LMFDB - Embedded newform 1000.2.o.a.149.20

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			149.20
Character	$\chi$	$=$	1000.149
Dual form			1000.2.o.a.349.20

$q$-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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

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

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	−0.174602	−	0.984639i	$-0.555864\pi$
$3$	−2.01785	−	1.46605i	−1.16500	−	0.846425i	−0.990402	+	0.138214i	$0.955864\pi$
$4$	−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	$-0.993327\pi$
$7$		−	0.110917i		−	0.0419227i	0.999780	−	0.0209613i	$-0.00667269\pi$
$8$	−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	0.545219	−	0.838294i	$-0.316446\pi$
$11$	1.63700	+	0.531893i	0.493574	+	0.160372i	−0.0516452	+	0.998665i	$0.516446\pi$
$12$	3.59372	−	3.45966i	1.03742	−	0.998718i
$13$	−1.48445	−	4.56868i	−0.411713	−	1.26712i	−0.915158	−	0.403096i	$-0.867934\pi$
$13$	−1.48445	−	4.56868i	−0.411713	−	1.26712i	0.503445	−	0.864027i	$-0.332066\pi$
$14$	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	0.775072	−	0.631873i	$-0.217713\pi$
$17$	−0.269588	−	0.371056i	−0.0653848	−	0.0899944i	−0.840457	+	0.541878i	$0.817713\pi$
$18$	−2.41688	+	3.86116i	−0.569665	+	0.910084i
$19$	2.40052	+	3.30403i	0.550716	+	0.757996i	0.990109	−	0.140299i	$-0.0448064\pi$
$19$	2.40052	+	3.30403i	0.550716	+	0.757996i	−0.439393	+	0.898295i	$0.644806\pi$
$20$		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	0.866318	−	0.499492i	$-0.166480\pi$
$23$	6.10792	+	1.98459i	1.27359	+	0.413815i	0.407272	+	0.913307i	$0.366480\pi$
$24$	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	0.0485566	−	0.998820i	$-0.484538\pi$
$29$	5.29624	−	7.28964i	0.983486	−	1.35365i	0.934930	−	0.354833i	$-0.115462\pi$
$30$		0			0
$31$	2.87291	−	2.08729i	0.515990	−	0.374889i	−0.299101	−	0.954221i	$-0.596687\pi$
$31$	2.87291	−	2.08729i	0.515990	−	0.374889i	0.815091	+	0.579333i	$0.196687\pi$
$32$	−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	0.983721	−	0.179704i	$-0.0575139\pi$
$37$	0.500287	+	1.53972i	0.0822467	+	0.253129i	−0.901474	+	0.432833i	$0.857514\pi$
$38$	−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	−0.711188	−	0.703002i	$-0.751843\pi$
$41$	−3.51556	−	10.8198i	−0.549039	−	1.68977i	0.162149	−	0.986766i	$-0.448157\pi$
$42$	−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	−0.921040	−	0.389467i	$-0.872659\pi$
$47$	−1.82373	+	2.51014i	−0.266018	+	0.366142i	0.655022	+	0.755609i	$0.272659\pi$
$48$	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	0.812905	−	0.582397i	$-0.197885\pi$
$53$	3.71441	+	2.69868i	0.510213	+	0.370692i	−0.302691	+	0.953089i	$0.597885\pi$
$54$	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	−0.521026	−	0.853541i	$-0.674451\pi$
$59$	−3.38621	+	1.10025i	−0.440847	+	0.143240i	0.0801796	+	0.996780i	$0.474451\pi$
$60$		0			0
$61$	11.1816	+	3.63312i	1.43166	+	0.465174i	0.919286	−	0.393590i	$-0.128767\pi$
$61$	11.1816	+	3.63312i	1.43166	+	0.465174i	0.512372	+	0.858764i	$0.328767\pi$
$62$	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	−0.387414	−	0.921906i	$-0.626632\pi$
$67$	3.02574	−	2.19833i	0.369653	−	0.268569i	0.757067	+	0.653337i	$0.226632\pi$
$68$	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	0.976601	−	0.215060i	$-0.0689948\pi$
$71$	9.04844	+	6.57408i	1.07385	+	0.780200i	0.0972518	+	0.995260i	$0.468995\pi$
$72$	−6.75615	−	6.11178i	−0.796220	−	0.720280i
$73$	−9.85476	−	3.20201i	−1.15341	−	0.374766i	−0.330985	−	0.943636i	$-0.607381\pi$
$73$	−9.85476	−	3.20201i	−1.15341	−	0.374766i	−0.822428	+	0.568870i	$0.807381\pi$
