LMFDB - Embedded newform 640.2.bm.a.221.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			221.13
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12716 - 0.854120i) q^{2} +(-2.15347 - 0.212098i) q^{3} +(0.540959 + 1.92545i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(2.24614 + 2.07839i) q^{6} +(-0.288072 - 1.44823i) q^{7} +(1.03482 - 2.63233i) q^{8} +(1.65009 + 0.328224i) q^{9} +O(q^{10})$	\(q+(-1.12716 - 0.854120i) q^{2} +(-2.15347 - 0.212098i) q^{3} +(0.540959 + 1.92545i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(2.24614 + 2.07839i) q^{6} +(-0.288072 - 1.44823i) q^{7} +(1.03482 - 2.63233i) q^{8} +(1.65009 + 0.328224i) q^{9} +(-0.221929 + 1.39669i) q^{10} +(3.98738 + 3.27236i) q^{11} +(-0.756554 - 4.26114i) q^{12} +(-1.20910 - 0.646279i) q^{13} +(-0.912264 + 1.87843i) q^{14} +(0.828085 + 1.99917i) q^{15} +(-3.41473 + 2.08318i) q^{16} +(-1.15931 + 2.79882i) q^{17} +(-1.57957 - 1.77934i) q^{18} +(7.24505 - 2.19776i) q^{19} +(1.44309 - 1.38473i) q^{20} +(0.313186 + 3.17983i) q^{21} +(-1.69941 - 7.09416i) q^{22} +(1.64225 - 1.09732i) q^{23} +(-2.78677 + 5.44916i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.810848 + 1.76118i) q^{26} +(2.72833 + 0.827629i) q^{27} +(2.63267 - 1.33810i) q^{28} +(-5.91382 - 7.20600i) q^{29} +(0.774154 - 2.96066i) q^{30} +(-4.70893 + 4.70893i) q^{31} +(5.62821 + 0.568518i) q^{32} +(-7.89264 - 7.89264i) q^{33} +(3.69725 - 2.16452i) q^{34} +(-1.14143 + 0.936750i) q^{35} +(0.260654 + 3.35473i) q^{36} +(3.28174 - 10.8184i) q^{37} +(-10.0434 - 3.71092i) q^{38} +(2.46669 + 1.64819i) q^{39} +(-2.80932 + 0.328239i) q^{40} +(-6.08751 - 9.11060i) q^{41} +(2.36295 - 3.85166i) q^{42} +(0.174512 - 0.0171880i) q^{43} +(-4.14376 + 9.44772i) q^{44} +(-0.488381 - 1.60998i) q^{45} +(-2.78831 - 0.165832i) q^{46} +(-8.95796 - 3.71051i) q^{47} +(7.79535 - 3.76181i) q^{48} +(4.45276 - 1.84439i) q^{49} +(1.33639 - 0.462672i) q^{50} +(3.09016 - 5.78129i) q^{51} +(0.590304 - 2.67768i) q^{52} +(-5.24954 + 6.39659i) q^{53} +(-2.36835 - 3.26318i) q^{54} +(1.00632 - 5.05913i) q^{55} +(-4.11033 - 0.740365i) q^{56} +(-16.0681 + 3.19615i) q^{57} +(0.510998 + 13.1734i) q^{58} +(7.40464 - 3.95786i) q^{59} +(-3.40135 + 2.67591i) q^{60} +(-0.103219 + 1.04800i) q^{61} +(9.32968 - 1.28571i) q^{62} -2.48428i q^{63} +(-5.85829 - 5.44798i) q^{64} +1.37099i q^{65} +(2.15497 + 15.6375i) q^{66} +(0.270121 - 2.74258i) q^{67} +(-6.01613 - 0.718147i) q^{68} +(-3.76927 + 2.01472i) q^{69} +(2.08667 - 0.0809422i) q^{70} +(-5.60805 + 1.11551i) q^{71} +(2.57155 - 4.00394i) q^{72} +(-1.50291 + 7.55563i) q^{73} +(-12.9393 + 9.39106i) q^{74} +(1.37276 - 1.67271i) q^{75} +(8.15095 + 12.7611i) q^{76} +(3.59049 - 6.71733i) q^{77} +(-1.37259 - 3.96462i) q^{78} +(2.81833 - 1.16739i) q^{79} +(3.44689 + 2.02952i) q^{80} +(-10.3629 - 4.29245i) q^{81} +(-0.919975 + 15.4685i) q^{82} +(-4.75002 - 15.6587i) q^{83} +(-5.95319 + 2.32318i) q^{84} +(3.01483 - 0.296935i) q^{85} +(-0.211383 - 0.129681i) q^{86} +(11.2068 + 16.7722i) q^{87} +(12.7401 - 7.10978i) q^{88} +(-10.8488 - 7.24897i) q^{89} +(-0.824632 + 2.23183i) q^{90} +(-0.587655 + 1.93724i) q^{91} +(3.00122 + 2.56847i) q^{92} +(11.1393 - 9.14178i) q^{93} +(6.92779 + 11.8335i) q^{94} +(-5.35354 - 5.35354i) q^{95} +(-11.9996 - 2.41802i) q^{96} +(10.1666 - 10.1666i) q^{97} +(-6.59428 - 1.72427i) q^{98} +(5.50549 + 6.70845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	−1.12716	−	0.854120i	−0.797019	−	0.603954i
$2$	−1.12716	−	0.854120i	−0.797019	−	0.603954i
$3$	−2.15347	−	0.212098i	−1.24331	−	0.122455i	−0.545112	−	0.838363i	$-0.683513\pi$
$3$	−2.15347	−	0.212098i	−1.24331	−	0.122455i	−0.698195	+	0.715908i	$0.746013\pi$
$4$	0.540959	+	1.92545i	0.270479	+	0.962726i
$5$	−0.471397	−	0.881921i	−0.210815	−	0.394407i
$5$	−0.471397	−	0.881921i	−0.210815	−	0.394407i
$6$	2.24614	+	2.07839i	0.916982	+	0.848499i
$7$	−0.288072	−	1.44823i	−0.108881	−	0.547381i	−0.996265	−	0.0863500i	$-0.972480\pi$
$7$	−0.288072	−	1.44823i	−0.108881	−	0.547381i	0.887384	−	0.461031i	$-0.152520\pi$
$8$	1.03482	−	2.63233i	0.365865	−	0.930668i
$9$	1.65009	+	0.328224i	0.550032	+	0.109408i
$10$	−0.221929	+	1.39669i	−0.0701801	+	0.441673i
$11$	3.98738	+	3.27236i	1.20224	+	0.986653i	0.999973	+	0.00732250i	$0.00233084\pi$
$11$	3.98738	+	3.27236i	1.20224	+	0.986653i	0.202267	+	0.979330i	$0.435169\pi$
$12$	−0.756554	−	4.26114i	−0.218398	−	1.23009i
$13$	−1.20910	−	0.646279i	−0.335345	−	0.179246i	0.295126	−	0.955458i	$-0.404638\pi$
$13$	−1.20910	−	0.646279i	−0.335345	−	0.179246i	−0.630471	+	0.776213i	$0.717138\pi$
$14$	−0.912264	+	1.87843i	−0.243813	+	0.502032i
$15$	0.828085	+	1.99917i	0.213811	+	0.516185i
$16$	−3.41473	+	2.08318i	−0.853682	+	0.520795i
$17$	−1.15931	+	2.79882i	−0.281174	+	0.678814i	−0.999864	−	0.0165173i	$-0.994742\pi$
$17$	−1.15931	+	2.79882i	−0.281174	+	0.678814i	0.718690	+	0.695331i	$0.244742\pi$
$18$	−1.57957	−	1.77934i	−0.372308	−	0.419394i
$19$	7.24505	−	2.19776i	1.66213	−	0.504201i	0.687152	−	0.726514i	$-0.258861\pi$
$19$	7.24505	−	2.19776i	1.66213	−	0.504201i	0.974975	+	0.222313i	$0.0713606\pi$
$20$	1.44309	−	1.38473i	0.322685	−	0.309636i
$21$	0.313186	+	3.17983i	0.0683428	+	0.693896i
$22$	−1.69941	−	7.09416i	−0.362316	−	1.51248i
$23$	1.64225	−	1.09732i	0.342432	−	0.228806i	−0.372448	−	0.928053i	$-0.621481\pi$
$23$	1.64225	−	1.09732i	0.342432	−	0.228806i	0.714880	+	0.699247i	$0.246481\pi$
$24$	−2.78677	+	5.44916i	−0.568847	+	1.11230i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	0.810848	+	1.76118i	0.159020	+	0.345395i
$27$	2.72833	+	0.827629i	0.525067	+	0.159277i
$28$	2.63267	−	1.33810i	0.497528	−	0.252878i
$29$	−5.91382	−	7.20600i	−1.09817	−	1.33812i	−0.936257	−	0.351316i	$-0.885734\pi$
$29$	−5.91382	−	7.20600i	−1.09817	−	1.33812i	−0.161911	−	0.986805i	$-0.551766\pi$
$30$	0.774154	−	2.96066i	0.141340	−	0.540541i
$31$	−4.70893	+	4.70893i	−0.845749	+	0.845749i	−0.989599	−	0.143851i	$-0.954051\pi$
$31$	−4.70893	+	4.70893i	−0.845749	+	0.845749i	0.143851	+	0.989599i	$0.454051\pi$
$32$	5.62821	+	0.568518i	0.994937	+	0.100501i
$33$	−7.89264	−	7.89264i	−1.37393	−	1.37393i
$34$	3.69725	−	2.16452i	0.634073	−	0.371212i
$35$	−1.14143	+	0.936750i	−0.192937	+	0.158340i
$36$	0.260654	+	3.35473i	0.0434423	+	0.559122i
$37$	3.28174	−	10.8184i	0.539514	−	1.77854i	−0.0837026	−	0.996491i	$-0.526675\pi$
$37$	3.28174	−	10.8184i	0.539514	−	1.77854i	0.623217	−	0.782049i	$-0.285825\pi$
$38$	−10.0434	−	3.71092i	−1.62926	−	0.601991i
$39$	2.46669	+	1.64819i	0.394987	+	0.263922i
$40$	−2.80932	+	0.328239i	−0.444192	+	0.0518992i
$41$	−6.08751	−	9.11060i	−0.950709	−	1.42284i	−0.905733	−	0.423848i	$-0.860679\pi$
$41$	−6.08751	−	9.11060i	−0.950709	−	1.42284i	−0.0449758	−	0.998988i	$-0.514321\pi$
$42$	2.36295	−	3.85166i	0.364611	−	0.594324i
$43$	0.174512	−	0.0171880i	0.0266129	−	0.00262114i	−0.0847019	−	0.996406i	$-0.526994\pi$
$43$	0.174512	−	0.0171880i	0.0266129	−	0.00262114i	0.111315	+	0.993785i	$0.464494\pi$
$44$	−4.14376	+	9.44772i	−0.624695	+	1.42430i
$45$	−0.488381	−	1.60998i	−0.0728036	−	0.240001i
$46$	−2.78831	−	0.165832i	−0.411114	−	0.0244506i
$47$	−8.95796	−	3.71051i	−1.30665	−	0.541233i	−0.382747	−	0.923853i	$-0.625022\pi$
$47$	−8.95796	−	3.71051i	−1.30665	−	0.541233i	−0.923906	+	0.382620i	$0.875022\pi$
$48$	7.79535	−	3.76181i	1.12516	−	0.542970i
$49$	4.45276	−	1.84439i	0.636108	−	0.263485i
$50$	1.33639	−	0.462672i	0.188994	−	0.0654317i
$51$	3.09016	−	5.78129i	0.432709	−	0.809543i
$52$	0.590304	−	2.67768i	0.0818605	−	0.371328i
$53$	−5.24954	+	6.39659i	−0.721080	+	0.878639i	−0.996578	−	0.0826629i	$-0.973658\pi$
$53$	−5.24954	+	6.39659i	−0.721080	+	0.878639i	0.275497	+	0.961302i	$0.411158\pi$
$54$	−2.36835	−	3.26318i	−0.322292	−	0.444063i
$55$	1.00632	−	5.05913i	0.135693	−	0.682173i
$56$	−4.11033	−	0.740365i	−0.549266	−	0.0989354i
$57$	−16.0681	+	3.19615i	−2.12828	+	0.423341i
$58$	0.510998	+	13.1734i	0.0670974	+	1.72975i
$59$	7.40464	−	3.95786i	0.964002	−	0.515270i	0.0872366	−	0.996188i	$-0.472196\pi$
$59$	7.40464	−	3.95786i	0.964002	−	0.515270i	0.876766	+	0.480918i	$0.159696\pi$
$60$	−3.40135	+	2.67591i	−0.439113	+	0.345458i
$61$	−0.103219	+	1.04800i	−0.0132159	+	0.134183i	−0.999529	−	0.0307026i	$-0.990226\pi$
$61$	−0.103219	+	1.04800i	−0.0132159	+	0.134183i	0.986313	+	0.164886i	$0.0527255\pi$
$62$	9.32968	−	1.28571i	1.18487	−	0.163285i
$63$		−	2.48428i		−	0.312989i
$64$	−5.85829	−	5.44798i	−0.732286	−	0.680997i
$65$			1.37099i			0.170050i
$66$	2.15497	+	15.6375i	0.265259	+	1.92484i
$67$	0.270121	−	2.74258i	0.0330005	−	0.335060i	−0.964482	−	0.264148i	$-0.914909\pi$
$67$	0.270121	−	2.74258i	0.0330005	−	0.335060i	0.997483	−	0.0709117i	$-0.0225909\pi$
$68$	−6.01613	−	0.718147i	−0.729563	−	0.0870881i
$69$	−3.76927	+	2.01472i	−0.453767	+	0.242544i
$70$	2.08667	−	0.0809422i	0.249405	−	0.00967445i
$71$	−5.60805	+	1.11551i	−0.665553	+	0.132387i	−0.516294	−	0.856411i	$-0.672689\pi$
$71$	−5.60805	+	1.11551i	−0.665553	+	0.132387i	−0.149259	+	0.988798i	$0.547689\pi$
$72$	2.57155	−	4.00394i	0.303060	−	0.471868i
$73$	−1.50291	+	7.55563i	−0.175902	+	0.884320i	0.787511	+	0.616300i	$0.211369\pi$
$73$	−1.50291	+	7.55563i	−0.175902	+	0.884320i	−0.963413	+	0.268020i	$0.913631\pi$
$74$	−12.9393	+	9.39106i	−1.50416	+	1.09169i
$75$	1.37276	−	1.67271i	0.158512	−	0.193148i
$76$	8.15095	+	12.7611i	0.934979	+	1.46380i
