LMFDB - Embedded newform 104.2.r.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(29,104)]

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

lf = mfeigenbasis(mf)

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")

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

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			29.4
Character	$\chi$	$=$	104.29
Dual form			104.2.r.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.782694 - 1.17788i) q^{2} +(1.47584 - 0.852079i) q^{3} +(-0.774781 + 1.84383i) q^{4} -2.59989i q^{5} +(-2.15878 - 1.07144i) q^{6} +(-0.300588 + 0.520633i) q^{7} +(2.77822 - 0.530559i) q^{8} +(-0.0479214 + 0.0830022i) q^{9} +(-3.06235 + 2.03492i) 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} +(-2.79943 - 2.85713i) q^{16} +(-1.29402 + 2.24132i) q^{17} +(0.135274 - 0.00851993i) q^{18} +(4.38088 + 2.52930i) q^{19} +(4.79376 + 2.01435i) q^{20} +1.02450i q^{21} +(-3.52456 - 1.74931i) q^{22} +(2.94353 + 5.09835i) q^{23} +(3.64814 - 3.15029i) q^{24} -1.75942 q^{25} +(2.88440 + 4.20479i) q^{26} +5.27581i q^{27} +(-0.727070 - 0.957610i) q^{28} +(1.54071 - 0.889530i) q^{29} +(-2.78564 + 5.61258i) q^{30} +5.09421 q^{31} +(-1.17425 + 5.53364i) q^{32} +(2.37076 - 4.10627i) q^{33} +(3.65282 - 0.230064i) q^{34} +(1.35359 + 0.781495i) q^{35} +(-0.115914 - 0.152668i) 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} +(1.20673 - 0.801868i) q^{42} +(-8.44267 - 4.87438i) q^{43} +(0.698182 + 5.52066i) q^{44} +(0.215797 + 0.124590i) q^{45} +(3.70134 - 7.45756i) q^{46} +2.13951 q^{47} +(-6.56602 - 1.83135i) q^{48} +(3.31929 + 5.74919i) q^{49} +(1.37709 + 2.07238i) q^{50} +4.41045i q^{51} +(2.69512 - 6.68852i) q^{52} -6.01748i q^{53} +(6.21424 - 4.12934i) q^{54} +(-3.61686 - 6.26458i) q^{55} +(-0.558872 + 1.60591i) q^{56} +8.62067 q^{57} +(-2.25366 - 1.11854i) q^{58} +(-9.44349 - 5.45220i) q^{59} +(8.79122 - 1.11180i) q^{60} +(1.84865 + 1.06732i) q^{61} +(-3.98720 - 6.00034i) 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} +(-3.13002 - 4.12249i) q^{68} +(8.68840 + 5.01625i) q^{69} +(-0.138942 - 2.20603i) q^{70} +(0.230832 - 0.399814i) q^{71} +(-0.0890985 + 0.256024i) q^{72} -14.8806 q^{73} +(12.9119 + 6.40843i) q^{74} +(-2.59664 + 1.49917i) q^{75} +(-8.05784 + 6.11795i) q^{76} +1.67266i q^{77} +(7.83974 + 3.74788i) q^{78} -7.83968 q^{79} +(-7.42823 + 7.27820i) q^{80} +(4.35164 + 7.53727i) q^{81} +(-6.61721 + 13.3325i) q^{82} -0.930501i q^{83} +(-1.88900 - 0.793762i) q^{84} +(5.82717 + 3.36432i) q^{85} +(0.866614 + 13.7596i) q^{86} +(1.51590 - 2.62562i) q^{87} +(5.95619 - 5.14336i) 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} +(-1.67458 - 2.52008i) q^{94} +(6.57591 - 11.3898i) q^{95} +(2.98209 + 9.16734i) q^{96} +(5.91151 - 10.2390i) q^{97} +(4.17383 - 8.40957i) 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 $

$2$	−0.782694	−	1.17788i	−0.553448	−	0.832884i
$2$	−0.782694	−	1.17788i	−0.553448	−	0.832884i
$3$	1.47584	−	0.852079i	0.852079	−	0.491948i	−0.00927251	−	0.999957i	$-0.502952\pi$
$3$	1.47584	−	0.852079i	0.852079	−	0.491948i	0.861352	+	0.508009i	$0.169618\pi$
$4$	−0.774781	+	1.84383i	−0.387391	+	0.921916i
$5$		−	2.59989i		−	1.16271i	−0.813651	−	0.581353i	$-0.802524\pi$
$5$		−	2.59989i		−	1.16271i	0.813651	−	0.581353i	$-0.197476\pi$
$6$	−2.15878	−	1.07144i	−0.881317	−	0.437415i
$7$	−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
$10$	−3.06235	+	2.03492i	−0.968399	+	0.643497i
$11$	2.40956	−	1.39116i	0.726509	−	0.419450i	−0.0906348	−	0.995884i	$-0.528890\pi$
$11$	2.40956	−	1.39116i	0.726509	−	0.419450i	0.817144	+	0.576434i	$0.195556\pi$
$12$	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
$16$	−2.79943	−	2.85713i	−0.699857	−	0.714283i
$17$	−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	0.909737	−	0.415186i	$-0.136283\pi$
$19$	4.38088	+	2.52930i	1.00504	+	0.580262i	0.0953071	+	0.995448i	$0.469617\pi$
$20$	4.79376	+	2.01435i	1.07192	+	0.450421i
$21$			1.02450i			0.223564i
$22$	−3.52456	−	1.74931i	−0.751438	−	0.372954i
$23$	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	$0.622986\pi$
$24$	3.64814	−	3.15029i	0.744674	−	0.643050i
$25$	−1.75942			−0.351885
$26$	2.88440	+	4.20479i	0.565677	+	0.824627i
$27$			5.27581i			1.01533i
$28$	−0.727070	−	0.957610i	−0.137403	−	0.180971i
$29$	1.54071	−	0.889530i	0.286103	−	0.165182i	−0.350080	−	0.936720i	$-0.613846\pi$
$29$	1.54071	−	0.889530i	0.286103	−	0.165182i	0.636183	+	0.771538i	$0.280512\pi$
$30$	−2.78564	+	5.61258i	−0.508585	+	1.02471i
$31$	5.09421			0.914947			0.457473	−	0.889223i	$-0.348755\pi$
$31$	5.09421			0.914947			0.457473	+	0.889223i	$0.348755\pi$
$32$	−1.17425	+	5.53364i	−0.207580	+	0.978218i
$33$	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
$36$	−0.115914	−	0.152668i	−0.0193189	−	0.0254446i
$37$	−8.82719	+	5.09638i	−1.45118	+	0.837840i	−0.998549	−	0.0538570i	$-0.982848\pi$
$37$	−8.82719	+	5.09638i	−1.45118	+	0.837840i	−0.452633	+	0.891697i	$0.649515\pi$
$38$	−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	$-0.473725\pi$
$42$	1.20673	−	0.801868i	0.186203	−	0.123731i
$43$	−8.44267	−	4.87438i	−1.28749	−	0.743335i	−0.309288	−	0.950968i	$-0.600091\pi$
$43$	−8.44267	−	4.87438i	−1.28749	−	0.743335i	−0.978207	+	0.207633i	$0.933424\pi$
$44$	0.698182	+	5.52066i	0.105255	+	0.832271i
$45$	0.215797	+	0.124590i	0.0321691	+	0.0185728i
$46$	3.70134	−	7.45756i	0.545732	−	1.09956i
$47$	2.13951			0.312080			0.156040	−	0.987751i	$-0.450127\pi$
$47$	2.13951			0.312080			0.156040	+	0.987751i	$0.450127\pi$
$48$	−6.56602	−	1.83135i	−0.947724	−	0.264332i
$49$	3.31929	+	5.74919i	0.474185	+	0.821312i
$50$	1.37709	+	2.07238i	0.194750	+	0.293079i
$51$			4.41045i			0.617586i
$52$	2.69512	−	6.68852i	0.373746	−	0.927531i
$53$		−	6.01748i		−	0.826565i	−0.910603	−	0.413282i	$-0.864382\pi$
$53$		−	6.01748i		−	0.826565i	0.910603	−	0.413282i	$-0.135618\pi$
$54$	6.21424	−	4.12934i	0.845652	−	0.561932i
$55$	−3.61686	−	6.26458i	−0.487697	−	0.844716i
$56$	−0.558872	+	1.60591i	−0.0746824	+	0.214599i
$57$	8.62067			1.14184
$58$	−2.25366	−	1.11854i	−0.295920	−	0.146871i
$59$	−9.44349	−	5.45220i	−1.22944	−	0.709816i	−0.262526	−	0.964925i	$-0.584555\pi$
$59$	−9.44349	−	5.45220i	−1.22944	−	0.709816i	−0.966912	+	0.255109i	$0.917889\pi$
$60$	8.79122	−	1.11180i	1.13494	−	0.143533i
$61$	1.84865	+	1.06732i	0.236696	+	0.136656i	0.613657	−	0.789573i	$-0.289698\pi$
$61$	1.84865	+	1.06732i	0.236696	+	0.136656i	−0.376961	+	0.926229i	$0.623031\pi$
$62$	−3.98720	−	6.00034i	−0.506375	−	0.762044i
