LMFDB - Embedded newform 1000.2.t.b.101.20

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			101.20
Character	$\chi$	$=$	1000.101
Dual form			1000.2.t.b.901.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.625006 - 1.26861i) q^{2} +(-1.48079 + 2.03813i) q^{3} +(-1.21874 + 1.58578i) q^{4} +(3.51109 + 0.604697i) q^{6} +3.58786 q^{7} +(2.77344 + 0.554981i) q^{8} +(-1.03418 - 3.18289i) q^{9} +O(q^{10})$	\(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	$0.459201\pi$
$3$	−1.48079	+	2.03813i	−0.854932	+	1.17671i	−0.982754	+	0.184916i	$0.940799\pi$
$4$	−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	$-0.262829\pi$
$7$	3.58786			1.35608			0.678042	+	0.735024i	$0.262829\pi$
$8$	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	0.804900	−	0.593410i	$-0.202219\pi$
$13$	6.50757	−	2.11444i	1.80488	−	0.586440i	0.999976	+	0.00697033i	$0.00221874\pi$
$14$	−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	−0.762036	−	0.647534i	$-0.775800\pi$
$17$	−1.57369	+	1.14335i	−0.381677	+	0.277304i	0.380360	+	0.924839i	$0.375800\pi$
$18$	−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	−0.922943	−	0.384936i	$-0.874224\pi$
$23$	0.239759	−	0.737902i	0.0499932	−	0.153863i	0.972936	+	0.231073i	$0.0742236\pi$
$24$	−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	0.481551	−	0.876418i	$-0.340074\pi$
$37$	8.43241	−	2.73986i	1.38628	−	0.450430i	0.904729	+	0.425988i	$0.140074\pi$
$38$	−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	$-0.984165\pi$
$43$		−	0.652170i		−	0.0994550i	0.998763	−	0.0497275i	$-0.0158353\pi$
$44$	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	0.532119	−	0.846670i	$-0.321396\pi$
$47$	−0.745059	−	0.541317i	−0.108678	−	0.0789592i	−0.640797	+	0.767710i	$0.721396\pi$
$48$	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	−0.728445	−	0.685104i	$-0.759757\pi$
$53$	1.07913	−	1.48529i	0.148229	−	0.204020i	0.876675	+	0.481084i	$0.159757\pi$
$54$	−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	0.948220	−	0.317615i	$-0.102882\pi$
$67$	2.89052	+	3.97847i	0.353134	+	0.486047i	−0.595086	+	0.803662i	$0.702882\pi$
$68$	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	$-0.565555\pi$
$73$	4.58222	−	14.1026i	0.536309	−	1.65059i	0.740804	−	0.671721i	$-0.234445\pi$
$74$	−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	0.985414	−	0.170176i	$-0.0544335\pi$
$83$	4.72884	+	6.50869i	0.519058	+	0.714422i	−0.466356	+	0.884597i	$0.654433\pi$
$84$	−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	0.794846	−	0.606811i	$-0.207551\pi$
$97$	4.56353	+	3.31560i	0.463356	+	0.336648i	−0.331490	+	0.943459i	$0.607551\pi$
$98$	−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	0.972668	−	0.232201i	$-0.0745926\pi$
$103$	10.6807	+	7.76000i	1.05240	+	0.764616i	0.0797351	+	0.996816i	$0.474593\pi$
$104$	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	$0.256368\pi$
$107$			14.9185i			1.44222i	−0.692819	+	0.721111i	$0.743632\pi$
$108$	−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	0.999471	−	0.0325164i	$-0.0103521\pi$
$113$	1.82593	+	5.61964i	0.171769	+	0.528652i	−0.827702	+	0.561168i	$0.810352\pi$
$114$	−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	−0.890849	−	0.454299i	$-0.849890\pi$
$127$	1.09193	−	3.36061i	0.0968930	−	0.298206i	0.987742	+	0.156093i	$0.0498899\pi$
$128$	−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	$-0.985472\pi$
