LMFDB - Embedded newform 273.2.by.d.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.1
Character	$\chi$	$=$	273.223
Dual form			273.2.by.d.202.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16866 - 0.581092i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(-2.16866 + 0.581092i) q^{6} +(1.25762 - 2.32774i) q^{7} +(-1.65230 - 1.65230i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.16866 - 0.581092i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(-2.16866 + 0.581092i) q^{6} +(1.25762 - 2.32774i) q^{7} +(-1.65230 - 1.65230i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.98130 - 5.16377i) q^{10} +(-1.20979 + 4.51499i) q^{11} +3.04077 q^{12} +(1.52548 + 3.26694i) q^{13} +(-4.07999 + 4.31730i) q^{14} +(2.56526 + 0.687359i) q^{15} +(-0.417624 - 0.723346i) q^{16} +(-2.18729 + 3.78849i) q^{17} +(-1.58757 + 1.58757i) q^{18} +(0.194491 - 0.0521138i) q^{19} +(2.09010 + 7.80037i) q^{20} +(-0.0747386 - 2.64470i) q^{21} +(5.24724 - 9.08849i) q^{22} +(7.20237 - 4.15829i) q^{23} +(-2.25709 - 0.604784i) q^{24} +2.05302i q^{25} +(-1.40986 - 7.97134i) q^{26} -1.00000i q^{27} +(6.85087 - 4.21777i) q^{28} +(-5.20380 - 9.01325i) q^{29} +(-5.16377 - 2.98130i) q^{30} +(6.75799 + 6.75799i) q^{31} +(1.69492 + 6.32554i) q^{32} +(1.20979 + 4.51499i) q^{33} +(6.94495 - 6.94495i) q^{34} +(6.73296 - 2.00958i) q^{35} +(2.63339 - 1.52039i) q^{36} +(1.22755 - 4.58128i) q^{37} -0.452070 q^{38} +(2.95458 + 2.06651i) q^{39} -6.20572i q^{40} +(-0.136339 + 0.508825i) q^{41} +(-1.37473 + 5.77889i) q^{42} +(2.49507 + 1.44053i) q^{43} +(-10.0504 + 10.0504i) q^{44} +(2.56526 - 0.687359i) q^{45} +(-18.0359 + 4.83270i) q^{46} +(-0.928461 + 0.928461i) q^{47} +(-0.723346 - 0.417624i) q^{48} +(-3.83677 - 5.85484i) q^{49} +(1.19299 - 4.45231i) q^{50} +4.37458i q^{51} +(-0.949833 + 10.9224i) q^{52} +1.95082 q^{53} +(-0.581092 + 2.16866i) q^{54} +(-10.7506 + 6.20683i) q^{55} +(-5.92410 + 1.76816i) q^{56} +(0.142378 - 0.142378i) q^{57} +(6.04777 + 22.5706i) q^{58} +(-1.76081 - 6.57142i) q^{59} +(5.71027 + 5.71027i) q^{60} +(-2.13306 - 1.23152i) q^{61} +(-10.7288 - 18.5828i) q^{62} +(-1.38707 - 2.25300i) q^{63} -13.0324i q^{64} +(-3.27029 + 8.99969i) q^{65} -10.4945i q^{66} +(-1.40878 - 0.377482i) q^{67} +(-11.5199 + 6.65104i) q^{68} +(4.15829 - 7.20237i) q^{69} +(-15.7693 + 0.445637i) q^{70} +(-1.44014 - 5.37468i) q^{71} +(-2.25709 + 0.604784i) q^{72} +(-8.75032 + 8.75032i) q^{73} +(-5.32429 + 9.22194i) q^{74} +(1.02651 + 1.77797i) q^{75} +(0.591404 + 0.158466i) q^{76} +(8.98827 + 8.49422i) q^{77} +(-5.20665 - 6.19846i) q^{78} -4.46495 q^{79} +(0.574115 - 2.14263i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.591348 - 1.02425i) q^{82} +(5.42187 + 5.42187i) q^{83} +(3.82414 - 7.07814i) q^{84} +(-11.2219 + 3.00690i) q^{85} +(-4.57389 - 4.57389i) q^{86} +(-9.01325 - 5.20380i) q^{87} +(9.45905 - 5.46119i) q^{88} +(-15.0461 - 4.03159i) q^{89} -5.96261 q^{90} +(9.52308 + 0.557652i) q^{91} +25.2888 q^{92} +(9.23159 + 2.47360i) q^{93} +(2.55304 - 1.47400i) q^{94} +(0.463100 + 0.267371i) q^{95} +(4.63062 + 4.63062i) q^{96} +(2.84925 - 0.763454i) q^{97} +(4.91847 + 14.9267i) q^{98} +(3.30520 + 3.30520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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 $

$2$	−2.16866	−	0.581092i	−1.53348	−	0.410894i	−0.609326	−	0.792920i	$-0.708560\pi$
$2$	−2.16866	−	0.581092i	−1.53348	−	0.410894i	−0.924152	+	0.382026i	$0.875226\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	2.63339	+	1.52039i	1.31669	+	0.760193i
$5$	1.87790	+	1.87790i	0.839823	+	0.839823i	0.988835	−	0.149013i	$-0.0476095\pi$
$5$	1.87790	+	1.87790i	0.839823	+	0.839823i	−0.149013	+	0.988835i	$0.547610\pi$
$6$	−2.16866	+	0.581092i	−0.885353	+	0.237230i
$7$	1.25762	−	2.32774i	0.475337	−	0.879804i
$7$	1.25762	−	2.32774i	0.475337	−	0.879804i
$8$	−1.65230	−	1.65230i	−0.584177	−	0.584177i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.98130	−	5.16377i	−0.942771	−	1.63293i
$11$	−1.20979	+	4.51499i	−0.364764	+	1.36132i	0.502975	+	0.864301i	$0.332239\pi$
$11$	−1.20979	+	4.51499i	−0.364764	+	1.36132i	−0.867740	+	0.497019i	$0.834428\pi$
$12$	3.04077			0.877795
$13$	1.52548	+	3.26694i	0.423092	+	0.906087i
$13$	1.52548	+	3.26694i	0.423092	+	0.906087i
$14$	−4.07999	+	4.31730i	−1.09042	+	1.15385i
$15$	2.56526	+	0.687359i	0.662347	+	0.177475i
$16$	−0.417624	−	0.723346i	−0.104406	−	0.180836i
$17$	−2.18729	+	3.78849i	−0.530495	+	0.918845i	0.468872	+	0.883266i	$0.344661\pi$
$17$	−2.18729	+	3.78849i	−0.530495	+	0.918845i	−0.999367	+	0.0355783i	$0.988673\pi$
$18$	−1.58757	+	1.58757i	−0.374194	+	0.374194i
$19$	0.194491	−	0.0521138i	0.0446194	−	0.0119557i	−0.236440	−	0.971646i	$-0.575981\pi$
$19$	0.194491	−	0.0521138i	0.0446194	−	0.0119557i	0.281060	+	0.959690i	$0.409314\pi$
$20$	2.09010	+	7.80037i	0.467361	+	1.74422i
$21$	−0.0747386	−	2.64470i	−0.0163093	−	0.577120i
$22$	5.24724	−	9.08849i	1.11872	−	1.93767i
$23$	7.20237	−	4.15829i	1.50180	−	0.867064i	0.501801	−	0.864983i	$-0.332671\pi$
$23$	7.20237	−	4.15829i	1.50180	−	0.867064i	0.999998	−	0.00208060i	$-0.000662276\pi$
$24$	−2.25709	−	0.604784i	−0.460726	−	0.123451i
$25$			2.05302i			0.410604i
$26$	−1.40986	−	7.97134i	−0.276497	−	1.56331i
$27$		−	1.00000i		−	0.192450i
$28$	6.85087	−	4.21777i	1.29469	−	0.797084i
$29$	−5.20380	−	9.01325i	−0.966322	−	1.67372i	−0.706022	−	0.708190i	$-0.749512\pi$
$29$	−5.20380	−	9.01325i	−0.966322	−	1.67372i	−0.260300	−	0.965528i	$-0.583821\pi$
$30$	−5.16377	−	2.98130i	−0.942771	−	0.544309i
$31$	6.75799	+	6.75799i	1.21377	+	1.21377i	0.969777	+	0.243995i	$0.0784579\pi$
$31$	6.75799	+	6.75799i	1.21377	+	1.21377i	0.243995	+	0.969777i	$0.421542\pi$
$32$	1.69492	+	6.32554i	0.299623	+	1.11821i
$33$	1.20979	+	4.51499i	0.210597	+	0.785958i
$34$	6.94495	−	6.94495i	1.19105	−	1.19105i
$35$	6.73296	−	2.00958i	1.13808	−	0.339681i
$36$	2.63339	−	1.52039i	0.438898	−	0.253398i
$37$	1.22755	−	4.58128i	0.201808	−	0.753158i	−0.788591	−	0.614919i	$-0.789189\pi$
$37$	1.22755	−	4.58128i	0.201808	−	0.753158i	0.990399	−	0.138240i	$-0.0441444\pi$
$38$	−0.452070			−0.0733354
$39$	2.95458	+	2.06651i	0.473111	+	0.330907i
$40$		−	6.20572i		−	0.981210i
$41$	−0.136339	+	0.508825i	−0.0212926	+	0.0794651i	−0.975755	−	0.218867i	$-0.929764\pi$
$41$	−0.136339	+	0.508825i	−0.0212926	+	0.0794651i	0.954462	+	0.298333i	$0.0964304\pi$
$42$	−1.37473	+	5.77889i	−0.212125	+	0.891702i
$43$	2.49507	+	1.44053i	0.380494	+	0.219678i	0.678033	−	0.735031i	$-0.262832\pi$
$43$	2.49507	+	1.44053i	0.380494	+	0.219678i	−0.297539	+	0.954710i	$0.596166\pi$
$44$	−10.0504	+	10.0504i	−1.51515	+	1.51515i
$45$	2.56526	−	0.687359i	0.382406	−	0.102465i
$46$	−18.0359	+	4.83270i	−2.65925	+	0.712543i
$47$	−0.928461	+	0.928461i	−0.135430	+	0.135430i	−0.771572	−	0.636142i	$-0.780529\pi$
$47$	−0.928461	+	0.928461i	−0.135430	+	0.135430i	0.636142	+	0.771572i	$0.280529\pi$
$48$	−0.723346	−	0.417624i	−0.104406	−	0.0602788i
$49$	−3.83677	−	5.85484i	−0.548110	−	0.836406i
$50$	1.19299	−	4.45231i	0.168715	−	0.629651i
$51$			4.37458i			0.612563i
$52$	−0.949833	+	10.9224i	−0.131718	+	1.51467i
$53$	1.95082			0.267966			0.133983	−	0.990984i	$-0.457223\pi$
$53$	1.95082			0.267966			0.133983	+	0.990984i	$0.457223\pi$
$54$	−0.581092	+	2.16866i	−0.0790766	+	0.295118i
$55$	−10.7506	+	6.20683i	−1.44960	+	0.836929i
$56$	−5.92410	+	1.76816i	−0.791642	+	0.236281i
$57$	0.142378	−	0.142378i	0.0188584	−	0.0188584i
$58$	6.04777	+	22.5706i	0.794111	+	2.96366i
$59$	−1.76081	−	6.57142i	−0.229237	−	0.855526i	−0.980662	−	0.195707i	$-0.937300\pi$
$59$	−1.76081	−	6.57142i	−0.229237	−	0.855526i	0.751425	−	0.659819i	$-0.229367\pi$
$60$	5.71027	+	5.71027i	0.737192	+	0.737192i
$61$	−2.13306	−	1.23152i	−0.273111	−	0.157681i	0.357190	−	0.934032i	$-0.383735\pi$
$61$	−2.13306	−	1.23152i	−0.273111	−	0.157681i	−0.630300	+	0.776351i	$0.717068\pi$
$62$	−10.7288	−	18.5828i	−1.36256	−	2.36002i
$63$	−1.38707	−	2.25300i	−0.174755	−	0.283852i
$64$		−	13.0324i		−	1.62905i
$65$	−3.27029	+	8.99969i	−0.405630	+	1.11627i
$66$		−	10.4945i		−	1.29178i
$67$	−1.40878	−	0.377482i	−0.172110	−	0.0461168i	0.171735	−	0.985143i	$-0.445063\pi$
$67$	−1.40878	−	0.377482i	−0.172110	−	0.0461168i	−0.343845	+	0.939026i	$0.611729\pi$
$68$	−11.5199	+	6.65104i	−1.39700	+	0.806558i
$69$	4.15829	−	7.20237i	0.500600	−	0.867064i
$70$	−15.7693	+	0.445637i	−1.88479	+	0.0532638i
$71$	−1.44014	−	5.37468i	−0.170913	−	0.637857i	−0.997212	−	0.0746244i	$-0.976224\pi$
$71$	−1.44014	−	5.37468i	−0.170913	−	0.637857i	0.826299	−	0.563232i	$-0.190442\pi$
$72$	−2.25709	+	0.604784i	−0.266000	+	0.0712745i
$73$	−8.75032	+	8.75032i	−1.02415	+	1.02415i	−0.0244465	+	0.999701i	$0.507782\pi$
$73$	−8.75032	+	8.75032i	−1.02415	+	1.02415i	−0.999701	+	0.0244465i	$0.992218\pi$
$74$	−5.32429	+	9.22194i	−0.618936	+	1.07203i
$75$	1.02651	+	1.77797i	0.118531	+	0.205302i
$76$	0.591404	+	0.158466i	0.0678387	+	0.0181773i
$77$	8.98827	+	8.49422i	1.02431	+	0.968006i
$78$	−5.20665	−	6.19846i	−0.589537	−	0.701837i
$79$	−4.46495			−0.502346			−0.251173	−	0.967942i	$-0.580816\pi$
$79$	−4.46495			−0.502346			−0.251173	+	0.967942i	$0.580816\pi$
$80$	0.574115	−	2.14263i	0.0641880	−	0.239553i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.591348	−	1.02425i	0.0653035	−	0.113109i
