LMFDB - Embedded newform 87.2.g.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			16.2
Root			$0.719749 + 0.902536i$ of defining polynomial
Character	$\chi$	$=$	87.16
Dual form			87.2.g.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04007 - 0.500870i) q^{2} +(-0.623490 + 0.781831i) q^{3} +(-0.416111 - 0.521786i) q^{4} +(3.10796 + 1.49671i) q^{5} +(1.04007 - 0.500870i) q^{6} +(2.81664 - 3.53195i) q^{7} +(0.685187 + 3.00200i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-2.48283 - 3.11337i) q^{10} +(0.123323 - 0.540315i) q^{11} +0.667390 q^{12} +(-0.614154 + 2.69078i) q^{13} +(-4.69854 + 2.26270i) q^{14} +(-3.10796 + 1.49671i) q^{15} +(0.493954 - 2.16416i) q^{16} -2.99688 q^{17} +(-0.256875 + 1.12544i) q^{18} +(-0.173453 - 0.217503i) q^{19} +(-0.512290 - 2.24449i) q^{20} +(1.00525 + 4.40427i) q^{21} +(-0.398892 + 0.500195i) q^{22} +(-0.836001 + 0.402597i) q^{23} +(-2.77426 - 1.33602i) q^{24} +(4.30181 + 5.39430i) q^{25} +(1.98649 - 2.49098i) q^{26} +(0.900969 + 0.433884i) q^{27} -3.01496 q^{28} +(-5.37860 + 0.265855i) q^{29} +3.98215 q^{30} +(-8.21748 - 3.95733i) q^{31} +(2.24199 - 2.81137i) q^{32} +(0.345544 + 0.433299i) q^{33} +(3.11696 + 1.50105i) q^{34} +(14.0403 - 6.76146i) q^{35} +(-0.416111 + 0.521786i) q^{36} +(1.52987 + 6.70278i) q^{37} +(0.0714618 + 0.313095i) q^{38} +(-1.72082 - 2.15784i) q^{39} +(-2.36360 + 10.3556i) q^{40} -2.85317 q^{41} +(1.16044 - 5.08423i) q^{42} +(10.1079 - 4.86770i) q^{43} +(-0.333245 + 0.160482i) q^{44} +(0.767603 - 3.36309i) q^{45} +1.07115 q^{46} +(-0.933590 + 4.09033i) q^{47} +(1.38403 + 1.73552i) q^{48} +(-2.98359 - 13.0720i) q^{49} +(-1.77233 - 7.76508i) q^{50} +(1.86853 - 2.34306i) q^{51} +(1.65957 - 0.799207i) q^{52} +(1.87299 + 0.901986i) q^{53} +(-0.719749 - 0.902536i) q^{54} +(1.19198 - 1.49470i) q^{55} +(12.5328 + 6.03550i) q^{56} +0.278196 q^{57} +(5.72726 + 2.41747i) q^{58} -14.2670 q^{59} +(2.07422 + 0.998892i) q^{60} +(-4.50873 + 5.65377i) q^{61} +(6.56462 + 8.23177i) q^{62} +(-4.07016 - 1.96009i) q^{63} +(-7.73992 + 3.72735i) q^{64} +(-5.93610 + 7.44363i) q^{65} +(-0.142363 - 0.623732i) q^{66} +(2.73383 + 11.9777i) q^{67} +(1.24704 + 1.56373i) q^{68} +(0.206475 - 0.904626i) q^{69} -17.9895 q^{70} +(0.530060 - 2.32234i) q^{71} +(2.77426 - 1.33602i) q^{72} +(0.822693 - 0.396188i) q^{73} +(1.76606 - 7.73761i) q^{74} -6.89956 q^{75} +(-0.0413145 + 0.181010i) q^{76} +(-1.56101 - 1.95744i) q^{77} +(0.708971 + 3.10621i) q^{78} +(-0.460193 - 2.01624i) q^{79} +(4.77431 - 5.98680i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(2.96749 + 1.42907i) q^{82} +(-6.83994 - 8.57702i) q^{83} +(1.87979 - 2.35719i) q^{84} +(-9.31420 - 4.48548i) q^{85} -12.9510 q^{86} +(3.14565 - 4.37092i) q^{87} +1.70652 q^{88} +(6.13283 + 2.95341i) q^{89} +(-2.48283 + 3.11337i) q^{90} +(7.77387 + 9.74812i) q^{91} +(0.557938 + 0.268689i) q^{92} +(8.21748 - 3.95733i) q^{93} +(3.01972 - 3.78661i) q^{94} +(-0.213544 - 0.935599i) q^{95} +(0.800159 + 3.50572i) q^{96} +(-2.19244 - 2.74924i) q^{97} +(-3.44422 + 15.0901i) q^{98} -0.554210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

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 $

$2$	−1.04007	−	0.500870i	−0.735438	−	0.354169i	0.0283821	−	0.999597i	$-0.490964\pi$
$2$	−1.04007	−	0.500870i	−0.735438	−	0.354169i	−0.763821	+	0.645429i	$0.776679\pi$
$3$	−0.623490	+	0.781831i	−0.359972	+	0.451391i
$3$	−0.623490	+	0.781831i	−0.359972	+	0.451391i
$4$	−0.416111	−	0.521786i	−0.208055	−	0.260893i
$5$	3.10796	+	1.49671i	1.38992	+	0.669351i	0.971090	−	0.238713i	$-0.0767255\pi$
$5$	3.10796	+	1.49671i	1.38992	+	0.669351i	0.418831	+	0.908064i	$0.362440\pi$
$6$	1.04007	−	0.500870i	0.424606	−	0.204479i
$7$	2.81664	−	3.53195i	1.06459	−	1.33495i	0.125187	−	0.992133i	$-0.460047\pi$
$7$	2.81664	−	3.53195i	1.06459	−	1.33495i	0.939402	−	0.342819i	$-0.111382\pi$
$8$	0.685187	+	3.00200i	0.242250	+	1.06137i
$9$	−0.222521	−	0.974928i	−0.0741736	−	0.324976i
$10$	−2.48283	−	3.11337i	−0.785139	−	0.984533i
$11$	0.123323	−	0.540315i	0.0371834	−	0.162911i	−0.952927	−	0.303198i	$-0.901946\pi$
$11$	0.123323	−	0.540315i	0.0371834	−	0.162911i	0.990111	+	0.140287i	$0.0448027\pi$
$12$	0.667390			0.192659
$13$	−0.614154	+	2.69078i	−0.170336	+	0.746289i	0.815525	+	0.578722i	$0.196448\pi$
$13$	−0.614154	+	2.69078i	−0.170336	+	0.746289i	−0.985861	+	0.167567i	$0.946409\pi$
$14$	−4.69854	+	2.26270i	−1.25574	+	0.604731i
$15$	−3.10796	+	1.49671i	−0.802472	+	0.386450i
$16$	0.493954	−	2.16416i	0.123489	−	0.541039i
$17$	−2.99688			−0.726851			−0.363426	−	0.931623i	$-0.618393\pi$
$17$	−2.99688			−0.726851			−0.363426	+	0.931623i	$0.618393\pi$
$18$	−0.256875	+	1.12544i	−0.0605461	+	0.265270i
$19$	−0.173453	−	0.217503i	−0.0397928	−	0.0498985i	0.761537	−	0.648122i	$-0.224445\pi$
$19$	−0.173453	−	0.217503i	−0.0397928	−	0.0498985i	−0.801330	+	0.598223i	$0.795874\pi$
$20$	−0.512290	−	2.24449i	−0.114552	−	0.501883i
$21$	1.00525	+	4.40427i	0.219363	+	0.961091i
$22$	−0.398892	+	0.500195i	−0.0850440	+	0.106642i
$23$	−0.836001	+	0.402597i	−0.174318	+	0.0839472i	−0.519008	−	0.854770i	$-0.673698\pi$
$23$	−0.836001	+	0.402597i	−0.174318	+	0.0839472i	0.344690	+	0.938717i	$0.387984\pi$
$24$	−2.77426	−	1.33602i	−0.566294	−	0.272713i
$25$	4.30181	+	5.39430i	0.860362	+	1.07886i
$26$	1.98649	−	2.49098i	0.389583	−	0.488522i
$27$	0.900969	+	0.433884i	0.173392	+	0.0835010i
$28$	−3.01496			−0.569773
$29$	−5.37860	+	0.265855i	−0.998781	+	0.0493681i
$29$	−5.37860	+	0.265855i	−0.998781	+	0.0493681i
$30$	3.98215			0.727037
$31$	−8.21748	−	3.95733i	−1.47590	−	0.710757i	−0.489031	−	0.872266i	$-0.662650\pi$
$31$	−8.21748	−	3.95733i	−1.47590	−	0.710757i	−0.986871	+	0.161509i	$0.948364\pi$
$32$	2.24199	−	2.81137i	0.396332	−	0.496985i
$33$	0.345544	+	0.433299i	0.0601515	+	0.0754276i
$34$	3.11696	+	1.50105i	0.534554	+	0.257428i
$35$	14.0403	−	6.76146i	2.37325	−	1.14290i
$36$	−0.416111	+	0.521786i	−0.0693518	+	0.0869644i
$37$	1.52987	+	6.70278i	0.251509	+	1.10193i	0.930069	+	0.367386i	$0.119747\pi$
$37$	1.52987	+	6.70278i	0.251509	+	1.10193i	−0.678560	+	0.734545i	$0.737396\pi$
$38$	0.0714618	+	0.313095i	0.0115926	+	0.0507907i
$39$	−1.72082	−	2.15784i	−0.275552	−	0.345531i
$40$	−2.36360	+	10.3556i	−0.373718	+	1.63737i
$41$	−2.85317			−0.445591			−0.222795	−	0.974865i	$-0.571518\pi$
$41$	−2.85317			−0.445591			−0.222795	+	0.974865i	$0.571518\pi$
$42$	1.16044	−	5.08423i	0.179060	−	0.784514i
$43$	10.1079	−	4.86770i	1.54144	−	0.742317i	0.546004	−	0.837783i	$-0.316148\pi$
$43$	10.1079	−	4.86770i	1.54144	−	0.742317i	0.995433	+	0.0954657i	$0.0304340\pi$
$44$	−0.333245	+	0.160482i	−0.0502386	+	0.0241936i
$45$	0.767603	−	3.36309i	0.114427	−	0.501339i
$46$	1.07115			0.157932
$47$	−0.933590	+	4.09033i	−0.136178	+	0.596635i	0.860076	+	0.510165i	$0.170416\pi$
$47$	−0.933590	+	4.09033i	−0.136178	+	0.596635i	−0.996254	+	0.0864700i	$0.972441\pi$
$48$	1.38403	+	1.73552i	0.199767	+	0.250500i
$49$	−2.98359	−	13.0720i	−0.426227	−	1.86742i
$50$	−1.77233	−	7.76508i	−0.250645	−	1.09815i
$51$	1.86853	−	2.34306i	0.261646	−	0.328094i
$52$	1.65957	−	0.799207i	0.230141	−	0.110830i