$63$	−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	−0.278366	−	0.960475i	$-0.589793\pi$
$67$	3.39076	−	1.95766i	0.414247	−	0.239166i	0.692613	+	0.721309i	$0.256459\pi$
$68$	−3.13002	−	4.12249i	−0.379571	−	0.499926i
$69$	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	$0.157946\pi$
$72$	−0.0890985	+	0.256024i	−0.0105004	+	0.0301727i
$73$	−14.8806			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$73$	−14.8806			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$74$	12.9119	+	6.40843i	1.50098	+	0.744965i
$75$	−2.59664	+	1.49917i	−0.299834	+	0.173109i
$76$	−8.05784	+	6.11795i	−0.924297	+	0.701777i
$77$			1.67266i			0.190617i
$78$	7.83974	+	3.74788i	0.887675	+	0.424364i
$79$	−7.83968			−0.882033			−0.441017	−	0.897499i	$-0.645382\pi$
$79$	−7.83968			−0.882033			−0.441017	+	0.897499i	$0.645382\pi$
$80$	−7.42823	+	7.27820i	−0.830501	+	0.813728i
$81$	4.35164	+	7.53727i	0.483516	+	0.837474i
$82$	−6.61721	+	13.3325i	−0.730748	+	1.47233i
$83$		−	0.930501i		−	0.102136i	−0.998695	−	0.0510679i	$-0.983738\pi$
$83$		−	0.930501i		−	0.102136i	0.998695	−	0.0510679i	$-0.0162625\pi$
$84$	−1.88900	−	0.793762i	−0.206107	−	0.0866065i
$85$	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
$88$	5.95619	−	5.14336i	0.634932	−	0.548284i
$89$	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
$94$	−1.67458	−	2.52008i	−0.172720	−	0.259926i
$95$	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	$-0.0382549\pi$
$98$	4.17383	−	8.40957i	0.421621	−	0.849495i
$99$			0.266665i			0.0268008i
$100$	1.36317	−	3.24408i	0.136317	−	0.324408i
$101$	11.2176	−	6.47646i	1.11619	−	0.644432i	0.175763	−	0.984432i	$-0.443761\pi$
$101$	11.2176	−	6.47646i	1.11619	−	0.644432i	0.940425	+	0.340001i	$0.110427\pi$
$102$	5.19496	−	3.45203i	0.514377	−	0.341802i
$103$	6.61141			0.651441			0.325721	−	0.945466i	$-0.394393\pi$
$103$	6.61141			0.651441			0.325721	+	0.945466i	$0.394393\pi$
$104$	−9.98770	+	2.06055i	−0.979374	+	0.202054i
$105$	2.66358			0.259939
$106$	−7.08785	+	4.70985i	−0.688432	+	0.457461i
$107$	−8.87612	+	5.12463i	−0.858087	+	0.495417i	−0.863371	−	0.504569i	$-0.831651\pi$
$107$	−8.87612	+	5.12463i	−0.858087	+	0.495417i	0.00528438	+	0.999986i	$0.498318\pi$
$108$	−9.72770	−	4.08760i	−0.936048	−	0.393329i
$109$			10.8192i			1.03630i	0.855291	+	0.518148i	$0.173378\pi$
$109$			10.8192i			1.03630i	−0.855291	+	0.518148i	$0.826622\pi$
$110$	−4.54801	+	9.16346i	−0.433635	+	0.873701i
$111$	−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	$0.0189780\pi$
$114$	−6.74735	−	10.1541i	−0.631947	−	0.951017i
$115$	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
$120$	−8.19040	−	9.48477i	−0.747678	−	0.865837i
$121$	−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
$124$	−3.94690	+	9.39286i	−0.354442	+	0.843504i
$125$		−	8.42514i		−	0.753567i
$126$	−0.0362260	+	0.0729891i	−0.00322727	+	0.00650239i
$127$	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	$0.528765\pi$
$128$	−9.29330	−	6.45248i	−0.821420	−	0.570324i
$129$	−16.6134			−1.46273
$130$	10.9320	−	7.49911i	0.958799	−	0.657716i
$131$			0.795820i			0.0695311i	0.999395	+	0.0347655i	$0.0110684\pi$
$131$			0.795820i			0.0695311i	−0.999395	+	0.0347655i	$0.988932\pi$
$132$	5.73445	+	7.55273i	0.499120	+	0.657381i
$133$	−2.63368	+	1.52056i	−0.228369	+	0.131849i
$134$	−4.95980	−	2.46165i	−0.428461	−	0.212654i
$135$	13.7165			1.18053
$136$	−2.40593	+	6.91343i	−0.206307	+	0.592822i
$137$	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	0.576876	−	0.816832i	$-0.304272\pi$
$139$	1.86181	+	1.07491i	0.157916	+	0.0911731i	−0.418959	+	0.908005i	$0.637605\pi$
$140$	−2.48968	+	1.89030i	−0.210416	+	0.159760i
$141$	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
$146$	11.6470	+	17.5275i	0.963911	+	1.45059i
$147$	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	0.377480	−	0.926018i	$-0.376791\pi$
$149$	−2.87752	−	1.66134i	−0.235736	−	0.136102i	−0.613215	+	0.789916i	$0.710124\pi$
$150$	3.79821	+	1.88513i	0.310122	+	0.153920i
$151$	−6.66412			−0.542318			−0.271159	−	0.962535i	$-0.587407\pi$
$151$	−6.66412			−0.542318			−0.271159	+	0.962535i	$0.587407\pi$
$152$	13.5130	+	4.70265i	1.09605	+	0.381435i
$153$	−0.124023	−	0.214814i	−0.0100267	−	0.0173667i
$154$	1.97019	−	1.30918i	0.158762	−	0.105497i
$155$		−	13.2444i		−	1.06381i
$156$	−1.72158	−	12.1677i	−0.137836	−	0.974194i
$157$		−	1.24154i		−	0.0990854i	−0.998772	−	0.0495427i	$-0.984224\pi$
$157$		−	1.24154i		−	0.0990854i	0.998772	−	0.0495427i	$-0.0157764\pi$
$158$	6.13607	+	9.23417i	0.488159	+	0.734631i
$159$	−5.12737	−	8.88087i	−0.406627	−	0.704299i
$160$	14.3868	+	3.05292i	1.13738	+	0.241355i
$161$	−3.53916			−0.278925
$162$	5.47196	−	11.0251i	0.429918	−	0.866211i
$163$	9.43363	+	5.44651i	0.738899	+	0.426604i	0.821669	−	0.569965i	$-0.193043\pi$
$163$	9.43363	+	5.44651i	0.738899	+	0.426604i	−0.0827698	+	0.996569i	$0.526377\pi$
$164$	20.8833	−	2.64105i	1.63071	−	0.206232i
$165$	−10.6758	−	6.16370i	−0.831113	−	0.479843i
$166$	−1.09601	+	0.728297i	−0.0850672	+	0.0565268i
$167$	−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
$172$	15.5287	−	11.7903i	1.18406	−	0.899000i
$173$	−5.66761	−	3.27220i	−0.430901	−	0.248781i	0.268830	−	0.963188i	$-0.413363\pi$
$173$	−5.66761	−	3.27220i	−0.430901	−	0.248781i	−0.699730	+	0.714407i	$0.746696\pi$
$174$	−4.27913	+	0.269511i	−0.324400	+	0.0204316i
$175$	0.528861	−	0.916015i	0.0399782	−	0.0692442i
$176$	−10.7201	−	2.98997i	−0.808058	−	0.225378i
$177$	−18.5828			−1.39677
$178$	1.48115	−	2.98427i	0.111017	−	0.223681i
$179$	−13.5832	+	7.84225i	−1.01525	+	0.586157i	−0.912726	−	0.408573i	$-0.866027\pi$
$179$	−13.5832	+	7.84225i	−1.01525	+	0.586157i	−0.102528	+	0.994730i	$0.532693\pi$
$180$	−0.396919	+	0.301362i	−0.0295846	+	0.0224622i
$181$			4.65816i			0.346238i	0.984901	+	0.173119i	$0.0553846\pi$
$181$			4.65816i			0.346238i	−0.984901	+	0.173119i	$0.944615\pi$
$182$	−3.05617	+	0.237805i	−0.226538	+	0.0176273i
$183$	3.63776			0.268911
$184$	10.8828	+	12.6026i	0.802288	+	0.929077i
$185$	13.2500	+	22.9497i	0.974162	+	1.68730i
$186$	−10.9973	−	5.45816i	−0.806358	−	0.400212i
$187$			7.20077i			0.526573i
$188$	−1.65765	+	3.94490i	−0.120897	+	0.287711i
$189$	−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	$0.0649297\pi$
$192$	8.46393	−	10.6877i	0.610832	−	0.771322i
$193$	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	$0.697994\pi$
$197$	−22.1460	+	12.7860i	−1.57784	+	0.910964i	−0.995161	+	0.0982592i	$0.968673\pi$
$198$	0.314098	−	0.208717i	0.0223220	−	0.0148329i
$199$	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
