LMFDB - Embedded newform 91.2.f.c.29.4

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			29.4
Root			$1.37054 + 2.37385i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.2.f.c.22.4

$q$-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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

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

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	0.698116	+	0.715984i	$0.254022\pi$
$2$	1.37054	+	2.37385i	0.969119	+	1.67856i	0.271003	+	0.962579i	$0.412645\pi$
$3$	−0.682410	−	1.18197i	−0.393989	−	0.682410i	0.598982	−	0.800762i	$-0.295572\pi$
$3$	−0.682410	−	1.18197i	−0.393989	−	0.682410i	−0.992972	+	0.118353i	$0.962239\pi$
$4$	−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	0.950373	−	0.311113i	$-0.100702\pi$
$11$	0.682410	+	1.18197i	0.205754	+	0.356377i	−0.744619	+	0.667490i	$0.767369\pi$
$12$	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	−0.496888	−	0.867814i	$-0.665524\pi$
$17$	2.07436	−	3.59289i	0.503105	−	0.871404i	0.999994	−	0.00358919i	$-0.00114248\pi$
$18$	3.11734			0.734765
$19$	−3.63303	+	6.29259i	−0.833474	+	1.44362i	0.0617933	+	0.998089i	$0.480318\pi$
$19$	−3.63303	+	6.29259i	−0.833474	+	1.44362i	−0.895267	+	0.445530i	$0.853015\pi$
$20$	−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	0.961646	−	0.274292i	$-0.0884435\pi$
$23$	1.16673	+	2.02083i	0.243279	+	0.421372i	−0.718367	+	0.695664i	$0.755110\pi$
$24$	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	0.884329	−	0.466865i	$-0.154617\pi$
$29$	0.203815	+	0.353017i	0.0378474	+	0.0655536i	−0.846481	+	0.532419i	$0.821283\pi$
$30$	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	0.999998	+	0.00219764i	$0.000699531\pi$
$37$	3.05295	+	5.28787i	0.501902	+	0.869320i	−0.498096	+	0.867122i	$0.665967\pi$
$38$	−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	0.812875	−	0.582438i	$-0.197901\pi$
$41$	−0.627306	−	1.08653i	−0.0979688	−	0.169687i	−0.910844	+	0.412751i	$0.864568\pi$
$42$	−1.87054	−	3.23987i	−0.288631	−	0.499923i
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	−0.791982	−	0.610545i	$-0.790951\pi$
$43$	0.870541	−	1.50782i	0.132756	−	0.229941i	0.924738	+	0.380604i	$0.124284\pi$
$44$	−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	−0.247940	−	0.968775i	$-0.579754\pi$
$59$	5.49213	−	9.51264i	0.715014	−	1.23844i	0.962954	−	0.269665i	$-0.0869130\pi$
$60$	5.57662			0.719939
$61$	−3.26249	+	5.65079i	−0.417719	+	0.723510i	−0.995710	−	0.0925333i	$-0.970504\pi$
$61$	−3.26249	+	5.65079i	−0.417719	+	0.723510i	0.577991	+	0.816043i	$0.303837\pi$
$62$	−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	0.889468	+	0.456997i	$0.151075\pi$
$67$	6.87983	+	11.9162i	0.840505	+	1.45580i	−0.0489630	+	0.998801i	$0.515592\pi$
$68$	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	−0.687054	−	0.726607i	$-0.741096\pi$
$71$	2.40763	−	4.17014i	0.285733	−	0.494904i	0.972787	+	0.231703i	$0.0744296\pi$
$72$	−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	0.908912	−	0.416989i	$-0.136915\pi$
$89$	0.880503	+	1.52508i	0.0933331	+	0.161658i	−0.815579	+	0.578646i	$0.803581\pi$
$90$	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	−0.999831	−	0.0183708i	$-0.994152\pi$
$97$	−4.76691	+	8.25652i	−0.484006	+	0.838323i	0.515825	+	0.856694i	$0.327485\pi$
$98$	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	0.989998	−	0.141079i	$-0.0450573\pi$
$101$	3.74680	+	6.48965i	0.372821	+	0.645745i	−0.617177	+	0.786824i	$0.711724\pi$
$102$	−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	0.827861	−	0.560933i	$-0.189557\pi$
$107$	−0.743235	−	1.28732i	−0.0718512	−	0.124450i	−0.899713	+	0.436483i	$0.856224\pi$
$108$	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	−0.410819	−	0.911717i	$-0.634757\pi$
$113$	6.20972	−	10.7555i	0.584161	−	1.01180i	0.994979	−	0.100079i	$-0.0319096\pi$
$114$	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	0.720042	−	0.693930i	$-0.244122\pi$
$127$	−2.71526	−	4.70296i	−0.240940	−	0.417321i	−0.960982	+	0.276610i	$0.910789\pi$
