LMFDB - Embedded newform 288.2.bc.a.13.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			13.18
Character	$\chi$	$=$	288.13
Dual form			288.2.bc.a.133.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.515291 + 1.31699i) q^{2} +(0.925920 + 1.46379i) q^{3} +(-1.46895 - 1.35727i) q^{4} +(-0.0503714 + 0.382609i) q^{5} +(-2.40492 + 0.465155i) q^{6} +(-2.21592 - 0.593754i) q^{7} +(2.54446 - 1.23521i) q^{8} +(-1.28535 + 2.71070i) q^{9} +O(q^{10})$	\(q+(-0.515291 + 1.31699i) q^{2} +(0.925920 + 1.46379i) q^{3} +(-1.46895 - 1.35727i) q^{4} +(-0.0503714 + 0.382609i) q^{5} +(-2.40492 + 0.465155i) q^{6} +(-2.21592 - 0.593754i) q^{7} +(2.54446 - 1.23521i) q^{8} +(-1.28535 + 2.71070i) q^{9} +(-0.477938 - 0.263494i) q^{10} +(-3.74995 + 4.88703i) q^{11} +(0.626626 - 3.40695i) q^{12} +(-1.75873 + 1.34952i) q^{13} +(1.92381 - 2.61240i) q^{14} +(-0.606698 + 0.280532i) q^{15} +(0.315630 + 3.98753i) q^{16} +2.11575i q^{17} +(-2.90765 - 3.08959i) q^{18} +(-3.81157 - 1.57881i) q^{19} +(0.593297 - 0.493666i) q^{20} +(-1.18263 - 3.79340i) q^{21} +(-4.50387 - 7.45690i) q^{22} +(8.01688 - 2.14812i) q^{23} +(4.16405 + 2.58084i) q^{24} +(4.68578 + 1.25555i) q^{25} +(-0.871054 - 3.01163i) q^{26} +(-5.15801 + 0.628416i) q^{27} +(2.44919 + 3.87980i) q^{28} +(7.98435 - 1.05116i) q^{29} +(-0.0568332 - 0.943574i) q^{30} +(-0.751135 + 1.30100i) q^{31} +(-5.41419 - 1.63905i) q^{32} +(-10.6257 - 0.964131i) q^{33} +(-2.78644 - 1.09023i) q^{34} +(0.338795 - 0.817922i) q^{35} +(5.56726 - 2.23732i) q^{36} +(-1.70259 + 0.705235i) q^{37} +(4.04335 - 4.20628i) q^{38} +(-3.60385 - 1.32486i) q^{39} +(0.344435 + 1.03575i) q^{40} +(7.77264 - 2.08267i) q^{41} +(5.60529 + 0.397184i) q^{42} +(0.200243 - 0.260962i) q^{43} +(12.1415 - 2.08910i) q^{44} +(-0.972393 - 0.628326i) q^{45} +(-1.30197 + 11.6651i) q^{46} +(-3.68618 + 2.12822i) q^{47} +(-5.54464 + 4.15415i) q^{48} +(-1.50442 - 0.868578i) q^{49} +(-4.06809 + 5.52417i) q^{50} +(-3.09701 + 1.95902i) q^{51} +(4.41515 + 0.404694i) q^{52} +(0.374914 + 0.905123i) q^{53} +(1.83026 - 7.11689i) q^{54} +(-1.68093 - 1.68093i) q^{55} +(-6.37172 + 1.22635i) q^{56} +(-1.21818 - 7.04118i) q^{57} +(-2.72989 + 11.0570i) q^{58} +(-1.68217 + 12.7774i) q^{59} +(1.27197 + 0.411366i) q^{60} +(6.31250 - 0.831057i) q^{61} +(-1.32636 - 1.65964i) q^{62} +(4.45771 - 5.24351i) q^{63} +(4.94851 - 6.28588i) q^{64} +(-0.427749 - 0.740883i) q^{65} +(6.74509 - 13.4972i) q^{66} +(2.03968 + 2.65816i) q^{67} +(2.87165 - 3.10794i) q^{68} +(10.5674 + 9.74602i) q^{69} +(0.902622 + 0.867659i) q^{70} +(-6.03843 + 6.03843i) q^{71} +(0.0777766 + 8.48492i) q^{72} +(-1.63191 - 1.63191i) q^{73} +(-0.0514625 - 2.60570i) q^{74} +(2.50079 + 8.02152i) q^{75} +(3.45615 + 7.49253i) q^{76} +(11.2113 - 8.60271i) q^{77} +(3.60187 - 4.06357i) q^{78} +(11.1128 - 6.41597i) q^{79} +(-1.54156 - 0.0800946i) q^{80} +(-5.69577 - 6.96837i) q^{81} +(-1.26230 + 11.3097i) q^{82} +(1.33597 + 10.1477i) q^{83} +(-3.41145 + 7.17748i) q^{84} +(-0.809506 - 0.106574i) q^{85} +(0.240502 + 0.398191i) q^{86} +(8.93154 + 10.7141i) q^{87} +(-3.50507 + 17.0668i) q^{88} +(4.37368 - 4.37368i) q^{89} +(1.32857 - 0.956865i) q^{90} +(4.69849 - 1.94618i) q^{91} +(-14.6920 - 7.72560i) q^{92} +(-2.59988 + 0.105123i) q^{93} +(-0.903395 - 5.95133i) q^{94} +(0.796059 - 1.37882i) q^{95} +(-2.61388 - 9.44286i) q^{96} +(1.80672 + 3.12934i) q^{97} +(1.91913 - 1.53374i) q^{98} +(-8.42728 - 16.4465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.515291	+	1.31699i	−0.364366	+	0.931256i
$2$	−0.515291	+	1.31699i	−0.364366	+	0.931256i
$3$	0.925920	+	1.46379i	0.534580	+	0.845118i
$3$	0.925920	+	1.46379i	0.534580	+	0.845118i
$4$	−1.46895	−	1.35727i	−0.734475	−	0.678636i
$5$	−0.0503714	+	0.382609i	−0.0225268	+	0.171108i	−0.999010	−	0.0444854i	$-0.985835\pi$
$5$	−0.0503714	+	0.382609i	−0.0225268	+	0.171108i	0.976483	+	0.215593i	$0.0691685\pi$
$6$	−2.40492	+	0.465155i	−0.981804	+	0.189899i
$7$	−2.21592	−	0.593754i	−0.837539	−	0.224418i	−0.185539	−	0.982637i	$-0.559403\pi$
$7$	−2.21592	−	0.593754i	−0.837539	−	0.224418i	−0.652000	+	0.758219i	$0.726070\pi$
$8$	2.54446	−	1.23521i	0.899601	−	0.436713i
$9$	−1.28535	+	2.71070i	−0.428449	+	0.903566i
$10$	−0.477938	−	0.263494i	−0.151137	−	0.0833241i
$11$	−3.74995	+	4.88703i	−1.13065	+	1.47349i	−0.271024	+	0.962573i	$0.587362\pi$
$11$	−3.74995	+	4.88703i	−1.13065	+	1.47349i	−0.859628	+	0.510921i	$0.829304\pi$
$12$	0.626626	−	3.40695i	0.180891	−	0.983503i
$13$	−1.75873	+	1.34952i	−0.487784	+	0.374290i	−0.823174	−	0.567790i	$-0.807799\pi$
$13$	−1.75873	+	1.34952i	−0.487784	+	0.374290i	0.335390	+	0.942079i	$0.391132\pi$
$14$	1.92381	−	2.61240i	0.514161	−	0.698193i
$15$	−0.606698	+	0.280532i	−0.156649	+	0.0724331i
$16$	0.315630	+	3.98753i	0.0789075	+	0.996882i
$17$			2.11575i			0.513146i	0.966525	+	0.256573i	$0.0825933\pi$
$17$			2.11575i			0.513146i	−0.966525	+	0.256573i	$0.917407\pi$
$18$	−2.90765	−	3.08959i	−0.685339	−	0.728224i
$19$	−3.81157	−	1.57881i	−0.874435	−	0.362203i	−0.100099	−	0.994977i	$-0.531916\pi$
$19$	−3.81157	−	1.57881i	−0.874435	−	0.362203i	−0.774336	+	0.632775i	$0.781916\pi$
$20$	0.593297	−	0.493666i	0.132665	−	0.110387i
$21$	−1.18263	−	3.79340i	−0.258072	−	0.827788i
$22$	−4.50387	−	7.45690i	−0.960229	−	1.58982i
$23$	8.01688	−	2.14812i	1.67163	−	0.447913i	0.706084	−	0.708128i	$-0.250460\pi$
$23$	8.01688	−	2.14812i	1.67163	−	0.447913i	0.965551	+	0.260215i	$0.0837936\pi$
$24$	4.16405	+	2.58084i	0.849982	+	0.526811i
$25$	4.68578	+	1.25555i	0.937155	+	0.251110i
$26$	−0.871054	−	3.01163i	−0.170828	−	0.590630i
$27$	−5.15801	+	0.628416i	−0.992660	+	0.120939i
$28$	2.44919	+	3.87980i	0.462854	+	0.733213i
$29$	7.98435	−	1.05116i	1.48266	−	0.195195i	0.654657	−	0.755926i	$-0.272813\pi$
$29$	7.98435	−	1.05116i	1.48266	−	0.195195i	0.827998	+	0.560730i	$0.189480\pi$
$30$	−0.0568332	−	0.943574i	−0.0103763	−	0.172272i
$31$	−0.751135	+	1.30100i	−0.134908	+	0.233667i	−0.925562	−	0.378596i	$-0.876407\pi$
$31$	−0.751135	+	1.30100i	−0.134908	+	0.233667i	0.790654	+	0.612263i	$0.209740\pi$
$32$	−5.41419	−	1.63905i	−0.957103	−	0.289747i
$33$	−10.6257	−	0.964131i	−1.84970	−	0.167834i
$34$	−2.78644	−	1.09023i	−0.477870	−	0.186973i
$35$	0.338795	−	0.817922i	0.0572667	−	0.138254i
$36$	5.56726	−	2.23732i	0.927877	−	0.372886i
$37$	−1.70259	+	0.705235i	−0.279904	+	0.115940i	−0.518219	−	0.855248i	$-0.673405\pi$
$37$	−1.70259	+	0.705235i	−0.279904	+	0.115940i	0.238315	+	0.971188i	$0.423405\pi$
$38$	4.04335	−	4.20628i	0.655918	−	0.682348i
$39$	−3.60385	−	1.32486i	−0.577078	−	0.212147i
$40$	0.344435	+	1.03575i	0.0544599	+	0.163767i
$41$	7.77264	−	2.08267i	1.21388	−	0.325259i	0.405599	−	0.914051i	$-0.367063\pi$
$41$	7.77264	−	2.08267i	1.21388	−	0.325259i	0.808284	+	0.588792i	$0.200396\pi$
$42$	5.60529	+	0.397184i	0.864915	+	0.0612868i
$43$	0.200243	−	0.260962i	0.0305368	−	0.0397964i	−0.777835	−	0.628468i	$-0.783682\pi$
$43$	0.200243	−	0.260962i	0.0305368	−	0.0397964i	0.808372	+	0.588672i	$0.200349\pi$
$44$	12.1415	−	2.08910i	1.83040	−	0.314944i
$45$	−0.972393	−	0.628326i	−0.144956	−	0.0936654i
$46$	−1.30197	+	11.6651i	−0.191965	+	1.71992i
$47$	−3.68618	+	2.12822i	−0.537685	+	0.310432i	−0.744140	−	0.668024i	$-0.767141\pi$
$47$	−3.68618	+	2.12822i	−0.537685	+	0.310432i	0.206455	+	0.978456i	$0.433807\pi$
$48$	−5.54464	+	4.15415i	−0.800300	+	0.599599i
$49$	−1.50442	−	0.868578i	−0.214917	−	0.124083i
$50$	−4.06809	+	5.52417i	−0.575315	+	0.781236i
$51$	−3.09701	+	1.95902i	−0.433669	+	0.274317i
$52$	4.41515	+	0.404694i	0.612271	+	0.0561210i
$53$	0.374914	+	0.905123i	0.0514984	+	0.124328i	0.947535	−	0.319652i	$-0.103566\pi$
$53$	0.374914	+	0.905123i	0.0514984	+	0.124328i	−0.896037	+	0.443980i	$0.853566\pi$
$54$	1.83026	−	7.11689i	0.249066	−	0.968486i
$55$	−1.68093	−	1.68093i	−0.226656	−	0.226656i
$56$	−6.37172	+	1.22635i	−0.851457	+	0.163877i
$57$	−1.21818	−	7.04118i	−0.161351	−	0.932627i
$58$	−2.72989	+	11.0570i	−0.358452	+	1.45185i
$59$	−1.68217	+	12.7774i	−0.219000	+	1.66347i	0.430109	+	0.902777i	$0.358475\pi$
$59$	−1.68217	+	12.7774i	−0.219000	+	1.66347i	−0.649109	+	0.760695i	$0.724858\pi$
$60$	1.27197	+	0.411366i	0.164210	+	0.0531071i
$61$	6.31250	−	0.831057i	0.808233	−	0.106406i	0.284925	−	0.958550i	$-0.408031\pi$
$61$	6.31250	−	0.831057i	0.808233	−	0.106406i	0.523308	+	0.852144i	$0.324698\pi$
$62$	−1.32636	−	1.65964i	−0.168448	−	0.210774i
$63$	4.45771	−	5.24351i	0.561619	−	0.660620i
$64$	4.94851	−	6.28588i	0.618564	−	0.785734i
$65$	−0.427749	−	0.740883i	−0.0530557	−	0.0918952i
$66$	6.74509	−	13.4972i	0.830263	−	1.66139i
$67$	2.03968	+	2.65816i	0.249186	+	0.324746i	0.901153	−	0.433502i	$-0.142722\pi$
$67$	2.03968	+	2.65816i	0.249186	+	0.324746i	−0.651966	+	0.758248i	$0.726056\pi$
$68$	2.87165	−	3.10794i	0.348239	−	0.376893i
$69$	10.5674	+	9.74602i	1.27216	+	1.17328i
$70$	0.902622	+	0.867659i	0.107884	+	0.103705i
$71$	−6.03843	+	6.03843i	−0.716630	+	0.716630i	−0.967913	−	0.251284i	$-0.919147\pi$
$71$	−6.03843	+	6.03843i	−0.716630	+	0.716630i	0.251284	+	0.967913i	$0.419147\pi$
$72$	0.0777766	+	8.48492i	0.00916605	+	0.999958i
$73$	−1.63191	−	1.63191i	−0.191001	−	0.191001i	0.605128	−	0.796128i	$-0.293122\pi$
$73$	−1.63191	−	1.63191i	−0.191001	−	0.191001i	−0.796128	+	0.605128i	$0.793122\pi$
$74$	−0.0514625	−	2.60570i	−0.00598240	−	0.302907i
$75$	2.50079	+	8.02152i	0.288767	+	0.926245i
$76$	3.45615	+	7.49253i	0.396447	+	0.859452i
