LMFDB - Embedded newform 1000.2.o.a.349.10

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			349.10
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.658957 + 1.25131i) q^{2} +(2.03813 - 1.48079i) q^{3} +(-1.13155 - 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} +3.58786i q^{7} +(2.80920 - 0.329223i) q^{8} +(1.03418 - 3.18289i) q^{9} +O(q^{10})$	\(q+(-0.658957 + 1.25131i) q^{2} +(2.03813 - 1.48079i) q^{3} +(-1.13155 - 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} +3.58786i q^{7} +(2.80920 - 0.329223i) q^{8} +(1.03418 - 3.18289i) q^{9} +(2.49567 - 0.810891i) q^{11} +(-4.74824 - 1.68553i) q^{12} +(-2.11444 + 6.50757i) q^{13} +(-4.48952 - 2.36424i) q^{14} +(-1.43918 + 3.73212i) q^{16} +(1.14335 - 1.57369i) q^{17} +(3.30130 + 3.39148i) q^{18} +(-3.00859 + 4.14097i) q^{19} +(5.31285 + 7.31251i) q^{21} +(-0.629861 + 3.65719i) q^{22} +(0.737902 - 0.239759i) q^{23} +(5.23800 - 4.83083i) q^{24} +(-6.74966 - 6.93403i) q^{26} +(-0.269899 - 0.830663i) q^{27} +(5.91680 - 4.05985i) q^{28} +(3.28631 + 4.52322i) q^{29} +(1.72253 + 1.25149i) q^{31} +(-3.72168 - 4.26017i) q^{32} +(3.88573 - 5.34825i) q^{33} +(1.21576 + 2.46769i) q^{34} +(-6.41920 + 1.89612i) q^{36} +(2.73986 - 8.43241i) q^{37} +(-3.19910 - 6.49339i) q^{38} +(5.32683 + 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(-12.6512 + 1.82939i) q^{42} -0.652170 q^{43} +(-4.16123 - 3.19808i) q^{44} +(-0.186233 + 1.08133i) q^{46} +(-0.541317 - 0.745059i) q^{47} +(2.59324 + 9.73767i) q^{48} -5.87273 q^{49} -4.90045i q^{51} +(13.1244 - 3.87669i) q^{52} +(-1.48529 + 1.07913i) q^{53} +(1.21727 + 0.209644i) q^{54} +(1.18121 + 10.0790i) q^{56} +12.8949i q^{57} +(-7.82548 + 1.13159i) q^{58} +(3.74706 + 1.21749i) q^{59} +(-6.21266 + 2.01862i) q^{61} +(-2.70108 + 1.33074i) q^{62} +(11.4198 + 3.71051i) q^{63} +(7.78322 - 1.84971i) q^{64} +(4.13179 + 8.38651i) q^{66} +(-3.97847 - 2.89052i) q^{67} +(-3.88897 - 0.104813i) q^{68} +(1.14891 - 1.58133i) q^{69} +(4.48762 - 3.26045i) q^{71} +(1.85735 - 9.28187i) q^{72} +(14.1026 - 4.58222i) q^{73} +(8.74611 + 8.98500i) q^{74} +(10.2333 + 0.275801i) q^{76} +(2.90936 + 8.95410i) q^{77} +(-24.0245 - 4.13762i) q^{78} +(7.65406 - 5.56100i) q^{79} +(6.34247 + 4.60807i) q^{81} +(3.58506 + 3.68298i) q^{82} +(6.50869 + 4.72884i) q^{83} +(6.04743 - 17.0360i) q^{84} +(0.429752 - 0.816067i) q^{86} +(13.3958 + 4.35257i) q^{87} +(6.74386 - 3.09959i) q^{88} +(3.35636 + 10.3298i) q^{89} +(-23.3483 - 7.58631i) q^{91} +(-1.23036 - 0.945588i) q^{92} +5.36393 q^{93} +(1.28900 - 0.186393i) q^{94} +(-13.8937 - 3.17175i) q^{96} +(3.31560 + 4.56353i) q^{97} +(3.86988 - 7.34861i) q^{98} -8.78205i 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 $

$2$	−0.658957	+	1.25131i	−0.465953	+	0.884810i
$2$	−0.658957	+	1.25131i	−0.465953	+	0.884810i
$3$	2.03813	−	1.48079i	1.17671	−	0.854932i	0.184916	−	0.982754i	$-0.440799\pi$
$3$	2.03813	−	1.48079i	1.17671	−	0.854932i	0.991797	+	0.127822i	$0.0407986\pi$
$4$	−1.13155	−	1.64912i	−0.565776	−	0.824559i
$5$		0			0
$5$		0			0
$6$	0.509884	+	3.52610i	0.208159	+	1.43953i
$7$			3.58786i			1.35608i	0.735024	+	0.678042i	$0.237171\pi$
$7$			3.58786i			1.35608i	−0.735024	+	0.678042i	$0.762829\pi$
$8$	2.80920	−	0.329223i	0.993203	−	0.116398i
$9$	1.03418	−	3.18289i	0.344728	−	1.06096i
$10$		0			0
$11$	2.49567	−	0.810891i	0.752472	−	0.244493i	0.0924272	−	0.995719i	$-0.470537\pi$
$11$	2.49567	−	0.810891i	0.752472	−	0.244493i	0.660044	+	0.751227i	$0.270537\pi$
$12$	−4.74824	−	1.68553i	−1.37070	−	0.486570i
$13$	−2.11444	+	6.50757i	−0.586440	+	1.80488i	0.00697033	+	0.999976i	$0.497781\pi$
$13$	−2.11444	+	6.50757i	−0.586440	+	1.80488i	−0.593410	+	0.804900i	$0.702219\pi$
$14$	−4.48952	−	2.36424i	−1.19988	−	0.631871i
$15$		0			0
$16$	−1.43918	+	3.73212i	−0.359796	+	0.933031i
$17$	1.14335	−	1.57369i	0.277304	−	0.381677i	−0.647534	−	0.762036i	$-0.724200\pi$
$17$	1.14335	−	1.57369i	0.277304	−	0.381677i	0.924839	+	0.380360i	$0.124200\pi$
$18$	3.30130	+	3.39148i	0.778124	+	0.799378i
$19$	−3.00859	+	4.14097i	−0.690218	+	0.950003i	−1.00000		0.000804663i	$-0.999744\pi$
$19$	−3.00859	+	4.14097i	−0.690218	+	0.950003i	0.309782	+	0.950808i	$0.399744\pi$
$20$		0			0
$21$	5.31285	+	7.31251i	1.15936	+	1.59572i
$22$	−0.629861	+	3.65719i	−0.134287	+	0.779716i
$23$	0.737902	−	0.239759i	0.153863	−	0.0499932i	−0.231073	−	0.972936i	$-0.574224\pi$
$23$	0.737902	−	0.239759i	0.153863	−	0.0499932i	0.384936	+	0.922943i	$0.374224\pi$
$24$	5.23800	−	4.83083i	1.06920	−	0.986088i
$25$		0			0
$26$	−6.74966	−	6.93403i	−1.32372	−	1.35987i
$27$	−0.269899	−	0.830663i	−0.0519421	−	0.159861i
$28$	5.91680	−	4.05985i	1.11817	−	0.767239i
$29$	3.28631	+	4.52322i	0.610252	+	0.839940i	0.996598	−	0.0824137i	$-0.0262629\pi$
$29$	3.28631	+	4.52322i	0.610252	+	0.839940i	−0.386346	+	0.922354i	$0.626263\pi$
$30$		0			0
$31$	1.72253	+	1.25149i	0.309376	+	0.224775i	0.731629	−	0.681704i	$-0.238761\pi$
$31$	1.72253	+	1.25149i	0.309376	+	0.224775i	−0.422253	+	0.906478i	$0.638761\pi$
$32$	−3.72168	−	4.26017i	−0.657907	−	0.753099i
$33$	3.88573	−	5.34825i	0.676419	−	0.931010i
$34$	1.21576	+	2.46769i	0.208500	+	0.423205i
$35$		0			0
$36$	−6.41920	+	1.89612i	−1.06987	+	0.316019i
$37$	2.73986	−	8.43241i	0.450430	−	1.38628i	−0.425988	−	0.904729i	$-0.640074\pi$
$37$	2.73986	−	8.43241i	0.450430	−	1.38628i	0.876418	−	0.481551i	$-0.159926\pi$
$38$	−3.19910	−	6.49339i	−0.518963	−	1.05337i
$39$	5.32683	+	16.3943i	0.852975	+	2.62519i
$40$		0			0
$41$	1.12308	−	3.45647i	0.175395	−	0.539811i	−0.824256	−	0.566217i	$-0.808406\pi$
$41$	1.12308	−	3.45647i	0.175395	−	0.539811i	0.999651	+	0.0264065i	$0.00840642\pi$
$42$	−12.6512	+	1.82939i	−1.95212	+	0.282281i
$43$	−0.652170			−0.0994550			−0.0497275	−	0.998763i	$-0.515835\pi$
$43$	−0.652170			−0.0994550			−0.0497275	+	0.998763i	$0.515835\pi$
$44$	−4.16123	−	3.19808i	−0.627329	−	0.482129i
$45$		0			0
$46$	−0.186233	+	1.08133i	−0.0274585	+	0.159434i
$47$	−0.541317	−	0.745059i	−0.0789592	−	0.108678i	0.767710	−	0.640797i	$-0.221396\pi$
$47$	−0.541317	−	0.745059i	−0.0789592	−	0.108678i	−0.846670	+	0.532119i	$0.821396\pi$
$48$	2.59324	+	9.73767i	0.374302	+	1.40551i
$49$	−5.87273			−0.838962
$50$		0			0
$51$		−	4.90045i		−	0.686201i
$52$	13.1244	−	3.87669i	1.82002	−	0.537601i
$53$	−1.48529	+	1.07913i	−0.204020	+	0.148229i	−0.685104	−	0.728445i	$-0.740243\pi$
$53$	−1.48529	+	1.07913i	−0.204020	+	0.148229i	0.481084	+	0.876675i	$0.340243\pi$
$54$	1.21727	+	0.209644i	0.165649	+	0.0285290i
$55$		0			0
$56$	1.18121	+	10.0790i	0.157845	+	1.34687i
$57$			12.8949i			1.70797i
$58$	−7.82548	+	1.13159i	−1.02754	+	0.148584i
$59$	3.74706	+	1.21749i	0.487826	+	0.158504i	0.542594	−	0.839995i	$-0.317442\pi$
$59$	3.74706	+	1.21749i	0.487826	+	0.158504i	−0.0547685	+	0.998499i	$0.517442\pi$
$60$		0			0
$61$	−6.21266	+	2.01862i	−0.795449	+	0.258457i	−0.678423	−	0.734672i	$-0.737336\pi$
$61$	−6.21266	+	2.01862i	−0.795449	+	0.258457i	−0.117027	+	0.993129i	$0.537336\pi$
$62$	−2.70108	+	1.33074i	−0.343037	+	0.169004i
$63$	11.4198	+	3.71051i	1.43876	+	0.467480i
$64$	7.78322	−	1.84971i	0.972903	−	0.231214i
$65$		0			0
$66$	4.13179	+	8.38651i	0.508588	+	1.03231i
$67$	−3.97847	−	2.89052i	−0.486047	−	0.353134i	0.317615	−	0.948220i	$-0.397118\pi$
$67$	−3.97847	−	2.89052i	−0.486047	−	0.353134i	−0.803662	+	0.595086i	$0.797118\pi$
$68$	−3.88897	−	0.104813i	−0.471607	−	0.0127104i
$69$	1.14891	−	1.58133i	0.138312	−	0.190370i
$70$		0			0
$71$	4.48762	−	3.26045i	0.532582	−	0.386944i	−0.288740	−	0.957407i	$-0.593236\pi$
$71$	4.48762	−	3.26045i	0.532582	−	0.386944i	0.821323	+	0.570464i	$0.193236\pi$
$72$	1.85735	−	9.28187i	0.218891	−	1.09388i
$73$	14.1026	−	4.58222i	1.65059	−	0.536309i	0.671721	−	0.740804i	$-0.265555\pi$
$73$	14.1026	−	4.58222i	1.65059	−	0.536309i	0.978868	+	0.204496i	$0.0655554\pi$
$74$	8.74611	+	8.98500i	1.01671	+	1.04449i
$75$		0			0
$76$	10.2333	+	0.275801i	1.17384	+	0.0316365i
$77$	2.90936	+	8.95410i	0.331553	+	1.02041i
$78$	−24.0245	−	4.13762i	−2.72024	−	0.468493i
$79$	7.65406	−	5.56100i	0.861148	−	0.625661i	−0.0670487	−	0.997750i	$-0.521358\pi$
$79$	7.65406	−	5.56100i	0.861148	−	0.625661i	0.928197	+	0.372089i	$0.121358\pi$
$80$		0			0
$81$	6.34247	+	4.60807i	0.704719	+	0.512008i
