LMFDB - Embedded newform 1000.2.t.b.901.9

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			901.9
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25131 - 0.658957i) q^{2} +(-1.48079 - 2.03813i) q^{3} +(1.13155 + 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} -3.58786 q^{7} +(-0.329223 - 2.80920i) q^{8} +(-1.03418 + 3.18289i) q^{9} +O(q^{10})$	\(q+(-1.25131 - 0.658957i) q^{2} +(-1.48079 - 2.03813i) q^{3} +(1.13155 + 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} -3.58786 q^{7} +(-0.329223 - 2.80920i) q^{8} +(-1.03418 + 3.18289i) q^{9} +(2.49567 - 0.810891i) q^{11} +(1.68553 - 4.74824i) q^{12} +(6.50757 + 2.11444i) q^{13} +(4.48952 + 2.36424i) q^{14} +(-1.43918 + 3.73212i) 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} +(-3.65719 - 0.629861i) 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} +(-4.05985 - 5.91680i) 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} +(-1.21576 - 2.46769i) q^{34} +(-6.41920 + 1.89612i) q^{36} +(8.43241 + 2.73986i) q^{37} +(-6.49339 + 3.19910i) q^{38} +(-5.32683 - 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(-1.82939 - 12.6512i) q^{42} +0.652170i q^{43} +(4.16123 + 3.19808i) q^{44} +(-0.186233 + 1.08133i) q^{46} +(0.745059 - 0.541317i) q^{47} +(9.73767 - 2.59324i) q^{48} +5.87273 q^{49} -4.90045i q^{51} +(3.87669 + 13.1244i) q^{52} +(1.07913 + 1.48529i) q^{53} +(-1.21727 - 0.209644i) q^{54} +(1.18121 + 10.0790i) q^{56} -12.8949 q^{57} +(1.13159 + 7.82548i) q^{58} +(-3.74706 - 1.21749i) q^{59} +(-6.21266 + 2.01862i) q^{61} +(-1.33074 - 2.70108i) q^{62} +(3.71051 - 11.4198i) q^{63} +(-7.78322 + 1.84971i) q^{64} +(4.13179 + 8.38651i) 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} +(9.28187 + 1.85735i) 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} +(-4.13762 + 24.0245i) 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} +(-6.04743 + 17.0360i) q^{84} +(0.429752 - 0.816067i) q^{86} +(-4.35257 + 13.3958i) q^{87} +(-3.09959 - 6.74386i) q^{88} +(-3.35636 - 10.3298i) q^{89} +(-23.3483 - 7.58631i) q^{91} +(0.945588 - 1.23036i) q^{92} -5.36393i q^{93} +(-1.28900 + 0.186393i) q^{94} +(-13.8937 - 3.17175i) q^{96} +(-4.56353 + 3.31560i) q^{97} +(-7.34861 - 3.86988i) 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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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 $

$2$	−1.25131	−	0.658957i	−0.884810	−	0.465953i
$2$	−1.25131	−	0.658957i	−0.884810	−	0.465953i
$3$	−1.48079	−	2.03813i	−0.854932	−	1.17671i	−0.982754	−	0.184916i	$-0.940799\pi$
$3$	−1.48079	−	2.03813i	−0.854932	−	1.17671i	0.127822	−	0.991797i	$-0.459201\pi$
$4$	1.13155	+	1.64912i	0.565776	+	0.824559i
$5$		0			0
$5$		0			0
$6$	0.509884	+	3.52610i	0.208159	+	1.43953i
$7$	−3.58786			−1.35608			−0.678042	−	0.735024i	$-0.737171\pi$
$7$	−3.58786			−1.35608			−0.678042	+	0.735024i	$0.737171\pi$
$8$	−0.329223	−	2.80920i	−0.116398	−	0.993203i
$9$	−1.03418	+	3.18289i	−0.344728	+	1.06096i
$10$		0			0
$11$	2.49567	−	0.810891i	0.752472	−	0.244493i	0.0924272	−	0.995719i	$-0.470537\pi$
$11$	2.49567	−	0.810891i	0.752472	−	0.244493i	0.660044	+	0.751227i	$0.270537\pi$
$12$	1.68553	−	4.74824i	0.486570	−	1.37070i
$13$	6.50757	+	2.11444i	1.80488	+	0.586440i	0.999976	−	0.00697033i	$-0.00221874\pi$
$13$	6.50757	+	2.11444i	1.80488	+	0.586440i	0.804900	+	0.593410i	$0.202219\pi$
$14$	4.48952	+	2.36424i	1.19988	+	0.631871i
$15$		0			0
$16$	−1.43918	+	3.73212i	−0.359796	+	0.933031i
$17$	1.57369	+	1.14335i	0.381677	+	0.277304i	0.762036	−	0.647534i	$-0.224200\pi$
$17$	1.57369	+	1.14335i	0.381677	+	0.277304i	−0.380360	+	0.924839i	$0.624200\pi$
$18$	3.39148	−	3.30130i	0.799378	−	0.778124i
$19$	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
$22$	−3.65719	−	0.629861i	−0.779716	−	0.134287i
$23$	−0.239759	−	0.737902i	−0.0499932	−	0.153863i	0.922943	−	0.384936i	$-0.125776\pi$
$23$	−0.239759	−	0.737902i	−0.0499932	−	0.153863i	−0.972936	+	0.231073i	$0.925776\pi$
$24$	−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
$28$	−4.05985	−	5.91680i	−0.767239	−	1.11817i
$29$	−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	$0.638761\pi$
$32$	4.26017	−	3.72168i	0.753099	−	0.657907i
$33$	−5.34825	−	3.88573i	−0.931010	−	0.676419i
$34$	−1.21576	−	2.46769i	−0.208500	−	0.423205i
$35$		0			0
$36$	−6.41920	+	1.89612i	−1.06987	+	0.316019i
$37$	8.43241	+	2.73986i	1.38628	+	0.450430i	0.904729	−	0.425988i	$-0.140074\pi$
$37$	8.43241	+	2.73986i	1.38628	+	0.450430i	0.481551	+	0.876418i	$0.340074\pi$
$38$	−6.49339	+	3.19910i	−1.05337	+	0.518963i
$39$	−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	$0.00840642\pi$
$42$	−1.82939	−	12.6512i	−0.282281	−	1.95212i
$43$			0.652170i			0.0994550i	0.998763	+	0.0497275i	$0.0158353\pi$
$43$			0.652170i			0.0994550i	−0.998763	+	0.0497275i	$0.984165\pi$
$44$	4.16123	+	3.19808i	0.627329	+	0.482129i
$45$		0			0
$46$	−0.186233	+	1.08133i	−0.0274585	+	0.159434i
$47$	0.745059	−	0.541317i	0.108678	−	0.0789592i	−0.532119	−	0.846670i	$-0.678604\pi$
$47$	0.745059	−	0.541317i	0.108678	−	0.0789592i	0.640797	+	0.767710i	$0.278604\pi$
$48$	9.73767	−	2.59324i	1.40551	−	0.374302i
$49$	5.87273			0.838962
$50$		0			0
$51$		−	4.90045i		−	0.686201i
$52$	3.87669	+	13.1244i	0.537601	+	1.82002i
$53$	1.07913	+	1.48529i	0.148229	+	0.204020i	0.876675	−	0.481084i	$-0.159757\pi$
$53$	1.07913	+	1.48529i	0.148229	+	0.204020i	−0.728445	+	0.685104i	$0.759757\pi$
$54$	−1.21727	−	0.209644i	−0.165649	−	0.0285290i
$55$		0			0
$56$	1.18121	+	10.0790i	0.157845	+	1.34687i
$57$	−12.8949			−1.70797
$58$	1.13159	+	7.82548i	0.148584	+	1.02754i
$59$	−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	−0.678423	−	0.734672i	$-0.737336\pi$
$61$	−6.21266	+	2.01862i	−0.795449	+	0.258457i	−0.117027	+	0.993129i	$0.537336\pi$
$62$	−1.33074	−	2.70108i	−0.169004	−	0.343037i
$63$	3.71051	−	11.4198i	0.467480	−	1.43876i
$64$	−7.78322	+	1.84971i	−0.972903	+	0.231214i
$65$		0			0
$66$	4.13179	+	8.38651i	0.508588	+	1.03231i
$67$	2.89052	−	3.97847i	0.353134	−	0.486047i	−0.595086	−	0.803662i	$-0.702882\pi$
$67$	2.89052	−	3.97847i	0.353134	−	0.486047i	0.948220	+	0.317615i	$0.102882\pi$
$68$	−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	−0.288740	−	0.957407i	$-0.593236\pi$
$71$	4.48762	−	3.26045i	0.532582	−	0.386944i	0.821323	+	0.570464i	$0.193236\pi$
$72$	9.28187	+	1.85735i	1.09388	+	0.218891i
$73$	−4.58222	−	14.1026i	−0.536309	−	1.65059i	−0.740804	−	0.671721i	$-0.765555\pi$
$73$	−4.58222	−	14.1026i	−0.536309	−	1.65059i	0.204496	−	0.978868i	$-0.434445\pi$
