590i		−	1.37368i
$372$	1.27202	+	1.15413i	0.0659510	+	0.0598391i
$373$			16.1839i			0.837973i	0.907992	+	0.418986i	$0.137615\pi$
$373$			16.1839i			0.837973i	−0.907992	+	0.418986i	$0.862385\pi$
$374$	3.30717	−	1.46490i	0.171010	−	0.0757484i
$375$		0			0
$376$	12.6090	+	4.17672i	0.650259	+	0.215398i
$377$	−15.3032			−0.788153
$378$	−4.36016	+	1.93133i	−0.224262	+	0.0993367i
$379$			10.9692i			0.563449i	0.959495	+	0.281724i	$0.0909063\pi$
$379$			10.9692i			0.563449i	−0.959495	+	0.281724i	$0.909094\pi$
$380$		0			0
$381$			0.813190i			0.0416610i
$382$	7.69859	+	17.3803i	0.393894	+	0.889255i
$383$	18.3816			0.939256			0.469628	−	0.882864i	$-0.344388\pi$
$383$	18.3816			0.939256			0.469628	+	0.882864i	$0.344388\pi$
$384$	2.28637	+	0.517937i	0.116676	+	0.0264308i
$385$		0			0
$386$	−11.4676	−	25.8892i	−0.583685	−	1.31773i
$387$			10.5032i			0.533909i
$388$	−16.3873	+	18.0611i	−0.831937	+	0.916911i
$389$		−	30.2480i		−	1.53364i	−0.641865	−	0.766818i	$-0.721839\pi$
$389$		−	30.2480i		−	1.53364i	0.641865	−	0.766818i	$-0.278161\pi$
$390$		0			0
$391$	19.1051			0.966186
$392$	1.24251	+	0.411579i	0.0627561	+	0.0207879i
$393$	3.49619			0.176360
$394$	−17.4512	+	7.72999i	−0.879180	+	0.389431i
$395$		0			0
$396$	3.81659	+	3.46289i	0.191791	+	0.174017i
$397$		−	39.1270i		−	1.96373i	−0.189582	−	0.981865i	$-0.560713\pi$
$397$		−	39.1270i		−	1.96373i	0.189582	−	0.981865i	$-0.439287\pi$
$398$	8.07948	+	18.2402i	0.404988	+	0.914301i
$399$	0.512508			0.0256575
$400$		0			0
$401$	−10.2607			−0.512397			−0.256198	−	0.966624i	$-0.582470\pi$
$401$	−10.2607			−0.512397			−0.256198	+	0.966624i	$0.582470\pi$
$402$	−1.21771	−	2.74909i	−0.0607336	−	0.137112i
$403$		−	8.21966i		−	0.409451i
$404$	8.16771	+	7.41077i	0.406359	+	0.368700i
$405$		0			0
$406$	−27.2563	+	12.0731i	−1.35271	+	0.599180i
$407$	−0.380609			−0.0188661
$408$	0.540925	−	1.63299i	0.0267798	−	0.0808448i
$409$	10.4383			0.516140			0.258070	−	0.966126i	$-0.416913\pi$
$409$	10.4383			0.516140			0.258070	+	0.966126i	$0.416913\pi$
$410$		0			0
$411$		−	1.41267i		−	0.0696818i
$412$	−6.70049	+	7.38488i	−0.330110	+	0.363827i
$413$		−	35.0211i		−	1.72327i
$414$	11.0240	+	24.8877i	0.541799	+	1.22316i
$415$		0			0
$416$	−5.51668	−	9.76887i	−0.270478	−	0.478958i
$417$	2.78935			0.136595
$418$	−0.451872	−	1.02015i	−0.0221018	−	0.0498969i
$419$			36.6607i			1.79099i	0.445067	+	0.895497i	$0.353180\pi$
$419$			36.6607i			1.79099i	−0.445067	+	0.895497i	$0.646820\pi$
$420$		0			0
$421$		−	10.4070i		−	0.507207i	−0.967308	−	0.253603i	$-0.918384\pi$
$421$		−	10.4070i		−	0.507207i	0.967308	−	0.253603i	$-0.0816158\pi$
$422$	16.9848	−	7.52339i	0.826807	−	0.366233i
$423$	13.8869			0.675202
$424$	−8.61422	+	26.0053i	−0.418343	+	1.26293i
$425$		0			0
$426$	−3.46123	+	1.53315i	−0.167697	+	0.0742812i
$427$		−	34.8047i		−	1.68432i
$428$	−18.4313	−	16.7232i	−0.890910	−	0.808345i
$429$			0.358089i			0.0172887i
$430$		0			0
$431$	−10.3866			−0.500306			−0.250153	−	0.968206i	$-0.580481\pi$
$431$	−10.3866			−0.500306			−0.250153	+	0.968206i	$0.580481\pi$
$432$	4.91416	−	0.478674i	0.236433	−	0.0230302i
$433$	7.01402			0.337072			0.168536	−	0.985695i	$-0.446096\pi$
$433$	7.01402			0.337072			0.168536	+	0.985695i	$0.446096\pi$
$434$	−6.48474	−	14.6400i	−0.311278	−	0.702740i
$435$		0			0
$436$	−6.87330	−	6.23633i	−0.329172	−	0.298666i
$437$		−	5.89325i		−	0.281912i
$438$	−2.61644	+	1.15895i	−0.125018	+	0.0553766i
$439$	−3.40264			−0.162399			−0.0811995	−	0.996698i	$-0.525875\pi$
$439$	−3.40264			−0.162399			−0.0811995	+	0.996698i	$0.525875\pi$
$440$		0			0
$441$	1.36843			0.0651633
$442$	−7.52709	+	3.33411i	−0.358027	+	0.158587i
$443$		−	14.1103i		−	0.670399i	−0.942147	−	0.335199i	$-0.891196\pi$
$443$		−	14.1103i		−	0.670399i	0.942147	−	0.335199i	$-0.108804\pi$
$444$	−0.121633	+	0.134057i	−0.00577245	+	0.00636205i
$445$		0			0
$446$	−0.411723	−	0.929506i	−0.0194956	−	0.0440134i
$447$	4.06506			0.192271
$448$	−17.5327	−	13.0469i	−0.828341	−	0.616410i
$449$	−18.9957			−0.896463			−0.448231	−	0.893918i	$-0.647946\pi$
$449$	−18.9957			−0.896463			−0.448231	+	0.893918i	$0.647946\pi$
$450$		0			0
$451$		−	5.09617i		−	0.239969i
$452$	22.9342	−	25.2767i	1.07873	−	1.18891i
$453$		−	4.53066i		−	0.212869i
$454$	−15.6086	+	6.91382i	−0.732550	+	0.324482i
$455$		0			0