$53$	1.87299	+	0.901986i	0.257275	+	0.123897i	0.558076	−	0.829790i	$-0.311540\pi$
$53$	1.87299	+	0.901986i	0.257275	+	0.123897i	−0.300801	+	0.953687i	$0.597254\pi$
$54$	−0.719749	−	0.902536i	−0.0979454	−	0.122820i
$55$	1.19198	−	1.49470i	0.160727	−	0.201545i
$56$	12.5328	+	6.03550i	1.67477	+	0.806527i
$57$	0.278196			0.0368480
$58$	5.72726	+	2.41747i	0.752026	+	0.317429i
$59$	−14.2670			−1.85741			−0.928703	−	0.370824i	$-0.879075\pi$
$59$	−14.2670			−1.85741			−0.928703	+	0.370824i	$0.879075\pi$
$60$	2.07422	+	0.998892i	0.267781	+	0.128956i
$61$	−4.50873	+	5.65377i	−0.577284	+	0.723891i	−0.981647	−	0.190707i	$-0.938922\pi$
$61$	−4.50873	+	5.65377i	−0.577284	+	0.723891i	0.404363	+	0.914599i	$0.367493\pi$
$62$	6.56462	+	8.23177i	0.833708	+	1.04544i
$63$	−4.07016	−	1.96009i	−0.512792	−	0.246948i
$64$	−7.73992	+	3.72735i	−0.967490	+	0.465919i
$65$	−5.93610	+	7.44363i	−0.736282	+	0.923269i
$66$	−0.142363	−	0.623732i	−0.0175237	−	0.0767762i
$67$	2.73383	+	11.9777i	0.333990	+	1.46331i	0.811330	+	0.584588i	$0.198744\pi$
$67$	2.73383	+	11.9777i	0.333990	+	1.46331i	−0.477340	+	0.878719i	$0.658399\pi$
$68$	1.24704	+	1.56373i	0.151225	+	0.189631i
$69$	0.206475	−	0.904626i	0.0248567	−	0.108904i
$70$	−17.9895			−2.15015
$71$	0.530060	−	2.32234i	0.0629065	−	0.275611i	−0.933686	−	0.358092i	$-0.883427\pi$
$71$	0.530060	−	2.32234i	0.0629065	−	0.275611i	0.996593	+	0.0824811i	$0.0262844\pi$
$72$	2.77426	−	1.33602i	0.326950	−	0.157451i
$73$	0.822693	−	0.396188i	0.0962889	−	0.0463703i	−0.385119	−	0.922867i	$-0.625840\pi$
$73$	0.822693	−	0.396188i	0.0962889	−	0.0463703i	0.481408	+	0.876496i	$0.340125\pi$
$74$	1.76606	−	7.73761i	0.205300	−	0.899479i
$75$	−6.89956			−0.796693
$76$	−0.0413145	+	0.181010i	−0.00473909	+	0.0207633i
$77$	−1.56101	−	1.95744i	−0.177893	−	0.223071i
$78$	0.708971	+	3.10621i	0.0802752	+	0.351709i
$79$	−0.460193	−	2.01624i	−0.0517758	−	0.226845i	0.942420	−	0.334432i	$-0.108545\pi$
$79$	−0.460193	−	2.01624i	−0.0517758	−	0.226845i	−0.994196	+	0.107588i	$0.965687\pi$
$80$	4.77431	−	5.98680i	0.533784	−	0.669345i
$81$	−0.900969	+	0.433884i	−0.100108	+	0.0482093i
$82$	2.96749	+	1.42907i	0.327705	+	0.157814i
$83$	−6.83994	−	8.57702i	−0.750781	−	0.941450i	0.248852	−	0.968542i	$-0.419947\pi$
$83$	−6.83994	−	8.57702i	−0.750781	−	0.941450i	−0.999633	+	0.0270916i	$0.991375\pi$
$84$	1.87979	−	2.35719i	0.205102	−	0.257190i
$85$	−9.31420	−	4.48548i	−1.01027	−	0.486519i
$86$	−12.9510			−1.39654
$87$	3.14565	−	4.37092i	0.337249	−	0.468611i
$88$	1.70652			0.181916
$89$	6.13283	+	2.95341i	0.650078	+	0.313061i	0.729703	−	0.683764i	$-0.239658\pi$
$89$	6.13283	+	2.95341i	0.650078	+	0.313061i	−0.0796253	+	0.996825i	$0.525372\pi$
$90$	−2.48283	+	3.11337i	−0.261713	+	0.328178i
$91$	7.77387	+	9.74812i	0.814923	+	1.02188i
$92$	0.557938	+	0.268689i	0.0581691	+	0.0280128i
$93$	8.21748	−	3.95733i	0.852113	−	0.410356i
$94$	3.01972	−	3.78661i	0.311460	−	0.390559i
$95$	−0.213544	−	0.935599i	−0.0219092	−	0.0959904i
$96$	0.800159	+	3.50572i	0.0816658	+	0.357801i
$97$	−2.19244	−	2.74924i	−0.222609	−	0.279143i	0.657968	−	0.753046i	$-0.271416\pi$
$97$	−2.19244	−	2.74924i	−0.222609	−	0.279143i	−0.880577	+	0.473903i	$0.842845\pi$
$98$	−3.44422	+	15.0901i	−0.347918	+	1.52433i
$99$	−0.554210			−0.0557002
$100$	1.02464	−	4.48925i	0.102464	−	0.448925i
$101$	11.4159	−	5.49760i	1.13592	−	0.547032i	0.231147	−	0.972919i	$-0.425752\pi$
$101$	11.4159	−	5.49760i	1.13592	−	0.547032i	0.904776	+	0.425887i	$0.140038\pi$
$102$	−3.11696	+	1.50105i	−0.308625	+	0.148626i
$103$	−0.448946	+	1.96696i	−0.0442359	+	0.193810i	−0.992218	−	0.124514i	$-0.960263\pi$
$103$	−0.448946	+	1.96696i	−0.0442359	+	0.193810i	0.947982	+	0.318324i	$0.103120\pi$
$104$	−8.49854			−0.833350
$105$	−3.46767	+	15.1929i	−0.338410	+	1.48267i
$106$	−1.49626	−	1.87625i	−0.145330	−	0.182238i
$107$	0.127292	+	0.557702i	0.0123058	+	0.0539151i	0.980708	−	0.195478i	$-0.0626259\pi$
$107$	0.127292	+	0.557702i	0.0123058	+	0.0539151i	−0.968402	+	0.249393i	$0.919769\pi$
$108$	−0.148508	−	0.650657i	−0.0142902	−	0.0626095i
$109$	12.1384	−	15.2210i	1.16264	−	1.45791i	0.298682	−	0.954353i	$-0.403453\pi$
$109$	12.1384	−	15.2210i	1.16264	−	1.45791i	0.863962	−	0.503557i	$-0.167976\pi$
$110$	−1.98839	+	0.957557i	−0.189585	+	0.0912995i
$111$	−6.19430	−	2.98302i	−0.587937	−	0.283136i
$112$	−6.25240	−	7.84026i	−0.590797	−	0.740835i
$113$	1.51936	−	1.90522i	0.142929	−	0.179228i	−0.705214	−	0.708994i	$-0.749149\pi$
$113$	1.51936	−	1.90522i	0.142929	−	0.179228i	0.848143	+	0.529767i	$0.177721\pi$
$114$	−0.289343	−	0.139340i	−0.0270994	−	0.0130504i
$115$	−3.20083			−0.298479
$116$	2.37681	+	2.69585i	0.220681	+	0.250304i
$117$	2.75998			0.255160
$118$	14.8386	+	7.14592i	1.36601	+	0.657835i
$119$	−8.44114	+	10.5849i	−0.773798	+	0.970312i
$120$	−6.62267	−	8.30456i	−0.604564	−	0.758099i
$121$	9.63393	+	4.63945i	0.875811	+	0.421769i
$122$	7.52119	−	3.62201i	0.680936	−	0.327922i
$123$	1.77893	−	2.23070i	0.160400	−	0.201136i
$124$	1.35450	+	5.93446i	0.121638	+	0.532930i
$125$	1.45811	+	6.38840i	0.130417	+	0.571396i
$126$	3.25149	+	4.07724i	0.289666	+	0.363229i
$127$	2.04476	−	8.95869i	0.181443	−	0.794955i	−0.799501	−	0.600665i	$-0.794903\pi$
$127$	2.04476	−	8.95869i	0.181443	−	0.794955i	0.980944	−	0.194290i	$-0.0622403\pi$
$128$	2.72519			0.240875
$129$	−2.49644	+	10.9376i	−0.219799	+	0.963003i
$130$	9.90223	−	4.76866i	0.868483	−	0.418240i
$131$	11.7972	−	5.68123i	1.03073	−	0.496372i	0.159471	−	0.987203i	$-0.449021\pi$
$131$	11.7972	−	5.68123i	1.03073	−	0.496372i	0.871255	+	0.490831i	$0.163307\pi$
$132$	0.0823047	−	0.360601i	0.00716371	−	0.0313862i
$133$	−1.25676			−0.108975
$134$	3.15590	−	13.8269i	0.272628	−	1.19446i
$135$	2.15077	+	2.69699i	0.185109	+	0.232120i
$136$	−2.05343	−	8.99665i	−0.176080	−	0.771456i
$137$	1.69127	+	7.40992i	0.144495	+	0.633072i	0.994359	+	0.106070i	$0.0338268\pi$
$137$	1.69127	+	7.40992i	0.144495	+	0.633072i	−0.849864	+	0.527002i	$0.823316\pi$
$138$	−0.667848	+	0.837455i	−0.0568510	+	0.0712889i
$139$	−7.97635	+	3.84121i	−0.676545	+	0.325807i	−0.740414	−	0.672151i	$-0.765370\pi$
$139$	−7.97635	+	3.84121i	−0.676545	+	0.325807i	0.0638687	+	0.997958i	$0.479656\pi$
$140$	−9.37036	−	4.51253i	−0.791940	−	0.381378i
$141$	−2.61586	−	3.28019i	−0.220295	−	0.276242i
$142$	−1.71449	+	2.14990i	−0.143877	+	0.180416i
$143$	1.37813	+	0.663673i	0.115245	+	0.0554991i
$144$	−2.21981			−0.184984
$145$	−17.1144	−	7.22396i	−1.42127	−	0.599917i
$146$	−1.05409			−0.0872375
$147$	12.0803	+	5.81757i	0.996366	+	0.479825i
$148$	2.86083	−	3.58736i	0.235159	−	0.294879i
$149$	4.96925	+	6.23124i	0.407097	+	0.510483i	0.942542	−	0.334087i	$-0.108428\pi$
$149$	4.96925	+	6.23124i	0.407097	+	0.510483i	−0.535446	+	0.844570i	$0.679856\pi$
$150$	7.17601	+	3.45578i	0.585919	+	0.282164i
$151$	0.0950717	−	0.0457841i	0.00773683	−	0.00372586i	−0.430011	−	0.902823i	$-0.641490\pi$
$151$	0.0950717	−	0.0457841i	0.00773683	−	0.00372586i	0.437748	+	0.899098i	$0.355776\pi$
$152$	0.534096	−	0.669735i	0.0433209	−	0.0543226i
$153$	0.666870	+	2.92175i	0.0539132	+	0.236209i
$154$	0.643129	+	2.81773i	0.0518248	+	0.227059i
