LMFDB - Embedded newform 1000.2.o.a.349.5

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			349.5
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26861 - 0.625006i) q^{2} +(-2.03813 + 1.48079i) q^{3} +(1.21874 + 1.58578i) q^{4} +(3.51109 - 0.604697i) q^{6} +3.58786i q^{7} +(-0.554981 - 2.77344i) q^{8} +(1.03418 - 3.18289i) q^{9} +O(q^{10})$	\(q+(-1.26861 - 0.625006i) q^{2} +(-2.03813 + 1.48079i) q^{3} +(1.21874 + 1.58578i) q^{4} +(3.51109 - 0.604697i) q^{6} +3.58786i q^{7} +(-0.554981 - 2.77344i) q^{8} +(1.03418 - 3.18289i) q^{9} +(-2.49567 + 0.810891i) q^{11} +(-4.83213 - 1.42732i) q^{12} +(2.11444 - 6.50757i) q^{13} +(2.24243 - 4.55159i) q^{14} +(-1.02937 + 3.86528i) 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} +(3.67283 + 0.531102i) 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} +(-5.68954 + 4.37265i) 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} +(-2.43404 + 1.28180i) q^{34} +(6.30775 - 2.23912i) q^{36} +(-2.73986 + 8.43241i) q^{37} +(-6.40485 + 3.37288i) q^{38} +(5.32683 + 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(2.16957 + 12.5973i) q^{42} +0.652170 q^{43} +(-4.32745 - 2.96930i) q^{44} +(-1.08596 - 0.157033i) q^{46} +(-0.541317 - 0.745059i) q^{47} +(-3.62568 - 9.40221i) q^{48} -5.87273 q^{49} +4.90045i q^{51} +(12.8965 - 4.57799i) q^{52} +(1.48529 - 1.07913i) q^{53} +(0.176773 - 1.22247i) q^{54} +(9.95073 - 1.99119i) q^{56} +12.8949i q^{57} +(1.34200 + 7.79215i) q^{58} +(-3.74706 - 1.21749i) q^{59} +(6.21266 - 2.01862i) q^{61} +(-1.40303 - 2.66424i) q^{62} +(11.4198 + 3.71051i) q^{63} +(-7.38399 + 3.07842i) q^{64} +(-8.27215 + 4.35623i) 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} +(-9.40153 - 1.10181i) 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} +(3.48886 - 24.1272i) 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} +(5.12104 - 17.3370i) q^{84} +(-0.827349 - 0.407610i) q^{86} +(13.3958 + 4.35257i) q^{87} +(3.63401 + 6.47156i) q^{88} +(3.35636 + 10.3298i) q^{89} +(23.3483 + 7.58631i) q^{91} +(1.27951 + 0.877943i) q^{92} -5.36393 q^{93} +(0.221053 + 1.28351i) q^{94} +(-1.27686 + 14.1938i) q^{96} +(3.31560 + 4.56353i) q^{97} +(7.45020 + 3.67049i) 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 $

$2$	−1.26861	−	0.625006i	−0.897042	−	0.441946i
$2$	−1.26861	−	0.625006i	−0.897042	−	0.441946i
$3$	−2.03813	+	1.48079i	−1.17671	+	0.854932i	−0.991797	−	0.127822i	$-0.959201\pi$
$3$	−2.03813	+	1.48079i	−1.17671	+	0.854932i	−0.184916	+	0.982754i	$0.559201\pi$
$4$	1.21874	+	1.58578i	0.609368	+	0.792888i
$5$		0			0
$5$		0			0
$6$	3.51109	−	0.604697i	1.43339	−	0.246867i
$7$			3.58786i			1.35608i	0.735024	+	0.678042i	$0.237171\pi$
$7$			3.58786i			1.35608i	−0.735024	+	0.678042i	$0.762829\pi$
$8$	−0.554981	−	2.77344i	−0.196215	−	0.980561i
$9$	1.03418	−	3.18289i	0.344728	−	1.06096i
$10$		0			0
$11$	−2.49567	+	0.810891i	−0.752472	+	0.244493i	−0.660044	−	0.751227i	$-0.729463\pi$
$11$	−2.49567	+	0.810891i	−0.752472	+	0.244493i	−0.0924272	+	0.995719i	$0.529463\pi$
$12$	−4.83213	−	1.42732i	−1.39492	−	0.412033i
$13$	2.11444	−	6.50757i	0.586440	−	1.80488i	−0.00697033	−	0.999976i	$-0.502219\pi$
$13$	2.11444	−	6.50757i	0.586440	−	1.80488i	0.593410	−	0.804900i	$-0.297781\pi$
$14$	2.24243	−	4.55159i	0.599315	−	1.21646i
$15$		0			0
$16$	−1.02937	+	3.86528i	−0.257341	+	0.966321i
$17$	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	−0.309782	−	0.950808i	$-0.600256\pi$
$19$	3.00859	−	4.14097i	0.690218	−	0.950003i	1.00000		0.000804663i	$0.000256132\pi$
$20$		0			0
$21$	−5.31285	−	7.31251i	−1.15936	−	1.59572i
$22$	3.67283	+	0.531102i	0.783051	+	0.113231i
$23$	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
$28$	−5.68954	+	4.37265i	−1.07522	+	0.826354i
$29$	−3.28631	−	4.52322i	−0.610252	−	0.839940i	0.386346	−	0.922354i	$-0.373737\pi$
$29$	−3.28631	−	4.52322i	−0.610252	−	0.839940i	−0.996598	+	0.0824137i	$0.973737\pi$
$30$		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
$34$	−2.43404	+	1.28180i	−0.417434	+	0.219826i
$35$		0			0
$36$	6.30775	−	2.23912i	1.05129	−	0.373187i
$37$	−2.73986	+	8.43241i	−0.450430	+	1.38628i	0.425988	+	0.904729i	$0.359926\pi$
$37$	−2.73986	+	8.43241i	−0.450430	+	1.38628i	−0.876418	+	0.481551i	$0.840074\pi$
$38$	−6.40485	+	3.37288i	−1.03900	+	0.547154i
$39$	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	$0.00840642\pi$
$42$	2.16957	+	12.5973i	0.334772	+	1.94380i
$43$	0.652170			0.0994550			0.0497275	−	0.998763i	$-0.484165\pi$
$43$	0.652170			0.0994550			0.0497275	+	0.998763i	$0.484165\pi$
$44$	−4.32745	−	2.96930i	−0.652387	−	0.447639i
$45$		0			0
$46$	−1.08596	−	0.157033i	−0.160116	−	0.0231532i
$47$	−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	$0.821396\pi$
$48$	−3.62568	−	9.40221i	−0.523322	−	1.35709i
$49$	−5.87273			−0.838962
$50$		0			0
$51$			4.90045i			0.686201i
$52$	12.8965	−	4.57799i	1.78842	−	0.634853i
$53$	1.48529	−	1.07913i	0.204020	−	0.148229i	−0.481084	−	0.876675i	$-0.659757\pi$
$53$	1.48529	−	1.07913i	0.204020	−	0.148229i	0.685104	+	0.728445i	$0.259757\pi$
$54$	0.176773	−	1.22247i	0.0240558	−	0.166358i
$55$		0			0
$56$	9.95073	−	1.99119i	1.32972	−	0.266084i
$57$			12.8949i			1.70797i
$58$	1.34200	+	7.79215i	0.176214	+	1.02316i
$59$	−3.74706	−	1.21749i	−0.487826	−	0.158504i	0.0547685	−	0.998499i	$-0.482558\pi$
$59$	−3.74706	−	1.21749i	−0.487826	−	0.158504i	−0.542594	+	0.839995i	$0.682558\pi$
$60$		0			0
$61$	6.21266	−	2.01862i	0.795449	−	0.258457i	0.117027	−	0.993129i	$-0.462664\pi$
$61$	6.21266	−	2.01862i	0.795449	−	0.258457i	0.678423	+	0.734672i	$0.262664\pi$
$62$	−1.40303	−	2.66424i	−0.178185	−	0.338359i
$63$	11.4198	+	3.71051i	1.43876	+	0.467480i
$64$	−7.38399	+	3.07842i	−0.922999	+	0.384802i
$65$		0			0
$66$	−8.27215	+	4.35623i	−1.01823	+	0.536215i
$67$	3.97847	+	2.89052i	0.486047	+	0.353134i	0.803662	−	0.595086i	$-0.202882\pi$
$67$	3.97847	+	2.89052i	0.486047	+	0.353134i	−0.317615	+	0.948220i	$0.602882\pi$
