LMFDB - Embedded newform 1000.2.o.a.349.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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, 1]))

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.20
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908199 - 1.08405i) q^{2} +(-2.01785 + 1.46605i) q^{3} +(-0.350349 - 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} +0.110917i q^{7} +(-2.45277 - 1.40851i) q^{8} +(0.995348 - 3.06337i) q^{9} +O(q^{10})$	\(q+(0.908199 - 1.08405i) q^{2} +(-2.01785 + 1.46605i) q^{3} +(-0.350349 - 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} +0.110917i q^{7} +(-2.45277 - 1.40851i) q^{8} +(0.995348 - 3.06337i) q^{9} +(1.63700 - 0.531893i) q^{11} +(3.59372 + 3.45966i) q^{12} +(-1.48445 + 4.56868i) q^{13} +(0.120240 + 0.100735i) q^{14} +(-3.75451 + 1.37973i) q^{16} +(-0.269588 + 0.371056i) q^{17} +(-2.41688 - 3.86116i) q^{18} +(2.40052 - 3.30403i) q^{19} +(-0.162610 - 0.223814i) q^{21} +(0.910120 - 2.25766i) q^{22} +(6.10792 - 1.98459i) q^{23} +(7.01427 - 0.753724i) q^{24} +(3.60452 + 5.75850i) q^{26} +(0.170346 + 0.524271i) q^{27} +(0.218404 - 0.0388597i) q^{28} +(5.29624 + 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(-1.91414 + 5.32316i) q^{32} +(-2.52343 + 3.47320i) q^{33} +(0.157406 + 0.629242i) q^{34} +(-6.38072 - 0.886667i) q^{36} +(0.500287 - 1.53972i) q^{37} +(-1.40160 - 5.60300i) q^{38} +(-3.70252 - 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(-0.390308 - 0.0269890i) q^{42} +10.5304 q^{43} +(-1.62086 - 3.03703i) q^{44} +(3.39581 - 8.42372i) q^{46} +(-1.82373 - 2.51014i) q^{47} +(5.55328 - 8.28839i) q^{48} +6.98770 q^{49} -1.14397i q^{51} +(9.51614 + 1.32237i) q^{52} +(3.71441 - 2.69868i) q^{53} +(0.723047 + 0.291478i) q^{54} +(0.156228 - 0.272054i) q^{56} +10.1863i q^{57} +(12.7124 + 0.879037i) q^{58} +(-3.38621 - 1.10025i) q^{59} +(11.1816 - 3.63312i) q^{61} +(4.87191 - 1.21872i) q^{62} +(0.339779 + 0.110401i) q^{63} +(4.03218 + 6.90953i) q^{64} +(1.47337 + 5.88990i) q^{66} +(3.02574 + 2.19833i) q^{67} +(0.825088 + 0.400840i) q^{68} +(-9.41535 + 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-6.75615 + 6.11178i) q^{72} +(-9.85476 + 3.20201i) q^{73} +(-1.21479 - 1.94072i) q^{74} +(-7.34690 - 3.56923i) q^{76} +(0.0589960 + 0.181571i) q^{77} +(-15.7156 - 6.33536i) q^{78} +(-4.45472 + 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(8.53642 + 13.6376i) q^{82} +(9.91061 + 7.20048i) q^{83} +(-0.383735 + 0.398604i) q^{84} +(9.56373 - 11.4156i) q^{86} +(-21.3740 - 6.94483i) q^{87} +(-4.76436 - 1.00112i) q^{88} +(-2.07551 - 6.38776i) q^{89} +(-0.506744 - 0.164651i) q^{91} +(-6.04770 - 11.3317i) q^{92} -8.85717 q^{93} +(-4.37744 - 0.302691i) q^{94} +(-3.94158 - 13.5476i) q^{96} +(3.30362 + 4.54704i) q^{97} +(6.34622 - 7.57505i) q^{98} -5.54415i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	0.908199	−	1.08405i	0.642194	−	0.766542i
$2$	0.908199	−	1.08405i	0.642194	−	0.766542i
$3$	−2.01785	+	1.46605i	−1.16500	+	0.846425i	−0.990402	−	0.138214i	$-0.955864\pi$
$3$	−2.01785	+	1.46605i	−1.16500	+	0.846425i	−0.174602	+	0.984639i	$0.555864\pi$
$4$	−0.350349	−	1.96907i	−0.175175	−	0.984537i
$5$		0			0
$5$		0			0
$6$	−0.243326	+	3.51892i	−0.0993376	+	1.43659i
$7$			0.110917i			0.0419227i	0.999780	+	0.0209613i	$0.00667269\pi$
$7$			0.110917i			0.0419227i	−0.999780	+	0.0209613i	$0.993327\pi$
$8$	−2.45277	−	1.40851i	−0.867186	−	0.497985i
$9$	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	$0.316446\pi$
$12$	3.59372	+	3.45966i	1.03742	+	0.998718i
$13$	−1.48445	+	4.56868i	−0.411713	+	1.26712i	0.503445	+	0.864027i	$0.332066\pi$
$13$	−1.48445	+	4.56868i	−0.411713	+	1.26712i	−0.915158	+	0.403096i	$0.867934\pi$
$14$	0.120240	+	0.100735i	0.0321355	+	0.0269225i
$15$		0			0
$16$	−3.75451	+	1.37973i	−0.938628	+	0.344932i
$17$	−0.269588	+	0.371056i	−0.0653848	+	0.0899944i	−0.840457	−	0.541878i	$-0.817713\pi$
$17$	−0.269588	+	0.371056i	−0.0653848	+	0.0899944i	0.775072	+	0.631873i	$0.217713\pi$
$18$	−2.41688	−	3.86116i	−0.569665	−	0.910084i
$19$	2.40052	−	3.30403i	0.550716	−	0.757996i	−0.439393	−	0.898295i	$-0.644806\pi$
$19$	2.40052	−	3.30403i	0.550716	−	0.757996i	0.990109	+	0.140299i	$0.0448064\pi$
$20$		0			0
$21$	−0.162610	−	0.223814i	−0.0354844	−	0.0488401i
$22$	0.910120	−	2.25766i	0.194038	−	0.481335i
$23$	6.10792	−	1.98459i	1.27359	−	0.413815i	0.407272	−	0.913307i	$-0.366480\pi$
$23$	6.10792	−	1.98459i	1.27359	−	0.413815i	0.866318	+	0.499492i	$0.166480\pi$
$24$	7.01427	−	0.753724i	1.43178	−	0.153853i
$25$		0			0
$26$	3.60452	+	5.75850i	0.706904	+	1.12933i
$27$	0.170346	+	0.524271i	0.0327831	+	0.100896i
$28$	0.218404	−	0.0388597i	0.0412745	−	0.00734379i
$29$	5.29624	+	7.28964i	0.983486	+	1.35365i	0.934930	+	0.354833i	$0.115462\pi$
$29$	5.29624	+	7.28964i	0.983486	+	1.35365i	0.0485566	+	0.998820i	$0.484538\pi$
$30$		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	$0.596687\pi$
$32$	−1.91414	+	5.32316i	−0.338376	+	0.941011i
$33$	−2.52343	+	3.47320i	−0.439273	+	0.604607i
$34$	0.157406	+	0.629242i	0.0269949	+	0.107914i
$35$		0			0
$36$	−6.38072	−	0.886667i	−1.06345	−	0.147778i
$37$	0.500287	−	1.53972i	0.0822467	−	0.253129i	−0.901474	−	0.432833i	$-0.857514\pi$
$37$	0.500287	−	1.53972i	0.0822467	−	0.253129i	0.983721	+	0.179704i	$0.0575139\pi$
$38$	−1.40160	−	5.60300i	−0.227370	−	0.908927i
$39$	−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	$0.751843\pi$
$42$	−0.390308	−	0.0269890i	−0.0602259	−	0.00416450i
$43$	10.5304			1.60588			0.802938	−	0.596063i	$-0.203269\pi$
$43$	10.5304			1.60588			0.802938	+	0.596063i	$0.203269\pi$
$44$	−1.62086	−	3.03703i	−0.244354	−	0.457849i
$45$		0			0
$46$	3.39581	−	8.42372i	0.500685	−	1.24201i
$47$	−1.82373	−	2.51014i	−0.266018	−	0.366142i	0.655022	−	0.755609i	$-0.272659\pi$
$47$	−1.82373	−	2.51014i	−0.266018	−	0.366142i	−0.921040	+	0.389467i	$0.872659\pi$
$48$	5.55328	−	8.28839i	0.801546	−	1.19633i
$49$	6.98770			0.998242
$50$		0			0
$51$		−	1.14397i		−	0.160187i
$52$	9.51614	+	1.32237i	1.31965	+	0.183379i
$53$	3.71441	−	2.69868i	0.510213	−	0.370692i	−0.302691	−	0.953089i	$-0.597885\pi$
$53$	3.71441	−	2.69868i	0.510213	−	0.370692i	0.812905	+	0.582397i	$0.197885\pi$
$54$	0.723047	+	0.291478i	0.0983942	+	0.0396651i
$55$		0			0
$56$	0.156228	−	0.272054i	0.0208769	−	0.0363548i
$57$			10.1863i			1.34921i
$58$	12.7124	+	0.879037i	1.66922	+	0.115423i
$59$	−3.38621	−	1.10025i	−0.440847	−	0.143240i	0.0801796	−	0.996780i	$-0.474451\pi$
$59$	−3.38621	−	1.10025i	−0.440847	−	0.143240i	−0.521026	+	0.853541i	$0.674451\pi$
$60$		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	$0.128767\pi$
$62$	4.87191	−	1.21872i	0.618734	−	0.154777i
$63$	0.339779	+	0.110401i	0.0428082	+	0.0139092i
$64$	4.03218	+	6.90953i	0.504022	+	0.863691i
$65$		0			0
$66$	1.47337	+	5.88990i	0.181359	+	0.724996i
$67$	3.02574	+	2.19833i	0.369653	+	0.268569i	0.757067	−	0.653337i	$-0.226632\pi$
$67$	3.02574	+	2.19833i	0.369653	+	0.268569i	−0.387414	+	0.921906i	$0.626632\pi$
$68$	0.825088	+	0.400840i	0.100057	+	0.0486090i
$69$	−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	$0.0689948\pi$
$72$	−6.75615	+	6.11178i	−0.796220	+	0.720280i
$73$	−9.85476	+	3.20201i	−1.15341	+	0.374766i	−0.822428	−	0.568870i	$-0.807381\pi$
$73$	−9.85476	+	3.20201i	−1.15341	+	0.374766i	−0.330985	+	0.943636i	$0.607381\pi$
$74$	−1.21479	−	1.94072i	−0.141216	−	0.225604i
$75$		0			0
$76$	−7.34690	−	3.56923i	−0.842747	−	0.409419i
$77$	0.0589960	+	0.181571i	0.00672322	+	0.0206919i
$78$	−15.7156	−	6.33536i	−1.77944	−	0.717338i
