LMFDB - Embedded newform 418.2.q.a.21.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.6
Character	$\chi$	$=$	418.21
Dual form			418.2.q.a.219.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.0268646 - 0.0320160i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.843173 + 0.306890i) q^{5} +(0.0268646 + 0.0320160i) q^{6} +(2.35018 - 1.35688i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.520641 + 2.95270i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0268646 - 0.0320160i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.843173 + 0.306890i) q^{5} +(0.0268646 + 0.0320160i) q^{6} +(2.35018 - 1.35688i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.520641 + 2.95270i) q^{9} +(-0.155812 - 0.883655i) q^{10} +(-1.48055 + 2.96782i) q^{11} +(-0.0361945 + 0.0208969i) q^{12} +(1.74073 - 1.46065i) q^{13} +(0.928158 + 2.55009i) q^{14} +(-0.0128261 + 0.0352395i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.35271 + 0.767500i) q^{17} -2.99825 q^{18} +(-2.41240 + 3.63047i) q^{19} +0.897286 q^{20} +(0.0196949 - 0.111695i) q^{21} +(-2.66564 - 1.97342i) q^{22} +(7.94098 + 2.89028i) q^{23} +(-0.0142943 - 0.0392734i) q^{24} +(-3.21346 + 2.69642i) q^{25} +(1.13618 + 1.96793i) q^{26} +(0.217104 + 0.125345i) q^{27} +(-2.67252 + 0.471238i) q^{28} +(0.228566 + 1.29626i) q^{29} +(-0.0324769 - 0.0187505i) q^{30} +(-4.92457 + 2.84320i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.0552433 + 0.127131i) q^{33} +(-1.51168 + 4.15331i) q^{34} +(-1.56520 + 1.86533i) q^{35} +(0.520641 - 2.95270i) q^{36} -3.73539i q^{37} +(-3.15640 - 3.00618i) q^{38} -0.0949710i q^{39} +(-0.155812 + 0.883655i) q^{40} +(5.23763 + 4.39489i) q^{41} +(0.106578 + 0.0387913i) q^{42} +(-3.20971 - 8.81861i) q^{43} +(2.40632 - 2.28246i) q^{44} +(-1.34515 - 2.32986i) q^{45} +(-4.22531 + 7.31845i) q^{46} +(0.547427 + 3.10461i) q^{47} +(0.0411589 - 0.00725743i) q^{48} +(0.182227 - 0.315626i) q^{49} +(-2.09744 - 3.63287i) q^{50} +(0.141506 - 0.118738i) q^{51} +(-2.13533 + 0.777195i) q^{52} +(2.08830 - 5.73755i) q^{53} +(-0.161141 + 0.192040i) q^{54} +(0.337567 - 2.95675i) q^{55} -2.71375i q^{56} +(0.0514247 + 0.174766i) q^{57} -1.31626 q^{58} +(-3.52865 - 0.622197i) q^{59} +(0.0241052 - 0.0287275i) q^{60} +(4.68333 - 12.8673i) q^{61} +(-1.94486 - 5.34347i) q^{62} +(5.23005 + 6.23293i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01948 + 1.76579i) q^{65} +(-0.134792 + 0.0323280i) q^{66} +(10.1808 - 1.79514i) q^{67} +(-3.82771 - 2.20993i) q^{68} +(0.305866 - 0.176592i) q^{69} +(-1.56520 - 1.86533i) q^{70} +(-3.82341 - 10.5047i) q^{71} +(2.81744 + 1.02546i) q^{72} +(-3.20646 + 3.82131i) q^{73} +(3.67864 + 0.648643i) q^{74} +0.175320i q^{75} +(3.50861 - 2.58643i) q^{76} +(0.547406 + 8.98384i) q^{77} +(0.0935282 + 0.0164915i) q^{78} +(0.352076 + 0.295427i) q^{79} +(-0.843173 - 0.306890i) q^{80} +(-8.44246 + 3.07281i) q^{81} +(-5.23763 + 4.39489i) q^{82} +(-3.56527 + 2.05841i) q^{83} +(-0.0567091 + 0.0982230i) q^{84} +(-3.90563 + 0.688667i) q^{85} +(9.24199 - 1.62961i) q^{86} +(0.0476414 + 0.0275058i) q^{87} +(1.82993 + 2.76611i) q^{88} +(5.32414 + 6.34506i) q^{89} +(2.52805 - 0.920134i) q^{90} +(2.10912 - 5.79475i) q^{91} +(-6.47355 - 5.43195i) q^{92} +(-0.0412686 + 0.234046i) q^{93} -3.15251 q^{94} +(0.919920 - 3.80146i) q^{95} +0.0417939i q^{96} +(10.1556 + 1.79070i) q^{97} +(0.279188 + 0.234266i) q^{98} +(-9.53393 - 2.82646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.0268646	−	0.0320160i	0.0155103	−	0.0184844i	−0.758234	−	0.651983i	$-0.773937\pi$
$3$	0.0268646	−	0.0320160i	0.0155103	−	0.0184844i	0.773744	+	0.633499i	$0.218382\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.843173	+	0.306890i	−0.377079	+	0.137245i	−0.523605	−	0.851961i	$-0.675413\pi$
$5$	−0.843173	+	0.306890i	−0.377079	+	0.137245i	0.146526	+	0.989207i	$0.453191\pi$
$6$	0.0268646	+	0.0320160i	0.0109674	+	0.0130705i
$7$	2.35018	−	1.35688i	0.888284	−	0.512851i	0.0149032	−	0.999889i	$-0.495256\pi$
$7$	2.35018	−	1.35688i	0.888284	−	0.512851i	0.873381	+	0.487038i	$0.161923\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.520641	+	2.95270i	0.173547	+	0.984234i
$10$	−0.155812	−	0.883655i	−0.0492721	−	0.279436i
$11$	−1.48055	+	2.96782i	−0.446403	+	0.894832i
$11$	−1.48055	+	2.96782i	−0.446403	+	0.894832i
$12$	−0.0361945	+	0.0208969i	−0.0104485	+	0.00603242i
$13$	1.74073	−	1.46065i	0.482793	−	0.405111i	−0.368642	−	0.929571i	$-0.620177\pi$
$13$	1.74073	−	1.46065i	0.482793	−	0.405111i	0.851435	+	0.524460i	$0.175733\pi$
$14$	0.928158	+	2.55009i	0.248061	+	0.681541i
$15$	−0.0128261	+	0.0352395i	−0.00331169	+	0.00909879i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.35271	+	0.767500i	1.05569	+	0.186146i	0.674442	−	0.738328i	$-0.264384\pi$
$17$	4.35271	+	0.767500i	1.05569	+	0.186146i	0.381245	+	0.924474i	$0.375495\pi$
$18$	−2.99825			−0.706695
$19$	−2.41240	+	3.63047i	−0.553443	+	0.832887i
$19$	−2.41240	+	3.63047i	−0.553443	+	0.832887i
$20$	0.897286			0.200639
$21$	0.0196949	−	0.111695i	0.00429777	−	0.0243739i
$22$	−2.66564	−	1.97342i	−0.568316	−	0.420734i
$23$	7.94098	+	2.89028i	1.65581	+	0.602665i	0.989696	−	0.143185i	$-0.0457343\pi$
$23$	7.94098	+	2.89028i	1.65581	+	0.602665i	0.666114	+	0.745850i	$0.267957\pi$
$24$	−0.0142943	−	0.0392734i	−0.00291782	−	0.00801665i
$25$	−3.21346	+	2.69642i	−0.642692	+	0.539283i
$26$	1.13618	+	1.96793i	0.222824	+	0.385942i
$27$	0.217104	+	0.125345i	0.0417817	+	0.0241227i
$28$	−2.67252	+	0.471238i	−0.505060	+	0.0890556i
$29$	0.228566	+	1.29626i	0.0424436	+	0.240710i	0.998648	−	0.0519917i	$-0.0165569\pi$
$29$	0.228566	+	1.29626i	0.0424436	+	0.240710i	−0.956204	+	0.292701i	$0.905446\pi$
$30$	−0.0324769	−	0.0187505i	−0.00592944	−	0.00342336i
$31$	−4.92457	+	2.84320i	−0.884478	+	0.510654i	−0.872132	−	0.489270i	$-0.837263\pi$
$31$	−4.92457	+	2.84320i	−0.884478	+	0.510654i	−0.0123459	+	0.999924i	$0.503930\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	0.0552433	+	0.127131i	0.00961662	+	0.0221306i
$34$	−1.51168	+	4.15331i	−0.259251	+	0.712286i
$35$	−1.56520	+	1.86533i	−0.264566	+	0.315298i
$36$	0.520641	−	2.95270i	0.0867735	−	0.492117i
$37$		−	3.73539i		−	0.614094i	−0.951694	−	0.307047i	$-0.900659\pi$
$37$		−	3.73539i		−	0.614094i	0.951694	−	0.307047i	$-0.0993408\pi$
$38$	−3.15640	−	3.00618i	−0.512036	−	0.487667i
$39$		−	0.0949710i		−	0.0152075i
$40$	−0.155812	+	0.883655i	−0.0246361	+	0.139718i
$41$	5.23763	+	4.39489i	0.817980	+	0.686367i	0.952498	−	0.304545i	$-0.0985043\pi$
$41$	5.23763	+	4.39489i	0.817980	+	0.686367i	−0.134518	+	0.990911i	$0.542949\pi$
$42$	0.106578	+	0.0387913i	0.0164454	+	0.00598563i
$43$	−3.20971	−	8.81861i	−0.489476	−	1.34482i	−0.901155	−	0.433496i	$-0.857280\pi$
$43$	−3.20971	−	8.81861i	−0.489476	−	1.34482i	0.411679	−	0.911329i	$-0.364942\pi$
$44$	2.40632	−	2.28246i	0.362766	−	0.344094i
$45$	−1.34515	−	2.32986i	−0.200523	−	0.347315i
$46$	−4.22531	+	7.31845i	−0.622988	+	1.07905i
$47$	0.547427	+	3.10461i	0.0798504	+	0.452854i	0.998349	+	0.0574310i	$0.0182909\pi$
$47$	0.547427	+	3.10461i	0.0798504	+	0.452854i	−0.918499	+	0.395423i	$0.870598\pi$
$48$	0.0411589	−	0.00725743i	0.00594078	−	0.00104752i
$49$	0.182227	−	0.315626i	0.0260324	−	0.0450894i
$50$	−2.09744	−	3.63287i	−0.296623	−	0.513765i
$51$	0.141506	−	0.118738i	0.0198148	−	0.0166266i
$52$	−2.13533	+	0.777195i	−0.296117	+	0.107778i
$53$	2.08830	−	5.73755i	0.286850	−	0.788113i	−0.709653	−	0.704552i	$-0.751148\pi$
$53$	2.08830	−	5.73755i	0.286850	−	0.788113i	0.996503	−	0.0835617i	$-0.0266296\pi$
$54$	−0.161141	+	0.192040i	−0.0219284	+	0.0261333i
$55$	0.337567	−	2.95675i	0.0455175	−	0.398689i
$56$		−	2.71375i		−	0.362640i
$57$	0.0514247	+	0.174766i	0.00681137	+	0.0231484i
$58$	−1.31626			−0.172833
$59$	−3.52865	−	0.622197i	−0.459391	−	0.0810031i	−0.0608369	−	0.998148i	$-0.519377\pi$
$59$	−3.52865	−	0.622197i	−0.459391	−	0.0810031i	−0.398555	+	0.917145i	$0.630488\pi$
$60$	0.0241052	−	0.0287275i	0.00311197	−	0.00370870i
$61$	4.68333	−	12.8673i	0.599639	−	1.64749i	−0.152356	−	0.988326i	$-0.548686\pi$
$61$	4.68333	−	12.8673i	0.599639	−	1.64749i	0.751995	−	0.659169i	$-0.229092\pi$
$62$	−1.94486	−	5.34347i	−0.246998	−	0.678621i
$63$	5.23005	+	6.23293i	0.658925	+	0.785276i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.01948	+	1.76579i	−0.126451	+	0.219020i
$66$	−0.134792	+	0.0323280i	−0.0165918	+	0.00397930i
$67$	10.1808	−	1.79514i	1.24378	−	0.219312i	0.487244	−	0.873266i	$-0.338002\pi$
$67$	10.1808	−	1.79514i	1.24378	−	0.219312i	0.756534	+	0.653954i	$0.226891\pi$
$68$	−3.82771	−	2.20993i	−0.464178	−	0.267993i
$69$	0.305866	−	0.176592i	0.0368220	−	0.0212592i
$70$	−1.56520	−	1.86533i	−0.187077	−	0.222949i
$71$	−3.82341	−	10.5047i	−0.453755	−	1.24668i	−0.930062	−	0.367402i	$-0.880247\pi$
$71$	−3.82341	−	10.5047i	−0.453755	−	1.24668i	0.476307	−	0.879279i	$-0.341975\pi$
$72$	2.81744	+	1.02546i	0.332038	+	0.120852i
$73$	−3.20646	+	3.82131i	−0.375288	+	0.447251i	−0.920321	−	0.391164i	$-0.872073\pi$
$73$	−3.20646	+	3.82131i	−0.375288	+	0.447251i	0.545033	+	0.838414i	$0.316517\pi$
$74$	3.67864	+	0.648643i	0.427633	+	0.0754032i
$75$			0.175320i			0.0202442i
$76$	3.50861	−	2.58643i	0.402465	−	0.296684i
$77$	0.547406	+	8.98384i	0.0623827	+	1.02380i
$78$	0.0935282	+	0.0164915i	0.0105900	+	0.00186730i