$74$	−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
$78$	−4.13762	+	24.0245i	−0.468493	+	2.72024i
$79$	−7.65406	+	5.56100i	−0.861148	+	0.625661i	−0.928197	−	0.372089i	$-0.878642\pi$
$79$	−7.65406	+	5.56100i	−0.861148	+	0.625661i	0.0670487	+	0.997750i	$0.478642\pi$
$80$		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	$-0.654433\pi$
$83$	4.72884	−	6.50869i	0.519058	−	0.714422i	0.985414	+	0.170176i	$0.0544335\pi$
$84$	−6.04743	+	17.0360i	−0.659829	+	1.85878i
$85$		0			0
$86$	0.429752	−	0.816067i	0.0463414	−	0.0879988i
$87$	−4.35257	+	13.3958i	−0.466645	+	1.43618i
$88$	−3.09959	−	6.74386i	−0.330417	−	0.718898i
$89$	−3.35636	−	10.3298i	−0.355773	−	1.09496i	−0.955560	−	0.294797i	$-0.904748\pi$
$89$	−3.35636	−	10.3298i	−0.355773	−	1.09496i	0.599787	−	0.800160i	$-0.295252\pi$
$90$		0			0
$91$	−23.3483	−	7.58631i	−2.44756	−	0.795261i
$92$	0.945588	−	1.23036i	0.0985843	−	0.128274i
$93$		−	5.36393i		−	0.556213i
$94$	−1.28900	+	0.186393i	−0.132951	+	0.0192250i
$95$		0			0
$96$	−13.8937	−	3.17175i	−1.41802	−	0.323716i
$97$	−4.56353	+	3.31560i	−0.463356	+	0.336648i	−0.794846	−	0.606811i	$-0.792449\pi$
$97$	−4.56353	+	3.31560i	−0.463356	+	0.336648i	0.331490	+	0.943459i	$0.392449\pi$
$98$	−7.34861	−	3.86988i	−0.742321	−	0.390917i
$99$			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	$-0.00321383\pi$
$102$	−3.22919	+	6.13198i	−0.319737	+	0.607157i
$103$	−10.6807	+	7.76000i	−1.05240	+	0.764616i	−0.972668	−	0.232201i	$-0.925407\pi$
$103$	−10.6807	+	7.76000i	−1.05240	+	0.764616i	−0.0797351	+	0.996816i	$0.525407\pi$
$104$	3.79744	−	18.9772i	0.372369	−	1.86087i
$105$		0			0
$106$	−0.371579	−	2.56966i	−0.0360910	−	0.249587i
$107$		−	14.9185i		−	1.44222i	−0.692819	−	0.721111i	$-0.743632\pi$
$107$		−	14.9185i		−	1.44222i	0.692819	−	0.721111i	$-0.256368\pi$
$108$	1.38503	+	1.06446i	0.133275	+	0.102427i
$109$	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
$112$	5.16358	−	13.3903i	0.487913	−	1.26527i
$113$	−1.82593	+	5.61964i	−0.171769	+	0.528652i	−0.999471	−	0.0325164i	$-0.989648\pi$
$113$	−1.82593	+	5.61964i	−0.171769	+	0.528652i	0.827702	+	0.561168i	$0.189648\pi$
$114$	16.1355	+	8.49718i	1.51123	+	0.795834i
$115$		0			0
$116$	3.74069	−	10.5378i	0.347314	−	0.978407i
$117$	−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
$122$	9.10414	+	1.56796i	0.824250	+	0.141957i
$123$	−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	0.890849	−	0.454299i	$-0.150110\pi$
$127$	−1.09193	−	3.36061i	−0.0968930	−	0.298206i	−0.987742	+	0.156093i	$0.950110\pi$
$128$	10.9581	+	2.81425i	0.968569	+	0.248747i
$129$	1.32921	−	0.965725i	0.117030	−	0.0850273i
$130$		0			0
$131$	3.96559	−	5.45817i	0.346475	−	0.476883i	−0.599843	−	0.800118i	$-0.704770\pi$
$131$	3.96559	−	5.45817i	0.346475	−	0.476883i	0.946319	+	0.323235i	$0.104770\pi$
$132$	0.356209	−	13.2168i	0.0310040	−	1.15037i
$133$	−10.7944	+	14.8572i	−0.935992	+	1.28828i
$134$	−6.23858	+	3.07356i	−0.538931	+	0.265515i
$135$		0			0
$136$	2.69382	−	4.79724i	0.230993	−	0.411360i
$137$	2.54696	−	7.83872i	0.217601	−	0.669707i	−0.781358	−	0.624084i	$-0.785472\pi$
$137$	2.54696	−	7.83872i	0.217601	−	0.669707i	0.998959	−	0.0456237i	$-0.0145275\pi$
$138$	2.47967	−	1.22166i	0.211083	−	0.103994i
$139$	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
$142$	−7.76389	+	1.12268i	−0.651531	+	0.0942132i
$143$	17.9553			1.50150
$144$	−10.3906	−	8.44047i	−0.865881	−	0.703373i
$145$		0			0
$146$	−3.55925	+	20.6663i	−0.294565	+	1.71035i
$147$	−8.69626	−	11.9694i	−0.717256	−	0.987218i
$148$	5.02336	+	17.0063i	0.412918	+	1.39791i
$149$		−	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	$0.394525\pi$
$152$	−12.6233	−	7.08843i	−1.02389	−	0.574947i
$153$	−5.26667	+	3.82646i	−0.425785	+	0.309351i
$154$	13.1215	+	2.25985i	1.05736	+	0.182104i
$155$		0			0
$156$	21.0086	−	27.3356i	1.68203	−	2.18860i
$157$		−	7.78075i		−	0.620971i	−0.950578	−	0.310486i	$-0.899508\pi$
$157$		−	7.78075i		−	0.620971i	0.950578	−	0.310486i	$-0.100492\pi$
$158$	13.2421	−	1.91484i	1.05348	−	0.152336i
$159$	1.42926	−	4.39880i	0.113347	−	0.348847i
$160$		0			0
$161$	0.860221	+	2.64749i	0.0677949	+	0.208651i
$162$	−4.89987	−	9.94554i	−0.384970	−	0.781396i
$163$	−21.8518	−	7.10008i	−1.71157	−	0.556121i	−0.720973	−	0.692964i	$-0.756305\pi$
$163$	−21.8518	−	7.10008i	−1.71157	−	0.556121i	−0.990593	+	0.136842i	$0.956305\pi$
$164$	6.97095	−	2.05909i	0.544340	−	0.160788i
$165$		0			0
$166$	−10.2062	+	5.02828i	−0.792154	+	0.390271i
$167$	9.78464	+	7.10896i	0.757158	+	0.550108i	0.898037	−	0.439919i	$-0.144993\pi$
$167$	9.78464	+	7.10896i	0.757158	+	0.550108i	−0.140879	+	0.990027i	$0.544993\pi$
$168$	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
$172$	−1.07551	+	0.737964i	−0.0820065	+	0.0562692i
$173$	15.0391	−	4.88649i	1.14340	−	0.371513i	0.324747	−	0.945801i	$-0.394721\pi$
$173$	15.0391	−	4.88649i	1.14340	−	0.371513i	0.818653	+	0.574288i	$0.194721\pi$
$174$	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
$178$	−2.60705	+	15.1375i	−0.195407	+	1.13460i
$179$	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	−0.675053	−	0.737769i	$-0.735879\pi$
$181$	3.16443	−	4.35546i	0.235210	−	0.323739i	0.910263	+	0.414030i	$0.135879\pi$
$182$	24.2168	+	24.8783i	1.79507	+	1.84410i
$183$	13.3138	+	9.67305i	0.984186	+	0.715053i
$184$	−1.99398	+	0.916465i	−0.146998	+	0.0675627i
$185$		0			0
$186$	−3.53460	+	6.71194i	−0.259169	+	0.492143i
$187$	4.85455	+	1.57734i	0.355000	+	0.115346i
$188$	1.73577	+	0.616162i	0.126594	+	0.0449382i
$189$	−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	$-0.0223832\pi$
$192$	15.2952	+	13.1242i	1.10384	+	0.947156i
$193$	−0.720451			−0.0518592			−0.0259296	−	0.999664i	$-0.508255\pi$
$193$	−0.720451			−0.0518592			−0.0259296	+	0.999664i	$0.508255\pi$
$194$	7.89523	−	1.14167i	0.566844	−	0.0819672i
$195$		0			0
$196$	6.64530	+	9.68483i	0.474664	+	0.691774i
$197$	−3.51179	−	4.83357i	−0.250205	−	0.344377i	0.665378	−	0.746506i	$-0.268270\pi$
$197$	−3.51179	−	4.83357i	−0.250205	−	0.344377i	−0.915583	+	0.402129i	$0.868270\pi$
$198$	5.78699	−	10.9891i	0.411264	−	0.780959i
$199$	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
$202$	−0.133725	+	0.253934i	−0.00940888	+	0.0178668i
$203$	11.7908	+	16.2287i	0.827553	+	1.13903i
$204$	8.08142	−	5.54511i	0.565813	−	0.388236i
$205$		0			0
$206$	18.4784	−	2.67203i	1.28745	−	0.186169i
$207$	2.59662			0.180477
$208$	−17.2569	+	21.2440i	−1.19655	+	1.47301i
$209$	4.15056	−	12.7741i	0.287100	−	0.883603i
$210$		0			0
