LMFDB - Embedded newform 968.2.o.c.269.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.7
Character	$\chi$	$=$	968.269
Dual form			968.2.o.c.493.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.784666 + 1.17656i) q^{2} +(0.866175 - 1.19219i) q^{3} +(-0.768600 + 1.84642i) q^{4} +(3.38352 + 1.09937i) q^{5} +(2.08234 + 0.0836407i) q^{6} +(-3.11534 + 2.26343i) q^{7} +(-2.77552 + 0.544514i) q^{8} +(0.255998 + 0.787881i) q^{9} +(1.36145 + 4.84357i) q^{10} +(1.53553 + 2.51564i) q^{12} +(4.54406 - 1.47646i) q^{13} +(-5.10756 - 1.88936i) q^{14} +(4.24139 - 3.08155i) q^{15} +(-2.81851 - 2.83831i) q^{16} +(-0.492895 + 1.51697i) q^{17} +(-0.726119 + 0.919421i) q^{18} +(-2.43570 + 3.35245i) q^{19} +(-4.63048 + 5.40242i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(-1.75492 + 3.78059i) q^{24} +(6.19453 + 4.50059i) q^{25} +(5.30271 + 4.18785i) q^{26} +(5.36555 + 1.74337i) q^{27} +(-1.78478 - 7.49188i) q^{28} +(-4.34434 - 5.97947i) q^{29} +(6.95370 + 2.57227i) q^{30} +(-1.10807 - 3.41029i) q^{31} +(1.12786 - 5.54328i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(-13.0292 + 4.23343i) q^{35} +(-1.65152 - 0.132886i) q^{36} +(0.358782 + 0.493821i) q^{37} +(-5.85558 - 0.235199i) q^{38} +(2.17574 - 6.69625i) q^{39} +(-9.98966 - 1.20896i) q^{40} +(7.52109 + 5.46439i) q^{41} +(-6.67652 + 4.45266i) q^{42} -3.06147i q^{43} +2.94725i q^{45} +(-2.54439 - 3.81517i) q^{46} +(3.90628 + 2.83808i) q^{47} +(-5.82512 + 0.901717i) q^{48} +(2.41912 - 7.44528i) q^{49} +(-0.434591 + 10.8197i) q^{50} +(1.38159 + 1.90159i) q^{51} +(-0.766414 + 9.52504i) q^{52} +(3.96404 - 1.28800i) q^{53} +(2.15897 + 7.68087i) q^{54} +(7.41421 - 7.97852i) q^{56} +(1.88701 + 5.80763i) q^{57} +(3.62637 - 9.80328i) q^{58} +(3.31609 + 4.56421i) q^{59} +(2.42989 + 10.1998i) q^{60} +(-2.05883 - 0.668955i) q^{61} +(3.14295 - 3.97965i) q^{62} +(-2.58083 - 1.87508i) q^{63} +(7.40701 - 3.02262i) q^{64} +16.9981 q^{65} +1.47363i q^{67} +(-2.42213 - 2.07604i) q^{68} +(-2.80870 + 3.86584i) q^{69} +(-15.2044 - 12.0078i) q^{70} +(3.21817 - 9.90451i) q^{71} +(-1.13954 - 2.04738i) q^{72} +(7.52109 - 5.46439i) q^{73} +(-0.299487 + 0.809613i) q^{74} +(10.7311 - 3.48674i) q^{75} +(-4.31795 - 7.07401i) q^{76} +(9.58579 - 2.69442i) q^{78} +(0.985790 + 3.03395i) q^{79} +(-6.41613 - 12.7021i) q^{80} +(4.71530 - 3.42586i) q^{81} +(-0.527659 + 13.1368i) q^{82} +(11.9998 + 3.89896i) q^{83} +(-10.4777 - 4.36149i) q^{84} +(-3.33544 + 4.59084i) q^{85} +(3.60201 - 2.40223i) q^{86} -10.8916 q^{87} -10.6569 q^{89} +(-3.46763 + 2.31261i) q^{90} +(-10.8144 + 14.8848i) q^{91} +(2.49229 - 5.98727i) q^{92} +(-5.02548 - 1.63288i) q^{93} +(-0.274054 + 6.82293i) q^{94} +(-11.9268 + 8.66536i) q^{95} +(-5.63170 - 6.14608i) q^{96} +(-5.29721 - 16.3031i) q^{97} +(10.6580 - 2.99581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.784666	+	1.17656i	0.554842	+	0.831956i
$2$	0.784666	+	1.17656i	0.554842	+	0.831956i
$3$	0.866175	−	1.19219i	0.500087	−	0.688310i	−0.482122	−	0.876104i	$-0.660134\pi$
$3$	0.866175	−	1.19219i	0.500087	−	0.688310i	0.982208	+	0.187794i	$0.0601337\pi$
$4$	−0.768600	+	1.84642i	−0.384300	+	0.923208i
$5$	3.38352	+	1.09937i	1.51316	+	0.491655i	0.943823	−	0.330451i	$-0.107201\pi$
$5$	3.38352	+	1.09937i	1.51316	+	0.491655i	0.569335	+	0.822106i	$0.307201\pi$
$6$	2.08234	+	0.0836407i	0.850113	+	0.0341462i
$7$	−3.11534	+	2.26343i	−1.17749	+	0.855494i	−0.991886	−	0.127131i	$-0.959423\pi$
$7$	−3.11534	+	2.26343i	−1.17749	+	0.855494i	−0.185601	+	0.982625i	$0.559423\pi$
$8$	−2.77552	+	0.544514i	−0.981294	+	0.192515i
$9$	0.255998	+	0.787881i	0.0853327	+	0.262627i
$10$	1.36145	+	4.84357i	0.430529	+	1.53167i
$11$		0			0
$11$		0			0
$12$	1.53553	+	2.51564i	0.443270	+	0.726202i
$13$	4.54406	−	1.47646i	1.26030	−	0.409495i	0.398696	−	0.917083i	$-0.369463\pi$
$13$	4.54406	−	1.47646i	1.26030	−	0.409495i	0.861600	+	0.507588i	$0.169463\pi$
$14$	−5.10756	−	1.88936i	−1.36505	−	0.504952i
$15$	4.24139	−	3.08155i	1.09512	−	0.795652i
$16$	−2.81851	−	2.83831i	−0.704627	−	0.709578i
$17$	−0.492895	+	1.51697i	−0.119545	+	0.367920i	−0.992868	−	0.119221i	$-0.961960\pi$
$17$	−0.492895	+	1.51697i	−0.119545	+	0.367920i	0.873323	+	0.487141i	$0.161960\pi$
$18$	−0.726119	+	0.919421i	−0.171148	+	0.216710i
$19$	−2.43570	+	3.35245i	−0.558788	+	0.769105i	−0.991172	−	0.132584i	$-0.957673\pi$
$19$	−2.43570	+	3.35245i	−0.558788	+	0.769105i	0.432384	+	0.901690i	$0.357673\pi$
$20$	−4.63048	+	5.40242i	−1.03541	+	1.20802i
$21$			5.67459i			1.23830i
$22$		0			0
$23$	−3.24264			−0.676137			−0.338069	−	0.941121i	$-0.609774\pi$
$23$	−3.24264			−0.676137			−0.338069	+	0.941121i	$0.609774\pi$
$24$	−1.75492	+	3.78059i	−0.358222	+	0.771709i
$25$	6.19453	+	4.50059i	1.23891	+	0.900117i
$26$	5.30271	+	4.18785i	1.03995	+	0.821305i
$27$	5.36555	+	1.74337i	1.03260	+	0.335512i
$28$	−1.78478	−	7.49188i	−0.337291	−	1.41583i
$29$	−4.34434	−	5.97947i	−0.806724	−	1.11036i	−0.991821	−	0.127640i	$-0.959260\pi$
$29$	−4.34434	−	5.97947i	−0.806724	−	1.11036i	0.185096	−	0.982720i	$-0.440740\pi$
$30$	6.95370	+	2.57227i	1.26957	+	0.469631i
$31$	−1.10807	−	3.41029i	−0.199015	−	0.612505i	−0.999906	−	0.0136954i	$-0.995640\pi$
$31$	−1.10807	−	3.41029i	−0.199015	−	0.612505i	0.800891	−	0.598810i	$-0.204360\pi$
$32$	1.12786	−	5.54328i	0.199380	−	0.979922i
$33$		0			0
$34$	−2.17157	+	0.610396i	−0.372422	+	0.104682i
$35$	−13.0292	+	4.23343i	−2.20233	+	0.715581i
$36$	−1.65152	−	0.132886i	−0.275253	−	0.0221477i
$37$	0.358782	+	0.493821i	0.0589833	+	0.0811836i	0.837490	−	0.546453i	$-0.184022\pi$
$37$	0.358782	+	0.493821i	0.0589833	+	0.0811836i	−0.778506	+	0.627637i	$0.784022\pi$
$38$	−5.85558	−	0.235199i	−0.949901	−	0.0381543i
$39$	2.17574	−	6.69625i	0.348398	−	1.07226i
$40$	−9.98966	−	1.20896i	−1.57950	−	0.191153i
$41$	7.52109	+	5.46439i	1.17460	+	0.853395i	0.991552	−	0.129710i	$-0.0414045\pi$
$41$	7.52109	+	5.46439i	1.17460	+	0.853395i	0.183045	+	0.983105i	$0.441405\pi$
$42$	−6.67652	+	4.45266i	−1.03021	+	0.687060i
$43$		−	3.06147i		−	0.466869i	−0.972372	−	0.233435i	$-0.925003\pi$
$43$		−	3.06147i		−	0.466869i	0.972372	−	0.233435i	$-0.0749965\pi$
$44$		0			0
$45$			2.94725i			0.439350i
$46$	−2.54439	−	3.81517i	−0.375150	−	0.562516i
$47$	3.90628	+	2.83808i	0.569789	+	0.413976i	0.835029	−	0.550206i	$-0.185451\pi$
$47$	3.90628	+	2.83808i	0.569789	+	0.413976i	−0.265239	+	0.964183i	$0.585451\pi$
$48$	−5.82512	+	0.901717i	−0.840784	+	0.130152i
$49$	2.41912	−	7.44528i	0.345588	−	1.06361i
$50$	−0.434591	+	10.8197i	−0.0614605	+	1.53014i
$51$	1.38159	+	1.90159i	0.193461	+	0.266276i
$52$	−0.766414	+	9.52504i	−0.106282	+	1.32088i
$53$	3.96404	−	1.28800i	0.544503	−	0.176920i	−0.0238333	−	0.999716i	$-0.507587\pi$
$53$	3.96404	−	1.28800i	0.544503	−	0.176920i	0.568337	+	0.822796i	$0.307587\pi$
$54$	2.15897	+	7.68087i	0.293799	+	1.04523i
$55$		0			0
$56$	7.41421	−	7.97852i	0.990766	−	1.06618i
$57$	1.88701	+	5.80763i	0.249941	+	0.769239i
$58$	3.62637	−	9.80328i	0.476166	−	1.28723i
$59$	3.31609	+	4.56421i	0.431718	+	0.594209i	0.968347	−	0.249610i	$-0.0803023\pi$
$59$	3.31609	+	4.56421i	0.431718	+	0.594209i	−0.536628	+	0.843819i	$0.680302\pi$
$60$	2.42989	+	10.1998i	0.313698	+	1.31679i
$61$	−2.05883	−	0.668955i	−0.263606	−	0.0856509i	0.174232	−	0.984705i	$-0.444256\pi$
$61$	−2.05883	−	0.668955i	−0.263606	−	0.0856509i	−0.437838	+	0.899054i	$0.644256\pi$
$62$	3.14295	−	3.97965i	0.399155	−	0.505416i
$63$	−2.58083	−	1.87508i	−0.325154	−	0.236238i
$64$	7.40701	−	3.02262i	0.925876	−	0.377827i
$65$	16.9981			2.10836
$66$		0			0
$67$			1.47363i			0.180032i	0.995940	+	0.0900160i	$0.0286918\pi$
$67$			1.47363i			0.180032i	−0.995940	+	0.0900160i	$0.971308\pi$
$68$	−2.42213	−	2.07604i	−0.293726	−	0.251756i
$69$	−2.80870	+	3.86584i	−0.338127	+	0.465392i
$70$	−15.2044	−	12.0078i	−1.81728	−	1.43521i
$71$	3.21817	−	9.90451i	0.381926	−	1.17545i	−0.556759	−	0.830674i	$-0.687955\pi$
$71$	3.21817	−	9.90451i	0.381926	−	1.17545i	0.938686	−	0.344775i	$-0.112045\pi$
$72$	−1.13954	−	2.04738i	−0.134296	−	0.241287i
$73$	7.52109	−	5.46439i	0.880277	−	0.639559i	−0.0530476	−	0.998592i	$-0.516894\pi$
$73$	7.52109	−	5.46439i	0.880277	−	0.639559i	0.933325	+	0.359033i	$0.116894\pi$
$74$	−0.299487	+	0.809613i	−0.0348147	+	0.0941156i
$75$	10.7311	−	3.48674i	1.23912	−	0.402614i
$76$	−4.31795	−	7.07401i	−0.495302	−	0.811445i
$77$		0			0
$78$	9.58579	−	2.69442i	1.08538	−	0.305083i
$79$	0.985790	+	3.03395i	0.110910	+	0.341346i	0.991072	−	0.133327i	$-0.0425662\pi$
$79$	0.985790	+	3.03395i	0.110910	+	0.341346i	−0.880162	+	0.474673i	$0.842566\pi$
$80$	−6.41613	−	12.7021i	−0.717345	−	1.42014i
$81$	4.71530	−	3.42586i	0.523922	−	0.380652i
$82$	−0.527659	+	13.1368i	−0.0582702	+	1.45071i