$155$	−19.6166	−	24.5984i	−1.57564	−	1.97579i
$156$	−0.409880	+	1.79580i	−0.0328167	+	0.143779i
$157$	−13.5037			−1.07771			−0.538857	−	0.842397i	$-0.681144\pi$
$157$	−13.5037			−1.07771			−0.538857	+	0.842397i	$0.681144\pi$
$158$	−0.531241	+	2.32752i	−0.0422633	+	0.185168i
$159$	−1.87299	+	0.901986i	−0.148538	+	0.0715321i
$160$	11.1758	−	5.38201i	0.883528	−	0.425485i
$161$	−0.932758	+	4.08668i	−0.0735117	+	0.322076i
$162$	1.15439			0.0906972
$163$	0.581624	−	2.54826i	0.0455563	−	0.199595i	−0.947028	−	0.321150i	$-0.895931\pi$
$163$	0.581624	−	2.54826i	0.0455563	−	0.199595i	0.992585	+	0.121554i	$0.0387879\pi$
$164$	1.18724	+	1.48875i	0.0927076	+	0.116252i
$165$	0.425413	+	1.86386i	0.0331184	+	0.145101i
$166$	2.81803	+	12.3466i	0.218722	+	0.958282i
$167$	−6.37129	+	7.98935i	−0.493026	+	0.618235i	−0.964640	−	0.263570i	$-0.915100\pi$
$167$	−6.37129	+	7.98935i	−0.493026	+	0.618235i	0.471615	+	0.881805i	$0.343671\pi$
$168$	−12.5328	+	6.03550i	−0.966929	+	0.465649i
$169$	4.84946	+	2.33538i	0.373036	+	0.179645i
$170$	7.44075	+	9.33040i	0.570679	+	0.715609i
$171$	−0.173453	+	0.217503i	−0.0132643	+	0.0166328i
$172$	−6.74589	−	3.24865i	−0.514370	−	0.247707i
$173$	23.0919			1.75564			0.877822	−	0.478987i	$-0.158996\pi$
$173$	23.0919			1.75564			0.877822	+	0.478987i	$0.158996\pi$
$174$	−5.46094	+	2.97049i	−0.413993	+	0.225192i
$175$	31.1690			2.35616
$176$	−1.10841	−	0.533782i	−0.0835495	−	0.0402353i
$177$	8.89533	−	11.1544i	0.668614	−	0.838416i
$178$	−4.89927	−	6.14350i	−0.367216	−	0.460474i
$179$	−13.3241	−	6.41655i	−0.995891	−	0.479596i	−0.136349	−	0.990661i	$-0.543537\pi$
$179$	−13.3241	−	6.41655i	−0.995891	−	0.479596i	−0.859542	+	0.511065i	$0.829251\pi$
$180$	−2.07422	+	0.998892i	−0.154603	+	0.0744530i
$181$	1.80146	−	2.25895i	0.133901	−	0.167907i	−0.710360	−	0.703838i	$-0.751468\pi$
$181$	1.80146	−	2.25895i	0.133901	−	0.167907i	0.844261	+	0.535931i	$0.180039\pi$
$182$	−3.20280	−	14.0324i	−0.237408	−	1.04015i
$183$	−1.60915	−	7.05014i	−0.118952	−	0.521161i
$184$	−1.78141	−	2.23382i	−0.131327	−	0.164679i
$185$	−5.27739	+	23.1218i	−0.388001	+	1.69994i
$186$	−10.5288			−0.772012
$187$	−0.369586	+	1.61926i	−0.0270268	+	0.118412i
$188$	2.52275	−	1.21489i	0.183991	−	0.0886052i
$189$	4.07016	−	1.96009i	0.296060	−	0.142575i
$190$	−0.246513	+	1.08004i	−0.0178839	+	0.0783546i
$191$	−4.66376			−0.337458			−0.168729	−	0.985663i	$-0.553966\pi$
$191$	−4.66376			−0.337458			−0.168729	+	0.985663i	$0.553966\pi$
$192$	1.91160	−	8.37528i	0.137958	−	0.604433i
$193$	−9.09293	−	11.4022i	−0.654523	−	0.820746i	0.338212	−	0.941070i	$-0.390178\pi$
$193$	−9.09293	−	11.4022i	−0.654523	−	0.820746i	−0.992735	+	0.120324i	$0.961607\pi$
$194$	0.903278	+	3.95752i	0.0648516	+	0.284133i
$195$	−2.11857	−	9.28206i	−0.151714	−	0.664702i
$196$	−5.57926	+	6.99618i	−0.398519	+	0.499727i
$197$	−2.60517	+	1.25458i	−0.185611	+	0.0893855i	−0.524381	−	0.851484i	$-0.675703\pi$
$197$	−2.60517	+	1.25458i	−0.185611	+	0.0893855i	0.338770	+	0.940869i	$0.389989\pi$
$198$	0.576415	+	0.277587i	0.0409641	+	0.0197273i
$199$	2.52561	+	3.16701i	0.179036	+	0.224504i	0.863249	−	0.504778i	$-0.168426\pi$
$199$	2.52561	+	3.16701i	0.179036	+	0.224504i	−0.684213	+	0.729282i	$0.739854\pi$
$200$	−13.2461	+	16.6101i	−0.936643	+	1.17451i
$201$	−11.0690	−	5.33057i	−0.780750	−	0.375989i
$202$	−14.6269			−1.02914
$203$	−14.2106	+	19.7458i	−0.997387	+	1.38588i
$204$	−2.00009			−0.140034
$205$	−8.86755	−	4.27039i	−0.619336	−	0.298257i
$206$	1.45212	−	1.82091i	0.101174	−	0.126869i
$207$	0.578530	+	0.725454i	0.0402106	+	0.0504225i
$208$	5.51991	+	2.65825i	0.382737	+	0.184316i
$209$	−0.138911	+	0.0668958i	−0.00960865	+	0.00462728i
$210$	11.2163	−	14.0647i	0.773995	−	0.970559i
$211$	2.93029	+	12.8385i	0.201730	+	0.883836i	0.969883	+	0.243570i	$0.0783186\pi$
$211$	2.93029	+	12.8385i	0.201730	+	0.883836i	−0.768154	+	0.640266i	$0.778824\pi$
$212$	−0.308728	−	1.35263i	−0.0212036	−	0.0928989i
$213$	1.48519	+	1.86237i	0.101764	+	0.127608i
$214$	0.146944	−	0.643805i	0.0100449	−	0.0440096i
$215$	38.7004			2.63935
$216$	−0.685187	+	3.00200i	−0.0466211	+	0.204260i
$217$	−37.1227	+	17.8774i	−2.52006	+	1.21360i
$218$	−20.2485	+	9.75115i	−1.37140	+	0.660431i
$219$	−0.203188	+	0.890227i	−0.0137302	+	0.0601559i
$220$	−1.27591			−0.0860217
$221$	1.84055	−	8.06397i	0.123809	−	0.542441i
$222$	4.94839	+	6.20508i	0.332114	+	0.416458i
$223$	3.39933	+	14.8934i	0.227636	+	0.997338i	0.951561	+	0.307459i	$0.0994788\pi$
$223$	3.39933	+	14.8934i	0.227636	+	0.997338i	−0.723925	+	0.689878i	$0.757664\pi$
$224$	−3.61474	−	15.8372i	−0.241520	−	1.05817i
$225$	4.30181	−	5.39430i	0.286787	−	0.359620i
$226$	−2.53450	+	1.22055i	−0.168593	+	0.0811899i
$227$	13.2896	+	6.39993i	0.882061	+	0.424778i	0.819377	−	0.573255i	$-0.194320\pi$
$227$	13.2896	+	6.39993i	0.882061	+	0.424778i	0.0626842	+	0.998033i	$0.480034\pi$
$228$	−0.115761	−	0.145159i	−0.00766643	−	0.00961340i
$229$	6.46791	−	8.11051i	0.427412	−	0.535957i	−0.520765	−	0.853700i	$-0.674353\pi$
$229$	6.46791	−	8.11051i	0.427412	−	0.535957i	0.948177	+	0.317742i	$0.102925\pi$
$230$	3.32908	+	1.60320i	0.219513	+	0.105712i
$231$	2.50366			0.164729
$232$	−4.48344	−	15.9644i	−0.294352	−	1.04811i
$233$	0.280226			0.0183582			0.00917911	−	0.999958i	$-0.497078\pi$
$233$	0.280226			0.0183582			0.00917911	+	0.999958i	$0.497078\pi$
$234$	−2.87057	−	1.38239i	−0.187655	−	0.0903698i
$235$	−9.02361	+	11.3152i	−0.588635	+	0.738125i
$236$	5.93666	+	7.44433i	0.386443	+	0.484585i
$237$	1.86329	+	0.897311i	0.121033	+	0.0582866i
$238$	14.0810	−	6.78104i	0.912734	−	0.439550i
$239$	4.01459	−	5.03414i	0.259682	−	0.325631i	−0.634849	−	0.772636i	$-0.718938\pi$
$239$	4.01459	−	5.03414i	0.259682	−	0.325631i	0.894532	+	0.447005i	$0.147509\pi$
$240$	1.70393	+	7.46542i	0.109988	+	0.481891i
$241$	3.43240	+	15.0383i	0.221101	+	0.968705i	0.956651	+	0.291235i	$0.0940663\pi$
$241$	3.43240	+	15.0383i	0.221101	+	0.968705i	−0.735551	+	0.677470i	$0.763077\pi$
$242$	−7.69617	−	9.65069i	−0.494728	−	0.620370i
$243$	0.222521	−	0.974928i	0.0142747	−	0.0625417i
$244$	4.82619			0.308965
$245$	10.2921	−	45.0927i	0.657539	−	2.88087i
$246$	−2.96749	+	1.42907i	−0.189200	+	0.0911141i
$247$	0.691779	−	0.333143i	0.0440169	−	0.0211974i
$248$	6.24939	−	27.3804i	0.396837	−	1.73866i
$249$	10.9704			0.695222
$250$	1.68322	−	7.37469i	0.106456	−	0.466416i
$251$	−2.05218	−	2.57336i	−0.129533	−	0.162429i	0.712836	−	0.701331i	$-0.247411\pi$
$251$	−2.05218	−	2.57336i	−0.129533	−	0.162429i	−0.842368	+	0.538902i	$0.818839\pi$
$252$	0.670891	+	2.93937i	0.0422622	+	0.185163i
$253$	0.114431	+	0.501353i	0.00719419	+	0.0315198i
$254$	−6.61383	+	8.29347i	−0.414988	+	0.520379i
$255$	9.31420	−	4.48548i	0.583278	−	0.280892i
$256$	12.6455	+	6.08973i	0.790341	+	0.380608i
$257$	−0.246680	−	0.309326i	−0.0153874	−	0.0192953i	0.774078	−	0.633090i	$-0.218214\pi$
$257$	−0.246680	−	0.309326i	−0.0153874	−	0.0192953i	−0.789466	+	0.613795i	$0.789642\pi$
$258$	8.07479	−	10.1255i	0.502714	−	0.630384i
$259$	27.9830	+	13.4759i	1.73878	+	0.837351i
$260$	6.35406			0.394062
$261$	1.45604	+	5.18459i	0.0901266	+	0.320918i