$211$	5.22662	−	1.69823i	0.359816	−	0.116911i	−0.123530	−	0.992341i	$-0.539421\pi$
$211$	5.22662	−	1.69823i	0.359816	−	0.116911i	0.483346	+	0.875430i	$0.339421\pi$
$212$	−1.22833	+	3.46029i	−0.0843622	+	0.237654i
$213$	−13.2904	−	4.31832i	−0.910644	−	0.295886i
$214$	−9.83063	+	18.6676i	−0.672008	+	1.27609i
$215$		0			0
$216$	−1.03167	−	2.24464i	−0.0701965	−	0.152729i
$217$	−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
$222$	−5.36147	+	31.1306i	−0.359838	+	2.08935i
$223$	−6.29390	−	19.3706i	−0.421471	−	1.29715i	−0.906333	−	0.422564i	$-0.861130\pi$
$223$	−6.29390	−	19.3706i	−0.421471	−	1.29715i	0.484862	−	0.874590i	$-0.338870\pi$
$224$	−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	$-0.423954\pi$
$227$	15.0541	−	4.89137i	0.999175	−	0.324652i	0.762536	+	0.646946i	$0.223954\pi$
$228$	−14.5912	−	21.2652i	−0.966328	−	1.40832i
$229$	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
$232$	−11.6247	+	10.7211i	−0.763199	+	0.703872i
$233$	−14.2284	−	10.3375i	−0.932133	−	0.677234i	0.0143813	−	0.999897i	$-0.495422\pi$
$233$	−14.2284	−	10.3375i	−0.932133	−	0.677234i	−0.946514	+	0.322662i	$0.895422\pi$
$234$	29.0507	−	14.3124i	1.89910	−	0.935631i
$235$		0			0
$236$	−2.23220	−	7.55701i	−0.145304	−	0.491919i
$237$	22.6680	+	7.36529i	1.47245	+	0.478427i
$238$	4.36196	+	8.85371i	0.282744	+	0.573901i
$239$	2.60748	+	8.02498i	0.168664	+	0.519093i	0.999288	−	0.0377406i	$-0.0120161\pi$
$239$	2.60748	+	8.02498i	0.168664	+	0.519093i	−0.830624	+	0.556834i	$0.812016\pi$
$240$		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	$0.0642022\pi$
$242$	5.75834	−	0.832671i	0.370160	−	0.0535261i
$243$		−	22.3706i		−	1.43507i
$244$	−10.3589	−	7.96124i	−0.663159	−	0.509666i
$245$		0			0
$246$	12.7605	+	2.19768i	0.813581	+	0.140119i
$247$	28.3344	−	20.5862i	1.80288	−	1.30987i
$248$	2.94859	−	5.25096i	0.187236	−	0.333436i
$249$	−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	$-0.178797\pi$
$252$	23.0312	−	6.80299i	1.45083	−	0.428548i
$253$	−1.19672	−	1.64714i	−0.0752369	−	0.103555i
$254$	−0.848157	+	4.92470i	−0.0532181	+	0.309003i
$255$		0			0
$256$	−11.8575	−	10.7424i	−0.741094	−	0.671401i
$257$	−4.42621			−0.276099			−0.138050	−	0.990425i	$-0.544083\pi$
$257$	−4.42621			−0.276099			−0.138050	+	0.990425i	$0.544083\pi$
$258$	−2.29962	+	0.332531i	−0.143168	+	0.0207025i
$259$	−30.2543	−	9.83022i	−1.87991	−	0.610820i
$260$		0			0
$261$	17.7956	−	5.78213i	1.10152	−	0.357905i
$262$	−8.55888	+	4.21671i	−0.528770	+	0.260509i
$263$	3.79412	−	11.6771i	0.233956	−	0.720041i	−0.763303	−	0.646041i	$-0.776423\pi$
$263$	3.79412	−	11.6771i	0.233956	−	0.720041i	0.997258	−	0.0740002i	$-0.0235766\pi$
$264$	−9.15503	+	16.3036i	−0.563453	+	1.00342i
$265$		0			0
$266$	23.2974	−	11.4779i	1.42845	−	0.703757i
$267$	−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	0.122591	−	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	$0.335523\pi$
$272$	−6.53197	+	4.22772i	−0.396059	+	0.256343i
$273$	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	$-0.561796\pi$
$277$	3.79042	−	1.23158i	0.227744	−	0.0739986i	0.420666	+	0.907216i	$0.361796\pi$
$278$	−1.89834	−	0.326942i	−0.113855	−	0.0196087i
$279$	−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	$-0.622283\pi$
$282$	2.28863	+	2.35115i	0.136286	+	0.140009i
$283$	7.67233	−	10.5601i	0.456073	−	0.627730i	−0.517616	−	0.855613i	$-0.673180\pi$
$283$	7.67233	−	10.5601i	0.456073	−	0.627730i	0.973689	+	0.227883i	$0.0731804\pi$
$284$	10.4548	+	3.71125i	0.620380	+	0.220222i
$285$		0			0
$286$	−22.4676	−	11.8318i	−1.32854	−	0.699627i
$287$	−4.02944	+	12.4013i	−0.237850	+	0.732028i
$288$	7.43992	+	17.4086i	0.438402	+	1.02581i
$289$	−4.08404	−	12.5694i	−0.240238	−	0.739375i
$290$		0			0
$291$	13.5152	+	4.39136i	0.792277	+	0.257426i
$292$	18.0719	−	23.5145i	1.05758	−	1.37608i
$293$			27.0373i			1.57954i	0.613404	+	0.789769i	$0.289800\pi$
$293$			27.0373i			1.57954i	−0.613404	+	0.789769i	$0.710200\pi$
$294$	2.99441	+	20.7079i	0.174638	+	1.20771i
$295$		0			0
$296$	4.92066	−	24.5904i	0.286008	−	1.42929i
$297$	1.85420	−	1.34715i	0.107592	−	0.0781698i
$298$	−6.23554	+	11.8408i	−0.361215	+	0.685920i
$299$		−	5.30890i		−	0.307022i
$300$		0			0
$301$		−	2.33989i		−	0.134869i
$302$	−10.0047	−	5.26864i	−0.575708	−	0.303176i
$303$	−0.413607	+	0.300503i	−0.0237611	+	0.0172635i
$304$	11.1247	+	17.1880i	0.638045	+	0.985801i
$305$		0			0
$306$	9.11170	−	1.31758i	0.520881	−	0.0753208i
$307$			23.1194i			1.31949i	0.751488	+	0.659747i	$0.229336\pi$
$307$			23.1194i			1.31949i	−0.751488	+	0.659747i	$0.770664\pi$
$308$	−14.9299	−	11.4743i	−0.850710	−	0.653807i
$309$	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	$0.801929\pi$
$312$	−44.3012	+	20.3615i	−2.50806	+	1.15274i
$313$	−2.15115	+	6.62056i	−0.121590	+	0.374216i	−0.993264	−	0.115870i	$-0.963035\pi$
$313$	−2.15115	+	6.62056i	−0.121590	+	0.374216i	0.871674	+	0.490086i	$0.163035\pi$
$314$	−5.12718	+	9.73613i	−0.289343	+	0.549441i
$315$		0			0
$316$	−17.8317	−	6.32989i	−1.00311	−	0.356084i
$317$	1.64686	−	2.26671i	0.0924971	−	0.127311i	−0.760260	−	0.649619i	$-0.774929\pi$
$317$	1.64686	−	2.26671i	0.0924971	−	0.127311i	0.852757	+	0.522307i	$0.174929\pi$
$318$	−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
$322$	0.668177	−	3.87967i	0.0372361	−	0.216206i
$323$	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
$328$	−10.0797	−	2.01700i	−0.556557	−	0.111370i
$329$	−2.67317	+	1.94217i	−0.147376	+	0.107075i
$330$		0			0
$331$	−15.6066	+	21.4807i	−0.857819	+	1.18069i	0.124266	+	0.992249i	$0.460342\pi$
$331$	−15.6066	+	21.4807i	−0.857819	+	1.18069i	−0.982085	+	0.188437i	$0.939658\pi$
$332$	16.0845	+	0.433498i	0.882753	+	0.0237913i
$333$	−17.4413	+	24.0060i	−0.955780	+	1.31552i
$334$	−7.55912	−	15.3432i	−0.413616	−	0.839540i
$335$		0			0
$336$	−34.9374	+	9.30419i	−1.90599	+	0.507585i
$337$	−5.89820	+	18.1528i	−0.321295	+	0.988845i	0.651790	+	0.758400i	$0.274018\pi$
$337$	−5.89820	+	18.1528i	−0.321295	+	0.988845i	−0.973085	+	0.230446i	$0.925982\pi$
$338$	−21.1373	−	42.9035i	−1.14972	−	2.33364i
$339$	14.1574	−	4.60001i	0.768923	−	0.249838i
$340$		0			0
$341$	5.31368	+	1.72652i	0.287752	+	0.0934963i
$342$	−3.46703	−	23.9762i	−0.187475	−	1.29649i
$343$	4.04448			0.218381
$344$	1.83208	−	0.214710i	0.0987790	−	0.0115764i
$345$		0			0
$346$	−22.0385	−	3.79559i	−1.18480	−	0.204052i
$347$	11.3134	+	15.5716i	0.607336	+	0.835926i	0.996355	−	0.0853039i	$-0.0271861\pi$
$347$	11.3134	+	15.5716i	0.607336	+	0.835926i	−0.389019	+	0.921230i	$0.627186\pi$
$348$	−27.0165	+	7.98018i	−1.44824	+	0.427782i
