LMFDB - Embedded newform 968.2.o.j.245.7

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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.7
Character	$\chi$	$=$	968.245
Dual form			968.2.o.j.565.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05579 - 0.940911i) q^{2} +(2.42981 - 0.789492i) q^{3} +(0.229373 - 1.98680i) q^{4} +(-1.58432 + 2.18063i) q^{5} +(1.82252 - 3.11977i) q^{6} +(1.22033 - 3.75580i) q^{7} +(-1.62724 - 2.31346i) q^{8} +(2.85361 - 2.07327i) q^{9} +(0.379074 + 3.79299i) q^{10} +(-1.01123 - 5.00864i) q^{12} +(-0.257423 - 0.354312i) q^{13} +(-2.24546 - 5.11355i) q^{14} +(-2.12801 + 6.54933i) q^{15} +(-3.89478 - 0.911440i) q^{16} +(1.93640 + 1.40688i) q^{17} +(1.06205 - 4.87393i) q^{18} +(5.08557 - 1.65240i) q^{19} +(3.96909 + 3.64792i) q^{20} -10.0893i q^{21} -1.35153 q^{23} +(-5.78033 - 4.33658i) q^{24} +(-0.699997 - 2.15437i) q^{25} +(-0.605160 - 0.131866i) q^{26} +(0.791790 - 1.08980i) q^{27} +(-7.18212 - 3.28604i) q^{28} +(-0.140131 - 0.0455314i) q^{29} +(3.91561 + 8.91696i) q^{30} +(-1.28045 + 0.930300i) q^{31} +(-4.96964 + 2.70235i) q^{32} +(3.36818 - 0.336618i) q^{34} +(6.25662 + 8.61150i) q^{35} +(-3.46464 - 6.14512i) q^{36} +(-7.01837 - 2.28041i) q^{37} +(3.81452 - 6.52966i) q^{38} +(-0.905215 - 0.657677i) q^{39} +(7.62288 + 0.116867i) q^{40} +(-1.11646 - 3.43612i) q^{41} +(-9.49314 - 10.6522i) q^{42} +6.62197i q^{43} +9.50742i q^{45} +(-1.42693 + 1.27167i) q^{46} +(0.934673 + 2.87663i) q^{47} +(-10.1831 + 0.860272i) q^{48} +(-6.95369 - 5.05215i) q^{49} +(-2.76612 - 1.61592i) q^{50} +(5.81581 + 1.88967i) q^{51} +(-0.762995 + 0.430179i) q^{52} +(2.72682 + 3.75314i) q^{53} +(-0.189448 - 1.89561i) q^{54} +(-10.6747 + 3.28838i) q^{56} +(11.0524 - 8.03004i) q^{57} +(-0.190790 + 0.0837795i) q^{58} +(11.8952 + 3.86498i) q^{59} +(12.5241 + 5.73017i) q^{60} +(0.387808 - 0.533772i) q^{61} +(-0.476551 + 2.18699i) q^{62} +(-4.30443 - 13.2477i) q^{63} +(-2.70421 + 7.52909i) q^{64} +1.18047 q^{65} -3.00157i q^{67} +(3.23935 - 3.52455i) q^{68} +(-3.28396 + 1.06702i) q^{69} +(14.7083 + 3.20499i) q^{70} +(8.54816 + 6.21060i) q^{71} +(-9.43994 - 3.22803i) q^{72} +(3.28894 - 10.1223i) q^{73} +(-9.55557 + 4.19604i) q^{74} +(-3.40172 - 4.68206i) q^{75} +(-2.11650 - 10.4830i) q^{76} +(-1.57453 + 0.157359i) q^{78} +(5.21464 - 3.78866i) q^{79} +(8.15810 - 7.04906i) q^{80} +(-2.20645 + 6.79075i) q^{81} +(-4.41183 - 2.57732i) q^{82} +(-1.34279 + 1.84820i) q^{83} +(-20.0455 - 2.31422i) q^{84} +(-6.13577 + 1.99363i) q^{85} +(6.23068 + 6.99139i) q^{86} -0.376438 q^{87} +11.5827 q^{89} +(8.94563 + 10.0378i) q^{90} +(-1.64487 + 0.534450i) q^{91} +(-0.310006 + 2.68523i) q^{92} +(-2.37678 + 3.27135i) q^{93} +(3.69347 + 2.15766i) q^{94} +(-4.45390 + 13.7077i) q^{95} +(-9.94178 + 10.4897i) q^{96} +(-7.02442 + 5.10354i) q^{97} +(-12.0952 + 1.20881i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} + 8 q^{6} + 5 q^{8} + 10 q^{9} - 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} + 4 q^{17} + 25 q^{18} + 8 q^{20} - 8 q^{23} - 40 q^{24} + 6 q^{25} - 20 q^{26} - 18 q^{28}+ \cdots - 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 + 8 * q^6 + 5 * q^8 + 10 * q^9 - 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 + 4 * q^17 + 25 * q^18 + 8 * q^20 - 8 * q^23 - 40 * q^24 + 6 * q^25 - 20 * q^26 - 18 * q^28 + 12 * q^30 + 4 * q^31 + 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 + 6 * q^39 - 20 * q^40 + 16 * q^41 - 20 * q^42 - 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 - 39 * q^50 + 108 * q^54 - 32 * q^56 + 4 * q^57 - 16 * q^58 + 94 * q^60 - 52 * q^62 - 30 * q^63 + 11 * q^64 - 36 * q^65 + 63 * q^68 + 52 * q^70 + 12 * q^71 + 44 * q^72 + 4 * q^73 - 26 * q^74 - 134 * q^76 - 12 * q^78 - 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 + 72 * q^84 - 10 * q^86 + 68 * q^87 - 16 * q^89 + 126 * q^90 - 64 * q^92 + 40 * q^94 + 26 * q^95 - 5 * q^96 - 20 * q^97 - 144 * q^98

Character values

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

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.05579	−	0.940911i	0.746554	−	0.665324i
$2$	1.05579	−	0.940911i	0.746554	−	0.665324i
$3$	2.42981	−	0.789492i	1.40285	−	0.455814i	0.492739	−	0.870177i	$-0.335996\pi$
$3$	2.42981	−	0.789492i	1.40285	−	0.455814i	0.910111	+	0.414364i	$0.135996\pi$
$4$	0.229373	−	1.98680i	0.114687	−	0.993402i
$5$	−1.58432	+	2.18063i	−0.708531	+	0.975209i	0.291297	+	0.956633i	$0.405913\pi$
$5$	−1.58432	+	2.18063i	−0.708531	+	0.975209i	−0.999827	+	0.0185761i	$0.994087\pi$
$6$	1.82252	−	3.11977i	0.744040	−	1.27364i
$7$	1.22033	−	3.75580i	0.461243	−	1.41956i	−0.402405	−	0.915462i	$-0.631826\pi$
$7$	1.22033	−	3.75580i	0.461243	−	1.41956i	0.863647	−	0.504097i	$-0.168174\pi$
$8$	−1.62724	−	2.31346i	−0.575315	−	0.817932i
$9$	2.85361	−	2.07327i	0.951205	−	0.691091i
$10$	0.379074	+	3.79299i	0.119874	+	1.19945i
$11$		0			0
$11$		0			0
$12$	−1.01123	−	5.00864i	−0.291918	−	1.44587i
$13$	−0.257423	−	0.354312i	−0.0713963	−	0.0982685i	0.771825	−	0.635834i	$-0.219344\pi$
$13$	−0.257423	−	0.354312i	−0.0713963	−	0.0982685i	−0.843222	+	0.537566i	$0.819344\pi$
$14$	−2.24546	−	5.11355i	−0.600124	−	1.36665i
$15$	−2.12801	+	6.54933i	−0.549449	+	1.69103i
$16$	−3.89478	−	0.911440i	−0.973694	−	0.227860i
$17$	1.93640	+	1.40688i	0.469647	+	0.341218i	0.797304	−	0.603578i	$-0.206259\pi$
$17$	1.93640	+	1.40688i	0.469647	+	0.341218i	−0.327657	+	0.944797i	$0.606259\pi$
$18$	1.06205	−	4.87393i	0.250326	−	1.14880i
$19$	5.08557	−	1.65240i	1.16671	−	0.379087i	0.339296	−	0.940680i	$-0.389811\pi$
$19$	5.08557	−	1.65240i	1.16671	−	0.379087i	0.827414	+	0.561592i	$0.189811\pi$
$20$	3.96909	+	3.64792i	0.887515	+	0.815699i
$21$		−	10.0893i		−	2.20167i
$22$		0			0
$23$	−1.35153			−0.281814			−0.140907	−	0.990023i	$-0.545002\pi$
$23$	−1.35153			−0.281814			−0.140907	+	0.990023i	$0.545002\pi$
$24$	−5.78033	−	4.33658i	−1.17990	−	0.885200i
$25$	−0.699997	−	2.15437i	−0.139999	−	0.430874i
$26$	−0.605160	−	0.131866i	−0.118682	−	0.0258611i
$27$	0.791790	−	1.08980i	0.152380	−	0.209733i
$28$	−7.18212	−	3.28604i	−1.35729	−	0.621004i
$29$	−0.140131	−	0.0455314i	−0.0260217	−	0.00845496i	0.295977	−	0.955195i	$-0.404355\pi$
$29$	−0.140131	−	0.0455314i	−0.0260217	−	0.00845496i	−0.321999	+	0.946740i	$0.604355\pi$
$30$	3.91561	+	8.91696i	0.714890	+	1.62801i
$31$	−1.28045	+	0.930300i	−0.229975	+	0.167087i	−0.696805	−	0.717260i	$-0.745396\pi$
$31$	−1.28045	+	0.930300i	−0.229975	+	0.167087i	0.466830	+	0.884347i	$0.345396\pi$
$32$	−4.96964	+	2.70235i	−0.878516	+	0.477713i
$33$		0			0
$34$	3.36818	−	0.336618i	0.577638	−	0.0577294i
$35$	6.25662	+	8.61150i	1.05756	+	1.45561i
$36$	−3.46464	−	6.14512i	−0.577440	−	1.02419i
$37$	−7.01837	−	2.28041i	−1.15381	−	0.374897i	−0.331235	−	0.943548i	$-0.607465\pi$
$37$	−7.01837	−	2.28041i	−1.15381	−	0.374897i	−0.822578	+	0.568652i	$0.807465\pi$
$38$	3.81452	−	6.52966i	0.618797	−	1.05925i
$39$	−0.905215	−	0.657677i	−0.144950	−	0.105313i
$40$	7.62288	+	0.116867i	1.20528	+	0.0184782i
$41$	−1.11646	−	3.43612i	−0.174362	−	0.536632i	0.825241	−	0.564780i	$-0.191039\pi$
$41$	−1.11646	−	3.43612i	−0.174362	−	0.536632i	−0.999604	+	0.0281481i	$0.991039\pi$
$42$	−9.49314	−	10.6522i	−1.46482	−	1.64366i
$43$			6.62197i			1.00984i	0.863166	+	0.504920i	$0.168478\pi$
$43$			6.62197i			1.00984i	−0.863166	+	0.504920i	$0.831522\pi$
$44$		0			0
$45$			9.50742i			1.41728i
$46$	−1.42693	+	1.27167i	−0.210389	+	0.187498i
$47$	0.934673	+	2.87663i	0.136336	+	0.419599i	0.995795	−	0.0916047i	$-0.0291996\pi$
$47$	0.934673	+	2.87663i	0.136336	+	0.419599i	−0.859459	+	0.511204i	$0.829200\pi$
$48$	−10.1831	+	0.860272i	−1.46981	+	0.124170i
$49$	−6.95369	−	5.05215i	−0.993385	−	0.721736i
$50$	−2.76612	−	1.61592i	−0.391188	−	0.228526i
$51$	5.81581	+	1.88967i	0.814376	+	0.264607i
$52$	−0.762995	+	0.430179i	−0.105808	+	0.0596551i
$53$	2.72682	+	3.75314i	0.374557	+	0.515534i	0.954132	−	0.299385i	$-0.0967815\pi$
$53$	2.72682	+	3.75314i	0.374557	+	0.515534i	−0.579575	+	0.814919i	$0.696781\pi$
$54$	−0.189448	−	1.89561i	−0.0257806	−	0.257959i
$55$		0			0
$56$	−10.6747	+	3.28838i	−1.42646	+	0.439428i
$57$	11.0524	−	8.03004i	1.46393	−	1.06360i
$58$	−0.190790	+	0.0837795i	−0.0250519	+	0.0110008i
$59$	11.8952	+	3.86498i	1.54862	+	0.503177i	0.953739	−	0.300637i	$-0.0971992\pi$
$59$	11.8952	+	3.86498i	1.54862	+	0.503177i	0.594881	+	0.803814i	$0.297199\pi$
$60$	12.5241	+	5.73017i	1.61686	+	0.739762i
$61$	0.387808	−	0.533772i	0.0496537	−	0.0683425i	−0.783468	−	0.621432i	$-0.786551\pi$
$61$	0.387808	−	0.533772i	0.0496537	−	0.0683425i	0.833122	+	0.553089i	$0.186551\pi$
$62$	−0.476551	+	2.18699i	−0.0605221	+	0.277748i
$63$	−4.30443	−	13.2477i	−0.542308	−	1.66905i
$64$	−2.70421	+	7.52909i	−0.338026	+	0.941137i
$65$	1.18047			0.146419
$66$		0			0
$67$		−	3.00157i		−	0.366701i	−0.983048	−	0.183350i	$-0.941306\pi$
$67$		−	3.00157i		−	0.366701i	0.983048	−	0.183350i	$-0.0586942\pi$
$68$	3.23935	−	3.52455i	0.392829	−	0.427415i
$69$	−3.28396	+	1.06702i	−0.395343	+	0.128455i
$70$	14.7083	+	3.20499i	1.75798	+	0.383069i
$71$	8.54816	+	6.21060i	1.01448	+	0.737063i	0.965144	−	0.261720i	$-0.0842896\pi$