$128$	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	−0.396261	−	0.918138i	$-0.629693\pi$
$137$	6.98771	−	12.1031i	0.597000	−	1.03403i	0.993261	−	0.115897i	$-0.0369741\pi$
$138$	8.72964			0.743116
$139$	−5.21544	+	9.03340i	−0.442368	+	0.766203i	−0.997865	−	0.0653153i	$-0.979195\pi$
$139$	−5.21544	+	9.03340i	−0.442368	+	0.766203i	0.555497	+	0.831518i	$0.312528\pi$
$140$	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	−0.983374	−	0.181592i	$-0.941875\pi$
$149$	−4.08216	+	7.07052i	−0.334424	+	0.579239i	0.648950	+	0.760831i	$0.275208\pi$
$150$	−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	−0.723526	−	0.690297i	$-0.757480\pi$
$163$	3.01371	−	5.21990i	0.236052	−	0.408854i	0.959578	+	0.281443i	$0.0908131\pi$
$164$	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	0.679192	−	0.733960i	$-0.262330\pi$
$167$	−3.82558	−	6.62610i	−0.296032	−	0.512743i	−0.975224	+	0.221218i	$0.928997\pi$
$168$	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	−0.862883	−	0.505404i	$-0.831343\pi$
$173$	0.0822298	−	0.142426i	0.00625182	−	0.0108285i	0.869134	+	0.494576i	$0.164677\pi$
$174$	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	0.851305	−	0.524670i	$-0.175811\pi$
$179$	−0.384316	−	0.665655i	−0.0287252	−	0.0497534i	−0.880031	+	0.474917i	$0.842478\pi$
$180$	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	−0.987636	−	0.156762i	$-0.949894\pi$
$191$	−4.94847	+	8.57099i	−0.358058	+	0.620175i	0.629578	+	0.776937i	$0.283228\pi$
$192$	−21.8069	−	37.7706i	−1.57378	−	2.72586i
$193$	−4.35037	−	7.53507i	−0.313147	−	0.542386i	0.665895	−	0.746045i	$-0.268050\pi$
$193$	−4.35037	−	7.53507i	−0.313147	−	0.542386i	−0.979042	+	0.203659i	$0.934716\pi$
$194$	−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	0.788520	+	0.615009i	$0.210848\pi$
$197$	13.0093	+	22.5328i	0.926874	+	1.60539i	0.138354	+	0.990383i	$0.455819\pi$
$198$	2.12731	+	3.68460i	0.151181	+	0.261853i
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	−0.987820	−	0.155603i	$-0.950268\pi$
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	0.628666	+	0.777675i	$0.283601\pi$
$200$	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	−0.996140	−	0.0877779i	$-0.972023\pi$
$211$	−8.33911	−	14.4438i	−0.574088	−	0.994349i	0.422052	−	0.906572i	$-0.361310\pi$
$212$	−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	0.847550	−	0.530716i	$-0.178077\pi$
$223$	−0.535180	−	0.926959i	−0.0358383	−	0.0620738i	−0.883388	+	0.468642i	$0.844743\pi$
$224$	−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	−0.0995534	−	0.995032i	$-0.531741\pi$
$227$	12.2332	−	21.1885i	0.811947	−	1.40633i	0.911500	−	0.411300i	$-0.134925\pi$
$228$	−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	−0.601456	−	0.798906i	$-0.705412\pi$
$241$	6.07220	−	10.5174i	0.391145	−	0.677483i	0.992601	+	0.121423i	$0.0387458\pi$
$242$	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	−0.749015	−	0.662553i	$-0.769473\pi$
$251$	3.15719	−	5.46842i	0.199280	−	0.345163i	0.948295	+	0.317390i	$0.102806\pi$
$252$	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	−0.943030	−	0.332709i	$-0.892037\pi$
$257$	−12.1781	−	21.0931i	−0.759649	−	1.31575i	0.183380	−	0.983042i	$-0.441296\pi$
$258$	−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	0.975063	−	0.221928i	$-0.0712350\pi$
$263$	4.78955	+	8.29574i	0.295336	+	0.511537i	−0.679727	+	0.733465i	$0.737902\pi$
$264$	−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	−0.0639886	+	0.997951i	$0.520382\pi$
$269$	−14.6995	+	25.4603i	−0.896245	+	1.55234i	−0.832256	+	0.554391i	$0.812951\pi$
$270$	−5.73518	−	9.93362i	−0.349032	−	0.604541i
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	0.870551	−	0.492078i	$-0.163763\pi$
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	−0.861428	+	0.507880i	$0.830429\pi$
$272$	−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	0.340408	−	0.940278i	$-0.389435\pi$
$277$	16.3855	−	28.3805i	0.984509	−	1.70522i	0.644100	−	0.764941i	$-0.277232\pi$
$278$	−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	0.988123	+	0.153666i	$0.0491079\pi$
