LMFDB - Embedded newform 1000.2.t.b.101.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			101.37
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.625006 + 1.26861i) q^{2} +(1.48079 - 2.03813i) q^{3} +(-1.21874 + 1.58578i) q^{4} +(3.51109 + 0.604697i) q^{6} -3.58786 q^{7} +(-2.77344 - 0.554981i) q^{8} +(-1.03418 - 3.18289i) q^{9} +O(q^{10})$	\(q+(0.625006 + 1.26861i) q^{2} +(1.48079 - 2.03813i) q^{3} +(-1.21874 + 1.58578i) q^{4} +(3.51109 + 0.604697i) q^{6} -3.58786 q^{7} +(-2.77344 - 0.554981i) q^{8} +(-1.03418 - 3.18289i) q^{9} +(-2.49567 - 0.810891i) q^{11} +(1.42732 + 4.83213i) q^{12} +(-6.50757 + 2.11444i) q^{13} +(-2.24243 - 4.55159i) q^{14} +(-1.02937 - 3.86528i) q^{16} +(1.57369 - 1.14335i) q^{17} +(3.39148 - 3.30130i) q^{18} +(-3.00859 - 4.14097i) q^{19} +(-5.31285 + 7.31251i) q^{21} +(-0.531102 - 3.67283i) q^{22} +(-0.239759 + 0.737902i) q^{23} +(-5.23800 + 4.83083i) q^{24} +(-6.74966 - 6.93403i) q^{26} +(-0.830663 - 0.269899i) q^{27} +(4.37265 - 5.68954i) q^{28} +(3.28631 - 4.52322i) q^{29} +(1.72253 - 1.25149i) q^{31} +(4.26017 - 3.72168i) q^{32} +(-5.34825 + 3.88573i) q^{33} +(2.43404 + 1.28180i) q^{34} +(6.30775 + 2.23912i) q^{36} +(-8.43241 + 2.73986i) q^{37} +(3.37288 - 6.40485i) q^{38} +(-5.32683 + 16.3943i) q^{39} +(1.12308 + 3.45647i) q^{41} +(-12.5973 - 2.16957i) q^{42} +0.652170i q^{43} +(4.32745 - 2.96930i) q^{44} +(-1.08596 + 0.157033i) q^{46} +(0.745059 + 0.541317i) q^{47} +(-9.40221 - 3.62568i) q^{48} +5.87273 q^{49} -4.90045i q^{51} +(4.57799 - 12.8965i) q^{52} +(-1.07913 + 1.48529i) q^{53} +(-0.176773 - 1.22247i) q^{54} +(9.95073 + 1.99119i) q^{56} -12.8949 q^{57} +(7.79215 + 1.34200i) q^{58} +(3.74706 - 1.21749i) q^{59} +(6.21266 + 2.01862i) q^{61} +(2.66424 + 1.40303i) q^{62} +(3.71051 + 11.4198i) q^{63} +(7.38399 + 3.07842i) q^{64} +(-8.27215 - 4.35623i) q^{66} +(-2.89052 - 3.97847i) q^{67} +(-0.104813 + 3.88897i) q^{68} +(1.14891 + 1.58133i) q^{69} +(4.48762 + 3.26045i) q^{71} +(1.10181 + 9.40153i) q^{72} +(-4.58222 + 14.1026i) q^{73} +(-8.74611 - 8.98500i) q^{74} +(10.2333 + 0.275801i) q^{76} +(8.95410 + 2.90936i) q^{77} +(-24.1272 + 3.48886i) q^{78} +(-7.65406 - 5.56100i) q^{79} +(6.34247 - 4.60807i) q^{81} +(-3.68298 + 3.58506i) q^{82} +(-4.72884 - 6.50869i) q^{83} +(-5.12104 - 17.3370i) q^{84} +(-0.827349 + 0.407610i) q^{86} +(-4.35257 - 13.3958i) q^{87} +(6.47156 + 3.63401i) q^{88} +(-3.35636 + 10.3298i) q^{89} +(23.3483 - 7.58631i) q^{91} +(-0.877943 - 1.27951i) q^{92} -5.36393i q^{93} +(-0.221053 + 1.28351i) q^{94} +(-1.27686 - 14.1938i) q^{96} +(-4.56353 - 3.31560i) q^{97} +(3.67049 + 7.45020i) q^{98} +8.78205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.625006	+	1.26861i	0.441946	+	0.897042i
$2$	0.625006	+	1.26861i	0.441946	+	0.897042i
$3$	1.48079	−	2.03813i	0.854932	−	1.17671i	−0.127822	−	0.991797i	$-0.540799\pi$
$3$	1.48079	−	2.03813i	0.854932	−	1.17671i	0.982754	−	0.184916i	$-0.0592014\pi$
$4$	−1.21874	+	1.58578i	−0.609368	+	0.792888i
$5$		0			0
$5$		0			0
$6$	3.51109	+	0.604697i	1.43339	+	0.246867i
$7$	−3.58786			−1.35608			−0.678042	−	0.735024i	$-0.737171\pi$
$7$	−3.58786			−1.35608			−0.678042	+	0.735024i	$0.737171\pi$
$8$	−2.77344	−	0.554981i	−0.980561	−	0.196215i
$9$	−1.03418	−	3.18289i	−0.344728	−	1.06096i
$10$		0			0
$11$	−2.49567	−	0.810891i	−0.752472	−	0.244493i	−0.0924272	−	0.995719i	$-0.529463\pi$
$11$	−2.49567	−	0.810891i	−0.752472	−	0.244493i	−0.660044	+	0.751227i	$0.729463\pi$
$12$	1.42732	+	4.83213i	0.412033	+	1.39492i
$13$	−6.50757	+	2.11444i	−1.80488	+	0.586440i	−0.999976	−	0.00697033i	$-0.997781\pi$
$13$	−6.50757	+	2.11444i	−1.80488	+	0.586440i	−0.804900	+	0.593410i	$0.797781\pi$
$14$	−2.24243	−	4.55159i	−0.599315	−	1.21646i
$15$		0			0
$16$	−1.02937	−	3.86528i	−0.257341	−	0.966321i
$17$	1.57369	−	1.14335i	0.381677	−	0.277304i	−0.380360	−	0.924839i	$-0.624200\pi$
$17$	1.57369	−	1.14335i	0.381677	−	0.277304i	0.762036	+	0.647534i	$0.224200\pi$
$18$	3.39148	−	3.30130i	0.799378	−	0.778124i
$19$	−3.00859	−	4.14097i	−0.690218	−	0.950003i	0.309782	−	0.950808i	$-0.399744\pi$
$19$	−3.00859	−	4.14097i	−0.690218	−	0.950003i	−1.00000		0.000804663i	$0.999744\pi$
$20$		0			0
$21$	−5.31285	+	7.31251i	−1.15936	+	1.59572i
$22$	−0.531102	−	3.67283i	−0.113231	−	0.783051i
$23$	−0.239759	+	0.737902i	−0.0499932	+	0.153863i	−0.972936	−	0.231073i	$-0.925776\pi$
$23$	−0.239759	+	0.737902i	−0.0499932	+	0.153863i	0.922943	+	0.384936i	$0.125776\pi$
$24$	−5.23800	+	4.83083i	−1.06920	+	0.986088i
$25$		0			0
$26$	−6.74966	−	6.93403i	−1.32372	−	1.35987i
$27$	−0.830663	−	0.269899i	−0.159861	−	0.0519421i
$28$	4.37265	−	5.68954i	0.826354	−	1.07522i
$29$	3.28631	−	4.52322i	0.610252	−	0.839940i	−0.386346	−	0.922354i	$-0.626263\pi$
$29$	3.28631	−	4.52322i	0.610252	−	0.839940i	0.996598	+	0.0824137i	$0.0262629\pi$
$30$		0			0
$31$	1.72253	−	1.25149i	0.309376	−	0.224775i	−0.422253	−	0.906478i	$-0.638761\pi$
$31$	1.72253	−	1.25149i	0.309376	−	0.224775i	0.731629	+	0.681704i	$0.238761\pi$
$32$	4.26017	−	3.72168i	0.753099	−	0.657907i
$33$	−5.34825	+	3.88573i	−0.931010	+	0.676419i
$34$	2.43404	+	1.28180i	0.417434	+	0.219826i
$35$		0			0
$36$	6.30775	+	2.23912i	1.05129	+	0.373187i
$37$	−8.43241	+	2.73986i	−1.38628	+	0.450430i	−0.904729	−	0.425988i	$-0.859926\pi$
$37$	−8.43241	+	2.73986i	−1.38628	+	0.450430i	−0.481551	+	0.876418i	$0.659926\pi$
$38$	3.37288	−	6.40485i	0.547154	−	1.03900i
$39$	−5.32683	+	16.3943i	−0.852975	+	2.62519i
$40$		0			0
$41$	1.12308	+	3.45647i	0.175395	+	0.539811i	0.999651	−	0.0264065i	$-0.00840642\pi$
$41$	1.12308	+	3.45647i	0.175395	+	0.539811i	−0.824256	+	0.566217i	$0.808406\pi$
$42$	−12.5973	−	2.16957i	−1.94380	−	0.334772i
$43$			0.652170i			0.0994550i	0.998763	+	0.0497275i	$0.0158353\pi$
$43$			0.652170i			0.0994550i	−0.998763	+	0.0497275i	$0.984165\pi$
$44$	4.32745	−	2.96930i	0.652387	−	0.447639i
$45$		0			0
$46$	−1.08596	+	0.157033i	−0.160116	+	0.0231532i
$47$	0.745059	+	0.541317i	0.108678	+	0.0789592i	0.640797	−	0.767710i	$-0.278604\pi$
$47$	0.745059	+	0.541317i	0.108678	+	0.0789592i	−0.532119	+	0.846670i	$0.678604\pi$
$48$	−9.40221	−	3.62568i	−1.35709	−	0.523322i
$49$	5.87273			0.838962
$50$		0			0
$51$		−	4.90045i		−	0.686201i
$52$	4.57799	−	12.8965i	0.634853	−	1.78842i
$53$	−1.07913	+	1.48529i	−0.148229	+	0.204020i	−0.876675	−	0.481084i	$-0.840243\pi$
$53$	−1.07913	+	1.48529i	−0.148229	+	0.204020i	0.728445	+	0.685104i	$0.240243\pi$
$54$	−0.176773	−	1.22247i	−0.0240558	−	0.166358i
$55$		0			0
$56$	9.95073	+	1.99119i	1.32972	+	0.266084i
$57$	−12.8949			−1.70797
$58$	7.79215	+	1.34200i	1.02316	+	0.176214i
$59$	3.74706	−	1.21749i	0.487826	−	0.158504i	−0.0547685	−	0.998499i	$-0.517442\pi$
$59$	3.74706	−	1.21749i	0.487826	−	0.158504i	0.542594	+	0.839995i	$0.317442\pi$
$60$		0			0
$61$	6.21266	+	2.01862i	0.795449	+	0.258457i	0.678423	−	0.734672i	$-0.262664\pi$
$61$	6.21266	+	2.01862i	0.795449	+	0.258457i	0.117027	+	0.993129i	$0.462664\pi$
$62$	2.66424	+	1.40303i	0.338359	+	0.178185i
$63$	3.71051	+	11.4198i	0.467480	+	1.43876i
$64$	7.38399	+	3.07842i	0.922999	+	0.384802i
$65$		0			0
$66$	−8.27215	−	4.35623i	−1.01823	−	0.536215i
$67$	−2.89052	−	3.97847i	−0.353134	−	0.486047i	0.595086	−	0.803662i	$-0.297118\pi$
$67$	−2.89052	−	3.97847i	−0.353134	−	0.486047i	−0.948220	+	0.317615i	$0.897118\pi$
$68$	−0.104813	+	3.88897i	−0.0127104	+	0.471607i
$69$	1.14891	+	1.58133i	0.138312	+	0.190370i
$70$		0			0
$71$	4.48762	+	3.26045i	0.532582	+	0.386944i	0.821323	−	0.570464i	$-0.193236\pi$
$71$	4.48762	+	3.26045i	0.532582	+	0.386944i	−0.288740	+	0.957407i	$0.593236\pi$
$72$	1.10181	+	9.40153i	0.129850	+	1.10798i
$73$	−4.58222	+	14.1026i	−0.536309	+	1.65059i	0.204496	+	0.978868i	$0.434445\pi$
$73$	−4.58222	+	14.1026i	−0.536309	+	1.65059i	−0.740804	+	0.671721i	$0.765555\pi$
$74$	−8.74611	−	8.98500i	−1.01671	−	1.04449i
$75$		0			0
$76$	10.2333	+	0.275801i	1.17384	+	0.0316365i
$77$	8.95410	+	2.90936i	1.02041	+	0.331553i
$78$	−24.1272	+	3.48886i	−2.73187	+	0.395036i
$79$	−7.65406	−	5.56100i	−0.861148	−	0.625661i	0.0670487	−	0.997750i	$-0.478642\pi$
$79$	−7.65406	−	5.56100i	−0.861148	−	0.625661i	−0.928197	+	0.372089i	$0.878642\pi$