$68$	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	$0.193236\pi$
$72$	−9.40153	−	1.10181i	−1.10798	−	0.129850i
$73$	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
$78$	3.48886	−	24.1272i	0.395036	−	2.73187i
$79$	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	0.170176	−	0.985414i	$-0.445567\pi$
$83$	−6.50869	−	4.72884i	−0.714422	−	0.519058i	−0.884597	+	0.466356i	$0.845567\pi$
$84$	5.12104	−	17.3370i	0.558751	−	1.89162i
$85$		0			0
$86$	−0.827349	−	0.407610i	−0.0892153	−	0.0439537i
$87$	13.3958	+	4.35257i	1.43618	+	0.466645i
$88$	3.63401	+	6.47156i	0.387387	+	0.689871i
$89$	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
$92$	1.27951	+	0.877943i	0.133398	+	0.0915319i
$93$	−5.36393			−0.556213
$94$	0.221053	+	1.28351i	0.0227999	+	0.132384i
$95$		0			0
$96$	−1.27686	+	14.1938i	−0.130319	+	1.44865i
$97$	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	$0.707551\pi$
$98$	7.45020	+	3.67049i	0.752584	+	0.370776i
$99$			8.78205i			0.882629i
$100$		0			0
$101$			0.202935i			0.0201928i	0.999949	+	0.0100964i	$0.00321383\pi$
$101$			0.202935i			0.0201928i	−0.999949	+	0.0100964i	$0.996786\pi$
$102$	3.06281	−	6.21676i	0.303263	−	0.615551i
$103$	−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	$-0.425407\pi$
$104$	−19.2219	−	2.25270i	−1.88486	−	0.220895i
$105$		0			0
$106$	−2.55871	+	0.440675i	−0.248524	+	0.0428021i
$107$	14.9185			1.44222			0.721111	−	0.692819i	$-0.243632\pi$
$107$	14.9185			1.44222			0.721111	+	0.692819i	$0.243632\pi$
$108$	−0.988310	+	1.44036i	−0.0951001	+	0.138599i
$109$	8.22423	+	2.67221i	0.787738	+	0.255952i	0.675141	−	0.737689i	$-0.264083\pi$
$109$	8.22423	+	2.67221i	0.787738	+	0.255952i	0.112598	+	0.993641i	$0.464083\pi$
$110$		0			0
$111$	−6.90242	−	21.2435i	−0.655149	−	2.01634i
$112$	−13.8681	−	3.69322i	−1.31041	−	0.348976i
$113$	−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	$0.689648\pi$
$114$	8.05938	−	16.3586i	0.754830	−	1.53212i
$115$		0			0
$116$	3.16766	−	10.7240i	0.294110	−	0.995694i
$117$	−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
$122$	−9.14308	−	1.32211i	−0.827775	−	0.119699i
$123$	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	$0.450110\pi$
$128$	11.2914	+	0.709730i	0.998030	+	0.0627318i
$129$	−1.32921	+	0.965725i	−0.117030	+	0.0850273i
$130$		0			0
$131$	−3.96559	+	5.45817i	−0.346475	+	0.476883i	−0.946319	−	0.323235i	$-0.895230\pi$
$131$	−3.96559	+	5.45817i	−0.346475	+	0.476883i	0.599843	+	0.800118i	$0.295230\pi$
$132$	13.2168	−	0.356209i	1.15037	−	0.0310040i
$133$	14.8572	+	10.7944i	1.28828	+	0.935992i
$134$	−3.24052	−	6.15351i	−0.279938	−	0.531582i
$135$		0			0
$136$	−4.99909	−	2.29766i	−0.428669	−	0.197023i
$137$	−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	$0.714528\pi$
$138$	2.44585	−	1.28802i	0.208205	−	0.109644i
$139$	1.29543	−	0.420910i	0.109877	−	0.0357011i	−0.253563	−	0.967319i	$-0.581602\pi$
$139$	1.29543	−	0.420910i	0.109877	−	0.0357011i	0.363439	+	0.931618i	$0.381602\pi$
$140$		0			0
$141$	2.20655	+	0.716950i	0.185825	+	0.0603781i
$142$	−7.73083	+	1.33144i	−0.648757	+	0.111732i
$143$			17.9553i			1.50150i
$144$	11.2382	+	7.27378i	0.936519	+	0.606148i
$145$		0			0
$146$	−20.7546	−	3.00118i	−1.71767	−	0.248379i
$147$	11.9694	−	8.69626i	0.987218	−	0.717256i
$148$	−16.7111	+	5.93209i	−1.37364	+	0.487615i
$149$		−	9.46274i		−	0.775218i	−0.921824	−	0.387609i	$-0.873301\pi$
$149$		−	9.46274i		−	0.775218i	0.921824	−	0.387609i	$-0.126699\pi$
$150$		0			0
$151$	7.99542			0.650658			0.325329	−	0.945601i	$-0.394525\pi$
$151$	7.99542			0.650658			0.325329	+	0.945601i	$0.394525\pi$
$152$	−13.1545	−	6.04600i	−1.06697	−	0.490395i
$153$	−3.82646	−	5.26667i	−0.309351	−	0.425785i
$154$	−1.90552	+	13.1776i	−0.153551	+	1.06188i
$155$		0			0
$156$	−19.5057	+	28.4275i	−1.56170	+	2.27602i
$157$	7.78075			0.620971			0.310486	−	0.950578i	$-0.399508\pi$
$157$	7.78075			0.620971			0.310486	+	0.950578i	$0.399508\pi$
$158$	−13.1857	+	2.27090i	−1.04899	+	0.180663i
$159$	−1.42926	+	4.39880i	−0.113347	+	0.348847i
$160$		0			0
$161$	0.860221	+	2.64749i	0.0677949	+	0.208651i
$162$	−5.16604	−	9.80992i	−0.405883	−	0.770740i
$163$	−7.10008	+	21.8518i	−0.556121	+	1.71157i	0.136842	+	0.990593i	$0.456305\pi$
$163$	−7.10008	+	21.8518i	−0.556121	+	1.71157i	−0.692964	+	0.720973i	$0.743695\pi$
$164$	6.84992	−	2.43158i	0.534889	−	0.189875i
$165$		0			0
$166$	5.30143	+	10.0670i	0.411471	+	0.781352i
$167$	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
$172$	0.794823	+	1.03420i	0.0606047	+	0.0788566i
$173$	−4.88649	−	15.0391i	−0.371513	−	1.14340i	−0.945801	−	0.324747i	$-0.894721\pi$
$173$	−4.88649	−	15.0391i	−0.371513	−	1.14340i	0.574288	−	0.818653i	$-0.305279\pi$
$174$	−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
$178$	2.19828	−	15.2022i	0.164768	−	1.13945i
$179$	8.68076	+	11.9480i	0.648830	+	0.893038i	0.999048	−	0.0436301i	$-0.0138923\pi$
$179$	8.68076	+	11.9480i	0.648830	+	0.893038i	−0.350217	+	0.936668i	$0.613892\pi$
$180$		0			0
$181$	−3.16443	+	4.35546i	−0.235210	+	0.323739i	−0.910263	−	0.414030i	$-0.864121\pi$
$181$	−3.16443	+	4.35546i	−0.235210	+	0.323739i	0.675053	+	0.737769i	$0.264121\pi$
$182$	−24.8783	−	24.2168i	−1.84410	−	1.79507i
$183$	−9.67305	+	13.3138i	−0.715053	+	0.984186i
$184$	−1.07448	−	1.91347i	−0.0792116	−	0.141063i
$185$		0			0
$186$	6.80473	+	3.35249i	0.498947	+	0.245816i
$187$	−1.57734	+	4.85455i	−0.115346	+	0.355000i
$188$	0.521773	−	1.76644i	0.0380542	−	0.128831i
$189$	−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	$-0.0223832\pi$
$192$	10.4910	−	17.2083i	0.757126	−	1.24190i
$193$		−	0.720451i		−	0.0518592i	−0.999664	−	0.0259296i	$-0.991745\pi$
$193$		−	0.720451i		−	0.0518592i	0.999664	−	0.0259296i	$-0.00825458\pi$
$194$	−1.35397	−	7.86160i	−0.0972091	−	0.564430i
$195$		0			0
$196$	−7.15731	−	9.31283i	−0.511236	−	0.665202i
$197$	4.83357	−	3.51179i	0.344377	−	0.250205i	−0.402129	−	0.915583i	$-0.631730\pi$
