LMFDB - Embedded newform 1045.2.b.d.419.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.7
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.60597i q^{2} -0.776012i q^{3} -0.579148 q^{4} +(-1.81070 - 1.31201i) q^{5} -1.24625 q^{6} +0.953282i q^{7} -2.28185i q^{8} +2.39780 q^{9} +O(q^{10})$	\(q-1.60597i q^{2} -0.776012i q^{3} -0.579148 q^{4} +(-1.81070 - 1.31201i) q^{5} -1.24625 q^{6} +0.953282i q^{7} -2.28185i q^{8} +2.39780 q^{9} +(-2.10704 + 2.90794i) q^{10} -1.00000 q^{11} +0.449426i q^{12} -4.91628i q^{13} +1.53094 q^{14} +(-1.01813 + 1.40513i) q^{15} -4.82288 q^{16} -1.30378i q^{17} -3.85081i q^{18} +1.00000 q^{19} +(1.04866 + 0.759845i) q^{20} +0.739759 q^{21} +1.60597i q^{22} -1.40028i q^{23} -1.77074 q^{24} +(1.55728 + 4.75130i) q^{25} -7.89541 q^{26} -4.18876i q^{27} -0.552091i q^{28} -10.3935 q^{29} +(2.25660 + 1.63509i) q^{30} -0.261368 q^{31} +3.18172i q^{32} +0.776012i q^{33} -2.09384 q^{34} +(1.25071 - 1.72611i) q^{35} -1.38868 q^{36} +2.27980i q^{37} -1.60597i q^{38} -3.81509 q^{39} +(-2.99380 + 4.13175i) q^{40} -3.22255 q^{41} -1.18803i q^{42} +1.39520i q^{43} +0.579148 q^{44} +(-4.34171 - 3.14593i) q^{45} -2.24882 q^{46} -1.24624i q^{47} +3.74262i q^{48} +6.09125 q^{49} +(7.63046 - 2.50096i) q^{50} -1.01175 q^{51} +2.84725i q^{52} +9.04663i q^{53} -6.72704 q^{54} +(1.81070 + 1.31201i) q^{55} +2.17525 q^{56} -0.776012i q^{57} +16.6917i q^{58} -10.7584 q^{59} +(0.589649 - 0.813776i) q^{60} +13.6260 q^{61} +0.419750i q^{62} +2.28578i q^{63} -4.53601 q^{64} +(-6.45018 + 8.90192i) q^{65} +1.24625 q^{66} -3.94074i q^{67} +0.755082i q^{68} -1.08664 q^{69} +(-2.77208 - 2.00861i) q^{70} -5.54955 q^{71} -5.47143i q^{72} -2.78271i q^{73} +3.66130 q^{74} +(3.68707 - 1.20847i) q^{75} -0.579148 q^{76} -0.953282i q^{77} +6.12693i q^{78} -7.73676 q^{79} +(8.73280 + 6.32765i) q^{80} +3.94288 q^{81} +5.17532i q^{82} -9.84690i q^{83} -0.428430 q^{84} +(-1.71057 + 2.36076i) q^{85} +2.24066 q^{86} +8.06548i q^{87} +2.28185i q^{88} +8.73496 q^{89} +(-5.05228 + 6.97267i) q^{90} +4.68660 q^{91} +0.810972i q^{92} +0.202825i q^{93} -2.00143 q^{94} +(-1.81070 - 1.31201i) q^{95} +2.46905 q^{96} +0.370936i q^{97} -9.78239i q^{98} -2.39780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.60597i		−	1.13559i	−0.823169	−	0.567797i	$-0.807796\pi$
$2$		−	1.60597i		−	1.13559i	0.823169	−	0.567797i	$-0.192204\pi$
$3$		−	0.776012i		−	0.448031i	−0.974586	−	0.224015i	$-0.928083\pi$
$3$		−	0.776012i		−	0.448031i	0.974586	−	0.224015i	$-0.0719166\pi$
$4$	−0.579148			−0.289574
$5$	−1.81070	−	1.31201i	−0.809771	−	0.586747i
$5$	−1.81070	−	1.31201i	−0.809771	−	0.586747i
$6$	−1.24625			−0.508781
$7$			0.953282i			0.360307i	0.983639	+	0.180153i	$0.0576594\pi$
$7$			0.953282i			0.360307i	−0.983639	+	0.180153i	$0.942341\pi$
$8$		−	2.28185i		−	0.806756i
$9$	2.39780			0.799268
$10$	−2.10704	+	2.90794i	−0.666306	+	0.919571i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			0.449426i			0.129738i
$13$		−	4.91628i		−	1.36353i	−0.731571	−	0.681765i	$-0.761213\pi$
$13$		−	4.91628i		−	1.36353i	0.731571	−	0.681765i	$-0.238787\pi$
$14$	1.53094			0.409162
$15$	−1.01813	+	1.40513i	−0.262881	+	0.362802i
$16$	−4.82288			−1.20572
$17$		−	1.30378i		−	0.316213i	−0.987422	−	0.158107i	$-0.949461\pi$
$17$		−	1.30378i		−	0.316213i	0.987422	−	0.158107i	$-0.0505390\pi$
$18$		−	3.85081i		−	0.907644i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.04866	+	0.759845i	0.234488	+	0.169906i
$21$	0.739759			0.161429
$22$			1.60597i			0.342394i
$23$		−	1.40028i		−	0.291980i	−0.989286	−	0.145990i	$-0.953363\pi$
$23$		−	1.40028i		−	0.291980i	0.989286	−	0.145990i	$-0.0466367\pi$
$24$	−1.77074			−0.361452
$25$	1.55728	+	4.75130i	0.311457	+	0.950260i
$26$	−7.89541			−1.54842
$27$		−	4.18876i		−	0.806128i
$28$		−	0.552091i		−	0.104335i
$29$	−10.3935			−1.93002			−0.965011	−	0.262208i	$-0.915549\pi$
$29$	−10.3935			−1.93002			−0.965011	+	0.262208i	$0.915549\pi$
$30$	2.25660	+	1.63509i	0.411996	+	0.298526i
$31$	−0.261368			−0.0469431			−0.0234716	−	0.999725i	$-0.507472\pi$
$31$	−0.261368			−0.0469431			−0.0234716	+	0.999725i	$0.507472\pi$
$32$			3.18172i			0.562454i
$33$			0.776012i			0.135086i
$34$	−2.09384			−0.359090
$35$	1.25071	−	1.72611i	0.211409	−	0.291766i
$36$	−1.38868			−0.231447
$37$			2.27980i			0.374797i	0.982284	+	0.187399i	$0.0600056\pi$
$37$			2.27980i			0.374797i	−0.982284	+	0.187399i	$0.939994\pi$
$38$		−	1.60597i		−	0.260523i
$39$	−3.81509			−0.610904
$40$	−2.99380	+	4.13175i	−0.473361	+	0.653287i
$41$	−3.22255			−0.503278			−0.251639	−	0.967821i	$-0.580969\pi$
$41$	−3.22255			−0.503278			−0.251639	+	0.967821i	$0.580969\pi$
$42$		−	1.18803i		−	0.183317i
$43$			1.39520i			0.212766i	0.994325	+	0.106383i	$0.0339270\pi$
$43$			1.39520i			0.212766i	−0.994325	+	0.106383i	$0.966073\pi$
$44$	0.579148			0.0873098
$45$	−4.34171	−	3.14593i	−0.647224	−	0.468968i
$46$	−2.24882			−0.331570
$47$		−	1.24624i		−	0.181783i	−0.995861	−	0.0908915i	$-0.971028\pi$
$47$		−	1.24624i		−	0.181783i	0.995861	−	0.0908915i	$-0.0289716\pi$
$48$			3.74262i			0.540200i
$49$	6.09125			0.870179
$50$	7.63046	−	2.50096i	1.07911	−	0.353689i
$51$	−1.01175			−0.141673
$52$			2.84725i			0.394843i
$53$			9.04663i			1.24265i	0.783553	+	0.621325i	$0.213405\pi$
$53$			9.04663i			1.24265i	−0.783553	+	0.621325i	$0.786595\pi$
$54$	−6.72704			−0.915434
$55$	1.81070	+	1.31201i	0.244155	+	0.176911i
$56$	2.17525			0.290680
$57$		−	0.776012i		−	0.102785i
$58$			16.6917i			2.19172i
$59$	−10.7584			−1.40062			−0.700310	−	0.713839i	$-0.746955\pi$
$59$	−10.7584			−1.40062			−0.700310	+	0.713839i	$0.746955\pi$
$60$	0.589649	−	0.813776i	0.0761234	−	0.105058i
$61$	13.6260			1.74463			0.872316	−	0.488942i	$-0.162617\pi$
$61$	13.6260			1.74463			0.872316	+	0.488942i	$0.162617\pi$
$62$			0.419750i			0.0533083i
$63$			2.28578i			0.287982i
$64$	−4.53601			−0.567002
$65$	−6.45018	+	8.90192i	−0.800047	+	1.10415i
$66$	1.24625			0.153403
$67$		−	3.94074i		−	0.481437i	−0.970595	−	0.240719i	$-0.922617\pi$
$67$		−	3.94074i		−	0.481437i	0.970595	−	0.240719i	$-0.0773831\pi$
$68$			0.755082i			0.0915671i
$69$	−1.08664			−0.130816
$70$	−2.77208	−	2.00861i	−0.331328	−	0.240075i
$71$	−5.54955			−0.658610			−0.329305	−	0.944224i	$-0.606814\pi$
$71$	−5.54955			−0.658610			−0.329305	+	0.944224i	$0.606814\pi$
$72$		−	5.47143i		−	0.644814i
$73$		−	2.78271i		−	0.325692i	−0.986652	−	0.162846i	$-0.947933\pi$
$73$		−	2.78271i		−	0.325692i	0.986652	−	0.162846i	$-0.0520673\pi$
$74$	3.66130			0.425617
$75$	3.68707	−	1.20847i	0.425746	−	0.139542i
$76$	−0.579148			−0.0664328
$77$		−	0.953282i		−	0.108637i
$78$			6.12693i			0.693739i
$79$	−7.73676			−0.870454			−0.435227	−	0.900321i	$-0.643332\pi$
$79$	−7.73676			−0.870454			−0.435227	+	0.900321i	$0.643332\pi$
