LMFDB - Embedded newform 126.2.h.c.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(67,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("126.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.h (of order $3$, degree $2$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	126.79
Dual form			126.2.h.c.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} +(1.09097 - 1.34528i) q^{6} +(-1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} +(1.09097 - 1.34528i) q^{6} +(-1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-2.23229 + 2.00422i) q^{9} +(-0.880438 - 1.52496i) q^{10} +6.12476 q^{11} +(-1.71053 - 0.272169i) q^{12} +(-0.380438 - 0.658939i) q^{13} +(2.56238 + 0.658939i) q^{14} +(1.09097 + 2.84813i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(2.85185 + 0.931107i) q^{18} +(0.971410 - 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(-4.20370 - 1.82454i) q^{21} +(-3.06238 - 5.30420i) q^{22} -0.421067 q^{23} +(0.619562 + 1.61745i) q^{24} -1.89931 q^{25} +(-0.380438 + 0.658939i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.710533 - 2.54856i) q^{28} +(0.732287 - 1.26836i) q^{29} +(1.92107 - 2.36887i) q^{30} +(-3.85185 + 6.67160i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.79467 + 9.90650i) q^{33} +(-3.42107 + 5.92546i) q^{34} +(-3.26088 + 3.32738i) q^{35} +(-0.619562 - 2.93533i) q^{36} +(1.44282 - 2.49904i) q^{37} -1.94282 q^{38} +(0.830095 - 1.02359i) q^{39} +1.76088 q^{40} +(-3.47141 - 6.01266i) q^{41} +(0.521753 + 4.55278i) q^{42} +(4.33009 - 7.49994i) q^{43} +(-3.06238 + 5.30420i) q^{44} +(-3.93078 + 3.52918i) q^{45} +(0.210533 + 0.364654i) q^{46} +(-0.830095 - 1.43777i) q^{47} +(1.09097 - 1.34528i) q^{48} +(-0.141315 - 6.99857i) q^{49} +(0.949657 + 1.64485i) q^{50} +(7.46457 - 9.20459i) q^{51} +0.760877 q^{52} +(-0.112725 - 0.195246i) q^{53} +(0.260877 + 5.18960i) q^{54} +10.7850 q^{55} +(-1.85185 + 1.88962i) q^{56} +(3.32326 + 0.528775i) q^{57} -1.46457 q^{58} +(-0.993163 + 1.72021i) q^{59} +(-3.01204 - 0.479256i) q^{60} +(5.17511 + 8.96355i) q^{61} +7.70370 q^{62} +(0.346647 - 7.92968i) q^{63} +1.00000 q^{64} +(-0.669905 - 1.16031i) q^{65} +(6.68194 - 8.23953i) q^{66} +(-3.39248 + 5.87594i) q^{67} +6.84213 q^{68} +(-0.260877 - 0.681054i) q^{69} +(4.51204 + 1.16031i) q^{70} +10.7850 q^{71} +(-2.23229 + 2.00422i) q^{72} +(0.153353 + 0.265616i) q^{73} -2.88564 q^{74} +(-1.17674 - 3.07204i) q^{75} +(0.971410 + 1.68253i) q^{76} +(-11.3421 + 11.5735i) q^{77} +(-1.30150 - 0.207087i) q^{78} +(6.72257 + 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(0.966208 - 8.94799i) q^{81} +(-3.47141 + 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(3.68194 - 2.72824i) q^{84} +(-6.02408 - 10.4340i) q^{85} -8.66019 q^{86} +(2.50520 + 0.398611i) q^{87} +6.12476 q^{88} +(1.30150 - 2.25427i) q^{89} +(5.02175 + 1.63957i) q^{90} +(1.94966 + 0.501371i) q^{91} +(0.210533 - 0.364654i) q^{92} +(-13.1774 - 2.09671i) q^{93} +(-0.830095 + 1.43777i) q^{94} +(1.71053 - 2.96273i) q^{95} +(-1.71053 - 0.272169i) q^{96} +(-1.81806 + 3.14897i) q^{97} +(-5.99028 + 3.62167i) q^{98} +(-13.6722 + 12.2754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.619562	+	1.61745i	0.357704	+	0.933835i
$3$	0.619562	+	1.61745i	0.357704	+	0.933835i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.76088			0.787488			0.393744	−	0.919220i	$-0.371180\pi$
$5$	1.76088			0.787488			0.393744	+	0.919220i	$0.371180\pi$
$6$	1.09097	−	1.34528i	0.445387	−	0.549209i
$7$	−1.85185	+	1.88962i	−0.699933	+	0.714209i
$7$	−1.85185	+	1.88962i	−0.699933	+	0.714209i
$8$	1.00000			0.353553
$9$	−2.23229	+	2.00422i	−0.744096	+	0.668073i
$10$	−0.880438	−	1.52496i	−0.278419	−	0.482236i
$11$	6.12476			1.84669			0.923343	−	0.383977i	$-0.125446\pi$
$11$	6.12476			1.84669			0.923343	+	0.383977i	$0.125446\pi$
$12$	−1.71053	−	0.272169i	−0.493788	−	0.0785683i
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	0.808434	−	0.588587i	$-0.200316\pi$
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	−0.913948	+	0.405831i	$0.866982\pi$
$14$	2.56238	+	0.658939i	0.684825	+	0.176109i
$15$	1.09097	+	2.84813i	0.281688	+	0.735384i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	−0.898250	−	0.439486i	$-0.855161\pi$
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	0.0685191	−	0.997650i	$-0.478173\pi$
$18$	2.85185	+	0.931107i	0.672187	+	0.219464i
$19$	0.971410	−	1.68253i	0.222857	−	0.385999i	−0.732818	−	0.680425i	$-0.761795\pi$
$19$	0.971410	−	1.68253i	0.222857	−	0.385999i	0.955674	+	0.294426i	$0.0951285\pi$
$20$	−0.880438	+	1.52496i	−0.196872	+	0.340992i
$21$	−4.20370	−	1.82454i	−0.917322	−	0.398147i
$22$	−3.06238	−	5.30420i	−0.652902	−	1.13086i
$23$	−0.421067			−0.0877985			−0.0438992	−	0.999036i	$-0.513978\pi$
$23$	−0.421067			−0.0877985			−0.0438992	+	0.999036i	$0.513978\pi$
$24$	0.619562	+	1.61745i	0.126467	+	0.330161i
$25$	−1.89931			−0.379863
$26$	−0.380438	+	0.658939i	−0.0746101	+	0.129228i
$27$	−4.62476	−	2.36887i	−0.890036	−	0.455890i
$28$	−0.710533	−	2.54856i	−0.134278	−	0.481632i
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	−0.789990	−	0.613120i	$-0.789914\pi$
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	0.925972	+	0.377592i	$0.123248\pi$
$30$	1.92107	−	2.36887i	0.350737	−	0.432495i
$31$	−3.85185	+	6.67160i	−0.691812	+	1.19825i	0.279431	+	0.960166i	$0.409854\pi$
$31$	−3.85185	+	6.67160i	−0.691812	+	1.19825i	−0.971243	+	0.238088i	$0.923479\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.79467	+	9.90650i	0.660567	+	1.72450i
$34$	−3.42107	+	5.92546i	−0.586708	+	1.01621i
$35$	−3.26088	+	3.32738i	−0.551189	+	0.562431i
$36$	−0.619562	−	2.93533i	−0.103260	−	0.489221i
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	−0.722711	−	0.691150i	$-0.757104\pi$
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	0.959909	+	0.280311i	$0.0904376\pi$
$38$	−1.94282			−0.315167
$39$	0.830095	−	1.02359i	0.132922	−	0.163906i
$40$	1.76088			0.278419
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	−0.998781	−	0.0493667i	$-0.984280\pi$
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	0.456638	−	0.889653i	$-0.349054\pi$
$42$	0.521753	+	4.55278i	0.0805083	+	0.702509i
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	−0.320195	−	0.947352i	$-0.603748\pi$
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	0.980528	−	0.196379i	$-0.0629183\pi$
$44$	−3.06238	+	5.30420i	−0.461671	+	0.799638i
$45$	−3.93078	+	3.52918i	−0.585966	+	0.526100i
$46$	0.210533	+	0.364654i	0.0310414	+	0.0537654i
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	0.799113	−	0.601181i	$-0.205303\pi$
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	−0.920195	+	0.391461i	$0.871970\pi$
$48$	1.09097	−	1.34528i	0.157468	−	0.194175i
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$	0.949657	+	1.64485i	0.134302	+	0.232617i
$51$	7.46457	−	9.20459i	1.04525	−	1.28890i
$52$	0.760877			0.105515
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	0.858180	−	0.513350i	$-0.171596\pi$
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	−0.873664	+	0.486531i	$0.838262\pi$
$54$	0.260877	+	5.18960i	0.0355008	+	0.706215i
$55$	10.7850			1.45424
$56$	−1.85185	+	1.88962i	−0.247464	+	0.252511i
$57$	3.32326	+	0.528775i	0.440176	+	0.0700379i
$58$	−1.46457			−0.192308
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	−0.923405	−	0.383827i	$-0.874606\pi$
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	0.794106	+	0.607779i	$0.207939\pi$
$60$	−3.01204	−	0.479256i	−0.388852	−	0.0618716i
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	0.979929	+	0.199348i	$0.0638823\pi$
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	−0.317324	+	0.948317i	$0.602784\pi$
$62$	7.70370			0.978370
$63$	0.346647	−	7.92968i	0.0436734	−	0.999046i
$64$	1.00000			0.125000
$65$	−0.669905	−	1.16031i	−0.0830915	−	0.143919i
$66$	6.68194	−	8.23953i	0.822490	−	1.01422i
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	−0.995371	−	0.0961042i	$-0.969362\pi$
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	0.580914	+	0.813965i	$0.302695\pi$
$68$	6.84213			0.829731
$69$	−0.260877	−	0.681054i	−0.0314059	−	0.0819893i
$70$	4.51204	+	1.16031i	0.539292	+	0.138684i
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$	−2.23229	+	2.00422i	−0.263078	+	0.236200i
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	0.874860	−	0.484375i	$-0.160953\pi$
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	−0.856912	+	0.515463i	$0.827620\pi$
$74$	−2.88564			−0.335449
$75$	−1.17674	−	3.07204i	−0.135878	−	0.354729i
$76$	0.971410	+	1.68253i	0.111428	+	0.193000i
$77$	−11.3421	+	11.5735i	−1.29256	+	1.31892i
$78$	−1.30150	−	0.207087i	−0.147366	−	0.0234480i
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	0.944701	+	0.327932i	$0.106352\pi$
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	−0.188353	+	0.982101i	$0.560315\pi$
$80$	−0.880438	−	1.52496i	−0.0984360	−	0.170496i