$83$	11.9998	+	3.89896i	1.31714	+	0.427966i	0.881513	−	0.472159i	$-0.156525\pi$
$83$	11.9998	+	3.89896i	1.31714	+	0.427966i	0.435631	+	0.900125i	$0.356525\pi$
$84$	−10.4777	−	4.36149i	−1.14321	−	0.475878i
$85$	−3.33544	+	4.59084i	−0.361780	+	0.497947i
$86$	3.60201	−	2.40223i	0.388415	−	0.259039i
$87$	−10.8916			−1.16770
$88$		0			0
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	−3.46763	+	2.31261i	−0.365520	+	0.243770i
$91$	−10.8144	+	14.8848i	−1.13366	+	1.56035i
$92$	2.49229	−	5.98727i	0.259840	−	0.624216i
$93$	−5.02548	−	1.63288i	−0.521118	−	0.169322i
$94$	−0.274054	+	6.82293i	−0.0282665	+	0.703731i
$95$	−11.9268	+	8.66536i	−1.22367	+	0.889047i
$96$	−5.63170	−	6.14608i	−0.574783	−	0.627281i
$97$	−5.29721	−	16.3031i	−0.537850	−	1.65533i	−0.737408	−	0.675447i	$-0.763951\pi$
$97$	−5.29721	−	16.3031i	−0.537850	−	1.65533i	0.199558	−	0.979886i	$-0.436049\pi$
$98$	10.6580	−	2.99581i	1.07662	−	0.302622i
$99$		0			0
$100$	−13.0711	+	7.97852i	−1.30711	+	0.797852i
$101$	4.54406	−	1.47646i	0.452151	−	0.146913i	−0.0740838	−	0.997252i	$-0.523603\pi$
$101$	4.54406	−	1.47646i	0.452151	−	0.146913i	0.526235	+	0.850339i	$0.323603\pi$
$102$	−1.15326	+	3.11763i	−0.114189	+	0.308692i
$103$	−7.53495	+	5.47446i	−0.742441	+	0.539415i	−0.893474	−	0.449114i	$-0.851740\pi$
$103$	−7.53495	+	5.47446i	−0.742441	+	0.539415i	0.151034	+	0.988529i	$0.451740\pi$
$104$	−11.8082	+	6.57223i	−1.15789	+	0.644461i
$105$	−6.23850	+	19.2001i	−0.608815	+	1.87374i
$106$	4.62586	+	3.65330i	0.449303	+	0.354840i
$107$	4.23519	−	5.82923i	0.409431	−	0.563533i	−0.553649	−	0.832750i	$-0.686765\pi$
$107$	4.23519	−	5.82923i	0.409431	−	0.563533i	0.963079	+	0.269217i	$0.0867649\pi$
$108$	−7.34295	+	8.56708i	−0.706575	+	0.824367i
$109$		−	4.32957i		−	0.414697i	−0.978267	−	0.207349i	$-0.933517\pi$
$109$		−	4.32957i		−	0.414697i	0.978267	−	0.207349i	$-0.0664835\pi$
$110$		0			0
$111$	0.899495			0.0853763
$112$	15.2049	+	2.46281i	1.43673	+	0.232714i
$113$	−2.81965	−	2.04860i	−0.265251	−	0.192716i	0.447208	−	0.894430i	$-0.352418\pi$
$113$	−2.81965	−	2.04860i	−0.265251	−	0.192716i	−0.712459	+	0.701714i	$0.752418\pi$
$114$	−5.35236	+	6.77723i	−0.501295	+	0.634746i
$115$	−10.9716	−	3.56487i	−1.02310	−	0.332426i
$116$	14.3797	−	3.42564i	1.33512	−	0.318063i
$117$	2.32654	+	3.20221i	0.215089	+	0.296045i
$118$	−2.76805	+	7.48296i	−0.254820	+	0.688863i
$119$	−1.89802	−	5.84152i	−0.173992	−	0.535491i
$120$	−10.0941	+	10.8624i	−0.921461	+	0.991595i
$121$		0			0
$122$	−0.828427	−	2.94725i	−0.0750023	−	0.266832i
$123$	13.0292	−	4.23343i	1.17480	−	0.381716i
$124$	7.14847	+	0.575188i	0.641952	+	0.0516534i
$125$	5.55583	+	7.64695i	0.496929	+	0.683964i
$126$	0.181064	−	4.50782i	0.0161305	−	0.401589i
$127$	4.55565	−	14.0208i	0.404249	−	1.24415i	−0.517273	−	0.855821i	$-0.673053\pi$
$127$	4.55565	−	14.0208i	0.404249	−	1.24415i	0.921521	−	0.388328i	$-0.126947\pi$
$128$	9.36832	+	6.34307i	0.828051	+	0.560653i
$129$	−3.64985	−	2.65177i	−0.321351	−	0.233475i
$130$	13.3378	+	19.9994i	1.16981	+	1.75406i
$131$			10.6382i			0.929465i	0.885451	+	0.464732i	$0.153850\pi$
$131$			10.6382i			0.929465i	−0.885451	+	0.464732i	$0.846150\pi$
$132$		0			0
$133$		−	15.9570i		−	1.38365i
$134$	−1.73381	+	1.15630i	−0.149779	+	0.0998894i
$135$	16.2378	+	11.7975i	1.39753	+	1.01537i
$136$	0.542026	−	4.47878i	0.0464783	−	0.384052i
$137$	0.927051	−	2.85317i	0.0792033	−	0.243763i	−0.903613	−	0.428350i	$-0.859095\pi$
$137$	0.927051	−	2.85317i	0.0792033	−	0.243763i	0.982816	+	0.184588i	$0.0590949\pi$
$138$	−6.75229	−	0.271217i	−0.574793	−	0.0230875i
$139$	−4.98056	−	6.85515i	−0.422445	−	0.581446i	0.543753	−	0.839245i	$-0.317003\pi$
$139$	−4.98056	−	6.85515i	−0.422445	−	0.581446i	−0.966199	+	0.257799i	$0.917003\pi$
$140$	2.19754	−	27.3111i	0.185726	−	2.30821i
$141$	6.76705	−	2.19875i	0.569888	−	0.185168i
$142$	14.1785	−	3.98535i	1.18983	−	0.334443i
$143$		0			0
$144$	1.51472	−	2.94725i	0.126227	−	0.245604i
$145$	−8.12551	−	25.0077i	−0.674787	−	2.07678i
$146$	12.3307	+	4.56132i	1.02050	+	0.377497i
$147$	−6.78079	−	9.33296i	−0.559270	−	0.769769i
$148$	−1.18756	+	0.282910i	−0.0976167	+	0.0232551i
$149$	−18.2494	−	5.92959i	−1.49505	−	0.485771i	−0.556480	−	0.830861i	$-0.687848\pi$
$149$	−18.2494	−	5.92959i	−1.49505	−	0.485771i	−0.938570	+	0.345090i	$0.887848\pi$
$150$	12.5227	+	9.88988i	1.02247	+	0.807505i
$151$	−6.23068	−	4.52685i	−0.507045	−	0.368390i	0.304656	−	0.952462i	$-0.401458\pi$
$151$	−6.23068	−	4.52685i	−0.507045	−	0.368390i	−0.811702	+	0.584072i	$0.801458\pi$
$152$	4.93487	−	10.6311i	0.400271	−	0.862293i
$153$	−1.32138			−0.106827
$154$		0			0
$155$		−	12.7570i		−	1.02466i
$156$	10.6918	+	9.16406i	0.856028	+	0.733712i
$157$	−8.00575	+	11.0190i	−0.638928	+	0.879409i	−0.998558	−	0.0536858i	$-0.982903\pi$
$157$	−8.00575	+	11.0190i	−0.638928	+	0.879409i	0.359630	+	0.933095i	$0.382903\pi$
$158$	−2.79612	+	3.54048i	−0.222447	+	0.281665i
$159$	1.89802	−	5.84152i	0.150523	−	0.463263i
$160$	9.91029	−	17.5159i	0.783477	−	1.38475i
$161$	10.1019	−	7.33948i	0.796143	−	0.578432i
$162$	7.73067	+	2.85969i	0.607379	+	0.224678i
$163$	−19.1401	+	6.21900i	−1.49917	+	0.487109i	−0.939775	−	0.341793i	$-0.888966\pi$
$163$	−19.1401	+	6.21900i	−1.49917	+	0.487109i	−0.559393	+	0.828902i	$0.688966\pi$
$164$	−15.8703	+	9.68714i	−1.23926	+	0.756438i
$165$		0			0
$166$	4.82843	+	17.1778i	0.374759	+	1.33326i
$167$	1.18995	+	3.66230i	0.0920813	+	0.283397i	0.986482	−	0.163869i	$-0.0523975\pi$
$167$	1.18995	+	3.66230i	0.0920813	+	0.283397i	−0.894401	+	0.447267i	$0.852398\pi$
$168$	−3.08989	−	15.7499i	−0.238390	−	1.21513i
$169$	7.95136	−	5.77700i	0.611643	−	0.444385i
$170$	−8.01862	−	0.322081i	−0.615000	−	0.0247025i
$171$	−3.26487	−	1.06082i	−0.249671	−	0.0811229i
$172$	5.65274	+	2.35304i	0.431018	+	0.179418i
$173$	−3.07191	+	4.22813i	−0.233553	+	0.321459i	−0.909667	−	0.415339i	$-0.863663\pi$
$173$	−3.07191	+	4.22813i	−0.233553	+	0.321459i	0.676113	+	0.736798i	$0.263663\pi$
$174$	−8.54628	−	12.8147i	−0.647892	−	0.971478i
$175$	−29.4848			−2.22884
$176$		0			0
$177$	8.31371			0.624897
$178$	−8.36207	−	12.5385i	−0.626763	−	0.939797i
$179$	11.6806	−	16.0770i	0.873051	−	1.20165i	−0.105247	−	0.994446i	$-0.533563\pi$
$179$	11.6806	−	16.0770i	0.873051	−	1.20165i	0.978298	−	0.207205i	$-0.0664367\pi$
$180$	−5.44185	−	2.26526i	−0.405612	−	0.168842i
$181$	14.5955	+	4.74238i	1.08488	+	0.352498i	0.796265	−	0.604948i	$-0.206806\pi$
$181$	14.5955	+	4.74238i	1.08488	+	0.352498i	0.288612	+	0.957446i	$0.406806\pi$
$182$	−25.9986	−	1.04428i	−1.92715	−	0.0774070i
$183$	−2.58083	+	1.87508i	−0.190780	+	0.138610i
$184$	9.00001	−	1.76566i	0.663490	−	0.130166i
$185$	0.671053	+	2.06529i	0.0493368	+	0.151843i
$186$	−2.02214	−	7.19406i	−0.148271	−	0.527494i
$187$		0			0
$188$	−8.24264	+	5.03127i	−0.601156	+	0.366943i
$189$	−20.6615	+	6.71332i	−1.50290	+	0.488322i
$190$	−19.5539	−	7.23327i	−1.41859	−	0.524757i
$191$	9.76570	−	7.09520i	0.706621	−	0.513390i	−0.175461	−	0.984486i	$-0.556141\pi$
$191$	9.76570	−	7.09520i	0.706621	−	0.513390i	0.882082	+	0.471096i	$0.156141\pi$
$192$	2.81224	−	11.4487i	0.202956	−	0.826236i
$193$	−0.985790	+	3.03395i	−0.0709587	+	0.218388i	−0.980247	−	0.197779i	$-0.936627\pi$
$193$	−0.985790	+	3.03395i	−0.0709587	+	0.218388i	0.909288	+	0.416168i	$0.136627\pi$
$194$	15.0251	−	19.0250i	1.07874	−	1.36592i
$195$	14.7234	−	20.2650i	1.05436	−	1.45120i
$196$	11.8877	+	10.1891i	0.849125	+	0.727795i
$197$		−	15.6788i		−	1.11707i	−0.829483	−	0.558533i	$-0.811365\pi$
$197$		−	15.6788i		−	1.11707i	0.829483	−	0.558533i	$-0.188635\pi$
$198$		0			0
$199$	16.8284			1.19294			0.596468	−	0.802637i	$-0.296570\pi$
$199$	16.8284			1.19294			0.596468	+	0.802637i	$0.296570\pi$
$200$	−19.6437	−	9.11846i	−1.38902	−	0.644772i
$201$	1.75684	+	1.27642i	0.123918	+	0.0900316i
$202$	5.30271	+	4.18785i	0.373098	+	0.294656i
$203$	27.0682	+	8.79499i	1.89981	+	0.617287i
$204$	−4.57301	+	1.08942i	−0.320175	+	0.0762747i
$205$	19.4404	+	26.7574i	1.35778	+	1.86882i
$206$	−12.3535	−	4.56972i	−0.860706	−	0.318387i
$207$	−0.830110	−	2.55482i	−0.0576966	−	0.177572i
$208$	−16.9981	−	8.73606i	−1.17861	−	0.605737i
$209$		0			0
$210$	−27.4853	+	7.72569i	−1.89666	+	0.533123i
$211$	21.9407	−	7.12896i	1.51046	−	0.490778i	0.567411	−	0.823435i	$-0.307945\pi$
$211$	21.9407	−	7.12896i	1.51046	−	0.490778i	0.943048	+	0.332657i	$0.107945\pi$
$212$	−0.668587	+	8.30923i	−0.0459187	+	0.570680i
$213$	−9.02054	−	12.4157i	−0.618077	−	0.850710i
$214$	10.1817	+	0.408963i	0.696004	+	0.0279561i
$215$	3.36570	−	10.3585i	0.229539	−	0.706447i
$216$	−15.8415	−	1.91715i	−1.07788	−	0.130445i
$217$	11.1709	+	8.11616i	0.758333	+	0.550961i
$218$	5.09401	−	3.39726i	0.345010	−	0.230092i
$219$		−	13.6997i		−	0.925739i
$220$		0			0
$221$			7.62096i			0.512641i