$137$	−2.54696	−	7.83872i	−0.217601	−	0.669707i	0.781358	−	0.624084i	$-0.214528\pi$
$138$	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	$0.100492\pi$
$157$			7.78075i			0.620971i	−0.950578	+	0.310486i	$0.899508\pi$
$158$	−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	−0.990593	−	0.136842i	$-0.956305\pi$
$163$	−21.8518	+	7.10008i	−1.71157	+	0.556121i	−0.720973	+	0.692964i	$0.756305\pi$
$164$	−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	−0.898037	−	0.439919i	$-0.855007\pi$
$167$	−9.78464	+	7.10896i	−0.757158	+	0.550108i	0.140879	+	0.990027i	$0.455007\pi$
$168$	−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	0.818653	−	0.574288i	$-0.194721\pi$
$173$	15.0391	+	4.88649i	1.14340	+	0.371513i	0.324747	+	0.945801i	$0.394721\pi$
$174$	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	$-0.491745\pi$
$193$	0.720451			0.0518592			0.0259296	+	0.999664i	$0.491745\pi$
$194$	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	−0.915583	−	0.402129i	$-0.868270\pi$
$197$	−3.51179	+	4.83357i	−0.250205	+	0.344377i	0.665378	+	0.746506i	$0.268270\pi$
$198$	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	$-0.661130\pi$
$223$	6.29390	−	19.3706i	0.421471	−	1.29715i	0.906333	−	0.422564i	$-0.138870\pi$
$224$	−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	0.762536	−	0.646946i	$-0.223954\pi$
$227$	15.0541	+	4.89137i	0.999175	+	0.324652i	0.236639	+	0.971598i	$0.423954\pi$
$228$	−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	−0.0143813	−	0.999897i	$-0.504578\pi$
$233$	14.2284	−	10.3375i	0.932133	−	0.677234i	0.946514	+	0.322662i	$0.104578\pi$
$234$	−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	$-0.455917\pi$
$257$	4.42621			0.276099			0.138050	+	0.990425i	$0.455917\pi$
$258$	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	$-0.976423\pi$
$263$	−3.79412	−	11.6771i	−0.233956	−	0.720041i	0.763303	−	0.646041i	$-0.223577\pi$
$264$	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	0.420666	−	0.907216i	$-0.361796\pi$
$277$	3.79042	+	1.23158i	0.227744	+	0.0739986i	−0.192922	+	0.981214i	$0.561796\pi$
$278$	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	0.973689	−	0.227883i	$-0.0731804\pi$
$283$	7.67233	+	10.5601i	0.456073	+	0.627730i	−0.517616	+	0.855613i	$0.673180\pi$
$284$	−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	$-0.710200\pi$
$293$		−	27.0373i		−	1.57954i	0.613404	−	0.789769i	$-0.289800\pi$
$294$	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	$-0.770664\pi$
$307$		−	23.1194i		−	1.31949i	0.751488	−	0.659747i	$-0.229336\pi$
$308$	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	0.993264	−	0.115870i	$-0.0369655\pi$
$313$	2.15115	+	6.62056i	0.121590	+	0.374216i	−0.871674	+	0.490086i	$0.836965\pi$
$314$	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	0.852757	−	0.522307i	$-0.174929\pi$
$317$	1.64686	+	2.26671i	0.0924971	+	0.127311i	−0.760260	+	0.649619i	$0.774929\pi$
$318$	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	$0.0740184\pi$
$337$	5.89820	+	18.1528i	0.321295	+	0.988845i	−0.651790	+	0.758400i	$0.725982\pi$
$338$	−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	−0.389019	−	0.921230i	$-0.627186\pi$
$347$	11.3134	−	15.5716i	0.607336	−	0.835926i	0.996355	+	0.0853039i	$0.0271861\pi$
$348$	−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	0.0834537	−	0.996512i	$-0.473405\pi$