$83$	5.42187	+	5.42187i	0.595128	+	0.595128i	0.939012	−	0.343884i	$-0.111743\pi$
$83$	5.42187	+	5.42187i	0.595128	+	0.595128i	−0.343884	+	0.939012i	$0.611743\pi$
$84$	3.82414	−	7.07814i	0.417248	−	0.772288i
$85$	−11.2219	+	3.00690i	−1.21719	+	0.326145i
$86$	−4.57389	−	4.57389i	−0.493215	−	0.493215i
$87$	−9.01325	−	5.20380i	−0.966322	−	0.557906i
$88$	9.45905	−	5.46119i	1.00834	−	0.582164i
$89$	−15.0461	−	4.03159i	−1.59488	−	0.427347i	−0.651390	−	0.758743i	$-0.725814\pi$
$89$	−15.0461	−	4.03159i	−1.59488	−	0.427347i	−0.943492	+	0.331396i	$0.892480\pi$
$90$	−5.96261			−0.628514
$91$	9.52308	+	0.557652i	0.998290	+	0.0584578i
$92$	25.2888			2.63654
$93$	9.23159	+	2.47360i	0.957271	+	0.256500i
$94$	2.55304	−	1.47400i	0.263326	−	0.152031i
$95$	0.463100	+	0.267371i	0.0475131	+	0.0274317i
$96$	4.63062	+	4.63062i	0.472611	+	0.472611i
$97$	2.84925	−	0.763454i	0.289297	−	0.0775170i	−0.111252	−	0.993792i	$-0.535486\pi$
$97$	2.84925	−	0.763454i	0.289297	−	0.0775170i	0.400549	+	0.916275i	$0.368819\pi$
$98$	4.91847	+	14.9267i	0.496841	+	1.50782i
$99$	3.30520	+	3.30520i	0.332185	+	0.332185i
$100$	−3.12138	+	5.40639i	−0.312138	+	0.540639i
$101$	−0.316767	−	0.548657i	−0.0315195	−	0.0545934i	0.849835	−	0.527048i	$-0.176701\pi$
$101$	−0.316767	−	0.548657i	−0.0315195	−	0.0545934i	−0.881355	+	0.472455i	$0.843368\pi$
$102$	2.54203	−	9.48698i	0.251698	−	0.939351i
$103$	−1.95716			−0.192845			−0.0964223	−	0.995341i	$-0.530740\pi$
$103$	−1.95716			−0.192845			−0.0964223	+	0.995341i	$0.530740\pi$
$104$	2.87742	−	7.91853i	0.282154	−	0.776475i
$105$	4.82612	−	5.10683i	0.470981	−	0.498375i
$106$	−4.23068	−	1.13361i	−0.410920	−	0.110106i
$107$	−3.59988	−	6.23517i	−0.348013	−	0.602777i	0.637883	−	0.770133i	$-0.279810\pi$
$107$	−3.59988	−	6.23517i	−0.348013	−	0.602777i	−0.985896	+	0.167357i	$0.946477\pi$
$108$	1.52039	−	2.63339i	0.146299	−	0.253398i
$109$	−2.42207	+	2.42207i	−0.231992	+	0.231992i	−0.813524	−	0.581531i	$-0.802454\pi$
$109$	−2.42207	+	2.42207i	−0.231992	+	0.231992i	0.581531	+	0.813524i	$0.302454\pi$
$110$	26.9211	−	7.21348i	2.56682	−	0.687778i
$111$	−1.22755	−	4.58128i	−0.116514	−	0.434836i
$112$	−2.20898	+	0.0624252i	−0.208729	+	0.00589863i
$113$	0.379755	−	0.657754i	0.0357243	−	0.0618763i	−0.847610	−	0.530619i	$-0.821960\pi$
$113$	0.379755	−	0.657754i	0.0357243	−	0.0618763i	0.883335	+	0.468743i	$0.155293\pi$
$114$	−0.391504	+	0.226035i	−0.0366677	+	0.0211701i
$115$	21.3342	+	5.71648i	1.98942	+	0.533065i
$116$		−	31.6471i		−	2.93836i
$117$	3.59199	+	0.312366i	0.332080	+	0.0288782i
$118$			15.2744i			1.40612i
$119$	6.06786	+	9.85594i	0.556239	+	0.903492i
$120$	−3.10286	−	5.37431i	−0.283251	−	0.490605i
$121$	−9.39523	−	5.42434i	−0.854112	−	0.493122i
$122$	3.91027	+	3.91027i	0.354019	+	0.354019i
$123$	0.136339	+	0.508825i	0.0122933	+	0.0458792i
$124$	7.52164	+	28.0712i	0.675464	+	2.52086i
$125$	5.53414	−	5.53414i	0.494988	−	0.494988i
$126$	1.69889	+	5.69203i	0.151349	+	0.507086i
$127$	−1.04032	+	0.600626i	−0.0923131	+	0.0532970i	−0.545446	−	0.838146i	$-0.683640\pi$
$127$	−1.04032	+	0.600626i	−0.0923131	+	0.0532970i	0.453133	+	0.891443i	$0.350306\pi$
$128$	−4.18317	+	15.6118i	−0.369743	+	1.37990i
$129$	2.88106			0.253663
$130$	12.3218	−	17.6170i	1.08069	−	1.54511i
$131$		−	3.03417i		−	0.265097i	−0.991177	−	0.132548i	$-0.957684\pi$
$131$		−	3.03417i		−	0.265097i	0.991177	−	0.132548i	$-0.0423160\pi$
$132$	−3.67869	+	13.7290i	−0.320189	+	1.19496i
$133$	0.123289	−	0.518266i	0.0106905	−	0.0449393i
$134$	2.83582	+	1.63726i	0.244978	+	0.141438i
$135$	1.87790	−	1.87790i	0.161624	−	0.161624i
$136$	9.87379	−	2.64567i	0.846671	−	0.226865i
$137$	−11.2793	+	3.02227i	−0.963654	+	0.258210i	−0.706146	−	0.708066i	$-0.749568\pi$
$137$	−11.2793	+	3.02227i	−0.963654	+	0.258210i	−0.257508	+	0.966276i	$0.582901\pi$
$138$	−13.2032	+	13.2032i	−1.12393	+	1.12393i
$139$	−5.80746	−	3.35294i	−0.492582	−	0.284393i	0.233063	−	0.972462i	$-0.425125\pi$
$139$	−5.80746	−	3.35294i	−0.492582	−	0.284393i	−0.725645	+	0.688069i	$0.758459\pi$
$140$	20.7858	+	4.94470i	1.75672	+	0.417903i
$141$	−0.339840	+	1.26830i	−0.0286197	+	0.106810i
$142$			12.4927i			1.04837i
$143$	−16.5957	+	2.93522i	−1.38780	+	0.245455i
$144$	−0.835248			−0.0696040
$145$	7.15376	−	26.6982i	0.594087	−	2.21716i
$146$	24.0612	−	13.8918i	1.99132	−	1.14969i
$147$	−6.25016	−	3.15206i	−0.515505	−	0.259977i
$148$	10.1979	−	10.1979i	0.838265	−	0.838265i
$149$	−1.23932	−	4.62521i	−0.101529	−	0.378912i	0.896399	−	0.443248i	$-0.146174\pi$
$149$	−1.23932	−	4.62521i	−0.101529	−	0.378912i	−0.997928	+	0.0643356i	$0.979507\pi$
$150$	−1.19299	−	4.45231i	−0.0974074	−	0.363529i
$151$	−7.66300	−	7.66300i	−0.623606	−	0.623606i	0.322845	−	0.946452i	$-0.395361\pi$
$151$	−7.66300	−	7.66300i	−0.623606	−	0.623606i	−0.946452	+	0.322845i	$0.895361\pi$
$152$	−0.407466	−	0.235251i	−0.0330499	−	0.0190814i
$153$	2.18729	+	3.78849i	0.176832	+	0.306282i
$154$	−14.5566	−	23.6441i	−1.17301	−	1.90530i
$155$			25.3817i			2.03870i
$156$	4.63864	+	9.93403i	0.371388	+	0.795359i
$157$		−	8.00601i		−	0.638949i	−0.947595	−	0.319475i	$-0.896494\pi$
$157$		−	8.00601i		−	0.638949i	0.947595	−	0.319475i	$-0.103506\pi$
$158$	9.68297	+	2.59455i	0.770336	+	0.206411i
$159$	1.68946	−	0.975412i	0.133983	−	0.0773552i
$160$	−8.69584	+	15.0616i	−0.687467	+	1.19073i
$161$	−0.621570	−	21.9948i	−0.0489865	−	1.73344i
$162$	0.581092	+	2.16866i	0.0456549	+	0.170386i
$163$	18.3794	−	4.92475i	1.43959	−	0.385736i	0.547199	−	0.837003i	$-0.315694\pi$
$163$	18.3794	−	4.92475i	1.43959	−	0.385736i	0.892389	+	0.451266i	$0.149028\pi$
$164$	−1.13264	+	1.13264i	−0.0884447	+	0.0884447i
$165$	−6.20683	+	10.7506i	−0.483201	+	0.836929i
$166$	−8.60761	−	14.9088i	−0.668080	−	1.15715i
$167$	−10.5127	−	2.81688i	−0.813500	−	0.217977i	−0.171997	−	0.985097i	$-0.555022\pi$
$167$	−10.5127	−	2.81688i	−0.813500	−	0.217977i	−0.641503	+	0.767121i	$0.721689\pi$
$168$	−4.24634	+	4.49333i	−0.327613	+	0.346668i
$169$	−8.34582	+	9.96731i	−0.641986	+	0.766716i
$170$	26.0839			2.00054
$171$	0.0521138	−	0.194491i	0.00398524	−	0.0148731i
$172$	4.38032	+	7.58693i	0.333996	+	0.578498i
$173$	−4.07283	+	7.05435i	−0.309651	+	0.536332i	−0.978286	−	0.207259i	$-0.933546\pi$
$173$	−4.07283	+	7.05435i	−0.309651	+	0.536332i	0.668635	+	0.743591i	$0.266879\pi$
$174$	16.5228	+	16.5228i	1.25259	+	1.25259i
$175$	4.77890	+	2.58192i	0.361251	+	0.195175i
$176$	3.77113	−	1.01047i	0.284260	−	0.0761672i
$177$	−4.81061	−	4.81061i	−0.361588	−	0.361588i
$178$	30.2872	+	17.4863i	2.27012	+	1.31065i
$179$	10.2340	−	5.90863i	0.764928	−	0.441631i	−0.0661342	−	0.997811i	$-0.521067\pi$
$179$	10.2340	−	5.90863i	0.764928	−	0.441631i	0.831062	+	0.556179i	$0.187733\pi$
$180$	7.80037	+	2.09010i	0.581405	+	0.155787i
$181$	10.4995			0.780423			0.390212	−	0.920725i	$-0.372402\pi$
$181$	10.4995			0.780423			0.390212	+	0.920725i	$0.372402\pi$
$182$	−20.3283	−	6.74314i	−1.50683	−	0.499835i
$183$	−2.46305			−0.182074
$184$	−18.7712	−	5.02974i	−1.38383	−	0.370797i
$185$	10.9084	−	6.29797i	0.802002	−	0.463036i
$186$	−18.5828	−	10.7288i	−1.36256	−	0.786674i
$187$	−14.4588	−	14.4588i	−1.05734	−	1.05734i
$188$	−3.85661	+	1.03338i	−0.281272	+	0.0753667i
$189$	−2.32774	−	1.25762i	−0.169318	−	0.0914786i
$190$	−0.848942	−	0.848942i	−0.0615887	−	0.0615887i
$191$	−6.67464	+	11.5608i	−0.482960	+	0.836511i	−0.999809	−	0.0195655i	$-0.993772\pi$
$191$	−6.67464	+	11.5608i	−0.482960	+	0.836511i	0.516849	+	0.856077i	$0.327105\pi$
$192$	−6.51620	−	11.2864i	−0.470266	−	0.814525i
$193$	−2.08783	+	7.79189i	−0.150285	+	0.560872i	0.849178	+	0.528107i	$0.177098\pi$
$193$	−2.08783	+	7.79189i	−0.150285	+	0.560872i	−0.999463	+	0.0327652i	$0.989569\pi$
$194$	−6.62270			−0.475482
$195$	1.66769	+	9.42911i	0.119426	+	0.675232i
$196$	−1.20208	−	21.2514i	−0.0858631	−	1.51796i
$197$	−12.2629	−	3.28585i	−0.873699	−	0.234107i	−0.206012	−	0.978549i	$-0.566049\pi$
$197$	−12.2629	−	3.28585i	−0.873699	−	0.234107i	−0.667686	+	0.744443i	$0.732715\pi$
$198$	−5.24724	−	9.08849i	−0.372905	−	0.645891i
$199$	−10.8366	+	18.7696i	−0.768188	+	1.33054i	0.170356	+	0.985383i	$0.445508\pi$
$199$	−10.8366	+	18.7696i	−0.768188	+	1.33054i	−0.938544	+	0.345158i	$0.887825\pi$
$200$	3.39221	−	3.39221i	0.239865	−	0.239865i
$201$	−1.40878	+	0.377482i	−0.0993678	+	0.0266255i
$202$	0.368142	+	1.37392i	0.0259024	+	0.0966689i
$203$	−27.5249	+	0.777849i	−1.93187	+	0.0545943i
$204$	−6.65104	+	11.5199i	−0.465666	+	0.806558i
$205$	−1.21155	+	0.699491i	−0.0846186	+	0.0488546i
$206$	4.24442	+	1.13729i	0.295723	+	0.0792387i
$207$		−	8.31658i		−	0.578043i
$208$	1.72605	−	2.46780i	0.119680	−	0.171111i
$209$			0.941173i			0.0651023i
$210$	−13.4338	+	8.27057i	−0.927019	+	0.570724i
$211$	6.50914	+	11.2742i	0.448108	+	0.776145i	0.998263	−	0.0589170i	$-0.0187647\pi$
$211$	6.50914	+	11.2742i	0.448108	+	0.776145i	−0.550155	+	0.835062i	$0.685431\pi$
$212$	5.13727	+	2.96601i	0.352829	+	0.203706i
$213$	−3.93454	−	3.93454i	−0.269590	−	0.269590i
$214$	4.18372	+	15.6138i	0.285993	+	1.06734i
$215$	1.98032	+	7.39066i	0.135057	+	0.504039i
$216$	−1.65230	+	1.65230i	−0.112425	+	0.112425i
$217$	24.2299	−	7.23187i	1.64483	−	0.490931i
$218$	6.66011	−	3.84521i	0.451079	−	0.260431i
$219$	−3.20284	+	11.9532i	−0.216428	+	0.807720i
$220$	−37.7471			−2.54491
$221$	−15.7135	−	1.36647i	−1.05700	−	0.0919186i