$79$	−4.45472	+	3.23655i	−0.501196	+	0.364140i	−0.809474	−	0.587156i	$-0.800247\pi$
$79$	−4.45472	+	3.23655i	−0.501196	+	0.364140i	0.308278	+	0.951296i	$0.400247\pi$
$80$		0			0
$81$	6.70522	+	4.87163i	0.745025	+	0.541292i
$82$	8.53642	+	13.6376i	0.942690	+	1.50602i
$83$	9.91061	+	7.20048i	1.08783	+	0.790356i	0.979032	−	0.203708i	$-0.0652993\pi$
$83$	9.91061	+	7.20048i	1.08783	+	0.790356i	0.108800	+	0.994064i	$0.465299\pi$
$84$	−0.383735	+	0.398604i	−0.0418690	+	0.0434913i
$85$		0			0
$86$	9.56373	−	11.4156i	1.03128	−	1.23097i
$87$	−21.3740	−	6.94483i	−2.29153	−	0.744564i
$88$	−4.76436	−	1.00112i	−0.507883	−	0.106720i
$89$	−2.07551	−	6.38776i	−0.220003	−	0.677101i	−0.998760	−	0.0497752i	$-0.984150\pi$
$89$	−2.07551	−	6.38776i	−0.220003	−	0.677101i	0.778757	−	0.627326i	$-0.215850\pi$
$90$		0			0
$91$	−0.506744	−	0.164651i	−0.0531212	−	0.0172601i
$92$	−6.04770	−	11.3317i	−0.630517	−	1.18141i
$93$	−8.85717			−0.918446
$94$	−4.37744	−	0.302691i	−0.451499	−	0.0312202i
$95$		0			0
$96$	−3.94158	−	13.5476i	−0.402286	−	1.38269i
$97$	3.30362	+	4.54704i	0.335431	+	0.461682i	0.943100	−	0.332509i	$-0.107895\pi$
$97$	3.30362	+	4.54704i	0.335431	+	0.461682i	−0.607669	+	0.794191i	$0.707895\pi$
$98$	6.34622	−	7.57505i	0.641065	−	0.765195i
$99$		−	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	$-0.0246727\pi$
$102$	−1.24012	−	1.03895i	−0.122790	−	0.102871i
$103$	−2.77316	−	3.81692i	−0.273247	−	0.376092i	0.650235	−	0.759733i	$-0.274670\pi$
$103$	−2.77316	−	3.81692i	−0.273247	−	0.376092i	−0.923483	+	0.383640i	$0.874670\pi$
$104$	10.0761	−	9.11505i	0.988040	−	0.893804i
$105$		0			0
$106$	0.447910	−	6.47756i	0.0435049	−	0.629156i
$107$	−11.5454			−1.11614			−0.558070	−	0.829794i	$-0.688458\pi$
$107$	−11.5454			−1.11614			−0.558070	+	0.829794i	$0.688458\pi$
$108$	0.972648	−	0.519102i	0.0935931	−	0.0499506i
$109$	−1.79379	−	0.582837i	−0.171814	−	0.0558256i	0.221847	−	0.975081i	$-0.428791\pi$
$109$	−1.79379	−	0.582837i	−0.171814	−	0.0558256i	−0.393661	+	0.919256i	$0.628791\pi$
$110$		0			0
$111$	1.24781	+	3.84038i	0.118437	+	0.364512i
$112$	−0.153035	−	0.416439i	−0.0144605	−	0.0393498i
$113$	−4.37045	−	1.42005i	−0.411137	−	0.133587i	0.0961433	−	0.995367i	$-0.469349\pi$
$113$	−4.37045	−	1.42005i	−0.411137	−	0.133587i	−0.507281	+	0.861781i	$0.669349\pi$
$114$	11.0425	+	9.25119i	1.03423	+	0.866453i
$115$		0			0
$116$	12.4983	−	12.9826i	1.16044	−	1.20540i
$117$	12.5180	+	9.09485i	1.15729	+	0.840819i
$118$	−4.26808	+	2.67159i	−0.392908	+	0.245940i
$119$	−0.0411565	−	0.0299019i	−0.00377281	−	0.00274111i
$120$		0			0
$121$	−6.50233	+	4.72422i	−0.591121	+	0.429475i
$122$	6.21662	−	15.4211i	0.562826	−	1.39616i
$123$	−8.76851	−	26.9867i	−0.790630	−	2.43331i
$124$	3.10351	−	6.38826i	0.278704	−	0.573683i
$125$		0			0
$126$	0.428268	−	0.268073i	0.0381531	−	0.0238819i
$127$	7.73794	−	2.51421i	0.686631	−	0.223100i	0.0551347	−	0.998479i	$-0.482441\pi$
$127$	7.73794	−	2.51421i	0.686631	−	0.223100i	0.631496	+	0.775379i	$0.282441\pi$
$128$	11.1523	+	1.90412i	0.985735	+	0.168302i
$129$	−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	$0.801122\pi$
$132$	7.72308	+	3.75199i	0.672208	+	0.326569i
$133$	0.366473	+	0.266258i	0.0317772	+	0.0230875i
$134$	5.13108	−	1.28355i	0.443258	−	0.110882i
$135$		0			0
$136$	1.18388	−	0.530398i	0.101517	−	0.0454812i
$137$	−8.72303	−	2.83428i	−0.745259	−	0.242149i	−0.0883189	−	0.996092i	$-0.528149\pi$
$137$	−8.72303	−	2.83428i	−0.745259	−	0.242149i	−0.656940	+	0.753943i	$0.728149\pi$
$138$	5.49738	+	21.9762i	0.467968	+	1.87074i
$139$	−13.0150	+	4.22884i	−1.10392	+	0.358685i	−0.803610	−	0.595156i	$-0.797090\pi$
$139$	−13.0150	+	4.22884i	−1.10392	+	0.358685i	−0.300310	+	0.953842i	$0.597090\pi$
$140$		0			0
$141$	7.36000	+	2.39141i	0.619824	+	0.201393i
$142$	1.09113	−	15.7796i	0.0915652	−	1.32419i
$143$			8.26849i			0.691446i
$144$	0.489566	+	12.8747i	0.0407972	+	1.07290i
$145$		0			0
$146$	−5.47893	+	13.5912i	−0.453440	+	1.12481i
$147$	−14.1001	+	10.2443i	−1.16296	+	0.844938i
$148$	−3.20711	−	0.445661i	−0.263623	−	0.0366331i
$149$		−	14.8397i		−	1.21572i	−0.794045	−	0.607859i	$-0.792028\pi$
$149$		−	14.8397i		−	1.21572i	0.794045	−	0.607859i	$-0.207972\pi$
$150$		0			0
$151$	−8.87251			−0.722035			−0.361017	−	0.932559i	$-0.617570\pi$
$151$	−8.87251			−0.722035			−0.361017	+	0.932559i	$0.617570\pi$
$152$	−10.5417	+	4.72286i	−0.855044	+	0.383075i
$153$	0.868348	+	1.19518i	0.0702017	+	0.0966244i
$154$	0.250413	+	0.100948i	0.0201789	+	0.00813460i
$155$		0			0
$156$	−21.1408	+	11.2828i	−1.69262	+	0.903349i
$157$	−4.71374			−0.376197			−0.188099	−	0.982150i	$-0.560232\pi$
$157$	−4.71374			−0.376197			−0.188099	+	0.982150i	$0.560232\pi$
$158$	−0.537182	+	7.76859i	−0.0427359	+	0.618036i
$159$	−3.53871	+	10.8910i	−0.280638	+	0.863715i
$160$		0			0
$161$	0.220124	+	0.677473i	0.0173482	+	0.0533923i
$162$	11.3708	−	2.84442i	0.893374	−	0.223479i
$163$	3.09987	−	9.54040i	0.242800	−	0.747262i	−0.753190	−	0.657803i	$-0.771486\pi$
$163$	3.09987	−	9.54040i	0.242800	−	0.747262i	0.995990	−	0.0894595i	$-0.0285139\pi$
$164$	22.5367	+	3.13170i	1.75982	+	0.244545i
$165$		0			0
$166$	16.8065	−	4.20418i	1.30444	−	0.326307i
$167$	−4.72830	+	6.50795i	−0.365887	+	0.503601i	−0.951777	−	0.306790i	$-0.900745\pi$
$167$	−4.72830	+	6.50795i	−0.365887	+	0.503601i	0.585890	+	0.810391i	$0.300745\pi$
$168$	0.0836008	+	0.778002i	0.00644994	+	0.0600242i
$169$	−8.15199	−	5.92277i	−0.627076	−	0.455597i
$170$		0			0
$171$	−7.73210	−	10.6423i	−0.591288	−	0.813838i
$172$	−3.68933	−	20.7352i	−0.281309	−	1.58104i
$173$	3.07351	+	9.45929i	0.233675	+	0.719176i	0.997294	+	0.0735104i	$0.0234202\pi$
$173$	3.07351	+	9.45929i	0.233675	+	0.719176i	−0.763620	+	0.645666i	$0.776580\pi$
$174$	−26.9404	+	16.8633i	−2.04235	+	1.27840i
$175$		0			0
$176$	−5.41226	+	4.25561i	−0.407965	+	0.320779i
$177$	8.44586	−	2.74423i	0.634830	−	0.206269i
$178$	−8.80965	−	3.55139i	−0.660311	−	0.266188i
$179$	−7.39861	−	10.1833i	−0.552998	−	0.761136i	0.437417	−	0.899259i	$-0.355893\pi$
$179$	−7.39861	−	10.1833i	−0.552998	−	0.761136i	−0.990415	+	0.138122i	$0.955893\pi$
$180$		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	$0.361296\pi$
$182$	−0.638715	+	0.399802i	−0.0473447	+	0.0296353i
$183$	−17.2364	+	23.7239i	−1.27415	+	1.75372i
$184$	−17.7767	−	3.73536i	−1.31051	−	0.275375i
$185$		0			0
$186$	−8.04408	+	9.60166i	−0.589820	+	0.704028i
$187$	−0.243953	+	0.750811i	−0.0178396	+	0.0549048i
$188$	−4.30372	+	4.47048i	−0.313881	+	0.326043i
$189$	−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	$0.0668058\pi$
$192$	−18.2660	−	8.03099i	−1.31824	−	0.579587i
$193$			15.9019i			1.14464i	0.820029	+	0.572322i	$0.193957\pi$
$193$			15.9019i			1.14464i	−0.820029	+	0.572322i	$0.806043\pi$
$194$	7.92958	+	0.548314i	0.569310	+	0.0393667i
$195$		0			0
$196$	−2.44813	−	13.7593i	−0.174867	−	0.982807i
$197$	3.78454	−	2.74963i	0.269637	−	0.195903i	−0.444748	−	0.895656i	$-0.646707\pi$
$197$	3.78454	−	2.74963i	0.269637	−	0.195903i	0.714385	+	0.699753i	$0.246707\pi$
$198$	−6.01016	−	5.03519i	−0.427123	−	0.357835i
$199$	28.0439			1.98798			0.993988	−	0.109488i	$-0.0349211\pi$
$199$	28.0439			1.98798			0.993988	+	0.109488i	$0.0349211\pi$
$200$		0			0
$201$	−9.32834			−0.657971
$202$	−1.68723	−	1.41352i	−0.118713	−	0.0994551i
$203$	−0.808546	+	0.587443i	−0.0567488	+	0.0412304i
$204$	−2.25255	+	0.400787i	−0.157710	+	0.0280607i
$205$		0			0
$206$	−6.65633	−	0.460272i	−0.463768	−	0.0320686i
$207$		−	20.6862i		−	1.43779i
$208$	−0.730135	−	19.2013i	−0.0506257	−	1.33137i
$209$	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	$0.403576\pi$
