LMFDB - Embedded newform 104.2.r.a.29.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(29,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.29"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.5
Character	$\chi$	$=$	104.29
Dual form			104.2.r.a.61.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.628723 - 1.26677i) q^{2} +(-1.47584 + 0.852079i) q^{3} +(-1.20941 + 1.59290i) q^{4} +2.59989i q^{5} +(2.00729 + 1.33383i) q^{6} +(-0.300588 + 0.520633i) q^{7} +(2.77822 + 0.530559i) q^{8} +(-0.0479214 + 0.0830022i) q^{9} +(3.29346 - 1.63461i) q^{10} +(-2.40956 + 1.39116i) q^{11} +(0.427634 - 3.38138i) q^{12} +(3.60516 - 0.0531995i) q^{13} +(0.848509 + 0.0534414i) q^{14} +(-2.21531 - 3.83703i) q^{15} +(-1.07463 - 3.85294i) q^{16} +(-1.29402 + 2.24132i) q^{17} +(0.135274 + 0.00851993i) q^{18} +(-4.38088 - 2.52930i) q^{19} +(-4.14135 - 3.14434i) q^{20} -1.02450i q^{21} +(3.27722 + 2.17770i) q^{22} +(2.94353 + 5.09835i) q^{23} +(-4.55230 + 1.58424i) q^{24} -1.75942 q^{25} +(-2.33404 - 4.53346i) q^{26} -5.27581i q^{27} +(-0.465779 - 1.10847i) q^{28} +(-1.54071 + 0.889530i) q^{29} +(-3.46782 + 5.21872i) q^{30} +5.09421 q^{31} +(-4.20514 + 3.78375i) q^{32} +(2.37076 - 4.10627i) q^{33} +(3.65282 + 0.230064i) q^{34} +(-1.35359 - 0.781495i) q^{35} +(-0.0742572 - 0.176718i) q^{36} +(8.82719 - 5.09638i) q^{37} +(-0.449684 + 7.13981i) q^{38} +(-5.27532 + 3.15040i) q^{39} +(-1.37940 + 7.22306i) q^{40} +(-5.26242 - 9.11477i) q^{41} +(-1.29780 + 0.644126i) q^{42} +(8.44267 + 4.87438i) q^{43} +(0.698182 - 5.52066i) q^{44} +(-0.215797 - 0.124590i) q^{45} +(4.60777 - 6.93423i) q^{46} +2.13951 q^{47} +(4.86901 + 4.77067i) q^{48} +(3.31929 + 5.74919i) q^{49} +(1.10619 + 2.22879i) q^{50} -4.41045i q^{51} +(-4.27539 + 5.80698i) q^{52} +6.01748i q^{53} +(-6.68324 + 3.31702i) q^{54} +(-3.61686 - 6.26458i) q^{55} +(-1.11133 + 1.28695i) q^{56} +8.62067 q^{57} +(2.09551 + 1.39246i) q^{58} +(9.44349 + 5.45220i) q^{59} +(8.79122 + 1.11180i) q^{60} +(-1.84865 - 1.06732i) q^{61} +(-3.20285 - 6.45319i) q^{62} +(-0.0288091 - 0.0498989i) q^{63} +(7.43701 + 2.94802i) q^{64} +(0.138313 + 9.37301i) q^{65} +(-6.69225 - 0.421496i) q^{66} +(-3.39076 + 1.95766i) q^{67} +(-2.00517 - 4.77193i) q^{68} +(-8.68840 - 5.01625i) q^{69} +(-0.138942 + 2.20603i) q^{70} +(0.230832 - 0.399814i) q^{71} +(-0.177174 + 0.205173i) q^{72} -14.8806 q^{73} +(-12.0058 - 7.97781i) q^{74} +(2.59664 - 1.49917i) q^{75} +(9.32722 - 3.91932i) q^{76} -1.67266i q^{77} +(7.30755 + 4.70190i) q^{78} -7.83968 q^{79} +(10.0172 - 2.79393i) q^{80} +(4.35164 + 7.53727i) q^{81} +(-8.23772 + 12.3969i) q^{82} +0.930501i q^{83} +(1.63192 + 1.23904i) q^{84} +(-5.82717 - 3.36432i) q^{85} +(0.866614 - 13.7596i) q^{86} +(1.51590 - 2.62562i) q^{87} +(-7.43237 + 2.58653i) q^{88} +(1.17791 + 2.04019i) q^{89} +(-0.0221509 + 0.351698i) q^{90} +(-1.05597 + 1.89296i) q^{91} +(-11.6811 - 1.47727i) q^{92} +(-7.51826 + 4.34067i) q^{93} +(-1.34516 - 2.71027i) q^{94} +(6.57591 - 11.3898i) q^{95} +(2.98209 - 9.16734i) q^{96} +(5.91151 - 10.2390i) q^{97} +(5.19598 - 7.81943i) q^{98} -0.266665i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) $ 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.628723	−	1.26677i	−0.444574	−	0.895742i
$2$	−0.628723	−	1.26677i	−0.444574	−	0.895742i
$3$	−1.47584	+	0.852079i	−0.852079	+	0.491948i	−0.861352	−	0.508009i	$-0.830382\pi$
$3$	−1.47584	+	0.852079i	−0.852079	+	0.491948i	0.00927251	+	0.999957i	$0.497048\pi$
$4$	−1.20941	+	1.59290i	−0.604707	+	0.796448i
$5$			2.59989i			1.16271i	0.813651	+	0.581353i	$0.197476\pi$
$5$			2.59989i			1.16271i	−0.813651	+	0.581353i	$0.802524\pi$
$6$	2.00729	+	1.33383i	0.819471	+	0.544536i
$7$	−0.300588	+	0.520633i	−0.113611	+	0.196781i	−0.917224	−	0.398372i	$-0.869575\pi$
$7$	−0.300588	+	0.520633i	−0.113611	+	0.196781i	0.803612	+	0.595153i	$0.202909\pi$
$8$	2.77822	+	0.530559i	0.982249	+	0.187581i
$9$	−0.0479214	+	0.0830022i	−0.0159738	+	0.0276674i
$10$	3.29346	−	1.63461i	1.04148	−	0.516909i
$11$	−2.40956	+	1.39116i	−0.726509	+	0.419450i	−0.817144	−	0.576434i	$-0.804444\pi$
$11$	−2.40956	+	1.39116i	−0.726509	+	0.419450i	0.0906348	+	0.995884i	$0.471110\pi$
$12$	0.427634	−	3.38138i	0.123447	−	0.976122i
$13$	3.60516	−	0.0531995i	0.999891	−	0.0147549i
$13$	3.60516	−	0.0531995i	0.999891	−	0.0147549i
$14$	0.848509	+	0.0534414i	0.226774	+	0.0142828i
$15$	−2.21531	−	3.83703i	−0.571991	−	0.990718i
$16$	−1.07463	−	3.85294i	−0.268659	−	0.963235i
$17$	−1.29402	+	2.24132i	−0.313847	+	0.543599i	−0.979192	−	0.202937i	$-0.934951\pi$
$17$	−1.29402	+	2.24132i	−0.313847	+	0.543599i	0.665345	+	0.746536i	$0.268285\pi$
$18$	0.135274	+	0.00851993i	0.0318844	+	0.00200817i
$19$	−4.38088	−	2.52930i	−1.00504	−	0.580262i	−0.0953071	−	0.995448i	$-0.530383\pi$
$19$	−4.38088	−	2.52930i	−1.00504	−	0.580262i	−0.909737	+	0.415186i	$0.863717\pi$
$20$	−4.14135	−	3.14434i	−0.926035	−	0.703096i
$21$		−	1.02450i		−	0.223564i
$22$	3.27722	+	2.17770i	0.698706	+	0.464288i
$23$	2.94353	+	5.09835i	0.613769	+	1.06308i	0.990599	+	0.136797i	$0.0436808\pi$
$23$	2.94353	+	5.09835i	0.613769	+	1.06308i	−0.376830	+	0.926282i	$0.622986\pi$
$24$	−4.55230	+	1.58424i	−0.929234	+	0.323382i
$25$	−1.75942			−0.351885
$26$	−2.33404	−	4.53346i	−0.457743	−	0.889085i
$27$		−	5.27581i		−	1.01533i
$28$	−0.465779	−	1.10847i	−0.0880240	−	0.209480i
$29$	−1.54071	+	0.889530i	−0.286103	+	0.165182i	−0.636183	−	0.771538i	$-0.719488\pi$
$29$	−1.54071	+	0.889530i	−0.286103	+	0.165182i	0.350080	+	0.936720i	$0.386154\pi$
$30$	−3.46782	+	5.21872i	−0.633135	+	0.952804i
$31$	5.09421			0.914947			0.457473	−	0.889223i	$-0.348755\pi$
$31$	5.09421			0.914947			0.457473	+	0.889223i	$0.348755\pi$
$32$	−4.20514	+	3.78375i	−0.743372	+	0.668879i
$33$	2.37076	−	4.10627i	0.412696	−	0.714810i
$34$	3.65282	+	0.230064i	0.626453	+	0.0394557i
$35$	−1.35359	−	0.781495i	−0.228798	−	0.132097i
$36$	−0.0742572	−	0.176718i	−0.0123762	−	0.0294530i
$37$	8.82719	−	5.09638i	1.45118	−	0.837840i	0.452633	−	0.891697i	$-0.350485\pi$
$37$	8.82719	−	5.09638i	1.45118	−	0.837840i	0.998549	+	0.0538570i	$0.0171515\pi$
$38$	−0.449684	+	7.13981i	−0.0729484	+	1.15823i
$39$	−5.27532	+	3.15040i	−0.844728	+	0.504467i
$40$	−1.37940	+	7.22306i	−0.218102	+	1.14207i
$41$	−5.26242	−	9.11477i	−0.821851	−	1.42349i	−0.904302	−	0.426893i	$-0.859608\pi$
$41$	−5.26242	−	9.11477i	−0.821851	−	1.42349i	0.0824509	−	0.996595i	$-0.473725\pi$
$42$	−1.29780	+	0.644126i	−0.200256	+	0.0993908i
$43$	8.44267	+	4.87438i	1.28749	+	0.743335i	0.978207	−	0.207633i	$-0.0665759\pi$
$43$	8.44267	+	4.87438i	1.28749	+	0.743335i	0.309288	+	0.950968i	$0.399909\pi$
$44$	0.698182	−	5.52066i	0.105255	−	0.832271i
$45$	−0.215797	−	0.124590i	−0.0321691	−	0.0185728i
$46$	4.60777	−	6.93423i	0.679379	−	1.02240i
$47$	2.13951			0.312080			0.156040	−	0.987751i	$-0.450127\pi$
$47$	2.13951			0.312080			0.156040	+	0.987751i	$0.450127\pi$
$48$	4.86901	+	4.77067i	0.702781	+	0.688587i
$49$	3.31929	+	5.74919i	0.474185	+	0.821312i
$50$	1.10619	+	2.22879i	0.156439	+	0.315198i
$51$		−	4.41045i		−	0.617586i
$52$	−4.27539	+	5.80698i	−0.592890	+	0.805284i
$53$			6.01748i			0.826565i	0.910603	+	0.413282i	$0.135618\pi$
$53$			6.01748i			0.826565i	−0.910603	+	0.413282i	$0.864382\pi$
$54$	−6.68324	+	3.31702i	−0.909473	+	0.451390i
$55$	−3.61686	−	6.26458i	−0.487697	−	0.844716i
$56$	−1.11133	+	1.28695i	−0.148507	+	0.171976i
$57$	8.62067			1.14184
$58$	2.09551	+	1.39246i	0.275154	+	0.182839i
$59$	9.44349	+	5.45220i	1.22944	+	0.709816i	0.966912	−	0.255109i	$-0.0821112\pi$
$59$	9.44349	+	5.45220i	1.22944	+	0.709816i	0.262526	+	0.964925i	$0.415445\pi$
$60$	8.79122	+	1.11180i	1.13494	+	0.143533i
$61$	−1.84865	−	1.06732i	−0.236696	−	0.136656i	0.376961	−	0.926229i	$-0.376969\pi$
$61$	−1.84865	−	1.06732i	−0.236696	−	0.136656i	−0.613657	+	0.789573i	$0.710302\pi$
$62$	−3.20285	−	6.45319i	−0.406762	−	0.819556i
$63$	−0.0288091	−	0.0498989i	−0.00362961	−	0.00628667i
$64$	7.43701	+	2.94802i	0.929627	+	0.368503i
$65$	0.138313	+	9.37301i	0.0171556	+	1.16258i
$66$	−6.69225	−	0.421496i	−0.823759	−	0.0518826i
$67$	−3.39076	+	1.95766i	−0.414247	+	0.239166i	−0.692613	−	0.721309i	$-0.743541\pi$
$67$	−3.39076	+	1.95766i	−0.414247	+	0.239166i	0.278366	+	0.960475i	$0.410207\pi$
$68$	−2.00517	−	4.77193i	−0.243163	−	0.578681i
$69$	−8.68840	−	5.01625i	−1.04596	−	0.603885i
$70$	−0.138942	+	2.20603i	−0.0166067	+	0.263671i
$71$	0.230832	−	0.399814i	0.0273948	−	0.0474491i	−0.852003	−	0.523537i	$-0.824612\pi$
$71$	0.230832	−	0.399814i	0.0273948	−	0.0474491i	0.879398	+	0.476088i	$0.157946\pi$
$72$	−0.177174	+	0.205173i	−0.0208801	+	0.0241799i
$73$	−14.8806			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$73$	−14.8806			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$74$	−12.0058	−	7.97781i	−1.39565	−	0.927402i
$75$	2.59664	−	1.49917i	0.299834	−	0.173109i
$76$	9.32722	−	3.91932i	1.06991	−	0.449576i
$77$		−	1.67266i		−	0.190617i
$78$	7.30755	+	4.70190i	0.827417	+	0.532385i