$82$	3.58506	+	3.68298i	0.395904	+	0.406718i
$83$	6.50869	+	4.72884i	0.714422	+	0.519058i	0.884597	−	0.466356i	$-0.154433\pi$
$83$	6.50869	+	4.72884i	0.714422	+	0.519058i	−0.170176	+	0.985414i	$0.554433\pi$
$84$	6.04743	−	17.0360i	0.659829	−	1.85878i
$85$		0			0
$86$	0.429752	−	0.816067i	0.0463414	−	0.0879988i
$87$	13.3958	+	4.35257i	1.43618	+	0.466645i
$88$	6.74386	−	3.09959i	0.718898	−	0.330417i
$89$	3.35636	+	10.3298i	0.355773	+	1.09496i	0.955560	+	0.294797i	$0.0952521\pi$
$89$	3.35636	+	10.3298i	0.355773	+	1.09496i	−0.599787	+	0.800160i	$0.704748\pi$
$90$		0			0
$91$	−23.3483	−	7.58631i	−2.44756	−	0.795261i
$92$	−1.23036	−	0.945588i	−0.128274	−	0.0985843i
$93$	5.36393			0.556213
$94$	1.28900	−	0.186393i	0.132951	−	0.0192250i
$95$		0			0
$96$	−13.8937	−	3.17175i	−1.41802	−	0.323716i
$97$	3.31560	+	4.56353i	0.336648	+	0.463356i	0.943459	−	0.331490i	$-0.107551\pi$
$97$	3.31560	+	4.56353i	0.336648	+	0.463356i	−0.606811	+	0.794846i	$0.707551\pi$
$98$	3.86988	−	7.34861i	0.390917	−	0.742321i
$99$		−	8.78205i		−	0.882629i
$100$		0			0
$101$		−	0.202935i		−	0.0201928i	−0.999949	−	0.0100964i	$-0.996786\pi$
$101$		−	0.202935i		−	0.0201928i	0.999949	−	0.0100964i	$-0.00321383\pi$
$102$	6.13198	+	3.22919i	0.607157	+	0.319737i
$103$	−7.76000	−	10.6807i	−0.764616	−	1.05240i	−0.996816	−	0.0797351i	$-0.974593\pi$
$103$	−7.76000	−	10.6807i	−0.764616	−	1.05240i	0.232201	−	0.972668i	$-0.425407\pi$
$104$	−3.79744	+	18.9772i	−0.372369	+	1.86087i
$105$		0			0
$106$	−0.371579	−	2.56966i	−0.0360910	−	0.249587i
$107$	−14.9185			−1.44222			−0.721111	−	0.692819i	$-0.756368\pi$
$107$	−14.9185			−1.44222			−0.721111	+	0.692819i	$0.756368\pi$
$108$	−1.06446	+	1.38503i	−0.102427	+	0.133275i
$109$	−8.22423	−	2.67221i	−0.787738	−	0.255952i	−0.112598	−	0.993641i	$-0.535917\pi$
$109$	−8.22423	−	2.67221i	−0.787738	−	0.255952i	−0.675141	+	0.737689i	$0.735917\pi$
$110$		0			0
$111$	−6.90242	−	21.2435i	−0.655149	−	2.01634i
$112$	−13.3903	−	5.16358i	−1.26527	−	0.487913i
$113$	−5.61964	−	1.82593i	−0.528652	−	0.171769i	0.0325164	−	0.999471i	$-0.489648\pi$
$113$	−5.61964	−	1.82593i	−0.528652	−	0.171769i	−0.561168	+	0.827702i	$0.689648\pi$
$114$	−16.1355	−	8.49718i	−1.51123	−	0.795834i
$115$		0			0
$116$	3.74069	−	10.5378i	0.347314	−	0.978407i
$117$	18.5262	+	13.4601i	1.71275	+	1.24438i
$118$	−3.99261	+	3.88646i	−0.367550	+	0.357778i
$119$	5.64619	+	4.10220i	0.517585	+	0.376048i
$120$		0			0
$121$	−3.32838	+	2.41821i	−0.302580	+	0.219837i
$122$	1.56796	−	9.10414i	0.141957	−	0.824250i
$123$	−2.82933	−	8.70777i	−0.255112	−	0.785153i
$124$	0.114726	−	4.25678i	0.0103027	−	0.382270i
$125$		0			0
$126$	−12.1681	+	11.8446i	−1.08402	+	1.05520i
$127$	−3.36061	+	1.09193i	−0.298206	+	0.0968930i	−0.454299	−	0.890849i	$-0.650110\pi$
$127$	−3.36061	+	1.09193i	−0.298206	+	0.0968930i	0.156093	+	0.987742i	$0.450110\pi$
$128$	−2.81425	+	10.9581i	−0.248747	+	0.968569i
$129$	−1.32921	+	0.965725i	−0.117030	+	0.0850273i
$130$		0			0
$131$	3.96559	−	5.45817i	0.346475	−	0.476883i	−0.599843	−	0.800118i	$-0.704770\pi$
$131$	3.96559	−	5.45817i	0.346475	−	0.476883i	0.946319	+	0.323235i	$0.104770\pi$
$132$	−13.2168	−	0.356209i	−1.15037	−	0.0310040i
$133$	−14.8572	−	10.7944i	−1.28828	−	0.935992i
$134$	6.23858	−	3.07356i	0.538931	−	0.265515i
$135$		0			0
$136$	2.69382	−	4.79724i	0.230993	−	0.411360i
$137$	−7.83872	−	2.54696i	−0.669707	−	0.217601i	−0.0456237	−	0.998959i	$-0.514528\pi$
$137$	−7.83872	−	2.54696i	−0.669707	−	0.217601i	−0.624084	+	0.781358i	$0.714528\pi$
$138$	1.22166	+	2.47967i	0.103994	+	0.211083i
$139$	−1.29543	+	0.420910i	−0.109877	+	0.0357011i	−0.363439	−	0.931618i	$-0.618398\pi$
$139$	−1.29543	+	0.420910i	−0.109877	+	0.0357011i	0.253563	+	0.967319i	$0.418398\pi$
$140$		0			0
$141$	−2.20655	−	0.716950i	−0.185825	−	0.0603781i
$142$	1.12268	+	7.76389i	0.0942132	+	0.651531i
$143$			17.9553i			1.50150i
$144$	10.3906	+	8.44047i	0.865881	+	0.703373i
$145$		0			0
$146$	−3.55925	+	20.6663i	−0.294565	+	1.71035i
$147$	−11.9694	+	8.69626i	−0.987218	+	0.717256i
$148$	−17.0063	+	5.02336i	−1.39791	+	0.412918i
$149$			9.46274i			0.775218i	0.921824	+	0.387609i	$0.126699\pi$
$149$			9.46274i			0.775218i	−0.921824	+	0.387609i	$0.873301\pi$
$150$		0			0
$151$	7.99542			0.650658			0.325329	−	0.945601i	$-0.394525\pi$
$151$	7.99542			0.650658			0.325329	+	0.945601i	$0.394525\pi$
$152$	−7.08843	+	12.6233i	−0.574947	+	1.02389i
$153$	−3.82646	−	5.26667i	−0.309351	−	0.425785i
$154$	−13.1215	−	2.25985i	−1.05736	−	0.182104i
$155$		0			0
$156$	21.0086	−	27.3356i	1.68203	−	2.18860i
$157$	−7.78075			−0.620971			−0.310486	−	0.950578i	$-0.600492\pi$
$157$	−7.78075			−0.620971			−0.310486	+	0.950578i	$0.600492\pi$
$158$	1.91484	+	13.2421i	0.152336	+	1.05348i
$159$	−1.42926	+	4.39880i	−0.113347	+	0.348847i
$160$		0			0
$161$	0.860221	+	2.64749i	0.0677949	+	0.208651i
$162$	−9.94554	+	4.89987i	−0.781396	+	0.384970i
$163$	7.10008	−	21.8518i	0.556121	−	1.71157i	−0.136842	−	0.990593i	$-0.543695\pi$
$163$	7.10008	−	21.8518i	0.556121	−	1.71157i	0.692964	−	0.720973i	$-0.256305\pi$
$164$	−6.97095	+	2.05909i	−0.544340	+	0.160788i
$165$		0			0
$166$	−10.2062	+	5.02828i	−0.792154	+	0.390271i
$167$	7.10896	−	9.78464i	0.550108	−	0.757158i	−0.439919	−	0.898037i	$-0.644993\pi$
$167$	7.10896	−	9.78464i	0.550108	−	0.757158i	0.990027	+	0.140879i	$0.0449929\pi$
$168$	17.3323	+	18.7932i	1.33722	+	1.44993i
$169$	−27.3604	−	19.8785i	−2.10465	−	1.52912i
$170$		0			0
$171$	10.0688	+	13.8585i	0.769982	+	1.05979i
$172$	0.737964	+	1.07551i	0.0562692	+	0.0820065i
$173$	4.88649	+	15.0391i	0.371513	+	1.14340i	0.945801	+	0.324747i	$0.105279\pi$
$173$	4.88649	+	15.0391i	0.371513	+	1.14340i	−0.574288	+	0.818653i	$0.694721\pi$
$174$	−14.2737	+	13.8942i	−1.08209	+	1.05332i
$175$		0			0
$176$	−0.565371	+	10.4812i	−0.0426165	+	0.790047i
$177$	9.43984	−	3.06719i	0.709542	−	0.230544i
$178$	−15.1375	−	2.60705i	−1.13460	−	0.195407i
$179$	−8.68076	−	11.9480i	−0.648830	−	0.893038i	0.350217	−	0.936668i	$-0.386108\pi$
$179$	−8.68076	−	11.9480i	−0.648830	−	0.893038i	−0.999048	+	0.0436301i	$0.986108\pi$
$180$		0			0
$181$	3.16443	−	4.35546i	0.235210	−	0.323739i	−0.675053	−	0.737769i	$-0.735879\pi$
$181$	3.16443	−	4.35546i	0.235210	−	0.323739i	0.910263	+	0.414030i	$0.135879\pi$
$182$	24.8783	−	24.2168i	1.84410	−	1.79507i
$183$	−9.67305	+	13.3138i	−0.715053	+	0.984186i
$184$	1.99398	−	0.916465i	0.146998	−	0.0675627i
$185$		0			0
$186$	−3.53460	+	6.71194i	−0.259169	+	0.492143i
$187$	1.57734	−	4.85455i	0.115346	−	0.355000i
$188$	−0.616162	+	1.73577i	−0.0449382	+	0.126594i
$189$	2.98030	−	0.968359i	0.216785	−	0.0704378i
$190$		0			0
$191$	3.20367	−	9.85988i	0.231809	−	0.713436i	−0.765719	−	0.643175i	$-0.777617\pi$
$191$	3.20367	−	9.85988i	0.231809	−	0.713436i	0.997529	−	0.0702610i	$-0.0223832\pi$
$192$	13.1242	−	15.2952i	0.947156	−	1.10384i
$193$		−	0.720451i		−	0.0518592i	−0.999664	−	0.0259296i	$-0.991745\pi$
$193$		−	0.720451i		−	0.0518592i	0.999664	−	0.0259296i	$-0.00825458\pi$
$194$	−7.89523	+	1.14167i	−0.566844	+	0.0819672i
$195$		0			0
$196$	6.64530	+	9.68483i	0.474664	+	0.691774i
$197$	−4.83357	+	3.51179i	−0.344377	+	0.250205i	−0.746506	−	0.665378i	$-0.768270\pi$
$197$	−4.83357	+	3.51179i	−0.344377	+	0.250205i	0.402129	+	0.915583i	$0.368270\pi$
$198$	10.9891	+	5.78699i	0.780959	+	0.411264i
$199$	−13.1660			−0.933311			−0.466655	−	0.884439i	$-0.654541\pi$
$199$	−13.1660			−0.933311			−0.466655	+	0.884439i	$0.654541\pi$
$200$		0			0
$201$	−12.3889			−0.873843
$202$	0.253934	+	0.133725i	0.0178668	+	0.00940888i
$203$	−16.2287	+	11.7908i	−1.13903	+	0.827553i
$204$	−8.08142	+	5.54511i	−0.565813	+	0.388236i
$205$		0			0
$206$	18.4784	−	2.67203i	1.28745	−	0.186169i
$207$		−	2.59662i		−	0.180477i
$208$	−21.2440	−	17.2569i	−1.47301	−	1.19655i
$209$	−4.15056	+	12.7741i	−0.287100	+	0.883603i
$210$		0			0
$211$	5.22662	−	1.69823i	0.359816	−	0.116911i	−0.123530	−	0.992341i	$-0.539421\pi$
$211$	5.22662	−	1.69823i	0.359816	−	0.116911i	0.483346	+	0.875430i	$0.339421\pi$
$212$	3.46029	+	1.22833i	0.237654	+	0.0843622i
$213$	4.31832	−	13.2904i	0.295886	−	0.910644i
$214$	9.83063	−	18.6676i	0.672008	−	1.27609i
$215$		0			0
$216$	−1.03167	−	2.24464i	−0.0701965	−	0.152729i
$217$	−4.49018	+	6.18020i	−0.304813	+	0.419539i
