LMFDB - Embedded newform 399.2.k.c.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(64,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("399.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.k (of order $3$, 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:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} - 10 x^{9} + 90 x^{8} - 79 x^{7} + 275 x^{6} - 177 x^{5} + 560 x^{4} + \cdots + 9 $ x^12 - x^11 + 11x^10 - 10x^9 + 90x^8 - 79x^7 + 275x^6 - 177x^5 + 560x^4 - 320x^3 + 421x^2 + 57x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.3
Root			$0.597305 + 1.03456i$ of defining polynomial
Character	$\chi$	$=$	399.64
Dual form			399.2.k.c.106.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.597305 - 1.03456i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.286453 - 0.496151i) q^{4} +(0.0760004 + 0.131637i) q^{5} +(-0.597305 + 1.03456i) q^{6} -1.00000 q^{7} -3.07362 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0907909 - 0.157254i) q^{10} -4.35742 q^{11} -0.572906 q^{12} +(0.191130 - 0.331047i) q^{13} +(0.597305 + 1.03456i) q^{14} +(0.0760004 - 0.131637i) q^{15} +(1.26298 + 2.18755i) q^{16} +(-0.710452 - 1.23054i) q^{17} +1.19461 q^{18} +(-3.81189 - 2.11411i) q^{19} +0.0870821 q^{20} +(0.500000 + 0.866025i) q^{21} +(2.60271 + 4.50802i) q^{22} +(-0.195662 + 0.338896i) q^{23} +(1.53681 + 2.66183i) q^{24} +(2.48845 - 4.31012i) q^{25} -0.456652 q^{26} +1.00000 q^{27} +(-0.286453 + 0.496151i) q^{28} +(-2.29279 + 3.97122i) q^{29} -0.181582 q^{30} -2.38016 q^{31} +(-1.56485 + 2.71039i) q^{32} +(2.17871 + 3.77363i) q^{33} +(-0.848714 + 1.47002i) q^{34} +(-0.0760004 - 0.131637i) q^{35} +(0.286453 + 0.496151i) q^{36} +4.84114 q^{37} +(0.0896785 + 5.20641i) q^{38} -0.382260 q^{39} +(-0.233596 - 0.404601i) q^{40} +(-4.15977 - 7.20493i) q^{41} +(0.597305 - 1.03456i) q^{42} +(2.70200 + 4.67999i) q^{43} +(-1.24819 + 2.16193i) q^{44} -0.152001 q^{45} +0.467480 q^{46} +(-6.29279 + 10.8994i) q^{47} +(1.26298 - 2.18755i) q^{48} +1.00000 q^{49} -5.94545 q^{50} +(-0.710452 + 1.23054i) q^{51} +(-0.109499 - 0.189659i) q^{52} +(6.77910 - 11.7417i) q^{53} +(-0.597305 - 1.03456i) q^{54} +(-0.331165 - 0.573595i) q^{55} +3.07362 q^{56} +(0.0750692 + 4.35825i) q^{57} +5.47797 q^{58} +(-5.80973 - 10.0627i) q^{59} +(-0.0435410 - 0.0754153i) q^{60} +(-2.04116 + 3.53539i) q^{61} +(1.42168 + 2.46242i) q^{62} +(0.500000 - 0.866025i) q^{63} +8.79070 q^{64} +0.0581038 q^{65} +(2.60271 - 4.50802i) q^{66} +(7.59723 - 13.1588i) q^{67} -0.814044 q^{68} +0.391324 q^{69} +(-0.0907909 + 0.157254i) q^{70} +(-2.79948 - 4.84884i) q^{71} +(1.53681 - 2.66183i) q^{72} +(1.21808 + 2.10978i) q^{73} +(-2.89164 - 5.00846i) q^{74} -4.97690 q^{75} +(-2.14085 + 1.28568i) q^{76} +4.35742 q^{77} +(0.228326 + 0.395472i) q^{78} +(-4.21230 - 7.29592i) q^{79} +(-0.191975 + 0.332510i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.96931 + 8.60709i) q^{82} +3.44575 q^{83} +0.572906 q^{84} +(0.107989 - 0.187043i) q^{85} +(3.22783 - 5.59077i) q^{86} +4.58557 q^{87} +13.3930 q^{88} +(-1.70940 + 2.96077i) q^{89} +(0.0907909 + 0.157254i) q^{90} +(-0.191130 + 0.331047i) q^{91} +(0.112096 + 0.194156i) q^{92} +(1.19008 + 2.06128i) q^{93} +15.0349 q^{94} +(-0.0114106 - 0.662458i) q^{95} +3.12969 q^{96} +(-8.63195 - 14.9510i) q^{97} +(-0.597305 - 1.03456i) q^{98} +(2.17871 - 3.77363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{11} + 18 q^{12} - 2 q^{13} + q^{14} - 19 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 26 q^{20} + 6 q^{21} + 2 q^{22}+ \cdots - 4 q^{99}+O(q^{100}) $ 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^11 + 18 * q^12 - 2 * q^13 + q^14 - 19 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 26 * q^20 + 6 * q^21 + 2 * q^22 + 5 * q^23 + 3 * q^24 - 16 * q^25 + 98 * q^26 + 12 * q^27 + 9 * q^28 + 11 * q^29 + 8 * q^30 - 10 * q^31 - 4 * q^33 - 6 * q^34 - 9 * q^36 - 10 * q^37 - 26 * q^38 + 4 * q^39 - 62 * q^40 + 5 * q^41 + q^42 - q^43 + 15 * q^44 - 24 * q^46 - 37 * q^47 - 19 * q^48 + 12 * q^49 + 6 * q^50 + 3 * q^51 + 9 * q^52 + 9 * q^53 - q^54 + 9 * q^55 + 6 * q^56 + 3 * q^57 + 18 * q^58 + 6 * q^59 + 13 * q^60 + 19 * q^61 + 5 * q^62 + 6 * q^63 + 118 * q^64 + 48 * q^65 + 2 * q^66 + 8 * q^67 - 130 * q^68 - 10 * q^69 + 4 * q^70 - 19 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 + 32 * q^75 - 6 * q^76 - 8 * q^77 - 49 * q^78 + 27 * q^79 - 11 * q^80 - 6 * q^81 - 46 * q^82 + 70 * q^83 - 18 * q^84 - 59 * q^85 - 3 * q^86 - 22 * q^87 - 14 * q^88 - 4 * q^89 - 4 * q^90 + 2 * q^91 - 9 * q^92 + 5 * q^93 + 34 * q^94 - 55 * q^97 - q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.597305	−	1.03456i	−0.422359	−	0.731547i	0.573811	−	0.818988i	$-0.305464\pi$
$2$	−0.597305	−	1.03456i	−0.422359	−	0.731547i	−0.996170	+	0.0874411i	$0.972131\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.286453	−	0.496151i	0.143226	−	0.248075i
$5$	0.0760004	+	0.131637i	0.0339884	+	0.0588696i	0.882519	−	0.470276i	$-0.155846\pi$
$5$	0.0760004	+	0.131637i	0.0339884	+	0.0588696i	−0.848531	+	0.529146i	$0.822512\pi$
$6$	−0.597305	+	1.03456i	−0.243849	+	0.422359i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−3.07362			−1.08669
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0907909	−	0.157254i	0.0287106	−	0.0497282i
$11$	−4.35742			−1.31381			−0.656905	−	0.753973i	$-0.728135\pi$
$11$	−4.35742			−1.31381			−0.656905	+	0.753973i	$0.728135\pi$
$12$	−0.572906			−0.165384
$13$	0.191130	−	0.331047i	0.0530099	−	0.0918158i	−0.838303	−	0.545205i	$-0.816452\pi$
$13$	0.191130	−	0.331047i	0.0530099	−	0.0918158i	0.891313	+	0.453389i	$0.149785\pi$
$14$	0.597305	+	1.03456i	0.159637	+	0.276499i
$15$	0.0760004	−	0.131637i	0.0196232	−	0.0339884i
$16$	1.26298	+	2.18755i	0.315746	+	0.546888i
$17$	−0.710452	−	1.23054i	−0.172310	−	0.298450i	0.766917	−	0.641746i	$-0.221790\pi$
$17$	−0.710452	−	1.23054i	−0.172310	−	0.298450i	−0.939227	+	0.343297i	$0.888456\pi$
$18$	1.19461			0.281572
$19$	−3.81189	−	2.11411i	−0.874508	−	0.485011i
$19$	−3.81189	−	2.11411i	−0.874508	−	0.485011i
$20$	0.0870821			0.0194721
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	2.60271	+	4.50802i	0.554899	+	0.961113i
$23$	−0.195662	+	0.338896i	−0.0407983	+	0.0706648i	−0.885704	−	0.464251i	$-0.846323\pi$
$23$	−0.195662	+	0.338896i	−0.0407983	+	0.0706648i	0.844905	+	0.534916i	$0.179657\pi$
$24$	1.53681	+	2.66183i	0.313700	+	0.543344i
$25$	2.48845	−	4.31012i	0.497690	−	0.862024i
$26$	−0.456652			−0.0895568
$27$	1.00000			0.192450
$28$	−0.286453	+	0.496151i	−0.0541345	+	0.0937637i
$29$	−2.29279	+	3.97122i	−0.425760	+	0.737437i	−0.996491	−	0.0836995i	$-0.973326\pi$
$29$	−2.29279	+	3.97122i	−0.425760	+	0.737437i	0.570731	+	0.821137i	$0.306660\pi$
$30$	−0.181582			−0.0331521
$31$	−2.38016			−0.427489			−0.213744	−	0.976890i	$-0.568566\pi$
$31$	−2.38016			−0.427489			−0.213744	+	0.976890i	$0.568566\pi$
$32$	−1.56485	+	2.71039i	−0.276628	+	0.479134i
$33$	2.17871	+	3.77363i	0.379264	+	0.656905i
$34$	−0.848714	+	1.47002i	−0.145553	+	0.252106i
$35$	−0.0760004	−	0.131637i	−0.0128464	−	0.0222506i
$36$	0.286453	+	0.496151i	0.0477421	+	0.0826918i
$37$	4.84114			0.795878			0.397939	−	0.917412i	$-0.369726\pi$
$37$	4.84114			0.795878			0.397939	+	0.917412i	$0.369726\pi$
$38$	0.0896785	+	5.20641i	0.0145478	+	0.844592i
$39$	−0.382260			−0.0612106
$40$	−0.233596	−	0.404601i	−0.0369348	−	0.0639730i
$41$	−4.15977	−	7.20493i	−0.649647	−	1.12522i	−0.983207	−	0.182493i	$-0.941583\pi$
$41$	−4.15977	−	7.20493i	−0.649647	−	1.12522i	0.333560	−	0.942729i	$-0.391750\pi$
$42$	0.597305	−	1.03456i	0.0921662	−	0.159637i
$43$	2.70200	+	4.67999i	0.412050	+	0.713692i	0.995114	−	0.0987344i	$-0.0314794\pi$
$43$	2.70200	+	4.67999i	0.412050	+	0.713692i	−0.583063	+	0.812427i	$0.698146\pi$
$44$	−1.24819	+	2.16193i	−0.188172	+	0.325924i
$45$	−0.152001			−0.0226589
$46$	0.467480			0.0689261
$47$	−6.29279	+	10.8994i	−0.917897	+	1.58984i	−0.115294	+	0.993331i	$0.536781\pi$
$47$	−6.29279	+	10.8994i	−0.917897	+	1.58984i	−0.802603	+	0.596513i	$0.796552\pi$
$48$	1.26298	−	2.18755i	0.182296	−	0.315746i
$49$	1.00000			0.142857
$50$	−5.94545			−0.840814
$51$	−0.710452	+	1.23054i	−0.0994832	+	0.172310i
$52$	−0.109499	−	0.189659i	−0.0151848	−	0.0263009i
$53$	6.77910	−	11.7417i	0.931180	−	1.61285i	0.149873	−	0.988705i	$-0.452113\pi$
$53$	6.77910	−	11.7417i	0.931180	−	1.61285i	0.781307	−	0.624147i	$-0.214553\pi$
$54$	−0.597305	−	1.03456i	−0.0812830	−	0.140786i
$55$	−0.331165	−	0.573595i	−0.0446543	−	0.0773435i
$56$	3.07362			0.410730
$57$	0.0750692	+	4.35825i	0.00994316	+	0.577265i
$58$	5.47797			0.719293
$59$	−5.80973	−	10.0627i	−0.756362	−	1.31006i	−0.944694	−	0.327952i	$-0.893641\pi$
$59$	−5.80973	−	10.0627i	−0.756362	−	1.31006i	0.188332	−	0.982105i	$-0.439692\pi$
$60$	−0.0435410	−	0.0754153i	−0.00562112	−	0.00973607i