$81$	0.966208	−	8.94799i	0.107356	−	0.994221i
$82$	−3.47141	+	6.01266i	−0.383353	+	0.663987i
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	−0.938942	−	0.344075i	$-0.888193\pi$
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	0.767449	+	0.641110i	$0.221526\pi$
$84$	3.68194	−	2.72824i	0.401733	−	0.297675i
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$	−8.66019			−0.933852
$87$	2.50520	+	0.398611i	0.268586	+	0.0427356i
$88$	6.12476			0.652902
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	−0.788765	−	0.614695i	$-0.789279\pi$
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	0.926724	+	0.375743i	$0.122612\pi$
$90$	5.02175	+	1.63957i	0.529339	+	0.172825i
$91$	1.94966	+	0.501371i	0.204380	+	0.0525580i
$92$	0.210533	−	0.364654i	0.0219496	−	0.0380178i
$93$	−13.1774	−	2.09671i	−1.36644	−	0.217418i
$94$	−0.830095	+	1.43777i	−0.0856178	+	0.148294i
$95$	1.71053	−	2.96273i	0.175497	−	0.303970i
$96$	−1.71053	−	0.272169i	−0.174581	−	0.0277781i
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	−0.943440	−	0.331543i	$-0.892431\pi$
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	0.758845	+	0.651272i	$0.225764\pi$
$98$	−5.99028	+	3.62167i	−0.605110	+	0.365844i
$99$	−13.6722	+	12.2754i	−1.37411	+	1.23372i
$100$	0.949657	−	1.64485i	0.0949657	−	0.164485i
$101$	−8.01040			−0.797065			−0.398532	−	0.917154i	$-0.630480\pi$
$101$	−8.01040			−0.797065			−0.398532	+	0.917154i	$0.630480\pi$
$102$	−11.7037	−	1.86221i	−1.15884	−	0.184387i
$103$	−6.82846			−0.672828			−0.336414	−	0.941714i	$-0.609214\pi$
$103$	−6.82846			−0.672828			−0.336414	+	0.941714i	$0.609214\pi$
$104$	−0.380438	−	0.658939i	−0.0373051	−	0.0646142i
$105$	−7.40219	−	3.21278i	−0.722380	−	0.313536i
$106$	−0.112725	+	0.195246i	−0.0109488	+	0.0189639i
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	−0.767513	−	0.641033i	$-0.778506\pi$
$107$	1.77292	−	3.07078i	0.171394	−	0.296863i	0.938908	+	0.344170i	$0.111840\pi$
$108$	4.36389	−	2.82073i	0.419915	−	0.271424i
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	0.882384	−	0.470530i	$-0.155937\pi$
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	−0.848683	+	0.528902i	$0.822604\pi$
$110$	−5.39248	−	9.34004i	−0.514152	−	0.890538i
$111$	4.93598	+	0.785381i	0.468503	+	0.0745451i
$112$	2.56238	+	0.658939i	0.242122	+	0.0622638i
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	0.993715	−	0.111939i	$-0.0357061\pi$
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	−0.593799	+	0.804613i	$0.702373\pi$
$114$	−1.20370	−	3.14241i	−0.112737	−	0.294314i
$115$	−0.741446			−0.0691402
$116$	0.732287	+	1.26836i	0.0679911	+	0.117764i
$117$	2.16991	+	0.708458i	0.200608	+	0.0654970i
$118$	1.98633			0.182856
$119$	17.5322	+	4.50855i	1.60717	+	0.413298i
$120$	1.09097	+	2.84813i	0.0995916	+	0.259997i
$121$	26.5127			2.41025
$122$	5.17511	−	8.96355i	0.468532	−	0.811521i
$123$	7.57442	−	9.34004i	0.682962	−	0.842163i
$124$	−3.85185	−	6.67160i	−0.345906	−	0.599127i
$125$	−12.1488			−1.08663
$126$	−7.04063	+	3.66464i	−0.627229	+	0.326472i
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	14.8135	+	2.35703i	1.30426	+	0.207525i
$130$	−0.669905	+	1.16031i	−0.0587546	+	0.101766i
$131$	−7.29303			−0.637195			−0.318598	−	0.947890i	$-0.603212\pi$
$131$	−7.29303			−0.637195			−0.318598	+	0.947890i	$0.603212\pi$
$132$	−10.4766	−	1.66697i	−0.911872	−	0.145091i
$133$	1.38044	+	4.95139i	0.119699	+	0.429340i
$134$	6.78495			0.586131
$135$	−8.14364	−	4.17129i	−0.700893	−	0.359008i
$136$	−3.42107	−	5.92546i	−0.293354	−	0.508104i
$137$	−8.18194			−0.699031			−0.349515	−	0.936931i	$-0.613654\pi$
$137$	−8.18194			−0.699031			−0.349515	+	0.936931i	$0.613654\pi$
$138$	−0.459372	+	0.566453i	−0.0391043	+	0.0482197i
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	−0.999443	−	0.0333640i	$-0.989378\pi$
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	0.470828	−	0.882225i	$-0.343955\pi$
$140$	−1.25116	−	4.48769i	−0.105742	−	0.379279i
$141$	1.81122	−	2.23342i	0.152532	−	0.188088i
$142$	−5.39248	−	9.34004i	−0.452527	−	0.783799i
$143$	−2.33009	−	4.03584i	−0.194852	−	0.337494i
$144$	2.85185	+	0.931107i	0.237654	+	0.0775923i
$145$	1.28947	−	2.23342i	0.107084	−	0.185476i
$146$	0.153353	−	0.265616i	0.0126916	−	0.0219825i
$147$	11.2323	−	4.56462i	0.926423	−	0.376483i
$148$	1.44282	+	2.49904i	0.118599	+	0.205420i
$149$	8.82846			0.723256			0.361628	−	0.932323i	$-0.382221\pi$
$149$	8.82846			0.723256			0.361628	+	0.932323i	$0.382221\pi$
$150$	−2.07210	+	2.55511i	−0.169186	+	0.208624i
$151$	−14.9863			−1.21957			−0.609785	−	0.792567i	$-0.708744\pi$
$151$	−14.9863			−1.21957			−0.609785	+	0.792567i	$0.708744\pi$
$152$	0.971410	−	1.68253i	0.0787918	−	0.136471i
$153$	19.5127	+	6.37076i	1.57751	+	0.515045i
$154$	15.6940	+	4.03584i	1.26466	+	0.325217i
$155$	−6.78263	+	11.7479i	−0.544794	+	0.943611i
$156$	0.471410	+	1.23068i	0.0377430	+	0.0985332i
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	0.186761	+	0.982405i	$0.440201\pi$
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	−0.944169	+	0.329462i	$0.893132\pi$
$158$	6.72257	−	11.6438i	0.534819	−	0.926334i
$159$	0.245960	−	0.303294i	0.0195059	−	0.0240528i
$160$	−0.880438	+	1.52496i	−0.0696048	+	0.120559i
$161$	0.779752	−	0.795655i	0.0614530	−	0.0627064i
$162$	−8.23229	+	3.63723i	−0.646790	+	0.285768i
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	0.405450	+	0.914117i	$0.367115\pi$
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	−0.994374	+	0.105929i	$0.966219\pi$
$164$	6.94282			0.542143
$165$	6.68194	+	17.4441i	0.520189	+	1.35802i
$166$	3.12476			0.242529
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	0.887311	−	0.461171i	$-0.152570\pi$
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	−0.843041	+	0.537849i	$0.819237\pi$
$168$	−4.20370	−	1.82454i	−0.324322	−	0.140766i
$169$	6.21053	−	10.7570i	0.477733	−	0.827458i
$170$	−6.02408	+	10.4340i	−0.462026	+	0.800252i
$171$	1.20370	+	5.70281i	0.0920490	+	0.436105i
$172$	4.33009	+	7.49994i	0.330167	+	0.571865i
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	0.856411	−	0.516295i	$-0.172689\pi$
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	−0.875330	+	0.483526i	$0.839356\pi$
$174$	−0.907394	−	2.36887i	−0.0687893	−	0.179584i
$175$	3.51724	−	3.58898i	0.265878	−	0.271301i
$176$	−3.06238	−	5.30420i	−0.230836	−	0.399819i
$177$	−3.39768	−	0.540616i	−0.255385	−	0.0406352i
$178$	−2.60301			−0.195104
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	0.982499	−	0.186270i	$-0.0596398\pi$
$179$	4.41423	+	7.64567i	0.329935	+	0.571464i	−0.652564	+	0.757734i	$0.726306\pi$
$180$	−1.09097	−	5.16875i	−0.0813162	−	0.385256i
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$	−0.540628	−	1.93914i	−0.0400740	−	0.143738i
$183$	−11.2918	+	13.9239i	−0.834713	+	1.02929i
$184$	−0.421067			−0.0310414
$185$	2.54063	−	4.40050i	0.186791	−	0.323531i
$186$	4.77292	+	12.4603i	0.349967	+	0.913637i
$187$	−20.9532	−	36.2920i	−1.53225	−	2.65394i
$188$	1.66019			0.121082
$189$	13.0406	−	4.35224i	0.948566	−	0.316579i
$190$	−3.42107			−0.248190
$191$	8.08414	+	14.0021i	0.584947	+	1.01316i	0.994882	+	0.101044i	$0.0322182\pi$
$191$	8.08414	+	14.0021i	0.584947	+	1.01316i	−0.409934	+	0.912115i	$0.634448\pi$
$192$	0.619562	+	1.61745i	0.0447130	+	0.116729i
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	−0.490007	−	0.871719i	$-0.663006\pi$
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	0.999934	−	0.0115011i	$-0.00366101\pi$
$194$	3.63611			0.261058
$195$	1.46169	−	1.80242i	0.104674	−	0.129074i
$196$	6.13160	+	3.37690i	0.437971	+	0.241207i
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$	17.4669	+	5.70281i	1.24132	+	0.405281i
$199$	−4.47141	−	7.74471i	−0.316970	−	0.549008i	0.662884	−	0.748722i	$-0.269332\pi$
$199$	−4.47141	−	7.74471i	−0.316970	−	0.549008i	−0.979854	+	0.199714i	$0.935999\pi$
$200$	−1.89931			−0.134302
$201$	−11.6059	−	1.84665i	−0.818616	−	0.130253i
$202$	4.00520	+	6.93721i	0.281805	+	0.488101i
$203$	1.04063	+	3.73255i	0.0730378	+	0.261974i
$204$	4.23912	+	11.0668i	0.296798	+	0.774831i
$205$	−6.11273	−	10.5876i	−0.426931	−	0.739467i
$206$	3.41423	+	5.91362i	0.237881	+	0.412021i
$207$	0.939941	−	0.843910i	0.0653304	−	0.0586558i
$208$	−0.380438	+	0.658939i	−0.0263787	+	0.0456892i
$209$	5.94966	−	10.3051i	0.411546	−	0.712819i
$210$	0.918743	+	8.01688i	0.0633993	+	0.553217i
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	0.929702	+	0.368314i	$0.120065\pi$
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	−0.145882	+	0.989302i	$0.546602\pi$
$212$	0.225450			0.0154840
$213$	6.68194	+	17.4441i	0.457839	+	1.19525i
$214$	−3.54583			−0.242388
$215$	7.62476	−	13.2065i	0.520005	−	0.900674i
$216$	−4.62476	−	2.36887i	−0.314675	−	0.161181i
$217$	−5.47373	−	19.6333i	−0.371581	−	1.33280i
$218$	0.351848	−	0.609419i	0.0238302	−	0.0412751i
$219$	−0.334608	+	0.412607i	−0.0226107	+	0.0278814i
