LMFDB - Embedded newform 288.2.bf.a.11.23

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			11.23
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.200844 - 1.39988i) q^{2} +(-1.56060 + 0.751351i) q^{3} +(-1.91932 + 0.562314i) q^{4} +(-0.202788 - 1.54033i) q^{5} +(1.36524 + 2.03375i) q^{6} +(1.17766 + 4.39511i) q^{7} +(1.17266 + 2.57388i) q^{8} +(1.87094 - 2.34512i) q^{9} +O(q^{10})$	\(q+(-0.200844 - 1.39988i) q^{2} +(-1.56060 + 0.751351i) q^{3} +(-1.91932 + 0.562314i) q^{4} +(-0.202788 - 1.54033i) q^{5} +(1.36524 + 2.03375i) q^{6} +(1.17766 + 4.39511i) q^{7} +(1.17266 + 2.57388i) q^{8} +(1.87094 - 2.34512i) q^{9} +(-2.11554 + 0.593244i) q^{10} +(3.93681 - 3.02082i) q^{11} +(2.57280 - 2.31963i) q^{12} +(0.682021 - 0.888828i) q^{13} +(5.91609 - 2.53132i) q^{14} +(1.47380 + 2.25147i) q^{15} +(3.36761 - 2.15853i) q^{16} -4.08402 q^{17} +(-3.65865 - 2.14809i) q^{18} +(2.37867 - 0.985278i) q^{19} +(1.25536 + 2.84235i) q^{20} +(-5.14013 - 5.97416i) q^{21} +(-5.01947 - 4.90434i) q^{22} +(5.35870 + 1.43586i) q^{23} +(-3.76394 - 3.13573i) q^{24} +(2.49815 - 0.669376i) q^{25} +(-1.38123 - 0.776232i) q^{26} +(-1.15779 + 5.06552i) q^{27} +(-4.73175 - 7.77341i) q^{28} +(9.39407 + 1.23675i) q^{29} +(2.85578 - 2.51533i) q^{30} +(-0.512694 + 0.296004i) q^{31} +(-3.69804 - 4.28071i) q^{32} +(-3.87409 + 7.67221i) q^{33} +(0.820250 + 5.71713i) q^{34} +(6.53108 - 2.70526i) q^{35} +(-2.27226 + 5.55309i) q^{36} +(-1.95073 + 4.70947i) q^{37} +(-1.85701 - 3.13197i) q^{38} +(-0.396542 + 1.89954i) q^{39} +(3.72682 - 2.32823i) q^{40} +(-1.25344 + 4.67789i) q^{41} +(-7.33074 + 8.39543i) q^{42} +(1.63054 + 2.12496i) q^{43} +(-5.85736 + 8.01165i) q^{44} +(-3.99165 - 2.40630i) q^{45} +(0.933768 - 7.78992i) q^{46} +(-2.20325 - 1.27205i) q^{47} +(-3.63367 + 5.89885i) q^{48} +(-11.8679 + 6.85192i) q^{49} +(-1.43878 - 3.36266i) q^{50} +(6.37352 - 3.06853i) q^{51} +(-0.809219 + 2.08946i) q^{52} +(2.74153 - 6.61863i) q^{53} +(7.32365 + 0.603391i) q^{54} +(-5.45138 - 5.45138i) q^{55} +(-9.93149 + 8.18512i) q^{56} +(-2.97187 + 3.32484i) q^{57} +(-0.155437 - 13.3990i) q^{58} +(-0.630820 + 0.0830490i) q^{59} +(-4.09472 - 3.49256i) q^{60} +(1.61659 - 12.2792i) q^{61} +(0.517341 + 0.658259i) q^{62} +(12.5104 + 5.46124i) q^{63} +(-5.24975 + 6.03656i) q^{64} +(-1.50739 - 0.870292i) q^{65} +(11.5183 + 3.88234i) q^{66} +(-5.85104 + 7.62523i) q^{67} +(7.83855 - 2.29650i) q^{68} +(-9.44162 + 1.78546i) q^{69} +(-5.09877 - 8.59939i) q^{70} +(1.64564 + 1.64564i) q^{71} +(8.23003 + 2.06558i) q^{72} +(-0.361810 + 0.361810i) q^{73} +(6.98448 + 1.78491i) q^{74} +(-3.39567 + 2.92161i) q^{75} +(-4.01141 + 3.22863i) q^{76} +(17.9131 + 13.7452i) q^{77} +(2.73877 + 0.173599i) q^{78} +(-3.24123 + 5.61397i) q^{79} +(-4.00774 - 4.74949i) q^{80} +(-1.99913 - 8.77516i) q^{81} +(6.80022 + 0.815134i) q^{82} +(-12.0094 - 1.58106i) q^{83} +(13.2249 + 8.57598i) q^{84} +(0.828189 + 6.29072i) q^{85} +(2.64720 - 2.70934i) q^{86} +(-15.5896 + 5.12816i) q^{87} +(12.3918 + 6.59050i) q^{88} +(-2.45638 + 2.45638i) q^{89} +(-2.56684 + 6.07112i) q^{90} +(4.70968 + 1.95082i) q^{91} +(-11.0925 + 0.257395i) q^{92} +(0.577707 - 0.847156i) q^{93} +(-1.33820 + 3.33977i) q^{94} +(-2.00002 - 3.46413i) q^{95} +(8.98748 + 3.90196i) q^{96} +(8.51749 - 14.7527i) q^{97} +(11.9755 + 15.2374i) q^{98} +(0.281381 - 14.8841i) 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.200844	−	1.39988i	−0.142018	−	0.989864i
$2$	−0.200844	−	1.39988i	−0.142018	−	0.989864i
$3$	−1.56060	+	0.751351i	−0.901013	+	0.433792i
$3$	−1.56060	+	0.751351i	−0.901013	+	0.433792i
$4$	−1.91932	+	0.562314i	−0.959662	+	0.281157i
$5$	−0.202788	−	1.54033i	−0.0906895	−	0.688855i	−0.975040	−	0.222031i	$-0.928731\pi$
$5$	−0.202788	−	1.54033i	−0.0906895	−	0.688855i	0.884350	−	0.466824i	$-0.154602\pi$
$6$	1.36524	+	2.03375i	0.557356	+	0.830274i
$7$	1.17766	+	4.39511i	0.445116	+	1.66119i	0.715631	+	0.698478i	$0.246139\pi$
$7$	1.17766	+	4.39511i	0.445116	+	1.66119i	−0.270516	+	0.962716i	$0.587194\pi$
$8$	1.17266	+	2.57388i	0.414597	+	0.910005i
$9$	1.87094	−	2.34512i	0.623648	−	0.781705i
$10$	−2.11554	+	0.593244i	−0.668993	+	0.187600i
$11$	3.93681	−	3.02082i	1.18699	−	0.910811i	0.189521	−	0.981877i	$-0.439307\pi$
$11$	3.93681	−	3.02082i	1.18699	−	0.910811i	0.997472	+	0.0710656i	$0.0226400\pi$
$12$	2.57280	−	2.31963i	0.742704	−	0.669620i
$13$	0.682021	−	0.888828i	0.189159	−	0.246516i	−0.689141	−	0.724628i	$-0.742012\pi$
$13$	0.682021	−	0.888828i	0.189159	−	0.246516i	0.878299	+	0.478111i	$0.158678\pi$
$14$	5.91609	−	2.53132i	1.58114	−	0.676523i
$15$	1.47380	+	2.25147i	0.380532	+	0.581327i
$16$	3.36761	−	2.15853i	0.841901	−	0.539632i
$17$	−4.08402			−0.990519			−0.495260	−	0.868745i	$-0.664927\pi$
$17$	−4.08402			−0.990519			−0.495260	+	0.868745i	$0.664927\pi$
$18$	−3.65865	−	2.14809i	−0.862351	−	0.506311i
$19$	2.37867	−	0.985278i	0.545705	−	0.226038i	−0.0927611	−	0.995688i	$-0.529569\pi$
$19$	2.37867	−	0.985278i	0.545705	−	0.226038i	0.638466	+	0.769650i	$0.279569\pi$
$20$	1.25536	+	2.84235i	0.280708	+	0.635570i
$21$	−5.14013	−	5.97416i	−1.12167	−	1.30367i
$22$	−5.01947	−	4.90434i	−1.07015	−	1.04561i
$23$	5.35870	+	1.43586i	1.11737	+	0.299397i	0.769817	−	0.638264i	$-0.220347\pi$
$23$	5.35870	+	1.43586i	1.11737	+	0.299397i	0.347549	+	0.937662i	$0.387014\pi$
$24$	−3.76394	−	3.13573i	−0.768310	−	0.640078i
$25$	2.49815	−	0.669376i	0.499629	−	0.133875i
$26$	−1.38123	−	0.776232i	−0.270882	−	0.152232i
$27$	−1.15779	+	5.06552i	−0.222817	+	0.974860i
$28$	−4.73175	−	7.77341i	−0.894217	−	1.46904i
$29$	9.39407	+	1.23675i	1.74444	+	0.229659i	0.934276	−	0.356551i	$-0.116047\pi$
$29$	9.39407	+	1.23675i	1.74444	+	0.229659i	0.810159	+	0.586210i	$0.199381\pi$
$30$	2.85578	−	2.51533i	0.521392	−	0.459234i
$31$	−0.512694	+	0.296004i	−0.0920825	+	0.0531639i	−0.545334	−	0.838219i	$-0.683597\pi$
$31$	−0.512694	+	0.296004i	−0.0920825	+	0.0531639i	0.453252	+	0.891383i	$0.350264\pi$
$32$	−3.69804	−	4.28071i	−0.653727	−	0.756730i
$33$	−3.87409	+	7.67221i	−0.674392	+	1.33556i
$34$	0.820250	+	5.71713i	0.140672	+	0.980480i
$35$	6.53108	−	2.70526i	1.10395	−	0.457273i
$36$	−2.27226	+	5.55309i	−0.378709	+	0.925516i
$37$	−1.95073	+	4.70947i	−0.320698	+	0.774233i	0.678516	+	0.734586i	$0.262623\pi$
$37$	−1.95073	+	4.70947i	−0.320698	+	0.774233i	−0.999214	+	0.0396471i	$0.987377\pi$
$38$	−1.85701	−	3.13197i	−0.301247	−	0.508072i
$39$	−0.396542	+	1.89954i	−0.0634975	+	0.304170i
$40$	3.72682	−	2.32823i	0.589262	−	0.368125i
$41$	−1.25344	+	4.67789i	−0.195754	+	0.730563i	0.796317	+	0.604880i	$0.206779\pi$
$41$	−1.25344	+	4.67789i	−0.195754	+	0.730563i	−0.992070	+	0.125683i	$0.959888\pi$
$42$	−7.33074	+	8.39543i	−1.13116	+	1.29544i
$43$	1.63054	+	2.12496i	0.248654	+	0.324053i	0.900959	−	0.433904i	$-0.142864\pi$
$43$	1.63054	+	2.12496i	0.248654	+	0.324053i	−0.652305	+	0.757957i	$0.726198\pi$
$44$	−5.85736	+	8.01165i	−0.883030	+	1.20780i
$45$	−3.99165	−	2.40630i	−0.595040	−	0.358711i
$46$	0.933768	−	7.78992i	0.137677	−	1.14856i
$47$	−2.20325	−	1.27205i	−0.321377	−	0.185547i	0.330629	−	0.943761i	$-0.392739\pi$
$47$	−2.20325	−	1.27205i	−0.321377	−	0.185547i	−0.652006	+	0.758214i	$0.726072\pi$
$48$	−3.63367	+	5.89885i	−0.524476	+	0.851425i
$49$	−11.8679	+	6.85192i	−1.69541	+	0.978846i
$50$	−1.43878	−	3.36266i	−0.203475	−	0.475552i
$51$	6.37352	−	3.06853i	0.892471	−	0.429680i
$52$	−0.809219	+	2.08946i	−0.112219	+	0.289756i
$53$	2.74153	−	6.61863i	0.376578	−	0.909139i	−0.616024	−	0.787727i	$-0.711258\pi$
$53$	2.74153	−	6.61863i	0.376578	−	0.909139i	0.992602	−	0.121412i	$-0.0387423\pi$
$54$	7.32365	+	0.603391i	0.996623	+	0.0821111i
$55$	−5.45138	−	5.45138i	−0.735064	−	0.735064i
$56$	−9.93149	+	8.18512i	−1.32715	+	1.09378i
$57$	−2.97187	+	3.32484i	−0.393633	+	0.440386i
$58$	−0.155437	−	13.3990i	−0.0204099	−	1.75937i
$59$	−0.630820	+	0.0830490i	−0.0821257	+	0.0108121i	−0.171477	−	0.985188i	$-0.554854\pi$
$59$	−0.630820	+	0.0830490i	−0.0821257	+	0.0108121i	0.0893513	+	0.996000i	$0.471521\pi$
$60$	−4.09472	−	3.49256i	−0.528627	−	0.450888i
$61$	1.61659	−	12.2792i	0.206983	−	1.57219i	−0.500675	−	0.865636i	$-0.666915\pi$
$61$	1.61659	−	12.2792i	0.206983	−	1.57219i	0.707658	−	0.706556i	$-0.249752\pi$
$62$	0.517341	+	0.658259i	0.0657024	+	0.0835990i
$63$	12.5104	+	5.46124i	1.57616	+	0.688051i
$64$	−5.24975	+	6.03656i	−0.656219	+	0.754570i
$65$	−1.50739	−	0.870292i	−0.186969	−	0.107946i
$66$	11.5183	+	3.88234i	1.41780	+	0.477883i
$67$	−5.85104	+	7.62523i	−0.714819	+	0.931570i	−0.999635	−	0.0270123i	$-0.991401\pi$
$67$	−5.85104	+	7.62523i	−0.714819	+	0.931570i	0.284816	+	0.958582i	$0.408067\pi$
$68$	7.83855	−	2.29650i	0.950564	−	0.278492i
$69$	−9.44162	+	1.78546i	−1.13664	+	0.214944i
$70$	−5.09877	−	8.59939i	−0.609419	−	1.02782i
$71$	1.64564	+	1.64564i	0.195301	+	0.195301i	0.797982	−	0.602681i	$-0.205901\pi$
$71$	1.64564	+	1.64564i	0.195301	+	0.195301i	−0.602681	+	0.797982i	$0.705901\pi$
$72$	8.23003	+	2.06558i	0.969918	+	0.243431i
$73$	−0.361810	+	0.361810i	−0.0423466	+	0.0423466i	−0.727963	−	0.685616i	$-0.759533\pi$
$73$	−0.361810	+	0.361810i	−0.0423466	+	0.0423466i	0.685616	+	0.727963i	$0.259533\pi$
$74$	6.98448	+	1.78491i	0.811930	+	0.207492i
$75$	−3.39567	+	2.92161i	−0.392098	+	0.337359i
$76$	−4.01141	+	3.22863i	−0.460140	+	0.370349i
$77$	17.9131	+	13.7452i	2.04138	+	1.56641i
$78$	2.73877	+	0.173599i	0.310105	+	0.0196562i
