LMFDB - Embedded newform 91.2.f.c.22.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.4
Root			$1.37054 - 2.37385i$ of defining polynomial
Character	$\chi$	$=$	91.22
Dual form			91.2.f.c.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37054 - 2.37385i) q^{2} +(-0.682410 + 1.18197i) q^{3} +(-2.75677 - 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 + 3.23987i) q^{6} +(0.500000 + 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +O(q^{10})$	\(q+(1.37054 - 2.37385i) q^{2} +(-0.682410 + 1.18197i) q^{3} +(-2.75677 - 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 + 3.23987i) q^{6} +(0.500000 + 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +(1.01568 - 1.75921i) q^{10} +(0.682410 - 1.18197i) q^{11} +7.52497 q^{12} +(0.301907 + 3.59289i) q^{13} +2.74108 q^{14} +(-0.505722 + 0.875935i) q^{15} +(-7.68598 + 13.3125i) q^{16} +(2.07436 + 3.59289i) q^{17} +3.11734 q^{18} +(-3.63303 - 6.29259i) q^{19} +(-2.04299 - 3.53856i) q^{20} -1.36482 q^{21} +(-1.87054 - 3.23987i) q^{22} +(1.16673 - 2.02083i) q^{23} +(6.57220 - 11.3834i) q^{24} -4.45080 q^{25} +(8.94274 + 4.20752i) q^{26} -5.64662 q^{27} +(2.75677 - 4.77486i) q^{28} +(0.203815 - 0.353017i) q^{29} +(1.38622 + 2.40101i) q^{30} -2.77245 q^{31} +(11.4370 + 19.8095i) q^{32} +(0.931366 + 1.61317i) q^{33} +11.3720 q^{34} +(0.370541 + 0.641796i) q^{35} +(3.13518 - 5.43029i) q^{36} +(3.05295 - 5.28787i) q^{37} -19.9169 q^{38} +(-4.45271 - 2.09498i) q^{39} -7.13727 q^{40} +(-0.627306 + 1.08653i) q^{41} +(-1.87054 + 3.23987i) q^{42} +(0.870541 + 1.50782i) q^{43} -7.52497 q^{44} +(0.421404 + 0.729894i) q^{45} +(-3.19809 - 5.53926i) q^{46} -5.85843 q^{47} +(-10.4900 - 18.1692i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.10000 + 10.5655i) q^{50} -5.66224 q^{51} +(16.3232 - 11.3463i) q^{52} +4.56778 q^{53} +(-7.73893 + 13.4042i) q^{54} +(0.505722 - 0.875935i) q^{55} +(-4.81544 - 8.34058i) q^{56} +9.91685 q^{57} +(-0.558672 - 0.967649i) q^{58} +(5.49213 + 9.51264i) q^{59} +5.57662 q^{60} +(-3.26249 - 5.65079i) q^{61} +(-3.79975 + 6.58137i) q^{62} +(-0.568634 + 0.984903i) q^{63} +31.9557 q^{64} +(0.223738 + 2.66263i) q^{65} +5.10590 q^{66} +(6.87983 - 11.9162i) q^{67} +(11.4370 - 19.8095i) q^{68} +(1.59237 + 2.75807i) q^{69} +2.03137 q^{70} +(2.40763 + 4.17014i) q^{71} +(-5.47644 - 9.48548i) q^{72} +6.06987 q^{73} +(-8.36839 - 14.4945i) q^{74} +(3.03727 - 5.26070i) q^{75} +(-20.0308 + 34.6944i) q^{76} +1.36482 q^{77} +(-11.0758 + 7.69879i) q^{78} -9.12582 q^{79} +(-5.69594 + 9.86566i) q^{80} +(2.14741 - 3.71942i) q^{81} +(1.71950 + 2.97826i) q^{82} +11.7368 q^{83} +(3.76249 + 6.51682i) q^{84} +(1.53727 + 2.66263i) q^{85} +4.77245 q^{86} +(0.278170 + 0.481805i) q^{87} +(-6.57220 + 11.3834i) q^{88} +(0.880503 - 1.52508i) q^{89} +2.31021 q^{90} +(-2.96058 + 2.05790i) q^{91} -12.8656 q^{92} +(1.89195 - 3.27695i) q^{93} +(-8.02921 + 13.9070i) q^{94} +(-2.69237 - 4.66332i) q^{95} -31.2189 q^{96} +(-4.76691 - 8.25652i) q^{97} +(1.37054 + 2.37385i) q^{98} +1.55217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.37054	−	2.37385i	0.969119	−	1.67856i	0.271003	−	0.962579i	$-0.412645\pi$
$2$	1.37054	−	2.37385i	0.969119	−	1.67856i	0.698116	−	0.715984i	$-0.254022\pi$
$3$	−0.682410	+	1.18197i	−0.393989	+	0.682410i	−0.992972	−	0.118353i	$-0.962239\pi$
$3$	−0.682410	+	1.18197i	−0.393989	+	0.682410i	0.598982	+	0.800762i	$0.295572\pi$
$4$	−2.75677	−	4.77486i	−1.37838	−	2.38743i
$5$	0.741082			0.331422			0.165711	−	0.986174i	$-0.447008\pi$
$5$	0.741082			0.331422			0.165711	+	0.986174i	$0.447008\pi$
$6$	1.87054	+	3.23987i	0.763645	+	1.32267i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−9.63087			−3.40503
$9$	0.568634	+	0.984903i	0.189545	+	0.328301i
$10$	1.01568	−	1.75921i	0.321187	−	0.556313i
$11$	0.682410	−	1.18197i	0.205754	−	0.356377i	−0.744619	−	0.667490i	$-0.767369\pi$
$11$	0.682410	−	1.18197i	0.205754	−	0.356377i	0.950373	+	0.311113i	$0.100702\pi$
$12$	7.52497			2.17227
$13$	0.301907	+	3.59289i	0.0837339	+	0.996488i
$13$	0.301907	+	3.59289i	0.0837339	+	0.996488i
$14$	2.74108			0.732585
$15$	−0.505722	+	0.875935i	−0.130577	+	0.226166i
$16$	−7.68598	+	13.3125i	−1.92149	+	3.32813i
$17$	2.07436	+	3.59289i	0.503105	+	0.871404i	0.999994	+	0.00358919i	$0.00114248\pi$
$17$	2.07436	+	3.59289i	0.503105	+	0.871404i	−0.496888	+	0.867814i	$0.665524\pi$
$18$	3.11734			0.734765
$19$	−3.63303	−	6.29259i	−0.833474	−	1.44362i	−0.895267	−	0.445530i	$-0.853015\pi$
$19$	−3.63303	−	6.29259i	−0.833474	−	1.44362i	0.0617933	−	0.998089i	$-0.480318\pi$
$20$	−2.04299	−	3.53856i	−0.456826	−	0.791246i
$21$	−1.36482			−0.297828
$22$	−1.87054	−	3.23987i	−0.398801	−	0.690743i
$23$	1.16673	−	2.02083i	0.243279	−	0.421372i	−0.718367	−	0.695664i	$-0.755110\pi$
$23$	1.16673	−	2.02083i	0.243279	−	0.421372i	0.961646	+	0.274292i	$0.0884435\pi$
$24$	6.57220	−	11.3834i	1.34155	−	2.32362i
$25$	−4.45080			−0.890159
$26$	8.94274	+	4.20752i	1.75382	+	0.825163i
$27$	−5.64662			−1.08669
$28$	2.75677	−	4.77486i	0.520980	−	0.902363i
$29$	0.203815	−	0.353017i	0.0378474	−	0.0655536i	−0.846481	−	0.532419i	$-0.821283\pi$
$29$	0.203815	−	0.353017i	0.0378474	−	0.0655536i	0.884329	+	0.466865i	$0.154617\pi$
$30$	1.38622	+	2.40101i	0.253089	+	0.438363i
$31$	−2.77245			−0.497946			−0.248973	−	0.968510i	$-0.580093\pi$
$31$	−2.77245			−0.497946			−0.248973	+	0.968510i	$0.580093\pi$
$32$	11.4370	+	19.8095i	2.02180	+	3.50186i
$33$	0.931366	+	1.61317i	0.162130	+	0.280817i
$34$	11.3720			1.95027
$35$	0.370541	+	0.641796i	0.0626329	+	0.108483i
$36$	3.13518	−	5.43029i	0.522530	−	0.905049i
$37$	3.05295	−	5.28787i	0.501902	−	0.869320i	−0.498096	−	0.867122i	$-0.665967\pi$
$37$	3.05295	−	5.28787i	0.501902	−	0.869320i	0.999998	−	0.00219764i	$-0.000699531\pi$
$38$	−19.9169			−3.23094
$39$	−4.45271	−	2.09498i	−0.713003	−	0.335465i
$40$	−7.13727			−1.12850
$41$	−0.627306	+	1.08653i	−0.0979688	+	0.169687i	−0.910844	−	0.412751i	$-0.864568\pi$
$41$	−0.627306	+	1.08653i	−0.0979688	+	0.169687i	0.812875	+	0.582438i	$0.197901\pi$
$42$	−1.87054	+	3.23987i	−0.288631	+	0.499923i
$43$	0.870541	+	1.50782i	0.132756	+	0.229941i	0.924738	−	0.380604i	$-0.124284\pi$
$43$	0.870541	+	1.50782i	0.132756	+	0.229941i	−0.791982	+	0.610545i	$0.790951\pi$
$44$	−7.52497			−1.13443
$45$	0.421404	+	0.729894i	0.0628193	+	0.108806i
$46$	−3.19809	−	5.53926i	−0.471533	−	0.816719i
$47$	−5.85843			−0.854539			−0.427270	−	0.904124i	$-0.640525\pi$
$47$	−5.85843			−0.854539			−0.427270	+	0.904124i	$0.640525\pi$
$48$	−10.4900	−	18.1692i	−1.51410	−	2.62249i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−6.10000	+	10.5655i	−0.862670	+	1.49419i
$51$	−5.66224			−0.792872