$79$	−7.83968			−0.882033			−0.441017	−	0.897499i	$-0.645382\pi$
$79$	−7.83968			−0.882033			−0.441017	+	0.897499i	$0.645382\pi$
$80$	10.0172	−	2.79393i	1.11996	−	0.312371i
$81$	4.35164	+	7.53727i	0.483516	+	0.837474i
$82$	−8.23772	+	12.3969i	−0.909704	+	1.36901i
$83$			0.930501i			0.102136i	0.998695	+	0.0510679i	$0.0162625\pi$
$83$			0.930501i			0.102136i	−0.998695	+	0.0510679i	$0.983738\pi$
$84$	1.63192	+	1.23904i	0.178057	+	0.135191i
$85$	−5.82717	−	3.36432i	−0.632046	−	0.364912i
$86$	0.866614	−	13.7596i	0.0934494	−	1.48373i
$87$	1.51590	−	2.62562i	0.162522	−	0.281496i
$88$	−7.43237	+	2.58653i	−0.792294	+	0.275725i
$89$	1.17791	+	2.04019i	0.124858	+	0.216260i	0.921677	−	0.387957i	$-0.126819\pi$
$89$	1.17791	+	2.04019i	0.124858	+	0.216260i	−0.796820	+	0.604217i	$0.793486\pi$
$90$	−0.0221509	+	0.351698i	−0.00233491	+	0.0370722i
$91$	−1.05597	+	1.89296i	−0.110696	+	0.198436i
$92$	−11.6811	−	1.47727i	−1.21784	−	0.154016i
$93$	−7.51826	+	4.34067i	−0.779607	+	0.450106i
$94$	−1.34516	−	2.71027i	−0.138743	−	0.279543i
$95$	6.57591	−	11.3898i	0.674674	−	1.16857i
$96$	2.98209	−	9.16734i	0.304358	−	0.935638i
$97$	5.91151	−	10.2390i	0.600223	−	1.03962i	−0.392564	−	0.919725i	$-0.628412\pi$
$97$	5.91151	−	10.2390i	0.600223	−	1.03962i	0.992787	−	0.119892i	$-0.0382549\pi$
$98$	5.19598	−	7.81943i	0.524873	−	0.789882i
$99$		−	0.266665i		−	0.0268008i
$100$	2.12787	−	2.80258i	0.212787	−	0.280258i
$101$	−11.2176	+	6.47646i	−1.11619	+	0.644432i	−0.940425	−	0.340001i	$-0.889573\pi$
$101$	−11.2176	+	6.47646i	−1.11619	+	0.644432i	−0.175763	+	0.984432i	$0.556239\pi$
$102$	−5.58702	+	2.77295i	−0.553198	+	0.274563i
$103$	6.61141			0.651441			0.325721	−	0.945466i	$-0.394393\pi$
$103$	6.61141			0.651441			0.325721	+	0.945466i	$0.394393\pi$
$104$	10.0442	+	1.76495i	0.984910	+	0.173068i
$105$	2.66358			0.259939
$106$	7.62277	−	3.78333i	0.740389	−	0.367470i
$107$	8.87612	−	5.12463i	0.858087	−	0.495417i	−0.00528438	−	0.999986i	$-0.501682\pi$
$107$	8.87612	−	5.12463i	0.858087	−	0.495417i	0.863371	+	0.504569i	$0.168349\pi$
$108$	8.40381	+	6.38064i	0.808657	+	0.613977i
$109$		−	10.8192i		−	1.03630i	−0.855291	−	0.518148i	$-0.826622\pi$
$109$		−	10.8192i		−	1.03630i	0.855291	−	0.518148i	$-0.173378\pi$
$110$	−5.66178	+	8.52042i	−0.539830	+	0.812390i
$111$	−8.68504	+	15.0429i	−0.824348	+	1.42781i
$112$	2.32899	+	0.598656i	0.220069	+	0.0565677i
$113$	4.75708	−	8.23951i	0.447509	−	0.775108i	−0.550714	−	0.834694i	$-0.685645\pi$
$113$	4.75708	−	8.23951i	0.447509	−	0.775108i	0.998223	+	0.0595859i	$0.0189780\pi$
$114$	−5.42002	−	10.9204i	−0.507631	−	1.02279i
$115$	−13.2551	+	7.65286i	−1.23605	+	0.713633i
$116$	0.446429	−	3.53000i	0.0414499	−	0.327752i
$117$	−0.168348	+	0.301786i	−0.0155638	+	0.0279001i
$118$	0.969346	−	15.3907i	0.0892355	−	1.41683i
$119$	−0.777936	−	1.34742i	−0.0713133	−	0.123518i
$120$	−4.11885	−	11.8355i	−0.375998	−	1.08043i
$121$	−1.62936	+	2.82213i	−0.148123	+	0.256557i
$122$	−0.189758	+	3.01287i	−0.0171799	+	0.272772i
$123$	15.5330	+	8.96799i	1.40057	+	0.808617i
$124$	−6.16101	+	8.11454i	−0.553275	+	0.728707i
$125$			8.42514i			0.753567i
$126$	−0.0450975	+	0.0678672i	−0.00401760	+	0.00604609i
$127$	9.21128	+	15.9544i	0.817369	+	1.41572i	0.907614	+	0.419805i	$0.137902\pi$
$127$	9.21128	+	15.9544i	0.817369	+	1.41572i	−0.0902451	+	0.995920i	$0.528765\pi$
$128$	−0.941358	−	11.2745i	−0.0832051	−	0.996532i
$129$	−16.6134			−1.46273
$130$	11.7865	−	6.06824i	1.03374	−	0.532220i
$131$		−	0.795820i		−	0.0695311i	−0.999395	−	0.0347655i	$-0.988932\pi$
$131$		−	0.795820i		−	0.0695311i	0.999395	−	0.0347655i	$-0.0110684\pi$
$132$	3.67363	+	8.74255i	0.319749	+	0.760941i
$133$	2.63368	−	1.52056i	0.228369	−	0.131849i
$134$	4.61175	+	3.06449i	0.398394	+	0.264732i
$135$	13.7165			1.18053
$136$	−4.78424	+	5.54031i	−0.410245	+	0.475078i
$137$	1.77845	−	3.08037i	0.151943	−	0.263174i	−0.779998	−	0.625781i	$-0.784780\pi$
$137$	1.77845	−	3.08037i	0.151943	−	0.263174i	0.931942	+	0.362608i	$0.118114\pi$
$138$	−0.891837	+	14.1600i	−0.0759182	+	1.20538i
$139$	−1.86181	−	1.07491i	−0.157916	−	0.0911731i	0.418959	−	0.908005i	$-0.362395\pi$
$139$	−1.86181	−	1.07491i	−0.157916	−	0.0911731i	−0.576876	+	0.816832i	$0.695728\pi$
$140$	2.88189	−	1.21097i	0.243564	−	0.102346i
$141$	−3.15759	+	1.82303i	−0.265917	+	0.153527i
$142$	−0.651602	−	0.0410396i	−0.0546812	−	0.00344397i
$143$	−8.61283	+	5.14353i	−0.720241	+	0.430124i
$144$	0.371301	+	0.0954411i	0.0309417	+	0.00795343i
$145$	−2.31268	−	4.00568i	−0.192058	−	0.332653i
$146$	9.35581	+	18.8504i	0.774292	+	1.56007i
$147$	−9.79753	−	5.65660i	−0.808086	−	0.466549i
$148$	−2.55773	+	20.2244i	−0.210244	+	1.66244i
$149$	2.87752	+	1.66134i	0.235736	+	0.136102i	0.613215	−	0.789916i	$-0.289876\pi$
$149$	2.87752	+	1.66134i	0.235736	+	0.136102i	−0.377480	+	0.926018i	$0.623209\pi$
$150$	−3.53167	−	2.34678i	−0.288360	−	0.191614i
$151$	−6.66412			−0.542318			−0.271159	−	0.962535i	$-0.587407\pi$
$151$	−6.66412			−0.542318			−0.271159	+	0.962535i	$0.587407\pi$
$152$	−10.8291	−	9.35128i	−0.878357	−	0.758489i
$153$	−0.124023	−	0.214814i	−0.0100267	−	0.0173667i
$154$	−2.11888	+	1.05164i	−0.170744	+	0.0847436i
$155$			13.2444i			1.06381i
$156$	1.36180	−	12.2132i	0.109031	−	0.977837i
$157$			1.24154i			0.0990854i	0.998772	+	0.0495427i	$0.0157764\pi$
$157$			1.24154i			0.0990854i	−0.998772	+	0.0495427i	$0.984224\pi$
$158$	4.92899	+	9.93108i	0.392129	+	0.790074i
$159$	−5.12737	−	8.88087i	−0.406627	−	0.704299i
$160$	−9.83733	−	10.9329i	−0.777709	−	0.864322i
$161$	−3.53916			−0.278925
$162$	6.81201	−	10.2514i	0.535202	−	0.805425i
$163$	−9.43363	−	5.44651i	−0.738899	−	0.426604i	0.0827698	−	0.996569i	$-0.473623\pi$
$163$	−9.43363	−	5.44651i	−0.738899	−	0.426604i	−0.821669	+	0.569965i	$0.806957\pi$
$164$	20.8833	+	2.64105i	1.63071	+	0.206232i
$165$	10.6758	+	6.16370i	0.831113	+	0.479843i
$166$	1.17873	−	0.585028i	0.0914873	−	0.0454070i
$167$	−6.68150	−	11.5727i	−0.517030	−	0.895522i	−0.999804	−	0.0197773i	$-0.993704\pi$
$167$	−6.68150	−	11.5727i	−0.517030	−	0.895522i	0.482775	−	0.875745i	$-0.339629\pi$
$168$	0.543557	−	2.84628i	0.0419363	−	0.219595i
$169$	12.9943	−	0.383585i	0.999565	−	0.0295065i
$170$	−0.598142	+	9.49692i	−0.0458754	+	0.728380i
$171$	0.419876	−	0.242415i	0.0321087	−	0.0185380i
$172$	−17.9751	+	7.55315i	−1.37059	+	0.575922i
$173$	5.66761	+	3.27220i	0.430901	+	0.248781i	0.699730	−	0.714407i	$-0.253304\pi$
$173$	5.66761	+	3.27220i	0.430901	+	0.248781i	−0.268830	+	0.963188i	$0.586637\pi$
$174$	−4.27913	−	0.269511i	−0.324400	−	0.0204316i
$175$	0.528861	−	0.916015i	0.0399782	−	0.0692442i
$176$	7.94945	+	7.78890i	0.599212	+	0.587110i
$177$	−18.5828			−1.39677
$178$	1.84388	−	2.77485i	0.138205	−	0.207984i
$179$	13.5832	−	7.84225i	1.01525	−	0.586157i	0.102528	−	0.994730i	$-0.467307\pi$
$179$	13.5832	−	7.84225i	1.01525	−	0.586157i	0.912726	+	0.408573i	$0.133973\pi$
$180$	0.459447	−	0.193060i	0.0342451	−	0.0143899i
$181$		−	4.65816i		−	0.346238i	−0.984901	−	0.173119i	$-0.944615\pi$
$181$		−	4.65816i		−	0.346238i	0.984901	−	0.173119i	$-0.0553846\pi$
$182$	3.06185	+	0.147525i	0.226960	+	0.0109352i
$183$	3.63776			0.268911
$184$	5.47281	+	15.7261i	0.403461	+	1.15934i
$185$	13.2500	+	22.9497i	0.974162	+	1.68730i
$186$	10.2255	+	6.79483i	0.749773	+	0.498221i
$187$		−	7.20077i		−	0.526573i
$188$	−2.58755	+	3.40802i	−0.188717	+	0.248555i
$189$	2.74676	+	1.58584i	0.199797	+	0.115353i
$190$	−18.5627	−	1.16913i	−1.34668	−	0.0848176i
$191$	4.34236	−	7.52119i	0.314202	−	0.544214i	−0.665066	−	0.746785i	$-0.731596\pi$
$191$	4.34236	−	7.52119i	0.314202	−	0.544214i	0.979268	+	0.202571i	$0.0649297\pi$
$192$	−13.4878	+	1.98610i	−0.973400	+	0.143335i
$193$	0.788692	+	1.36605i	0.0567713	+	0.0983308i	0.893014	−	0.450028i	$-0.148586\pi$
$193$	0.788692	+	1.36605i	0.0567713	+	0.0983308i	−0.836243	+	0.548359i	$0.815253\pi$
$194$	−16.6872	−	1.05101i	−1.19807	−	0.0754578i
$195$	−8.19068	−	13.7153i	−0.586547	−	0.982170i
$196$	−13.1723	−	1.66586i	−0.940875	−	0.118990i
$197$	22.1460	−	12.7860i	1.57784	−	0.910964i	0.582675	−	0.812705i	$-0.302006\pi$
$197$	22.1460	−	12.7860i	1.57784	−	0.910964i	0.995161	−	0.0982592i	$-0.0313274\pi$
$198$	−0.337803	+	0.167658i	−0.0240066	+	0.0119150i
$199$	10.3516	−	17.9295i	0.733807	−	1.27099i	−0.221438	−	0.975174i	$-0.571075\pi$
$199$	10.3516	−	17.9295i	0.733807	−	1.27099i	0.955245	−	0.295816i	$-0.0955915\pi$
$200$	−4.88807	−	0.933479i	−0.345639	−	0.0660069i
$201$	3.33616	−	5.77839i	0.235314	−	0.407576i
$202$	15.2569	+	10.1382i	1.07347	+	0.713319i
$203$		−	1.06953i		−	0.0750661i
$204$	7.02538	+	5.33406i	0.491875	+	0.373459i
$205$	23.6974	−	13.6817i	1.65510	−	0.955571i
$206$	−4.15675	−	8.37513i	−0.289614	−	0.583523i
$207$	−0.564233			−0.0392169
$208$	−4.07920	−	13.8333i	−0.282842	−	0.959167i
$209$	14.0747			0.973564
$210$	−1.67466	−	3.37415i	−0.115562	−	0.232838i
$211$	−18.3083	+	10.5703i	−1.26040	+	0.727691i	−0.973151	−	0.230166i	$-0.926073\pi$