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	−0.988723	−	0.149758i	$-0.952150\pi$
$79$	−3.24123	+	5.61397i	−0.364667	+	0.631622i	0.624056	+	0.781380i	$0.285484\pi$
$80$	−4.00774	−	4.74949i	−0.448079	−	0.531009i
$81$	−1.99913	−	8.77516i	−0.222126	−	0.975018i
$82$	6.80022	+	0.815134i	0.750959	+	0.0900165i
$83$	−12.0094	−	1.58106i	−1.31820	−	0.173544i	−0.561593	−	0.827414i	$-0.689811\pi$
$83$	−12.0094	−	1.58106i	−1.31820	−	0.173544i	−0.756607	+	0.653870i	$0.773144\pi$
$84$	13.2249	+	8.57598i	1.44296	+	0.935716i
$85$	0.828189	+	6.29072i	0.0898297	+	0.682324i
$86$	2.64720	−	2.70934i	0.285455	−	0.292155i
$87$	−15.5896	+	5.12816i	−1.67138	+	0.549797i
$88$	12.3918	+	6.59050i	1.32097	+	0.702550i
$89$	−2.45638	+	2.45638i	−0.260376	+	0.260376i	−0.825207	−	0.564831i	$-0.808941\pi$
$89$	−2.45638	+	2.45638i	−0.260376	+	0.260376i	0.564831	+	0.825207i	$0.308941\pi$
$90$	−2.56684	+	6.07112i	−0.270568	+	0.639952i
$91$	4.70968	+	1.95082i	0.493709	+	0.204501i
$92$	−11.0925	+	0.257395i	−1.15647	+	0.0268353i
$93$	0.577707	−	0.847156i	0.0599055	−	0.0878460i
$94$	−1.33820	+	3.33977i	−0.138025	+	0.344471i
$95$	−2.00002	−	3.46413i	−0.205197	−	0.355412i
$96$	8.98748	+	3.90196i	0.917280	+	0.398242i
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	−0.00240483	−	0.999997i	$-0.500765\pi$
$97$	8.51749	−	14.7527i	0.864820	−	1.49791i	0.867225	−	0.497916i	$-0.165901\pi$
$98$	11.9755	+	15.2374i	1.20970	+	1.53921i
$99$	0.281381	−	14.8841i	0.0282799	−	1.49590i
$100$	−4.41835	+	2.68949i	−0.441835	+	0.268949i
$101$	3.20048	−	2.45582i	0.318460	−	0.244363i	−0.437144	−	0.899391i	$-0.644010\pi$
$101$	3.20048	−	2.45582i	0.318460	−	0.244363i	0.755604	+	0.655028i	$0.227343\pi$
$102$	−5.57565	−	8.30586i	−0.552072	−	0.822402i
$103$	15.3404	+	4.11044i	1.51153	+	0.405013i	0.916943	−	0.399018i	$-0.130649\pi$
$103$	15.3404	+	4.11044i	1.51153	+	0.405013i	0.594587	+	0.804031i	$0.297316\pi$
$104$	3.08752	+	0.713154i	0.302756	+	0.0699305i
$105$	−8.15980	+	9.12896i	−0.796315	+	0.890896i
$106$	−9.81591	−	2.50850i	−0.953405	−	0.243647i
$107$	−2.60587	−	1.07939i	−0.251919	−	0.104348i	0.253150	−	0.967427i	$-0.418533\pi$
$107$	−2.60587	−	1.07939i	−0.251919	−	0.104348i	−0.505070	+	0.863079i	$0.668533\pi$
$108$	−0.626237	−	10.3734i	−0.0602597	−	0.998183i
$109$	−0.946606	−	2.28531i	−0.0906684	−	0.218893i	0.872040	−	0.489435i	$-0.162797\pi$
$109$	−0.946606	−	2.28531i	−0.0906684	−	0.218893i	−0.962708	+	0.270542i	$0.912797\pi$
$110$	−6.53640	+	8.72616i	−0.623221	+	0.832006i
$111$	−0.494160	−	8.81528i	−0.0469036	−	0.836710i
$112$	13.4529	+	12.2590i	1.27118	+	1.15836i
$113$	−8.13956	−	14.0981i	−0.765705	−	1.32624i	−0.939873	−	0.341525i	$-0.889057\pi$
$113$	−8.13956	−	14.0981i	−0.765705	−	1.32624i	0.174167	−	0.984716i	$-0.444277\pi$
$114$	5.25126	+	3.49248i	0.491825	+	0.327101i
$115$	1.12501	−	8.54533i	0.104908	−	0.796856i
$116$	−18.7257	+	2.90869i	−1.73864	+	0.270065i
$117$	−0.808379	−	3.26237i	−0.0747347	−	0.301606i
$118$	0.242955	+	0.866392i	0.0223658	+	0.0797578i
$119$	−4.80960	−	17.9497i	−0.440896	−	1.64544i
$120$	−4.06676	+	6.43358i	−0.371243	+	0.587303i
$121$	3.52610	−	13.1596i	0.320554	−	1.19633i
$122$	−17.5141	+	0.203175i	−1.58565	+	0.0183946i
$123$	−1.55862	−	8.24208i	−0.140536	−	0.743164i
$124$	0.817578	−	0.856422i	0.0734207	−	0.0769090i
$125$	−4.51037	−	10.8890i	−0.403420	−	0.973942i
$126$	5.13244	−	18.6099i	0.457234	−	1.65790i
$127$			21.9679i			1.94934i	0.223651	+	0.974669i	$0.428202\pi$
$127$			21.9679i			1.94934i	−0.223651	+	0.974669i	$0.571798\pi$
$128$	9.50484	+	6.13661i	0.840117	+	0.542405i
$129$	−4.14120	−	2.09110i	−0.364613	−	0.184111i
$130$	−0.915554	+	2.28496i	−0.0802994	+	0.200404i
$131$	−2.58818	−	1.98598i	−0.226130	−	0.173516i	0.489482	−	0.872013i	$-0.337186\pi$
$131$	−2.58818	−	1.98598i	−0.226130	−	0.173516i	−0.715613	+	0.698497i	$0.753852\pi$
$132$	3.12143	−	16.9039i	0.271686	−	1.47130i
$133$	7.13168	+	9.29419i	0.618395	+	0.805908i
$134$	11.8495	+	6.65927i	1.02364	+	0.575274i
$135$	8.03734	+	0.756152i	0.691744	+	0.0650792i
$136$	−4.78915	−	10.5118i	−0.410666	−	0.901378i
$137$	−3.35747	+	0.899631i	−0.286848	+	0.0768606i	−0.399374	−	0.916788i	$-0.630772\pi$
$137$	−3.35747	+	0.899631i	−0.286848	+	0.0768606i	0.112526	+	0.993649i	$0.464106\pi$
$138$	4.39572	+	12.8585i	0.374189	+	1.09459i
$139$	−16.1894	+	2.13138i	−1.37317	+	0.180781i	−0.780748	−	0.624846i	$-0.785162\pi$
$139$	−16.1894	+	2.13138i	−1.37317	+	0.180781i	−0.592423	+	0.805627i	$0.701828\pi$
$140$	−11.0140	+	8.86479i	−0.930857	+	0.749212i
$141$	4.39415	+	0.329743i	0.370054	+	0.0277694i
$142$	1.97318	−	2.63421i	0.165586	−	0.221058i
$143$		−	5.55941i		−	0.464901i
$144$	1.23861	−	11.9359i	0.103217	−	0.994659i
$145$		−	14.7207i		−	1.22249i
$146$	0.579157	+	0.433823i	0.0479314	+	0.0359034i
$147$	13.3728	−	19.6100i	1.10297	−	1.61741i
$148$	1.09587	−	10.1359i	0.0900802	−	0.833168i
$149$	−9.88347	+	1.30118i	−0.809685	+	0.106597i	−0.523991	−	0.851724i	$-0.675557\pi$
$149$	−9.88347	+	1.30118i	−0.809685	+	0.106597i	−0.285694	+	0.958321i	$0.592224\pi$
$150$	4.77190	+	4.16674i	0.389624	+	0.340213i
$151$	−4.32703	+	1.15942i	−0.352129	+	0.0943526i	−0.430548	−	0.902568i	$-0.641680\pi$
$151$	−4.32703	+	1.15942i	−0.352129	+	0.0943526i	0.0784188	+	0.996921i	$0.475013\pi$
$152$	5.32536	+	4.96703i	0.431944	+	0.402880i
$153$	−7.64097	+	9.57749i	−0.617736	+	0.774294i
$154$	15.6439	−	27.8368i	1.26062	−	2.24315i
$155$	0.559911	+	0.729690i	0.0449731	+	0.0586101i
$156$	−0.307048	−	3.86882i	−0.0245835	−	0.309753i
$157$	6.14501	+	4.71523i	0.490425	+	0.376317i	0.824166	−	0.566348i	$-0.191644\pi$
$157$	6.14501	+	4.71523i	0.490425	+	0.376317i	−0.333741	+	0.942665i	$0.608311\pi$
$158$	8.50987	+	3.40980i	0.677009	+	0.271269i
$159$	0.694486	+	12.3889i	0.0550763	+	0.982503i
$160$	−5.84378	+	6.56426i	−0.461991	+	0.518951i
$161$			25.2430i			1.98943i
$162$	−11.8827	+	4.56098i	−0.933589	+	0.358344i
$163$	−4.51520	−	10.9007i	−0.353658	−	0.853806i	−0.996162	−	0.0875240i	$-0.972105\pi$
$163$	−4.51520	−	10.9007i	−0.353658	−	0.853806i	0.642504	−	0.766282i	$-0.277895\pi$
$164$	−0.224694	−	9.68321i	−0.0175456	−	0.756131i
$165$	12.6033	+	4.41153i	0.981168	+	0.343437i
$166$	0.198711	+	17.1292i	0.0154229	+	1.32949i
$167$	0.234682	−	0.875847i	0.0181603	−	0.0677751i	−0.956251	−	0.292547i	$-0.905497\pi$
$167$	0.234682	−	0.875847i	0.0181603	−	0.0677751i	0.974411	+	0.224772i	$0.0721638\pi$
$168$	9.34919	−	20.2357i	0.721306	−	1.56122i
$169$	3.03979	+	11.3446i	0.233830	+	0.872664i
$170$	8.63991	−	2.42282i	0.662651	−	0.185822i
$171$	2.13977	−	7.42166i	0.163633	−	0.567549i
$172$	−4.32442	−	3.16160i	−0.329734	−	0.241070i
$173$	0.137639	−	1.04547i	0.0104645	−	0.0794859i	−0.985416	−	0.170164i	$-0.945570\pi$
$173$	0.137639	−	1.04547i	0.0104645	−	0.0794859i	0.995880	+	0.0906783i	$0.0289035\pi$
$174$	10.3099	+	20.7936i	0.781591	+	1.57636i
$175$	5.88396	+	10.1913i	0.444785	+	0.770391i
$176$	6.73710	−	18.6706i	0.507828	−	1.40735i
$177$	0.922058	−	0.603573i	0.0693062	−	0.0453673i
$178$	3.93199	+	2.94529i	0.294715	+	0.220759i
$179$	−8.10504	−	19.5673i	−0.605799	−	1.46253i	−0.867529	−	0.497387i	$-0.834293\pi$
$179$	−8.10504	−	19.5673i	−0.605799	−	1.46253i	0.261730	−	0.965141i	$-0.415707\pi$
$180$	9.01436	+	2.37392i	0.671891	+	0.176941i
$181$	4.74472	+	1.96533i	0.352672	+	0.146082i	0.551984	−	0.833854i	$-0.313871\pi$
$181$	4.74472	+	1.96533i	0.352672	+	0.146082i	−0.199312	+	0.979936i	$0.563871\pi$
$182$	1.78499	−	6.98480i	0.132313	−	0.517748i
$183$	6.70314	+	20.3776i	0.495510	+	1.50635i
$184$	2.58818	+	15.4764i	0.190803	+	1.14094i
$185$	7.64971	+	2.04973i	0.562418	+	0.150699i
$186$	−1.30195	−	0.638574i	−0.0954633	−	0.0468225i
$187$	−16.0780	+	12.3371i	−1.17574	+	0.902176i
$188$	4.94404	+	1.20255i	0.360581	+	0.0877050i
$189$	−23.6270	+	0.876868i	−1.71861	+	0.0637827i
$190$	−4.44767	+	3.49553i	−0.322668	+	0.253592i
$191$	2.81155	−	4.86975i	0.203437	−	0.352363i	−0.746197	−	0.665725i	$-0.768122\pi$
$191$	2.81155	−	4.86975i	0.203437	−	0.352363i	0.949634	+	0.313363i	$0.101456\pi$
$192$	3.65719	−	13.3651i	0.263935	−	0.964540i
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	0.885187	−	0.465236i	$-0.154031\pi$
$193$	0.551350	+	0.954966i	0.0396870	+	0.0687399i	−0.845500	+	0.533976i	$0.820697\pi$
$194$	−22.3627	−	8.96047i	−1.60555	−	0.643324i
$195$	3.00633	+	0.225599i	0.215288	+	0.0161555i
$196$	18.9254	−	19.8245i	1.35181	−	1.41604i
$197$	−7.02701	−	2.91068i	−0.500653	−	0.207377i	0.118042	−	0.993009i	$-0.462338\pi$
$197$	−7.02701	−	2.91068i	−0.500653	−	0.207377i	−0.618695	+	0.785631i	$0.712338\pi$
$198$	−20.8924	+	2.59547i	−1.48476	+	0.184452i
$199$	1.84792	−	1.84792i	0.130996	−	0.130996i	−0.638569	−	0.769565i	$-0.720473\pi$
$199$	1.84792	−	1.84792i	0.130996	−	0.130996i	0.769565	+	0.638569i	$0.220473\pi$
$200$	4.65236	+	5.64499i	0.328972	+	0.399161i
$201$	3.40192	−	16.2961i	0.239953	−	1.14944i
$202$	−4.08065	−	3.98705i	−0.287113	−	0.280528i
$203$	5.62741	+	42.7444i	0.394967	+	3.00007i
$204$	−10.5074	+	9.47342i	−0.735662	+	0.663272i
$205$	7.45966	+	0.982082i	0.521005	+	0.0685916i
$206$	2.67310	−	22.3002i	0.186243	−	1.55373i
$207$	13.3931	−	9.88036i	0.930884	−	0.686732i
$208$	0.378221	−	4.46538i	0.0262249	−	0.309619i
$209$	6.38803	−	11.0644i	0.441869	−	0.765340i
$210$	14.4183	+	9.58924i	0.994957	+	0.661721i
$211$	0.862538	+	0.661849i	0.0593796	+	0.0455635i	0.638025	−	0.770016i	$-0.279752\pi$