$222$	0.705803	+	1.05831i	0.0473704	+	0.0710293i
$223$	−20.8143	−	15.1225i	−1.39383	−	1.01268i	−0.995433	−	0.0954642i	$-0.969566\pi$
$223$	−20.8143	−	15.1225i	−1.39383	−	1.01268i	−0.398398	−	0.917213i	$-0.630434\pi$
$224$	9.03312	+	19.8220i	0.603551	+	1.32441i
$225$	−1.96014	+	6.03269i	−0.130676	+	0.402179i
$226$	0.197819	−	4.92496i	0.0131587	−	0.327604i
$227$	1.69033	+	2.32654i	0.112191	+	0.154418i	0.861420	−	0.507894i	$-0.169576\pi$
$227$	1.69033	+	2.32654i	0.112191	+	0.154418i	−0.749229	+	0.662311i	$0.769576\pi$
$228$	−12.1737	−	0.979530i	−0.806220	−	0.0648709i
$229$	−19.7206	+	6.40762i	−1.30318	+	0.423427i	−0.876685	−	0.481065i	$-0.840250\pi$
$229$	−19.7206	+	6.40762i	−1.30318	+	0.423427i	−0.426490	+	0.904492i	$0.640250\pi$
$230$	−4.41470	−	15.7060i	−0.291097	−	1.03562i
$231$		0			0
$232$	15.3137	+	14.2306i	1.00539	+	0.934284i
$233$	3.36570	+	10.3585i	0.220494	+	0.678611i	0.998718	+	0.0506239i	$0.0161210\pi$
$233$	3.36570	+	10.3585i	0.220494	+	0.678611i	−0.778224	+	0.627987i	$0.783879\pi$
$234$	−1.94204	+	5.24999i	−0.126955	+	0.343202i
$235$	10.0969	+	13.8972i	0.658648	+	0.906551i
$236$	−10.9762	+	2.61484i	−0.714488	+	0.170211i
$237$	4.47090	+	1.45268i	0.290416	+	0.0943620i
$238$	5.38360	−	6.81678i	0.348967	−	0.441866i
$239$	−18.6920	−	13.5806i	−1.20909	−	0.878453i	−0.213939	−	0.976847i	$-0.568629\pi$
$239$	−18.6920	−	13.5806i	−1.20909	−	0.878453i	−0.995148	+	0.0983940i	$0.968629\pi$
$240$	−20.7008	−	3.35300i	−1.33623	−	0.216436i
$241$	29.4848			1.89928			0.949641	−	0.313340i	$-0.101448\pi$
$241$	29.4848			1.89928			0.949641	+	0.313340i	$0.101448\pi$
$242$		0			0
$243$			8.33609i			0.534760i
$244$	2.81759	−	3.28730i	0.180378	−	0.210448i
$245$	16.3703	−	22.5318i	1.04586	−	1.43950i
$246$	15.2044	+	12.0078i	0.969400	+	0.765590i
$247$	−6.11822	+	18.8300i	−0.389293	+	1.19812i
$248$	4.93241	+	8.86195i	0.313209	+	0.562735i
$249$	15.0422	−	10.9288i	0.953260	−	0.692584i
$250$	−4.63764	+	12.5371i	−0.293310	+	0.792915i
$251$	13.7746	−	4.47562i	0.869442	−	0.282499i	0.159875	−	0.987137i	$-0.448891\pi$
$251$	13.7746	−	4.47562i	0.869442	−	0.282499i	0.709567	+	0.704638i	$0.248891\pi$
$252$	5.44581	−	3.32410i	0.343054	−	0.209399i
$253$		0			0
$254$	20.0711	−	5.64167i	1.25937	−	0.353990i
$255$	2.58407	+	7.95295i	0.161821	+	0.498033i
$256$	−0.112019	+	15.9996i	−0.00700117	+	0.999975i
$257$	−14.9549	+	10.8654i	−0.932861	+	0.677764i	−0.946692	−	0.322141i	$-0.895598\pi$
$257$	−14.9549	+	10.8654i	−0.932861	+	0.677764i	0.0138303	+	0.999904i	$0.495598\pi$
$258$	0.256063	−	6.37502i	0.0159418	−	0.396892i
$259$	−2.23545	−	0.726342i	−0.138904	−	0.0451327i
$260$	−13.0648	+	31.3856i	−0.810242	+	1.94645i
$261$	3.59897	−	4.95356i	0.222771	−	0.306618i
$262$	−12.5165	+	8.34744i	−0.773273	+	0.515707i
$263$	−7.04085			−0.434158			−0.217079	−	0.976154i	$-0.569653\pi$
$263$	−7.04085			−0.434158			−0.217079	+	0.976154i	$0.569653\pi$
$264$		0			0
$265$	14.8284			0.910903
$266$	18.7745	−	12.5209i	1.15114	−	0.767709i
$267$	−9.23071	+	12.7050i	−0.564910	+	0.777532i
$268$	−2.72093	−	1.13263i	−0.166207	−	0.0691863i
$269$	−7.24797	−	2.35501i	−0.441916	−	0.143587i	0.0796033	−	0.996827i	$-0.474635\pi$
$269$	−7.24797	−	2.35501i	−0.441916	−	0.143587i	−0.521520	+	0.853239i	$0.674635\pi$
$270$	−1.13920	+	28.3619i	−0.0693297	+	1.72605i
$271$	12.9959	−	9.44204i	0.789442	−	0.573563i	−0.118356	−	0.992971i	$-0.537762\pi$
$271$	12.9959	−	9.44204i	0.789442	−	0.573563i	0.907798	+	0.419408i	$0.137762\pi$
$272$	5.69487	−	2.87662i	0.345302	−	0.174420i
$273$	8.37828	+	25.7857i	0.507077	+	1.56062i
$274$	4.08436	−	1.14805i	0.246745	−	0.0693563i
$275$		0			0
$276$	−4.97918	−	8.15731i	−0.299712	−	0.491012i
$277$	−5.32370	+	1.72978i	−0.319870	+	0.103932i	−0.464551	−	0.885546i	$-0.653784\pi$
$277$	−5.32370	+	1.72978i	−0.319870	+	0.103932i	0.144681	+	0.989478i	$0.453784\pi$
$278$	4.15744	−	11.2389i	0.249347	−	0.674067i
$279$	2.40324	−	1.74605i	0.143878	−	0.104533i
$280$	33.8575	−	18.8445i	2.02338	−	1.12618i
$281$	−7.13972	+	21.9738i	−0.425920	+	1.31085i	0.476191	+	0.879342i	$0.342017\pi$
$281$	−7.13972	+	21.9738i	−0.425920	+	1.31085i	−0.902111	+	0.431505i	$0.857983\pi$
$282$	7.89683	+	6.23657i	0.470250	+	0.371383i
$283$	−10.4882	+	14.4357i	−0.623457	+	0.858115i	−0.997599	−	0.0692566i	$-0.977937\pi$
$283$	−10.4882	+	14.4357i	−0.623457	+	0.858115i	0.374142	+	0.927371i	$0.377937\pi$
$284$	15.8144	+	13.5547i	0.938410	+	0.804322i
$285$			21.7248i			1.28686i
$286$		0			0
$287$	−35.7990			−2.11315
$288$	4.65617	−	0.530445i	0.274368	−	0.0312568i
$289$	11.6950	+	8.49693i	0.687943	+	0.499820i
$290$	23.0474	−	29.1829i	1.35339	−	1.71368i
$291$	−24.0247	−	7.80611i	−1.40835	−	0.457602i
$292$	4.30884	+	18.0870i	0.252156	+	1.05846i
$293$	1.75427	+	2.41455i	0.102486	+	0.141059i	0.857180	−	0.515018i	$-0.172215\pi$
$293$	1.75427	+	2.41455i	0.102486	+	0.141059i	−0.754694	+	0.656077i	$0.772215\pi$
$294$	5.66016	−	15.3013i	0.330107	−	0.892389i
$295$	6.20230	+	19.0887i	0.361112	+	1.11139i
$296$	−1.26470	−	1.17525i	−0.0735090	−	0.0683098i
$297$		0			0
$298$	−7.34315	−	26.1243i	−0.425377	−	1.51334i
$299$	−14.7348	+	4.78761i	−0.852133	+	0.276875i
$300$	−1.80994	+	22.4940i	−0.104497	+	1.29869i
$301$	6.92940	+	9.53751i	0.399404	+	0.549733i
$302$	0.437127	−	10.8828i	0.0251539	−	0.626237i
$303$	2.17574	−	6.69625i	0.124993	−	0.384689i
$304$	16.3803	−	2.53564i	0.939477	−	0.145429i
$305$	−6.23068	−	4.52685i	−0.356767	−	0.259207i
$306$	−1.03684	−	1.55468i	−0.0592721	−	0.0888752i
$307$		−	28.1103i		−	1.60434i	−0.597095	−	0.802171i	$-0.703678\pi$
$307$		−	28.1103i		−	1.60434i	0.597095	−	0.802171i	$-0.296322\pi$
$308$		0			0
$309$			13.7249i			0.780783i
$310$	15.0094	−	10.0100i	0.852475	−	0.568527i
$311$	−8.48277	−	6.16309i	−0.481014	−	0.349477i	0.320704	−	0.947179i	$-0.396080\pi$
$311$	−8.48277	−	6.16309i	−0.481014	−	0.349477i	−0.801718	+	0.597702i	$0.796080\pi$
$312$	−2.39262	+	19.7703i	−0.135455	+	1.11927i
$313$	−0.565015	+	1.73894i	−0.0319365	+	0.0982906i	−0.965754	−	0.259459i	$-0.916456\pi$
$313$	−0.565015	+	1.73894i	−0.0319365	+	0.0982906i	0.933818	+	0.357749i	$0.116456\pi$
$314$	−19.2463	−	0.773061i	−1.08613	−	0.0436264i
$315$	−6.67088	−	9.18168i	−0.375862	−	0.517329i
$316$	−6.35961	−	0.511714i	−0.357756	−	0.0287862i
$317$	−1.74156	+	0.565868i	−0.0978159	+	0.0317823i	−0.357516	−	0.933907i	$-0.616376\pi$
$317$	−1.74156	+	0.565868i	−0.0978159	+	0.0317823i	0.259700	+	0.965689i	$0.416376\pi$
$318$	8.36223	−	2.35049i	0.468930	−	0.131809i
$319$		0			0
$320$	28.3848	−	2.08402i	1.58676	−	0.116500i
$321$	−3.28113	−	10.0983i	−0.183135	−	0.563631i
$322$	16.5620	+	6.12651i	0.922963	+	0.341417i
$323$	−3.88504	−	5.34730i	−0.216169	−	0.297532i
$324$	2.70140	+	11.3395i	0.150078	+	0.629973i
$325$	34.7932	+	11.3050i	1.92998	+	0.627089i
$326$	−22.3356	−	17.6397i	−1.23706	−	0.976972i
$327$	−5.16166	−	3.75017i	−0.285441	−	0.207385i
$328$	−23.8504	−	11.0712i	−1.31692	−	0.611304i
$329$	−18.5932			−1.02507
$330$		0			0
$331$			12.7570i			0.701186i	0.936528	+	0.350593i	$0.114020\pi$
$331$			12.7570i			0.701186i	−0.936528	+	0.350593i	$0.885980\pi$
$332$	−16.4221	+	19.1598i	−0.901280	+	1.05153i
$333$	−0.297224	+	0.409094i	−0.0162878	+	0.0224182i
$334$	−3.37521	+	4.27374i	−0.184683	+	0.233848i
$335$	−1.62007	+	4.98605i	−0.0885136	+	0.272417i
$336$	16.1063	−	15.9939i	0.878669	−	0.872538i
$337$	−4.94026	+	3.58931i	−0.269113	+	0.195522i	−0.714155	−	0.699988i	$-0.753189\pi$
$337$	−4.94026	+	3.58931i	−0.269113	+	0.195522i	0.445042	+	0.895510i	$0.353189\pi$
$338$	13.0362	+	4.82226i	0.709074	+	0.262297i
$339$	−4.88463	+	1.58711i	−0.265297	+	0.0862001i
$340$	−5.91299	−	9.68714i	−0.320677	−	0.525359i
$341$		0			0
$342$	−1.31371	−	4.67371i	−0.0710372	−	0.252725i
$343$	0.985790	+	3.03395i	0.0532276	+	0.163818i
$344$	1.66701	+	8.49716i	0.0898792	+	0.458136i
$345$	−13.7533	+	9.99235i	−0.740452	+	0.537970i
$346$	−7.38508	−	0.296634i	−0.397024	−	0.0159471i
$347$	−1.02942	−	0.334478i	−0.0552620	−	0.0179557i	0.281256	−	0.959633i	$-0.409249\pi$
$347$	−1.02942	−	0.334478i	−0.0552620	−	0.0179557i	−0.336518	+	0.941677i	$0.609249\pi$
$348$	8.37130	−	20.1105i	0.448749	−	1.07803i
$349$	10.9700	−	15.0989i	0.587211	−	0.808227i	−0.407252	−	0.913316i	$-0.633513\pi$
$349$	10.9700	−	15.0989i	0.587211	−	0.808227i	0.994463	+	0.105089i	$0.0335128\pi$
$350$	−23.1357	−	34.6907i	−1.23665	−	1.85430i
$351$	26.9554			1.43877
$352$		0			0
$353$	−16.7990			−0.894120			−0.447060	−	0.894504i	$-0.647529\pi$
$353$	−16.7990			−0.894120			−0.447060	+	0.894504i	$0.647529\pi$
$354$	6.52348	+	9.78160i	0.346719	+	0.519886i
$355$	21.7775	−	29.9742i	1.15583	−	1.59086i
$356$	8.19086	−	19.6770i	0.434115	−	1.04288i
$357$	−8.60821	−	2.79698i	−0.455595	−	0.148032i
$358$	28.0810	+	1.12792i	1.48413	+	0.0596123i