$212$	−6.61524	−	6.36847i	−0.454336	−	0.437388i
$213$	−8.62043	+	26.5310i	−0.590662	+	1.81787i
$214$	−10.4856	+	12.5159i	−0.716777	+	0.855568i
$215$		0			0
$216$	0.320623	−	1.52585i	0.0218157	−	0.103821i
$217$	−0.231516	+	0.318655i	−0.0157163	+	0.0216317i
$218$	−2.26094	+	1.41523i	−0.153130	+	0.0958516i
$219$	15.1911	−	20.9087i	1.02652	−	1.41288i
$220$		0			0
$221$	−1.29505	−	1.78248i	−0.0871142	−	0.119902i
$222$	5.29644	+	2.13513i	0.355474	+	0.143300i
$223$	11.2099	−	3.64231i	0.750669	−	0.243907i	0.0914002	−	0.995814i	$-0.470866\pi$
$223$	11.2099	−	3.64231i	0.750669	−	0.243907i	0.659269	+	0.751907i	$0.270866\pi$
$224$	−0.590429	−	0.212311i	−0.0394497	−	0.0141856i
$225$		0			0
$226$	−5.50865	+	3.44812i	−0.366430	+	0.229366i
$227$	0.324287	+	0.998051i	0.0215237	+	0.0662430i	0.961241	−	0.275708i	$-0.0889123\pi$
$227$	0.324287	+	0.998051i	0.0215237	+	0.0662430i	−0.939718	+	0.341951i	$0.888912\pi$
$228$	20.0576	−	3.56876i	1.32835	−	0.236347i
$229$	11.8902	+	16.3654i	0.785723	+	1.08146i	0.994627	+	0.103519i	$0.0330104\pi$
$229$	11.8902	+	16.3654i	0.785723	+	1.08146i	−0.208904	+	0.977936i	$0.566990\pi$
$230$		0			0
$231$	−0.385237	−	0.279891i	−0.0253468	−	0.0184155i
$232$	−2.72289	−	25.3397i	−0.178767	−	1.66363i
$233$	15.4318	−	21.2400i	1.01097	−	1.39148i	0.0926216	−	0.995701i	$-0.470475\pi$
$233$	15.4318	−	21.2400i	1.01097	−	1.39148i	0.918347	−	0.395777i	$-0.129525\pi$
$234$	21.2281	−	5.31025i	1.38773	−	0.347142i
$235$		0			0
$236$	−0.980110	+	7.05316i	−0.0637997	+	0.459122i
$237$	4.24401	−	13.0617i	0.275678	−	0.848449i
$238$	−0.0697936	+	0.0174590i	−0.00452405	+	0.00113170i
$239$	−2.69865	−	8.30559i	−0.174561	−	0.537244i	0.825052	−	0.565057i	$-0.191146\pi$
$239$	−2.69865	−	8.30559i	−0.174561	−	0.537244i	−0.999613	+	0.0278129i	$0.991146\pi$
$240$		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	$0.0963323\pi$
$242$	−0.784097	+	11.3394i	−0.0504037	+	0.728925i
$243$	−22.3259			−1.43221
$244$	−11.0714	−	20.7446i	−0.708771	−	1.32803i
$245$		0			0
$246$	−37.2186	−	15.0037i	−2.37297	−	0.956604i
$247$	11.5316	+	15.8719i	0.733737	+	1.00990i
$248$	−4.10661	−	9.16619i	−0.260770	−	0.582053i
$249$	−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	$-0.217915\pi$
$252$	0.0983464	−	0.707730i	0.00619524	−	0.0445828i
$253$	8.94308	−	6.49753i	0.562247	−	0.408496i
$254$	4.30205	−	10.6717i	0.269934	−	0.669605i
$255$		0			0
$256$	12.1927	−	10.3604i	0.762044	−	0.647525i
$257$		−	18.7305i		−	1.16838i	−0.811617	−	0.584190i	$-0.801412\pi$
$257$		−	18.7305i		−	1.16838i	0.811617	−	0.584190i	$-0.198588\pi$
$258$	−2.56233	+	37.0558i	−0.159524	+	2.30699i
$259$	0.170782	+	0.0554903i	0.0106119	+	0.00344800i
$260$		0			0
$261$	27.6024	−	8.96858i	1.70855	−	0.555141i
$262$	7.46293	+	29.8337i	0.461061	+	1.84313i
$263$	15.6804	+	5.09486i	0.966892	+	0.314162i	0.749561	−	0.661936i	$-0.230265\pi$
$263$	15.6804	+	5.09486i	0.966892	+	0.314162i	0.217331	+	0.976098i	$0.430265\pi$
$264$	11.0815	−	4.96469i	0.682016	−	0.305556i
$265$		0			0
$266$	0.621469	−	0.155461i	0.0381047	−	0.00953194i
$267$	13.5528	+	9.84671i	0.829420	+	0.602609i
$268$	3.26861	−	6.72809i	0.199662	−	0.410984i
$269$	−0.0856192	+	0.117845i	−0.00522029	+	0.00718512i	−0.811619	−	0.584187i	$-0.801414\pi$
$269$	−0.0856192	+	0.117845i	−0.00522029	+	0.00718512i	0.806399	+	0.591372i	$0.201414\pi$
$270$		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	$0.454234\pi$
$272$	0.500215	−	1.76509i	0.0303300	−	0.107025i
$273$	1.26392	−	0.410672i	0.0764958	−	0.0248550i
$274$	−10.9948	+	6.88215i	−0.664218	+	0.415766i
$275$		0			0
$276$	28.8161	+	13.9993i	1.73453	+	0.842660i
$277$	−6.39942	−	19.6954i	−0.384504	−	1.18338i	−0.936840	−	0.349759i	$-0.886263\pi$
$277$	−6.39942	−	19.6954i	−0.384504	−	1.18338i	0.552336	−	0.833622i	$-0.313737\pi$
$278$	−7.23594	+	17.9496i	−0.433983	+	1.07655i
$279$	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	$0.802251\pi$
$282$	9.27677	−	5.80677i	0.552423	−	0.345788i
$283$	16.6426	+	12.0915i	0.989298	+	0.718767i	0.959767	−	0.280797i	$-0.0905988\pi$
$283$	16.6426	+	12.0915i	0.989298	+	0.718767i	0.0295305	+	0.999564i	$0.490599\pi$
$284$	−16.1150	−	15.5138i	−0.956247	−	0.920577i
$285$		0			0
$286$	8.96350	+	7.50943i	0.530023	+	0.444042i
$287$	−1.20010	−	0.389936i	−0.0708396	−	0.0230172i
$288$	14.4016	+	11.1621i	0.848620	+	0.657734i
$289$	5.18828	+	15.9679i	0.305193	+	0.939288i
$290$		0			0
$291$	−13.3324	−	4.33195i	−0.781558	−	0.253944i
$292$	9.75760	+	18.2829i	0.571020	+	1.06993i
$293$	0.603128			0.0352351			0.0176176	−	0.999845i	$-0.494392\pi$
$293$	0.603128			0.0352351			0.0176176	+	0.999845i	$0.494392\pi$
$294$	−1.70029	+	24.5892i	−0.0991630	+	1.43407i
$295$		0			0
$296$	−3.39581	+	3.07193i	−0.197378	+	0.178552i
$297$	0.557713	+	0.767625i	0.0323618	+	0.0445421i
$298$	−16.0871	−	13.4774i	−0.931900	−	0.780727i
$299$			30.8512i			1.78417i
$300$		0			0
$301$			1.16800i			0.0673226i
$302$	−8.05801	+	9.61829i	−0.463686	+	0.553470i
$303$	2.28177	+	3.14058i	0.131084	+	0.180422i
$304$	−4.45411	+	15.7171i	−0.255461	+	0.901435i
$305$		0			0
$306$	2.08427	+	0.144123i	0.119150	+	0.00823897i
$307$	−9.96251			−0.568591			−0.284295	−	0.958737i	$-0.591760\pi$
$307$	−9.96251			−0.568591			−0.284295	+	0.958737i	$0.591760\pi$
$308$	0.336858	−	0.179781i	0.0191943	−	0.0102440i
$309$	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	$-0.342689\pi$
$312$	−6.96884	+	33.1648i	−0.394533	+	1.87759i
$313$	−17.7993	−	5.78333i	−1.00607	−	0.326893i	−0.240784	−	0.970579i	$-0.577404\pi$
$313$	−17.7993	−	5.78333i	−1.00607	−	0.326893i	−0.765290	+	0.643686i	$0.777404\pi$
$314$	−4.28101	+	5.10995i	−0.241592	+	0.288371i
$315$		0			0
$316$	7.93371	+	7.63776i	0.446306	+	0.429658i
$317$	23.0942	+	16.7789i	1.29710	+	0.942397i	0.999923	−	0.0124261i	$-0.00395545\pi$
$317$	23.0942	+	16.7789i	1.29710	+	0.942397i	0.297175	+	0.954823i	$0.403955\pi$
$318$	8.59262	+	13.7274i	0.481850	+	0.769793i
$319$	12.5472	+	9.11611i	0.702511	+	0.510404i
$320$		0			0
$321$	23.2969	−	16.9262i	1.30031	−	0.944728i
$322$	0.934334	+	0.376653i	0.0520684	+	0.0209901i
$323$	0.578830	+	1.78145i	0.0322069	+	0.0991228i
$324$	7.24343	−	14.9099i	0.402413	−	0.828325i
$325$		0			0
$326$	−7.52703	−	12.0250i	−0.416883	−	0.666004i
$327$	4.47406	−	1.45371i	0.247416	−	0.0803903i
$328$	23.8627	−	21.5868i	1.31760	−	1.19193i
$329$	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	$0.231339\pi$
$332$	10.7061	−	22.0374i	0.587574	−	1.20946i
$333$	−4.21878	−	3.06512i	−0.231188	−	0.167968i
$334$	2.76074	+	11.0363i	0.151061	+	0.603877i
$335$		0			0
$336$	0.919323	+	0.615953i	0.0501532	+	0.0336030i
$337$	9.35059	+	3.03819i	0.509359	+	0.165501i	0.552411	−	0.833572i	$-0.313708\pi$
$337$	9.35059	+	3.03819i	0.509359	+	0.165501i	−0.0430517	+	0.999073i	$0.513708\pi$
$338$	−13.8242	+	3.45815i	−0.751939	+	0.188099i
$339$	10.9008	−	3.54187i	0.592048	−	0.192368i
$340$		0			0
$341$	5.81317	+	1.88881i	0.314801	+	0.102285i
$342$	−18.5591	−	1.28333i	−1.00356	−	0.0693943i
$343$			1.55147i			0.0837717i
$344$	−25.8287	−	14.8323i	−1.39259	−	0.799702i
$345$		0			0
$346$	13.0457	+	5.25906i	0.701344	+	0.282729i
$347$	−12.7780	+	9.28373i	−0.685957	+	0.498377i	−0.875329	−	0.483529i	$-0.839355\pi$
$347$	−12.7780	+	9.28373i	−0.685957	+	0.498377i	0.189372	+	0.981905i	$0.439355\pi$
$348$	−6.18653	+	44.5201i	−0.331633	+	2.38653i
$349$			7.78786i			0.416875i	0.978036	+	0.208437i	$0.0668377\pi$
$349$			7.78786i			0.416875i	−0.978036	+	0.208437i	$0.933162\pi$
$350$		0			0
$351$	−2.64810			−0.141345
$352$	−0.302096	+	9.73213i	−0.0161017	+	0.518724i