$349$		−	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
$352$	7.61408	−	12.7426i	0.405832	−	0.679184i
$353$	15.7539	−	11.4459i	0.838497	−	0.609203i	−0.0834537	−	0.996512i	$-0.526595\pi$
$353$	15.7539	−	11.4459i	0.838497	−	0.609203i	0.921950	+	0.387308i	$0.126595\pi$
$354$	2.38244	−	13.8333i	0.126625	−	0.735232i
$355$		0			0
$356$	13.2372	−	17.2237i	0.701569	−	0.912856i
$357$			17.5821i			0.930545i
$358$	−2.98907	−	20.6709i	−0.157977	−	1.09249i
$359$	−7.90364	+	24.3249i	−0.417138	+	1.28382i	0.493186	+	0.869924i	$0.335832\pi$
$359$	−7.90364	+	24.3249i	−0.417138	+	1.28382i	−0.910324	+	0.413896i	$0.864168\pi$
$360$		0			0
$361$	−2.22468	−	6.84685i	−0.117088	−	0.360361i
$362$	−6.82974	+	3.36481i	−0.358963	+	0.176850i
$363$	9.85725	+	3.20281i	0.517371	+	0.168104i
$364$	−13.9090	−	47.0883i	−0.729032	−	2.46810i
$365$		0			0
$366$	−10.2856	−	20.8772i	−0.537636	−	1.09127i
$367$	23.3737	+	16.9820i	1.22010	+	0.886453i	0.996108	−	0.0881385i	$-0.0280918\pi$
$367$	23.3737	+	16.9820i	1.22010	+	0.886453i	0.223990	+	0.974592i	$0.428092\pi$
$368$	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
$372$	8.84575	−	6.06956i	0.458631	−	0.314692i
$373$	23.6625	−	7.68840i	1.22520	−	0.398090i	0.376224	−	0.926529i	$-0.377222\pi$
$373$	23.6625	−	7.68840i	1.22520	−	0.398090i	0.848972	+	0.528438i	$0.177222\pi$
$374$	−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
$378$	4.36739	+	0.752174i	0.224634	+	0.0386877i
$379$	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
$382$	−10.5060	+	10.2267i	−0.537535	+	0.523243i
$383$	2.47525	+	1.79838i	0.126480	+	0.0918928i	0.649227	−	0.760595i	$-0.275093\pi$
$383$	2.47525	+	1.79838i	0.126480	+	0.0918928i	−0.522747	+	0.852488i	$0.675093\pi$
$384$	−10.4908	−	26.5013i	−0.535357	−	1.35239i
$385$		0			0
$386$	0.901508	+	0.474746i	0.0458855	+	0.0241640i
$387$	−2.07579	−	0.674465i	−0.105518	−	0.0342850i
$388$	−10.6317	−	3.77403i	−0.539742	−	0.191597i
$389$	−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
$392$	−1.93344	−	16.4977i	−0.0976535	−	0.833259i
$393$	−16.9966			−0.857367
$394$	1.20923	+	8.36241i	0.0609200	+	0.421292i
$395$		0			0
$396$	−14.4826	+	9.93734i	−0.727780	+	0.499370i
$397$	−20.5622	−	28.3014i	−1.03199	−	1.42041i	−0.903446	−	0.428701i	$-0.858971\pi$
$397$	−20.5622	−	28.3014i	−1.03199	−	1.42041i	−0.128539	−	0.991704i	$-0.541029\pi$
$398$	−16.4747	−	8.67581i	−0.825802	−	0.434879i
$399$	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	$0.391635\pi$
$402$	15.5023	+	8.16373i	0.773185	+	0.407170i
$403$	8.56329	+	11.7864i	0.426568	+	0.587120i
$404$	0.334663	−	0.229631i	0.0166501	−	0.0114246i
$405$		0			0
$406$	−4.05997	−	28.0767i	−0.201493	−	1.39342i
$407$	23.2662			1.15326
$408$	−13.7664	+	1.61334i	−0.681536	+	0.0798724i
$409$	−8.50186	+	26.1660i	−0.420390	+	1.29383i	0.486950	+	0.873430i	$0.338109\pi$
$409$	−8.50186	+	26.1660i	−0.420390	+	1.29383i	−0.907340	+	0.420397i	$0.861891\pi$
$410$		0			0
$411$	−19.7478	+	6.41645i	−0.974088	+	0.316500i
$412$	−24.8829	−	8.83294i	−1.22589	−	0.435168i
$413$	13.4439	+	4.36820i	0.661533	+	0.214945i
$414$	−3.24917	−	1.71106i	−0.159688	−	0.0840940i
$415$		0			0
$416$	35.5927	−	15.2113i	1.74507	−	0.745793i
$417$	−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	0.375649	−	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	0.870764	−	0.491701i	$-0.163625\pi$
$421$	2.75042	+	3.78563i	0.134047	+	0.184500i	−0.736717	+	0.676202i	$0.763625\pi$
$422$	−7.65919	−	1.31910i	−0.372843	−	0.0642130i
$423$	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
$428$	24.6023	−	16.8810i	1.18920	−	0.815975i
$429$	−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	$0.860983\pi$
$432$	−0.188180	+	3.48857i	−0.00905379	+	0.167844i
$433$	−1.13838	−	0.827085i	−0.0547073	−	0.0397472i	0.560096	−	0.828428i	$-0.310764\pi$
$433$	−1.13838	−	0.827085i	−0.0547073	−	0.0397472i	−0.614803	+	0.788681i	$0.710764\pi$
$434$	4.77451	+	9.69108i	0.229184	+	0.465187i
$435$		0			0
$436$	4.89934	+	16.5865i	0.234636	+	0.794348i
$437$	−3.77696	−	1.22721i	−0.180677	−	0.0587054i
$438$	47.3909	−	23.3481i	2.26443	−	1.11562i
$439$	4.33963	+	13.3560i	0.207119	+	0.637447i	0.999620	+	0.0275762i	$0.00877888\pi$
$439$	4.33963	+	13.3560i	0.207119	+	0.637447i	−0.792500	+	0.609871i	$0.791221\pi$
$440$		0			0
$441$	−6.07349	+	18.6923i	−0.289214	+	0.890109i
$442$	−2.69385	−	18.6293i	−0.128133	−	0.886105i
$443$		−	9.37158i		−	0.445257i	−0.974903	−	0.222629i	$-0.928536\pi$
$443$		−	9.37158i		−	0.445257i	0.974903	−	0.222629i	$-0.0714637\pi$
$444$	27.2226	−	35.4210i	1.29193	−	1.68101i
$445$		0			0
$446$	−4.88880	+	28.3861i	−0.231491	+	1.34412i
$447$	−19.2863	+	14.0123i	−0.912210	+	0.662759i
$448$	27.9251	−	6.63650i	1.31934	−	0.313545i
$449$	−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
$452$	−11.3336	+	3.34774i	−0.533088	+	0.157464i
$453$	−11.8395	−	16.2957i	−0.556269	−	0.765638i
$454$	−22.0605	−	3.79938i	−1.03535	−	0.178314i
$455$		0			0
$456$	4.24530	+	36.2244i	0.198804	+	1.69636i
$457$	32.1890			1.50574			0.752869	−	0.658170i	$-0.228669\pi$
$457$	32.1890			1.50574			0.752869	+	0.658170i	$0.228669\pi$
$458$	−1.29675	−	8.96768i	−0.0605932	−	0.419032i
$459$	1.61580	+	0.525005i	0.0754190	+	0.0245051i
$460$		0			0
$461$	2.49963	−	0.812178i	0.116419	−	0.0378269i	−0.250228	−	0.968187i	$-0.580506\pi$
$461$	2.49963	−	0.812178i	0.116419	−	0.0378269i	0.366647	+	0.930360i	$0.380506\pi$
$462$	−14.8243	−	30.0896i	−0.689687	−	1.39990i
$463$	−9.34875	+	28.7725i	−0.434473	+	1.33717i	0.459152	+	0.888358i	$0.348153\pi$
$463$	−9.34875	+	28.7725i	−0.434473	+	1.33717i	−0.893625	+	0.448814i	$0.851847\pi$
$464$	21.6108	−	5.75518i	1.00326	−	0.267178i
$465$		0			0
$466$	10.9921	+	22.3113i	0.509201	+	1.03355i
$467$	−24.2441	+	33.3692i	−1.12188	+	1.54414i	−0.319250	+	0.947671i	$0.603431\pi$
$467$	−24.2441	+	33.3692i	−1.12188	+	1.54414i	−0.802635	+	0.596471i	$0.796569\pi$
$468$	−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
$472$	−2.18657	+	10.9271i	−0.100645	+	0.502960i
$473$	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
$478$	2.02536	−	11.7600i	0.0926378	−	0.537888i
$479$	−12.7715	+	9.27902i	−0.583544	+	0.423969i	−0.840000	−	0.542586i	$-0.817445\pi$
$479$	−12.7715	+	9.27902i	−0.583544	+	0.423969i	0.256456	+	0.966556i	$0.417445\pi$
$480$		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
$484$	−7.75416	−	2.75257i	−0.352462	−	0.125117i
$485$		0			0
$486$	−14.7412	+	27.9925i	−0.668676	+	1.26977i
$487$	11.0724	−	34.0773i	0.501738	−	1.54419i	−0.304449	−	0.952529i	$-0.598472\pi$