$220$	−5.39248	+	9.34004i	−0.363561	+	0.629706i
$221$	−2.60301	+	4.50855i	−0.175097	+	0.303278i
$222$	−1.78783	−	4.66738i	−0.119991	−	0.313254i
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	−0.996998	−	0.0774293i	$-0.975329\pi$
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	0.565555	+	0.824711i	$0.308662\pi$
$224$	−0.710533	−	2.54856i	−0.0474745	−	0.170283i
$225$	4.23981	−	3.80664i	0.282654	−	0.253776i
$226$	4.25116	−	7.36323i	0.282783	−	0.489795i
$227$	21.9967			1.45997			0.729987	−	0.683461i	$-0.239526\pi$
$227$	21.9967			1.45997			0.729987	+	0.683461i	$0.239526\pi$
$228$	−2.11956	+	2.61364i	−0.140371	+	0.173092i
$229$	−3.79863			−0.251020			−0.125510	−	0.992092i	$-0.540057\pi$
$229$	−3.79863			−0.251020			−0.125510	+	0.992092i	$0.540057\pi$
$230$	0.370723	+	0.642111i	0.0244448	+	0.0423396i
$231$	−25.7466	−	11.1749i	−1.69401	−	0.735251i
$232$	0.732287	−	1.26836i	0.0480770	−	0.0832718i
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	−0.954350	−	0.298689i	$-0.903451\pi$
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	0.735848	+	0.677147i	$0.236784\pi$
$234$	−0.471410	−	2.23342i	−0.0308170	−	0.146003i
$235$	−1.46169	−	2.53173i	−0.0953505	−	0.165152i
$236$	−0.993163	−	1.72021i	−0.0646494	−	0.111976i
$237$	−14.6683	+	18.0875i	−0.952807	+	1.17491i
$238$	−4.86156	−	17.4376i	−0.315128	−	1.13031i
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	−0.999977	−	0.00677786i	$-0.997843\pi$
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	0.494119	−	0.869394i	$-0.335491\pi$
$240$	1.92107	−	2.36887i	0.124004	−	0.152910i
$241$	21.4120			1.37927			0.689635	−	0.724157i	$-0.257771\pi$
$241$	21.4120			1.37927			0.689635	+	0.724157i	$0.257771\pi$
$242$	−13.2564	−	22.9607i	−0.852151	−	1.47597i
$243$	15.0715	−	3.98104i	0.966840	−	0.255384i
$244$	−10.3502			−0.662605
$245$	−0.248838	−	12.3236i	−0.0158977	−	0.787328i
$246$	−11.8759	−	1.88962i	−0.757181	−	0.120478i
$247$	−1.47825			−0.0940586
$248$	−3.85185	+	6.67160i	−0.244593	+	0.423647i
$249$	−5.34501	−	0.850463i	−0.338726	−	0.0538959i
$250$	6.07442	+	10.5212i	0.384180	+	0.665419i
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$	6.69398	+	4.26505i	0.421681	+	0.268673i
$253$	−2.57893			−0.162136
$254$	9.47661	+	16.4140i	0.594616	+	1.02990i
$255$	13.1442	−	16.2082i	0.823121	−	1.01499i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.2599			1.26378			0.631890	−	0.775058i	$-0.282279\pi$
$257$	20.2599			1.26378			0.631890	+	0.775058i	$0.282279\pi$
$258$	−5.36552	−	14.0074i	−0.334043	−	0.872064i
$259$	2.05034	+	7.35422i	0.127402	+	0.456969i
$260$	1.33981			0.0830915
$261$	0.907394	+	4.29900i	0.0561663	+	0.266102i
$262$	3.64652	+	6.31595i	0.225283	+	0.390201i
$263$	−22.4887			−1.38671			−0.693355	−	0.720596i	$-0.743868\pi$
$263$	−22.4887			−1.38671			−0.693355	+	0.720596i	$0.743868\pi$
$264$	3.79467	+	9.90650i	0.233546	+	0.609703i
$265$	−0.198495	−	0.343803i	−0.0121935	−	0.0211197i
$266$	3.59781	−	3.67119i	0.220596	−	0.225095i
$267$	4.45254	+	0.708458i	0.272491	+	0.0433569i
$268$	−3.39248	−	5.87594i	−0.207228	−	0.358930i
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	−0.936167	−	0.351556i	$-0.885653\pi$
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	0.163627	−	0.986522i	$-0.447681\pi$
$270$	0.459372	+	9.13825i	0.0279565	+	0.556136i
$271$	−6.87880	+	11.9144i	−0.417858	+	0.723751i	−0.995724	−	0.0923810i	$-0.970552\pi$
$271$	−6.87880	+	11.9144i	−0.417858	+	0.723751i	0.577866	+	0.816132i	$0.303886\pi$
$272$	−3.42107	+	5.92546i	−0.207433	+	0.359284i
$273$	0.396990	+	3.46410i	0.0240269	+	0.209657i
$274$	4.09097	+	7.08577i	0.247145	+	0.428067i
$275$	−11.6328			−0.701487
$276$	0.720248	+	0.114601i	0.0433539	+	0.00689818i
$277$	−3.28263			−0.197234			−0.0986171	−	0.995125i	$-0.531442\pi$
$277$	−3.28263			−0.197234			−0.0986171	+	0.995125i	$0.531442\pi$
$278$	−6.23229	+	10.7946i	−0.373788	+	0.647419i
$279$	−4.77292	−	22.6129i	−0.285747	−	1.35380i
$280$	−3.26088	+	3.32738i	−0.194875	+	0.198849i
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	−0.846480	−	0.532421i	$-0.821282\pi$
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	0.884330	+	0.466863i	$0.154616\pi$
$282$	−2.83981	−	0.451852i	−0.169108	−	0.0269074i
$283$	4.09617	−	7.09478i	0.243492	−	0.421741i	−0.718214	−	0.695822i	$-0.755040\pi$
$283$	4.09617	−	7.09478i	0.243492	−	0.421741i	0.961707	+	0.274081i	$0.0883736\pi$
$284$	−5.39248	+	9.34004i	−0.319985	+	0.554230i
$285$	5.85185	+	0.931107i	0.346634	+	0.0551540i
$286$	−2.33009	+	4.03584i	−0.137781	+	0.238644i
$287$	17.7902	+	4.57489i	1.05012	+	0.270047i
$288$	−0.619562	−	2.93533i	−0.0365080	−	0.172966i
$289$	−14.9074	+	25.8204i	−0.876906	+	1.51884i
$290$	−2.57893			−0.151440
$291$	−6.21969	−	0.989636i	−0.364605	−	0.0580135i
$292$	−0.306707			−0.0179487
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	0.998469	−	0.0553202i	$-0.0176180\pi$
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	−0.547143	+	0.837039i	$0.684285\pi$
$294$	−9.56922	−	7.44514i	−0.558088	−	0.434209i
$295$	−1.74884	+	3.02908i	−0.101821	+	0.176360i
$296$	1.44282	−	2.49904i	0.0838622	−	0.145254i
$297$	−28.3256	−	14.5088i	−1.64362	−	0.841886i
$298$	−4.41423	−	7.64567i	−0.255709	−	0.442902i
$299$	0.160190	+	0.277457i	0.00926402	+	0.0160458i
$300$	3.24884	+	0.516934i	0.187572	+	0.0298452i
$301$	6.15335	+	22.0710i	0.354673	+	1.27215i
$302$	7.49316	+	12.9785i	0.431183	+	0.746831i
$303$	−4.96294	−	12.9564i	−0.285113	−	0.744327i
$304$	−1.94282			−0.111428
$305$	9.11273	+	15.7837i	0.521793	+	0.903772i
$306$	−4.23912	−	20.0839i	−0.242335	−	1.14812i
$307$	4.89931			0.279619			0.139809	−	0.990178i	$-0.455351\pi$
$307$	4.89931			0.279619			0.139809	+	0.990178i	$0.455351\pi$
$308$	−4.35185	−	15.6093i	−0.247970	−	0.889423i
$309$	−4.23065	−	11.0447i	−0.240673	−	0.628310i
$310$	13.5653			0.770455
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	−0.736175	−	0.676791i	$-0.763370\pi$
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	0.954206	+	0.299151i	$0.0967034\pi$
$312$	0.830095	−	1.02359i	0.0469949	−	0.0579495i
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	0.889347	−	0.457233i	$-0.151159\pi$
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	−0.840649	+	0.541581i	$0.817826\pi$
$314$	18.9806			1.07114
$315$	0.610402	−	13.9632i	0.0343923	−	0.786737i
$316$	−13.4451			−0.756348
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.779161	−	0.626824i	$-0.784354\pi$
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.153266	−	0.988185i	$-0.548979\pi$
$318$	−0.385640	−	0.0613605i	−0.0216256	−	0.00344093i
$319$	4.48508	−	7.76839i	0.251116	−	0.434946i
$320$	1.76088			0.0984360
$321$	6.06526	+	0.965064i	0.338530	+	0.0538646i
$322$	−1.07893	−	0.277457i	−0.0601266	−	0.0154621i
$323$	−13.2930			−0.739644
$324$	7.26608	+	5.31075i	0.403671	+	0.295042i
$325$	0.722572	+	1.25153i	0.0400811	+	0.0694224i
$326$	15.0377			0.832864
$327$	−0.767713	+	0.946670i	−0.0424546	+	0.0523510i
$328$	−3.47141	−	6.01266i	−0.191677	−	0.331994i
$329$	4.25404	+	1.09396i	0.234533	+	0.0603121i
$330$	11.7661	−	14.5088i	0.647701	−	0.798683i
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	0.823594	−	0.567179i	$-0.191965\pi$
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	−0.902989	+	0.429664i	$0.858632\pi$
$332$	−1.56238	−	2.70612i	−0.0857468	−	0.148518i
$333$	1.78783	+	8.47030i	0.0979726	+	0.464169i
$334$	0.572097	−	0.990901i	0.0313037	−	0.0542197i
$335$	−5.97373	+	10.3468i	−0.326380	+	0.565307i
$336$	0.521753	+	4.55278i	0.0284640	+	0.248374i
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$	−12.4211			−0.675617
$339$	−9.27579	+	11.4380i	−0.503792	+	0.621228i
$340$	12.0482			0.653403
$341$	−23.5917	+	40.8620i	−1.27756	+	2.21280i
$342$	4.33693	−	3.89384i	0.234514	−	0.210555i
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$	4.33009	−	7.49994i	0.233463	−	0.404370i
$345$	−0.459372	−	1.19925i	−0.0247317	−	0.0645656i
$346$	−0.248838	+	0.431001i	−0.0133776	+	0.0231707i
$347$	−4.84733	+	8.39583i	−0.260219	+	0.450712i	−0.966300	−	0.257419i	$-0.917128\pi$
$347$	−4.84733	+	8.39583i	−0.260219	+	0.450712i	0.706081	+	0.708131i	$0.250461\pi$
$348$	−1.59781	+	1.97026i	−0.0856515	+	0.105617i
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	−0.182752	−	0.983159i	$-0.558500\pi$
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	0.942817	−	0.333312i	$-0.108166\pi$
$350$	−4.86677	−	1.25153i	−0.260140	−	0.0668971i
$351$	0.198495	+	3.94865i	0.0105949	+	0.210763i
$352$	−3.06238	+	5.30420i	−0.163225	+	0.282715i
$353$	−4.39372			−0.233854			−0.116927	−	0.993141i	$-0.537304\pi$
$353$	−4.39372			−0.233854			−0.116927	+	0.993141i	$0.537304\pi$
$354$	1.23065	+	3.21278i	0.0654084	+	0.170758i
$355$	18.9910			1.00794
$356$	1.30150	+	2.25427i	0.0689796	+	0.119476i
$357$	3.56991	+	31.1507i	0.188939	+	1.64867i
$358$	4.41423	−	7.64567i	0.233299	−	0.404086i