$77$	3.59049	−	6.71733i	0.409174	−	0.765511i
$78$	−1.37259	−	3.96462i	−0.155416	−	0.448905i
$79$	2.81833	−	1.16739i	0.317087	−	0.131342i	−0.218463	−	0.975845i	$-0.570104\pi$
$79$	2.81833	−	1.16739i	0.317087	−	0.131342i	0.535550	+	0.844504i	$0.320104\pi$
$80$	3.44689	+	2.02952i	0.385374	+	0.226907i
$81$	−10.3629	−	4.29245i	−1.15143	−	0.476939i
$82$	−0.919975	+	15.4685i	−0.101594	+	1.70821i
$83$	−4.75002	−	15.6587i	−0.521382	−	1.71877i	−0.681637	−	0.731691i	$-0.738732\pi$
$83$	−4.75002	−	15.6587i	−0.521382	−	1.71877i	0.160255	−	0.987076i	$-0.448768\pi$
$84$	−5.95319	+	2.32318i	−0.649546	+	0.253480i
$85$	3.01483	−	0.296935i	0.327005	−	0.0322071i
$86$	−0.211383	−	0.129681i	−0.0227940	−	0.0139838i
$87$	11.2068	+	16.7722i	1.20150	+	1.79817i
$88$	12.7401	−	7.10978i	1.35810	−	0.757905i
$89$	−10.8488	−	7.24897i	−1.14998	−	0.768389i	−0.173674	−	0.984803i	$-0.555564\pi$
$89$	−10.8488	−	7.24897i	−1.14998	−	0.768389i	−0.976302	+	0.216415i	$0.930564\pi$
$90$	−0.824632	+	2.23183i	−0.0869238	+	0.235256i
$91$	−0.587655	+	1.93724i	−0.0616030	+	0.203078i
$92$	3.00122	+	2.56847i	0.312898	+	0.267781i
$93$	11.1393	−	9.14178i	1.15509	−	0.947959i
$94$	6.92779	+	11.8335i	0.714547	+	1.22053i
$95$	−5.35354	−	5.35354i	−0.549262	−	0.549262i
$96$	−11.9996	−	2.41802i	−1.22471	−	0.246788i
$97$	10.1666	−	10.1666i	1.03226	−	1.03226i	0.0327968	−	0.999462i	$-0.489559\pi$
$97$	10.1666	−	10.1666i	1.03226	−	1.03226i	0.999462	−	0.0327968i	$-0.0104414\pi$
$98$	−6.59428	−	1.72427i	−0.666123	−	0.174178i
$99$	5.50549	+	6.70845i	0.553322	+	0.674225i
$100$	−1.90150	−	0.619933i	−0.190150	−	0.0619933i
$101$	−7.63939	−	2.31738i	−0.760147	−	0.230588i	−0.113667	−	0.993519i	$-0.536260\pi$
$101$	−7.63939	−	2.31738i	−0.760147	−	0.230588i	−0.646480	+	0.762931i	$0.723760\pi$
$102$	−8.42101	+	3.87704i	−0.833804	+	0.383884i
$103$	1.49122	−	2.23178i	0.146935	−	0.219903i	−0.750700	−	0.660643i	$-0.770284\pi$
$103$	1.49122	−	2.23178i	0.146935	−	0.219903i	0.897635	+	0.440740i	$0.145284\pi$
$104$	−2.95242	+	2.51397i	−0.289509	+	0.246515i
$105$	2.65672	−	1.77517i	0.259270	−	0.173239i
$106$	11.3805	−	2.72621i	1.10537	−	0.264793i
$107$	−0.131973	−	1.33994i	−0.0127583	−	0.129537i	0.986696	−	0.162578i	$-0.0519808\pi$
$107$	−0.131973	−	1.33994i	−0.0127583	−	0.129537i	−0.999454	+	0.0330409i	$0.989481\pi$
$108$	−0.117647	+	5.70098i	−0.0113206	+	0.548577i
$109$	18.0023	−	5.46094i	1.72431	−	0.523063i	0.736193	−	0.676772i	$-0.236622\pi$
$109$	18.0023	−	5.46094i	1.72431	−	0.523063i	0.988116	+	0.153709i	$0.0491217\pi$
$110$	−5.45539	+	4.84291i	−0.520151	+	0.461753i
$111$	−9.36170	+	22.6011i	−0.888573	+	2.14520i
$112$	4.00062	+	4.34522i	0.378023	+	0.410585i
$113$	3.61328	+	8.72322i	0.339908	+	0.820611i	0.997724	+	0.0674323i	$0.0214807\pi$
$113$	3.61328	+	8.72322i	0.339908	+	0.820611i	−0.657815	+	0.753179i	$0.728519\pi$
$114$	20.8412	+	10.1216i	1.95196	+	0.947970i
$115$	−1.74190	−	0.931063i	−0.162433	−	0.0868221i
$116$	10.6757	−	15.2849i	0.991212	−	1.41917i
$117$	−1.78301	−	1.46328i	−0.164839	−	0.135280i
$118$	−11.7267	−	1.86332i	−1.07953	−	0.171533i
$119$	4.38731	+	0.872691i	0.402184	+	0.0799994i
$120$	6.11940	−	0.111002i	0.558622	−	0.0101331i
$121$	3.04488	+	15.3076i	0.276807	+	1.39160i
$122$	1.01147	−	1.09310i	0.0915738	−	0.0989648i
$123$	11.1769	+	20.9106i	1.00779	+	1.88544i
$124$	−11.6142	−	6.51948i	−1.04298	−	0.585466i
$125$	0.995185	+	0.0980171i	0.0890120	+	0.00876692i
$126$	−2.12187	+	2.80017i	−0.189031	+	0.249459i
$127$	6.08477			0.539936			0.269968	−	0.962869i	$-0.412987\pi$
$127$	6.08477			0.539936			0.269968	+	0.962869i	$0.412987\pi$
$128$	1.94998	+	11.1444i	0.172355	+	0.985035i
$129$	−0.379453			−0.0334089
$130$	1.17099	−	1.54532i	0.102702	−	0.135533i
$131$	11.5984	+	1.14234i	1.01335	+	0.0998065i	0.591039	−	0.806643i	$-0.298718\pi$
$131$	11.5984	+	1.14234i	1.01335	+	0.0998065i	0.422314	+	0.906450i	$0.361218\pi$
$132$	10.9273	−	19.4665i	0.951100	−	1.69434i
$133$	−5.26997	−	9.85941i	−0.456964	−	0.854919i
$134$	−2.64696	+	2.86060i	−0.228663	+	0.247119i
$135$	−0.556221	−	2.79631i	−0.0478719	−	0.240668i
$136$	6.16773	+	5.94796i	0.528879	+	0.510033i
$137$	6.94391	+	1.38123i	0.593258	+	0.118006i	0.482583	−	0.875850i	$-0.339699\pi$
$137$	6.94391	+	1.38123i	0.593258	+	0.118006i	0.110675	+	0.993857i	$0.464699\pi$
$138$	5.96937	+	0.948509i	0.508146	+	0.0807425i
$139$	−4.31845	−	3.54406i	−0.366286	−	0.300603i	0.433188	−	0.901304i	$-0.357389\pi$
$139$	−4.31845	−	3.54406i	−0.366286	−	0.300603i	−0.799474	+	0.600700i	$0.794889\pi$
$140$	−2.42113	−	1.69103i	−0.204623	−	0.142918i
$141$	18.5037	+	9.89044i	1.55829	+	0.832925i
$142$	7.27393	+	3.53259i	0.610414	+	0.296449i
$143$	−2.70630	−	6.53358i	−0.226312	−	0.546365i
$144$	−6.31837	+	2.31665i	−0.526531	+	0.193054i
$145$	−3.56738	+	8.61241i	−0.296254	+	0.715221i
$146$	8.14743	−	7.23271i	0.674286	−	0.598583i
$147$	−9.98008	+	3.02742i	−0.823143	+	0.249698i
$148$	22.6057	+	0.466495i	1.85817	+	0.0383457i
$149$	0.147979	+	1.50246i	0.0121229	+	0.123086i	0.999341	−	0.0362865i	$-0.0115529\pi$
$149$	0.147979	+	1.50246i	0.0121229	+	0.123086i	−0.987218	+	0.159373i	$0.949053\pi$
$150$	−2.97601	+	0.712905i	−0.242990	+	0.0582084i
$151$	4.35888	−	2.91251i	0.354721	−	0.237017i	−0.365423	−	0.930842i	$-0.619076\pi$
$151$	4.35888	−	2.91251i	0.354721	−	0.237017i	0.720144	+	0.693825i	$0.244076\pi$
$152$	1.71210	−	21.3456i	0.138870	−	1.73136i
$153$	−2.83161	+	4.23781i	−0.228922	+	0.342606i
$154$	−9.78445	+	4.50477i	−0.788453	+	0.363005i
$155$	6.37268	+	1.93313i	0.511866	+	0.155273i
$156$	−1.83913	+	5.64111i	−0.147249	+	0.451650i
$157$	−2.28996	−	2.79032i	−0.182759	−	0.222692i	0.673570	−	0.739124i	$-0.264760\pi$
$157$	−2.28996	−	2.79032i	−0.182759	−	0.222692i	−0.856328	+	0.516432i	$0.827260\pi$
$158$	−4.17378	−	1.09136i	−0.332048	−	0.0868239i
$159$	12.6614	−	12.6614i	1.00412	−	1.00412i
$160$	−2.15173	−	5.23164i	−0.170109	−	0.413597i
$161$	−2.06225	−	2.06225i	−0.162528	−	0.162528i
$162$	8.01433	+	13.6894i	0.629665	+	1.07554i
$163$	2.88511	−	2.36775i	0.225979	−	0.185456i	−0.514590	−	0.857436i	$-0.672056\pi$
$163$	2.88511	−	2.36775i	0.225979	−	0.185456i	0.740569	+	0.671980i	$0.234556\pi$
$164$	14.2489	−	16.6497i	1.11265	−	1.30012i
$165$	−3.24012	+	10.6813i	−0.252243	+	0.831535i
$166$	−8.02040	+	21.7069i	−0.622504	+	1.68478i
$167$	0.980523	+	0.655165i	0.0758752	+	0.0506982i	0.592929	−	0.805255i	$-0.297971\pi$
$167$	0.980523	+	0.655165i	0.0758752	+	0.0506982i	−0.517054	+	0.855953i	$0.672971\pi$
$168$	8.69444	+	2.46615i	0.670791	+	0.190267i
$169$	−6.17816	−	9.24627i	−0.475243	−	0.711251i
$170$	−3.65180	−	2.24034i	−0.280081	−	0.171826i
$171$	12.6764	−	1.24851i	0.969386	−	0.0954762i
$172$	0.127499	+	0.326717i	0.00972167	+	0.0249119i
$173$	−1.20716	−	3.97949i	−0.0917790	−	0.302555i	0.899018	−	0.437912i	$-0.144282\pi$
$173$	−1.20716	−	3.97949i	−0.0917790	−	0.302555i	−0.990797	+	0.135357i	$0.956782\pi$
$174$	1.69364	−	28.4769i	0.128394	−	2.15883i
$175$	1.36421	+	0.565073i	0.103124	+	0.0427155i
$176$	−20.4327	−	2.86778i	−1.54017	−	0.216167i
$177$	−16.7851	+	6.95263i	−1.26165	+	0.522592i
$178$	6.03685	+	17.4369i	0.452481	+	1.30695i
$179$	4.76716	−	8.91873i	0.356314	−	0.666617i	−0.638354	−	0.769743i	$-0.720384\pi$
$179$	4.76716	−	8.91873i	0.356314	−	0.666617i	0.994668	+	0.103126i	$0.0328844\pi$
$180$	2.83574	−	1.81129i	0.211364	−	0.135005i
$181$	2.13038	−	2.59587i	0.158350	−	0.192950i	−0.687792	−	0.725908i	$-0.741420\pi$
$181$	2.13038	−	2.59587i	0.158350	−	0.192950i	0.846141	+	0.532958i	$0.178920\pi$
$182$	2.31701	−	1.68164i	0.171749	−	0.124652i
$183$	0.444560	−	2.23495i	0.0328628	−	0.165213i
$184$	−1.18906	−	5.45846i	−0.0876586	−	0.402403i
$185$	−11.0880	+	2.20554i	−0.815207	+	0.162155i
$186$	−20.3639	+	0.789919i	−1.49315	+	0.0579197i
$187$	−13.7813	+	7.36628i	−1.00779	+	0.538676i
$188$	2.29851	−	19.2553i	0.167636	−	1.40434i
$189$	0.412647	−	4.18967i	0.0300156	−	0.304754i
$190$	1.46171	+	10.6068i	0.106043	+	0.769501i
$191$			16.8891i			1.22205i	0.791611	+	0.611025i	$0.209243\pi$
$191$			16.8891i			1.22205i	−0.791611	+	0.611025i	$0.790757\pi$
$192$	11.4601	+	12.9746i	0.827065	+	0.936360i
$193$			10.3090i			0.742057i	0.928621	+	0.371029i	$0.120995\pi$
$193$			10.3090i			0.742057i	−0.928621	+	0.371029i	$0.879005\pi$
$194$	−20.1428	+	2.77584i	−1.44617	+	0.199293i
$195$	0.290784	−	2.95238i	0.0208235	−	0.211425i
$196$	5.96005	+	7.57583i	0.425718	+	0.541131i
$197$	−13.3177	+	7.11847i	−0.948848	+	0.507170i	−0.871802	−	0.489858i	$-0.837049\pi$
$197$	−13.3177	+	7.11847i	−0.948848	+	0.507170i	−0.0770458	+	0.997028i	$0.524549\pi$
$198$	−0.475716	−	12.2638i	−0.0338076	−	0.871551i
$199$	−17.8997	+	3.56047i	−1.26888	+	0.252395i	−0.783214	−	0.621752i	$-0.786421\pi$
$199$	−17.8997	+	3.56047i	−1.26888	+	0.252395i	−0.485662	+	0.874147i	$0.661421\pi$
$200$	1.61378	+	2.32286i	0.114112	+	0.164251i
$201$	−1.16340	+	5.84878i	−0.0820596	+	0.412541i
$202$	6.63145	+	9.13700i	0.466587	+	0.642877i
$203$	−8.73238	+	10.6404i	−0.612893	+	0.746812i
$204$	12.8032	+	2.82252i	0.896406	+	0.197616i
$205$	−5.16520	+	9.66341i	−0.360753	+	0.674922i
$206$	−3.58705	+	1.24187i	−0.249921	+	0.0865254i
$207$	3.07003	−	1.27165i	0.213382	−	0.0883857i
$208$	5.47508	−	0.311913i	0.379628	−	0.0216273i
$209$	36.0806	+	14.9451i	2.49575	+	1.03377i
$210$	−4.51075	−	0.268272i	−0.311271	−	0.0185125i
