LMFDB - Embedded newform 273.2.by.c.202.1

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			202.1
Character	$\chi$	$=$	273.202
Dual form			273.2.by.c.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16866 + 0.581092i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(2.16866 + 0.581092i) q^{6} +(2.25300 - 1.38707i) q^{7} +(-1.65230 + 1.65230i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(2.25300 - 1.38707i) 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} +(-2.64470 + 0.0747386i) 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} +(3.82414 - 7.07814i) 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} +(-1.62613 + 6.83570i) 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} +(5.69203 - 1.69889i) 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} +(3.15206 - 6.25016i) 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} +(-1.43078 + 6.01451i) 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} +(2.32774 + 1.25762i) 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} +(-0.445637 - 15.7693i) 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} +(-6.85087 + 4.21777i) 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} +(1.09457 + 9.47639i) 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} +(-3.20383 + 15.3861i) 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} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 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} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 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 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * 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 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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	−0.924152	−	0.382026i	$-0.875226\pi$
$2$	−2.16866	+	0.581092i	−1.53348	+	0.410894i	−0.609326	+	0.792920i	$0.708560\pi$
$3$	−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	$-0.952390\pi$
$5$	−1.87790	+	1.87790i	−0.839823	+	0.839823i	0.149013	+	0.988835i	$0.452390\pi$
$6$	2.16866	+	0.581092i	0.885353	+	0.237230i
$7$	2.25300	−	1.38707i	0.851556	−	0.524264i
$7$	2.25300	−	1.38707i	0.851556	−	0.524264i
$8$	−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	−0.867740	−	0.497019i	$-0.834428\pi$
$11$	−1.20979	−	4.51499i	−0.364764	−	1.36132i	0.502975	−	0.864301i	$-0.332239\pi$
$12$	−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	0.999367	+	0.0355783i	$0.0113273\pi$
$17$	2.18729	+	3.78849i	0.530495	+	0.918845i	−0.468872	+	0.883266i	$0.655339\pi$
$18$	−1.58757	−	1.58757i	−0.374194	−	0.374194i
$19$	−0.194491	−	0.0521138i	−0.0446194	−	0.0119557i	0.236440	−	0.971646i	$-0.424019\pi$
$19$	−0.194491	−	0.0521138i	−0.0446194	−	0.0119557i	−0.281060	+	0.959690i	$0.590686\pi$
$20$	−2.09010	+	7.80037i	−0.467361	+	1.74422i
$21$	−2.64470	+	0.0747386i	−0.577120	+	0.0163093i
$22$	5.24724	+	9.08849i	1.11872	+	1.93767i
$23$	7.20237	+	4.15829i	1.50180	+	0.867064i	0.999998	+	0.00208060i	$0.000662276\pi$
$23$	7.20237	+	4.15829i	1.50180	+	0.867064i	0.501801	+	0.864983i	$0.332671\pi$
$24$	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
$28$	3.82414	−	7.07814i	0.722695	−	1.33764i
$29$	−5.20380	+	9.01325i	−0.966322	+	1.67372i	−0.260300	+	0.965528i	$0.583821\pi$
$29$	−5.20380	+	9.01325i	−0.966322	+	1.67372i	−0.706022	+	0.708190i	$0.749512\pi$
$30$	−5.16377	+	2.98130i	−0.942771	+	0.544309i
$31$	−6.75799	+	6.75799i	−1.21377	+	1.21377i	−0.243995	+	0.969777i	$0.578458\pi$
$31$	−6.75799	+	6.75799i	−1.21377	+	1.21377i	−0.969777	+	0.243995i	$0.921542\pi$
$32$	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
$35$	−1.62613	+	6.83570i	−0.274866	+	1.15544i
$36$	2.63339	+	1.52039i	0.438898	+	0.253398i
$37$	1.22755	+	4.58128i	0.201808	+	0.753158i	0.990399	+	0.138240i	$0.0441444\pi$
$37$	1.22755	+	4.58128i	0.201808	+	0.753158i	−0.788591	+	0.614919i	$0.789189\pi$
$38$	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	$-0.0702362\pi$
$41$	0.136339	+	0.508825i	0.0212926	+	0.0794651i	−0.954462	+	0.298333i	$0.903570\pi$
$42$	5.69203	−	1.69889i	0.878299	−	0.262145i
$43$	2.49507	−	1.44053i	0.380494	−	0.219678i	−0.297539	−	0.954710i	$-0.596166\pi$
$43$	2.49507	−	1.44053i	0.380494	−	0.219678i	0.678033	+	0.735031i	$0.262832\pi$
$44$	−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	$-0.219471\pi$
$47$	0.928461	+	0.928461i	0.135430	+	0.135430i	−0.636142	+	0.771572i	$0.719471\pi$
$48$	0.723346	−	0.417624i	0.104406	−	0.0602788i
$49$	3.15206	−	6.25016i	0.450294	−	0.892881i
$50$	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
$56$	−1.43078	+	6.01451i	−0.191196	+	0.803722i
$57$	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	−0.751425	−	0.659819i	$-0.770633\pi$
$59$	1.76081	−	6.57142i	0.229237	−	0.855526i	0.980662	−	0.195707i	$-0.0627002\pi$
$60$	5.71027	−	5.71027i	0.737192	−	0.737192i
$61$	2.13306	−	1.23152i	0.273111	−	0.157681i	−0.357190	−	0.934032i	$-0.616265\pi$
$61$	2.13306	−	1.23152i	0.273111	−	0.157681i	0.630300	+	0.776351i	$0.282932\pi$
$62$	10.7288	−	18.5828i	1.36256	−	2.36002i
$63$	2.32774	+	1.25762i	0.293268	+	0.158446i
$64$			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	−0.343845	−	0.939026i	$-0.611729\pi$
$67$	−1.40878	+	0.377482i	−0.172110	+	0.0461168i	0.171735	+	0.985143i	$0.445063\pi$
$68$	11.5199	+	6.65104i	1.39700	+	0.806558i
$69$	−4.15829	−	7.20237i	−0.500600	−	0.867064i
$70$	−0.445637	−	15.7693i	−0.0532638	−	1.88479i