$218$	8.76318	−	8.53018i	0.593517	−	0.577737i
$219$	21.9577	−	30.2221i	1.48376	−	2.04222i
$220$		0			0
$221$	7.82337	+	10.7679i	0.526257	+	0.724330i
$222$	31.1306	+	5.36147i	2.08935	+	0.359838i
$223$	19.3706	−	6.29390i	1.29715	−	0.421471i	0.422564	−	0.906333i	$-0.361130\pi$
$223$	19.3706	−	6.29390i	1.29715	−	0.421471i	0.874590	+	0.484862i	$0.161130\pi$
$224$	15.2849	−	13.3529i	1.02127	−	0.892177i
$225$		0			0
$226$	5.98791	−	5.82870i	0.398310	−	0.387720i
$227$	−4.89137	−	15.0541i	−0.324652	−	0.999175i	−0.971598	−	0.236639i	$-0.923954\pi$
$227$	−4.89137	−	15.0541i	−0.324652	−	0.999175i	0.646946	−	0.762536i	$-0.276046\pi$
$228$	21.2652	−	14.5912i	1.40832	−	0.966328i
$229$	−3.76598	−	5.18342i	−0.248863	−	0.342530i	0.666250	−	0.745729i	$-0.267898\pi$
$229$	−3.76598	−	5.18342i	−0.248863	−	0.342530i	−0.915113	+	0.403198i	$0.867898\pi$
$230$		0			0
$231$	19.1888	+	13.9414i	1.26253	+	0.917280i
$232$	10.7211	+	11.6247i	0.703872	+	0.763199i
$233$	10.3375	−	14.2284i	0.677234	−	0.932133i	−0.322662	−	0.946514i	$-0.604578\pi$
$233$	10.3375	−	14.2284i	0.677234	−	0.932133i	0.999897	+	0.0143813i	$0.00457787\pi$
$234$	−29.0507	+	14.3124i	−1.89910	+	0.935631i
$235$		0			0
$236$	−2.23220	−	7.55701i	−0.145304	−	0.491919i
$237$	7.36529	−	22.6680i	0.478427	−	1.47245i
$238$	−8.85371	+	4.36196i	−0.573901	+	0.282744i
$239$	−2.60748	−	8.02498i	−0.168664	−	0.519093i	0.830624	−	0.556834i	$-0.187984\pi$
$239$	−2.60748	−	8.02498i	−0.168664	−	0.519093i	−0.999288	+	0.0377406i	$0.987984\pi$
$240$		0			0
$241$	1.07674	−	3.31387i	0.0693591	−	0.213465i	−0.910369	−	0.413797i	$-0.864202\pi$
$241$	1.07674	−	3.31387i	0.0693591	−	0.213465i	0.979728	+	0.200332i	$0.0642022\pi$
$242$	−0.832671	−	5.75834i	−0.0535261	−	0.370160i
$243$	22.3706			1.43507
$244$	10.3589	+	7.96124i	0.663159	+	0.509666i
$245$		0			0
$246$	12.7605	+	2.19768i	0.813581	+	0.140119i
$247$	−20.5862	−	28.3344i	−1.30987	−	1.80288i
$248$	5.25096	+	2.94859i	0.333436	+	0.187236i
$249$	20.2679			1.28443
$250$		0			0
$251$		−	16.8769i		−	1.06526i	−0.846347	−	0.532632i	$-0.821203\pi$
$251$		−	16.8769i		−	1.06526i	0.846347	−	0.532632i	$-0.178797\pi$
$252$	−6.80299	−	23.0312i	−0.428548	−	1.45083i
$253$	1.64714	−	1.19672i	0.103555	−	0.0752369i
$254$	0.848157	−	4.92470i	0.0532181	−	0.309003i
$255$		0			0
$256$	−11.8575	−	10.7424i	−0.741094	−	0.671401i
$257$			4.42621i			0.276099i	0.990425	+	0.138050i	$0.0440833\pi$
$257$			4.42621i			0.276099i	−0.990425	+	0.138050i	$0.955917\pi$
$258$	−0.332531	−	2.29962i	−0.0207025	−	0.143168i
$259$	30.2543	+	9.83022i	1.87991	+	0.610820i
$260$		0			0
$261$	17.7956	−	5.78213i	1.10152	−	0.357905i
$262$	4.21671	+	8.55888i	0.260509	+	0.528770i
$263$	11.6771	+	3.79412i	0.720041	+	0.233956i	0.646041	−	0.763303i	$-0.276423\pi$
$263$	11.6771	+	3.79412i	0.720041	+	0.233956i	0.0740002	+	0.997258i	$0.476423\pi$
$264$	9.15503	−	16.3036i	0.563453	−	1.00342i
$265$		0			0
$266$	23.2974	−	11.4779i	1.42845	−	0.703757i
$267$	22.1369	+	16.0834i	1.35476	+	0.984289i
$268$	−0.264978	+	9.83174i	−0.0161861	+	0.600569i
$269$	−16.8702	+	23.2198i	−1.02859	+	1.41573i	−0.122591	+	0.992457i	$0.539120\pi$
$269$	−16.8702	+	23.2198i	−1.02859	+	1.41573i	−0.906000	+	0.423277i	$0.860880\pi$
$270$		0			0
$271$	−2.96640	+	2.15522i	−0.180196	+	0.130920i	−0.674227	−	0.738524i	$-0.735523\pi$
$271$	−2.96640	+	2.15522i	−0.180196	+	0.130920i	0.494031	+	0.869444i	$0.335523\pi$
$272$	4.22772	+	6.53197i	0.256343	+	0.396059i
$273$	−58.8204	+	19.1119i	−3.55997	+	1.15671i
$274$	8.35241	−	8.13034i	0.504588	−	0.491172i
$275$		0			0
$276$	−3.90785	−	0.105322i	−0.235225	−	0.00633961i
$277$	−1.23158	−	3.79042i	−0.0739986	−	0.227744i	0.907216	−	0.420666i	$-0.138204\pi$
$277$	−1.23158	−	3.79042i	−0.0739986	−	0.227744i	−0.981214	+	0.192922i	$0.938204\pi$
$278$	0.326942	−	1.89834i	0.0196087	−	0.113855i
$279$	5.76478	−	4.18836i	0.345128	−	0.250750i
$280$		0			0
$281$	−23.0045	−	16.7138i	−1.37234	−	0.997060i	−0.997551	−	0.0699483i	$-0.977717\pi$
$281$	−23.0045	−	16.7138i	−1.37234	−	0.997060i	−0.374785	−	0.927112i	$-0.622283\pi$
$282$	2.35115	−	2.28863i	0.140009	−	0.136286i
$283$	10.5601	+	7.67233i	0.627730	+	0.456073i	0.855613	−	0.517616i	$-0.173180\pi$
$283$	10.5601	+	7.67233i	0.627730	+	0.456073i	−0.227883	+	0.973689i	$0.573180\pi$
$284$	−10.4548	−	3.71125i	−0.620380	−	0.220222i
$285$		0			0
$286$	−22.4676	−	11.8318i	−1.32854	−	0.699627i
$287$	12.4013	+	4.02944i	0.732028	+	0.237850i
$288$	−17.4086	+	7.43992i	−1.02581	+	0.438402i
$289$	4.08404	+	12.5694i	0.240238	+	0.739375i
$290$		0			0
$291$	13.5152	+	4.39136i	0.792277	+	0.257426i
$292$	−23.5145	−	18.0719i	−1.37608	−	1.05758i
$293$	−27.0373			−1.57954			−0.789769	−	0.613404i	$-0.789800\pi$
$293$	−27.0373			−1.57954			−0.789769	+	0.613404i	$0.789800\pi$
$294$	−2.99441	−	20.7079i	−0.174638	−	1.20771i
$295$		0			0
$296$	4.92066	−	24.5904i	0.286008	−	1.42929i
$297$	−1.34715	−	1.85420i	−0.0781698	−	0.107592i
$298$	−11.8408	−	6.23554i	−0.685920	−	0.361215i
$299$			5.30890i			0.307022i
$300$		0			0
$301$		−	2.33989i		−	0.134869i
$302$	−5.26864	+	10.0047i	−0.303176	+	0.575708i
$303$	−0.300503	−	0.413607i	−0.0172635	−	0.0237611i
$304$	−11.1247	−	17.1880i	−0.638045	−	0.985801i
$305$		0			0
$306$	9.11170	−	1.31758i	0.520881	−	0.0753208i
$307$	23.1194			1.31949			0.659747	−	0.751488i	$-0.270664\pi$
$307$	23.1194			1.31949			0.659747	+	0.751488i	$0.270664\pi$
$308$	11.4743	−	14.9299i	0.653807	−	0.850710i
$309$	−31.6317	−	10.2778i	−1.79947	−	0.584682i
$310$		0			0
$311$	3.30515	+	10.1722i	0.187418	+	0.576813i	0.999982	−	0.00605932i	$-0.00192875\pi$
$311$	3.30515	+	10.1722i	0.187418	+	0.576813i	−0.812564	+	0.582872i	$0.801929\pi$
$312$	20.3615	+	44.3012i	1.15274	+	2.50806i
$313$	−6.62056	−	2.15115i	−0.374216	−	0.121590i	0.115870	−	0.993264i	$-0.463035\pi$
$313$	−6.62056	−	2.15115i	−0.374216	−	0.121590i	−0.490086	+	0.871674i	$0.663035\pi$
$314$	5.12718	−	9.73613i	0.289343	−	0.549441i
$315$		0			0
$316$	−17.8317	−	6.32989i	−1.00311	−	0.356084i
$317$	−2.26671	−	1.64686i	−0.127311	−	0.0924971i	0.522307	−	0.852757i	$-0.325071\pi$
$317$	−2.26671	−	1.64686i	−0.127311	−	0.0924971i	−0.649619	+	0.760260i	$0.725071\pi$
$318$	−4.56244	−	4.68706i	−0.255849	−	0.262837i
$319$	11.8694	+	8.62360i	0.664557	+	0.482829i
$320$		0			0
$321$	−30.4057	+	22.0911i	−1.69708	+	1.23300i
$322$	−3.87967	−	0.668177i	−0.216206	−	0.0372361i
$323$	3.07673	+	9.46919i	0.171194	+	0.526880i
$324$	0.422428	−	15.6738i	0.0234682	−	0.870764i
$325$		0			0
$326$	22.6647	+	23.2838i	1.25528	+	1.28957i
$327$	−20.7190	+	6.73201i	−1.14576	+	0.372281i
$328$	2.01700	−	10.0797i	0.111370	−	0.556557i
$329$	2.67317	−	1.94217i	0.147376	−	0.107075i
$330$		0			0
$331$	−15.6066	+	21.4807i	−0.857819	+	1.18069i	0.124266	+	0.992249i	$0.460342\pi$
$331$	−15.6066	+	21.4807i	−0.857819	+	1.18069i	−0.982085	+	0.188437i	$0.939658\pi$
$332$	0.433498	−	16.0845i	0.0237913	−	0.882753i
$333$	−24.0060	−	17.4413i	−1.31552	−	0.955780i
$334$	7.55912	+	15.3432i	0.413616	+	0.839540i
$335$		0			0
$336$	−34.9374	+	9.30419i	−1.90599	+	0.507585i
$337$	18.1528	+	5.89820i	0.988845	+	0.321295i	0.758400	−	0.651790i	$-0.225982\pi$
$337$	18.1528	+	5.89820i	0.988845	+	0.321295i	0.230446	+	0.973085i	$0.425982\pi$
$338$	42.9035	−	21.1373i	2.33364	−	1.14972i
$339$	−14.1574	+	4.60001i	−0.768923	+	0.249838i
$340$		0			0
$341$	5.31368	+	1.72652i	0.287752	+	0.0934963i
$342$	−23.9762	+	3.46703i	−1.29649	+	0.187475i
$343$			4.04448i			0.218381i
$344$	−1.83208	+	0.214710i	−0.0987790	+	0.0115764i
$345$		0			0
$346$	−22.0385	−	3.79559i	−1.18480	−	0.204052i
$347$	15.5716	−	11.3134i	0.835926	−	0.607336i	−0.0853039	−	0.996355i	$-0.527186\pi$
$347$	15.5716	−	11.3134i	0.835926	−	0.607336i	0.921230	+	0.389019i	$0.127186\pi$
$348$	−7.98018	−	27.0165i	−0.427782	−	1.44824i
$349$			0.0595710i			0.00318876i	0.999999	+	0.00159438i	$0.000507507\pi$
$349$			0.0595710i			0.00318876i	−0.999999	+	0.00159438i	$0.999492\pi$
$350$		0			0
$351$	5.97629			0.318991
$352$	−12.7426	−	7.61408i	−0.679184	−	0.405832i
$353$	11.4459	+	15.7539i	0.609203	+	0.838497i	0.996512	−	0.0834537i	$-0.0265951\pi$
$353$	11.4459	+	15.7539i	0.609203	+	0.838497i	−0.387308	+	0.921950i	$0.626595\pi$
$354$	−2.38244	+	13.8333i	−0.126625	+	0.735232i
$355$		0			0