$80$		0			0
$81$	6.34247	−	4.60807i	0.704719	−	0.512008i
$82$	−3.68298	+	3.58506i	−0.406718	+	0.395904i
$83$	−4.72884	−	6.50869i	−0.519058	−	0.714422i	0.466356	−	0.884597i	$-0.345567\pi$
$83$	−4.72884	−	6.50869i	−0.519058	−	0.714422i	−0.985414	+	0.170176i	$0.945567\pi$
$84$	−5.12104	−	17.3370i	−0.558751	−	1.89162i
$85$		0			0
$86$	−0.827349	+	0.407610i	−0.0892153	+	0.0439537i
$87$	−4.35257	−	13.3958i	−0.466645	−	1.43618i
$88$	6.47156	+	3.63401i	0.689871	+	0.387387i
$89$	−3.35636	+	10.3298i	−0.355773	+	1.09496i	0.599787	+	0.800160i	$0.295252\pi$
$89$	−3.35636	+	10.3298i	−0.355773	+	1.09496i	−0.955560	+	0.294797i	$0.904748\pi$
$90$		0			0
$91$	23.3483	−	7.58631i	2.44756	−	0.795261i
$92$	−0.877943	−	1.27951i	−0.0915319	−	0.133398i
$93$		−	5.36393i		−	0.556213i
$94$	−0.221053	+	1.28351i	−0.0227999	+	0.132384i
$95$		0			0
$96$	−1.27686	−	14.1938i	−0.130319	−	1.44865i
$97$	−4.56353	−	3.31560i	−0.463356	−	0.336648i	0.331490	−	0.943459i	$-0.392449\pi$
$97$	−4.56353	−	3.31560i	−0.463356	−	0.336648i	−0.794846	+	0.606811i	$0.792449\pi$
$98$	3.67049	+	7.45020i	0.370776	+	0.752584i
$99$			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	$-0.00321383\pi$
$102$	6.21676	−	3.06281i	0.615551	−	0.303263i
$103$	−10.6807	−	7.76000i	−1.05240	−	0.764616i	−0.0797351	−	0.996816i	$-0.525407\pi$
$103$	−10.6807	−	7.76000i	−1.05240	−	0.764616i	−0.972668	+	0.232201i	$0.925407\pi$
$104$	19.2219	−	2.25270i	1.88486	−	0.220895i
$105$		0			0
$106$	−2.55871	−	0.440675i	−0.248524	−	0.0428021i
$107$		−	14.9185i		−	1.44222i	−0.692819	−	0.721111i	$-0.743632\pi$
$107$		−	14.9185i		−	1.44222i	0.692819	−	0.721111i	$-0.256368\pi$
$108$	1.44036	−	0.988310i	0.138599	−	0.0951001i
$109$	−8.22423	+	2.67221i	−0.787738	+	0.255952i	−0.675141	−	0.737689i	$-0.735917\pi$
$109$	−8.22423	+	2.67221i	−0.787738	+	0.255952i	−0.112598	+	0.993641i	$0.535917\pi$
$110$		0			0
$111$	−6.90242	+	21.2435i	−0.655149	+	2.01634i
$112$	3.69322	+	13.8681i	0.348976	+	1.31041i
$113$	−1.82593	−	5.61964i	−0.171769	−	0.528652i	0.827702	−	0.561168i	$-0.189648\pi$
$113$	−1.82593	−	5.61964i	−0.171769	−	0.528652i	−0.999471	+	0.0325164i	$0.989648\pi$
$114$	−8.05938	−	16.3586i	−0.754830	−	1.53212i
$115$		0			0
$116$	3.16766	+	10.7240i	0.294110	+	0.995694i
$117$	13.4601	+	18.5262i	1.24438	+	1.71275i
$118$	3.88646	+	3.99261i	0.357778	+	0.367550i
$119$	−5.64619	+	4.10220i	−0.517585	+	0.376048i
$120$		0			0
$121$	−3.32838	−	2.41821i	−0.302580	−	0.219837i
$122$	1.32211	+	9.14308i	0.119699	+	0.827775i
$123$	8.70777	+	2.82933i	0.785153	+	0.255112i
$124$	−0.114726	+	4.25678i	−0.0103027	+	0.382270i
$125$		0			0
$126$	−12.1681	+	11.8446i	−1.08402	+	1.05520i
$127$	−1.09193	+	3.36061i	−0.0968930	+	0.298206i	−0.987742	−	0.156093i	$-0.950110\pi$
$127$	−1.09193	+	3.36061i	−0.0968930	+	0.298206i	0.890849	+	0.454299i	$0.150110\pi$
$128$	0.709730	+	11.2914i	0.0627318	+	0.998030i
$129$	1.32921	+	0.965725i	0.117030	+	0.0850273i
$130$		0			0
$131$	−3.96559	−	5.45817i	−0.346475	−	0.476883i	0.599843	−	0.800118i	$-0.295230\pi$
$131$	−3.96559	−	5.45817i	−0.346475	−	0.476883i	−0.946319	+	0.323235i	$0.895230\pi$
$132$	0.356209	−	13.2168i	0.0310040	−	1.15037i
$133$	10.7944	+	14.8572i	0.935992	+	1.28828i
$134$	3.24052	−	6.15351i	0.279938	−	0.531582i
$135$		0			0
$136$	−4.99909	+	2.29766i	−0.428669	+	0.197023i
$137$	2.54696	+	7.83872i	0.217601	+	0.669707i	0.998959	+	0.0456237i	$0.0145275\pi$
$137$	2.54696	+	7.83872i	0.217601	+	0.669707i	−0.781358	+	0.624084i	$0.785472\pi$
$138$	−1.28802	+	2.44585i	−0.109644	+	0.208205i
$139$	−1.29543	−	0.420910i	−0.109877	−	0.0357011i	0.253563	−	0.967319i	$-0.418398\pi$
$139$	−1.29543	−	0.420910i	−0.109877	−	0.0357011i	−0.363439	+	0.931618i	$0.618398\pi$
$140$		0			0
$141$	2.20655	−	0.716950i	0.185825	−	0.0603781i
$142$	−1.33144	+	7.73083i	−0.111732	+	0.648757i
$143$	17.9553			1.50150
$144$	−11.2382	+	7.27378i	−0.936519	+	0.606148i
$145$		0			0
$146$	−20.7546	+	3.00118i	−1.71767	+	0.248379i
$147$	8.69626	−	11.9694i	0.717256	−	0.987218i
$148$	5.93209	−	16.7111i	0.487615	−	1.37364i
$149$		−	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	$0.394525\pi$
$152$	6.04600	+	13.1545i	0.490395	+	1.06697i
$153$	−5.26667	−	3.82646i	−0.425785	−	0.309351i
$154$	1.90552	+	13.1776i	0.153551	+	1.06188i
$155$		0			0
$156$	−19.5057	−	28.4275i	−1.56170	−	2.27602i
$157$		−	7.78075i		−	0.620971i	−0.950578	−	0.310486i	$-0.899508\pi$
$157$		−	7.78075i		−	0.620971i	0.950578	−	0.310486i	$-0.100492\pi$
$158$	2.27090	−	13.1857i	0.180663	−	1.04899i
$159$	1.42926	+	4.39880i	0.113347	+	0.348847i
$160$		0			0
$161$	0.860221	−	2.64749i	0.0677949	−	0.208651i
$162$	9.80992	+	5.16604i	0.770740	+	0.405883i
$163$	21.8518	−	7.10008i	1.71157	−	0.556121i	0.720973	−	0.692964i	$-0.243695\pi$
$163$	21.8518	−	7.10008i	1.71157	−	0.556121i	0.990593	+	0.136842i	$0.0436953\pi$
$164$	−6.84992	−	2.43158i	−0.534889	−	0.189875i
$165$		0			0
$166$	5.30143	−	10.0670i	0.411471	−	0.781352i
$167$	9.78464	−	7.10896i	0.757158	−	0.550108i	−0.140879	−	0.990027i	$-0.544993\pi$
$167$	9.78464	−	7.10896i	0.757158	−	0.550108i	0.898037	+	0.439919i	$0.144993\pi$
$168$	18.7932	−	17.3323i	1.44993	−	1.33722i
$169$	27.3604	−	19.8785i	2.10465	−	1.52912i
$170$		0			0
$171$	−10.0688	+	13.8585i	−0.769982	+	1.05979i
$172$	−1.03420	−	0.794823i	−0.0788566	−	0.0606047i
$173$	−15.0391	−	4.88649i	−1.14340	−	0.371513i	−0.324747	−	0.945801i	$-0.605279\pi$
$173$	−15.0391	−	4.88649i	−1.14340	−	0.371513i	−0.818653	+	0.574288i	$0.805279\pi$
$174$	14.2737	−	13.8942i	1.08209	−	1.05332i
$175$		0			0
$176$	−0.565371	+	10.4812i	−0.0426165	+	0.790047i
$177$	3.06719	−	9.43984i	0.230544	−	0.709542i
$178$	−15.2022	+	2.19828i	−1.13945	+	0.164768i
$179$	−8.68076	+	11.9480i	−0.648830	+	0.893038i	−0.999048	−	0.0436301i	$-0.986108\pi$
$179$	−8.68076	+	11.9480i	−0.648830	+	0.893038i	0.350217	+	0.936668i	$0.386108\pi$
$180$		0			0
$181$	−3.16443	−	4.35546i	−0.235210	−	0.323739i	0.675053	−	0.737769i	$-0.264121\pi$
$181$	−3.16443	−	4.35546i	−0.235210	−	0.323739i	−0.910263	+	0.414030i	$0.864121\pi$
$182$	24.2168	+	24.8783i	1.79507	+	1.84410i
$183$	13.3138	−	9.67305i	0.984186	−	0.715053i
$184$	1.07448	−	1.91347i	0.0792116	−	0.141063i
$185$		0			0
$186$	6.80473	−	3.35249i	0.498947	−	0.245816i
$187$	−4.85455	+	1.57734i	−0.355000	+	0.115346i
$188$	−1.76644	+	0.521773i	−0.128831	+	0.0380542i
$189$	2.98030	+	0.968359i	0.216785	+	0.0704378i
$190$		0			0
$191$	3.20367	+	9.85988i	0.231809	+	0.713436i	0.997529	+	0.0702610i	$0.0223832\pi$
$191$	3.20367	+	9.85988i	0.231809	+	0.713436i	−0.765719	+	0.643175i	$0.777617\pi$
$192$	17.2083	−	10.4910i	1.24190	−	0.757126i
$193$	−0.720451			−0.0518592			−0.0259296	−	0.999664i	$-0.508255\pi$
$193$	−0.720451			−0.0518592			−0.0259296	+	0.999664i	$0.508255\pi$
$194$	1.35397	−	7.86160i	0.0972091	−	0.564430i
$195$		0			0
$196$	−7.15731	+	9.31283i	−0.511236	+	0.665202i
$197$	3.51179	−	4.83357i	0.250205	−	0.344377i	−0.665378	−	0.746506i	$-0.731730\pi$
$197$	3.51179	−	4.83357i	0.250205	−	0.344377i	0.915583	+	0.402129i	$0.131730\pi$
$198$	−11.1410	+	5.48883i	−0.791755	+	0.390074i
$199$	13.1660			0.933311			0.466655	−	0.884439i	$-0.345459\pi$
$199$	13.1660			0.933311			0.466655	+	0.884439i	$0.345459\pi$
$200$		0			0
$201$	−12.3889			−0.873843
$202$	0.257445	−	0.126835i	0.0181138	−	0.00892411i
$203$	−11.7908	+	16.2287i	−0.827553	+	1.13903i
$204$	7.77101	+	5.97236i	0.544080	+	0.418149i
$205$		0			0
$206$	3.16889	−	18.3997i	0.220787	−	1.28197i
$207$	2.59662			0.180477
$208$	14.8716	+	22.9771i	1.03116	+	1.59317i
$209$	4.15056	+	12.7741i	0.287100	+	0.883603i
$210$		0			0
$211$	−5.22662	−	1.69823i	−0.359816	−	0.116911i	0.123530	−	0.992341i	$-0.460579\pi$
$211$	−5.22662	−	1.69823i	−0.359816	−	0.116911i	−0.483346	+	0.875430i	$0.660579\pi$
$212$	−1.04017	−	3.52143i	−0.0714389	−	0.241853i
$213$	13.2904	−	4.31832i	0.910644	−	0.295886i
$214$	18.9257	−	9.32412i	1.29373	−	0.637384i
$215$		0			0
$216$	2.15401	+	1.20955i	0.146562	+	0.0822996i
$217$	−6.18020	+	4.49018i	−0.419539	+	0.304813i
$218$	−8.53018	−	8.76318i	−0.577737	−	0.593517i
$219$	21.9577	+	30.2221i	1.48376	+	2.04222i