$71$	−1.44014	+	5.37468i	−0.170913	+	0.637857i	0.826299	+	0.563232i	$0.190442\pi$
$71$	−1.44014	+	5.37468i	−0.170913	+	0.637857i	−0.997212	+	0.0746244i	$0.976224\pi$
$72$	−2.25709	−	0.604784i	−0.266000	−	0.0712745i
$73$	8.75032	+	8.75032i	1.02415	+	1.02415i	0.999701	+	0.0244465i	$0.00778234\pi$
$73$	8.75032	+	8.75032i	1.02415	+	1.02415i	0.0244465	+	0.999701i	$0.492218\pi$
$74$	−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	$-0.888257\pi$
$83$	−5.42187	+	5.42187i	−0.595128	+	0.595128i	0.343884	+	0.939012i	$0.388257\pi$
$84$	−6.85087	+	4.21777i	−0.747492	+	0.460197i
$85$	−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	$-0.274186\pi$
$89$	15.0461	−	4.03159i	1.59488	−	0.427347i	0.943492	+	0.331396i	$0.107520\pi$
$90$	5.96261			0.628514
$91$	1.09457	+	9.47639i	0.114742	+	0.993395i
$92$	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	$-0.464514\pi$
$97$	−2.84925	−	0.763454i	−0.289297	−	0.0775170i	−0.400549	+	0.916275i	$0.631181\pi$
$98$	−3.20383	+	15.3861i	−0.323636	+	1.55423i
$99$	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	$-0.823299\pi$
$101$	0.316767	−	0.548657i	0.0315195	−	0.0545934i	0.881355	+	0.472455i	$0.156632\pi$
$102$	2.54203	+	9.48698i	0.251698	+	0.939351i
$103$	1.95716			0.192845			0.0964223	−	0.995341i	$-0.469260\pi$
$103$	1.95716			0.192845			0.0964223	+	0.995341i	$0.469260\pi$
$104$	−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	−0.985896	−	0.167357i	$-0.946477\pi$
$107$	−3.59988	+	6.23517i	−0.348013	+	0.602777i	0.637883	+	0.770133i	$0.279810\pi$
$108$	−1.52039	−	2.63339i	−0.146299	−	0.253398i
$109$	−2.42207	−	2.42207i	−0.231992	−	0.231992i	0.581531	−	0.813524i	$-0.302454\pi$
$109$	−2.42207	−	2.42207i	−0.231992	−	0.231992i	−0.813524	+	0.581531i	$0.802454\pi$
$110$	−26.9211	−	7.21348i	−2.56682	−	0.687778i
$111$	1.22755	−	4.58128i	0.116514	−	0.434836i
$112$	0.0624252	+	2.20898i	0.00589863	+	0.208729i
$113$	0.379755	+	0.657754i	0.0357243	+	0.0618763i	0.883335	−	0.468743i	$-0.155293\pi$
$113$	0.379755	+	0.657754i	0.0357243	+	0.0618763i	−0.847610	+	0.530619i	$0.821960\pi$
$114$	−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
$119$	10.1829	+	5.50156i	0.933464	+	0.504327i
$120$	−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
$126$	−5.77889	−	1.37473i	−0.514824	−	0.122471i
$127$	−1.04032	−	0.600626i	−0.0923131	−	0.0532970i	0.453133	−	0.891443i	$-0.350306\pi$
$127$	−1.04032	−	0.600626i	−0.0923131	−	0.0532970i	−0.545446	+	0.838146i	$0.683640\pi$
$128$	−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
$133$	−0.510476	+	0.152361i	−0.0442639	+	0.0132114i
$134$	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	−0.257508	−	0.966276i	$-0.582901\pi$
$137$	−11.2793	−	3.02227i	−0.963654	−	0.258210i	−0.706146	+	0.708066i	$0.749568\pi$
$138$	13.2032	+	13.2032i	1.12393	+	1.12393i
$139$	5.80746	−	3.35294i	0.492582	−	0.284393i	−0.233063	−	0.972462i	$-0.574875\pi$
$139$	5.80746	−	3.35294i	0.492582	−	0.284393i	0.725645	+	0.688069i	$0.241541\pi$
$140$	6.11067	+	20.4734i	0.516446	+	1.73032i
$141$	−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
$147$	−5.85484	+	3.83677i	−0.482899	+	0.316452i
$148$	10.1979	+	10.1979i	0.838265	+	0.838265i
$149$	−1.23932	+	4.62521i	−0.101529	+	0.378912i	−0.997928	−	0.0643356i	$-0.979507\pi$
$149$	−1.23932	+	4.62521i	−0.101529	+	0.378912i	0.896399	+	0.443248i	$0.146174\pi$
$150$	1.19299	−	4.45231i	0.0974074	−	0.363529i
$151$	−7.66300	+	7.66300i	−0.623606	+	0.623606i	−0.946452	−	0.322845i	$-0.895361\pi$
$151$	−7.66300	+	7.66300i	−0.623606	+	0.623606i	0.322845	+	0.946452i	$0.395361\pi$
$152$	0.407466	−	0.235251i	0.0330499	−	0.0190814i
$153$	−2.18729	+	3.78849i	−0.176832	+	0.306282i
$154$	24.4285	+	13.1981i	1.96850	+	1.06353i
$155$		−	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
$161$	21.9948	−	0.621570i	1.73344	−	0.0489865i
$162$	0.581092	−	2.16866i	0.0456549	−	0.170386i
$163$	18.3794	+	4.92475i	1.43959	+	0.385736i	0.892389	−	0.451266i	$-0.149028\pi$
$163$	18.3794	+	4.92475i	1.43959	+	0.385736i	0.547199	+	0.837003i	$0.315694\pi$
$164$	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	$-0.444978\pi$
$167$	10.5127	−	2.81688i	0.813500	−	0.217977i	0.641503	+	0.767121i	$0.278311\pi$
$168$	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	$-0.0664543\pi$
$173$	4.07283	+	7.05435i	0.309651	+	0.536332i	−0.668635	+	0.743591i	$0.733121\pi$
$174$	−16.5228	+	16.5228i	−1.25259	+	1.25259i
$175$	−2.84769	−	4.62546i	−0.215265	−	0.349652i
$176$	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	0.831062	−	0.556179i	$-0.187733\pi$
$179$	10.2340	+	5.90863i	0.764928	+	0.441631i	−0.0661342	+	0.997811i	$0.521067\pi$
$180$	−7.80037	+	2.09010i	−0.581405	+	0.155787i
$181$	−10.4995			−0.780423			−0.390212	−	0.920725i	$-0.627598\pi$
$181$	−10.4995			−0.780423			−0.390212	+	0.920725i	$0.627598\pi$
$182$	−7.88041	−	19.9151i	−0.584135	−	1.47620i
$183$	−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
$189$	−1.38707	−	2.25300i	−0.100895	−	0.163882i
$190$	−0.848942	+	0.848942i	−0.0615887	+	0.0615887i
$191$	−6.67464	−	11.5608i	−0.482960	−	0.836511i	0.516849	−	0.856077i	$-0.327105\pi$
$191$	−6.67464	−	11.5608i	−0.482960	−	0.836511i	−0.999809	+	0.0195655i	$0.993772\pi$
$192$	6.51620	−	11.2864i	0.470266	−	0.814525i
$193$	−2.08783	−	7.79189i	−0.150285	−	0.560872i	−0.999463	−	0.0327652i	$-0.989569\pi$
$193$	−2.08783	−	7.79189i	−0.150285	−	0.560872i	0.849178	−	0.528107i	$-0.177098\pi$