$222$			10.6486i			0.714686i
$223$	−4.38178	+	16.3530i	−0.293426	+	1.09508i	0.649034	+	0.760759i	$0.275173\pi$
$223$	−4.38178	+	16.3530i	−0.293426	+	1.09508i	−0.942460	+	0.334320i	$0.891493\pi$
$224$	16.8558	+	4.00980i	1.12623	+	0.267916i
$225$	1.77797	+	1.02651i	0.118531	+	0.0684340i
$226$	−1.20578	+	1.20578i	−0.0802070	+	0.0802070i
$227$	18.2910	−	4.90106i	1.21402	−	0.325295i	0.405679	−	0.914015i	$-0.367035\pi$
$227$	18.2910	−	4.90106i	1.21402	−	0.325295i	0.808336	+	0.588721i	$0.200368\pi$
$228$	0.591404	−	0.158466i	0.0391667	−	0.0104947i
$229$	0.181433	−	0.181433i	0.0119894	−	0.0119894i	−0.701087	−	0.713076i	$-0.747301\pi$
$229$	0.181433	−	0.181433i	0.0119894	−	0.0119894i	0.713076	+	0.701087i	$0.247301\pi$
$230$	−42.9449	−	24.7943i	−2.83170	−	1.63488i
$231$	12.0312	+	2.86207i	0.791594	+	0.188311i
$232$	−6.29435	+	23.4909i	−0.413245	+	1.54225i
$233$		−	11.3848i		−	0.745842i	−0.927863	−	0.372921i	$-0.878356\pi$
$233$		−	11.3848i		−	0.745842i	0.927863	−	0.372921i	$-0.121644\pi$
$234$	−7.60832	−	2.76470i	−0.497371	−	0.180734i
$235$	−3.48711			−0.227474
$236$	5.35421	−	19.9822i	0.348529	−	1.30073i
$237$	−3.86676	+	2.23247i	−0.251173	+	0.145015i
$238$	−7.43194	−	24.9002i	−0.481741	−	1.61404i
$239$	−12.2181	+	12.2181i	−0.790322	+	0.790322i	−0.981546	−	0.191224i	$-0.938754\pi$
$239$	−12.2181	+	12.2181i	−0.790322	+	0.790322i	0.191224	+	0.981546i	$0.438754\pi$
$240$	−0.574115	−	2.14263i	−0.0370590	−	0.138306i
$241$	−7.89185	−	29.4528i	−0.508359	−	1.89722i	−0.436254	−	0.899824i	$-0.643695\pi$
$241$	−7.89185	−	29.4528i	−0.508359	−	1.89722i	−0.0721047	−	0.997397i	$-0.522972\pi$
$242$	17.2231	+	17.2231i	1.10714	+	1.10714i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.74479	−	6.48616i	−0.239735	−	0.415234i
$245$	3.78973	−	18.1999i	0.242117	−	1.16275i
$246$		−	1.18270i		−	0.0754060i
$247$	0.466946	+	0.555894i	0.0297111	+	0.0353707i
$248$		−	22.3325i		−	1.41811i
$249$	7.40641	+	1.98454i	0.469362	+	0.125765i
$250$	−15.2175	+	8.78584i	−0.962441	+	0.555666i
$251$	5.46171	−	9.45996i	0.344740	−	0.597107i	−0.640566	−	0.767903i	$-0.721300\pi$
$251$	5.46171	−	9.45996i	0.344740	−	0.597107i	0.985307	+	0.170795i	$0.0546337\pi$
$252$	−0.227263	−	8.04192i	−0.0143162	−	0.506593i
$253$	10.0613	+	37.5493i	0.632548	+	2.36070i
$254$	2.60511	−	0.698038i	0.163459	−	0.0437988i
$255$	−8.21502	+	8.21502i	−0.514444	+	0.514444i
$256$	5.11138	−	8.85317i	0.319461	−	0.553323i
$257$	14.2035	+	24.6012i	0.885991	+	1.53458i	0.844574	+	0.535439i	$0.179854\pi$
$257$	14.2035	+	24.6012i	0.885991	+	1.53458i	0.0414174	+	0.999142i	$0.486813\pi$
$258$	−6.24804	−	1.67416i	−0.388986	−	0.104229i
$259$	−9.12025	−	8.61895i	−0.566705	−	0.535555i
$260$	−22.2949	+	18.7276i	−1.38267	+	1.16143i
$261$	−10.4076			−0.644214
$262$	−1.76313	+	6.58009i	−0.108927	+	0.406520i
$263$	10.8579	+	18.8064i	0.669526	+	1.15965i	0.978037	+	0.208433i	$0.0668363\pi$
$263$	10.8579	+	18.8064i	0.669526	+	1.15965i	−0.308510	+	0.951221i	$0.599830\pi$
$264$	5.46119	−	9.45905i	0.336113	−	0.582164i
$265$	3.66345	+	3.66345i	0.225044	+	0.225044i
$266$	−0.568533	+	1.05230i	−0.0348590	+	0.0645208i
$267$	−15.0461	+	4.03159i	−0.920805	+	0.246729i
$268$	−3.13595	−	3.13595i	−0.191559	−	0.191559i
$269$	−10.7149	−	6.18625i	−0.653298	−	0.377182i	0.136420	−	0.990651i	$-0.456440\pi$
$269$	−10.7149	−	6.18625i	−0.653298	−	0.377182i	−0.789719	+	0.613469i	$0.789774\pi$
$270$	−5.16377	+	2.98130i	−0.314257	+	0.181436i
$271$	7.64449	+	2.04834i	0.464370	+	0.124427i	0.483415	−	0.875391i	$-0.339396\pi$
$271$	7.64449	+	2.04834i	0.464370	+	0.124427i	−0.0190456	+	0.999819i	$0.506063\pi$
$272$	3.65385			0.221547
$273$	8.52605	−	4.27860i	0.516020	−	0.258953i
$274$	26.2172			1.58384
$275$	−9.26935	−	2.48371i	−0.558963	−	0.149774i
$276$	21.9008	−	12.6444i	1.31827	−	0.761105i
$277$	9.70888	+	5.60543i	0.583350	+	0.336797i	0.762464	−	0.647031i	$-0.223990\pi$
$277$	9.70888	+	5.60543i	0.583350	+	0.336797i	−0.179113	+	0.983828i	$0.557323\pi$
$278$	10.6461	+	10.6461i	0.638509	+	0.638509i
$279$	9.23159	−	2.47360i	0.552681	−	0.148090i
$280$	−14.4453	−	7.80445i	−0.863272	−	0.466405i
$281$	−15.1948	−	15.1948i	−0.906448	−	0.906448i	0.0895355	−	0.995984i	$-0.471462\pi$
$281$	−15.1948	−	15.1948i	−0.906448	−	0.906448i	−0.995984	+	0.0895355i	$0.971462\pi$
$282$	1.47400	−	2.55304i	0.0877753	−	0.152031i
$283$	−7.64747	−	13.2458i	−0.454595	−	0.787382i	0.544070	−	0.839040i	$-0.316883\pi$
$283$	−7.64747	−	13.2458i	−0.454595	−	0.787382i	−0.998665	+	0.0516583i	$0.983549\pi$
$284$	4.37914	−	16.3432i	0.259854	−	0.969789i
$285$	0.534742			0.0316754
$286$	37.6961	+	3.27812i	2.22902	+	0.193839i
$287$	1.01295	+	0.957272i	0.0597926	+	0.0565060i
$288$	6.32554	+	1.69492i	0.372736	+	0.0998744i
$289$	−1.06845	−	1.85062i	−0.0628502	−	0.108860i
$290$	−31.0282	+	53.7424i	−1.82204	+	3.15586i
$291$	2.08580	−	2.08580i	0.122271	−	0.122271i
$292$	−36.3468	+	9.73911i	−2.12704	+	0.569938i
$293$	−5.44000	−	20.3023i	−0.317808	−	1.18608i	−0.921347	−	0.388742i	$-0.872910\pi$
$293$	−5.44000	−	20.3023i	−0.317808	−	1.18608i	0.603539	−	0.797334i	$-0.293757\pi$
$294$	11.7229	+	10.4677i	0.683692	+	0.610487i
$295$	9.03385	−	15.6471i	0.525971	−	0.911009i
$296$	−9.59795	+	5.54138i	−0.557869	+	0.322086i
$297$	4.51499	+	1.20979i	0.261986	+	0.0701989i
$298$			10.7507i			0.622771i
$299$	24.5720	+	17.1863i	1.42103	+	0.993912i
$300$			6.24276i			0.360426i
$301$	6.49103	−	3.99624i	0.374137	−	0.230339i
$302$	12.1656	+	21.0714i	0.700050	+	1.21252i
$303$	−0.548657	−	0.316767i	−0.0315195	−	0.0181978i
$304$	−0.118921	−	0.118921i	−0.00682057	−	0.00682057i
$305$	−1.69300	−	6.31836i	−0.0969409	−	0.361788i
$306$	−2.54203	−	9.48698i	−0.145318	−	0.542335i
$307$	12.7905	−	12.7905i	0.729995	−	0.729995i	−0.240624	−	0.970618i	$-0.577352\pi$
$307$	12.7905	−	12.7905i	0.729995	−	0.729995i	0.970618	+	0.240624i	$0.0773520\pi$
$308$	10.7551	+	36.0342i	0.612828	+	2.05324i
$309$	−1.69495	+	0.978579i	−0.0964223	+	0.0556694i
$310$	14.7491	−	55.0443i	0.837692	−	3.12631i
$311$	19.5517			1.10868			0.554338	−	0.832292i	$-0.312972\pi$
$311$	19.5517			1.10868			0.554338	+	0.832292i	$0.312972\pi$
$312$	−1.46735	−	8.29636i	−0.0830721	−	0.469689i
$313$		−	13.2495i		−	0.748904i	−0.927246	−	0.374452i	$-0.877831\pi$
$313$		−	13.2495i		−	0.748904i	0.927246	−	0.374452i	$-0.122169\pi$
$314$	−4.65223	+	17.3624i	−0.262540	+	0.979814i
$315$	1.62613	−	6.83570i	0.0916222	−	0.385148i
$316$	−11.7579	−	6.78845i	−0.661435	−	0.381880i
$317$	17.8861	−	17.8861i	1.00458	−	1.00458i	0.00459262	−	0.999989i	$-0.498538\pi$
$317$	17.8861	−	17.8861i	1.00458	−	1.00458i	0.999989	−	0.00459262i	$-0.00146188\pi$
$318$	−4.23068	+	1.13361i	−0.237245	+	0.0635696i
$319$	46.9902	−	12.5910i	2.63094	−	0.704959i
$320$	24.4735	−	24.4735i	1.36811	−	1.36811i
$321$	−6.23517	−	3.59988i	−0.348013	−	0.200926i
$322$	−11.4330	+	48.0606i	−0.637139	+	2.67831i
$323$	−0.227976	+	0.850818i	−0.0126849	+	0.0473408i
$324$		−	3.04077i		−	0.168932i
$325$	−6.70709	+	3.13184i	−0.372043	+	0.173723i
$326$	−42.7206			−2.36607
$327$	−0.886540	+	3.30861i	−0.0490258	+	0.182967i
$328$	1.06601	−	0.615459i	0.0588603	−	0.0339830i
$329$	0.993565	+	3.32887i	0.0547770	+	0.183527i
$330$	19.7076	−	19.7076i	1.08487	−	1.08487i
$331$	−3.51837	−	13.1307i	−0.193387	−	0.721731i	−0.992678	−	0.120787i	$-0.961458\pi$
$331$	−3.51837	−	13.1307i	−0.193387	−	0.721731i	0.799291	−	0.600944i	$-0.205208\pi$
$332$	6.03454	+	22.5212i	0.331189	+	1.23601i
$333$	−3.35373	−	3.35373i	−0.183783	−	0.183783i
$334$	21.1617	+	12.2177i	1.15792	+	0.668524i
$335$	−1.93668	−	3.35443i	−0.105812	−	0.183272i
$336$	−1.88182	+	1.15855i	−0.102662	+	0.0632041i
$337$			1.75678i			0.0956980i	0.998855	+	0.0478490i	$0.0152366\pi$
$337$			1.75678i			0.0956980i	−0.998855	+	0.0478490i	$0.984763\pi$
$338$	23.8912	−	16.7661i	1.29951	−	0.911954i
$339$		−	0.759509i		−	0.0412509i
$340$	−34.1233	−	9.14331i	−1.85060	−	0.495866i
$341$	−38.6880	+	22.3365i	−2.09507	+	1.20959i
$342$	−0.226035	+	0.391504i	−0.0122226	+	0.0211701i
$343$	−18.4538	+	1.56784i	−0.996410	+	0.0846554i
$344$	−1.74242	−	6.50279i	−0.0939449	−	0.350607i
$345$	21.3342	−	5.71648i	1.14859	−	0.307765i
$346$	12.9318	−	12.9318i	0.695219	−	0.695219i
$347$	5.43920	−	9.42098i	0.291992	−	0.505744i	−0.682289	−	0.731083i	$-0.739015\pi$
$347$	5.43920	−	9.42098i	0.291992	−	0.505744i	0.974281	+	0.225338i	$0.0723487\pi$
$348$	−15.8236	−	27.4072i	−0.848233	−	1.46918i
$349$	11.9450	+	3.20064i	0.639399	+	0.171326i	0.563931	−	0.825822i	$-0.309288\pi$
$349$	11.9450	+	3.20064i	0.639399	+	0.171326i	0.0754676	+	0.997148i	$0.475955\pi$
$350$	−8.86349	−	8.37630i	−0.473774	−	0.447732i
$351$	3.26694	−	1.52548i	0.174376	−	0.0814241i
$352$	−30.6102			−1.63153
$353$	−4.55715	+	17.0075i	−0.242552	+	0.905218i	0.732045	+	0.681256i	$0.238566\pi$
$353$	−4.55715	+	17.0075i	−0.242552	+	0.905218i	−0.974598	+	0.223962i	$0.928101\pi$
$354$	7.63720	+	13.2280i	0.405912	+	0.703061i
$355$	7.38867	−	12.7975i	0.392150	−	0.679223i
$356$	−33.4926	−	33.4926i	−1.77510	−	1.77510i
$357$	10.1829	+	5.50156i	0.538935	+	0.291174i
$358$	−25.6277	+	6.86691i	−1.35446	+	0.362927i
$359$	11.4993	+	11.4993i	0.606911	+	0.606911i	0.942137	−	0.335227i	$-0.108813\pi$
$359$	11.4993	+	11.4993i	0.606911	+	0.606911i	−0.335227	+	0.942137i	$0.608813\pi$