$202$	−16.4084	−	8.14380i	−1.15449	−	0.572996i
$203$			1.06953i			0.0750661i
$204$	−8.13212	−	3.41713i	−0.569362	−	0.239247i
$205$	−23.6974	+	13.6817i	−1.65510	+	0.955571i
$206$	−5.17471	−	7.78741i	−0.360539	−	0.542575i
$207$	−0.564233			−0.0392169
$208$	10.2444	+	10.1515i	0.710320	+	0.703879i
$209$	14.0747			0.973564
$210$	−2.08477	−	3.13737i	−0.143863	−	0.216499i
$211$	18.3083	−	10.5703i	1.26040	−	0.727691i	0.287246	−	0.957857i	$-0.407260\pi$
$211$	18.3083	−	10.5703i	1.26040	−	0.727691i	0.973151	+	0.230166i	$0.0739270\pi$
$212$	11.0952	+	4.66223i	0.762023	+	0.320203i
$213$		−	0.786750i		−	0.0539072i
$214$	12.9835	+	6.44395i	0.887531	+	0.440499i
$215$	−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
$218$	12.7437	−	8.46816i	0.863114	−	0.573536i
$219$	−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	$0.746200\pi$
$224$	−2.52803	−	2.27470i	−0.168911	−	0.151985i
$225$	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	0.983344	−	0.181752i	$-0.0581768\pi$
$227$	19.8519	+	11.4615i	1.31761	+	0.760725i	0.334270	+	0.942477i	$0.391510\pi$
$228$	−6.67914	+	15.8951i	−0.442337	+	1.05268i
$229$			0.594709i			0.0392995i	0.999807	+	0.0196497i	$0.00625511\pi$
$229$			0.594709i			0.0392995i	−0.999807	+	0.0196497i	$0.993745\pi$
$230$	−19.3888	−	9.62306i	−1.27846	−	0.634526i
$231$	1.42524	+	2.46859i	0.0937739	+	0.162421i
$232$	3.80849	−	3.28875i	0.250039	−	0.215917i
$233$	−0.0945847			−0.00619645			−0.00309823	−	0.999995i	$-0.500986\pi$
$233$	−0.0945847			−0.00619645			−0.00309823	+	0.999995i	$0.500986\pi$
$234$	−0.487231	+	0.0379122i	−0.0318513	+	0.00247840i
$235$		−	5.56249i		−	0.362857i
$236$	17.3696	−	13.1879i	1.13066	−	0.858462i
$237$	−11.5702	+	6.68003i	−0.751562	+	0.433915i
$238$	−0.978213	+	1.97093i	−0.0634081	+	0.127757i
$239$	−15.3694			−0.994166			−0.497083	−	0.867703i	$-0.665596\pi$
$239$	−15.3694			−0.994166			−0.497083	+	0.867703i	$0.665596\pi$
$240$	−4.76130	+	17.0709i	−0.307341	+	1.10192i
$241$	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
$244$	−3.40026	+	2.58166i	−0.217679	+	0.165274i
$245$	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
$250$	−9.92376	+	6.59430i	−0.627634	+	0.417060i
$251$	14.8114	+	8.55135i	0.934886	+	0.539757i	0.888353	−	0.459160i	$-0.151850\pi$
$251$	14.8114	+	8.55135i	0.934886	+	0.539757i	0.0465324	+	0.998917i	$0.485183\pi$
$252$	0.114326	−	0.0144585i	0.00720186	−	0.000910798i
$253$	14.1852	+	8.18984i	0.891818	+	0.514891i
$254$	11.5827	−	23.3372i	0.726763	−	1.46430i
$255$	11.4667			0.718071
$256$	−0.326406	+	15.9967i	−0.0204003	+	0.999792i
$257$	−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	$-0.390066\pi$
$258$	13.0032	+	19.5685i	0.809545	+	1.21828i
$259$		−	6.12764i		−	0.380753i
$260$	−17.3894	−	7.00701i	−1.07845	−	0.434556i
$261$			0.170510i			0.0105543i
$262$	0.937376	−	0.622883i	0.0579113	−	0.0384818i
$263$	−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	$0.843456\pi$
$264$	4.40786	−	12.6659i	0.271285	−	0.779535i
$265$	−15.6448			−0.961052
$266$	3.85239	+	1.91202i	0.236205	+	0.117233i
$267$	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	0.654034	−	0.756465i	$-0.273075\pi$
$269$	5.34569	+	3.08633i	0.325932	+	0.188177i	−0.328101	+	0.944642i	$0.606409\pi$
$270$	−10.7358	−	16.1563i	−0.653362	−	0.983244i
$271$	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
$276$	−15.9807	+	12.1334i	−0.961927	+	0.730348i
$277$	−24.4764	−	14.1314i	−1.47064	−	0.849076i	−0.471187	−	0.882033i	$-0.656174\pi$
$277$	−24.4764	−	14.1314i	−1.47064	−	0.849076i	−0.999457	+	0.0329570i	$0.989508\pi$
$278$	−0.191109	−	3.03430i	−0.0114619	−	0.181986i
$279$	−0.244121	+	0.422831i	−0.0146152	+	0.0253142i
$280$	4.17520	+	1.45301i	0.249516	+	0.0868337i
$281$	−12.3330			−0.735724			−0.367862	−	0.929880i	$-0.619910\pi$
$281$	−12.3330			−0.735724			−0.367862	+	0.929880i	$0.619910\pi$
$282$	−4.61873	−	2.29237i	−0.275041	−	0.136508i
$283$	17.0408	−	9.83851i	1.01297	−	0.584838i	0.100910	−	0.994896i	$-0.467825\pi$
$283$	17.0408	−	9.83851i	1.01297	−	0.584838i	0.912060	+	0.410057i	$0.134491\pi$
$284$	0.558344	+	0.735384i	0.0331316	+	0.0436370i
$285$		−	22.4128i		−	1.32762i
$286$	12.7996	+	6.11903i	0.756859	+	0.361826i
$287$	6.32727			0.373487
$288$	−0.403033	−	0.362645i	−0.0237489	−	0.0213691i
$289$	5.15100	+	8.92179i	0.303000	+	0.524811i
$290$	−2.90807	+	5.85927i	−0.170768	+	0.344068i
$291$		−	20.1483i		−	1.18111i
$292$	11.5292	−	27.4374i	0.674698	−	1.60565i
$293$	10.1639	+	5.86812i	0.593780	+	0.342819i	0.766591	−	0.642136i	$-0.221952\pi$
$293$	10.1639	+	5.86812i	0.593780	+	0.342819i	−0.172811	+	0.984955i	$0.555285\pi$
$294$	−1.00569	−	15.9677i	−0.0586528	−	0.931252i
$295$	−14.1751	+	24.5520i	−0.825308	+	1.42947i
$296$	−21.8200	+	18.8422i	−1.26826	+	1.09518i
$297$	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
$302$	5.21596	+	7.84950i	0.300145	+	0.451688i
$303$	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
$306$	−0.155952	+	0.314217i	−0.00891519	+	0.0179626i
$307$			5.08990i			0.290496i	0.989395	+	0.145248i	$0.0463980\pi$
$307$			5.08990i			0.290496i	−0.989395	+	0.145248i	$0.953602\pi$
$308$	−3.08410	−	1.29595i	−0.175733	−	0.0738434i
$309$	9.75741	−	5.63344i	0.555080	−	0.320475i
$310$	−15.6002	+	10.3663i	−0.886033	+	0.588766i
$311$	25.1578			1.42657			0.713284	−	0.700875i	$-0.247207\pi$
$311$	25.1578			1.42657			0.713284	+	0.700875i	$0.247207\pi$
$312$	−12.9845	+	11.5514i	−0.735105	+	0.653967i
$313$	12.4651			0.704569			0.352285	−	0.935893i	$-0.385405\pi$
$313$	12.4651			0.704569			0.352285	+	0.935893i	$0.385405\pi$
$314$	−1.46237	+	0.971742i	−0.0825266	+	0.0548386i
$315$	−0.129732	+	0.0749006i	−0.00730955	+	0.00422017i
$316$	6.07404	−	14.4550i	0.341691	−	0.813160i
$317$		−	11.0238i		−	0.619160i	−0.950873	−	0.309580i	$-0.899811\pi$
$317$		−	11.0238i		−	0.619160i	0.950873	−	0.309580i	$-0.100189\pi$
$318$	−6.44740	+	12.9904i	−0.361552	+	0.728466i
$319$	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
$322$	2.77008	+	4.16869i	0.154370	+	0.232312i
$323$	−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
$328$	−19.4561	−	22.5308i	−1.07428	−	1.24406i
$329$	−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	0.0493848	−	0.998780i	$-0.484274\pi$
$331$	−14.3890	−	8.30750i	−0.790891	−	0.456621i	−0.840276	+	0.542158i	$0.817607\pi$
$332$	1.71569	+	0.720935i	0.0941606	+	0.0395664i
$333$		−	0.976902i		−	0.0535339i
$334$	−8.40163	+	16.9278i	−0.459717	+	0.926251i
$335$	−5.08969	−	8.81560i	−0.278079	−	0.481647i
$336$	2.92713	−	2.86801i	0.159688	−	0.156463i