$194$	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	−0.667686	−	0.744443i	$-0.732715\pi$
$197$	−12.2629	+	3.28585i	−0.873699	+	0.234107i	−0.206012	+	0.978549i	$0.566049\pi$
$198$	−5.24724	+	9.08849i	−0.372905	+	0.645891i
$199$	10.8366	+	18.7696i	0.768188	+	1.33054i	0.938544	+	0.345158i	$0.112175\pi$
$199$	10.8366	+	18.7696i	0.768188	+	1.33054i	−0.170356	+	0.985383i	$0.554492\pi$
$200$	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
$203$	0.777849	+	27.5249i	0.0545943	+	1.93187i
$204$	−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
$210$	−7.49871	+	13.8794i	−0.517460	+	0.957770i
$211$	6.50914	−	11.2742i	0.448108	−	0.776145i	−0.550155	−	0.835062i	$-0.685431\pi$
$211$	6.50914	−	11.2742i	0.448108	−	0.776145i	0.998263	+	0.0589170i	$0.0187647\pi$
$212$	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
$217$	−5.85195	+	24.5996i	−0.397257	+	1.66993i
$218$	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	0.942460	+	0.334320i	$0.108507\pi$
$223$	4.38178	+	16.3530i	0.293426	+	1.09508i	−0.649034	+	0.760759i	$0.724827\pi$
$224$	−4.95532	−	16.6025i	−0.331091	−	1.10930i
$225$	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	$-0.632965\pi$
$227$	−18.2910	−	4.90106i	−1.21402	−	0.325295i	−0.808336	+	0.588721i	$0.799632\pi$
$228$	0.591404	+	0.158466i	0.0391667	+	0.0104947i
$229$	−0.181433	−	0.181433i	−0.0119894	−	0.0119894i	0.701087	−	0.713076i	$-0.252699\pi$
$229$	−0.181433	−	0.181433i	−0.0119894	−	0.0119894i	−0.713076	+	0.701087i	$0.752699\pi$
$230$	42.9449	−	24.7943i	2.83170	−	1.63488i
$231$	3.53696	+	11.8503i	0.232715	+	0.779695i
$232$	−6.29435	−	23.4909i	−0.413245	−	1.54225i
$233$			11.3848i			0.745842i	0.927863	+	0.372921i	$0.121644\pi$
$233$			11.3848i			0.745842i	−0.927863	+	0.372921i	$0.878356\pi$
$234$	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
$238$	−25.2802	−	6.01385i	−1.63867	−	0.389820i
$239$	−12.2181	−	12.2181i	−0.790322	−	0.790322i	0.191224	−	0.981546i	$-0.438754\pi$
$239$	−12.2181	−	12.2181i	−0.790322	−	0.790322i	−0.981546	+	0.191224i	$0.938754\pi$
$240$	−0.574115	+	2.14263i	−0.0370590	+	0.138306i
$241$	7.89185	−	29.4528i	0.508359	−	1.89722i	0.0721047	−	0.997397i	$-0.477028\pi$
$241$	7.89185	−	29.4528i	0.508359	−	1.89722i	0.436254	−	0.899824i	$-0.356305\pi$
$242$	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
$245$	5.81794	+	17.6564i	0.371694	+	1.12803i
$246$			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	$-0.278700\pi$
$251$	−5.46171	−	9.45996i	−0.344740	−	0.597107i	−0.985307	+	0.170795i	$0.945366\pi$
$252$	8.04192	−	0.227263i	0.506593	−	0.0143162i
$253$	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	−0.0414174	+	0.999142i	$0.513187\pi$
$257$	−14.2035	+	24.6012i	−0.885991	+	1.53458i	−0.844574	+	0.535439i	$0.820146\pi$
$258$	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	−0.308510	−	0.951221i	$-0.599830\pi$
$263$	10.8579	−	18.8064i	0.669526	−	1.15965i	0.978037	−	0.208433i	$-0.0668363\pi$
$264$	−5.46119	−	9.45905i	−0.336113	−	0.582164i
$265$	−3.66345	+	3.66345i	−0.225044	+	0.225044i
$266$	1.01851	−	0.627054i	0.0624491	−	0.0384471i
$267$	−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	$-0.543560\pi$
$269$	10.7149	−	6.18625i	0.653298	−	0.377182i	0.789719	+	0.613469i	$0.210226\pi$
$270$	−5.16377	−	2.98130i	−0.314257	−	0.181436i
$271$	−7.64449	+	2.04834i	−0.464370	+	0.124427i	−0.483415	−	0.875391i	$-0.660604\pi$
$271$	−7.64449	+	2.04834i	−0.464370	+	0.124427i	0.0190456	+	0.999819i	$0.493937\pi$
$272$	−3.65385			−0.221547
$273$	3.79027	−	8.75408i	0.229397	−	0.529821i
$274$	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	−0.179113	−	0.983828i	$-0.557323\pi$
$277$	9.70888	−	5.60543i	0.583350	−	0.336797i	0.762464	+	0.647031i	$0.223990\pi$
$278$	−10.6461	+	10.6461i	−0.638509	+	0.638509i
$279$	−9.23159	−	2.47360i	−0.552681	−	0.148090i
$280$	−8.60778	−	13.9815i	−0.514413	−	0.835555i
$281$	−15.1948	+	15.1948i	−0.906448	+	0.906448i	−0.995984	−	0.0895355i	$-0.971462\pi$
$281$	−15.1948	+	15.1948i	−0.906448	+	0.906448i	0.0895355	+	0.995984i	$0.471462\pi$
$282$	1.47400	+	2.55304i	0.0877753	+	0.152031i
$283$	7.64747	−	13.2458i	0.454595	−	0.787382i	−0.544070	−	0.839040i	$-0.683117\pi$
$283$	7.64747	−	13.2458i	0.454595	−	0.787382i	0.998665	+	0.0516583i	$0.0164507\pi$
$284$	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	−0.603539	−	0.797334i	$-0.706243\pi$
$293$	5.44000	−	20.3023i	0.317808	−	1.18608i	0.921347	−	0.388742i	$-0.127090\pi$
$294$	10.4677	−	11.7229i	0.610487	−	0.683692i
$295$	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
$301$	3.62328	−	6.70636i	0.208842	−	0.386548i
$302$	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	$-0.422648\pi$
$307$	−12.7905	−	12.7905i	−0.729995	−	0.729995i	−0.970618	+	0.240624i	$0.922648\pi$
$308$	−36.5841	−	8.70292i	−2.08457	−	0.495895i
$309$	−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	$-0.687028\pi$
$311$	−19.5517			−1.10868			−0.554338	+	0.832292i	$0.687028\pi$
$312$	−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
$315$	−6.73296	+	2.00958i	−0.379359	+	0.113227i
$316$	−11.7579	+	6.78845i	−0.661435	+	0.381880i
$317$	17.8861	+	17.8861i	1.00458	+	1.00458i	0.999989	+	0.00459262i	$0.00146188\pi$
$317$	17.8861	+	17.8861i	1.00458	+	1.00458i	0.00459262	+	0.999989i	$0.498538\pi$
$318$	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
$322$	−47.3382	+	14.1290i	−2.63806	+	0.787378i
$323$	−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