$211$	0.862538	+	0.661849i	0.0593796	+	0.0455635i	−0.578645	+	0.815579i	$0.696418\pi$
$212$	−1.54013	+	14.2449i	−0.105776	+	0.978344i
$213$	−3.80464	−	1.33173i	−0.260689	−	0.0912488i
$214$	−0.987640	+	3.86470i	−0.0675137	+	0.264185i
$215$	2.94247	−	2.94247i	0.200675	−	0.200675i
$216$	−14.3958	+	2.96009i	−0.979507	+	0.201409i
$217$	−1.90475	−	1.90475i	−0.129303	−	0.129303i
$218$	−3.00904	+	1.78412i	−0.203798	+	0.120836i
$219$	0.292794	−	0.836486i	0.0197852	−	0.0565245i
$220$	13.5284	+	7.39758i	0.912082	+	0.498745i
$221$	−2.78539	+	3.62999i	−0.187365	+	0.244179i
$222$	−12.2411	+	2.46226i	−0.821568	+	0.165256i
$223$	5.00046	+	2.88701i	0.334855	+	0.193329i	0.657995	−	0.753023i	$-0.271405\pi$
$223$	5.00046	+	2.88701i	0.334855	+	0.193329i	−0.323139	+	0.946351i	$0.604738\pi$
$224$	14.4591	−	21.2945i	0.966092	−	1.42280i
$225$	3.10413	−	7.11081i	0.206942	−	0.474054i
$226$	−18.1009	+	14.2259i	−1.20405	+	0.946294i
$227$	−0.802907	+	6.09868i	−0.0532908	+	0.404784i	0.943922	+	0.330169i	$0.107106\pi$
$227$	−0.802907	+	6.09868i	−0.0532908	+	0.404784i	−0.997212	+	0.0746142i	$0.976227\pi$
$228$	3.83437	−	8.05257i	0.253937	−	0.533295i
$229$	−14.7068	+	1.93618i	−0.971851	+	0.127947i	−0.599700	−	0.800225i	$-0.704713\pi$
$229$	−14.7068	+	1.93618i	−0.971851	+	0.127947i	−0.372152	+	0.928172i	$0.621380\pi$
$230$	−12.1884	+	0.141393i	−0.803678	+	0.00932321i
$231$	−38.2826	−	7.99173i	−2.51881	−	0.525817i
$232$	7.83276	+	25.6295i	0.514246	+	1.68266i
$233$	14.8047	+	14.8047i	0.969888	+	0.969888i	0.999560	−	0.0296721i	$-0.00944630\pi$
$233$	14.8047	+	14.8047i	0.969888	+	0.969888i	−0.0296721	+	0.999560i	$0.509446\pi$
$234$	−4.40456	+	1.78686i	−0.287935	+	0.116811i
$235$	−1.51258	+	3.65168i	−0.0986695	+	0.238209i
$236$	1.16405	−	0.514117i	0.0757730	−	0.0334662i
$237$	0.840200	−	11.1965i	0.0545769	−	0.727289i
$238$	−24.1614	+	10.3379i	−1.56615	+	0.670110i
$239$	5.86397	−	3.38557i	0.379309	−	0.218994i	−0.298209	−	0.954501i	$-0.596389\pi$
$239$	5.86397	−	3.38557i	0.379309	−	0.218994i	0.677518	+	0.735507i	$0.263056\pi$
$240$	9.82302	+	4.40083i	0.634073	+	0.284072i
$241$	25.0688	+	14.4735i	1.61482	+	0.932318i	0.988231	+	0.152970i	$0.0488839\pi$
$241$	25.0688	+	14.4735i	1.61482	+	0.932318i	0.626592	+	0.779348i	$0.284449\pi$
$242$	−19.1300	−	2.29309i	−1.22972	−	0.147406i
$243$	9.71307	+	12.1925i	0.623094	+	0.782147i
$244$	3.80202	+	24.4768i	0.243399	+	1.56697i
$245$	12.9609	+	16.8909i	0.828039	+	1.07912i
$246$	−11.2249	+	3.83725i	−0.715672	+	0.244654i
$247$	0.746563	−	2.78621i	0.0475027	−	0.177282i
$248$	−1.36309	−	0.972503i	−0.0865565	−	0.0617540i
$249$	19.9298	−	6.55584i	1.26300	−	0.415459i
$250$	−14.3374	+	8.50096i	−0.906777	+	0.537648i
$251$	1.10999	−	2.67976i	0.0700622	−	0.169145i	−0.884969	−	0.465649i	$-0.845821\pi$
$251$	1.10999	−	2.67976i	0.0700622	−	0.169145i	0.955032	+	0.296504i	$0.0958208\pi$
$252$	−27.0824	−	3.44712i	−1.70603	−	0.217148i
$253$	25.4337	−	10.5350i	1.59900	−	0.662327i
$254$	30.7524	−	4.41212i	1.92958	−	0.276841i
$255$	−6.01901	−	9.19503i	−0.376925	−	0.575815i
$256$	6.68153	−	14.5381i	0.417596	−	0.908633i
$257$	−19.8010	+	11.4321i	−1.23515	+	0.713115i	−0.968099	−	0.250567i	$-0.919383\pi$
$257$	−19.8010	+	11.4321i	−1.23515	+	0.713115i	−0.267052	+	0.963682i	$0.586050\pi$
$258$	−2.09556	+	6.21717i	−0.130464	+	0.387064i
$259$	−22.9959	−	3.02747i	−1.42890	−	0.188118i
$260$	3.38255	+	0.822745i	0.209777	+	0.0510245i
$261$	20.4761	−	19.7163i	1.26744	−	1.22041i
$262$	−2.26031	+	4.02201i	−0.139643	+	0.248481i
$263$	0.590968	−	0.158349i	0.0364407	−	0.00976425i	−0.240553	−	0.970636i	$-0.577329\pi$
$263$	0.590968	−	0.158349i	0.0364407	−	0.00976425i	0.276993	+	0.960872i	$0.410662\pi$
$264$	−24.2904	−	0.974582i	−1.49497	−	0.0599814i
$265$	−10.7508	−	2.88067i	−0.660417	−	0.176958i
$266$	11.5784	−	11.8502i	0.709916	−	0.726581i
$267$	1.98783	−	5.67904i	0.121653	−	0.347551i
$268$	6.94227	−	17.9254i	0.424067	−	1.09497i
$269$	−1.42907	+	0.591941i	−0.0871321	+	0.0360913i	−0.425824	−	0.904806i	$-0.640016\pi$
$269$	−1.42907	+	0.591941i	−0.0871321	+	0.0360913i	0.338692	+	0.940897i	$0.390016\pi$
$270$	−0.555730	−	11.4032i	−0.0338206	−	0.693975i
$271$	12.8060			0.777912			0.388956	−	0.921256i	$-0.372836\pi$
$271$	12.8060			0.777912			0.388956	+	0.921256i	$0.372836\pi$
$272$	−13.7534	+	8.81546i	−0.833920	+	0.534516i
$273$	−8.81568	+	0.494182i	−0.533549	+	0.0299092i
$274$	1.93370	+	4.51936i	0.116819	+	0.273025i
$275$	7.81266	−	10.1817i	0.471121	−	0.613977i
$276$	17.1175	−	8.73604i	1.03035	−	0.525848i
$277$	−8.33871	+	6.39852i	−0.501025	+	0.384450i	−0.828128	−	0.560539i	$-0.810594\pi$
$277$	−8.33871	+	6.39852i	−0.501025	+	0.384450i	0.327103	+	0.944989i	$0.393927\pi$
$278$	6.23523	+	22.2352i	0.373964	+	1.33358i
$279$	−0.265058	+	1.75613i	−0.0158686	+	0.105137i
$280$	14.6217	+	13.6379i	0.873816	+	0.815020i
$281$	2.09852	+	7.83178i	0.125187	+	0.467205i	0.999846	−	0.0175337i	$-0.00558145\pi$
$281$	2.09852	+	7.83178i	0.125187	+	0.467205i	−0.874659	+	0.484738i	$0.838915\pi$
$282$	−0.420936	−	6.21750i	−0.0250664	−	0.370247i
$283$	−1.51058	−	11.4740i	−0.0897947	−	0.682059i	−0.975844	−	0.218468i	$-0.929894\pi$
$283$	−1.51058	−	11.4740i	−0.0897947	−	0.682059i	0.886049	−	0.463591i	$-0.153439\pi$
$284$	−4.08388	−	2.23315i	−0.242334	−	0.132513i
$285$	5.72400	+	3.90341i	0.339061	+	0.231218i
$286$	−7.78250	+	1.11657i	−0.460189	+	0.0660243i
$287$	−22.0359			−1.30074
$288$	−16.9576	+	0.663349i	−0.999236	+	0.0390882i
$289$	−0.320814			−0.0188714
$290$	−20.6073	+	2.95657i	−1.21010	+	0.173616i
$291$	−2.20793	+	29.4227i	−0.129431	+	1.72479i
$292$	0.490979	−	0.897881i	0.0287324	−	0.0525445i
$293$	0.378280	+	2.87332i	0.0220993	+	0.167861i	0.998936	−	0.0461271i	$-0.0146879\pi$
$293$	0.378280	+	2.87332i	0.0220993	+	0.167861i	−0.976836	+	0.213988i	$0.931355\pi$
$294$	−30.1375	−	14.7818i	−1.75766	−	0.862090i
$295$	0.255845	+	0.954827i	0.0148959	+	0.0555922i
$296$	−14.4092	+	0.501649i	−0.837516	+	0.0291577i
$297$	10.7440	+	23.4395i	0.623431	+	1.36010i
$298$	3.80653	+	13.5743i	0.220507	+	0.786340i
$299$	4.93098	−	3.78368i	0.285166	−	0.218816i
$300$	4.87453	−	7.51695i	0.281431	−	0.433992i
$301$	−7.41918	+	9.66887i	−0.427635	+	0.557304i
$302$	2.49211	+	5.82446i	0.143405	+	0.335160i
$303$	−3.14949	+	6.23723i	−0.180934	+	0.358320i
$304$	5.88368	−	8.45246i	0.337452	−	0.484782i
$305$	−19.2418			−1.10178
$306$	14.9420	+	8.77285i	0.854175	+	0.501511i
$307$	−25.8180	+	10.6941i	−1.47351	+	0.610347i	−0.967656	−	0.252273i	$-0.918822\pi$
$307$	−25.8180	+	10.6941i	−1.47351	+	0.610347i	−0.505852	+	0.862620i	$0.668822\pi$
$308$	−42.1101	−	16.3087i	−2.39944	−	0.929272i
$309$	−27.0285	+	5.11124i	−1.53760	+	0.290768i
$310$	0.909023	−	0.930361i	0.0516290	−	0.0528410i
$311$	−32.4549	−	8.69628i	−1.84035	−	0.493121i	−0.841465	−	0.540311i	$-0.818306\pi$
$311$	−32.4549	−	8.69628i	−1.84035	−	0.493121i	−0.998886	+	0.0471908i	$0.984973\pi$
$312$	−5.35421	+	1.20686i	−0.303122	+	0.0683249i
$313$	−11.2593	+	3.01691i	−0.636412	+	0.170526i	−0.562578	−	0.826745i	$-0.690190\pi$
$313$	−11.2593	+	3.01691i	−0.636412	+	0.170526i	−0.0738342	+	0.997271i	$0.523524\pi$
$314$	5.36657	−	9.54930i	0.302853	−	0.538898i
$315$	5.87514	−	20.3775i	0.331027	−	1.14814i
$316$	3.06415	−	12.5976i	0.172372	−	0.708672i
$317$	25.9981	+	3.42271i	1.46020	+	0.192239i	0.818406	−	0.574640i	$-0.194858\pi$
$317$	25.9981	+	3.42271i	1.46020	+	0.192239i	0.641792	+	0.766879i	$0.278191\pi$
$318$	17.2035	−	3.46043i	0.964722	−	0.194051i
$319$	40.7187	−	23.5089i	2.27981	−	1.31625i
$320$	10.3629	+	6.86219i	0.579302	+	0.383608i
$321$	4.87773	−	0.273431i	0.272248	−	0.0152615i
$322$	35.3372	−	5.06991i	1.96926	−	0.282535i
$323$	−9.71454	+	4.02389i	−0.540531	+	0.223895i
$324$	8.77138	+	15.7182i	0.487299	+	0.873235i
$325$	1.10883	−	2.67695i	0.0615068	−	0.148491i
$326$	−14.3528	+	8.51007i	−0.794926	+	0.471329i
$327$	3.19434	+	2.85522i	0.176647	+	0.157894i
$328$	−13.5102	+	2.25936i	−0.745975	+	0.124752i
$329$	2.99609	−	11.1816i	0.165180	−	0.616460i
$330$	3.64431	−	18.5292i	0.200612	−	1.02000i
$331$	−20.5227	−	26.7458i	−1.12803	−	1.47008i	−0.862555	−	0.505963i	$-0.831137\pi$
$331$	−20.5227	−	26.7458i	−1.12803	−	1.47008i	−0.265477	−	0.964117i	$-0.585529\pi$
$332$	23.9389	−	3.71847i	1.31382	−	0.204078i
$333$	7.39455	+	13.3858i	0.405219	+	0.733540i
$334$	−1.27321	−	0.152619i	−0.0696672	−	0.00835092i
$335$	12.9319	+	7.46621i	0.706543	+	0.407923i
$336$	−30.2053	−	9.02352i	−1.64783	−	0.492273i
$337$	2.73282	−	1.57779i	0.148866	−	0.0859478i	−0.423717	−	0.905795i	$-0.639275\pi$
$337$	2.73282	−	1.57779i	0.148866	−	0.0859478i	0.572583	+	0.819847i	$0.305942\pi$
$338$	15.2706	−	6.53383i	0.830611	−	0.355394i
$339$	23.2952	+	15.8859i	1.26522	+	0.862803i
$340$	−5.12692	−	11.6082i	−0.278046	−	0.629544i
$341$	−1.12420	+	2.71407i	−0.0608790	+	0.146975i
$342$	−10.8192	−	1.50483i	−0.585035	−	0.0813718i
$343$	−21.5692	−	21.5692i	−1.16463	−	1.16463i
$344$	−3.55733	+	6.68866i	−0.191798	+	0.360628i
$345$	4.66484	+	14.1811i	0.251146	+	0.763486i
$346$	−1.49118	+	0.0172987i	−0.0801664	+	0.000929985i
$347$	−25.4794	+	3.35443i	−1.36781	+	0.180075i	−0.778404	−	0.627764i	$-0.783970\pi$
$347$	−25.4794	+	3.35443i	−1.36781	+	0.180075i	−0.589403	+	0.807839i	$0.700637\pi$
$348$	27.0379	−	18.6089i	1.44938	−	0.997540i
$349$	−1.58498	+	12.0391i	−0.0848420	+	0.644439i	0.895202	+	0.445660i	$0.147031\pi$