$353$	−15.7539	−	11.4459i	−0.838497	−	0.609203i	−0.921950	+	0.387308i	$0.873405\pi$
$354$	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	−0.996108	−	0.0881385i	$-0.971908\pi$
$367$	−23.3737	+	16.9820i	−1.22010	+	0.886453i	−0.223990	+	0.974592i	$0.571908\pi$
$368$	−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	0.848972	−	0.528438i	$-0.177222\pi$
$373$	23.6625	+	7.68840i	1.22520	+	0.398090i	0.376224	+	0.926529i	$0.377222\pi$
$374$	−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	−0.649227	−	0.760595i	$-0.724907\pi$
$383$	−2.47525	+	1.79838i	−0.126480	+	0.0918928i	0.522747	+	0.852488i	$0.324907\pi$
$384$	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	$0.541029\pi$
$397$	−20.5622	+	28.3014i	−1.03199	+	1.42041i	−0.903446	+	0.428701i	$0.858971\pi$
$398$	−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	−0.560096	−	0.828428i	$-0.689236\pi$
$433$	1.13838	−	0.827085i	0.0547073	−	0.0397472i	0.614803	+	0.788681i	$0.289236\pi$
$434$	−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	$0.0714637\pi$
$443$			9.37158i			0.445257i	−0.974903	+	0.222629i	$0.928536\pi$
$444$	−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	$-0.771331\pi$
$457$	−32.1890			−1.50574			−0.752869	+	0.658170i	$0.771331\pi$
$458$	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	$0.148153\pi$
$463$	9.34875	+	28.7725i	0.434473	+	1.33717i	−0.459152	+	0.888358i	$0.651847\pi$
$464$	−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	$-0.796569\pi$
$467$	−24.2441	−	33.3692i	−1.12188	−	1.54414i	−0.319250	−	0.947671i	$-0.603431\pi$
$468$	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	$-0.798472\pi$
$487$	−11.0724	−	34.0773i	−0.501738	−	1.54419i	0.304449	−	0.952529i	$-0.401528\pi$
$488$	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	0.976158	−	0.217062i	$-0.0696473\pi$
$503$	24.0283	+	17.4576i	1.07137	+	0.778395i	0.0952114	+	0.995457i	$0.469647\pi$
$504$	−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	−0.140753	−	0.990045i	$-0.544952\pi$
$523$	−19.1314	−	6.21617i	−0.836558	−	0.271814i	−0.695805	+	0.718230i	$0.744952\pi$
$524$	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	$0.507129\pi$
$547$	−22.5997	+	31.1058i	−0.966293	+	1.32999i	−0.943897	+	0.330239i	$0.892871\pi$
$548$	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	$-0.925335\pi$
$557$		−	10.9707i		−	0.464844i	0.972615	−	0.232422i	$-0.0746650\pi$
$558$	−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	−0.287838	−	0.957679i	$-0.592936\pi$
$563$	1.00145	−	0.325391i	0.0422061	−	0.0137136i	0.330044	+	0.943966i	$0.392936\pi$
$564$	−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	$0.301971\pi$
$577$	−8.80026	+	27.0844i	−0.366360	+	1.12754i	−0.949125	+	0.314899i	$0.898029\pi$
$578$	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	0.463491	−	0.886101i	$-0.346597\pi$
$587$	32.9333	−	10.7007i	1.35930	−	0.441664i	0.895810	+	0.444438i	$0.146597\pi$
$588$	−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	$-0.755164\pi$
$593$	−34.9925			−1.43697			−0.718484	+	0.695543i	$0.755164\pi$
$594$	−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	$-0.207218\pi$
$607$	39.1971			1.59096			0.795481	+	0.605979i	$0.207218\pi$
$608$	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	0.135575	−	0.990767i	$-0.456712\pi$
$613$	20.4908	−	6.65786i	0.827615	−	0.268909i	0.692041	+	0.721859i	$0.256712\pi$
$614$	−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	0.0154563	−	0.999881i	$-0.495080\pi$
