LMFDB - Embedded newform 882.2.bk.a.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(5,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("882.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bk (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	882.101
Dual form			882.2.bk.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 + 0.623490i) q^{2} +(-1.72915 - 0.100272i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.305069 - 4.07086i) q^{5} +(1.41442 - 0.999709i) q^{6} +(-0.770817 - 2.53098i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.97989 + 0.346769i) q^{9} +O(q^{10})$	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.72915 - 0.100272i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.305069 - 4.07086i) q^{5} +(1.41442 - 0.999709i) q^{6} +(-0.770817 - 2.53098i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.97989 + 0.346769i) q^{9} +(2.29963 + 3.37294i) q^{10} +(2.21561 + 0.869564i) q^{11} +(-0.482529 + 1.66348i) q^{12} +(3.62176 + 1.42143i) q^{13} +(2.18069 + 1.49820i) q^{14} +(-0.935701 + 7.00853i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(7.07536 + 2.18246i) q^{17} +(-2.54598 + 1.58682i) q^{18} +(1.05396 - 0.608506i) q^{19} +(-3.90091 - 1.20327i) q^{20} +(1.07907 + 4.45372i) q^{21} +(-2.27440 + 0.701559i) q^{22} +(2.61048 - 2.81342i) q^{23} +(-0.659907 - 1.60141i) q^{24} +(-11.5347 - 1.73858i) q^{25} +(-3.71785 + 1.14681i) q^{26} +(-5.11790 - 0.898413i) q^{27} +(-2.63904 + 0.188296i) q^{28} +(2.24347 - 7.27314i) q^{29} +(-3.63819 - 6.06289i) q^{30} -7.48579i q^{31} +(0.974928 - 0.222521i) q^{32} +(-3.74392 - 1.72577i) q^{33} +(-6.89248 + 2.70510i) q^{34} +(-10.5384 + 2.36577i) q^{35} +(1.00116 - 2.82802i) q^{36} +(2.94529 - 2.73283i) q^{37} +(-0.444624 + 1.13288i) q^{38} +(-6.12001 - 2.82103i) q^{39} +(3.80009 - 1.49142i) q^{40} +(7.80796 + 5.32338i) q^{41} +(-3.62050 - 2.80927i) q^{42} +(-1.96956 + 1.34283i) q^{43} +(1.34078 - 1.96657i) q^{44} +(2.32072 - 12.0249i) q^{45} +(-0.286811 + 3.82723i) q^{46} +(2.97133 + 3.72594i) q^{47} +(1.51440 + 0.840590i) q^{48} +(-5.81168 + 3.90184i) q^{49} +(10.1022 - 5.83250i) q^{50} +(-12.0155 - 4.48325i) q^{51} +(2.19171 - 3.21465i) q^{52} +(-7.15775 + 7.71422i) q^{53} +(4.56148 - 2.48855i) q^{54} +(4.21579 - 8.75418i) q^{55} +(1.94589 - 1.79263i) q^{56} +(-1.88347 + 0.946513i) q^{57} +(2.78072 + 7.08515i) q^{58} +(-2.90645 - 1.39967i) q^{59} +(6.62460 + 2.47179i) q^{60} +(7.59246 - 1.73293i) q^{61} +(4.66731 + 5.85263i) q^{62} +(-1.41929 - 7.80933i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.89135 - 14.3100i) q^{65} +(4.00311 - 0.985040i) q^{66} -15.1936 q^{67} +(3.70216 - 6.41232i) q^{68} +(-4.79600 + 4.60306i) q^{69} +(6.76423 - 8.42023i) q^{70} +(-6.44655 - 1.47138i) q^{71} +(0.980498 + 2.83525i) q^{72} +(-5.03785 + 1.97721i) q^{73} +(-0.598829 + 3.97297i) q^{74} +(19.7709 + 4.16286i) q^{75} +(-0.358720 - 1.16294i) q^{76} +(0.493014 - 6.27794i) q^{77} +(6.54370 - 1.61020i) q^{78} +3.63132 q^{79} +(-2.04114 + 3.53536i) q^{80} +(8.75950 + 2.06667i) q^{81} +(-9.42359 + 0.706200i) q^{82} +(2.09352 + 5.33419i) q^{83} +(4.58217 - 0.0609697i) q^{84} +(11.0430 - 28.1370i) q^{85} +(0.702629 - 2.27787i) q^{86} +(-4.60857 + 12.3514i) q^{87} +(0.177868 + 2.37349i) q^{88} +(10.7527 + 1.62072i) q^{89} +(5.68302 + 10.8484i) q^{90} +(0.805906 - 10.2622i) q^{91} +(-2.16200 - 3.17107i) q^{92} +(-0.750613 + 12.9440i) q^{93} +(-4.64617 - 1.06046i) q^{94} +(-2.15561 - 4.47618i) q^{95} +(-1.70811 + 0.287013i) q^{96} +(-7.24090 - 4.18054i) q^{97} +(2.11100 - 6.67411i) q^{98} +(6.30074 + 3.35951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9	$ 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) $ 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^15 - 112 * q^16 + 18 * q^17 + 8 * q^18 + 12 * q^21 + 18 * q^23 + 56 * q^25 - 12 * q^26 + 48 * q^27 + 2 * q^28 - 6 * q^29 + 4 * q^30 - 30 * q^35 - 10 * q^36 - 26 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^42 + 2 * q^43 + 58 * q^45 + 78 * q^46 - 90 * q^47 + 8 * q^49 + 24 * q^50 + 6 * q^51 - 22 * q^52 + 12 * q^53 - 18 * q^54 - 42 * q^55 - 6 * q^56 - 28 * q^57 + 78 * q^58 - 60 * q^59 - 6 * q^60 + 98 * q^61 - 36 * q^62 - 36 * q^63 + 112 * q^64 - 24 * q^66 + 28 * q^67 - 18 * q^68 + 14 * q^69 + 18 * q^70 + 126 * q^71 - 8 * q^72 - 18 * q^74 - 102 * q^75 + 42 * q^77 - 8 * q^78 - 8 * q^79 + 26 * q^81 + 30 * q^84 + 80 * q^87 - 186 * q^89 - 102 * q^90 + 12 * q^91 - 18 * q^92 - 224 * q^93 - 6 * q^97 + 24 * q^98 + 194 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.781831	+	0.623490i	−0.552838	+	0.440874i
$2$	−0.781831	+	0.623490i	−0.552838	+	0.440874i
$3$	−1.72915	−	0.100272i	−0.998323	−	0.0578919i
$3$	−1.72915	−	0.100272i	−0.998323	−	0.0578919i
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	0.305069	−	4.07086i	0.136431	−	1.82055i	−0.338993	−	0.940789i	$-0.610086\pi$
$5$	0.305069	−	4.07086i	0.136431	−	1.82055i	0.475424	−	0.879757i	$-0.342295\pi$
$6$	1.41442	−	0.999709i	0.577434	−	0.408130i
$7$	−0.770817	−	2.53098i	−0.291341	−	0.956619i
$7$	−0.770817	−	2.53098i	−0.291341	−	0.956619i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$	2.97989	+	0.346769i	0.993297	+	0.115590i
$10$	2.29963	+	3.37294i	0.727207	+	1.06662i
$11$	2.21561	+	0.869564i	0.668032	+	0.262183i	0.675028	−	0.737792i	$-0.264132\pi$
$11$	2.21561	+	0.869564i	0.668032	+	0.262183i	−0.00699573	+	0.999976i	$0.502227\pi$
$12$	−0.482529	+	1.66348i	−0.139294	+	0.480205i
$13$	3.62176	+	1.42143i	1.00449	+	0.394235i	0.809849	−	0.586639i	$-0.199549\pi$
$13$	3.62176	+	1.42143i	1.00449	+	0.394235i	0.194645	+	0.980874i	$0.437644\pi$
$14$	2.18069	+	1.49820i	0.582813	+	0.400411i
$15$	−0.935701	+	7.00853i	−0.241597	+	1.80959i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	7.07536	+	2.18246i	1.71603	+	0.529324i	0.987762	−	0.155971i	$-0.0498505\pi$
$17$	7.07536	+	2.18246i	1.71603	+	0.529324i	0.728266	+	0.685295i	$0.240327\pi$
$18$	−2.54598	+	1.58682i	−0.600093	+	0.374016i
$19$	1.05396	−	0.608506i	0.241796	−	0.139601i	−0.374206	−	0.927346i	$-0.622085\pi$
$19$	1.05396	−	0.608506i	0.241796	−	0.139601i	0.616002	+	0.787745i	$0.288751\pi$
$20$	−3.90091	−	1.20327i	−0.872271	−	0.269060i
$21$	1.07907	+	4.45372i	0.235472	+	0.971881i
$22$	−2.27440	+	0.701559i	−0.484904	+	0.149573i
$23$	2.61048	−	2.81342i	0.544322	−	0.586639i	−0.399649	−	0.916668i	$-0.630868\pi$
$23$	2.61048	−	2.81342i	0.544322	−	0.586639i	0.943971	+	0.330029i	$0.107058\pi$
$24$	−0.659907	−	1.60141i	−0.134703	−	0.326887i
$25$	−11.5347	−	1.73858i	−2.30694	−	0.347716i
$26$	−3.71785	+	1.14681i	−0.729131	+	0.224907i
$27$	−5.11790	−	0.898413i	−0.984939	−	0.172900i
$28$	−2.63904	+	0.188296i	−0.498732	+	0.0355846i
$29$	2.24347	−	7.27314i	0.416601	−	1.35059i	−0.467789	−	0.883840i	$-0.654949\pi$
$29$	2.24347	−	7.27314i	0.416601	−	1.35059i	0.884390	−	0.466748i	$-0.154575\pi$
$30$	−3.63819	−	6.06289i	−0.664239	−	1.10693i
$31$		−	7.48579i		−	1.34449i	−0.740330	−	0.672244i	$-0.765331\pi$
$31$		−	7.48579i		−	1.34449i	0.740330	−	0.672244i	$-0.234669\pi$
$32$	0.974928	−	0.222521i	0.172345	−	0.0393365i
$33$	−3.74392	−	1.72577i	−0.651733	−	0.300417i
$34$	−6.89248	+	2.70510i	−1.18205	+	0.463921i
$35$	−10.5384	+	2.36577i	−1.78132	+	0.399888i
$36$	1.00116	−	2.82802i	0.166860	−	0.471336i
$37$	2.94529	−	2.73283i	0.484203	−	0.449275i	−0.399906	−	0.916556i	$-0.630957\pi$
$37$	2.94529	−	2.73283i	0.484203	−	0.449275i	0.884108	+	0.467282i	$0.154767\pi$
$38$	−0.444624	+	1.13288i	−0.0721276	+	0.183778i
$39$	−6.12001	−	2.82103i	−0.979986	−	0.451726i
$40$	3.80009	−	1.49142i	0.600846	−	0.235815i
$41$	7.80796	+	5.32338i	1.21940	+	0.831372i	0.989877	−	0.141931i	$-0.0453311\pi$
$41$	7.80796	+	5.32338i	1.21940	+	0.831372i	0.229523	+	0.973303i	$0.426284\pi$
$42$	−3.62050	−	2.80927i	−0.558655	−	0.433480i
$43$	−1.96956	+	1.34283i	−0.300356	+	0.204779i	−0.704115	−	0.710086i	$-0.748656\pi$
$43$	−1.96956	+	1.34283i	−0.300356	+	0.204779i	0.403759	+	0.914865i	$0.367703\pi$
$44$	1.34078	−	1.96657i	0.202130	−	0.296471i
$45$	2.32072	−	12.0249i	0.345953	−	1.79257i
$46$	−0.286811	+	3.82723i	−0.0422880	+	0.564294i
$47$	2.97133	+	3.72594i	0.433414	+	0.543484i	0.949794	−	0.312876i	$-0.101292\pi$
$47$	2.97133	+	3.72594i	0.433414	+	0.543484i	−0.516380	+	0.856359i	$0.672721\pi$
$48$	1.51440	+	0.840590i	0.218585	+	0.121329i
$49$	−5.81168	+	3.90184i	−0.830240	+	0.557406i
$50$	10.1022	−	5.83250i	1.42867	−	0.824840i
$51$	−12.0155	−	4.48325i	−1.68251	−	0.627781i
$52$	2.19171	−	3.21465i	0.303936	−	0.445792i
$53$	−7.15775	+	7.71422i	−0.983192	+	1.05963i	0.0150214	+	0.999887i	$0.495218\pi$
$53$	−7.15775	+	7.71422i	−0.983192	+	1.05963i	−0.998214	+	0.0597422i	$0.980972\pi$
$54$	4.56148	−	2.48855i	0.620739	−	0.338649i
$55$	4.21579	−	8.75418i	0.568457	−	1.18041i
$56$	1.94589	−	1.79263i	0.260030	−	0.239550i
$57$	−1.88347	+	0.946513i	−0.249472	+	0.125369i
$58$	2.78072	+	7.08515i	0.365126	+	0.930326i
$59$	−2.90645	−	1.39967i	−0.378387	−	0.182222i	0.235016	−	0.971992i	$-0.424486\pi$
$59$	−2.90645	−	1.39967i	−0.378387	−	0.182222i	−0.613403	+	0.789770i	$0.710200\pi$
$60$	6.62460	+	2.47179i	0.855232	+	0.319106i
$61$	7.59246	−	1.73293i	0.972115	−	0.221879i	0.293164	−	0.956062i	$-0.405292\pi$
$61$	7.59246	−	1.73293i	0.972115	−	0.221879i	0.678951	+	0.734183i	$0.262435\pi$
$62$	4.66731	+	5.85263i	0.592750	+	0.743284i
$63$	−1.41929	−	7.80933i	−0.178813	−	0.983883i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	6.89135	−	14.3100i	0.854767	−	1.77494i
$66$	4.00311	−	0.985040i	0.492749	−	0.121250i
$67$	−15.1936			−1.85619			−0.928097	−	0.372339i	$-0.878556\pi$