$197$	4.83357	−	3.51179i	0.344377	−	0.250205i	0.746506	+	0.665378i	$0.231730\pi$
$198$	5.48883	−	11.1410i	0.390074	−	0.791755i
$199$	−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
$202$	0.126835	−	0.257445i	0.00892411	−	0.0181138i
$203$	16.2287	−	11.7908i	1.13903	−	0.827553i
$204$	−7.77101	+	5.97236i	−0.544080	+	0.418149i
$205$		0			0
$206$	3.16889	+	18.3997i	0.220787	+	1.28197i
$207$		−	2.59662i		−	0.180477i
$208$	22.9771	+	14.8716i	1.59317	+	1.03116i
$209$	−4.15056	+	12.7741i	−0.287100	+	0.883603i
$210$		0			0
$211$	−5.22662	+	1.69823i	−0.359816	+	0.116911i	−0.483346	−	0.875430i	$-0.660579\pi$
$211$	−5.22662	+	1.69823i	−0.359816	+	0.116911i	0.123530	+	0.992341i	$0.460579\pi$
$212$	3.52143	+	1.04017i	0.241853	+	0.0714389i
$213$	−4.31832	+	13.2904i	−0.295886	+	0.910644i
$214$	−18.9257	−	9.32412i	−1.29373	−	0.637384i
$215$		0			0
$216$	2.15401	−	1.20955i	0.146562	−	0.0822996i
$217$	−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
$222$	−4.52082	+	31.2637i	−0.303417	+	2.09828i
$223$	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	$0.0760460\pi$
$227$	4.89137	+	15.0541i	0.324652	+	0.999175i	−0.646946	+	0.762536i	$0.723954\pi$
$228$	−20.4484	+	15.7155i	−1.35423	+	1.04078i
$229$	3.76598	+	5.18342i	0.248863	+	0.342530i	0.915113	−	0.403198i	$-0.132102\pi$
$229$	3.76598	+	5.18342i	0.248863	+	0.342530i	−0.666250	+	0.745729i	$0.732102\pi$
$230$		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	$0.00457787\pi$
$234$	15.0899	+	28.6545i	0.986456	+	1.87321i
$235$		0			0
$236$	−2.63601	−	7.42580i	−0.171589	−	0.483379i
$237$	−7.36529	+	22.6680i	−0.478427	+	1.47245i
$238$	−4.59891	−	8.73298i	−0.298103	−	0.566075i
$239$	−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	$0.0642022\pi$
$242$	5.73381	−	0.987507i	0.368583	−	0.0634793i
$243$	−22.3706			−1.43507
$244$	10.7727	+	7.39172i	0.689649	+	0.473206i
$245$		0			0
$246$	1.85310	−	12.8151i	0.118149	−	0.817061i
$247$	−20.5862	−	28.3344i	−1.30987	−	1.80288i
$248$	2.51497	−	5.47190i	0.159701	−	0.347466i
$249$	20.2679			1.28443
$250$		0			0
$251$			16.8769i			1.06526i	0.846347	+	0.532632i	$0.178797\pi$
$251$			16.8769i			1.06526i	−0.846347	+	0.532632i	$0.821203\pi$
$252$	8.03366	+	22.6313i	0.506073	+	1.42564i
$253$	−1.64714	+	1.19672i	−0.103555	+	0.0752369i
$254$	4.94576	+	0.715170i	0.310325	+	0.0448738i
$255$		0			0
$256$	−13.8808	−	7.95757i	−0.867551	−	0.497348i
$257$			4.42621i			0.276099i	0.990425	+	0.138050i	$0.0440833\pi$
$257$			4.42621i			0.276099i	−0.990425	+	0.138050i	$0.955917\pi$
$258$	2.28983	−	0.394366i	0.142558	−	0.0245521i
$259$	−30.2543	−	9.83022i	−1.87991	−	0.610820i
$260$		0			0
$261$	−17.7956	+	5.78213i	−1.10152	+	0.357905i
$262$	8.44217	−	4.44576i	0.521559	−	0.274660i
$263$	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	$0.476423\pi$
$264$	−16.9896	−	7.80868i	−1.04564	−	0.480591i
$265$		0			0
$266$	−12.1014	−	22.9797i	−0.741986	−	1.40898i
$267$	−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	$-0.460880\pi$
$269$	16.8702	−	23.2198i	1.02859	−	1.41573i	0.906000	−	0.423277i	$-0.139120\pi$
$270$		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	$0.335523\pi$
$272$	4.90584	+	6.03929i	0.297460	+	0.366186i
$273$	−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	0.981214	−	0.192922i	$-0.0617964\pi$
$277$	1.23158	+	3.79042i	0.0739986	+	0.227744i	−0.907216	+	0.420666i	$0.861796\pi$
$278$	−1.90646	−	0.275679i	−0.114342	−	0.0165341i
$279$	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	0.227883	−	0.973689i	$-0.426820\pi$
$283$	−10.5601	−	7.67233i	−0.627730	−	0.456073i	−0.855613	+	0.517616i	$0.826820\pi$
$284$	10.6396	+	3.14273i	0.631342	+	0.186487i
$285$		0			0
$286$	11.2222	−	22.7783i	0.663581	−	1.34691i
$287$	12.4013	+	4.02944i	0.732028	+	0.237850i
$288$	−9.71077	−	16.2515i	−0.572212	−	0.957631i
$289$	4.08404	+	12.5694i	0.240238	+	0.739375i
$290$		0			0
$291$	−13.5152	−	4.39136i	−0.792277	−	0.257426i
$292$	24.4538	+	16.7791i	1.43105	+	0.981922i
$293$	27.0373			1.57954			0.789769	−	0.613404i	$-0.210200\pi$
$293$	27.0373			1.57954			0.789769	+	0.613404i	$0.210200\pi$
$294$	−20.6197	+	3.55123i	−1.20256	+	0.207112i
$295$		0			0
$296$	24.9074	+	2.91901i	1.44771	+	0.169664i
$297$	−1.34715	−	1.85420i	−0.0781698	−	0.107592i
$298$	−5.91427	+	12.0045i	−0.342604	+	0.695403i
$299$		−	5.30890i		−	0.307022i
$300$		0			0
$301$			2.33989i			0.134869i
$302$	−10.1431	−	4.99718i	−0.583667	−	0.287556i
$303$	−0.300503	−	0.413607i	−0.0172635	−	0.0237611i
$304$	12.9091	+	15.8916i	0.740386	+	0.911446i
$305$		0			0
$306$	1.56258	+	9.07290i	0.0893268	+	0.518663i
$307$	−23.1194			−1.31949			−0.659747	−	0.751488i	$-0.729336\pi$
$307$	−23.1194			−1.31949			−0.659747	+	0.751488i	$0.729336\pi$
$308$	10.6534	−	15.5263i	0.607036	−	0.884692i
$309$	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	$0.801929\pi$
$312$	42.5124	−	23.8722i	2.40679	−	1.35150i
$313$	−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	$0.663035\pi$
$314$	−9.87073	−	4.86301i	−0.557037	−	0.274436i
$315$		0			0
$316$	18.1468	+	5.36022i	1.02084	+	0.301536i
$317$	2.26671	+	1.64686i	0.127311	+	0.0924971i	0.649619	−	0.760260i	$-0.274929\pi$
$317$	2.26671	+	1.64686i	0.127311	+	0.0924971i	−0.522307	+	0.852757i	$0.674929\pi$
$318$	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
$322$	0.563411	−	3.89627i	0.0313977	−	0.217131i
$323$	−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
$328$	−10.2096	−	1.19651i	−0.563732	−	0.0660664i
$329$	2.67317	−	1.94217i	0.147376	−	0.107075i
$330$		0			0
$331$	15.6066	−	21.4807i	0.857819	−	1.18069i	−0.124266	−	0.992249i	$-0.539658\pi$
$331$	15.6066	−	21.4807i	0.857819	−	1.18069i	0.982085	−	0.188437i	$-0.0603422\pi$
$332$	−0.433498	−	16.0845i	−0.0237913	−	0.882753i
$333$	24.0060	+	17.4413i	1.31552	+	0.955780i
$334$	−15.1339	+	7.96974i	−0.828092	+	0.436085i
$335$		0			0
$336$	33.7338	−	13.0084i	1.84033	−	0.709668i