$337$	−11.0591			−0.602427			−0.301214	−	0.953557i	$-0.597392\pi$
$337$	−11.0591			−0.602427			−0.301214	+	0.953557i	$0.597392\pi$
$338$	−10.6224	−	15.0055i	−0.577783	−	0.816191i
$339$		−	16.2136i		−	0.880605i
$340$	−10.7180	+	8.13771i	−0.581267	+	0.441330i
$341$	12.2748	−	7.08685i	0.664717	−	0.383774i
$342$	0.614170	+	0.304825i	0.0332105	+	0.0164830i
$343$	−8.19918			−0.442714
$344$	−26.0417	−	9.06276i	−1.40408	−	0.488631i
$345$	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	0.447481	−	0.894293i	$-0.352321\pi$
$347$	−1.92350	−	1.11054i	−0.103259	−	0.0596167i	−0.550740	+	0.834677i	$0.685655\pi$
$348$	3.66670	+	4.82934i	0.196556	+	0.258880i
$349$	11.6899	−	6.74919i	0.625748	−	0.361276i	−0.153355	−	0.988171i	$-0.549008\pi$
$349$	11.6899	−	6.74919i	0.625748	−	0.361276i	0.779104	+	0.626895i	$0.215675\pi$
$350$	−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	$0.863111\pi$
$354$	14.5447	+	21.8883i	0.773041	+	1.16335i
$355$	−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
$358$	19.8687	+	9.86121i	1.05009	+	0.521181i
$359$	25.0138			1.32018			0.660090	−	0.751187i	$-0.270518\pi$
$359$	25.0138			1.32018			0.660090	+	0.751187i	$0.270518\pi$
$360$	0.665633	+	0.231646i	0.0350819	+	0.0122088i
$361$	3.29476	+	5.70670i	0.173409	+	0.300353i
$362$	5.48673	−	3.64591i	0.288376	−	0.191625i
$363$			5.55336i			0.291476i
$364$	2.67215	+	3.41366i	0.140059	+	0.178924i
$365$			38.6880i			2.02502i
$366$	−2.84725	−	4.28483i	−0.148828	−	0.223972i
$367$	−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	$-0.347179\pi$
$368$	6.32645	−	22.6825i	0.329789	−	1.18241i
$369$	1.00873			0.0525123
$370$	16.6612	−	33.5695i	0.866175	−	1.74519i
$371$	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	0.783437	−	0.621471i	$-0.213465\pi$
$373$	12.3015	+	7.10225i	0.636946	+	0.367741i	−0.146491	+	0.989212i	$0.546798\pi$
$374$	8.48162	−	5.63600i	0.438574	−	0.291431i
$375$	−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	−0.651552	−	0.758604i	$-0.725882\pi$
$379$	−6.23669	+	3.60075i	−0.320357	+	0.184958i	0.331195	+	0.943562i	$0.392548\pi$
$380$	15.9060	+	20.9495i	0.815961	+	1.07469i
$381$	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	$0.959099\pi$
$384$	−19.2135	−	1.60422i	−0.980485	−	0.0818652i
$385$	4.34873			0.221632
$386$	0.991738	−	1.99818i	0.0504781	−	0.101705i
$387$	0.809168	−	0.467174i	0.0411323	−	0.0237478i
$388$	14.2989	+	18.8328i	0.725918	+	0.956093i
$389$			20.6264i			1.04580i	0.852394	+	0.522900i	$0.175150\pi$
$389$			20.6264i			1.04580i	−0.852394	+	0.522900i	$0.824850\pi$
$390$	9.74408	−	20.3824i	0.493410	−	1.03211i
$391$	−15.2360			−0.770519
$392$	12.2720	+	14.2114i	0.619830	+	0.717785i
$393$	0.678101	+	1.17451i	0.0342057	+	0.0592460i
$394$	32.3938	+	16.0777i	1.63198	+	0.809983i
$395$			20.3823i			1.02554i
$396$	−0.491685	−	0.206607i	−0.0247081	−	0.0103824i
$397$	−25.6669	−	14.8188i	−1.28819	−	0.743734i	−0.309855	−	0.950784i	$-0.600280\pi$
$397$	−25.6669	−	14.8188i	−1.28819	−	0.743734i	−0.978330	+	0.207050i	$0.933614\pi$
$398$	−29.2209	+	1.84041i	−1.46471	+	0.0922515i
$399$	−2.59127	+	4.48821i	−0.129726	+	0.224691i
$400$	4.92538	+	5.02691i	0.246269	+	0.251345i
$401$	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
$406$	1.25977	−	0.837112i	0.0625213	−	0.0415452i
$407$	−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	$0.170938\pi$
$410$	34.6631	+	17.2040i	1.71189	+	0.849645i
$411$		−	6.06153i		−	0.298993i
$412$	−5.12239	+	12.1903i	−0.252362	+	0.600574i
$413$	5.67720	−	3.27773i	0.279357	−	0.161287i
$414$	0.441621	+	0.664596i	0.0217045	+	0.0326631i
$415$	−2.41920			−0.118754
$416$	3.93897	−	20.0121i	0.193124	−	0.981174i
$417$	3.66365			0.179410
$418$	−11.0161	−	16.5782i	−0.538817	−	0.810866i
$419$	−17.8473	+	10.3042i	−0.871900	+	0.503392i	−0.867979	−	0.496601i	$-0.834581\pi$
$419$	−17.8473	+	10.3042i	−0.871900	+	0.503392i	−0.00392074	+	0.999992i	$0.501248\pi$
$420$	−2.06369	+	4.91120i	−0.100698	+	0.239642i
$421$		−	2.14198i		−	0.104394i	−0.998637	−	0.0521968i	$-0.983378\pi$
$421$		−	2.14198i		−	0.104394i	0.998637	−	0.0521968i	$-0.0166223\pi$
$422$	−26.7803	−	13.2916i	−1.30365	−	0.647025i
$423$	−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
$426$	−0.926694	+	0.615784i	−0.0448985	+	0.0298349i
$427$	−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	$0.922315\pi$
$432$	15.0737	−	14.7692i	0.725233	−	0.710586i
$433$	−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
$436$	−19.9489	−	8.38255i	−0.955378	−	0.401451i
$437$			29.7804i			1.42459i
$438$	32.1240	+	15.9438i	1.53494	+	0.761823i
$439$	−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	$0.853743\pi$
$440$	−13.3722	−	15.4854i	−0.637493	−	0.738239i
$441$	−0.636260			−0.0302981
$442$	−13.1567	+	1.02375i	−0.625803	+	0.0486946i
$443$			14.6679i			0.696891i	0.937329	+	0.348446i	$0.113290\pi$
$443$			14.6679i			0.696891i	−0.937329	+	0.348446i	$0.886710\pi$
$444$	−21.0076	−	27.6687i	−0.996978	−	1.31310i
$445$	5.30428	−	3.06242i	0.251447	−	0.145173i
$446$	5.07621	−	10.2277i	0.240365	−	0.484295i
$447$	−5.66237			−0.267821
$448$	−0.700637	+	4.75809i	−0.0331020	+	0.224799i
$449$	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
$452$	11.5066	+	15.1551i	0.541223	+	0.712835i
$453$	−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	$0.681120\pi$
$458$	0.700493	−	0.465475i	0.0327319	−	0.0217502i
$459$	−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	0.244916	−	0.969544i	$-0.421240\pi$
$461$	−10.1402	−	5.85445i	−0.472277	−	0.272669i	−0.717192	+	0.696875i	$0.754573\pi$
$462$	1.79216	−	3.61090i	0.0833789	−	0.167994i
$463$	20.0915			0.933731			0.466866	−	0.884328i	$-0.345383\pi$
$463$	20.0915			0.933731			0.466866	+	0.884328i	$0.345383\pi$
$464$	−6.85461	−	1.91184i	−0.318217	−	0.0887549i
$465$	−11.2853	−	19.5466i	−0.523341	−	0.906454i
$466$	0.0740309	+	0.111409i	0.00342941	+	0.00516092i
$467$			38.0472i			1.76061i	0.474405	+	0.880307i	$0.342663\pi$
$467$			38.0472i			1.76061i	−0.474405	+	0.880307i	$0.657337\pi$
$468$	0.426009	+	0.544224i	0.0196923	+	0.0251568i
$469$			2.35379i			0.108688i
$470$	−6.55192	+	4.35373i	−0.302218	+	0.200822i
$471$	−1.05789	−	1.83231i	−0.0487449	−	0.0844286i
$472$	−29.1288	−	10.1371i	−1.34076	−	0.466597i
$473$	−27.1241			−1.24717
$474$	16.9241	+	8.39978i	0.777351	+	0.385815i
$475$	−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
$478$	12.0296	+	18.1033i	0.550219	+	0.828025i
$479$	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
$484$	−3.94113	−	5.19079i	−0.179142	−	0.235945i