$349$	−1.58498	+	12.0391i	−0.0848420	+	0.644439i	−0.980044	+	0.198779i	$0.936302\pi$
$350$	13.0849	−	10.2837i	0.699415	−	0.549687i
$351$	3.71274	+	4.48387i	0.198171	+	0.239331i
$352$	−27.4897	−	5.68124i	−1.46521	−	0.302811i
$353$	−3.33343	−	1.92456i	−0.177421	−	0.102434i	0.408660	−	0.912687i	$-0.365996\pi$
$353$	−3.33343	−	1.92456i	−0.177421	−	0.102434i	−0.586080	+	0.810253i	$0.699330\pi$
$354$	−1.03012	−	1.16955i	−0.0547502	−	0.0621607i
$355$	2.20111	−	2.86854i	0.116823	−	0.152246i
$356$	3.33333	−	6.09585i	0.176666	−	0.323080i
$357$	20.9924	+	24.3986i	1.11103	+	1.29131i
$358$	−25.7640	+	15.2760i	−1.36167	+	0.807364i
$359$	−14.3336	−	14.3336i	−0.756497	−	0.756497i	0.219186	−	0.975683i	$-0.429660\pi$
$359$	−14.3336	−	14.3336i	−0.756497	−	0.756497i	−0.975683	+	0.219186i	$0.929660\pi$
$360$	1.51272	−	13.0958i	0.0797271	−	0.690210i
$361$	−8.74772	+	8.74772i	−0.460406	+	0.460406i
$362$	1.79827	−	7.03676i	0.0945151	−	0.369844i
$363$	4.38463	+	23.1862i	0.230133	+	1.21696i
$364$	−10.1364	−	1.09592i	−0.531291	−	0.0574419i
$365$	0.630676	+	0.483935i	0.0330111	+	0.0253303i
$366$	27.1798	−	13.4763i	1.42071	−	0.704417i
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	−0.717837	−	0.696212i	$-0.754868\pi$
$367$	4.67472	−	8.09686i	0.244019	−	0.422652i	0.961855	+	0.273559i	$0.0882009\pi$
$368$	21.1453	−	6.73149i	1.10228	−	0.350903i
$369$	8.62508	+	11.6915i	0.449004	+	0.608636i
$370$	1.33298	−	11.1203i	0.0692984	−	0.578119i
$371$	32.3182	+	4.25477i	1.67788	+	0.220897i
$372$	−0.632439	+	1.95082i	−0.0327904	+	0.101145i
$373$	−0.741285	−	5.63062i	−0.0383823	−	0.291542i	−0.999861	−	0.0166635i	$-0.994696\pi$
$373$	−0.741285	−	5.63062i	−0.0383823	−	0.291542i	0.961479	−	0.274879i	$-0.0886377\pi$
$374$	20.4996	+	20.0294i	1.06001	+	1.03570i
$375$	15.2203	+	13.6045i	0.785975	+	0.702533i
$376$	0.690445	−	7.16258i	0.0356070	−	0.369382i
$377$	7.50622	−	7.50622i	0.386590	−	0.386590i
$378$	5.97285	+	32.8988i	0.307210	+	1.69213i
$379$	21.3058	+	8.82516i	1.09441	+	0.453318i	0.855541	−	0.517735i	$-0.173225\pi$
$379$	21.3058	+	8.82516i	1.09441	+	0.453318i	0.238865	+	0.971053i	$0.423225\pi$
$380$	5.78661	+	5.52415i	0.296847	+	0.283383i
$381$	−16.5056	−	34.2832i	−0.845608	−	1.75638i
$382$	−7.38175	−	2.95777i	−0.377683	−	0.151333i
$383$	−11.6397	−	20.1606i	−0.594762	−	1.03016i	−0.993580	−	0.113128i	$-0.963913\pi$
$383$	−11.6397	−	20.1606i	−0.594762	−	1.03016i	0.398818	−	0.917030i	$-0.369420\pi$
$384$	−19.4440	−	2.43533i	−0.992247	−	0.124278i
$385$	17.5395	−	30.3793i	0.893896	−	1.54827i
$386$	1.22610	−	0.963622i	0.0624069	−	0.0490471i
$387$	8.03391	+	0.151880i	0.408387	+	0.00772050i
$388$	−8.05215	+	33.1048i	−0.408786	+	1.68064i
$389$	−2.18552	+	1.67701i	−0.110810	+	0.0850275i	−0.662680	−	0.748903i	$-0.730581\pi$
$389$	−2.18552	+	1.67701i	−0.110810	+	0.0850275i	0.551870	+	0.833930i	$0.313914\pi$
$390$	−0.287991	−	4.25381i	−0.0145830	−	0.215400i
$391$	−21.8850	−	5.86407i	−1.10677	−	0.296559i
$392$	−31.5530	−	22.5116i	−1.59367	−	1.13701i
$393$	5.53128	+	1.15469i	0.279016	+	0.0582465i
$394$	−2.66327	+	10.4216i	−0.134174	+	0.525030i
$395$	9.30464	+	3.85411i	0.468167	+	0.193921i
$396$	7.82946	+	28.7255i	0.393445	+	1.44351i
$397$	−7.43673	−	17.9539i	−0.373239	−	0.901078i	−0.993197	−	0.116444i	$-0.962851\pi$
$397$	−7.43673	−	17.9539i	−0.373239	−	0.901078i	0.619958	−	0.784635i	$-0.287149\pi$
$398$	−2.95802	−	2.21573i	−0.148272	−	0.111064i
$399$	−18.1129	−	9.14612i	−0.906779	−	0.457879i
$400$	6.96790	−	7.64651i	0.348395	−	0.382325i
$401$	10.3222	+	17.8787i	0.515468	+	0.892817i	0.999839	+	0.0179544i	$0.00571538\pi$
$401$	10.3222	+	17.8787i	0.515468	+	0.892817i	−0.484370	+	0.874863i	$0.660951\pi$
$402$	−23.4958	−	1.48930i	−1.17187	−	0.0742795i
$403$	−0.0865717	+	0.657577i	−0.00431244	+	0.0327563i
$404$	−4.76182	+	6.51319i	−0.236909	+	0.324043i
$405$	−13.1112	+	4.85881i	−0.651502	+	0.241436i
$406$	58.7068	−	16.4626i	2.91357	−	0.817027i
$407$	6.54683	+	24.4331i	0.324514	+	1.21110i
$408$	15.3720	+	12.8064i	0.761026	+	0.634009i
$409$	4.93596	−	18.4213i	0.244068	−	0.910873i	−0.729782	−	0.683680i	$-0.760378\pi$
$409$	4.93596	−	18.4213i	0.244068	−	0.910873i	0.973850	−	0.227193i	$-0.0729549\pi$
$410$	−0.123430	−	10.6399i	−0.00609576	−	0.525465i
$411$	4.56373	−	3.92660i	0.225112	−	0.193685i
$412$	−31.7545	+	0.736846i	−1.56443	+	0.0363018i
$413$	−1.10790	−	2.67472i	−0.0545164	−	0.131614i
$414$	−16.5212	−	16.7643i	−0.811974	−	0.823920i
$415$			18.8190i			0.923787i
$416$	−6.32696	+	0.367381i	−0.310205	+	0.0180123i
$417$	23.6638	−	15.4902i	1.15882	−	0.758557i
$418$	−16.7718	−	6.72025i	−0.820336	−	0.328698i
$419$	23.1211	+	17.7415i	1.12954	+	0.866728i	0.992306	−	0.123811i	$-0.0395116\pi$
$419$	23.1211	+	17.7415i	1.12954	+	0.866728i	0.137236	+	0.990538i	$0.456178\pi$
$420$	10.5280	−	22.1098i	0.513712	−	1.07885i
$421$	16.3019	+	21.2451i	0.794506	+	1.03542i	0.998407	+	0.0564291i	$0.0179715\pi$
$421$	16.3019	+	21.2451i	0.794506	+	1.03542i	−0.203900	+	0.978992i	$0.565362\pi$
$422$	0.753273	−	1.34038i	0.0366687	−	0.0652485i
$423$	−7.10526	+	2.78695i	−0.345469	+	0.135506i
$424$	20.2505	−	0.705011i	0.983450	−	0.0342383i
$425$	−10.2025	+	2.73374i	−0.494892	+	0.132606i
$426$	−1.10013	+	5.59350i	−0.0533013	+	0.271006i
$427$	55.8722	−	7.35571i	2.70385	−	0.355968i
$428$	5.60847	+	0.606375i	0.271096	+	0.0293102i
$429$	4.17706	+	8.67601i	0.201671	+	0.418882i
$430$	−4.71009	−	3.52813i	−0.227141	−	0.170142i
$431$			0.846314i			0.0407655i	0.999792	+	0.0203828i	$0.00648848\pi$
$431$			0.846314i			0.0407655i	−0.999792	+	0.0203828i	$0.993512\pi$
$432$	7.03507	+	19.5578i	0.338475	+	0.940975i
$433$		−	35.1194i		−	1.68773i	−0.536554	−	0.843866i	$-0.680274\pi$
$433$		−	35.1194i		−	1.68773i	0.536554	−	0.843866i	$-0.319726\pi$
$434$	−2.28386	+	3.04898i	−0.109629	+	0.146356i
$435$	11.0604	+	22.9732i	0.530307	+	1.10148i
$436$	3.10191	+	3.85396i	0.148554	+	0.184571i
$437$	14.1613	−	1.86437i	0.677428	−	0.0891851i
$438$	−1.22979	−	0.241874i	−0.0587614	−	0.0115572i
$439$	−6.15039	+	1.64799i	−0.293542	+	0.0786544i	−0.402585	−	0.915383i	$-0.631888\pi$
$439$	−6.15039	+	1.64799i	−0.293542	+	0.0786544i	0.109043	+	0.994037i	$0.465221\pi$
$440$	7.63863	−	20.4238i	0.364157	−	0.973668i
$441$	−6.13560	+	40.6511i	−0.292171	+	1.93577i
$442$	5.64097	+	3.17014i	0.268314	+	0.150788i
$443$	−12.2314	−	15.9403i	−0.581132	−	0.757346i	0.406583	−	0.913614i	$-0.366720\pi$
$443$	−12.2314	−	15.9403i	−0.581132	−	0.757346i	−0.987715	+	0.156268i	$0.950054\pi$
$444$	5.90541	+	16.6415i	0.280258	+	0.789771i
$445$	4.28176	+	3.28551i	0.202975	+	0.155748i
$446$	3.03716	−	7.57987i	0.143814	−	0.358917i
$447$	14.4465	−	9.45658i	0.683296	−	0.447281i
$448$	−32.7138	−	15.9642i	−1.54558	−	0.754236i
$449$			2.52101i			0.118974i	0.998229	+	0.0594870i	$0.0189465\pi$
$449$			2.52101i			0.118974i	−0.998229	+	0.0594870i	$0.981054\pi$
$450$	−10.5777	−	2.91724i	−0.498638	−	0.137520i
$451$	9.19651	+	22.2023i	0.433047	+	1.04547i
$452$	23.5500	+	22.4819i	1.10770	+	1.05746i
$453$	5.88163	−	5.06051i	0.276343	−	0.237764i
$454$	8.69867	−	0.100911i	0.408249	−	0.00473597i
$455$	2.04983	−	7.65005i	0.0960973	−	0.358640i
$456$	−12.0427	−	3.75034i	−0.563953	−	0.175626i
$457$	−5.70405	−	21.2878i	−0.266824	−	0.995801i	−0.961124	−	0.276116i	$-0.910953\pi$
$457$	−5.70405	−	21.2878i	−0.266824	−	0.995801i	0.694300	−	0.719686i	$-0.255714\pi$
$458$	5.66419	+	20.1988i	0.264670	+	0.943830i
$459$	4.72844	−	20.6877i	0.220705	−	0.965618i
$460$	2.64589	+	17.0339i	0.123365	+	0.794208i
$461$	−0.0909258	+	0.690650i	−0.00423484	+	0.0321668i	−0.993432	−	0.114426i	$-0.963497\pi$
$461$	−0.0909258	+	0.690650i	−0.00423484	+	0.0321668i	0.989197	+	0.146592i	$0.0468306\pi$
$462$	−3.49864	+	55.1961i	−0.162771	+	2.56795i
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	0.640798	−	0.767710i	$-0.278604\pi$
$463$	−7.41183	−	12.8377i	−0.344457	−	0.596617i	−0.985255	+	0.171092i	$0.945270\pi$
$464$	34.3051	−	16.1125i	1.59257	−	0.748002i
$465$	−1.42205	−	0.718065i	−0.0659460	−	0.0332995i
$466$	17.7513	−	23.6982i	0.822315	−	1.09780i
$467$	−0.222565	−	0.537320i	−0.0102991	−	0.0248642i	0.918646	−	0.395081i	$-0.129283\pi$
$467$	−0.222565	−	0.537320i	−0.0102991	−	0.0248642i	−0.928945	+	0.370217i	$0.879283\pi$
$468$	3.38602	+	5.80697i	0.156519	+	0.268427i
$469$	−40.4042	−	16.7360i	−1.86569	−	0.772796i
$470$	5.41570	+	1.38401i	0.249808	+	0.0638394i
$471$	−13.1327	−	2.74153i	−0.605123	−	0.126323i
$472$	−0.953493	−	1.52627i	−0.0438881	−	0.0702522i
$473$	12.8382	+	3.43999i	0.590302	+	0.158171i
$474$	−15.8425	+	1.07256i	−0.727668	+	0.0492645i
$475$	5.28275	−	4.05360i	0.242389	−	0.185992i
$476$	19.3245	+	31.7467i	0.885739	+	1.45511i
$477$	−10.3922	−	18.8123i	−0.475827	−	0.861356i
$478$	−5.91713	−	7.52888i	−0.270643	−	0.344363i
$479$	−18.1501	+	31.4369i	−0.829300	+	1.43639i	0.0692877	+	0.997597i	$0.477927\pi$
$479$	−18.1501	+	31.4369i	−0.829300	+	1.43639i	−0.898588	+	0.438793i	$0.855406\pi$
$480$	4.18774	−	14.6349i	0.191143	−	0.667989i
$481$	2.85547	+	4.94582i	0.130198	+	0.225510i
$482$	15.2262	−	38.0002i	0.693534	−	1.73086i
$483$	−18.9664	−	39.3943i	−0.862999	−	1.79250i
$484$	0.632097	+	27.2403i	0.0287317	+	1.23819i
$485$	−24.4513	−	10.1280i	−1.11027	−	0.459891i
$486$	15.1172	−	16.0459i	0.685729	−	0.727857i
$487$	5.14815	−	5.14815i	0.233285	−	0.233285i	−0.580777	−	0.814062i	$-0.697251\pi$
$487$	5.14815	−	5.14815i	0.233285	−	0.233285i	0.814062	+	0.580777i	$0.197251\pi$
