LMFDB - Embedded newform 1000.2.t.b.901.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			901.43
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08405 + 0.908199i) q^{2} +(1.46605 + 2.01785i) q^{3} +(0.350349 + 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} -0.110917 q^{7} +(-1.40851 + 2.45277i) q^{8} +(-0.995348 + 3.06337i) q^{9} +O(q^{10})$	\(q+(1.08405 + 0.908199i) q^{2} +(1.46605 + 2.01785i) q^{3} +(0.350349 + 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} -0.110917 q^{7} +(-1.40851 + 2.45277i) q^{8} +(-0.995348 + 3.06337i) q^{9} +(1.63700 - 0.531893i) q^{11} +(-3.45966 + 3.59372i) q^{12} +(4.56868 + 1.48445i) q^{13} +(-0.120240 - 0.100735i) q^{14} +(-3.75451 + 1.37973i) q^{16} +(-0.371056 - 0.269588i) q^{17} +(-3.86116 + 2.41688i) q^{18} +(-2.40052 + 3.30403i) q^{19} +(-0.162610 - 0.223814i) q^{21} +(2.25766 + 0.910120i) q^{22} +(-1.98459 - 6.10792i) q^{23} +(-7.01427 + 0.753724i) q^{24} +(3.60452 + 5.75850i) q^{26} +(-0.524271 + 0.170346i) q^{27} +(-0.0388597 - 0.218404i) q^{28} +(-5.29624 - 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(-5.32316 - 1.91414i) q^{32} +(3.47320 + 2.52343i) q^{33} +(-0.157406 - 0.629242i) q^{34} +(-6.38072 - 0.886667i) q^{36} +(1.53972 + 0.500287i) q^{37} +(-5.60300 + 1.40160i) q^{38} +(3.70252 + 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(0.0269890 - 0.390308i) q^{42} -10.5304i q^{43} +(1.62086 + 3.03703i) q^{44} +(3.39581 - 8.42372i) q^{46} +(2.51014 - 1.82373i) q^{47} +(-8.28839 - 5.55328i) q^{48} -6.98770 q^{49} -1.14397i q^{51} +(-1.32237 + 9.51614i) q^{52} +(-2.69868 - 3.71441i) q^{53} +(-0.723047 - 0.291478i) q^{54} +(0.156228 - 0.272054i) q^{56} -10.1863 q^{57} +(0.879037 - 12.7124i) q^{58} +(3.38621 + 1.10025i) q^{59} +(11.1816 - 3.63312i) q^{61} +(1.21872 + 4.87191i) q^{62} +(0.110401 - 0.339779i) q^{63} +(-4.03218 - 6.90953i) q^{64} +(1.47337 + 5.88990i) q^{66} +(-2.19833 + 3.02574i) q^{67} +(0.400840 - 0.825088i) q^{68} +(9.41535 - 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-6.11178 - 6.75615i) q^{72} +(3.20201 + 9.85476i) q^{73} +(1.21479 + 1.94072i) q^{74} +(-7.34690 - 3.56923i) q^{76} +(-0.181571 + 0.0589960i) q^{77} +(-6.33536 + 15.7156i) q^{78} +(4.45472 - 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(-13.6376 + 8.53642i) q^{82} +(7.20048 - 9.91061i) q^{83} +(0.383735 - 0.398604i) q^{84} +(9.56373 - 11.4156i) q^{86} +(6.94483 - 21.3740i) q^{87} +(-1.00112 + 4.76436i) q^{88} +(2.07551 + 6.38776i) q^{89} +(-0.506744 - 0.164651i) q^{91} +(11.3317 - 6.04770i) q^{92} +8.85717i q^{93} +(4.37744 + 0.302691i) q^{94} +(-3.94158 - 13.5476i) q^{96} +(-4.54704 + 3.30362i) q^{97} +(-7.57505 - 6.34622i) q^{98} +5.54415i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.08405	+	0.908199i	0.766542	+	0.642194i
$2$	1.08405	+	0.908199i	0.766542	+	0.642194i
$3$	1.46605	+	2.01785i	0.846425	+	1.16500i	0.984639	+	0.174602i	$0.0558639\pi$
$3$	1.46605	+	2.01785i	0.846425	+	1.16500i	−0.138214	+	0.990402i	$0.544136\pi$
$4$	0.350349	+	1.96907i	0.175175	+	0.984537i
$5$		0			0
$5$		0			0
$6$	−0.243326	+	3.51892i	−0.0993376	+	1.43659i
$7$	−0.110917			−0.0419227			−0.0209613	−	0.999780i	$-0.506673\pi$
$7$	−0.110917			−0.0419227			−0.0209613	+	0.999780i	$0.506673\pi$
$8$	−1.40851	+	2.45277i	−0.497985	+	0.867186i
$9$	−0.995348	+	3.06337i	−0.331783	+	1.02112i
$10$		0			0
$11$	1.63700	−	0.531893i	0.493574	−	0.160372i	−0.0516452	−	0.998665i	$-0.516446\pi$
$11$	1.63700	−	0.531893i	0.493574	−	0.160372i	0.545219	+	0.838294i	$0.316446\pi$
$12$	−3.45966	+	3.59372i	−0.998718	+	1.03742i
$13$	4.56868	+	1.48445i	1.26712	+	0.411713i	0.864027	−	0.503445i	$-0.167934\pi$
$13$	4.56868	+	1.48445i	1.26712	+	0.411713i	0.403096	+	0.915158i	$0.367934\pi$
$14$	−0.120240	−	0.100735i	−0.0321355	−	0.0269225i
$15$		0			0
$16$	−3.75451	+	1.37973i	−0.938628	+	0.344932i
$17$	−0.371056	−	0.269588i	−0.0899944	−	0.0653848i	0.541878	−	0.840457i	$-0.317713\pi$
$17$	−0.371056	−	0.269588i	−0.0899944	−	0.0653848i	−0.631873	+	0.775072i	$0.717713\pi$
$18$	−3.86116	+	2.41688i	−0.910084	+	0.569665i
$19$	−2.40052	+	3.30403i	−0.550716	+	0.757996i	−0.990109	−	0.140299i	$-0.955194\pi$
$19$	−2.40052	+	3.30403i	−0.550716	+	0.757996i	0.439393	+	0.898295i	$0.355194\pi$
$20$		0			0
$21$	−0.162610	−	0.223814i	−0.0354844	−	0.0488401i
$22$	2.25766	+	0.910120i	0.481335	+	0.194038i
$23$	−1.98459	−	6.10792i	−0.413815	−	1.27359i	−0.913307	−	0.407272i	$-0.866480\pi$
$23$	−1.98459	−	6.10792i	−0.413815	−	1.27359i	0.499492	−	0.866318i	$-0.333520\pi$
$24$	−7.01427	+	0.753724i	−1.43178	+	0.153853i
$25$		0			0
$26$	3.60452	+	5.75850i	0.706904	+	1.12933i
$27$	−0.524271	+	0.170346i	−0.100896	+	0.0327831i
$28$	−0.0388597	−	0.218404i	−0.00734379	−	0.0412745i
$29$	−5.29624	−	7.28964i	−0.983486	−	1.35365i	−0.934930	−	0.354833i	$-0.884538\pi$
$29$	−5.29624	−	7.28964i	−0.983486	−	1.35365i	−0.0485566	−	0.998820i	$-0.515462\pi$
$30$		0			0
$31$	2.87291	+	2.08729i	0.515990	+	0.374889i	0.815091	−	0.579333i	$-0.196687\pi$
$31$	2.87291	+	2.08729i	0.515990	+	0.374889i	−0.299101	+	0.954221i	$0.596687\pi$
$32$	−5.32316	−	1.91414i	−0.941011	−	0.338376i
$33$	3.47320	+	2.52343i	0.604607	+	0.439273i
$34$	−0.157406	−	0.629242i	−0.0269949	−	0.107914i
$35$		0			0
$36$	−6.38072	−	0.886667i	−1.06345	−	0.147778i
$37$	1.53972	+	0.500287i	0.253129	+	0.0822467i	0.432833	−	0.901474i	$-0.357514\pi$
$37$	1.53972	+	0.500287i	0.253129	+	0.0822467i	−0.179704	+	0.983721i	$0.557514\pi$
$38$	−5.60300	+	1.40160i	−0.908927	+	0.227370i
$39$	3.70252	+	11.3952i	0.592877	+	1.82469i
$40$		0			0
$41$	−3.51556	+	10.8198i	−0.549039	+	1.68977i	0.162149	+	0.986766i	$0.448157\pi$
$41$	−3.51556	+	10.8198i	−0.549039	+	1.68977i	−0.711188	+	0.703002i	$0.751843\pi$
$42$	0.0269890	−	0.390308i	0.00416450	−	0.0602259i
$43$		−	10.5304i		−	1.60588i	−0.596063	−	0.802938i	$-0.703269\pi$
$43$		−	10.5304i		−	1.60588i	0.596063	−	0.802938i	$-0.296731\pi$
$44$	1.62086	+	3.03703i	0.244354	+	0.457849i
$45$		0			0
$46$	3.39581	−	8.42372i	0.500685	−	1.24201i
$47$	2.51014	−	1.82373i	0.366142	−	0.266018i	−0.389467	−	0.921040i	$-0.627341\pi$
$47$	2.51014	−	1.82373i	0.366142	−	0.266018i	0.755609	+	0.655022i	$0.227341\pi$
$48$	−8.28839	−	5.55328i	−1.19633	−	0.801546i
$49$	−6.98770			−0.998242
$50$		0			0
$51$		−	1.14397i		−	0.160187i
$52$	−1.32237	+	9.51614i	−0.183379	+	1.31965i
$53$	−2.69868	−	3.71441i	−0.370692	−	0.510213i	0.582397	−	0.812905i	$-0.302115\pi$
$53$	−2.69868	−	3.71441i	−0.370692	−	0.510213i	−0.953089	+	0.302691i	$0.902115\pi$
$54$	−0.723047	−	0.291478i	−0.0983942	−	0.0396651i
$55$		0			0
$56$	0.156228	−	0.272054i	0.0208769	−	0.0363548i
$57$	−10.1863			−1.34921
$58$	0.879037	−	12.7124i	0.115423	−	1.66922i
$59$	3.38621	+	1.10025i	0.440847	+	0.143240i	0.521026	−	0.853541i	$-0.325549\pi$
$59$	3.38621	+	1.10025i	0.440847	+	0.143240i	−0.0801796	+	0.996780i	$0.525549\pi$
$60$		0			0
$61$	11.1816	−	3.63312i	1.43166	−	0.465174i	0.512372	−	0.858764i	$-0.328767\pi$
$61$	11.1816	−	3.63312i	1.43166	−	0.465174i	0.919286	+	0.393590i	$0.128767\pi$
$62$	1.21872	+	4.87191i	0.154777	+	0.618734i
$63$	0.110401	−	0.339779i	0.0139092	−	0.0428082i
$64$	−4.03218	−	6.90953i	−0.504022	−	0.863691i
$65$		0			0
$66$	1.47337	+	5.88990i	0.181359	+	0.724996i
$67$	−2.19833	+	3.02574i	−0.268569	+	0.369653i	−0.921906	−	0.387414i	$-0.873368\pi$
$67$	−2.19833	+	3.02574i	−0.268569	+	0.369653i	0.653337	+	0.757067i	$0.273368\pi$
$68$	0.400840	−	0.825088i	0.0486090	−	0.100057i
$69$	9.41535	−	12.9591i	1.13348	−	1.56009i
$70$		0			0
$71$	9.04844	−	6.57408i	1.07385	−	0.780200i	0.0972518	−	0.995260i	$-0.468995\pi$
$71$	9.04844	−	6.57408i	1.07385	−	0.780200i	0.976601	+	0.215060i	$0.0689948\pi$
$72$	−6.11178	−	6.75615i	−0.720280	−	0.796220i
$73$	3.20201	+	9.85476i	0.374766	+	1.15341i	0.943636	+	0.330985i	$0.107381\pi$
$73$	3.20201	+	9.85476i	0.374766	+	1.15341i	−0.568870	+	0.822428i	$0.692619\pi$
$74$	1.21479	+	1.94072i	0.141216	+	0.225604i
$75$		0			0
$76$	−7.34690	−	3.56923i	−0.842747	−	0.409419i
$77$	−0.181571	+	0.0589960i	−0.0206919	+	0.00672322i
$78$	−6.33536	+	15.7156i	−0.717338	+	1.77944i
$79$	4.45472	−	3.23655i	0.501196	−	0.364140i	−0.308278	−	0.951296i	$-0.599753\pi$
$79$	4.45472	−	3.23655i	0.501196	−	0.364140i	0.809474	+	0.587156i	$0.199753\pi$
$80$		0			0
$81$	6.70522	+	4.87163i	0.745025	+	0.541292i