$485$	−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	$-0.0119924\pi$
$488$	5.70224	+	1.98443i	0.258128	+	0.0898309i
$489$	18.5634			0.839468
$490$	−21.8639	−	10.8515i	−0.987712	−	0.490221i
$491$	26.6538	−	15.3886i	1.20287	−	0.694478i	0.241679	−	0.970356i	$-0.422302\pi$
$491$	26.6538	−	15.3886i	1.20287	−	0.694478i	0.961193	+	0.275878i	$0.0889687\pi$
$492$	28.5702	−	21.6920i	1.28804	−	0.977952i
$493$			4.60429i			0.207367i
$494$	2.00102	+	25.7162i	0.0900300	+	1.15703i
$495$	0.693299			0.0311615
$496$	−14.2609	−	14.5548i	−0.640332	−	0.653531i
$497$	0.138771	+	0.240358i	0.00622472	+	0.0107815i
$498$	−0.996980	+	2.00875i	−0.0446757	+	0.0900140i
$499$		−	4.61772i		−	0.206718i	−0.994644	−	0.103359i	$-0.967041\pi$
$499$		−	4.61772i		−	0.206718i	0.994644	−	0.103359i	$-0.0329590\pi$
$500$	15.5345	+	6.52764i	0.694725	+	0.291925i
$501$	−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	$-0.0635683\pi$
$504$	−0.106512	−	0.123345i	−0.00474444	−	0.00549423i
$505$	−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	0.0244475	−	0.999701i	$-0.492217\pi$
$509$	20.3599	−	11.7548i	0.902438	−	0.521023i	0.877990	+	0.478678i	$0.158884\pi$
$510$	−8.97489	−	13.5063i	−0.397415	−	0.598070i
$511$	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
$514$	−13.0146	+	26.2222i	−0.574049	+	1.15661i
$515$		−	17.1889i		−	0.757435i
$516$	12.8718	−	30.6324i	0.566648	−	1.34851i
$517$	5.15527	−	2.97640i	0.226729	−	0.130902i
$518$	−7.21759	+	4.79606i	−0.317123	+	0.210727i
$519$	−11.1527			−0.489549
$520$	5.35720	+	25.9669i	0.234929	+	1.13872i
$521$	−11.7037			−0.512747			−0.256374	−	0.966578i	$-0.582528\pi$
$521$	−11.7037			−0.512747			−0.256374	+	0.966578i	$0.582528\pi$
$522$	0.200839	−	0.133457i	0.00879050	−	0.00584126i
$523$	−10.9235	+	6.30668i	−0.477651	+	0.275772i	−0.719437	−	0.694558i	$-0.755600\pi$
$523$	−10.9235	+	6.30668i	−0.477651	+	0.275772i	0.241786	+	0.970330i	$0.422267\pi$
$524$	−1.46736	−	0.616586i	−0.0641018	−	0.0269357i
$525$		−	1.80253i		−	0.0786688i
$526$	−0.648378	+	1.30637i	−0.0282706	+	0.0569605i
$527$	−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
$530$	12.2451	+	18.4276i	0.531892	+	0.800444i
$531$	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
$536$	8.38162	−	7.23780i	0.362031	−	0.312625i
$537$	−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
$540$	−10.6273	+	25.2909i	−0.457326	+	1.08835i
$541$		−	40.4799i		−	1.74037i	−0.492728	−	0.870183i	$-0.664000\pi$
$541$		−	40.4799i		−	1.74037i	0.492728	−	0.870183i	$-0.336000\pi$
$542$	8.61712	−	17.3620i	0.370137	−	0.745763i
$543$	3.96912	+	6.87472i	0.170331	+	0.295023i
$544$	−10.8831	−	9.79253i	−0.466610	−	0.419851i
$545$	28.1288			1.20491
$546$	−4.30780	+	2.95506i	−0.184357	+	0.126465i
$547$		−	27.1567i		−	1.16114i	−0.814212	−	0.580568i	$-0.802831\pi$
$547$		−	27.1567i		−	1.16114i	0.814212	−	0.580568i	$-0.197169\pi$
$548$	4.30177	+	5.66578i	0.183763	+	0.242030i
$549$	−0.177180	+	0.102295i	−0.00756185	+	0.00436584i
$550$	6.20119	+	3.07778i	0.264420	+	0.131237i
$551$	8.99957			0.383394
$552$	26.7997	+	9.32653i	1.14067	+	0.396964i
$553$	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
$556$	−3.42445	+	2.60003i	−0.145229	+	0.110266i
$557$	−26.2789	+	15.1721i	−1.11347	+	0.642863i	−0.939726	−	0.341927i	$-0.888920\pi$
$557$	−26.2789	+	15.1721i	−1.11347	+	0.642863i	−0.173746	+	0.984791i	$0.555587\pi$
$558$	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
$562$	9.65294	+	14.5267i	0.407185	+	0.612772i
$563$	−7.83182	−	4.52170i	−0.330072	−	0.190567i	0.325801	−	0.945438i	$-0.394366\pi$
$563$	−7.83182	−	4.52170i	−0.330072	−	0.190567i	−0.655873	+	0.754871i	$0.727699\pi$
$564$	0.914927	+	7.23451i	0.0385254	+	0.304628i
$565$	−21.4218	−	12.3679i	−0.901222	−	0.520321i
$566$	−24.9263	−	12.3714i	−1.04773	−	0.520008i
$567$	−5.23220			−0.219732
$568$	0.429179	−	1.23324i	0.0180079	−	0.0517456i
$569$	−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	$-0.441895\pi$
$570$	−26.3995	+	17.5424i	−1.10575	+	0.734768i
$571$			24.9740i			1.04513i	0.852599	+	0.522566i	$0.175025\pi$
$571$			24.9740i			1.04513i	−0.852599	+	0.522566i	$0.824975\pi$
$572$	−2.81075	−	19.8657i	−0.117523	−	0.830627i
$573$		−	14.8001i		−	0.618285i
$574$	−4.95231	−	7.45273i	−0.206706	−	0.311071i
$575$	−5.17893	−	8.97016i	−0.215976	−	0.374082i
$576$	−0.111700	+	0.758562i	−0.00465415	+	0.0316068i
$577$	14.7654			0.614692			0.307346	−	0.951598i	$-0.400559\pi$
$577$	14.7654			0.614692			0.307346	+	0.951598i	$0.400559\pi$
$578$	6.47711	−	13.0503i	0.269412	−	0.542820i
$579$	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
$582$	−23.7322	+	15.7700i	−0.983731	+	0.653686i
$583$	−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	0.398460	−	0.917186i	$-0.369545\pi$
$587$	33.7254	−	19.4714i	1.39200	−	0.803669i	0.993536	+	0.113517i	$0.0362115\pi$
$588$	−18.0208	+	13.6824i	−0.743164	+	0.564251i
$589$	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
$592$	39.2721	+	10.9535i	1.61407	+	0.450186i
$593$	19.6722			0.807842			0.403921	−	0.914794i	$-0.367647\pi$
$593$	19.6722			0.807842			0.403921	+	0.914794i	$0.367647\pi$
$594$	9.22901	−	18.5949i	0.378671	−	0.762957i
$595$	−3.50315	+	2.02255i	−0.143615	+	0.0829163i
$596$	5.29268	−	4.01849i	0.216796	−	0.164604i
$597$		−	35.2816i		−	1.44398i
$598$	−12.9472	+	27.0826i	−0.529449	+	1.10749i
$599$	−0.289136			−0.0118138			−0.00590689	−	0.999983i	$-0.501880\pi$
$599$	−0.289136			−0.0118138			−0.00590689	+	0.999983i	$0.501880\pi$
$600$	−6.41863	+	5.54269i	−0.262040	+	0.226280i
$601$	−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	$-0.349305\pi$
$602$	−7.42417	−	3.68476i	−0.302587	−	0.150180i
$603$			0.375254i			0.0152815i
$604$	5.16324	−	12.2875i	0.210089	−	0.499972i
$605$	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	$0.221620\pi$
$608$	−19.1405	+	21.2722i	−0.776250	+	0.862701i
$609$	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	−0.707453	−	0.706760i	$-0.750156\pi$
$613$	−11.1194	+	6.41977i	−0.449107	+	0.259292i	0.258346	+	0.966053i	$0.416823\pi$
$614$	5.99527	−	3.98383i	0.241949	−	0.160774i
$615$	−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	$0.198900\pi$
$618$	−14.2726	−	7.08375i	−0.574127	−	0.284950i
$619$			25.2782i			1.01602i	0.861353	+	0.508008i	$0.169618\pi$
$619$			25.2782i			1.01602i	−0.861353	+	0.508008i	$0.830382\pi$
$620$	24.4204	+	10.2615i	0.980747	+	0.412111i
$621$	−26.8979	+	15.5295i	−1.07938	+	0.623178i
$622$	−19.6909	−	29.6328i	−0.789531	−	1.18817i
$623$	−1.41626			−0.0567411
$624$	23.7690	+	6.25299i	0.951521	+	0.250320i
$625$	−30.7015			−1.22806