$283$	10.5501	+	18.2734i	0.627140	+	1.08624i	−0.360983	+	0.932572i	$0.617559\pi$
$284$	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	0.480872	+	0.876791i	$0.340320\pi$
$293$	−8.88192	+	15.3839i	−0.518887	+	0.898739i	−0.999759	+	0.0219482i	$0.993013\pi$
$294$	−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	−0.821926	−	0.569594i	$-0.807101\pi$
$331$	1.49767	−	2.59404i	0.0823193	−	0.142581i	0.904246	+	0.427012i	$0.140434\pi$
$332$	−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	−0.774423	−	0.632668i	$-0.781960\pi$
$347$	2.99343	−	5.18477i	0.160696	−	0.278333i	0.935118	+	0.354336i	$0.115293\pi$
$348$	1.53370	+	2.65644i	0.0822149	+	0.142400i
$349$	15.1681	+	26.2719i	0.811929	+	1.40630i	0.911513	+	0.411272i	$0.134915\pi$
$349$	15.1681	+	26.2719i	0.811929	+	1.40630i	−0.0995840	+	0.995029i	$0.531751\pi$
$350$	−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	0.942191	+	0.335075i	$0.108762\pi$
$353$	14.3031	+	24.7738i	0.761280	+	1.31857i	−0.180912	+	0.983499i	$0.557905\pi$
$354$	−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	−0.738533	−	0.674218i	$-0.764481\pi$
$367$	−18.2598	−	31.6270i	−0.953156	−	1.65091i	−0.214623	−	0.976697i	$-0.568852\pi$
$368$	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	−0.646181	−	0.763185i	$-0.723635\pi$
$373$	6.52491	−	11.3015i	0.337847	−	0.585168i	0.984028	+	0.178017i	$0.0569680\pi$
$374$	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	−0.928398	−	0.371587i	$-0.878814\pi$
$379$	−15.3018	−	26.5036i	−0.786003	−	1.36140i	0.142395	−	0.989810i	$-0.454520\pi$
$380$	−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	−0.796836	−	0.604196i	$-0.793495\pi$
$383$	2.44299	−	4.23138i	0.124831	−	0.216213i	0.921667	+	0.387982i	$0.126828\pi$
$384$	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	0.459048	+	0.888412i	$0.348191\pi$
$397$	−10.7567	+	18.6312i	−0.539863	+	0.935071i	−0.998911	+	0.0466590i	$0.985143\pi$
$398$	−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	0.988563	−	0.150808i	$-0.0481874\pi$
$401$	7.28266	+	12.6139i	0.363678	+	0.629910i	−0.624885	+	0.780717i	$0.714854\pi$
$402$	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	−0.451366	−	0.892339i	$-0.649063\pi$
$409$	11.0645	−	19.1643i	0.547105	−	0.947613i	0.998471	−	0.0552745i	$-0.0176034\pi$
$410$	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	0.821845	−	0.569711i	$-0.192945\pi$
$419$	−1.68795	−	2.92362i	−0.0824618	−	0.142828i	−0.904307	+	0.426883i	$0.859612\pi$
$420$	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	0.706253	−	0.707960i	$-0.250384\pi$
$431$	−5.39742	−	9.34861i	−0.259985	−	0.450307i	−0.966238	+	0.257653i	$0.917051\pi$
$432$	43.3998	+	75.1707i	2.08808	+	3.61665i
$433$	7.25910	−	12.5731i	0.348850	−	0.604226i	−0.637195	−	0.770702i	$-0.719906\pi$
$433$	7.25910	−	12.5731i	0.348850	−	0.604226i	0.986045	+	0.166476i	$0.0532389\pi$
$434$	−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	0.985240	−	0.171180i	$-0.0547578\pi$
$439$	7.21544	+	12.4975i	0.344374	+	0.596473i	−0.640866	+	0.767653i	$0.721425\pi$
$440$	−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	0.215390	+	0.976528i	$0.430898\pi$
$449$	−15.6380	+	27.0858i	−0.738003	+	1.27826i	−0.953393	+	0.301731i	$0.902435\pi$
$450$	−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	0.516903	−	0.856044i	$-0.327085\pi$
$457$	−10.3233	−	17.8805i	−0.482904	−	0.836415i	−0.999807	+	0.0196293i	$0.993751\pi$
$458$	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	0.350724	+	0.936479i	$0.385936\pi$
$461$	−13.6480	+	23.6391i	−0.635653	+	1.10098i	−0.986376	+	0.164504i	$0.947398\pi$
$462$	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	−0.951029	−	0.309101i	$-0.899972\pi$
$479$	−16.2658	−	28.1732i	−0.743204	−	1.28727i	0.207825	−	0.978166i	$-0.433361\pi$
$480$	−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	0.382950	+	0.923769i	$0.374908\pi$
$487$	−13.4291	+	23.2600i	−0.608533	+	1.05401i	−0.991482	+	0.130240i	$0.958425\pi$