$456$	−0.503719	−	0.166856i	−0.0235888	−	0.00781376i
$457$	28.3050			1.32405			0.662027	−	0.749480i	$-0.269697\pi$
$457$	28.3050			1.32405			0.662027	+	0.749480i	$0.269697\pi$
$458$	−13.3711	+	5.92273i	−0.624793	+	0.276751i
$459$		−	3.62308i		−	0.169111i
$460$		0			0
$461$		−	11.2576i		−	0.524320i	−0.965024	−	0.262160i	$-0.915565\pi$
$461$		−	11.2576i		−	0.524320i	0.965024	−	0.262160i	$-0.0844348\pi$
$462$	0.282507	+	0.637788i	0.0131434	+	0.0296726i
$463$	−1.11665			−0.0518950			−0.0259475	−	0.999663i	$-0.508260\pi$
$463$	−1.11665			−0.0518950			−0.0259475	+	0.999663i	$0.508260\pi$
$464$	30.7195	−	2.99230i	1.42612	−	0.138914i
$465$		0			0
$466$	−2.30988	−	5.21479i	−0.107003	−	0.241570i
$467$			1.34496i			0.0622374i	0.999516	+	0.0311187i	$0.00990699\pi$
$467$			1.34496i			0.0622374i	−0.999516	+	0.0311187i	$0.990093\pi$
$468$	−8.68652	−	7.88150i	−0.401534	−	0.364322i
$469$			28.0297i			1.29429i
$470$		0			0
$471$	1.10679			0.0509983
$472$	−11.4017	+	34.4205i	−0.524808	+	1.58433i
$473$	3.09505			0.142311
$474$	0.809620	−	0.358620i	0.0371871	−	0.0164720i
$475$		0			0
$476$	−10.7760	+	11.8767i	−0.493919	+	0.544367i
$477$			28.6408i			1.31137i
$478$	6.71650	+	15.1632i	0.307205	+	0.693547i
$479$	26.2181			1.19794			0.598968	−	0.800773i	$-0.295578\pi$
$479$	26.2181			1.19794			0.598968	+	0.800773i	$0.295578\pi$
$480$		0			0
$481$	0.866263			0.0394982
$482$	−7.31385	−	16.5118i	−0.333137	−	0.752090i
$483$			3.68442i			0.167647i
$484$	−13.7626	+	15.1683i	−0.625574	+	0.689470i
$485$		0			0
$486$	7.09654	−	3.14340i	0.321906	−	0.142588i
$487$	12.2782			0.556378			0.278189	−	0.960526i	$-0.410266\pi$
$487$	12.2782			0.556378			0.278189	+	0.960526i	$0.410266\pi$
$488$	−11.3313	+	34.2078i	−0.512944	+	1.54852i
$489$	−3.61945			−0.163677
$490$		0			0
$491$			32.3053i			1.45792i	0.684558	+	0.728959i	$0.259995\pi$
$491$			32.3053i			1.45792i	−0.684558	+	0.728959i	$0.740005\pi$
$492$	−1.79495	−	1.62861i	−0.0809228	−	0.0734233i
$493$		−	22.6486i		−	1.02004i
$494$	1.02846	+	2.32184i	0.0462724	+	0.104465i
$495$		0			0
$496$	1.60723	+	16.5001i	0.0721666	+	0.740876i
$497$	35.2907			1.58300
$498$	1.17274	+	2.64758i	0.0525518	+	0.118641i
$499$			6.14059i			0.274890i	0.990509	+	0.137445i	$0.0438891\pi$
$499$			6.14059i			0.274890i	−0.990509	+	0.137445i	$0.956111\pi$
$500$		0			0
$501$			2.40270i			0.107345i
$502$	−29.4847	+	13.0602i	−1.31597	+	0.582905i
$503$	26.1226			1.16475			0.582375	−	0.812921i	$-0.302124\pi$
$503$	26.1226			1.16475			0.582375	+	0.812921i	$0.302124\pi$
$504$	−21.6894	−	7.18460i	−0.966123	−	0.320027i
$505$		0			0
$506$	7.33382	−	3.24850i	0.326028	−	0.144414i
$507$			1.87870i			0.0834362i
$508$	−5.27419	+	5.81289i	−0.234004	+	0.257905i
$509$			8.02196i			0.355567i	0.984070	+	0.177784i	$0.0568927\pi$
$509$			8.02196i			0.355567i	−0.984070	+	0.177784i	$0.943107\pi$
$510$		0			0
$511$	26.6772			1.18013
$512$	12.9843	+	18.5313i	0.573831	+	0.818974i
$513$	−1.11759			−0.0493429
$514$	12.9920	+	29.3307i	0.573051	+	1.29372i
$515$		0			0
$516$	0.989101	−	1.09013i	0.0435427	−	0.0479902i
$517$		−	4.09213i		−	0.179972i
$518$	1.54289	−	0.683421i	0.0677907	−	0.0300278i
$519$	−1.88049			−0.0825446
$520$		0			0
$521$	−37.3348			−1.63567			−0.817833	−	0.575456i	$-0.804825\pi$
$521$	−37.3348			−1.63567			−0.817833	+	0.575456i	$0.804825\pi$
$522$	29.5038	−	13.0687i	1.29135	−	0.572000i
$523$		−	41.8753i		−	1.83108i	−0.402230	−	0.915539i	$-0.631765\pi$
$523$		−	41.8753i		−	1.83108i	0.402230	−	0.915539i	$-0.368235\pi$
$524$	24.9917	+	22.6756i	1.09177	+	0.990589i
$525$		0			0
$526$	8.59503	+	19.4041i	0.374761	+	0.846061i
$527$	12.1651			0.529919
$528$	−0.0700187	−	0.718825i	−0.00304717	−	0.0312829i
$529$	19.3666			0.842025
$530$		0			0
$531$			37.9088i			1.64510i
$532$	3.66354	+	3.32403i	0.158835	+	0.144115i
$533$			11.5988i			0.502401i
$534$	−2.15580	+	0.954908i	−0.0932906	+	0.0413229i
$535$		0			0
$536$	9.12558	−	27.5490i	0.394165	−	1.18994i
$537$	2.07698			0.0896283
$538$	19.9051	−	8.81694i	0.858171	−	0.380125i
$539$		−	0.403244i		−	0.0173690i
$540$		0			0
$541$			33.1542i			1.42541i	0.701464	+	0.712705i	$0.252530\pi$
$541$			33.1542i			1.42541i	−0.701464	+	0.712705i	$0.747470\pi$
$542$	8.68494	+	19.6071i	0.373050	+	0.842198i
$543$	−2.96291			−0.127151
$544$	14.4579	−	8.16468i	0.619877	−	0.350058i