$626$	−9.75636	−	14.6823i	−0.389943	−	0.586824i
$627$	20.7720	−	11.9927i	0.829554	−	0.478943i
$628$	2.28918	+	0.961919i	0.0913483	+	0.0383847i
$629$		−	26.3794i		−	1.05181i
$630$	0.189764	+	0.0941835i	0.00756037	+	0.00375236i
$631$	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
$634$	−12.9847	+	8.62829i	−0.515689	+	0.342673i
$635$	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
$640$	−16.7757	+	24.1616i	−0.663119	+	0.955070i
$641$	−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	0.952103	−	0.305778i	$-0.0989167\pi$
$643$	29.4994	+	17.0315i	1.16334	+	0.671656i	0.211239	+	0.977434i	$0.432250\pi$
$644$	2.74207	−	6.52561i	0.108053	−	0.257145i
$645$			43.1931i			1.70073i
$646$	16.5845	+	8.23120i	0.652507	+	0.323852i
$647$	−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	$-0.453095\pi$
$648$	16.0888	+	18.6314i	0.632027	+	0.731910i
$649$	−30.3395			−1.19093
$650$	−5.07488	−	7.39801i	−0.199053	−	0.290174i
$651$			5.21901i			0.204549i
$652$	−17.3514	+	13.1742i	−0.679535	+	0.515940i
$653$	−17.1513	+	9.90232i	−0.671183	+	0.387508i	−0.796525	−	0.604606i	$-0.793331\pi$
$653$	−17.1513	+	9.90232i	−0.671183	+	0.387508i	0.125342	+	0.992114i	$0.459997\pi$
$654$	11.5922	−	23.3564i	0.453292	−	0.913306i
$655$	2.06904			0.0808442
$656$	−11.3103	+	40.5516i	−0.441595	+	1.58327i
$657$	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	−0.0506442	−	0.998717i	$-0.516127\pi$
$659$	−24.1533	−	13.9449i	−0.940880	−	0.543218i	−0.890236	+	0.455499i	$0.849461\pi$
$660$	19.6363	−	14.9089i	0.764341	−	0.580330i
$661$	17.0661	−	9.85313i	0.663795	−	0.383242i	−0.129926	−	0.991524i	$-0.541474\pi$
$661$	17.0661	−	9.85313i	0.663795	−	0.383242i	0.793722	+	0.608281i	$0.208141\pi$
$662$	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
$666$	−1.15067	+	0.764615i	−0.0445875	+	0.0296282i
$667$	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
$670$	−6.40001	+	12.8949i	−0.247254	+	0.498175i
$671$	5.93924			0.229282
$672$	−5.66920	−	1.20302i	−0.218694	−	0.0464074i
$673$	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	$0.587857\pi$
$674$	8.65589	+	13.0262i	0.333412	+	0.501752i
$675$		−	9.28239i		−	0.357279i
$676$	−9.36050	+	24.2566i	−0.360019	+	0.932945i
$677$		−	43.5560i		−	1.67399i	−0.547209	−	0.836996i	$-0.684310\pi$
$677$		−	43.5560i		−	1.67399i	0.547209	−	0.836996i	$-0.315690\pi$
$678$	−19.0977	+	12.6903i	−0.733441	+	0.487369i
$679$	3.55386	+	6.15546i	0.136384	+	0.236225i
$680$	17.9741	+	6.25516i	0.689277	+	0.239875i
$681$	39.0644			1.49695
$682$	−17.9548	−	8.91133i	−0.687526	−	0.341233i
$683$	6.89615	+	3.98149i	0.263874	+	0.152348i	0.626100	−	0.779742i	$-0.284650\pi$
$683$	6.89615	+	3.98149i	0.263874	+	0.152348i	−0.362227	+	0.932090i	$0.617983\pi$
$684$	−0.121661	−	0.961999i	−0.00465183	−	0.0367830i
$685$	−8.00862	−	4.62378i	−0.305994	−	0.176666i
$686$	6.41745	+	9.65762i	0.245019	+	0.368730i
$687$	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	−0.949267	−	0.314471i	$-0.898173\pi$
$691$	−30.2709	+	17.4769i	−1.15156	+	0.664854i	−0.202294	+	0.979325i	$0.564840\pi$
$692$	10.4245	−	7.91488i	0.396282	−	0.300879i
$693$	−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
$696$	2.81846	−	8.09881i	0.106833	−	0.306985i
$697$	27.2388			1.03174
$698$	−17.0993	−	8.48675i	−0.647220	−	0.321228i
$699$	−0.139592	+	0.0805937i	−0.00527987	+	0.00304833i
$700$	1.27922	+	1.68484i	0.0483502	+	0.0636811i
$701$			10.8831i			0.411050i	0.978652	+	0.205525i	$0.0658901\pi$
$701$			10.8831i			0.411050i	−0.978652	+	0.205525i	$0.934110\pi$
$702$	−22.1837	+	15.2175i	−0.837268	+	0.574348i
$703$	−51.5612			−1.94467
$704$	13.8187	−	17.4495i	0.520814	−	0.657652i
$705$	−4.73968	−	8.20937i	−0.178507	−	0.309183i
$706$	−2.20694	+	4.44660i	−0.0830592	+	0.167350i
$707$			7.78698i			0.292859i
$708$	14.3976	−	34.2636i	0.541096	−	1.28771i
$709$	31.1767	+	17.9999i	1.17087	+	0.676000i	0.953884	−	0.300176i	$-0.0970454\pi$
$709$	31.1767	+	17.9999i	1.17087	+	0.676000i	0.216982	+	0.976176i	$0.430379\pi$
$710$	0.106699	+	1.69409i	0.00400432	+	0.0635781i
$711$	0.375688	−	0.650711i	0.0140894	−	0.0244036i
$712$	4.35492	+	5.04316i	0.163208	+	0.189000i
$713$	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
$718$	−19.5782	−	29.4632i	−0.730651	−	1.09956i
$719$	−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
$722$	4.14299	−	8.34742i	0.154186	−	0.310659i
$723$		−	17.1132i		−	0.636447i
$724$	−8.58887	−	3.60906i	−0.319203	−	0.134130i
$725$	−2.71076	+	1.56506i	−0.100675	+	0.0581249i
$726$	6.54117	−	4.34658i	0.242766	−	0.161317i
$727$	34.3229			1.27297			0.636484	−	0.771290i	$-0.280388\pi$
$727$	34.3229			1.27297			0.636484	+	0.771290i	$0.280388\pi$
$728$	1.92939	−	5.81930i	0.0715079	−	0.215678i
$729$	−27.8066			−1.02987
$730$	45.5697	−	30.2809i	1.68661	−	1.12075i
$731$	21.8500	−	12.6151i	0.808153	−	0.466587i
$732$	−2.81847	+	6.70742i	−0.104174	+	0.247913i
$733$			6.24499i			0.230664i	0.993327	+	0.115332i	$0.0367932\pi$
$733$			6.24499i			0.230664i	−0.993327	+	0.115332i	$0.963207\pi$
$734$	−12.9404	+	26.0727i	−0.477639	+	0.962360i
$735$	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
$738$	−0.789526	−	1.18816i	−0.0290628	−	0.0437367i
$739$	−5.26210	+	3.03807i	−0.193569	+	0.111757i	−0.593652	−	0.804722i	$-0.702315\pi$
$739$	−5.26210	+	3.03807i	−0.193569	+	0.111757i	0.400083	+	0.916479i	$0.368981\pi$
$740$	−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	$0.881492\pi$
$744$	18.5844	−	16.0482i	0.681337	−	0.588356i
$745$	−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
$748$	−13.2770	−	5.57902i	−0.485456	−	0.203989i
$749$		−	6.16160i		−	0.225140i
$750$	−9.02706	+	18.1880i	−0.329622	+	0.664132i
$751$	−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	$0.963878\pi$
$752$	−5.98941	−	6.11286i	−0.218411	−	0.222913i
$753$	29.1457			1.06213
$754$	8.18431	+	3.91261i	0.298055	+	0.142489i
$755$			17.3260i			0.630557i
$756$	5.05216	−	3.83588i	0.183745	−	0.139510i
$757$	18.5854	−	10.7303i	0.675498	−	0.389999i	−0.122659	−	0.992449i	$-0.539142\pi$
$757$	18.5854	−	10.7303i	0.675498	−	0.389999i	0.798157	+	0.602450i	$0.205809\pi$
$758$	9.12266	+	4.52776i	0.331350	+	0.164456i
$759$	27.9136			1.01320
$760$	12.2264	−	35.1323i	0.443497	−	1.27438i
$761$	−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
$764$	10.5034	+	13.8338i	0.380000	+	0.500491i
$765$	−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	$0.902165\pi$
$770$	−3.40373	−	5.12227i	−0.122662	−	0.184594i
$771$	−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	0.262623	−	0.964898i	$-0.415412\pi$
