LMFDB - Embedded newform 98.2.e.a.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(15,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("98.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.e (of order $7$, degree $6$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 15 x^{16} - 23 x^{15} + 72 x^{14} - 85 x^{13} + 432 x^{12} - 282 x^{11} + 1786 x^{10} + \cdots + 729 $ x^18 - 6x^17 + 15x^16 - 23x^15 + 72x^14 - 85x^13 + 432x^12 - 282x^11 + 1786x^10 - 1092x^9 + 7272x^8 - 10168x^7 + 25378x^6 - 43359x^5 + 57726x^4 - 56565x^3 + 38232x^2 - 6804*x + 729
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			57.3
Root			$3.47467 - 1.67331i$ of defining polynomial
Character	$\chi$	$=$	98.57
Dual form			98.2.e.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 + 0.781831i) q^{2} +(2.57370 - 1.23943i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-2.64206 + 1.27235i) q^{5} +(2.57370 + 1.23943i) q^{6} +(-2.49104 - 0.891482i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(3.21729 - 4.03436i) q^{9} +O(q^{10})$	\(q+(0.623490 + 0.781831i) q^{2} +(2.57370 - 1.23943i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-2.64206 + 1.27235i) q^{5} +(2.57370 + 1.23943i) q^{6} +(-2.49104 - 0.891482i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(3.21729 - 4.03436i) q^{9} +(-2.64206 - 1.27235i) q^{10} +(-2.98073 - 3.73772i) q^{11} +(0.635652 + 2.78497i) q^{12} +(3.28098 + 4.11422i) q^{13} +(-0.856146 - 2.50340i) q^{14} +(-5.22290 + 6.54930i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(0.472600 + 2.07060i) q^{17} +5.16013 q^{18} +3.82308 q^{19} +(-0.652536 - 2.85895i) q^{20} +(-7.51612 + 0.793054i) q^{21} +(1.06381 - 4.66086i) q^{22} +(0.351636 - 1.54062i) q^{23} +(-1.78106 + 2.23338i) q^{24} +(2.24417 - 2.81410i) q^{25} +(-1.17097 + 5.13035i) q^{26} +(1.37309 - 6.01592i) q^{27} +(1.42344 - 2.23021i) q^{28} +(-0.132859 - 0.582092i) q^{29} -8.37687 q^{30} -0.0848956 q^{31} +(-0.222521 - 0.974928i) q^{32} +(-12.3042 - 5.92537i) q^{33} +(-1.32420 + 1.66049i) q^{34} +(7.71575 - 0.814118i) q^{35} +(3.21729 + 4.03436i) q^{36} +(-1.14296 - 5.00766i) q^{37} +(2.38365 + 2.98900i) q^{38} +(13.5436 + 6.52224i) q^{39} +(1.82836 - 2.29270i) q^{40} +(-6.48181 + 3.12147i) q^{41} +(-5.30626 - 5.38188i) q^{42} +(3.87857 + 1.86782i) q^{43} +(4.30728 - 2.07428i) q^{44} +(-3.36717 + 14.7525i) q^{45} +(1.42374 - 0.685639i) q^{46} +(0.628687 + 0.788349i) q^{47} -2.85659 q^{48} +(5.41052 + 4.44143i) q^{49} +3.59937 q^{50} +(3.78269 + 4.74335i) q^{51} +(-4.74116 + 2.28322i) q^{52} +(-0.641220 + 2.80937i) q^{53} +(5.55954 - 2.67733i) q^{54} +(12.6310 + 6.08275i) q^{55} +(2.63115 - 0.277622i) q^{56} +(9.83947 - 4.73844i) q^{57} +(0.372262 - 0.466801i) q^{58} +(-1.82448 - 0.878624i) q^{59} +(-5.22290 - 6.54930i) q^{60} +(-0.826391 - 3.62066i) q^{61} +(-0.0529315 - 0.0663741i) q^{62} +(-11.6109 + 7.18157i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-13.9033 - 6.69548i) q^{65} +(-3.03888 - 13.3142i) q^{66} -11.9726 q^{67} -2.12385 q^{68} +(-1.00448 - 4.40092i) q^{69} +(5.44720 + 5.52482i) q^{70} +(0.746863 - 3.27222i) q^{71} +(-1.14824 + 5.03076i) q^{72} +(4.76836 - 5.97933i) q^{73} +(3.20252 - 4.01583i) q^{74} +(2.28795 - 10.0242i) q^{75} +(-0.850715 + 3.72722i) q^{76} +(4.09300 + 11.9681i) q^{77} +(3.34499 + 14.6553i) q^{78} +10.8827 q^{79} +2.93247 q^{80} +(-0.477659 - 2.09276i) q^{81} +(-6.48181 - 3.12147i) q^{82} +(6.72146 - 8.42844i) q^{83} +(0.899323 - 7.50414i) q^{84} +(-3.88316 - 4.86933i) q^{85} +(0.957927 + 4.19695i) q^{86} +(-1.06340 - 1.33346i) q^{87} +(4.30728 + 2.07428i) q^{88} +(-7.48671 + 9.38804i) q^{89} +(-13.6334 + 6.56550i) q^{90} +(-4.50529 - 13.1736i) q^{91} +(1.42374 + 0.685639i) q^{92} +(-0.218496 + 0.105222i) q^{93} +(-0.224376 + 0.983055i) q^{94} +(-10.1008 + 4.86429i) q^{95} +(-1.78106 - 2.23338i) q^{96} +10.5542 q^{97} +(-0.0990455 + 6.99930i) q^{98} -24.6692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{5} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^5 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{5} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 4 q^{12} - 7 q^{14} - 9 q^{15} - 3 q^{16} - 11 q^{17} + 24 q^{18} + 36 q^{19} + q^{20} - 21 q^{21} - q^{22} + 5 q^{23} - 4 q^{24} - 23 q^{25} - 7 q^{26} - 12 q^{27} - 13 q^{29} - 16 q^{30} - 4 q^{31} - 3 q^{32} - 34 q^{33} - 11 q^{34} - 7 q^{35} + 10 q^{36} + 33 q^{37} + 15 q^{38} + 21 q^{39} + q^{40} - 28 q^{41} + 35 q^{42} - 20 q^{43} + 6 q^{44} + 20 q^{45} + 5 q^{46} + 36 q^{47} + 10 q^{48} + 49 q^{49} + 26 q^{50} - 20 q^{51} + 48 q^{53} + 2 q^{54} + 47 q^{55} + 7 q^{56} - 37 q^{57} + 36 q^{58} - 25 q^{59} - 9 q^{60} + q^{61} - 11 q^{62} - 35 q^{63} - 3 q^{64} - 56 q^{65} - 27 q^{66} + 34 q^{67} + 38 q^{68} + 23 q^{69} - 14 q^{70} - 6 q^{71} - 11 q^{72} - 39 q^{73} - 23 q^{74} - 47 q^{75} - 20 q^{76} - 28 q^{77} - 14 q^{78} - 2 q^{79} + 8 q^{80} - 34 q^{81} - 28 q^{82} + 35 q^{83} - 7 q^{84} + 33 q^{85} + 36 q^{86} + 48 q^{87} + 6 q^{88} - 6 q^{89} - 57 q^{90} - 35 q^{91} + 5 q^{92} + 36 q^{93} - 13 q^{94} - 17 q^{95} - 4 q^{96} + 56 q^{97} + 28 q^{98} + 106 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^5 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 4 * q^12 - 7 * q^14 - 9 * q^15 - 3 * q^16 - 11 * q^17 + 24 * q^18 + 36 * q^19 + q^20 - 21 * q^21 - q^22 + 5 * q^23 - 4 * q^24 - 23 * q^25 - 7 * q^26 - 12 * q^27 - 13 * q^29 - 16 * q^30 - 4 * q^31 - 3 * q^32 - 34 * q^33 - 11 * q^34 - 7 * q^35 + 10 * q^36 + 33 * q^37 + 15 * q^38 + 21 * q^39 + q^40 - 28 * q^41 + 35 * q^42 - 20 * q^43 + 6 * q^44 + 20 * q^45 + 5 * q^46 + 36 * q^47 + 10 * q^48 + 49 * q^49 + 26 * q^50 - 20 * q^51 + 48 * q^53 + 2 * q^54 + 47 * q^55 + 7 * q^56 - 37 * q^57 + 36 * q^58 - 25 * q^59 - 9 * q^60 + q^61 - 11 * q^62 - 35 * q^63 - 3 * q^64 - 56 * q^65 - 27 * q^66 + 34 * q^67 + 38 * q^68 + 23 * q^69 - 14 * q^70 - 6 * q^71 - 11 * q^72 - 39 * q^73 - 23 * q^74 - 47 * q^75 - 20 * q^76 - 28 * q^77 - 14 * q^78 - 2 * q^79 + 8 * q^80 - 34 * q^81 - 28 * q^82 + 35 * q^83 - 7 * q^84 + 33 * q^85 + 36 * q^86 + 48 * q^87 + 6 * q^88 - 6 * q^89 - 57 * q^90 - 35 * q^91 + 5 * q^92 + 36 * q^93 - 13 * q^94 - 17 * q^95 - 4 * q^96 + 56 * q^97 + 28 * q^98 + 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$3$	2.57370	−	1.23943i	1.48593	−	0.715585i	0.497527	−	0.867449i	$-0.334242\pi$
$3$	2.57370	−	1.23943i	1.48593	−	0.715585i	0.988401	+	0.151863i	$0.0485274\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	−2.64206	+	1.27235i	−1.18157	+	0.569012i	−0.918367	−	0.395729i	$-0.870492\pi$
$5$	−2.64206	+	1.27235i	−1.18157	+	0.569012i	−0.263199	+	0.964742i	$0.584778\pi$
$6$	2.57370	+	1.23943i	1.05071	+	0.505995i
$7$	−2.49104	−	0.891482i	−0.941523	−	0.336949i
$7$	−2.49104	−	0.891482i	−0.941523	−	0.336949i
$8$	−0.900969	+	0.433884i	−0.318541	+	0.153401i
$9$	3.21729	−	4.03436i	1.07243	−	1.34479i
$10$	−2.64206	−	1.27235i	−0.835494	−	0.402353i
$11$	−2.98073	−	3.73772i	−0.898724	−	1.12696i	−0.991348	−	0.131263i	$-0.958097\pi$
$11$	−2.98073	−	3.73772i	−0.898724	−	1.12696i	0.0926234	−	0.995701i	$-0.470475\pi$
$12$	0.635652	+	2.78497i	0.183497	+	0.803953i
$13$	3.28098	+	4.11422i	0.909981	+	1.14108i	0.989541	+	0.144250i	$0.0460771\pi$
$13$	3.28098	+	4.11422i	0.909981	+	1.14108i	−0.0795598	+	0.996830i	$0.525351\pi$
$14$	−0.856146	−	2.50340i	−0.228815	−	0.669062i
$15$	−5.22290	+	6.54930i	−1.34855	+	1.69102i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	0.472600	+	2.07060i	0.114622	+	0.502193i	0.999349	+	0.0360828i	$0.0114880\pi$
$17$	0.472600	+	2.07060i	0.114622	+	0.502193i	−0.884726	+	0.466111i	$0.845655\pi$
$18$	5.16013			1.21626
$19$	3.82308			0.877074			0.438537	−	0.898713i	$-0.355497\pi$
$19$	3.82308			0.877074			0.438537	+	0.898713i	$0.355497\pi$
$20$	−0.652536	−	2.85895i	−0.145911	−	0.639280i
$21$	−7.51612	+	0.793054i	−1.64015	+	0.173059i
$22$	1.06381	−	4.66086i	0.226805	−	0.993698i
$23$	0.351636	−	1.54062i	0.0733211	−	0.321241i	−0.924945	−	0.380101i	$-0.875889\pi$
$23$	0.351636	−	1.54062i	0.0733211	−	0.321241i	0.998266	+	0.0588599i	$0.0187465\pi$
$24$	−1.78106	+	2.23338i	−0.363557	+	0.455886i
$25$	2.24417	−	2.81410i	0.448834	−	0.562821i
$26$	−1.17097	+	5.13035i	−0.229646	+	1.00615i
$27$	1.37309	−	6.01592i	0.264252	−	1.15776i
$28$	1.42344	−	2.23021i	0.269005	−	0.421469i
$29$	−0.132859	−	0.582092i	−0.0246712	−	0.108092i	0.961093	−	0.276225i	$-0.0890834\pi$
$29$	−0.132859	−	0.582092i	−0.0246712	−	0.108092i	−0.985764	+	0.168133i	$0.946226\pi$
$30$	−8.37687			−1.52940
$31$	−0.0848956			−0.0152477			−0.00762385	−	0.999971i	$-0.502427\pi$
$31$	−0.0848956			−0.0152477			−0.00762385	+	0.999971i	$0.502427\pi$
$32$	−0.222521	−	0.974928i	−0.0393365	−	0.172345i
$33$	−12.3042	−	5.92537i	−2.14188	−	1.03147i
$34$	−1.32420	+	1.66049i	−0.227098	+	0.284772i
$35$	7.71575	−	0.814118i	1.30420	−	0.137611i
$36$	3.21729	+	4.03436i	0.536215	+	0.672393i
$37$	−1.14296	−	5.00766i	−0.187902	−	0.823254i	−0.977720	−	0.209912i	$-0.932682\pi$
$37$	−1.14296	−	5.00766i	−0.187902	−	0.823254i	0.789818	−	0.613341i	$-0.210175\pi$
$38$	2.38365	+	2.98900i	0.386679	+	0.484880i
$39$	13.5436	+	6.52224i	2.16871	+	1.04439i
$40$	1.82836	−	2.29270i	0.289090	−	0.362507i
$41$	−6.48181	+	3.12147i	−1.01229	+	0.487492i	−0.865091	−	0.501615i	$-0.832739\pi$
$41$	−6.48181	+	3.12147i	−1.01229	+	0.487492i	−0.147197	+	0.989107i	$0.547025\pi$
$42$	−5.30626	−	5.38188i	−0.818773	−	0.830441i
$43$	3.87857	+	1.86782i	0.591476	+	0.284840i	0.705582	−	0.708629i	$-0.250686\pi$
$43$	3.87857	+	1.86782i	0.591476	+	0.284840i	−0.114105	+	0.993469i	$0.536400\pi$
$44$	4.30728	−	2.07428i	0.649347	−	0.312709i
$45$	−3.36717	+	14.7525i	−0.501948	+	2.19918i
$46$	1.42374	−	0.685639i	0.209920	−	0.101092i