$359$	−14.5077	+	10.5404i	−0.765686	+	0.556303i	−0.900649	−	0.434547i	$-0.856908\pi$
$359$	−14.5077	+	10.5404i	−0.765686	+	0.556303i	0.134963	+	0.990851i	$0.456908\pi$
$360$	−1.60482	−	8.18015i	−0.0845814	−	0.431132i
$361$	0.565015	+	1.73894i	0.0297376	+	0.0915230i
$362$	5.87291	+	20.8937i	0.308673	+	1.09815i
$363$		0			0
$364$	−19.1716	−	31.4084i	−1.00486	−	1.64625i
$365$	31.4552	−	10.2204i	1.64644	−	0.534961i
$366$	−4.23124	−	1.56520i	−0.221171	−	0.0818141i
$367$	4.79661	−	3.48494i	0.250381	−	0.181912i	−0.455515	−	0.890228i	$-0.650545\pi$
$367$	4.79661	−	3.48494i	0.250381	−	0.181912i	0.705896	+	0.708316i	$0.250545\pi$
$368$	9.13941	+	9.20362i	0.476425	+	0.479772i
$369$	−2.37991	+	7.32460i	−0.123893	+	0.381303i
$370$	−1.90339	+	2.41010i	−0.0989525	+	0.125295i
$371$	−9.43406	+	12.9849i	−0.489792	+	0.674141i
$372$	6.87756	−	8.02411i	0.356585	−	0.416031i
$373$			28.7444i			1.48833i	0.667997	+	0.744164i	$0.267152\pi$
$373$			28.7444i			1.48833i	−0.667997	+	0.744164i	$0.732848\pi$
$374$		0			0
$375$	13.9289			0.719287
$376$	−12.3873	−	5.75012i	−0.638828	−	0.296540i
$377$	−28.5694	−	20.7569i	−1.47140	−	1.06903i
$378$	−24.1110	−	19.0418i	−1.24014	−	0.979405i
$379$	−2.56254	−	0.832621i	−0.131629	−	0.0427689i	0.242462	−	0.970161i	$-0.422045\pi$
$379$	−2.56254	−	0.832621i	−0.131629	−	0.0427689i	−0.374091	+	0.927392i	$0.622045\pi$
$380$	−6.83289	−	28.6821i	−0.350520	−	1.47136i
$381$	−12.7695	−	17.5757i	−0.654201	−	0.900431i
$382$	16.0108	+	5.92260i	0.819181	+	0.303027i
$383$	0.383997	+	1.18182i	0.0196213	+	0.0603883i	0.960388	−	0.278667i	$-0.0898926\pi$
$383$	0.383997	+	1.18182i	0.0196213	+	0.0603883i	−0.940766	+	0.339055i	$0.889893\pi$
$384$	15.6767	−	5.67459i	0.800001	−	0.289580i
$385$		0			0
$386$	−4.34315	+	1.22079i	−0.221060	+	0.0621367i
$387$	2.41207	−	0.783730i	0.122613	−	0.0398392i
$388$	34.1738	+	2.74973i	1.73491	+	0.139596i
$389$	−9.73810	−	13.4033i	−0.493741	−	0.679577i	0.487331	−	0.873217i	$-0.337970\pi$
$389$	−9.73810	−	13.4033i	−0.493741	−	0.679577i	−0.981073	+	0.193641i	$0.937970\pi$
$390$	35.3959	+	1.42173i	1.79234	+	0.0719923i
$391$	1.59828	−	4.91900i	0.0808285	−	0.248765i
$392$	−2.66025	+	21.9817i	−0.134363	+	1.11025i
$393$	12.6828	+	9.21456i	0.639760	+	0.464813i
$394$	18.4470	−	12.3026i	0.929348	−	0.619795i
$395$			11.3492i			0.571040i
$396$		0			0
$397$			36.0821i			1.81091i	0.424441	+	0.905455i	$0.360470\pi$
$397$			36.0821i			1.81091i	−0.424441	+	0.905455i	$0.639530\pi$
$398$	13.2047	+	19.7997i	0.661891	+	0.992469i
$399$	−19.0238	−	13.8216i	−0.952382	−	0.691946i
$400$	−4.68526	−	30.2669i	−0.234263	−	1.51335i
$401$	−3.54005	+	10.8952i	−0.176782	+	0.544078i	−0.999710	−	0.0240666i	$-0.992339\pi$
$401$	−3.54005	+	10.8952i	−0.176782	+	0.544078i	0.822929	+	0.568145i	$0.192339\pi$
$402$	−0.123255	+	3.06859i	−0.00614741	+	0.153048i
$403$	−10.0703	−	13.8605i	−0.501636	−	0.690443i
$404$	−0.766414	+	9.52504i	−0.0381305	+	0.473888i
$405$	19.7206	−	6.40762i	0.979926	−	0.318397i
$406$	10.8916	+	38.7485i	0.540542	+	1.92306i
$407$		0			0
$408$	−4.87006	−	4.52560i	−0.241104	−	0.224051i
$409$	−1.97158	−	6.06790i	−0.0974883	−	0.300038i	0.890406	−	0.455167i	$-0.150421\pi$
$409$	−1.97158	−	6.06790i	−0.0974883	−	0.300038i	−0.987894	+	0.155129i	$0.950421\pi$
$410$	−16.2276	+	43.8684i	−0.801422	+	2.16651i
$411$	−2.59853	−	3.57656i	−0.128176	−	0.176419i
$412$	−4.31677	−	18.1203i	−0.212672	−	0.892724i
$413$	−20.6615	−	6.71332i	−1.01669	−	0.330341i
$414$	2.35454	−	2.98135i	0.115719	−	0.146525i
$415$	36.3150	+	26.3844i	1.78264	+	1.29516i
$416$	−3.05932	−	26.8542i	−0.149995	−	1.31664i
$417$	−12.4867			−0.611474
$418$		0			0
$419$			11.7890i			0.575931i	0.957641	+	0.287965i	$0.0929788\pi$
$419$			11.7890i			0.575931i	−0.957641	+	0.287965i	$0.907021\pi$
$420$	−30.6565	−	26.2761i	−1.49588	−	1.28214i
$421$	−2.44991	+	3.37202i	−0.119402	+	0.164342i	−0.864534	−	0.502574i	$-0.832386\pi$
$421$	−2.44991	+	3.37202i	−0.119402	+	0.164342i	0.745132	+	0.666917i	$0.232386\pi$
$422$	25.6038	+	20.2207i	1.24637	+	0.984330i
$423$	−1.23607	+	3.80423i	−0.0600997	+	0.184968i
$424$	−10.3009	+	5.73333i	−0.500258	+	0.278435i
$425$	−9.88052	+	7.17862i	−0.479276	+	0.348214i
$426$	7.52975	−	20.3554i	0.364818	−	0.986222i
$427$	7.92809	−	2.57599i	0.383667	−	0.124661i
$428$	7.50803	+	12.3003i	0.362914	+	0.594556i
$429$		0			0
$430$	14.8284	−	4.16804i	0.715090	−	0.201001i
$431$	−7.92135	−	24.3794i	−0.381558	−	1.17431i	−0.938947	−	0.344063i	$-0.888197\pi$
$431$	−7.92135	−	24.3794i	−0.381558	−	1.17431i	0.557389	−	0.830252i	$-0.311803\pi$
$432$	−10.1746	−	20.1428i	−0.489526	−	0.969121i
$433$	2.70466	−	1.96505i	0.129978	−	0.0944344i	−0.520897	−	0.853620i	$-0.674402\pi$
$433$	2.70466	−	1.96505i	0.129978	−	0.0944344i	0.650875	+	0.759185i	$0.274402\pi$
$434$	−0.783723	+	19.5118i	−0.0376199	+	0.936595i
$435$	−36.8521	−	11.9740i	−1.76692	−	0.574107i
$436$	7.99419	+	3.32771i	0.382852	+	0.159368i
$437$	7.89810	−	10.8708i	0.377817	−	0.520021i
$438$	16.1185	−	10.7497i	0.770173	−	0.513639i
$439$	−4.51146			−0.215320			−0.107660	−	0.994188i	$-0.534336\pi$
$439$	−4.51146			−0.215320			−0.107660	+	0.994188i	$0.534336\pi$
$440$		0			0
$441$	6.48528			0.308823
$442$	−8.96654	+	5.97991i	−0.426495	+	0.284435i
$443$	−3.61331	+	4.97330i	−0.171674	+	0.236289i	−0.886181	−	0.463340i	$-0.846651\pi$
$443$	−3.61331	+	4.97330i	−0.171674	+	0.236289i	0.714507	+	0.699628i	$0.246651\pi$
$444$	−0.691352	+	1.66084i	−0.0328101	+	0.0788201i
$445$	−36.0577	−	11.7159i	−1.70930	−	0.555385i
$446$	1.46028	−	36.3555i	0.0691461	−	1.72148i
$447$	−22.8764	+	16.6207i	−1.08202	+	0.786130i
$448$	−16.2339	+	26.1817i	−0.766978	+	1.23697i
$449$	5.35933	+	16.4943i	0.252922	+	0.778415i	0.994232	+	0.107252i	$0.0342050\pi$
$449$	5.35933	+	16.4943i	0.252922	+	0.778415i	−0.741310	+	0.671163i	$0.765795\pi$
$450$	−8.63589	+	2.42742i	−0.407100	+	0.114430i
$451$		0			0
$452$	5.94975	−	3.63170i	0.279853	−	0.170821i
$453$	−10.7937	+	3.50709i	−0.507133	+	0.164778i
$454$	−1.41097	+	3.81433i	−0.0662203	+	0.179015i
$455$	−52.9549	+	38.4740i	−2.48256	+	1.80369i
$456$	−8.39977	−	15.0917i	−0.393355	−	0.706732i
$457$	8.12551	−	25.0077i	0.380095	−	1.16981i	−0.559881	−	0.828573i	$-0.689153\pi$
$457$	8.12551	−	25.0077i	0.380095	−	1.16981i	0.939976	−	0.341240i	$-0.110847\pi$
$458$	−23.0131	−	18.1747i	−1.07533	−	0.849248i
$459$	−5.28930	+	7.28010i	−0.246883	+	0.339806i
$460$	15.0150	−	17.5181i	0.700077	−	0.816785i
$461$			4.85483i			0.226112i	0.993589	+	0.113056i	$0.0360640\pi$
$461$			4.85483i			0.226112i	−0.993589	+	0.113056i	$0.963936\pi$
$462$		0			0
$463$	7.72792			0.359147			0.179573	−	0.983745i	$-0.442528\pi$
$463$	7.72792			0.359147			0.179573	+	0.983745i	$0.442528\pi$
$464$	−4.72704	+	29.1838i	−0.219447	+	1.35482i
$465$	−15.2087	−	11.0498i	−0.705287	−	0.512421i
$466$	−9.54654	+	12.0879i	−0.442235	+	0.559963i
$467$	−27.3086	−	8.87312i	−1.26369	−	0.410599i	−0.400884	−	0.916129i	$-0.631297\pi$
$467$	−27.3086	−	8.87312i	−1.26369	−	0.410599i	−0.862809	+	0.505530i	$0.831297\pi$
$468$	−7.70080	+	1.83455i	−0.355969	+	0.0848020i
$469$	−3.33544	−	4.59084i	−0.154016	−	0.211985i
$470$	−8.42821	+	22.7842i	−0.388764	+	1.05096i
$471$	6.20230	+	19.0887i	0.285787	+	0.879562i
$472$	−11.6891	−	10.8624i	−0.538036	−	0.499982i
$473$		0			0
$474$	1.79899	+	6.40017i	0.0826303	+	0.293970i
$475$	−30.1760	+	9.80478i	−1.38457	+	0.449874i
$476$	12.2447	+	0.985246i	0.561235	+	0.0451587i
$477$	2.02958	+	2.79347i	0.0929279	+	0.127904i
$478$	1.31138	−	32.6485i	0.0599812	−	1.49331i
$479$	−1.18995	+	3.66230i	−0.0543704	+	0.167335i	−0.974554	−	0.224152i	$-0.928039\pi$
$479$	−1.18995	+	3.66230i	−0.0543704	+	0.167335i	0.920184	+	0.391486i	$0.128039\pi$
$480$	−12.2982	−	26.9867i	−0.561332	−	1.23177i
$481$	2.35943	+	1.71423i	0.107581	+	0.0781620i
$482$	23.1357	+	34.6907i	1.05380	+	1.58012i
$483$		−	18.4007i		−	0.837259i
$484$		0			0
$485$		−	60.9857i		−	2.76922i
$486$	−9.80793	+	6.54104i	−0.444897	+	0.296708i
$487$	28.2343	+	20.5134i	1.27942	+	0.929551i	0.999535	−	0.0304831i	$-0.00970456\pi$
$487$	28.2343	+	20.5134i	1.27942	+	0.929551i	0.279882	+	0.960034i	$0.409705\pi$
$488$	6.07858	+	0.735635i	0.275165	+	0.0333007i
$489$	−9.16447	+	28.2053i	−0.414432	+	1.27549i
$490$	39.3552	+	1.58077i	1.77789	+	0.0714118i
$491$	13.7784	+	18.9643i	0.621810	+	0.855849i	0.997483	−	0.0709038i	$-0.0225883\pi$
$491$	13.7784	+	18.9643i	0.621810	+	0.855849i	−0.375673	+	0.926752i	$0.622588\pi$
$492$	−2.19754	+	27.3111i	−0.0990725	+	1.23128i
$493$	11.2120	−	3.64300i	0.504964	−	0.164073i
$494$	−26.9554	+	7.57675i	−1.21278	+	0.340894i
$495$		0			0
$496$	−6.55635	+	12.7570i	−0.294389	+	0.572805i
$497$	12.3924	+	38.1400i	0.555876	+	1.71081i
$498$	24.6615	+	9.12263i	1.10511	+	0.408795i