$773$	−12.2803	−	7.09004i	−0.441692	−	0.255011i	−0.704315	+	0.709888i	$0.748746\pi$
$774$	−1.18360	−	0.587446i	−0.0425437	−	0.0211153i
$775$	−8.96287			−0.321956
$776$	10.9911	−	31.5827i	0.394556	−	1.13375i
$777$	−5.22123	−	9.04344i	−0.187311	−	0.324432i
$778$	24.2953	−	16.1442i	0.871030	−	0.578796i
$779$		−	53.2410i		−	1.90756i
$780$	−31.6346	+	4.47591i	−1.13270	+	0.160263i
$781$		−	1.28450i		−	0.0459630i
$782$	11.9251	+	17.9461i	0.426442	+	0.641752i
$783$	4.69299	+	8.12849i	0.167714	+	0.290489i
$784$	7.13406	−	25.5781i	0.254788	−	0.913503i
$785$	−3.22786			−0.115207
$786$	0.852676	−	1.71800i	0.0304140	−	0.0612789i
$787$	−7.12142	−	4.11155i	−0.253851	−	0.146561i	0.367675	−	0.929954i	$-0.380154\pi$
$787$	−7.12142	−	4.11155i	−0.253851	−	0.146561i	−0.621526	+	0.783393i	$0.713487\pi$
$788$	−6.41692	−	50.7398i	−0.228593	−	1.80753i
$789$	−1.52198	−	0.878717i	−0.0541840	−	0.0312832i
$790$	24.0078	−	15.9531i	0.854160	−	0.567586i
$791$	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
$796$	25.0388	+	32.9781i	0.887476	+	1.16888i
$797$	1.61224	+	0.930825i	0.0571083	+	0.0329715i	0.528282	−	0.849069i	$-0.322836\pi$
$797$	1.61224	+	0.930825i	0.0571083	+	0.0329715i	−0.471174	+	0.882040i	$0.656170\pi$
$798$	7.31472	−	0.460701i	0.258938	−	0.0163086i
$799$	−2.76858	+	4.79532i	−0.0979453	+	0.169646i
$800$	2.06601	−	9.73602i	0.0730444	−	0.344220i
$801$	−0.225787			−0.00797781
$802$	6.69568	−	13.4907i	0.236433	−	0.476372i
$803$	−35.8558	+	20.7013i	−1.26532	+	0.730534i
$804$	8.06959	+	10.6283i	0.284592	+	0.374831i
$805$			9.20142i			0.324308i
$806$	14.6937	+	21.4201i	0.517564	+	0.754490i
$807$	10.5192			0.370294
$808$	27.7287	−	23.9446i	0.975492	−	0.842368i
$809$	−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	$-0.398428\pi$
$810$	−28.6639	−	14.2265i	−1.00715	−	0.499868i
$811$			16.1872i			0.568409i	0.958764	+	0.284205i	$0.0917295\pi$
$811$			16.1872i			0.568409i	−0.958764	+	0.284205i	$0.908270\pi$
$812$	−1.97203	−	0.828649i	−0.0692046	−	0.0290799i
$813$	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
$816$	12.6012	−	12.3467i	0.441131	−	0.432222i
$817$	−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	−0.855725	−	0.517431i	$-0.826889\pi$
$821$	−23.9391	+	13.8212i	−0.835479	+	0.482364i	0.0202456	+	0.999795i	$0.493555\pi$
$822$	−7.13973	+	4.74432i	−0.249027	+	0.165477i
$823$	−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
$826$	−8.30426	−	4.12157i	−0.288942	−	0.143408i
$827$		−	1.10220i		−	0.0383272i	−0.999816	−	0.0191636i	$-0.993900\pi$
$827$		−	1.10220i		−	0.0383272i	0.999816	−	0.0191636i	$-0.00610034\pi$
$828$	0.437157	−	1.04035i	0.0151923	−	0.0361547i
$829$	17.1870	−	9.92292i	0.596929	−	0.344637i	−0.170903	−	0.985288i	$-0.554669\pi$
$829$	17.1870	−	9.92292i	0.596929	−	0.344637i	0.767833	+	0.640650i	$0.221335\pi$
$830$	1.89349	+	2.84952i	0.0657241	+	0.0989082i
$831$	−48.1645			−1.67081
$832$	−26.6548	+	11.0237i	−0.924088	+	0.382179i
$833$	−17.1810			−0.595286
$834$	−2.86752	−	4.31532i	−0.0992939	−	0.149427i
$835$	−30.0877	+	17.3712i	−1.04123	+	0.601154i
$836$	−10.9048	+	25.9513i	−0.377150	+	0.897544i
$837$			26.8761i			0.928972i
$838$	26.1060	+	12.9569i	0.901818	+	0.447590i
$839$	−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
$842$	−2.52298	+	1.67651i	−0.0869478	+	0.0577764i
$843$	−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
$848$	−17.1927	+	16.8455i	−0.590401	+	0.578477i
$849$	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
$852$	1.45063	+	0.609559i	0.0496979	+	0.0208832i
$853$		−	12.5392i		−	0.429333i	−0.976687	−	0.214666i	$-0.931134\pi$
$853$		−	12.5392i		−	0.429333i	0.976687	−	0.214666i	$-0.0688664\pi$
$854$	1.62564	+	0.806836i	0.0556281	+	0.0276093i
$855$	0.630253	+	1.09163i	0.0215542	+	0.0373330i
$856$	−21.9409	+	18.9467i	−0.749924	+	0.647583i
$857$	34.8182			1.18937			0.594684	−	0.803960i	$-0.297277\pi$
$857$	34.8182			1.18937			0.594684	+	0.803960i	$0.297277\pi$
$858$	24.1042	−	1.87558i	0.822904	−	0.0640314i
$859$			33.1090i			1.12966i	0.825206	+	0.564832i	$0.191059\pi$
$859$			33.1090i			1.12966i	−0.825206	+	0.564832i	$0.808941\pi$
$860$	−30.6534	−	40.3730i	−1.04527	−	1.37671i
$861$	9.33807	−	5.39134i	0.318240	−	0.183736i
$862$	−7.20293	+	14.5127i	−0.245333	+	0.494304i
$863$	−48.3902			−1.64722			−0.823611	−	0.567155i	$-0.808044\pi$
$863$	−48.3902			−1.64722			−0.823611	+	0.567155i	$0.808044\pi$
$864$	−29.1944	−	6.19512i	−0.993214	−	0.210762i
$865$	−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
$868$	−3.70384	−	4.87826i	−0.125717	−	0.165579i
$869$	−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
$874$	35.0776	−	23.3089i	1.18652	−	0.788436i
$875$	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	0.969661	−	0.244454i	$-0.0786087\pi$
$877$	36.8042	+	21.2489i	1.24279	+	0.717524i	0.273127	+	0.961978i	$0.411942\pi$
$878$	−1.68815	+	3.40134i	−0.0569723	+	0.114790i
$879$	20.0004			0.674597
$880$	−7.77360	+	27.8711i	−0.262048	+	0.939534i
$881$	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	$0.830608\pi$
$882$	0.497997	+	0.749436i	0.0167684	+	0.0252348i
$883$		−	47.2885i		−	1.59139i	−0.605700	−	0.795693i	$-0.707107\pi$
$883$		−	47.2885i		−	1.59139i	0.605700	−	0.795693i	$-0.292893\pi$
$884$	11.5035	+	14.6957i	0.386906	+	0.494271i
$885$			48.3133i			1.62403i
$886$	17.2769	−	11.4804i	0.580430	−	0.385693i
$887$	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	$0.777310\pi$
$888$	−16.1478	+	46.4005i	−0.541884	+	1.55710i
$889$	−11.0752			−0.371450
$890$	−7.75878	−	3.85084i	−0.260075	−	0.129080i
$891$	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
$894$	4.43190	+	6.66956i	0.148225	+	0.223064i
$895$	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
$900$	0.203941	+	0.268607i	0.00679804	+	0.00895357i
$901$	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
$904$	8.84468	−	25.4151i	0.294170	−	0.845293i
$905$	12.1107			0.402573
$906$	14.3864	+	7.14023i	0.477955	+	0.237218i
$907$	−20.2878	+	11.7132i	−0.673646	+	0.388930i	−0.797457	−	0.603376i	$-0.793822\pi$
$907$	−20.2878	+	11.7132i	−0.673646	+	0.388930i	0.123811	+	0.992306i	$0.460488\pi$
$908$	−36.5139	+	27.7234i	−1.21176	+	0.920032i
$909$			1.24144i			0.0411761i
$910$	0.618267	+	7.94570i	0.0204953	+	0.263397i
$911$	53.8994			1.78577			0.892883	−	0.450289i	$-0.148679\pi$
$911$	53.8994			1.78577			0.892883	+	0.450289i	$0.148679\pi$
$912$	−24.1330	−	24.6304i	−0.799122	−	0.815594i
$913$	−1.29447	−	2.24210i	−0.0428409	−	0.0742025i
$914$	12.3700	−	24.9235i	0.409165	−	0.824397i
$915$		−	9.45778i		−	0.312665i