$488$	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	−0.638317	−	0.769774i	$-0.720369\pi$
$491$	−21.8439	−	37.8348i	−0.985802	−	1.70746i	−0.347485	−	0.937685i	$-0.612964\pi$
$492$	−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	−0.353341	−	0.935495i	$-0.614954\pi$
$503$	14.2077	−	24.6085i	0.633492	−	1.09724i	0.986833	−	0.161745i	$-0.0517123\pi$
$504$	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	0.604721	−	0.796437i	$-0.293285\pi$
$509$	−8.73956	−	15.1374i	−0.387374	−	0.670952i	−0.992095	+	0.125485i	$0.959951\pi$
$510$	−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	0.954544	−	0.298071i	$-0.0963431\pi$
$523$	5.01144	+	8.68007i	0.219135	+	0.379553i	−0.735409	+	0.677624i	$0.763010\pi$
$524$	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	0.778871	−	0.627184i	$-0.215793\pi$
$557$	−3.62798	−	6.28384i	−0.153722	−	0.266255i	−0.932593	+	0.360930i	$0.882459\pi$
$558$	−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	−0.907585	−	0.419868i	$-0.862076\pi$
$563$	−2.13967	+	3.70601i	−0.0901762	+	0.156190i	0.817409	+	0.576058i	$0.195410\pi$
$564$	−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	0.995349	−	0.0963347i	$-0.0307119\pi$
$569$	9.88131	+	17.1149i	0.414246	+	0.717495i	−0.581103	+	0.813830i	$0.697379\pi$
$570$	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	−0.982912	−	0.184078i	$-0.941070\pi$
$587$	−15.7694	−	27.3134i	−0.650872	−	1.12734i	0.332040	−	0.943265i	$-0.392263\pi$
$588$	−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	0.877735	−	0.479146i	$-0.159053\pi$
$601$	0.586291	+	1.01548i	0.0239153	+	0.0414225i	−0.853820	+	0.520568i	$0.825720\pi$
$602$	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	−0.872385	−	0.488819i	$-0.837428\pi$
$607$	−0.316919	+	0.548920i	−0.0128633	+	0.0222800i	0.859522	+	0.511099i	$0.170761\pi$
$608$	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	0.988903	+	0.148562i	$0.0474646\pi$
$613$	15.4275	+	26.7212i	0.623110	+	1.07926i	−0.365793	+	0.930696i	$0.619202\pi$
$614$	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	0.293951	+	0.955821i	$0.405030\pi$
$617$	−16.9105	+	29.2898i	−0.680790	+	1.17916i	−0.974740	+	0.223341i	$0.928304\pi$
$618$	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	0.385761	+	0.922599i	$0.373939\pi$
$631$	−15.2254	+	26.3712i	−0.606114	+	1.04982i	−0.991874	+	0.127221i	$0.959394\pi$
$632$	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	−0.945413	−	0.325875i	$-0.894341\pi$
$641$	−4.82282	+	8.35337i	−0.190490	+	0.329938i	0.754923	+	0.655814i	$0.227674\pi$
$642$	−5.56100			−0.219475
$643$	−4.06648	+	7.04335i	−0.160366	+	0.277763i	−0.935000	−	0.354647i	$-0.884601\pi$
$643$	−4.06648	+	7.04335i	−0.160366	+	0.277763i	0.774634	+	0.632410i	$0.217934\pi$
$644$	−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	0.956769	−	0.290848i	$-0.0939375\pi$
$647$	5.76136	+	9.97898i	0.226503	+	0.392314i	−0.730267	+	0.683162i	$0.760604\pi$
$648$	−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	−0.898276	−	0.439431i	$-0.855180\pi$
$653$	−21.2020	−	36.7229i	−0.829697	−	1.43708i	0.0685797	−	0.997646i	$-0.478153\pi$
$654$	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	−0.840642	−	0.541591i	$-0.817822\pi$
$659$	1.25044	−	2.16582i	0.0487101	−	0.0843684i	0.889352	+	0.457222i	$0.151156\pi$
$660$	3.80554	+	6.59139i	0.148130	+	0.256570i
$661$	−7.41968	−	12.8513i	−0.288592	−	0.499856i	0.684882	−	0.728654i	$-0.259854\pi$
$661$	−7.41968	−	12.8513i	−0.288592	−	0.499856i	−0.973474	+	0.228798i	$0.926520\pi$
$662$	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	−0.941083	−	0.338175i	$-0.890190\pi$
$673$	−19.8046	−	34.3025i	−0.763410	−	1.32226i	0.177674	−	0.984089i	$-0.443143\pi$
$674$	−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	0.358426	+	0.933558i	$0.383314\pi$
$683$	−16.4456	+	28.4846i	−0.629272	+	1.08993i	−0.987698	+	0.156374i	$0.950020\pi$
$684$	−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	0.998544	−	0.0539500i	$-0.0171812\pi$
$691$	11.8961	+	20.6047i	0.452550	+	0.783839i	−0.545994	+	0.837789i	$0.683848\pi$