$47$	0.628687	+	0.788349i	0.0917035	+	0.114993i	0.825566	−	0.564305i	$-0.190856\pi$
$47$	0.628687	+	0.788349i	0.0917035	+	0.114993i	−0.733863	+	0.679298i	$0.762284\pi$
$48$	−2.85659			−0.412314
$49$	5.41052	+	4.44143i	0.772931	+	0.634490i
$50$	3.59937			0.509028
$51$	3.78269	+	4.74335i	0.529683	+	0.664201i
$52$	−4.74116	+	2.28322i	−0.657481	+	0.316626i
$53$	−0.641220	+	2.80937i	−0.0880783	+	0.385896i	−0.999683	−	0.0251714i	$-0.991987\pi$
$53$	−0.641220	+	2.80937i	−0.0880783	+	0.385896i	0.911605	+	0.411068i	$0.134844\pi$
$54$	5.55954	−	2.67733i	0.756558	−	0.364339i
$55$	12.6310	+	6.08275i	1.70316	+	0.820198i
$56$	2.63115	−	0.277622i	0.351602	−	0.0370988i
$57$	9.83947	−	4.73844i	1.30327	−	0.627621i
$58$	0.372262	−	0.466801i	0.0488804	−	0.0612940i
$59$	−1.82448	−	0.878624i	−0.237527	−	0.114387i	0.311334	−	0.950301i	$-0.399224\pi$
$59$	−1.82448	−	0.878624i	−0.237527	−	0.114387i	−0.548861	+	0.835913i	$0.684938\pi$
$60$	−5.22290	−	6.54930i	−0.674273	−	0.845512i
$61$	−0.826391	−	3.62066i	−0.105809	−	0.463578i	−0.999878	−	0.0156483i	$-0.995019\pi$
$61$	−0.826391	−	3.62066i	−0.105809	−	0.463578i	0.894069	−	0.447929i	$-0.147838\pi$
$62$	−0.0529315	−	0.0663741i	−0.00672231	−	0.00842951i
$63$	−11.6109	+	7.18157i	−1.46284	+	0.904792i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−13.9033	−	6.69548i	−1.72449	−	0.830472i
$66$	−3.03888	−	13.3142i	−0.374060	−	1.63886i
$67$	−11.9726			−1.46269			−0.731344	−	0.682008i	$-0.761107\pi$
$67$	−11.9726			−1.46269			−0.731344	+	0.682008i	$0.761107\pi$
$68$	−2.12385			−0.257554
$69$	−1.00448	−	4.40092i	−0.120925	−	0.529808i
$70$	5.44720	+	5.52482i	0.651064	+	0.660343i
$71$	0.746863	−	3.27222i	0.0886363	−	0.388341i	−0.911078	−	0.412234i	$-0.864749\pi$
$71$	0.746863	−	3.27222i	0.0886363	−	0.388341i	0.999715	+	0.0238925i	$0.00760593\pi$
$72$	−1.14824	+	5.03076i	−0.135321	+	0.592881i
$73$	4.76836	−	5.97933i	0.558094	−	0.699828i	−0.420110	−	0.907473i	$-0.638009\pi$
$73$	4.76836	−	5.97933i	0.558094	−	0.699828i	0.978204	+	0.207645i	$0.0665800\pi$
$74$	3.20252	−	4.01583i	0.372285	−	0.466831i
$75$	2.28795	−	10.0242i	0.264190	−	1.15749i
$76$	−0.850715	+	3.72722i	−0.0975837	+	0.427542i
$77$	4.09300	+	11.9681i	0.466440	+	1.36389i
$78$	3.34499	+	14.6553i	0.378745	+	1.65939i
$79$	10.8827			1.22440			0.612199	−	0.790704i	$-0.290285\pi$
$79$	10.8827			1.22440			0.612199	+	0.790704i	$0.290285\pi$
$80$	2.93247			0.327860
$81$	−0.477659	−	2.09276i	−0.0530732	−	0.232529i
$82$	−6.48181	−	3.12147i	−0.715796	−	0.344709i
$83$	6.72146	−	8.42844i	0.737776	−	0.925141i	−0.261421	−	0.965225i	$-0.584191\pi$
$83$	6.72146	−	8.42844i	0.737776	−	0.925141i	0.999196	+	0.0400836i	$0.0127624\pi$
$84$	0.899323	−	7.50414i	0.0981242	−	0.818769i
$85$	−3.88316	−	4.86933i	−0.421188	−	0.528153i
$86$	0.957927	+	4.19695i	0.103296	+	0.452569i
$87$	−1.06340	−	1.33346i	−0.114009	−	0.142962i
$88$	4.30728	+	2.07428i	0.459158	+	0.221119i
$89$	−7.48671	+	9.38804i	−0.793590	+	0.995130i	0.206272	+	0.978495i	$0.433867\pi$
$89$	−7.48671	+	9.38804i	−0.793590	+	0.995130i	−0.999862	+	0.0166355i	$0.994705\pi$
$90$	−13.6334	+	6.56550i	−1.43709	+	0.692064i
$91$	−4.50529	−	13.1736i	−0.472283	−	1.38097i
$92$	1.42374	+	0.685639i	0.148436	+	0.0714828i
$93$	−0.218496	+	0.105222i	−0.0226570	+	0.0109110i
$94$	−0.224376	+	0.983055i	−0.0231426	+	0.101394i
$95$	−10.1008	+	4.86429i	−1.03632	+	0.499066i
$96$	−1.78106	−	2.23338i	−0.181778	−	0.227943i
$97$	10.5542			1.07162			0.535809	−	0.844339i	$-0.320007\pi$
$97$	10.5542			1.07162			0.535809	+	0.844339i	$0.320007\pi$
$98$	−0.0990455	+	6.99930i	−0.0100051	+	0.707036i
$99$	−24.6692			−2.47934
$100$	2.24417	+	2.81410i	0.224417	+	0.281410i
$101$	−7.65882	+	3.68829i	−0.762081	+	0.366999i	−0.774211	−	0.632928i	$-0.781853\pi$
$101$	−7.65882	+	3.68829i	−0.762081	+	0.366999i	0.0121301	+	0.999926i	$0.496139\pi$
$102$	−1.35003	+	5.91486i	−0.133673	+	0.585658i
$103$	−4.79203	+	2.30772i	−0.472173	+	0.227387i	−0.654810	−	0.755794i	$-0.727251\pi$
$103$	−4.79203	+	2.30772i	−0.472173	+	0.227387i	0.182636	+	0.983181i	$0.441537\pi$
$104$	−4.74116	−	2.28322i	−0.464909	−	0.223888i
$105$	18.8490	−	11.6584i	1.83948	−	1.13775i
$106$	−2.59625	+	1.25029i	−0.252170	+	0.121439i
$107$	0.992337	−	1.24435i	0.0959328	−	0.120296i	−0.731548	−	0.681790i	$-0.761202\pi$
$107$	0.992337	−	1.24435i	0.0959328	−	0.120296i	0.827481	+	0.561494i	$0.189773\pi$
$108$	5.55954	+	2.67733i	0.534967	+	0.257627i
$109$	−8.60783	−	10.7939i	−0.824481	−	1.03387i	−0.998790	−	0.0491753i	$-0.984341\pi$
$109$	−8.60783	−	10.7939i	−0.824481	−	1.03387i	0.174309	−	0.984691i	$-0.444231\pi$
$110$	3.11959	+	13.6678i	0.297441	+	1.30318i
$111$	−9.14829	−	11.4716i	−0.868317	−	1.08884i
$112$	1.85755	+	1.88402i	0.175522	+	0.178023i
$113$	−3.65557	+	4.58394i	−0.343887	+	0.431221i	−0.923457	−	0.383702i	$-0.874649\pi$
$113$	−3.65557	+	4.58394i	−0.343887	+	0.431221i	0.579570	+	0.814922i	$0.303221\pi$
$114$	9.83947	+	4.73844i	0.921550	+	0.443795i
$115$	1.03116	+	4.51781i	0.0961562	+	0.421288i
$116$	0.597061			0.0554358
$117$	27.1541			2.51040
$118$	−0.450609	−	1.97425i	−0.0414820	−	0.181744i
$119$	0.668636	−	5.57925i	0.0612938	−	0.511449i
$120$	1.86403	−	8.16685i	0.170162	−	0.745528i
$121$	−2.63805	+	11.5581i	−0.239823	+	1.05073i
$122$	2.31550	−	2.90354i	0.209635	−	0.262874i
$123$	−12.8134	+	16.0675i	−1.15535	+	1.44876i
$124$	0.0188910	−	0.0827671i	0.00169647	−	0.00743270i
$125$	0.913959	−	4.00432i	0.0817470	−	0.358157i
$126$	−12.8541	−	4.60017i	−1.14513	−	0.409816i
$127$	−2.95291	−	12.9375i	−0.262028	−	1.14802i	−0.919047	−	0.394147i	$-0.871040\pi$
$127$	−2.95291	−	12.9375i	−0.262028	−	1.14802i	0.657019	−	0.753874i	$-0.271817\pi$
$128$	1.00000			0.0883883
$129$	12.2973			1.08272
$130$	−3.43383	−	15.0446i	−0.301167	−	1.31950i
$131$	15.5667	+	7.49652i	1.36007	+	0.654974i	0.964652	−	0.263528i	$-0.0848862\pi$
$131$	15.5667	+	7.49652i	1.36007	+	0.654974i	0.395416	+	0.918502i	$0.370600\pi$
$132$	8.51474	−	10.6771i	0.741113	−	0.929326i
$133$	−9.52342	−	3.40821i	−0.825785	−	0.295529i
$134$	−7.46481	−	9.36057i	−0.644861	−	0.808630i
$135$	4.02655	+	17.6415i	0.346551	+	1.51834i
$136$	−1.32420	−	1.66049i	−0.113549	−	0.142386i
$137$	2.13510	+	1.02821i	0.182414	+	0.0878458i	0.522862	−	0.852418i	$-0.324864\pi$
$137$	2.13510	+	1.02821i	0.182414	+	0.0878458i	−0.340448	+	0.940263i	$0.610579\pi$
$138$	2.81449	−	3.52926i	0.239585	−	0.300431i
$139$	−14.0637	+	6.77272i	−1.19287	+	0.574455i	−0.921635	−	0.388059i	$-0.873146\pi$
$139$	−14.0637	+	6.77272i	−1.19287	+	0.574455i	−0.271233	+	0.962514i	$0.587431\pi$
$140$	−0.923210	+	7.70346i	−0.0780255	+	0.651061i
$141$	2.59516	+	1.24976i	0.218552	+	0.105249i
$142$	3.02399	−	1.45627i	0.253767	−	0.122208i
$143$	5.59808	−	24.5268i	0.468135	−	2.05103i
$144$	−4.64912	+	2.23890i	−0.387427	+	0.186575i
$145$	1.09165	+	1.36888i	0.0906562	+	0.113679i
$146$	7.64785			0.632941
$147$	19.4299	+	4.72496i	1.60255	+	0.389708i
$148$	5.13644			0.422213
$149$	−7.73206	−	9.69570i	−0.633435	−	0.794302i	0.356730	−	0.934208i	$-0.383892\pi$
$149$	−7.73206	−	9.69570i	−0.633435	−	0.794302i	−0.990165	+	0.139905i	$0.955320\pi$
$150$	9.26372	−	4.46117i	0.756379	−	0.364253i
$151$	−5.04679	+	22.1114i	−0.410702	+	1.79940i	0.170178	+	0.985413i	$0.445566\pi$
$151$	−5.04679	+	22.1114i	−0.410702	+	1.79940i	−0.580880	+	0.813989i	$0.697291\pi$
$152$	−3.44447	+	1.65877i	−0.279384	+	0.134544i
$153$	9.87401	+	4.75507i	0.798267	+	0.384425i
$154$	−6.80506	+	10.6620i	−0.548368	+	0.859168i
$155$	0.224300	−	0.108017i	0.0180162	−	0.00867613i
$156$	−9.37244	+	11.7527i	−0.750396	+	0.940967i
$157$	−6.05492	−	2.91589i	−0.483235	−	0.232714i	0.176373	−	0.984323i	$-0.443563\pi$
$157$	−6.05492	−	2.91589i	−0.483235	−	0.232714i	−0.659608	+	0.751610i	$0.729278\pi$
$158$	6.78525	+	8.50843i	0.539805	+	0.676894i
$159$	1.83171	+	8.02522i	0.145264	+	0.636442i
$160$	1.82836	+	2.29270i	0.144545	+	0.181254i
$161$	−2.24937	+	3.52425i	−0.177275	+	0.277750i
$162$	1.33837	−	1.67826i	0.105152	−	0.131857i
$163$	5.49389	+	2.64572i	0.430315	+	0.207229i	0.636488	−	0.771287i	$-0.280387\pi$
$163$	5.49389	+	2.64572i	0.430315	+	0.207229i	−0.206173	+	0.978516i	$0.566101\pi$
$164$	−1.60087	−	7.01389i	−0.125007	−	0.547693i
$165$	40.0475			3.11769
$166$	10.7804			0.836720
$167$	3.01288	+	13.2003i	0.233144	+	1.02147i	0.947014	+	0.321191i	$0.104083\pi$
$167$	3.01288	+	13.2003i	0.233144	+	1.02147i	−0.713871	+	0.700277i	$0.753060\pi$
$168$	6.42769	−	3.97564i	0.495907	−	0.306727i
$169$	−3.26921	+	14.3234i	−0.251478	+	1.10180i
$170$	1.38589	−	6.07196i	0.106293	−	0.465698i
$171$	12.3000	−	15.4237i	0.940601	−	1.17948i
$172$	−2.68405	+	3.36570i	−0.204657	+	0.256632i
$173$	4.91705	−	21.5430i	0.373836	−	1.63788i	−0.342061	−	0.939678i	$-0.611125\pi$
$173$	4.91705	−	21.5430i	0.373836	−	1.63788i	0.715897	−	0.698206i	$-0.246018\pi$
$174$	0.379523	−	1.66280i	0.0287716	−	0.126057i
$175$	−8.09904	+	5.00939i	−0.612230	+	0.378674i
$176$	1.06381	+	4.66086i	0.0801877	+	0.351325i
$177$	−5.78466			−0.434802
$178$	−12.0078			−0.900019
$179$	−4.64395	−	20.3465i	−0.347105	−	1.52077i	−0.783718	−	0.621117i	$-0.786679\pi$
$179$	−4.64395	−	20.3465i	−0.347105	−	1.52077i	0.436613	−	0.899649i	$-0.356178\pi$
$180$	−13.6334	−	6.56550i	−1.01617	−	0.489363i
$181$	−13.2686	+	16.6383i	−0.986246	+	1.23671i	−0.0146921	+	0.999892i	$0.504677\pi$
$181$	−13.2686	+	16.6383i	−0.986246	+	1.23671i	−0.971553	+	0.236821i	$0.923895\pi$
$182$	7.49055	−	11.7360i	0.555236	−	0.869930i
$183$	−6.61444	−	8.29424i	−0.488953	−	0.613128i
$184$	0.351636	+	1.54062i	0.0259229	+	0.113576i
$185$	9.39128	+	11.7763i	0.690461	+	0.865810i
$186$	−0.218496	−	0.105222i	−0.0160209	−	0.00771526i
$187$	6.33061	−	7.93834i	0.462940	−	0.580509i
$188$	−0.908479	+	0.437501i	−0.0662577	+	0.0319080i
$189$	−8.78351	+	13.7618i	−0.638906	+	1.00102i
$190$	−10.1008	−	4.86429i	−0.732790	−	0.352893i