$329$	3.37967	+	0.803983i	0.186327	+	0.0443250i
$330$	19.7076	+	19.7076i	1.08487	+	1.08487i
$331$	−3.51837	+	13.1307i	−0.193387	+	0.721731i	0.799291	+	0.600944i	$0.205208\pi$
$331$	−3.51837	+	13.1307i	−0.193387	+	0.721731i	−0.992678	+	0.120787i	$0.961458\pi$
$332$	−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
$336$	1.05043	−	1.94424i	0.0573055	−	0.106067i
$337$		−	1.75678i		−	0.0956980i	−0.998855	−	0.0478490i	$-0.984763\pi$
$337$		−	1.75678i		−	0.0956980i	0.998855	−	0.0478490i	$-0.0152366\pi$
$338$	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
$343$	−1.56784	−	18.4538i	−0.0846554	−	0.996410i
$344$	−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	0.974281	−	0.225338i	$-0.0723487\pi$
$347$	5.43920	+	9.42098i	0.291992	+	0.505744i	−0.682289	+	0.731083i	$0.739015\pi$
$348$	15.8236	−	27.4072i	0.848233	−	1.46918i
$349$	−11.9450	+	3.20064i	−0.639399	+	0.171326i	−0.563931	−	0.825822i	$-0.690712\pi$
$349$	−11.9450	+	3.20064i	−0.639399	+	0.171326i	−0.0754676	+	0.997148i	$0.524045\pi$
$350$	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	0.974598	+	0.223962i	$0.0718992\pi$
$353$	4.55715	+	17.0075i	0.242552	+	0.905218i	−0.732045	+	0.681256i	$0.761434\pi$
$354$	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
$357$	−6.06786	−	9.85594i	−0.321145	−	0.521631i
$358$	−25.6277	−	6.86691i	−1.35446	−	0.362927i
$359$	11.4993	−	11.4993i	0.606911	−	0.606911i	−0.335227	−	0.942137i	$-0.608813\pi$
$359$	11.4993	−	11.4993i	0.606911	−	0.606911i	0.942137	+	0.335227i	$0.108813\pi$
$360$	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
$364$	17.2902	+	23.2908i	0.906253	+	1.22077i
$365$	−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	$-0.444850\pi$
$367$	−11.3884	−	6.57510i	−0.594470	−	0.343217i	−0.766863	+	0.641811i	$0.778183\pi$
$368$	−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
$371$	4.39522	−	2.70594i	0.228188	−	0.140485i
$372$	20.5495	−	20.5495i	1.06544	−	1.06544i
$373$	4.81532	+	8.34037i	0.249328	+	0.431848i	0.963339	−	0.268286i	$-0.0864571\pi$
$373$	4.81532	+	8.34037i	0.249328	+	0.431848i	−0.714012	+	0.700134i	$0.753124\pi$
$374$	−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	−0.960037	−	0.279872i	$-0.909708\pi$
$379$	−32.1516	+	8.61500i	−1.65152	+	0.442523i	−0.691481	+	0.722395i	$0.743041\pi$
$380$	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	$-0.448141\pi$
$383$	−3.73221	−	1.00004i	−0.190707	−	0.0510998i	−0.352908	+	0.935658i	$0.614807\pi$
$384$	−4.18317	+	15.6118i	−0.213471	+	0.796686i
$385$	32.8304	−	0.927780i	1.67319	−	0.0472840i
$386$	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	$0.103332\pi$
$389$			12.5816i			0.637911i	−0.947770	+	0.318955i	$0.896668\pi$
$390$	−1.86251	−	21.4176i	−0.0943121	−	1.08452i
$391$			36.3815i			1.83989i
$392$	5.11901	+	15.5353i	0.258549	+	0.784651i
$393$	−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	0.547882	+	0.836556i	$0.315434\pi$
$397$	−6.87160	+	25.6452i	−0.344876	+	1.28709i	−0.892757	+	0.450538i	$0.851232\pi$
$398$	−34.4079	−	34.4079i	−1.72471	−	1.72471i
$399$	0.518266	+	0.123289i	0.0259457	+	0.00617218i
$400$	1.48504	+	0.857390i	0.0742521	+	0.0428695i
$401$	−3.89519	−	14.5370i	−0.194517	−	0.725946i	−0.992391	−	0.123123i	$-0.960709\pi$
$401$	−3.89519	−	14.5370i	−0.194517	−	0.725946i	0.797875	−	0.602823i	$-0.205957\pi$
$402$	−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
$406$	−17.6814	−	59.2403i	−0.877514	−	2.94005i
$407$	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	$-0.206139\pi$
$409$	23.9970	+	6.42996i	1.18657	+	0.317941i	0.389042	+	0.921220i	$0.372806\pi$
$410$	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
$413$	−5.14793	−	17.2478i	−0.253313	−	0.848709i
$414$	−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	$-0.189021\pi$
$419$	15.5289	+	8.96562i	0.758637	+	0.437999i	−0.0701691	+	0.997535i	$0.522354\pi$
$420$	4.94470	−	20.7858i	0.241277	−	1.01424i
$421$	0.833811	+	0.833811i	0.0406375	+	0.0406375i	0.727134	−	0.686496i	$-0.240852\pi$
$421$	0.833811	+	0.833811i	0.0406375	+	0.0406375i	−0.686496	+	0.727134i	$0.740852\pi$
$422$	−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
$427$	3.09758	−	5.73334i	0.149903	−	0.277456i
$428$			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	0.0802899	−	0.996772i	$-0.474415\pi$
$431$	13.4572	−	3.60584i	0.648209	−	0.173687i	0.567919	+	0.823085i	$0.307749\pi$
$432$	0.723346	+	0.417624i	0.0348020	+	0.0200929i
$433$	−0.380141	−	0.658423i	−0.0182684	−	0.0316418i	0.856747	−	0.515737i	$-0.172482\pi$
$433$	−0.380141	−	0.658423i	−0.0182684	−	0.0316418i	−0.875015	+	0.484096i	$0.839149\pi$
$434$	−1.60371	−	56.7488i	−0.0769806	−	2.72403i
$435$	−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	−0.180518	−	0.983572i	$-0.557777\pi$
$439$	15.9560	−	27.6366i	0.761539	−	1.31902i	0.942057	−	0.335453i	$-0.108889\pi$
$440$	−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
$448$	18.0769	+	29.3620i	0.854052	+	1.38723i
$449$	37.3413	+	10.0056i	1.76224	+	0.472192i	0.987169	−	0.159677i	$-0.0510451\pi$
$449$	37.3413	+	10.0056i	1.76224	+	0.472192i	0.775075	+	0.631869i	$0.217712\pi$
$450$	−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
$455$	−19.8512	−	15.7402i	−0.930639	−	0.737912i
$456$	−0.470502			−0.0220333
$457$	−11.2913	+	3.02549i	−0.528183	+	0.141526i	−0.513049	−	0.858359i	$-0.671484\pi$
$457$	−11.2913	+	3.02549i	−0.528183	+	0.141526i	−0.0151341	+	0.999885i	$0.504818\pi$