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	−0.0337633	−	0.999430i	$-0.510749\pi$
$359$	16.0796	−	27.8507i	0.848650	−	1.46990i	0.882413	−	0.470475i	$-0.155917\pi$
$360$	−3.93078	+	3.52918i	−0.207170	+	0.186004i
$361$	7.61273	+	13.1856i	0.400670	+	0.693980i
$362$	−0.664703	−	1.15130i	−0.0349360	−	0.0605110i
$363$	16.4263	+	42.8830i	0.862155	+	2.25077i
$364$	−1.40903	+	1.43777i	−0.0738532	+	0.0753594i
$365$	0.270036	+	0.467717i	0.0141343	+	0.0244814i
$366$	17.7044	+	2.81700i	0.925423	+	0.147247i
$367$	34.6030			1.80626			0.903131	−	0.429365i	$-0.141262\pi$
$367$	34.6030			1.80626			0.903131	+	0.429365i	$0.141262\pi$
$368$	0.210533	+	0.364654i	0.0109748	+	0.0190089i
$369$	19.7999	+	6.46451i	1.03074	+	0.336529i
$370$	−5.08126			−0.264162
$371$	0.577690	+	0.148558i	0.0299921	+	0.00771274i
$372$	8.40451	−	10.3636i	0.435754	−	0.537330i
$373$	10.9759			0.568312			0.284156	−	0.958778i	$-0.408287\pi$
$373$	10.9759			0.568312			0.284156	+	0.958778i	$0.408287\pi$
$374$	−20.9532	+	36.2920i	−1.08347	+	1.87662i
$375$	−7.52696	−	19.6501i	−0.388690	−	1.01473i
$376$	−0.830095	−	1.43777i	−0.0428089	−	0.0741472i
$377$	−1.11436			−0.0573925
$378$	−10.2895	−	9.11739i	−0.529233	−	0.468948i
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	1.71053	+	2.96273i	0.0877485	+	0.151985i
$381$	−11.7427	−	30.6559i	−0.601596	−	1.57055i
$382$	8.08414	−	14.0021i	0.413620	−	0.716411i
$383$	−21.0241			−1.07428			−0.537140	−	0.843493i	$-0.680495\pi$
$383$	−21.0241			−1.07428			−0.537140	+	0.843493i	$0.680495\pi$
$384$	1.09097	−	1.34528i	0.0556734	−	0.0686511i
$385$	−19.9721	+	20.3794i	−1.01787	+	1.03863i
$386$	−14.1683			−0.721146
$387$	5.36552	+	25.4205i	0.272745	+	1.29220i
$388$	−1.81806	−	3.14897i	−0.0922978	−	0.159865i
$389$	13.7382			0.696553			0.348277	−	0.937392i	$-0.386767\pi$
$389$	13.7382			0.696553			0.348277	+	0.937392i	$0.386767\pi$
$390$	−2.29179	−	0.364654i	−0.116049	−	0.0184650i
$391$	1.44050	+	2.49501i	0.0728491	+	0.126178i
$392$	−0.141315	−	6.99857i	−0.00713749	−	0.353481i
$393$	−4.51848	−	11.7961i	−0.227927	−	0.595035i
$394$	−7.92107	−	13.7197i	−0.399058	−	0.691188i
$395$	11.8376	+	20.5034i	0.595615	+	1.03164i
$396$	−3.79467	−	17.9782i	−0.190689	−	0.903438i
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	−0.941751	−	0.336311i	$-0.890821\pi$
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$398$	−4.47141	+	7.74471i	−0.224132	+	0.388207i
$399$	−7.15335	+	5.30048i	−0.358116	+	0.265356i
$400$	0.949657	+	1.64485i	0.0474828	+	0.0822427i
$401$	−9.27936			−0.463389			−0.231695	−	0.972789i	$-0.574427\pi$
$401$	−9.27936			−0.463389			−0.231695	+	0.972789i	$0.574427\pi$
$402$	4.20370	+	10.9743i	0.209661	+	0.547349i
$403$	5.86156			0.291985
$404$	4.00520	−	6.93721i	0.199266	−	0.345139i
$405$	1.70137	−	15.7563i	0.0845419	−	0.782937i
$406$	2.71217	−	2.76748i	0.134603	−	0.137348i
$407$	8.83693	−	15.3060i	0.438030	−	0.758691i
$408$	7.46457	−	9.20459i	0.369551	−	0.455695i
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	−0.990329	−	0.138741i	$-0.955695\pi$
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	0.615317	+	0.788279i	$0.289028\pi$
$410$	−6.11273	+	10.5876i	−0.301886	+	0.522882i
$411$	−5.06922	−	13.2339i	−0.250046	−	0.652779i
$412$	3.41423	−	5.91362i	0.168207	−	0.291343i
$413$	−1.41135	−	5.06227i	−0.0694481	−	0.249098i
$414$	−1.20082	−	0.392058i	−0.0590170	−	0.0192686i
$415$	−2.75116	+	4.76515i	−0.135049	+	0.233912i
$416$	0.760877			0.0373051
$417$	13.5985	−	16.7684i	0.665921	−	0.821150i
$418$	−11.8993			−0.582014
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	0.746063	−	0.665875i	$-0.231942\pi$
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	−0.949696	+	0.313172i	$0.898608\pi$
$420$	6.48345	−	4.80409i	0.316360	−	0.234416i
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$	11.3856	−	19.7205i	0.554244	−	0.959979i
$423$	4.73461	+	1.54581i	0.230205	+	0.0751601i
$424$	−0.112725	−	0.195246i	−0.00547442	−	0.00948197i
$425$	6.49768	+	11.2543i	0.315184	+	0.545914i
$426$	11.7661	−	14.5088i	0.570068	−	0.702953i
$427$	−26.5212	−	6.82015i	−1.28345	−	0.330050i
$428$	1.77292	+	3.07078i	0.0856971	+	0.148432i
$429$	5.08414	−	6.26926i	0.245464	−	0.302683i
$430$	−15.2495			−0.735397
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	0.821473	−	0.570247i	$-0.193153\pi$
$431$	−1.72545	−	2.98857i	−0.0831120	−	0.143954i	−0.904585	+	0.426293i	$0.859819\pi$
$432$	0.260877	+	5.18960i	0.0125514	+	0.249685i
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$	−14.2661	+	14.5570i	−0.684794	+	0.698761i
$435$	4.41135	+	0.701905i	0.211508	+	0.0336538i
$436$	−0.703697			−0.0337010
$437$	−0.409028	+	0.708458i	−0.0195665	+	0.0338901i
$438$	0.524632	+	0.0834760i	0.0250679	+	0.00398864i
$439$	14.4480	+	25.0247i	0.689566	+	1.19436i	0.971978	+	0.235071i	$0.0755322\pi$
$439$	14.4480	+	25.0247i	0.689566	+	1.19436i	−0.282412	+	0.959293i	$0.591134\pi$
$440$	10.7850			0.514152
$441$	14.3421	+	15.3396i	0.682959	+	0.730457i
$442$	5.20602			0.247625
$443$	6.88044	+	11.9173i	0.326899	+	0.566207i	0.981895	−	0.189426i	$-0.0606628\pi$
$443$	6.88044	+	11.9173i	0.326899	+	0.566207i	−0.654995	+	0.755633i	$0.727329\pi$
$444$	−3.14815	+	3.88200i	−0.149405	+	0.184231i
$445$	2.29179	−	3.96950i	0.108641	−	0.188172i
$446$	12.8856			0.610153
$447$	5.46978	+	14.2796i	0.258711	+	0.675401i
$448$	−1.85185	+	1.88962i	−0.0874916	+	0.0892761i
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$	−5.41655	−	1.76846i	−0.255339	−	0.0833662i
$451$	−21.2616	−	36.8261i	−1.00117	−	1.73407i
$452$	−8.50232			−0.399916
$453$	−9.28495	−	24.2396i	−0.436245	−	1.13888i
$454$	−10.9984	−	19.0497i	−0.516179	−	0.894048i
$455$	3.43310	+	0.882853i	0.160946	+	0.0413888i
$456$	3.32326	+	0.528775i	0.155626	+	0.0247621i
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	0.530873	−	0.847451i	$-0.321864\pi$
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	−0.999351	+	0.0360237i	$0.988531\pi$
$458$	1.89931	+	3.28971i	0.0887491	+	0.153718i
$459$	1.78495	+	35.5079i	0.0833145	+	1.65737i
$460$	0.370723	−	0.642111i	0.0172851	−	0.0299386i
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	−0.692618	−	0.721304i	$-0.743543\pi$
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	0.970977	+	0.239173i	$0.0768763\pi$
$462$	3.19562	+	27.8847i	0.148674	+	1.29731i
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	0.978107	−	0.208102i	$-0.0667286\pi$
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	−0.669275	+	0.743015i	$0.733395\pi$
$464$	−1.46457			−0.0679911
$465$	−23.2038	−	3.69204i	−1.07605	−	0.171214i
$466$	6.67059			0.309009
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$468$	−1.69850	+	1.52496i	−0.0785130	+	0.0704915i
$469$	−4.82094	−	17.2918i	−0.222610	−	0.798463i
$470$	−1.46169	+	2.53173i	−0.0674230	+	0.116780i
$471$	−32.4669	−	5.16592i	−1.49600	−	0.238033i
$472$	−0.993163	+	1.72021i	−0.0457141	+	0.0791791i
$473$	26.5208	−	45.9354i	1.21943	−	2.11211i
$474$	22.9984	+	3.65935i	1.05635	+	0.168079i
$475$	−1.84501	+	3.19565i	−0.0846550	+	0.146627i
$476$	−12.6706	+	12.9290i	−0.580756	+	0.592601i
$477$	0.642950	+	0.209918i	0.0294387	+	0.00961150i
$478$	−7.82038	+	13.5453i	−0.357696	+	0.619547i
$479$	−32.6271			−1.49077			−0.745385	−	0.666634i	$-0.767734\pi$
$479$	−32.6271			−1.49077			−0.745385	+	0.666634i	$0.767734\pi$
$480$	−3.01204	−	0.479256i	−0.137480	−	0.0218749i
$481$	−2.19562			−0.100111
$482$	−10.7060	−	18.5434i	−0.487646	−	0.844627i
$483$	1.77004	+	0.768251i	0.0805394	+	0.0349566i
$484$	−13.2564	+	22.9607i	−0.602562	+	1.04367i
$485$	−3.20137	+	5.54494i	−0.145367	+	0.251783i
$486$	−10.9834	−	11.0618i	−0.498219	−	0.501774i
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	0.904873	−	0.425682i	$-0.139966\pi$
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	−0.821088	+	0.570802i	$0.806632\pi$
$488$	5.17511	+	8.96355i	0.234266	+	0.405761i
$489$	−25.7226	−	4.09280i	−1.16321	−	0.185083i
$490$	−10.5482	+	6.37731i	−0.476517	+	0.288098i
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	−0.883389	−	0.468641i	$-0.844744\pi$
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	0.0358393	−	0.999358i	$-0.488590\pi$
$492$	4.30150	+	11.2297i	0.193927	+	0.506272i
$493$	−10.0208			−0.451314
$494$	0.739123	+	1.28020i	0.0332547	+	0.0575989i
$495$	−24.0751	+	21.6154i	−1.08210	+	0.971541i
$496$	7.70370			0.345906
$497$	−19.9721	+	20.3794i	−0.895871	+	0.914143i
$498$	1.93598	+	5.05415i	0.0867535	+	0.226482i
$499$	−31.7954			−1.42336			−0.711678	−	0.702506i	$-0.752064\pi$
$499$	−31.7954			−1.42336			−0.711678	+	0.702506i	$0.752064\pi$
$500$	6.07442	−	10.5212i	0.271656	−	0.470523i
$501$	−1.24828	+	1.53926i	−0.0557692	+	0.0687692i
$502$	11.8015	+	20.4408i	0.526727	+	0.912318i
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$	0.346647	−	7.92968i	0.0154409	−	0.353216i
$505$	−14.1053			−0.627679
$506$	1.28947	+	2.23342i	0.0573238	+	0.0992877i
$507$	21.2466	+	3.38063i	0.943597	+	0.150139i