$191$	−14.8533	+	7.15295i	−1.07474	+	0.517569i	−0.885633	−	0.464386i	$-0.846275\pi$
$191$	−14.8533	+	7.15295i	−1.07474	+	0.517569i	−0.189111	+	0.981956i	$0.560561\pi$
$192$	0.635652	−	2.78497i	0.0458742	−	0.200988i
$193$	−2.29785	+	1.10658i	−0.165403	+	0.0796537i	−0.514753	−	0.857338i	$-0.672116\pi$
$193$	−2.29785	+	1.10658i	−0.165403	+	0.0796537i	0.349351	+	0.936992i	$0.386402\pi$
$194$	6.58044	+	8.25161i	0.472448	+	0.592431i
$195$	−44.0816			−3.15675
$196$	−5.53403	+	4.28655i	−0.395288	+	0.306182i
$197$	26.4015			1.88103			0.940515	−	0.339752i	$-0.110343\pi$
$197$	26.4015			1.88103			0.940515	+	0.339752i	$0.110343\pi$
$198$	−15.3810	−	19.2871i	−1.09308	−	1.37068i
$199$	−13.3961	+	6.45121i	−0.949623	+	0.457314i	−0.843554	−	0.537044i	$-0.819541\pi$
$199$	−13.3961	+	6.45121i	−0.949623	+	0.457314i	−0.106069	+	0.994359i	$0.533826\pi$
$200$	−0.800936	+	3.50913i	−0.0566347	+	0.248133i
$201$	−30.8140	+	14.8392i	−2.17345	+	1.04668i
$202$	−7.65882	−	3.68829i	−0.538873	−	0.259507i
$203$	−0.187969	+	1.56845i	−0.0131928	+	0.110084i
$204$	−5.46615	+	2.63236i	−0.382707	+	0.184302i
$205$	13.1537	−	16.4943i	0.918697	−	1.15201i
$206$	−4.79203	−	2.30772i	−0.333877	−	0.160787i
$207$	−5.08408	−	6.37523i	−0.353368	−	0.443109i
$208$	−1.17097	−	5.13035i	−0.0811922	−	0.355726i
$209$	−11.3956	−	14.2896i	−0.788248	−	0.988431i
$210$	20.8671	+	7.46784i	1.43997	+	0.515330i
$211$	15.3529	−	19.2519i	1.05694	−	1.32536i	0.113596	−	0.993527i	$-0.463763\pi$
$211$	15.3529	−	19.2519i	1.05694	−	1.32536i	0.943340	−	0.331828i	$-0.107666\pi$
$212$	−2.59625	−	1.25029i	−0.178311	−	0.0858700i
$213$	−2.13348	−	9.34741i	−0.146184	−	0.640474i
$214$	1.59158			0.108799
$215$	−12.6239			−0.860946
$216$	1.37309	+	6.01592i	0.0934272	+	0.409331i
$217$	0.211478	+	0.0756829i	0.0143561	+	0.00513769i
$218$	3.07210	−	13.4597i	0.208069	−	0.911609i
$219$	4.86137	−	21.2991i	0.328501	−	1.43926i
$220$	−8.74090	+	10.9607i	−0.589311	+	0.738973i
$221$	−6.96831	+	8.73798i	−0.468739	+	0.587780i
$222$	3.26499	−	14.3048i	0.219132	−	0.960078i
$223$	−2.72346	+	11.9323i	−0.182377	+	0.799044i	0.798118	+	0.602501i	$0.205829\pi$
$223$	−2.72346	+	11.9323i	−0.182377	+	0.799044i	−0.980495	+	0.196544i	$0.937028\pi$
$224$	−0.314823	+	2.62695i	−0.0210350	+	0.175521i
$225$	−4.13294	−	18.1076i	−0.275529	−	1.20717i
$226$	−5.86308			−0.390006
$227$	7.82425			0.519314			0.259657	−	0.965701i	$-0.416391\pi$
$227$	7.82425			0.519314			0.259657	+	0.965701i	$0.416391\pi$
$228$	2.43015	+	10.6472i	0.160940	+	0.705126i
$229$	9.88718	+	4.76142i	0.653363	+	0.314643i	0.731039	−	0.682335i	$-0.239036\pi$
$229$	9.88718	+	4.76142i	0.653363	+	0.314643i	−0.0776759	+	0.996979i	$0.524750\pi$
$230$	−2.88925	+	3.62300i	−0.190511	+	0.238894i
$231$	25.3677	+	25.7292i	1.66907	+	1.69286i
$232$	0.372262	+	0.466801i	0.0244402	+	0.0306470i
$233$	4.81551	+	21.0981i	0.315474	+	1.38218i	0.845397	+	0.534138i	$0.179364\pi$
$233$	4.81551	+	21.0981i	0.315474	+	1.38218i	−0.529923	+	0.848046i	$0.677779\pi$
$234$	16.9303	+	21.2299i	1.10677	+	1.38785i
$235$	−2.66409	−	1.28296i	−0.173786	−	0.0836909i
$236$	1.26258	−	1.58322i	0.0821869	−	0.103059i
$237$	28.0088	−	13.4883i	1.81937	−	0.876162i
$238$	4.77892	−	2.95584i	0.309771	−	0.191599i
$239$	14.4011	+	6.93520i	0.931529	+	0.448601i	0.837173	−	0.546938i	$-0.184207\pi$
$239$	14.4011	+	6.93520i	0.931529	+	0.448601i	0.0943560	+	0.995539i	$0.469921\pi$
$240$	7.54730	−	3.63459i	0.487176	−	0.234612i
$241$	−5.29208	+	23.1861i	−0.340893	+	1.49355i	0.456301	+	0.889826i	$0.349174\pi$
$241$	−5.29208	+	23.1861i	−0.340893	+	1.49355i	−0.797193	+	0.603724i	$0.793683\pi$
$242$	−10.6812	+	5.14382i	−0.686617	+	0.330657i
$243$	7.71879	+	9.67905i	0.495160	+	0.620911i
$244$	3.71377			0.237750
$245$	−19.9460	−	4.85046i	−1.27430	−	0.309884i
$246$	−20.5511			−1.31029
$247$	12.5435	+	15.7290i	0.798121	+	1.00081i
$248$	0.0764883	−	0.0368348i	0.00485701	−	0.00233901i
$249$	6.85257	−	30.0231i	0.434264	−	1.90264i
$250$	3.70055	−	1.78209i	0.234043	−	0.112709i
$251$	−11.4348	−	5.50670i	−0.721757	−	0.347580i	0.0366794	−	0.999327i	$-0.488322\pi$
$251$	−11.4348	−	5.50670i	−0.721757	−	0.347580i	−0.758436	+	0.651747i	$0.774036\pi$
$252$	−4.41783	−	12.9179i	−0.278297	−	0.813750i
$253$	−6.80652	+	3.27785i	−0.427922	+	0.206077i
$254$	8.27387	−	10.3751i	0.519149	−	0.650992i
$255$	−16.0293	−	7.71931i	−1.00379	−	0.483402i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−3.24183	−	14.2034i	−0.202220	−	0.885982i	−0.969582	−	0.244768i	$-0.921288\pi$
$257$	−3.24183	−	14.2034i	−0.202220	−	0.885982i	0.767362	−	0.641214i	$-0.221569\pi$
$258$	7.66725	+	9.61443i	0.477342	+	0.598568i
$259$	−1.61707	+	13.4932i	−0.100480	+	0.838426i
$260$	9.62138	−	12.0648i	0.596693	−	0.748229i
$261$	−2.77581	−	1.33676i	−0.171818	−	0.0827433i
$262$	3.84465	+	16.8445i	0.237523	+	1.04066i
$263$	18.7309			1.15500			0.577499	−	0.816392i	$-0.304029\pi$
$263$	18.7309			1.15500			0.577499	+	0.816392i	$0.304029\pi$
$264$	13.6566			0.840505
$265$	−1.88036	−	8.23838i	−0.115509	−	0.506080i
$266$	−3.27311	−	9.57069i	−0.200687	−	0.586817i
$267$	−7.63275	+	33.4413i	−0.467117	+	2.04657i
$268$	2.66416	−	11.6724i	0.162739	−	0.713008i
$269$	7.82086	−	9.80705i	0.476846	−	0.597946i	−0.483986	−	0.875076i	$-0.660812\pi$
$269$	7.82086	−	9.80705i	0.476846	−	0.597946i	0.960833	+	0.277129i	$0.0893830\pi$
$270$	−11.2822	+	14.1474i	−0.686610	+	0.860982i
$271$	3.89895	−	17.0824i	0.236845	−	1.03768i	−0.706979	−	0.707234i	$-0.749943\pi$
$271$	3.89895	−	17.0824i	0.236845	−	1.03768i	0.943824	−	0.330449i	$-0.107200\pi$
$272$	0.472600	−	2.07060i	0.0286556	−	0.125548i
$273$	−27.9231	−	28.3210i	−1.68998	−	1.71406i
$274$	0.527326	+	2.31037i	0.0318569	+	0.139574i
$275$	−17.2076			−1.03766
$276$	4.51409			0.271717
$277$	−0.812834	−	3.56126i	−0.0488384	−	0.213975i	0.944621	−	0.328165i	$-0.106430\pi$
$277$	−0.812834	−	3.56126i	−0.0488384	−	0.213975i	−0.993459	+	0.114189i	$0.963573\pi$
$278$	−14.0637	−	6.77272i	−0.843485	−	0.406201i
$279$	−0.273134	+	0.342499i	−0.0163521	+	0.0205049i
$280$	−6.59842	+	4.08123i	−0.394331	+	0.243900i
$281$	12.1302	+	15.2108i	0.723625	+	0.907397i	0.998537	−	0.0540720i	$-0.0172201\pi$
$281$	12.1302	+	15.2108i	0.723625	+	0.907397i	−0.274912	+	0.961469i	$0.588649\pi$
$282$	0.640951	+	2.80819i	0.0381681	+	0.167225i
$283$	−6.82695	−	8.56072i	−0.405820	−	0.508882i	0.536360	−	0.843989i	$-0.319799\pi$
$283$	−6.82695	−	8.56072i	−0.405820	−	0.508882i	−0.942180	+	0.335107i	$0.891228\pi$
$284$	3.02399	+	1.45627i	0.179441	+	0.0864140i
$285$	−19.9675	+	25.0385i	−1.18277	+	1.48315i
$286$	22.6662	−	10.9154i	1.34028	−	0.645444i
$287$	18.9291	−	1.99729i	1.11735	−	0.117896i
$288$	−4.64912	−	2.23890i	−0.273952	−	0.131928i
$289$	11.2525	−	5.41889i	0.661909	−	0.318759i
$290$	−0.389604	+	1.70697i	−0.0228783	+	0.100236i
$291$	27.1634	−	13.0812i	1.59235	−	0.766834i
$292$	4.76836	+	5.97933i	0.279047	+	0.349914i
$293$	21.2866			1.24357			0.621787	−	0.783186i	$-0.286407\pi$
$293$	21.2866			1.24357			0.621787	+	0.783186i	$0.286407\pi$
$294$	8.42023	+	18.1369i	0.491078	+	1.05776i
$295$	5.93831			0.345742
$296$	3.20252	+	4.01583i	0.186142	+	0.233415i
$297$	−26.5786	+	12.7996i	−1.54225	+	0.742708i
$298$	2.75954	−	12.0903i	0.159856	−	0.700374i
$299$	7.49215	−	3.60803i	0.433282	−	0.208658i
$300$	9.26372	+	4.46117i	0.534841	+	0.257566i
$301$	−7.99653	−	8.11048i	−0.460912	−	0.467480i
$302$	−20.4340	+	9.84051i	−1.17585	+	0.566258i
$303$	−15.1401	+	18.9851i	−0.869778	+	1.09067i
$304$	−3.44447	−	1.65877i	−0.197554	−	0.0951370i
$305$	6.79012	+	8.51454i	0.388801	+	0.487541i
$306$	2.43868	+	10.6846i	0.139410	+	0.610795i
$307$	9.65162	+	12.1027i	0.550847	+	0.690740i	0.976836	−	0.213988i	$-0.0686453\pi$
$307$	9.65162	+	12.1027i	0.550847	+	0.690740i	−0.425989	+	0.904728i	$0.640074\pi$
$308$	−12.5788	+	1.32723i	−0.716742	+	0.0756262i
$309$	−9.47301	+	11.8788i	−0.538901	+	0.675760i
$310$	0.224300	+	0.108017i	0.0127394	+	0.00613495i
$311$	−3.74297	−	16.3990i	−0.212244	−	0.929904i	−0.963038	−	0.269367i	$-0.913186\pi$
$311$	−3.74297	−	16.3990i	−0.212244	−	0.929904i	0.750793	−	0.660537i	$-0.229671\pi$
$312$	−15.0322			−0.851033
$313$	19.6300			1.10955			0.554776	−	0.832000i	$-0.312804\pi$
$313$	19.6300			1.10955			0.554776	+	0.832000i	$0.312804\pi$
$314$	−1.49544	−	6.55196i	−0.0843926	−	0.369748i
$315$	21.5394	−	33.7473i	1.21361	−	1.90145i
$316$	−2.42163	+	10.6098i	−0.136227	+	0.596850i
$317$	−3.66557	+	16.0599i	−0.205879	+	0.902015i	0.761397	+	0.648286i	$0.224514\pi$
$317$	−3.66557	+	16.0599i	−0.205879	+	0.902015i	−0.967276	+	0.253728i	$0.918343\pi$
$318$	−5.13232	+	6.43573i	−0.287806	+	0.360898i
$319$	−1.77968	+	2.23165i	−0.0996429	+	0.124948i
$320$	−0.652536	+	2.85895i	−0.0364779	+	0.159820i
$321$	1.01169	−	4.43252i	0.0564673	−	0.247399i
$322$	−4.15783	+	0.438709i	−0.231707	+	0.0244483i
$323$	1.80679	+	7.91605i	0.100532	+	0.440461i
$324$	2.14658			0.119254
$325$	18.9409			1.05065
$326$	1.35688	+	5.94488i	0.0751506	+	0.329256i
$327$	−35.5323	−	17.1114i	−1.96494	−	0.946265i
$328$	4.48555	−	5.62470i	0.247673	−	0.310572i
$329$	−0.863283	−	2.52427i	−0.0475944	−	0.139167i
$330$	24.9692	+	31.3104i	1.37451	+	1.72358i
$331$	−6.79972	−	29.7915i	−0.373746	−	1.63749i	−0.716157	−	0.697939i	$-0.754100\pi$
$331$	−6.79972	−	29.7915i	−0.373746	−	1.63749i	0.342410	−	0.939551i	$-0.388757\pi$
$332$	6.72146	+	8.42844i	0.368888	+	0.462571i
$333$	−23.8799	−	11.5000i	−1.30861	−	0.630194i
$334$	−8.44190	+	10.5858i	−0.461920	+	0.579230i
$335$	31.6324	−	15.2334i	1.72826	−	0.832288i
$336$	7.11588	+	2.54660i	0.388203	+	0.138929i
$337$	−18.3513	−	8.83751i	−0.999657	−	0.481410i	−0.138835	−	0.990315i	$-0.544336\pi$
$337$	−18.3513	−	8.83751i	−0.999657	−	0.481410i	−0.860822	+	0.508906i	$0.830050\pi$
$338$	−13.2368	+	6.37449i	−0.719985	+	0.346727i