$74$	−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	0.308278	−	0.951296i	$-0.400247\pi$
$79$	−4.45472	−	3.23655i	−0.501196	−	0.364140i	−0.809474	+	0.587156i	$0.800247\pi$
$80$		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	0.108800	−	0.994064i	$-0.465299\pi$
$83$	9.91061	−	7.20048i	1.08783	−	0.790356i	0.979032	+	0.203708i	$0.0652993\pi$
$84$	−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	0.778757	+	0.627326i	$0.215850\pi$
$89$	−2.07551	+	6.38776i	−0.220003	+	0.677101i	−0.998760	+	0.0497752i	$0.984150\pi$
$90$		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	−0.607669	−	0.794191i	$-0.707895\pi$
$97$	3.30362	−	4.54704i	0.335431	−	0.461682i	0.943100	+	0.332509i	$0.107895\pi$
$98$	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	$0.0246727\pi$
$101$			1.55640i			0.154868i	−0.996997	+	0.0774339i	$0.975327\pi$
$102$	−1.24012	+	1.03895i	−0.122790	+	0.102871i
$103$	−2.77316	+	3.81692i	−0.273247	+	0.376092i	−0.923483	−	0.383640i	$-0.874670\pi$
$103$	−2.77316	+	3.81692i	−0.273247	+	0.376092i	0.650235	+	0.759733i	$0.274670\pi$
$104$	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	−0.393661	−	0.919256i	$-0.628791\pi$
$109$	−1.79379	+	0.582837i	−0.171814	+	0.0558256i	0.221847	+	0.975081i	$0.428791\pi$
$110$		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	−0.507281	−	0.861781i	$-0.669349\pi$
$113$	−4.37045	+	1.42005i	−0.411137	+	0.133587i	0.0961433	+	0.995367i	$0.469349\pi$
$114$	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	0.631496	−	0.775379i	$-0.282441\pi$
$127$	7.73794	+	2.51421i	0.686631	+	0.223100i	0.0551347	+	0.998479i	$0.482441\pi$
$128$	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	−0.811085	−	0.584929i	$-0.801122\pi$
$131$	−12.7817	−	17.5926i	−1.11675	−	1.53707i	−0.305661	−	0.952140i	$-0.598878\pi$
$132$	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	−0.656940	−	0.753943i	$-0.728149\pi$
$137$	−8.72303	+	2.83428i	−0.745259	+	0.242149i	−0.0883189	+	0.996092i	$0.528149\pi$
$138$	5.49738	−	21.9762i	0.467968	−	1.87074i
$139$	−13.0150	−	4.22884i	−1.10392	−	0.358685i	−0.300310	−	0.953842i	$-0.597090\pi$
$139$	−13.0150	−	4.22884i	−1.10392	−	0.358685i	−0.803610	+	0.595156i	$0.797090\pi$
$140$		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	$0.207972\pi$
$149$			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	$0.617570\pi$
$152$	−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	0.995990	+	0.0894595i	$0.0285139\pi$
$163$	3.09987	+	9.54040i	0.242800	+	0.747262i	−0.753190	+	0.657803i	$0.771486\pi$
$164$	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	0.585890	−	0.810391i	$-0.300745\pi$
$167$	−4.72830	−	6.50795i	−0.365887	−	0.503601i	−0.951777	+	0.306790i	$0.900745\pi$
$168$	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	−0.763620	−	0.645666i	$-0.776580\pi$
$173$	3.07351	−	9.45929i	0.233675	−	0.719176i	0.997294	−	0.0735104i	$-0.0234202\pi$
$174$	−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	−0.990415	−	0.138122i	$-0.955893\pi$
$179$	−7.39861	+	10.1833i	−0.552998	+	0.761136i	0.437417	+	0.899259i	$0.355893\pi$
$180$		0			0
$181$	−7.67562	−	10.5646i	−0.570524	−	0.785259i	0.422092	−	0.906553i	$-0.361296\pi$
$181$	−7.67562	−	10.5646i	−0.570524	−	0.785259i	−0.992617	+	0.121293i	$0.961296\pi$
$182$	−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	0.978057	−	0.208339i	$-0.0668058\pi$
$191$	0.889107	+	2.73639i	0.0643335	+	0.197998i	−0.913723	+	0.406337i	$0.866806\pi$
$192$	−18.2660	+	8.03099i	−1.31824	+	0.579587i
$193$		−	15.9019i		−	1.14464i	−0.820029	−	0.572322i	$-0.806043\pi$
$193$		−	15.9019i		−	1.14464i	0.820029	−	0.572322i	$-0.193957\pi$