$67$	−15.1936			−1.85619			−0.928097	+	0.372339i	$0.878556\pi$
$68$	3.70216	−	6.41232i	0.448953	−	0.777609i
$69$	−4.79600	+	4.60306i	−0.577371	+	0.554144i
$70$	6.76423	−	8.42023i	0.808480	−	1.00641i
$71$	−6.44655	−	1.47138i	−0.765064	−	0.174621i	−0.177856	−	0.984057i	$-0.556916\pi$
$71$	−6.44655	−	1.47138i	−0.765064	−	0.174621i	−0.587209	+	0.809436i	$0.699773\pi$
$72$	0.980498	+	2.83525i	0.115553	+	0.334137i
$73$	−5.03785	+	1.97721i	−0.589636	+	0.231415i	−0.641352	−	0.767247i	$-0.721626\pi$
$73$	−5.03785	+	1.97721i	−0.589636	+	0.231415i	0.0517160	+	0.998662i	$0.483531\pi$
$74$	−0.598829	+	3.97297i	−0.0696125	+	0.461849i
$75$	19.7709	+	4.16286i	2.28294	+	0.480686i
$76$	−0.358720	−	1.16294i	−0.0411481	−	0.133399i
$77$	0.493014	−	6.27794i	0.0561841	−	0.715437i
$78$	6.54370	−	1.61020i	0.740928	−	0.182319i
$79$	3.63132			0.408555			0.204277	−	0.978913i	$-0.434516\pi$
$79$	3.63132			0.408555			0.204277	+	0.978913i	$0.434516\pi$
$80$	−2.04114	+	3.53536i	−0.228206	+	0.395265i
$81$	8.75950	+	2.06667i	0.973278	+	0.229630i
$82$	−9.42359	+	0.706200i	−1.04066	+	0.0779868i
$83$	2.09352	+	5.33419i	0.229793	+	0.585504i	0.998538	−	0.0540518i	$-0.0172136\pi$
$83$	2.09352	+	5.33419i	0.229793	+	0.585504i	−0.768745	+	0.639556i	$0.779118\pi$
$84$	4.58217	−	0.0609697i	0.499956	−	0.00665234i
$85$	11.0430	−	28.1370i	1.19778	−	3.05189i
$86$	0.702629	−	2.27787i	0.0757664	−	0.245629i
$87$	−4.60857	+	12.3514i	−0.494091	+	1.32421i
$88$	0.177868	+	2.37349i	0.0189608	+	0.253015i
$89$	10.7527	+	1.62072i	1.13979	+	0.171796i	0.691694	−	0.722191i	$-0.256865\pi$
$89$	10.7527	+	1.62072i	1.13979	+	0.171796i	0.448095	+	0.893986i	$0.352103\pi$
$90$	5.68302	+	10.8484i	0.599043	+	1.14352i
$91$	0.805906	−	10.2622i	0.0844819	−	1.07578i
$92$	−2.16200	−	3.17107i	−0.225404	−	0.330607i
$93$	−0.750613	+	12.9440i	−0.0778349	+	1.34223i
$94$	−4.64617	−	1.06046i	−0.479215	−	0.109378i
$95$	−2.15561	−	4.47618i	−0.221161	−	0.459246i
$96$	−1.70811	+	0.287013i	−0.174333	+	0.0292932i
$97$	−7.24090	−	4.18054i	−0.735202	−	0.424469i	0.0851201	−	0.996371i	$-0.472873\pi$
$97$	−7.24090	−	4.18054i	−0.735202	−	0.424469i	−0.820322	+	0.571902i	$0.806206\pi$
$98$	2.11100	−	6.67411i	0.213243	−	0.674186i
$99$	6.30074	+	3.35951i	0.633249	+	0.337643i
$100$	−4.26170	+	10.8586i	−0.426170	+	1.08586i
$101$	8.24538	+	5.62160i	0.820446	+	0.559370i	0.899207	−	0.437523i	$-0.144144\pi$
$101$	8.24538	+	5.62160i	0.820446	+	0.559370i	−0.0787615	+	0.996893i	$0.525097\pi$
$102$	12.1894	−	3.98639i	1.20693	−	0.394712i
$103$	−3.14465	−	0.235659i	−0.309852	−	0.0232202i	−0.0811033	−	0.996706i	$-0.525844\pi$
$103$	−3.14465	−	0.235659i	−0.309852	−	0.0232202i	−0.228749	+	0.973486i	$0.573463\pi$
$104$	0.290753	+	3.87983i	0.0285107	+	0.380448i
$105$	18.4597	−	3.03405i	1.80148	−	0.296093i
$106$	0.786417	−	10.4940i	0.0763835	−	1.01927i
$107$	0.348969	−	2.31526i	0.0337361	−	0.223825i	−0.965609	−	0.259997i	$-0.916278\pi$
$107$	0.348969	−	2.31526i	0.0337361	−	0.223825i	0.999346	+	0.0361724i	$0.0115165\pi$
$108$	−2.01473	+	4.78966i	−0.193867	+	0.460886i
$109$	−16.5851	+	2.49980i	−1.58856	+	0.239438i	−0.883057	−	0.469265i	$-0.844519\pi$
$109$	−16.5851	+	2.49980i	−1.58856	+	0.239438i	−0.705507	+	0.708703i	$0.749281\pi$
$110$	2.16210	+	9.47279i	0.206148	+	0.903195i
$111$	−5.36686	+	4.43013i	−0.509400	+	0.420490i
$112$	−0.403667	+	2.61478i	−0.0381430	+	0.247073i
$113$	0.721934	−	4.78972i	0.0679139	−	0.450579i	−0.928868	−	0.370412i	$-0.879217\pi$
$113$	0.721934	−	4.78972i	0.0679139	−	0.450579i	0.996781	−	0.0801671i	$-0.0255454\pi$
$114$	0.882416	−	1.91434i	0.0826459	−	0.179294i
$115$	−10.6567	−	11.4852i	−0.993741	−	1.07100i
$116$	−6.59157	−	3.80565i	−0.612012	−	0.353345i
$117$	10.2995	+	5.49163i	0.952192	+	0.507701i
$118$	3.14503	−	0.717834i	0.289524	−	0.0660819i
$119$	0.0699456	−	19.5899i	0.00641190	−	1.79580i
$120$	−6.72045	+	2.19785i	−0.613490	+	0.200635i
$121$	−3.91078	−	3.62867i	−0.355525	−	0.329879i
$122$	−4.85556	+	6.08868i	−0.439602	+	0.551243i
$123$	−12.9673	−	9.98782i	−1.16922	−	0.900571i
$124$	−7.29811	−	1.66575i	−0.655389	−	0.149588i
$125$	−6.05444	+	26.5262i	−0.541525	+	2.37258i
$126$	5.97868	+	5.22067i	0.532623	+	0.465094i
$127$	4.53417	+	19.8655i	0.402343	+	1.76278i	0.617869	+	0.786281i	$0.287996\pi$
$127$	4.53417	+	19.8655i	0.402343	+	1.76278i	−0.215526	+	0.976498i	$0.569147\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.54031	−	2.12445i	0.311707	−	0.187047i
$130$	3.53429	+	15.4847i	0.309978	+	1.35810i
$131$	1.69553	−	1.15599i	0.148139	−	0.100999i	−0.486983	−	0.873412i	$-0.661902\pi$
$131$	1.69553	−	1.15599i	0.148139	−	0.100999i	0.635121	+	0.772412i	$0.280950\pi$
$132$	−2.51560	+	3.26604i	−0.218955	+	0.284272i
$133$	−2.35253	−	2.19851i	−0.203990	−	0.190635i
$134$	11.8788	−	9.47306i	1.02618	−	0.818347i
$135$	−5.21863	+	20.5602i	−0.449148	+	1.76954i
$136$	1.10356	+	7.32161i	0.0946291	+	0.627823i
$137$	5.38132	−	0.403274i	0.459757	−	0.0344541i	0.157161	−	0.987573i	$-0.449766\pi$
$137$	5.38132	−	0.403274i	0.459757	−	0.0344541i	0.302596	+	0.953119i	$0.402147\pi$
$138$	0.879701	−	6.58908i	0.0748851	−	0.560899i
$139$	9.52553	−	13.9714i	0.807945	−	1.18504i	−0.171868	−	0.985120i	$-0.554980\pi$
$139$	9.52553	−	13.9714i	0.807945	−	1.18504i	0.979813	−	0.199918i	$-0.0640675\pi$
$140$	−0.0385636	+	10.8006i	−0.00325922	+	0.912820i
$141$	−4.76427	−	6.74063i	−0.401224	−	0.567663i
$142$	5.95751	−	2.86898i	0.499943	−	0.240760i
$143$	6.78838	+	6.29869i	0.567673	+	0.526723i
$144$	−2.53433	−	1.60535i	−0.211194	−	0.133780i
$145$	−28.9236	−	11.3517i	−2.40197	−	0.942704i
$146$	2.70598	−	4.68690i	0.223949	−	0.387890i
$147$	10.4405	−	6.16410i	0.861117	−	0.508407i
$148$	−2.00892	−	3.47956i	−0.165133	−	0.286018i
$149$	−1.04232	−	6.91536i	−0.0853904	−	0.566528i	−0.990085	−	0.140468i	$-0.955139\pi$
$149$	−1.04232	−	6.91536i	−0.0853904	−	0.566528i	0.904695	−	0.426060i	$-0.140099\pi$
$150$	−18.0530	+	9.07228i	−1.47402	+	0.740749i
$151$	2.15270	−	0.664020i	0.175184	−	0.0540372i	−0.205922	−	0.978568i	$-0.566019\pi$
$151$	2.15270	−	0.664020i	0.175184	−	0.0540372i	0.381106	+	0.924531i	$0.375543\pi$
$152$	1.00554	+	0.685567i	0.0815602	+	0.0556068i
$153$	20.3270	+	8.95701i	1.64334	+	0.724131i
$154$	3.52878	+	5.21568i	0.284357	+	0.420291i
$155$	−30.4736	−	2.28368i	−2.44770	−	0.183430i
$156$	−4.11213	+	5.33883i	−0.329234	+	0.427449i
$157$	−4.17400	+	8.66741i	−0.333122	+	0.691734i	−0.998499	−	0.0547731i	$-0.982556\pi$
$157$	−4.17400	+	8.66741i	−0.333122	+	0.691734i	0.665377	+	0.746507i	$0.268271\pi$
$158$	−2.83908	+	2.26409i	−0.225865	+	0.180121i
$159$	13.1503	−	12.6213i	1.04289	−	1.00093i
$160$	−0.608432	−	4.03668i	−0.0481008	−	0.319128i
$161$	−9.13291	−	4.43842i	−0.719774	−	0.349796i
$162$	−8.13700	+	3.84568i	−0.639303	+	0.302145i
$163$	0.958172	+	12.7859i	0.0750499	+	1.00147i	0.899893	+	0.436110i	$0.143644\pi$
$163$	0.958172	+	12.7859i	0.0750499	+	1.00147i	−0.824844	+	0.565361i	$0.808737\pi$
$164$	6.92735	−	6.42764i	0.540935	−	0.501914i
$165$	−8.16751	+	14.7145i	−0.635840	+	1.14552i
$166$	−4.96259	−	2.86515i	−0.385172	−	0.222379i
$167$	−4.33640	+	4.02359i	−0.335561	+	0.311355i	−0.829898	−	0.557915i	$-0.811601\pi$
$167$	−4.33640	+	4.02359i	−0.335561	+	0.311355i	0.494337	+	0.869270i	$0.335411\pi$
$168$	−3.54447	+	2.90460i	−0.273462	+	0.224095i
$169$	1.56696	+	1.45393i	0.120536	+	0.111841i
$170$	8.90941	+	28.8836i	0.683321	+	2.21527i
$171$	3.35171	−	1.44780i	0.256311	−	0.110716i
$172$	0.870890	+	2.21899i	0.0664047	+	0.169196i
$173$	−2.09746	+	9.18955i	−0.159467	+	0.698669i	0.830459	+	0.557080i	$0.188078\pi$
$173$	−2.09746	+	9.18955i	−0.159467	+	0.698669i	−0.989926	+	0.141589i	$0.954779\pi$
$174$	−4.09783	−	12.5301i	−0.310655	−	0.949904i
$175$	4.49085	+	30.5342i	0.339477	+	2.30817i
$176$	−1.61891	−	1.74477i	−0.122030	−	0.131517i
$177$	4.88533	+	2.71167i	0.367204	+	0.203822i
$178$	−9.41734	+	5.43710i	−0.705859	+	0.407528i
$179$	−5.00947	+	16.2403i	−0.374425	+	1.21386i	0.550864	+	0.834595i	$0.314298\pi$
$179$	−5.00947	+	16.2403i	−0.374425	+	1.21386i	−0.925289	+	0.379262i	$0.876178\pi$
$180$	−11.2070	−	4.93834i	−0.835324	−	0.368082i
$181$	−4.97565	−	3.96795i	−0.369837	−	0.294936i	0.420881	−	0.907116i	$-0.361721\pi$
$181$	−4.97565	−	3.96795i	−0.369837	−	0.294936i	−0.790718	+	0.612181i	$0.790293\pi$
$182$	5.76832	+	8.52582i	0.427576	+	0.631976i
$183$	−13.3022	+	2.23518i	−0.983329	+	0.165229i
$184$	3.66745	+	1.13126i	0.270368	+	0.0833975i
$185$	−10.2265	−	12.8236i	−0.751865	−	0.942809i
$186$	−7.48361	−	10.5880i	−0.548725	−	0.776353i
$187$	13.7785	+	10.9880i	1.00758	+	0.803519i
$188$	4.29370	−	2.06774i	0.313150	−	0.150805i
$189$	1.67110	+	13.6458i	0.121555	+	0.992585i
$190$	4.47618	+	2.15561i	0.324736	+	0.156385i
$191$	−0.345532	−	0.717505i	−0.0250018	−	0.0519168i	0.888094	−	0.459662i	$-0.152029\pi$
$191$	−0.345532	−	0.717505i	−0.0250018	−	0.0519168i	−0.913096	+	0.407745i	$0.866315\pi$
$192$	1.15650	−	1.28938i	0.0834632	−	0.0930532i
$193$	−5.70814	+	2.74889i	−0.410881	+	0.197870i	−0.627894	−	0.778299i	$-0.716083\pi$
$193$	−5.70814	+	2.74889i	−0.410881	+	0.197870i	0.217013	+	0.976169i	$0.430369\pi$
$194$	8.26769	−	1.24615i	0.593585	−	0.0894686i
$195$	−13.3510	+	24.0531i	−0.956088	+	1.72248i
$196$	2.51079	+	6.53421i	0.179342	+	0.466729i
$197$		−	9.06447i		−	0.645817i	−0.946430	−	0.322908i	$-0.895339\pi$
$197$		−	9.06447i		−	0.645817i	0.946430	−	0.322908i	$-0.104661\pi$
$198$	−7.02074	+	1.30188i	−0.498942	+	0.0925205i
$199$	6.79866	+	0.509489i	0.481945	+	0.0361167i	0.313488	−	0.949592i	$-0.398503\pi$
$199$	6.79866	+	0.509489i	0.481945	+	0.0361167i	0.168457	+	0.985709i	$0.446122\pi$