$545$		0			0
$546$	−0.642984	−	1.45160i	−0.0275172	−	0.0621227i
$547$			21.2749i			0.909650i	0.890581	+	0.454825i	$0.150298\pi$
$547$			21.2749i			0.909650i	−0.890581	+	0.454825i	$0.849702\pi$
$548$	9.16228	−	10.0981i	0.391393	−	0.431370i
$549$			37.6746i			1.60791i
$550$		0			0
$551$	−6.98631			−0.297627
$552$	1.19953	−	3.62123i	0.0510554	−	0.154130i
$553$	−8.25489			−0.351034
$554$	12.6835	−	5.61814i	0.538871	−	0.238692i
$555$		0			0
$556$	19.9390	+	18.0912i	0.845602	+	0.767237i
$557$			1.73333i			0.0734437i	0.999326	+	0.0367219i	$0.0116916\pi$
$557$			1.73333i			0.0734437i	−0.999326	+	0.0367219i	$0.988308\pi$
$558$	7.01946	+	15.8471i	0.297157	+	0.670862i
$559$	−7.04431			−0.297943
$560$		0			0
$561$	−0.529970			−0.0223754
$562$	−1.95858	−	4.42168i	−0.0826176	−	0.186517i
$563$			47.0184i			1.98159i	0.135369	+	0.990795i	$0.456778\pi$
$563$			47.0184i			1.98159i	−0.135369	+	0.990795i	$0.543222\pi$
$564$	−1.44132	−	1.30774i	−0.0606903	−	0.0550659i
$565$		0			0
$566$	−31.7398	+	14.0591i	−1.33412	+	0.590948i
$567$	−23.5357			−0.988405
$568$	−34.6855	−	11.4895i	−1.45537	−	0.482090i
$569$	−0.301785			−0.0126515			−0.00632573	−	0.999980i	$-0.502014\pi$
$569$	−0.301785			−0.0126515			−0.00632573	+	0.999980i	$0.502014\pi$
$570$		0			0
$571$		−	30.2200i		−	1.26467i	−0.774697	−	0.632333i	$-0.782097\pi$
$571$		−	30.2200i		−	1.26467i	0.774697	−	0.632333i	$-0.217903\pi$
$572$	−2.32249	+	2.55971i	−0.0971083	+	0.107027i
$573$		−	2.78518i		−	0.116353i
$574$	9.15067	+	20.6586i	0.381942	+	0.862272i
$575$		0			0
$576$	18.9784	+	14.1228i	0.790765	+	0.588448i
$577$	−4.58089			−0.190705			−0.0953524	−	0.995444i	$-0.530398\pi$
$577$	−4.58089			−0.190705			−0.0953524	+	0.995444i	$0.530398\pi$
$578$	4.80229	+	10.8416i	0.199749	+	0.450953i
$579$			4.14872i			0.172415i
$580$		0			0
$581$		−	26.9947i		−	1.11993i
$582$	3.26705	−	1.44713i	0.135423	−	0.0599856i
$583$	8.43976			0.349539
$584$	−26.2197	−	8.68524i	−1.08498	−	0.359398i
$585$		0			0
$586$	−29.6782	+	13.1459i	−1.22600	+	0.543052i
$587$		−	0.387716i		−	0.0160028i	−0.999968	−	0.00800138i	$-0.997453\pi$
$587$		−	0.387716i		−	0.0160028i	0.999968	−	0.00800138i	$-0.00254695\pi$
$588$	−0.142029	−	0.128867i	−0.00585718	−	0.00531437i
$589$		−	3.75250i		−	0.154619i
$590$		0			0
$591$	2.79654			0.115034
$592$	−1.73893	+	0.169384i	−0.0714696	+	0.00696165i
$593$	14.5864			0.598994			0.299497	−	0.954097i	$-0.403181\pi$
$593$	14.5864			0.598994			0.299497	+	0.954097i	$0.403181\pi$
$594$	−0.616044	−	1.39078i	−0.0252766	−	0.0570644i
$595$		0			0
$596$	29.0581	+	26.3652i	1.19027	+	1.07996i
$597$		−	2.92298i		−	0.119630i
$598$	−16.6917	+	7.39357i	−0.682575	+	0.302345i
$599$	5.66881			0.231621			0.115811	−	0.993271i	$-0.463053\pi$
$599$	5.66881			0.231621			0.115811	+	0.993271i	$0.463053\pi$
$600$		0			0
$601$	−29.8385			−1.21714			−0.608569	−	0.793501i	$-0.708256\pi$
$601$	−29.8385			−1.21714			−0.608569	+	0.793501i	$0.708256\pi$
$602$	−12.5465	+	5.55747i	−0.511359	+	0.226506i
$603$		−	30.3410i		−	1.23558i
$604$	29.3850	−	32.3864i	1.19566	−	1.31778i
$605$		0			0
$606$	−0.654433	−	1.47745i	−0.0265845	−	0.0600172i
$607$	19.4752			0.790474			0.395237	−	0.918579i	$-0.370662\pi$
$607$	19.4752			0.790474			0.395237	+	0.918579i	$0.370662\pi$
$608$	−2.51852	−	4.45975i	−0.102139	−	0.180867i
$609$	4.36779			0.176992
$610$		0			0
$611$			9.31365i			0.376790i
$612$	11.6646	−	12.8560i	0.471513	−	0.519674i
$613$		−	39.6234i		−	1.60037i	−0.599752	−	0.800186i	$-0.704734\pi$
$613$		−	39.6234i		−	1.60037i	0.599752	−	0.800186i	$-0.295266\pi$
$614$	−2.98929	+	1.32410i	−0.120638	+	0.0534363i
$615$		0			0
$616$	−2.11713	+	6.39136i	−0.0853017	+	0.257515i
$617$	−32.0519			−1.29036			−0.645180	−	0.764031i	$-0.723218\pi$
$617$	−32.0519			−1.29036			−0.645180	+	0.764031i	$0.723218\pi$
$618$	1.33584	−	0.591710i	0.0537355	−	0.0238021i
$619$			17.9597i			0.721861i	0.932593	+	0.360930i	$0.117541\pi$
$619$			17.9597i			0.721861i	−0.932593	+	0.360930i	$0.882459\pi$
$620$		0			0
$621$		−	8.03437i		−	0.322408i
$622$	−0.228044	−	0.514832i	−0.00914374	−	0.0206429i
$623$	21.9805			0.880632
$624$	0.159362	+	1.63604i	0.00637958	+	0.0654940i
$625$		0			0
$626$	−15.9165	−	35.9331i	−0.636152	−	1.43618i
$627$			0.163477i			0.00652865i
$628$	7.91164	+	7.17843i	0.315709	+	0.286451i