$692$	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	−0.956027	−	0.293278i	$-0.905254\pi$
$709$	−5.96518	+	10.3320i	−0.224027	+	0.388026i	0.732000	+	0.681305i	$0.238587\pi$
$710$	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	0.388805	+	0.921320i	$0.372888\pi$
$719$	−16.1819	+	28.0279i	−0.603484	+	1.04526i	−0.992289	+	0.123945i	$0.960446\pi$
$720$	−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	0.982027	+	0.188739i	$0.0604402\pi$
$739$	17.7914	+	30.8156i	0.654467	+	1.13357i	−0.327560	+	0.944830i	$0.606226\pi$
$740$	−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	0.553378	−	0.832930i	$-0.313339\pi$
$743$	−12.1203	−	20.9929i	−0.444650	−	0.770156i	−0.998028	+	0.0627740i	$0.980005\pi$
$744$	−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	0.999316	+	0.0369807i	$0.0117740\pi$
$751$	14.5705	+	25.2368i	0.531684	+	0.920904i	−0.467632	+	0.883923i	$0.654893\pi$
$752$	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	0.907798	−	0.419408i	$-0.137762\pi$
$757$	2.49495	+	4.32138i	0.0906805	+	0.157063i	−0.817117	+	0.576472i	$0.804429\pi$
$758$	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	−0.738584	−	0.674161i	$-0.764505\pi$
$761$	5.91858	−	10.2513i	0.214548	−	0.371609i	0.953133	+	0.302552i	$0.0978387\pi$
$762$	−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	0.984111	+	0.177553i	$0.0568180\pi$
$769$	17.9092	+	31.0196i	0.645821	+	1.11859i	−0.338291	+	0.941042i	$0.609849\pi$
$770$	1.38622	+	2.40101i	0.0499561	+	0.0865264i
$771$	−16.6209	+	28.7883i	−0.598588	+	1.03678i
$772$	47.9718			1.72654
$773$	9.97669	−	17.2801i	0.358837	−	0.621523i	−0.628930	−	0.777462i	$-0.716507\pi$
$773$	9.97669	−	17.2801i	0.358837	−	0.621523i	0.987767	+	0.155939i	$0.0498402\pi$
$774$	2.71378	−	4.70040i	0.0975447	−	0.168952i
$775$	12.3396			0.443252
$776$	45.9095	−	79.5176i	1.64805	−	2.85451i
$777$	−4.16673	−	7.21698i	−0.149480	−	0.258908i
$778$	−2.54133	−	4.40171i	−0.0911110	−	0.157809i
$779$	9.11608			0.326618
$780$	1.68362	−	20.0362i	0.0602833	−	0.717411i
$781$	6.57196			0.235163
$782$	13.2680	+	22.9808i	0.474461	+	0.821791i
$783$	−1.15086	−	1.99335i	−0.0411285	−	0.0712367i
$784$	−7.68598	+	13.3125i	−0.274499	+	0.475447i
$785$	−9.57464			−0.341734
$786$	−21.1783	+	36.6819i	−0.755404	+	1.30840i
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	−0.889868	−	0.456219i	$-0.849203\pi$
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	0.840031	+	0.542539i	$0.182537\pi$
$788$	−143.454			−5.11035
$789$	6.53687	−	11.3222i	0.232719	−	0.403081i
$790$	−9.26895	−	16.0543i	−0.329774	−	0.571186i
$791$	−6.20972	−	10.7555i	−0.220792	−	0.382423i
$792$	−14.9487			−0.531179
$793$	19.3177	+	13.4278i	0.685992	+	0.476834i
$794$	−58.9700			−2.09277
$795$	−2.31003	−	4.00108i	−0.0819282	−	0.141904i
$796$	−27.9342	−	48.3835i	−0.990101	−	1.71491i
$797$	−0.842809	+	1.45979i	−0.0298538	+	0.0517083i	−0.880566	−	0.473923i	$-0.842838\pi$
$797$	−0.842809	+	1.45979i	−0.0298538	+	0.0517083i	0.850712	+	0.525631i	$0.176171\pi$
$798$	27.1829			0.962265
$799$	−12.1525	+	21.0487i	−0.429923	+	0.744649i
$800$	−50.9039	+	88.1681i	−1.79972	+	3.11721i
$801$	2.00273			0.0707632
$802$	−19.9624	+	34.5758i	−0.704895	+	1.22091i
$803$	4.14214	+	7.17439i	0.146173	+	0.253179i
$804$	51.7705	+	89.6692i	1.82581	+	3.16239i
$805$	1.72928			0.0609491
$806$	−24.7933	+	11.6651i	−0.873307	+	0.410887i
$807$	40.1244			1.41244
$808$	−36.0850	−	62.5010i	−1.26947	−	2.19878i
$809$	21.7186	+	37.6177i	0.763585	+	1.32257i	0.940992	+	0.338430i	$0.109896\pi$
$809$	21.7186	+	37.6177i	0.763585	+	1.32257i	−0.177407	+	0.984138i	$0.556771\pi$
$810$	−4.36217	+	7.55551i	−0.153271	+	0.265473i
$811$	5.60812			0.196928			0.0984639	−	0.995141i	$-0.468607\pi$
$811$	5.60812			0.196928			0.0984639	+	0.995141i	$0.468607\pi$
$812$	−1.12374	+	1.94637i	−0.0394355	+	0.0683042i
$813$	0.204986	−	0.355045i	0.00718916	−	0.0124520i
$814$	−22.8427			−0.800635
$815$	2.23341	−	3.86837i	0.0782328	−	0.135503i
$816$	43.5199	+	75.3786i	1.52350	+	2.63878i
$817$	6.32540	+	10.9559i	0.221298	+	0.383299i