$80$	8.73280	+	6.32765i	0.976357	+	0.707453i
$81$	3.94288			0.438098
$82$			5.17532i			0.571519i
$83$		−	9.84690i		−	1.08084i	−0.841396	−	0.540419i	$-0.818266\pi$
$83$		−	9.84690i		−	1.08084i	0.841396	−	0.540419i	$-0.181734\pi$
$84$	−0.428430			−0.0467455
$85$	−1.71057	+	2.36076i	−0.185537	+	0.256060i
$86$	2.24066			0.241616
$87$			8.06548i			0.864710i
$88$			2.28185i			0.243246i
$89$	8.73496			0.925904			0.462952	−	0.886383i	$-0.346790\pi$
$89$	8.73496			0.925904			0.462952	+	0.886383i	$0.346790\pi$
$90$	−5.05228	+	6.97267i	−0.532557	+	0.734984i
$91$	4.68660			0.491289
$92$			0.810972i			0.0845496i
$93$			0.202825i			0.0210320i
$94$	−2.00143			−0.206432
$95$	−1.81070	−	1.31201i	−0.185774	−	0.134609i
$96$	2.46905			0.251997
$97$			0.370936i			0.0376629i	0.999823	+	0.0188314i	$0.00599459\pi$
$97$			0.370936i			0.0376629i	−0.999823	+	0.0188314i	$0.994005\pi$
$98$		−	9.78239i		−	0.988170i
$99$	−2.39780			−0.240988
$100$	−0.901897	−	2.75171i	−0.0901897	−	0.275171i
$101$	7.08288			0.704773			0.352386	−	0.935855i	$-0.385370\pi$
$101$	7.08288			0.704773			0.352386	+	0.935855i	$0.385370\pi$
$102$			1.62484i			0.160883i
$103$		−	1.20600i		−	0.118831i	−0.998233	−	0.0594155i	$-0.981076\pi$
$103$		−	1.20600i		−	0.118831i	0.998233	−	0.0594155i	$-0.0189237\pi$
$104$	−11.2182			−1.10004
$105$	−1.33948	−	0.970567i	−0.130720	−	0.0947177i
$106$	14.5286			1.41115
$107$		−	15.3457i		−	1.48352i	−0.670663	−	0.741762i	$-0.733990\pi$
$107$		−	15.3457i		−	1.48352i	0.670663	−	0.741762i	$-0.266010\pi$
$108$			2.42591i			0.233434i
$109$	9.71582			0.930607			0.465304	−	0.885151i	$-0.345945\pi$
$109$	9.71582			0.930607			0.465304	+	0.885151i	$0.345945\pi$
$110$	2.10704	−	2.90794i	0.200899	−	0.277261i
$111$	1.76916			0.167921
$112$		−	4.59757i		−	0.434429i
$113$		−	2.45283i		−	0.230742i	−0.993322	−	0.115371i	$-0.963194\pi$
$113$		−	2.45283i		−	0.230742i	0.993322	−	0.115371i	$-0.0368058\pi$
$114$	−1.24625			−0.116722
$115$	−1.83718	+	2.53550i	−0.171318	+	0.236436i
$116$	6.01936			0.558884
$117$		−	11.7883i		−	1.08983i
$118$			17.2776i			1.59053i
$119$	1.24287			0.113934
$120$	3.20629	+	2.32323i	0.292693	+	0.212080i
$121$	1.00000			0.0909091
$122$		−	21.8830i		−	1.98119i
$123$			2.50074i			0.225484i
$124$	0.151371			0.0135935
$125$	3.41395	−	10.6464i	0.305353	−	0.952239i
$126$	3.67091			0.327030
$127$			8.92365i			0.791846i	0.918284	+	0.395923i	$0.129575\pi$
$127$			8.92365i			0.791846i	−0.918284	+	0.395923i	$0.870425\pi$
$128$			13.6482i			1.20634i
$129$	1.08269			0.0953259
$130$	14.2962	+	10.3588i	1.25386	+	0.908528i
$131$	20.5764			1.79777			0.898883	−	0.438189i	$-0.144380\pi$
$131$	20.5764			1.79777			0.898883	+	0.438189i	$0.144380\pi$
$132$		−	0.449426i		−	0.0391175i
$133$			0.953282i			0.0826600i
$134$	−6.32871			−0.546718
$135$	−5.49568	+	7.58460i	−0.472993	+	0.652779i
$136$	−2.97503			−0.255107
$137$		−	13.2463i		−	1.13171i	−0.824506	−	0.565853i	$-0.808547\pi$
$137$		−	13.2463i		−	1.13171i	0.824506	−	0.565853i	$-0.191453\pi$
$138$			1.74511i			0.148554i
$139$	−8.43868			−0.715760			−0.357880	−	0.933768i	$-0.616500\pi$
$139$	−8.43868			−0.715760			−0.357880	+	0.933768i	$0.616500\pi$
$140$	−0.724346	+	0.999672i	−0.0612184	+	0.0844877i
$141$	−0.967099			−0.0814444
$142$			8.91242i			0.747914i
$143$			4.91628i			0.411120i
$144$	−11.5643			−0.963694
$145$	18.8195	+	13.6363i	1.56288	+	1.13243i
$146$	−4.46896			−0.369854
$147$		−	4.72689i		−	0.389867i
$148$		−	1.32034i		−	0.108531i
$149$	1.29553			0.106134			0.0530670	−	0.998591i	$-0.483100\pi$
$149$	1.29553			0.106134			0.0530670	+	0.998591i	$0.483100\pi$
$150$	−1.94077	−	5.92133i	−0.158463	−	0.483475i
$151$	−15.7521			−1.28189			−0.640945	−	0.767587i	$-0.721457\pi$
$151$	−15.7521			−1.28189			−0.640945	+	0.767587i	$0.721457\pi$
$152$		−	2.28185i		−	0.185082i
$153$		−	3.12621i		−	0.252739i
$154$	−1.53094			−0.123367
$155$	0.473260	+	0.342916i	0.0380132	+	0.0275437i
$156$	2.20950			0.176902
$157$			13.3994i			1.06939i	0.845045	+	0.534696i	$0.179574\pi$
$157$			13.3994i			1.06939i	−0.845045	+	0.534696i	$0.820426\pi$
$158$			12.4250i			0.988482i
$159$	7.02029			0.556746
$160$	4.17443	−	5.76114i	0.330018	−	0.455458i
$161$	1.33487			0.105202
$162$		−	6.33216i		−	0.497501i
$163$		−	17.1342i		−	1.34206i	−0.741432	−	0.671028i	$-0.765853\pi$
$163$		−	17.1342i		−	1.34206i	0.741432	−	0.671028i	$-0.234147\pi$
$164$	1.86633			0.145736
$165$	1.01813	−	1.40513i	0.0792615	−	0.109389i
$166$	−15.8138			−1.22739
$167$			11.5688i			0.895222i	0.894228	+	0.447611i	$0.147725\pi$
$167$			11.5688i			0.895222i	−0.894228	+	0.447611i	$0.852275\pi$
$168$		−	1.68802i		−	0.130233i
$169$	−11.1698			−0.859215
$170$	3.79131	+	2.74712i	0.290780	+	0.210695i
$171$	2.39780			0.183365
$172$		−	0.808028i		−	0.0616116i
$173$			0.975419i			0.0741597i	0.999312	+	0.0370799i	$0.0118056\pi$
$173$			0.975419i			0.0741597i	−0.999312	+	0.0370799i	$0.988194\pi$
$174$	12.9529			0.981959
$175$	−4.52933	+	1.48453i	−0.342385	+	0.112220i
$176$	4.82288			0.363539
$177$			8.34862i			0.627521i
$178$		−	14.0281i		−	1.05145i
$179$	2.73488			0.204414			0.102207	−	0.994763i	$-0.467410\pi$
$179$	2.73488			0.204414			0.102207	+	0.994763i	$0.467410\pi$
$180$	2.51449	+	1.82196i	0.187419	+	0.135801i
$181$	2.61845			0.194628			0.0973138	−	0.995254i	$-0.468975\pi$
$181$	2.61845			0.194628			0.0973138	+	0.995254i	$0.468975\pi$
$182$		−	7.52655i		−	0.557905i
$183$		−	10.5740i		−	0.781650i
$184$	−3.19524			−0.235556
$185$	2.99111	−	4.12804i	0.219911	−	0.303500i
$186$	0.325731			0.0238838
$187$			1.30378i			0.0953419i
$188$			0.721758i			0.0526396i
$189$	3.99307			0.290453
$190$	−2.10704	+	2.90794i	−0.152861	+	0.210964i
$191$	1.30263			0.0942553			0.0471276	−	0.998889i	$-0.484993\pi$
$191$	1.30263			0.0942553			0.0471276	+	0.998889i	$0.484993\pi$
$192$			3.52000i			0.254034i
$193$		−	13.9892i		−	1.00697i	−0.864005	−	0.503483i	$-0.832052\pi$
$193$		−	13.9892i		−	1.00697i	0.864005	−	0.503483i	$-0.167948\pi$
$194$	0.595714			0.0427697
$195$	6.90800	+	5.00542i	0.494692	+	0.358446i
$196$	−3.52773			−0.251981
$197$		−	24.1085i		−	1.71766i	−0.512261	−	0.858830i	$-0.671192\pi$
$197$		−	24.1085i		−	1.71766i	0.512261	−	0.858830i	$-0.328808\pi$
$198$			3.85081i			0.273665i
$199$	5.97076			0.423256			0.211628	−	0.977350i	$-0.432123\pi$
$199$	5.97076			0.423256			0.211628	+	0.977350i	$0.432123\pi$
$200$	10.8418	−	3.55349i	0.766628	−	0.251270i
$201$	−3.05806			−0.215699
$202$		−	11.3749i		−	0.800336i
$203$		−	9.90793i		−	0.695400i
$204$	0.585953			0.0410249
$205$	5.83508	+	4.22800i	0.407539	+	0.295296i
$206$	−1.93681			−0.134944
$207$		−	3.35761i		−	0.233370i
$208$			23.7106i			1.64404i
$209$	−1.00000			−0.0691714
$210$	−1.55870	+	2.15117i	−0.107561	+	0.148445i
$211$	6.76945			0.466028			0.233014	−	0.972473i	$-0.425141\pi$