$194$	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	0.714385	−	0.699753i	$-0.246707\pi$
$197$	3.78454	+	2.74963i	0.269637	+	0.195903i	−0.444748	+	0.895656i	$0.646707\pi$
$198$	−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	0.298315	−	0.954468i	$-0.403576\pi$
$211$	−0.310359	−	0.100842i	−0.0213660	−	0.00694223i	−0.319680	+	0.947525i	$0.603576\pi$
$212$	−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	0.659269	−	0.751907i	$-0.270866\pi$
$223$	11.2099	+	3.64231i	0.750669	+	0.243907i	0.0914002	+	0.995814i	$0.470866\pi$
$224$	−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	−0.939718	−	0.341951i	$-0.888912\pi$
$227$	0.324287	−	0.998051i	0.0215237	−	0.0662430i	0.961241	+	0.275708i	$0.0889123\pi$
$228$	20.0576	+	3.56876i	1.32835	+	0.236347i
$229$	11.8902	−	16.3654i	0.785723	−	1.08146i	−0.208904	−	0.977936i	$-0.566990\pi$
$229$	11.8902	−	16.3654i	0.785723	−	1.08146i	0.994627	−	0.103519i	$-0.0330104\pi$
$230$		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	0.918347	+	0.395777i	$0.129525\pi$
$233$	15.4318	+	21.2400i	1.01097	+	1.39148i	0.0926216	+	0.995701i	$0.470475\pi$
$234$	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	−0.999613	−	0.0278129i	$-0.991146\pi$
$239$	−2.69865	+	8.30559i	−0.174561	+	0.537244i	0.825052	+	0.565057i	$0.191146\pi$
$240$		0			0
$241$	0.110550	+	0.340238i	0.00712115	+	0.0219166i	0.954554	−	0.298038i	$-0.0963323\pi$
$241$	0.110550	+	0.340238i	0.00712115	+	0.0219166i	−0.947433	+	0.319955i	$0.896332\pi$
$242$	−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	$0.217915\pi$
$251$			20.0370i			1.26473i	−0.774672	+	0.632363i	$0.782085\pi$
$252$	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	$0.198588\pi$
$257$			18.7305i			1.16838i	−0.811617	+	0.584190i	$0.801412\pi$
$258$	−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	0.217331	−	0.976098i	$-0.430265\pi$
$263$	15.6804	−	5.09486i	0.966892	−	0.314162i	0.749561	+	0.661936i	$0.230265\pi$
$264$	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	0.806399	−	0.591372i	$-0.201414\pi$
$269$	−0.0856192	−	0.117845i	−0.00522029	−	0.00718512i	−0.811619	+	0.584187i	$0.801414\pi$
$270$		0			0
$271$	−12.4072	−	9.01437i	−0.753684	−	0.547584i	0.143282	−	0.989682i	$-0.454234\pi$
$271$	−12.4072	−	9.01437i	−0.753684	−	0.547584i	−0.896967	+	0.442098i	$0.854234\pi$
$272$	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	0.552336	+	0.833622i	$0.313737\pi$
$277$	−6.39942	+	19.6954i	−0.384504	+	1.18338i	−0.936840	+	0.349759i	$0.886263\pi$
$278$	−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	−0.813153	−	0.582049i	$-0.802251\pi$
$281$	−8.56374	+	6.22192i	−0.510870	+	0.371169i	0.302284	+	0.953218i	$0.402251\pi$
$282$	9.27677	+	5.80677i	0.552423	+	0.345788i
$283$	16.6426	−	12.0915i	0.989298	−	0.718767i	0.0295305	−	0.999564i	$-0.490599\pi$
$283$	16.6426	−	12.0915i	0.989298	−	0.718767i	0.959767	+	0.280797i	$0.0905988\pi$
$284$	−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	0.474335	+	0.880344i	$0.342689\pi$
$311$	−7.52782	+	23.1683i	−0.426864	+	1.31375i	−0.901198	+	0.433407i	$0.857311\pi$
$312$	−6.96884	−	33.1648i	−0.394533	−	1.87759i
$313$	−17.7993	+	5.78333i	−1.00607	+	0.326893i	−0.765290	−	0.643686i	$-0.777404\pi$
$313$	−17.7993	+	5.78333i	−1.00607	+	0.326893i	−0.240784	+	0.970579i	$0.577404\pi$
$314$	−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	0.297175	−	0.954823i	$-0.403955\pi$
$317$	23.0942	−	16.7789i	1.29710	−	0.942397i	0.999923	+	0.0124261i	$0.00395545\pi$
$318$	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	0.747323	−	0.664461i	$-0.231339\pi$
$331$	−2.10228	−	2.89354i	−0.115552	−	0.159043i	−0.862875	+	0.505417i	$0.831339\pi$