$262$	−15.1154			−0.933835
$263$	7.33709	+	3.53336i	0.452425	+	0.217876i	0.646198	−	0.763170i	$-0.276358\pi$
$263$	7.33709	+	3.53336i	0.452425	+	0.217876i	−0.193773	+	0.981046i	$0.562073\pi$
$264$	−1.06400	+	1.33421i	−0.0654847	+	0.0821152i
$265$	4.47117	+	5.60667i	0.274662	+	0.344415i
$266$	1.30712	+	0.629474i	0.0801445	+	0.0385955i
$267$	−6.13283	+	2.95341i	−0.375323	+	0.180746i
$268$	5.11222	−	6.41052i	0.312278	−	0.391585i
$269$	−1.99769	−	8.75246i	−0.121801	−	0.533647i	−0.998605	−	0.0527984i	$-0.983186\pi$
$269$	−1.99769	−	8.75246i	−0.121801	−	0.533647i	0.876804	−	0.480848i	$-0.159671\pi$
$270$	−0.886111	−	3.88230i	−0.0539270	−	0.236270i
$271$	3.14213	+	3.94011i	0.190871	+	0.239344i	0.868054	−	0.496470i	$-0.165371\pi$
$271$	3.14213	+	3.94011i	0.190871	+	0.239344i	−0.677183	+	0.735815i	$0.736799\pi$
$272$	−1.48032	+	6.48573i	−0.0897579	+	0.393255i
$273$	−12.4683			−0.754617
$274$	1.95238	−	8.55391i	0.117947	−	0.516761i
$275$	3.44513	−	1.65909i	0.207749	−	0.100047i
$276$	−0.557938	+	0.268689i	−0.0335839	+	0.0161732i
$277$	−0.452859	+	1.98410i	−0.0272097	+	0.119213i	−0.986709	−	0.162498i	$-0.948045\pi$
$277$	−0.452859	+	1.98410i	−0.0272097	+	0.119213i	0.959499	+	0.281711i	$0.0909020\pi$
$278$	10.2199			0.612948
$279$	−2.02955	+	8.89204i	−0.121506	+	0.532352i
$280$	29.9181	+	37.5162i	1.78795	+	2.24202i
$281$	−5.30139	−	23.2269i	−0.316255	−	1.38560i	−0.844065	−	0.536240i	$-0.819844\pi$
$281$	−5.30139	−	23.2269i	−0.316255	−	1.38560i	0.527811	−	0.849362i	$-0.323013\pi$
$282$	1.07772	+	4.72182i	0.0641776	+	0.281180i
$283$	−9.34352	+	11.7164i	−0.555414	+	0.696468i	−0.977703	−	0.209994i	$-0.932656\pi$
$283$	−9.34352	+	11.7164i	−0.555414	+	0.696468i	0.422288	+	0.906462i	$0.361227\pi$
$284$	−1.43233	+	0.689774i	−0.0849932	+	0.0409306i
$285$	0.864623	+	0.416381i	0.0512159	+	0.0246643i
$286$	−1.10093	−	1.38053i	−0.0650996	−	0.0816323i
$287$	−8.03636	+	10.0773i	−0.474371	+	0.594843i
$288$	−3.23978	−	1.56019i	−0.190906	−	0.0919353i
$289$	−8.01868			−0.471687
$290$	14.1818	+	16.0855i	0.832786	+	0.944572i
$291$	3.51641			0.206135
$292$	−0.549057	−	0.264412i	−0.0321311	−	0.0154735i
$293$	18.9354	−	23.7443i	1.10622	−	1.38715i	0.192261	−	0.981344i	$-0.438418\pi$
$293$	18.9354	−	23.7443i	1.10622	−	1.38715i	0.913957	−	0.405810i	$-0.133011\pi$
$294$	−9.65048	−	12.1013i	−0.562827	−	0.705763i
$295$	−44.3413	−	21.3536i	−2.58165	−	1.24326i
$296$	−19.0735	+	9.18532i	−1.10863	+	0.533886i
$297$	0.345544	−	0.433299i	0.0200505	−	0.0251425i
$298$	−2.04731	−	8.96985i	−0.118598	−	0.519610i
$299$	−0.569868	−	2.49675i	−0.0329563	−	0.144391i
$300$	2.87098	+	3.60010i	0.165756	+	0.207852i
$301$	11.2778	−	49.4111i	0.650039	−	2.84801i
$302$	−0.121813			−0.00700954
$303$	−2.81949	+	12.3530i	−0.161976	+	0.709662i
$304$	−0.556387	+	0.267942i	−0.0319110	+	0.0153675i
$305$	−22.4750	+	10.8234i	−1.28692	+	0.619746i
$306$	0.769826	−	3.37283i	0.0440080	−	0.192812i
$307$	2.10479			0.120127			0.0600635	−	0.998195i	$-0.480870\pi$
$307$	2.10479			0.120127			0.0600635	+	0.998195i	$0.480870\pi$
$308$	−0.371814	+	1.62903i	−0.0211861	+	0.0928223i
$309$	−1.25792	−	1.57738i	−0.0715604	−	0.0897339i
$310$	8.08196	+	35.4094i	0.459025	+	2.01112i
$311$	−3.75530	−	16.4530i	−0.212943	−	0.932965i	−0.962555	−	0.271087i	$-0.912617\pi$
$311$	−3.75530	−	16.4530i	−0.212943	−	0.932965i	0.749611	−	0.661878i	$-0.230240\pi$
$312$	5.29875	−	6.64443i	0.299983	−	0.376167i
$313$	−13.3609	+	6.43428i	−0.755203	+	0.363687i	−0.771541	−	0.636180i	$-0.780514\pi$
$313$	−13.3609	+	6.43428i	−0.755203	+	0.363687i	0.0163375	+	0.999867i	$0.494799\pi$
$314$	14.0448	+	6.76361i	0.792593	+	0.381693i
$315$	−9.71620	−	12.1837i	−0.547446	−	0.686475i
$316$	−0.860555	+	1.07910i	−0.0484100	+	0.0607042i
$317$	4.96094	+	2.38906i	0.278634	+	0.134183i	0.567982	−	0.823041i	$-0.307724\pi$
$317$	4.96094	+	2.38906i	0.278634	+	0.134183i	−0.289348	+	0.957224i	$0.593439\pi$
$318$	2.39981			0.134575
$319$	−0.519661	+	2.93892i	−0.0290954	+	0.164548i
$320$	−29.6341			−1.65660
$321$	−0.515395	−	0.248201i	−0.0287665	−	0.0138532i
$322$	3.01703	−	3.78323i	0.168132	−	0.210831i
$323$	0.519818	+	0.651831i	0.0289234	+	0.0362688i
$324$	0.601297	+	0.289570i	0.0334054	+	0.0160872i
$325$	−17.1569	+	8.26231i	−0.951691	+	0.458310i
$326$	−1.88127	+	2.35904i	−0.104194	+	0.130655i
$327$	4.33213	+	18.9803i	0.239567	+	1.04961i
$328$	−1.95496	−	8.56523i	−0.107944	−	0.472936i
$329$	11.8172	+	14.8184i	0.651506	+	0.816963i
$330$	0.491091	−	2.15161i	0.0270337	−	0.118442i
$331$	−5.88833			−0.323652			−0.161826	−	0.986819i	$-0.551738\pi$
$331$	−5.88833			−0.323652			−0.161826	+	0.986819i	$0.551738\pi$
$332$	−1.62920	+	7.13798i	−0.0894138	+	0.391747i
$333$	6.19430	−	2.98302i	0.339446	−	0.163468i
$334$	10.6282	−	5.11827i	0.581549	−	0.280059i
$335$	−9.43054	+	41.3179i	−0.515246	+	2.25744i
$336$	10.0281			0.547076
$337$	−3.87848	+	16.9927i	−0.211274	+	0.925652i	0.752428	+	0.658674i	$0.228882\pi$
$337$	−3.87848	+	16.9927i	−0.211274	+	0.925652i	−0.963703	+	0.266978i	$0.913975\pi$
$338$	−3.87405	−	4.85790i	−0.210720	−	0.264235i
$339$	0.542253	+	2.37577i	0.0294512	+	0.129034i
$340$	1.53527	+	6.72648i	0.0832619	+	0.364794i
$341$	−3.15161	+	3.95199i	−0.170669	+	0.214012i
$342$	0.289343	−	0.139340i	0.0156459	−	0.00753466i
$343$	−26.0821	−	12.5605i	−1.40830	−	0.678201i
$344$	21.5386	+	27.0086i	1.16128	+	1.45620i
$345$	1.99568	−	2.50251i	0.107444	−	0.134731i
$346$	−24.0171	−	11.5660i	−1.29117	−	0.621794i
$347$	−2.81562			−0.151150			−0.0755751	−	0.997140i	$-0.524079\pi$
$347$	−2.81562			−0.151150			−0.0755751	+	0.997140i	$0.524079\pi$
$348$	−3.58962	+	0.177429i	−0.192424	+	0.00951120i
$349$	23.4949			1.25765			0.628826	−	0.777546i	$-0.283536\pi$
$349$	23.4949			1.25765			0.628826	+	0.777546i	$0.283536\pi$
$350$	−32.4179	−	15.6116i	−1.73281	−	0.834477i
$351$	−1.72082	+	2.15784i	−0.0918506	+	0.115177i
$352$	−1.24254	−	1.55809i	−0.0662274	−	0.0830465i
$353$	−14.5563	−	7.00993i	−0.774752	−	0.373101i	0.00435584	−	0.999991i	$-0.498613\pi$
$353$	−14.5563	−	7.00993i	−0.774752	−	0.373101i	−0.779108	+	0.626889i	$0.784328\pi$
$354$	−14.8386	+	7.14592i	−0.788665	+	0.379801i
$355$	5.12329	−	6.42440i	0.271916	−	0.340972i
$356$	−1.01088	−	4.42897i	−0.0535767	−	0.234735i
$357$	−3.01261	−	13.1991i	−0.159444	−	0.698570i
$358$	10.6441	+	13.3473i	0.562559	+	0.705426i
$359$	1.92263	−	8.42361i	0.101473	−	0.444581i	−0.898511	−	0.438950i	$-0.855350\pi$
$359$	1.92263	−	8.42361i	0.101473	−	0.444581i	0.999984	−	0.00563099i	$-0.00179241\pi$
$360$	10.6219			0.559825
$361$	4.21068	−	18.4482i	0.221615	−	0.970957i
$362$	−3.00508	+	1.44717i	−0.157943	+	0.0760615i
$363$	−9.63393	+	4.63945i	−0.505650	+	0.243508i
$364$	1.85165	−	8.11260i	0.0970527	−	0.425216i
$365$	3.14988			0.164872
$366$	−1.85758	+	8.13859i	−0.0970973	+	0.425411i
$367$	8.38364	+	10.5127i	0.437622	+	0.548761i	0.950915	−	0.309453i	$-0.100146\pi$
$367$	8.38364	+	10.5127i	0.437622	+	0.548761i	−0.513293	+	0.858214i	$0.671574\pi$
$368$	0.458336	+	2.00810i	0.0238924	+	0.104679i
$369$	0.634891	+	2.78164i	0.0330511	+	0.144806i
$370$	17.0698	−	21.4049i	0.887418	−	1.11279i
$371$	8.46131	−	4.07475i	0.439289	−	0.211551i