$200$	−3.43832	−	11.1468i	−0.243126	−	0.788195i
$201$	26.2720	+	1.52349i	1.85308	+	0.107459i
$202$	−9.95151	+	0.745762i	−0.700186	+	0.0524717i
$203$	−20.1375	−	0.0719008i	−1.41337	−	0.00504645i
$204$	−7.04455	+	10.7166i	−0.493217	+	0.750314i
$205$	24.0527	−	30.1612i	1.67992	−	2.10655i
$206$	2.60552	−	1.77641i	0.181535	−	0.123769i
$207$	8.75454	−	7.47846i	0.608483	−	0.519789i
$208$	−2.64635	−	2.85209i	−0.183491	−	0.197757i
$209$	2.86431	−	0.431725i	0.198128	−	0.0298630i
$210$	−12.5407	+	13.8815i	−0.865387	+	0.957917i
$211$	−1.15334	−	0.173839i	−0.0793994	−	0.0119675i	0.109222	−	0.994017i	$-0.465164\pi$
$211$	−1.15334	−	0.173839i	−0.0793994	−	0.0119675i	−0.188622	+	0.982050i	$0.560402\pi$
$212$	5.92806	+	8.69486i	0.407141	+	0.597166i
$213$	10.9995	+	3.19064i	0.753672	+	0.218619i
$214$	1.17071	+	2.02772i	0.0800278	+	0.138612i
$215$	4.86561	+	8.42748i	0.331832	+	0.574750i
$216$	−1.41113	−	5.00087i	−0.0960152	−	0.340266i
$217$	−18.9464	+	5.77017i	−1.28616	+	0.391705i
$218$	11.4082	−	12.2951i	0.772658	−	0.832727i
$219$	8.90944	−	2.91373i	0.602044	−	0.196892i
$220$	−7.59659	−	6.05808i	−0.512162	−	0.408436i
$221$	22.5230	+	17.9615i	1.51506	+	1.20822i
$222$	1.43384	−	6.80980i	0.0962330	−	0.457044i
$223$	2.59306	−	2.79466i	0.173644	−	0.187144i	−0.640233	−	0.768181i	$-0.721162\pi$
$223$	2.59306	−	2.79466i	0.173644	−	0.187144i	0.813877	+	0.581037i	$0.197353\pi$
$224$	−1.31469	−	2.29600i	−0.0878412	−	0.153408i
$225$	−33.7693	−	9.18065i	−2.25129	−	0.612044i
$226$	2.42191	+	4.19487i	0.161103	+	0.279039i
$227$	−5.92584	−	10.2639i	−0.393312	−	0.681236i	0.599572	−	0.800321i	$-0.295337\pi$
$227$	−5.92584	−	10.2639i	−0.393312	−	0.681236i	−0.992884	+	0.119084i	$0.962004\pi$
$228$	0.503670	+	2.04687i	0.0333563	+	0.135557i
$229$	−2.45681	−	3.60348i	−0.162351	−	0.238125i	0.736440	−	0.676503i	$-0.236505\pi$
$229$	−2.45681	−	3.60348i	−0.162351	−	0.238125i	−0.898791	+	0.438378i	$0.855553\pi$
$230$	15.4926	+	2.33514i	1.02155	+	0.153974i
$231$	−1.48199	+	10.8060i	−0.0975079	+	0.710985i
$232$	7.52628	−	1.13440i	0.494124	−	0.0744773i
$233$	10.1733	+	10.9643i	0.666478	+	0.718292i	0.972284	−	0.233801i	$-0.0751165\pi$
$233$	10.1733	+	10.9643i	0.666478	+	0.718292i	−0.305806	+	0.952094i	$0.598926\pi$
$234$	−11.4765	+	2.12812i	−0.750240	+	0.139120i
$235$	16.0742	−	10.9592i	1.04857	−	0.714901i
$236$	−2.01133	+	2.52212i	−0.130926	+	0.164176i
$237$	−6.27907	−	0.364118i	−0.407870	−	0.0236520i
$238$	12.1594	+	15.3596i	0.788176	+	0.995613i
$239$	16.9874	−	1.27303i	1.09882	−	0.0823453i	0.487046	−	0.873377i	$-0.338075\pi$
$239$	16.9874	−	1.27303i	1.09882	−	0.0823453i	0.611776	+	0.791031i	$0.290456\pi$
$240$	3.88392	−	5.90848i	0.250706	−	0.381391i
$241$	4.93713	+	16.0058i	0.318028	+	1.03102i	0.963606	+	0.267327i	$0.0861405\pi$
$241$	4.93713	+	16.0058i	0.318028	+	1.03102i	−0.645578	+	0.763695i	$0.723383\pi$
$242$	5.32001	+	0.398679i	0.341983	+	0.0256281i
$243$	−14.9392	−	4.45190i	−0.958352	−	0.285589i
$244$		−	7.78771i		−	0.498557i
$245$	14.1109	+	24.8489i	0.901512	+	1.58754i
$246$	16.3656	−	0.276204i	1.04343	−	0.0176101i
$247$	4.68215	−	0.705720i	0.297918	−	0.0449039i
$248$	6.74446	−	3.24796i	0.428274	−	0.206246i
$249$	−3.08513	−	9.43352i	−0.195512	−	0.597825i
$250$	−11.8053	−	24.5139i	−0.746632	−	1.55040i
$251$	−18.3774	−	8.85010i	−1.15997	−	0.558614i	−0.247958	−	0.968771i	$-0.579760\pi$
$251$	−18.3774	−	8.85010i	−1.15997	−	0.558614i	−0.912015	+	0.410157i	$0.865474\pi$
$252$	−7.92935	−	0.354037i	−0.499502	−	0.0223022i
$253$	8.23025	−	3.96348i	0.517431	−	0.249182i
$254$	−15.9309	−	12.7045i	−0.999594	−	0.797149i
$255$	−21.9163	+	47.5457i	−1.37245	+	2.97743i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	1.57618	+	0.486187i	0.0983194	+	0.0303275i	0.343525	−	0.939144i	$-0.388379\pi$
$257$	1.57618	+	0.486187i	0.0983194	+	0.0303275i	−0.245205	+	0.969471i	$0.578855\pi$
$258$	−1.44335	+	3.86831i	−0.0898593	+	0.240831i
$259$	−9.18701	−	5.34795i	−0.570853	−	0.332305i
$260$	−12.4178	−	9.90285i	−0.770118	−	0.614149i
$261$	9.20739	−	20.8952i	0.569923	−	1.29338i
$262$	−0.604867	+	1.96093i	−0.0373688	+	0.121147i
$263$	−14.4020	+	8.31499i	−0.888065	+	0.512724i	−0.873309	−	0.487167i	$-0.838030\pi$
$263$	−14.4020	+	8.31499i	−0.888065	+	0.512724i	−0.0147557	+	0.999891i	$0.504697\pi$
$264$	−0.0695666	−	4.12194i	−0.00428153	−	0.253688i
$265$	29.2199	+	31.4916i	1.79497	+	1.93451i
$266$	3.21003	+	0.252087i	0.196819	+	0.0154565i
$267$	−18.4306	−	3.88065i	−1.12793	−	0.237492i
$268$	−3.38089	+	14.8127i	−0.206521	+	0.904828i
$269$	−10.2311	−	26.0684i	−0.623801	−	1.58942i	−0.796630	−	0.604467i	$-0.793386\pi$
$269$	−10.2311	−	26.0684i	−0.623801	−	1.58942i	0.172830	−	0.984952i	$-0.444709\pi$
$270$	−8.73898	−	19.3284i	−0.531837	−	1.17629i
$271$	1.51196	+	4.90165i	0.0918449	+	0.297754i	0.989827	−	0.142279i	$-0.0454430\pi$
$271$	1.51196	+	4.90165i	0.0918449	+	0.297754i	−0.897982	+	0.440033i	$0.854967\pi$
$272$	−5.42775	−	5.03621i	−0.329106	−	0.305365i
$273$	−2.42254	+	17.6641i	−0.146619	+	1.06908i
$274$	−3.95585	+	3.67049i	−0.238982	+	0.221743i
$275$	−24.0446	−	13.8822i	−1.44995	−	0.837127i
$276$	3.42044	+	5.70003i	0.205887	+	0.343102i
$277$	20.7801	−	19.2811i	1.24856	−	1.15849i	0.267752	−	0.963488i	$-0.413719\pi$
$277$	20.7801	−	19.2811i	1.24856	−	1.15849i	0.980803	−	0.195002i	$-0.0624714\pi$
$278$	1.26366	+	16.8623i	0.0757892	+	1.01134i
$279$	2.59584	−	22.3068i	0.155409	−	1.33548i
$280$	−6.70393	−	8.46831i	−0.400636	−	0.506079i
$281$	−2.02634	−	13.4439i	−0.120881	−	0.801994i	−0.964314	−	0.264760i	$-0.914707\pi$
$281$	−2.02634	−	13.4439i	−0.120881	−	0.801994i	0.843433	−	0.537234i	$-0.180531\pi$
$282$	7.92757	+	2.29956i	0.472080	+	0.136937i
$283$	7.54455	−	6.01657i	0.448477	−	0.357648i	−0.373057	−	0.927809i	$-0.621690\pi$
$283$	7.54455	−	6.01657i	0.448477	−	0.357648i	0.821533	+	0.570160i	$0.193119\pi$
$284$	−2.86898	+	5.95751i	−0.170243	+	0.353513i
$285$	3.27854	+	7.95611i	0.194204	+	0.471279i
$286$	−9.23454	−	0.692033i	−0.546050	−	0.0409208i
$287$	7.45484	−	23.8651i	0.440045	−	1.40871i
$288$	2.98234	−	0.325014i	0.175736	−	0.0191516i
$289$	31.2516	+	21.3070i	1.83833	+	1.25335i
$290$	29.6910	−	9.15846i	1.74352	−	0.537803i
$291$	12.1014	+	7.95482i	0.709396	+	0.466320i
$292$	0.806611	+	5.35151i	0.0472033	+	0.313174i
$293$	−4.72297	−	8.18042i	−0.275919	−	0.477905i	0.694448	−	0.719543i	$-0.255649\pi$
$293$	−4.72297	−	8.18042i	−0.275919	−	0.477905i	−0.970367	+	0.241638i	$0.922315\pi$
$294$	−4.31945	+	11.3288i	−0.251915	+	0.660711i
$295$	−6.58454	+	11.4048i	−0.383367	+	0.664011i
$296$	3.74011	+	1.46788i	0.217389	+	0.0853191i
$297$	−10.5580	−	6.44087i	−0.612640	−	0.373737i
$298$	5.12658	+	4.75677i	0.296975	+	0.275552i
$299$	13.4536	−	6.47891i	0.778042	−	0.374685i
$300$	8.45792	−	18.3489i	0.488318	−	1.05937i
$301$	4.91684	+	3.94985i	0.283402	+	0.227665i
$302$	−1.26904	+	1.86134i	−0.0730250	+	0.107108i
$303$	−13.6938	−	10.5473i	−0.786687	−	0.605929i
$304$	−1.21361	+	0.0909474i	−0.0696052	+	0.00521619i
$305$	−4.73829	−	31.4365i	−0.271314	−	1.80005i
$306$	−21.4769	+	5.67081i	−1.22775	+	0.324178i
$307$	−11.9426	+	9.52390i	−0.681600	+	0.543558i	−0.901938	−	0.431866i	$-0.857855\pi$
$307$	−11.9426	+	9.52390i	−0.681600	+	0.543558i	0.220338	+	0.975424i	$0.429284\pi$
$308$	−6.01083	−	1.87762i	−0.342499	−	0.106988i
$309$	5.41394	+	0.722809i	0.307988	+	0.0411192i
$310$	25.2491	−	17.2145i	1.43405	−	0.977721i
$311$	2.44833	+	10.7268i	0.138832	+	0.608262i	0.995693	+	0.0927143i	$0.0295543\pi$
$311$	2.44833	+	10.7268i	0.138832	+	0.608262i	−0.856861	+	0.515548i	$0.827589\pi$
$312$	−0.113717	−	6.73794i	−0.00643797	−	0.381461i
$313$		−	0.673555i		−	0.0380716i	−0.999819	−	0.0190358i	$-0.993940\pi$
$313$		−	0.673555i		−	0.0380716i	0.999819	−	0.0190358i	$-0.00605965\pi$
$314$	−2.14067	−	9.37890i	−0.120805	−	0.529282i
$315$	−32.2237	+	3.39534i	−1.81560	+	0.191306i
$316$	0.808044	−	3.54027i	0.0454560	−	0.199156i
$317$	−9.02952	−	2.06093i	−0.507148	−	0.115753i	−0.0387117	−	0.999250i	$-0.512325\pi$
$317$	−9.02952	−	2.06093i	−0.507148	−	0.115753i	−0.468437	+	0.883497i	$0.655183\pi$
$318$	−2.41208	+	18.0668i	−0.135263	+	1.01314i
$319$	11.2951	−	14.1636i	0.632405	−	0.793011i
$320$	2.99252	+	2.77665i	0.167287	+	0.155220i
$321$	−0.835573	+	3.96843i	−0.0466372	+	0.221496i
$322$	9.90770	−	2.22418i	0.552135	−	0.123949i
$323$	8.78521	−	2.00517i	0.488822	−	0.111570i
$324$	3.96402	−	8.08001i	0.220224	−	0.448889i
$325$	−39.3046	−	22.6925i	−2.18023	−	1.25876i
$326$	−8.72102	−	9.39903i	−0.483013	−	0.520564i
$327$	28.9287	−	2.65951i	1.59976	−	0.147071i
$328$	−1.40845	+	9.34446i	−0.0777687	+	0.515962i
$329$	7.13990	−	10.3924i	0.393635	−	0.572951i
$330$	−2.78874	−	16.5966i	−0.153515	−	0.913615i
$331$	7.49205	+	32.8248i	0.411801	+	1.80422i	0.575610	+	0.817724i	$0.304765\pi$
$331$	7.49205	+	32.8248i	0.411801	+	1.80422i	−0.163810	+	0.986492i	$0.552378\pi$
$332$	5.66631	−	0.854058i	0.310979	−	0.0468725i
$333$	9.72431	−	7.12220i	0.532889	−	0.390294i
$334$	0.881666	−	5.84947i	0.0482426	−	0.320069i
$335$	−4.63510	+	61.8511i	−0.253242	+	3.37929i
$336$	0.960188	−	4.48085i	0.0523825	−	0.244451i
$337$	0.0843084	+	1.12502i	0.00459257	+	0.0612836i	0.999029	−	0.0440530i	$-0.0140270\pi$
$337$	0.0843084	+	1.12502i	0.00459257	+	0.0612836i	−0.994437	+	0.105337i	$0.966408\pi$
$338$	−2.13161	−	0.159742i	−0.115944	−	0.00868882i
$339$	−1.72860	+	8.20974i	−0.0938849	+	0.445892i
$340$	−24.9743	−	17.0272i	−1.35442	−	0.923429i
$341$	6.50937	−	16.5856i	0.352502	−	0.898161i
$342$	−1.71778	+	3.22169i	−0.0928869	+	0.174209i
$343$	14.3552	+	11.7016i	0.775108	+	0.631828i
$344$	−2.06441	−	1.19189i	−0.111305	−	0.0642622i