$82$	−13.6376	+	8.53642i	−1.50602	+	0.942690i
$83$	7.20048	−	9.91061i	0.790356	−	1.08783i	−0.203708	−	0.979032i	$-0.565299\pi$
$83$	7.20048	−	9.91061i	0.790356	−	1.08783i	0.994064	−	0.108800i	$-0.0347007\pi$
$84$	0.383735	−	0.398604i	0.0418690	−	0.0434913i
$85$		0			0
$86$	9.56373	−	11.4156i	1.03128	−	1.23097i
$87$	6.94483	−	21.3740i	0.744564	−	2.29153i
$88$	−1.00112	+	4.76436i	−0.106720	+	0.507883i
$89$	2.07551	+	6.38776i	0.220003	+	0.677101i	0.998760	+	0.0497752i	$0.0158505\pi$
$89$	2.07551	+	6.38776i	0.220003	+	0.677101i	−0.778757	+	0.627326i	$0.784150\pi$
$90$		0			0
$91$	−0.506744	−	0.164651i	−0.0531212	−	0.0172601i
$92$	11.3317	−	6.04770i	1.18141	−	0.630517i
$93$			8.85717i			0.918446i
$94$	4.37744	+	0.302691i	0.451499	+	0.0312202i
$95$		0			0
$96$	−3.94158	−	13.5476i	−0.402286	−	1.38269i
$97$	−4.54704	+	3.30362i	−0.461682	+	0.335431i	−0.794191	−	0.607669i	$-0.792105\pi$
$97$	−4.54704	+	3.30362i	−0.461682	+	0.335431i	0.332509	+	0.943100i	$0.392105\pi$
$98$	−7.57505	−	6.34622i	−0.765195	−	0.641065i
$99$			5.54415i			0.557208i
$100$		0			0
$101$		−	1.55640i		−	0.154868i	−0.996997	−	0.0774339i	$-0.975327\pi$
$101$		−	1.55640i		−	0.154868i	0.996997	−	0.0774339i	$-0.0246727\pi$
$102$	1.03895	−	1.24012i	0.102871	−	0.122790i
$103$	−3.81692	+	2.77316i	−0.376092	+	0.273247i	−0.759733	−	0.650235i	$-0.774670\pi$
$103$	−3.81692	+	2.77316i	−0.376092	+	0.273247i	0.383640	+	0.923483i	$0.374670\pi$
$104$	−10.0761	+	9.11505i	−0.988040	+	0.893804i
$105$		0			0
$106$	0.447910	−	6.47756i	0.0435049	−	0.629156i
$107$		−	11.5454i		−	1.11614i	−0.829794	−	0.558070i	$-0.811542\pi$
$107$		−	11.5454i		−	1.11614i	0.829794	−	0.558070i	$-0.188458\pi$
$108$	−0.519102	−	0.972648i	−0.0499506	−	0.0935931i
$109$	1.79379	+	0.582837i	0.171814	+	0.0558256i	0.393661	−	0.919256i	$-0.371209\pi$
$109$	1.79379	+	0.582837i	0.171814	+	0.0558256i	−0.221847	+	0.975081i	$0.571209\pi$
$110$		0			0
$111$	1.24781	+	3.84038i	0.118437	+	0.364512i
$112$	0.416439	−	0.153035i	0.0393498	−	0.0144605i
$113$	−1.42005	+	4.37045i	−0.133587	+	0.411137i	−0.995367	−	0.0961433i	$-0.969349\pi$
$113$	−1.42005	+	4.37045i	−0.133587	+	0.411137i	0.861781	+	0.507281i	$0.169349\pi$
$114$	−11.0425	−	9.25119i	−1.03423	−	0.866453i
$115$		0			0
$116$	12.4983	−	12.9826i	1.16044	−	1.20540i
$117$	−9.09485	+	12.5180i	−0.840819	+	1.15729i
$118$	2.67159	+	4.26808i	0.245940	+	0.392908i
$119$	0.0411565	+	0.0299019i	0.00377281	+	0.00274111i
$120$		0			0
$121$	−6.50233	+	4.72422i	−0.591121	+	0.429475i
$122$	15.4211	+	6.21662i	1.39616	+	0.562826i
$123$	−26.9867	+	8.76851i	−2.43331	+	0.790630i
$124$	−3.10351	+	6.38826i	−0.278704	+	0.573683i
$125$		0			0
$126$	0.428268	−	0.268073i	0.0381531	−	0.0238819i
$127$	2.51421	+	7.73794i	0.223100	+	0.686631i	0.998479	+	0.0551347i	$0.0175588\pi$
$127$	2.51421	+	7.73794i	0.223100	+	0.686631i	−0.775379	+	0.631496i	$0.782441\pi$
$128$	1.90412	−	11.1523i	0.168302	−	0.985735i
$129$	21.2488	−	15.4382i	1.87085	−	1.35925i
$130$		0			0
$131$	−12.7817	+	17.5926i	−1.11675	+	1.53707i	−0.305661	+	0.952140i	$0.598878\pi$
$131$	−12.7817	+	17.5926i	−1.11675	+	1.53707i	−0.811085	+	0.584929i	$0.801122\pi$
$132$	−3.75199	+	7.72308i	−0.326569	+	0.672208i
$133$	0.266258	−	0.366473i	0.0230875	−	0.0317772i
$134$	−5.13108	+	1.28355i	−0.443258	+	0.110882i
$135$		0			0
$136$	1.18388	−	0.530398i	0.101517	−	0.0454812i
$137$	2.83428	−	8.72303i	0.242149	−	0.745259i	−0.753943	−	0.656940i	$-0.771851\pi$
$137$	2.83428	−	8.72303i	0.242149	−	0.745259i	0.996092	−	0.0883189i	$-0.0281494\pi$
$138$	21.9762	−	5.49738i	1.87074	−	0.467968i
$139$	13.0150	−	4.22884i	1.10392	−	0.358685i	0.300310	−	0.953842i	$-0.402910\pi$
$139$	13.0150	−	4.22884i	1.10392	−	0.358685i	0.803610	+	0.595156i	$0.202910\pi$
$140$		0			0
$141$	7.36000	+	2.39141i	0.619824	+	0.201393i
$142$	15.7796	+	1.09113i	1.32419	+	0.0915652i
$143$	8.26849			0.691446
$144$	−0.489566	−	12.8747i	−0.0407972	−	1.07290i
$145$		0			0
$146$	−5.47893	+	13.5912i	−0.453440	+	1.12481i
$147$	−10.2443	−	14.1001i	−0.844938	−	1.16296i
$148$	−0.445661	+	3.20711i	−0.0366331	+	0.263623i
$149$			14.8397i			1.21572i	0.794045	+	0.607859i	$0.207972\pi$
$149$			14.8397i			1.21572i	−0.794045	+	0.607859i	$0.792028\pi$
$150$		0			0
$151$	−8.87251			−0.722035			−0.361017	−	0.932559i	$-0.617570\pi$
$151$	−8.87251			−0.722035			−0.361017	+	0.932559i	$0.617570\pi$
$152$	−4.72286	−	10.5417i	−0.383075	−	0.855044i
$153$	1.19518	−	0.868348i	0.0966244	−	0.0702017i
$154$	−0.250413	−	0.100948i	−0.0201789	−	0.00813460i
$155$		0			0
$156$	−21.1408	+	11.2828i	−1.69262	+	0.903349i
$157$		−	4.71374i		−	0.376197i	−0.982150	−	0.188099i	$-0.939768\pi$
$157$		−	4.71374i		−	0.376197i	0.982150	−	0.188099i	$-0.0602325\pi$
$158$	7.76859	+	0.537182i	0.618036	+	0.0427359i
$159$	3.53871	−	10.8910i	0.280638	−	0.863715i
$160$		0			0
$161$	0.220124	+	0.677473i	0.0173482	+	0.0533923i
$162$	2.84442	+	11.3708i	0.223479	+	0.893374i
$163$	−9.54040	−	3.09987i	−0.747262	−	0.242800i	−0.0894595	−	0.995990i	$-0.528514\pi$
$163$	−9.54040	−	3.09987i	−0.747262	−	0.242800i	−0.657803	+	0.753190i	$0.728514\pi$
$164$	−22.5367	−	3.13170i	−1.75982	−	0.244545i
$165$		0			0
$166$	16.8065	−	4.20418i	1.30444	−	0.326307i
$167$	−6.50795	−	4.72830i	−0.503601	−	0.365887i	0.306790	−	0.951777i	$-0.400745\pi$
$167$	−6.50795	−	4.72830i	−0.503601	−	0.365887i	−0.810391	+	0.585890i	$0.800745\pi$
$168$	0.778002	−	0.0836008i	0.0600242	−	0.00644994i
$169$	8.15199	+	5.92277i	0.627076	+	0.455597i
$170$		0			0
$171$	−7.73210	−	10.6423i	−0.591288	−	0.813838i
$172$	20.7352	−	3.68933i	1.58104	−	0.281309i
$173$	9.45929	−	3.07351i	0.719176	−	0.233675i	0.0735104	−	0.997294i	$-0.476580\pi$
$173$	9.45929	−	3.07351i	0.719176	−	0.233675i	0.645666	+	0.763620i	$0.276580\pi$
$174$	26.9404	−	16.8633i	2.04235	−	1.27840i
$175$		0			0
$176$	−5.41226	+	4.25561i	−0.407965	+	0.320779i
$177$	2.74423	+	8.44586i	0.206269	+	0.634830i
$178$	−3.55139	+	8.80965i	−0.266188	+	0.660311i
$179$	7.39861	+	10.1833i	0.552998	+	0.761136i	0.990415	−	0.138122i	$-0.0441068\pi$
$179$	7.39861	+	10.1833i	0.552998	+	0.761136i	−0.437417	+	0.899259i	$0.644107\pi$
$180$		0			0
$181$	−7.67562	+	10.5646i	−0.570524	+	0.785259i	−0.992617	−	0.121293i	$-0.961296\pi$
$181$	−7.67562	+	10.5646i	−0.570524	+	0.785259i	0.422092	+	0.906553i	$0.361296\pi$
$182$	−0.399802	−	0.638715i	−0.0296353	−	0.0473447i
$183$	23.7239	+	17.2364i	1.75372	+	1.27415i
$184$	17.7767	+	3.73536i	1.31051	+	0.275375i
$185$		0			0
$186$	−8.04408	+	9.60166i	−0.589820	+	0.704028i
$187$	−0.750811	−	0.243953i	−0.0549048	−	0.0178396i
$188$	4.47048	+	4.30372i	0.326043	+	0.313881i
$189$	0.0581506	−	0.0188943i	0.00422983	−	0.00137436i
$190$		0			0
$191$	0.889107	−	2.73639i	0.0643335	−	0.197998i	−0.913723	−	0.406337i	$-0.866806\pi$
$191$	0.889107	−	2.73639i	0.0643335	−	0.197998i	0.978057	+	0.208339i	$0.0668058\pi$
$192$	8.03099	−	18.2660i	0.579587	−	1.31824i
$193$	15.9019			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$193$	15.9019			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$194$	−7.92958	−	0.548314i	−0.569310	−	0.0393667i
$195$		0			0
$196$	−2.44813	−	13.7593i	−0.174867	−	0.982807i
$197$	2.74963	+	3.78454i	0.195903	+	0.269637i	0.895656	−	0.444748i	$-0.146707\pi$
$197$	2.74963	+	3.78454i	0.195903	+	0.269637i	−0.699753	+	0.714385i	$0.746707\pi$
$198$	−5.03519	+	6.01016i	−0.357835	+	0.427123i
$199$	−28.0439			−1.98798			−0.993988	−	0.109488i	$-0.965079\pi$
$199$	−28.0439			−1.98798			−0.993988	+	0.109488i	$0.965079\pi$
$200$		0			0
$201$	−9.32834			−0.657971
$202$	1.41352	−	1.68723i	0.0994551	−	0.118713i
$203$	0.587443	+	0.808546i	0.0412304	+	0.0567488i
$204$	2.25255	−	0.400787i	0.157710	−	0.0280607i
$205$		0			0
$206$	−6.65633	−	0.460272i	−0.463768	−	0.0320686i
$207$	20.6862			1.43779
$208$	−19.2013	+	0.730135i	−1.33137	+	0.0506257i
$209$	−2.17225	+	6.68551i	−0.150258	+	0.462446i
$210$		0			0
$211$	−0.310359	+	0.100842i	−0.0213660	+	0.00694223i	−0.319680	−	0.947525i	$-0.603576\pi$
$211$	−0.310359	+	0.100842i	−0.0213660	+	0.00694223i	0.298315	+	0.954468i	$0.403576\pi$
$212$	6.36847	−	6.61524i	0.437388	−	0.454336i
$213$	26.5310	+	8.62043i	1.81787	+	0.590662i
$214$	10.4856	−	12.5159i	0.716777	−	0.855568i
$215$		0			0
$216$	0.320623	−	1.52585i	0.0218157	−	0.103821i
$217$	−0.318655	−	0.231516i	−0.0216317	−	0.0157163i