$77$	11.2113	−	8.60271i	1.27764	−	0.980370i
$78$	3.60187	−	4.06357i	0.407831	−	0.460109i
$79$	11.1128	−	6.41597i	1.25029	−	0.721853i	0.279120	−	0.960256i	$-0.409957\pi$
$79$	11.1128	−	6.41597i	1.25029	−	0.721853i	0.971166	+	0.238403i	$0.0766239\pi$
$80$	−1.54156	−	0.0800946i	−0.172352	−	0.00895485i
$81$	−5.69577	−	6.96837i	−0.632864	−	0.774263i
$82$	−1.26230	+	11.3097i	−0.139398	+	1.24895i
$83$	1.33597	+	10.1477i	0.146642	+	1.11386i	0.893561	+	0.448942i	$0.148199\pi$
$83$	1.33597	+	10.1477i	0.146642	+	1.11386i	−0.746919	+	0.664915i	$0.768468\pi$
$84$	−3.41145	+	7.17748i	−0.372219	+	0.783127i
$85$	−0.809506	−	0.106574i	−0.0878033	−	0.0115595i
$86$	0.240502	+	0.398191i	0.0259340	+	0.0429380i
$87$	8.93154	+	10.7141i	0.957561	+	1.14867i
$88$	−3.50507	+	17.0668i	−0.373642	+	1.81933i
$89$	4.37368	−	4.37368i	0.463609	−	0.463609i	−0.436227	−	0.899837i	$-0.643686\pi$
$89$	4.37368	−	4.37368i	0.463609	−	0.463609i	0.899837	+	0.436227i	$0.143686\pi$
$90$	1.32857	−	0.956865i	0.140043	−	0.100862i
$91$	4.69849	−	1.94618i	0.492535	−	0.204015i
$92$	−14.6920	−	7.72560i	−1.53174	−	0.805449i
$93$	−2.59988	+	0.105123i	−0.269595	+	0.0109008i
$94$	−0.903395	−	5.95133i	−0.0931781	−	0.613833i
$95$	0.796059	−	1.37882i	0.0816740	−	0.141463i
$96$	−2.61388	−	9.44286i	−0.266778	−	0.963758i
$97$	1.80672	+	3.12934i	0.183445	+	0.317736i	0.943051	−	0.332647i	$-0.107942\pi$
$97$	1.80672	+	3.12934i	0.183445	+	0.317736i	−0.759606	+	0.650383i	$0.774608\pi$
$98$	1.91913	−	1.53374i	0.193861	−	0.154932i
$99$	−8.42728	−	16.4465i	−0.846973	−	1.65293i
$100$	−5.17905	−	8.20421i	−0.517905	−	0.820421i
$101$	−11.3904	−	8.74013i	−1.13338	−	0.869676i	−0.140656	−	0.990059i	$-0.544921\pi$
$101$	−11.3904	−	8.74013i	−1.13338	−	0.869676i	−0.992728	+	0.120383i	$0.961588\pi$
$102$	−0.984153	−	5.08821i	−0.0974457	−	0.503808i
$103$	−1.77974	−	6.64208i	−0.175363	−	0.654464i	−0.996490	−	0.0837176i	$-0.973321\pi$
$103$	−1.77974	−	6.64208i	−0.175363	−	0.654464i	0.821126	−	0.570746i	$-0.193346\pi$
$104$	−2.80807	+	5.60620i	−0.275354	+	0.549733i
$105$	1.51096	−	0.261407i	0.147455	−	0.0255107i
$106$	−1.38523	+	0.0273583i	−0.134546	+	0.00265727i
$107$	3.36941	+	8.13448i	0.325733	+	0.786390i	0.998900	+	0.0468988i	$0.0149338\pi$
$107$	3.36941	+	8.13448i	0.325733	+	0.786390i	−0.673166	+	0.739491i	$0.735066\pi$
$108$	8.42980	+	6.07771i	0.811157	+	0.584828i
$109$	5.05069	+	2.09206i	0.483768	+	0.200383i	0.611219	−	0.791462i	$-0.290679\pi$
$109$	5.05069	+	2.09206i	0.483768	+	0.200383i	−0.127451	+	0.991845i	$0.540679\pi$
$110$	3.07994	−	1.34761i	0.293661	−	0.128489i
$111$	−2.60877	−	1.83924i	−0.247614	−	0.174572i
$112$	1.66820	−	9.02345i	0.157630	−	0.852636i
$113$	4.79412	+	2.76788i	0.450993	+	0.260381i	0.708249	−	0.705962i	$-0.249485\pi$
$113$	4.79412	+	2.76788i	0.450993	+	0.260381i	−0.257257	+	0.966343i	$0.582819\pi$
$114$	9.90091	+	2.02393i	0.927305	+	0.189558i
$115$	0.418067	+	3.17553i	0.0389849	+	0.296120i
$116$	−13.1553	−	9.29282i	−1.22144	−	0.862817i
$117$	−1.39757	−	6.50199i	−0.129205	−	0.601109i
$118$	−15.9609	−	8.79948i	−1.46932	−	0.810058i
$119$	1.25624	−	4.68834i	0.115159	−	0.429779i
$120$	−1.19720	+	1.46320i	−0.109289	+	0.133571i
$121$	−6.97391	−	26.0270i	−0.633992	−	2.36609i
$122$	−2.15828	+	8.74177i	−0.195401	+	0.791443i
$123$	10.2454	+	9.44911i	0.923800	+	0.851997i
$124$	2.86919	−	0.891616i	0.257661	−	0.0800695i
$125$	−1.45482	+	3.51225i	−0.130123	+	0.314145i
$126$	4.60866	+	8.57272i	0.410572	+	0.763718i
$127$	−20.9358			−1.85775			−0.928876	−	0.370391i	$-0.879224\pi$
$127$	−20.9358			−1.85775			−0.928876	+	0.370391i	$0.879224\pi$
$128$	5.72854	+	9.75622i	0.506336	+	0.862336i
$129$	0.567402	+	0.0514836i	0.0499570	+	0.00453288i
$130$	1.19615	−	0.181573i	0.104910	−	0.0159250i
$131$	−10.4603	−	13.6321i	−0.913921	−	1.19104i	−0.981138	−	0.193306i	$-0.938079\pi$
$131$	−10.4603	−	13.6321i	−0.913921	−	1.19104i	0.0672177	−	0.997738i	$-0.478588\pi$
$132$	14.3001	+	15.8382i	1.24466	+	1.37854i
$133$	7.50872	+	5.76164i	0.651089	+	0.499598i
$134$	−4.55181	+	1.31652i	−0.393216	+	0.113730i
$135$	0.0193788	−	2.00516i	0.00166786	−	0.172576i
$136$	2.61340	+	5.38344i	0.224097	+	0.461626i
$137$	−3.59334	+	13.4105i	−0.307000	+	1.14574i	0.624210	+	0.781257i	$0.285421\pi$
$137$	−3.59334	+	13.4105i	−0.307000	+	1.14574i	−0.931210	+	0.364483i	$0.881246\pi$
$138$	−18.2807	+	8.89513i	−1.55616	+	0.757204i
$139$	5.21767	+	0.686919i	0.442557	+	0.0582637i	0.348512	−	0.937304i	$-0.386687\pi$
$139$	5.21767	+	0.686919i	0.442557	+	0.0582637i	0.0940446	+	0.995568i	$0.470020\pi$
$140$	−1.60781	+	0.741651i	−0.135885	+	0.0626810i
$141$	−6.52836	−	3.42523i	−0.549787	−	0.288456i
$142$	−4.84103	−	11.0641i	−0.406250	−	0.928481i
$143$		−	13.6556i		−	1.14194i
$144$	−11.2147	−	4.26977i	−0.934557	−	0.355815i
$145$			3.10783i			0.258091i
$146$	2.99013	−	1.30831i	0.247465	−	0.108277i
$147$	−0.121560	−	3.00639i	−0.0100261	−	0.247963i
$148$	3.45821	+	1.27492i	0.284263	+	0.104798i
$149$	0.467810	+	0.0615883i	0.0383245	+	0.00504551i	0.149664	−	0.988737i	$-0.452181\pi$
$149$	0.467810	+	0.0615883i	0.0383245	+	0.00504551i	−0.111340	+	0.993782i	$0.535514\pi$
$150$	−11.8529	−	0.839883i	−0.967788	−	0.0685762i
$151$	3.64015	−	13.5852i	0.296231	−	1.10555i	−0.644003	−	0.765023i	$-0.722728\pi$
$151$	3.64015	−	13.5852i	0.296231	−	1.10555i	0.940234	−	0.340528i	$-0.110606\pi$
$152$	−11.6485	+	0.690894i	−0.944821	+	0.0560389i
$153$	−5.73517	−	2.71948i	−0.463661	−	0.219857i
$154$	5.55266	+	19.1981i	0.447446	+	1.54703i
$155$	−0.459940	−	0.352924i	−0.0369433	−	0.0283476i
$156$	3.49569	+	6.83756i	0.279879	+	0.547443i
$157$	12.9430	+	16.8676i	1.03296	+	1.34618i	0.936432	+	0.350850i	$0.114107\pi$
$157$	12.9430	+	16.8676i	1.03296	+	1.34618i	0.0965292	+	0.995330i	$0.469226\pi$
$158$	2.72348	+	17.9416i	0.216668	+	1.42736i
$159$	−0.977767	+	1.38687i	−0.0775420	+	0.109986i
$160$	0.899837	−	1.98896i	0.0711384	−	0.157241i
$161$	−19.0402			−1.50058
$162$	12.1123	−	3.91056i	0.951631	−	0.307243i
$163$	1.37390	−	3.31690i	0.107612	−	0.259800i	−0.860896	−	0.508782i	$-0.830096\pi$
$163$	1.37390	−	3.31690i	0.107612	−	0.259800i	0.968508	+	0.248982i	$0.0800960\pi$
$164$	−14.2444	−	7.49024i	−1.11230	−	0.584890i
$165$	0.904117	−	4.01693i	0.0703854	−	0.312717i
$166$	−14.0529	−	3.46956i	−1.09072	−	0.269290i
$167$	−1.80553	−	6.73833i	−0.139716	−	0.521428i	−0.999934	−	0.0115009i	$-0.996339\pi$
$167$	−1.80553	−	6.73833i	−0.139716	−	0.521428i	0.860218	−	0.509927i	$-0.170328\pi$
$168$	−7.69481	−	8.19135i	−0.593668	−	0.631976i
$169$	−2.09272	+	7.81015i	−0.160979	+	0.600781i
$170$	0.557488	−	1.01120i	0.0427574	−	0.0775554i
$171$	9.17886	−	8.30272i	0.701925	−	0.634925i
$172$	−0.648344	+	0.111556i	−0.0494358	+	0.00850606i
$173$	0.522211	+	3.96658i	0.0397029	+	0.301574i	0.999763	+	0.0217791i	$0.00693304\pi$
$173$	0.522211	+	3.96658i	0.0397029	+	0.301574i	−0.960060	+	0.279795i	$0.909734\pi$
$174$	−18.7127	+	6.24191i	−1.41861	+	0.473198i
$175$	−9.63782	−	5.56440i	−0.728550	−	0.420629i
$176$	−20.6707	−	13.4105i	−1.55812	−	1.01086i
$177$	−20.2609	+	9.36848i	−1.52290	+	0.704178i
$178$	3.50640	+	8.01383i	0.262816	+	0.600662i
$179$	−2.98374	−	1.23591i	−0.223015	−	0.0923760i	0.268378	−	0.963314i	$-0.413512\pi$
$179$	−2.98374	−	1.23591i	−0.223015	−	0.0923760i	−0.491394	+	0.870938i	$0.663512\pi$
$180$	0.575587	+	2.24278i	0.0429017	+	0.167167i
$181$	−0.280293	−	0.676687i	−0.0208340	−	0.0502977i	0.913120	−	0.407691i	$-0.133666\pi$
$181$	−0.280293	−	0.676687i	−0.0208340	−	0.0502977i	−0.933954	+	0.357393i	$0.883666\pi$
$182$	0.142017	+	7.19073i	0.0105270	+	0.533012i
$183$	7.06136	+	8.47067i	0.521991	+	0.626170i
$184$	17.7452	−	15.3683i	1.30819	−	1.13297i
$185$	−0.184067	−	0.686949i	−0.0135329	−	0.0505055i
$186$	1.20125	−	3.47820i	0.0880799	−	0.255034i
$187$	−10.3397	−	7.93396i	−0.756117	−	0.580189i
$188$	8.30338	+	1.87690i	0.605587	+	0.136887i
$189$	11.8029	+	1.67007i	0.858532	+	0.121480i
$190$	1.40569	+	1.75890i	0.101979	+	0.127604i
$191$	7.76876	+	13.4559i	0.562128	+	0.973634i	0.997311	+	0.0732921i	$0.0233505\pi$
$191$	7.76876	+	13.4559i	0.562128	+	0.973634i	−0.435182	+	0.900342i	$0.643316\pi$
$192$	13.7831	+	1.42335i	0.994710	+	0.102722i
$193$	1.96702	−	3.40698i	0.141589	−	0.245240i	−0.786506	−	0.617583i	$-0.788112\pi$
$193$	1.96702	−	3.40698i	0.141589	−	0.245240i	0.928095	+	0.372343i	$0.121445\pi$
$194$	−5.05231	+	0.766926i	−0.362735	+	0.0550621i
$195$	0.688434	−	1.31213i	0.0492998	−	0.0939637i
$196$	1.03102	+	3.31781i	0.0736446	+	0.236986i
$197$	−2.68609	+	1.11261i	−0.191376	+	0.0792705i	−0.476313	−	0.879276i	$-0.658027\pi$
$197$	−2.68609	+	1.11261i	−0.191376	+	0.0792705i	0.284937	+	0.958546i	$0.408027\pi$
$198$	26.0024	−	2.62395i	1.84791	−	0.186476i
$199$	9.08039	−	9.08039i	0.643692	−	0.643692i	−0.307769	−	0.951461i	$-0.599582\pi$
$199$	9.08039	−	9.08039i	0.643692	−	0.643692i	0.951461	+	0.307769i	$0.0995824\pi$
$200$	13.4736	−	2.59323i	0.952729	−	0.183369i
$201$	−2.00240	+	5.44689i	−0.141239	+	0.384194i
$202$	17.3801	−	10.4973i	1.22286	−	0.738590i
$203$	−18.3168	−	2.41145i	−1.28559	−	0.169251i
$204$	7.20828	+	1.32579i	0.504680	+	0.0928236i
$205$	0.405330	+	3.07879i	0.0283095	+	0.215032i
$206$	9.66467	+	1.07870i	0.673370	+	0.0751564i
$207$	−4.48156	+	24.4924i	−0.311490	+	1.70234i
$208$	−5.93636	−	6.58703i	−0.411612	−	0.456729i
$209$	22.0089	−	12.7068i	1.52238	−	0.878949i
$210$	−0.434313	+	2.12463i	−0.0299704	+	0.146613i