$337$	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	$0.425982\pi$
$338$	22.2855	+	42.3185i	1.21217	+	2.30182i
$339$	14.1574	−	4.60001i	0.768923	−	0.249838i
$340$		0			0
$341$	−5.31368	−	1.72652i	−0.287752	−	0.0934963i
$342$	4.11173	+	23.8741i	0.222337	+	1.29097i
$343$			4.04448i			0.218381i
$344$	−0.361942	−	1.80876i	−0.0195146	−	0.0975217i
$345$		0			0
$346$	−3.20046	+	22.1328i	−0.172058	+	1.18987i
$347$	−15.5716	+	11.3134i	−0.835926	+	0.607336i	−0.921230	−	0.389019i	$-0.872814\pi$
$347$	−15.5716	+	11.3134i	−0.835926	+	0.607336i	0.0853039	+	0.996355i	$0.472814\pi$
$348$	9.42379	+	26.5474i	0.505168	+	1.42309i
$349$		−	0.0595710i		−	0.00318876i	−0.999999	−	0.00159438i	$-0.999492\pi$
$349$		−	0.0595710i		−	0.00318876i	0.999999	−	0.00159438i	$-0.000507507\pi$
$350$		0			0
$351$	5.97629			0.318991
$352$	−5.83355	+	13.6498i	−0.310929	+	0.727539i
$353$	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	$0.626595\pi$
$354$	−13.8925	−	2.00889i	−0.738377	−	0.106771i
$355$		0			0
$356$	−12.2902	+	17.9117i	−0.651381	+	0.949320i
$357$	−17.5821			−0.930545
$358$	−3.54489	−	20.5829i	−0.187353	−	1.08784i
$359$	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
$362$	6.73660	−	3.54759i	0.354068	−	0.186457i
$363$	3.20281	−	9.85725i	0.168104	−	0.517371i
$364$	16.4252	+	46.2708i	0.860913	+	2.42525i
$365$		0			0
$366$	20.5925	−	10.8443i	1.07639	−	0.566841i
$367$	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
$372$	−6.53721	−	8.50598i	−0.338939	−	0.441015i
$373$	−7.68840	−	23.6625i	−0.398090	−	1.22520i	−0.926529	−	0.376224i	$-0.877222\pi$
$373$	−7.68840	−	23.6625i	−0.398090	−	1.22520i	0.528438	−	0.848972i	$-0.322778\pi$
$374$	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
$378$	4.38607	+	0.634237i	0.225595	+	0.0326216i
$379$	3.80553	+	5.23786i	0.195477	+	0.269051i	0.895492	−	0.445077i	$-0.146824\pi$
$379$	3.80553	+	5.23786i	0.195477	+	0.269051i	−0.700016	+	0.714128i	$0.746824\pi$
$380$		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	$0.224907\pi$
$384$	−24.0643	+	15.2737i	−1.22803	+	0.779431i
$385$		0			0
$386$	−0.450286	+	0.913971i	−0.0229190	+	0.0465199i
$387$	0.674465	−	2.07579i	0.0342850	−	0.105518i
$388$	−3.19589	+	10.8195i	−0.162247	+	0.549279i
$389$	−26.7250	+	8.68349i	−1.35501	+	0.440270i	−0.894375	−	0.447318i	$-0.852379\pi$
$389$	−26.7250	+	8.68349i	−1.35501	+	0.440270i	−0.460637	+	0.887588i	$0.652379\pi$
$390$		0			0
$391$	0.466377	−	1.43536i	0.0235857	−	0.0725893i
$392$	3.25925	+	16.2877i	0.164617	+	0.822653i
$393$		−	16.9966i		−	0.857367i
$394$	−8.32680	+	1.43408i	−0.419498	+	0.0722481i
$395$		0			0
$396$	−13.9264	+	10.7030i	−0.699826	+	0.537846i
$397$	28.3014	−	20.5622i	1.42041	−	1.03199i	0.428701	−	0.903446i	$-0.358971\pi$
$397$	28.3014	−	20.5622i	1.42041	−	1.03199i	0.991704	−	0.128539i	$-0.0410288\pi$
$398$	16.7025	+	8.22881i	0.837219	+	0.412473i
$399$	−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	$0.391635\pi$
$402$	15.7166	+	7.74311i	0.783874	+	0.386191i
$403$	11.7864	−	8.56329i	0.587120	−	0.426568i
$404$	−0.321809	+	0.247324i	−0.0160106	+	0.0123048i
$405$		0			0
$406$	−27.9572	+	4.81492i	−1.38749	+	0.238961i
$407$		−	23.2662i		−	1.15326i
$408$	13.5911	−	2.71966i	0.672861	−	0.134643i
$409$	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
$412$	7.47983	−	25.3226i	0.368505	−	1.24755i
$413$	4.36820	−	13.4439i	0.214945	−	0.661533i
$414$	−1.62290	+	3.29409i	−0.0797612	+	0.161896i
$415$		0			0
$416$	−19.8541	−	33.2270i	−0.973428	−	1.62909i
$417$	−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	$-0.377420\pi$
$419$	23.3551	−	32.1455i	1.14097	−	1.57041i	0.765321	−	0.643648i	$-0.222580\pi$
$420$		0			0
$421$	−2.75042	−	3.78563i	−0.134047	−	0.184500i	0.736717	−	0.676202i	$-0.236375\pi$
$421$	−2.75042	−	3.78563i	−0.134047	−	0.184500i	−0.870764	+	0.491701i	$0.836375\pi$
$422$	7.69195	+	1.11228i	0.374438	+	0.0541448i
$423$	−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
$428$	18.1817	+	23.6573i	0.878844	+	1.14352i
$429$	−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	$0.189236\pi$
$434$	9.55893	−	5.03387i	0.458843	−	0.241633i
$435$		0			0
$436$	5.78563	+	16.2985i	0.277082	+	0.780557i
$437$	1.22721	−	3.77696i	0.0587054	−	0.180677i
$438$	46.7447	−	24.6164i	2.23355	−	1.17622i
$439$	−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
$442$	3.19477	+	18.5500i	0.151960	+	0.882331i
$443$	−9.37158			−0.445257			−0.222629	−	0.974903i	$-0.571464\pi$
$443$	−9.37158			−0.445257			−0.222629	+	0.974903i	$0.571464\pi$
$444$	25.2751	−	36.8359i	1.19950	−	1.74815i
$445$		0			0
$446$	−28.5075	−	4.12226i	−1.34987	−	0.195195i
$447$	14.0123	+	19.2863i	0.662759	+	0.912210i
$448$	−11.0449	−	26.4927i	−0.521824	−	1.25166i
$449$	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
$452$	−3.95334	−	11.1368i	−0.185950	−	0.523832i
$453$	−16.2957	+	11.8395i	−0.765638	+	0.556269i
$454$	3.20366	−	22.1549i	0.150355	−	1.03978i
$455$		0			0
$456$	35.7633	−	7.15642i	1.67477	−	0.335130i
$457$		−	32.1890i		−	1.50574i	−0.658170	−	0.752869i	$-0.728669\pi$
$457$		−	32.1890i		−	1.50574i	0.658170	−	0.752869i	$-0.271331\pi$
$458$	−1.53788	−	8.92949i	−0.0718605	−	0.417248i
$459$	1.61580	+	0.525005i	0.0754190	+	0.0245051i
$460$		0			0
$461$	−2.49963	+	0.812178i	−0.116419	+	0.0378269i	−0.366647	−	0.930360i	$-0.619494\pi$
$461$	−2.49963	+	0.812178i	−0.116419	+	0.0378269i	0.250228	+	0.968187i	$0.419494\pi$
$462$	−15.6295	−	29.6793i	−0.727152	−	1.38081i
$463$	−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	$0.848153\pi$
$464$	20.8663	−	8.04647i	0.968695	−	0.373548i
$465$		0			0
$466$	−22.0071	+	11.5892i	−1.01946	+	0.536861i
$467$	−33.3692	−	24.2441i	−1.54414	−	1.12188i	−0.947671	−	0.319250i	$-0.896569\pi$
$467$	−33.3692	−	24.2441i	−1.54414	−	1.12188i	−0.596471	−	0.802635i	$-0.703431\pi$
$468$	−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
$472$	−1.29711	+	11.0680i	−0.0597041	+	0.509444i
$473$	−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