$52$	16.3232	−	11.3463i	2.26363	−	1.57345i
$53$	4.56778			0.627433			0.313717	−	0.949517i	$-0.398426\pi$
$53$	4.56778			0.627433			0.313717	+	0.949517i	$0.398426\pi$
$54$	−7.73893	+	13.4042i	−1.05313	+	1.82408i
$55$	0.505722	−	0.875935i	0.0681915	−	0.118111i
$56$	−4.81544	−	8.34058i	−0.643490	−	1.11456i
$57$	9.91685			1.31352
$58$	−0.558672	−	0.967649i	−0.0733573	−	0.127059i
$59$	5.49213	+	9.51264i	0.715014	+	1.23844i	0.962954	+	0.269665i	$0.0869130\pi$
$59$	5.49213	+	9.51264i	0.715014	+	1.23844i	−0.247940	+	0.968775i	$0.579754\pi$
$60$	5.57662			0.719939
$61$	−3.26249	−	5.65079i	−0.417719	−	0.723510i	0.577991	−	0.816043i	$-0.303837\pi$
$61$	−3.26249	−	5.65079i	−0.417719	−	0.723510i	−0.995710	+	0.0925333i	$0.970504\pi$
$62$	−3.79975	+	6.58137i	−0.482569	+	0.835834i
$63$	−0.568634	+	0.984903i	−0.0716411	+	0.124086i
$64$	31.9557			3.99446
$65$	0.223738	+	2.66263i	0.0277513	+	0.330258i
$66$	5.10590			0.628493
$67$	6.87983	−	11.9162i	0.840505	−	1.45580i	−0.0489630	−	0.998801i	$-0.515592\pi$
$67$	6.87983	−	11.9162i	0.840505	−	1.45580i	0.889468	−	0.456997i	$-0.151075\pi$
$68$	11.4370	−	19.8095i	1.38694	−	2.40226i
$69$	1.59237	+	2.75807i	0.191699	+	0.332032i
$70$	2.03137			0.242795
$71$	2.40763	+	4.17014i	0.285733	+	0.494904i	0.972787	−	0.231703i	$-0.0744296\pi$
$71$	2.40763	+	4.17014i	0.285733	+	0.494904i	−0.687054	+	0.726607i	$0.741096\pi$
$72$	−5.47644	−	9.48548i	−0.645405	−	1.11787i
$73$	6.06987			0.710425			0.355212	−	0.934786i	$-0.384409\pi$
$73$	6.06987			0.710425			0.355212	+	0.934786i	$0.384409\pi$
$74$	−8.36839	−	14.4945i	−0.972805	−	1.68495i
$75$	3.03727	−	5.26070i	0.350713	−	0.607453i
$76$	−20.0308	+	34.6944i	−2.29769	+	3.97972i
$77$	1.36482			0.155536
$78$	−11.0758	+	7.69879i	−1.25408	+	0.871716i
$79$	−9.12582			−1.02674			−0.513368	−	0.858169i	$-0.671602\pi$
$79$	−9.12582			−1.02674			−0.513368	+	0.858169i	$0.671602\pi$
$80$	−5.69594	+	9.86566i	−0.636825	+	1.10301i
$81$	2.14741	−	3.71942i	0.238601	−	0.413269i
$82$	1.71950	+	2.97826i	0.189887	+	0.328894i
$83$	11.7368			1.28828			0.644139	−	0.764908i	$-0.277216\pi$
$83$	11.7368			1.28828			0.644139	+	0.764908i	$0.277216\pi$
$84$	3.76249	+	6.51682i	0.410521	+	0.711043i
$85$	1.53727	+	2.66263i	0.166740	+	0.288802i
$86$	4.77245			0.514626
$87$	0.278170	+	0.481805i	0.0298230	+	0.0516549i
$88$	−6.57220	+	11.3834i	−0.700599	+	1.21347i
$89$	0.880503	−	1.52508i	0.0933331	−	0.161658i	−0.815579	−	0.578646i	$-0.803581\pi$
$89$	0.880503	−	1.52508i	0.0933331	−	0.161658i	0.908912	+	0.416989i	$0.136915\pi$
$90$	2.31021			0.243517
$91$	−2.96058	+	2.05790i	−0.310353	+	0.215727i
$92$	−12.8656			−1.34133
$93$	1.89195	−	3.27695i	0.196186	−	0.339803i
$94$	−8.02921	+	13.9070i	−0.828150	+	1.43440i
$95$	−2.69237	−	4.66332i	−0.276231	−	0.478447i
$96$	−31.2189			−3.18627
$97$	−4.76691	−	8.25652i	−0.484006	−	0.838323i	0.515825	−	0.856694i	$-0.327485\pi$
$97$	−4.76691	−	8.25652i	−0.484006	−	0.838323i	−0.999831	+	0.0183708i	$0.994152\pi$
$98$	1.37054	+	2.37385i	0.138446	+	0.239795i
$99$	1.55217			0.155998
$100$	12.2698	+	21.2519i	1.22698	+	2.12519i
$101$	3.74680	−	6.48965i	0.372821	−	0.645745i	−0.617177	−	0.786824i	$-0.711724\pi$
$101$	3.74680	−	6.48965i	0.372821	−	0.645745i	0.989998	+	0.141079i	$0.0450573\pi$
$102$	−7.76033	+	13.4413i	−0.768388	+	1.33089i
$103$	2.80848			0.276728			0.138364	−	0.990381i	$-0.455816\pi$
$103$	2.80848			0.276728			0.138364	+	0.990381i	$0.455816\pi$
$104$	−2.90763	−	34.6027i	−0.285116	−	3.39307i
$105$	−1.01144			−0.0987067
$106$	6.26033	−	10.8432i	0.608057	−	1.05319i
$107$	−0.743235	+	1.28732i	−0.0718512	+	0.124450i	−0.899713	−	0.436483i	$-0.856224\pi$
$107$	−0.743235	+	1.28732i	−0.0718512	+	0.124450i	0.827861	+	0.560933i	$0.189557\pi$
$108$	15.5664	+	26.9618i	1.49788	+	2.59440i
$109$	2.87121			0.275012			0.137506	−	0.990501i	$-0.456091\pi$
$109$	2.87121			0.275012			0.137506	+	0.990501i	$0.456091\pi$
$110$	−1.38622	−	2.40101i	−0.132171	−	0.228927i
$111$	4.16673	+	7.21698i	0.395488	+	0.685006i
$112$	−15.3720			−1.45251
$113$	6.20972	+	10.7555i	0.584161	+	1.01180i	0.994979	+	0.100079i	$0.0319096\pi$
$113$	6.20972	+	10.7555i	0.584161	+	1.01180i	−0.410819	+	0.911717i	$0.634757\pi$
$114$	13.5915	−	23.5411i	1.27296	−	2.20483i
$115$	0.864640	−	1.49760i	0.0806281	−	0.139652i
$116$	−2.24747			−0.208673
$117$	−3.36697	+	2.34039i	−0.311277	+	0.216369i
$118$	30.1087			2.77173
$119$	−2.07436	+	3.59289i	−0.190156	+	0.329360i
$120$	4.87054	−	8.43602i	0.444618	−	0.770100i
$121$	4.56863	+	7.91311i	0.415330	+	0.719373i
$122$	−17.8855			−1.61928
$123$	−0.856160	−	1.48291i	−0.0771973	−	0.133710i
$124$	7.64299	+	13.2380i	0.686361	+	1.18881i
$125$	−7.00382			−0.626440
$126$	1.55867	+	2.69970i	0.138858	+	0.240508i
$127$	−2.71526	+	4.70296i	−0.240940	+	0.417321i	−0.960982	−	0.276610i	$-0.910789\pi$
$127$	−2.71526	+	4.70296i	−0.240940	+	0.417321i	0.720042	+	0.693930i	$0.244122\pi$
$128$	20.9226	−	36.2390i	1.84931	−	3.20310i
$129$	−2.37626			−0.209218
$130$	6.62731	+	3.11812i	0.581253	+	0.273477i
$131$	−11.3220			−0.989209			−0.494604	−	0.869118i	$-0.664687\pi$
$131$	−11.3220			−0.989209			−0.494604	+	0.869118i	$0.664687\pi$
$132$	5.13512	−	8.89428i	0.446954	−	0.774148i
$133$	3.63303	−	6.29259i	0.315023	−	0.545637i
$134$	−18.8582	−	32.6633i	−1.62910	−	2.82168i
$135$	−4.18461			−0.360154
$136$	−19.9779	−	34.6027i	−1.71309	−	2.96715i
$137$	6.98771	+	12.1031i	0.597000	+	1.03403i	0.993261	+	0.115897i	$0.0369741\pi$
$137$	6.98771	+	12.1031i	0.597000	+	1.03403i	−0.396261	+	0.918138i	$0.629693\pi$
$138$	8.72964			0.743116
$139$	−5.21544	−	9.03340i	−0.442368	−	0.766203i	0.555497	−	0.831518i	$-0.312528\pi$
$139$	−5.21544	−	9.03340i	−0.442368	−	0.766203i	−0.997865	+	0.0653153i	$0.979195\pi$
$140$	2.04299	−	3.53856i	0.172664	−	0.299063i
$141$	3.99785	−	6.92447i	0.336679	−	0.583146i
$142$	13.1990			1.10764
$143$	4.45271	+	2.09498i	0.372354	+	0.175191i
$144$	−17.4820			−1.45684
$145$	0.151043	−	0.261615i	0.0125435	−	0.0217259i
$146$	8.31901	−	14.4089i	0.688486	−	1.19249i
$147$	−0.682410	−	1.18197i	−0.0562842	−	0.0974871i
$148$	−33.6651			−2.76725
$149$	−4.08216	−	7.07052i	−0.334424	−	0.579239i	0.648950	−	0.760831i	$-0.275208\pi$
$149$	−4.08216	−	7.07052i	−0.334424	−	0.579239i	−0.983374	+	0.181592i	$0.941875\pi$
$150$	−8.32540	−	14.4200i	−0.679766	−	1.17739i
$151$	−2.46188			−0.200345			−0.100173	−	0.994970i	$-0.531939\pi$
$151$	−2.46188			−0.200345			−0.100173	+	0.994970i	$0.531939\pi$
$152$	34.9892	+	60.6031i	2.83800	+	4.91556i
$153$	−2.35910	+	4.08608i	−0.190722	+	0.330340i
$154$	1.87054	−	3.23987i	0.150732	−	0.261076i
$155$	−2.05461			−0.165030
$156$	2.27184	+	27.0364i	0.181893	+	2.16464i