$211$	−18.3083	+	10.5703i	−1.26040	+	0.727691i	−0.287246	+	0.957857i	$0.592740\pi$
$212$	−9.58522	−	7.27763i	−0.658316	−	0.499830i
$213$			0.786750i			0.0539072i
$214$	−12.0724	−	8.02203i	−0.825249	−	0.548375i
$215$	−12.6728	+	21.9500i	−0.864281	+	1.49698i
$216$	2.79913	−	14.6574i	0.190457	−	0.997307i
$217$	−1.53126	+	2.65221i	−0.103948	+	0.180044i
$218$	−13.7055	+	6.80231i	−0.928254	+	0.460711i
$219$	21.9615	−	12.6795i	1.48402	−	0.856800i
$220$	14.3531	+	1.81520i	0.967686	+	0.122380i
$221$	−4.54593	+	8.14914i	−0.305792	+	0.548171i
$222$	24.5164	+	1.54411i	1.64544	+	0.103634i
$223$	4.03692	+	6.99214i	0.270332	+	0.468229i	0.968947	−	0.247269i	$-0.0795332\pi$
$223$	4.03692	+	6.99214i	0.270332	+	0.468229i	−0.698615	+	0.715498i	$0.746200\pi$
$224$	−0.705931	−	3.32669i	−0.0471670	−	0.222274i
$225$	0.0843141	−	0.146036i	0.00562094	−	0.00973575i
$226$	−13.4285	−	0.845760i	−0.893248	−	0.0562591i
$227$	−19.8519	−	11.4615i	−1.31761	−	0.760725i	−0.334270	−	0.942477i	$-0.608490\pi$
$227$	−19.8519	−	11.4615i	−1.31761	−	0.760725i	−0.983344	+	0.181752i	$0.941823\pi$
$228$	−10.4260	+	13.7318i	−0.690476	+	0.909413i
$229$		−	0.594709i		−	0.0392995i	−0.999807	−	0.0196497i	$-0.993745\pi$
$229$		−	0.594709i		−	0.0392995i	0.999807	−	0.0196497i	$-0.00625511\pi$
$230$	18.0282	+	11.9797i	1.18875	+	0.789918i
$231$	1.42524	+	2.46859i	0.0937739	+	0.162421i
$232$	−4.75238	+	1.65387i	−0.312009	+	0.108582i
$233$	−0.0945847			−0.00619645			−0.00309823	−	0.999995i	$-0.500986\pi$
$233$	−0.0945847			−0.00619645			−0.00309823	+	0.999995i	$0.500986\pi$
$234$	0.488138	+	0.0235192i	0.0319106	+	0.00153750i
$235$			5.56249i			0.362857i
$236$	−20.1059	+	8.44853i	−1.30878	+	0.549952i
$237$	11.5702	−	6.68003i	0.751562	−	0.433915i
$238$	−1.21777	+	1.83262i	−0.0789364	+	0.118791i
$239$	−15.3694			−0.994166			−0.497083	−	0.867703i	$-0.665596\pi$
$239$	−15.3694			−0.994166			−0.497083	+	0.867703i	$0.665596\pi$
$240$	−12.4032	+	12.6589i	−0.800624	+	0.817127i
$241$	5.02102	−	8.69665i	0.323432	−	0.560201i	−0.657762	−	0.753226i	$-0.728497\pi$
$241$	5.02102	−	8.69665i	0.323432	−	0.560201i	0.981194	+	0.193025i	$0.0618300\pi$
$242$	4.59940	+	0.289683i	0.295661	+	0.0186215i
$243$	0.862251	+	0.497821i	0.0553134	+	0.0319352i
$244$	3.93591	−	1.65388i	0.251971	−	0.105879i
$245$	−14.9472	+	8.62980i	−0.954945	+	0.551338i
$246$	1.59442	−	25.3152i	0.101656	−	1.61404i
$247$	−15.9283	−	8.88548i	−1.01350	−	0.565370i
$248$	14.1528	+	2.70278i	0.898705	+	0.171627i
$249$	−0.792861	−	1.37328i	−0.0502455	−	0.0870278i
$250$	10.6727	−	5.29708i	0.675002	−	0.335017i
$251$	−14.8114	−	8.55135i	−0.934886	−	0.539757i	−0.0465324	−	0.998917i	$-0.514817\pi$
$251$	−14.8114	−	8.55135i	−0.934886	−	0.539757i	−0.888353	+	0.459160i	$0.848150\pi$
$252$	0.114326	+	0.0144585i	0.00720186	+	0.000910798i
$253$	−14.1852	−	8.18984i	−0.891818	−	0.514891i
$254$	14.4192	−	21.6995i	0.904743	−	1.36155i
$255$	11.4667			0.718071
$256$	−13.6903	+	8.28101i	−0.855645	+	0.517563i
$257$	−10.3500	−	17.9267i	−0.645616	−	1.11824i	−0.984159	−	0.177288i	$-0.943267\pi$
$257$	−10.3500	−	17.9267i	−0.645616	−	1.11824i	0.338543	−	0.940951i	$-0.390066\pi$
$258$	10.4452	+	21.0454i	0.650293	+	1.31023i
$259$			6.12764i			0.380753i
$260$	−15.0975	−	11.1155i	−0.936308	−	0.689356i
$261$		−	0.170510i		−	0.0105543i
$262$	−1.00812	+	0.500350i	−0.0622819	+	0.0309117i
$263$	−0.515631	−	0.893099i	−0.0317952	−	0.0550708i	0.849690	−	0.527283i	$-0.176789\pi$
$263$	−0.515631	−	0.893099i	−0.0317952	−	0.0550708i	−0.881485	+	0.472212i	$0.843456\pi$
$264$	8.76510	−	10.1503i	0.539455	−	0.624707i
$265$	−15.6448			−0.961052
$266$	−3.58205	−	2.38026i	−0.219630	−	0.145943i
$267$	−3.47681	−	2.00734i	−0.212777	−	0.122847i
$268$	0.982490	−	7.76874i	0.0600151	−	0.474551i
$269$	−5.34569	−	3.08633i	−0.325932	−	0.188177i	0.328101	−	0.944642i	$-0.393591\pi$
$269$	−5.34569	−	3.08633i	−0.325932	−	0.188177i	−0.654034	+	0.756465i	$0.726925\pi$
$270$	−8.62389	−	17.3757i	−0.524833	−	1.05745i
$271$	6.85287	+	11.8695i	0.416282	+	0.721022i	0.995562	−	0.0941065i	$-0.0299994\pi$
$271$	6.85287	+	11.8695i	0.416282	+	0.721022i	−0.579280	+	0.815129i	$0.696666\pi$
$272$	10.0263	+	2.57720i	0.607932	+	0.156266i
$273$	−0.0545028	−	3.69348i	−0.00329866	−	0.223540i
$274$	−5.02027	−	0.316191i	−0.303286	−	0.0191018i
$275$	4.23944	−	2.44764i	0.255648	−	0.147598i
$276$	18.4982	−	7.77299i	1.11346	−	0.467879i
$277$	24.4764	+	14.1314i	1.47064	+	0.849076i	0.999457	−	0.0329570i	$-0.0104924\pi$
$277$	24.4764	+	14.1314i	1.47064	+	0.849076i	0.471187	+	0.882033i	$0.343826\pi$
$278$	−0.191109	+	3.03430i	−0.0114619	+	0.181986i
$279$	−0.244121	+	0.422831i	−0.0146152	+	0.0253142i
$280$	−3.34594	−	2.88932i	−0.199958	−	0.172670i
$281$	−12.3330			−0.735724			−0.367862	−	0.929880i	$-0.619910\pi$
$281$	−12.3330			−0.735724			−0.367862	+	0.929880i	$0.619910\pi$
$282$	4.29461	+	2.85375i	0.255740	+	0.169938i
$283$	−17.0408	+	9.83851i	−1.01297	+	0.584838i	−0.912060	−	0.410057i	$-0.865509\pi$
$283$	−17.0408	+	9.83851i	−1.01297	+	0.584838i	−0.100910	+	0.994896i	$0.532175\pi$
$284$	0.357689	+	0.851232i	0.0212250	+	0.0505113i
$285$			22.4128i			1.32762i
$286$	11.9308	+	7.67662i	0.705481	+	0.453928i
$287$	6.32727			0.373487
$288$	−0.112543	−	0.530359i	−0.00663169	−	0.0312517i
$289$	5.15100	+	8.92179i	0.303000	+	0.524811i
$290$	−3.62024	+	5.44810i	−0.212588	+	0.319923i
$291$			20.1483i			1.18111i
$292$	17.9969	−	23.7033i	1.05319	−	1.38713i
$293$	−10.1639	−	5.86812i	−0.593780	−	0.342819i	0.172811	−	0.984955i	$-0.444715\pi$
$293$	−10.1639	−	5.86812i	−0.593780	−	0.342819i	−0.766591	+	0.642136i	$0.778048\pi$
$294$	−1.00569	+	15.9677i	−0.0586528	+	0.931252i
$295$	−14.1751	+	24.5520i	−0.825308	+	1.42947i
$296$	27.2278	−	9.47552i	1.58258	−	0.550754i
$297$	7.33949	+	12.7124i	0.425880	+	0.737646i
$298$	0.295369	−	4.68968i	0.0171103	−	0.271666i
$299$	10.8831	+	18.2238i	0.629388	+	1.05391i
$300$	−0.752390	+	5.94929i	−0.0434392	+	0.343482i
$301$	−5.07552	+	2.93036i	−0.292548	+	0.168903i
$302$	4.18989	+	8.44191i	0.241101	+	0.485777i
$303$	11.0369	−	19.1165i	0.634054	−	1.09821i
$304$	−5.03741	+	19.5974i	−0.288915	+	1.12399i
$305$	2.77491	−	4.80629i	0.158891	−	0.275207i
$306$	−0.194144	+	0.292167i	−0.0110985	+	0.0167021i
$307$		−	5.08990i		−	0.290496i	−0.989395	−	0.145248i	$-0.953602\pi$
$307$		−	5.08990i		−	0.290496i	0.989395	−	0.145248i	$-0.0463980\pi$
$308$	2.66437	+	2.02294i	0.151817	+	0.115268i
$309$	−9.75741	+	5.63344i	−0.555080	+	0.320475i
$310$	16.7776	−	8.32705i	0.952902	−	0.472944i
$311$	25.1578			1.42657			0.713284	−	0.700875i	$-0.247207\pi$
$311$	25.1578			1.42657			0.713284	+	0.700875i	$0.247207\pi$
$312$	−16.3275	+	5.95362i	−0.924362	+	0.337057i
$313$	12.4651			0.704569			0.352285	−	0.935893i	$-0.385405\pi$
$313$	12.4651			0.704569			0.352285	+	0.935893i	$0.385405\pi$
$314$	1.57274	−	0.780583i	0.0887549	−	0.0440508i
$315$	0.129732	−	0.0749006i	0.00730955	−	0.00422017i
$316$	9.48142	−	12.4878i	0.533372	−	0.702493i
$317$			11.0238i			0.619160i	0.950873	+	0.309580i	$0.100189\pi$
$317$			11.0238i			0.619160i	−0.950873	+	0.309580i	$0.899811\pi$
$318$	−8.02633	+	12.0788i	−0.450094	+	0.677346i
$319$	2.47495	−	4.28675i	0.138571	−	0.240012i
$320$	−7.66453	+	19.3354i	−0.428460	+	1.08088i
$321$	−8.73318	+	15.1263i	−0.487439	+	0.844269i
$322$	2.22515	+	4.48330i	0.124003	+	0.249845i
$323$	11.3379	−	6.54597i	0.630860	−	0.364227i
$324$	−17.2690	−	2.18396i	−0.959390	−	0.121331i
$325$	−6.34301	+	0.0936005i	−0.351847	+	0.00519202i
$326$	−0.968334	+	15.3746i	−0.0536310	+	0.851520i
$327$	9.21886	+	15.9675i	0.509804	+	0.883006i
$328$	−9.78422	−	28.1149i	−0.540243	−	1.55238i
$329$	−0.643110	+	1.11390i	−0.0354558	+	0.0614113i
$330$	1.09584	−	17.3991i	0.0603242	−	0.957789i
$331$	14.3890	+	8.30750i	0.790891	+	0.456621i	0.840276	−	0.542158i	$-0.182393\pi$
$331$	14.3890	+	8.30750i	0.790891	+	0.456621i	−0.0493848	+	0.998780i	$0.515726\pi$
$332$	−1.48219	−	1.12536i	−0.0813458	−	0.0617622i
$333$			0.976902i			0.0535339i
$334$	−10.4591	+	15.7399i	−0.572298	+	0.861251i
$335$	−5.08969	−	8.81560i	−0.278079	−	0.481647i
$336$	−3.94733	+	1.10096i	−0.215345	+	0.0600624i
$337$	−11.0591			−0.602427			−0.301214	−	0.953557i	$-0.597392\pi$
$337$	−11.0591			−0.602427			−0.301214	+	0.953557i	$0.597392\pi$
$338$	−8.65576	−	16.2197i	−0.470811	−	0.882234i
$339$			16.2136i			0.880605i
$340$	12.4065	−	5.21323i	0.672836	−	0.282727i
$341$	−12.2748	+	7.08685i	−0.664717	+	0.383774i
$342$	−0.571071	−	0.379474i	−0.0308800	−	0.0205196i
$343$	−8.19918			−0.442714
$344$	20.8694	+	18.0214i	1.12521	+	0.971650i
$345$	13.0417	−	22.5889i	0.702141	−	1.21614i
$346$	0.581763	−	9.23687i	0.0312758	−	0.496577i
$347$	1.92350	+	1.11054i	0.103259	+	0.0596167i	0.550740	−	0.834677i	$-0.314345\pi$
$347$	1.92350	+	1.11054i	0.103259	+	0.0596167i	−0.447481	+	0.894293i	$0.647679\pi$
$348$	2.34898	+	5.59013i	0.125919	+	0.299662i
$349$	−11.6899	+	6.74919i	−0.625748	+	0.361276i	−0.779104	−	0.626895i	$-0.784325\pi$
$349$	−11.6899	+	6.74919i	−0.625748	+	0.361276i	0.153355	+	0.988171i	$0.450992\pi$