$61$	−2.04116	+	3.53539i	−0.261344	+	0.452661i	−0.966599	−	0.256292i	$-0.917499\pi$
$61$	−2.04116	+	3.53539i	−0.261344	+	0.452661i	0.705255	+	0.708953i	$0.250832\pi$
$62$	1.42168	+	2.46242i	0.180554	+	0.312728i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	8.79070			1.09884
$65$	0.0581038			0.00720689
$66$	2.60271	−	4.50802i	0.320371	−	0.554899i
$67$	7.59723	−	13.1588i	0.928150	−	1.60760i	0.141734	−	0.989905i	$-0.454732\pi$
$67$	7.59723	−	13.1588i	0.928150	−	1.60760i	0.786416	−	0.617698i	$-0.211934\pi$
$68$	−0.814044			−0.0987174
$69$	0.391324			0.0471098
$70$	−0.0907909	+	0.157254i	−0.0108516	+	0.0187955i
$71$	−2.79948	−	4.84884i	−0.332237	−	0.575452i	0.650713	−	0.759324i	$-0.274470\pi$
$71$	−2.79948	−	4.84884i	−0.332237	−	0.575452i	−0.982950	+	0.183872i	$0.941137\pi$
$72$	1.53681	−	2.66183i	0.181115	−	0.313700i
$73$	1.21808	+	2.10978i	0.142565	+	0.246930i	0.928462	−	0.371427i	$-0.121132\pi$
$73$	1.21808	+	2.10978i	0.142565	+	0.246930i	−0.785897	+	0.618358i	$0.787798\pi$
$74$	−2.89164	−	5.00846i	−0.336146	−	0.582222i
$75$	−4.97690			−0.574682
$76$	−2.14085	+	1.28568i	−0.245572	+	0.147478i
$77$	4.35742			0.496574
$78$	0.228326	+	0.395472i	0.0258528	+	0.0447784i
$79$	−4.21230	−	7.29592i	−0.473921	−	0.820855i	0.525633	−	0.850711i	$-0.323828\pi$
$79$	−4.21230	−	7.29592i	−0.473921	−	0.820855i	−0.999554	+	0.0298559i	$0.990495\pi$
$80$	−0.191975	+	0.332510i	−0.0214634	+	0.0371757i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.96931	+	8.60709i	−0.548768	+	0.950494i
$83$	3.44575			0.378220			0.189110	−	0.981956i	$-0.439440\pi$
$83$	3.44575			0.378220			0.189110	+	0.981956i	$0.439440\pi$
$84$	0.572906			0.0625091
$85$	0.107989	−	0.187043i	0.0117131	−	0.0202877i
$86$	3.22783	−	5.59077i	0.348066	−	0.602868i
$87$	4.58557			0.491625
$88$	13.3930			1.42770
$89$	−1.70940	+	2.96077i	−0.181196	+	0.313841i	−0.942288	−	0.334803i	$-0.891330\pi$
$89$	−1.70940	+	2.96077i	−0.181196	+	0.313841i	0.761092	+	0.648644i	$0.224664\pi$
$90$	0.0907909	+	0.157254i	0.00957020	+	0.0165761i
$91$	−0.191130	+	0.331047i	−0.0200359	+	0.0347031i
$92$	0.112096	+	0.194156i	0.0116868	+	0.0202421i
$93$	1.19008	+	2.06128i	0.123405	+	0.213744i
$94$	15.0349			1.55073
$95$	−0.0114106	−	0.662458i	−0.00117070	−	0.0679667i
$96$	3.12969			0.319423
$97$	−8.63195	−	14.9510i	−0.876442	−	1.51804i	−0.855219	−	0.518267i	$-0.826577\pi$
$97$	−8.63195	−	14.9510i	−0.876442	−	1.51804i	−0.0212231	−	0.999775i	$-0.506756\pi$
$98$	−0.597305	−	1.03456i	−0.0603369	−	0.104507i
$99$	2.17871	−	3.77363i	0.218968	−	0.379264i
$100$	−1.42565	−	2.46929i	−0.142565	−	0.246929i
$101$	4.70609	−	8.15119i	0.468273	−	0.811073i	−0.531069	−	0.847328i	$-0.678210\pi$
$101$	4.70609	−	8.15119i	0.468273	−	0.811073i	0.999343	+	0.0362551i	$0.0115429\pi$
$102$	1.69743			0.168070
$103$	−2.86719			−0.282513			−0.141257	−	0.989973i	$-0.545114\pi$
$103$	−2.86719			−0.282513			−0.141257	+	0.989973i	$0.545114\pi$
$104$	−0.587461	+	1.01751i	−0.0576053	+	0.0997753i
$105$	−0.0760004	+	0.131637i	−0.00741688	+	0.0128464i
$106$	−16.1968			−1.57317
$107$	10.8517			1.04907			0.524537	−	0.851388i	$-0.324239\pi$
$107$	10.8517			1.04907			0.524537	+	0.851388i	$0.324239\pi$
$108$	0.286453	−	0.496151i	0.0275639	−	0.0477421i
$109$	−3.12026	−	5.40444i	−0.298866	−	0.517652i	0.677011	−	0.735973i	$-0.263275\pi$
$109$	−3.12026	−	5.40444i	−0.298866	−	0.517652i	−0.975877	+	0.218322i	$0.929942\pi$
$110$	−0.395613	+	0.685223i	−0.0377203	+	0.0653334i
$111$	−2.42057	−	4.19255i	−0.229750	−	0.397939i
$112$	−1.26298	−	2.18755i	−0.119341	−	0.206704i
$113$	4.95084			0.465736			0.232868	−	0.972508i	$-0.425189\pi$
$113$	4.95084			0.465736			0.232868	+	0.972508i	$0.425189\pi$
$114$	4.46405	−	2.68087i	0.418096	−	0.251087i
$115$	−0.0594815			−0.00554668
$116$	1.31355	+	2.27513i	0.121960	+	0.211241i
$117$	0.191130	+	0.331047i	0.0176700	+	0.0306053i
$118$	−6.94036	+	12.0211i	−0.638912	+	1.10663i
$119$	0.710452	+	1.23054i	0.0651271	+	0.112803i
$120$	−0.233596	+	0.404601i	−0.0213243	+	0.0369348i
$121$	7.98707			0.726097
$122$	4.87678			0.441523
$123$	−4.15977	+	7.20493i	−0.375074	+	0.649647i
$124$	−0.681803	+	1.18092i	−0.0612277	+	0.106049i
$125$	1.51650			0.135639
$126$	−1.19461			−0.106424
$127$	−9.87970	+	17.1121i	−0.876682	+	1.51846i	−0.0217212	+	0.999764i	$0.506915\pi$
$127$	−9.87970	+	17.1121i	−0.876682	+	1.51846i	−0.854960	+	0.518693i	$0.826419\pi$
$128$	−2.12104	−	3.67375i	−0.187475	−	0.324717i
$129$	2.70200	−	4.67999i	0.237897	−	0.412050i
$130$	−0.0347057	−	0.0601120i	−0.00304389	−	0.00527217i
$131$	−2.46672	−	4.27248i	−0.215518	−	0.373288i	0.737915	−	0.674894i	$-0.235811\pi$
$131$	−2.46672	−	4.27248i	−0.215518	−	0.373288i	−0.953433	+	0.301606i	$0.902477\pi$
$132$	2.49639			0.217283
$133$	3.81189	+	2.11411i	0.330533	+	0.183317i
$134$	−18.1515			−1.56805
$135$	0.0760004	+	0.131637i	0.00654107	+	0.0113295i
$136$	2.18366	+	3.78221i	0.187247	+	0.324322i
$137$	0.789042	−	1.36666i	0.0674124	−	0.116762i	−0.830349	−	0.557243i	$-0.811859\pi$
$137$	0.789042	−	1.36666i	0.0674124	−	0.116762i	0.897762	+	0.440482i	$0.145192\pi$
$138$	−0.233740	−	0.404849i	−0.0198973	−	0.0344631i
$139$	−1.26840	+	2.19693i	−0.107584	+	0.186341i	−0.914791	−	0.403927i	$-0.867645\pi$
$139$	−1.26840	+	2.19693i	−0.107584	+	0.186341i	0.807207	+	0.590269i	$0.200978\pi$
$140$	−0.0870821			−0.00735978
$141$	12.5856			1.05990
$142$	−3.34429	+	5.79248i	−0.280647	+	0.486094i
$143$	−0.832832	+	1.44251i	−0.0696450	+	0.120629i
$144$	−2.52597			−0.210497
$145$	−0.697010			−0.0578836
$146$	1.45513	−	2.52036i	0.120427	−	0.208586i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	1.38676	−	2.40193i	0.113991	−	0.197438i
$149$	−0.542104	−	0.938952i	−0.0444109	−	0.0769219i	0.842965	−	0.537968i	$-0.180808\pi$
$149$	−0.542104	−	0.938952i	−0.0444109	−	0.0769219i	−0.887376	+	0.461046i	$0.847474\pi$
$150$	2.97273	+	5.14891i	0.242722	+	0.420407i
$151$	1.64906			0.134199			0.0670994	−	0.997746i	$-0.478626\pi$
$151$	1.64906			0.134199			0.0670994	+	0.997746i	$0.478626\pi$
$152$	11.7163	+	6.49798i	0.950318	+	0.527056i
$153$	1.42090			0.114873
$154$	−2.60271	−	4.50802i	−0.209732	−	0.363267i
$155$	−0.180893	−	0.313316i	−0.0145297	−	0.0251661i
$156$	−0.109499	+	0.189659i	−0.00876697	+	0.0151848i
$157$	−9.20495	−	15.9434i	−0.734635	−	1.27242i	−0.954883	−	0.296981i	$-0.904020\pi$
$157$	−9.20495	−	15.9434i	−0.734635	−	1.27242i	0.220249	−	0.975444i	$-0.429313\pi$
$158$	−5.03206	+	8.71579i	−0.400329	+	0.693391i
$159$	−13.5582			−1.07523
$160$	−0.475716			−0.0376086
$161$	0.195662	−	0.338896i	0.0154203	−	0.0267088i
$162$	−0.597305	+	1.03456i	−0.0469287	+	0.0812830i
$163$	−11.8661			−0.929423			−0.464712	−	0.885462i	$-0.653842\pi$
$163$	−11.8661			−0.929423			−0.464712	+	0.885462i	$0.653842\pi$
$164$	−4.76631			−0.372186
$165$	−0.331165	+	0.573595i	−0.0257812	+	0.0446543i
$166$	−2.05816	−	3.56485i	−0.159745	−	0.276686i
$167$	5.20019	−	9.00700i	0.402403	−	0.696983i	−0.591612	−	0.806223i	$-0.701508\pi$
$167$	5.20019	−	9.00700i	0.402403	−	0.696983i	0.994015	+	0.109240i	$0.0348417\pi$
$168$	−1.53681	−	2.66183i	−0.118567	−	0.205365i
$169$	6.42694	+	11.1318i	0.494380	+	0.856291i
$170$	−0.258010			−0.0197885
$171$	3.73682	−	2.24414i	0.285762	−	0.171614i
$172$	3.09598			0.236066
$173$	6.02433	+	10.4344i	0.458021	+	0.793316i	0.998856	−	0.0478128i	$-0.0152251\pi$
$173$	6.02433	+	10.4344i	0.458021	+	0.793316i	−0.540835	+	0.841129i	$0.681892\pi$
$174$	−2.73899	−	4.74406i	−0.207642	−	0.359647i
$175$	−2.48845	+	4.31012i	−0.188109	+	0.325814i
$176$	−5.50335	−	9.53208i	−0.414830	−	0.718507i
$177$	−5.80973	+	10.0627i	−0.436686	+	0.756362i
$178$	4.08414			0.306119
$179$	3.04546			0.227628			0.113814	−	0.993502i	$-0.463693\pi$
$179$	3.04546			0.227628			0.113814	+	0.993502i	$0.463693\pi$
$180$	−0.0435410	+	0.0754153i	−0.00324536	+	0.00562112i
$181$	−6.48950	+	11.2401i	−0.482361	+	0.835473i	−0.999795	−	0.0202498i	$-0.993554\pi$
$181$	−6.48950	+	11.2401i	−0.482361	+	0.835473i	0.517434	+	0.855723i	$0.326887\pi$
$182$	0.456652			0.0338493
$183$	4.08232			0.301774
$184$	0.601390	−	1.04164i	0.0443351	−	0.0767906i
$185$	0.367928	+	0.637270i	0.0270506	+	0.0468530i
$186$	1.42168	−	2.46242i	0.104243	−	0.180554i
$187$	3.09574	+	5.36197i	0.226383	+	0.392106i
$188$	3.60517	+	6.24434i	0.262934	+	0.455415i
$189$	−1.00000			−0.0727393
$190$	−0.678539	+	0.407494i	−0.0492264	+	0.0295628i
$191$	15.0370			1.08804			0.544018	−	0.839073i	$-0.316902\pi$
$191$	15.0370			1.08804			0.544018	+	0.839073i	$0.316902\pi$
$192$	−4.39535	−	7.61297i	−0.317207	−	0.549419i
$193$	11.9088	+	20.6267i	0.857216	+	1.48474i	0.874574	+	0.484892i	$0.161141\pi$
$193$	11.9088	+	20.6267i	0.857216	+	1.48474i	−0.0173582	+	0.999849i	$0.505526\pi$
$194$	−10.3118	+	17.8606i	−0.740346	+	1.28232i
$195$	−0.0290519	−	0.0503194i	−0.00208045	−	0.00360344i