$211$	6.76945			0.466028			0.233014	+	0.972473i	$0.425141\pi$
$212$		−	5.23933i		−	0.359839i
$213$			4.30652i			0.295078i
$214$	−24.6448			−1.68468
$215$	1.83051	−	2.52630i	0.124840	−	0.172292i
$216$	−9.55813			−0.650348
$217$		−	0.249158i		−	0.0169139i
$218$		−	15.6033i		−	1.05679i
$219$	−2.15942			−0.145920
$220$	−1.04866	−	0.759845i	−0.0707009	−	0.0512287i
$221$	−6.40975			−0.431166
$222$		−	2.84121i		−	0.190690i
$223$			6.37180i			0.426687i	0.976977	+	0.213344i	$0.0684354\pi$
$223$			6.37180i			0.426687i	−0.976977	+	0.213344i	$0.931565\pi$
$224$	−3.03307			−0.202656
$225$	3.73406	+	11.3927i	0.248938	+	0.759513i
$226$	−3.93917			−0.262030
$227$		−	11.6362i		−	0.772321i	−0.922432	−	0.386160i	$-0.873801\pi$
$227$		−	11.6362i		−	0.772321i	0.922432	−	0.386160i	$-0.126199\pi$
$228$			0.449426i			0.0297639i
$229$	−2.02431			−0.133770			−0.0668851	−	0.997761i	$-0.521306\pi$
$229$	−2.02431			−0.133770			−0.0668851	+	0.997761i	$0.521306\pi$
$230$	4.07194	+	2.95046i	0.268496	+	0.194548i
$231$	−0.739759			−0.0486726
$232$			23.7164i			1.55706i
$233$		−	19.9653i		−	1.30797i	−0.756507	−	0.653986i	$-0.773095\pi$
$233$		−	19.9653i		−	1.30797i	0.756507	−	0.653986i	$-0.226905\pi$
$234$	−18.9316			−1.23760
$235$	−1.63508	+	2.25657i	−0.106661	+	0.147203i
$236$	6.23068			0.405583
$237$			6.00382i			0.389990i
$238$		−	1.99602i		−	0.129383i
$239$	2.02025			0.130679			0.0653395	−	0.997863i	$-0.479187\pi$
$239$	2.02025			0.130679			0.0653395	+	0.997863i	$0.479187\pi$
$240$	4.91033	−	6.77676i	0.316961	−	0.437438i
$241$	9.17120			0.590769			0.295385	−	0.955378i	$-0.404552\pi$
$241$	9.17120			0.590769			0.295385	+	0.955378i	$0.404552\pi$
$242$		−	1.60597i		−	0.103236i
$243$		−	15.6260i		−	1.00241i
$244$	−7.89148			−0.505200
$245$	−11.0294	−	7.99176i	−0.704645	−	0.510575i
$246$	4.01612			0.256058
$247$		−	4.91628i		−	0.312815i
$248$			0.596403i			0.0378716i
$249$	−7.64131			−0.484249
$250$	−17.0978	−	5.48272i	−1.08136	−	0.346758i
$251$	25.0453			1.58085			0.790424	−	0.612560i	$-0.209860\pi$
$251$	25.0453			1.58085			0.790424	+	0.612560i	$0.209860\pi$
$252$		−	1.32381i		−	0.0833920i
$253$			1.40028i			0.0880352i
$254$	14.3311			0.899215
$255$	1.83198	+	1.32742i	0.114723	+	0.0831264i
$256$	12.8465			0.802908
$257$			9.28363i			0.579097i	0.957163	+	0.289549i	$0.0935052\pi$
$257$			9.28363i			0.579097i	−0.957163	+	0.289549i	$0.906495\pi$
$258$		−	1.73878i		−	0.108252i
$259$	−2.17329			−0.135042
$260$	3.73561	−	5.15552i	0.231673	−	0.319732i
$261$	−24.9216			−1.54261
$262$		−	33.0451i		−	2.04153i
$263$			25.1698i			1.55204i	0.630709	+	0.776020i	$0.282764\pi$
$263$			25.1698i			1.55204i	−0.630709	+	0.776020i	$0.717236\pi$
$264$	1.77074			0.108982
$265$	11.8692	−	16.3807i	0.729120	−	1.00626i
$266$	1.53094			0.0938682
$267$		−	6.77844i		−	0.414834i
$268$			2.28227i			0.139412i
$269$	−3.24410			−0.197796			−0.0988980	−	0.995098i	$-0.531532\pi$
$269$	−3.24410			−0.197796			−0.0988980	+	0.995098i	$0.531532\pi$
$270$	12.1807	+	8.82591i	0.741292	+	0.537128i
$271$	24.2047			1.47033			0.735166	−	0.677887i	$-0.237104\pi$
$271$	24.2047			1.47033			0.735166	+	0.677887i	$0.237104\pi$
$272$			6.28798i			0.381265i
$273$		−	3.63686i		−	0.220113i
$274$	−21.2732			−1.28516
$275$	−1.55728	−	4.75130i	−0.0939078	−	0.286514i
$276$	0.629324			0.0378809
$277$		−	29.6571i		−	1.78192i	−0.454080	−	0.890961i	$-0.650032\pi$
$277$		−	29.6571i		−	1.78192i	0.454080	−	0.890961i	$-0.349968\pi$
$278$			13.5523i			0.812812i
$279$	−0.626710			−0.0375201
$280$	−3.93872	−	2.85393i	−0.235384	−	0.170555i
$281$	5.43639			0.324308			0.162154	−	0.986765i	$-0.448156\pi$
$281$	5.43639			0.324308			0.162154	+	0.986765i	$0.448156\pi$
$282$			1.55313i			0.0924878i
$283$		−	27.0240i		−	1.60641i	−0.595701	−	0.803206i	$-0.703126\pi$
$283$		−	27.0240i		−	1.60641i	0.595701	−	0.803206i	$-0.296874\pi$
$284$	3.21401			0.190716
$285$	−1.01813	+	1.40513i	−0.0603090	+	0.0832326i
$286$	7.89541			0.466865
$287$		−	3.07200i		−	0.181334i
$288$			7.62914i			0.449551i
$289$	15.3002			0.900009
$290$	21.8995	−	30.2236i	1.28599	−	1.77479i
$291$	0.287851			0.0168741
$292$			1.61160i			0.0943118i
$293$		−	16.8015i		−	0.981551i	−0.871286	−	0.490776i	$-0.836713\pi$
$293$		−	16.8015i		−	0.981551i	0.871286	−	0.490776i	$-0.163287\pi$
$294$	−7.59125			−0.442731
$295$	19.4802	+	14.1150i	1.13418	+	0.821809i
$296$	5.20217			0.302370
$297$			4.18876i			0.243057i
$298$		−	2.08059i		−	0.120525i
$299$	−6.88419			−0.398123
$300$	−2.13536	+	0.699884i	−0.123285	+	0.0404078i
$301$	−1.33002			−0.0766612
$302$			25.2975i			1.45571i
$303$		−	5.49640i		−	0.315760i
$304$	−4.82288			−0.276611
$305$	−24.6727	−	17.8774i	−1.41275	−	1.02366i
$306$	−5.02061			−0.287009
$307$			20.2363i			1.15495i	0.816409	+	0.577474i	$0.195962\pi$
$307$			20.2363i			1.15495i	−0.816409	+	0.577474i	$0.804038\pi$
$308$			0.552091i			0.0314583i
$309$	−0.935873			−0.0532400
$310$	0.550714	−	0.760042i	0.0312785	−	0.0431675i
$311$	−4.83984			−0.274442			−0.137221	−	0.990540i	$-0.543817\pi$
$311$	−4.83984			−0.274442			−0.137221	+	0.990540i	$0.543817\pi$
$312$			8.70547i			0.492850i
$313$			1.99173i			0.112579i	0.998414	+	0.0562896i	$0.0179270\pi$
$313$			1.99173i			0.112579i	−0.998414	+	0.0562896i	$0.982073\pi$
$314$	21.5191			1.21439
$315$	2.99896	−	4.13887i	0.168972	−	0.233199i
$316$	4.48073			0.252061
$317$		−	4.31468i		−	0.242337i	−0.992632	−	0.121168i	$-0.961336\pi$
$317$		−	4.31468i		−	0.242337i	0.992632	−	0.121168i	$-0.0386641\pi$
$318$		−	11.2744i		−	0.632237i
$319$	10.3935			0.581924
$320$	8.21337	+	5.95128i	0.459141	+	0.332686i
$321$	−11.9084			−0.664665
$322$		−	2.14376i		−	0.119467i
$323$		−	1.30378i		−	0.0725443i
$324$	−2.28351			−0.126862
$325$	23.3587	−	7.65604i	1.29571	−	0.424681i
$326$	−27.5171			−1.52403
$327$		−	7.53960i		−	0.416941i
$328$			7.35337i			0.406022i
$329$	1.18802			0.0654976
$330$	−2.25660	−	1.63509i	−0.124222	−	0.0900089i
$331$	29.4038			1.61618			0.808090	−	0.589058i	$-0.200501\pi$
$331$	29.4038			1.61618			0.808090	+	0.589058i	$0.200501\pi$
$332$			5.70281i			0.312982i
$333$			5.46652i			0.299564i
$334$	18.5792			1.01661
$335$	−5.17027	+	7.13550i	−0.282482	+	0.389854i
$336$	−3.56777			−0.194638
$337$		−	34.9078i		−	1.90155i	−0.309882	−	0.950775i	$-0.600290\pi$
$337$		−	34.9078i		−	1.90155i	0.309882	−	0.950775i	$-0.399710\pi$
$338$			17.9384i			0.975719i
$339$	−1.90342			−0.103380
$340$	0.990671	−	1.36723i	0.0537267	−	0.0741483i
$341$	0.261368			0.0141539
$342$		−	3.85081i		−	0.208228i
$343$			12.4797i			0.673838i
$344$	3.18364			0.171650
$345$	1.96758	+	1.42568i	0.105931	+	0.0767558i
$346$	1.56650			0.0842153
$347$		−	1.69558i		−	0.0910237i	−0.998964	−	0.0455118i	$-0.985508\pi$
$347$		−	1.69558i		−	0.0910237i	0.998964	−	0.0455118i	$-0.0144919\pi$
$348$		−	4.67110i		−	0.250397i