$360$	−5.37431	−	3.10286i	−0.283251	−	0.163535i
$361$	−16.4194	+	9.47973i	−0.864177	+	0.498933i
$362$	−22.7699	−	6.10119i	−1.19676	−	0.320671i
$363$	−10.8487			−0.569408
$364$	24.2301	+	15.9473i	1.27000	+	0.835864i
$365$	−32.8645			−1.72020
$366$	5.34153	+	1.43126i	0.279206	+	0.0748130i
$367$	11.3884	−	6.57510i	0.594470	−	0.343217i	−0.172393	−	0.985028i	$-0.555150\pi$
$367$	11.3884	−	6.57510i	0.594470	−	0.343217i	0.766863	+	0.641811i	$0.221817\pi$
$368$	−6.01577	−	3.47320i	−0.313594	−	0.181053i
$369$	0.372486	+	0.372486i	0.0193908	+	0.0193908i
$370$	−27.3164	+	7.31940i	−1.42011	+	0.380518i
$371$	2.45340	−	4.54102i	0.127374	−	0.235758i
$372$	20.5495	+	20.5495i	1.06544	+	1.06544i
$373$	4.81532	−	8.34037i	0.249328	−	0.431848i	−0.714012	−	0.700134i	$-0.753124\pi$
$373$	4.81532	−	8.34037i	0.249328	−	0.431848i	0.963339	+	0.268286i	$0.0864571\pi$
$374$	22.9545	+	39.7583i	1.18695	+	2.05585i
$375$	2.02563	−	7.55977i	0.104603	−	0.390385i
$376$	3.06819			0.158230
$377$	21.5075	−	30.7500i	1.10769	−	1.58371i
$378$	4.31730	+	4.07999i	0.222058	+	0.209852i
$379$	−32.1516	−	8.61500i	−1.65152	−	0.442523i	−0.691481	−	0.722395i	$-0.743041\pi$
$379$	−32.1516	−	8.61500i	−1.65152	−	0.442523i	−0.960037	+	0.279872i	$0.909708\pi$
$380$	0.813014	+	1.40818i	0.0417068	+	0.0722382i
$381$	−0.600626	+	1.04032i	−0.0307710	+	0.0532970i
$382$	21.1930	−	21.1930i	1.08433	−	1.08433i
$383$	3.73221	−	1.00004i	0.190707	−	0.0510998i	−0.162201	−	0.986758i	$-0.551859\pi$
$383$	3.73221	−	1.00004i	0.190707	−	0.0510998i	0.352908	+	0.935658i	$0.385193\pi$
$384$	4.18317	+	15.6118i	0.213471	+	0.796686i
$385$	0.927780	+	32.8304i	0.0472840	+	1.67319i
$386$	9.05560	−	15.6848i	0.460918	−	0.798334i
$387$	2.49507	−	1.44053i	0.126831	−	0.0732262i
$388$	8.66392	+	2.32149i	0.439844	+	0.117856i
$389$		−	12.5816i		−	0.637911i	−0.947770	−	0.318955i	$-0.896668\pi$
$389$		−	12.5816i		−	0.637911i	0.947770	−	0.318955i	$-0.103332\pi$
$390$	1.86251	−	21.4176i	0.0943121	−	1.08452i
$391$			36.3815i			1.83989i
$392$	−3.33446	+	16.0135i	−0.168416	+	0.808802i
$393$	−1.51708	−	2.62767i	−0.0765268	−	0.132548i
$394$	24.6848	+	14.2518i	1.24360	+	0.717995i
$395$	−8.38473	−	8.38473i	−0.421881	−	0.421881i
$396$	3.67869	+	13.7290i	0.184861	+	0.689910i
$397$	6.87160	+	25.6452i	0.344876	+	1.28709i	0.892757	+	0.450538i	$0.148768\pi$
$397$	6.87160	+	25.6452i	0.344876	+	1.28709i	−0.547882	+	0.836556i	$0.684566\pi$
$398$	34.4079	−	34.4079i	1.72471	−	1.72471i
$399$	−0.152361	−	0.510476i	−0.00762760	−	0.0255558i
$400$	1.48504	−	0.857390i	0.0742521	−	0.0428695i
$401$	−3.89519	+	14.5370i	−0.194517	+	0.725946i	0.797875	+	0.602823i	$0.205957\pi$
$401$	−3.89519	+	14.5370i	−0.194517	+	0.725946i	−0.992391	+	0.123123i	$0.960709\pi$
$402$	3.27453			0.163319
$403$	−11.7688	+	32.3872i	−0.586245	+	1.61332i
$404$		−	1.92643i		−	0.0958437i
$405$	0.687359	−	2.56526i	0.0341552	−	0.127469i
$406$	60.1443	+	14.3076i	2.98491	+	0.710075i
$407$	19.1994	+	11.0848i	0.951676	+	0.549451i
$408$	7.22812	−	7.22812i	0.357845	−	0.357845i
$409$	−23.9970	+	6.42996i	−1.18657	+	0.317941i	−0.797531	−	0.603279i	$-0.793861\pi$
$409$	−23.9970	+	6.42996i	−1.18657	+	0.317941i	−0.389042	+	0.921220i	$0.627194\pi$
$410$	3.03392	−	0.812937i	0.149835	−	0.0401481i
$411$	−8.25701	+	8.25701i	−0.407288	+	0.407288i
$412$	−5.15395	−	2.97564i	−0.253917	−	0.146599i
$413$	−17.5110	−	4.16566i	−0.861660	−	0.204979i
$414$	−4.83270	+	18.0359i	−0.237514	+	0.886415i
$415$			20.3635i			0.999603i
$416$	−18.0796	+	15.1867i	−0.886426	+	0.744590i
$417$	−6.70588			−0.328388
$418$	0.546908	−	2.04109i	0.0267501	−	0.0998329i
$419$	−15.5289	+	8.96562i	−0.758637	+	0.437999i	−0.828806	−	0.559536i	$-0.810979\pi$
$419$	−15.5289	+	8.96562i	−0.758637	+	0.437999i	0.0701691	+	0.997535i	$0.477646\pi$
$420$	20.4734	−	6.11067i	0.998999	−	0.298170i
$421$	0.833811	−	0.833811i	0.0406375	−	0.0406375i	−0.686496	−	0.727134i	$-0.740852\pi$
$421$	0.833811	−	0.833811i	0.0406375	−	0.0406375i	0.727134	+	0.686496i	$0.240852\pi$
$422$	−7.56482	−	28.2323i	−0.368250	−	1.37433i
$423$	0.339840	+	1.26830i	0.0165236	+	0.0616669i
$424$	−3.22335	−	3.22335i	−0.156540	−	0.156540i
$425$	−7.77785	−	4.49054i	−0.377281	−	0.217823i
$426$	6.24636	+	10.8190i	0.302637	+	0.524183i
$427$	−5.54926	+	3.41643i	−0.268547	+	0.165333i
$428$		−	21.8928i		−	1.05823i
$429$	−12.9047	+	10.8398i	−0.623044	+	0.523352i
$430$		−	17.1786i		−	0.828426i
$431$	13.4572	+	3.60584i	0.648209	+	0.173687i	0.567919	−	0.823085i	$-0.307749\pi$
$431$	13.4572	+	3.60584i	0.648209	+	0.173687i	0.0802899	+	0.996772i	$0.474415\pi$
$432$	−0.723346	+	0.417624i	−0.0348020	+	0.0200929i
$433$	0.380141	−	0.658423i	0.0182684	−	0.0316418i	−0.856747	−	0.515737i	$-0.827518\pi$
$433$	0.380141	−	0.658423i	0.0182684	−	0.0316418i	0.875015	+	0.484096i	$0.160851\pi$
$434$	−56.7488	+	1.60371i	−2.72403	+	0.0769806i
$435$	−7.15376	−	26.6982i	−0.342997	−	1.28008i
$436$	−10.0607	+	2.69577i	−0.481822	+	0.129104i
$437$	1.18410	−	1.18410i	0.0566430	−	0.0566430i
$438$	13.8918	−	24.0612i	0.663774	−	1.14969i
$439$	−15.9560	−	27.6366i	−0.761539	−	1.31902i	−0.942057	−	0.335453i	$-0.891111\pi$
$439$	−15.9560	−	27.6366i	−0.761539	−	1.31902i	0.180518	−	0.983572i	$-0.442223\pi$
$440$	28.0187	+	7.50759i	1.33574	+	0.357910i
$441$	−6.98883	+	0.395322i	−0.332801	+	0.0188248i
$442$	33.2832	+	12.0944i	1.58312	+	0.575270i
$443$	13.9082			0.660799			0.330399	−	0.943841i	$-0.392817\pi$
$443$	13.9082			0.660799			0.330399	+	0.943841i	$0.392817\pi$
$444$	3.73270	−	13.9306i	0.177146	−	0.661119i
$445$	−20.6841	−	35.8260i	−0.980522	−	1.69831i
$446$	19.0052	−	32.9180i	0.899923	−	1.55871i
$447$	−3.38589	−	3.38589i	−0.160147	−	0.160147i
$448$	−30.3361	−	16.3898i	−1.43324	−	0.774347i
$449$	37.3413	−	10.0056i	1.76224	−	0.472192i	0.775075	−	0.631869i	$-0.217712\pi$
$449$	37.3413	−	10.0056i	1.76224	−	0.472192i	0.987169	+	0.159677i	$0.0510451\pi$
$450$	−3.25932	−	3.25932i	−0.153646	−	0.153646i
$451$	−2.13240	−	1.23114i	−0.100411	−	0.0579721i
$452$	2.00008	−	1.15475i	0.0940759	−	0.0543148i
$453$	−10.4679	−	2.80485i	−0.491823	−	0.131784i
$454$	−42.5150			−1.99533
$455$	16.8362	+	18.9306i	0.789292	+	0.887481i
$456$	−0.470502			−0.0220333
$457$	−11.2913	−	3.02549i	−0.528183	−	0.141526i	−0.0151341	−	0.999885i	$-0.504818\pi$
$457$	−11.2913	−	3.02549i	−0.528183	−	0.141526i	−0.513049	+	0.858359i	$0.671484\pi$
$458$	−0.498897	+	0.288038i	−0.0233119	+	0.0134591i
$459$	3.78849	+	2.18729i	0.176832	+	0.102094i
$460$	47.4899	+	47.4899i	2.21423	+	2.21423i
$461$	−33.0727	+	8.86180i	−1.54035	+	0.412735i	−0.926379	−	0.376594i	$-0.877095\pi$
$461$	−33.0727	+	8.86180i	−1.54035	+	0.412735i	−0.613971	+	0.789329i	$0.710429\pi$
$462$	−24.4285	−	13.1981i	−1.13651	−	0.614031i
$463$	−18.1263	−	18.1263i	−0.842399	−	0.842399i	0.146772	−	0.989170i	$-0.453112\pi$
$463$	−18.1263	−	18.1263i	−0.842399	−	0.842399i	−0.989170	+	0.146772i	$0.953112\pi$
$464$	−4.34646	+	7.52830i	−0.201780	+	0.349492i
$465$	12.6908	+	21.9812i	0.588523	+	1.01935i
$466$	−6.61561	+	24.6898i	−0.306462	+	1.14373i
$467$	20.4427			0.945975			0.472988	−	0.881069i	$-0.343176\pi$
$467$	20.4427			0.945975			0.472988	+	0.881069i	$0.343176\pi$
$468$	8.98419	+	6.28380i	0.415294	+	0.290469i
$469$	−2.65040	+	2.80455i	−0.122384	+	0.129502i
$470$	7.56238	+	2.02633i	0.348826	+	0.0934678i
$471$	−4.00301	−	6.93341i	−0.184449	−	0.319475i
$472$	−7.94858	+	13.7673i	−0.365863	+	0.633694i
$473$	−9.52246	+	9.52246i	−0.437843	+	0.437843i
$474$	9.68297	−	2.59455i	0.444754	−	0.119171i
$475$	0.106991	+	0.399295i	0.00490907	+	0.0183209i
$476$	0.994179	+	35.1800i	0.0455681	+	1.61247i
$477$	0.975412	−	1.68946i	0.0446611	−	0.0773552i
$478$	33.5967	−	19.3971i	1.53668	−	0.887202i
$479$	11.4241	+	3.06108i	0.521980	+	0.139864i	0.510182	−	0.860066i	$-0.329578\pi$
$479$	11.4241	+	3.06108i	0.521980	+	0.139864i	0.0117979	+	0.999930i	$0.496245\pi$
$480$			17.3917i			0.793818i
$481$	16.8394	−	2.97832i	0.767810	−	0.135800i
$482$			68.4591i			3.11823i
$483$	−11.5357	−	18.7373i	−0.524893	−	0.852577i
$484$	−16.4942	−	28.5688i	−0.749736	−	1.29858i
$485$	6.78430	+	3.91692i	0.308059	+	0.177858i
$486$	1.58757	+	1.58757i	0.0720137	+	0.0720137i
$487$	0.0483236	+	0.180346i	0.00218975	+	0.00817226i	0.967012	−	0.254731i	$-0.0819868\pi$
$487$	0.0483236	+	0.180346i	0.00218975	+	0.00817226i	−0.964822	+	0.262903i	$0.915320\pi$
$488$	1.48961	+	5.55931i	0.0674316	+	0.251658i
$489$	13.4547	−	13.4547i	0.608442	−	0.608442i
$490$	−18.7945	+	37.2673i	−0.849047	+	1.68356i
$491$	−2.43785	+	1.40749i	−0.110019	+	0.0635193i	−0.554000	−	0.832517i	$-0.686899\pi$
$491$	−2.43785	+	1.40749i	−0.110019	+	0.0635193i	0.443981	+	0.896036i	$0.353566\pi$
$492$	−0.414577	+	1.54722i	−0.0186906	+	0.0697541i
$493$	45.5288			2.05052
$494$	−0.689624	−	1.47689i	−0.0310276	−	0.0664482i
$495$			12.4137i			0.557953i
$496$	2.06607	−	7.71067i	0.0927691	−	0.346219i
$497$	−14.3220	−	3.40704i	−0.642430	−	0.152826i
$498$	−14.9088	−	8.60761i	−0.668080	−	0.385716i
$499$	1.80207	−	1.80207i	0.0806719	−	0.0806719i	−0.665619	−	0.746291i	$-0.731833\pi$
$499$	1.80207	−	1.80207i	0.0806719	−	0.0806719i	0.746291	+	0.665619i	$0.231833\pi$
$500$	22.9875	−	6.15949i	1.02803	−	0.275461i
$501$	−10.5127	+	2.81688i	−0.469674	+	0.125849i
$502$	−17.3417	+	17.3417i	−0.773999	+	0.773999i
$503$	−6.33177	−	3.65565i	−0.282320	−	0.162997i	0.352153	−	0.935942i	$-0.385450\pi$