$339$	−3.72688	+	16.3285i	−0.202416	+	0.886844i
$340$	5.61133	−	2.70228i	0.304317	−	0.146552i
$341$	0.253051	+	0.317316i	0.0137035	+	0.0171836i
$342$	19.7276			1.06675
$343$	−9.51834	−	15.8871i	−0.513942	−	0.857825i
$344$	−4.30489			−0.232104
$345$	8.25341	+	10.3494i	0.444349	+	0.557196i
$346$	19.9087	−	9.58753i	1.07030	−	0.515429i
$347$	−1.73736	+	7.61188i	−0.0932665	+	0.408627i	−0.999912	−	0.0132660i	$-0.995777\pi$
$347$	−1.73736	+	7.61188i	−0.0932665	+	0.408627i	0.906646	+	0.421893i	$0.138634\pi$
$348$	1.53666	−	0.740016i	0.0823736	−	0.0396690i
$349$	−17.9053	−	8.62276i	−0.958451	−	0.461566i	−0.111810	−	0.993730i	$-0.535665\pi$
$349$	−17.9053	−	8.62276i	−0.958451	−	0.461566i	−0.846641	+	0.532164i	$0.821379\pi$
$350$	−8.96617	−	3.20878i	−0.479262	−	0.171516i
$351$	29.2559	−	14.0889i	1.56157	−	0.752011i
$352$	−2.98073	+	3.73772i	−0.158873	+	0.199221i
$353$	14.1851	+	6.83120i	0.754998	+	0.363588i	0.771461	−	0.636276i	$-0.219526\pi$
$353$	14.1851	+	6.83120i	0.754998	+	0.363588i	−0.0164627	+	0.999864i	$0.505240\pi$
$354$	−3.60668	−	4.52263i	−0.191693	−	0.240375i
$355$	2.19015	+	9.59568i	0.116241	+	0.509286i
$356$	−7.48671	−	9.38804i	−0.396795	−	0.497565i
$357$	−5.19421	−	15.1880i	−0.274907	−	0.803837i
$358$	13.0121	−	16.3166i	0.687708	−	0.862359i
$359$	7.46113	+	3.59309i	0.393783	+	0.189636i	0.620288	−	0.784374i	$-0.287016\pi$
$359$	7.46113	+	3.59309i	0.393783	+	0.189636i	−0.226505	+	0.974010i	$0.572730\pi$
$360$	−3.36717	−	14.7525i	−0.177466	−	0.777527i
$361$	−4.38408			−0.230741
$362$	−21.2811			−1.11851
$363$	7.53584	+	33.0167i	0.395529	+	1.73293i
$364$	13.8459	−	1.46093i	0.725720	−	0.0765735i
$365$	−4.99050	+	21.8648i	−0.261215	+	1.14446i
$366$	2.36066	−	10.3427i	0.123394	−	0.540624i
$367$	−7.05604	+	8.84800i	−0.368322	+	0.461862i	−0.931109	−	0.364740i	$-0.881158\pi$
$367$	−7.05604	+	8.84800i	−0.368322	+	0.461862i	0.562787	+	0.826602i	$0.309729\pi$
$368$	−0.985261	+	1.23548i	−0.0513603	+	0.0644038i
$369$	−8.26072	+	36.1926i	−0.430036	+	1.88411i
$370$	−3.35171	+	14.6848i	−0.174247	+	0.763426i
$371$	4.10180	−	6.42660i	0.212955	−	0.333652i
$372$	−0.0539641	−	0.236432i	−0.00279791	−	0.0122584i
$373$	11.1939			0.579601			0.289800	−	0.957087i	$-0.406411\pi$
$373$	11.1939			0.579601			0.289800	+	0.957087i	$0.406411\pi$
$374$	10.1535			0.525026
$375$	−2.61081	−	11.4387i	−0.134822	−	0.590692i
$376$	−0.908479	−	0.437501i	−0.0468513	−	0.0225624i
$377$	1.95895	−	2.45644i	0.100891	−	0.126513i
$378$	−16.2358	+	1.71310i	−0.835080	+	0.0881125i
$379$	−15.7623	−	19.7653i	−0.809657	−	1.01528i	−0.999440	−	0.0334517i	$-0.989350\pi$
$379$	−15.7623	−	19.7653i	−0.809657	−	1.01528i	0.189783	−	0.981826i	$-0.439221\pi$
$380$	−2.49469	−	10.9300i	−0.127975	−	0.560696i
$381$	−23.6351	−	29.6375i	−1.21086	−	1.51837i
$382$	−14.8533	−	7.15295i	−0.759959	−	0.365977i
$383$	−2.97517	+	3.73074i	−0.152024	+	0.190632i	−0.852012	−	0.523523i	$-0.824617\pi$
$383$	−2.97517	+	3.73074i	−0.152024	+	0.190632i	0.699988	+	0.714155i	$0.253189\pi$
$384$	2.57370	−	1.23943i	0.131339	−	0.0632494i
$385$	−26.0415	−	26.4126i	−1.32720	−	1.34611i
$386$	−2.29785	−	1.10658i	−0.116957	−	0.0563237i
$387$	20.0139	−	9.63820i	1.01737	−	0.489937i
$388$	−2.34853	+	10.2896i	−0.119229	+	0.522375i
$389$	1.62271	−	0.781455i	0.0822746	−	0.0396213i	−0.392294	−	0.919840i	$-0.628318\pi$
$389$	1.62271	−	0.781455i	0.0822746	−	0.0396213i	0.474569	+	0.880219i	$0.342604\pi$
$390$	−27.4844	−	34.4643i	−1.39173	−	1.74517i
$391$	3.35618			0.169729
$392$	−6.80177	−	1.65405i	−0.343541	−	0.0835423i
$393$	49.3554			2.48965
$394$	16.4611	+	20.6415i	0.829297	+	1.03991i
$395$	−28.7528	+	13.8466i	−1.44671	+	0.696698i
$396$	5.48940	−	24.0507i	0.275853	−	1.20859i
$397$	−11.1066	+	5.34864i	−0.557422	+	0.268441i	−0.691313	−	0.722556i	$-0.742967\pi$
$397$	−11.1066	+	5.34864i	−0.557422	+	0.268441i	0.133890	+	0.990996i	$0.457253\pi$
$398$	−13.3961	−	6.45121i	−0.671485	−	0.323370i
$399$	−28.7347	+	3.03191i	−1.43853	+	0.151785i
$400$	−3.24292	+	1.56171i	−0.162146	+	0.0780855i
$401$	−2.53321	+	3.17654i	−0.126502	+	0.158629i	−0.841049	−	0.540959i	$-0.818062\pi$
$401$	−2.53321	+	3.17654i	−0.126502	+	0.158629i	0.714547	+	0.699588i	$0.246633\pi$
$402$	−30.8140	−	14.8392i	−1.53686	−	0.740113i
$403$	−0.278541	−	0.349280i	−0.0138751	−	0.0173989i
$404$	−1.89157	−	8.28752i	−0.0941092	−	0.412319i
$405$	3.92473	+	4.92146i	0.195021	+	0.244549i
$406$	−1.34346	+	0.830954i	−0.0666749	+	0.0412396i
$407$	−15.3103	+	19.1986i	−0.758905	+	0.951637i
$408$	−5.46615	−	2.63236i	−0.270615	−	0.130321i
$409$	4.20059	+	18.4040i	0.207706	+	0.910019i	0.966089	+	0.258210i	$0.0831325\pi$
$409$	4.20059	+	18.4040i	0.207706	+	0.910019i	−0.758383	+	0.651809i	$0.774010\pi$
$410$	21.0969			1.04190
$411$	6.76950			0.333915
$412$	−1.18353	−	5.18540i	−0.0583086	−	0.255467i
$413$	3.76157	+	3.81517i	0.185095	+	0.187732i
$414$	1.81449	−	7.94979i	0.0891772	−	0.390711i
$415$	−7.03458	+	30.8205i	−0.345314	+	1.51292i
$416$	3.28098	−	4.11422i	0.160864	−	0.201716i
$417$	−27.8015	+	34.8620i	−1.36144	+	1.70720i
$418$	4.06703	−	17.8188i	0.198925	−	0.871547i
$419$	−4.07528	+	17.8550i	−0.199091	+	0.872273i	0.772389	+	0.635150i	$0.219062\pi$
$419$	−4.07528	+	17.8550i	−0.199091	+	0.872273i	−0.971480	+	0.237123i	$0.923795\pi$
$420$	7.17183	+	20.9707i	0.349950	+	1.02326i
$421$	7.06512	+	30.9543i	0.344333	+	1.50862i	0.789823	+	0.613334i	$0.210172\pi$
$421$	7.06512	+	30.9543i	0.344333	+	1.50862i	−0.445490	+	0.895287i	$0.646971\pi$
$422$	24.6241			1.19868
$423$	5.20315			0.252986
$424$	−0.641220	−	2.80937i	−0.0311404	−	0.136435i
$425$	6.88747	+	3.31683i	0.334091	+	0.160890i
$426$	5.97789	−	7.49604i	0.289630	−	0.363184i
$427$	−1.16918	+	9.75590i	−0.0565806	+	0.472121i
$428$	0.992337	+	1.24435i	0.0479664	+	0.0601480i
$429$	−15.9914	−	70.0631i	−0.772074	−	3.38268i
$430$	−7.87090	−	9.86980i	−0.379569	−	0.475964i
$431$	18.2603	+	8.79371i	0.879569	+	0.423578i	0.818467	−	0.574553i	$-0.194824\pi$
$431$	18.2603	+	8.79371i	0.879569	+	0.423578i	0.0611019	+	0.998132i	$0.480539\pi$
$432$	−3.84732	+	4.82439i	−0.185104	+	0.232114i
$433$	3.37812	−	1.62682i	0.162342	−	0.0781798i	−0.350948	−	0.936395i	$-0.614141\pi$
$433$	3.37812	−	1.62682i	0.162342	−	0.0781798i	0.513290	+	0.858215i	$0.328426\pi$
$434$	0.0726831	+	0.212528i	0.00348890	+	0.0102017i
$435$	4.50620	+	2.17007i	0.216056	+	0.104047i
$436$	12.4387	−	5.99015i	0.595705	−	0.286876i
$437$	1.34433	−	5.88990i	0.0643080	−	0.281752i
$438$	19.6833	−	9.47898i	0.940505	−	0.452923i
$439$	−2.87917	−	3.61036i	−0.137415	−	0.172313i	0.708362	−	0.705849i	$-0.249434\pi$
$439$	−2.87917	−	3.61036i	−0.137415	−	0.172313i	−0.845777	+	0.533536i	$0.820863\pi$
$440$	−14.0193			−0.668345
$441$	35.3255	−	7.53859i	1.68217	−	0.358980i
$442$	−11.1763			−0.531602
$443$	−18.1534	−	22.7636i	−0.862493	−	1.08153i	−0.995899	−	0.0904709i	$-0.971163\pi$
$443$	−18.1534	−	22.7636i	−0.862493	−	1.08153i	0.133406	−	0.991061i	$-0.457409\pi$
$444$	13.2197	−	6.36626i	0.627378	−	0.302129i
$445$	7.83549	−	34.3295i	0.371438	−	1.62738i
$446$	−11.0271	+	5.31036i	−0.522147	+	0.251453i
$447$	−31.9172	−	15.3705i	−1.50963	−	0.726999i
$448$	−2.25012	+	1.39174i	−0.106308	+	0.0657535i
$449$	−30.1826	+	14.5352i	−1.42440	+	0.685957i	−0.977948	−	0.208848i	$-0.933029\pi$
$449$	−30.1826	+	14.5352i	−1.42440	+	0.685957i	−0.446457	+	0.894805i	$0.647314\pi$
$450$	11.5802	−	14.5211i	0.545897	−	0.684534i
$451$	30.9877	+	14.9229i	1.45915	+	0.702692i
$452$	−3.65557	−	4.58394i	−0.171944	−	0.215610i
$453$	14.4166	+	63.1634i	0.677352	+	2.96768i
$454$	4.87834	+	6.11725i	0.228952	+	0.287097i
$455$	28.6647	+	29.0732i	1.34382	+	1.36297i
$456$	−6.80912	+	8.53837i	−0.318866	+	0.399846i
$457$	−4.54017	−	2.18643i	−0.212380	−	0.102277i	0.324669	−	0.945828i	$-0.394747\pi$
$457$	−4.54017	−	2.18643i	−0.212380	−	0.102277i	−0.537050	+	0.843551i	$0.680461\pi$
$458$	2.44193	+	10.6988i	0.114104	+	0.499922i
$459$	13.1055			0.611711
$460$	−4.63399			−0.216061
$461$	1.83823	+	8.05383i	0.0856151	+	0.375104i	0.999525	−	0.0308124i	$-0.00980945\pi$
$461$	1.83823	+	8.05383i	0.0856151	+	0.375104i	−0.913910	+	0.405917i	$0.866952\pi$
$462$	−4.29941	+	35.8752i	−0.200027	+	1.66907i
$463$	8.72611	−	38.2316i	0.405537	−	1.77677i	−0.198797	−	0.980041i	$-0.563703\pi$
$463$	8.72611	−	38.2316i	0.405537	−	1.77677i	0.604334	−	0.796731i	$-0.293439\pi$
$464$	−0.132859	+	0.582092i	−0.00616781	+	0.0270229i
$465$	0.443401	−	0.556007i	0.0205622	−	0.0257842i
$466$	−13.4928	+	16.9194i	−0.625040	+	0.783775i
$467$	3.26661	−	14.3120i	0.151161	−	0.662278i	−0.841388	−	0.540431i	$-0.818261\pi$
$467$	3.26661	−	14.3120i	0.151161	−	0.662278i	0.992549	−	0.121847i	$-0.0388817\pi$
$468$	−6.04236	+	26.4733i	−0.279308	+	1.22373i
$469$	29.8242	+	10.6734i	1.37715	+	0.492851i
$470$	−0.657975	−	2.88278i	−0.0303501	−	0.132973i
$471$	−19.1976			−0.884579
$472$	2.02502			0.0932091
$473$	−4.57958	−	20.0645i	−0.210569	−	0.922565i
$474$	28.0088	+	13.4883i	1.28649	+	0.619540i
$475$	8.57964	−	10.7585i	0.393661	−	0.493635i
$476$	5.29058	+	1.89337i	0.242493	+	0.0867825i
$477$	9.27100	+	11.6255i	0.424490	+	0.532293i
$478$	3.55678	+	15.5833i	0.162683	+	0.712762i
$479$	1.98373	+	2.48752i	0.0906389	+	0.113658i	0.825083	−	0.565012i	$-0.191128\pi$
$479$	1.98373	+	2.48752i	0.0906389	+	0.113658i	−0.734444	+	0.678669i	$0.762557\pi$
$480$	7.54730	+	3.63459i	0.344486	+	0.165896i
$481$	16.8526	−	21.1325i	0.768411	−	0.963557i
$482$	−21.4272	+	10.3188i	−0.975982	+	0.470008i
$483$	−1.42114	+	11.8583i	−0.0646642	+	0.539572i
$484$	−10.6812	−	5.14382i	−0.485511	−	0.233810i
$485$	−27.8849	+	13.4287i	−1.26619	+	0.609764i
$486$	−2.75480	+	12.0696i	−0.124960	+	0.547487i
$487$	25.0587	−	12.0676i	1.13552	−	0.546836i	0.230865	−	0.972986i	$-0.425845\pi$