$345$	17.2753	+	20.9281i	0.930073	+	1.12673i
$346$	−4.08974	−	8.49242i	−0.219866	−	0.456556i
$347$	−3.12343	−	0.712903i	−0.167675	−	0.0382706i	0.137859	−	0.990452i	$-0.455978\pi$
$347$	−3.12343	−	0.712903i	−0.167675	−	0.0382706i	−0.305534	+	0.952181i	$0.598835\pi$
$348$	11.0162	+	7.24147i	0.590530	+	0.388183i
$349$	−10.0790	−	14.7832i	−0.539517	−	0.791327i	0.455583	−	0.890193i	$-0.349431\pi$
$349$	−10.0790	−	14.7832i	−0.539517	−	0.791327i	−0.995101	+	0.0988665i	$0.968478\pi$
$350$	−22.5489	−	21.0726i	−1.20529	−	1.12638i
$351$	−17.2587	−	10.5286i	−0.921203	−	0.561974i
$352$	2.35356	+	0.354742i	0.125445	+	0.0189078i
$353$	2.22373	+	29.6737i	0.118357	+	1.57937i	0.668123	+	0.744051i	$0.267098\pi$
$353$	2.22373	+	29.6737i	0.118357	+	1.57937i	−0.549765	+	0.835319i	$0.685283\pi$
$354$	−5.51020	+	0.925881i	−0.292864	+	0.0492100i
$355$	−7.95644	+	25.7941i	−0.422284	+	1.36901i
$356$	3.97279	−	10.1225i	0.210558	−	0.536492i
$357$	−2.08525	+	33.8667i	−0.110363	+	1.79242i
$358$	−6.20910	−	15.8205i	−0.328161	−	0.836141i
$359$	17.9344	−	1.34400i	0.946541	−	0.0709335i	0.407493	−	0.913208i	$-0.366403\pi$
$359$	17.9344	−	1.34400i	0.946541	−	0.0709335i	0.539048	+	0.842275i	$0.318784\pi$
$360$	11.8410	−	3.12653i	0.624077	−	0.164783i
$361$	−8.75944	+	15.1718i	−0.461023	+	0.798516i
$362$	6.36410			0.334490
$363$	6.39845	+	6.66664i	0.335831	+	0.349908i
$364$	−9.82562	−	3.06926i	−0.515002	−	0.160873i
$365$	6.51207	+	21.1116i	0.340857	+	1.10503i
$366$	9.00649	−	10.0413i	0.470777	−	0.524869i
$367$	−4.12847	+	27.3906i	−0.215505	+	1.42978i	0.575416	+	0.817861i	$0.304840\pi$
$367$	−4.12847	+	27.3906i	−0.215505	+	1.42978i	−0.790921	+	0.611919i	$0.790398\pi$
$368$	−3.57266	+	1.40216i	−0.186238	+	0.0730929i
$369$	21.4209	+	18.5707i	1.11513	+	0.966750i
$370$	15.9907	+	3.64978i	0.831319	+	0.189743i
$371$	25.0418	+	12.1698i	1.30011	+	0.631827i
$372$	12.4525	+	3.61211i	0.645630	+	0.187279i
$373$	−14.2765	+	24.7277i	−0.739211	+	1.28035i	0.213640	+	0.976912i	$0.431468\pi$
$373$	−14.2765	+	24.7277i	−0.739211	+	1.28035i	−0.952851	+	0.303438i	$0.901865\pi$
$374$	−17.6233			−0.911280
$375$	13.1288	−	45.2606i	0.677970	−	2.33725i
$376$	−2.06774	+	4.29370i	−0.106635	+	0.221431i
$377$	18.4636	−	23.1526i	0.950923	−	1.19242i
$378$	−9.81453	−	9.62679i	−0.504805	−	0.495149i
$379$	−9.91491	−	12.4329i	−0.509295	−	0.638635i	0.459003	−	0.888435i	$-0.348207\pi$
$379$	−9.91491	−	12.4329i	−0.509295	−	0.638635i	−0.968298	+	0.249800i	$0.919635\pi$
$380$	−4.84362	+	1.10552i	−0.248472	+	0.0567122i
$381$	−5.84830	−	34.8050i	−0.299617	−	1.78312i
$382$	0.717505	+	0.345532i	0.0367107	+	0.0176790i
$383$	−5.24202	−	13.3564i	−0.267855	−	0.682482i	−0.999999	−	0.00133292i	$-0.999576\pi$
$383$	−5.24202	−	13.3564i	−0.267855	−	0.682482i	0.732145	−	0.681149i	$-0.238520\pi$
$384$	−0.100272	+	1.72915i	−0.00511697	+	0.0882401i
$385$	−25.4062	−	3.92220i	−1.29482	−	0.199894i
$386$	2.74889	−	5.70814i	0.139915	−	0.290537i
$387$	−6.33474	+	3.31849i	−0.322013	+	0.168688i
$388$	−5.68697	+	6.12910i	−0.288712	+	0.311158i
$389$	19.0008	−	27.8691i	0.963381	−	1.41302i	0.0533058	−	0.998578i	$-0.483024\pi$
$389$	19.0008	−	27.8691i	0.963381	−	1.41302i	0.910075	−	0.414443i	$-0.136023\pi$
$390$	−4.55862	−	27.1297i	−0.230835	−	1.37377i
$391$	24.6102	−	14.2087i	1.24459	−	0.718566i
$392$	−6.03703	−	3.54320i	−0.304916	−	0.178959i
$393$	−3.04772	+	1.82886i	−0.153737	+	0.0922539i
$394$	5.65160	+	7.08689i	0.284724	+	0.357032i
$395$	1.10780	−	14.7826i	0.0557396	−	0.743793i
$396$	4.67733	−	5.39521i	0.235045	−	0.271120i
$397$	−3.19927	+	4.69247i	−0.160567	+	0.235508i	−0.898088	−	0.439816i	$-0.855044\pi$
$397$	−3.19927	+	4.69247i	−0.160567	+	0.235508i	0.737521	+	0.675324i	$0.235996\pi$
$398$	−5.63307	+	3.84056i	−0.282360	+	0.192510i
$399$	3.84741	+	4.03743i	0.192612	+	0.202125i
$400$	9.63808	+	6.57113i	0.481904	+	0.328556i
$401$	−36.3017	+	14.2474i	−1.81282	+	0.711479i	−0.823202	+	0.567749i	$0.807814\pi$
$401$	−36.3017	+	14.2474i	−1.81282	+	0.711479i	−0.989617	+	0.143730i	$0.954090\pi$
$402$	−21.4901	+	15.1892i	−1.07183	+	0.757568i
$403$	10.6406	−	27.1117i	0.530044	−	1.35053i
$404$	7.31543	−	6.78772i	0.363956	−	0.337702i
$405$	11.0854	−	35.0283i	0.550837	−	1.74057i
$406$	15.7889	−	12.4993i	0.783591	−	0.620329i
$407$	8.90199	−	3.49377i	0.441255	−	0.173180i
$408$	−1.17406	−	12.7708i	−0.0581246	−	0.632249i
$409$	18.7954	−	4.28992i	0.929371	−	0.212123i	0.269067	−	0.963121i	$-0.413285\pi$
$409$	18.7954	−	4.28992i	0.929371	−	0.212123i	0.660304	+	0.750999i	$0.270428\pi$
$410$			38.5776i			1.90521i
$411$	−9.34553	+	0.157726i	−0.460981	+	0.00778005i
$412$	−0.929502	+	3.01337i	−0.0457933	+	0.148458i
$413$	−1.30220	+	8.43505i	−0.0640769	+	0.415061i
$414$	−2.18183	+	11.3053i	−0.107231	+	0.555624i
$415$	22.3534	−	6.89512i	1.09729	−	0.338468i
$416$	3.84725	+	0.579880i	0.188627	+	0.0284309i
$417$	−17.8720	+	23.2034i	−0.875194	+	1.13628i
$418$	−1.97023	+	2.12340i	−0.0963671	+	0.103859i
$419$	−7.18454	+	2.21614i	−0.350988	+	0.108265i	−0.465236	−	0.885187i	$-0.654030\pi$
$419$	−7.18454	+	2.21614i	−0.350988	+	0.108265i	0.114248	+	0.993452i	$0.463554\pi$
$420$	1.14968	−	18.6720i	0.0560986	−	0.911100i
$421$	22.2816	+	6.87296i	1.08594	+	0.334967i	0.785518	−	0.618839i	$-0.212397\pi$
$421$	22.2816	+	6.87296i	1.08594	+	0.334967i	0.300420	+	0.953807i	$0.402873\pi$
$422$	1.01011	−	0.583185i	0.0491712	−	0.0283890i
$423$	7.56222	+	12.1333i	0.367688	+	0.589939i
$424$	−10.0559	−	3.10183i	−0.488358	−	0.150638i
$425$	−77.8179	−	37.4751i	−3.77472	−	1.81781i
$426$	−10.5891	+	4.36352i	−0.513042	+	0.211413i
$427$	−10.2384	−	17.8806i	−0.495471	−	0.865301i
$428$	−2.17956	−	0.855413i	−0.105353	−	0.0413480i
$429$	−11.1065	−	11.5720i	−0.536228	−	0.558703i
$430$	−9.05854	−	3.55521i	−0.436842	−	0.171448i
$431$	11.6835	+	17.1366i	0.562775	+	0.825439i	0.997162	−	0.0752873i	$-0.0239874\pi$
$431$	11.6835	+	17.1366i	0.562775	+	0.825439i	−0.434387	+	0.900726i	$0.643035\pi$
$432$	4.22126	+	3.03001i	0.203095	+	0.145782i
$433$	−5.22003	−	10.8395i	−0.250859	−	0.520913i	0.737071	−	0.675815i	$-0.236208\pi$
$433$	−5.22003	−	10.8395i	−0.250859	−	0.520913i	−0.987930	+	0.154902i	$0.950494\pi$
$434$	11.2152	−	16.3242i	0.538348	−	0.783585i
$435$	48.8748	+	22.5289i	2.34337	+	1.08018i
$436$	−1.25341	+	16.7255i	−0.0600273	+	0.801008i
$437$	1.03936	−	4.55373i	0.0497193	−	0.217835i
$438$	−5.14900	+	7.83299i	−0.246029	+	0.374275i
$439$	17.7511	−	14.1560i	0.847212	−	0.675629i	−0.100437	−	0.994943i	$-0.532024\pi$
$439$	17.7511	−	14.1560i	0.847212	−	0.675629i	0.947649	+	0.319315i	$0.103453\pi$
$440$	9.71640			0.463211
$441$	−18.6712	+	9.61175i	−0.889106	+	0.457702i
$442$	−28.8080			−1.37026
$443$	8.51634	−	6.79155i	0.404623	−	0.322676i	−0.399942	−	0.916540i	$-0.630970\pi$
$443$	8.51634	−	6.79155i	0.404623	−	0.322676i	0.804565	+	0.593864i	$0.202398\pi$
$444$	3.12482	+	6.21810i	0.148297	+	0.295098i
$445$	9.87804	−	43.2785i	0.468264	−	2.05160i
$446$	−0.284898	+	3.80170i	−0.0134903	+	0.180016i
$447$	1.10891	+	12.0622i	0.0524498	+	0.570522i
$448$	2.45939	+	0.975389i	0.116195	+	0.0460828i
$449$	−1.51564	−	3.14726i	−0.0715275	−	0.148528i	0.862139	−	0.506671i	$-0.169124\pi$
$449$	−1.51564	−	3.14726i	−0.0715275	−	0.148528i	−0.933667	+	0.358143i	$0.883410\pi$
$450$	32.1259	−	13.8771i	1.51443	−	0.654172i
$451$	12.6704	+	18.5841i	0.596626	+	0.875089i
$452$	−4.50899	−	1.76965i	−0.212085	−	0.0832372i
$453$	−3.78891	+	0.932332i	−0.178019	+	0.0438048i
$454$	11.0324	+	4.32991i	0.517777	+	0.203213i
$455$	−41.5303	−	6.41143i	−1.94697	−	0.300572i
$456$	−1.66999	−	1.28627i	−0.0782043	−	0.0602352i
$457$	−26.0534	−	12.5467i	−1.21873	−	0.586909i	−0.289771	−	0.957096i	$-0.593579\pi$
$457$	−26.0534	−	12.5467i	−1.21873	−	0.586909i	−0.928957	+	0.370187i	$0.879294\pi$
$458$	4.16755	+	1.28552i	0.194737	+	0.0600683i
$459$	−34.2502	−	17.5262i	−1.59866	−	0.818053i
$460$	−13.5686	+	7.83381i	−0.632637	+	0.365253i
$461$	5.03000	+	1.55155i	0.234270	+	0.0722628i	0.409667	−	0.912235i	$-0.365645\pi$
$461$	5.03000	+	1.55155i	0.234270	+	0.0722628i	−0.175397	+	0.984498i	$0.556121\pi$
$462$	−5.57878	−	9.37250i	−0.259548	−	0.436048i
$463$	8.74280	−	2.69680i	0.406312	−	0.125331i	−0.0848606	−	0.996393i	$-0.527044\pi$
$463$	8.74280	−	2.69680i	0.406312	−	0.125331i	0.491173	+	0.871062i	$0.336568\pi$
$464$	−5.17699	+	5.57947i	−0.240336	+	0.259020i
$465$	52.4644	+	7.00447i	2.43298	+	0.324824i
$466$	−14.7899	−	2.22923i	−0.685131	−	0.103267i
$467$	−11.0249	+	3.40074i	−0.510173	+	0.157368i	−0.539146	−	0.842213i	$-0.681253\pi$
$467$	−11.0249	+	3.40074i	−0.510173	+	0.157368i	0.0289722	+	0.999580i	$0.490777\pi$
$468$	7.64580	−	8.81929i	0.353427	−	0.407672i
$469$	11.7115	+	38.4546i	0.540786	+	1.77567i
$470$	−5.73438	+	18.5904i	−0.264507	+	0.857511i
$471$	8.08656	−	14.5687i	0.372609	−	0.671289i
$472$		−	3.22592i		−	0.148485i
$473$	−5.53146	+	1.26252i	−0.254337	+	0.0580508i
$474$	5.13620	−	3.63026i	0.235914	−	0.166743i
$475$	−13.2151	+	5.18654i	−0.606350	+	0.237975i
$476$	−19.0831	−	4.42734i	−0.874674	−	0.202927i
$477$	−24.0044	+	20.5054i	−1.09908	+	0.938880i
$478$	−12.4875	+	11.5867i	−0.571167	+	0.529965i
$479$	−7.56822	+	19.2835i	−0.345801	+	0.881086i	0.647129	+	0.762381i	$0.275970\pi$
$479$	−7.56822	+	19.2835i	−0.345801	+	0.881086i	−0.992930	+	0.118705i	$0.962126\pi$
$480$	0.647303	+	7.04102i	0.0295452	+	0.321377i
$481$	14.5517	−	5.71111i	0.663499	−	0.260404i
$482$	−13.8394	−	9.43557i	−0.630369	−	0.429778i
$483$	15.3471	+	8.59044i	0.698316	+	0.390879i
$484$	−4.40792	+	3.00527i	−0.200360	+	0.136603i
$485$	−19.2274	+	28.2014i	−0.873070	+	1.28056i
$486$	14.4557	−	5.83382i	0.655723	−	0.264628i