$79$	0.352076	+	0.295427i	0.0396117	+	0.0332382i	0.662379	−	0.749169i	$-0.269547\pi$
$79$	0.352076	+	0.295427i	0.0396117	+	0.0332382i	−0.622767	+	0.782407i	$0.713991\pi$
$80$	−0.843173	−	0.306890i	−0.0942696	−	0.0343113i
$81$	−8.44246	+	3.07281i	−0.938052	+	0.341423i
$82$	−5.23763	+	4.39489i	−0.578399	+	0.485334i
$83$	−3.56527	+	2.05841i	−0.391339	+	0.225940i	−0.682740	−	0.730661i	$-0.739212\pi$
$83$	−3.56527	+	2.05841i	−0.391339	+	0.225940i	0.291401	+	0.956601i	$0.405879\pi$
$84$	−0.0567091	+	0.0982230i	−0.00618747	+	0.0107170i
$85$	−3.90563	+	0.688667i	−0.423625	+	0.0746964i
$86$	9.24199	−	1.62961i	0.996590	−	0.175726i
$87$	0.0476414	+	0.0275058i	0.00510769	+	0.00294893i
$88$	1.82993	+	2.76611i	0.195072	+	0.294868i
$89$	5.32414	+	6.34506i	0.564358	+	0.672575i	0.970463	−	0.241251i	$-0.0775577\pi$
$89$	5.32414	+	6.34506i	0.564358	+	0.672575i	−0.406105	+	0.913826i	$0.633113\pi$
$90$	2.52805	−	0.920134i	0.266480	−	0.0969906i
$91$	2.10912	−	5.79475i	0.221095	−	0.607455i
$92$	−6.47355	−	5.43195i	−0.674914	−	0.566320i
$93$	−0.0412686	+	0.234046i	−0.00427936	+	0.0242694i
$94$	−3.15251			−0.325156
$95$	0.919920	−	3.80146i	0.0943818	−	0.390021i
$96$			0.0417939i			0.00426557i
$97$	10.1556	+	1.79070i	1.03114	+	0.181818i	0.663522	−	0.748157i	$-0.269061\pi$
$97$	10.1556	+	1.79070i	1.03114	+	0.181818i	0.367622	+	0.929976i	$0.380172\pi$
$98$	0.279188	+	0.234266i	0.0282022	+	0.0236645i
$99$	−9.53393	−	2.82646i	−0.958196	−	0.284070i
$100$	3.94190	−	1.43473i	0.394190	−	0.143473i
$101$	5.58046	+	6.65053i	0.555277	+	0.661753i	0.968540	−	0.248859i	$-0.0800555\pi$
$101$	5.58046	+	6.65053i	0.555277	+	0.661753i	−0.413263	+	0.910612i	$0.635611\pi$
$102$	0.0923614	+	0.159975i	0.00914514	+	0.0158399i
$103$	−12.3964	−	7.15706i	−1.22145	−	0.705206i	−0.256226	−	0.966617i	$-0.582479\pi$
$103$	−12.3964	−	7.15706i	−1.22145	−	0.705206i	−0.965228	+	0.261411i	$0.915812\pi$
$104$	−0.394592	−	2.23785i	−0.0386930	−	0.219439i
$105$	0.0176719	+	0.100223i	0.00172460	+	0.00978072i
$106$	5.28776	+	3.05289i	0.513592	+	0.296523i
$107$	−9.34493	−	16.1859i	−0.903408	−	1.56475i	−0.823040	−	0.567984i	$-0.807724\pi$
$107$	−9.34493	−	16.1859i	−0.903408	−	1.56475i	−0.0803686	−	0.996765i	$-0.525610\pi$
$108$	−0.161141	−	0.192040i	−0.0155058	−	0.0184790i
$109$	16.1883	−	5.89205i	1.55056	−	0.564356i	0.582008	−	0.813183i	$-0.302267\pi$
$109$	16.1883	−	5.89205i	1.55056	−	0.564356i	0.968548	+	0.248827i	$0.0800452\pi$
$110$	2.85322	+	0.845874i	0.272044	+	0.0806509i
$111$	−0.119592	−	0.100350i	−0.0113512	−	0.00952476i
$112$	2.67252	+	0.471238i	0.252530	+	0.0445278i
$113$		−	7.84800i		−	0.738278i	−0.929374	−	0.369139i	$-0.879653\pi$
$113$		−	7.84800i		−	0.738278i	0.929374	−	0.369139i	$-0.120347\pi$
$114$	−0.181041	+	0.0202956i	−0.0169561	+	0.00190086i
$115$	−7.58263			−0.707083
$116$	0.228566	−	1.29626i	0.0212218	−	0.120355i
$117$	5.21916	+	4.37940i	0.482512	+	0.404875i
$118$	1.22549	−	3.36700i	0.112815	−	0.309958i
$119$	11.2710	−	4.10232i	1.03322	−	0.376060i
$120$	0.0241052	+	0.0287275i	0.00220050	+	0.00262245i
$121$	−6.61593	−	8.78803i	−0.601449	−	0.798912i
$122$	11.8586	+	6.84657i	1.07363	+	0.619859i
$123$	0.281413	−	0.0496207i	0.0253742	−	0.00447415i
$124$	5.60001	−	0.987433i	0.502896	−	0.0886741i
$125$	4.12522	−	7.14509i	0.368971	−	0.639076i
$126$	−7.04643	+	4.06826i	−0.627746	+	0.362429i
$127$	8.01016	−	6.72132i	0.710786	−	0.596421i	−0.214033	−	0.976826i	$-0.568660\pi$
$127$	8.01016	−	6.72132i	0.710786	−	0.596421i	0.924820	+	0.380406i	$0.124216\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−0.368564	−	0.134146i	−0.0324502	−	0.0118109i
$130$	−1.56194	−	1.31062i	−0.136991	−	0.114949i
$131$	−10.1404	−	1.78803i	−0.885974	−	0.156221i	−0.287898	−	0.957661i	$-0.592957\pi$
$131$	−10.1404	−	1.78803i	−0.885974	−	0.156221i	−0.598075	+	0.801440i	$0.704068\pi$
$132$	−0.00843048	−	0.138358i	−0.000733779	−	0.0120425i
$133$	−0.743483	+	11.8056i	−0.0644681	+	1.02367i
$134$			10.3378i			0.893051i
$135$	−0.221524	−	0.0390606i	−0.0190657	−	0.00336180i
$136$	2.84103	−	3.38581i	0.243616	−	0.290330i
$137$	10.0848	+	3.67056i	0.861601	+	0.313597i	0.734761	−	0.678326i	$-0.237294\pi$
$137$	10.0848	+	3.67056i	0.861601	+	0.313597i	0.126840	+	0.991923i	$0.459516\pi$
$138$	0.120796	+	0.331884i	0.0102828	+	0.0282519i
$139$	−11.2136	−	13.3639i	−0.951126	−	1.13351i	−0.990941	−	0.134301i	$-0.957121\pi$
$139$	−11.2136	−	13.3639i	−0.951126	−	1.13351i	0.0398142	−	0.999207i	$-0.487323\pi$
$140$	2.10878	−	1.21751i	0.178225	−	0.102898i
$141$	0.114103	+	0.0658777i	0.00960925	+	0.00554790i
$142$	11.0091	−	1.94119i	0.923860	−	0.162901i
$143$	1.75770	+	7.32876i	0.146986	+	0.612861i
$144$	−1.49913	+	2.59656i	−0.124927	+	0.216380i
$145$	−0.590530	−	1.02283i	−0.0490409	−	0.0849413i
$146$	−3.20646	−	3.82131i	−0.265369	−	0.316254i
$147$	−0.00520962	−	0.0143133i	−0.000429683	−	0.00118054i
$148$	−1.27758	+	3.51011i	−0.105016	+	0.288530i
$149$	−0.875460	+	1.04333i	−0.0717205	+	0.0854732i	−0.800712	−	0.599050i	$-0.795545\pi$
$149$	−0.875460	+	1.04333i	−0.0717205	+	0.0854732i	0.728991	+	0.684523i	$0.239990\pi$
$150$	−0.172657	−	0.0304440i	−0.0140974	−	0.00248574i
$151$	−21.0348			−1.71179			−0.855893	−	0.517152i	$-0.826992\pi$
$151$	−21.0348			−1.71179			−0.855893	+	0.517152i	$0.826992\pi$
$152$	1.93788	+	3.90444i	0.157183	+	0.316692i
$153$			13.2518i			1.07135i
$154$	−8.94241	−	1.02094i	−0.720600	−	0.0822694i
$155$	3.27971	−	3.90861i	0.263433	−	0.313947i
$156$	−0.0324820	+	0.0892436i	−0.00260064	+	0.00714520i
$157$	−10.7679	+	3.91918i	−0.859369	+	0.312785i	−0.733854	−	0.679307i	$-0.762280\pi$
$157$	−10.7679	+	3.91918i	−0.859369	+	0.312785i	−0.125515	+	0.992092i	$0.540058\pi$
$158$	−0.352076	+	0.295427i	−0.0280097	+	0.0235029i
$159$	−0.127592	−	0.220996i	−0.0101187	−	0.0175261i
$160$	0.448643	−	0.777073i	0.0354684	−	0.0614330i
$161$	22.5845	−	3.98225i	1.77991	−	0.313846i
$162$	−1.56010	−	8.84779i	−0.122573	−	0.695148i
$163$	−2.08548	+	3.61215i	−0.163347	+	0.282926i	−0.936067	−	0.351822i	$-0.885562\pi$
$163$	−2.08548	+	3.61215i	−0.163347	+	0.282926i	0.772720	+	0.634747i	$0.218896\pi$
$164$	−3.41862	−	5.92122i	−0.266949	−	0.462370i
$165$	−0.0855947	−	0.0902395i	−0.00666354	−	0.00702513i
$166$	−1.40803	−	3.86854i	−0.109285	−	0.300257i
$167$	−3.97800	−	1.44787i	−0.307827	−	0.112040i	0.183488	−	0.983022i	$-0.441261\pi$
$167$	−3.97800	−	1.44787i	−0.307827	−	0.112040i	−0.491315	+	0.870982i	$0.663483\pi$
$168$	−0.0868834	−	0.0729038i	−0.00670320	−	0.00562465i
$169$	−1.36077	+	7.71729i	−0.104674	+	0.593638i
$170$		−	3.96588i		−	0.304169i
$171$	−11.9757	−	5.23294i	−0.915804	−	0.400173i
$172$			9.38457i			0.715566i
$173$	−2.71735	+	15.4109i	−0.206597	+	1.17167i	0.688311	+	0.725416i	$0.258353\pi$
$173$	−2.71735	+	15.4109i	−0.206597	+	1.17167i	−0.894907	+	0.446252i	$0.852759\pi$
$174$	−0.0353607	+	0.0421413i	−0.00268069	+	0.00319472i
$175$	−3.89351	+	10.6973i	−0.294322	+	0.808642i
$176$	−3.04185	+	1.32180i	−0.229288	+	0.0996347i
$177$	−0.114716	+	0.0962581i	−0.00862258	+	0.00723520i
$178$	−7.17319	+	4.14145i	−0.537654	+	0.310414i
$179$	22.1656	+	12.7973i	1.65673	+	0.956516i	0.974207	+	0.225656i	$0.0724526\pi$
$179$	22.1656	+	12.7973i	1.65673	+	0.956516i	0.682528	+	0.730860i	$0.260881\pi$
$180$	0.467164	+	2.64942i	0.0348204	+	0.197476i
$181$	−16.2432	+	2.86412i	−1.20735	+	0.212888i	−0.740873	−	0.671645i	$-0.765588\pi$
$181$	−16.2432	+	2.86412i	−1.20735	+	0.212888i	−0.466476	+	0.884534i	$0.654477\pi$
$182$	5.34047	+	3.08332i	0.395862	+	0.228551i
$183$	−0.286145	−	0.495617i	−0.0211524	−	0.0366371i
$184$	6.47355	−	5.43195i	0.477236	−	0.400449i
$185$	1.14635	+	3.14958i	0.0842815	+	0.231562i
$186$	−0.223324	−	0.0812833i	−0.0163749	−	0.00595998i
$187$	−8.72221	+	11.7817i	−0.637831	+	0.861566i
$188$	0.547427	−	3.10461i	0.0399252	−	0.226427i
$189$	0.680311			0.0494854
$190$	3.58396	+	1.56606i	0.260008	+	0.113614i
$191$	−3.15867			−0.228553			−0.114277	−	0.993449i	$-0.536455\pi$
$191$	−3.15867			−0.228553			−0.114277	+	0.993449i	$0.536455\pi$
$192$	−0.0411589	−	0.00725743i	−0.00297039	−	0.000523760i
$193$	−10.1524	−	8.51889i	−0.730787	−	0.613203i	0.199559	−	0.979886i	$-0.436049\pi$
$193$	−10.1524	−	8.51889i	−0.730787	−	0.613203i	−0.930346	+	0.366683i	$0.880493\pi$
$194$	−3.52700	+	9.69034i	−0.253224	+	0.695726i
$195$	0.0291457	+	0.0800770i	0.00208716	+	0.00573443i
$196$	−0.279188	+	0.234266i	−0.0199420	+	0.0167333i
$197$	−7.62536	+	4.40250i	−0.543284	+	0.313665i	−0.746409	−	0.665488i	$-0.768224\pi$
$197$	−7.62536	+	4.40250i	−0.543284	+	0.313665i	0.203125	+	0.979153i	$0.434890\pi$
$198$	4.43907	−	8.89828i	0.315471	−	0.632373i
$199$	2.15156	+	12.2021i	0.152520	+	0.864983i	0.961018	+	0.276485i	$0.0891695\pi$
$199$	2.15156	+	12.2021i	0.152520	+	0.864983i	−0.808499	+	0.588498i	$0.799719\pi$
$200$	0.728433	+	4.13115i	0.0515080	+	0.292116i
$201$	0.216029	−	0.374172i	0.0152375	−	0.0263921i
$202$	−7.51853	+	4.34083i	−0.529002	+	0.305420i
$203$	2.29604	+	2.73631i	0.161150	+	0.192051i
$204$	−0.173583	+	0.0631789i	−0.0121532	+	0.00442341i
$205$	−5.76498	−	2.09828i	−0.402643	−	0.146550i
$206$	9.20094	−	10.9653i	0.641060	−	0.763986i
$207$	−4.39974	+	24.9522i	−0.305803	+	1.73430i
$208$	2.27237			0.157560
$209$	−7.20290	−	12.5347i	−0.498235	−	0.867042i
$210$	−0.101769			−0.00702270
$211$	2.48768	−	14.1083i	0.171259	−	0.971257i	−0.771115	−	0.636696i	$-0.780301\pi$