$350$	−1.49289	−	0.0940261i	−0.0797982	−	0.00502591i
$351$	−0.280670	−	19.0201i	−0.0149811	−	1.01522i
$352$	4.86874	−	14.9672i	0.259505	−	0.797754i
$353$	−1.75509	−	3.03991i	−0.0934143	−	0.161798i	0.815531	−	0.578713i	$-0.196445\pi$
$353$	−1.75509	−	3.03991i	−0.0934143	−	0.161798i	−0.908946	+	0.416915i	$0.863111\pi$
$354$	11.6835	+	23.5402i	0.620969	+	1.25115i
$355$	1.03947	+	0.600139i	0.0551694	+	0.0318521i
$356$	−4.67439	−	0.591157i	−0.247742	−	0.0313312i
$357$	2.29622	+	1.32573i	0.121529	+	0.0701649i
$358$	−18.4744	−	12.2762i	−0.976401	−	0.648815i
$359$	25.0138			1.32018			0.660090	−	0.751187i	$-0.270518\pi$
$359$	25.0138			1.32018			0.660090	+	0.751187i	$0.270518\pi$
$360$	−0.533428	−	0.460632i	−0.0281141	−	0.0242774i
$361$	3.29476	+	5.70670i	0.173409	+	0.300353i
$362$	−5.90082	+	2.92869i	−0.310140	+	0.153929i
$363$		−	5.55336i		−	0.291476i
$364$	−1.73818	−	3.97142i	−0.0911053	−	0.208159i
$365$		−	38.6880i		−	2.02502i
$366$	−2.28715	−	4.60821i	−0.119551	−	0.240875i
$367$	−10.2910	−	17.8245i	−0.537186	−	0.930434i	−0.999054	−	0.0434851i	$-0.986154\pi$
$367$	−10.2910	−	17.8245i	−0.537186	−	0.930434i	0.461868	−	0.886949i	$-0.347179\pi$
$368$	16.4804	−	16.8201i	0.859101	−	0.876810i
$369$	1.00873			0.0525123
$370$	20.7414	−	31.2138i	1.07830	−	1.62273i
$371$	−3.13290	−	1.80878i	−0.162652	−	0.0939072i
$372$	2.17845	−	17.2255i	0.112948	−	0.893099i
$373$	−12.3015	−	7.10225i	−0.636946	−	0.367741i	0.146491	−	0.989212i	$-0.453202\pi$
$373$	−12.3015	−	7.10225i	−0.636946	−	0.367741i	−0.783437	+	0.621471i	$0.786535\pi$
$374$	−9.12173	+	4.52729i	−0.471673	+	0.234101i
$375$	−7.17889	−	12.4342i	−0.370716	−	0.642099i
$376$	5.94403	+	1.13514i	0.306540	+	0.0585402i
$377$	−5.50718	+	3.28886i	−0.283634	+	0.169385i
$378$	0.281947	−	4.47657i	0.0145018	−	0.230250i
$379$	6.23669	−	3.60075i	0.320357	−	0.184958i	−0.331195	−	0.943562i	$-0.607452\pi$
$379$	6.23669	−	3.60075i	0.320357	−	0.184958i	0.651552	+	0.758604i	$0.274118\pi$
$380$	10.1898	+	24.2497i	0.522725	+	1.24399i
$381$	−27.1888	−	15.6975i	−1.39293	−	0.804207i
$382$	−12.2578	−	0.772027i	−0.627161	−	0.0395003i
$383$	−11.8763	+	20.5704i	−0.606852	+	1.05110i	0.384903	+	0.922957i	$0.374235\pi$
$383$	−11.8763	+	20.5704i	−0.606852	+	1.05110i	−0.991756	+	0.128142i	$0.959099\pi$
$384$	10.9960	+	15.8373i	0.561140	+	0.808192i
$385$	4.34873			0.221632
$386$	1.23461	−	1.85796i	0.0628399	−	0.0945678i
$387$	−0.809168	+	0.467174i	−0.0411323	+	0.0237478i
$388$	9.16026	+	21.7997i	0.465042	+	1.10671i
$389$		−	20.6264i		−	1.04580i	−0.852394	−	0.522900i	$-0.824850\pi$
$389$		−	20.6264i		−	1.04580i	0.852394	−	0.522900i	$-0.175150\pi$
$390$	−12.2244	+	18.9988i	−0.619007	+	0.962042i
$391$	−15.2360			−0.770519
$392$	6.17145	+	17.7336i	0.311705	+	0.895681i
$393$	0.678101	+	1.17451i	0.0342057	+	0.0592460i
$394$	−30.1206	−	20.0150i	−1.51745	−	1.00834i
$395$		−	20.3823i		−	1.02554i
$396$	0.424769	+	0.322508i	0.0213455	+	0.0162067i
$397$	25.6669	+	14.8188i	1.28819	+	0.743734i	0.978330	−	0.207050i	$-0.0663862\pi$
$397$	25.6669	+	14.8188i	1.28819	+	0.743734i	0.309855	+	0.950784i	$0.399720\pi$
$398$	−29.2209	−	1.84041i	−1.46471	−	0.0922515i
$399$	−2.59127	+	4.48821i	−0.129726	+	0.224691i
$400$	1.89074	+	6.77896i	0.0945370	+	0.338948i
$401$	5.32482	+	9.22286i	0.265909	+	0.460568i	0.967801	−	0.251715i	$-0.0809946\pi$
$401$	5.32482	+	9.22286i	0.265909	+	0.460568i	−0.701892	+	0.712283i	$0.747661\pi$
$402$	−9.41741	−	0.593134i	−0.469698	−	0.0295828i
$403$	18.3654	−	0.271009i	0.914847	−	0.0134999i
$404$	3.25035	−	25.7011i	0.161711	−	1.27868i
$405$	−19.5961	+	11.3138i	−0.973736	+	0.562187i
$406$	−1.35484	+	0.672436i	−0.0672398	+	0.0333725i
$407$	−14.1798	+	24.5600i	−0.702864	+	1.21740i
$408$	2.34000	−	12.2532i	0.115847	−	0.606623i
$409$	−0.271387	+	0.470056i	−0.0134192	+	0.0232428i	−0.872657	−	0.488334i	$-0.837605\pi$
$409$	−0.271387	+	0.470056i	−0.0134192	+	0.0232428i	0.859238	+	0.511576i	$0.170938\pi$
$410$	−32.2307	−	21.4172i	−1.59176	−	1.05772i
$411$			6.06153i			0.298993i
$412$	−7.99593	+	10.5313i	−0.393931	+	0.518839i
$413$	−5.67720	+	3.27773i	−0.279357	+	0.161287i
$414$	0.354746	+	0.714753i	0.0174348	+	0.0351282i
$415$	−2.41920			−0.118754
$416$	−14.9589	+	13.8647i	−0.733421	+	0.679774i
$417$	3.66365			0.179410
$418$	−8.84906	−	17.8294i	−0.432822	−	0.872062i
$419$	17.8473	−	10.3042i	0.871900	−	0.503392i	0.00392074	−	0.999992i	$-0.498752\pi$
$419$	17.8473	−	10.3042i	0.871900	−	0.503392i	0.867979	+	0.496601i	$0.165419\pi$
$420$	−3.22137	+	4.24281i	−0.157187	+	0.207028i
$421$			2.14198i			0.104394i	0.998637	+	0.0521968i	$0.0166223\pi$
$421$			2.14198i			0.104394i	−0.998637	+	0.0521968i	$0.983378\pi$
$422$	24.9010	+	16.5466i	1.21216	+	0.805478i
$423$	−0.102528	+	0.177584i	−0.00498510	+	0.00863444i
$424$	−3.19263	+	16.7179i	−0.155048	+	0.811893i
$425$	2.27674	−	3.94343i	0.110438	−	0.191284i
$426$	0.996632	−	0.494648i	0.0482870	−	0.0239658i
$427$	1.11136	−	0.641646i	0.0537827	−	0.0310514i
$428$	−2.57190	+	20.3365i	−0.124318	+	0.983003i
$429$	8.32850	−	14.9299i	0.402104	−	0.720821i
$430$	35.7733	+	2.25310i	1.72514	+	0.108654i
$431$	−5.72822	−	9.92157i	−0.275919	−	0.477905i	0.694448	−	0.719543i	$-0.255649\pi$
$431$	−5.72822	−	9.92157i	−0.275919	−	0.477905i	−0.970366	+	0.241638i	$0.922315\pi$
$432$	−20.3274	+	5.66957i	−0.978002	+	0.272777i
$433$	−8.14866	+	14.1139i	−0.391600	+	0.678270i	−0.992661	−	0.120933i	$-0.961411\pi$
$433$	−8.14866	+	14.1139i	−0.391600	+	0.678270i	0.601061	+	0.799203i	$0.294745\pi$
$434$	4.32248	+	0.272242i	0.207486	+	0.0130680i
$435$	6.82631	+	3.94117i	0.327297	+	0.188965i
$436$	17.2339	+	13.0850i	0.825356	+	0.626656i
$437$		−	29.7804i		−	1.42459i
$438$	−29.8697	−	19.8483i	−1.42723	−	0.948389i
$439$	−1.34252	−	2.32532i	−0.0640751	−	0.110981i	0.832208	−	0.554463i	$-0.187076\pi$
$439$	−1.34252	−	2.32532i	−0.0640751	−	0.110981i	−0.896283	+	0.443482i	$0.853743\pi$
$440$	−6.72470	−	19.3233i	−0.320587	−	0.921204i
$441$	−0.636260			−0.0302981
$442$	13.1812	+	0.635090i	0.626967	+	0.0302082i
$443$		−	14.6679i		−	0.696891i	−0.937329	−	0.348446i	$-0.886710\pi$
$443$		−	14.6679i		−	0.696891i	0.937329	−	0.348446i	$-0.113290\pi$
$444$	−13.4580	−	32.0275i	−0.638689	−	1.51996i
$445$	−5.30428	+	3.06242i	−0.251447	+	0.145173i
$446$	6.31934	−	9.50997i	0.299229	−	0.450310i
$447$	−5.66237			−0.267821
$448$	−3.77031	+	2.98582i	−0.178130	+	0.141067i
$449$	0.656457	−	1.13702i	0.0309801	−	0.0536591i	−0.850120	−	0.526590i	$-0.823470\pi$
$449$	0.656457	−	1.13702i	0.0309801	−	0.0536591i	0.881100	+	0.472930i	$0.156804\pi$
$450$	−0.238005	−	0.0149902i	−0.0112196	−	0.000706643i
$451$	25.3602	+	14.6417i	1.19416	+	0.689451i
$452$	7.37140	+	17.5425i	0.346721	+	0.825131i
$453$	9.83521	−	5.67836i	0.462098	−	0.266793i
$454$	−2.03773	+	32.3539i	−0.0956356	+	1.51844i
$455$	−4.92148	−	2.74540i	−0.230722	−	0.128706i
$456$	23.9501	+	4.57378i	1.12157	+	0.214187i
$457$	9.83743	+	17.0389i	0.460176	+	0.797048i	0.998969	−	0.0453901i	$-0.0144531\pi$
$457$	9.83743	+	17.0389i	0.460176	+	0.797048i	−0.538794	+	0.842438i	$0.681120\pi$
$458$	−0.753360	+	0.373907i	−0.0352022	+	0.0174715i
$459$	11.8248	+	6.82703i	0.551932	+	0.318658i
$460$	3.84075	−	30.3695i	0.179076	−	1.41599i
$461$	10.1402	+	5.85445i	0.472277	+	0.272669i	0.717192	−	0.696875i	$-0.245427\pi$
$461$	10.1402	+	5.85445i	0.472277	+	0.272669i	−0.244916	+	0.969544i	$0.578760\pi$
$462$	2.23105	−	3.35751i	0.103798	−	0.156205i
$463$	20.0915			0.933731			0.466866	−	0.884328i	$-0.345383\pi$
$463$	20.0915			0.933731			0.466866	+	0.884328i	$0.345383\pi$
$464$	5.08301	+	4.98035i	0.235973	+	0.231207i
$465$	−11.2853	−	19.5466i	−0.523341	−	0.906454i
$466$	0.0594676	+	0.119817i	0.00275478	+	0.00555042i
$467$		−	38.0472i		−	1.76061i	−0.474405	−	0.880307i	$-0.657337\pi$
$467$		−	38.0472i		−	1.76061i	0.474405	−	0.880307i	$-0.342663\pi$
$468$	−0.277110	−	0.633145i	−0.0128094	−	0.0292672i
$469$		−	2.35379i		−	0.108688i
$470$	7.04640	−	3.49727i	0.325026	−	0.161317i
$471$	−1.05789	−	1.83231i	−0.0487449	−	0.0844286i
$472$	23.3434	+	20.1578i	1.07447	+	0.927836i
$473$	−27.1241			−1.24717
$474$	−15.7365	−	10.4568i	−0.722801	−	0.480298i
$475$	7.70784	+	4.45012i	0.353660	+	0.204186i
$476$	3.08715	+	0.390423i	0.141499	+	0.0178950i
$477$	−0.499465	−	0.288366i	−0.0228689	−	0.0132034i
$478$	9.66312	+	19.4695i	0.441981	+	0.890516i
$479$	4.96607	+	8.60149i	0.226906	+	0.393012i	0.956889	−	0.290452i	$-0.0938057\pi$
$479$	4.96607	+	8.60149i	0.226906	+	0.393012i	−0.729984	+	0.683465i	$0.760472\pi$
$480$	23.8341	+	7.75309i	1.08787	+	0.353879i
$481$	31.5523	−	18.8429i	1.43866	−	0.859161i
$482$	−14.1735	−	0.892685i	−0.645585	−	0.0406607i
$483$	5.22325	−	3.01565i	0.237666	−	0.137217i
$484$	−2.52479	−	6.00851i	−0.114763	−	0.273114i
$485$	26.6204	+	15.3693i	1.20877	+	0.697883i
$486$	0.0885074	−	1.40527i	0.00401478	−	0.0637441i
$487$	11.7461	−	20.3448i	0.532265	−	0.921910i	−0.467025	−	0.884244i	$-0.654674\pi$