$487$	0.954683	−	12.7394i	0.0432608	−	0.577275i	−0.932887	−	0.360169i	$-0.882719\pi$
$487$	0.954683	−	12.7394i	0.0432608	−	0.577275i	0.976148	−	0.217106i	$-0.0696619\pi$
$488$	4.85556	+	6.08868i	0.219801	+	0.275622i
$489$	−0.374754	−	22.2048i	−0.0169470	−	1.00414i
$490$	−26.5254	−	10.6297i	−1.19829	−	0.480199i
$491$	−0.803790	+	0.464069i	−0.0362745	+	0.0209431i	−0.518028	−	0.855364i	$-0.673334\pi$
$491$	−0.803790	+	0.464069i	−0.0362745	+	0.0209431i	0.481753	+	0.876307i	$0.340000\pi$
$492$	−12.6229	+	10.4197i	−0.569084	+	0.469757i
$493$	31.7467	−	46.5638i	1.42980	−	2.09713i
$494$	−3.22064	+	3.47102i	−0.144903	+	0.156169i
$495$	15.5983	−	24.6246i	0.701090	−	1.10679i
$496$	−3.24796	+	6.74446i	−0.145838	+	0.302835i
$497$	1.24507	+	17.4502i	0.0558492	+	0.782750i
$498$	8.29375	+	5.45188i	0.371652	+	0.244304i
$499$	−13.6974	−	34.9005i	−0.613181	−	1.56236i	−0.812836	−	0.582493i	$-0.802077\pi$
$499$	−13.6974	−	34.9005i	−0.613181	−	1.56236i	0.199655	−	0.979866i	$-0.436018\pi$
$500$	24.5139	+	11.8053i	1.09630	+	0.527948i
$501$	7.90173	−	6.52256i	0.353023	−	0.291407i
$502$	19.8860	−	4.53885i	0.887556	−	0.202579i
$503$	26.8464	+	33.6643i	1.19702	+	1.50102i	0.817592	+	0.575798i	$0.195309\pi$
$503$	26.8464	+	33.6643i	1.19702	+	1.50102i	0.379430	+	0.925220i	$0.376120\pi$
$504$	6.42016	−	4.66707i	0.285977	−	0.207888i
$505$	25.4002	−	31.8508i	1.13029	−	1.41734i
$506$	−3.96348	+	8.23025i	−0.176198	+	0.365879i
$507$	−2.56372	−	2.67118i	−0.113859	−	0.118631i
$508$	20.3764			0.904056
$509$	11.9303	−	20.6639i	0.528802	−	0.915912i	−0.470634	−	0.882329i	$-0.655975\pi$
$509$	11.9303	−	20.6639i	0.528802	−	0.915912i	0.999436	−	0.0335833i	$-0.0106919\pi$
$510$	−12.5095	−	50.8373i	−0.553928	−	2.25111i
$511$	8.88754	+	11.2266i	0.393162	+	0.496636i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$	−5.94076	+	2.16738i	−0.262291	+	0.0956920i
$514$	−1.53544	+	0.602616i	−0.0677253	+	0.0265802i
$515$	−1.91867	+	12.7296i	−0.0845469	+	0.560932i
$516$	−1.28339	−	3.92428i	−0.0564982	−	0.172757i
$517$	3.34339	+	10.8390i	0.147042	+	0.476698i
$518$	10.5171	−	1.54681i	0.462094	−	0.0679630i
$519$	4.54826	−	15.6798i	0.199646	−	0.688265i
$520$	15.8829			0.696513
$521$	0.853130	−	1.47766i	0.0373763	−	0.0647376i	−0.846732	−	0.532019i	$-0.821433\pi$
$521$	0.853130	−	1.47766i	0.0373763	−	0.0647376i	0.884108	+	0.467282i	$0.154767\pi$
$522$	5.82932	+	22.0772i	0.255143	+	0.966295i
$523$	12.2870	−	0.920784i	0.537273	−	0.0402631i	0.196669	−	0.980470i	$-0.436988\pi$
$523$	12.2870	−	0.920784i	0.537273	−	0.0402631i	0.340604	+	0.940207i	$0.389368\pi$
$524$	−0.749717	−	1.91025i	−0.0327515	−	0.0834495i
$525$	−4.70362	−	53.2484i	−0.205283	−	2.32395i
$526$	6.07562	−	15.4804i	0.264909	−	0.674978i
$527$	16.3374	−	52.9647i	0.711670	−	2.30718i
$528$	2.62438	+	3.17929i	0.114211	+	0.138361i
$529$	0.618023	+	8.24694i	0.0268706	+	0.358563i
$530$	−42.4797	−	6.40279i	−1.84520	−	0.278119i
$531$	−8.17554	−	5.17874i	−0.354788	−	0.224738i
$532$	−2.66687	+	1.80433i	−0.115624	+	0.0782276i
$533$	20.7117	+	30.3785i	0.897123	+	1.31584i
$534$	16.8291	−	8.45725i	0.728268	−	0.365981i
$535$	−9.31864	−	2.12692i	−0.402880	−	0.0919548i
$536$	−6.59226	−	13.6890i	−0.284742	−	0.591273i
$537$	10.2905	−	27.5795i	0.444070	−	1.19014i
$538$	24.2524	+	14.0021i	1.04559	+	0.603674i
$539$	−16.2693	+	3.59133i	−0.700770	+	0.154690i
$540$	18.8834	+	9.66286i	0.812614	+	0.415823i
$541$	4.75805	−	12.1233i	0.204565	−	0.521222i	−0.791366	−	0.611342i	$-0.790630\pi$
$541$	4.75805	−	12.1233i	0.204565	−	0.521222i	0.995931	+	0.0901200i	$0.0287251\pi$
$542$	−4.23822	−	2.88957i	−0.182047	−	0.124118i
$543$	8.20576	+	7.36009i	0.352143	+	0.315851i
$544$	7.38361	+	0.553325i	0.316570	+	0.0237236i
$545$	5.11675	+	68.2783i	0.219178	+	2.92472i
$546$	−9.11937	−	15.3208i	−0.390273	−	0.655669i
$547$	−0.861846	+	11.5005i	−0.0368499	+	0.491727i	0.947995	+	0.318287i	$0.103107\pi$
$547$	−0.861846	+	11.5005i	−0.0368499	+	0.491727i	−0.984844	+	0.173440i	$0.944512\pi$
$548$	0.804293	−	5.33614i	0.0343577	−	0.227949i
$549$	23.2256	−	2.53111i	0.991245	−	0.108025i
$550$	27.4543	−	4.13806i	1.17065	−	0.176448i
$551$	−2.06122	−	9.03079i	−0.0878108	−	0.384724i
$552$	−6.22812	−	2.32385i	−0.265087	−	0.0989097i
$553$	−2.79908	−	9.19077i	−0.119029	−	0.390831i
$554$	−4.22496	+	28.0308i	−0.179501	+	1.19091i
$555$	16.3972	+	23.1993i	0.696023	+	0.984754i
$556$	−11.5015	−	12.3956i	−0.487771	−	0.525692i
$557$	−24.4072	−	14.0915i	−1.03417	−	0.597077i	−0.115992	−	0.993250i	$-0.537005\pi$
$557$	−24.4072	−	14.0915i	−1.03417	−	0.597077i	−0.918176	+	0.396173i	$0.870338\pi$
$558$	11.8786	+	19.0587i	0.502860	+	0.806818i
$559$	−9.04202	+	2.06378i	−0.382437	+	0.0872887i
$560$	10.5213	+	2.44096i	0.444604	+	0.103149i
$561$	−22.7232	−	20.3814i	−0.959374	−	0.860503i
$562$	9.96637	+	9.24744i	0.420406	+	0.390080i
$563$	−6.41234	+	8.04082i	−0.270248	+	0.338880i	−0.898374	−	0.439231i	$-0.855251\pi$
$563$	−6.41234	+	8.04082i	−0.270248	+	0.338880i	0.628126	+	0.778112i	$0.283822\pi$
$564$	−7.63178	+	3.14488i	−0.321356	+	0.132424i
$565$	−19.2781	−	4.40009i	−0.811034	−	0.185113i
$566$	−2.14729	+	9.40789i	−0.0902574	+	0.395443i
$567$	−1.52129	−	23.7631i	−0.0638882	−	0.997957i
$568$	−1.47138	−	6.44655i	−0.0617378	−	0.270491i
$569$			32.9303i			1.38051i	0.723567	+	0.690254i	$0.242501\pi$
$569$			32.9303i			1.38051i	−0.723567	+	0.690254i	$0.757499\pi$
$570$	−7.52381	−	4.17620i	−0.315138	−	0.174922i
$571$	6.69949	+	29.3524i	0.280365	+	1.22836i	0.897327	+	0.441367i	$0.145506\pi$
$571$	6.69949	+	29.3524i	0.280365	+	1.22836i	−0.616962	+	0.786993i	$0.711637\pi$
$572$	7.65133	−	5.21659i	0.319918	−	0.218116i
$573$	0.525530	+	1.27532i	0.0219543	+	0.0532772i
$574$	9.05124	+	23.3065i	0.377791	+	0.972795i
$575$	−35.0024	+	27.9135i	−1.45970	+	1.16407i
$576$	−2.12905	+	2.11357i	−0.0887103	+	0.0880652i
$577$	−1.01957	−	6.76441i	−0.0424453	−	0.281606i	0.957532	−	0.288327i	$-0.0930989\pi$
$577$	−1.01957	−	6.76441i	−0.0424453	−	0.281606i	−0.999977	+	0.00672055i	$0.997861\pi$
$578$	−37.7181	+	2.82658i	−1.56887	+	0.117570i
$579$	10.1458	−	4.18087i	0.421647	−	0.173751i
$580$	−17.5032	+	25.6724i	−0.726779	+	1.06599i
$581$	11.8870	−	9.41033i	0.493156	−	0.390406i
$582$	−14.4210	+	1.32577i	−0.597769	+	0.0549548i
$583$	−22.5668	+	10.8676i	−0.934621	+	0.450090i
$584$	−3.96725	−	3.68107i	−0.164166	−	0.152324i
$585$	25.4978	−	40.2526i	1.05420	−	1.66424i
$586$	8.79297	+	3.45099i	0.363234	+	0.142559i
$587$	15.7720	−	27.3179i	0.650980	−	1.12753i	−0.331905	−	0.943313i	$-0.607691\pi$
$587$	15.7720	−	27.3179i	0.650980	−	1.12753i	0.982885	−	0.184218i	$-0.0589753\pi$
$588$	−3.68633	−	11.5504i	−0.152022	−	0.476329i
$589$	−4.55515	−	7.88975i	−0.187692	−	0.325091i
$590$	−1.96275	−	13.0220i	−0.0808052	−	0.536107i
$591$	−0.908910	+	15.6738i	−0.0373875	+	0.644733i
$592$	−3.83935	+	1.18428i	−0.157796	+	0.0486737i
$593$	14.1900	+	9.67461i	0.582715	+	0.397289i	0.818491	−	0.574519i	$-0.194811\pi$
$593$	14.1900	+	9.67461i	0.582715	+	0.397289i	−0.235776	+	0.971807i	$0.575763\pi$
$594$	12.2704	−	1.54716i	0.503462	−	0.0634807i
$595$	−79.7263	−	6.26100i	−3.26846	−	0.256676i
$596$	−6.97391	−	0.522623i	−0.285663	−	0.0214075i
$597$	−11.7048	−	1.56270i	−0.479045	−	0.0639569i
$598$	−6.47891	+	13.4536i	−0.264942	+	0.550159i
$599$	−25.2066	+	20.1016i	−1.02991	+	0.821328i	−0.984099	−	0.177621i	$-0.943160\pi$
$599$	−25.2066	+	20.1016i	−1.02991	+	0.821328i	−0.0458145	+	0.998950i	$0.514588\pi$
$600$	4.82765	+	19.6191i	0.197088	+	0.800948i
$601$	0.193413	+	1.28321i	0.00788947	+	0.0523432i	0.992429	−	0.122818i	$-0.0391933\pi$
$601$	0.193413	+	1.28321i	0.00788947	+	0.0523432i	−0.984540	+	0.175162i	$0.943955\pi$
$602$	−6.30683	−	0.0225185i	−0.257047	−	0.000917786i
$603$	−45.2753	−	5.26867i	−1.84375	−	0.214557i
$604$	−0.168351	−	2.24648i	−0.00685009	−	0.0914082i
$605$	−15.9649	+	14.8132i	−0.649064	+	0.602244i
$606$	17.2824	−	0.291677i	0.702049	−	0.0118486i
$607$	8.45700	+	4.88265i	0.343259	+	0.198181i	0.661712	−	0.749758i	$-0.269830\pi$
$607$	8.45700	+	4.88265i	0.343259	+	0.198181i	−0.318453	+	0.947939i	$0.603163\pi$
$608$	0.892133	−	0.827778i	0.0361808	−	0.0335708i
$609$	34.8134	+	2.14354i	1.41071	+	0.0868608i
$610$	23.3049	+	21.6238i	0.943588	+	0.875522i
$611$	5.46527	+	17.7180i	0.221101	+	0.716793i
$612$	13.2556	−	17.8242i	0.535827	−	0.720502i
$613$	6.29893	+	16.0494i	0.254411	+	0.648229i	0.999831	−	0.0183658i	$-0.00584633\pi$
$613$	6.29893	+	16.0494i	0.254411	+	0.648229i	−0.745420	+	0.666595i	$0.767751\pi$
$614$	3.39904	−	14.8922i	0.137174	−	0.600999i
$615$	−44.6150	+	49.7412i	−1.79905	+	2.00576i
$616$	5.87014	−	2.27970i	0.236514	−	0.0918519i
$617$	−8.09995	−	8.72967i	−0.326092	−	0.351443i	0.548633	−	0.836063i	$-0.315148\pi$
$617$	−8.09995	−	8.72967i	−0.326092	−	0.351443i	−0.874725	+	0.484620i	$0.838958\pi$
$618$	−4.68345	+	2.81042i	−0.188396	+	0.113052i
$619$	11.6837	−	6.74557i	0.469606	−	0.271127i	−0.246469	−	0.969151i	$-0.579270\pi$
$619$	11.6837	−	6.74557i	0.469606	−	0.271127i	0.716075	+	0.698023i	$0.245937\pi$
$620$	−9.00745	+	29.2014i	−0.361748	+	1.17276i
$621$	−15.8878	+	12.0535i	−0.637554	+	0.483691i
$622$	−8.60224	−	6.86006i	−0.344918	−	0.275063i
$623$	−4.18641	−	28.4642i	−0.167725	−	1.14040i
$624$	4.28994	+	5.19703i	0.171735	+	0.208048i
$625$	50.4038	+	15.5475i	2.01615	+	0.621901i
$626$	0.419955	+	0.526607i	0.0167848	+	0.0210474i
$627$	−4.99609	+	0.459306i	−0.199525	+	0.0183429i
$628$	7.52129	+	5.99803i	0.300132	+	0.239347i
$629$	26.8033	−	12.9078i	1.06872	−	0.514667i
$630$	23.0765	−	22.7457i	0.919391	−	0.906212i
$631$	−19.3550	−	9.32088i	−0.770510	−	0.371058i	0.00696157	−	0.999976i	$-0.497784\pi$