$211$	2.48768	−	14.1083i	0.171259	−	0.971257i	0.942374	−	0.334562i	$-0.108588\pi$
$212$	−3.92472	+	4.67729i	−0.269551	+	0.321238i
$213$	−0.439033	−	0.159795i	−0.0300820	−	0.0109490i
$214$	17.5627	−	6.39231i	1.20056	−	0.436969i
$215$	5.41268	+	6.45059i	0.369142	+	0.439926i
$216$	0.217104	−	0.125345i	0.0147721	−	0.00852865i
$217$	−7.71574	+	13.3641i	−0.523779	+	0.907211i
$218$	2.99147	+	16.9655i	0.202608	+	1.14905i
$219$	0.0362027	+	0.205316i	0.00244635	+	0.0138740i
$220$	−1.32848	+	2.66299i	−0.0895660	+	0.179538i
$221$	8.69796	−	5.02177i	0.585088	−	0.337801i
$222$	0.119592	−	0.100350i	0.00802648	−	0.00673502i
$223$	0.996244	+	2.73716i	0.0667134	+	0.183294i	0.968570	−	0.248743i	$-0.0800174\pi$
$223$	0.996244	+	2.73716i	0.0667134	+	0.183294i	−0.901856	+	0.432036i	$0.857795\pi$
$224$	−0.928158	+	2.55009i	−0.0620152	+	0.170385i
$225$	−9.63477	−	8.08454i	−0.642318	−	0.538969i
$226$	7.72877	+	1.36279i	0.514110	+	0.0906515i
$227$	−19.5384			−1.29681			−0.648406	−	0.761295i	$-0.724564\pi$
$227$	−19.5384			−1.29681			−0.648406	+	0.761295i	$0.724564\pi$
$228$	0.0114502	−	0.181815i	0.000758308	−	0.0120410i
$229$	29.6336			1.95825			0.979123	−	0.203270i	$-0.0651568\pi$
$229$	29.6336			1.95825			0.979123	+	0.203270i	$0.0651568\pi$
$230$	1.31671	−	7.46743i	0.0868212	−	0.492388i
$231$	0.302332	+	0.223821i	0.0198920	+	0.0147264i
$232$	1.23688	+	0.450187i	0.0812050	+	0.0295562i
$233$	−5.36726	−	14.7464i	−0.351621	−	0.966070i	−0.981850	−	0.189661i	$-0.939261\pi$
$233$	−5.36726	−	14.7464i	−0.351621	−	0.966070i	0.630229	−	0.776409i	$-0.282961\pi$
$234$	−5.21916	+	4.37940i	−0.341187	+	0.286290i
$235$	−1.41435	−	2.44973i	−0.0922620	−	0.159803i
$236$	3.10305	+	1.79154i	0.201991	+	0.116620i
$237$	0.0189168	−	0.00333554i	0.00122878	−	0.000216666i
$238$	2.08280	+	11.8122i	0.135008	+	0.765670i
$239$	9.25680	+	5.34442i	0.598773	+	0.345702i	0.768559	−	0.639779i	$-0.220974\pi$
$239$	9.25680	+	5.34442i	0.598773	+	0.345702i	−0.169786	+	0.985481i	$0.554308\pi$
$240$	−0.0324769	+	0.0187505i	−0.00209637	+	0.00121034i
$241$	16.3719	−	13.7377i	1.05461	−	0.884921i	0.0610375	−	0.998135i	$-0.480559\pi$
$241$	16.3719	−	13.7377i	1.05461	−	0.884921i	0.993571	+	0.113214i	$0.0361146\pi$
$242$	9.80336	−	4.98940i	0.630184	−	0.320731i
$243$	−0.385648	+	1.05956i	−0.0247393	+	0.0679707i
$244$	−8.80178	+	10.4896i	−0.563476	+	0.671525i
$245$	−0.0567863	+	0.322051i	−0.00362794	+	0.0205751i
$246$			0.285754i			0.0182190i
$247$	1.10349	+	9.84336i	0.0702133	+	0.626318i
$248$			5.68640i			0.361087i
$249$	−0.0298775	+	0.169444i	−0.00189341	+	0.0107381i
$250$	6.32020	+	5.30328i	0.399725	+	0.335409i
$251$	−2.62030	−	0.953709i	−0.165392	−	0.0601976i	0.257997	−	0.966146i	$-0.416937\pi$
$251$	−2.62030	−	0.953709i	−0.165392	−	0.0601976i	−0.423389	+	0.905948i	$0.639160\pi$
$252$	−2.78285	−	7.64583i	−0.175303	−	0.481642i
$253$	−20.3349	+	19.2882i	−1.27844	+	1.21264i
$254$	5.22826	+	9.05561i	0.328050	+	0.568199i
$255$	−0.0828746	+	0.143543i	−0.00518981	+	0.00898902i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−5.92321	+	1.04442i	−0.369479	+	0.0651492i	−0.355305	−	0.934750i	$-0.615623\pi$
$257$	−5.92321	+	1.04442i	−0.369479	+	0.0651492i	−0.0141743	+	0.999900i	$0.504512\pi$
$258$	0.196109	−	0.339670i	0.0122092	−	0.0211469i
$259$	−5.06846	−	8.77882i	−0.314939	−	0.545490i
$260$	1.56194	−	1.31062i	0.0968672	−	0.0812813i
$261$	−3.70847	+	1.34977i	−0.229549	+	0.0835489i
$262$	3.52174	−	9.67589i	0.217574	−	0.597778i
$263$	−12.2887	+	14.6452i	−0.757756	+	0.903059i	−0.997704	−	0.0677270i	$-0.978425\pi$
$263$	−12.2887	+	14.6452i	−0.757756	+	0.903059i	0.239947	+	0.970786i	$0.422870\pi$
$264$	0.137720	+	0.0157232i	0.00847607	+	0.000967697i
$265$			5.47863i			0.336549i
$266$	−11.4971	−	2.78221i	−0.704934	−	0.170588i
$267$	0.346174			0.0211855
$268$	−10.1808	−	1.79514i	−0.621889	−	0.109656i
$269$	5.21014	−	6.20920i	0.317668	−	0.378582i	−0.583455	−	0.812145i	$-0.698300\pi$
$269$	5.21014	−	6.20920i	0.317668	−	0.378582i	0.901123	+	0.433564i	$0.142744\pi$
$270$	0.0769343	−	0.211375i	0.00468207	−	0.0128639i
$271$	−3.42805	−	9.41848i	−0.208239	−	0.572132i	0.790972	−	0.611852i	$-0.209575\pi$
$271$	−3.42805	−	9.41848i	−0.208239	−	0.572132i	−0.999211	+	0.0397208i	$0.987353\pi$
$272$	2.84103	+	3.38581i	0.172263	+	0.205295i
$273$	−0.128864	−	0.223199i	−0.00779920	−	0.0135086i
$274$	−5.36600	+	9.29419i	−0.324172	+	0.561482i
$275$	−3.24478	−	13.5292i	−0.195668	−	0.815839i
$276$	−0.347818	+	0.0613298i	−0.0209362	+	0.00369162i
$277$	7.04243	+	4.06595i	0.423139	+	0.244299i	0.696419	−	0.717635i	$-0.254775\pi$
$277$	7.04243	+	4.06595i	0.423139	+	0.244299i	−0.273281	+	0.961934i	$0.588109\pi$
$278$	15.1081	−	8.72264i	0.906121	−	0.523149i
$279$	−10.9591	−	13.0605i	−0.656102	−	0.781911i
$280$	0.832824	+	2.28816i	0.0497707	+	0.136744i
$281$	13.2095	+	4.80785i	0.788011	+	0.286812i	0.704509	−	0.709695i	$-0.251167\pi$
$281$	13.2095	+	4.80785i	0.788011	+	0.286812i	0.0835018	+	0.996508i	$0.473390\pi$
$282$	−0.0846907	+	0.100930i	−0.00504326	+	0.00601032i
$283$	23.3488	+	4.11702i	1.38794	+	0.244731i	0.817179	−	0.576384i	$-0.195537\pi$
$283$	23.3488	+	4.11702i	1.38794	+	0.244731i	0.570762	+	0.821116i	$0.306648\pi$
$284$			11.1789i			0.663345i
$285$	−0.0969940	−	0.131577i	−0.00574543	−	0.00779393i
$286$	−7.52264	+	0.458372i	−0.444823	+	0.0271041i
$287$	18.2727	+	3.22197i	1.07860	+	0.190187i
$288$	−2.29680	−	1.92724i	−0.135340	−	0.113564i
$289$	2.38224	+	0.867064i	0.140132	+	0.0510038i
$290$	1.10983	−	0.403946i	0.0651717	−	0.0237205i
$291$	0.330156	−	0.277034i	0.0193541	−	0.0162400i
$292$	4.32005	−	2.49418i	0.252812	−	0.145961i
$293$	3.22532	−	5.58643i	0.188425	−	0.326363i	−0.756300	−	0.654225i	$-0.772995\pi$
$293$	3.22532	−	5.58643i	0.188425	−	0.326363i	0.944725	+	0.327862i	$0.106328\pi$
$294$	0.0150005	−	0.00264500i	0.000874848	−	0.000154259i
$295$	3.16621	−	0.558289i	0.184344	−	0.0325048i
$296$	−3.23494	−	1.86769i	−0.188027	−	0.108557i
$297$	−0.693436	+	0.458746i	−0.0402372	+	0.0266192i
$298$	−0.875460	−	1.04333i	−0.0507140	−	0.0604386i
$299$	18.0448	−	6.56778i	1.04356	−	0.379825i
$300$	0.0599630	−	0.164747i	0.00346197	−	0.00951167i
$301$	−19.5092	−	16.3701i	−1.12449	−	0.943558i
$302$	3.65265	−	20.7152i	0.210187	−	1.19203i
$303$	0.362840			0.0208446
$304$	−4.18163	+	1.23044i	−0.239833	+	0.0705704i
$305$			12.2867i			0.703532i
$306$	−13.0505	−	2.30116i	−0.746049	−	0.131549i
$307$	−4.80276	−	4.02999i	−0.274108	−	0.230004i	0.495362	−	0.868686i	$-0.335035\pi$
$307$	−4.80276	−	4.02999i	−0.274108	−	0.230004i	−0.769470	+	0.638683i	$0.779480\pi$
$308$	2.55826	−	8.62927i	0.145770	−	0.491698i
$309$	−0.562164	+	0.204611i	−0.0319804	+	0.0116399i
$310$	3.27971	+	3.90861i	0.186275	+	0.221994i
$311$	−13.1486	−	22.7741i	−0.745591	−	1.29140i	−0.949918	−	0.312499i	$-0.898834\pi$
$311$	−13.1486	−	22.7741i	−0.745591	−	1.29140i	0.204327	−	0.978903i	$-0.434499\pi$
$312$	−0.0822473	−	0.0474855i	−0.00465634	−	0.00268834i
$313$	0.231603	+	1.31349i	0.0130910	+	0.0742427i	0.990653	−	0.136403i	$-0.0435543\pi$
$313$	0.231603	+	1.31349i	0.0130910	+	0.0742427i	−0.977562	+	0.210646i	$0.932443\pi$
$314$	−1.98982	−	11.2848i	−0.112292	−	0.636840i
$315$	−6.32267	−	3.65039i	−0.356242	−	0.205676i
$316$	−0.229802	−	0.398028i	−0.0129274	−	0.0223908i
$317$	16.0267	+	19.0998i	0.900148	+	1.07275i	0.996996	+	0.0774551i	$0.0246794\pi$
$317$	16.0267	+	19.0998i	0.900148	+	1.07275i	−0.0968481	+	0.995299i	$0.530876\pi$
$318$	0.239794	−	0.0872780i	0.0134470	−	0.00489431i
$319$	−4.18548	−	1.24084i	−0.234342	−	0.0694736i
$320$	0.687361	+	0.576765i	0.0384247	+	0.0322421i
$321$	−0.769254	−	0.135640i	−0.0429356	−	0.00757070i
$322$			22.9329i			1.27800i
$323$	−13.2869	+	13.9509i	−0.739302	+	0.776246i
$324$	8.98428			0.499127
$325$	−1.65527	+	9.38749i	−0.0918177	+	0.520724i
$326$	−3.19514	−	2.68104i	−0.176962	−	0.148489i
$327$	0.246252	−	0.676570i	0.0136177	−	0.0374144i
$328$	6.42490	−	2.33847i	0.354756	−	0.129121i
$329$	5.49912	+	6.55360i	0.303177	+	0.361312i
$330$	0.103732	−	0.0686244i	0.00571025	−	0.00377765i
$331$	11.7611	+	6.79025i	0.646446	+	0.373226i	0.787093	−	0.616834i	$-0.211585\pi$
$331$	11.7611	+	6.79025i	0.646446	+	0.373226i	−0.140647	+	0.990060i	$0.544918\pi$
$332$	4.05427	−	0.714877i	0.222507	−	0.0392340i
$333$	11.0295	−	1.94480i	0.604412	−	0.106574i
$334$	2.11665	−	3.66614i	0.115818	−	0.200602i
$335$	−8.03323	+	4.63799i	−0.438902	+	0.253400i
$336$	0.0868834	−	0.0729038i	0.00473988	−	0.00397723i
$337$	28.0104	−	10.1949i	1.52582	−	0.555354i	0.563228	−	0.826302i	$-0.309559\pi$
$337$	28.0104	−	10.1949i	1.52582	−	0.555354i	0.962594	+	0.270948i	$0.0873372\pi$
$338$	−7.36376	−	2.68019i	−0.400536	−	0.145783i
$339$	−0.251261	−	0.210833i	−0.0136466	−	0.0114509i
$340$	3.90563	+	0.688667i	0.211812	+	0.0373482i
$341$	−1.14704	−	18.8247i	−0.0621155	−	1.01942i
$342$	7.23300	−	10.8851i	0.391116	−	0.588597i
$343$			18.0072i			0.972299i
$344$	−9.24199	−	1.62961i	−0.498295	−	0.0878628i
$345$	−0.203704	+	0.242765i	−0.0109671	+	0.0130700i
$346$	−14.7049	−	5.35214i	−0.790540	−	0.287733i
$347$	−2.18771	−	6.01068i	−0.117442	−	0.322670i	0.867018	−	0.498277i	$-0.166034\pi$
$347$	−2.18771	−	6.01068i	−0.117442	−	0.322670i	−0.984460	+	0.175606i	$0.943811\pi$
$348$	−0.0353607	−	0.0421413i	−0.00189553	−	0.00225901i
$349$	3.53283	−	2.03968i	0.189108	−	0.109182i	−0.402457	−	0.915439i	$-0.631844\pi$