$499$	−18.7586	−	25.8190i	−0.839752	−	1.15582i	−0.986029	−	0.166576i	$-0.946729\pi$
$499$	−18.7586	−	25.8190i	−0.839752	−	1.15582i	0.146277	−	0.989244i	$-0.453271\pi$
$500$	−18.3897	+	4.38094i	−0.822411	+	0.195922i
$501$	5.39686	+	1.75355i	0.241114	+	0.0783426i
$502$	16.0743	+	12.6948i	0.717430	+	0.566595i
$503$	−8.81151	−	6.40193i	−0.392886	−	0.285448i	0.373751	−	0.927529i	$-0.378071\pi$
$503$	−8.81151	−	6.40193i	−0.392886	−	0.285448i	−0.766637	+	0.642081i	$0.778071\pi$
$504$	8.18415	+	3.79903i	0.364551	+	0.169222i
$505$	16.9981			0.756406
$506$		0			0
$507$		−	14.4834i		−	0.643231i
$508$	22.3869	+	19.1880i	0.993256	+	0.851332i
$509$	1.79391	−	2.46910i	0.0795136	−	0.109441i	−0.767407	−	0.641160i	$-0.778454\pi$
$509$	1.79391	−	2.46910i	0.0795136	−	0.109441i	0.846921	+	0.531719i	$0.178454\pi$
$510$	−7.32951	+	9.28073i	−0.324556	+	0.410958i
$511$	−11.0625	+	34.0469i	−0.489376	+	1.50614i
$512$	−18.9124	+	12.4225i	−0.835820	+	0.549004i
$513$	−18.9134	+	13.7414i	−0.835048	+	0.606698i
$514$	−24.5184	−	9.06970i	−1.08146	−	0.400047i
$515$	−31.5132	+	10.2392i	−1.38864	+	0.451195i
$516$	7.70154	−	4.70099i	0.339041	−	0.206949i
$517$		0			0
$518$	−0.899495	−	3.20009i	−0.0395215	−	0.140604i
$519$	2.37991	+	7.32460i	0.104466	+	0.321514i
$520$	−47.1786	+	9.25571i	−2.06892	+	0.405890i
$521$	−1.20162	+	0.873026i	−0.0526438	+	0.0382480i	−0.613796	−	0.789465i	$-0.710358\pi$
$521$	−1.20162	+	0.873026i	−0.0526438	+	0.0382480i	0.561152	+	0.827713i	$0.310358\pi$
$522$	8.65216	+	0.347528i	0.378695	+	0.0152109i
$523$	27.4410	+	8.91612i	1.19991	+	0.389875i	0.839728	−	0.543007i	$-0.182714\pi$
$523$	27.4410	+	8.91612i	1.19991	+	0.389875i	0.360183	+	0.932882i	$0.382714\pi$
$524$	−19.6426	−	8.17653i	−0.858090	−	0.357193i
$525$	−25.5390	+	35.1514i	−1.11461	+	1.53413i
$526$	−5.52471	−	8.28400i	−0.240889	−	0.361200i
$527$	5.71948			0.249144
$528$		0			0
$529$	−12.4853			−0.542838
$530$	11.6354	+	17.4466i	0.505408	+	0.757831i
$531$	−2.74714	+	3.78111i	−0.119216	+	0.164086i
$532$	29.4634	+	12.2646i	1.27740	+	0.531737i
$533$	42.2442	+	13.7260i	1.82980	+	0.594539i
$534$	−22.1912	−	0.891347i	−0.960308	−	0.0385723i
$535$	20.7384	−	15.0673i	0.896597	−	0.651416i
$536$	−0.802409	−	4.09008i	−0.0346588	−	0.176664i
$537$	−9.04934	−	27.8510i	−0.390508	−	1.20186i
$538$	−2.91642	−	10.3756i	−0.125736	−	0.447323i
$539$		0			0
$540$	−34.2635	+	20.9143i	−1.47446	+	0.900007i
$541$	4.54406	−	1.47646i	0.195365	−	0.0634778i	−0.209700	−	0.977766i	$-0.567249\pi$
$541$	4.54406	−	1.47646i	0.195365	−	0.0634778i	0.405065	+	0.914288i	$0.367249\pi$
$542$	21.3066	+	7.88160i	0.915195	+	0.338544i
$543$	18.2961	−	13.2929i	0.785161	−	0.570453i
$544$	7.85309	+	4.44319i	0.336698	+	0.190500i
$545$	4.75981	−	14.6492i	0.203888	−	0.627503i
$546$	−23.7644	+	30.0907i	−1.01702	+	1.28776i
$547$	−23.8299	+	32.7991i	−1.01889	+	1.40239i	−0.105919	+	0.994375i	$0.533778\pi$
$547$	−23.8299	+	32.7991i	−1.01889	+	1.40239i	−0.912976	+	0.408013i	$0.866222\pi$
$548$	4.55561	+	3.90467i	0.194606	+	0.166799i
$549$		−	1.79337i		−	0.0765390i
$550$		0			0
$551$	30.6274			1.30477
$552$	5.69059	−	12.2591i	0.242207	−	0.521781i
$553$	−9.93818	−	7.22051i	−0.422615	−	0.307047i
$554$	−6.21251	−	4.90637i	−0.263944	−	0.208452i
$555$	3.04346	+	0.988881i	0.129188	+	0.0419757i
$556$	16.4855	−	3.92732i	0.699141	−	0.166555i
$557$	−14.3507	−	19.7520i	−0.608057	−	0.836919i	0.388359	−	0.921508i	$-0.373042\pi$
$557$	−14.3507	−	19.7520i	−0.608057	−	0.836919i	−0.996416	+	0.0845892i	$0.973042\pi$
$558$	3.94008	+	1.45749i	0.166797	+	0.0617005i
$559$	−4.52012	−	13.9115i	−0.191181	−	0.588394i
$560$	48.7386	+	25.0489i	2.05958	+	1.05851i
$561$		0			0
$562$	−31.4558	+	8.84175i	−1.32688	+	0.372967i
$563$	−17.3235	+	5.62873i	−0.730097	+	0.237223i	−0.650395	−	0.759596i	$-0.725397\pi$
$563$	−17.3235	+	5.62873i	−0.730097	+	0.237223i	−0.0797014	+	0.996819i	$0.525397\pi$
$564$	−1.14135	+	14.1847i	−0.0480594	+	0.597286i
$565$	−7.28819	−	10.0313i	−0.306616	−	0.422021i
$566$	−25.2142	−	1.01277i	−1.05983	−	0.0425700i
$567$	−6.93556	+	21.3454i	−0.291266	+	0.896424i
$568$	−3.53895	+	29.2425i	−0.148491	+	1.22699i
$569$	−11.3923	−	8.27702i	−0.477592	−	0.346991i	0.322801	−	0.946467i	$-0.395376\pi$
$569$	−11.3923	−	8.27702i	−0.477592	−	0.346991i	−0.800393	+	0.599476i	$0.795376\pi$
$570$	−25.5606	+	17.0467i	−1.07061	+	0.714007i
$571$			40.3881i			1.69019i	0.534618	+	0.845094i	$0.320456\pi$
$571$			40.3881i			1.69019i	−0.534618	+	0.845094i	$0.679544\pi$
$572$		0			0
$573$		−	17.7882i		−	0.743114i
$574$	−28.0902	−	42.1198i	−1.17246	−	1.75804i
$575$	−20.0866	−	14.5938i	−0.837670	−	0.608603i
$576$	4.27764	+	5.06206i	0.178235	+	0.210919i
$577$	−7.83146	+	24.1028i	−0.326028	+	1.00341i	0.644946	+	0.764228i	$0.276880\pi$
$577$	−7.83146	+	24.1028i	−0.326028	+	1.00341i	−0.970974	+	0.239183i	$0.923120\pi$
$578$	−0.820491	+	20.4272i	−0.0341279	+	0.849659i
$579$	2.76317	+	3.80318i	0.114833	+	0.158055i
$580$	52.4200	+	4.21787i	2.17662	+	0.175138i
$581$	−46.2083	+	15.0140i	−1.91704	+	0.622885i
$582$	−9.66700	−	34.3918i	−0.400710	−	1.42559i
$583$		0			0
$584$	−17.8995	+	19.2619i	−0.740686	+	0.797062i
$585$	4.35149	+	13.3925i	0.179912	+	0.553712i
$586$	−1.46435	+	3.95862i	−0.0604917	+	0.163529i
$587$	−3.88504	−	5.34730i	−0.160353	−	0.220707i	0.721279	−	0.692645i	$-0.243555\pi$
$587$	−3.88504	−	5.34730i	−0.160353	−	0.220707i	−0.881632	+	0.471938i	$0.843555\pi$
$588$	22.4442	−	5.34686i	0.925585	−	0.220501i
$589$	14.1317	+	4.59168i	0.582288	+	0.189197i
$590$	−17.5923	+	22.2757i	−0.724265	+	0.917074i
$591$	−18.6920	−	13.5806i	−0.768887	−	0.558629i
$592$	0.390387	−	2.41017i	0.0160448	−	0.0990574i
$593$	−21.7832			−0.894531			−0.447265	−	0.894401i	$-0.647602\pi$
$593$	−21.7832			−0.894531			−0.447265	+	0.894401i	$0.647602\pi$
$594$		0			0
$595$		−	21.8516i		−	0.895826i
$596$	24.9750	−	29.1385i	1.02302	−	1.19356i
$597$	14.5764	−	20.0627i	0.596571	−	0.821110i
$598$	−17.1948	−	13.5797i	−0.703147	−	0.555315i
$599$	13.2165	−	40.6763i	0.540012	−	1.66199i	−0.192550	−	0.981287i	$-0.561676\pi$
$599$	13.2165	−	40.6763i	0.540012	−	1.66199i	0.732562	−	0.680700i	$-0.238324\pi$
$600$	−27.8858	+	15.5207i	−1.13843	+	0.633632i
$601$	−21.4943	+	15.6165i	−0.876769	+	0.637010i	−0.932395	−	0.361442i	$-0.882285\pi$
$601$	−21.4943	+	15.6165i	−0.876769	+	0.637010i	0.0556256	+	0.998452i	$0.482285\pi$
$602$	−5.78421	+	15.6366i	−0.235747	+	0.637302i
$603$	−1.16104	+	0.377245i	−0.0472813	+	0.0153626i
$604$	13.1474	−	8.02509i	0.534958	−	0.326536i
$605$		0			0
$606$	9.58579	−	2.69442i	0.389396	−	0.109453i
$607$	10.0971	+	31.0756i	0.409828	+	1.26132i	0.916796	+	0.399356i	$0.130766\pi$
$607$	10.0971	+	31.0756i	0.409828	+	1.26132i	−0.506968	+	0.861965i	$0.669234\pi$
$608$	15.8364	+	17.2829i	0.642252	+	0.700913i
$609$	33.9311	−	24.6524i	1.37496	−	0.998965i
$610$	0.437127	−	10.8828i	0.0176988	−	0.440634i
$611$	21.9407	+	7.12896i	0.887625	+	0.288407i
$612$	1.01561	−	2.43981i	0.0410536	−	0.0986234i
$613$	−11.2335	+	15.4616i	−0.453718	+	0.624490i	−0.973191	−	0.229997i	$-0.926128\pi$
$613$	−11.2335	+	15.4616i	−0.453718	+	0.624490i	0.519473	+	0.854487i	$0.326128\pi$
$614$	33.0736	−	22.0572i	1.33474	−	0.890157i
$615$	48.7386			1.96533
$616$		0			0
$617$	13.7990			0.555526			0.277763	−	0.960650i	$-0.410407\pi$
$617$	13.7990			0.555526			0.277763	+	0.960650i	$0.410407\pi$
$618$	−16.1482	+	10.7695i	−0.649577	+	0.433212i
$619$	−1.58374	+	2.17983i	−0.0636558	+	0.0876147i	−0.839658	−	0.543116i	$-0.817245\pi$
$619$	−1.58374	+	2.17983i	−0.0636558	+	0.0876147i	0.776002	+	0.630730i	$0.217245\pi$
$620$	23.5547	+	9.80500i	0.945978	+	0.393778i
$621$	−17.3985	−	5.65313i	−0.698179	−	0.226852i
$622$	0.595128	−	14.8165i	0.0238625	−	0.594087i
$623$	33.1997	−	24.1210i	1.33012	−	0.966387i
$624$	−25.1384	+	12.6980i	−1.00634	+	0.508327i
$625$	−1.43905	−	4.42893i	−0.0575619	−	0.177157i
$626$	−2.48932	+	0.699709i	−0.0994931	+	0.0279660i
$627$		0			0
$628$	−14.1924	−	23.2511i	−0.566338	−	0.927821i
$629$	−0.925955	+	0.300861i	−0.0369202	+	0.0119961i
$630$	5.56841	−	15.0533i	0.221851	−	0.599736i
$631$	−5.35183	+	3.88833i	−0.213053	+	0.154792i	−0.689194	−	0.724577i	$-0.742035\pi$
$631$	−5.35183	+	3.88833i	−0.213053	+	0.154792i	0.476141	+	0.879369i	$0.342035\pi$
$632$	−4.38810	−	7.88400i	−0.174549	−	0.313609i
$633$	10.5054	−	32.3323i	0.417553	−	1.28510i
$634$	−2.03232	−	1.60504i	−0.0807139	−	0.0637443i
$635$	30.8283	−	42.4315i	1.22338	−	1.68384i
$636$	9.32705	+	7.99433i	0.369842	+	0.316996i
$637$		−	37.4035i		−	1.48198i
$638$		0			0
$639$	8.62742			0.341295
$640$	24.7245	+	31.7612i	0.977323	+	1.25547i
$641$	−1.75684	−	1.27642i	−0.0693910	−	0.0504155i	0.552549	−	0.833480i	$-0.313655\pi$
$641$	−1.75684	−	1.27642i	−0.0693910	−	0.0504155i	−0.621940	+	0.783065i	$0.713655\pi$
