LMFDB - Embedded newform 288.2.bf.a.59.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (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			59.43
Character	$\chi$	$=$	288.59
Dual form			288.2.bf.a.83.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36986 + 0.351406i) q^{2} +(-0.197306 - 1.72078i) q^{3} +(1.75303 + 0.962754i) q^{4} +(1.98789 + 2.59067i) q^{5} +(0.334409 - 2.42656i) q^{6} +(-0.0424520 - 0.0113750i) q^{7} +(2.06308 + 1.93486i) q^{8} +(-2.92214 + 0.679040i) q^{9} +O(q^{10})$	\(q+(1.36986 + 0.351406i) q^{2} +(-0.197306 - 1.72078i) q^{3} +(1.75303 + 0.962754i) q^{4} +(1.98789 + 2.59067i) q^{5} +(0.334409 - 2.42656i) q^{6} +(-0.0424520 - 0.0113750i) q^{7} +(2.06308 + 1.93486i) q^{8} +(-2.92214 + 0.679040i) q^{9} +(1.81275 + 4.24741i) q^{10} +(-1.93779 + 0.255115i) q^{11} +(1.31080 - 3.20653i) q^{12} +(0.252285 - 1.91630i) q^{13} +(-0.0541561 - 0.0305000i) q^{14} +(4.06574 - 3.93187i) q^{15} +(2.14621 + 3.37547i) q^{16} -0.829919 q^{17} +(-4.24154 - 0.0966687i) q^{18} +(-2.63304 - 6.35672i) q^{19} +(0.990651 + 6.45537i) q^{20} +(-0.0111978 + 0.0752948i) q^{21} +(-2.74415 - 0.331481i) q^{22} +(-1.56000 - 5.82202i) q^{23} +(2.92240 - 3.93186i) q^{24} +(-1.46577 + 5.47032i) q^{25} +(1.01899 - 2.53640i) q^{26} +(1.74503 + 4.89437i) q^{27} +(-0.0634683 - 0.0608115i) q^{28} +(3.95073 + 3.03150i) q^{29} +(6.95118 - 3.95739i) q^{30} +(-0.805036 - 0.464788i) q^{31} +(1.75385 + 5.37811i) q^{32} +(0.821335 + 3.28417i) q^{33} +(-1.13687 - 0.291639i) q^{34} +(-0.0549212 - 0.132592i) q^{35} +(-5.77634 - 1.62293i) q^{36} +(-7.69054 - 3.18552i) q^{37} +(-1.37310 - 9.63308i) q^{38} +(-3.34730 - 0.0560288i) q^{39} +(-0.911405 + 9.19107i) q^{40} +(-0.106160 + 0.0284456i) q^{41} +(-0.0417984 + 0.0992083i) q^{42} +(1.18682 + 9.01477i) q^{43} +(-3.64262 - 1.41839i) q^{44} +(-7.56807 - 6.22045i) q^{45} +(-0.0910939 - 8.52354i) q^{46} +(5.45988 - 3.15226i) q^{47} +(5.38496 - 4.35915i) q^{48} +(-6.06051 - 3.49903i) q^{49} +(-3.93020 + 6.97849i) q^{50} +(0.163748 + 1.42810i) q^{51} +(2.28719 - 3.11643i) q^{52} +(0.857129 + 0.355035i) q^{53} +(0.670538 + 7.31781i) q^{54} +(-4.51304 - 4.51304i) q^{55} +(-0.0655730 - 0.105606i) q^{56} +(-10.4190 + 5.78510i) q^{57} +(4.34666 + 5.54105i) q^{58} +(-8.95089 + 6.86826i) q^{59} +(10.9128 - 2.97837i) q^{60} +(-6.60666 + 8.60997i) q^{61} +(-0.939457 - 0.919589i) q^{62} +(0.131775 + 0.00441267i) q^{63} +(0.512621 + 7.98356i) q^{64} +(5.46601 - 3.15580i) q^{65} +(-0.0289648 + 4.78748i) q^{66} +(0.0234347 - 0.178004i) q^{67} +(-1.45487 - 0.799007i) q^{68} +(-9.71059 + 3.83314i) q^{69} +(-0.0286408 - 0.200931i) q^{70} +(9.64167 + 9.64167i) q^{71} +(-7.34247 - 4.25302i) q^{72} +(5.88713 - 5.88713i) q^{73} +(-9.41554 - 7.06622i) q^{74} +(9.70241 + 1.44293i) q^{75} +(1.50417 - 13.6785i) q^{76} +(0.0851652 + 0.0112122i) q^{77} +(-4.56563 - 1.25301i) q^{78} +(-7.32756 - 12.6917i) q^{79} +(-4.47829 + 12.2702i) q^{80} +(8.07781 - 3.96850i) q^{81} +(-0.155421 + 0.00166103i) q^{82} +(6.13499 + 4.70755i) q^{83} +(-0.0921203 + 0.121213i) q^{84} +(-1.64979 - 2.15005i) q^{85} +(-1.54207 + 12.7660i) q^{86} +(4.43703 - 7.39646i) q^{87} +(-4.49144 - 3.22304i) q^{88} +(9.80410 - 9.80410i) q^{89} +(-8.18129 - 11.1806i) q^{90} +(-0.0325079 + 0.0784810i) q^{91} +(2.87044 - 11.7081i) q^{92} +(-0.640957 + 1.47699i) q^{93} +(8.58699 - 2.39952i) q^{94} +(11.2340 - 19.4578i) q^{95} +(8.90847 - 4.07911i) q^{96} +(9.02297 + 15.6282i) q^{97} +(-7.07246 - 6.92288i) q^{98} +(5.48927 - 2.06132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.36986	+	0.351406i	0.968637	+	0.248482i
$2$	1.36986	+	0.351406i	0.968637	+	0.248482i
$3$	−0.197306	−	1.72078i	−0.113915	−	0.993491i
$3$	−0.197306	−	1.72078i	−0.113915	−	0.993491i
$4$	1.75303	+	0.962754i	0.876514	+	0.481377i
$5$	1.98789	+	2.59067i	0.889013	+	1.15858i	0.986568	+	0.163354i	$0.0522311\pi$
$5$	1.98789	+	2.59067i	0.889013	+	1.15858i	−0.0975551	+	0.995230i	$0.531102\pi$
$6$	0.334409	−	2.42656i	0.136522	−	0.990637i
$7$	−0.0424520	−	0.0113750i	−0.0160454	−	0.00429934i	0.250787	−	0.968042i	$-0.419310\pi$
$7$	−0.0424520	−	0.0113750i	−0.0160454	−	0.00429934i	−0.266833	+	0.963743i	$0.585977\pi$
$8$	2.06308	+	1.93486i	0.729410	+	0.684077i
$9$	−2.92214	+	0.679040i	−0.974047	+	0.226347i
$10$	1.81275	+	4.24741i	0.573243	+	1.34315i
$11$	−1.93779	+	0.255115i	−0.584267	+	0.0769202i	−0.416865	−	0.908969i	$-0.636871\pi$
$11$	−1.93779	+	0.255115i	−0.584267	+	0.0769202i	−0.167402	+	0.985889i	$0.553538\pi$
$12$	1.31080	−	3.20653i	0.378395	−	0.925644i
$13$	0.252285	−	1.91630i	0.0699713	−	0.531485i	−0.920181	−	0.391493i	$-0.871959\pi$
$13$	0.252285	−	1.91630i	0.0699713	−	0.531485i	0.990153	−	0.139992i	$-0.0447078\pi$
$14$	−0.0541561	−	0.0305000i	−0.0144738	−	0.00815148i
$15$	4.06574	−	3.93187i	1.04977	−	1.01521i
$16$	2.14621	+	3.37547i	0.536553	+	0.843867i
$17$	−0.829919			−0.201285			−0.100642	−	0.994923i	$-0.532090\pi$
$17$	−0.829919			−0.201285			−0.100642	+	0.994923i	$0.532090\pi$
$18$	−4.24154	−	0.0966687i	−0.999740	−	0.0227850i
$19$	−2.63304	−	6.35672i	−0.604061	−	1.45833i	−0.869366	−	0.494168i	$-0.835473\pi$
$19$	−2.63304	−	6.35672i	−0.604061	−	1.45833i	0.265305	−	0.964164i	$-0.414527\pi$
$20$	0.990651	+	6.45537i	0.221516	+	1.44346i
$21$	−0.0111978	+	0.0752948i	−0.00244355	+	0.0164307i
$22$	−2.74415	−	0.331481i	−0.585055	−	0.0706719i
$23$	−1.56000	−	5.82202i	−0.325283	−	1.21397i	−0.914027	−	0.405654i	$-0.867044\pi$
$23$	−1.56000	−	5.82202i	−0.325283	−	1.21397i	0.588743	−	0.808320i	$-0.299623\pi$
$24$	2.92240	−	3.93186i	0.596533	−	0.802588i
$25$	−1.46577	+	5.47032i	−0.293154	+	1.09406i
$26$	1.01899	−	2.53640i	0.199841	−	0.497429i
$27$	1.74503	+	4.89437i	0.335832	+	0.941922i
$28$	−0.0634683	−	0.0608115i	−0.0119944	−	0.0114923i
$29$	3.95073	+	3.03150i	0.733633	+	0.562936i	0.906600	−	0.421991i	$-0.138669\pi$
$29$	3.95073	+	3.03150i	0.733633	+	0.562936i	−0.172967	+	0.984928i	$0.555335\pi$
$30$	6.95118	−	3.95739i	1.26911	−	0.722516i
$31$	−0.805036	−	0.464788i	−0.144589	−	0.0834784i	0.425960	−	0.904742i	$-0.359936\pi$
$31$	−0.805036	−	0.464788i	−0.144589	−	0.0834784i	−0.570549	+	0.821263i	$0.693270\pi$
$32$	1.75385	+	5.37811i	0.310039	+	0.950724i
$33$	0.821335	+	3.28417i	0.142976	+	0.571701i
$34$	−1.13687	−	0.291639i	−0.194972	−	0.0500156i
$35$	−0.0549212	−	0.132592i	−0.00928338	−	0.0224121i
$36$	−5.77634	−	1.62293i	−0.962723	−	0.270488i
$37$	−7.69054	−	3.18552i	−1.26432	−	0.523697i	−0.353085	−	0.935591i	$-0.614867\pi$
$37$	−7.69054	−	3.18552i	−1.26432	−	0.523697i	−0.911232	+	0.411894i	$0.864867\pi$
$38$	−1.37310	−	9.63308i	−0.222747	−	1.56269i
$39$	−3.34730	−	0.0560288i	−0.535996	−	0.00897179i
$40$	−0.911405	+	9.19107i	−0.144106	+	1.45324i
$41$	−0.106160	+	0.0284456i	−0.0165795	+	0.00444245i	−0.267099	−	0.963669i	$-0.586065\pi$
$41$	−0.106160	+	0.0284456i	−0.0165795	+	0.00444245i	0.250520	+	0.968111i	$0.419398\pi$
$42$	−0.0417984	+	0.0992083i	−0.00644963	+	0.0153082i
$43$	1.18682	+	9.01477i	0.180988	+	1.37474i	0.804977	+	0.593306i	$0.202178\pi$
$43$	1.18682	+	9.01477i	0.180988	+	1.37474i	−0.623989	+	0.781433i	$0.714489\pi$
$44$	−3.64262	−	1.41839i	−0.549145	−	0.213831i
$45$	−7.56807	−	6.22045i	−1.12818	−	0.927290i
$46$	−0.0910939	−	8.52354i	−0.0134311	−	1.25673i
$47$	5.45988	−	3.15226i	0.796405	−	0.459805i	−0.0458073	−	0.998950i	$-0.514586\pi$
$47$	5.45988	−	3.15226i	0.796405	−	0.459805i	0.842213	+	0.539145i	$0.181253\pi$
$48$	5.38496	−	4.35915i	0.777252	−	0.629189i
$49$	−6.06051	−	3.49903i	−0.865786	−	0.499862i
$50$	−3.93020	+	6.97849i	−0.555815	+	0.986908i
$51$	0.163748	+	1.42810i	0.0229293	+	0.199975i
$52$	2.28719	−	3.11643i	0.317176	−	0.432171i
$53$	0.857129	+	0.355035i	0.117736	+	0.0487678i	0.440774	−	0.897618i	$-0.354704\pi$
$53$	0.857129	+	0.355035i	0.117736	+	0.0487678i	−0.323038	+	0.946386i	$0.604704\pi$
$54$	0.670538	+	7.31781i	0.0912486	+	0.995828i
$55$	−4.51304	−	4.51304i	−0.608539	−	0.608539i
$56$	−0.0655730	−	0.105606i	−0.00876257	−	0.0141122i
$57$	−10.4190	+	5.78510i	−1.38003	+	0.766255i
$58$	4.34666	+	5.54105i	0.570744	+	0.727575i
$59$	−8.95089	+	6.86826i	−1.16531	+	0.894171i	−0.995818	−	0.0913608i	$-0.970878\pi$
$59$	−8.95089	+	6.86826i	−1.16531	+	0.894171i	−0.169489	+	0.985532i	$0.554212\pi$
$60$	10.9128	−	2.97837i	1.40883	−	0.384506i
$61$	−6.60666	+	8.60997i	−0.845896	+	1.10239i	0.147658	+	0.989038i	$0.452826\pi$
$61$	−6.60666	+	8.60997i	−0.845896	+	1.10239i	−0.993555	+	0.113355i	$0.963840\pi$
$62$	−0.939457	−	0.919589i	−0.119311	−	0.116788i
$63$	0.131775	+	0.00441267i	0.0166021	+	0.000555945i
$64$	0.512621	+	7.98356i	0.0640776	+	0.997945i
$65$	5.46601	−	3.15580i	0.677975	−	0.391429i
$66$	−0.0289648	+	4.78748i	−0.00356532	+	0.589298i
$67$	0.0234347	−	0.178004i	0.00286300	−	0.0217466i	−0.989954	−	0.141392i	$-0.954842\pi$
$67$	0.0234347	−	0.178004i	0.00286300	−	0.0217466i	0.992817	+	0.119645i	$0.0381756\pi$
$68$	−1.45487	−	0.799007i	−0.176429	−	0.0968939i
$69$	−9.71059	+	3.83314i	−1.16902	+	0.461456i
$70$	−0.0286408	−	0.200931i	−0.00342324	−	0.0240159i
$71$	9.64167	+	9.64167i	1.14426	+	1.14426i	0.987663	+	0.156592i	$0.0500509\pi$
$71$	9.64167	+	9.64167i	1.14426	+	1.14426i	0.156592	+	0.987663i	$0.449949\pi$
$72$	−7.34247	−	4.25302i	−0.865318	−	0.501223i
$73$	5.88713	−	5.88713i	0.689037	−	0.689037i	−0.272982	−	0.962019i	$-0.588010\pi$
$73$	5.88713	−	5.88713i	0.689037	−	0.689037i	0.962019	+	0.272982i	$0.0880101\pi$
$74$	−9.41554	−	7.06622i	−1.09453	−	0.821432i
$75$	9.70241	+	1.44293i	1.12034	+	0.166615i