$916$	−1.09654	−	0.460769i	−0.0362308	−	0.0152242i
$917$	−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	$0.910241\pi$
$920$	32.7654	−	28.2940i	1.08024	−	0.932825i
$921$	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
$926$	−15.7255	−	23.6653i	−0.516772	−	0.777690i
$927$	−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	$0.193062\pi$
$930$	−14.1906	+	28.5917i	−0.465328	+	0.937557i
$931$			33.5820i			1.10061i
$932$	0.0732825	−	0.174398i	0.00240045	−	0.00571260i
$933$	37.1290	−	21.4364i	1.21555	−	0.701798i
$934$	44.8148	−	29.7793i	1.46639	−	0.974408i
$935$	18.7212			0.612249
$936$	0.307594	−	0.927746i	0.0100540	−	0.0303243i
$937$	44.5775			1.45628			0.728141	−	0.685427i	$-0.240385\pi$
$937$	44.5775			1.45628			0.728141	+	0.685427i	$0.240385\pi$
$938$	2.77247	−	1.84230i	0.0905243	−	0.0601531i
$939$	18.3966	−	10.6213i	0.600349	−	0.346612i
$940$	10.2563	+	4.30971i	0.334523	+	0.140567i
$941$			58.1679i			1.89622i	0.317943	+	0.948110i	$0.397008\pi$
$941$			58.1679i			1.89622i	−0.317943	+	0.948110i	$0.602992\pi$
$942$	−1.33024	+	2.68020i	−0.0433415	+	0.0873256i
$943$	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
$946$	21.2299	+	31.9488i	0.690243	+	1.03875i
$947$	8.18618	−	4.72629i	0.266015	−	0.153584i	−0.361060	−	0.932542i	$-0.617585\pi$
$947$	8.18618	−	4.72629i	0.266015	−	0.153584i	0.627075	+	0.778959i	$0.284252\pi$
$948$	−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
$952$	−2.87617	−	3.33070i	−0.0932170	−	0.107949i
$953$	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
$956$	11.9079	−	28.3386i	0.385131	−	0.916537i
$957$		−	8.43543i		−	0.272679i
$958$	6.24457	−	12.5818i	0.201753	−	0.406498i
$959$	1.06916	+	1.85184i	0.0345250	+	0.0597991i
$960$	−27.7870	−	22.0053i	−0.896820	−	0.710217i
$961$	−5.04906			−0.162873
$962$	−46.8903	−	22.4165i	−1.51181	−	0.722737i
$963$		−	0.982317i		−	0.0316547i
$964$	12.1450	+	15.9959i	0.391163	+	0.515194i
$965$	3.55159	−	2.05051i	0.114330	−	0.0660083i
$966$	7.64026	+	3.79201i	0.245821	+	0.122006i
$967$	13.9692			0.449218			0.224609	−	0.974449i	$-0.427889\pi$
$967$	13.9692			0.449218			0.224609	+	0.974449i	$0.427889\pi$
$968$	−3.02940	+	8.70496i	−0.0973687	+	0.279788i
$969$	−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	0.663555	−	0.748128i	$-0.269047\pi$
$971$	10.8263	+	6.25059i	0.347434	+	0.200591i	−0.316121	+	0.948719i	$0.602380\pi$
$972$	1.58595	−	1.20414i	0.0508695	−	0.0386229i
$973$	−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	$0.905593\pi$
$978$	−14.5295	−	21.8654i	−0.464602	−	0.699179i
$979$	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
$982$	−38.9877	−	19.3503i	−1.24415	−	0.617494i
$983$	−42.4961			−1.35541			−0.677707	−	0.735332i	$-0.737026\pi$
$983$	−42.4961			−1.35541			−0.677707	+	0.735332i	$0.737026\pi$
$984$	−47.9122	−	16.6739i	−1.52738	−	0.531544i
$985$	33.2422	+	57.5771i	1.05918	+	1.83456i
$986$	5.42328	−	3.60375i	0.172713	−	0.114767i
$987$			2.19192i			0.0697697i
$988$	28.7243	−	22.4849i	0.913842	−	0.715339i
$989$		−	57.3916i		−	1.82495i
$990$	−0.542641	−	0.816620i	−0.0172463	−	0.0259539i
$991$	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	$0.785502\pi$
$992$	−5.98188	+	28.1895i	−0.189925	+	0.895017i
$993$	−28.3146			−0.898536
$994$	0.174497	−	0.351581i	0.00553470	−	0.0111515i
$995$	−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	0.397105	−	0.917773i	$-0.370015\pi$
$997$	−6.28844	−	3.63063i	−0.199157	−	0.114983i	−0.596262	+	0.802790i	$0.703348\pi$
$998$	−5.43910	+	3.61426i	−0.172172	+	0.114408i
$999$	−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.29.4	✓	24
3.2	odd	2		936.2.be.a.757.9		24
4.3	odd	2		416.2.z.a.81.3		24
8.3	odd	2		416.2.z.a.81.10		24
8.5	even	2	inner	104.2.r.a.29.5	yes	24
13.9	even	3	inner	104.2.r.a.61.5	yes	24
24.5	odd	2		936.2.be.a.757.8		24
39.35	odd	6		936.2.be.a.685.8		24
52.35	odd	6		416.2.z.a.113.10		24
104.35	odd	6		416.2.z.a.113.3		24
104.61	even	6	inner	104.2.r.a.61.4	yes	24
312.269	odd	6		936.2.be.a.685.9		24

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

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

\(f(q)\)	\(=\)	\(q+(-0.782694 - 1.17788i) q^{2} +(1.47584 - 0.852079i) q^{3} +(-0.774781 + 1.84383i) q^{4} -2.59989i q^{5} +(-2.15878 - 1.07144i) q^{6} +(-0.300588 + 0.520633i) q^{7} +(2.77822 - 0.530559i) q^{8} +(-0.0479214 + 0.0830022i) q^{9} +(-3.06235 + 2.03492i) 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} +(-2.79943 - 2.85713i) q^{16} +(-1.29402 + 2.24132i) q^{17} +(0.135274 - 0.00851993i) q^{18} +(4.38088 + 2.52930i) q^{19} +(4.79376 + 2.01435i) q^{20} +1.02450i q^{21} +(-3.52456 - 1.74931i) q^{22} +(2.94353 + 5.09835i) q^{23} +(3.64814 - 3.15029i) q^{24} -1.75942 q^{25} +(2.88440 + 4.20479i) q^{26} +5.27581i q^{27} +(-0.727070 - 0.957610i) q^{28} +(1.54071 - 0.889530i) q^{29} +(-2.78564 + 5.61258i) q^{30} +5.09421 q^{31} +(-1.17425 + 5.53364i) q^{32} +(2.37076 - 4.10627i) q^{33} +(3.65282 - 0.230064i) q^{34} +(1.35359 + 0.781495i) q^{35} +(-0.115914 - 0.152668i) 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} +(1.20673 - 0.801868i) q^{42} +(-8.44267 - 4.87438i) q^{43} +(0.698182 + 5.52066i) q^{44} +(0.215797 + 0.124590i) q^{45} +(3.70134 - 7.45756i) q^{46} +2.13951 q^{47} +(-6.56602 - 1.83135i) q^{48} +(3.31929 + 5.74919i) q^{49} +(1.37709 + 2.07238i) q^{50} +4.41045i q^{51} +(2.69512 - 6.68852i) q^{52} -6.01748i q^{53} +(6.21424 - 4.12934i) q^{54} +(-3.61686 - 6.26458i) q^{55} +(-0.558872 + 1.60591i) q^{56} +8.62067 q^{57} +(-2.25366 - 1.11854i) q^{58} +(-9.44349 - 5.45220i) q^{59} +(8.79122 - 1.11180i) q^{60} +(1.84865 + 1.06732i) q^{61} +(-3.98720 - 6.00034i) 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} +(-3.13002 - 4.12249i) q^{68} +(8.68840 + 5.01625i) q^{69} +(-0.138942 - 2.20603i) q^{70} +(0.230832 - 0.399814i) q^{71} +(-0.0890985 + 0.256024i) q^{72} -14.8806 q^{73} +(12.9119 + 6.40843i) q^{74} +(-2.59664 + 1.49917i) q^{75} +(-8.05784 + 6.11795i) q^{76} +1.67266i q^{77} +(7.83974 + 3.74788i) q^{78} -7.83968 q^{79} +(-7.42823 + 7.27820i) q^{80} +(4.35164 + 7.53727i) q^{81} +(-6.61721 + 13.3325i) q^{82} -0.930501i q^{83} +(-1.88900 - 0.793762i) q^{84} +(5.82717 + 3.36432i) q^{85} +(0.866614 + 13.7596i) q^{86} +(1.51590 - 2.62562i) q^{87} +(5.95619 - 5.14336i) 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} +(-1.67458 - 2.52008i) q^{94} +(6.57591 - 11.3898i) q^{95} +(2.98209 + 9.16734i) q^{96} +(5.91151 - 10.2390i) q^{97} +(4.17383 - 8.40957i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more