$211$	2.68439	+	8.84924i	0.184801	+	0.609207i	0.999567	+	0.0294174i	$0.00936519\pi$
$211$	2.68439	+	8.84924i	0.184801	+	0.609207i	−0.814766	+	0.579789i	$0.803135\pi$
$212$	−15.1561	−	6.64745i	−1.04093	−	0.456549i
$213$	12.3134	−	1.21276i	0.843698	−	0.0830970i
$214$	−0.995715	+	1.62304i	−0.0680657	+	0.110949i
$215$	−0.0974229	−	0.145804i	−0.00664419	−	0.00994373i
$216$	5.00192	−	6.32540i	0.340338	−	0.430389i
$217$	8.17614	+	5.46312i	0.555033	+	0.370861i
$218$	−24.9557	−	9.22080i	−1.69021	−	0.624511i
$219$	4.83901	−	15.9521i	0.326990	−	1.07794i
$220$	10.2855	−	0.799155i	0.693448	−	0.0538790i
$221$	3.21054	−	2.63483i	0.215965	−	0.177238i
$222$	29.8562	−	17.4790i	2.00381	−	1.17311i
$223$	−9.31621	−	9.31621i	−0.623859	−	0.623859i	0.322657	−	0.946516i	$-0.395424\pi$
$223$	−9.31621	−	9.31621i	−0.623859	−	0.623859i	−0.946516	+	0.322657i	$0.895424\pi$
$224$	−0.797982	−	8.31475i	−0.0533174	−	0.555552i
$225$	−1.18965	+	1.18965i	−0.0793101	+	0.0793101i
$226$	3.37795	−	12.9186i	0.224698	−	0.859332i
$227$	−4.59372	−	5.59746i	−0.304896	−	0.371517i	0.597911	−	0.801562i	$-0.295997\pi$
$227$	−4.59372	−	5.59746i	−0.304896	−	0.371517i	−0.902807	+	0.430046i	$0.858497\pi$
$228$	−14.8462	−	29.2094i	−0.983216	−	1.93444i
$229$	−0.484283	−	0.146906i	−0.0320024	−	0.00970781i	0.274243	−	0.961660i	$-0.411573\pi$
$229$	−0.484283	−	0.146906i	−0.0320024	−	0.00970781i	−0.306245	+	0.951953i	$0.599073\pi$
$230$	1.16815	+	2.53724i	0.0770254	+	0.167301i
$231$	−9.15675	+	13.7040i	−0.602470	+	0.901660i
$232$	−25.0883	+	8.11017i	−1.64713	+	0.532459i
$233$	1.67083	−	1.11641i	0.109460	−	0.0731386i	−0.499636	−	0.866236i	$-0.666533\pi$
$233$	1.67083	−	1.11641i	0.109460	−	0.0731386i	0.609095	+	0.793097i	$0.291533\pi$
$234$	0.759915	+	3.17225i	0.0496772	+	0.207376i
$235$	0.950376	+	9.64933i	0.0619957	+	0.629453i
$236$	11.6263	+	12.1162i	0.756807	+	0.788700i
$237$	−6.31678	+	1.91618i	−0.410319	+	0.124469i
$238$	−4.19980	−	4.73095i	−0.272233	−	0.306662i
$239$	10.7704	−	26.0022i	0.696682	−	1.68194i	−0.0341811	−	0.999416i	$-0.510882\pi$
$239$	10.7704	−	26.0022i	0.696682	−	1.68194i	0.730863	−	0.682524i	$-0.239118\pi$
$240$	−6.99232	−	5.10158i	−0.451353	−	0.329306i
$241$	−10.1813	−	24.5798i	−0.655834	−	1.58332i	−0.804178	−	0.594388i	$-0.797394\pi$
$241$	−10.1813	−	24.5798i	−0.655834	−	1.58332i	0.148344	−	0.988936i	$-0.452606\pi$
$242$	9.64250	−	19.8548i	0.619843	−	1.27631i
$243$	13.8625	+	7.40964i	0.889277	+	0.475328i
$244$	−2.07372	+	0.368183i	−0.132756	+	0.0235705i
$245$	−3.72563	−	3.05754i	−0.238022	−	0.195339i
$246$	5.26199	−	33.1159i	0.335492	−	2.11139i
$247$	−10.1804	−	2.02500i	−0.647762	−	0.128848i
$248$	7.52254	+	17.2683i	0.477682	+	1.09654i
$249$	6.90784	+	34.7280i	0.437766	+	2.20080i
$250$	−1.03801	−	0.960487i	−0.0656495	−	0.0607466i
$251$	12.0233	+	22.4940i	0.758903	+	1.41981i	0.902731	+	0.430205i	$0.141559\pi$
$251$	12.0233	+	22.4940i	0.758903	+	1.41981i	−0.143829	+	0.989603i	$0.545941\pi$
$252$	4.78335	−	1.34389i	0.301323	−	0.0846572i
$253$	10.1391	+	0.998612i	0.637438	+	0.0627822i
$254$	−6.85848	−	5.19712i	−0.430339	−	0.326096i
$255$	−6.55534			−0.410511
$256$	7.32072	−	14.2270i	0.457545	−	0.889186i
$257$	−14.6423			−0.913362			−0.456681	−	0.889631i	$-0.650962\pi$
$257$	−14.6423			−0.913362			−0.456681	+	0.889631i	$0.650962\pi$
$258$	0.427702	+	0.324098i	0.0266276	+	0.0201775i
$259$	−16.6130	−	1.63624i	−1.03228	−	0.101671i
$260$	−2.63977	+	0.741648i	−0.163712	+	0.0459951i
$261$	−7.39317	−	13.8316i	−0.457626	−	0.856158i
$262$	−12.0975	−	11.1940i	−0.747383	−	0.691566i
$263$	2.16757	+	10.8971i	0.133658	+	0.671946i	0.988275	+	0.152686i	$0.0487924\pi$
$263$	2.16757	+	10.8971i	0.133658	+	0.671946i	−0.854616	+	0.519260i	$0.826208\pi$
$264$	−28.9435	+	12.6085i	−1.78135	+	0.776002i
$265$	8.11590	+	1.61435i	0.498556	+	0.0991690i
$266$	−2.48105	+	15.6143i	−0.152123	+	0.957372i
$267$	21.8252	+	17.9115i	1.33568	+	1.09616i
$268$	5.42684	−	0.963521i	0.331497	−	0.0588564i
$269$	−10.2266	−	5.46622i	−0.623525	−	0.333281i	0.129197	−	0.991619i	$-0.458760\pi$
$269$	−10.2266	−	5.46622i	−0.623525	−	0.333281i	−0.752723	+	0.658338i	$0.771260\pi$
$270$	−1.76144	+	3.62696i	−0.107198	+	0.220730i
$271$	−7.47237	−	18.0399i	−0.453914	−	1.09585i	−0.970821	−	0.239804i	$-0.922917\pi$
$271$	−7.47237	−	18.0399i	−0.453914	−	1.09585i	0.516907	−	0.856041i	$-0.327083\pi$
$272$	−1.87172	−	11.9723i	−0.113490	−	0.725925i
$273$	1.67638	−	4.04715i	0.101459	−	0.244945i
$274$	−6.64713	−	7.48779i	−0.401568	−	0.452354i
$275$	−4.93614	+	1.49736i	−0.297660	+	0.0902942i
$276$	−5.91826	−	6.16767i	−0.356238	−	0.371250i
$277$	0.599539	+	6.08722i	0.0360228	+	0.365746i	0.996250	+	0.0865249i	$0.0275762\pi$
$277$	0.599539	+	6.08722i	0.0360228	+	0.365746i	−0.960227	+	0.279221i	$0.909924\pi$
$278$	1.84051	+	7.68318i	0.110387	+	0.460807i
$279$	−9.31576	+	6.22459i	−0.557720	+	0.372657i
$280$	1.28465	+	3.97399i	0.0767726	+	0.237491i
$281$	7.65799	−	11.4610i	0.456837	−	0.683705i	−0.529525	−	0.848294i	$-0.677630\pi$
$281$	7.65799	−	11.4610i	0.456837	−	0.683705i	0.986362	+	0.164589i	$0.0526299\pi$
$282$	−12.4089	−	26.9524i	−0.738941	−	1.60499i
$283$	15.7465	+	4.77666i	0.936035	+	0.283943i	0.721215	−	0.692711i	$-0.243584\pi$
$283$	15.7465	+	4.77666i	0.936035	+	0.283943i	0.214819	+	0.976654i	$0.431084\pi$
$284$	−5.18159	−	10.1946i	−0.307471	−	0.604937i
$285$	10.3932	+	12.6642i	0.615641	+	0.750161i
$286$	−2.53004	+	9.67586i	−0.149605	+	0.572146i
$287$	−11.4406	+	11.4406i	−0.675320	+	0.675320i
$288$	9.10048	+	2.78542i	0.536251	+	0.164133i
$289$	5.53142	+	5.53142i	0.325378	+	0.325378i
$290$	11.3770	−	6.66056i	0.668081	−	0.391121i
$291$	−24.0497	+	19.7371i	−1.40982	+	1.15701i
$292$	−15.3610	+	1.19351i	−0.898936	+	0.0698448i
$293$	1.34654	−	4.43894i	0.0786657	−	0.259326i	−0.908782	−	0.417271i	$-0.862987\pi$
$293$	1.34654	−	4.43894i	0.0786657	−	0.259326i	0.987448	+	0.157945i	$0.0504868\pi$
$294$	13.8349	+	5.11181i	0.806867	+	0.298127i
$295$	−6.98105	−	4.66459i	−0.406452	−	0.271583i
$296$	−25.0816	−	19.8338i	−1.45784	−	1.15281i
$297$	8.17058	+	12.2281i	0.474105	+	0.709548i
$298$	1.11648	−	1.81990i	0.0646762	−	0.105424i
$299$	−2.69482	+	0.265417i	−0.155845	+	0.0153494i
$300$	3.96333	+	1.73831i	0.228823	+	0.100361i
$301$	−0.0751642	−	0.247783i	−0.00433239	−	0.0142820i
$302$	−7.40078	−	0.440154i	−0.425867	−	0.0253280i
$303$	15.9597	+	6.61072i	0.916860	+	0.379776i
$304$	−20.1615	+	22.5975i	−1.15634	+	1.29605i
$305$	0.972914	−	0.402994i	0.0557089	−	0.0230754i
$306$	6.81126	−	2.35813i	0.389374	−	0.134805i
$307$	−6.50587	+	12.1716i	−0.371310	+	0.694672i	−0.996298	−	0.0859620i	$-0.972604\pi$
$307$	−6.50587	+	12.1716i	−0.371310	+	0.694672i	0.624989	+	0.780634i	$0.285104\pi$
$308$	14.8762	+	3.27951i	0.847651	+	0.186868i
$309$	−3.68466	+	4.48978i	−0.209613	+	0.255414i
$310$	−5.53187	−	7.62197i	−0.314189	−	0.432899i
$311$	−2.61472	+	13.1451i	−0.148267	+	0.745390i	0.833081	+	0.553151i	$0.186575\pi$
$311$	−2.61472	+	13.1451i	−0.148267	+	0.745390i	−0.981348	+	0.192239i	$0.938425\pi$
$312$	6.89117	−	4.78756i	0.390136	−	0.271042i
$313$	−15.6494	+	3.11285i	−0.884554	+	0.175949i	−0.616405	−	0.787429i	$-0.711412\pi$
$313$	−15.6494	+	3.11285i	−0.884554	+	0.175949i	−0.268148	+	0.963378i	$0.586412\pi$
$314$	0.197870	+	5.10103i	0.0111664	+	0.287868i
$315$	−2.19094	+	1.17108i	−0.123445	+	0.0659829i
$316$	3.77235	+	4.79504i	0.212211	+	0.269742i
$317$	1.10765	−	11.2462i	0.0622120	−	0.631649i	−0.912635	−	0.408775i	$-0.865956\pi$
$317$	1.10765	−	11.2462i	0.0622120	−	0.631649i	0.974847	−	0.222874i	$-0.0715439\pi$
$318$	−25.0858	+	3.45703i	−1.40674	+	0.193860i
$319$		−	48.0852i		−	2.69225i
$320$	−2.04311	+	7.73471i	−0.114213	+	0.432383i
$321$			2.91351i			0.162616i
$322$	0.563069	+	4.08589i	0.0313786	+	0.227698i
$323$	−2.24811	+	22.8255i	−0.125088	+	1.27004i
$324$	2.65901	−	22.2753i	0.147723	−	1.23752i
$325$	1.20910	−	0.646279i	0.0670690	−	0.0358491i
$326$	−5.27431	+	0.204591i	−0.292117	+	0.0113313i
$327$	−39.9257	+	7.94172i	−2.20790	+	0.439178i
$328$	−30.2816	+	6.59647i	−1.67202	+	0.364229i
$329$	−2.79315	+	14.0421i	−0.153991	+	0.774167i
$330$	12.7752	−	9.27198i	0.703251	−	0.510406i
$331$	13.5983	−	16.5695i	0.747428	−	0.910744i	−0.250931	−	0.968005i	$-0.580737\pi$
$331$	13.5983	−	16.5695i	0.747428	−	0.910744i	0.998359	+	0.0572611i	$0.0182368\pi$
$332$	27.5805	−	17.6166i	1.51368	−	0.966839i
$333$	8.96605	−	16.7743i	0.491336	−	0.919226i
$334$	−0.545613	−	1.57596i	−0.0298546	−	0.0862325i
$335$	−2.54608	+	1.05462i	−0.139107	+	0.0576200i
$336$	−7.69360	−	10.2058i	−0.419720	−	0.556774i
$337$	0.0283055	+	0.0117245i	0.00154190	+	0.000638675i	0.383454	−	0.923560i	$-0.374734\pi$
$337$	0.0283055	+	0.0117245i	0.00154190	+	0.000638675i	−0.381912	+	0.924199i	$0.624734\pi$
$338$	−0.933675	+	15.6989i	−0.0507852	+	0.853906i
$339$	−5.93090	−	19.5516i	−0.322122	−	1.06190i
$340$	2.20264	+	5.64429i	0.119455	+	0.306104i
$341$	−34.1856	+	3.36699i	−1.85125	+	0.182333i
$342$	−15.3546	−	9.41987i	−0.830283	−	0.509368i
$343$	−9.69634	−	14.5116i	−0.523553	−	0.783553i
$344$	0.135345	−	0.477160i	0.00729730	−	0.0257267i
$345$	3.55365	+	2.37447i	0.191322	+	0.127837i
$346$	−2.03830	+	5.51656i	−0.109580	+	0.296572i
$347$	−3.63523	+	11.9838i	−0.195150	+	0.643322i	0.803685	+	0.595055i	$0.202870\pi$
$347$	−3.63523	+	11.9838i	−0.195150	+	0.643322i	−0.998834	+	0.0482668i	$0.984630\pi$