$349$	−10.3070			−0.551719			−0.275860	−	0.961198i	$-0.588963\pi$
$349$	−10.3070			−0.551719			−0.275860	+	0.961198i	$0.588963\pi$
$350$	2.38412	+	7.27398i	0.127436	+	0.388811i
$351$	−20.5931			−1.09918
$352$		−	3.18172i		−	0.169586i
$353$			18.6861i			0.994560i	0.867590	+	0.497280i	$0.165668\pi$
$353$			18.6861i			0.994560i	−0.867590	+	0.497280i	$0.834332\pi$
$354$	13.4077			0.712609
$355$	10.0486	+	7.28103i	0.533323	+	0.386437i
$356$	−5.05883			−0.268117
$357$		−	0.964483i		−	0.0510459i
$358$		−	4.39214i		−	0.232132i
$359$	8.10093			0.427551			0.213775	−	0.976883i	$-0.431424\pi$
$359$	8.10093			0.427551			0.213775	+	0.976883i	$0.431424\pi$
$360$	−7.17855	+	9.90713i	−0.378343	+	0.522152i
$361$	1.00000			0.0526316
$362$		−	4.20515i		−	0.221018i
$363$		−	0.776012i		−	0.0407301i
$364$	−2.71423			−0.142264
$365$	−3.65093	+	5.03866i	−0.191099	+	0.263736i
$366$	−16.9815			−0.887637
$367$			24.1369i			1.25993i	0.776622	+	0.629967i	$0.216932\pi$
$367$			24.1369i			1.25993i	−0.776622	+	0.629967i	$0.783068\pi$
$368$			6.75341i			0.352046i
$369$	−7.72704			−0.402254
$370$	−6.62952	−	4.80365i	−0.344653	−	0.249730i
$371$	−8.62399			−0.447735
$372$		−	0.117466i		−	0.00609031i
$373$		−	30.0560i		−	1.55624i	−0.628116	−	0.778120i	$-0.716174\pi$
$373$		−	30.0560i		−	1.55624i	0.628116	−	0.778120i	$-0.283826\pi$
$374$	2.09384			0.108270
$375$	−8.26170	−	2.64927i	−0.426633	−	0.136808i
$376$	−2.84374			−0.146654
$377$			51.0973i			2.63164i
$378$		−	6.41277i		−	0.329837i
$379$	−29.7401			−1.52765			−0.763824	−	0.645424i	$-0.776681\pi$
$379$	−29.7401			−1.52765			−0.763824	+	0.645424i	$0.776681\pi$
$380$	1.04866	+	0.759845i	0.0537953	+	0.0389792i
$381$	6.92486			0.354771
$382$		−	2.09199i		−	0.107036i
$383$			1.33591i			0.0682617i	0.999417	+	0.0341308i	$0.0108663\pi$
$383$			1.33591i			0.0682617i	−0.999417	+	0.0341308i	$0.989134\pi$
$384$	10.5911			0.540477
$385$	−1.25071	+	1.72611i	−0.0637421	+	0.0879707i
$386$	−22.4663			−1.14350
$387$			3.34542i			0.170057i
$388$		−	0.214827i		−	0.0109062i
$389$	−26.5639			−1.34685			−0.673423	−	0.739258i	$-0.735177\pi$
$389$	−26.5639			−1.34685			−0.673423	+	0.739258i	$0.735177\pi$
$390$	8.03857	−	11.0941i	0.407049	−	0.561769i
$391$	−1.82566			−0.0923278
$392$		−	13.8993i		−	0.702022i
$393$		−	15.9675i		−	0.805455i
$394$	−38.7176			−1.95056
$395$	14.0090	+	10.1507i	0.704868	+	0.510736i
$396$	1.38868			0.0697839
$397$			18.7036i			0.938705i	0.883011	+	0.469353i	$0.155513\pi$
$397$			18.7036i			0.938705i	−0.883011	+	0.469353i	$0.844487\pi$
$398$		−	9.58888i		−	0.480647i
$399$	0.739759			0.0370343
$400$	−7.51060	−	22.9150i	−0.375530	−	1.14575i
$401$	25.5327			1.27504			0.637520	−	0.770434i	$-0.279960\pi$
$401$	25.5327			1.27504			0.637520	+	0.770434i	$0.279960\pi$
$402$			4.91116i			0.244946i
$403$			1.28496i			0.0640084i
$404$	−4.10203			−0.204084
$405$	−7.13938	−	5.17308i	−0.354759	−	0.257052i
$406$	−15.9119			−0.789692
$407$		−	2.27980i		−	0.113006i
$408$			2.30866i			0.114296i
$409$	−5.16668			−0.255476			−0.127738	−	0.991808i	$-0.540772\pi$
$409$	−5.16668			−0.255476			−0.127738	+	0.991808i	$0.540772\pi$
$410$	6.79005	−	9.37097i	0.335337	−	0.462799i
$411$	−10.2793			−0.507040
$412$			0.698454i			0.0344104i
$413$		−	10.2558i		−	0.504653i
$414$	−5.39223			−0.265014
$415$	−12.9192	+	17.8298i	−0.634178	+	0.875230i
$416$	15.6422			0.766923
$417$			6.54852i			0.320683i
$418$			1.60597i			0.0785507i
$419$	−14.8764			−0.726761			−0.363381	−	0.931641i	$-0.618378\pi$
$419$	−14.8764			−0.726761			−0.363381	+	0.931641i	$0.618378\pi$
$420$	0.775758	+	0.562102i	0.0378531	+	0.0274278i
$421$	13.6728			0.666374			0.333187	−	0.942861i	$-0.391876\pi$
$421$	13.6728			0.666374			0.333187	+	0.942861i	$0.391876\pi$
$422$		−	10.8715i		−	0.529219i
$423$		−	2.98824i		−	0.145293i
$424$	20.6430			1.00251
$425$	6.19466	−	2.03036i	0.300485	−	0.0984868i
$426$	6.91615			0.335088
$427$			12.9894i			0.628603i
$428$			8.88742i			0.429590i
$429$	3.81509			0.184194
$430$	−4.05716	−	2.93975i	−0.195654	−	0.141767i
$431$	−23.1499			−1.11509			−0.557545	−	0.830147i	$-0.688257\pi$
$431$	−23.1499			−1.11509			−0.557545	+	0.830147i	$0.688257\pi$
$432$			20.2019i			0.971965i
$433$			23.5874i			1.13354i	0.823877	+	0.566769i	$0.191807\pi$
$433$			23.5874i			1.13354i	−0.823877	+	0.566769i	$0.808193\pi$
$434$	−0.400140			−0.0192073
$435$	10.5819	−	14.6042i	0.507366	−	0.700217i
$436$	−5.62690			−0.269479
$437$		−	1.40028i		−	0.0669847i
$438$			3.46797i			0.165706i
$439$	−10.4135			−0.497008			−0.248504	−	0.968631i	$-0.579939\pi$
$439$	−10.4135			−0.497008			−0.248504	+	0.968631i	$0.579939\pi$
$440$	2.99380	−	4.13175i	0.142724	−	0.196973i
$441$	14.6056			0.695506
$442$			10.2939i			0.489630i
$443$			34.7243i			1.64980i	0.565277	+	0.824901i	$0.308769\pi$
$443$			34.7243i			1.64980i	−0.565277	+	0.824901i	$0.691231\pi$
$444$	−1.02460			−0.0486255
$445$	−15.8164	−	11.4603i	−0.749770	−	0.543271i
$446$	10.2329			0.484544
$447$		−	1.00535i		−	0.0475513i
$448$		−	4.32410i		−	0.204295i
$449$	−9.24213			−0.436163			−0.218082	−	0.975931i	$-0.569980\pi$
$449$	−9.24213			−0.436163			−0.218082	+	0.975931i	$0.569980\pi$
$450$	18.2964	−	5.99680i	0.862498	−	0.282692i
$451$	3.22255			0.151744
$452$			1.42055i			0.0668170i
$453$			12.2239i			0.574327i
$454$	−18.6874			−0.877043
$455$	−8.48604	−	6.14884i	−0.397832	−	0.288262i
$456$	−1.77074			−0.0829227
$457$			19.8593i			0.928977i	0.885579	+	0.464489i	$0.153762\pi$
$457$			19.8593i			0.928977i	−0.885579	+	0.464489i	$0.846238\pi$
$458$			3.25099i			0.151909i
$459$	−5.46123			−0.254908
$460$	1.06400	−	1.46843i	0.0496092	−	0.0684658i
$461$	29.7527			1.38572			0.692862	−	0.721071i	$-0.256350\pi$
$461$	29.7527			1.38572			0.692862	+	0.721071i	$0.256350\pi$
$462$			1.18803i			0.0552723i
$463$			23.7046i			1.10165i	0.834622	+	0.550824i	$0.185686\pi$
$463$			23.7046i			1.10165i	−0.834622	+	0.550824i	$0.814314\pi$
$464$	50.1266			2.32707
$465$	0.266107	−	0.367256i	0.0123404	−	0.0170311i
$466$	−32.0638			−1.48533
$467$			3.26892i			0.151268i	0.997136	+	0.0756339i	$0.0240980\pi$
$467$			3.26892i			0.151268i	−0.997136	+	0.0756339i	$0.975902\pi$
$468$			6.82715i			0.315585i
$469$	3.75663			0.173465
$470$	3.62399	+	2.62589i	0.167162	+	0.121123i
$471$	10.3981			0.479120
$472$			24.5490i			1.12996i
$473$		−	1.39520i		−	0.0641515i
$474$	9.64197			0.442871
$475$	1.55728	+	4.75130i	0.0714531	+	0.218005i
$476$	−0.719806			−0.0329922
$477$			21.6920i			0.993210i
$478$		−	3.24447i		−	0.148398i
$479$	24.7933			1.13284			0.566418	−	0.824118i	$-0.308329\pi$
$479$	24.7933			1.13284			0.566418	+	0.824118i	$0.308329\pi$
$480$	−4.47072	−	3.23941i	−0.204059	−	0.147858i
$481$	11.2081			0.511047
$482$		−	14.7287i		−	0.670874i
$483$		−	1.03587i		−	0.0471339i
$484$	−0.579148			−0.0263249