$487$	11.0724	−	34.0773i	0.501738	−	1.54419i	0.806187	−	0.591661i	$-0.201528\pi$
$488$	7.71605	+	16.7880i	0.349289	+	0.759959i
$489$	17.8870	+	55.0505i	0.808877	+	2.48947i
$490$		0			0
$491$	−7.10672	−	2.30911i	−0.320722	−	0.104209i	0.144232	−	0.989544i	$-0.453929\pi$
$491$	−7.10672	−	2.30911i	−0.320722	−	0.104209i	−0.464954	+	0.885335i	$0.653929\pi$
$492$	−14.5192	−	11.1586i	−0.654575	−	0.503069i
$493$		−	10.8756i		−	0.489811i
$494$	−49.0205	+	7.08850i	−2.20554	+	0.318927i
$495$		0			0
$496$	−7.14976	+	4.62757i	−0.321034	+	0.207784i
$497$	−16.1009	+	11.6980i	−0.722226	+	0.524728i
$498$	25.3615	+	13.3557i	1.13647	+	0.598483i
$499$			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
$502$	−11.1212	+	21.1183i	−0.496363	+	0.942555i
$503$	−24.0283	+	17.4576i	−1.07137	+	0.778395i	−0.976158	−	0.217062i	$-0.930353\pi$
$503$	−24.0283	+	17.4576i	−1.07137	+	0.778395i	−0.0952114	+	0.995457i	$0.530353\pi$
$504$	−33.3020	−	6.66391i	−1.48339	−	0.296834i
$505$		0			0
$506$	0.412069	+	2.84966i	0.0183187	+	0.126683i
$507$		−	85.1999i		−	3.78386i
$508$	4.30647	−	5.60342i	0.191069	−	0.248612i
$509$	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
$512$	7.75863	+	21.2557i	0.342886	+	0.939377i
$513$	1.38148	−	4.25176i	0.0609939	−	0.187720i
$514$	5.53856	+	2.91668i	0.244295	+	0.128649i
$515$		0			0
$516$	3.09666	+	1.09925i	0.136323	+	0.0483918i
$517$	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	−0.361326	−	0.932440i	$-0.617676\pi$
$521$	9.44563	−	6.86265i	0.413821	−	0.300658i	0.775147	+	0.631781i	$0.217676\pi$
$522$	−26.0779	−	4.49128i	−1.14140	−	0.196578i
$523$	−19.1314	+	6.21617i	−0.836558	+	0.271814i	−0.695805	−	0.718230i	$-0.744952\pi$
$523$	−19.1314	+	6.21617i	−0.836558	+	0.271814i	−0.140753	+	0.990045i	$0.544952\pi$
$524$	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
$528$	22.1991	−	14.3681i	0.966093	−	0.625289i
$529$	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
$534$	34.7126	−	17.1019i	1.50216	−	0.740070i
$535$		0			0
$536$	−12.1279	−	6.81026i	−0.523847	−	0.294158i
$537$	11.4973	−	35.3850i	0.496144	−	1.52697i
$538$	−36.4106	+	17.9384i	−1.56977	+	0.773380i
$539$	14.6564	−	4.76215i	0.631295	−	0.205120i
$540$		0			0
$541$	−19.0637	−	6.19417i	−0.819612	−	0.266308i	−0.130949	−	0.991389i	$-0.541802\pi$
$541$	−19.0637	−	6.19417i	−0.819612	−	0.266308i	−0.688664	+	0.725081i	$0.741802\pi$
$542$	5.13208	−	0.742113i	0.220442	−	0.0318765i
$543$	−13.5628			−0.582036
$544$	10.9594	−	0.985901i	0.469881	−	0.0422701i
$545$		0			0
$546$	14.8452	−	86.1965i	0.635316	−	3.68887i
$547$	−22.5997	−	31.1058i	−0.966293	−	1.32999i	−0.943897	−	0.330239i	$-0.892871\pi$
$547$	−22.5997	−	31.1058i	−0.966293	−	1.32999i	−0.0223953	−	0.999749i	$-0.507129\pi$
$548$	15.8090	−	4.66969i	0.675327	−	0.199479i
$549$		−	21.8619i		−	0.933041i
$550$		0			0
$551$	−28.6176			−1.21915
$552$	4.82053	+	2.70690i	0.205175	+	0.115213i
$553$	27.4617	−	19.9521i	1.16779	−	0.848448i
$554$	−5.55455	−	0.956633i	−0.235990	−	0.0406434i
$555$		0			0
$556$	2.15997	+	1.66003i	0.0916032	+	0.0704010i
$557$			10.9707i			0.464844i	0.972615	+	0.232422i	$0.0746650\pi$
$557$			10.9707i			0.464844i	−0.972615	+	0.232422i	$0.925335\pi$
$558$	9.97347	−	1.44219i	0.422211	−	0.0610528i
$559$	−1.37897	+	4.24405i	−0.0583244	+	0.179504i
$560$		0			0
$561$	−3.97373	−	12.2299i	−0.167771	−	0.516346i
$562$	17.7721	+	36.0731i	0.749672	+	1.52165i
$563$	1.00145	+	0.325391i	0.0422061	+	0.0137136i	0.330044	−	0.943966i	$-0.392936\pi$
$563$	1.00145	+	0.325391i	0.0422061	+	0.0137136i	−0.287838	+	0.957679i	$0.592936\pi$
$564$	−1.31448	−	4.45012i	−0.0553498	−	0.187384i
$565$		0			0
$566$	−16.5591	+	8.15816i	−0.696030	+	0.342913i
$567$	−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	0.187188	−	0.982324i	$-0.440063\pi$
$569$	−16.4403	−	11.9446i	−0.689213	−	0.500743i	−0.876401	+	0.481581i	$0.840063\pi$
$570$		0			0
$571$	8.81803	+	12.1370i	0.369023	+	0.507917i	0.952635	−	0.304116i	$-0.0983610\pi$
$571$	8.81803	+	12.1370i	0.369023	+	0.507917i	−0.583612	+	0.812033i	$0.698361\pi$
$572$	20.3174	+	29.6104i	0.849511	+	1.23807i
$573$	−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	0.949125	+	0.314899i	$0.101971\pi$
$577$	8.80026	+	27.0844i	0.366360	+	1.12754i	−0.582765	+	0.812640i	$0.698029\pi$
$578$	−3.17228	+	18.4194i	−0.131950	+	0.766146i
$579$	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
$584$	−38.1086	+	17.5153i	−1.57694	+	0.724789i
$585$		0			0
$586$	17.8164	−	33.8321i	0.735990	−	1.39759i
$587$	32.9333	+	10.7007i	1.35930	+	0.441664i	0.895810	−	0.444438i	$-0.146597\pi$
$587$	32.9333	+	10.7007i	1.35930	+	0.441664i	0.463491	+	0.886101i	$0.346597\pi$
$588$	9.89865	−	27.8851i	0.408213	−	1.14996i
$589$	10.3648	−	3.36772i	0.427073	−	0.138764i
$590$		0			0
$591$	−4.65121	+	14.3150i	−0.191325	+	0.588839i
$592$	−22.3613	+	27.5277i	−0.919042	+	1.13138i
$593$	34.9925			1.43697			0.718484	−	0.695543i	$-0.244836\pi$
$593$	34.9925			1.43697			0.718484	+	0.695543i	$0.244836\pi$
$594$	−3.20789	+	0.463870i	−0.131621	+	0.0190328i
$595$		0			0
$596$	15.6052	−	10.7076i	0.639213	−	0.438600i
$597$	−19.4960	−	26.8339i	−0.797918	−	1.09824i
$598$	−3.49834	+	6.64308i	−0.143058	+	0.271656i
$599$	−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	$0.513086\pi$
$602$	−1.54189	+	2.92793i	−0.0628427	+	0.119334i
$603$	9.67370	+	13.3147i	0.393943	+	0.542217i
$604$	9.04723	+	13.1854i	0.368127	+	0.536506i
$605$		0			0
$606$	0.715569	−	0.103473i	0.0290680	−	0.00420331i
$607$	−39.1971			−1.59096			−0.795481	−	0.605979i	$-0.792782\pi$
$607$	−39.1971			−1.59096			−0.795481	+	0.605979i	$0.792782\pi$
$608$	−2.59427	−	28.8382i	−0.105211	−	1.16955i
$609$	15.6164	−	48.0624i	0.632809	−	1.94759i
$610$		0			0
$611$	5.99311	−	1.94728i	0.242455	−	0.0787785i
$612$	−12.2698	−	4.35552i	−0.495977	−	0.176062i
$613$	20.4908	+	6.65786i	0.827615	+	0.268909i	0.692041	−	0.721859i	$-0.256712\pi$
$613$	20.4908	+	6.65786i	0.827615	+	0.268909i	0.135575	+	0.990767i	$0.456712\pi$
$614$	15.2347	−	28.9295i	0.614822	−	1.16750i
$615$		0			0
$616$	11.1209	+	24.1960i	0.448073	+	0.974886i
$617$	−24.1235	−	17.5267i	−0.971175	−	0.705600i	−0.0154563	−	0.999881i	$-0.504920\pi$
$617$	−24.1235	−	17.5267i	−0.971175	−	0.705600i	−0.955719	+	0.294280i	$0.904920\pi$
$618$	−32.8085	−	33.7046i	−1.31975	−	1.35580i
$619$	−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
$622$	2.56728	−	14.9065i	0.102939	−	0.597698i
$623$	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
$628$	12.8314	−	8.80432i	0.512028	−	0.351331i