$71$	8.54816	+	6.21060i	1.01448	+	0.737063i	0.0493358	+	0.998782i	$0.484290\pi$
$72$	−9.43994	−	3.22803i	−1.11251	−	0.380426i
$73$	3.28894	−	10.1223i	0.384941	−	1.18473i	−0.551582	−	0.834120i	$-0.685976\pi$
$73$	3.28894	−	10.1223i	0.384941	−	1.18473i	0.936523	−	0.350606i	$-0.114024\pi$
$74$	−9.55557	+	4.19604i	−1.11081	+	0.487779i
$75$	−3.40172	−	4.68206i	−0.392797	−	0.540638i
$76$	−2.11650	−	10.4830i	−0.242780	−	1.20249i
$77$		0			0
$78$	−1.57453	+	0.157359i	−0.178280	+	0.0178174i
$79$	5.21464	−	3.78866i	0.586693	−	0.426257i	−0.254438	−	0.967089i	$-0.581890\pi$
$79$	5.21464	−	3.78866i	0.586693	−	0.426257i	0.841131	+	0.540832i	$0.181890\pi$
$80$	8.15810	−	7.04906i	0.912103	−	0.788109i
$81$	−2.20645	+	6.79075i	−0.245161	+	0.754527i
$82$	−4.41183	−	2.57732i	−0.487205	−	0.284617i
$83$	−1.34279	+	1.84820i	−0.147391	+	0.202866i	−0.876328	−	0.481714i	$-0.840014\pi$
$83$	−1.34279	+	1.84820i	−0.147391	+	0.202866i	0.728938	+	0.684580i	$0.240014\pi$
$84$	−20.0455	−	2.31422i	−2.18714	−	0.252502i
$85$	−6.13577	+	1.99363i	−0.665518	+	0.216240i
$86$	6.23068	+	6.99139i	0.671872	+	0.753901i
$87$	−0.376438			−0.0403584
$88$		0			0
$89$	11.5827			1.22777			0.613883	−	0.789397i	$-0.289607\pi$
$89$	11.5827			1.22777			0.613883	+	0.789397i	$0.289607\pi$
$90$	8.94563	+	10.0378i	0.942952	+	1.05808i
$91$	−1.64487	+	0.534450i	−0.172429	+	0.0560256i
$92$	−0.310006	+	2.68523i	−0.0323203	+	0.279954i
$93$	−2.37678	+	3.27135i	−0.246460	+	0.339224i
$94$	3.69347	+	2.15766i	0.380952	+	0.222546i
$95$	−4.45390	+	13.7077i	−0.456961	+	1.40638i
$96$	−9.94178	+	10.4897i	−1.01468	+	1.07060i
$97$	−7.02442	+	5.10354i	−0.713222	+	0.518186i	−0.884211	−	0.467087i	$-0.845304\pi$
$97$	−7.02442	+	5.10354i	−0.713222	+	0.518186i	0.170990	+	0.985273i	$0.445304\pi$
$98$	−12.0952	+	1.20881i	−1.22180	+	0.122108i
$99$		0			0
$100$	−4.44087	+	0.896602i	−0.444087	+	0.0896602i
$101$	−3.31000	−	4.55582i	−0.329357	−	0.453321i	0.611938	−	0.790906i	$-0.290390\pi$
$101$	−3.31000	−	4.55582i	−0.329357	−	0.453321i	−0.941295	+	0.337585i	$0.890390\pi$
$102$	7.91827	−	3.47707i	0.784025	−	0.344281i
$103$	−4.78383	+	14.7231i	−0.471364	+	1.45071i	0.379434	+	0.925219i	$0.376119\pi$
$103$	−4.78383	+	14.7231i	−0.471364	+	1.45071i	−0.850799	+	0.525492i	$0.823881\pi$
$104$	−0.400800	+	1.17209i	−0.0393017	+	0.114933i
$105$	22.0011	+	15.9847i	2.14709	+	1.55995i
$106$	6.41031	+	1.39683i	0.622625	+	0.135672i
$107$	−2.98631	+	0.970311i	−0.288697	+	0.0938035i	−0.449786	−	0.893137i	$-0.648500\pi$
$107$	−2.98631	+	0.970311i	−0.288697	+	0.0938035i	0.161088	+	0.986940i	$0.448500\pi$
$108$	−1.98361	−	1.82310i	−0.190873	−	0.175428i
$109$			16.0246i			1.53488i	0.641124	+	0.767438i	$0.278469\pi$
$109$			16.0246i			1.53488i	−0.641124	+	0.767438i	$0.721531\pi$
$110$		0			0
$111$	−18.8537			−1.78951
$112$	−8.17611	+	13.5157i	−0.772570	+	1.27712i
$113$	5.15214	+	15.8567i	0.484673	+	1.49167i	0.832454	+	0.554094i	$0.186935\pi$
$113$	5.15214	+	15.8567i	0.484673	+	1.49167i	−0.347781	+	0.937576i	$0.613065\pi$
$114$	4.11343	−	18.8773i	0.385258	−	1.76802i
$115$	2.14126	−	2.94720i	0.199674	−	0.274827i
$116$	−0.122604	+	0.267969i	−0.0113835	+	0.0248803i
$117$	−1.46917	−	0.477363i	−0.135825	−	0.0441322i
$118$	16.1954	−	7.11171i	1.49090	−	0.654686i
$119$	7.64701	−	5.55588i	0.701000	−	0.509307i
$120$	18.6144	−	5.73424i	1.69925	−	0.523462i
$121$		0			0
$122$	−0.0927891	−	0.928443i	−0.00840073	−	0.0840572i
$123$	−5.42558	−	7.46767i	−0.489208	−	0.673337i
$124$	1.55462	+	2.75738i	0.139609	+	0.247620i
$125$	−7.01053	−	2.27786i	−0.627041	−	0.203738i
$126$	−17.0095	−	9.93665i	−1.51532	−	0.885227i
$127$	2.08907	+	1.51780i	0.185375	+	0.134683i	0.676602	−	0.736349i	$-0.263452\pi$
$127$	2.08907	+	1.51780i	0.185375	+	0.134683i	−0.491228	+	0.871031i	$0.663452\pi$
$128$	4.22914	+	10.4935i	0.373806	+	0.927507i
$129$	5.22799	+	16.0901i	0.460299	+	1.41666i
$130$	1.24632	−	1.11071i	0.109310	−	0.0974160i
$131$			5.37550i			0.469659i	0.972037	+	0.234830i	$0.0754533\pi$
$131$			5.37550i			0.469659i	−0.972037	+	0.234830i	$0.924547\pi$
$132$		0			0
$133$		−	21.1169i		−	1.83106i
$134$	−2.82421	−	3.16902i	−0.243975	−	0.273762i
$135$	1.12201	+	3.45321i	0.0965676	+	0.297205i
$136$	0.103778	−	6.76912i	0.00889885	−	0.580447i
$137$	−1.34744	−	0.978973i	−0.115120	−	0.0836393i	0.528736	−	0.848786i	$-0.322666\pi$
$137$	−1.34744	−	0.978973i	−0.115120	−	0.0836393i	−0.643856	+	0.765147i	$0.722666\pi$
$138$	−2.46319	+	4.21647i	−0.209681	+	0.358929i
$139$	−12.0200	−	3.90554i	−1.01953	−	0.331264i	−0.248884	−	0.968533i	$-0.580064\pi$
$139$	−12.0200	−	3.90554i	−1.01953	−	0.331264i	−0.770641	+	0.637269i	$0.780064\pi$
$140$	18.5445	−	10.4554i	1.56729	−	0.883644i
$141$	4.54215	+	6.25173i	0.382518	+	0.526491i
$142$	14.8687	−	1.48598i	1.24775	−	0.124701i
$143$		0			0
$144$	−13.0038	+	5.47403i	−1.08365	+	0.456169i
$145$	0.321300	−	0.233438i	0.0266825	−	0.0193860i
$146$	−6.05177	−	13.7816i	−0.500848	−	1.14057i
$147$	−20.8848	−	6.78587i	−1.72255	−	0.559689i
$148$	−6.14055	+	13.4211i	−0.504750	+	1.10320i
$149$	−11.4128	+	15.7084i	−0.934973	+	1.28688i	0.0229153	+	0.999737i	$0.492705\pi$
$149$	−11.4128	+	15.7084i	−0.934973	+	1.28688i	−0.957888	+	0.287142i	$0.907295\pi$
$150$	−7.99689	−	1.74255i	−0.652944	−	0.142279i
$151$	−5.60489	−	17.2501i	−0.456119	−	1.40379i	−0.869816	−	0.493376i	$-0.835763\pi$
$151$	−5.60489	−	17.2501i	−0.456119	−	1.40379i	0.413697	−	0.910415i	$-0.364237\pi$
$152$	−12.0982	−	9.07643i	−0.981293	−	0.736195i
$153$	8.44259			0.682543
$154$		0			0
$155$		−	4.26608i		−	0.342660i
$156$	−1.51431	+	1.64763i	−0.121242	+	0.131916i
$157$	−2.78601	+	0.905229i	−0.222348	+	0.0722451i	−0.418072	−	0.908414i	$-0.637294\pi$
$157$	−2.78601	+	0.905229i	−0.222348	+	0.0722451i	0.195725	+	0.980659i	$0.437294\pi$
$158$	1.94076	−	8.90653i	0.154399	−	0.708566i
$159$	9.58872	+	6.96661i	0.760435	+	0.552488i
$160$	1.98068	−	15.1184i	0.156586	−	1.19521i
$161$	−1.64932	+	5.07608i	−0.129985	+	0.400051i
$162$	4.05995	+	9.24565i	0.318980	+	0.726407i
$163$	−2.13905	−	2.94415i	−0.167543	−	0.230603i	0.716987	−	0.697087i	$-0.245521\pi$
$163$	−2.13905	−	2.94415i	−0.167543	−	0.230603i	−0.884530	+	0.466483i	$0.845521\pi$
$164$	−7.08299	+	1.43004i	−0.553088	+	0.111667i
$165$		0			0
$166$	0.321284	+	3.21475i	0.0249365	+	0.249513i
$167$	−11.1647	+	8.11167i	−0.863954	+	0.627700i	−0.928958	−	0.370186i	$-0.879294\pi$
$167$	−11.1647	+	8.11167i	−0.863954	+	0.627700i	0.0650036	+	0.997885i	$0.479294\pi$
$168$	−23.3412	+	16.4177i	−1.80082	+	1.26665i
$169$	3.95795	−	12.1813i	0.304458	−	0.937025i
$170$	−4.60224	+	7.87807i	−0.352976	+	0.604220i
$171$	11.0864	−	15.2591i	0.847797	−	1.16689i
$172$	13.1566	+	1.51890i	1.00318	+	0.115815i
$173$	7.15127	−	2.32359i	0.543701	−	0.176659i	−0.0242734	−	0.999705i	$-0.507727\pi$
$173$	7.15127	−	2.32359i	0.543701	−	0.176659i	0.567974	+	0.823046i	$0.307727\pi$
$174$	−0.397439	+	0.354195i	−0.0301298	+	0.0268515i
$175$	−8.94561			−0.676225
$176$		0			0
$177$	31.9543			2.40184
$178$	12.2289	−	10.8983i	0.916594	−	0.816863i
$179$	−17.7897	+	5.78022i	−1.32966	+	0.432034i	−0.885802	−	0.464063i	$-0.846391\pi$
$179$	−17.7897	+	5.78022i	−1.32966	+	0.432034i	−0.443860	+	0.896096i	$0.646391\pi$
$180$	18.8894	+	2.18075i	1.40793	+	0.162543i
$181$	13.7016	−	18.8587i	1.01843	−	1.40175i	0.105137	−	0.994458i	$-0.466472\pi$
$181$	13.7016	−	18.8587i	1.01843	−	1.40175i	0.913296	−	0.407296i	$-0.133528\pi$
$182$	−1.23376	+	2.11194i	−0.0914524	+	0.156547i
$183$	0.520890	−	1.60313i	0.0385053	−	0.118507i
$184$	2.19926	+	3.12672i	0.162132	+	0.230505i
$185$	16.0921	−	11.6916i	1.18311	−	0.859583i
$186$	0.568681	+	5.69019i	0.0416977	+	0.417225i
$187$		0			0
$188$	5.92968	−	1.19719i	0.432467	−	0.0873140i
$189$	−3.12684	−	4.30373i	−0.227444	−	0.313050i
$190$	8.19535	+	18.6631i	0.594553	+	1.35397i
$191$	4.38778	−	13.5042i	0.317488	−	0.977129i	−0.657230	−	0.753690i	$-0.728272\pi$
$191$	4.38778	−	13.5042i	0.317488	−	0.977129i	0.974718	−	0.223439i	$-0.0717282\pi$
$192$	−0.626549	+	20.4292i	−0.0452173	+	1.47435i
$193$	1.22768	+	0.891963i	0.0883705	+	0.0642049i	0.631093	−	0.775707i	$-0.282607\pi$
$193$	1.22768	+	0.891963i	0.0883705	+	0.0642049i	−0.542723	+	0.839912i	$0.682607\pi$
$194$	−2.61432	+	11.9976i	−0.187697	+	0.861378i
$195$	2.86830	−	0.931969i	0.205404	−	0.0667397i
$196$	−11.6326	+	12.6568i	−0.830902	+	0.904057i
$197$		−	8.05669i		−	0.574016i	−0.957928	−	0.287008i	$-0.907339\pi$
$197$		−	8.05669i		−	0.574016i	0.957928	−	0.287008i	$-0.0926606\pi$
$198$		0			0
$199$	9.70147			0.687719			0.343860	−	0.939021i	$-0.388266\pi$
$199$	9.70147			0.687719			0.343860	+	0.939021i	$0.388266\pi$
$200$	−3.84499	+	5.12509i	−0.271882	+	0.362398i
$201$	−2.36972	−	7.29324i	−0.167147	−	0.514426i
$202$	−7.78127	−	1.69556i	−0.547489	−	0.119300i
$203$	−0.342013	+	0.470741i	−0.0240046	+	0.0330395i
$204$	5.08839	−	11.1214i	0.356259	−	0.778655i
$205$	9.26176	+	3.00933i	0.646869	+	0.210181i
$206$	8.80242	+	20.0456i	0.613294	+	1.39664i
$207$	−3.85675	+	2.80209i	−0.268063	+	0.194759i
$208$	0.679670	+	1.61459i	0.0471266	+	0.111952i