$485$	0.486670	−	0.671655i	0.0220986	−	0.0304983i
$486$	−25.0950			−1.13833
$487$			41.9236i			1.89974i	0.312647	+	0.949869i	$0.398784\pi$
$487$			41.9236i			1.89974i	−0.312647	+	0.949869i	$0.601216\pi$
$488$		−	31.0925i		−	1.40749i
$489$	−13.2964			−0.601283
$490$	−12.8345	+	17.7130i	−0.579805	+	0.800191i
$491$	29.1574			1.31585			0.657927	−	0.753081i	$-0.271433\pi$
$491$	29.1574			1.31585			0.657927	+	0.753081i	$0.271433\pi$
$492$		−	1.44830i		−	0.0652942i
$493$			13.5508i			0.610299i
$494$	−7.89541			−0.355231
$495$	4.34171	+	3.14593i	0.195145	+	0.141399i
$496$	1.26055			0.0566003
$497$		−	5.29028i		−	0.237302i
$498$			12.2717i			0.549910i
$499$	−12.1684			−0.544733			−0.272367	−	0.962194i	$-0.587806\pi$
$499$	−12.1684			−0.544733			−0.272367	+	0.962194i	$0.587806\pi$
$500$	−1.97718	+	6.16581i	−0.0884224	+	0.275744i
$501$	8.97755			0.401087
$502$		−	40.2221i		−	1.79520i
$503$			14.6468i			0.653068i	0.945185	+	0.326534i	$0.105881\pi$
$503$			14.6468i			0.653068i	−0.945185	+	0.326534i	$0.894119\pi$
$504$	5.21582			0.232331
$505$	−12.8250	−	9.29278i	−0.570704	−	0.413523i
$506$	2.24882			0.0999722
$507$			8.66790i			0.384955i
$508$		−	5.16811i		−	0.229298i
$509$	35.5192			1.57436			0.787181	−	0.616722i	$-0.211540\pi$
$509$	35.5192			1.57436			0.787181	+	0.616722i	$0.211540\pi$
$510$	2.13180	−	2.94211i	0.0943978	−	0.130279i
$511$	2.65271			0.117349
$512$			6.66513i			0.294560i
$513$		−	4.18876i		−	0.184938i
$514$	14.9093			0.657619
$515$	−1.58228	+	2.18371i	−0.0697237	+	0.0962259i
$516$	−0.627040			−0.0276039
$517$			1.24624i			0.0548096i
$518$			3.49025i			0.153353i
$519$	0.756937			0.0332259
$520$	20.3128	+	14.7183i	0.890777	+	0.645442i
$521$	29.5346			1.29393			0.646967	−	0.762518i	$-0.276037\pi$
$521$	29.5346			1.29393			0.646967	+	0.762518i	$0.276037\pi$
$522$			40.0233i			1.75177i
$523$		−	0.494856i		−	0.0216385i	−0.999941	−	0.0108193i	$-0.996556\pi$
$523$		−	0.494856i		−	0.0216385i	0.999941	−	0.0108193i	$-0.00344395\pi$
$524$	−11.9168			−0.520586
$525$	1.15201	+	3.51482i	0.0502780	+	0.153399i
$526$	40.4221			1.76249
$527$			0.340767i			0.0148440i
$528$		−	3.74262i		−	0.162877i
$529$	21.0392			0.914748
$530$	−26.3070	−	19.0616i	−1.14270	−	0.827985i
$531$	−25.7964			−1.11947
$532$		−	0.552091i		−	0.0239362i
$533$			15.8429i			0.686234i
$534$	−10.8860			−0.471083
$535$	−20.1336	+	27.7865i	−0.870453	+	1.20131i
$536$	−8.99217			−0.388402
$537$		−	2.12230i		−	0.0915840i
$538$			5.20993i			0.224616i
$539$	−6.09125			−0.262369
$540$	3.18281	−	4.39260i	0.136966	−	0.189028i
$541$	−26.6748			−1.14684			−0.573419	−	0.819262i	$-0.694383\pi$
$541$	−26.6748			−1.14684			−0.573419	+	0.819262i	$0.694383\pi$
$542$		−	38.8721i		−	1.66970i
$543$		−	2.03195i		−	0.0871992i
$544$	4.14826			0.177855
$545$	−17.5925	−	12.7472i	−0.753578	−	0.546031i
$546$	−5.84070			−0.249959
$547$			46.5485i			1.99027i	0.0985296	+	0.995134i	$0.468586\pi$
$547$			46.5485i			1.99027i	−0.0985296	+	0.995134i	$0.531414\pi$
$548$			7.67156i			0.327713i
$549$	32.6725			1.39443
$550$	−7.63046	+	2.50096i	−0.325364	+	0.106641i
$551$	−10.3935			−0.442778
$552$			2.47955i			0.105536i
$553$		−	7.37532i		−	0.313630i
$554$	−47.6285			−2.02354
$555$	−3.20341	−	2.32114i	−0.135977	−	0.0985269i
$556$	4.88724			0.207265
$557$			19.0216i			0.805971i	0.915206	+	0.402986i	$0.132028\pi$
$557$			19.0216i			0.805971i	−0.915206	+	0.402986i	$0.867972\pi$
$558$			1.00648i			0.0426076i
$559$	6.85920			0.290113
$560$	−6.03203	+	8.32483i	−0.254900	+	0.351788i
$561$	1.01175			0.0427161
$562$		−	8.73069i		−	0.368282i
$563$		−	6.64301i		−	0.279969i	−0.990154	−	0.139985i	$-0.955295\pi$
$563$		−	6.64301i		−	0.279969i	0.990154	−	0.139985i	$-0.0447053\pi$
$564$	0.560093			0.0235842
$565$	−3.21812	+	4.44134i	−0.135387	+	0.186848i
$566$	−43.3999			−1.82423
$567$			3.75868i			0.157850i
$568$			12.6632i			0.531337i
$569$	5.71266			0.239487			0.119744	−	0.992805i	$-0.461793\pi$
$569$	5.71266			0.239487			0.119744	+	0.992805i	$0.461793\pi$
$570$	2.25660	+	1.63509i	0.0945184	+	0.0684865i
$571$	−12.3081			−0.515076			−0.257538	−	0.966268i	$-0.582911\pi$
$571$	−12.3081			−0.515076			−0.257538	+	0.966268i	$0.582911\pi$
$572$		−	2.84725i		−	0.119050i
$573$		−	1.01086i		−	0.0422293i
$574$	−4.93354			−0.205922
$575$	6.65318	−	2.18064i	0.277457	−	0.0909390i
$576$	−10.8765			−0.453187
$577$			4.02812i			0.167693i	0.996479	+	0.0838464i	$0.0267205\pi$
$577$			4.02812i			0.167693i	−0.996479	+	0.0838464i	$0.973280\pi$
$578$		−	24.5716i		−	1.02205i
$579$	−10.8558			−0.451152
$580$	−10.8993	−	7.89744i	−0.452568	−	0.327923i
$581$	9.38687			0.389433
$582$		−	0.462281i		−	0.0191622i
$583$		−	9.04663i		−	0.374673i
$584$	−6.34973			−0.262754
$585$	−15.4663	+	21.3451i	−0.639452	+	0.882509i
$586$	−26.9827			−1.11464
$587$			8.60688i			0.355244i	0.984099	+	0.177622i	$0.0568404\pi$
$587$			8.60688i			0.355244i	−0.984099	+	0.177622i	$0.943160\pi$
$588$			2.73757i			0.112895i
$589$	−0.261368			−0.0107695
$590$	22.6683	−	31.2846i	0.933241	−	1.28797i
$591$	−18.7085			−0.769565
$592$		−	10.9952i		−	0.451901i
$593$			14.0989i			0.578972i	0.957182	+	0.289486i	$0.0934844\pi$
$593$			14.0989i			0.578972i	−0.957182	+	0.289486i	$0.906516\pi$
$594$	6.72704			0.276014
$595$	−2.25047	−	1.63065i	−0.0922602	−	0.0668503i
$596$	−0.750304			−0.0307336
$597$		−	4.63339i		−	0.189632i
$598$			11.0558i			0.452106i
$599$	−41.6567			−1.70204			−0.851022	−	0.525130i	$-0.824017\pi$
$599$	−41.6567			−1.70204			−0.851022	+	0.525130i	$0.824017\pi$
$600$	−2.75755	−	8.41334i	−0.112577	−	0.343473i
$601$	46.2275			1.88566			0.942829	−	0.333276i	$-0.108154\pi$
$601$	46.2275			1.88566			0.942829	+	0.333276i	$0.108154\pi$
$602$			2.13598i			0.0870560i
$603$		−	9.44911i		−	0.384798i
$604$	9.12281			0.371202
$605$	−1.81070	−	1.31201i	−0.0736155	−	0.0533406i
$606$	−8.82707			−0.358575
$607$		−	40.2730i		−	1.63463i	−0.576191	−	0.817315i	$-0.695461\pi$
$607$		−	40.2730i		−	1.63463i	0.576191	−	0.817315i	$-0.304539\pi$
$608$			3.18172i			0.129036i
$609$	−7.68867			−0.311561
$610$	−28.7106	+	39.6236i	−1.16246	+	1.60431i
$611$	−6.12687			−0.247867
$612$			1.81054i			0.0731867i
$613$		−	18.8063i		−	0.759578i	−0.925073	−	0.379789i	$-0.875997\pi$
$613$		−	18.8063i		−	0.759578i	0.925073	−	0.379789i	$-0.124003\pi$
$614$	32.4990			1.31155
$615$	3.28098	−	4.52809i	0.132302	−	0.182590i
$616$	−2.17525			−0.0876432
$617$			17.9716i			0.723510i	0.932273	+	0.361755i	$0.117822\pi$
$617$			17.9716i			0.723510i	−0.932273	+	0.361755i	$0.882178\pi$
$618$			1.50299i			0.0604590i
$619$	−31.2480			−1.25596			−0.627981	−	0.778228i	$-0.716119\pi$
$619$	−31.2480			−1.25596			−0.627981	+	0.778228i	$0.716119\pi$
$620$	−0.274087	−	0.198599i	−0.0110076	−	0.00797594i
$621$	−5.86546			−0.235373
$622$			7.77266i			0.311655i
$623$			8.32688i			0.333609i