$458$	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	$-0.122905\pi$
$461$	33.0727	+	8.86180i	1.54035	+	0.412735i	0.613971	+	0.789329i	$0.289571\pi$
$462$	−14.5566	−	23.6441i	−0.677235	−	1.10002i
$463$	−18.1263	+	18.1263i	−0.842399	+	0.842399i	−0.989170	−	0.146772i	$-0.953112\pi$
$463$	−18.1263	+	18.1263i	−0.842399	+	0.842399i	0.146772	+	0.989170i	$0.453112\pi$
$464$	−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	$-0.656824\pi$
$467$	−20.4427			−0.945975			−0.472988	+	0.881069i	$0.656824\pi$
$468$	−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
$476$	35.1800	−	0.994179i	1.61247	−	0.0455681i
$477$	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	$-0.670422\pi$
$479$	−11.4241	+	3.06108i	−0.521980	+	0.139864i	−0.0117979	+	0.999930i	$0.503755\pi$
$480$		−	17.3917i		−	0.793818i
$481$	−16.8394	−	2.97832i	−0.767810	−	0.135800i
$482$			68.4591i			3.11823i
$483$	−19.3589	−	10.4591i	−0.880859	−	0.475906i
$484$	−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	−0.964822	−	0.262903i	$-0.915320\pi$
$487$	0.0483236	−	0.180346i	0.00218975	−	0.00817226i	0.967012	+	0.254731i	$0.0819868\pi$
$488$	−1.48961	+	5.55931i	−0.0674316	+	0.251658i
$489$	−13.4547	−	13.4547i	−0.608442	−	0.608442i
$490$	−22.8772	−	34.9101i	−1.03348	−	1.57708i
$491$	−2.43785	−	1.40749i	−0.110019	−	0.0635193i	0.443981	−	0.896036i	$-0.353566\pi$
$491$	−2.43785	−	1.40749i	−0.110019	−	0.0635193i	−0.554000	+	0.832517i	$0.686899\pi$
$492$	−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
$497$	4.21043	+	14.1067i	0.188864	+	0.632774i
$498$	−14.9088	+	8.60761i	−0.668080	+	0.385716i
$499$	1.80207	+	1.80207i	0.0806719	+	0.0806719i	0.746291	−	0.665619i	$-0.231833\pi$
$499$	1.80207	+	1.80207i	0.0806719	+	0.0806719i	−0.665619	+	0.746291i	$0.731833\pi$
$500$	−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	$-0.614550\pi$
$503$	6.33177	−	3.65565i	0.282320	−	0.162997i	0.634473	+	0.772945i	$0.281217\pi$
$504$	−5.92410	+	1.76816i	−0.263881	+	0.0787602i
$505$	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	0.937689	+	0.347477i	$0.112961\pi$
$509$	6.75398	+	25.2062i	0.299365	+	1.11724i	−0.638324	+	0.769768i	$0.720372\pi$
$510$	−22.5893	−	13.0419i	−1.00027	−	0.577506i
$511$	31.8518	+	7.57717i	1.40904	+	0.335194i
$512$	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
$518$	−24.7872	−	13.3919i	−1.08909	−	0.588406i
$519$		−	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	−0.999238	−	0.0390336i	$-0.987572\pi$
$523$	−35.0507	−	20.2365i	−1.53266	−	0.884882i	−0.533423	−	0.845849i	$-0.679095\pi$
$524$	−4.61311	−	7.99014i	−0.201525	−	0.349051i
$525$	0.153440	+	5.42961i	0.00669666	+	0.236968i
$526$	−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
$539$	−32.0327	−	6.67012i	−1.37975	−	0.287302i
$540$	7.80037	+	2.09010i	0.335674	+	0.0899437i
$541$	25.7367	−	25.7367i	1.10651	−	1.10651i	0.112900	−	0.993606i	$-0.463986\pi$
$541$	25.7367	−	25.7367i	1.10651	−	1.10651i	0.993606	−	0.112900i	$-0.0360139\pi$
$542$	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
$546$	−3.13289	+	21.1871i	−0.134075	+	0.906726i
$547$	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
$553$	−10.0595	+	6.19321i	−0.427775	+	0.263362i
$554$	−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	0.962237	−	0.272214i	$-0.0877559\pi$
$557$	−0.169733	−	0.633453i	−0.00719183	−	0.0268403i	−0.969429	+	0.245374i	$0.921089\pi$
$558$	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	−0.999375	−	0.0353593i	$-0.988742\pi$
$563$	−12.5830	−	21.7944i	−0.530309	−	0.918523i	0.469065	−	0.883164i	$-0.344591\pi$
$564$	−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
$567$	0.0747386	+	2.64470i	0.00313872	+	0.111067i
$568$	−6.50104	−	11.2601i	−0.272778	−	0.472465i
$569$	−3.46005	−	1.99766i	−0.145053	−	0.0837463i	0.425717	−	0.904856i	$-0.360022\pi$
$569$	−3.46005	−	1.99766i	−0.145053	−	0.0837463i	−0.570770	+	0.821110i	$0.693355\pi$
$570$	1.15968	−	0.310734i	0.0485735	−	0.0130152i
$571$		−	17.9370i		−	0.750640i	−0.926895	−	0.375320i	$-0.877533\pi$
$571$		−	17.9370i		−	0.750640i	0.926895	−	0.375320i	$-0.122467\pi$
$572$	48.1656	−	17.5023i	2.01390	−	0.731808i
$573$			13.3493i			0.557674i
$574$	−2.75301	−	1.48739i	−0.114909	−	0.0620823i
$575$	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	0.270389	−	0.962751i	$-0.412848\pi$
$577$	29.6210	−	29.6210i	1.23314	−	1.23314i	0.962751	−	0.270389i	$-0.0871524\pi$
$578$	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
$581$	−4.69497	+	19.7360i	−0.194780	+	0.818789i
$582$	−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	$-0.0978528\pi$
$587$	−0.571868	−	2.13424i	−0.0236035	−	0.0880895i	−0.976723	+	0.214505i	$0.931186\pi$
$588$	−9.58468	+	19.0053i	−0.395266	+	0.783766i
$589$	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	$-0.236230\pi$
$593$	1.48928	+	1.48928i	0.0611573	+	0.0611573i	−0.675867	+	0.737024i	$0.736230\pi$
$594$	9.08849	−	5.24724i	0.372905	−	0.215297i
$595$	−29.4538	+	8.79106i	−1.20749	+	0.360398i
$596$	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	$-0.398234\pi$
$601$	−8.59776	−	4.96392i	−0.350710	−	0.202482i	−0.664998	+	0.746845i	$0.731568\pi$
$602$	−3.96067	+	16.6493i	−0.161425	+	0.678575i
$603$	−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	$-0.452427\pi$
$607$	26.6015	−	15.3584i	1.07972	−	0.623378i	0.930821	+	0.365475i	$0.119093\pi$
$608$	−0.659297	+	1.14194i	−0.0267380	+	0.0463116i
$609$	13.0888	−	24.2262i	0.530386	−	0.981696i