$348$	−26.2317	+	30.6513i	−1.40617	+	1.64308i
$349$	18.3587	−	15.0666i	0.982719	−	0.806497i	0.00161901	−	0.999999i	$-0.499485\pi$
$349$	18.3587	−	15.0666i	0.982719	−	0.806497i	0.981100	+	0.193502i	$0.0619847\pi$
$350$	−1.05503	−	1.80212i	−0.0563939	−	0.0963274i
$351$	−2.76395	−	2.76395i	−0.147529	−	0.147529i
$352$	20.5814	+	20.6844i	1.09699	+	1.10248i
$353$	2.27883	−	2.27883i	0.121290	−	0.121290i	−0.643856	−	0.765146i	$-0.722667\pi$
$353$	2.27883	−	2.27883i	0.121290	−	0.121290i	0.765146	+	0.643856i	$0.222667\pi$
$354$	24.8578	+	6.49982i	1.32118	+	0.345462i
$355$	3.62741	+	4.42001i	0.192523	+	0.234590i
$356$	8.08875	−	24.8103i	0.428703	−	1.31494i
$357$	−9.26285	−	2.80986i	−0.490242	−	0.148713i
$358$	−12.9910	+	5.98107i	−0.686596	+	0.316109i
$359$	14.3907	−	21.5372i	0.759511	−	1.13669i	−0.227143	−	0.973861i	$-0.572939\pi$
$359$	14.3907	−	21.5372i	0.759511	−	1.13669i	0.986655	−	0.162828i	$-0.0520614\pi$
$360$	−4.74337	−	0.380460i	−0.249998	−	0.0200520i
$361$	31.8626	−	21.2899i	1.67698	−	1.12052i
$362$	−4.61845	+	1.10635i	−0.242740	+	0.0581486i
$363$	−3.31033	−	33.6103i	−0.173747	−	1.76408i
$364$	−4.04796	−	0.0835346i	−0.212171	−	0.00437840i
$365$	7.37194	−	2.23625i	0.385865	−	0.117051i
$366$	−2.41001	+	2.13943i	−0.125973	+	0.111830i
$367$	3.83234	−	9.25208i	0.200046	−	0.482955i	−0.791740	−	0.610858i	$-0.790825\pi$
$367$	3.83234	−	9.25208i	0.200046	−	0.482955i	0.991787	+	0.127903i	$0.0408246\pi$
$368$	−3.32192	+	7.16813i	−0.173167	+	0.373665i
$369$	−7.05464	−	17.0314i	−0.367250	−	0.886620i
$370$	14.3817	+	6.98450i	0.747669	+	0.363107i
$371$	10.7760	+	5.75989i	0.559462	+	0.299039i
$372$	23.6280	+	16.5028i	1.22505	+	0.855633i
$373$	14.5680	+	11.9556i	0.754301	+	0.619039i	0.930913	−	0.365241i	$-0.119014\pi$
$373$	14.5680	+	11.9556i	0.754301	+	0.619039i	−0.176611	+	0.984281i	$0.556514\pi$
$374$	21.8254	+	3.46797i	1.12856	+	0.179325i
$375$	−2.12231	−	0.422154i	−0.109596	−	0.0217999i
$376$	−19.0372	+	19.7406i	−0.981766	+	1.01804i
$377$	2.49332	+	12.5348i	0.128413	+	0.645574i
$378$	−4.04360	+	4.36996i	−0.207980	+	0.224767i
$379$	11.8508	+	22.1712i	0.608733	+	1.13886i	0.977817	+	0.209463i	$0.0671716\pi$
$379$	11.8508	+	22.1712i	0.608733	+	1.13886i	−0.369084	+	0.929396i	$0.620328\pi$
$380$	7.41194	−	13.2040i	0.380225	−	0.677353i
$381$	−13.1034	−	1.29057i	−0.671306	−	0.0661178i
$382$	14.4253	−	19.0366i	0.738062	−	0.973998i
$383$	1.75134			0.0894893			0.0447446	−	0.998998i	$-0.485753\pi$
$383$	1.75134			0.0894893			0.0447446	+	0.998998i	$0.485753\pi$
$384$	−1.83551	−	24.4127i	−0.0936682	−	1.24581i
$385$	−7.61670			−0.388183
$386$	8.80511	−	11.6198i	0.448168	−	0.591434i
$387$	0.293603	+	0.0289174i	0.0149247	+	0.00146995i
$388$	25.0749	+	14.0755i	1.27299	+	0.714577i
$389$	2.26535	+	4.23817i	0.114858	+	0.214884i	0.932781	−	0.360444i	$-0.117375\pi$
$389$	2.26535	+	4.23817i	0.114858	+	0.214884i	−0.817923	+	0.575327i	$0.804875\pi$
$390$	−2.84945	+	3.07943i	−0.144287	+	0.155933i
$391$	1.16731	+	5.86848i	0.0590336	+	0.296782i
$392$	−0.247236	−	13.6297i	−0.0124873	−	0.688406i
$393$	−24.7344	−	4.91998i	−1.24769	−	0.248180i
$394$	21.0912	+	3.35131i	1.06256	+	0.168836i
$395$	−2.35810	−	1.93524i	−0.118649	−	0.0973724i
$396$	−9.93856	+	14.2295i	−0.499432	+	0.715062i
$397$	−20.4596	−	10.9359i	−1.02684	−	0.548856i	−0.130138	−	0.991496i	$-0.541542\pi$
$397$	−20.4596	−	10.9359i	−1.02684	−	0.548856i	−0.896700	+	0.442640i	$0.854042\pi$
$398$	23.2168	+	11.2753i	1.16375	+	0.565179i
$399$	9.25755	+	22.3497i	0.463457	+	1.11888i
$400$	0.165020	−	3.99659i	0.00825098	−	0.199830i
$401$	10.4458	−	25.2185i	0.521640	−	1.25935i	−0.415244	−	0.909710i	$-0.636304\pi$
$401$	10.4458	−	25.2185i	0.521640	−	1.25935i	0.936884	−	0.349640i	$-0.113696\pi$
$402$	6.30689	−	5.59881i	0.314559	−	0.279243i
$403$	8.73687	−	2.65030i	0.435214	−	0.132021i
$404$	0.329414	−	15.9629i	0.0163889	−	0.794183i
$405$	1.09943	+	11.1627i	0.0546312	+	0.554680i
$406$	18.9310	−	4.53493i	0.939528	−	0.225065i
$407$	48.4873	−	32.3982i	2.40343	−	1.60592i
$408$	−12.0205	−	14.1169i	−0.595102	−	0.698892i
$409$	−8.88507	+	13.2975i	−0.439339	+	0.657517i	−0.983384	−	0.181539i	$-0.941892\pi$
$409$	−8.88507	+	13.2975i	−0.439339	+	0.657517i	0.544045	+	0.839056i	$0.316892\pi$
$410$	14.0757	−	6.48047i	0.695149	−	0.320047i
$411$	−14.6605	−	4.44723i	−0.723151	−	0.219366i
$412$	5.10387	+	1.66398i	0.251449	+	0.0819785i
$413$	−7.86498	−	9.58351i	−0.387011	−	0.471574i
$414$	−4.54654	−	1.18883i	−0.223450	−	0.0584277i
$415$	−11.5706	+	11.5706i	−0.567979	+	0.567979i
$416$	−6.43767	−	4.32480i	−0.315633	−	0.212041i
$417$	8.54797	+	8.54797i	0.418596	+	0.418596i
$418$	−27.9036	−	47.6626i	−1.36481	−	2.33125i
$419$	−19.1693	+	15.7318i	−0.936481	+	0.768550i	−0.973005	−	0.230783i	$-0.925871\pi$
$419$	−19.1693	+	15.7318i	−0.936481	+	0.768550i	0.0365245	+	0.999333i	$0.488371\pi$
$420$	4.85518	+	4.15510i	0.236908	+	0.202748i
$421$	0.0313736	−	0.103425i	0.00152905	−	0.00504061i	−0.956172	−	0.292804i	$-0.905412\pi$
$421$	0.0313736	−	0.103425i	0.00152905	−	0.00504061i	0.957702	+	0.287763i	$0.0929117\pi$
$422$	4.53259	−	12.2673i	0.220643	−	0.597161i
$423$	−13.5636	−	9.06291i	−0.659485	−	0.440654i
$424$	11.4056	+	20.4378i	0.553903	+	0.992549i
$425$	−1.68306	−	2.51887i	−0.0816402	−	0.122183i
$426$	−14.9149	−	9.15012i	−0.722631	−	0.443325i
$427$	1.54749	−	0.152414i	0.0748883	−	0.00737585i
$428$	2.50860	−	0.978959i	0.121258	−	0.0473198i
$429$	4.44217	+	14.6439i	0.214470	+	0.707013i
$430$	−0.0147230	+	0.247554i	−0.000710008	+	0.0119381i
$431$	4.70890	+	1.95049i	0.226820	+	0.0939518i	0.493199	−	0.869916i	$-0.335827\pi$
$431$	4.70890	+	1.95049i	0.226820	+	0.0939518i	−0.266379	+	0.963868i	$0.585827\pi$
$432$	−11.0406	+	2.85747i	−0.531191	+	0.137480i
$433$	14.2378	−	5.89750i	0.684227	−	0.283416i	−0.0133659	−	0.999911i	$-0.504255\pi$
$433$	14.2378	−	5.89750i	0.684227	−	0.283416i	0.697592	+	0.716495i	$0.254255\pi$
$434$	−4.54962	−	13.1412i	−0.218389	−	0.630797i
$435$	9.50892	−	17.7899i	0.455918	−	0.852962i
$436$	20.2533	+	31.7084i	0.969957	+	1.51856i
$437$	9.48653	−	11.5594i	0.453802	−	0.552960i
$438$	−19.0793	+	13.8474i	−0.911644	+	0.661653i
$439$	−4.46102	+	22.4271i	−0.212913	+	1.07039i	0.715437	+	0.698678i	$0.246228\pi$
$439$	−4.46102	+	22.4271i	−0.212913	+	1.07039i	−0.928350	+	0.371708i	$0.878772\pi$
$440$	−12.2759	−	7.88427i	−0.585232	−	0.375868i
$441$	7.95285	−	1.58192i	0.378707	−	0.0753295i
$442$	−5.86924	+	0.227669i	−0.279171	+	0.0108291i
$443$	−30.3577	+	16.2265i	−1.44234	+	0.770946i	−0.992509	−	0.122169i	$-0.961015\pi$
$443$	−30.3577	+	16.2265i	−1.44234	+	0.770946i	−0.449829	+	0.893115i	$0.648515\pi$
$444$	−48.5817	−	5.79921i	−2.30558	−	0.275218i
$445$	−1.27891	+	12.9850i	−0.0606260	+	0.615546i
$446$	2.54366	+	18.4580i	0.120446	+	0.874010i
$447$		−	3.26689i		−	0.154518i
$448$	−6.20234	+	10.0536i	−0.293033	+	0.474987i
$449$			23.9990i			1.13258i	0.824205	+	0.566292i	$0.191623\pi$
$449$			23.9990i			1.13258i	−0.824205	+	0.566292i	$0.808377\pi$
$450$	2.35703	−	0.324817i	0.111111	−	0.0153120i
$451$	5.53994	−	56.2479i	0.260865	−	2.64861i
$452$	−14.8415	+	11.6761i	−0.698086	+	0.549197i
$453$	−10.0045	+	5.34750i	−0.470051	+	0.251247i
$454$	0.396932	+	10.2328i	0.0186289	+	0.480249i
$455$	1.98551	−	0.394943i	0.0930822	−	0.0185152i
$456$	−8.21434	+	45.6040i	−0.384672	+	2.13560i
$457$	0.492478	−	2.47586i	0.0230372	−	0.115816i	−0.967556	−	0.252658i	$-0.918695\pi$
$457$	0.492478	−	2.47586i	0.0230372	−	0.115816i	0.990593	+	0.136842i	$0.0436953\pi$
$458$	0.420388	+	0.579222i	0.0196434	+	0.0270653i
$459$	−5.47936	+	6.67662i	−0.255755	+	0.311638i
$460$	0.850422	−	3.85760i	0.0396511	−	0.179862i
$461$	13.1208	−	24.5472i	0.611095	−	1.14328i	−0.366028	−	0.930604i	$-0.619283\pi$
$461$	13.1208	−	24.5472i	0.611095	−	1.14328i	0.977123	−	0.212675i	$-0.0682174\pi$
$462$	22.0260	−	7.62563i	1.02474	−	0.354776i
$463$	10.5352	−	4.36383i	0.489613	−	0.202805i	−0.124198	−	0.992258i	$-0.539636\pi$
$463$	10.5352	−	4.36383i	0.489613	−	0.202805i	0.613811	+	0.789453i	$0.289636\pi$
$464$	35.2055	+	12.2870i	1.63437	+	0.570409i
$465$	−13.3134	−	5.51458i	−0.617392	−	0.255732i
$466$	−2.83683	−	0.168718i	−0.131414	−	0.00781571i
$467$	−7.21764	−	23.7934i	−0.333992	−	1.10103i	−0.949729	−	0.313073i	$-0.898641\pi$
$467$	−7.21764	−	23.7934i	−0.333992	−	1.10103i	0.615737	−	0.787952i	$-0.288859\pi$
$468$	1.85294	−	4.22468i	0.0856521	−	0.195286i
$469$	−4.04972	+	0.398863i	−0.186999	+	0.0184178i
$470$	7.17046	−	11.6880i	0.330749	−	0.539129i
$471$	4.33954	+	6.49457i	0.199955	+	0.299254i
$472$	−2.75591	−	23.5871i	−0.126851	−	1.08569i
$473$	0.752092	+	0.502532i	0.0345812	+	0.0231064i
$474$	8.75664	+	3.23546i	0.402206	+	0.148610i
$475$	−2.19776	+	7.24505i	−0.100840	+	0.332426i
$476$	0.693032	+	8.91965i	0.0317651	+	0.408831i
$477$	−10.7618	+	8.83195i	−0.492747	+	0.404387i
$478$	−34.3489	+	20.1092i	−1.57108	+	0.919774i
$479$	−0.240684	−	0.240684i	−0.0109972	−	0.0109972i	0.701587	−	0.712584i	$-0.252475\pi$
$479$	−0.240684	−	0.240684i	−0.0109972	−	0.0109972i	−0.712584	+	0.701587i	$0.752475\pi$
$480$	3.52407	+	11.7226i	0.160851	+	0.535059i
$481$	−10.9597	+	10.9597i	−0.499719	+	0.499719i
$482$	−9.51820	+	36.4013i	−0.433542	+	1.65803i
$483$	4.00360	+	4.87841i	0.182170	+	0.221975i
$484$	−27.8269	+	14.1436i	−1.26486	+	0.642889i
$485$	−13.7586	−	4.17363i	−0.624746	−	0.189515i