$196$	0.286453	−	0.496151i	0.0204609	−	0.0354393i
$197$	−1.90086			−0.135431			−0.0677154	−	0.997705i	$-0.521571\pi$
$197$	−1.90086			−0.135431			−0.0677154	+	0.997705i	$0.521571\pi$
$198$	−5.20541			−0.369933
$199$	−8.22002	+	14.2375i	−0.582702	+	1.00927i	0.412456	+	0.910978i	$0.364671\pi$
$199$	−8.22002	+	14.2375i	−0.582702	+	1.00927i	−0.995158	+	0.0982918i	$0.968662\pi$
$200$	−7.64854	+	13.2477i	−0.540834	+	0.936751i
$201$	−15.1945			−1.07173
$202$	−11.2439			−0.791117
$203$	2.29279	−	3.97122i	0.160922	−	0.278725i
$204$	0.407022	+	0.704983i	0.0284972	+	0.0493587i
$205$	0.632288	−	1.09516i	0.0441609	−	0.0764890i
$206$	1.71259	+	2.96629i	0.119322	+	0.206671i
$207$	−0.195662	−	0.338896i	−0.0135994	−	0.0235549i
$208$	0.965576			0.0669507
$209$	16.6100	+	9.21207i	1.14894	+	0.637213i
$210$	0.181582			0.0125303
$211$	−12.0784	−	20.9205i	−0.831514	−	1.44023i	−0.896837	−	0.442361i	$-0.854141\pi$
$211$	−12.0784	−	20.9205i	−0.831514	−	1.44023i	0.0653225	−	0.997864i	$-0.479192\pi$
$212$	−3.88378	−	6.72691i	−0.266739	−	0.462006i
$213$	−2.79948	+	4.84884i	−0.191817	+	0.332237i
$214$	−6.48178	−	11.2268i	−0.443085	−	0.767446i
$215$	−0.410705	+	0.711362i	−0.0280099	+	0.0485145i
$216$	−3.07362			−0.209133
$217$	2.38016			0.161576
$218$	−3.72749	+	6.45620i	−0.252458	+	0.437269i
$219$	1.21808	−	2.10978i	0.0823102	−	0.142565i
$220$	−0.379453			−0.0255827
$221$	−0.543155			−0.0365365
$222$	−2.89164	+	5.00846i	−0.194074	+	0.336146i
$223$	3.18103	+	5.50970i	0.213017	+	0.368957i	0.952657	−	0.304046i	$-0.0983376\pi$
$223$	3.18103	+	5.50970i	0.213017	+	0.368957i	−0.739640	+	0.673003i	$0.765004\pi$
$224$	1.56485	−	2.71039i	0.104556	−	0.181096i
$225$	2.48845	+	4.31012i	0.165897	+	0.287341i
$226$	−2.95716	−	5.12195i	−0.196707	−	0.340707i
$227$	−5.72133			−0.379738			−0.189869	−	0.981809i	$-0.560806\pi$
$227$	−5.72133			−0.379738			−0.189869	+	0.981809i	$0.560806\pi$
$228$	2.18385	+	1.21119i	0.144629	+	0.0802129i
$229$	4.90284			0.323989			0.161994	−	0.986792i	$-0.448207\pi$
$229$	4.90284			0.323989			0.161994	+	0.986792i	$0.448207\pi$
$230$	0.0355286	+	0.0615374i	0.00234269	+	0.00405765i
$231$	−2.17871	−	3.77363i	−0.143348	−	0.248287i
$232$	7.04715	−	12.2060i	0.462668	−	0.801365i
$233$	8.76247	+	15.1770i	0.574048	+	0.994281i	0.996144	+	0.0877297i	$0.0279612\pi$
$233$	8.76247	+	15.1770i	0.574048	+	0.994281i	−0.422096	+	0.906551i	$0.638706\pi$
$234$	0.228326	−	0.395472i	0.0149261	−	0.0258528i
$235$	−1.91302			−0.124791
$236$	−6.65685			−0.433324
$237$	−4.21230	+	7.29592i	−0.273618	+	0.473921i
$238$	0.848714	−	1.47002i	0.0550140	−	0.0952870i
$239$	−10.0256			−0.648502			−0.324251	−	0.945971i	$-0.605112\pi$
$239$	−10.0256			−0.648502			−0.324251	+	0.945971i	$0.605112\pi$
$240$	0.383949			0.0247838
$241$	−10.7721	+	18.6578i	−0.693890	+	1.20185i	0.276664	+	0.960967i	$0.410771\pi$
$241$	−10.7721	+	18.6578i	−0.693890	+	1.20185i	−0.970554	+	0.240885i	$0.922562\pi$
$242$	−4.77072	−	8.26313i	−0.306673	−	0.531174i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.16939	+	2.02545i	0.0748627	+	0.129666i
$245$	0.0760004	+	0.131637i	0.00485549	+	0.00840995i
$246$	9.93861			0.633663
$247$	−1.42844	+	0.857844i	−0.0908893	+	0.0545833i
$248$	7.31570			0.464547
$249$	−1.72287	−	2.98411i	−0.109183	−	0.189110i
$250$	−0.905811	−	1.56891i	−0.0572885	−	0.0992266i
$251$	−6.42613	+	11.1304i	−0.405613	+	0.702543i	−0.994393	−	0.105751i	$-0.966275\pi$
$251$	−6.42613	+	11.1304i	−0.405613	+	0.702543i	0.588779	+	0.808294i	$0.299609\pi$
$252$	−0.286453	−	0.496151i	−0.0180448	−	0.0312546i
$253$	0.852580	−	1.47671i	0.0536013	−	0.0928401i
$254$	23.6048			1.48110
$255$	−0.215979			−0.0135251
$256$	6.25688	−	10.8372i	0.391055	−	0.677327i
$257$	9.84276	−	17.0482i	0.613974	−	1.06343i	−0.376589	−	0.926380i	$-0.622903\pi$
$257$	9.84276	−	17.0482i	0.613974	−	1.06343i	0.990564	−	0.137054i	$-0.0437635\pi$
$258$	−6.45566			−0.401912
$259$	−4.84114			−0.300814
$260$	0.0166440	−	0.0288282i	0.00103222	−	0.00178785i
$261$	−2.29279	−	3.97122i	−0.141920	−	0.245812i
$262$	−2.94677	+	5.10395i	−0.182052	+	0.315323i
$263$	9.49582	+	16.4472i	0.585537	+	1.01418i	0.994808	+	0.101768i	$0.0324498\pi$
$263$	9.49582	+	16.4472i	0.585537	+	1.01418i	−0.409271	+	0.912413i	$0.634217\pi$
$264$	−6.69652	−	11.5987i	−0.412142	−	0.713851i
$265$	2.06086			0.126597
$266$	−0.0896785	−	5.20641i	−0.00549854	−	0.319226i
$267$	3.41880			0.209227
$268$	−4.35250	−	7.53874i	−0.265871	−	0.460502i
$269$	−5.58464	−	9.67288i	−0.340502	−	0.589766i	0.644024	−	0.765005i	$-0.277264\pi$
$269$	−5.58464	−	9.67288i	−0.340502	−	0.589766i	−0.984526	+	0.175239i	$0.943930\pi$
$270$	0.0907909	−	0.157254i	0.00552536	−	0.00957020i
$271$	−8.03378	−	13.9149i	−0.488017	−	0.845271i	0.511888	−	0.859052i	$-0.328946\pi$
$271$	−8.03378	−	13.9149i	−0.488017	−	0.845271i	−0.999905	+	0.0137818i	$0.995613\pi$
$272$	1.79458	−	3.10830i	0.108812	−	0.188469i
$273$	0.382260			0.0231354
$274$	−1.88520			−0.113889
$275$	−10.8432	+	18.7810i	−0.653870	+	1.13254i
$276$	0.112096	−	0.194156i	0.00674737	−	0.0116868i
$277$	7.51483			0.451522			0.225761	−	0.974183i	$-0.427513\pi$
$277$	7.51483			0.451522			0.225761	+	0.974183i	$0.427513\pi$
$278$	3.03048			0.181756
$279$	1.19008	−	2.06128i	0.0712481	−	0.123405i
$280$	0.233596	+	0.404601i	0.0139600	+	0.0241795i
$281$	3.03598	−	5.25846i	0.181111	−	0.313694i	−0.761148	−	0.648578i	$-0.775364\pi$
$281$	3.03598	−	5.25846i	0.181111	−	0.313694i	0.942259	+	0.334885i	$0.108697\pi$
$282$	−7.51743	−	13.0206i	−0.447656	−	0.775364i
$283$	−1.33044	−	2.30439i	−0.0790864	−	0.136982i	0.823770	−	0.566925i	$-0.191867\pi$
$283$	−1.33044	−	2.30439i	−0.0790864	−	0.136982i	−0.902856	+	0.429943i	$0.858534\pi$
$284$	−3.20768			−0.190341
$285$	−0.568000	+	0.341111i	−0.0336454	+	0.0202057i
$286$	1.98982			0.117661
$287$	4.15977	+	7.20493i	0.245544	+	0.425294i
$288$	−1.56485	−	2.71039i	−0.0922094	−	0.159711i
$289$	7.49051	−	12.9740i	0.440619	−	0.763174i
$290$	0.416328	+	0.721101i	0.0244476	+	0.0423445i
$291$	−8.63195	+	14.9510i	−0.506014	+	0.876442i
$292$	1.39569			0.0816765
$293$	27.2943			1.59455			0.797275	−	0.603617i	$-0.206274\pi$
$293$	27.2943			1.59455			0.797275	+	0.603617i	$0.206274\pi$
$294$	−0.597305	+	1.03456i	−0.0348356	+	0.0603369i
$295$	0.883083	−	1.52954i	0.0514151	−	0.0890535i
$296$	−14.8798			−0.864872
$297$	−4.35742			−0.252843
$298$	−0.647603	+	1.12168i	−0.0375146	+	0.0649773i
$299$	0.0747937	+	0.129546i	0.00432543	+	0.00749187i
$300$	−1.42565	+	2.46929i	−0.0823097	+	0.142565i
$301$	−2.70200	−	4.67999i	−0.155740	−	0.269750i
$302$	−0.984993	−	1.70606i	−0.0566800	−	0.0981726i
$303$	−9.41218			−0.540716
$304$	−0.189622	−	11.0088i	−0.0108756	−	0.631398i
$305$	−0.620516			−0.0355306
$306$	−0.848714	−	1.47002i	−0.0485177	−	0.0840352i
$307$	−10.3347	−	17.9002i	−0.589831	−	1.02162i	−0.994254	−	0.107045i	$-0.965861\pi$
$307$	−10.3347	−	17.9002i	−0.589831	−	1.02162i	0.404423	−	0.914572i	$-0.367472\pi$
$308$	1.24819	−	2.16193i	0.0711224	−	0.123188i
$309$	1.43360	+	2.48306i	0.0815545	+	0.141257i
$310$	−0.216097	+	0.374290i	−0.0122735	+	0.0212583i
$311$	12.7100			0.720716			0.360358	−	0.932814i	$-0.382654\pi$
$311$	12.7100			0.720716			0.360358	+	0.932814i	$0.382654\pi$
$312$	1.17492			0.0665168
$313$	−7.39943	+	12.8162i	−0.418241	+	0.724414i	−0.995763	−	0.0919611i	$-0.970686\pi$
$313$	−7.39943	+	12.8162i	−0.418241	+	0.724414i	0.577522	+	0.816375i	$0.304020\pi$
$314$	−10.9963	+	19.0462i	−0.620559	+	1.07484i
$315$	0.152001			0.00856427
$316$	−4.82650			−0.271512
$317$	8.21433	−	14.2276i	0.461363	−	0.799104i	−0.537666	−	0.843158i	$-0.680694\pi$
$317$	8.21433	−	14.2276i	0.461363	−	0.799104i	0.999029	+	0.0440537i	$0.0140273\pi$
$318$	8.09838	+	14.0268i	0.454135	+	0.786584i
$319$	9.99062	−	17.3043i	0.559367	−	0.968853i
$320$	0.668096	+	1.15718i	0.0373477	+	0.0646882i
$321$	−5.42585	−	9.39785i	−0.302841	−	0.524537i
$322$	−0.467480			−0.0260516
$323$	0.106666	+	6.19266i	0.00593506	+	0.344569i
$324$	−0.572906			−0.0318281
$325$	−0.951234	−	1.64759i	−0.0527650	−	0.0913916i
$326$	7.08767	+	12.2762i	0.392550	+	0.679916i
$327$	−3.12026	+	5.40444i	−0.172551	+	0.298866i
$328$	12.7856	+	22.1452i	0.705964	+	1.22277i
$329$	6.29279	−	10.8994i	0.346933	−	0.600905i
$330$	0.791227			0.0435556
$331$	11.5538			0.635054			0.317527	−	0.948249i	$-0.397148\pi$
$331$	11.5538			0.635054			0.317527	+	0.948249i	$0.397148\pi$
$332$	0.987044	−	1.70961i	0.0541711	−	0.0938271i
$333$	−2.42057	+	4.19255i	−0.132646	+	0.229750i
$334$	−12.4244			−0.679834
$335$	2.30957			0.126185
$336$	−1.26298	+	2.18755i	−0.0689014	+	0.119341i
$337$	9.06087	+	15.6939i	0.493577	+	0.854900i	0.999973	−	0.00740084i	$-0.00235578\pi$
$337$	9.06087	+	15.6939i	0.493577	+	0.854900i	−0.506396	+	0.862301i	$0.669022\pi$
$338$	7.67769	−	13.2981i	0.417611	−	0.723324i
$339$	−2.47542	−	4.28755i	−0.134446	−	0.232868i
