LMFDB - Embedded newform 196.2.p.a.103.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.15
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.253576 + 1.39129i) q^{2} +(1.97899 + 1.34925i) q^{3} +(-1.87140 + 0.705597i) q^{4} +(-0.0159493 - 0.00119524i) q^{5} +(-1.37538 + 3.09550i) q^{6} +(2.59622 - 0.509531i) q^{7} +(-1.45623 - 2.42474i) q^{8} +(0.999898 + 2.54770i) q^{9} +O(q^{10})$	\(q+(0.253576 + 1.39129i) q^{2} +(1.97899 + 1.34925i) q^{3} +(-1.87140 + 0.705597i) q^{4} +(-0.0159493 - 0.00119524i) q^{5} +(-1.37538 + 3.09550i) q^{6} +(2.59622 - 0.509531i) q^{7} +(-1.45623 - 2.42474i) q^{8} +(0.999898 + 2.54770i) q^{9} +(-0.00238144 - 0.0224933i) q^{10} +(-1.65591 - 0.649897i) q^{11} +(-4.65551 - 1.12862i) q^{12} +(-2.07204 + 1.65240i) q^{13} +(1.36725 + 3.48291i) q^{14} +(-0.0299509 - 0.0238850i) q^{15} +(3.00427 - 2.64091i) q^{16} +(-3.29762 - 3.55399i) q^{17} +(-3.29105 + 2.03719i) q^{18} +(0.682883 - 1.18279i) q^{19} +(0.0306909 - 0.00901703i) q^{20} +(5.82539 + 2.49461i) q^{21} +(0.484299 - 2.46866i) q^{22} +(3.75388 - 4.04572i) q^{23} +(0.389718 - 6.76337i) q^{24} +(-4.94390 - 0.745173i) q^{25} +(-2.82439 - 2.46381i) q^{26} +(0.140232 - 0.614395i) q^{27} +(-4.49905 + 2.78542i) q^{28} +(0.487147 + 2.13433i) q^{29} +(0.0256363 - 0.0477272i) q^{30} +(4.96153 + 8.59362i) q^{31} +(4.43609 + 3.51015i) q^{32} +(-2.40016 - 3.52038i) q^{33} +(4.10844 - 5.48916i) q^{34} +(-0.0420170 + 0.00502358i) q^{35} +(-3.66886 - 4.06224i) q^{36} +(1.78032 + 0.549155i) q^{37} +(1.81877 + 0.650165i) q^{38} +(-6.33006 + 0.474372i) q^{39} +(0.0203278 + 0.0404136i) q^{40} +(-1.78963 - 3.71620i) q^{41} +(-1.99355 + 8.73740i) q^{42} +(-4.01716 + 8.34173i) q^{43} +(3.55744 + 0.0478108i) q^{44} +(-0.0129026 - 0.0418292i) q^{45} +(6.58068 + 4.19686i) q^{46} +(9.62933 - 1.45139i) q^{47} +(9.50867 - 1.17282i) q^{48} +(6.48076 - 2.64571i) q^{49} +(-0.216899 - 7.06738i) q^{50} +(-1.73073 - 11.4826i) q^{51} +(2.71169 - 4.55432i) q^{52} +(-8.11554 + 2.50331i) q^{53} +(0.890364 + 0.0393078i) q^{54} +(0.0256339 + 0.0123446i) q^{55} +(-5.01619 - 5.55318i) q^{56} +(2.94730 - 1.41935i) q^{57} +(-2.84595 + 1.21898i) q^{58} +(-0.462993 - 6.17821i) q^{59} +(0.0729033 + 0.0235652i) q^{60} +(2.72001 - 8.81806i) q^{61} +(-10.6981 + 9.08207i) q^{62} +(3.89409 + 6.10492i) q^{63} +(-3.75876 + 7.06199i) q^{64} +(0.0350227 - 0.0238781i) q^{65} +(4.28927 - 4.23201i) q^{66} +(-4.78628 + 2.76336i) q^{67} +(8.67884 + 4.32414i) q^{68} +(12.8876 - 2.94151i) q^{69} +(-0.0176438 - 0.0571842i) q^{70} +(-13.9367 - 3.18096i) q^{71} +(4.72143 - 6.13454i) q^{72} +(-1.28303 + 8.51233i) q^{73} +(-0.312591 + 2.61620i) q^{74} +(-8.77851 - 8.14527i) q^{75} +(-0.443375 + 2.69531i) q^{76} +(-4.63026 - 0.843540i) q^{77} +(-2.26514 - 8.68668i) q^{78} +(0.651250 + 0.376000i) q^{79} +(-0.0510725 + 0.0385299i) q^{80} +(7.12534 - 6.61135i) q^{81} +(4.71652 - 3.43224i) q^{82} +(-2.16800 + 2.71859i) q^{83} +(-12.6618 - 0.558023i) q^{84} +(0.0483469 + 0.0606251i) q^{85} +(-12.6245 - 3.47380i) q^{86} +(-1.91569 + 4.88111i) q^{87} +(0.835561 + 4.96156i) q^{88} +(1.89685 - 0.744461i) q^{89} +(0.0549249 - 0.0285582i) q^{90} +(-4.53754 + 5.34577i) q^{91} +(-4.17036 + 10.2199i) q^{92} +(-1.77615 + 23.7010i) q^{93} +(4.46107 + 13.0292i) q^{94} +(-0.0123052 + 0.0180485i) q^{95} +(4.04290 + 12.9320i) q^{96} -12.1281i q^{97} +(5.32433 + 8.34575i) q^{98} -4.86859i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	0.253576	+	1.39129i	0.179305	+	0.983794i
$2$	0.253576	+	1.39129i	0.179305	+	0.983794i
$3$	1.97899	+	1.34925i	1.14257	+	0.778992i	0.978253	−	0.207416i	$-0.0665053\pi$
$3$	1.97899	+	1.34925i	1.14257	+	0.778992i	0.164318	+	0.986407i	$0.447458\pi$
$4$	−1.87140	+	0.705597i	−0.935699	+	0.352799i
$5$	−0.0159493	−	0.00119524i	−0.00713275	−	0.000534526i	0.0711632	−	0.997465i	$-0.477329\pi$
$5$	−0.0159493	−	0.00119524i	−0.00713275	−	0.000534526i	−0.0782960	+	0.996930i	$0.524948\pi$
$6$	−1.37538	+	3.09550i	−0.561498	+	1.26373i
$7$	2.59622	−	0.509531i	0.981280	−	0.192585i
$7$	2.59622	−	0.509531i	0.981280	−	0.192585i
$8$	−1.45623	−	2.42474i	−0.514857	−	0.857276i
$9$	0.999898	+	2.54770i	0.333299	+	0.849233i
$10$	−0.00238144	−	0.0224933i	−0.000753077	−	0.00711300i
$11$	−1.65591	−	0.649897i	−0.499276	−	0.195951i	0.102321	−	0.994751i	$-0.467373\pi$
$11$	−1.65591	−	0.649897i	−0.499276	−	0.195951i	−0.601597	+	0.798800i	$0.705468\pi$
$12$	−4.65551	−	1.12862i	−1.34393	−	0.325805i
$13$	−2.07204	+	1.65240i	−0.574681	+	0.458293i	−0.867195	−	0.497968i	$-0.834080\pi$
$13$	−2.07204	+	1.65240i	−0.574681	+	0.458293i	0.292514	+	0.956261i	$0.405508\pi$
$14$	1.36725	+	3.48291i	0.365412	+	0.930846i
$15$	−0.0299509	−	0.0238850i	−0.00773329	−	0.00616709i
$16$	3.00427	−	2.64091i	0.751066	−	0.660227i
$17$	−3.29762	−	3.55399i	−0.799790	−	0.861968i	0.193079	−	0.981183i	$-0.438153\pi$