$211$	13.9832	−	10.7297i	0.962644	−	0.738663i	−0.00260442	−	0.999997i	$-0.500829\pi$
$211$	13.9832	−	10.7297i	0.962644	−	0.738663i	0.965248	+	0.261334i	$0.0841623\pi$
$212$	0.677767	−	1.83844i	0.0465492	−	0.126265i
$213$	−14.4301	−	3.24787i	−0.988732	−	0.222541i
$214$	−12.4493	+	0.245873i	−0.851016	+	0.0168075i
$215$	0.0897599	+	0.0897599i	0.00612158	+	0.00612158i
$216$	−12.3481	+	7.97021i	−0.840182	+	0.542304i
$217$	2.43693	−	2.43693i	0.165430	−	0.165430i
$218$	−5.35781	+	5.57371i	−0.362877	+	0.377499i
$219$	0.877753	−	3.89979i	0.0593130	−	0.263524i
$220$	0.187725	+	4.75068i	0.0126564	+	0.320291i
$221$	−2.85525	−	3.72104i	−0.192065	−	0.250304i
$222$	3.76654	−	2.48800i	0.252794	−	0.166984i
$223$	−7.46985	−	12.9382i	−0.500218	−	0.866404i	−1.00000		0.000252106i	$-0.999920\pi$
$223$	−7.46985	−	12.9382i	−0.500218	−	0.866404i	0.499782	−	0.866151i	$-0.333414\pi$
$224$	11.0242	+	6.84671i	0.736587	+	0.457465i
$225$	−9.42626	+	11.0879i	−0.628417	+	0.739194i
$226$	−6.11566	+	4.88756i	−0.406807	+	0.325116i
$227$	24.4041	−	3.21286i	1.61976	−	0.213245i	0.734587	−	0.678515i	$-0.237376\pi$
$227$	24.4041	−	3.21286i	1.61976	−	0.213245i	0.885169	+	0.465270i	$0.154043\pi$
$228$	−7.76735	+	11.9965i	−0.514405	+	0.794490i
$229$	2.06478	−	15.6835i	0.136444	−	1.03640i	−0.777020	−	0.629476i	$-0.783269\pi$
$229$	2.06478	−	15.6835i	0.136444	−	1.03640i	0.913464	−	0.406920i	$-0.133397\pi$
$230$	−4.39758	−	1.08573i	−0.289968	−	0.0715910i
$231$	22.9733	+	8.44550i	1.51153	+	0.555673i
$232$	19.0174	−	12.5370i	1.24855	−	0.823093i
$233$	−1.00722	−	1.00722i	−0.0659851	−	0.0659851i	0.673344	−	0.739329i	$-0.264857\pi$
$233$	−1.00722	−	1.00722i	−0.0659851	−	0.0659851i	−0.739329	+	0.673344i	$0.764857\pi$
$234$	9.28324	+	1.50983i	0.606864	+	0.0987004i
$235$	−0.628597	−	1.51757i	−0.0410051	−	0.0989951i
$236$	19.8134	−	16.4862i	1.28974	−	1.07316i
$237$	19.6812	+	10.3261i	1.27843	+	0.670751i
$238$	5.52719	+	4.07032i	0.358275	+	0.263839i
$239$	16.4825	+	9.51615i	1.06616	+	0.615549i	0.927130	−	0.374739i	$-0.122268\pi$
$239$	16.4825	+	9.51615i	1.06616	+	0.615549i	0.139032	+	0.990288i	$0.455601\pi$
$240$	−1.31012	−	2.33068i	−0.0845680	−	0.150445i
$241$	−12.6153	+	7.28345i	−0.812623	+	0.469168i	−0.847866	−	0.530210i	$-0.822113\pi$
$241$	−12.6153	+	7.28345i	−0.812623	+	0.469168i	0.0352427	+	0.999379i	$0.488780\pi$
$242$	37.8710	+	4.22687i	2.43444	+	0.271714i
$243$	4.92638	−	14.7895i	0.316028	−	0.948750i
$244$	−10.4007	−	7.34700i	−0.665838	−	0.470343i
$245$	0.408106	−	0.531854i	0.0260729	−	0.0339789i
$246$	−17.7238	+	8.62414i	−1.13003	+	0.549855i
$247$	8.83416	−	2.36711i	0.562104	−	0.150615i
$248$	−0.304216	+	4.23816i	−0.0193178	+	0.269123i
$249$	−13.6171	+	11.3516i	−0.862949	+	0.719375i
$250$	−3.87596	−	3.72582i	−0.245137	−	0.235642i
$251$	−13.3517	+	5.53046i	−0.842753	+	0.349080i	−0.761939	−	0.647649i	$-0.775752\pi$
$251$	−13.3517	+	5.53046i	−0.842753	+	0.349080i	−0.0808147	+	0.996729i	$0.525752\pi$
$252$	−13.6650	+	1.65213i	−0.860815	+	0.104075i
$253$	−19.5650	+	47.2340i	−1.23004	+	2.96958i
$254$	10.7880	−	27.5723i	0.676901	−	1.73004i
$255$	−0.593537	−	1.28362i	−0.0371687	−	0.0803836i
$256$	−15.8008	+	2.51717i	−0.987547	+	0.157323i
$257$	2.04278	−	3.53820i	0.127425	−	0.220707i	−0.795253	−	0.606277i	$-0.792662\pi$
$257$	2.04278	−	3.53820i	0.127425	−	0.220707i	0.922678	+	0.385571i	$0.125995\pi$
$258$	−0.360181	+	0.720737i	−0.0224239	+	0.0448711i
$259$	4.19153	−	0.551826i	0.260449	−	0.0342888i
$260$	−0.377237	+	1.66889i	−0.0233953	+	0.103500i
$261$	−7.41327	+	22.9943i	−0.458870	+	1.42331i
$262$	23.3435	−	6.75165i	1.44217	−	0.417118i
$263$	−0.885195	−	0.237187i	−0.0545835	−	0.0146256i	0.231424	−	0.972853i	$-0.425662\pi$
$263$	−0.885195	−	0.237187i	−0.0545835	−	0.0146256i	−0.286007	+	0.958227i	$0.592328\pi$
$264$	−28.2276	+	10.6718i	−1.73729	+	0.656804i
$265$	−0.365193	+	0.0978532i	−0.0224336	+	0.00601107i
$266$	−11.4572	+	6.92002i	−0.702488	+	0.424294i
$267$	10.4518	+	2.35246i	0.639641	+	0.143968i
$268$	0.611658	−	6.67310i	0.0373630	−	0.407624i
$269$	2.14502	+	0.888497i	0.130784	+	0.0541726i	0.447116	−	0.894476i	$-0.352451\pi$
$269$	2.14502	+	0.888497i	0.130784	+	0.0541726i	−0.316332	+	0.948649i	$0.602451\pi$
$270$	2.63079	+	1.05876i	0.160105	+	0.0644341i
$271$		−	23.6782i		−	1.43835i	−0.694831	−	0.719173i	$-0.744521\pi$
$271$		−	23.6782i		−	1.43835i	0.694831	−	0.719173i	$-0.255479\pi$
$272$	−8.43663	+	0.667795i	−0.511546	+	0.0404910i
$273$	7.19921	+	5.07558i	0.435716	+	0.307188i
$274$	−15.8100	−	11.6427i	−0.955116	−	0.703364i
$275$	−23.7073	+	18.1913i	−1.42961	+	1.09697i
$276$	−2.29495	−	28.6592i	−0.138140	−	1.72508i
$277$	−1.88337	+	2.45445i	−0.113161	+	0.147474i	−0.846500	−	0.532389i	$-0.821294\pi$
$277$	−1.88337	+	2.45445i	−0.113161	+	0.147474i	0.733339	+	0.679863i	$0.237961\pi$
$278$	−3.59328	+	6.51767i	−0.215511	+	0.390904i
$279$	−2.56116	−	3.70834i	−0.153333	−	0.222012i
$280$	−0.148258	−	2.49965i	−0.00886013	−	0.149383i
$281$	8.29077	+	2.22150i	0.494586	+	0.132524i	0.497486	−	0.867472i	$-0.334257\pi$
$281$	8.29077	+	2.22150i	0.494586	+	0.132524i	−0.00290040	+	0.999996i	$0.500923\pi$
$282$	7.87501	−	6.83283i	0.468950	−	0.406889i
$283$	−3.51159	+	26.6732i	−0.208742	+	1.58555i	0.491000	+	0.871159i	$0.336631\pi$
$283$	−3.51159	+	26.6732i	−0.208742	+	1.58555i	−0.699742	+	0.714395i	$0.746702\pi$
$284$	17.0659	−	0.674366i	1.01268	−	0.0400163i
$285$	2.75538	−	0.111411i	0.163215	−	0.00659939i
$286$	17.9843	+	7.03660i	1.06344	+	0.416083i
$287$	−18.4602			−1.08967
$288$	11.4021	−	12.5695i	0.671875	−	0.740665i
$289$	12.5236			0.736682
$290$	−4.09300	−	1.60144i	−0.240349	−	0.0940396i
$291$	−2.90780	+	5.54218i	−0.170458	+	0.324888i
$292$	0.182251	+	4.61215i	0.0106654	+	0.269905i
$293$	1.09987	−	8.35432i	0.0642549	−	0.488064i	−0.928815	−	0.370543i	$-0.879172\pi$
$293$	1.09987	−	8.35432i	0.0642549	−	0.488064i	0.993070	−	0.117522i	$-0.0374949\pi$
$294$	4.02203	+	1.38907i	0.234570	+	0.0810122i
$295$	−4.80400	−	1.28723i	−0.279700	−	0.0749454i
$296$	−3.46105	+	3.89749i	−0.201169	+	0.226537i
$297$	16.2712	−	27.5639i	0.944150	−	1.59942i
$298$	−0.322170	+	0.584367i	−0.0186628	+	0.0338515i
$299$	−11.2006	+	14.5969i	−0.647747	+	0.844160i
$300$	7.21383	−	15.1775i	0.416491	−	0.876272i
$301$	−0.598670	+	0.459376i	−0.0345068	+	0.0264780i
$302$	16.0159	+	11.7944i	0.921614	+	0.678692i
$303$	2.24713	−	24.7657i	0.129094	−	1.42275i
$304$	5.09248	−	15.6971i	0.292074	−	0.900289i
$305$			2.45708i			0.140692i
$306$	6.53682	−	6.15187i	0.373685	−	0.351679i
$307$	23.0211	+	9.53564i	1.31388	+	0.544228i	0.926015	−	0.377487i	$-0.123212\pi$
$307$	23.0211	+	9.53564i	1.31388	+	0.544228i	0.387868	+	0.921715i	$0.373212\pi$
$308$	−28.1450	−	2.57978i	−1.60371	−	0.146997i
$309$	8.07470	−	8.75520i	0.459354	−	0.498066i
$310$	0.701802	−	0.423880i	0.0398597	−	0.0240747i
$311$	5.22983	−	1.40133i	0.296556	−	0.0794620i	−0.107473	−	0.994208i	$-0.534276\pi$
$311$	5.22983	−	1.40133i	0.296556	−	0.0794620i	0.404029	+	0.914746i	$0.367609\pi$
$312$	−10.8063	+	1.08047i	−0.611788	+	0.0611697i
$313$	13.9965	+	3.75035i	0.791129	+	0.211982i	0.631686	−	0.775225i	$-0.282363\pi$
$313$	13.9965	+	3.75035i	0.791129	+	0.211982i	0.159443	+	0.987207i	$0.449030\pi$
$314$	−28.8839	+	8.35409i	−1.63001	+	0.471449i
$315$	1.78167	+	1.96968i	0.100386	+	0.110979i
$316$	−25.0323	−	5.65832i	−1.40818	−	0.318306i
$317$	−21.2996	+	2.80415i	−1.19631	+	0.157497i	−0.702248	−	0.711933i	$-0.747820\pi$
$317$	−21.2996	+	2.80415i	−1.19631	+	0.157497i	−0.494057	+	0.869429i	$0.664487\pi$
$318$	−1.32266	−	2.00235i	−0.0741711	−	0.112286i
$319$	−24.8038	+	42.9615i	−1.38875	+	2.40538i
$320$	2.15577	+	2.20997i	0.120511	+	0.123541i
$321$	−8.78734	+	12.4640i	−0.490462	+	0.695671i
$322$	9.81125	−	25.0759i	0.546759	−	1.39742i
$323$	3.34036	−	8.06435i	0.185863	−	0.448713i
$324$	−1.09116	+	17.9669i	−0.0606201	+	0.998161i
$325$	−9.93541	+	4.11538i	−0.551117	+	0.228280i
$326$	3.66038	+	3.51859i	0.202730	+	0.194877i
$327$	1.61420	+	9.33021i	0.0892652	+	0.515962i
$328$	17.2046	−	14.9001i	0.949966	−	0.822722i
$329$	9.43192	−	2.52727i	0.519998	−	0.139333i
$330$	4.82439	+	3.26061i	0.265574	+	0.179490i
$331$	7.71921	−	10.0599i	0.424286	−	0.552941i	−0.531479	−	0.847072i	$-0.678364\pi$
$331$	7.71921	−	10.0599i	0.424286	−	0.552941i	0.955765	+	0.294131i	$0.0950302\pi$
$332$	11.8107	−	16.7198i	0.648198	−	0.917617i
$333$	0.276735	−	5.52167i	0.0151650	−	0.302586i
$334$	9.80472	+	1.09433i	0.536491	+	0.0598790i
$335$	−1.11978	+	0.646503i	−0.0611799	+	0.0353223i
$336$	14.7530	−	5.91310i	0.804844	−	0.322586i
$337$	4.88939	+	2.82289i	0.266342	+	0.153773i	0.627224	−	0.778839i	$-0.284191\pi$
$337$	4.88939	+	2.82289i	0.266342	+	0.153773i	−0.360882	+	0.932611i	$0.617524\pi$
$338$	−9.20757	−	6.78061i	−0.500826	−	0.368816i
$339$	0.387373	+	9.58041i	0.0210392	+	0.520336i
$340$	1.04448	+	1.25527i	0.0566446	+	0.0680766i
$341$	−3.54132	−	8.54951i	−0.191773	−	0.462982i
$342$	6.20485	+	16.3668i	0.335520	+	0.885016i
$343$	14.1731	+	14.1731i	0.765276	+	0.765276i
$344$	0.187167	−	0.911349i	0.0100914	−	0.0491367i
$345$	−4.26121	+	3.55225i	−0.229416	+	0.191247i
$346$	−5.49306	−	1.35620i	−0.295309	−	0.0729096i
$347$	1.18070	−	8.96828i	0.0633831	−	0.481443i	−0.930086	−	0.367342i	$-0.880268\pi$
$347$	1.18070	−	8.96828i	0.0633831	−	0.481443i	0.993469	−	0.114101i	$-0.0363987\pi$
$348$	1.42195	−	27.8610i	0.0762245	−	1.49351i
$349$	−23.3895	+	3.07929i	−1.25201	+	0.164830i	−0.727222	−	0.686402i	$-0.759189\pi$