$487$	25.0587	−	12.0676i	1.13552	−	0.546836i	0.904653	+	0.426149i	$0.140130\pi$
$488$	2.31550	+	2.90354i	0.104818	+	0.131437i
$489$	17.4188			0.787707
$490$	−8.64388	−	18.6186i	−0.390491	−	0.841103i
$491$	−10.7719			−0.486130			−0.243065	−	0.970010i	$-0.578153\pi$
$491$	−10.7719			−0.486130			−0.243065	+	0.970010i	$0.578153\pi$
$492$	−12.8134	−	16.0675i	−0.577673	−	0.724378i
$493$	1.14249	−	0.550193i	0.0514551	−	0.0247795i
$494$	−4.47671	+	19.6137i	−0.201417	+	0.882464i
$495$	65.1775	−	31.3878i	2.92951	−	1.41078i
$496$	0.0764883	+	0.0368348i	0.00343443	+	0.00165393i
$497$	−4.77759	+	7.48540i	−0.214304	+	0.335766i
$498$	27.7455	−	13.3615i	1.24331	−	0.598744i
$499$	−12.4838	+	15.6541i	−0.558849	+	0.700775i	−0.978345	−	0.206983i	$-0.933636\pi$
$499$	−12.4838	+	15.6541i	−0.558849	+	0.700775i	0.419495	+	0.907758i	$0.362207\pi$
$500$	3.70055	+	1.78209i	0.165493	+	0.0796974i
$501$	24.1151	+	30.2394i	1.07738	+	1.35099i
$502$	−2.82416	−	12.3734i	−0.126048	−	0.552254i
$503$	−13.3386	−	16.7261i	−0.594740	−	0.745780i	0.389808	−	0.920896i	$-0.372541\pi$
$503$	−13.3386	−	16.7261i	−0.594740	−	0.745780i	−0.984548	+	0.175116i	$0.943970\pi$
$504$	7.34513	−	11.5082i	0.327178	−	0.512614i
$505$	15.5423	−	19.4894i	0.691622	−	0.867267i
$506$	−6.80652	−	3.27785i	−0.302587	−	0.145718i
$507$	9.33881	+	40.9160i	0.414751	+	1.81714i
$508$	13.2703			0.588772
$509$	−12.2471			−0.542842			−0.271421	−	0.962461i	$-0.587494\pi$
$509$	−12.2471			−0.542842			−0.271421	+	0.962461i	$0.587494\pi$
$510$	−3.95891	−	17.3451i	−0.175304	−	0.768055i
$511$	−17.2086	+	10.6438i	−0.761265	+	0.470855i
$512$	−0.222521	+	0.974928i	−0.00983413	+	0.0430861i
$513$	5.24944	−	22.9993i	0.231769	−	1.01544i
$514$	9.08339	−	11.3902i	0.400651	−	0.502401i
$515$	9.72462	−	12.1943i	0.428518	−	0.537345i
$516$	−2.73641	+	11.9890i	−0.120464	+	0.527786i
$517$	1.07268	−	4.69971i	0.0471763	−	0.206693i
$518$	−11.5576	+	7.14859i	−0.507813	+	0.314091i
$519$	−14.0460	−	61.5396i	−0.616552	−	2.70129i
$520$	15.4315			0.676716
$521$	−33.3427			−1.46077			−0.730385	−	0.683036i	$-0.760659\pi$
$521$	−33.3427			−1.46077			−0.730385	+	0.683036i	$0.760659\pi$
$522$	−0.685568	−	3.00367i	−0.0300065	−	0.131467i
$523$	−16.7910	−	8.08610i	−0.734218	−	0.353581i	0.0291237	−	0.999576i	$-0.490728\pi$
$523$	−16.7910	−	8.08610i	−0.734218	−	0.353581i	−0.763342	+	0.645995i	$0.776443\pi$
$524$	−10.7725	+	13.5083i	−0.470598	+	0.590111i
$525$	−14.6357	+	22.9309i	−0.638755	+	1.00079i
$526$	11.6785	+	14.6444i	0.509208	+	0.638527i
$527$	−0.0401217	−	0.175785i	−0.00174773	−	0.00765730i
$528$	8.51474	+	10.6771i	0.370556	+	0.464663i
$529$	18.4724	+	8.89585i	0.803149	+	0.386776i
$530$	5.26864	−	6.60667i	0.228855	−	0.286975i
$531$	−9.41456	+	4.53382i	−0.408557	+	0.196751i
$532$	5.44192	−	8.52625i	0.235937	−	0.369660i
$533$	−34.1091	−	16.4261i	−1.47743	−	0.711493i
$534$	−30.9044	+	14.8828i	−1.33736	+	0.644040i
$535$	−1.03857	+	4.55025i	−0.0449011	+	0.196725i
$536$	10.7870	−	5.19473i	0.465926	−	0.224378i
$537$	−37.1702	−	46.6099i	−1.60401	−	2.01137i
$538$	12.5437			0.540797
$539$	0.473509	−	33.4617i	0.0203955	−	1.44130i
$540$	−18.0952			−0.778692
$541$	−5.32759	−	6.68058i	−0.229051	−	0.287221i	0.654003	−	0.756492i	$-0.273088\pi$
$541$	−5.32759	−	6.68058i	−0.229051	−	0.287221i	−0.883054	+	0.469271i	$0.844517\pi$
$542$	15.7865	−	7.60240i	0.678090	−	0.326551i
$543$	−13.5274	+	59.2674i	−0.580517	+	2.54341i
$544$	1.91352	−	0.921502i	0.0820415	−	0.0395091i
$545$	36.4760	+	17.5659i	1.56246	+	0.752442i
$546$	4.73250	−	39.4890i	0.202532	−	1.68997i
$547$	15.8937	−	7.65398i	0.679564	−	0.327261i	−0.0620641	−	0.998072i	$-0.519768\pi$
$547$	15.8937	−	7.65398i	0.679564	−	0.327261i	0.741628	+	0.670811i	$0.234054\pi$
$548$	−1.47753	+	1.85277i	−0.0631171	+	0.0791464i
$549$	−17.2658	−	8.31475i	−0.736884	−	0.354865i
$550$	−10.7288	−	13.4534i	−0.457476	−	0.573657i
$551$	−0.507929	−	2.22538i	−0.0216385	−	0.0948045i
$552$	2.81449	+	3.52926i	0.119793	+	0.150215i
$553$	−27.1092	−	9.70173i	−1.15280	−	0.412559i
$554$	2.27751	−	2.85591i	0.0967621	−	0.121336i
$555$	38.7663	+	18.6688i	1.64554	+	0.792448i
$556$	−3.47345	−	15.2182i	−0.147307	−	0.645394i
$557$	−7.63613			−0.323553			−0.161777	−	0.986827i	$-0.551722\pi$
$557$	−7.63613			−0.323553			−0.161777	+	0.986827i	$0.551722\pi$
$558$	−0.438073			−0.0185451
$559$	5.04089	+	22.0856i	0.213207	+	0.934121i
$560$	−7.30488	−	2.61424i	−0.308688	−	0.110472i
$561$	6.45410	−	28.2773i	0.272492	−	1.19387i
$562$	−4.32921	+	18.9675i	−0.182617	+	0.800096i
$563$	1.48375	−	1.86056i	0.0625326	−	0.0784134i	−0.749582	−	0.661912i	$-0.769745\pi$
$563$	1.48375	−	1.86056i	0.0625326	−	0.0784134i	0.812114	+	0.583499i	$0.198317\pi$
$564$	−1.79590	+	2.25199i	−0.0756212	+	0.0948260i
$565$	3.82587	−	16.7622i	0.160956	−	0.705192i
$566$	2.43651	−	10.6750i	0.102414	−	0.448706i
$567$	−0.675794	+	5.63897i	−0.0283807	+	0.236814i
$568$	0.746863	+	3.27222i	0.0313377	+	0.137299i
$569$	45.1248			1.89173			0.945865	−	0.324560i	$-0.105216\pi$
$569$	45.1248			1.89173			0.945865	+	0.324560i	$0.105216\pi$
$570$	−32.0254			−1.34140
$571$	6.36161	+	27.8720i	0.266225	+	1.16641i	0.914366	+	0.404888i	$0.132689\pi$
$571$	6.36161	+	27.8720i	0.266225	+	1.16641i	−0.648142	+	0.761520i	$0.724453\pi$
$572$	22.6662	+	10.9154i	0.947720	+	0.456398i
$573$	−29.3623	+	36.8191i	−1.22663	+	1.53814i
$574$	13.3637	+	13.5541i	0.557789	+	0.565738i
$575$	−3.54632	−	4.44695i	−0.147892	−	0.185451i
$576$	−1.14824	−	5.03076i	−0.0478432	−	0.209615i
$577$	6.59190	+	8.26598i	0.274424	+	0.344117i	0.899876	−	0.436145i	$-0.143657\pi$
$577$	6.59190	+	8.26598i	0.274424	+	0.344117i	−0.625452	+	0.780263i	$0.715085\pi$
$578$	11.2525	+	5.41889i	0.468040	+	0.225396i
$579$	−4.54244	+	5.69604i	−0.188777	+	0.236719i
$580$	−1.57747	+	0.759671i	−0.0655010	+	0.0315436i
$581$	−24.2572	+	15.0035i	−1.00636	+	0.622449i
$582$	27.1634	+	13.0812i	1.12596	+	0.542233i
$583$	12.4119	−	5.97727i	0.514049	−	0.247553i
$584$	−1.70181	+	7.45611i	−0.0704213	+	0.308536i
$585$	−71.7429	+	34.5496i	−2.96620	+	1.42845i
$586$	13.2720	+	16.6425i	0.548259	+	0.687496i
$587$	−29.3440			−1.21116			−0.605578	−	0.795786i	$-0.707058\pi$
$587$	−29.3440			−1.21116			−0.605578	+	0.795786i	$0.707058\pi$
$588$	−8.93006	+	17.8914i	−0.368269	+	0.737827i
$589$	−0.324562			−0.0133734
$590$	3.70248	+	4.64276i	0.152429	+	0.191139i
$591$	67.9496	−	32.7228i	2.79508	−	1.34604i
$592$	−1.14296	+	5.00766i	−0.0469756	+	0.205813i
$593$	7.49816	−	3.61092i	0.307913	−	0.148283i	−0.273546	−	0.961859i	$-0.588197\pi$
$593$	7.49816	−	3.61092i	0.307913	−	0.148283i	0.581458	+	0.813576i	$0.302482\pi$
$594$	−26.5786	−	12.7996i	−1.09053	−	0.525174i
$595$	5.33218	+	15.5915i	0.218598	+	0.639187i
$596$	11.1731	−	5.38071i	0.457670	−	0.220402i
$597$	−26.4817	+	33.2070i	−1.08382	+	1.35907i
$598$	7.49215	+	3.60803i	0.306377	+	0.147543i
$599$	0.00281797	+	0.00353363i	0.000115139	+	0.000144380i	0.781889	−	0.623418i	$-0.214256\pi$
$599$	0.00281797	+	0.00353363i	0.000115139	+	0.000144380i	−0.781774	+	0.623562i	$0.785685\pi$
$600$	2.28795	+	10.0242i	0.0934051	+	0.409235i
$601$	−17.8901	−	22.4335i	−0.729752	−	0.915080i	0.269094	−	0.963114i	$-0.413276\pi$
$601$	−17.8901	−	22.4335i	−0.729752	−	0.915080i	−0.998846	+	0.0480343i	$0.984704\pi$
$602$	1.35528	−	11.3087i	0.0552370	−	0.460910i
$603$	−38.5194	+	48.3018i	−1.56863	+	1.96700i
$604$	−20.4340	−	9.84051i	−0.831449	−	0.400405i
$605$	−7.73600	−	33.8936i	−0.314513	−	1.37797i
$606$	−24.2829			−0.986425
$607$	−19.0992			−0.775213			−0.387606	−	0.921825i	$-0.626698\pi$
$607$	−19.0992			−0.775213			−0.387606	+	0.921825i	$0.626698\pi$
$608$	−0.850715	−	3.72722i	−0.0345010	−	0.151159i
$609$	1.46021	+	4.26971i	0.0591707	+	0.173017i
$610$	−2.42337	+	10.6175i	−0.0981192	+	0.429888i
$611$	−1.18073	+	5.17312i	−0.0477673	+	0.209282i
$612$	−6.83303	+	8.56835i	−0.276209	+	0.346355i
$613$	26.9282	−	33.7669i	1.08762	−	1.36383i	0.161385	−	0.986892i	$-0.448404\pi$
$613$	26.9282	−	33.7669i	1.08762	−	1.36383i	0.926237	−	0.376943i	$-0.123025\pi$
$614$	−3.44462	+	15.0919i	−0.139014	+	0.609059i
$615$	13.4103	−	58.7545i	0.540756	−	2.36921i
$616$	−8.88041	−	9.00696i	−0.357802	−	0.362901i
$617$	0.268135	+	1.17478i	0.0107947	+	0.0472947i	0.980038	−	0.198808i	$-0.0637071\pi$
$617$	0.268135	+	1.17478i	0.0107947	+	0.0472947i	−0.969244	+	0.246103i	$0.920850\pi$
$618$	−15.1935			−0.611174
$619$	5.48067			0.220287			0.110143	−	0.993916i	$-0.464869\pi$
$619$	5.48067			0.220287			0.110143	+	0.993916i	$0.464869\pi$
$620$	0.0553974	+	0.242712i	0.00222481	+	0.00974754i
$621$	−8.78539	−	4.23082i	−0.352546	−	0.169777i
$622$	10.4876	−	13.1510i	0.420513	−	0.527307i
$623$	27.0189	−	16.7117i	1.08249	−	0.669539i
$624$	−9.37244	−	11.7527i	−0.375198	−	0.470483i
$625$	6.68484	+	29.2882i	0.267393	+	1.17153i
$626$	12.2391	+	15.3473i	0.489172	+	0.613403i
$627$	−47.0397	−	22.6531i	−1.87859	−	0.904679i
$628$	4.19013	−	5.25426i	0.167205	−	0.209668i
$629$	9.82867	−	4.73324i	0.391895	−	0.188727i
$630$	39.8143	−	4.20096i	1.58624	−	0.167370i
$631$	−10.7504	−	5.17710i	−0.427965	−	0.206097i	0.207486	−	0.978238i	$-0.433472\pi$
$631$	−10.7504	−	5.17710i	−0.427965	−	0.206097i	−0.635452	+	0.772141i	$0.719186\pi$
$632$	−9.80497	+	4.72182i	−0.390021	+	0.187824i
$633$	15.6524	−	68.5775i	0.622126	−	2.72571i
$634$	−14.8416	+	7.14734i	−0.589435	+	0.283857i
$635$	24.2629	+	30.4247i	0.962842	+	1.20737i
$636$	−8.23161			−0.326404
$637$	−0.521206	+	36.8323i	−0.0206509	+	1.45935i
$638$	−2.85438			−0.113006
$639$	−10.7984	−	13.5408i	−0.427179	−	0.535666i
$640$	−2.64206	+	1.27235i	−0.104437	+	0.0502941i
$641$	11.1022	−	48.6419i	0.438510	−	1.92124i	0.0528390	−	0.998603i	$-0.483173\pi$
$641$	11.1022	−	48.6419i	0.438510	−	1.92124i	0.385671	−	0.922636i	$-0.373970\pi$
$642$	4.09627	−	1.97266i	0.161667	−	0.0778546i