$629$			1.28207i			0.0511193i
$630$		0			0
$631$	28.0265			1.11572			0.557858	−	0.829936i	$-0.311623\pi$
$631$	28.0265			1.11572			0.557858	+	0.829936i	$0.311623\pi$
$632$	8.11332	+	2.68753i	0.322730	+	0.106904i
$633$	−2.72180			−0.108182
$634$	21.6189	−	9.57606i	0.858596	−	0.380314i
$635$		0			0
$636$	2.69714	−	2.97262i	0.106948	−	0.117872i
$637$			0.917780i			0.0363638i
$638$	−3.85103	−	8.69408i	−0.152464	−	0.344202i
$639$	−38.2007			−1.51120
$640$		0			0
$641$	−11.2647			−0.444929			−0.222465	−	0.974941i	$-0.571410\pi$
$641$	−11.2647			−0.444929			−0.222465	+	0.974941i	$0.571410\pi$
$642$	1.47680	+	3.33402i	0.0582845	+	0.131583i
$643$			48.2471i			1.90268i	0.308141	+	0.951341i	$0.400293\pi$
$643$			48.2471i			1.90268i	−0.308141	+	0.951341i	$0.599707\pi$
$644$	−23.8964	+	26.3372i	−0.941651	+	1.03783i
$645$		0			0
$646$	−3.43632	+	1.52211i	−0.135200	+	0.0598867i
$647$	−31.8798			−1.25333			−0.626663	−	0.779291i	$-0.715580\pi$
$647$	−31.8798			−1.25333			−0.626663	+	0.779291i	$0.715580\pi$
$648$	23.1320	+	7.66246i	0.908712	+	0.301010i
$649$	11.1708			0.438494
$650$		0			0
$651$			2.34604i			0.0919484i
$652$	−25.8727	−	23.4750i	−1.01325	−	0.919352i
$653$			36.3662i			1.42312i	0.702627	+	0.711559i	$0.252010\pi$
$653$			36.3662i			1.42312i	−0.702627	+	0.711559i	$0.747990\pi$
$654$	0.550720	+	1.24331i	0.0215349	+	0.0486171i
$655$		0			0
$656$	−2.26797	−	23.2834i	−0.0885494	−	0.909065i
$657$	−28.8769			−1.12660
$658$	7.34783	+	16.5884i	0.286448	+	0.646685i
$659$			5.48884i			0.213815i	0.994269	+	0.106907i	$0.0340949\pi$
$659$			5.48884i			0.213815i	−0.994269	+	0.106907i	$0.965905\pi$
$660$		0			0
$661$		−	29.5221i		−	1.14828i	−0.818759	−	0.574138i	$-0.805337\pi$
$661$		−	29.5221i		−	1.14828i	0.818759	−	0.574138i	$-0.194663\pi$
$662$	16.5303	−	7.32206i	0.642467	−	0.284580i
$663$	1.20621			0.0468452
$664$	−8.78862	+	26.5318i	−0.341065	+	1.02963i
$665$		0			0
$666$	−1.67011	+	0.739774i	−0.0647156	+	0.0286657i
$667$		−	50.2246i		−	1.94470i
$668$	−15.5835	+	17.1752i	−0.602942	+	0.664527i
$669$			0.148952i			0.00575883i
$670$		0			0
$671$	11.1018			0.428581
$672$	1.57456	+	2.78821i	0.0607399	+	0.107557i
$673$	−41.5796			−1.60278			−0.801389	−	0.598144i	$-0.795905\pi$
$673$	−41.5796			−1.60278			−0.801389	+	0.598144i	$0.795905\pi$
$674$	−2.71282	−	6.12446i	−0.104494	−	0.235905i
$675$		0			0
$676$	−12.1849	+	13.4295i	−0.468650	+	0.516518i
$677$			35.3724i			1.35947i	0.733457	+	0.679736i	$0.237906\pi$
$677$			35.3724i			1.35947i	−0.733457	+	0.679736i	$0.762094\pi$
$678$	−4.57227	+	2.02528i	−0.175597	+	0.0777804i
$679$	−33.3108			−1.27835
$680$		0			0
$681$	2.50127			0.0958488
$682$	4.66977	−	2.06847i	0.178815	−	0.0792058i
$683$		−	22.5077i		−	0.861233i	−0.902535	−	0.430617i	$-0.858296\pi$
$683$		−	22.5077i		−	0.861233i	0.902535	−	0.430617i	$-0.141704\pi$
$684$	−3.96563	−	3.59812i	−0.151630	−	0.137577i
$685$		0			0
$686$	−10.2284	−	23.0917i	−0.390524	−	0.881646i
$687$	2.14271			0.0817496
$688$	14.1407	−	1.37740i	0.539109	−	0.0525131i
$689$	−19.2088			−0.731798
$690$		0			0
$691$			0.855355i			0.0325392i	0.999868	+	0.0162696i	$0.00517901\pi$
$691$			0.855355i			0.0325392i	−0.999868	+	0.0162696i	$0.994821\pi$
$692$	−13.4423	−	12.1965i	−0.510998	−	0.463642i
$693$			7.03910i			0.267393i
$694$	33.2415	−	14.7243i	1.26183	−	0.558925i
$695$		0			0
$696$	−4.29289	−	1.42201i	−0.162721	−	0.0539013i
$697$	−17.1662			−0.650218
$698$	9.29103	−	4.11545i	0.351671	−	0.155772i
$699$			0.835664i			0.0316077i
$700$		0			0
$701$		−	16.7658i		−	0.633236i	−0.948553	−	0.316618i	$-0.897453\pi$
$701$		−	16.7658i		−	0.633236i	0.948553	−	0.316618i	$-0.102547\pi$
$702$	1.40211	+	3.16540i	0.0529193	+	0.119471i
$703$	0.395472			0.0149155
$704$	4.16165	−	5.59248i	0.156848	−	0.210774i
$705$		0			0
$706$	−3.42311	−	7.72801i	−0.128830	−	0.290848i
$707$			15.0641i			0.566542i
$708$	3.56992	−	3.93455i	0.134166	−	0.147870i
$709$			21.8389i			0.820177i	0.912046	+	0.410088i	$0.134502\pi$
$709$			21.8389i			0.820177i	−0.912046	+	0.410088i	$0.865498\pi$
$710$		0			0
$711$	8.93557			0.335110
$712$	−21.6036	−	7.15616i	−0.809628	−	0.268188i
$713$	26.9767			1.01029
$714$	2.14836	−	0.951614i	0.0804005	−	0.0356133i
$715$		0			0
$716$	14.8468	+	13.4709i	0.554851	+	0.503430i
$717$		−	2.42988i		−	0.0907456i