$486$	−9.29643	−	20.1920i	−0.421694	−	0.915928i
$487$	−2.53373	+	3.79199i	−0.114814	+	0.171831i	−0.884426	−	0.466681i	$-0.845450\pi$
$487$	−2.53373	+	3.79199i	−0.114814	+	0.171831i	0.769612	+	0.638512i	$0.220450\pi$
$488$	2.65188	+	1.35620i	0.120045	+	0.0613925i
$489$	−6.71520	+	4.48695i	−0.303672	+	0.202907i
$490$	1.58785	+	6.62846i	0.0717319	+	0.299443i
$491$	−2.01551	−	20.4638i	−0.0909587	−	0.923519i	−0.927052	−	0.374932i	$-0.877666\pi$
$491$	−2.01551	−	20.4638i	−0.0909587	−	0.923519i	0.836093	−	0.548587i	$-0.184834\pi$
$492$	−34.2160	+	32.8324i	−1.54258	+	1.48020i
$493$	27.0243	−	8.19772i	1.21711	−	0.369207i
$494$	9.74527	+	10.9778i	0.438461	+	0.493913i
$495$	3.32106	−	8.01775i	0.149271	−	0.360371i
$496$	6.27016	−	25.8893i	0.281538	−	1.16246i
$497$	3.23104	+	7.80043i	0.144932	+	0.349897i
$498$	21.8757	−	45.0440i	0.980273	−	2.01847i
$499$	−2.97655	−	1.59100i	−0.133249	−	0.0712228i	0.403425	−	0.915013i	$-0.367819\pi$
$499$	−2.97655	−	1.59100i	−0.133249	−	0.0712228i	−0.536674	+	0.843790i	$0.680319\pi$
$500$	0.349627	+	1.96920i	0.0156358	+	0.0880654i
$501$	−1.97257	−	1.61885i	−0.0881279	−	0.0723247i
$502$	5.66044	−	35.6235i	0.252638	−	1.58996i
$503$	28.2261	+	5.61453i	1.25854	+	0.250339i	0.778913	−	0.627132i	$-0.215772\pi$
$503$	28.2261	+	5.61453i	1.25854	+	0.250339i	0.479628	+	0.877472i	$0.340772\pi$
$504$	−6.53943	−	2.57078i	−0.291289	−	0.114512i
$505$	1.55743	+	7.82974i	0.0693049	+	0.348419i
$506$	−10.5754	−	9.78557i	−0.470133	−	0.435022i
$507$	11.3434	+	21.2219i	0.503777	+	0.942500i
$508$	3.29161	+	11.7159i	0.146042	+	0.519810i
$509$	−18.0896	−	1.78167i	−0.801806	−	0.0789710i	−0.311191	−	0.950347i	$-0.600728\pi$
$509$	−18.0896	−	1.78167i	−0.801806	−	0.0789710i	−0.490615	+	0.871376i	$0.663228\pi$
$510$	7.38888	+	5.59904i	0.327185	+	0.247930i
$511$	11.3753			0.503213
$512$	−20.4031	+	9.78325i	−0.901700	+	0.432363i
$513$	21.5858			0.953036
$514$	16.5042	+	12.5063i	0.727967	+	0.551628i
$515$	−2.67121	−	0.263091i	−0.117708	−	0.0115932i
$516$	−0.205268	−	0.730617i	−0.00903643	−	0.0321636i
$517$	−23.5767	−	44.1088i	−1.03690	−	1.93990i
$518$	17.3279	+	16.0338i	0.761344	+	0.704484i
$519$	1.75555	+	8.82575i	0.0770601	+	0.387407i
$520$	3.60889	+	1.41873i	0.158260	+	0.0622153i
$521$	18.0798	+	3.59630i	0.792091	+	0.157557i	0.574523	−	0.818488i	$-0.305188\pi$
$521$	18.0798	+	3.59630i	0.792091	+	0.157557i	0.217568	+	0.976045i	$0.430188\pi$
$522$	−3.48063	+	21.9051i	−0.152343	+	0.958759i
$523$	30.1825	+	24.7701i	1.31979	+	1.08312i	0.990298	+	0.138963i	$0.0443768\pi$
$523$	30.1825	+	24.7701i	1.31979	+	1.08312i	0.329490	+	0.944159i	$0.393123\pi$
$524$	4.07472	+	22.9500i	0.178005	+	1.00258i
$525$	−2.81793	−	1.50621i	−0.122984	−	0.0657366i
$526$	6.86426	−	14.1341i	0.299296	−	0.616278i
$527$	−7.72034	−	18.6385i	−0.336303	−	0.811908i
$528$	43.3930	+	10.5094i	1.88844	+	0.457364i
$529$	−7.30884	+	17.6451i	−0.317776	+	0.767178i
$530$	−7.76904	−	8.75158i	−0.337465	−	0.380144i
$531$	13.5174	−	4.10047i	0.586606	−	0.177945i
$532$	16.1330	−	15.4806i	0.699454	−	0.671169i
$533$	1.47244	+	14.9499i	0.0637783	+	0.647552i
$534$	−9.30183	−	38.8303i	−0.402530	−	1.68035i
$535$	−1.11951	+	0.748033i	−0.0484006	+	0.0323403i
$536$	−6.93985	−	3.54913i	−0.299756	−	0.153299i
$537$	−12.1576	+	18.1951i	−0.524639	+	0.785178i
$538$	6.85813	+	14.8960i	0.295675	+	0.642212i
$539$	23.7904	+	7.21673i	1.02472	+	0.310846i
$540$	5.08327	−	2.58367i	0.218749	−	0.111183i
$541$	1.90565	+	2.32204i	0.0819302	+	0.0998323i	0.812362	−	0.583153i	$-0.198181\pi$
$541$	1.90565	+	2.32204i	0.0819302	+	0.0998323i	−0.730432	+	0.682985i	$0.760681\pi$
$542$	−6.98571	+	26.7161i	−0.300062	+	1.14755i
$543$	−5.13828	+	5.13828i	−0.220505	+	0.220505i
$544$	−8.11602	+	15.0933i	−0.347971	+	0.647119i
$545$	−13.3024	−	13.3024i	−0.569810	−	0.569810i
$546$	−5.34630	+	3.12993i	−0.228800	+	0.133949i
$547$	1.84824	−	1.51681i	0.0790248	−	0.0648540i	−0.594052	−	0.804427i	$-0.702473\pi$
$547$	1.84824	−	1.51681i	0.0790248	−	0.0648540i	0.673076	+	0.739573i	$0.264973\pi$
$548$	1.09688	+	14.1173i	0.0468563	+	0.603063i
$549$	−0.514302	+	1.69543i	−0.0219499	+	0.0723591i
$550$	6.84272	+	2.52829i	0.291774	+	0.107807i
$551$	−58.6829	−	39.2107i	−2.49998	−	1.67043i
$552$	1.40287	+	12.0068i	0.0597102	+	0.511045i
$553$	−2.50253	−	3.74531i	−0.106419	−	0.159267i
$554$	4.52344	−	7.37333i	0.192183	−	0.313263i
$555$	24.3455	−	2.39782i	1.03341	−	0.101782i
$556$	4.48781	−	10.2322i	0.190326	−	0.433940i
$557$	8.09261	+	26.6778i	0.342895	+	1.13037i	0.943651	+	0.330941i	$0.107366\pi$
$557$	8.09261	+	26.6778i	0.342895	+	1.13037i	−0.600757	+	0.799432i	$0.705134\pi$
$558$	15.8169	+	0.940692i	0.669581	+	0.0398227i
$559$	−0.222112	−	0.0920016i	−0.00939432	−	0.00389125i
$560$	1.94626	−	5.57655i	0.0822446	−	0.235652i
$561$	31.2401	−	12.9401i	1.31896	−	0.546330i
$562$	−18.4208	+	6.37748i	−0.777034	+	0.269018i
$563$	−8.20815	+	15.3564i	−0.345932	+	0.647194i	−0.993375	−	0.114920i	$-0.963339\pi$
$563$	−8.20815	+	15.3564i	−0.345932	+	0.647194i	0.647442	+	0.762115i	$0.275839\pi$
$564$	−9.03381	+	40.9783i	−0.380392	+	1.72550i
$565$	5.98991	−	7.29872i	0.251997	−	0.307060i
$566$	−13.6690	−	18.8335i	−0.574549	−	0.791630i
$567$	−3.23122	+	16.2444i	−0.135699	+	0.682202i
$568$	−2.86694	+	15.9166i	−0.120294	+	0.667845i
$569$	−23.4726	+	4.66900i	−0.984024	+	0.195735i	−0.660779	−	0.750581i	$-0.729774\pi$
$569$	−23.4726	+	4.66900i	−0.984024	+	0.195735i	−0.323245	+	0.946315i	$0.604774\pi$
$570$	−0.898053	−	23.1516i	−0.0376153	−	0.969712i
$571$	−7.36072	+	3.93439i	−0.308037	+	0.164649i	−0.618171	−	0.786044i	$-0.712126\pi$
$571$	−7.36072	+	3.93439i	−0.308037	+	0.164649i	0.310134	+	0.950693i	$0.399626\pi$
$572$	11.1161	−	8.74524i	0.464787	−	0.365657i
$573$	3.58215	−	36.3701i	0.149646	−	1.51938i
$574$	22.6671	−	3.12370i	0.946105	−	0.130381i
$575$			1.97512i			0.0823680i
$576$	−7.87857	−	10.9125i	−0.328274	−	0.454688i
$577$			24.5219i			1.02086i	0.859919	+	0.510431i	$0.170514\pi$
$577$			24.5219i			1.02086i	−0.859919	+	0.510431i	$0.829486\pi$
$578$	−1.51027	−	10.9593i	−0.0628192	−	0.455845i
$579$	2.18652	−	22.2001i	0.0908686	−	0.922605i
$580$	−18.5126	−	2.20985i	−0.768693	−	0.0917591i
$581$	−21.3091	+	11.3900i	−0.884052	+	0.472535i
$582$	43.9656	−	1.70543i	1.82243	−	0.0706925i
$583$	−41.8638	+	8.32724i	−1.73382	+	0.344879i
$584$	18.3337	+	11.7749i	0.758652	+	0.487248i
$585$	−0.449992	+	2.26226i	−0.0186049	+	0.0935330i
$586$	−5.30915	+	3.85327i	−0.219319	+	0.159177i
$587$	0.811743	−	0.989111i	0.0335042	−	0.0408250i	−0.755989	−	0.654585i	$-0.772844\pi$
$587$	0.811743	−	0.989111i	0.0335042	−	0.0408250i	0.789493	+	0.613760i	$0.210344\pi$
$588$	−11.2280	−	17.5784i	−0.463034	−	0.724923i
$589$	−23.7673	+	44.4655i	−0.979315	+	1.83217i
$590$	3.88461	+	11.2204i	0.159927	+	0.461935i
$591$	30.1891	−	12.5048i	1.24182	−	0.514377i
$592$	11.3305	+	43.7785i	0.465681	+	1.79928i
$593$	−16.6751	−	6.90706i	−0.684765	−	0.283639i	0.0130520	−	0.999915i	$-0.495845\pi$
$593$	−16.6751	−	6.90706i	−0.684765	−	0.283639i	−0.697817	+	0.716276i	$0.745845\pi$
$594$	1.23478	−	20.7617i	0.0506636	−	0.851861i
$595$	−1.29852	−	4.28065i	−0.0532341	−	0.175489i
$596$	−2.81286	+	1.09769i	−0.115219	+	0.0449633i
$597$	39.3016	−	3.87087i	1.60851	−	0.158424i
$598$	3.26418	+	2.00253i	0.133482	+	0.0818897i
$599$	6.58970	+	9.86218i	0.269248	+	0.402958i	0.941313	−	0.337534i	$-0.109593\pi$
$599$	6.58970	+	9.86218i	0.269248	+	0.402958i	−0.672066	+	0.740492i	$0.734593\pi$
$600$	−2.98256	−	5.34450i	−0.121763	−	0.218188i
$601$	1.45941	+	0.975144i	0.0595304	+	0.0397769i	0.584979	−	0.811048i	$-0.301103\pi$
$601$	1.45941	+	0.975144i	0.0595304	+	0.0397769i	−0.525449	+	0.850825i	$0.676103\pi$
$602$	−0.126915	+	0.343489i	−0.00517266	+	0.0139996i
$603$	1.34591	−	4.43686i	0.0548096	−	0.180683i
$604$	7.96588	+	6.81727i	0.324127	+	0.277391i
$605$	12.0648	−	9.90130i	0.490503	−	0.402545i
$606$	−12.3427	−	21.0828i	−0.501388	−	0.856430i
$607$	27.5069	+	27.5069i	1.11647	+	1.11647i	0.992255	+	0.124214i	$0.0396410\pi$
$607$	27.5069	+	27.5069i	1.11647	+	1.11647i	0.124214	+	0.992255i	$0.460359\pi$
$608$	42.0261	−	8.25053i	1.70438	−	0.334603i
$609$	21.0617	−	21.0617i	0.853465	−	0.853465i
$610$	−1.44083	−	0.376748i	−0.0583375	−	0.0152541i
$611$	8.43307	+	10.2757i	0.341166	+	0.415712i
$612$	−9.69147	−	3.15965i	−0.391755	−	0.127721i
$613$	26.9132	+	8.16403i	1.08701	+	0.329742i	0.782427	−	0.622742i	$-0.213981\pi$
$613$	26.9132	+	8.16403i	1.08701	+	0.329742i	0.304587	+	0.952484i	$0.401481\pi$
$614$	17.7292	−	8.16253i	0.715491	−	0.329413i
$615$	13.1727	−	19.7143i	0.531175	−	0.794959i
$616$	−13.9667	−	16.4026i	−0.562734	−	0.660879i
$617$	25.4758	−	17.0224i	1.02562	−	0.685296i	0.0754864	−	0.997147i	$-0.475949\pi$
$617$	25.4758	−	17.0224i	1.02562	−	0.685296i	0.950131	+	0.311851i	$0.100949\pi$
$618$	7.98800	−	1.91353i	0.321324	−	0.0769735i
$619$	−2.88013	−	29.2425i	−0.115762	−	1.17535i	−0.861018	−	0.508575i	$-0.830173\pi$
$619$	−2.88013	−	29.2425i	−0.115762	−	1.17535i	0.745256	−	0.666779i	$-0.232327\pi$
$620$	−0.274793	+	13.3160i	−0.0110359	+	0.534784i
$621$	5.38876	−	1.63466i	0.216244	−	0.0655968i
$622$	14.1747	−	12.5833i	0.568353	−	0.504543i
$623$	−7.37296	+	17.7999i	−0.295391	+	0.713137i
$624$	−11.8566	−	0.489558i	−0.474643	−	0.0195980i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	20.2980	+	9.85775i	0.811271	+	0.393995i