$643$	−15.8104	−	7.61388i	−0.623500	−	0.300262i	0.0953319	−	0.995446i	$-0.469609\pi$
$643$	−15.8104	−	7.61388i	−0.623500	−	0.300262i	−0.718832	+	0.695184i	$0.755323\pi$
$644$	−2.93536	−	2.97719i	−0.115669	−	0.117318i
$645$	−32.4903	+	15.6465i	−1.27930	+	0.616080i
$646$	−5.06250	+	6.34818i	−0.199182	+	0.249766i
$647$	−4.17523	−	2.01069i	−0.164145	−	0.0790483i	0.350007	−	0.936747i	$-0.386179\pi$
$647$	−4.17523	−	2.01069i	−0.164145	−	0.0790483i	−0.514152	+	0.857699i	$0.671893\pi$
$648$	1.33837	+	1.67826i	0.0525762	+	0.0659284i
$649$	2.15424	+	9.43833i	0.0845612	+	0.370487i
$650$	11.8095	+	14.8086i	0.463206	+	0.580842i
$651$	0.638085	−	0.0673268i	0.0250085	−	0.00263874i
$652$	−3.80189	+	4.76742i	−0.148894	+	0.186707i
$653$	24.9126	+	11.9973i	0.974904	+	0.469489i	0.852349	−	0.522973i	$-0.175177\pi$
$653$	24.9126	+	11.9973i	0.974904	+	0.469489i	0.122554	+	0.992462i	$0.460891\pi$
$654$	−8.77574	−	38.4490i	−0.343159	−	1.50348i
$655$	−50.6664			−1.97970
$656$	7.19426			0.280889
$657$	−8.78155	−	38.4745i	−0.342601	−	1.50103i
$658$	1.43530	−	2.24880i	0.0559540	−	0.0876673i
$659$	2.89556	−	12.6863i	0.112795	−	0.494187i	−0.886698	−	0.462349i	$-0.847007\pi$
$659$	2.89556	−	12.6863i	0.112795	−	0.494187i	0.999493	−	0.0318383i	$-0.0101362\pi$
$660$	−8.91141	+	39.0434i	−0.346876	+	1.51976i
$661$	10.5455	−	13.2236i	0.410171	−	0.514338i	−0.533240	−	0.845964i	$-0.679026\pi$
$661$	10.5455	−	13.2236i	0.410171	−	0.514338i	0.943411	+	0.331626i	$0.107597\pi$
$662$	19.0524	−	23.8909i	0.740492	−	0.928548i
$663$	−7.10424	+	31.1257i	−0.275906	+	1.20882i
$664$	−2.39886	+	10.5101i	−0.0930938	+	0.407871i
$665$	29.4979	−	3.11244i	1.14388	−	0.120695i
$666$	−5.89785	−	25.8402i	−0.228537	−	1.00129i
$667$	−0.943498			−0.0365324
$668$	−13.5398			−0.523869
$669$	7.77983	+	34.0857i	0.300786	+	1.31783i
$670$	31.6324	+	15.2334i	1.22207	+	0.588516i
$671$	−11.0697	+	13.8810i	−0.427343	+	0.535871i
$672$	2.44566	+	7.15120i	0.0943435	+	0.275864i
$673$	−8.94417	−	11.2156i	−0.344772	−	0.432331i	0.578968	−	0.815350i	$-0.303456\pi$
$673$	−8.94417	−	11.2156i	−0.344772	−	0.432331i	−0.923740	+	0.383019i	$0.874884\pi$
$674$	−4.53239	−	19.8577i	−0.174581	−	0.764890i
$675$	−13.8480	−	17.3648i	−0.533008	−	0.668371i
$676$	−13.2368	−	6.37449i	−0.509106	−	0.245173i
$677$	12.2269	−	15.3320i	0.469918	−	0.589258i	−0.489233	−	0.872153i	$-0.662723\pi$
$677$	12.2269	−	15.3320i	0.469918	−	0.589258i	0.959151	+	0.282895i	$0.0912948\pi$
$678$	−15.0898	+	7.26688i	−0.579521	+	0.279083i
$679$	−26.2909	−	9.40889i	−1.00895	−	0.361080i
$680$	5.61133	+	2.70228i	0.215185	+	0.103628i
$681$	20.1373	−	9.69761i	0.771663	−	0.371613i
$682$	−0.0903128	+	0.395686i	−0.00345826	+	0.0151516i
$683$	−21.3227	+	10.2685i	−0.815889	+	0.392911i	−0.794804	−	0.606866i	$-0.792426\pi$
$683$	−21.3227	+	10.2685i	−0.815889	+	0.392911i	−0.0210850	+	0.999778i	$0.506712\pi$
$684$	12.3000	+	15.4237i	0.470300	+	0.589738i
$685$	−6.94931			−0.265519
$686$	6.48648	−	17.3472i	0.247655	−	0.662319i
$687$	31.3481			1.19600
$688$	−2.68405	−	3.36570i	−0.102329	−	0.128316i
$689$	−13.6622	+	6.57937i	−0.520488	+	0.250654i
$690$	−2.94561	+	12.9056i	−0.112137	+	0.491306i
$691$	−8.92111	+	4.29618i	−0.339375	+	0.163434i	−0.595807	−	0.803128i	$-0.703168\pi$
$691$	−8.92111	+	4.29618i	−0.339375	+	0.163434i	0.256431	+	0.966562i	$0.417453\pi$
$692$	19.9087	+	9.58753i	0.756816	+	0.364463i
$693$	61.4518	+	21.9921i	2.33436	+	0.835412i
$694$	−7.03444	+	3.38761i	−0.267024	+	0.128592i
$695$	28.5399	−	35.7879i	1.08258	−	1.35751i
$696$	1.53666	+	0.740016i	0.0582469	+	0.0280502i
$697$	−9.52661	−	11.9460i	−0.360846	−	0.452487i
$698$	−4.42225	−	19.3752i	−0.167385	−	0.733361i
$699$	38.5433	+	48.3318i	1.45784	+	1.82808i
$700$	−3.08159	−	9.01067i	−0.116473	−	0.340571i
$701$	−2.68991	+	3.37304i	−0.101597	+	0.127398i	−0.830031	−	0.557718i	$-0.811677\pi$
$701$	−2.68991	+	3.37304i	−0.101597	+	0.127398i	0.728434	+	0.685116i	$0.240249\pi$
$702$	29.2559	+	14.0889i	1.10419	+	0.531752i
$703$	−4.36964	−	19.1447i	−0.164804	−	0.722054i
$704$	−4.78072			−0.180180
$705$	−8.44671			−0.318121
$706$	3.50344	+	15.3496i	0.131854	+	0.577689i
$707$	22.3664	−	2.35997i	0.841176	−	0.0887557i
$708$	1.28721	−	5.63963i	0.0483763	−	0.211950i
$709$	2.64768	−	11.6003i	0.0994358	−	0.435657i	−0.900564	−	0.434724i	$-0.856846\pi$
$709$	2.64768	−	11.6003i	0.0994358	−	0.435657i	1.00000		0.000932684i	$-0.000296883\pi$
$710$	−6.13667	+	7.69514i	−0.230305	+	0.288793i
$711$	35.0128	−	43.9046i	1.31308	−	1.64655i
$712$	2.67198	−	11.7067i	0.100137	−	0.438727i
$713$	−0.0298523	+	0.130792i	−0.00111798	+	0.00489818i
$714$	8.63596	−	13.5306i	0.323193	−	0.506370i
$715$	16.4162	+	71.9240i	0.613931	+	2.68981i
$716$	20.8697			0.779938
$717$	45.6598			1.70520
$718$	1.84275	+	8.07360i	0.0687707	+	0.301304i
$719$	−3.08546	−	1.48588i	−0.115068	−	0.0554139i	0.375464	−	0.926837i	$-0.377483\pi$
$719$	−3.08546	−	1.48588i	−0.115068	−	0.0554139i	−0.490532	+	0.871423i	$0.663198\pi$
$720$	9.43460	−	11.8306i	0.351607	−	0.440901i
$721$	13.9944	−	1.47660i	0.521180	−	0.0549916i
$722$	−2.73343	−	3.42761i	−0.101728	−	0.127563i
$723$	15.1173	+	66.2334i	0.562220	+	2.46325i
$724$	−13.2686	−	16.6383i	−0.493123	−	0.618356i
$725$	−1.93622	−	0.932436i	−0.0719096	−	0.0346298i
$726$	−21.1150	+	26.4773i	−0.783650	+	0.982666i
$727$	−1.29493	+	0.623603i	−0.0480261	+	0.0231282i	−0.457743	−	0.889085i	$-0.651342\pi$
$727$	−1.29493	+	0.623603i	−0.0480261	+	0.0231282i	0.409717	+	0.912213i	$0.365628\pi$
$728$	9.77495	+	9.91425i	0.362284	+	0.367447i
$729$	37.6644	+	18.1382i	1.39498	+	0.671785i
$730$	−20.2061	+	9.73075i	−0.747862	+	0.360151i
$731$	−2.03449	+	8.91368i	−0.0752483	+	0.329685i
$732$	9.55814	−	4.60296i	0.353279	−	0.170130i
$733$	6.04406	+	7.57901i	0.223242	+	0.279937i	0.880822	−	0.473448i	$-0.156991\pi$
$733$	6.04406	+	7.57901i	0.223242	+	0.279937i	−0.657579	+	0.753385i	$0.728420\pi$
$734$	−11.3170			−0.417719
$735$	−57.3468	+	12.2380i	−2.11527	+	0.451406i
$736$	−1.58024			−0.0582483
$737$	35.6872	+	44.7503i	1.31455	+	1.64840i
$738$	−33.4470	+	16.1072i	−1.23120	+	0.592915i
$739$	−6.64119	+	29.0970i	−0.244300	+	1.07035i	0.692756	+	0.721172i	$0.256396\pi$
$739$	−6.64119	+	29.0970i	−0.244300	+	1.07035i	−0.937057	+	0.349178i	$0.886461\pi$
$740$	−13.5708	+	6.53535i	−0.498872	+	0.240244i
$741$	51.7781	+	24.9350i	1.90212	+	0.916011i
$742$	7.58195	−	0.800000i	0.278342	−	0.0293689i
$743$	−40.9193	+	19.7057i	−1.50118	+	0.722932i	−0.990587	−	0.136888i	$-0.956290\pi$
$743$	−40.9193	+	19.7057i	−1.50118	+	0.722932i	−0.510598	+	0.859820i	$0.670576\pi$
$744$	0.151204	−	0.189604i	0.00554341	−	0.00695121i
$745$	32.7649	+	15.7787i	1.20041	+	0.578089i
$746$	6.97931	+	8.75178i	0.255531	+	0.320425i
$747$	−12.3784	−	54.2335i	−0.452903	−	1.98430i
$748$	6.33061	+	7.93834i	0.231470	+	0.290254i
$749$	−3.58126	+	2.21507i	−0.130857	+	0.0809370i
$750$	7.31533	−	9.17313i	0.267118	−	0.334955i
$751$	−17.3397	−	8.35037i	−0.632736	−	0.304709i	0.0898873	−	0.995952i	$-0.471349\pi$
$751$	−17.3397	−	8.35037i	−0.632736	−	0.304709i	−0.722623	+	0.691243i	$0.757064\pi$
$752$	−0.224376	−	0.983055i	−0.00818215	−	0.0358483i
$753$	−36.2549			−1.32120
$754$	3.14191			0.114422
$755$	−14.7996	−	64.8411i	−0.538611	−	2.35981i
$756$	−11.4622	−	11.6256i	−0.416877	−	0.422818i
$757$	5.10424	−	22.3631i	0.185517	−	0.812802i	−0.793426	−	0.608667i	$-0.791705\pi$
$757$	5.10424	−	22.3631i	0.185517	−	0.812802i	0.978943	−	0.204135i	$-0.0654382\pi$
$758$	5.62551	−	24.6470i	0.204328	−	0.895219i
$759$	−13.4553	+	16.8724i	−0.488396	+	0.612430i
$760$	6.98998	−	8.76516i	0.253553	−	0.317946i
$761$	0.922553	−	4.04197i	0.0334425	−	0.146521i	−0.955450	−	0.295152i	$-0.904630\pi$
$761$	0.922553	−	4.04197i	0.0334425	−	0.146521i	0.988893	+	0.148631i	$0.0474867\pi$
$762$	8.43527	−	36.9573i	0.305577	−	1.33882i
$763$	11.8199	+	34.5617i	0.427908	+	1.25122i
$764$	−3.66845	−	16.0725i	−0.132720	−	0.581484i
$765$	−32.1379			−1.16195
$766$	−4.77180			−0.172412
$767$	−2.37124	−	10.3891i	−0.0856204	−	0.375128i
$768$	2.57370	+	1.23943i	0.0928705	+	0.0447241i
$769$	−13.8780	+	17.4024i	−0.500453	+	0.627548i	−0.966331	−	0.257301i	$-0.917167\pi$
$769$	−13.8780	+	17.4024i	−0.500453	+	0.627548i	0.465879	+	0.884849i	$0.345738\pi$
$770$	4.41361	−	36.8281i	0.159055	−	1.32719i
$771$	−25.9476	−	32.5372i	−0.934479	−	1.17180i
$772$	−0.567521	−	2.48647i	−0.0204255	−	0.0894901i
$773$	30.4984	+	38.2438i	1.09695	+	1.37553i	0.920278	+	0.391264i	$0.127962\pi$
$773$	30.4984	+	38.2438i	1.09695	+	1.37553i	0.176673	+	0.984270i	$0.443466\pi$
$774$	20.0139	+	9.63820i	0.719386	+	0.346438i
$775$	−0.190520	+	0.238905i	−0.00684369	+	0.00858172i
$776$	−9.50901	+	4.57930i	−0.341354	+	0.164387i
$777$	12.5620	+	36.7317i	0.450659	+	1.31774i
$778$	1.62271	+	0.781455i	0.0581769	+	0.0280165i
$779$	−24.7804	+	11.9336i	−0.887852	+	0.427567i
$780$	9.80907	−	42.9763i	0.351221	−	1.53880i
$781$	−14.4568	+	6.96204i	−0.517306	+	0.249122i
$782$	2.09254	+	2.62397i	0.0748292	+	0.0938328i
$783$	−3.68424			−0.131664
$784$	−2.94765	−	6.34912i	−0.105273	−	0.226754i
$785$	19.7075			0.703391
$786$	30.7726	+	38.5876i	1.09762	+	1.37638i
$787$	−38.8605	+	18.7142i	−1.38523	+	0.667090i	−0.970107	−	0.242677i	$-0.921975\pi$
$787$	−38.8605	+	18.7142i	−1.38523	+	0.667090i	−0.415120	+	0.909767i	$0.636260\pi$
$788$	−5.87489	+	25.7396i	−0.209284	+	0.916934i
$789$	48.2078	−	23.2156i	1.71624	−	0.826499i
$790$	−28.7528	−	13.8466i	−1.02298	−	0.492640i
$791$	13.1927	−	8.15988i	0.469077	−	0.290132i
$792$	22.2261	−	10.7035i	0.789772	−	0.380334i
$793$	12.1848	−	15.2793i	0.432696	−	0.542583i
$794$	−11.1066	−	5.34864i	−0.394157	−	0.189816i
$795$	−15.0504	−	18.8726i	−0.533782	−	0.669341i
$796$	−3.30856	−	14.4957i	−0.117269	−	0.513788i
$797$	7.74431	+	9.71106i	0.274318	+	0.343983i	0.899838	−	0.436225i	$-0.143685\pi$