$503$	−6.33177	−	3.65565i	−0.282320	−	0.162997i	−0.634473	+	0.772945i	$0.718783\pi$
$504$	−1.43078	+	6.01451i	−0.0637320	+	0.267907i
$505$	0.435466	−	1.62518i	0.0193780	−	0.0723196i
$506$		−	87.2783i		−	3.87999i
$507$	−2.24403	+	12.8049i	−0.0996610	+	0.568684i
$508$	−3.65274			−0.162064
$509$	−6.75398	+	25.2062i	−0.299365	+	1.11724i	0.638324	+	0.769768i	$0.279628\pi$
$509$	−6.75398	+	25.2062i	−0.299365	+	1.11724i	−0.937689	+	0.347477i	$0.887039\pi$
$510$	22.5893	−	13.0419i	1.00027	−	0.577506i
$511$	9.36390	+	31.3731i	0.414234	+	1.38786i
$512$	6.62788	−	6.62788i	0.292914	−	0.292914i
$513$	−0.0521138	−	0.194491i	−0.00230088	−	0.00858701i
$514$	−16.5071	−	61.6053i	−0.728097	−	2.71729i
$515$	−3.67535	−	3.67535i	−0.161955	−	0.161955i
$516$	7.58693	+	4.38032i	0.333996	+	0.192833i
$517$	−3.06875	−	5.31523i	−0.134963	−	0.233763i
$518$	14.7704	+	23.9913i	0.648973	+	1.05412i
$519$			8.14566i			0.357555i
$520$	20.2737	−	9.46670i	0.889061	−	0.415142i
$521$			5.50223i			0.241057i	0.992710	+	0.120529i	$0.0384589\pi$
$521$			5.50223i			0.241057i	−0.992710	+	0.120529i	$0.961541\pi$
$522$	22.5706	+	6.04777i	0.987888	+	0.264704i
$523$	35.0507	−	20.2365i	1.53266	−	0.884882i	0.533423	−	0.845849i	$-0.320905\pi$
$523$	35.0507	−	20.2365i	1.53266	−	0.884882i	0.999238	−	0.0390336i	$-0.0124279\pi$
$524$	4.61311	−	7.99014i	0.201525	−	0.349051i
$525$	5.42961	−	0.153440i	0.236968	−	0.00669666i
$526$	−12.6189	−	47.0943i	−0.550209	−	2.05341i
$527$	−40.3843	+	10.8209i	−1.75917	+	0.471367i
$528$	2.76066	−	2.76066i	0.120142	−	0.120142i
$529$	23.0828	−	39.9806i	1.00360	−	1.73829i
$530$	−5.81600	−	10.0736i	−0.252631	−	0.437569i
$531$	−6.57142	−	1.76081i	−0.285175	−	0.0764125i
$532$	1.11263	−	1.17735i	0.0482387	−	0.0510444i
$533$	−1.87028	+	0.330790i	−0.0810110	+	0.0143281i
$534$	34.9726			1.51341
$535$	4.94882	−	18.4692i	0.213956	−	0.798495i
$536$	1.70402	+	2.95145i	0.0736024	+	0.127483i
$537$	5.90863	−	10.2340i	0.254976	−	0.441631i
$538$	19.6422	+	19.6422i	0.846836	+	0.846836i
$539$	31.0762	−	10.2399i	1.33855	−	0.441062i
$540$	7.80037	−	2.09010i	0.335674	−	0.0899437i
$541$	25.7367	+	25.7367i	1.10651	+	1.10651i	0.993606	+	0.112900i	$0.0360139\pi$
$541$	25.7367	+	25.7367i	1.10651	+	1.10651i	0.112900	+	0.993606i	$0.463986\pi$
$542$	−15.3881	−	8.88430i	−0.660974	−	0.381613i
$543$	9.09285	−	5.24976i	0.390212	−	0.225289i
$544$	−27.6716	−	7.41457i	−1.18641	−	0.317897i
$545$	−9.09682			−0.389665
$546$	−20.9764	+	4.32442i	−0.897707	+	0.185068i
$547$	31.3852			1.34193			0.670967	−	0.741487i	$-0.265879\pi$
$547$	31.3852			1.34193			0.670967	+	0.741487i	$0.265879\pi$
$548$	−34.2977	−	9.19005i	−1.46513	−	0.392579i
$549$	−2.13306	+	1.23152i	−0.0910369	+	0.0525602i
$550$	18.6588	+	10.7727i	0.795616	+	0.459349i
$551$	−1.48181	−	1.48181i	−0.0631272	−	0.0631272i
$552$	−18.7712	+	5.02974i	−0.798957	+	0.214080i
$553$	−5.61522	+	10.3933i	−0.238783	+	0.441966i
$554$	−17.7980	−	17.7980i	−0.756166	−	0.756166i
$555$	6.29797	−	10.9084i	0.267334	−	0.463036i
$556$	−10.1955	−	17.6592i	−0.432387	−	0.748916i
$557$	−0.169733	+	0.633453i	−0.00719183	+	0.0268403i	−0.969429	−	0.245374i	$-0.921089\pi$
$557$	−0.169733	+	0.633453i	−0.00719183	+	0.0268403i	0.962237	+	0.272214i	$0.0877559\pi$
$558$	−21.4576			−0.908373
$559$	−0.899944	+	10.3487i	−0.0380636	+	0.437705i
$560$	−4.26547	−	4.03101i	−0.180249	−	0.170341i
$561$	−19.7511	−	5.29230i	−0.833894	−	0.223441i
$562$	24.1229	+	41.7821i	1.01756	+	1.76247i
$563$	12.5830	−	21.7944i	0.530309	−	0.918523i	−0.469065	−	0.883164i	$-0.655409\pi$
$563$	12.5830	−	21.7944i	0.530309	−	0.918523i	0.999375	−	0.0353593i	$-0.0112576\pi$
$564$	−2.82324	+	2.82324i	−0.118880	+	0.118880i
$565$	1.94834	−	0.522056i	0.0819672	−	0.0219630i
$566$	8.88777	+	33.1696i	0.373581	+	1.39422i
$567$	−2.64470	+	0.0747386i	−0.111067	+	0.00313872i
$568$	−6.50104	+	11.2601i	−0.272778	+	0.472465i
$569$	−3.46005	+	1.99766i	−0.145053	+	0.0837463i	−0.570770	−	0.821110i	$-0.693355\pi$
$569$	−3.46005	+	1.99766i	−0.145053	+	0.0837463i	0.425717	+	0.904856i	$0.360022\pi$
$570$	−1.15968	−	0.310734i	−0.0485735	−	0.0130152i
$571$			17.9370i			0.750640i	0.926895	+	0.375320i	$0.122467\pi$
$571$			17.9370i			0.750640i	−0.926895	+	0.375320i	$0.877533\pi$
$572$	−48.1656	−	17.5023i	−2.01390	−	0.731808i
$573$			13.3493i			0.557674i
$574$	−1.64049	−	2.66462i	−0.0684726	−	0.111219i
$575$	8.53705	+	14.7866i	0.356020	+	0.616644i
$576$	−11.2864	−	6.51620i	−0.470266	−	0.271508i
$577$	−29.6210	−	29.6210i	−1.23314	−	1.23314i	−0.962751	−	0.270389i	$-0.912848\pi$
$577$	−29.6210	−	29.6210i	−1.23314	−	1.23314i	−0.270389	−	0.962751i	$-0.587152\pi$
$578$	1.24174	+	4.63424i	0.0516496	+	0.192759i
$579$	2.08783	+	7.79189i	0.0867672	+	0.323820i
$580$	59.4302	−	59.4302i	2.46770	−	2.46770i
$581$	19.4394	−	5.80206i	0.806482	−	0.240710i
$582$	−5.73543	+	3.31135i	−0.237741	+	0.137260i
$583$	−2.36008	+	8.80794i	−0.0977446	+	0.364788i
$584$	28.9163			1.19657
$585$	6.15882	+	7.33200i	0.254636	+	0.303141i
$586$			47.1901i			1.94941i
$587$	0.571868	−	2.13424i	0.0236035	−	0.0880895i	−0.953119	−	0.302595i	$-0.902147\pi$
$587$	0.571868	−	2.13424i	0.0236035	−	0.0880895i	0.976723	+	0.214505i	$0.0688138\pi$
$588$	−11.6668	−	17.8032i	−0.481129	−	0.734193i
$589$	1.66656	+	0.962187i	0.0686693	+	0.0396462i
$590$	−28.6838	+	28.6838i	−1.18089	+	1.18089i
$591$	−12.2629	+	3.28585i	−0.504430	+	0.135162i
$592$	−3.82651	+	1.02531i	−0.157268	+	0.0421400i
$593$	−1.48928	+	1.48928i	−0.0611573	+	0.0611573i	−0.737024	−	0.675867i	$-0.763770\pi$
$593$	−1.48928	+	1.48928i	−0.0611573	+	0.0611573i	0.675867	+	0.737024i	$0.263770\pi$
$594$	−9.08849	−	5.24724i	−0.372905	−	0.215297i
$595$	−7.11364	+	29.9033i	−0.291631	+	1.22592i
$596$	3.76850	−	14.0642i	0.154364	−	0.576093i
$597$			21.6733i			0.887027i
$598$	−43.3015	−	51.5500i	−1.77073	−	2.10804i
$599$	13.9002			0.567945			0.283973	−	0.958832i	$-0.408347\pi$
$599$	13.9002			0.567945			0.283973	+	0.958832i	$0.408347\pi$
$600$	1.24163	−	4.63384i	0.0506895	−	0.189176i
$601$	8.59776	−	4.96392i	0.350710	−	0.202482i	−0.314288	−	0.949328i	$-0.601766\pi$
$601$	8.59776	−	4.96392i	0.350710	−	0.202482i	0.664998	+	0.746845i	$0.268432\pi$
$602$	−16.3991	+	4.89461i	−0.668375	+	0.199489i
$603$	−1.03130	+	1.03130i	−0.0419978	+	0.0419978i
$604$	−8.52892	−	31.8304i	−0.347037	−	1.29516i
$605$	−7.45694	−	27.8297i	−0.303168	−	1.13144i
$606$	1.00578	+	1.00578i	0.0408571	+	0.0408571i
$607$	−26.6015	−	15.3584i	−1.07972	−	0.623378i	−0.148900	−	0.988852i	$-0.547573\pi$
$607$	−26.6015	−	15.3584i	−1.07972	−	0.623378i	−0.930821	+	0.365475i	$0.880907\pi$
$608$	0.659297	+	1.14194i	0.0267380	+	0.0463116i
$609$	−23.4484	+	14.4361i	−0.950176	+	0.584981i
$610$			14.6862i			0.594626i
$611$	−4.44958	−	1.61688i	−0.180011	−	0.0654119i
$612$			13.3021i			0.537705i
$613$	9.42794	+	2.52621i	0.380791	+	0.102033i	0.444137	−	0.895959i	$-0.353510\pi$
$613$	9.42794	+	2.52621i	0.380791	+	0.102033i	−0.0633459	+	0.997992i	$0.520177\pi$
$614$	−35.1709	+	20.3059i	−1.41938	+	0.819480i
$615$	−0.699491	+	1.21155i	−0.0282062	+	0.0488546i
$616$	−0.816322	−	28.8863i	−0.0328906	−	1.16386i
$617$	6.69956	+	25.0031i	0.269714	+	1.00659i	0.959301	+	0.282384i	$0.0911253\pi$
$617$	6.69956	+	25.0031i	0.269714	+	1.00659i	−0.689587	+	0.724203i	$0.742208\pi$
$618$	4.24442	−	1.13729i	0.170736	−	0.0457485i
$619$	−25.5525	+	25.5525i	−1.02704	+	1.02704i	−0.0274172	+	0.999624i	$0.508728\pi$
$619$	−25.5525	+	25.5525i	−1.02704	+	1.02704i	−0.999624	+	0.0274172i	$0.991272\pi$
$620$	−38.5899	+	66.8397i	−1.54981	+	2.68435i
$621$	−4.15829	−	7.20237i	−0.166867	−	0.289021i
$622$	−42.4011	−	11.3613i	−1.70013	−	0.455548i
$623$	−28.3068	+	29.9532i	−1.13409	+	1.20005i
$624$	0.260903	−	3.00021i	0.0104445	−	0.120104i
$625$	31.0502			1.24201
$626$	−7.69915	+	28.7336i	−0.307720	+	1.14843i
$627$	0.470586	+	0.815080i	0.0187934	+	0.0325511i
$628$	12.1722	−	21.0829i	0.485725	−	0.841300i
$629$	14.6712	+	14.6712i	0.584977	+	0.584977i
$630$	−7.49871	+	13.8794i	−0.298756	+	0.552969i
$631$	9.92759	−	2.66009i	0.395211	−	0.105897i	−0.0557396	−	0.998445i	$-0.517752\pi$
$631$	9.92759	−	2.66009i	0.395211	−	0.105897i	0.450951	+	0.892549i	$0.351085\pi$
$632$	7.37744	+	7.37744i	0.293459	+	0.293459i
$633$	11.2742	+	6.50914i	0.448108	+	0.258715i
$634$	−49.1823	+	28.3954i	−1.95328	+	1.12773i
$635$	−3.08153	−	0.825692i	−0.122287	−	0.0327666i
$636$	5.93201			0.235220
$637$	13.2745	−	21.4660i	0.525955	−	0.850512i
$638$	−109.222			−4.32416
$639$	−5.37468	−	1.44014i	−0.212619	−	0.0569711i
$640$	−37.1730	+	21.4618i	−1.46939	+	0.848353i
$641$	−26.2509	−	15.1559i	−1.03685	−	0.598624i	−0.117908	−	0.993025i	$-0.537619\pi$
$641$	−26.2509	−	15.1559i	−1.03685	−	0.598624i	−0.918939	+	0.394401i	$0.870952\pi$
$642$	11.4301	+	11.4301i	0.451111	+	0.451111i
$643$	−35.0393	+	9.38876i	−1.38182	+	0.370256i	−0.871780	−	0.489897i	$-0.837034\pi$
$643$	−35.0393	+	9.38876i	−1.38182	+	0.370256i	−0.510035	+	0.860153i	$0.670368\pi$
$644$	31.8038	−	58.8659i	1.25325	−	2.31964i
$645$	5.41034	+	5.41034i	0.213032	+	0.213032i
$646$	0.988806	−	1.71266i	0.0389041	−	0.0673838i
$647$	9.62979	+	16.6793i	0.378586	+	0.655730i	0.990857	−	0.134918i	$-0.0430771\pi$
$647$	9.62979	+	16.6793i	0.378586	+	0.655730i	−0.612271	+	0.790648i	$0.709744\pi$