$372$	−5.48426	−	2.64108i	−0.284346	−	0.136934i
$373$	−1.99095	−	2.49657i	−0.103088	−	0.129268i	0.727611	−	0.685989i	$-0.240630\pi$
$373$	−1.99095	−	2.49657i	−0.103088	−	0.129268i	−0.830699	+	0.556722i	$0.812059\pi$
$374$	1.19543	−	1.49903i	0.0618144	−	0.0775128i
$375$	−5.90377	−	2.84310i	−0.304869	−	0.146817i
$376$	−12.9188			−0.666238
$377$	2.58793	−	14.6359i	0.133285	−	0.753788i
$378$	−5.21499			−0.268230
$379$	14.8677	+	7.15991i	0.763703	+	0.367780i	0.774839	−	0.632158i	$-0.217831\pi$
$379$	14.8677	+	7.15991i	0.763703	+	0.367780i	−0.0111367	+	0.999938i	$0.503545\pi$
$380$	−0.399325	+	0.500737i	−0.0204849	+	0.0256873i
$381$	5.72929	+	7.18431i	0.293521	+	0.368063i
$382$	4.85062	+	2.33594i	0.248179	+	0.119517i
$383$	−1.42189	+	0.684747i	−0.0726553	+	0.0349889i	−0.469859	−	0.882742i	$-0.655695\pi$
$383$	−1.42189	+	0.684747i	−0.0726553	+	0.0349889i	0.397203	+	0.917731i	$0.369981\pi$
$384$	−1.69913	+	2.13064i	−0.0867083	+	0.108729i
$385$	−1.92182	−	8.42003i	−0.0979449	−	0.429125i
$386$	3.74625	+	16.4134i	0.190679	+	0.835420i
$387$	−6.99487	−	8.77129i	−0.355569	−	0.445870i
$388$	−0.522215	+	2.28797i	−0.0265114	+	0.116154i
$389$	−14.0108			−0.710375			−0.355188	−	0.934795i	$-0.615583\pi$
$389$	−14.0108			−0.710375			−0.355188	+	0.934795i	$0.615583\pi$
$390$	−2.44565	+	10.7151i	−0.123840	+	0.542580i
$391$	2.50540	−	1.20654i	0.126703	−	0.0610171i
$392$	37.1977	−	17.9135i	1.87877	−	0.904766i
$393$	−2.91367	+	12.7656i	−0.146975	+	0.643940i
$394$	3.33794			0.168163
$395$	1.58747	−	6.95517i	0.0798744	−	0.349952i
$396$	0.230613	+	0.289179i	0.0115887	+	0.0145318i
$397$	−5.32177	−	23.3162i	−0.267092	−	1.17021i	−0.913378	−	0.407112i	$-0.866536\pi$
$397$	−5.32177	−	23.3162i	−0.267092	−	1.17021i	0.646286	−	0.763095i	$-0.276321\pi$
$398$	−1.04054	−	4.55891i	−0.0521576	−	0.228517i
$399$	0.783578	−	0.982576i	0.0392280	−	0.0491903i
$400$	13.7990	−	6.64525i	0.689950	−	0.332262i
$401$	32.3263	+	15.5675i	1.61430	+	0.777406i	0.999933	−	0.0116132i	$-0.00369666\pi$
$401$	32.3263	+	15.5675i	1.61430	+	0.777406i	0.614368	+	0.789019i	$0.289411\pi$
$402$	8.84263	+	11.0883i	0.441030	+	0.553034i
$403$	15.6951	−	19.6810i	0.781829	−	0.980383i
$404$	−7.61885	−	3.66904i	−0.379052	−	0.182542i
$405$	−3.44957			−0.171411
$406$	24.6700	−	13.4193i	1.22435	−	0.665987i
$407$	3.81028			0.188869
$408$	8.31415	+	4.00388i	0.411612	+	0.198222i
$409$	9.36367	−	11.7417i	0.463004	−	0.580588i	−0.494439	−	0.869212i	$-0.664626\pi$
$409$	9.36367	−	11.7417i	0.463004	−	0.580588i	0.957442	+	0.288624i	$0.0931978\pi$
$410$	7.08394	+	8.88298i	0.349851	+	0.438699i
$411$	−6.84779	−	3.29772i	−0.337777	−	0.162665i
$412$	1.21314	−	0.584219i	0.0597673	−	0.0287824i
$413$	−40.1850	+	50.3904i	−1.97737	+	2.47955i
$414$	−0.238352	−	1.04429i	−0.0117144	−	0.0513240i
$415$	−8.42092	−	36.8945i	−0.413367	−	1.81108i
$416$	6.18786	+	7.75934i	0.303385	+	0.380433i
$417$	1.97000	−	8.63111i	0.0964711	−	0.422667i
$418$	0.177983			0.00870541
$419$	−8.22309	+	36.0277i	−0.401724	+	1.76007i	0.218691	+	0.975794i	$0.429821\pi$
$419$	−8.22309	+	36.0277i	−0.401724	+	1.76007i	−0.620415	+	0.784274i	$0.713036\pi$
$420$	9.37036	−	4.51253i	0.457227	−	0.220189i
$421$	−1.15916	+	0.558222i	−0.0564940	+	0.0272061i	−0.461917	−	0.886923i	$-0.652838\pi$
$421$	−1.15916	+	0.558222i	−0.0564940	+	0.0272061i	0.405423	+	0.914129i	$0.367124\pi$
$422$	3.38269	−	14.8206i	0.164667	−	0.721453i
$423$	4.19552			0.203993
$424$	−1.42441	+	6.24075i	−0.0691755	+	0.303078i
$425$	−12.8920	−	16.1661i	−0.625355	−	0.784170i
$426$	−0.611894	−	2.68088i	−0.0296464	−	0.129889i
$427$	7.26938	+	31.8492i	0.351790	+	1.54129i
$428$	0.238034	−	0.298485i	0.0115058	−	0.0144278i
$429$	−1.37813	+	0.663673i	−0.0665368	+	0.0320424i
$430$	−40.2510	−	19.3839i	−1.94108	−	0.934774i
$431$	−15.7634	−	19.7667i	−0.759298	−	0.952130i	0.240531	−	0.970642i	$-0.422679\pi$
$431$	−15.7634	−	19.7667i	−0.759298	−	0.952130i	−0.999829	+	0.0185118i	$0.994107\pi$
$432$	1.38403	−	1.73552i	0.0665892	−	0.0835002i
$433$	9.33295	+	4.49451i	0.448513	+	0.215993i	0.644485	−	0.764617i	$-0.277072\pi$
$433$	9.33295	+	4.49451i	0.448513	+	0.215993i	−0.195972	+	0.980610i	$0.562786\pi$
$434$	47.5644			2.28316
$435$	16.3186	−	8.87649i	0.782415	−	0.425595i
$436$	−12.9930			−0.622253
$437$	0.232572	+	0.112001i	0.0111254	+	0.00535773i
$438$	0.657217	−	0.824124i	0.0314031	−	0.0393782i
$439$	−8.35161	−	10.4726i	−0.398601	−	0.499829i	0.541512	−	0.840693i	$-0.317852\pi$
$439$	−8.35161	−	10.4726i	−0.398601	−	0.499829i	−0.940113	+	0.340864i	$0.889281\pi$
$440$	5.30381	+	2.55418i	0.252849	+	0.121766i
$441$	−12.0803	+	5.81757i	−0.575252	+	0.277027i
$442$	−5.95329	+	7.46519i	−0.283169	+	0.355083i
$443$	−6.85215	−	30.0213i	−0.325556	−	1.42635i	−0.827506	−	0.561456i	$-0.810241\pi$
$443$	−6.85215	−	30.0213i	−0.325556	−	1.42635i	0.501951	−	0.864896i	$-0.332616\pi$
$444$	1.02102	+	4.47337i	0.0484553	+	0.212297i
$445$	14.6402	+	18.3582i	0.694010	+	0.870261i
$446$	3.92414	−	17.1928i	0.185813	−	0.814102i
$447$	−7.97006			−0.376971
$448$	−8.63573	+	37.8356i	−0.408000	+	1.78756i
$449$	−5.54036	+	2.66810i	−0.261466	+	0.125915i	−0.560025	−	0.828476i	$-0.689208\pi$
$449$	−5.54036	+	2.66810i	−0.261466	+	0.125915i	0.298559	+	0.954391i	$0.403494\pi$
$450$	−7.17601	+	3.45578i	−0.338280	+	0.162907i
$451$	−0.351863	+	1.54161i	−0.0165686	+	0.0725917i
$452$	−1.62634			−0.0764965
$453$	−0.0234808	+	0.102876i	−0.00110322	+	0.00483354i
$454$	−10.6165	−	13.3127i	−0.498259	−	0.624797i
$455$	9.57071	+	41.9320i	0.448682	+	1.96580i
$456$	0.190616	+	0.835145i	0.00892643	+	0.0391093i
$457$	−10.6275	+	13.3265i	−0.497134	+	0.623386i	−0.965580	−	0.260106i	$-0.916242\pi$
$457$	−10.6275	+	13.3265i	−0.497134	+	0.623386i	0.468446	+	0.883492i	$0.344814\pi$
$458$	−10.7894	+	5.19589i	−0.504154	+	0.242788i
$459$	−2.70010	−	1.30030i	−0.126030	−	0.0606928i
$460$	1.33190	+	1.67015i	0.0621001	+	0.0778711i
$461$	−10.3278	+	12.9506i	−0.481012	+	0.603170i	−0.961829	−	0.273651i	$-0.911769\pi$
$461$	−10.3278	+	12.9506i	−0.481012	+	0.603170i	0.480817	+	0.876821i	$0.340340\pi$
$462$	−2.60398	−	1.25401i	−0.121148	−	0.0583418i
$463$	28.9072			1.34343			0.671715	−	0.740809i	$-0.265558\pi$
$463$	28.9072			1.34343			0.671715	+	0.740809i	$0.265558\pi$
$464$	−2.08143	+	11.7714i	−0.0966280	+	0.546476i
$465$	31.4626			1.45904
$466$	−0.291454	−	0.140357i	−0.0135013	−	0.00650190i
$467$	14.1479	−	17.7409i	0.654688	−	0.820953i	−0.338065	−	0.941123i	$-0.609772\pi$
$467$	14.1479	−	17.7409i	0.654688	−	0.820953i	0.992753	+	0.120170i	$0.0383438\pi$
$468$	−1.14846	−	1.44012i	−0.0530875	−	0.0665696i
$469$	50.0048	+	24.0810i	2.30901	+	1.11196i
$470$	15.0526	−	7.24896i	0.694326	−	0.334370i
$471$	8.41944	−	10.5576i	0.387947	−	0.486470i
$472$	−9.77556	−	42.8295i	−0.449957	−	1.97139i
$473$	−1.38355	−	6.06173i	−0.0636158	−	0.278719i
$474$	−1.48851	−	1.86653i	−0.0683693	−	0.0857324i
$475$	0.427114	−	1.87131i	0.0195973	−	0.0858616i
$476$	9.03548			0.414140
$477$	0.462591	−	2.02674i	0.0211806	−	0.0927982i
$478$	−6.69689	+	3.22505i	−0.306309	+	0.147511i
$479$	−5.87751	+	2.83046i	−0.268550	+	0.129327i	−0.563313	−	0.826243i	$-0.690474\pi$