$627$	−74.5287	−	39.8364i	−2.97639	−	1.59091i
$628$	4.13386	−	5.91865i	0.164959	−	0.236180i
$629$	26.4743	+	21.7269i	1.05560	+	0.866308i
$630$	3.46977	+	0.551333i	0.138239	+	0.0219656i
$631$	−6.98314	−	1.38903i	−0.277994	−	0.0552965i	0.0541240	−	0.998534i	$-0.482763\pi$
$631$	−6.98314	−	1.38903i	−0.277994	−	0.0552965i	−0.332118	+	0.943238i	$0.607763\pi$
$632$	−0.156485	−	8.62680i	−0.00622464	−	0.343156i
$633$	−3.90384	−	19.6259i	−0.155164	−	0.780061i
$634$	−10.8541	+	11.7301i	−0.431071	+	0.465863i
$635$	−2.86834	−	5.36628i	−0.113827	−	0.212955i
$636$	31.2283	+	17.5297i	1.23828	+	0.695097i
$637$	−6.57584	−	0.647664i	−0.260544	−	0.0256614i
$638$	−41.0705	+	54.1995i	−1.62600	+	2.14578i
$639$	−9.61995			−0.380560
$640$	8.90927	−	6.97316i	0.352170	−	0.275638i
$641$	17.7872			0.702553			0.351276	−	0.936272i	$-0.385748\pi$
$641$	17.7872			0.702553			0.351276	+	0.936272i	$0.385748\pi$
$642$	2.48849	−	3.28398i	0.0982128	−	0.129608i
$643$	−7.68967	−	0.757366i	−0.303251	−	0.0298676i	−0.0547527	−	0.998500i	$-0.517437\pi$
$643$	−7.68967	−	0.757366i	−0.303251	−	0.0298676i	−0.248498	+	0.968632i	$0.579937\pi$
$644$	2.85518	−	5.08637i	0.112510	−	0.200431i
$645$	0.178873	+	0.334647i	0.00704311	+	0.0131767i
$646$	22.0297	−	23.8077i	0.866745	−	0.936701i
$647$	8.22879	+	41.3689i	0.323507	+	1.62638i	0.710080	+	0.704121i	$0.248659\pi$
$647$	8.22879	+	41.3689i	0.323507	+	1.62638i	−0.386573	+	0.922259i	$0.626341\pi$
$648$	−22.0229	+	22.8366i	−0.865141	+	0.897107i
$649$	42.4767	+	8.44913i	1.66736	+	0.331658i
$650$	−1.91485	−	0.304262i	−0.0751065	−	0.0119341i
$651$	−16.4484	−	13.4988i	−0.644662	−	0.529061i
$652$	6.11971	+	4.27429i	0.239666	+	0.167394i
$653$	42.0171	+	22.4586i	1.64426	+	0.878874i	0.992745	+	0.120235i	$0.0383648\pi$
$653$	42.0171	+	22.4586i	1.64426	+	0.878874i	0.651512	+	0.758639i	$0.274135\pi$
$654$	51.7857	+	25.1498i	2.02498	+	0.983434i
$655$	−4.45997	−	10.7673i	−0.174266	−	0.420714i
$656$	39.7662	+	18.4288i	1.55261	+	0.719525i
$657$	−4.95988	+	11.9742i	−0.193504	+	0.467159i
$658$	15.1420	−	13.4420i	0.590295	−	0.524022i
$659$	−13.6071	+	4.12766i	−0.530056	+	0.160791i	−0.543958	−	0.839113i	$-0.683075\pi$
$659$	−13.6071	+	4.12766i	−0.530056	+	0.160791i	0.0139018	+	0.999903i	$0.495575\pi$
$660$	−22.3190	−	0.460580i	−0.868766	−	0.0179281i
$661$	4.90652	+	49.8167i	0.190841	+	1.93764i	0.322964	+	0.946411i	$0.395321\pi$
$661$	4.90652	+	49.8167i	0.190841	+	1.93764i	−0.132123	+	0.991233i	$0.542179\pi$
$662$	−29.4797	+	7.06189i	−1.14576	+	0.274468i
$663$	−7.47266	+	4.99307i	−0.290214	+	0.193915i
$664$	−46.1342	−	3.70037i	−1.79036	−	0.143602i
$665$	−6.21098	+	9.29539i	−0.240851	+	0.360460i
$666$	−24.4334	+	11.2492i	−0.946775	+	0.435896i
$667$	−17.6192	−	5.34473i	−0.682219	−	0.206949i
$668$	−0.731065	+	2.24237i	−0.0282858	+	0.0867598i
$669$	18.0862	+	22.0381i	0.699254	+	0.852043i
$670$	3.77060	+	0.985935i	0.145671	+	0.0380900i
$671$	−3.84102	+	3.84102i	−0.148281	+	0.148281i
$672$	−0.0451123	+	18.0748i	−0.00174024	+	0.697251i
$673$	−17.5365	−	17.5365i	−0.675983	−	0.675983i	0.283106	−	0.959089i	$-0.408635\pi$
$673$	−17.5365	−	17.5365i	−0.675983	−	0.675983i	−0.959089	+	0.283106i	$0.908635\pi$
$674$	−0.0218905	−	0.0373916i	−0.000843192	−	0.00144027i
$675$	−2.20393	+	1.80872i	−0.0848291	+	0.0696175i
$676$	14.4611	−	16.8976i	0.556197	−	0.649908i
$677$	11.4332	−	37.6901i	0.439412	−	1.44855i	−0.405723	−	0.913996i	$-0.632980\pi$
$677$	11.4332	−	37.6901i	0.439412	−	1.44855i	0.845135	−	0.534552i	$-0.179520\pi$
$678$	−10.0143	+	27.1034i	−0.384598	+	1.04090i
$679$	−17.6523	−	11.7949i	−0.677432	−	0.452646i
$680$	2.33818	−	8.24330i	0.0896653	−	0.316116i
$681$	8.70523	+	13.0283i	0.333585	+	0.499245i
$682$	41.4083	+	25.4035i	1.58560	+	0.972749i
$683$	25.4599	−	2.50759i	0.974198	−	0.0959501i	0.401625	−	0.915804i	$-0.368445\pi$
$683$	25.4599	−	2.50759i	0.974198	−	0.0959501i	0.572573	+	0.819854i	$0.305945\pi$
$684$	9.26135	+	23.7323i	0.354116	+	0.907429i
$685$	−2.05520	−	6.77508i	−0.0785251	−	0.258863i
$686$	−1.46536	+	24.6387i	−0.0559477	+	0.940708i
$687$	1.01173	+	0.419073i	0.0386000	+	0.0159886i
$688$	−0.560106	+	0.422233i	−0.0213538	+	0.0160975i
$689$	10.4812	−	4.34147i	0.399303	−	0.165397i
$690$	−1.97743	−	5.71164i	−0.0752794	−	0.217438i
$691$	0.0571303	−	0.106883i	0.00217334	−	0.00406603i	−0.880832	−	0.473428i	$-0.843016\pi$
$691$	0.0571303	−	0.106883i	0.00217334	−	0.00406603i	0.883006	+	0.469362i	$0.155516\pi$
$692$	7.00928	−	4.47708i	0.266453	−	0.170193i
$693$	8.12944	−	9.90575i	0.308812	−	0.376288i
$694$	14.3330	−	10.4026i	0.544075	−	0.394879i
$695$	−1.08988	+	5.47919i	−0.0413415	+	0.207838i
$696$	55.7471	−	12.1438i	2.11309	−	0.460310i
$697$	32.5562	−	6.47584i	1.23316	−	0.245290i
$698$	−33.5618	+	1.30187i	−1.27033	+	0.0492764i
$699$	−3.83487	+	2.04978i	−0.145048	+	0.0775299i
$700$	−0.350041	+	2.93240i	−0.0132303	+	0.110834i
$701$	−1.40013	+	14.2157i	−0.0528820	+	0.536920i	0.931850	+	0.362843i	$0.118194\pi$
$701$	−1.40013	+	14.2157i	−0.0528820	+	0.536920i	−0.984732	+	0.174077i	$0.944306\pi$
$702$	0.754657	+	5.47615i	0.0284827	+	0.206684i
$703$		−	85.5925i		−	3.22818i
$704$	−5.53150	−	40.8936i	−0.208476	−	1.54123i
$705$		−	20.9811i		−	0.790195i
$706$	−4.51500	+	0.622203i	−0.169924	+	0.0234169i
$707$	−1.15542	+	11.7312i	−0.0434541	+	0.441197i
$708$	−22.4670	−	28.5579i	−0.844363	−	1.07327i
$709$	−15.2770	+	8.16573i	−0.573740	+	0.306670i	−0.732631	−	0.680626i	$-0.761708\pi$
$709$	−15.2770	+	8.16573i	−0.573740	+	0.306670i	0.158891	+	0.987296i	$0.449208\pi$
$710$	−0.313436	−	8.08028i	−0.0117630	−	0.303248i
$711$	5.03367	−	1.00126i	0.188777	−	0.0375502i
$712$	−30.3083	+	21.0563i	−1.13585	+	0.789119i
$713$	−2.56605	+	12.9004i	−0.0960994	+	0.483124i
$714$	8.04072	+	11.0787i	0.300916	+	0.414611i
$715$	−4.48636	+	5.46665i	−0.167780	+	0.204441i
$716$	19.7514	+	4.35427i	0.738145	+	0.162727i
$717$	−28.7089	+	53.7105i	−1.07215	+	2.00585i
$718$	−34.6159	+	11.9844i	−1.29185	+	0.447253i
$719$	2.07942	−	0.861322i	0.0775491	−	0.0321219i	−0.343572	−	0.939126i	$-0.611637\pi$
$719$	2.07942	−	0.861322i	0.0775491	−	0.0321219i	0.421121	+	0.907005i	$0.361637\pi$
$720$	5.02156	+	4.48025i	0.187143	+	0.166969i
$721$	−3.66171	−	1.51673i	−0.136369	−	0.0564860i
$722$	−54.0983	−	3.21744i	−2.01333	−	0.119741i
$723$	16.7118	+	55.0913i	0.621517	+	2.04887i
$724$	6.15067	+	2.69768i	0.228588	+	0.100258i
$725$	9.27711	−	0.913716i	0.344543	−	0.0339346i
$726$	−24.9760	+	40.7115i	−0.926946	+	1.51095i
$727$	−1.58006	−	2.36473i	−0.0586012	−	0.0877029i	0.801012	−	0.598648i	$-0.204295\pi$
$727$	−1.58006	−	2.36473i	−0.0586012	−	0.0877029i	−0.859613	+	0.510946i	$0.829295\pi$
$728$	4.49133	+	3.55160i	0.166460	+	0.131631i
$729$	−0.301733	−	0.201612i	−0.0111753	−	0.00746710i
$730$	−10.2194	−	3.77591i	−0.378235	−	0.139753i
$731$	−0.154208	+	0.508355i	−0.00570358	+	0.0188022i
$732$	4.54378	−	0.353039i	0.167943	−	0.0130487i
$733$	23.6825	−	19.4358i	0.874734	−	0.717876i	−0.0857183	−	0.996319i	$-0.527319\pi$
$733$	23.6825	−	19.4358i	0.874734	−	0.717876i	0.960453	+	0.278444i	$0.0898185\pi$
$734$	−12.2220	+	7.15526i	−0.451123	+	0.264106i
$735$	7.37453	+	7.37453i	0.272014	+	0.272014i
$736$	9.86677	−	5.24228i	0.363694	−	0.193233i
$737$	10.0518	−	10.0518i	0.370263	−	0.370263i
$738$	−6.59519	+	25.2226i	−0.242772	+	0.928456i
$739$	19.6932	+	23.9963i	0.724427	+	0.882717i	0.996838	−	0.0794638i	$-0.0253208\pi$
$739$	19.6932	+	23.9963i	0.724427	+	0.882717i	−0.272410	+	0.962181i	$0.587821\pi$
$740$	−10.2448	−	20.1563i	−0.376607	−	0.740961i
$741$	21.4936	+	6.52003i	0.789589	+	0.239519i
$742$	−7.22659	−	15.6963i	−0.265297	−	0.576229i
$743$	−19.5751	+	29.2963i	−0.718143	+	1.07478i	0.275402	+	0.961329i	$0.411189\pi$
$743$	−19.5751	+	29.2963i	−0.718143	+	1.07478i	−0.993544	+	0.113447i	$0.963811\pi$
$744$	−12.5370	−	38.7824i	−0.459628	−	1.42183i
$745$	1.25529	−	0.838760i	0.0459904	−	0.0307298i
$746$	−6.20884	−	25.9187i	−0.227322	−	0.948949i
$747$	−2.69841	−	27.3974i	−0.0987297	−	1.00242i
$748$	−21.6386	−	22.5505i	−0.791184	−	0.824526i
$749$	−1.90253	+	0.577126i	−0.0695169	+	0.0210877i
$750$	2.03161	+	2.28854i	0.0741837	+	0.0835657i
$751$	−9.09692	+	21.9619i	−0.331951	+	0.801401i	0.666486	+	0.745518i	$0.267798\pi$
$751$	−9.09692	+	21.9619i	−0.331951	+	0.801401i	−0.998437	+	0.0558837i	$0.982202\pi$
$752$	38.3186	−	5.99067i	1.39734	−	0.218457i
$753$	−21.1208	−	50.9902i	−0.769686	−	1.85819i
$754$	7.89584	−	16.2582i	0.287550	−	0.592090i
$755$	−4.62337	−	2.47124i	−0.168262	−	0.0899378i
$756$	8.29024	−	1.47191i	0.301513	−	0.0535328i
$757$	−36.2141	−	29.7201i	−1.31622	−	1.08020i	−0.990901	−	0.134593i	$-0.957027\pi$
$757$	−36.2141	−	29.7201i	−1.31622	−	1.08020i	−0.325322	−	0.945603i	$-0.605473\pi$
$758$	5.57922	−	35.1124i	0.202647	−	1.27534i
$759$	−21.6224	−	4.30096i	−0.784843	−	0.156115i
$760$	−19.6322	+	8.55231i	−0.712136	+	0.310225i
$761$	4.67395	+	23.4975i	0.169430	+	0.851784i	0.968206	+	0.250155i	$0.0804816\pi$
$761$	4.67395	+	23.4975i	0.169430	+	0.851784i	−0.798775	+	0.601629i	$0.794518\pi$
$762$	13.6672	+	12.6465i	0.495112	+	0.458135i
$763$	−13.0947	−	24.4984i	−0.474059	−	0.886902i
$764$	−32.5191	+	9.13630i	−1.17650	+	0.330540i
$765$	5.07222	+	0.499570i	0.183387	+	0.0180620i
$766$	−1.97403	−	1.49585i	−0.0713247	−	0.0540474i
$767$	−11.5109			−0.415633