$340$	−0.0618677	−	0.107158i	−0.00335524	−	0.00581145i
$341$	10.3713			0.561639
$342$	−4.55373	−	2.52554i	−0.246237	−	0.136566i
$343$	−1.00000			−0.0539949
$344$	−8.30491	−	14.3845i	−0.447771	−	0.775561i
$345$	0.0297408	+	0.0515125i	0.00160119	+	0.00277334i
$346$	7.19672	−	12.4651i	0.386898	−	0.670128i
$347$	−8.81970	−	15.2762i	−0.473466	−	0.820068i	0.526072	−	0.850440i	$-0.323664\pi$
$347$	−8.81970	−	15.2762i	−0.473466	−	0.820068i	−0.999539	+	0.0303722i	$0.990331\pi$
$348$	1.31355	−	2.27513i	0.0704137	−	0.121960i
$349$	2.81083			0.150460			0.0752301	−	0.997166i	$-0.476031\pi$
$349$	2.81083			0.150460			0.0752301	+	0.997166i	$0.476031\pi$
$350$	5.94545			0.317798
$351$	0.191130	−	0.331047i	0.0102018	−	0.0176700i
$352$	6.81868	−	11.8103i	0.363437	−	0.629491i
$353$	−19.2746			−1.02588			−0.512941	−	0.858424i	$-0.671444\pi$
$353$	−19.2746			−1.02588			−0.512941	+	0.858424i	$0.671444\pi$
$354$	13.8807			0.737752
$355$	0.425523	−	0.737028i	0.0225844	−	0.0391174i
$356$	0.979325	+	1.69624i	0.0519041	+	0.0899006i
$357$	0.710452	−	1.23054i	0.0376011	−	0.0651271i
$358$	−1.81907	−	3.15072i	−0.0961408	−	0.166521i
$359$	−2.58957	−	4.48527i	−0.136672	−	0.236723i	0.789563	−	0.613670i	$-0.210307\pi$
$359$	−2.58957	−	4.48527i	−0.136672	−	0.236723i	−0.926235	+	0.376946i	$0.876974\pi$
$360$	0.467193			0.0246232
$361$	10.0610	+	16.1176i	0.529528	+	0.848292i
$362$	15.5048			0.814917
$363$	−3.99353	−	6.91701i	−0.209606	−	0.363049i
$364$	0.109499	+	0.189659i	0.00573933	+	0.00994081i
$365$	−0.185149	+	0.320687i	−0.00969114	+	0.0167855i
$366$	−2.43839	−	4.22342i	−0.127457	−	0.220762i
$367$	15.9492	−	27.6248i	0.832542	−	1.44201i	−0.0634737	−	0.997984i	$-0.520218\pi$
$367$	15.9492	−	27.6248i	0.832542	−	1.44201i	0.896016	−	0.444022i	$-0.146449\pi$
$368$	−0.988472			−0.0515276
$369$	8.31954			0.433098
$370$	0.439531	−	0.761290i	0.0228501	−	0.0395776i
$371$	−6.77910	+	11.7417i	−0.351953	+	0.609601i
$372$	1.36361			0.0706996
$373$	8.13943			0.421444			0.210722	−	0.977546i	$-0.432419\pi$
$373$	8.13943			0.421444			0.210722	+	0.977546i	$0.432419\pi$
$374$	3.69820	−	6.40547i	0.191229	−	0.331219i
$375$	−0.758248	−	1.31332i	−0.0391557	−	0.0678197i
$376$	19.3416	−	33.5007i	0.997469	−	1.72767i
$377$	0.876440	+	1.51804i	0.0451390	+	0.0781830i
$378$	0.597305	+	1.03456i	0.0307221	+	0.0532122i
$379$	1.23889			0.0636375			0.0318188	−	0.999494i	$-0.489870\pi$
$379$	1.23889			0.0636375			0.0318188	+	0.999494i	$0.489870\pi$
$380$	−0.331947	−	0.184101i	−0.0170285	−	0.00944421i
$381$	19.7594			1.01230
$382$	−8.98166	−	15.5567i	−0.459542	−	0.795949i
$383$	7.02202	+	12.1625i	0.358808	+	0.621474i	0.987762	−	0.155968i	$-0.0498498\pi$
$383$	7.02202	+	12.1625i	0.358808	+	0.621474i	−0.628954	+	0.777443i	$0.716516\pi$
$384$	−2.12104	+	3.67375i	−0.108239	+	0.187475i
$385$	0.331165	+	0.573595i	0.0168777	+	0.0292331i
$386$	14.2264	−	24.6409i	0.724105	−	1.25419i
$387$	−5.40399			−0.274700
$388$	−9.89059			−0.502118
$389$	−6.51900	+	11.2912i	−0.330526	+	0.572488i	−0.982615	−	0.185654i	$-0.940560\pi$
$389$	−6.51900	+	11.2912i	−0.330526	+	0.572488i	0.652089	+	0.758143i	$0.273893\pi$
$390$	−0.0347057	+	0.0601120i	−0.00175739	+	0.00304389i
$391$	0.556034			0.0281198
$392$	−3.07362			−0.155241
$393$	−2.46672	+	4.27248i	−0.124429	+	0.215518i
$394$	1.13540	+	1.96656i	0.0572004	+	0.0990740i
$395$	0.640273	−	1.10899i	0.0322156	−	0.0557991i
$396$	−1.24819	−	2.16193i	−0.0627241	−	0.108641i
$397$	3.28053	+	5.68205i	0.164645	+	0.285174i	0.936529	−	0.350589i	$-0.114019\pi$
$397$	3.28053	+	5.68205i	0.164645	+	0.285174i	−0.771884	+	0.635763i	$0.780685\pi$
$398$	19.6395			0.984437
$399$	−0.0750692	−	4.35825i	−0.00375816	−	0.218186i
$400$	12.5715			0.628574
$401$	−1.84991	−	3.20414i	−0.0923800	−	0.160007i	0.816132	−	0.577865i	$-0.196114\pi$
$401$	−1.84991	−	3.20414i	−0.0923800	−	0.160007i	−0.908512	+	0.417858i	$0.862781\pi$
$402$	9.07573	+	15.7196i	0.452656	+	0.784024i
$403$	−0.454919	+	0.787943i	−0.0226611	+	0.0392503i
$404$	−2.69614	−	4.66986i	−0.134138	−	0.232334i
$405$	0.0760004	−	0.131637i	0.00377649	−	0.00654107i
$406$	−5.47797			−0.271867
$407$	−21.0948			−1.04563
$408$	2.18366	−	3.78221i	0.108107	−	0.187247i
$409$	−8.19114	+	14.1875i	−0.405026	+	0.701525i	−0.994324	−	0.106390i	$-0.966071\pi$
$409$	−8.19114	+	14.1875i	−0.405026	+	0.701525i	0.589299	+	0.807915i	$0.299404\pi$
$410$	−1.51068			−0.0746070
$411$	−1.57808			−0.0778411
$412$	−0.821316	+	1.42256i	−0.0404633	+	0.0700845i
$413$	5.80973	+	10.0627i	0.285878	+	0.495155i
$414$	−0.233740	+	0.404849i	−0.0114877	+	0.0198973i
$415$	0.261878	+	0.453586i	0.0128551	+	0.0222657i
$416$	0.598178	+	1.03607i	0.0293281	+	0.0507977i
$417$	2.53680			0.124227
$418$	−0.390766	−	22.6865i	−0.0191130	−	1.10963i
$419$	−3.24051			−0.158309			−0.0791547	−	0.996862i	$-0.525222\pi$
$419$	−3.24051			−0.158309			−0.0791547	+	0.996862i	$0.525222\pi$
$420$	0.0435410	+	0.0754153i	0.00212458	+	0.00367989i
$421$	10.3568	+	17.9386i	0.504761	+	0.874272i	0.999985	+	0.00550656i	$0.00175280\pi$
$421$	10.3568	+	17.9386i	0.504761	+	0.874272i	−0.495224	+	0.868766i	$0.664914\pi$
$422$	−14.4290	+	24.9918i	−0.702395	+	1.21658i
$423$	−6.29279	−	10.8994i	−0.305966	−	0.529948i
$424$	−20.8364	+	36.0896i	−1.01190	+	1.75267i
$425$	−7.07169			−0.343028
$426$	6.68858			0.324063
$427$	2.04116	−	3.53539i	0.0987787	−	0.171090i
$428$	3.10850	−	5.38408i	0.150255	−	0.260249i
$429$	1.66566			0.0804191
$430$	0.981266			0.0473208
$431$	13.0935	−	22.6787i	0.630694	−	1.09239i	−0.356717	−	0.934213i	$-0.616104\pi$
$431$	13.0935	−	22.6787i	0.630694	−	1.09239i	0.987410	−	0.158181i	$-0.0505628\pi$
$432$	1.26298	+	2.18755i	0.0607654	+	0.105249i
$433$	−4.52689	+	7.84080i	−0.217548	+	0.376805i	−0.954058	−	0.299622i	$-0.903139\pi$
$433$	−4.52689	+	7.84080i	−0.217548	+	0.376805i	0.736510	+	0.676427i	$0.236473\pi$
$434$	−1.42168	−	2.46242i	−0.0682429	−	0.118200i
$435$	0.348505	+	0.603629i	0.0167095	+	0.0289418i
$436$	−3.57522			−0.171222
$437$	1.46231	−	0.878185i	0.0699517	−	0.0420093i
$438$	−2.91026			−0.139058
$439$	−8.04180	−	13.9288i	−0.383814	−	0.664786i	0.607790	−	0.794098i	$-0.292056\pi$
$439$	−8.04180	−	13.9288i	−0.383814	−	0.664786i	−0.991604	+	0.129312i	$0.958723\pi$
$440$	1.01788	+	1.76301i	0.0485253	+	0.0840483i
$441$	−0.500000	+	0.866025i	−0.0238095	+	0.0412393i
$442$	0.324429	+	0.561928i	0.0154315	+	0.0267282i
$443$	−4.80730	+	8.32649i	−0.228402	+	0.395603i	−0.957335	−	0.288982i	$-0.906683\pi$
$443$	−4.80730	+	8.32649i	−0.228402	+	0.395603i	0.728933	+	0.684585i	$0.240017\pi$
$444$	−2.77351			−0.131625
$445$	−0.519660			−0.0246343
$446$	3.80009	−	6.58195i	0.179939	−	0.311664i
$447$	−0.542104	+	0.938952i	−0.0256406	+	0.0444109i
$448$	−8.79070			−0.415322
$449$	−13.9383			−0.657790			−0.328895	−	0.944367i	$-0.606676\pi$
$449$	−13.9383			−0.657790			−0.328895	+	0.944367i	$0.606676\pi$
$450$	2.97273	−	5.14891i	0.140136	−	0.242722i
$451$	18.1259	+	31.3949i	0.853513	+	1.47833i
$452$	1.41818	−	2.45636i	0.0667056	−	0.115538i
$453$	−0.824531	−	1.42813i	−0.0387398	−	0.0670994i
$454$	3.41738	+	5.91908i	0.160386	+	0.277796i
$455$	−0.0581038			−0.00272395
$456$	−0.230734	−	13.3956i	−0.0108051	−	0.627307i
$457$	−26.2618			−1.22848			−0.614238	−	0.789121i	$-0.710536\pi$
$457$	−26.2618			−1.22848			−0.614238	+	0.789121i	$0.710536\pi$
$458$	−2.92849	−	5.07230i	−0.136840	−	0.237013i
$459$	−0.710452	−	1.23054i	−0.0331611	−	0.0574367i
$460$	−0.0170386	+	0.0295118i	−0.000794431	+	0.00137599i
$461$	−0.0322523	−	0.0558626i	−0.00150214	−	0.00260178i	0.865273	−	0.501300i	$-0.167145\pi$
$461$	−0.0322523	−	0.0558626i	−0.00150214	−	0.00260178i	−0.866775	+	0.498699i	$0.833811\pi$
$462$	−2.60271	+	4.50802i	−0.121089	+	0.209732i
$463$	37.7314			1.75353			0.876764	−	0.480921i	$-0.159698\pi$
$463$	37.7314			1.75353			0.876764	+	0.480921i	$0.159698\pi$
$464$	−11.5830			−0.537728
$465$	−0.180893	+	0.313316i	−0.00838870	+	0.0145297i
$466$	10.4677	−	18.1306i	0.484908	−	0.839886i
$467$	38.0543			1.76094			0.880471	−	0.474101i	$-0.157227\pi$
$467$	38.0543			1.76094			0.880471	+	0.474101i	$0.157227\pi$
$468$	0.218999			0.0101232
$469$	−7.59723	+	13.1588i	−0.350808	+	0.607617i
$470$	1.14265	+	1.97914i	0.0527067	+	0.0912907i
$471$	−9.20495	+	15.9434i	−0.424142	+	0.734635i
$472$	17.8569	+	30.9291i	0.821930	+	1.42363i
$473$	−11.7737	−	20.3927i	−0.541356	−	0.937656i
$474$	10.0641			0.462260
$475$	−18.5978	+	11.1688i	−0.853325	+	0.512462i
$476$	0.814044			0.0373117
$477$	6.77910	+	11.7417i	0.310393	+	0.537617i
$478$	5.98834	+	10.3721i	0.273900	+	0.474409i
$479$	−13.8240	+	23.9438i	−0.631634	+	1.09402i	0.355584	+	0.934644i	$0.384282\pi$
$479$	−13.8240	+	23.9438i	−0.631634	+	1.09402i	−0.987218	+	0.159377i	$0.949051\pi$
$480$	0.237858	+	0.411982i	0.0108567	+	0.0188043i
$481$	0.925286	−	1.60264i	0.0421894	−	0.0730742i