$349$	3.53283	−	2.03968i	0.189108	−	0.109182i	0.591565	+	0.806257i	$0.298510\pi$
$350$	−9.85871	−	5.69193i	−0.526970	−	0.304246i
$351$	0.561006	−	0.0989204i	0.0299443	−	0.00527998i
$352$	−0.773511	−	3.22516i	−0.0412283	−	0.171902i
$353$	8.02125	−	13.8932i	0.426928	−	0.739461i	−0.569670	−	0.821873i	$-0.692929\pi$
$353$	8.02125	−	13.8932i	0.426928	−	0.739461i	0.996598	+	0.0824125i	$0.0262625\pi$
$354$	−0.0748755	−	0.129688i	−0.00397959	−	0.00689285i
$355$	6.44759	+	7.68394i	0.342202	+	0.407821i
$356$	−2.83292	−	7.78337i	−0.150144	−	0.412518i
$357$	0.171452	−	0.471060i	0.00907420	−	0.0249312i
$358$	−16.4519	+	19.6066i	−0.869510	+	1.03624i
$359$	25.9093	+	4.56850i	1.36744	+	0.241116i	0.808697	−	0.588226i	$-0.200173\pi$
$359$	25.9093	+	4.56850i	1.36744	+	0.241116i	0.558741	+	0.829342i	$0.311284\pi$
$360$	−2.69029			−0.141791
$361$	−7.36061	−	17.5163i	−0.387401	−	0.921911i
$362$		−	16.4938i		−	0.866895i
$363$	−0.459091	−	0.0242712i	−0.0240960	−	0.00127391i
$364$	−3.96384	+	4.72392i	−0.207762	+	0.247601i
$365$	1.53088	−	4.20606i	0.0801299	−	0.220155i
$366$	0.537776	−	0.195734i	0.0281100	−	0.0102312i
$367$	5.50631	−	4.62034i	0.287427	−	0.241180i	−0.487661	−	0.873033i	$-0.662150\pi$
$367$	5.50631	−	4.62034i	0.287427	−	0.241180i	0.775088	+	0.631853i	$0.217705\pi$
$368$	4.22531	+	7.31845i	0.220259	+	0.381501i
$369$	−10.2499	+	17.7533i	−0.533588	+	0.924201i
$370$	−3.30079	+	0.582018i	−0.171600	+	0.0302577i
$371$	−2.87727	−	16.3178i	−0.149381	−	0.847180i
$372$	0.118828	−	0.205817i	0.00616096	−	0.0106711i
$373$	−11.9925	−	20.7716i	−0.620947	−	1.07551i	−0.989310	−	0.145830i	$-0.953415\pi$
$373$	−11.9925	−	20.7716i	−0.620947	−	1.07551i	0.368362	−	0.929682i	$-0.379919\pi$
$374$	−10.0882	−	10.6356i	−0.521646	−	0.549953i
$375$	−0.117935	−	0.324023i	−0.00609012	−	0.0167325i
$376$	2.96239	+	1.07822i	0.152773	+	0.0556050i
$377$	2.29126	+	1.92259i	0.118006	+	0.0990185i
$378$	−0.118135	+	0.669976i	−0.00607620	+	0.0344598i
$379$		−	25.2410i		−	1.29654i	−0.761410	−	0.648270i	$-0.775493\pi$
$379$		−	25.2410i		−	1.29654i	0.761410	−	0.648270i	$-0.224507\pi$
$380$	−2.16462	+	3.25757i	−0.111043	+	0.167110i
$381$		−	0.437018i		−	0.0223891i
$382$	0.548497	−	3.11068i	0.0280635	−	0.159156i
$383$	10.5292	−	12.5482i	0.538016	−	0.641182i	−0.426726	−	0.904381i	$-0.640333\pi$
$383$	10.5292	−	12.5482i	0.538016	−	0.641182i	0.964742	+	0.263199i	$0.0847775\pi$
$384$	0.0142943	−	0.0392734i	0.000729455	−	0.00200416i
$385$	−3.21861	−	7.40694i	−0.164035	−	0.377493i
$386$	10.1524	−	8.51889i	0.516744	−	0.433600i
$387$	24.3676	−	14.0687i	1.23868	−	0.715150i
$388$	−8.93067	−	5.15612i	−0.453386	−	0.261763i
$389$	1.92619	+	10.9239i	0.0976615	+	0.553866i	0.993899	+	0.110292i	$0.0351785\pi$
$389$	1.92619	+	10.9239i	0.0976615	+	0.553866i	−0.896238	+	0.443574i	$0.853710\pi$
$390$	−0.0839216	+	0.0147976i	−0.00424953	+	0.000749307i
$391$	32.3465	+	18.6753i	1.63583	+	0.944448i
$392$	−0.182227	−	0.315626i	−0.00920384	−	0.0159415i
$393$	−0.329664	+	0.276621i	−0.0166293	+	0.0139537i
$394$	−3.01149	−	8.27400i	−0.151717	−	0.416838i
$395$	−0.387525	−	0.141048i	−0.0194985	−	0.00709688i
$396$	7.99226	+	5.91680i	0.401626	+	0.297330i
$397$	−0.135022	+	0.765748i	−0.00677656	+	0.0384318i	−0.988009	−	0.154399i	$-0.950656\pi$
$397$	−0.135022	+	0.765748i	−0.00677656	+	0.0384318i	0.981232	+	0.192831i	$0.0617669\pi$
$398$	−12.3903			−0.621071
$399$	0.357994	+	0.340955i	0.0179221	+	0.0170691i
$400$	−4.19488			−0.209744
$401$	−1.42992	−	0.252133i	−0.0714066	−	0.0125909i	0.137831	−	0.990456i	$-0.455987\pi$
$401$	−1.42992	−	0.252133i	−0.0714066	−	0.0125909i	−0.209237	+	0.977865i	$0.567098\pi$
$402$	0.330975	+	0.277721i	0.0165075	+	0.0138515i
$403$	−4.41944	+	12.1423i	−0.220148	+	0.604852i
$404$	−2.96930	−	8.15809i	−0.147728	−	0.405880i
$405$	6.17545	−	5.18182i	0.306860	−	0.257486i
$406$	−3.09344	+	1.78600i	−0.153525	+	0.0886377i
$407$	11.0860	+	5.53043i	0.549511	+	0.274133i
$408$	−0.0320768	−	0.181916i	−0.00158804	−	0.00900621i
$409$	−1.70352	−	9.66113i	−0.0842336	−	0.477712i	−0.997519	−	0.0703929i	$-0.977575\pi$
$409$	−1.70352	−	9.66113i	−0.0842336	−	0.477712i	0.913286	−	0.407319i	$-0.133536\pi$
$410$	3.06748	−	5.31303i	0.151492	−	0.262392i
$411$	0.388440	−	0.224266i	0.0191603	−	0.0110622i
$412$	9.20094	+	10.9653i	0.453298	+	0.540219i
$413$	−9.13721	+	3.32567i	−0.449613	+	0.163646i
$414$	−23.8091	−	8.66580i	−1.17015	−	0.425901i
$415$	2.37443	−	2.82974i	0.116556	−	0.138906i
$416$	−0.394592	+	2.23785i	−0.0193465	+	0.109719i
$417$	−0.729106			−0.0357045
$418$	13.5950	−	4.91684i	0.664954	−	0.240491i
$419$	−34.6110			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$419$	−34.6110			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$420$	0.0176719	−	0.100223i	0.000862302	−	0.00489036i
$421$	−8.40885	+	10.0213i	−0.409822	+	0.488407i	−0.930989	−	0.365048i	$-0.881053\pi$
$421$	−8.40885	+	10.0213i	−0.409822	+	0.488407i	0.521166	+	0.853455i	$0.325497\pi$
$422$	13.4620	+	4.89977i	0.655320	+	0.238517i
$423$	−8.88198	+	3.23278i	−0.431857	+	0.157183i
$424$	−3.92472	−	4.67729i	−0.190601	−	0.227150i
$425$	−16.0568	+	9.27038i	−0.778867	+	0.449679i
$426$	0.233604	−	0.404615i	0.0113182	−	0.0196037i
$427$	−6.45273	−	36.5952i	−0.312269	−	1.77097i
$428$	3.24546	+	18.4059i	0.156875	+	0.889683i
$429$	0.281857	+	0.140609i	0.0136082	+	0.00678869i
$430$	−7.29249	+	4.21032i	−0.351675	+	0.203040i
$431$	14.4193	−	12.0993i	0.694555	−	0.582801i	−0.225663	−	0.974205i	$-0.572455\pi$
$431$	14.4193	−	12.0993i	0.694555	−	0.582801i	0.920219	+	0.391404i	$0.128011\pi$
$432$	0.0857411	+	0.235572i	0.00412522	+	0.0113339i
$433$	9.77508	−	26.8568i	0.469760	−	1.29066i	−0.448182	−	0.893942i	$-0.647928\pi$
$433$	9.77508	−	26.8568i	0.469760	−	1.29066i	0.917942	−	0.396714i	$-0.129849\pi$
$434$	−11.8212	−	9.91916i	−0.567436	−	0.476135i
$435$	−0.0486112	−	0.00857146i	−0.00233073	−	0.000410970i
$436$	−17.2272			−0.825033
$437$	−29.6499	+	21.8570i	−1.41835	+	1.04556i
$438$	−0.208483			−0.00996171
$439$	−5.12055	+	29.0401i	−0.244391	+	1.38601i	0.577513	+	0.816381i	$0.304023\pi$
$439$	−5.12055	+	29.0401i	−0.244391	+	1.38601i	−0.821904	+	0.569626i	$0.807088\pi$
$440$	−2.39184	−	1.77072i	−0.114027	−	0.0844157i
$441$	1.02682	+	0.373734i	0.0488964	+	0.0177968i
$442$	3.43509	+	9.43784i	0.163391	+	0.448912i
$443$	10.1951	−	8.55472i	0.484385	−	0.406447i	−0.367624	−	0.929974i	$-0.619829\pi$
$443$	10.1951	−	8.55472i	0.484385	−	0.406447i	0.852009	+	0.523527i	$0.175384\pi$
$444$	0.0780581	+	0.135201i	0.00370447	+	0.00641634i
$445$	−6.43641	−	3.71606i	−0.305115	−	0.176158i
$446$	−2.86857	+	0.505806i	−0.135831	+	0.0239506i
$447$	0.00988443	+	0.0560574i	0.000467517	+	0.00265142i
$448$	−2.35018	−	1.35688i	−0.111036	−	0.0641064i
$449$	−22.3719	+	12.9164i	−1.05580	+	0.609565i	−0.924267	−	0.381748i	$-0.875322\pi$
$449$	−22.3719	+	12.9164i	−1.05580	+	0.609565i	−0.131530	+	0.991312i	$0.541989\pi$
$450$	9.63477	−	8.08454i	0.454188	−	0.381109i
$451$	−20.7978	+	9.03748i	−0.979331	+	0.425558i
$452$	−2.68417	+	7.37471i	−0.126253	+	0.346877i
$453$	−0.565091	+	0.673449i	−0.0265503	+	0.0316414i
$454$	3.39281	−	19.2416i	0.159233	−	0.903053i
$455$			5.53324i			0.259403i
$456$	0.177065	+	0.0428481i	0.00829181	+	0.00200655i
$457$			13.3420i			0.624112i	0.950064	+	0.312056i	$0.101018\pi$
$457$			13.3420i			0.624112i	−0.950064	+	0.312056i	$0.898982\pi$
$458$	−5.14583	+	29.1834i	−0.240449	+	1.36365i
$459$	0.848788	+	0.712218i	0.0396180	+	0.0332435i
$460$	7.12534	+	2.59341i	0.332221	+	0.120918i
$461$	0.901787	+	2.47764i	0.0420004	+	0.115395i	0.958920	−	0.283677i	$-0.0915544\pi$
$461$	0.901787	+	2.47764i	0.0420004	+	0.115395i	−0.916919	+	0.399072i	$0.869332\pi$
$462$	−0.272920	+	0.258873i	−0.0126974	+	0.0120438i
$463$	−5.34893	−	9.26462i	−0.248586	−	0.430564i	0.714548	−	0.699587i	$-0.246633\pi$
$463$	−5.34893	−	9.26462i	−0.248586	−	0.430564i	−0.963134	+	0.269023i	$0.913299\pi$
$464$	−0.658129	+	1.13991i	−0.0305529	+	0.0529191i
$465$	−0.0370298	−	0.210006i	−0.00171721	−	0.00973881i
$466$	15.4544	−	2.72503i	0.715911	−	0.126235i
$467$	−5.96133	+	10.3253i	−0.275858	+	0.477799i	−0.970351	−	0.241700i	$-0.922295\pi$
$467$	−5.96133	+	10.3253i	−0.275858	+	0.477799i	0.694494	+	0.719499i	$0.255628\pi$
$468$	−3.40657	−	5.90035i	−0.157469	−	0.272744i
$469$	21.4908	−	18.0329i	0.992354	−	0.832684i
$470$	2.65811	−	0.967472i	0.122609	−	0.0446262i
$471$	−0.163798	+	0.450031i	−0.00754740	+	0.0207363i
$472$	−2.30316	+	2.74480i	−0.106012	+	0.126340i
$473$	30.9242	+	3.53055i	1.42190	+	0.162335i
$474$			0.0192086i			0.000882280i
$475$	−2.03708	−	18.1712i	−0.0934678	−	0.833753i
$476$	−11.9944			−0.549762
$477$	18.0285	+	3.17892i	0.825470	+	0.145553i
$478$	−6.87065	+	8.18812i	−0.314256	+	0.374516i
$479$	0.916169	−	2.51715i	0.0418608	−	0.115012i	−0.917001	−	0.398885i	$-0.869397\pi$
$479$	0.916169	−	2.51715i	0.0418608	−	0.115012i	0.958862	+	0.283873i	$0.0916195\pi$
$480$	−0.0128261	−	0.0352395i	−0.000585430	−	0.00160845i
$481$	−5.45609	−	6.50231i	−0.248776	−	0.296480i
$482$	10.6860	+	18.5087i	0.486734	+	0.843049i
$483$	0.479227	−	0.830046i	0.0218056	−	0.0377684i
$484$	3.21126	+	10.5208i	0.145966	+	0.478219i
$485$	−9.11246	+	1.60677i	−0.413776	+	0.0729598i
$486$	−0.976494	−	0.563779i	−0.0442947	−	0.0255735i
$487$	19.6599	−	11.3506i	0.890874	−	0.514346i	0.0166457	−	0.999861i	$-0.494701\pi$