$487$	11.7461	−	20.3448i	0.532265	−	0.921910i	0.999290	−	0.0376664i	$-0.0119924\pi$
$488$	−4.56968	−	3.94607i	−0.206860	−	0.178630i
$489$	18.5634			0.839468
$490$	20.3297	+	13.5090i	0.918400	+	0.610273i
$491$	−26.6538	+	15.3886i	−1.20287	+	0.694478i	−0.961193	−	0.275878i	$-0.911031\pi$
$491$	−26.6538	+	15.3886i	−1.20287	+	0.694478i	−0.241679	+	0.970356i	$0.577698\pi$
$492$	−33.0709	+	13.8965i	−1.49095	+	0.626501i
$493$		−	4.60429i		−	0.207367i
$494$	−1.24135	+	25.7641i	−0.0558510	+	1.15918i
$495$	0.693299			0.0311615
$496$	−5.47441	−	19.6277i	−0.245808	−	0.881309i
$497$	0.138771	+	0.240358i	0.00622472	+	0.0107815i
$498$	−1.24113	+	1.86778i	−0.0556166	+	0.0836973i
$499$			4.61772i			0.206718i	0.994644	+	0.103359i	$0.0329590\pi$
$499$			4.61772i			0.206718i	−0.994644	+	0.103359i	$0.967041\pi$
$500$	−13.4204	−	10.1895i	−0.600177	−	0.455687i
$501$	19.7217	+	11.3863i	0.881101	+	0.508704i
$502$	−1.52034	+	24.1390i	−0.0678562	+	1.07738i
$503$	14.8441	−	25.7107i	0.661865	−	1.14638i	−0.318260	−	0.948004i	$-0.603098\pi$
$503$	14.8441	−	25.7107i	0.661865	−	1.14638i	0.980125	−	0.198381i	$-0.0635683\pi$
$504$	−0.0535638	−	0.153915i	−0.00238592	−	0.00685592i
$505$	−16.8381	−	29.1644i	−0.749285	−	1.29780i
$506$	−1.45607	+	23.1186i	−0.0647302	+	1.02775i
$507$	−18.8508	+	11.6383i	−0.837193	+	0.516876i
$508$	−36.5540	−	4.62287i	−1.62182	−	0.205107i
$509$	−20.3599	+	11.7548i	−0.902438	+	0.521023i	−0.877990	−	0.478678i	$-0.841116\pi$
$509$	−20.3599	+	11.7548i	−0.902438	+	0.521023i	−0.0244475	+	0.999701i	$0.507783\pi$
$510$	−7.20936	−	14.5256i	−0.319236	−	0.643206i
$511$	4.47294	−	7.74736i	0.197871	−	0.342723i
$512$	19.0976	+	12.1360i	0.844001	+	0.536342i
$513$	−13.3441	+	23.1127i	−0.589158	+	1.02045i
$514$	−16.2018	+	24.3820i	−0.714629	+	1.07545i
$515$			17.1889i			0.757435i
$516$	20.0925	−	26.4635i	0.884523	−	1.16499i
$517$	−5.15527	+	2.97640i	−0.226729	+	0.130902i
$518$	7.76231	−	3.85259i	0.341056	−	0.169273i
$519$	−11.1527			−0.489549
$520$	−4.58868	+	26.1137i	−0.201227	+	1.14516i
$521$	−11.7037			−0.512747			−0.256374	−	0.966578i	$-0.582528\pi$
$521$	−11.7037			−0.512747			−0.256374	+	0.966578i	$0.582528\pi$
$522$	−0.215997	+	0.107204i	−0.00945393	+	0.00469217i
$523$	10.9235	−	6.30668i	0.477651	−	0.275772i	−0.241786	−	0.970330i	$-0.577733\pi$
$523$	10.9235	−	6.30668i	0.477651	−	0.275772i	0.719437	+	0.694558i	$0.244400\pi$
$524$	1.26766	+	0.962475i	0.0553779	+	0.0420459i
$525$			1.80253i			0.0786688i
$526$	−0.807162	+	1.21470i	−0.0351939	+	0.0529633i
$527$	−6.59203	+	11.4177i	−0.287153	+	0.497364i
$528$	−18.3689	−	4.72164i	−0.799404	−	0.205483i
$529$	−5.82878	+	10.0957i	−0.253425	+	0.438945i
$530$	9.83624	+	19.8184i	0.427259	+	0.860854i
$531$	−0.905090	+	0.522554i	−0.0392776	+	0.0226769i
$532$	−0.763123	+	6.03416i	−0.0330856	+	0.261614i
$533$	−19.4567	−	32.5802i	−0.842765	−	1.41121i
$534$	−0.356884	+	5.66638i	−0.0154439	+	0.245208i
$535$	13.3235	+	23.0769i	0.576024	+	0.997703i
$536$	−10.4589	+	3.63980i	−0.451757	+	0.157215i
$537$	−13.3644	+	23.1479i	−0.576718	+	0.998905i
$538$	−0.548718	+	8.71221i	−0.0236569	+	0.375610i
$539$	−15.9961	−	9.23533i	−0.688999	−	0.397794i
$540$	−16.5889	+	21.8490i	−0.713875	+	0.940231i
$541$			40.4799i			1.74037i	0.492728	+	0.870183i	$0.336000\pi$
$541$			40.4799i			1.74037i	−0.492728	+	0.870183i	$0.664000\pi$
$542$	10.7274	−	16.1437i	0.460781	−	0.693430i
$543$	3.96912	+	6.87472i	0.170331	+	0.295023i
$544$	−3.03902	−	14.3213i	−0.130297	−	0.614022i
$545$	28.1288			1.20491
$546$	−4.64452	+	2.39122i	−0.198767	+	0.102335i
$547$			27.1567i			1.16114i	0.814212	+	0.580568i	$0.197169\pi$
$547$			27.1567i			1.16114i	−0.814212	+	0.580568i	$0.802831\pi$
$548$	2.75582	+	6.55833i	0.117723	+	0.280158i
$549$	0.177180	−	0.102295i	0.00756185	−	0.00436584i
$550$	−5.76603	−	3.83150i	−0.245864	−	0.163376i
$551$	8.99957			0.383394
$552$	−21.4769	−	18.5460i	−0.914116	−	0.789368i
$553$	2.35651	−	4.08160i	0.100209	−	0.173567i
$554$	2.51243	−	39.8907i	0.106743	−	1.69479i
$555$	−39.1100	−	22.5802i	−1.66013	−	0.958474i
$556$	3.96392	−	1.66565i	0.168108	−	0.0706392i
$557$	26.2789	−	15.1721i	1.11347	−	0.642863i	0.173746	−	0.984791i	$-0.444413\pi$
$557$	26.2789	−	15.1721i	1.11347	−	0.642863i	0.939726	+	0.341927i	$0.111080\pi$
$558$	0.689114	+	0.0434023i	0.0291725	+	0.00183736i
$559$	30.6965	+	17.1238i	1.29832	+	0.724258i
$560$	−1.55644	+	6.05512i	−0.0657716	+	0.255875i
$561$	6.13563	+	10.6272i	0.259047	+	0.448682i
$562$	7.75403	+	15.6230i	0.327084	+	0.659018i
$563$	7.83182	+	4.52170i	0.330072	+	0.190567i	0.655873	−	0.754871i	$-0.272301\pi$
$563$	7.83182	+	4.52170i	0.330072	+	0.190567i	−0.325801	+	0.945438i	$0.605634\pi$
$564$	0.914927	−	7.23451i	0.0385254	−	0.304628i
$565$	21.4218	+	12.3679i	0.901222	+	0.520321i
$566$	23.1771	+	15.4011i	0.974205	+	0.647355i
$567$	−5.23220			−0.219732
$568$	0.853428	−	0.988300i	0.0358090	−	0.0414681i
$569$	−18.1496	−	31.4361i	−0.760872	−	1.31787i	−0.942401	−	0.334484i	$-0.891438\pi$
$569$	−18.1496	−	31.4361i	−0.760872	−	1.31787i	0.181529	−	0.983386i	$-0.441895\pi$
$570$	28.3919	−	14.0914i	1.18920	−	0.590226i
$571$		−	24.9740i		−	1.04513i	−0.852599	−	0.522566i	$-0.824975\pi$
$571$		−	24.9740i		−	1.04513i	0.852599	−	0.522566i	$-0.175025\pi$
$572$	2.22336	−	19.9400i	0.0929634	−	0.833733i
$573$			14.8001i			0.618285i
$574$	−3.97810	−	8.01520i	−0.166043	−	0.334548i
$575$	−5.17893	−	8.97016i	−0.215976	−	0.374082i
$576$	−0.601084	+	0.476016i	−0.0250452	+	0.0198340i
$577$	14.7654			0.614692			0.307346	−	0.951598i	$-0.400559\pi$
$577$	14.7654			0.614692			0.307346	+	0.951598i	$0.400559\pi$
$578$	8.06331	−	12.1345i	0.335390	−	0.504728i
$579$	−2.32797	−	1.34406i	−0.0967473	−	0.0558571i
$580$	9.17761	+	1.16067i	0.381080	+	0.0481940i
$581$	−0.484450	−	0.279697i	−0.0200984	−	0.0116038i
$582$	25.5233	−	12.6677i	1.05797	−	0.525094i
$583$	−8.37127	−	14.4995i	−0.346703	−	0.600507i
$584$	−41.3417	−	7.89506i	−1.71073	−	0.326700i
$585$	−0.784609	−	0.437687i	−0.0324396	−	0.0180961i
$586$	−1.04329	+	16.5647i	−0.0430979	+	0.684282i
$587$	−33.7254	+	19.4714i	−1.39200	+	0.803669i	−0.993536	−	0.113517i	$-0.963788\pi$
$587$	−33.7254	+	19.4714i	−1.39200	+	0.803669i	−0.398460	+	0.917186i	$0.630455\pi$
$588$	20.8596	−	8.76526i	0.860237	−	0.361473i
$589$	−22.3171	−	12.8848i	−0.919561	−	0.530909i
$590$	40.0140	+	2.52019i	1.64735	+	0.103755i
$591$	−21.7894	+	37.7403i	−0.896295	+	1.55243i
$592$	−29.1221	−	28.5339i	−1.19691	−	1.17274i
$593$	19.6722			0.807842			0.403921	−	0.914794i	$-0.367647\pi$
$593$	19.6722			0.807842			0.403921	+	0.914794i	$0.367647\pi$
$594$	11.4891	−	17.2900i	0.471405	−	0.709417i
$595$	3.50315	−	2.02255i	0.143615	−	0.0829163i
$596$	−6.12645	+	2.57435i	−0.250949	+	0.105449i
$597$			35.2816i			1.44398i
$598$	16.2428	−	25.2441i	0.664219	−	1.03231i
$599$	−0.289136			−0.0118138			−0.00590689	−	0.999983i	$-0.501880\pi$
$599$	−0.289136			−0.0118138			−0.00590689	+	0.999983i	$0.501880\pi$
$600$	8.00943	−	2.78735i	0.326984	−	0.113793i
$601$	−13.3071	−	23.0486i	−0.542808	−	0.940171i	−0.998741	−	0.0501569i	$-0.984028\pi$
$601$	−13.3071	−	23.0486i	−0.542808	−	0.940171i	0.455933	−	0.890014i	$-0.349305\pi$
$602$	6.90319	+	4.58714i	0.281353	+	0.186958i
$603$		−	0.375254i		−	0.0152815i
$604$	8.05968	−	10.6152i	0.327944	−	0.431928i
$605$	−7.33722	−	4.23614i	−0.298300	−	0.172224i
$606$	−31.1554	−	1.96225i	−1.26560	−	0.0797110i
$607$	−4.23231	+	7.33058i	−0.171784	+	0.297539i	−0.939044	−	0.343798i	$-0.888287\pi$
$607$	−4.23231	+	7.33058i	−0.171784	+	0.297539i	0.767259	+	0.641337i	$0.221620\pi$
$608$	27.9925	−	5.94008i	1.13525	−	0.240902i
$609$	0.911322	+	1.57846i	0.0369286	+	0.0639622i
$610$	−7.83312	−	0.493351i	−0.317154	−	0.0199752i
$611$	7.71327	−	0.113821i	0.312046	−	0.00460470i
$612$	0.492171	+	0.0622435i	0.0198948	+	0.00251604i
$613$	11.1194	−	6.41977i	0.449107	−	0.259292i	−0.258346	−	0.966053i	$-0.583177\pi$
$613$	11.1194	−	6.41977i	0.449107	−	0.259292i	0.707453	+	0.706760i	$0.249844\pi$
$614$	−6.44774	+	3.20014i	−0.260209	+	0.129147i
$615$	−23.3158	+	40.3841i	−0.940183	+	1.62845i
$616$	0.887446	−	4.64702i	0.0357562	−	0.187234i
$617$	−2.51106	+	4.34928i	−0.101091	+	0.175095i	−0.912135	−	0.409891i	$-0.865567\pi$
$617$	−2.51106	+	4.34928i	−0.101091	+	0.175095i	0.811043	+	0.584986i	$0.198900\pi$
$618$	13.2710	+	8.81852i	0.533838	+	0.354733i
$619$		−	25.2782i		−	1.01602i	−0.861353	−	0.508008i	$-0.830382\pi$
$619$		−	25.2782i		−	1.01602i	0.861353	−	0.508008i	$-0.169618\pi$
$620$	−21.0969	−	16.0179i	−0.847272	−	0.643296i
$621$	26.8979	−	15.5295i	1.07938	−	0.623178i
$622$	−15.8173	−	31.8692i	−0.634216	−	1.27784i
$623$	−1.41626			−0.0567411
$624$	17.8073	+	16.9400i	0.712864	+	0.678142i
$625$	−30.7015			−1.22806
$626$	−7.83710	−	15.7904i	−0.313234	−	0.631112i
$627$	−20.7720	+	11.9927i	−0.829554	+	0.478943i
$628$	−1.97764	−	1.50153i	−0.0789163	−	0.0599176i
$629$			26.3794i			1.05181i
$630$	−0.176447	−	0.117248i	−0.00702982	−	0.00467129i
$631$	16.7070	−	28.9374i	0.665097	−	1.15198i	−0.314163	−	0.949369i	$-0.601724\pi$