$797$	7.74431	+	9.71106i	0.274318	+	0.343983i	−0.625520	+	0.780208i	$0.715113\pi$
$798$	−20.2862	−	20.5753i	−0.718125	−	0.728359i
$799$	−1.33523	+	1.67433i	−0.0472372	+	0.0592336i
$800$	−3.24292	−	1.56171i	−0.114655	−	0.0552148i
$801$	13.7878	+	60.4081i	0.487166	+	2.13442i
$802$	−4.06295			−0.143468
$803$	−36.5623			−1.29025
$804$	−7.61042	−	33.3434i	−0.268399	−	1.17593i
$805$	1.45889	−	12.1733i	0.0514191	−	0.429052i
$806$	0.0994102	−	0.435544i	0.00350157	−	0.0153414i
$807$	7.97342	−	34.9338i	0.280678	−	1.22973i
$808$	5.30007	−	6.64607i	0.186456	−	0.233808i
$809$	−19.8626	+	24.9069i	−0.698331	+	0.875679i	−0.996898	−	0.0787094i	$-0.974920\pi$
$809$	−19.8626	+	24.9069i	−0.698331	+	0.875679i	0.298567	+	0.954389i	$0.403492\pi$
$810$	−1.40072	+	6.13696i	−0.0492163	+	0.215631i
$811$	7.02307	−	30.7701i	0.246613	−	1.08048i	−0.688250	−	0.725474i	$-0.741621\pi$
$811$	7.02307	−	30.7701i	0.246613	−	1.08048i	0.934863	−	0.355009i	$-0.115522\pi$
$812$	−1.48730	−	0.532270i	−0.0521940	−	0.0186790i
$813$	−11.1377	−	48.7976i	−0.390617	−	1.71141i
$814$	−24.5559			−0.860683
$815$	−17.8815			−0.626361
$816$	−1.35003	−	5.91486i	−0.0472604	−	0.207061i
$817$	14.8281	+	7.14082i	0.518768	+	0.249826i
$818$	−11.7698	+	14.7589i	−0.411521	+	0.516031i
$819$	−67.6419	−	24.2074i	−2.36360	−	0.845876i
$820$	13.1537	+	16.4943i	0.459348	+	0.576004i
$821$	2.36765	+	10.3733i	0.0826315	+	0.362032i	0.999292	−	0.0376357i	$-0.0119826\pi$
$821$	2.36765	+	10.3733i	0.0826315	+	0.362032i	−0.916660	+	0.399668i	$0.869125\pi$
$822$	4.22072	+	5.29261i	0.147214	+	0.184601i
$823$	16.1347	+	7.77008i	0.562422	+	0.270848i	0.693419	−	0.720535i	$-0.256104\pi$
$823$	16.1347	+	7.77008i	0.562422	+	0.270848i	−0.130997	+	0.991383i	$0.541818\pi$
$824$	3.31619	−	4.15837i	0.115525	−	0.144864i
$825$	−44.2872	+	21.3276i	−1.54188	+	0.742532i
$826$	−0.637524	+	5.31964i	−0.0221823	+	0.185094i
$827$	34.3841	+	16.5585i	1.19565	+	0.575796i	0.922434	−	0.386155i	$-0.126197\pi$
$827$	34.3841	+	16.5585i	1.19565	+	0.575796i	0.273220	+	0.961952i	$0.411911\pi$
$828$	7.34671	−	3.53799i	0.255316	−	0.122954i
$829$	−1.63659	+	7.17035i	−0.0568410	+	0.249037i	−0.995364	−	0.0961802i	$-0.969337\pi$
$829$	−1.63659	+	7.17035i	−0.0568410	+	0.249037i	0.938523	+	0.345217i	$0.112195\pi$
$830$	−28.4824	+	13.7164i	−0.988640	+	0.476104i
$831$	−6.50592	−	8.15817i	−0.225688	−	0.283004i
$832$	5.26229			0.182437
$833$	−6.63940	+	13.3020i	−0.230041	+	0.460888i
$834$	−44.5901			−1.54403
$835$	−24.7556	−	31.0425i	−0.856703	−	1.07427i
$836$	16.4671	−	7.93012i	0.569525	−	0.274269i
$837$	−0.116570	+	0.510725i	−0.00402924	+	0.0176532i
$838$	−16.5005	+	7.94622i	−0.570000	+	0.274497i
$839$	25.3285	+	12.1976i	0.874438	+	0.421107i	0.816590	−	0.577218i	$-0.195862\pi$
$839$	25.3285	+	12.1976i	0.874438	+	0.421107i	0.0578480	+	0.998325i	$0.481576\pi$
$840$	−11.9240	+	18.6822i	−0.411416	+	0.644596i
$841$	25.8069	−	12.4280i	0.889894	−	0.428550i
$842$	−19.7960	+	24.8234i	−0.682216	+	0.855472i
$843$	50.0721	+	24.1135i	1.72458	+	0.830512i
$844$	15.3529	+	19.2519i	0.528468	+	0.662678i
$845$	−9.58686	−	42.0028i	−0.329798	−	1.44494i
$846$	3.24411	+	4.06799i	0.111535	+	0.139860i
$847$	16.8753	−	26.4398i	0.579841	−	0.908481i
$848$	1.79666	−	2.25294i	0.0616975	−	0.0773662i
$849$	−28.1810	−	13.5712i	−0.967168	−	0.465764i
$850$	1.70106	+	7.45285i	0.0583460	+	0.255631i
$851$	−8.11679			−0.278240
$852$	9.58779			0.328472
$853$	−8.17623	−	35.8224i	−0.279949	−	1.22654i	−0.897858	−	0.440286i	$-0.854877\pi$
$853$	−8.17623	−	35.8224i	−0.279949	−	1.22654i	0.617909	−	0.786250i	$-0.287980\pi$
$854$	−8.35644	+	5.16860i	−0.285952	+	0.176866i
$855$	−12.8730	+	56.4001i	−0.440246	+	1.92884i
$856$	−0.354161	+	1.55168i	−0.0121050	+	0.0530354i
$857$	−16.9033	+	21.1961i	−0.577407	+	0.724046i	−0.981668	−	0.190598i	$-0.938957\pi$
$857$	−16.9033	+	21.1961i	−0.577407	+	0.724046i	0.404261	+	0.914644i	$0.367529\pi$
$858$	44.8070	−	56.1862i	1.52969	−	1.91817i
$859$	−7.22109	+	31.6377i	−0.246380	+	1.07946i	0.688705	+	0.725041i	$0.258179\pi$
$859$	−7.22109	+	31.6377i	−0.246380	+	1.07946i	−0.935086	+	0.354421i	$0.884678\pi$
$860$	2.80909	−	12.3074i	0.0957893	−	0.419680i
$861$	46.2425	−	28.6018i	1.57594	−	0.974746i
$862$	4.50993	+	19.7593i	0.153609	+	0.673004i
$863$	0.995757			0.0338960			0.0169480	−	0.999856i	$-0.494605\pi$
$863$	0.995757			0.0338960			0.0169480	+	0.999856i	$0.494605\pi$
$864$	−6.17063			−0.209929
$865$	14.4191	+	63.1742i	0.490264	+	2.14799i
$866$	3.37812	+	1.62682i	0.114793	+	0.0552815i
$867$	22.2441	−	27.8933i	0.755450	−	0.947304i
$868$	−0.120844	+	0.189335i	−0.00410170	+	0.00642644i
$869$	−32.4384	−	40.6764i	−1.10040	−	1.37985i
$870$	1.11294	+	4.87611i	0.0377322	+	0.165316i
$871$	−39.2820	−	49.2581i	−1.33102	−	1.66905i
$872$	12.4387	+	5.99015i	0.421227	+	0.202852i
$873$	33.9560	−	42.5794i	1.14924	−	1.44110i
$874$	5.44308	−	2.62125i	0.184115	−	0.0886651i
$875$	−5.84648	+	9.16012i	−0.197647	+	0.309668i
$876$	19.6833	+	9.47898i	0.665037	+	0.320265i
$877$	−23.9811	+	11.5487i	−0.809785	+	0.389972i	−0.792495	−	0.609878i	$-0.791218\pi$
$877$	−23.9811	+	11.5487i	−0.809785	+	0.389972i	−0.0172903	+	0.999851i	$0.505504\pi$
$878$	1.02756	−	4.50205i	0.0346786	−	0.151937i
$879$	54.7853	−	26.3832i	1.84786	−	0.889884i
$880$	−8.74090	−	10.9607i	−0.294656	−	0.369487i
$881$	−35.7880			−1.20573			−0.602863	−	0.797844i	$-0.705974\pi$
$881$	−35.7880			−1.20573			−0.602863	+	0.797844i	$0.705974\pi$
$882$	27.9190	+	22.9184i	0.940082	+	0.771702i
$883$	−34.0987			−1.14751			−0.573757	−	0.819026i	$-0.694515\pi$
$883$	−34.0987			−1.14751			−0.573757	+	0.819026i	$0.694515\pi$
$884$	−6.96831	−	8.73798i	−0.234369	−	0.293890i
$885$	15.2834	−	7.36012i	0.513747	−	0.247408i
$886$	6.47887	−	28.3858i	0.217662	−	0.953639i
$887$	−11.6921	+	5.63064i	−0.392583	+	0.189058i	−0.619753	−	0.784797i	$-0.712767\pi$
$887$	−11.6921	+	5.63064i	−0.392583	+	0.189058i	0.227169	+	0.973855i	$0.427053\pi$
$888$	13.2197	+	6.36626i	0.443623	+	0.213638i
$889$	−4.17779	+	34.8604i	−0.140118	+	1.16918i
$890$	31.7252	−	15.2781i	1.06343	−	0.512122i
$891$	−6.39838	+	8.02331i	−0.214354	+	0.268791i
$892$	−11.0271	−	5.31036i	−0.369214	−	0.177804i
$893$	2.40352	+	3.01392i	0.0804307	+	0.100857i
$894$	−7.88289	−	34.5372i	−0.263643	−	1.15510i
$895$	38.1574	+	47.8479i	1.27546	+	1.59938i
$896$	−2.49104	−	0.891482i	−0.0832197	−	0.0297823i
$897$	14.8107	−	18.5720i	0.494514	−	0.620101i
$898$	−30.1826	−	14.5352i	−1.00721	−	0.485045i
$899$	0.0112791	+	0.0494170i	0.000376180	+	0.00164815i
$900$	18.5732			0.619108
$901$	−6.12011			−0.203890
$902$	7.65333	+	33.5314i	0.254828	+	1.11647i
$903$	−30.6331	−	10.9628i	−1.01940	−	0.364821i
$904$	1.30466	−	5.71608i	0.0433923	−	0.190114i
$905$	13.8867	−	60.8416i	0.461610	−	2.02244i
$906$	−40.3945	+	50.6531i	−1.34202	+	1.68284i
$907$	1.24119	−	1.55640i	0.0412130	−	0.0516794i	−0.760798	−	0.648989i	$-0.775192\pi$
$907$	1.24119	−	1.55640i	0.0412130	−	0.0516794i	0.802011	+	0.597309i	$0.203764\pi$
$908$	−1.74106	+	7.62808i	−0.0577791	+	0.253147i
$909$	−9.76076	+	42.7647i	−0.323744	+	1.41842i
$910$	−4.85820	+	40.5378i	−0.161048	+	1.34382i
$911$	9.95483	+	43.6150i	0.329818	+	1.44503i	0.819476	+	0.573113i	$0.194265\pi$
$911$	9.95483	+	43.6150i	0.329818	+	1.44503i	−0.489658	+	0.871915i	$0.662878\pi$
$912$	−10.9210			−0.361630
$913$	−51.5380			−1.70566
$914$	−1.12133	−	4.91287i	−0.0370903	−	0.162503i
$915$	28.0289	+	13.4980i	0.926608	+	0.446231i
$916$	−6.84214	+	8.57977i	−0.226071	+	0.283484i
$917$	−32.0942	−	32.5515i	−1.05984	−	1.07495i
$918$	8.17112	+	10.2463i	0.269687	+	0.338177i
$919$	−3.87305	−	16.9689i	−0.127760	−	0.559753i	−0.997772	−	0.0667218i	$-0.978746\pi$
$919$	−3.87305	−	16.9689i	−0.127760	−	0.559753i	0.870012	−	0.493031i	$-0.164111\pi$
$920$	−2.88925	−	3.62300i	−0.0952557	−	0.119447i
$921$	39.8409	+	19.1864i	1.31280	+	0.632212i
$922$	−5.15062	+	6.45867i	−0.169627	+	0.212705i
$923$	15.9131	−	7.66334i	0.523786	−	0.252242i
$924$	−30.7290	+	19.0064i	−1.01091	+	0.625265i
$925$	−16.6571	−	8.02162i	−0.547681	−	0.263749i
$926$	35.3313	−	17.0147i	1.16106	−	0.559136i
$927$	−6.10720	+	26.7574i	−0.200587	+	0.878828i
$928$	−0.537934	+	0.259055i	−0.0176585	+	0.00850390i
$929$	−24.6174	−	30.8692i	−0.807671	−	1.01279i	−0.999508	−	0.0313604i	$-0.990016\pi$
$929$	−24.6174	−	30.8692i	−0.807671	−	1.01279i	0.191837	−	0.981427i	$-0.438555\pi$
$930$	0.711160			0.0233198
$931$	20.6848	+	16.9799i	0.677918	+	0.556495i
$932$	−21.6407			−0.708864
$933$	−29.9588	−	37.5671i	−0.980805	−	1.22989i
$934$	13.2262	−	6.36942i	0.432776	−	0.208414i
$935$	−6.62553	+	29.0283i	−0.216678	+	0.949328i
$936$	−24.4650	+	11.7817i	−0.799664	+	0.385098i
$937$	−7.95065	−	3.82883i	−0.259736	−	0.125082i	0.299485	−	0.954101i	$-0.403185\pi$
$937$	−7.95065	−	3.82883i	−0.259736	−	0.125082i	−0.559221	+	0.829019i	$0.688900\pi$
$938$	10.2503	+	29.9723i	0.334685	+	0.978629i
$939$	50.5217	−	24.3300i	1.64871	−	0.793979i
$940$	1.84361	−	2.31181i	0.0601318	−	0.0754029i
$941$	−38.2981	−	18.4434i	−1.24848	−	0.601237i	−0.311378	−	0.950286i	$-0.600790\pi$
$941$	−38.2981	−	18.4434i	−1.24848	−	0.601237i	−0.937104	+	0.349049i	$0.886505\pi$
$942$	−11.9695	−	15.0093i	−0.389988	−	0.489029i
$943$	2.52976	+	11.0836i	0.0823803	+	0.360932i
$944$	1.26258	+	1.58322i	0.0410935	+	0.0515296i
$945$	5.69678	−	47.5352i	0.185316	−	1.54632i
$946$	12.8317	−	16.0905i	0.417195	−	0.523146i
$947$	−15.2745	−	7.35582i	−0.496355	−	0.239032i	0.168921	−	0.985630i	$-0.445972\pi$
$947$	−15.2745	−	7.35582i	−0.496355	−	0.239032i	−0.665276	+	0.746598i	$0.731686\pi$
$948$	6.91761	+	30.3080i	0.224673	+	0.984359i
$949$	40.2452			1.30642
$950$	13.7607			0.446455
$951$	10.4711	+	45.8767i	0.339547	+	1.48765i
$952$	1.81832	+	5.31684i	0.0589322	+	0.172320i
$953$	0.216469	−	0.948414i	0.00701213	−	0.0307221i	−0.971301	−	0.237854i	$-0.923556\pi$