$209$		0			0
$210$	38.2687	−	3.82459i	2.64079	−	0.263922i
$211$	−11.4242	−	15.7240i	−0.786473	−	1.08249i	−0.994538	−	0.104373i	$-0.966717\pi$
$211$	−11.4242	−	15.7240i	−0.786473	−	1.08249i	0.208065	−	0.978115i	$-0.433283\pi$
$212$	8.08222	−	4.55678i	0.555089	−	0.312961i
$213$	25.6736	+	8.34186i	1.75913	+	0.571575i
$214$	−2.23993	+	3.83429i	−0.153119	+	0.262107i
$215$	−14.4401	−	10.4913i	−0.984806	−	0.715503i
$216$	−3.80965	−	0.0584059i	−0.259214	−	0.00397402i
$217$	1.93145	+	5.94438i	0.131115	+	0.403531i
$218$	15.0777	+	16.9185i	1.02119	+	1.14587i
$219$		−	27.1918i		−	1.83745i
$220$		0			0
$221$		−	1.04825i		−	0.0705132i
$222$	−19.9054	+	17.7396i	−1.33597	+	1.19060i
$223$	6.90793	+	21.2604i	0.462590	+	1.42370i	0.861989	+	0.506927i	$0.169219\pi$
$223$	6.90793	+	21.2604i	0.462590	+	1.42370i	−0.399399	+	0.916777i	$0.630781\pi$
$224$	4.08487	+	21.9627i	0.272932	+	1.46745i
$225$	−6.46412	−	4.69646i	−0.430941	−	0.313097i
$226$	20.3593	+	11.8936i	1.35428	+	0.791148i
$227$	−13.1934	−	4.28680i	−0.875677	−	0.284525i	−0.163516	−	0.986541i	$-0.552283\pi$
$227$	−13.1934	−	4.28680i	−0.875677	−	0.284525i	−0.712161	+	0.702016i	$0.752283\pi$
$228$	−13.4190	−	23.8008i	−0.888694	−	1.57625i
$229$	−10.4684	−	14.4085i	−0.691769	−	0.952138i	−1.00000		0.000826338i	$-0.999737\pi$
$229$	−10.4684	−	14.4085i	−0.691769	−	0.952138i	0.308231	−	0.951312i	$-0.400263\pi$
$230$	−0.512330	−	5.12635i	−0.0337821	−	0.338021i
$231$		0			0
$232$	0.122691	+	0.398278i	0.00805508	+	0.0261483i
$233$	−2.45239	+	1.78177i	−0.160661	+	0.116727i	−0.665211	−	0.746655i	$-0.731659\pi$
$233$	−2.45239	+	1.78177i	−0.160661	+	0.116727i	0.504550	+	0.863383i	$0.331659\pi$
$234$	−2.00029	+	0.878366i	−0.130763	+	0.0574206i
$235$	−7.75370	−	2.51933i	−0.505795	−	0.164343i
$236$	10.4074	−	22.7468i	0.677463	−	1.48069i
$237$	9.67946	−	13.3226i	0.628748	−	0.865398i
$238$	2.84603	−	13.0610i	0.184481	−	0.846618i
$239$	−2.50779	−	7.71817i	−0.162215	−	0.499247i	0.836605	−	0.547806i	$-0.184537\pi$
$239$	−2.50779	−	7.71817i	−0.162215	−	0.499247i	−0.998820	+	0.0485594i	$0.984537\pi$
$240$	14.2574	−	23.5686i	0.920313	−	1.52135i
$241$	−10.6765			−0.687734			−0.343867	−	0.939018i	$-0.611737\pi$
$241$	−10.6765			−0.687734			−0.343867	+	0.939018i	$0.611737\pi$
$242$		0			0
$243$			22.2834i			1.42948i
$244$	−0.971547	−	0.892932i	−0.0621969	−	0.0571641i
$245$	22.0338	−	7.15921i	1.40769	−	0.457385i
$246$	−12.7547	−	2.77929i	−0.813208	−	0.177201i
$247$	−1.89461	−	1.37651i	−0.120551	−	0.0875855i
$248$	4.23580	+	1.44845i	0.268974	+	0.0919767i
$249$	−1.80359	+	5.55089i	−0.114298	+	0.351773i
$250$	−9.54489	+	4.19135i	−0.603672	+	0.265084i
$251$	3.36199	+	4.62738i	0.212207	+	0.292078i	0.901830	−	0.432090i	$-0.142224\pi$
$251$	3.36199	+	4.62738i	0.212207	+	0.292078i	−0.689623	+	0.724168i	$0.742224\pi$
$252$	−27.3079	+	5.51340i	−1.72023	+	0.347311i
$253$		0			0
$254$	3.63372	−	0.363156i	0.228000	−	0.0227865i
$255$	−13.3348	+	9.68829i	−0.835057	+	0.606704i
$256$	14.3386	+	7.09971i	0.896160	+	0.443732i
$257$	7.47232	−	22.9974i	0.466111	−	1.43454i	−0.391470	−	0.920191i	$-0.628033\pi$
$257$	7.47232	−	22.9974i	0.466111	−	1.43454i	0.857580	−	0.514350i	$-0.171967\pi$
$258$	20.6590	+	12.0687i	1.28617	+	0.751362i
$259$	−17.1295	+	23.5767i	−1.06438	+	1.46499i
$260$	0.270768	−	2.34535i	0.0167923	−	0.145453i
$261$	−0.494279	+	0.160601i	−0.0305951	+	0.00994096i
$262$	5.05786	+	5.67538i	0.312476	+	0.350626i
$263$	22.3674			1.37923			0.689616	−	0.724175i	$-0.257779\pi$
$263$	22.3674			1.37923			0.689616	+	0.724175i	$0.257779\pi$
$264$		0			0
$265$	−12.5044			−0.768138
$266$	−19.8691	−	22.2949i	−1.21825	−	1.36699i
$267$	28.1438	−	9.14447i	1.72237	−	0.559632i
$268$	−5.96354	−	0.688481i	−0.364281	−	0.0420557i
$269$	−9.88522	+	13.6058i	−0.602712	+	0.829562i	−0.995953	−	0.0898731i	$-0.971354\pi$
$269$	−9.88522	+	13.6058i	−0.602712	+	0.829562i	0.393241	+	0.919435i	$0.371354\pi$
$270$	4.43377	+	2.59013i	0.269830	+	0.157631i
$271$	−1.12118	+	3.45064i	−0.0681069	+	0.209611i	−0.979318	−	0.202329i	$-0.935149\pi$
$271$	−1.12118	+	3.45064i	−0.0681069	+	0.209611i	0.911211	+	0.411941i	$0.135149\pi$
$272$	−6.25957	−	7.24439i	−0.379542	−	0.439256i
$273$	−3.57477	+	2.59722i	−0.216355	+	0.157191i
$274$	−2.34374	+	0.234235i	−0.141590	+	0.0141506i
$275$		0			0
$276$	1.36671	+	6.76933i	0.0822665	+	0.407466i
$277$	18.5009	+	25.4643i	1.11161	+	1.53000i	0.819021	+	0.573764i	$0.194517\pi$
$277$	18.5009	+	25.4643i	1.11161	+	1.53000i	0.292591	+	0.956238i	$0.405483\pi$
$278$	−16.3654	+	7.18635i	−0.981529	+	0.431009i
$279$	−1.72514	+	5.30943i	−0.103281	+	0.317867i
$280$	9.74138	−	28.4874i	0.582159	−	1.70245i
$281$	−5.02923	−	3.65395i	−0.300019	−	0.217976i	0.427583	−	0.903976i	$-0.359365\pi$
$281$	−5.02923	−	3.65395i	−0.300019	−	0.217976i	−0.727602	+	0.686000i	$0.759365\pi$
$282$	10.6779	+	2.32674i	0.635858	+	0.138556i
$283$	−21.3744	+	6.94497i	−1.27058	+	0.412836i	−0.865252	−	0.501337i	$-0.832842\pi$
$283$	−21.3744	+	6.94497i	−1.27058	+	0.412836i	−0.405326	+	0.914172i	$0.632842\pi$
$284$	14.3000	−	15.5590i	0.848547	−	0.923255i
$285$			36.8234i			2.18123i
$286$		0			0
$287$	−14.2678			−0.842204
$288$	−8.57872	+	18.0149i	−0.505506	+	1.06154i
$289$	−3.48294	−	10.7194i	−0.204879	−	0.630552i
$290$	0.119580	−	0.548776i	0.00702198	−	0.0322252i
$291$	−13.0388	+	17.9463i	−0.764347	+	1.05203i
$292$	−19.3566	−	8.85626i	−1.13276	−	0.518273i
$293$	−10.8174	−	3.51480i	−0.631962	−	0.205337i	−0.0245180	−	0.999699i	$-0.507805\pi$
$293$	−10.8174	−	3.51480i	−0.631962	−	0.205337i	−0.607444	+	0.794362i	$0.707805\pi$
$294$	−28.4348	+	12.4863i	−1.65835	+	0.728214i
$295$	−27.2739	+	19.8156i	−1.58795	+	1.15371i
$296$	6.14491	+	19.9475i	0.357166	+	1.15942i
$297$		0			0
$298$	2.73069	+	27.3231i	0.158185	+	1.58279i
$299$	0.347915	+	0.478864i	0.0201205	+	0.0276934i
$300$	−10.0826	+	5.68460i	−0.582119	+	0.328201i
$301$	24.8708	+	8.08101i	1.43353	+	0.465782i
$302$	−22.1483	−	12.9387i	−1.27449	−	0.744539i
$303$	−11.6394	−	8.45655i	−0.668668	−	0.485816i
$304$	−21.3132	+	1.80054i	−1.22240	+	0.103268i
$305$	0.549548	+	1.69133i	0.0314670	+	0.0968455i
$306$	8.91358	−	7.94372i	0.509555	−	0.454113i
$307$		−	14.1471i		−	0.807418i	−0.914887	−	0.403709i	$-0.867721\pi$
$307$		−	14.1471i		−	0.807418i	0.914887	−	0.403709i	$-0.132279\pi$
$308$		0			0
$309$			39.5511i			2.24998i
$310$	−4.01400	−	4.50408i	−0.227980	−	0.255814i
$311$	−4.52493	−	13.9263i	−0.256585	−	0.789688i	−0.993513	−	0.113717i	$-0.963724\pi$
$311$	−4.52493	−	13.9263i	−0.256585	−	0.789688i	0.736928	−	0.675971i	$-0.236276\pi$
$312$	−0.0485131	+	3.16438i	−0.00274652	+	0.179147i
$313$	−18.3845	−	13.3571i	−1.03915	−	0.754990i	−0.0690342	−	0.997614i	$-0.521992\pi$
$313$	−18.3845	−	13.3571i	−1.03915	−	0.754990i	−0.970120	+	0.242624i	$0.921992\pi$
$314$	−2.08969	+	3.57711i	−0.117928	+	0.201868i
$315$	35.7079	+	11.6022i	2.01191	+	0.653711i
$316$	−6.33122	−	11.2295i	−0.356159	−	0.631708i
$317$	−2.40072	−	3.30431i	−0.134838	−	0.185589i	0.736259	−	0.676700i	$-0.236591\pi$
$317$	−2.40072	−	3.30431i	−0.134838	−	0.185589i	−0.871097	+	0.491112i	$0.836591\pi$
$318$	16.6786	−	1.66687i	0.935290	−	0.0934734i
$319$		0			0
$320$	−12.1338	−	17.8254i	−0.678303	−	0.996470i
$321$	−6.49010	+	4.71534i	−0.362242	+	0.263184i
$322$	3.03481	+	6.91113i	0.169123	+	0.385142i
$323$	12.1724	+	3.95507i	0.677293	+	0.220066i
$324$	12.9858	+	5.94139i	0.721432	+	0.330077i
$325$	−0.583125	+	0.802602i	−0.0323459	+	0.0445204i
$326$	−5.02856	−	1.09574i	−0.278506	−	0.0606874i
$327$	12.6513	+	38.9366i	0.699617	+	2.15320i
$328$	−6.13259	+	8.17427i	−0.338615	+	0.451349i
$329$	11.9447			0.658530
$330$		0			0
$331$		−	7.57089i		−	0.416133i	−0.978115	−	0.208067i	$-0.933283\pi$
$331$		−	7.57089i		−	0.416133i	0.978115	−	0.208067i	$-0.0667171\pi$
$332$	3.36400	+	3.09179i	0.184624	+	0.169684i
$333$	−24.7556	+	8.04359i	−1.35660	+	0.440786i
$334$	−4.15525	+	19.0692i	−0.227365	+	1.04342i
$335$	6.54533	+	4.75546i	0.357610	+	0.259819i
$336$	−9.19580	+	39.2956i	−0.501672	+	2.14375i
$337$	0.391015	−	1.20342i	0.0213000	−	0.0655546i	−0.939842	−	0.341611i	$-0.889028\pi$
$337$	0.391015	−	1.20342i	0.0213000	−	0.0655546i	0.961142	+	0.276056i	$0.0890276\pi$
$338$	−7.28278	−	16.5850i	−0.396131	−	0.902103i
$339$	25.0374	+	34.4611i	1.35985	+	1.87167i
$340$	2.55358	+	12.6479i	0.138487	+	0.685927i
$341$		0			0
$342$	−2.65259	−	26.5416i	−0.143436	−	1.43521i
$343$	−5.09659	+	3.70289i	−0.275190	+	0.199937i
$344$	15.3197	−	10.7755i	0.825981	−	0.580976i
$345$	2.87607	−	8.85163i	0.154842	−	0.476556i
$346$	5.36393	−	9.18192i	0.288367	−	0.493623i
$347$	4.05895	−	5.58667i	0.217896	−	0.299908i	−0.686050	−	0.727554i	$-0.740657\pi$
$347$	4.05895	−	5.58667i	0.217896	−	0.299908i	0.903946	+	0.427646i	$0.140657\pi$
$348$	−0.0863450	+	0.747909i	−0.00462858	+	0.0400921i
$349$	15.1128	−	4.91044i	0.808969	−	0.262850i	0.124808	−	0.992181i	$-0.460169\pi$
$349$	15.1128	−	4.91044i	0.808969	−	0.262850i	0.684161	+	0.729331i	$0.260169\pi$
$350$	−9.44466	+	8.41702i	−0.504839	+	0.449909i
$351$	−0.589956			−0.0314895
$352$		0			0
$353$	2.35416			0.125300			0.0626498	−	0.998036i	$-0.480045\pi$