$76$	1.50417	−	13.6785i	0.172540	−	1.56903i
$77$	0.0851652	+	0.0112122i	0.00970548	+	0.00127775i
$78$	−4.56563	−	1.25301i	−0.516956	−	0.141876i
$79$	−7.32756	−	12.6917i	−0.824415	−	1.42793i	−0.902366	−	0.430971i	$-0.858171\pi$
$79$	−7.32756	−	12.6917i	−0.824415	−	1.42793i	0.0779513	−	0.996957i	$-0.475162\pi$
$80$	−4.47829	+	12.2702i	−0.500688	+	1.37185i
$81$	8.07781	−	3.96850i	0.897534	−	0.440945i
$82$	−0.155421	+	0.00166103i	−0.0171633	+	0.000183430i
$83$	6.13499	+	4.70755i	0.673403	+	0.516720i	0.887919	−	0.460000i	$-0.152151\pi$
$83$	6.13499	+	4.70755i	0.673403	+	0.516720i	−0.214516	+	0.976721i	$0.568817\pi$
$84$	−0.0921203	+	0.121213i	−0.0100512	+	0.0132254i
$85$	−1.64979	−	2.15005i	−0.178945	−	0.233205i
$86$	−1.54207	+	12.7660i	−0.166286	+	1.37659i
$87$	4.43703	−	7.39646i	0.475700	−	0.792984i
$88$	−4.49144	−	3.22304i	−0.478789	−	0.343577i
$89$	9.80410	−	9.80410i	1.03923	−	1.03923i	0.0400337	−	0.999198i	$-0.487253\pi$
$89$	9.80410	−	9.80410i	1.03923	−	1.03923i	0.999198	−	0.0400337i	$-0.0127465\pi$
$90$	−8.18129	−	11.1806i	−0.862383	−	1.17854i
$91$	−0.0325079	+	0.0784810i	−0.00340775	+	0.00822704i
$92$	2.87044	−	11.7081i	0.299264	−	1.22065i
$93$	−0.640957	+	1.47699i	−0.0664642	+	0.153157i
$94$	8.58699	−	2.39952i	0.885680	−	0.247492i
$95$	11.2340	−	19.4578i	1.15258	−	1.99633i
$96$	8.90847	−	4.07911i	0.909217	−	0.416322i
$97$	9.02297	+	15.6282i	0.916144	+	1.58681i	0.805218	+	0.592979i	$0.202048\pi$
$97$	9.02297	+	15.6282i	0.916144	+	1.58681i	0.110926	+	0.993829i	$0.464618\pi$
$98$	−7.07246	−	6.92288i	−0.714426	−	0.699317i
$99$	5.48927	−	2.06132i	0.551692	−	0.207171i
$100$	−7.83611	+	8.17845i	−0.783611	+	0.817845i
$101$	9.83486	−	1.29478i	0.978605	−	0.128836i	0.375780	−	0.926709i	$-0.377375\pi$
$101$	9.83486	−	1.29478i	0.978605	−	0.128836i	0.602825	+	0.797873i	$0.294042\pi$
$102$	−0.277533	+	2.01384i	−0.0274798	+	0.199400i
$103$	−0.454795	−	1.69732i	−0.0448123	−	0.167242i	0.939893	−	0.341468i	$-0.110924\pi$
$103$	−0.454795	−	1.69732i	−0.0448123	−	0.167242i	−0.984706	+	0.174226i	$0.944258\pi$
$104$	4.22825	−	3.46534i	0.414615	−	0.339805i
$105$	−0.217324	+	0.120668i	−0.0212087	+	0.0117760i
$106$	1.04939	+	0.787548i	0.101925	+	0.0764934i
$107$	−2.82452	+	6.81899i	−0.273057	+	0.659217i	−0.999611	−	0.0278920i	$-0.991121\pi$
$107$	−2.82452	+	6.81899i	−0.273057	+	0.659217i	0.726554	+	0.687109i	$0.241121\pi$
$108$	−1.65298	+	10.2600i	−0.159058	+	0.987269i
$109$	−9.72168	+	4.02685i	−0.931168	+	0.385702i	−0.796121	−	0.605137i	$-0.793118\pi$
$109$	−9.72168	+	4.02685i	−0.931168	+	0.385702i	−0.135046	+	0.990839i	$0.543118\pi$
$110$	−4.59632	−	7.76815i	−0.438242	−	0.740664i
$111$	−3.96418	+	13.8622i	−0.376264	+	1.31574i
$112$	−0.0527151	−	0.167709i	−0.00498111	−	0.0158470i
$113$	8.19337	−	14.1913i	0.770768	−	1.33501i	−0.166375	−	0.986063i	$-0.553206\pi$
$113$	8.19337	−	14.1913i	0.770768	−	1.33501i	0.937143	−	0.348946i	$-0.113460\pi$
$114$	−16.3055	+	4.26347i	−1.52715	+	0.399311i
$115$	11.9818	−	15.6150i	1.11731	−	1.45611i
$116$	4.00715	+	9.11789i	0.372055	+	0.846575i
$117$	0.564030	+	5.77100i	0.0521446	+	0.533529i
$118$	−14.6750	+	6.26315i	−1.35094	+	0.576570i
$119$	0.0352317	+	0.00944032i	0.00322969	+	0.000865393i
$120$	15.9956	−	0.245133i	1.46019	−	0.0223774i
$121$	−6.93522	+	1.85829i	−0.630475	+	0.168935i
$122$	−12.0758	+	9.47282i	−1.09329	+	0.857629i
$123$	0.0698946	+	0.177066i	0.00630218	+	0.0159655i
$124$	−0.963775	−	1.58984i	−0.0865495	−	0.142772i
$125$	−2.00110	+	0.828883i	−0.178984	+	0.0741375i
$126$	0.178962	+	0.0523513i	0.0159432	+	0.00466382i
$127$			3.51345i			0.311769i	0.987775	+	0.155884i	$0.0498227\pi$
$127$			3.51345i			0.311769i	−0.987775	+	0.155884i	$0.950177\pi$
$128$	−2.10325	+	11.1165i	−0.185903	+	0.982568i
$129$	15.2782	−	3.82092i	1.34517	−	0.336413i
$130$	8.59664	−	2.40222i	0.753975	−	0.210688i
$131$	2.03095	+	0.267380i	0.177445	+	0.0233611i	0.218725	−	0.975787i	$-0.429810\pi$
$131$	2.03095	+	0.267380i	0.177445	+	0.0233611i	−0.0412799	+	0.999148i	$0.513144\pi$
$132$	−1.72203	+	6.54799i	−0.149883	+	0.569929i
$133$	0.0394703	+	0.299807i	0.00342251	+	0.0259965i
$134$	0.0946538	−	0.235605i	0.00817685	−	0.0203532i
$135$	−9.21077	+	14.2503i	−0.792737	+	1.22647i
$136$	−1.71219	−	1.60578i	−0.146819	−	0.137694i
$137$	−3.65523	+	13.6415i	−0.312287	+	1.16547i	0.614201	+	0.789149i	$0.289478\pi$
$137$	−3.65523	+	13.6415i	−0.312287	+	1.16547i	−0.926489	+	0.376323i	$0.877188\pi$
$138$	−14.6491	+	1.83850i	−1.24702	+	0.156504i
$139$	10.2956	−	7.90005i	0.873257	−	0.670074i	−0.0716437	−	0.997430i	$-0.522824\pi$
$139$	10.2956	−	7.90005i	0.873257	−	0.670074i	0.944901	+	0.327356i	$0.106158\pi$
$140$	0.0313746	−	0.285312i	0.00265164	−	0.0241133i
$141$	−6.50161	−	8.77327i	−0.547534	−	0.738843i
$142$	9.81959	+	16.5959i	0.824041	+	1.39269i
$143$			3.77775i			0.315911i
$144$	−8.56361	−	8.40623i	−0.713634	−	0.700519i
$145$			16.2614i			1.35043i
$146$	10.1333	−	5.99577i	0.838639	−	0.496213i
$147$	−4.82528	+	11.1192i	−0.397982	+	0.917092i
$148$	−10.4148	−	12.9884i	−0.856095	−	1.06764i
$149$	−7.16140	+	5.49514i	−0.586685	+	0.450179i	−0.858962	−	0.512040i	$-0.828890\pi$
$149$	−7.16140	+	5.49514i	−0.586685	+	0.450179i	0.272277	+	0.962219i	$0.412223\pi$
$150$	12.7839	+	5.38610i	1.04380	+	0.439773i
$151$	3.76889	−	14.0657i	0.306708	−	1.14465i	−0.624757	−	0.780819i	$-0.714802\pi$
$151$	3.76889	−	14.0657i	0.306708	−	1.14465i	0.931465	−	0.363831i	$-0.118531\pi$
$152$	6.86720	−	18.2090i	0.557003	−	1.47695i
$153$	2.42514	−	0.563548i	0.196061	−	0.0455602i
$154$	0.112724	+	0.0452867i	0.00908358	+	0.00364931i
$155$	−0.396213	−	3.00953i	−0.0318246	−	0.241732i
$156$	−5.81396	−	3.32084i	−0.465489	−	0.265880i
$157$	17.2201	+	2.26707i	1.37432	+	0.180932i	0.781248	−	0.624221i	$-0.214583\pi$
$157$	17.2201	+	2.26707i	1.37432	+	0.180932i	0.593068	+	0.805153i	$0.297917\pi$
$158$	−5.57778	−	19.9608i	−0.443744	−	1.58800i
$159$	0.441818	−	1.54498i	0.0350384	−	0.122525i
$160$	−10.4465	+	15.2347i	−0.825865	+	1.20441i
$161$			0.264902i			0.0208772i
$162$	12.4600	−	2.59770i	0.978951	−	0.204094i
$163$	−13.7314	+	5.68773i	−1.07553	+	0.445498i	−0.848938	−	0.528493i	$-0.822757\pi$
$163$	−13.7314	+	5.68773i	−1.07553	+	0.445498i	−0.226589	+	0.973990i	$0.572757\pi$
$164$	−0.213488	−	0.0523404i	−0.0166706	−	0.00408710i
$165$	−6.87549	+	8.65639i	−0.535256	+	0.673899i
$166$	6.74982	+	8.60455i	0.523887	+	0.667843i
$167$	−14.5179	+	3.89005i	−1.12343	+	0.301021i	−0.772269	−	0.635296i	$-0.780878\pi$
$167$	−14.5179	+	3.89005i	−1.12343	+	0.301021i	−0.351157	+	0.936317i	$0.614212\pi$
$168$	−0.168787	+	0.133673i	−0.0130222	+	0.0103131i
$169$	8.94849	+	2.39774i	0.688345	+	0.184442i
$170$	−1.50444	−	3.52501i	−0.115385	−	0.270356i
$171$	12.0106	+	16.7873i	0.918473	+	1.28376i
$172$	−6.59848	+	16.9457i	−0.503129	+	1.29210i
$173$	−6.79944	+	8.86121i	−0.516952	+	0.673705i	−0.976766	−	0.214310i	$-0.931250\pi$
$173$	−6.79944	+	8.86121i	−0.516952	+	0.673705i	0.459814	+	0.888015i	$0.347916\pi$
$174$	8.67727	−	8.57291i	0.657823	−	0.649911i
$175$	0.124450	−	0.215553i	0.00940752	−	0.0162943i
$176$	−5.02005	−	5.99343i	−0.378400	−	0.451772i
$177$	13.5848	+	14.0473i	1.02110	+	1.05586i
$178$	16.8754	−	9.98501i	1.26487	−	0.748408i
$179$	−14.2382	+	5.89766i	−1.06421	+	0.440811i	−0.844945	−	0.534853i	$-0.820367\pi$
$179$	−14.2382	+	5.89766i	−1.06421	+	0.440811i	−0.219268	+	0.975665i	$0.570367\pi$
$180$	−7.27828	−	18.1908i	−0.542491	−	1.35586i
$181$	8.12586	−	19.6176i	0.603990	−	1.45816i	−0.265451	−	0.964124i	$-0.585521\pi$
$181$	8.12586	−	19.6176i	0.603990	−	1.45816i	0.869441	−	0.494037i	$-0.164479\pi$
$182$	−0.0721099	+	0.0960844i	−0.00534514	+	0.00712225i
$183$	16.1194	+	9.66978i	1.19158	+	0.714811i
$184$	8.04638	−	15.0297i	0.593187	−	1.10800i
$185$	−7.03531	−	26.2561i	−0.517246	−	1.93039i
$186$	−1.39705	+	1.79804i	−0.102436	+	0.131838i
$187$	1.60821	−	0.211725i	0.117604	−	0.0154829i
$188$	12.6062	−	0.269484i	0.919400	−	0.0196541i
$189$	−0.0184068	−	0.227626i	−0.00133890	−	0.0165573i
$190$	22.2266	−	22.7068i	1.61249	−	1.64732i
$191$	−6.41903	−	11.1181i	−0.464465	−	0.804477i	0.534712	−	0.845034i	$-0.320420\pi$
$191$	−6.41903	−	11.1181i	−0.464465	−	0.804477i	−0.999177	+	0.0405575i	$0.987087\pi$
$192$	13.6368	−	2.45731i	0.984149	−	0.177341i
$193$	0.0443081	−	0.0767438i	0.00318937	−	0.00552414i	−0.864426	−	0.502760i	$-0.832318\pi$
$193$	0.0443081	−	0.0767438i	0.00318937	−	0.00552414i	0.867616	+	0.497235i	$0.165651\pi$
$194$	6.86834	+	24.5792i	0.493118	+	1.76468i
$195$	−6.50891	−	8.78312i	−0.466113	−	0.628973i
$196$	−7.25552	−	11.9687i	−0.518252	−	0.854906i
$197$	6.14152	−	14.8269i	0.437565	−	1.05638i	−0.539222	−	0.842164i	$-0.681282\pi$
$197$	6.14152	−	14.8269i	0.437565	−	1.05638i	0.976787	−	0.214212i	$-0.0687184\pi$
$198$	8.24389	−	0.894758i	0.585868	−	0.0635877i
$199$	9.42883	−	9.42883i	0.668392	−	0.668392i	−0.288952	−	0.957344i	$-0.593307\pi$
$199$	9.42883	−	9.42883i	0.668392	−	0.668392i	0.957344	+	0.288952i	$0.0933068\pi$
$200$	−13.6083	+	8.44967i	−0.962254	+	0.597482i
$201$	−0.310929	−	0.00520449i	−0.0219312	−	0.000367096i
$202$	13.9274	+	1.68236i	0.979926	+	0.118370i
$203$	−0.133233	−	0.173633i	−0.00935115	−	0.0121867i
$204$	−1.08786	+	2.66116i	−0.0761653	+	0.186318i
$205$	−0.284728	−	0.218480i	−0.0198863	−	0.0152593i
$206$	−0.0265570	−	2.48490i	−0.00185031	−	0.173132i
$207$	8.51194	+	15.9534i	0.591621	+	1.10884i
$208$	7.00986	−	3.26120i	0.486046	−	0.226123i
$209$	6.72399	+	11.6463i	0.465108	+	0.805591i
$210$	−0.340107	+	0.0889295i	−0.0234696	+	0.00613672i