$356$	13.2372	−	17.2237i	0.701569	−	0.912856i
$357$	17.5821			0.930545
$358$	20.6709	−	2.98907i	1.09249	−	0.157977i
$359$	7.90364	−	24.3249i	0.417138	−	1.28382i	−0.493186	−	0.869924i	$-0.664168\pi$
$359$	7.90364	−	24.3249i	0.417138	−	1.28382i	0.910324	−	0.413896i	$-0.135832\pi$
$360$		0			0
$361$	−2.22468	−	6.84685i	−0.117088	−	0.360361i
$362$	3.36481	+	6.82974i	0.176850	+	0.358963i
$363$	−3.20281	+	9.85725i	−0.168104	+	0.517371i
$364$	13.9090	+	47.0883i	0.729032	+	2.46810i
$365$		0			0
$366$	−10.2856	−	20.8772i	−0.537636	−	1.09127i
$367$	16.9820	−	23.3737i	0.886453	−	1.22010i	−0.0881385	−	0.996108i	$-0.528092\pi$
$367$	16.9820	−	23.3737i	0.886453	−	1.22010i	0.974592	−	0.223990i	$-0.0719082\pi$
$368$	−0.167165	+	3.09900i	−0.00871409	+	0.161546i
$369$	−9.84012	−	7.14927i	−0.512256	−	0.372176i
$370$		0			0
$371$	−3.87175	−	5.32901i	−0.201011	−	0.276669i
$372$	−6.06956	−	8.84575i	−0.314692	−	0.458631i
$373$	7.68840	+	23.6625i	0.398090	+	1.22520i	0.926529	+	0.376224i	$0.122778\pi$
$373$	7.68840	+	23.6625i	0.398090	+	1.22520i	−0.528438	+	0.848972i	$0.677222\pi$
$374$	5.03514	+	5.17268i	0.260361	+	0.267473i
$375$		0			0
$376$	−1.76596	−	1.91481i	−0.0910724	−	0.0987486i
$377$	−36.3839	+	11.8218i	−1.87386	+	0.608855i
$378$	−0.752174	+	4.36739i	−0.0386877	+	0.224634i
$379$	−3.80553	−	5.23786i	−0.195477	−	0.269051i	0.700016	−	0.714128i	$-0.253176\pi$
$379$	−3.80553	−	5.23786i	−0.195477	−	0.269051i	−0.895492	+	0.445077i	$0.853176\pi$
$380$		0			0
$381$	−5.23244	+	7.20183i	−0.268066	+	0.368961i
$382$	10.2267	+	10.5060i	0.523243	+	0.537535i
$383$	−1.79838	+	2.47525i	−0.0918928	+	0.126480i	−0.852488	−	0.522747i	$-0.824907\pi$
$383$	−1.79838	+	2.47525i	−0.0918928	+	0.126480i	0.760595	+	0.649227i	$0.224907\pi$
$384$	10.4908	+	26.5013i	0.535357	+	1.35239i
$385$		0			0
$386$	0.901508	+	0.474746i	0.0458855	+	0.0241640i
$387$	−0.674465	+	2.07579i	−0.0342850	+	0.105518i
$388$	3.77403	−	10.6317i	0.191597	−	0.539742i
$389$	26.7250	−	8.68349i	1.35501	−	0.440270i	0.460637	−	0.887588i	$-0.347621\pi$
$389$	26.7250	−	8.68349i	1.35501	−	0.440270i	0.894375	+	0.447318i	$0.147621\pi$
$390$		0			0
$391$	0.466377	−	1.43536i	0.0235857	−	0.0725893i
$392$	−16.4977	+	1.93344i	−0.833259	+	0.0976535i
$393$		−	16.9966i		−	0.857367i
$394$	−1.20923	−	8.36241i	−0.0609200	−	0.421292i
$395$		0			0
$396$	−14.4826	+	9.93734i	−0.727780	+	0.499370i
$397$	−28.3014	+	20.5622i	−1.42041	+	1.03199i	−0.428701	+	0.903446i	$0.641029\pi$
$397$	−28.3014	+	20.5622i	−1.42041	+	1.03199i	−0.991704	+	0.128539i	$0.958971\pi$
$398$	8.67581	−	16.4747i	0.434879	−	0.825802i
$399$	−46.2651			−2.31615
$400$		0			0
$401$	13.3727			0.667799			0.333900	−	0.942609i	$-0.391635\pi$
$401$	13.3727			0.667799			0.333900	+	0.942609i	$0.391635\pi$
$402$	8.16373	−	15.5023i	0.407170	−	0.773185i
$403$	−11.7864	+	8.56329i	−0.587120	+	0.426568i
$404$	−0.334663	+	0.229631i	−0.0166501	+	0.0114246i
$405$		0			0
$406$	−4.05997	−	28.0767i	−0.201493	−	1.39342i
$407$		−	23.2662i		−	1.15326i
$408$	−1.61334	−	13.7664i	−0.0798724	−	0.681536i
$409$	8.50186	−	26.1660i	0.420390	−	1.29383i	−0.486950	−	0.873430i	$-0.661891\pi$
$409$	8.50186	−	26.1660i	0.420390	−	1.29383i	0.907340	−	0.420397i	$-0.138109\pi$
$410$		0			0
$411$	−19.7478	+	6.41645i	−0.974088	+	0.316500i
$412$	−8.83294	+	24.8829i	−0.435168	+	1.22589i
$413$	−4.36820	+	13.4439i	−0.214945	+	0.661533i
$414$	3.24917	+	1.71106i	0.159688	+	0.0840940i
$415$		0			0
$416$	35.5927	−	15.2113i	1.74507	−	0.745793i
$417$	−2.01697	+	2.77612i	−0.0987713	+	0.135947i
$418$	−13.2493	−	13.6112i	−0.648046	−	0.665746i
$419$	−23.3551	+	32.1455i	−1.14097	+	1.57041i	−0.375649	+	0.926762i	$0.622580\pi$
$419$	−23.3551	+	32.1455i	−1.14097	+	1.57041i	−0.765321	+	0.643648i	$0.777420\pi$
$420$		0			0
$421$	2.75042	+	3.78563i	0.134047	+	0.184500i	0.870764	−	0.491701i	$-0.163625\pi$
$421$	2.75042	+	3.78563i	0.134047	+	0.184500i	−0.736717	+	0.676202i	$0.763625\pi$
$422$	−1.31910	+	7.65919i	−0.0642130	+	0.372843i
$423$	−2.93127	+	0.952426i	−0.142523	+	0.0463085i
$424$	−3.81721	+	3.52048i	−0.185380	+	0.170969i
$425$		0			0
$426$	13.7848	+	14.1614i	0.667877	+	0.686120i
$427$	−7.24251	−	22.2901i	−0.350489	−	1.07870i
$428$	16.8810	+	24.6023i	0.815975	+	1.18920i
$429$	26.5880	+	36.5952i	1.28368	+	1.76683i
$430$		0			0
$431$	−16.2735	−	11.8234i	−0.783869	−	0.569514i	0.122269	−	0.992497i	$-0.460983\pi$
$431$	−16.2735	−	11.8234i	−0.783869	−	0.569514i	−0.906138	+	0.422983i	$0.860983\pi$
$432$	3.48857	+	0.188180i	0.167844	+	0.00905379i
$433$	0.827085	−	1.13838i	0.0397472	−	0.0547073i	−0.788681	−	0.614803i	$-0.789236\pi$
$433$	0.827085	−	1.13838i	0.0397472	−	0.0547073i	0.828428	+	0.560096i	$0.189236\pi$
$434$	−4.77451	−	9.69108i	−0.229184	−	0.465187i
$435$		0			0
$436$	4.89934	+	16.5865i	0.234636	+	0.794348i
$437$	−1.22721	+	3.77696i	−0.0587054	+	0.180677i
$438$	23.3481	+	47.3909i	1.11562	+	2.26443i
$439$	−4.33963	−	13.3560i	−0.207119	−	0.637447i	−0.999620	−	0.0275762i	$-0.991221\pi$
$439$	−4.33963	−	13.3560i	−0.207119	−	0.637447i	0.792500	−	0.609871i	$-0.208779\pi$
$440$		0			0
$441$	−6.07349	+	18.6923i	−0.289214	+	0.890109i
$442$	−18.6293	+	2.69385i	−0.886105	+	0.128133i
$443$	9.37158			0.445257			0.222629	−	0.974903i	$-0.428536\pi$
$443$	9.37158			0.445257			0.222629	+	0.974903i	$0.428536\pi$
$444$	−27.2226	+	35.4210i	−1.29193	+	1.68101i
$445$		0			0
$446$	−4.88880	+	28.3861i	−0.231491	+	1.34412i
$447$	14.0123	+	19.2863i	0.662759	+	0.912210i
$448$	6.63650	+	27.9251i	0.313545	+	1.31934i
$449$	27.0993			1.27889			0.639447	−	0.768835i	$-0.279163\pi$
$449$	27.0993			1.27889			0.639447	+	0.768835i	$0.279163\pi$
$450$		0			0
$451$		−	9.53690i		−	0.449075i
$452$	3.34774	+	11.3336i	0.157464	+	0.533088i
$453$	16.2957	−	11.8395i	0.765638	−	0.556269i
$454$	22.0605	+	3.79938i	1.03535	+	0.178314i
$455$		0			0
$456$	4.24530	+	36.2244i	0.198804	+	1.69636i
$457$		−	32.1890i		−	1.50574i	−0.658170	−	0.752869i	$-0.728669\pi$
$457$		−	32.1890i		−	1.50574i	0.658170	−	0.752869i	$-0.271331\pi$
$458$	8.96768	−	1.29675i	0.419032	−	0.0605932i
$459$	−1.61580	−	0.525005i	−0.0754190	−	0.0245051i
$460$		0			0
$461$	2.49963	−	0.812178i	0.116419	−	0.0378269i	−0.250228	−	0.968187i	$-0.580506\pi$
$461$	2.49963	−	0.812178i	0.116419	−	0.0378269i	0.366647	+	0.930360i	$0.380506\pi$
$462$	−30.0896	+	14.8243i	−1.39990	+	0.689687i
$463$	−28.7725	−	9.34875i	−1.33717	−	0.434473i	−0.448814	−	0.893625i	$-0.648153\pi$
$463$	−28.7725	−	9.34875i	−1.33717	−	0.434473i	−0.888358	+	0.459152i	$0.848153\pi$
$464$	−21.6108	+	5.75518i	−1.00326	+	0.267178i
$465$		0			0
$466$	10.9921	+	22.3113i	0.509201	+	1.03355i
$467$	33.3692	+	24.2441i	1.54414	+	1.12188i	0.947671	+	0.319250i	$0.103431\pi$
$467$	33.3692	+	24.2441i	1.54414	+	1.12188i	0.596471	+	0.802635i	$0.296569\pi$
$468$	1.23390	−	45.7826i	0.0570371	−	2.11630i
$469$	10.3708	−	14.2742i	0.478879	−	0.659120i
$470$		0			0
$471$	−15.8582	+	11.5216i	−0.730705	+	0.530889i
$472$	10.9271	+	2.18657i	0.502960	+	0.100645i
$473$	−1.62760	+	0.528839i	−0.0748371	+	0.0243160i
$474$	23.5113	+	24.1535i	1.07991	+	1.10941i
$475$		0			0
$476$	0.376053	−	13.9531i	0.0172364	−	0.639538i
$477$	1.89868	+	5.84354i	0.0869346	+	0.267557i
$478$	11.7600	+	2.02536i	0.537888	+	0.0926378i
$479$	12.7715	−	9.27902i	0.583544	−	0.423969i	−0.256456	−	0.966556i	$-0.582555\pi$
$479$	12.7715	−	9.27902i	0.583544	−	0.423969i	0.840000	+	0.542586i	$0.182555\pi$
$480$		0			0
$481$	49.0813	+	35.6596i	2.23791	+	1.62594i
$482$	3.43715	+	3.53104i	0.156558	+	0.160834i
$483$	5.67360	+	4.12211i	0.258158	+	0.187563i
$484$	7.75416	+	2.75257i	0.352462	+	0.125117i
$485$		0			0
$486$	−14.7412	+	27.9925i	−0.668676	+	1.26977i
$487$	−34.0773	−	11.0724i	−1.54419	−	0.501738i	−0.591661	−	0.806187i	$-0.701528\pi$
$487$	−34.0773	−	11.0724i	−1.54419	−	0.501738i	−0.952529	+	0.304449i	$0.901528\pi$
$488$	−16.7880	+	7.71605i	−0.759959	+	0.349289i
$489$	−17.8870	−	55.0505i	−0.808877	−	2.48947i
$490$		0			0
$491$	−7.10672	−	2.30911i	−0.320722	−	0.104209i	0.144232	−	0.989544i	$-0.453929\pi$
$491$	−7.10672	−	2.30911i	−0.320722	−	0.104209i	−0.464954	+	0.885335i	$0.653929\pi$
$492$	−11.1586	+	14.5192i	−0.503069	+	0.654575i
$493$	10.8756			0.489811
$494$	49.0205	−	7.08850i	2.20554	−	0.318927i
$495$		0			0