$353$	6.60894	+	9.09643i	0.351759	+	0.484154i	0.947830	−	0.318778i	$-0.103272\pi$
$353$	6.60894	+	9.09643i	0.351759	+	0.484154i	−0.596071	+	0.802932i	$0.703272\pi$
$354$	4.69563	−	11.6481i	0.249570	−	0.619089i
$355$		0			0
$356$	−11.8508	+	6.32478i	−0.628092	+	0.335212i
$357$	0.126885			0.00671548
$358$	−17.7587	−	1.22798i	−0.938575	−	0.0649005i
$359$	−3.14405	+	9.67639i	−0.165937	+	0.510700i	−0.999104	−	0.0423204i	$-0.986525\pi$
$359$	−3.14405	+	9.67639i	−0.165937	+	0.510700i	0.833167	+	0.553021i	$0.186525\pi$
$360$		0			0
$361$	0.717206	+	2.20733i	0.0377477	+	0.116175i
$362$	4.48160	+	17.9155i	0.235548	+	0.941620i
$363$	6.19476	−	19.0655i	0.325141	−	1.00068i
$364$	−0.146673	+	1.05550i	−0.00768775	+	0.0553233i
$365$		0			0
$366$	10.0639	+	40.2312i	0.526049	+	2.10292i
$367$	7.13356	−	9.81851i	0.372369	−	0.512522i	−0.581174	−	0.813779i	$-0.697406\pi$
$367$	7.13356	−	9.81851i	0.372369	−	0.512522i	0.953543	+	0.301257i	$0.0974064\pi$
$368$	−20.1941	+	15.8784i	−1.05269	+	0.827720i
$369$	29.6458	+	21.5389i	1.54330	+	1.12127i
$370$		0			0
$371$	0.299329	+	0.411991i	0.0155404	+	0.0213895i
$372$	3.10310	+	17.4404i	0.160888	+	0.904244i
$373$	2.30235	+	7.08589i	0.119211	+	0.366894i	0.992802	−	0.119767i	$-0.0382148\pi$
$373$	2.30235	+	7.08589i	0.119211	+	0.366894i	−0.873591	+	0.486661i	$0.838215\pi$
$374$	0.592362	+	0.946345i	0.0306303	+	0.0489343i
$375$		0			0
$376$	0.937612	+	8.72556i	0.0483536	+	0.449986i
$377$	−41.1660	+	13.3757i	−2.12016	+	0.688881i
$378$	−0.0323299	+	0.0801982i	−0.00166287	+	0.00412495i
$379$	3.70220	+	5.09564i	0.190169	+	0.261746i	0.893446	−	0.449171i	$-0.148281\pi$
$379$	3.70220	+	5.09564i	0.190169	+	0.261746i	−0.703277	+	0.710916i	$0.748281\pi$
$380$		0			0
$381$	−11.9280	+	16.4175i	−0.611091	+	0.841094i
$382$	−2.15891	−	3.44903i	−0.110460	−	0.176468i
$383$	16.8385	−	23.1761i	0.860405	−	1.18425i	−0.121068	−	0.992644i	$-0.538632\pi$
$383$	16.8385	−	23.1761i	0.860405	−	1.18425i	0.981473	−	0.191601i	$-0.0613681\pi$
$384$	−25.2952	+	12.5077i	−1.29084	+	0.638278i
$385$		0			0
$386$	17.2385	+	14.4421i	0.877418	+	0.735083i
$387$	10.4814	−	32.2586i	0.532802	−	1.63979i
$388$	7.79603	−	8.09812i	0.395784	−	0.411120i
$389$	0.660483	−	0.214604i	0.0334878	−	0.0108808i	−0.292225	−	0.956350i	$-0.594396\pi$
$389$	0.660483	−	0.214604i	0.0334878	−	0.0108808i	0.325713	+	0.945469i	$0.394396\pi$
$390$		0			0
$391$	−0.910232	+	2.80141i	−0.0460324	+	0.141673i
$392$	−17.1392	−	9.84227i	−0.865662	−	0.497110i
$393$		−	54.2378i		−	2.73593i
$394$	0.456366	−	6.59985i	0.0229914	−	0.332496i
$395$		0			0
$396$	−10.9168	+	1.94239i	−0.548592	+	0.0976086i
$397$	16.9780	−	12.3352i	0.852099	−	0.619086i	−0.0736250	−	0.997286i	$-0.523457\pi$
$397$	16.9780	−	12.3352i	0.852099	−	0.619086i	0.925724	+	0.378200i	$0.123457\pi$
$398$	25.4694	−	30.4011i	1.27667	−	1.52387i
$399$	−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	$0.344722\pi$
$402$	−8.47199	+	10.1124i	−0.422545	+	0.504362i
$403$	−13.8009	+	10.0269i	−0.687470	+	0.499476i
$404$	−3.06467	+	0.545284i	−0.152473	+	0.0271289i
$405$		0			0
$406$	−0.0975002	+	1.41002i	−0.00483885	+	0.0699782i
$407$		−	2.78663i		−	0.138128i
$408$	−1.61129	+	2.80589i	−0.0797708	+	0.138912i
$409$	11.2943	−	34.7602i	0.558465	−	1.71878i	−0.128146	−	0.991755i	$-0.540903\pi$
$409$	11.2943	−	34.7602i	0.558465	−	1.71878i	0.686611	−	0.727025i	$-0.259097\pi$
$410$		0			0
$411$	21.7569	−	7.06926i	1.07319	−	0.348701i
$412$	−6.54423	+	6.79781i	−0.322411	+	0.334904i
$413$	0.122036	−	0.375588i	0.00600499	−	0.0184815i
$414$	−22.4249	−	18.7872i	−1.10213	−	0.923338i
$415$		0			0
$416$	−21.4784	−	16.6471i	−1.05306	−	0.816190i
$417$	20.0626	−	27.6138i	0.982471	−	1.35226i
$418$	−5.27462	−	8.42661i	−0.257990	−	0.412159i
$419$	−6.06690	+	8.35037i	−0.296387	+	0.407942i	−0.931076	−	0.364826i	$-0.881128\pi$
$419$	−6.06690	+	8.35037i	−0.296387	+	0.407942i	0.634688	+	0.772768i	$0.281128\pi$
$420$		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	$0.704494\pi$
$422$	−0.172550	+	0.428030i	−0.00839958	+	0.0208362i
$423$	−9.50473	+	3.08828i	−0.462136	+	0.150157i
$424$	−12.9117	+	1.38744i	−0.627049	+	0.0673800i
$425$		0			0
$426$	20.9320	+	33.4404i	1.01416	+	1.62019i
$427$	0.402975	+	1.24023i	0.0195013	+	0.0600189i
$428$	4.04493	+	22.7338i	0.195519	+	1.09888i
$429$	−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	$0.965417\pi$
$432$	−1.36292	−	1.73335i	−0.0655734	−	0.0833959i
$433$	−2.65013	+	3.64760i	−0.127357	+	0.175292i	−0.867934	−	0.496680i	$-0.834552\pi$
$433$	−2.65013	+	3.64760i	−0.127357	+	0.175292i	0.740577	+	0.671972i	$0.234552\pi$
$434$	0.135176	+	0.540378i	0.00648867	+	0.0259390i
$435$		0			0
$436$	−0.519197	+	3.73630i	−0.0248650	+	0.178936i
$437$	8.10505	−	24.9448i	0.387717	−	1.19327i
$438$	−8.86969	−	35.4573i	−0.423810	−	1.69421i
$439$	3.68407	+	11.3384i	0.175831	+	0.541153i	0.999670	−	0.0256706i	$-0.00817212\pi$
$439$	3.68407	+	11.3384i	0.175831	+	0.541153i	−0.823839	+	0.566824i	$0.808172\pi$
$440$		0			0
$441$	6.95519	−	21.4059i	0.331200	−	1.01933i
$442$	−3.10846	−	0.214944i	−0.147854	−	0.0102238i
$443$	−4.00502			−0.190284			−0.0951422	−	0.995464i	$-0.530331\pi$
$443$	−4.00502			−0.190284			−0.0951422	+	0.995464i	$0.530331\pi$
$444$	7.12482	−	3.80251i	0.338129	−	0.180459i
$445$		0			0
$446$	6.23234	−	15.4601i	0.295110	−	0.732056i
$447$	21.7558	+	29.9443i	1.02902	+	1.41632i
$448$	−0.766384	+	0.447237i	−0.0362082	+	0.0211300i
$449$	6.20695			0.292924			0.146462	−	0.989216i	$-0.453211\pi$
$449$	6.20695			0.292924			0.146462	+	0.989216i	$0.453211\pi$
$450$		0			0
$451$			19.5819i			0.922076i
$452$	−1.26499	+	9.10326i	−0.0595002	+	0.428181i
$453$	17.9034	−	13.0076i	0.841174	−	0.611148i
$454$	1.37646	+	0.554885i	0.0646004	+	0.0260420i
$455$		0			0
$456$	14.3475	−	24.9847i	0.671885	−	1.17001i
$457$			34.1526i			1.59759i	0.601604	+	0.798795i	$0.294529\pi$
$457$			34.1526i			1.59759i	−0.601604	+	0.798795i	$0.705471\pi$
$458$	28.5396	+	1.97346i	1.33357	+	0.0922135i
$459$	−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	$0.497992\pi$
$462$	−0.653290	+	0.163421i	−0.0303938	+	0.00760305i
$463$	0.474013	+	0.154016i	0.0220292	+	0.00715774i	0.320011	−	0.947414i	$-0.396313\pi$
$463$	0.474013	+	0.154016i	0.0220292	+	0.00715774i	−0.297982	+	0.954572i	$0.596313\pi$
$464$	−29.9425	−	20.0617i	−1.39005	−	0.931340i
$465$		0			0
$466$	−9.01021	−	36.0190i	−0.417390	−	1.66855i
$467$	−22.0431	−	16.0152i	−1.02003	−	0.741096i	−0.0537419	−	0.998555i	$-0.517115\pi$
$467$	−22.0431	−	16.0152i	−1.02003	−	0.741096i	−0.966289	+	0.257459i	$0.917115\pi$
$468$	13.5228	−	27.8352i	0.625090	−	1.28668i
$469$	−0.243832	+	0.335606i	−0.0112591	+	0.0154968i
$470$		0			0
$471$	9.51161	−	6.91059i	0.438272	−	0.318423i
$472$	6.75588	+	7.46817i	0.310965	+	0.343750i
$473$	17.2383	−	5.60106i	0.792618	−	0.257537i
$474$	−10.3052	−	16.4634i	−0.473334	−	0.756188i
$475$		0			0
$476$	−0.0444600	+	0.0915163i	−0.00203782	+	0.00419464i
$477$	−4.56990	−	14.0647i	−0.209242	−	0.643979i
$478$	−11.4546	−	4.61764i	−0.523922	−	0.211206i
$479$	23.5204	−	17.0886i	1.07468	−	0.780797i	0.0979285	−	0.995193i	$-0.468778\pi$
$479$	23.5204	−	17.0886i	1.07468	−	0.780797i	0.976747	+	0.214396i	$0.0687784\pi$
$480$		0			0
$481$	6.29185	+	4.57130i	0.286884	+	0.208433i
$482$	−0.268435	−	0.428846i	−0.0122269	−	0.0195334i
$483$	−1.43739	−	1.04432i	−0.0654034	−	0.0475183i
$484$	11.5804	+	11.1484i	0.526383	+	0.506748i
$485$		0			0
$486$	−20.2764	+	24.2025i	−0.919756	+	1.09785i
$487$	24.7645	+	8.04647i	1.12219	+	0.364620i	0.810601	−	0.585598i	$-0.199140\pi$
$487$	24.7645	+	8.04647i	1.12219	+	0.364620i	0.311584	+	0.950219i	$0.399140\pi$