$211$	−8.36721	−	1.10156i	−0.576023	−	0.0758348i	−0.163114	−	0.986607i	$-0.552154\pi$
$211$	−8.36721	−	1.10156i	−0.576023	−	0.0758348i	−0.412909	+	0.910772i	$0.635487\pi$
$212$	1.16076	+	1.44759i	0.0797213	+	0.0994209i
$213$	14.6888	−	18.4935i	1.00646	−	1.26716i
$214$	−6.26543	+	8.34851i	−0.428296	+	0.570692i
$215$	−20.9950	+	20.9950i	−1.43185	+	1.43185i
$216$	−5.86978	+	13.4739i	−0.399388	+	0.916782i
$217$	0.0288885	+	0.0288885i	0.00196108	+	0.00196108i
$218$	−14.7324	+	2.09996i	−0.997803	+	0.142227i
$219$	−11.2920	−	8.96887i	−0.763043	−	0.606060i
$220$	−3.56654	−	12.2564i	−0.240456	−	0.826329i
$221$	−0.209376	+	1.59037i	−0.0140842	+	0.106980i
$222$	−10.3016	+	17.5962i	−0.691401	+	1.18098i
$223$	−4.43724	+	2.56184i	−0.297140	+	0.171554i	−0.641157	−	0.767410i	$-0.721545\pi$
$223$	−4.43724	+	2.56184i	−0.297140	+	0.171554i	0.344017	+	0.938963i	$0.388212\pi$
$224$	−0.0132784	−	0.248262i	−0.000887201	−	0.0165877i
$225$	0.568612	−	16.9804i	0.0379075	−	1.13202i
$226$	16.2107	−	16.5609i	1.07832	−	1.10162i
$227$	−12.3049	+	16.0361i	−0.816708	+	1.06435i	0.180031	+	0.983661i	$0.442380\pi$
$227$	−12.3049	+	16.0361i	−0.816708	+	1.06435i	−0.996739	+	0.0806936i	$0.974286\pi$
$228$	−23.8344	+	0.110518i	−1.57847	+	0.00731924i
$229$	16.8325	−	12.9160i	1.11232	−	0.853514i	0.122030	−	0.992526i	$-0.461059\pi$
$229$	16.8325	−	12.9160i	1.11232	−	0.853514i	0.990291	+	0.139012i	$0.0443928\pi$
$230$	21.9006	−	17.1799i	1.44408	−	1.13281i
$231$	0.00249007	−	0.148763i	0.000163834	−	0.00978785i
$232$	2.28515	+	13.8984i	0.150027	+	0.912472i
$233$	−4.42491	−	4.42491i	−0.289885	−	0.289885i	0.547150	−	0.837035i	$-0.315713\pi$
$233$	−4.42491	−	4.42491i	−0.289885	−	0.289885i	−0.837035	+	0.547150i	$0.815713\pi$
$234$	−1.25532	+	8.10366i	−0.0820631	+	0.529753i
$235$	19.0201	+	7.87840i	1.24074	+	0.513930i
$236$	−22.3036	+	3.42274i	−1.45184	+	0.222802i
$237$	−20.3938	+	15.1132i	−1.32472	+	0.981710i
$238$	0.0449451	+	0.0253126i	0.00291336	+	0.00164077i
$239$	13.2506	+	7.65022i	0.857108	+	0.494852i	0.863043	−	0.505131i	$-0.168556\pi$
$239$	13.2506	+	7.65022i	0.857108	+	0.494852i	−0.00593456	+	0.999982i	$0.501889\pi$
$240$	21.9978	+	5.28515i	1.41996	+	0.341155i
$241$	−0.640516	+	0.369802i	−0.0412593	+	0.0238211i	−0.520488	−	0.853869i	$-0.674250\pi$
$241$	−0.640516	+	0.369802i	−0.0412593	+	0.0238211i	0.479228	+	0.877690i	$0.340917\pi$
$242$	−10.1533	+	0.108512i	−0.652678	+	0.00697539i
$243$	−8.42271	−	13.1171i	−0.540317	−	0.841462i
$244$	−19.8709	+	8.73292i	−1.27211	+	0.559068i
$245$	−2.98278	−	22.6565i	−0.190563	−	1.44747i
$246$	0.0335237	+	0.267116i	0.00213740	+	0.0170307i
$247$	−12.8456	+	3.44198i	−0.817349	+	0.219008i
$248$	−0.761556	−	2.51653i	−0.0483589	−	0.159800i
$249$	6.89016	−	11.4858i	0.436646	−	0.727882i
$250$	−3.03250	+	0.432254i	−0.191792	+	0.0273381i
$251$	−13.3530	−	5.53099i	−0.842833	−	0.349113i	−0.0808630	−	0.996725i	$-0.525768\pi$
$251$	−13.3530	−	5.53099i	−0.842833	−	0.349113i	−0.761970	+	0.647612i	$0.775768\pi$
$252$	0.226757	+	0.134602i	0.0142843	+	0.00847915i
$253$	4.50825	+	10.8839i	0.283431	+	0.684264i
$254$	−1.23465	+	4.81294i	−0.0774688	+	0.301990i
$255$	−3.37424	+	3.26314i	−0.211303	+	0.204345i
$256$	−6.78756	+	14.4889i	−0.424223	+	0.905558i
$257$	10.9376	+	6.31485i	0.682271	+	0.393910i	0.800710	−	0.599052i	$-0.204456\pi$
$257$	10.9376	+	6.31485i	0.682271	+	0.393910i	−0.118439	+	0.992961i	$0.537789\pi$
$258$	22.2717	+	0.134746i	1.38658	+	0.00838895i
$259$	0.290244	+	0.222712i	0.0180349	+	0.0138386i
$260$	12.6203	−	0.269786i	0.782680	−	0.0167314i
$261$	−13.6031	−	6.17577i	−0.842011	−	0.382271i
$262$	2.68816	+	1.07996i	0.166075	+	0.0667203i
$263$	−0.0292140	+	0.109028i	−0.00180141	+	0.00672296i	−0.966821	−	0.255456i	$-0.917774\pi$
$263$	−0.0292140	+	0.109028i	−0.00180141	+	0.00672296i	0.965019	+	0.262179i	$0.0844411\pi$
$264$	−4.65994	+	8.36469i	−0.286799	+	0.514811i
$265$	0.784103	+	2.92631i	0.0481671	+	0.179762i
$266$	−0.0512852	+	0.424563i	−0.00314450	+	0.0260316i
$267$	−18.8051	−	14.9362i	−1.15085	−	0.914083i
$268$	0.212456	−	0.289484i	0.0129778	−	0.0176830i
$269$	2.21983	+	5.35915i	0.135346	+	0.326753i	0.976992	−	0.213276i	$-0.0684133\pi$
$269$	2.21983	+	5.35915i	0.135346	+	0.326753i	−0.841646	+	0.540029i	$0.818413\pi$
$270$	−17.6251	+	16.2842i	−1.07263	+	0.991023i
$271$	15.2679			0.927461			0.463731	−	0.885976i	$-0.346511\pi$
$271$	15.2679			0.927461			0.463731	+	0.885976i	$0.346511\pi$
$272$	−1.78118	−	2.80136i	−0.108000	−	0.169858i
$273$	0.141462	+	0.0404540i	0.00856168	+	0.00244839i
$274$	−9.80085	+	17.4025i	−0.592091	+	1.05132i
$275$	1.44479	−	10.9743i	0.0871243	−	0.661775i
$276$	−20.7133	−	2.62931i	−1.24679	−	0.158266i
$277$	4.65221	−	0.612476i	0.279524	−	0.0368001i	0.0105394	−	0.999944i	$-0.496645\pi$
$277$	4.65221	−	0.612476i	0.279524	−	0.0368001i	0.268985	+	0.963144i	$0.413312\pi$
$278$	16.8796	−	7.20404i	1.01237	−	0.432070i
$279$	2.66804	+	0.811524i	0.159731	+	0.0485846i
$280$	0.143239	−	0.379812i	0.00856018	−	0.0226981i
$281$	−9.31303	−	2.49542i	−0.555569	−	0.148864i	−0.0298990	−	0.999553i	$-0.509519\pi$
$281$	−9.31303	−	2.49542i	−0.555569	−	0.148864i	−0.525670	+	0.850689i	$0.676185\pi$
$282$	−5.82331	−	14.3028i	−0.346773	−	0.851722i
$283$	9.76968	+	12.7321i	0.580747	+	0.756844i	0.987658	−	0.156623i	$-0.0500609\pi$
$283$	9.76968	+	12.7321i	0.580747	+	0.756844i	−0.406911	+	0.913468i	$0.633394\pi$
$284$	7.61956	+	26.1847i	0.452138	+	1.55377i
$285$	−35.6991	−	15.4920i	−2.11463	−	0.917668i
$286$	−1.32752	+	5.17498i	−0.0784982	+	0.306003i
$287$	0.00483029			0.000285123
$288$	−8.77693	−	14.5246i	−0.517186	−	0.855873i
$289$	−16.3112			−0.959484
$290$	−5.71434	+	22.2758i	−0.335558	+	1.30808i
$291$	25.1124	−	18.6101i	1.47212	−	1.09094i
$292$	15.9882	−	4.65245i	0.935636	−	0.272264i
$293$	−2.39828	−	3.12551i	−0.140109	−	0.182594i	0.718028	−	0.696014i	$-0.245045\pi$
$293$	−2.39828	−	3.12551i	−0.140109	−	0.182594i	−0.858137	+	0.513420i	$0.828378\pi$
$294$	−10.5173	+	13.5360i	−0.613381	+	0.789438i
$295$	−35.5868	−	9.53546i	−2.07194	−	0.555176i
$296$	−9.70267	−	21.4521i	−0.563956	−	1.24688i
$297$	−4.63014	−	9.03909i	−0.268668	−	0.524501i
$298$	−11.7411	+	5.01100i	−0.680146	+	0.290279i
$299$	−11.5503	+	1.52062i	−0.667970	+	0.0879399i
$300$	15.6194	+	11.8705i	0.901787	+	0.685345i
$301$	0.0521601	−	0.396195i	0.00300646	−	0.0228363i
$302$	10.1056	−	17.9436i	0.581513	−	1.03254i
$303$	−4.16851	−	16.6681i	−0.239475	−	0.957559i
$304$	15.8059	−	22.5306i	0.906528	−	1.29222i
$305$	−35.4389			−2.02923
$306$	3.52013	+	0.0802272i	0.201233	+	0.00458628i
$307$	1.76033	+	4.24981i	0.100467	+	0.242550i	0.966119	−	0.258097i	$-0.0830955\pi$
$307$	1.76033	+	4.24981i	0.100467	+	0.242550i	−0.865652	+	0.500647i	$0.833095\pi$
$308$	0.138502	+	0.101648i	0.00789190	+	0.00579196i
$309$	−2.83097	+	1.11749i	−0.161048	+	0.0635719i
$310$	0.514813	−	4.26187i	0.0292394	−	0.242058i
$311$	1.37536	+	5.13290i	0.0779893	+	0.291060i	0.993894	−	0.110335i	$-0.0351923\pi$
$311$	1.37536	+	5.13290i	0.0779893	+	0.291060i	−0.915905	+	0.401395i	$0.868526\pi$
$312$	−6.79734	−	6.59215i	−0.384824	−	0.373207i
$313$	−2.67793	+	9.99418i	−0.151366	+	0.564905i	0.848023	+	0.529959i	$0.177793\pi$
$313$	−2.67793	+	9.99418i	−0.151366	+	0.564905i	−0.999389	+	0.0349459i	$0.988874\pi$
$314$	22.7925	+	9.15683i	1.28625	+	0.516750i
$315$	0.250523	+	0.350157i	0.0141153	+	0.0197291i
$316$	−0.626425	−	29.3035i	−0.0352391	−	1.64845i
$317$	17.6724	+	13.5605i	0.992580	+	0.761633i	0.971231	−	0.238139i	$-0.0765373\pi$
$317$	17.6724	+	13.5605i	0.992580	+	0.761633i	0.0213488	+	0.999772i	$0.493204\pi$
$318$	1.14814	−	1.96114i	0.0643847	−	0.109976i
$319$	−8.42909	−	4.86654i	−0.471938	−	0.272474i
$320$	−19.6637	+	17.1985i	−1.09924	+	0.961425i
$321$	12.2913	+	3.51493i	0.686031	+	0.196185i
$322$	−0.0930880	+	0.362878i	−0.00518759	+	0.0202224i
$323$	2.18521	+	5.27557i	0.121588	+	0.293540i
$324$	17.9813	+	0.820048i	0.998962	+	0.0455582i
$325$	10.1130	+	4.18893i	0.560967	+	0.232360i
$326$	−20.8088	+	2.96609i	−1.15249	+	0.164277i
$327$	8.84746	+	15.9343i	0.489265	+	0.881169i
$328$	−0.274056	−	0.146720i	−0.0151322	−	0.00810125i
$329$	−0.267640	+	0.0717139i	−0.0147555	+	0.00395372i
$330$	−12.4604	+	9.44195i	−0.685920	+	0.519762i
$331$	0.346909	+	2.63504i	0.0190678	+	0.144835i	0.998330	−	0.0577602i	$-0.0183959\pi$
$331$	0.346909	+	2.63504i	0.0190678	+	0.144835i	−0.979263	+	0.202595i	$0.935063\pi$
$332$	6.22260	+	14.1589i	0.341510	+	0.777073i
$333$	24.6359	+	4.08637i	1.35004	+	0.223931i
$334$	−21.2544	+	0.227153i	−1.16299	+	0.0124293i
$335$	0.507735	−	0.293141i	0.0277405	−	0.0160160i
$336$	−0.278188	+	0.123801i	−0.0151764	+	0.00675389i
$337$	−16.6902	−	9.63607i	−0.909172	−	0.524910i	−0.0290070	−	0.999579i	$-0.509235\pi$
$337$	−16.6902	−	9.63607i	−0.909172	−	0.524910i	−0.880164	+	0.474669i	$0.842568\pi$
$338$	11.4156	+	6.42912i	0.620926	+	0.349698i
$339$	−26.0367	−	11.2989i	−1.41412	−	0.613673i
$340$	−0.822160	−	5.35743i	−0.0445879	−	0.290548i
$341$	1.67857	+	0.695286i	0.0908996	+	0.0376518i
$342$	10.5537	+	27.2168i	0.570676	+	1.47172i
$343$	0.435019	+	0.435019i	0.0234888	+	0.0234888i
$344$	−14.9938	+	20.8945i	−0.808413	+	1.12656i
$345$	−29.2340	−	17.5371i	−1.57391	−	0.944165i
$346$	−12.4282	+	9.74924i	−0.668142	+	0.524122i
$347$	−18.3995	+	14.1185i	−0.987739	+	0.757919i	−0.970294	−	0.241929i	$-0.922220\pi$
$347$	−18.3995	+	14.1185i	−0.987739	+	0.757919i	−0.0174453	+	0.999848i	$0.505553\pi$
$348$	14.8992	−	8.69443i	0.798682	−	0.466070i