$631$	16.7070	−	28.9374i	0.665097	−	1.15198i	0.979259	−	0.202612i	$-0.0649430\pi$
$632$	−21.7804	−	4.15942i	−0.866376	−	0.165453i
$633$	18.0135	−	31.2003i	0.715972	−	1.24010i
$634$	13.9647	−	6.93094i	0.554608	−	0.275263i
$635$	−41.4797	+	23.9483i	−1.64607	+	0.950360i
$636$	20.3474	+	2.57328i	0.806828	+	0.102037i
$637$	12.2724	+	20.5501i	0.486252	+	0.814226i
$638$	−6.98638	−	0.440021i	−0.276594	−	0.0174206i
$639$	0.0221236	+	0.0383192i	0.000875197	+	0.00151589i
$640$	29.3124	−	2.44743i	1.15867	−	0.0967430i
$641$	−5.95235	+	10.3098i	−0.235104	+	0.407212i	−0.959303	−	0.282379i	$-0.908876\pi$
$641$	−5.95235	+	10.3098i	−0.235104	+	0.407212i	0.724199	+	0.689591i	$0.242210\pi$
$642$	24.6523	+	1.55267i	0.972950	+	0.0612790i
$643$	−29.4994	−	17.0315i	−1.16334	−	0.671656i	−0.211239	−	0.977434i	$-0.567750\pi$
$643$	−29.4994	−	17.0315i	−1.16334	−	0.671656i	−0.952103	+	0.305778i	$0.901083\pi$
$644$	4.28031	−	5.63751i	0.168668	−	0.222149i
$645$		−	43.1931i		−	1.70073i
$646$	−15.4207	−	10.2470i	−0.606718	−	0.403162i
$647$	−19.9224	−	34.5065i	−0.783229	−	1.35659i	−0.930052	−	0.367429i	$-0.880238\pi$
$647$	−19.9224	−	34.5065i	−0.783229	−	1.35659i	0.146823	−	0.989163i	$-0.453095\pi$
$648$	8.09086	+	23.2490i	0.317839	+	0.913307i
$649$	−30.3395			−1.19093
$650$	4.10657	+	7.97628i	0.161073	+	0.312856i
$651$		−	5.21901i		−	0.204549i
$652$	20.0849	−	8.43971i	0.786585	−	0.330524i
$653$	17.1513	−	9.90232i	0.671183	−	0.387508i	−0.125342	−	0.992114i	$-0.540003\pi$
$653$	17.1513	−	9.90232i	0.671183	−	0.387508i	0.796525	+	0.604606i	$0.206669\pi$
$654$	14.4311	−	21.7173i	0.564300	−	0.849215i
$655$	2.06904			0.0808442
$656$	−29.4635	+	30.0708i	−1.15036	+	1.17407i
$657$	0.713101	−	1.23513i	0.0278207	−	0.0481869i
$658$	1.81539	+	0.114338i	0.0707714	+	0.00445738i
$659$	24.1533	+	13.9449i	0.940880	+	0.543218i	0.890236	−	0.455499i	$-0.150539\pi$
$659$	24.1533	+	13.9449i	0.940880	+	0.543218i	0.0506442	+	0.998717i	$0.483873\pi$
$660$	−22.7297	+	9.55104i	−0.884750	+	0.371774i
$661$	−17.0661	+	9.85313i	−0.663795	+	0.383242i	−0.793722	−	0.608281i	$-0.791859\pi$
$661$	−17.0661	+	9.85313i	−0.663795	+	0.383242i	0.129926	+	0.991524i	$0.458526\pi$
$662$	1.47699	−	23.4507i	0.0574048	−	0.911437i
$663$	−0.234633	−	15.9004i	−0.00911241	−	0.617519i
$664$	−0.493686	+	2.58514i	−0.0191587	+	0.100323i
$665$	3.95328	+	6.84728i	0.153301	+	0.265526i
$666$	1.23751	−	0.614201i	0.0479526	−	0.0237998i
$667$	−9.07027	−	5.23672i	−0.351202	−	0.202767i
$668$	26.5148	+	3.35325i	1.02589	+	0.129741i
$669$	−11.9157	−	6.87955i	−0.460688	−	0.265979i
$670$	−7.96733	+	11.9900i	−0.307805	+	0.463215i
$671$	5.93924			0.229282
$672$	3.87644	+	4.30816i	0.149537	+	0.166191i
$673$	18.0814	+	31.3179i	0.696986	+	1.20722i	0.969507	+	0.245065i	$0.0788094\pi$
$673$	18.0814	+	31.3179i	0.696986	+	1.20722i	−0.272521	+	0.962150i	$0.587857\pi$
$674$	6.95311	+	14.0093i	0.267824	+	0.539619i
$675$			9.28239i			0.357279i
$676$	−15.1045	+	21.1625i	−0.580943	+	0.813944i
$677$			43.5560i			1.67399i	0.547209	+	0.836996i	$0.315690\pi$
$677$			43.5560i			1.67399i	−0.547209	+	0.836996i	$0.684310\pi$
$678$	20.5390	−	10.1939i	0.788794	−	0.391494i
$679$	3.55386	+	6.15546i	0.136384	+	0.236225i
$680$	−14.4042	−	12.4385i	−0.552376	−	0.476994i
$681$	39.0644			1.49695
$682$	16.6949	+	11.0937i	0.639279	+	0.424798i
$683$	−6.89615	−	3.98149i	−0.263874	−	0.152348i	0.362227	−	0.932090i	$-0.382017\pi$
$683$	−6.89615	−	3.98149i	−0.263874	−	0.152348i	−0.626100	+	0.779742i	$0.715350\pi$
$684$	−0.121661	+	0.961999i	−0.00465183	+	0.0367830i
$685$	8.00862	+	4.62378i	0.305994	+	0.176666i
$686$	5.15502	+	10.3865i	0.196819	+	0.396558i
$687$	0.506739	+	0.877698i	0.0193333	+	0.0334863i
$688$	9.70790	−	37.7673i	0.370110	−	1.43986i
$689$	0.320127	+	21.6940i	0.0121959	+	0.826475i
$690$	−36.8145	−	2.31868i	−1.40151	−	0.0882706i
$691$	30.2709	−	17.4769i	1.15156	−	0.664854i	0.202294	−	0.979325i	$-0.435160\pi$
$691$	30.2709	−	17.4769i	1.15156	−	0.664854i	0.949267	+	0.314471i	$0.101827\pi$
$692$	−12.0668	+	5.07047i	−0.458709	+	0.192751i
$693$	0.138835	+	0.0801562i	0.00527389	+	0.00304488i
$694$	0.197442	−	3.13486i	0.00749479	−	0.118998i
$695$	2.79466	−	4.84049i	0.106007	−	0.183610i
$696$	5.60455	−	6.49026i	0.212440	−	0.246013i
$697$	27.2388			1.03174
$698$	15.8994	+	10.5651i	0.601802	+	0.399895i
$699$	0.139592	−	0.0805937i	0.00527987	−	0.00304833i
$700$	0.819504	+	1.95026i	0.0309743	+	0.0737130i
$701$		−	10.8831i		−	0.411050i	−0.978652	−	0.205525i	$-0.934110\pi$
$701$		−	10.8831i		−	0.411050i	0.978652	−	0.205525i	$-0.0658901\pi$
$702$	−23.9177	+	12.3139i	−0.902714	+	0.464760i
$703$	−51.5612			−1.94467
$704$	−22.0211	+	3.24264i	−0.829951	+	0.122212i
$705$	−4.73968	−	8.20937i	−0.178507	−	0.309183i
$706$	−2.74740	+	4.13457i	−0.103400	+	0.155606i
$707$		−	7.78698i		−	0.292859i
$708$	22.4744	−	29.6005i	0.844638	−	1.11246i
$709$	−31.1767	−	17.9999i	−1.17087	−	0.676000i	−0.216982	−	0.976176i	$-0.569621\pi$
$709$	−31.1767	−	17.9999i	−1.17087	−	0.676000i	−0.953884	+	0.300176i	$0.902955\pi$
$710$	0.106699	−	1.69409i	0.00400432	−	0.0635781i
$711$	0.375688	−	0.650711i	0.0140894	−	0.0244036i
$712$	2.19004	+	6.29305i	0.0820752	+	0.235842i
$713$	14.9950	+	25.9720i	0.561566	+	0.972661i
$714$	0.235700	−	3.74230i	0.00882087	−	0.140052i
$715$	−13.3726	−	22.3924i	−0.500108	−	0.837428i
$716$	−3.93580	+	31.1211i	−0.147088	+	1.16305i
$717$	22.6829	−	13.0960i	0.847108	−	0.489078i
$718$	−15.7268	−	31.6868i	−0.586918	−	1.18254i
$719$	−2.97642	+	5.15531i	−0.111002	+	0.192261i	−0.916174	−	0.400780i	$-0.868739\pi$
$719$	−2.97642	+	5.15531i	−0.111002	+	0.192261i	0.805173	+	0.593040i	$0.202073\pi$
$720$	−0.248136	+	0.965341i	−0.00924750	+	0.0359761i
$721$	−1.98731	+	3.44212i	−0.0740112	+	0.128191i
$722$	5.15758	−	7.76164i	0.191945	−	0.288858i
$723$			17.1132i			0.636447i
$724$	7.41997	+	5.63365i	0.275761	+	0.209373i
$725$	2.71076	−	1.56506i	0.100675	−	0.0581249i
$726$	−7.03483	+	3.49153i	−0.261087	+	0.129583i
$727$	34.3229			1.27297			0.636484	−	0.771290i	$-0.280388\pi$
$727$	34.3229			1.27297			0.636484	+	0.771290i	$0.280388\pi$
$728$	−3.93804	+	4.69879i	−0.145953	+	0.174149i
$729$	−27.8066			−1.02987
$730$	−49.0088	+	24.3241i	−1.81390	+	0.900274i
$731$	−21.8500	+	12.6151i	−0.808153	+	0.466587i
$732$	−4.39956	+	5.79458i	−0.162613	+	0.214174i
$733$		−	6.24499i		−	0.230664i	−0.993327	−	0.115332i	$-0.963207\pi$
$733$		−	6.24499i		−	0.230664i	0.993327	−	0.115332i	$-0.0367932\pi$
$734$	−16.1094	+	24.2431i	−0.594609	+	0.894827i
$735$	14.7065	−	25.4725i	0.542459	−	0.939567i
$736$	−31.6689	−	10.3017i	−1.16733	−	0.379726i
$737$	5.44682	−	9.43417i	0.200636	−	0.347512i
$738$	−0.634211	−	1.27783i	−0.0233456	−	0.0470375i
$739$	5.26210	−	3.03807i	0.193569	−	0.111757i	−0.400083	−	0.916479i	$-0.631019\pi$
$739$	5.26210	−	3.03807i	0.193569	−	0.111757i	0.593652	+	0.804722i	$0.297685\pi$
$740$	−52.5813	−	6.64980i	−1.93293	−	0.244452i
$741$	31.0789	−	0.458615i	1.14171	−	0.0168476i
$742$	−0.321583	+	5.10589i	−0.0118057	+	0.187443i
$743$	−4.10832	−	7.11582i	−0.150720	−	0.261054i	0.780773	−	0.624815i	$-0.214826\pi$
$743$	−4.10832	−	7.11582i	−0.150720	−	0.261054i	−0.931492	+	0.363761i	$0.881492\pi$
$744$	−23.1904	+	8.07045i	−0.850200	+	0.295877i
$745$	−4.31929	+	7.48124i	−0.158247	+	0.274091i
$746$	−1.26271	+	20.0485i	−0.0462310	+	0.734027i
$747$	−0.0772337	−	0.0445909i	−0.00282583	−	0.00163150i
$748$	11.4701	+	8.70872i	0.419388	+	0.318422i
$749$			6.16160i			0.225140i
$750$	−11.2377	+	16.9117i	−0.410344	+	0.617527i
$751$	−10.9266	−	18.9254i	−0.398717	−	0.690599i	0.594851	−	0.803836i	$-0.297211\pi$
$751$	−10.9266	−	18.9254i	−0.398717	−	0.690599i	−0.993568	+	0.113238i	$0.963878\pi$
$752$	−2.29919	−	8.24341i	−0.0838429	−	0.300606i
$753$	29.1457			1.06213
$754$	7.62873	+	4.90855i	0.277822	+	0.178759i
$755$		−	17.3260i		−	0.630557i
$756$	−5.84805	+	2.45736i	−0.212692	+	0.0893734i
$757$	−18.5854	+	10.7303i	−0.675498	+	0.389999i	−0.798157	−	0.602450i	$-0.794191\pi$
$757$	−18.5854	+	10.7303i	−0.675498	+	0.389999i	0.122659	+	0.992449i	$0.460858\pi$
$758$	−8.48248	−	5.63658i	−0.308098	−	0.204730i
$759$	27.9136			1.01320
$760$	24.3123	−	28.1545i	0.881900	−	1.02127i
$761$	−11.7372	+	20.3294i	−0.425472	+	0.736939i	−0.996464	−	0.0840166i	$-0.973225\pi$
$761$	−11.7372	+	20.3294i	−0.425472	+	0.736939i	0.570993	+	0.820955i	$0.306558\pi$
$762$	−2.79085	+	44.3114i	−0.101102	+	1.60523i
$763$	5.63286	+	3.25213i	0.203923	+	0.117735i
$764$	6.72876	+	16.0132i	0.243438	+	0.579336i
$765$	0.558492	−	0.322446i	0.0201923	−	0.0116581i
$766$	33.5249	+	2.11149i	1.21130	+	0.0762912i
$767$	34.3353	+	19.1537i	1.23978	+	0.691599i
$768$	13.1487	−	23.8867i	0.474463	−	0.861938i
$769$	−5.94997	−	10.3056i	−0.214561	−	0.371631i	0.738575	−	0.674171i	$-0.235499\pi$
$769$	−5.94997	−	10.3056i	−0.214561	−	0.371631i	−0.953137	+	0.302540i	$0.902165\pi$
$770$	−2.73415	−	5.50885i	−0.0985319	−	0.198525i
$771$	30.5500	+	17.6381i	1.10023	+	0.635219i