$220$		0			0
$221$	−7.82337	+	10.7679i	−0.526257	+	0.724330i
$222$	−31.2637	+	4.52082i	−2.09828	+	0.303417i
$223$	−6.29390	+	19.3706i	−0.421471	+	1.29715i	0.484862	+	0.874590i	$0.338870\pi$
$223$	−6.29390	+	19.3706i	−0.421471	+	1.29715i	−0.906333	+	0.422564i	$0.861130\pi$
$224$	−15.2849	+	13.3529i	−1.02127	+	0.892177i
$225$		0			0
$226$	5.98791	−	5.82870i	0.398310	−	0.387720i
$227$	−15.0541	−	4.89137i	−0.999175	−	0.324652i	−0.236639	−	0.971598i	$-0.576046\pi$
$227$	−15.0541	−	4.89137i	−0.999175	−	0.324652i	−0.762536	+	0.646946i	$0.776046\pi$
$228$	15.7155	−	20.4484i	1.04078	−	1.35423i
$229$	−3.76598	+	5.18342i	−0.248863	+	0.342530i	−0.915113	−	0.403198i	$-0.867898\pi$
$229$	−3.76598	+	5.18342i	−0.248863	+	0.342530i	0.666250	+	0.745729i	$0.267898\pi$
$230$		0			0
$231$	19.1888	−	13.9414i	1.26253	−	0.917280i
$232$	−11.6247	+	10.7211i	−0.763199	+	0.703872i
$233$	−14.2284	+	10.3375i	−0.932133	+	0.677234i	−0.946514	−	0.322662i	$-0.895422\pi$
$233$	−14.2284	+	10.3375i	−0.932133	+	0.677234i	0.0143813	+	0.999897i	$0.495422\pi$
$234$	−15.0899	+	28.6545i	−0.986456	+	1.87321i
$235$		0			0
$236$	−2.63601	+	7.42580i	−0.171589	+	0.483379i
$237$	−22.6680	+	7.36529i	−1.47245	+	0.478427i
$238$	−8.73298	−	4.59891i	−0.566075	−	0.298103i
$239$	2.60748	−	8.02498i	0.168664	−	0.519093i	−0.830624	−	0.556834i	$-0.812016\pi$
$239$	2.60748	−	8.02498i	0.168664	−	0.519093i	0.999288	+	0.0377406i	$0.0120161\pi$
$240$		0			0
$241$	1.07674	+	3.31387i	0.0693591	+	0.213465i	0.979728	−	0.200332i	$-0.0642022\pi$
$241$	1.07674	+	3.31387i	0.0693591	+	0.213465i	−0.910369	+	0.413797i	$0.864202\pi$
$242$	0.987507	−	5.73381i	0.0634793	−	0.368583i
$243$		−	22.3706i		−	1.43507i
$244$	−10.7727	+	7.39172i	−0.689649	+	0.473206i
$245$		0			0
$246$	1.85310	+	12.8151i	0.118149	+	0.817061i
$247$	28.3344	+	20.5862i	1.80288	+	1.30987i
$248$	−5.47190	+	2.51497i	−0.347466	+	0.159701i
$249$	−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	$-0.178797\pi$
$252$	−22.6313	−	8.03366i	−1.42564	−	0.506073i
$253$	1.19672	−	1.64714i	0.0752369	−	0.103555i
$254$	−4.94576	+	0.715170i	−0.310325	+	0.0448738i
$255$		0			0
$256$	−13.8808	+	7.95757i	−0.867551	+	0.497348i
$257$	−4.42621			−0.276099			−0.138050	−	0.990425i	$-0.544083\pi$
$257$	−4.42621			−0.276099			−0.138050	+	0.990425i	$0.544083\pi$
$258$	−0.394366	+	2.28983i	−0.0245521	+	0.142558i
$259$	30.2543	−	9.83022i	1.87991	−	0.610820i
$260$		0			0
$261$	−17.7956	−	5.78213i	−1.10152	−	0.357905i
$262$	4.44576	−	8.44217i	0.274660	−	0.521559i
$263$	3.79412	+	11.6771i	0.233956	+	0.720041i	0.997258	+	0.0740002i	$0.0235766\pi$
$263$	3.79412	+	11.6771i	0.233956	+	0.720041i	−0.763303	+	0.646041i	$0.776423\pi$
$264$	16.9896	−	7.80868i	1.04564	−	0.480591i
$265$		0			0
$266$	−12.1014	+	22.9797i	−0.741986	+	1.40898i
$267$	16.0834	+	22.1369i	0.984289	+	1.35476i
$268$	9.83174	+	0.264978i	0.600569	+	0.0161861i
$269$	−16.8702	−	23.2198i	−1.02859	−	1.41573i	−0.906000	−	0.423277i	$-0.860880\pi$
$269$	−16.8702	−	23.2198i	−1.02859	−	1.41573i	−0.122591	−	0.992457i	$-0.539120\pi$
$270$		0			0
$271$	−2.96640	−	2.15522i	−0.180196	−	0.130920i	0.494031	−	0.869444i	$-0.335523\pi$
$271$	−2.96640	−	2.15522i	−0.180196	−	0.130920i	−0.674227	+	0.738524i	$0.735523\pi$
$272$	−6.03929	−	4.90584i	−0.366186	−	0.297460i
$273$	19.1119	−	58.8204i	1.15671	−	3.55997i
$274$	−8.35241	+	8.13034i	−0.504588	+	0.491172i
$275$		0			0
$276$	−3.90785	−	0.105322i	−0.235225	−	0.00633961i
$277$	−3.79042	−	1.23158i	−0.227744	−	0.0739986i	0.192922	−	0.981214i	$-0.438204\pi$
$277$	−3.79042	−	1.23158i	−0.227744	−	0.0739986i	−0.420666	+	0.907216i	$0.638204\pi$
$278$	−0.275679	−	1.90646i	−0.0165341	−	0.114342i
$279$	−5.76478	−	4.18836i	−0.345128	−	0.250750i
$280$		0			0
$281$	−23.0045	+	16.7138i	−1.37234	+	0.997060i	−0.374785	+	0.927112i	$0.622283\pi$
$281$	−23.0045	+	16.7138i	−1.37234	+	0.997060i	−0.997551	+	0.0699483i	$0.977717\pi$
$282$	2.28863	+	2.35115i	0.136286	+	0.140009i
$283$	−7.67233	−	10.5601i	−0.456073	−	0.627730i	0.517616	−	0.855613i	$-0.326820\pi$
$283$	−7.67233	−	10.5601i	−0.456073	−	0.627730i	−0.973689	+	0.227883i	$0.926820\pi$
$284$	−10.6396	+	3.14273i	−0.631342	+	0.186487i
$285$		0			0
$286$	11.2222	+	22.7783i	0.663581	+	1.34691i
$287$	−4.02944	−	12.4013i	−0.237850	−	0.732028i
$288$	−16.2515	−	9.71077i	−0.957631	−	0.572212i
$289$	−4.08404	+	12.5694i	−0.240238	+	0.739375i
$290$		0			0
$291$	−13.5152	+	4.39136i	−0.792277	+	0.257426i
$292$	−16.7791	−	24.4538i	−0.981922	−	1.43105i
$293$			27.0373i			1.57954i	0.613404	+	0.789769i	$0.289800\pi$
$293$			27.0373i			1.57954i	−0.613404	+	0.789769i	$0.710200\pi$
$294$	20.6197	+	3.55123i	1.20256	+	0.207112i
$295$		0			0
$296$	24.9074	−	2.91901i	1.44771	−	0.169664i
$297$	1.85420	+	1.34715i	0.107592	+	0.0781698i
$298$	12.0045	−	5.91427i	0.695403	−	0.342604i
$299$		−	5.30890i		−	0.307022i
$300$		0			0
$301$		−	2.33989i		−	0.134869i
$302$	4.99718	+	10.1431i	0.287556	+	0.583667i
$303$	−0.413607	−	0.300503i	−0.0237611	−	0.0172635i
$304$	−12.9091	+	15.8916i	−0.740386	+	0.911446i
$305$		0			0
$306$	1.56258	−	9.07290i	0.0893268	−	0.518663i
$307$			23.1194i			1.31949i	0.751488	+	0.659747i	$0.229336\pi$
$307$			23.1194i			1.31949i	−0.751488	+	0.659747i	$0.770664\pi$
$308$	−15.5263	+	10.6534i	−0.884692	+	0.607036i
$309$	−31.6317	+	10.2778i	−1.79947	+	0.584682i
$310$		0			0
$311$	3.30515	−	10.1722i	0.187418	−	0.576813i	−0.812564	−	0.582872i	$-0.801929\pi$
$311$	3.30515	−	10.1722i	0.187418	−	0.576813i	0.999982	+	0.00605932i	$0.00192875\pi$
$312$	23.8722	−	42.5124i	1.35150	−	2.40679i
$313$	−2.15115	−	6.62056i	−0.121590	−	0.374216i	0.871674	−	0.490086i	$-0.163035\pi$
$313$	−2.15115	−	6.62056i	−0.121590	−	0.374216i	−0.993264	+	0.115870i	$0.963035\pi$
$314$	9.87073	−	4.86301i	0.557037	−	0.274436i
$315$		0			0
$316$	18.1468	−	5.36022i	1.02084	−	0.301536i
$317$	−1.64686	−	2.26671i	−0.0924971	−	0.127311i	0.760260	−	0.649619i	$-0.225071\pi$
$317$	−1.64686	−	2.26671i	−0.0924971	−	0.127311i	−0.852757	+	0.522307i	$0.825071\pi$
$318$	−4.68706	+	4.56244i	−0.262837	+	0.255849i
$319$	−11.8694	+	8.62360i	−0.664557	+	0.482829i
$320$		0			0
$321$	−30.4057	−	22.0911i	−1.69708	−	1.23300i
$322$	3.89627	−	0.563411i	0.217131	−	0.0313977i
$323$	−9.46919	−	3.07673i	−0.526880	−	0.171194i
$324$	−0.422428	+	15.6738i	−0.0234682	+	0.870764i
$325$		0			0
$326$	22.6647	+	23.2838i	1.25528	+	1.28957i
$327$	−6.73201	+	20.7190i	−0.372281	+	1.14576i
$328$	−1.19651	−	10.2096i	−0.0660664	−	0.563732i
$329$	−2.67317	−	1.94217i	−0.147376	−	0.107075i
$330$		0			0
$331$	15.6066	+	21.4807i	0.857819	+	1.18069i	0.982085	+	0.188437i	$0.0603422\pi$
$331$	15.6066	+	21.4807i	0.857819	+	1.18069i	−0.124266	+	0.992249i	$0.539658\pi$
$332$	16.0845	+	0.433498i	0.882753	+	0.0237913i
$333$	17.4413	+	24.0060i	0.955780	+	1.31552i
$334$	15.1339	+	7.96974i	0.828092	+	0.436085i
$335$		0			0
$336$	33.7338	+	13.0084i	1.84033	+	0.709668i
$337$	−5.89820	−	18.1528i	−0.321295	−	0.988845i	−0.973085	−	0.230446i	$-0.925982\pi$
$337$	−5.89820	−	18.1528i	−0.321295	−	0.988845i	0.651790	−	0.758400i	$-0.274018\pi$
$338$	42.3185	+	22.2855i	2.30182	+	1.21217i
$339$	−14.1574	−	4.60001i	−0.768923	−	0.249838i
$340$		0			0
$341$	−5.31368	+	1.72652i	−0.287752	+	0.0934963i
$342$	−23.8741	−	4.11173i	−1.29097	−	0.222337i
$343$	4.04448			0.218381
$344$	0.361942	−	1.80876i	0.0195146	−	0.0975217i
$345$		0			0
$346$	−3.20046	−	22.1328i	−0.172058	−	1.18987i
$347$	−11.3134	+	15.5716i	−0.607336	+	0.835926i	−0.996355	−	0.0853039i	$-0.972814\pi$
$347$	−11.3134	+	15.5716i	−0.607336	+	0.835926i	0.389019	+	0.921230i	$0.372814\pi$
$348$	26.5474	+	9.42379i	1.42309	+	0.505168i
$349$		−	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
$352$	−13.6498	+	5.83355i	−0.727539	+	0.310929i
$353$	15.7539	+	11.4459i	0.838497	+	0.609203i	0.921950	−	0.387308i	$-0.126595\pi$
$353$	15.7539	+	11.4459i	0.838497	+	0.609203i	−0.0834537	+	0.996512i	$0.526595\pi$
$354$	13.8925	−	2.00889i	0.738377	−	0.106771i
$355$		0			0
$356$	−12.2902	−	17.9117i	−0.651381	−	0.949320i
$357$			17.5821i			0.930545i
$358$	−20.5829	−	3.54489i	−1.08784	−	0.187353i