$487$	19.6599	−	11.3506i	0.890874	−	0.514346i	0.874228	+	0.485515i	$0.161368\pi$
$488$	−8.80178	−	10.4896i	−0.398438	−	0.474840i
$489$	0.0596210	+	0.163807i	0.00269616	+	0.00740763i
$490$	−0.307298	−	0.111847i	−0.0138823	−	0.00505274i
$491$	6.33654	−	7.55159i	0.285964	−	0.340799i	−0.603870	−	0.797083i	$-0.706375\pi$
$491$	6.33654	−	7.55159i	0.285964	−	0.340799i	0.889834	+	0.456284i	$0.150820\pi$
$492$	−0.281413	−	0.0496207i	−0.0126871	−	0.00223708i
$493$			5.81767i			0.262015i
$494$	−9.88544	−	0.622557i	−0.444767	−	0.0280102i
$495$	8.90617	−	0.542674i	0.400303	−	0.0243914i
$496$	−5.60001	−	0.987433i	−0.251448	−	0.0443370i
$497$	−23.2393	−	19.5001i	−1.04242	−	0.874698i
$498$	−0.161681	−	0.0588471i	−0.00724511	−	0.00263700i
$499$	−2.49909	+	0.909593i	−0.111874	+	0.0407190i	−0.397351	−	0.917667i	$-0.630070\pi$
$499$	−2.49909	+	0.909593i	−0.111874	+	0.0407190i	0.285476	+	0.958386i	$0.407848\pi$
$500$	−6.32020	+	5.30328i	−0.282648	+	0.237170i
$501$	−0.153222	+	0.0884629i	−0.00684547	+	0.00395223i
$502$	1.39423	−	2.41488i	0.0622275	−	0.107781i
$503$	38.1310	−	6.72352i	1.70018	−	0.299787i	0.762421	−	0.647082i	$-0.224011\pi$
$503$	38.1310	−	6.72352i	1.70018	−	0.299787i	0.937756	+	0.347295i	$0.112900\pi$
$504$	8.01291	−	1.41289i	0.356923	−	0.0629352i
$505$	−6.74628	−	3.89497i	−0.300205	−	0.173324i
$506$	−15.4641	−	23.3753i	−0.687462	−	1.03916i
$507$	0.210520	+	0.250888i	0.00934953	+	0.0111423i
$508$	−9.82591	+	3.57634i	−0.435954	+	0.158674i
$509$	−5.57609	+	15.3202i	−0.247156	+	0.679055i	0.752632	+	0.658442i	$0.228784\pi$
$509$	−5.57609	+	15.3202i	−0.247156	+	0.679055i	−0.999788	+	0.0206134i	$0.993438\pi$
$510$	−0.126971	−	0.106542i	−0.00562238	−	0.00471774i
$511$	−2.35071	+	13.3315i	−0.103989	+	0.589752i
$512$	−1.00000			−0.0441942
$513$	−0.978804	+	0.485807i	−0.0432153	+	0.0214489i
$514$		−	6.01458i		−	0.265292i
$515$	12.6487	+	2.23031i	0.557370	+	0.0982794i
$516$	0.300456	+	0.252112i	0.0132268	+	0.0110986i
$517$	−10.0244	−	2.97187i	−0.440874	−	0.130703i
$518$	9.52558	−	3.46703i	0.418530	−	0.152332i
$519$	0.420394	+	0.501006i	0.0184532	+	0.0219917i
$520$	1.01948	+	1.76579i	0.0447072	+	0.0774352i
$521$	−21.3965	−	12.3533i	−0.937398	−	0.541207i	−0.0482543	−	0.998835i	$-0.515366\pi$
$521$	−21.3965	−	12.3533i	−0.937398	−	0.541207i	−0.889144	+	0.457628i	$0.848699\pi$
$522$	−0.685298	−	3.88652i	−0.0299947	−	0.170108i
$523$	−0.0314977	−	0.178633i	−0.00137730	−	0.00781106i	0.984111	−	0.177552i	$-0.0568179\pi$
$523$	−0.0314977	−	0.178633i	−0.00137730	−	0.00781106i	−0.985489	+	0.169741i	$0.945707\pi$
$524$	8.91735	+	5.14843i	0.389556	+	0.224910i
$525$	0.237888	+	0.412034i	0.0103823	+	0.0179826i
$526$	−12.2887	−	14.6452i	−0.535815	−	0.638559i
$527$	−23.6174	+	8.59601i	−1.02879	+	0.374448i
$528$	−0.0393991	+	0.132897i	−0.00171463	+	0.00578361i
$529$	37.0865	+	31.1193i	1.61246	+	1.35301i
$530$	−5.39540	−	0.951354i	−0.234361	−	0.0413242i
$531$		−	10.7430i		−	0.466207i
$532$	4.73639	−	10.8393i	0.205349	−	0.469945i
$533$	15.5367			0.672970
$534$	−0.0601125	+	0.340915i	−0.00260132	+	0.0147528i
$535$	12.8467	+	10.7796i	0.555411	+	0.466045i
$536$	3.53574	−	9.71437i	0.152721	−	0.419597i
$537$	1.00519	−	0.365858i	0.0433770	−	0.0157880i
$538$	5.21014	+	6.20920i	0.224625	+	0.267698i
$539$	0.666926	+	1.00812i	0.0287265	+	0.0434227i
$540$	0.194805	+	0.112470i	0.00838305	+	0.00483996i
$541$	20.4361	−	3.60343i	0.878616	−	0.154924i	0.283894	−	0.958856i	$-0.408373\pi$
$541$	20.4361	−	3.60343i	0.878616	−	0.154924i	0.594721	+	0.803932i	$0.297262\pi$
$542$	9.87066	−	1.74046i	0.423981	−	0.0747593i
$543$	−0.344670	+	0.596986i	−0.0147912	+	0.0256191i
$544$	−3.82771	+	2.20993i	−0.164112	+	0.0947499i
$545$	−11.8413	+	9.93604i	−0.507226	+	0.425613i
$546$	0.242185	−	0.0881481i	0.0103646	−	0.00377239i
$547$	−3.79957	−	1.38293i	−0.162458	−	0.0591298i	0.259511	−	0.965740i	$-0.416439\pi$
$547$	−3.79957	−	1.38293i	−0.162458	−	0.0591298i	−0.421969	+	0.906610i	$0.638661\pi$
$548$	−8.22119	−	6.89840i	−0.351192	−	0.294685i
$549$	40.4318	+	7.12921i	1.72559	+	0.304267i
$550$	13.8871	−	0.846172i	0.592147	−	0.0360809i
$551$	−5.25743	−	2.29730i	−0.223974	−	0.0978684i
$552$		−	0.353184i		−	0.0150325i
$553$	1.22830	+	0.216583i	0.0522327	+	0.00921003i
$554$	−5.22708	+	6.22939i	−0.222077	+	0.264662i
$555$	0.131633	+	0.0479105i	0.00558751	+	0.00203369i
$556$	5.96664	+	16.3932i	0.253042	+	0.695227i
$557$	−5.83473	−	6.95356i	−0.247225	−	0.294632i	0.628133	−	0.778106i	$-0.283819\pi$
$557$	−5.83473	−	6.95356i	−0.247225	−	0.294632i	−0.875359	+	0.483474i	$0.839375\pi$
$558$	14.7651	−	8.52463i	0.625056	−	0.360876i
$559$	−18.4681	−	10.6626i	−0.781119	−	0.450980i
$560$	−2.39802	+	0.422836i	−0.101335	+	0.0178681i
$561$	0.142885	+	0.595761i	0.00603261	+	0.0251531i
$562$	−7.02861	+	12.1739i	−0.296484	+	0.513525i
$563$	−13.6114	−	23.5756i	−0.573650	−	0.993591i	−0.996187	−	0.0872454i	$-0.972194\pi$
$563$	−13.6114	−	23.5756i	−0.573650	−	0.993591i	0.422537	−	0.906346i	$-0.361140\pi$
$564$	−0.0846907	−	0.100930i	−0.00356612	−	0.00424994i
$565$	2.40847	+	6.61723i	0.101325	+	0.278389i
$566$	−8.10894	+	22.2791i	−0.340844	+	0.936462i
$567$	−15.6719	+	18.6770i	−0.658157	+	0.784361i
$568$	−11.0091	−	1.94119i	−0.461930	−	0.0814507i
$569$	−23.1409			−0.970116			−0.485058	−	0.874482i	$-0.661202\pi$
$569$	−23.1409			−0.970116			−0.485058	+	0.874482i	$0.661202\pi$
$570$	0.146421	−	0.0726724i	0.00613288	−	0.00304391i
$571$			26.8470i			1.12351i	0.827303	+	0.561755i	$0.189874\pi$
$571$			26.8470i			1.12351i	−0.827303	+	0.561755i	$0.810126\pi$
$572$	0.854884	−	7.48795i	0.0357445	−	0.313087i
$573$	−0.0848563	+	0.101128i	−0.00354492	+	0.00422467i
$574$	−6.34604	+	17.4356i	−0.264878	+	0.727747i
$575$	−33.3115	+	12.1244i	−1.38918	+	0.505622i
$576$	2.29680	−	1.92724i	0.0956998	−	0.0803017i
$577$	2.75378	+	4.76969i	0.114641	+	0.198565i	0.917636	−	0.397421i	$-0.130095\pi$
$577$	2.75378	+	4.76969i	0.114641	+	0.198565i	−0.802995	+	0.595986i	$0.796761\pi$
$578$	−1.26756	+	2.19548i	−0.0527237	+	0.0913201i
$579$	−0.545481	+	0.0961830i	−0.0226694	+	0.00399723i
$580$	0.205089	+	1.16312i	0.00851586	+	0.0482958i
$581$	−5.58601	+	9.67525i	−0.231747	+	0.401397i
$582$	0.215494	+	0.373247i	0.00893253	+	0.0154716i
$583$	13.9362	+	14.6924i	0.577178	+	0.608499i
$584$	1.70612	+	4.68753i	0.0705998	+	0.193971i
$585$	−5.74465	−	2.09088i	−0.237512	−	0.0864473i
$586$	4.94148	+	4.14640i	0.204131	+	0.171286i
$587$	−3.61685	+	20.5122i	−0.149284	+	0.846629i	0.814544	+	0.580102i	$0.196987\pi$
$587$	−3.61685	+	20.5122i	−0.149284	+	0.846629i	−0.963827	+	0.266527i	$0.914124\pi$
$588$			0.0152319i			0.000628154i
$589$	1.55789	−	24.7374i	0.0641919	−	1.01929i
$590$			3.21506i			0.132362i
$591$	−0.0639017	+	0.362405i	−0.00262856	+	0.0149073i
$592$	2.40106	−	2.86147i	0.0986829	−	0.117606i
$593$	−0.288279	+	0.792040i	−0.0118382	+	0.0325252i	−0.945471	−	0.325706i	$-0.894398\pi$
$593$	−0.288279	+	0.792040i	−0.0118382	+	0.0325252i	0.933633	+	0.358232i	$0.116620\pi$
$594$	−0.331363	−	0.762561i	−0.0135960	−	0.0312883i
$595$	−8.24448	+	6.91794i	−0.337991	+	0.283608i
$596$	1.17950	−	0.680987i	0.0483144	−	0.0278943i
$597$	0.448462	+	0.258920i	0.0183543	+	0.0105969i
$598$	3.33455	+	18.9112i	0.136360	+	0.773336i
$599$	−2.70186	+	0.476411i	−0.110395	+	0.0194656i	−0.228573	−	0.973527i	$-0.573406\pi$
$599$	−2.70186	+	0.476411i	−0.110395	+	0.0194656i	0.118178	+	0.992992i	$0.462295\pi$
$600$	0.151832	+	0.0876601i	0.00619850	+	0.00357871i
$601$	−3.59963	−	6.23474i	−0.146832	−	0.254320i	0.783223	−	0.621741i	$-0.213574\pi$
$601$	−3.59963	−	6.23474i	−0.146832	−	0.254320i	−0.930055	+	0.367421i	$0.880241\pi$
$602$	19.5092	−	16.3701i	0.795134	−	0.667196i
$603$	10.6010	+	29.1261i	0.431708	+	1.18611i
$604$	19.7662	+	7.19432i	0.804277	+	0.292733i
$605$	8.27534	+	5.37947i	0.336440	+	0.218706i
$606$	−0.0630065	+	0.357328i	−0.00255946	+	0.0145154i
$607$	10.7816			0.437610			0.218805	−	0.975769i	$-0.429784\pi$
$607$	10.7816			0.437610			0.218805	+	0.975769i	$0.429784\pi$
$608$	−0.485612	−	4.33176i	−0.0196942	−	0.175676i
$609$	0.149288			0.00604944
$610$	−12.1000	−	2.13356i	−0.489915	−	0.0863852i
$611$	5.48767	+	4.60471i	0.222008	+	0.186286i
$612$	4.53240	−	12.4527i	0.183211	−	0.503369i
$613$	0.979402	+	2.69088i	0.0395577	+	0.108684i	0.957899	−	0.287106i	$-0.0926932\pi$
$613$	0.979402	+	2.69088i	0.0395577	+	0.108684i	−0.918341	+	0.395790i	$0.870471\pi$
$614$	4.80276	−	4.02999i	0.193824	−	0.162637i
$615$	−0.222052	+	0.128202i	−0.00895400	+	0.00516960i
$616$	8.05393	+	4.01785i	0.324502	+	0.161884i
$617$	−1.38194	−	7.83734i	−0.0556346	−	0.315520i	0.944272	−	0.329165i	$-0.106767\pi$
$617$	−1.38194	−	7.83734i	−0.0556346	−	0.315520i	−0.999907	+	0.0136458i	$0.995656\pi$
$618$	−0.103884	−	0.589154i	−0.00417882	−	0.0236992i
$619$	−14.8469	+	25.7156i	−0.596748	+	1.03360i	0.396550	+	0.918013i	$0.370207\pi$
$619$	−14.8469	+	25.7156i	−0.596748	+	1.03360i	−0.993298	+	0.115585i	$0.963126\pi$
$620$	−4.41875	+	2.55116i	−0.177461	+	0.102457i
$621$	1.36174	+	1.62286i	0.0546446	+	0.0651229i
$622$	24.7114	−	8.99420i	0.990835	−	0.360635i
$623$	21.1221	+	7.68783i	0.846241	+	0.308007i
$624$	0.0610462	−	0.0727520i	0.00244380	−	0.00291241i
$625$	2.35665	−	13.3652i	0.0942658	−	0.534608i
$626$	−1.33375			−0.0533074
$627$	−0.594813	−	0.106131i	−0.0237545	−	0.00423847i
