LMFDB - Embedded newform 418.2.b.c.417.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(417,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("418.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.b (of order $2$, degree $1$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14584320320.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} + 11x^{5} - 11x^{4} + 32x^{3} + 44x^{2} - 18x + 46 $ x^8 - x^7 + 4x^6 + 11x^5 - 11x^4 + 32x^3 + 44x^2 - 18x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			417.2
Root			$0.682410 + 2.29682i$ of defining polynomial
Character	$\chi$	$=$	418.417
Dual form			418.2.b.c.417.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.00783i q^{3} +1.00000 q^{4} +1.36482 q^{5} +2.00783i q^{6} +0.331974i q^{7} -1.00000 q^{8} -1.03137 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.00783i q^{3} +1.00000 q^{4} +1.36482 q^{5} +2.00783i q^{6} +0.331974i q^{7} -1.00000 q^{8} -1.03137 q^{9} -1.36482 q^{10} +(3.31544 + 0.0887375i) q^{11} -2.00783i q^{12} +5.11734 q^{13} -0.331974i q^{14} -2.74032i q^{15} +1.00000 q^{16} +2.58582i q^{17} +1.03137 q^{18} +(-1.77245 - 3.98226i) q^{19} +1.36482 q^{20} +0.666547 q^{21} +(-3.31544 - 0.0887375i) q^{22} -2.10590 q^{23} +2.00783i q^{24} -3.13727 q^{25} -5.11734 q^{26} -3.95267i q^{27} +0.331974i q^{28} +0.741082 q^{29} +2.74032i q^{30} +5.22421i q^{31} -1.00000 q^{32} +(0.178170 - 6.65682i) q^{33} -2.58582i q^{34} +0.453085i q^{35} -1.03137 q^{36} -6.14459i q^{37} +(1.77245 + 3.98226i) q^{38} -10.2747i q^{39} -1.36482 q^{40} -2.49361 q^{41} -0.666547 q^{42} -10.2518i q^{43} +(3.31544 + 0.0887375i) q^{44} -1.40763 q^{45} +2.10590 q^{46} -4.21180 q^{47} -2.00783i q^{48} +6.88979 q^{49} +3.13727 q^{50} +5.19188 q^{51} +5.11734 q^{52} +7.44290i q^{53} +3.95267i q^{54} +(4.52497 + 0.121111i) q^{55} -0.331974i q^{56} +(-7.99569 + 3.55877i) q^{57} -0.741082 q^{58} -1.84953i q^{59} -2.74032i q^{60} -2.61541i q^{61} -5.22421i q^{62} -0.342387i q^{63} +1.00000 q^{64} +6.98425 q^{65} +(-0.178170 + 6.65682i) q^{66} +2.28344i q^{67} +2.58582i q^{68} +4.22828i q^{69} -0.453085i q^{70} +12.1385i q^{71} +1.03137 q^{72} +9.08536i q^{73} +6.14459i q^{74} +6.29909i q^{75} +(-1.77245 - 3.98226i) q^{76} +(-0.0294586 + 1.10064i) q^{77} +10.2747i q^{78} -5.96397 q^{79} +1.36482 q^{80} -11.0304 q^{81} +2.49361 q^{82} -13.2221i q^{83} +0.666547 q^{84} +3.52918i q^{85} +10.2518i q^{86} -1.48796i q^{87} +(-3.31544 - 0.0887375i) q^{88} +16.4879i q^{89} +1.40763 q^{90} +1.69883i q^{91} -2.10590 q^{92} +10.4893 q^{93} +4.21180 q^{94} +(-2.41907 - 5.43507i) q^{95} +2.00783i q^{96} -3.52918i q^{97} -6.88979 q^{98} +(-3.41943 - 0.0915209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	2.00783i		−	1.15922i	−0.814894	−	0.579610i	$-0.803205\pi$
$3$		−	2.00783i		−	1.15922i	0.814894	−	0.579610i	$-0.196795\pi$
$4$	1.00000			0.500000
$5$	1.36482			0.610366			0.305183	−	0.952294i	$-0.401282\pi$
$5$	1.36482			0.610366			0.305183	+	0.952294i	$0.401282\pi$
$6$			2.00783i			0.819692i
$7$			0.331974i			0.125475i	0.998030	+	0.0627373i	$0.0199830\pi$
$7$			0.331974i			0.125475i	−0.998030	+	0.0627373i	$0.980017\pi$
$8$	−1.00000			−0.353553
$9$	−1.03137			−0.343789
$10$	−1.36482			−0.431594
$11$	3.31544	+	0.0887375i	0.999642	+	0.0267554i
$11$	3.31544	+	0.0887375i	0.999642	+	0.0267554i
$12$		−	2.00783i		−	0.579610i
$13$	5.11734			1.41930			0.709648	−	0.704556i	$-0.248854\pi$
$13$	5.11734			1.41930			0.709648	+	0.704556i	$0.248854\pi$
$14$		−	0.331974i		−	0.0887239i
$15$		−	2.74032i		−	0.707548i
$16$	1.00000			0.250000
$17$			2.58582i			0.627154i	0.949563	+	0.313577i	$0.101527\pi$
$17$			2.58582i			0.627154i	−0.949563	+	0.313577i	$0.898473\pi$
$18$	1.03137			0.243095
$19$	−1.77245	−	3.98226i	−0.406628	−	0.913594i
$19$	−1.77245	−	3.98226i	−0.406628	−	0.913594i
$20$	1.36482			0.305183
$21$	0.666547			0.145452
$22$	−3.31544	−	0.0887375i	−0.706854	−	0.0189189i
$23$	−2.10590			−0.439111			−0.219555	−	0.975600i	$-0.570461\pi$
$23$	−2.10590			−0.439111			−0.219555	+	0.975600i	$0.570461\pi$
$24$			2.00783i			0.409846i
$25$	−3.13727			−0.627454
$26$	−5.11734			−1.00359
$27$		−	3.95267i		−	0.760693i
$28$			0.331974i			0.0627373i
$29$	0.741082			0.137615			0.0688077	−	0.997630i	$-0.478080\pi$
$29$	0.741082			0.137615			0.0688077	+	0.997630i	$0.478080\pi$
$30$			2.74032i			0.500312i
$31$			5.22421i			0.938295i	0.883120	+	0.469148i	$0.155439\pi$
$31$			5.22421i			0.938295i	−0.883120	+	0.469148i	$0.844561\pi$
$32$	−1.00000			−0.176777
$33$	0.178170	−	6.65682i	0.0310153	−	1.15880i
$34$		−	2.58582i		−	0.443465i
$35$			0.453085i			0.0765854i
$36$	−1.03137			−0.171894
$37$		−	6.14459i		−	1.01016i	−0.863071	−	0.505082i	$-0.831462\pi$
$37$		−	6.14459i		−	1.01016i	0.863071	−	0.505082i	$-0.168538\pi$
$38$	1.77245	+	3.98226i	0.287529	+	0.646009i
$39$		−	10.2747i		−	1.64527i
$40$	−1.36482			−0.215797
$41$	−2.49361			−0.389436			−0.194718	−	0.980859i	$-0.562379\pi$
$41$	−2.49361			−0.389436			−0.194718	+	0.980859i	$0.562379\pi$
$42$	−0.666547			−0.102850
$43$		−	10.2518i		−	1.56338i	−0.623668	−	0.781690i	$-0.714358\pi$
$43$		−	10.2518i		−	1.56338i	0.623668	−	0.781690i	$-0.285642\pi$
$44$	3.31544	+	0.0887375i	0.499821	+	0.0133777i
$45$	−1.40763			−0.209837
$46$	2.10590			0.310498
$47$	−4.21180			−0.614355			−0.307177	−	0.951652i	$-0.599384\pi$
$47$	−4.21180			−0.614355			−0.307177	+	0.951652i	$0.599384\pi$
$48$		−	2.00783i		−	0.289805i
$49$	6.88979			0.984256
$50$	3.13727			0.443677
$51$	5.19188			0.727009
$52$	5.11734			0.709648
$53$			7.44290i			1.02236i	0.859473	+	0.511180i	$0.170792\pi$
$53$			7.44290i			1.02236i	−0.859473	+	0.511180i	$0.829208\pi$
$54$			3.95267i			0.537891i
$55$	4.52497	+	0.121111i	0.610147	+	0.0163306i
$56$		−	0.331974i		−	0.0443620i
$57$	−7.99569	+	3.55877i	−1.05906	+	0.471370i
$58$	−0.741082			−0.0973088
$59$		−	1.84953i		−	0.240788i	−0.992726	−	0.120394i	$-0.961584\pi$
$59$		−	1.84953i		−	0.240788i	0.992726	−	0.120394i	$-0.0384158\pi$
$60$		−	2.74032i		−	0.353774i
$61$		−	2.61541i		−	0.334869i	−0.985883	−	0.167435i	$-0.946452\pi$
$61$		−	2.61541i		−	0.334869i	0.985883	−	0.167435i	$-0.0535483\pi$
$62$		−	5.22421i		−	0.663475i
$63$		−	0.342387i		−	0.0431367i
$64$	1.00000			0.125000
$65$	6.98425			0.866290
$66$	−0.178170	+	6.65682i	−0.0219312	+	0.819398i
$67$			2.28344i			0.278966i	0.990224	+	0.139483i	$0.0445441\pi$
$67$			2.28344i			0.278966i	−0.990224	+	0.139483i	$0.955456\pi$
$68$			2.58582i			0.313577i
$69$			4.22828i			0.509026i
$70$		−	0.453085i		−	0.0541540i
$71$			12.1385i			1.44057i	0.693677	+	0.720286i	$0.255990\pi$
$71$			12.1385i			1.44057i	−0.693677	+	0.720286i	$0.744010\pi$
$72$	1.03137			0.121548
$73$			9.08536i			1.06336i	0.846945	+	0.531681i	$0.178439\pi$
