LMFDB - Embedded newform 930.2.bg.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 $ x^16 + 40x^14 + 654x^12 + 5650x^10 + 27831x^8 + 78445x^6 + 119819x^4 + 87030*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.1
Root			$-3.17690i$ of defining polynomial
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.c.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.89605 + 0.403018i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.89605 + 0.403018i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(0.662442 + 0.735716i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(3.59101 - 1.59882i) q^{13} +(1.29705 - 1.44052i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.32709 - 1.47388i) q^{17} +(0.913545 - 0.406737i) q^{18} +(-3.68670 - 1.64142i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(0.202619 + 1.92779i) q^{21} +(-0.968370 - 0.205833i) q^{22} +(-0.256838 - 0.790465i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.96543 + 3.40422i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.202619 + 1.92779i) q^{28} +(5.80144 - 4.21499i) q^{29} +1.00000 q^{30} +(5.00360 - 2.44212i) q^{31} +1.00000 q^{32} +(0.800930 - 0.581910i) q^{33} +(-0.207312 + 1.97244i) q^{34} +(-0.599002 + 1.84354i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.84779 - 10.1287i) q^{37} +(3.94741 - 0.839047i) q^{38} +(-1.21470 - 3.73846i) q^{39} +(0.978148 + 0.207912i) q^{40} +(0.392166 + 3.73121i) q^{41} +(-1.29705 - 1.44052i) q^{42} +(-9.85284 - 4.38677i) q^{43} +(0.904413 - 0.402671i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(0.672410 + 0.488534i) q^{46} +(-8.50120 - 6.17648i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-2.96223 + 1.31887i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-1.32709 - 1.47388i) q^{51} +(-0.410886 - 3.90932i) q^{52} +(2.55555 + 0.543200i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.968370 - 0.205833i) q^{55} +(-0.969206 - 1.67871i) q^{56} +(-2.01780 + 3.49493i) q^{57} +(-2.21595 + 6.82000i) q^{58} +(-0.329023 + 3.13045i) q^{59} +(-0.809017 + 0.587785i) q^{60} -3.14596 q^{61} +(-2.61255 + 4.91676i) q^{62} +1.93841 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.410886 - 3.90932i) q^{65} +(-0.305928 + 0.941549i) q^{66} +(-4.08861 + 7.08167i) q^{67} +(-0.991653 - 1.71759i) q^{68} +(-0.812982 + 0.172805i) q^{69} +(-0.599002 - 1.84354i) q^{70} +(8.87799 + 1.88707i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-7.84748 - 8.71551i) q^{73} +(10.6844 + 4.75702i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(-2.70034 + 2.99903i) q^{76} +(-1.55253 - 1.12798i) q^{77} +(3.18013 + 2.31050i) q^{78} +(3.77541 - 4.19302i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-2.51042 - 2.78811i) q^{82} +(-0.434582 - 4.13478i) q^{83} +(1.89605 + 0.403018i) q^{84} +(-0.612875 - 1.88624i) q^{85} +(10.5496 - 2.24238i) q^{86} +(-3.58549 - 6.21025i) q^{87} +(-0.495002 + 0.857368i) q^{88} +(4.05819 - 12.4898i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-6.16440 + 4.47870i) q^{91} -0.831144 q^{92} +(-1.90573 - 5.23146i) q^{93} +10.5081 q^{94} +(-3.26486 + 2.37206i) q^{95} +(0.104528 - 0.994522i) q^{96} +(5.42487 - 16.6960i) q^{97} +(1.62128 - 2.80814i) q^{98} +(-0.495002 - 0.857368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−1.89605	+	0.403018i	−0.716641	+	0.152327i	−0.551779	−	0.833990i	$-0.686051\pi$
$7$	−1.89605	+	0.403018i	−0.716641	+	0.152327i	−0.164861	+	0.986317i	$0.552718\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.104528	+	0.994522i	0.0330548	+	0.314495i
$11$	0.662442	+	0.735716i	0.199734	+	0.221827i	0.834688	−	0.550723i	$-0.185648\pi$
$11$	0.662442	+	0.735716i	0.199734	+	0.221827i	−0.634955	+	0.772550i	$0.718981\pi$
$12$	−0.913545	−	0.406737i	−0.263718	−	0.117415i
$13$	3.59101	−	1.59882i	0.995968	−	0.443434i	0.156991	−	0.987600i	$-0.449821\pi$
$13$	3.59101	−	1.59882i	0.995968	−	0.443434i	0.838977	+	0.544166i	$0.183154\pi$
$14$	1.29705	−	1.44052i	0.346651	−	0.384995i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.32709	−	1.47388i	0.321867	−	0.357469i	−0.560397	−	0.828224i	$-0.689352\pi$
$17$	1.32709	−	1.47388i	0.321867	−	0.357469i	0.882264	+	0.470755i	$0.156018\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	−3.68670	−	1.64142i	−0.845787	−	0.376568i	−0.0623607	−	0.998054i	$-0.519863\pi$
$19$	−3.68670	−	1.64142i	−0.845787	−	0.376568i	−0.783426	+	0.621485i	$0.786530\pi$
$20$	−0.669131	−	0.743145i	−0.149622	−	0.166172i
$21$	0.202619	+	1.92779i	0.0442151	+	0.420679i
$22$	−0.968370	−	0.205833i	−0.206457	−	0.0438838i
$23$	−0.256838	−	0.790465i	−0.0535544	−	0.164823i	0.920702	−	0.390266i	$-0.127617\pi$
$23$	−0.256838	−	0.790465i	−0.0535544	−	0.164823i	−0.974256	+	0.225443i	$0.927617\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.96543	+	3.40422i	−0.385452	+	0.667622i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.202619	+	1.92779i	−0.0382914	+	0.364319i
$29$	5.80144	−	4.21499i	1.07730	−	0.782705i	0.100090	−	0.994978i	$-0.468087\pi$
$29$	5.80144	−	4.21499i	1.07730	−	0.782705i	0.977210	+	0.212274i	$0.0680868\pi$
$30$	1.00000			0.182574
$31$	5.00360	−	2.44212i	0.898673	−	0.438618i
$31$	5.00360	−	2.44212i	0.898673	−	0.438618i
$32$	1.00000			0.176777
$33$	0.800930	−	0.581910i	0.139424	−	0.101297i
$34$	−0.207312	+	1.97244i	−0.0355537	+	0.338271i
$35$	−0.599002	+	1.84354i	−0.101250	+	0.311615i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.84779	−	10.1287i	−0.961370	−	1.66514i	−0.719066	−	0.694942i	$-0.755430\pi$
$37$	−5.84779	−	10.1287i	−0.961370	−	1.66514i	−0.242304	−	0.970200i	$-0.577903\pi$
$38$	3.94741	−	0.839047i	0.640354	−	0.136111i
$39$	−1.21470	−	3.73846i	−0.194508	−	0.598633i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	0.392166	+	3.73121i	0.0612461	+	0.582718i	0.981509	+	0.191417i	$0.0613082\pi$
$41$	0.392166	+	3.73121i	0.0612461	+	0.582718i	−0.920263	+	0.391301i	$0.872025\pi$
$42$	−1.29705	−	1.44052i	−0.200139	−	0.222277i
$43$	−9.85284	−	4.38677i	−1.50254	−	0.668975i	−0.519857	−	0.854253i	$-0.674015\pi$
$43$	−9.85284	−	4.38677i	−1.50254	−	0.668975i	−0.982686	+	0.185278i	$0.940682\pi$
$44$	0.904413	−	0.402671i	0.136345	−	0.0607049i
$45$	−0.669131	+	0.743145i	−0.0997481	+	0.110781i
$46$	0.672410	+	0.488534i	0.0991414	+	0.0720305i
$47$	−8.50120	−	6.17648i	−1.24003	−	0.900933i	−0.242427	−	0.970170i	$-0.577944\pi$
$47$	−8.50120	−	6.17648i	−1.24003	−	0.900933i	−0.997600	+	0.0692367i	$0.977944\pi$
$48$	−0.669131	+	0.743145i	−0.0965807	+	0.107264i
$49$	−2.96223	+	1.31887i	−0.423175	+	0.188410i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	−1.32709	−	1.47388i	−0.185830	−	0.206385i
$52$	−0.410886	−	3.90932i	−0.0569797	−	0.542125i
$53$	2.55555	+	0.543200i	0.351032	+	0.0746142i	0.380053	−	0.924965i	$-0.375906\pi$
$53$	2.55555	+	0.543200i	0.351032	+	0.0746142i	−0.0290211	+	0.999579i	$0.509239\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	0.968370	−	0.205833i	0.130575	−	0.0277546i
$56$	−0.969206	−	1.67871i	−0.129516	−	0.224328i
$57$	−2.01780	+	3.49493i	−0.267264	+	0.462914i
$58$	−2.21595	+	6.82000i	−0.290969	+	0.895510i
$59$	−0.329023	+	3.13045i	−0.0428352	+	0.407549i	0.952004	+	0.306085i	$0.0990193\pi$
$59$	−0.329023	+	3.13045i	−0.0428352	+	0.407549i	−0.994839	+	0.101464i	$0.967647\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−3.14596			−0.402799			−0.201400	−	0.979509i	$-0.564549\pi$
$61$	−3.14596			−0.402799			−0.201400	+	0.979509i	$0.564549\pi$
$62$	−2.61255	+	4.91676i	−0.331795	+	0.624430i
$63$	1.93841			0.244217
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.410886	−	3.90932i	0.0509642	−	0.484892i
$66$	−0.305928	+	0.941549i	−0.0376571	+	0.115897i
$67$	−4.08861	+	7.08167i	−0.499503	+	0.865164i	−1.00000		0.000574109i	$-0.999817\pi$
$67$	−4.08861	+	7.08167i	−0.499503	+	0.865164i	0.500497	+	0.865738i	$0.333151\pi$
$68$	−0.991653	−	1.71759i	−0.120256	−	0.208289i
$69$	−0.812982	+	0.172805i	−0.0978715	+	0.0208032i
$70$	−0.599002	−	1.84354i	−0.0715944	−	0.220345i
$71$	8.87799	+	1.88707i	1.05362	+	0.223955i	0.701993	−	0.712184i	$-0.252294\pi$
$71$	8.87799	+	1.88707i	1.05362	+	0.223955i	0.351631	+	0.936139i	$0.385627\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	−7.84748	−	8.71551i	−0.918479	−	1.02007i	−0.999727	−	0.0233799i	$-0.992557\pi$
$73$	−7.84748	−	8.71551i	−0.918479	−	1.02007i	0.0812480	−	0.996694i	$-0.474109\pi$
$74$	10.6844	+	4.75702i	1.24204	+	0.552992i
$75$	−0.913545	+	0.406737i	−0.105487	+	0.0469659i
$76$	−2.70034	+	2.99903i	−0.309750	+	0.344012i
$77$	−1.55253	−	1.12798i	−0.176927	−	0.128545i
$78$	3.18013	+	2.31050i	0.360079	+	0.261612i
$79$	3.77541	−	4.19302i	0.424767	−	0.471751i	−0.492334	−	0.870406i	$-0.663856\pi$
$79$	3.77541	−	4.19302i	0.424767	−	0.471751i	0.917101	+	0.398655i	$0.130523\pi$
$80$	−0.913545	+	0.406737i	−0.102137	+	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−2.51042	−	2.78811i	−0.277230	−	0.307895i
$83$	−0.434582	−	4.13478i	−0.0477016	−	0.453851i	−0.992137	−	0.125154i	$-0.960057\pi$
$83$	−0.434582	−	4.13478i	−0.0477016	−	0.453851i	0.944436	−	0.328696i	$-0.106609\pi$
$84$	1.89605	+	0.403018i	0.206876	+	0.0439729i