$478$	−1.70779	+	11.8103i	−0.0781127	+	0.540188i
$479$	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
$484$	−7.89116	−	2.33091i	−0.358689	−	0.105950i
$485$		0			0
$486$	28.3795	+	13.9817i	1.28732	+	0.634224i
$487$	−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	$0.901528\pi$
$488$	−9.04642	−	16.1102i	−0.409512	−	0.729273i
$489$	−17.8870	−	55.0505i	−0.808877	−	2.48947i
$490$		0			0
$491$	7.10672	+	2.30911i	0.320722	+	0.104209i	0.464954	−	0.885335i	$-0.346071\pi$
$491$	7.10672	+	2.30911i	0.320722	+	0.104209i	−0.144232	+	0.989544i	$0.546071\pi$
$492$	−10.3604	+	15.0992i	−0.467081	+	0.680722i
$493$	−10.8756			−0.489811
$494$	8.40661	+	48.8118i	0.378231	+	2.19615i
$495$		0			0
$496$	−6.61048	+	5.36982i	−0.296819	+	0.241112i
$497$	11.6980	+	16.1009i	0.524728	+	0.722226i
$498$	−25.7121	−	12.6676i	−1.15219	−	0.567648i
$499$			1.61567i			0.0723272i	0.999346	+	0.0361636i	$0.0115137\pi$
$499$			1.61567i			0.0723272i	−0.999346	+	0.0361636i	$0.988486\pi$
$500$		0			0
$501$			30.4692i			1.36126i
$502$	10.5482	−	21.4102i	0.470789	−	0.955586i
$503$	−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	$-0.430353\pi$
$504$	3.95314	−	33.7314i	0.176087	−	1.50252i
$505$		0			0
$506$	2.83753	−	0.488693i	0.126143	−	0.0217251i
$507$	85.1999			3.78386
$508$	−5.82725	−	3.99840i	−0.258542	−	0.177400i
$509$	1.21315	+	0.394177i	0.0537721	+	0.0174716i	0.335780	−	0.941941i	$-0.391000\pi$
$509$	1.21315	+	0.394177i	0.0537721	+	0.0174716i	−0.282007	+	0.959412i	$0.591000\pi$
$510$		0			0
$511$	16.4404	+	50.5983i	0.727279	+	2.23834i
$512$	12.6358	+	18.7706i	0.558429	+	0.829553i
$513$	4.25176	+	1.38148i	0.187720	+	0.0609939i
$514$	2.76640	−	5.61512i	0.122021	−	0.247673i
$515$		0			0
$516$	−3.15137	−	0.930858i	−0.138731	−	0.0409788i
$517$	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	$0.217676\pi$
$522$	26.1895	+	3.78707i	1.14628	+	0.165756i
$523$	6.21617	+	19.1314i	0.271814	+	0.836558i	0.990045	+	0.140753i	$0.0449524\pi$
$523$	6.21617	+	19.1314i	0.271814	+	0.836558i	−0.718230	+	0.695805i	$0.755048\pi$
$524$	−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
$528$	16.6727	+	20.5247i	0.725584	+	0.893225i
$529$	−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
$534$	18.0309	+	34.2393i	0.780272	+	1.48168i
$535$		0			0
$536$	5.80874	−	12.6382i	0.250899	−	0.545889i
$537$	−35.3850	−	11.4973i	−1.52697	−	0.496144i
$538$	−35.9141	+	18.9129i	−1.54837	+	0.815391i
$539$	14.6564	−	4.76215i	0.631295	−	0.205120i
$540$		0			0
$541$	19.0637	+	6.19417i	0.819612	+	0.266308i	0.688664	−	0.725081i	$-0.258198\pi$
$541$	19.0637	+	6.19417i	0.819612	+	0.266308i	0.130949	+	0.991389i	$0.458198\pi$
$542$	5.11023	−	0.880109i	0.219503	−	0.0378039i
$543$		−	13.5628i		−	0.582036i
$544$	−2.44900	−	10.7277i	−0.105000	−	0.459945i
$545$		0			0
$546$	86.5652	+	12.5176i	3.70465	+	0.535702i
$547$	31.1058	−	22.5997i	1.32999	−	0.966293i	0.330239	−	0.943897i	$-0.392871\pi$
$547$	31.1058	−	22.5997i	1.32999	−	0.966293i	0.999749	−	0.0223953i	$-0.00712924\pi$
$548$	−5.51444	−	15.5345i	−0.235565	−	0.663602i
$549$		−	21.8619i		−	0.933041i
$550$		0			0
$551$	−28.6176			−1.21915
$552$	5.02336	+	2.30882i	0.213809	+	0.0982698i
$553$	19.9521	+	27.4617i	0.848448	+	1.16779i
$554$	0.806638	−	5.57830i	0.0342708	−	0.236999i
$555$		0			0
$556$	2.24625	+	1.54128i	0.0952623	+	0.0653647i
$557$	−10.9707			−0.464844			−0.232422	−	0.972615i	$-0.574665\pi$
$557$	−10.9707			−0.464844			−0.232422	+	0.972615i	$0.574665\pi$
$558$	−9.93100	+	1.71037i	−0.420413	+	0.0724056i
$559$	1.37897	−	4.24405i	0.0583244	−	0.179504i
$560$		0			0
$561$	−3.97373	−	12.2299i	−0.167771	−	0.516346i
$562$	18.7376	+	35.5812i	0.790396	+	1.50090i
$563$	0.325391	−	1.00145i	0.0137136	−	0.0422061i	−0.943966	−	0.330044i	$-0.892936\pi$
$563$	0.325391	−	1.00145i	0.0137136	−	0.0422061i	0.957679	+	0.287838i	$0.0929364\pi$
$564$	1.55228	+	4.37286i	0.0653626	+	0.184131i
$565$		0			0
$566$	8.60133	+	16.3333i	0.361541	+	0.686539i
$567$	−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	0.583612	−	0.812033i	$-0.301639\pi$
$571$	−8.81803	−	12.1370i	−0.369023	−	0.507917i	−0.952635	+	0.304116i	$0.901639\pi$
$572$	−28.4731	+	21.8828i	−1.19052	+	0.914965i
$573$	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	$0.198029\pi$
$578$	2.67489	−	18.4982i	0.111261	−	0.769423i
$579$	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
$584$	−20.5352	−	36.5698i	−0.849754	−	1.51327i
$585$		0			0
$586$	−34.2998	−	16.8985i	−1.41691	−	0.698070i
$587$	−10.7007	+	32.9333i	−0.441664	+	1.35930i	0.444438	+	0.895810i	$0.353403\pi$
$587$	−10.7007	+	32.9333i	−0.441664	+	1.35930i	−0.886101	+	0.463491i	$0.846597\pi$
$588$	28.3778	+	8.38229i	1.17028	+	0.345680i
$589$	10.3648	−	3.36772i	0.427073	−	0.138764i
$590$		0			0
$591$	−4.65121	+	14.3150i	−0.191325	+	0.588839i
$592$	−29.7733	−	19.2703i	−1.22368	−	0.792006i
$593$			34.9925i			1.43697i	0.695543	+	0.718484i	$0.255164\pi$
$593$			34.9925i			1.43697i	−0.695543	+	0.718484i	$0.744836\pi$
$594$	0.550127	+	3.19423i	0.0225720	+	0.131061i
$595$		0			0
$596$	15.0058	−	11.5326i	0.614661	−	0.472393i
$597$	26.8339	−	19.4960i	1.09824	−	0.797918i
$598$	−3.31809	+	6.73492i	−0.135687	+	0.275411i
$599$	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	$0.513086\pi$
$602$	1.46245	−	2.96841i	0.0596049	−	0.120983i
$603$	13.3147	−	9.67370i	0.542217	−	0.393943i
$604$	9.74431	+	12.6789i	0.396490	+	0.515899i
$605$		0			0
$606$	0.122714	+	0.712522i	0.00498492	+	0.0289442i
$607$			39.1971i			1.59096i	0.605979	+	0.795481i	$0.292782\pi$
$607$			39.1971i			1.59096i	−0.605979	+	0.795481i	$0.707218\pi$
$608$	−6.44421	−	28.2285i	−0.261347	−	1.14482i
$609$	−15.6164	+	48.0624i	−0.632809	+	1.94759i
$610$		0			0
$611$	−5.99311	+	1.94728i	−0.242455	+	0.0787785i
$612$	3.68831	−	12.4866i	0.149091	−	0.504740i
$613$	6.65786	−	20.4908i	0.268909	−	0.827615i	−0.721859	−	0.692041i	$-0.756712\pi$