$631$	−19.3550	−	9.32088i	−0.770510	−	0.371058i	−0.777472	+	0.628917i	$0.783498\pi$
$632$	1.57557	+	3.27170i	0.0626728	+	0.130141i
$633$	1.97687	+	0.416240i	0.0785734	+	0.0165441i
$634$	8.34453	−	4.01851i	0.331404	−	0.159596i
$635$	82.2530	−	12.3977i	3.26411	−	0.491986i
$636$	−9.37863	−	15.6291i	−0.371887	−	0.619734i
$637$	−26.5947	+	5.87058i	−1.05372	+	0.232601i
$638$			18.1160i			0.717218i
$639$	−18.6998	−	6.62002i	−0.739752	−	0.261884i
$640$	−4.07086	−	0.305069i	−0.160915	−	0.0120589i
$641$	6.03279	+	19.5578i	0.238281	+	0.772487i	0.993174	+	0.116640i	$0.0372123\pi$
$641$	6.03279	+	19.5578i	0.238281	+	0.772487i	−0.754894	+	0.655847i	$0.772311\pi$
$642$	−1.82100	−	3.62361i	−0.0718690	−	0.143013i
$643$	−2.19190	+	0.164261i	−0.0864403	+	0.00647780i	−0.117880	−	0.993028i	$-0.537610\pi$
$643$	−2.19190	+	0.164261i	−0.0864403	+	0.00647780i	0.0314397	+	0.999506i	$0.489991\pi$
$644$	−6.35940	+	7.91629i	−0.250595	+	0.311945i
$645$	−7.56831	−	15.0602i	−0.298002	−	0.592996i
$646$	−5.61835	+	7.04519i	−0.221051	+	0.277189i
$647$	16.0117	−	10.9166i	0.629484	−	0.429175i	−0.206105	−	0.978530i	$-0.566079\pi$
$647$	16.0117	−	10.9166i	0.629484	−	0.429175i	0.835589	+	0.549355i	$0.185127\pi$
$648$	1.93860	+	8.78873i	0.0761555	+	0.345254i
$649$	−5.22246	−	5.62847i	−0.204999	−	0.220937i
$650$	44.8782	−	6.76430i	1.76027	−	0.265317i
$651$	33.3396	−	8.07769i	1.30668	−	0.316590i
$652$	12.6786	+	1.91099i	0.496531	+	0.0748400i
$653$	−21.2350	−	31.1461i	−0.830991	−	1.21884i	−0.973418	−	0.229034i	$-0.926443\pi$
$653$	−21.2350	−	31.1461i	−0.830991	−	1.21884i	0.142428	−	0.989805i	$-0.454509\pi$
$654$	−20.9592	+	20.1161i	−0.819570	+	0.786600i
$655$	−4.18862	−	7.25491i	−0.163663	−	0.283473i
$656$	−4.72500	−	8.18395i	−0.184480	−	0.319530i
$657$	−15.6979	+	4.14491i	−0.612433	+	0.161708i
$658$	0.897352	+	12.5768i	0.0349824	+	0.490293i
$659$	−6.18208	+	6.66270i	−0.240820	+	0.259542i	−0.841884	−	0.539659i	$-0.818553\pi$
$659$	−6.18208	+	6.66270i	−0.240820	+	0.259542i	0.601064	+	0.799201i	$0.294744\pi$
$660$	12.5282	+	11.2370i	0.487658	+	0.437401i
$661$	4.12460	+	3.28926i	0.160428	+	0.127937i	0.700414	−	0.713737i	$-0.252999\pi$
$661$	4.12460	+	3.28926i	0.160428	+	0.127937i	−0.539985	+	0.841674i	$0.681570\pi$
$662$	−26.3235	−	20.9923i	−1.02309	−	0.815888i
$663$	−37.1445	−	33.3165i	−1.44257	−	1.29390i
$664$	−3.89760	+	4.20061i	−0.151256	+	0.163015i
$665$	−9.66751	+	8.90612i	−0.374890	+	0.345364i
$666$	−3.16215	+	11.6314i	−0.122531	+	0.450706i
$667$	−14.6059	−	25.2982i	−0.565543	−	0.979550i
$668$	2.95777	+	5.12301i	0.114440	+	0.198215i
$669$	−4.76401	+	4.57236i	−0.184187	+	0.176778i
$670$	−34.9397	−	51.2471i	−1.34984	−	1.97985i
$671$	18.3288	+	2.76263i	0.707577	+	0.106650i
$672$	2.04306	+	4.10194i	0.0788128	+	0.158236i
$673$	−30.2458	+	4.55883i	−1.16589	+	0.175730i	−0.703334	−	0.710859i	$-0.748306\pi$
$673$	−30.2458	+	4.55883i	−1.16589	+	0.175730i	−0.462557	+	0.886589i	$0.653068\pi$
$674$	−0.767352	−	0.827008i	−0.0295573	−	0.0318552i
$675$	57.4715	+	19.2608i	2.21208	+	0.741348i
$676$	1.76616	−	1.20415i	0.0679291	−	0.0463133i
$677$	−5.77635	+	7.24332i	−0.222003	+	0.278383i	−0.880343	−	0.474338i	$-0.842688\pi$
$677$	−5.77635	+	7.24332i	−0.222003	+	0.278383i	0.658340	+	0.752721i	$0.271259\pi$
$678$	−3.76721	−	7.49640i	−0.144679	−	0.287897i
$679$	−4.99943	+	21.5490i	−0.191860	+	0.826974i
$680$	30.1420	−	2.25883i	1.15589	−	0.0866221i
$681$	9.21747	+	18.3419i	0.353214	+	0.702863i
$682$	5.25173	+	17.0257i	0.201099	+	0.651947i
$683$	21.1514	+	1.58508i	0.809337	+	0.0606514i	0.472969	−	0.881079i	$-0.343182\pi$
$683$	21.1514	+	1.58508i	0.809337	+	0.0606514i	0.336368	+	0.941731i	$0.390801\pi$
$684$	−0.665676	−	3.58984i	−0.0254527	−	0.137261i
$685$		−	22.0297i		−	0.841710i
$686$	−18.5192	−	0.198375i	−0.707066	−	0.00757400i
$687$	3.88686	+	6.47729i	0.148293	+	0.247124i
$688$	2.35715	−	0.355283i	0.0898654	−	0.0135450i
$689$	−36.8889	+	17.7647i	−1.40535	+	0.676783i
$690$	−26.5549	−	5.59127i	−1.01093	−	0.212856i
$691$	−10.7996	−	22.4256i	−0.410836	−	0.853110i	−0.999015	−	0.0443791i	$-0.985869\pi$
$691$	−10.7996	−	22.4256i	−0.410836	−	0.853110i	0.588179	−	0.808731i	$-0.299845\pi$
$692$	8.49242	+	4.08974i	0.322834	+	0.155468i
$693$	3.64612	−	18.5366i	0.138505	−	0.704147i
$694$	2.88648	−	1.39006i	0.109569	−	0.0527659i
$695$	−53.9697	−	43.0394i	−2.04719	−	1.63258i
$696$	−13.1278	+	1.20688i	−0.497607	+	0.0457466i
$697$	43.6261	+	54.7054i	1.65246	+	2.07212i
$698$	17.0973	+	5.27381i	0.647141	+	0.199617i
$699$	−16.4918	−	19.9789i	−0.623777	−	0.755671i
$700$	30.7680	+	2.41624i	1.16292	+	0.0913254i
$701$	40.1476	+	32.0167i	1.51635	+	1.20925i	0.910383	+	0.413767i	$0.135787\pi$
$701$	40.1476	+	32.0167i	1.51635	+	1.20925i	0.605972	+	0.795486i	$0.292784\pi$
$702$	20.0579	−	2.52907i	0.757036	−	0.0954534i
$703$	1.44128	−	4.67253i	0.0543591	−	0.176228i
$704$	−2.06126	+	1.19007i	−0.0776868	+	0.0448525i
$705$	−28.8936	+	17.3383i	−1.08820	+	0.652999i
$706$	−20.2398	−	21.8133i	−0.761736	−	0.820956i
$707$	7.87247	−	25.2021i	0.296075	−	0.947822i
$708$	3.73077	−	4.15944i	0.140211	−	0.156321i
$709$	5.85655	−	25.6592i	0.219947	−	0.963652i	−0.737569	−	0.675272i	$-0.764026\pi$
$709$	5.85655	−	25.6592i	0.219947	−	0.963652i	0.957516	−	0.288380i	$-0.0931166\pi$
$710$	−9.86179	−	25.1274i	−0.370106	−	0.943016i
$711$	10.8209	+	1.25923i	0.405816	+	0.0472247i
$712$	3.20523	+	10.3911i	0.120121	+	0.389423i
$713$	−21.0607	−	19.5415i	−0.788729	−	0.731834i
$714$	−19.4852	−	27.7782i	−0.729216	−	1.03957i
$715$	27.7120	−	25.7130i	1.03637	−	0.961613i
$716$	14.7184	+	8.49767i	0.550052	+	0.317573i
$717$	−29.5013	+	0.497898i	−1.10175	+	0.0185943i
$718$	−13.1837	+	12.2327i	−0.492012	+	0.456520i
$719$	−0.472677	−	6.30744i	−0.0176279	−	0.235228i	−0.999058	−	0.0434053i	$-0.986179\pi$
$719$	−0.472677	−	6.30744i	−0.0176279	−	0.235228i	0.981430	−	0.191822i	$-0.0614397\pi$
$720$	−7.30833	+	9.82718i	−0.272365	+	0.366237i
$721$	1.82750	+	8.14070i	0.0680598	+	0.303175i
$722$	−2.61105	−	17.3232i	−0.0971734	−	0.644703i
$723$	−6.93209	−	28.1714i	−0.257807	−	1.04770i
$724$	−4.97565	+	3.96795i	−0.184919	+	0.147468i
$725$	−38.5227	+	79.9932i	−1.43070	+	2.97087i
$726$	−9.15909	−	1.22282i	−0.339926	−	0.0453831i
$727$	17.0386	+	1.27687i	0.631928	+	0.0473564i	0.386844	−	0.922145i	$-0.373565\pi$
$727$	17.0386	+	1.27687i	0.631928	+	0.0473564i	0.245084	+	0.969502i	$0.421184\pi$
$728$	9.59563	−	3.72652i	0.355638	−	0.138114i
$729$	25.3857	+	9.19596i	0.940211	+	0.340591i
$730$	−18.2542	−	12.4455i	−0.675619	−	0.460629i
$731$	−16.8660	+	5.20249i	−0.623813	+	0.192421i
$732$	−0.780887	+	13.4661i	−0.0288624	+	0.497721i
$733$	6.85446	+	45.4764i	0.253175	+	1.67971i	0.648537	+	0.761183i	$0.275381\pi$
$733$	6.85446	+	45.4764i	0.253175	+	1.67971i	−0.395362	+	0.918525i	$0.629381\pi$
$734$	−13.8500	−	23.9889i	−0.511213	−	0.885447i
$735$	−21.9082	−	44.3823i	−0.808094	−	1.63707i
$736$	1.91898	−	3.32377i	0.0707345	−	0.122516i
$737$	−33.6631	−	13.2118i	−1.24000	−	0.486663i
$738$	−28.3261	−	1.16341i	−1.04270	−	0.0428256i
$739$	4.61213	+	4.27943i	0.169660	+	0.157421i	0.760433	−	0.649416i	$-0.224987\pi$
$739$	4.61213	+	4.27943i	0.169660	+	0.157421i	−0.590773	+	0.806838i	$0.701177\pi$
$740$	−14.7777	+	7.11655i	−0.543238	+	0.261610i
$741$	−8.16688	+	0.750806i	−0.300018	+	0.0275816i
$742$	−27.1663	+	6.09855i	−0.997305	+	0.223885i
$743$	17.8911	−	26.2414i	0.656359	−	0.962702i	−0.343365	−	0.939202i	$-0.611567\pi$
$743$	17.8911	−	26.2414i	0.656359	−	0.962702i	0.999724	−	0.0234999i	$-0.00748094\pi$
$744$	−11.9878	+	4.93992i	−0.439496	+	0.181106i
$745$	−28.4695	+	2.13349i	−1.04304	+	0.0781651i
$746$	−4.25561	−	28.2341i	−0.155809	−	1.03373i
$747$	4.38872	+	16.6213i	0.160575	+	0.608141i
$748$	13.7785	−	10.9880i	0.503791	−	0.401760i
$749$	−6.12886	+	0.901408i	−0.223944	+	0.0329367i
$750$	17.9550	+	43.5719i	0.655624	+	1.59102i
$751$	−31.1318	+	21.2253i	−1.13602	+	0.774522i	−0.977102	−	0.212770i	$-0.931751\pi$
$751$	−31.1318	+	21.2253i	−1.13602	+	0.774522i	−0.158914	+	0.987293i	$0.550799\pi$
$752$	−1.06046	−	4.64617i	−0.0386709	−	0.169428i
$753$	30.8898	+	17.1459i	1.12569	+	0.624830i
$754$			29.6133i			1.07845i
$755$	−2.04641	−	8.96592i	−0.0744766	−	0.326303i
$756$	13.6755	+	1.40727i	0.497374	+	0.0511819i
$757$	−4.72842	+	20.7166i	−0.171857	+	0.752956i	0.813376	+	0.581738i	$0.197627\pi$
$757$	−4.72842	+	20.7166i	−0.171857	+	0.752956i	−0.985233	+	0.171218i	$0.945230\pi$
$758$	15.5036	+	3.53859i	0.563115	+	0.128527i
$759$	−14.6287	+	6.02817i	−0.530989	+	0.218809i
$760$	3.09761	−	3.88428i	0.112362	−	0.140898i
$761$	4.24821	+	3.94177i	0.153998	+	0.142889i	0.753409	−	0.657552i	$-0.228408\pi$
$761$	4.24821	+	3.94177i	0.153998	+	0.142889i	−0.599411	+	0.800441i	$0.704599\pi$
$762$	26.2730	+	23.5653i	0.951769	+	0.853681i
$763$	19.1110	+	40.0496i	0.691865	+	1.44989i
$764$	−0.776404	+	0.177209i	−0.0280893	+	0.00641120i
$765$	42.6639	−	80.0159i	1.54252	−	2.89298i
$766$	12.4260	+	7.17414i	0.448969	+	0.259212i
$767$	−8.53691	−	9.20060i	−0.308250	−	0.332214i
$768$	−0.999709	−	1.41442i	−0.0360739	−	0.0510385i
$769$	−0.725348	+	4.81237i	−0.0261567	+	0.173538i	−0.998095	−	0.0616982i	$-0.980348\pi$
$769$	−0.725348	+	4.81237i	−0.0261567	+	0.173538i	0.971938	+	0.235237i	$0.0755865\pi$
$770$	22.3088	−	12.7740i	0.803954	−	0.460344i
$771$	−2.67669	−	0.998734i	−0.0963988	−	0.0359685i
$772$	1.40979	+	6.17671i	0.0507396	+	0.222305i
$773$	−6.02405	+	0.907979i	−0.216670	+	0.0326577i	−0.256480	−	0.966550i	$-0.582563\pi$
$773$	−6.02405	+	0.907979i	−0.216670	+	0.0326577i	0.0398101	+	0.999207i	$0.487325\pi$