$85$	−0.612875	−	1.88624i	−0.0664757	−	0.204591i
$86$	10.5496	−	2.24238i	1.13759	−	0.241802i
$87$	−3.58549	−	6.21025i	−0.384405	−	0.665808i
$88$	−0.495002	+	0.857368i	−0.0527674	+	0.0913958i
$89$	4.05819	−	12.4898i	0.430167	−	1.32392i	−0.467791	−	0.883839i	$-0.654950\pi$
$89$	4.05819	−	12.4898i	0.430167	−	1.32392i	0.897958	−	0.440080i	$-0.145050\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	−6.16440	+	4.47870i	−0.646204	+	0.469495i
$92$	−0.831144			−0.0866528
$93$	−1.90573	−	5.23146i	−0.197615	−	0.542477i
$94$	10.5081			1.08382
$95$	−3.26486	+	2.37206i	−0.334968	+	0.243368i
$96$	0.104528	−	0.994522i	0.0106684	−	0.101503i
$97$	5.42487	−	16.6960i	0.550812	−	1.69523i	−0.155942	−	0.987766i	$-0.549841\pi$
$97$	5.42487	−	16.6960i	0.550812	−	1.69523i	0.706754	−	0.707459i	$-0.250159\pi$
$98$	1.62128	−	2.80814i	0.163774	−	0.283665i
$99$	−0.495002	−	0.857368i	−0.0497496	−	0.0861688i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	2.85594	+	8.78967i	0.284176	+	0.874605i	0.986644	+	0.162890i	$0.0520815\pi$
$101$	2.85594	+	8.78967i	0.284176	+	0.874605i	−0.702468	+	0.711716i	$0.747919\pi$
$102$	1.93997	+	0.412353i	0.192085	+	0.0408290i
$103$	−0.112606	−	1.07138i	−0.0110954	−	0.105566i	0.987573	−	0.157164i	$-0.0502351\pi$
$103$	−0.112606	−	1.07138i	−0.0110954	−	0.105566i	−0.998668	+	0.0515983i	$0.983568\pi$
$104$	2.63026	+	2.92119i	0.257918	+	0.286447i
$105$	1.77083	+	0.788423i	0.172815	+	0.0769422i
$106$	−2.38677	+	1.06266i	−0.231824	+	0.103215i
$107$	8.52962	−	9.47310i	0.824589	−	0.915799i	−0.173019	−	0.984918i	$-0.555352\pi$
$107$	8.52962	−	9.47310i	0.824589	−	0.915799i	0.997608	+	0.0691195i	$0.0220190\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	0.275724	+	0.200325i	0.0264096	+	0.0191877i	0.600912	−	0.799315i	$-0.294804\pi$
$109$	0.275724	+	0.200325i	0.0264096	+	0.0191877i	−0.574502	+	0.818503i	$0.694804\pi$
$110$	−0.662442	+	0.735716i	−0.0631613	+	0.0701478i
$111$	−10.6844	+	4.75702i	−1.01412	+	0.451516i
$112$	1.77083	+	0.788423i	0.167327	+	0.0744990i
$113$	13.6539	+	15.1642i	1.28445	+	1.42652i	0.850843	+	0.525420i	$0.176092\pi$
$113$	13.6539	+	15.1642i	1.28445	+	1.42652i	0.433605	+	0.901103i	$0.357241\pi$
$114$	−0.421834	−	4.01349i	−0.0395084	−	0.375897i
$115$	−0.812982	−	0.172805i	−0.0758109	−	0.0161141i
$116$	−2.21595	−	6.82000i	−0.205746	−	0.633221i
$117$	−3.84496	+	0.817271i	−0.355466	+	0.0755567i
$118$	−1.57384	−	2.72598i	−0.144884	−	0.250947i
$119$	−1.92223	+	3.32940i	−0.176211	+	0.305206i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	1.04736	−	9.96500i	0.0952149	−	0.905909i
$122$	2.54514	−	1.84915i	0.230426	−	0.167414i
$123$	3.75177			0.338285
$124$	−0.776400	−	5.51337i	−0.0697228	−	0.495115i
$125$	−1.00000			−0.0894427
$126$	−1.56821	+	1.13937i	−0.139707	+	0.101503i
$127$	−0.847793	+	8.06621i	−0.0752295	+	0.715761i	0.890284	+	0.455406i	$0.150506\pi$
$127$	−0.847793	+	8.06621i	−0.0752295	+	0.715761i	−0.965513	+	0.260354i	$0.916161\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−5.39264	+	9.34032i	−0.474795	+	0.822369i
$130$	1.96543	+	3.40422i	0.172379	+	0.298570i
$131$	6.83815	−	1.45349i	0.597452	−	0.126992i	0.100747	−	0.994912i	$-0.467877\pi$
$131$	6.83815	−	1.45349i	0.597452	−	0.126992i	0.496705	+	0.867920i	$0.334543\pi$
$132$	−0.305928	−	0.941549i	−0.0266276	−	0.0819514i
$133$	7.65170	+	1.62642i	0.663486	+	0.141028i
$134$	−0.854751	−	8.13242i	−0.0738393	−	0.702534i
$135$	0.669131	+	0.743145i	0.0575896	+	0.0639597i
$136$	1.81184	+	0.806683i	0.155364	+	0.0691725i
$137$	7.50897	−	3.34321i	0.641535	−	0.285630i	−0.0600719	−	0.998194i	$-0.519133\pi$
$137$	7.50897	−	3.34321i	0.641535	−	0.285630i	0.701607	+	0.712564i	$0.252466\pi$
$138$	0.556144	−	0.617661i	0.0473421	−	0.0525788i
$139$	6.57678	+	4.77831i	0.557835	+	0.405291i	0.830666	−	0.556771i	$-0.187960\pi$
$139$	6.57678	+	4.77831i	0.557835	+	0.405291i	−0.272831	+	0.962062i	$0.587960\pi$
$140$	1.56821	+	1.13937i	0.132538	+	0.0962943i
$141$	−7.03127	+	7.80901i	−0.592139	+	0.657637i
$142$	−8.29164	+	3.69168i	−0.695819	+	0.309798i
$143$	3.55512	+	1.58284i	0.297294	+	0.132364i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	−0.749571	−	7.13169i	−0.0622485	−	0.592255i
$146$	11.4716	+	2.43836i	0.949396	+	0.201800i
$147$	1.00201	+	3.08386i	0.0826441	+	0.254352i
$148$	−11.4400	+	2.43165i	−0.940362	+	0.199880i
$149$	7.38511	+	12.7914i	0.605012	+	1.04791i	0.992050	+	0.125848i	$0.0401650\pi$
$149$	7.38511	+	12.7914i	0.605012	+	1.04791i	−0.387038	+	0.922064i	$0.626502\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	1.31174	−	4.03711i	0.106748	−	0.328536i	−0.883389	−	0.468641i	$-0.844744\pi$
$151$	1.31174	−	4.03711i	0.106748	−	0.328536i	0.990137	+	0.140105i	$0.0447440\pi$
$152$	0.421834	−	4.01349i	0.0342153	−	0.325537i
$153$	−1.60453	+	1.16576i	−0.129718	+	0.0942460i
$154$	1.91903			0.154640
$155$	0.386860	−	5.55431i	0.0310733	−	0.446133i
$156$	−3.93085			−0.314720
$157$	−19.8421	+	14.4161i	−1.58357	+	1.15053i	−0.671119	+	0.741349i	$0.734186\pi$
$157$	−19.8421	+	14.4161i	−1.58357	+	1.15053i	−0.912452	+	0.409183i	$0.865814\pi$
$158$	−0.589777	+	5.61135i	−0.0469201	+	0.446415i
$159$	0.807352	−	2.48477i	0.0640272	−	0.197055i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.805550	+	1.39525i	0.0634862	+	0.109961i
$162$	−0.978148	+	0.207912i	−0.0768505	+	0.0163351i
$163$	4.78591	+	14.7295i	0.374861	+	1.15370i	0.943572	+	0.331167i	$0.107442\pi$
$163$	4.78591	+	14.7295i	0.374861	+	1.15370i	−0.568711	+	0.822538i	$0.692558\pi$
$164$	3.66978	+	0.780036i	0.286562	+	0.0609106i
$165$	−0.103484	−	0.984580i	−0.00805618	−	0.0766495i
$166$	2.78194	+	3.08966i	0.215921	+	0.239804i
$167$	−7.99166	−	3.55811i	−0.618413	−	0.275335i	0.0735237	−	0.997293i	$-0.476576\pi$
$167$	−7.99166	−	3.55811i	−0.618413	−	0.275335i	−0.691937	+	0.721958i	$0.743242\pi$
$168$	−1.77083	+	0.788423i	−0.136622	+	0.0608282i
$169$	1.64045	−	1.82191i	0.126189	−	0.140147i
$170$	1.60453	+	1.16576i	0.123062	+	0.0894096i
$171$	3.26486	+	2.37206i	0.249670	+	0.181396i
$172$	−7.21676	+	8.01502i	−0.550272	+	0.611139i
$173$	2.64735	−	1.17867i	0.201274	−	0.0896129i	−0.303624	−	0.952792i	$-0.598197\pi$
$173$	2.64735	−	1.17867i	0.201274	−	0.0896129i	0.504898	+	0.863179i	$0.331530\pi$
$174$	6.55101	+	2.91670i	0.496631	+	0.221114i
$175$	1.29705	+	1.44052i	0.0980478	+	0.108893i
$176$	−0.103484	−	0.984580i	−0.00780037	−	0.0742155i
$177$	3.07890	+	0.654441i	0.231425	+	0.0491908i
$178$	4.05819	+	12.4898i	0.304174	+	0.936152i
$179$	−8.21502	+	1.74616i	−0.614019	+	0.130514i	−0.504415	−	0.863462i	$-0.668292\pi$
$179$	−8.21502	+	1.74616i	−0.614019	+	0.130514i	−0.109604	+	0.993975i	$0.534958\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	4.76038	−	8.24522i	0.353836	−	0.612862i	−0.633082	−	0.774085i	$-0.718210\pi$
$181$	4.76038	−	8.24522i	0.353836	−	0.612862i	0.986918	+	0.161222i	$0.0515437\pi$
$182$	2.35459	−	7.24668i	0.174534	−	0.537160i
$183$	−0.328842	+	3.12873i	−0.0243087	+	0.231282i
$184$	0.672410	−	0.488534i	0.0495707	−	0.0360152i
$185$	−11.6956			−0.859876
$186$	4.61674	+	3.11218i	0.338516	+	0.228196i
$187$	1.96348			0.143584
$188$	−8.50120	+	6.17648i	−0.620014	+	0.450466i
$189$	0.202619	−	1.92779i	0.0147384	−	0.140226i
$190$	1.24707	−	3.83808i	0.0904717	−	0.278443i
$191$	−11.8019	+	20.4415i	−0.853957	+	1.47910i	0.0236526	+	0.999720i	$0.492470\pi$
$191$	−11.8019	+	20.4415i	−0.853957	+	1.47910i	−0.877609	+	0.479376i	$0.840863\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	18.4984	−	3.93196i	1.33154	−	0.283029i	0.513454	−	0.858117i	$-0.328366\pi$
$193$	18.4984	−	3.93196i	1.33154	−	0.283029i	0.818091	+	0.575089i	$0.195032\pi$
$194$	5.42487	+	16.6960i	0.389483	+	1.19871i
$195$	−3.84496	−	0.817271i	−0.275343	−	0.0585260i
$196$	0.338940	+	3.22480i	0.0242100	+	0.230343i
$197$	−3.10907	−	3.45297i	−0.221512	−	0.246014i	0.622138	−	0.782908i	$-0.286264\pi$
$197$	−3.10907	−	3.45297i	−0.221512	−	0.246014i	−0.843650	+	0.536894i	$0.819598\pi$
$198$	0.904413	+	0.402671i	0.0642739	+	0.0286166i
$199$	−3.80388	+	1.69360i	−0.269650	+	0.120056i	−0.537108	−	0.843514i	$-0.680483\pi$
$199$	−3.80388	+	1.69360i	−0.269650	+	0.120056i	0.267458	+	0.963570i	$0.413816\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	6.61550	+	4.80644i	0.466622	+	0.339020i
$202$	−7.47694	−	5.43232i	−0.526076	−	0.382217i
$203$	−9.30112	+	10.3299i	−0.652810	+	0.725020i
$204$	−1.81184	+	0.806683i	−0.126854	+	0.0564791i
$205$	3.42741	+	1.52598i	0.239381	+	0.106579i
$206$	0.720839	+	0.800573i	0.0502232	+	0.0557785i
$207$	0.0868782	+	0.826591i	0.00603846	+	0.0574521i
$208$	−3.84496	−	0.817271i	−0.266600	−	0.0566675i
$209$	−1.23460	−	3.79971i	−0.0853991	−	0.262832i
$210$	−1.89605	+	0.403018i	−0.130840	+	0.0278109i
$211$	2.12131	+	3.67421i	0.146037	+	0.252943i	0.929759	−	0.368168i	$-0.120015\pi$
$211$	2.12131	+	3.67421i	0.146037	+	0.252943i	−0.783723	+	0.621111i	$0.786682\pi$
$212$	1.30632	−	2.26262i	0.0897186	−	0.155397i
$213$	2.80474	−	8.63210i	0.192178	−	0.591462i
$214$	−1.33246	+	12.6775i	−0.0910849	+	0.866615i
$215$	−8.72547	+	6.33942i	−0.595072	+	0.432345i
$216$	−1.00000			−0.0680414
$217$	−8.50287	+	6.64694i	−0.577213	+	0.451224i