$488$	−32.5432	−	6.83822i	−1.47316	−	0.309552i
$489$	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	$0.787550\pi$
$492$	−50.0668	+	26.7206i	−2.25718	+	1.20466i
$493$	−4.13267			−0.186126
$494$	27.6789	+	1.91394i	1.24533	+	0.0861123i
$495$		0			0
$496$	−13.6663	−	3.87293i	−0.613634	−	0.173900i
$497$	0.729177	+	1.00363i	0.0327081	+	0.0450188i
$498$	−27.7495	+	33.1226i	−1.24348	+	1.48426i
$499$		−	18.4619i		−	0.826469i	−0.910625	−	0.413234i	$-0.864399\pi$
$499$		−	18.4619i		−	0.826469i	0.910625	−	0.413234i	$-0.135601\pi$
$500$		0			0
$501$		−	20.0640i		−	0.896393i
$502$	−21.7212	−	18.1976i	−0.969466	−	0.812199i
$503$	−14.1453	−	19.4694i	−0.630709	−	0.868097i	0.367368	−	0.930076i	$-0.380259\pi$
$503$	−14.1453	−	19.4694i	−0.630709	−	0.868097i	−0.998077	+	0.0619786i	$0.980259\pi$
$504$	−0.677900	−	0.749372i	−0.0301961	−	0.0333797i
$505$		0			0
$506$	1.07842	−	15.5958i	0.0479416	−	0.693320i
$507$	25.1325			1.11618
$508$	−7.66164	−	14.3557i	−0.339930	−	0.636932i
$509$	−0.950881	−	0.308960i	−0.0421471	−	0.0136944i	0.287868	−	0.957670i	$-0.407054\pi$
$509$	−0.950881	−	0.308960i	−0.0421471	−	0.0136944i	−0.330015	+	0.943976i	$0.607054\pi$
$510$		0			0
$511$	−0.355157	−	1.09306i	−0.0157112	−	0.0483541i
$512$	−0.157845	−	22.6269i	−0.00697584	−	0.999976i
$513$	2.14112	+	0.695693i	0.0945330	+	0.0307156i
$514$	−20.3049	−	17.0111i	−0.895612	−	0.750326i
$515$		0			0
$516$	37.8434	+	36.4317i	1.66596	+	1.60382i
$517$	−4.32057	−	3.13908i	−0.190018	−	0.138056i
$518$	0.215258	−	0.134740i	0.00945791	−	0.00592015i
$519$	−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	$0.415672\pi$
$522$	15.3461	−	38.0678i	0.671680	−	1.66618i
$523$	−0.338728	−	1.04250i	−0.0148115	−	0.0455852i	0.943378	−	0.331721i	$-0.107629\pi$
$523$	−0.338728	−	1.04250i	−0.0148115	−	0.0455852i	−0.958189	+	0.286136i	$0.907629\pi$
$524$	39.1191	+	19.0047i	1.70893	+	0.830223i
$525$		0			0
$526$	19.7640	−	12.3712i	0.861751	−	0.539411i
$527$	−1.54901	+	0.503303i	−0.0674758	+	0.0219242i
$528$	4.68217	−	16.5218i	0.203765	−	0.719020i
$529$	14.7608	−	10.7243i	0.641773	−	0.466275i
$530$		0			0
$531$	−6.74091	+	9.27806i	−0.292530	+	0.402634i
$532$	0.395889	−	0.814896i	0.0171639	−	0.0353302i
$533$	−44.2135	−	32.1230i	−1.91510	−	1.39140i
$534$	22.9830	−	5.74924i	0.994574	−	0.248794i
$535$		0			0
$536$	−4.32507	−	9.65379i	−0.186815	−	0.416980i
$537$	29.8585	+	9.70162i	1.28849	+	0.418656i
$538$	0.0499908	+	0.199842i	0.00215526	+	0.00861581i
$539$	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	$0.772552\pi$
$542$	−1.49615	+	21.6369i	−0.0642651	+	0.929386i
$543$		−	32.5706i		−	1.39774i
$544$	−1.45916	−	2.14532i	−0.0625611	−	0.0919797i
$545$		0			0
$546$	0.702699	−	1.74313i	0.0300727	−	0.0745990i
$547$	−20.6852	+	15.0286i	−0.884434	+	0.642579i	−0.934421	−	0.356171i	$-0.884082\pi$
$547$	−20.6852	+	15.0286i	−0.884434	+	0.642579i	0.0499871	+	0.998750i	$0.484082\pi$
$548$	−2.52481	+	18.1693i	−0.107855	+	0.776153i
$549$		−	37.8696i		−	1.61623i
$550$		0			0
$551$	36.7989			1.56769
$552$	41.3468	−	18.5241i	1.75984	−	0.788438i
$553$	−0.358988	−	0.494105i	−0.0152657	−	0.0210115i
$554$	−27.1628	−	10.9500i	−1.15404	−	0.465221i
$555$		0			0
$556$	12.8867	+	24.1460i	0.546518	+	1.02402i
$557$	−39.1180			−1.65748			−0.828742	−	0.559631i	$-0.810943\pi$
$557$	−39.1180			−1.65748			−0.828742	+	0.559631i	$0.810943\pi$
$558$	1.11588	−	16.1375i	0.0472388	−	0.683155i
$559$	−15.6319	+	48.1101i	−0.661160	+	2.03484i
$560$		0			0
$561$	−0.608468	−	1.87267i	−0.0256895	−	0.0790642i
$562$	−14.5225	+	3.63282i	−0.612594	+	0.153241i
$563$	−9.45014	+	29.0845i	−0.398276	+	1.22577i	0.528105	+	0.849179i	$0.322903\pi$
$563$	−9.45014	+	29.0845i	−0.398276	+	1.22577i	−0.926381	+	0.376588i	$0.877097\pi$
$564$	2.13029	−	15.3302i	0.0897015	−	0.645519i
$565$		0			0
$566$	28.2226	−	7.05993i	1.18629	−	0.296751i
$567$	−0.540347	+	0.743723i	−0.0226924	+	0.0312334i
$568$	−31.4534	+	3.37986i	−1.31976	+	0.141816i
$569$	0.511882	+	0.371904i	0.0214592	+	0.0155910i	0.598463	−	0.801150i	$-0.295778\pi$
$569$	0.511882	+	0.371904i	0.0214592	+	0.0155910i	−0.577004	+	0.816741i	$0.695778\pi$
$570$		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	$0.766953\pi$
$572$	16.2813	−	2.89686i	0.680754	−	0.121124i
$573$	2.21761	+	6.82510i	0.0926419	+	0.285122i
$574$	−1.51264	+	0.946834i	−0.0631364	+	0.0395201i
$575$		0			0
$576$	25.1798	−	5.47465i	1.04916	−	0.228110i
$577$	15.2638	−	4.95951i	0.635440	−	0.206467i	0.0264569	−	0.999650i	$-0.491578\pi$
$577$	15.2638	−	4.95951i	0.635440	−	0.206467i	0.608984	+	0.793183i	$0.291578\pi$
$578$	22.0221	+	8.87764i	0.915997	+	0.369261i
$579$	−23.3130	−	32.0876i	−0.968855	−	1.33352i
$580$		0			0
$581$	−0.798656	+	1.09926i	−0.0331338	+	0.0456048i
$582$	−16.8045	+	10.5188i	−0.696570	+	0.436016i
$583$	4.64508	−	6.39340i	0.192379	−	0.264788i
$584$	28.6815	+	6.02678i	1.18685	+	0.249390i
$585$		0			0
$586$	0.547760	−	0.653824i	0.0226278	−	0.0270092i
$587$	7.22818	−	22.2461i	0.298339	−	0.918193i	−0.683740	−	0.729725i	$-0.739648\pi$
$587$	7.22818	−	22.2461i	0.298339	−	0.918193i	0.982079	−	0.188468i	$-0.0603521\pi$
$588$	25.1118	+	24.1751i	1.03559	+	0.996963i
$589$	13.7929	−	4.48160i	0.568328	−	0.184661i
$590$		0			0
$591$	−3.60552	+	11.0967i	−0.148311	+	0.456455i
$592$	0.246068	+	6.47117i	0.0101133	+	0.265964i
$593$			7.54773i			0.309948i	0.987919	+	0.154974i	$0.0495294\pi$
$593$			7.54773i			0.309948i	−0.987919	+	0.154974i	$0.950471\pi$
$594$	1.33866	+	0.0925658i	0.0549260	+	0.00379802i
$595$		0			0
$596$	−29.2206	+	5.19909i	−1.19692	+	0.212963i
$597$	−56.5882	+	41.1137i	−2.31600	+	1.68267i
$598$	33.4443	+	28.0190i	1.36764	+	1.14578i
$599$	0.302745			0.0123698			0.00618491	−	0.999981i	$-0.498031\pi$
$599$	0.302745			0.0123698			0.00618491	+	0.999981i	$0.498031\pi$
$600$		0			0
$601$	−32.7273			−1.33497			−0.667487	−	0.744622i	$-0.732630\pi$
$601$	−32.7273			−1.33497			−0.667487	+	0.744622i	$0.732630\pi$
$602$	1.26618	+	1.06078i	0.0516056	+	0.0432342i
$603$	9.74595	−	7.08085i	0.396886	−	0.288354i
$604$	3.10848	+	17.4706i	0.126482	+	0.710870i
$605$		0			0
$606$	5.47686	+	0.378714i	0.222482	+	0.0153842i
$607$			26.9091i			1.09221i	0.837718	+	0.546103i	$0.183889\pi$
$607$			26.9091i			1.09221i	−0.837718	+	0.546103i	$0.816111\pi$
$608$	12.9929	+	19.1027i	0.526933	+	0.774717i
$609$	0.770300	−	2.37074i	0.0312141	−	0.0960672i
$610$		0			0
$611$	14.1753	−	4.60583i	0.573470	−	0.186332i
$612$	2.04917	−	2.12857i	0.0828328	−	0.0860424i
$613$	2.61296	−	8.04187i	0.105537	−	0.324808i	−0.884319	−	0.466882i	$-0.845377\pi$
$613$	2.61296	−	8.04187i	0.105537	−	0.324808i	0.989856	+	0.142074i	$0.0453772\pi$
$614$	−9.04794	+	10.7999i	−0.365145	+	0.435849i
$615$		0			0
$616$	0.111042	−	0.528449i	0.00447399	−	0.0212918i
$617$	11.3137	−	15.5720i	0.455472	−	0.626904i	−0.518090	−	0.855326i	$-0.673357\pi$
$617$	11.3137	−	15.5720i	0.455472	−	0.626904i	0.973562	+	0.228422i	$0.0733567\pi$
$618$	14.1062	−	8.82976i	0.567436	−	0.355185i
$619$	19.2261	−	26.4625i	0.772763	−	1.06362i	−0.223281	−	0.974754i	$-0.571677\pi$
$619$	19.2261	−	26.4625i	0.772763	−	1.06362i	0.996044	−	0.0888631i	$-0.0283233\pi$
$620$		0			0
$621$	2.08092	+	2.86414i	0.0835045	+	0.114934i
$622$	−31.9524	−	12.8808i	−1.28118	−	0.516474i
$623$	0.708511	−	0.230209i	0.0283859	−	0.00922313i
$624$	29.6234	+	37.6748i	1.18588	+	1.50820i
$625$		0			0
$626$	−22.4347	+	14.0430i	−0.896672	+	0.561270i
$627$	5.41803	+	16.6750i	0.216375	+	0.665934i
$628$	1.65146	+	9.28171i	0.0659002	+	0.370380i
$629$	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	$0.443116\pi$