$157$	−12.9198			−1.03111			−0.515557	−	0.856855i	$-0.672415\pi$
$157$	−12.9198			−1.03111			−0.515557	+	0.856855i	$0.672415\pi$
$158$	−12.5073	+	21.6633i	−0.995029	+	1.72344i
$159$	−3.11710	+	5.39897i	−0.247202	+	0.428167i
$160$	8.47577	+	14.6805i	0.670069	+	1.16059i
$161$	2.33345			0.183902
$162$	−5.88622	−	10.1952i	−0.462465	−	0.801014i
$163$	3.01371	+	5.21990i	0.236052	+	0.408854i	0.959578	−	0.281443i	$-0.0908131\pi$
$163$	3.01371	+	5.21990i	0.236052	+	0.408854i	−0.723526	+	0.690297i	$0.757480\pi$
$164$	6.91734			0.540154
$165$	0.690219	+	1.19549i	0.0537334	+	0.0930691i
$166$	16.0857	−	27.8613i	1.24850	−	2.16246i
$167$	−3.82558	+	6.62610i	−0.296032	+	0.512743i	−0.975224	−	0.221218i	$-0.928997\pi$
$167$	−3.82558	+	6.62610i	−0.296032	+	0.512743i	0.679192	+	0.733960i	$0.262330\pi$
$168$	13.1444			1.01411
$169$	−12.8177	+	2.16944i	−0.985977	+	0.166880i
$170$	8.42755			0.646364
$171$	4.13173	−	7.15636i	0.315961	−	0.547260i
$172$	4.79975	−	8.31342i	0.365978	−	0.633892i
$173$	0.0822298	+	0.142426i	0.00625182	+	0.0108285i	0.869134	−	0.494576i	$-0.164677\pi$
$173$	0.0822298	+	0.142426i	0.00625182	+	0.0108285i	−0.862883	+	0.505404i	$0.831343\pi$
$174$	1.52497			0.115608
$175$	−2.22540	−	3.85450i	−0.168224	−	0.291373i
$176$	10.4900	+	18.1692i	0.790711	+	1.36955i
$177$	−14.9915			−1.12683
$178$	−2.41353	−	4.18036i	−0.180902	−	0.313331i
$179$	−0.384316	+	0.665655i	−0.0287252	+	0.0497534i	−0.880031	−	0.474917i	$-0.842478\pi$
$179$	−0.384316	+	0.665655i	−0.0287252	+	0.0497534i	0.851305	+	0.524670i	$0.175811\pi$
$180$	2.32343	−	4.02429i	0.173178	−	0.299953i
$181$	−9.92152			−0.737461			−0.368730	−	0.929536i	$-0.620207\pi$
$181$	−9.92152			−0.737461			−0.368730	+	0.929536i	$0.620207\pi$
$182$	0.827552	+	9.84840i	0.0613422	+	0.730012i
$183$	8.90541			0.658307
$184$	−11.2366	+	19.4624i	−0.828373	+	1.43478i
$185$	2.26249	−	3.91874i	0.166341	−	0.288112i
$186$	−5.18598	−	8.98238i	−0.380254	−	0.658620i
$187$	5.66224			0.414064
$188$	16.1503	+	27.9732i	1.17788	+	2.04015i
$189$	−2.82331	−	4.89012i	−0.205366	−	0.355704i
$190$	−14.7600			−1.07080
$191$	−4.94847	−	8.57099i	−0.358058	−	0.620175i	0.629578	−	0.776937i	$-0.283228\pi$
$191$	−4.94847	−	8.57099i	−0.358058	−	0.620175i	−0.987636	+	0.156762i	$0.949894\pi$
$192$	−21.8069	+	37.7706i	−1.57378	+	2.72586i
$193$	−4.35037	+	7.53507i	−0.313147	+	0.542386i	−0.979042	−	0.203659i	$-0.934716\pi$
$193$	−4.35037	+	7.53507i	−0.313147	+	0.542386i	0.665895	+	0.746045i	$0.268050\pi$
$194$	−26.1330			−1.87624
$195$	−3.29982	−	1.55255i	−0.236305	−	0.111180i
$196$	5.51353			0.393824
$197$	13.0093	−	22.5328i	0.926874	−	1.60539i	0.138354	−	0.990383i	$-0.455819\pi$
$197$	13.0093	−	22.5328i	0.926874	−	1.60539i	0.788520	−	0.615009i	$-0.210848\pi$
$198$	2.12731	−	3.68460i	0.151181	−	0.261853i
$199$	−5.06648	−	8.77540i	−0.359153	−	0.622072i	0.628666	−	0.777675i	$-0.283601\pi$
$199$	−5.06648	−	8.77540i	−0.359153	−	0.622072i	−0.987820	+	0.155603i	$0.950268\pi$
$200$	42.8651			3.03102
$201$	9.38973	+	16.2635i	0.662300	+	1.14714i
$202$	−10.2703	−	17.7887i	−0.722615	−	1.25161i
$203$	0.407629			0.0286099
$204$	15.6095	+	27.0364i	1.09288	+	1.89293i
$205$	−0.464885	+	0.805205i	−0.0324690	+	0.0562380i
$206$	3.84914	−	6.66690i	0.268182	−	0.464505i
$207$	2.65376			0.184449
$208$	−50.1508	−	23.5957i	−3.47733	−	1.63607i
$209$	−9.91685			−0.685963
$210$	−1.38622	+	2.40101i	−0.0956586	+	0.165685i
$211$	−8.33911	+	14.4438i	−0.574088	+	0.994349i	0.422052	+	0.906572i	$0.361310\pi$
$211$	−8.33911	+	14.4438i	−0.574088	+	0.994349i	−0.996140	+	0.0877779i	$0.972023\pi$
$212$	−12.5923	−	21.8105i	−0.864843	−	1.49795i
$213$	−6.57196			−0.450303
$214$	2.03727	+	3.52865i	0.139265	+	0.241214i
$215$	0.645142	+	1.11742i	0.0439983	+	0.0762074i
$216$	54.3819			3.70022
$217$	−1.38622	−	2.40101i	−0.0941030	−	0.162991i
$218$	3.93511	−	6.81582i	0.266520	−	0.461625i
$219$	−4.14214	+	7.17439i	−0.279900	+	0.484801i
$220$	−5.57662			−0.375976
$221$	−12.2826	+	8.53765i	−0.826216	+	0.574304i
$222$	22.8427			1.53310
$223$	−0.535180	+	0.926959i	−0.0358383	+	0.0620738i	−0.883388	−	0.468642i	$-0.844743\pi$
$223$	−0.535180	+	0.926959i	−0.0358383	+	0.0620738i	0.847550	+	0.530716i	$0.178077\pi$
$224$	−11.4370	+	19.8095i	−0.764168	+	1.32358i
$225$	−2.53087	−	4.38360i	−0.168725	−	0.292240i
$226$	34.0427			2.26449
$227$	12.2332	+	21.1885i	0.811947	+	1.40633i	0.911500	+	0.411300i	$0.134925\pi$
$227$	12.2332	+	21.1885i	0.811947	+	1.40633i	−0.0995534	+	0.995032i	$0.531741\pi$
$228$	−27.3384	−	47.3516i	−1.81053	−	3.13593i
$229$	4.72964			0.312543			0.156272	−	0.987714i	$-0.450052\pi$
$229$	4.72964			0.312543			0.156272	+	0.987714i	$0.450052\pi$
$230$	−2.37005	−	4.10505i	−0.156276	−	0.270679i
$231$	−0.931366	+	1.61317i	−0.0612794	+	0.106139i
$232$	−1.96291	+	3.39986i	−0.128871	+	0.223212i
$233$	20.5507			1.34632			0.673160	−	0.739497i	$-0.264936\pi$
$233$	20.5507			1.34632			0.673160	+	0.739497i	$0.264936\pi$
$234$	0.941148	+	11.2003i	0.0615248	+	0.732185i
$235$	−4.34157			−0.283213
$236$	30.2810	−	52.4482i	1.97113	−	3.41409i
$237$	6.22755	−	10.7864i	0.404523	−	0.700654i
$238$	5.68598	+	9.84840i	0.368567	+	0.638377i
$239$	6.25461			0.404577			0.202289	−	0.979326i	$-0.435162\pi$
$239$	6.25461			0.404577			0.202289	+	0.979326i	$0.435162\pi$
$240$	−7.77393	−	13.4648i	−0.501805	−	0.869152i
$241$	6.07220	+	10.5174i	0.391145	+	0.677483i	0.992601	−	0.121423i	$-0.0387458\pi$
$241$	6.07220	+	10.5174i	0.391145	+	0.677483i	−0.601456	+	0.798906i	$0.705412\pi$
$242$	25.0460			1.61002
$243$	−5.53911	−	9.59402i	−0.355334	−	0.615457i
$244$	−17.9878	+	31.1558i	−1.15155	+	1.99455i
$245$	−0.370541	+	0.641796i	−0.0236730	+	0.0410028i
$246$	−4.69361			−0.299254
$247$	21.5117	−	14.9528i	1.36876	−	0.951427i
$248$	26.7011			1.69552
$249$	−8.00929	+	13.8725i	−0.507568	+	0.879134i
$250$	−9.59902	+	16.6260i	−0.607095	+	1.05152i
$251$	3.15719	+	5.46842i	0.199280	+	0.345163i	0.948295	−	0.317390i	$-0.102806\pi$
$251$	3.15719	+	5.46842i	0.199280	+	0.345163i	−0.749015	+	0.662553i	$0.769473\pi$
$252$	6.27036			0.394996
$253$	−1.59237	−	2.75807i	−0.100112	−	0.173398i
$254$	7.44274	+	12.8912i	0.466999	+	0.808866i
$255$	−4.19619			−0.262775
$256$	−25.3948	−	43.9850i	−1.58717	−	2.74907i
$257$	−12.1781	+	21.0931i	−0.759649	+	1.31575i	0.183380	+	0.983042i	$0.441296\pi$
$257$	−12.1781	+	21.0931i	−0.759649	+	1.31575i	−0.943030	+	0.332709i	$0.892037\pi$
$258$	−3.25677	+	5.64088i	−0.202757	+	0.351186i
$259$	6.10590			0.379402
$260$	12.0969	−	8.40855i	0.750216	−	0.521476i
$261$	0.463583			0.0286951
$262$	−15.5173	+	26.8767i	−0.958661	+	1.66045i
$263$	4.78955	−	8.29574i	0.295336	−	0.511537i	−0.679727	−	0.733465i	$-0.737902\pi$