$218$	−0.340814			−0.0230828
$219$	−9.48806	+	6.89348i	−0.641143	+	0.465818i
$220$	0.103484	−	0.984580i	0.00697686	−	0.0663804i
$221$	2.40912	−	7.41452i	0.162055	−	0.498755i
$222$	5.84779	−	10.1287i	0.392478	−	0.679791i
$223$	10.0076	+	17.3337i	0.670161	+	1.16075i	0.977858	+	0.209269i	$0.0671084\pi$
$223$	10.0076	+	17.3337i	0.670161	+	1.16075i	−0.307697	+	0.951484i	$0.599558\pi$
$224$	−1.89605	+	0.403018i	−0.126685	+	0.0269278i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−19.9595	−	4.24252i	−1.32768	−	0.282208i
$227$	−0.600613	−	5.71445i	−0.0398641	−	0.379281i	−0.996206	−	0.0870301i	$-0.972262\pi$
$227$	−0.600613	−	5.71445i	−0.0398641	−	0.379281i	0.956342	−	0.292251i	$-0.0944043\pi$
$228$	2.70034	+	2.99903i	0.178834	+	0.198616i
$229$	6.33125	+	2.81885i	0.418380	+	0.186275i	0.605120	−	0.796135i	$-0.293125\pi$
$229$	6.33125	+	2.81885i	0.418380	+	0.186275i	−0.186739	+	0.982410i	$0.559792\pi$
$230$	0.759288	−	0.338057i	0.0500660	−	0.0222908i
$231$	−1.28408	+	1.42612i	−0.0844866	+	0.0938318i
$232$	5.80144	+	4.21499i	0.380883	+	0.276728i
$233$	−17.6636	−	12.8333i	−1.15718	−	0.840740i	−0.167761	−	0.985828i	$-0.553654\pi$
$233$	−17.6636	−	12.8333i	−1.15718	−	0.840740i	−0.989419	+	0.145087i	$0.953654\pi$
$234$	2.63026	−	2.92119i	0.171945	−	0.190964i
$235$	−9.59959	+	4.27401i	−0.626208	+	0.278806i
$236$	2.87556	+	1.28028i	0.187183	+	0.0833392i
$237$	−3.77541	−	4.19302i	−0.245239	−	0.272366i
$238$	−0.401856	−	3.82340i	−0.0260484	−	0.247834i
$239$	0.677273	+	0.143959i	0.0438092	+	0.00931192i	0.229764	−	0.973246i	$-0.426205\pi$
$239$	0.677273	+	0.143959i	0.0438092	+	0.00931192i	−0.185955	+	0.982558i	$0.559538\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	28.6393	−	6.08748i	1.84482	−	0.392129i	0.853229	−	0.521536i	$-0.174641\pi$
$241$	28.6393	−	6.08748i	1.84482	−	0.392129i	0.991592	+	0.129407i	$0.0413074\pi$
$242$	5.00995	+	8.67748i	0.322052	+	0.557810i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.972155	+	2.99199i	−0.0622359	+	0.191542i
$245$	−0.338940	+	3.22480i	−0.0216541	+	0.206025i
$246$	−3.03524	+	2.20523i	−0.193520	+	0.140601i
$247$	−15.8633			−1.00936
$248$	3.86880	+	4.00405i	0.245669	+	0.254257i
$249$	−4.15755			−0.263474
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−1.10796	+	10.5415i	−0.0699337	+	0.665375i	0.902259	+	0.431194i	$0.141908\pi$
$251$	−1.10796	+	10.5415i	−0.0699337	+	0.665375i	−0.972193	+	0.234181i	$0.924759\pi$
$252$	0.599002	−	1.84354i	0.0377336	−	0.116132i
$253$	0.411418	−	0.712597i	0.0258656	−	0.0448006i
$254$	−4.05532	−	7.02402i	−0.254454	−	0.440726i
$255$	−1.93997	+	0.412353i	−0.121485	+	0.0258225i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.19238	+	0.253447i	0.0743784	+	0.0158096i	0.244951	−	0.969536i	$-0.421228\pi$
$257$	1.19238	+	0.253447i	0.0743784	+	0.0158096i	−0.170572	+	0.985345i	$0.554562\pi$
$258$	−1.12737	−	10.7262i	−0.0701869	−	0.667783i
$259$	15.1697	+	16.8477i	0.942602	+	1.04687i
$260$	−3.59101	−	1.59882i	−0.222705	−	0.0991548i
$261$	−6.55101	+	2.91670i	−0.405497	+	0.180539i
$262$	−4.67784	+	5.19527i	−0.288998	+	0.320965i
$263$	4.39568	+	3.19365i	0.271049	+	0.196929i	0.715004	−	0.699120i	$-0.246425\pi$
$263$	4.39568	+	3.19365i	0.271049	+	0.196929i	−0.443955	+	0.896049i	$0.646425\pi$
$264$	0.800930	+	0.581910i	0.0492938	+	0.0358141i
$265$	1.74820	−	1.94157i	0.107391	−	0.119270i
$266$	−7.14634	+	3.18175i	−0.438170	+	0.195086i
$267$	−11.9972	−	5.34150i	−0.734218	−	0.326895i
$268$	5.47162	+	6.07685i	0.334233	+	0.371203i
$269$	2.18450	+	20.7841i	0.133191	+	1.26723i	0.833151	+	0.553046i	$0.186535\pi$
$269$	2.18450	+	20.7841i	0.133191	+	1.26723i	−0.699959	+	0.714183i	$0.746799\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	0.0791185	+	0.243502i	0.00480611	+	0.0147917i	0.953431	−	0.301612i	$-0.0975247\pi$
$271$	0.0791185	+	0.243502i	0.00480611	+	0.0147917i	−0.948625	+	0.316403i	$0.897525\pi$
$272$	−1.93997	+	0.412353i	−0.117628	+	0.0250025i
$273$	3.80981	+	6.59878i	0.230580	+	0.399376i
$274$	−4.10980	+	7.11838i	−0.248282	+	0.430037i
$275$	0.305928	−	0.941549i	0.0184482	−	0.0567776i
$276$	−0.0868782	+	0.826591i	−0.00522946	+	0.0497549i
$277$	−3.47856	+	2.52732i	−0.209007	+	0.151852i	−0.687364	−	0.726313i	$-0.741232\pi$
$277$	−3.47856	+	2.52732i	−0.209007	+	0.151852i	0.478357	+	0.878165i	$0.341232\pi$
$278$	−8.12934			−0.487566
$279$	−5.40201	+	1.34845i	−0.323410	+	0.0807296i
$280$	−1.93841			−0.115842
$281$	−1.72401	+	1.25256i	−0.102846	+	0.0747217i	−0.638019	−	0.770020i	$-0.720246\pi$
$281$	−1.72401	+	1.25256i	−0.102846	+	0.0747217i	0.535174	+	0.844742i	$0.320246\pi$
$282$	1.09839	−	10.4505i	0.0654083	−	0.622318i
$283$	−1.48483	+	4.56983i	−0.0882639	+	0.271648i	−0.985440	−	0.170025i	$-0.945615\pi$
$283$	−1.48483	+	4.56983i	−0.0882639	+	0.271648i	0.897176	+	0.441674i	$0.145615\pi$
$284$	4.53816	−	7.86033i	0.269290	−	0.466425i
$285$	2.01780	+	3.49493i	0.119524	+	0.207022i
$286$	−3.80652	+	0.809101i	−0.225084	+	0.0478431i
$287$	−2.24732	−	6.91653i	−0.132655	−	0.408270i
$288$	−0.978148	−	0.207912i	−0.0576379	−	0.0122513i
$289$	1.36582	+	12.9949i	0.0803424	+	0.764407i
$290$	4.79832	+	5.32907i	0.281767	+	0.312934i
$291$	−16.0375	−	7.14036i	−0.940136	−	0.418575i
$292$	−10.7140	+	4.77016i	−0.626987	+	0.279152i
$293$	8.38145	−	9.30855i	0.489650	−	0.543811i	−0.446790	−	0.894639i	$-0.647433\pi$
$293$	8.38145	−	9.30855i	0.489650	−	0.543811i	0.936440	+	0.350828i	$0.114100\pi$
$294$	−2.62329	−	1.90593i	−0.152993	−	0.111156i
$295$	2.54653	+	1.85017i	0.148265	+	0.107721i
$296$	7.82587	−	8.69150i	0.454869	−	0.505183i
$297$	−0.904413	+	0.402671i	−0.0524794	+	0.0233653i
$298$	−13.4933	−	6.00759i	−0.781644	−	0.348010i
$299$	−2.18612	−	2.42793i	−0.126427	−	0.140411i
$300$	0.104528	+	0.994522i	0.00603495	+	0.0574187i
$301$	20.4494	+	4.34666i	1.17869	+	0.250537i
$302$	1.31174	+	4.03711i	0.0754820	+	0.232310i
$303$	9.04005	−	1.92152i	0.519337	−	0.110389i
$304$	2.01780	+	3.49493i	0.115729	+	0.200448i
$305$	−1.57298	+	2.72448i	−0.0900686	+	0.156003i
$306$	0.612875	−	1.88624i	0.0350358	−	0.107829i
$307$	0.961221	−	9.14541i	0.0548598	−	0.521956i	−0.932239	−	0.361843i	$-0.882148\pi$
$307$	0.961221	−	9.14541i	0.0548598	−	0.521956i	0.987099	−	0.160113i	$-0.0511858\pi$
$308$	−1.55253	+	1.12798i	−0.0884637	+	0.0642726i
$309$	−1.07728			−0.0612841
$310$	2.95176	+	4.72092i	0.167649	+	0.268130i
$311$	19.9975			1.13396			0.566978	−	0.823733i	$-0.308112\pi$
$311$	19.9975			1.13396			0.566978	+	0.823733i	$0.308112\pi$
$312$	3.18013	−	2.31050i	0.180039	−	0.130806i
$313$	1.74624	−	16.6143i	0.0987032	−	0.939098i	−0.827345	−	0.561694i	$-0.810150\pi$
$313$	1.74624	−	16.6143i	0.0987032	−	0.939098i	0.926048	−	0.377405i	$-0.123183\pi$
$314$	7.57901	−	23.3258i	0.427708	−	1.31635i
$315$	0.969206	−	1.67871i	0.0546086	−	0.0945848i
$316$	−2.82113	−	4.88634i	−0.158701	−	0.274878i
$317$	−11.2265	+	2.38627i	−0.630544	+	0.134026i	−0.512088	−	0.858933i	$-0.671128\pi$
$317$	−11.2265	+	2.38627i	−0.630544	+	0.134026i	−0.118456	+	0.992959i	$0.537794\pi$
$318$	0.807352	+	2.48477i	0.0452740	+	0.139339i
$319$	6.94416	+	1.47603i	0.388798	+	0.0826416i
$320$	0.104528	+	0.994522i	0.00584332	+	0.0555955i
$321$	−8.52962	−	9.47310i	−0.476077	−	0.528737i
$322$	−1.47181	−	0.655293i	−0.0820209	−	0.0365181i
$323$	−7.31185	+	3.25545i	−0.406842	+	0.181138i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	−3.18013	−	2.31050i	−0.176402	−	0.128163i
$326$	−12.5297	−	9.10334i	−0.693954	−	0.504187i
$327$	0.228049	−	0.253274i	0.0126111	−	0.0140061i
$328$	−3.42741	+	1.52598i	−0.189247	+	0.0842582i
$329$	18.6080	+	8.28480i	1.02589	+	0.456756i
$330$	0.662442	+	0.735716i	0.0364662	+	0.0404998i
$331$	−2.55375	−	24.2973i	−0.140367	−	1.33550i	−0.807192	−	0.590288i	$-0.799014\pi$
$331$	−2.55375	−	24.2973i	−0.140367	−	1.33550i	0.666825	−	0.745214i	$-0.267653\pi$
$332$	−4.06670	−	0.864403i	−0.223189	−	0.0474403i
$333$	3.61413	+	11.1232i	0.198053	+	0.609545i
$334$	8.55679	−	1.81880i	0.468207	−	0.0995204i
$335$	4.08861	+	7.08167i	0.223384	+	0.386913i
$336$	0.969206	−	1.67871i	0.0528745	−	0.0915813i
$337$	−5.64515	+	17.3740i	−0.307511	+	0.946421i	0.671218	+	0.741260i	$0.265772\pi$
$337$	−5.64515	+	17.3740i	−0.307511	+	0.946421i	−0.978728	+	0.205160i	$0.934228\pi$
$338$	−0.256264	+	2.43819i	−0.0139389	+	0.132620i
$339$	16.5083	−	11.9940i	0.896608	−	0.651424i
$340$	−1.98331			−0.107560
$341$	5.11130	+	2.06347i	0.276793	+	0.111743i
$342$	−4.03559			−0.218220
$343$	16.0625	−	11.6701i	0.867292	−	0.630124i
$344$	1.12737	−	10.7262i	0.0607836	−	0.578317i
$345$	−0.256838	+	0.790465i	−0.0138277	+	0.0425572i
$346$	−1.44894	+	2.50964i	−0.0778955	+	0.134919i
$347$	−1.96005	−	3.39490i	−0.105221	−	0.182248i	0.808608	−	0.588348i	$-0.200222\pi$
$347$	−1.96005	−	3.39490i	−0.105221	−	0.182248i	−0.913828	+	0.406101i	$0.866888\pi$
$348$	−7.01427	+	1.49093i	−0.376004	+	0.0799222i
$349$	3.05773	+	9.41072i	0.163676	+	0.503744i	0.998936	−	0.0461111i	$-0.0146828\pi$
$349$	3.05773	+	9.41072i	0.163676	+	0.503744i	−0.835260	+	0.549855i	$0.814683\pi$
$350$	−1.89605	−	0.403018i	−0.101348	−	0.0215422i
$351$	0.410886	+	3.90932i	0.0219315	+	0.208664i