$218$	1.41523	+	2.26094i	0.0958516	+	0.153130i
$219$	−15.1911	+	20.9087i	−1.02652	+	1.41288i
$220$		0			0
$221$	−1.29505	−	1.78248i	−0.0871142	−	0.119902i
$222$	−2.13513	+	5.29644i	−0.143300	+	0.355474i
$223$	−3.64231	−	11.2099i	−0.243907	−	0.750669i	−0.995814	−	0.0914002i	$-0.970866\pi$
$223$	−3.64231	−	11.2099i	−0.243907	−	0.750669i	0.751907	−	0.659269i	$-0.229134\pi$
$224$	0.590429	+	0.212311i	0.0394497	+	0.0141856i
$225$		0			0
$226$	−5.50865	+	3.44812i	−0.366430	+	0.229366i
$227$	−0.998051	+	0.324287i	−0.0662430	+	0.0215237i	−0.341951	−	0.939718i	$-0.611088\pi$
$227$	−0.998051	+	0.324287i	−0.0662430	+	0.0215237i	0.275708	+	0.961241i	$0.411088\pi$
$228$	−3.56876	−	20.0576i	−0.236347	−	1.32835i
$229$	−11.8902	−	16.3654i	−0.785723	−	1.08146i	−0.994627	−	0.103519i	$-0.966990\pi$
$229$	−11.8902	−	16.3654i	−0.785723	−	1.08146i	0.208904	−	0.977936i	$-0.433010\pi$
$230$		0			0
$231$	−0.385237	−	0.279891i	−0.0253468	−	0.0184155i
$232$	25.3397	−	2.72289i	1.66363	−	0.178767i
$233$	−21.2400	−	15.4318i	−1.39148	−	1.01097i	−0.995701	−	0.0926216i	$-0.970475\pi$
$233$	−21.2400	−	15.4318i	−1.39148	−	1.01097i	−0.395777	−	0.918347i	$-0.629525\pi$
$234$	−21.2281	+	5.31025i	−1.38773	+	0.347142i
$235$		0			0
$236$	−0.980110	+	7.05316i	−0.0637997	+	0.459122i
$237$	13.0617	+	4.24401i	0.848449	+	0.275678i
$238$	0.0174590	+	0.0697936i	0.00113170	+	0.00452405i
$239$	2.69865	+	8.30559i	0.174561	+	0.537244i	0.999613	−	0.0278129i	$-0.00885425\pi$
$239$	2.69865	+	8.30559i	0.174561	+	0.537244i	−0.825052	+	0.565057i	$0.808854\pi$
$240$		0			0
$241$	0.110550	−	0.340238i	0.00712115	−	0.0219166i	−0.947433	−	0.319955i	$-0.896332\pi$
$241$	0.110550	−	0.340238i	0.00712115	−	0.0219166i	0.954554	+	0.298038i	$0.0963323\pi$
$242$	−11.3394	−	0.784097i	−0.728925	−	0.0504037i
$243$			22.3259i			1.43221i
$244$	11.0714	+	20.7446i	0.708771	+	1.32803i
$245$		0			0
$246$	−37.2186	−	15.0037i	−2.37297	−	0.956604i
$247$	−15.8719	+	11.5316i	−1.00990	+	0.733737i
$248$	−9.16619	+	4.10661i	−0.582053	+	0.260770i
$249$	30.5544			1.93631
$250$		0			0
$251$		−	20.0370i		−	1.26473i	−0.774672	−	0.632363i	$-0.782085\pi$
$251$		−	20.0370i		−	1.26473i	0.774672	−	0.632363i	$-0.217915\pi$
$252$	0.707730	+	0.0983464i	0.0445828	+	0.00619524i
$253$	−6.49753	−	8.94308i	−0.408496	−	0.562247i
$254$	−4.30205	+	10.6717i	−0.269934	+	0.669605i
$255$		0			0
$256$	12.1927	−	10.3604i	0.762044	−	0.647525i
$257$	18.7305			1.16838			0.584190	−	0.811617i	$-0.301412\pi$
$257$	18.7305			1.16838			0.584190	+	0.811617i	$0.301412\pi$
$258$	37.0558	+	2.56233i	2.30699	+	0.159524i
$259$	−0.170782	−	0.0554903i	−0.0106119	−	0.00344800i
$260$		0			0
$261$	27.6024	−	8.96858i	1.70855	−	0.555141i
$262$	−29.8337	+	7.46293i	−1.84313	+	0.461061i
$263$	5.09486	−	15.6804i	0.314162	−	0.966892i	−0.661936	−	0.749561i	$-0.730265\pi$
$263$	5.09486	−	15.6804i	0.314162	−	0.966892i	0.976098	−	0.217331i	$-0.0697352\pi$
$264$	−11.0815	+	4.96469i	−0.682016	+	0.305556i
$265$		0			0
$266$	0.621469	−	0.155461i	0.0381047	−	0.00953194i
$267$	−9.84671	+	13.5528i	−0.602609	+	0.829420i
$268$	−6.72809	−	3.26861i	−0.410984	−	0.199662i
$269$	0.0856192	−	0.117845i	0.00522029	−	0.00718512i	−0.806399	−	0.591372i	$-0.798586\pi$
$269$	0.0856192	−	0.117845i	0.00522029	−	0.00718512i	0.811619	+	0.584187i	$0.198586\pi$
$270$		0			0
$271$	−12.4072	+	9.01437i	−0.753684	+	0.547584i	−0.896967	−	0.442098i	$-0.854234\pi$
$271$	−12.4072	+	9.01437i	−0.753684	+	0.547584i	0.143282	+	0.989682i	$0.454234\pi$
$272$	1.76509	+	0.500215i	0.107025	+	0.0303300i
$273$	−0.410672	−	1.26392i	−0.0248550	−	0.0764958i
$274$	10.9948	−	6.88215i	0.664218	−	0.415766i
$275$		0			0
$276$	28.8161	+	13.9993i	1.73453	+	0.842660i
$277$	19.6954	−	6.39942i	1.18338	−	0.384504i	0.349759	−	0.936840i	$-0.386263\pi$
$277$	19.6954	−	6.39942i	1.18338	−	0.384504i	0.833622	+	0.552336i	$0.186263\pi$
$278$	17.9496	+	7.23594i	1.07655	+	0.433983i
$279$	−9.25369	+	6.72320i	−0.554004	+	0.402507i
$280$		0			0
$281$	−8.56374	−	6.22192i	−0.510870	−	0.371169i	0.302284	−	0.953218i	$-0.402251\pi$
$281$	−8.56374	−	6.22192i	−0.510870	−	0.371169i	−0.813153	+	0.582049i	$0.802251\pi$
$282$	5.80677	+	9.27677i	0.345788	+	0.552423i
$283$	12.0915	−	16.6426i	0.718767	−	0.989298i	−0.280797	−	0.959767i	$-0.590599\pi$
$283$	12.0915	−	16.6426i	0.718767	−	0.989298i	0.999564	−	0.0295305i	$-0.00940123\pi$
$284$	16.1150	+	15.5138i	0.956247	+	0.920577i
$285$		0			0
$286$	8.96350	+	7.50943i	0.530023	+	0.444042i
$287$	0.389936	−	1.20010i	0.0230172	−	0.0708396i
$288$	11.1621	−	14.4016i	0.657734	−	0.848620i
$289$	−5.18828	−	15.9679i	−0.305193	−	0.939288i
$290$		0			0
$291$	−13.3324	−	4.33195i	−0.781558	−	0.253944i
$292$	−18.2829	+	9.75760i	−1.06993	+	0.571020i
$293$		−	0.603128i		−	0.0352351i	−0.999845	−	0.0176176i	$-0.994392\pi$
$293$		−	0.603128i		−	0.0352351i	0.999845	−	0.0176176i	$-0.00560813\pi$
$294$	1.70029	−	24.5892i	0.0991630	−	1.43407i
$295$		0			0
$296$	−3.39581	+	3.07193i	−0.197378	+	0.178552i
$297$	−0.767625	+	0.557713i	−0.0445421	+	0.0323618i
$298$	−13.4774	+	16.0871i	−0.780727	+	0.931900i
$299$		−	30.8512i		−	1.78417i
$300$		0			0
$301$			1.16800i			0.0673226i
$302$	−9.61829	−	8.05801i	−0.553470	−	0.463686i
$303$	3.14058	−	2.28177i	0.180422	−	0.131084i
$304$	4.45411	−	15.7171i	0.255461	−	0.901435i
$305$		0			0
$306$	2.08427	+	0.144123i	0.119150	+	0.00823897i
$307$		−	9.96251i		−	0.568591i	−0.958737	−	0.284295i	$-0.908240\pi$
$307$		−	9.96251i		−	0.568591i	0.958737	−	0.284295i	$-0.0917596\pi$
$308$	−0.179781	−	0.336858i	−0.0102440	−	0.0191943i
$309$	−11.1916	−	3.63637i	−0.636668	−	0.206866i
$310$		0			0
$311$	−7.52782	−	23.1683i	−0.426864	−	1.31375i	−0.901198	−	0.433407i	$-0.857311\pi$
$311$	−7.52782	−	23.1683i	−0.426864	−	1.31375i	0.474335	−	0.880344i	$-0.342689\pi$
$312$	−33.1648	−	6.96884i	−1.87759	−	0.394533i
$313$	−5.78333	+	17.7993i	−0.326893	+	1.00607i	0.643686	+	0.765290i	$0.277404\pi$
$313$	−5.78333	+	17.7993i	−0.326893	+	1.00607i	−0.970579	+	0.240784i	$0.922596\pi$
$314$	4.28101	−	5.10995i	0.241592	−	0.288371i
$315$		0			0
$316$	7.93371	+	7.63776i	0.446306	+	0.429658i
$317$	−16.7789	+	23.0942i	−0.942397	+	1.29710i	0.0124261	+	0.999923i	$0.496045\pi$
$317$	−16.7789	+	23.0942i	−0.942397	+	1.29710i	−0.954823	+	0.297175i	$0.903955\pi$
$318$	13.7274	−	8.59262i	0.769793	−	0.481850i
$319$	−12.5472	−	9.11611i	−0.702511	−	0.510404i
$320$		0			0
$321$	23.2969	−	16.9262i	1.30031	−	0.944728i
$322$	−0.376653	+	0.934334i	−0.0209901	+	0.0520684i
$323$	1.78145	−	0.578830i	0.0991228	−	0.0322069i
$324$	−7.24343	+	14.9099i	−0.402413	+	0.828325i
$325$		0			0
$326$	−7.52703	−	12.0250i	−0.416883	−	0.666004i
$327$	1.45371	+	4.47406i	0.0803903	+	0.247416i
$328$	−21.5868	−	23.8627i	−1.19193	−	1.31760i
$329$	−0.278418	+	0.202282i	−0.0153497	+	0.0111522i
$330$		0			0
$331$	−2.10228	+	2.89354i	−0.115552	+	0.159043i	−0.862875	−	0.505417i	$-0.831339\pi$
$331$	−2.10228	+	2.89354i	−0.115552	+	0.159043i	0.747323	+	0.664461i	$0.231339\pi$
$332$	22.0374	+	10.7061i	1.20946	+	0.587574i
$333$	−3.06512	+	4.21878i	−0.167968	+	0.231188i
$334$	−2.76074	−	11.0363i	−0.151061	−	0.603877i
$335$		0			0
$336$	0.919323	+	0.615953i	0.0501532	+	0.0336030i
$337$	−3.03819	+	9.35059i	−0.165501	+	0.509359i	−0.999073	−	0.0430517i	$-0.986292\pi$
$337$	−3.03819	+	9.35059i	−0.165501	+	0.509359i	0.833572	+	0.552411i	$0.186292\pi$
$338$	3.45815	+	13.8242i	0.188099	+	0.751939i
$339$	−10.9008	+	3.54187i	−0.592048	+	0.192368i
$340$		0			0
$341$	5.81317	+	1.88881i	0.314801	+	0.102285i
$342$	1.28333	−	18.5591i	0.0693943	−	1.00356i
$343$	1.55147			0.0837717
$344$	25.8287	+	14.8323i	1.39259	+	0.799702i
$345$		0			0
$346$	13.0457	+	5.25906i	0.701344	+	0.282729i
$347$	−9.28373	−	12.7780i	−0.498377	−	0.685957i	0.483529	−	0.875329i	$-0.339355\pi$
$347$	−9.28373	−	12.7780i	−0.498377	−	0.685957i	−0.981905	+	0.189372i	$0.939355\pi$
$348$	44.5201	+	6.18653i	2.38653	+	0.331633i
$349$		−	7.78786i		−	0.416875i	−0.978036	−	0.208437i	$-0.933162\pi$
$349$		−	7.78786i		−	0.416875i	0.978036	−	0.208437i	$-0.0668377\pi$
$350$		0			0
$351$	−2.64810			−0.141345
$352$	−9.73213	−	0.302096i	−0.518724	−	0.0161017i
$353$	9.09643	−	6.60894i	0.484154	−	0.351759i	−0.318778	−	0.947830i	$-0.603272\pi$
$353$	9.09643	−	6.60894i	0.484154	−	0.351759i	0.802932	+	0.596071i	$0.203272\pi$