$359$	−7.90364	−	24.3249i	−0.417138	−	1.28382i	−0.910324	−	0.413896i	$-0.864168\pi$
$359$	−7.90364	−	24.3249i	−0.417138	−	1.28382i	0.493186	−	0.869924i	$-0.335832\pi$
$360$		0			0
$361$	−2.22468	+	6.84685i	−0.117088	+	0.360361i
$362$	3.54759	−	6.73660i	0.186457	−	0.354068i
$363$	−9.85725	+	3.20281i	−0.517371	+	0.168104i
$364$	−16.4252	+	46.2708i	−0.860913	+	2.42525i
$365$		0			0
$366$	20.5925	+	10.8443i	1.07639	+	0.566841i
$367$	23.3737	−	16.9820i	1.22010	−	0.886453i	0.223990	−	0.974592i	$-0.428092\pi$
$367$	23.3737	−	16.9820i	1.22010	−	0.886453i	0.996108	+	0.0881385i	$0.0280918\pi$
$368$	3.09900	+	0.167165i	0.161546	+	0.00871409i
$369$	9.84012	−	7.14927i	0.512256	−	0.372176i
$370$		0			0
$371$	3.87175	−	5.32901i	0.201011	−	0.276669i
$372$	8.50598	+	6.53721i	0.441015	+	0.338939i
$373$	−23.6625	−	7.68840i	−1.22520	−	0.398090i	−0.376224	−	0.926529i	$-0.622778\pi$
$373$	−23.6625	−	7.68840i	−1.22520	−	0.398090i	−0.848972	+	0.528438i	$0.822778\pi$
$374$	−5.03514	−	5.17268i	−0.260361	−	0.267473i
$375$		0			0
$376$	−1.76596	−	1.91481i	−0.0910724	−	0.0987486i
$377$	−11.8218	+	36.3839i	−0.608855	+	1.87386i
$378$	0.634237	+	4.38607i	0.0326216	+	0.225595i
$379$	−3.80553	+	5.23786i	−0.195477	+	0.269051i	−0.895492	−	0.445077i	$-0.853176\pi$
$379$	−3.80553	+	5.23786i	−0.195477	+	0.269051i	0.700016	+	0.714128i	$0.253176\pi$
$380$		0			0
$381$	5.23244	+	7.20183i	0.268066	+	0.368961i
$382$	−10.5060	+	10.2267i	−0.537535	+	0.523243i
$383$	2.47525	−	1.79838i	0.126480	−	0.0918928i	−0.522747	−	0.852488i	$-0.675093\pi$
$383$	2.47525	−	1.79838i	0.126480	−	0.0918928i	0.649227	+	0.760595i	$0.275093\pi$
$384$	24.0643	+	15.2737i	1.22803	+	0.779431i
$385$		0			0
$386$	−0.450286	−	0.913971i	−0.0229190	−	0.0465199i
$387$	2.07579	−	0.674465i	0.105518	−	0.0342850i
$388$	10.8195	−	3.19589i	0.549279	−	0.162247i
$389$	26.7250	+	8.68349i	1.35501	+	0.440270i	0.894375	−	0.447318i	$-0.147621\pi$
$389$	26.7250	+	8.68349i	1.35501	+	0.440270i	0.460637	+	0.887588i	$0.347621\pi$
$390$		0			0
$391$	0.466377	+	1.43536i	0.0235857	+	0.0725893i
$392$	−16.2877	−	3.25925i	−0.822653	−	0.164617i
$393$	−16.9966			−0.857367
$394$	8.32680	+	1.43408i	0.419498	+	0.0722481i
$395$		0			0
$396$	−13.9264	−	10.7030i	−0.699826	−	0.537846i
$397$	20.5622	−	28.3014i	1.03199	−	1.42041i	0.128539	−	0.991704i	$-0.458971\pi$
$397$	20.5622	−	28.3014i	1.03199	−	1.42041i	0.903446	−	0.428701i	$-0.141029\pi$
$398$	8.22881	+	16.7025i	0.412473	+	0.837219i
$399$	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	$0.391635\pi$
$402$	−7.74311	−	15.7166i	−0.386191	−	0.783874i
$403$	−8.56329	+	11.7864i	−0.426568	+	0.587120i
$404$	0.321809	+	0.247324i	0.0160106	+	0.0123048i
$405$		0			0
$406$	−27.9572	−	4.81492i	−1.38749	−	0.238961i
$407$	23.2662			1.15326
$408$	−2.71966	+	13.5911i	−0.134643	+	0.672861i
$409$	−8.50186	−	26.1660i	−0.420390	−	1.29383i	−0.907340	−	0.420397i	$-0.861891\pi$
$409$	−8.50186	−	26.1660i	−0.420390	−	1.29383i	0.486950	−	0.873430i	$-0.338109\pi$
$410$		0			0
$411$	19.7478	+	6.41645i	0.974088	+	0.316500i
$412$	25.3226	−	7.47983i	1.24755	−	0.368505i
$413$	−13.4439	+	4.36820i	−0.661533	+	0.214945i
$414$	1.62290	+	3.29409i	0.0797612	+	0.161896i
$415$		0			0
$416$	−19.8541	+	33.2270i	−0.973428	+	1.62909i
$417$	−2.77612	+	2.01697i	−0.135947	+	0.0987713i
$418$	−13.6112	+	13.2493i	−0.665746	+	0.648046i
$419$	−23.3551	−	32.1455i	−1.14097	−	1.57041i	−0.765321	−	0.643648i	$-0.777420\pi$
$419$	−23.3551	−	32.1455i	−1.14097	−	1.57041i	−0.375649	−	0.926762i	$-0.622580\pi$
$420$		0			0
$421$	−2.75042	+	3.78563i	−0.134047	+	0.184500i	−0.870764	−	0.491701i	$-0.836375\pi$
$421$	−2.75042	+	3.78563i	−0.134047	+	0.184500i	0.736717	+	0.676202i	$0.236375\pi$
$422$	−1.11228	−	7.69195i	−0.0541448	−	0.374438i
$423$	0.952426	−	2.93127i	0.0463085	−	0.142523i
$424$	3.81721	−	3.52048i	0.185380	−	0.170969i
$425$		0			0
$426$	13.7848	+	14.1614i	0.667877	+	0.686120i
$427$	−22.2901	−	7.24251i	−1.07870	−	0.350489i
$428$	23.6573	+	18.1817i	1.14352	+	0.878844i
$429$	26.5880	−	36.5952i	1.28368	−	1.76683i
$430$		0			0
$431$	−16.2735	+	11.8234i	−0.783869	+	0.569514i	−0.906138	−	0.422983i	$-0.860983\pi$
$431$	−16.2735	+	11.8234i	−0.783869	+	0.569514i	0.122269	+	0.992497i	$0.460983\pi$
$432$	−0.188180	+	3.48857i	−0.00905379	+	0.167844i
$433$	−1.13838	+	0.827085i	−0.0547073	+	0.0397472i	−0.614803	−	0.788681i	$-0.710764\pi$
$433$	−1.13838	+	0.827085i	−0.0547073	+	0.0397472i	0.560096	+	0.828428i	$0.310764\pi$
$434$	−9.55893	−	5.03387i	−0.458843	−	0.241633i
$435$		0			0
$436$	5.78563	−	16.2985i	0.277082	−	0.780557i
$437$	3.77696	−	1.22721i	0.180677	−	0.0587054i
$438$	−24.6164	+	46.7447i	−1.17622	+	2.23355i
$439$	4.33963	−	13.3560i	0.207119	−	0.637447i	−0.792500	−	0.609871i	$-0.791221\pi$
$439$	4.33963	−	13.3560i	0.207119	−	0.637447i	0.999620	−	0.0275762i	$-0.00877888\pi$
$440$		0			0
$441$	−6.07349	−	18.6923i	−0.289214	−	0.890109i
$442$	−18.5500	−	3.19477i	−0.882331	−	0.151960i
$443$		−	9.37158i		−	0.445257i	−0.974903	−	0.222629i	$-0.928536\pi$
$443$		−	9.37158i		−	0.445257i	0.974903	−	0.222629i	$-0.0714637\pi$
$444$	−25.2751	−	36.8359i	−1.19950	−	1.74815i
$445$		0			0
$446$	−28.5075	+	4.12226i	−1.34987	+	0.195195i
$447$	−19.2863	−	14.0123i	−0.912210	−	0.662759i
$448$	−26.4927	−	11.0449i	−1.25166	−	0.521824i
$449$	−27.0993			−1.27889			−0.639447	−	0.768835i	$-0.720837\pi$
$449$	−27.0993			−1.27889			−0.639447	+	0.768835i	$0.720837\pi$
$450$		0			0
$451$		−	9.53690i		−	0.449075i
$452$	11.1368	+	3.95334i	0.523832	+	0.185950i
$453$	11.8395	−	16.2957i	0.556269	−	0.765638i
$454$	−3.20366	−	22.1549i	−0.150355	−	1.03978i
$455$		0			0
$456$	35.7633	+	7.15642i	1.67477	+	0.335130i
$457$	32.1890			1.50574			0.752869	−	0.658170i	$-0.228669\pi$
$457$	32.1890			1.50574			0.752869	+	0.658170i	$0.228669\pi$
$458$	−8.92949	−	1.53788i	−0.417248	−	0.0718605i
$459$	−1.61580	+	0.525005i	−0.0754190	+	0.0245051i
$460$		0			0
$461$	−2.49963	−	0.812178i	−0.116419	−	0.0378269i	0.250228	−	0.968187i	$-0.419494\pi$
$461$	−2.49963	−	0.812178i	−0.116419	−	0.0378269i	−0.366647	+	0.930360i	$0.619494\pi$
$462$	29.6793	+	15.6295i	1.38081	+	0.727152i
$463$	−9.34875	−	28.7725i	−0.434473	−	1.33717i	−0.893625	−	0.448814i	$-0.851847\pi$
$463$	−9.34875	−	28.7725i	−0.434473	−	1.33717i	0.459152	−	0.888358i	$-0.348153\pi$
$464$	−20.8663	−	8.04647i	−0.968695	−	0.373548i
$465$		0			0
$466$	−22.0071	−	11.5892i	−1.01946	−	0.536861i
$467$	24.2441	+	33.3692i	1.12188	+	1.54414i	0.802635	+	0.596471i	$0.203431\pi$
$467$	24.2441	+	33.3692i	1.12188	+	1.54414i	0.319250	+	0.947671i	$0.396569\pi$
$468$	−45.7826	−	1.23390i	−2.11630	−	0.0570371i
$469$	10.3708	+	14.2742i	0.478879	+	0.659120i
$470$		0			0
$471$	−15.8582	−	11.5216i	−0.730705	−	0.530889i
$472$	−11.0680	+	1.29711i	−0.509444	+	0.0597041i
$473$	0.528839	−	1.62760i	0.0243160	−	0.0748371i
$474$	−23.5113	−	24.1535i	−1.07991	−	1.10941i
$475$		0			0
$476$	0.376053	−	13.9531i	0.0172364	−	0.639538i
$477$	5.84354	+	1.89868i	0.267557	+	0.0869346i
$478$	11.8103	−	1.70779i	0.540188	−	0.0781127i
$479$	−12.7715	−	9.27902i	−0.583544	−	0.423969i	0.256456	−	0.966556i	$-0.417445\pi$
$479$	−12.7715	−	9.27902i	−0.583544	−	0.423969i	−0.840000	+	0.542586i	$0.817445\pi$
$480$		0			0
$481$	49.0813	−	35.6596i	2.23791	−	1.62594i
$482$	−3.53104	+	3.43715i	−0.160834	+	0.156558i
$483$	−4.12211	−	5.67360i	−0.187563	−	0.258158i
$484$	7.89116	−	2.33091i	0.358689	−	0.105950i
$485$		0			0
$486$	28.3795	−	13.9817i	1.28732	−	0.634224i
$487$	11.0724	+	34.0773i	0.501738	+	1.54419i	0.806187	+	0.591661i	$0.201528\pi$
$487$	11.0724	+	34.0773i	0.501738	+	1.54419i	−0.304449	+	0.952529i	$0.598472\pi$
$488$	−16.1102	−	9.04642i	−0.729273	−	0.409512i
$489$	17.8870	−	55.0505i	0.808877	−	2.48947i
$490$		0			0
$491$	7.10672	−	2.30911i	0.320722	−	0.104209i	−0.144232	−	0.989544i	$-0.546071\pi$
$491$	7.10672	−	2.30911i	0.320722	−	0.104209i	0.464954	+	0.885335i	$0.346071\pi$
$492$	−15.0992	+	10.3604i	−0.680722	+	0.467081i
$493$		−	10.8756i		−	0.489811i
$494$	−8.40661	+	48.8118i	−0.378231	+	2.19615i
$495$		0			0
$496$	−6.61048	−	5.36982i	−0.296819	−	0.241112i
$497$	−16.1009	−	11.6980i	−0.722226	−	0.524728i