$718$	−17.6275	−	39.7958i	−0.657852	−	1.48517i
$719$	28.2838			1.05481			0.527403	−	0.849615i	$-0.323166\pi$
$719$	28.2838			1.05481			0.527403	+	0.849615i	$0.323166\pi$
$720$		0			0
$721$	−13.6203			−0.507245
$722$	−10.4127	−	23.5078i	−0.387522	−	0.874870i
$723$			2.64599i			0.0984055i
$724$	−21.1796	−	19.2168i	−0.787135	−	0.714188i
$725$		0			0
$726$	2.74378	−	1.21535i	0.101831	−	0.0451060i
$727$	18.7205			0.694305			0.347152	−	0.937809i	$-0.387149\pi$
$727$	18.7205			0.694305			0.347152	+	0.937809i	$0.387149\pi$
$728$	4.81857	−	14.5467i	0.178588	−	0.539136i
$729$	24.7091			0.915150
$730$		0			0
$731$		−	10.4256i		−	0.385603i
$732$	3.54787	−	3.91025i	0.131133	−	0.144527i
$733$			3.61353i			0.133469i	0.997771	+	0.0667344i	$0.0212580\pi$
$733$			3.61353i			0.133469i	−0.997771	+	0.0667344i	$0.978742\pi$
$734$	−12.8271	−	28.9584i	−0.473456	−	1.06887i
$735$		0			0
$736$	32.0611	−	18.1056i	1.18179	−	0.667381i
$737$	−8.94077			−0.329338
$738$	−9.90522	−	22.3620i	−0.364616	−	0.823157i
$739$		−	31.3284i		−	1.15243i	−0.817296	−	0.576217i	$-0.804528\pi$
$739$		−	31.3284i		−	1.15243i	0.817296	−	0.576217i	$-0.195472\pi$
$740$		0			0
$741$		−	0.372073i		−	0.0136684i
$742$	−34.2126	+	15.1544i	−1.25599	+	0.556337i
$743$	−44.8723			−1.64621			−0.823103	−	0.567892i	$-0.807759\pi$
$743$	−44.8723			−1.64621			−0.823103	+	0.567892i	$0.807759\pi$
$744$	0.763795	−	2.30580i	0.0280021	−	0.0845348i
$745$		0			0
$746$	20.9265	−	9.26936i	0.766174	−	0.339376i
$747$			29.2206i			1.06913i
$748$	−3.78837	−	3.43728i	−0.138516	−	0.125679i
$749$		−	33.9936i		−	1.24210i
$750$		0			0
$751$	29.7771			1.08658			0.543292	−	0.839544i	$-0.317178\pi$
$751$	29.7771			1.08658			0.543292	+	0.839544i	$0.317178\pi$
$752$	−1.82114	−	18.6962i	−0.0664101	−	0.681779i
$753$	4.72489			0.172185
$754$	8.76490	+	19.7876i	0.319199	+	0.720623i
$755$		0			0
$756$	4.99457	+	4.53170i	0.181651	+	0.164816i
$757$		−	33.1452i		−	1.20468i	−0.798239	−	0.602341i	$-0.794235\pi$
$757$		−	33.1452i		−	1.20468i	0.798239	−	0.602341i	$-0.205765\pi$
$758$	14.1836	−	6.28260i	0.515171	−	0.228194i
$759$	−1.17524			−0.0426584
$760$		0			0
$761$	−14.1986			−0.514699			−0.257350	−	0.966318i	$-0.582849\pi$
$761$	−14.1986			−0.514699			−0.257350	+	0.966318i	$0.582849\pi$
$762$	1.05149	−	0.465755i	0.0380914	−	0.0168725i
$763$		−	12.6767i		−	0.458929i
$764$	18.0641	−	19.9092i	0.653537	−	0.720289i
$765$		0			0
$766$	−10.5281	−	23.7682i	−0.380395	−	0.858779i
$767$	−25.4247			−0.918034
$768$	−0.639804	−	3.25302i	−0.0230869	−	0.117383i
$769$	5.12825			0.184930			0.0924648	−	0.995716i	$-0.470525\pi$
$769$	5.12825			0.184930			0.0924648	+	0.995716i	$0.470525\pi$
$770$		0			0
$771$		−	4.70021i		−	0.169274i
$772$	−26.9078	+	29.6561i	−0.968432	+	1.06735i
$773$			1.17666i			0.0423216i	0.999776	+	0.0211608i	$0.00673619\pi$
$773$			1.17666i			0.0423216i	−0.999776	+	0.0211608i	$0.993264\pi$
$774$	13.5811	−	6.01572i	0.488163	−	0.216231i
$775$		0			0
$776$	32.7395	+	10.8449i	1.17528	+	0.389310i
$777$	−0.247247			−0.00886992
$778$	−39.1119	+	17.3246i	−1.40223	+	0.621116i
$779$			5.29518i			0.189720i
$780$		0			0
$781$			11.2568i			0.402801i
$782$	−10.9425	−	24.7037i	−0.391301	−	0.883402i
$783$	−9.52455			−0.340380
$784$	−0.179458	−	1.84235i	−0.00640920	−	0.0657981i
$785$		0			0
$786$	−2.00245	−	4.52072i	−0.0714249	−	0.161249i
$787$		−	0.644823i		−	0.0229854i	−0.999934	−	0.0114927i	$-0.996342\pi$
$787$		−	0.644823i		−	0.0229854i	0.999934	−	0.0114927i	$-0.00365833\pi$
$788$	19.9904	+	18.1378i	0.712128	+	0.646132i
$789$		−	3.10949i		−	0.110701i
$790$		0			0
$791$	46.6189			1.65758
$792$	2.29171	−	6.91838i	0.0814322	−	0.245834i
$793$	−25.2677			−0.897281
$794$	−50.5929	+	22.4100i	−1.79547	+	0.795302i
$795$		0			0
$796$	18.9579	−	20.8942i	0.671944	−	0.740576i
$797$		−	0.822745i		−	0.0291431i	−0.999894	−	0.0145716i	$-0.995362\pi$
$797$		−	0.822745i		−	0.0291431i	0.999894	−	0.0145716i	$-0.00463844\pi$
$798$	−0.293539	−	0.662695i	−0.0103912	−	0.0234591i
$799$	−13.7842			−0.487649
$800$		0			0
$801$	−23.7930			−0.840684
$802$	5.87684	+	13.2676i	0.207518	+	0.468494i
$803$			8.50934i			0.300288i
$804$	−2.85725	+	3.14909i	−0.100767	+	0.111060i
$805$		0			0
$806$	−10.6284	+	4.70782i	−0.374368	+	0.165826i
$807$	−3.18978			−0.112285