$332$	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	−0.0430517	−	0.999073i	$-0.513708\pi$
$337$	9.35059	−	3.03819i	0.509359	−	0.165501i	0.552411	+	0.833572i	$0.313708\pi$
$338$	−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	0.189372	−	0.981905i	$-0.439355\pi$
$347$	−12.7780	−	9.28373i	−0.685957	−	0.498377i	−0.875329	+	0.483529i	$0.839355\pi$
$348$	−6.18653	−	44.5201i	−0.331633	−	2.38653i
$349$		−	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
$352$	−0.302096	−	9.73213i	−0.0161017	−	0.518724i
$353$	6.60894	−	9.09643i	0.351759	−	0.484154i	−0.596071	−	0.802932i	$-0.703272\pi$
$353$	6.60894	−	9.09643i	0.351759	−	0.484154i	0.947830	+	0.318778i	$0.103272\pi$
$354$	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	0.833167	−	0.553021i	$-0.186525\pi$
$359$	−3.14405	−	9.67639i	−0.165937	−	0.510700i	−0.999104	+	0.0423204i	$0.986525\pi$
$360$		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	0.953543	−	0.301257i	$-0.0974064\pi$
$367$	7.13356	+	9.81851i	0.372369	+	0.512522i	−0.581174	+	0.813779i	$0.697406\pi$
$368$	−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	−0.873591	−	0.486661i	$-0.838215\pi$
$373$	2.30235	−	7.08589i	0.119211	−	0.366894i	0.992802	+	0.119767i	$0.0382148\pi$
$374$	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	−0.703277	−	0.710916i	$-0.748281\pi$
$379$	3.70220	−	5.09564i	0.190169	−	0.261746i	0.893446	+	0.449171i	$0.148281\pi$
$380$		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	0.981473	+	0.191601i	$0.0613681\pi$
$383$	16.8385	+	23.1761i	0.860405	+	1.18425i	−0.121068	+	0.992644i	$0.538632\pi$
$384$	−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	0.325713	−	0.945469i	$-0.394396\pi$
$389$	0.660483	+	0.214604i	0.0334878	+	0.0108808i	−0.292225	+	0.956350i	$0.594396\pi$
$390$		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	0.925724	−	0.378200i	$-0.123457\pi$
$397$	16.9780	+	12.3352i	0.852099	+	0.619086i	−0.0736250	+	0.997286i	$0.523457\pi$
$398$	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	0.686611	+	0.727025i	$0.259097\pi$
$409$	11.2943	+	34.7602i	0.558465	+	1.71878i	−0.128146	+	0.991755i	$0.540903\pi$
$410$		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	0.634688	−	0.772768i	$-0.281128\pi$
$419$	−6.06690	−	8.35037i	−0.296387	−	0.407942i	−0.931076	+	0.364826i	$0.881128\pi$
$420$		0			0
$421$	7.12906	−	9.81232i	0.347449	−	0.478223i	−0.599149	−	0.800637i	$-0.704494\pi$
$421$	7.12906	−	9.81232i	0.347449	−	0.478223i	0.946599	+	0.322414i	$0.104494\pi$
$422$	−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	−0.994104	−	0.108432i	$-0.965417\pi$
$431$	−24.8747	+	18.0726i	−1.19817	+	0.870525i	−0.204070	+	0.978956i	$0.565417\pi$
$432$	−1.36292	+	1.73335i	−0.0655734	+	0.0833959i
$433$	−2.65013	−	3.64760i	−0.127357	−	0.175292i	0.740577	−	0.671972i	$-0.234552\pi$
$433$	−2.65013	−	3.64760i	−0.127357	−	0.175292i	−0.867934	+	0.496680i	$0.834552\pi$
$434$	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	−0.823839	−	0.566824i	$-0.808172\pi$
$439$	3.68407	−	11.3384i	0.175831	−	0.541153i	0.999670	+	0.0256706i	$0.00817212\pi$
$440$		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	$-0.705471\pi$
$457$		−	34.1526i		−	1.59759i	0.601604	−	0.798795i	$-0.294529\pi$
$458$	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	0.00630961	−	0.999980i	$-0.497992\pi$
$461$	−12.3750	−	4.02087i	−0.576359	−	0.187271i	−0.582669	+	0.812710i	$0.697992\pi$
$462$	−0.653290	−	0.163421i	−0.0303938	−	0.00760305i
$463$	0.474013	−	0.154016i	0.0220292	−	0.00715774i	−0.297982	−	0.954572i	$-0.596313\pi$
$463$	0.474013	−	0.154016i	0.0220292	−	0.00715774i	0.320011	+	0.947414i	$0.396313\pi$