$628$	11.4589			0.457261
$629$	2.86691	−	16.2590i	0.114311	−	0.648290i
$630$	4.69286	−	5.59273i	0.186968	−	0.222820i
$631$	13.8465	+	5.03971i	0.551220	+	0.200628i	0.602589	−	0.798052i	$-0.294136\pi$
$631$	13.8465	+	5.03971i	0.551220	+	0.200628i	−0.0513683	+	0.998680i	$0.516358\pi$
$632$	0.431886	−	0.157194i	0.0171795	−	0.00625282i
$633$	−0.384861	−	0.458660i	−0.0152969	−	0.0182301i
$634$	−21.5927	+	12.4665i	−0.857555	+	0.495110i
$635$	−4.69124	+	8.12547i	−0.186166	+	0.322450i
$636$	0.0443122	+	0.251307i	0.00175709	+	0.00996497i
$637$	−0.143811	−	0.815591i	−0.00569798	−	0.0323149i
$638$	1.94879	−	3.90642i	0.0771532	−	0.154657i
$639$	29.0267	−	16.7586i	1.14828	−	0.662959i
$640$	−0.687361	+	0.576765i	−0.0271703	+	0.0227986i
$641$	−0.324060	−	0.890348i	−0.0127996	−	0.0351666i	0.933128	−	0.359544i	$-0.117068\pi$
$641$	−0.324060	−	0.890348i	−0.0127996	−	0.0351666i	−0.945928	+	0.324377i	$0.894845\pi$
$642$	0.267159	−	0.734014i	0.0105439	−	0.0289692i
$643$	33.5989	+	28.1928i	1.32501	+	1.11182i	0.985216	+	0.171316i	$0.0548019\pi$
$643$	33.5989	+	28.1928i	1.32501	+	1.11182i	0.339794	+	0.940500i	$0.389643\pi$
$644$	−22.5845	−	3.98225i	−0.889954	−	0.156923i
$645$	0.351931			0.0138573
$646$	−11.4317	−	15.5076i	−0.449773	−	0.610137i
$647$	−22.4094			−0.881005			−0.440503	−	0.897751i	$-0.645200\pi$
$647$	−22.4094			−0.881005			−0.440503	+	0.897751i	$0.645200\pi$
$648$	−1.56010	+	8.84779i	−0.0612867	+	0.347574i
$649$	7.07092	−	9.55122i	0.277558	−	0.374918i
$650$	−8.95743	−	3.26024i	−0.351339	−	0.127877i
$651$	0.220583	+	0.606046i	0.00864532	+	0.0237528i
$652$	3.19514	−	2.68104i	0.125131	−	0.104998i
$653$	15.5562	+	26.9442i	0.608763	+	1.05441i	0.991445	+	0.130528i	$0.0416672\pi$
$653$	15.5562	+	26.9442i	0.608763	+	1.05441i	−0.382682	+	0.923880i	$0.624999\pi$
$654$	0.623531	+	0.359996i	0.0243820	+	0.0140769i
$655$	9.09887	−	1.60438i	0.355522	−	0.0626882i
$656$	1.18727	+	6.73336i	0.0463552	+	0.262894i
$657$	−12.9526	−	7.47819i	−0.505329	−	0.291752i
$658$	−7.40895	+	4.27756i	−0.288831	+	0.166757i
$659$	−4.07825	+	3.42206i	−0.158866	+	0.133304i	−0.718756	−	0.695263i	$-0.755288\pi$
$659$	−4.07825	+	3.42206i	−0.158866	+	0.133304i	0.559890	+	0.828567i	$0.310844\pi$
$660$	0.0495690	+	0.114073i	0.00192947	+	0.00444027i
$661$	1.14861	−	3.15578i	0.0446758	−	0.122746i	−0.915348	−	0.402663i	$-0.868085\pi$
$661$	1.14861	−	3.15578i	0.0446758	−	0.122746i	0.960024	+	0.279917i	$0.0903070\pi$
$662$	−8.72937	+	10.4033i	−0.339277	+	0.404334i
$663$	0.0728902	−	0.413381i	0.00283082	−	0.0160544i
$664$			4.11681i			0.159763i
$665$	−2.99613	−	10.1823i	−0.116185	−	0.394854i
$666$			11.1996i			0.433977i
$667$	−1.93152	+	10.9542i	−0.0747888	+	0.424149i
$668$	3.24289	+	2.72111i	0.125471	+	0.105283i
$669$	0.114396	+	0.0416369i	0.00442282	+	0.00160977i
$670$	−3.17257	−	8.71657i	−0.122567	−	0.336750i
$671$	31.2541	+	32.9500i	1.20655	+	1.27202i
$672$	0.0567091	+	0.0982230i	0.00218760	+	0.00378904i
$673$	15.1517	−	26.2435i	0.584055	−	1.01161i	−0.410937	−	0.911664i	$-0.634798\pi$
$673$	15.1517	−	26.2435i	0.584055	−	1.01161i	0.994992	−	0.0999498i	$-0.0318682\pi$
$674$	5.17611	+	29.3552i	0.199376	+	1.13072i
$675$	−1.03564	+	0.182611i	−0.0398617	+	0.00702870i
$676$	3.91817	−	6.78648i	0.150699	−	0.261018i
$677$	9.36313	+	16.2174i	0.359854	+	0.623286i	0.987936	−	0.154861i	$-0.0494930\pi$
$677$	9.36313	+	16.2174i	0.359854	+	0.623286i	−0.628082	+	0.778147i	$0.716160\pi$
$678$	0.251261	−	0.210833i	0.00964963	−	0.00809700i
$679$	26.2972	−	9.57140i	1.00919	−	0.367316i
$680$	−1.35641	+	3.72670i	−0.0520159	+	0.142913i
$681$	−0.524892	+	0.625541i	−0.0201139	+	0.0239708i
$682$	18.7379	+	2.13927i	0.717512	+	0.0819170i
$683$			4.14767i			0.158706i	0.996847	+	0.0793531i	$0.0252854\pi$
$683$			4.14767i			0.158706i	−0.996847	+	0.0793531i	$0.974715\pi$
$684$	9.46370	+	9.01328i	0.361854	+	0.344632i
$685$	−9.62968			−0.367931
$686$	−17.7337	−	3.12692i	−0.677074	−	0.119386i
$687$	0.796095	−	0.948749i	0.0303729	−	0.0361970i
$688$	3.20971	−	8.81861i	0.122369	−	0.336206i
$689$	−4.74538	−	13.0378i	−0.180785	−	0.496702i
$690$	−0.203704	−	0.242765i	−0.00775488	−	0.00924191i
$691$	7.07991	+	12.2628i	0.269332	+	0.466497i	0.968690	−	0.248275i	$-0.0798636\pi$
$691$	7.07991	+	12.2628i	0.269332	+	0.466497i	−0.699357	+	0.714772i	$0.746530\pi$
$692$	7.82431	−	13.5521i	0.297436	−	0.515174i
$693$	−26.2416	+	6.29368i	−0.996836	+	0.239077i
$694$	6.29926	−	1.11073i	0.239117	−	0.0421627i
$695$	13.5563	+	7.82671i	0.514218	+	0.296884i
$696$	0.0476414	−	0.0275058i	0.00180584	−	0.00104260i
$697$	19.4248	+	23.1496i	0.735766	+	0.876852i
$698$	1.39522	+	3.83334i	0.0528100	+	0.145094i
$699$	−0.616310	−	0.224318i	−0.0233110	−	0.00848450i
$700$	7.31740	−	8.72054i	0.276572	−	0.329606i
$701$	−49.9111	−	8.80067i	−1.88512	−	0.332397i	−0.892241	−	0.451559i	$-0.850868\pi$
$701$	−49.9111	−	8.80067i	−1.88512	−	0.332397i	−0.992875	+	0.119162i	$0.961979\pi$
$702$			0.569660i			0.0215004i
$703$	13.5612	+	9.01126i	0.511470	+	0.339866i
$704$	3.31048	−	0.201716i	0.124769	−	0.00760244i
$705$	−0.116426	−	0.0205291i	−0.00438487	−	0.000773170i
$706$	12.2893	+	10.3119i	0.462512	+	0.388094i
$707$	22.1390	+	8.05795i	0.832624	+	0.303050i
$708$	0.140720	−	0.0512179i	0.00528858	−	0.00192489i
$709$	5.36413	−	4.50104i	0.201454	−	0.169040i	−0.536480	−	0.843913i	$-0.680246\pi$
$709$	5.36413	−	4.50104i	0.201454	−	0.169040i	0.737934	+	0.674873i	$0.235802\pi$
$710$	−8.68681	+	5.01533i	−0.326010	+	0.188222i
$711$	−0.689003	+	1.19339i	−0.0258396	+	0.0447556i
$712$	8.15706	−	1.43831i	0.305699	−	0.0539029i
$713$	−47.3236	+	8.34442i	−1.77228	+	0.312501i
$714$	0.434132	+	0.250646i	0.0162470	+	0.00938019i
$715$	−3.73117	−	5.63999i	−0.139538	−	0.210924i
$716$	−16.4519	−	19.6066i	−0.614837	−	0.732734i
$717$	0.419787	−	0.152790i	0.0156772	−	0.00570604i
$718$	−8.99819	+	24.7223i	−0.335810	+	0.922629i
$719$	27.8373	+	23.3582i	1.03815	+	0.871115i	0.991799	−	0.127810i	$-0.0407948\pi$
$719$	27.8373	+	23.3582i	1.03815	+	0.871115i	0.0463556	+	0.998925i	$0.485239\pi$
$720$	0.467164	−	2.64942i	0.0174102	−	0.0987381i
$721$	−38.8450			−1.44666
$722$	18.5284	−	4.20711i	0.689554	−	0.156573i
$723$		−	0.893219i		−	0.0332192i
$724$	16.2432	+	2.86412i	0.603675	+	0.106444i
$725$	−4.22975	−	3.54918i	−0.157089	−	0.131813i
$726$	0.103623	−	0.447902i	0.00384580	−	0.0166232i
$727$	−22.1181	+	8.05032i	−0.820314	+	0.298570i	−0.717877	−	0.696170i	$-0.754886\pi$
$727$	−22.1181	+	8.05032i	−0.820314	+	0.298570i	−0.102437	+	0.994740i	$0.532664\pi$
$728$	−3.96384	−	4.72392i	−0.146910	−	0.175080i
$729$	−13.4529	−	23.3010i	−0.498254	−	0.863001i
$730$	3.87632	+	2.23800i	0.143469	+	0.0828320i
$731$	−7.20265	−	40.8483i	−0.266400	−	1.51083i
$732$	0.0993770	+	0.563595i	0.00367308	+	0.0208311i
$733$	−36.3907	−	21.0102i	−1.34412	−	0.776028i	−0.356711	−	0.934215i	$-0.616102\pi$
$733$	−36.3907	−	21.0102i	−1.34412	−	0.776028i	−0.987409	+	0.158187i	$0.949435\pi$
$734$	3.59399	+	6.22497i	0.132657	+	0.229768i
$735$	0.00878523	+	0.0104698i	0.000324048	+	0.000386186i
$736$	−7.94098	+	2.89028i	−0.292709	+	0.106537i
$737$	−9.74548	+	32.8725i	−0.358979	+	1.21087i
$738$	−15.7037	−	13.1770i	−0.578062	−	0.485052i
$739$	−30.8141	−	5.43336i	−1.13352	−	0.199869i	−0.424748	−	0.905311i	$-0.639637\pi$
$739$	−30.8141	−	5.43336i	−1.13352	−	0.199869i	−0.708768	+	0.705442i	$0.750749\pi$
$740$		−	3.35171i		−	0.123211i
$741$	0.344789	+	0.229108i	0.0126662	+	0.00841651i
$742$	16.5696			0.608288
$743$	8.87782	−	50.3486i	0.325696	−	1.84711i	−0.179046	−	0.983841i	$-0.557301\pi$
$743$	8.87782	−	50.3486i	0.325696	−	1.84711i	0.504741	−	0.863271i	$-0.331588\pi$
$744$	0.182055	+	0.152763i	0.00667448	+	0.00560055i
$745$	0.417976	−	1.14838i	0.0153135	−	0.0420734i
$746$	22.5385	−	8.20334i	0.825193	−	0.300346i
$747$	−7.93409	−	9.45548i	−0.290293	−	0.345958i
$748$	12.2258	−	8.08804i	0.447019	−	0.295728i
$749$	−43.9245	−	25.3598i	−1.60497	−	0.926628i
$750$	0.339579	−	0.0598770i	0.0123997	−	0.00218640i
$751$	−47.5223	+	8.37947i	−1.73411	+	0.305771i	−0.949396	−	0.314081i	$-0.898304\pi$
$751$	−47.5223	+	8.37947i	−1.73411	+	0.305771i	−0.784718	+	0.619852i	$0.787192\pi$
$752$	−1.57625	+	2.73015i	−0.0574800	+	0.0995583i
$753$	−0.100927	+	0.0582703i	−0.00367799	+	0.00212349i
$754$	−2.29126	+	1.92259i	−0.0834426	+	0.0700167i
$755$	17.7360	−	6.45537i	0.645478	−	0.234935i
$756$	−0.639283	−	0.232680i	−0.0232505	−	0.00846249i
$757$	−20.6895	−	17.3606i	−0.751974	−	0.630981i	0.184050	−	0.982917i	$-0.441079\pi$
$757$	−20.6895	−	17.3606i	−0.751974	−	0.630981i	−0.936024	+	0.351935i	$0.885524\pi$
$758$	24.8575	+	4.38305i	0.902865	+	0.159199i
$759$	0.0712427	+	1.16921i	0.00258595	+	0.0424396i
$760$	−2.83220	−	2.69740i	−0.102735	−	0.0978451i
$761$			39.2062i			1.42122i	0.703584	+	0.710612i	$0.251582\pi$
$761$			39.2062i			1.42122i	−0.703584	+	0.710612i	$0.748418\pi$
$762$	0.430379	+	0.0758874i	0.0155910	+	0.00274911i
$763$	30.0506	−	35.8129i	1.08790	−	1.29651i
$764$	2.96818	+	1.08033i	0.107385	+	0.0390849i
$765$	−4.06686	−	11.1736i	−0.147038	−	0.403983i
$766$	10.5292	+	12.5482i	0.380435	+	0.453384i
$767$	−7.05126	+	4.07105i	−0.254606	+	0.146997i
$768$	0.0361945	+	0.0208969i	0.00130606	+	0.000754053i
$769$	−34.2081	+	6.03180i	−1.23357	+	0.217512i	−0.752160	−	0.658981i	$-0.770988\pi$