$772$	−3.12984	−	0.395822i	−0.112645	−	0.0142459i
$773$	12.2803	+	7.09004i	0.441692	+	0.255011i	0.704315	−	0.709888i	$-0.251254\pi$
$773$	12.2803	+	7.09004i	0.441692	+	0.255011i	−0.262623	+	0.964898i	$0.584588\pi$
$774$	1.10054	+	0.731308i	0.0395583	+	0.0262863i
$775$	−8.96287			−0.321956
$776$	21.8559	−	25.3099i	0.784581	−	0.908572i
$777$	−5.22123	−	9.04344i	−0.187311	−	0.324432i
$778$	−26.1289	+	12.9683i	−0.936767	+	0.464936i
$779$			53.2410i			1.90756i
$780$	31.7529	+	3.54053i	1.13694	+	0.126771i
$781$			1.28450i			0.0459630i
$782$	9.57924	+	19.3005i	0.342553	+	0.690186i
$783$	4.69299	+	8.12849i	0.167714	+	0.290489i
$784$	18.5842	−	18.9673i	0.663723	−	0.677404i
$785$	−3.22786			−0.115207
$786$	1.06149	−	1.59744i	0.0378621	−	0.0569787i
$787$	7.12142	+	4.11155i	0.253851	+	0.146561i	0.621526	−	0.783393i	$-0.286513\pi$
$787$	7.12142	+	4.11155i	0.253851	+	0.146561i	−0.367675	+	0.929954i	$0.619846\pi$
$788$	−6.41692	+	50.7398i	−0.228593	+	1.80753i
$789$	1.52198	+	0.878717i	0.0541840	+	0.0312832i
$790$	−25.8197	+	12.8148i	−0.918624	+	0.455931i
$791$	2.85984	+	4.95339i	0.101684	+	0.176122i
$792$	0.141482	−	0.740854i	0.00502733	−	0.0263251i
$793$	−6.72146	−	3.74951i	−0.238686	−	0.133149i
$794$	2.63463	−	41.8310i	0.0934995	−	1.48453i
$795$	23.0893	−	13.3306i	0.818892	−	0.472788i
$796$	16.0405	+	38.1733i	0.568540	+	1.35302i
$797$	−1.61224	−	0.930825i	−0.0571083	−	0.0329715i	0.471174	−	0.882040i	$-0.343830\pi$
$797$	−1.61224	−	0.930825i	−0.0571083	−	0.0329715i	−0.528282	+	0.849069i	$0.677164\pi$
$798$	7.31472	+	0.460701i	0.258938	+	0.0163086i
$799$	−2.76858	+	4.79532i	−0.0979453	+	0.169646i
$800$	7.39864	−	6.65722i	0.261581	−	0.235368i
$801$	−0.225787			−0.00797781
$802$	8.33541	−	12.5440i	0.294334	−	0.442942i
$803$	35.8558	−	20.7013i	1.26532	−	0.730534i
$804$	5.16958	+	12.3026i	0.182317	+	0.433880i
$805$		−	9.20142i		−	0.324308i
$806$	−11.8901	−	23.0944i	−0.418810	−	0.813465i
$807$	10.5192			0.370294
$808$	−34.6010	+	12.0415i	−1.21726	+	0.423617i
$809$	−18.9274	−	32.7832i	−0.665452	−	1.15260i	−0.979163	−	0.203078i	$-0.934906\pi$
$809$	−18.9274	−	32.7832i	−0.665452	−	1.15260i	0.313711	−	0.949519i	$-0.398428\pi$
$810$	26.6525	+	17.7105i	0.936472	+	0.622282i
$811$		−	16.1872i		−	0.568409i	−0.958764	−	0.284205i	$-0.908270\pi$
$811$		−	16.1872i		−	0.568409i	0.958764	−	0.284205i	$-0.0917295\pi$
$812$	1.70364	+	1.29350i	0.0597862	+	0.0453930i
$813$	−20.2276	−	11.6784i	−0.709411	−	0.409579i
$814$	40.0271	+	2.52101i	1.40295	+	0.0883615i
$815$	14.1603	−	24.5264i	0.496015	−	0.859122i
$816$	−16.9932	+	4.73962i	−0.594881	+	0.165920i
$817$	−24.6576	−	42.7082i	−0.862659	−	1.49417i
$818$	0.766080	+	0.0482498i	0.0267854	+	0.00168702i
$819$	−0.106516	−	0.178361i	−0.00372198	−	0.00623243i
$820$	−6.86645	+	54.2943i	−0.239787	+	1.89604i
$821$	23.9391	−	13.8212i	0.835479	−	0.482364i	−0.0202456	−	0.999795i	$-0.506445\pi$
$821$	23.9391	−	13.8212i	0.835479	−	0.482364i	0.855725	+	0.517431i	$0.173111\pi$
$822$	7.67857	−	3.81102i	0.267821	−	0.132925i
$823$	−16.9386	+	29.3385i	−0.590442	+	1.02268i	0.403731	+	0.914878i	$0.367713\pi$
$823$	−16.9386	+	29.3385i	−0.590442	+	1.02268i	−0.994173	+	0.107797i	$0.965620\pi$
$824$	18.3679	+	3.50774i	0.639878	+	0.122198i
$825$	−4.17117	+	7.22467i	−0.145221	+	0.251531i
$826$	7.72152	+	5.13092i	0.268666	+	0.178527i
$827$			1.10220i			0.0383272i	0.999816	+	0.0191636i	$0.00610034\pi$
$827$			1.10220i			0.0383272i	−0.999816	+	0.0191636i	$0.993900\pi$
$828$	0.682391	−	0.898764i	0.0237147	−	0.0312342i
$829$	−17.1870	+	9.92292i	−0.596929	+	0.344637i	−0.767833	−	0.640650i	$-0.778665\pi$
$829$	−17.1870	+	9.92292i	−0.596929	+	0.344637i	0.170903	+	0.985288i	$0.445331\pi$
$830$	1.52101	+	3.06457i	0.0527949	+	0.106373i
$831$	−48.1645			−1.67081
$832$	26.9684	+	10.2324i	0.934963	+	0.354746i
$833$	−17.1810			−0.595286
$834$	−2.30342	−	4.64100i	−0.0797610	−	0.160705i
$835$	30.0877	−	17.3712i	1.04123	−	0.601154i
$836$	−17.0221	+	22.4195i	−0.588721	+	0.775393i
$837$		−	26.8761i		−	0.928972i
$838$	−24.2741	−	16.1300i	−0.838533	−	0.557202i
$839$	−8.38043	+	14.5153i	−0.289325	+	0.501125i	−0.973649	−	0.228053i	$-0.926764\pi$
$839$	−8.38043	+	14.5153i	−0.289325	+	0.501125i	0.684324	+	0.729178i	$0.260097\pi$
$840$	7.40002	+	1.41319i	0.255325	+	0.0487596i
$841$	−12.9175	+	22.3737i	−0.445430	+	0.771508i
$842$	2.71339	−	1.34671i	0.0935097	−	0.0464107i
$843$	18.2016	−	10.5087i	0.626895	−	0.361938i
$844$	5.30493	−	41.9471i	0.182603	−	1.44388i
$845$	0.997279	+	33.7838i	0.0343074	+	1.16220i
$846$	0.289420	+	0.0182285i	0.00995047	+	0.000626708i
$847$	−0.979528	−	1.69659i	−0.0336570	−	0.0582956i
$848$	23.1850	−	6.46660i	0.796177	−	0.222064i
$849$	16.7664	−	29.0402i	0.575421	−	0.996658i
$850$	−6.42686	−	0.404781i	−0.220439	−	0.0138839i
$851$	51.9663	+	30.0027i	1.78138	+	1.02848i
$852$	−1.25321	−	0.951507i	−0.0429343	−	0.0325981i
$853$			12.5392i			0.429333i	0.976687	+	0.214666i	$0.0688664\pi$
$853$			12.5392i			0.429333i	−0.976687	+	0.214666i	$0.931134\pi$
$854$	−1.51156	−	1.00442i	−0.0517245	−	0.0343707i
$855$	0.630253	+	1.09163i	0.0215542	+	0.0373330i
$856$	27.3787	−	9.52804i	0.935786	−	0.325662i
$857$	34.8182			1.18937			0.594684	−	0.803960i	$-0.297277\pi$
$857$	34.8182			1.18937			0.594684	+	0.803960i	$0.297277\pi$
$858$	−24.1490	−	1.16354i	−0.824435	−	0.0397225i
$859$		−	33.1090i		−	1.12966i	−0.825206	−	0.564832i	$-0.808941\pi$
$859$		−	33.1090i		−	1.12966i	0.825206	−	0.564832i	$-0.191059\pi$
$860$	−19.6374	−	46.7332i	−0.669628	−	1.59359i
$861$	−9.33807	+	5.39134i	−0.318240	+	0.183736i
$862$	−8.96689	+	13.4943i	−0.305413	+	0.459616i
$863$	−48.3902			−1.64722			−0.823611	−	0.567155i	$-0.808044\pi$
$863$	−48.3902			−1.64722			−0.823611	+	0.567155i	$0.808044\pi$
$864$	19.9623	+	22.1855i	0.679132	+	0.754767i
$865$	−8.50735	+	14.7352i	−0.289259	+	0.501011i
$866$	23.0023	+	1.44875i	0.781650	+	0.0492305i
$867$	−15.2042	−	8.77812i	−0.516360	−	0.298121i
$868$	−2.37278	−	5.64675i	−0.0805373	−	0.191663i
$869$	18.8902	−	10.9062i	0.640805	−	0.369969i
$870$	0.700700	−	11.1253i	0.0237560	−	0.377182i
$871$	−12.1201	+	7.23804i	−0.410673	+	0.245252i
$872$	5.74025	−	30.0583i	0.194389	−	1.01790i
$873$	0.566576	+	0.981338i	0.0191757	+	0.0332132i
$874$	−37.7249	+	18.7236i	−1.27606	+	0.633336i
$875$	−4.38641	−	2.53249i	−0.148288	−	0.0856139i
$876$	−6.36347	+	50.3172i	−0.215002	+	1.70006i
$877$	−36.8042	−	21.2489i	−1.24279	−	0.717524i	−0.273127	−	0.961978i	$-0.588058\pi$
$877$	−36.8042	−	21.2489i	−1.24279	−	0.717524i	−0.969661	+	0.244454i	$0.921391\pi$
$878$	−2.10157	+	3.16265i	−0.0709245	+	0.106734i
$879$	20.0004			0.674597
$880$	−20.2503	+	20.6677i	−0.682636	+	0.696707i
$881$	0.254151	+	0.440202i	0.00856257	+	0.0148308i	0.870275	−	0.492566i	$-0.163941\pi$
$881$	0.254151	+	0.440202i	0.00856257	+	0.0148308i	−0.861712	+	0.507397i	$0.830608\pi$
$882$	0.400032	+	0.805996i	0.0134698	+	0.0271393i
$883$			47.2885i			1.59139i	0.605700	+	0.795693i	$0.292893\pi$
$883$			47.2885i			1.59139i	−0.605700	+	0.795693i	$0.707107\pi$
$884$	−7.48283	−	17.0969i	−0.251675	−	0.575030i
$885$		−	48.3133i		−	1.62403i
$886$	−18.5808	+	9.22203i	−0.624235	+	0.309820i
$887$	5.21481	+	9.03232i	0.175096	+	0.303276i	0.940195	−	0.340638i	$-0.110643\pi$
$887$	5.21481	+	9.03232i	0.175096	+	0.303276i	−0.765098	+	0.643914i	$0.777310\pi$
$888$	−32.1101	+	37.1847i	−1.07755	+	1.24784i
$889$	−11.0752			−0.371450
$890$	7.21431	+	4.79388i	0.241824	+	0.160691i
$891$	−20.9711	−	12.1077i	−0.702557	−	0.405622i
$892$	−16.0201	−	2.02601i	−0.536391	−	0.0678358i
$893$	−9.37295	−	5.41147i	−0.313654	−	0.181088i
$894$	3.56006	+	7.17292i	0.119066	+	0.239898i
$895$	20.3890	+	35.3147i	0.681528	+	1.18044i
$896$	6.15283	+	2.89887i	0.205552	+	0.0968443i
$897$	−31.5899	−	17.6222i	−1.05476	−	0.588387i
$898$	−1.85307	−	0.116711i	−0.0618377	−	0.00389470i
$899$	−7.84870	+	4.53145i	−0.261769	+	0.151132i
$900$	0.130650	+	0.310922i	0.00435500	+	0.0103641i
$901$	−13.4871	−	7.78677i	−0.449320	−	0.259415i
$902$	2.60315	−	41.3311i	0.0866753	−	1.37618i
$903$	4.99379	−	8.64950i	0.166183	−	0.287837i
$904$	17.5878	−	20.3673i	0.584961	−	0.677405i
$905$	12.1107			0.402573
$906$	−13.3768	−	8.88883i	−0.444414	−	0.295312i
$907$	20.2878	−	11.7132i	0.673646	−	0.388930i	−0.123811	−	0.992306i	$-0.539512\pi$
$907$	20.2878	−	11.7132i	0.673646	−	0.388930i	0.797457	+	0.603376i	$0.206178\pi$
$908$	42.2661	−	17.7603i	1.40265	−	0.589396i
$909$		−	1.24144i		−	0.0411761i
$910$	−0.383547	+	7.96048i	−0.0127145	+	0.263887i
$911$	53.8994			1.78577			0.892883	−	0.450289i	$-0.148679\pi$
$911$	53.8994			1.78577			0.892883	+	0.450289i	$0.148679\pi$
$912$	−9.26408	−	33.2150i	−0.306764	−	1.09986i
$913$	−1.29447	−	2.24210i	−0.0428409	−	0.0742025i
$914$	15.3994	−	23.1745i	0.509367	−	0.766546i
$915$			9.45778i			0.312665i
$916$	0.947310	+	0.719249i	0.0313000	+	0.0237647i
$917$	0.414330	+	0.239214i	0.0136824	+	0.00789953i
$918$	1.21377	−	19.2716i	0.0400605	−	0.636056i
$919$	−21.8643	+	37.8701i	−0.721237	+	1.24922i	0.239268	+	0.970954i	$0.423093\pi$