$352$	0.662442	+	0.735716i	0.0353083	+	0.0392138i
$353$	16.7457	+	7.45567i	0.891284	+	0.396825i	0.800701	−	0.599064i	$-0.204460\pi$
$353$	16.7457	+	7.45567i	0.891284	+	0.396825i	0.0905829	+	0.995889i	$0.471127\pi$
$354$	−2.87556	+	1.28028i	−0.152834	+	0.0680461i
$355$	6.07325	−	6.74503i	0.322335	−	0.357989i
$356$	−10.6245	−	7.71914i	−0.563097	−	0.409114i
$357$	3.11024	+	2.25972i	0.164611	+	0.119597i
$358$	5.61972	−	6.24133i	0.297012	−	0.329865i
$359$	−3.90293	+	1.73770i	−0.205989	+	0.0917121i	−0.507138	−	0.861865i	$-0.669296\pi$
$359$	−3.90293	+	1.73770i	−0.205989	+	0.0917121i	0.301149	+	0.953577i	$0.402630\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	−1.81601	−	2.01688i	−0.0955795	−	0.106152i
$362$	0.995191	+	9.46861i	0.0523061	+	0.497659i
$363$	−9.80093	−	2.08325i	−0.514416	−	0.109342i
$364$	2.35459	+	7.24668i	0.123414	+	0.379829i
$365$	−11.4716	+	2.43836i	−0.600451	+	0.127630i
$366$	−1.57298	−	2.72448i	−0.0822210	−	0.142411i
$367$	−6.42411	+	11.1269i	−0.335336	+	0.580819i	−0.983549	−	0.180640i	$-0.942183\pi$
$367$	−6.42411	+	11.1269i	−0.335336	+	0.580819i	0.648213	+	0.761459i	$0.275516\pi$
$368$	−0.256838	+	0.790465i	−0.0133886	+	0.0412058i
$369$	0.392166	−	3.73121i	0.0204154	−	0.194239i
$370$	9.46192	−	6.87449i	0.491902	−	0.357387i
$371$	−5.06438			−0.262930
$372$	−5.56432	+	0.195843i	−0.288496	+	0.0101540i
$373$	17.2124			0.891227			0.445613	−	0.895226i	$-0.352986\pi$
$373$	17.2124			0.891227			0.445613	+	0.895226i	$0.352986\pi$
$374$	−1.58849	+	1.15410i	−0.0821388	+	0.0596773i
$375$	−0.104528	+	0.994522i	−0.00539783	+	0.0513569i
$376$	3.24717	−	9.99376i	0.167460	−	0.515389i
$377$	14.0940	−	24.4116i	0.725880	−	1.25726i
$378$	0.969206	+	1.67871i	0.0498506	+	0.0863437i
$379$	−23.6673	+	5.03064i	−1.21571	+	0.258407i	−0.770746	−	0.637143i	$-0.780116\pi$
$379$	−23.6673	+	5.03064i	−1.21571	+	0.258407i	−0.444962	+	0.895549i	$0.646783\pi$
$380$	1.24707	+	3.83808i	0.0639732	+	0.196889i
$381$	7.93341	+	1.68630i	0.406441	+	0.0863916i
$382$	−2.46727	−	23.4745i	−0.126237	−	1.20106i
$383$	14.1536	+	15.7192i	0.723217	+	0.803214i	0.986889	−	0.161398i	$-0.0516004\pi$
$383$	14.1536	+	15.7192i	0.723217	+	0.803214i	−0.263672	+	0.964612i	$0.584934\pi$
$384$	−0.913545	−	0.406737i	−0.0466192	−	0.0207562i
$385$	−1.75313	+	0.780542i	−0.0893475	+	0.0397801i
$386$	−12.6544	+	14.0541i	−0.644091	+	0.715336i
$387$	8.72547	+	6.33942i	0.443540	+	0.322251i
$388$	−14.2025	−	10.3187i	−0.721022	−	0.523853i
$389$	−23.2987	+	25.8758i	−1.18129	+	1.31196i	−0.241420	+	0.970421i	$0.577613\pi$
$389$	−23.2987	+	25.8758i	−1.18129	+	1.31196i	−0.939869	+	0.341535i	$0.889053\pi$
$390$	3.59101	−	1.59882i	0.181838	−	0.0809595i
$391$	−1.50590	−	0.670470i	−0.0761567	−	0.0339071i
$392$	−2.16970	−	2.40969i	−0.109586	−	0.121708i
$393$	−0.730750	−	6.95262i	−0.0368615	−	0.350713i
$394$	4.54490	+	0.966048i	0.228969	+	0.0486688i
$395$	−1.74355	−	5.36611i	−0.0877277	−	0.269998i
$396$	−0.968370	+	0.205833i	−0.0486624	+	0.0103435i
$397$	−0.724278	−	1.25449i	−0.0363505	−	0.0629609i	0.847278	−	0.531150i	$-0.178240\pi$
$397$	−0.724278	−	1.25449i	−0.0363505	−	0.0629609i	−0.883628	+	0.468189i	$0.844907\pi$
$398$	2.08193	−	3.60601i	0.104358	−	0.180753i
$399$	2.41733	−	7.43977i	0.121018	−	0.372455i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	17.3862	−	12.6318i	0.868227	−	0.630804i	−0.0618838	−	0.998083i	$-0.519711\pi$
$401$	17.3862	−	12.6318i	0.868227	−	0.630804i	0.930111	+	0.367280i	$0.119711\pi$
$402$	−8.17721			−0.407842
$403$	14.0635	−	16.7696i	0.700552	−	0.835352i
$404$	9.24201			0.459807
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	1.45298	−	13.8242i	0.0721101	−	0.686081i
$407$	3.57800	−	11.0120i	0.177355	−	0.545843i
$408$	0.991653	−	1.71759i	0.0490941	−	0.0850336i
$409$	1.86853	+	3.23639i	0.0923929	+	0.160029i	0.908518	−	0.417847i	$-0.137215\pi$
$409$	1.86853	+	3.23639i	0.0923929	+	0.160029i	−0.816125	+	0.577876i	$0.803882\pi$
$410$	−3.66978	+	0.780036i	−0.181238	+	0.0385232i
$411$	−2.53999	−	7.81730i	−0.125289	−	0.385599i
$412$	−1.05374	−	0.223978i	−0.0519138	−	0.0110346i
$413$	−0.637782	−	6.06809i	−0.0313832	−	0.298591i
$414$	−0.556144	−	0.617661i	−0.0273330	−	0.0303564i
$415$	−3.79811	−	1.69103i	−0.186442	−	0.0830093i
$416$	3.59101	−	1.59882i	0.176064	−	0.0783887i
$417$	5.43959	−	6.04128i	0.266378	−	0.295843i
$418$	3.23223	+	2.34835i	0.158093	+	0.114862i
$419$	−17.4557	−	12.6823i	−0.852768	−	0.619572i	0.0731396	−	0.997322i	$-0.476698\pi$
$419$	−17.4557	−	12.6823i	−0.852768	−	0.619572i	−0.925908	+	0.377749i	$0.876698\pi$
$420$	1.29705	−	1.44052i	0.0632896	−	0.0702902i
$421$	−2.14882	+	0.956718i	−0.104727	+	0.0466276i	−0.458432	−	0.888730i	$-0.651589\pi$
$421$	−2.14882	+	0.956718i	−0.104727	+	0.0466276i	0.353704	+	0.935357i	$0.384922\pi$
$422$	−3.87582	−	1.72563i	−0.188672	−	0.0840021i
$423$	7.03127	+	7.80901i	0.341872	+	0.379687i
$424$	0.273096	+	2.59833i	0.0132627	+	0.126186i
$425$	−1.93997	−	0.412353i	−0.0941022	−	0.0200020i
$426$	2.80474	+	8.63210i	0.135890	+	0.418227i
$427$	5.96491	−	1.26788i	0.288662	−	0.0613570i
$428$	−6.37366	−	11.0395i	−0.308082	−	0.533614i
$429$	1.94578	−	3.37019i	0.0939432	−	0.162714i
$430$	3.33283	−	10.2574i	0.160723	−	0.494656i
$431$	1.06986	−	10.1790i	0.0515333	−	0.490306i	−0.938066	−	0.346456i	$-0.887385\pi$
$431$	1.06986	−	10.1790i	0.0515333	−	0.490306i	0.989599	−	0.143850i	$-0.0459484\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	21.9143			1.05313			0.526566	−	0.850134i	$-0.323479\pi$
$433$	21.9143			1.05313			0.526566	+	0.850134i	$0.323479\pi$
$434$	2.97199	−	10.3753i	0.142660	−	0.498033i
$435$	−7.17098			−0.343822
$436$	0.275724	−	0.200325i	0.0132048	−	0.00959385i
$437$	−0.350605	+	3.33579i	−0.0167717	+	0.159572i
$438$	3.62411	−	11.1539i	0.173167	−	0.532953i
$439$	−4.98576	+	8.63558i	−0.237957	+	0.412154i	−0.960128	−	0.279561i	$-0.909811\pi$
$439$	−4.98576	+	8.63558i	−0.237957	+	0.412154i	0.722171	+	0.691715i	$0.243144\pi$
$440$	0.495002	+	0.857368i	0.0235983	+	0.0408734i
$441$	3.17170	−	0.674166i	0.151033	−	0.0321032i
$442$	2.40912	+	7.41452i	0.114590	+	0.352673i
$443$	−30.7700	−	6.54036i	−1.46193	−	0.310742i	−0.592806	−	0.805345i	$-0.701980\pi$
$443$	−30.7700	−	6.54036i	−1.46193	−	0.310742i	−0.869119	+	0.494603i	$0.835313\pi$
$444$	1.22252	+	11.6315i	0.0580182	+	0.552007i
$445$	−8.78741	−	9.75941i	−0.416563	−	0.462641i
$446$	−18.2849	−	8.14095i	−0.865814	−	0.385485i
$447$	13.4933	−	6.00759i	0.638210	−	0.284149i
$448$	1.29705	−	1.44052i	0.0612799	−	0.0680582i
$449$	9.41379	+	6.83952i	0.444264	+	0.322777i	0.787327	−	0.616536i	$-0.211464\pi$
$449$	9.41379	+	6.83952i	0.444264	+	0.322777i	−0.343063	+	0.939312i	$0.611464\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	−2.48533	+	2.76024i	−0.117029	+	0.129974i
$452$	18.6412	−	8.29962i	0.876810	−	0.390381i
$453$	−3.87788	−	1.72655i	−0.182199	−	0.0811202i
$454$	3.84477	+	4.27005i	0.180444	+	0.200404i
$455$	0.796467	+	7.57787i	0.0373389	+	0.355256i
$456$	−3.94741	−	0.839047i	−0.184854	−	0.0392920i
$457$	6.95641	+	21.4096i	0.325407	+	1.00150i	0.971256	+	0.238035i	$0.0765034\pi$
$457$	6.95641	+	21.4096i	0.325407	+	1.00150i	−0.645849	+	0.763465i	$0.723497\pi$
$458$	−6.77896	+	1.44091i	−0.316760	+	0.0673295i
$459$	0.991653	+	1.71759i	0.0462864	+	0.0801704i
$460$	−0.415572	+	0.719792i	−0.0193762	+	0.0335605i
$461$	12.9799	−	39.9481i	0.604535	−	1.86057i	0.104577	−	0.994517i	$-0.466651\pi$
$461$	12.9799	−	39.9481i	0.604535	−	1.86057i	0.499958	−	0.866050i	$-0.333349\pi$
$462$	0.200594	−	1.90852i	0.00933247	−	0.0887925i
$463$	−14.6521	+	10.6453i	−0.680939	+	0.494731i	−0.873669	−	0.486521i	$-0.838266\pi$
$463$	−14.6521	+	10.6453i	−0.680939	+	0.494731i	0.192730	+	0.981252i	$0.438266\pi$
$464$	−7.17098			−0.332904
$465$	−5.48344	−	0.965324i	−0.254289	−	0.0447658i
$466$	21.8334			1.01141
$467$	1.14562	−	0.832344i	0.0530131	−	0.0385163i	−0.560963	−	0.827841i	$-0.689569\pi$
$467$	1.14562	−	0.832344i	0.0530131	−	0.0385163i	0.613976	+	0.789325i	$0.289569\pi$
$468$	−0.410886	+	3.90932i	−0.0189932	+	0.180708i
$469$	4.89817	−	15.0750i	0.226176	−	0.696099i
$470$	5.25403	−	9.10025i	0.242350	−	0.419763i
$471$	12.2631	+	21.2403i	0.565053	+	0.978701i
$472$	−3.07890	+	0.654441i	−0.141718	+	0.0301231i
$473$	−3.29952	−	10.1549i	−0.151712	−	0.466921i
$474$	5.51896	+	1.17309i	0.253494	+	0.0538819i
$475$	0.421834	+	4.01349i	0.0193551	+	0.184151i
$476$	2.57245	+	2.85699i	0.117908	+	0.130950i
$477$	−2.38677	−	1.06266i	−0.109283	−	0.0486558i
$478$	−0.632542	+	0.281626i	−0.0289318	+	0.0128813i
$479$	−1.80663	+	2.00646i	−0.0825469	+	0.0916777i	−0.783003	−	0.622018i	$-0.786313\pi$
$479$	−1.80663	+	2.00646i	−0.0825469	+	0.0916777i	0.700456	+	0.713695i	$0.252980\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−37.1934	−	27.0226i	−1.69587	−	1.23212i
$482$	−19.5916	+	21.7586i	−0.892372	+	0.991079i
$483$	1.47181	−	0.655293i	0.0669698	−	0.0298169i
$484$	−9.15363	−	4.07546i	−0.416074	−	0.185248i
$485$	−11.7468	−	13.0461i	−0.533393	−	0.592392i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	28.8539	+	6.13308i	1.30749	+	0.277916i	0.808401	−	0.588632i	$-0.200333\pi$