$464$	−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	−0.966289	−	0.257459i	$-0.917115\pi$
$467$	−22.0431	+	16.0152i	−1.02003	+	0.741096i	−0.0537419	+	0.998555i	$0.517115\pi$
$468$	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	0.976747	−	0.214396i	$-0.0687784\pi$
$479$	23.5204	+	17.0886i	1.07468	+	0.780797i	0.0979285	+	0.995193i	$0.468778\pi$
$480$		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	0.311584	−	0.950219i	$-0.399140\pi$
$487$	24.7645	−	8.04647i	1.12219	−	0.364620i	0.810601	+	0.585598i	$0.199140\pi$
$488$	−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	−0.785414	−	0.618971i	$-0.787550\pi$
$491$	−23.4217	+	7.61016i	−1.05700	+	0.343442i	−0.271591	+	0.962413i	$0.587550\pi$
$492$	−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	$0.135601\pi$
$499$			18.4619i			0.826469i	−0.910625	+	0.413234i	$0.864399\pi$
$500$		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	−0.998077	−	0.0619786i	$-0.980259\pi$
$503$	−14.1453	+	19.4694i	−0.630709	+	0.868097i	0.367368	+	0.930076i	$0.380259\pi$
$504$	−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	−0.330015	−	0.943976i	$-0.607054\pi$
$509$	−0.950881	+	0.308960i	−0.0421471	+	0.0136944i	0.287868	+	0.957670i	$0.407054\pi$
$510$		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	0.261836	−	0.965112i	$-0.415672\pi$
$521$	−13.1276	−	9.53774i	−0.575129	−	0.417856i	−0.836965	+	0.547257i	$0.815672\pi$
$522$	15.3461	+	38.0678i	0.671680	+	1.66618i
$523$	−0.338728	+	1.04250i	−0.0148115	+	0.0455852i	−0.958189	−	0.286136i	$-0.907629\pi$
$523$	−0.338728	+	1.04250i	−0.0148115	+	0.0455852i	0.943378	+	0.331721i	$0.107629\pi$
$524$	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	−0.755389	−	0.655277i	$-0.772552\pi$
$541$	−22.8256	+	7.41649i	−0.981349	+	0.318860i	−0.225961	+	0.974136i	$0.572552\pi$
$542$	−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	0.0499871	−	0.998750i	$-0.484082\pi$
$547$	−20.6852	−	15.0286i	−0.884434	−	0.642579i	−0.934421	+	0.356171i	$0.884082\pi$
$548$	−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	−0.926381	−	0.376588i	$-0.877097\pi$
$563$	−9.45014	−	29.0845i	−0.398276	−	1.22577i	0.528105	−	0.849179i	$-0.322903\pi$
$564$	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	−0.577004	−	0.816741i	$-0.695778\pi$
$569$	0.511882	−	0.371904i	0.0214592	−	0.0155910i	0.598463	+	0.801150i	$0.295778\pi$
$570$		0			0
$571$	2.91121	−	4.00694i	0.121830	−	0.167685i	−0.743746	−	0.668463i	$-0.766953\pi$
$571$	2.91121	−	4.00694i	0.121830	−	0.167685i	0.865576	+	0.500778i	$0.166953\pi$
$572$	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	0.608984	−	0.793183i	$-0.291578\pi$
$577$	15.2638	+	4.95951i	0.635440	+	0.206467i	0.0264569	+	0.999650i	$0.491578\pi$
$578$	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	0.982079	+	0.188468i	$0.0603521\pi$
$587$	7.22818	+	22.2461i	0.298339	+	0.918193i	−0.683740	+	0.729725i	$0.739648\pi$
$588$	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	$-0.950471\pi$
$593$		−	7.54773i		−	0.309948i	0.987919	−	0.154974i	$-0.0495294\pi$
$594$	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	$-0.816111\pi$
$607$		−	26.9091i		−	1.09221i	0.837718	−	0.546103i	$-0.183889\pi$
$608$	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	0.989856	−	0.142074i	$-0.0453772\pi$
$613$	2.61296	+	8.04187i	0.105537	+	0.324808i	−0.884319	+	0.466882i	$0.845377\pi$
$614$	−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	0.973562	−	0.228422i	$-0.0733567\pi$
$617$	11.3137	+	15.5720i	0.455472	+	0.626904i	−0.518090	+	0.855326i	$0.673357\pi$
$618$	14.1062	+	8.82976i	0.567436	+	0.355185i