$488$	33.5009	−	10.2384i	1.51652	−	0.463470i
$489$	15.2366	+	13.6191i	0.689025	+	0.615876i
$490$	21.0421	−	21.5361i	0.950587	−	0.972901i
$491$	2.81970	+	21.4178i	0.127251	+	0.966570i	0.929304	+	0.369316i	$0.120408\pi$
$491$	2.81970	+	21.4178i	0.127251	+	0.966570i	−0.802052	+	0.597254i	$0.796259\pi$
$492$	7.62614	+	14.9428i	0.343813	+	0.673673i
$493$	−38.3655	−	5.05092i	−1.72790	−	0.227482i
$494$	−4.05030	−	0.485505i	−0.182232	−	0.0218439i
$495$	−22.9834	+	2.58489i	−1.03303	+	0.116182i
$496$	−1.08762	+	2.10349i	−0.0488355	+	0.0944494i
$497$	−5.29475	+	9.17077i	−0.237502	+	0.411365i
$498$	−13.1802	−	26.5826i	−0.590617	−	1.19119i
$499$	−26.8946	−	20.6370i	−1.20397	−	0.923838i	−0.205474	−	0.978663i	$-0.565873\pi$
$499$	−26.8946	−	20.6370i	−1.20397	−	0.923838i	−0.998496	+	0.0548242i	$0.982540\pi$
$500$	14.7799	+	18.3633i	0.660977	+	0.821230i
$501$	0.291823	+	1.54318i	0.0130377	+	0.0689440i
$502$	−3.97428	−	1.01564i	−0.177381	−	0.0453304i
$503$	8.18706	−	8.18706i	0.365043	−	0.365043i	−0.500623	−	0.865666i	$-0.666896\pi$
$503$	8.18706	−	8.18706i	0.365043	−	0.365043i	0.865666	+	0.500623i	$0.166896\pi$
$504$	0.613780	+	38.6044i	0.0273399	+	1.71958i
$505$	−4.43178	−	4.43178i	−0.197212	−	0.197212i
$506$	−19.8559	−	33.4882i	−0.882701	−	1.48873i
$507$	−13.2677	−	15.4205i	−0.589239	−	0.684848i
$508$	−12.3529	−	42.1636i	−0.548071	−	1.87071i
$509$	−12.6432	+	16.4770i	−0.560401	+	0.730328i	−0.984519	−	0.175278i	$-0.943917\pi$
$509$	−12.6432	+	16.4770i	−0.560401	+	0.730328i	0.424118	+	0.905607i	$0.360584\pi$
$510$	−11.6631	+	10.2726i	−0.516449	+	0.454880i
$511$	−2.01628	−	1.16410i	−0.0891951	−	0.0514968i
$512$	−21.6936	−	6.43344i	−0.958729	−	0.284321i
$513$	2.23694	+	13.1900i	0.0987633	+	0.582351i
$514$	19.9805	+	25.4229i	0.881301	+	1.12136i
$515$	3.22058	−	24.4627i	0.141916	−	1.07796i
$516$	9.12416	+	1.68484i	0.401669	+	0.0741712i
$517$	−12.5164	+	1.64781i	−0.550471	+	0.0724708i
$518$	0.380498	+	32.7996i	0.0167181	+	1.44113i
$519$	0.570718	+	1.73498i	0.0250517	+	0.0761573i
$520$	0.472380	−	4.90040i	0.0207152	−	0.214897i
$521$	−20.7314	−	20.7314i	−0.908261	−	0.908261i	0.0878707	−	0.996132i	$-0.471994\pi$
$521$	−20.7314	−	20.7314i	−0.908261	−	0.908261i	−0.996132	+	0.0878707i	$0.971994\pi$
$522$	−31.7129	−	24.7042i	−1.38804	−	1.08127i
$523$	−5.99966	+	14.4845i	−0.262347	+	0.633361i	−0.999083	−	0.0428191i	$-0.986366\pi$
$523$	−5.99966	+	14.4845i	−0.262347	+	0.633361i	0.736736	+	0.676181i	$0.236366\pi$
$524$	6.08430	+	2.35637i	0.265794	+	0.102938i
$525$	−16.8398	−	11.4837i	−0.734947	−	0.501188i
$526$	−0.340362	−	0.795481i	−0.0148405	−	0.0346846i
$527$	2.09385	−	1.20888i	0.0912095	−	0.0526598i
$528$	3.51427	+	34.1993i	0.152939	+	1.48833i
$529$	6.73541	+	3.88869i	0.292844	+	0.169073i
$530$	−1.87336	+	15.6284i	−0.0813734	+	0.678854i
$531$	−0.985469	+	1.63473i	−0.0427657	+	0.0709410i
$532$	−18.9143	−	13.8283i	−0.820037	−	0.599533i
$533$	3.30297	+	4.30451i	0.143067	+	0.186449i
$534$	−8.34921	−	1.64212i	−0.361306	−	0.0710614i
$535$	−1.13417	+	4.23278i	−0.0490345	+	0.182999i
$536$	−26.4877	−	6.11813i	−1.14409	−	0.264263i
$537$	27.3506	+	24.4470i	1.18027	+	1.05497i
$538$	1.11567	+	1.88164i	0.0480998	+	0.0811233i
$539$	−26.0231	+	62.8254i	−1.12090	+	2.70608i
$540$	−15.8515	+	3.06821i	−0.682138	+	0.132035i
$541$	−4.63048	+	1.91801i	−0.199080	+	0.0824617i	−0.479996	−	0.877271i	$-0.659362\pi$
$541$	−4.63048	+	1.91801i	−0.199080	+	0.0824617i	0.280916	+	0.959732i	$0.409362\pi$
$542$	−2.57202	−	17.9269i	−0.110478	−	0.770027i
$543$	−8.88126	+	0.497858i	−0.381131	+	0.0213651i
$544$	15.1028	+	17.4825i	0.647529	+	0.749556i
$545$	−3.32816	+	1.92152i	−0.142563	+	0.0823087i
$546$	2.46237	+	12.2416i	0.105380	+	0.523894i
$547$	32.3265	+	4.25586i	1.38218	+	0.181968i	0.784680	−	0.619901i	$-0.212827\pi$
$547$	32.3265	+	4.25586i	1.38218	+	0.181968i	0.597501	+	0.801868i	$0.296160\pi$
$548$	5.93819	−	3.61463i	0.253667	−	0.154410i
$549$	−25.7716	−	26.7648i	−1.09991	−	1.14229i
$550$	−15.8222	−	8.89185i	−0.674661	−	0.379150i
$551$	23.5640	−	6.31395i	1.00386	−	0.268983i
$552$	−15.6674	−	22.2079i	−0.666847	−	0.945231i
$553$	−28.4911	−	7.63417i	−1.21156	−	0.324638i
$554$	10.6319	+	10.3881i	0.451708	+	0.441348i
$555$	−13.4782	+	2.54880i	−0.572118	+	0.108191i
$556$	29.8743	−	13.1944i	1.26695	−	0.559566i
$557$	29.0633	−	12.0384i	1.23145	−	0.510083i	0.330418	−	0.943835i	$-0.392810\pi$
$557$	29.0633	−	12.0384i	1.23145	−	0.510083i	0.901033	+	0.433751i	$0.142810\pi$
$558$	2.51161	+	0.0183412i	0.106325	+	0.000776446i
$559$	3.00078			0.126920
$560$	16.1547	−	23.2078i	0.682662	−	0.980707i
$561$	15.8218	−	31.3334i	0.667999	−	1.32290i
$562$	10.5421	−	4.51064i	0.444690	−	0.190270i
$563$	0.193257	−	0.251857i	0.00814479	−	0.0106145i	−0.789263	−	0.614055i	$-0.789537\pi$
$563$	0.193257	−	0.251857i	0.00814479	−	0.0106145i	0.797408	+	0.603441i	$0.206204\pi$
$564$	−8.61921	+	1.83801i	−0.362934	+	0.0773940i
$565$	−20.0651	+	15.3965i	−0.844146	+	0.647736i
$566$	−15.7588	+	4.41911i	−0.662393	+	0.185749i
$567$	36.2135	−	19.1206i	1.52082	−	0.802990i
$568$	−2.30591	+	6.16546i	−0.0967540	+	0.258697i
$569$	−11.4624	−	42.7781i	−0.480527	−	1.79335i	−0.599408	−	0.800444i	$-0.704597\pi$
$569$	−11.4624	−	42.7781i	−0.480527	−	1.79335i	0.118881	−	0.992909i	$-0.462069\pi$
$570$	4.31467	−	8.79689i	0.180722	−	0.368461i
$571$	−0.837628	−	6.36242i	−0.0350537	−	0.266259i	−0.999993	−	0.00378539i	$-0.998795\pi$
$571$	−0.837628	−	6.36242i	−0.0350537	−	0.266259i	0.964939	−	0.262474i	$-0.0845383\pi$
$572$	3.12613	+	10.6703i	0.130710	+	0.446148i
$573$	−0.728818	+	9.71220i	−0.0304468	+	0.405733i
$574$	4.42578	+	30.8477i	0.184729	+	1.28756i
$575$	14.3480			0.598351
$576$	4.33444	+	23.6054i	0.180602	+	0.983556i
$577$	6.71403			0.279509			0.139754	−	0.990186i	$-0.455369\pi$
$577$	6.71403			0.279509			0.139754	+	0.990186i	$0.455369\pi$
$578$	0.0644335	+	0.449101i	0.00268008	+	0.0186801i
$579$	−1.57795	−	1.07606i	−0.0655774	−	0.0447196i
$580$	8.27768	+	28.2539i	0.343712	+	1.17318i
$581$	−7.19407	−	54.6444i	−0.298460	−	2.26703i
$582$	41.6317	−	2.81855i	1.72569	−	0.116832i
$583$	−9.20083	−	34.3380i	−0.381059	−	1.42213i
$584$	−1.35553	−	0.506978i	−0.0560924	−	0.0209789i
$585$	−4.86118	+	1.90674i	−0.200985	+	0.0788338i
$586$	3.94633	−	1.10663i	0.163021	−	0.0457147i
$587$	−8.36957	+	6.42220i	−0.345449	+	0.265072i	−0.766883	−	0.641787i	$-0.778194\pi$
$587$	−8.36957	+	6.42220i	−0.345449	+	0.265072i	0.421434	+	0.906859i	$0.361527\pi$
$588$	−14.6397	+	45.1578i	−0.603733	+	1.86227i
$589$	−0.927884	+	1.20924i	−0.0382328	+	0.0498260i
$590$	1.28526	−	0.549923i	0.0529132	−	0.0226400i
$591$	13.1533	−	0.737336i	0.541054	−	0.0303299i
$592$	3.59624	+	20.0703i	0.147805	+	0.824886i
$593$	−13.6954			−0.562403			−0.281202	−	0.959649i	$-0.590733\pi$
$593$	−13.6954			−0.562403			−0.281202	+	0.959649i	$0.590733\pi$
$594$	30.6546	−	19.7480i	1.25777	−	0.810270i
$595$	−26.6730	+	11.0483i	−1.09349	+	0.452938i
$596$	18.2379	−	8.05501i	0.747053	−	0.329946i
$597$	−1.49543	+	4.27231i	−0.0612040	+	0.174854i
$598$	−6.28705	−	6.14285i	−0.257096	−	0.251200i
$599$	39.5590	+	10.5998i	1.61634	+	0.433096i	0.949923	−	0.312485i	$-0.101161\pi$
$599$	39.5590	+	10.5998i	1.61634	+	0.433096i	0.666415	+	0.745581i	$0.267828\pi$
$600$	−11.5018	−	5.31401i	−0.469561	−	0.216944i
$601$	22.5982	−	6.05516i	0.921798	−	0.246995i	0.233444	−	0.972370i	$-0.425000\pi$
$601$	22.5982	−	6.05516i	0.921798	−	0.246995i	0.688354	+	0.725375i	$0.258334\pi$
$602$	15.0253	+	8.44403i	0.612387	+	0.344153i
$603$	6.93506	+	27.9877i	0.282417	+	1.13975i
$604$	7.65301	−	4.65846i	0.311397	−	0.189550i
$605$	−20.9851	−	2.76274i	−0.853166	−	0.112321i
$606$	9.36393	+	3.15620i	0.380384	+	0.128212i
$607$	−16.3379	+	9.43267i	−0.663133	+	0.382860i	−0.793470	−	0.608610i	$-0.791728\pi$
$607$	−16.3379	+	9.43267i	−0.663133	+	0.382860i	0.130337	+	0.991470i	$0.458394\pi$
$608$	−13.0141	−	6.53882i	−0.527792	−	0.265184i
$609$	−40.8982	−	62.4788i	−1.65728	−	2.53177i
$610$	3.86460	+	26.9362i	0.156473	+	1.09062i
$611$	−2.63329	+	1.09075i	−0.106532	+	0.0441269i
$612$	9.27993	−	22.6789i	0.375119	−	0.916741i
$613$	−9.88791	+	23.8715i	−0.399369	+	0.964162i	0.588447	+	0.808536i	$0.299740\pi$
$613$	−9.88791	+	23.8715i	−0.399369	+	0.964162i	−0.987816	+	0.155626i	$0.950260\pi$
$614$	20.1559	+	33.9942i	0.813426	+	1.37189i
$615$	−12.3794	+	4.07218i	−0.499187	+	0.164206i
$616$	−14.3726	+	62.2245i	−0.579089	+	2.50710i
$617$	0.271173	−	1.01203i	0.0109170	−	0.0407428i	−0.960252	−	0.279133i	$-0.909953\pi$
$617$	0.271173	−	1.01203i	0.0109170	−	0.0407428i	0.971169	+	0.238390i	$0.0766197\pi$
$618$	12.5836	+	36.8101i	0.506188	+	1.48072i
$619$	−4.92501	−	6.41840i	−0.197953	−	0.257977i	0.683821	−	0.729650i	$-0.260317\pi$
$619$	−4.92501	−	6.41840i	−0.197953	−	0.257977i	−0.881774	+	0.471673i	$0.843650\pi$
$620$	−1.48496	−	1.08567i	−0.0596376	−	0.0436014i
$621$	−13.4776	+	25.4822i	−0.540839	+	1.02257i
$622$	−5.65536	+	47.1796i	−0.226759	+	1.89173i
$623$	−13.6889	−	7.90327i	−0.548433	−	0.316638i
$624$	2.76482	+	7.25285i	0.110681	+	0.290346i
$625$	−4.65908	+	2.68992i	−0.186363	+	0.107597i
$626$	6.48467	+	15.1557i	0.259180	+	0.605743i
$627$	−1.65592	+	22.0667i	−0.0661312	+	0.881261i
$628$	−14.4457	−	5.59463i	−0.576446	−	0.223250i
$629$	7.96680	−	19.2336i	0.317657	−	0.766892i
$630$	−29.7061	−	4.13178i	−1.18352	−	0.164614i
$631$	−2.84039	−	2.84039i	−0.113074	−	0.113074i	0.648306	−	0.761380i	$-0.275478\pi$