$487$	28.8539	+	6.13308i	1.30749	+	0.277916i	0.499093	+	0.866549i	$0.333667\pi$
$488$	−0.972155	−	2.99199i	−0.0440074	−	0.135441i
$489$	15.1491	−	3.22004i	0.685065	−	0.145615i
$490$	−1.62128	−	2.80814i	−0.0732420	−	0.126859i
$491$	−9.29616	+	16.1014i	−0.419530	+	0.726647i	−0.995892	−	0.0905474i	$-0.971138\pi$
$491$	−9.29616	+	16.1014i	−0.419530	+	0.726647i	0.576362	+	0.817194i	$0.304472\pi$
$492$	1.15936	−	3.56814i	0.0522680	−	0.160864i
$493$	1.48663	−	14.1443i	0.0669544	−	0.637029i
$494$	12.8337	−	9.32423i	0.577416	−	0.419517i
$495$	−0.990004			−0.0444974
$496$	−5.48344	−	0.965324i	−0.246214	−	0.0433443i
$497$	−17.5937			−0.789183
$498$	3.36353	−	2.44375i	0.150723	−	0.109507i
$499$	2.99215	−	28.4684i	0.133947	−	1.27442i	−0.696594	−	0.717465i	$-0.745302\pi$
$499$	2.99215	−	28.4684i	0.133947	−	1.27442i	0.830541	−	0.556957i	$-0.188031\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−4.37398	+	7.57595i	−0.195415	+	0.338469i
$502$	−5.29979	−	9.17951i	−0.236541	−	0.409702i
$503$	−21.3916	+	4.54693i	−0.953805	+	0.202738i	−0.658428	−	0.752643i	$-0.728778\pi$
$503$	−21.3916	+	4.54693i	−0.953805	+	0.202738i	−0.295377	+	0.955381i	$0.595445\pi$
$504$	0.599002	+	1.84354i	0.0266817	+	0.0821178i
$505$	9.04005	+	1.92152i	0.402277	+	0.0855066i
$506$	0.0860098	+	0.818328i	0.00382360	+	0.0363791i
$507$	−1.64045	−	1.82191i	−0.0728550	−	0.0809137i
$508$	7.40944	+	3.29890i	0.328741	+	0.146365i
$509$	6.23185	−	2.77460i	0.276222	−	0.122982i	−0.263951	−	0.964536i	$-0.585026\pi$
$509$	6.23185	−	2.77460i	0.276222	−	0.122982i	0.540173	+	0.841554i	$0.318359\pi$
$510$	1.32709	−	1.47388i	0.0587646	−	0.0652647i
$511$	18.3918	+	13.3624i	0.813603	+	0.591117i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	2.70034	−	2.99903i	0.119223	−	0.132410i
$514$	−1.11362	+	0.495818i	−0.0491199	+	0.0218696i
$515$	−0.984141	−	0.438168i	−0.0433664	−	0.0193080i
$516$	7.21676	+	8.01502i	0.317700	+	0.352842i
$517$	−1.08741	−	10.3460i	−0.0478243	−	0.455018i
$518$	−22.1754	−	4.71353i	−0.974332	−	0.207101i
$519$	−0.895494	−	2.75605i	−0.0393078	−	0.120977i
$520$	3.84496	−	0.817271i	0.168612	−	0.0358397i
$521$	9.13612	+	15.8242i	0.400261	+	0.693272i	0.993757	−	0.111565i	$-0.0355863\pi$
$521$	9.13612	+	15.8242i	0.400261	+	0.693272i	−0.593497	+	0.804837i	$0.702253\pi$
$522$	3.58549	−	6.21025i	0.156933	−	0.271815i
$523$	10.9393	−	33.6676i	0.478340	−	1.47218i	−0.363059	−	0.931766i	$-0.618268\pi$
$523$	10.9393	−	33.6676i	0.478340	−	1.47218i	0.841399	−	0.540414i	$-0.181732\pi$
$524$	0.730750	−	6.95262i	0.0319230	−	0.303727i
$525$	1.56821	−	1.13937i	0.0684422	−	0.0497262i
$526$	−5.43336			−0.236906
$527$	3.04083	−	10.6156i	0.132461	−	0.462425i
$528$	−0.990004			−0.0430844
$529$	18.0485	−	13.1130i	0.784718	−	0.570131i
$530$	−0.273096	+	2.59833i	−0.0118625	+	0.112864i
$531$	0.972689	−	2.99363i	0.0422111	−	0.129912i
$532$	3.91132	−	6.77461i	0.169577	−	0.293716i
$533$	7.37383	+	12.7718i	0.319396	+	0.553210i
$534$	12.8456	−	2.73042i	0.555884	−	0.118157i
$535$	−3.93914	−	12.1234i	−0.170304	−	0.524141i
$536$	−7.99852	−	1.70014i	−0.345483	−	0.0734348i
$537$	0.877887	+	8.35254i	0.0378836	+	0.360439i
$538$	−13.9839	−	15.5307i	−0.602888	−	0.669575i
$539$	−2.93262	−	1.30568i	−0.126317	−	0.0562398i
$540$	0.913545	−	0.406737i	0.0393127	−	0.0175032i
$541$	24.2092	−	26.8871i	1.04084	−	1.15597i	0.0532989	−	0.998579i	$-0.483026\pi$
$541$	24.2092	−	26.8871i	1.04084	−	1.15597i	0.987537	−	0.157387i	$-0.0503069\pi$
$542$	−0.207135	−	0.150492i	−0.00889721	−	0.00646420i
$543$	−7.70246	−	5.59616i	−0.330544	−	0.240154i
$544$	1.32709	−	1.47388i	0.0568986	−	0.0631922i
$545$	0.311349	−	0.138622i	0.0133367	−	0.00593790i
$546$	−6.96086	−	3.09918i	−0.297897	−	0.132632i
$547$	26.5590	+	29.4967i	1.13558	+	1.26119i	0.961001	+	0.276546i	$0.0891898\pi$
$547$	26.5590	+	29.4967i	1.13558	+	1.26119i	0.174579	+	0.984643i	$0.444144\pi$
$548$	−0.859182	−	8.17457i	−0.0367024	−	0.349200i
$549$	3.07721	+	0.654082i	0.131332	+	0.0279155i
$550$	0.305928	+	0.941549i	0.0130448	+	0.0401478i
$551$	−28.3068	+	6.01679i	−1.20591	+	0.256324i
$552$	−0.415572	−	0.719792i	−0.0176879	−	0.0306364i
$553$	−5.46851	+	9.47174i	−0.232545	+	0.402779i
$554$	1.32869	−	4.08930i	0.0564508	−	0.173738i
$555$	−1.22252	+	11.6315i	−0.0518931	+	0.493730i
$556$	6.57678	−	4.77831i	0.278917	−	0.202645i
$557$	20.9574			0.887994			0.443997	−	0.896028i	$-0.353560\pi$
$557$	20.9574			0.887994			0.443997	+	0.896028i	$0.353560\pi$
$558$	3.57772	−	4.26614i	0.151457	−	0.180600i
$559$	−42.3953			−1.79313
$560$	1.56821	−	1.13937i	0.0662689	−	0.0481472i
$561$	0.205240	−	1.95272i	0.00866522	−	0.0824441i
$562$	0.658512	−	2.02669i	0.0277776	−	0.0854908i
$563$	21.7457	−	37.6647i	0.916473	−	1.58738i	0.111742	−	0.993737i	$-0.464357\pi$
$563$	21.7457	−	37.6647i	0.916473	−	1.58738i	0.804730	−	0.593640i	$-0.202310\pi$
$564$	5.25403	+	9.10025i	0.221235	+	0.383190i
$565$	19.9595	−	4.24252i	0.839701	−	0.178484i
$566$	−1.48483	−	4.56983i	−0.0624120	−	0.192084i
$567$	−1.89605	−	0.403018i	−0.0796267	−	0.0169252i
$568$	0.948735	+	9.02661i	0.0398080	+	0.378748i
$569$	−12.6547	−	14.0544i	−0.530512	−	0.589193i	0.417003	−	0.908905i	$-0.363080\pi$
$569$	−12.6547	−	14.0544i	−0.530512	−	0.589193i	−0.947515	+	0.319712i	$0.896414\pi$
$570$	−3.68670	−	1.64142i	−0.154419	−	0.0687517i
$571$	21.2154	−	9.44571i	0.887837	−	0.395291i	0.0884317	−	0.996082i	$-0.471814\pi$
$571$	21.2154	−	9.44571i	0.887837	−	0.395291i	0.799406	+	0.600792i	$0.205148\pi$
$572$	2.60396	−	2.89199i	0.108877	−	0.120920i
$573$	19.0959	+	13.8740i	0.797743	+	0.579594i
$574$	5.88355	+	4.27465i	0.245575	+	0.178420i
$575$	−0.556144	+	0.617661i	−0.0231928	+	0.0257582i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	13.2283	+	5.88960i	0.550700	+	0.245187i	0.663171	−	0.748468i	$-0.269210\pi$
$577$	13.2283	+	5.88960i	0.550700	+	0.245187i	−0.112472	+	0.993655i	$0.535877\pi$
$578$	−8.74319	−	9.71030i	−0.363669	−	0.403895i
$579$	−1.97681	−	18.8081i	−0.0821534	−	0.781637i
$580$	−7.01427	−	1.49093i	−0.291252	−	0.0619075i
$581$	2.49038	+	7.66461i	0.103318	+	0.317981i
$582$	17.1716	−	3.64994i	0.711787	−	0.151295i
$583$	1.29326	+	2.24000i	0.0535615	+	0.0927713i
$584$	5.86394	−	10.1566i	0.242652	−	0.420285i
$585$	−1.21470	+	3.73846i	−0.0502217	+	0.154566i
$586$	−1.30931	+	12.4573i	−0.0540872	+	0.514605i
$587$	3.23387	−	2.34955i	0.133476	−	0.0969761i	−0.519044	−	0.854748i	$-0.673712\pi$
$587$	3.23387	−	2.34955i	0.133476	−	0.0969761i	0.652520	+	0.757772i	$0.273712\pi$
$588$	3.24256			0.133721
$589$	−22.4553	+	0.790342i	−0.925256	+	0.0325655i
$590$	−3.14769			−0.129588
$591$	−3.75904	+	2.73110i	−0.154626	+	0.112343i
$592$	−1.22252	+	11.6315i	−0.0502453	+	0.478052i
$593$	−8.99538	+	27.6849i	−0.369396	+	1.13688i	0.577786	+	0.816188i	$0.303917\pi$
$593$	−8.99538	+	27.6849i	−0.369396	+	1.13688i	−0.947182	+	0.320696i	$0.896083\pi$
$594$	0.495002	−	0.857368i	0.0203102	−	0.0351782i
$595$	1.92223	+	3.32940i	0.0788038	+	0.136492i
$596$	14.4475	−	3.07090i	0.591791	−	0.125789i
$597$	1.28671	+	3.96007i	0.0526613	+	0.162075i
$598$	3.19571	+	0.679270i	0.130682	+	0.0277774i
$599$	0.978343	+	9.30831i	0.0399740	+	0.380327i	0.996159	+	0.0875638i	$0.0279082\pi$
$599$	0.978343	+	9.30831i	0.0399740	+	0.380327i	−0.956185	+	0.292763i	$0.905425\pi$
$600$	−0.669131	−	0.743145i	−0.0273171	−	0.0303388i
$601$	−27.0757	−	12.0549i	−1.10444	−	0.491730i	−0.228207	−	0.973613i	$-0.573286\pi$
$601$	−27.0757	−	12.0549i	−1.10444	−	0.491730i	−0.876236	+	0.481883i	$0.839953\pi$
$602$	−19.0989	+	8.50336i	−0.778411	+	0.346571i
$603$	5.47162	−	6.07685i	0.222822	−	0.247469i
$604$	−3.43417	−	2.49507i	−0.139735	−	0.101523i
$605$	−8.10626	−	5.88955i	−0.329566	−	0.239444i
$606$	−6.18411	+	6.86815i	−0.251212	+	0.279000i
$607$	−32.4913	+	14.4660i	−1.31878	+	0.587159i	−0.940897	−	0.338694i	$-0.890015\pi$
$607$	−32.4913	+	14.4660i	−1.31878	+	0.587159i	−0.377884	+	0.925853i	$0.623348\pi$
$608$	−3.68670	−	1.64142i	−0.149515	−	0.0665685i
$609$	9.30112	+	10.3299i	0.376900	+	0.418590i
$610$	−0.328842	−	3.12873i	−0.0133144	−	0.126678i
$611$	−40.4030	−	8.58793i	−1.63453	−	0.347431i
$612$	0.612875	+	1.88624i	0.0247740	+	0.0762466i
$613$	−25.8315	+	5.49066i	−1.04333	+	0.221766i	−0.697539	−	0.716547i	$-0.745722\pi$
$613$	−25.8315	+	5.49066i	−1.04333	+	0.221766i	−0.345787	+	0.938313i	$0.612388\pi$
$614$	4.59789	+	7.96378i	0.185556	+	0.321392i
$615$	1.87588	−	3.24913i	0.0756429	−	0.131017i
$616$	0.593014	−	1.82511i	0.0238932	−	0.0735358i
$617$	−5.01041	+	47.6709i	−0.201712	+	1.91916i	0.160454	+	0.987043i	$0.448704\pi$
$617$	−5.01041	+	47.6709i	−0.201712	+	1.91916i	−0.362166	+	0.932114i	$0.617963\pi$
$618$	0.871535	−	0.633207i	0.0350583	−	0.0254713i
$619$	−31.2154			−1.25465			−0.627327	−	0.778756i	$-0.715851\pi$
$619$	−31.2154			−1.25465			−0.627327	+	0.778756i	$0.715851\pi$
$620$	−5.16291	−	2.08430i	−0.207348	−	0.0837075i
$621$	0.831144			0.0333527
$622$	−16.1784	+	11.7543i	−0.648693	+	0.471303i
$623$	−2.66091	+	25.3169i	−0.106607	+	1.01430i
$624$	−1.21470	+	3.73846i	−0.0486270	+	0.149658i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.35293	+	14.4677i	0.333850	+	0.578246i