$73$			9.08536i			1.06336i	−0.846945	+	0.531681i	$0.821561\pi$
$74$			6.14459i			0.714294i
$75$			6.29909i			0.727356i
$76$	−1.77245	−	3.98226i	−0.203314	−	0.456797i
$77$	−0.0294586	+	1.10064i	−0.00335712	+	0.125430i
$78$			10.2747i			1.16339i
$79$	−5.96397			−0.670999			−0.335499	−	0.942040i	$-0.608905\pi$
$79$	−5.96397			−0.670999			−0.335499	+	0.942040i	$0.608905\pi$
$80$	1.36482			0.152591
$81$	−11.0304			−1.22560
$82$	2.49361			0.275373
$83$		−	13.2221i		−	1.45132i	−0.688055	−	0.725658i	$-0.741535\pi$
$83$		−	13.2221i		−	1.45132i	0.688055	−	0.725658i	$-0.258465\pi$
$84$	0.666547			0.0727262
$85$			3.52918i			0.382793i
$86$			10.2518i			1.10548i
$87$		−	1.48796i		−	0.159526i
$88$	−3.31544	−	0.0887375i	−0.353427	−	0.00945945i
$89$			16.4879i			1.74771i	0.486186	+	0.873856i	$0.338388\pi$
$89$			16.4879i			1.74771i	−0.486186	+	0.873856i	$0.661612\pi$
$90$	1.40763			0.148377
$91$			1.69883i			0.178086i
$92$	−2.10590			−0.219555
$93$	10.4893			1.08769
$94$	4.21180			0.434414
$95$	−2.41907	−	5.43507i	−0.248192	−	0.557627i
$96$			2.00783i			0.204923i
$97$		−	3.52918i		−	0.358334i	−0.983819	−	0.179167i	$-0.942660\pi$
$97$		−	3.52918i		−	0.358334i	0.983819	−	0.179167i	$-0.0573402\pi$
$98$	−6.88979			−0.695974
$99$	−3.41943	−	0.0915209i	−0.343666	−	0.00919820i
$100$	−3.13727			−0.313727
$101$			16.4879i			1.64060i	0.571930	+	0.820302i	$0.306195\pi$
$101$			16.4879i			1.64060i	−0.571930	+	0.820302i	$0.693805\pi$
$102$	−5.19188			−0.514073
$103$		−	9.20647i		−	0.907141i	−0.891221	−	0.453570i	$-0.850150\pi$
$103$		−	9.20647i		−	0.907141i	0.891221	−	0.453570i	$-0.149850\pi$
$104$	−5.11734			−0.501797
$105$	0.909716			0.0887792
$106$		−	7.44290i		−	0.722918i
$107$	−5.77245			−0.558044			−0.279022	−	0.960285i	$-0.590010\pi$
$107$	−5.77245			−0.558044			−0.279022	+	0.960285i	$0.590010\pi$
$108$		−	3.95267i		−	0.380346i
$109$	11.5291			1.10429			0.552146	−	0.833747i	$-0.313809\pi$
$109$	11.5291			1.10429			0.552146	+	0.833747i	$0.313809\pi$
$110$	−4.52497	−	0.121111i	−0.431439	−	0.0115475i
$111$	−12.3373			−1.17100
$112$			0.331974i			0.0313686i
$113$			3.17423i			0.298606i	0.988791	+	0.149303i	$0.0477030\pi$
$113$			3.17423i			0.298606i	−0.988791	+	0.149303i	$0.952297\pi$
$114$	7.99569	−	3.55877i	0.748865	−	0.333309i
$115$	−2.87418			−0.268018
$116$	0.741082			0.0688077
$117$	−5.27786			−0.487938
$118$			1.84953i			0.170263i
$119$	−0.858427			−0.0786918
$120$			2.74032i			0.250156i
$121$	10.9843	+	0.588408i	0.998568	+	0.0534916i
$122$			2.61541i			0.236788i
$123$			5.00673i			0.451442i
$124$			5.22421i			0.469148i
$125$	−11.1059			−0.993342
$126$			0.342387i			0.0305023i
$127$	4.50469			0.399727			0.199863	−	0.979824i	$-0.435950\pi$
$127$	4.50469			0.399727			0.199863	+	0.979824i	$0.435950\pi$
$128$	−1.00000			−0.0883883
$129$	−20.5838			−1.81230
$130$	−6.98425			−0.612559
$131$			11.2637i			0.984111i	0.870564	+	0.492056i	$0.163754\pi$
$131$			11.2637i			0.984111i	−0.870564	+	0.492056i	$0.836246\pi$
$132$	0.178170	−	6.65682i	0.0155077	−	0.579402i
$133$	1.32201	−	0.588408i	0.114633	−	0.0510214i
$134$		−	2.28344i		−	0.197259i
$135$		−	5.39469i		−	0.464301i
$136$		−	2.58582i		−	0.221732i
$137$	−11.5364			−0.985623			−0.492811	−	0.870136i	$-0.664031\pi$
$137$	−11.5364			−0.985623			−0.492811	+	0.870136i	$0.664031\pi$
$138$		−	4.22828i		−	0.359935i
$139$			15.3511i			1.30206i	0.759052	+	0.651030i	$0.225663\pi$
$139$			15.3511i			1.30206i	−0.759052	+	0.651030i	$0.774337\pi$
$140$			0.453085i			0.0382927i
$141$			8.45657i			0.712172i
$142$		−	12.1385i		−	1.01864i
$143$	16.9662	+	0.454101i	1.41879	+	0.0379738i
$144$	−1.03137			−0.0859472
$145$	1.01144			0.0839958
$146$		−	9.08536i		−	0.751910i
$147$		−	13.8335i		−	1.14097i
$148$		−	6.14459i		−	0.505082i
$149$			9.05577i			0.741878i	0.928657	+	0.370939i	$0.120964\pi$
$149$			9.05577i			0.741878i	−0.928657	+	0.370939i	$0.879036\pi$
$150$		−	6.29909i		−	0.514318i
$151$	14.1758			1.15361			0.576804	−	0.816883i	$-0.304300\pi$
$151$	14.1758			1.15361			0.576804	+	0.816883i	$0.304300\pi$
$152$	1.77245	+	3.98226i	0.143765	+	0.323004i
$153$		−	2.66693i		−	0.215608i
$154$	0.0294586	−	1.10064i	0.00237384	−	0.0886921i
$155$			7.13010i			0.572703i
$156$		−	10.2747i		−	0.822637i
$157$	−14.8966			−1.18888			−0.594438	−	0.804142i	$-0.702625\pi$
$157$	−14.8966			−1.18888			−0.594438	+	0.804142i	$0.702625\pi$
$158$	5.96397			0.474468
$159$	14.9440			1.18514
$160$	−1.36482			−0.107898
$161$		−	0.699105i		−	0.0550972i
$162$	11.0304			0.866629
$163$	3.54108			0.277359			0.138679	−	0.990337i	$-0.455714\pi$
$163$	3.54108			0.277359			0.138679	+	0.990337i	$0.455714\pi$
$164$	−2.49361			−0.194718
$165$	0.243169	−	9.08536i	0.0189307	−	0.707294i
$166$			13.2221i			1.02624i
$167$	−10.3876			−0.803815			−0.401907	−	0.915680i	$-0.631653\pi$
$167$	−10.3876			−0.803815			−0.401907	+	0.915680i	$0.631653\pi$
$168$	−0.666547			−0.0514252
$169$	13.1872			1.01440
$170$		−	3.52918i		−	0.270676i
$171$	1.82804	+	4.10717i	0.139794	+	0.314083i
$172$		−	10.2518i		−	0.781690i
$173$	11.1804			0.850033			0.425016	−	0.905186i	$-0.360268\pi$
$173$	11.1804			0.850033			0.425016	+	0.905186i	$0.360268\pi$
$174$			1.48796i			0.112802i
$175$		−	1.04149i		−	0.0787295i
$176$	3.31544	+	0.0887375i	0.249911	+	0.00668884i
$177$	−3.71353			−0.279126
$178$		−	16.4879i		−	1.23582i
$179$			2.25385i			0.168460i	0.996446	+	0.0842302i	$0.0268431\pi$
$179$			2.25385i			0.168460i	−0.996446	+	0.0842302i	$0.973157\pi$
$180$	−1.40763			−0.104918
$181$		−	24.3153i		−	1.80734i	−0.428227	−	0.903671i	$-0.640861\pi$
$181$		−	24.3153i		−	1.80734i	0.428227	−	0.903671i	$-0.359139\pi$
$182$		−	1.69883i		−	0.125925i
$183$	−5.25129			−0.388187
$184$	2.10590			0.155249
$185$		−	8.38626i		−	0.616570i
$186$	−10.4893			−0.769113
$187$	−0.229459	+	8.57313i	−0.0167797	+	0.626929i
$188$	−4.21180			−0.307177
$189$	1.31219			0.0954475
$190$	2.41907	+	5.43507i	0.175498	+	0.394302i
$191$	21.4533			1.55230			0.776152	−	0.630546i	$-0.217169\pi$
$191$	21.4533			1.55230			0.776152	+	0.630546i	$0.217169\pi$
$192$		−	2.00783i		−	0.144902i
$193$	−20.6664			−1.48760			−0.743801	−	0.668402i	$-0.766979\pi$
$193$	−20.6664			−1.48760			−0.743801	+	0.668402i	$0.766979\pi$
$194$			3.52918i			0.253380i
$195$		−	14.0232i		−	1.00422i
$196$	6.88979			0.492128
$197$			8.03131i			0.572207i	0.958199	+	0.286103i	$0.0923601\pi$
$197$			8.03131i			0.572207i	−0.958199	+	0.286103i	$0.907640\pi$
$198$	3.41943	+	0.0915209i	0.243008	+	0.00650411i
$199$	0.263583			0.0186849			0.00934244	−	0.999956i	$-0.497026\pi$
$199$	0.263583			0.0186849			0.00934244	+	0.999956i	$0.497026\pi$
$200$	3.13727			0.221838
$201$	4.58474			0.323383
$202$		−	16.4879i		−	1.16008i
$203$			0.246020i			0.0172672i
$204$	5.19188			0.363504