$619$	19.2261	+	26.4625i	0.772763	+	1.06362i	0.996044	+	0.0888631i	$0.0283233\pi$
$619$	19.2261	+	26.4625i	0.772763	+	1.06362i	−0.223281	+	0.974754i	$0.571677\pi$
$620$		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	0.177756	−	0.984075i	$-0.443116\pi$
$631$	29.3548	−	21.3275i	1.16860	−	0.849035i	0.990840	+	0.135040i	$0.0431162\pi$
$632$	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	0.950024	−	0.312176i	$-0.101058\pi$
$641$	−0.0519999	−	0.160039i	−0.00205387	−	0.00632117i	−0.952078	+	0.305855i	$0.901058\pi$
$642$	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	−0.995676	−	0.0928983i	$-0.970387\pi$
$647$	−15.2526	+	20.9935i	−0.599643	+	0.825338i	0.396032	+	0.918237i	$0.370387\pi$
$648$	−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	0.840286	−	0.542143i	$-0.182387\pi$
$653$	14.9322	+	10.8488i	0.584340	+	0.424548i	−0.255946	+	0.966691i	$0.582387\pi$
$654$	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	−0.462520	−	0.886609i	$-0.653055\pi$
$659$	−8.10100	+	2.63217i	−0.315570	+	0.102535i	0.146950	+	0.989144i	$0.453055\pi$
$660$		0			0
$661$	−38.1202	−	12.3860i	−1.48270	−	0.481760i	−0.547785	−	0.836619i	$-0.684529\pi$
$661$	−38.1202	−	12.3860i	−1.48270	−	0.481760i	−0.934920	+	0.354859i	$0.884529\pi$
$662$	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	−0.671367	−	0.741125i	$-0.734292\pi$
$673$	−42.8082	−	13.9092i	−1.65014	−	0.536162i	−0.978770	+	0.204964i	$0.934292\pi$
$674$	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	−0.208808	−	0.977957i	$-0.566958\pi$
$677$	13.9190	−	42.8382i	0.534950	−	1.64641i	0.743758	−	0.668450i	$-0.233042\pi$
$678$	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	−0.695112	−	0.718901i	$-0.744645\pi$
$683$	−5.91153	+	4.29498i	−0.226199	+	0.164343i	0.468914	+	0.883244i	$0.344645\pi$
$684$	−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	0.398455	−	0.917188i	$-0.369546\pi$
$691$	33.1194	−	10.7611i	1.25992	−	0.409373i	0.861467	+	0.507814i	$0.169546\pi$
$692$	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	$0.138803\pi$
$701$			22.3659i			0.844750i	−0.906421	+	0.422375i	$0.861197\pi$
$702$	−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	0.0322662	−	0.999479i	$-0.489728\pi$
$709$	17.1971	−	5.58767i	0.645849	−	0.209849i	0.613583	+	0.789630i	$0.289728\pi$
$710$		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	−0.992995	−	0.118158i	$-0.962301\pi$
$719$	−31.8411	+	23.1339i	−1.18747	+	0.862749i	−0.194477	+	0.980907i	$0.562301\pi$
$720$		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	0.603401	−	0.797438i	$-0.293812\pi$
$727$	16.7936	+	5.45658i	0.622841	+	0.202373i	0.0194399	+	0.999811i	$0.493812\pi$
$728$	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	−0.445382	−	0.895341i	$-0.646932\pi$
$733$	7.26956	−	5.28165i	0.268507	−	0.195082i	0.713889	+	0.700259i	$0.246932\pi$
$734$	−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	−0.0846720	−	0.996409i	$-0.526984\pi$
$739$	−20.0852	−	6.52609i	−0.738848	−	0.240066i	−0.654176	+	0.756343i	$0.726984\pi$
$740$		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	$0.0498868\pi$
$743$			8.50903i			0.312166i	−0.987744	+	0.156083i	$0.950113\pi$
$744$	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	0.779146	+	0.626842i	$0.215653\pi$
$761$	−6.05917	+	18.6482i	−0.219645	+	0.675997i	−0.998791	+	0.0491552i	$0.984347\pi$
$762$	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	−0.276936	−	0.960888i	$-0.589319\pi$
$769$	15.2893	−	11.1083i	0.551345	−	0.400576i	0.828281	+	0.560313i	$0.189319\pi$
$770$		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	−0.984269	−	0.176677i	$-0.943465\pi$