$263$	4.78955	−	8.29574i	0.295336	−	0.511537i	0.975063	+	0.221928i	$0.0712350\pi$
$264$	−8.96987	−	15.5363i	−0.552057	−	0.956191i
$265$	3.38510			0.207945
$266$	−9.95843	−	17.2485i	−0.610590	−	1.05757i
$267$	1.20173	+	2.08145i	0.0735445	+	0.127383i
$268$	−75.8643			−4.63415
$269$	−14.6995	−	25.4603i	−0.896245	−	1.55234i	−0.832256	−	0.554391i	$-0.812951\pi$
$269$	−14.6995	−	25.4603i	−0.896245	−	1.55234i	−0.0639886	−	0.997951i	$-0.520382\pi$
$270$	−5.73518	+	9.93362i	−0.349032	+	0.604541i
$271$	0.150192	−	0.260141i	0.00912354	−	0.0158024i	−0.861428	−	0.507880i	$-0.830429\pi$
$271$	0.150192	−	0.260141i	0.00912354	−	0.0158024i	0.870551	+	0.492078i	$0.163763\pi$
$272$	−63.7738			−3.86686
$273$	−0.412049	−	4.90364i	−0.0249383	−	0.296782i
$274$	38.3078			2.31426
$275$	−3.03727	+	5.26070i	−0.183154	+	0.317232i
$276$	8.77959	−	15.2067i	0.528469	−	0.915335i
$277$	16.3855	+	28.3805i	0.984509	+	1.70522i	0.644100	+	0.764941i	$0.277232\pi$
$277$	16.3855	+	28.3805i	0.984509	+	1.70522i	0.340408	+	0.940278i	$0.389435\pi$
$278$	−28.5919			−1.71483
$279$	−1.57651	−	2.73059i	−0.0943831	−	0.163476i
$280$	−3.56863	−	6.18106i	−0.213267	−	0.369389i
$281$	4.29482			0.256207			0.128104	−	0.991761i	$-0.459111\pi$
$281$	4.29482			0.256207			0.128104	+	0.991761i	$0.459111\pi$
$282$	−10.9584	−	18.9806i	−0.652565	−	1.13028i
$283$	10.5501	−	18.2734i	0.627140	−	1.08624i	−0.360983	−	0.932572i	$-0.617559\pi$
$283$	10.5501	−	18.2734i	0.627140	−	1.08624i	0.988123	−	0.153666i	$-0.0491079\pi$
$284$	13.2745	−	22.9922i	0.787699	−	1.36433i
$285$	7.34920			0.435329
$286$	11.0758	−	7.69879i	0.654924	−	0.455239i
$287$	−1.25461			−0.0740574
$288$	−13.0070	+	22.5287i	−0.766442	+	1.32752i
$289$	−0.105901	+	0.183427i	−0.00622950	+	0.0107898i
$290$	−0.414022	−	0.717107i	−0.0243122	−	0.0421100i
$291$	13.0119			0.762773
$292$	−16.7332	−	28.9828i	−0.979237	−	1.69609i
$293$	−8.88192	−	15.3839i	−0.518887	−	0.898739i	−0.999759	−	0.0219482i	$-0.993013\pi$
$293$	−8.88192	−	15.3839i	−0.518887	−	0.898739i	0.480872	−	0.876791i	$-0.340320\pi$
$294$	−3.74108			−0.218184
$295$	4.07012	+	7.04965i	0.236971	+	0.410446i
$296$	−29.4026	+	50.9268i	−1.70899	+	2.96006i
$297$	−3.85331	+	6.67413i	−0.223592	+	0.387272i
$298$	−22.3791			−1.29639
$299$	7.61286	+	3.58182i	0.440263	+	0.207142i
$300$	−33.4921			−1.93367
$301$	−0.870541	+	1.50782i	−0.0501771	+	0.0869094i
$302$	−3.37411	+	5.84413i	−0.194158	+	0.336292i
$303$	5.11371	+	8.85721i	0.293775	+	0.508833i
$304$	111.693			6.40606
$305$	−2.41777	−	4.18770i	−0.138441	−	0.239787i
$306$	6.46648	+	11.2003i	0.369664	+	0.640277i
$307$	18.0156			1.02821			0.514103	−	0.857729i	$-0.328125\pi$
$307$	18.0156			1.02821			0.514103	+	0.857729i	$0.328125\pi$
$308$	−3.76249	−	6.51682i	−0.214388	−	0.371330i
$309$	−1.91653	+	3.31953i	−0.109028	+	0.188842i
$310$	−2.81593	+	4.87733i	−0.159934	+	0.277014i
$311$	17.2545			0.978412			0.489206	−	0.872168i	$-0.337287\pi$
$311$	17.2545			0.978412			0.489206	+	0.872168i	$0.337287\pi$
$312$	42.8834	+	20.1765i	2.42780	+	1.14227i
$313$	6.81526			0.385221			0.192611	−	0.981275i	$-0.438305\pi$
$313$	6.81526			0.385221			0.192611	+	0.981275i	$0.438305\pi$
$314$	−17.7071	+	30.6697i	−0.999272	+	1.73079i
$315$	−0.421404	+	0.729894i	−0.0237434	+	0.0411249i
$316$	25.1578	+	43.5745i	1.41523	+	2.45126i
$317$	−25.0770			−1.40847			−0.704233	−	0.709969i	$-0.748709\pi$
$317$	−25.0770			−1.40847			−0.704233	+	0.709969i	$0.748709\pi$
$318$	8.54423	+	14.7990i	0.479136	+	0.829889i
$319$	−0.278170	−	0.481805i	−0.0155745	−	0.0269759i
$320$	23.6818			1.32385
$321$	−1.01438	−	1.75696i	−0.0566172	−	0.0980639i
$322$	3.19809	−	5.53926i	0.178223	−	0.308691i
$323$	15.0724	−	26.1061i	0.838650	−	1.45258i
$324$	−23.6796			−1.31553
$325$	−1.34373	−	15.9912i	−0.0745366	−	0.887033i
$326$	16.5217			0.915050
$327$	−1.95934	+	3.39368i	−0.108352	+	0.187671i
$328$	6.04151	−	10.4642i	0.333586	−	0.577789i
$329$	−2.92921	−	5.07355i	−0.161493	−	0.279714i
$330$	3.78389			0.208296
$331$	1.49767	+	2.59404i	0.0823193	+	0.142581i	0.904246	−	0.427012i	$-0.140434\pi$
$331$	1.49767	+	2.59404i	0.0823193	+	0.142581i	−0.821926	+	0.569594i	$0.807101\pi$
$332$	−32.3555	−	56.0414i	−1.77574	−	3.07567i
$333$	6.94405			0.380531
$334$	10.4862	+	18.1627i	0.573781	+	0.993817i
$335$	5.09852	−	8.83089i	0.278562	−	0.482483i
$336$	10.4900	−	18.1692i	0.572275	−	0.991209i
$337$	−29.4888			−1.60636			−0.803179	−	0.595738i	$-0.796860\pi$
$337$	−29.4888			−1.60636			−0.803179	+	0.595738i	$0.796860\pi$
$338$	−12.4173	+	33.4006i	−0.675411	+	1.81675i
$339$	−16.9503			−0.920613
$340$	8.47577	−	14.6805i	0.459663	−	0.796160i
$341$	−1.89195	+	3.27695i	−0.102455	+	0.177457i
$342$	−11.3254	−	19.6162i	−0.612407	−	1.06072i
$343$	−1.00000			−0.0539949
$344$	−8.38407	−	14.5216i	−0.452039	−	0.782954i
$345$	1.18008	+	2.04395i	0.0635332	+	0.110043i
$346$	0.450797			0.0242350
$347$	2.99343	+	5.18477i	0.160696	+	0.278333i	0.935118	−	0.354336i	$-0.115293\pi$
$347$	2.99343	+	5.18477i	0.160696	+	0.278333i	−0.774423	+	0.632668i	$0.781960\pi$
$348$	1.53370	−	2.65644i	0.0822149	−	0.142400i
$349$	15.1681	−	26.2719i	0.811929	−	1.40630i	−0.0995840	−	0.995029i	$-0.531751\pi$
$349$	15.1681	−	26.2719i	0.811929	−	1.40630i	0.911513	−	0.411272i	$-0.134915\pi$
$350$	−12.2000			−0.652117
$351$	−1.70476	−	20.2877i	−0.0909931	−	1.08288i
$352$	31.2189			1.66398
$353$	14.3031	−	24.7738i	0.761280	−	1.31857i	−0.180912	−	0.983499i	$-0.557905\pi$
$353$	14.3031	−	24.7738i	0.761280	−	1.31857i	0.942191	−	0.335075i	$-0.108762\pi$
$354$	−20.5465	+	35.5876i	−1.09203	+	1.89146i
$355$	1.78425	+	3.09041i	0.0946982	+	0.164022i
$356$	−9.70936			−0.514595
$357$	−2.83112	−	4.90364i	−0.149839	−	0.259528i
$358$	1.05344	+	1.82462i	0.0556762	+	0.0964340i
$359$	23.4618			1.23826			0.619132	−	0.785287i	$-0.287485\pi$
$359$	23.4618			1.23826			0.619132	+	0.785287i	$0.287485\pi$
$360$	−4.05849	−	7.02952i	−0.213901	−	0.370488i
$361$	−16.8978	+	29.2678i	−0.889357	+	1.54041i
$362$	−13.5978	+	23.5522i	−0.714687	+	1.23787i
$363$	−12.4707			−0.654543
$364$	17.9878	+	8.46319i	0.942818	+	0.443592i
$365$	4.49827			0.235450
$366$	12.2052	−	21.1401i	0.637978	−	1.10501i
$367$	−18.2598	+	31.6270i	−0.953156	+	1.65091i	−0.214623	+	0.976697i	$0.568852\pi$
$367$	−18.2598	+	31.6270i	−0.953156	+	1.65091i	−0.738533	+	0.674218i	$0.764481\pi$
$368$	17.9349	+	31.0641i	0.934920	+	1.61933i
$369$	−1.42683			−0.0742778
$370$	−6.20166	−	10.7416i	−0.322409	−	0.558429i
$371$	2.28389	+	3.95582i	0.118574	+	0.205376i
$372$	−20.8626			−1.08168
$373$	6.52491	+	11.3015i	0.337847	+	0.585168i	0.984028	−	0.178017i	$-0.0569680\pi$