$205$	−3.40332			−0.237698
$206$			9.20647i			0.641445i
$207$	2.17196			0.150961
$208$	5.11734			0.354824
$209$	−5.52307	−	13.3602i	−0.382038	−	0.924146i
$210$	−0.909716			−0.0627764
$211$	−16.7825			−1.15536			−0.577679	−	0.816264i	$-0.696042\pi$
$211$	−16.7825			−1.15536			−0.577679	+	0.816264i	$0.696042\pi$
$212$			7.44290i			0.511180i
$213$	24.3720			1.66994
$214$	5.77245			0.394596
$215$		−	13.9918i		−	0.954233i
$216$			3.95267i			0.268945i
$217$	−1.73430			−0.117732
$218$	−11.5291			−0.780852
$219$	18.2418			1.23267
$220$	4.52497	+	0.121111i	0.305074	+	0.00816528i
$221$			13.2325i			0.890117i
$222$	12.3373			0.828023
$223$		−	3.91052i		−	0.261868i	−0.991391	−	0.130934i	$-0.958202\pi$
$223$		−	3.91052i		−	0.261868i	0.991391	−	0.130934i	$-0.0417976\pi$
$224$		−	0.331974i		−	0.0221810i
$225$	3.23567			0.215712
$226$		−	3.17423i		−	0.211147i
$227$	18.5791			1.23314			0.616569	−	0.787301i	$-0.288522\pi$
$227$	18.5791			1.23314			0.616569	+	0.787301i	$0.288522\pi$
$228$	−7.99569	+	3.55877i	−0.529528	+	0.235685i
$229$	−3.22325			−0.212998			−0.106499	−	0.994313i	$-0.533964\pi$
$229$	−3.22325			−0.212998			−0.106499	+	0.994313i	$0.533964\pi$
$230$	2.87418			0.189518
$231$	2.20989	+	0.0591477i	0.145400	+	0.00389164i
$232$	−0.741082			−0.0486544
$233$		−	8.59012i		−	0.562758i	−0.959597	−	0.281379i	$-0.909208\pi$
$233$		−	8.59012i		−	0.562758i	0.959597	−	0.281379i	$-0.0907918\pi$
$234$	5.27786			0.345024
$235$	−5.74835			−0.374981
$236$		−	1.84953i		−	0.120394i
$237$			11.9746i			0.777835i
$238$	0.858427			0.0556435
$239$		−	5.42428i		−	0.350867i	−0.984491	−	0.175434i	$-0.943867\pi$
$239$		−	5.42428i		−	0.350867i	0.984491	−	0.175434i	$-0.0561327\pi$
$240$		−	2.74032i		−	0.176887i
$241$	−0.436523			−0.0281189			−0.0140594	−	0.999901i	$-0.504475\pi$
$241$	−0.436523			−0.0281189			−0.0140594	+	0.999901i	$0.504475\pi$
$242$	−10.9843	−	0.588408i	−0.706094	−	0.0378243i
$243$			10.2891i			0.660044i
$244$		−	2.61541i		−	0.167435i
$245$	9.40332			0.600756
$246$		−	5.00673i		−	0.319217i
$247$	−9.07023	−	20.3786i	−0.577125	−	1.29666i
$248$		−	5.22421i		−	0.331738i
$249$	−26.5477			−1.68239
$250$	11.1059			0.702399
$251$	−26.0541			−1.64452			−0.822261	−	0.569111i	$-0.807288\pi$
$251$	−26.0541			−1.64452			−0.822261	+	0.569111i	$0.807288\pi$
$252$		−	0.342387i		−	0.0215684i
$253$	−6.98198	−	0.186873i	−0.438954	−	0.0117486i
$254$	−4.50469			−0.282649
$255$	7.08598			0.443741
$256$	1.00000			0.0625000
$257$		−	14.9965i		−	0.935456i	−0.883873	−	0.467728i	$-0.845073\pi$
$257$		−	14.9965i		−	0.935456i	0.883873	−	0.467728i	$-0.154927\pi$
$258$	20.5838			1.28149
$259$	2.03985			0.126750
$260$	6.98425			0.433145
$261$	−0.764327			−0.0473107
$262$		−	11.2637i		−	0.695872i
$263$		−	15.3531i		−	0.946712i	−0.880871	−	0.473356i	$-0.843042\pi$
$263$		−	15.3531i		−	0.946712i	0.880871	−	0.473356i	$-0.156958\pi$
$264$	−0.178170	+	6.65682i	−0.0109656	+	0.409699i
$265$			10.1582i			0.624014i
$266$	−1.32201	+	0.588408i	−0.0810576	+	0.0360776i
$267$	33.1048			2.02598
$268$			2.28344i			0.139483i
$269$		−	16.1329i		−	0.983642i	−0.870696	−	0.491821i	$-0.836331\pi$
$269$		−	16.1329i		−	0.983642i	0.870696	−	0.491821i	$-0.163669\pi$
$270$			5.39469i			0.328310i
$271$			19.6795i			1.19545i	0.801703	+	0.597723i	$0.203928\pi$
$271$			19.6795i			1.19545i	−0.801703	+	0.597723i	$0.796072\pi$
$272$			2.58582i			0.156788i
$273$	3.41095			0.206440
$274$	11.5364			0.696940
$275$	−10.4014	−	0.278393i	−0.627229	−	0.0167878i
$276$			4.22828i			0.254513i
$277$			24.1642i			1.45189i	0.687754	+	0.725944i	$0.258597\pi$
$277$			24.1642i			1.45189i	−0.687754	+	0.725944i	$0.741403\pi$
$278$		−	15.3511i		−	0.920695i
$279$		−	5.38807i		−	0.322575i
$280$		−	0.453085i		−	0.0270770i
$281$	−23.1313			−1.37990			−0.689948	−	0.723859i	$-0.742366\pi$
$281$	−23.1313			−1.37990			−0.689948	+	0.723859i	$0.742366\pi$
$282$		−	8.45657i		−	0.503581i
$283$			5.62638i			0.334453i	0.985918	+	0.167227i	$0.0534812\pi$
$283$			5.62638i			0.334453i	−0.985918	+	0.167227i	$0.946519\pi$
$284$			12.1385i			0.720286i
$285$	−10.9127	+	4.85708i	−0.646411	+	0.287708i
$286$	−16.9662	−	0.454101i	−1.00323	−	0.0268515i
$287$		−	0.827814i		−	0.0488643i
$288$	1.03137			0.0607739
$289$	10.3135			0.606678
$290$	−1.01144			−0.0593940
$291$	−7.08598			−0.415387
$292$			9.08536i			0.531681i
$293$	15.9953			0.934457			0.467229	−	0.884136i	$-0.345252\pi$
$293$	15.9953			0.934457			0.467229	+	0.884136i	$0.345252\pi$
$294$			13.8335i			0.806787i
$295$		−	2.52427i		−	0.146969i
$296$			6.14459i			0.357147i
$297$	0.350751	−	13.1048i	0.0203526	−	0.760420i
$298$		−	9.05577i		−	0.524587i
$299$	−10.7766			−0.623228
$300$			6.29909i			0.363678i
$301$	3.40332			0.196164
$302$	−14.1758			−0.815724
$303$	33.1048			1.90182
$304$	−1.77245	−	3.98226i	−0.101657	−	0.228399i
$305$		−	3.56956i		−	0.204393i
$306$			2.66693i			0.152458i
$307$	−17.8829			−1.02063			−0.510315	−	0.859988i	$-0.670471\pi$
$307$	−17.8829			−1.02063			−0.510315	+	0.859988i	$0.670471\pi$
$308$	−0.0294586	+	1.10064i	−0.00167856	+	0.0627148i
$309$	−18.4850			−1.05157
$310$		−	7.13010i		−	0.404962i
$311$	−22.9846			−1.30334			−0.651669	−	0.758504i	$-0.725931\pi$
$311$	−22.9846			−1.30334			−0.651669	+	0.758504i	$0.725931\pi$
$312$			10.2747i			0.581693i
$313$	−20.2507			−1.14464			−0.572318	−	0.820032i	$-0.693956\pi$
$313$	−20.2507			−1.14464			−0.572318	+	0.820032i	$0.693956\pi$
$314$	14.8966			0.840662
$315$		−	0.467297i		−	0.0263292i
$316$	−5.96397			−0.335499
$317$			10.1690i			0.571148i	0.958357	+	0.285574i	$0.0921843\pi$
$317$			10.1690i			0.571148i	−0.958357	+	0.285574i	$0.907816\pi$
$318$	−14.9440			−0.838020
$319$	2.45701	+	0.0657618i	0.137566	+	0.00368195i
$320$	1.36482			0.0762957
$321$			11.5901i			0.646895i
$322$			0.699105i			0.0389596i
$323$	10.2974	−	4.58323i	0.572964	−	0.255018i
$324$	−11.0304			−0.612799
$325$	−16.0545			−0.890542
$326$	−3.54108			−0.196122
$327$		−	23.1485i		−	1.28012i
$328$	2.49361			0.137686
$329$		−	1.39821i		−	0.0770859i
$330$	−0.243169	+	9.08536i	−0.0133860	+	0.500133i
$331$			19.2264i			1.05678i	0.849002	+	0.528390i	$0.177204\pi$
$331$			19.2264i			1.05678i	−0.849002	+	0.528390i	$0.822796\pi$
$332$		−	13.2221i		−	0.725658i
$333$			6.33732i			0.347283i
$334$	10.3876			0.568383
$335$			3.11648i			0.170271i
$336$	0.666547			0.0363631
$337$	1.38474			0.0754317			0.0377159	−	0.999289i	$-0.487992\pi$
$337$	1.38474			0.0754317			0.0377159	+	0.999289i	$0.487992\pi$
$338$	−13.1872			−0.717290
$339$	6.37330			0.346150
$340$			3.52918i			0.191397i
$341$	−0.463583	+	17.3205i	−0.0251044	+	0.937959i
$342$	−1.82804	−	4.10717i	−0.0988493	−	0.222091i
$343$			4.61106i			0.248974i
$344$			10.2518i			0.552738i
$345$			5.77084i			0.310692i