$919$	−21.8643	+	37.8701i	−0.721237	+	1.24922i	−0.960504	+	0.278265i	$0.910241\pi$
$920$	−40.8860	+	14.2287i	−1.34797	+	0.469106i
$921$	4.33700	+	7.51190i	0.142909	+	0.247526i
$922$	1.04086	−	16.5261i	0.0342789	−	0.544260i
$923$	0.810918	−	1.45367i	0.0266917	−	0.0478482i
$924$	−5.65591	−	0.715286i	−0.186066	−	0.0235312i
$925$	−15.5308	+	8.96670i	−0.510649	+	0.294823i
$926$	−12.6320	−	25.4513i	−0.415113	−	0.836382i
$927$	−0.316828	+	0.548762i	−0.0104060	+	0.0180237i
$928$	3.11315	−	9.57026i	0.102194	−	0.314159i
$929$	−2.52459	+	4.37272i	−0.0828291	+	0.143464i	−0.904464	−	0.426550i	$-0.859729\pi$
$929$	−2.52459	+	4.37272i	−0.0828291	+	0.143464i	0.821635	+	0.570014i	$0.193062\pi$
$930$	−17.6658	+	26.5853i	−0.579284	+	0.871765i
$931$		−	33.5820i		−	1.10061i
$932$	0.114392	−	0.150664i	0.00374704	−	0.00493515i
$933$	−37.1290	+	21.4364i	−1.21555	+	0.701798i
$934$	−48.1970	+	23.9211i	−1.57706	+	0.782724i
$935$	18.7212			0.612249
$936$	−0.627824	+	0.749108i	−0.0205211	+	0.0244854i
$937$	44.5775			1.45628			0.728141	−	0.685427i	$-0.240385\pi$
$937$	44.5775			1.45628			0.728141	+	0.685427i	$0.240385\pi$
$938$	−2.98171	+	1.47988i	−0.0973562	+	0.0483198i
$939$	−18.3966	+	10.6213i	−0.600349	+	0.346612i
$940$	−8.86047	−	6.72735i	−0.288997	−	0.219422i
$941$		−	58.1679i		−	1.89622i	−0.317943	−	0.948110i	$-0.602992\pi$
$941$		−	58.1679i		−	1.89622i	0.317943	−	0.948110i	$-0.397008\pi$
$942$	−1.65600	+	2.49212i	−0.0539555	+	0.0811976i
$943$	30.9802	−	53.6593i	1.00885	−	1.74739i
$944$	10.8587	−	42.2444i	0.353421	−	1.37494i
$945$	−4.12302	+	7.14127i	−0.134122	+	0.232306i
$946$	17.0536	+	34.3600i	0.554459	+	1.11714i
$947$	−8.18618	+	4.72629i	−0.266015	+	0.153584i	−0.627075	−	0.778959i	$-0.715748\pi$
$947$	−8.18618	+	4.72629i	−0.266015	+	0.153584i	0.361060	+	0.932542i	$0.382415\pi$
$948$	−3.35251	+	26.5090i	−0.108885	+	0.860971i
$949$	−53.6471	+	0.791642i	−1.74146	+	0.0256978i
$950$	0.791186	−	12.5620i	0.0256695	−	0.407564i
$951$	−9.39319	−	16.2695i	−0.304595	−	0.527574i
$952$	−1.44639	−	4.15618i	−0.0468777	−	0.134703i
$953$	9.38165	−	16.2495i	0.303901	−	0.526373i	−0.673115	−	0.739538i	$-0.735044\pi$
$953$	9.38165	−	16.2495i	0.303901	−	0.526373i	0.977016	+	0.213165i	$0.0683773\pi$
$954$	−0.0512685	+	0.814009i	−0.00165988	+	0.0263545i
$955$	19.5542	+	11.2897i	0.632761	+	0.365325i
$956$	18.5880	−	24.4819i	0.601179	−	0.791801i
$957$			8.43543i			0.272679i
$958$	7.77383	−	11.6988i	0.251161	−	0.377972i
$959$	1.06916	+	1.85184i	0.0345250	+	0.0597991i
$960$	−5.16365	−	35.0669i	−0.166656	−	1.13178i
$961$	−5.04906			−0.162873
$962$	−43.7073	−	28.1226i	−1.40918	−	0.906708i
$963$			0.982317i			0.0316547i
$964$	7.78038	+	18.5158i	0.250589	+	0.596354i
$965$	−3.55159	+	2.05051i	−0.114330	+	0.0660083i
$966$	−7.10411	−	4.72065i	−0.228571	−	0.151885i
$967$	13.9692			0.449218			0.224609	−	0.974449i	$-0.427889\pi$
$967$	13.9692			0.449218			0.224609	+	0.974449i	$0.427889\pi$
$968$	−6.02401	+	6.97602i	−0.193619	+	0.224218i
$969$	−11.1554	+	19.3217i	−0.358362	+	0.620701i
$970$	2.73250	−	43.3849i	0.0877353	−	1.39301i
$971$	−10.8263	−	6.25059i	−0.347434	−	0.200591i	0.316121	−	0.948719i	$-0.397620\pi$
$971$	−10.8263	−	6.25059i	−0.347434	−	0.200591i	−0.663555	+	0.748128i	$0.730953\pi$
$972$	−1.83580	+	0.771404i	−0.0588832	+	0.0247428i
$973$	1.11927	−	0.646212i	0.0358822	−	0.0207166i
$974$	−33.1572	−	2.08833i	−1.06243	−	0.0669144i
$975$	9.28154	−	5.54288i	0.297247	−	0.177514i
$976$	−2.12569	+	8.26973i	−0.0680418	+	0.264707i
$977$	−7.03484	−	12.1847i	−0.225065	−	0.389823i	0.731274	−	0.682084i	$-0.238926\pi$
$977$	−7.03484	−	12.1847i	−0.225065	−	0.389823i	−0.956339	+	0.292260i	$0.905593\pi$
$978$	−11.6713	−	23.5156i	−0.373206	−	0.751946i
$979$	−5.67646	−	3.27731i	−0.181421	−	0.104743i
$980$	4.33104	−	34.2464i	0.138350	−	1.09396i
$981$	0.898022	+	0.518473i	0.0286716	+	0.0165536i
$982$	36.2517	+	24.0891i	1.15684	+	0.768715i
$983$	−42.4961			−1.35541			−0.677707	−	0.735332i	$-0.737026\pi$
$983$	−42.4961			−1.35541			−0.677707	+	0.735332i	$0.737026\pi$
$984$	38.3961	+	33.1562i	1.22402	+	1.05698i
$985$	33.2422	+	57.5771i	1.05918	+	1.83456i
$986$	−5.83258	+	2.89483i	−0.185747	+	0.0921901i
$987$		−	2.19192i		−	0.0697697i
$988$	33.4176	−	14.6260i	1.06316	−	0.465314i
$989$			57.3916i			1.82495i
$990$	−0.435893	−	0.878251i	−0.0138536	−	0.0279126i
$991$	4.71260	+	8.16245i	0.149701	+	0.259289i	0.931117	−	0.364721i	$-0.118836\pi$
$991$	4.71260	+	8.16245i	0.149701	+	0.259289i	−0.781416	+	0.624010i	$0.785502\pi$
$992$	−21.4219	+	19.2752i	−0.680145	+	0.611988i
$993$	−28.3146			−0.898536
$994$	0.217230	−	0.326909i	0.00689012	−	0.0103689i
$995$	46.6148	+	26.9131i	1.47779	+	0.853201i
$996$	3.14638	+	0.397914i	0.0996969	+	0.0126084i
$997$	6.28844	+	3.63063i	0.199157	+	0.114983i	0.596262	−	0.802790i	$-0.296652\pi$
$997$	6.28844	+	3.63063i	0.199157	+	0.114983i	−0.397105	+	0.917773i	$0.629985\pi$
$998$	5.84960	−	2.90327i	0.185166	−	0.0919014i
$999$	−26.8875	−	46.5706i	−0.850684	−	1.47343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.r.a.29.5	yes	24
3.2	odd	2		936.2.be.a.757.8		24
4.3	odd	2		416.2.z.a.81.10		24
8.3	odd	2		416.2.z.a.81.3		24
8.5	even	2	inner	104.2.r.a.29.4	✓	24
13.9	even	3	inner	104.2.r.a.61.4	yes	24
24.5	odd	2		936.2.be.a.757.9		24
39.35	odd	6		936.2.be.a.685.9		24
52.35	odd	6		416.2.z.a.113.3		24
104.35	odd	6		416.2.z.a.113.10		24
104.61	even	6	inner	104.2.r.a.61.5	yes	24
312.269	odd	6		936.2.be.a.685.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.4	✓	24	8.5	even	2	inner
104.2.r.a.29.5	yes	24	1.1	even	1	trivial
104.2.r.a.61.4	yes	24	13.9	even	3	inner
104.2.r.a.61.5	yes	24	104.61	even	6	inner
416.2.z.a.81.3		24	8.3	odd	2
416.2.z.a.81.10		24	4.3	odd	2
416.2.z.a.113.3		24	52.35	odd	6
416.2.z.a.113.10		24	104.35	odd	6
936.2.be.a.685.8		24	312.269	odd	6
936.2.be.a.685.9		24	39.35	odd	6
936.2.be.a.757.8		24	3.2	odd	2
936.2.be.a.757.9		24	24.5	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.628723 - 1.26677i) q^{2} +(-1.47584 + 0.852079i) q^{3} +(-1.20941 + 1.59290i) q^{4} +2.59989i q^{5} +(2.00729 + 1.33383i) q^{6} +(-0.300588 + 0.520633i) q^{7} +(2.77822 + 0.530559i) q^{8} +(-0.0479214 + 0.0830022i) q^{9} +(3.29346 - 1.63461i) q^{10} +(-2.40956 + 1.39116i) q^{11} +(0.427634 - 3.38138i) q^{12} +(3.60516 - 0.0531995i) q^{13} +(0.848509 + 0.0534414i) q^{14} +(-2.21531 - 3.83703i) q^{15} +(-1.07463 - 3.85294i) q^{16} +(-1.29402 + 2.24132i) q^{17} +(0.135274 + 0.00851993i) q^{18} +(-4.38088 - 2.52930i) q^{19} +(-4.14135 - 3.14434i) q^{20} -1.02450i q^{21} +(3.27722 + 2.17770i) q^{22} +(2.94353 + 5.09835i) q^{23} +(-4.55230 + 1.58424i) q^{24} -1.75942 q^{25} +(-2.33404 - 4.53346i) q^{26} -5.27581i q^{27} +(-0.465779 - 1.10847i) q^{28} +(-1.54071 + 0.889530i) q^{29} +(-3.46782 + 5.21872i) q^{30} +5.09421 q^{31} +(-4.20514 + 3.78375i) q^{32} +(2.37076 - 4.10627i) q^{33} +(3.65282 + 0.230064i) q^{34} +(-1.35359 - 0.781495i) q^{35} +(-0.0742572 - 0.176718i) q^{36} +(8.82719 - 5.09638i) q^{37} +(-0.449684 + 7.13981i) q^{38} +(-5.27532 + 3.15040i) q^{39} +(-1.37940 + 7.22306i) q^{40} +(-5.26242 - 9.11477i) q^{41} +(-1.29780 + 0.644126i) q^{42} +(8.44267 + 4.87438i) q^{43} +(0.698182 - 5.52066i) q^{44} +(-0.215797 - 0.124590i) q^{45} +(4.60777 - 6.93423i) q^{46} +2.13951 q^{47} +(4.86901 + 4.77067i) q^{48} +(3.31929 + 5.74919i) q^{49} +(1.10619 + 2.22879i) q^{50} -4.41045i q^{51} +(-4.27539 + 5.80698i) q^{52} +6.01748i q^{53} +(-6.68324 + 3.31702i) q^{54} +(-3.61686 - 6.26458i) q^{55} +(-1.11133 + 1.28695i) q^{56} +8.62067 q^{57} +(2.09551 + 1.39246i) q^{58} +(9.44349 + 5.45220i) q^{59} +(8.79122 + 1.11180i) q^{60} +(-1.84865 - 1.06732i) q^{61} +(-3.20285 - 6.45319i) q^{62} +(-0.0288091 - 0.0498989i) q^{63} +(7.43701 + 2.94802i) q^{64} +(0.138313 + 9.37301i) q^{65} +(-6.69225 - 0.421496i) q^{66} +(-3.39076 + 1.95766i) q^{67} +(-2.00517 - 4.77193i) q^{68} +(-8.68840 - 5.01625i) q^{69} +(-0.138942 + 2.20603i) q^{70} +(0.230832 - 0.399814i) q^{71} +(-0.177174 + 0.205173i) q^{72} -14.8806 q^{73} +(-12.0058 - 7.97781i) q^{74} +(2.59664 - 1.49917i) q^{75} +(9.32722 - 3.91932i) q^{76} -1.67266i q^{77} +(7.30755 + 4.70190i) q^{78} -7.83968 q^{79} +(10.0172 - 2.79393i) q^{80} +(4.35164 + 7.53727i) q^{81} +(-8.23772 + 12.3969i) q^{82} +0.930501i q^{83} +(1.63192 + 1.23904i) q^{84} +(-5.82717 - 3.36432i) q^{85} +(0.866614 - 13.7596i) q^{86} +(1.51590 - 2.62562i) q^{87} +(-7.43237 + 2.58653i) q^{88} +(1.17791 + 2.04019i) q^{89} +(-0.0221509 + 0.351698i) q^{90} +(-1.05597 + 1.89296i) q^{91} +(-11.6811 - 1.47727i) q^{92} +(-7.51826 + 4.34067i) q^{93} +(-1.34516 - 2.71027i) q^{94} +(6.57591 - 11.3898i) q^{95} +(2.98209 - 9.16734i) q^{96} +(5.91151 - 10.2390i) q^{97} +(5.19598 - 7.81943i) q^{98} -0.266665i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) \) 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Introduction

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