$354$	−4.69563	+	11.6481i	−0.249570	+	0.619089i
$355$		0			0
$356$	−11.8508	+	6.32478i	−0.628092	+	0.335212i
$357$			0.126885i			0.00671548i
$358$	−1.22798	+	17.7587i	−0.0649005	+	0.938575i
$359$	3.14405	−	9.67639i	0.165937	−	0.510700i	−0.833167	−	0.553021i	$-0.813475\pi$
$359$	3.14405	−	9.67639i	0.165937	−	0.510700i	0.999104	+	0.0423204i	$0.0134750\pi$
$360$		0			0
$361$	0.717206	+	2.20733i	0.0377477	+	0.116175i
$362$	−17.9155	+	4.48160i	−0.941620	+	0.235548i
$363$	−19.0655	−	6.19476i	−1.00068	−	0.325141i
$364$	0.146673	−	1.05550i	0.00768775	−	0.0553233i
$365$		0			0
$366$	10.0639	+	40.2312i	0.526049	+	2.10292i
$367$	9.81851	+	7.13356i	0.512522	+	0.372369i	0.813779	−	0.581174i	$-0.197406\pi$
$367$	9.81851	+	7.13356i	0.512522	+	0.372369i	−0.301257	+	0.953543i	$0.597406\pi$
$368$	15.8784	+	20.1941i	0.827720	+	1.05269i
$369$	−29.6458	−	21.5389i	−1.54330	−	1.12127i
$370$		0			0
$371$	0.299329	+	0.411991i	0.0155404	+	0.0213895i
$372$	−17.4404	+	3.10310i	−0.904244	+	0.160888i
$373$	7.08589	−	2.30235i	0.366894	−	0.119211i	−0.119767	−	0.992802i	$-0.538215\pi$
$373$	7.08589	−	2.30235i	0.366894	−	0.119211i	0.486661	+	0.873591i	$0.338215\pi$
$374$	−0.592362	−	0.946345i	−0.0306303	−	0.0489343i
$375$		0			0
$376$	0.937612	+	8.72556i	0.0483536	+	0.449986i
$377$	−13.3757	−	41.1660i	−0.688881	−	2.12016i
$378$	0.0801982	+	0.0323299i	0.00412495	+	0.00166287i
$379$	−3.70220	−	5.09564i	−0.190169	−	0.261746i	0.703277	−	0.710916i	$-0.251719\pi$
$379$	−3.70220	−	5.09564i	−0.190169	−	0.261746i	−0.893446	+	0.449171i	$0.851719\pi$
$380$		0			0
$381$	−11.9280	+	16.4175i	−0.611091	+	0.841094i
$382$	3.44903	−	2.15891i	0.176468	−	0.110460i
$383$	−23.1761	−	16.8385i	−1.18425	−	0.860405i	−0.191601	−	0.981473i	$-0.561368\pi$
$383$	−23.1761	−	16.8385i	−1.18425	−	0.860405i	−0.992644	+	0.121068i	$0.961368\pi$
$384$	25.2952	−	12.5077i	1.29084	−	0.638278i
$385$		0			0
$386$	17.2385	+	14.4421i	0.877418	+	0.735083i
$387$	32.2586	+	10.4814i	1.63979	+	0.532802i
$388$	−8.09812	−	7.79603i	−0.411120	−	0.395784i
$389$	−0.660483	+	0.214604i	−0.0334878	+	0.0108808i	−0.325713	−	0.945469i	$-0.605604\pi$
$389$	−0.660483	+	0.214604i	−0.0334878	+	0.0108808i	0.292225	+	0.956350i	$0.405604\pi$
$390$		0			0
$391$	−0.910232	+	2.80141i	−0.0460324	+	0.141673i
$392$	9.84227	−	17.1392i	0.497110	−	0.865662i
$393$	−54.2378			−2.73593
$394$	−0.456366	+	6.59985i	−0.0229914	+	0.332496i
$395$		0			0
$396$	−10.9168	+	1.94239i	−0.548592	+	0.0976086i
$397$	12.3352	+	16.9780i	0.619086	+	0.852099i	0.997286	−	0.0736250i	$-0.0234568\pi$
$397$	12.3352	+	16.9780i	0.619086	+	0.852099i	−0.378200	+	0.925724i	$0.623457\pi$
$398$	−30.4011	−	25.4694i	−1.52387	−	1.27667i
$399$	1.12983			0.0565625
$400$		0			0
$401$	18.7715			0.937404			0.468702	−	0.883356i	$-0.344722\pi$
$401$	18.7715			0.937404			0.468702	+	0.883356i	$0.344722\pi$
$402$	−10.1124	−	8.47199i	−0.504362	−	0.422545i
$403$	10.0269	+	13.8009i	0.499476	+	0.687470i
$404$	3.06467	−	0.545284i	0.152473	−	0.0271289i
$405$		0			0
$406$	−0.0975002	+	1.41002i	−0.00483885	+	0.0699782i
$407$	2.78663			0.138128
$408$	2.80589	+	1.61129i	0.138912	+	0.0797708i
$409$	−11.2943	+	34.7602i	−0.558465	+	1.71878i	0.128146	+	0.991755i	$0.459097\pi$
$409$	−11.2943	+	34.7602i	−0.558465	+	1.71878i	−0.686611	+	0.727025i	$0.740903\pi$
$410$		0			0
$411$	21.7569	−	7.06926i	1.07319	−	0.348701i
$412$	−6.79781	−	6.54423i	−0.334904	−	0.322411i
$413$	−0.375588	−	0.122036i	−0.0184815	−	0.00600499i
$414$	22.4249	+	18.7872i	1.10213	+	0.923338i
$415$		0			0
$416$	−21.4784	−	16.6471i	−1.05306	−	0.816190i
$417$	27.6138	+	20.0626i	1.35226	+	0.982471i
$418$	−8.42661	+	5.27462i	−0.412159	+	0.257990i
$419$	6.06690	−	8.35037i	0.296387	−	0.407942i	−0.634688	−	0.772768i	$-0.718872\pi$
$419$	6.06690	−	8.35037i	0.296387	−	0.407942i	0.931076	+	0.364826i	$0.118872\pi$
$420$		0			0
$421$	7.12906	+	9.81232i	0.347449	+	0.478223i	0.946599	−	0.322414i	$-0.104494\pi$
$421$	7.12906	+	9.81232i	0.347449	+	0.478223i	−0.599149	+	0.800637i	$0.704494\pi$
$422$	−0.428030	−	0.172550i	−0.0208362	−	0.00839958i
$423$	3.08828	+	9.50473i	0.150157	+	0.462136i
$424$	12.9117	−	1.38744i	0.627049	−	0.0673800i
$425$		0			0
$426$	20.9320	+	33.4404i	1.01416	+	1.62019i
$427$	−1.24023	+	0.402975i	−0.0600189	+	0.0195013i
$428$	22.7338	−	4.04493i	1.09888	−	0.195519i
$429$	12.1220	+	16.6845i	0.585257	+	0.805538i
$430$		0			0
$431$	−24.8747	−	18.0726i	−1.19817	−	0.870525i	−0.204070	−	0.978956i	$-0.565417\pi$
$431$	−24.8747	−	18.0726i	−1.19817	−	0.870525i	−0.994104	+	0.108432i	$0.965417\pi$
$432$	1.73335	−	1.36292i	0.0833959	−	0.0655734i
$433$	3.64760	+	2.65013i	0.175292	+	0.127357i	0.671972	−	0.740577i	$-0.265448\pi$
$433$	3.64760	+	2.65013i	0.175292	+	0.127357i	−0.496680	+	0.867934i	$0.665448\pi$
$434$	−0.135176	−	0.540378i	−0.00648867	−	0.0259390i
$435$		0			0
$436$	−0.519197	+	3.73630i	−0.0248650	+	0.178936i
$437$	24.9448	+	8.10505i	1.19327	+	0.387717i
$438$	−35.4573	+	8.86969i	−1.69421	+	0.423810i
$439$	−3.68407	−	11.3384i	−0.175831	−	0.541153i	0.823839	−	0.566824i	$-0.191828\pi$
$439$	−3.68407	−	11.3384i	−0.175831	−	0.541153i	−0.999670	+	0.0256706i	$0.991828\pi$
$440$		0			0
$441$	6.95519	−	21.4059i	0.331200	−	1.01933i
$442$	0.214944	−	3.10846i	0.0102238	−	0.147854i
$443$			4.00502i			0.190284i	0.995464	+	0.0951422i	$0.0303306\pi$
$443$			4.00502i			0.190284i	−0.995464	+	0.0951422i	$0.969669\pi$
$444$	−7.12482	+	3.80251i	−0.338129	+	0.180459i
$445$		0			0
$446$	6.23234	−	15.4601i	0.295110	−	0.732056i
$447$	−29.9443	+	21.7558i	−1.41632	+	1.02902i
$448$	0.447237	+	0.766384i	0.0211300	+	0.0362082i
$449$	−6.20695			−0.292924			−0.146462	−	0.989216i	$-0.546789\pi$
$449$	−6.20695			−0.292924			−0.146462	+	0.989216i	$0.546789\pi$
$450$		0			0
$451$			19.5819i			0.922076i
$452$	−9.10326	−	1.26499i	−0.428181	−	0.0595002i
$453$	−13.0076	−	17.9034i	−0.611148	−	0.841174i
$454$	−1.37646	−	0.554885i	−0.0646004	−	0.0260420i
$455$		0			0
$456$	14.3475	−	24.9847i	0.671885	−	1.17001i
$457$	−34.1526			−1.59759			−0.798795	−	0.601604i	$-0.794529\pi$
$457$	−34.1526			−1.59759			−0.798795	+	0.601604i	$0.794529\pi$
$458$	1.97346	−	28.5396i	0.0922135	−	1.33357i
$459$	0.240457	+	0.0781294i	0.0112236	+	0.00364677i
$460$		0			0
$461$	−12.3750	+	4.02087i	−0.576359	+	0.187271i	−0.582669	−	0.812710i	$-0.697992\pi$
$461$	−12.3750	+	4.02087i	−0.576359	+	0.187271i	0.00630961	+	0.999980i	$0.497992\pi$
$462$	−0.163421	−	0.653290i	−0.00760305	−	0.0303938i
$463$	0.154016	−	0.474013i	0.00715774	−	0.0220292i	−0.947414	−	0.320011i	$-0.896313\pi$
$463$	0.154016	−	0.474013i	0.00715774	−	0.0220292i	0.954572	+	0.297982i	$0.0963134\pi$
$464$	29.9425	+	20.0617i	1.39005	+	0.931340i
$465$		0			0
$466$	−9.01021	−	36.0190i	−0.417390	−	1.66855i
$467$	16.0152	−	22.0431i	0.741096	−	1.02003i	−0.257459	−	0.966289i	$-0.582885\pi$
$467$	16.0152	−	22.0431i	0.741096	−	1.02003i	0.998555	−	0.0537419i	$-0.0171148\pi$
$468$	−27.8352	−	13.5228i	−1.28668	−	0.625090i
$469$	0.243832	−	0.335606i	0.0112591	−	0.0154968i
$470$		0			0
$471$	9.51161	−	6.91059i	0.438272	−	0.318423i
$472$	−7.46817	+	6.75588i	−0.343750	+	0.310965i
$473$	−5.60106	−	17.2383i	−0.257537	−	0.792618i
$474$	10.3052	+	16.4634i	0.473334	+	0.756188i
$475$		0			0
$476$	−0.0444600	+	0.0915163i	−0.00203782	+	0.00419464i
$477$	14.0647	−	4.56990i	0.643979	−	0.209242i
$478$	−4.61764	+	11.4546i	−0.211206	+	0.523922i
$479$	−23.5204	+	17.0886i	−1.07468	+	0.780797i	−0.976747	−	0.214396i	$-0.931222\pi$
$479$	−23.5204	+	17.0886i	−1.07468	+	0.780797i	−0.0979285	+	0.995193i	$0.531222\pi$
$480$		0			0
$481$	6.29185	+	4.57130i	0.286884	+	0.208433i
$482$	0.428846	−	0.268435i	0.0195334	−	0.0122269i
$483$	−1.04432	+	1.43739i	−0.0475183	+	0.0654034i
$484$	−11.5804	−	11.1484i	−0.526383	−	0.506748i
$485$		0			0
$486$	−20.2764	+	24.2025i	−0.919756	+	1.09785i
$487$	−8.04647	+	24.7645i	−0.364620	+	1.12219i	0.585598	+	0.810601i	$0.300860\pi$
$487$	−8.04647	+	24.7645i	−0.364620	+	1.12219i	−0.950219	+	0.311584i	$0.899140\pi$
$488$	−6.83822	+	32.5432i	−0.309552	+	1.47316i
$489$	−7.73167	−	23.7956i	−0.349638	−	1.07608i
$490$		0			0
$491$	−23.4217	−	7.61016i	−1.05700	−	0.343442i	−0.271591	−	0.962413i	$-0.587550\pi$
$491$	−23.4217	−	7.61016i	−1.05700	−	0.343442i	−0.785414	+	0.618971i	$0.787550\pi$
$492$	−26.7206	−	50.0668i	−1.20466	−	2.25718i
$493$			4.13267i			0.186126i