$773$	−2.33908	+	7.19893i	−0.0841307	+	0.258928i	0.900138	+	0.435604i	$0.143465\pi$
$774$	−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	0.877903	+	0.478839i	$0.158942\pi$
$787$	12.5994	+	38.7769i	0.449119	+	1.38225i	−0.428784	+	0.903407i	$0.641058\pi$
$788$	−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	0.656507	−	0.754320i	$-0.272033\pi$
$797$	4.00819	+	2.91212i	0.141977	+	0.103153i	−0.514529	+	0.857473i	$0.672033\pi$
$798$	−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	0.991302	+	0.131603i	$0.0420126\pi$
$809$	7.58506	+	23.3444i	0.266676	+	0.820746i	−0.724626	+	0.689142i	$0.757987\pi$
$810$		0			0
$811$	0.736311	+	0.239242i	0.0258554	+	0.00840092i	0.321916	−	0.946768i	$-0.395673\pi$
$811$	0.736311	+	0.239242i	0.0258554	+	0.00840092i	−0.296061	+	0.955169i	$0.595673\pi$
$812$	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	−0.729935	−	0.683516i	$-0.760450\pi$
$821$	4.17446	−	5.74566i	0.145690	−	0.200525i	0.875625	+	0.482992i	$0.160450\pi$
$822$	12.0962	+	30.0060i	0.421902	+	1.04658i
$823$	−7.47765	−	2.42963i	−0.260654	−	0.0846917i	0.175775	−	0.984430i	$-0.443757\pi$
$823$	−7.47765	−	2.42963i	−0.260654	−	0.0846917i	−0.436429	+	0.899739i	$0.643757\pi$
$824$	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	−0.967217	−	0.253953i	$-0.918269\pi$
$827$	−1.01952	+	3.13777i	−0.0354523	+	0.109111i	0.931764	+	0.363064i	$0.118269\pi$
$828$	−40.7326	−	7.24738i	−1.41556	−	0.251864i
$829$	−19.0835	+	26.2662i	−0.662798	+	0.912263i	−0.999570	−	0.0293232i	$-0.990665\pi$
$829$	−19.0835	+	26.2662i	−0.662798	+	0.912263i	0.336772	+	0.941586i	$0.390665\pi$
$830$		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	−0.877219	−	0.480091i	$-0.840604\pi$
$839$	3.32108	−	10.2212i	0.114656	−	0.352876i	0.991875	+	0.127215i	$0.0406037\pi$
$840$		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	0.219528	−	0.975606i	$-0.429548\pi$
$853$	−18.7063	−	13.5909i	−0.640491	−	0.465344i	−0.860019	+	0.510262i	$0.829548\pi$
$854$	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	$-0.912492\pi$
$857$		−	15.8941i		−	0.542932i	0.962448	−	0.271466i	$-0.0875084\pi$
$858$	−29.0962	+	2.01194i	−0.993327	+	0.0686866i
$859$	−3.46524	+	1.12593i	−0.118233	+	0.0384161i	−0.367536	−	0.930009i	$-0.619798\pi$
$859$	−3.46524	+	1.12593i	−0.118233	+	0.0384161i	0.249303	+	0.968425i	$0.419798\pi$
$860$		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	−0.894968	−	0.446131i	$-0.852802\pi$
$863$	−39.8580	+	12.9507i	−1.35678	+	0.440845i	−0.461815	+	0.886976i	$0.652802\pi$
$864$	−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	0.683516	+	0.729936i	$0.260450\pi$
$877$	−8.84000	+	27.2067i	−0.298505	+	0.918705i	−0.982021	+	0.188770i	$0.939550\pi$
$878$	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	−0.293718	−	0.955892i	$-0.594893\pi$
$881$	15.5718	−	11.3135i	0.524626	−	0.381163i	0.818344	+	0.574729i	$0.194893\pi$
$882$	−16.8884	+	26.9806i	−0.568663	+	0.908484i
$883$	−10.5069	+	7.63372i	−0.353586	+	0.256895i	−0.750372	−	0.661016i	$-0.770126\pi$
$883$	−10.5069	+	7.63372i	−0.353586	+	0.256895i	0.396786	+	0.917911i	$0.370126\pi$
$884$	−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	−0.566205	−	0.824264i	$-0.691589\pi$
$887$	−16.0762	+	5.22346i	−0.539785	+	0.175387i	0.0264205	+	0.999651i	$0.491589\pi$
$888$	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	−0.990833	−	0.135091i	$-0.956867\pi$
$911$	−3.31491	+	10.2022i	−0.109828	+	0.338015i	0.881005	+	0.473106i	$0.156867\pi$
$912$	−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	−0.973896	−	0.226995i	$-0.927110\pi$
$919$	−32.1024	+	23.3238i	−1.05896	+	0.769380i	−0.0850654	+	0.996375i	$0.527110\pi$