$482$	25.7368			1.17228
$483$	−0.391324			−0.0178058
$484$	2.28792	−	3.96279i	0.103996	−	0.180127i
$485$	1.31206	−	2.27256i	0.0595777	−	0.103192i
$486$	1.19461			0.0541886
$487$	−35.8936			−1.62649			−0.813247	−	0.581919i	$-0.802302\pi$
$487$	−35.8936			−1.62649			−0.813247	+	0.581919i	$0.802302\pi$
$488$	6.27375	−	10.8665i	0.283999	−	0.491902i
$489$	5.93304	+	10.2763i	0.268301	+	0.464712i
$490$	0.0907909	−	0.157254i	0.00410151	−	0.00710403i
$491$	−6.12650	−	10.6114i	−0.276485	−	0.478886i	0.694024	−	0.719952i	$-0.255836\pi$
$491$	−6.12650	−	10.6114i	−0.276485	−	0.478886i	−0.970509	+	0.241066i	$0.922503\pi$
$492$	2.38316	+	4.12775i	0.107441	+	0.186093i
$493$	6.51566			0.293451
$494$	1.74071	+	0.965414i	0.0783181	+	0.0434360i
$495$	0.662330			0.0297695
$496$	−3.00610	−	5.20672i	−0.134978	−	0.233789i
$497$	2.79948	+	4.84884i	0.125574	+	0.217500i
$498$	−2.05816	+	3.56485i	−0.0922285	+	0.159745i
$499$	−7.37222	−	12.7691i	−0.330026	−	0.571621i	0.652491	−	0.757797i	$-0.273724\pi$
$499$	−7.37222	−	12.7691i	−0.330026	−	0.571621i	−0.982517	+	0.186175i	$0.940391\pi$
$500$	0.434404	−	0.752410i	0.0194272	−	0.0336488i
$501$	−10.4004			−0.464655
$502$	15.3534			0.685257
$503$	−7.89127	+	13.6681i	−0.351854	+	0.609429i	−0.986574	−	0.163313i	$-0.947782\pi$
$503$	−7.89127	+	13.6681i	−0.351854	+	0.609429i	0.634720	+	0.772742i	$0.281115\pi$
$504$	−1.53681	+	2.66183i	−0.0684550	+	0.118567i
$505$	1.43066			0.0636635
$506$	−2.03700			−0.0905558
$507$	6.42694	−	11.1318i	0.285430	−	0.494380i
$508$	5.66013	+	9.80364i	0.251128	+	0.434966i
$509$	18.9548	−	32.8306i	0.840156	−	1.45519i	−0.0496067	−	0.998769i	$-0.515797\pi$
$509$	18.9548	−	32.8306i	0.840156	−	1.45519i	0.889763	−	0.456424i	$-0.150870\pi$
$510$	0.129005	+	0.223443i	0.00571244	+	0.00989424i
$511$	−1.21808	−	2.10978i	−0.0538847	−	0.0933310i
$512$	−23.4332			−1.03561
$513$	−3.81189	−	2.11411i	−0.168299	−	0.0933404i
$514$	−23.5165			−1.03727
$515$	−0.217908	−	0.377427i	−0.00960217	−	0.0166314i
$516$	−1.54799	−	2.68119i	−0.0681464	−	0.118033i
$517$	27.4203	−	47.4933i	1.20594	−	2.08875i
$518$	2.89164	+	5.00846i	0.127051	+	0.220059i
$519$	6.02433	−	10.4344i	0.264439	−	0.458021i
$520$	−0.178589			−0.00783164
$521$	−41.8605			−1.83394			−0.916970	−	0.398956i	$-0.869372\pi$
$521$	−41.8605			−1.83394			−0.916970	+	0.398956i	$0.869372\pi$
$522$	−2.73899	+	4.74406i	−0.119882	+	0.207642i
$523$	−14.5229	+	25.1544i	−0.635042	+	1.09992i	0.351465	+	0.936201i	$0.385684\pi$
$523$	−14.5229	+	25.1544i	−0.635042	+	1.09992i	−0.986506	+	0.163723i	$0.947650\pi$
$524$	−2.82639			−0.123472
$525$	4.97690			0.217210
$526$	11.3438	−	19.6481i	0.494614	−	0.856696i
$527$	1.69099	+	2.92888i	0.0736606	+	0.127584i
$528$	−5.50335	+	9.53208i	−0.239502	+	0.414830i
$529$	11.4234	+	19.7860i	0.496671	+	0.860259i
$530$	−1.23096	−	2.13208i	−0.0534695	−	0.0926119i
$531$	11.6195			0.504241
$532$	2.14085	−	1.28568i	0.0928175	−	0.0557413i
$533$	−3.18023			−0.137751
$534$	−2.04207	−	3.53697i	−0.0883690	−	0.153060i
$535$	0.824733	+	1.42848i	0.0356563	+	0.0617586i
$536$	−23.3510	+	40.4451i	−1.00861	+	1.74696i
$537$	−1.52273	−	2.63745i	−0.0657106	−	0.113814i
$538$	−6.67147	+	11.5553i	−0.287628	+	0.498186i
$539$	−4.35742			−0.187687
$540$	0.0870821			0.00374742
$541$	−15.8711	+	27.4895i	−0.682350	+	1.18187i	0.291911	+	0.956445i	$0.405709\pi$
$541$	−15.8711	+	27.4895i	−0.682350	+	1.18187i	−0.974262	+	0.225420i	$0.927625\pi$
$542$	−9.59723	+	16.6229i	−0.412237	+	0.714015i
$543$	12.9790			0.556982
$544$	4.44699			0.190663
$545$	0.474281	−	0.821479i	0.0203160	−	0.0351883i
$546$	−0.228326	−	0.395472i	−0.00977144	−	0.0169246i
$547$	4.47020	−	7.74261i	0.191132	−	0.331050i	−0.754494	−	0.656307i	$-0.772118\pi$
$547$	4.47020	−	7.74261i	0.191132	−	0.331050i	0.945626	+	0.325257i	$0.105451\pi$
$548$	−0.452046	−	0.782967i	−0.0193105	−	0.0334467i
$549$	−2.04116	−	3.53539i	−0.0871146	−	0.150887i
$550$	25.9068			1.10467
$551$	17.1355	−	10.2907i	0.729996	−	0.438397i
$552$	−1.20278			−0.0511937
$553$	4.21230	+	7.29592i	0.179125	+	0.310254i
$554$	−4.48865	−	7.77456i	−0.190704	−	0.330309i
$555$	0.367928	−	0.637270i	0.0156177	−	0.0270506i
$556$	0.726672	+	1.25863i	0.0308178	+	0.0533779i
$557$	3.20848	−	5.55725i	0.135948	−	0.235468i	−0.790011	−	0.613092i	$-0.789925\pi$
$557$	3.20848	−	5.55725i	0.135948	−	0.235468i	0.925959	+	0.377624i	$0.123259\pi$
$558$	−2.84336			−0.120369
$559$	2.06573			0.0873710
$560$	0.191975	−	0.332510i	0.00811240	−	0.0140511i
$561$	3.09574	−	5.36197i	0.130702	−	0.226383i
$562$	−7.25362			−0.305975
$563$	−41.9161			−1.76655			−0.883276	−	0.468853i	$-0.844668\pi$
$563$	−41.9161			−1.76655			−0.883276	+	0.468853i	$0.844668\pi$
$564$	3.60517	−	6.24434i	0.151805	−	0.262934i
$565$	0.376266	+	0.651711i	0.0158296	+	0.0274177i
$566$	−1.58936	+	2.75284i	−0.0668056	+	0.115711i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	8.60454	+	14.9035i	0.361039	+	0.625337i
$569$	−8.47478			−0.355281			−0.177641	−	0.984095i	$-0.556846\pi$
$569$	−8.47478			−0.355281			−0.177641	+	0.984095i	$0.556846\pi$
$570$	0.692170	+	0.383884i	0.0289918	+	0.0160792i
$571$	−44.9870			−1.88265			−0.941323	−	0.337507i	$-0.890416\pi$
$571$	−44.9870			−1.88265			−0.941323	+	0.337507i	$0.890416\pi$
$572$	0.477134	+	0.826421i	0.0199500	+	0.0345544i
$573$	−7.51848	−	13.0224i	−0.314089	−	0.544018i
$574$	4.96931	−	8.60709i	0.207415	−	0.359253i
$575$	0.973789	+	1.68665i	0.0406098	+	0.0703382i
$576$	−4.39535	+	7.61297i	−0.183140	+	0.317207i
$577$	−28.1625			−1.17242			−0.586209	−	0.810160i	$-0.699380\pi$
$577$	−28.1625			−1.17242			−0.586209	+	0.810160i	$0.699380\pi$
$578$	−17.8965			−0.744396
$579$	11.9088	−	20.6267i	0.494914	−	0.857216i
$580$	−0.199661	+	0.345822i	−0.00829045	+	0.0143595i
$581$	−3.44575			−0.142954
$582$	20.6236			0.854877
$583$	−29.5393	+	51.1636i	−1.22339	+	2.11898i
$584$	−3.74391	−	6.48465i	−0.154924	−	0.268337i
$585$	−0.0290519	+	0.0503194i	−0.00120115	+	0.00208045i
$586$	−16.3030	−	28.2377i	−0.673472	−	1.16649i
$587$	−18.8817	−	32.7040i	−0.779329	−	1.34984i	−0.932329	−	0.361612i	$-0.882227\pi$
$587$	−18.8817	−	32.7040i	−0.779329	−	1.34984i	0.152999	−	0.988226i	$-0.451107\pi$
$588$	−0.572906			−0.0236262
$589$	9.07290	+	5.03192i	0.373842	+	0.207337i
$590$	−2.10988			−0.0868624
$591$	0.950431	+	1.64619i	0.0390955	+	0.0677154i
$592$	6.11428	+	10.5902i	0.251295	+	0.435256i
$593$	9.32589	−	16.1529i	0.382968	−	0.663321i	−0.608517	−	0.793541i	$-0.708235\pi$
$593$	9.32589	−	16.1529i	0.382968	−	0.663321i	0.991485	+	0.130220i	$0.0415685\pi$
$594$	2.60271	+	4.50802i	0.106790	+	0.184966i
$595$	−0.107989	+	0.187043i	−0.00442713	+	0.00766801i
$596$	−0.621149			−0.0254432
$597$	16.4400			0.672846
$598$	0.0893493	−	0.154758i	0.00365377	−	0.00632851i
$599$	−1.48454	+	2.57129i	−0.0606565	+	0.105060i	−0.894759	−	0.446549i	$-0.852653\pi$
$599$	−1.48454	+	2.57129i	−0.0606565	+	0.105060i	0.834103	+	0.551609i	$0.185986\pi$
$600$	15.2971			0.624501
$601$	−3.07231			−0.125322			−0.0626610	−	0.998035i	$-0.519959\pi$
$601$	−3.07231			−0.125322			−0.0626610	+	0.998035i	$0.519959\pi$
$602$	−3.22783	+	5.59077i	−0.131557	+	0.227863i
$603$	7.59723	+	13.1588i	0.309383	+	0.535867i
$604$	0.472378	−	0.818183i	0.0192208	−	0.0332914i
$605$	0.607020	+	1.05139i	0.0246789	+	0.0427451i
$606$	5.62194	+	9.73749i	0.228376	+	0.395559i
$607$	−14.3398			−0.582035			−0.291017	−	0.956718i	$-0.593994\pi$
$607$	−14.3398			−0.582035			−0.291017	+	0.956718i	$0.593994\pi$
$608$	11.6951	−	7.02346i	0.474299	−	0.284839i
$609$	−4.58557			−0.185817
$610$	0.370637	+	0.641963i	0.0150067	+	0.0259923i
$611$	2.40548	+	4.16641i	0.0973153	+	0.168555i
$612$	0.407022	−	0.704983i	0.0164529	−	0.0284972i
$613$	−7.12510	−	12.3410i	−0.287780	−	0.498449i	0.685500	−	0.728073i	$-0.259584\pi$
$613$	−7.12510	−	12.3410i	−0.287780	−	0.498449i	−0.973280	+	0.229624i	$0.926251\pi$
$614$	−12.3459	+	21.3837i	−0.498240	+	0.862978i
$615$	−1.26458			−0.0509927
$616$	−13.3930			−0.539621
$617$	−20.6696	+	35.8008i	−0.832127	+	1.44129i	0.0642218	+	0.997936i	$0.479543\pi$
$617$	−20.6696	+	35.8008i	−0.832127	+	1.44129i	−0.896349	+	0.443350i	$0.853790\pi$
$618$	1.71259	−	2.96629i	0.0688905	−	0.119322i
$619$	40.1692			1.61454			0.807268	−	0.590185i	$-0.200945\pi$
$619$	40.1692			1.61454			0.807268	+	0.590185i	$0.200945\pi$
$620$	−0.207269			−0.00832412
$621$	−0.195662	+	0.338896i	−0.00785164	+	0.0135994i
$622$	−7.59173	−	13.1493i	−0.304401	−	0.527238i
$623$	1.70940	−	2.96077i	0.0684857	−	0.118621i
$624$	−0.482788	−	0.836214i	−0.0193270	−	0.0334753i
$625$	−12.3270	−	21.3510i	−0.493079	−	0.854039i
$626$	17.6789			0.706590
$627$	−0.327108	−	18.9907i	−0.0130634	−	0.758416i
$628$	−10.5471			−0.420876
$629$	−3.43940	−	5.95721i	−0.137138	−	0.237530i
$630$	−0.0907909	−	0.157254i	−0.00361719	−	0.00626516i