$617$	24.1235	−	17.5267i	0.971175	−	0.705600i	0.955719	+	0.294280i	$0.0950799\pi$
$618$	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	$-0.959291\pi$
$643$		−	6.46830i		−	0.255085i	0.991833	−	0.127542i	$-0.0407089\pi$
$644$	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	0.800122	−	0.599838i	$-0.204768\pi$
$647$	12.1303	+	8.81321i	0.476893	+	0.346483i	−0.323229	+	0.946321i	$0.604768\pi$
$648$	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	$0.472638\pi$
$653$	−22.6975	+	31.2404i	−0.888220	+	1.22253i	−0.974076	+	0.226223i	$0.927362\pi$
$654$	−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	$-0.730792\pi$
$673$	8.12719	−	25.0129i	0.313280	−	0.964177i	0.976457	−	0.215714i	$-0.0692079\pi$
$674$	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	0.614119	−	0.789213i	$-0.289511\pi$
$677$	16.8361	+	5.47038i	0.647064	+	0.210244i	0.0329450	+	0.999457i	$0.489511\pi$
$678$	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	$-0.860545\pi$
$683$	−26.8971	−	37.0207i	−1.02919	−	1.41656i	−0.123635	−	0.992328i	$-0.539455\pi$
$684$	−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	$0.386857\pi$
$727$	−13.0656	+	40.2119i	−0.484578	+	1.49138i	−0.832591	+	0.553888i	$0.813143\pi$
$728$	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	0.994058	−	0.108854i	$-0.0347180\pi$
$733$	15.7936	+	21.7381i	0.583351	+	0.802914i	−0.410707	+	0.911768i	$0.634718\pi$
$734$	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	$-0.208635\pi$
$743$	43.2190			1.58555			0.792776	+	0.609513i	$0.208635\pi$
$744$	−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	$0.152903\pi$
$757$			25.4279i			0.924193i	−0.886830	+	0.462096i	$0.847097\pi$
$758$	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	−0.0610199	−	0.998137i	$-0.519435\pi$
$773$	−19.3807	−	6.29718i	−0.697076	−	0.226494i	−0.636056	+	0.771643i	$0.719435\pi$
$774$	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	−0.342223	−	0.939619i	$-0.611180\pi$
$787$	−1.87380	+	0.608835i	−0.0667938	+	0.0217026i	0.275430	+	0.961321i	$0.411180\pi$
$788$	−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	−0.503975	−	0.863718i	$-0.668130\pi$
$797$	13.3592	−	18.3873i	0.473206	−	0.651313i	0.977182	+	0.212405i	$0.0681297\pi$
$798$	−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	−0.929687	−	0.368350i	$-0.879923\pi$
$823$	1.11758	−	3.43957i	0.0389565	−	0.119896i	0.968644	+	0.248455i	$0.0799227\pi$
$824$	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	0.735819	−	0.677178i	$-0.236797\pi$
$827$	26.8330	+	8.71857i	0.933075	+	0.303174i	0.197255	+	0.980352i	$0.436797\pi$
$828$	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	−0.364492	−	0.931206i	$-0.618757\pi$
$853$	18.5100	−	25.4769i	0.633772	−	0.872312i	0.998264	+	0.0588942i	$0.0187574\pi$
$854$	−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	$-0.805207\pi$
$857$	−47.9238			−1.63705			−0.818523	+	0.574473i	$0.805207\pi$
$858$	−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	$0.159283\pi$
$863$	13.2070	+	40.6471i	0.449573	+	1.38364i	−0.427817	+	0.903865i	$0.640717\pi$
$864$	−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	$-0.965181\pi$
$877$	−55.1526	−	17.9202i	−1.86237	−	0.605121i	−0.868349	−	0.495953i	$-0.834819\pi$
$878$	−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	$0.0540882\pi$