$610$		−	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	−0.0633459	−	0.997992i	$-0.520177\pi$
$613$	9.42794	−	2.52621i	0.380791	−	0.102033i	0.444137	+	0.895959i	$0.353510\pi$
$614$	35.1709	+	20.3059i	1.41938	+	0.819480i
$615$	0.699491	+	1.21155i	0.0282062	+	0.0488546i
$616$	28.8863	−	0.816322i	1.16386	−	0.0328906i
$617$	6.69956	−	25.0031i	0.269714	−	1.00659i	−0.689587	−	0.724203i	$-0.742208\pi$
$617$	6.69956	−	25.0031i	0.269714	−	1.00659i	0.959301	−	0.282384i	$-0.0911253\pi$
$618$	4.24442	+	1.13729i	0.170736	+	0.0457485i
$619$	25.5525	+	25.5525i	1.02704	+	1.02704i	0.999624	+	0.0274172i	$0.00872826\pi$
$619$	25.5525	+	25.5525i	1.02704	+	1.02704i	0.0274172	+	0.999624i	$0.491272\pi$
$620$	−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
$630$	13.4338	−	8.27057i	0.535214	−	0.329507i
$631$	9.92759	+	2.66009i	0.395211	+	0.105897i	0.450951	−	0.892549i	$-0.351085\pi$
$631$	9.92759	+	2.66009i	0.395211	+	0.105897i	−0.0557396	+	0.998445i	$0.517752\pi$
$632$	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
$637$	15.6105	+	19.8321i	0.618511	+	0.785776i
$638$	−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	−0.918939	−	0.394401i	$-0.870952\pi$
$641$	−26.2509	+	15.1559i	−1.03685	+	0.598624i	−0.117908	+	0.993025i	$0.537619\pi$
$642$	−11.4301	+	11.4301i	−0.451111	+	0.451111i
$643$	35.0393	+	9.38876i	1.38182	+	0.370256i	0.871780	−	0.489897i	$-0.162966\pi$
$643$	35.0393	+	9.38876i	1.38182	+	0.370256i	0.510035	+	0.860153i	$0.329632\pi$
$644$	56.9759	−	35.0775i	2.24516	−	1.38225i
$645$	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	$-0.956923\pi$
$647$	−9.62979	+	16.6793i	−0.378586	+	0.655730i	0.612271	+	0.790648i	$0.290256\pi$
$648$	−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	−0.866637	−	0.498939i	$-0.833723\pi$
$653$	−0.0312823	+	0.0541825i	−0.00122417	+	0.00212033i	0.865413	+	0.501060i	$0.167056\pi$
$654$	−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
$658$	−7.79655	+	0.220329i	−0.303941	+	0.00858932i
$659$	3.09067	+	5.35320i	0.120395	+	0.208531i	0.919924	−	0.392098i	$-0.128250\pi$
$659$	3.09067	+	5.35320i	0.120395	+	0.208531i	−0.799528	+	0.600628i	$0.794917\pi$
$660$	−32.6900	−	18.8736i	−1.27246	−	0.734653i
$661$	−6.90812	+	1.85103i	−0.268695	+	0.0719965i	−0.390651	−	0.920539i	$-0.627750\pi$
$661$	−6.90812	+	1.85103i	−0.268695	+	0.0719965i	0.121956	+	0.992536i	$0.461083\pi$
$662$		−	30.5207i		−	1.18622i
$663$	14.2915	+	6.67333i	0.555035	+	0.259171i
$664$		−	17.9171i		−	0.695320i
$665$	0.672503	−	1.24474i	0.0260786	−	0.0482690i
$666$	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
$672$	−4.00980	+	16.8558i	−0.154681	+	0.650227i
$673$	−4.05354	−	2.34031i	−0.156253	−	0.0902125i	0.419835	−	0.907600i	$-0.362088\pi$
$673$	−4.05354	−	2.34031i	−0.156253	−	0.0902125i	−0.576088	+	0.817388i	$0.695421\pi$
$674$	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
$679$	−7.47834	+	2.23205i	−0.286992	+	0.0856583i
$680$	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	0.939148	−	0.343512i	$-0.111617\pi$
$683$	41.3109	+	11.0692i	1.58072	+	0.423552i	0.641570	+	0.767064i	$0.278283\pi$
$684$	−0.432938	−	0.432938i	−0.0165538	−	0.0165538i
$685$	26.8569	−	15.5058i	1.02615	−	0.592447i
$686$	14.1235	+	39.1090i	0.539236	+	1.49319i
$687$	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	0.996195	+	0.0871512i	$0.0277763\pi$
$691$	4.65384	+	17.3684i	0.177040	+	0.660724i	−0.819155	+	0.573573i	$0.805557\pi$
$692$	21.4507	+	12.3845i	0.815432	+	0.470790i
$693$	2.86207	−	12.0312i	0.108721	−	0.457027i
$694$	−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
$700$	−14.5315	−	7.85104i	−0.549241	−	0.296741i
$701$		−	34.0110i		−	1.28458i	−0.766462	−	0.642290i	$-0.777985\pi$
$701$		−	34.0110i		−	1.28458i	0.766462	−	0.642290i	$-0.222015\pi$
$702$	−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
$707$	−0.0473495	−	1.67551i	−0.00178076	−	0.0630139i
$708$	−5.35421	+	19.9822i	−0.201224	+	0.750977i
$709$	−2.70932	−	0.725960i	−0.101751	−	0.0272640i	0.207584	−	0.978217i	$-0.433440\pi$
$709$	−2.70932	−	0.725960i	−0.101751	−	0.0272640i	−0.309335	+	0.950953i	$0.600106\pi$
$710$	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	$-0.298256\pi$
$719$	−10.7719	−	18.6575i	−0.401725	−	0.695809i	−0.993934	+	0.109976i	$0.964923\pi$
$720$	1.56851	−	1.56851i	0.0584550	−	0.0584550i
$721$	4.40949	−	2.71472i	0.164218	−	0.101102i
$722$	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	$-0.344786\pi$
$727$	25.2656			0.937048			0.468524	+	0.883451i	$0.344786\pi$
$728$	−17.4664	−	13.8493i	−0.647348	−	0.513289i
$729$	−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	$-0.953603\pi$
$733$	−22.8545	+	22.8545i	−0.844152	+	0.844152i	0.145244	+	0.989396i	$0.453603\pi$
$734$	28.5184	+	7.64147i	1.05263	+	0.282052i
$735$	3.78973	−	18.1999i	0.139786	−	0.671313i
$736$	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	0.999781	−	0.0209450i	$-0.00666750\pi$
$739$	3.35655	+	12.5268i	0.123473	+	0.460806i	−0.876308	+	0.481751i	$0.840001\pi$
$740$	−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	0.360751	−	0.932662i	$-0.382520\pi$
$743$	31.0606	−	8.32266i	1.13950	−	0.305329i	0.778751	+	0.627333i	$0.215854\pi$
$744$	−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
$749$	0.538099	+	19.0412i	0.0196617	+	0.695749i
$750$	−8.78584	−	15.2175i	−0.320814	−	0.555666i
$751$	−13.1305	−	7.58091i	−0.479140	−	0.276631i	0.240918	−	0.970545i	$-0.422551\pi$