$349$	−2.40758	+	3.13762i	−0.128875	+	0.167953i	−0.853334	−	0.521365i	$-0.825423\pi$
$349$	−2.40758	+	3.13762i	−0.128875	+	0.167953i	0.724459	+	0.689318i	$0.242090\pi$
$350$	0.246225	−	0.251545i	0.0131613	−	0.0134457i
$351$	9.81931	−	2.10922i	0.524116	−	0.112582i
$352$	−4.77063	−	9.97423i	−0.254275	−	0.531628i
$353$	10.6169	−	6.12969i	0.565082	−	0.326250i	−0.190101	−	0.981765i	$-0.560881\pi$
$353$	10.6169	−	6.12969i	0.565082	−	0.326250i	0.755183	+	0.655514i	$0.227548\pi$
$354$	13.6730	+	24.0166i	0.726709	+	1.27647i
$355$	−5.81180	+	44.1450i	−0.308458	+	2.34297i
$356$	26.6258	−	7.74792i	1.41116	−	0.410639i
$357$	0.00929322	−	0.0624886i	0.000491850	−	0.00330725i
$358$	−21.5768	+	3.07557i	−1.14037	+	0.162549i
$359$	−22.5779	−	22.5779i	−1.19161	−	1.19161i	−0.976614	−	0.215000i	$-0.931025\pi$
$359$	−22.5779	−	22.5779i	−1.19161	−	1.19161i	−0.215000	−	0.976614i	$-0.568975\pi$
$360$	−3.57785	−	27.4765i	−0.188569	−	1.44814i
$361$	−20.0400	+	20.0400i	−1.05474	+	1.05474i
$362$	18.0250	−	24.0178i	0.947373	−	1.26235i
$363$	4.56606	+	11.5673i	0.239656	+	0.607127i
$364$	−0.132545	+	0.106282i	−0.00694725	+	0.00557070i
$365$	26.9546	+	3.54864i	1.41087	+	0.185744i
$366$	18.6832	+	18.9107i	0.976588	+	0.988477i
$367$	3.87237	+	6.70715i	0.202136	+	0.350110i	0.949217	−	0.314624i	$-0.101878\pi$
$367$	3.87237	+	6.70715i	0.202136	+	0.350110i	−0.747080	+	0.664734i	$0.768545\pi$
$368$	16.3039	−	17.7610i	0.849901	−	0.925857i
$369$	0.290900	−	0.155209i	0.0151436	−	0.00807986i
$370$	−0.410815	−	38.4395i	−0.0213573	−	1.99837i
$371$	−0.0323484	−	0.0248218i	−0.00167944	−	0.00128868i
$372$	−2.54560	+	1.97213i	−0.131983	+	0.102250i
$373$	−5.02837	−	6.55309i	−0.260359	−	0.339306i	0.644822	−	0.764333i	$-0.276931\pi$
$373$	−5.02837	−	6.55309i	−0.260359	−	0.339306i	−0.905181	+	0.425026i	$0.860265\pi$
$374$	2.27742	+	0.275102i	0.117763	+	0.0142252i
$375$	1.82115	+	3.27990i	0.0940439	+	0.169373i
$376$	17.3634	+	4.06073i	0.895448	+	0.209416i
$377$	6.80597	−	6.80597i	0.350526	−	0.350526i
$378$	0.0547744	−	0.318283i	0.00281729	−	0.0163707i
$379$	−0.908381	+	2.19302i	−0.0466604	+	0.112648i	−0.945491	−	0.325648i	$-0.894418\pi$
$379$	−0.908381	+	2.19302i	−0.0466604	+	0.112648i	0.898831	+	0.438296i	$0.144418\pi$
$380$	38.4266	−	23.2946i	1.97124	−	1.19499i
$381$	6.04587	−	0.693227i	0.309739	−	0.0355151i
$382$	−4.88620	−	17.4859i	−0.250000	−	0.894656i
$383$	5.86455	−	10.1577i	0.299664	−	0.519034i	−0.676395	−	0.736539i	$-0.736459\pi$
$383$	5.86455	−	10.1577i	0.299664	−	0.519034i	0.976059	+	0.217505i	$0.0697920\pi$
$384$	19.5440	+	1.42587i	0.997349	+	0.0727638i
$385$	0.140252	+	0.242924i	0.00714791	+	0.0123805i
$386$	0.0876641	−	0.0895581i	0.00446198	−	0.00455839i
$387$	−9.58943	−	25.5365i	−0.487458	−	1.29809i
$388$	0.771364	+	36.0836i	0.0391601	+	1.83187i
$389$	16.4521	−	2.16596i	0.834153	−	0.109818i	0.298662	−	0.954359i	$-0.403460\pi$
$389$	16.4521	−	2.16596i	0.834153	−	0.109818i	0.535491	+	0.844541i	$0.320126\pi$
$390$	−5.82985	−	14.3189i	−0.295206	−	0.725066i
$391$	1.29468	+	4.83180i	0.0654746	+	0.244355i
$392$	−5.73318	−	18.9450i	−0.289569	−	0.956869i
$393$	0.0593811	−	3.54757i	0.00299538	−	0.178951i
$394$	13.6233	−	18.1526i	0.686332	−	0.914517i
$395$	18.3136	−	44.2130i	0.921459	−	2.22460i
$396$	11.6074	+	1.67126i	0.583293	+	0.0839840i
$397$	−11.3617	+	4.70618i	−0.570229	+	0.236197i	−0.649119	−	0.760687i	$-0.724862\pi$
$397$	−11.3617	+	4.70618i	−0.570229	+	0.236197i	0.0788901	+	0.996883i	$0.474862\pi$
$398$	16.2295	−	9.60281i	0.813512	−	0.481346i
$399$	0.508113	−	0.127073i	0.0254374	−	0.00636162i
$400$	−21.6108	+	6.79281i	−1.08054	+	0.339641i
$401$	−5.98123	+	10.3598i	−0.298688	+	0.517343i	−0.975836	−	0.218504i	$-0.929882\pi$
$401$	−5.98123	+	10.3598i	−0.298688	+	0.517343i	0.677148	+	0.735847i	$0.263216\pi$
$402$	−0.424099	−	0.116392i	−0.0211522	−	0.00580509i
$403$	−1.09377	+	1.42543i	−0.0544846	+	0.0710057i
$404$	18.4873	+	7.19876i	0.919779	+	0.358152i
$405$	26.3389	+	13.0380i	1.30879	+	0.647863i
$406$	−0.121495	−	0.284672i	−0.00602970	−	0.0141280i
$407$	15.7153	+	4.21092i	0.778981	+	0.208727i
$408$	−2.42536	+	3.26313i	−0.120073	+	0.161549i
$409$	15.0424	−	4.03059i	0.743798	−	0.199300i	0.133033	−	0.991112i	$-0.457529\pi$
$409$	15.0424	−	4.03059i	0.743798	−	0.199300i	0.610765	+	0.791812i	$0.290862\pi$
$410$	−0.313263	−	0.399342i	−0.0154709	−	0.0197221i
$411$	24.1952	+	3.59827i	1.19346	+	0.177490i
$412$	0.836831	−	3.41330i	0.0412277	−	0.168161i
$413$	0.458110	−	0.189755i	0.0225421	−	0.00933725i
$414$	6.05401	+	24.8451i	0.297539	+	1.22107i
$415$			25.2519i			1.23956i
$416$	10.7485	−	2.00407i	0.526989	−	0.0982577i
$417$	−15.6256	−	16.1576i	−0.765189	−	0.791241i
$418$	5.11834	+	18.3166i	0.250346	+	0.895895i
$419$	25.8380	+	3.40163i	1.26227	+	0.166181i	0.731797	−	0.681523i	$-0.238682\pi$
$419$	25.8380	+	3.40163i	1.26227	+	0.166181i	0.530470	+	0.847704i	$0.322015\pi$
$420$	−0.497149	+	0.00230524i	−0.0242584	+	0.000112484i
$421$	−2.12525	−	16.1429i	−0.103578	−	0.786756i	−0.961853	−	0.273566i	$-0.911797\pi$
$421$	−2.12525	−	16.1429i	−0.103578	−	0.786756i	0.858275	−	0.513190i	$-0.171536\pi$
$422$	−11.0748	−	4.44928i	−0.539113	−	0.216587i
$423$	−13.8140	+	12.9188i	−0.671661	+	0.628135i
$424$	1.08139	+	2.39089i	0.0525167	+	0.116112i
$425$	1.21647	−	4.53993i	0.0590074	−	0.220219i
$426$	26.6203	−	20.1718i	1.28976	−	0.977326i
$427$	0.378405	−	0.290360i	0.0183123	−	0.0140515i
$428$	−11.5165	+	9.23457i	−0.556670	+	0.446370i
$429$	6.50066	−	0.745374i	0.313855	−	0.0359870i
$430$	−36.1380	+	21.3825i	−1.74273	+	1.03115i
$431$			1.28136i			0.0617207i	0.999524	+	0.0308604i	$0.00982472\pi$
$431$			1.28136i			0.0617207i	−0.999524	+	0.0308604i	$0.990175\pi$
$432$	−12.7756	+	16.3947i	−0.614665	+	0.788788i
$433$		−	38.2898i		−	1.84009i	−0.391815	−	0.920044i	$-0.628153\pi$
$433$		−	38.2898i		−	1.84009i	0.391815	−	0.920044i	$-0.371847\pi$
$434$	0.0294216	+	0.0497247i	0.00141228	+	0.00238686i
$435$	27.9822	−	3.20847i	1.34164	−	0.153834i
$436$	−20.9192	−	2.30040i	−1.00185	−	0.110169i
$437$	−32.9014	+	25.2461i	−1.57389	+	1.20769i
$438$	−12.3167	−	16.2542i	−0.588517	−	0.776654i
$439$	0.237258	−	0.885457i	0.0113237	−	0.0422606i	−0.960033	−	0.279887i	$-0.909703\pi$
$439$	0.237258	−	0.885457i	0.0113237	−	0.0422606i	0.971357	+	0.237627i	$0.0763695\pi$
$440$	−0.578668	−	18.0429i	−0.0275869	−	0.860162i
$441$	20.0856	+	6.10934i	0.956459	+	0.290921i
$442$	−0.845682	+	2.10501i	−0.0402250	+	0.100125i
$443$	2.83987	+	21.5709i	0.134926	+	1.02487i	0.916212	+	0.400693i	$0.131231\pi$
$443$	2.83987	+	21.5709i	0.134926	+	1.02487i	−0.781286	+	0.624173i	$0.785436\pi$
$444$	−20.2952	+	20.4843i	−0.963169	+	0.972143i
$445$	44.8887	+	5.90971i	2.12793	+	0.280147i
$446$	−6.97865	+	1.95009i	−0.330448	+	0.0923394i
$447$	10.8689	+	11.2389i	0.514081	+	0.531584i
$448$	0.0690511	−	0.344749i	0.00326236	−	0.0162879i
$449$			36.1061i			1.70395i	0.523582	+	0.851976i	$0.324596\pi$
$449$			36.1061i			1.70395i	−0.523582	+	0.851976i	$0.675404\pi$
$450$	6.74593	−	23.0609i	0.318006	−	1.08710i
$451$	0.198460	−	0.0822048i	0.00934511	−	0.00387087i
$452$	28.0260	−	16.9896i	1.31823	−	0.799124i
$453$	−24.9475	−	3.71017i	−1.17214	−	0.174319i
$454$	−22.4912	+	17.6432i	−1.05557	+	0.828036i
$455$	−0.267941	+	0.0717945i	−0.0125612	+	0.00336578i
$456$	−32.6886	−	8.22416i	−1.53078	−	0.385131i
$457$	−11.3587	−	3.04354i	−0.531336	−	0.142371i	−0.0168307	−	0.999858i	$-0.505358\pi$
$457$	−11.3587	−	3.04354i	−0.531336	−	0.142371i	−0.514505	+	0.857487i	$0.672024\pi$
$458$	27.5969	−	11.7781i	1.28952	−	0.550353i
$459$	−1.44824	−	4.06193i	−0.0675979	−	0.189595i
$460$	36.0379	−	15.8380i	1.68027	−	0.738450i
$461$	16.7934	−	21.8856i	0.782146	−	1.01931i	−0.216923	−	0.976189i	$-0.569602\pi$
$461$	16.7934	−	21.8856i	0.782146	−	1.01931i	0.999070	−	0.0431243i	$-0.0137312\pi$
$462$	0.0556871	−	0.202909i	0.00259080	−	0.00944016i
$463$	3.29312	−	5.70386i	0.153044	−	0.265081i	−0.779301	−	0.626650i	$-0.784426\pi$
$463$	3.29312	−	5.70386i	0.153044	−	0.265081i	0.932345	+	0.361569i	$0.117759\pi$
$464$	−1.75364	+	19.8418i	−0.0814107	+	0.921133i
$465$	−5.10056	+	1.27559i	−0.236533	+	0.0591542i
$466$	−4.50656	−	7.61644i	−0.208762	−	0.352825i
$467$	−16.4088	+	6.79674i	−0.759308	+	0.314516i	−0.728533	−	0.685011i	$-0.759798\pi$
$467$	−16.4088	+	6.79674i	−0.759308	+	0.314516i	−0.0307749	+	0.999526i	$0.509798\pi$
$468$	−4.56729	+	10.6597i	−0.211123	+	0.492747i
$469$	−0.00301964	+	0.00729006i	−0.000139434	+	0.000336624i
$470$	23.2864	+	17.4761i	1.07412	+	0.806112i
$471$	0.503483	−	30.0793i	0.0231993	−	1.38598i
$472$	−31.7556	−	3.14895i	−1.46167	−	0.144942i
$473$	−4.59961	−	17.1660i	−0.211490	−	0.789293i
$474$	−33.2475	+	13.5365i	−1.52711	+	0.621752i
$475$	38.6328	−	5.08610i	1.77259	−	0.233366i
$476$	0.0526735	+	0.0504686i	0.00241429	+	0.00231323i
$477$	−2.74574	−	0.455436i	−0.125719	−	0.0208530i
$478$	15.4631	+	15.1361i	0.707265	+	0.692307i
$479$	8.08524	+	14.0040i	0.369424	+	0.639861i	0.989476	−	0.144700i	$-0.0462217\pi$
$479$	8.08524	+	14.0040i	0.369424	+	0.639861i	−0.620052	+	0.784561i	$0.712888\pi$
$480$	28.2767	+	14.9701i	1.29065	+	0.683288i
$481$	−8.04462	+	13.9337i	−0.366803	+	0.635322i
$482$	−1.00737	+	0.281496i	−0.0458843	+	0.0128218i
$483$	0.455836	−	0.0522668i	0.0207413	−	0.00237822i
$484$	−13.9467	−	3.41928i	−0.633941	−	0.155422i
$485$	−22.5510	+	54.4428i	−1.02399	+	2.47212i
$486$	−6.92849	−	20.9284i	−0.314283	−	0.949329i
$487$	7.19888	−	7.19888i	0.326213	−	0.326213i	−0.524932	−	0.851144i	$-0.675909\pi$