$613$	6.65786	−	20.4908i	0.268909	−	0.827615i	0.990767	−	0.135575i	$-0.0432881\pi$
$614$	29.3295	+	14.4498i	1.18364	+	0.583145i
$615$		0			0
$616$	−23.2191	+	13.0383i	−0.935522	+	0.525328i
$617$	−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	−0.862768	−	0.505599i	$-0.831271\pi$
$619$	−2.86875	+	3.94849i	−0.115305	+	0.158703i	0.747464	+	0.664303i	$0.231271\pi$
$620$		0			0
$621$	0.398318	+	0.548237i	0.0159839	+	0.0220000i
$622$	2.16474	−	14.9703i	0.0867983	−	0.600254i
$623$	−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
$628$	9.48268	+	12.3385i	0.378400	+	0.492360i
$629$	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
$634$	−1.84627	−	3.50594i	−0.0733249	−	0.139239i
$635$		0			0
$636$	−8.71739	+	3.09449i	−0.345667	+	0.122705i
$637$	−12.4175	+	38.2172i	−0.492001	+	1.51422i
$638$	−9.66778	−	18.3584i	−0.382751	−	0.726816i
$639$	−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	$0.150298\pi$
$642$	52.3800	−	9.02116i	2.06727	−	0.356037i
$643$	6.46830			0.255085			0.127542	−	0.991833i	$-0.459291\pi$
$643$	6.46830			0.255085			0.127542	+	0.991833i	$0.459291\pi$
$644$	−3.14994	+	4.59070i	−0.124125	+	0.180899i
$645$		0			0
$646$	−2.01513	+	13.9357i	−0.0792844	+	0.548291i
$647$	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	$0.704768\pi$
$648$	9.26029	−	20.1479i	0.363779	−	0.791484i
$649$	10.3387			0.405828
$650$		0			0
$651$		−	19.2450i		−	0.754272i
$652$	−43.3052	+	15.3724i	−1.69596	+	0.602032i
$653$	−31.2404	+	22.6975i	−1.22253	+	0.888220i	−0.996308	−	0.0858552i	$-0.972638\pi$
$653$	−31.2404	+	22.6975i	−1.22253	+	0.888220i	−0.226223	+	0.974076i	$0.572638\pi$
$654$	30.4919	+	4.40920i	1.19233	+	0.172414i
$655$		0			0
$656$	12.2042	+	7.89898i	0.476494	+	0.308403i
$657$		−	49.6261i		−	1.93610i
$658$	−4.60507	+	0.793109i	−0.179524	+	0.0309186i
$659$	−32.1885	−	10.4587i	−1.25389	−	0.407412i	−0.394574	−	0.918864i	$-0.629108\pi$
$659$	−32.1885	−	10.4587i	−1.25389	−	0.407412i	−0.859312	+	0.511452i	$0.829108\pi$
$660$		0			0
$661$	1.06103	−	0.344750i	0.0412693	−	0.0134092i	−0.288310	−	0.957537i	$-0.593093\pi$
$661$	1.06103	−	0.344750i	0.0412693	−	0.0134092i	0.329579	+	0.944128i	$0.393093\pi$
$662$	−33.2243	+	17.4964i	−1.29130	+	0.680016i
$663$	31.8900	+	10.3617i	1.23851	+	0.402415i
$664$	−9.50298	+	20.6759i	−0.368787	+	0.802381i
$665$		0			0
$666$	−19.5532	−	37.1301i	−0.757672	−	1.43876i
$667$	−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
$672$	−50.9253	−	4.58121i	−1.96449	−	0.176724i
$673$	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	$0.0104886\pi$
$677$	5.47038	+	16.8361i	0.210244	+	0.647064i	−0.789213	+	0.614119i	$0.789511\pi$
$678$	−20.8352	−	3.01283i	−0.800171	−	0.115707i
$679$	−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	$0.0394553\pi$
$683$	37.0207	+	26.8971i	1.41656	+	1.02919i	0.424230	+	0.905554i	$0.360545\pi$
$684$	9.70530	−	32.8568i	0.371091	−	1.25631i
$685$		0			0
$686$	2.52782	−	5.13086i	0.0965127	−	0.195897i
$687$	−15.3511	−	4.98787i	−0.585680	−	0.190299i
$688$	−0.671321	+	2.52082i	−0.0255939	+	0.0961054i
$689$	−3.88194	−	11.9474i	−0.147890	−	0.455159i
$690$		0			0
$691$	5.90130	+	1.91745i	0.224496	+	0.0729432i	0.419105	−	0.907938i	$-0.362344\pi$
$691$	5.90130	+	1.91745i	0.224496	+	0.0729432i	−0.194609	+	0.980881i	$0.562344\pi$
$692$	17.8933	−	26.0776i	0.680199	−	0.991320i
$693$	−31.5088			−1.19692
$694$	26.8252	−	4.61997i	1.01827	−	0.175372i
$695$		0			0
$696$	4.63718	−	39.5682i	0.175772	−	1.49983i
$697$	−4.15535	−	5.71935i	−0.157395	−	0.216636i
$698$	−0.0372322	+	0.0755723i	−0.00140926	+	0.00286045i
$699$			44.3069i			1.67584i
$700$		0			0
$701$		−	21.2933i		−	0.804238i	−0.915587	−	0.402119i	$-0.868274\pi$
$701$		−	21.2933i		−	0.804238i	0.915587	−	0.402119i	$-0.131726\pi$
$702$	−7.58157	−	3.73521i	−0.286148	−	0.140977i
$703$	26.6752	+	36.7153i	1.00608	+	1.38474i
$704$	15.9317	−	13.6703i	0.600449	−	0.515219i
$705$		0			0
$706$	−4.67407	−	27.1393i	−0.175911	−	1.02140i
$707$	−0.728101			−0.0273831
$708$	16.3685	+	11.2314i	0.615168	+	0.422101i
$709$	10.0050	+	3.25084i	0.375747	+	0.122088i	0.490801	−	0.871272i	$-0.336704\pi$
$709$	10.0050	+	3.25084i	0.375747	+	0.122088i	−0.115054	+	0.993359i	$0.536704\pi$
$710$		0			0
$711$	−9.78435	−	30.1131i	−0.366942	−	1.12933i
$712$	26.7864	−	15.0415i	1.00386	−	0.563705i
$713$	1.57111	+	0.510486i	0.0588387	+	0.0191178i
$714$	22.3048	+	10.9889i	0.834738	+	0.411250i
$715$		0			0
$716$	−8.36735	+	28.3272i	−0.312703	+	1.05864i
$717$	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
$722$	−1.45708	+	10.0764i	−0.0542268	+	0.375005i
$723$	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	$0.113143\pi$
$728$	8.08237	−	68.9654i	0.299553	−	2.55603i
$729$	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	0.108854	−	0.994058i	$-0.465282\pi$
$733$	−21.7381	−	15.7936i	−0.802914	−	0.583351i	−0.911768	+	0.410707i	$0.865282\pi$
$734$	−36.1522	+	19.0383i	−1.33440	+	0.702715i
$735$		0			0
$736$	1.72482	−	4.03589i	0.0635778	−	0.148765i
$737$	−12.2728	−	3.98768i	−0.452075	−	0.146888i
$738$	8.01493	+	15.2198i	0.295034	+	0.560247i
$739$	13.3854	−	4.34919i	0.492391	−	0.159988i	−0.0522881	−	0.998632i	$-0.516651\pi$
$739$	13.3854	−	4.34919i	0.492391	−	0.159988i	0.544679	+	0.838644i	$0.316651\pi$
$740$		0			0
$741$	83.9145	+	27.2655i	3.08268	+	1.00162i
$742$	−1.58108	−	9.18030i	−0.0580432	−	0.337019i
$743$		−	43.2190i		−	1.58555i	−0.609513	−	0.792776i	$-0.708635\pi$
$743$		−	43.2190i		−	1.58555i	0.609513	−	0.792776i	$-0.291365\pi$
$744$	2.97688	+	14.8766i	0.109138	+	0.545401i
$745$		0			0
$746$	−5.03560	+	34.8237i	−0.184366	+	1.27499i
$747$	−21.7826	+	15.8260i	−0.796983	+	0.579042i
$748$	−9.62058	+	3.41511i	−0.351763	+	0.124869i
$749$			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	$0.518842\pi$
$752$	3.43708	−	1.32541i	0.125337	−	0.0483326i
$753$	−24.9912	−	34.3974i	−0.910728	−	1.25351i
$754$	53.5456	+	7.74284i	1.95002	+	0.281977i
$755$		0			0