$818$	60.6574			2.12084
$819$	−3.71032	+	1.74569i	−0.129649	+	0.0609993i
$820$	5.12632			0.179019
$821$	11.9724	+	20.7368i	0.417839	+	0.723718i	0.995722	−	0.0924014i	$-0.0294543\pi$
$821$	11.9724	+	20.7368i	0.417839	+	0.723718i	−0.577883	+	0.816120i	$0.696121\pi$
$822$	−26.1416	−	45.2785i	−0.911792	−	1.57927i
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	0.372810	+	0.927908i	$0.378394\pi$
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	−0.989997	+	0.141091i	$0.954939\pi$
$824$	−27.0481			−0.942266
$825$	−4.14532	+	7.17991i	−0.144322	+	0.249972i
$826$	15.0544	−	26.0749i	0.523808	−	0.907263i
$827$	−16.1563			−0.561811			−0.280905	−	0.959735i	$-0.590635\pi$
$827$	−16.1563			−0.561811			−0.280905	+	0.959735i	$0.590635\pi$
$828$	−7.31580	+	12.6713i	−0.254242	+	0.440359i
$829$	26.3505	+	45.6404i	0.915190	+	1.58516i	0.806623	+	0.591067i	$0.201293\pi$
$829$	26.3505	+	45.6404i	0.915190	+	1.58516i	0.108568	+	0.994089i	$0.465374\pi$
$830$	11.9208	+	20.6475i	0.413779	+	0.716686i
$831$	−44.7265			−1.55154
$832$	9.64766	−	114.813i	0.334472	−	3.98044i
$833$	−4.14871			−0.143744
$834$	19.5114	+	33.7947i	0.675624	+	1.17021i
$835$	−2.83507	−	4.91048i	−0.0981116	−	0.169934i
$836$	27.3384	−	47.3516i	0.945520	−	1.63769i
$837$	15.6550			0.541115
$838$	4.62681	−	8.01388i	0.159831	−	0.276835i
$839$	11.2169	−	19.4283i	0.387251	−	0.670738i	−0.604828	−	0.796356i	$-0.706758\pi$
$839$	11.2169	−	19.4283i	0.387251	−	0.670738i	0.992079	+	0.125618i	$0.0400913\pi$
$840$	9.74108			0.336099
$841$	14.4169	−	24.9708i	0.497135	−	0.861063i
$842$	−34.4144	−	59.6075i	−1.18600	−	2.05421i
$843$	−2.93083	−	5.07634i	−0.100943	−	0.174838i
$844$	91.9559			3.16525
$845$	−9.49897	−	1.60773i	−0.326774	−	0.0553076i
$846$	−18.2627			−0.627886
$847$	−4.56863	−	7.91311i	−0.156980	−	0.271898i
$848$	−35.1079	−	60.8086i	−1.20561	−	2.08818i
$849$	14.3990	−	24.9398i	0.494173	−	0.855933i
$850$	−50.6143			−1.73606
$851$	−7.12392	+	12.3390i	−0.244205	+	0.422975i
$852$	18.1173	−	31.3802i	0.620690	−	1.07507i
$853$	30.8521			1.05635			0.528177	−	0.849134i	$-0.322876\pi$
$853$	30.8521			1.05635			0.528177	+	0.849134i	$0.322876\pi$
$854$	−8.94274	+	15.4893i	−0.306014	+	0.530032i
$855$	3.06195	+	5.30345i	0.104716	+	0.181374i
$856$	7.15800	+	12.3980i	0.244655	+	0.423756i
$857$	26.7400			0.913420			0.456710	−	0.889616i	$-0.349028\pi$
$857$	26.7400			0.913420			0.456710	+	0.889616i	$0.349028\pi$
$858$	1.54151	−	18.3449i	0.0526262	−	0.626286i
$859$	−5.15804			−0.175990			−0.0879950	−	0.996121i	$-0.528046\pi$
$859$	−5.15804			−0.175990			−0.0879950	+	0.996121i	$0.528046\pi$
$860$	3.55701	+	6.16092i	0.121293	+	0.210086i
$861$	0.856160	+	1.48291i	0.0291778	+	0.0505375i
$862$	14.7948	−	25.6253i	0.503912	−	0.872801i
$863$	8.16814			0.278047			0.139023	−	0.990289i	$-0.455604\pi$
$863$	8.16814			0.278047			0.139023	+	0.990289i	$0.455604\pi$
$864$	−64.5806	+	111.857i	−2.19708	+	3.80545i
$865$	0.0609391	−	0.105550i	0.00207199	−	0.00358879i
$866$	39.7956			1.35231
$867$	−0.144536	+	0.250344i	−0.00490871	+	0.00850214i
$868$	−7.64299	−	13.2380i	−0.259420	−	0.449329i
$869$	−6.22755	−	10.7864i	−0.211255	−	0.365905i
$870$	1.13013			0.0383150
$871$	44.8907	−	21.1209i	1.52106	−	0.715654i
$872$	−27.6523			−0.936425
$873$	5.42125	+	9.38988i	0.183481	+	0.317799i
$874$	−23.2375	−	40.2486i	−0.786021	−	1.36143i
$875$	−3.50191	+	6.06548i	−0.118386	+	0.205051i
$876$	45.6756			1.54324
$877$	−7.80922	+	13.5260i	−0.263699	+	0.456740i	−0.967222	−	0.253933i	$-0.918276\pi$
$877$	−7.80922	+	13.5260i	−0.263699	+	0.456740i	0.703523	+	0.710672i	$0.251609\pi$
$878$	−19.7781	+	34.2567i	−0.667479	+	1.15611i
$879$	24.2444			0.817744
$880$	7.77393	−	13.4648i	0.262059	−	0.453900i
$881$	23.2188	+	40.2161i	0.782260	+	1.35491i	0.930622	+	0.365981i	$0.119266\pi$
$881$	23.2188	+	40.2161i	0.782260	+	1.35491i	−0.148362	+	0.988933i	$0.547400\pi$
$882$	−1.55867	−	2.69970i	−0.0524832	−	0.0909036i
$883$	15.6588			0.526960			0.263480	−	0.964665i	$-0.415130\pi$
$883$	15.6588			0.526960			0.263480	+	0.964665i	$0.415130\pi$