$808$	4.90438	−	14.8057i	0.172535	−	0.520863i
$809$	−11.5085			−0.404619			−0.202309	−	0.979322i	$-0.564845\pi$
$809$	−11.5085			−0.404619			−0.202309	+	0.979322i	$0.564845\pi$
$810$		0			0
$811$			51.7936i			1.81872i	0.416011	+	0.909360i	$0.363428\pi$
$811$			51.7936i			1.81872i	−0.416011	+	0.909360i	$0.636572\pi$
$812$	31.2221	+	28.3287i	1.09568	+	0.994141i
$813$		−	3.14202i		−	0.110195i
$814$	0.217994	+	0.492143i	0.00764069	+	0.0172496i
$815$		0			0
$816$	−2.42133	+	0.235855i	−0.0847636	+	0.00825658i
$817$	−3.21592			−0.112511
$818$	−5.97853	−	13.4971i	−0.209035	−	0.471916i
$819$		−	16.0209i		−	0.559816i
$820$		0			0
$821$		−	1.66017i		−	0.0579403i	−0.999580	−	0.0289702i	$-0.990777\pi$
$821$		−	1.66017i		−	0.0579403i	0.999580	−	0.0289702i	$-0.00922278\pi$
$822$	−1.82664	+	0.809106i	−0.0637113	+	0.0282208i
$823$	−33.9444			−1.18323			−0.591613	−	0.806222i	$-0.701509\pi$
$823$	−33.9444			−1.18323			−0.591613	+	0.806222i	$0.701509\pi$
$824$	13.3867	+	4.43432i	0.466347	+	0.154477i
$825$		0			0
$826$	−45.2837	+	20.0583i	−1.57562	+	0.697919i
$827$		−	35.2510i		−	1.22580i	−0.790162	−	0.612898i	$-0.790004\pi$
$827$		−	35.2510i		−	1.22580i	0.790162	−	0.612898i	$-0.209996\pi$
$828$	25.8669	−	28.5089i	0.898936	−	0.990753i
$829$		−	36.8215i		−	1.27886i	−0.768847	−	0.639432i	$-0.779169\pi$
$829$		−	36.8215i		−	1.27886i	0.768847	−	0.639432i	$-0.220831\pi$
$830$		0			0
$831$	−2.03252			−0.0705073
$832$	−9.47187	+	12.7284i	−0.328378	+	0.441279i
$833$	−1.35831			−0.0470627
$834$	−1.59760	−	3.60675i	−0.0553205	−	0.124891i
$835$		0			0
$836$	−1.06028	+	1.16858i	−0.0366706	+	0.0404161i
$837$		−	5.11584i		−	0.176829i
$838$	47.4039	−	20.9975i	1.63754	−	0.725345i
$839$	40.2678			1.39020			0.695100	−	0.718913i	$-0.255360\pi$
$839$	40.2678			1.39020			0.695100	+	0.718913i	$0.255360\pi$
$840$		0			0
$841$	−30.5401			−1.05311
$842$	−13.4567	+	5.96062i	−0.463748	+	0.205417i
$843$			0.708570i			0.0244044i
$844$	−19.4561	−	17.6530i	−0.669707	−	0.607642i
$845$		0			0
$846$	−7.95371	−	17.9563i	−0.273454	−	0.617350i
$847$	−27.9756			−0.961253
$848$	38.5597	−	3.75599i	1.32414	−	0.128981i
$849$	5.08627			0.174560
$850$		0			0
$851$			2.84305i			0.0974585i
$852$	3.96484	+	3.59740i	0.135833	+	0.123245i
$853$			52.0753i			1.78302i	0.452997	+	0.891512i	$0.350355\pi$
$853$			52.0753i			1.78302i	−0.452997	+	0.891512i	$0.649645\pi$
$854$	−45.0040	+	19.9344i	−1.54000	+	0.682142i
$855$		0			0
$856$	−11.0672	+	33.4106i	−0.378270	+	1.14195i
$857$	48.7275			1.66450			0.832250	−	0.554400i	$-0.187052\pi$
$857$	48.7275			1.66450			0.832250	+	0.554400i	$0.187052\pi$
$858$	0.463024	−	0.205096i	0.0158074	−	0.00700185i
$859$		−	34.8415i		−	1.18878i	−0.804178	−	0.594389i	$-0.797394\pi$
$859$		−	34.8415i		−	1.18878i	0.804178	−	0.594389i	$-0.202606\pi$
$860$		0			0
$861$		−	3.31051i		−	0.112822i
$862$	5.94895	+	13.4303i	0.202622	+	0.457439i
$863$	−14.8198			−0.504473			−0.252237	−	0.967666i	$-0.581166\pi$
$863$	−14.8198			−0.504473			−0.252237	+	0.967666i	$0.581166\pi$
$864$	−3.43353	−	6.08005i	−0.116811	−	0.206848i
$865$		0			0
$866$	−4.01729	−	9.06943i	−0.136513	−	0.308192i
$867$		−	1.73736i		−	0.0590039i
$868$	−15.2159	+	16.7701i	−0.516462	+	0.569214i
$869$		−	2.63310i		−	0.0893218i
$870$		0			0
$871$	20.3491			0.689504
$872$	−4.12714	+	12.4593i	−0.139763	+	0.421926i
$873$	36.0575			1.22036
$874$	−7.62022	+	3.37536i	−0.257758	+	0.114173i
$875$		0			0
$876$	2.99713	+	2.71937i	0.101264	+	0.0918791i
$877$		−	5.24283i		−	0.177038i	−0.996074	−	0.0885189i	$-0.971787\pi$
$877$		−	5.24283i		−	0.177038i	0.996074	−	0.0885189i	$-0.0282134\pi$
$878$	1.94886	+	4.39975i	0.0657709	+	0.148484i
$879$	4.75590			0.160413
$880$		0			0
$881$	−24.2313			−0.816374			−0.408187	−	0.912898i	$-0.633839\pi$
$881$	−24.2313			−0.816374			−0.408187	+	0.912898i	$0.633839\pi$
$882$	−0.783769	−	1.76944i	−0.0263909	−	0.0595801i
$883$			40.7796i			1.37234i	0.727439	+	0.686172i	$0.240710\pi$
$883$			40.7796i			1.37234i	−0.727439	+	0.686172i	$0.759290\pi$
$884$	8.62229	+	7.82322i	0.289999	+	0.263123i
$885$		0			0
$886$	−18.2451	+	8.08166i	−0.612958	+	0.271509i
$887$	−4.68906			−0.157443			−0.0787216	−	0.996897i	$-0.525084\pi$
$887$	−4.68906			−0.157443			−0.0787216	+	0.996897i	$0.525084\pi$
$888$	0.243006	+	0.0804956i	0.00815476	+	0.00270126i
$889$	−10.7210			−0.359570