$632$	15.4851	−	1.66397i	0.615966	−	0.0661891i
$633$	0.478417	−	0.658485i	0.0190154	−	0.0261724i
$634$	39.1633	−	9.79677i	1.55538	−	0.389079i
$635$		0			0
$636$	22.6850	+	3.15232i	0.899521	+	0.124998i
$637$	−10.3729	+	31.9245i	−0.410990	+	1.26490i
$638$	21.2778	−	5.32266i	0.842394	−	0.210726i
$639$	−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	$0.101058\pi$
$642$	2.80931	−	40.6275i	0.110875	−	1.60344i
$643$	6.95566			0.274305			0.137152	−	0.990550i	$-0.456205\pi$
$643$	6.95566			0.274305			0.137152	+	0.990550i	$0.456205\pi$
$644$	1.25687	−	0.670793i	0.0495278	−	0.0264330i
$645$		0			0
$646$	2.45689	+	0.990432i	0.0966649	+	0.0389680i
$647$	−15.2526	−	20.9935i	−0.599643	−	0.825338i	0.396032	−	0.918237i	$-0.370387\pi$
$647$	−15.2526	−	20.9935i	−0.599643	−	0.825338i	−0.995676	+	0.0928983i	$0.970387\pi$
$648$	−9.58462	−	21.3934i	−0.376520	−	0.840412i
$649$	−6.12843			−0.240562
$650$		0			0
$651$		−	0.982411i		−	0.0385037i
$652$	−19.8718	−	2.76139i	−0.778240	−	0.108145i
$653$	14.9322	−	10.8488i	0.584340	−	0.424548i	−0.255946	−	0.966691i	$-0.582387\pi$
$653$	14.9322	−	10.8488i	0.584340	−	0.424548i	0.840286	+	0.542143i	$0.182387\pi$
$654$	2.48743	−	6.17038i	0.0972663	−	0.241281i
$655$		0			0
$656$	−1.72915	−	45.4736i	−0.0675118	−	1.77544i
$657$			33.3758i			1.30212i
$658$	0.0335736	−	0.485533i	0.00130884	−	0.0189280i
$659$	−8.10100	−	2.63217i	−0.315570	−	0.102535i	0.146950	−	0.989144i	$-0.453055\pi$
$659$	−8.10100	−	2.63217i	−0.315570	−	0.102535i	−0.462520	+	0.886609i	$0.653055\pi$
$660$		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	$0.684529\pi$
$662$	1.22747	+	4.90690i	0.0477069	+	0.190712i
$663$	5.22641	+	1.69816i	0.202977	+	0.0659512i
$664$	−14.1665	−	31.6204i	−0.549767	−	1.22711i
$665$		0			0
$666$	−7.15426	+	1.78965i	−0.277222	+	0.0693474i
$667$	46.8159	+	34.0138i	1.81272	+	1.31702i
$668$	14.4712	+	7.03033i	0.559908	+	0.272012i
$669$	−17.2800	+	23.7839i	−0.668084	+	0.919539i
$670$		0			0
$671$	16.3718	−	11.8948i	0.632028	−	0.459195i
$672$	1.50265	−	0.437189i	0.0579662	−	0.0168649i
$673$	−42.8082	+	13.9092i	−1.65014	+	0.536162i	−0.978770	−	0.204964i	$-0.934292\pi$
$673$	−42.8082	+	13.9092i	−1.65014	+	0.536162i	−0.671367	+	0.741125i	$0.734292\pi$
$674$	11.7858	−	7.37727i	0.453970	−	0.284162i
$675$		0			0
$676$	−8.80633	+	18.1269i	−0.338705	+	0.697189i
$677$	13.9190	+	42.8382i	0.534950	+	1.64641i	0.743758	+	0.668450i	$0.233042\pi$
$677$	13.9190	+	42.8382i	0.534950	+	1.64641i	−0.208808	+	0.977957i	$0.566958\pi$
$678$	6.06048	−	15.0337i	0.232751	−	0.577368i
$679$	−0.504344	+	0.366427i	−0.0193549	+	0.0140622i
$680$		0			0
$681$	−2.11756	−	1.53849i	−0.0811449	−	0.0589552i
$682$	7.32709	−	4.58638i	0.280569	−	0.175621i
$683$	−5.91153	−	4.29498i	−0.226199	−	0.164343i	0.468914	−	0.883244i	$-0.344645\pi$
$683$	−5.91153	−	4.29498i	−0.226199	−	0.164343i	−0.695112	+	0.718901i	$0.744645\pi$
$684$	−18.2466	+	18.9536i	−0.697676	+	0.724709i
$685$		0			0
$686$	1.68188	+	1.40905i	0.0642146	+	0.0537977i
$687$	−47.9850	−	15.5913i	−1.83074	−	0.594844i
$688$	−39.5366	+	14.5291i	−1.50732	+	0.553918i
$689$	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	$0.369546\pi$
$692$	17.5492	−	9.36602i	0.667122	−	0.356043i
$693$	0.614940			0.0233596
$694$	−1.54086	+	22.2835i	−0.0584901	+	0.845869i
$695$		0			0
$696$	42.6436	+	47.1396i	1.61640	+	1.78682i
$697$	−3.06700	−	4.22136i	−0.116171	−	0.159896i
$698$	8.44247	+	7.07293i	0.319552	+	0.267714i
$699$			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	$-0.138803\pi$
$702$	−2.40500	+	2.87068i	−0.0907708	+	0.108347i
$703$	−3.88635	−	5.34910i	−0.146576	−	0.201745i
$704$	10.2758	+	9.16620i	0.387284	+	0.345464i
$705$		0			0
$706$	15.8633	+	1.09691i	0.597022	+	0.0412828i
$707$	0.172631			0.00649248
$708$	−8.36259	−	15.6691i	−0.314285	−	0.588881i
$709$	17.1971	+	5.58767i	0.645849	+	0.209849i	0.613583	−	0.789630i	$-0.289728\pi$
$709$	17.1971	+	5.58767i	0.645849	+	0.209849i	0.0322662	+	0.999479i	$0.489728\pi$
$710$		0			0
$711$	5.48073	+	16.8679i	0.205543	+	0.632597i
$712$	−3.90650	+	18.5911i	−0.146402	+	0.696730i
$713$	21.6899	+	7.04749i	0.812294	+	0.263930i
$714$	0.115237	−	0.137551i	0.00431264	−	0.00514770i
$715$		0			0
$716$	−17.4596	+	18.1361i	−0.652496	+	0.677779i
$717$	17.6219	+	12.8030i	0.658101	+	0.478139i
$718$	7.63431	+	12.1964i	0.284910	+	0.455166i
$719$	−31.8411	−	23.1339i	−1.18747	−	0.862749i	−0.194477	−	0.980907i	$-0.562301\pi$
$719$	−31.8411	−	23.1339i	−1.18747	−	0.862749i	−0.992995	+	0.118158i	$0.962301\pi$
$720$		0			0
$721$	0.423362	−	0.307590i	0.0157668	−	0.0114553i
$722$	3.04424	+	1.22721i	0.113295	+	0.0456719i
$723$	0.275733	+	0.848620i	0.0102546	+	0.0315605i
$724$	23.4916	+	11.4126i	0.873059	+	0.424145i
$725$		0			0
$726$	−15.0420	−	24.0307i	−0.558260	−	0.891864i
$727$	16.7936	−	5.45658i	0.622841	−	0.202373i	0.0194399	−	0.999811i	$-0.493812\pi$
$727$	16.7936	−	5.45658i	0.622841	−	0.202373i	0.603401	+	0.797438i	$0.293812\pi$
$728$	1.01101	+	1.11761i	0.0374707	+	0.0414213i
$729$	24.9346	−	18.1161i	0.923505	−	0.670966i
$730$		0			0
$731$	−2.83888	+	3.90738i	−0.105000	+	0.144520i
$732$	52.7529	+	25.6281i	1.94980	+	0.947244i
$733$	7.26956	+	5.28165i	0.268507	+	0.195082i	0.713889	−	0.700259i	$-0.246932\pi$
$733$	7.26956	+	5.28165i	0.268507	+	0.195082i	−0.445382	+	0.895341i	$0.646932\pi$
$734$	−4.16510	−	16.6503i	−0.153737	−	0.614575i
$735$		0			0
$736$	−1.12717	+	36.3123i	−0.0415481	+	1.33849i
$737$	6.12241	+	1.98929i	0.225522	+	0.0732765i
$738$	50.2736	−	12.5760i	1.85060	−	0.462930i
$739$	−20.0852	+	6.52609i	−0.738848	+	0.240066i	−0.654176	−	0.756343i	$-0.726984\pi$
$739$	−20.0852	+	6.52609i	−0.738848	+	0.240066i	−0.0846720	+	0.996409i	$0.526984\pi$
$740$		0			0
$741$	−46.5379	−	15.1211i	−1.70961	−	0.555487i
$742$	0.718472	+	0.0496808i	0.0263759	+	0.00182384i
$743$		−	8.50903i		−	0.312166i	−0.987744	−	0.156083i	$-0.950113\pi$
$743$		−	8.50903i		−	0.312166i	0.987744	−	0.156083i	$-0.0498868\pi$
$744$	21.7246	+	12.4755i	0.796463	+	0.457372i
$745$		0			0
$746$	9.77249	+	3.93953i	0.357796	+	0.144237i
$747$	31.9222	−	23.1929i	1.16797	−	0.848582i
$748$	1.56387	+	0.217316i	0.0571808	+	0.00794587i
$749$		−	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	$0.601043\pi$
$752$	10.3105	+	6.90812i	0.375986	+	0.251913i
$753$	29.3753	+	40.4317i	1.07050	+	1.47341i
$754$	−22.8870	+	56.7740i	−0.833496	+	2.06759i
$755$		0			0
$756$	0.0575772	+	0.107883i	0.00209406	+	0.00392368i
$757$	2.28693			0.0831199			0.0415599	−	0.999136i	$-0.486767\pi$
$757$	2.28693			0.0831199			0.0415599	+	0.999136i	$0.486767\pi$
$758$	8.88629	+	0.614469i	0.322765	+	0.0223185i
$759$	−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	$-0.215653\pi$
$762$	6.96446	+	27.8410i	0.252296	+	1.00857i
$763$	0.0646465	−	0.198961i	0.00234036	−	0.00720289i
$764$	−5.69966	−	0.792026i	−0.206206	−	0.0286545i
$765$		0			0
$766$	−9.83154	−	39.3024i	−0.355228	−	1.42005i
$767$	10.0533	−	13.8372i	0.363005	−	0.499633i
$768$	−9.41412	+	38.7808i	−0.339703	+	1.39938i
$769$	15.2893	+	11.1083i	0.551345	+	0.400576i	0.828281	−	0.560313i	$-0.189319\pi$
$769$	15.2893	+	11.1083i	0.551345	+	0.400576i	−0.276936	+	0.960888i	$0.589319\pi$
$770$		0			0
$771$	27.4599	+	37.7954i	0.988946	+	1.36117i
$772$	31.3120	−	5.57122i	1.12694	−	0.200513i
$773$	−2.33908	−	7.19893i	−0.0841307	−	0.258928i	0.900138	−	0.435604i	$-0.143465\pi$
$773$	−2.33908	−	7.19893i	−0.0841307	−	0.258928i	−0.984269	+	0.176677i	$0.943465\pi$
$774$	−25.4508	−	40.6597i	−0.914811	−	1.46148i
$775$		0			0
$776$	−1.69845	−	15.8060i	−0.0609708	−	0.567403i