$498$	−12.6676	−	25.7121i	−0.567648	−	1.15219i
$499$			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
$502$	21.4102	−	10.5482i	0.955586	−	0.470789i
$503$	−24.0283	−	17.4576i	−1.07137	−	0.778395i	−0.0952114	−	0.995457i	$-0.530353\pi$
$503$	−24.0283	−	17.4576i	−1.07137	−	0.778395i	−0.976158	+	0.217062i	$0.930353\pi$
$504$	−3.95314	−	33.7314i	−0.176087	−	1.50252i
$505$		0			0
$506$	2.83753	+	0.488693i	0.126143	+	0.0217251i
$507$		−	85.1999i		−	3.78386i
$508$	−3.99840	−	5.82725i	−0.177400	−	0.258542i
$509$	−1.21315	+	0.394177i	−0.0537721	+	0.0174716i	−0.335780	−	0.941941i	$-0.609000\pi$
$509$	−1.21315	+	0.394177i	−0.0537721	+	0.0174716i	0.282007	+	0.959412i	$0.409000\pi$
$510$		0			0
$511$	16.4404	−	50.5983i	0.727279	−	2.23834i
$512$	−18.7706	−	12.6358i	−0.829553	−	0.558429i
$513$	1.38148	+	4.25176i	0.0609939	+	0.187720i
$514$	−2.76640	−	5.61512i	−0.122021	−	0.247673i
$515$		0			0
$516$	−3.15137	+	0.930858i	−0.138731	+	0.0409788i
$517$	−1.42047	−	1.95511i	−0.0624722	−	0.0859855i
$518$	31.3798	+	32.2369i	1.37875	+	1.41641i
$519$	−32.2290	+	23.4157i	−1.41469	+	1.02784i
$520$		0			0
$521$	9.44563	+	6.86265i	0.413821	+	0.300658i	0.775147	−	0.631781i	$-0.217676\pi$
$521$	9.44563	+	6.86265i	0.413821	+	0.300658i	−0.361326	+	0.932440i	$0.617676\pi$
$522$	−3.78707	−	26.1895i	−0.165756	−	1.14628i
$523$	19.1314	+	6.21617i	0.836558	+	0.271814i	0.695805	−	0.718230i	$-0.255048\pi$
$523$	19.1314	+	6.21617i	0.836558	+	0.271814i	0.140753	+	0.990045i	$0.455048\pi$
$524$	13.4884	+	0.363531i	0.589245	+	0.0158809i
$525$		0			0
$526$	−12.4423	+	12.1115i	−0.542512	+	0.528087i
$527$	1.27984	−	3.93893i	0.0557505	−	0.171582i
$528$	20.5247	+	16.6727i	0.893225	+	0.725584i
$529$	18.1204	+	13.1652i	0.787842	+	0.572401i
$530$		0			0
$531$	−7.75031	−	10.6674i	−0.336335	−	0.462925i
$532$	−36.7157	−	0.989534i	−1.59183	−	0.0429018i
$533$	−14.6170	−	20.1186i	−0.633133	−	0.871432i
$534$	−18.0309	+	34.2393i	−0.780272	+	1.48168i
$535$		0			0
$536$	5.80874	+	12.6382i	0.250899	+	0.545889i
$537$	11.4973	+	35.3850i	0.496144	+	1.52697i
$538$	18.9129	−	35.9141i	0.815391	−	1.54837i
$539$	−14.6564	−	4.76215i	−0.631295	−	0.205120i
$540$		0			0
$541$	19.0637	−	6.19417i	0.819612	−	0.266308i	0.130949	−	0.991389i	$-0.458198\pi$
$541$	19.0637	−	6.19417i	0.819612	−	0.266308i	0.688664	+	0.725081i	$0.258198\pi$
$542$	0.880109	−	5.11023i	0.0378039	−	0.219503i
$543$	−13.5628			−0.582036
$544$	2.44900	−	10.7277i	0.105000	−	0.459945i
$545$		0			0
$546$	86.5652	−	12.5176i	3.70465	−	0.535702i
$547$	22.5997	−	31.1058i	0.966293	−	1.32999i	0.0223953	−	0.999749i	$-0.492871\pi$
$547$	22.5997	−	31.1058i	0.966293	−	1.32999i	0.943897	−	0.330239i	$-0.107129\pi$
$548$	−15.5345	−	5.51444i	−0.663602	−	0.235565i
$549$		−	21.8619i		−	0.933041i
$550$		0			0
$551$	−28.6176			−1.21915
$552$	−2.30882	−	5.02336i	−0.0982698	−	0.213809i
$553$	27.4617	+	19.9521i	1.16779	+	0.848448i
$554$	−0.806638	−	5.57830i	−0.0342708	−	0.236999i
$555$		0			0
$556$	2.24625	−	1.54128i	0.0952623	−	0.0653647i
$557$			10.9707i			0.464844i	0.972615	+	0.232422i	$0.0746650\pi$
$557$			10.9707i			0.464844i	−0.972615	+	0.232422i	$0.925335\pi$
$558$	1.71037	−	9.93100i	0.0724056	−	0.420413i
$559$	−1.37897	−	4.24405i	−0.0583244	−	0.179504i
$560$		0			0
$561$	−3.97373	+	12.2299i	−0.167771	+	0.516346i
$562$	−35.5812	−	18.7376i	−1.50090	−	0.790396i
$563$	−1.00145	+	0.325391i	−0.0422061	+	0.0137136i	−0.330044	−	0.943966i	$-0.607064\pi$
$563$	−1.00145	+	0.325391i	−0.0422061	+	0.0137136i	0.287838	+	0.957679i	$0.407064\pi$
$564$	−1.55228	+	4.37286i	−0.0653626	+	0.184131i
$565$		0			0
$566$	8.60133	−	16.3333i	0.361541	−	0.686539i
$567$	−22.7559	+	16.5331i	−0.955658	+	0.694326i
$568$	−10.6367	−	11.5332i	−0.446305	−	0.483923i
$569$	−16.4403	+	11.9446i	−0.689213	+	0.500743i	−0.876401	−	0.481581i	$-0.840063\pi$
$569$	−16.4403	+	11.9446i	−0.689213	+	0.500743i	0.187188	+	0.982324i	$0.440063\pi$
$570$		0			0
$571$	−8.81803	+	12.1370i	−0.369023	+	0.507917i	−0.952635	−	0.304116i	$-0.901639\pi$
$571$	−8.81803	+	12.1370i	−0.369023	+	0.507917i	0.583612	+	0.812033i	$0.301639\pi$
$572$	−21.8828	+	28.4731i	−0.914965	+	1.19052i
$573$	24.8396	+	8.07089i	1.03769	+	0.337166i
$574$	13.2140	−	12.8627i	0.551543	−	0.536878i
$575$		0			0
$576$	2.16186	−	26.6861i	0.0900776	−	1.11192i
$577$	8.80026	−	27.0844i	0.366360	−	1.12754i	−0.582765	−	0.812640i	$-0.698029\pi$
$577$	8.80026	−	27.0844i	0.366360	−	1.12754i	0.949125	−	0.314899i	$-0.101971\pi$
$578$	−18.4982	+	2.67489i	−0.769423	+	0.111261i
$579$	−1.06683	+	1.46837i	−0.0443361	+	0.0610235i
$580$		0			0
$581$	16.9664	+	23.3523i	0.703885	+	0.968815i
$582$	−14.0180	−	14.4009i	−0.581065	−	0.596937i
$583$	3.89755	−	2.83173i	0.161420	−	0.117278i
$584$	20.5352	−	36.5698i	0.849754	−	1.51327i
$585$		0			0
$586$	−34.2998	+	16.8985i	−1.41691	+	0.698070i
$587$	−32.9333	+	10.7007i	−1.35930	+	0.441664i	−0.895810	−	0.444438i	$-0.853403\pi$
$587$	−32.9333	+	10.7007i	−1.35930	+	0.441664i	−0.463491	+	0.886101i	$0.653403\pi$
$588$	8.38229	+	28.3778i	0.345680	+	1.17028i
$589$	−10.3648	−	3.36772i	−0.427073	−	0.138764i
$590$		0			0
$591$	−4.65121	−	14.3150i	−0.191325	−	0.588839i
$592$	19.2703	+	29.7733i	0.792006	+	1.22368i
$593$	34.9925			1.43697			0.718484	−	0.695543i	$-0.244836\pi$
$593$	34.9925			1.43697			0.718484	+	0.695543i	$0.244836\pi$
$594$	−0.550127	+	3.19423i	−0.0225720	+	0.131061i
$595$		0			0
$596$	15.0058	+	11.5326i	0.614661	+	0.472393i
$597$	19.4960	−	26.8339i	0.797918	−	1.09824i
$598$	6.73492	−	3.31809i	0.275411	−	0.135687i
$599$	−17.7341			−0.724596			−0.362298	−	0.932062i	$-0.618008\pi$
$599$	−17.7341			−0.724596			−0.362298	+	0.932062i	$0.618008\pi$
$600$		0			0
$601$	−2.01505			−0.0821957			−0.0410979	−	0.999155i	$-0.513086\pi$
$601$	−2.01505			−0.0821957			−0.0410979	+	0.999155i	$0.513086\pi$
$602$	2.96841	−	1.46245i	0.120983	−	0.0596049i
$603$	−9.67370	+	13.3147i	−0.393943	+	0.542217i
$604$	−9.74431	+	12.6789i	−0.396490	+	0.515899i
$605$		0			0
$606$	0.122714	−	0.712522i	0.00498492	−	0.0289442i
$607$	−39.1971			−1.59096			−0.795481	−	0.605979i	$-0.792782\pi$
$607$	−39.1971			−1.59096			−0.795481	+	0.605979i	$0.792782\pi$
$608$	−28.2285	−	6.44421i	−1.14482	−	0.261347i
$609$	15.6164	+	48.0624i	0.632809	+	1.94759i
$610$		0			0
$611$	−5.99311	−	1.94728i	−0.242455	−	0.0787785i
$612$	12.4866	−	3.68831i	0.504740	−	0.149091i
$613$	−20.4908	+	6.65786i	−0.827615	+	0.268909i	−0.692041	−	0.721859i	$-0.743288\pi$
$613$	−20.4908	+	6.65786i	−0.827615	+	0.268909i	−0.135575	+	0.990767i	$0.543288\pi$
$614$	−29.3295	+	14.4498i	−1.18364	+	0.583145i
$615$		0			0
$616$	−23.2191	−	13.0383i	−0.935522	−	0.525328i
$617$	−24.1235	+	17.5267i	−0.971175	+	0.705600i	−0.955719	−	0.294280i	$-0.904920\pi$
$617$	−24.1235	+	17.5267i	−0.971175	+	0.705600i	−0.0154563	+	0.999881i	$0.504920\pi$
$618$	−32.8085	−	33.7046i	−1.31975	−	1.35580i
$619$	2.86875	+	3.94849i	0.115305	+	0.158703i	0.862768	−	0.505599i	$-0.168729\pi$
$619$	2.86875	+	3.94849i	0.115305	+	0.158703i	−0.747464	+	0.664303i	$0.768729\pi$
$620$		0			0
$621$	0.398318	−	0.548237i	0.0159839	−	0.0220000i
$622$	14.9703	−	2.16474i	0.600254	−	0.0867983i
$623$	12.0421	−	37.0619i	0.482458	−	1.48485i
$624$	68.8518	+	3.71399i	2.75628	+	0.148678i
$625$		0			0
$626$	7.05442	−	6.86685i	0.281951	−	0.274455i
$627$	32.1813	+	10.4564i	1.28520	+	0.417587i
$628$	12.3385	+	9.48268i	0.492360	+	0.378400i
$629$	−10.1374	+	13.9529i	−0.404205	+	0.556340i
$630$		0			0
$631$	−12.3860	+	8.99897i	−0.493080	+	0.358243i	−0.806367	−	0.591415i	$-0.798570\pi$
$631$	−12.3860	+	8.99897i	−0.493080	+	0.358243i	0.313288	+	0.949658i	$0.398570\pi$
$632$	18.1419	+	19.6710i	0.721644	+	0.782469i
$633$	−11.2007	+	8.13781i	−0.445189	+	0.323449i
$634$	1.84627	−	3.50594i	0.0733249	−	0.139239i
$635$		0			0
$636$	−8.71739	−	3.09449i	−0.345667	−	0.122705i
$637$	−38.2172	+	12.4175i	−1.51422	+	0.492001i
$638$	−18.3584	−	9.66778i	−0.726816	−	0.382751i
$639$	5.73663	−	17.6555i	0.226937	−	0.698442i
$640$		0			0
$641$	−2.46226	−	7.57805i	−0.0972533	−	0.299315i	0.890581	−	0.454825i	$-0.150298\pi$
$641$	−2.46226	−	7.57805i	−0.0972533	−	0.299315i	−0.987834	+	0.155510i	$0.950298\pi$