$883$	25.0162	+	34.4318i	0.841861	+	1.15872i	−0.143736	+	0.989616i	$0.545912\pi$
$884$	−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	$0.132049\pi$
$887$	12.2612	+	37.7360i	0.411689	+	1.26705i	−0.503489	+	0.864001i	$0.667951\pi$
$888$	−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	$-0.803220\pi$
$907$		−	34.9093i		−	1.15914i	0.814921	−	0.579571i	$-0.196780\pi$
$908$	−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	0.901886	−	0.431974i	$-0.142183\pi$
$937$	−2.49974	−	7.69340i	−0.0816628	−	0.251332i	−0.983549	+	0.180641i	$0.942183\pi$
$938$	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	−0.639380	−	0.768890i	$-0.720809\pi$
$947$	8.90757	−	12.2602i	0.289457	−	0.398404i	0.928838	+	0.370487i	$0.120809\pi$
$948$	−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	$-0.956024\pi$
$953$	−44.0685	−	32.0176i	−1.42752	−	1.03715i	−0.437047	−	0.899439i	$-0.643976\pi$
$954$	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	−0.836710	−	0.547647i	$-0.815524\pi$
$967$	−17.8627	+	12.9780i	−0.574424	+	0.417344i	0.262285	+	0.964990i	$0.415524\pi$
$968$	−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	−0.999989	−	0.00460737i	$-0.998533\pi$
$977$	−5.88484	+	18.1117i	−0.188273	+	0.579444i	0.811717	+	0.584052i	$0.198533\pi$
$978$	−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	−0.820553	−	0.571571i	$-0.806334\pi$
$983$	−16.6333	+	12.0848i	−0.530521	+	0.385446i	0.290032	+	0.957017i	$0.406334\pi$
$984$	−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	−0.592396	−	0.805647i	$-0.701818\pi$
$997$	11.2686	−	15.5099i	0.356881	−	0.491204i	0.949276	+	0.314443i	$0.101818\pi$
$998$	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.101.20		224
5.2	odd	4		200.2.o.a.29.24	yes	112
5.3	odd	4		1000.2.o.a.149.5		112
5.4	even	2	inner	1000.2.t.b.101.37		224
8.5	even	2	inner	1000.2.t.b.101.48		224
20.7	even	4		800.2.be.a.529.4		112
25.6	even	5	inner	1000.2.t.b.901.48		224
25.8	odd	20		200.2.o.a.69.19	yes	112
25.17	odd	20		1000.2.o.a.349.10		112
25.19	even	10	inner	1000.2.t.b.901.9		224
40.13	odd	4		1000.2.o.a.149.10		112
40.27	even	4		800.2.be.a.529.25		112
40.29	even	2	inner	1000.2.t.b.101.9		224
40.37	odd	4		200.2.o.a.29.19	✓	112
100.83	even	20		800.2.be.a.369.25		112
200.69	even	10	inner	1000.2.t.b.901.37		224
200.83	even	20		800.2.be.a.369.4		112
200.117	odd	20		1000.2.o.a.349.5		112
200.133	odd	20		200.2.o.a.69.24	yes	112
200.181	even	10	inner	1000.2.t.b.901.20		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.19	✓	112	40.37	odd	4
200.2.o.a.29.24	yes	112	5.2	odd	4
200.2.o.a.69.19	yes	112	25.8	odd	20
200.2.o.a.69.24	yes	112	200.133	odd	20
800.2.be.a.369.4		112	200.83	even	20
800.2.be.a.369.25		112	100.83	even	20
800.2.be.a.529.4		112	20.7	even	4
800.2.be.a.529.25		112	40.27	even	4
1000.2.o.a.149.5		112	5.3	odd	4
1000.2.o.a.149.10		112	40.13	odd	4
1000.2.o.a.349.5		112	200.117	odd	20
1000.2.o.a.349.10		112	25.17	odd	20
1000.2.t.b.101.9		224	40.29	even	2	inner
1000.2.t.b.101.20		224	1.1	even	1	trivial
1000.2.t.b.101.37		224	5.4	even	2	inner
1000.2.t.b.101.48		224	8.5	even	2	inner
1000.2.t.b.901.9		224	25.19	even	10	inner
1000.2.t.b.901.20		224	200.181	even	10	inner
1000.2.t.b.901.37		224	200.69	even	10	inner
1000.2.t.b.901.48		224	25.6	even	5	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

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Database

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