$494$	−27.6789	−	1.91394i	−1.24533	−	0.0861123i
$495$		0			0
$496$	−13.6663	−	3.87293i	−0.613634	−	0.173900i
$497$	−1.00363	+	0.729177i	−0.0450188	+	0.0327081i
$498$	33.1226	+	27.7495i	1.48426	+	1.24348i
$499$			18.4619i			0.826469i	0.910625	+	0.413234i	$0.135601\pi$
$499$			18.4619i			0.826469i	−0.910625	+	0.413234i	$0.864399\pi$
$500$		0			0
$501$		−	20.0640i		−	0.896393i
$502$	18.1976	−	21.7212i	0.812199	−	0.969466i
$503$	−19.4694	+	14.1453i	−0.868097	+	0.630709i	−0.930076	−	0.367368i	$-0.880259\pi$
$503$	−19.4694	+	14.1453i	−0.868097	+	0.630709i	0.0619786	+	0.998077i	$0.480259\pi$
$504$	0.677900	+	0.749372i	0.0301961	+	0.0333797i
$505$		0			0
$506$	1.07842	−	15.5958i	0.0479416	−	0.693320i
$507$			25.1325i			1.11618i
$508$	−14.3557	+	7.66164i	−0.636932	+	0.339930i
$509$	0.950881	+	0.308960i	0.0421471	+	0.0136944i	0.330015	−	0.943976i	$-0.392946\pi$
$509$	0.950881	+	0.308960i	0.0421471	+	0.0136944i	−0.287868	+	0.957670i	$0.592946\pi$
$510$		0			0
$511$	−0.355157	−	1.09306i	−0.0157112	−	0.0483541i
$512$	22.6269	−	0.157845i	0.999976	−	0.00697584i
$513$	0.695693	−	2.14112i	0.0307156	−	0.0945330i
$514$	20.3049	+	17.0111i	0.895612	+	0.750326i
$515$		0			0
$516$	37.8434	+	36.4317i	1.66596	+	1.60382i
$517$	3.13908	−	4.32057i	0.138056	−	0.190018i
$518$	−0.134740	−	0.215258i	−0.00592015	−	0.00945791i
$519$	20.0697	+	14.5815i	0.880961	+	0.640056i
$520$		0			0
$521$	−13.1276	+	9.53774i	−0.575129	+	0.417856i	−0.836965	−	0.547257i	$-0.815672\pi$
$521$	−13.1276	+	9.53774i	−0.575129	+	0.417856i	0.261836	+	0.965112i	$0.415672\pi$
$522$	38.0678	+	15.3461i	1.66618	+	0.671680i
$523$	−1.04250	+	0.338728i	−0.0455852	+	0.0148115i	−0.331721	−	0.943378i	$-0.607629\pi$
$523$	−1.04250	+	0.338728i	−0.0455852	+	0.0148115i	0.286136	+	0.958189i	$0.407629\pi$
$524$	−39.1191	−	19.0047i	−1.70893	−	0.830223i
$525$		0			0
$526$	19.7640	−	12.3712i	0.861751	−	0.539411i
$527$	−0.503303	−	1.54901i	−0.0219242	−	0.0674758i
$528$	−16.5218	−	4.68217i	−0.719020	−	0.203765i
$529$	−14.7608	+	10.7243i	−0.641773	+	0.466275i
$530$		0			0
$531$	−6.74091	+	9.27806i	−0.292530	+	0.402634i
$532$	0.814896	+	0.395889i	0.0353302	+	0.0171639i
$533$	−32.1230	+	44.2135i	−1.39140	+	1.91510i
$534$	−22.9830	+	5.74924i	−0.994574	+	0.248794i
$535$		0			0
$536$	−4.32507	−	9.65379i	−0.186815	−	0.416980i
$537$	−9.70162	+	29.8585i	−0.418656	+	1.28849i
$538$	0.199842	−	0.0499908i	0.00861581	−	0.00215526i
$539$	−11.4389	+	3.71671i	−0.492706	+	0.160090i
$540$		0			0
$541$	−22.8256	−	7.41649i	−0.981349	−	0.318860i	−0.225961	−	0.974136i	$-0.572552\pi$
$541$	−22.8256	−	7.41649i	−0.981349	−	0.318860i	−0.755389	+	0.655277i	$0.772552\pi$
$542$	−21.6369	−	1.49615i	−0.929386	−	0.0642651i
$543$	−32.5706			−1.39774
$544$	1.45916	+	2.14532i	0.0625611	+	0.0919797i
$545$		0			0
$546$	0.702699	−	1.74313i	0.0300727	−	0.0745990i
$547$	−15.0286	−	20.6852i	−0.642579	−	0.884434i	0.356171	−	0.934421i	$-0.384082\pi$
$547$	−15.0286	−	20.6852i	−0.642579	−	0.884434i	−0.998750	+	0.0499871i	$0.984082\pi$
$548$	18.1693	+	2.52481i	0.776153	+	0.107855i
$549$			37.8696i			1.61623i
$550$		0			0
$551$	36.7989			1.56769
$552$	18.5241	+	41.3468i	0.788438	+	1.75984i
$553$	−0.494105	+	0.358988i	−0.0210115	+	0.0152657i
$554$	27.1628	+	10.9500i	1.15404	+	0.465221i
$555$		0			0
$556$	12.8867	+	24.1460i	0.546518	+	1.02402i
$557$		−	39.1180i		−	1.65748i	−0.559631	−	0.828742i	$-0.689057\pi$
$557$		−	39.1180i		−	1.65748i	0.559631	−	0.828742i	$-0.310943\pi$
$558$	−16.1375	−	1.11588i	−0.683155	−	0.0472388i
$559$	15.6319	−	48.1101i	0.661160	−	2.03484i
$560$		0			0
$561$	−0.608468	−	1.87267i	−0.0256895	−	0.0790642i
$562$	−3.63282	−	14.5225i	−0.153241	−	0.612594i
$563$	29.0845	+	9.45014i	1.22577	+	0.398276i	0.849179	−	0.528105i	$-0.177097\pi$
$563$	29.0845	+	9.45014i	1.22577	+	0.398276i	0.376588	+	0.926381i	$0.377097\pi$
$564$	−2.13029	+	15.3302i	−0.0897015	+	0.645519i
$565$		0			0
$566$	28.2226	−	7.05993i	1.18629	−	0.296751i
$567$	−0.743723	−	0.540347i	−0.0312334	−	0.0226924i
$568$	3.37986	+	31.4534i	0.141816	+	1.31976i
$569$	−0.511882	−	0.371904i	−0.0214592	−	0.0155910i	0.577004	−	0.816741i	$-0.304222\pi$
$569$	−0.511882	−	0.371904i	−0.0214592	−	0.0155910i	−0.598463	+	0.801150i	$0.704222\pi$
$570$		0			0
$571$	2.91121	+	4.00694i	0.121830	+	0.167685i	0.865576	−	0.500778i	$-0.166953\pi$
$571$	2.91121	+	4.00694i	0.121830	+	0.167685i	−0.743746	+	0.668463i	$0.766953\pi$
$572$	2.89686	+	16.2813i	0.121124	+	0.680754i
$573$	6.82510	−	2.21761i	0.285122	−	0.0926419i
$574$	1.51264	−	0.946834i	0.0631364	−	0.0395201i
$575$		0			0
$576$	25.1798	−	5.47465i	1.04916	−	0.228110i
$577$	4.95951	+	15.2638i	0.206467	+	0.635440i	0.999650	+	0.0264569i	$0.00842246\pi$
$577$	4.95951	+	15.2638i	0.206467	+	0.635440i	−0.793183	+	0.608984i	$0.791578\pi$
$578$	8.87764	−	22.0221i	0.369261	−	0.915997i
$579$	23.3130	+	32.0876i	0.968855	+	1.33352i
$580$		0			0
$581$	−0.798656	+	1.09926i	−0.0331338	+	0.0456048i
$582$	−10.5188	−	16.8045i	−0.436016	−	0.696570i
$583$	−6.39340	−	4.64508i	−0.264788	−	0.192379i
$584$	−28.6815	−	6.02678i	−1.18685	−	0.249390i
$585$		0			0
$586$	0.547760	−	0.653824i	0.0226278	−	0.0270092i
$587$	22.2461	+	7.22818i	0.918193	+	0.298339i	0.729725	−	0.683740i	$-0.239648\pi$
$587$	22.2461	+	7.22818i	0.918193	+	0.298339i	0.188468	+	0.982079i	$0.439648\pi$
$588$	24.1751	−	25.1118i	0.996963	−	1.03559i
$589$	−13.7929	+	4.48160i	−0.568328	+	0.184661i
$590$		0			0
$591$	−3.60552	+	11.0967i	−0.148311	+	0.456455i
$592$	−6.47117	+	0.246068i	−0.265964	+	0.0101133i
$593$	7.54773			0.309948			0.154974	−	0.987919i	$-0.450471\pi$
$593$	7.54773			0.309948			0.154974	+	0.987919i	$0.450471\pi$
$594$	−1.33866	−	0.0925658i	−0.0549260	−	0.00379802i
$595$		0			0
$596$	−29.2206	+	5.19909i	−1.19692	+	0.212963i
$597$	−41.1137	−	56.5882i	−1.68267	−	2.31600i
$598$	28.0190	−	33.4443i	1.14578	−	1.36764i
$599$	−0.302745			−0.0123698			−0.00618491	−	0.999981i	$-0.501969\pi$
$599$	−0.302745			−0.0123698			−0.00618491	+	0.999981i	$0.501969\pi$
$600$		0			0
$601$	−32.7273			−1.33497			−0.667487	−	0.744622i	$-0.732630\pi$
$601$	−32.7273			−1.33497			−0.667487	+	0.744622i	$0.732630\pi$
$602$	−1.06078	+	1.26618i	−0.0432342	+	0.0516056i
$603$	−7.08085	−	9.74595i	−0.288354	−	0.396886i
$604$	−3.10848	−	17.4706i	−0.126482	−	0.710870i
$605$		0			0
$606$	5.47686	+	0.378714i	0.222482	+	0.0153842i
$607$	−26.9091			−1.09221			−0.546103	−	0.837718i	$-0.683889\pi$
$607$	−26.9091			−1.09221			−0.546103	+	0.837718i	$0.683889\pi$
$608$	19.1027	−	12.9929i	0.774717	−	0.526933i
$609$	−0.770300	+	2.37074i	−0.0312141	+	0.0960672i
$610$		0			0
$611$	14.1753	−	4.60583i	0.573470	−	0.186332i
$612$	2.12857	+	2.04917i	0.0860424	+	0.0828328i
$613$	−8.04187	−	2.61296i	−0.324808	−	0.105537i	0.142074	−	0.989856i	$-0.454623\pi$
$613$	−8.04187	−	2.61296i	−0.324808	−	0.105537i	−0.466882	+	0.884319i	$0.654623\pi$
$614$	9.04794	−	10.7999i	0.365145	−	0.435849i
$615$		0			0
$616$	0.111042	−	0.528449i	0.00447399	−	0.0212918i
$617$	15.5720	+	11.3137i	0.626904	+	0.455472i	0.855326	−	0.518090i	$-0.173357\pi$
$617$	15.5720	+	11.3137i	0.626904	+	0.455472i	−0.228422	+	0.973562i	$0.573357\pi$
$618$	−8.82976	−	14.1062i	−0.355185	−	0.567436i
$619$	−19.2261	+	26.4625i	−0.772763	+	1.06362i	0.223281	+	0.974754i	$0.428323\pi$
$619$	−19.2261	+	26.4625i	−0.772763	+	1.06362i	−0.996044	+	0.0888631i	$0.971677\pi$
$620$		0			0
$621$	2.08092	+	2.86414i	0.0835045	+	0.114934i
$622$	12.8808	−	31.9524i	0.516474	−	1.28118i
$623$	−0.230209	−	0.708511i	−0.00922313	−	0.0283859i
$624$	−29.6234	−	37.6748i	−1.18588	−	1.50820i
$625$		0			0
$626$	−22.4347	+	14.0430i	−0.896672	+	0.561270i
$627$	−16.6750	+	5.41803i	−0.665934	+	0.216375i
$628$	9.28171	−	1.65146i	0.370380	−	0.0659002i
$629$	−0.436453	−	0.600727i	−0.0174025	−	0.0239525i
$630$		0			0
$631$	29.3548	+	21.3275i	1.16860	+	0.849035i	0.990840	−	0.135040i	$-0.0431162\pi$
$631$	29.3548	+	21.3275i	1.16860	+	0.849035i	0.177756	+	0.984075i	$0.443116\pi$
$632$	1.66397	+	15.4851i	0.0661891	+	0.615966i
$633$	−0.658485	−	0.478417i	−0.0261724	−	0.0190154i
$634$	−39.1633	+	9.79677i	−1.55538	+	0.389079i
$635$		0			0
$636$	22.6850	+	3.15232i	0.899521	+	0.124998i
$637$	−31.9245	−	10.3729i	−1.26490	−	0.410990i
$638$	−5.32266	−	21.2778i	−0.210726	−	0.842394i
$639$	11.1325	+	34.2622i	0.440393	+	1.35539i