$642$	9.02116	−	52.3800i	0.356037	−	2.06727i
$643$			6.46830i			0.255085i	0.991833	+	0.127542i	$0.0407089\pi$
$643$			6.46830i			0.255085i	−0.991833	+	0.127542i	$0.959291\pi$
$644$	3.14994	+	4.59070i	0.124125	+	0.180899i
$645$		0			0
$646$	−2.01513	−	13.9357i	−0.0792844	−	0.548291i
$647$	−12.1303	−	8.81321i	−0.476893	−	0.346483i	0.323229	−	0.946321i	$-0.395232\pi$
$647$	−12.1303	−	8.81321i	−0.476893	−	0.346483i	−0.800122	+	0.599838i	$0.795232\pi$
$648$	−20.1479	+	9.26029i	−0.791484	+	0.363779i
$649$	−10.3387			−0.405828
$650$		0			0
$651$			19.2450i			0.754272i
$652$	−15.3724	+	43.3052i	−0.602032	+	1.69596i
$653$	22.6975	−	31.2404i	0.888220	−	1.22253i	−0.0858552	−	0.996308i	$-0.527362\pi$
$653$	22.6975	−	31.2404i	0.888220	−	1.22253i	0.974076	−	0.226223i	$-0.0726378\pi$
$654$	−30.4919	+	4.40920i	−1.19233	+	0.172414i
$655$		0			0
$656$	12.2042	−	7.89898i	0.476494	−	0.308403i
$657$	49.6261			1.93610
$658$	0.793109	−	4.60507i	0.0309186	−	0.179524i
$659$	32.1885	−	10.4587i	1.25389	−	0.407412i	0.394574	−	0.918864i	$-0.370892\pi$
$659$	32.1885	−	10.4587i	1.25389	−	0.407412i	0.859312	+	0.511452i	$0.170892\pi$
$660$		0			0
$661$	1.06103	+	0.344750i	0.0412693	+	0.0134092i	0.329579	−	0.944128i	$-0.393093\pi$
$661$	1.06103	+	0.344750i	0.0412693	+	0.0134092i	−0.288310	+	0.957537i	$0.593093\pi$
$662$	−17.4964	+	33.2243i	−0.680016	+	1.29130i
$663$	10.3617	+	31.8900i	0.402415	+	1.23851i
$664$	9.50298	+	20.6759i	0.368787	+	0.802381i
$665$		0			0
$666$	−19.5532	+	37.1301i	−0.757672	+	1.43876i
$667$	2.54977	+	3.50945i	0.0987274	+	0.135887i
$668$	−0.651686	+	24.1802i	−0.0252145	+	0.935559i
$669$	30.1599	+	41.5116i	1.16605	+	1.60493i
$670$		0			0
$671$	−13.8678	−	10.0756i	−0.535362	−	0.388963i
$672$	4.58121	+	50.9253i	0.176724	+	1.96449i
$673$	−8.12719	+	25.0129i	−0.313280	+	0.964177i	0.663177	+	0.748463i	$0.269208\pi$
$673$	−8.12719	+	25.0129i	−0.313280	+	0.964177i	−0.976457	+	0.215714i	$0.930792\pi$
$674$	19.3424	−	18.8281i	0.745040	−	0.725231i
$675$		0			0
$676$	−1.82229	+	67.6142i	−0.0700880	+	2.60054i
$677$	−16.8361	−	5.47038i	−0.647064	−	0.210244i	−0.0329450	−	0.999457i	$-0.510489\pi$
$677$	−16.8361	−	5.47038i	−0.647064	−	0.210244i	−0.614119	+	0.789213i	$0.710489\pi$
$678$	−3.01283	−	20.8352i	−0.115707	−	0.800171i
$679$	16.3733	+	11.8959i	0.628350	+	0.456523i
$680$		0			0
$681$	−32.2611	+	23.4391i	−1.23625	+	0.898188i
$682$	−5.51136	−	5.66190i	−0.211041	−	0.216805i
$683$	26.8971	+	37.0207i	1.02919	+	1.41656i	0.905554	+	0.424230i	$0.139455\pi$
$683$	26.8971	+	37.0207i	1.02919	+	1.41656i	0.123635	+	0.992328i	$0.460545\pi$
$684$	−9.70530	−	32.8568i	−0.371091	−	1.25631i
$685$		0			0
$686$	2.52782	+	5.13086i	0.0965127	+	0.195897i
$687$	4.98787	+	15.3511i	0.190299	+	0.585680i
$688$	2.52082	−	0.671321i	0.0961054	−	0.0255939i
$689$	3.88194	−	11.9474i	0.147890	−	0.455159i
$690$		0			0
$691$	5.90130	−	1.91745i	0.224496	−	0.0729432i	−0.194609	−	0.980881i	$-0.562344\pi$
$691$	5.90130	−	1.91745i	0.224496	−	0.0729432i	0.419105	+	0.907938i	$0.362344\pi$
$692$	26.0776	−	17.8933i	0.991320	−	0.680199i
$693$		−	31.5088i		−	1.19692i
$694$	−26.8252	−	4.61997i	−1.01827	−	0.175372i
$695$		0			0
$696$	4.63718	+	39.5682i	0.175772	+	1.49983i
$697$	5.71935	+	4.15535i	0.216636	+	0.157395i
$698$	0.0755723	−	0.0372322i	0.00286045	−	0.00140926i
$699$			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	$0.868274\pi$
$702$	3.73521	+	7.58157i	0.140977	+	0.286148i
$703$	36.7153	+	26.6752i	1.38474	+	1.00608i
$704$	−15.9317	−	13.6703i	−0.600449	−	0.515219i
$705$		0			0
$706$	−4.67407	+	27.1393i	−0.175911	+	1.02140i
$707$			0.728101i			0.0273831i
$708$	11.2314	+	16.3685i	0.422101	+	0.615168i
$709$	−10.0050	+	3.25084i	−0.375747	+	0.122088i	−0.490801	−	0.871272i	$-0.663296\pi$
$709$	−10.0050	+	3.25084i	−0.375747	+	0.122088i	0.115054	+	0.993359i	$0.463296\pi$
$710$		0			0
$711$	−9.78435	+	30.1131i	−0.366942	+	1.12933i
$712$	15.0415	−	26.7864i	0.563705	−	1.00386i
$713$	0.510486	+	1.57111i	0.0191178	+	0.0588387i
$714$	−22.3048	+	10.9889i	−0.834738	+	0.411250i
$715$		0			0
$716$	−8.36735	−	28.3272i	−0.312703	−	1.05864i
$717$	−12.4948	−	17.1977i	−0.466628	−	0.642258i
$718$	25.9190	−	25.2298i	0.967287	−	0.941569i
$719$	−5.42565	+	3.94197i	−0.202343	+	0.147011i	−0.684342	−	0.729161i	$-0.739911\pi$
$719$	−5.42565	+	3.94197i	−0.202343	+	0.147011i	0.482000	+	0.876171i	$0.339911\pi$
$720$		0			0
$721$	38.3209	+	27.8418i	1.42715	+	1.03688i
$722$	−10.0764	+	1.45708i	−0.375005	+	0.0542268i
$723$	8.34852	+	2.71260i	0.310485	+	0.100883i
$724$	10.7634	+	0.290087i	0.400018	+	0.0107810i
$725$		0			0
$726$	−10.2240	−	10.5032i	−0.379447	−	0.389811i
$727$	13.0656	−	40.2119i	0.484578	−	1.49138i	−0.348013	−	0.937490i	$-0.613143\pi$
$727$	13.0656	−	40.2119i	0.484578	−	1.49138i	0.832591	−	0.553888i	$-0.186857\pi$
$728$	−68.9654	+	8.08237i	−2.55603	+	0.299553i
$729$	−26.5667	−	19.3018i	−0.983951	−	0.714882i
$730$		0			0
$731$	0.745662	+	1.02632i	0.0275793	+	0.0379597i
$732$	−0.886740	+	32.9016i	−0.0327749	+	1.21608i
$733$	−15.7936	−	21.7381i	−0.583351	−	0.802914i	0.410707	−	0.911768i	$-0.365282\pi$
$733$	−15.7936	−	21.7381i	−0.583351	−	0.802914i	−0.994058	+	0.108854i	$0.965282\pi$
$734$	36.1522	+	19.0383i	1.33440	+	0.702715i
$735$		0			0
$736$	1.72482	+	4.03589i	0.0635778	+	0.148765i
$737$	3.98768	+	12.2728i	0.146888	+	0.452075i
$738$	15.2198	+	8.01493i	0.560247	+	0.295034i
$739$	−13.3854	−	4.34919i	−0.492391	−	0.159988i	0.0522881	−	0.998632i	$-0.483349\pi$
$739$	−13.3854	−	4.34919i	−0.492391	−	0.159988i	−0.544679	+	0.838644i	$0.683349\pi$
$740$		0			0
$741$	83.9145	−	27.2655i	3.08268	−	1.00162i
$742$	9.18030	+	1.58108i	0.337019	+	0.0580432i
$743$	−43.2190			−1.58555			−0.792776	−	0.609513i	$-0.791365\pi$
$743$	−43.2190			−1.58555			−0.792776	+	0.609513i	$0.791365\pi$
$744$	−2.97688	+	14.8766i	−0.109138	+	0.545401i
$745$		0			0
$746$	−5.03560	−	34.8237i	−0.184366	−	1.27499i
$747$	−15.8260	+	21.7826i	−0.579042	+	0.796983i
$748$	3.41511	−	9.62058i	0.124869	−	0.351763i
$749$			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	$0.518842\pi$
$752$	1.32541	−	3.43708i	0.0483326	−	0.125337i
$753$	−34.3974	−	24.9912i	−1.25351	−	0.910728i
$754$	−53.5456	+	7.74284i	−1.95002	+	0.281977i
$755$		0			0
$756$	−5.16780	+	3.54592i	−0.187951	+	0.128964i
$757$		−	25.4279i		−	0.924193i	−0.886830	−	0.462096i	$-0.847097\pi$
$757$		−	25.4279i		−	0.924193i	0.886830	−	0.462096i	$-0.152903\pi$
$758$	−9.02327	−	1.55403i	−0.327740	−	0.0564451i
$759$	−1.58500	−	4.87812i	−0.0575317	−	0.177064i
$760$		0			0
$761$	5.54324	−	17.0603i	0.200942	−	0.618437i	−0.798913	−	0.601446i	$-0.794591\pi$
$761$	5.54324	−	17.0603i	0.200942	−	0.618437i	0.999856	−	0.0169909i	$-0.00540862\pi$
$762$	−5.86601	+	11.1391i	−0.212503	+	0.403527i
$763$	29.5074	−	9.58753i	1.06824	−	0.347092i
$764$	−19.5400	−	6.93629i	−0.706932	−	0.250946i
$765$		0			0
$766$	3.82849	+	2.01613i	0.138329	+	0.0728459i
$767$	−21.8100	+	15.8459i	−0.787512	+	0.572161i
$768$	−4.33597	+	40.0743i	−0.156461	+	1.44606i
$769$	9.85987	−	7.16362i	0.355556	−	0.258327i	−0.395640	−	0.918406i	$-0.629477\pi$
$769$	9.85987	−	7.16362i	0.355556	−	0.258327i	0.751196	+	0.660079i	$0.229477\pi$
$770$		0			0
$771$	−6.55427	+	9.02118i	−0.236046	+	0.324890i
$772$	0.878040	−	1.14247i	0.0316014	−	0.0411185i
$773$	19.3807	+	6.29718i	0.697076	+	0.226494i	0.636056	−	0.771643i	$-0.280565\pi$
$773$	19.3807	+	6.29718i	0.697076	+	0.226494i	0.0610199	+	0.998137i	$0.480565\pi$
$774$	2.15301	+	2.21182i	0.0773884	+	0.0795022i
$775$		0			0
$776$	10.8166	+	11.7283i	0.388294	+	0.421022i
$777$	24.7649	−	76.2186i	0.888437	−	2.73433i
$778$	5.68734	+	39.3308i	0.203901	+	1.41008i
$779$	10.9343	−	15.0497i	0.391761	−	0.539213i
$780$		0			0
$781$	−8.55573	−	11.7760i	−0.306148	−	0.421377i
$782$	−1.52942	+	1.48876i	−0.0546920	+	0.0532379i
$783$	−3.95063	+	2.87030i	−0.141184	+	0.102576i
$784$	−6.04519	−	22.6998i	−0.215899	−	0.810706i
$785$		0			0
$786$	−10.6230	−	21.5621i	−0.378910	−	0.769094i
$787$	1.87380	−	0.608835i	0.0667938	−	0.0217026i	−0.275430	−	0.961321i	$-0.588820\pi$