$508$	9.47661	−	16.4140i	0.420457	−	0.728252i
$509$	8.01616			0.355310			0.177655	−	0.984093i	$-0.443149\pi$
$509$	8.01616			0.355310			0.177655	+	0.984093i	$0.443149\pi$
$510$	−20.6088	−	3.27913i	−0.912572	−	0.145202i
$511$	−0.785900	−	0.202101i	−0.0347662	−	0.00894042i
$512$	1.00000			0.0441942
$513$	−8.47825	+	5.48016i	−0.374324	+	0.241955i
$514$	−10.1300	−	17.5456i	−0.446814	−	0.773904i
$515$	−12.0241			−0.529844
$516$	−9.44802	+	11.6504i	−0.415926	+	0.512880i
$517$	−5.08414	−	8.80598i	−0.223600	−	0.387287i
$518$	5.34377	−	5.45276i	0.234792	−	0.239580i
$519$	0.542951	−	0.669515i	0.0238329	−	0.0293885i
$520$	−0.669905	−	1.16031i	−0.0293773	−	0.0508829i
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	0.982825	+	0.184540i	$0.0590795\pi$
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	−0.331596	+	0.943421i	$0.607587\pi$
$522$	3.26935	−	2.93533i	0.143095	−	0.128476i
$523$	13.4698	−	23.3303i	0.588992	−	1.02016i	−0.405373	−	0.914152i	$-0.632858\pi$
$523$	13.4698	−	23.3303i	0.588992	−	1.02016i	0.994365	−	0.106013i	$-0.0338084\pi$
$524$	3.64652	−	6.31595i	0.159299	−	0.275914i
$525$	7.98414	+	3.46537i	0.348456	+	0.151241i
$526$	11.2443	+	19.4757i	0.490276	+	0.849183i
$527$	52.7097			2.29607
$528$	6.68194	−	8.23953i	0.290794	−	0.358579i
$529$	−22.8227			−0.992291
$530$	−0.198495	+	0.343803i	−0.00862207	+	0.0149339i
$531$	−1.23065	−	5.83052i	−0.0534057	−	0.253023i
$532$	−4.97825	−	1.28020i	−0.215834	−	0.0555037i
$533$	−2.64132	+	4.57489i	−0.114408	+	0.198161i
$534$	−1.61273	−	4.21024i	−0.0697894	−	0.182195i
$535$	3.12188	−	5.40726i	0.134971	−	0.233776i
$536$	−3.39248	+	5.87594i	−0.146533	+	0.253802i
$537$	−9.63160	+	11.8768i	−0.415634	+	0.512520i
$538$	−12.6706	+	21.9461i	−0.546268	+	0.946164i
$539$	−0.865521	−	42.8646i	−0.0372806	−	1.84631i
$540$	7.68427	−	4.96695i	0.330678	−	0.213744i
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	−0.670201	−	0.742180i	$-0.733792\pi$
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	0.977847	+	0.209321i	$0.0671252\pi$
$542$	13.7576			0.590940
$543$	0.823649	+	2.15025i	0.0353462	+	0.0922760i
$544$	6.84213			0.293354
$545$	0.619562	+	1.07311i	0.0265391	+	0.0459671i
$546$	2.80150	−	2.07585i	0.119893	−	0.0888384i
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	−0.843289	−	0.537461i	$-0.819384\pi$
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	0.887099	+	0.461579i	$0.152717\pi$
$548$	4.09097	−	7.08577i	0.174758	−	0.302689i
$549$	−29.5172	−	9.63716i	−1.25977	−	0.411304i
$550$	5.81642	+	10.0743i	0.248013	+	0.429571i
$551$	−1.42270	−	2.46419i	−0.0606091	−	0.104978i
$552$	−0.260877	−	0.681054i	−0.0111037	−	0.0289876i
$553$	−34.4516	−	8.85952i	−1.46503	−	0.376745i
$554$	1.64132	+	2.84284i	0.0697328	+	0.120781i
$555$	8.69166	+	1.38296i	0.368940	+	0.0587033i
$556$	12.4646			0.528616
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	0.990283	−	0.139067i	$-0.0444103\pi$
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	−0.615577	+	0.788077i	$0.711077\pi$
$558$	−17.1969	+	15.4399i	−0.728001	+	0.653623i
$559$	−6.58934			−0.278699
$560$	4.51204	+	1.16031i	0.190668	+	0.0490320i
$561$	45.7187	−	56.3759i	1.93025	−	2.38019i
$562$	−1.26896			−0.0535277
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	−0.875730	−	0.482802i	$-0.839619\pi$
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	0.855983	+	0.517003i	$0.172952\pi$
$564$	1.02859	+	2.68527i	0.0433115	+	0.113070i
$565$	7.48577	+	12.9657i	0.314929	+	0.545473i
$566$	−8.19235			−0.344350
$567$	15.1190	+	18.3961i	0.634939	+	0.772563i
$568$	10.7850			0.452527
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	0.506830	−	0.862046i	$-0.330817\pi$
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	−0.999969	+	0.00790437i	$0.997484\pi$
$570$	−2.11956	−	5.53340i	−0.0887787	−	0.231769i
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	−0.860917	−	0.508745i	$-0.830110\pi$
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	0.871045	+	0.491204i	$0.163443\pi$
$572$	4.66019			0.194852
$573$	−17.6391	+	21.7509i	−0.736885	+	0.908655i
$574$	−4.93310	−	17.6942i	−0.205904	−	0.738540i
$575$	0.799737			0.0333514
$576$	−2.23229	+	2.00422i	−0.0930119	+	0.0835091i
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	0.815852	−	0.578261i	$-0.196269\pi$
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	−0.908715	+	0.417417i	$0.862935\pi$
$578$	29.8148			1.24013
$579$	24.2353	+	3.85616i	1.00718	+	0.160257i
$580$	1.28947	+	2.23342i	0.0535422	+	0.0927378i
$581$	−2.22025	−	7.96364i	−0.0921114	−	0.330387i
$582$	2.25280	+	5.88123i	0.0933814	+	0.243785i
$583$	−0.690415	−	1.19583i	−0.0285941	−	0.0495264i
$584$	0.153353	+	0.265616i	0.00634581	+	0.0109913i
$585$	3.82094	+	1.24751i	0.157976	+	0.0515781i
$586$	7.72545	−	13.3809i	0.319135	−	0.552759i
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	−0.641822	−	0.766854i	$-0.721821\pi$
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	0.985026	+	0.172407i	$0.0551544\pi$
$588$	−1.66307	+	12.0098i	−0.0685838	+	0.495274i
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$	3.49768			0.143997
$591$	9.81518	+	25.6239i	0.403742	+	1.05402i
$592$	−2.88564			−0.118599
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	−0.0261726	−	0.999657i	$-0.508332\pi$
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	0.878815	−	0.477163i	$-0.158335\pi$
$594$	1.59781	+	31.7851i	0.0655589	+	1.30416i
$595$	30.8720	+	7.93899i	1.26563	+	0.325467i
$596$	−4.41423	+	7.64567i	−0.180814	+	0.313179i
$597$	9.75636	−	12.0306i	0.399301	−	0.492380i
$598$	0.160190	−	0.277457i	0.00655065	−	0.0113461i
$599$	−7.53831	+	13.0567i	−0.308007	+	0.533483i	−0.977926	−	0.208950i	$-0.932995\pi$
$599$	−7.53831	+	13.0567i	−0.308007	+	0.533483i	0.669919	+	0.742434i	$0.266329\pi$
$600$	−1.17674	−	3.07204i	−0.0480403	−	0.125416i
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$602$	16.0374	−	16.3645i	0.653634	−	0.666965i
$603$	−4.20370	−	19.9161i	−0.171188	−	0.811044i
$604$	7.49316	−	12.9785i	0.304892	−	0.528089i
$605$	46.6856			1.89804
$606$	−8.73912	+	10.7762i	−0.355003	+	0.437755i
$607$	19.5732			0.794451			0.397225	−	0.917721i	$-0.369973\pi$
$607$	19.5732			0.794451			0.397225	+	0.917721i	$0.369973\pi$
$608$	0.971410	+	1.68253i	0.0393959	+	0.0682357i
$609$	−5.39248	+	3.99571i	−0.218514	+	0.161914i
$610$	9.11273	−	15.7837i	0.368963	−	0.639063i
$611$	−0.631600	+	1.09396i	−0.0255518	+	0.0442570i
$612$	−15.2736	+	13.7131i	−0.617399	+	0.554321i
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	0.804509	−	0.593941i	$-0.202429\pi$
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	−0.916622	+	0.399755i	$0.869095\pi$
$614$	−2.44966	−	4.24293i	−0.0988601	−	0.171231i
$615$	13.3376	−	16.4467i	0.537825	−	0.663194i
$616$	−11.3421	+	11.5735i	−0.456988	+	0.466308i
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	0.878514	−	0.477716i	$-0.158535\pi$
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	−0.852971	+	0.521958i	$0.825202\pi$
$618$	−7.44966	+	9.18620i	−0.299669	+	0.369523i
$619$	4.50232			0.180964			0.0904818	−	0.995898i	$-0.471159\pi$
$619$	4.50232			0.180964			0.0904818	+	0.995898i	$0.471159\pi$
$620$	−6.78263	−	11.7479i	−0.272397	−	0.471805i
$621$	1.94733	+	0.997454i	0.0781438	+	0.0400264i
$622$	−7.69002			−0.308342
$623$	1.84953	+	6.63392i	0.0740997	+	0.265782i
$624$	−1.30150	−	0.207087i	−0.0521019	−	0.00829011i
$625$	−11.8960			−0.475842
$626$	0.861564	−	1.49227i	0.0344350	−	0.0596432i
$627$	20.3542	+	3.23862i	0.812867	+	0.129338i
$628$	−9.49028	−	16.4377i	−0.378704	−	0.655934i
$629$	−19.7439			−0.787242
$630$	−12.3977	+	6.45297i	−0.493935	+	0.257093i
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	6.72257	+	11.6438i	0.267410	+	0.463167i
$633$	−24.8428	+	30.6338i	−0.987414	+	1.21758i
$634$	−16.6014	+	28.7544i	−0.659325	+	1.14198i
$635$	−33.3743			−1.32442
$636$	0.139680	+	0.364654i	0.00553868	+	0.0144595i
$637$	−4.55787	+	2.75564i	−0.180589	+	0.109183i
$638$	−8.97017			−0.355132
$639$	−24.0751	+	21.6154i	−0.952397	+	0.855093i
$640$	−0.880438	−	1.52496i	−0.0348024	−	0.0602795i
$641$	−0.948577			−0.0374666			−0.0187333	−	0.999825i	$-0.505963\pi$
$641$	−0.948577			−0.0374666			−0.0187333	+	0.999825i	$0.505963\pi$
$642$	−2.19686	−	5.73520i	−0.0867032	−	0.226350i
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	0.603830	−	0.797113i	$-0.293641\pi$
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	−0.992235	+	0.124375i	$0.960307\pi$
$644$	0.299182	+	1.07311i	0.0117894	+	0.0422865i
$645$	26.0848	+	4.15044i	1.02709	+	0.163424i
$646$	6.64652	+	11.5121i	0.261504	+	0.452938i
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	0.999013	−	0.0444181i	$-0.0141434\pi$
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	−0.537974	+	0.842962i	$0.680810\pi$
$648$	0.966208	−	8.94799i	0.0379562	−	0.351510i
$649$	−6.08289	+	10.5359i	−0.238774	+	0.413569i
$650$	0.722572	−	1.25153i	0.0283416	−	0.0490891i