$768$	−18.7825	+	29.0847i	−0.677754	+	1.04950i
$769$	−45.6955			−1.64782			−0.823910	−	0.566720i	$-0.808212\pi$
$769$	−45.6955			−1.64782			−0.823910	+	0.566720i	$0.808212\pi$
$770$	8.58521	+	6.50558i	0.309389	+	0.234445i
$771$	31.5318	+	3.10561i	1.13559	+	0.111846i
$772$	−19.8495	+	5.57674i	−0.714398	+	0.200711i
$773$	−16.2922	−	30.4806i	−0.585990	−	1.09631i	−0.983872	−	0.178874i	$-0.942755\pi$
$773$	−16.2922	−	30.4806i	−0.585990	−	1.09631i	0.397882	−	0.917437i	$-0.369745\pi$
$774$	−0.306238	−	0.283367i	−0.0110075	−	0.0101854i
$775$	−1.29919	−	6.53147i	−0.0466683	−	0.234617i
$776$	−16.2412	−	37.2823i	−0.583023	−	1.33836i
$777$	35.4286	+	7.04718i	1.27099	+	0.252816i
$778$	1.06650	−	6.71196i	0.0382360	−	0.240635i
$779$	−64.1272	−	52.6278i	−2.29760	−	1.88559i
$780$	5.84197	−	1.03723i	0.209176	−	0.0371387i
$781$	−26.0118	−	13.9036i	−0.930775	−	0.497509i
$782$	3.69664	−	7.61172i	0.132192	−	0.272195i
$783$	−10.1709	−	24.5548i	−0.363479	−	0.877516i
$784$	−11.3628	+	15.5740i	−0.405813	+	0.556214i
$785$	−1.38137	+	3.33491i	−0.0493031	+	0.119028i
$786$	23.6773	+	26.6717i	0.844541	+	0.951350i
$787$	−40.3254	+	12.2326i	−1.43744	+	0.436044i	−0.910377	−	0.413780i	$-0.864208\pi$
$787$	−40.3254	+	12.2326i	−1.43744	+	0.436044i	−0.527067	+	0.849824i	$0.676708\pi$
$788$	−20.9106	−	21.7918i	−0.744910	−	0.776302i
$789$	−2.35654	−	23.9264i	−0.0838952	−	0.851802i
$790$	1.00501	+	4.19541i	0.0357568	+	0.149266i
$791$	11.5924	−	7.74578i	0.412178	−	0.275408i
$792$	23.3560	−	7.55019i	0.829921	−	0.268284i
$793$	0.802106	−	1.20044i	0.0284836	−	0.0426288i
$794$	13.7206	+	29.8014i	0.486926	+	1.05761i
$795$	−17.1350	−	5.19783i	−0.607714	−	0.184348i
$796$	−16.5385	−	32.5389i	−0.586192	−	1.15331i
$797$	15.5958	+	19.0035i	0.552431	+	0.673139i	0.972108	−	0.234535i	$-0.0753567\pi$
$797$	15.5958	+	19.0035i	0.552431	+	0.673139i	−0.419677	+	0.907673i	$0.637857\pi$
$798$	8.65463	−	33.0987i	0.306370	−	1.17168i
$799$	20.7701	−	20.7701i	0.734793	−	0.734793i
$800$	−3.59957	+	4.36384i	−0.127264	+	0.154285i
$801$	−15.5223	−	15.5223i	−0.548455	−	0.548455i
$802$	−33.3137	+	19.5032i	−1.17635	+	0.688680i
$803$	−30.7174	+	25.2091i	−1.08399	+	0.889611i
$804$	−11.8909	+	0.923890i	−0.419360	+	0.0325831i
$805$	−0.846606	+	2.79089i	−0.0298389	+	0.0983658i
$806$	−12.1115	−	4.47503i	−0.426609	−	0.157626i
$807$	20.8633	+	13.9404i	0.734421	+	0.490725i
$808$	−14.0055	+	17.7113i	−0.492712	+	0.623081i
$809$	−1.08422	−	1.62265i	−0.0381193	−	0.0570495i	0.811921	−	0.583768i	$-0.198422\pi$
$809$	−1.08422	−	1.62265i	−0.0381193	−	0.0570495i	−0.850040	+	0.526718i	$0.823422\pi$
$810$	8.29506	−	13.5212i	0.291459	−	0.475085i
$811$	−9.54056	+	0.939663i	−0.335014	+	0.0329960i	−0.264126	−	0.964488i	$-0.585083\pi$
$811$	−9.54056	+	0.939663i	−0.335014	+	0.0329960i	−0.0708885	+	0.997484i	$0.522583\pi$
$812$	−25.2115	−	11.0577i	−0.884750	−	0.388050i
$813$	12.2653	+	40.4333i	0.430163	+	1.41806i
$814$	−82.3247	−	4.89618i	−2.88548	−	0.171611i
$815$	−3.44820	−	1.42829i	−0.120785	−	0.0500309i
$816$	1.49140	+	26.1789i	0.0522096	+	0.916445i
$817$	1.22657	−	0.508064i	0.0429124	−	0.0177749i
$818$	21.3725	−	7.39938i	0.747271	−	0.258713i
$819$	−1.60554	+	3.00375i	−0.0561020	+	0.104959i
$820$	−21.4006	−	4.71783i	−0.747341	−	0.164754i
$821$	−6.31259	+	7.69192i	−0.220311	+	0.268450i	−0.871423	−	0.490532i	$-0.836803\pi$
$821$	−6.31259	+	7.69192i	−0.220311	+	0.268450i	0.651112	+	0.758981i	$0.274303\pi$
$822$	12.7262	+	17.5346i	0.443879	+	0.611588i
$823$	0.745470	−	3.74773i	0.0259854	−	0.130638i	−0.965615	−	0.259976i	$-0.916285\pi$
$823$	0.745470	−	3.74773i	0.0259854	−	0.130638i	0.991601	+	0.129338i	$0.0412853\pi$
$824$	−4.33161	−	6.23488i	−0.150899	−	0.217202i
$825$	10.9474	−	2.17758i	0.381140	−	0.0758134i
$826$	0.679594	+	17.5197i	0.0236461	+	0.609590i
$827$	11.2788	−	6.02863i	0.392201	−	0.209636i	−0.263495	−	0.964661i	$-0.584875\pi$
$827$	11.2788	−	6.02863i	0.392201	−	0.209636i	0.655696	+	0.755025i	$0.272375\pi$
$828$	4.10926	+	5.22329i	0.142807	+	0.181522i
$829$	4.82557	−	48.9949i	0.167599	−	1.70166i	−0.432417	−	0.901674i	$-0.642339\pi$
$829$	4.82557	−	48.9949i	0.167599	−	1.70166i	0.600016	−	0.799988i	$-0.295161\pi$
$830$	22.9245	−	3.15919i	0.795723	−	0.109657i
$831$		−	13.2358i		−	0.459146i
$832$	3.56236	+	10.3733i	0.123503	+	0.359628i
$833$			14.6007i			0.505884i
$834$	−2.33390	−	16.9359i	−0.0808164	−	0.586442i
$835$	0.115588	−	1.17359i	0.00400010	−	0.0406137i
$836$	−9.25789	+	77.5561i	−0.320191	+	2.68233i
$837$	−16.7447	+	8.95025i	−0.578783	+	0.309366i
$838$	35.0436	−	1.35935i	1.21056	−	0.0469579i
$839$	−29.8125	+	5.93008i	−1.02924	+	0.204729i	−0.680699	−	0.732563i	$-0.738324\pi$
$839$	−29.8125	+	5.93008i	−1.02924	+	0.204729i	−0.348544	+	0.937292i	$0.613324\pi$
$840$	−1.92358	−	8.83035i	−0.0663699	−	0.304676i
$841$	−11.2957	+	56.7872i	−0.389506	+	1.95818i
$842$	−0.123700	+	0.0897790i	−0.00426298	+	0.00309399i
$843$	−18.9221	+	23.0566i	−0.651712	+	0.794113i
$844$	−15.5866	+	9.95573i	−0.536514	+	0.342690i
$845$	−5.24212	+	9.80731i	−0.180334	+	0.337382i
$846$	7.54748	+	21.8002i	0.259488	+	0.749508i
$847$	21.2919	−	8.81939i	0.731598	−	0.303038i
$848$	4.60051	−	32.7783i	0.157982	−	1.12561i
$849$	−32.8966	−	13.6262i	−1.12901	−	0.467650i
$850$	−0.254352	+	4.27669i	−0.00872420	+	0.146689i
$851$	−6.48181	−	21.3677i	−0.222194	−	0.732474i
$852$	8.99614	+	23.0527i	0.308203	+	0.789774i
$853$	1.34713	−	0.132681i	0.0461249	−	0.00454291i	−0.0749284	−	0.997189i	$-0.523873\pi$
$853$	1.34713	−	0.132681i	0.0461249	−	0.00454291i	0.121053	+	0.992646i	$0.461373\pi$
$854$	−1.87444	−	1.14995i	−0.0641421	−	0.0393504i
$855$	−7.07669	−	10.5910i	−0.242018	−	0.362205i
$856$	−3.66373	−	1.03920i	−0.125224	−	0.0355192i
$857$	−30.8042	−	20.5827i	−1.05225	−	0.703091i	−0.0959229	−	0.995389i	$-0.530580\pi$
$857$	−30.8042	−	20.5827i	−1.05225	−	0.703091i	−0.956327	+	0.292298i	$0.905580\pi$
$858$	7.50061	−	20.3001i	0.256066	−	0.693033i
$859$	2.60524	−	8.58834i	0.0888897	−	0.293030i	−0.901213	−	0.433377i	$-0.857322\pi$
$859$	2.60524	−	8.58834i	0.0888897	−	0.293030i	0.990102	+	0.140347i	$0.0448218\pi$
$860$	0.228036	−	0.266457i	0.00777597	−	0.00908611i
$861$	27.0636	−	22.2105i	0.922326	−	0.756933i
$862$	−3.64171	−	6.22047i	−0.124037	−	0.211870i
$863$	39.3261	+	39.3261i	1.33867	+	1.33867i	0.897345	+	0.441330i	$0.145493\pi$
$863$	39.3261	+	39.3261i	1.33867	+	1.33867i	0.441330	+	0.897345i	$0.354507\pi$
$864$	14.8851	+	6.20918i	0.506401	+	0.211240i
$865$	−2.94054	+	2.94054i	−0.0999814	+	0.0999814i
$866$	−21.0854	−	5.51341i	−0.716512	−	0.187353i
$867$	−10.7385	−	13.0850i	−0.364700	−	0.444388i
$868$	−6.09602	+	18.6981i	−0.206912	+	0.634654i
$869$	15.0579	+	4.56775i	0.510803	+	0.154950i
$870$	−25.9128	+	11.9303i	−0.878525	+	0.404474i
$871$	−2.09908	+	3.14150i	−0.0711246	+	0.106446i
$872$	4.25419	−	53.0391i	0.144065	−	1.79613i
$873$	20.1127	−	13.4389i	0.680712	−	0.454837i
$874$	−20.5659	+	4.92657i	−0.695651	+	0.166644i
$875$	−0.144733	−	1.46950i	−0.00489286	−	0.0496781i
$876$	33.3326	+	0.687860i	1.12621	+	0.0232406i
$877$	22.5022	−	6.82596i	0.759844	−	0.230496i	0.113496	−	0.993538i	$-0.463795\pi$
$877$	22.5022	−	6.82596i	0.759844	−	0.230496i	0.646349	+	0.763042i	$0.276295\pi$
$878$	24.1837	−	21.4686i	0.816160	−	0.724529i
$879$	−3.84123	+	9.27354i	−0.129561	+	0.312789i
$880$	7.10276	+	19.3719i	0.239434	+	0.653027i
$881$	−9.44939	−	22.8128i	−0.318358	−	0.768584i	−0.999341	−	0.0362853i	$-0.988447\pi$
$881$	−9.44939	−	22.8128i	−0.318358	−	0.768584i	0.680984	−	0.732299i	$-0.261553\pi$
$882$	−10.3152	−	5.00962i	−0.347332	−	0.168683i
$883$	−22.9831	−	12.2847i	−0.773444	−	0.413415i	0.0369370	−	0.999318i	$-0.488240\pi$
$883$	−22.9831	−	12.2847i	−0.773444	−	0.413415i	−0.810381	+	0.585903i	$0.800740\pi$
$884$	6.81000	+	4.75642i	0.229045	+	0.159976i
$885$	14.0441	+	11.5257i	0.472088	+	0.387433i
$886$	48.0773	+	7.63929i	1.61519	+	0.256647i
$887$	−4.30917	−	0.857147i	−0.144688	−	0.0287802i	0.122215	−	0.992504i	$-0.461000\pi$
$887$	−4.30917	−	0.857147i	−0.144688	−	0.0287802i	−0.266903	+	0.963723i	$0.586000\pi$
$888$	49.8059	+	48.0312i	1.67138	+	1.61182i
$889$	−1.75285	−	8.81217i	−0.0587887	−	0.295551i
$890$	12.5322	−	13.5437i	0.420082	−	0.453987i
$891$	−27.2744	−	51.0268i	−0.913726	−	1.70946i
$892$	12.8982	−	22.9776i	0.431864	−	0.769347i
$893$	−73.0556	−	7.19535i	−2.44471	−	0.240783i
$894$	−2.79031	+	3.68229i	−0.0933220	+	0.123154i
$895$	−10.1128			−0.338035
$896$	15.5780	−	6.03441i	0.520423	−	0.201596i
$897$	5.85951			0.195643
$898$	20.4980	−	27.0506i	0.684028	−	0.902691i
$899$	61.7803	+	6.08483i	2.06049	+	0.202940i
$900$	−2.93417	−	1.64706i	−0.0978057	−	0.0549021i
$901$	−11.8171	−	22.1082i	−0.393683	−	0.736529i
$902$	−54.2868	+	58.6684i	−1.80755	+	1.95344i
$903$	0.109310	+	0.549536i	0.00363759	+	0.0182874i
$904$	26.7015	−	0.484349i	0.888077	−	0.0161092i
$905$	−3.29361	−	0.655139i	−0.109483	−	0.0217776i
$906$	15.8440	+	2.51755i	0.526382	+	0.0836400i
$907$	11.0193	+	9.04330i	0.365889	+	0.300278i	0.799316	−	0.600911i	$-0.205196\pi$
$907$	11.0193	+	9.04330i	0.365889	+	0.300278i	−0.433426	+	0.901189i	$0.642696\pi$
$908$	8.29263	−	11.8730i	0.275201	−	0.394019i
$909$	−11.8451	−	6.33133i	−0.392877	−	0.209997i
$910$	−2.57531	−	1.25070i	−0.0853707	−	0.0414604i
$911$	17.3161	+	41.8048i	0.573709	+	1.38506i	0.898376	+	0.439227i	$0.144748\pi$