$496$	−7.14976	+	4.62757i	−0.321034	+	0.207784i
$497$	11.6980	+	16.1009i	0.524728	+	0.722226i
$498$	−13.3557	+	25.3615i	−0.598483	+	1.13647i
$499$		−	1.61567i		−	0.0723272i	−0.999346	−	0.0361636i	$-0.988486\pi$
$499$		−	1.61567i		−	0.0723272i	0.999346	−	0.0361636i	$-0.0115137\pi$
$500$		0			0
$501$		−	30.4692i		−	1.36126i
$502$	21.1183	+	11.1212i	0.942555	+	0.496363i
$503$	−17.4576	−	24.0283i	−0.778395	−	1.07137i	−0.995457	−	0.0952114i	$-0.969647\pi$
$503$	−17.4576	−	24.0283i	−0.778395	−	1.07137i	0.217062	−	0.976158i	$-0.430353\pi$
$504$	33.3020	+	6.66391i	1.48339	+	0.296834i
$505$		0			0
$506$	0.412069	+	2.84966i	0.0183187	+	0.126683i
$507$	−85.1999			−3.78386
$508$	5.60342	+	4.30647i	0.248612	+	0.191069i
$509$	−1.21315	−	0.394177i	−0.0537721	−	0.0174716i	0.282007	−	0.959412i	$-0.409000\pi$
$509$	−1.21315	−	0.394177i	−0.0537721	−	0.0174716i	−0.335780	+	0.941941i	$0.609000\pi$
$510$		0			0
$511$	16.4404	+	50.5983i	0.727279	+	2.23834i
$512$	21.2557	−	7.75863i	0.939377	−	0.342886i
$513$	4.25176	+	1.38148i	0.187720	+	0.0609939i
$514$	−5.53856	−	2.91668i	−0.244295	−	0.128649i
$515$		0			0
$516$	3.09666	+	1.09925i	0.136323	+	0.0483918i
$517$	−1.95511	−	1.42047i	−0.0859855	−	0.0624722i
$518$	−32.2369	+	31.3798i	−1.41641	+	1.37875i
$519$	32.2290	+	23.4157i	1.41469	+	1.02784i
$520$		0			0
$521$	9.44563	−	6.86265i	0.413821	−	0.300658i	−0.361326	−	0.932440i	$-0.617676\pi$
$521$	9.44563	−	6.86265i	0.413821	−	0.300658i	0.775147	+	0.631781i	$0.217676\pi$
$522$	−4.49128	+	26.0779i	−0.196578	+	1.14140i
$523$	−6.21617	−	19.1314i	−0.271814	−	0.836558i	−0.990045	−	0.140753i	$-0.955048\pi$
$523$	−6.21617	−	19.1314i	−0.271814	−	0.836558i	0.718230	−	0.695805i	$-0.244952\pi$
$524$	−13.4884	−	0.363531i	−0.589245	−	0.0158809i
$525$		0			0
$526$	−12.4423	+	12.1115i	−0.542512	+	0.528087i
$527$	3.93893	−	1.27984i	0.171582	−	0.0557505i
$528$	14.3681	+	22.1991i	0.625289	+	0.966093i
$529$	−18.1204	+	13.1652i	−0.787842	+	0.572401i
$530$		0			0
$531$	7.75031	−	10.6674i	0.336335	−	0.462925i
$532$	−0.989534	+	36.7157i	−0.0429018	+	1.59183i
$533$	20.1186	+	14.6170i	0.871432	+	0.633133i
$534$	−34.7126	+	17.1019i	−1.50216	+	0.740070i
$535$		0			0
$536$	−12.1279	−	6.81026i	−0.523847	−	0.294158i
$537$	−35.3850	−	11.4973i	−1.52697	−	0.496144i
$538$	−17.9384	−	36.4106i	−0.773380	−	1.56977i
$539$	−14.6564	+	4.76215i	−0.631295	+	0.205120i
$540$		0			0
$541$	−19.0637	−	6.19417i	−0.819612	−	0.266308i	−0.130949	−	0.991389i	$-0.541802\pi$
$541$	−19.0637	−	6.19417i	−0.819612	−	0.266308i	−0.688664	+	0.725081i	$0.741802\pi$
$542$	−0.742113	−	5.13208i	−0.0318765	−	0.220442i
$543$		−	13.5628i		−	0.582036i
$544$	−10.9594	+	0.985901i	−0.469881	+	0.0422701i
$545$		0			0
$546$	14.8452	−	86.1965i	0.635316	−	3.68887i
$547$	−31.1058	+	22.5997i	−1.32999	+	0.966293i	−0.330239	+	0.943897i	$0.607129\pi$
$547$	−31.1058	+	22.5997i	−1.32999	+	0.966293i	−0.999749	+	0.0223953i	$0.992871\pi$
$548$	4.66969	+	15.8090i	0.199479	+	0.675327i
$549$			21.8619i			0.933041i
$550$		0			0
$551$	−28.6176			−1.21915
$552$	2.70690	−	4.82053i	0.115213	−	0.205175i
$553$	19.9521	+	27.4617i	0.848448	+	1.16779i
$554$	5.55455	+	0.956633i	0.235990	+	0.0406434i
$555$		0			0
$556$	2.15997	+	1.66003i	0.0916032	+	0.0704010i
$557$	10.9707			0.464844			0.232422	−	0.972615i	$-0.425335\pi$
$557$	10.9707			0.464844			0.232422	+	0.972615i	$0.425335\pi$
$558$	1.44219	+	9.97347i	0.0610528	+	0.422211i
$559$	1.37897	−	4.24405i	0.0583244	−	0.179504i
$560$		0			0
$561$	−3.97373	−	12.2299i	−0.167771	−	0.516346i
$562$	36.0731	−	17.7721i	1.52165	−	0.749672i
$563$	−0.325391	+	1.00145i	−0.0137136	+	0.0422061i	−0.957679	−	0.287838i	$-0.907064\pi$
$563$	−0.325391	+	1.00145i	−0.0137136	+	0.0422061i	0.943966	+	0.330044i	$0.107064\pi$
$564$	1.31448	+	4.45012i	0.0553498	+	0.187384i
$565$		0			0
$566$	−16.5591	+	8.15816i	−0.696030	+	0.342913i
$567$	−16.5331	+	22.7559i	−0.694326	+	0.955658i
$568$	11.5332	−	10.6367i	0.483923	−	0.446305i
$569$	16.4403	+	11.9446i	0.689213	+	0.500743i	0.876401	−	0.481581i	$-0.159937\pi$
$569$	16.4403	+	11.9446i	0.689213	+	0.500743i	−0.187188	+	0.982324i	$0.559937\pi$
$570$		0			0
$571$	8.81803	+	12.1370i	0.369023	+	0.507917i	0.952635	−	0.304116i	$-0.0983610\pi$
$571$	8.81803	+	12.1370i	0.369023	+	0.507917i	−0.583612	+	0.812033i	$0.698361\pi$
$572$	29.6104	−	20.3174i	1.23807	−	0.849511i
$573$	−8.07089	−	24.8396i	−0.337166	−	1.03769i
$574$	−13.2140	+	12.8627i	−0.551543	+	0.536878i
$575$		0			0
$576$	2.16186	−	26.6861i	0.0900776	−	1.11192i
$577$	27.0844	−	8.80026i	1.12754	−	0.366360i	0.314899	−	0.949125i	$-0.398029\pi$
$577$	27.0844	−	8.80026i	1.12754	−	0.366360i	0.812640	+	0.582765i	$0.198029\pi$
$578$	−18.4194	−	3.17228i	−0.766146	−	0.131950i
$579$	−1.06683	−	1.46837i	−0.0443361	−	0.0610235i
$580$		0			0
$581$	−16.9664	+	23.3523i	−0.703885	+	0.968815i
$582$	−14.4009	+	14.0180i	−0.596937	+	0.581065i
$583$	−2.83173	+	3.89755i	−0.117278	+	0.161420i
$584$	38.1086	−	17.5153i	1.57694	−	0.724789i
$585$		0			0
$586$	17.8164	−	33.8321i	0.735990	−	1.39759i
$587$	10.7007	−	32.9333i	0.441664	−	1.35930i	−0.444438	−	0.895810i	$-0.646597\pi$
$587$	10.7007	−	32.9333i	0.441664	−	1.35930i	0.886101	−	0.463491i	$-0.153403\pi$
$588$	27.8851	+	9.89865i	1.14996	+	0.408213i
$589$	−10.3648	+	3.36772i	−0.427073	+	0.138764i
$590$		0			0
$591$	−4.65121	+	14.3150i	−0.191325	+	0.588839i
$592$	27.5277	+	22.3613i	1.13138	+	0.919042i
$593$			34.9925i			1.43697i	0.695543	+	0.718484i	$0.255164\pi$
$593$			34.9925i			1.43697i	−0.695543	+	0.718484i	$0.744836\pi$
$594$	3.20789	−	0.463870i	0.131621	−	0.0190328i
$595$		0			0
$596$	15.6052	−	10.7076i	0.639213	−	0.438600i
$597$	−26.8339	+	19.4960i	−1.09824	+	0.797918i
$598$	−6.64308	−	3.49834i	−0.271656	−	0.143058i
$599$	17.7341			0.724596			0.362298	−	0.932062i	$-0.381992\pi$
$599$	17.7341			0.724596			0.362298	+	0.932062i	$0.381992\pi$
$600$		0			0
$601$	−2.01505			−0.0821957			−0.0410979	−	0.999155i	$-0.513086\pi$
$601$	−2.01505			−0.0821957			−0.0410979	+	0.999155i	$0.513086\pi$
$602$	2.92793	+	1.54189i	0.119334	+	0.0628427i
$603$	−13.3147	+	9.67370i	−0.542217	+	0.393943i
$604$	−9.04723	−	13.1854i	−0.368127	−	0.536506i
$605$		0			0
$606$	0.715569	−	0.103473i	0.0290680	−	0.00420331i
$607$			39.1971i			1.59096i	0.605979	+	0.795481i	$0.292782\pi$
$607$			39.1971i			1.59096i	−0.605979	+	0.795481i	$0.707218\pi$
$608$	28.8382	−	2.59427i	1.16955	−	0.105211i
$609$	−15.6164	+	48.0624i	−0.632809	+	1.94759i
$610$		0			0
$611$	5.99311	−	1.94728i	0.242455	−	0.0787785i
$612$	−4.35552	+	12.2698i	−0.176062	+	0.495977i
$613$	−6.65786	+	20.4908i	−0.268909	+	0.827615i	0.721859	+	0.692041i	$0.243288\pi$
$613$	−6.65786	+	20.4908i	−0.268909	+	0.827615i	−0.990767	+	0.135575i	$0.956712\pi$
$614$	−15.2347	+	28.9295i	−0.614822	+	1.16750i
$615$		0			0
$616$	11.1209	+	24.1960i	0.448073	+	0.974886i
$617$	−17.5267	+	24.1235i	−0.705600	+	0.971175i	0.294280	+	0.955719i	$0.404920\pi$
$617$	−17.5267	+	24.1235i	−0.705600	+	0.971175i	−0.999881	+	0.0154563i	$0.995080\pi$
$618$	33.7046	−	32.8085i	1.35580	−	1.31975i
$619$	2.86875	−	3.94849i	0.115305	−	0.158703i	−0.747464	−	0.664303i	$-0.768729\pi$
$619$	2.86875	−	3.94849i	0.115305	−	0.158703i	0.862768	+	0.505599i	$0.168729\pi$
$620$		0			0
$621$	−0.398318	−	0.548237i	−0.0159839	−	0.0220000i
$622$	−14.9065	−	2.56728i	−0.597698	−	0.102939i
$623$	−37.0619	+	12.0421i	−1.48485	+	0.482458i
$624$	−68.8518	−	3.71399i	−2.75628	−	0.148678i
$625$		0			0
$626$	7.05442	−	6.86685i	0.281951	−	0.274455i
$627$	10.4564	+	32.1813i	0.417587	+	1.28520i
$628$	8.80432	+	12.8314i	0.351331	+	0.512028i
$629$	−10.1374	−	13.9529i	−0.404205	−	0.556340i
$630$		0			0
$631$	−12.3860	−	8.99897i	−0.493080	−	0.358243i	0.313288	−	0.949658i	$-0.398570\pi$
$631$	−12.3860	−	8.99897i	−0.493080	−	0.358243i	−0.806367	+	0.591415i	$0.798570\pi$
$632$	19.6710	−	18.1419i	0.782469	−	0.721644i
$633$	8.13781	−	11.2007i	0.323449	−	0.445189i
$634$	3.55441	−	1.75115i	0.141163	−	0.0695470i
$635$		0			0
$636$	8.87141	−	2.62045i	0.351774	−	0.103908i
$637$	12.4175	−	38.2172i	0.492001	−	1.51422i
$638$	−18.6122	+	9.16967i	−0.736864	+	0.363031i
$639$	−5.73663	−	17.6555i	−0.226937	−	0.698442i
$640$		0			0
$641$	−2.46226	+	7.57805i	−0.0972533	+	0.299315i	−0.987834	−	0.155510i	$-0.950298\pi$