$651$	28.3646	−	21.0175i	1.11170	−	0.823742i
$652$	−7.51887	−	13.0231i	−0.294462	−	0.510023i
$653$	22.7907			0.891869			0.445935	−	0.895065i	$-0.352871\pi$
$653$	22.7907			0.891869			0.445935	+	0.895065i	$0.352871\pi$
$654$	1.20370	+	0.191524i	0.0470683	+	0.00748919i
$655$	−12.8421			−0.501784
$656$	−3.47141	+	6.01266i	−0.135536	+	0.234755i
$657$	−0.874681	−	0.285577i	−0.0341246	−	0.0111414i
$658$	−1.17962	−	4.23109i	−0.0459864	−	0.164945i
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	0.484083	+	0.875022i	$0.339153\pi$
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	−0.999833	+	0.0182828i	$0.994180\pi$
$660$	−18.4480	−	2.93533i	−0.718088	−	0.114257i
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	−0.479732	−	0.877415i	$-0.659266\pi$
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	0.999730	−	0.0232469i	$-0.00740038\pi$
$662$	−1.44445	+	2.50187i	−0.0561403	+	0.0972379i
$663$	−8.90507	−	1.41692i	−0.345844	−	0.0550284i
$664$	−1.56238	+	2.70612i	−0.0606322	+	0.105018i
$665$	2.43078	+	8.71878i	0.0942617	+	0.338100i
$666$	6.44158	−	5.78346i	0.249606	−	0.224104i
$667$	−0.308342	+	0.534063i	−0.0119390	+	0.0206790i
$668$	−1.14419			−0.0442702
$669$	−22.0413	−	3.50707i	−0.852167	−	0.135591i
$670$	11.9475			0.461571
$671$	31.6963	+	54.8996i	1.22362	+	2.11938i
$672$	3.68194	−	2.72824i	0.142034	−	0.105244i
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$	−4.36156	+	7.55445i	−0.168001	+	0.290987i
$675$	8.78387	+	4.49923i	0.338091	+	0.173176i
$676$	6.21053	+	10.7570i	0.238867	+	0.413729i
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	0.993447	−	0.114293i	$-0.0364602\pi$
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	−0.595704	+	0.803204i	$0.703127\pi$
$678$	14.5435	+	2.31407i	0.558540	+	0.0888712i
$679$	−2.58358	−	9.26684i	−0.0991487	−	0.355629i
$680$	−6.02408	−	10.4340i	−0.231013	−	0.400126i
$681$	13.6283	+	35.5786i	0.522239	+	1.36338i
$682$	47.1833			1.80674
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	0.998487	+	0.0549828i	$0.0175104\pi$
$683$	14.2918	+	24.7541i	0.546860	+	0.947190i	−0.451627	+	0.892207i	$0.649156\pi$
$684$	−5.54063	−	1.80897i	−0.211851	−	0.0691678i
$685$	−14.4074			−0.550478
$686$	4.24953	−	18.0261i	0.162248	−	0.688241i
$687$	−2.35348	−	6.14409i	−0.0897910	−	0.234412i
$688$	−8.66019			−0.330167
$689$	−0.0857699	+	0.148558i	−0.00326757	+	0.00565960i
$690$	−0.808897	+	0.997454i	−0.0307942	+	0.0379724i
$691$	3.34897	+	5.80059i	0.127401	+	0.220665i	0.922669	−	0.385593i	$-0.126003\pi$
$691$	3.34897	+	5.80059i	0.127401	+	0.220665i	−0.795268	+	0.606258i	$0.792670\pi$
$692$	0.497677			0.0189188
$693$	2.12313	−	48.5674i	0.0806510	−	1.84492i
$694$	9.69467			0.368005
$695$	−10.9743	−	19.0080i	−0.416278	−	0.721016i
$696$	2.50520	+	0.398611i	0.0949594	+	0.0151093i
$697$	−23.7518	+	41.1394i	−0.899665	+	1.55827i
$698$	−28.3984			−1.07489
$699$	−11.4103	−	1.81553i	−0.431576	−	0.0686695i
$700$	1.34953	+	4.84051i	0.0510073	+	0.182954i
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$	3.32038	−	2.14622i	0.125320	−	0.0810040i
$703$	−2.80314	−	4.85518i	−0.105722	−	0.183117i
$704$	6.12476			0.230836
$705$	3.18934	−	3.93278i	0.120117	−	0.148117i
$706$	2.19686	+	3.80507i	0.0826799	+	0.143206i
$707$	14.8341	−	15.1366i	0.557892	−	0.569271i
$708$	2.16703	−	2.67217i	0.0814418	−	0.100426i
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	0.770694	−	0.637205i	$-0.219910\pi$
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	−0.937183	+	0.348838i	$0.886576\pi$
$710$	−9.49549	−	16.4467i	−0.356359	−	0.617232i
$711$	−38.3435	−	12.5189i	−1.43799	−	0.469494i
$712$	1.30150	−	2.25427i	0.0487760	−	0.0844824i
$713$	1.62188	−	2.80919i	0.0607401	−	0.105205i
$714$	25.1923	−	18.6670i	0.942800	−	0.698594i
$715$	−4.10301	−	7.10662i	−0.153444	−	0.265773i
$716$	−8.82846			−0.329935
$717$	17.0636	−	21.0412i	0.637253	−	0.785799i
$718$	−32.1592			−1.20017
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	−0.557576	−	0.830126i	$-0.688269\pi$
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	0.997698	+	0.0678123i	$0.0216019\pi$
$720$	5.02175	+	1.63957i	0.187150	+	0.0611030i
$721$	12.6453	−	12.9032i	0.470935	−	0.480540i
$722$	7.61273	−	13.1856i	0.283316	−	0.490718i
$723$	13.2661	+	34.6329i	0.493371	+	1.28801i
$724$	−0.664703	+	1.15130i	−0.0247035	+	0.0427877i
$725$	−1.39084	+	2.40901i	−0.0516546	+	0.0894683i
$726$	28.9246	−	35.6671i	1.07349	−	1.32373i
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	−0.799288	−	0.600948i	$-0.794790\pi$
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	0.920080	+	0.391730i	$0.128123\pi$
$728$	1.94966	+	0.501371i	0.0722591	+	0.0185820i
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	0.270036	−	0.467717i	0.00999449	−	0.0173110i
$731$	−59.2542			−2.19159
$732$	−6.41260	−	16.7409i	−0.237016	−	0.618763i
$733$	−23.1981			−0.856842			−0.428421	−	0.903579i	$-0.640930\pi$
$733$	−23.1981			−0.856842			−0.428421	+	0.903579i	$0.640930\pi$
$734$	−17.3015	−	29.9671i	−0.638610	−	1.10611i
$735$	19.7787	−	8.03773i	0.729547	−	0.296476i
$736$	0.210533	−	0.364654i	0.00776036	−	0.0134413i
$737$	−20.7781	+	35.9888i	−0.765372	+	1.32566i
$738$	−4.30150	−	20.3794i	−0.158341	−	0.750178i
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	0.692305	−	0.721605i	$-0.256595\pi$
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	−0.971081	+	0.238752i	$0.923262\pi$
$740$	2.54063	+	4.40050i	0.0933954	+	0.161765i
$741$	−0.915865	−	2.39099i	−0.0336451	−	0.0878352i
$742$	−0.160190	−	0.574573i	−0.00588076	−	0.0210932i
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	0.754310	−	0.656518i	$-0.227972\pi$
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	−0.945717	+	0.324992i	$0.894638\pi$
$744$	−13.1774	−	2.09671i	−0.483108	−	0.0768689i
$745$	15.5458			0.569555
$746$	−5.48796	−	9.50543i	−0.200929	−	0.348018i
$747$	−1.93598	−	9.17220i	−0.0708339	−	0.335593i
$748$	41.9064			1.53225
$749$	2.51943	+	9.03675i	0.0920580	+	0.330196i
$750$	−13.2540	+	16.3436i	−0.483969	+	0.596784i
$751$	40.2118			1.46735			0.733674	−	0.679501i	$-0.237804\pi$
$751$	40.2118			1.46735			0.733674	+	0.679501i	$0.237804\pi$
$752$	−0.830095	+	1.43777i	−0.0302704	+	0.0524300i
$753$	−14.6235	−	38.1767i	−0.532911	−	1.39124i
$754$	0.557180	+	0.965064i	0.0202913	+	0.0351456i
$755$	−26.3891			−0.960397
$756$	−2.75116	+	13.4696i	−0.100059	+	0.489886i
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	−16.9939	−	29.4342i	−0.617244	−	1.06910i
$759$	−1.59781	−	4.17129i	−0.0579968	−	0.151408i
$760$	1.71053	−	2.96273i	0.0620476	−	0.107470i
$761$	−23.6627			−0.857771			−0.428886	−	0.903359i	$-0.641094\pi$
$761$	−23.6627			−0.857771			−0.428886	+	0.903359i	$0.641094\pi$
$762$	−20.6774	+	25.4974i	−0.749064	+	0.923674i
$763$	−1.80314	−	0.463693i	−0.0652780	−	0.0167868i
$764$	−16.1683			−0.584947
$765$	34.3595	+	11.2181i	1.24227	+	0.405592i
$766$	10.5120	+	18.2074i	0.379815	+	0.657860i
$767$	1.51135			0.0545717
$768$	−1.71053	−	0.272169i	−0.0617236	−	0.00982104i
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	0.746536	−	0.665345i	$-0.231716\pi$
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	−0.949474	+	0.313846i	$0.898382\pi$
$770$	27.6352	+	7.10662i	0.995902	+	0.256105i
$771$	12.5523	+	32.7694i	0.452059	+	1.18016i
$772$	7.08414	+	12.2701i	0.254964	+	0.441610i
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	0.868514	−	0.495664i	$-0.165075\pi$
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	−0.863515	+	0.504323i	$0.831742\pi$
$774$	19.3320	−	17.3569i	0.694875	−	0.623882i
$775$	7.31587	−	12.6715i	0.262794	−	0.455172i
$776$	−1.81806	+	3.14897i	−0.0652644	+	0.113041i
$777$	−10.6248	+	7.87272i	−0.381161	+	0.282432i
$778$	−6.86909	−	11.8976i	−0.246269	−	0.426550i
$779$	−13.4887			−0.483281
$780$	0.830095	+	2.16708i	0.0297222	+	0.0775937i
$781$	66.0553			2.36364
$782$	1.44050	−	2.49501i	0.0515121	−	0.0892215i
$783$	−6.39123	+	4.13116i	−0.228404	+	0.147636i
$784$	−5.99028	+	3.62167i	−0.213939	+	0.129345i
$785$	−16.7112	+	28.9447i	−0.596449	+	1.03308i
$786$	−7.95649	+	9.81118i	−0.283799	+	0.349953i
$787$	14.6940	−	25.4507i	0.523784	−	0.907220i	−0.475833	−	0.879536i	$-0.657853\pi$
$787$	14.6940	−	25.4507i	0.523784	−	0.907220i	0.999617	−	0.0276845i	$-0.00881339\pi$
$788$	−7.92107	+	13.7197i	−0.282176	+	0.488744i
$789$	−13.9331	−	36.3743i	−0.496032	−	1.29496i
$790$	11.8376	−	20.5034i	0.421164	−	0.729477i
$791$	−21.7862	−	5.60251i	−0.774628	−	0.199202i
$792$	−13.6722	+	12.2754i	−0.485821	+	0.436186i
$793$	3.93762	−	6.82015i	0.139829	−	0.242191i
$794$	7.15787			0.254023
$795$	0.433105	−	0.534063i	0.0153606	−	0.0189413i
$796$	8.94282			0.316970
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	0.873594	−	0.486655i	$-0.161783\pi$
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	−0.858253	+	0.513227i	$0.828450\pi$
$798$	8.16703	+	3.54475i	0.289110	+	0.125483i
$799$	−5.67962	+	9.83739i	−0.200931	+	0.348022i