$787$	1.87380	−	0.608835i	0.0667938	−	0.0217026i	0.342223	+	0.939619i	$0.388820\pi$
$788$	3.38500	+	11.4598i	0.120586	+	0.408237i
$789$	29.4177	+	9.55840i	1.04730	+	0.340288i
$790$		0			0
$791$	6.55119	+	20.1625i	0.232934	+	0.716896i
$792$	4.87387	−	24.3565i	0.173185	−	0.865472i
$793$	−44.6976			−1.58726
$794$	48.7549	+	8.39681i	1.73024	+	0.297992i
$795$		0			0
$796$	−16.0458	+	20.8783i	−0.568730	+	0.740011i
$797$	−13.3592	+	18.3873i	−0.473206	+	0.651313i	−0.977182	−	0.212405i	$-0.931870\pi$
$797$	−13.3592	+	18.3873i	−0.473206	+	0.651313i	0.503975	+	0.863718i	$0.331870\pi$
$798$	28.9159	+	58.6923i	1.02361	+	2.07768i
$799$	1.79141			0.0633756
$800$		0			0
$801$	36.3498			1.28436
$802$	8.35799	+	16.9647i	0.295131	+	0.599044i
$803$	22.8714	−	31.4798i	0.807114	−	1.11090i
$804$	15.0988	−	19.6460i	0.532492	−	0.692860i
$805$		0			0
$806$	−20.3044	−	3.49692i	−0.715191	−	0.123174i
$807$	−72.3059			−2.54529
$808$	−0.112625	+	0.562828i	−0.00396213	+	0.0198002i
$809$	15.7618	+	48.5099i	0.554156	+	1.70552i	0.698163	+	0.715939i	$0.254001\pi$
$809$	15.7618	+	48.5099i	0.554156	+	1.70552i	−0.144007	+	0.989577i	$0.545999\pi$
$810$		0			0
$811$	−42.6096	−	13.8447i	−1.49622	−	0.486153i	−0.557310	−	0.830305i	$-0.688166\pi$
$811$	−42.6096	−	13.8447i	−1.49622	−	0.486153i	−0.938914	+	0.344152i	$0.888166\pi$
$812$	−11.3651	−	38.4760i	−0.398838	−	1.35024i
$813$	−8.78521	+	2.85449i	−0.308111	+	0.100111i
$814$	14.5415	+	29.5157i	0.509680	+	1.03453i
$815$		0			0
$816$	−18.9416	+	5.04435i	−0.663090	+	0.176588i
$817$	2.70061	−	1.96211i	0.0944826	−	0.0686456i
$818$	27.8808	−	27.1395i	0.974828	−	0.948909i
$819$	−48.2928	−	66.4694i	−1.68749	−	2.32263i
$820$		0			0
$821$	−16.5666	+	22.8020i	−0.578180	+	0.795796i	−0.993494	−	0.113881i	$-0.963672\pi$
$821$	−16.5666	+	22.8020i	−0.578180	+	0.795796i	0.415314	+	0.909678i	$0.363672\pi$
$822$	4.20253	+	29.0626i	0.146580	+	1.01367i
$823$	−1.11758	+	3.43957i	−0.0389565	+	0.119896i	−0.968644	−	0.248455i	$-0.920077\pi$
$823$	−1.11758	+	3.43957i	−0.0389565	+	0.119896i	0.929687	+	0.368350i	$0.120077\pi$
$824$	25.3157	+	27.4495i	0.881916	+	0.956250i
$825$		0			0
$826$	−13.9441	−	14.3249i	−0.485176	−	0.498428i
$827$	−26.8330	−	8.71857i	−0.933075	−	0.303174i	−0.197255	−	0.980352i	$-0.563203\pi$
$827$	−26.8330	−	8.71857i	−0.933075	−	0.303174i	−0.735819	+	0.677178i	$0.763203\pi$
$828$	−3.16459	+	4.11765i	−0.109977	+	0.143098i
$829$	−31.0042	+	42.6736i	−1.07682	+	1.48212i	−0.213846	+	0.976867i	$0.568599\pi$
$829$	−31.0042	+	42.6736i	−1.07682	+	1.48212i	−0.862974	+	0.505248i	$0.831401\pi$
$830$		0			0
$831$	−8.12292	+	5.90165i	−0.281781	+	0.204726i
$832$	−54.5610	−	4.42003i	−1.89156	−	0.153237i
$833$	9.24188	−	6.71462i	0.320212	−	0.232648i
$834$	−4.29383	−	2.26119i	−0.148683	−	0.0782987i
$835$		0			0
$836$	−25.3153	−	8.98641i	−0.875548	−	0.310802i
$837$	−1.76862	+	0.574659i	−0.0611324	+	0.0198631i
$838$	26.1830	−	49.7196i	0.904477	−	1.71753i
$839$	−2.76644	+	8.51422i	−0.0955081	+	0.293944i	−0.987386	−	0.158333i	$-0.949388\pi$
$839$	−2.76644	+	8.51422i	−0.0955081	+	0.293944i	0.891878	+	0.452277i	$0.149388\pi$
$840$		0			0
$841$	−0.698169	−	2.14874i	−0.0240748	−	0.0740946i
$842$	−6.52151	−	1.12317i	−0.224746	−	0.0387069i
$843$			71.6357i			2.46726i
$844$	9.06289	−	6.21855i	0.311958	−	0.214051i
$845$		0			0
$846$	4.31390	−	0.623802i	0.148315	−	0.0214467i
$847$	11.9418	+	8.67620i	0.410324	+	0.298118i
$848$	6.85188	+	2.64222i	0.235295	+	0.0907343i
$849$	−32.8838			−1.12857
$850$		0			0
$851$		−	6.87919i		−	0.235816i
$852$	−9.34962	+	26.3385i	−0.320313	+	0.902342i
$853$	−18.5100	+	25.4769i	−0.633772	+	0.872312i	−0.998264	−	0.0588942i	$-0.981243\pi$
$853$	−18.5100	+	25.4769i	−0.633772	+	0.872312i	0.364492	+	0.931206i	$0.381243\pi$
$854$	−4.74356	−	32.8041i	−0.162321	−	1.12253i
$855$		0			0
$856$	−8.27946	+	41.3755i	−0.282986	+	1.41419i
$857$	47.9238			1.63705			0.818523	−	0.574473i	$-0.194793\pi$
$857$	47.9238			1.63705			0.818523	+	0.574473i	$0.194793\pi$
$858$	63.0426	+	10.8575i	2.15224	+	0.370670i
$859$	−25.9430	+	8.42940i	−0.885164	+	0.287607i	−0.716100	−	0.697998i	$-0.754075\pi$
$859$	−25.9430	+	8.42940i	−0.885164	+	0.287607i	−0.169064	+	0.985605i	$0.554075\pi$
$860$		0			0
$861$	−31.2423	−	10.1512i	−1.06473	−	0.345953i
$862$	−25.1703	−	13.2550i	−0.857305	−	0.451469i
$863$	−13.2070	−	40.6471i	−0.449573	−	1.38364i	−0.877390	−	0.479778i	$-0.840717\pi$
$863$	−13.2070	−	40.6471i	−0.449573	−	1.38364i	0.427817	−	0.903865i	$-0.359283\pi$
$864$	−4.54325	+	1.94165i	−0.154564	+	0.0660563i
$865$		0			0
$866$	−1.76074	−	0.927232i	−0.0598325	−	0.0315086i
$867$	19.5704	+	26.9364i	0.664646	+	0.914807i
$868$	0.411620	−	15.2727i	0.0139713	−	0.518391i
$869$	14.5926	+	20.0850i	0.495020	+	0.681337i
$870$		0			0
$871$	27.2225	+	19.7783i	0.922400	+	0.670163i
$872$	24.2925	−	2.84695i	0.822647	−	0.0964099i
$873$	−5.83367	+	17.9542i	−0.197440	+	0.607657i
$874$	3.91747	+	4.02447i	0.132510	+	0.136130i
$875$		0			0
$876$	−74.6861	−	2.01289i	−2.52341	−	0.0680091i
$877$	55.1526	+	17.9202i	1.86237	+	0.605121i	0.994023	+	0.109168i	$0.0348187\pi$
$877$	55.1526	+	17.9202i	1.86237	+	0.605121i	0.868349	+	0.495953i	$0.165181\pi$
$878$	19.6558	−	2.84229i	0.663352	−	0.0959225i
$879$	55.1055	+	40.0365i	1.85866	+	1.35040i
$880$		0			0
$881$	14.3649	−	10.4367i	0.483965	−	0.351621i	−0.318894	−	0.947790i	$-0.603311\pi$
$881$	14.3649	−	10.4367i	0.483965	−	0.351621i	0.802859	+	0.596169i	$0.203311\pi$
$882$	19.9172	−	19.3877i	0.670648	−	0.652817i
$883$	−25.0162	−	34.4318i	−0.841861	−	1.15872i	−0.985598	−	0.169107i	$-0.945912\pi$
$883$	−25.0162	−	34.4318i	−0.841861	−	1.15872i	0.143736	−	0.989616i	$-0.454088\pi$
$884$	−7.54091	−	25.5294i	−0.253628	−	0.858646i
$885$		0			0
$886$	11.8889	−	5.85729i	0.399414	−	0.196780i
$887$	−12.2612	−	37.7360i	−0.411689	−	1.26705i	−0.915179	−	0.403048i	$-0.867951\pi$
$887$	−12.2612	−	37.7360i	−0.411689	−	1.26705i	0.503489	−	0.864001i	$-0.332049\pi$
$888$	30.9332	−	55.0869i	1.03805	−	1.84859i
$889$	3.91768	−	12.0574i	0.131395	−	0.404392i
$890$		0			0
$891$	−19.5653	+	6.35716i	−0.655463	+	0.212973i
$892$	−23.0469	−	33.5884i	−0.771666	−	1.12462i
$893$		−	4.71386i		−	0.157743i
$894$	5.72210	−	33.2245i	0.191375	−	1.11119i
$895$		0			0
$896$	−2.54641	−	40.5120i	−0.0850696	−	1.35341i
$897$	−10.8202	−	7.86135i	−0.361277	−	0.262483i
$898$	−16.9372	−	34.3784i	−0.565202	−	1.14722i
$899$		−	11.9042i		−	0.397026i
$900$		0			0
$901$			3.57122i			0.118974i
$902$	12.0986	−	5.96061i	0.402839	−	0.198467i
$903$	−4.76900	−	3.46488i	−0.158703	−	0.115304i
$904$	1.94533	+	16.5991i	0.0647007	+	0.552079i
$905$		0			0
$906$	28.0726	+	4.83481i	0.932650	+	0.160626i
$907$			34.9093i			1.15914i	0.814921	+	0.579571i	$0.196780\pi$
$907$			34.9093i			1.15914i	−0.814921	+	0.579571i	$0.803220\pi$
$908$	26.1036	−	17.9111i	0.866278	−	0.594401i
$909$	−0.645920	+	0.209872i	−0.0214238	+	0.00696102i
$910$		0			0
$911$	−7.05588	+	21.7158i	−0.233772	+	0.719476i	0.763510	+	0.645796i	$0.223474\pi$
$911$	−7.05588	+	21.7158i	−0.233772	+	0.719476i	−0.997282	+	0.0736799i	$0.976526\pi$
$912$	13.2736	+	49.8424i	0.439531	+	1.65045i
$913$	6.52377	+	20.0781i	0.215905	+	0.664488i
$914$	20.1183	+	40.8353i	0.665455	+	1.35071i
$915$		0			0
$916$	−3.63001	−	12.2892i	−0.119939	−	0.406047i
$917$	14.2280	+	19.5831i	0.469850	+	0.646692i
$918$	−1.67591	−	1.72169i	−0.0553133	−	0.0568241i
$919$	44.3337	−	32.2104i	1.46244	−	1.06252i	0.479715	−	0.877424i	$-0.340740\pi$
$919$	44.3337	−	32.2104i	1.46244	−	1.06252i	0.982720	−	0.185097i	$-0.0592600\pi$
$920$		0			0
$921$	47.1203	+	34.2349i	1.55267	+	1.12808i
$922$	−0.531945	−	3.67867i	−0.0175187	−	0.121150i
$923$	−36.0975	−	11.7288i	−1.18816	−	0.386058i
$924$	−1.27803	+	47.4200i	−0.0420441	+	1.56000i
$925$		0			0
$926$	30.6580	−	29.8429i	1.00748	−	0.980698i
$927$	−13.6534	+	42.0209i	−0.448437	+	1.38015i
$928$	−2.83374	−	31.5003i	−0.0930222	−	1.03405i
$929$	26.3740	+	19.1618i	0.865301	+	0.628678i	0.929322	−	0.369270i	$-0.120392\pi$
$929$	26.3740	+	19.1618i	0.865301	+	0.628678i	−0.0640206	+	0.997949i	$0.520392\pi$
$930$		0			0
$931$	−17.6686	−	24.3188i	−0.579066	−	0.797016i
$932$	0.947653	−	35.1617i	0.0310414	−	1.15176i