$920$		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	0.833042	−	0.553210i	$-0.186597\pi$
$929$	17.2005	+	12.4969i	0.564331	+	0.410011i	−0.268710	+	0.963221i	$0.586597\pi$
$930$		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	−0.735312	−	0.677729i	$-0.762964\pi$
$937$	−28.5238	+	9.26796i	−0.931833	+	0.302771i	−0.196521	+	0.980500i	$0.562964\pi$
$938$	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	0.0481695	−	0.998839i	$-0.484661\pi$
$941$	20.6829	−	6.72027i	0.674242	−	0.219075i	0.626073	+	0.779765i	$0.284661\pi$
$942$	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	0.232899	−	0.972501i	$-0.425179\pi$
$947$	−19.0805	−	13.8628i	−0.620034	−	0.450481i	−0.852934	+	0.522020i	$0.825179\pi$
$948$	−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	−0.987147	−	0.159817i	$-0.948909\pi$
$953$	−16.3647	+	22.5241i	−0.530106	+	0.729629i	0.457040	+	0.889446i	$0.348909\pi$
$954$	−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	−0.722707	−	0.691154i	$-0.757103\pi$
$967$	−35.9696	−	49.5079i	−1.15671	−	1.59207i	−0.433998	−	0.900914i	$-0.642897\pi$
$968$	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	−0.357364	−	0.933965i	$-0.616324\pi$
$971$	19.9841	−	27.5058i	0.641321	−	0.882703i	0.998685	+	0.0512621i	$0.0163244\pi$
$972$	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	−0.644702	−	0.764434i	$-0.723018\pi$
$977$	−50.4988	−	16.4081i	−1.61560	−	0.524940i	−0.970898	+	0.239494i	$0.923018\pi$
$978$	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	0.416472	−	0.909149i	$-0.363266\pi$
$983$	−18.0867	−	24.8942i	−0.576877	−	0.794003i	−0.993349	+	0.115146i	$0.963266\pi$
$984$	−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	0.870597	−	0.491997i	$-0.163733\pi$
$991$	−3.86953	−	11.9092i	−0.122920	−	0.378308i	−0.993516	+	0.113690i	$0.963733\pi$
$992$	−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	0.734657	−	0.678439i	$-0.237343\pi$
$997$	9.99182	+	7.25948i	0.316444	+	0.229910i	−0.418212	+	0.908349i	$0.637343\pi$
$998$	−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.149.20		112
5.2	odd	4		1000.2.t.b.101.14		224
5.3	odd	4		1000.2.t.b.101.43		224
5.4	even	2		200.2.o.a.29.9	yes	112
8.5	even	2	inner	1000.2.o.a.149.27		112
20.19	odd	2		800.2.be.a.529.5		112
25.6	even	5		200.2.o.a.69.2	yes	112
25.8	odd	20		1000.2.t.b.901.27		224
25.17	odd	20		1000.2.t.b.901.30		224
25.19	even	10	inner	1000.2.o.a.349.27		112
40.13	odd	4		1000.2.t.b.101.27		224
40.19	odd	2		800.2.be.a.529.24		112
40.29	even	2		200.2.o.a.29.2	✓	112
40.37	odd	4		1000.2.t.b.101.30		224
100.31	odd	10		800.2.be.a.369.24		112
200.69	even	10	inner	1000.2.o.a.349.20		112
200.117	odd	20		1000.2.t.b.901.14		224
200.131	odd	10		800.2.be.a.369.5		112
200.133	odd	20		1000.2.t.b.901.43		224
200.181	even	10		200.2.o.a.69.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.2	✓	112	40.29	even	2
200.2.o.a.29.9	yes	112	5.4	even	2
200.2.o.a.69.2	yes	112	25.6	even	5
200.2.o.a.69.9	yes	112	200.181	even	10
800.2.be.a.369.5		112	200.131	odd	10
800.2.be.a.369.24		112	100.31	odd	10
800.2.be.a.529.5		112	20.19	odd	2
800.2.be.a.529.24		112	40.19	odd	2
1000.2.o.a.149.20		112	1.1	even	1	trivial
1000.2.o.a.149.27		112	8.5	even	2	inner
1000.2.o.a.349.20		112	200.69	even	10	inner
1000.2.o.a.349.27		112	25.19	even	10	inner
1000.2.t.b.101.14		224	5.2	odd	4
1000.2.t.b.101.27		224	40.13	odd	4
1000.2.t.b.101.30		224	40.37	odd	4
1000.2.t.b.101.43		224	5.3	odd	4
1000.2.t.b.901.14		224	200.117	odd	20
1000.2.t.b.901.27		224	25.8	odd	20
1000.2.t.b.901.30		224	25.17	odd	20
1000.2.t.b.901.43		224	200.133	odd	20

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

Related objects

Downloads

Learn more