$346$	−11.1804			−0.601064
$347$			21.7263i			1.16633i	0.812354	+	0.583164i	$0.198186\pi$
$347$			21.7263i			1.16633i	−0.812354	+	0.583164i	$0.801814\pi$
$348$		−	1.48796i		−	0.0797632i
$349$		−	8.38626i		−	0.448906i	−0.974485	−	0.224453i	$-0.927940\pi$
$349$		−	8.38626i		−	0.448906i	0.974485	−	0.224453i	$-0.0720595\pi$
$350$			1.04149i			0.0556701i
$351$		−	20.2272i		−	1.07965i
$352$	−3.31544	−	0.0887375i	−0.176713	−	0.00472973i
$353$	−13.1101			−0.697779			−0.348889	−	0.937164i	$-0.613441\pi$
$353$	−13.1101			−0.697779			−0.348889	+	0.937164i	$0.613441\pi$
$354$	3.71353			0.197372
$355$			16.5668i			0.879276i
$356$			16.4879i			0.873856i
$357$			1.72357i			0.0912211i
$358$		−	2.25385i		−	0.119119i
$359$		−	29.8474i		−	1.57528i	−0.616134	−	0.787641i	$-0.711302\pi$
$359$		−	29.8474i		−	1.57528i	0.616134	−	0.787641i	$-0.288698\pi$
$360$	1.40763			0.0741886
$361$	−12.7169	+	14.1167i	−0.669308	+	0.742985i
$362$			24.3153i			1.27798i
$363$	1.18142	−	22.0545i	0.0620085	−	1.15756i
$364$			1.69883i			0.0890428i
$365$			12.3999i			0.649039i
$366$	5.25129			0.274489
$367$	3.49912			0.182653			0.0913264	−	0.995821i	$-0.470889\pi$
$367$	3.49912			0.182653			0.0913264	+	0.995821i	$0.470889\pi$
$368$	−2.10590			−0.109778
$369$	2.57182			0.133884
$370$			8.38626i			0.435981i
$371$	−2.47085			−0.128280
$372$	10.4893			0.543845
$373$	14.2004			0.735267			0.367633	−	0.929971i	$-0.380168\pi$
$373$	14.2004			0.735267			0.367633	+	0.929971i	$0.380168\pi$
$374$	0.229459	−	8.57313i	0.0118651	−	0.443306i
$375$			22.2987i			1.15150i
$376$	4.21180			0.217207
$377$	3.79237			0.195317
$378$	−1.31219			−0.0674916
$379$		−	19.7199i		−	1.01294i	−0.862257	−	0.506472i	$-0.830950\pi$
$379$		−	19.7199i		−	1.01294i	0.862257	−	0.506472i	$-0.169050\pi$
$380$	−2.41907	−	5.43507i	−0.124096	−	0.278813i
$381$		−	9.04464i		−	0.463371i
$382$	−21.4533			−1.09764
$383$			28.8108i			1.47216i	0.676892	+	0.736082i	$0.263326\pi$
$383$			28.8108i			1.47216i	−0.676892	+	0.736082i	$0.736674\pi$
$384$			2.00783i			0.102461i
$385$	−0.0402057	+	1.50218i	−0.00204907	+	0.0765580i
$386$	20.6664			1.05189
$387$			10.5733i			0.537472i
$388$		−	3.52918i		−	0.179167i
$389$	9.71255			0.492446			0.246223	−	0.969213i	$-0.420810\pi$
$389$	9.71255			0.492446			0.246223	+	0.969213i	$0.420810\pi$
$390$			14.0232i			0.710090i
$391$		−	5.44548i		−	0.275390i
$392$	−6.88979			−0.347987
$393$	22.6155			1.14080
$394$		−	8.03131i		−	0.404611i
$395$	−8.13974			−0.409555
$396$	−3.41943	−	0.0915209i	−0.171833	−	0.00459910i
$397$	21.8815			1.09820			0.549102	−	0.835756i	$-0.314970\pi$
$397$	21.8815			1.09820			0.549102	+	0.835756i	$0.314970\pi$
$398$	−0.263583			−0.0132122
$399$	−1.18142	−	2.65437i	−0.0591450	−	0.132885i
$400$	−3.13727			−0.156863
$401$			20.9308i			1.04524i	0.852567	+	0.522618i	$0.175044\pi$
$401$			20.9308i			1.04524i	−0.852567	+	0.522618i	$0.824956\pi$
$402$	−4.58474			−0.228666
$403$			26.7341i			1.33172i
$404$			16.4879i			0.820302i
$405$	−15.0545			−0.748063
$406$		−	0.246020i		−	0.0122098i
$407$	0.545256	−	20.3720i	0.0270273	−	1.00980i
$408$	−5.19188			−0.257036
$409$	25.6935			1.27046			0.635230	−	0.772323i	$-0.280905\pi$
$409$	25.6935			1.27046			0.635230	+	0.772323i	$0.280905\pi$
$410$	3.40332			0.168078
$411$			23.1631i			1.14255i
$412$		−	9.20647i		−	0.453570i
$413$	0.613996			0.0302128
$414$	−2.17196			−0.106746
$415$		−	18.0458i		−	0.885834i
$416$	−5.11734			−0.250898
$417$	30.8223			1.50937
$418$	5.52307	+	13.3602i	0.270142	+	0.653470i
$419$	10.6766			0.521588			0.260794	−	0.965394i	$-0.416016\pi$
$419$	10.6766			0.521588			0.260794	+	0.965394i	$0.416016\pi$
$420$	0.909716			0.0443896
$421$			11.2866i			0.550077i	0.961433	+	0.275039i	$0.0886906\pi$
$421$			11.2866i			0.550077i	−0.961433	+	0.275039i	$0.911309\pi$
$422$	16.7825			0.816962
$423$	4.34391			0.211208
$424$		−	7.44290i		−	0.361459i
$425$		−	8.11241i		−	0.393510i
$426$	−24.3720			−1.18083
$427$	0.868250			0.0420175
$428$	−5.77245			−0.279022
$429$	0.911755	−	34.0653i	0.0440200	−	1.64469i
$430$			13.9918i			0.674745i
$431$	33.5141			1.61432			0.807159	−	0.590334i	$-0.201004\pi$
$431$	33.5141			1.61432			0.807159	+	0.590334i	$0.201004\pi$
$432$		−	3.95267i		−	0.190173i
$433$			1.36828i			0.0657555i	0.999459	+	0.0328777i	$0.0104672\pi$
$433$			1.36828i			0.0657555i	−0.999459	+	0.0328777i	$0.989533\pi$
$434$	1.73430			0.0832492
$435$		−	2.03080i		−	0.0973695i
$436$	11.5291			0.552146
$437$	3.73260	+	8.38626i	0.178555	+	0.401169i
$438$	−18.2418			−0.871628
$439$	−37.1544			−1.77328			−0.886641	−	0.462459i	$-0.846967\pi$
$439$	−37.1544			−1.77328			−0.886641	+	0.462459i	$0.846967\pi$
$440$	−4.52497	−	0.121111i	−0.215720	−	0.00577373i
$441$	−7.10590			−0.338376
$442$		−	13.2325i		−	0.629408i
$443$	−6.38376			−0.303302			−0.151651	−	0.988434i	$-0.548459\pi$
$443$	−6.38376			−0.303302			−0.151651	+	0.988434i	$0.548459\pi$
$444$	−12.3373			−0.585501
$445$			22.5030i			1.06674i
$446$			3.91052i			0.185169i
$447$	18.1824			0.859999
$448$			0.331974i			0.0156843i
$449$		−	14.6943i		−	0.693468i	−0.937963	−	0.346734i	$-0.887291\pi$
$449$		−	14.6943i		−	0.693468i	0.937963	−	0.346734i	$-0.112709\pi$
$450$	−3.23567			−0.152531
$451$	−8.26740	−	0.221277i	−0.389297	−	0.0104195i
$452$			3.17423i			0.149303i
$453$		−	28.4625i		−	1.33728i
$454$	−18.5791			−0.871960
$455$			2.31859i			0.108697i
$456$	7.99569	−	3.55877i	0.374433	−	0.166655i
$457$			22.5097i			1.05296i	0.850188	+	0.526480i	$0.176488\pi$
$457$			22.5097i			1.05296i	−0.850188	+	0.526480i	$0.823512\pi$
$458$	3.22325			0.150612
$459$	10.2209			0.477071
$460$	−2.87418			−0.134009
$461$		−	18.1532i		−	0.845479i	−0.906251	−	0.422739i	$-0.861069\pi$
$461$		−	18.1532i		−	0.845479i	0.906251	−	0.422739i	$-0.138931\pi$
$462$	−2.20989	−	0.0591477i	−0.102814	−	0.00275180i
$463$	2.87799			0.133752			0.0668758	−	0.997761i	$-0.478697\pi$
$463$	2.87799			0.133752			0.0668758	+	0.997761i	$0.478697\pi$
$464$	0.741082			0.0344039
$465$	14.3160			0.663889
$466$			8.59012i			0.397930i
$467$	−9.14010			−0.422953			−0.211477	−	0.977383i	$-0.567827\pi$
$467$	−9.14010			−0.422953			−0.211477	+	0.977383i	$0.567827\pi$
$468$	−5.27786			−0.243969
$469$	−0.758043			−0.0350032
$470$	5.74835			0.265152
$471$			29.9097i			1.37817i
$472$			1.84953i			0.0851314i
$473$	0.909716	−	33.9891i	0.0418288	−	1.56282i
$474$		−	11.9746i		−	0.550012i
$475$	5.56065	+	12.4934i	0.255140	+	0.573238i
$476$	−0.858427			−0.0393459
$477$		−	7.67636i		−	0.351476i
$478$			5.42428i			0.248101i
$479$			4.65982i			0.212913i	0.994317	+	0.106456i	$0.0339505\pi$
$479$			4.65982i			0.212913i	−0.994317	+	0.106456i	$0.966050\pi$
$480$			2.74032i			0.125078i
$481$		−	31.4440i		−	1.43372i
$482$	0.436523			0.0198831