$756$	−5.16780	−	3.54592i	−0.187951	−	0.128964i
$757$	25.4279			0.924193			0.462096	−	0.886830i	$-0.347097\pi$
$757$	25.4279			0.924193			0.462096	+	0.886830i	$0.347097\pi$
$758$	−1.55403	−	9.02327i	−0.0564451	−	0.327740i
$759$	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	$0.794591\pi$
$762$	−11.1391	+	5.86601i	−0.403527	+	0.212503i
$763$	−9.58753	+	29.5074i	−0.347092	+	1.06824i
$764$	19.5400	−	6.93629i	0.706932	−	0.250946i
$765$		0			0
$766$	3.82849	−	2.01613i	0.138329	−	0.0728459i
$767$	−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
$772$	1.14247	−	0.878040i	0.0411185	−	0.0316014i
$773$	6.29718	+	19.3807i	0.226494	+	0.697076i	0.998137	+	0.0610199i	$0.0194353\pi$
$773$	6.29718	+	19.3807i	0.226494	+	0.697076i	−0.771643	+	0.636056i	$0.780565\pi$
$774$	−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
$778$	39.3308	+	5.68734i	1.41008	+	0.203901i
$779$	−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
$784$	6.04519	−	22.6998i	0.215899	−	0.810706i
$785$		0			0
$786$	−10.6230	+	21.5621i	−0.378910	+	0.769094i
$787$	0.608835	−	1.87380i	0.0217026	−	0.0667938i	−0.939619	−	0.342223i	$-0.888820\pi$
$787$	0.608835	−	1.87380i	0.0217026	−	0.0667938i	0.961321	+	0.275430i	$0.0888201\pi$
$788$	11.4598	+	3.38500i	0.408237	+	0.120586i
$789$	−29.4177	+	9.55840i	−1.04730	+	0.340288i
$790$		0			0
$791$	6.55119	−	20.1625i	0.232934	−	0.716896i
$792$	24.3565	−	4.87387i	0.865472	−	0.173185i
$793$		−	44.6976i		−	1.58726i
$794$	−48.7549	+	8.39681i	−1.73024	+	0.297992i
$795$		0			0
$796$	−16.0458	−	20.8783i	−0.568730	−	0.740011i
$797$	−18.3873	+	13.3592i	−0.651313	+	0.473206i	−0.863718	−	0.503975i	$-0.831870\pi$
$797$	−18.3873	+	13.3592i	−0.651313	+	0.473206i	0.212405	+	0.977182i	$0.431870\pi$
$798$	58.6923	+	28.9159i	2.07768	+	1.02361i
$799$	−1.79141			−0.0633756
$800$		0			0
$801$	36.3498			1.28436
$802$	−16.9647	−	8.35799i	−0.599044	−	0.295131i
$803$	−31.4798	+	22.8714i	−1.11090	+	0.807114i
$804$	−15.0988	−	19.6460i	−0.532492	−	0.692860i
$805$		0			0
$806$	−20.3044	+	3.49692i	−0.715191	+	0.123174i
$807$			72.3059i			2.54529i
$808$	0.562828	−	0.112625i	0.0198002	−	0.00396213i
$809$	−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	−0.938914	−	0.344152i	$-0.888166\pi$
$811$	−42.6096	+	13.8447i	−1.49622	+	0.486153i	−0.557310	+	0.830305i	$0.688166\pi$
$812$	38.4760	+	11.3651i	1.35024	+	0.398838i
$813$	2.85449	−	8.78521i	0.100111	−	0.308111i
$814$	−14.5415	+	29.5157i	−0.509680	+	1.03453i
$815$		0			0
$816$	−18.9416	−	5.04435i	−0.663090	−	0.176588i
$817$	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	0.415314	−	0.909678i	$-0.363672\pi$
$821$	−16.5666	−	22.8020i	−0.578180	−	0.795796i	−0.993494	+	0.113881i	$0.963672\pi$
$822$	−29.0626	−	4.20253i	−1.01367	−	0.146580i
$823$	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	$0.0632028\pi$
$827$	8.71857	+	26.8330i	0.303174	+	0.933075i	−0.677178	+	0.735819i	$0.736797\pi$
$828$	4.11765	−	3.16459i	0.143098	−	0.109977i
$829$	31.0042	+	42.6736i	1.07682	+	1.48212i	0.862974	+	0.505248i	$0.168599\pi$
$829$	31.0042	+	42.6736i	1.07682	+	1.48212i	0.213846	+	0.976867i	$0.431401\pi$
$830$		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
$834$	4.29383	−	2.26119i	0.148683	−	0.0782987i
$835$		0			0
$836$	−25.3153	+	8.98641i	−0.875548	+	0.310802i
$837$	−0.574659	+	1.76862i	−0.0198631	+	0.0611324i
$838$	−49.7196	+	26.1830i	−1.71753	+	0.904477i
$839$	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
$842$	1.12317	+	6.52151i	0.0387069	+	0.224746i
$843$	71.6357			2.46726
$844$	−9.06289	−	6.21855i	−0.311958	−	0.214051i
$845$		0			0
$846$	4.31390	+	0.623802i	0.148315	+	0.0214467i
$847$	−8.67620	−	11.9418i	−0.298118	−	0.410324i
$848$	2.64222	+	6.85188i	0.0907343	+	0.235295i
$849$	32.8838			1.12857
$850$		0			0
$851$			6.87919i			0.235816i
$852$	−26.3385	+	9.34962i	−0.902342	+	0.320313i
$853$	25.4769	−	18.5100i	0.872312	−	0.633772i	−0.0588942	−	0.998264i	$-0.518757\pi$
$853$	25.4769	−	18.5100i	0.872312	−	0.633772i	0.931206	+	0.364492i	$0.118757\pi$
$854$	4.74356	−	32.8041i	0.162321	−	1.12253i
$855$		0			0
$856$	−8.27946	−	41.3755i	−0.282986	−	1.41419i
$857$		−	47.9238i		−	1.63705i	−0.574473	−	0.818523i	$-0.694793\pi$
$857$		−	47.9238i		−	1.63705i	0.574473	−	0.818523i	$-0.305207\pi$
$858$	10.8575	+	63.0426i	0.370670	+	2.15224i
$859$	25.9430	+	8.42940i	0.885164	+	0.287607i	0.716100	−	0.697998i	$-0.245925\pi$
$859$	25.9430	+	8.42940i	0.885164	+	0.287607i	0.169064	+	0.985605i	$0.445925\pi$
$860$		0			0
$861$	−31.2423	+	10.1512i	−1.06473	+	0.345953i
$862$	13.2550	+	25.1703i	0.451469	+	0.857305i
$863$	−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	$0.859283\pi$
$864$	4.54325	+	1.94165i	0.154564	+	0.0660563i
$865$		0			0
$866$	−1.76074	+	0.927232i	−0.0598325	+	0.0315086i
$867$	−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
$872$	2.84695	−	24.2925i	0.0964099	−	0.822647i
$873$	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	$-0.665181\pi$
$877$	−17.9202	−	55.1526i	−0.605121	−	1.86237i	−0.109168	−	0.994023i	$-0.534819\pi$
$878$	−2.84229	+	19.6558i	−0.0959225	+	0.663352i
$879$	−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	−0.169107	−	0.985598i	$-0.554088\pi$
$883$	−34.4318	−	25.0162i	−1.15872	−	0.841861i	−0.989616	+	0.143736i	$0.954088\pi$
$884$	7.54091	−	25.5294i	0.253628	−	0.858646i
$885$		0			0
$886$	11.8889	+	5.85729i	0.399414	+	0.196780i
$887$	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	$0.367951\pi$
$888$	−55.0869	+	30.9332i	−1.84859	+	1.03805i
$889$	−3.91768	−	12.0574i	−0.131395	−	0.404392i
$890$		0			0
$891$	−19.5653	−	6.35716i	−0.655463	−	0.212973i
$892$	33.5884	+	23.0469i	1.12462	+	0.771666i
$893$	−4.71386			−0.157743
$894$	−5.72210	−	33.2245i	−0.191375	−	1.11119i
$895$		0			0
$896$	−2.54641	+	40.5120i	−0.0850696	+	1.35341i
$897$	7.86135	+	10.8202i	0.262483	+	0.361277i
$898$	−34.3784	−	16.9372i	−1.14722	−	0.565202i
$899$		−	11.9042i		−	0.397026i
$900$		0			0