$911$	17.3161	+	41.8048i	0.573709	+	1.38506i	−0.324667	+	0.945828i	$0.605252\pi$
$912$	48.2101	−	44.3868i	1.59640	−	1.46979i
$913$	32.3008	−	77.9809i	1.06900	−	2.58079i
$914$	−2.66978	+	2.37004i	−0.0883084	+	0.0783939i
$915$	−2.18062	+	0.661483i	−0.0720890	+	0.0218680i
$916$	0.0208825	−	1.01193i	0.000689977	−	0.0334353i
$917$	−1.68678	−	17.1262i	−0.0557025	−	0.565557i
$918$	11.8787	−	2.84556i	0.392056	−	0.0939174i
$919$	2.48726	−	1.66193i	0.0820470	−	0.0548220i	−0.513870	−	0.857868i	$-0.671789\pi$
$919$	2.48726	−	1.66193i	0.0820470	−	0.0548220i	0.595917	+	0.803046i	$0.296789\pi$
$920$	−4.25341	+	3.62176i	−0.140231	+	0.119406i
$921$	16.5918	−	24.8314i	0.546718	−	0.818222i
$922$	−35.7554	+	16.4618i	−1.17754	+	0.542142i
$923$	7.50165	+	2.27560i	0.246920	+	0.0749023i
$924$	−31.3399	−	10.2176i	−1.03101	−	0.336133i
$925$	7.17197	+	8.73907i	0.235813	+	0.287339i
$926$	−15.6021	−	4.07963i	−0.512716	−	0.134065i
$927$	3.19318	−	3.19318i	0.104878	−	0.104878i
$928$	−29.1875	−	43.9190i	−0.958126	−	1.44171i
$929$	5.61102	+	5.61102i	0.184091	+	0.184091i	0.793136	−	0.609045i	$-0.208447\pi$
$929$	5.61102	+	5.61102i	0.184091	+	0.184091i	−0.609045	+	0.793136i	$0.708447\pi$
$930$	10.2961	+	17.5870i	0.337623	+	0.576700i
$931$	28.2069	−	23.1488i	0.924444	−	0.758672i
$932$	3.05345	+	2.61317i	0.100019	+	0.0855971i
$933$	8.41878	−	27.7530i	0.275618	−	0.908592i
$934$	−12.1870	+	32.9835i	−0.398770	+	1.07925i
$935$	12.9930	+	8.68162i	0.424915	+	0.283919i
$936$	−5.69693	+	3.17924i	−0.186210	+	0.103917i
$937$	6.24954	+	9.35310i	0.204164	+	0.305552i	0.919395	−	0.393335i	$-0.128679\pi$
$937$	6.24954	+	9.35310i	0.204164	+	0.305552i	−0.715232	+	0.698888i	$0.753679\pi$
$938$	4.90534	+	3.00937i	0.160165	+	0.0982593i
$939$	34.3606	−	3.38423i	1.12132	−	0.110440i
$940$	−18.0652	+	7.04980i	−0.589222	+	0.229939i
$941$	4.54279	+	14.9756i	0.148091	+	0.488190i	0.999330	−	0.0365873i	$-0.0116487\pi$
$941$	4.54279	+	14.9756i	0.148091	+	0.488190i	−0.851240	+	0.524777i	$0.824149\pi$
$942$	0.655813	−	11.0269i	0.0213675	−	0.359275i
$943$	−19.9944	−	8.28195i	−0.651107	−	0.269697i
$944$	−17.0399	+	28.9402i	−0.554601	+	0.941924i
$945$	−3.88948	+	1.61108i	−0.126525	+	0.0524083i
$946$	−0.418502	−	1.20881i	−0.0136067	−	0.0393017i
$947$	11.9379	−	22.3342i	0.387929	−	0.725764i	−0.609840	−	0.792525i	$-0.708766\pi$
$947$	11.9379	−	22.3342i	0.387929	−	0.725764i	0.997769	+	0.0667603i	$0.0212663\pi$
$948$	−7.10662	−	11.1261i	−0.230812	−	0.361359i
$949$	6.70022	−	8.16425i	0.217498	−	0.265023i
$950$	8.66536	−	6.28914i	0.281141	−	0.204047i
$951$	−4.77060	+	23.9834i	−0.154697	+	0.777716i
$952$	6.83729	−	10.6458i	0.221598	−	0.345031i
$953$	5.76131	−	1.14600i	0.186627	−	0.0371224i	−0.100892	−	0.994897i	$-0.532170\pi$
$953$	5.76131	−	1.14600i	0.186627	−	0.0371224i	0.287519	+	0.957775i	$0.407170\pi$
$954$	19.6737	−	0.763147i	0.636960	−	0.0247078i
$955$	14.8948	−	7.96146i	0.481986	−	0.257627i
$956$	55.8923	+	6.67187i	1.80768	+	0.215784i
$957$	−10.1988	+	103.550i	−0.329680	+	3.34730i
$958$	0.0657154	+	0.476862i	0.00212317	+	0.0154067i
$959$		−	10.4543i		−	0.337587i
$960$	6.04029	−	16.2231i	0.194950	−	0.523599i
$961$		−	13.3480i		−	0.430581i
$962$	21.7142	−	2.99239i	0.700093	−	0.0964784i
$963$	0.222034	−	2.25434i	0.00715493	−	0.0726452i
$964$	41.8196	−	32.9002i	1.34692	−	1.05965i
$965$	9.09172	−	4.85962i	0.292673	−	0.156437i
$966$	−0.345942	−	8.91828i	−0.0111305	−	0.286941i
$967$	40.3803	−	8.03214i	1.29854	−	0.258296i	0.503049	−	0.864258i	$-0.332211\pi$
$967$	40.3803	−	8.03214i	1.29854	−	0.258296i	0.795494	+	0.605961i	$0.207211\pi$
$968$	43.4456	+	7.82555i	1.39639	+	0.251523i
$969$	9.68249	−	48.6772i	0.311046	−	1.56374i
$970$	11.9433	+	16.4558i	0.383476	+	0.528365i
$971$	−7.29999	+	8.89507i	−0.234268	+	0.285456i	−0.876854	−	0.480758i	$-0.840362\pi$
$971$	−7.29999	+	8.89507i	−0.234268	+	0.285456i	0.642586	+	0.766214i	$0.277862\pi$
$972$	−6.76788	+	30.6998i	−0.217080	+	0.984696i
$973$	−3.88861	+	7.27507i	−0.124663	+	0.233228i
$974$	6.09472	−	2.11006i	0.195287	−	0.0676106i
$975$	−2.74084	+	1.13529i	−0.0877773	+	0.0363585i
$976$	−1.83072	−	3.79367i	−0.0585998	−	0.121432i
$977$	−32.7508	−	13.5658i	−1.04779	−	0.434009i	−0.208689	−	0.977982i	$-0.566920\pi$
$977$	−32.7508	−	13.5658i	−1.04779	−	0.434009i	−0.839103	+	0.543973i	$0.816920\pi$
$978$	11.4015	+	0.678091i	0.364579	+	0.0216830i
$979$	−19.5372	−	64.4057i	−0.624413	−	2.05841i
$980$	3.87174	−	8.82752i	0.123678	−	0.281985i
$981$	31.4979	−	3.10228i	1.00565	−	0.0990480i
$982$	−15.2068	+	24.7874i	−0.485267	+	0.790998i
$983$	1.30850	+	1.95831i	0.0417347	+	0.0624604i	0.851750	−	0.523948i	$-0.175541\pi$
$983$	1.30850	+	1.95831i	0.0417347	+	0.0624604i	−0.810016	+	0.586408i	$0.800541\pi$
$984$	66.6095	−	7.78263i	2.12343	−	0.248101i
$985$	12.5559	+	8.38956i	0.400063	+	0.267314i
$986$	−37.4624	−	13.8418i	−1.19304	−	0.440814i
$987$	8.99327	−	29.6469i	0.286259	−	0.943670i
$988$	−1.60812	−	20.6973i	−0.0511611	−	0.658468i
$989$	0.267732	−	0.219722i	0.00851338	−	0.00698675i
$990$	−10.5915	+	6.20067i	−0.336619	+	0.197070i
$991$	−11.8977	−	11.8977i	−0.377943	−	0.377943i	0.492417	−	0.870360i	$-0.336114\pi$
$991$	−11.8977	−	11.8977i	−0.377943	−	0.377943i	−0.870360	+	0.492417i	$0.836114\pi$
$992$	−29.1800	+	23.8257i	−0.926465	+	0.756468i
$993$	−32.7978	+	32.7978i	−1.04081	+	1.04081i
$994$	3.02061	−	11.5520i	0.0958080	−	0.366407i
$995$	11.5779	+	14.1077i	0.367045	+	0.447245i
$996$	−63.1303	+	32.0871i	−2.00036	+	1.01672i
$997$	51.6897	+	15.6799i	1.63703	+	0.496587i	0.968899	−	0.247457i	$-0.0795948\pi$
$997$	51.6897	+	15.6799i	1.63703	+	0.496587i	0.668130	+	0.744044i	$0.267095\pi$
$998$	1.99613	+	4.33563i	0.0631864	+	0.137242i
$999$	17.9073	−	26.8002i	0.566562	−	0.847920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.13	✓	1024
128.117	even	32	inner	640.2.bm.a.501.13	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.13	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.13	yes	1024	128.117	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12716 - 0.854120i) q^{2} +(-2.15347 - 0.212098i) q^{3} +(0.540959 + 1.92545i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(2.24614 + 2.07839i) q^{6} +(-0.288072 - 1.44823i) q^{7} +(1.03482 - 2.63233i) q^{8} +(1.65009 + 0.328224i) q^{9} +O(q^{10})\)	\(q+(-1.12716 - 0.854120i) q^{2} +(-2.15347 - 0.212098i) q^{3} +(0.540959 + 1.92545i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(2.24614 + 2.07839i) q^{6} +(-0.288072 - 1.44823i) q^{7} +(1.03482 - 2.63233i) q^{8} +(1.65009 + 0.328224i) q^{9} +(-0.221929 + 1.39669i) q^{10} +(3.98738 + 3.27236i) q^{11} +(-0.756554 - 4.26114i) q^{12} +(-1.20910 - 0.646279i) q^{13} +(-0.912264 + 1.87843i) q^{14} +(0.828085 + 1.99917i) q^{15} +(-3.41473 + 2.08318i) q^{16} +(-1.15931 + 2.79882i) q^{17} +(-1.57957 - 1.77934i) q^{18} +(7.24505 - 2.19776i) q^{19} +(1.44309 - 1.38473i) q^{20} +(0.313186 + 3.17983i) q^{21} +(-1.69941 - 7.09416i) q^{22} +(1.64225 - 1.09732i) q^{23} +(-2.78677 + 5.44916i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.810848 + 1.76118i) q^{26} +(2.72833 + 0.827629i) q^{27} +(2.63267 - 1.33810i) q^{28} +(-5.91382 - 7.20600i) q^{29} +(0.774154 - 2.96066i) q^{30} +(-4.70893 + 4.70893i) q^{31} +(5.62821 + 0.568518i) q^{32} +(-7.89264 - 7.89264i) q^{33} +(3.69725 - 2.16452i) q^{34} +(-1.14143 + 0.936750i) q^{35} +(0.260654 + 3.35473i) q^{36} +(3.28174 - 10.8184i) q^{37} +(-10.0434 - 3.71092i) q^{38} +(2.46669 + 1.64819i) q^{39} +(-2.80932 + 0.328239i) q^{40} +(-6.08751 - 9.11060i) q^{41} +(2.36295 - 3.85166i) q^{42} +(0.174512 - 0.0171880i) q^{43} +(-4.14376 + 9.44772i) q^{44} +(-0.488381 - 1.60998i) q^{45} +(-2.78831 - 0.165832i) q^{46} +(-8.95796 - 3.71051i) q^{47} +(7.79535 - 3.76181i) q^{48} +(4.45276 - 1.84439i) q^{49} +(1.33639 - 0.462672i) q^{50} +(3.09016 - 5.78129i) q^{51} +(0.590304 - 2.67768i) q^{52} +(-5.24954 + 6.39659i) q^{53} +(-2.36835 - 3.26318i) q^{54} +(1.00632 - 5.05913i) q^{55} +(-4.11033 - 0.740365i) q^{56} +(-16.0681 + 3.19615i) q^{57} +(0.510998 + 13.1734i) q^{58} +(7.40464 - 3.95786i) q^{59} +(-3.40135 + 2.67591i) q^{60} +(-0.103219 + 1.04800i) q^{61} +(9.32968 - 1.28571i) q^{62} -2.48428i q^{63} +(-5.85829 - 5.44798i) q^{64} +1.37099i q^{65} +(2.15497 + 15.6375i) q^{66} +(0.270121 - 2.74258i) q^{67} +(-6.01613 - 0.718147i) q^{68} +(-3.76927 + 2.01472i) q^{69} +(2.08667 - 0.0809422i) q^{70} +(-5.60805 + 1.11551i) q^{71} +(2.57155 - 4.00394i) q^{72} +(-1.50291 + 7.55563i) q^{73} +(-12.9393 + 9.39106i) q^{74} +(1.37276 - 1.67271i) q^{75} +(8.15095 + 12.7611i) q^{76} +(3.59049 - 6.71733i) q^{77} +(-1.37259 - 3.96462i) q^{78} +(2.81833 - 1.16739i) q^{79} +(3.44689 + 2.02952i) q^{80} +(-10.3629 - 4.29245i) q^{81} +(-0.919975 + 15.4685i) q^{82} +(-4.75002 - 15.6587i) q^{83} +(-5.95319 + 2.32318i) q^{84} +(3.01483 - 0.296935i) q^{85} +(-0.211383 - 0.129681i) q^{86} +(11.2068 + 16.7722i) q^{87} +(12.7401 - 7.10978i) q^{88} +(-10.8488 - 7.24897i) q^{89} +(-0.824632 + 2.23183i) q^{90} +(-0.587655 + 1.93724i) q^{91} +(3.00122 + 2.56847i) q^{92} +(11.1393 - 9.14178i) q^{93} +(6.92779 + 11.8335i) q^{94} +(-5.35354 - 5.35354i) q^{95} +(-11.9996 - 2.41802i) q^{96} +(10.1666 - 10.1666i) q^{97} +(-6.59428 - 1.72427i) q^{98} +(5.50549 + 6.70845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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