$640$		0			0
$641$	−0.0519999	+	0.160039i	−0.00205387	+	0.00632117i	−0.952078	−	0.305855i	$-0.901058\pi$
$641$	−0.0519999	+	0.160039i	−0.00205387	+	0.00632117i	0.950024	+	0.312176i	$0.101058\pi$
$642$	40.6275	+	2.80931i	1.60344	+	0.110875i
$643$		−	6.95566i		−	0.274305i	−0.990550	−	0.137152i	$-0.956205\pi$
$643$		−	6.95566i		−	0.274305i	0.990550	−	0.137152i	$-0.0437950\pi$
$644$	−1.25687	+	0.670793i	−0.0495278	+	0.0264330i
$645$		0			0
$646$	2.45689	+	0.990432i	0.0966649	+	0.0389680i
$647$	20.9935	−	15.2526i	0.825338	−	0.599643i	−0.0928983	−	0.995676i	$-0.529613\pi$
$647$	20.9935	−	15.2526i	0.825338	−	0.599643i	0.918237	+	0.396032i	$0.129613\pi$
$648$	−21.3934	+	9.58462i	−0.840412	+	0.376520i
$649$	6.12843			0.240562
$650$		0			0
$651$		−	0.982411i		−	0.0385037i
$652$	2.76139	−	19.8718i	0.108145	−	0.778240i
$653$	−10.8488	−	14.9322i	−0.424548	−	0.584340i	0.542143	−	0.840286i	$-0.317613\pi$
$653$	−10.8488	−	14.9322i	−0.424548	−	0.584340i	−0.966691	+	0.255946i	$0.917613\pi$
$654$	−2.48743	+	6.17038i	−0.0972663	+	0.241281i
$655$		0			0
$656$	−1.72915	−	45.4736i	−0.0675118	−	1.77544i
$657$	−33.3758			−1.30212
$658$	−0.485533	−	0.0335736i	−0.0189280	−	0.00130884i
$659$	8.10100	+	2.63217i	0.315570	+	0.102535i	0.462520	−	0.886609i	$-0.346945\pi$
$659$	8.10100	+	2.63217i	0.315570	+	0.102535i	−0.146950	+	0.989144i	$0.546945\pi$
$660$		0			0
$661$	−38.1202	+	12.3860i	−1.48270	+	0.481760i	−0.934920	−	0.354859i	$-0.884529\pi$
$661$	−38.1202	+	12.3860i	−1.48270	+	0.481760i	−0.547785	+	0.836619i	$0.684529\pi$
$662$	−4.90690	+	1.22747i	−0.190712	+	0.0477069i
$663$	1.69816	−	5.22641i	0.0659512	−	0.202977i
$664$	14.1665	+	31.6204i	0.549767	+	1.22711i
$665$		0			0
$666$	−7.15426	+	1.78965i	−0.277222	+	0.0693474i
$667$	−34.0138	+	46.8159i	−1.31702	+	1.81272i
$668$	7.03033	−	14.4712i	0.272012	−	0.559908i
$669$	17.2800	−	23.7839i	0.668084	−	0.919539i
$670$		0			0
$671$	16.3718	−	11.8948i	0.632028	−	0.459195i
$672$	0.437189	+	1.50265i	0.0168649	+	0.0579662i
$673$	13.9092	+	42.8082i	0.536162	+	1.65014i	0.741125	+	0.671367i	$0.234292\pi$
$673$	13.9092	+	42.8082i	0.536162	+	1.65014i	−0.204964	+	0.978770i	$0.565708\pi$
$674$	−11.7858	+	7.37727i	−0.453970	+	0.284162i
$675$		0			0
$676$	−8.80633	+	18.1269i	−0.338705	+	0.697189i
$677$	−42.8382	+	13.9190i	−1.64641	+	0.534950i	−0.977957	−	0.208808i	$-0.933042\pi$
$677$	−42.8382	+	13.9190i	−1.64641	+	0.534950i	−0.668450	+	0.743758i	$0.733042\pi$
$678$	−15.0337	−	6.06048i	−0.577368	−	0.232751i
$679$	0.504344	−	0.366427i	0.0193549	−	0.0140622i
$680$		0			0
$681$	−2.11756	−	1.53849i	−0.0811449	−	0.0589552i
$682$	4.58638	+	7.32709i	0.175621	+	0.280569i
$683$	−4.29498	+	5.91153i	−0.164343	+	0.226199i	−0.883244	−	0.468914i	$-0.844645\pi$
$683$	−4.29498	+	5.91153i	−0.164343	+	0.226199i	0.718901	+	0.695112i	$0.244645\pi$
$684$	18.2466	−	18.9536i	0.697676	−	0.724709i
$685$		0			0
$686$	1.68188	+	1.40905i	0.0642146	+	0.0537977i
$687$	15.5913	−	47.9850i	0.594844	−	1.83074i
$688$	14.5291	+	39.5366i	0.553918	+	1.50732i
$689$	−6.81552	−	20.9760i	−0.259650	−	0.799122i
$690$		0			0
$691$	33.1194	+	10.7611i	1.25992	+	0.409373i	0.861467	−	0.507814i	$-0.169546\pi$
$691$	33.1194	+	10.7611i	1.25992	+	0.409373i	0.398455	+	0.917188i	$0.369546\pi$
$692$	9.36602	+	17.5492i	0.356043	+	0.667122i
$693$		−	0.614940i		−	0.0233596i
$694$	1.54086	−	22.2835i	0.0584901	−	0.845869i
$695$		0			0
$696$	42.6436	+	47.1396i	1.61640	+	1.78682i
$697$	4.22136	−	3.06700i	0.159896	−	0.116171i
$698$	7.07293	−	8.44247i	0.267714	−	0.319552i
$699$		−	65.4828i		−	2.47679i
$700$		0			0
$701$		−	22.3659i		−	0.844750i	−0.906421	−	0.422375i	$-0.861197\pi$
$701$		−	22.3659i		−	0.844750i	0.906421	−	0.422375i	$-0.138803\pi$
$702$	−2.87068	−	2.40500i	−0.108347	−	0.0907708i
$703$	−5.34910	+	3.88635i	−0.201745	+	0.146576i
$704$	−10.2758	−	9.16620i	−0.387284	−	0.345464i
$705$		0			0
$706$	15.8633	+	1.09691i	0.597022	+	0.0412828i
$707$			0.172631i			0.00649248i
$708$	−15.6691	+	8.36259i	−0.588881	+	0.314285i
$709$	−17.1971	−	5.58767i	−0.645849	−	0.209849i	−0.0322662	−	0.999479i	$-0.510272\pi$
$709$	−17.1971	−	5.58767i	−0.645849	−	0.209849i	−0.613583	+	0.789630i	$0.710272\pi$
$710$		0			0
$711$	5.48073	+	16.8679i	0.205543	+	0.632597i
$712$	−18.5911	−	3.90650i	−0.696730	−	0.146402i
$713$	7.04749	−	21.6899i	0.263930	−	0.812294i
$714$	−0.115237	+	0.137551i	−0.00431264	+	0.00514770i
$715$		0			0
$716$	−17.4596	+	18.1361i	−0.652496	+	0.677779i
$717$	−12.8030	+	17.6219i	−0.478139	+	0.658101i
$718$	12.1964	−	7.63431i	0.455166	−	0.284910i
$719$	31.8411	+	23.1339i	1.18747	+	0.862749i	0.992995	−	0.118158i	$-0.0376991\pi$
$719$	31.8411	+	23.1339i	1.18747	+	0.862749i	0.194477	+	0.980907i	$0.437699\pi$
$720$		0			0
$721$	0.423362	−	0.307590i	0.0157668	−	0.0114553i
$722$	−1.22721	+	3.04424i	−0.0456719	+	0.113295i
$723$	0.848620	−	0.275733i	0.0315605	−	0.0102546i
$724$	−23.4916	−	11.4126i	−0.873059	−	0.424145i
$725$		0			0
$726$	−15.0420	−	24.0307i	−0.558260	−	0.891864i
$727$	5.45658	+	16.7936i	0.202373	+	0.622841i	0.999811	+	0.0194399i	$0.00618830\pi$
$727$	5.45658	+	16.7936i	0.202373	+	0.622841i	−0.797438	+	0.603401i	$0.793812\pi$
$728$	1.11761	−	1.01101i	0.0414213	−	0.0374707i
$729$	−24.9346	+	18.1161i	−0.923505	+	0.670966i
$730$		0			0
$731$	−2.83888	+	3.90738i	−0.105000	+	0.144520i
$732$	−25.6281	+	52.7529i	−0.947244	+	1.94980i
$733$	5.28165	−	7.26956i	0.195082	−	0.268507i	−0.700259	−	0.713889i	$-0.746932\pi$
$733$	5.28165	−	7.26956i	0.195082	−	0.268507i	0.895341	+	0.445382i	$0.146932\pi$
$734$	4.16510	+	16.6503i	0.153737	+	0.614575i
$735$		0			0
$736$	−1.12717	+	36.3123i	−0.0415481	+	1.33849i
$737$	−1.98929	+	6.12241i	−0.0732765	+	0.225522i
$738$	−12.5760	−	50.2736i	−0.462930	−	1.85060i
$739$	20.0852	−	6.52609i	0.738848	−	0.240066i	0.0846720	−	0.996409i	$-0.473016\pi$
$739$	20.0852	−	6.52609i	0.738848	−	0.240066i	0.654176	+	0.756343i	$0.273016\pi$
$740$		0			0
$741$	−46.5379	−	15.1211i	−1.70961	−	0.555487i
$742$	−0.0496808	+	0.718472i	−0.00182384	+	0.0263759i
$743$	−8.50903			−0.312166			−0.156083	−	0.987744i	$-0.549887\pi$
$743$	−8.50903			−0.312166			−0.156083	+	0.987744i	$0.549887\pi$
$744$	−21.7246	−	12.4755i	−0.796463	−	0.457372i
$745$		0			0
$746$	9.77249	+	3.93953i	0.357796	+	0.144237i
$747$	23.1929	+	31.9222i	0.848582	+	1.16797i
$748$	0.217316	−	1.56387i	0.00794587	−	0.0571808i
$749$			1.28058i			0.0467916i
$750$		0			0
$751$	−17.1075			−0.624262			−0.312131	−	0.950039i	$-0.601043\pi$
$751$	−17.1075			−0.624262			−0.312131	+	0.950039i	$0.601043\pi$
$752$	−6.90812	+	10.3105i	−0.251913	+	0.375986i
$753$	40.4317	−	29.3753i	1.47341	−	1.07050i
$754$	22.8870	−	56.7740i	0.833496	−	2.06759i
$755$		0			0
$756$	0.0575772	+	0.107883i	0.00209406	+	0.00392368i
$757$			2.28693i			0.0831199i	0.999136	+	0.0415599i	$0.0132328\pi$
$757$			2.28693i			0.0831199i	−0.999136	+	0.0415599i	$0.986767\pi$
$758$	0.614469	−	8.88629i	0.0223185	−	0.322765i
$759$	8.52006	−	26.2220i	0.309258	−	0.951800i
$760$		0			0
$761$	−6.05917	−	18.6482i	−0.219645	−	0.675997i	−0.998791	−	0.0491552i	$-0.984347\pi$
$761$	−6.05917	−	18.6482i	−0.219645	−	0.675997i	0.779146	−	0.626842i	$-0.215653\pi$
$762$	−27.8410	+	6.96446i	−1.00857	+	0.252296i
$763$	−0.198961	−	0.0646465i	−0.00720289	−	0.00234036i
$764$	5.69966	+	0.792026i	0.206206	+	0.0286545i
$765$		0			0
$766$	−9.83154	−	39.3024i	−0.355228	−	1.42005i
$767$	13.8372	+	10.0533i	0.499633	+	0.363005i
$768$	38.7808	+	9.41412i	1.39938	+	0.339703i
$769$	−15.2893	−	11.1083i	−0.551345	−	0.400576i	0.276936	−	0.960888i	$-0.410681\pi$
$769$	−15.2893	−	11.1083i	−0.551345	−	0.400576i	−0.828281	+	0.560313i	$0.810681\pi$
$770$		0			0
$771$	27.4599	+	37.7954i	0.988946	+	1.36117i
$772$	5.57122	+	31.3120i	0.200513	+	1.12694i
$773$	−7.19893	+	2.33908i	−0.258928	+	0.0841307i	−0.435604	−	0.900138i	$-0.643465\pi$
$773$	−7.19893	+	2.33908i	−0.258928	+	0.0841307i	0.176677	+	0.984269i	$0.443465\pi$
$774$	25.4508	+	40.6597i	0.914811	+	1.46148i
$775$		0			0
$776$	−1.69845	−	15.8060i	−0.0609708	−	0.567403i
$777$	−0.138404	−	0.425963i	−0.00496521	−	0.0152813i
$778$	−0.910902	−	0.367207i	−0.0326574	−	0.0131650i
$779$	−27.3097	−	37.5886i	−0.978473	−	1.34675i
$780$		0			0
$781$	11.3156	−	15.5746i	0.404903	−	0.557302i
$782$	−3.53098	+	2.21021i	−0.126267	+	0.0790368i
$783$	4.01843	+	2.91956i	0.143607	+	0.104336i