$373$	6.52491	+	11.3015i	0.337847	+	0.585168i	−0.646181	+	0.763185i	$0.723635\pi$
$374$	7.76033	−	13.4413i	0.401277	−	0.695033i
$375$	4.77947	−	8.27829i	0.246811	−	0.427489i
$376$	56.4218			2.90973
$377$	1.32988	+	0.625705i	0.0684925	+	0.0322254i
$378$	−15.4779			−0.796095
$379$	−15.3018	+	26.5036i	−0.786003	+	1.36140i	0.142395	+	0.989810i	$0.454520\pi$
$379$	−15.3018	+	26.5036i	−0.786003	+	1.36140i	−0.928398	+	0.371587i	$0.878814\pi$
$380$	−14.8445	+	25.7114i	−0.761505	+	1.31897i
$381$	−3.70584	−	6.41870i	−0.189856	−	0.328840i
$382$	−27.1283			−1.38800
$383$	2.44299	+	4.23138i	0.124831	+	0.216213i	0.921667	−	0.387982i	$-0.126828\pi$
$383$	2.44299	+	4.23138i	0.124831	+	0.216213i	−0.796836	+	0.604196i	$0.793495\pi$
$384$	28.5555	+	49.4596i	1.45722	+	2.52398i
$385$	1.01144			0.0515479
$386$	11.9247	+	20.6542i	0.606953	+	1.05127i
$387$	−0.990038	+	1.71480i	−0.0503265	+	0.0871680i
$388$	−26.2825	+	45.5226i	−1.33429	+	2.31106i
$389$	−1.85425			−0.0940143			−0.0470072	−	0.998895i	$-0.514968\pi$
$389$	−1.85425			−0.0940143			−0.0470072	+	0.998895i	$0.514968\pi$
$390$	−8.20805	+	5.70543i	−0.415631	+	0.288906i
$391$	9.68082			0.489580
$392$	4.81544	−	8.34058i	0.243216	−	0.421263i
$393$	7.72625	−	13.3823i	0.389738	−	0.675046i
$394$	−35.6595	−	61.7641i	−1.79650	−	3.11163i
$395$	−6.76298			−0.340283
$396$	−4.27896	−	7.41137i	−0.215026	−	0.372435i
$397$	−10.7567	−	18.6312i	−0.539863	−	0.935071i	−0.998911	−	0.0466590i	$-0.985143\pi$
$397$	−10.7567	−	18.6312i	−0.539863	−	0.935071i	0.459048	−	0.888412i	$-0.348191\pi$
$398$	−27.7753			−1.39225
$399$	4.95843	+	8.58825i	0.248232	+	0.429950i
$400$	34.2087	−	59.2513i	1.71044	−	2.96256i
$401$	7.28266	−	12.6139i	0.363678	−	0.629910i	−0.624885	−	0.780717i	$-0.714854\pi$
$401$	7.28266	−	12.6139i	0.363678	−	0.629910i	0.988563	+	0.150808i	$0.0481874\pi$
$402$	51.4760			2.56739
$403$	−0.837022	−	9.96110i	−0.0416950	−	0.496198i
$404$	−41.3162			−2.05556
$405$	1.59141	−	2.75640i	0.0790776	−	0.136966i
$406$	0.558672	−	0.967649i	0.0277264	−	0.0480236i
$407$	−4.16673	−	7.21698i	−0.206537	−	0.357733i
$408$	54.5323			2.69975
$409$	11.0645	+	19.1643i	0.547105	+	0.947613i	0.998471	+	0.0552745i	$0.0176034\pi$
$409$	11.0645	+	19.1643i	0.547105	+	0.947613i	−0.451366	+	0.892339i	$0.649063\pi$
$410$	1.27429	+	2.20713i	0.0629326	+	0.109003i
$411$	−19.0739			−0.940847
$412$	−7.74232	−	13.4101i	−0.381437	−	0.660668i
$413$	−5.49213	+	9.51264i	−0.270250	+	0.468086i
$414$	3.63709	−	6.29962i	0.178753	−	0.309610i
$415$	8.69791			0.426964
$416$	−67.7204	+	47.0726i	−3.32027	+	2.30792i
$417$	14.2363			0.697153
$418$	−13.5915	+	23.5411i	−0.664780	+	1.15143i
$419$	−1.68795	+	2.92362i	−0.0824618	+	0.142828i	−0.904307	−	0.426883i	$-0.859612\pi$
$419$	−1.68795	+	2.92362i	−0.0824618	+	0.142828i	0.821845	+	0.569711i	$0.192945\pi$
$420$	2.78831	+	4.82950i	0.136056	+	0.235655i
$421$	−25.1101			−1.22379			−0.611895	−	0.790939i	$-0.709593\pi$
$421$	−25.1101			−1.22379			−0.611895	+	0.790939i	$0.709593\pi$
$422$	22.8582	+	39.5915i	1.11272	+	1.92729i
$423$	−3.33130	−	5.76998i	−0.161973	−	0.280546i
$424$	−43.9917			−2.13643
$425$	−9.23254	−	15.9912i	−0.447844	−	0.775688i
$426$	−9.00714	+	15.6008i	−0.436397	+	0.755862i
$427$	3.26249	−	5.65079i	0.157883	−	0.273461i
$428$	8.19570			0.396154
$429$	−5.51477	+	3.83332i	−0.266255	+	0.185075i
$430$	3.53678			0.170558
$431$	−5.39742	+	9.34861i	−0.259985	+	0.450307i	−0.966238	−	0.257653i	$-0.917051\pi$
$431$	−5.39742	+	9.34861i	−0.259985	+	0.450307i	0.706253	+	0.707960i	$0.250384\pi$
$432$	43.3998	−	75.1707i	2.08808	−	3.61665i
$433$	7.25910	+	12.5731i	0.348850	+	0.604226i	0.986045	−	0.166476i	$-0.0532389\pi$
$433$	7.25910	+	12.5731i	0.348850	+	0.604226i	−0.637195	+	0.770702i	$0.719906\pi$
$434$	−7.59951			−0.364788
$435$	0.206147	+	0.357057i	0.00988398	+	0.0171196i
$436$	−7.91526	−	13.7096i	−0.379072	−	0.656572i
$437$	−16.9550			−0.811068
$438$	11.3539	+	19.6656i	0.542512	+	0.939659i
$439$	7.21544	−	12.4975i	0.344374	−	0.596473i	−0.640866	−	0.767653i	$-0.721425\pi$
$439$	7.21544	−	12.4975i	0.344374	−	0.596473i	0.985240	+	0.171180i	$0.0547578\pi$
$440$	−4.87054	+	8.43602i	−0.232194	+	0.402172i
$441$	−1.13727			−0.0541556
$442$	3.43327	+	40.8582i	0.163304	+	1.94343i
$443$	−30.2430			−1.43689			−0.718445	−	0.695584i	$-0.755146\pi$
$443$	−30.2430			−1.43689			−0.718445	+	0.695584i	$0.755146\pi$
$444$	22.9734	−	39.7910i	1.09027	−	1.88840i
$445$	0.652525	−	1.13021i	0.0309326	−	0.0535769i
$446$	1.46697	+	2.54087i	0.0694632	+	0.120314i
$447$	11.1428			0.527038
$448$	15.9779	+	27.6745i	0.754883	+	1.30750i
$449$	−15.6380	−	27.0858i	−0.738003	−	1.27826i	−0.953393	−	0.301731i	$-0.902435\pi$
$449$	−15.6380	−	27.0858i	−0.738003	−	1.27826i	0.215390	−	0.976528i	$-0.430898\pi$
$450$	−13.8747			−0.654058
$451$	0.856160	+	1.48291i	0.0403150	+	0.0698276i
$452$	34.2375	−	59.3010i	1.61039	−	2.78928i
$453$	1.68001	−	2.90987i	0.0789338	−	0.136717i
$454$	67.0645			3.14749
$455$	−2.19403	+	1.52508i	−0.102858	+	0.0714966i
$456$	−95.5080			−4.47257
$457$	−10.3233	+	17.8805i	−0.482904	+	0.836415i	−0.999807	−	0.0196293i	$-0.993751\pi$
$457$	−10.3233	+	17.8805i	−0.482904	+	0.836415i	0.516903	+	0.856044i	$0.327085\pi$
$458$	6.48216	−	11.2274i	0.302892	−	0.524624i
$459$	−11.7131	−	20.2877i	−0.546721	−	0.946948i
$460$	−9.53444			−0.444545
$461$	−13.6480	−	23.6391i	−0.635653	−	1.10098i	−0.986376	−	0.164504i	$-0.947398\pi$
$461$	−13.6480	−	23.6391i	−0.635653	−	1.10098i	0.350724	−	0.936479i	$-0.385936\pi$
$462$	2.55295	+	4.42184i	0.118774	+	0.205723i
$463$	5.65977			0.263032			0.131516	−	0.991314i	$-0.458016\pi$
$463$	5.65977			0.263032			0.131516	+	0.991314i	$0.458016\pi$
$464$	3.13303	+	5.42656i	0.145447	+	0.251922i
$465$	1.40209	−	2.42849i	0.0650202	−	0.112618i
$466$	28.1656	−	48.7842i	1.30474	−	2.25988i
$467$	42.2145			1.95345			0.976727	−	0.214486i	$-0.0688075\pi$
$467$	42.2145			1.95345			0.976727	+	0.214486i	$0.0688075\pi$
$468$	20.4570	+	9.62491i	0.945624	+	0.444912i
$469$	13.7597			0.635362
$470$	−5.95031	+	10.3062i	−0.274467	+	0.475391i
$471$	8.81661	−	15.2708i	0.406248	−	0.703642i
$472$	−52.8940	−	91.6151i	−2.43464	−	4.21692i
$473$	2.37626			0.109261
$474$	−17.0702	−	29.5665i	−0.784062	−	1.35803i
$475$	16.1699	+	28.0070i	0.741925	+	1.28505i
$476$	22.8740			1.04843
$477$	2.59740	+	4.49882i	0.118927	+	0.205987i
$478$	8.57220	−	14.8475i	0.392083	−	0.679108i
$479$	−16.2658	+	28.1732i	−0.743204	+	1.28727i	0.207825	+	0.978166i	$0.433361\pi$
$479$	−16.2658	+	28.1732i	−0.743204	+	1.28727i	−0.951029	+	0.309101i	$0.899972\pi$
$480$	−23.1358			−1.05600
$481$	19.9204	+	9.37247i	0.908293	+	0.427348i
$482$	33.2888			1.51626
$483$	−1.59237	+	2.75807i	−0.0724554	+	0.125496i