$353$	2.35416			0.125300			0.0626498	+	0.998036i	$0.480045\pi$
$354$	33.7370	−	30.0662i	1.79310	−	1.59800i
$355$	−27.0861	+	8.80080i	−1.43758	+	0.467098i
$356$	2.65677	−	23.0126i	0.140808	−	1.21966i
$357$	14.1944	−	19.5370i	0.751249	−	1.03401i
$358$	−13.3434	+	22.8412i	−0.705223	+	1.20719i
$359$	7.87550	−	24.2383i	0.415653	−	1.27925i	−0.496012	−	0.868315i	$-0.665203\pi$
$359$	7.87550	−	24.2383i	0.415653	−	1.27925i	0.911665	−	0.410933i	$-0.134797\pi$
$360$	21.9950	−	15.4708i	1.15924	−	0.815383i
$361$	7.76128	−	5.63890i	0.408489	−	0.296784i
$362$	−3.27833	−	32.8027i	−0.172305	−	1.72407i
$363$		0			0
$364$	0.684558	+	3.39062i	0.0358806	+	0.177717i
$365$	16.8623	+	23.2090i	0.882613	+	1.21481i
$366$	−0.958458	−	2.18268i	−0.0500994	−	0.114091i
$367$	−1.74025	+	5.35594i	−0.0908403	+	0.279578i	−0.986147	−	0.165872i	$-0.946956\pi$
$367$	−1.74025	+	5.35594i	−0.0908403	+	0.279578i	0.895307	+	0.445450i	$0.146956\pi$
$368$	5.26391	+	1.23184i	0.274400	+	0.0642141i
$369$	−10.3100	−	7.49063i	−0.536716	−	0.389947i
$370$	5.98908	−	27.4851i	0.311358	−	1.42888i
$371$	17.4237	−	5.66129i	0.904592	−	0.293920i
$372$	5.95437	+	5.47255i	0.308719	+	0.283739i
$373$		−	33.3480i		−	1.72669i	−0.504611	−	0.863347i	$-0.668364\pi$
$373$		−	33.3480i		−	1.72669i	0.504611	−	0.863347i	$-0.331636\pi$
$374$		0			0
$375$	−18.8326			−0.972510
$376$	5.13404	−	6.84328i	0.264768	−	0.352915i
$377$	0.0199407	+	0.0613710i	0.00102700	+	0.00316077i
$378$	−7.35070	−	1.60174i	−0.378079	−	0.0823847i
$379$	−11.1620	+	15.3631i	−0.573351	+	0.789150i	−0.992947	−	0.118561i	$-0.962172\pi$
$379$	−11.1620	+	15.3631i	−0.573351	+	0.789150i	0.419596	+	0.907711i	$0.362172\pi$
$380$	26.2129	+	11.9932i	1.34469	+	0.615239i
$381$	6.27432	+	2.03865i	0.321443	+	0.104443i
$382$	−8.07368	−	18.3861i	−0.413085	−	0.940713i
$383$	23.4100	−	17.0083i	1.19619	−	0.869086i	0.202289	−	0.979326i	$-0.435162\pi$
$383$	23.4100	−	17.0083i	1.19619	−	0.869086i	0.993905	+	0.110240i	$0.0351619\pi$
$384$	18.5606	+	22.1584i	0.947164	+	1.13077i
$385$		0			0
$386$	2.13543	−	0.213416i	0.108690	−	0.0108626i
$387$	13.7291	+	18.8965i	0.697892	+	0.960565i
$388$	8.52852	+	15.1268i	0.432970	+	0.767945i
$389$	−23.3288	−	7.57997i	−1.18281	−	0.384320i	−0.349403	−	0.936972i	$-0.613616\pi$
$389$	−23.3288	−	7.57997i	−1.18281	−	0.384320i	−0.833412	+	0.552653i	$0.813616\pi$
$390$	2.15142	−	3.68278i	0.108941	−	0.186485i
$391$	−2.61711	−	1.90144i	−0.132353	−	0.0961601i
$392$	−0.372669	+	24.3081i	−0.0188226	+	1.22775i
$393$	4.24391	+	13.0614i	0.214077	+	0.658862i
$394$	−7.58063	−	8.50615i	−0.381907	−	0.428534i
$395$			17.3737i			0.874165i
$396$		0			0
$397$		−	1.08190i		−	0.0542989i	−0.999631	−	0.0271495i	$-0.991357\pi$
$397$		−	1.08190i		−	0.0542989i	0.999631	−	0.0271495i	$-0.00864300\pi$
$398$	10.2427	−	9.12822i	0.513420	−	0.457556i
$399$	−16.6716	−	51.3099i	−0.834624	−	2.56871i
$400$	0.762754	+	9.02880i	0.0381377	+	0.451440i
$401$	16.8769	+	12.2618i	0.842792	+	0.612324i	0.923149	−	0.384442i	$-0.125606\pi$
$401$	16.8769	+	12.2618i	0.842792	+	0.612324i	−0.0803573	+	0.996766i	$0.525606\pi$
$402$	−9.36421	−	5.47042i	−0.467044	−	0.272840i
$403$	0.659233	+	0.214198i	0.0328388	+	0.0106700i
$404$	−9.81074	+	5.53133i	−0.488103	+	0.275194i
$405$	−11.3124	−	15.5702i	−0.562118	−	0.773689i
$406$	0.0818320	+	0.818807i	0.00406125	+	0.0406367i
$407$		0			0
$408$	−5.09201	−	16.5296i	−0.252092	−	0.818336i
$409$	−21.9502	+	15.9477i	−1.08537	+	0.788565i	−0.978611	−	0.205720i	$-0.934046\pi$
$409$	−21.9502	+	15.9477i	−1.08537	+	0.788565i	−0.106756	+	0.994285i	$0.534046\pi$
$410$	12.6100	−	5.53728i	0.622761	−	0.273467i
$411$	−4.04691	−	1.31492i	−0.199620	−	0.0648603i
$412$	28.1546	+	12.8816i	1.38708	+	0.634631i
$413$	29.0321	−	39.9593i	1.42858	−	1.96627i
$414$	−1.43539	+	6.58727i	−0.0705455	+	0.323747i
$415$	−1.90282	−	5.85628i	−0.0934058	−	0.287474i
$416$	2.23677	+	1.06516i	0.109667	+	0.0522236i
$417$	−32.2897			−1.58124
$418$		0			0
$419$		−	13.9742i		−	0.682686i	−0.939939	−	0.341343i	$-0.889118\pi$
$419$		−	13.9742i		−	0.682686i	0.939939	−	0.341343i	$-0.110882\pi$
$420$	36.8050	−	40.0454i	1.79590	−	1.95401i
$421$	24.4937	−	7.95850i	1.19375	−	0.387874i	0.356293	−	0.934374i	$-0.384040\pi$
$421$	24.4937	−	7.95850i	1.19375	−	0.387874i	0.837459	+	0.546501i	$0.184040\pi$
$422$	−26.8564	−	5.85210i	−1.30735	−	0.284876i
$423$	8.63123	+	6.27096i	0.419665	+	0.304904i
$424$	4.24558	−	12.4156i	0.206183	−	0.602956i
$425$	1.67546	−	5.15654i	0.0812718	−	0.250129i
$426$	34.9548	−	15.3493i	1.69357	−	0.743678i
$427$	−1.53149	−	2.10791i	−0.0741138	−	0.102009i
$428$	1.24284	+	6.15577i	0.0600748	+	0.297551i
$429$		0			0
$430$	−25.1171	+	2.51021i	−1.21125	+	0.121053i
$431$	14.7992	−	10.7523i	0.712855	−	0.517919i	−0.171239	−	0.985230i	$-0.554777\pi$
$431$	14.7992	−	10.7523i	0.712855	−	0.517919i	0.884093	+	0.467310i	$0.154777\pi$
$432$	−4.07713	+	3.52288i	−0.196161	+	0.169494i
$433$	−3.03401	+	9.33771i	−0.145805	+	0.448742i	−0.997114	−	0.0759234i	$-0.975810\pi$
$433$	−3.03401	+	9.33771i	−0.145805	+	0.448742i	0.851309	+	0.524665i	$0.175810\pi$
$434$	7.63233	+	4.45868i	0.366364	+	0.214024i
$435$	0.596400	−	0.820874i	0.0285952	−	0.0393579i
$436$	31.8377	+	3.67561i	1.52475	+	0.176030i
$437$	−6.87331	+	2.23327i	−0.328795	+	0.106832i
$438$	−25.5851	−	28.7088i	−1.22250	−	1.37176i
$439$	−32.0228			−1.52836			−0.764182	−	0.645001i	$-0.776857\pi$
$439$	−32.0228			−1.52836			−0.764182	+	0.645001i	$0.776857\pi$
$440$		0			0
$441$	−30.3176			−1.44370
$442$	−0.986314	−	1.10673i	−0.0469142	−	0.0526419i
$443$	16.1114	−	5.23490i	0.765474	−	0.248718i	0.0998477	−	0.995003i	$-0.468164\pi$
$443$	16.1114	−	5.23490i	0.765474	−	0.248718i	0.665626	+	0.746285i	$0.268164\pi$
$444$	−4.32453	+	37.4585i	−0.205233	+	1.77770i
$445$	−18.3508	+	25.2577i	−0.869910	+	1.19733i
$446$	27.2975	+	15.9467i	1.29257	+	0.755100i
$447$	−15.3293	+	47.1786i	−0.725049	+	2.23147i
$448$	24.9777	+	19.3445i	1.18009	+	0.913940i
$449$	−16.8333	+	12.2301i	−0.794414	+	0.577176i	−0.909270	−	0.416207i	$-0.863359\pi$
$449$	−16.8333	+	12.2301i	−0.794414	+	0.577176i	0.114856	+	0.993382i	$0.463359\pi$
$450$	−11.2437	+	1.12370i	−0.530032	+	0.0529717i
$451$		0			0
$452$	32.6858	−	6.59920i	1.53741	−	0.310400i
$453$	−27.2376	−	37.4893i	−1.27973	−	1.76140i
$454$	−17.9629	+	7.88787i	−0.843042	+	0.370196i
$455$	1.44056	−	4.43359i	0.0675346	−	0.207850i
$456$	−36.5620	−	12.5025i	−1.71217	−	0.585485i
$457$	4.07218	+	2.95861i	0.190489	+	0.138398i	0.678942	−	0.734192i	$-0.262439\pi$
$457$	4.07218	+	2.95861i	0.190489	+	0.138398i	−0.488453	+	0.872590i	$0.662439\pi$
$458$	−24.6094	−	5.36248i	−1.14992	−	0.250572i
$459$	3.06645	−	0.996349i	0.143130	−	0.0465056i
$460$	−5.36435	−	4.93028i	−0.250114	−	0.229875i
$461$		−	12.9071i		−	0.601144i	−0.953759	−	0.300572i	$-0.902822\pi$
$461$		−	12.9071i		−	0.601144i	0.953759	−	0.300572i	$-0.0971775\pi$
$462$		0			0
$463$	2.39020			0.111082			0.0555410	−	0.998456i	$-0.482312\pi$
$463$	2.39020			0.111082			0.0555410	+	0.998456i	$0.482312\pi$
$464$	0.504280	+	0.305056i	0.0234106	+	0.0141619i
$465$	−3.36804	−	10.3658i	−0.156189	−	0.480701i
$466$	−0.912720	+	4.18865i	−0.0422809	+	0.194035i
$467$	4.85951	−	6.68854i	0.224871	−	0.309509i	−0.681642	−	0.731686i	$-0.738734\pi$
$467$	4.85951	−	6.68854i	0.224871	−	0.309509i	0.906513	+	0.422177i	$0.138734\pi$
$468$	−1.28541	+	2.80946i	−0.0594183	+	0.129867i
$469$	−11.2733	−	3.66292i	−0.520553	−	0.169138i
$470$	−10.5567	+	4.63566i	−0.486945	+	0.213827i
$471$	−6.05479	+	4.39906i	−0.278990	+	0.202698i
$472$	−10.4148	−	33.8083i	−0.479379	−	1.55615i
$473$		0			0
$474$	−2.31596	−	23.1734i	−0.106376	−	1.06439i
$475$	−7.11977	−	9.79953i	−0.326678	−	0.449633i
$476$	−9.28442	−	16.4675i	−0.425551	−	0.754786i
$477$	15.5626	+	5.05659i	0.712561	+	0.231525i
$478$	−9.90980	−	5.78914i	−0.453264	−	0.264789i
$479$	−17.5499	−	12.7507i	−0.801874	−	0.582596i	0.109589	−	0.993977i	$-0.465046\pi$
$479$	−17.5499	−	12.7507i	−0.801874	−	0.582596i	−0.911463	+	0.411381i	$0.865046\pi$
$480$	−7.12316	−	38.2984i	−0.325126	−	1.74808i
$481$	0.998714	+	3.07372i	0.0455374	+	0.140150i
$482$	−11.2721	+	10.0456i	−0.513431	+	0.457566i
$483$			13.6360i			0.620461i
$484$		0			0
$485$		−	23.4033i		−	1.06269i
$486$	20.9667	+	23.5265i	0.951068	+	1.06718i
$487$	4.47921	+	13.7856i	0.202972	+	0.624685i	0.999791	+	0.0204656i	$0.00651487\pi$
$487$	4.47921	+	13.7856i	0.202972	+	0.624685i	−0.796818	+	0.604219i	$0.793485\pi$
$488$	−1.86592	−	0.0286064i	−0.0844661	−	0.00129495i
$489$	−7.52185	−	5.46495i	−0.340150	−	0.247133i
$490$	16.5268	−	28.2904i	0.746605	−	1.27803i
$491$	−32.2546	−	10.4801i	−1.45563	−	0.472962i	−0.528896	−	0.848687i	$-0.677394\pi$
$491$	−32.2546	−	10.4801i	−1.45563	−	0.472962i	−0.926731	+	0.375725i	$0.877394\pi$
$492$	−16.0813	+	9.06668i	−0.725000	+	0.408757i
$493$	−0.207293	−	0.285315i	−0.00933602	−	0.0128499i
$494$	−3.29548	+	0.329352i	−0.148271	+	0.0148183i
$495$		0			0
$496$	5.83497	−	2.45626i	0.261998	−	0.110289i
$497$	33.7574	−	24.5262i	1.51422	−	1.10015i
$498$	3.31868	+	7.55758i	0.148714	+	0.338663i