$479$	−5.87751	+	2.83046i	−0.268550	+	0.129327i	0.294763	+	0.955570i	$0.404759\pi$
$480$	−2.76021	+	12.0933i	−0.125986	+	0.551979i
$481$	−18.9753			−0.865200
$482$	3.96232	−	17.3601i	0.180479	−	0.790730i
$483$	−2.61353	−	3.27726i	−0.118920	−	0.149121i
$484$	−1.58798	−	6.95738i	−0.0721807	−	0.316244i
$485$	−2.69920	−	11.8260i	−0.122564	−	0.536990i
$486$	−0.719749	+	0.902536i	−0.0326485	+	0.0409399i
$487$	21.1411	−	10.1810i	0.957996	−	0.461346i	0.111513	−	0.993763i	$-0.464430\pi$
$487$	21.1411	−	10.1810i	0.957996	−	0.461346i	0.846482	+	0.532417i	$0.178716\pi$
$488$	−20.0619	−	9.66132i	−0.908161	−	0.437347i
$489$	1.62967	+	2.04355i	0.0736964	+	0.0924123i
$490$	−33.2900	+	41.7444i	−1.50389	+	1.88582i
$491$	27.0162	+	13.0103i	1.21923	+	0.587148i	0.929096	−	0.369839i	$-0.120587\pi$
$491$	27.0162	+	13.0103i	1.21923	+	0.587148i	0.290130	+	0.956987i	$0.406301\pi$
$492$	−1.90418			−0.0858470
$493$	16.1190	−	0.796738i	0.725965	−	0.0358833i
$494$	−0.886358			−0.0398791
$495$	−1.72246	−	0.829494i	−0.0774189	−	0.0372830i
$496$	−12.6233	+	15.8292i	−0.566805	+	0.710750i
$497$	−6.70942	−	8.41334i	−0.300958	−	0.377390i
$498$	−11.4100	−	5.49475i	−0.511293	−	0.246226i
$499$	−13.9764	+	6.73068i	−0.625669	+	0.301307i	−0.719724	−	0.694261i	$-0.755732\pi$
$499$	−13.9764	+	6.73068i	−0.625669	+	0.301307i	0.0940543	+	0.995567i	$0.470017\pi$
$500$	2.72664	−	3.41910i	0.121939	−	0.152907i
$501$	−2.27389	−	9.96256i	−0.101590	−	0.445094i
$502$	0.845492	+	3.70434i	0.0377361	+	0.165333i
$503$	−9.15733	−	11.4829i	−0.408305	−	0.511999i	0.534579	−	0.845118i	$-0.320470\pi$
$503$	−9.15733	−	11.4829i	−0.408305	−	0.511999i	−0.942885	+	0.333120i	$0.891899\pi$
$504$	3.09535	−	13.5616i	0.137878	−	0.604083i
$505$	43.7085			1.94500
$506$	0.132097	−	0.578755i	0.00587244	−	0.0257288i
$507$	−4.84946	+	2.33538i	−0.215372	+	0.103718i
$508$	−5.52537	+	2.66088i	−0.245149	+	0.118057i
$509$	−7.27387	+	31.8689i	−0.322408	+	1.41256i	0.510845	+	0.859673i	$0.329333\pi$
$509$	−7.27387	+	31.8689i	−0.322408	+	1.41256i	−0.833254	+	0.552891i	$0.813525\pi$
$510$	−11.9340			−0.528448
$511$	0.917911	−	4.02163i	0.0406060	−	0.177906i
$512$	−13.5002	−	16.9287i	−0.596631	−	0.748151i
$513$	−0.0619045	−	0.271221i	−0.00273315	−	0.0119747i
$514$	0.101631	+	0.445275i	0.00448275	+	0.0196402i
$515$	−4.33928	+	5.44129i	−0.191212	+	0.239772i
$516$	6.74589	−	3.24865i	0.296971	−	0.143014i
$517$	2.09493	+	1.00886i	0.0921349	+	0.0443698i
$518$	−22.3545	−	28.0317i	−0.982201	−	1.23164i
$519$	−14.3976	+	18.0540i	−0.631983	+	0.792481i
$520$	−26.4131	−	12.7199i	−1.15829	−	0.557804i
$521$	−33.5048			−1.46787			−0.733937	−	0.679218i	$-0.762319\pi$
$521$	−33.5048			−1.46787			−0.733937	+	0.679218i	$0.762319\pi$
$522$	1.08242	−	6.12161i	0.0473764	−	0.267935i
$523$	−23.3879			−1.02268			−0.511341	−	0.859378i	$-0.670851\pi$
$523$	−23.3879			−1.02268			−0.511341	+	0.859378i	$0.670851\pi$
$524$	−7.87333	−	3.79160i	−0.343948	−	0.165637i
$525$	−19.4336	+	24.3689i	−0.848150	+	1.06355i
$526$	−5.86132	−	7.34986i	−0.255566	−	0.320469i
$527$	24.6268	+	11.8597i	1.07276	+	0.516615i
$528$	1.10841	−	0.533782i	0.0482373	−	0.0232299i
$529$	−13.8035	+	17.3090i	−0.600150	+	0.752564i
$530$	−1.84210	−	8.07079i	−0.0800159	−	0.350573i
$531$	3.17471	+	13.9093i	0.137771	+	0.603612i
$532$	0.522952	+	0.655761i	0.0226729	+	0.0284309i
$533$	1.75229	−	7.67727i	0.0759000	−	0.332540i
$534$	7.85783			0.340041
$535$	−0.439103	+	1.92384i	−0.0189841	+	0.0831747i
$536$	−34.0838	+	16.4139i	−1.47220	+	0.708972i
$537$	13.3241	−	6.41655i	0.574978	−	0.276895i
$538$	−2.30611	+	10.1037i	−0.0994234	+	0.435602i
$539$	−7.43091			−0.320072
$540$	0.512290	−	2.24449i	0.0220455	−	0.0965875i
$541$	−9.10698	−	11.4198i	−0.391540	−	0.490975i	0.546521	−	0.837445i	$-0.315952\pi$
$541$	−9.10698	−	11.4198i	−0.391540	−	0.490975i	−0.938061	+	0.346470i	$0.887380\pi$
$542$	−1.29455	−	5.67177i	−0.0556055	−	0.243624i
$543$	0.642932	+	2.81687i	0.0275908	+	0.120883i
$544$	−6.71900	+	8.42536i	−0.288075	+	0.361234i
$545$	60.5071	−	29.1387i	2.59184	−	1.24816i
$546$	12.9679	+	6.24500i	0.554974	+	0.267262i
$547$	7.68546	+	9.63726i	0.328607	+	0.412060i	0.918500	−	0.395422i	$-0.129402\pi$
$547$	7.68546	+	9.63726i	0.328607	+	0.412060i	−0.589893	+	0.807481i	$0.700830\pi$
$548$	3.16264	−	3.96583i	0.135101	−	0.169412i
$549$	6.51531	+	3.13761i	0.278067	+	0.133910i
$550$	−4.41415			−0.188220
$551$	0.990756	+	1.12375i	0.0422076	+	0.0478732i
$552$	2.85716			0.121609
$553$	−8.41746	−	4.05363i	−0.357947	−	0.172378i
$554$	1.46478	−	1.83678i	0.0622326	−	0.0780372i
$555$	−14.7869	−	18.5422i	−0.627670	−	0.787073i
$556$	5.32333	+	2.56358i	0.225760	+	0.108720i
$557$	22.4253	−	10.7994i	0.950190	−	0.457587i	0.106437	−	0.994319i	$-0.466056\pi$
$557$	22.4253	−	10.7994i	0.950190	−	0.457587i	0.843753	+	0.536732i	$0.180341\pi$
$558$	6.56462	−	8.23177i	0.277903	−	0.348479i
$559$	6.89013	+	30.1876i	0.291421	+	1.27680i
$560$	−7.69758	−	33.7253i	−0.325282	−	1.42515i
$561$	−1.03556	−	1.29855i	−0.0437212	−	0.0548247i
$562$	−6.11986	+	26.8129i	−0.258151	+	1.13103i
$563$	16.2217			0.683662			0.341831	−	0.939762i	$-0.388953\pi$
$563$	16.2217			0.683662			0.341831	+	0.939762i	$0.388953\pi$
$564$	−0.623069	+	2.72984i	−0.0262359	+	0.114947i
$565$	7.57368	−	3.64729i	0.318627	−	0.153443i
$566$	15.5863	−	7.50596i	0.655140	−	0.315499i
$567$	−1.00525	+	4.40427i	−0.0422164	+	0.184962i
$568$	7.33486			0.307764
$569$	9.97556	−	43.7058i	0.418197	−	1.83224i	−0.124378	−	0.992235i	$-0.539693\pi$
$569$	9.97556	−	43.7058i	0.418197	−	1.83224i	0.542575	−	0.840007i	$-0.317449\pi$
$570$	−0.690714	−	0.866127i	−0.0289308	−	0.0362781i
$571$	3.78155	+	16.5681i	0.158253	+	0.693352i	0.990335	+	0.138699i	$0.0442920\pi$
$571$	3.78155	+	16.5681i	0.158253	+	0.693352i	−0.832081	+	0.554653i	$0.812851\pi$
$572$	−0.227160	−	0.995251i	−0.00949802	−	0.0416135i
$573$	2.90781	−	3.64627i	0.121475	−	0.152325i
$574$	13.4058	−	6.45587i	0.559545	−	0.269463i
$575$	−5.76804	−	2.77774i	−0.240544	−	0.115840i
$576$	5.35619	+	6.71645i	0.223175	+	0.279852i
$577$	−3.45830	+	4.33657i	−0.143971	+	0.180534i	−0.848589	−	0.529053i	$-0.822547\pi$
$577$	−3.45830	+	4.33657i	−0.143971	+	0.180534i	0.704618	+	0.709587i	$0.251119\pi$
$578$	8.33997	+	4.01632i	0.346897	+	0.167057i
$579$	14.5839			0.606087
$580$	3.35211	+	11.9360i	0.139189	+	0.495616i
$581$	−49.5592			−2.05606
$582$	−3.65730	−	1.76126i	−0.151600	−	0.0730066i
$583$	0.718340	−	0.900769i	0.0297506	−	0.0373061i
$584$	1.75305	+	2.19826i	0.0725419	+	0.0909647i
$585$	8.57791	+	4.13090i	0.354653	+	0.170792i
$586$	−31.5869	+	15.2114i	−1.30484	+	0.628379i
$587$	−11.9358	+	14.9671i	−0.492644	+	0.617756i	−0.964552	−	0.263891i	$-0.914994\pi$
$587$	−11.9358	+	14.9671i	−0.492644	+	0.617756i	0.471908	+	0.881648i	$0.343565\pi$
$588$	−1.99122	−	8.72409i	−0.0821164	−	0.359775i
$589$	0.564613	+	2.47373i	0.0232645	+	0.101928i
$590$	35.4225	+	44.4184i	1.45832	+	1.82868i
$591$	0.643424	−	2.81903i	0.0264669	−	0.115959i
$592$	15.2616			0.627246
$593$	−7.05758	+	30.9213i	−0.289820	+	1.26978i	0.594952	+	0.803761i	$0.297171\pi$