$487$	7.19888	−	7.19888i	0.326213	−	0.326213i	0.851144	+	0.524932i	$0.175909\pi$
$488$	−30.2892	+	4.98010i	−1.37113	+	0.225439i
$489$	12.4966	+	22.5064i	0.565116	+	1.01778i
$490$	3.87564	−	32.0844i	0.175083	−	1.44942i
$491$	1.31390	+	1.71231i	0.0592956	+	0.0772755i	0.822060	−	0.569401i	$-0.192825\pi$
$491$	1.31390	+	1.71231i	0.0592956	+	0.0772755i	−0.762764	+	0.646677i	$0.776158\pi$
$492$	−0.0479435	+	0.377692i	−0.00216146	+	0.0170277i
$493$	−3.27879	−	2.51590i	−0.147669	−	0.113311i
$494$	−18.8063	+	0.200989i	−0.846134	+	0.00904291i
$495$	16.2523	+	10.1232i	0.730486	+	0.455005i
$496$	−0.158901	−	3.71491i	−0.00713485	−	0.166804i
$497$	−0.299635	−	0.518982i	−0.0134405	−	0.0232795i
$498$	13.4747	−	13.3127i	0.603817	−	0.596554i
$499$	11.5227	+	1.51700i	0.515829	+	0.0679101i	0.383947	−	0.923355i	$-0.374565\pi$
$499$	11.5227	+	1.51700i	0.515829	+	0.0679101i	0.131882	+	0.991265i	$0.457898\pi$
$500$	−4.30599	−	0.473512i	−0.192570	−	0.0211761i
$501$	9.55837	+	24.2145i	0.427037	+	1.08182i
$502$	−16.3481	−	12.2690i	−0.729651	−	0.547592i
$503$	−10.4320	+	10.4320i	−0.465139	+	0.465139i	−0.900336	−	0.435196i	$-0.856679\pi$
$503$	−10.4320	+	10.4320i	−0.465139	+	0.465139i	0.435196	+	0.900336i	$0.356679\pi$
$504$	0.263325	+	0.264070i	0.0117294	+	0.0117626i
$505$	22.9050	+	22.9050i	1.01926	+	1.01926i
$506$	2.35101	+	16.4936i	0.104515	+	0.733231i
$507$	2.36038	−	15.8714i	0.104828	−	0.704875i
$508$	−3.38259	+	6.15918i	−0.150078	+	0.273269i
$509$	−0.774630	+	5.88390i	−0.0343349	+	0.260799i	0.965665	+	0.259792i	$0.0836540\pi$
$509$	−0.774630	+	5.88390i	−0.0343349	+	0.260799i	−0.999999	+	0.00100728i	$0.999679\pi$
$510$	−5.76891	+	3.28431i	−0.255452	+	0.145432i
$511$	−0.316887	+	0.182955i	−0.0140182	+	0.00809344i
$512$	−14.3895	+	17.4626i	−0.635932	+	0.771745i
$513$	26.5174	−	23.9798i	1.17077	−	1.05873i
$514$	12.7639	+	12.4940i	0.562994	+	0.551087i
$515$	3.49311	−	4.55231i	0.153925	−	0.200599i
$516$	30.4618	+	8.01100i	1.34100	+	0.352665i
$517$	−9.77593	+	7.50133i	−0.429945	+	0.329908i
$518$	0.319331	+	0.407077i	0.0140306	+	0.0178859i
$519$	16.5897	+	9.95195i	0.728208	+	0.436842i
$520$	17.3829	+	4.06529i	0.762290	+	0.178275i
$521$	−14.8417	−	14.8417i	−0.650226	−	0.650226i	0.302821	−	0.953047i	$-0.402071\pi$
$521$	−14.8417	−	14.8417i	−0.650226	−	0.650226i	−0.953047	+	0.302821i	$0.902071\pi$
$522$	−16.4641	−	13.2402i	−0.720616	−	0.579506i
$523$	−1.30351	−	0.539932i	−0.0569986	−	0.0236096i	0.354002	−	0.935245i	$-0.384821\pi$
$523$	−1.30351	−	0.539932i	−0.0569986	−	0.0236096i	−0.411001	+	0.911635i	$0.634821\pi$
$524$	3.30290	+	2.42403i	0.144288	+	0.105894i
$525$	−0.395474	−	0.171620i	−0.0172599	−	0.00749012i
$526$	−0.0783322	+	0.139087i	−0.00341545	+	0.00606449i
$527$	0.668115	+	0.385736i	0.0291035	+	0.0168029i
$528$	−9.32286	+	9.82092i	−0.405725	+	0.427401i
$529$	−11.5437	+	6.66475i	−0.501899	+	0.289772i
$530$	0.0457864	+	4.28417i	0.00198883	+	0.186093i
$531$	21.4919	−	26.1480i	0.932671	−	1.13473i
$532$	−0.219448	+	0.563570i	−0.00951426	+	0.0244338i
$533$	0.0277275	+	0.210611i	0.00120101	+	0.00912258i
$534$	−20.5116	−	27.0688i	−0.887624	−	1.17138i
$535$	−23.2806	+	6.23802i	−1.00651	+	0.269693i
$536$	0.392761	−	0.321894i	0.0169647	−	0.0139037i
$537$	12.9578	+	23.3371i	0.559172	+	1.00707i
$538$	1.15762	+	8.12134i	0.0499085	+	0.350136i
$539$	12.6367	+	5.23428i	0.544300	+	0.225456i
$540$	−29.8663	+	16.1134i	−1.28524	+	0.693412i
$541$	−10.4544	−	25.2393i	−0.449472	−	1.08512i	−0.972520	−	0.232818i	$-0.925205\pi$
$541$	−10.4544	−	25.2393i	−0.449472	−	1.08512i	0.523049	−	0.852303i	$-0.324795\pi$
$542$	20.9149	+	5.36525i	0.898373	+	0.230457i
$543$	−35.3607	−	10.1121i	−1.51747	−	0.433952i
$544$	−1.45555	−	4.46339i	−0.0624062	−	0.191366i
$545$	−29.7579	−	17.1807i	−1.27469	−	0.735941i
$546$	0.179567	+	0.105127i	0.00768478	+	0.00449902i
$547$	−16.8566	−	12.9345i	−0.720734	−	0.553039i	0.181968	−	0.983304i	$-0.441753\pi$
$547$	−16.8566	−	12.9345i	−0.720734	−	0.553039i	−0.902702	+	0.430266i	$0.858420\pi$
$548$	−19.5411	+	20.3948i	−0.834755	+	0.871224i
$549$	13.4591	−	29.6457i	0.574419	−	1.26525i
$550$	5.83560	−	14.5255i	0.248831	−	0.619371i
$551$	8.86799	−	33.0958i	0.377789	−	1.40993i
$552$	−27.4503	−	10.8806i	−1.16836	−	0.463107i
$553$	0.166702	+	0.622139i	0.00708888	+	0.0264561i
$554$	6.58810	+	0.795811i	0.279902	+	0.0338108i
$555$	−43.7928	+	17.2867i	−1.85890	+	0.733780i
$556$	25.6542	−	3.93693i	1.08798	−	0.166963i
$557$	5.95462	+	14.3757i	0.252305	+	0.609119i	0.998389	−	0.0567329i	$-0.0180684\pi$
$557$	5.95462	+	14.3757i	0.252305	+	0.609119i	−0.746084	+	0.665852i	$0.768068\pi$
$558$	3.36966	+	2.04924i	0.142649	+	0.0867512i
$559$	17.5744			0.743317
$560$	0.329686	−	0.469954i	0.0139318	−	0.0198592i
$561$	−0.681642	−	2.72560i	−0.0287789	−	0.115075i
$562$	−11.8806	−	6.69103i	−0.501154	−	0.282244i
$563$	0.199033	−	1.51180i	0.00838823	−	0.0637150i	−0.986739	−	0.162316i	$-0.948104\pi$
$563$	0.199033	−	1.51180i	0.00838823	−	0.0637150i	0.995127	+	0.0986013i	$0.0314369\pi$
$564$	−2.95100	−	21.6392i	−0.124259	−	0.911176i
$565$	53.0526	−	6.98451i	2.23194	−	0.293841i
$566$	8.90894	+	20.8743i	0.374471	+	0.877412i
$567$	−0.388061	+	0.0765860i	−0.0162970	+	0.00321631i
$568$	1.23627	+	38.5469i	0.0518726	+	1.61739i
$569$	−7.26619	−	1.94697i	−0.304615	−	0.0816213i	0.103274	−	0.994653i	$-0.467068\pi$
$569$	−7.26619	−	1.94697i	−0.304615	−	0.0816213i	−0.407889	+	0.913032i	$0.633735\pi$
$570$	−43.4588	−	33.7668i	−1.82029	−	1.41433i
$571$	−14.4146	−	18.7854i	−0.603231	−	0.786146i	0.387516	−	0.921863i	$-0.373333\pi$
$571$	−14.4146	−	18.7854i	−0.603231	−	0.786146i	−0.990748	+	0.135716i	$0.956666\pi$
$572$	−3.63704	+	6.62250i	−0.152072	+	0.276901i
$573$	−17.8652	+	13.2394i	−0.746330	+	0.553083i
$574$	0.00661682	+	0.00169739i	0.000276181	+	7.08478e-5i
$575$	34.1349			1.42352
$576$	−6.91911	−	22.9810i	−0.288296	−	0.957541i
$577$	−34.3158			−1.42859			−0.714294	−	0.699846i	$-0.753252\pi$
$577$	−34.3158			−1.42859			−0.714294	+	0.699846i	$0.753252\pi$
$578$	−22.3441	−	5.73187i	−0.929392	−	0.238414i
$579$	−0.140801	−	0.0611022i	−0.00585150	−	0.00253932i
$580$	−15.6557	+	28.5066i	−0.650067	+	1.18367i
$581$	−0.206895	−	0.269630i	−0.00858344	−	0.0111862i
$582$	40.9402	−	16.6685i	1.69702	−	0.690932i
$583$	−1.75151	−	0.469317i	−0.0725403	−	0.0194371i
$584$	23.5364	−	0.754855i	0.973944	−	0.0312361i
$585$	−13.8295	+	12.9333i	−0.571781	+	0.534728i
$586$	−2.18699	−	5.12427i	−0.0903437	−	0.211682i
$587$	−10.9830	+	1.44595i	−0.453319	+	0.0596805i	−0.353729	−	0.935348i	$-0.615086\pi$
$587$	−10.9830	+	1.44595i	−0.453319	+	0.0596805i	−0.0995899	+	0.995029i	$0.531753\pi$
$588$	−19.1639	+	14.8466i	−0.790304	+	0.612265i
$589$	−0.834835	+	6.34120i	−0.0343988	+	0.261285i
$590$	−45.3981	−	25.5677i	−1.86901	−	1.05260i
$591$	−26.7256	−	7.64273i	−1.09934	−	0.314380i
$592$	−5.75287	−	32.7960i	−0.236442	−	1.34791i
$593$	11.5734			0.475264			0.237632	−	0.971355i	$-0.423629\pi$
$593$	11.5734			0.475264			0.237632	+	0.971355i	$0.423629\pi$
$594$	−3.16625	−	14.0093i	−0.129913	−	0.574810i
$595$	0.0455802	+	0.110040i	0.00186860	+	0.00451121i
$596$	−17.8446	+	2.73846i	−0.730943	+	0.112172i
$597$	−18.0853	−	14.3645i	−0.740181	−	0.587901i
$598$	−16.3566	−	1.97580i	−0.668872	−	0.0807965i
$599$	0.646487	+	2.41272i	0.0264147	+	0.0985811i	0.977875	−	0.209191i	$-0.0670831\pi$
$599$	0.646487	+	2.41272i	0.0264147	+	0.0985811i	−0.951460	+	0.307772i	$0.900416\pi$
$600$	17.2250	+	21.7497i	0.703208	+	0.887928i
$601$	−5.51738	+	20.5911i	−0.225059	+	0.839930i	0.757322	+	0.653041i	$0.226507\pi$
$601$	−5.51738	+	20.5911i	−0.225059	+	0.839930i	−0.982381	+	0.186889i	$0.940160\pi$
$602$	0.210677	−	0.524402i	0.00858657	−	0.0213730i
$603$	0.0523924	+	0.536065i	0.00213359	+	0.0218303i
$604$	20.1488	−	21.0290i	0.819842	−	0.855659i
$605$	−18.6007	−	14.2728i	−0.756226	−	0.580272i
$606$	0.147005	−	24.2978i	0.00597165	−	0.987031i
$607$	14.6199	+	8.44080i	0.593403	+	0.342601i	0.766442	−	0.642314i	$-0.222025\pi$
$607$	14.6199	+	8.44080i	0.593403	+	0.342601i	−0.173039	+	0.984915i	$0.555359\pi$
$608$	29.5692	−	25.3095i	1.19919	−	1.02644i
$609$	−0.272496	+	0.263524i	−0.0110421	+	0.0106785i
$610$	−48.5463	−	12.4535i	−1.96558	−	0.504226i
$611$	−4.66322	−	11.2580i	−0.188654	−	0.455451i
$612$	4.79389	+	1.34690i	0.193782	+	0.0544451i
$613$	20.4698	+	8.47887i	0.826768	+	0.342458i	0.755622	−	0.655008i	$-0.227335\pi$
$613$	20.4698	+	8.47887i	0.826768	+	0.342458i	0.0711454	+	0.997466i	$0.477335\pi$
$614$	0.917994	+	6.44024i	0.0370472	+	0.259907i
$615$	−0.319776	+	0.533061i	−0.0128946	+	0.0214951i
$616$	0.154009	+	0.187915i	0.00620519	+	0.00757130i
$617$	−12.8852	+	3.45258i	−0.518738	+	0.138995i	−0.508683	−	0.860954i	$-0.669867\pi$
$617$	−12.8852	+	3.45258i	−0.518738	+	0.138995i	−0.0100552	+	0.999949i	$0.503201\pi$
$618$	−4.27072	+	0.535986i	−0.171794	+	0.0215605i
$619$	−3.01970	−	22.9369i	−0.121372	−	0.921912i	−0.938457	−	0.345395i	$-0.887745\pi$
$619$	−3.01970	−	22.9369i	−0.121372	−	0.921912i	0.817085	−	0.576517i	$-0.195588\pi$
$620$	2.20287	−	5.65725i	0.0884693	−	0.227201i
$621$	25.7728	−	17.7949i	1.03423	−	0.714083i
$622$	0.0803116	+	7.51466i	0.00322020	+	0.301310i
$623$	−0.527725	+	0.304682i	−0.0211429	+	0.0122068i
$624$	−6.99488	−	11.4189i	−0.280019	−	0.457123i
$625$	18.3975	+	10.6218i	0.735898	+	0.424871i
$626$	−7.18041	+	12.7496i	−0.286987	+	0.509576i
$627$	18.7140	−	13.8684i	0.747364	−	0.553849i
$628$	28.0047	+	20.5530i	1.11751	+	0.820153i
$629$	6.38252	+	2.64373i	0.254488	+	0.105412i