$631$	3.27073	−	5.66507i	0.130206	−	0.225523i	−0.793550	−	0.608505i	$-0.791770\pi$
$631$	3.27073	−	5.66507i	0.130206	−	0.225523i	0.923756	+	0.382982i	$0.125103\pi$
$632$	12.9470	+	22.4249i	0.515005	+	0.892014i
$633$	−12.0784	+	20.9205i	−0.480075	+	0.831514i
$634$	−19.6259			−0.779443
$635$	−3.00344			−0.119188
$636$	−3.88378	+	6.72691i	−0.154002	+	0.266739i
$637$	0.191130	−	0.331047i	0.00757284	−	0.0131165i
$638$	−23.8698			−0.945015
$639$	5.59896			0.221492
$640$	0.322400	−	0.558412i	0.0127440	−	0.0220732i
$641$	−20.9583	−	36.3009i	−0.827804	−	1.43380i	−0.899757	−	0.436391i	$-0.856256\pi$
$641$	−20.9583	−	36.3009i	−0.827804	−	1.43380i	0.0719528	−	0.997408i	$-0.477077\pi$
$642$	−6.48178	+	11.2268i	−0.255815	+	0.443085i
$643$	−15.8285	−	27.4158i	−0.624215	−	1.08117i	−0.988692	−	0.149960i	$-0.952086\pi$
$643$	−15.8285	−	27.4158i	−0.624215	−	1.08117i	0.364477	−	0.931212i	$-0.381248\pi$
$644$	−0.112096	−	0.194156i	−0.00441719	−	0.00765080i
$645$	0.821411			0.0323430
$646$	6.34299	−	3.80926i	0.249561	−	0.149873i
$647$	26.5647			1.04437			0.522183	−	0.852833i	$-0.325118\pi$
$647$	26.5647			1.04437			0.522183	+	0.852833i	$0.325118\pi$
$648$	1.53681	+	2.66183i	0.0603716	+	0.104567i
$649$	25.3154	+	43.8476i	0.993716	+	1.72117i
$650$	−1.13635	+	1.96822i	−0.0445715	+	0.0772000i
$651$	−1.19008	−	2.06128i	−0.0466429	−	0.0807878i
$652$	−3.39907	+	5.88736i	−0.133118	+	0.230567i
$653$	27.9865			1.09519			0.547597	−	0.836742i	$-0.315543\pi$
$653$	27.9865			1.09519			0.547597	+	0.836742i	$0.315543\pi$
$654$	7.45498			0.291513
$655$	0.374943	−	0.649420i	0.0146502	−	0.0253749i
$656$	10.5074	−	18.1994i	0.410247	−	0.710569i
$657$	−2.43616			−0.0950436
$658$	−15.0349			−0.586120
$659$	0.534319	−	0.925468i	0.0208141	−	0.0360511i	−0.855431	−	0.517917i	$-0.826708\pi$
$659$	0.534319	−	0.925468i	0.0208141	−	0.0360511i	0.876245	+	0.481866i	$0.160041\pi$
$660$	0.189726	+	0.328616i	0.00738509	+	0.0127913i
$661$	8.56235	−	14.8304i	0.333037	−	0.576837i	−0.650069	−	0.759875i	$-0.725260\pi$
$661$	8.56235	−	14.8304i	0.333037	−	0.576837i	0.983106	+	0.183039i	$0.0585933\pi$
$662$	−6.90114	−	11.9531i	−0.268220	−	0.464571i
$663$	0.271577	+	0.470386i	0.0105472	+	0.0182683i
$664$	−10.5909			−0.411008
$665$	0.0114106	+	0.662458i	0.000442483	+	0.0256890i
$666$	5.78327			0.224097
$667$	−0.897222	−	1.55403i	−0.0347406	−	0.0601724i
$668$	−2.97922	−	5.16016i	−0.115269	−	0.199653i
$669$	3.18103	−	5.50970i	0.122986	−	0.213017i
$670$	−1.37952	−	2.38940i	−0.0532954	−	0.0923104i
$671$	8.89419	−	15.4052i	0.343356	−	0.594710i
$672$	−3.12969			−0.120730
$673$	20.9247			0.806586			0.403293	−	0.915071i	$-0.367865\pi$
$673$	20.9247			0.806586			0.403293	+	0.915071i	$0.367865\pi$
$674$	10.8242	−	18.7481i	0.416933	−	0.722149i
$675$	2.48845	−	4.31012i	0.0957804	−	0.165897i
$676$	7.36406			0.283233
$677$	−7.00773			−0.269329			−0.134665	−	0.990891i	$-0.542996\pi$
$677$	−7.00773			−0.269329			−0.134665	+	0.990891i	$0.542996\pi$
$678$	−2.95716	+	5.12195i	−0.113569	+	0.196707i
$679$	8.63195	+	14.9510i	0.331264	+	0.573766i
$680$	−0.331918	+	0.574899i	−0.0127285	+	0.0220464i
$681$	2.86067	+	4.95482i	0.109621	+	0.189869i
$682$	−6.19485	−	10.7298i	−0.237213	−	0.410865i
$683$	−7.30884			−0.279665			−0.139832	−	0.990175i	$-0.544656\pi$
$683$	−7.30884			−0.279665			−0.139832	+	0.990175i	$0.544656\pi$
$684$	−0.0430076	−	2.49687i	−0.00164444	−	0.0954701i
$685$	0.239870			0.00916496
$686$	0.597305	+	1.03456i	0.0228052	+	0.0394998i
$687$	−2.45142	−	4.24599i	−0.0935276	−	0.161994i
$688$	−6.82515	+	11.8215i	−0.260207	+	0.450691i
$689$	−2.59138	−	4.48840i	−0.0987236	−	0.170994i
$690$	0.0355286	−	0.0615374i	0.00135255	−	0.00234269i
$691$	39.3070			1.49531			0.747655	−	0.664087i	$-0.231180\pi$
$691$	39.3070			1.49531			0.747655	+	0.664087i	$0.231180\pi$
$692$	6.90274			0.262403
$693$	−2.17871	+	3.77363i	−0.0827623	+	0.143348i
$694$	−10.5361	+	18.2491i	−0.399945	+	0.692725i
$695$	−0.385595			−0.0146264
$696$	−14.0943			−0.534243
$697$	−5.91064	+	10.2375i	−0.223881	+	0.387774i
$698$	−1.67892	−	2.90798i	−0.0635481	−	0.110069i
$699$	8.76247	−	15.1770i	0.331427	−	0.574048i
$700$	1.42565	+	2.46929i	0.0538843	+	0.0933304i
$701$	−20.2709	−	35.1102i	−0.765621	−	1.32610i	−0.939917	−	0.341402i	$-0.889098\pi$
$701$	−20.2709	−	35.1102i	−0.765621	−	1.32610i	0.174296	−	0.984693i	$-0.444235\pi$
$702$	−0.456652			−0.0172352
$703$	−18.4539	−	10.2347i	−0.696002	−	0.386010i
$704$	−38.3047			−1.44366
$705$	0.956508	+	1.65672i	0.0360242	+	0.0623957i
$706$	11.5128	+	19.9408i	0.433290	+	0.750481i
$707$	−4.70609	+	8.15119i	−0.176991	+	0.306557i
$708$	3.32843	+	5.76500i	0.125090	+	0.216662i
$709$	−17.4985	+	30.3083i	−0.657171	+	1.13825i	0.324174	+	0.945998i	$0.394914\pi$
$709$	−17.4985	+	30.3083i	−0.657171	+	1.13825i	−0.981345	+	0.192256i	$0.938420\pi$
$710$	−1.01667			−0.0381549
$711$	8.42461			0.315947
$712$	5.25405	−	9.10028i	0.196904	−	0.341047i
$713$	0.465706	−	0.806627i	0.0174408	−	0.0302084i
$714$	−1.69743			−0.0635246
$715$	−0.253182			−0.00946848
$716$	0.872380	−	1.51101i	0.0326024	−	0.0564690i
$717$	5.01280	+	8.68242i	0.187206	+	0.324251i
$718$	−3.09353	+	5.35815i	−0.115449	+	0.199964i
$719$	17.8906	+	30.9874i	0.667207	+	1.15564i	0.978682	+	0.205382i	$0.0658436\pi$
$719$	17.8906	+	30.9874i	0.667207	+	1.15564i	−0.311475	+	0.950254i	$0.600823\pi$
$720$	−0.191975	−	0.332510i	−0.00715447	−	0.0123919i
$721$	2.86719			0.106780
$722$	10.6651	−	20.0359i	0.396914	−	0.745658i
$723$	21.5441			0.801235
$724$	3.71787	+	6.43954i	0.138174	+	0.239324i
$725$	11.4110	+	19.7644i	0.423792	+	0.734030i
$726$	−4.77072	+	8.26313i	−0.177058	+	0.306673i
$727$	−5.86331	−	10.1555i	−0.217458	−	0.376648i	0.736572	−	0.676359i	$-0.236443\pi$
$727$	−5.86331	−	10.1555i	−0.217458	−	0.376648i	−0.954030	+	0.299711i	$0.903110\pi$
$728$	0.587461	−	1.01751i	0.0217727	−	0.0377115i
$729$	1.00000			0.0370370
$730$	0.442362			0.0163725
$731$	3.83928	−	6.64982i	0.142001	−	0.245953i
$732$	1.16939	−	2.02545i	0.0432220	−	0.0748627i
$733$	13.9576			0.515536			0.257768	−	0.966207i	$-0.417013\pi$
$733$	13.9576			0.515536			0.257768	+	0.966207i	$0.417013\pi$
$734$	−38.1062			−1.40653
$735$	0.0760004	−	0.131637i	0.00280332	−	0.00485549i
$736$	−0.612361	−	1.06064i	−0.0225719	−	0.0390958i
$737$	−33.1043	+	57.3383i	−1.21941	+	2.11208i
$738$	−4.96931	−	8.60709i	−0.182923	−	0.316831i
$739$	5.15998	+	8.93734i	0.189813	+	0.328765i	0.945188	−	0.326527i	$-0.105879\pi$
$739$	5.15998	+	8.93734i	0.189813	+	0.328765i	−0.755375	+	0.655293i	$0.772545\pi$
$740$	0.421576			0.0154974
$741$	1.45713	+	0.808141i	0.0535291	+	0.0296878i
$742$	16.1968			0.594602
$743$	23.3692	+	40.4767i	0.857333	+	1.48494i	0.874464	+	0.485091i	$0.161214\pi$
$743$	23.3692	+	40.4767i	0.857333	+	1.48494i	−0.0171304	+	0.999853i	$0.505453\pi$
$744$	−3.65785	−	6.33558i	−0.134103	−	0.232274i
$745$	0.0824002	−	0.142721i	0.00301891	−	0.00522891i
$746$	−4.86173	−	8.42076i	−0.178000	−	0.308306i
$747$	−1.72287	+	2.98411i	−0.0630367	+	0.109183i
$748$	3.54713			0.129696
$749$	−10.8517			−0.396512
$750$	−0.905811	+	1.56891i	−0.0330755	+	0.0572885i
$751$	26.8798	−	46.5573i	0.980860	−	1.69890i	0.321800	−	0.946808i	$-0.395712\pi$
$751$	26.8798	−	46.5573i	0.980860	−	1.69890i	0.659059	−	0.752091i	$-0.270955\pi$
$752$	−31.7908			−1.15929
$753$	12.8523			0.468362
$754$	1.04700	−	1.81347i	0.0381297	−	0.0660425i
$755$	0.125329	+	0.217077i	0.00456120	+	0.00790023i
$756$	−0.286453	+	0.496151i	−0.0104182	+	0.0180448i
$757$	−8.06664	−	13.9718i	−0.293187	−	0.507815i	0.681374	−	0.731935i	$-0.261383\pi$
$757$	−8.06664	−	13.9718i	−0.293187	−	0.507815i	−0.974562	+	0.224120i	$0.928049\pi$
$758$	−0.739996	−	1.28171i	−0.0268779	−	0.0465538i
$759$	−1.70516			−0.0618934
$760$	0.0350718	+	2.03614i	0.00127219	+	0.0738587i
$761$	−37.0513			−1.34311			−0.671554	−	0.740955i	$-0.734373\pi$
$761$	−37.0513			−1.34311			−0.671554	+	0.740955i	$0.734373\pi$
$762$	−11.8024	−	20.4423i	−0.427556	−	0.740548i
$763$	3.12026	+	5.40444i	0.112961	+	0.195654i
$764$	4.30738	−	7.46060i	0.155835	−	0.269915i
$765$	0.107989	+	0.187043i	0.00390436	+	0.00676255i
$766$	8.38858	−	14.5294i	0.303092	−	0.524970i
$767$	−4.44165			−0.160379
$768$	−12.5138			−0.451552
$769$	25.1285	−	43.5239i	0.906158	−	1.56951i	0.0868022	−	0.996226i	$-0.472335\pi$
$769$	25.1285	−	43.5239i	0.906158	−	1.56951i	0.819356	−	0.573286i	$-0.194331\pi$
$770$	0.395613	−	0.685223i	0.0142569	−	0.0246937i
$771$	−19.6855			−0.708956
$772$	13.6453			0.491104
$773$	15.8715	−	27.4903i	0.570859	−	0.988757i	−0.425619	−	0.904902i	$-0.639944\pi$
$773$	15.8715	−	27.4903i	0.570859	−	0.988757i	0.996478	−	0.0838542i	$-0.0267230\pi$
$774$	3.22783	+	5.59077i	0.116022	+	0.200956i
$775$	−5.92290	+	10.2588i	−0.212757	+	0.368506i
$776$	26.5313	+	45.9536i	0.952420	+	1.64964i
$777$	2.42057	+	4.19255i	0.0868374	+	0.150407i