$648$	−0.604784	+	2.25709i	−0.0237582	+	0.0886667i
$649$	31.8001			1.24826
$650$	16.3653	−	2.89447i	0.641901	−	0.113531i
$651$	17.3677	−	18.3779i	0.680696	−	0.720287i
$652$	55.8877	+	14.9751i	2.18873	+	0.586468i
$653$	−0.0312823	−	0.0541825i	−0.00122417	−	0.00212033i	0.865413	−	0.501060i	$-0.167056\pi$
$653$	−0.0312823	−	0.0541825i	−0.00122417	−	0.00212033i	−0.866637	+	0.498939i	$0.833723\pi$
$654$	3.84521	−	6.66011i	0.150360	−	0.260431i
$655$	5.69787	−	5.69787i	0.222634	−	0.222634i
$656$	0.424995	−	0.113877i	0.0165933	−	0.00444615i
$657$	3.20284	+	11.9532i	0.124955	+	0.466337i
$658$	−0.220329	−	7.79655i	−0.00858932	−	0.303941i
$659$	3.09067	−	5.35320i	0.120395	−	0.208531i	−0.799528	−	0.600628i	$-0.794917\pi$
$659$	3.09067	−	5.35320i	0.120395	−	0.208531i	0.919924	+	0.392098i	$0.128250\pi$
$660$	−32.6900	+	18.8736i	−1.27246	+	0.734653i
$661$	6.90812	+	1.85103i	0.268695	+	0.0719965i	0.390651	−	0.920539i	$-0.372250\pi$
$661$	6.90812	+	1.85103i	0.268695	+	0.0719965i	−0.121956	+	0.992536i	$0.538917\pi$
$662$			30.5207i			1.18622i
$663$	−14.2915	+	6.67333i	−0.555035	+	0.259171i
$664$		−	17.9171i		−	0.695320i
$665$	1.20478	−	0.741726i	0.0467192	−	0.0287629i
$666$	5.32429	+	9.22194i	0.206312	+	0.357343i
$667$	−74.9594	−	43.2778i	−2.90244	−	1.67572i
$668$	−23.4013	−	23.4013i	−0.905425	−	0.905425i
$669$	4.38178	+	16.3530i	0.169409	+	0.632244i
$670$	2.25078	+	8.40001i	0.0869551	+	0.324521i
$671$	8.14087	−	8.14087i	0.314275	−	0.314275i
$672$	16.6025	−	4.95532i	0.640454	−	0.191156i
$673$	−4.05354	+	2.34031i	−0.156253	+	0.0902125i	−0.576088	−	0.817388i	$-0.695421\pi$
$673$	−4.05354	+	2.34031i	−0.156253	+	0.0902125i	0.419835	+	0.907600i	$0.362088\pi$
$674$	1.02085	−	3.80987i	0.0393217	−	0.146751i
$675$	2.05302			0.0790207
$676$	−37.1319	+	13.5589i	−1.42815	+	0.521497i
$677$		−	31.1590i		−	1.19754i	−0.800922	−	0.598769i	$-0.795657\pi$
$677$		−	31.1590i		−	1.19754i	0.800922	−	0.598769i	$-0.204343\pi$
$678$	−0.441345	+	1.64712i	−0.0169497	+	0.0632573i
$679$	1.80615	−	7.59246i	0.0693139	−	0.291372i
$680$	23.5103	+	13.5737i	0.901579	+	0.520527i
$681$	13.3899	−	13.3899i	0.513103	−	0.513103i
$682$	96.8808	−	25.9591i	3.70976	−	0.994026i
$683$	41.3109	−	11.0692i	1.58072	−	0.423552i	0.641570	−	0.767064i	$-0.278283\pi$
$683$	41.3109	−	11.0692i	1.58072	−	0.423552i	0.939148	+	0.343512i	$0.111617\pi$
$684$	0.432938	−	0.432938i	0.0165538	−	0.0165538i
$685$	−26.8569	−	15.5058i	−1.02615	−	0.592447i
$686$	40.9311	+	7.32322i	1.56276	+	0.279602i
$687$	0.0664091	−	0.247842i	0.00253367	−	0.00945577i
$688$		−	2.40640i		−	0.0917430i
$689$	2.97595	+	6.37323i	0.113374	+	0.242801i
$690$	−49.5885			−1.88780
$691$	−4.65384	+	17.3684i	−0.177040	+	0.660724i	0.819155	+	0.573573i	$0.194443\pi$
$691$	−4.65384	+	17.3684i	−0.177040	+	0.660724i	−0.996195	+	0.0871512i	$0.972224\pi$
$692$	−21.4507	+	12.3845i	−0.815432	+	0.470790i
$693$	11.8503	−	3.53696i	0.450157	−	0.134358i
$694$	−17.2703	+	17.2703i	−0.655570	+	0.655570i
$695$	−4.60935	−	17.2023i	−0.174843	−	0.652521i
$696$	6.29435	+	23.4909i	0.238587	+	0.890418i
$697$	−1.62947	−	1.62947i	−0.0617205	−	0.0617205i
$698$	−24.0447	−	13.8822i	−0.910106	−	0.525450i
$699$	−5.69240	−	9.85952i	−0.215306	−	0.372921i
$700$	8.65917	+	14.0650i	0.327286	+	0.531606i
$701$			34.0110i			1.28458i	0.766462	+	0.642290i	$0.222015\pi$
$701$			34.0110i			1.28458i	−0.766462	+	0.642290i	$0.777985\pi$
$702$	−7.97134	+	1.40986i	−0.300859	+	0.0532118i
$703$		−	0.954993i		−	0.0360182i
$704$	58.8411	+	15.7664i	2.21766	+	0.594219i
$705$	−3.01993	+	1.74356i	−0.113737	+	0.0656661i
$706$	19.7658	−	34.2354i	0.743897	−	1.28847i
$707$	−1.67551	+	0.0473495i	−0.0630139	+	0.00178076i
$708$	−5.35421	−	19.9822i	−0.201224	−	0.750977i
$709$	−2.70932	+	0.725960i	−0.101751	+	0.0272640i	−0.309335	−	0.950953i	$-0.600106\pi$
$709$	−2.70932	+	0.725960i	−0.101751	+	0.0272640i	0.207584	+	0.978217i	$0.433440\pi$
$710$	−23.4601	+	23.4601i	−0.880441	+	0.880441i
$711$	−2.23247	+	3.86676i	−0.0837243	+	0.145015i
$712$	18.1993	+	31.5221i	0.682047	+	1.18134i
$713$	76.7753	+	20.5719i	2.87526	+	0.770423i
$714$	−18.8863	−	17.8482i	−0.706804	−	0.667953i
$715$	−36.6771	−	25.6530i	−1.37165	−	0.959369i
$716$	35.9336			1.34290
$717$	−4.47213	+	16.6902i	−0.167015	+	0.623307i
$718$	−18.2560	−	31.6203i	−0.681308	−	1.18006i
$719$	10.7719	−	18.6575i	0.401725	−	0.695809i	−0.592209	−	0.805784i	$-0.701744\pi$
$719$	10.7719	−	18.6575i	0.401725	−	0.695809i	0.993934	+	0.109976i	$0.0350773\pi$
$720$	−1.56851	−	1.56851i	−0.0584550	−	0.0584550i
$721$	−2.46137	+	4.55576i	−0.0916661	+	0.169665i
$722$	41.1167	−	11.0172i	1.53021	−	0.410017i
$723$	−21.5609	−	21.5609i	−0.801860	−	0.801860i
$724$	27.6493	+	15.9633i	1.02758	+	0.593272i
$725$	18.5044	−	10.6835i	0.687235	−	0.396775i
$726$	23.5271	+	6.30408i	0.873174	+	0.233966i
$727$	−25.2656			−0.937048			−0.468524	−	0.883451i	$-0.655214\pi$
$727$	−25.2656			−0.937048			−0.468524	+	0.883451i	$0.655214\pi$
$728$	−14.8136	−	16.6564i	−0.549028	−	0.617328i
$729$	−1.00000			−0.0370370
$730$	71.2720	+	19.0973i	2.63789	+	0.706822i
$731$	−10.9149	+	6.30170i	−0.403701	+	0.233077i
$732$	−6.48616	−	3.74479i	−0.239735	−	0.138411i
$733$	22.8545	+	22.8545i	0.844152	+	0.844152i	0.989396	−	0.145244i	$-0.0463967\pi$
$733$	22.8545	+	22.8545i	0.844152	+	0.844152i	−0.145244	+	0.989396i	$0.546397\pi$
$734$	−28.5184	+	7.64147i	−1.05263	+	0.282052i
$735$	−5.81794	−	17.6564i	−0.214598	−	0.651267i
$736$	38.5109	+	38.5109i	1.41953	+	1.41953i
$737$	3.40865	−	5.90396i	0.125559	−	0.217475i
$738$	−0.591348	−	1.02425i	−0.0217678	−	0.0377030i
$739$	3.35655	−	12.5268i	0.123473	−	0.460806i	−0.876308	−	0.481751i	$-0.840001\pi$
$739$	3.35655	−	12.5268i	0.123473	−	0.460806i	0.999781	+	0.0209450i	$0.00666750\pi$
$740$	38.3014			1.40799
$741$	0.682334	+	0.247945i	0.0250662	+	0.00910849i
$742$	−7.95935	+	8.42229i	−0.292197	+	0.309192i
$743$	31.0606	+	8.32266i	1.13950	+	0.305329i	0.778751	−	0.627333i	$-0.215854\pi$
$743$	31.0606	+	8.32266i	1.13950	+	0.305329i	0.360751	+	0.932662i	$0.382520\pi$
$744$	−11.1662	−	19.3405i	−0.409374	−	0.709057i
$745$	6.35837	−	11.0130i	0.232953	−	0.403486i
$746$	−15.2893	+	15.2893i	−0.559782	+	0.559782i
$747$	7.40641	−	1.98454i	0.270987	−	0.0726106i
$748$	−16.0927	−	60.0587i	−0.588407	−	2.19596i
$749$	−19.0412	+	0.538099i	−0.695749	+	0.0196617i
$750$	−8.78584	+	15.2175i	−0.320814	+	0.555666i
$751$	−13.1305	+	7.58091i	−0.479140	+	0.276631i	−0.720058	−	0.693914i	$-0.755885\pi$
$751$	−13.1305	+	7.58091i	−0.479140	+	0.276631i	0.240918	+	0.970545i	$0.422551\pi$
$752$	1.05935	+	0.283851i	0.0386304	+	0.0103510i
$753$		−	10.9234i		−	0.398072i
$754$	−64.5111	+	54.1887i	−2.34935	+	1.97344i
$755$		−	28.7807i		−	1.04744i
$756$	−4.21777	−	6.85087i	−0.153399	−	0.249164i
$757$	−17.8529	−	30.9221i	−0.648875	−	1.12388i	−0.983392	−	0.181494i	$-0.941907\pi$
$757$	−17.8529	−	30.9221i	−0.648875	−	1.12388i	0.334517	−	0.942390i	$-0.391427\pi$
$758$	64.7200	+	37.3661i	2.35074	+	1.35720i
$759$	27.4880	+	27.4880i	0.997750	+	0.997750i
$760$	−0.323404	−	1.20696i	−0.0117311	−	0.0437810i
$761$	0.802382	+	2.99453i	0.0290863	+	0.108552i	0.978943	−	0.204134i	$-0.0654379\pi$
$761$	0.802382	+	2.99453i	0.0290863	+	0.108552i	−0.949857	+	0.312686i	$0.898771\pi$
$762$	1.90708	−	1.90708i	0.0690861	−	0.0690861i
$763$	2.59191	+	8.68401i	0.0938334	+	0.314382i
$764$	−35.1538	+	20.2961i	−1.27182	+	0.734286i
$765$	−3.00690	+	11.2219i	−0.108715	+	0.405729i
$766$	−8.67503			−0.313442
$767$	18.7824	−	15.7770i	0.678192	−	0.569675i
$768$		−	10.2228i		−	0.368882i
$769$	−8.07284	+	30.1282i	−0.291114	+	1.08645i	0.653141	+	0.757237i	$0.273451\pi$
$769$	−8.07284	+	30.1282i	−0.291114	+	1.08645i	−0.944255	+	0.329216i	$0.893216\pi$
$770$	17.0654	−	71.7372i	0.614995	−	2.58523i
$771$	24.6012	+	14.2035i	0.885991	+	0.511527i
$772$	−17.3447	+	17.3447i	−0.624251	+	0.624251i
$773$	−5.18000	+	1.38798i	−0.186312	+	0.0499220i	−0.350768	−	0.936462i	$-0.614080\pi$
$773$	−5.18000	+	1.38798i	−0.186312	+	0.0499220i	0.164457	+	0.986384i	$0.447413\pi$
$774$	−6.24804	+	1.67416i	−0.224581	+	0.0601764i
$775$	−13.8743	+	13.8743i	−0.498379	+	0.498379i
$776$	−5.96928	−	3.44636i	−0.214284	−	0.123717i
$777$	−12.2078	−	2.90410i	−0.437954	−	0.104184i
$778$	−7.31105	+	27.2852i	−0.262114	+	0.978222i
$779$			0.106067i			0.00380026i
$780$	−9.94421	+	27.3660i	−0.356060	+	0.979860i
$781$	26.0089			0.930670
$782$	21.1410	−	78.8993i	0.756001	−	2.82143i
$783$	−9.01325	+	5.20380i	−0.322107	+	0.185969i
$784$	−2.63275	+	5.22044i	−0.0940267	+	0.186444i
$785$	15.0345	−	15.0345i	0.536604	−	0.536604i
$786$	1.76313	+	6.58009i	0.0628888	+	0.234704i
$787$	3.63938	+	13.5824i	0.129730	+	0.484159i	0.999964	−	0.00847973i	$-0.00269922\pi$
$787$	3.63938	+	13.5824i	0.129730	+	0.484159i	−0.870234	+	0.492638i	$0.836033\pi$
$788$	−27.2973	−	27.2973i	−0.972426	−	0.972426i
$789$	18.8064	+	10.8579i	0.669526	+	0.386551i
$790$	13.3114	+	23.0560i	0.473597	+	0.820294i
$791$	−1.05350	−	1.71118i	−0.0374580	−	0.0608425i
$792$		−	10.9224i		−	0.388110i
$793$	0.769372	−	8.84726i	0.0273212	−	0.314175i
$794$		−	59.6088i		−	2.11544i
$795$	5.00437	+	1.34092i	0.177487	+	0.0475574i
$796$	−57.0740	+	32.9517i	−2.02294	+	1.16794i
$797$	−14.0098	+	24.2657i	−0.496252	+	0.859534i	−0.999991	−	0.00432247i	$-0.998624\pi$