$593$	−7.05758	+	30.9213i	−0.289820	+	1.26978i	−0.884772	+	0.466024i	$0.845686\pi$
$594$	−0.576415	+	0.277587i	−0.0236506	+	0.0113895i
$595$	−42.0772	+	20.2633i	−1.72500	+	0.830715i
$596$	1.18362	−	5.18577i	0.0484829	−	0.212418i
$597$	−4.05076			−0.165787
$598$	−0.657848	+	2.88222i	−0.0269014	+	0.117863i
$599$	−29.4026	−	36.8696i	−1.20136	−	1.50645i	−0.810227	−	0.586117i	$-0.800656\pi$
$599$	−29.4026	−	36.8696i	−1.20136	−	1.50645i	−0.391129	−	0.920336i	$-0.627915\pi$
$600$	−4.72749	−	20.7125i	−0.192999	−	0.845584i
$601$	−3.29442	−	14.4338i	−0.134382	−	0.588766i	−0.996612	−	0.0822488i	$-0.973790\pi$
$601$	−3.29442	−	14.4338i	−0.134382	−	0.588766i	0.862230	−	0.506517i	$-0.169067\pi$
$602$	−36.4781	+	45.7421i	−1.48674	+	1.86431i
$603$	11.0690	−	5.33057i	0.450766	−	0.217078i
$604$	−0.0634499	−	0.0305559i	−0.00258174	−	0.00124330i
$605$	22.9979	+	28.8385i	0.934998	+	1.17245i
$606$	9.11971	−	11.4358i	0.370463	−	0.464546i
$607$	−10.5442	−	5.07781i	−0.427975	−	0.206102i	0.207481	−	0.978239i	$-0.433474\pi$
$607$	−10.5442	−	5.07781i	−0.427975	−	0.206102i	−0.635456	+	0.772137i	$0.719188\pi$
$608$	−1.00036			−0.0405700
$609$	−6.57771	−	23.4216i	−0.266542	−	0.949089i
$610$	28.7967			1.16594
$611$	−10.4328	−	5.02418i	−0.422066	−	0.203256i
$612$	1.24704	−	1.56373i	0.0504084	−	0.0632102i
$613$	−28.6483	−	35.9238i	−1.15709	−	1.45095i	−0.870003	−	0.493046i	$-0.835883\pi$
$613$	−28.6483	−	35.9238i	−1.15709	−	1.45095i	−0.287091	−	0.957903i	$-0.592688\pi$
$614$	−2.18913	−	1.05423i	−0.0883460	−	0.0425452i
$615$	8.86755	−	4.27039i	0.357574	−	0.172199i
$616$	4.80666	−	6.02736i	0.193666	−	0.242849i
$617$	9.15351	+	40.1041i	0.368506	+	1.61453i	0.730885	+	0.682501i	$0.239108\pi$
$617$	9.15351	+	40.1041i	0.368506	+	1.61453i	−0.362378	+	0.932031i	$0.618035\pi$
$618$	0.518257	+	2.27063i	0.0208474	+	0.0913382i
$619$	−1.85196	−	2.32229i	−0.0744367	−	0.0933407i	0.743219	−	0.669048i	$-0.233298\pi$
$619$	−1.85196	−	2.32229i	−0.0744367	−	0.0933407i	−0.817656	+	0.575708i	$0.804727\pi$
$620$	−4.67245	+	20.4713i	−0.187650	+	0.822149i
$621$	−0.927891			−0.0372350
$622$	−4.33507	+	18.9932i	−0.173820	+	0.761557i
$623$	27.7053	−	13.3421i	1.10999	−	0.534542i
$624$	−5.51991	+	2.65825i	−0.220973	+	0.106415i
$625$	2.64663	−	11.5956i	0.105865	−	0.463825i
$626$	17.1190			0.684212
$627$	0.0343081	−	0.150314i	0.00137013	−	0.00600295i
$628$	5.61905	+	7.04606i	0.224224	+	0.281168i
$629$	−4.58483	−	20.0875i	−0.182809	−	0.800940i
$630$	4.00304	+	17.5384i	0.159485	+	0.698748i
$631$	13.4129	−	16.8192i	0.533959	−	0.669563i	−0.439549	−	0.898219i	$-0.644862\pi$
$631$	13.4129	−	16.8192i	0.533959	−	0.669563i	0.973507	+	0.228656i	$0.0734330\pi$
$632$	5.73743	−	2.76300i	0.228223	−	0.109906i
$633$	−11.8645	−	5.71365i	−0.471572	−	0.227097i
$634$	−3.96310	−	4.96957i	−0.157395	−	0.197367i
$635$	19.7636	−	24.7828i	0.784296	−	0.983476i
$636$	1.25002	+	0.601976i	0.0495664	+	0.0238699i
$637$	37.0062			1.46624
$638$	2.01250	−	2.79639i	0.0796756	−	0.110710i
$639$	−2.38207			−0.0942331
$640$	8.46978	+	4.07883i	0.334797	+	0.161230i
$641$	−20.0815	+	25.1814i	−0.793172	+	0.994606i	0.206697	+	0.978405i	$0.433729\pi$
$641$	−20.0815	+	25.1814i	−0.793172	+	0.994606i	−0.999869	+	0.0162011i	$0.994843\pi$
$642$	0.411729	+	0.516291i	0.0162496	+	0.0203764i
$643$	−35.1799	−	16.9417i	−1.38736	−	0.668117i	−0.416803	−	0.908997i	$-0.636850\pi$
$643$	−35.1799	−	16.9417i	−1.38736	−	0.668117i	−0.970555	+	0.240880i	$0.922564\pi$
$644$	2.52051	−	1.21381i	0.0993218	−	0.0478309i
$645$	−24.1293	+	30.2572i	−0.950091	+	1.19138i
$646$	−0.214163	−	0.938308i	−0.00842612	−	0.0369173i
$647$	0.917446	+	4.01959i	0.0360685	+	0.158027i	0.989755	−	0.142776i	$-0.0456027\pi$
$647$	0.917446	+	4.01959i	0.0360685	+	0.158027i	−0.953687	+	0.300802i	$0.902746\pi$
$648$	−1.91985	−	2.40742i	−0.0754188	−	0.0945722i
$649$	−1.75945	+	7.70867i	−0.0690646	+	0.302592i
$650$	21.9826			0.862229
$651$	9.16856	−	40.1701i	0.359344	−	1.57439i
$652$	−1.57167	+	0.756875i	−0.0615512	+	0.0296415i
$653$	13.7671	−	6.62990i	0.538749	−	0.259448i	−0.144663	−	0.989481i	$-0.546210\pi$
$653$	13.7671	−	6.62990i	0.538749	−	0.259448i	0.683412	+	0.730033i	$0.260495\pi$
$654$	5.00096	−	21.9106i	0.195553	−	0.856773i
$655$	45.1684			1.76488
$656$	−1.40934	+	6.17471i	−0.0550254	+	0.241082i
$657$	−0.569321	−	0.713906i	−0.0222113	−	0.0278521i
$658$	−4.86866	−	21.3310i	−0.189800	−	0.831569i
$659$	7.68022	+	33.6492i	0.299179	+	1.31079i	0.871353	+	0.490656i	$0.163243\pi$
$659$	7.68022	+	33.6492i	0.299179	+	1.31079i	−0.572175	+	0.820132i	$0.693900\pi$
$660$	0.795516	−	0.997545i	0.0309654	−	0.0388294i
$661$	−10.7766	+	5.18973i	−0.419160	+	0.201857i	−0.631562	−	0.775325i	$-0.717586\pi$
$661$	−10.7766	+	5.18973i	−0.419160	+	0.201857i	0.212401	+	0.977182i	$0.431872\pi$
$662$	6.12425	+	2.94928i	0.238026	+	0.114627i
$663$	5.15710	+	6.46680i	0.200285	+	0.251150i
$664$	21.0616	−	26.4104i	0.817347	−	1.02492i
$665$	−3.90597	−	1.88101i	−0.151467	−	0.0729426i
$666$	−7.93660			−0.307537
$667$	4.38948	−	2.38766i	0.169961	−	0.0924506i
$668$	6.81990			0.263870
$669$	−13.7636	−	6.62820i	−0.532131	−	0.256261i
$670$	30.5033	−	38.2499i	1.17845	−	1.47772i
$671$	2.49878	+	3.13338i	0.0964645	+	0.120963i
$672$	14.6358	+	7.04823i	0.564588	+	0.271891i
$673$	15.9364	−	7.67456i	0.614303	−	0.295833i	−0.100741	−	0.994913i	$-0.532121\pi$
$673$	15.9364	−	7.67456i	0.614303	−	0.295833i	0.715043	+	0.699080i	$0.246407\pi$
$674$	12.5450	−	15.7310i	0.483216	−	0.605934i
$675$	1.53530	+	6.72658i	0.0590936	+	0.258906i
$676$	−0.799345	−	3.50216i	−0.0307440	−	0.134698i
$677$	18.5642	+	23.2788i	0.713480	+	0.894675i	0.997949	−	0.0640097i	$-0.0203889\pi$
$677$	18.5642	+	23.2788i	0.713480	+	0.894675i	−0.284469	+	0.958685i	$0.591817\pi$
$678$	0.625970	−	2.74256i	0.0240403	−	0.105327i
$679$	−15.8855			−0.609629
$680$	7.08344	−	31.0346i	0.271638	−	1.19012i
$681$	−13.2896	+	6.39993i	−0.509258	+	0.245246i
$682$	5.25732	−	2.53179i	0.201313	−	0.0969473i
$683$	3.77624	−	16.5448i	0.144494	−	0.633069i	−0.849865	−	0.527000i	$-0.823317\pi$
$683$	3.77624	−	16.5448i	0.144494	−	0.633069i	0.994359	−	0.106068i	$-0.0338262\pi$
$684$	0.185665			0.00709910
$685$	−5.83414	+	25.5611i	−0.222911	+	0.976638i
$686$	20.8360	+	26.1275i	0.795520	+	0.997551i
$687$	2.30837	+	10.1136i	0.0880699	+	0.385859i
$688$	−5.54162	−	24.2794i	−0.211272	−	0.925645i
$689$	−3.57735	+	4.48586i	−0.136286	+	0.170898i
$690$	−3.32908	+	1.60320i	−0.126736	+	0.0610327i
$691$	22.2454	+	10.7128i	0.846254	+	0.407534i	0.806186	−	0.591662i	$-0.201528\pi$
$691$	22.2454	+	10.7128i	0.846254	+	0.407534i	0.0400683	+	0.999197i	$0.487242\pi$
$692$	−9.60878	−	12.0490i	−0.365271	−	0.458036i
$693$	−1.56101	+	1.95744i	−0.0592978	+	0.0743571i
$694$	2.92843	+	1.41026i	0.111162	+	0.0535327i
$695$	−30.5394			−1.15842
$696$	15.2768	+	6.44834i	0.579067	+	0.244424i
$697$	8.55063			0.323878
$698$	−24.4363	−	11.7679i	−0.924926	−	0.445421i
$699$	−0.174718	+	0.219090i	−0.00660844	+	0.00828673i
$700$	−12.9698	−	16.2636i	−0.490211	−	0.614705i
$701$	−22.7891	−	10.9746i	−0.860732	−	0.414507i	−0.0491820	−	0.998790i	$-0.515661\pi$
$701$	−22.7891	−	10.9746i	−0.860732	−	0.414507i	−0.811550	+	0.584283i	$0.801376\pi$