$777$	−0.425963	+	0.138404i	−0.0152813	+	0.00496521i
$778$	0.367207	−	0.910902i	0.0131650	−	0.0326574i
$779$	27.3097	+	37.5886i	0.978473	+	1.34675i
$780$		0			0
$781$	11.3156	−	15.5746i	0.404903	−	0.557302i
$782$	2.21021	+	3.53098i	0.0790368	+	0.126267i
$783$	−2.91956	+	4.01843i	−0.104336	+	0.143607i
$784$	−26.2354	+	9.64112i	−0.936978	+	0.344326i
$785$		0			0
$786$	−58.7967	−	49.2587i	−2.09721	−	1.75700i
$787$	12.5994	−	38.7769i	0.449119	−	1.38225i	−0.428784	−	0.903407i	$-0.641058\pi$
$787$	12.5994	−	38.7769i	0.449119	−	1.38225i	0.877903	−	0.478839i	$-0.158942\pi$
$788$	−6.74013	−	6.48870i	−0.240107	−	0.231151i
$789$	−39.1099	+	12.7076i	−1.39235	+	0.452401i
$790$		0			0
$791$	0.157507	−	0.484757i	0.00560031	−	0.0172360i
$792$	−7.80901	+	13.5985i	−0.277481	+	0.483203i
$793$			56.4783i			2.00560i
$794$	2.04732	−	29.6079i	0.0726568	−	1.05074i
$795$		0			0
$796$	−9.82514	−	55.2204i	−0.348243	−	1.95724i
$797$	4.00819	−	2.91212i	0.141977	−	0.103153i	−0.514529	−	0.857473i	$-0.672033\pi$
$797$	4.00819	−	2.91212i	0.141977	−	0.103153i	0.656507	+	0.754320i	$0.272033\pi$
$798$	−1.02611	+	1.22480i	−0.0363240	+	0.0433575i
$799$	1.42306			0.0503443
$800$		0			0
$801$	−21.6339			−0.764396
$802$	17.0483	−	20.3493i	0.601995	−	0.718560i
$803$	−14.4291	+	10.4834i	−0.509192	+	0.369950i
$804$	3.26818	+	18.3682i	0.115260	+	0.647797i
$805$		0			0
$806$	−1.66421	+	24.0673i	−0.0586192	+	0.847735i
$807$		−	0.363315i		−	0.0127893i
$808$	−2.19221	+	3.81750i	−0.0771218	+	0.134299i
$809$	7.58506	−	23.3444i	0.266676	−	0.820746i	−0.724626	−	0.689142i	$-0.757987\pi$
$809$	7.58506	−	23.3444i	0.266676	−	0.820746i	0.991302	−	0.131603i	$-0.0420126\pi$
$810$		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	$0.395673\pi$
$812$	1.43999	+	1.38628i	0.0505338	+	0.0486488i
$813$	11.8203	−	36.3792i	0.414557	−	1.27588i
$814$	−3.02086	−	2.53081i	−0.105881	−	0.0887049i
$815$		0			0
$816$	1.57836	+	4.29503i	0.0552537	+	0.150356i
$817$	25.2785	−	34.7928i	0.884382	−	1.21725i
$818$	−27.4245	−	43.8128i	−0.958875	−	1.53188i
$819$	−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	$0.760450\pi$
$822$	12.0962	−	30.0060i	0.421902	−	1.04658i
$823$	−7.47765	+	2.42963i	−0.260654	+	0.0846917i	−0.436429	−	0.899739i	$-0.643757\pi$
$823$	−7.47765	+	2.42963i	−0.260654	+	0.0846917i	0.175775	+	0.984430i	$0.443757\pi$
$824$	1.42573	+	13.2681i	0.0496677	+	0.462215i
$825$		0			0
$826$	−0.296325	−	0.473402i	−0.0103105	−	0.0164718i
$827$	−1.01952	−	3.13777i	−0.0354523	−	0.109111i	0.931764	−	0.363064i	$-0.118269\pi$
$827$	−1.01952	−	3.13777i	−0.0354523	−	0.109111i	−0.967217	+	0.253953i	$0.918269\pi$
$828$	−40.7326	+	7.24738i	−1.41556	+	0.251864i
$829$	−19.0835	−	26.2662i	−0.662798	−	0.912263i	0.336772	−	0.941586i	$-0.390665\pi$
$829$	−19.0835	−	26.2662i	−0.662798	−	0.912263i	−0.999570	+	0.0293232i	$0.990665\pi$
$830$		0			0
$831$	41.7875	+	30.3604i	1.44959	+	1.05319i
$832$	−37.5530	+	8.16485i	−1.30192	+	0.283065i
$833$	−1.88380	+	2.59283i	−0.0652699	+	0.0898362i
$834$	−11.7141	−	46.8279i	−0.405625	−	1.62152i
$835$		0			0
$836$	−13.9253	−	1.93507i	−0.481617	−	0.0669257i
$837$	−0.604918	+	1.86175i	−0.0209090	+	0.0643514i
$838$	3.54231	+	14.1606i	0.122367	+	0.489171i
$839$	3.32108	+	10.2212i	0.114656	+	0.352876i	0.991875	−	0.127215i	$-0.0406037\pi$
$839$	3.32108	+	10.2212i	0.114656	+	0.352876i	−0.877219	+	0.480091i	$0.840604\pi$
$840$		0			0
$841$	−16.1273	+	49.6347i	−0.556114	+	1.71154i
$842$	17.1117	+	1.18324i	0.589708	+	0.0407771i
$843$	26.4020			0.909332
$844$	0.307299	+	0.575790i	0.0105777	+	0.0198195i
$845$		0			0
$846$	−5.28433	+	13.1084i	−0.181679	+	0.450677i
$847$	−0.523996	−	0.721219i	−0.0180047	−	0.0247814i
$848$	−10.2224	+	15.2571i	−0.351037	+	0.523931i
$849$	−51.3090			−1.76092
$850$		0			0
$851$		−	10.3974i		−	0.356418i
$852$	55.2616	+	7.67917i	1.89323	+	0.263084i
$853$	−18.7063	+	13.5909i	−0.640491	+	0.465344i	−0.860019	−	0.510262i	$-0.829548\pi$
$853$	−18.7063	+	13.5909i	−0.640491	+	0.465344i	0.219528	+	0.975606i	$0.429548\pi$
$854$	1.71046	+	0.689528i	0.0585307	+	0.0235952i
$855$		0			0
$856$	28.3183	+	16.2619i	0.967900	+	0.555820i
$857$			15.8941i			0.542932i	0.962448	+	0.271466i	$0.0875084\pi$
$857$			15.8941i			0.542932i	−0.962448	+	0.271466i	$0.912492\pi$
$858$	−29.0962	−	2.01194i	−0.993327	−	0.0686866i
$859$	−3.46524	−	1.12593i	−0.118233	−	0.0384161i	0.249303	−	0.968425i	$-0.419798\pi$
$859$	−3.46524	−	1.12593i	−0.118233	−	0.0384161i	−0.367536	+	0.930009i	$0.619798\pi$
$860$		0			0
$861$	2.99328	−	0.972577i	0.102011	−	0.0331453i
$862$	−42.1829	+	10.5521i	−1.43675	+	0.359406i
$863$	−39.8580	−	12.9507i	−1.35678	−	0.440845i	−0.461815	−	0.886976i	$-0.652802\pi$
$863$	−39.8580	−	12.9507i	−1.35678	−	0.440845i	−0.894968	+	0.446131i	$0.852802\pi$
$864$	−3.11685	−	0.0967502i	−0.106037	−	0.00329151i
$865$		0			0
$866$	1.54734	+	6.18563i	0.0525809	+	0.210196i
$867$	−33.8789	−	24.6145i	−1.15059	−	0.835951i
$868$	0.708566	+	0.344232i	0.0240503	+	0.0116840i
$869$	−5.57088	+	7.66766i	−0.188979	+	0.260108i
$870$		0			0
$871$	−14.5350	+	10.5603i	−0.492500	+	0.357823i
$872$	3.57882	+	3.95614i	0.121194	+	0.133972i
$873$	17.2175	−	5.59430i	0.582723	−	0.189338i
$874$	−19.6805	−	31.4411i	−0.665703	−	1.06351i
$875$		0			0
$876$	−46.4931	−	22.5870i	−1.57086	−	0.763145i
$877$	−8.84000	−	27.2067i	−0.298505	−	0.918705i	−0.982021	−	0.188770i	$-0.939550\pi$
$877$	−8.84000	−	27.2067i	−0.298505	−	0.918705i	0.683516	−	0.729936i	$-0.260450\pi$
$878$	15.6373	+	6.30380i	0.527734	+	0.212743i
$879$	−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	$0.594893\pi$
$882$	−16.8884	−	26.9806i	−0.568663	−	0.908484i
$883$	−10.5069	−	7.63372i	−0.353586	−	0.256895i	0.396786	−	0.917911i	$-0.370126\pi$
$883$	−10.5069	−	7.63372i	−0.353586	−	0.256895i	−0.750372	+	0.661016i	$0.770126\pi$
$884$	−3.05611	+	3.17453i	−0.102788	+	0.106771i
$885$		0			0
$886$	−3.63736	+	4.34167i	−0.122199	+	0.145861i
$887$	−16.0762	−	5.22346i	−0.539785	−	0.175387i	0.0264205	−	0.999651i	$-0.491589\pi$
$887$	−16.0762	−	5.22346i	−0.539785	−	0.175387i	−0.566205	+	0.824264i	$0.691589\pi$
$888$	2.34862	−	11.1771i	0.0788146	−	0.375080i
$889$	0.278868	+	0.858269i	0.00935295	+	0.0287854i
$890$		0			0
$891$	13.5676	+	4.40839i	0.454533	+	0.147687i
$892$	−11.0994	−	20.7970i	−0.371634	−	0.696336i
$893$	−12.6715			−0.424035
$894$	52.2199	+	3.61090i	1.74649	+	0.120767i
$895$		0			0
$896$	−0.211200	+	1.23698i	−0.00705569	+	0.0413247i
$897$	−45.2294	−	62.2529i	−1.51017	−	2.07856i
$898$	5.63715	−	6.72868i	0.188114	−	0.224539i
$899$			31.9973i			1.06717i
$900$		0			0
$901$			2.10579i			0.0701540i
$902$	21.2279	+	17.7843i	0.706810	+	0.592151i
$903$	−1.71235	−	2.35685i	−0.0569836	−	0.0784312i
$904$	8.71956	+	9.63889i	0.290008	+	0.320585i
$905$		0			0
$906$	2.15892	−	31.2217i	0.0717252	−	1.03727i
$907$	36.2209			1.20269			0.601347	−	0.798988i	$-0.294631\pi$
$907$	36.2209			1.20269			0.601347	+	0.798988i	$0.294631\pi$
$908$	1.85162	−	0.988211i	0.0614483	−	0.0327949i
$909$	−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	$0.956867\pi$
$912$	−14.0543	−	38.2446i	−0.465385	−	1.26640i
$913$	20.0536	+	6.51579i	0.663676	+	0.215641i
$914$	37.0232	+	31.0173i	1.22462	+	1.02596i
$915$		0			0
$916$	28.0590	−	29.1462i	0.927095	−	0.963018i
$917$	−1.95131	−	1.41771i	−0.0644381	−	0.0468170i
$918$	−0.303080	+	0.189712i	−0.0100031	+	0.00626143i
$919$	−32.1024	−	23.3238i	−1.05896	−	0.769380i	−0.0850654	−	0.996375i	$-0.527110\pi$
$919$	−32.1024	−	23.3238i	−1.05896	−	0.769380i	−0.973896	+	0.226995i	$0.927110\pi$
$920$		0			0
$921$	20.1028	−	14.6056i	0.662411	−	0.481270i