$630$	0.220133	+	0.567701i	0.00877031	+	0.0226178i
$631$	−6.76574	−	6.76574i	−0.269340	−	0.269340i	0.559494	−	0.828834i	$-0.310995\pi$
$631$	−6.76574	−	6.76574i	−0.269340	−	0.269340i	−0.828834	+	0.559494i	$0.810995\pi$
$632$	9.43933	−	40.3618i	0.375476	−	1.60551i
$633$	−0.244641	+	14.6154i	−0.00972361	+	0.580912i
$634$	19.4434	+	24.7862i	0.772197	+	0.984384i
$635$	−9.10221	+	6.98437i	−0.361210	+	0.277166i
$636$	2.26195	−	2.28303i	0.0896923	−	0.0905279i
$637$	−8.23416	+	10.7310i	−0.326249	+	0.425177i
$638$	−9.83653	−	9.62850i	−0.389432	−	0.381196i
$639$	−34.7214	−	21.6272i	−1.37356	−	0.855560i
$640$	−32.9802	+	16.6495i	−1.30366	+	0.658131i
$641$	−22.9259	+	13.2363i	−0.905518	+	0.522801i	−0.878986	−	0.476847i	$-0.841780\pi$
$641$	−22.9259	+	13.2363i	−0.905518	+	0.522801i	−0.0265317	+	0.999648i	$0.508446\pi$
$642$	15.6021	+	9.13419i	0.615767	+	0.360498i
$643$	−0.841130	+	6.38902i	−0.0331709	+	0.251958i	−0.999994	−	0.00348903i	$-0.998889\pi$
$643$	−0.841130	+	6.38902i	−0.0331709	+	0.251958i	0.966823	+	0.255447i	$0.0822227\pi$
$644$	−0.255035	+	0.464380i	−0.0100498	+	0.0182991i
$645$	40.2702	+	31.9853i	1.58564	+	1.25942i
$646$	1.13956	+	7.99468i	0.0448356	+	0.314546i
$647$	30.0499	+	30.0499i	1.18138	+	1.18138i	0.979386	+	0.201997i	$0.0647431\pi$
$647$	30.0499	+	30.0499i	1.18138	+	1.18138i	0.201997	+	0.979386i	$0.435257\pi$
$648$	24.3437	+	7.44209i	0.956310	+	0.292353i
$649$	15.5928	−	15.5928i	0.612070	−	0.612070i
$650$	12.3813	+	9.29201i	0.485636	+	0.364462i
$651$	0.0440107	−	0.0554105i	0.00172492	−	0.00217171i
$652$	−29.5474	−	3.24921i	−1.15717	−	0.127249i
$653$	40.6261	+	5.34853i	1.58982	+	0.209304i	0.872918	−	0.487866i	$-0.162225\pi$
$653$	40.6261	+	5.34853i	1.58982	+	0.209304i	0.716905	+	0.697171i	$0.245558\pi$
$654$	6.52035	+	24.9368i	0.254966	+	0.975106i
$655$	3.34462	+	5.79306i	0.130685	+	0.226353i
$656$	−0.323859	−	0.297290i	−0.0126446	−	0.0116072i
$657$	−13.2054	+	21.2006i	−0.515193	+	0.827115i
$658$	−0.391830	+	0.00418762i	−0.0152751	+	0.000163250i
$659$	−16.6762	−	12.7961i	−0.649614	−	0.498467i	0.230596	−	0.973049i	$-0.425932\pi$
$659$	−16.6762	−	12.7961i	−0.649614	−	0.498467i	−0.880211	+	0.474583i	$0.842599\pi$
$660$	−20.3869	+	8.55549i	−0.793559	+	0.333022i
$661$	−18.0821	−	23.5650i	−0.703311	−	0.916572i	0.295943	−	0.955206i	$-0.404366\pi$
$661$	−18.0821	−	23.5650i	−0.703311	−	0.916572i	−0.999253	+	0.0386335i	$0.987700\pi$
$662$	−0.450751	+	3.73153i	−0.0175189	+	0.145030i
$663$	2.77798	+	0.0464994i	0.107888	+	0.00180589i
$664$	3.54855	+	21.5824i	0.137710	+	0.837561i
$665$	−0.698238	+	0.698238i	−0.0270765	+	0.0270765i
$666$	32.3118	+	14.2550i	1.25206	+	0.552369i
$667$	11.4863	−	27.7304i	0.444752	−	1.07373i
$668$	−29.1954	−	7.15776i	−1.12960	−	0.276942i
$669$	5.28386	+	7.13003i	0.204286	+	0.275663i
$670$	0.798537	−	0.223141i	0.0308502	−	0.00862067i
$671$	10.6058	−	18.3698i	0.409433	−	0.709158i
$672$	−0.424583	+	0.0718328i	−0.0163786	+	0.00277101i
$673$	5.55088	+	9.61440i	0.213971	+	0.370608i	0.952954	−	0.303116i	$-0.0980270\pi$
$673$	5.55088	+	9.61440i	0.213971	+	0.370608i	−0.738983	+	0.673724i	$0.764694\pi$
$674$	−19.4770	−	19.0651i	−0.750226	−	0.734360i
$675$	−29.3316	+	2.37188i	−1.12897	+	0.0912938i
$676$	13.3785	+	12.8185i	0.514558	+	0.493019i
$677$	−49.1351	+	6.46876i	−1.88842	+	0.248615i	−0.984017	−	0.178073i	$-0.943014\pi$
$677$	−49.1351	+	6.46876i	−1.88842	+	0.248615i	−0.904399	+	0.426688i	$0.859680\pi$
$678$	−31.6961	−	24.6274i	−1.21728	−	0.945809i
$679$	−0.205272	−	0.766087i	−0.00787763	−	0.0293997i
$680$	0.756392	−	7.62784i	0.0290063	−	0.292514i
$681$	30.0224	+	18.0100i	1.15046	+	0.690146i
$682$	2.05507	+	1.54230i	0.0786929	+	0.0590578i
$683$	18.6218	−	44.9571i	0.712545	−	1.72024i	0.0190023	−	0.999819i	$-0.493951\pi$
$683$	18.6218	−	44.9571i	0.712545	−	1.72024i	0.693542	−	0.720416i	$-0.256049\pi$
$684$	4.89285	+	40.9918i	0.187083	+	1.56736i
$685$	−42.6068	+	17.6483i	−1.62792	+	0.674308i
$686$	0.443046	+	0.748782i	0.0169156	+	0.0285886i
$687$	−25.5467	−	26.4165i	−0.974668	−	1.00785i
$688$	−27.8819	+	23.3536i	−1.06299	+	0.890349i
$689$	0.896593	−	1.55294i	0.0341575	−	0.0591625i
$690$	−33.8838	−	34.2963i	−1.28994	−	1.30564i
$691$	8.32169	−	10.8450i	0.316572	−	0.412565i	−0.607780	−	0.794105i	$-0.707940\pi$
$691$	8.32169	−	10.8450i	0.316572	−	0.412565i	0.924352	+	0.381541i	$0.124606\pi$
$692$	−20.4508	+	8.98775i	−0.777422	+	0.341663i
$693$	−0.256478	+	0.0250669i	−0.00974280	+	0.000952215i
$694$	−30.1661	+	12.8746i	−1.14509	+	0.488713i
$695$	40.9329	+	10.9679i	1.55267	+	0.416038i
$696$	23.4651	−	6.67447i	0.889442	−	0.252995i
$697$	0.0881044	−	0.0236075i	0.00333719	−	0.000894198i
$698$	−4.40063	+	3.45206i	−0.166566	+	0.130662i
$699$	−6.74121	+	8.48734i	−0.254976	+	0.321021i
$700$	0.425689	−	0.258056i	0.0160895	−	0.00975361i
$701$	9.91068	−	4.10514i	0.374321	−	0.155049i	−0.187588	−	0.982248i	$-0.560067\pi$
$701$	9.91068	−	4.10514i	0.374321	−	0.155049i	0.561909	+	0.827199i	$0.310067\pi$
$702$	14.1923	+	0.561227i	0.535653	+	0.0211822i
$703$			57.2742i			2.16014i
$704$	−3.03008	−	15.3397i	−0.114201	−	0.578137i
$705$	9.80416	−	34.2838i	0.369246	−	1.29120i
$706$	16.6977	−	4.66595i	0.628426	−	0.175605i
$707$	−0.432238	−	0.0569052i	−0.0162560	−	0.00214014i
$708$	10.2904	+	37.7042i	0.386738	+	1.41701i
$709$	2.89583	+	21.9960i	0.108755	+	0.826078i	0.955689	+	0.294379i	$0.0951128\pi$
$709$	2.89583	+	21.9960i	0.108755	+	0.826078i	−0.846934	+	0.531699i	$0.821554\pi$
$710$	−23.4742	+	58.4301i	−0.880970	+	2.19284i
$711$	30.0303	+	32.1112i	1.12623	+	1.20427i
$712$	39.1962	−	1.25709i	1.46894	−	0.0471115i
$713$	−1.45014	+	5.41201i	−0.0543083	+	0.202681i
$714$	0.0346893	−	0.0823348i	0.00129821	−	0.00308130i
$715$	−9.78691	+	7.50976i	−0.366010	+	0.280849i
$716$	−30.6379	−	3.36913i	−1.14499	−	0.125910i
$717$	10.5499	−	24.3107i	0.393993	−	0.907900i
$718$	−22.9945	−	38.8625i	−0.858147	−	1.45034i
$719$		−	2.14383i		−	0.0799514i	−0.999201	−	0.0399757i	$-0.987272\pi$
$719$		−	2.14383i		−	0.0799514i	0.999201	−	0.0399757i	$-0.0127280\pi$
$720$	4.75425	−	38.8962i	0.177180	−	1.44957i
$721$			0.0772279i			0.00287612i
$722$	−34.4942	+	20.4098i	−1.28374	+	0.759574i
$723$	0.762725	+	1.02922i	0.0283660	+	0.0382771i
$724$	33.1317	−	26.5669i	1.23133	−	0.987351i
$725$	−22.3742	+	17.1683i	−0.830956	+	0.637615i
$726$	2.19003	+	17.4501i	0.0812798	+	0.647635i
$727$	−6.63681	+	24.7689i	−0.246146	+	0.918628i	0.726659	+	0.686999i	$0.241072\pi$
$727$	−6.63681	+	24.7689i	−0.246146	+	0.918628i	−0.972804	+	0.231629i	$0.925594\pi$
$728$	−0.218916	+	0.0990145i	−0.00811358	+	0.00366972i
$729$	−20.9097	+	17.0817i	−0.774434	+	0.632655i
$730$	35.6770	+	14.3332i	1.32047	+	0.530494i
$731$	−0.984961	−	7.48152i	−0.0364301	−	0.276714i
$732$	18.9481	+	32.4704i	0.700341	+	1.20014i
$733$	−37.0303	−	4.87513i	−1.36774	−	0.180067i	−0.589368	−	0.807865i	$-0.700623\pi$
$733$	−37.0303	−	4.87513i	−1.36774	−	0.180067i	−0.778377	+	0.627797i	$0.783957\pi$
$734$	2.94767	+	10.5486i	0.108801	+	0.389357i
$735$	−38.3982	+	9.60297i	−1.41634	+	0.354211i
$736$	28.5754	−	18.6008i	1.05330	−	0.685634i
$737$			0.350913i			0.0129261i
$738$	0.453033	−	0.110391i	0.0166764	−	0.00406353i
$739$	47.1295	−	19.5217i	1.73368	−	0.718116i	0.734464	−	0.678648i	$-0.237434\pi$
$739$	47.1295	−	19.5217i	1.73368	−	0.718116i	0.999221	−	0.0394681i	$-0.0125664\pi$
$740$	12.9451	−	52.8010i	0.475872	−	1.94100i
$741$	8.45741	+	21.4254i	0.310691	+	0.787080i
$742$	−0.0355902	−	0.0453698i	−0.00130656	−	0.00166558i
$743$	2.19241	−	0.587455i	0.0804317	−	0.0215516i	−0.218379	−	0.975864i	$-0.570077\pi$
$743$	2.19241	−	0.587455i	0.0804317	−	0.0215516i	0.298810	+	0.954312i	$0.403410\pi$
$744$	−4.18013	+	1.80700i	−0.153251	+	0.0662477i
$745$	−28.4722	−	7.62910i	−1.04314	−	0.279509i
$746$	−4.58535	−	10.7438i	−0.167882	−	0.393359i
$747$	−21.1239	−	9.59020i	−0.772884	−	0.350887i
$748$	3.02308	+	1.17715i	0.110535	+	0.0430409i
$749$	0.197473	−	0.257351i	0.00721549	−	0.00940341i
$750$	1.34214	+	5.13297i	0.0490081	+	0.187429i
$751$	−3.46698	+	6.00499i	−0.126512	+	0.219125i	−0.922323	−	0.386420i	$-0.873712\pi$
$751$	−3.46698	+	6.00499i	−0.126512	+	0.219125i	0.795811	+	0.605545i	$0.207045\pi$
$752$	22.3584	+	11.6642i	0.815327	+	0.425351i
$753$	−6.88296	+	24.0688i	−0.250829	+	0.877116i
$754$	11.7149	−	6.93156i	0.426631	−	0.252433i
$755$	43.9318	−	18.1971i	1.59884	−	0.662261i
$756$	0.186880	−	0.416755i	0.00679676	−	0.0151572i
$757$	3.84097	−	9.27292i	0.139602	−	0.337030i	−0.838580	−	0.544779i	$-0.816614\pi$
$757$	3.84097	−	9.27292i	0.139602	−	0.337030i	0.978182	+	0.207749i	$0.0666136\pi$
$758$	−2.01500	+	2.68492i	−0.0731879	+	0.0975208i
$759$	17.8392	−	9.90515i	0.647523	−	0.359534i
$760$	60.8248	−	18.4069i	2.20635	−	0.667689i
$761$	−3.28801	−	12.2710i	−0.119190	−	0.444825i	0.880376	−	0.474277i	$-0.157290\pi$
$761$	−3.28801	−	12.2710i	−0.119190	−	0.444825i	−0.999566	+	0.0294522i	$0.990624\pi$
$762$	8.52559	+	1.17493i	0.308850	+	0.0425633i
$763$	0.458510	−	0.0603640i	0.0165992	−	0.00218532i
$764$	−0.548756	−	25.6703i	−0.0198533	−	0.928717i
$765$	6.28088	+	5.16247i	0.227086	+	0.186649i
$766$	11.6031	−	11.8538i	0.419236	−	0.428294i
$767$	10.9034	+	18.8853i	0.393701	+	0.681910i
$768$	26.2714	+	8.82112i	0.947988	+	0.318305i
$769$	21.4273	−	37.1132i	0.772689	−	1.33834i	−0.163395	−	0.986561i	$-0.552244\pi$
$769$	21.4273	−	37.1132i	0.772689	−	1.33834i	0.936084	−	0.351776i	$-0.114422\pi$
$770$	0.106761	+	0.382057i	0.00384739	+	0.0137684i
$771$	8.70838	−	20.0672i	0.313625	−	0.722702i