$349$	−23.3895	+	3.07929i	−1.25201	+	0.164830i	−0.524789	+	0.851232i	$0.675856\pi$
$350$	12.2946	−	9.82567i	0.657172	−	0.525204i
$351$	8.22349	−	8.06606i	0.438937	−	0.430534i
$352$	28.3130	−	20.3129i	1.50909	−	1.08268i
$353$	5.37147	+	9.30366i	0.285894	+	0.495184i	0.972826	−	0.231539i	$-0.0743760\pi$
$353$	5.37147	+	9.30366i	0.285894	+	0.495184i	−0.686931	+	0.726722i	$0.741043\pi$
$354$	−1.89797	−	31.5110i	−0.100876	−	1.67479i
$355$	−2.00619	−	2.61452i	−0.106478	−	0.138764i
$356$	−12.3610	+	0.488449i	−0.655131	+	0.0258877i
$357$	8.02591	−	2.50216i	0.424776	−	0.132428i
$358$	3.16518	−	3.29272i	0.167285	−	0.174026i
$359$	13.7896	−	13.7896i	0.727789	−	0.727789i	−0.242390	−	0.970179i	$-0.577931\pi$
$359$	13.7896	−	13.7896i	0.727789	−	0.727789i	0.970179	+	0.242390i	$0.0779312\pi$
$360$	−3.25033	−	0.397640i	−0.171307	−	0.0209575i
$361$	−1.39956	−	1.39956i	−0.0736610	−	0.0736610i
$362$	1.03563	−	0.0204536i	0.0544313	−	0.00107502i
$363$	31.6407	−	34.3072i	1.66071	−	1.80066i
$364$	−9.54333	−	3.51828i	−0.500207	−	0.184408i
$365$	0.706586	−	0.542182i	0.0369844	−	0.0283791i
$366$	−14.7945	+	4.93492i	−0.773320	+	0.257952i
$367$	−31.0542	+	17.9292i	−1.62102	+	0.935895i	−0.634370	+	0.773029i	$0.718741\pi$
$367$	−31.0542	+	17.9292i	−1.62102	+	0.935895i	−0.986648	+	0.162866i	$0.947926\pi$
$368$	11.0960	+	31.2895i	0.578421	+	1.63108i
$369$	−4.34504	+	23.7463i	−0.226194	+	1.23618i
$370$	0.999556	+	0.111563i	0.0519645	+	0.00579987i
$371$	−0.293359	−	2.22829i	−0.0152305	−	0.115687i
$372$	3.96178	+	3.37433i	0.205409	+	0.174951i
$373$	−18.0901	−	2.38161i	−0.936672	−	0.123315i	−0.353291	−	0.935514i	$-0.614937\pi$
$373$	−18.0901	−	2.38161i	−0.936672	−	0.123315i	−0.583381	+	0.812198i	$0.698271\pi$
$374$	15.7770	−	9.52909i	0.815807	−	0.492737i
$375$	−6.48823	+	1.12251i	−0.335051	+	0.0579663i
$376$	−6.75053	+	9.96836i	−0.348132	+	0.514079i
$377$	−12.6237	+	12.6237i	−0.650156	+	0.650156i
$378$	−8.28138	+	14.6837i	−0.425948	+	0.755250i
$379$	18.3121	−	7.58511i	0.940628	−	0.389621i	0.140927	−	0.990020i	$-0.454992\pi$
$379$	18.3121	−	7.58511i	0.940628	−	0.389621i	0.799700	+	0.600399i	$0.204992\pi$
$380$	−3.04080	+	0.944943i	−0.155990	+	0.0484745i
$381$	−19.3849	−	30.6456i	−0.993117	−	1.57002i
$382$	−21.7245	+	3.29772i	−1.11152	+	0.168726i
$383$	12.1542	−	21.0517i	0.621051	−	1.07569i	−0.368239	−	0.929731i	$-0.620039\pi$
$383$	12.1542	−	21.0517i	0.621051	−	1.07569i	0.989290	−	0.145961i	$-0.0466273\pi$
$384$	−8.97686	+	17.4188i	−0.458098	+	0.888901i
$385$	2.72675	+	4.72286i	0.138968	+	0.240699i
$386$	3.47339	+	4.34615i	0.176791	+	0.221213i
$387$	0.450008	+	0.878226i	0.0228752	+	0.0446427i
$388$	1.59337	−	7.04906i	0.0808912	−	0.357862i
$389$	−17.5246	−	13.4471i	−0.888533	−	0.681796i	0.0600935	−	0.998193i	$-0.480860\pi$
$389$	−17.5246	−	13.4471i	−0.888533	−	0.681796i	−0.948627	+	0.316397i	$0.897527\pi$
$390$	1.37333	+	1.58279i	0.0695411	+	0.0801479i
$391$	4.54488	+	16.9617i	0.229845	+	0.857792i
$392$	−4.90081	−	0.351782i	−0.247528	−	0.0177677i
$393$	10.2691	−	27.9339i	0.518010	−	1.40908i
$394$	−0.0811899	−	4.11089i	−0.00409029	−	0.207103i
$395$	1.89504	+	4.57503i	0.0953499	+	0.230195i
$396$	−9.94310	+	35.5972i	−0.499660	+	1.78883i
$397$	−23.4787	−	9.72519i	−1.17836	−	0.488093i	−0.294413	−	0.955678i	$-0.595124\pi$
$397$	−23.4787	−	9.72519i	−1.17836	−	0.488093i	−0.883948	+	0.467585i	$0.845124\pi$
$398$	7.27979	+	16.6379i	0.364903	+	0.833981i
$399$	−1.48135	+	16.3260i	−0.0741602	+	0.817322i
$400$	−3.52757	+	19.0810i	−0.176378	+	0.954048i
$401$	−1.94283	−	1.12170i	−0.0970205	−	0.0560148i	0.450705	−	0.892673i	$-0.351173\pi$
$401$	−1.94283	−	1.12170i	−0.0970205	−	0.0560148i	−0.547725	+	0.836658i	$0.684506\pi$
$402$	−6.14171	−	5.44389i	−0.306321	−	0.271517i
$403$	−0.434688	−	3.30179i	−0.0216534	−	0.164474i
$404$	4.86915	+	28.2986i	0.242249	+	1.40791i
$405$	2.95306	−	1.82825i	0.146739	−	0.0908463i
$406$	12.6144	−	22.8805i	0.626040	−	1.13554i
$407$	2.93811	−	10.9652i	0.145637	−	0.543524i
$408$	−5.46041	+	8.81010i	−0.270331	+	0.436165i
$409$	−1.27014	−	4.74021i	−0.0628042	−	0.234388i	0.927388	−	0.374101i	$-0.122049\pi$
$409$	−1.27014	−	4.74021i	−0.0628042	−	0.234388i	−0.990192	+	0.139713i	$0.955382\pi$
$410$	−4.26361	−	1.05265i	−0.210565	−	0.0519869i
$411$	−22.9573	+	7.15719i	−1.13240	+	0.353038i
$412$	−6.40076	+	12.1725i	−0.315343	+	0.599695i
$413$	11.3142	−	27.3148i	0.556734	−	1.34408i
$414$	−29.9471	−	18.5229i	−1.47182	−	0.910352i
$415$	−3.94990			−0.193893
$416$	11.7340	−	4.42391i	0.575309	−	0.216900i
$417$	3.82564	+	8.27358i	0.187342	+	0.405159i
$418$	5.39385	+	35.5333i	0.263822	+	1.73799i
$419$	−8.74569	−	11.3976i	−0.427255	−	0.556810i	0.529272	−	0.848452i	$-0.322465\pi$
$419$	−8.74569	−	11.3976i	−0.427255	−	0.556810i	−0.956527	+	0.291642i	$0.905798\pi$
$420$	−2.57433	−	1.66679i	−0.125614	−	0.0813310i
$421$	20.4642	+	15.7028i	0.997365	+	0.765305i	0.972146	−	0.234377i	$-0.0753049\pi$
$421$	20.4642	+	15.7028i	0.997365	+	0.765305i	0.0252194	+	0.999682i	$0.491972\pi$
$422$	6.92553	+	23.9447i	0.337130	+	1.16561i
$423$	−1.03094	−	12.7276i	−0.0501260	−	0.618838i
$424$	2.07197	+	1.83995i	0.100624	+	0.0893558i
$425$	−2.65643	+	9.91395i	−0.128856	+	0.480897i
$426$	11.7131	−	17.3307i	0.567503	−	0.839676i
$427$	−14.4814	−	1.90652i	−0.700806	−	0.0922629i
$428$	6.09120	−	16.5224i	0.294429	−	0.798638i
$429$	19.9889	−	12.6440i	0.965072	−	0.610457i
$430$	−0.164466	+	0.0719609i	−0.00793125	+	0.00347026i
$431$			5.30385i			0.255477i	0.991808	+	0.127739i	$0.0407719\pi$
$431$			5.30385i			0.255477i	−0.991808	+	0.127739i	$0.959228\pi$
$432$	−4.13385	−	20.3694i	−0.198890	−	0.980022i
$433$			12.9183i			0.620814i	0.950604	+	0.310407i	$0.100465\pi$
$433$			12.9183i			0.620814i	−0.950604	+	0.310407i	$0.899535\pi$
$434$	1.95370	+	4.46515i	0.0937804	+	0.214334i
$435$	−4.54920	+	2.87760i	−0.218118	+	0.137970i
$436$	−4.57971	−	9.92829i	−0.219328	−	0.475479i
$437$	−33.9484	−	4.46939i	−1.62397	−	0.213800i
$438$	4.68371	+	3.16552i	0.223796	+	0.151255i
$439$	−7.47734	+	27.9058i	−0.356874	+	1.33187i	0.521236	+	0.853412i	$0.325471\pi$
$439$	−7.47734	+	27.9058i	−0.356874	+	1.33187i	−0.878110	+	0.478459i	$0.841196\pi$
$440$	−6.35335	−	2.20075i	−0.302884	−	0.104917i
$441$	4.28816	−	2.96161i	0.204198	−	0.141029i
$442$	6.37188	−	1.84294i	0.303079	−	0.0876595i
$443$	−5.59626	−	4.29416i	−0.265886	−	0.204022i	0.467210	−	0.884146i	$-0.345259\pi$
$443$	−5.59626	−	4.29416i	−0.265886	−	0.204022i	−0.733097	+	0.680124i	$0.761926\pi$
$444$	1.33582	+	6.24256i	0.0633951	+	0.296259i
$445$	1.45310	+	1.89372i	0.0688836	+	0.0897708i
$446$	20.8886	−	3.17084i	0.989106	−	0.150143i
$447$	0.343002	+	0.741800i	0.0162234	+	0.0350859i
$448$	−14.6978	+	10.9908i	−0.694404	+	0.519266i
$449$	−20.9724			−0.989751			−0.494875	−	0.868964i	$-0.664786\pi$
$449$	−20.9724			−0.989751			−0.494875	+	0.868964i	$0.664786\pi$
$450$	−9.74545	−	18.1278i	−0.459405	−	0.854554i
$451$	−18.9689	+	45.7950i	−0.893212	+	2.15640i
$452$	−3.28555	−	10.5728i	−0.154539	−	0.497303i
$453$	23.2564	−	7.25043i	1.09268	−	0.340655i
$454$	−8.34389	+	33.7956i	−0.391598	+	1.58611i
$455$	0.507955	+	1.89571i	0.0238133	+	0.0888725i
$456$	−11.7969	−	16.4113i	−0.552442	−	0.768528i
$457$	0.0377770	−	0.140986i	0.00176713	−	0.00659503i	−0.965037	−	0.262115i	$-0.915580\pi$
$457$	0.0377770	−	0.140986i	0.00176713	−	0.00659503i	0.966804	+	0.255520i	$0.0822467\pi$
$458$	19.5912	+	10.8009i	0.915435	+	0.504692i
$459$	−1.32957	−	10.9131i	−0.0620592	−	0.509379i
$460$	3.69594	−	5.23213i	0.172324	−	0.243949i
$461$	−0.208485	−	1.58360i	−0.00971012	−	0.0737557i	0.985904	−	0.167314i	$-0.0535093\pi$
$461$	−0.208485	−	1.58360i	−0.00971012	−	0.0737557i	−0.995614	+	0.0935580i	$0.970176\pi$
$462$	−22.9606	+	25.9038i	−1.06822	+	1.20515i
$463$	1.33115	+	0.768541i	0.0618639	+	0.0357171i	0.530613	−	0.847614i	$-0.321962\pi$
$463$	1.33115	+	0.768541i	0.0618639	+	0.0357171i	−0.468749	+	0.883331i	$0.655295\pi$
$464$	6.71163	+	31.5060i	0.311579	+	1.46263i
$465$	0.0907387	−	1.00003i	0.00420791	−	0.0463754i
$466$	1.84551	−	0.807491i	0.0854917	−	0.0374063i
$467$	−1.51389	−	0.627075i	−0.0700546	−	0.0290176i	0.347381	−	0.937724i	$-0.387071\pi$
$467$	−1.51389	−	0.627075i	−0.0700546	−	0.0290176i	−0.417436	+	0.908707i	$0.637071\pi$
$468$	−6.77200	+	11.4480i	−0.313036	+	0.529183i
$469$	−2.94147	−	7.10133i	−0.135824	−	0.327909i
$470$	2.32254	−	0.0458701i	0.107131	−	0.00211583i
$471$	−12.7064	+	34.5638i	−0.585481	+	1.59261i
$472$	11.5025	+	34.5893i	0.529447	+	1.59210i
$473$	0.524427	+	1.95719i	0.0241132	+	0.0899916i
$474$	−23.7409	+	20.5991i	−1.09046	+	0.946146i
$475$	−15.8779	−	12.1836i	−0.728529	−	0.559020i
$476$	−8.20870	+	5.18188i	−0.376245	+	0.237511i
$477$	−2.93541	−	0.147117i	−0.134403	−	0.00673601i
$478$	−21.0260	+	16.8037i	−0.961706	+	0.768585i
$479$	12.1761	+	21.0897i	0.556341	+	0.963611i	0.997798	+	0.0663285i	$0.0211285\pi$
$479$	12.1761	+	21.0897i	0.556341	+	0.963611i	−0.441457	+	0.897283i	$0.645538\pi$
$480$	3.74459	−	0.524444i	0.170916	−	0.0239375i
$481$	2.04266	−	3.53800i	0.0931374	−	0.161319i
$482$	−3.09171	−	20.3674i	−0.140824	−	0.927709i
$483$	−17.6297	−	27.8708i	−0.802179	−	1.26817i
$484$	−25.0814	+	47.6978i	−1.14006	+	2.16808i
$485$	−1.28832	+	0.533640i	−0.0584996	+	0.0242313i
$486$	16.9392	+	14.1089i	0.768379	+	0.639995i
$487$	19.8649	−	19.8649i	0.900166	−	0.900166i	−0.0952843	−	0.995450i	$-0.530376\pi$