$624$	18.3997			0.736579
$625$	−20.1497	+	14.7983i	−0.805989	+	0.591930i
$626$	3.19866			0.127844
$627$			0.776012i			0.0309910i
$628$		−	7.76025i		−	0.309668i
$629$	2.97236			0.118516
$630$	−6.64692	−	4.81625i	−0.264820	−	0.191884i
$631$	1.58270			0.0630062			0.0315031	−	0.999504i	$-0.489971\pi$
$631$	1.58270			0.0630062			0.0315031	+	0.999504i	$0.489971\pi$
$632$			17.6541i			0.702244i
$633$		−	5.25318i		−	0.208795i
$634$	−6.92926			−0.275196
$635$	11.7079	−	16.1581i	0.464613	−	0.641213i
$636$	−4.06579			−0.161219
$637$		−	29.9463i		−	1.18652i
$638$		−	16.6917i		−	0.660829i
$639$	−13.3067			−0.526406
$640$	17.9064	−	24.7127i	0.707814	−	0.976857i
$641$	−24.1720			−0.954738			−0.477369	−	0.878703i	$-0.658409\pi$
$641$	−24.1720			−0.954738			−0.477369	+	0.878703i	$0.658409\pi$
$642$			19.1246i			0.754789i
$643$		−	17.5234i		−	0.691057i	−0.938408	−	0.345528i	$-0.887700\pi$
$643$		−	17.5234i		−	0.691057i	0.938408	−	0.345528i	$-0.112300\pi$
$644$	−0.773085			−0.0304638
$645$	−1.96044	−	1.42050i	−0.0771921	−	0.0559322i
$646$	−2.09384			−0.0823809
$647$		−	32.9959i		−	1.29720i	−0.761128	−	0.648601i	$-0.775354\pi$
$647$		−	32.9959i		−	1.29720i	0.761128	−	0.648601i	$-0.224646\pi$
$648$		−	8.99706i		−	0.353438i
$649$	10.7584			0.422303
$650$	−12.2954	−	37.5135i	−0.482265	−	1.47140i
$651$	−0.193349			−0.00757796
$652$			9.92325i			0.388624i
$653$		−	33.1058i		−	1.29553i	−0.761839	−	0.647766i	$-0.775703\pi$
$653$		−	33.1058i		−	1.29553i	0.761839	−	0.647766i	$-0.224297\pi$
$654$	−12.1084			−0.473475
$655$	−37.2577	−	26.9963i	−1.45578	−	1.05483i
$656$	15.5420			0.606812
$657$		−	6.67240i		−	0.260315i
$658$		−	1.90793i		−	0.0743787i
$659$	7.15649			0.278777			0.139389	−	0.990238i	$-0.455486\pi$
$659$	7.15649			0.278777			0.139389	+	0.990238i	$0.455486\pi$
$660$	−0.589649	+	0.813776i	−0.0229521	+	0.0316762i
$661$	13.0442			0.507362			0.253681	−	0.967288i	$-0.418359\pi$
$661$	13.0442			0.507362			0.253681	+	0.967288i	$0.418359\pi$
$662$		−	47.2218i		−	1.83533i
$663$			4.97404i			0.193176i
$664$	−22.4691			−0.871972
$665$	1.25071	−	1.72611i	0.0485005	−	0.0669357i
$666$	8.77908			0.340183
$667$			14.5538i			0.563527i
$668$		−	6.70006i		−	0.259233i
$669$	4.94460			0.191169
$670$	11.4594	+	8.30330i	0.442716	+	0.320785i
$671$	−13.6260			−0.526027
$672$			2.35370i			0.0907961i
$673$			24.5295i			0.945542i	0.881185	+	0.472771i	$0.156746\pi$
$673$			24.5295i			0.945542i	−0.881185	+	0.472771i	$0.843254\pi$
$674$	−56.0610			−2.15939
$675$	19.9021	−	6.52310i	0.766031	−	0.251074i
$676$	6.46896			0.248806
$677$			47.0489i			1.80824i	0.427283	+	0.904118i	$0.359471\pi$
$677$			47.0489i			1.80824i	−0.427283	+	0.904118i	$0.640529\pi$
$678$			3.05685i			0.117397i
$679$	−0.353607			−0.0135702
$680$	5.38690	+	3.90326i	0.206578	+	0.149683i
$681$	−9.02982			−0.346024
$682$		−	0.419750i		−	0.0160731i
$683$			18.9622i			0.725569i	0.931873	+	0.362784i	$0.118174\pi$
$683$			18.9622i			0.725569i	−0.931873	+	0.362784i	$0.881826\pi$
$684$	−1.38868			−0.0530976
$685$	−17.3792	+	23.9851i	−0.664025	+	0.916423i
$686$	20.0420			0.765207
$687$			1.57089i			0.0599332i
$688$		−	6.72890i		−	0.256537i
$689$	44.4757			1.69439
$690$	2.28960	−	3.15988i	0.0871634	−	0.120294i
$691$	13.3011			0.505997			0.252999	−	0.967467i	$-0.418583\pi$
$691$	13.3011			0.505997			0.252999	+	0.967467i	$0.418583\pi$
$692$		−	0.564912i		−	0.0214747i
$693$		−	2.28578i		−	0.0868298i
$694$	−2.72306			−0.103366
$695$	15.2799	+	11.0716i	0.579601	+	0.419970i
$696$	18.4042			0.697610
$697$			4.20150i			0.159143i
$698$			16.5527i			0.626529i
$699$	−15.4933			−0.586012
$700$	2.62315	−	0.859763i	0.0991458	−	0.0324960i
$701$	32.4520			1.22570			0.612848	−	0.790201i	$-0.290024\pi$
$701$	32.4520			1.22570			0.612848	+	0.790201i	$0.290024\pi$
$702$			33.0720i			1.24822i
$703$			2.27980i			0.0859844i
$704$	4.53601			0.170957
$705$	1.75113	+	1.26884i	0.0659513	+	0.0477872i
$706$	30.0093			1.12942
$707$			6.75198i			0.253934i
$708$		−	4.83508i		−	0.181714i
$709$	9.03547			0.339334			0.169667	−	0.985501i	$-0.445731\pi$
$709$	9.03547			0.339334			0.169667	+	0.985501i	$0.445731\pi$
$710$	11.6931	−	16.1377i	0.438836	−	0.605638i
$711$	−18.5512			−0.695726
$712$		−	19.9319i		−	0.746978i
$713$			0.365990i			0.0137064i
$714$	−1.54893			−0.0579674
$715$	6.45018	−	8.90192i	0.241223	−	0.332913i
$716$	−1.58390			−0.0591930
$717$		−	1.56774i		−	0.0585483i
$718$		−	13.0099i		−	0.485524i
$719$	−11.3168			−0.422046			−0.211023	−	0.977481i	$-0.567679\pi$
$719$	−11.3168			−0.422046			−0.211023	+	0.977481i	$0.567679\pi$
$720$	20.9396	+	15.1725i	0.780371	+	0.565444i
$721$	1.14966			0.0428156
$722$		−	1.60597i		−	0.0597681i
$723$		−	7.11697i		−	0.264683i
$724$	−1.51647			−0.0563591
$725$	−16.1856	−	49.3826i	−0.601119	−	1.83402i
$726$	−1.24625			−0.0462528
$727$			21.4938i			0.797163i	0.917133	+	0.398581i	$0.130497\pi$
$727$			21.4938i			0.797163i	−0.917133	+	0.398581i	$0.869503\pi$
$728$		−	10.6941i		−	0.396350i
$729$	−0.297337			−0.0110125
$730$	8.09195	+	5.86330i	0.299497	+	0.217010i
$731$	1.81904			0.0672795
$732$			6.12388i			0.226345i
$733$			4.17977i			0.154383i	0.997016	+	0.0771917i	$0.0245953\pi$
$733$			4.17977i			0.154383i	−0.997016	+	0.0771917i	$0.975405\pi$
$734$	38.7631			1.43077
$735$	−6.20170	+	8.55899i	−0.228753	+	0.315703i
$736$	4.45531			0.164225
$737$			3.94074i			0.145159i
$738$			12.4094i			0.456797i
$739$	−14.5013			−0.533438			−0.266719	−	0.963774i	$-0.585940\pi$
$739$	−14.5013			−0.533438			−0.266719	+	0.963774i	$0.585940\pi$
$740$	−1.73230	+	2.39075i	−0.0636805	+	0.0878856i
$741$	−3.81509			−0.140151
$742$			13.8499i			0.508445i
$743$		−	17.6019i		−	0.645751i	−0.946441	−	0.322875i	$-0.895351\pi$
$743$		−	17.6019i		−	0.645751i	0.946441	−	0.322875i	$-0.104649\pi$
$744$	0.462816			0.0169677
$745$	−2.34582	−	1.69974i	−0.0859442	−	0.0622738i
$746$	−48.2691			−1.76726
$747$		−	23.6109i		−	0.863879i
$748$		−	0.755082i		−	0.0276085i
$749$	14.6288			0.534524
$750$	−4.25466	+	13.2681i	−0.155358	+	0.484481i
$751$	3.15382			0.115084			0.0575422	−	0.998343i	$-0.481674\pi$
$751$	3.15382			0.115084			0.0575422	+	0.998343i	$0.481674\pi$
$752$			6.01048i			0.219180i
$753$		−	19.4355i		−	0.708269i
$754$	82.0608			2.98848
$755$	28.5224	+	20.6669i	1.03804	+	0.752145i
$756$	−2.31258			−0.0841077
$757$			16.2302i			0.589898i	0.955513	+	0.294949i	$0.0953027\pi$
$757$			16.2302i			0.589898i	−0.955513	+	0.294949i	$0.904697\pi$
$758$			47.7618i			1.73479i
$759$	1.08664			0.0394425
$760$	−2.99380	+	4.13175i	−0.108597	+	0.149874i
$761$	−29.8717			−1.08285			−0.541425	−	0.840749i	$-0.682115\pi$
$761$	−29.8717			−1.08285			−0.541425	+	0.840749i	$0.682115\pi$
$762$		−	11.1211i		−	0.402876i
$763$			9.26192i			0.335304i
$764$	−0.754417			−0.0272939
$765$	−4.10161	+	5.66064i	−0.148294	+	0.204661i