$772$	0.151559	−	0.0918763i	0.00545472	−	0.00330670i
$773$	11.9365	−	28.8173i	0.429327	−	1.03649i	−0.550174	−	0.835050i	$-0.685439\pi$
$773$	11.9365	−	28.8173i	0.429327	−	1.03649i	0.979501	−	0.201437i	$-0.0645612\pi$
$774$	−4.16248	−	38.3512i	−0.149617	−	1.37851i
$775$	3.72254	−	3.72254i	0.133718	−	0.133718i
$776$	−11.6234	+	49.7006i	−0.417254	+	1.78415i
$777$	0.325970	−	0.543387i	0.0116941	−	0.0194939i
$778$	23.2981	+	2.81430i	0.835279	+	0.100898i
$779$	0.460345	+	0.599933i	0.0164936	+	0.0214948i
$780$	−2.95431	−	21.6635i	−0.105781	−	0.775679i
$781$	−21.1433	−	16.2238i	−0.756567	−	0.580534i
$782$	0.0756005	+	7.07384i	0.00270347	+	0.252960i
$783$	−7.94314	+	24.6264i	−0.283865	+	0.880077i
$784$	−1.19624	−	27.9667i	−0.0427229	−	0.998811i
$785$	28.3585	+	49.1184i	1.01216	+	1.75311i
$786$	1.32798	−	4.83881i	0.0473676	−	0.172595i
$787$	−24.7511	−	3.25854i	−0.882281	−	0.116155i	−0.324247	−	0.945972i	$-0.605111\pi$
$787$	−24.7511	−	3.25854i	−0.882281	−	0.116155i	−0.558034	+	0.829818i	$0.688444\pi$
$788$	25.0409	−	20.0793i	0.892047	−	0.715294i
$789$	0.193377	+	0.0287588i	0.00688441	+	0.00102384i
$790$	40.6238	−	54.1301i	1.44533	−	1.92586i
$791$	−0.509252	+	0.509252i	−0.0181069	+	0.0181069i
$792$	15.3132	+	6.36830i	0.544131	+	0.226288i
$793$	14.8325	+	14.8325i	0.526717	+	0.526717i
$794$	−17.2178	+	2.45423i	−0.611035	+	0.0870972i
$795$	4.88082	−	1.92665i	0.173105	−	0.0683311i
$796$	25.6066	−	7.45135i	0.907603	−	0.264106i
$797$	1.05359	−	8.00281i	0.0373201	−	0.283474i	−0.962601	−	0.270923i	$-0.912671\pi$
$797$	1.05359	−	8.00281i	0.0373201	−	0.283474i	0.999921	−	0.0125516i	$-0.00399540\pi$
$798$	0.740697	+	0.00448130i	0.0262204	+	0.000158636i
$799$	−4.53126	+	2.61612i	−0.160304	+	0.0925518i
$800$	−31.9907	+	1.71104i	−1.13104	+	0.0604944i
$801$	−21.9916	+	35.3063i	−0.777034	+	1.24749i
$802$	−11.8339	+	12.0896i	−0.417871	+	0.426899i
$803$	−9.90615	+	12.9099i	−0.349580	+	0.455582i
$804$	−0.540056	−	0.308471i	−0.0190463	−	0.0108789i
$805$	−0.686273	+	0.526596i	−0.0241879	+	0.0185601i
$806$	−1.99922	+	1.56828i	−0.0704194	+	0.0552403i
$807$	8.78391	−	4.87723i	0.309208	−	0.171687i
$808$	22.7954	+	16.3578i	0.801938	+	0.575467i
$809$	−20.5380	−	20.5380i	−0.722076	−	0.722076i	0.246952	−	0.969028i	$-0.420571\pi$
$809$	−20.5380	−	20.5380i	−0.722076	−	0.722076i	−0.969028	+	0.246952i	$0.920571\pi$
$810$	31.4989	+	27.1159i	1.10676	+	0.952755i
$811$	6.08418	+	2.52015i	0.213645	+	0.0884945i	0.486939	−	0.873436i	$-0.338113\pi$
$811$	6.08418	+	2.52015i	0.213645	+	0.0884945i	−0.273295	+	0.961930i	$0.588113\pi$
$812$	−0.0663958	−	0.432654i	−0.00233004	−	0.0151832i
$813$	−3.01246	−	26.2727i	−0.105652	−	0.921424i
$814$	20.0481	+	11.2908i	0.702685	+	0.395743i
$815$	−42.0316	−	24.2670i	−1.47230	−	0.850035i
$816$	−4.46908	+	3.61774i	−0.156449	+	0.126646i
$817$	54.1794	−	31.2805i	1.89550	−	1.09437i
$818$	22.0223	−	0.235360i	0.769992	−	0.00822917i
$819$	0.0417009	−	0.251407i	0.00145715	−	0.00878486i
$820$	−0.288794	−	0.657124i	−0.0100851	−	0.0229478i
$821$	−3.88627	−	29.5192i	−0.135632	−	1.03023i	−0.914941	−	0.403587i	$-0.867763\pi$
$821$	−3.88627	−	29.5192i	−0.135632	−	1.03023i	0.779309	−	0.626639i	$-0.215570\pi$
$822$	31.8795	+	13.4315i	1.11193	+	0.468476i
$823$	35.9077	−	9.62144i	1.25166	−	0.335382i	0.428685	−	0.903454i	$-0.358977\pi$
$823$	35.9077	−	9.62144i	1.25166	−	0.335382i	0.822979	+	0.568072i	$0.192311\pi$
$824$	2.34580	−	4.38167i	0.0817197	−	0.152643i
$825$	−19.1694	−	0.320867i	−0.667392	−	0.0111712i
$826$	0.694227	−	0.0989554i	0.0241553	−	0.00344310i
$827$	−12.7739	−	5.29114i	−0.444193	−	0.183991i	0.149365	−	0.988782i	$-0.452277\pi$
$827$	−12.7739	−	5.29114i	−0.444193	−	0.183991i	−0.593558	+	0.804791i	$0.702277\pi$
$828$	−0.437581	+	36.1617i	−0.0152070	+	1.25671i
$829$	−13.1509	−	31.7491i	−0.456750	−	1.10269i	−0.969705	−	0.244277i	$-0.921449\pi$
$829$	−13.1509	−	31.7491i	−0.456750	−	1.10269i	0.512955	−	0.858415i	$-0.328551\pi$
$830$	−8.87366	+	34.5915i	−0.308009	+	1.20069i
$831$	−1.97184	−	7.88457i	−0.0684025	−	0.273513i
$832$	15.4282	+	1.03180i	0.534877	+	0.0357712i
$833$	5.02973	+	2.90391i	0.174270	+	0.100615i
$834$	−15.7270	−	27.6246i	−0.544581	−	0.956561i
$835$	−38.9378	−	29.8780i	−1.34750	−	1.03397i
$836$	0.574826	+	26.8898i	0.0198808	+	0.930004i
$837$	0.870029	−	4.75122i	0.0300726	−	0.164226i
$838$	34.1990	+	13.7394i	1.18139	+	0.474619i
$839$	10.9720	−	40.9479i	0.378794	−	1.41368i	−0.468928	−	0.883237i	$-0.655359\pi$
$839$	10.9720	−	40.9479i	0.378794	−	1.41368i	0.847722	−	0.530442i	$-0.177974\pi$
$840$	−0.681834	−	0.171543i	−0.0235255	−	0.00591881i
$841$	−1.08748	−	4.05852i	−0.0374992	−	0.139949i
$842$	2.76141	−	22.8603i	0.0951646	−	0.787818i
$843$	−2.45654	+	16.5180i	−0.0846076	+	0.568910i
$844$	−13.6074	−	9.98664i	−0.468387	−	0.343754i
$845$	11.5769	+	27.9490i	0.398257	+	0.961477i
$846$	−23.4630	+	12.8426i	−0.806675	+	0.441539i
$847$	0.315552			0.0108425
$848$	0.641172	+	3.65519i	0.0220179	+	0.125520i
$849$	19.9815	−	19.3235i	0.685762	−	0.663182i
$850$	3.26175	−	5.79158i	0.111877	−	0.198650i
$851$	−6.54891	+	49.7439i	−0.224494	+	1.70520i
$852$	43.5546	−	18.2780i	1.49215	−	0.626192i
$853$	−22.7023	+	2.98882i	−0.777312	+	0.102335i	−0.508735	−	0.860923i	$-0.669887\pi$
$853$	−22.7023	+	2.98882i	−0.777312	+	0.102335i	−0.268577	+	0.963258i	$0.586553\pi$
$854$	0.620395	−	0.264779i	0.0212295	−	0.00906054i
$855$	−19.6146	+	64.4868i	−0.670806	+	2.20540i
$856$	−19.0210	+	8.60309i	−0.650125	+	0.294048i
$857$	−40.0689	−	10.7364i	−1.36873	−	0.366750i	−0.501715	−	0.865033i	$-0.667297\pi$
$857$	−40.0689	−	10.7364i	−1.36873	−	0.366750i	−0.867014	+	0.498283i	$0.833964\pi$
$858$	9.16692	+	1.26331i	0.312953	+	0.0431289i
$859$	−12.2262	−	15.9334i	−0.417151	−	0.543642i	0.536759	−	0.843736i	$-0.319649\pi$
$859$	−12.2262	−	15.9334i	−0.417151	−	0.543642i	−0.953910	+	0.300094i	$0.902982\pi$
$860$	−57.0179	+	16.5918i	−1.94430	+	0.565777i
$861$	−0.000953047	−	0.00831185i	−3.24798e−5	−	0.000283267i
$862$	−0.450276	+	1.75528i	−0.0153365	+	0.0597849i
$863$	8.80230			0.299634			0.149817	−	0.988714i	$-0.452132\pi$
$863$	8.80230			0.299634			0.149817	+	0.988714i	$0.452132\pi$
$864$	−23.2619	+	17.9689i	−0.791387	+	0.611316i
$865$	−36.4730			−1.24012
$866$	13.4553	−	52.4516i	0.457228	−	1.78238i
$867$	3.21831	+	28.0680i	0.109300	+	0.953239i
$868$	0.0228298	+	0.0784548i	0.000774894	+	0.00266293i
$869$	17.4371	+	22.7245i	0.591514	+	0.770877i
$870$	39.4591	+	5.43795i	1.33779	+	0.184364i
$871$	−0.335196	−	0.0898155i	−0.0113577	−	0.00304328i
$872$	−27.8480	−	10.5024i	−0.943053	−	0.355655i
$873$	−36.9786	−	39.5410i	−1.25154	−	1.33826i
$874$	−53.9419	+	23.0219i	−1.82461	+	0.778727i
$875$	0.0943793	−	0.0124253i	0.00319060	−	0.000420051i
$876$	−11.1604	−	26.5941i	−0.377074	−	0.898531i
$877$	0.825102	−	6.26727i	0.0278617	−	0.211631i	−0.971851	−	0.235596i	$-0.924296\pi$
$877$	0.825102	−	6.26727i	0.0278617	−	0.211631i	0.999713	+	0.0239653i	$0.00762913\pi$
$878$	0.636164	−	1.12958i	0.0214695	−	0.0381214i
$879$	−4.90510	+	4.74359i	−0.165445	+	0.159997i
$880$	5.54769	−	24.9196i	0.187013	−	0.840039i
$881$	−30.5633			−1.02970			−0.514852	−	0.857279i	$-0.672153\pi$
$881$	−30.5633			−1.02970			−0.514852	+	0.857279i	$0.672153\pi$
$882$	25.3676	+	15.4272i	0.854172	+	0.519459i
$883$	20.8857	+	50.4226i	0.702861	+	1.69686i	0.717112	+	0.696958i	$0.245464\pi$
$883$	20.8857	+	50.4226i	0.702861	+	1.69686i	−0.0142511	+	0.999898i	$0.504536\pi$
$884$	−1.89818	+	2.58639i	−0.0638426	+	0.0869896i
$885$	−9.38688	+	63.1183i	−0.315537	+	2.12170i
$886$	−3.68994	+	30.5471i	−0.123966	+	1.02625i
$887$	−4.58318	−	17.1047i	−0.153888	−	0.574319i	−0.999198	−	0.0400423i	$-0.987251\pi$
$887$	−4.58318	−	17.1047i	−0.153888	−	0.574319i	0.845310	−	0.534277i	$-0.179416\pi$
$888$	−34.9999	+	20.9288i	−1.17452	+	0.702323i
$889$	0.0399655	−	0.149153i	0.00134040	−	0.00500244i
$890$	59.4145	+	23.8696i	1.99158	+	0.800112i
$891$	−14.6407	+	9.75091i	−0.490482	+	0.326668i
$892$	−10.2450	+	0.219009i	−0.343029	+	0.00733297i
$893$	−34.4142	−	26.4069i	−1.15163	−	0.883674i
$894$	10.9394	+	19.2152i	0.365869	+	0.642651i
$895$	−43.5829	−	25.1626i	−1.45682	−	0.841093i
$896$	0.215737	−	0.447993i	0.00720728	−	0.0149664i
$897$	4.89560	+	19.5754i	0.163459	+	0.653604i
$898$	−12.6879	+	49.4602i	−0.423401	+	1.65051i
$899$	−1.77148	−	4.27672i	−0.0590821	−	0.142637i
$900$	17.3447	−	29.2196i	0.578157	−	0.973987i
$901$	−0.711348	−	0.294650i	−0.0236984	−	0.00981621i
$902$	0.300749	−	0.0428689i	0.0100139	−	0.00142738i
$903$	−0.692055	−	0.0115840i	−0.0230301	−	0.000385491i
$904$	44.3619	−	13.4249i	1.47545	−	0.446504i
$905$	66.9760	−	17.9462i	2.22636	−	0.596550i
$906$	−32.8708	−	13.8491i	−1.09206	−	0.460106i
$907$	5.79925	+	44.0497i	0.192561	+	1.46265i	0.765705	+	0.643191i	$0.222390\pi$
$907$	5.79925	+	44.0497i	0.192561	+	1.46265i	−0.573144	+	0.819454i	$0.694277\pi$
$908$	−37.0097	+	16.2651i	−1.22821	+	0.539777i
$909$	−27.8596	+	10.4618i	−0.924046	+	0.346996i
$910$	−0.392270	+	0.00419232i	−0.0130036	+	0.000138974i
$911$	−10.8789	+	6.28091i	−0.360432	+	0.208096i	−0.669270	−	0.743019i	$-0.733393\pi$
$911$	−10.8789	+	6.28091i	−0.360432	+	0.208096i	0.308838	+	0.951115i	$0.400060\pi$
$912$	−41.8887	−	22.7529i	−1.38707	−	0.753424i
$913$	−13.0893	−	7.55712i	−0.433193	−	0.250104i
$914$	−14.4902	−	8.16073i	−0.479295	−	0.269933i
$915$	6.99233	+	60.9825i	0.231159	+	2.01602i
$916$	41.9427	−	6.43659i	1.38583	−	0.212671i
$917$	−0.0831767	−	0.0344529i	−0.00274674	−	0.00113774i
$918$	−0.556492	−	6.07319i	−0.0183670	−	0.200445i