$499$	−7.35370	−	2.38936i	−0.329197	−	0.106963i	0.139755	−	0.990186i	$-0.455368\pi$
$499$	−7.35370	−	2.38936i	−0.329197	−	0.106963i	−0.468952	+	0.883224i	$0.655368\pi$
$500$	−6.13368	+	13.4061i	−0.274307	+	0.599537i
$501$	−20.7241	+	28.5243i	−0.925884	+	1.27437i
$502$	7.90350	+	1.72220i	0.352751	+	0.0768655i
$503$	4.70838	+	14.4909i	0.209936	+	0.646117i	0.999474	+	0.0324159i	$0.0103201\pi$
$503$	4.70838	+	14.4909i	0.209936	+	0.646117i	−0.789538	+	0.613701i	$0.789680\pi$
$504$	−23.6437	+	31.5152i	−1.05317	+	1.40380i
$505$	15.1787			0.675442
$506$		0			0
$507$		−	32.7230i		−	1.45328i
$508$	3.49474	−	3.80242i	0.155054	−	0.168705i
$509$	−33.0294	+	10.7319i	−1.46400	+	0.475684i	−0.929290	−	0.369350i	$-0.879580\pi$
$509$	−33.0294	+	10.7319i	−1.46400	+	0.475684i	−0.534713	+	0.845034i	$0.679580\pi$
$510$	−4.96288	+	22.7756i	−0.219760	+	1.00852i
$511$	−34.0037	−	24.7052i	−1.50424	−	1.09289i
$512$	21.8187	−	5.99552i	0.964257	−	0.264967i
$513$	2.22591	−	6.85064i	0.0982762	−	0.302463i
$514$	−13.7494	−	31.3112i	−0.606458	−	1.38108i
$515$	−24.5266	−	33.7579i	−1.08077	−	1.48755i
$516$	33.1670	−	6.69635i	1.46010	−	0.294790i
$517$		0			0
$518$	4.09850	+	41.0094i	0.180078	+	1.80185i
$519$	15.5418	−	11.2917i	0.682207	−	0.495653i
$520$	−1.92090	−	2.73096i	−0.0842369	−	0.119761i
$521$	−9.61132	+	29.5806i	−0.421080	+	1.29595i	0.485619	+	0.874171i	$0.338594\pi$
$521$	−9.61132	+	29.5806i	−0.421080	+	1.29595i	−0.906699	+	0.421779i	$0.861406\pi$
$522$	−0.370742	+	0.634633i	−0.0162270	+	0.0277771i
$523$	5.80762	−	7.99350i	0.253949	−	0.349531i	−0.662940	−	0.748672i	$-0.730692\pi$
$523$	5.80762	−	7.99350i	0.253949	−	0.349531i	0.916890	+	0.399141i	$0.130692\pi$
$524$	10.6801	+	1.23300i	0.466561	+	0.0538637i
$525$	−21.7361	+	7.06249i	−0.948642	+	0.308232i
$526$	23.6152	−	21.0457i	1.02967	−	0.917637i
$527$	−3.78828			−0.165020
$528$		0			0
$529$	−21.1734			−0.920581
$530$	−13.2020	+	11.7655i	−0.573457	+	0.511061i
$531$	41.9574	−	13.6328i	1.82080	−	0.591612i
$532$	−41.9551	−	4.84365i	−1.81898	−	0.209999i
$533$	−0.930057	+	1.28011i	−0.0402852	+	0.0554479i
$534$	21.1097	−	36.1354i	0.913507	−	1.56373i
$535$	2.61539	−	8.04933i	0.113073	−	0.348003i
$536$	−6.94402	+	4.88427i	−0.299936	+	0.210968i
$537$	−38.6620	+	28.0896i	−1.66839	+	1.21216i
$538$	2.36519	+	23.6660i	0.101971	+	1.02031i
$539$		0			0
$540$	7.11820	−	1.43715i	0.306319	−	0.0618450i
$541$	−4.92883	−	6.78395i	−0.211907	−	0.291665i	0.689811	−	0.723989i	$-0.257694\pi$
$541$	−4.92883	−	6.78395i	−0.211907	−	0.291665i	−0.901718	+	0.432325i	$0.857694\pi$
$542$	2.06302	+	4.69807i	0.0886141	+	0.201800i
$543$	18.4035	−	56.6402i	0.789771	−	2.43067i
$544$	−13.4251	−	1.75884i	−0.575597	−	0.0754097i
$545$	−34.9437	−	25.3881i	−1.49682	−	1.08751i
$546$	−1.33044	+	6.10565i	−0.0569376	+	0.261298i
$547$	3.22553	−	1.04804i	0.137914	−	0.0448108i	−0.239247	−	0.970959i	$-0.576901\pi$
$547$	3.22553	−	1.04804i	0.137914	−	0.0448108i	0.377160	+	0.926148i	$0.376901\pi$
$548$	−2.25410	+	2.45255i	−0.0962902	+	0.104768i
$549$		−	2.32721i		−	0.0993230i
$550$		0			0
$551$	−0.787883			−0.0335650
$552$	7.81230	+	5.86102i	0.332514	+	0.249462i
$553$	−7.86584	−	24.2086i	−0.334490	−	1.02945i
$554$	43.4927	+	9.47719i	1.84783	+	0.402647i
$555$	29.8703	−	41.1129i	1.26792	−	1.74515i
$556$	−10.5166	+	22.9856i	−0.446004	+	0.974807i
$557$	26.6653	+	8.66407i	1.12984	+	0.367108i	0.813517	−	0.581542i	$-0.197550\pi$
$557$	26.6653	+	8.66407i	1.12984	+	0.367108i	0.316327	+	0.948650i	$0.397550\pi$
$558$	3.17432	+	7.22883i	0.134380	+	0.306021i
$559$	2.34624	−	1.70465i	0.0992356	−	0.0720989i
$560$	−16.5193	−	39.2424i	−0.698066	−	1.65829i
$561$		0			0
$562$	−8.74784	+	0.874264i	−0.369005	+	0.0368786i
$563$	−5.17851	−	7.12760i	−0.218248	−	0.300393i	0.685829	−	0.727763i	$-0.259440\pi$
$563$	−5.17851	−	7.12760i	−0.218248	−	0.300393i	−0.904077	+	0.427371i	$0.859440\pi$
$564$	13.4628	−	7.59038i	0.566887	−	0.319613i
$565$	−42.7402	−	13.8871i	−1.79810	−	0.584237i
$566$	−16.0323	+	27.4438i	−0.673886	+	1.15355i
$567$	22.8121	+	16.5739i	0.958017	+	0.696040i
$568$	0.458121	−	29.8819i	0.0192223	−	1.25382i
$569$	6.41754	+	19.7512i	0.269037	+	0.828011i	0.990736	+	0.135804i	$0.0433617\pi$
$569$	6.41754	+	19.7512i	0.269037	+	0.828011i	−0.721699	+	0.692207i	$0.756638\pi$
$570$	34.6475	+	38.8777i	1.45123	+	1.62841i
$571$			2.93591i			0.122864i	0.998111	+	0.0614321i	$0.0195668\pi$
$571$			2.93591i			0.122864i	−0.998111	+	0.0614321i	$0.980433\pi$
$572$		0			0
$573$		−	36.2767i		−	1.51548i
$574$	−15.0638	+	13.4248i	−0.628751	+	0.560339i
$575$	0.946069	+	2.91170i	0.0394538	+	0.121426i
$576$	7.89309	+	27.0917i	0.328879	+	1.12882i
$577$	8.85175	+	6.43118i	0.368503	+	0.267733i	0.756590	−	0.653890i	$-0.226864\pi$
$577$	8.85175	+	6.43118i	0.368503	+	0.267733i	−0.388087	+	0.921623i	$0.626864\pi$
$578$	−13.7632	−	8.04026i	−0.572475	−	0.334431i
$579$	3.68723	+	1.19805i	0.153236	+	0.0497894i
$580$	−0.390098	−	0.691905i	−0.0161979	−	0.0287298i
$581$	5.30280	+	7.29868i	0.219997	+	0.302800i
$582$	3.11973	+	31.2159i	0.129317	+	1.29394i
$583$		0			0
$584$	−28.7694	+	8.86254i	−1.19049	+	0.366735i
$585$	3.36859	−	2.44743i	0.139274	−	0.101189i
$586$	−14.7280	+	6.46737i	−0.608410	+	0.267165i
$587$	19.7525	+	6.41796i	0.815271	+	0.264898i	0.686829	−	0.726819i	$-0.259002\pi$
$587$	19.7525	+	6.41796i	0.815271	+	0.264898i	0.128443	+	0.991717i	$0.459002\pi$
$588$	−18.2726	+	39.9374i	−0.753550	+	1.64699i
$589$	−4.97458	+	6.84692i	−0.204974	+	0.282122i
$590$	−10.1507	+	46.5834i	−0.417897	+	1.91781i
$591$	−6.36070	−	19.5762i	−0.261644	−	0.805258i
$592$	25.2565	+	15.2785i	1.03804	+	0.627943i
$593$	29.8145			1.22433			0.612167	−	0.790729i	$-0.290298\pi$
$593$	29.8145			1.22433			0.612167	+	0.790729i	$0.290298\pi$
$594$		0			0
$595$			25.4776i			1.04448i
$596$	28.5916	+	26.2781i	1.17116	+	1.07639i
$597$	23.5727	−	7.65924i	0.964767	−	0.313472i
$598$	0.817893	+	0.178222i	0.0334461	+	0.00728802i
$599$	4.40781	+	3.20246i	0.180098	+	0.130849i	0.674182	−	0.738565i	$-0.264496\pi$
$599$	4.40781	+	3.20246i	0.180098	+	0.130849i	−0.494084	+	0.869414i	$0.664496\pi$
$600$	−5.29638	+	15.4886i	−0.216224	+	0.632318i
$601$	5.13576	−	15.8062i	0.209492	−	0.644750i	−0.790007	−	0.613098i	$-0.789923\pi$
$601$	5.13576	−	15.8062i	0.209492	−	0.644750i	0.999499	−	0.0316523i	$-0.0100769\pi$
$602$	33.8618	−	14.8694i	1.38010	−	0.606030i
$603$	−6.22308	−	8.56533i	−0.253423	−	0.348807i
$604$	−35.5581	+	7.17910i	−1.44684	+	0.292113i
$605$		0			0
$606$	−20.2456	+	2.02336i	−0.822423	+	0.0821934i
$607$	−24.7007	+	17.9461i	−1.00257	+	0.728410i	−0.962638	−	0.270793i	$-0.912714\pi$
$607$	−24.7007	+	17.9461i	−1.00257	+	0.728410i	−0.0399322	+	0.999202i	$0.512714\pi$
$608$	−20.8081	+	21.9548i	−0.843879	+	0.890386i
$609$	−0.459380	+	1.41383i	−0.0186150	+	0.0572912i
$610$	2.17160	+	1.26861i	0.0879255	+	0.0513647i
$611$	0.778618	−	1.07168i	0.0314995	−	0.0433554i
$612$	1.93651	−	16.7738i	0.0782786	−	0.678039i
$613$	−1.51574	+	0.492493i	−0.0612201	+	0.0198916i	−0.339467	−	0.940618i	$-0.610247\pi$
$613$	−1.51574	+	0.492493i	−0.0612201	+	0.0198916i	0.278247	+	0.960510i	$0.410247\pi$
$614$	−13.3112	−	14.9363i	−0.537195	−	0.602782i
$615$	24.8801			1.00326
$616$		0			0
$617$	8.83199			0.355562			0.177781	−	0.984070i	$-0.443108\pi$
$617$	8.83199			0.355562			0.177781	+	0.984070i	$0.443108\pi$
$618$	37.2140	+	41.7575i	1.49697	+	1.67973i
$619$	−26.7273	+	8.68424i	−1.07426	+	0.349049i	−0.792146	−	0.610331i	$-0.791036\pi$
$619$	−26.7273	+	8.68424i	−1.07426	+	0.349049i	−0.282116	+	0.959380i	$0.591036\pi$
$620$	−8.47587	−	0.978526i	−0.340399	−	0.0392986i
$621$	−1.07013	+	1.47291i	−0.0429428	+	0.0591057i
$622$	−17.8808	−	10.4457i	−0.716953	−	0.418833i
$623$	14.1348	−	43.5024i	0.566298	−	1.74289i
$624$	2.92618	+	3.38655i	0.117141	+	0.135571i
$625$	25.2372	−	18.3359i	1.00949	−	0.733436i
$626$	−31.9780	+	3.19590i	−1.27810	+	0.127734i
$627$		0			0
$628$	1.15948	+	5.74289i	0.0462681	+	0.229166i
$629$	−10.3821	−	14.2898i	−0.413963	−	0.569771i
$630$	48.6166	−	21.3485i	1.93693	−	0.850546i
$631$	−4.00063	+	12.3127i	−0.159263	+	0.490160i	−0.998568	−	0.0535006i	$-0.982962\pi$
$631$	−4.00063	+	12.3127i	−0.159263	+	0.490160i	0.839305	+	0.543661i	$0.182962\pi$
$632$	−17.2504	−	5.89883i	−0.686183	−	0.234643i
$633$	−40.1726	−	29.1871i	−1.59672	−	1.16008i
$634$	−5.64371	−	1.22978i	−0.224140	−	0.0488409i
$635$	−6.61951	+	2.15081i	−0.262687	+	0.0853523i
$636$	16.0407	−	17.4529i	0.636054	−	0.692054i
$637$			3.76432i			0.149148i
$638$		0			0
$639$	37.2694			1.47435
$640$	−29.5829	−	7.40296i	−1.16937	−	0.292628i
$641$	−7.00300	−	21.5530i	−0.276602	−	0.851293i	−0.988791	−	0.149305i	$-0.952296\pi$
$641$	−7.00300	−	21.5530i	−0.276602	−	0.851293i	0.712189	−	0.701987i	$-0.247704\pi$
$642$	−2.41546	+	11.0850i	−0.0953305	+	0.437490i
$643$	19.6312	−	27.0200i	0.774177	−	1.06556i	−0.221723	−	0.975110i	$-0.571168\pi$
$643$	19.6312	−	27.0200i	0.774177	−	1.06556i	0.995901	−	0.0904539i	$-0.0288318\pi$
$644$	9.70687	+	4.44119i	0.382504	+	0.175007i
$645$	−43.3695	−	14.0916i	−1.70767	−	0.554856i
$646$	16.5729	−	7.27748i	0.652051	−	0.286329i