$627$	−3.90795	+	0.830660i	−0.156068	+	0.0331734i
$628$	7.57901	+	23.3258i	0.302435	+	0.930800i
$629$	−22.6890	−	4.82270i	−0.904670	−	0.192294i
$630$	0.202619	+	1.92779i	0.00807254	+	0.0768051i
$631$	−5.38188	−	5.97718i	−0.214249	−	0.237948i	0.626435	−	0.779474i	$-0.284513\pi$
$631$	−5.38188	−	5.97718i	−0.214249	−	0.237948i	−0.840684	+	0.541526i	$0.817847\pi$
$632$	5.15446	+	2.29491i	0.205033	+	0.0912868i
$633$	3.87582	−	1.72563i	0.154050	−	0.0685874i
$634$	7.67983	−	8.52931i	0.305005	−	0.338742i
$635$	6.56165	+	4.76732i	0.260391	+	0.189185i
$636$	−2.11367	−	1.53567i	−0.0838126	−	0.0608935i
$637$	−8.52876	+	9.47215i	−0.337922	+	0.375300i
$638$	−6.48553	+	2.88754i	−0.256764	+	0.114319i
$639$	−8.29164	−	3.69168i	−0.328012	−	0.146040i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	0.344909	+	3.28159i	0.0136231	+	0.129615i	0.999220	−	0.0394988i	$-0.0125761\pi$
$641$	0.344909	+	3.28159i	0.0136231	+	0.129615i	−0.985597	+	0.169114i	$0.945909\pi$
$642$	12.4688	+	2.65031i	0.492102	+	0.104600i
$643$	2.13241	+	6.56288i	0.0840941	+	0.258815i	0.984258	−	0.176736i	$-0.0565537\pi$
$643$	2.13241	+	6.56288i	0.0840941	+	0.258815i	−0.900164	+	0.435550i	$0.856554\pi$
$644$	1.57589	−	0.334966i	0.0620989	−	0.0131995i
$645$	5.39264	+	9.34032i	0.212335	+	0.367775i
$646$	4.00191	−	6.93151i	0.157453	−	0.272717i
$647$	10.5575	−	32.4927i	0.415059	−	1.27742i	−0.497140	−	0.867671i	$-0.665616\pi$
$647$	10.5575	−	32.4927i	0.415059	−	1.27742i	0.912198	−	0.409749i	$-0.134384\pi$
$648$	−0.104528	+	0.994522i	−0.00410627	+	0.0390685i
$649$	−2.52108	+	1.83167i	−0.0989610	+	0.0718994i
$650$	3.93085			0.154181
$651$	5.72173	+	9.15109i	0.224252	+	0.358659i
$652$	15.4875			0.606538
$653$	9.20723	−	6.68944i	0.360307	−	0.261778i	−0.392873	−	0.919593i	$-0.628519\pi$
$653$	9.20723	−	6.68944i	0.360307	−	0.261778i	0.753180	+	0.657814i	$0.228519\pi$
$654$	−0.0356248	+	0.338947i	−0.00139304	+	0.0132539i
$655$	2.16031	−	6.64876i	0.0844104	−	0.259789i
$656$	1.87588	−	3.24913i	0.0732410	−	0.126857i
$657$	5.86394	+	10.1566i	0.228774	+	0.396248i
$658$	−19.9238	+	4.23494i	−0.776712	+	0.165095i
$659$	5.26998	+	16.2193i	0.205289	+	0.631815i	0.999701	+	0.0244360i	$0.00777901\pi$
$659$	5.26998	+	16.2193i	0.205289	+	0.631815i	−0.794412	+	0.607379i	$0.792221\pi$
$660$	−0.968370	−	0.205833i	−0.0376937	−	0.00801205i
$661$	−2.26486	−	21.5487i	−0.0880927	−	0.838146i	−0.945962	−	0.324278i	$-0.894879\pi$
$661$	−2.26486	−	21.5487i	−0.0880927	−	0.838146i	0.857869	−	0.513868i	$-0.171788\pi$
$662$	16.3476	+	18.1559i	0.635369	+	0.705649i
$663$	−7.12208	−	3.17095i	−0.276599	−	0.123150i
$664$	3.79811	−	1.69103i	0.147395	−	0.0656246i
$665$	5.23437	−	5.81336i	0.202980	−	0.225432i
$666$	−9.46192	−	6.87449i	−0.366642	−	0.266381i
$667$	−4.82184	−	3.50327i	−0.186702	−	0.135647i
$668$	−5.85353	+	6.50100i	−0.226480	+	0.251531i
$669$	18.2849	−	8.14095i	0.706934	−	0.314747i
$670$	−7.47025	−	3.32597i	−0.288601	−	0.128493i
$671$	−2.08402	−	2.31453i	−0.0804525	−	0.0893516i
$672$	0.202619	+	1.92779i	0.00781620	+	0.0743662i
$673$	39.2284	+	8.33824i	1.51214	+	0.321416i	0.887981	−	0.459880i	$-0.152108\pi$
$673$	39.2284	+	8.33824i	1.51214	+	0.321416i	0.624161	+	0.781296i	$0.285441\pi$
$674$	−5.64515	−	17.3740i	−0.217443	−	0.669220i
$675$	0.978148	−	0.207912i	0.0376489	−	0.00800252i
$676$	−1.22581	−	2.12316i	−0.0471465	−	0.0816601i
$677$	−3.60695	+	6.24743i	−0.138627	+	0.240108i	−0.926977	−	0.375118i	$-0.877602\pi$
$677$	−3.60695	+	6.24743i	−0.138627	+	0.240108i	0.788350	+	0.615226i	$0.210935\pi$
$678$	−6.30561	+	19.4067i	−0.242165	+	0.745309i
$679$	−3.55703	+	33.8429i	−0.136506	+	1.29877i
$680$	1.60453	−	1.16576i	0.0615309	−	0.0447048i
$681$	−5.74592			−0.220184
$682$	−5.34801	+	1.33497i	−0.204786	+	0.0511187i
$683$	−9.20534			−0.352233			−0.176116	−	0.984369i	$-0.556353\pi$
$683$	−9.20534			−0.352233			−0.176116	+	0.984369i	$0.556353\pi$
$684$	3.26486	−	2.37206i	0.124835	−	0.0906981i
$685$	0.859182	−	8.17457i	0.0328276	−	0.312334i
$686$	−6.13532	+	18.8826i	−0.234247	+	0.720939i
$687$	3.46521	−	6.00191i	0.132206	−	0.228987i
$688$	5.39264	+	9.34032i	0.205592	+	0.356096i
$689$	10.0455	−	2.13524i	0.382703	−	0.0813461i
$690$	−0.256838	−	0.790465i	−0.00977764	−	0.0300925i
$691$	37.7437	+	8.02266i	1.43584	+	0.305196i	0.859131	−	0.511756i	$-0.171005\pi$
$691$	37.7437	+	8.02266i	1.43584	+	0.305196i	0.576705	+	0.816952i	$0.304338\pi$
$692$	−0.302911	−	2.88201i	−0.0115149	−	0.109557i
$693$	1.28408	+	1.42612i	0.0487783	+	0.0541738i
$694$	3.58118	+	1.59445i	0.135940	+	0.0605243i
$695$	7.42652	−	3.30650i	0.281704	−	0.125423i
$696$	4.79832	−	5.32907i	0.181880	−	0.201998i
$697$	6.01982	+	4.37365i	0.228017	+	0.165664i
$698$	−8.00524	−	5.81614i	−0.303003	−	0.220144i
$699$	−14.6094	+	16.2254i	−0.552578	+	0.613700i
$700$	1.77083	−	0.788423i	0.0669310	−	0.0297996i
$701$	−34.9273	−	15.5506i	−1.31919	−	0.587339i	−0.378180	−	0.925732i	$-0.623450\pi$
$701$	−34.9273	−	15.5506i	−1.31919	−	0.587339i	−0.941005	+	0.338393i	$0.890117\pi$
$702$	−2.63026	−	2.92119i	−0.0992726	−	0.110253i
$703$	4.93360	+	46.9400i	0.186074	+	1.77038i
$704$	−0.968370	−	0.205833i	−0.0364968	−	0.00775764i
$705$	3.24717	+	9.99376i	0.122295	+	0.376387i
$706$	−17.9299	+	3.81112i	−0.674801	+	0.143433i
$707$	−8.95741	−	15.5147i	−0.336878	−	0.583490i
$708$	1.57384	−	2.72598i	0.0591487	−	0.102449i
$709$	3.07117	−	9.45210i	0.115340	−	0.354981i	−0.876677	−	0.481079i	$-0.840245\pi$
$709$	3.07117	−	9.45210i	0.115340	−	0.354981i	0.992018	+	0.126097i	$0.0402452\pi$
$710$	−0.948735	+	9.02661i	−0.0356054	+	0.338763i
$711$	−4.56468	+	3.31644i	−0.171189	+	0.124376i
$712$	13.1326			0.492164
$713$	−3.21553	−	3.32794i	−0.120422	−	0.124632i
$714$	−3.84446			−0.143875
$715$	3.14834	−	2.28740i	0.117741	−	0.0855440i
$716$	−0.877887	+	8.35254i	−0.0328082	+	0.312149i
$717$	0.213965	−	0.658515i	0.00799065	−	0.0245927i
$718$	2.13614	−	3.69991i	0.0797202	−	0.138079i
$719$	4.83318	+	8.37132i	0.180247	+	0.312197i	0.941965	−	0.335712i	$-0.108977\pi$
$719$	4.83318	+	8.37132i	0.180247	+	0.312197i	−0.761717	+	0.647909i	$0.775644\pi$
$720$	0.978148	−	0.207912i	0.0364534	−	0.00774841i
$721$	0.645291	+	1.98600i	0.0240319	+	0.0739626i
$722$	2.65468	+	0.564269i	0.0987969	+	0.0209999i
$723$	−3.06050	−	29.1187i	−0.113821	−	1.08294i
$724$	−6.37063	−	7.07530i	−0.236763	−	0.262952i
$725$	−6.55101	−	2.91670i	−0.243298	−	0.108323i
$726$	9.15363	−	4.07546i	0.339723	−	0.151254i
$727$	13.5659	−	15.0665i	0.503133	−	0.558786i	−0.437058	−	0.899433i	$-0.643980\pi$
$727$	13.5659	−	15.0665i	0.503133	−	0.558786i	0.940191	+	0.340647i	$0.110646\pi$
$728$	−6.16440	−	4.47870i	−0.228468	−	0.165992i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	7.84748	−	8.71551i	0.290448	−	0.322576i
$731$	−19.5412	+	8.70030i	−0.722757	+	0.321792i
$732$	2.87398	+	1.27958i	0.106225	+	0.0472945i
$733$	4.93347	+	5.47918i	0.182222	+	0.202378i	0.827334	−	0.561710i	$-0.189856\pi$
$733$	4.93347	+	5.47918i	0.182222	+	0.202378i	−0.645113	+	0.764088i	$0.723190\pi$
$734$	−1.34301	−	12.7778i	−0.0495712	−	0.471639i
$735$	3.17170	+	0.674166i	0.116990	+	0.0248670i
$736$	−0.256838	−	0.790465i	−0.00946716	−	0.0291369i
$737$	−7.91856	+	1.68314i	−0.291684	+	0.0619994i
$738$	1.87588	+	3.24913i	0.0690522	+	0.119602i
$739$	−11.9891	+	20.7656i	−0.441024	+	0.763877i	−0.997766	−	0.0668092i	$-0.978718\pi$
$739$	−11.9891	+	20.7656i	−0.441024	+	0.763877i	0.556741	+	0.830686i	$0.312051\pi$
$740$	−3.61413	+	11.1232i	−0.132858	+	0.408895i
$741$	−1.65817	+	15.7764i	−0.0609144	+	0.579562i
$742$	4.09717	−	2.97677i	0.150412	−	0.109281i
$743$	−21.2624			−0.780041			−0.390020	−	0.920806i	$-0.627532\pi$
$743$	−21.2624			−0.780041			−0.390020	+	0.920806i	$0.627532\pi$
$744$	4.38652	−	3.42906i	0.160817	−	0.125716i
$745$	14.7702			0.541139
$746$	−13.9252	+	10.1172i	−0.509836	+	0.370418i
$747$	−0.434582	+	4.13478i	−0.0159005	+	0.151284i
$748$	0.606749	−	1.86738i	0.0221849	−	0.0682782i
$749$	−12.3548	+	21.3991i	−0.451433	+	0.781906i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−10.2581	+	2.18044i	−0.374325	+	0.0795652i	−0.391233	−	0.920292i	$-0.627951\pi$
$751$	−10.2581	+	2.18044i	−0.374325	+	0.0795652i	0.0169077	+	0.999857i	$0.494618\pi$
$752$	3.24717	+	9.99376i	0.118412	+	0.364435i
$753$	10.3680	+	2.20378i	0.377830	+	0.0803102i
$754$	2.94645	+	28.0336i	0.107304	+	1.02093i
$755$	−2.84037	−	3.15455i	−0.103372	−	0.114806i
$756$	−1.77083	−	0.788423i	−0.0644044	−	0.0286747i
$757$	−30.4949	+	13.5772i	−1.10836	+	0.493472i	−0.877530	−	0.479522i	$-0.840810\pi$
$757$	−30.4949	+	13.5772i	−1.10836	+	0.493472i	−0.230827	+	0.972995i	$0.574143\pi$
$758$	16.1903	−	17.9812i	0.588059	−	0.653106i
$759$	−0.665688	−	0.483651i	−0.0241630	−	0.0175554i
$760$	−3.26486	−	2.37206i	−0.118429	−	0.0860437i
$761$	−0.542444	+	0.602445i	−0.0196636	+	0.0218386i	−0.752896	−	0.658139i	$-0.771344\pi$
$761$	−0.542444	+	0.602445i	−0.0196636	+	0.0218386i	0.733233	+	0.679978i	$0.238011\pi$
$762$	−7.40944	+	3.29890i	−0.268416	+	0.119506i
$763$	−0.603523	−	0.268706i	−0.0218490	−	0.00972780i
$764$	15.7940	+	17.5411i	0.571409	+	0.634614i
$765$	0.207312	+	1.97244i	0.00749538	+	0.0713138i