$642$	9.30667	−	11.7842i	0.367305	−	0.465086i
$643$	38.5207	+	12.5161i	1.51911	+	0.493588i	0.945522	−	0.325559i	$-0.105552\pi$
$643$	38.5207	+	12.5161i	1.51911	+	0.493588i	0.573585	+	0.819146i	$0.305552\pi$
$644$	5.78739	+	24.2935i	0.228055	+	0.957297i
$645$	−9.43406	−	12.9849i	−0.371466	−	0.511278i
$646$	3.24298	−	8.76684i	0.127593	−	0.344927i
$647$	8.46236	+	26.0445i	0.332690	+	1.02391i	0.967849	+	0.251532i	$0.0809345\pi$
$647$	8.46236	+	26.0445i	0.332690	+	1.02391i	−0.635159	+	0.772381i	$0.719065\pi$
$648$	−11.2220	+	12.0761i	−0.440840	+	0.474394i
$649$		0			0
$650$	14.0000	+	49.8071i	0.549125	+	1.95359i
$651$	19.3520	−	6.28784i	0.758464	−	0.246440i
$652$	3.22822	−	40.1205i	0.126427	−	1.57124i
$653$	−1.79391	−	2.46910i	−0.0702011	−	0.0966235i	0.772473	−	0.635048i	$-0.219020\pi$
$653$	−1.79391	−	2.46910i	−0.0702011	−	0.0966235i	−0.842674	+	0.538425i	$0.819020\pi$
$654$	0.362128	−	9.01564i	0.0141603	−	0.352540i
$655$	−11.6954	+	35.9946i	−0.456976	+	1.40643i
$656$	−5.68861	−	36.7486i	−0.222103	−	1.43479i
$657$	6.23068	+	4.52685i	0.243082	+	0.176609i
$658$	−14.5894	−	21.8760i	−0.568755	−	0.852816i
$659$			49.2011i			1.91660i	0.285763	+	0.958300i	$0.407753\pi$
$659$			49.2011i			1.91660i	−0.285763	+	0.958300i	$0.592247\pi$
$660$		0			0
$661$			28.5659i			1.11108i	0.831488	+	0.555542i	$0.187489\pi$
$661$			28.5659i			1.11108i	−0.831488	+	0.555542i	$0.812511\pi$
$662$	−15.0094	+	10.0100i	−0.583356	+	0.389048i
$663$	9.08562	+	6.60109i	0.352856	+	0.256365i
$664$	−35.4286	−	4.28760i	−1.37490	−	0.166391i
$665$	17.5428	−	53.9911i	0.680279	−	2.09368i
$666$	−0.714547	−	0.0287010i	−0.0276881	−	0.00111214i
$667$	14.0871	+	19.3893i	0.545456	+	0.750756i
$668$	−7.67673	−	0.617693i	−0.297022	−	0.0238993i
$669$	−36.0577	+	11.7159i	−1.39407	+	0.452961i
$670$	−7.13761	+	2.00627i	−0.275750	+	0.0775090i
$671$		0			0
$672$	31.4558	+	6.40017i	1.21344	+	0.246892i
$673$	−2.95737	−	9.10184i	−0.113998	−	0.350850i	0.877739	−	0.479140i	$-0.159051\pi$
$673$	−2.95737	−	9.10184i	−0.113998	−	0.350850i	−0.991737	+	0.128290i	$0.959051\pi$
$674$	−8.09950	−	2.99612i	−0.311981	−	0.115406i
$675$	25.3908	+	34.9475i	0.977293	+	1.34513i
$676$	4.55534	+	19.1217i	0.175205	+	0.735451i
$677$	−31.4552	−	10.2204i	−1.20892	−	0.392802i	−0.365886	−	0.930660i	$-0.619234\pi$
$677$	−31.4552	−	10.2204i	−1.20892	−	0.392802i	−0.843036	+	0.537857i	$0.819234\pi$
$678$	−5.70013	−	4.50172i	−0.218912	−	0.172887i
$679$	53.4035	+	38.7999i	2.04944	+	1.48901i
$680$	6.75781	−	14.5582i	0.259150	−	0.558280i
$681$	4.23779			0.162393
$682$		0			0
$683$		−	16.6722i		−	0.637943i	−0.947764	−	0.318971i	$-0.896663\pi$
$683$		−	16.6722i		−	0.637943i	0.947764	−	0.318971i	$-0.103337\pi$
$684$	4.46809	−	5.21296i	0.170842	−	0.199323i
$685$	6.27340	−	8.63459i	0.239694	−	0.329911i
$686$	−2.79612	+	3.54048i	−0.106756	+	0.135176i
$687$	−9.44243	+	29.0608i	−0.360251	+	1.10874i
$688$	−8.68940	+	8.62877i	−0.331280	+	0.328969i
$689$	16.1112	−	11.7055i	0.613788	−	0.445943i
$690$	−22.5484	−	8.34095i	−0.858401	−	0.317535i
$691$	22.1836	−	7.20788i	0.843902	−	0.274201i	0.145013	−	0.989430i	$-0.453678\pi$
$691$	22.1836	−	7.20788i	0.843902	−	0.274201i	0.698890	+	0.715229i	$0.253678\pi$
$692$	−5.44581	−	8.92177i	−0.207019	−	0.339155i
$693$		0			0
$694$	−0.414214	−	1.47363i	−0.0157233	−	0.0559381i
$695$	−9.31546	−	28.6700i	−0.353356	−	1.08752i
$696$	30.2299	−	5.93064i	1.14586	−	0.224800i
$697$	−11.9964	+	8.71593i	−0.454398	+	0.330139i
$698$	26.3726	+	1.05930i	0.998219	+	0.0400951i
$699$	15.2646	+	4.95978i	0.577361	+	0.187596i
$700$	22.6620	−	54.4412i	0.856543	−	2.05768i
$701$	16.3685	−	22.5293i	0.618229	−	0.850919i	−0.378994	−	0.925399i	$-0.623730\pi$
$701$	16.3685	−	22.5293i	0.618229	−	0.850919i	0.997222	+	0.0744806i	$0.0237299\pi$
$702$	21.1510	+	31.7147i	0.798292	+	1.19699i
$703$	−2.52939			−0.0953979
$704$		0			0
$705$	25.3137			0.953369
$706$	−13.1816	−	19.7651i	−0.496096	−	0.743868i
$707$	−10.8144	+	14.8848i	−0.406719	+	0.559801i
$708$	−6.38991	+	15.3506i	−0.240148	+	0.576910i
$709$	−7.34757	−	2.38737i	−0.275944	−	0.0896595i	0.167776	−	0.985825i	$-0.446341\pi$
$709$	−7.34757	−	2.38737i	−0.275944	−	0.0896595i	−0.443720	+	0.896166i	$0.646341\pi$
$710$	52.3545	+	2.10291i	1.96483	+	0.0789207i
$711$	−2.13803	+	1.55337i	−0.0801824	+	0.0582559i
$712$	29.5783	−	5.80280i	1.10849	−	0.217469i
$713$	3.59307	+	11.0583i	0.134562	+	0.414138i
$714$	−3.46375	−	12.3228i	−0.129628	−	0.461169i
$715$		0			0
$716$	20.7071	+	33.9241i	0.773861	+	1.26780i
$717$	−32.3812	+	10.5213i	−1.20930	+	0.392924i
$718$	−23.7852	−	8.79847i	−0.887655	−	0.328356i
$719$	28.7895	−	20.9168i	1.07367	−	0.780065i	0.0970995	−	0.995275i	$-0.469043\pi$
$719$	28.7895	−	20.9168i	1.07367	−	0.780065i	0.976568	+	0.215210i	$0.0690435\pi$
$720$	8.36522	−	8.30685i	0.311753	−	0.309578i
$721$	11.0829	−	34.1096i	0.412748	−	1.27031i
$722$	−1.60262	+	2.02926i	−0.0596434	+	0.0755212i
$723$	25.5390	−	35.1514i	0.949805	−	1.30730i
$724$	−19.9745	+	23.3044i	−0.742348	+	0.866103i
$725$		−	56.5921i		−	2.10178i
$726$		0			0
$727$	−8.07107			−0.299339			−0.149670	−	0.988736i	$-0.547821\pi$
$727$	−8.07107			−0.299339			−0.149670	+	0.988736i	$0.547821\pi$
$728$	21.9107	−	47.2017i	0.812065	−	1.74941i
$729$	24.0841	+	17.4981i	0.892003	+	0.648078i
$730$	36.7068	+	28.9894i	1.35858	+	1.07295i
$731$	4.64417	+	1.50898i	0.171771	+	0.0558117i
$732$	−1.47856	−	6.20648i	−0.0546491	−	0.229398i
$733$	3.81729	+	5.25404i	0.140995	+	0.194062i	0.873674	−	0.486511i	$-0.161731\pi$
$733$	3.81729	+	5.25404i	0.140995	+	0.194062i	−0.732680	+	0.680574i	$0.761731\pi$
$734$	7.86398	+	2.90900i	0.290265	+	0.107373i
$735$	−12.6826	−	39.0329i	−0.467803	−	1.43975i
$736$	−3.65726	+	17.9749i	−0.134808	+	0.662562i
$737$		0			0
$738$	−10.4853	+	2.94725i	−0.385969	+	0.108490i
$739$	21.9407	−	7.12896i	0.807101	−	0.262243i	0.123731	−	0.992316i	$-0.460514\pi$
$739$	21.9407	−	7.12896i	0.807101	−	0.262243i	0.683369	+	0.730073i	$0.260514\pi$
$740$	−4.32915	−	0.348337i	−0.159143	−	0.0128051i
$741$	17.1494	+	23.6041i	0.629999	+	0.867119i
$742$	−22.6801	−	0.910983i	−0.832612	−	0.0334432i
$743$	−11.8995	+	36.6230i	−0.436552	+	1.34357i	0.454937	+	0.890524i	$0.349662\pi$
$743$	−11.8995	+	36.6230i	−0.436552	+	1.34357i	−0.891488	+	0.453044i	$0.850338\pi$
$744$	14.8375	+	1.79564i	0.543967	+	0.0658314i
$745$	−55.2285	−	40.1258i	−2.02341	−	1.47010i
$746$	−33.8196	+	22.5547i	−1.23822	+	0.825787i
$747$			10.4525i			0.382437i
$748$		0			0
$749$			27.7461i			1.01382i
$750$	10.9296	+	16.3883i	0.399091	+	0.598415i
$751$	−11.9390	−	8.67416i	−0.435659	−	0.316525i	0.348249	−	0.937402i	$-0.386776\pi$
$751$	−11.9390	−	8.67416i	−0.435659	−	0.316525i	−0.783908	+	0.620878i	$0.786776\pi$
$752$	−2.95453	−	19.0864i	−0.107741	−	0.696009i
$753$	6.59539	−	20.2985i	0.240350	−	0.739720i
$754$	2.00435	−	49.9009i	0.0729942	−	1.81728i
$755$	−16.1049	−	22.1665i	−0.586119	−	0.806723i
$756$	3.48482	−	43.3096i	0.126742	−	1.57515i
$757$	46.8884	−	15.2350i	1.70419	−	0.553724i	0.714840	−	0.699289i	$-0.246500\pi$
$757$	46.8884	−	15.2350i	1.70419	−	0.553724i	0.989349	+	0.145564i	$0.0464997\pi$
$758$	−1.03111	−	3.66832i	−0.0374516	−	0.133239i
$759$		0			0
$760$	28.3848	−	30.5452i	1.02962	−	1.10799i
$761$	−9.02673	−	27.7814i	−0.327219	−	1.00708i	−0.970429	−	0.241386i	$-0.922398\pi$
$761$	−9.02673	−	27.7814i	−0.327219	−	1.00708i	0.643210	−	0.765690i	$-0.277602\pi$
$762$	10.6591	−	28.8152i	0.386140	−	1.04386i
$763$	9.79966	+	13.4881i	0.354771	+	0.488301i
$764$	5.59477	+	23.4849i	0.202412	+	0.849654i
$765$	−4.47090	−	1.45268i	−0.161646	−	0.0525219i
$766$	−1.08918	+	1.37913i	−0.0393536	+	0.0498300i
$767$	21.8074	+	15.8440i	0.787418	+	0.572093i
$768$	18.9775	+	13.9920i	0.684792	+	0.504893i
$769$	−40.1027			−1.44614			−0.723071	−	0.690774i	$-0.757270\pi$
$769$	−40.1027			−1.44614			−0.723071	+	0.690774i	$0.757270\pi$
$770$		0			0
$771$			27.2404i			0.981039i
$772$	−4.84425	−	4.15207i	−0.174349	−	0.149436i
$773$	−28.5583	+	39.3071i	−1.02717	+	1.41378i	−0.120119	+	0.992760i	$0.538328\pi$
$773$	−28.5583	+	39.3071i	−1.02717	+	1.41378i	−0.907052	+	0.421019i	$0.861672\pi$
$774$	2.81478	+	2.22299i	0.101175	+	0.0799037i
$775$	8.48432	−	26.1121i	0.304766	−	0.937973i
$776$	23.5798	+	42.3653i	0.846465	+	1.52082i
$777$	−2.80223	+	2.03594i	−0.100529	+	0.0730389i
$778$	8.12872	−	21.9746i	0.291429	−	0.787829i
$779$	−36.6382	+	11.9045i	−1.31270	+	0.426522i
$780$	26.1012	+	42.7611i	0.934572	+	1.53109i
$781$		0			0
$782$	7.04163	−	1.97929i	0.251808	−	0.0707794i
$783$	−12.8853	−	39.6569i	−0.460484	−	1.41722i
$784$	−27.9503	+	14.1184i	−0.998225	+	0.504227i
$785$	−39.2016	+	28.4816i	−1.39917	+	1.01655i
$786$	−0.889788	+	22.1524i	−0.0317377	+	0.790150i