$647$	−14.8073	+	10.7581i	−0.582133	+	0.422945i	−0.839493	−	0.543371i	$-0.817148\pi$
$647$	−14.8073	+	10.7581i	−0.582133	+	0.422945i	0.257359	+	0.966316i	$0.417148\pi$
$648$	19.3005	−	5.94561i	0.758197	−	0.233566i
$649$		0			0
$650$	0.139522	+	1.39605i	0.00547249	+	0.0547574i
$651$	9.38608	+	12.9188i	0.367870	+	0.506329i
$652$	−6.34008	+	3.57456i	−0.248297	+	0.139991i
$653$	−21.8018	−	7.08385i	−0.853172	−	0.277212i	−0.150398	−	0.988626i	$-0.548056\pi$
$653$	−21.8018	−	7.08385i	−0.853172	−	0.277212i	−0.702774	+	0.711413i	$0.748056\pi$
$654$	49.9929	+	29.2051i	1.95488	+	1.14201i
$655$	−11.7220	−	8.51652i	−0.458016	−	0.332768i
$656$	1.21656	+	14.4005i	0.0474986	+	0.562246i
$657$	−11.6009	−	35.7040i	−0.452596	−	1.39295i
$658$	12.6110	−	11.2389i	0.491628	−	0.438136i
$659$			29.7976i			1.16075i	0.814349	+	0.580375i	$0.197094\pi$
$659$			29.7976i			1.16075i	−0.814349	+	0.580375i	$0.802906\pi$
$660$		0			0
$661$			14.8182i			0.576361i	0.957576	+	0.288181i	$0.0930503\pi$
$661$			14.8182i			0.576361i	−0.957576	+	0.288181i	$0.906950\pi$
$662$	−7.12353	−	7.99324i	−0.276864	−	0.310666i
$663$	−0.827589	−	2.54706i	−0.0321409	−	0.0989195i
$664$	6.46077	+	0.0990503i	0.250727	+	0.00384390i
$665$	46.0481	+	33.4559i	1.78567	+	1.29737i
$666$	−18.5684	+	31.7852i	−0.719510	+	1.23165i
$667$	0.189392	+	0.0615371i	0.00733328	+	0.00238273i
$668$	13.5554	+	24.0428i	0.524474	+	0.930242i
$669$	33.5699	+	46.2050i	1.29789	+	1.78639i
$670$	11.3849	−	1.13782i	0.439839	−	0.0439577i
$671$		0			0
$672$	27.2648	+	50.1402i	1.05176	+	1.93420i
$673$	−10.2724	+	7.46334i	−0.395972	+	0.287691i	−0.767898	−	0.640572i	$-0.778697\pi$
$673$	−10.2724	+	7.46334i	−0.395972	+	0.287691i	0.371926	+	0.928262i	$0.378697\pi$
$674$	−0.719483	−	1.63847i	−0.0277135	−	0.0631114i
$675$	−2.90209	−	0.942948i	−0.111702	−	0.0362941i
$676$	−23.2940	−	10.6577i	−0.895924	−	0.409913i
$677$	−15.3716	+	21.1571i	−0.590777	+	0.813135i	−0.994825	−	0.101603i	$-0.967603\pi$
$677$	−15.3716	+	21.1571i	−0.590777	+	0.813135i	0.404048	+	0.914738i	$0.367603\pi$
$678$	58.8590	+	12.8256i	2.26047	+	0.492563i
$679$	10.5957	+	32.6103i	0.406627	+	1.25147i
$680$	14.5965	+	10.9508i	0.559752	+	0.419943i
$681$	−35.4418			−1.35813
$682$		0			0
$683$			40.9743i			1.56784i	0.620863	+	0.783919i	$0.286782\pi$
$683$			40.9743i			1.56784i	−0.620863	+	0.783919i	$0.713218\pi$
$684$	−27.7739	−	25.5265i	−1.06196	−	0.976030i
$685$	4.26956	−	1.38727i	0.163132	−	0.0530047i
$686$	−1.89682	+	8.70489i	−0.0724211	+	0.332354i
$687$	−36.8115	−	26.7451i	−1.40444	−	1.02039i
$688$	6.03553	−	25.7911i	0.230102	−	0.983276i
$689$	0.627839	−	1.93229i	0.0239188	−	0.0736144i
$690$	−5.29208	−	12.0516i	−0.201466	−	0.458795i
$691$	−6.68706	−	9.20395i	−0.254388	−	0.350135i	0.662654	−	0.748926i	$-0.269430\pi$
$691$	−6.68706	−	9.20395i	−0.254388	−	0.350135i	−0.917042	+	0.398791i	$0.869430\pi$
$692$	−2.97620	−	14.7411i	−0.113138	−	0.560374i
$693$		0			0
$694$	−0.971167	−	9.71745i	−0.0368650	−	0.368869i
$695$	27.5602	−	20.0236i	1.04542	−	0.759539i
$696$	0.612554	+	0.870876i	0.0232188	+	0.0330105i
$697$	2.67228	−	8.22445i	0.101220	−	0.311523i
$698$	11.3356	−	19.4042i	0.429059	−	0.734458i
$699$	−4.55215	+	6.26549i	−0.172178	+	0.236983i
$700$	−2.05189	+	17.7732i	−0.0775540	+	0.671763i
$701$	−42.7680	+	13.8962i	−1.61532	+	0.524851i	−0.970832	−	0.239760i	$-0.922931\pi$
$701$	−42.7680	+	13.8962i	−1.61532	+	0.524851i	−0.644492	+	0.764611i	$0.722931\pi$
$702$	−0.622868	+	0.555096i	−0.0235086	+	0.0209508i
$703$	−39.4606			−1.48828
$704$		0			0
$705$	−20.8290			−0.784465
$706$	2.48550	−	2.21506i	0.0935429	−	0.0833648i
$707$	−21.1500	+	6.87207i	−0.795429	+	0.258451i
$708$	7.32948	−	63.4870i	0.275459	−	2.38599i
$709$	24.1486	−	33.2378i	0.906921	−	1.24827i	−0.0612857	−	0.998120i	$-0.519520\pi$
$709$	24.1486	−	33.2378i	0.906921	−	1.24827i	0.968207	−	0.250150i	$-0.0804799\pi$
$710$	−20.3164	+	34.7774i	−0.762460	+	1.30517i
$711$	7.02566	−	21.6227i	0.263483	−	0.810916i
$712$	−18.8478	−	26.7962i	−0.706352	−	1.00423i
$713$	1.73057	−	1.25733i	0.0648102	−	0.0470874i
$714$	−3.39624	−	33.9826i	−0.127101	−	1.27177i
$715$		0			0
$716$	7.40367	+	36.6704i	0.276688	+	1.37044i
$717$	−12.1869	−	16.7738i	−0.455127	−	0.626429i
$718$	−14.4912	−	33.0006i	−0.540808	−	1.23157i
$719$	−4.06174	+	12.5007i	−0.151477	+	0.466199i	−0.997787	−	0.0664921i	$-0.978819\pi$
$719$	−4.06174	+	12.5007i	−0.151477	+	0.466199i	0.846310	+	0.532691i	$0.178819\pi$
$720$	8.66544	−	37.0293i	0.322942	−	1.38000i
$721$	49.4591	+	35.9342i	1.84195	+	1.33826i
$722$	2.88856	−	13.2562i	0.107501	−	0.493343i
$723$	−25.9418	+	8.42901i	−0.964787	+	0.313478i
$724$	−34.3257	−	31.5481i	−1.27570	−	1.17248i
$725$			0.333766i			0.0123958i
$726$		0			0
$727$	24.2293			0.898616			0.449308	−	0.893377i	$-0.351671\pi$
$727$	24.2293			0.898616			0.449308	+	0.893377i	$0.351671\pi$
$728$	3.91302	+	2.93566i	0.145026	+	0.108803i
$729$	10.9732	+	33.7721i	0.406416	+	1.25082i
$730$	39.6406	+	8.63780i	1.46716	+	0.319700i
$731$	−9.31631	+	12.8228i	−0.344576	+	0.474268i
$732$	−3.06564	−	1.40262i	−0.113309	−	0.0518424i
$733$	27.9929	+	9.09545i	1.03394	+	0.335948i	0.776347	−	0.630305i	$-0.217070\pi$
$733$	27.9929	+	9.09545i	1.03394	+	0.335948i	0.257594	+	0.966253i	$0.417070\pi$
$734$	3.20213	+	7.29215i	0.118193	+	0.269158i
$735$	47.8857	−	34.7910i	1.76629	−	1.28329i
$736$	6.71663	−	3.65231i	0.247578	−	0.134626i
$737$		0			0
$738$	−17.9332	+	1.79225i	−0.660128	+	0.0659736i
$739$	19.6547	+	27.0524i	0.723010	+	0.995138i	0.999418	+	0.0340981i	$0.0108559\pi$
$739$	19.6547	+	27.0524i	0.723010	+	0.995138i	−0.276408	+	0.961040i	$0.589144\pi$
$740$	−19.5378	−	34.6536i	−0.718224	−	1.27389i
$741$	−5.69028	−	1.84888i	−0.209038	−	0.0679205i
$742$	13.0689	−	22.3712i	0.479775	−	0.821274i
$743$	27.7234	+	20.1422i	1.01707	+	0.738947i	0.965681	−	0.259732i	$-0.0836341\pi$
$743$	27.7234	+	20.1422i	1.01707	+	0.738947i	0.0513924	+	0.998679i	$0.483634\pi$
$744$	11.4357	+	0.175321i	0.419254	+	0.00642760i
$745$	−16.1726	−	49.7742i	−0.592519	−	1.82359i
$746$	−31.3775	−	35.2084i	−1.14881	−	1.28907i
$747$			8.05802i			0.294827i
$748$		0			0
$749$			12.4001i			0.453089i
$750$	−19.8832	+	17.7198i	−0.726032	+	0.647035i
$751$	−4.49020	−	13.8194i	−0.163850	−	0.504278i	0.835100	−	0.550098i	$-0.185410\pi$
$751$	−4.49020	−	13.8194i	−0.163850	−	0.504278i	−0.998950	+	0.0458204i	$0.985410\pi$
$752$	−1.01847	−	12.0557i	−0.0371397	−	0.439627i
$753$	11.8223	+	8.58938i	0.430828	+	0.313015i
$754$	0.0787977	+	0.0460324i	0.00286964	+	0.00167640i
$755$	46.4960	+	15.1075i	1.69216	+	0.549817i
$756$	−9.26787	+	5.22526i	−0.337069	+	0.190041i
$757$	7.85067	+	10.8055i	0.285338	+	0.392734i	0.927493	−	0.373841i	$-0.121959\pi$
$757$	7.85067	+	10.8055i	0.285338	+	0.392734i	−0.642155	+	0.766575i	$0.721959\pi$
$758$	2.67067	+	26.7226i	0.0970031	+	0.970608i
$759$		0			0
$760$	38.9598	−	12.0017i	1.41322	−	0.435348i
$761$	−23.6765	+	17.2020i	−0.858273	+	0.623572i	−0.927415	−	0.374035i	$-0.877974\pi$
$761$	−23.6765	+	17.2020i	−0.858273	+	0.623572i	0.0691416	+	0.997607i	$0.477974\pi$
$762$	8.54254	−	3.75120i	0.309463	−	0.135891i
$763$	60.1851	+	19.5553i	2.17885	+	0.707950i
$764$	−25.8237	−	11.8152i	−0.934270	−	0.427457i
$765$	−13.3758	+	18.4102i	−0.483603	+	0.665622i
$766$	8.71262	−	39.9839i	0.314800	−	1.44468i
$767$	−1.69268	−	5.20954i	−0.0611192	−	0.188106i
$768$	40.4451	+	5.93074i	1.45944	+	0.214007i
$769$	13.2263			0.476952			0.238476	−	0.971148i	$-0.423352\pi$
$769$	13.2263			0.476952			0.238476	+	0.971148i	$0.423352\pi$
$770$		0			0
$771$		−	61.7787i		−	2.22491i
$772$	2.05375	−	2.23457i	0.0739162	−	0.0804239i
$773$	12.2575	−	3.98270i	0.440871	−	0.143248i	−0.0801666	−	0.996781i	$-0.525545\pi$
$773$	12.2575	−	3.98270i	0.440871	−	0.143248i	0.521037	+	0.853534i	$0.325545\pi$
$774$	32.2750	+	7.03283i	1.16010	+	0.252790i
$775$	2.90052	+	2.10735i	0.104190	+	0.0756983i
$776$	23.2372	+	7.94607i	0.834168	+	0.285247i
$777$	−23.0077	+	70.8105i	−0.825398	+	2.54031i
$778$	−31.7623	+	13.9474i	−1.13873	+	0.500040i
$779$	−11.3557	−	15.6298i	−0.406861	−	0.559996i
$780$	−1.19373	−	5.91253i	−0.0427422	−	0.211702i
$781$		0			0
$782$	−4.55220	+	0.454949i	−0.162786	+	0.0162690i
$783$	−0.160575	+	0.116664i	−0.00573847	+	0.00416924i
$784$	22.4783	+	26.0149i	0.802798	+	0.929103i
$785$	2.43996	−	7.50944i	0.0870860	−	0.268023i
$786$	16.7703	+	9.79694i	0.598177	+	0.349445i
$787$	28.0435	−	38.5985i	0.999642	−	1.37589i	0.0740976	−	0.997251i	$-0.476392\pi$
$787$	28.0435	−	38.5985i	0.999642	−	1.37589i	0.925545	−	0.378639i	$-0.123608\pi$
$788$	−16.0071	−	1.84799i	−0.570228	−	0.0658320i
$789$	54.3484	−	17.6589i	1.93485	−	0.628672i
$790$	16.3471	+	18.3429i	0.581603	+	0.652611i
$791$	65.8418			2.34106
$792$		0			0
$793$	−0.288953			−0.0102610
$794$	−1.01797	−	1.14225i	−0.0361264	−	0.0405371i
$795$	−30.3832	+	9.87212i	−1.07758	+	0.350128i
$796$	2.22526	−	19.2749i	0.0788722	−	0.683181i
$797$	0.0183825	−	0.0253014i	0.000651143	−	0.000896222i	−0.808691	−	0.588233i	$-0.799824\pi$
$797$	0.0183825	−	0.0253014i	0.000651143	−	0.000896222i	0.809342	+	0.587337i	$0.199824\pi$
$798$	−65.8797	−	38.4859i	−2.33212	−	1.36238i