$766$	2.14543			0.0775176
$767$			52.8911i			1.90979i
$768$		−	9.96906i		−	0.359728i
$769$	−30.1488			−1.08719			−0.543597	−	0.839347i	$-0.682938\pi$
$769$	−30.1488			−1.08719			−0.543597	+	0.839347i	$0.682938\pi$
$770$	2.77208	+	2.00861i	0.0998990	+	0.0723852i
$771$	7.20422			0.259453
$772$			8.10182i			0.291591i
$773$		−	39.7833i		−	1.43091i	−0.698661	−	0.715453i	$-0.746220\pi$
$773$		−	39.7833i		−	1.43091i	0.698661	−	0.715453i	$-0.253780\pi$
$774$	5.37266			0.193116
$775$	−0.407025	−	1.24184i	−0.0146208	−	0.0446082i
$776$	0.846421			0.0303847
$777$			1.68650i			0.0605030i
$778$			42.6610i			1.52947i
$779$	−3.22255			−0.115460
$780$	−4.00075	−	2.89888i	−0.143250	−	0.103796i
$781$	5.54955			0.198578
$782$			2.93197i			0.104847i
$783$			43.5359i			1.55585i
$784$	−29.3774			−1.04919
$785$	17.5801	−	24.2624i	0.627462	−	0.865962i
$786$	−25.6434			−0.914670
$787$		−	35.6139i		−	1.26950i	−0.772718	−	0.634749i	$-0.781103\pi$
$787$		−	35.6139i		−	1.26950i	0.772718	−	0.634749i	$-0.218897\pi$
$788$			13.9624i			0.497389i
$789$	19.5321			0.695362
$790$	16.3017	−	22.4980i	0.579988	−	0.800444i
$791$	2.33824			0.0831381
$792$			5.47143i			0.194419i
$793$		−	66.9893i		−	2.37886i
$794$	30.0374			1.06599
$795$	−12.7117	−	9.21066i	−0.450836	−	0.326669i
$796$	−3.45795			−0.122564
$797$		−	20.7634i		−	0.735478i	−0.929929	−	0.367739i	$-0.880132\pi$
$797$		−	20.7634i		−	0.735478i	0.929929	−	0.367739i	$-0.119868\pi$
$798$		−	1.18803i		−	0.0420559i
$799$	−1.62483			−0.0574822
$800$	−15.1173	+	4.95484i	−0.534477	+	0.175180i
$801$	20.9447			0.740045
$802$		−	41.0047i		−	1.44793i
$803$			2.78271i			0.0981998i
$804$	1.77107			0.0624608
$805$	−2.41705	−	1.75135i	−0.0851897	−	0.0617270i
$806$	2.06361			0.0726875
$807$			2.51746i			0.0886187i
$808$		−	16.1621i		−	0.568580i
$809$	−14.1210			−0.496468			−0.248234	−	0.968700i	$-0.579850\pi$
$809$	−14.1210			−0.496468			−0.248234	+	0.968700i	$0.579850\pi$
$810$	−8.30783	+	11.4657i	−0.291907	+	0.402862i
$811$	−42.0097			−1.47516			−0.737579	−	0.675261i	$-0.764031\pi$
$811$	−42.0097			−1.47516			−0.737579	+	0.675261i	$0.764031\pi$
$812$			5.73815i			0.201370i
$813$		−	18.7832i		−	0.658754i
$814$	−3.66130			−0.128329
$815$	−22.4802	+	31.0250i	−0.787447	+	1.08676i
$816$	4.87955			0.170818
$817$			1.39520i			0.0488120i
$818$			8.29754i			0.290117i
$819$	11.2376			0.392672
$820$	−3.37937	−	2.44864i	−0.118013	−	0.0855101i
$821$	−41.5973			−1.45176			−0.725878	−	0.687823i	$-0.758566\pi$
$821$	−41.5973			−1.45176			−0.725878	+	0.687823i	$0.758566\pi$
$822$			16.5082i			0.575791i
$823$			3.45339i			0.120378i	0.998187	+	0.0601888i	$0.0191703\pi$
$823$			3.45339i			0.120378i	−0.998187	+	0.0601888i	$0.980830\pi$
$824$	−2.75192			−0.0958676
$825$	−3.68707	+	1.20847i	−0.128367	+	0.0420736i
$826$	−16.4705			−0.573080
$827$		−	12.4022i		−	0.431266i	−0.976475	−	0.215633i	$-0.930819\pi$
$827$		−	12.4022i		−	0.431266i	0.976475	−	0.215633i	$-0.0691814\pi$
$828$			1.94455i			0.0675778i
$829$	−19.4569			−0.675765			−0.337883	−	0.941188i	$-0.609711\pi$
$829$	−19.4569			−0.675765			−0.337883	+	0.941188i	$0.609711\pi$
$830$	28.6342	+	20.7479i	0.993906	+	0.720168i
$831$	−23.0143			−0.798356
$832$			22.3003i			0.773124i
$833$		−	7.94166i		−	0.275162i
$834$	10.5167			0.364165
$835$	15.1784	−	20.9477i	0.525269	−	0.724925i
$836$	0.579148			0.0200302
$837$			1.09481i			0.0378422i
$838$			23.8911i			0.825306i
$839$	−42.8834			−1.48050			−0.740249	−	0.672333i	$-0.765292\pi$
$839$	−42.8834			−1.48050			−0.740249	+	0.672333i	$0.765292\pi$
$840$	−2.21469	+	3.05650i	−0.0764140	+	0.105459i
$841$	79.0246			2.72499
$842$		−	21.9582i		−	0.756730i
$843$		−	4.21871i		−	0.145300i
$844$	−3.92051			−0.134949
$845$	20.2252	+	14.6548i	0.695767	+	0.504141i
$846$	−4.79904			−0.164994
$847$			0.953282i			0.0327552i
$848$		−	43.6308i		−	1.49829i
$849$	−20.9710			−0.719723
$850$	−3.26070	−	9.94845i	−0.111841	−	0.341229i
$851$	3.19237			0.109433
$852$		−	2.49411i		−	0.0854468i
$853$		−	44.6288i		−	1.52806i	−0.645180	−	0.764031i	$-0.723218\pi$
$853$		−	44.6288i		−	1.52806i	0.645180	−	0.764031i	$-0.276782\pi$
$854$	20.8607			0.713838
$855$	−4.34171	−	3.14593i	−0.148483	−	0.107589i
$856$	−35.0166			−1.19684
$857$		−	35.7235i		−	1.22029i	−0.792289	−	0.610146i	$-0.791111\pi$
$857$		−	35.7235i		−	1.22029i	0.792289	−	0.610146i	$-0.208889\pi$
$858$		−	6.12693i		−	0.209170i
$859$	44.1430			1.50614			0.753071	−	0.657940i	$-0.228572\pi$
$859$	44.1430			1.50614			0.753071	+	0.657940i	$0.228572\pi$
$860$	−1.06014	+	1.46310i	−0.0361504	+	0.0498912i
$861$	−2.38391			−0.0812434
$862$			37.1781i			1.26629i
$863$		−	19.8560i		−	0.675905i	−0.941163	−	0.337952i	$-0.890266\pi$
$863$		−	19.8560i		−	0.675905i	0.941163	−	0.337952i	$-0.109734\pi$
$864$	13.3275			0.453410
$865$	1.27975	−	1.76619i	0.0435130	−	0.0600524i
$866$	37.8807			1.28724
$867$		−	11.8731i		−	0.403232i
$868$			0.144299i			0.00489783i
$869$	7.73676			0.262452
$870$	−23.4539	−	16.9943i	−0.795162	−	0.576161i
$871$	−19.3738			−0.656455
$872$		−	22.1700i		−	0.750773i
$873$			0.889433i			0.0301027i
$874$	−2.24882			−0.0760674
$875$	10.1490	+	3.25446i	0.343098	+	0.110021i
$876$	1.25062			0.0422546
$877$		−	19.6775i		−	0.664460i	−0.943198	−	0.332230i	$-0.892199\pi$
$877$		−	19.6775i		−	0.664460i	0.943198	−	0.332230i	$-0.107801\pi$
$878$			16.7238i			0.564399i
$879$	−13.0381			−0.439765
$880$	−8.73280	−	6.32765i	−0.294383	−	0.213305i
$881$	−17.3011			−0.582888			−0.291444	−	0.956588i	$-0.594136\pi$
$881$	−17.3011			−0.582888			−0.291444	+	0.956588i	$0.594136\pi$
$882$		−	23.4562i		−	0.789813i
$883$		−	14.6246i		−	0.492158i	−0.969250	−	0.246079i	$-0.920858\pi$
$883$		−	14.6246i		−	0.492158i	0.969250	−	0.246079i	$-0.0791422\pi$
$884$	3.71219			0.124854
$885$	10.9534	−	15.1169i	0.368196	−	0.508148i
$886$	55.7663			1.87351
$887$			0.991426i			0.0332888i	0.999861	+	0.0166444i	$0.00529833\pi$
$887$			0.991426i			0.0332888i	−0.999861	+	0.0166444i	$0.994702\pi$
$888$		−	4.03695i		−	0.135471i
$889$	−8.50675			−0.285307
$890$	−18.4049	+	25.4007i	−0.616935	+	0.851434i
$891$	−3.94288			−0.132092
$892$		−	3.69021i		−	0.123557i
$893$		−	1.24624i		−	0.0417039i
$894$	−1.61456			−0.0539990
$895$	−4.95205	−	3.58817i	−0.165529	−	0.119939i
$896$	−13.0105			−0.434652
$897$			5.34222i			0.178371i
$898$			14.8426i			0.495304i
$899$	2.71653			0.0906013
$900$	−2.16257	−	6.59805i	−0.0720858	−	0.219935i
$901$	11.7948			0.392942
$902$		−	5.17532i		−	0.172319i
$903$			1.03211i			0.0343466i
$904$	−5.59698			−0.186153
$905$	−4.74123	−	3.43542i	−0.157604	−	0.114197i
$906$	19.6312			0.652202
$907$			8.54420i			0.283706i	0.989888	+	0.141853i	$0.0453060\pi$
$907$			8.54420i			0.283706i	−0.989888	+	0.141853i	$0.954694\pi$
$908$			6.73907i			0.223644i
$909$	16.9834			0.563303