$919$	−24.4591	−	24.4591i	−0.806830	−	0.806830i	0.177323	−	0.984153i	$-0.443256\pi$
$919$	−24.4591	−	24.4591i	−0.806830	−	0.806830i	−0.984153	+	0.177323i	$0.943256\pi$
$920$	54.9323	−	9.03189i	1.81107	−	0.297773i
$921$	6.96565	−	3.86765i	0.229526	−	0.127443i
$922$	30.6953	−	24.0789i	1.01090	−	0.792995i
$923$	20.9088	−	16.0439i	0.688220	−	0.528090i
$924$	0.147587	−	0.258387i	0.00485525	−	0.00850032i
$925$	28.6984	−	37.4005i	0.943598	−	1.22972i
$926$	6.51548	−	6.65625i	0.214112	−	0.218738i
$927$	2.48152	+	4.65098i	0.0815039	+	0.152758i
$928$	−9.37478	+	26.5643i	−0.307742	+	0.872014i
$929$	2.93209	−	1.69284i	0.0961988	−	0.0555404i	−0.451129	−	0.892459i	$-0.648979\pi$
$929$	2.93209	−	1.69284i	0.0961988	−	0.0555404i	0.547328	+	0.836918i	$0.315645\pi$
$930$	−7.43530	−	0.0449844i	−0.243813	−	0.00147510i
$931$	−6.28484	+	47.7381i	−0.205977	+	1.56455i
$932$	−3.49689	−	12.0171i	−0.114544	−	0.393633i
$933$	8.56120	−	3.37943i	0.280281	−	0.110638i
$934$	−24.8661	+	3.54443i	−0.813645	+	0.115977i
$935$	3.74546	+	3.74546i	0.122490	+	0.122490i
$936$	−10.0024	+	12.9974i	−0.326940	+	0.424832i
$937$	39.1233	−	39.1233i	1.27810	−	1.27810i	0.336372	−	0.941729i	$-0.390800\pi$
$937$	39.1233	−	39.1233i	1.27810	−	1.27810i	0.941729	−	0.336372i	$-0.109200\pi$
$938$	−0.00669825	+	0.00892523i	−0.000218706	+	0.000291419i
$939$	17.7261	+	2.63621i	0.578470	+	0.0860294i
$940$	25.7579	+	32.1228i	0.840129	+	1.04773i
$941$	−53.9489	−	7.10250i	−1.75868	−	0.231535i	−0.819051	−	0.573721i	$-0.805499\pi$
$941$	−53.9489	−	7.10250i	−1.75868	−	0.231535i	−0.939632	+	0.342186i	$0.888833\pi$
$942$	11.2597	−	41.0275i	0.366862	−	1.33675i
$943$	0.331221	+	0.573692i	0.0107860	+	0.0186820i
$944$	−42.3941	−	15.4727i	−1.37981	−	0.503594i
$945$	0.553113	−	0.500181i	0.0179928	−	0.0162709i
$946$	−0.268587	−	25.1313i	−0.00873250	−	0.817089i
$947$	34.0832	+	26.1530i	1.10756	+	0.849857i	0.989698	−	0.143173i	$-0.0457306\pi$
$947$	34.0832	+	26.1530i	1.10756	+	0.849857i	0.117858	+	0.993030i	$0.462397\pi$
$948$	−50.3012	+	6.85971i	−1.63371	+	0.222793i
$949$	−9.79626	−	12.7667i	−0.318000	−	0.414426i
$950$	54.7087	+	6.60855i	1.77499	+	0.214410i
$951$	19.8477	−	33.0858i	0.643606	−	1.07288i
$952$	0.0544203	+	0.0876447i	0.00176377	+	0.00284058i
$953$	12.9963	−	12.9963i	0.420991	−	0.420991i	−0.464554	−	0.885545i	$-0.653785\pi$
$953$	12.9963	−	12.9963i	0.420991	−	0.420991i	0.885545	+	0.464554i	$0.153785\pi$
$954$	−3.60123	−	1.58875i	−0.116594	−	0.0514377i
$955$	16.0430	−	38.7312i	0.519138	−	1.25331i
$956$	15.8633	+	26.1681i	0.513057	+	0.846336i
$957$	−6.71111	+	15.4648i	−0.216939	+	0.499905i
$958$	6.15453	+	22.0248i	0.198844	+	0.711588i
$959$	0.310344	−	0.537531i	0.0100215	−	0.0173578i
$960$	33.4745	+	30.4435i	1.08039	+	0.982561i
$961$	−15.0679	−	26.0984i	−0.486063	−	0.841885i
$962$	−15.9164	+	16.2603i	−0.513165	+	0.524252i
$963$	3.62327	−	21.8440i	0.116758	−	0.703914i
$964$	−1.47887	+	0.0316140i	−0.0476312	+	0.00101822i
$965$	0.286898	−	0.0377708i	0.00923557	−	0.00121589i
$966$	0.642798	+	0.0885856i	0.0206817	+	0.00285019i
$967$	4.97590	+	18.5703i	0.160014	+	0.597181i	0.998624	+	0.0524482i	$0.0167024\pi$
$967$	4.97590	+	18.5703i	0.160014	+	0.597181i	−0.838609	+	0.544733i	$0.816631\pi$
$968$	−17.9035	−	9.58490i	−0.575439	−	0.308070i
$969$	8.64691	−	4.80116i	0.277779	−	0.154236i
$970$	−50.0232	+	66.6544i	−1.60615	+	2.14014i
$971$	−4.50813	+	10.8836i	−0.144673	+	0.349271i	−0.979561	−	0.201149i	$-0.935532\pi$
$971$	−4.50813	+	10.8836i	−0.144673	+	0.349271i	0.834888	+	0.550420i	$0.185532\pi$
$972$	−2.13671	−	31.1036i	−0.0685349	−	0.997649i
$973$	−0.526930	+	0.218262i	−0.0168926	+	0.00699715i
$974$	12.3912	−	7.33172i	0.397039	−	0.234924i
$975$	5.21286	−	18.2287i	0.166945	−	0.583785i
$976$	−43.2420	−	3.82177i	−1.38414	−	0.122332i
$977$	18.1652	−	31.4631i	0.581157	−	1.00659i	−0.414186	−	0.910192i	$-0.635934\pi$
$977$	18.1652	−	31.4631i	0.581157	−	1.00659i	0.995343	−	0.0964004i	$-0.0307329\pi$
$978$	9.20969	+	35.2220i	0.294493	+	1.12628i
$979$	−16.4971	+	21.4995i	−0.527251	+	0.687127i
$980$	16.5837	−	42.5891i	0.529747	−	1.36046i
$981$	25.6737	−	18.3684i	0.819698	−	0.586459i
$982$	1.19814	+	2.80734i	0.0382343	+	0.0895858i
$983$	−14.1474	−	3.79077i	−0.451231	−	0.120907i	0.0260445	−	0.999661i	$-0.491709\pi$
$983$	−14.1474	−	3.79077i	−0.451231	−	0.120907i	−0.477275	+	0.878754i	$0.658376\pi$
$984$	−0.198399	+	0.500537i	−0.00632474	+	0.0159565i
$985$	50.6204	−	13.5637i	1.61290	−	0.432175i
$986$	−3.60737	−	4.59862i	−0.114882	−	0.146450i
$987$	0.176211	+	0.446399i	0.00560885	+	0.0142090i
$988$	−25.8326	−	6.33331i	−0.821843	−	0.201489i
$989$	50.6327	−	20.9727i	1.61003	−	0.666894i
$990$	18.7060	+	19.5785i	0.594515	+	0.622246i
$991$			1.68682i			0.0535835i	0.999641	+	0.0267918i	$0.00852910\pi$
$991$			1.68682i			0.0535835i	−0.999641	+	0.0267918i	$0.991471\pi$
$992$	1.08777	−	5.14474i	0.0345367	−	0.163346i
$993$	4.46586	−	1.11686i	0.141720	−	0.0354426i
$994$	−0.228084	−	0.816226i	−0.00723437	−	0.0258891i
$995$	43.1705	+	5.68350i	1.36860	+	0.180179i
$996$	23.1366	−	13.5014i	0.733112	−	0.427807i
$997$	−7.74799	−	58.8518i	−0.245381	−	1.86386i	−0.461030	−	0.887385i	$-0.652520\pi$
$997$	−7.74799	−	58.8518i	−0.245381	−	1.86386i	0.215648	−	0.976471i	$-0.430814\pi$
$998$	15.2514	+	6.12723i	0.482776	+	0.193954i
$999$	2.17089	−	43.1992i	0.0686841	−	1.36676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.59.43	✓	368
3.2	odd	2		864.2.bn.a.827.4		368
9.2	odd	6	inner	288.2.bf.a.155.29	yes	368
9.7	even	3		864.2.bn.a.251.18		368
32.19	odd	8	inner	288.2.bf.a.275.29	yes	368
96.83	even	8		864.2.bn.a.179.18		368
288.83	even	24	inner	288.2.bf.a.83.43	yes	368
288.115	odd	24		864.2.bn.a.467.4		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.43	✓	368	1.1	even	1	trivial
288.2.bf.a.83.43	yes	368	288.83	even	24	inner
288.2.bf.a.155.29	yes	368	9.2	odd	6	inner
288.2.bf.a.275.29	yes	368	32.19	odd	8	inner
864.2.bn.a.179.18		368	96.83	even	8
864.2.bn.a.251.18		368	9.7	even	3
864.2.bn.a.467.4		368	288.115	odd	24
864.2.bn.a.827.4		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.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36986 + 0.351406i) q^{2} +(-0.197306 - 1.72078i) q^{3} +(1.75303 + 0.962754i) q^{4} +(1.98789 + 2.59067i) q^{5} +(0.334409 - 2.42656i) q^{6} +(-0.0424520 - 0.0113750i) q^{7} +(2.06308 + 1.93486i) q^{8} +(-2.92214 + 0.679040i) q^{9} +O(q^{10})\)	\(q+(1.36986 + 0.351406i) q^{2} +(-0.197306 - 1.72078i) q^{3} +(1.75303 + 0.962754i) q^{4} +(1.98789 + 2.59067i) q^{5} +(0.334409 - 2.42656i) q^{6} +(-0.0424520 - 0.0113750i) q^{7} +(2.06308 + 1.93486i) q^{8} +(-2.92214 + 0.679040i) q^{9} +(1.81275 + 4.24741i) q^{10} +(-1.93779 + 0.255115i) q^{11} +(1.31080 - 3.20653i) q^{12} +(0.252285 - 1.91630i) q^{13} +(-0.0541561 - 0.0305000i) q^{14} +(4.06574 - 3.93187i) q^{15} +(2.14621 + 3.37547i) q^{16} -0.829919 q^{17} +(-4.24154 - 0.0966687i) q^{18} +(-2.63304 - 6.35672i) q^{19} +(0.990651 + 6.45537i) q^{20} +(-0.0111978 + 0.0752948i) q^{21} +(-2.74415 - 0.331481i) q^{22} +(-1.56000 - 5.82202i) q^{23} +(2.92240 - 3.93186i) q^{24} +(-1.46577 + 5.47032i) q^{25} +(1.01899 - 2.53640i) q^{26} +(1.74503 + 4.89437i) q^{27} +(-0.0634683 - 0.0608115i) q^{28} +(3.95073 + 3.03150i) q^{29} +(6.95118 - 3.95739i) q^{30} +(-0.805036 - 0.464788i) q^{31} +(1.75385 + 5.37811i) q^{32} +(0.821335 + 3.28417i) q^{33} +(-1.13687 - 0.291639i) q^{34} +(-0.0549212 - 0.132592i) q^{35} +(-5.77634 - 1.62293i) q^{36} +(-7.69054 - 3.18552i) q^{37} +(-1.37310 - 9.63308i) q^{38} +(-3.34730 - 0.0560288i) q^{39} +(-0.911405 + 9.19107i) q^{40} +(-0.106160 + 0.0284456i) q^{41} +(-0.0417984 + 0.0992083i) q^{42} +(1.18682 + 9.01477i) q^{43} +(-3.64262 - 1.41839i) q^{44} +(-7.56807 - 6.22045i) q^{45} +(-0.0910939 - 8.52354i) q^{46} +(5.45988 - 3.15226i) q^{47} +(5.38496 - 4.35915i) q^{48} +(-6.06051 - 3.49903i) q^{49} +(-3.93020 + 6.97849i) q^{50} +(0.163748 + 1.42810i) q^{51} +(2.28719 - 3.11643i) q^{52} +(0.857129 + 0.355035i) q^{53} +(0.670538 + 7.31781i) q^{54} +(-4.51304 - 4.51304i) q^{55} +(-0.0655730 - 0.105606i) q^{56} +(-10.4190 + 5.78510i) q^{57} +(4.34666 + 5.54105i) q^{58} +(-8.95089 + 6.86826i) q^{59} +(10.9128 - 2.97837i) q^{60} +(-6.60666 + 8.60997i) q^{61} +(-0.939457 - 0.919589i) q^{62} +(0.131775 + 0.00441267i) q^{63} +(0.512621 + 7.98356i) q^{64} +(5.46601 - 3.15580i) q^{65} +(-0.0289648 + 4.78748i) q^{66} +(0.0234347 - 0.178004i) q^{67} +(-1.45487 - 0.799007i) q^{68} +(-9.71059 + 3.83314i) q^{69} +(-0.0286408 - 0.200931i) q^{70} +(9.64167 + 9.64167i) q^{71} +(-7.34247 - 4.25302i) q^{72} +(5.88713 - 5.88713i) q^{73} +(-9.41554 - 7.06622i) q^{74} +(9.70241 + 1.44293i) q^{75} +(1.50417 - 13.6785i) q^{76} +(0.0851652 + 0.0112122i) q^{77} +(-4.56563 - 1.25301i) q^{78} +(-7.32756 - 12.6917i) q^{79} +(-4.47829 + 12.2702i) q^{80} +(8.07781 - 3.96850i) q^{81} +(-0.155421 + 0.00166103i) q^{82} +(6.13499 + 4.70755i) q^{83} +(-0.0921203 + 0.121213i) q^{84} +(-1.64979 - 2.15005i) q^{85} +(-1.54207 + 12.7660i) q^{86} +(4.43703 - 7.39646i) q^{87} +(-4.49144 - 3.22304i) q^{88} +(9.80410 - 9.80410i) q^{89} +(-8.18129 - 11.1806i) q^{90} +(-0.0325079 + 0.0784810i) q^{91} +(2.87044 - 11.7081i) q^{92} +(-0.640957 + 1.47699i) q^{93} +(8.58699 - 2.39952i) q^{94} +(11.2340 - 19.4578i) q^{95} +(8.90847 - 4.07911i) q^{96} +(9.02297 + 15.6282i) q^{97} +(-7.07246 - 6.92288i) q^{98} +(5.48927 - 2.06132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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