$751$	−13.1305	−	7.58091i	−0.479140	−	0.276631i	−0.720058	+	0.693914i	$0.755885\pi$
$752$	−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
$756$	−7.07814	−	3.82414i	−0.257429	−	0.139083i
$757$	−17.8529	+	30.9221i	−0.648875	+	1.12388i	0.334517	+	0.942390i	$0.391427\pi$
$757$	−17.8529	+	30.9221i	−0.648875	+	1.12388i	−0.983392	+	0.181494i	$0.941907\pi$
$758$	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	$-0.934562\pi$
$761$	−0.802382	+	2.99453i	−0.0290863	+	0.108552i	0.949857	+	0.312686i	$0.101229\pi$
$762$	−1.90708	−	1.90708i	−0.0690861	−	0.0690861i
$763$	−8.81653	−	2.09735i	−0.319180	−	0.0759291i
$764$	−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	0.944255	+	0.329216i	$0.106784\pi$
$769$	8.07284	+	30.1282i	0.291114	+	1.08645i	−0.653141	+	0.757237i	$0.726549\pi$
$770$	−70.6589	+	21.0895i	−2.54637	+	0.760013i
$771$	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	$-0.385920\pi$
$773$	5.18000	+	1.38798i	0.186312	+	0.0499220i	−0.164457	+	0.986384i	$0.552587\pi$
$774$	−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
$777$	−3.58890	−	12.0244i	−0.128751	−	0.431371i
$778$	−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
$784$	3.20466	+	4.89024i	0.114452	+	0.174652i
$785$	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	$-0.997301\pi$
$787$	−3.63938	+	13.5824i	−0.129730	+	0.484159i	0.870234	+	0.492638i	$0.163967\pi$
$788$	−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
$791$	1.76794	+	0.955176i	0.0628608	+	0.0339621i
$792$			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	$-0.00137589\pi$
$797$	14.0098	+	24.2657i	0.496252	+	0.859534i	−0.503739	+	0.863856i	$0.668043\pi$
$798$	−1.19559	+	0.0337870i	−0.0423233	+	0.00119605i
$799$	−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	−0.114441	−	0.993430i	$-0.536508\pi$
$809$	22.8429	−	39.5651i	0.803115	−	1.39104i	0.917556	−	0.397606i	$-0.130159\pi$
$810$	2.98130	+	5.16377i	0.104752	+	0.181436i
$811$	−7.85623	+	7.85623i	−0.275870	+	0.275870i	−0.831458	−	0.555588i	$-0.812493\pi$
$811$	−7.85623	+	7.85623i	−0.275870	+	0.275870i	0.555588	+	0.831458i	$0.312493\pi$
$812$	43.8969	+	71.3012i	1.54048	+	2.50218i
$813$	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
$819$	−7.65951	+	5.68612i	−0.267645	+	0.198689i
$820$	−4.25399			−0.148556
$821$	25.7120	−	6.88952i	0.897356	−	0.240446i	0.219476	−	0.975618i	$-0.429565\pi$
$821$	25.7120	−	6.88952i	0.897356	−	0.240446i	0.677881	+	0.735172i	$0.262899\pi$
$822$	−22.7048	−	13.1086i	−0.791919	−	0.457215i
$823$	38.5488	−	22.2561i	1.34373	−	0.775800i	0.356373	−	0.934344i	$-0.384013\pi$
$823$	38.5488	−	22.2561i	1.34373	−	0.775800i	0.987352	+	0.158543i	$0.0506798\pi$
$824$	−3.23382	+	3.23382i	−0.112655	+	0.112655i
$825$	9.26935	+	2.48371i	0.322717	+	0.0864719i
$826$	21.1867	+	34.4133i	0.737179	+	1.19739i
$827$	−10.7544	+	10.7544i	−0.373966	+	0.373966i	−0.868920	−	0.494953i	$-0.835185\pi$
$827$	−10.7544	+	10.7544i	−0.373966	+	0.373966i	0.494953	+	0.868920i	$0.335185\pi$
$828$	12.6444	+	21.9008i	0.439424	+	0.761105i
$829$	−22.8384	+	39.5572i	−0.793209	+	1.37388i	0.130761	+	0.991414i	$0.458258\pi$
$829$	−22.8384	+	39.5572i	−0.793209	+	1.37388i	−0.923970	+	0.382464i	$0.875076\pi$
$830$	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	$-0.928262\pi$
$839$	−0.546041	+	2.03785i	−0.0188514	+	0.0703546i	0.955859	+	0.293825i	$0.0949282\pi$
$840$	0.463806	+	16.4122i	0.0160028	+	0.566276i
$841$	−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
$847$	−13.6435	+	25.2529i	−0.468798	+	0.867701i
$848$	−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	0.995652	+	0.0931541i	$0.0296949\pi$
$853$	31.7998	+	31.7998i	1.08881	+	1.08881i	0.0931541	+	0.995652i	$0.470305\pi$
$854$	−3.38602	+	14.2337i	−0.115867	+	0.487066i
$855$	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	$-0.501712\pi$
$857$	−0.314991			−0.0107599			−0.00537994	+	0.999986i	$0.501712\pi$
$858$	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
$861$	−0.398605	−	1.33550i	−0.0135844	−	0.0455136i
$862$	−27.0887	+	15.6397i	−0.922646	+	0.532690i
$863$	−10.5474	−	10.5474i	−0.359038	−	0.359038i	0.504420	−	0.863458i	$-0.331706\pi$
$863$	−10.5474	−	10.5474i	−0.359038	−	0.359038i	−0.863458	+	0.504420i	$0.831706\pi$
$864$	−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
$868$	21.9905	+	73.6775i	0.746405	+	2.50078i
$869$	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
$875$	−20.1447	−	4.79218i	−0.681015	−	0.162005i
$876$	−26.6077	−	26.6077i	−0.898992	−	0.898992i
$877$	13.5647	−	50.6241i	0.458047	−	1.70945i	−0.220925	−	0.975291i	$-0.570908\pi$
$877$	13.5647	−	50.6241i	0.458047	−	1.70945i	0.678972	−	0.734164i	$-0.262426\pi$
$878$	−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	$-0.856290\pi$
$881$	−2.13878	+	3.70447i	−0.0720572	+	0.124807i	0.827746	+	0.561104i	$0.189623\pi$
$882$	−14.9267	+	4.91847i	−0.502608	+	0.165614i
$883$			33.8768i			1.14004i	0.821630	+	0.570022i	$0.193065\pi$
$883$			33.8768i			1.14004i	−0.821630	+	0.570022i	$0.806935\pi$
$884$	−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	$-0.309314\pi$
$887$	3.88879	+	2.24520i	0.130573	+	0.0753863i	−0.433291	+	0.901254i	$0.642648\pi$
$888$	5.54138	+	9.59795i	0.185956	+	0.322086i
$889$	−3.17695	+	0.0897799i	−0.106551	+	0.00301112i
$890$	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
$903$	−6.49103	+	3.99624i	−0.216008	+	0.132986i
$904$	−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	0.703640	−	0.710557i	$-0.251557\pi$