$799$	−2.23716	+	6.88528i	−0.0791452	+	0.243584i
$800$	9.30060	+	8.81480i	0.328826	+	0.311650i
$801$	33.0526	−	24.0141i	1.16786	−	0.848498i
$802$	29.3557	−	2.93382i	1.03658	−	0.103597i
$803$		0			0
$804$	−15.0338	+	3.03529i	−0.530201	+	0.107046i
$805$	−8.45602	−	11.6387i	−0.298036	−	0.410211i
$806$	0.897551	−	0.394132i	0.0316149	−	0.0138827i
$807$	−13.2775	+	40.8639i	−0.467389	+	1.43848i
$808$	−5.15357	+	15.0709i	−0.181302	+	0.530194i
$809$	−24.3067	−	17.6599i	−0.854579	−	0.620888i	0.0718261	−	0.997417i	$-0.477117\pi$
$809$	−24.3067	−	17.6599i	−0.854579	−	0.620888i	−0.926405	+	0.376530i	$0.877117\pi$
$810$	−26.5936	−	5.79484i	−0.934405	−	0.203610i
$811$	24.4225	−	7.93534i	0.857589	−	0.278647i	0.152968	−	0.988231i	$-0.451117\pi$
$811$	24.4225	−	7.93534i	0.857589	−	0.278647i	0.704621	+	0.709584i	$0.251117\pi$
$812$	0.856821	+	0.787489i	0.0300685	+	0.0276354i
$813$			9.26955i			0.325097i
$814$		0			0
$815$	9.80905			0.343596
$816$	−20.9289	−	12.6606i	−0.732659	−	0.443210i
$817$	10.9422	+	33.6765i	0.382818	+	1.17819i
$818$	−8.16932	+	37.4906i	−0.285634	+	1.31083i
$819$	−3.58576	+	4.93537i	−0.125296	+	0.172456i
$820$	8.10334	−	17.7110i	0.282981	−	0.618496i
$821$	13.5652	+	4.40760i	0.473429	+	0.153826i	0.536007	−	0.844214i	$-0.319932\pi$
$821$	13.5652	+	4.40760i	0.473429	+	0.153826i	−0.0625779	+	0.998040i	$0.519932\pi$
$822$	−5.50991	+	2.41951i	−0.192180	+	0.0843900i
$823$	−37.2934	+	27.0953i	−1.29997	+	0.944481i	−0.999955	−	0.00945414i	$-0.996991\pi$
$823$	−37.2934	+	27.0953i	−1.29997	+	0.944481i	−0.300012	+	0.953936i	$0.596991\pi$
$824$	41.8457	−	12.8908i	1.45777	−	0.449071i
$825$		0			0
$826$	−6.94639	−	69.5052i	−0.241696	−	2.41840i
$827$	−11.5365	−	15.8787i	−0.401165	−	0.552156i	0.559871	−	0.828580i	$-0.310851\pi$
$827$	−11.5365	−	15.8787i	−0.401165	−	0.552156i	−0.961036	+	0.276424i	$0.910851\pi$
$828$	4.68257	+	8.30533i	0.162731	+	0.288630i
$829$	−1.14259	−	0.371248i	−0.0396836	−	0.0128940i	0.289108	−	0.957297i	$-0.406641\pi$
$829$	−1.14259	−	0.371248i	−0.0396836	−	0.0128940i	−0.328792	+	0.944403i	$0.606641\pi$
$830$	−7.51921	−	4.39260i	−0.260996	−	0.152469i
$831$	65.0575	+	47.2670i	2.25682	+	1.63968i
$832$	3.36378	−	0.980026i	0.116618	−	0.0339763i
$833$	−6.35738	−	19.5660i	−0.220270	−	0.677922i
$834$	−34.0911	+	30.3818i	−1.18048	+	1.05203i
$835$		−	37.1977i		−	1.28728i
$836$		0			0
$837$			2.13204i			0.0736941i
$838$	−13.1485	−	14.7538i	−0.454207	−	0.509662i
$839$	7.92940	+	24.4042i	0.273753	+	0.842526i	0.989547	+	0.144214i	$0.0460652\pi$
$839$	7.92940	+	24.4042i	0.273753	+	0.842526i	−0.715793	+	0.698312i	$0.753935\pi$
$840$	1.17910	−	76.9096i	0.0406829	−	2.65363i
$841$	−23.4439	−	17.0330i	−0.808411	−	0.587345i
$842$	18.3719	−	31.4489i	0.633139	−	1.08380i
$843$	−15.1048	−	4.90786i	−0.520238	−	0.169036i
$844$	−33.8610	+	19.0909i	−1.16554	+	0.657137i
$845$	20.2923	+	27.9300i	0.698077	+	0.960820i
$846$	15.0132	−	1.50042i	0.516163	−	0.0515856i
$847$		0			0
$848$	−7.19958	−	17.1030i	−0.247235	−	0.587319i
$849$	−46.4527	+	33.7499i	−1.59425	+	1.15829i
$850$	−3.08291	−	7.02067i	−0.105743	−	0.240807i
$851$	9.48556	+	3.08204i	0.325161	+	0.105651i
$852$	22.4625	−	49.0950i	0.769552	−	1.68197i
$853$	27.7449	−	38.1876i	0.949967	−	1.30752i	−0.00157486	−	0.999999i	$-0.500501\pi$
$853$	27.7449	−	38.1876i	0.949967	−	1.30752i	0.951542	−	0.307519i	$-0.0994987\pi$
$854$	−3.60028	−	0.784512i	−0.123199	−	0.0268455i
$855$	15.7101	+	48.3507i	0.537273	+	1.65356i
$856$	7.10421	+	5.32979i	0.242817	+	0.182168i
$857$	−28.7877			−0.983370			−0.491685	−	0.870773i	$-0.663619\pi$
$857$	−28.7877			−0.983370			−0.491685	+	0.870773i	$0.663619\pi$
$858$		0			0
$859$			50.4595i			1.72165i	0.508897	+	0.860827i	$0.330053\pi$
$859$			50.4595i			1.72165i	−0.508897	+	0.860827i	$0.669947\pi$
$860$	−24.1564	+	26.2832i	−0.823726	+	0.896249i
$861$	−34.6681	+	11.2643i	−1.18149	+	0.383888i
$862$	5.50792	−	25.2769i	0.187600	−	0.860934i
$863$	18.9772	+	13.7877i	0.645990	+	0.469339i	0.861903	−	0.507073i	$-0.169273\pi$
$863$	18.9772	+	13.7877i	0.645990	+	0.469339i	−0.215913	+	0.976413i	$0.569273\pi$
$864$	−0.989874	+	7.55563i	−0.0336762	+	0.257048i
$865$	−6.26303	+	19.2756i	−0.212949	+	0.655391i
$866$	5.58269	+	12.7134i	0.189708	+	0.432018i
$867$	−16.9258	−	23.2963i	−0.574829	−	0.791184i
$868$	12.2533	−	2.47392i	0.415905	−	0.0839704i
$869$		0			0
$870$	−0.142698	−	1.42783i	−0.00483791	−	0.0484079i
$871$	−1.06349	+	0.772674i	−0.0360351	+	0.0261811i
$872$	37.0722	−	26.0757i	1.25542	−	0.883036i
$873$	−9.46396	+	29.1271i	−0.320306	+	0.985802i
$874$	−5.15544	+	8.82504i	−0.174385	+	0.298511i
$875$	−17.1104	+	23.5504i	−0.578436	+	0.796148i
$876$	−54.0248	−	6.23709i	−1.82533	−	0.210732i
$877$	27.5850	−	8.96292i	0.931480	−	0.302656i	0.196312	−	0.980541i	$-0.437103\pi$
$877$	27.5850	−	8.96292i	0.931480	−	0.302656i	0.735168	+	0.677885i	$0.237103\pi$
$878$	−33.8092	+	30.1306i	−1.14101	+	1.01686i
$879$	−29.0592			−0.980143
$880$		0			0
$881$	−30.9774			−1.04365			−0.521827	−	0.853051i	$-0.674749\pi$
$881$	−30.9774			−1.04365			−0.521827	+	0.853051i	$0.674749\pi$
$882$	−32.0090	+	28.5262i	−1.07780	+	0.960527i
$883$	39.1926	−	12.7344i	1.31893	−	0.428548i	0.436806	−	0.899556i	$-0.356110\pi$
$883$	39.1926	−	12.7344i	1.31893	−	0.428548i	0.882129	+	0.471008i	$0.156110\pi$
$884$	−2.08268	−	0.240442i	−0.0700479	−	0.00808693i
$885$	−50.6260	+	69.6807i	−1.70177	+	2.34229i
$886$	12.0846	−	20.6863i	0.405990	−	0.694970i
$887$	−2.64584	+	8.14306i	−0.0888386	+	0.273417i	−0.985599	−	0.169099i	$-0.945914\pi$
$887$	−2.64584	+	8.14306i	−0.0888386	+	0.273417i	0.896760	+	0.442516i	$0.145914\pi$
$888$	30.6793	+	43.6172i	1.02953	+	1.46370i
$889$	8.24990	−	5.99390i	0.276693	−	0.201029i
$890$	4.39070	+	43.9332i	0.147177	+	1.47264i
$891$		0			0
$892$	43.8248	−	8.84813i	1.46736	−	0.296257i
$893$	9.50670	+	13.0848i	0.318129	+	0.437868i
$894$	28.2064	+	64.2340i	0.943364	+	2.14831i
$895$	15.5801	−	47.9505i	0.520784	−	1.60281i
$896$	44.5726	−	3.07817i	1.48907	−	0.102834i
$897$	1.22343	+	0.888872i	0.0408490	+	0.0296786i
$898$	−6.26495	+	28.7511i	−0.209064	+	0.959436i
$899$	0.221789	−	0.0720635i	0.00739706	−	0.00240345i
$900$	−10.8136	+	11.7657i	−0.360454	+	0.392190i
$901$			11.1039i			0.369925i
$902$		0			0
$903$	66.8111			2.22333
$904$	28.3000	−	37.7218i	0.941246	−	1.25461i
$905$	19.4160	+	59.7564i	0.645411	+	1.98637i
$906$	−64.0312	−	13.9526i	−2.12729	−	0.463544i
$907$	−28.9131	+	39.7955i	−0.960045	+	1.32139i	−0.0131266	+	0.999914i	$0.504178\pi$
$907$	−28.9131	+	39.7955i	−0.960045	+	1.32139i	−0.946918	+	0.321474i	$0.895822\pi$
$908$	−11.5432	+	25.2294i	−0.383076	+	0.837268i
$909$	−18.8909	−	6.13803i	−0.626572	−	0.203586i
$910$	−2.65069	−	6.03637i	−0.0878695	−	0.200104i
$911$	39.8498	−	28.9526i	1.32028	−	0.959241i	0.320354	−	0.947298i	$-0.396198\pi$
$911$	39.8498	−	28.9526i	1.32028	−	0.959241i	0.999929	−	0.0119435i	$-0.00380182\pi$
$912$	−50.3655	+	21.2016i	−1.66777	+	0.702055i
$913$		0			0
$914$	7.08314	−	0.707894i	0.234290	−	0.0234150i
$915$	2.67059	+	3.67575i	0.0882870	+	0.121517i
$916$	−31.0279	+	17.4937i	−1.02519	+	0.578007i
$917$	20.1893	+	6.55990i	0.666709	+	0.216627i
$918$	2.30004	−	3.93719i	0.0759126	−	0.129947i
$919$	−1.01052	−	0.734187i	−0.0333340	−	0.0242186i	0.570993	−	0.820955i	$-0.306558\pi$
$919$	−1.01052	−	0.734187i	−0.0333340	−	0.0242186i	−0.604328	+	0.796736i	$0.706558\pi$
$920$	−10.3026	−	0.157949i	−0.339665	−	0.00520742i
$921$	−11.1690	−	34.3747i	−0.368032	−	1.13269i
$922$	−12.1444	−	13.6272i	−0.399956	−	0.448786i
$923$		−	4.62747i		−	0.152315i
$924$		0			0
$925$			16.7165i			0.549634i
$926$	2.52354	−	2.24896i	0.0829287	−	0.0739056i
$927$	16.8738	+	51.9322i	0.554208	+	1.70568i
$928$	0.819443	−	0.152409i	0.0268995	−	0.00500307i
$929$	−17.6605	−	12.8311i	−0.579421	−	0.420974i	0.259095	−	0.965852i	$-0.416576\pi$
$929$	−17.6605	−	12.8311i	−0.579421	−	0.420974i	−0.838515	+	0.544878i	$0.816576\pi$
$930$	−13.3092	−	7.77501i	−0.436425	−	0.254953i
$931$	−43.7117	−	14.2028i	−1.43259	−	0.465478i
$932$	2.97751	+	5.28111i	0.0975314	+	0.172988i
$933$	−21.9894	−	30.2658i	−0.719901	−	0.990859i
$934$	−1.16271	−	11.6340i	−0.0380451	−	0.380677i
$935$		0			0
$936$	1.28633	+	4.17565i	0.0420449	+	0.136485i
$937$	36.3148	−	26.3843i	1.18635	−	0.861936i	0.193479	−	0.981104i	$-0.438023\pi$
$937$	36.3148	−	26.3843i	1.18635	−	0.861936i	0.992874	+	0.119168i	$0.0380228\pi$
$938$	−15.3487	+	6.73991i	−0.501153	+	0.220066i
$939$	−55.2162	−	17.9408i	−1.80191	−	0.585477i
$940$	−6.78390	+	14.8272i	−0.221266	+	0.483610i
$941$	9.48471	−	13.0546i	0.309193	−	0.425567i	−0.625937	−	0.779874i	$-0.715283\pi$
$941$	9.48471	−	13.0546i	0.309193	−	0.425567i	0.935129	+	0.354307i	$0.115283\pi$
$942$	−2.25344	+	10.3415i	−0.0734212	+	0.336944i
$943$	1.50894	+	4.64403i	0.0491377	+	0.151230i
$944$	−42.8063	−	25.8950i	−1.39323	−	0.842809i
$945$	14.3388			0.466440
$946$		0			0
$947$			38.3800i			1.24718i	0.781751	+	0.623591i	$0.214327\pi$
$947$			38.3800i			1.24718i	−0.781751	+	0.623591i	$0.785673\pi$
$948$	−24.2492	−	22.2870i	−0.787579	−	0.723849i
$949$	−4.43310	+	1.44040i	−0.143905	+	0.0467574i