$483$	−1.40368			−0.0638698
$484$	10.9843	+	0.588408i	0.499284	+	0.0267458i
$485$		−	4.81669i		−	0.218715i
$486$		−	10.2891i		−	0.466722i
$487$			0.648308i			0.0293776i	0.999892	+	0.0146888i	$0.00467576\pi$
$487$			0.648308i			0.0293776i	−0.999892	+	0.0146888i	$0.995324\pi$
$488$			2.61541i			0.118394i
$489$		−	7.10988i		−	0.321520i
$490$	−9.40332			−0.424799
$491$			22.1546i			0.999825i	0.866076	+	0.499912i	$0.166634\pi$
$491$			22.1546i			0.999825i	−0.866076	+	0.499912i	$0.833366\pi$
$492$			5.00673i			0.225721i
$493$			1.91631i			0.0863061i
$494$	9.07023	+	20.3786i	0.408089	+	0.916877i
$495$	−4.66691	−	0.124910i	−0.209762	−	0.00561427i
$496$			5.22421i			0.234574i
$497$	−4.02966			−0.180755
$498$	26.5477			1.18963
$499$	14.5550			0.651571			0.325786	−	0.945444i	$-0.394371\pi$
$499$	14.5550			0.651571			0.325786	+	0.945444i	$0.394371\pi$
$500$	−11.1059			−0.496671
$501$			20.8564i			0.931797i
$502$	26.0541			1.16285
$503$		−	24.5088i		−	1.09279i	−0.837527	−	0.546396i	$-0.815999\pi$
$503$		−	24.5088i		−	1.09279i	0.837527	−	0.546396i	$-0.184001\pi$
$504$			0.342387i			0.0152511i
$505$			22.5030i			1.00137i
$506$	6.98198	+	0.186873i	0.310387	+	0.00830750i
$507$		−	26.4776i		−	1.17591i
$508$	4.50469			0.199863
$509$		−	25.8471i		−	1.14565i	−0.819677	−	0.572826i	$-0.805847\pi$
$509$		−	25.8471i		−	1.14565i	0.819677	−	0.572826i	$-0.194153\pi$
$510$	−7.08598			−0.313772
$511$	−3.01611			−0.133425
$512$	−1.00000			−0.0441942
$513$	−15.7406	+	7.00591i	−0.694964	+	0.309319i
$514$			14.9965i			0.661467i
$515$		−	12.5652i		−	0.553688i
$516$	−20.5838			−0.906149
$517$	−13.9640	−	0.373745i	−0.614135	−	0.0164373i
$518$	−2.03985			−0.0896257
$519$		−	22.4484i		−	0.985374i
$520$	−6.98425			−0.306280
$521$		−	2.18249i		−	0.0956165i	−0.998857	−	0.0478082i	$-0.984776\pi$
$521$		−	2.18249i		−	0.0956165i	0.998857	−	0.0478082i	$-0.0152236\pi$
$522$	0.764327			0.0334537
$523$	−5.84451			−0.255563			−0.127781	−	0.991802i	$-0.540786\pi$
$523$	−5.84451			−0.255563			−0.127781	+	0.991802i	$0.540786\pi$
$524$			11.2637i			0.492056i
$525$	−2.09114			−0.0912647
$526$			15.3531i			0.669427i
$527$	−13.5089			−0.588455
$528$	0.178170	−	6.65682i	0.00775384	−	0.289701i
$529$	−18.5652			−0.807182
$530$		−	10.1582i		−	0.441245i
$531$			1.90754i			0.0827802i
$532$	1.32201	−	0.588408i	0.0573164	−	0.0255107i
$533$	−12.7606			−0.552725
$534$	−33.1048			−1.43258
$535$	−7.87835			−0.340611
$536$		−	2.28344i		−	0.0986294i
$537$	4.52533			0.195283
$538$			16.1329i			0.695540i
$539$	22.8427	+	0.611383i	0.983904	+	0.0263341i
$540$		−	5.39469i		−	0.232150i
$541$		−	29.6720i		−	1.27570i	−0.770161	−	0.637850i	$-0.779824\pi$
$541$		−	29.6720i		−	1.27570i	0.770161	−	0.637850i	$-0.220176\pi$
$542$		−	19.6795i		−	0.845307i
$543$	−48.8209			−2.09511
$544$		−	2.58582i		−	0.110866i
$545$	15.7352			0.674022
$546$	−3.41095			−0.145975
$547$	−16.9102			−0.723028			−0.361514	−	0.932367i	$-0.617740\pi$
$547$	−16.9102			−0.723028			−0.361514	+	0.932367i	$0.617740\pi$
$548$	−11.5364			−0.492811
$549$			2.69745i			0.115124i
$550$	10.4014	+	0.278393i	0.443518	+	0.0118707i
$551$	−1.31353	−	2.95118i	−0.0559582	−	0.125725i
$552$		−	4.22828i		−	0.179968i
$553$		−	1.97989i		−	0.0841933i
$554$		−	24.1642i		−	1.02664i
$555$	−16.8381			−0.714739
$556$			15.3511i			0.651030i
$557$		−	36.0053i		−	1.52559i	−0.646639	−	0.762797i	$-0.723826\pi$
$557$		−	36.0053i		−	1.52559i	0.646639	−	0.762797i	$-0.276174\pi$
$558$			5.38807i			0.228095i
$559$		−	52.4618i		−	2.21890i
$560$			0.453085i			0.0191463i
$561$	17.2134	+	0.460715i	0.726748	+	0.0194514i
$562$	23.1313			0.975733
$563$	−43.0192			−1.81304			−0.906521	−	0.422161i	$-0.861272\pi$
$563$	−43.0192			−1.81304			−0.906521	+	0.422161i	$0.861272\pi$
$564$			8.45657i			0.356086i
$565$			4.33225i			0.182259i
$566$		−	5.62638i		−	0.236494i
$567$		−	3.66181i		−	0.153781i
$568$		−	12.1385i		−	0.509319i
$569$	43.7422			1.83377			0.916884	−	0.399153i	$-0.130696\pi$
$569$	43.7422			1.83377			0.916884	+	0.399153i	$0.130696\pi$
$570$	10.9127	−	4.85708i	0.457082	−	0.203441i
$571$			31.8799i			1.33413i	0.744998	+	0.667067i	$0.232450\pi$
$571$			31.8799i			1.33413i	−0.744998	+	0.667067i	$0.767550\pi$
$572$	16.9662	+	0.454101i	0.709394	+	0.0189869i
$573$		−	43.0744i		−	1.79946i
$574$			0.827814i			0.0345523i
$575$	6.60678			0.275522
$576$	−1.03137			−0.0429736
$577$	33.8574			1.40950			0.704752	−	0.709454i	$-0.251058\pi$
$577$	33.8574			1.40950			0.704752	+	0.709454i	$0.251058\pi$
$578$	−10.3135			−0.428986
$579$			41.4946i			1.72446i
$580$	1.01144			0.0419979
$581$	4.38941			0.182103
$582$	7.08598			0.293723
$583$	−0.660464	+	24.6765i	−0.0273536	+	1.02199i
$584$		−	9.08536i		−	0.375955i
$585$	−7.20332			−0.297821
$586$	−15.9953			−0.660761
$587$	2.61278			0.107841			0.0539206	−	0.998545i	$-0.482828\pi$
$587$	2.61278			0.107841			0.0539206	+	0.998545i	$0.482828\pi$
$588$		−	13.8335i		−	0.570484i
$589$	20.8042	−	9.25964i	0.857221	−	0.381537i
$590$			2.52427i			0.103923i
$591$	16.1255			0.663313
$592$		−	6.14459i		−	0.252541i
$593$		−	12.1597i		−	0.499338i	−0.968331	−	0.249669i	$-0.919678\pi$
$593$		−	12.1597i		−	0.499338i	0.968331	−	0.249669i	$-0.0803219\pi$
$594$	−0.350751	+	13.1048i	−0.0143915	+	0.537698i
$595$	−1.17160			−0.0480308
$596$			9.05577i			0.370939i
$597$		−	0.529228i		−	0.0216599i
$598$	10.7766			0.440689
$599$			17.5907i			0.718736i	0.933196	+	0.359368i	$0.117008\pi$
$599$			17.5907i			0.718736i	−0.933196	+	0.359368i	$0.882992\pi$
$600$		−	6.29909i		−	0.257159i
$601$	−27.3356			−1.11504			−0.557521	−	0.830163i	$-0.688247\pi$
$601$	−27.3356			−1.11504			−0.557521	+	0.830163i	$0.688247\pi$
$602$	−3.40332			−0.138709
$603$		−	2.35506i		−	0.0959054i
$604$	14.1758			0.576804
$605$	14.9915	+	0.803070i	0.609492	+	0.0326494i
$606$	−33.1048			−1.34479
$607$	−29.0905			−1.18075			−0.590374	−	0.807130i	$-0.701020\pi$
$607$	−29.0905			−1.18075			−0.590374	+	0.807130i	$0.701020\pi$
$608$	1.77245	+	3.98226i	0.0718823	+	0.161502i
$609$	0.493966			0.0200165
$610$			3.56956i			0.144527i
$611$	−21.5532			−0.871951
$612$		−	2.66693i		−	0.107804i
$613$			36.7152i			1.48291i	0.671001	+	0.741456i	$0.265865\pi$
$613$			36.7152i			1.48291i	−0.671001	+	0.741456i	$0.734135\pi$
$614$	17.8829			0.721694
$615$			6.83328i			0.275545i
$616$	0.0294586	−	1.10064i	0.00118692	−	0.0443461i
$617$	37.8396			1.52336			0.761682	−	0.647951i	$-0.224374\pi$
$617$	37.8396			1.52336			0.761682	+	0.647951i	$0.224374\pi$
$618$	18.4850			0.743576
$619$	−38.5731			−1.55038			−0.775192	−	0.631726i	$-0.782347\pi$
$619$	−38.5731			−1.55038			−0.775192	+	0.631726i	$0.782347\pi$
$620$			7.13010i			0.286352i
$621$			8.32394i			0.334028i
$622$	22.9846			0.921599
$623$	−5.47355			−0.219293