$797$	−14.0098	+	24.2657i	−0.496252	+	0.859534i	0.503739	+	0.863856i	$0.331957\pi$
$798$	0.0337870	+	1.19559i	0.00119605	+	0.0423233i
$799$	−1.48666	−	5.54828i	−0.0525941	−	0.196284i
$800$	−12.9865	+	3.47971i	−0.459141	+	0.123026i
$801$	−11.0145	+	11.0145i	−0.389178	+	0.389178i
$802$	16.8947	−	29.2625i	0.596573	−	1.03330i
$803$	−28.9216	−	50.0936i	−1.02062	−	1.76776i
$804$	−4.28378	−	1.14784i	−0.151077	−	0.0404811i
$805$	40.1369	−	42.4713i	1.41464	−	1.49692i
$806$	44.3424	−	63.3981i	1.56190	−	2.23310i
$807$	−12.3725			−0.435532
$808$	−0.383152	+	1.42994i	−0.0134792	+	0.0503052i
$809$	22.8429	+	39.5651i	0.803115	+	1.39104i	0.917556	+	0.397606i	$0.130159\pi$
$809$	22.8429	+	39.5651i	0.803115	+	1.39104i	−0.114441	+	0.993430i	$0.536508\pi$
$810$	−2.98130	+	5.16377i	−0.104752	+	0.181436i
$811$	7.85623	+	7.85623i	0.275870	+	0.275870i	0.831458	−	0.555588i	$-0.187507\pi$
$811$	7.85623	+	7.85623i	0.275870	+	0.275870i	−0.555588	+	0.831458i	$0.687507\pi$
$812$	−73.6664	−	39.8002i	−2.58518	−	1.39671i
$813$	7.64449	−	2.04834i	0.268104	−	0.0718382i
$814$	−35.1957	−	35.1957i	−1.23361	−	1.23361i
$815$	43.7629	+	25.2665i	1.53295	+	0.885048i
$816$	3.16433	−	1.82693i	0.110774	−	0.0639553i
$817$	0.560341	+	0.150143i	0.0196038	+	0.00525284i
$818$	55.7777			1.95022
$819$	5.24448	−	7.96840i	0.183257	−	0.278438i
$820$	−4.25399			−0.148556
$821$	25.7120	+	6.88952i	0.897356	+	0.240446i	0.677881	−	0.735172i	$-0.262899\pi$
$821$	25.7120	+	6.88952i	0.897356	+	0.240446i	0.219476	+	0.975618i	$0.429565\pi$
$822$	22.7048	−	13.1086i	0.791919	−	0.457215i
$823$	38.5488	+	22.2561i	1.34373	+	0.775800i	0.987352	−	0.158543i	$-0.0506798\pi$
$823$	38.5488	+	22.2561i	1.34373	+	0.775800i	0.356373	+	0.934344i	$0.384013\pi$
$824$	3.23382	+	3.23382i	0.112655	+	0.112655i
$825$	−9.26935	+	2.48371i	−0.322717	+	0.0864719i
$826$	35.5549	+	19.2094i	1.23711	+	0.668381i
$827$	−10.7544	−	10.7544i	−0.373966	−	0.373966i	0.494953	−	0.868920i	$-0.335185\pi$
$827$	−10.7544	−	10.7544i	−0.373966	−	0.373966i	−0.868920	+	0.494953i	$0.835185\pi$
$828$	12.6444	−	21.9008i	0.439424	−	0.761105i
$829$	22.8384	+	39.5572i	0.793209	+	1.37388i	0.923970	+	0.382464i	$0.124924\pi$
$829$	22.8384	+	39.5572i	0.793209	+	1.37388i	−0.130761	+	0.991414i	$0.541742\pi$
$830$	11.8330	−	44.1615i	0.410731	−	1.53287i
$831$	11.2109			0.388900
$832$	42.5761	−	19.8807i	1.47606	−	0.689238i
$833$	30.5732	−	1.72936i	1.05930	−	0.0599189i
$834$	14.5428	+	3.89673i	0.503576	+	0.134933i
$835$	−14.4521	−	25.0317i	−0.500134	−	0.866257i
$836$	−1.43095	+	2.47847i	−0.0494903	+	0.0857197i
$837$	6.75799	−	6.75799i	0.233590	−	0.233590i
$838$	38.8869	−	10.4197i	1.34332	−	0.359943i
$839$	0.546041	+	2.03785i	0.0188514	+	0.0703546i	0.974711	−	0.223470i	$-0.0717385\pi$
$839$	0.546041	+	2.03785i	0.0188514	+	0.0703546i	−0.955859	+	0.293825i	$0.905072\pi$
$840$	−16.4122	+	0.463806i	−0.566276	+	0.0160028i
$841$	−39.6591	+	68.6916i	−1.36755	+	2.36867i
$842$	−2.29278	+	1.32374i	−0.0790144	+	0.0456190i
$843$	−20.7565	−	5.56170i	−0.714893	−	0.191555i
$844$			39.5856i			1.36259i
$845$	−34.3902	+	3.04501i	−1.18306	+	0.104751i
$846$		−	2.94800i		−	0.101354i
$847$	−24.4421	+	15.0479i	−0.839841	+	0.517052i
$848$	−0.814711	−	1.41112i	−0.0279773	−	0.0484581i
$849$	−13.2458	−	7.64747i	−0.454595	−	0.262461i
$850$	14.2581	+	14.2581i	0.489050	+	0.489050i
$851$	−10.2090	−	38.1006i	−0.349961	−	1.30607i
$852$	−4.37914	−	16.3432i	−0.150027	−	0.559908i
$853$	−31.7998	+	31.7998i	−1.08881	+	1.08881i	−0.0931541	+	0.995652i	$0.529695\pi$
$853$	−31.7998	+	31.7998i	−1.08881	+	1.08881i	−0.995652	+	0.0931541i	$0.970305\pi$
$854$	14.0197	−	4.18446i	0.479746	−	0.143189i
$855$	0.463100	−	0.267371i	0.0158377	−	0.00914390i
$856$	−4.35430	+	16.2505i	−0.148827	+	0.555429i
$857$	0.314991			0.0107599			0.00537994	−	0.999986i	$-0.498288\pi$
$857$	0.314991			0.0107599			0.00537994	+	0.999986i	$0.498288\pi$
$858$	34.2849	−	16.0091i	1.17047	−	0.546543i
$859$		−	11.6151i		−	0.396303i	−0.980171	−	0.198151i	$-0.936506\pi$
$859$		−	11.6151i		−	0.396303i	0.980171	−	0.198151i	$-0.0634938\pi$
$860$	−6.02170	+	22.4733i	−0.205338	+	0.766333i
$861$	1.35588	+	0.322547i	0.0462082	+	0.0109924i
$862$	−27.0887	−	15.6397i	−0.922646	−	0.532690i
$863$	−10.5474	+	10.5474i	−0.359038	+	0.359038i	−0.863458	−	0.504420i	$-0.831706\pi$
$863$	−10.5474	+	10.5474i	−0.359038	+	0.359038i	0.504420	+	0.863458i	$0.331706\pi$
$864$	6.32554	−	1.69492i	0.215199	−	0.0576625i
$865$	−20.8957	+	5.59899i	−0.710476	+	0.190371i
$866$	−1.20700	+	1.20700i	−0.0410156	+	0.0410156i
$867$	−1.85062	−	1.06845i	−0.0628502	−	0.0362866i
$868$	74.8018	+	17.7945i	2.53894	+	0.603983i
$869$	5.40164	−	20.1592i	0.183238	−	0.683853i
$870$			62.0564i			2.10391i
$871$	−0.915858	−	5.17825i	−0.0310327	−	0.175458i
$872$	8.00399			0.271049
$873$	0.763454	−	2.84925i	0.0258390	−	0.0964325i
$874$	−3.25597	+	1.87984i	−0.110135	+	0.0635865i
$875$	−5.92219	−	19.8419i	−0.200207	−	0.670779i
$876$	−26.6077	+	26.6077i	−0.898992	+	0.898992i
$877$	13.5647	+	50.6241i	0.458047	+	1.70945i	0.678972	+	0.734164i	$0.262426\pi$
$877$	13.5647	+	50.6241i	0.458047	+	1.70945i	−0.220925	+	0.975291i	$0.570908\pi$
$878$	18.5438	+	69.2065i	0.625824	+	2.33561i
$879$	−14.8624	−	14.8624i	−0.501295	−	0.501295i
$880$	8.97938	+	5.18425i	0.302695	+	0.174761i
$881$	2.13878	+	3.70447i	0.0720572	+	0.124807i	0.899803	−	0.436297i	$-0.143710\pi$
$881$	2.13878	+	3.70447i	0.0720572	+	0.124807i	−0.827746	+	0.561104i	$0.810377\pi$
$882$	15.3861	+	3.20383i	0.518078	+	0.107879i
$883$		−	33.8768i		−	1.14004i	−0.821630	−	0.570022i	$-0.806935\pi$
$883$		−	33.8768i		−	1.14004i	0.821630	−	0.570022i	$-0.193065\pi$
$884$	−39.3020	−	27.4890i	−1.32187	−	0.924554i
$885$		−	18.0677i		−	0.607339i
$886$	−30.1622	−	8.08195i	−1.01332	−	0.271518i
$887$	−3.88879	+	2.24520i	−0.130573	+	0.0753863i	−0.563864	−	0.825868i	$-0.690686\pi$
$887$	−3.88879	+	2.24520i	−0.130573	+	0.0753863i	0.433291	+	0.901254i	$0.357352\pi$
$888$	−5.54138	+	9.59795i	−0.185956	+	0.322086i
$889$	0.0897799	+	3.17695i	0.00301112	+	0.106551i
$890$	24.0388	+	89.7139i	0.805781	+	3.00722i
$891$	4.51499	−	1.20979i	0.151258	−	0.0405294i
$892$	−36.4018	+	36.4018i	−1.21882	+	1.21882i
$893$	−0.132192	+	0.228963i	−0.00442364	+	0.00766197i
$894$	5.37535	+	9.31038i	0.179779	+	0.311386i
$895$	30.3143	+	8.12270i	1.01330	+	0.271512i
$896$	31.0794	+	29.3711i	1.03829	+	0.981219i
$897$	29.8731	+	2.59782i	0.997435	+	0.0867386i
$898$	−86.7949			−2.89638
$899$	25.7442	−	96.0787i	0.858617	−	3.20440i
$900$	3.12138	+	5.40639i	0.104046	+	0.180213i
$901$	−4.26701	+	7.39069i	−0.142155	+	0.246219i
$902$	3.90905	+	3.90905i	0.130157	+	0.130157i
$903$	3.62328	−	6.70636i	0.120575	−	0.223174i
$904$	−1.71428	+	0.459339i	−0.0570160	+	0.0152774i
$905$	19.7171	+	19.7171i	0.655417	+	0.655417i
$906$	21.0714	+	12.1656i	0.700050	+	0.404174i
$907$	13.2542	−	7.65232i	0.440099	−	0.254091i	−0.263541	−	0.964648i	$-0.584890\pi$
$907$	13.2542	−	7.65232i	0.440099	−	0.254091i	0.703640	+	0.710557i	$0.251557\pi$
$908$	55.6187	+	14.9030i	1.84577	+	0.494573i
$909$	−0.633535			−0.0210130
$910$	−25.5116	−	50.8375i	−0.845701	−	1.68525i
$911$	15.6790			0.519470			0.259735	−	0.965680i	$-0.416365\pi$
$911$	15.6790			0.519470			0.259735	+	0.965680i	$0.416365\pi$
$912$	−0.162449	−	0.0435280i	−0.00537921	−	0.00144136i
$913$	−31.0390	+	17.9204i	−1.02724	+	0.593077i
$914$	22.7289	+	13.1225i	0.751805	+	0.434055i
$915$	−4.62536	−	4.62536i	−0.152910	−	0.152910i
$916$	0.753632	−	0.201935i	0.0249007	−	0.00667212i
$917$	−7.06277	−	3.81584i	−0.233233	−	0.126010i
$918$	−6.94495	−	6.94495i	−0.229218	−	0.229218i
$919$	−26.1402	+	45.2762i	−0.862287	+	1.49352i	0.00742976	+	0.999972i	$0.497635\pi$
$919$	−26.1402	+	45.2762i	−0.862287	+	1.49352i	−0.869716	+	0.493552i	$0.835698\pi$
$920$	−25.8052	−	44.6959i	−0.850771	−	1.47358i
$921$	4.68166	−	17.4722i	0.154266	−	0.575729i
$922$	76.8731			2.53168
$923$	15.3619	−	12.9038i	0.505641	−	0.424734i
$924$	27.3313	+	25.8290i	0.899133	+	0.849711i
$925$	9.40546	+	2.52019i	0.309250	+	0.0828632i
$926$	28.7768	+	49.8428i	0.945663	+	1.63794i
$927$	−0.978579	+	1.69495i	−0.0321408	+	0.0556694i
$928$	48.1936	−	48.1936i	1.58203	−	1.58203i
$929$	19.0687	−	5.10945i	0.625625	−	0.167636i	0.0679414	−	0.997689i	$-0.478357\pi$
$929$	19.0687	−	5.10945i	0.625625	−	0.167636i	0.557684	+	0.830054i	$0.311690\pi$
$930$	−14.7491	−	55.0443i	−0.483641	−	1.80497i
$931$	−1.05134	−	0.938768i	−0.0344562	−	0.0307669i
$932$	17.3093	−	29.9806i	0.566984	−	0.982046i
$933$	16.9323	−	9.77585i	0.554338	−	0.320047i
$934$	−44.3333	−	11.8791i	−1.45063	−	0.388696i
$935$		−	54.3045i		−	1.77595i
$936$	−5.41894	−	6.45118i	−0.177123	−	0.210863i
$937$			32.0301i			1.04638i	0.852217	+	0.523189i	$0.175258\pi$
$937$			32.0301i			1.04638i	−0.852217	+	0.523189i	$0.824742\pi$
$938$	7.37752	−	4.54201i	0.240885	−	0.148302i
$939$	−6.62473	−	11.4744i	−0.216190	−	0.374452i
$940$	−9.18291	−	5.30176i	−0.299514	−	0.172924i
$941$	−16.4141	−	16.4141i	−0.535083	−	0.535083i	0.386998	−	0.922081i	$-0.373512\pi$
$941$	−16.4141	−	16.4141i	−0.535083	−	0.535083i	−0.922081	+	0.386998i	$0.873512\pi$
$942$	4.65223	+	17.3624i	0.151578	+	0.565696i
$943$	1.13388	+	4.23169i	0.0369241	+	0.137803i
$944$	−4.01805	+	4.01805i	−0.130777	+	0.130777i
$945$	−2.00958	−	6.73296i	−0.0653716	−	0.219023i
$946$	26.1845	−	15.1176i	0.851330	−	0.491516i