$787$	−0.852796	−	0.277090i	−0.0303989	−	0.00987720i	0.293778	−	0.955874i	$-0.405087\pi$
$787$	−0.852796	−	0.277090i	−0.0303989	−	0.00987720i	−0.324177	+	0.945996i	$0.605087\pi$
$788$	28.9495	+	12.0507i	1.03128	+	0.429288i
$789$	−6.09861	+	8.39402i	−0.217116	+	0.298835i
$790$	−13.3530	+	8.90532i	−0.475080	+	0.316837i
$791$	13.4210			0.477196
$792$		0			0
$793$	−10.3431			−0.367296
$794$	−42.4529	+	28.3124i	−1.50660	+	1.00477i
$795$	12.8440	−	17.6783i	0.455530	−	0.626984i
$796$	−12.9343	+	31.0723i	−0.458445	+	1.10133i
$797$	5.70561	+	1.85386i	0.202103	+	0.0656672i	0.408319	−	0.912839i	$-0.366115\pi$
$797$	5.70561	+	1.85386i	0.202103	+	0.0656672i	−0.206216	+	0.978506i	$0.566115\pi$
$798$	1.33466	−	33.2280i	0.0472464	−	1.17626i
$799$	−6.23068	+	4.52685i	−0.220425	+	0.160148i
$800$	31.9346	−	29.2619i	1.12906	−	1.03457i
$801$	−2.72813	−	8.39633i	−0.0963939	−	0.296670i
$802$	−15.5966	+	4.38396i	−0.550735	+	0.154803i
$803$		0			0
$804$	−3.70711	+	2.26280i	−0.130740	+	0.0798029i
$805$	42.2489	−	13.7275i	1.48908	−	0.483831i
$806$	8.40600	−	22.7242i	0.296089	−	0.800425i
$807$	−9.08562	+	6.60109i	−0.319829	+	0.232369i
$808$	−11.8082	+	6.57223i	−0.415410	+	0.231210i
$809$	2.87280	−	8.84157i	0.101002	−	0.310853i	−0.887769	−	0.460289i	$-0.847746\pi$
$809$	2.87280	−	8.84157i	0.101002	−	0.310853i	0.988771	+	0.149436i	$0.0477458\pi$
$810$	23.0131	+	18.1747i	0.808596	+	0.638594i
$811$	1.58117	−	2.17630i	0.0555224	−	0.0764201i	−0.780353	−	0.625339i	$-0.784961\pi$
$811$	1.58117	−	2.17630i	0.0555224	−	0.0764201i	0.835875	+	0.548919i	$0.184961\pi$
$812$	−37.0438	+	43.2193i	−1.29998	+	1.51670i
$813$		−	23.6720i		−	0.830213i
$814$		0			0
$815$	−71.5980			−2.50797
$816$	1.50329	−	9.28101i	0.0526257	−	0.324901i
$817$	10.2634	+	7.45682i	0.359072	+	0.260881i
$818$	5.59223	−	7.08096i	0.195528	−	0.247580i
$819$	−14.4959	−	4.71001i	−0.506529	−	0.164581i
$820$	−64.3472	+	15.3293i	−2.24710	+	0.535323i
$821$	1.05411	+	1.45086i	0.0367888	+	0.0506355i	0.827015	−	0.562180i	$-0.190037\pi$
$821$	1.05411	+	1.45086i	0.0367888	+	0.0506355i	−0.790226	+	0.612815i	$0.790037\pi$
$822$	2.16908	−	5.86374i	0.0756553	−	0.204521i
$823$	−0.702111	−	2.16087i	−0.0244740	−	0.0753234i	0.938074	−	0.346436i	$-0.112608\pi$
$823$	−0.702111	−	2.16087i	−0.0244740	−	0.0753234i	−0.962548	+	0.271113i	$0.912608\pi$
$824$	17.9325	−	19.2974i	0.624707	−	0.672255i
$825$		0			0
$826$	−8.31371	−	29.5772i	−0.289271	−	1.02912i
$827$	21.7641	−	7.07157i	0.756810	−	0.245903i	0.0949013	−	0.995487i	$-0.469746\pi$
$827$	21.7641	−	7.07157i	0.756810	−	0.245903i	0.661909	+	0.749584i	$0.269746\pi$
$828$	5.35528	+	0.430902i	0.186109	+	0.0149749i
$829$	18.5230	+	25.4947i	0.643329	+	0.885467i	0.998788	−	0.0492253i	$-0.0156752\pi$
$829$	18.5230	+	25.4947i	0.643329	+	0.885467i	−0.355458	+	0.934692i	$0.615675\pi$
$830$	−2.54777	+	63.4299i	−0.0884342	+	2.20168i
$831$	−2.54904	+	7.84514i	−0.0884253	+	0.272145i
$832$	29.1952	−	24.6711i	1.01216	−	0.855316i
$833$	10.1019	+	7.33948i	0.350011	+	0.254298i
$834$	−9.79785	−	14.6913i	−0.339272	−	0.508720i
$835$			13.6997i			0.474097i
$836$		0			0
$837$		−	20.2298i		−	0.699245i
$838$	−13.8705	+	9.25043i	−0.479149	+	0.319551i
$839$	4.24139	+	3.08155i	0.146429	+	0.106387i	0.658588	−	0.752504i	$-0.271154\pi$
$839$	4.24139	+	3.08155i	0.146429	+	0.106387i	−0.512159	+	0.858891i	$0.671154\pi$
$840$	6.86034	−	56.6872i	0.236704	−	1.95590i
$841$	−7.91931	+	24.3731i	−0.273080	+	0.840452i
$842$	−5.88975	−	0.236572i	−0.202974	−	0.00815280i
$843$	20.0127	+	27.5451i	0.689272	+	0.948702i
$844$	−3.70057	+	45.9909i	−0.127379	+	1.58307i
$845$	33.2547	−	10.8051i	1.14400	−	0.371707i
$846$	−5.44581	+	1.53073i	−0.187231	+	0.0526277i
$847$		0			0
$848$	−14.8284	−	7.62096i	−0.509210	−	0.261705i
$849$	8.12551	+	25.0077i	0.278867	+	0.858264i
$850$	−16.1990	−	5.99224i	−0.555621	−	0.205532i
$851$	−1.16340	−	1.60128i	−0.0398808	−	0.0548913i
$852$	29.8577	−	7.11296i	1.02291	−	0.243686i
$853$	−30.5292	−	9.91955i	−1.04530	−	0.339639i	−0.264479	−	0.964392i	$-0.585200\pi$
$853$	−30.5292	−	9.91955i	−1.04530	−	0.339639i	−0.780823	+	0.624753i	$0.785200\pi$
$854$	9.25172	+	7.30660i	0.316587	+	0.250027i
$855$	−9.88052	−	7.17862i	−0.337907	−	0.245504i
$856$	−8.58074	+	18.4853i	−0.293284	+	0.631813i
$857$	−24.9733			−0.853073			−0.426536	−	0.904470i	$-0.640266\pi$
$857$	−24.9733			−0.853073			−0.426536	+	0.904470i	$0.640266\pi$
$858$		0			0
$859$			49.5542i			1.69077i	0.534159	+	0.845384i	$0.320628\pi$
$859$			49.5542i			1.69077i	−0.534159	+	0.845384i	$0.679372\pi$
$860$	16.5393	+	14.1761i	0.563986	+	0.483399i
$861$	−31.0082	+	42.6791i	−1.05676	+	1.45450i
$862$	22.4683	−	28.4496i	0.765273	−	0.968998i
$863$	10.3566	−	31.8744i	0.352543	−	1.08502i	−0.604877	−	0.796319i	$-0.706778\pi$
$863$	10.3566	−	31.8744i	0.352543	−	1.08502i	0.957420	−	0.288698i	$-0.0932223\pi$
$864$	15.7156	−	27.7764i	0.534656	−	0.944973i
$865$	−15.0422	+	10.9288i	−0.511450	+	0.371590i
$866$	4.43426	+	1.64030i	0.150682	+	0.0557395i
$867$	20.2599	−	6.58284i	0.688062	−	0.223565i
$868$	−23.5718	+	14.3881i	−0.800079	+	0.488365i
$869$		0			0
$870$	−14.8284	−	52.7543i	−0.502731	−	1.78854i
$871$	2.17574	+	6.69625i	0.0737222	+	0.226894i
$872$	2.35751	+	12.0168i	0.0798353	+	0.406940i
$873$	11.4889	−	8.34714i	0.388839	−	0.282508i
$874$	18.9875	+	0.762666i	0.642263	+	0.0257976i
$875$	−34.6166	−	11.2476i	−1.17025	−	0.380239i
$876$	25.2953	+	10.5296i	0.854650	+	0.355761i
$877$	8.20684	−	11.2957i	0.277125	−	0.381430i	−0.647654	−	0.761935i	$-0.724250\pi$
$877$	8.20684	−	11.2957i	0.277125	−	0.381430i	0.924779	+	0.380504i	$0.124250\pi$
$878$	−3.53999	−	5.30801i	−0.119469	−	0.179137i
$879$	4.39810			0.148344
$880$		0			0
$881$	−24.1716			−0.814361			−0.407180	−	0.913348i	$-0.633488\pi$
$881$	−24.1716			−0.814361			−0.407180	+	0.913348i	$0.633488\pi$
$882$	5.08878	+	7.63034i	0.171348	+	0.256927i
$883$	−15.7143	+	21.6288i	−0.528827	+	0.727868i	−0.986951	−	0.161020i	$-0.948522\pi$
$883$	−15.7143	+	21.6288i	−0.528827	+	0.727868i	0.458124	+	0.888888i	$0.348522\pi$
$884$	−14.0715	−	5.85747i	−0.473275	−	0.197008i
$885$	28.1296	+	9.13987i	0.945567	+	0.307233i
$886$	−8.68664	−	0.348913i	−0.291833	−	0.0117220i
$887$	33.7342	−	24.5093i	1.13268	−	0.822943i	0.146601	−	0.989196i	$-0.453167\pi$
$887$	33.7342	−	24.5093i	1.13268	−	0.822943i	0.986083	+	0.166253i	$0.0531667\pi$
$888$	−2.49657	+	0.489787i	−0.0837792	+	0.0164362i
$889$	17.5428	+	53.9911i	0.588365	+	1.81080i
$890$	−14.5088	−	51.6172i	−0.486336	−	1.73021i
$891$		0			0
$892$	43.9203	−	26.8088i	1.47056	−	0.897624i
$893$	−19.0290	+	6.18291i	−0.636783	+	0.206903i
$894$	−37.5056	−	13.8738i	−1.25437	−	0.464010i
$895$	57.1963	−	41.5555i	1.91186	−	1.38905i
$896$	−43.5426	+	1.44370i	−1.45465	+	0.0482305i
$897$	−7.05515	+	21.7135i	−0.235565	+	0.724994i
$898$	−15.2013	+	19.2481i	−0.507274	+	0.642318i
$899$	−15.5779	+	21.4411i	−0.519551	+	0.715101i
$900$	−9.63230	−	8.25596i	−0.321077	−	0.275199i
$901$			6.64820i			0.221484i
$902$		0			0
$903$	17.3726			0.578123
$904$	8.94149	+	4.15058i	0.297389	+	0.138046i
$905$	44.1707	+	32.0919i	1.46828	+	1.06677i
$906$	−12.5958	−	9.94759i	−0.418467	−	0.330487i
$907$	−42.9244	−	13.9470i	−1.42528	−	0.463102i	−0.508005	−	0.861354i	$-0.669617\pi$
$907$	−42.9244	−	13.9470i	−1.42528	−	0.463102i	−0.917276	+	0.398253i	$0.869617\pi$
$908$	−5.59494	+	1.33287i	−0.185675	+	0.0442330i
$909$	2.32654	+	3.20221i	0.0771665	+	0.106211i
$910$	−86.8189	−	32.1155i	−2.87802	−	1.06462i
$911$	−7.16041	−	22.0375i	−0.237235	−	0.730134i	−0.996817	−	0.0797227i	$-0.974597\pi$
$911$	−7.16041	−	22.0375i	−0.237235	−	0.730134i	0.759582	−	0.650411i	$-0.225403\pi$
$912$	11.1653	−	21.7248i	0.369720	−	0.719379i
$913$		0			0
$914$	35.7990	−	10.0625i	1.18413	−	0.332839i
$915$	−10.7937	+	3.50709i	−0.356829	+	0.115941i
$916$	3.32613	−	41.3374i	0.109899	−	1.36583i
$917$	−24.0788	−	33.1416i	−0.795152	−	1.09443i
$918$	−12.7158	−	0.510752i	−0.419685	−	0.0168573i
$919$	−10.0971	+	31.0756i	−0.333072	+	1.02509i	0.634592	+	0.772848i	$0.281168\pi$
$919$	−10.0971	+	31.0756i	−0.333072	+	1.02509i	−0.967664	+	0.252243i	$0.918832\pi$
$920$	32.3929	+	3.92021i	1.06796	+	0.129246i
$921$	−33.5128	−	24.3485i	−1.10428	−	0.802310i
$922$	−5.71202	+	3.80942i	−0.188115	+	0.125457i
$923$		−	49.7582i		−	1.63781i
$924$		0			0
$925$			4.67371i			0.153671i
$926$	6.06383	+	9.09239i	0.199270	+	0.298794i
$927$	−6.24216	−	4.53519i	−0.205019	−	0.148955i
$928$	−38.0457	+	17.3379i	−1.24891	+	0.569143i
$929$	17.9487	−	55.2405i	0.588878	−	1.81238i	0.00577421	−	0.999983i	$-0.498162\pi$
$929$	17.9487	−	55.2405i	0.588878	−	1.81238i	0.583104	−	0.812398i	$-0.301838\pi$
$930$	1.06700	−	26.5644i	0.0349884	−	0.871080i
$931$	19.0677	+	26.2444i	0.624919	+	0.860127i
$932$	−21.7131	−	1.74710i	−0.711235	−	0.0572282i