$774$	2.88365	−	6.54415i	0.103651	−	0.235225i
$775$	−13.0146	+	86.3465i	−0.467499	+	3.10166i
$776$	0.624824	−	8.33769i	0.0224299	−	0.299306i
$777$	15.3494	+	10.1686i	0.550658	+	0.364796i
$778$	2.52065	+	33.6358i	0.0903698	+	1.20590i
$779$	11.4686	+	0.859454i	0.410906	+	0.0307931i
$780$	20.4792	+	18.3686i	0.733273	+	0.657702i
$781$	−13.0036	−	8.86570i	−0.465305	−	0.317240i
$782$	−10.3821	+	26.4531i	−0.371262	+	0.945960i
$783$	−18.0161	+	35.2076i	−0.643843	+	1.25822i
$784$	6.92909	−	0.993841i	0.247467	−	0.0354943i
$785$	34.0105	+	19.6360i	1.21389	+	0.700837i
$786$	1.24253	−	3.33009i	0.0443196	−	0.118780i
$787$	−18.9652	−	39.3817i	−0.676038	−	1.40381i	−0.902887	−	0.429877i	$-0.858557\pi$
$787$	−18.9652	−	39.3817i	−0.676038	−	1.40381i	0.226849	−	0.973930i	$-0.427158\pi$
$788$	−8.83720	−	2.01703i	−0.314812	−	0.0718539i
$789$	25.7369	−	12.9337i	0.916258	−	0.460453i
$790$	8.35068	+	12.2482i	0.297104	+	0.435771i
$791$	−12.6792	+	1.86480i	−0.450819	+	0.0663047i
$792$	−0.293023	+	7.13441i	−0.0104121	+	0.253510i
$793$	29.9613	+	4.51593i	1.06396	+	0.160366i
$794$	−0.424415	−	5.66343i	−0.0150619	−	0.200988i
$795$	−47.3678	−	57.3835i	−1.67996	−	2.03518i
$796$	2.00956	−	6.51484i	0.0712270	−	0.230912i
$797$	−10.7465	+	27.3815i	−0.380659	+	0.969904i	0.604244	+	0.796799i	$0.293475\pi$
$797$	−10.7465	+	27.3815i	−0.380659	+	0.969904i	−0.984903	+	0.173105i	$0.944620\pi$
$798$	−5.52533	−	0.757770i	−0.195594	−	0.0268248i
$799$	12.8916	+	32.8472i	0.456071	+	1.16205i
$800$	−11.6324	+	0.871727i	−0.411267	+	0.0308202i
$801$	31.4800	+	8.55827i	1.11229	+	0.302392i
$802$	19.4987	−	33.7727i	0.688523	−	1.19256i
$803$	−12.8812			−0.454569
$804$	7.33135	−	25.2743i	0.258557	−	0.891354i
$805$	−20.8544	+	35.8248i	−0.735020	+	1.26266i
$806$	8.58475	+	27.8311i	0.302385	+	0.980307i
$807$	15.0771	+	46.1020i	0.530740	+	1.62287i
$808$	−1.48735	+	9.86795i	−0.0523249	+	0.347153i
$809$	5.98549	−	2.34913i	0.210439	−	0.0825911i	−0.257780	−	0.966204i	$-0.582991\pi$
$809$	5.98549	−	2.34913i	0.210439	−	0.0825911i	0.468219	+	0.883612i	$0.344896\pi$
$810$	13.1729	+	34.2978i	0.462848	+	1.20510i
$811$	10.6607	+	2.43325i	0.374350	+	0.0854428i	0.405556	−	0.914070i	$-0.367078\pi$
$811$	10.6607	+	2.43325i	0.374350	+	0.0854428i	−0.0312066	+	0.999513i	$0.509935\pi$
$812$	−4.55110	+	19.6166i	−0.159712	+	0.688407i
$813$	−2.12290	−	8.62727i	−0.0744534	−	0.302572i
$814$	−4.78153	+	8.28185i	−0.167592	+	0.290279i
$815$	52.3421			1.83346
$816$	8.88038	+	9.25260i	0.310875	+	0.323906i
$817$	−1.25873	+	2.61378i	−0.0440374	+	0.0914446i
$818$	−12.0201	+	15.0727i	−0.420272	+	0.527005i
$819$	5.96014	−	30.3009i	0.208264	−	1.05880i
$820$	−24.0527	−	30.1612i	−0.839958	−	1.05327i
$821$	−53.8218	+	12.2845i	−1.87840	+	0.428731i	−0.998888	−	0.0471534i	$-0.984985\pi$
$821$	−53.8218	+	12.2845i	−1.87840	+	0.428731i	−0.879508	+	0.475885i	$0.842128\pi$
$822$	7.20829	−	5.95016i	0.251418	−	0.207536i
$823$	2.14481	+	1.03289i	0.0747634	+	0.0360041i	0.470892	−	0.882191i	$-0.343932\pi$
$823$	2.14481	+	1.03289i	0.0747634	+	0.0360041i	−0.396128	+	0.918195i	$0.629646\pi$
$824$	−1.15209	−	2.93548i	−0.0401350	−	0.102262i
$825$	40.1847	+	26.4153i	1.39905	+	0.919663i
$826$	−4.24107	−	7.40669i	−0.147566	−	0.257712i
$827$	24.3832	−	50.6323i	0.847889	−	1.76066i	0.232202	−	0.972668i	$-0.425407\pi$
$827$	24.3832	−	50.6323i	0.847889	−	1.76066i	0.615687	−	0.787991i	$-0.288879\pi$
$828$	−5.34290	−	10.1992i	−0.185678	−	0.354445i
$829$	2.53151	−	2.72832i	0.0879229	−	0.0947584i	−0.687558	−	0.726130i	$-0.741317\pi$
$829$	2.53151	−	2.72832i	0.0879229	−	0.0947584i	0.775481	+	0.631371i	$0.217508\pi$
$830$	−13.1776	+	19.3280i	−0.457401	+	0.670884i
$831$	−37.8652	+	31.2562i	−1.31353	+	1.08427i
$832$	−3.36945	+	1.94535i	−0.116815	+	0.0674430i
$833$	−49.6354	+	14.9232i	−1.71976	+	0.517057i
$834$	−0.494233	−	29.2842i	−0.0171139	−	1.01403i
$835$	15.0566	+	18.8804i	0.521055	+	0.653382i
$836$	0.216468	−	2.88856i	0.00748669	−	0.0999030i
$837$	−6.72533	+	38.3115i	−0.232461	+	1.32424i
$838$	4.23536	−	6.21213i	0.146308	−	0.214595i
$839$	−27.0097	+	18.4149i	−0.932478	+	0.635753i	−0.931303	−	0.364247i	$-0.881327\pi$
$839$	−27.0097	+	18.4149i	−0.932478	+	0.635753i	−0.00117542	+	0.999999i	$0.500374\pi$
$840$	10.7429	+	15.3152i	0.370667	+	0.528423i
$841$	−23.9045	−	16.2978i	−0.824295	−	0.561995i
$842$	−21.7057	+	8.51884i	−0.748027	+	0.293579i
$843$	2.15579	+	23.4496i	0.0742494	+	0.807647i
$844$	−0.426123	+	1.08574i	−0.0146678	+	0.0373728i
$845$	6.39677	−	5.93534i	0.220056	−	0.204182i
$846$	−13.4773	−	4.77119i	−0.463360	−	0.164037i
$847$	−6.16958	+	12.6951i	−0.211989	+	0.436209i
$848$	9.79598	−	3.84464i	0.336395	−	0.132025i
$849$	−13.6489	+	9.64703i	−0.468429	+	0.331085i
$850$	84.2058	−	19.2194i	2.88824	−	0.659221i
$851$		−	15.4203i		−	0.528602i
$852$	5.55826	−	10.0137i	0.190423	−	0.343064i
$853$	−11.6936	+	37.9097i	−0.400381	+	1.29800i	0.501178	+	0.865344i	$0.332900\pi$
$853$	−11.6936	+	37.9097i	−0.400381	+	1.29800i	−0.901558	+	0.432658i	$0.857576\pi$
$854$	19.1530	+	7.59605i	0.655404	+	0.259931i
$855$	−4.87129	−	14.0860i	−0.166595	−	0.481732i
$856$	2.23739	−	0.690143i	0.0764723	−	0.0235886i
$857$	17.0264	+	2.56631i	0.581609	+	0.0876635i	0.433256	−	0.901271i	$-0.357365\pi$
$857$	17.0264	+	2.56631i	0.581609	+	0.0876635i	0.148353	+	0.988934i	$0.452603\pi$
$858$	15.8985	+	2.12259i	0.542765	+	0.0724640i
$859$	2.36623	−	2.55018i	0.0807346	−	0.0870112i	−0.691392	−	0.722479i	$-0.743002\pi$
$859$	2.36623	−	2.55018i	0.0807346	−	0.0870112i	0.772127	+	0.635468i	$0.219193\pi$
$860$	9.29889	−	2.86833i	0.317090	−	0.0978092i
$861$	−15.2835	+	40.5188i	−0.520860	+	1.38088i
$862$	−19.8190	−	6.11335i	−0.675038	−	0.208222i
$863$	17.8584	−	10.3105i	0.607906	−	0.350975i	−0.164240	−	0.986420i	$-0.552517\pi$
$863$	17.8584	−	10.3105i	0.607906	−	0.350975i	0.772145	+	0.635446i	$0.219184\pi$
$864$	−5.18949	+	0.262951i	−0.176550	+	0.00894579i
$865$	36.7696	+	11.3419i	1.25020	+	0.385636i
$866$	10.8395	+	5.22003i	0.368341	+	0.177384i
$867$	−51.9020	−	39.9765i	−1.76268	−	1.35767i
$868$	1.40954	+	19.7553i	0.0478430	+	0.670539i
$869$	8.04559	+	3.15766i	0.272928	+	0.107116i
$870$	−52.2584	+	12.8591i	−1.77173	+	0.435966i
$871$	−55.0275	−	21.5967i	−1.86454	−	0.731776i
$872$	−9.44825	−	13.8580i	−0.319958	−	0.469292i
$873$	−20.1274	−	14.9685i	−0.681210	−	0.506606i
$874$	2.02660	+	4.20828i	0.0685508	+	0.142347i
$875$	71.8041	−	5.12323i	2.42742	−	0.173197i
$876$	−0.858143	−	9.33443i	−0.0289940	−	0.315381i
$877$	3.10142	−	41.3856i	0.104728	−	1.39749i	−0.659092	−	0.752063i	$-0.729059\pi$
$877$	3.10142	−	41.3856i	0.104728	−	1.39749i	0.763819	−	0.645430i	$-0.223322\pi$
$878$	−5.05222	+	22.1352i	−0.170504	+	0.747027i
$879$	7.34644	+	14.6187i	0.247789	+	0.493077i
$880$	−7.59659	+	6.05808i	−0.256081	+	0.204218i
$881$	49.0799			1.65354			0.826772	−	0.562538i	$-0.190175\pi$
$881$	49.0799			1.65354			0.826772	+	0.562538i	$0.190175\pi$
$882$	8.60492	−	19.1561i	0.289743	−	0.645019i
$883$	9.64520			0.324587			0.162293	−	0.986743i	$-0.448111\pi$
$883$	9.64520			0.324587			0.162293	+	0.986743i	$0.448111\pi$
$884$	22.5230	−	17.9615i	0.757531	−	0.604111i
$885$	12.5292	−	19.0603i	0.421165	−	0.640704i
$886$	−2.42388	+	10.6197i	−0.0814317	+	0.356776i
$887$	2.34085	−	31.2364i	0.0785980	−	1.04882i	−0.808882	−	0.587971i	$-0.799927\pi$
$887$	2.34085	−	31.2364i	0.0785980	−	1.04882i	0.887480	−	0.460846i	$-0.152454\pi$
$888$	−6.32001	−	2.91321i	−0.212086	−	0.0977611i
$889$	46.7841	−	26.7886i	1.56909	−	0.898459i
$890$	19.2608	+	39.9954i	0.645622	+	1.34065i
$891$	17.6106	+	12.1959i	0.589976	+	0.408577i
$892$	−2.14758	−	3.14992i	−0.0719063	−	0.105467i
$893$	5.39893	+	2.11892i	0.180668	+	0.0709071i
$894$	−8.38763	−	8.73920i	−0.280524	−	0.292282i
$895$	64.5838	+	25.3473i	2.15880	+	0.847266i
$896$	−2.53098	+	0.770817i	−0.0845540	+	0.0257512i
$897$	−23.9129	+	9.85397i	−0.798428	+	0.329014i
$898$	3.14726	+	1.51564i	0.105025	+	0.0505776i
$899$	−54.4452	−	16.7941i	−1.81585	−	0.560116i
$900$	−16.4649	+	30.8798i	−0.548828	+	1.02933i
$901$	−67.4796	+	38.9594i	−2.24807	+	1.29793i
$902$	−21.4931	−	6.62974i	−0.715642	−	0.220746i
$903$	−8.10587	−	7.32288i	−0.269746	−	0.243690i
$904$	4.62863	−	1.42774i	0.153946	−	0.0474860i
$905$	−17.6709	+	19.0447i	−0.587401	+	0.633068i
$906$	2.38099	−	3.09128i	0.0791032	−	0.102701i
$907$	19.0153	+	2.86610i	0.631394	+	0.0951674i	0.456939	−	0.889498i	$-0.348946\pi$
$907$	19.0153	+	2.86610i	0.631394	+	0.0951674i	0.174455	+	0.984665i	$0.444184\pi$
$908$	−11.3251	+	3.49335i	−0.375838	+	0.115931i
$909$	22.6209	+	19.6110i	0.750289	+	0.650456i
$910$	36.4672	−	20.8811i	1.20888	−	0.692201i
$911$	−0.0307091	+	0.0995566i	−0.00101744	+	0.00329846i	−0.956080	−	0.293106i	$-0.905311\pi$
$911$	−0.0307091	+	0.0995566i	−0.00101744	+	0.00329846i	0.955063	+	0.296404i	$0.0957875\pi$
$912$	2.10763	−	0.0355707i	0.0697905	−	0.00117786i
$913$			13.6389i			0.451383i
$914$	28.1921	−	6.43467i	0.932513	−	0.212840i
$915$	5.04101	+	54.8335i	0.166651	+	1.81274i
$916$	−4.05983	+	1.59336i	−0.134140	+	0.0526462i
$917$	−4.23272	−	3.40028i	−0.139777	−	0.112287i
$918$	37.7053	−	7.65213i	1.24446	−	0.252558i
$919$	−13.8063	+	12.8103i	−0.455427	+	0.422574i	−0.874237	−	0.485499i	$-0.838638\pi$
$919$	−13.8063	+	12.8103i	−0.455427	+	0.422574i	0.418810	+	0.908074i	$0.362447\pi$
$920$	5.72403	−	14.5846i	0.188716	−	0.480839i
$921$	21.6055	−	15.2707i	0.711925	−	0.503187i
$922$	−4.89998	+	1.92310i	−0.161372	+	0.0633340i
$923$	−21.2563	−	14.4923i	−0.699661	−	0.477021i
$924$	10.2053	+	3.84940i	0.335731	+	0.126636i
$925$	−38.7243	+	26.4018i	−1.27325	+	0.868086i
$926$	−5.15397	+	7.55949i	−0.169370	+	0.248420i