$487$	19.8649	−	19.8649i	0.900166	−	0.900166i	0.995450	+	0.0952843i	$0.0303760\pi$
$488$	15.0354	−	9.91186i	0.680619	−	0.448689i
$489$	6.12736	−	1.06008i	0.277089	−	0.0479384i
$490$	0.490155	+	0.811532i	0.0221430	+	0.0366613i
$491$	15.4199	+	2.03006i	0.695889	+	0.0916155i	0.470168	−	0.882577i	$-0.344193\pi$
$491$	15.4199	+	2.03006i	0.695889	+	0.0916155i	0.225720	+	0.974192i	$0.427526\pi$
$492$	−2.22503	−	27.7861i	−0.100312	−	1.25269i
$493$	2.22399	+	16.8929i	0.100164	+	0.760818i
$494$	−1.43470	+	12.8543i	−0.0645501	+	0.578342i
$495$	6.71707	−	2.39592i	0.301910	−	0.107688i
$496$	−5.42487	−	2.58454i	−0.243584	−	0.116049i
$497$	16.9660	−	9.79533i	0.761030	−	0.439381i
$498$	−7.93317	−	23.7830i	−0.355494	−	1.06574i
$499$	14.6029	−	11.2052i	0.653716	−	0.501614i	−0.227837	−	0.973699i	$-0.573165\pi$
$499$	14.6029	−	11.2052i	0.653716	−	0.501614i	0.881553	+	0.472086i	$0.156499\pi$
$500$	6.90414	−	3.18473i	0.308762	−	0.142426i
$501$	8.19171	−	8.88207i	0.365979	−	0.396822i
$502$	−0.403570	−	20.4339i	−0.0180122	−	0.912012i
$503$	−30.2428	−	30.2428i	−1.34846	−	1.34846i	−0.887335	−	0.461125i	$-0.847446\pi$
$503$	−30.2428	−	30.2428i	−1.34846	−	1.34846i	−0.461125	−	0.887335i	$-0.652554\pi$
$504$	4.86561	−	18.8481i	0.216732	−	0.839561i
$505$	3.91780	−	3.91780i	0.174340	−	0.174340i
$506$	−52.1253	−	50.1062i	−2.31725	−	2.22749i
$507$	−13.3701	+	4.16827i	−0.593787	+	0.185119i
$508$	30.7536	+	28.4156i	1.36447	+	1.26074i
$509$	6.58505	+	8.58180i	0.291877	+	0.380382i	0.916157	−	0.400819i	$-0.131274\pi$
$509$	6.58505	+	8.58180i	0.291877	+	0.380382i	−0.624280	+	0.781200i	$0.714608\pi$
$510$	1.99637	−	0.120245i	0.0884007	−	0.00532454i
$511$	2.64723	+	4.58514i	0.117107	+	0.202835i
$512$	4.82689	−	22.1066i	0.213321	−	0.976982i
$513$	20.6523	+	5.74825i	0.911821	+	0.253791i
$514$	3.60716	+	4.51353i	0.159105	+	0.199083i
$515$	2.63097	−	0.346374i	0.115934	−	0.0152630i
$516$	−0.763609	−	0.845746i	−0.0336160	−	0.0372319i
$517$	3.42233	−	25.9952i	0.150514	−	1.14327i
$518$	−1.43311	+	5.80458i	−0.0629671	+	0.255039i
$519$	−5.32271	+	4.43714i	−0.233641	+	0.194769i
$520$	−2.00353	−	1.35678i	−0.0878608	−	0.0594989i
$521$	24.9497	+	24.9497i	1.09307	+	1.09307i	0.995200	+	0.0978664i	$0.0312018\pi$
$521$	24.9497	+	24.9497i	1.09307	+	1.09307i	0.0978664	+	0.995200i	$0.468798\pi$
$522$	−26.4633	−	21.6120i	−1.15827	−	0.945930i
$523$	3.60064	+	8.69271i	0.157445	+	0.380106i	0.982843	−	0.184446i	$-0.0590491\pi$
$523$	3.60064	+	8.69271i	0.157445	+	0.380106i	−0.825398	+	0.564552i	$0.809049\pi$
$524$	−3.13683	+	34.2224i	−0.137033	+	1.49501i
$525$	−0.778752	−	19.2599i	−0.0339875	−	0.840571i
$526$	0.768508	−	1.04358i	0.0335085	−	0.0455021i
$527$	−2.75260	−	1.58922i	−0.119905	−	0.0692273i
$528$	0.490705	−	42.6746i	0.0213552	−	1.85718i
$529$	39.7373	−	22.9424i	1.72771	−	0.997494i
$530$	0.0593086	−	0.531380i	0.00257620	−	0.0230817i
$531$	−32.4734	−	20.9832i	−1.40923	−	0.910594i
$532$	−3.20982	−	18.6549i	−0.139164	−	0.808794i
$533$	−10.8594	+	14.1522i	−0.470372	+	0.613000i
$534$	−8.48391	+	12.5528i	−0.367135	+	0.543212i
$535$	−3.28205	+	0.879422i	−0.141895	+	0.0380207i
$536$	8.47325	+	4.24414i	0.365989	+	0.183319i
$537$	−0.953602	−	5.51192i	−0.0411509	−	0.237857i
$538$	−2.27546	+	2.36715i	−0.0981018	+	0.102055i
$539$	9.88627	−	4.09503i	0.425832	−	0.176385i
$540$	−2.75001	+	2.91917i	−0.118341	+	0.125621i
$541$	11.5319	−	27.8404i	0.495794	−	1.19695i	−0.455934	−	0.890013i	$-0.650695\pi$
$541$	11.5319	−	27.8404i	0.495794	−	1.19695i	0.951729	−	0.306940i	$-0.0993052\pi$
$542$	31.1840	+	12.2011i	1.33947	+	0.524084i
$543$	0.730997	−	1.03685i	0.0313701	−	0.0444954i
$544$	3.46783	−	11.4551i	0.148682	−	0.491133i
$545$	−1.05485	+	1.82706i	−0.0451849	+	0.0782626i
$546$	−10.3942	+	6.86592i	−0.444831	+	0.293834i
$547$	−15.5192	+	2.04314i	−0.663552	+	0.0873582i	−0.454777	−	0.890606i	$-0.650281\pi$
$547$	−15.5192	+	2.04314i	−0.663552	+	0.0873582i	−0.208775	+	0.977964i	$0.566948\pi$
$548$	23.4802	−	14.8223i	1.00302	−	0.633176i
$549$	−5.86101	+	18.1795i	−0.250142	+	0.775882i
$550$	−11.7416	−	40.5962i	−0.500665	−	1.73103i
$551$	−32.0925	−	8.59916i	−1.36719	−	0.366337i
$552$	38.9266	+	11.7454i	1.65683	+	0.499917i
$553$	−28.4346	+	7.61902i	−1.20916	+	0.323994i
$554$	−2.26202	−	3.74514i	−0.0961040	−	0.159116i
$555$	0.835115	−	0.905495i	0.0354487	−	0.0384361i
$556$	−6.73216	−	8.09084i	−0.285507	−	0.343128i
$557$	31.2452	+	12.9422i	1.32390	+	0.548378i	0.928910	−	0.370306i	$-0.120747\pi$
$557$	31.2452	+	12.9422i	1.32390	+	0.548378i	0.394992	+	0.918684i	$0.370747\pi$
$558$	6.20361	−	1.46216i	0.262620	−	0.0618982i
$559$			0.729195i			0.0308416i
$560$	3.36842	+	1.09279i	0.142342	+	0.0461789i
$561$	2.03986	−	22.4814i	0.0861231	−	0.949165i
$562$	−7.19787	+	9.77418i	−0.303624	+	0.412299i
$563$	25.7114	−	19.7290i	1.08360	−	0.831479i	0.0971104	−	0.995274i	$-0.469040\pi$
$563$	25.7114	−	19.7290i	1.08360	−	0.831479i	0.986495	+	0.163794i	$0.0523733\pi$
$564$	4.94088	+	13.8922i	0.208049	+	0.584969i
$565$	−1.30050	+	1.69485i	−0.0547126	+	0.0713029i
$566$	−33.3189	−	18.3692i	−1.40050	−	0.772114i
$567$	8.48388	+	18.8232i	0.356289	+	0.790502i
$568$	−7.90579	+	22.8232i	−0.331719	+	0.957642i
$569$	42.1891	+	11.3045i	1.76866	+	0.473910i	0.988442	−	0.151601i	$-0.0484428\pi$
$569$	42.1891	+	11.3045i	1.76866	+	0.473910i	0.780215	+	0.625511i	$0.215109\pi$
$570$	−1.27310	+	3.68623i	−0.0533241	+	0.154399i
$571$	3.17720	−	24.1332i	0.132962	−	1.00994i	−0.786728	−	0.617299i	$-0.788227\pi$
$571$	3.17720	−	24.1332i	0.132962	−	1.00994i	0.919690	−	0.392645i	$-0.128440\pi$
$572$	−18.5343	+	20.0594i	−0.774960	+	0.838725i
$573$	−12.5033	+	23.8309i	−0.522333	+	0.995550i
$574$	9.51235	−	24.3119i	0.397038	−	1.01476i
$575$	40.2624			1.67906
$576$	10.6786	+	21.4934i	0.444940	+	0.895560i
$577$	32.2758			1.34366			0.671830	−	0.740706i	$-0.265509\pi$
$577$	32.2758			1.34366			0.671830	+	0.740706i	$0.265509\pi$
$578$	−6.45329	+	16.4935i	−0.268422	+	0.686039i
$579$	6.80840	−	0.275290i	0.282948	−	0.0114407i
$580$	4.21817	−	4.56525i	0.175150	−	0.189562i
$581$	3.06484	−	23.2798i	0.127151	−	0.965808i
$582$	−5.80065	−	6.68540i	−0.240445	−	0.277119i
$583$	−5.82927	−	1.56195i	−0.241424	−	0.0646893i
$584$	−6.16808	−	2.13657i	−0.255237	−	0.0884121i
$585$	2.55812	−	0.207208i	0.105765	−	0.00856698i
$586$	10.4358	+	5.75342i	0.431101	+	0.237672i
$587$	1.96635	−	2.56260i	0.0811600	−	0.105770i	−0.751009	−	0.660292i	$-0.770432\pi$
$587$	1.96635	−	2.56260i	0.0811600	−	0.105770i	0.832169	+	0.554522i	$0.187099\pi$
$588$	−3.90192	+	4.58122i	−0.160912	+	0.188926i
$589$	4.91704	−	3.77298i	0.202603	−	0.155463i
$590$	4.17073	−	5.66355i	0.171706	−	0.233165i
$591$	−4.11573	−	2.90167i	−0.169299	−	0.119359i
$592$	−3.34953	−	6.56652i	−0.137665	−	0.269882i
$593$		−	33.4867i		−	1.37513i	−0.726120	−	0.687567i	$-0.758679\pi$
$593$		−	33.4867i		−	1.37513i	0.726120	−	0.687567i	$-0.241321\pi$
$594$	27.9171	+	35.6325i	1.14545	+	1.46202i
$595$	1.73052	+	0.716806i	0.0709445	+	0.0293862i
$596$	−0.603597	−	0.725415i	−0.0247243	−	0.0297141i
$597$	21.6995	+	4.88405i	0.888101	+	0.199891i
$598$	−13.4525	−	22.2728i	−0.550112	−	0.910801i
$599$	35.8461	−	9.60493i	1.46463	−	0.392447i	0.563545	−	0.826085i	$-0.309437\pi$
$599$	35.8461	−	9.60493i	1.46463	−	0.392447i	0.901087	+	0.433638i	$0.142770\pi$
$600$	16.2714	+	17.3214i	0.664278	+	0.707143i
$601$	−12.7682	−	3.42122i	−0.520824	−	0.139555i	−0.0111765	−	0.999938i	$-0.503558\pi$
$601$	−12.7682	−	3.42122i	−0.520824	−	0.139555i	−0.509648	+	0.860383i	$0.670224\pi$
$602$	−0.296506	−	1.02516i	−0.0120847	−	0.0417823i
$603$	−9.82716	+	2.11230i	−0.400193	+	0.0860193i
$604$	−23.7861	+	15.0154i	−0.967841	+	0.610966i
$605$	10.3094	−	1.35726i	0.419139	−	0.0551806i
$606$	31.4584	+	15.7210i	1.27791	+	0.638623i
$607$	−3.94505	+	6.83302i	−0.160125	+	0.277344i	−0.934913	−	0.354876i	$-0.884523\pi$
$607$	−3.94505	+	6.83302i	−0.160125	+	0.277344i	0.774789	+	0.632220i	$0.217856\pi$
$608$	18.0489	+	14.7953i	0.731978	+	0.600030i
$609$	−13.4300	−	29.0447i	−0.544212	−	1.17695i
$610$	−3.23596	−	1.26611i	−0.131020	−	0.0512634i
$611$	3.61092	−	8.71754i	0.146082	−	0.352674i
$612$	4.73361	+	11.7790i	0.191345	+	0.476136i
$613$	−6.66660	+	2.76140i	−0.269261	+	0.111532i	−0.513229	−	0.858252i	$-0.671551\pi$
$613$	−6.66660	+	2.76140i	−0.269261	+	0.111532i	0.243968	+	0.969783i	$0.421551\pi$
$614$	−24.4209	+	25.4050i	−0.985549	+	1.02526i
$615$	−4.13139	+	3.44403i	−0.166594	+	0.138877i
$616$	17.9004	−	35.7375i	0.721229	−	1.43990i
$617$	−20.9966	+	5.62601i	−0.845289	+	0.226495i	−0.655373	−	0.755306i	$-0.727488\pi$
$617$	−20.9966	+	5.62601i	−0.845289	+	0.226495i	−0.189917	+	0.981800i	$0.560822\pi$
$618$	7.36973	+	15.1458i	0.296454	+	0.609254i
$619$	−18.6991	+	24.3692i	−0.751581	+	0.979480i	0.248360	+	0.968668i	$0.420108\pi$
$619$	−18.6991	+	24.3692i	−0.751581	+	0.979480i	−0.999942	+	0.0108121i	$0.996558\pi$
$620$	0.196615	+	1.14269i	0.00789624	+	0.0458916i
$621$	−40.0012	+	16.1179i	−1.60519	+	0.646791i
$622$	−0.849341	+	7.60975i	−0.0340555	+	0.305123i
$623$	−12.2886	+	7.09484i	−0.492333	+	0.284249i
$624$	4.14543	−	14.7886i	0.165950	−	0.592019i
$625$	19.7352	+	11.3941i	0.789409	+	0.455766i
$626$	−12.1515	+	16.5008i	−0.485670	+	0.659504i
$627$	38.9785	+	20.4508i	1.55665	+	0.816726i
$628$	3.88133	−	42.3448i	0.154882	−	1.68974i
$629$	−1.49210	−	3.60226i	−0.0594941	−	0.143631i
$630$	−3.51214	+	1.33149i	−0.139927	+	0.0530480i