$769$	−34.2081	+	6.03180i	−1.23357	+	0.217512i	−0.481414	+	0.876493i	$0.659877\pi$
$770$	7.85332	−	1.88351i	0.283014	−	0.0678770i
$771$	−0.125686	+	0.217695i	−0.00452648	+	0.00784010i
$772$	6.62652	+	11.4775i	0.238494	+	0.413083i
$773$	−20.6616	−	24.6235i	−0.743146	−	0.885647i	0.253512	−	0.967332i	$-0.418414\pi$
$773$	−20.6616	−	24.6235i	−0.743146	−	0.885647i	−0.996658	+	0.0816850i	$0.973970\pi$
$774$	9.62352	+	26.4404i	0.345910	+	0.950381i
$775$	8.15846	−	22.4152i	0.293061	−	0.805177i
$776$	6.62859	−	7.89964i	0.237952	−	0.283581i
$777$	−0.417224	−	0.0735679i	−0.0149678	−	0.00263923i
$778$	−11.0925			−0.397684
$779$	−28.5908	+	8.41279i	−1.02437	+	0.301420i
$780$		−	0.0852162i		−	0.00305123i
$781$	36.8369	+	4.20559i	1.31813	+	0.150488i
$782$	−24.0085	+	28.6122i	−0.858540	+	1.02317i
$783$	−0.112857	+	0.310073i	−0.00403319	+	0.0110811i
$784$	0.342474	−	0.124650i	0.0122312	−	0.00445180i
$785$	7.87642	−	6.60910i	0.281121	−	0.235889i
$786$	−0.215173	−	0.372690i	−0.00767496	−	0.0132934i
$787$	−11.0447	+	19.1301i	−0.393703	+	0.681913i	−0.992935	−	0.118662i	$-0.962139\pi$
$787$	−11.0447	+	19.1301i	−0.393703	+	0.681913i	0.599232	+	0.800576i	$0.295473\pi$
$788$	8.67124	−	1.52897i	0.308900	−	0.0544674i
$789$	0.138747	+	0.786872i	0.00493951	+	0.0280134i
$790$	0.206198	−	0.357145i	0.00733619	−	0.0127067i
$791$	−10.6488	−	18.4442i	−0.378627	−	0.655800i
$792$	−7.21475	+	6.84340i	−0.256365	+	0.243170i
$793$	−10.6422	−	29.2393i	−0.377917	−	1.03832i
$794$	−0.730668	−	0.265942i	−0.0259304	−	0.00943791i
$795$	0.175404	+	0.147181i	0.00622092	+	0.00521997i
$796$	2.15156	−	12.2021i	0.0762599	−	0.432491i
$797$		−	1.39103i		−	0.0492729i	−0.999696	−	0.0246365i	$-0.992157\pi$
$797$		−	1.39103i		−	0.0492729i	0.999696	−	0.0246365i	$-0.00784282\pi$
$798$	−0.397940	+	0.293349i	−0.0140869	+	0.0103844i
$799$			13.9336i			0.492936i
$800$	0.728433	−	4.13115i	0.0257540	−	0.146058i
$801$	−15.9631	+	19.0241i	−0.564029	+	0.672184i
$802$	0.496605	−	1.36441i	0.0175357	−	0.0481790i
$803$	−6.59364	−	15.1738i	−0.232684	−	0.535474i
$804$	−0.330975	+	0.277721i	−0.0116726	+	0.00979446i
$805$	−17.8205	+	10.2887i	−0.628091	+	0.362628i
$806$	−11.1904	−	6.46079i	−0.394166	−	0.227572i
$807$	−0.0588253	−	0.333615i	−0.00207075	−	0.0117438i
$808$	8.54976	−	1.50755i	0.300780	−	0.0530356i
$809$	38.9419	+	22.4831i	1.36913	+	0.790465i	0.990816	−	0.135214i	$-0.0431723\pi$
$809$	38.9419	+	22.4831i	1.36913	+	0.790465i	0.378309	+	0.925679i	$0.376506\pi$
$810$	4.03074	+	6.98144i	0.141626	+	0.245303i
$811$	−17.7897	+	14.9274i	−0.624683	+	0.524171i	−0.899272	−	0.437391i	$-0.855903\pi$
$811$	−17.7897	+	14.9274i	−0.624683	+	0.524171i	0.274589	+	0.961562i	$0.411458\pi$
$812$	−1.22170	−	3.35658i	−0.0428731	−	0.117793i
$813$	−0.393635	−	0.143271i	−0.0138054	−	0.00502474i
$814$	−7.37147	+	9.95719i	−0.258370	+	0.348999i
$815$	0.649885	−	3.68568i	0.0227645	−	0.129104i
$816$	0.184723			0.00646659
$817$	39.7588	+	9.62129i	1.39098	+	0.336606i
$818$	9.81017			0.343005
$819$	18.2083	+	3.21061i	0.636248	+	0.112188i
$820$	4.69965	+	3.94348i	0.164119	+	0.137712i
$821$	−1.75730	+	4.82815i	−0.0613302	+	0.168503i	−0.966573	−	0.256391i	$-0.917467\pi$
$821$	−1.75730	+	4.82815i	−0.0613302	+	0.168503i	0.905243	+	0.424894i	$0.139689\pi$
$822$	0.153407	+	0.421482i	0.00535068	+	0.0147009i
$823$	13.7954	−	11.5758i	0.480879	−	0.403505i	−0.369865	−	0.929085i	$-0.620596\pi$
$823$	13.7954	−	11.5758i	0.480879	−	0.403505i	0.850744	+	0.525580i	$0.176152\pi$
$824$	−12.3964	+	7.15706i	−0.431849	+	0.249328i
$825$	−0.520319	−	0.259570i	−0.0181152	−	0.00903708i
$826$	−1.68849	−	9.57589i	−0.0587500	−	0.333188i
$827$	6.60225	+	37.4432i	0.229583	+	1.30203i	0.853728	+	0.520719i	$0.174336\pi$
$827$	6.60225	+	37.4432i	0.229583	+	1.30203i	−0.624145	+	0.781308i	$0.714553\pi$
$828$	12.6685	−	21.9426i	0.440262	−	0.762557i
$829$	45.1458	−	26.0649i	1.56798	−	0.905272i	0.571572	−	0.820552i	$-0.306334\pi$
$829$	45.1458	−	26.0649i	1.56798	−	0.905272i	0.996405	−	0.0847203i	$-0.0269997\pi$
$830$	2.37443	+	2.82974i	0.0824177	+	0.0982216i
$831$	0.319367	−	0.116240i	0.0110787	−	0.00403232i
$832$	−2.13533	−	0.777195i	−0.0740291	−	0.0269444i
$833$	1.03542	−	1.23397i	0.0358753	−	0.0427545i
$834$	0.126608	−	0.718029i	0.00438407	−	0.0248633i
$835$	3.79848			0.131452
$836$	2.48140	+	14.2423i	0.0858209	+	0.492580i
$837$	−1.42552			−0.0492733
$838$	6.01013	−	34.0852i	0.207617	−	1.17745i
$839$	−14.0082	+	16.6943i	−0.483615	+	0.576350i	−0.951582	−	0.307396i	$-0.900542\pi$
$839$	−14.0082	+	16.6943i	−0.483615	+	0.576350i	0.467966	+	0.883746i	$0.344987\pi$
$840$	0.0956312	+	0.0348069i	0.00329959	+	0.00120095i
$841$	25.6230	−	9.32602i	0.883553	−	0.321587i
$842$	−8.40885	−	10.0213i	−0.289788	−	0.345356i
$843$	0.508795	−	0.293753i	0.0175238	−	0.0101174i
$844$	−7.16299	+	12.4067i	−0.246560	+	0.427055i
$845$	−1.22100	−	6.92462i	−0.0420036	−	0.238214i
$846$	−1.64132	−	9.30841i	−0.0564299	−	0.320030i
$847$	−27.4729	−	11.6764i	−0.943980	−	0.401207i
$848$	5.28776	−	3.05289i	0.181582	−	0.104837i
$849$	0.759065	−	0.636931i	0.0260510	−	0.0218594i
$850$	−6.34131	−	17.4226i	−0.217505	−	0.597591i
$851$	10.7963	−	29.6626i	0.370093	−	1.01682i
$852$	0.357903	+	0.300316i	0.0122615	+	0.0102887i
$853$	−49.6597	−	8.75635i	−1.70032	−	0.299812i	−0.762512	−	0.646974i	$-0.776034\pi$
$853$	−49.6597	−	8.75635i	−1.70032	−	0.299812i	−0.937805	+	0.347163i	$0.887145\pi$
$854$	37.1598			1.27158
$855$	11.7035	+	0.737055i	0.400252	+	0.0252068i
$856$	−18.6899			−0.638806
$857$	−7.93738	+	45.0151i	−0.271136	+	1.53769i	0.479840	+	0.877356i	$0.340695\pi$
$857$	−7.93738	+	45.0151i	−0.271136	+	1.53769i	−0.750975	+	0.660330i	$0.770416\pi$
$858$	−0.187417	+	0.253158i	−0.00639832	+	0.00864269i
$859$	−21.6671	−	7.88619i	−0.739273	−	0.269073i	−0.0551884	−	0.998476i	$-0.517576\pi$
$859$	−21.6671	−	7.88619i	−0.739273	−	0.269073i	−0.684085	+	0.729403i	$0.739798\pi$
$860$	−2.88003	−	7.91282i	−0.0982082	−	0.269825i
$861$	0.594042	−	0.498461i	0.0202449	−	0.0169875i
$862$	9.41156	+	16.3013i	0.320559	+	0.555224i
$863$	20.1318	+	11.6231i	0.685295	+	0.395655i	0.801847	−	0.597529i	$-0.203851\pi$
$863$	20.1318	+	11.6231i	0.685295	+	0.395655i	−0.116552	+	0.993185i	$0.537184\pi$
$864$	−0.246882	+	0.0435319i	−0.00839908	+	0.00148098i
$865$	−2.43824	−	13.8280i	−0.0829028	−	0.470165i
$866$	24.7514	+	14.2902i	0.841086	+	0.485601i
$867$	0.0917577	−	0.0529764i	0.00311626	−	0.00179917i
$868$	11.8212	−	9.91916i	0.401238	−	0.336678i
$869$	−1.39804	+	0.607505i	−0.0474254	+	0.0206082i
$870$	0.0168825	−	0.0463842i	0.000572370	−	0.00157257i
$871$	15.0999	−	17.9954i	0.511641	−	0.609750i
$872$	2.99147	−	16.9655i	0.101304	−	0.574524i
$873$			30.9187i			1.04644i
$874$	−16.3763	−	32.9949i	−0.553935	−	1.11607i
$875$		−	22.3896i		−	0.756908i
$876$	0.0362027	−	0.205316i	0.00122318	−	0.00693698i
$877$	3.92886	+	3.29670i	0.132668	+	0.111322i	0.706707	−	0.707506i	$-0.250180\pi$
$877$	3.92886	+	3.29670i	0.132668	+	0.111322i	−0.574039	+	0.818828i	$0.694624\pi$
$878$	−27.7097	−	10.0855i	−0.935158	−	0.340370i
$879$	−0.0922078	−	0.253339i	−0.00311009	−	0.00854491i
$880$	2.15916	−	2.04802i	0.0727852	−	0.0690388i
$881$	−23.0524	−	39.9279i	−0.776654	−	1.34520i	−0.933860	−	0.357638i	$-0.883582\pi$
$881$	−23.0524	−	39.9279i	−0.776654	−	1.34520i	0.157206	−	0.987566i	$-0.449751\pi$
$882$	−0.546362	+	0.946327i	−0.0183970	+	0.0318645i
$883$	−2.74441	−	15.5643i	−0.0923566	−	0.523780i	−0.995525	−	0.0944947i	$-0.969876\pi$
$883$	−2.74441	−	15.5643i	−0.0923566	−	0.523780i	0.903169	−	0.429286i	$-0.141235\pi$
$884$	−9.89095	+	1.74404i	−0.332669	+	0.0586585i
$885$	0.0671848	−	0.116367i	0.00225839	−	0.00391165i
$886$	6.65439	+	11.5257i	0.223559	+	0.387215i
$887$	−27.8260	+	23.3488i	−0.934306	+	0.783976i	−0.976585	−	0.215130i	$-0.930982\pi$
$887$	−27.8260	+	23.3488i	−0.934306	+	0.783976i	0.0422796	+	0.999106i	$0.486538\pi$
$888$	−0.146701	+	0.0533949i	−0.00492297	+	0.00179181i
$889$	9.70530	−	26.6651i	0.325505	−	0.894319i
$890$	4.77728	−	5.69334i	0.160135	−	0.190841i
$891$	3.37996	−	29.6052i	0.113233	−	0.991811i
$892$		−	2.91282i		−	0.0975285i
$893$	−12.5918	−	5.50216i	−0.421369	−	0.184123i
$894$	−0.0569222			−0.00190376
$895$	−22.6168	−	3.98795i	−0.755997	−	0.133303i
$896$	1.74437	−	2.07886i	0.0582752	−	0.0694497i
$897$	0.274493	−	0.754163i	0.00916505	−	0.0251808i
$898$	−8.83537	−	24.2750i	−0.294840	−	0.810066i
$899$	−4.81112	−	5.73366i	−0.160460	−	0.191228i
$900$	6.28865	+	10.8923i	0.209622	+	0.363076i
$901$	13.4933	−	23.3711i	0.449528	−	0.778605i
$902$	−5.28868	−	22.0512i	−0.176094	−	0.734225i
$903$	−1.04821	+	0.184828i	−0.0348823	+	0.00615068i
$904$	−6.79657	−	3.92400i	−0.226051	−	0.130510i
$905$	12.8169	−	7.39983i	0.426048	−	0.245979i
$906$	−0.565091	−	0.673449i	−0.0187739	−	0.0223738i
$907$	13.8719	+	38.1127i	0.460608	+	1.26551i	0.925029	+	0.379896i	$0.124040\pi$
$907$	13.8719	+	38.1127i	0.460608	+	1.26551i	−0.464421	+	0.885614i	$0.653738\pi$
$908$	18.3601	+	6.68254i	0.609302	+	0.221768i
$909$	−16.7316	+	19.9400i	−0.554953	+	0.661368i
$910$	−5.44918	−	0.960838i	−0.180639	−	0.0318515i
$911$		−	10.9703i		−	0.363462i	−0.983348	−	0.181731i	$-0.941830\pi$
$911$		−	10.9703i		−	0.363462i	0.983348	−	0.181731i	$-0.0581701\pi$
$912$	−0.0729441	+	0.166934i	−0.00241542	+	0.00552774i
$913$	−0.830426	−	13.6286i	−0.0274831	−	0.451042i
$914$	−13.1393	−	2.31681i	−0.434609	−	0.0766334i