$800$	0.949657	−	1.64485i	0.0335754	−	0.0581544i
$801$	1.61273	+	7.64068i	0.0569828	+	0.269970i
$802$	4.63968	+	8.03616i	0.163833	+	0.283767i
$803$	0.939253	+	1.62683i	0.0331455	+	0.0574097i
$804$	7.40219	−	9.12767i	0.261055	−	0.321908i
$805$	1.37305	−	1.40105i	0.0483935	−	0.0493805i
$806$	−2.93078	−	5.07626i	−0.103232	−	0.178804i
$807$	27.6465	−	34.0910i	0.973203	−	1.20006i
$808$	−8.01040			−0.281805
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	0.984409	−	0.175895i	$-0.0562820\pi$
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	−0.644534	+	0.764575i	$0.722949\pi$
$810$	−14.4960	+	6.40472i	−0.509339	+	0.225039i
$811$	−47.0391			−1.65177			−0.825884	−	0.563841i	$-0.809323\pi$
$811$	−47.0391			−1.65177			−0.825884	+	0.563841i	$0.809323\pi$
$812$	−3.75280	−	0.965064i	−0.131697	−	0.0338671i
$813$	−23.5328	−	3.74439i	−0.825333	−	0.131321i
$814$	−17.6739			−0.619469
$815$	−13.2398	+	22.9320i	−0.463770	+	0.803274i
$816$	−11.7037	−	1.86221i	−0.409711	−	0.0651905i
$817$	−8.41260	−	14.5710i	−0.294319	−	0.509776i
$818$	15.1683			0.530346
$819$	−5.35705	+	2.78834i	−0.187190	+	0.0974323i
$820$	12.2255			0.426931
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	0.853455	−	0.521167i	$-0.174503\pi$
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	−0.878071	+	0.478530i	$0.841170\pi$
$822$	−8.92627	+	11.0070i	−0.311339	+	0.383914i
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	−0.380430	−	0.924810i	$-0.624224\pi$
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	0.991124	−	0.132943i	$-0.0424426\pi$
$824$	−6.82846			−0.237881
$825$	−7.20726	−	18.8155i	−0.250925	−	0.655073i
$826$	−3.67838	+	3.75340i	−0.127987	+	0.130597i
$827$	−18.5997			−0.646776			−0.323388	−	0.946266i	$-0.604822\pi$
$827$	−18.5997			−0.646776			−0.323388	+	0.946266i	$0.604822\pi$
$828$	0.260877	+	1.23597i	0.00906609	+	0.0429529i
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	0.979865	+	0.199660i	$0.0639838\pi$
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	−0.317022	+	0.948418i	$0.602683\pi$
$830$	5.50232			0.190988
$831$	−2.03379	−	5.30949i	−0.0705515	−	0.184184i
$832$	−0.380438	−	0.658939i	−0.0131893	−	0.0228446i
$833$	−40.9863	+	24.7799i	−1.42009	+	0.858574i
$834$	−21.3211	−	3.39247i	−0.738288	−	0.117472i
$835$	1.00739	+	1.74485i	0.0348622	+	0.0603832i
$836$	5.94966	+	10.3051i	0.205773	+	0.356410i
$837$	33.6181	−	21.7300i	1.16201	−	0.751099i
$838$	−4.16827	+	7.21966i	−0.143991	+	0.249399i
$839$	17.3691	−	30.0841i	0.599648	−	1.03862i	−0.393225	−	0.919442i	$-0.628641\pi$
$839$	17.3691	−	30.0841i	0.599648	−	1.03862i	0.992873	−	0.119178i	$-0.0380259\pi$
$840$	−7.40219	−	3.21278i	−0.255400	−	0.110852i
$841$	13.4275	+	23.2571i	0.463018	+	0.801970i
$842$	7.00465			0.241396
$843$	2.17059	+	0.345370i	0.0747592	+	0.0118952i
$844$	−22.7713			−0.783820
$845$	10.9360	−	18.9417i	0.376209	−	0.651614i
$846$	−1.02859	−	4.87320i	−0.0353637	−	0.167544i
$847$	−49.0976	+	50.0989i	−1.68701	+	1.72142i
$848$	−0.112725	+	0.195246i	−0.00387100	+	0.00670476i
$849$	14.0133	+	2.22970i	0.480935	+	0.0765231i
$850$	6.49768	−	11.2543i	0.222868	−	0.386020i
$851$	−0.607523	+	1.05226i	−0.0208256	+	0.0360711i
$852$	−18.4480	−	2.93533i	−0.632019	−	0.100563i
$853$	−21.1586	+	36.6477i	−0.724455	+	1.25479i	0.234743	+	0.972058i	$0.424575\pi$
$853$	−21.1586	+	36.6477i	−0.724455	+	1.25479i	−0.959198	+	0.282736i	$0.908758\pi$
$854$	7.35417	+	26.3781i	0.251655	+	0.902640i
$855$	2.11956	+	10.0419i	0.0724875	+	0.343427i
$856$	1.77292	−	3.07078i	0.0605970	−	0.104957i
$857$	14.9234			0.509773			0.254887	−	0.966971i	$-0.417962\pi$
$857$	14.9234			0.509773			0.254887	+	0.966971i	$0.417962\pi$
$858$	−7.97141	−	1.26836i	−0.272139	−	0.0433010i
$859$	19.4132			0.662368			0.331184	−	0.943566i	$-0.392552\pi$
$859$	19.4132			0.662368			0.331184	+	0.943566i	$0.392552\pi$
$860$	7.62476	+	13.2065i	0.260002	+	0.450337i
$861$	3.62244	+	31.6091i	0.123452	+	1.07724i
$862$	−1.72545	+	2.98857i	−0.0587691	+	0.101791i
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	−0.875107	−	0.483929i	$-0.839209\pi$
$863$	−0.542263	+	0.939227i	−0.0184588	+	0.0319717i	0.856648	+	0.515901i	$0.172543\pi$
$864$	4.36389	−	2.82073i	0.148462	−	0.0959630i
$865$	−0.438174	−	0.758939i	−0.0148984	−	0.0258047i
$866$	−14.1300	−	24.4738i	−0.480156	−	0.831654i
$867$	−50.9992	−	8.11465i	−1.73202	−	0.275588i
$868$	19.7398	+	5.07626i	0.670013	+	0.172300i
$869$	41.1742	+	71.3157i	1.39674	+	2.41922i
$870$	−1.59781	−	4.17129i	−0.0541708	−	0.141420i
$871$	5.16251			0.174925
$872$	0.351848	+	0.609419i	0.0119151	+	0.0206375i
$873$	−2.25280	−	10.6732i	−0.0762456	−	0.361232i
$874$	0.818057			0.0276712
$875$	22.4978	−	22.9567i	0.760565	−	0.776077i
$876$	−0.190024	−	0.496083i	−0.00642031	−	0.0167611i
$877$	−28.5699			−0.964737			−0.482369	−	0.875968i	$-0.660223\pi$
$877$	−28.5699			−0.964737			−0.482369	+	0.875968i	$0.660223\pi$
$878$	14.4480	−	25.0247i	0.487597	−	0.844543i
$879$	−16.8565	+	20.7858i	−0.568555	+	0.701088i
$880$	−5.39248	−	9.34004i	−0.181780	−	0.314853i
$881$	45.9967			1.54967			0.774835	−	0.632164i	$-0.217833\pi$
$881$	45.9967			1.54967			0.774835	+	0.632164i	$0.217833\pi$
$882$	6.11341	−	20.0904i	0.205849	−	0.676481i
$883$	32.9384			1.10847			0.554233	−	0.832361i	$-0.313012\pi$
$883$	32.9384			1.10847			0.554233	+	0.832361i	$0.313012\pi$
$884$	−2.60301	−	4.50855i	−0.0875487	−	0.151639i
$885$	−5.98289	−	0.951958i	−0.201113	−	0.0319997i
$886$	6.88044	−	11.9173i	0.231153	−	0.400368i
$887$	−28.3398			−0.951558			−0.475779	−	0.879565i	$-0.657834\pi$
$887$	−28.3398			−0.951558			−0.475779	+	0.879565i	$0.657834\pi$
$888$	4.93598	+	0.785381i	0.165641	+	0.0263557i
$889$	35.0985	−	35.8144i	1.17717	−	1.20118i
$890$	−4.58358			−0.153642
$891$	5.91780	−	54.8043i	0.198254	−	1.83601i
$892$	−6.44282	−	11.1593i	−0.215722	−	0.373641i
$893$	−3.22545			−0.107936
$894$	9.63160	−	11.8768i	0.322129	−	0.397218i
$895$	7.77292	+	13.4631i	0.259820	+	0.450021i
$896$	2.56238	+	0.658939i	0.0856032	+	0.0220136i
$897$	−0.349525	+	0.431001i	−0.0116703	+	0.0143907i
$898$	10.1001	+	17.4939i	0.337046	+	0.583780i
$899$	5.64132	+	9.77104i	0.188148	+	0.325883i
$900$	1.17674	+	5.57510i	0.0392247	+	0.185837i
$901$	−0.771280	+	1.33590i	−0.0256951	+	0.0445052i
$902$	−21.2616	+	36.8261i	−0.707933	+	1.22618i
$903$	−31.8863	+	23.6271i	−1.06111	+	0.786260i
$904$	4.25116	+	7.36323i	0.141392	+	0.244897i
$905$	2.34092			0.0778149
$906$	−16.3497	+	20.1608i	−0.543181	+	0.669798i
$907$	7.94747			0.263891			0.131946	−	0.991257i	$-0.457878\pi$
$907$	7.94747			0.263891			0.131946	+	0.991257i	$0.457878\pi$
$908$	−10.9984	+	19.0497i	−0.364994	+	0.632187i
$909$	17.8815	−	16.0546i	0.593093	−	0.532498i
$910$	−0.951980	−	3.41458i	−0.0315578	−	0.113192i
$911$	−4.00808	+	6.94220i	−0.132794	+	0.230005i	−0.924752	−	0.380569i	$-0.875728\pi$
$911$	−4.00808	+	6.94220i	−0.132794	+	0.230005i	0.791959	+	0.610575i	$0.209061\pi$
$912$	−1.20370	−	3.14241i	−0.0398584	−	0.104056i
$913$	−9.56922	+	16.5744i	−0.316695	+	0.548532i
$914$	−10.0149	+	17.3463i	−0.331264	+	0.573766i
$915$	−19.8834	+	24.5184i	−0.657327	+	0.810552i
$916$	1.89931	−	3.28971i	0.0627551	−	0.108695i
$917$	13.5056	−	13.7811i	0.445994	−	0.455090i
$918$	29.8583	−	19.2998i	0.985471	−	0.636988i
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	−0.993302	−	0.115548i	$-0.963138\pi$
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	0.596718	+	0.802451i	$0.296471\pi$
$920$	−0.741446			−0.0244448
$921$	3.03543	+	7.92439i	0.100021	+	0.261118i
$922$	−11.9532			−0.393658
$923$	−4.10301	−	7.10662i	−0.135052	−	0.233917i
$924$	22.5510	−	16.7098i	0.741874	−	0.549713i
$925$	−2.74037	+	4.74646i	−0.0901027	+	0.156062i
$926$	6.64527	−	11.5100i	0.218377	−	0.378240i
$927$	15.2431	−	13.6857i	0.500648	−	0.449498i
$928$	0.732287	+	1.26836i	0.0240385	+	0.0416359i
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	0.541678	−	0.840586i	$-0.317789\pi$
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	−0.998808	+	0.0488134i	$0.984456\pi$
$930$	8.40451	+	21.9411i	0.275595	+	0.719478i
$931$	−11.9126	−	6.56072i	−0.390420	−	0.215019i
$932$	−3.33530	−	5.77690i	−0.109251	−	0.189229i
$933$	13.1540	+	2.09298i	0.430644	+	0.0685212i
$934$	11.2301			0.367460
$935$	−36.8960	−	63.9058i	−1.20663	−	2.08994i
$936$	2.16991	+	0.708458i	0.0709256	+	0.0231567i
$937$	53.2211			1.73866			0.869328	−	0.494235i	$-0.164552\pi$
$937$	53.2211			1.73866			0.869328	+	0.494235i	$0.164552\pi$
$938$	−12.5647	+	12.8210i	−0.410252	+	0.418620i
$939$	−1.87988	+	2.31809i	−0.0613477	+	0.0756480i
$940$	2.92339			0.0953505
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	−0.510160	−	0.860080i	$-0.670414\pi$
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	0.999931	+	0.0117715i	$0.00374709\pi$
$942$	11.7596	+	30.7001i	0.383150	+	1.00026i
$943$	1.46169	+	2.53173i	0.0475993	+	0.0824445i
$944$	1.98633			0.0646494
$945$	22.9629	−	7.66376i	0.746984	−	0.249302i