$953$	0.216469	−	0.948414i	0.00701213	−	0.0307221i	0.978313	+	0.207132i	$0.0664130\pi$
$954$	−3.30878	+	14.4967i	−0.107126	+	0.469348i
$955$	30.1422	−	37.7971i	0.975378	−	1.22309i
$956$	−9.96587	+	12.4968i	−0.322319	+	0.404175i
$957$	−1.81440	+	7.94938i	−0.0586511	+	0.256967i
$958$	−0.707985	+	3.10188i	−0.0228740	+	0.100217i
$959$	−4.40198	−	4.46471i	−0.142147	−	0.144173i
$960$	1.86403	+	8.16685i	0.0601613	+	0.263584i
$961$	−30.9928			−0.999768
$962$	27.0294			0.871464
$963$	−1.82752	−	8.00688i	−0.0588909	−	0.258018i
$964$	−21.4272	−	10.3188i	−0.690124	−	0.332346i
$965$	4.66309	−	5.84733i	0.150110	−	0.188232i
$966$	−10.1573	+	6.28245i	−0.326805	+	0.202134i
$967$	−8.02548	−	10.0636i	−0.258082	−	0.323625i	0.635862	−	0.771802i	$-0.280645\pi$
$967$	−8.02548	−	10.0636i	−0.258082	−	0.323625i	−0.893944	+	0.448178i	$0.852073\pi$
$968$	−2.63805	−	11.5581i	−0.0847902	−	0.371490i
$969$	14.4615	+	18.1342i	0.464571	+	0.582554i
$970$	−27.8849	−	13.4287i	−0.895330	−	0.431168i
$971$	8.06688	−	10.1155i	0.258878	−	0.324623i	−0.635358	−	0.772217i	$-0.719148\pi$
$971$	8.06688	−	10.1155i	0.258878	−	0.324623i	0.894237	+	0.447594i	$0.147719\pi$
$972$	−11.1540	+	5.37147i	−0.357764	+	0.172290i
$973$	41.0710	−	4.33355i	1.31667	−	0.138927i
$974$	25.0587	+	12.0676i	0.802932	+	0.386672i
$975$	48.7484	−	23.4760i	1.56120	−	0.751833i
$976$	−0.826391	+	3.62066i	−0.0264521	+	0.115894i
$977$	26.7629	−	12.8883i	0.856220	−	0.412334i	0.0463372	−	0.998926i	$-0.485245\pi$
$977$	26.7629	−	12.8883i	0.856220	−	0.412334i	0.809882	+	0.586592i	$0.199531\pi$
$978$	10.8605	+	13.6186i	0.347279	+	0.435475i
$979$	57.4057			1.83469
$980$	9.16725	−	18.3666i	0.292837	−	0.586699i
$981$	−71.2402			−2.27453
$982$	−6.71618	−	8.42182i	−0.214322	−	0.268751i
$983$	−1.28783	+	0.620187i	−0.0410754	+	0.0197809i	−0.454309	−	0.890844i	$-0.650114\pi$
$983$	−1.28783	+	0.620187i	−0.0410754	+	0.0197809i	0.413233	+	0.910625i	$0.364399\pi$
$984$	4.57305	−	20.0358i	0.145783	−	0.638719i
$985$	−69.7545	+	33.5920i	−2.22256	+	1.07033i
$986$	1.14249	+	0.550193i	0.0363842	+	0.0175217i
$987$	−5.35049	−	5.42674i	−0.170308	−	0.172735i
$988$	−18.1258	+	8.72894i	−0.576659	+	0.277704i
$989$	4.24144	−	5.31860i	0.134870	−	0.169121i
$990$	65.1775	+	31.3878i	2.07148	+	0.997570i
$991$	−31.7489	−	39.8119i	−1.00854	−	1.26467i	−0.964068	−	0.265657i	$-0.914411\pi$
$991$	−31.7489	−	39.8119i	−1.00854	−	1.26467i	−0.0444707	−	0.999011i	$-0.514160\pi$
$992$	0.0188910	+	0.0827671i	0.000599791	+	0.00262786i
$993$	−54.4250	−	68.2467i	−1.72712	−	2.16575i
$994$	−8.83110	+	0.931803i	−0.280106	+	0.0295550i
$995$	27.1851	−	34.0890i	0.861825	−	1.08069i
$996$	27.7455	+	13.3615i	0.879150	+	0.423376i
$997$	5.28181	+	23.1411i	0.167276	+	0.732886i	0.987078	+	0.160239i	$0.0512264\pi$
$997$	5.28181	+	23.1411i	0.167276	+	0.732886i	−0.819802	+	0.572647i	$0.805916\pi$
$998$	−20.0224			−0.633797
$999$	−31.6950			−1.00279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.e.a.57.3	yes	18
3.2	odd	2		882.2.u.j.253.3		18
4.3	odd	2		784.2.u.c.449.1		18
7.2	even	3		686.2.g.i.557.1		36
7.3	odd	6		686.2.g.j.79.3		36
7.4	even	3		686.2.g.i.79.1		36
7.5	odd	6		686.2.g.j.557.3		36
7.6	odd	2		686.2.e.a.393.1		18
49.6	odd	14		686.2.e.a.295.1		18
49.10	odd	42		686.2.g.j.569.3		36
49.16	even	21		686.2.g.i.165.1		36
49.22	even	7		4802.2.a.h.1.1		9
49.27	odd	14		4802.2.a.e.1.9		9
49.33	odd	42		686.2.g.j.165.3		36
49.39	even	21		686.2.g.i.569.1		36
49.43	even	7	inner	98.2.e.a.43.3	✓	18
147.92	odd	14		882.2.u.j.631.3		18
196.43	odd	14		784.2.u.c.337.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.a.43.3	✓	18	49.43	even	7	inner
98.2.e.a.57.3	yes	18	1.1	even	1	trivial
686.2.e.a.295.1		18	49.6	odd	14
686.2.e.a.393.1		18	7.6	odd	2
686.2.g.i.79.1		36	7.4	even	3
686.2.g.i.165.1		36	49.16	even	21
686.2.g.i.557.1		36	7.2	even	3
686.2.g.i.569.1		36	49.39	even	21
686.2.g.j.79.3		36	7.3	odd	6
686.2.g.j.165.3		36	49.33	odd	42
686.2.g.j.557.3		36	7.5	odd	6
686.2.g.j.569.3		36	49.10	odd	42
784.2.u.c.337.1		18	196.43	odd	14
784.2.u.c.449.1		18	4.3	odd	2
882.2.u.j.253.3		18	3.2	odd	2
882.2.u.j.631.3		18	147.92	odd	14
4802.2.a.e.1.9		9	49.27	odd	14
4802.2.a.h.1.1		9	49.22	even	7

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 + 0.781831i) q^{2} +(2.57370 - 1.23943i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-2.64206 + 1.27235i) q^{5} +(2.57370 + 1.23943i) q^{6} +(-2.49104 - 0.891482i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(3.21729 - 4.03436i) q^{9} +O(q^{10})\)	\(q+(0.623490 + 0.781831i) q^{2} +(2.57370 - 1.23943i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-2.64206 + 1.27235i) q^{5} +(2.57370 + 1.23943i) q^{6} +(-2.49104 - 0.891482i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(3.21729 - 4.03436i) q^{9} +(-2.64206 - 1.27235i) q^{10} +(-2.98073 - 3.73772i) q^{11} +(0.635652 + 2.78497i) q^{12} +(3.28098 + 4.11422i) q^{13} +(-0.856146 - 2.50340i) q^{14} +(-5.22290 + 6.54930i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(0.472600 + 2.07060i) q^{17} +5.16013 q^{18} +3.82308 q^{19} +(-0.652536 - 2.85895i) q^{20} +(-7.51612 + 0.793054i) q^{21} +(1.06381 - 4.66086i) q^{22} +(0.351636 - 1.54062i) q^{23} +(-1.78106 + 2.23338i) q^{24} +(2.24417 - 2.81410i) q^{25} +(-1.17097 + 5.13035i) q^{26} +(1.37309 - 6.01592i) q^{27} +(1.42344 - 2.23021i) q^{28} +(-0.132859 - 0.582092i) q^{29} -8.37687 q^{30} -0.0848956 q^{31} +(-0.222521 - 0.974928i) q^{32} +(-12.3042 - 5.92537i) q^{33} +(-1.32420 + 1.66049i) q^{34} +(7.71575 - 0.814118i) q^{35} +(3.21729 + 4.03436i) q^{36} +(-1.14296 - 5.00766i) q^{37} +(2.38365 + 2.98900i) q^{38} +(13.5436 + 6.52224i) q^{39} +(1.82836 - 2.29270i) q^{40} +(-6.48181 + 3.12147i) q^{41} +(-5.30626 - 5.38188i) q^{42} +(3.87857 + 1.86782i) q^{43} +(4.30728 - 2.07428i) q^{44} +(-3.36717 + 14.7525i) q^{45} +(1.42374 - 0.685639i) q^{46} +(0.628687 + 0.788349i) q^{47} -2.85659 q^{48} +(5.41052 + 4.44143i) q^{49} +3.59937 q^{50} +(3.78269 + 4.74335i) q^{51} +(-4.74116 + 2.28322i) q^{52} +(-0.641220 + 2.80937i) q^{53} +(5.55954 - 2.67733i) q^{54} +(12.6310 + 6.08275i) q^{55} +(2.63115 - 0.277622i) q^{56} +(9.83947 - 4.73844i) q^{57} +(0.372262 - 0.466801i) q^{58} +(-1.82448 - 0.878624i) q^{59} +(-5.22290 - 6.54930i) q^{60} +(-0.826391 - 3.62066i) q^{61} +(-0.0529315 - 0.0663741i) q^{62} +(-11.6109 + 7.18157i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-13.9033 - 6.69548i) q^{65} +(-3.03888 - 13.3142i) q^{66} -11.9726 q^{67} -2.12385 q^{68} +(-1.00448 - 4.40092i) q^{69} +(5.44720 + 5.52482i) q^{70} +(0.746863 - 3.27222i) q^{71} +(-1.14824 + 5.03076i) q^{72} +(4.76836 - 5.97933i) q^{73} +(3.20252 - 4.01583i) q^{74} +(2.28795 - 10.0242i) q^{75} +(-0.850715 + 3.72722i) q^{76} +(4.09300 + 11.9681i) q^{77} +(3.34499 + 14.6553i) q^{78} +10.8827 q^{79} +2.93247 q^{80} +(-0.477659 - 2.09276i) q^{81} +(-6.48181 - 3.12147i) q^{82} +(6.72146 - 8.42844i) q^{83} +(0.899323 - 7.50414i) q^{84} +(-3.88316 - 4.86933i) q^{85} +(0.957927 + 4.19695i) q^{86} +(-1.06340 - 1.33346i) q^{87} +(4.30728 + 2.07428i) q^{88} +(-7.48671 + 9.38804i) q^{89} +(-13.6334 + 6.56550i) q^{90} +(-4.50529 - 13.1736i) q^{91} +(1.42374 + 0.685639i) q^{92} +(-0.218496 + 0.105222i) q^{93} +(-0.224376 + 0.983055i) q^{94} +(-10.1008 + 4.86429i) q^{95} +(-1.78106 - 2.23338i) q^{96} +10.5542 q^{97} +(-0.0990455 + 6.99930i) q^{98} -24.6692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{5} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^5 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{5} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 4 q^{12} - 7 q^{14} - 9 q^{15} - 3 q^{16} - 11 q^{17} + 24 q^{18} + 36 q^{19} + q^{20} - 21 q^{21} - q^{22} + 5 q^{23} - 4 q^{24} - 23 q^{25} - 7 q^{26} - 12 q^{27} - 13 q^{29} - 16 q^{30} - 4 q^{31} - 3 q^{32} - 34 q^{33} - 11 q^{34} - 7 q^{35} + 10 q^{36} + 33 q^{37} + 15 q^{38} + 21 q^{39} + q^{40} - 28 q^{41} + 35 q^{42} - 20 q^{43} + 6 q^{44} + 20 q^{45} + 5 q^{46} + 36 q^{47} + 10 q^{48} + 49 q^{49} + 26 q^{50} - 20 q^{51} + 48 q^{53} + 2 q^{54} + 47 q^{55} + 7 q^{56} - 37 q^{57} + 36 q^{58} - 25 q^{59} - 9 q^{60} + q^{61} - 11 q^{62} - 35 q^{63} - 3 q^{64} - 56 q^{65} - 27 q^{66} + 34 q^{67} + 38 q^{68} + 23 q^{69} - 14 q^{70} - 6 q^{71} - 11 q^{72} - 39 q^{73} - 23 q^{74} - 47 q^{75} - 20 q^{76} - 28 q^{77} - 14 q^{78} - 2 q^{79} + 8 q^{80} - 34 q^{81} - 28 q^{82} + 35 q^{83} - 7 q^{84} + 33 q^{85} + 36 q^{86} + 48 q^{87} + 6 q^{88} - 6 q^{89} - 57 q^{90} - 35 q^{91} + 5 q^{92} + 36 q^{93} - 13 q^{94} - 17 q^{95} - 4 q^{96} + 56 q^{97} + 28 q^{98} + 106 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^5 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 4 * q^12 - 7 * q^14 - 9 * q^15 - 3 * q^16 - 11 * q^17 + 24 * q^18 + 36 * q^19 + q^20 - 21 * q^21 - q^22 + 5 * q^23 - 4 * q^24 - 23 * q^25 - 7 * q^26 - 12 * q^27 - 13 * q^29 - 16 * q^30 - 4 * q^31 - 3 * q^32 - 34 * q^33 - 11 * q^34 - 7 * q^35 + 10 * q^36 + 33 * q^37 + 15 * q^38 + 21 * q^39 + q^40 - 28 * q^41 + 35 * q^42 - 20 * q^43 + 6 * q^44 + 20 * q^45 + 5 * q^46 + 36 * q^47 + 10 * q^48 + 49 * q^49 + 26 * q^50 - 20 * q^51 + 48 * q^53 + 2 * q^54 + 47 * q^55 + 7 * q^56 - 37 * q^57 + 36 * q^58 - 25 * q^59 - 9 * q^60 + q^61 - 11 * q^62 - 35 * q^63 - 3 * q^64 - 56 * q^65 - 27 * q^66 + 34 * q^67 + 38 * q^68 + 23 * q^69 - 14 * q^70 - 6 * q^71 - 11 * q^72 - 39 * q^73 - 23 * q^74 - 47 * q^75 - 20 * q^76 - 28 * q^77 - 14 * q^78 - 2 * q^79 + 8 * q^80 - 34 * q^81 - 28 * q^82 + 35 * q^83 - 7 * q^84 + 33 * q^85 + 36 * q^86 + 48 * q^87 + 6 * q^88 - 6 * q^89 - 57 * q^90 - 35 * q^91 + 5 * q^92 + 36 * q^93 - 13 * q^94 - 17 * q^95 - 4 * q^96 + 56 * q^97 + 28 * q^98 + 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more