$631$	−18.4600	−	18.4600i	−0.734883	−	0.734883i	0.236700	−	0.971583i	$-0.423934\pi$
$631$	−18.4600	−	18.4600i	−0.734883	−	0.734883i	−0.971583	+	0.236700i	$0.923934\pi$
$632$	20.3509	−	30.0518i	0.809516	−	1.19540i
$633$	28.6533	+	10.5336i	1.13887	+	0.418673i
$634$	7.28245	−	29.4964i	0.289223	−	1.17145i
$635$	1.05457	−	8.01022i	0.0418492	−	0.317876i
$636$	3.31864	−	0.710142i	0.131593	−	0.0281590i
$637$	3.81804	−	0.502654i	0.151276	−	0.0199159i
$638$	−43.7989	−	54.8042i	−1.73401	−	2.16972i
$639$	−8.60689	−	24.1298i	−0.340483	−	0.954561i
$640$	−4.02137	+	1.70036i	−0.158959	+	0.0672125i
$641$	15.8520	+	27.4564i	0.626116	+	1.08446i	0.988324	+	0.152367i	$0.0486896\pi$
$641$	15.8520	+	27.4564i	0.626116	+	1.08446i	−0.362208	+	0.932097i	$0.617977\pi$
$642$	−11.8870	−	17.9955i	−0.469141	−	0.710224i
$643$	25.0600	+	32.6589i	0.988271	+	1.28794i	0.957506	+	0.288413i	$0.0931276\pi$
$643$	25.0600	+	32.6589i	0.988271	+	1.28794i	0.0307648	+	0.999527i	$0.490206\pi$
$644$	27.9691	+	25.8427i	1.10214	+	1.01835i
$645$	−0.0482789	+	0.214500i	−0.00190098	+	0.00844592i
$646$	8.89945	+	8.55473i	0.350144	+	0.336581i
$647$	−28.0284	+	28.0284i	−1.10191	+	1.10191i	−0.107731	+	0.994180i	$0.534359\pi$
$647$	−28.0284	+	28.0284i	−1.10191	+	1.10191i	−0.994180	+	0.107731i	$0.965641\pi$
$648$	−23.1000	−	10.6952i	−0.907455	−	0.420148i
$649$	−56.1353	−	56.1353i	−2.20350	−	2.20350i
$650$	−0.300308	−	15.2055i	−0.0117791	−	0.596409i
$651$	5.82355	+	1.31075i	0.228243	+	0.0513722i
$652$	−6.52013	+	3.00760i	−0.255348	+	0.117787i
$653$	−38.2667	+	29.3631i	−1.49749	+	1.14907i	−0.547493	+	0.836811i	$0.684418\pi$
$653$	−38.2667	+	29.3631i	−1.49749	+	1.14907i	−0.949998	+	0.312255i	$0.898916\pi$
$654$	−13.1196	−	2.68189i	−0.513018	−	0.104870i
$655$	5.74267	−	3.31553i	0.224385	−	0.129549i
$656$	10.7580	+	30.3363i	0.420029	+	1.18443i
$657$	6.52119	−	2.32605i	0.254416	−	0.0907479i
$658$	−1.53178	+	13.7241i	−0.0597148	+	0.535020i
$659$	−4.83930	−	36.7581i	−0.188512	−	1.43189i	−0.780101	−	0.625653i	$-0.784832\pi$
$659$	−4.83930	−	36.7581i	−0.188512	−	1.43189i	0.591589	−	0.806240i	$-0.298501\pi$
$660$	−6.78016	+	4.67354i	−0.263918	+	0.181917i
$661$	7.83530	+	1.03154i	0.304758	+	0.0401221i	0.281354	−	0.959604i	$-0.409216\pi$
$661$	7.83530	+	1.03154i	0.304758	+	0.0401221i	0.0234035	+	0.999726i	$0.492550\pi$
$662$	9.27116	+	15.3499i	0.360334	+	0.596592i
$663$	2.80307	−	7.62487i	0.108862	−	0.296125i
$664$	15.9339	+	24.1702i	0.618355	+	0.937987i
$665$	−2.58268	+	2.58268i	−0.100152	+	0.100152i
$666$	7.12942	+	3.20973i	0.276259	+	0.124374i
$667$	61.7515	−	25.5783i	2.39103	−	0.990396i
$668$	−6.49351	+	12.3489i	−0.251241	+	0.477792i
$669$	12.0222	−	22.9140i	0.464806	−	0.885905i
$670$	−0.274431	−	1.80788i	−0.0106022	−	0.0698444i
$671$	−19.6102	+	33.9658i	−0.757042	+	1.31123i
$672$	0.185417	+	22.4766i	0.00715264	+	0.867055i
$673$	−21.3570	−	36.9914i	−0.823252	−	1.42591i	−0.903248	−	0.429119i	$-0.858824\pi$
$673$	−21.3570	−	36.9914i	−0.823252	−	1.42591i	0.0799957	−	0.996795i	$-0.474509\pi$
$674$	−6.23720	+	4.98469i	−0.240248	+	0.192003i
$675$	−24.9583	−	3.53153i	−0.960646	−	0.135928i
$676$	13.6746	−	8.63233i	0.525946	−	0.332013i
$677$	−26.7492	−	20.5254i	−1.02806	−	0.788855i	−0.0503278	−	0.998733i	$-0.516027\pi$
$677$	−26.7492	−	20.5254i	−1.02806	−	0.788855i	−0.977728	+	0.209878i	$0.932693\pi$
$678$	−12.8170	−	4.42653i	−0.492232	−	0.170000i
$679$	−2.14550	−	8.00711i	−0.0823367	−	0.307285i
$680$	−2.19139	+	0.728739i	−0.0840361	+	0.0279459i
$681$	27.2992	+	32.7475i	1.04611	+	1.25489i
$682$	13.0845	−	0.258418i	0.501030	−	0.00989533i
$683$	15.0100	+	36.2374i	0.574342	+	1.38658i	0.897826	+	0.440350i	$0.145146\pi$
$683$	15.0100	+	36.2374i	0.574342	+	1.38658i	−0.323484	+	0.946234i	$0.604854\pi$
$684$	−24.7523	−	0.261920i	−0.946429	−	0.0100147i
$685$	−4.94999	−	2.05035i	−0.189129	−	0.0783399i
$686$	−25.9692	+	11.3626i	−0.991509	+	0.433828i
$687$	24.8692	−	11.4993i	0.948818	−	0.438725i
$688$	1.10380	+	0.716108i	0.0420819	+	0.0273014i
$689$	−1.88086	−	1.08591i	−0.0716549	−	0.0413700i
$690$	−2.48253	−	7.44243i	−0.0945083	−	0.283328i
$691$	0.500425	+	3.80111i	0.0190371	+	0.144601i	0.998324	−	0.0578782i	$-0.0184335\pi$
$691$	0.500425	+	3.80111i	0.0190371	+	0.144601i	−0.979287	+	0.202479i	$0.935100\pi$
$692$	4.61663	−	6.53549i	0.175498	−	0.248442i
$693$	8.90899	+	41.4478i	0.338425	+	1.57447i
$694$	11.2028	+	6.17625i	0.425252	+	0.234447i
$695$	−0.525642	+	1.96172i	−0.0199388	+	0.0744124i
$696$	35.9601	+	16.2292i	1.36306	+	0.615167i
$697$	4.40642	+	16.4450i	0.166905	+	0.622899i
$698$	7.99700	−	32.3906i	0.302691	−	1.22600i
$699$	0.541750	−	2.40696i	0.0204909	−	0.0910395i
$700$	6.60508	+	21.2550i	0.249649	+	0.803362i
$701$	11.8470	−	28.6011i	0.447454	−	1.08025i	−0.525819	−	0.850597i	$-0.676241\pi$
$701$	11.8470	−	28.6011i	0.447454	−	1.08025i	0.973273	−	0.229653i	$-0.0737591\pi$
$702$	6.38547	+	14.9867i	0.241004	+	0.565635i
$703$	7.60297			0.286751
$704$	12.1626	+	47.7552i	0.458395	+	1.79984i
$705$	1.63936	−	2.32528i	0.0617421	−	0.0875750i
$706$	−15.0207	+	2.28011i	−0.565313	+	0.0858129i
$707$	20.0506	+	26.1305i	0.754082	+	0.982739i
$708$	42.4778	+	13.7377i	1.59641	+	0.516295i
$709$	−18.0138	−	13.8225i	−0.676524	−	0.519115i	0.212393	−	0.977184i	$-0.431874\pi$
$709$	−18.0138	−	13.8225i	−0.676524	−	0.519115i	−0.888916	+	0.458070i	$0.848541\pi$
$710$	4.47708	−	1.29491i	0.168022	−	0.0485969i
$711$	3.10799	+	38.3702i	0.116559	+	1.43899i
$712$	5.72622	−	16.5311i	0.214599	−	0.619527i
$713$	−3.22705	+	12.0435i	−0.120854	+	0.451033i
$714$	−0.840343	+	11.8594i	−0.0314490	+	0.443828i
$715$	5.22475	+	0.687851i	0.195395	+	0.0257242i
$716$	2.70551	+	5.86523i	0.101110	+	0.219194i
$717$	1.33181	+	32.9380i	0.0497374	+	1.23009i
$718$	11.0552	+	25.2666i	0.412577	+	0.942940i
$719$			2.08263i			0.0776690i	0.999246	+	0.0388345i	$0.0123645\pi$
$719$			2.08263i			0.0776690i	−0.999246	+	0.0388345i	$0.987635\pi$
$720$	2.19855	−	4.07576i	0.0819352	−	0.151895i
$721$			15.7751i			0.587494i
$722$	2.56439	−	1.12203i	0.0954368	−	0.0417577i
$723$	−22.3422	−	11.7222i	−0.830915	−	0.435955i
$724$	−0.506711	+	1.37445i	−0.0188318	+	0.0510811i
$725$	38.7326	+	5.09925i	1.43849	+	0.189381i
$726$	28.8783	+	59.3488i	1.07177	+	2.20264i
$727$	−3.92859	+	14.6617i	−0.145703	+	0.543772i	0.854020	+	0.520241i	$0.174158\pi$
$727$	−3.92859	+	14.6617i	−0.145703	+	0.543772i	−0.999723	+	0.0235317i	$0.992509\pi$
$728$	9.55116	−	10.7556i	0.353989	−	0.398628i
$729$	26.2102	−	6.48276i	0.970748	−	0.240102i
$730$	0.349954	+	1.20995i	0.0129524	+	0.0447823i
$731$	0.552132	+	0.423666i	0.0204213	+	0.0156698i
$732$	1.12421	−	22.0272i	0.0415519	−	0.814148i
$733$	17.4514	+	22.7431i	0.644581	+	0.840034i	0.995340	−	0.0964320i	$-0.0307430\pi$
$733$	17.4514	+	22.7431i	0.644581	+	0.840034i	−0.350759	+	0.936466i	$0.614076\pi$
$734$	−7.61066	−	50.1370i	−0.280915	−	1.85059i
$735$	1.15639	+	0.104926i	0.0426542	+	0.00387026i
$736$	−46.9258	−	1.50978i	−1.72971	−	0.0556512i
$737$	−20.6392			−0.760254
$738$	−29.0347	−	17.9586i	−1.06878	−	0.661066i
$739$	4.91715	−	11.8711i	0.180880	−	0.436684i	−0.807268	−	0.590185i	$-0.799055\pi$
$739$	4.91715	−	11.8711i	0.180880	−	0.436684i	0.988148	+	0.153501i	$0.0490549\pi$
$740$	−0.661990	+	1.25892i	−0.0243352	+	0.0462789i
$741$	11.6447	+	10.7396i	0.427777	+	0.394528i
$742$	3.08581	+	0.761863i	0.113284	+	0.0279689i
$743$	6.69375	+	24.9814i	0.245570	+	0.916479i	0.973096	+	0.230399i	$0.0740031\pi$
$743$	6.69375	+	24.9814i	0.245570	+	0.916479i	−0.727527	+	0.686080i	$0.759330\pi$
$744$	−6.48544	+	3.47888i	−0.237768	+	0.127542i
$745$	−0.0471285	+	0.175886i	−0.00172665	+	0.00644396i
$746$	12.4583	−	22.5974i	0.456129	−	0.827349i
$747$	−29.2246	−	9.42191i	−1.06927	−	0.344730i
$748$	4.42003	+	25.6884i	0.161612	+	0.939262i
$749$	−2.63647	−	20.0260i	−0.0963344	−	0.731733i
$750$	1.86499	−	9.12339i	0.0680997	−	0.333139i
$751$	6.79698	+	3.92424i	0.248025	+	0.143198i	0.618860	−	0.785501i	$-0.287595\pi$
$751$	6.79698	+	3.92424i	0.248025	+	0.143198i	−0.370834	+	0.928699i	$0.620928\pi$
$752$	−9.64980	−	14.0270i	−0.351892	−	0.511513i
$753$	−20.4580	−	14.4233i	−0.745533	−	0.525615i
$754$	−10.1205	−	23.1303i	−0.368567	−	0.842356i
$755$	5.01447	+	2.07706i	0.182495	+	0.0755920i
$756$	−15.0711	−	18.4729i	−0.548130	−	0.671854i
$757$	8.75571	+	21.1382i	0.318232	+	0.768279i	0.999348	+	0.0361040i	$0.0114948\pi$
$757$	8.75571	+	21.1382i	0.318232	+	0.768279i	−0.681116	+	0.732175i	$0.738505\pi$
$758$	0.553502	+	28.0254i	0.0201041	+	1.01793i
$759$	−87.2561	+	15.0959i	−3.16720	+	0.547948i
$760$	0.322411	−	4.49164i	0.0116951	−	0.162929i
$761$	−1.79209	−	6.68816i	−0.0649631	−	0.242445i	0.925807	−	0.377995i	$-0.123387\pi$
$761$	−1.79209	−	6.68816i	−0.0649631	−	0.242445i	−0.990771	+	0.135550i	$0.956720\pi$
$762$	50.3489	−	9.73839i	1.82395	−	0.352785i
$763$	−9.94975	−	7.63471i	−0.360205	−	0.276395i
$764$	6.85137	−	30.3104i	0.247874	−	1.09659i
$765$	1.32938	−	2.05734i	0.0480640	−	0.0743834i
$766$	21.4620	+	26.8548i	0.775455	+	0.970303i
$767$	−14.2848	−	24.7421i	−0.515796	−	0.893385i
$768$	−18.3148	−	20.7982i	−0.660879	−	0.750492i
$769$	17.9673	−	31.1202i	0.647916	−	1.12222i	−0.335704	−	0.941968i	$-0.608974\pi$
$769$	17.9673	−	31.1202i	0.647916	−	1.12222i	0.983620	−	0.180256i	$-0.0576926\pi$
$770$	−7.62505	+	1.15746i	−0.274788	+	0.0417120i
$771$	7.07062	−	0.285892i	0.254642	−	0.0102962i
$772$	−7.51366	+	2.33491i	−0.270422	+	0.0840351i