$641$	−2.46226	+	7.57805i	−0.0972533	+	0.299315i	0.890581	+	0.454825i	$0.150298\pi$
$642$	−7.60669	−	52.6041i	−0.300212	−	2.07612i
$643$	−6.46830			−0.255085			−0.127542	−	0.991833i	$-0.540709\pi$
$643$	−6.46830			−0.255085			−0.127542	+	0.991833i	$0.540709\pi$
$644$	3.39263	−	4.41437i	0.133689	−	0.173951i
$645$		0			0
$646$	−13.8763	−	2.38985i	−0.545956	−	0.0940274i
$647$	8.81321	+	12.1303i	0.346483	+	0.476893i	0.946321	−	0.323229i	$-0.104768\pi$
$647$	8.81321	+	12.1303i	0.346483	+	0.476893i	−0.599838	+	0.800122i	$0.704768\pi$
$648$	19.3344	+	10.8569i	0.759526	+	0.426500i
$649$	10.3387			0.405828
$650$		0			0
$651$			19.2450i			0.754272i
$652$	−44.0703	+	13.0176i	−1.72593	+	0.509807i
$653$	31.2404	−	22.6975i	1.22253	−	0.888220i	0.226223	−	0.974076i	$-0.427362\pi$
$653$	31.2404	−	22.6975i	1.22253	−	0.888220i	0.996308	+	0.0858552i	$0.0273622\pi$
$654$	5.22910	−	30.3620i	0.204474	−	1.18725i
$655$		0			0
$656$	11.2837	+	9.16596i	0.440554	+	0.357870i
$657$		−	49.6261i		−	1.93610i
$658$	0.668753	+	4.62476i	0.0260707	+	0.180292i
$659$	32.1885	+	10.4587i	1.25389	+	0.407412i	0.859312	−	0.511452i	$-0.170892\pi$
$659$	32.1885	+	10.4587i	1.25389	+	0.407412i	0.394574	+	0.918864i	$0.370892\pi$
$660$		0			0
$661$	−1.06103	+	0.344750i	−0.0412693	+	0.0134092i	−0.329579	−	0.944128i	$-0.606907\pi$
$661$	−1.06103	+	0.344750i	−0.0412693	+	0.0134092i	0.288310	+	0.957537i	$0.406907\pi$
$662$	−16.5949	−	33.6836i	−0.644979	−	1.30915i
$663$	31.8900	+	10.3617i	1.23851	+	0.402415i
$664$	19.8411	+	11.1415i	0.769983	+	0.432372i
$665$		0			0
$666$	37.6434	−	18.5458i	1.45865	−	0.718635i
$667$	3.50945	+	2.54977i	0.135887	+	0.0987274i
$668$	−24.1802	−	0.651686i	−0.935559	−	0.0252145i
$669$	30.1599	−	41.5116i	1.16605	−	1.60493i
$670$		0			0
$671$	−13.8678	+	10.0756i	−0.535362	+	0.388963i
$672$	11.3798	−	49.8485i	0.438986	−	1.92295i
$673$	25.0129	−	8.12719i	0.964177	−	0.313280i	0.215714	−	0.976457i	$-0.430792\pi$
$673$	25.0129	−	8.12719i	0.964177	−	0.313280i	0.748463	+	0.663177i	$0.230792\pi$
$674$	−19.3424	+	18.8281i	−0.745040	+	0.725231i
$675$		0			0
$676$	−1.82229	+	67.6142i	−0.0700880	+	2.60054i
$677$	−5.47038	−	16.8361i	−0.210244	−	0.647064i	−0.999457	−	0.0329450i	$-0.989511\pi$
$677$	−5.47038	−	16.8361i	−0.210244	−	0.647064i	0.789213	−	0.614119i	$-0.210489\pi$
$678$	3.57306	−	20.7465i	0.137223	−	0.796763i
$679$	−16.3733	+	11.8959i	−0.628350	+	0.456523i
$680$		0			0
$681$	−32.2611	−	23.4391i	−1.23625	−	0.898188i
$682$	−5.66190	+	5.51136i	−0.216805	+	0.211041i
$683$	−37.0207	−	26.8971i	−1.41656	−	1.02919i	−0.992328	−	0.123635i	$-0.960545\pi$
$683$	−37.0207	−	26.8971i	−1.41656	−	1.02919i	−0.424230	−	0.905554i	$-0.639455\pi$
$684$	11.4610	−	32.2863i	0.438222	−	1.23450i
$685$		0			0
$686$	−5.06089	−	2.66514i	−0.193226	−	0.101755i
$687$	−15.3511	−	4.98787i	−0.585680	−	0.190299i
$688$	0.938592	−	2.43398i	0.0357835	−	0.0927946i
$689$	−3.88194	−	11.9474i	−0.147890	−	0.455159i
$690$		0			0
$691$	−5.90130	−	1.91745i	−0.224496	−	0.0729432i	0.194609	−	0.980881i	$-0.437656\pi$
$691$	−5.90130	−	1.91745i	−0.224496	−	0.0729432i	−0.419105	+	0.907938i	$0.637656\pi$
$692$	19.2719	−	25.0759i	0.732608	−	0.953243i
$693$	31.5088			1.19692
$694$	3.89558	+	26.9399i	0.147874	+	1.02262i
$695$		0			0
$696$	39.0646	+	7.81702i	1.48074	+	0.296304i
$697$	−4.15535	−	5.71935i	−0.157395	−	0.216636i
$698$	−0.0745417	−	0.0392547i	−0.00282145	−	0.00148581i
$699$		−	44.3069i		−	1.67584i
$700$		0			0
$701$			21.2933i			0.804238i	0.915587	+	0.402119i	$0.131726\pi$
$701$			21.2933i			0.804238i	−0.915587	+	0.402119i	$0.868274\pi$
$702$	−3.93812	+	7.47818i	−0.148635	+	0.282246i
$703$	26.6752	+	36.7153i	1.00608	+	1.38474i
$704$	17.9244	−	10.9276i	0.675552	−	0.411850i
$705$		0			0
$706$	−27.2554	+	3.94120i	−1.02577	+	0.148329i
$707$	0.728101			0.0273831
$708$	−15.7398	−	12.0967i	−0.591539	−	0.454623i
$709$	−10.0050	−	3.25084i	−0.375747	−	0.122088i	0.115054	−	0.993359i	$-0.463296\pi$
$709$	−10.0050	−	3.25084i	−0.375747	−	0.122088i	−0.490801	+	0.871272i	$0.663296\pi$
$710$		0			0
$711$	−9.78435	−	30.1131i	−0.366942	−	1.12933i
$712$	12.8295	+	27.9135i	0.480806	+	1.04610i
$713$	1.57111	+	0.510486i	0.0588387	+	0.0191178i
$714$	−11.5859	+	22.0007i	−0.433590	+	0.823355i
$715$		0			0
$716$	−9.88100	+	27.8354i	−0.369270	+	1.04026i
$717$	−17.1977	−	12.4948i	−0.642258	−	0.466628i
$718$	25.2298	+	25.9190i	0.941569	+	0.967287i
$719$	5.42565	+	3.94197i	0.202343	+	0.147011i	0.684342	−	0.729161i	$-0.260089\pi$
$719$	5.42565	+	3.94197i	0.202343	+	0.147011i	−0.482000	+	0.876171i	$0.660089\pi$
$720$		0			0
$721$	38.3209	−	27.8418i	1.42715	−	1.03688i
$722$	10.0335	+	1.72802i	0.373408	+	0.0643103i
$723$	−2.71260	−	8.34852i	−0.100883	−	0.310485i
$724$	−10.7634	−	0.290087i	−0.400018	−	0.0107810i
$725$		0			0
$726$	−10.2240	−	10.5032i	−0.379447	−	0.389811i
$727$	40.2119	−	13.0656i	1.49138	−	0.484578i	0.553888	−	0.832591i	$-0.313143\pi$
$727$	40.2119	−	13.0656i	1.49138	−	0.484578i	0.937490	+	0.348013i	$0.113143\pi$
$728$	−68.0875	−	13.6247i	−2.52349	−	0.504964i
$729$	26.5667	−	19.3018i	0.983951	−	0.714882i
$730$		0			0
$731$	−0.745662	+	1.02632i	−0.0275793	+	0.0379597i
$732$	32.9016	+	0.886740i	1.21608	+	0.0327749i
$733$	21.7381	+	15.7936i	0.802914	+	0.583351i	0.911768	−	0.410707i	$-0.134718\pi$
$733$	21.7381	+	15.7936i	0.802914	+	0.583351i	−0.108854	+	0.994058i	$0.534718\pi$
$734$	18.0573	+	36.6520i	0.666509	+	1.35285i
$735$		0			0
$736$	−3.76765	−	2.25128i	−0.138877	−	0.0829833i
$737$	−12.2728	−	3.98768i	−0.452075	−	0.146888i
$738$	15.4302	−	7.60198i	0.567992	−	0.279833i
$739$	−13.3854	+	4.34919i	−0.492391	+	0.159988i	−0.544679	−	0.838644i	$-0.683349\pi$
$739$	−13.3854	+	4.34919i	−0.492391	+	0.159988i	0.0522881	+	0.998632i	$0.483349\pi$
$740$		0			0
$741$	−83.9145	−	27.2655i	−3.08268	−	1.00162i
$742$	9.21956	−	1.33317i	0.338461	−	0.0489423i
$743$		−	43.2190i		−	1.58555i	−0.609513	−	0.792776i	$-0.708635\pi$
$743$		−	43.2190i		−	1.58555i	0.609513	−	0.792776i	$-0.291365\pi$
$744$	15.0684	−	1.76593i	0.552433	−	0.0647422i
$745$		0			0
$746$	−34.6754	−	5.97197i	−1.26956	−	0.218650i
$747$	21.7826	−	15.8260i	0.796983	−	0.579042i
$748$	−9.79056	+	2.89195i	−0.357978	+	0.105740i
$749$		−	53.5254i		−	1.95577i
$750$		0			0
$751$	−3.24240			−0.118317			−0.0591584	−	0.998249i	$-0.518842\pi$
$751$	−3.24240			−0.118317			−0.0591584	+	0.998249i	$0.518842\pi$
$752$	3.55971	−	0.947987i	0.129809	−	0.0345695i
$753$	−24.9912	−	34.3974i	−0.910728	−	1.25351i
$754$	9.18262	−	53.3176i	0.334411	−	1.94171i
$755$		0			0
$756$	−4.96930	−	3.81912i	−0.180732	−	0.138900i
$757$	−25.4279			−0.924193			−0.462096	−	0.886830i	$-0.652903\pi$
$757$	−25.4279			−0.924193			−0.462096	+	0.886830i	$0.652903\pi$
$758$	9.06187	−	1.31037i	0.329142	−	0.0475948i
$759$	1.58500	−	4.87812i	0.0575317	−	0.177064i
$760$		0			0
$761$	5.54324	+	17.0603i	0.200942	+	0.618437i	0.999856	+	0.0169909i	$0.00540862\pi$
$761$	5.54324	+	17.0603i	0.200942	+	0.618437i	−0.798913	+	0.601446i	$0.794591\pi$
$762$	−5.56377	−	11.2931i	−0.201554	−	0.409106i
$763$	9.58753	−	29.5074i	0.347092	−	1.06824i
$764$	−19.8852	+	5.87373i	−0.719422	+	0.212504i
$765$		0			0
$766$	−1.91226	−	3.88141i	−0.0690926	−	0.140241i
$767$	−15.8459	+	21.8100i	−0.572161	+	0.787512i
$768$	−40.0743	−	4.33597i	−1.44606	−	0.156461i
$769$	−9.85987	−	7.16362i	−0.355556	−	0.258327i	0.395640	−	0.918406i	$-0.370523\pi$
$769$	−9.85987	−	7.16362i	−0.355556	−	0.258327i	−0.751196	+	0.660079i	$0.770523\pi$
$770$		0			0
$771$	6.55427	+	9.02118i	0.236046	+	0.324890i
$772$	−1.18811	+	0.815228i	−0.0427610	+	0.0293407i
$773$	−6.29718	−	19.3807i	−0.226494	−	0.697076i	−0.998137	−	0.0610199i	$-0.980565\pi$
$773$	−6.29718	−	19.3807i	−0.226494	−	0.697076i	0.771643	−	0.636056i	$-0.219435\pi$
$774$	−2.15301	−	2.21182i	−0.0773884	−	0.0795022i
$775$		0			0
$776$	10.8166	+	11.7283i	0.388294	+	0.421022i
$777$	76.2186	−	24.7649i	2.73433	−	0.888437i
$778$	−6.74491	+	39.1633i	−0.241817	+	1.40407i
$779$	10.9343	+	15.0497i	0.391761	+	0.539213i
$780$		0			0
$781$	8.55573	−	11.7760i	0.306148	−	0.421377i
$782$	1.48876	+	1.52942i	0.0532379	+	0.0546920i
$783$	2.87030	−	3.95063i	0.102576	−	0.141184i
$784$	8.45193	−	21.9178i	0.301855	−	0.782777i
$785$		0			0