$933$	−14.6951	+	4.77474i	−0.481097	+	0.156318i
$934$	−10.9884	−	39.0928i	−0.359551	−	1.27915i
$935$		0			0
$936$	−8.20101	−	7.62096i	−0.268058	−	0.249099i
$937$	−11.9841	−	36.8833i	−0.391503	−	1.20492i	−0.931651	−	0.363354i	$-0.881632\pi$
$937$	−11.9841	−	36.8833i	−0.391503	−	1.20492i	0.540148	−	0.841570i	$-0.318368\pi$
$938$	2.78421	−	7.52663i	0.0909076	−	0.245753i
$939$	1.58374	+	2.17983i	0.0516834	+	0.0711360i
$940$	−33.4204	+	7.96169i	−1.09005	+	0.259682i
$941$	50.0578	+	16.2648i	1.63184	+	0.530217i	0.974693	−	0.223547i	$-0.0717635\pi$
$941$	50.0578	+	16.2648i	1.63184	+	0.530217i	0.657146	+	0.753763i	$0.271763\pi$
$942$	−17.5923	+	22.2757i	−0.573190	+	0.725780i
$943$	−24.3882	−	17.7191i	−0.794189	−	0.577012i
$944$	3.60821	−	22.2763i	0.117437	−	0.725033i
$945$	−77.2891			−2.51421
$946$		0			0
$947$		−	29.9348i		−	0.972750i	−0.873750	−	0.486375i	$-0.838319\pi$
$947$		−	29.9348i		−	0.972750i	0.873750	−	0.486375i	$-0.161681\pi$
$948$	−6.11860	+	7.13862i	−0.198723	+	0.231852i
$949$	26.1084	−	35.9351i	0.847514	−	1.16650i
$950$	−35.2140	−	27.8105i	−1.14249	−	0.902291i
$951$	−0.833878	+	2.56641i	−0.0270403	+	0.0832216i
$952$	8.44879	+	15.1797i	0.273827	+	0.491978i
$953$	−36.0936	+	26.2236i	−1.16919	+	0.849465i	−0.990911	−	0.134516i	$-0.957052\pi$
$953$	−36.0936	+	26.2236i	−1.16919	+	0.849465i	−0.178276	+	0.983980i	$0.557052\pi$
$954$	−1.69416	+	4.57986i	−0.0548503	+	0.148279i
$955$	40.8427	−	13.2706i	1.32164	−	0.429427i
$956$	39.4421	−	24.0753i	1.27565	−	0.778650i
$957$		0			0
$958$	−5.24264	+	1.47363i	−0.169382	+	0.0476107i
$959$	3.56986	+	10.9869i	0.115277	+	0.354785i
$960$	22.1017	−	35.6451i	0.713328	−	1.15044i
$961$	14.6773	−	10.6637i	0.473461	−	0.343990i
$962$	−0.165531	+	4.12111i	−0.00533694	+	0.132870i
$963$	5.67694	+	1.84455i	0.182937	+	0.0594398i
$964$	−22.6620	+	54.4412i	−0.729894	+	1.75343i
$965$	−6.67088	+	9.18168i	−0.214743	+	0.295569i
$966$	21.6495	−	14.4384i	0.696563	−	0.464547i
$967$	−33.9962			−1.09325			−0.546623	−	0.837379i	$-0.684087\pi$
$967$	−33.9962			−1.09325			−0.546623	+	0.837379i	$0.684087\pi$
$968$		0			0
$969$	−9.74012			−0.312898
$970$	71.7535	−	47.8534i	2.30387	−	1.53648i
$971$	14.4278	−	19.8581i	0.463009	−	0.637277i	−0.512121	−	0.858914i	$-0.671140\pi$
$971$	14.4278	−	19.8581i	0.463009	−	0.637277i	0.975129	+	0.221637i	$0.0711399\pi$
$972$	−15.3919	−	6.40711i	−0.493695	−	0.205508i
$973$	31.0322	+	10.0830i	0.994848	+	0.323246i
$974$	−1.98084	+	49.3156i	−0.0634702	+	1.58017i
$975$	43.6147	−	31.6880i	1.39679	−	1.01483i
$976$	3.90413	+	7.72906i	0.124968	+	0.247401i
$977$	−18.6380	−	57.3617i	−0.596281	−	1.83516i	−0.548243	−	0.836319i	$-0.684703\pi$
$977$	−18.6380	−	57.3617i	−0.596281	−	1.83516i	−0.0480386	−	0.998845i	$-0.515297\pi$
$978$	−40.3764	+	11.3492i	−1.29110	+	0.362907i
$979$		0			0
$980$	29.0208	+	47.5443i	0.927036	+	1.51875i
$981$	3.41119	−	1.10836i	0.108911	−	0.0353873i
$982$	−11.5013	+	31.0918i	−0.367021	+	0.992180i
$983$	−35.3766	+	25.7026i	−1.12834	+	0.819787i	−0.985452	−	0.169952i	$-0.945639\pi$
$983$	−35.3766	+	25.7026i	−1.12834	+	0.819787i	−0.142887	+	0.989739i	$0.545639\pi$
$984$	−33.8575	+	18.8445i	−1.07934	+	0.600742i
$985$	17.2368	−	53.0494i	0.549210	−	1.69030i
$986$	13.0839	+	10.3331i	0.416676	+	0.329073i
$987$	−16.1049	+	22.1665i	−0.512626	+	0.705569i
$988$	−30.0655	−	25.7695i	−0.956510	−	0.819837i
$989$			9.92724i			0.315668i
$990$		0			0
$991$	−39.4558			−1.25336			−0.626678	−	0.779278i	$-0.715586\pi$
$991$	−39.4558			−1.25336			−0.626678	+	0.779278i	$0.715586\pi$
$992$	−20.1539	+	2.29599i	−0.639887	+	0.0728979i
$993$	15.2087	+	11.0498i	0.482634	+	0.350654i
$994$	−35.1502	+	44.5076i	−1.11490	+	1.41170i
$995$	56.9394	+	18.5007i	1.80510	+	0.586512i
$996$	8.61767	+	36.1740i	0.273061	+	1.14622i
$997$	7.15273	+	9.84488i	0.226529	+	0.311791i	0.907119	−	0.420874i	$-0.138276\pi$
$997$	7.15273	+	9.84488i	0.226529	+	0.311791i	−0.680590	+	0.732664i	$0.738276\pi$
$998$	15.6585	−	42.3300i	0.495660	−	1.33993i
$999$	1.06415	+	3.27511i	0.0336681	+	0.103620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.c.269.7		32
8.5	even	2	inner	968.2.o.c.269.5		32
11.2	odd	10	inner	968.2.o.c.493.4		32
11.3	even	5		968.2.c.c.485.7	yes	8
11.4	even	5	inner	968.2.o.c.245.3		32
11.5	even	5	inner	968.2.o.c.565.2		32
11.6	odd	10	inner	968.2.o.c.565.7		32
11.7	odd	10	inner	968.2.o.c.245.6		32
11.8	odd	10		968.2.c.c.485.2	yes	8
11.9	even	5	inner	968.2.o.c.493.5		32
11.10	odd	2	inner	968.2.o.c.269.2		32
44.3	odd	10		3872.2.c.c.1937.3		8
44.19	even	10		3872.2.c.c.1937.4		8
88.3	odd	10		3872.2.c.c.1937.5		8
88.5	even	10	inner	968.2.o.c.565.3		32
88.13	odd	10	inner	968.2.o.c.493.2		32
88.19	even	10		3872.2.c.c.1937.6		8
88.21	odd	2	inner	968.2.o.c.269.4		32
88.29	odd	10	inner	968.2.o.c.245.7		32
88.37	even	10	inner	968.2.o.c.245.2		32
88.53	even	10	inner	968.2.o.c.493.7		32
88.61	odd	10	inner	968.2.o.c.565.6		32
88.69	even	10		968.2.c.c.485.8	yes	8
88.85	odd	10		968.2.c.c.485.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.c.c.485.1	✓	8	88.85	odd	10
968.2.c.c.485.2	yes	8	11.8	odd	10
968.2.c.c.485.7	yes	8	11.3	even	5
968.2.c.c.485.8	yes	8	88.69	even	10
968.2.o.c.245.2		32	88.37	even	10	inner
968.2.o.c.245.3		32	11.4	even	5	inner
968.2.o.c.245.6		32	11.7	odd	10	inner
968.2.o.c.245.7		32	88.29	odd	10	inner
968.2.o.c.269.2		32	11.10	odd	2	inner
968.2.o.c.269.4		32	88.21	odd	2	inner
968.2.o.c.269.5		32	8.5	even	2	inner
968.2.o.c.269.7		32	1.1	even	1	trivial
968.2.o.c.493.2		32	88.13	odd	10	inner
968.2.o.c.493.4		32	11.2	odd	10	inner
968.2.o.c.493.5		32	11.9	even	5	inner
968.2.o.c.493.7		32	88.53	even	10	inner
968.2.o.c.565.2		32	11.5	even	5	inner
968.2.o.c.565.3		32	88.5	even	10	inner
968.2.o.c.565.6		32	88.61	odd	10	inner
968.2.o.c.565.7		32	11.6	odd	10	inner
3872.2.c.c.1937.3		8	44.3	odd	10
3872.2.c.c.1937.4		8	44.19	even	10
3872.2.c.c.1937.5		8	88.3	odd	10
3872.2.c.c.1937.6		8	88.19	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.784666 + 1.17656i) q^{2} +(0.866175 - 1.19219i) q^{3} +(-0.768600 + 1.84642i) q^{4} +(3.38352 + 1.09937i) q^{5} +(2.08234 + 0.0836407i) q^{6} +(-3.11534 + 2.26343i) q^{7} +(-2.77552 + 0.544514i) q^{8} +(0.255998 + 0.787881i) q^{9} +(1.36145 + 4.84357i) q^{10} +(1.53553 + 2.51564i) q^{12} +(4.54406 - 1.47646i) q^{13} +(-5.10756 - 1.88936i) q^{14} +(4.24139 - 3.08155i) q^{15} +(-2.81851 - 2.83831i) q^{16} +(-0.492895 + 1.51697i) q^{17} +(-0.726119 + 0.919421i) q^{18} +(-2.43570 + 3.35245i) q^{19} +(-4.63048 + 5.40242i) q^{20} +5.67459i q^{21} -3.24264 q^{23} +(-1.75492 + 3.78059i) q^{24} +(6.19453 + 4.50059i) q^{25} +(5.30271 + 4.18785i) q^{26} +(5.36555 + 1.74337i) q^{27} +(-1.78478 - 7.49188i) q^{28} +(-4.34434 - 5.97947i) q^{29} +(6.95370 + 2.57227i) q^{30} +(-1.10807 - 3.41029i) q^{31} +(1.12786 - 5.54328i) q^{32} +(-2.17157 + 0.610396i) q^{34} +(-13.0292 + 4.23343i) q^{35} +(-1.65152 - 0.132886i) q^{36} +(0.358782 + 0.493821i) q^{37} +(-5.85558 - 0.235199i) q^{38} +(2.17574 - 6.69625i) q^{39} +(-9.98966 - 1.20896i) q^{40} +(7.52109 + 5.46439i) q^{41} +(-6.67652 + 4.45266i) q^{42} -3.06147i q^{43} +2.94725i q^{45} +(-2.54439 - 3.81517i) q^{46} +(3.90628 + 2.83808i) q^{47} +(-5.82512 + 0.901717i) q^{48} +(2.41912 - 7.44528i) q^{49} +(-0.434591 + 10.8197i) q^{50} +(1.38159 + 1.90159i) q^{51} +(-0.766414 + 9.52504i) q^{52} +(3.96404 - 1.28800i) q^{53} +(2.15897 + 7.68087i) q^{54} +(7.41421 - 7.97852i) q^{56} +(1.88701 + 5.80763i) q^{57} +(3.62637 - 9.80328i) q^{58} +(3.31609 + 4.56421i) q^{59} +(2.42989 + 10.1998i) q^{60} +(-2.05883 - 0.668955i) q^{61} +(3.14295 - 3.97965i) q^{62} +(-2.58083 - 1.87508i) q^{63} +(7.40701 - 3.02262i) q^{64} +16.9981 q^{65} +1.47363i q^{67} +(-2.42213 - 2.07604i) q^{68} +(-2.80870 + 3.86584i) q^{69} +(-15.2044 - 12.0078i) q^{70} +(3.21817 - 9.90451i) q^{71} +(-1.13954 - 2.04738i) q^{72} +(7.52109 - 5.46439i) q^{73} +(-0.299487 + 0.809613i) q^{74} +(10.7311 - 3.48674i) q^{75} +(-4.31795 - 7.07401i) q^{76} +(9.58579 - 2.69442i) q^{78} +(0.985790 + 3.03395i) q^{79} +(-6.41613 - 12.7021i) q^{80} +(4.71530 - 3.42586i) q^{81} +(-0.527659 + 13.1368i) q^{82} +(11.9998 + 3.89896i) q^{83} +(-10.4777 - 4.36149i) q^{84} +(-3.33544 + 4.59084i) q^{85} +(3.60201 - 2.40223i) q^{86} -10.8916 q^{87} -10.6569 q^{89} +(-3.46763 + 2.31261i) q^{90} +(-10.8144 + 14.8848i) q^{91} +(2.49229 - 5.98727i) q^{92} +(-5.02548 - 1.63288i) q^{93} +(-0.274054 + 6.82293i) q^{94} +(-11.9268 + 8.66536i) q^{95} +(-5.63170 - 6.14608i) q^{96} +(-5.29721 - 16.3031i) q^{97} +(10.6580 - 2.99581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49}+ \cdots + 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

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