$624$		−	10.2747i		−	0.411319i
$625$	0.528789			0.0211516
$626$	20.2507			0.809379
$627$	−26.8250	+	11.0894i	−1.07129	+	0.442866i
$628$	−14.8966			−0.594438
$629$	15.8888			0.633528
$630$			0.467297i			0.0186176i
$631$	7.98573			0.317907			0.158953	−	0.987286i	$-0.449188\pi$
$631$	7.98573			0.317907			0.158953	+	0.987286i	$0.449188\pi$
$632$	5.96397			0.237234
$633$			33.6964i			1.33931i
$634$		−	10.1690i		−	0.403863i
$635$	6.14809			0.243980
$636$	14.9440			0.592570
$637$	35.2574			1.39695
$638$	−2.45701	−	0.0657618i	−0.0972740	−	0.00260353i
$639$		−	12.5192i		−	0.495253i
$640$	−1.36482			−0.0539492
$641$		−	19.1625i		−	0.756872i	−0.925627	−	0.378436i	$-0.876462\pi$
$641$		−	19.1625i		−	0.756872i	0.925627	−	0.378436i	$-0.123538\pi$
$642$		−	11.5901i		−	0.457424i
$643$	32.1803			1.26907			0.634534	−	0.772895i	$-0.281192\pi$
$643$	32.1803			1.26907			0.634534	+	0.772895i	$0.281192\pi$
$644$		−	0.699105i		−	0.0275486i
$645$	−28.0931			−1.10617
$646$	−10.2974	+	4.58323i	−0.405147	+	0.180325i
$647$	22.8329			0.897652			0.448826	−	0.893619i	$-0.351842\pi$
$647$	22.8329			0.897652			0.448826	+	0.893619i	$0.351842\pi$
$648$	11.0304			0.433314
$649$	0.164123	−	6.13199i	0.00644238	−	0.240702i
$650$	16.0545			0.629709
$651$			3.48218i			0.136477i
$652$	3.54108			0.138679
$653$	−1.30505			−0.0510705			−0.0255353	−	0.999674i	$-0.508129\pi$
$653$	−1.30505			−0.0510705			−0.0255353	+	0.999674i	$0.508129\pi$
$654$			23.1485i			0.905179i
$655$			15.3729i			0.600668i
$656$	−2.49361			−0.0973590
$657$		−	9.37034i		−	0.365572i
$658$			1.39821i			0.0545079i
$659$	−42.5739			−1.65844			−0.829222	−	0.558920i	$-0.811216\pi$
$659$	−42.5739			−1.65844			−0.829222	+	0.558920i	$0.811216\pi$
$660$	0.243169	−	9.08536i	0.00946535	−	0.353647i
$661$		−	22.3990i		−	0.871220i	−0.900135	−	0.435610i	$-0.856533\pi$
$661$		−	22.3990i		−	0.871220i	0.900135	−	0.435610i	$-0.143467\pi$
$662$		−	19.2264i		−	0.747256i
$663$	26.5686			1.03184
$664$			13.2221i			0.513118i
$665$	1.80430	−	0.803070i	0.0699679	−	0.0311417i
$666$		−	6.33732i		−	0.245566i
$667$	−1.56065			−0.0604284
$668$	−10.3876			−0.401907
$669$	−7.85165			−0.303562
$670$		−	3.11648i		−	0.120400i
$671$	0.232085	−	8.67123i	0.00895955	−	0.334749i
$672$	−0.666547			−0.0257126
$673$	11.3449			0.437314			0.218657	−	0.975802i	$-0.429832\pi$
$673$	11.3449			0.437314			0.218657	+	0.975802i	$0.429832\pi$
$674$	−1.38474			−0.0533383
$675$			12.4006i			0.477299i
$676$	13.1872			0.507201
$677$	−6.72412			−0.258429			−0.129214	−	0.991617i	$-0.541246\pi$
$677$	−6.72412			−0.258429			−0.129214	+	0.991617i	$0.541246\pi$
$678$	−6.37330			−0.244765
$679$	1.17160			0.0449618
$680$		−	3.52918i		−	0.135338i
$681$		−	37.3036i		−	1.42948i
$682$	0.463583	−	17.3205i	0.0177515	−	0.663238i
$683$		−	40.1776i		−	1.53735i	−0.639638	−	0.768676i	$-0.720916\pi$
$683$		−	40.1776i		−	1.53735i	0.639638	−	0.768676i	$-0.279084\pi$
$684$	1.82804	+	4.10717i	0.0698970	+	0.157042i
$685$	−15.7451			−0.601590
$686$		−	4.61106i		−	0.176051i
$687$			6.47172i			0.246911i
$688$		−	10.2518i		−	0.390845i
$689$			38.0879i			1.45103i
$690$		−	5.77084i		−	0.219692i
$691$	15.6846			0.596672			0.298336	−	0.954461i	$-0.403568\pi$
$691$	15.6846			0.596672			0.298336	+	0.954461i	$0.403568\pi$
$692$	11.1804			0.425016
$693$	0.0303826	−	1.13516i	0.00115414	−	0.0431213i
$694$		−	21.7263i		−	0.824719i
$695$			20.9514i			0.794733i
$696$			1.48796i			0.0564011i
$697$		−	6.44802i		−	0.244236i
$698$			8.38626i			0.317424i
$699$	−17.2475			−0.652359
$700$		−	1.04149i		−	0.0393647i
$701$			14.3270i			0.541122i	0.962703	+	0.270561i	$0.0872093\pi$
$701$			14.3270i			0.541122i	−0.962703	+	0.270561i	$0.912791\pi$
$702$			20.2272i			0.763426i
$703$	−24.4694	+	10.8910i	−0.922880	+	0.410761i
$704$	3.31544	+	0.0887375i	0.124955	+	0.00334442i
$705$			11.5417i			0.434685i
$706$	13.1101			0.493404
$707$	−5.47355			−0.205854
$708$	−3.71353			−0.139563
$709$	2.48315			0.0932566			0.0466283	−	0.998912i	$-0.485152\pi$
$709$	2.48315			0.0932566			0.0466283	+	0.998912i	$0.485152\pi$
$710$		−	16.5668i		−	0.621742i
$711$	6.15104			0.230682
$712$		−	16.4879i		−	0.617909i
$713$		−	11.0017i		−	0.412016i
$714$		−	1.72357i		−	0.0645030i
$715$	23.1558	+	0.619765i	0.865980	+	0.0231779i
$716$			2.25385i			0.0842302i
$717$	−10.8910			−0.406732
$718$			29.8474i			1.11389i
$719$	−17.3932			−0.648658			−0.324329	−	0.945944i	$-0.605138\pi$
$719$	−17.3932			−0.648658			−0.324329	+	0.945944i	$0.605138\pi$
$720$	−1.40763			−0.0524592
$721$	3.05631			0.113823
$722$	12.7169	−	14.1167i	0.473272	−	0.525370i
$723$			0.876461i			0.0325960i
$724$		−	24.3153i		−	0.903671i
$725$	−2.32497			−0.0863473
$726$	−1.18142	+	22.0545i	−0.0438466	+	0.818518i
$727$	48.5116			1.79919			0.899597	−	0.436721i	$-0.143860\pi$
$727$	48.5116			1.79919			0.899597	+	0.436721i	$0.143860\pi$
$728$		−	1.69883i		−	0.0629627i
$729$	−12.4325			−0.460462
$730$		−	12.3999i		−	0.458940i
$731$	26.5092			0.980479
$732$	−5.25129			−0.194093
$733$		−	29.7137i		−	1.09750i	−0.835987	−	0.548750i	$-0.815104\pi$
$733$		−	29.7137i		−	1.09750i	0.835987	−	0.548750i	$-0.184896\pi$
$734$	−3.49912			−0.129155
$735$		−	18.8802i		−	0.696408i
$736$	2.10590			0.0776246
$737$	−0.202627	+	7.57059i	−0.00746384	+	0.278866i
$738$	−2.57182			−0.0946701
$739$			12.1001i			0.445110i	0.974920	+	0.222555i	$0.0714397\pi$
$739$			12.1001i			0.445110i	−0.974920	+	0.222555i	$0.928560\pi$
$740$		−	8.38626i		−	0.308285i
$741$	−40.9167	+	18.2114i	−1.50311	+	0.669014i
$742$	2.47085			0.0907078
$743$	29.3218			1.07571			0.537856	−	0.843037i	$-0.319234\pi$
$743$	29.3218			1.07571			0.537856	+	0.843037i	$0.319234\pi$
$744$	−10.4893			−0.384556
$745$			12.3595i			0.452817i
$746$	−14.2004			−0.519912
$747$			13.6369i			0.498946i
$748$	−0.229459	+	8.57313i	−0.00838987	+	0.313465i
$749$		−	1.91631i		−	0.0700203i
$750$		−	22.2987i		−	0.814234i
$751$			30.5782i			1.11581i	0.829903	+	0.557907i	$0.188395\pi$
$751$			30.5782i			1.11581i	−0.829903	+	0.557907i	$0.811605\pi$
$752$	−4.21180			−0.153589
$753$			52.3122i			1.90636i
$754$	−3.79237			−0.138110
$755$	19.3474			0.704123
$756$	1.31219			0.0477238
$757$	39.5549			1.43765			0.718823	−	0.695193i	$-0.244681\pi$
$757$	39.5549			1.43765			0.718823	+	0.695193i	$0.244681\pi$
$758$			19.7199i			0.716259i
$759$	−0.375208	+	14.0186i	−0.0136192	+	0.508843i
$760$	2.41907	+	5.43507i	0.0877490	+	0.197151i
$761$			33.3088i			1.20744i	0.797196	+	0.603721i	$0.206316\pi$
$761$			33.3088i			1.20744i	−0.797196	+	0.603721i	$0.793684\pi$
$762$			9.04464i			0.327653i
$763$			3.82738i			0.138561i
$764$	21.4533			0.776152
$765$		−	3.63988i		−	0.131600i
$766$		−	28.8108i		−	1.04098i
$767$		−	9.46467i		−	0.341750i
$768$		−	2.00783i		−	0.0724512i