$631$	−2.84039	−	2.84039i	−0.113074	−	0.113074i	−0.761380	+	0.648306i	$0.775478\pi$
$632$	−18.2506	−	1.75928i	−0.725969	−	0.0699806i
$633$	−1.84336	−	0.384813i	−0.0732669	−	0.0152949i
$634$	−0.430172	−	37.0816i	−0.0170843	−	1.47270i
$635$	33.8378	−	4.45483i	1.34281	−	0.176784i
$636$	−8.29939	−	23.3878i	−0.329092	−	0.927385i
$637$	−2.00397	+	15.2217i	−0.0794002	+	0.603104i
$638$	−41.0878	−	52.2796i	−1.62668	−	2.06977i
$639$	6.93812	−	0.780314i	0.274468	−	0.0308687i
$640$	7.52492	−	15.8850i	0.297449	−	0.627909i
$641$	−18.8927	−	10.9077i	−0.746215	−	0.430828i	0.0781094	−	0.996945i	$-0.475112\pi$
$641$	−18.8927	−	10.9077i	−0.746215	−	0.430828i	−0.824325	+	0.566117i	$0.808445\pi$
$642$	−1.36243	−	6.77331i	−0.0537709	−	0.267321i
$643$	1.96897	−	2.56601i	0.0776485	−	0.101193i	−0.752914	−	0.658119i	$-0.771352\pi$
$643$	1.96897	−	2.56601i	0.0776485	−	0.101193i	0.830563	+	0.556925i	$0.188019\pi$
$644$	−14.1945	−	48.4495i	−0.559342	−	1.90918i
$645$	−2.38120	+	6.80285i	−0.0937595	+	0.267862i
$646$	7.58407	+	12.7910i	0.298391	+	0.503255i
$647$	16.3835	+	16.3835i	0.644101	+	0.644101i	0.951561	−	0.307460i	$-0.0994790\pi$
$647$	16.3835	+	16.3835i	0.644101	+	0.644101i	−0.307460	+	0.951561i	$0.599479\pi$
$648$	20.2420	−	15.4358i	0.795179	−	0.606375i
$649$	−2.23254	+	2.23254i	−0.0876349	+	0.0876349i
$650$	−3.97011	−	1.01458i	−0.155720	−	0.0397950i
$651$	4.40369	+	1.54142i	0.172594	+	0.0604129i
$652$	14.7957	+	18.3829i	0.579446	+	0.719932i
$653$	−19.1626	−	14.7040i	−0.749890	−	0.575411i	0.161540	−	0.986866i	$-0.448354\pi$
$653$	−19.1626	−	14.7040i	−0.749890	−	0.575411i	−0.911430	+	0.411456i	$0.865021\pi$
$654$	3.35540	−	5.04515i	0.131206	−	0.197281i
$655$	−2.53421	+	4.38938i	−0.0990197	+	0.171507i
$656$	5.87627	+	18.4589i	0.229430	+	0.720697i
$657$	0.171560	+	1.52541i	0.00669318	+	0.0595120i
$658$	−16.2546	−	1.94842i	−0.633670	−	0.0759572i
$659$	−7.02331	−	0.924636i	−0.273589	−	0.0360187i	−0.00751688	−	0.999972i	$-0.502393\pi$
$659$	−7.02331	−	0.924636i	−0.273589	−	0.0360187i	−0.266072	+	0.963953i	$0.585726\pi$
$660$	−26.6705	−	1.38012i	−1.03815	−	0.0537210i
$661$	5.03887	+	38.2740i	0.195989	+	1.48869i	0.752911	+	0.658122i	$0.228649\pi$
$661$	5.03887	+	38.2740i	0.195989	+	1.48869i	−0.556922	+	0.830565i	$0.688018\pi$
$662$	−33.3190	+	34.1011i	−1.29498	+	1.32538i
$663$	1.61948	−	7.75776i	0.0628955	−	0.301286i
$664$	−10.0134	−	32.7648i	−0.388595	−	1.27152i
$665$	12.8699	−	12.8699i	0.499072	−	0.499072i
$666$	17.2534	−	13.0399i	0.668556	−	0.505288i
$667$	48.5642	+	20.1160i	1.88041	+	0.778893i
$668$	0.0420697	+	1.81300i	0.00162773	+	0.0701470i
$669$	−9.97287	−	0.748380i	−0.385573	−	0.0289340i
$670$	7.85451	−	19.6026i	0.303446	−	0.757314i
$671$	−30.7291	−	53.2243i	−1.18628	−	2.05470i
$672$	−6.56528	+	44.0961i	−0.253261	+	1.70104i
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	−0.944443	−	0.328675i	$-0.893398\pi$
$673$	−4.86626	+	8.42860i	−0.187580	+	0.324899i	0.756863	+	0.653574i	$0.226731\pi$
$674$	−2.75759	−	3.50872i	−0.106218	−	0.135151i
$675$	0.498405	+	13.4294i	0.0191836	+	0.516898i
$676$	−12.2136	−	20.0647i	−0.469753	−	0.771720i
$677$	−21.1827	+	16.2540i	−0.814116	+	0.624693i	−0.929581	−	0.368618i	$-0.879831\pi$
$677$	−21.1827	+	16.2540i	−0.814116	+	0.624693i	0.115465	+	0.993312i	$0.463164\pi$
$678$	17.5596	−	35.8011i	0.674373	−	1.37493i
$679$	74.8706	+	20.0615i	2.87327	+	0.769890i
$680$	−15.2204	+	9.50851i	−0.583675	+	0.364635i
$681$	−3.32923	−	10.1209i	−0.127576	−	0.387832i
$682$	4.02515	+	1.02864i	0.154131	+	0.0393888i
$683$	13.9691	+	5.78620i	0.534513	+	0.221403i	0.633579	−	0.773678i	$-0.281585\pi$
$683$	13.9691	+	5.78620i	0.534513	+	0.221403i	−0.0990653	+	0.995081i	$0.531585\pi$
$684$	0.0663906	+	15.4478i	0.00253851	+	0.590661i
$685$	2.06658	+	4.98916i	0.0789599	+	0.190626i
$686$	−25.8623	+	34.5264i	−0.987426	+	1.31822i
$687$	21.4966	−	14.0716i	0.820148	−	0.536863i
$688$	10.0778	+	3.63646i	0.384212	+	0.138639i
$689$	−4.01304	−	6.95080i	−0.152885	−	0.264804i
$690$	18.9149	−	9.37840i	0.720080	−	0.357030i
$691$	−4.39444	+	33.3791i	−0.167172	+	1.26980i	0.677902	+	0.735152i	$0.262889\pi$
$691$	−4.39444	+	33.3791i	−0.167172	+	1.26980i	−0.845075	+	0.534648i	$0.820444\pi$
$692$	0.323711	+	2.08400i	0.0123056	+	0.0792218i
$693$	65.7484	−	16.2917i	2.49757	−	0.618872i
$694$	9.81318	+	34.9944i	0.372503	+	1.32837i
$695$	6.56604	+	24.5048i	0.249064	+	0.929520i
$696$	−31.4806	−	34.1123i	−1.19327	−	1.29302i
$697$	5.11905	−	19.1046i	0.193898	−	0.723637i
$698$	17.1716	−	0.199203i	0.649956	−	0.00753994i
$699$	−34.2277	−	11.9807i	−1.29461	−	0.453151i
$700$	−17.0239	−	16.2518i	−0.643445	−	0.614260i
$701$	8.97900	+	21.6772i	0.339132	+	0.818737i	0.997800	+	0.0663032i	$0.0211205\pi$
$701$	8.97900	+	21.6772i	0.339132	+	0.818737i	−0.658667	+	0.752434i	$0.728880\pi$
$702$	5.53120	−	6.09794i	0.208762	−	0.230152i
$703$			13.1243i			0.494993i
$704$	−2.43191	+	39.6233i	−0.0916559	+	1.49336i
$705$	−0.383167	−	6.83529i	−0.0144309	−	0.257432i
$706$	−2.02465	+	5.05293i	−0.0761986	+	0.190170i
$707$	14.5627	+	11.1743i	0.547686	+	0.420254i
$708$	−1.43033	+	1.67694i	−0.0537551	+	0.0630232i
$709$	−18.2360	−	23.7656i	−0.684868	−	0.892537i	0.313503	−	0.949587i	$-0.398497\pi$
$709$	−18.2360	−	23.7656i	−0.684868	−	0.892537i	−0.998371	+	0.0570496i	$0.981831\pi$
$710$	−4.45769	−	2.50516i	−0.167294	−	0.0940168i
$711$	7.10126	+	18.1045i	0.266318	+	0.678972i
$712$	−9.20294	−	3.44195i	−0.344895	−	0.128993i
$713$	−3.17239	+	0.850040i	−0.118807	+	0.0318343i
$714$	29.9389	−	34.2871i	1.12043	−	1.28316i
$715$	−8.56330	+	1.12738i	−0.320249	+	0.0421616i
$716$	26.5592	+	32.9984i	0.992562	+	1.23321i
$717$	−6.60757	+	9.68941i	−0.246764	+	0.361858i
$718$	−17.1865	+	22.9441i	−0.641393	+	0.856265i
$719$			40.2309i			1.50036i	0.661234	+	0.750180i	$0.270033\pi$
$719$			40.2309i			1.50036i	−0.661234	+	0.750180i	$0.729967\pi$
$720$	−18.6364	+	0.512593i	−0.694536	+	0.0191032i
$721$			72.2632i			2.69122i
$722$	14.0027	+	10.4888i	0.521126	+	0.390354i
$723$	−49.9970	−	3.75185i	−1.85941	−	0.139533i
$724$	−10.2118	−	1.10407i	−0.379518	−	0.0410326i
$725$	24.2956	−	3.19858i	0.902317	−	0.118792i
$726$	31.5772	−	10.7948i	1.17194	−	0.400631i
$727$	−14.5365	+	3.89504i	−0.539129	+	0.144459i	−0.518100	−	0.855320i	$-0.673361\pi$
$727$	−14.5365	+	3.89504i	−0.539129	+	0.144459i	−0.0210282	+	0.999779i	$0.506694\pi$
$728$	0.501671	+	14.4098i	0.0185932	+	0.534063i
$729$	−24.3190	−	11.7296i	−0.900705	−	0.434431i
$730$	0.550783	−	0.980065i	0.0203854	−	0.0362738i
$731$	−6.65914	−	8.67836i	−0.246297	−	0.320981i
$732$	−24.3241	−	35.3418i	−0.899044	−	1.30627i
$733$	1.04651	+	0.803017i	0.0386538	+	0.0296601i	0.627908	−	0.778288i	$-0.283912\pi$
$733$	1.04651	+	0.803017i	0.0386538	+	0.0296601i	−0.589254	+	0.807948i	$0.700578\pi$
$734$	−12.2735	−	4.91784i	−0.453024	−	0.181521i
$735$	−32.9177	−	16.6218i	−1.21419	−	0.613105i
$736$	−13.6702	−	28.2489i	−0.503890	−	1.04127i
$737$			47.6940i			1.75683i
$738$	14.6344	−	14.4222i	0.538701	−	0.530890i
$739$	−11.4907	−	27.7409i	−0.422691	−	1.02047i	−0.981550	−	0.191204i	$-0.938761\pi$
$739$	−11.4907	−	27.7409i	−0.422691	−	1.02047i	0.558860	−	0.829262i	$-0.311239\pi$
$740$	−15.8349	+	0.367440i	−0.582101	+	0.0135074i
$741$	0.928335	+	4.90909i	0.0341032	+	0.180340i
$742$	−0.534746	−	46.0961i	−0.0196312	−	1.69224i
$743$	1.46392	−	5.46342i	0.0537060	−	0.200433i	−0.933860	−	0.357639i	$-0.883582\pi$
$743$	1.46392	−	5.46342i	0.0537060	−	0.200433i	0.987566	+	0.157206i	$0.0502485\pi$
$744$	2.85793	+	0.493528i	0.104777	+	0.0180936i
$745$	4.00849	+	14.9599i	0.146860	+	0.548089i
$746$	−7.73330	+	2.16858i	−0.283136	+	0.0793975i
$747$	−26.1766	+	25.2053i	−0.957753	+	0.922213i
$748$	23.9215	−	32.7197i	0.874658	−	1.19635i
$749$	1.67518	−	12.7243i	0.0612097	−	0.464934i
$750$	15.9877	−	24.0390i	0.583790	−	0.877781i
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.650098	−	0.759850i	$-0.725272\pi$
$751$	−26.9412	−	46.6635i	−0.983099	−	1.70278i	−0.333001	−	0.942927i	$-0.608061\pi$
$752$	−10.1654	+	0.472021i	−0.370695	+	0.0172128i
$753$	0.281185	+	5.01603i	0.0102469	+	0.182794i
$754$	−12.0154	−	9.00022i	−0.437574	−	0.327769i
$755$	2.66336	+	6.42992i	0.0969296	+	0.234009i
$756$	44.8548	−	14.9688i	1.63135	−	0.544410i
$757$	34.5808	+	14.3238i	1.25686	+	0.520609i	0.908945	−	0.416917i	$-0.136889\pi$
$757$	34.5808	+	14.3238i	1.25686	+	0.520609i	0.347916	+	0.937526i	$0.386889\pi$
$758$	8.07501	−	31.5981i	0.293298	−	1.14769i
$759$	−31.7763	+	35.5505i	−1.15341	+	1.29040i
$760$	6.57093	−	9.21004i	0.238353	−	0.334083i
$761$	−20.7070	−	5.54843i	−0.750629	−	0.201130i	−0.136832	−	0.990594i	$-0.543692\pi$
$761$	−20.7070	−	5.54843i	−0.750629	−	0.201130i	−0.613797	+	0.789464i	$0.710359\pi$
$762$	−44.6772	+	29.9914i	−1.61848	+	1.08647i
$763$	8.92939	−	6.85176i	0.323266	−	0.248050i
$764$	−2.65795	+	10.9276i	−0.0961612	+	0.395347i
$765$	16.3020	+	9.82739i	0.589398	+	0.355310i
$766$	−25.8846	+	20.3433i	−0.935250	+	0.735035i
$767$	−0.356416	+	0.617331i	−0.0128695	+	0.0222905i
$768$	0.496037	+	27.7084i	0.0178992	+	0.999840i
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	0.896566	+	0.442910i	$0.146054\pi$
$769$	23.0680	+	39.9550i	0.831854	+	1.44081i	−0.0647118	+	0.997904i	$0.520613\pi$
$770$	−46.0501	−	18.4517i	−1.65953	−	0.664953i
$771$	22.3119	−	32.7184i	0.803544	−	1.17833i
$772$	−1.59521	−	1.52286i	−0.0574128	−	0.0548088i