$890$		0			0
$891$		−	7.50729i		−	0.251504i
$892$	−0.966075	+	1.06475i	−0.0323466	+	0.0356505i
$893$			4.25194i			0.142286i
$894$	−2.32827	−	5.25629i	−0.0778689	−	0.175797i
$895$		0			0
$896$	−6.82840	+	30.1431i	−0.228121	+	1.00701i
$897$	2.67483			0.0893100
$898$	10.8798	+	24.5622i	0.363064	+	0.819652i
$899$		−	31.9802i		−	1.06660i
$900$		0			0
$901$		−	28.4290i		−	0.947108i
$902$	−6.58956	+	2.91883i	−0.219408	+	0.0971865i
$903$	2.01057			0.0669076
$904$	−45.8193	−	15.1776i	−1.52393	−	0.504800i
$905$		0			0
$906$	−5.85834	+	2.59494i	−0.194630	+	0.0862111i
$907$			3.54602i			0.117744i	0.998266	+	0.0588718i	$0.0187503\pi$
$907$			3.54602i			0.117744i	−0.998266	+	0.0588718i	$0.981250\pi$
$908$	17.8797	+	16.2227i	0.593359	+	0.538370i
$909$		−	16.3062i		−	0.540843i
$910$		0			0
$911$	24.9437			0.826420			0.413210	−	0.910636i	$-0.364407\pi$
$911$	24.9437			0.826420			0.413210	+	0.910636i	$0.364407\pi$
$912$	0.0727530	+	0.746896i	0.00240909	+	0.0247322i
$913$	8.61063			0.284970
$914$	−16.2117	−	36.5996i	−0.536236	−	1.21061i
$915$		0			0
$916$	15.3167	+	13.8972i	0.506077	+	0.459177i
$917$			46.0933i			1.52213i
$918$	−4.68479	+	2.07512i	−0.154621	+	0.0684892i
$919$	−4.92584			−0.162488			−0.0812442	−	0.996694i	$-0.525889\pi$
$919$	−4.92584			−0.162488			−0.0812442	+	0.996694i	$0.525889\pi$
$920$		0			0
$921$	0.479030			0.0157846
$922$	−14.5566	+	6.44781i	−0.479395	+	0.212347i
$923$		−	25.6205i		−	0.843308i
$924$	0.662880	−	0.730587i	0.0218072	−	0.0240345i
$925$		0			0
$926$	0.639560	+	1.44387i	0.0210172	+	0.0474485i
$927$	14.7434			0.484235
$928$	−21.4638	−	38.0077i	−0.704583	−	1.24767i
$929$	−39.6646			−1.30135			−0.650677	−	0.759354i	$-0.725515\pi$
$929$	−39.6646			−1.30135			−0.650677	+	0.759354i	$0.725515\pi$
$930$		0			0
$931$			0.418991i			0.0137319i
$932$	−5.41995	+	5.97354i	−0.177536	+	0.195670i
$933$			0.0825014i			0.00270097i
$934$	1.73909	−	0.770328i	0.0569048	−	0.0252059i
$935$		0			0
$936$	−5.21590	+	15.7462i	−0.170487	+	0.514679i
$937$	31.3308			1.02353			0.511767	−	0.859125i	$-0.328991\pi$
$937$	31.3308			1.02353			0.511767	+	0.859125i	$0.328991\pi$
$938$	36.2436	−	16.0540i	1.18340	−	0.524183i
$939$			5.75824i			0.187913i
$940$		0			0
$941$		−	13.1179i		−	0.427630i	−0.976874	−	0.213815i	$-0.931411\pi$
$941$		−	13.1179i		−	0.427630i	0.976874	−	0.213815i	$-0.0685889\pi$
$942$	−0.633916	−	1.43113i	−0.0206541	−	0.0466287i
$943$	−38.0671			−1.23963
$944$	51.0374	−	4.97141i	1.66113	−	0.161806i
$945$		0			0
$946$	−1.77269	−	4.00203i	−0.0576352	−	0.130117i
$947$			32.0477i			1.04141i	0.853737	+	0.520705i	$0.174331\pi$
$947$			32.0477i			1.04141i	−0.853737	+	0.520705i	$0.825669\pi$
$948$	−0.927421	−	0.841473i	−0.0301212	−	0.0273298i
$949$		−	19.3672i		−	0.628686i
$950$		0			0
$951$	−3.46441			−0.112341
$952$	21.5290	+	7.13147i	0.697760	+	0.231132i
$953$	−33.0115			−1.06935			−0.534674	−	0.845059i	$-0.679565\pi$
$953$	−33.0115			−1.06935			−0.534674	+	0.845059i	$0.679565\pi$
$954$	37.0337	−	16.4040i	1.19901	−	0.531100i
$955$		0			0
$956$	15.7597	−	17.3694i	0.509706	−	0.561767i
$957$			1.39322i			0.0450363i
$958$	−15.0164	−	33.9011i	−0.485159	−	1.09530i
$959$	18.6244			0.601413
$960$		0			0
$961$	−13.8227			−0.445894
$962$	−0.496152	−	1.12011i	−0.0159966	−	0.0361139i
$963$			36.7967i			1.18576i
$964$	−17.1614	+	18.9142i	−0.552731	+	0.609186i
$965$		0			0
$966$	4.76411	−	2.11025i	0.153283	−	0.0678963i
$967$	58.2596			1.87350			0.936751	−	0.349995i	$-0.113817\pi$
$967$	58.2596			1.87350			0.936751	+	0.349995i	$0.113817\pi$
$968$	27.4958	+	9.10797i	0.883749	+	0.292741i
$969$	0.550666			0.0176900
$970$		0			0
$971$			25.2784i			0.811223i	0.914046	+	0.405612i	$0.132941\pi$
$971$			25.2784i			0.811223i	−0.914046	+	0.405612i	$0.867059\pi$
$972$	−8.12910	−	7.37574i	−0.260741	−	0.236577i
$973$			36.7744i			1.17893i
$974$	−7.03235	−	15.8762i	−0.225331	−	0.508707i
$975$		0			0
$976$	50.7222	−	4.94070i	1.62358	−	0.158148i
$977$	−17.7917			−0.569207			−0.284604	−	0.958645i	$-0.591862\pi$
$977$	−17.7917			−0.569207			−0.284604	+	0.958645i	$0.591862\pi$
$978$	2.07304	+	4.68009i	0.0662885	+	0.149653i
$979$			7.01124i			0.224080i
$980$		0			0
$981$			13.7220i			0.438111i
$982$	41.7721	−	18.5029i	1.33300	−	0.590450i
$983$	−33.3339			−1.06319			−0.531594	−	0.846999i	$-0.678407\pi$