$778$	15.5753			0.558403
$779$	0.624541	+	36.2587i	0.0223765	+	1.29910i
$780$	−0.0332880			−0.00119190
$781$	12.1985	+	21.1284i	0.436497	+	0.756035i
$782$	−0.332122	−	0.575252i	−0.0118767	−	0.0205710i
$783$	−2.29279	+	3.97122i	−0.0819375	+	0.141920i
$784$	1.26298	+	2.18755i	0.0451066	+	0.0781269i
$785$	1.39916	−	2.42341i	0.0499381	−	0.0864954i
$786$	5.89353			0.210215
$787$	47.7296			1.70138			0.850688	−	0.525671i	$-0.176186\pi$
$787$	47.7296			1.70138			0.850688	+	0.525671i	$0.176186\pi$
$788$	−0.544507	+	0.943114i	−0.0193973	+	0.0335971i
$789$	9.49582	−	16.4472i	0.338060	−	0.585537i
$790$	−1.52975			−0.0544262
$791$	−4.95084			−0.176032
$792$	−6.69652	+	11.5987i	−0.237950	+	0.412142i
$793$	0.780254	+	1.35144i	0.0277076	+	0.0479910i
$794$	3.91896	−	6.78784i	0.139079	−	0.240891i
$795$	−1.03043	−	1.78475i	−0.0365455	−	0.0632987i
$796$	4.70930	+	8.15674i	0.166917	+	0.289108i
$797$	−44.3597			−1.57130			−0.785651	−	0.618670i	$-0.787672\pi$
$797$	−44.3597			−1.57130			−0.785651	+	0.618670i	$0.787672\pi$
$798$	−4.46405	+	2.68087i	−0.158026	+	0.0949018i
$799$	17.8829			0.632651
$800$	7.78808	+	13.4893i	0.275350	+	0.476920i
$801$	−1.70940	−	2.96077i	−0.0603987	−	0.104614i
$802$	−2.20992	+	3.82769i	−0.0780350	+	0.135161i
$803$	−5.30768	−	9.19317i	−0.187304	−	0.324420i
$804$	−4.35250	+	7.53874i	−0.153501	+	0.265871i
$805$	0.0594815			0.00209645
$806$	1.08690			0.0382845
$807$	−5.58464	+	9.67288i	−0.196589	+	0.340502i
$808$	−14.4647	+	25.0537i	−0.508868	+	0.881384i
$809$	37.6374			1.32326			0.661631	−	0.749830i	$-0.269865\pi$
$809$	37.6374			1.32326			0.661631	+	0.749830i	$0.269865\pi$
$810$	−0.181582			−0.00638013
$811$	8.92112	−	15.4518i	0.313263	−	0.542587i	−0.665804	−	0.746127i	$-0.731911\pi$
$811$	8.92112	−	15.4518i	0.313263	−	0.542587i	0.979067	+	0.203540i	$0.0652446\pi$
$812$	−1.31355	−	2.27513i	−0.0460966	−	0.0798416i
$813$	−8.03378	+	13.9149i	−0.281757	+	0.488017i
$814$	12.6001	+	21.8239i	0.441632	+	0.764929i
$815$	−0.901826	−	1.56201i	−0.0315896	−	0.0547148i
$816$	−3.58916			−0.125646
$817$	−0.405673	−	23.5520i	−0.0141927	−	0.823979i
$818$	19.5704			0.684265
$819$	−0.191130	−	0.331047i	−0.00667862	−	0.0115677i
$820$	−0.362241	−	0.627421i	−0.0126500	−	0.0219105i
$821$	17.5737	−	30.4385i	0.613325	−	1.06231i	−0.377351	−	0.926070i	$-0.623165\pi$
$821$	17.5737	−	30.4385i	0.613325	−	1.06231i	0.990676	−	0.136239i	$-0.0435016\pi$
$822$	0.942598	+	1.63263i	0.0328769	+	0.0569444i
$823$	−12.7823	+	22.1396i	−0.445564	+	0.771740i	−0.998091	−	0.0617553i	$-0.980330\pi$
$823$	−12.7823	+	22.1396i	−0.445564	+	0.771740i	0.552527	+	0.833495i	$0.313663\pi$
$824$	8.81267			0.307004
$825$	21.6864			0.755024
$826$	6.94036	−	12.0211i	0.241486	−	0.418266i
$827$	5.44816	−	9.43648i	0.189451	−	0.328139i	−0.755616	−	0.655014i	$-0.772663\pi$
$827$	5.44816	−	9.43648i	0.189451	−	0.328139i	0.945067	+	0.326876i	$0.105996\pi$
$828$	−0.224192			−0.00779120
$829$	22.9851			0.798304			0.399152	−	0.916885i	$-0.369305\pi$
$829$	22.9851			0.798304			0.399152	+	0.916885i	$0.369305\pi$
$830$	0.312843	−	0.541859i	0.0108589	−	0.0188082i
$831$	−3.75741	−	6.50803i	−0.130343	−	0.225761i
$832$	1.68017	−	2.91013i	0.0582493	−	0.100891i
$833$	−0.710452	−	1.23054i	−0.0246157	−	0.0426357i
$834$	−1.51524	−	2.62448i	−0.0524685	−	0.0908782i
$835$	1.58087			0.0547081
$836$	9.32856	−	5.60224i	0.322635	−	0.193757i
$837$	−2.38016			−0.0822703
$838$	1.93558	+	3.35251i	0.0668633	+	0.115811i
$839$	−19.4350	−	33.6625i	−0.670972	−	1.16216i	−0.977629	−	0.210338i	$-0.932544\pi$
$839$	−19.4350	−	33.6625i	−0.670972	−	1.16216i	0.306656	−	0.951820i	$-0.400790\pi$
$840$	0.233596	−	0.404601i	0.00805984	−	0.0139600i
$841$	3.98626	+	6.90441i	0.137457	+	0.238083i
$842$	12.3724	−	21.4296i	0.426381	−	0.738513i
$843$	−6.07195			−0.209129
$844$	−13.8396			−0.476379
$845$	−0.976899	+	1.69204i	−0.0336064	+	0.0582079i
$846$	−7.51743	+	13.0206i	−0.258455	+	0.447656i
$847$	−7.98707			−0.274439
$848$	34.2476			1.17607
$849$	−1.33044	+	2.30439i	−0.0456605	+	0.0790864i
$850$	4.22396	+	7.31611i	0.144881	+	0.250941i
$851$	−0.947226	+	1.64064i	−0.0324705	+	0.0562405i
$852$	1.60384	+	2.77793i	0.0549466	+	0.0951703i
$853$	3.49550	+	6.05438i	0.119683	+	0.207298i	0.919642	−	0.392757i	$-0.128479\pi$
$853$	3.49550	+	6.05438i	0.119683	+	0.207298i	−0.799959	+	0.600055i	$0.795145\pi$
$854$	−4.87678			−0.166880
$855$	0.579410	+	0.321347i	0.0198154	+	0.0109898i
$856$	−33.3540			−1.14002
$857$	−4.86683	−	8.42959i	−0.166248	−	0.287949i	0.770850	−	0.637017i	$-0.219832\pi$
$857$	−4.86683	−	8.42959i	−0.166248	−	0.287949i	−0.937098	+	0.349067i	$0.886498\pi$
$858$	−0.994911	−	1.72324i	−0.0339657	−	0.0588303i
$859$	6.84144	−	11.8497i	0.233427	−	0.404307i	−0.725387	−	0.688341i	$-0.758339\pi$
$859$	6.84144	−	11.8497i	0.233427	−	0.404307i	0.958814	+	0.284033i	$0.0916727\pi$
$860$	0.235295	+	0.407543i	0.00802350	+	0.0138971i
$861$	4.15977	−	7.20493i	0.141765	−	0.245544i
$862$	−31.2834			−1.06552
$863$	3.08754			0.105101			0.0525506	−	0.998618i	$-0.483265\pi$
$863$	3.08754			0.105101			0.0525506	+	0.998618i	$0.483265\pi$
$864$	−1.56485	+	2.71039i	−0.0532371	+	0.0922094i
$865$	−0.915702	+	1.58604i	−0.0311348	+	0.0539271i
$866$	10.8157			0.367534
$867$	−14.9810			−0.508782
$868$	0.681803	−	1.18092i	0.0231419	−	0.0400829i
$869$	18.3548	+	31.7914i	0.622642	+	1.07845i
$870$	0.416328	−	0.721101i	0.0141148	−	0.0244476i
$871$	−2.90412	−	5.03008i	−0.0984022	−	0.170438i
$872$	9.59048	+	16.6112i	0.324775	+	0.562526i
$873$	17.2639			0.584295
$874$	−1.78198	−	0.988305i	−0.0602764	−	0.0334299i
$875$	−1.51650			−0.0512669
$876$	−0.697844	−	1.20870i	−0.0235780	−	0.0408382i
$877$	−10.6253	−	18.4036i	−0.358792	−	0.621445i	0.628968	−	0.777432i	$-0.283478\pi$
$877$	−10.6253	−	18.4036i	−0.358792	−	0.621445i	−0.987759	+	0.155986i	$0.950144\pi$
$878$	−9.60683	+	16.6395i	−0.324215	+	0.561556i
$879$	−13.6471	−	23.6375i	−0.460307	−	0.797275i
$880$	0.836513	−	1.44888i	0.0281988	−	0.0488418i
$881$	29.9975			1.01064			0.505320	−	0.862932i	$-0.331374\pi$
$881$	29.9975			1.01064			0.505320	+	0.862932i	$0.331374\pi$
$882$	1.19461			0.0402246
$883$	12.2001	−	21.1312i	0.410565	−	0.711120i	−0.584386	−	0.811476i	$-0.698665\pi$
$883$	12.2001	−	21.1312i	0.410565	−	0.711120i	0.994952	+	0.100355i	$0.0319980\pi$
$884$	−0.155588	+	0.269487i	−0.00523300	+	0.00906382i
$885$	−1.76617			−0.0593690
$886$	11.4857			0.385870
$887$	−0.801001	+	1.38737i	−0.0268950	+	0.0465835i	−0.879160	−	0.476527i	$-0.841895\pi$
$887$	−0.801001	+	1.38737i	−0.0268950	+	0.0465835i	0.852265	+	0.523111i	$0.175229\pi$
$888$	7.43991	+	12.8863i	0.249667	+	0.432436i
$889$	9.87970	−	17.1121i	0.331355	−	0.573923i
$890$	0.310396	+	0.537622i	0.0104045	+	0.0180211i
$891$	2.17871	+	3.77363i	0.0729895	+	0.126421i
$892$	3.64486			0.122039
$893$	47.0301	−	28.2438i	1.57380	−	0.945141i
$894$	1.29521			0.0433182
$895$	0.231456	+	0.400894i	0.00773672	+	0.0134004i
$896$	2.12104	+	3.67375i	0.0708590	+	0.122731i
$897$	0.0747937	−	0.129546i	0.00249729	−	0.00432543i
$898$	8.32543	+	14.4201i	0.277823	+	0.481204i
$899$	5.45719	−	9.45213i	0.182008	−	0.315246i
$900$	2.85129			0.0950430
$901$	−19.2649			−0.641807
$902$	21.6533	−	37.5047i	0.720977	−	1.24877i
$903$	−2.70200	+	4.67999i	−0.0899168	+	0.155740i
$904$	−15.2170			−0.506110
$905$	−1.97282			−0.0655787
$906$	−0.984993	+	1.70606i	−0.0327242	+	0.0566800i
$907$	−12.0635	−	20.8946i	−0.400563	−	0.693795i	0.593231	−	0.805032i	$-0.297852\pi$
$907$	−12.0635	−	20.8946i	−0.400563	−	0.693795i	−0.993794	+	0.111237i	$0.964519\pi$
$908$	−1.63889	+	2.83864i	−0.0543885	+	0.0942037i
$909$	4.70609	+	8.15119i	0.156091	+	0.270358i
$910$	0.0347057	+	0.0601120i	0.00115048	+	0.00199269i
$911$	−33.0678			−1.09559			−0.547793	−	0.836614i	$-0.684532\pi$
$911$	−33.0678			−1.09559			−0.547793	+	0.836614i	$0.684532\pi$
$912$	−9.43910	+	5.66862i	−0.312560	+	0.187707i
$913$	−15.0146			−0.496909
$914$	15.6863	+	27.1695i	0.518857	+	0.898687i
$915$	0.310258	+	0.537383i	0.0102568	+	0.0177653i
$916$	1.40443	−	2.43255i	0.0464038	−	0.0803737i
$917$	2.46672	+	4.27248i	0.0814582	+	0.141090i
$918$	−0.848714	+	1.47002i	−0.0280117	+	0.0485177i
$919$	51.9138			1.71248			0.856239	−	0.516580i	$-0.172795\pi$
$919$	51.9138			1.71248			0.856239	+	0.516580i	$0.172795\pi$
$920$	0.182824			0.00602751
$921$	−10.3347	+	17.9002i	−0.340539	+	0.589831i
$922$	−0.0385289	+	0.0667341i	−0.00126888	+	0.00219777i
$923$	−2.14026			−0.0704475
$924$	−2.49639			−0.0821251
$925$	12.0469	−	20.8659i	0.396100	−	0.686066i
$926$	−22.5372	−	39.0355i	−0.740618	−	1.28279i
$927$	1.43360	−	2.48306i	0.0470855	−	0.0815545i
$928$	−7.17571	−	12.4287i	−0.235554	−	0.407992i
$929$	−0.173965	−	0.301316i	−0.00570760	−	0.00988585i	0.863157	−	0.504935i	$-0.168483\pi$
$929$	−0.173965	−	0.301316i	−0.00570760	−	0.00988585i	−0.868865	+	0.495049i	$0.835150\pi$