$786$	21.2681	+	11.2001i	0.758607	+	0.399493i
$787$	−0.608835	+	1.87380i	−0.0217026	+	0.0667938i	−0.961321	−	0.275430i	$-0.911180\pi$
$787$	−0.608835	+	1.87380i	−0.0217026	+	0.0667938i	0.939619	+	0.342223i	$0.111180\pi$
$788$	11.2608	+	3.99735i	0.401149	+	0.142400i
$789$	29.4177	−	9.55840i	1.04730	−	0.340288i
$790$		0			0
$791$	6.55119	−	20.1625i	0.232934	−	0.716896i
$792$	−2.89126	−	24.6705i	−0.102736	−	0.876630i
$793$		−	44.6976i		−	1.58726i
$794$	−7.08024	−	48.9634i	−0.251268	−	1.73765i
$795$		0			0
$796$	14.8980	+	21.7122i	0.528045	+	0.769570i
$797$	18.3873	−	13.3592i	0.651313	−	0.473206i	−0.212405	−	0.977182i	$-0.568130\pi$
$797$	18.3873	−	13.3592i	0.651313	−	0.473206i	0.863718	+	0.503975i	$0.168130\pi$
$798$	30.4867	−	57.8919i	1.07922	−	2.04935i
$799$	−1.79141			−0.0633756
$800$		0			0
$801$	36.3498			1.28436
$802$	−8.81201	+	16.7334i	−0.311163	+	0.590875i
$803$	31.4798	−	22.8714i	1.11090	−	0.807114i
$804$	14.0186	+	20.4307i	0.494399	+	0.720536i
$805$		0			0
$806$	−2.94863	−	20.3912i	−0.103861	−	0.718250i
$807$			72.3059i			2.54529i
$808$	−0.0668109	−	0.570085i	−0.00235040	−	0.0200555i
$809$	−15.7618	+	48.5099i	−0.554156	+	1.70552i	0.144007	+	0.989577i	$0.454001\pi$
$809$	−15.7618	+	48.5099i	−0.554156	+	1.70552i	−0.698163	+	0.715939i	$0.745999\pi$
$810$		0			0
$811$	42.6096	−	13.8447i	1.49622	−	0.486153i	0.557310	−	0.830305i	$-0.311834\pi$
$811$	42.6096	−	13.8447i	1.49622	−	0.486153i	0.938914	+	0.344152i	$0.111834\pi$
$812$	37.8080	+	13.4211i	1.32680	+	0.470987i
$813$	−2.85449	+	8.78521i	−0.100111	+	0.308111i
$814$	29.1132	+	15.3314i	1.02042	+	0.537366i
$815$		0			0
$816$	18.2891	+	7.05264i	0.640246	+	0.246892i
$817$	1.96211	−	2.70061i	0.0686456	−	0.0944826i
$818$	27.1395	+	27.8808i	0.948909	+	0.974828i
$819$	−48.2928	+	66.4694i	−1.68749	+	2.32263i
$820$		0			0
$821$	16.5666	+	22.8020i	0.578180	+	0.795796i	0.993494	−	0.113881i	$-0.0363284\pi$
$821$	16.5666	+	22.8020i	0.578180	+	0.795796i	−0.415314	+	0.909678i	$0.636328\pi$
$822$	4.98399	−	28.9388i	0.173837	−	1.00936i
$823$	3.43957	−	1.11758i	0.119896	−	0.0389565i	−0.248455	−	0.968644i	$-0.579923\pi$
$823$	3.43957	−	1.11758i	0.119896	−	0.0389565i	0.368350	+	0.929687i	$0.379923\pi$
$824$	−25.3157	−	27.4495i	−0.881916	−	0.956250i
$825$		0			0
$826$	−13.9441	−	14.3249i	−0.485176	−	0.498428i
$827$	−8.71857	−	26.8330i	−0.303174	−	0.933075i	−0.980352	−	0.197255i	$-0.936797\pi$
$827$	−8.71857	−	26.8330i	−0.303174	−	0.933075i	0.677178	−	0.735819i	$-0.263203\pi$
$828$	−4.28213	+	2.93821i	−0.148814	+	0.102110i
$829$	−31.0042	−	42.6736i	−1.07682	−	1.48212i	−0.862974	−	0.505248i	$-0.831401\pi$
$829$	−31.0042	−	42.6736i	−1.07682	−	1.48212i	−0.213846	−	0.976867i	$-0.568599\pi$
$830$		0			0
$831$	−8.12292	−	5.90165i	−0.281781	−	0.204726i
$832$	−4.42003	+	54.5610i	−0.153237	+	1.89156i
$833$	−6.71462	+	9.24188i	−0.232648	+	0.320212i
$834$	−2.14469	−	4.35319i	−0.0742645	−	0.150739i
$835$		0			0
$836$	25.7626	−	7.60980i	0.891018	−	0.263190i
$837$	0.574659	−	1.76862i	0.0198631	−	0.0611324i
$838$	−24.8340	−	50.4069i	−0.857876	−	1.74128i
$839$	2.76644	+	8.51422i	0.0955081	+	0.293944i	0.987386	−	0.158333i	$-0.0506120\pi$
$839$	2.76644	+	8.51422i	0.0955081	+	0.293944i	−0.891878	+	0.452277i	$0.850612\pi$
$840$		0			0
$841$	−0.698169	+	2.14874i	−0.0240748	+	0.0740946i
$842$	−6.54940	+	0.947061i	−0.225707	+	0.0326379i
$843$	−71.6357			−2.46726
$844$	−8.71478	−	6.69768i	−0.299975	−	0.230544i
$845$		0			0
$846$	0.739798	−	4.29553i	0.0254348	−	0.147683i
$847$	−8.67620	−	11.9418i	−0.298118	−	0.410324i
$848$	−1.88983	−	7.09635i	−0.0648971	−	0.243690i
$849$	32.8838			1.12857
$850$		0			0
$851$		−	6.87919i		−	0.235816i
$852$	−26.8039	+	7.91737i	−0.918285	+	0.271245i
$853$	−25.4769	+	18.5100i	−0.872312	+	0.633772i	−0.931206	−	0.364492i	$-0.881243\pi$
$853$	−25.4769	+	18.5100i	−0.872312	+	0.633772i	0.0588942	+	0.998264i	$0.481243\pi$
$854$	32.6644	+	5.62563i	1.11775	+	0.192505i
$855$		0			0
$856$	−41.9090	+	4.91151i	−1.43242	+	0.167872i
$857$		−	47.9238i		−	1.63705i	−0.574473	−	0.818523i	$-0.694793\pi$
$857$		−	47.9238i		−	1.63705i	0.574473	−	0.818523i	$-0.305207\pi$
$858$	−63.3123	+	9.15512i	−2.16145	+	0.312551i
$859$	−25.9430	−	8.42940i	−0.885164	−	0.287607i	−0.169064	−	0.985605i	$-0.554075\pi$
$859$	−25.9430	−	8.42940i	−0.885164	−	0.287607i	−0.716100	+	0.697998i	$0.754075\pi$
$860$		0			0
$861$	31.2423	−	10.1512i	1.06473	−	0.345953i
$862$	25.5183	−	12.5721i	0.869157	−	0.428208i
$863$	−40.6471	−	13.2070i	−1.38364	−	0.449573i	−0.479778	−	0.877390i	$-0.659283\pi$
$863$	−40.6471	−	13.2070i	−1.38364	−	0.449573i	−0.903865	+	0.427817i	$0.859283\pi$
$864$	−2.53429	+	4.24128i	−0.0862183	+	0.144291i
$865$		0			0
$866$	0.879458	+	1.78509i	0.0298852	+	0.0606597i
$867$	26.9364	+	19.5704i	0.914807	+	0.664646i
$868$	15.2727	+	0.411620i	0.518391	+	0.0139713i
$869$	14.5926	−	20.0850i	0.495020	−	0.681337i
$870$		0			0
$871$	27.2225	−	19.7783i	0.922400	−	0.670163i
$872$	−23.9833	−	4.79918i	−0.812176	−	0.162521i
$873$	17.9542	−	5.83367i	0.607657	−	0.197440i
$874$	−3.91747	−	4.02447i	−0.132510	−	0.136130i
$875$		0			0
$876$	−74.6861	−	2.01289i	−2.52341	−	0.0680091i
$877$	17.9202	+	55.1526i	0.605121	+	1.86237i	0.495953	+	0.868349i	$0.334819\pi$
$877$	17.9202	+	55.1526i	0.605121	+	1.86237i	0.109168	+	0.994023i	$0.465181\pi$
$878$	19.5721	+	3.37081i	0.660527	+	0.113759i
$879$	−55.1055	+	40.0365i	−1.85866	+	1.35040i
$880$		0			0
$881$	14.3649	+	10.4367i	0.483965	+	0.351621i	0.802859	−	0.596169i	$-0.203311\pi$
$881$	14.3649	+	10.4367i	0.483965	+	0.351621i	−0.318894	+	0.947790i	$0.603311\pi$
$882$	−19.3877	−	19.9172i	−0.652817	−	0.670648i
$883$	34.4318	+	25.0162i	1.15872	+	0.841861i	0.989616	−	0.143736i	$-0.0459118\pi$
$883$	34.4318	+	25.0162i	1.15872	+	0.841861i	0.169107	+	0.985598i	$0.445912\pi$
$884$	8.90507	−	25.0861i	0.299510	−	0.843738i
$885$		0			0
$886$	−6.17547	+	11.7267i	−0.207469	+	0.393968i
$887$	37.7360	+	12.2612i	1.26705	+	0.411689i	0.864001	−	0.503489i	$-0.167951\pi$
$887$	37.7360	+	12.2612i	1.26705	+	0.411689i	0.403048	+	0.915179i	$0.367951\pi$
$888$	−26.3841	−	57.4047i	−0.885394	−	1.92638i
$889$	−3.91768	−	12.0574i	−0.131395	−	0.404392i
$890$		0			0
$891$	19.5653	+	6.35716i	0.655463	+	0.212973i
$892$	−32.2983	−	24.8226i	−1.08143	−	0.831122i
$893$	4.71386			0.157743
$894$	−33.3666	+	4.82490i	−1.11595	+	0.161369i
$895$		0			0
$896$	−39.3161	−	10.0971i	−1.31346	−	0.337321i
$897$	7.86135	+	10.8202i	0.262483	+	0.361277i
$898$	−17.8573	+	33.9096i	−0.595904	+	1.13158i
$899$			11.9042i			0.397026i
$900$		0			0
$901$			3.57122i			0.118974i
$902$	11.9336	+	6.28440i	0.397346	+	0.209248i
$903$	−3.46488	−	4.76900i	−0.115304	−	0.158703i
$904$	−16.3879	−	3.27930i	−0.545052	−	0.109068i
$905$		0			0
$906$	4.07674	+	28.1927i	0.135440	+	0.936639i
$907$	34.9093			1.15914			0.579571	−	0.814921i	$-0.303220\pi$
$907$	34.9093			1.15914			0.579571	+	0.814921i	$0.303220\pi$
$908$	−19.2911	+	25.1009i	−0.640199	+	0.833004i
$909$	−0.645920	−	0.209872i	−0.0214238	−	0.00696102i
$910$		0			0
$911$	−7.05588	−	21.7158i	−0.233772	−	0.719476i	−0.997282	−	0.0736799i	$-0.976526\pi$
$911$	−7.05588	−	21.7158i	−0.233772	−	0.719476i	0.763510	−	0.645796i	$-0.223474\pi$
$912$	−48.1254	−	18.5581i	−1.59359	−	0.614520i
$913$	20.0781	+	6.52377i	0.664488	+	0.215905i
$914$	40.2784	+	21.2112i	1.33229	+	0.701603i
$915$		0			0
$916$	−4.28668	+	12.0758i	−0.141636	+	0.398997i
$917$	19.5831	+	14.2280i	0.646692	+	0.469850i
$918$	1.72169	−	1.67591i	0.0568241	−	0.0553133i
$919$	−44.3337	−	32.2104i	−1.46244	−	1.06252i	−0.982720	−	0.185097i	$-0.940740\pi$
$919$	−44.3337	−	32.2104i	−1.46244	−	1.06252i	−0.479715	−	0.877424i	$-0.659260\pi$
$920$		0			0
$921$	47.1203	−	34.2349i	1.55267	−	1.12808i
$922$	−0.630861	+	3.66300i	−0.0207763	+	0.120634i
$923$	11.7288	+	36.0975i	0.386058	+	1.18816i
$924$	1.27803	−	47.4200i	0.0420441	−	1.56000i
$925$		0			0
$926$	30.6580	−	29.8429i	1.00748	−	0.980698i
$927$	−42.0209	+	13.6534i	−1.38015	+	0.448437i
$928$	7.03907	−	30.8342i	0.231069	−	1.01218i
$929$	−26.3740	+	19.1618i	−0.865301	+	0.628678i	−0.929322	−	0.369270i	$-0.879608\pi$
$929$	−26.3740	+	19.1618i	−0.865301	+	0.628678i	0.0640206	+	0.997949i	$0.479608\pi$
$930$		0			0
$931$	17.6686	−	24.3188i	0.579066	−	0.797016i