$773$	−6.22198	+	2.57723i	−0.223789	+	0.0926964i	−0.491761	−	0.870730i	$-0.663647\pi$
$773$	−6.22198	+	2.57723i	−0.223789	+	0.0926964i	0.267972	+	0.963427i	$0.413647\pi$
$774$	−1.38850	+	0.140116i	−0.0499087	+	0.00503637i
$775$	−5.15313	+	5.15313i	−0.185106	+	0.185106i
$776$	8.46252	+	5.73078i	0.303787	+	0.205723i
$777$	4.68878	+	5.62457i	0.168209	+	0.201780i
$778$	26.7401	−	16.1507i	0.958677	−	0.579029i
$779$	−32.9141	−	4.33323i	−1.17927	−	0.155254i
$780$	−2.79219	+	0.993065i	−0.0999766	+	0.0355574i
$781$	−6.86617	−	52.1537i	−0.245691	−	1.86621i
$782$	−24.6805	−	2.75464i	−0.882571	−	0.0985058i
$783$	−40.5228	+	10.4394i	−1.44817	+	0.373073i
$784$	2.98864	−	6.27307i	0.106737	−	0.224038i
$785$	−7.10565	+	4.10245i	−0.253611	+	0.146423i
$786$	31.4972	+	27.9185i	1.12347	+	0.995820i
$787$	−11.5538	+	8.86557i	−0.411850	+	0.316023i	−0.793822	−	0.608150i	$-0.791912\pi$
$787$	−11.5538	+	8.86557i	−0.411850	+	0.316023i	0.381972	+	0.924174i	$0.375245\pi$
$788$	5.45585	+	2.01138i	0.194357	+	0.0716523i
$789$	−0.472428	−	1.51535i	−0.0168189	−	0.0539480i
$790$	−7.00179	+	0.138285i	−0.249113	+	0.00491997i
$791$	−8.97994	−	8.97994i	−0.319290	−	0.319290i
$792$	−41.7577	−	31.4379i	−1.48380	−	1.11710i
$793$	−9.98046	+	9.98046i	−0.354417	+	0.354417i
$794$	24.9064	−	25.9100i	0.883895	−	0.919512i
$795$	−0.481376	−	0.443961i	−0.0170726	−	0.0157457i
$796$	−25.6632	+	1.01409i	−0.909608	+	0.0359435i
$797$	3.35874	+	4.37719i	0.118973	+	0.155048i	0.849043	−	0.528324i	$-0.177179\pi$
$797$	3.35874	+	4.37719i	0.118973	+	0.155048i	−0.730070	+	0.683372i	$0.760513\pi$
$798$	−20.7379	−	10.3636i	−0.734114	−	0.366866i
$799$	−4.50278	−	7.79905i	−0.159297	−	0.275911i
$800$	−23.3118	−	14.4780i	−0.824196	−	0.511876i
$801$	6.23404	+	17.4774i	0.220269	+	0.617534i
$802$	2.47839	−	1.98070i	0.0875151	−	0.0699411i
$803$	14.0948	−	1.85561i	0.497394	−	0.0654832i
$804$	10.3343	−	5.28342i	0.364464	−	0.186332i
$805$	0.959082	−	7.28495i	0.0338032	−	0.256761i
$806$	4.57243	+	1.12890i	0.161057	+	0.0397638i
$807$	0.685547	+	3.96253i	0.0241324	+	0.139488i
$808$	−39.7782	−	8.16939i	−1.39939	−	0.287398i
$809$	−7.94720	−	7.94720i	−0.279409	−	0.279409i	0.553464	−	0.832873i	$-0.313306\pi$
$809$	−7.94720	−	7.94720i	−0.279409	−	0.279409i	−0.832873	+	0.553464i	$0.813306\pi$
$810$	0.886103	+	4.83125i	0.0311345	+	0.169753i
$811$	−13.1050	−	31.6383i	−0.460180	−	1.11097i	−0.968323	−	0.249699i	$-0.919668\pi$
$811$	−13.1050	−	31.6383i	−0.460180	−	1.11097i	0.508144	−	0.861272i	$-0.330332\pi$
$812$	23.6335	+	28.4032i	0.829372	+	0.996756i
$813$	34.6598	−	21.9241i	1.21557	−	0.768911i
$814$	12.9271	+	9.51974i	0.453095	+	0.333667i
$815$	1.19987	+	0.692745i	0.0420296	+	0.0242658i
$816$	−8.78915	−	11.7311i	−0.307682	−	0.410671i
$817$	−1.17525	+	0.678531i	−0.0411168	+	0.0237388i
$818$	6.89732	+	0.769826i	0.241159	+	0.0269163i
$819$	−0.763682	+	15.2377i	−0.0266852	+	0.532448i
$820$	3.58334	−	5.07273i	0.125136	−	0.177148i
$821$	−29.3159	+	38.2052i	−1.02313	+	1.33337i	−0.0815209	+	0.996672i	$0.525978\pi$
$821$	−29.3159	+	38.2052i	−1.02313	+	1.33337i	−0.941612	+	0.336701i	$0.890689\pi$
$822$	2.40372	−	33.9227i	0.0838393	−	1.18319i
$823$	5.31087	−	1.42304i	0.185125	−	0.0496042i	−0.165065	−	0.986283i	$-0.552783\pi$
$823$	5.31087	−	1.42304i	0.185125	−	0.0496042i	0.350191	+	0.936678i	$0.386117\pi$
$824$	−12.7328	−	14.7021i	−0.443570	−	0.512173i
$825$	−48.5792	−	17.8588i	−1.69131	−	0.621764i
$826$	30.1434	+	28.9758i	1.04882	+	1.00820i
$827$	−27.0968	+	11.2239i	−0.942249	+	0.390292i	−0.800312	−	0.599584i	$-0.795333\pi$
$827$	−27.0968	+	11.2239i	−0.942249	+	0.390292i	−0.141936	+	0.989876i	$0.545333\pi$
$828$	39.8260	−	29.8954i	1.38405	−	1.03894i
$829$	8.11239	−	19.5850i	0.281755	−	0.680216i	−0.718122	−	0.695917i	$-0.754998\pi$
$829$	8.11239	−	19.5850i	0.281755	−	0.680216i	0.999877	+	0.0157010i	$0.00499799\pi$
$830$	2.03535	−	5.20200i	0.0706480	−	0.180564i
$831$	−5.33664	−	0.484224i	−0.185126	−	0.0167975i
$832$	−0.220175	+	17.7333i	−0.00763318	+	0.614791i
$833$	1.83770	−	3.18299i	0.0636724	−	0.110284i
$834$	−12.8676	+	0.775039i	−0.445568	+	0.0268374i
$835$	2.66909	−	0.351393i	0.0923678	−	0.0121605i
$836$	−49.5765	−	11.2063i	−1.71464	−	0.387578i
$837$	3.05679	−	7.18262i	0.105658	−	0.248268i
$838$	19.5172	−	5.64494i	0.674209	−	0.195001i
$839$	−1.02595	−	0.274901i	−0.0354196	−	0.00949064i	0.241066	−	0.970509i	$-0.422503\pi$
$839$	−1.02595	−	0.274901i	−0.0354196	−	0.00949064i	−0.276485	+	0.961018i	$0.589170\pi$
$840$	3.52168	−	2.53149i	0.121510	−	0.0873448i
$841$	34.6330	−	9.27988i	1.19424	−	0.319996i
$842$	−31.2255	+	18.8598i	−1.07610	+	0.649951i
$843$	4.42477	+	14.1929i	0.152397	+	0.488828i
$844$	−35.1038	−	3.21762i	−1.20832	−	0.110755i
$845$	−2.88282	−	1.19410i	−0.0991720	−	0.0410784i
$846$	17.2934	+	5.20069i	0.594561	+	0.178803i
$847$			61.8145i			2.12397i
$848$	−3.49087	+	1.78066i	−0.119877	+	0.0611483i
$849$	−42.2953	+	19.5570i	−1.45157	+	0.671194i
$850$	−11.6878	−	8.60708i	−0.400888	−	0.295220i
$851$	−12.1345	+	9.31114i	−0.415966	+	0.319182i
$852$	16.7888	+	24.3565i	0.575175	+	0.834439i
$853$	34.7152	−	45.2417i	1.18863	−	1.54905i	0.422491	−	0.906367i	$-0.361156\pi$
$853$	34.7152	−	45.2417i	1.18863	−	1.54905i	0.766135	−	0.642680i	$-0.222177\pi$
$854$	9.97303	−	18.0896i	0.341270	−	0.619012i
$855$	2.71434	+	3.93013i	0.0928285	+	0.134408i
$856$	18.6211	+	16.5359i	0.636457	+	0.565185i
$857$	−28.8428	−	7.72840i	−0.985251	−	0.263997i	−0.269996	−	0.962861i	$-0.587022\pi$
$857$	−28.8428	−	7.72840i	−0.985251	−	0.263997i	−0.715254	+	0.698864i	$0.753689\pi$
$858$	6.35196	+	32.8406i	0.216852	+	1.12116i
$859$	−2.86770	+	21.7823i	−0.0978446	+	0.743203i	0.870249	+	0.492613i	$0.163958\pi$
$859$	−2.86770	+	21.7823i	−0.0978446	+	0.743203i	−0.968093	+	0.250591i	$0.919375\pi$
$860$	−0.0100243	−	0.253681i	−0.000341826	−	0.00865046i
$861$	−17.0926	−	27.0217i	−0.582515	−	0.920898i
$862$	−6.98514	−	2.73302i	−0.237915	−	0.0930872i
$863$	49.3938			1.68138			0.840692	−	0.541513i	$-0.182148\pi$
$863$	49.3938			1.68138			0.840692	+	0.541513i	$0.182148\pi$
$864$	28.9565	+	5.05190i	0.985120	+	0.171869i
$865$	−1.54395			−0.0524960
$866$	−17.0133	−	6.65668i	−0.578136	−	0.226203i
$867$	11.5958	+	18.3319i	0.393815	+	0.622583i
$868$	−6.88730	+	0.272154i	−0.233770	+	0.00923752i
$869$	−10.3173	+	78.3680i	−0.349992	+	2.65845i
$870$	−1.44562	−	7.47408i	−0.0490112	−	0.253395i
$871$	−7.17448	−	1.92240i	−0.243098	−	0.0651379i
$872$	15.4354	−	0.915498i	0.522708	−	0.0310027i
$873$	−10.8050	+	0.875203i	−0.365692	+	0.0296211i
$874$	23.3795	−	42.4068i	0.790822	−	1.43443i
$875$	5.30918	−	6.91906i	0.179483	−	0.233907i
$876$	−6.58245	+	4.53725i	−0.222400	+	0.153300i
$877$	−38.8330	+	29.7976i	−1.31130	+	1.00619i	−0.312890	+	0.949789i	$0.601297\pi$
$877$	−38.8330	+	29.7976i	−1.31130	+	1.00619i	−0.998408	+	0.0564047i	$0.982036\pi$
$878$	−32.8988	−	24.2272i	−1.11028	−	0.817629i
$879$	13.2473	−	6.12545i	0.446821	−	0.206606i
$880$	6.17220	−	7.23330i	0.208065	−	0.243835i
$881$			5.08722i			0.171393i	0.996321	+	0.0856963i	$0.0273115\pi$
$881$			5.08722i			0.171393i	−0.996321	+	0.0856963i	$0.972689\pi$
$882$	1.69078	+	7.17357i	0.0569314	+	0.241547i
$883$	−30.4828	−	12.6264i	−1.02583	−	0.424911i	−0.194622	−	0.980878i	$-0.562348\pi$
$883$	−30.4828	−	12.6264i	−1.02583	−	0.424911i	−0.831205	+	0.555967i	$0.812348\pi$
$884$	−0.856233	+	9.34137i	−0.0287982	+	0.314184i
$885$	−2.56389	−	8.22391i	−0.0861843	−	0.276444i
$886$	8.53909	−	5.15750i	0.286876	−	0.173270i
$887$	6.23699	−	1.67120i	0.209418	−	0.0561133i	−0.152585	−	0.988290i	$-0.548760\pi$
$887$	6.23699	−	1.67120i	0.209418	−	0.0561133i	0.362003	+	0.932177i	$0.382093\pi$
$888$	−8.90975	−	1.45747i	−0.298992	−	0.0489095i
$889$	46.3920	+	12.4307i	1.55594	+	0.416913i
$890$	−3.24279	+	0.937910i	−0.108698	+	0.0314388i
$891$	55.4134	−	1.70437i	1.85642	−	0.0570985i
$892$	−6.58775	+	29.1441i	−0.220574	+	0.975818i
$893$	17.4102	−	2.29210i	0.582610	−	0.0767020i
$894$	−1.15369	+	0.0694891i	−0.0385852	+	0.00232406i
$895$	0.623164	−	1.07935i	0.0208301	−	0.0360788i
$896$	−6.90119	−	25.0203i	−0.230553	−	0.835871i
$897$	−31.7376	−	2.87973i	−1.05969	−	0.0961514i
$898$	10.8069	−	27.6206i	0.360631	−	0.921711i
$899$	−4.62976	+	11.1772i	−0.154411	+	0.372781i
$900$	28.8960	−	3.49360i	0.963200	−	0.116453i
$901$	−1.91502	+	0.793226i	−0.0637985	+	0.0264262i
$902$	−50.5373	−	48.5797i	−1.68271	−	1.61753i
$903$	−1.22675	−	0.450981i	−0.0408237	−	0.0150077i
$904$	15.6173	+	1.12102i	0.519425	+	0.0372845i
$905$	0.273025	−	0.0731569i	0.00907567	−	0.00243182i
$906$	−2.43503	+	34.3646i	−0.0808985	+	1.14169i
$907$	12.1384	−	15.8190i	0.403048	−	0.525262i	−0.547098	−	0.837069i	$-0.684267\pi$
$907$	12.1384	−	15.8190i	0.403048	−	0.525262i	0.950146	+	0.311806i	$0.100934\pi$
$908$	−40.2091	−	28.4034i	−1.33439	−	0.942601i
$909$	38.3324	−	19.6417i	1.27141	−	0.651476i
$910$	−2.75839	−	0.307870i	−0.0914398	−	0.0102058i
$911$	32.4434	−	18.7312i	1.07490	−	0.620593i	0.145383	−	0.989375i	$-0.453559\pi$
$911$	32.4434	−	18.7312i	1.07490	−	0.620593i	0.929516	+	0.368783i	$0.120225\pi$
$912$	27.6924	−	7.07992i	0.916987	−	0.234439i
$913$	−54.6020	−	31.5245i	−1.80706	−	1.04331i
$914$	0.166211	+	0.122401i	0.00549778	+	0.00404865i
$915$	−3.59664	+	2.27506i	−0.118901	+	0.0752112i
$916$	−24.3198	+	20.2359i	−0.803550	+	0.668612i
$917$	15.0851	+	36.4185i	0.498152	+	1.20265i
$918$	15.0576	+	3.87237i	0.496975	+	0.127807i