$784$	26.2354	−	9.64112i	0.936978	−	0.344326i
$785$		0			0
$786$	−58.7967	−	49.2587i	−2.09721	−	1.75700i
$787$	38.7769	+	12.5994i	1.38225	+	0.449119i	0.903407	−	0.428784i	$-0.141058\pi$
$787$	38.7769	+	12.5994i	1.38225	+	0.449119i	0.478839	+	0.877903i	$0.341058\pi$
$788$	−6.48870	+	6.74013i	−0.231151	+	0.240107i
$789$	39.1099	−	12.7076i	1.39235	−	0.452401i
$790$		0			0
$791$	0.157507	−	0.484757i	0.00560031	−	0.0172360i
$792$	−13.5985	−	7.80901i	−0.483203	−	0.277481i
$793$	56.4783			2.00560
$794$	−2.04732	+	29.6079i	−0.0726568	+	1.05074i
$795$		0			0
$796$	−9.82514	−	55.2204i	−0.348243	−	1.95724i
$797$	2.91212	+	4.00819i	0.103153	+	0.141977i	0.857473	−	0.514529i	$-0.172033\pi$
$797$	2.91212	+	4.00819i	0.103153	+	0.141977i	−0.754320	+	0.656507i	$0.772033\pi$
$798$	1.22480	+	1.02611i	0.0433575	+	0.0363240i
$799$	−1.42306			−0.0503443
$800$		0			0
$801$	−21.6339			−0.764396
$802$	20.3493	+	17.0483i	0.718560	+	0.601995i
$803$	10.4834	+	14.4291i	0.369950	+	0.509192i
$804$	−3.26818	−	18.3682i	−0.115260	−	0.647797i
$805$		0			0
$806$	−1.66421	+	24.0673i	−0.0586192	+	0.847735i
$807$	0.363315			0.0127893
$808$	3.81750	+	2.19221i	0.134299	+	0.0771218i
$809$	−7.58506	+	23.3444i	−0.266676	+	0.820746i	0.724626	+	0.689142i	$0.242013\pi$
$809$	−7.58506	+	23.3444i	−0.266676	+	0.820746i	−0.991302	+	0.131603i	$0.957987\pi$
$810$		0			0
$811$	0.736311	−	0.239242i	0.0258554	−	0.00840092i	−0.296061	−	0.955169i	$-0.595673\pi$
$811$	0.736311	−	0.239242i	0.0258554	−	0.00840092i	0.321916	+	0.946768i	$0.395673\pi$
$812$	−1.38628	+	1.43999i	−0.0486488	+	0.0505338i
$813$	−36.3792	−	11.8203i	−1.27588	−	0.414557i
$814$	3.02086	+	2.53081i	0.105881	+	0.0887049i
$815$		0			0
$816$	1.57836	+	4.29503i	0.0552537	+	0.150356i
$817$	34.7928	+	25.2785i	1.21725	+	0.884382i
$818$	−43.8128	+	27.4245i	−1.53188	+	0.958875i
$819$	1.00877	−	1.38846i	0.0352494	−	0.0485166i
$820$		0			0
$821$	4.17446	+	5.74566i	0.145690	+	0.200525i	0.875625	−	0.482992i	$-0.160450\pi$
$821$	4.17446	+	5.74566i	0.145690	+	0.200525i	−0.729935	+	0.683516i	$0.760450\pi$
$822$	30.0060	+	12.0962i	1.04658	+	0.421902i
$823$	2.42963	+	7.47765i	0.0846917	+	0.260654i	0.984430	−	0.175775i	$-0.0562430\pi$
$823$	2.42963	+	7.47765i	0.0846917	+	0.260654i	−0.899739	+	0.436429i	$0.856243\pi$
$824$	−1.42573	−	13.2681i	−0.0496677	−	0.462215i
$825$		0			0
$826$	−0.296325	−	0.473402i	−0.0103105	−	0.0164718i
$827$	3.13777	−	1.01952i	0.109111	−	0.0354523i	−0.253953	−	0.967217i	$-0.581731\pi$
$827$	3.13777	−	1.01952i	0.109111	−	0.0354523i	0.363064	+	0.931764i	$0.381731\pi$
$828$	7.24738	+	40.7326i	0.251864	+	1.41556i
$829$	19.0835	+	26.2662i	0.662798	+	0.912263i	0.999570	−	0.0293232i	$-0.00933521\pi$
$829$	19.0835	+	26.2662i	0.662798	+	0.912263i	−0.336772	+	0.941586i	$0.609335\pi$
$830$		0			0
$831$	41.7875	+	30.3604i	1.44959	+	1.05319i
$832$	−8.16485	−	37.5530i	−0.283065	−	1.30192i
$833$	2.59283	+	1.88380i	0.0898362	+	0.0652699i
$834$	11.7141	+	46.8279i	0.405625	+	1.62152i
$835$		0			0
$836$	−13.9253	−	1.93507i	−0.481617	−	0.0669257i
$837$	−1.86175	−	0.604918i	−0.0643514	−	0.0209090i
$838$	14.1606	−	3.54231i	0.489171	−	0.122367i
$839$	−3.32108	−	10.2212i	−0.114656	−	0.352876i	0.877219	−	0.480091i	$-0.159396\pi$
$839$	−3.32108	−	10.2212i	−0.114656	−	0.352876i	−0.991875	+	0.127215i	$0.959396\pi$
$840$		0			0
$841$	−16.1273	+	49.6347i	−0.556114	+	1.71154i
$842$	−1.18324	+	17.1117i	−0.0407771	+	0.589708i
$843$		−	26.4020i		−	0.909332i
$844$	−0.307299	−	0.575790i	−0.0105777	−	0.0198195i
$845$		0			0
$846$	−5.28433	+	13.1084i	−0.181679	+	0.450677i
$847$	0.721219	−	0.523996i	0.0247814	−	0.0180047i
$848$	15.2571	+	10.2224i	0.523931	+	0.351037i
$849$	51.3090			1.76092
$850$		0			0
$851$		−	10.3974i		−	0.356418i
$852$	−7.67917	+	55.2616i	−0.263084	+	1.89323i
$853$	13.5909	+	18.7063i	0.465344	+	0.640491i	0.975606	−	0.219528i	$-0.0704517\pi$
$853$	13.5909	+	18.7063i	0.465344	+	0.640491i	−0.510262	+	0.860019i	$0.670452\pi$
$854$	−1.71046	−	0.689528i	−0.0585307	−	0.0235952i
$855$		0			0
$856$	28.3183	+	16.2619i	0.967900	+	0.555820i
$857$	−15.8941			−0.542932			−0.271466	−	0.962448i	$-0.587508\pi$
$857$	−15.8941			−0.542932			−0.271466	+	0.962448i	$0.587508\pi$
$858$	−2.01194	+	29.0962i	−0.0686866	+	0.993327i
$859$	3.46524	+	1.12593i	0.118233	+	0.0384161i	0.367536	−	0.930009i	$-0.380202\pi$
$859$	3.46524	+	1.12593i	0.118233	+	0.0384161i	−0.249303	+	0.968425i	$0.580202\pi$
$860$		0			0
$861$	2.99328	−	0.972577i	0.102011	−	0.0331453i
$862$	−10.5521	−	42.1829i	−0.359406	−	1.43675i
$863$	−12.9507	+	39.8580i	−0.440845	+	1.35678i	0.446131	+	0.894968i	$0.352802\pi$
$863$	−12.9507	+	39.8580i	−0.440845	+	1.35678i	−0.886976	+	0.461815i	$0.847198\pi$
$864$	3.11685	+	0.0967502i	0.106037	+	0.00329151i
$865$		0			0
$866$	1.54734	+	6.18563i	0.0525809	+	0.210196i
$867$	24.6145	−	33.8789i	0.835951	−	1.15059i
$868$	0.344232	−	0.708566i	0.0116840	−	0.0240503i
$869$	5.57088	−	7.66766i	0.188979	−	0.260108i
$870$		0			0
$871$	−14.5350	+	10.5603i	−0.492500	+	0.357823i
$872$	−3.95614	+	3.57882i	−0.133972	+	0.121194i
$873$	−5.59430	−	17.2175i	−0.189338	−	0.582723i
$874$	19.6805	+	31.4411i	0.665703	+	1.06351i
$875$		0			0
$876$	−46.4931	−	22.5870i	−1.57086	−	0.763145i
$877$	27.2067	−	8.84000i	0.918705	−	0.298505i	0.188770	−	0.982021i	$-0.439550\pi$
$877$	27.2067	−	8.84000i	0.918705	−	0.298505i	0.729936	+	0.683516i	$0.239550\pi$
$878$	6.30380	−	15.6373i	0.212743	−	0.527734i
$879$	1.21702	−	0.884217i	0.0410491	−	0.0298239i
$880$		0			0
$881$	15.5718	+	11.3135i	0.524626	+	0.381163i	0.818344	−	0.574729i	$-0.194893\pi$
$881$	15.5718	+	11.3135i	0.524626	+	0.381163i	−0.293718	+	0.955892i	$0.594893\pi$
$882$	26.9806	−	16.8884i	0.908484	−	0.568663i
$883$	−7.63372	+	10.5069i	−0.256895	+	0.353586i	−0.917911	−	0.396786i	$-0.870126\pi$
$883$	−7.63372	+	10.5069i	−0.256895	+	0.353586i	0.661016	+	0.750372i	$0.270126\pi$
$884$	3.05611	−	3.17453i	0.102788	−	0.106771i
$885$		0			0
$886$	−3.63736	+	4.34167i	−0.122199	+	0.145861i
$887$	5.22346	−	16.0762i	0.175387	−	0.539785i	−0.824264	−	0.566205i	$-0.808411\pi$
$887$	5.22346	−	16.0762i	0.175387	−	0.539785i	0.999651	+	0.0264205i	$0.00841087\pi$
$888$	−11.1771	−	2.34862i	−0.375080	−	0.0788146i
$889$	−0.278868	−	0.858269i	−0.00935295	−	0.0287854i
$890$		0			0
$891$	13.5676	+	4.40839i	0.454533	+	0.147687i
$892$	20.7970	−	11.0994i	0.696336	−	0.371634i
$893$			12.6715i			0.424035i
$894$	−52.2199	−	3.61090i	−1.74649	−	0.120767i
$895$		0			0
$896$	−0.211200	+	1.23698i	−0.00705569	+	0.0413247i
$897$	62.2529	−	45.2294i	2.07856	−	1.51017i
$898$	−6.72868	−	5.63715i	−0.224539	−	0.188114i
$899$		−	31.9973i		−	1.06717i
$900$		0			0
$901$			2.10579i			0.0701540i
$902$	−17.7843	+	21.2279i	−0.592151	+	0.706810i
$903$	−2.35685	+	1.71235i	−0.0784312	+	0.0569836i
$904$	−8.71956	−	9.63889i	−0.290008	−	0.320585i
$905$		0			0
$906$	2.15892	−	31.2217i	0.0717252	−	1.03727i
$907$			36.2209i			1.20269i	0.798988	+	0.601347i	$0.205369\pi$
$907$			36.2209i			1.20269i	−0.798988	+	0.601347i	$0.794631\pi$
$908$	−0.988211	−	1.85162i	−0.0327949	−	0.0614483i
$909$	4.76783	+	1.54916i	0.158139	+	0.0513825i
$910$		0			0
$911$	−3.31491	−	10.2022i	−0.109828	−	0.338015i	0.881005	−	0.473106i	$-0.156867\pi$
$911$	−3.31491	−	10.2022i	−0.109828	−	0.338015i	−0.990833	+	0.135091i	$0.956867\pi$
$912$	38.2446	−	14.0543i	1.26640	−	0.465385i
$913$	6.51579	−	20.0536i	0.215641	−	0.663676i
$914$	−37.0232	−	31.0173i	−1.22462	−	1.02596i
$915$		0			0
$916$	28.0590	−	29.1462i	0.927095	−	0.963018i
$917$	1.41771	−	1.95131i	0.0468170	−	0.0644381i
$918$	0.189712	+	0.303080i	0.00626143	+	0.0100031i
$919$	32.1024	+	23.3238i	1.05896	+	0.769380i	0.973896	−	0.226995i	$-0.0728901\pi$
$919$	32.1024	+	23.3238i	1.05896	+	0.769380i	0.0850654	+	0.996375i	$0.472890\pi$
$920$		0			0
$921$	20.1028	−	14.6056i	0.662411	−	0.481270i
$922$	−17.0669	−	6.88008i	−0.562068	−	0.226584i
$923$	51.0983	−	16.6029i	1.68192	−	0.546490i
$924$	0.416159	−	0.856621i	0.0136906	−	0.0281808i
$925$		0			0
$926$	0.597460	−	0.373979i	0.0196338	−	0.0122897i
$927$	−4.69603	−	14.4529i	−0.154238	−	0.474695i
$928$	14.2393	+	48.9417i	0.467428	+	1.60659i
$929$	−17.2005	+	12.4969i	−0.564331	+	0.410011i	−0.833042	−	0.553210i	$-0.813403\pi$
$929$	−17.2005	+	12.4969i	−0.564331	+	0.410011i	0.268710	+	0.963221i	$0.413403\pi$