$983$	−33.3339			−1.06319			−0.531594	+	0.846999i	$0.678407\pi$
$984$	−1.07780	+	3.25374i	−0.0343589	+	0.103725i
$985$		0			0
$986$	−29.2856	+	12.9720i	−0.932645	+	0.413113i
$987$		−	2.65828i		−	0.0846140i
$988$	2.41319	−	2.65967i	0.0767738	−	0.0846154i
$989$		−	23.1192i		−	0.735149i
$990$		0			0
$991$	−21.9753			−0.698069			−0.349034	−	0.937110i	$-0.613490\pi$
$991$	−21.9753			−0.698069			−0.349034	+	0.937110i	$0.613490\pi$
$992$	20.4148	−	11.5287i	0.648170	−	0.366035i
$993$	−2.64896			−0.0840622
$994$	−20.2128	−	45.6323i	−0.641110	−	1.44737i
$995$		0			0
$996$	2.75174	−	3.03281i	0.0871923	−	0.0960981i
$997$		−	42.6450i		−	1.35058i	−0.737553	−	0.675290i	$-0.764019\pi$
$997$		−	42.6450i		−	1.35058i	0.737553	−	0.675290i	$-0.235981\pi$
$998$	7.94004	−	3.51703i	0.251337	−	0.111330i
$999$	0.539154			0.0170581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.15	✓	40
4.3	odd	2		4000.2.d.c.2001.11		40
5.2	odd	4		1000.2.f.c.749.17		20
5.3	odd	4		1000.2.f.d.749.4		20
5.4	even	2	inner	1000.2.d.c.501.26	yes	40
8.3	odd	2		4000.2.d.c.2001.12		40
8.5	even	2	inner	1000.2.d.c.501.16	yes	40
20.3	even	4		4000.2.f.d.3249.9		20
20.7	even	4		4000.2.f.c.3249.12		20
20.19	odd	2		4000.2.d.c.2001.30		40
40.3	even	4		4000.2.f.c.3249.11		20
40.13	odd	4		1000.2.f.c.749.18		20
40.19	odd	2		4000.2.d.c.2001.29		40
40.27	even	4		4000.2.f.d.3249.10		20
40.29	even	2	inner	1000.2.d.c.501.25	yes	40
40.37	odd	4		1000.2.f.d.749.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.15	✓	40	1.1	even	1	trivial
1000.2.d.c.501.16	yes	40	8.5	even	2	inner
1000.2.d.c.501.25	yes	40	40.29	even	2	inner
1000.2.d.c.501.26	yes	40	5.4	even	2	inner
1000.2.f.c.749.17		20	5.2	odd	4
1000.2.f.c.749.18		20	40.13	odd	4
1000.2.f.d.749.3		20	40.37	odd	4
1000.2.f.d.749.4		20	5.3	odd	4
4000.2.d.c.2001.11		40	4.3	odd	2
4000.2.d.c.2001.12		40	8.3	odd	2
4000.2.d.c.2001.29		40	40.19	odd	2
4000.2.d.c.2001.30		40	20.19	odd	2
4000.2.f.c.3249.11		20	40.3	even	4
4000.2.f.c.3249.12		20	20.7	even	4
4000.2.f.d.3249.9		20	20.3	even	4
4000.2.f.d.3249.10		20	40.27	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.572751 - 1.29304i) q^{2} +0.207209i q^{3} +(-1.34391 + 1.48118i) q^{4} +(0.267929 - 0.118679i) q^{6} -2.73181 q^{7} +(2.68496 + 0.889389i) q^{8} +2.95706 q^{9} +O(q^{10})\)	\(q+(-0.572751 - 1.29304i) q^{2} +0.207209i q^{3} +(-1.34391 + 1.48118i) q^{4} +(0.267929 - 0.118679i) q^{6} -2.73181 q^{7} +(2.68496 + 0.889389i) q^{8} +2.95706 q^{9} -0.871377i q^{11} +(-0.306913 - 0.278470i) q^{12} +1.98325i q^{13} +(1.56464 + 3.53234i) q^{14} +(-0.387793 - 3.98116i) q^{16} -2.93520 q^{17} +(-1.69366 - 3.82361i) q^{18} +0.905406i q^{19} -0.566054i q^{21} +(-1.12673 + 0.499082i) q^{22} -6.50896 q^{23} +(-0.184289 + 0.556346i) q^{24} +(2.56442 - 1.13591i) q^{26} +1.23435i q^{27} +(3.67131 - 4.04630i) q^{28} +7.71622i q^{29} -4.14455 q^{31} +(-4.92569 + 2.78164i) q^{32} +0.180557 q^{33} +(1.68114 + 3.79533i) q^{34} +(-3.97404 + 4.37995i) q^{36} -0.436790i q^{37} +(1.17073 - 0.518572i) q^{38} -0.410946 q^{39} +5.84841 q^{41} +(-0.731931 + 0.324208i) q^{42} +3.55191i q^{43} +(1.29067 + 1.17106i) q^{44} +(3.72801 + 8.41636i) q^{46} +4.69617 q^{47} +(0.824930 - 0.0803540i) q^{48} +0.462766 q^{49} -0.608198i q^{51} +(-2.93755 - 2.66531i) q^{52} +9.68555i q^{53} +(1.59607 - 0.706977i) q^{54} +(-7.33478 - 2.42964i) q^{56} -0.187608 q^{57} +(9.97739 - 4.41947i) q^{58} +12.8197i q^{59} +12.7406i q^{61} +(2.37379 + 5.35907i) q^{62} -8.07813 q^{63} +(6.41797 + 4.77594i) q^{64} +(-0.103414 - 0.233467i) q^{66} -10.2605i q^{67} +(3.94465 - 4.34756i) q^{68} -1.34871i q^{69} -12.9184 q^{71} +(7.93959 + 2.62998i) q^{72} -9.76540 q^{73} +(-0.564788 + 0.250172i) q^{74} +(-1.34107 - 1.21679i) q^{76} +2.38043i q^{77} +(0.235369 + 0.531370i) q^{78} +3.02177 q^{79} +8.61542 q^{81} +(-3.34968 - 7.56223i) q^{82} +9.88164i q^{83} +(0.838428 + 0.760727i) q^{84} +(4.59276 - 2.03436i) q^{86} -1.59887 q^{87} +(0.774993 - 2.33961i) q^{88} -8.04615 q^{89} -5.41785i q^{91} +(8.74748 - 9.64095i) q^{92} -0.858786i q^{93} +(-2.68973 - 6.07234i) q^{94} +(-0.576380 - 1.02065i) q^{96} +12.1937 q^{97} +(-0.265050 - 0.598376i) q^{98} -2.57672i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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