$932$	−35.1617	−	0.947653i	−1.15176	−	0.0310414i
$933$	21.7992	+	15.8380i	0.713673	+	0.518514i
$934$	−52.3258	+	25.7793i	−1.71215	+	0.843526i
$935$		0			0
$936$	56.4752	+	31.7128i	1.84595	+	1.03656i
$937$	−7.69340	−	2.49974i	−0.251332	−	0.0816628i	0.180641	−	0.983549i	$-0.442183\pi$
$937$	−7.69340	−	2.49974i	−0.251332	−	0.0816628i	−0.431974	+	0.901886i	$0.642183\pi$
$938$	11.0275	+	22.3831i	0.360061	+	0.730835i
$939$	−16.6789	+	5.41932i	−0.544297	+	0.176853i
$940$		0			0
$941$	34.7042	+	11.2761i	1.13133	+	0.367590i	0.814080	−	0.580753i	$-0.197242\pi$
$941$	34.7042	+	11.2761i	1.13133	+	0.367590i	0.317246	+	0.948343i	$0.397242\pi$
$942$	−3.96728	−	27.4357i	−0.129261	−	0.893904i
$943$		−	2.81981i		−	0.0918255i
$944$	−9.93655	+	12.2323i	−0.323407	+	0.398128i
$945$		0			0
$946$	0.410776	−	2.38511i	0.0133555	−	0.0775467i
$947$	12.2602	−	8.90757i	0.398404	−	0.289457i	−0.370487	−	0.928838i	$-0.620809\pi$
$947$	12.2602	−	8.90757i	0.398404	−	0.289457i	0.768890	+	0.639380i	$0.220809\pi$
$948$	−45.7165	+	13.5038i	−1.48480	+	0.438584i
$949$			101.463i			3.29362i
$950$		0			0
$951$	−7.05851			−0.228888
$952$	17.2118	+	9.66504i	0.557838	+	0.313246i
$953$	32.0176	+	44.0685i	1.03715	+	1.42752i	0.899439	+	0.437047i	$0.143976\pi$
$953$	32.0176	+	44.0685i	1.03715	+	1.42752i	0.137714	+	0.990472i	$0.456024\pi$
$954$	−8.56323	−	1.47480i	−0.277245	−	0.0477485i
$955$		0			0
$956$	−10.2837	+	13.3807i	−0.332597	+	0.432763i
$957$	36.9610			1.19478
$958$	3.19508	+	22.0956i	0.103228	+	0.713875i
$959$	9.13812	−	28.1242i	0.295085	−	0.908179i
$960$		0			0
$961$	−8.17865	−	25.1713i	−0.263827	−	0.811977i
$962$	−76.9637	+	37.9177i	−2.48141	+	1.22252i
$963$	−15.4285	+	47.4839i	−0.497175	+	1.53015i
$964$	−6.68335	+	1.97414i	−0.215256	+	0.0635828i
$965$		0			0
$966$	−8.89670	+	4.38314i	−0.286247	+	0.141025i
$967$	12.9780	−	17.8627i	0.417344	−	0.574424i	−0.547647	−	0.836710i	$-0.684476\pi$
$967$	12.9780	−	17.8627i	0.417344	−	0.574424i	0.964990	+	0.262285i	$0.0844762\pi$
$968$	−8.55397	+	7.88903i	−0.274935	+	0.253563i
$969$	20.2926	+	14.7434i	0.651892	+	0.473628i
$970$		0			0
$971$	−5.05516	−	6.95783i	−0.162228	−	0.223287i	0.720163	−	0.693805i	$-0.244067\pi$
$971$	−5.05516	−	6.95783i	−0.162228	−	0.223287i	−0.882390	+	0.470518i	$0.844067\pi$
$972$	−25.3135	−	36.8917i	−0.811930	−	1.18330i
$973$	−1.51016	−	4.64781i	−0.0484137	−	0.149002i
$974$	36.3105	−	35.3450i	1.16346	−	1.13253i
$975$		0			0
$976$	1.40742	−	26.0916i	0.0450505	−	0.835171i
$977$	18.1117	−	5.88484i	0.579444	−	0.188273i	−0.00460737	−	0.999989i	$-0.501467\pi$
$977$	18.1117	−	5.88484i	0.579444	−	0.188273i	0.584052	+	0.811717i	$0.301467\pi$
$978$	80.6719	+	13.8937i	2.57960	+	0.444273i
$979$	16.7527	+	23.0581i	0.535418	+	0.736940i
$980$		0			0
$981$	−17.0107	+	23.4133i	−0.543111	+	0.747529i
$982$	7.57244	−	7.37111i	0.241646	−	0.235221i
$983$	−12.0848	+	16.6333i	−0.385446	+	0.530521i	−0.957017	−	0.290032i	$-0.906334\pi$
$983$	−12.0848	+	16.6333i	−0.385446	+	0.530521i	0.571571	+	0.820553i	$0.306334\pi$
$984$	−10.8150	−	23.5304i	−0.344768	−	0.750122i
$985$		0			0
$986$	−7.16653	+	13.6087i	−0.228229	+	0.433390i
$987$	2.57232	−	7.91678i	0.0818777	−	0.251994i
$988$	−23.4325	+	66.0109i	−0.745488	+	2.10009i
$989$	−0.481237	+	0.156364i	−0.0153025	+	0.00497207i
$990$		0			0
$991$	−7.98983	+	24.5902i	−0.253805	+	0.781132i	0.740258	+	0.672323i	$0.234704\pi$
$991$	−7.98983	+	24.5902i	−0.253805	+	0.781132i	−0.994063	+	0.108809i	$0.965296\pi$
$992$	−1.07915	−	11.9959i	−0.0342629	−	0.380871i
$993$			66.8905i			2.12271i
$994$	−27.8558	+	4.02802i	−0.883531	+	0.127761i
$995$		0			0
$996$	−22.9342	−	33.4242i	−0.726699	−	1.05909i
$997$	15.5099	−	11.2686i	0.491204	−	0.356881i	−0.314443	−	0.949276i	$-0.601818\pi$
$997$	15.5099	−	11.2686i	0.491204	−	0.356881i	0.805647	+	0.592396i	$0.201818\pi$
$998$	2.02170	+	1.06466i	0.0639958	+	0.0337011i
$999$	−7.74398			−0.245009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.349.10		112
5.2	odd	4		1000.2.t.b.901.9		224
5.3	odd	4		1000.2.t.b.901.48		224
5.4	even	2		200.2.o.a.69.19	yes	112
8.5	even	2	inner	1000.2.o.a.349.5		112
20.19	odd	2		800.2.be.a.369.25		112
25.3	odd	20		1000.2.t.b.101.20		224
25.4	even	10	inner	1000.2.o.a.149.5		112
25.21	even	5		200.2.o.a.29.24	yes	112
25.22	odd	20		1000.2.t.b.101.37		224
40.13	odd	4		1000.2.t.b.901.20		224
40.19	odd	2		800.2.be.a.369.4		112
40.29	even	2		200.2.o.a.69.24	yes	112
40.37	odd	4		1000.2.t.b.901.37		224
100.71	odd	10		800.2.be.a.529.4		112
200.21	even	10		200.2.o.a.29.19	✓	112
200.29	even	10	inner	1000.2.o.a.149.10		112
200.53	odd	20		1000.2.t.b.101.48		224
200.171	odd	10		800.2.be.a.529.25		112
200.197	odd	20		1000.2.t.b.101.9		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.19	✓	112	200.21	even	10
200.2.o.a.29.24	yes	112	25.21	even	5
200.2.o.a.69.19	yes	112	5.4	even	2
200.2.o.a.69.24	yes	112	40.29	even	2
800.2.be.a.369.4		112	40.19	odd	2
800.2.be.a.369.25		112	20.19	odd	2
800.2.be.a.529.4		112	100.71	odd	10
800.2.be.a.529.25		112	200.171	odd	10
1000.2.o.a.149.5		112	25.4	even	10	inner
1000.2.o.a.149.10		112	200.29	even	10	inner
1000.2.o.a.349.5		112	8.5	even	2	inner
1000.2.o.a.349.10		112	1.1	even	1	trivial
1000.2.t.b.101.9		224	200.197	odd	20
1000.2.t.b.101.20		224	25.3	odd	20
1000.2.t.b.101.37		224	25.22	odd	20
1000.2.t.b.101.48		224	200.53	odd	20
1000.2.t.b.901.9		224	5.2	odd	4
1000.2.t.b.901.20		224	40.13	odd	4
1000.2.t.b.901.37		224	40.37	odd	4
1000.2.t.b.901.48		224	5.3	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)

\(f(q)\)	\(=\)	\(q+(-0.658957 + 1.25131i) q^{2} +(2.03813 - 1.48079i) q^{3} +(-1.13155 - 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} +3.58786i q^{7} +(2.80920 - 0.329223i) q^{8} +(1.03418 - 3.18289i) q^{9} +O(q^{10})\)	\(q+(-0.658957 + 1.25131i) q^{2} +(2.03813 - 1.48079i) q^{3} +(-1.13155 - 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} +3.58786i q^{7} +(2.80920 - 0.329223i) q^{8} +(1.03418 - 3.18289i) q^{9} +(2.49567 - 0.810891i) q^{11} +(-4.74824 - 1.68553i) q^{12} +(-2.11444 + 6.50757i) q^{13} +(-4.48952 - 2.36424i) q^{14} +(-1.43918 + 3.73212i) q^{16} +(1.14335 - 1.57369i) q^{17} +(3.30130 + 3.39148i) q^{18} +(-3.00859 + 4.14097i) q^{19} +(5.31285 + 7.31251i) q^{21} +(-0.629861 + 3.65719i) q^{22} +(0.737902 - 0.239759i) q^{23} +(5.23800 - 4.83083i) q^{24} +(-6.74966 - 6.93403i) q^{26} +(-0.269899 - 0.830663i) q^{27} +(5.91680 - 4.05985i) q^{28} +(3.28631 + 4.52322i) q^{29} +(1.72253 + 1.25149i) q^{31} +(-3.72168 - 4.26017i) q^{32} +(3.88573 - 5.34825i) q^{33} +(1.21576 + 2.46769i) q^{34} +(-6.41920 + 1.89612i) q^{36} +(2.73986 - 8.43241i) q^{37} +(-3.19910 - 6.49339i) q^{38} +(5.32683 + 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(-12.6512 + 1.82939i) q^{42} -0.652170 q^{43} +(-4.16123 - 3.19808i) q^{44} +(-0.186233 + 1.08133i) q^{46} +(-0.541317 - 0.745059i) q^{47} +(2.59324 + 9.73767i) q^{48} -5.87273 q^{49} -4.90045i q^{51} +(13.1244 - 3.87669i) q^{52} +(-1.48529 + 1.07913i) q^{53} +(1.21727 + 0.209644i) q^{54} +(1.18121 + 10.0790i) q^{56} +12.8949i q^{57} +(-7.82548 + 1.13159i) q^{58} +(3.74706 + 1.21749i) q^{59} +(-6.21266 + 2.01862i) q^{61} +(-2.70108 + 1.33074i) q^{62} +(11.4198 + 3.71051i) q^{63} +(7.78322 - 1.84971i) q^{64} +(4.13179 + 8.38651i) q^{66} +(-3.97847 - 2.89052i) q^{67} +(-3.88897 - 0.104813i) q^{68} +(1.14891 - 1.58133i) q^{69} +(4.48762 - 3.26045i) q^{71} +(1.85735 - 9.28187i) q^{72} +(14.1026 - 4.58222i) q^{73} +(8.74611 + 8.98500i) q^{74} +(10.2333 + 0.275801i) q^{76} +(2.90936 + 8.95410i) q^{77} +(-24.0245 - 4.13762i) q^{78} +(7.65406 - 5.56100i) q^{79} +(6.34247 + 4.60807i) q^{81} +(3.58506 + 3.68298i) q^{82} +(6.50869 + 4.72884i) q^{83} +(6.04743 - 17.0360i) q^{84} +(0.429752 - 0.816067i) q^{86} +(13.3958 + 4.35257i) q^{87} +(6.74386 - 3.09959i) q^{88} +(3.35636 + 10.3298i) q^{89} +(-23.3483 - 7.58631i) q^{91} +(-1.23036 - 0.945588i) q^{92} +5.36393 q^{93} +(1.28900 - 0.186393i) q^{94} +(-13.8937 - 3.17175i) q^{96} +(3.31560 + 4.56353i) q^{97} +(3.86988 - 7.34861i) q^{98} -8.78205i 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

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Database

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