$930$		0			0
$931$	16.7741	−	23.0875i	0.549748	−	0.756664i
$932$	22.9449	−	47.2296i	0.751584	−	1.54706i
$933$	35.7138	−	49.1558i	1.16922	−	1.60929i
$934$	37.3809	−	9.35088i	1.22314	−	0.305970i
$935$		0			0
$936$	−17.8935	−	39.9393i	−0.584868	−	1.30546i
$937$	9.26796	−	28.5238i	0.302771	−	0.931833i	−0.677729	−	0.735312i	$-0.737036\pi$
$937$	9.26796	−	28.5238i	0.302771	−	0.931833i	0.980500	−	0.196521i	$-0.0629644\pi$
$938$	0.569124	−	0.142367i	0.0185826	−	0.00464846i
$939$	−44.3948	+	14.4248i	−1.44877	+	0.470734i
$940$		0			0
$941$	20.6829	+	6.72027i	0.674242	+	0.219075i	0.626073	−	0.779765i	$-0.284661\pi$
$941$	20.6829	+	6.72027i	0.674242	+	0.219075i	0.0481695	+	0.998839i	$0.484661\pi$
$942$	16.5873	+	1.14698i	0.540443	+	0.0373705i
$943$	73.0634			2.37927
$944$	−14.2316	+	0.541160i	−0.463199	+	0.0176133i
$945$		0			0
$946$	9.58395	−	23.7741i	0.311601	−	0.772964i
$947$	−13.8628	−	19.0805i	−0.450481	−	0.620034i	0.522020	−	0.852934i	$-0.325179\pi$
$947$	−13.8628	−	19.0805i	−0.450481	−	0.620034i	−0.972501	+	0.232899i	$0.925179\pi$
$948$	−3.78061	+	27.2064i	−0.122788	+	0.883622i
$949$			49.7764i			1.61581i
$950$		0			0
$951$	−71.1992			−2.30879
$952$	−0.131312	+	0.0588301i	−0.00425585	+	0.00190670i
$953$	−22.5241	+	16.3647i	−0.729629	+	0.530106i	−0.889446	−	0.457040i	$-0.848909\pi$
$953$	−22.5241	+	16.3647i	−0.729629	+	0.530106i	0.159817	+	0.987147i	$0.448909\pi$
$954$	19.3973	+	7.81954i	0.628011	+	0.253167i
$955$		0			0
$956$	−15.4089	+	8.22370i	−0.498358	+	0.265973i
$957$		−	38.6831i		−	1.25045i
$958$	−41.0173	−	2.83626i	−1.32521	−	0.0916354i
$959$	−0.314370	+	0.967532i	−0.0101515	+	0.0312432i
$960$		0			0
$961$	−5.68270	−	17.4895i	−0.183313	−	0.564179i
$962$	2.66906	+	10.6698i	0.0860541	+	0.344008i
$963$	35.3679	+	11.4917i	1.13971	+	0.370316i
$964$	0.708685	+	0.0984791i	0.0228252	+	0.00317180i
$965$		0			0
$966$	−2.43754	+	0.609753i	−0.0784265	+	0.0196185i
$967$	−49.5079	−	35.9696i	−1.59207	−	1.15671i	−0.900914	−	0.433998i	$-0.857103\pi$
$967$	−49.5079	−	35.9696i	−1.59207	−	1.15671i	−0.691154	−	0.722707i	$-0.742897\pi$
$968$	−2.42881	−	22.6029i	−0.0780649	−	0.726484i
$969$	3.77969	+	2.74611i	0.121421	+	0.0882177i
$970$		0			0
$971$	19.9841	+	27.5058i	0.641321	+	0.882703i	0.998685	−	0.0512621i	$-0.0163244\pi$
$971$	19.9841	+	27.5058i	0.641321	+	0.882703i	−0.357364	+	0.933965i	$0.616324\pi$
$972$	−43.9614	+	7.82187i	−1.41006	+	0.250887i
$973$	−1.44359	+	0.469050i	−0.0462793	+	0.0150371i
$974$	−31.2139	+	19.5383i	−1.00016	+	0.626046i
$975$		0			0
$976$	−36.9687	+	29.0682i	−1.18334	+	0.930449i
$977$	−16.4081	−	50.4988i	−0.524940	−	1.61560i	−0.764434	−	0.644702i	$-0.776982\pi$
$977$	−16.4081	−	50.4988i	−0.524940	−	1.61560i	0.239494	−	0.970898i	$-0.423018\pi$
$978$	13.2296	−	32.8177i	0.423037	−	1.04939i
$979$	6.79521	+	9.35280i	0.217176	+	0.298917i
$980$		0			0
$981$	−3.57088	+	4.91490i	−0.114010	+	0.156921i
$982$	−18.4788	−	29.5214i	−0.589683	−	0.942065i
$983$	24.8942	+	18.0867i	0.794003	+	0.576877i	0.909149	−	0.416472i	$-0.136734\pi$
$983$	24.8942	+	18.0867i	0.794003	+	0.576877i	−0.115146	+	0.993349i	$0.536734\pi$
$984$	16.5040	−	78.5428i	0.526128	−	2.50385i
$985$		0			0
$986$	−3.75329	+	4.48004i	−0.119529	+	0.142674i
$987$	−0.816350	−	0.265248i	−0.0259847	−	0.00844294i
$988$	−28.2672	−	27.2128i	−0.899301	−	0.865754i
$989$	−64.3191	+	20.8985i	−2.04523	+	0.664535i
$990$		0			0
$991$	−3.86953	+	11.9092i	−0.122920	+	0.378308i	−0.993516	−	0.113690i	$-0.963733\pi$
$991$	−3.86953	+	11.9092i	−0.122920	+	0.378308i	0.870597	+	0.491997i	$0.163733\pi$
$992$	−11.2976	−	16.6102i	−0.358699	−	0.527373i
$993$	−8.92077			−0.283092
$994$	−1.75022	−	0.121024i	−0.0555137	−	0.00383866i
$995$		0			0
$996$	10.7047	+	60.1639i	0.339192	+	1.90636i
$997$	7.25948	+	9.99182i	0.229910	+	0.316444i	0.908349	−	0.418212i	$-0.137343\pi$
$997$	7.25948	+	9.99182i	0.229910	+	0.316444i	−0.678439	+	0.734657i	$0.737343\pi$
$998$	−16.7671	+	20.0137i	−0.530753	+	0.633523i
$999$	−0.892455			−0.0282360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.901.43		224
5.2	odd	4		200.2.o.a.69.9	yes	112
5.3	odd	4		1000.2.o.a.349.20		112
5.4	even	2	inner	1000.2.t.b.901.14		224
8.5	even	2	inner	1000.2.t.b.901.27		224
20.7	even	4		800.2.be.a.369.5		112
25.3	odd	20		200.2.o.a.29.2	✓	112
25.4	even	10	inner	1000.2.t.b.101.30		224
25.21	even	5	inner	1000.2.t.b.101.27		224
25.22	odd	20		1000.2.o.a.149.27		112
40.13	odd	4		1000.2.o.a.349.27		112
40.27	even	4		800.2.be.a.369.24		112
40.29	even	2	inner	1000.2.t.b.901.30		224
40.37	odd	4		200.2.o.a.69.2	yes	112
100.3	even	20		800.2.be.a.529.24		112
200.3	even	20		800.2.be.a.529.5		112
200.21	even	10	inner	1000.2.t.b.101.43		224
200.29	even	10	inner	1000.2.t.b.101.14		224
200.53	odd	20		200.2.o.a.29.9	yes	112
200.197	odd	20		1000.2.o.a.149.20		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.2	✓	112	25.3	odd	20
200.2.o.a.29.9	yes	112	200.53	odd	20
200.2.o.a.69.2	yes	112	40.37	odd	4
200.2.o.a.69.9	yes	112	5.2	odd	4
800.2.be.a.369.5		112	20.7	even	4
800.2.be.a.369.24		112	40.27	even	4
800.2.be.a.529.5		112	200.3	even	20
800.2.be.a.529.24		112	100.3	even	20
1000.2.o.a.149.20		112	200.197	odd	20
1000.2.o.a.149.27		112	25.22	odd	20
1000.2.o.a.349.20		112	5.3	odd	4
1000.2.o.a.349.27		112	40.13	odd	4
1000.2.t.b.101.14		224	200.29	even	10	inner
1000.2.t.b.101.27		224	25.21	even	5	inner
1000.2.t.b.101.30		224	25.4	even	10	inner
1000.2.t.b.101.43		224	200.21	even	10	inner
1000.2.t.b.901.14		224	5.4	even	2	inner
1000.2.t.b.901.27		224	8.5	even	2	inner
1000.2.t.b.901.30		224	40.29	even	2	inner
1000.2.t.b.901.43		224	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.08405 + 0.908199i) q^{2} +(1.46605 + 2.01785i) q^{3} +(0.350349 + 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} -0.110917 q^{7} +(-1.40851 + 2.45277i) q^{8} +(-0.995348 + 3.06337i) q^{9} +O(q^{10})\)	\(q+(1.08405 + 0.908199i) q^{2} +(1.46605 + 2.01785i) q^{3} +(0.350349 + 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} -0.110917 q^{7} +(-1.40851 + 2.45277i) q^{8} +(-0.995348 + 3.06337i) q^{9} +(1.63700 - 0.531893i) q^{11} +(-3.45966 + 3.59372i) q^{12} +(4.56868 + 1.48445i) q^{13} +(-0.120240 - 0.100735i) q^{14} +(-3.75451 + 1.37973i) q^{16} +(-0.371056 - 0.269588i) q^{17} +(-3.86116 + 2.41688i) q^{18} +(-2.40052 + 3.30403i) q^{19} +(-0.162610 - 0.223814i) q^{21} +(2.25766 + 0.910120i) q^{22} +(-1.98459 - 6.10792i) q^{23} +(-7.01427 + 0.753724i) q^{24} +(3.60452 + 5.75850i) q^{26} +(-0.524271 + 0.170346i) q^{27} +(-0.0388597 - 0.218404i) q^{28} +(-5.29624 - 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(-5.32316 - 1.91414i) q^{32} +(3.47320 + 2.52343i) q^{33} +(-0.157406 - 0.629242i) q^{34} +(-6.38072 - 0.886667i) q^{36} +(1.53972 + 0.500287i) q^{37} +(-5.60300 + 1.40160i) q^{38} +(3.70252 + 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(0.0269890 - 0.390308i) q^{42} -10.5304i q^{43} +(1.62086 + 3.03703i) q^{44} +(3.39581 - 8.42372i) q^{46} +(2.51014 - 1.82373i) q^{47} +(-8.28839 - 5.55328i) q^{48} -6.98770 q^{49} -1.14397i q^{51} +(-1.32237 + 9.51614i) q^{52} +(-2.69868 - 3.71441i) q^{53} +(-0.723047 - 0.291478i) q^{54} +(0.156228 - 0.272054i) q^{56} -10.1863 q^{57} +(0.879037 - 12.7124i) q^{58} +(3.38621 + 1.10025i) q^{59} +(11.1816 - 3.63312i) q^{61} +(1.21872 + 4.87191i) q^{62} +(0.110401 - 0.339779i) q^{63} +(-4.03218 - 6.90953i) q^{64} +(1.47337 + 5.88990i) q^{66} +(-2.19833 + 3.02574i) q^{67} +(0.400840 - 0.825088i) q^{68} +(9.41535 - 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-6.11178 - 6.75615i) q^{72} +(3.20201 + 9.85476i) q^{73} +(1.21479 + 1.94072i) q^{74} +(-7.34690 - 3.56923i) q^{76} +(-0.181571 + 0.0589960i) q^{77} +(-6.33536 + 15.7156i) q^{78} +(4.45472 - 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(-13.6376 + 8.53642i) q^{82} +(7.20048 - 9.91061i) q^{83} +(0.383735 - 0.398604i) q^{84} +(9.56373 - 11.4156i) q^{86} +(6.94483 - 21.3740i) q^{87} +(-1.00112 + 4.76436i) q^{88} +(2.07551 + 6.38776i) q^{89} +(-0.506744 - 0.164651i) q^{91} +(11.3317 - 6.04770i) q^{92} +8.85717i q^{93} +(4.37744 + 0.302691i) q^{94} +(-3.94158 - 13.5476i) q^{96} +(-4.54704 + 3.30362i) q^{97} +(-7.57505 - 6.34622i) q^{98} +5.54415i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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