$629$	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	$0.798570\pi$
$632$	18.1419	+	19.6710i	0.721644	+	0.782469i
$633$	−11.2007	−	8.13781i	−0.445189	−	0.323449i
$634$	−3.55441	+	1.75115i	−0.141163	+	0.0695470i
$635$		0			0
$636$	8.87141	−	2.62045i	0.351774	−	0.103908i
$637$	38.2172	+	12.4175i	1.51422	+	0.492001i
$638$	9.16967	+	18.6122i	0.363031	+	0.736864i
$639$	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	$0.150298\pi$
$642$	52.6041	−	7.60669i	2.07612	−	0.300212i
$643$			6.46830i			0.255085i	0.991833	+	0.127542i	$0.0407089\pi$
$643$			6.46830i			0.255085i	−0.991833	+	0.127542i	$0.959291\pi$
$644$	−3.39263	+	4.41437i	−0.133689	+	0.173951i
$645$		0			0
$646$	−13.8763	−	2.38985i	−0.545956	−	0.0940274i
$647$	−12.1303	+	8.81321i	−0.476893	+	0.346483i	−0.800122	−	0.599838i	$-0.795232\pi$
$647$	−12.1303	+	8.81321i	−0.476893	+	0.346483i	0.323229	+	0.946321i	$0.395232\pi$
$648$	10.8569	−	19.3344i	0.426500	−	0.759526i
$649$	−10.3387			−0.405828
$650$		0			0
$651$			19.2450i			0.754272i
$652$	−13.0176	−	44.0703i	−0.509807	−	1.72593i
$653$	−22.6975	−	31.2404i	−0.888220	−	1.22253i	−0.974076	−	0.226223i	$-0.927362\pi$
$653$	−22.6975	−	31.2404i	−0.888220	−	1.22253i	0.0858552	−	0.996308i	$-0.472638\pi$
$654$	−5.22910	+	30.3620i	−0.204474	+	1.18725i
$655$		0			0
$656$	11.2837	+	9.16596i	0.440554	+	0.357870i
$657$	49.6261			1.93610
$658$	4.62476	−	0.668753i	0.180292	−	0.0260707i
$659$	−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	−0.329579	−	0.944128i	$-0.606907\pi$
$661$	−1.06103	+	0.344750i	−0.0412693	+	0.0134092i	0.288310	+	0.957537i	$0.406907\pi$
$662$	33.6836	−	16.5949i	1.30915	−	0.644979i
$663$	10.3617	−	31.8900i	0.402415	−	1.23851i
$664$	−19.8411	−	11.1415i	−0.769983	−	0.432372i
$665$		0			0
$666$	37.6434	−	18.5458i	1.45865	−	0.718635i
$667$	−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
$672$	49.8485	+	11.3798i	1.92295	+	0.438986i
$673$	−8.12719	−	25.0129i	−0.313280	−	0.964177i	−0.976457	−	0.215714i	$-0.930792\pi$
$673$	−8.12719	−	25.0129i	−0.313280	−	0.964177i	0.663177	−	0.748463i	$-0.269208\pi$
$674$	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	$-0.489511\pi$
$677$	16.8361	−	5.47038i	0.647064	−	0.210244i	0.614119	+	0.789213i	$0.289511\pi$
$678$	−20.7465	−	3.57306i	−0.796763	−	0.137223i
$679$	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	−0.123635	+	0.992328i	$0.539455\pi$
$683$	−26.8971	+	37.0207i	−1.02919	+	1.41656i	−0.905554	+	0.424230i	$0.860545\pi$
$684$	−11.4610	+	32.2863i	−0.438222	+	1.23450i
$685$		0			0
$686$	−5.06089	−	2.66514i	−0.193226	−	0.101755i
$687$	4.98787	−	15.3511i	0.190299	−	0.585680i
$688$	−2.43398	−	0.938592i	−0.0927946	−	0.0357835i
$689$	3.88194	+	11.9474i	0.147890	+	0.455159i
$690$		0			0
$691$	−5.90130	−	1.91745i	−0.224496	−	0.0729432i	0.194609	−	0.980881i	$-0.437656\pi$
$691$	−5.90130	−	1.91745i	−0.224496	−	0.0729432i	−0.419105	+	0.907938i	$0.637656\pi$
$692$	25.0759	+	19.2719i	0.953243	+	0.732608i
$693$		−	31.5088i		−	1.19692i
$694$	−3.89558	−	26.9399i	−0.147874	−	1.02262i
$695$		0			0
$696$	39.0646	+	7.81702i	1.48074	+	0.296304i
$697$	5.71935	−	4.15535i	0.216636	−	0.157395i
$698$	−0.0392547	+	0.0745417i	−0.00148581	+	0.00282145i
$699$			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	$0.868274\pi$
$702$	−7.47818	−	3.93812i	−0.282246	−	0.148635i
$703$	36.7153	−	26.6752i	1.38474	−	1.00608i
$704$	−17.9244	+	10.9276i	−0.675552	+	0.411850i
$705$		0			0
$706$	−27.2554	+	3.94120i	−1.02577	+	0.148329i
$707$			0.728101i			0.0273831i
$708$	−12.0967	+	15.7398i	−0.454623	+	0.591539i
$709$	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
$712$	−27.9135	+	12.8295i	−1.04610	+	0.480806i
$713$	0.510486	−	1.57111i	0.0191178	−	0.0588387i
$714$	11.5859	−	22.0007i	0.433590	−	0.823355i
$715$		0			0
$716$	−9.88100	+	27.8354i	−0.369270	+	1.04026i
$717$	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	0.482000	−	0.876171i	$-0.339911\pi$
$719$	−5.42565	−	3.94197i	−0.202343	−	0.147011i	−0.684342	+	0.729161i	$0.739911\pi$
$720$		0			0
$721$	38.3209	−	27.8418i	1.42715	−	1.03688i
$722$	−1.72802	+	10.0335i	−0.0643103	+	0.373408i
$723$	−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	0.832591	+	0.553888i	$0.186857\pi$
$727$	13.0656	+	40.2119i	0.484578	+	1.49138i	−0.348013	+	0.937490i	$0.613143\pi$
$728$	−13.6247	+	68.0875i	−0.504964	+	2.52349i
$729$	−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	$-0.634718\pi$
$733$	15.7936	−	21.7381i	0.583351	−	0.802914i	0.994058	+	0.108854i	$0.0347180\pi$
$734$	−18.0573	−	36.6520i	−0.666509	−	1.35285i
$735$		0			0
$736$	−3.76765	−	2.25128i	−0.138877	−	0.0829833i
$737$	3.98768	−	12.2728i	0.146888	−	0.452075i
$738$	−7.60198	−	15.4302i	−0.279833	−	0.567992i
$739$	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
$742$	1.33317	+	9.21956i	0.0489423	+	0.338461i
$743$	−43.2190			−1.58555			−0.792776	−	0.609513i	$-0.791365\pi$
$743$	−43.2190			−1.58555			−0.792776	+	0.609513i	$0.791365\pi$
$744$	−15.0684	+	1.76593i	−0.552433	+	0.0647422i
$745$		0			0
$746$	−34.6754	−	5.97197i	−1.26956	−	0.218650i
$747$	15.8260	+	21.7826i	0.579042	+	0.796983i
$748$	2.89195	+	9.79056i	0.105740	+	0.357978i
$749$			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	$0.518842\pi$
$752$	0.947987	+	3.55971i	0.0345695	+	0.129809i
$753$	−34.3974	+	24.9912i	−1.25351	+	0.910728i
$754$	−9.18262	+	53.3176i	−0.334411	+	1.94171i
$755$		0			0
$756$	−4.96930	−	3.81912i	−0.180732	−	0.138900i
$757$		−	25.4279i		−	0.924193i	−0.886830	−	0.462096i	$-0.847097\pi$
$757$		−	25.4279i		−	0.924193i	0.886830	−	0.462096i	$-0.152903\pi$
$758$	−1.31037	−	9.06187i	−0.0475948	−	0.329142i
$759$	−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	$0.794591\pi$
$762$	11.2931	−	5.56377i	0.409106	−	0.201554i
$763$	−29.5074	−	9.58753i	−1.06824	−	0.347092i
$764$	19.8852	−	5.87373i	0.719422	−	0.212504i
$765$		0			0
$766$	−1.91226	−	3.88141i	−0.0690926	−	0.140241i
$767$	−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	0.751196	−	0.660079i	$-0.229477\pi$
$769$	9.85987	+	7.16362i	0.355556	+	0.258327i	−0.395640	+	0.918406i	$0.629477\pi$
$770$		0			0
$771$	6.55427	+	9.02118i	0.236046	+	0.324890i
$772$	−0.815228	−	1.18811i	−0.0293407	−	0.0427610i
$773$	−19.3807	+	6.29718i	−0.697076	+	0.226494i	−0.636056	−	0.771643i	$-0.719435\pi$
$773$	−19.3807	+	6.29718i	−0.697076	+	0.226494i	−0.0610199	+	0.998137i	$0.519435\pi$
$774$	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
$778$	39.1633	+	6.74491i	1.40407	+	0.241817i
$779$	−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