$930$	0.432193			0.0141722
$931$	−3.81189	−	2.11411i	−0.124930	−	0.0692873i
$932$	10.0401			0.328875
$933$	−6.35499	−	11.0072i	−0.208053	−	0.360358i
$934$	−22.7300	−	39.3695i	−0.743749	−	1.28821i
$935$	−0.470554	+	0.815024i	−0.0153888	+	0.0266541i
$936$	−0.587461	−	1.01751i	−0.0192018	−	0.0332584i
$937$	21.6394	−	37.4805i	0.706927	−	1.22443i	−0.259065	−	0.965860i	$-0.583414\pi$
$937$	21.6394	−	37.4805i	0.706927	−	1.22443i	0.965992	−	0.258573i	$-0.0832524\pi$
$938$	18.1515			0.592666
$939$	14.7989			0.482943
$940$	−0.547989	+	0.949144i	−0.0178734	+	0.0309577i
$941$	−15.5041	+	26.8539i	−0.505420	+	0.875413i	0.494560	+	0.869143i	$0.335329\pi$
$941$	−15.5041	+	26.8539i	−0.505420	+	0.875413i	−0.999980	+	0.00626966i	$0.998004\pi$
$942$	21.9927			0.716559
$943$	3.25563			0.106018
$944$	14.6752	−	25.4182i	0.477637	−	0.827291i
$945$	−0.0760004	−	0.131637i	−0.00247229	−	0.00428214i
$946$	−14.0650	+	24.3613i	−0.457293	+	0.792054i
$947$	−17.3279	−	30.0128i	−0.563082	−	0.975286i	−0.997225	−	0.0744424i	$-0.976282\pi$
$947$	−17.3279	−	30.0128i	−0.563082	−	0.975286i	0.434144	−	0.900844i	$-0.357051\pi$
$948$	2.41325	+	4.17987i	0.0783788	+	0.135756i
$949$	0.931246			0.0302295
$950$	22.6634	+	12.5694i	0.735299	+	0.407804i
$951$	−16.4287			−0.532736
$952$	−2.18366	−	3.78221i	−0.0707729	−	0.122582i
$953$	−15.4442	−	26.7501i	−0.500285	−	0.866520i	−1.00000		0.000329698i	$-0.999895\pi$
$953$	−15.4442	−	26.7501i	−0.500285	−	0.866520i	0.499714	−	0.866190i	$-0.333438\pi$
$954$	8.09838	−	14.0268i	0.262195	−	0.454135i
$955$	1.14281	+	1.97941i	0.0369806	+	0.0640523i
$956$	−2.87186	+	4.97420i	−0.0928825	+	0.160877i
$957$	−19.9812			−0.645902
$958$	33.0285			1.06710
$959$	−0.789042	+	1.36666i	−0.0254795	+	0.0441318i
$960$	0.668096	−	1.15718i	0.0215627	−	0.0373477i
$961$	−25.3349			−0.817253
$962$	−2.21071			−0.0712762
$963$	−5.42585	+	9.39785i	−0.174846	+	0.302841i
$964$	6.17137	+	10.6891i	0.198767	+	0.344274i
$965$	−1.81015	+	3.13527i	−0.0582708	+	0.100928i
$966$	0.233740	+	0.404849i	0.00752045	+	0.0130258i
$967$	−17.6994	−	30.6563i	−0.569175	−	0.985840i	−0.996648	−	0.0818118i	$-0.973929\pi$
$967$	−17.6994	−	30.6563i	−0.569175	−	0.985840i	0.427473	−	0.904028i	$-0.359404\pi$
$968$	−24.5492			−0.789042
$969$	5.30967	−	3.18871i	0.170571	−	0.102436i
$970$	−3.13481			−0.100653
$971$	26.4357	+	45.7881i	0.848364	+	1.46941i	0.882668	+	0.469997i	$0.155745\pi$
$971$	26.4357	+	45.7881i	0.848364	+	1.46941i	−0.0343043	+	0.999411i	$0.510922\pi$
$972$	0.286453	+	0.496151i	0.00918798	+	0.0159140i
$973$	1.26840	−	2.19693i	0.0406630	−	0.0704303i
$974$	21.4394	+	37.1342i	0.686964	+	1.18986i
$975$	−0.951234	+	1.64759i	−0.0304639	+	0.0527650i
$976$	−10.3118			−0.330073
$977$	15.1975			0.486211			0.243105	−	0.970000i	$-0.421834\pi$
$977$	15.1975			0.486211			0.243105	+	0.970000i	$0.421834\pi$
$978$	7.08767	−	12.2762i	0.226639	−	0.392550i
$979$	7.44857	−	12.9013i	0.238057	−	0.412327i
$980$	0.0870821			0.00278173
$981$	6.24051			0.199244
$982$	−7.31878	+	12.6765i	−0.233552	+	0.404523i
$983$	14.4362	+	25.0043i	0.460444	+	0.797513i	0.998983	−	0.0450877i	$-0.0143567\pi$
$983$	14.4362	+	25.0043i	0.460444	+	0.797513i	−0.538539	+	0.842601i	$0.681023\pi$
$984$	12.7856	−	22.1452i	0.407589	−	0.705964i
$985$	−0.144466	−	0.250223i	−0.00460308	−	0.00797276i
$986$	−3.89184	−	6.74086i	−0.123941	−	0.214673i
$987$	−12.5856			−0.400603
$988$	0.0164401	+	0.954452i	0.000523028	+	0.0303652i
$989$	−2.11471			−0.0672439
$990$	−0.395613	−	0.685223i	−0.0125734	−	0.0217778i
$991$	−2.52755	−	4.37785i	−0.0802904	−	0.139067i	0.823084	−	0.567919i	$-0.192251\pi$
$991$	−2.52755	−	4.37785i	−0.0802904	−	0.139067i	−0.903375	+	0.428852i	$0.858918\pi$
$992$	3.72458	−	6.45116i	0.118256	−	0.204825i
$993$	−5.77690	−	10.0059i	−0.183324	−	0.317527i
$994$	3.34429	−	5.79248i	0.106074	−	0.183726i
$995$	−2.49890			−0.0792204
$996$	−1.97409			−0.0625514
$997$	26.6555	−	46.1686i	0.844187	−	1.46218i	−0.0421379	−	0.999112i	$-0.513417\pi$
$997$	26.6555	−	46.1686i	0.844187	−	1.46218i	0.886325	−	0.463063i	$-0.153250\pi$
$998$	−8.80693	+	15.2540i	−0.278778	+	0.482859i
$999$	4.84114			0.153167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.k.c.64.3	✓	12
3.2	odd	2		1197.2.k.i.64.4		12
19.7	even	3		7581.2.a.bc.1.4		6
19.11	even	3	inner	399.2.k.c.106.3	yes	12
19.12	odd	6		7581.2.a.ba.1.3		6
57.11	odd	6		1197.2.k.i.505.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.k.c.64.3	✓	12	1.1	even	1	trivial
399.2.k.c.106.3	yes	12	19.11	even	3	inner
1197.2.k.i.64.4		12	3.2	odd	2
1197.2.k.i.505.4		12	57.11	odd	6
7581.2.a.ba.1.3		6	19.12	odd	6
7581.2.a.bc.1.4		6	19.7	even	3

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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.597305 - 1.03456i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.286453 - 0.496151i) q^{4} +(0.0760004 + 0.131637i) q^{5} +(-0.597305 + 1.03456i) q^{6} -1.00000 q^{7} -3.07362 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0907909 - 0.157254i) q^{10} -4.35742 q^{11} -0.572906 q^{12} +(0.191130 - 0.331047i) q^{13} +(0.597305 + 1.03456i) q^{14} +(0.0760004 - 0.131637i) q^{15} +(1.26298 + 2.18755i) q^{16} +(-0.710452 - 1.23054i) q^{17} +1.19461 q^{18} +(-3.81189 - 2.11411i) q^{19} +0.0870821 q^{20} +(0.500000 + 0.866025i) q^{21} +(2.60271 + 4.50802i) q^{22} +(-0.195662 + 0.338896i) q^{23} +(1.53681 + 2.66183i) q^{24} +(2.48845 - 4.31012i) q^{25} -0.456652 q^{26} +1.00000 q^{27} +(-0.286453 + 0.496151i) q^{28} +(-2.29279 + 3.97122i) q^{29} -0.181582 q^{30} -2.38016 q^{31} +(-1.56485 + 2.71039i) q^{32} +(2.17871 + 3.77363i) q^{33} +(-0.848714 + 1.47002i) q^{34} +(-0.0760004 - 0.131637i) q^{35} +(0.286453 + 0.496151i) q^{36} +4.84114 q^{37} +(0.0896785 + 5.20641i) q^{38} -0.382260 q^{39} +(-0.233596 - 0.404601i) q^{40} +(-4.15977 - 7.20493i) q^{41} +(0.597305 - 1.03456i) q^{42} +(2.70200 + 4.67999i) q^{43} +(-1.24819 + 2.16193i) q^{44} -0.152001 q^{45} +0.467480 q^{46} +(-6.29279 + 10.8994i) q^{47} +(1.26298 - 2.18755i) q^{48} +1.00000 q^{49} -5.94545 q^{50} +(-0.710452 + 1.23054i) q^{51} +(-0.109499 - 0.189659i) q^{52} +(6.77910 - 11.7417i) q^{53} +(-0.597305 - 1.03456i) q^{54} +(-0.331165 - 0.573595i) q^{55} +3.07362 q^{56} +(0.0750692 + 4.35825i) q^{57} +5.47797 q^{58} +(-5.80973 - 10.0627i) q^{59} +(-0.0435410 - 0.0754153i) q^{60} +(-2.04116 + 3.53539i) q^{61} +(1.42168 + 2.46242i) q^{62} +(0.500000 - 0.866025i) q^{63} +8.79070 q^{64} +0.0581038 q^{65} +(2.60271 - 4.50802i) q^{66} +(7.59723 - 13.1588i) q^{67} -0.814044 q^{68} +0.391324 q^{69} +(-0.0907909 + 0.157254i) q^{70} +(-2.79948 - 4.84884i) q^{71} +(1.53681 - 2.66183i) q^{72} +(1.21808 + 2.10978i) q^{73} +(-2.89164 - 5.00846i) q^{74} -4.97690 q^{75} +(-2.14085 + 1.28568i) q^{76} +4.35742 q^{77} +(0.228326 + 0.395472i) q^{78} +(-4.21230 - 7.29592i) q^{79} +(-0.191975 + 0.332510i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.96931 + 8.60709i) q^{82} +3.44575 q^{83} +0.572906 q^{84} +(0.107989 - 0.187043i) q^{85} +(3.22783 - 5.59077i) q^{86} +4.58557 q^{87} +13.3930 q^{88} +(-1.70940 + 2.96077i) q^{89} +(0.0907909 + 0.157254i) q^{90} +(-0.191130 + 0.331047i) q^{91} +(0.112096 + 0.194156i) q^{92} +(1.19008 + 2.06128i) q^{93} +15.0349 q^{94} +(-0.0114106 - 0.662458i) q^{95} +3.12969 q^{96} +(-8.63195 - 14.9510i) q^{97} +(-0.597305 - 1.03456i) q^{98} +(2.17871 - 3.77363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 6 q^{3} - 9 q^{4} - q^{6} - 12 q^{7} - 6 q^{8} - 6 q^{9} - 4 q^{10} + 8 q^{11} + 18 q^{12} - 2 q^{13} + q^{14} - 19 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 26 q^{20} + 6 q^{21} + 2 q^{22}+ \cdots - 4 q^{99}+O(q^{100}) \) 12 * q - q^2 - 6 * q^3 - 9 * q^4 - q^6 - 12 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 + 8 * q^11 + 18 * q^12 - 2 * q^13 + q^14 - 19 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 26 * q^20 + 6 * q^21 + 2 * q^22 + 5 * q^23 + 3 * q^24 - 16 * q^25 + 98 * q^26 + 12 * q^27 + 9 * q^28 + 11 * q^29 + 8 * q^30 - 10 * q^31 - 4 * q^33 - 6 * q^34 - 9 * q^36 - 10 * q^37 - 26 * q^38 + 4 * q^39 - 62 * q^40 + 5 * q^41 + q^42 - q^43 + 15 * q^44 - 24 * q^46 - 37 * q^47 - 19 * q^48 + 12 * q^49 + 6 * q^50 + 3 * q^51 + 9 * q^52 + 9 * q^53 - q^54 + 9 * q^55 + 6 * q^56 + 3 * q^57 + 18 * q^58 + 6 * q^59 + 13 * q^60 + 19 * q^61 + 5 * q^62 + 6 * q^63 + 118 * q^64 + 48 * q^65 + 2 * q^66 + 8 * q^67 - 130 * q^68 - 10 * q^69 + 4 * q^70 - 19 * q^71 + 3 * q^72 + 24 * q^73 + 15 * q^74 + 32 * q^75 - 6 * q^76 - 8 * q^77 - 49 * q^78 + 27 * q^79 - 11 * q^80 - 6 * q^81 - 46 * q^82 + 70 * q^83 - 18 * q^84 - 59 * q^85 - 3 * q^86 - 22 * q^87 - 14 * q^88 - 4 * q^89 - 4 * q^90 + 2 * q^91 - 9 * q^92 + 5 * q^93 + 34 * q^94 - 55 * q^97 - q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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