$915$	0.393369	+	0.330076i	0.0130044	+	0.0109120i
$916$	−27.8465	−	10.1353i	−0.920074	−	0.334880i
$917$	−26.2580	+	9.55712i	−0.867114	+	0.315604i
$918$	−0.848788	+	0.712218i	−0.0280142	+	0.0235067i
$919$	7.67319	−	4.43012i	0.253115	−	0.146136i	−0.368075	−	0.929796i	$-0.619983\pi$
$919$	7.67319	−	4.43012i	0.253115	−	0.146136i	0.621190	+	0.783660i	$0.286650\pi$
$920$	−3.79131	+	6.56675i	−0.124996	+	0.216499i
$921$	−0.258048	+	0.0455009i	−0.00850298	+	0.00149930i
$922$	−2.59659	+	0.457849i	−0.0855142	+	0.0150785i
$923$	−21.9992	−	12.7013i	−0.724114	−	0.418067i
$924$	−0.207548	−	0.313727i	−0.00682782	−	0.0103209i
$925$	10.0721	+	12.0035i	0.331170	+	0.394673i
$926$	10.0527	−	3.65889i	0.330352	−	0.120238i
$927$	14.6786	−	40.3291i	0.482109	−	1.32458i
$928$	−1.00831	−	0.846074i	−0.0330995	−	0.0277737i
$929$	−8.05772	+	45.6976i	−0.264365	+	1.49929i	0.506472	+	0.862256i	$0.330949\pi$
$929$	−8.05772	+	45.6976i	−0.264365	+	1.49929i	−0.770837	+	0.637032i	$0.780162\pi$
$930$	0.213246			0.00699261
$931$	0.706266	+	1.42299i	0.0231469	+	0.0466365i
$932$			15.6928i			0.514035i
$933$	−1.08237	−	0.190851i	−0.0354351	−	0.00624817i
$934$	−9.13329	−	7.66374i	−0.298850	−	0.250765i
$935$	3.73864	−	12.6108i	0.122267	−	0.412418i
$936$	6.40225	−	2.33023i	0.209264	−	0.0761659i
$937$	−7.76961	−	9.25946i	−0.253822	−	0.302493i	0.624054	−	0.781381i	$-0.285484\pi$
$937$	−7.76961	−	9.25946i	−0.253822	−	0.302493i	−0.877876	+	0.478888i	$0.841040\pi$
$938$	14.0271	+	24.2957i	0.458002	+	0.793283i
$939$	0.0482745	+	0.0278713i	0.00157538	+	0.000909545i
$940$	0.491199	+	2.78573i	0.0160211	+	0.0908604i
$941$	1.37165	+	7.77899i	0.0447144	+	0.253588i	0.998968	−	0.0454090i	$-0.0144591\pi$
$941$	1.37165	+	7.77899i	0.0447144	+	0.253588i	−0.954254	+	0.298997i	$0.903348\pi$
$942$	−0.414750	−	0.239456i	−0.0135133	−	0.00780191i
$943$	28.8894	+	50.0380i	0.940770	+	1.62946i
$944$	−2.30316	−	2.74480i	−0.0749616	−	0.0893358i
$945$	−0.573620	+	0.208781i	−0.0186599	+	0.00679164i
$946$	−8.84685	+	29.8413i	−0.287636	+	0.970225i
$947$	−26.5533	−	22.2808i	−0.862865	−	0.724030i	0.0997180	−	0.995016i	$-0.468206\pi$
$947$	−26.5533	−	22.2808i	−0.862865	−	0.724030i	−0.962583	+	0.270986i	$0.912650\pi$
$948$	−0.0189168	−	0.00333554i	−0.000614388	−	0.000108333i
$949$			11.3354i			0.367963i
$950$	18.2489	+	1.14926i	0.592072	+	0.0372870i
$951$	1.04205			0.0337908
$952$	2.08280	−	11.8122i	0.0675041	−	0.382835i
$953$	−5.21285	−	4.37410i	−0.168861	−	0.141691i	0.554441	−	0.832223i	$-0.312932\pi$
$953$	−5.21285	−	4.37410i	−0.168861	−	0.141691i	−0.723302	+	0.690532i	$0.757377\pi$
$954$	−6.26125	+	17.2026i	−0.202715	+	0.556956i
$955$	2.66330	−	0.969364i	0.0861825	−	0.0313679i
$956$	−6.87065	−	8.18812i	−0.222213	−	0.264823i
$957$	−0.152168	+	0.100667i	−0.00491888	+	0.00325411i
$958$	2.31982	+	1.33935i	0.0749501	+	0.0432724i
$959$	28.6815	−	5.05733i	0.926175	−	0.163310i
$960$	0.0369313	−	0.00651199i	0.00119195	−	0.000210174i
$961$	0.667568	−	1.15626i	0.0215344	−	0.0372987i
$962$	7.35097	−	4.24408i	0.237005	−	0.136835i
$963$	42.9268	−	36.0198i	1.38330	−	1.16072i
$964$	−20.0831	+	7.30966i	−0.646834	+	0.235428i
$965$	11.1746	+	4.06722i	0.359723	+	0.130929i
$966$	0.734218	+	0.616082i	0.0236231	+	0.0198221i
$967$	28.8207	+	5.08187i	0.926811	+	0.163422i	0.616628	−	0.787255i	$-0.288498\pi$
$967$	28.8207	+	5.08187i	0.926811	+	0.163422i	0.310183	+	0.950677i	$0.399610\pi$
$968$	−10.9186	+	1.33555i	−0.350938	+	0.0429263i
$969$	0.0897036	+	0.800176i	0.00288170	+	0.0257053i
$970$		−	9.25304i		−	0.297097i
$971$	5.96777	+	1.05228i	0.191515	+	0.0337693i	0.268583	−	0.963257i	$-0.413445\pi$
$971$	5.96777	+	1.05228i	0.191515	+	0.0337693i	−0.0770678	+	0.997026i	$0.524556\pi$
$972$	0.724781	−	0.863760i	0.0232473	−	0.0277051i
$973$	−44.4871	−	16.1920i	−1.42619	−	0.519091i
$974$	7.76429	+	21.3322i	0.248784	+	0.683528i
$975$	0.256081	+	0.305186i	0.00820116	+	0.00977377i
$976$	11.8586	−	6.84657i	0.379585	−	0.219153i
$977$	19.3855	+	11.1922i	0.620197	+	0.358071i	0.776946	−	0.629568i	$-0.216768\pi$
$977$	19.3855	+	11.1922i	0.620197	+	0.358071i	−0.156749	+	0.987638i	$0.550101\pi$
$978$	−0.171672	+	0.0302704i	−0.00548946	+	0.000967940i
$979$	−26.7137	+	6.40691i	−0.853773	+	0.204766i
$980$	0.163510	−	0.283207i	0.00522312	−	0.00904671i
$981$	25.8258	+	44.7315i	0.824553	+	1.42817i
$982$	6.33654	+	7.55159i	0.202207	+	0.240981i
$983$	−0.00764237	−	0.0209972i	−0.000243754	−	0.000669708i	0.939571	−	0.342355i	$-0.111225\pi$
$983$	−0.00764237	−	0.0209972i	−0.000243754	−	0.000669708i	−0.939814	+	0.341685i	$0.889002\pi$
$984$	0.0977338	−	0.268521i	0.00311564	−	0.00856015i
$985$	5.07842	−	6.05222i	0.161812	−	0.192840i
$986$	−5.72929	−	1.01023i	−0.182458	−	0.0321722i
$987$	0.357551			0.0113810
$988$	2.32969	−	9.62715i	0.0741172	−	0.306280i
$989$		−	79.3054i		−	2.52176i
$990$	−1.01211	+	8.86510i	−0.0321670	+	0.281751i
$991$	3.71487	−	4.42721i	0.118007	−	0.140635i	−0.703807	−	0.710391i	$-0.748518\pi$
$991$	3.71487	−	4.42721i	0.118007	−	0.140635i	0.821814	+	0.569756i	$0.192962\pi$
$992$	1.94486	−	5.34347i	0.0617495	−	0.169655i
$993$	0.533352	−	0.194124i	0.0169254	−	0.00616035i
$994$	23.2393	−	19.5001i	0.737106	−	0.618505i
$995$	−5.55883	−	9.62818i	−0.176227	−	0.305234i
$996$	0.0860288	−	0.149006i	0.00272593	−	0.00472144i
$997$	10.5569	−	1.86147i	0.334341	−	0.0589533i	−0.00395758	−	0.999992i	$-0.501260\pi$
$997$	10.5569	−	1.86147i	0.334341	−	0.0589533i	0.338299	+	0.941039i	$0.390149\pi$
$998$	−0.461812	−	2.61907i	−0.0146184	−	0.0829051i
$999$	0.468212	−	0.810967i	0.0148136	−	0.0256579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.a.21.6	✓	60
11.10	odd	2		418.2.q.b.21.6	yes	60
19.10	odd	18		418.2.q.b.219.6	yes	60
209.10	even	18	inner	418.2.q.a.219.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.6	✓	60	1.1	even	1	trivial
418.2.q.a.219.6	yes	60	209.10	even	18	inner
418.2.q.b.21.6	yes	60	11.10	odd	2
418.2.q.b.219.6	yes	60	19.10	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0268646 - 0.0320160i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.843173 + 0.306890i) q^{5} +(0.0268646 + 0.0320160i) q^{6} +(2.35018 - 1.35688i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.520641 + 2.95270i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0268646 - 0.0320160i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.843173 + 0.306890i) q^{5} +(0.0268646 + 0.0320160i) q^{6} +(2.35018 - 1.35688i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.520641 + 2.95270i) q^{9} +(-0.155812 - 0.883655i) q^{10} +(-1.48055 + 2.96782i) q^{11} +(-0.0361945 + 0.0208969i) q^{12} +(1.74073 - 1.46065i) q^{13} +(0.928158 + 2.55009i) q^{14} +(-0.0128261 + 0.0352395i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.35271 + 0.767500i) q^{17} -2.99825 q^{18} +(-2.41240 + 3.63047i) q^{19} +0.897286 q^{20} +(0.0196949 - 0.111695i) q^{21} +(-2.66564 - 1.97342i) q^{22} +(7.94098 + 2.89028i) q^{23} +(-0.0142943 - 0.0392734i) q^{24} +(-3.21346 + 2.69642i) q^{25} +(1.13618 + 1.96793i) q^{26} +(0.217104 + 0.125345i) q^{27} +(-2.67252 + 0.471238i) q^{28} +(0.228566 + 1.29626i) q^{29} +(-0.0324769 - 0.0187505i) q^{30} +(-4.92457 + 2.84320i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.0552433 + 0.127131i) q^{33} +(-1.51168 + 4.15331i) q^{34} +(-1.56520 + 1.86533i) q^{35} +(0.520641 - 2.95270i) q^{36} -3.73539i q^{37} +(-3.15640 - 3.00618i) q^{38} -0.0949710i q^{39} +(-0.155812 + 0.883655i) q^{40} +(5.23763 + 4.39489i) q^{41} +(0.106578 + 0.0387913i) q^{42} +(-3.20971 - 8.81861i) q^{43} +(2.40632 - 2.28246i) q^{44} +(-1.34515 - 2.32986i) q^{45} +(-4.22531 + 7.31845i) q^{46} +(0.547427 + 3.10461i) q^{47} +(0.0411589 - 0.00725743i) q^{48} +(0.182227 - 0.315626i) q^{49} +(-2.09744 - 3.63287i) q^{50} +(0.141506 - 0.118738i) q^{51} +(-2.13533 + 0.777195i) q^{52} +(2.08830 - 5.73755i) q^{53} +(-0.161141 + 0.192040i) q^{54} +(0.337567 - 2.95675i) q^{55} -2.71375i q^{56} +(0.0514247 + 0.174766i) q^{57} -1.31626 q^{58} +(-3.52865 - 0.622197i) q^{59} +(0.0241052 - 0.0287275i) q^{60} +(4.68333 - 12.8673i) q^{61} +(-1.94486 - 5.34347i) q^{62} +(5.23005 + 6.23293i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01948 + 1.76579i) q^{65} +(-0.134792 + 0.0323280i) q^{66} +(10.1808 - 1.79514i) q^{67} +(-3.82771 - 2.20993i) q^{68} +(0.305866 - 0.176592i) q^{69} +(-1.56520 - 1.86533i) q^{70} +(-3.82341 - 10.5047i) q^{71} +(2.81744 + 1.02546i) q^{72} +(-3.20646 + 3.82131i) q^{73} +(3.67864 + 0.648643i) q^{74} +0.175320i q^{75} +(3.50861 - 2.58643i) q^{76} +(0.547406 + 8.98384i) q^{77} +(0.0935282 + 0.0164915i) q^{78} +(0.352076 + 0.295427i) q^{79} +(-0.843173 - 0.306890i) q^{80} +(-8.44246 + 3.07281i) q^{81} +(-5.23763 + 4.39489i) q^{82} +(-3.56527 + 2.05841i) q^{83} +(-0.0567091 + 0.0982230i) q^{84} +(-3.90563 + 0.688667i) q^{85} +(9.24199 - 1.62961i) q^{86} +(0.0476414 + 0.0275058i) q^{87} +(1.82993 + 2.76611i) q^{88} +(5.32414 + 6.34506i) q^{89} +(2.52805 - 0.920134i) q^{90} +(2.10912 - 5.79475i) q^{91} +(-6.47355 - 5.43195i) q^{92} +(-0.0412686 + 0.234046i) q^{93} -3.15251 q^{94} +(0.919920 - 3.80146i) q^{95} +0.0417939i q^{96} +(10.1556 + 1.79070i) q^{97} +(0.279188 + 0.234266i) q^{98} +(-9.53393 - 2.82646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

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