$947$	−11.1001	+	41.4261i	−0.360704	+	1.34617i	0.512447	+	0.858719i	$0.328739\pi$
$947$	−11.1001	+	41.4261i	−0.360704	+	1.34617i	−0.873152	+	0.487449i	$0.837928\pi$
$948$	−13.5769			−0.440957
$949$	−41.9352	−	15.2383i	−1.36128	−	0.494658i
$950$		−	0.928107i		−	0.0301118i
$951$	6.54676	−	24.4328i	0.212293	−	0.792289i
$952$	6.25905	−	26.3109i	0.202857	−	0.852741i
$953$	−10.3745	−	5.98973i	−0.336064	−	0.194026i	0.322466	−	0.946581i	$-0.395488\pi$
$953$	−10.3745	−	5.98973i	−0.336064	−	0.194026i	−0.658530	+	0.752554i	$0.728821\pi$
$954$	−3.09708	+	3.09708i	−0.100272	+	0.100272i
$955$	−34.2444	+	9.17575i	−1.10812	+	0.296920i
$956$	−50.7511	+	13.5987i	−1.64141	+	0.439814i
$957$	34.3992	−	34.3992i	1.11197	−	1.11197i
$958$	−22.9963	−	13.2769i	−0.742976	−	0.428957i
$959$	−7.15000	+	30.0561i	−0.230885	+	0.970563i
$960$	8.95793	−	33.4315i	0.289116	−	1.07900i
$961$			60.3409i			1.94648i
$962$	−38.2497	−	3.32625i	−1.23322	−	0.107243i
$963$	−7.19975			−0.232009
$964$	23.9973	−	89.5592i	0.772902	−	2.88451i
$965$	−18.5531	+	10.7117i	−0.597246	+	0.344820i
$966$	14.1290	+	47.3382i	0.454593	+	1.52308i
$967$	3.08553	−	3.08553i	0.0992241	−	0.0992241i	−0.655752	−	0.754976i	$-0.727648\pi$
$967$	3.08553	−	3.08553i	0.0992241	−	0.0992241i	0.754976	+	0.655752i	$0.227648\pi$
$968$	6.56111	+	24.4864i	0.210882	+	0.787023i
$969$	0.227976	+	0.850818i	0.00732364	+	0.0273322i
$970$	−12.4368	−	12.4368i	−0.399321	−	0.399321i
$971$	25.8972	+	14.9518i	0.831081	+	0.479825i	0.854223	−	0.519907i	$-0.174033\pi$
$971$	25.8972	+	14.9518i	0.831081	+	0.479825i	−0.0231414	+	0.999732i	$0.507367\pi$
$972$	−1.52039	−	2.63339i	−0.0487664	−	0.0844659i
$973$	−15.1084	+	9.30154i	−0.484352	+	0.298194i
$974$		−	0.419190i		−	0.0134317i
$975$	−4.24259	+	6.06580i	−0.135872	+	0.194261i
$976$			2.05726i			0.0658512i
$977$	−9.78075	−	2.62074i	−0.312914	−	0.0838450i	0.0989443	−	0.995093i	$-0.468453\pi$
$977$	−9.78075	−	2.62074i	−0.312914	−	0.0838450i	−0.411858	+	0.911248i	$0.635120\pi$
$978$	−36.9971	+	21.3603i	−1.18304	+	0.683026i
$979$	36.4051	−	63.0555i	1.16351	−	2.01526i
$980$	37.6507	−	42.1655i	1.20271	−	1.34693i
$981$	0.886540	+	3.30861i	0.0283050	+	0.105636i
$982$	6.10476	−	1.63577i	0.194811	−	0.0521994i
$983$	−5.97019	+	5.97019i	−0.190419	+	0.190419i	−0.795877	−	0.605458i	$-0.792990\pi$
$983$	−5.97019	+	5.97019i	−0.190419	+	0.190419i	0.605458	+	0.795877i	$0.292990\pi$
$984$	0.615459	−	1.06601i	0.0196201	−	0.0339830i
$985$	−16.8581	−	29.1991i	−0.537144	−	0.930360i
$986$	−98.7368	−	26.4564i	−3.14442	−	0.842545i
$987$	2.52489	+	2.38610i	0.0803681	+	0.0759505i
$988$	0.384476	+	2.17382i	0.0122318	+	0.0691585i
$989$	23.9605			0.761901
$990$	7.21348	−	26.9211i	0.229259	−	0.855608i
$991$	−27.8012	−	48.1532i	−0.883136	−	1.52964i	−0.847836	−	0.530259i	$-0.822095\pi$
$991$	−27.8012	−	48.1532i	−0.883136	−	1.52964i	−0.0353002	−	0.999377i	$-0.511239\pi$
$992$	−31.2937	+	54.2023i	−0.993576	+	1.72092i
$993$	−9.61237	−	9.61237i	−0.305039	−	0.305039i
$994$	29.0798	+	15.7111i	0.922357	+	0.498327i
$995$	−55.5975	+	14.8973i	−1.76256	+	0.472277i
$996$	16.4867	+	16.4867i	0.522400	+	0.522400i
$997$	9.66852	+	5.58213i	0.306205	+	0.176788i	0.645227	−	0.763991i	$-0.276763\pi$
$997$	9.66852	+	5.58213i	0.306205	+	0.176788i	−0.339022	+	0.940778i	$0.610096\pi$
$998$	−4.95526	+	2.86092i	−0.156856	+	0.0905609i
$999$	−4.58128	−	1.22755i	−0.144945	−	0.0388380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.d.223.1	yes	32
3.2	odd	2		819.2.fm.e.496.8		32
7.6	odd	2		273.2.by.c.223.1	yes	32
13.7	odd	12		273.2.by.c.202.1	✓	32
21.20	even	2		819.2.fm.f.496.8		32
39.20	even	12		819.2.fm.f.748.8		32
91.20	even	12	inner	273.2.by.d.202.1	yes	32
273.20	odd	12		819.2.fm.e.748.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.1	✓	32	13.7	odd	12
273.2.by.c.223.1	yes	32	7.6	odd	2
273.2.by.d.202.1	yes	32	91.20	even	12	inner
273.2.by.d.223.1	yes	32	1.1	even	1	trivial
819.2.fm.e.496.8		32	3.2	odd	2
819.2.fm.e.748.8		32	273.20	odd	12
819.2.fm.f.496.8		32	21.20	even	2
819.2.fm.f.748.8		32	39.20	even	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16866 - 0.581092i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(-2.16866 + 0.581092i) q^{6} +(1.25762 - 2.32774i) q^{7} +(-1.65230 - 1.65230i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.16866 - 0.581092i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.63339 + 1.52039i) q^{4} +(1.87790 + 1.87790i) q^{5} +(-2.16866 + 0.581092i) q^{6} +(1.25762 - 2.32774i) q^{7} +(-1.65230 - 1.65230i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.98130 - 5.16377i) q^{10} +(-1.20979 + 4.51499i) q^{11} +3.04077 q^{12} +(1.52548 + 3.26694i) q^{13} +(-4.07999 + 4.31730i) q^{14} +(2.56526 + 0.687359i) q^{15} +(-0.417624 - 0.723346i) q^{16} +(-2.18729 + 3.78849i) q^{17} +(-1.58757 + 1.58757i) q^{18} +(0.194491 - 0.0521138i) q^{19} +(2.09010 + 7.80037i) q^{20} +(-0.0747386 - 2.64470i) q^{21} +(5.24724 - 9.08849i) q^{22} +(7.20237 - 4.15829i) q^{23} +(-2.25709 - 0.604784i) q^{24} +2.05302i q^{25} +(-1.40986 - 7.97134i) q^{26} -1.00000i q^{27} +(6.85087 - 4.21777i) q^{28} +(-5.20380 - 9.01325i) q^{29} +(-5.16377 - 2.98130i) q^{30} +(6.75799 + 6.75799i) q^{31} +(1.69492 + 6.32554i) q^{32} +(1.20979 + 4.51499i) q^{33} +(6.94495 - 6.94495i) q^{34} +(6.73296 - 2.00958i) q^{35} +(2.63339 - 1.52039i) q^{36} +(1.22755 - 4.58128i) q^{37} -0.452070 q^{38} +(2.95458 + 2.06651i) q^{39} -6.20572i q^{40} +(-0.136339 + 0.508825i) q^{41} +(-1.37473 + 5.77889i) q^{42} +(2.49507 + 1.44053i) q^{43} +(-10.0504 + 10.0504i) q^{44} +(2.56526 - 0.687359i) q^{45} +(-18.0359 + 4.83270i) q^{46} +(-0.928461 + 0.928461i) q^{47} +(-0.723346 - 0.417624i) q^{48} +(-3.83677 - 5.85484i) q^{49} +(1.19299 - 4.45231i) q^{50} +4.37458i q^{51} +(-0.949833 + 10.9224i) q^{52} +1.95082 q^{53} +(-0.581092 + 2.16866i) q^{54} +(-10.7506 + 6.20683i) q^{55} +(-5.92410 + 1.76816i) q^{56} +(0.142378 - 0.142378i) q^{57} +(6.04777 + 22.5706i) q^{58} +(-1.76081 - 6.57142i) q^{59} +(5.71027 + 5.71027i) q^{60} +(-2.13306 - 1.23152i) q^{61} +(-10.7288 - 18.5828i) q^{62} +(-1.38707 - 2.25300i) q^{63} -13.0324i q^{64} +(-3.27029 + 8.99969i) q^{65} -10.4945i q^{66} +(-1.40878 - 0.377482i) q^{67} +(-11.5199 + 6.65104i) q^{68} +(4.15829 - 7.20237i) q^{69} +(-15.7693 + 0.445637i) q^{70} +(-1.44014 - 5.37468i) q^{71} +(-2.25709 + 0.604784i) q^{72} +(-8.75032 + 8.75032i) q^{73} +(-5.32429 + 9.22194i) q^{74} +(1.02651 + 1.77797i) q^{75} +(0.591404 + 0.158466i) q^{76} +(8.98827 + 8.49422i) q^{77} +(-5.20665 - 6.19846i) q^{78} -4.46495 q^{79} +(0.574115 - 2.14263i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.591348 - 1.02425i) q^{82} +(5.42187 + 5.42187i) q^{83} +(3.82414 - 7.07814i) q^{84} +(-11.2219 + 3.00690i) q^{85} +(-4.57389 - 4.57389i) q^{86} +(-9.01325 - 5.20380i) q^{87} +(9.45905 - 5.46119i) q^{88} +(-15.0461 - 4.03159i) q^{89} -5.96261 q^{90} +(9.52308 + 0.557652i) q^{91} +25.2888 q^{92} +(9.23159 + 2.47360i) q^{93} +(2.55304 - 1.47400i) q^{94} +(0.463100 + 0.267371i) q^{95} +(4.63062 + 4.63062i) q^{96} +(2.84925 - 0.763454i) q^{97} +(4.91847 + 14.9267i) q^{98} +(3.30520 + 3.30520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{10} - 4 q^{11} + 32 q^{12} + 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{19} + 44 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 4 q^{24} - 28 q^{26} - 32 q^{28} - 18 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{33} - 66 q^{34} + 22 q^{35} + 6 q^{36} - 24 q^{37} + 24 q^{38} + 8 q^{39} - 26 q^{42} - 6 q^{43} - 20 q^{44} + 4 q^{45} - 58 q^{46} - 28 q^{47} - 60 q^{48} + 8 q^{49} + 70 q^{50} + 28 q^{52} - 80 q^{53} - 4 q^{54} + 60 q^{55} - 54 q^{56} + 16 q^{57} - 4 q^{58} - 42 q^{59} - 58 q^{60} + 36 q^{61} + 52 q^{62} + 4 q^{63} + 14 q^{65} + 26 q^{67} - 72 q^{68} + 2 q^{69} - 116 q^{70} - 4 q^{71} + 4 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} - 48 q^{76} + 28 q^{77} - 14 q^{78} - 4 q^{79} - 98 q^{80} - 16 q^{81} + 20 q^{82} - 36 q^{83} - 18 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} - 54 q^{89} + 4 q^{90} + 148 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} + 22 q^{96} - 40 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^10 - 4 * q^11 + 32 * q^12 + 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^19 + 44 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 4 * q^24 - 28 * q^26 - 32 * q^28 - 18 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^33 - 66 * q^34 + 22 * q^35 + 6 * q^36 - 24 * q^37 + 24 * q^38 + 8 * q^39 - 26 * q^42 - 6 * q^43 - 20 * q^44 + 4 * q^45 - 58 * q^46 - 28 * q^47 - 60 * q^48 + 8 * q^49 + 70 * q^50 + 28 * q^52 - 80 * q^53 - 4 * q^54 + 60 * q^55 - 54 * q^56 + 16 * q^57 - 4 * q^58 - 42 * q^59 - 58 * q^60 + 36 * q^61 + 52 * q^62 + 4 * q^63 + 14 * q^65 + 26 * q^67 - 72 * q^68 + 2 * q^69 - 116 * q^70 - 4 * q^71 + 4 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 - 48 * q^76 + 28 * q^77 - 14 * q^78 - 4 * q^79 - 98 * q^80 - 16 * q^81 + 20 * q^82 - 36 * q^83 - 18 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 - 54 * q^89 + 4 * q^90 + 148 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 + 22 * q^96 - 40 * q^97 + 36 * q^98 + 4 * q^99

Introduction

L-functions

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