$784$	−8.45193	+	21.9178i	−0.301855	+	0.782777i
$785$		0			0
$786$	21.2681	+	11.2001i	0.758607	+	0.399493i
$787$	−1.87380	−	0.608835i	−0.0667938	−	0.0217026i	0.275430	−	0.961321i	$-0.411180\pi$
$787$	−1.87380	−	0.608835i	−0.0667938	−	0.0217026i	−0.342223	+	0.939619i	$0.611180\pi$
$788$	3.99735	−	11.2608i	0.142400	−	0.401149i
$789$	−29.4177	+	9.55840i	−1.04730	+	0.340288i
$790$		0			0
$791$	6.55119	−	20.1625i	0.232934	−	0.716896i
$792$	24.6705	−	2.89126i	0.876630	−	0.102736i
$793$	−44.6976			−1.58726
$794$	7.08024	+	48.9634i	0.251268	+	1.73765i
$795$		0			0
$796$	14.8980	+	21.7122i	0.528045	+	0.769570i
$797$	13.3592	+	18.3873i	0.473206	+	0.651313i	0.977182	−	0.212405i	$-0.0681297\pi$
$797$	13.3592	+	18.3873i	0.473206	+	0.651313i	−0.503975	+	0.863718i	$0.668130\pi$
$798$	−57.8919	−	30.4867i	−2.04935	−	1.07922i
$799$	1.79141			0.0633756
$800$		0			0
$801$	36.3498			1.28436
$802$	−16.7334	−	8.81201i	−0.590875	−	0.311163i
$803$	−22.8714	−	31.4798i	−0.807114	−	1.11090i
$804$	−14.0186	−	20.4307i	−0.494399	−	0.720536i
$805$		0			0
$806$	−2.94863	−	20.3912i	−0.103861	−	0.718250i
$807$	−72.3059			−2.54529
$808$	−0.570085	+	0.0668109i	−0.0200555	+	0.00235040i
$809$	15.7618	−	48.5099i	0.554156	−	1.70552i	−0.144007	−	0.989577i	$-0.545999\pi$
$809$	15.7618	−	48.5099i	0.554156	−	1.70552i	0.698163	−	0.715939i	$-0.254001\pi$
$810$		0			0
$811$	42.6096	−	13.8447i	1.49622	−	0.486153i	0.557310	−	0.830305i	$-0.311834\pi$
$811$	42.6096	−	13.8447i	1.49622	−	0.486153i	0.938914	+	0.344152i	$0.111834\pi$
$812$	−13.4211	+	37.8080i	−0.470987	+	1.32680i
$813$	8.78521	+	2.85449i	0.308111	+	0.100111i
$814$	−29.1132	−	15.3314i	−1.02042	−	0.537366i
$815$		0			0
$816$	18.2891	+	7.05264i	0.640246	+	0.246892i
$817$	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	$-0.0363284\pi$
$821$	16.5666	+	22.8020i	0.578180	+	0.795796i	−0.415314	+	0.909678i	$0.636328\pi$
$822$	28.9388	+	4.98399i	1.00936	+	0.173837i
$823$	−1.11758	−	3.43957i	−0.0389565	−	0.119896i	0.929687	−	0.368350i	$-0.120077\pi$
$823$	−1.11758	−	3.43957i	−0.0389565	−	0.119896i	−0.968644	+	0.248455i	$0.920077\pi$
$824$	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	$-0.436797\pi$
$827$	26.8330	−	8.71857i	0.933075	−	0.303174i	0.735819	+	0.677178i	$0.236797\pi$
$828$	2.93821	+	4.28213i	0.102110	+	0.148814i
$829$	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
$832$	−54.5610	−	4.42003i	−1.89156	−	0.153237i
$833$	9.24188	+	6.71462i	0.320212	+	0.232648i
$834$	2.14469	+	4.35319i	0.0742645	+	0.150739i
$835$		0			0
$836$	25.7626	−	7.60980i	0.891018	−	0.263190i
$837$	1.76862	+	0.574659i	0.0611324	+	0.0198631i
$838$	−50.4069	+	24.8340i	−1.74128	+	0.857876i
$839$	−2.76644	−	8.51422i	−0.0955081	−	0.293944i	0.891878	−	0.452277i	$-0.149388\pi$
$839$	−2.76644	−	8.51422i	−0.0955081	−	0.293944i	−0.987386	+	0.158333i	$0.949388\pi$
$840$		0			0
$841$	−0.698169	+	2.14874i	−0.0240748	+	0.0740946i
$842$	−0.947061	−	6.54940i	−0.0326379	−	0.225707i
$843$			71.6357i			2.46726i
$844$	8.71478	+	6.69768i	0.299975	+	0.230544i
$845$		0			0
$846$	0.739798	−	4.29553i	0.0254348	−	0.147683i
$847$	11.9418	−	8.67620i	0.410324	−	0.298118i
$848$	−7.09635	+	1.88983i	−0.243690	+	0.0648971i
$849$	−32.8838			−1.12857
$850$		0			0
$851$		−	6.87919i		−	0.235816i
$852$	−7.91737	−	26.8039i	−0.271245	−	0.918285i
$853$	18.5100	+	25.4769i	0.633772	+	0.872312i	0.998264	−	0.0588942i	$-0.0187574\pi$
$853$	18.5100	+	25.4769i	0.633772	+	0.872312i	−0.364492	+	0.931206i	$0.618757\pi$
$854$	−32.6644	−	5.62563i	−1.11775	−	0.192505i
$855$		0			0
$856$	−41.9090	+	4.91151i	−1.43242	+	0.167872i
$857$	47.9238			1.63705			0.818523	−	0.574473i	$-0.194793\pi$
$857$	47.9238			1.63705			0.818523	+	0.574473i	$0.194793\pi$
$858$	9.15512	+	63.3123i	0.312551	+	2.16145i
$859$	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
$862$	12.5721	+	25.5183i	0.428208	+	0.869157i
$863$	−13.2070	+	40.6471i	−0.449573	+	1.38364i	0.427817	+	0.903865i	$0.359283\pi$
$863$	−13.2070	+	40.6471i	−0.449573	+	1.38364i	−0.877390	+	0.479778i	$0.840717\pi$
$864$	2.53429	−	4.24128i	0.0862183	−	0.144291i
$865$		0			0
$866$	0.879458	+	1.78509i	0.0298852	+	0.0606597i
$867$	−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
$872$	4.79918	−	23.9833i	0.162521	−	0.812176i
$873$	−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	−0.868349	+	0.495953i	$0.834819\pi$
$877$	−55.1526	+	17.9202i	−1.86237	+	0.605121i	−0.994023	+	0.109168i	$0.965181\pi$
$878$	3.37081	−	19.5721i	0.113759	−	0.660527i
$879$	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	$0.603311\pi$
$882$	19.9172	−	19.3877i	0.670648	−	0.652817i
$883$	25.0162	−	34.4318i	0.841861	−	1.15872i	−0.143736	−	0.989616i	$-0.545912\pi$
$883$	25.0162	−	34.4318i	0.841861	−	1.15872i	0.985598	−	0.169107i	$-0.0540882\pi$
$884$	−8.90507	+	25.0861i	−0.299510	+	0.843738i
$885$		0			0
$886$	−6.17547	+	11.7267i	−0.207469	+	0.393968i
$887$	−12.2612	+	37.7360i	−0.411689	+	1.26705i	0.503489	+	0.864001i	$0.332049\pi$
$887$	−12.2612	+	37.7360i	−0.411689	+	1.26705i	−0.915179	+	0.403048i	$0.867951\pi$
$888$	−57.4047	+	26.3841i	−1.92638	+	0.885394i
$889$	3.91768	+	12.0574i	0.131395	+	0.404392i
$890$		0			0
$891$	19.5653	+	6.35716i	0.655463	+	0.212973i
$892$	24.8226	−	32.2983i	0.831122	−	1.08143i
$893$		−	4.71386i		−	0.157743i
$894$	33.3666	−	4.82490i	1.11595	−	0.161369i
$895$		0			0
$896$	−39.3161	−	10.0971i	−1.31346	−	0.337321i
$897$	−10.8202	+	7.86135i	−0.361277	+	0.262483i
$898$	33.9096	+	17.8573i	1.13158	+	0.595904i
$899$		−	11.9042i		−	0.397026i
$900$		0			0
$901$			3.57122i			0.118974i
$902$	−6.28440	+	11.9336i	−0.209248	+	0.397346i
$903$	−4.76900	+	3.46488i	−0.158703	+	0.115304i
$904$	16.3879	+	3.27930i	0.545052	+	0.109068i
$905$		0			0
$906$	4.07674	+	28.1927i	0.135440	+	0.936639i
$907$			34.9093i			1.15914i	0.814921	+	0.579571i	$0.196780\pi$
$907$			34.9093i			1.15914i	−0.814921	+	0.579571i	$0.803220\pi$
$908$	25.1009	+	19.2911i	0.833004	+	0.640199i
$909$	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	$-0.223474\pi$
$912$	18.5581	−	48.1254i	0.614520	−	1.59359i
$913$	6.52377	−	20.0781i	0.215905	−	0.664488i
$914$	−40.2784	−	21.2112i	−1.33229	−	0.701603i
$915$		0			0
$916$	−4.28668	+	12.0758i	−0.141636	+	0.398997i
$917$	−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	0.982720	+	0.185097i	$0.0592600\pi$
$919$	44.3337	+	32.2104i	1.46244	+	1.06252i	0.479715	+	0.877424i	$0.340740\pi$
$920$		0			0
$921$	47.1203	−	34.2349i	1.55267	−	1.12808i
$922$	−3.66300	−	0.630861i	−0.120634	−	0.0207763i