$907$	13.2542	+	7.65232i	0.440099	+	0.254091i	−0.263541	+	0.964648i	$0.584890\pi$
$908$	−55.6187	+	14.9030i	−1.84577	+	0.494573i
$909$	0.633535			0.0210130
$910$	52.1971	+	22.5999i	1.73032	+	0.749178i
$911$	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
$917$	−4.20861	−	6.83600i	−0.138981	−	0.225744i
$918$	−6.94495	+	6.94495i	−0.229218	+	0.229218i
$919$	−26.1402	−	45.2762i	−0.862287	−	1.49352i	−0.869716	−	0.493552i	$-0.835698\pi$
$919$	−26.1402	−	45.2762i	−0.862287	−	1.49352i	0.00742976	−	0.999972i	$-0.497635\pi$
$920$	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	$-0.521643\pi$
$929$	−19.0687	−	5.10945i	−0.625625	−	0.167636i	−0.557684	+	0.830054i	$0.688310\pi$
$930$	14.7491	−	55.0443i	0.483641	−	1.80497i
$931$	−0.938768	+	1.05134i	−0.0307669	+	0.0344562i
$932$	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	$0.824742\pi$
$938$	4.11812	−	7.62226i	0.134461	−	0.248875i
$939$	−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	$-0.626488\pi$
$941$	16.4141	−	16.4141i	0.535083	−	0.535083i	0.922081	+	0.386998i	$0.126488\pi$
$942$	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
$945$	6.83570	+	1.62613i	0.222365	+	0.0528981i
$946$	26.1845	+	15.1176i	0.851330	+	0.491516i
$947$	−11.1001	−	41.4261i	−0.360704	−	1.34617i	−0.873152	−	0.487449i	$-0.837928\pi$
$947$	−11.1001	−	41.4261i	−0.360704	−	1.34617i	0.512447	−	0.858719i	$-0.328739\pi$
$948$	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
$952$	−25.9154	+	7.73496i	−0.839924	+	0.250691i
$953$	−10.3745	+	5.98973i	−0.336064	+	0.194026i	−0.658530	−	0.752554i	$-0.728821\pi$
$953$	−10.3745	+	5.98973i	−0.336064	+	0.194026i	0.322466	+	0.946581i	$0.395488\pi$
$954$	−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
$959$	−29.6044	+	8.83599i	−0.955975	+	0.285329i
$960$	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
$966$	48.0606	+	11.4330i	1.54632	+	0.367852i
$967$	3.08553	+	3.08553i	0.0992241	+	0.0992241i	0.754976	−	0.655752i	$-0.227648\pi$
$967$	3.08553	+	3.08553i	0.0992241	+	0.0992241i	−0.655752	+	0.754976i	$0.727648\pi$
$968$	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	$-0.825967\pi$
$971$	−25.8972	+	14.9518i	−0.831081	+	0.479825i	0.0231414	+	0.999732i	$0.492633\pi$
$972$	1.52039	−	2.63339i	0.0487664	−	0.0844659i
$973$	8.43346	−	15.6096i	0.270364	−	0.500420i
$974$			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	−0.411858	−	0.911248i	$-0.635120\pi$
$977$	−9.78075	+	2.62074i	−0.312914	+	0.0838450i	0.0989443	+	0.995093i	$0.468453\pi$
$978$	36.9971	+	21.3603i	1.18304	+	0.683026i
$979$	−36.4051	−	63.0555i	−1.16351	−	2.01526i
$980$	42.1655	+	37.6507i	1.34693	+	1.20271i
$981$	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	$-0.207010\pi$
$983$	5.97019	+	5.97019i	0.190419	+	0.190419i	−0.605458	+	0.795877i	$0.707010\pi$
$984$	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	−0.0353002	+	0.999377i	$0.511239\pi$
$991$	−27.8012	+	48.1532i	−0.883136	+	1.52964i	−0.847836	+	0.530259i	$0.822095\pi$
$992$	31.2937	+	54.2023i	0.993576	+	1.72092i
$993$	9.61237	−	9.61237i	0.305039	−	0.305039i
$994$	−17.3283	−	28.1462i	−0.549621	−	0.892742i
$995$	−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	$-0.723237\pi$
$997$	−9.66852	+	5.58213i	−0.306205	+	0.176788i	0.339022	+	0.940778i	$0.389904\pi$
$998$	−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.c.202.1	✓	32
3.2	odd	2		819.2.fm.f.748.8		32
7.6	odd	2		273.2.by.d.202.1	yes	32
13.2	odd	12		273.2.by.d.223.1	yes	32
21.20	even	2		819.2.fm.e.748.8		32
39.2	even	12		819.2.fm.e.496.8		32
91.41	even	12	inner	273.2.by.c.223.1	yes	32
273.41	odd	12		819.2.fm.f.496.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.1	✓	32	1.1	even	1	trivial
273.2.by.c.223.1	yes	32	91.41	even	12	inner
273.2.by.d.202.1	yes	32	7.6	odd	2
273.2.by.d.223.1	yes	32	13.2	odd	12
819.2.fm.e.496.8		32	39.2	even	12
819.2.fm.e.748.8		32	21.20	even	2
819.2.fm.f.496.8		32	273.41	odd	12
819.2.fm.f.748.8		32	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16866 + 0.581092i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(2.16866 + 0.581092i) q^{6} +(2.25300 - 1.38707i) q^{7} +(-1.65230 + 1.65230i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(2.25300 - 1.38707i) 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} +(-2.64470 + 0.0747386i) 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} +(3.82414 - 7.07814i) 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} +(-1.62613 + 6.83570i) 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} +(5.69203 - 1.69889i) 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} +(3.15206 - 6.25016i) 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} +(-1.43078 + 6.01451i) 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} +(2.32774 + 1.25762i) 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} +(-0.445637 - 15.7693i) 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} +(-6.85087 + 4.21777i) 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} +(1.09457 + 9.47639i) 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} +(-3.20383 + 15.3861i) 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	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 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 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * 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 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more