$484$	25.1893	−	43.6292i	1.14497	−	1.98314i
$485$	−3.53267	−	6.11876i	−0.160410	−	0.277839i
$486$	−30.3663			−1.37744
$487$	−13.4291	−	23.2600i	−0.608533	−	1.05401i	−0.991482	−	0.130240i	$-0.958425\pi$
$487$	−13.4291	−	23.2600i	−0.608533	−	1.05401i	0.382950	−	0.923769i	$-0.374908\pi$
$488$	31.4206	+	54.4221i	1.42234	+	2.46357i
$489$	−8.22634			−0.372008
$490$	1.01568	+	1.75921i	0.0458839	+	0.0794732i
$491$	−21.8439	+	37.8348i	−0.985802	+	1.70746i	−0.347485	+	0.937685i	$0.612964\pi$
$491$	−21.8439	+	37.8348i	−0.985802	+	1.70746i	−0.638317	+	0.769774i	$0.720369\pi$
$492$	−4.72046	+	8.17608i	−0.212815	+	0.368606i
$493$	1.69113			0.0761649
$494$	−6.01304	−	71.5590i	−0.270539	−	3.21959i
$495$	1.15028			0.0517013
$496$	21.3090	−	36.9082i	0.956801	−	1.65723i
$497$	−2.40763	+	4.17014i	−0.107997	+	0.187056i
$498$	21.9541	+	38.0257i	0.983788	+	1.70397i
$499$	−18.1020			−0.810355			−0.405177	−	0.914238i	$-0.632790\pi$
$499$	−18.1020			−0.810355			−0.405177	+	0.914238i	$0.632790\pi$
$500$	19.3079	+	33.4422i	0.863474	+	1.49558i
$501$	−5.22122	−	9.04343i	−0.233267	−	0.404030i
$502$	17.3082			0.772505
$503$	14.2077	+	24.6085i	0.633492	+	1.09724i	0.986833	+	0.161745i	$0.0517123\pi$
$503$	14.2077	+	24.6085i	0.633492	+	1.09724i	−0.353341	+	0.935495i	$0.614954\pi$
$504$	5.47644	−	9.48548i	0.243940	−	0.422517i
$505$	2.77669	−	4.80937i	0.123561	−	0.214014i
$506$	−8.72964			−0.388080
$507$	6.18272	−	16.6306i	0.274584	−	0.738589i
$508$	29.9413			1.32843
$509$	−8.73956	+	15.1374i	−0.387374	+	0.670952i	−0.992095	−	0.125485i	$-0.959951\pi$
$509$	−8.73956	+	15.1374i	−0.387374	+	0.670952i	0.604721	+	0.796437i	$0.293285\pi$
$510$	−5.75104	+	9.96110i	−0.254660	+	0.441085i
$511$	3.03494	+	5.25666i	0.134258	+	0.232541i
$512$	−55.5280			−2.45402
$513$	20.5143	+	35.5319i	0.905730	+	1.56877i
$514$	33.3812	+	57.8179i	1.47238	+	2.55024i
$515$	2.08131			0.0917136
$516$	6.55080	+	11.3463i	0.288383	+	0.499494i
$517$	−3.99785	+	6.92447i	−0.175825	+	0.304538i
$518$	8.36839	−	14.4945i	0.367686	−	0.636851i
$519$	−0.224458			−0.00985260
$520$	−2.15479	−	25.6434i	−0.0944939	−	1.12454i
$521$	19.3087			0.845931			0.422966	−	0.906146i	$-0.360989\pi$
$521$	19.3087			0.845931			0.422966	+	0.906146i	$0.360989\pi$
$522$	0.635360	−	1.10048i	0.0278090	−	0.0481665i
$523$	5.01144	−	8.68007i	0.219135	−	0.379553i	−0.735409	−	0.677624i	$-0.763010\pi$
$523$	5.01144	−	8.68007i	0.219135	−	0.379553i	0.954544	+	0.298071i	$0.0963431\pi$
$524$	31.2121	+	54.0610i	1.36351	+	2.36167i
$525$	6.07453			0.265114
$526$	−13.1285	−	22.7393i	−0.572432	−	0.991481i
$527$	−5.75104	−	9.96110i	−0.250519	−	0.433912i
$528$	−28.6338			−1.24613
$529$	8.77750	+	15.2031i	0.381630	+	0.661003i
$530$	4.63942	−	8.03571i	0.201524	−	0.349049i
$531$	−6.24602	+	10.8184i	−0.271054	+	0.469479i
$532$	−40.0616			−1.73689
$533$	−4.09316	−	1.92581i	−0.177294	−	0.0834162i
$534$	6.58807			0.285093
$535$	−0.550798	+	0.954010i	−0.0238131	+	0.0412454i
$536$	−66.2588	+	114.764i	−2.86194	+	4.95703i
$537$	−0.524522	−	0.908500i	−0.0226348	−	0.0392046i
$538$	−80.5851			−3.47427
$539$	0.682410	+	1.18197i	0.0293935	+	0.0509110i
$540$	11.5360	+	19.9809i	0.496430	+	0.859842i
$541$	17.6153			0.757339			0.378670	−	0.925532i	$-0.376382\pi$
$541$	17.6153			0.757339			0.378670	+	0.925532i	$0.376382\pi$
$542$	−0.411690	−	0.713067i	−0.0176836	−	0.0306289i
$543$	6.77054	−	11.7269i	0.290552	−	0.503250i
$544$	−47.4489	+	82.1839i	−2.03435	+	3.52361i
$545$	2.12780			0.0911451
$546$	−12.2052	−	5.74251i	−0.522336	−	0.245757i
$547$	2.98425			0.127597			0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425			0.127597			0.0637987	+	0.997963i	$0.479678\pi$
$548$	38.5269	−	66.7306i	1.64579	−	2.85059i
$549$	3.71032	−	6.42647i	0.158353	−	0.274275i
$550$	8.32540	+	14.4200i	0.354996	+	0.614871i
$551$	−2.96185			−0.126179
$552$	−15.3359	−	26.5626i	−0.652740	−	1.13058i
$553$	−4.56291	−	7.90320i	−0.194035	−	0.336078i
$554$	89.8279			3.81642
$555$	3.08789	+	5.34838i	0.131073	+	0.227026i
$556$	−28.7555	+	49.8059i	−1.21950	+	2.11224i
$557$	−3.62798	+	6.28384i	−0.153722	+	0.266255i	−0.932593	−	0.360930i	$-0.882459\pi$
$557$	−3.62798	+	6.28384i	−0.153722	+	0.266255i	0.778871	+	0.627184i	$0.215793\pi$
$558$	−8.64268			−0.365874
$559$	−5.15461	+	3.58298i	−0.218017	+	0.151544i
$560$	−11.3919			−0.481395
$561$	−3.86397	+	6.69259i	−0.163137	+	0.282561i
$562$	5.88622	−	10.1952i	0.248295	−	0.430060i
$563$	−2.13967	−	3.70601i	−0.0901762	−	0.156190i	0.817409	−	0.576058i	$-0.195410\pi$
$563$	−2.13967	−	3.70601i	−0.0901762	−	0.156190i	−0.907585	+	0.419868i	$0.862076\pi$
$564$	−44.0845			−1.85629
$565$	4.60191	+	7.97074i	0.193604	+	0.335332i
$566$	−28.9188	−	50.0888i	−1.21555	−	2.10539i
$567$	4.29482			0.180365
$568$	−23.1876	−	40.1621i	−0.972929	−	1.68516i
$569$	9.88131	−	17.1149i	0.414246	−	0.717495i	−0.581103	−	0.813830i	$-0.697379\pi$
$569$	9.88131	−	17.1149i	0.414246	−	0.717495i	0.995349	+	0.0963347i	$0.0307119\pi$
$570$	10.0724	−	17.4459i	0.421886	−	0.730727i
$571$	−19.9236			−0.833778			−0.416889	−	0.908957i	$-0.636880\pi$
$571$	−19.9236			−0.833778			−0.416889	+	0.908957i	$0.636880\pi$
$572$	−2.27184	−	27.0364i	−0.0949905	−	1.13045i
$573$	13.5075			0.564285
$574$	−1.71950	+	2.97826i	−0.0717704	+	0.124310i
$575$	−5.19286	+	8.99430i	−0.216557	+	0.375088i
$576$	18.1711	+	31.4733i	0.757129	+	1.31139i
$577$	−28.7300			−1.19605			−0.598023	−	0.801479i	$-0.704047\pi$
$577$	−28.7300			−1.19605			−0.598023	+	0.801479i	$0.704047\pi$
$578$	0.290284	+	0.502787i	0.0120742	+	0.0209132i
$579$	−5.93747	−	10.2840i	−0.246753	−	0.427389i
$580$	−1.66556			−0.0691587
$581$	5.86839	+	10.1643i	0.243462	+	0.421688i
$582$	17.8334	−	30.8883i	0.739218	−	1.28036i
$583$	3.11710	−	5.39897i	0.129097	−	0.223603i
$584$	−58.4582			−2.41902
$585$	−2.49520	+	1.73442i	−0.103164	+	0.0717094i
$586$	−48.6921			−2.01145
$587$	−15.7694	+	27.3134i	−0.650872	+	1.12734i	0.332040	+	0.943265i	$0.392263\pi$
$587$	−15.7694	+	27.3134i	−0.650872	+	1.12734i	−0.982912	+	0.184078i	$0.941070\pi$
$588$	−3.76249	+	6.51682i	−0.155162	+	0.268749i
$589$	10.0724	+	17.4459i	0.415025	+	0.718845i
$590$	22.3130			0.918613
$591$	17.7553	+	30.7531i	0.730357	+	1.26502i
$592$	46.9298	+	81.2848i	1.92880	+	3.34079i
$593$	−11.1181			−0.456564			−0.228282	−	0.973595i	$-0.573311\pi$
$593$	−11.1181			−0.456564			−0.228282	+	0.973595i	$0.573311\pi$
$594$	10.5622	+	18.2943i	0.433374	+	0.750626i
$595$	−1.53727	+	2.66263i	−0.0630218	+	0.109157i
$596$	−22.5071	+	38.9835i	−0.921928	+	1.59683i
$597$	13.8297			0.566010
$598$	18.9364	−	13.1627i	0.774368	−	0.538264i
$599$	−7.29572			−0.298095			−0.149048	−	0.988830i	$-0.547621\pi$