$923$	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
$928$	−30.8342	−	7.03907i	−1.01218	−	0.231069i
$929$	26.3740	−	19.1618i	0.865301	−	0.628678i	−0.0640206	−	0.997949i	$-0.520392\pi$
$929$	26.3740	−	19.1618i	0.865301	−	0.628678i	0.929322	+	0.369270i	$0.120392\pi$
$930$		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
$934$	52.3258	−	25.7793i	1.71215	−	0.843526i
$935$		0			0
$936$	56.4752	+	31.7128i	1.84595	+	1.03656i
$937$	2.49974	−	7.69340i	0.0816628	−	0.251332i	−0.901886	−	0.431974i	$-0.857817\pi$
$937$	2.49974	−	7.69340i	0.0816628	−	0.251332i	0.983549	+	0.180641i	$0.0578173\pi$
$938$	22.3831	−	11.0275i	0.730835	−	0.360061i
$939$	16.6789	−	5.41932i	0.544297	−	0.176853i
$940$		0			0
$941$	34.7042	+	11.2761i	1.13133	+	0.367590i	0.814080	−	0.580753i	$-0.197242\pi$
$941$	34.7042	+	11.2761i	1.13133	+	0.367590i	0.317246	+	0.948343i	$0.397242\pi$
$942$	27.4357	−	3.96728i	0.893904	−	0.129261i
$943$	−2.81981			−0.0918255
$944$	9.93655	−	12.2323i	0.323407	−	0.398128i
$945$		0			0
$946$	0.410776	−	2.38511i	0.0133555	−	0.0775467i
$947$	8.90757	+	12.2602i	0.289457	+	0.398404i	0.928838	−	0.370487i	$-0.120809\pi$
$947$	8.90757	+	12.2602i	0.289457	+	0.398404i	−0.639380	+	0.768890i	$0.720809\pi$
$948$	13.5038	+	45.7165i	0.438584	+	1.48480i
$949$		−	101.463i		−	3.29362i
$950$		0			0
$951$	−7.05851			−0.228888
$952$	−9.66504	+	17.2118i	−0.313246	+	0.557838i
$953$	44.0685	−	32.0176i	1.42752	−	1.03715i	0.437047	−	0.899439i	$-0.356024\pi$
$953$	44.0685	−	32.0176i	1.42752	−	1.03715i	0.990472	−	0.137714i	$-0.0439755\pi$
$954$	8.56323	+	1.47480i	0.277245	+	0.0477485i
$955$		0			0
$956$	−10.2837	+	13.3807i	−0.332597	+	0.432763i
$957$			36.9610i			1.19478i
$958$	22.0956	−	3.19508i	0.713875	−	0.103228i
$959$	−9.13812	+	28.1242i	−0.295085	+	0.908179i
$960$		0			0
$961$	−8.17865	−	25.1713i	−0.263827	−	0.811977i
$962$	−37.9177	−	76.9637i	−1.22252	−	2.48141i
$963$	47.4839	+	15.4285i	1.53015	+	0.497175i
$964$	6.68335	−	1.97414i	0.215256	−	0.0635828i
$965$		0			0
$966$	−8.89670	+	4.38314i	−0.286247	+	0.141025i
$967$	17.8627	+	12.9780i	0.574424	+	0.417344i	0.836710	−	0.547647i	$-0.184476\pi$
$967$	17.8627	+	12.9780i	0.574424	+	0.417344i	−0.262285	+	0.964990i	$0.584476\pi$
$968$	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	$-0.244067\pi$
$971$	−5.05516	−	6.95783i	−0.162228	−	0.223287i	−0.882390	+	0.470518i	$0.844067\pi$
$972$	36.8917	−	25.3135i	1.18330	−	0.811930i
$973$	−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	0.999989	−	0.00460737i	$-0.00146658\pi$
$977$	5.88484	+	18.1117i	0.188273	+	0.579444i	−0.811717	+	0.584052i	$0.801467\pi$
$978$	13.8937	−	80.6719i	0.444273	−	2.57960i
$979$	−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	0.820553	−	0.571571i	$-0.193666\pi$
$983$	16.6333	+	12.0848i	0.530521	+	0.385446i	−0.290032	+	0.957017i	$0.593666\pi$
$984$	10.8150	+	23.5304i	0.344768	+	0.750122i
$985$		0			0
$986$	−7.16653	+	13.6087i	−0.228229	+	0.433390i
$987$	7.91678	+	2.57232i	0.251994	+	0.0818777i
$988$	66.0109	+	23.4325i	2.10009	+	0.745488i
$989$	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	$0.965296\pi$
$992$	11.9959	−	1.07915i	0.380871	−	0.0342629i
$993$	66.8905			2.12271
$994$	27.8558	−	4.02802i	0.883531	−	0.127761i
$995$		0			0
$996$	−22.9342	−	33.4242i	−0.726699	−	1.05909i
$997$	11.2686	+	15.5099i	0.356881	+	0.491204i	0.949276	−	0.314443i	$-0.101818\pi$
$997$	11.2686	+	15.5099i	0.356881	+	0.491204i	−0.592396	+	0.805647i	$0.701818\pi$
$998$	1.06466	−	2.02170i	0.0337011	−	0.0639958i
$999$	7.74398			0.245009

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.19	✓	112	200.53	odd	20
200.2.o.a.29.24	yes	112	25.3	odd	20
200.2.o.a.69.19	yes	112	5.2	odd	4
200.2.o.a.69.24	yes	112	40.37	odd	4
800.2.be.a.369.4		112	40.27	even	4
800.2.be.a.369.25		112	20.7	even	4
800.2.be.a.529.4		112	100.3	even	20
800.2.be.a.529.25		112	200.3	even	20
1000.2.o.a.149.5		112	25.22	odd	20
1000.2.o.a.149.10		112	200.197	odd	20
1000.2.o.a.349.5		112	40.13	odd	4
1000.2.o.a.349.10		112	5.3	odd	4
1000.2.t.b.101.9		224	200.21	even	10	inner
1000.2.t.b.101.20		224	25.4	even	10	inner
1000.2.t.b.101.37		224	25.21	even	5	inner
1000.2.t.b.101.48		224	200.29	even	10	inner
1000.2.t.b.901.9		224	1.1	even	1	trivial
1000.2.t.b.901.20		224	40.29	even	2	inner
1000.2.t.b.901.37		224	8.5	even	2	inner
1000.2.t.b.901.48		224	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-1.25131 - 0.658957i) q^{2} +(-1.48079 - 2.03813i) q^{3} +(1.13155 + 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} -3.58786 q^{7} +(-0.329223 - 2.80920i) q^{8} +(-1.03418 + 3.18289i) q^{9} +O(q^{10})\)	\(q+(-1.25131 - 0.658957i) q^{2} +(-1.48079 - 2.03813i) q^{3} +(1.13155 + 1.64912i) q^{4} +(0.509884 + 3.52610i) q^{6} -3.58786 q^{7} +(-0.329223 - 2.80920i) q^{8} +(-1.03418 + 3.18289i) q^{9} +(2.49567 - 0.810891i) q^{11} +(1.68553 - 4.74824i) q^{12} +(6.50757 + 2.11444i) q^{13} +(4.48952 + 2.36424i) q^{14} +(-1.43918 + 3.73212i) 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} +(-3.65719 - 0.629861i) 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} +(-4.05985 - 5.91680i) 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} +(-1.21576 - 2.46769i) q^{34} +(-6.41920 + 1.89612i) q^{36} +(8.43241 + 2.73986i) q^{37} +(-6.49339 + 3.19910i) q^{38} +(-5.32683 - 16.3943i) q^{39} +(1.12308 - 3.45647i) q^{41} +(-1.82939 - 12.6512i) q^{42} +0.652170i q^{43} +(4.16123 + 3.19808i) q^{44} +(-0.186233 + 1.08133i) q^{46} +(0.745059 - 0.541317i) q^{47} +(9.73767 - 2.59324i) q^{48} +5.87273 q^{49} -4.90045i q^{51} +(3.87669 + 13.1244i) q^{52} +(1.07913 + 1.48529i) q^{53} +(-1.21727 - 0.209644i) q^{54} +(1.18121 + 10.0790i) q^{56} -12.8949 q^{57} +(1.13159 + 7.82548i) q^{58} +(-3.74706 - 1.21749i) q^{59} +(-6.21266 + 2.01862i) q^{61} +(-1.33074 - 2.70108i) q^{62} +(3.71051 - 11.4198i) q^{63} +(-7.78322 + 1.84971i) q^{64} +(4.13179 + 8.38651i) 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} +(9.28187 + 1.85735i) 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} +(-4.13762 + 24.0245i) 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} +(-6.04743 + 17.0360i) q^{84} +(0.429752 - 0.816067i) q^{86} +(-4.35257 + 13.3958i) q^{87} +(-3.09959 - 6.74386i) q^{88} +(-3.35636 - 10.3298i) q^{89} +(-23.3483 - 7.58631i) q^{91} +(0.945588 - 1.23036i) q^{92} -5.36393i q^{93} +(-1.28900 + 0.186393i) q^{94} +(-13.8937 - 3.17175i) q^{96} +(-4.56353 + 3.31560i) q^{97} +(-7.34861 - 3.86988i) 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

Related objects

Downloads

Learn more