$769$		−	52.5268i		−	1.89417i	−0.320990	−	0.947083i	$-0.604016\pi$
$769$		−	52.5268i		−	1.89417i	0.320990	−	0.947083i	$-0.395984\pi$
$770$	0.0402057	−	1.50218i	0.00144891	−	0.0541347i
$771$	−30.1104			−1.08440
$772$	−20.6664			−0.743801
$773$		−	13.6467i		−	0.490836i	−0.969417	−	0.245418i	$-0.921075\pi$
$773$		−	13.6467i		−	0.490836i	0.969417	−	0.245418i	$-0.0789253\pi$
$774$		−	10.5733i		−	0.380050i
$775$		−	16.3897i		−	0.588737i
$776$			3.52918i			0.126690i
$777$		−	4.09566i		−	0.146931i
$778$	−9.71255			−0.348212
$779$	4.41979	+	9.93020i	0.158355	+	0.355786i
$780$		−	14.0232i		−	0.502110i
$781$	−1.07714	+	40.2444i	−0.0385431	+	1.44006i
$782$			5.44548i			0.194730i
$783$		−	2.92926i		−	0.104683i
$784$	6.88979			0.246064
$785$	−20.3311			−0.725649
$786$	−22.6155			−0.806668
$787$	−20.9801			−0.747859			−0.373929	−	0.927457i	$-0.621990\pi$
$787$	−20.9801			−0.747859			−0.373929	+	0.927457i	$0.621990\pi$
$788$			8.03131i			0.286103i
$789$	−30.8263			−1.09745
$790$	8.13974			0.289599
$791$	−1.05376			−0.0374675
$792$	3.41943	+	0.0915209i	0.121504	+	0.00325205i
$793$		−	13.3840i		−	0.475278i
$794$	−21.8815			−0.776547
$795$	20.3959			0.723369
$796$	0.263583			0.00934244
$797$		−	17.5648i		−	0.622177i	−0.950381	−	0.311088i	$-0.899307\pi$
$797$		−	17.5648i		−	0.622177i	0.950381	−	0.311088i	$-0.100693\pi$
$798$	1.18142	+	2.65437i	0.0418218	+	0.0939635i
$799$		−	10.8910i		−	0.385295i
$800$	3.13727			0.110919
$801$		−	17.0050i		−	0.600844i
$802$		−	20.9308i		−	0.739093i
$803$	−0.806213	+	30.1219i	−0.0284506	+	1.06298i
$804$	4.58474			0.161691
$805$		−	0.954153i		−	0.0336295i
$806$		−	26.7341i		−	0.941667i
$807$	−32.3921			−1.14026
$808$		−	16.4879i		−	0.580041i
$809$		−	6.97725i		−	0.245307i	−0.992450	−	0.122654i	$-0.960860\pi$
$809$		−	6.97725i		−	0.245307i	0.992450	−	0.122654i	$-0.0391404\pi$
$810$	15.0545			0.528961
$811$	56.5078			1.98426			0.992128	−	0.125230i	$-0.0399668\pi$
$811$	56.5078			1.98426			0.992128	+	0.125230i	$0.0399668\pi$
$812$			0.246020i			0.00863362i
$813$	39.5130			1.38578
$814$	−0.545256	+	20.3720i	−0.0191112	+	0.714038i
$815$	4.83294			0.169290
$816$	5.19188			0.181752
$817$	−40.8252	+	18.1707i	−1.42829	+	0.635713i
$818$	−25.6935			−0.898351
$819$		−	1.75211i		−	0.0612238i
$820$	−3.40332			−0.118849
$821$		−	20.3380i		−	0.709802i	−0.934904	−	0.354901i	$-0.884515\pi$
$821$		−	20.3380i		−	0.709802i	0.934904	−	0.354901i	$-0.115485\pi$
$822$		−	23.1631i		−	0.807907i
$823$	−22.7728			−0.793810			−0.396905	−	0.917860i	$-0.629916\pi$
$823$	−22.7728			−0.793810			−0.396905	+	0.917860i	$0.629916\pi$
$824$			9.20647i			0.320723i
$825$	−0.558966	+	20.8842i	−0.0194607	+	0.727096i
$826$	−0.613996			−0.0213637
$827$	−9.52915			−0.331361			−0.165680	−	0.986179i	$-0.552982\pi$
$827$	−9.52915			−0.331361			−0.165680	+	0.986179i	$0.552982\pi$
$828$	2.17196			0.0754807
$829$		−	6.05582i		−	0.210327i	−0.994455	−	0.105164i	$-0.966463\pi$
$829$		−	6.05582i		−	0.210327i	0.994455	−	0.105164i	$-0.0335366\pi$
$830$			18.0458i			0.626379i
$831$	48.5176			1.68306
$832$	5.11734			0.177412
$833$			17.8158i			0.617280i
$834$	−30.8223			−1.06729
$835$	−14.1772			−0.490621
$836$	−5.52307	−	13.3602i	−0.191019	−	0.462073i
$837$	20.6496			0.713754
$838$	−10.6766			−0.368819
$839$		−	22.5026i		−	0.776876i	−0.921475	−	0.388438i	$-0.873015\pi$
$839$		−	22.5026i		−	0.776876i	0.921475	−	0.388438i	$-0.126985\pi$
$840$	−0.909716			−0.0313882
$841$	−28.4508			−0.981062
$842$		−	11.2866i		−	0.388963i
$843$			46.4436i			1.59960i
$844$	−16.7825			−0.577679
$845$	17.9982			0.619156
$846$	−4.34391			−0.149347
$847$	−0.195336	+	3.64649i	−0.00671183	+	0.125295i
$848$			7.44290i			0.255590i
$849$	11.2968			0.387705
$850$			8.11241i			0.278253i
$851$			12.9399i			0.443574i
$852$	24.3720			0.834969
$853$		−	54.2908i		−	1.85888i	−0.368973	−	0.929440i	$-0.620290\pi$
$853$		−	54.2908i		−	1.85888i	0.368973	−	0.929440i	$-0.379710\pi$
$854$	−0.868250			−0.0297109
$855$	2.49495	+	5.60555i	0.0853255	+	0.191706i
$856$	5.77245			0.197298
$857$	25.5807			0.873821			0.436910	−	0.899505i	$-0.356073\pi$
$857$	25.5807			0.873821			0.436910	+	0.899505i	$0.356073\pi$
$858$	−0.911755	+	34.0653i	−0.0311268	+	1.16297i
$859$	−34.2659			−1.16914			−0.584569	−	0.811344i	$-0.698736\pi$
$859$	−34.2659			−1.16914			−0.584569	+	0.811344i	$0.698736\pi$
$860$		−	13.9918i		−	0.477117i
$861$	−1.66211			−0.0566444
$862$	−33.5141			−1.14150
$863$		−	8.18134i		−	0.278496i	−0.990258	−	0.139248i	$-0.955531\pi$
$863$		−	8.18134i		−	0.278496i	0.990258	−	0.139248i	$-0.0444685\pi$
$864$			3.95267i			0.134473i
$865$	15.2593			0.518831
$866$		−	1.36828i		−	0.0464961i
$867$		−	20.7078i		−	0.703273i
$868$	−1.73430			−0.0588661
$869$	−19.7732	−	0.529228i	−0.670759	−	0.0179528i
$870$			2.03080i			0.0688506i
$871$			11.6851i			0.395936i
$872$	−11.5291			−0.390426
$873$			3.63988i			0.123191i
$874$	−3.73260	−	8.38626i	−0.126257	−	0.283669i
$875$		−	3.68688i		−	0.124639i
$876$	18.2418			0.616334
$877$	23.5342			0.794693			0.397346	−	0.917669i	$-0.369931\pi$
$877$	23.5342			0.794693			0.397346	+	0.917669i	$0.369931\pi$
$878$	37.1544			1.25390
$879$		−	32.1159i		−	1.08324i
$880$	4.52497	+	0.121111i	0.152537	+	0.00408264i
$881$	24.2600			0.817342			0.408671	−	0.912682i	$-0.365992\pi$
$881$	24.2600			0.817342			0.408671	+	0.912682i	$0.365992\pi$
$882$	7.10590			0.239268
$883$	−41.9782			−1.41268			−0.706340	−	0.707873i	$-0.749655\pi$
$883$	−41.9782			−1.41268			−0.706340	+	0.707873i	$0.749655\pi$
$884$			13.2325i			0.445058i
$885$	−5.06830			−0.170369
$886$	6.38376			0.214467
$887$	−37.6410			−1.26386			−0.631930	−	0.775025i	$-0.717737\pi$
$887$	−37.6410			−1.26386			−0.631930	+	0.775025i	$0.717737\pi$
$888$	12.3373			0.414012
$889$			1.49544i			0.0501555i
$890$		−	22.5030i		−	0.754301i
$891$	−36.5705	−	0.978809i	−1.22516	−	0.0327913i
$892$		−	3.91052i		−	0.130934i
$893$	7.46520	+	16.7725i	0.249814	+	0.561271i
$894$	−18.1824			−0.608111
$895$			3.07609i			0.102822i
$896$		−	0.331974i		−	0.0110905i
$897$			21.6376i			0.722458i
$898$			14.6943i			0.490356i
$899$			3.87157i			0.129124i
$900$	3.23567			0.107856
$901$	−19.2460			−0.641177
$902$	8.26740	+	0.221277i	0.275274	+	0.00736770i
$903$		−	6.83328i		−	0.227397i
$904$		−	3.17423i		−	0.105573i
$905$		−	33.1860i		−	1.10314i
$906$			28.4625i			0.945603i
$907$			57.5321i			1.91032i	0.296086	+	0.955161i	$0.404318\pi$
$907$			57.5321i			1.91032i	−0.296086	+	0.955161i	$0.595682\pi$
$908$	18.5791			0.616569
$909$		−	17.0050i		−	0.564022i
$910$		−	2.31859i		−	0.0768606i
$911$		−	27.6266i		−	0.915311i	−0.889130	−	0.457656i	$-0.848689\pi$
$911$		−	27.6266i		−	0.915311i	0.889130	−	0.457656i	$-0.151311\pi$
$912$	−7.99569	+	3.55877i	−0.264764	+	0.117843i