$884$	74.6263	−	35.1113i	2.50995	−	1.18092i
$885$	−11.1099			−0.373457
$886$	−41.4493	−	71.7923i	−1.39252	−	2.41191i
$887$	−15.7554	−	27.2891i	−0.529013	−	0.916278i	−0.999428	−	0.0338320i	$-0.989229\pi$
$887$	−15.7554	−	27.2891i	−0.529013	−	0.916278i	0.470414	−	0.882446i	$-0.344104\pi$
$888$	−40.1292	+	69.5059i	−1.34665	+	2.33246i
$889$	−5.43052			−0.182134
$890$	−1.78862	+	3.09799i	−0.0599548	+	0.103845i
$891$	−2.93083	+	5.07634i	−0.0981864	+	0.170064i
$892$	5.90146			0.197596
$893$	21.2838	−	36.8647i	0.712236	−	1.23363i
$894$	15.2717	+	26.4514i	0.510762	+	0.884666i
$895$	−0.284810	−	0.493305i	−0.00952015	−	0.0164894i
$896$	41.8452			1.39795
$897$	−9.42868	−	6.55389i	−0.314815	−	0.218828i
$898$	−85.7301			−2.86085
$899$	−0.565065	−	0.978722i	−0.0188460	−	0.0326422i
$900$	−13.9541	−	24.1691i	−0.465135	−	0.805638i
$901$	9.47521	−	16.4115i	0.315665	−	0.546748i
$902$	4.69361			0.156280
$903$	−1.18813	+	2.05790i	−0.0395385	+	0.0684827i
$904$	−59.8050	+	103.585i	−1.98908	+	3.44520i
$905$	−7.35266			−0.244411
$906$	−4.60505	+	7.97618i	−0.152993	+	0.264991i
$907$	0.373996	+	0.647780i	0.0124183	+	0.0215092i	0.872168	−	0.489207i	$-0.162714\pi$
$907$	0.373996	+	0.647780i	0.0124183	+	0.0215092i	−0.859749	+	0.510716i	$0.829380\pi$
$908$	67.4482	+	116.824i	2.23835	+	3.87693i
$909$	8.52224			0.282665
$910$	0.613284	−	7.29847i	0.0203302	−	0.241942i
$911$	24.9000			0.824973			0.412486	−	0.910964i	$-0.364660\pi$
$911$	24.9000			0.824973			0.412486	+	0.910964i	$0.364660\pi$
$912$	−76.2207	−	132.018i	−2.52392	−	4.37156i
$913$	8.00929	+	13.8725i	0.265069	+	0.459113i
$914$	28.2970	−	49.0119i	0.935983	−	1.62117i
$915$	6.59964			0.218177
$916$	−13.0385	+	22.5834i	−0.430804	+	0.746175i
$917$	−5.66100	+	9.80515i	−0.186943	+	0.323795i
$918$	−64.2132			−2.11935
$919$	−0.293247	+	0.507919i	−0.00967334	+	0.0167547i	−0.870822	−	0.491599i	$-0.836412\pi$
$919$	−0.293247	+	0.507919i	−0.00967334	+	0.0167547i	0.861148	+	0.508354i	$0.169746\pi$
$920$	−8.32724	−	14.4232i	−0.274541	−	0.475519i
$921$	−12.2940	−	21.2939i	−0.405102	−	0.701658i
$922$	−74.8208			−2.46409
$923$	−14.2560	−	9.90934i	−0.469240	−	0.326170i
$924$	10.2702			0.337866
$925$	−13.5881	−	23.5352i	−0.446773	−	0.773833i
$926$	7.75694	+	13.4354i	0.254909	+	0.441515i
$927$	1.59700	−	2.76608i	0.0524523	−	0.0908500i
$928$	9.32412			0.306079
$929$	25.0975	−	43.4701i	0.823421	−	1.42621i	−0.0796986	−	0.996819i	$-0.525396\pi$
$929$	25.0975	−	43.4701i	0.823421	−	1.42621i	0.903120	−	0.429388i	$-0.141271\pi$
$930$	−3.84324	+	6.65668i	−0.126025	+	0.218281i
$931$	7.26606			0.238135
$932$	−56.6534	+	98.1266i	−1.85574	+	3.21424i
$933$	−11.7746	−	20.3943i	−0.385484	−	0.667678i
$934$	57.8567	+	100.211i	1.89313	+	3.27900i
$935$	4.19619			0.137230
$936$	32.4269	+	22.5400i	1.05991	+	0.736742i
$937$	22.7130			0.742003			0.371001	−	0.928632i	$-0.379015\pi$
$937$	22.7130			0.742003			0.371001	+	0.928632i	$0.379015\pi$
$938$	18.8582	+	32.6633i	0.615741	+	1.06650i
$939$	−4.65080	−	8.05542i	−0.151773	−	0.262879i
$940$	11.9687	−	20.7304i	0.390376	−	0.676151i
$941$	−49.8734			−1.62583			−0.812914	−	0.582384i	$-0.802120\pi$
$941$	−49.8734			−1.62583			−0.812914	+	0.582384i	$0.802120\pi$
$942$	−24.1670	+	41.8586i	−0.787405	+	1.36383i
$943$	1.46379	−	2.53536i	0.0476675	−	0.0825626i
$944$	−168.849			−5.49558
$945$	−2.09231	+	3.62398i	−0.0680627	+	0.117888i
$946$	3.25677	+	5.64088i	0.105887	+	0.183401i
$947$	−0.133207	−	0.230722i	−0.00432865	−	0.00749745i	0.863853	−	0.503744i	$-0.168045\pi$
$947$	−0.133207	−	0.230722i	−0.00432865	−	0.00749745i	−0.868182	+	0.496247i	$0.834711\pi$
$948$	−68.6716			−2.23035
$949$	1.83254	−	21.8084i	0.0594867	−	0.707930i
$950$	88.6459			2.87605
$951$	17.1128	+	29.6402i	0.554920	+	0.961150i
$952$	19.9779	+	34.6027i	0.647486	+	1.12148i
$953$	−3.91014	+	6.77257i	−0.126662	+	0.219385i	−0.922381	−	0.386281i	$-0.873760\pi$
$953$	−3.91014	+	6.77257i	−0.126662	+	0.219385i	0.795719	+	0.605665i	$0.207093\pi$
$954$	14.2394			0.461016
$955$	−3.66722	+	6.35181i	−0.118668	+	0.205540i