$766$	−20.6901	−	4.39781i	−0.747562	−	0.158899i
$767$	3.82350	+	11.7675i	0.138059	+	0.424901i
$768$	0.978148	−	0.207912i	0.0352959	−	0.00750237i
$769$	−19.2147	−	33.2808i	−0.692899	−	1.20014i	−0.970884	−	0.239550i	$-0.923000\pi$
$769$	−19.2147	−	33.2808i	−0.692899	−	1.20014i	0.277985	−	0.960585i	$-0.410333\pi$
$770$	0.959517	−	1.66193i	0.0345786	−	0.0598919i
$771$	0.376696	−	1.15935i	0.0135664	−	0.0417530i
$772$	1.97681	−	18.8081i	0.0711469	−	0.676917i
$773$	−19.4860	+	14.1574i	−0.700863	+	0.509206i	−0.880213	−	0.474579i	$-0.842600\pi$
$773$	−19.4860	+	14.1574i	−0.700863	+	0.509206i	0.179350	+	0.983785i	$0.442600\pi$
$774$	−10.7853			−0.387669
$775$	−4.61674	−	3.11218i	−0.165838	−	0.111793i
$776$	17.5552			0.630197
$777$	18.3411	−	13.3256i	0.657983	−	0.478053i
$778$	3.63961	−	34.6286i	0.130486	−	1.24149i
$779$	4.67871	−	14.3996i	0.167632	−	0.515918i
$780$	−1.96543	+	3.40422i	−0.0703736	+	0.121891i
$781$	4.49280	+	7.78176i	0.160765	+	0.278453i
$782$	1.61239	−	0.342724i	0.0576590	−	0.0122558i
$783$	2.21595	+	6.82000i	0.0791917	+	0.243727i
$784$	3.17170	+	0.674166i	0.113275	+	0.0240774i
$785$	2.56368	+	24.3918i	0.0915018	+	0.870582i
$786$	4.67784	+	5.19527i	0.166853	+	0.185309i
$787$	−8.07595	−	3.59564i	−0.287876	−	0.128171i	0.257718	−	0.966220i	$-0.417029\pi$
$787$	−8.07595	−	3.59564i	−0.287876	−	0.128171i	−0.545594	+	0.838049i	$0.683696\pi$
$788$	−4.24473	+	1.88987i	−0.151212	+	0.0673240i
$789$	3.63563	−	4.03777i	0.129432	−	0.143749i
$790$	4.56468	+	3.31644i	0.162404	+	0.117994i
$791$	−31.9999	−	23.2493i	−1.13778	−	0.826649i
$792$	0.662442	−	0.735716i	0.0235388	−	0.0261425i
$793$	−11.2972	+	5.02983i	−0.401175	+	0.178615i
$794$	1.32332	+	0.589181i	0.0469630	+	0.0209093i
$795$	−1.74820	−	1.94157i	−0.0620023	−	0.0688605i
$796$	0.435242	+	4.14106i	0.0154268	+	0.146776i
$797$	51.8073	+	11.0120i	1.83511	+	0.390064i	0.989594	−	0.143889i	$-0.0459607\pi$
$797$	51.8073	+	11.0120i	1.83511	+	0.390064i	0.845514	+	0.533953i	$0.179294\pi$
$798$	2.41733	+	7.43977i	0.0855725	+	0.263365i
$799$	−20.3853	+	4.33303i	−0.721180	+	0.153291i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−6.56629	+	11.3732i	−0.232009	+	0.401851i
$802$	−6.64095	+	20.4387i	−0.234500	+	0.721717i
$803$	1.21364	−	11.5470i	0.0428285	−	0.407486i
$804$	6.61550	−	4.80644i	0.233311	−	0.169510i
$805$	1.61110			0.0567838
$806$	−1.52069	+	21.8332i	−0.0535640	+	0.769041i
$807$	20.8986			0.735665
$808$	−7.47694	+	5.43232i	−0.263038	+	0.191108i
$809$	1.39268	−	13.2505i	0.0489641	−	0.465862i	−0.942377	−	0.334552i	$-0.891415\pi$
$809$	1.39268	−	13.2505i	0.0489641	−	0.465862i	0.991341	−	0.131310i	$-0.0419183\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	2.09296	−	3.62511i	0.0734937	−	0.127295i	−0.826937	−	0.562295i	$-0.809918\pi$
$811$	2.09296	−	3.62511i	0.0734937	−	0.127295i	0.900430	+	0.435000i	$0.143252\pi$
$812$	6.95015	+	12.0380i	0.243902	+	0.422452i
$813$	0.250438	−	0.0532322i	0.00878324	−	0.00186694i
$814$	3.57800	+	11.0120i	0.125409	+	0.385969i
$815$	15.1491	+	3.22004i	0.530649	+	0.112793i
$816$	0.207312	+	1.97244i	0.00725737	+	0.0690493i
$817$	29.1239	+	32.3454i	1.01892	+	1.13162i
$818$	−3.41398	−	1.52000i	−0.119367	−	0.0531456i
$819$	6.96086	−	3.09918i	0.243232	−	0.108294i
$820$	2.51042	−	2.78811i	0.0876678	−	0.0973649i
$821$	8.43717	+	6.12996i	0.294459	+	0.213937i	0.725200	−	0.688539i	$-0.241748\pi$
$821$	8.43717	+	6.12996i	0.294459	+	0.213937i	−0.430740	+	0.902476i	$0.641748\pi$
$822$	6.64979	+	4.83136i	0.231938	+	0.168513i
$823$	−14.9473	+	16.6006i	−0.521029	+	0.578662i	−0.945023	−	0.327004i	$-0.893961\pi$
$823$	−14.9473	+	16.6006i	−0.521029	+	0.578662i	0.423994	+	0.905665i	$0.360628\pi$
$824$	0.984141	−	0.438168i	0.0342842	−	0.0152643i
$825$	−0.904413	−	0.402671i	−0.0314876	−	0.0140192i
$826$	4.08271	+	4.53431i	0.142056	+	0.157769i
$827$	−3.89588	−	37.0668i	−0.135473	−	1.28894i	−0.825188	−	0.564859i	$-0.808931\pi$
$827$	−3.89588	−	37.0668i	−0.135473	−	1.28894i	0.689714	−	0.724081i	$-0.257736\pi$
$828$	0.812982	+	0.172805i	0.0282531	+	0.00600538i
$829$	3.23236	+	9.94818i	0.112264	+	0.345515i	0.991367	−	0.131119i	$-0.0418569\pi$
$829$	3.23236	+	9.94818i	0.112264	+	0.345515i	−0.879102	+	0.476633i	$0.841857\pi$
$830$	4.06670	−	0.864403i	0.141157	−	0.0300039i
$831$	2.14987	+	3.72369i	0.0745782	+	0.129173i
$832$	−1.96543	+	3.40422i	−0.0681389	+	0.118020i
$833$	−1.98729	+	6.11624i	−0.0688554	+	0.211915i
$834$	−0.849748	+	8.08481i	−0.0294244	+	0.279954i
$835$	−7.07725	+	5.14192i	−0.244918	+	0.177943i
$836$	−3.99525			−0.138179
$837$	0.776400	+	5.51337i	0.0268363	+	0.190570i
$838$	21.5765			0.745347
$839$	−33.0547	+	24.0156i	−1.14117	+	0.829112i	−0.987283	−	0.158976i	$-0.949181\pi$
$839$	−33.0547	+	24.0156i	−1.14117	+	0.829112i	−0.153892	+	0.988088i	$0.549181\pi$
$840$	−0.202619	+	1.92779i	−0.00699103	+	0.0665152i
$841$	6.92906	−	21.3254i	0.238933	−	0.735360i
$842$	1.17609	−	2.03705i	0.0405307	−	0.0702013i
$843$	1.06549	+	1.84549i	0.0366976	+	0.0635620i
$844$	4.14990	−	0.882088i	0.142845	−	0.0303627i
$845$	−0.757592	−	2.33163i	−0.0260619	−	0.0802104i
$846$	−10.2784	−	2.18475i	−0.353380	−	0.0751132i
$847$	2.03022	+	19.3163i	0.0697593	+	0.663715i
$848$	−1.74820	−	1.94157i	−0.0600335	−	0.0666739i
$849$	4.38959	+	1.95437i	0.150650	+	0.0670738i
$850$	1.81184	−	0.806683i	0.0621456	−	0.0276690i
$851$	−6.50442	+	7.22389i	−0.222969	+	0.247632i
$852$	−7.34290	−	5.33493i	−0.251564	−	0.182772i
$853$	−39.7099	−	28.8509i	−1.35964	−	0.987836i	−0.998468	−	0.0553369i	$-0.982377\pi$
$853$	−39.7099	−	28.8509i	−1.35964	−	0.987836i	−0.361172	−	0.932499i	$-0.617623\pi$
$854$	−4.08047	+	4.53182i	−0.139631	+	0.155076i
$855$	3.68670	−	1.64142i	0.126082	−	0.0561355i
$856$	11.6452	+	5.18480i	0.398026	+	0.177213i
$857$	−7.60715	−	8.44859i	−0.259855	−	0.288598i	0.599073	−	0.800694i	$-0.295536\pi$
$857$	−7.60715	−	8.44859i	−0.259855	−	0.288598i	−0.858928	+	0.512096i	$0.828869\pi$
$858$	0.406779	+	3.87024i	0.0138872	+	0.132128i
$859$	22.0352	+	4.68372i	0.751830	+	0.159806i	0.567860	−	0.823125i	$-0.307772\pi$
$859$	22.0352	+	4.68372i	0.751830	+	0.159806i	0.183971	+	0.982932i	$0.441105\pi$
$860$	3.33283	+	10.2574i	0.113649	+	0.349775i
$861$	−7.11355	+	1.51203i	−0.242429	+	0.0515299i
$862$	5.11755	+	8.86385i	0.174304	+	0.301904i
$863$	−7.03694	+	12.1883i	−0.239540	+	0.414896i	−0.960582	−	0.277995i	$-0.910330\pi$
$863$	−7.03694	+	12.1883i	−0.239540	+	0.414896i	0.721042	+	0.692891i	$0.243663\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	0.302911	−	2.88201i	0.0102993	−	0.0979911i
$866$	−17.7290	+	12.8809i	−0.602457	+	0.437710i
$867$	13.0665			0.443761
$868$	3.69408	+	10.1407i	0.125385	+	0.344199i
$869$	5.58586			0.189487
$870$	5.80144	−	4.21499i	0.196687	−	0.142902i
$871$	−3.35990	+	31.9673i	−0.113846	+	1.08317i
$872$	−0.105317	+	0.324133i	−0.00356649	+	0.0109765i
$873$	−8.77762	+	15.2033i	−0.297078	+	0.514553i
$874$	−1.67708	−	2.90479i	−0.0567281	−	0.0982559i
$875$	1.89605	−	0.403018i	0.0640983	−	0.0136245i
$876$	3.62411	+	11.1539i	0.122447	+	0.376855i
$877$	19.0966	+	4.05910i	0.644846	+	0.137066i	0.518715	−	0.854947i	$-0.326411\pi$
$877$	19.0966	+	4.05910i	0.644846	+	0.137066i	0.126131	+	0.992014i	$0.459744\pi$
$878$	−1.04231	−	9.91689i	−0.0351762	−	0.334679i
$879$	−8.38145	−	9.30855i	−0.282699	−	0.313970i
$880$	−0.904413	−	0.402671i	−0.0304878	−	0.0135740i
$881$	24.6887	−	10.9921i	0.831784	−	0.370334i	0.0537488	−	0.998554i	$-0.482883\pi$
$881$	24.6887	−	10.9921i	0.831784	−	0.370334i	0.778036	+	0.628220i	$0.216216\pi$
$882$	−2.16970	+	2.40969i	−0.0730575	+	0.0811386i
$883$	−33.0911	−	24.0421i	−1.11360	−	0.809081i	−0.130377	−	0.991465i	$-0.541619\pi$
$883$	−33.0911	−	24.0421i	−1.11360	−	0.809081i	−0.983227	+	0.182384i	$0.941619\pi$
$884$	−6.30717	−	4.58243i	−0.212133	−	0.154124i
$885$	2.10622	−	2.33919i	0.0707997	−	0.0786310i
$886$	28.7378	−	12.7949i	0.965464	−	0.429852i
$887$	21.6513	+	9.63978i	0.726979	+	0.323672i	0.736643	−	0.676281i	$-0.236410\pi$
$887$	21.6513	+	9.63978i	0.726979	+	0.323672i	−0.00966424	+	0.999953i	$0.503076\pi$
$888$	−7.82587	−	8.69150i	−0.262619	−	0.291668i
$889$	−1.64337	−	15.6356i	−0.0551169	−	0.524402i
$890$	12.8456	+	2.73042i	0.430586	+	0.0915238i
$891$	0.305928	+	0.941549i	0.0102490	+	0.0315431i
$892$	19.5779	−	4.16141i	0.655517	−	0.139334i
$893$	21.2031	+	36.7249i	0.709536	+	1.22895i
$894$	−7.38511	+	12.7914i	−0.246995	+	0.427808i
$895$	−2.59529	+	7.98749i	−0.0867511	+	0.266992i
$896$	−0.202619	+	1.92779i	−0.00676903	+	0.0644030i
$897$	−2.64315	+	1.92036i	−0.0882521	+	0.0641189i
$898$	−11.6361			−0.388301
$899$	18.7346	−	35.2580i	0.624833	−	1.17592i
$900$	1.00000			0.0333333
$901$	4.19206	−	3.04571i	0.139658	−	0.101467i
$902$	0.388246	−	3.69392i	0.0129272	−	0.122994i
$903$	6.46040	−	19.8831i	0.214989	−	0.661667i
$904$	−10.2027	+	17.6716i	−0.339336	+	0.587748i
$905$	−4.76038	−	8.24522i	−0.158240	−	0.274080i
$906$	4.15211	−	0.882559i	0.137945	−	0.0293210i
$907$	5.40024	+	16.6202i	0.179312	+	0.551866i	0.999804	−	0.0197922i	$-0.00630045\pi$
$907$	5.40024	+	16.6202i	0.179312	+	0.551866i	−0.820492	+	0.571658i	$0.806300\pi$
$908$	−5.62036	−	1.19464i	−0.186518	−	0.0396457i