$773$	−3.48172	−	1.44218i	−0.125229	−	0.0518715i	0.319189	−	0.947691i	$-0.396589\pi$
$773$	−3.48172	−	1.44218i	−0.125229	−	0.0518715i	−0.444418	+	0.895820i	$0.646589\pi$
$774$	−1.40095	−	11.2770i	−0.0503560	−	0.405344i
$775$	−1.08265	+	1.08265i	−0.0388898	+	0.0388898i
$776$	47.9599	+	4.62315i	1.72166	+	0.165961i
$777$	38.1621	−	12.5533i	1.36906	−	0.450348i
$778$	2.78655	+	2.72264i	0.0999027	+	0.0976114i
$779$	1.62751	+	12.3621i	0.0583115	+	0.442920i
$780$	−5.89697	+	1.25750i	−0.211146	+	0.0450258i
$781$	11.4497	+	1.50739i	0.409704	+	0.0539386i
$782$	−3.81352	+	31.8142i	−0.136371	+	1.13767i
$783$	−17.1412	+	46.1540i	−0.612576	+	1.64941i
$784$	−25.1763	+	48.6917i	−0.899153	+	1.73899i
$785$	6.01686	−	10.4215i	0.214751	−	0.371960i
$786$	0.505503	−	7.97504i	0.0180307	−	0.284460i
$787$	2.96828	+	2.27764i	0.105808	+	0.0811893i	0.660310	−	0.750993i	$-0.270425\pi$
$787$	2.96828	+	2.27764i	0.105808	+	0.0811893i	−0.554502	+	0.832182i	$0.687091\pi$
$788$	15.1238	+	1.63515i	0.538764	+	0.0582499i
$789$	−0.803289	+	0.691144i	−0.0285978	+	0.0246054i
$790$	3.52650	−	13.7994i	0.125467	−	0.490962i
$791$	52.3771	−	52.3771i	1.86232	−	1.86232i
$792$	38.6398	−	16.7296i	1.37300	−	0.594462i
$793$	−9.81155	−	9.81155i	−0.348418	−	0.348418i
$794$	−23.6396	+	14.0164i	−0.838938	+	0.497425i
$795$	18.9421	−	3.58205i	0.671807	−	0.127042i
$796$	−2.50765	+	4.58588i	−0.0888813	+	0.162542i
$797$	−17.8536	+	23.2672i	−0.632406	+	0.824168i	−0.994138	−	0.108114i	$-0.965519\pi$
$797$	−17.8536	+	23.2672i	−0.632406	+	0.824168i	0.361732	+	0.932282i	$0.382185\pi$
$798$	−9.16560	+	27.1928i	−0.324459	+	0.962615i
$799$	8.99811	+	5.19506i	0.318330	+	0.183788i
$800$	−12.1037	−	8.21847i	−0.427929	−	0.290567i
$801$	1.16474	+	10.3563i	0.0411542	+	0.365920i
$802$	22.9548	−	18.0407i	0.810562	−	0.637040i
$803$	−0.331414	+	2.51734i	−0.0116953	+	0.0888349i
$804$	2.63416	+	33.1905i	0.0928995	+	1.17054i
$805$	38.8825	−	5.11898i	1.37043	−	0.180420i
$806$	0.937916	−	0.0108805i	0.0330367	−	0.000383248i
$807$	1.78545	−	1.99752i	0.0628510	−	0.0703159i
$808$	10.0741	+	5.35784i	0.354404	+	0.188488i
$809$	−14.3467	−	14.3467i	−0.504404	−	0.504404i	0.408400	−	0.912803i	$-0.366087\pi$
$809$	−14.3467	−	14.3467i	−0.504404	−	0.504404i	−0.912803	+	0.408400i	$0.866087\pi$
$810$	9.43506	+	17.3783i	0.331514	+	0.610610i
$811$	13.2334	−	31.9483i	0.464688	−	1.12186i	−0.501763	−	0.865005i	$-0.667315\pi$
$811$	13.2334	−	31.9483i	0.464688	−	1.12186i	0.966451	−	0.256851i	$-0.0826848\pi$
$812$	−34.8366	−	78.8760i	−1.22253	−	2.76800i
$813$	−19.9851	+	9.62183i	−0.700909	+	0.337452i
$814$	32.8885	−	14.0720i	1.15274	−	0.493223i
$815$	−15.8750	+	9.16541i	−0.556075	+	0.321050i
$816$	14.8400	−	24.0910i	0.519503	−	0.843353i
$817$	5.97219	+	3.44804i	0.208940	+	0.120632i
$818$	−26.7789	−	3.20995i	−0.936303	−	0.112233i
$819$	13.3864	−	7.39489i	0.467760	−	0.258398i
$820$	−14.8697	+	2.30974i	−0.519274	+	0.0806596i
$821$	−17.1807	−	22.3903i	−0.599609	−	0.781426i	0.390668	−	0.920532i	$-0.372244\pi$
$821$	−17.1807	−	22.3903i	−0.599609	−	0.781426i	−0.990278	+	0.139105i	$0.955577\pi$
$822$	−6.41336	−	5.60003i	−0.223692	−	0.195324i
$823$	5.54918	−	20.7098i	0.193432	−	0.721899i	−0.799235	−	0.601019i	$-0.794762\pi$
$823$	5.54918	−	20.7098i	0.193432	−	0.721899i	0.992667	−	0.120880i	$-0.0385717\pi$
$824$	7.40918	+	44.3044i	0.258111	+	1.54342i
$825$	−4.54244	+	21.7595i	−0.158148	+	0.757570i
$826$	−3.52176	+	2.08813i	−0.122538	+	0.0726554i
$827$	−1.83537	+	4.43098i	−0.0638222	+	0.154080i	−0.952573	−	0.304310i	$-0.901574\pi$
$827$	−1.83537	+	4.43098i	−0.0638222	+	0.154080i	0.888751	+	0.458391i	$0.151574\pi$
$828$	−20.1498	+	26.4947i	−0.700254	+	0.920756i
$829$	31.7765	−	13.1623i	1.10364	−	0.457144i	0.244899	−	0.969549i	$-0.421245\pi$
$829$	31.7765	−	13.1623i	1.10364	−	0.457144i	0.858744	+	0.512405i	$0.171245\pi$
$830$	26.3443	−	3.77968i	0.914424	−	0.131194i
$831$	8.20587	−	16.2508i	0.284658	−	0.563735i
$832$	1.78502	+	8.78319i	0.0618844	+	0.304502i
$833$	48.4686	−	27.9834i	1.67934	−	0.969566i
$834$	−26.4371	−	30.0154i	−0.915442	−	1.03935i
$835$	−1.39668	−	0.183876i	−0.0483341	−	0.00636331i
$836$	−6.03903	+	24.8282i	−0.208864	+	0.858702i
$837$	−0.905821	−	2.93977i	−0.0313098	−	0.101613i
$838$	20.1922	−	35.9301i	0.697527	−	1.24118i
$839$	−6.05695	+	1.62295i	−0.209109	+	0.0560306i	−0.361853	−	0.932235i	$-0.617856\pi$
$839$	−6.05695	+	1.62295i	−0.209109	+	0.0560306i	0.152744	+	0.988266i	$0.451189\pi$
$840$	−33.0655	−	10.2972i	−1.14087	−	0.355289i
$841$	58.7072	+	15.7305i	2.02439	+	0.542432i
$842$	26.4664	−	27.0876i	0.912092	−	0.933502i
$843$	−9.15936	−	10.6455i	−0.315465	−	0.366652i
$844$	−2.02766	−	0.785284i	−0.0697948	−	0.0270306i
$845$	16.8580	−	6.98282i	0.579933	−	0.240216i
$846$	5.32844	+	9.38676i	0.183195	+	0.322723i
$847$	61.9903			2.13001
$848$	−5.05411	−	28.2066i	−0.173559	−	0.968619i
$849$	10.9784	+	16.7714i	0.376778	+	0.575591i
$850$	5.87601	+	13.7332i	0.201546	+	0.471044i
$851$	−17.2155	+	22.4357i	−0.590140	+	0.769086i
$852$	8.05118	+	0.416624i	0.275829	+	0.0142733i
$853$	36.9971	−	28.3888i	1.26675	−	0.972015i	0.266789	−	0.963755i	$-0.414037\pi$
$853$	36.9971	−	28.3888i	1.26675	−	0.972015i	0.999966	−	0.00826028i	$-0.00262936\pi$
$854$	−21.5187	−	76.7370i	−0.736355	−	2.62589i
$855$	−11.8657	−	1.79093i	−0.405799	−	0.0612484i
$856$	−0.277575	−	7.97297i	−0.00948733	−	0.272510i
$857$	−2.61101	−	9.74444i	−0.0891906	−	0.332864i	0.906884	−	0.421380i	$-0.138454\pi$
$857$	−2.61101	−	9.74444i	−0.0891906	−	0.332864i	−0.996075	+	0.0885163i	$0.971787\pi$
$858$	11.3064	−	7.58991i	0.385995	−	0.259115i
$859$	2.34801	+	17.8349i	0.0801131	+	0.608520i	0.983661	+	0.180032i	$0.0576201\pi$
$859$	2.34801	+	17.8349i	0.0801131	+	0.608520i	−0.903548	+	0.428488i	$0.859047\pi$
$860$	−3.99296	+	7.30215i	−0.136159	+	0.249001i
$861$	34.3893	−	16.5567i	1.17198	−	0.564251i
$862$	1.18474	−	0.169977i	0.0403523	−	0.00578944i
$863$	0.213637			0.00727230			0.00363615	−	0.999993i	$-0.498843\pi$
$863$	0.213637			0.00727230			0.00363615	+	0.999993i	$0.498843\pi$
$864$	25.9656	−	13.7763i	0.883368	−	0.468680i
$865$	−1.63828			−0.0557033
$866$	−49.1629	+	7.05352i	−1.67062	+	0.239688i
$867$	0.500662	−	0.241044i	0.0170034	−	0.00818627i
$868$	4.72690	+	2.58476i	0.160441	+	0.0877326i
$869$	4.19870	+	31.8923i	0.142431	+	1.08187i
$870$	29.9383	−	20.0973i	1.01500	−	0.681362i
$871$	2.78698	+	10.4011i	0.0944331	+	0.352429i
$872$	4.77208	−	5.11634i	0.161603	−	0.173261i
$873$	−18.6611	−	47.5761i	−0.631582	−	1.61021i
$874$	−5.45411	−	19.4497i	−0.184488	−	0.657896i
$875$	42.5466	−	32.6471i	1.43834	−	1.10368i
$876$	−0.0915988	+	1.77013i	−0.00309484	+	0.0598072i
$877$	−19.6882	+	25.6581i	−0.664823	+	0.866414i	−0.997048	−	0.0767862i	$-0.975534\pi$
$877$	−19.6882	+	25.6581i	−0.664823	+	0.866414i	0.332225	+	0.943200i	$0.392201\pi$
$878$	3.54226	+	8.27881i	0.119545	+	0.279396i
$879$	−2.74921	−	4.19988i	−0.0927287	−	0.141659i
$880$	−30.1251	−	6.59115i	−1.01552	−	0.222188i
$881$	40.2583			1.35634			0.678168	−	0.734907i	$-0.262774\pi$
$881$	40.2583			1.35634			0.678168	+	0.734907i	$0.262774\pi$
$882$	58.1389	+	0.424564i	1.95764	+	0.0142958i
$883$	25.3073	−	10.4826i	0.851660	−	0.352769i	0.0862196	−	0.996276i	$-0.472521\pi$
$883$	25.3073	−	10.4826i	0.851660	−	0.352769i	0.765440	+	0.643507i	$0.222521\pi$
$884$	3.30486	−	8.53338i	0.111155	−	0.287009i
$885$	−1.11668	−	1.29787i	−0.0375368	−	0.0436276i
$886$	−19.8579	+	20.3240i	−0.667138	+	0.682799i
$887$	−1.77186	−	0.474768i	−0.0594931	−	0.0159411i	0.228950	−	0.973438i	$-0.426471\pi$
$887$	−1.77186	−	0.474768i	−0.0594931	−	0.0159411i	−0.288443	+	0.957497i	$0.593138\pi$
$888$	22.1100	−	11.6092i	0.741964	−	0.389580i
$889$	−96.5514	+	25.8709i	−3.23823	+	0.867681i
$890$	3.73935	−	6.65382i	0.125343	−	0.223036i
$891$	−34.3784	−	28.5071i	−1.15172	−	0.955024i
$892$	−11.2209	−	2.72929i	−0.375704	−	0.0913833i
$893$	−6.49413	−	0.854969i	−0.217318	−	0.0286104i
$894$	−16.1396	−	18.3241i	−0.539787	−	0.612848i
$895$	−28.4964	+	16.4524i	−0.952530	+	0.549944i
$896$	−15.7775	+	49.0016i	−0.527091	+	1.63703i
$897$	−4.85242	+	9.60970i	−0.162018	+	0.320859i
$898$	3.52912	−	0.506330i	0.117768	−	0.0168965i
$899$	−5.18237	+	2.14661i	−0.172842	+	0.0715933i
$900$	−1.95932	+	15.3934i	−0.0653106	+	0.513115i
$901$	−11.1964	+	27.0306i	−0.373008	+	0.900520i
$902$	29.2335	−	17.3332i	0.973371	−	0.577133i
$903$	4.31367	−	20.6636i	0.143550	−	0.687643i
$904$	26.7420	−	37.4825i	0.889427	−	1.24665i
$905$	2.06507	−	7.70696i	0.0686454	−	0.256188i
$906$	−8.26540	−	7.21720i	−0.274599	−	0.239775i
$907$	−34.7536	−	45.2918i	−1.15397	−	1.50389i	−0.829948	−	0.557840i	$-0.811630\pi$
$907$	−34.7536	−	45.2918i	−1.15397	−	1.50389i	−0.324026	−	0.946048i	$-0.605036\pi$
$908$	−1.88834	−	12.1568i	−0.0626667	−	0.403438i
$909$	0.228753	−	12.1002i	0.00758725	−	0.401338i
$910$	−11.1208	−	1.33304i	−0.368652	−	0.0441899i
$911$	−3.88028	−	2.24028i	−0.128559	−	0.0742237i	0.434341	−	0.900748i	$-0.356981\pi$
$911$	−3.88028	−	2.24028i	−0.128559	−	0.0742237i	−0.562900	+	0.826525i	$0.690315\pi$
$912$	−2.83131	+	17.6116i	−0.0937542	+	0.583179i
$913$	−52.0547	+	30.0538i	−1.72276	+	0.994635i
$914$	−28.6547	+	12.2605i	−0.947814	+	0.405541i
$915$	30.0288	−	14.4573i	0.992720	−	0.477945i
$916$	27.1383	−	11.9860i	0.896675	−	0.396028i
$917$	5.68059	−	13.7142i	0.187590	−	0.452881i
$918$	−29.9099	−	2.46426i	−0.987175	−	0.0813326i