$956$	−17.2425	+	29.8649i	−0.557662	+	0.965899i
$957$	0.759304			0.0245448
$958$	44.5859	−	77.2251i	1.44051	−	2.49503i
$959$	−6.98771	−	12.1031i	−0.225645	−	0.390828i
$960$	−16.1607	−	27.9911i	−0.521584	−	0.903410i
$961$	−23.3135			−0.752049
$962$	49.5506	+	34.4427i	1.59757	+	1.11048i
$963$	−1.69051			−0.0544761
$964$	33.4793	+	57.9878i	1.07829	+	1.86766i
$965$	−3.22398	−	5.58410i	−0.103784	−	0.179759i
$966$	4.36482	−	7.56009i	0.140436	−	0.243242i
$967$	39.8224			1.28060			0.640301	−	0.768124i	$-0.278810\pi$
$967$	39.8224			1.28060			0.640301	+	0.768124i	$0.278810\pi$
$968$	−43.9999	+	76.2101i	−1.41421	+	2.44949i
$969$	20.5711	−	35.6302i	0.660838	−	1.14461i
$970$	−19.3667			−0.621826
$971$	22.9648	−	39.7761i	0.736974	−	1.27648i	−0.216878	−	0.976199i	$-0.569587\pi$
$971$	22.9648	−	39.7761i	0.736974	−	1.27648i	0.953852	−	0.300278i	$-0.0970794\pi$
$972$	−30.5401	−	52.8969i	−0.979573	−	1.69667i
$973$	5.21544	+	9.03340i	0.167199	+	0.289598i
$974$	−73.6208			−2.35896
$975$	19.8181	−	9.32432i	0.634687	−	0.298617i
$976$	100.302			3.21058
$977$	14.3314	+	24.8227i	0.458501	+	0.794147i	0.998882	−	0.0472734i	$-0.0150532\pi$
$977$	14.3314	+	24.8227i	0.458501	+	0.794147i	−0.540381	+	0.841420i	$0.681720\pi$
$978$	−11.2745	−	19.5281i	−0.360520	−	0.624439i
$979$	−1.20173	+	2.08145i	−0.0384074	+	0.0665235i
$980$	4.08598			0.130522
$981$	1.63267	−	2.82787i	0.0521271	−	0.0902868i
$982$	59.8760	−	103.708i	1.91072	−	3.30946i
$983$	−46.1200			−1.47100			−0.735500	−	0.677524i	$-0.763053\pi$
$983$	−46.1200			−1.47100			−0.735500	+	0.677524i	$0.763053\pi$
$984$	8.24557	−	14.2817i	0.262859	−	0.455285i
$985$	9.64095	+	16.6986i	0.307186	+	0.532062i
$986$	2.31777	+	4.01449i	0.0738128	+	0.127848i
$987$	7.99569			0.254506
$988$	−130.700	+	61.4940i	−4.15814	+	1.95638i
$989$	4.06273			0.129187
$990$	1.57651	+	2.73059i	0.0501047	+	0.0867839i
$991$	−18.9124	−	32.7573i	−0.600773	−	1.04057i	−0.992704	−	0.120575i	$-0.961526\pi$
$991$	−18.9124	−	32.7573i	−0.600773	−	1.04057i	0.391931	−	0.919995i	$-0.371807\pi$
$992$	−31.7086	+	54.9208i	−1.00675	+	1.74374i
$993$	−4.08809			−0.129732
$994$	6.59951	−	11.4307i	0.209324	−	0.362559i
$995$	−3.75468	+	6.50329i	−0.119031	+	0.206168i
$996$	88.3189			2.79849
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	0.383952	+	0.923353i	$0.374563\pi$
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	−0.991623	+	0.129164i	$0.958771\pi$
$998$	−24.8095	−	42.9713i	−0.785330	−	1.36023i
$999$	−17.2389	−	29.8586i	−0.545414	−	0.944684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.f.c.29.4	yes	8
3.2	odd	2		819.2.o.h.757.1		8
4.3	odd	2		1456.2.s.q.1121.3		8
7.2	even	3		637.2.g.k.263.4		8
7.3	odd	6		637.2.h.i.471.1		8
7.4	even	3		637.2.h.h.471.1		8
7.5	odd	6		637.2.g.j.263.4		8
7.6	odd	2		637.2.f.i.393.4		8
13.2	odd	12		1183.2.c.g.337.8		8
13.3	even	3		1183.2.a.k.1.1		4
13.9	even	3	inner	91.2.f.c.22.4	✓	8
13.10	even	6		1183.2.a.l.1.4		4
13.11	odd	12		1183.2.c.g.337.1		8
39.35	odd	6		819.2.o.h.568.1		8
52.35	odd	6		1456.2.s.q.113.3		8
91.9	even	3		637.2.h.h.165.1		8
91.48	odd	6		637.2.f.i.295.4		8
91.55	odd	6		8281.2.a.bp.1.1		4
91.61	odd	6		637.2.h.i.165.1		8
91.62	odd	6		8281.2.a.bt.1.4		4
91.74	even	3		637.2.g.k.373.4		8
91.87	odd	6		637.2.g.j.373.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	13.9	even	3	inner
91.2.f.c.29.4	yes	8	1.1	even	1	trivial
637.2.f.i.295.4		8	91.48	odd	6
637.2.f.i.393.4		8	7.6	odd	2
637.2.g.j.263.4		8	7.5	odd	6
637.2.g.j.373.4		8	91.87	odd	6
637.2.g.k.263.4		8	7.2	even	3
637.2.g.k.373.4		8	91.74	even	3
637.2.h.h.165.1		8	91.9	even	3
637.2.h.h.471.1		8	7.4	even	3
637.2.h.i.165.1		8	91.61	odd	6
637.2.h.i.471.1		8	7.3	odd	6
819.2.o.h.568.1		8	39.35	odd	6
819.2.o.h.757.1		8	3.2	odd	2
1183.2.a.k.1.1		4	13.3	even	3
1183.2.a.l.1.4		4	13.10	even	6
1183.2.c.g.337.1		8	13.11	odd	12
1183.2.c.g.337.8		8	13.2	odd	12
1456.2.s.q.113.3		8	52.35	odd	6
1456.2.s.q.1121.3		8	4.3	odd	2
8281.2.a.bp.1.1		4	91.55	odd	6
8281.2.a.bt.1.4		4	91.62	odd	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more