$901$		−	3.57122i		−	0.118974i
$902$	5.96061	−	12.0986i	0.198467	−	0.402839i
$903$	−3.46488	−	4.76900i	−0.115304	−	0.158703i
$904$	−1.94533	+	16.5991i	−0.0647007	+	0.552079i
$905$		0			0
$906$	28.0726	−	4.83481i	0.932650	−	0.160626i
$907$	−34.9093			−1.15914			−0.579571	−	0.814921i	$-0.696780\pi$
$907$	−34.9093			−1.15914			−0.579571	+	0.814921i	$0.696780\pi$
$908$	−17.9111	+	26.1036i	−0.594401	+	0.866278i
$909$	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	$-0.223474\pi$
$912$	−49.8424	−	13.2736i	−1.65045	−	0.439531i
$913$	20.0781	+	6.52377i	0.664488	+	0.215905i
$914$	−20.1183	+	40.8353i	−0.665455	+	1.35071i
$915$		0			0
$916$	−3.63001	+	12.2892i	−0.119939	+	0.406047i
$917$	−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
$922$	3.67867	+	0.531945i	0.121150	+	0.0175187i
$923$	−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
$928$	−31.5003	−	2.83374i	−1.03405	−	0.0930222i
$929$	−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
$934$	27.1797	+	51.6122i	0.889347	+	1.68880i
$935$		0			0
$936$	−27.0491	+	58.8515i	−0.884127	+	1.92362i
$937$	−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	$0.642183\pi$
$938$	22.0779	−	11.6265i	0.720870	−	0.379620i
$939$	16.6789	−	5.41932i	0.544297	−	0.176853i
$940$		0			0
$941$	−34.7042	−	11.2761i	−1.13133	−	0.367590i	−0.317246	−	0.948343i	$-0.602758\pi$
$941$	−34.7042	−	11.2761i	−1.13133	−	0.367590i	−0.814080	+	0.580753i	$0.802758\pi$
$942$	27.3189	−	4.70500i	0.890097	−	0.153297i
$943$		−	2.81981i		−	0.0918255i
$944$	8.56305	−	13.2302i	0.278704	−	0.430607i
$945$		0			0
$946$	2.39531	+	0.346369i	0.0778784	+	0.0112614i
$947$	−12.2602	+	8.90757i	−0.398404	+	0.289457i	−0.768890	−	0.639380i	$-0.779191\pi$
$947$	−12.2602	+	8.90757i	−0.398404	+	0.289457i	0.370487	+	0.928838i	$0.379191\pi$
$948$	−44.9228	+	15.9467i	−1.45902	+	0.517923i
$949$		−	101.463i		−	3.29362i
$950$		0			0
$951$	−7.05851			−0.228888
$952$	8.24369	−	17.9360i	0.267179	−	0.581310i
$953$	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	$0.456024\pi$
$954$	−1.24356	+	8.59985i	−0.0402618	+	0.278430i
$955$		0			0
$956$	9.54799	−	13.9152i	0.308804	−	0.450050i
$957$	−36.9610			−1.19478
$958$	−22.0015	+	3.78920i	−0.710835	+	0.122424i
$959$	9.13812	−	28.1242i	0.295085	−	0.908179i
$960$		0			0
$961$	−8.17865	−	25.1713i	−0.263827	−	0.811977i
$962$	−39.9775	−	75.9142i	−1.28892	−	2.44757i
$963$	15.4285	−	47.4839i	0.497175	−	1.53015i
$964$	6.56732	−	2.33126i	0.211519	−	0.0750849i
$965$		0			0
$966$	4.62124	+	8.77538i	0.148686	+	0.282343i
$967$	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	0.882390	−	0.470518i	$-0.155933\pi$
$971$	5.05516	+	6.95783i	0.162228	+	0.223287i	−0.720163	+	0.693805i	$0.755933\pi$
$972$	−27.2638	−	35.4747i	−0.874488	−	1.13785i
$973$	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	$0.301467\pi$
$978$	−11.7153	+	81.0170i	−0.374613	+	2.59064i
$979$	−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	$0.306334\pi$
$984$	22.5803	−	12.6796i	0.719834	−	0.404212i
$985$		0			0
$986$	13.7968	+	6.79729i	0.439381	+	0.216470i
$987$	−2.57232	+	7.91678i	−0.0818777	+	0.251994i
$988$	19.8429	−	67.1772i	0.631288	−	2.13719i
$989$	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	$0.965296\pi$
$992$	11.7423	−	2.68062i	0.372818	−	0.0851097i
$993$			66.8905i			2.12271i
$994$	−4.77703	−	27.7371i	−0.151518	−	0.879768i
$995$		0			0
$996$	24.7013	+	32.1404i	0.782690	+	1.01841i
$997$	−15.5099	+	11.2686i	−0.491204	+	0.356881i	−0.805647	−	0.592396i	$-0.798182\pi$
$997$	−15.5099	+	11.2686i	−0.491204	+	0.356881i	0.314443	+	0.949276i	$0.398182\pi$
$998$	1.00980	−	2.04965i	0.0319647	−	0.0648805i
$999$	−7.74398			−0.245009

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.26861 - 0.625006i) q^{2} +(-2.03813 + 1.48079i) q^{3} +(1.21874 + 1.58578i) q^{4} +(3.51109 - 0.604697i) q^{6} +3.58786i q^{7} +(-0.554981 - 2.77344i) q^{8} +(1.03418 - 3.18289i) q^{9} +O(q^{10})\)	\(q+(-1.26861 - 0.625006i) q^{2} +(-2.03813 + 1.48079i) q^{3} +(1.21874 + 1.58578i) q^{4} +(3.51109 - 0.604697i) q^{6} +3.58786i q^{7} +(-0.554981 - 2.77344i) q^{8} +(1.03418 - 3.18289i) q^{9} +(-2.49567 + 0.810891i) q^{11} +(-4.83213 - 1.42732i) q^{12} +(2.11444 - 6.50757i) q^{13} +(2.24243 - 4.55159i) q^{14} +(-1.02937 + 3.86528i) 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} +(3.67283 + 0.531102i) 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} +(-5.68954 + 4.37265i) 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} +(-2.43404 + 1.28180i) q^{34} +(6.30775 - 2.23912i) q^{36} +(-2.73986 + 8.43241i) q^{37} +(-6.40485 + 3.37288i) q^{38} +(5.32683 + 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(2.16957 + 12.5973i) q^{42} +0.652170 q^{43} +(-4.32745 - 2.96930i) q^{44} +(-1.08596 - 0.157033i) q^{46} +(-0.541317 - 0.745059i) q^{47} +(-3.62568 - 9.40221i) q^{48} -5.87273 q^{49} +4.90045i q^{51} +(12.8965 - 4.57799i) q^{52} +(1.48529 - 1.07913i) q^{53} +(0.176773 - 1.22247i) q^{54} +(9.95073 - 1.99119i) q^{56} +12.8949i q^{57} +(1.34200 + 7.79215i) q^{58} +(-3.74706 - 1.21749i) q^{59} +(6.21266 - 2.01862i) q^{61} +(-1.40303 - 2.66424i) q^{62} +(11.4198 + 3.71051i) q^{63} +(-7.38399 + 3.07842i) q^{64} +(-8.27215 + 4.35623i) 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} +(-9.40153 - 1.10181i) 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} +(3.48886 - 24.1272i) 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} +(5.12104 - 17.3370i) q^{84} +(-0.827349 - 0.407610i) q^{86} +(13.3958 + 4.35257i) q^{87} +(3.63401 + 6.47156i) q^{88} +(3.35636 + 10.3298i) q^{89} +(23.3483 + 7.58631i) q^{91} +(1.27951 + 0.877943i) q^{92} -5.36393 q^{93} +(0.221053 + 1.28351i) q^{94} +(-1.27686 + 14.1938i) q^{96} +(3.31560 + 4.56353i) q^{97} +(7.45020 + 3.67049i) 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

Fields

Representations

Groups

Database

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