$919$	12.8420	+	12.8420i	0.423620	+	0.423620i	0.886448	−	0.462828i	$-0.153165\pi$
$919$	12.8420	+	12.8420i	0.423620	+	0.423620i	−0.462828	+	0.886448i	$0.653165\pi$
$920$	23.3139	−	7.12508i	0.768637	−	0.234907i
$921$	32.2565	−	36.0876i	1.06289	−	1.18913i
$922$	0.985089	−	0.0114277i	0.0324422	−	0.000376351i
$923$	2.58505	−	0.340329i	0.0850880	−	0.0112020i
$924$	77.9705	−	6.18812i	2.56504	−	0.203574i
$925$	−1.72079	+	13.0707i	−0.0565793	+	0.429763i
$926$	−16.4826	+	12.9540i	−0.541651	+	0.425696i
$927$	38.3404	−	28.2845i	1.25926	−	0.928985i
$928$	−29.4455	−	44.7869i	−0.966594	−	1.47020i
$929$	−37.2662	−	21.5156i	−1.22266	−	0.705905i	−0.257178	−	0.966364i	$-0.582793\pi$
$929$	−37.2662	−	21.5156i	−1.22266	−	0.705905i	−0.965485	+	0.260459i	$0.916126\pi$
$930$	−0.719594	+	2.13492i	−0.0235964	+	0.0700067i
$931$	−21.4787	+	27.9916i	−0.703938	+	0.917389i
$932$	−36.7399	−	20.0901i	−1.20345	−	0.658073i
$933$	57.1831	−	10.8136i	1.87209	−	0.354022i
$934$	−0.707482	+	0.419482i	−0.0231495	+	0.0137259i
$935$	22.2635	+	22.2635i	0.728096	+	0.728096i
$936$	7.44900	−	5.90631i	0.243478	−	0.193054i
$937$	30.0408	−	30.0408i	0.981392	−	0.981392i	−0.0184383	−	0.999830i	$-0.505869\pi$
$937$	30.0408	−	30.0408i	0.981392	−	0.981392i	0.999830	+	0.0184383i	$0.00586941\pi$
$938$	−15.3134	+	59.9224i	−0.500001	+	1.95654i
$939$	15.3045	−	13.1679i	0.499442	−	0.429717i
$940$	0.849729	−	7.85930i	0.0277151	−	0.256342i
$941$	17.0028	+	13.0467i	0.554276	+	0.425311i	0.847548	−	0.530718i	$-0.178078\pi$
$941$	17.0028	+	13.0467i	0.554276	+	0.425311i	−0.293273	+	0.956029i	$0.594744\pi$
$942$	−1.20020	+	18.9348i	−0.0391045	+	0.616929i
$943$	−13.4336	+	23.2676i	−0.437458	+	0.757699i
$944$	−1.94509	+	1.64132i	−0.0633072	+	0.0534203i
$945$	6.14193	+	36.2155i	0.199797	+	1.17809i
$946$	2.23709	−	18.6629i	0.0727342	−	0.606782i
$947$	−12.8489	−	1.69158i	−0.417532	−	0.0549691i	−0.0811661	−	0.996701i	$-0.525864\pi$
$947$	−12.8489	−	1.69158i	−0.417532	−	0.0549691i	−0.336366	+	0.941732i	$0.609198\pi$
$948$	4.68332	+	21.9621i	0.152107	+	0.713296i
$949$	0.0748245	+	0.568349i	0.00242891	+	0.0184494i
$950$	−6.73555	−	6.58107i	−0.218530	−	0.213518i
$951$	−43.1443	+	14.1922i	−1.39905	+	0.460213i
$952$	40.5604	−	33.4282i	1.31457	−	1.08341i
$953$	17.4567	−	17.4567i	0.565477	−	0.565477i	−0.365381	−	0.930858i	$-0.619061\pi$
$953$	17.4567	−	17.4567i	0.565477	−	0.565477i	0.930858	+	0.365381i	$0.119061\pi$
$954$	−24.2477	+	18.3262i	−0.785049	+	0.593332i
$955$	−8.07116	−	3.34318i	−0.261176	−	0.108183i
$956$	−9.35111	+	9.79539i	−0.302436	+	0.316806i
$957$	−45.8821	+	67.2820i	−1.48316	+	2.17492i
$958$	47.6533	+	19.0941i	1.53961	+	0.616901i
$959$	−7.90794	−	13.6970i	−0.255361	−	0.442298i
$960$	−21.3282	−	2.92299i	−0.688365	−	0.0943392i
$961$	−15.3248	+	26.5433i	−0.494347	+	0.856234i
$962$	6.35005	−	4.99065i	0.204734	−	0.160905i
$963$	−7.40674	+	4.09160i	−0.238679	+	0.131850i
$964$	−56.2537	−	13.6827i	−1.81181	−	0.440691i
$965$	1.35915	−	1.04291i	0.0437527	−	0.0335726i
$966$	−51.3379	+	34.4627i	−1.65177	+	1.10882i
$967$	−43.2077	−	11.5775i	−1.38947	−	0.372306i	−0.514915	−	0.857241i	$-0.672177\pi$
$967$	−43.2077	−	11.5775i	−1.38947	−	0.372306i	−0.874550	+	0.484935i	$0.838843\pi$
$968$	38.0061	−	6.35590i	1.22156	−	0.204286i
$969$	12.1372	−	13.5787i	0.389902	−	0.436211i
$970$	−9.26715	+	36.2630i	−0.297550	+	1.16433i
$971$	−35.1496	−	14.5595i	−1.12801	−	0.467235i	−0.260903	−	0.965365i	$-0.584020\pi$
$971$	−35.1496	−	14.5595i	−1.12801	−	0.467235i	−0.867103	+	0.498130i	$0.834020\pi$
$972$	−25.4985	−	17.9395i	−0.817865	−	0.575410i
$973$	−28.4334	−	68.6443i	−0.911532	−	2.20063i
$974$	−8.24076	−	6.17282i	−0.264051	−	0.197790i
$975$	0.280889	+	5.01077i	0.00899566	+	0.160473i
$976$	−21.0610	−	44.8410i	−0.674145	−	1.43532i
$977$	−3.00365	−	5.20247i	−0.0960952	−	0.166442i	0.813970	−	0.580907i	$-0.197302\pi$
$977$	−3.00365	−	5.20247i	−0.0960952	−	0.166442i	−0.910065	+	0.414465i	$0.863969\pi$
$978$	16.0049	−	24.0648i	0.511780	−	0.769507i
$979$	−2.25002	+	17.0906i	−0.0719109	+	0.546218i
$980$	−34.3741	−	25.1311i	−1.09804	−	0.802782i
$981$	−7.13036	−	2.05579i	−0.227655	−	0.0656362i
$982$	29.4160	−	8.24887i	0.938701	−	0.263232i
$983$	7.48681	+	27.9412i	0.238792	+	0.891184i	0.976403	+	0.215958i	$0.0692874\pi$
$983$	7.48681	+	27.9412i	0.238792	+	0.891184i	−0.737611	+	0.675226i	$0.764046\pi$
$984$	19.3864	−	13.6768i	0.618017	−	0.436002i
$985$	−3.05841	+	11.4141i	−0.0974490	+	0.363685i
$986$	0.634807	+	54.7216i	0.0202164	+	1.74269i
$987$	3.72557	+	19.7011i	0.118586	+	0.627092i
$988$	0.133831	+	5.76744i	0.00425772	+	0.183487i
$989$	5.68642	+	13.7282i	0.180818	+	0.436532i
$990$	8.23460	+	31.6548i	0.261713	+	1.00605i
$991$			36.4148i			1.15675i	0.815770	+	0.578377i	$0.196314\pi$
$991$			36.4148i			1.15675i	−0.815770	+	0.578377i	$0.803686\pi$
$992$	3.16307	+	1.10006i	0.100428	+	0.0349270i
$993$	52.1232	+	26.3197i	1.65408	+	0.835229i
$994$	13.9014	+	5.57011i	0.440925	+	0.176673i
$995$	−3.22114	−	2.47167i	−0.102117	−	0.0783572i
$996$	−34.5652	+	23.7896i	−1.09524	+	0.753801i
$997$	−23.8237	−	31.0476i	−0.754503	−	0.983288i	−0.999904	−	0.0138661i	$-0.995586\pi$
$997$	−23.8237	−	31.0476i	−0.754503	−	0.983288i	0.245400	−	0.969422i	$-0.421081\pi$
$998$	−23.4877	+	41.7941i	−0.743489	+	1.32297i
$999$	−21.5974	−	15.3340i	−0.683312	−	0.485148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.23	✓	368
3.2	odd	2		864.2.bn.a.683.24		368
9.4	even	3		864.2.bn.a.395.40		368
9.5	odd	6	inner	288.2.bf.a.203.7	yes	368
32.3	odd	8	inner	288.2.bf.a.227.7	yes	368
96.35	even	8		864.2.bn.a.35.40		368
288.67	odd	24		864.2.bn.a.611.24		368
288.131	even	24	inner	288.2.bf.a.131.23	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.23	✓	368	1.1	even	1	trivial
288.2.bf.a.131.23	yes	368	288.131	even	24	inner
288.2.bf.a.203.7	yes	368	9.5	odd	6	inner
288.2.bf.a.227.7	yes	368	32.3	odd	8	inner
864.2.bn.a.35.40		368	96.35	even	8
864.2.bn.a.395.40		368	9.4	even	3
864.2.bn.a.611.24		368	288.67	odd	24
864.2.bn.a.683.24		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)

\(f(q)\)	\(=\)	\(q+(-0.200844 - 1.39988i) q^{2} +(-1.56060 + 0.751351i) q^{3} +(-1.91932 + 0.562314i) q^{4} +(-0.202788 - 1.54033i) q^{5} +(1.36524 + 2.03375i) q^{6} +(1.17766 + 4.39511i) q^{7} +(1.17266 + 2.57388i) q^{8} +(1.87094 - 2.34512i) q^{9} +O(q^{10})\)	\(q+(-0.200844 - 1.39988i) q^{2} +(-1.56060 + 0.751351i) q^{3} +(-1.91932 + 0.562314i) q^{4} +(-0.202788 - 1.54033i) q^{5} +(1.36524 + 2.03375i) q^{6} +(1.17766 + 4.39511i) q^{7} +(1.17266 + 2.57388i) q^{8} +(1.87094 - 2.34512i) q^{9} +(-2.11554 + 0.593244i) q^{10} +(3.93681 - 3.02082i) q^{11} +(2.57280 - 2.31963i) q^{12} +(0.682021 - 0.888828i) q^{13} +(5.91609 - 2.53132i) q^{14} +(1.47380 + 2.25147i) q^{15} +(3.36761 - 2.15853i) q^{16} -4.08402 q^{17} +(-3.65865 - 2.14809i) q^{18} +(2.37867 - 0.985278i) q^{19} +(1.25536 + 2.84235i) q^{20} +(-5.14013 - 5.97416i) q^{21} +(-5.01947 - 4.90434i) q^{22} +(5.35870 + 1.43586i) q^{23} +(-3.76394 - 3.13573i) q^{24} +(2.49815 - 0.669376i) q^{25} +(-1.38123 - 0.776232i) q^{26} +(-1.15779 + 5.06552i) q^{27} +(-4.73175 - 7.77341i) q^{28} +(9.39407 + 1.23675i) q^{29} +(2.85578 - 2.51533i) q^{30} +(-0.512694 + 0.296004i) q^{31} +(-3.69804 - 4.28071i) q^{32} +(-3.87409 + 7.67221i) q^{33} +(0.820250 + 5.71713i) q^{34} +(6.53108 - 2.70526i) q^{35} +(-2.27226 + 5.55309i) q^{36} +(-1.95073 + 4.70947i) q^{37} +(-1.85701 - 3.13197i) q^{38} +(-0.396542 + 1.89954i) q^{39} +(3.72682 - 2.32823i) q^{40} +(-1.25344 + 4.67789i) q^{41} +(-7.33074 + 8.39543i) q^{42} +(1.63054 + 2.12496i) q^{43} +(-5.85736 + 8.01165i) q^{44} +(-3.99165 - 2.40630i) q^{45} +(0.933768 - 7.78992i) q^{46} +(-2.20325 - 1.27205i) q^{47} +(-3.63367 + 5.89885i) q^{48} +(-11.8679 + 6.85192i) q^{49} +(-1.43878 - 3.36266i) q^{50} +(6.37352 - 3.06853i) q^{51} +(-0.809219 + 2.08946i) q^{52} +(2.74153 - 6.61863i) q^{53} +(7.32365 + 0.603391i) q^{54} +(-5.45138 - 5.45138i) q^{55} +(-9.93149 + 8.18512i) q^{56} +(-2.97187 + 3.32484i) q^{57} +(-0.155437 - 13.3990i) q^{58} +(-0.630820 + 0.0830490i) q^{59} +(-4.09472 - 3.49256i) q^{60} +(1.61659 - 12.2792i) q^{61} +(0.517341 + 0.658259i) q^{62} +(12.5104 + 5.46124i) q^{63} +(-5.24975 + 6.03656i) q^{64} +(-1.50739 - 0.870292i) q^{65} +(11.5183 + 3.88234i) q^{66} +(-5.85104 + 7.62523i) q^{67} +(7.83855 - 2.29650i) q^{68} +(-9.44162 + 1.78546i) q^{69} +(-5.09877 - 8.59939i) q^{70} +(1.64564 + 1.64564i) q^{71} +(8.23003 + 2.06558i) q^{72} +(-0.361810 + 0.361810i) q^{73} +(6.98448 + 1.78491i) q^{74} +(-3.39567 + 2.92161i) q^{75} +(-4.01141 + 3.22863i) q^{76} +(17.9131 + 13.7452i) q^{77} +(2.73877 + 0.173599i) q^{78} +(-3.24123 + 5.61397i) q^{79} +(-4.00774 - 4.74949i) q^{80} +(-1.99913 - 8.77516i) q^{81} +(6.80022 + 0.815134i) q^{82} +(-12.0094 - 1.58106i) q^{83} +(13.2249 + 8.57598i) q^{84} +(0.828189 + 6.29072i) q^{85} +(2.64720 - 2.70934i) q^{86} +(-15.5896 + 5.12816i) q^{87} +(12.3918 + 6.59050i) q^{88} +(-2.45638 + 2.45638i) q^{89} +(-2.56684 + 6.07112i) q^{90} +(4.70968 + 1.95082i) q^{91} +(-11.0925 + 0.257395i) q^{92} +(0.577707 - 0.847156i) q^{93} +(-1.33820 + 3.33977i) q^{94} +(-2.00002 - 3.46413i) q^{95} +(8.98748 + 3.90196i) q^{96} +(8.51749 - 14.7527i) q^{97} +(11.9755 + 15.2374i) q^{98} +(0.281381 - 14.8841i) 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

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