$946$	−53.0416			−1.72453
$947$	19.8445	+	34.3716i	0.644858	+	1.11693i	0.984334	+	0.176312i	$0.0564169\pi$
$947$	19.8445	+	34.3716i	0.644858	+	1.11693i	−0.339476	+	0.940615i	$0.610250\pi$
$948$	−8.33009	−	21.7468i	−0.270549	−	0.706305i
$949$	0.116683	−	0.202101i	0.00378769	−	0.00656047i
$950$	3.69002			0.119720
$951$	36.2233	−	44.6670i	1.17462	−	1.44843i
$952$	17.5322	+	4.50855i	0.568220	+	0.146123i
$953$	23.0643			0.747126			0.373563	−	0.927605i	$-0.378136\pi$
$953$	23.0643			0.747126			0.373563	+	0.927605i	$0.378136\pi$
$954$	−0.139680	−	0.661770i	−0.00452232	−	0.0214256i
$955$	14.2352	+	24.6560i	0.460639	+	0.797850i
$956$	15.6408			0.505858
$957$	15.3438	+	2.44140i	0.495994	+	0.0789192i
$958$	16.3135	+	28.2559i	0.527067	+	0.912906i
$959$	15.1517	−	15.4608i	0.489275	−	0.499254i
$960$	1.09097	+	2.84813i	0.0352110	+	0.0919230i
$961$	−14.1735	−	24.5492i	−0.457209	−	0.791909i
$962$	1.09781	+	1.90146i	0.0353948	+	0.0613055i
$963$	2.19686	+	10.4082i	0.0707928	+	0.335399i
$964$	−10.7060	+	18.5434i	−0.344818	+	0.597242i
$965$	12.4743	−	21.6061i	0.401562	−	0.695525i
$966$	−0.219693	−	1.91702i	−0.00706850	−	0.0616792i
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	0.999954	−	0.00955967i	$-0.00304298\pi$
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	−0.508256	+	0.861206i	$0.669710\pi$
$968$	26.5127			0.852151
$969$	−8.23585	−	21.5008i	−0.264574	−	0.690706i
$970$	6.40275			0.205580
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	−0.575492	−	0.817807i	$-0.695190\pi$
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	0.995988	+	0.0894874i	$0.0285229\pi$
$972$	−4.08809	+	15.0429i	−0.131126	+	0.482500i
$973$	31.9390	+	8.21339i	1.02392	+	0.263309i
$974$	1.84897	−	3.20251i	0.0592448	−	0.102615i
$975$	−1.57661	+	1.94412i	−0.0504919	+	0.0622618i
$976$	5.17511	−	8.96355i	0.165651	−	0.286916i
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	−0.983826	−	0.179124i	$-0.942674\pi$
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	0.647039	+	0.762457i	$0.276007\pi$
$978$	9.31681	+	24.3228i	0.297919	+	0.777757i
$979$	7.97141	−	13.8069i	0.254767	−	0.441270i
$980$	10.7970	+	5.94631i	0.344897	+	0.189948i
$981$	−2.00684	−	0.655217i	−0.0640734	−	0.0209195i
$982$	−18.7804	+	32.5287i	−0.599308	+	1.03803i
$983$	−19.5297			−0.622900			−0.311450	−	0.950263i	$-0.600815\pi$
$983$	−19.5297			−0.622900			−0.311450	+	0.950263i	$0.600815\pi$
$984$	7.57442	−	9.34004i	0.241464	−	0.297750i
$985$	27.8960			0.888842
$986$	5.01040	+	8.67827i	0.159564	+	0.276373i
$987$	0.866210	+	7.55847i	0.0275718	+	0.240589i
$988$	0.739123	−	1.28020i	0.0235146	−	0.0407286i
$989$	−1.82326	+	3.15798i	−0.0579762	+	0.100418i
$990$	30.7571	+	10.0419i	0.977523	+	0.319154i
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	0.722003	−	0.691890i	$-0.243222\pi$
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	−0.960196	+	0.279327i	$0.909889\pi$
$992$	−3.85185	−	6.67160i	−0.122296	−	0.211823i
$993$	3.15172	−	3.88640i	0.100017	−	0.123331i
$994$	27.6352	+	7.10662i	0.876534	+	0.225408i
$995$	−7.87360	−	13.6375i	−0.249610	−	0.432337i
$996$	3.40903	−	4.20368i	0.108019	−	0.133199i
$997$	−58.5641			−1.85475			−0.927373	−	0.374139i	$-0.877938\pi$
$997$	−58.5641			−1.85475			−0.927373	+	0.374139i	$0.877938\pi$
$998$	15.8977	+	27.5356i	0.503232	+	0.871624i
$999$	−12.5926	+	8.13960i	−0.398412	+	0.257526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.h.c.79.2	yes	6
3.2	odd	2		378.2.h.d.289.2		6
4.3	odd	2		1008.2.t.g.961.2		6
7.2	even	3		882.2.f.l.295.1		6
7.3	odd	6		882.2.e.p.655.1		6
7.4	even	3		126.2.e.d.25.3	✓	6
7.5	odd	6		882.2.f.m.295.3		6
7.6	odd	2		882.2.h.o.79.2		6
9.2	odd	6		1134.2.g.n.163.2		6
9.4	even	3		126.2.e.d.121.3	yes	6
9.5	odd	6		378.2.e.c.37.2		6
9.7	even	3		1134.2.g.k.163.2		6
12.11	even	2		3024.2.t.g.289.2		6
21.2	odd	6		2646.2.f.o.883.2		6
21.5	even	6		2646.2.f.n.883.2		6
21.11	odd	6		378.2.e.c.235.2		6
21.17	even	6		2646.2.e.o.2125.2		6
21.20	even	2		2646.2.h.p.667.2		6
28.11	odd	6		1008.2.q.h.529.1		6
36.23	even	6		3024.2.q.h.2305.2		6
36.31	odd	6		1008.2.q.h.625.1		6
63.2	odd	6		7938.2.a.bu.1.2		3
63.4	even	3	inner	126.2.h.c.67.2	yes	6
63.5	even	6		2646.2.f.n.1765.2		6
63.11	odd	6		1134.2.g.n.487.2		6
63.13	odd	6		882.2.e.p.373.1		6
63.16	even	3		7938.2.a.cb.1.2		3
63.23	odd	6		2646.2.f.o.1765.2		6
63.25	even	3		1134.2.g.k.487.2		6
63.31	odd	6		882.2.h.o.67.2		6
63.32	odd	6		378.2.h.d.361.2		6
63.40	odd	6		882.2.f.m.589.3		6
63.41	even	6		2646.2.e.o.1549.2		6
63.47	even	6		7938.2.a.bx.1.2		3
63.58	even	3		882.2.f.l.589.1		6
63.59	even	6		2646.2.h.p.361.2		6
63.61	odd	6		7938.2.a.by.1.2		3
84.11	even	6		3024.2.q.h.2881.2		6
252.67	odd	6		1008.2.t.g.193.2		6
252.95	even	6		3024.2.t.g.1873.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	7.4	even	3
126.2.e.d.121.3	yes	6	9.4	even	3
126.2.h.c.67.2	yes	6	63.4	even	3	inner
126.2.h.c.79.2	yes	6	1.1	even	1	trivial
378.2.e.c.37.2		6	9.5	odd	6
378.2.e.c.235.2		6	21.11	odd	6
378.2.h.d.289.2		6	3.2	odd	2
378.2.h.d.361.2		6	63.32	odd	6
882.2.e.p.373.1		6	63.13	odd	6
882.2.e.p.655.1		6	7.3	odd	6
882.2.f.l.295.1		6	7.2	even	3
882.2.f.l.589.1		6	63.58	even	3
882.2.f.m.295.3		6	7.5	odd	6
882.2.f.m.589.3		6	63.40	odd	6
882.2.h.o.67.2		6	63.31	odd	6
882.2.h.o.79.2		6	7.6	odd	2
1008.2.q.h.529.1		6	28.11	odd	6
1008.2.q.h.625.1		6	36.31	odd	6
1008.2.t.g.193.2		6	252.67	odd	6
1008.2.t.g.961.2		6	4.3	odd	2
1134.2.g.k.163.2		6	9.7	even	3
1134.2.g.k.487.2		6	63.25	even	3
1134.2.g.n.163.2		6	9.2	odd	6
1134.2.g.n.487.2		6	63.11	odd	6
2646.2.e.o.1549.2		6	63.41	even	6
2646.2.e.o.2125.2		6	21.17	even	6
2646.2.f.n.883.2		6	21.5	even	6
2646.2.f.n.1765.2		6	63.5	even	6
2646.2.f.o.883.2		6	21.2	odd	6
2646.2.f.o.1765.2		6	63.23	odd	6
2646.2.h.p.361.2		6	63.59	even	6
2646.2.h.p.667.2		6	21.20	even	2
3024.2.q.h.2305.2		6	36.23	even	6
3024.2.q.h.2881.2		6	84.11	even	6
3024.2.t.g.289.2		6	12.11	even	2
3024.2.t.g.1873.2		6	252.95	even	6
7938.2.a.bu.1.2		3	63.2	odd	6
7938.2.a.bx.1.2		3	63.47	even	6
7938.2.a.by.1.2		3	63.61	odd	6
7938.2.a.cb.1.2		3	63.16	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} +(1.09097 - 1.34528i) q^{6} +(-1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} +(1.09097 - 1.34528i) q^{6} +(-1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-2.23229 + 2.00422i) q^{9} +(-0.880438 - 1.52496i) q^{10} +6.12476 q^{11} +(-1.71053 - 0.272169i) q^{12} +(-0.380438 - 0.658939i) q^{13} +(2.56238 + 0.658939i) q^{14} +(1.09097 + 2.84813i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(2.85185 + 0.931107i) q^{18} +(0.971410 - 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(-4.20370 - 1.82454i) q^{21} +(-3.06238 - 5.30420i) q^{22} -0.421067 q^{23} +(0.619562 + 1.61745i) q^{24} -1.89931 q^{25} +(-0.380438 + 0.658939i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.710533 - 2.54856i) q^{28} +(0.732287 - 1.26836i) q^{29} +(1.92107 - 2.36887i) q^{30} +(-3.85185 + 6.67160i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.79467 + 9.90650i) q^{33} +(-3.42107 + 5.92546i) q^{34} +(-3.26088 + 3.32738i) q^{35} +(-0.619562 - 2.93533i) q^{36} +(1.44282 - 2.49904i) q^{37} -1.94282 q^{38} +(0.830095 - 1.02359i) q^{39} +1.76088 q^{40} +(-3.47141 - 6.01266i) q^{41} +(0.521753 + 4.55278i) q^{42} +(4.33009 - 7.49994i) q^{43} +(-3.06238 + 5.30420i) q^{44} +(-3.93078 + 3.52918i) q^{45} +(0.210533 + 0.364654i) q^{46} +(-0.830095 - 1.43777i) q^{47} +(1.09097 - 1.34528i) q^{48} +(-0.141315 - 6.99857i) q^{49} +(0.949657 + 1.64485i) q^{50} +(7.46457 - 9.20459i) q^{51} +0.760877 q^{52} +(-0.112725 - 0.195246i) q^{53} +(0.260877 + 5.18960i) q^{54} +10.7850 q^{55} +(-1.85185 + 1.88962i) q^{56} +(3.32326 + 0.528775i) q^{57} -1.46457 q^{58} +(-0.993163 + 1.72021i) q^{59} +(-3.01204 - 0.479256i) q^{60} +(5.17511 + 8.96355i) q^{61} +7.70370 q^{62} +(0.346647 - 7.92968i) q^{63} +1.00000 q^{64} +(-0.669905 - 1.16031i) q^{65} +(6.68194 - 8.23953i) q^{66} +(-3.39248 + 5.87594i) q^{67} +6.84213 q^{68} +(-0.260877 - 0.681054i) q^{69} +(4.51204 + 1.16031i) q^{70} +10.7850 q^{71} +(-2.23229 + 2.00422i) q^{72} +(0.153353 + 0.265616i) q^{73} -2.88564 q^{74} +(-1.17674 - 3.07204i) q^{75} +(0.971410 + 1.68253i) q^{76} +(-11.3421 + 11.5735i) q^{77} +(-1.30150 - 0.207087i) q^{78} +(6.72257 + 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(0.966208 - 8.94799i) q^{81} +(-3.47141 + 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(3.68194 - 2.72824i) q^{84} +(-6.02408 - 10.4340i) q^{85} -8.66019 q^{86} +(2.50520 + 0.398611i) q^{87} +6.12476 q^{88} +(1.30150 - 2.25427i) q^{89} +(5.02175 + 1.63957i) q^{90} +(1.94966 + 0.501371i) q^{91} +(0.210533 - 0.364654i) q^{92} +(-13.1774 - 2.09671i) q^{93} +(-0.830095 + 1.43777i) q^{94} +(1.71053 - 2.96273i) q^{95} +(-1.71053 - 0.272169i) q^{96} +(-1.81806 + 3.14897i) q^{97} +(-5.99028 + 3.62167i) q^{98} +(-13.6722 + 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more