$599$	−7.29572			−0.298095			−0.149048	+	0.988830i	$0.547621\pi$
$600$	−29.2515	+	50.6652i	−1.19419	+	2.06840i
$601$	0.586291	−	1.01548i	0.0239153	−	0.0414225i	−0.853820	−	0.520568i	$-0.825720\pi$
$601$	0.586291	−	1.01548i	0.0239153	−	0.0414225i	0.877735	+	0.479146i	$0.159053\pi$
$602$	2.38622	+	4.13306i	0.0972552	+	0.168451i
$603$	15.6484			0.637253
$604$	6.78683	+	11.7551i	0.276152	+	0.478310i
$605$	3.38573	+	5.86426i	0.137650	+	0.238416i
$606$	28.0342			1.13881
$607$	−0.316919	−	0.548920i	−0.0128633	−	0.0222800i	0.859522	−	0.511099i	$-0.170761\pi$
$607$	−0.316919	−	0.548920i	−0.0128633	−	0.0222800i	−0.872385	+	0.488819i	$0.837428\pi$
$608$	83.1020	−	143.937i	3.37023	−	5.83741i
$609$	−0.278170	+	0.481805i	−0.0112720	+	0.0195237i
$610$	−13.2546			−0.536664
$611$	−1.76870	−	21.0487i	−0.0715540	−	0.851538i
$612$	26.0139			1.05155
$613$	15.4275	−	26.7212i	0.623110	−	1.07926i	−0.365793	−	0.930696i	$-0.619202\pi$
$613$	15.4275	−	26.7212i	0.623110	−	1.07926i	0.988903	−	0.148562i	$-0.0474646\pi$
$614$	24.6911	−	42.7663i	0.996453	−	1.72591i
$615$	−0.634485	−	1.09896i	−0.0255849	−	0.0443143i
$616$	−13.1444			−0.529603
$617$	−16.9105	−	29.2898i	−0.680790	−	1.17916i	−0.974740	−	0.223341i	$-0.928304\pi$
$617$	−16.9105	−	29.2898i	−0.680790	−	1.17916i	0.293951	−	0.955821i	$-0.405030\pi$
$618$	5.25338	+	9.09911i	0.211322	+	0.366020i
$619$	−0.404797			−0.0162702			−0.00813509	−	0.999967i	$-0.502590\pi$
$619$	−0.404797			−0.0162702			−0.00813509	+	0.999967i	$0.502590\pi$
$620$	5.66408	+	9.81048i	0.227475	+	0.393998i
$621$	−6.58807	+	11.4109i	−0.264370	+	0.457902i
$622$	23.6480	−	40.9595i	0.948197	−	1.64233i
$623$	1.76101			0.0705532
$624$	62.1128	−	43.1747i	2.48650	−	1.72837i
$625$	17.0636			0.682543
$626$	9.34059	−	16.1784i	0.373325	−	0.646618i
$627$	6.76736	−	11.7214i	0.270262	−	0.468108i
$628$	35.6169	+	61.6903i	1.42127	+	2.46171i
$629$	25.3316			1.01004
$630$	1.15510	+	2.00070i	0.0460204	+	0.0797097i
$631$	−15.2254	−	26.3712i	−0.606114	−	1.04982i	−0.991874	−	0.127221i	$-0.959394\pi$
$631$	−15.2254	−	26.3712i	−0.606114	−	1.04982i	0.385761	−	0.922599i	$-0.373939\pi$
$632$	87.8897			3.49606
$633$	−11.3814	−	19.7131i	−0.452369	−	0.783526i
$634$	−34.3691	+	59.5290i	−1.36497	+	2.36420i
$635$	−2.01223	+	3.48528i	−0.0798529	+	0.138309i
$636$	34.3724			1.36296
$637$	−3.26249	−	1.53499i	−0.129264	−	0.0608183i
$638$	−1.52497			−0.0603743
$639$	−2.73812	+	4.74256i	−0.108318	+	0.187613i
$640$	15.5053	−	26.8560i	0.612903	−	1.06158i
$641$	−4.82282	−	8.35337i	−0.190490	−	0.329938i	0.754923	−	0.655814i	$-0.227674\pi$
$641$	−4.82282	−	8.35337i	−0.190490	−	0.329938i	−0.945413	+	0.325875i	$0.894341\pi$
$642$	−5.56100			−0.219475
$643$	−4.06648	−	7.04335i	−0.160366	−	0.277763i	0.774634	−	0.632410i	$-0.217934\pi$
$643$	−4.06648	−	7.04335i	−0.160366	−	0.277763i	−0.935000	+	0.354647i	$0.884601\pi$
$644$	−6.43278	−	11.1419i	−0.253487	−	0.439053i
$645$	−1.76101			−0.0693395
$646$	−41.3146	−	71.5590i	−1.62550	−	2.81545i
$647$	5.76136	−	9.97898i	0.226503	−	0.392314i	−0.730267	−	0.683162i	$-0.760604\pi$
$647$	5.76136	−	9.97898i	0.226503	−	0.392314i	0.956769	+	0.290848i	$0.0939375\pi$
$648$	−20.6814	+	35.8213i	−0.812443	+	1.40719i
$649$	14.9915			0.588469
$650$	−39.8023	−	18.7268i	−1.56118	−	0.734526i
$651$	3.78389			0.148302
$652$	16.6162	−	28.7801i	0.650740	−	1.12711i
$653$	−21.2020	+	36.7229i	−0.829697	+	1.43708i	0.0685797	+	0.997646i	$0.478153\pi$
$653$	−21.2020	+	36.7229i	−0.829697	+	1.43708i	−0.898276	+	0.439431i	$0.855180\pi$
$654$	5.37072	+	9.30236i	0.210012	+	0.363751i
$655$	−8.39054			−0.327845
$656$	−9.64292	−	16.7020i	−0.376493	−	0.652105i
$657$	3.45153	+	5.97823i	0.134657	+	0.233233i
$658$	−16.0584			−0.626023
$659$	1.25044	+	2.16582i	0.0487101	+	0.0843684i	0.889352	−	0.457222i	$-0.151156\pi$
$659$	1.25044	+	2.16582i	0.0487101	+	0.0843684i	−0.840642	+	0.541591i	$0.817822\pi$
$660$	3.80554	−	6.59139i	0.148130	−	0.256570i
$661$	−7.41968	+	12.8513i	−0.288592	+	0.499856i	−0.973474	−	0.228798i	$-0.926520\pi$
$661$	−7.41968	+	12.8513i	−0.288592	+	0.499856i	0.684882	+	0.728654i	$0.259854\pi$
$662$	8.21046			0.319109
$663$	−1.70947	−	20.3438i	−0.0663903	−	0.790088i
$664$	−113.035			−4.38663
$665$	2.69237	−	4.66332i	0.104406	−	0.180836i
$666$	9.51710	−	16.4841i	0.368780	−	0.638746i
$667$	−0.475592	−	0.823749i	−0.0184150	−	0.0318957i
$668$	42.1849			1.63218
$669$	−0.730424	−	1.26513i	−0.0282398	−	0.0489128i
$670$	−13.9755	−	24.2062i	−0.539919	−	0.935167i
$671$	−8.90541			−0.343790
$672$	−15.6095	−	27.0364i	−0.602148	−	1.04295i
$673$	−19.8046	+	34.3025i	−0.763410	+	1.32226i	0.177674	+	0.984089i	$0.443143\pi$
$673$	−19.8046	+	34.3025i	−0.763410	+	1.32226i	−0.941083	+	0.338175i	$0.890190\pi$
$674$	−40.4156	+	70.0019i	−1.55675	+	2.69637i
$675$	25.1320			0.967330
$676$	45.6942	+	55.2221i	1.75747	+	2.12393i
$677$	17.0321			0.654596			0.327298	−	0.944921i	$-0.393862\pi$
$677$	17.0321			0.654596			0.327298	+	0.944921i	$0.393862\pi$
$678$	−23.2311	+	40.2374i	−0.892183	+	1.54531i
$679$	4.76691	−	8.25652i	0.182937	−	0.316856i
$680$	−14.8052	−	25.6434i	−0.567755	−	0.983380i
$681$	−33.3922			−1.27959
$682$	5.18598	+	8.98238i	0.198581	+	0.343953i
$683$	−16.4456	−	28.4846i	−0.629272	−	1.08993i	−0.987698	−	0.156374i	$-0.950020\pi$
$683$	−16.4456	−	28.4846i	−0.629272	−	1.08993i	0.358426	−	0.933558i	$-0.383314\pi$
$684$	−45.5608			−1.74206
$685$	5.17846	+	8.96936i	0.197859	+	0.342702i
$686$	−1.37054	+	2.37385i	−0.0523275	+	0.0906339i
$687$	−3.22755	+	5.59028i	−0.123139	+	0.213283i
$688$	−26.7638			−1.02036
$689$	1.37905	+	16.4115i	0.0525375	+	0.625230i
$690$	6.46938			0.246285
$691$	11.8961	−	20.6047i	0.452550	−	0.783839i	−0.545994	−	0.837789i	$-0.683848\pi$
$691$	11.8961	−	20.6047i	0.452550	−	0.783839i	0.998544	+	0.0539500i	$0.0171812\pi$
$692$	0.453377	−	0.785272i	0.0172348	−	0.0298515i
$693$	0.776083	+	1.34421i	0.0294809	+	0.0510625i
$694$	16.4105			0.622933
$695$	−3.86507	−	6.69449i	−0.146610	−	0.253937i
$696$	−2.67902	−	4.64020i	−0.101548	−	0.175886i
$697$	−5.20502			−0.197154
$698$	−41.5769	−	72.0134i	−1.57371	−	2.72575i
$699$	−14.0240	+	24.2903i	−0.530436	+	0.918742i
$700$	−12.2698	+	21.2519i	−0.463755	+	0.803247i
$701$	29.7796			1.12476			0.562380	−	0.826879i	$-0.309886\pi$
$701$	29.7796			1.12476			0.562380	+	0.826879i	$0.309886\pi$
$702$	−50.4963	−	23.7583i	−1.90586	−	0.896699i
$703$	−44.3658			−1.67329
$704$	21.8069	−	37.7706i	0.821878	−	1.42353i
$705$	2.96273	−	5.13160i	0.111583	−	0.193267i
$706$	−39.2061	−	67.9069i	−1.47554	−	2.55571i
$707$	7.49361			0.281826
$708$	41.3281	+	71.5824i	1.55321	+	2.69023i
$709$	−5.96518	−	10.3320i	−0.224027	−	0.388026i	0.732000	−	0.681305i	$-0.238587\pi$