$702$	2.87057	−	1.38239i	0.108343	−	0.0521750i
$703$	1.19251	−	1.49537i	0.0449765	−	0.0563988i
$704$	1.05943	+	4.64166i	0.0399287	+	0.174939i
$705$	−3.22049	−	14.1099i	−0.121291	−	0.531409i
$706$	11.6284	+	14.5816i	0.437642	+	0.548786i
$707$	12.7372	−	55.8051i	0.479030	−	2.09877i
$708$	−9.52166			−0.357846
$709$	−0.443854	+	1.94465i	−0.0166693	+	0.0730329i	−0.982578	−	0.185848i	$-0.940497\pi$
$709$	−0.443854	+	1.94465i	−0.0166693	+	0.0730329i	0.965909	+	0.258881i	$0.0833538\pi$
$710$	−8.54635	+	4.11571i	−0.320739	+	0.154460i
$711$	−1.86329	+	0.897311i	−0.0698786	+	0.0336518i
$712$	−4.66401	+	20.4344i	−0.174791	+	0.765811i
$713$	8.46302			0.316943
$714$	−3.47772	+	15.2369i	−0.130150	+	0.570225i
$715$	3.28984	+	4.12533i	0.123033	+	0.154279i
$716$	2.19624	+	9.62234i	0.0820772	+	0.359604i
$717$	1.43279	+	6.27747i	0.0535086	+	0.234436i
$718$	−6.21880	+	7.79813i	−0.232084	+	0.291024i
$719$	−5.69960	+	2.74478i	−0.212559	+	0.102363i	−0.537134	−	0.843497i	$-0.680493\pi$
$719$	−5.69960	+	2.74478i	−0.212559	+	0.102363i	0.324575	+	0.945860i	$0.394779\pi$
$720$	−6.89908	−	3.32242i	−0.257114	−	0.123819i
$721$	5.68269	+	7.12586i	0.211634	+	0.265381i
$722$	−13.6195	+	17.0783i	−0.506866	+	0.635590i
$723$	−13.8975	−	6.69269i	−0.516854	−	0.248904i
$724$	−1.92830			−0.0716646
$725$	−24.5718	−	27.8701i	−0.912574	−	1.03507i
$726$	12.3437			0.458117
$727$	−16.3885	−	7.89230i	−0.607817	−	0.292709i	0.104547	−	0.994520i	$-0.466661\pi$
$727$	−16.3885	−	7.89230i	−0.607817	−	0.292709i	−0.712363	+	0.701811i	$0.752375\pi$
$728$	−23.9373	+	30.0164i	−0.887175	+	1.11248i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−3.27608	−	1.57768i	−0.121253	−	0.0583925i
$731$	−30.2921	+	14.5879i	−1.12040	+	0.539554i
$732$	−3.00908	+	3.77327i	−0.111219	+	0.139464i
$733$	8.06036	+	35.3148i	0.297716	+	1.30438i	0.873518	+	0.486791i	$0.161833\pi$
$733$	8.06036	+	35.3148i	0.297716	+	1.30438i	−0.575802	+	0.817589i	$0.695310\pi$
$734$	−3.45403	−	15.1331i	−0.127490	−	0.558572i
$735$	28.8379	+	36.1615i	1.06370	+	1.33384i
$736$	−0.742460	+	3.25293i	−0.0273674	+	0.119905i
$737$	6.80886			0.250808
$738$	0.732910	−	3.21109i	0.0269788	−	0.118202i
$739$	3.75343	−	1.80755i	0.138072	−	0.0664920i	−0.363572	−	0.931566i	$-0.618443\pi$
$739$	3.75343	−	1.80755i	0.138072	−	0.0664920i	0.501644	+	0.865074i	$0.332729\pi$
$740$	14.2606	−	6.86754i	0.524230	−	0.252456i
$741$	−0.170855	+	0.748566i	−0.00627653	+	0.0274993i
$742$	−10.8412			−0.397995
$743$	−5.47368	+	23.9818i	−0.200810	+	0.879806i	0.769635	+	0.638484i	$0.220438\pi$
$743$	−5.47368	+	23.9818i	−0.200810	+	0.879806i	−0.970445	+	0.241322i	$0.922419\pi$
$744$	17.5104	+	21.9574i	0.641963	+	0.804996i
$745$	6.11783	+	26.8040i	0.224140	+	0.982022i
$746$	0.820264	+	3.59381i	0.0300320	+	0.131579i
$747$	−6.83994	+	8.57702i	−0.250260	+	0.313817i
$748$	0.998697	−	0.480947i	0.0365160	−	0.0175852i
$749$	2.32831	+	1.12126i	0.0850747	+	0.0409698i
$750$	4.71629	+	5.91404i	0.172215	+	0.215950i
$751$	16.3234	−	20.4689i	0.595651	−	0.746922i	−0.389042	−	0.921220i	$-0.627194\pi$
$751$	16.3234	−	20.4689i	0.595651	−	0.746922i	0.984693	+	0.174297i	$0.0557654\pi$
$752$	8.39095	+	4.04087i	0.305987	+	0.147355i
$753$	3.29145			0.119947
$754$	−10.0223	+	13.9261i	−0.364991	+	0.507160i
$755$	0.364005			0.0132475
$756$	−2.71638	−	1.30814i	−0.0987939	−	0.0475766i
$757$	−32.5871	+	40.8630i	−1.18440	+	1.48519i	−0.347632	+	0.937631i	$0.613014\pi$
$757$	−32.5871	+	40.8630i	−1.18440	+	1.48519i	−0.836767	+	0.547559i	$0.815557\pi$
$758$	−11.8772	−	14.8936i	−0.431400	−	0.540959i
$759$	−0.463320	−	0.223123i	−0.0168174	−	0.00809885i
$760$	2.66235	−	1.28212i	0.0965735	−	0.0465074i
$761$	3.05680	−	3.83310i	0.110809	−	0.138950i	−0.723334	−	0.690498i	$-0.757391\pi$
$761$	3.05680	−	3.83310i	0.110809	−	0.138950i	0.834143	+	0.551548i	$0.185963\pi$
$762$	−2.36045	−	10.3418i	−0.0855100	−	0.374644i
$763$	−19.5706	−	85.7442i	−0.708502	−	3.10415i
$764$	1.94064	+	2.43348i	0.0702099	+	0.0880404i
$765$	−2.30042	+	10.0788i	−0.0831717	+	0.364399i
$766$	1.82183			0.0658255
$767$	8.76214	−	38.3894i	0.316382	−	1.38616i
$768$

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04007 - 0.500870i) q^{2} +(-0.623490 + 0.781831i) q^{3} +(-0.416111 - 0.521786i) q^{4} +(3.10796 + 1.49671i) q^{5} +(1.04007 - 0.500870i) q^{6} +(2.81664 - 3.53195i) q^{7} +(0.685187 + 3.00200i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-2.48283 - 3.11337i) q^{10} +(0.123323 - 0.540315i) q^{11} +0.667390 q^{12} +(-0.614154 + 2.69078i) q^{13} +(-4.69854 + 2.26270i) q^{14} +(-3.10796 + 1.49671i) q^{15} +(0.493954 - 2.16416i) q^{16} -2.99688 q^{17} +(-0.256875 + 1.12544i) q^{18} +(-0.173453 - 0.217503i) q^{19} +(-0.512290 - 2.24449i) q^{20} +(1.00525 + 4.40427i) q^{21} +(-0.398892 + 0.500195i) q^{22} +(-0.836001 + 0.402597i) q^{23} +(-2.77426 - 1.33602i) q^{24} +(4.30181 + 5.39430i) q^{25} +(1.98649 - 2.49098i) q^{26} +(0.900969 + 0.433884i) q^{27} -3.01496 q^{28} +(-5.37860 + 0.265855i) q^{29} +3.98215 q^{30} +(-8.21748 - 3.95733i) q^{31} +(2.24199 - 2.81137i) q^{32} +(0.345544 + 0.433299i) q^{33} +(3.11696 + 1.50105i) q^{34} +(14.0403 - 6.76146i) q^{35} +(-0.416111 + 0.521786i) q^{36} +(1.52987 + 6.70278i) q^{37} +(0.0714618 + 0.313095i) q^{38} +(-1.72082 - 2.15784i) q^{39} +(-2.36360 + 10.3556i) q^{40} -2.85317 q^{41} +(1.16044 - 5.08423i) q^{42} +(10.1079 - 4.86770i) q^{43} +(-0.333245 + 0.160482i) q^{44} +(0.767603 - 3.36309i) q^{45} +1.07115 q^{46} +(-0.933590 + 4.09033i) q^{47} +(1.38403 + 1.73552i) q^{48} +(-2.98359 - 13.0720i) q^{49} +(-1.77233 - 7.76508i) q^{50} +(1.86853 - 2.34306i) q^{51} +(1.65957 - 0.799207i) q^{52} +(1.87299 + 0.901986i) q^{53} +(-0.719749 - 0.902536i) q^{54} +(1.19198 - 1.49470i) q^{55} +(12.5328 + 6.03550i) q^{56} +0.278196 q^{57} +(5.72726 + 2.41747i) q^{58} -14.2670 q^{59} +(2.07422 + 0.998892i) q^{60} +(-4.50873 + 5.65377i) q^{61} +(6.56462 + 8.23177i) q^{62} +(-4.07016 - 1.96009i) q^{63} +(-7.73992 + 3.72735i) q^{64} +(-5.93610 + 7.44363i) q^{65} +(-0.142363 - 0.623732i) q^{66} +(2.73383 + 11.9777i) q^{67} +(1.24704 + 1.56373i) q^{68} +(0.206475 - 0.904626i) q^{69} -17.9895 q^{70} +(0.530060 - 2.32234i) q^{71} +(2.77426 - 1.33602i) q^{72} +(0.822693 - 0.396188i) q^{73} +(1.76606 - 7.73761i) q^{74} -6.89956 q^{75} +(-0.0413145 + 0.181010i) q^{76} +(-1.56101 - 1.95744i) q^{77} +(0.708971 + 3.10621i) q^{78} +(-0.460193 - 2.01624i) q^{79} +(4.77431 - 5.98680i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(2.96749 + 1.42907i) q^{82} +(-6.83994 - 8.57702i) q^{83} +(1.87979 - 2.35719i) q^{84} +(-9.31420 - 4.48548i) q^{85} -12.9510 q^{86} +(3.14565 - 4.37092i) q^{87} +1.70652 q^{88} +(6.13283 + 2.95341i) q^{89} +(-2.48283 + 3.11337i) q^{90} +(7.77387 + 9.74812i) q^{91} +(0.557938 + 0.268689i) q^{92} +(8.21748 - 3.95733i) q^{93} +(3.01972 - 3.78661i) q^{94} +(-0.213544 - 0.935599i) q^{95} +(0.800159 + 3.50572i) q^{96} +(-2.19244 - 2.74924i) q^{97} +(-3.44422 + 15.0901i) q^{98} -0.554210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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