$922$	−6.88008	+	17.0669i	−0.226584	+	0.562068i
$923$	16.6029	+	51.0983i	0.546490	+	1.68192i
$924$	−0.416159	+	0.856621i	−0.0136906	+	0.0281808i
$925$		0			0
$926$	0.597460	−	0.373979i	0.0196338	−	0.0122897i
$927$	−14.4529	+	4.69603i	−0.474695	+	0.154238i
$928$	−48.9417	+	14.2393i	−1.60659	+	0.467428i
$929$	17.2005	−	12.4969i	0.564331	−	0.410011i	−0.268710	−	0.963221i	$-0.586597\pi$
$929$	17.2005	−	12.4969i	0.564331	−	0.410011i	0.833042	+	0.553210i	$0.186597\pi$
$930$		0			0
$931$	16.7741	−	23.0875i	0.549748	−	0.756664i
$932$	−47.2296	−	22.9449i	−1.54706	−	0.751584i
$933$	49.1558	+	35.7138i	1.60929	+	1.16922i
$934$	−37.3809	+	9.35088i	−1.22314	+	0.305970i
$935$		0			0
$936$	−17.8935	−	39.9393i	−0.584868	−	1.30546i
$937$	−28.5238	−	9.26796i	−0.931833	−	0.302771i	−0.196521	−	0.980500i	$-0.562964\pi$
$937$	−28.5238	−	9.26796i	−0.931833	−	0.302771i	−0.735312	+	0.677729i	$0.762964\pi$
$938$	0.142367	+	0.569124i	0.00464846	+	0.0185826i
$939$	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	$0.484661\pi$
$942$	1.14698	−	16.5873i	0.0373705	−	0.540443i
$943$			73.0634i			2.37927i
$944$	14.2316	−	0.541160i	0.463199	−	0.0176133i
$945$		0			0
$946$	9.58395	−	23.7741i	0.311601	−	0.772964i
$947$	−19.0805	+	13.8628i	−0.620034	+	0.450481i	−0.852934	−	0.522020i	$-0.825179\pi$
$947$	−19.0805	+	13.8628i	−0.620034	+	0.450481i	0.232899	+	0.972501i	$0.425179\pi$
$948$	−27.2064	−	3.78061i	−0.883622	−	0.122788i
$949$		−	49.7764i		−	1.61581i
$950$		0			0
$951$	−71.1992			−2.30879
$952$	0.0588301	+	0.131312i	0.00190670	+	0.00425585i
$953$	−16.3647	−	22.5241i	−0.530106	−	0.729629i	0.457040	−	0.889446i	$-0.348909\pi$
$953$	−16.3647	−	22.5241i	−0.530106	−	0.729629i	−0.987147	+	0.159817i	$0.948909\pi$
$954$	−19.3973	−	7.81954i	−0.628011	−	0.253167i
$955$		0			0
$956$	−15.4089	+	8.22370i	−0.498358	+	0.265973i
$957$	−38.6831			−1.25045
$958$	2.83626	−	41.0173i	0.0916354	−	1.32521i
$959$	0.314370	−	0.967532i	0.0101515	−	0.0312432i
$960$		0			0
$961$	−5.68270	−	17.4895i	−0.183313	−	0.564179i
$962$	10.6698	−	2.66906i	0.344008	−	0.0860541i
$963$	−11.4917	+	35.3679i	−0.370316	+	1.13971i
$964$	−0.708685	−	0.0984791i	−0.0228252	−	0.00317180i
$965$		0			0
$966$	−2.43754	+	0.609753i	−0.0784265	+	0.0196185i
$967$	−35.9696	+	49.5079i	−1.15671	+	1.59207i	−0.433998	+	0.900914i	$0.642897\pi$
$967$	−35.9696	+	49.5079i	−1.15671	+	1.59207i	−0.722707	+	0.691154i	$0.757103\pi$
$968$	22.6029	−	2.42881i	0.726484	−	0.0780649i
$969$	−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	$0.616324\pi$
$972$	7.82187	+	43.9614i	0.250887	+	1.41006i
$973$	−0.469050	−	1.44359i	−0.0150371	−	0.0462793i
$974$	31.2139	−	19.5383i	1.00016	−	0.626046i
$975$		0			0
$976$	−36.9687	+	29.0682i	−1.18334	+	0.930449i
$977$	−50.4988	+	16.4081i	−1.61560	+	0.524940i	−0.970898	−	0.239494i	$-0.923018\pi$
$977$	−50.4988	+	16.4081i	−1.61560	+	0.524940i	−0.644702	+	0.764434i	$0.723018\pi$
$978$	32.8177	+	13.2296i	1.04939	+	0.423037i
$979$	−6.79521	−	9.35280i	−0.217176	−	0.298917i
$980$		0			0
$981$	−3.57088	+	4.91490i	−0.114010	+	0.156921i
$982$	−29.5214	+	18.4788i	−0.942065	+	0.589683i
$983$	−18.0867	+	24.8942i	−0.576877	+	0.794003i	−0.993349	−	0.115146i	$-0.963266\pi$
$983$	−18.0867	+	24.8942i	−0.576877	+	0.794003i	0.416472	+	0.909149i	$0.363266\pi$
$984$	−16.5040	+	78.5428i	−0.526128	+	2.50385i
$985$		0			0
$986$	−3.75329	+	4.48004i	−0.119529	+	0.142674i
$987$	−0.265248	+	0.816350i	−0.00844294	+	0.0259847i
$988$	27.2128	−	28.2672i	0.865754	−	0.899301i
$989$	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	$0.163733\pi$
$992$	−16.6102	+	11.2976i	−0.527373	+	0.358699i
$993$		−	8.92077i		−	0.283092i
$994$	1.75022	+	0.121024i	0.0555137	+	0.00383866i
$995$		0			0
$996$	10.7047	+	60.1639i	0.339192	+	1.90636i
$997$	9.99182	−	7.25948i	0.316444	−	0.229910i	−0.418212	−	0.908349i	$-0.637343\pi$
$997$	9.99182	−	7.25948i	0.316444	−	0.229910i	0.734657	+	0.678439i	$0.237343\pi$
$998$	−20.0137	−	16.7671i	−0.633523	−	0.530753i
$999$	0.892455			0.0282360

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.2	✓	112	25.21	even	5
200.2.o.a.29.9	yes	112	200.21	even	10
200.2.o.a.69.2	yes	112	40.29	even	2
200.2.o.a.69.9	yes	112	5.4	even	2
800.2.be.a.369.5		112	20.19	odd	2
800.2.be.a.369.24		112	40.19	odd	2
800.2.be.a.529.5		112	200.171	odd	10
800.2.be.a.529.24		112	100.71	odd	10
1000.2.o.a.149.20		112	200.29	even	10	inner
1000.2.o.a.149.27		112	25.4	even	10	inner
1000.2.o.a.349.20		112	1.1	even	1	trivial
1000.2.o.a.349.27		112	8.5	even	2	inner
1000.2.t.b.101.14		224	200.53	odd	20
1000.2.t.b.101.27		224	25.22	odd	20
1000.2.t.b.101.30		224	25.3	odd	20
1000.2.t.b.101.43		224	200.197	odd	20
1000.2.t.b.901.14		224	5.3	odd	4
1000.2.t.b.901.27		224	40.37	odd	4
1000.2.t.b.901.30		224	40.13	odd	4
1000.2.t.b.901.43		224	5.2	odd	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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.908199 - 1.08405i) q^{2} +(-2.01785 + 1.46605i) q^{3} +(-0.350349 - 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} +0.110917i q^{7} +(-2.45277 - 1.40851i) q^{8} +(0.995348 - 3.06337i) q^{9} +O(q^{10})\)	\(q+(0.908199 - 1.08405i) q^{2} +(-2.01785 + 1.46605i) q^{3} +(-0.350349 - 1.96907i) q^{4} +(-0.243326 + 3.51892i) q^{6} +0.110917i q^{7} +(-2.45277 - 1.40851i) q^{8} +(0.995348 - 3.06337i) q^{9} +(1.63700 - 0.531893i) q^{11} +(3.59372 + 3.45966i) q^{12} +(-1.48445 + 4.56868i) q^{13} +(0.120240 + 0.100735i) q^{14} +(-3.75451 + 1.37973i) q^{16} +(-0.269588 + 0.371056i) q^{17} +(-2.41688 - 3.86116i) q^{18} +(2.40052 - 3.30403i) q^{19} +(-0.162610 - 0.223814i) q^{21} +(0.910120 - 2.25766i) q^{22} +(6.10792 - 1.98459i) q^{23} +(7.01427 - 0.753724i) q^{24} +(3.60452 + 5.75850i) q^{26} +(0.170346 + 0.524271i) q^{27} +(0.218404 - 0.0388597i) q^{28} +(5.29624 + 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(-1.91414 + 5.32316i) q^{32} +(-2.52343 + 3.47320i) q^{33} +(0.157406 + 0.629242i) q^{34} +(-6.38072 - 0.886667i) q^{36} +(0.500287 - 1.53972i) q^{37} +(-1.40160 - 5.60300i) q^{38} +(-3.70252 - 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(-0.390308 - 0.0269890i) q^{42} +10.5304 q^{43} +(-1.62086 - 3.03703i) q^{44} +(3.39581 - 8.42372i) q^{46} +(-1.82373 - 2.51014i) q^{47} +(5.55328 - 8.28839i) q^{48} +6.98770 q^{49} -1.14397i q^{51} +(9.51614 + 1.32237i) q^{52} +(3.71441 - 2.69868i) q^{53} +(0.723047 + 0.291478i) q^{54} +(0.156228 - 0.272054i) q^{56} +10.1863i q^{57} +(12.7124 + 0.879037i) q^{58} +(-3.38621 - 1.10025i) q^{59} +(11.1816 - 3.63312i) q^{61} +(4.87191 - 1.21872i) q^{62} +(0.339779 + 0.110401i) q^{63} +(4.03218 + 6.90953i) q^{64} +(1.47337 + 5.88990i) q^{66} +(3.02574 + 2.19833i) q^{67} +(0.825088 + 0.400840i) q^{68} +(-9.41535 + 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-6.75615 + 6.11178i) q^{72} +(-9.85476 + 3.20201i) q^{73} +(-1.21479 - 1.94072i) q^{74} +(-7.34690 - 3.56923i) q^{76} +(0.0589960 + 0.181571i) q^{77} +(-15.7156 - 6.33536i) q^{78} +(-4.45472 + 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(8.53642 + 13.6376i) q^{82} +(9.91061 + 7.20048i) q^{83} +(-0.383735 + 0.398604i) q^{84} +(9.56373 - 11.4156i) q^{86} +(-21.3740 - 6.94483i) q^{87} +(-4.76436 - 1.00112i) q^{88} +(-2.07551 - 6.38776i) q^{89} +(-0.506744 - 0.164651i) q^{91} +(-6.04770 - 11.3317i) q^{92} -8.85717 q^{93} +(-4.37744 - 0.302691i) q^{94} +(-3.94158 - 13.5476i) q^{96} +(3.30362 + 4.54704i) q^{97} +(6.34622 - 7.57505i) q^{98} -5.54415i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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