$709$	−5.96518	−	10.3320i	−0.224027	−	0.388026i	−0.956027	+	0.293278i	$0.905254\pi$
$710$	9.78155			0.367095
$711$	−5.18925	−	8.98805i	−0.194612	−	0.337078i
$712$	−8.48001	+	14.6878i	−0.317802	+	0.550449i
$713$	−3.23469	+	5.60265i	−0.121140	+	0.209821i
$714$	−15.5207			−0.580846
$715$	3.29982	+	1.55255i	0.123406	+	0.0580621i
$716$	4.23788			0.158377
$717$	−4.26821	+	7.39275i	−0.159399	+	0.276087i
$718$	32.1553	−	55.6946i	1.20002	−	2.07850i
$719$	−16.1819	−	28.0279i	−0.603484	−	1.04526i	−0.992289	−	0.123945i	$-0.960446\pi$
$719$	−16.1819	−	28.0279i	−0.603484	−	1.04526i	0.388805	−	0.921320i	$-0.372888\pi$
$720$	−12.9556			−0.482827
$721$	1.40424	+	2.43221i	0.0522966	+	0.0905804i
$722$	46.3182	+	80.2255i	1.72379	+	2.98568i
$723$	−16.5749			−0.616428
$724$	27.3513	+	47.3738i	1.01650	+	1.76063i
$725$	−0.907137	+	1.57121i	−0.0336902	+	0.0583532i
$726$	−17.0916	+	29.6036i	−0.634330	+	1.09869i
$727$	−31.4897			−1.16789			−0.583943	−	0.811794i	$-0.698491\pi$
$727$	−31.4897			−1.16789			−0.583943	+	0.811794i	$0.698491\pi$
$728$	28.5130	−	19.8194i	1.05676	−	0.734556i
$729$	28.0042			1.03719
$730$	6.16507	−	10.6782i	0.228179	−	0.395218i
$731$	−3.61162	+	6.25551i	−0.133581	+	0.231369i
$732$	−24.5501	−	42.5221i	−0.907399	−	1.57166i
$733$	2.66224			0.0983321			0.0491661	−	0.998791i	$-0.484344\pi$
$733$	2.66224			0.0983321			0.0491661	+	0.998791i	$0.484344\pi$
$734$	50.0517	+	86.6921i	1.84744	+	3.19986i
$735$	−0.505722	−	0.875935i	−0.0186538	−	0.0323094i
$736$	53.3755			1.96745
$737$	−9.38973	−	16.2635i	−0.345875	−	0.599073i
$738$	−1.95553	+	3.38708i	−0.0719840	+	0.124680i
$739$	17.7914	−	30.8156i	0.654467	−	1.13357i	−0.327560	−	0.944830i	$-0.606226\pi$
$739$	17.7914	−	30.8156i	0.654467	−	1.13357i	0.982027	−	0.188739i	$-0.0604402\pi$
$740$	−24.9486			−0.917128
$741$	2.99397	+	35.6302i	0.109986	+	1.30891i
$742$	12.5207			0.459648
$743$	−12.1203	+	20.9929i	−0.444650	+	0.770156i	−0.998028	−	0.0627740i	$-0.980005\pi$
$743$	−12.1203	+	20.9929i	−0.444650	+	0.770156i	0.553378	+	0.832930i	$0.313339\pi$
$744$	−18.2211	+	31.5599i	−0.668018	+	1.15704i
$745$	−3.02522	−	5.23983i	−0.110835	−	0.191973i
$746$	35.7706			1.30966
$747$	6.67393	+	11.5596i	0.244186	+	0.422943i
$748$	−15.6095	−	27.0364i	−0.570739	−	0.988549i
$749$	−1.48647			−0.0543144
$750$	−13.1009	−	22.6915i	−0.478378	−	0.828575i
$751$	14.5705	−	25.2368i	0.531684	−	0.920904i	−0.467632	−	0.883923i	$-0.654893\pi$
$751$	14.5705	−	25.2368i	0.531684	−	0.920904i	0.999316	−	0.0369807i	$-0.0117740\pi$
$752$	45.0277	−	77.9903i	1.64199	−	2.84401i
$753$	−8.61799			−0.314057
$754$	3.30799	−	2.29939i	0.120470	−	0.0837388i
$755$	−1.82446			−0.0663988
$756$	−15.5664	+	26.9618i	−0.566145	+	0.980592i
$757$	2.49495	−	4.32138i	0.0906805	−	0.157063i	−0.817117	−	0.576472i	$-0.804429\pi$
$757$	2.49495	−	4.32138i	0.0906805	−	0.157063i	0.907798	+	0.419408i	$0.137762\pi$
$758$	41.9436	+	72.6485i	1.52346	+	2.63871i
$759$	4.34660			0.157772
$760$	25.9299	+	44.9119i	0.940576	+	1.62913i
$761$	5.91858	+	10.2513i	0.214548	+	0.371609i	0.953133	−	0.302552i	$-0.0978387\pi$
$761$	5.91858	+	10.2513i	0.214548	+	0.371609i	−0.738584	+	0.674161i	$0.764505\pi$
$762$	−20.3160			−0.735971
$763$	1.43561	+	2.48654i	0.0519724	+	0.0900189i
$764$	−27.2835	+	47.2564i	−0.987083	+	1.70968i
$765$	−1.74828	+	3.02812i	−0.0632094	+	0.109482i
$766$	13.3929			0.483904
$767$	−32.5198	+	22.6045i	−1.17422	+	0.816202i
$768$	69.3186			2.50132
$769$	17.9092	−	31.0196i	0.645821	−	1.11859i	−0.338291	−	0.941042i	$-0.609849\pi$
$769$	17.9092	−	31.0196i	0.645821	−	1.11859i	0.984111	−	0.177553i	$-0.0568180\pi$
$770$	1.38622	−	2.40101i	0.0499561	−	0.0865264i

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37054 - 2.37385i) q^{2} +(-0.682410 + 1.18197i) q^{3} +(-2.75677 - 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 + 3.23987i) q^{6} +(0.500000 + 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +O(q^{10})\)	\(q+(1.37054 - 2.37385i) q^{2} +(-0.682410 + 1.18197i) q^{3} +(-2.75677 - 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 + 3.23987i) q^{6} +(0.500000 + 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 + 0.984903i) q^{9} +(1.01568 - 1.75921i) q^{10} +(0.682410 - 1.18197i) q^{11} +7.52497 q^{12} +(0.301907 + 3.59289i) q^{13} +2.74108 q^{14} +(-0.505722 + 0.875935i) q^{15} +(-7.68598 + 13.3125i) q^{16} +(2.07436 + 3.59289i) q^{17} +3.11734 q^{18} +(-3.63303 - 6.29259i) q^{19} +(-2.04299 - 3.53856i) q^{20} -1.36482 q^{21} +(-1.87054 - 3.23987i) q^{22} +(1.16673 - 2.02083i) q^{23} +(6.57220 - 11.3834i) q^{24} -4.45080 q^{25} +(8.94274 + 4.20752i) q^{26} -5.64662 q^{27} +(2.75677 - 4.77486i) q^{28} +(0.203815 - 0.353017i) q^{29} +(1.38622 + 2.40101i) q^{30} -2.77245 q^{31} +(11.4370 + 19.8095i) q^{32} +(0.931366 + 1.61317i) q^{33} +11.3720 q^{34} +(0.370541 + 0.641796i) q^{35} +(3.13518 - 5.43029i) q^{36} +(3.05295 - 5.28787i) q^{37} -19.9169 q^{38} +(-4.45271 - 2.09498i) q^{39} -7.13727 q^{40} +(-0.627306 + 1.08653i) q^{41} +(-1.87054 + 3.23987i) q^{42} +(0.870541 + 1.50782i) q^{43} -7.52497 q^{44} +(0.421404 + 0.729894i) q^{45} +(-3.19809 - 5.53926i) q^{46} -5.85843 q^{47} +(-10.4900 - 18.1692i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-6.10000 + 10.5655i) q^{50} -5.66224 q^{51} +(16.3232 - 11.3463i) q^{52} +4.56778 q^{53} +(-7.73893 + 13.4042i) q^{54} +(0.505722 - 0.875935i) q^{55} +(-4.81544 - 8.34058i) q^{56} +9.91685 q^{57} +(-0.558672 - 0.967649i) q^{58} +(5.49213 + 9.51264i) q^{59} +5.57662 q^{60} +(-3.26249 - 5.65079i) q^{61} +(-3.79975 + 6.58137i) q^{62} +(-0.568634 + 0.984903i) q^{63} +31.9557 q^{64} +(0.223738 + 2.66263i) q^{65} +5.10590 q^{66} +(6.87983 - 11.9162i) q^{67} +(11.4370 - 19.8095i) q^{68} +(1.59237 + 2.75807i) q^{69} +2.03137 q^{70} +(2.40763 + 4.17014i) q^{71} +(-5.47644 - 9.48548i) q^{72} +6.06987 q^{73} +(-8.36839 - 14.4945i) q^{74} +(3.03727 - 5.26070i) q^{75} +(-20.0308 + 34.6944i) q^{76} +1.36482 q^{77} +(-11.0758 + 7.69879i) q^{78} -9.12582 q^{79} +(-5.69594 + 9.86566i) q^{80} +(2.14741 - 3.71942i) q^{81} +(1.71950 + 2.97826i) q^{82} +11.7368 q^{83} +(3.76249 + 6.51682i) q^{84} +(1.53727 + 2.66263i) q^{85} +4.77245 q^{86} +(0.278170 + 0.481805i) q^{87} +(-6.57220 + 11.3834i) q^{88} +(0.880503 - 1.52508i) q^{89} +2.31021 q^{90} +(-2.96058 + 2.05790i) q^{91} -12.8656 q^{92} +(1.89195 - 3.27695i) q^{93} +(-8.02921 + 13.9070i) q^{94} +(-2.69237 - 4.66332i) q^{95} -31.2189 q^{96} +(-4.76691 - 8.25652i) q^{97} +(1.37054 + 2.37385i) q^{98} +1.55217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

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