$919$	9.85400	+	9.85400i	0.325053	+	0.325053i	0.850702	−	0.525648i	$-0.176177\pi$
$919$	9.85400	+	9.85400i	0.325053	+	0.325053i	−0.525648	+	0.850702i	$0.676177\pi$
$920$	4.98620	+	7.56360i	0.164390	+	0.249365i
$921$	7.35752	+	42.5272i	0.242438	+	1.40132i
$922$	2.19303	+	0.541442i	0.0722235	+	0.0178314i
$923$	2.47098	−	18.7689i	0.0813333	−	0.617787i
$924$	−22.2838	−	43.5870i	−0.733082	−	1.43391i
$925$	−8.86340	+	1.16689i	−0.291427	+	0.0383671i
$926$	−1.69810	+	1.35710i	−0.0558029	+	0.0445970i
$927$	20.2923	+	3.71303i	0.666486	+	0.121952i
$928$	−44.9517	−	7.39560i	−1.47561	−	0.242772i
$929$	−24.0926	−	41.7296i	−0.790452	−	1.36910i	−0.925687	−	0.378290i	$-0.876512\pi$
$929$	−24.0926	−	41.7296i	−0.790452	−	1.36910i	0.135235	−	0.990814i	$-0.456821\pi$
$930$	1.27028	+	0.634811i	0.0416542	+	0.0208163i
$931$	4.36290	+	5.68584i	0.142988	+	0.186346i
$932$	0.112485	+	2.84662i	0.00368458	+	0.0932443i
$933$	6.89364	+	6.35784i	0.225688	+	0.208146i
$934$	1.60595	−	1.67066i	0.0525483	−	0.0546658i
$935$	3.55643	−	3.55643i	0.116308	−	0.116308i
$936$	−11.5874	−	14.8177i	−0.378745	−	0.484333i
$937$	−13.1474	−	13.1474i	−0.429508	−	0.429508i	0.458953	−	0.888461i	$-0.348225\pi$
$937$	−13.1474	−	13.1474i	−0.429508	−	0.429508i	−0.888461	+	0.458953i	$0.848225\pi$
$938$	10.8681	−	0.214645i	0.354857	−	0.00700842i
$939$	7.46992	+	23.9604i	0.243772	+	0.781919i
$940$	−1.13637	+	3.08241i	−0.0370644	+	0.100537i
$941$	−32.4165	+	24.8740i	−1.05675	+	0.810870i	−0.982480	−	0.186368i	$-0.940328\pi$
$941$	−32.4165	+	24.8740i	−1.05675	+	0.810870i	−0.0742668	+	0.997238i	$0.523662\pi$
$942$	−38.9728	−	34.5447i	−1.26980	−	1.12553i
$943$	57.8385	−	33.3931i	1.88348	−	1.08743i
$944$	−51.4811	−	2.67479i	−1.67557	−	0.0870570i
$945$	−1.23351	+	4.43176i	−0.0401261	+	0.144165i
$946$	−2.84784	−	0.317854i	−0.0925913	−	0.0103343i
$947$	−3.82066	−	29.0208i	−0.124155	−	0.943049i	−0.934217	−	0.356705i	$-0.883900\pi$
$947$	−3.82066	−	29.0208i	−0.124155	−	0.943049i	0.810062	−	0.586344i	$-0.199433\pi$
$948$	−14.8954	−	41.8812i	−0.483779	−	1.36024i
$949$	5.07239	+	0.667793i	0.164657	+	0.0216775i
$950$	24.2274	−	14.6331i	0.786041	−	0.474759i
$951$	−23.8264	−	28.5817i	−0.772624	−	0.926824i
$952$	−2.59465	−	13.4810i	−0.0840930	−	0.436921i
$953$	−35.0017	+	35.0017i	−1.13382	+	1.13382i	−0.144279	+	0.989537i	$0.546086\pi$
$953$	−35.0017	+	35.0017i	−1.13382	+	1.13382i	−0.989537	+	0.144279i	$0.953914\pi$
$954$	1.70634	−	3.79011i	0.0552449	−	0.122709i
$955$	−5.53967	+	2.29461i	−0.179259	+	0.0742517i
$956$	−11.2959	−	36.3499i	−0.365336	−	1.17564i
$957$	−85.8528	+	3.47136i	−2.77523	+	0.112213i
$958$	−34.0492	+	5.16857i	−1.10008	+	0.166989i
$959$	15.9251	−	27.5831i	0.514249	−	0.890705i
$960$	−1.23886	+	5.20184i	−0.0399841	+	0.167889i
$961$	14.3716	+	24.8923i	0.463600	+	0.802978i
$962$	3.60696	+	4.51327i	0.116293	+	0.145514i
$963$	−26.3810	−	1.32216i	−0.850115	−	0.0426060i
$964$	28.4169	+	6.42337i	0.915246	+	0.206883i
$965$	1.20446	+	0.924215i	0.0387729	+	0.0297515i
$966$	45.7901	−	8.85664i	1.47327	−	0.284958i
$967$	0.266753	+	0.995536i	0.00857820	+	0.0320143i	0.970082	−	0.242776i	$-0.0780581\pi$
$967$	0.266753	+	0.995536i	0.00857820	+	0.0320143i	−0.961504	+	0.274791i	$0.911391\pi$
$968$	−49.8936	−	57.6103i	−1.60364	−	1.85166i
$969$	14.8974	−	2.57736i	0.478574	−	0.0827967i
$970$	−0.0389408	−	1.97169i	−0.00125031	−	0.0633072i
$971$	16.3200	+	39.4000i	0.523735	+	1.26441i	0.935568	+	0.353148i	$0.114889\pi$
$971$	16.3200	+	39.4000i	0.523735	+	1.26441i	−0.411833	+	0.911259i	$0.635111\pi$
$972$	−27.3100	+	15.0387i	−0.875970	+	0.482366i
$973$	−11.1541	−	4.62017i	−0.357583	−	0.148116i
$974$	15.9258	+	36.3982i	0.510295	+	1.16627i
$975$	−15.2234	−	10.7328i	−0.487540	−	0.343725i
$976$	5.30628	+	24.9090i	0.169850	+	0.797317i
$977$	1.19187	+	0.688128i	0.0381314	+	0.0220152i	0.518945	−	0.854808i	$-0.326325\pi$
$977$	1.19187	+	0.688128i	0.0381314	+	0.0220152i	−0.480813	+	0.876823i	$0.659658\pi$
$978$	−1.76126	+	8.61595i	−0.0563188	+	0.275508i
$979$	4.97322	+	37.7754i	0.158945	+	1.20731i
$980$	−1.32136	+	0.227357i	−0.0422092	+	0.00726264i
$981$	−12.1628	+	11.0019i	−0.388329	+	0.351263i
$982$	−10.6193	+	19.2618i	−0.338875	+	0.614669i
$983$	−0.744300	+	2.77777i	−0.0237395	+	0.0885969i	−0.976779	−	0.214248i	$-0.931270\pi$
$983$	−0.744300	+	2.77777i	−0.0237395	+	0.0885969i	0.953040	+	0.302845i	$0.0979365\pi$
$984$	37.7407	+	11.3876i	1.20313	+	0.363023i
$985$	−0.290394	−	1.08377i	−0.00925273	−	0.0345316i
$986$	−23.3939	−	5.77578i	−0.745013	−	0.183938i
$987$	12.4326	+	11.4663i	0.395734	+	0.364975i
$988$	−16.1897	−	8.51319i	−0.515064	−	0.270841i
$989$	1.04475	−	2.52225i	0.0332211	−	0.0802028i
$990$	−0.305835	+	10.0809i	−0.00972007	+	0.320393i
$991$	33.4340			1.06207			0.531033	−	0.847351i	$-0.321804\pi$
$991$	33.4340			1.06207			0.531033	+	0.847351i	$0.321804\pi$
$992$	6.19921	−	5.81274i	0.196825	−	0.184555i
$993$	21.8729	+	1.98465i	0.694115	+	0.0629810i
$994$	4.15797	+	27.3916i	0.131883	+	0.868809i
$995$	3.01685	+	3.93163i	0.0956405	+	0.124641i
$996$	35.4100	+	1.80723i	1.12201	+	0.0572643i
$997$	17.8631	+	13.7068i	0.565729	+	0.434099i	0.851617	−	0.524164i	$-0.175622\pi$
$997$	17.8631	+	13.7068i	0.565729	+	0.434099i	−0.285889	+	0.958263i	$0.592289\pi$
$998$	7.23245	+	25.0059i	0.228939	+	0.791547i
$999$	8.33879	−	4.70754i	0.263828	−	0.148940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.13.18	✓	368
3.2	odd	2		864.2.bk.a.685.29		368
9.2	odd	6		864.2.bk.a.397.2		368
9.7	even	3	inner	288.2.bc.a.205.45	yes	368
32.5	even	8	inner	288.2.bc.a.229.45	yes	368
96.5	odd	8		864.2.bk.a.37.2		368
288.101	odd	24		864.2.bk.a.613.29		368
288.133	even	24	inner	288.2.bc.a.133.18	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.18	✓	368	1.1	even	1	trivial
288.2.bc.a.133.18	yes	368	288.133	even	24	inner
288.2.bc.a.205.45	yes	368	9.7	even	3	inner
288.2.bc.a.229.45	yes	368	32.5	even	8	inner
864.2.bk.a.37.2		368	96.5	odd	8
864.2.bk.a.397.2		368	9.2	odd	6
864.2.bk.a.613.29		368	288.101	odd	24
864.2.bk.a.685.29		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.515291 + 1.31699i) q^{2} +(0.925920 + 1.46379i) q^{3} +(-1.46895 - 1.35727i) q^{4} +(-0.0503714 + 0.382609i) q^{5} +(-2.40492 + 0.465155i) q^{6} +(-2.21592 - 0.593754i) q^{7} +(2.54446 - 1.23521i) q^{8} +(-1.28535 + 2.71070i) q^{9} +O(q^{10})\)	\(q+(-0.515291 + 1.31699i) q^{2} +(0.925920 + 1.46379i) q^{3} +(-1.46895 - 1.35727i) q^{4} +(-0.0503714 + 0.382609i) q^{5} +(-2.40492 + 0.465155i) q^{6} +(-2.21592 - 0.593754i) q^{7} +(2.54446 - 1.23521i) q^{8} +(-1.28535 + 2.71070i) q^{9} +(-0.477938 - 0.263494i) q^{10} +(-3.74995 + 4.88703i) q^{11} +(0.626626 - 3.40695i) q^{12} +(-1.75873 + 1.34952i) q^{13} +(1.92381 - 2.61240i) q^{14} +(-0.606698 + 0.280532i) q^{15} +(0.315630 + 3.98753i) q^{16} +2.11575i q^{17} +(-2.90765 - 3.08959i) q^{18} +(-3.81157 - 1.57881i) q^{19} +(0.593297 - 0.493666i) q^{20} +(-1.18263 - 3.79340i) q^{21} +(-4.50387 - 7.45690i) q^{22} +(8.01688 - 2.14812i) q^{23} +(4.16405 + 2.58084i) q^{24} +(4.68578 + 1.25555i) q^{25} +(-0.871054 - 3.01163i) q^{26} +(-5.15801 + 0.628416i) q^{27} +(2.44919 + 3.87980i) q^{28} +(7.98435 - 1.05116i) q^{29} +(-0.0568332 - 0.943574i) q^{30} +(-0.751135 + 1.30100i) q^{31} +(-5.41419 - 1.63905i) q^{32} +(-10.6257 - 0.964131i) q^{33} +(-2.78644 - 1.09023i) q^{34} +(0.338795 - 0.817922i) q^{35} +(5.56726 - 2.23732i) q^{36} +(-1.70259 + 0.705235i) q^{37} +(4.04335 - 4.20628i) q^{38} +(-3.60385 - 1.32486i) q^{39} +(0.344435 + 1.03575i) q^{40} +(7.77264 - 2.08267i) q^{41} +(5.60529 + 0.397184i) q^{42} +(0.200243 - 0.260962i) q^{43} +(12.1415 - 2.08910i) q^{44} +(-0.972393 - 0.628326i) q^{45} +(-1.30197 + 11.6651i) q^{46} +(-3.68618 + 2.12822i) q^{47} +(-5.54464 + 4.15415i) q^{48} +(-1.50442 - 0.868578i) q^{49} +(-4.06809 + 5.52417i) q^{50} +(-3.09701 + 1.95902i) q^{51} +(4.41515 + 0.404694i) q^{52} +(0.374914 + 0.905123i) q^{53} +(1.83026 - 7.11689i) q^{54} +(-1.68093 - 1.68093i) q^{55} +(-6.37172 + 1.22635i) q^{56} +(-1.21818 - 7.04118i) q^{57} +(-2.72989 + 11.0570i) q^{58} +(-1.68217 + 12.7774i) q^{59} +(1.27197 + 0.411366i) q^{60} +(6.31250 - 0.831057i) q^{61} +(-1.32636 - 1.65964i) q^{62} +(4.45771 - 5.24351i) q^{63} +(4.94851 - 6.28588i) q^{64} +(-0.427749 - 0.740883i) q^{65} +(6.74509 - 13.4972i) q^{66} +(2.03968 + 2.65816i) q^{67} +(2.87165 - 3.10794i) q^{68} +(10.5674 + 9.74602i) q^{69} +(0.902622 + 0.867659i) q^{70} +(-6.03843 + 6.03843i) q^{71} +(0.0777766 + 8.48492i) q^{72} +(-1.63191 - 1.63191i) q^{73} +(-0.0514625 - 2.60570i) q^{74} +(2.50079 + 8.02152i) q^{75} +(3.45615 + 7.49253i) q^{76} +(11.2113 - 8.60271i) q^{77} +(3.60187 - 4.06357i) q^{78} +(11.1128 - 6.41597i) q^{79} +(-1.54156 - 0.0800946i) q^{80} +(-5.69577 - 6.96837i) q^{81} +(-1.26230 + 11.3097i) q^{82} +(1.33597 + 10.1477i) q^{83} +(-3.41145 + 7.17748i) q^{84} +(-0.809506 - 0.106574i) q^{85} +(0.240502 + 0.398191i) q^{86} +(8.93154 + 10.7141i) q^{87} +(-3.50507 + 17.0668i) q^{88} +(4.37368 - 4.37368i) q^{89} +(1.32857 - 0.956865i) q^{90} +(4.69849 - 1.94618i) q^{91} +(-14.6920 - 7.72560i) q^{92} +(-2.59988 + 0.105123i) q^{93} +(-0.903395 - 5.95133i) q^{94} +(0.796059 - 1.37882i) q^{95} +(-2.61388 - 9.44286i) q^{96} +(1.80672 + 3.12934i) q^{97} +(1.91913 - 1.53374i) q^{98} +(-8.42728 - 16.4465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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