$950$	−16.7375	−	3.64714i	−0.543035	−	0.118329i
$951$	−8.44202	−	6.13349i	−0.273751	−	0.198892i
$952$	−25.2968	−	8.65035i	−0.819874	−	0.280359i
$953$	8.12386	−	25.0027i	0.263158	−	0.809916i	−0.728955	−	0.684562i	$-0.759993\pi$
$953$	8.12386	−	25.0027i	0.263158	−	0.809916i	0.992112	−	0.125354i	$-0.0400066\pi$
$954$	21.1886	−	9.30431i	0.686005	−	0.301238i
$955$	22.4960	+	30.9631i	0.727955	+	1.00194i
$956$	−15.9097	+	3.21213i	−0.514557	+	0.103888i
$957$		0			0
$958$	−30.5262	+	3.05081i	−0.986258	+	0.0985672i
$959$	−5.32115	+	3.86605i	−0.171829	+	0.124841i
$960$	−43.5559	−	33.7327i	−1.40576	−	1.08872i
$961$	−8.80544	+	27.1004i	−0.284046	+	0.874205i
$962$	3.94653	+	2.30550i	0.127241	+	0.0743323i
$963$	−6.51006	+	8.96032i	−0.209784	+	0.288742i
$964$	−2.44891	+	21.2121i	−0.0788739	+	0.683196i
$965$	−3.89009	+	1.26397i	−0.125226	+	0.0406885i
$966$	12.8303	+	14.3967i	0.412808	+	0.463208i
$967$	8.79993			0.282987			0.141493	−	0.989939i	$-0.454810\pi$
$967$	8.79993			0.282987			0.141493	+	0.989939i	$0.454810\pi$
$968$		0			0
$969$	32.6992			1.05045
$970$	−22.0205	−	24.7089i	−0.707034	−	0.793357i
$971$	−12.1675	+	3.95346i	−0.390474	+	0.126873i	−0.497673	−	0.867365i	$-0.665812\pi$
$971$	−12.1675	+	3.95346i	−0.390474	+	0.126873i	0.107199	+	0.994238i	$0.465812\pi$
$972$	44.2727	+	5.11122i	1.42005	+	0.163942i
$973$	−29.3369	+	40.3787i	−0.940497	+	1.29448i
$974$	17.7001	+	10.3401i	0.567148	+	0.331319i
$975$	−0.783232	+	2.41054i	−0.0250835	+	0.0771991i
$976$	−1.99693	+	1.72546i	−0.0639201	+	0.0552306i
$977$	−24.2515	+	17.6197i	−0.775874	+	0.563705i	−0.903738	−	0.428086i	$-0.859188\pi$
$977$	−24.2515	+	17.6197i	−0.775874	+	0.563705i	0.127864	+	0.991792i	$0.459188\pi$
$978$	−13.0835	+	1.30757i	−0.418364	+	0.0418116i
$979$		0			0
$980$	−9.16998	−	45.4189i	−0.292924	−	1.45085i
$981$	33.2233	+	45.7279i	1.06074	+	1.45998i
$982$	−43.9148	+	19.2839i	−1.40138	+	0.615373i
$983$	−2.57294	+	7.91871i	−0.0820642	+	0.252567i	−0.983667	−	0.179997i	$-0.942391\pi$
$983$	−2.57294	+	7.91871i	−0.0820642	+	0.252567i	0.901603	+	0.432564i	$0.142391\pi$
$984$	−8.44748	+	24.7035i	−0.269296	+	0.787520i
$985$	17.5687	+	12.7644i	0.559785	+	0.406708i
$986$	−0.487313	−	0.106187i	−0.0155192	−	0.00338169i
$987$	29.0232	−	9.43021i	0.923819	−	0.300167i
$988$	−3.16944	+	3.44848i	−0.100833	+	0.109711i
$989$		−	8.94980i		−	0.284587i
$990$		0			0
$991$	35.5599			1.12960			0.564798	−	0.825229i	$-0.308954\pi$
$991$	35.5599			1.12960			0.564798	+	0.825229i	$0.308954\pi$
$992$	3.84937	−	8.08347i	0.122218	−	0.256651i
$993$	−5.97715	−	18.3958i	−0.189679	−	0.583773i
$994$	12.5637	−	57.6571i	0.398495	−	1.82877i
$995$	−15.3703	+	21.1553i	−0.487270	+	0.670670i
$996$	10.6148	+	4.85661i	0.336344	+	0.153888i
$997$	4.47204	+	1.45306i	0.141631	+	0.0460187i	0.378975	−	0.925407i	$-0.376277\pi$
$997$	4.47204	+	1.45306i	0.141631	+	0.0460187i	−0.237344	+	0.971426i	$0.576277\pi$
$998$	−10.0121	+	4.39652i	−0.316928	+	0.139169i
$999$	−8.04227	+	5.84305i	−0.254446	+	0.184866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.j.245.7		40
8.5	even	2	inner	968.2.o.j.245.9		40
11.2	odd	10		968.2.c.i.485.19		20
11.3	even	5		88.2.o.a.5.4	✓	40
11.4	even	5	inner	968.2.o.j.565.9		40
11.5	even	5		88.2.o.a.53.5	yes	40
11.6	odd	10		968.2.o.i.493.6		40
11.7	odd	10		968.2.o.d.565.2		40
11.8	odd	10		968.2.o.i.269.7		40
11.9	even	5		968.2.c.h.485.2		20
11.10	odd	2		968.2.o.d.245.4		40
33.5	odd	10		792.2.br.b.757.6		40
33.14	odd	10		792.2.br.b.181.7		40
44.3	odd	10		352.2.w.a.49.9		40
44.27	odd	10		352.2.w.a.273.2		40
44.31	odd	10		3872.2.c.h.1937.18		20
44.35	even	10		3872.2.c.i.1937.18		20
88.3	odd	10		352.2.w.a.49.2		40
88.5	even	10		88.2.o.a.53.4	yes	40
88.13	odd	10		968.2.c.i.485.20		20
88.21	odd	2		968.2.o.d.245.2		40
88.27	odd	10		352.2.w.a.273.9		40
88.29	odd	10		968.2.o.d.565.4		40
88.35	even	10		3872.2.c.i.1937.3		20
88.37	even	10	inner	968.2.o.j.565.7		40
88.53	even	10		968.2.c.h.485.1		20
88.61	odd	10		968.2.o.i.493.7		40
88.69	even	10		88.2.o.a.5.5	yes	40
88.75	odd	10		3872.2.c.h.1937.3		20
88.85	odd	10		968.2.o.i.269.6		40
264.5	odd	10		792.2.br.b.757.7		40
264.245	odd	10		792.2.br.b.181.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.4	✓	40	11.3	even	5
88.2.o.a.5.5	yes	40	88.69	even	10
88.2.o.a.53.4	yes	40	88.5	even	10
88.2.o.a.53.5	yes	40	11.5	even	5
352.2.w.a.49.2		40	88.3	odd	10
352.2.w.a.49.9		40	44.3	odd	10
352.2.w.a.273.2		40	44.27	odd	10
352.2.w.a.273.9		40	88.27	odd	10
792.2.br.b.181.6		40	264.245	odd	10
792.2.br.b.181.7		40	33.14	odd	10
792.2.br.b.757.6		40	33.5	odd	10
792.2.br.b.757.7		40	264.5	odd	10
968.2.c.h.485.1		20	88.53	even	10
968.2.c.h.485.2		20	11.9	even	5
968.2.c.i.485.19		20	11.2	odd	10
968.2.c.i.485.20		20	88.13	odd	10
968.2.o.d.245.2		40	88.21	odd	2
968.2.o.d.245.4		40	11.10	odd	2
968.2.o.d.565.2		40	11.7	odd	10
968.2.o.d.565.4		40	88.29	odd	10
968.2.o.i.269.6		40	88.85	odd	10
968.2.o.i.269.7		40	11.8	odd	10
968.2.o.i.493.6		40	11.6	odd	10
968.2.o.i.493.7		40	88.61	odd	10
968.2.o.j.245.7		40	1.1	even	1	trivial
968.2.o.j.245.9		40	8.5	even	2	inner
968.2.o.j.565.7		40	88.37	even	10	inner
968.2.o.j.565.9		40	11.4	even	5	inner
3872.2.c.h.1937.3		20	88.75	odd	10
3872.2.c.h.1937.18		20	44.31	odd	10
3872.2.c.i.1937.3		20	88.35	even	10
3872.2.c.i.1937.18		20	44.35	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+(1.05579 - 0.940911i) q^{2} +(2.42981 - 0.789492i) q^{3} +(0.229373 - 1.98680i) q^{4} +(-1.58432 + 2.18063i) q^{5} +(1.82252 - 3.11977i) q^{6} +(1.22033 - 3.75580i) q^{7} +(-1.62724 - 2.31346i) q^{8} +(2.85361 - 2.07327i) q^{9} +(0.379074 + 3.79299i) q^{10} +(-1.01123 - 5.00864i) q^{12} +(-0.257423 - 0.354312i) q^{13} +(-2.24546 - 5.11355i) q^{14} +(-2.12801 + 6.54933i) q^{15} +(-3.89478 - 0.911440i) q^{16} +(1.93640 + 1.40688i) q^{17} +(1.06205 - 4.87393i) q^{18} +(5.08557 - 1.65240i) q^{19} +(3.96909 + 3.64792i) q^{20} -10.0893i q^{21} -1.35153 q^{23} +(-5.78033 - 4.33658i) q^{24} +(-0.699997 - 2.15437i) q^{25} +(-0.605160 - 0.131866i) q^{26} +(0.791790 - 1.08980i) q^{27} +(-7.18212 - 3.28604i) q^{28} +(-0.140131 - 0.0455314i) q^{29} +(3.91561 + 8.91696i) q^{30} +(-1.28045 + 0.930300i) q^{31} +(-4.96964 + 2.70235i) q^{32} +(3.36818 - 0.336618i) q^{34} +(6.25662 + 8.61150i) q^{35} +(-3.46464 - 6.14512i) q^{36} +(-7.01837 - 2.28041i) q^{37} +(3.81452 - 6.52966i) q^{38} +(-0.905215 - 0.657677i) q^{39} +(7.62288 + 0.116867i) q^{40} +(-1.11646 - 3.43612i) q^{41} +(-9.49314 - 10.6522i) q^{42} +6.62197i q^{43} +9.50742i q^{45} +(-1.42693 + 1.27167i) q^{46} +(0.934673 + 2.87663i) q^{47} +(-10.1831 + 0.860272i) q^{48} +(-6.95369 - 5.05215i) q^{49} +(-2.76612 - 1.61592i) q^{50} +(5.81581 + 1.88967i) q^{51} +(-0.762995 + 0.430179i) q^{52} +(2.72682 + 3.75314i) q^{53} +(-0.189448 - 1.89561i) q^{54} +(-10.6747 + 3.28838i) q^{56} +(11.0524 - 8.03004i) q^{57} +(-0.190790 + 0.0837795i) q^{58} +(11.8952 + 3.86498i) q^{59} +(12.5241 + 5.73017i) q^{60} +(0.387808 - 0.533772i) q^{61} +(-0.476551 + 2.18699i) q^{62} +(-4.30443 - 13.2477i) q^{63} +(-2.70421 + 7.52909i) q^{64} +1.18047 q^{65} -3.00157i q^{67} +(3.23935 - 3.52455i) q^{68} +(-3.28396 + 1.06702i) q^{69} +(14.7083 + 3.20499i) q^{70} +(8.54816 + 6.21060i) q^{71} +(-9.43994 - 3.22803i) q^{72} +(3.28894 - 10.1223i) q^{73} +(-9.55557 + 4.19604i) q^{74} +(-3.40172 - 4.68206i) q^{75} +(-2.11650 - 10.4830i) q^{76} +(-1.57453 + 0.157359i) q^{78} +(5.21464 - 3.78866i) q^{79} +(8.15810 - 7.04906i) q^{80} +(-2.20645 + 6.79075i) q^{81} +(-4.41183 - 2.57732i) q^{82} +(-1.34279 + 1.84820i) q^{83} +(-20.0455 - 2.31422i) q^{84} +(-6.13577 + 1.99363i) q^{85} +(6.23068 + 6.99139i) q^{86} -0.376438 q^{87} +11.5827 q^{89} +(8.94563 + 10.0378i) q^{90} +(-1.64487 + 0.534450i) q^{91} +(-0.310006 + 2.68523i) q^{92} +(-2.37678 + 3.27135i) q^{93} +(3.69347 + 2.15766i) q^{94} +(-4.45390 + 13.7077i) q^{95} +(-9.94178 + 10.4897i) q^{96} +(-7.02442 + 5.10354i) q^{97} +(-12.0952 + 1.20881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} + 8 q^{6} + 5 q^{8} + 10 q^{9} - 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} + 4 q^{17} + 25 q^{18} + 8 q^{20} - 8 q^{23} - 40 q^{24} + 6 q^{25} - 20 q^{26} - 18 q^{28}+ \cdots - 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 + 8 * q^6 + 5 * q^8 + 10 * q^9 - 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 + 4 * q^17 + 25 * q^18 + 8 * q^20 - 8 * q^23 - 40 * q^24 + 6 * q^25 - 20 * q^26 - 18 * q^28 + 12 * q^30 + 4 * q^31 + 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 + 6 * q^39 - 20 * q^40 + 16 * q^41 - 20 * q^42 - 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 - 39 * q^50 + 108 * q^54 - 32 * q^56 + 4 * q^57 - 16 * q^58 + 94 * q^60 - 52 * q^62 - 30 * q^63 + 11 * q^64 - 36 * q^65 + 63 * q^68 + 52 * q^70 + 12 * q^71 + 44 * q^72 + 4 * q^73 - 26 * q^74 - 134 * q^76 - 12 * q^78 - 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 + 72 * q^84 - 10 * q^86 + 68 * q^87 - 16 * q^89 + 126 * q^90 - 64 * q^92 + 40 * q^94 + 26 * q^95 - 5 * q^96 - 20 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more