$913$	1.17330	−	43.8371i	0.0388305	−	1.45080i
$914$		−	22.5097i		−	0.744555i
$915$	−7.16706			−0.236936
$916$	−3.22325			−0.106499
$917$	−3.73925			−0.123481
$918$	−10.2209			−0.337340
$919$			1.18723i			0.0391630i	0.999808	+	0.0195815i	$0.00623339\pi$
$919$			1.18723i			0.0391630i	−0.999808	+	0.0195815i	$0.993767\pi$
$920$	2.87418			0.0947588
$921$			35.9057i			1.18313i
$922$			18.1532i			0.597844i
$923$			62.1168i			2.04460i
$924$	2.20989	+	0.0591477i	0.0727002	+	0.00194582i
$925$			19.2772i			0.633831i
$926$	−2.87799			−0.0945767
$927$			9.49525i			0.311865i
$928$	−0.741082			−0.0243272
$929$	−21.6626			−0.710727			−0.355363	−	0.934728i	$-0.615643\pi$
$929$	−21.6626			−0.710727			−0.355363	+	0.934728i	$0.615643\pi$
$930$	−14.3160			−0.469440
$931$	−12.2118	−	27.4370i	−0.400226	−	0.899211i
$932$		−	8.59012i		−	0.281379i
$933$			46.1491i			1.51085i
$934$	9.14010			0.299073
$935$	−0.313171	+	11.7008i	−0.0102418	+	0.382656i
$936$	5.27786			0.172512
$937$			4.19836i			0.137154i	0.997646	+	0.0685772i	$0.0218459\pi$
$937$			4.19836i			0.137154i	−0.997646	+	0.0685772i	$0.978154\pi$
$938$	0.758043			0.0247510
$939$			40.6598i			1.32688i
$940$	−5.74835			−0.187491
$941$	−51.3865			−1.67515			−0.837575	−	0.546322i	$-0.816028\pi$
$941$	−51.3865			−1.67515			−0.837575	+	0.546322i	$0.816028\pi$
$942$		−	29.9097i		−	0.974512i
$943$	5.25129			0.171006
$944$		−	1.84953i		−	0.0601970i
$945$	1.79090			0.0582579
$946$	−0.909716	+	33.9891i	−0.0295774	+	1.10508i
$947$	24.3658			0.791783			0.395891	−	0.918297i	$-0.370436\pi$
$947$	24.3658			0.791783			0.395891	+	0.918297i	$0.370436\pi$
$948$			11.9746i			0.388917i
$949$			46.4929i			1.50922i
$950$	−5.56065	−	12.4934i	−0.180411	−	0.405340i
$951$	20.4176			0.662086
$952$	0.858427			0.0278218
$953$	−26.6316			−0.862682			−0.431341	−	0.902189i	$-0.641959\pi$
$953$	−26.6316			−0.862682			−0.431341	+	0.902189i	$0.641959\pi$
$954$			7.67636i			0.248531i
$955$	29.2798			0.947473
$956$		−	5.42428i		−	0.175434i
$957$	0.132038	−	4.93325i	0.00426819	−	0.159469i
$958$		−	4.65982i		−	0.150552i
$959$		−	3.82980i		−	0.123671i
$960$		−	2.74032i		−	0.0884435i
$961$	3.70765			0.119602
$962$			31.4440i			1.01379i
$963$	5.95351			0.191849
$964$	−0.436523			−0.0140594
$965$	−28.2059			−0.907981
$966$	1.40368			0.0451627
$967$			42.6864i			1.37270i	0.727271	+	0.686350i	$0.240788\pi$
$967$			42.6864i			1.37270i	−0.727271	+	0.686350i	$0.759212\pi$
$968$	−10.9843	−	0.588408i	−0.353047	−	0.0189121i
$969$	−9.20234	−	20.6754i	−0.295622	−	0.664191i
$970$			4.81669i			0.154655i
$971$		−	35.1642i		−	1.12847i	−0.825613	−	0.564237i	$-0.809170\pi$
$971$		−	35.1642i		−	1.12847i	0.825613	−	0.564237i	$-0.190830\pi$
$972$			10.2891i			0.330022i
$973$	−5.09616			−0.163375
$974$		−	0.648308i		−	0.0207731i
$975$			32.2346i			1.03233i
$976$		−	2.61541i		−	0.0837173i
$977$			11.7415i			0.375644i	0.982203	+	0.187822i	$0.0601428\pi$
$977$			11.7415i			0.375644i	−0.982203	+	0.187822i	$0.939857\pi$
$978$			7.10988i			0.227349i
$979$	−1.46309	+	54.6645i	−0.0467607	+	1.74709i
$980$	9.40332			0.300378
$981$	−11.8908			−0.379643
$982$		−	22.1546i		−	0.706983i
$983$			28.3815i			0.905229i	0.891706	+	0.452615i	$0.149509\pi$
$983$			28.3815i			0.905229i	−0.891706	+	0.452615i	$0.850491\pi$
$984$		−	5.00673i		−	0.159609i
$985$			10.9613i			0.349255i
$986$		−	1.91631i		−	0.0610276i
$987$	−2.80736			−0.0893594
$988$	−9.07023	−	20.3786i	−0.288562	−	0.648330i
$989$			21.5892i			0.686497i
$990$	4.66691	+	0.124910i	0.148324	+	0.00396989i
$991$			45.0141i			1.42992i	0.699166	+	0.714959i	$0.253555\pi$
$991$			45.0141i			1.42992i	−0.699166	+	0.714959i	$0.746445\pi$
$992$		−	5.22421i		−	0.165869i
$993$	38.6033			1.22504
$994$	4.02966			0.127813
$995$	0.359743			0.0114046
$996$	−26.5477			−0.841197
$997$			29.4506i			0.932711i	0.884597	+	0.466355i	$0.154433\pi$
$997$			29.4506i			0.932711i	−0.884597	+	0.466355i	$0.845567\pi$
$998$	−14.5550			−0.460730
$999$	−24.2876			−0.768424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.b.c.417.2	✓	8
3.2	odd	2		3762.2.g.h.2089.4		8
11.10	odd	2		418.2.b.d.417.2	yes	8
19.18	odd	2		418.2.b.d.417.7	yes	8
33.32	even	2		3762.2.g.g.2089.3		8
57.56	even	2		3762.2.g.g.2089.4		8
209.208	even	2	inner	418.2.b.c.417.7	yes	8
627.626	odd	2		3762.2.g.h.2089.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.b.c.417.2	✓	8	1.1	even	1	trivial
418.2.b.c.417.7	yes	8	209.208	even	2	inner
418.2.b.d.417.2	yes	8	11.10	odd	2
418.2.b.d.417.7	yes	8	19.18	odd	2
3762.2.g.g.2089.3		8	33.32	even	2
3762.2.g.g.2089.4		8	57.56	even	2
3762.2.g.h.2089.3		8	627.626	odd	2
3762.2.g.h.2089.4		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.00783i q^{3} +1.00000 q^{4} +1.36482 q^{5} +2.00783i q^{6} +0.331974i q^{7} -1.00000 q^{8} -1.03137 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.00783i q^{3} +1.00000 q^{4} +1.36482 q^{5} +2.00783i q^{6} +0.331974i q^{7} -1.00000 q^{8} -1.03137 q^{9} -1.36482 q^{10} +(3.31544 + 0.0887375i) q^{11} -2.00783i q^{12} +5.11734 q^{13} -0.331974i q^{14} -2.74032i q^{15} +1.00000 q^{16} +2.58582i q^{17} +1.03137 q^{18} +(-1.77245 - 3.98226i) q^{19} +1.36482 q^{20} +0.666547 q^{21} +(-3.31544 - 0.0887375i) q^{22} -2.10590 q^{23} +2.00783i q^{24} -3.13727 q^{25} -5.11734 q^{26} -3.95267i q^{27} +0.331974i q^{28} +0.741082 q^{29} +2.74032i q^{30} +5.22421i q^{31} -1.00000 q^{32} +(0.178170 - 6.65682i) q^{33} -2.58582i q^{34} +0.453085i q^{35} -1.03137 q^{36} -6.14459i q^{37} +(1.77245 + 3.98226i) q^{38} -10.2747i q^{39} -1.36482 q^{40} -2.49361 q^{41} -0.666547 q^{42} -10.2518i q^{43} +(3.31544 + 0.0887375i) q^{44} -1.40763 q^{45} +2.10590 q^{46} -4.21180 q^{47} -2.00783i q^{48} +6.88979 q^{49} +3.13727 q^{50} +5.19188 q^{51} +5.11734 q^{52} +7.44290i q^{53} +3.95267i q^{54} +(4.52497 + 0.121111i) q^{55} -0.331974i q^{56} +(-7.99569 + 3.55877i) q^{57} -0.741082 q^{58} -1.84953i q^{59} -2.74032i q^{60} -2.61541i q^{61} -5.22421i q^{62} -0.342387i q^{63} +1.00000 q^{64} +6.98425 q^{65} +(-0.178170 + 6.65682i) q^{66} +2.28344i q^{67} +2.58582i q^{68} +4.22828i q^{69} -0.453085i q^{70} +12.1385i q^{71} +1.03137 q^{72} +9.08536i q^{73} +6.14459i q^{74} +6.29909i q^{75} +(-1.77245 - 3.98226i) q^{76} +(-0.0294586 + 1.10064i) q^{77} +10.2747i q^{78} -5.96397 q^{79} +1.36482 q^{80} -11.0304 q^{81} +2.49361 q^{82} -13.2221i q^{83} +0.666547 q^{84} +3.52918i q^{85} +10.2518i q^{86} -1.48796i q^{87} +(-3.31544 - 0.0887375i) q^{88} +16.4879i q^{89} +1.40763 q^{90} +1.69883i q^{91} -2.10590 q^{92} +10.4893 q^{93} +4.21180 q^{94} +(-2.41907 - 5.43507i) q^{95} +2.00783i q^{96} -3.52918i q^{97} -6.88979 q^{98} +(-3.41943 - 0.0915209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

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