$927$	−9.28901	−	1.79271i	−0.305091	−	0.0588802i
$928$	0.568793	−	7.59001i	0.0186715	−	0.249154i
$929$	−12.2514	−	15.3628i	−0.401956	−	0.504036i	0.539122	−	0.842228i	$-0.318756\pi$
$929$	−12.2514	−	15.3628i	−0.401956	−	0.504036i	−0.941077	+	0.338191i	$0.890185\pi$
$930$	−45.3855	+	27.2347i	−1.48825	+	0.893061i
$931$	−3.75101	+	7.64884i	−0.122934	+	0.250680i
$932$	12.9531	−	7.47850i	0.424294	−	0.244966i
$933$	−3.15792	−	18.7937i	−0.103386	−	0.615279i
$934$	6.49932	−	9.53275i	0.212664	−	0.311921i
$935$	48.9339	−	52.7382i	1.60031	−	1.72472i
$936$	−0.478991	+	11.6623i	−0.0156563	+	0.381194i
$937$	5.56108	−	11.5477i	0.181673	−	0.377247i	−0.790167	−	0.612892i	$-0.790006\pi$
$937$	5.56108	−	11.5477i	0.181673	−	0.377247i	0.971839	+	0.235645i	$0.0757203\pi$
$938$	−33.1325	−	22.7631i	−1.08181	−	0.743240i
$939$	−0.0675385	+	1.16468i	−0.00220404	+	0.0380077i
$940$	−7.10761	−	18.1099i	−0.231825	−	0.590679i
$941$	31.0526	+	14.9542i	1.01229	+	0.487492i	0.865091	−	0.501615i	$-0.167261\pi$
$941$	31.0526	+	14.9542i	1.01229	+	0.487492i	0.147197	+	0.989107i	$0.452975\pi$
$942$	2.76110	+	16.4321i	0.0899614	+	0.535388i
$943$	35.3594	−	8.07056i	1.15146	−	0.262814i
$944$	2.01133	+	2.52212i	0.0654631	+	0.0820881i
$945$	56.0599	−	2.63991i	1.82363	−	0.0858764i
$946$	3.53750	−	4.43589i	0.115014	−	0.144223i
$947$	−18.6931	+	38.8166i	−0.607444	+	1.26137i	0.339691	+	0.940537i	$0.389678\pi$
$947$	−18.6931	+	38.8166i	−0.607444	+	1.26137i	−0.947135	+	0.320834i	$0.896037\pi$
$948$	−1.75221	+	6.04062i	−0.0569093	+	0.196190i
$949$	−21.0563			−0.683518
$950$	7.09822	−	12.2945i	0.230297	−	0.398886i
$951$	15.4067	+	4.46905i	0.499596	+	0.144919i
$952$	17.6802	−	8.43670i	0.573018	−	0.273435i
$953$	19.5979	+	4.47310i	0.634839	+	0.144898i	0.527816	−	0.849359i	$-0.323011\pi$
$953$	19.5979	+	4.47310i	0.634839	+	0.144898i	0.107023	+	0.994257i	$0.465868\pi$
$954$	5.98243	−	30.9983i	0.193688	−	1.00361i
$955$	−3.02628	+	1.18773i	−0.0979280	+	0.0384339i
$956$	2.53893	−	16.8447i	0.0821150	−	0.544798i
$957$	−20.9511	+	23.3584i	−0.677253	+	0.755070i
$958$	−6.10600	−	19.7952i	−0.197276	−	0.639553i
$959$	−5.16869	−	13.3091i	−0.166906	−	0.429775i
$960$	−4.89609	−	5.10131i	−0.158021	−	0.164644i
$961$	−25.0371			−0.807647
$962$	−7.81613	+	13.5379i	−0.252002	+	0.436481i
$963$	1.84275	−	6.77821i	0.0593818	−	0.218425i
$964$	16.7031	−	1.25172i	0.537970	−	0.0403153i
$965$	9.44900	+	24.0757i	0.304174	+	0.775023i
$966$	−17.3549	+	2.85247i	−0.558384	+	0.0917767i
$967$	11.0463	−	28.1454i	0.355224	−	0.905095i	−0.635854	−	0.771809i	$-0.719352\pi$
$967$	11.0463	−	28.1454i	0.355224	−	0.905095i	0.991078	−	0.133286i	$-0.0425528\pi$
$968$	1.57250	−	5.09791i	0.0505419	−	0.163853i
$969$	−15.3920	+	2.58632i	−0.494461	+	0.0830845i
$970$	−2.55071	−	34.0368i	−0.0818982	−	1.09286i
$971$	39.4931	+	5.95263i	1.26739	+	0.191029i	0.748111	−	0.663574i	$-0.230961\pi$
$971$	39.4931	+	5.95263i	1.26739	+	0.191029i	0.519283	+	0.854602i	$0.326199\pi$
$972$	−7.66457	+	13.5740i	−0.245841	+	0.435387i
$973$	−42.7037	−	13.3395i	−1.36902	−	0.427645i
$974$	7.19646	+	10.5553i	0.230589	+	0.338213i
$975$	65.6880	+	43.1799i	2.10370	+	1.38286i
$976$	−7.59246	−	1.73293i	−0.243029	−	0.0554697i
$977$	10.3155	+	21.4203i	0.330022	+	0.685297i	0.998280	−	0.0586325i	$-0.0186740\pi$
$977$	10.3155	+	21.4203i	0.330022	+	0.685297i	−0.668258	+	0.743930i	$0.732960\pi$
$978$	14.1375	+	17.1268i	0.452066	+	0.547653i
$979$	22.4146	+	12.9411i	0.716374	+	0.413599i
$980$	27.3659	−	8.22770i	0.874170	−	0.262824i
$981$	−50.2887	+	1.69794i	−1.60559	+	0.0542111i
$982$	0.339087	−	0.863978i	0.0108207	−	0.0275707i
$983$	50.3306	+	34.3148i	1.60530	+	1.09447i	0.936295	+	0.351214i	$0.114231\pi$
$983$	50.3306	+	34.3148i	1.60530	+	1.09447i	0.669003	+	0.743260i	$0.266721\pi$
$984$	3.37240	−	16.0167i	0.107508	−	0.510594i
$985$	−36.9002	−	2.76529i	−1.17574	−	0.0881094i
$986$	4.21152	+	56.1988i	0.134122	+	1.78973i
$987$	−13.3880	+	17.2540i	−0.426145	+	0.549202i
$988$	0.353849	−	4.72179i	0.0112575	−	0.150220i
$989$	−1.36356	+	9.04664i	−0.0433587	+	0.287666i
$990$	3.15796	+	28.9776i	0.100367	+	0.920970i
$991$	22.7758	−	3.43290i	0.723497	−	0.109050i	0.223038	−	0.974810i	$-0.428403\pi$
$991$	22.7758	−	3.43290i	0.723497	−	0.109050i	0.500459	+	0.865760i	$0.333165\pi$
$992$	−1.66575	−	7.29811i	−0.0528875	−	0.231715i
$993$	−9.66345	−	57.5102i	−0.306660	−	1.82503i
$994$	−11.8535	−	12.8668i	−0.375969	−	0.408112i
$995$	4.14812	−	27.5210i	0.131504	−	0.872475i
$996$	−9.88351	+	0.908621i	−0.313171	+	0.0287908i
$997$	−9.07336	−	9.77875i	−0.287356	−	0.309696i	0.572832	−	0.819673i	$-0.305845\pi$
$997$	−9.07336	−	9.77875i	−0.287356	−	0.309696i	−0.860188	+	0.509976i	$0.829654\pi$
$998$	32.4692	+	18.7461i	1.02779	+	0.593397i
$999$	−17.5289	+	11.3403i	−0.554590	+	0.358790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bk.a.101.1	yes	672
9.5	odd	6		882.2.bc.a.689.30	yes	672
49.33	odd	42		882.2.bc.a.425.30	✓	672
441.131	even	42	inner	882.2.bk.a.131.1	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bc.a.425.30	✓	672	49.33	odd	42
882.2.bc.a.689.30	yes	672	9.5	odd	6
882.2.bk.a.101.1	yes	672	1.1	even	1	trivial
882.2.bk.a.131.1	yes	672	441.131	even	42	inner

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bk (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.72915 - 0.100272i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.305069 - 4.07086i) q^{5} +(1.41442 - 0.999709i) q^{6} +(-0.770817 - 2.53098i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.97989 + 0.346769i) q^{9} +O(q^{10})\)	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.72915 - 0.100272i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.305069 - 4.07086i) q^{5} +(1.41442 - 0.999709i) q^{6} +(-0.770817 - 2.53098i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.97989 + 0.346769i) q^{9} +(2.29963 + 3.37294i) q^{10} +(2.21561 + 0.869564i) q^{11} +(-0.482529 + 1.66348i) q^{12} +(3.62176 + 1.42143i) q^{13} +(2.18069 + 1.49820i) q^{14} +(-0.935701 + 7.00853i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(7.07536 + 2.18246i) q^{17} +(-2.54598 + 1.58682i) q^{18} +(1.05396 - 0.608506i) q^{19} +(-3.90091 - 1.20327i) q^{20} +(1.07907 + 4.45372i) q^{21} +(-2.27440 + 0.701559i) q^{22} +(2.61048 - 2.81342i) q^{23} +(-0.659907 - 1.60141i) q^{24} +(-11.5347 - 1.73858i) q^{25} +(-3.71785 + 1.14681i) q^{26} +(-5.11790 - 0.898413i) q^{27} +(-2.63904 + 0.188296i) q^{28} +(2.24347 - 7.27314i) q^{29} +(-3.63819 - 6.06289i) q^{30} -7.48579i q^{31} +(0.974928 - 0.222521i) q^{32} +(-3.74392 - 1.72577i) q^{33} +(-6.89248 + 2.70510i) q^{34} +(-10.5384 + 2.36577i) q^{35} +(1.00116 - 2.82802i) q^{36} +(2.94529 - 2.73283i) q^{37} +(-0.444624 + 1.13288i) q^{38} +(-6.12001 - 2.82103i) q^{39} +(3.80009 - 1.49142i) q^{40} +(7.80796 + 5.32338i) q^{41} +(-3.62050 - 2.80927i) q^{42} +(-1.96956 + 1.34283i) q^{43} +(1.34078 - 1.96657i) q^{44} +(2.32072 - 12.0249i) q^{45} +(-0.286811 + 3.82723i) q^{46} +(2.97133 + 3.72594i) q^{47} +(1.51440 + 0.840590i) q^{48} +(-5.81168 + 3.90184i) q^{49} +(10.1022 - 5.83250i) q^{50} +(-12.0155 - 4.48325i) q^{51} +(2.19171 - 3.21465i) q^{52} +(-7.15775 + 7.71422i) q^{53} +(4.56148 - 2.48855i) q^{54} +(4.21579 - 8.75418i) q^{55} +(1.94589 - 1.79263i) q^{56} +(-1.88347 + 0.946513i) q^{57} +(2.78072 + 7.08515i) q^{58} +(-2.90645 - 1.39967i) q^{59} +(6.62460 + 2.47179i) q^{60} +(7.59246 - 1.73293i) q^{61} +(4.66731 + 5.85263i) q^{62} +(-1.41929 - 7.80933i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.89135 - 14.3100i) q^{65} +(4.00311 - 0.985040i) q^{66} -15.1936 q^{67} +(3.70216 - 6.41232i) q^{68} +(-4.79600 + 4.60306i) q^{69} +(6.76423 - 8.42023i) q^{70} +(-6.44655 - 1.47138i) q^{71} +(0.980498 + 2.83525i) q^{72} +(-5.03785 + 1.97721i) q^{73} +(-0.598829 + 3.97297i) q^{74} +(19.7709 + 4.16286i) q^{75} +(-0.358720 - 1.16294i) q^{76} +(0.493014 - 6.27794i) q^{77} +(6.54370 - 1.61020i) q^{78} +3.63132 q^{79} +(-2.04114 + 3.53536i) q^{80} +(8.75950 + 2.06667i) q^{81} +(-9.42359 + 0.706200i) q^{82} +(2.09352 + 5.33419i) q^{83} +(4.58217 - 0.0609697i) q^{84} +(11.0430 - 28.1370i) q^{85} +(0.702629 - 2.27787i) q^{86} +(-4.60857 + 12.3514i) q^{87} +(0.177868 + 2.37349i) q^{88} +(10.7527 + 1.62072i) q^{89} +(5.68302 + 10.8484i) q^{90} +(0.805906 - 10.2622i) q^{91} +(-2.16200 - 3.17107i) q^{92} +(-0.750613 + 12.9440i) q^{93} +(-4.64617 - 1.06046i) q^{94} +(-2.15561 - 4.47618i) q^{95} +(-1.70811 + 0.287013i) q^{96} +(-7.24090 - 4.18054i) q^{97} +(2.11100 - 6.67411i) q^{98} +(6.30074 + 3.35951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9	\( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) \) 672 * q + 112 * q^4 + 14 * q^6 - 2 * q^7 + 10 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^15 - 112 * q^16 + 18 * q^17 + 8 * q^18 + 12 * q^21 + 18 * q^23 + 56 * q^25 - 12 * q^26 + 48 * q^27 + 2 * q^28 - 6 * q^29 + 4 * q^30 - 30 * q^35 - 10 * q^36 - 26 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^42 + 2 * q^43 + 58 * q^45 + 78 * q^46 - 90 * q^47 + 8 * q^49 + 24 * q^50 + 6 * q^51 - 22 * q^52 + 12 * q^53 - 18 * q^54 - 42 * q^55 - 6 * q^56 - 28 * q^57 + 78 * q^58 - 60 * q^59 - 6 * q^60 + 98 * q^61 - 36 * q^62 - 36 * q^63 + 112 * q^64 - 24 * q^66 + 28 * q^67 - 18 * q^68 + 14 * q^69 + 18 * q^70 + 126 * q^71 - 8 * q^72 - 18 * q^74 - 102 * q^75 + 42 * q^77 - 8 * q^78 - 8 * q^79 + 26 * q^81 + 30 * q^84 + 80 * q^87 - 186 * q^89 - 102 * q^90 + 12 * q^91 - 18 * q^92 - 224 * q^93 - 6 * q^97 + 24 * q^98 + 194 * q^99

Introduction

L-functions

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