$933$	−15.8380	−	21.7992i	−0.518514	−	0.713673i
$934$	−27.1797	+	51.6122i	−0.889347	+	1.68880i
$935$		0			0
$936$	−27.0491	−	58.8515i	−0.884127	−	1.92362i
$937$	2.49974	+	7.69340i	0.0816628	+	0.251332i	0.983549	−	0.180641i	$-0.0578173\pi$
$937$	2.49974	+	7.69340i	0.0816628	+	0.251332i	−0.901886	+	0.431974i	$0.857817\pi$
$938$	−11.6265	+	22.0779i	−0.379620	+	0.720870i
$939$	−16.6789	−	5.41932i	−0.544297	−	0.176853i
$940$		0			0
$941$	−34.7042	+	11.2761i	−1.13133	+	0.367590i	−0.814080	−	0.580753i	$-0.802758\pi$
$941$	−34.7042	+	11.2761i	−1.13133	+	0.367590i	−0.317246	+	0.948343i	$0.602758\pi$
$942$	4.70500	−	27.3189i	0.153297	−	0.890097i
$943$	−2.81981			−0.0918255
$944$	−8.56305	−	13.2302i	−0.278704	−	0.430607i
$945$		0			0
$946$	2.39531	−	0.346369i	0.0778784	−	0.0112614i
$947$	−8.90757	+	12.2602i	−0.289457	+	0.398404i	−0.928838	−	0.370487i	$-0.879191\pi$
$947$	−8.90757	+	12.2602i	−0.289457	+	0.398404i	0.639380	+	0.768890i	$0.279191\pi$
$948$	15.9467	−	44.9228i	0.517923	−	1.45902i
$949$		−	101.463i		−	3.29362i
$950$		0			0
$951$	−7.05851			−0.228888
$952$	17.9360	−	8.24369i	0.581310	−	0.267179i
$953$	44.0685	+	32.0176i	1.42752	+	1.03715i	0.990472	+	0.137714i	$0.0439755\pi$
$953$	44.0685	+	32.0176i	1.42752	+	1.03715i	0.437047	+	0.899439i	$0.356024\pi$
$954$	1.24356	+	8.59985i	0.0402618	+	0.278430i
$955$		0			0
$956$	9.54799	+	13.9152i	0.308804	+	0.450050i
$957$			36.9610i			1.19478i
$958$	3.78920	−	22.0015i	0.122424	−	0.710835i
$959$	−9.13812	−	28.1242i	−0.295085	−	0.908179i
$960$		0			0
$961$	−8.17865	+	25.1713i	−0.263827	+	0.811977i
$962$	75.9142	+	39.9775i	2.44757	+	1.28892i
$963$	−47.4839	+	15.4285i	−1.53015	+	0.497175i
$964$	−6.56732	−	2.33126i	−0.211519	−	0.0750849i
$965$		0			0
$966$	4.62124	−	8.77538i	0.148686	−	0.282343i
$967$	17.8627	−	12.9780i	0.574424	−	0.417344i	−0.262285	−	0.964990i	$-0.584476\pi$
$967$	17.8627	−	12.9780i	0.574424	−	0.417344i	0.836710	+	0.547647i	$0.184476\pi$
$968$	7.88903	+	8.55397i	0.253563	+	0.274935i
$969$	−20.2926	+	14.7434i	−0.651892	+	0.473628i
$970$		0			0
$971$	5.05516	−	6.95783i	0.162228	−	0.223287i	−0.720163	−	0.693805i	$-0.755933\pi$
$971$	5.05516	−	6.95783i	0.162228	−	0.223287i	0.882390	+	0.470518i	$0.155933\pi$
$972$	35.4747	+	27.2638i	1.13785	+	0.874488i
$973$	4.64781	+	1.51016i	0.149002	+	0.0484137i
$974$	−36.3105	+	35.3450i	−1.16346	+	1.13253i
$975$		0			0
$976$	1.40742	−	26.0916i	0.0450505	−	0.835171i
$977$	5.88484	−	18.1117i	0.188273	−	0.579444i	−0.811717	−	0.584052i	$-0.801467\pi$
$977$	5.88484	−	18.1117i	0.188273	−	0.579444i	0.999989	+	0.00460737i	$0.00146658\pi$
$978$	81.0170	−	11.7153i	2.59064	−	0.374613i
$979$	16.7527	−	23.0581i	0.535418	−	0.736940i
$980$		0			0
$981$	17.0107	+	23.4133i	0.543111	+	0.747529i
$982$	7.37111	+	7.57244i	0.235221	+	0.241646i
$983$	16.6333	−	12.0848i	0.530521	−	0.385446i	−0.290032	−	0.957017i	$-0.593666\pi$
$983$	16.6333	−	12.0848i	0.530521	−	0.385446i	0.820553	+	0.571571i	$0.193666\pi$
$984$	−22.5803	−	12.6796i	−0.719834	−	0.404212i
$985$		0			0
$986$	13.7968	−	6.79729i	0.439381	−	0.216470i
$987$	−7.91678	+	2.57232i	−0.251994	+	0.0818777i
$988$	−67.1772	+	19.8429i	−2.13719	+	0.631288i
$989$	−0.481237	−	0.156364i	−0.0153025	−	0.00497207i
$990$		0			0
$991$	−7.98983	−	24.5902i	−0.253805	−	0.781132i	−0.994063	−	0.108809i	$-0.965296\pi$
$991$	−7.98983	−	24.5902i	−0.253805	−	0.781132i	0.740258	−	0.672323i	$-0.234704\pi$
$992$	2.68062	−	11.7423i	0.0851097	−	0.372818i
$993$	66.8905			2.12271
$994$	4.77703	−	27.7371i	0.151518	−	0.879768i
$995$		0			0
$996$	24.7013	−	32.1404i	0.782690	−	1.01841i
$997$	−11.2686	+	15.5099i	−0.356881	+	0.491204i	−0.949276	−	0.314443i	$-0.898182\pi$
$997$	−11.2686	+	15.5099i	−0.356881	+	0.491204i	0.592396	+	0.805647i	$0.298182\pi$
$998$	−2.04965	+	1.00980i	−0.0648805	+	0.0319647i
$999$	7.74398			0.245009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.101.37		224
5.2	odd	4		1000.2.o.a.149.5		112
5.3	odd	4		200.2.o.a.29.24	yes	112
5.4	even	2	inner	1000.2.t.b.101.20		224
8.5	even	2	inner	1000.2.t.b.101.9		224
20.3	even	4		800.2.be.a.529.4		112
25.6	even	5	inner	1000.2.t.b.901.9		224
25.8	odd	20		1000.2.o.a.349.10		112
25.17	odd	20		200.2.o.a.69.19	yes	112
25.19	even	10	inner	1000.2.t.b.901.48		224
40.3	even	4		800.2.be.a.529.25		112
40.13	odd	4		200.2.o.a.29.19	✓	112
40.29	even	2	inner	1000.2.t.b.101.48		224
40.37	odd	4		1000.2.o.a.149.10		112
100.67	even	20		800.2.be.a.369.25		112
200.67	even	20		800.2.be.a.369.4		112
200.69	even	10	inner	1000.2.t.b.901.20		224
200.117	odd	20		200.2.o.a.69.24	yes	112
200.133	odd	20		1000.2.o.a.349.5		112
200.181	even	10	inner	1000.2.t.b.901.37		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.19	✓	112	40.13	odd	4
200.2.o.a.29.24	yes	112	5.3	odd	4
200.2.o.a.69.19	yes	112	25.17	odd	20
200.2.o.a.69.24	yes	112	200.117	odd	20
800.2.be.a.369.4		112	200.67	even	20
800.2.be.a.369.25		112	100.67	even	20
800.2.be.a.529.4		112	20.3	even	4
800.2.be.a.529.25		112	40.3	even	4
1000.2.o.a.149.5		112	5.2	odd	4
1000.2.o.a.149.10		112	40.37	odd	4
1000.2.o.a.349.5		112	200.133	odd	20
1000.2.o.a.349.10		112	25.8	odd	20
1000.2.t.b.101.9		224	8.5	even	2	inner
1000.2.t.b.101.20		224	5.4	even	2	inner
1000.2.t.b.101.37		224	1.1	even	1	trivial
1000.2.t.b.101.48		224	40.29	even	2	inner
1000.2.t.b.901.9		224	25.6	even	5	inner
1000.2.t.b.901.20		224	200.69	even	10	inner
1000.2.t.b.901.37		224	200.181	even	10	inner
1000.2.t.b.901.48		224	25.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.625006 + 1.26861i) q^{2} +(1.48079 - 2.03813i) q^{3} +(-1.21874 + 1.58578i) q^{4} +(3.51109 + 0.604697i) q^{6} -3.58786 q^{7} +(-2.77344 - 0.554981i) q^{8} +(-1.03418 - 3.18289i) q^{9} +O(q^{10})\)	\(q+(0.625006 + 1.26861i) q^{2} +(1.48079 - 2.03813i) q^{3} +(-1.21874 + 1.58578i) q^{4} +(3.51109 + 0.604697i) q^{6} -3.58786 q^{7} +(-2.77344 - 0.554981i) q^{8} +(-1.03418 - 3.18289i) q^{9} +(-2.49567 - 0.810891i) q^{11} +(1.42732 + 4.83213i) q^{12} +(-6.50757 + 2.11444i) q^{13} +(-2.24243 - 4.55159i) q^{14} +(-1.02937 - 3.86528i) q^{16} +(1.57369 - 1.14335i) q^{17} +(3.39148 - 3.30130i) q^{18} +(-3.00859 - 4.14097i) q^{19} +(-5.31285 + 7.31251i) q^{21} +(-0.531102 - 3.67283i) q^{22} +(-0.239759 + 0.737902i) q^{23} +(-5.23800 + 4.83083i) q^{24} +(-6.74966 - 6.93403i) q^{26} +(-0.830663 - 0.269899i) q^{27} +(4.37265 - 5.68954i) q^{28} +(3.28631 - 4.52322i) q^{29} +(1.72253 - 1.25149i) q^{31} +(4.26017 - 3.72168i) q^{32} +(-5.34825 + 3.88573i) q^{33} +(2.43404 + 1.28180i) q^{34} +(6.30775 + 2.23912i) q^{36} +(-8.43241 + 2.73986i) q^{37} +(3.37288 - 6.40485i) q^{38} +(-5.32683 + 16.3943i) q^{39} +(1.12308 + 3.45647i) q^{41} +(-12.5973 - 2.16957i) q^{42} +0.652170i q^{43} +(4.32745 - 2.96930i) q^{44} +(-1.08596 + 0.157033i) q^{46} +(0.745059 + 0.541317i) q^{47} +(-9.40221 - 3.62568i) q^{48} +5.87273 q^{49} -4.90045i q^{51} +(4.57799 - 12.8965i) q^{52} +(-1.07913 + 1.48529i) q^{53} +(-0.176773 - 1.22247i) q^{54} +(9.95073 + 1.99119i) q^{56} -12.8949 q^{57} +(7.79215 + 1.34200i) q^{58} +(3.74706 - 1.21749i) q^{59} +(6.21266 + 2.01862i) q^{61} +(2.66424 + 1.40303i) q^{62} +(3.71051 + 11.4198i) q^{63} +(7.38399 + 3.07842i) q^{64} +(-8.27215 - 4.35623i) q^{66} +(-2.89052 - 3.97847i) q^{67} +(-0.104813 + 3.88897i) q^{68} +(1.14891 + 1.58133i) q^{69} +(4.48762 + 3.26045i) q^{71} +(1.10181 + 9.40153i) q^{72} +(-4.58222 + 14.1026i) q^{73} +(-8.74611 - 8.98500i) q^{74} +(10.2333 + 0.275801i) q^{76} +(8.95410 + 2.90936i) q^{77} +(-24.1272 + 3.48886i) q^{78} +(-7.65406 - 5.56100i) q^{79} +(6.34247 - 4.60807i) q^{81} +(-3.68298 + 3.58506i) q^{82} +(-4.72884 - 6.50869i) q^{83} +(-5.12104 - 17.3370i) q^{84} +(-0.827349 + 0.407610i) q^{86} +(-4.35257 - 13.3958i) q^{87} +(6.47156 + 3.63401i) q^{88} +(-3.35636 + 10.3298i) q^{89} +(23.3483 - 7.58631i) q^{91} +(-0.877943 - 1.27951i) q^{92} -5.36393i q^{93} +(-0.221053 + 1.28351i) q^{94} +(-1.27686 - 14.1938i) q^{96} +(-4.56353 - 3.31560i) q^{97} +(3.67049 + 7.45020i) q^{98} +8.78205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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