$910$	−9.87487	+	13.6283i	−0.327349	+	0.451775i
$911$	1.73213			0.0573882			0.0286941	−	0.999588i	$-0.490865\pi$
$911$	1.73213			0.0573882			0.0286941	+	0.999588i	$0.490865\pi$
$912$			3.74262i			0.123930i
$913$			9.84690i			0.325885i
$914$	31.8934			1.05494
$915$	−13.8731	+	19.1463i	−0.458630	+	0.632957i
$916$	1.17237			0.0387363
$917$			19.6151i			0.647747i
$918$			8.77058i			0.289472i
$919$	−34.0654			−1.12372			−0.561858	−	0.827234i	$-0.689913\pi$
$919$	−34.0654			−1.12372			−0.561858	+	0.827234i	$0.689913\pi$
$920$	5.78563	+	4.19217i	0.190746	+	0.138212i
$921$	15.7036			0.517453
$922$		−	47.7821i		−	1.57362i
$923$			27.2831i			0.898035i
$924$	0.428430			0.0140943
$925$	−10.8320	+	3.55030i	−0.356155	+	0.116733i
$926$	38.0690			1.25102
$927$		−	2.89176i		−	0.0949779i
$928$		−	33.0692i		−	1.08555i
$929$	14.3980			0.472384			0.236192	−	0.971706i	$-0.424101\pi$
$929$	14.3980			0.472384			0.236192	+	0.971706i	$0.424101\pi$
$930$	−0.589802	−	0.427361i	−0.0193404	−	0.0140137i
$931$	6.09125			0.199633
$932$			11.5629i			0.378755i
$933$			3.75578i			0.122959i
$934$	5.24980			0.171779
$935$	1.71057	−	2.36076i	0.0559415	−	0.0772051i
$936$	−26.8991			−0.879224
$937$		−	1.24615i		−	0.0407099i	−0.999793	−	0.0203549i	$-0.993520\pi$
$937$		−	1.24615i		−	0.0407099i	0.999793	−	0.0203549i	$-0.00647962\pi$
$938$		−	6.03305i		−	0.196986i
$939$	1.54561			0.0504389
$940$	0.946950	−	1.30689i	0.0308861	−	0.0426260i
$941$	14.4691			0.471680			0.235840	−	0.971792i	$-0.424216\pi$
$941$	14.4691			0.471680			0.235840	+	0.971792i	$0.424216\pi$
$942$		−	16.6991i		−	0.544086i
$943$			4.51249i			0.146947i
$944$	51.8863			1.68876
$945$	−7.23027	−	5.23893i	−0.235201	−	0.170423i
$946$	−2.24066			−0.0728500
$947$			39.9191i			1.29720i	0.761131	+	0.648598i	$0.224645\pi$
$947$			39.9191i			1.29720i	−0.761131	+	0.648598i	$0.775355\pi$
$948$		−	3.47710i		−	0.112931i
$949$	−13.6806			−0.444091
$950$	7.63046	−	2.50096i	0.247565	−	0.0811417i
$951$	−3.34825			−0.108574
$952$		−	2.83604i		−	0.0919167i
$953$			37.7433i			1.22262i	0.791390	+	0.611312i	$0.209358\pi$
$953$			37.7433i			1.22262i	−0.791390	+	0.611312i	$0.790642\pi$
$954$	34.8368			1.12788
$955$	−2.35868	−	1.70906i	−0.0763251	−	0.0553040i
$956$	−1.17002			−0.0378412
$957$		−	8.06548i		−	0.260720i
$958$		−	39.8174i		−	1.28644i
$959$	12.6274			0.407762
$960$	4.61826	−	6.37368i	0.149054	−	0.205710i
$961$	−30.9317			−0.997796
$962$		−	18.0000i		−	0.580342i
$963$		−	36.7960i		−	1.18573i
$964$	−5.31148			−0.171071
$965$	−18.3539	+	25.3303i	−0.590834	+	0.815412i
$966$	−1.66358			−0.0535249
$967$		−	24.0313i		−	0.772796i	−0.922332	−	0.386398i	$-0.873719\pi$
$967$		−	24.0313i		−	0.772796i	0.922332	−	0.386398i	$-0.126281\pi$
$968$		−	2.28185i		−	0.0733414i
$969$	−1.01175			−0.0325021
$970$	−1.07866	−	0.781579i	−0.0346337	−	0.0250950i
$971$	−6.37141			−0.204468			−0.102234	−	0.994760i	$-0.532599\pi$
$971$	−6.37141			−0.204468			−0.102234	+	0.994760i	$0.532599\pi$
$972$			9.04977i			0.290272i
$973$		−	8.04444i		−	0.257893i
$974$	67.3281			2.15733
$975$	−5.94118	−	18.1267i	−0.190270	−	0.580518i
$976$	−65.7167			−2.10354
$977$		−	30.5715i		−	0.978069i	−0.872264	−	0.489035i	$-0.837349\pi$
$977$		−	30.5715i		−	0.978069i	0.872264	−	0.489035i	$-0.162651\pi$
$978$			21.3536i			0.682813i
$979$	−8.73496			−0.279170
$980$	6.38768	+	4.62841i	0.204047	+	0.147849i
$981$	23.2966			0.743805
$982$		−	46.8260i		−	1.49428i
$983$			16.5777i			0.528748i	0.964420	+	0.264374i	$0.0851653\pi$
$983$			16.5777i			0.528748i	−0.964420	+	0.264374i	$0.914835\pi$
$984$	5.70631			0.181910
$985$	−31.6305	+	43.6533i	−1.00783	+	1.39091i
$986$	21.7623			0.693052
$987$		−	0.921918i		−	0.0293450i
$988$			2.84725i			0.0905831i
$989$	1.95368			0.0621234
$990$	5.05228	−	6.97267i	0.160572	−	0.221606i
$991$	50.4455			1.60245			0.801227	−	0.598360i	$-0.204181\pi$
$991$	50.4455			1.60245			0.801227	+	0.598360i	$0.204181\pi$
$992$		−	0.831600i		−	0.0264033i
$993$		−	22.8177i		−	0.724099i
$994$	−8.49605			−0.269478
$995$	−10.8113	−	7.83367i	−0.342740	−	0.248344i
$996$	4.42545			0.140226
$997$		−	5.98429i		−	0.189524i	−0.995500	−	0.0947622i	$-0.969791\pi$
$997$		−	5.98429i		−	0.189524i	0.995500	−	0.0947622i	$-0.0302091\pi$
$998$			19.5421i			0.618596i
$999$	9.54955			0.302135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.7	✓	22
5.2	odd	4		5225.2.a.bb.1.16		22
5.3	odd	4		5225.2.a.bb.1.7		22
5.4	even	2	inner	1045.2.b.d.419.16	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.7	✓	22	1.1	even	1	trivial
1045.2.b.d.419.16	yes	22	5.4	even	2	inner
5225.2.a.bb.1.7		22	5.3	odd	4
5225.2.a.bb.1.16		22	5.2	odd	4

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.60597i q^{2} -0.776012i q^{3} -0.579148 q^{4} +(-1.81070 - 1.31201i) q^{5} -1.24625 q^{6} +0.953282i q^{7} -2.28185i q^{8} +2.39780 q^{9} +O(q^{10})\)	\(q-1.60597i q^{2} -0.776012i q^{3} -0.579148 q^{4} +(-1.81070 - 1.31201i) q^{5} -1.24625 q^{6} +0.953282i q^{7} -2.28185i q^{8} +2.39780 q^{9} +(-2.10704 + 2.90794i) q^{10} -1.00000 q^{11} +0.449426i q^{12} -4.91628i q^{13} +1.53094 q^{14} +(-1.01813 + 1.40513i) q^{15} -4.82288 q^{16} -1.30378i q^{17} -3.85081i q^{18} +1.00000 q^{19} +(1.04866 + 0.759845i) q^{20} +0.739759 q^{21} +1.60597i q^{22} -1.40028i q^{23} -1.77074 q^{24} +(1.55728 + 4.75130i) q^{25} -7.89541 q^{26} -4.18876i q^{27} -0.552091i q^{28} -10.3935 q^{29} +(2.25660 + 1.63509i) q^{30} -0.261368 q^{31} +3.18172i q^{32} +0.776012i q^{33} -2.09384 q^{34} +(1.25071 - 1.72611i) q^{35} -1.38868 q^{36} +2.27980i q^{37} -1.60597i q^{38} -3.81509 q^{39} +(-2.99380 + 4.13175i) q^{40} -3.22255 q^{41} -1.18803i q^{42} +1.39520i q^{43} +0.579148 q^{44} +(-4.34171 - 3.14593i) q^{45} -2.24882 q^{46} -1.24624i q^{47} +3.74262i q^{48} +6.09125 q^{49} +(7.63046 - 2.50096i) q^{50} -1.01175 q^{51} +2.84725i q^{52} +9.04663i q^{53} -6.72704 q^{54} +(1.81070 + 1.31201i) q^{55} +2.17525 q^{56} -0.776012i q^{57} +16.6917i q^{58} -10.7584 q^{59} +(0.589649 - 0.813776i) q^{60} +13.6260 q^{61} +0.419750i q^{62} +2.28578i q^{63} -4.53601 q^{64} +(-6.45018 + 8.90192i) q^{65} +1.24625 q^{66} -3.94074i q^{67} +0.755082i q^{68} -1.08664 q^{69} +(-2.77208 - 2.00861i) q^{70} -5.54955 q^{71} -5.47143i q^{72} -2.78271i q^{73} +3.66130 q^{74} +(3.68707 - 1.20847i) q^{75} -0.579148 q^{76} -0.953282i q^{77} +6.12693i q^{78} -7.73676 q^{79} +(8.73280 + 6.32765i) q^{80} +3.94288 q^{81} +5.17532i q^{82} -9.84690i q^{83} -0.428430 q^{84} +(-1.71057 + 2.36076i) q^{85} +2.24066 q^{86} +8.06548i q^{87} +2.28185i q^{88} +8.73496 q^{89} +(-5.05228 + 6.97267i) q^{90} +4.68660 q^{91} +0.810972i q^{92} +0.202825i q^{93} -2.00143 q^{94} +(-1.81070 - 1.31201i) q^{95} +2.46905 q^{96} +0.370936i q^{97} -9.78239i q^{98} -2.39780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more