$909$	−0.966053	−	9.19138i	−0.0320420	−	0.304859i
$910$	−5.09852	−	5.66248i	−0.169014	−	0.187709i
$911$	22.6781	+	10.0969i	0.751358	+	0.334526i	0.746432	−	0.665462i	$-0.231765\pi$
$911$	22.6781	+	10.0969i	0.751358	+	0.334526i	0.00492599	+	0.999988i	$0.498432\pi$
$912$	3.68670	−	1.64142i	0.122079	−	0.0543530i
$913$	2.75414	−	3.05878i	0.0911486	−	0.101231i
$914$	−18.2121	−	13.2319i	−0.602403	−	0.437672i
$915$	2.54514	+	1.84915i	0.0841396	+	0.0611310i
$916$	4.63735	−	5.15030i	0.153222	−	0.170171i
$917$	−12.3797	+	5.51180i	−0.408814	+	0.182016i
$918$	−1.81184	−	0.806683i	−0.0597996	−	0.0266245i
$919$	−30.9682	−	34.3937i	−1.02155	−	1.13454i	−0.990844	−	0.135014i	$-0.956892\pi$
$919$	−30.9682	−	34.3937i	−1.02155	−	1.13454i	−0.0307033	−	0.999529i	$-0.509775\pi$
$920$	−0.0868782	−	0.826591i	−0.00286429	−	0.0272519i
$921$	−8.99484	−	1.91191i	−0.296390	−	0.0629996i
$922$	12.9799	+	39.9481i	0.427471	+	1.31562i
$923$	34.8981	−	7.41782i	1.14868	−	0.244160i
$924$	0.959517	+	1.66193i	0.0315658	+	0.0546736i
$925$	−5.84779	+	10.1287i	−0.192274	+	0.333028i
$926$	5.59659	−	17.2245i	0.183915	−	0.566033i
$927$	−0.112606	+	1.07138i	−0.00369847	+	0.0351886i
$928$	5.80144	−	4.21499i	0.190442	−	0.138364i
$929$	−26.5813			−0.872105			−0.436053	−	0.899921i	$-0.643624\pi$
$929$	−26.5813			−0.872105			−0.436053	+	0.899921i	$0.643624\pi$
$930$	5.00360	−	2.44212i	0.164075	−	0.0800804i
$931$	13.0857			0.428865
$932$	−17.6636	+	12.8333i	−0.578590	+	0.420370i
$933$	2.09031	−	19.8880i	0.0684338	−	0.651104i
$934$	−0.437589	+	1.34676i	−0.0143184	+	0.0440674i
$935$	0.981740	−	1.70042i	0.0321063	−	0.0556098i
$936$	−1.96543	−	3.40422i	−0.0642420	−	0.111270i
$937$	−15.1681	+	3.22407i	−0.495519	+	0.105326i	−0.448891	−	0.893586i	$-0.648181\pi$
$937$	−15.1681	+	3.22407i	−0.495519	+	0.105326i	−0.0466281	+	0.998912i	$0.514848\pi$
$938$	4.89817	+	15.0750i	0.159931	+	0.492216i
$939$	−16.3408	−	3.47334i	−0.533262	−	0.113348i
$940$	1.09839	+	10.4505i	0.0358256	+	0.340858i
$941$	13.7847	+	15.3094i	0.449368	+	0.499073i	0.924681	−	0.380743i	$-0.124332\pi$
$941$	13.7847	+	15.3094i	0.449368	+	0.499073i	−0.475313	+	0.879817i	$0.657665\pi$
$942$	−22.4058	−	9.97570i	−0.730020	−	0.325026i
$943$	2.84867	−	1.26831i	0.0927655	−	0.0413019i
$944$	2.10622	−	2.33919i	0.0685515	−	0.0761341i
$945$	−1.56821	−	1.13937i	−0.0510138	−	0.0370637i
$946$	8.63825	+	6.27605i	0.280854	+	0.204052i
$947$	30.6055	−	33.9908i	0.994545	−	1.10455i	2.54375e−5	−	1.00000i	$-0.499992\pi$
$947$	30.6055	−	33.9908i	0.994545	−	1.10455i	0.994519	−	0.104554i	$-0.0333414\pi$
$948$	−5.15446	+	2.29491i	−0.167409	+	0.0745353i
$949$	−42.1150	−	18.7508i	−1.36711	−	0.608677i
$950$	−2.70034	−	2.99903i	−0.0876106	−	0.0973014i
$951$	1.19971	+	11.4144i	0.0389032	+	0.370139i
$952$	−3.76045	−	0.799309i	−0.121877	−	0.0259058i
$953$	8.40103	+	25.8557i	0.272136	+	0.837548i	0.989963	+	0.141327i	$0.0451369\pi$
$953$	8.40103	+	25.8557i	0.272136	+	0.837548i	−0.717827	+	0.696221i	$0.754863\pi$
$954$	2.55555	−	0.543200i	0.0827391	−	0.0175867i
$955$	11.8019	+	20.4415i	0.381901	+	0.661472i
$956$	0.346202	−	0.599639i	0.0111970	−	0.0193937i
$957$	2.19380	−	6.75183i	0.0709155	−	0.218256i
$958$	0.282223	−	2.68517i	0.00911821	−	0.0867540i
$959$	−12.8900	+	9.36516i	−0.416241	+	0.302417i
$960$	1.00000			0.0322749
$961$	19.0721	−	24.4388i	0.615228	−	0.788349i
$962$	45.9736			1.48225
$963$	−10.3128	+	7.49268i	−0.332325	+	0.241448i
$964$	3.06050	−	29.1187i	0.0985722	−	0.937852i
$965$	5.84403	−	17.9861i	0.188126	−	0.578992i
$966$	−0.805550	+	1.39525i	−0.0259181	+	0.0448915i
$967$	12.9606	+	22.4484i	0.416784	+	0.721891i	0.995614	−	0.0935576i	$-0.0298239\pi$
$967$	12.9606	+	22.4484i	0.416784	+	0.721891i	−0.578830	+	0.815448i	$0.696491\pi$
$968$	9.80093	−	2.08325i	0.315014	−	0.0669583i
$969$	2.47332	+	7.61208i	0.0794544	+	0.244535i
$970$	17.1716	+	3.64994i	0.551348	+	0.117193i
$971$	2.24291	+	21.3398i	0.0719783	+	0.684828i	0.969706	+	0.244276i	$0.0785504\pi$
$971$	2.24291	+	21.3398i	0.0719783	+	0.684828i	−0.897727	+	0.440552i	$0.854783\pi$
$972$	−0.669131	−	0.743145i	−0.0214624	−	0.0238364i
$973$	−14.3957	−	6.40936i	−0.461504	−	0.205475i
$974$	−26.9482	+	11.9981i	−0.863476	+	0.384444i
$975$	−2.63026	+	2.92119i	−0.0842356	+	0.0935531i
$976$	2.54514	+	1.84915i	0.0814678	+	0.0591898i
$977$	−13.2033	−	9.59277i	−0.422411	−	0.306900i	0.356196	−	0.934411i	$-0.384074\pi$
$977$	−13.2033	−	9.59277i	−0.422411	−	0.306900i	−0.778607	+	0.627511i	$0.784074\pi$
$978$	−10.3632	+	11.5095i	−0.331378	+	0.368032i
$979$	11.8773	−	5.28811i	0.379600	−	0.169009i
$980$	2.96223	+	1.31887i	0.0946249	+	0.0421297i
$981$	−0.228049	−	0.253274i	−0.00728105	−	0.00808642i
$982$	−1.94343	−	18.4905i	−0.0620172	−	0.590054i
$983$	57.1676	+	12.1513i	1.82336	+	0.387568i	0.987014	−	0.160632i	$-0.0513533\pi$
$983$	57.1676	+	12.1513i	1.82336	+	0.387568i	0.836347	+	0.548200i	$0.184687\pi$
$984$	1.15936	+	3.56814i	0.0369590	+	0.113748i
$985$	−4.54490	+	0.966048i	−0.144812	+	0.0307808i
$986$	7.11112	+	12.3168i	0.226464	+	0.392248i
$987$	10.1845	−	17.6400i	0.324175	−	0.561488i
$988$	−4.90204	+	15.0869i	−0.155955	+	0.479979i
$989$	−0.937005	+	8.91501i	−0.0297950	+	0.283481i
$990$	0.800930	−	0.581910i	0.0254552	−	0.0184943i
$991$	4.58211			0.145555			0.0727777	−	0.997348i	$-0.476814\pi$
$991$	4.58211			0.145555			0.0727777	+	0.997348i	$0.476814\pi$
$992$	5.00360	−	2.44212i	0.158865	−	0.0775375i
$993$	−24.4312			−0.775300
$994$	14.2336	−	10.3413i	0.451461	−	0.328006i
$995$	−0.435242	+	4.14106i	−0.0137981	+	0.131280i
$996$	−1.28475	+	3.95407i	−0.0407090	+	0.125289i
$997$	−10.8854	+	18.8541i	−0.344744	+	0.597114i	−0.985307	−	0.170791i	$-0.945368\pi$
$997$	−10.8854	+	18.8541i	−0.344744	+	0.597114i	0.640563	+	0.767906i	$0.278701\pi$
$998$	14.3126	+	24.7902i	0.453058	+	0.784720i
$999$	11.4400	−	2.43165i	0.361945	−	0.0769339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.c.121.1	✓	16
31.10	even	15	inner	930.2.bg.c.661.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.c.121.1	✓	16	1.1	even	1	trivial
930.2.bg.c.661.1	yes	16	31.10	even	15	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.89605 + 0.403018i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.89605 + 0.403018i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(0.662442 + 0.735716i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(3.59101 - 1.59882i) q^{13} +(1.29705 - 1.44052i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.32709 - 1.47388i) q^{17} +(0.913545 - 0.406737i) q^{18} +(-3.68670 - 1.64142i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(0.202619 + 1.92779i) q^{21} +(-0.968370 - 0.205833i) q^{22} +(-0.256838 - 0.790465i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.96543 + 3.40422i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.202619 + 1.92779i) q^{28} +(5.80144 - 4.21499i) q^{29} +1.00000 q^{30} +(5.00360 - 2.44212i) q^{31} +1.00000 q^{32} +(0.800930 - 0.581910i) q^{33} +(-0.207312 + 1.97244i) q^{34} +(-0.599002 + 1.84354i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.84779 - 10.1287i) q^{37} +(3.94741 - 0.839047i) q^{38} +(-1.21470 - 3.73846i) q^{39} +(0.978148 + 0.207912i) q^{40} +(0.392166 + 3.73121i) q^{41} +(-1.29705 - 1.44052i) q^{42} +(-9.85284 - 4.38677i) q^{43} +(0.904413 - 0.402671i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(0.672410 + 0.488534i) q^{46} +(-8.50120 - 6.17648i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(-2.96223 + 1.31887i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-1.32709 - 1.47388i) q^{51} +(-0.410886 - 3.90932i) q^{52} +(2.55555 + 0.543200i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.968370 - 0.205833i) q^{55} +(-0.969206 - 1.67871i) q^{56} +(-2.01780 + 3.49493i) q^{57} +(-2.21595 + 6.82000i) q^{58} +(-0.329023 + 3.13045i) q^{59} +(-0.809017 + 0.587785i) q^{60} -3.14596 q^{61} +(-2.61255 + 4.91676i) q^{62} +1.93841 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.410886 - 3.90932i) q^{65} +(-0.305928 + 0.941549i) q^{66} +(-4.08861 + 7.08167i) q^{67} +(-0.991653 - 1.71759i) q^{68} +(-0.812982 + 0.172805i) q^{69} +(-0.599002 - 1.84354i) q^{70} +(8.87799 + 1.88707i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-7.84748 - 8.71551i) q^{73} +(10.6844 + 4.75702i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(-2.70034 + 2.99903i) q^{76} +(-1.55253 - 1.12798i) q^{77} +(3.18013 + 2.31050i) q^{78} +(3.77541 - 4.19302i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-2.51042 - 2.78811i) q^{82} +(-0.434582 - 4.13478i) q^{83} +(1.89605 + 0.403018i) q^{84} +(-0.612875 - 1.88624i) q^{85} +(10.5496 - 2.24238i) q^{86} +(-3.58549 - 6.21025i) q^{87} +(-0.495002 + 0.857368i) q^{88} +(4.05819 - 12.4898i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-6.16440 + 4.47870i) q^{91} -0.831144 q^{92} +(-1.90573 - 5.23146i) q^{93} +10.5081 q^{94} +(-3.26486 + 2.37206i) q^{95} +(0.104528 - 0.994522i) q^{96} +(5.42487 - 16.6960i) q^{97} +(1.62128 - 2.80814i) q^{98} +(-0.495002 - 0.857368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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