$17$	−3.29762	−	3.55399i	−0.799790	−	0.861968i	−0.992868	+	0.119215i	$0.961962\pi$
$18$	−3.29105	+	2.03719i	−0.775708	+	0.480170i
$19$	0.682883	−	1.18279i	0.156664	−	0.271350i	−0.777000	−	0.629501i	$-0.783259\pi$
$19$	0.682883	−	1.18279i	0.156664	−	0.271350i	0.933664	+	0.358151i	$0.116593\pi$
$20$	0.0306909	−	0.00901703i	0.00686269	−	0.00201627i
$21$	5.82539	+	2.49461i	1.27120	+	0.544368i
$22$	0.484299	−	2.46866i	0.103253	−	0.526320i
$23$	3.75388	−	4.04572i	0.782738	−	0.843591i	−0.208175	−	0.978092i	$-0.566752\pi$
$23$	3.75388	−	4.04572i	0.782738	−	0.843591i	0.990914	+	0.134500i	$0.0429429\pi$
$24$	0.389718	−	6.76337i	0.0795509	−	1.38057i
$25$	−4.94390	−	0.745173i	−0.988780	−	0.149035i
$26$	−2.82439	−	2.46381i	−0.553909	−	0.483193i
$27$	0.140232	−	0.614395i	0.0269876	−	0.118240i
$28$	−4.49905	+	2.78542i	−0.850240	+	0.526396i
$29$	0.487147	+	2.13433i	0.0904609	+	0.396335i	0.999806	−	0.0197080i	$-0.00627365\pi$
$29$	0.487147	+	2.13433i	0.0904609	+	0.396335i	−0.909345	+	0.416043i	$0.863417\pi$
$30$	0.0256363	−	0.0477272i	0.00468053	−	0.00871375i
$31$	4.96153	+	8.59362i	0.891116	+	1.54346i	0.838539	+	0.544842i	$0.183410\pi$
$31$	4.96153	+	8.59362i	0.891116	+	1.54346i	0.0525777	+	0.998617i	$0.483256\pi$
$32$	4.43609	+	3.51015i	0.784197	+	0.620512i
$33$	−2.40016	−	3.52038i	−0.417814	−	0.612820i
$34$	4.10844	−	5.48916i	0.704592	−	0.941383i
$35$	−0.0420170	+	0.00502358i	−0.00710217	+	0.000849140i
$36$	−3.66886	−	4.06224i	−0.611476	−	0.677039i
$37$	1.78032	+	0.549155i	0.292682	+	0.0902805i	0.437619	−	0.899160i	$-0.355822\pi$
$37$	1.78032	+	0.549155i	0.292682	+	0.0902805i	−0.144937	+	0.989441i	$0.546298\pi$
$38$	1.81877	+	0.650165i	0.295043	+	0.105471i
$39$	−6.33006	+	0.474372i	−1.01362	+	0.0759603i
$40$	0.0203278	+	0.0404136i	0.00321411	+	0.00638995i
$41$	−1.78963	−	3.71620i	−0.279493	−	0.580373i	0.713211	−	0.700949i	$-0.247240\pi$
$41$	−1.78963	−	3.71620i	−0.279493	−	0.580373i	−0.992704	+	0.120576i	$0.961526\pi$
$42$	−1.99355	+	8.73740i	−0.307612	+	1.34821i
$43$	−4.01716	+	8.34173i	−0.612612	+	1.27210i	0.331804	+	0.943348i	$0.392343\pi$
$43$	−4.01716	+	8.34173i	−0.612612	+	1.27210i	−0.944416	+	0.328753i	$0.893372\pi$
$44$	3.55744	+	0.0478108i	0.536304	+	0.00720775i
$45$	−0.0129026	−	0.0418292i	−0.00192341	−	0.00623553i
$46$	6.58068	+	4.19686i	0.970269	+	0.618793i
$47$	9.62933	−	1.45139i	1.40458	−	0.211707i	0.597369	−	0.801967i	$-0.296213\pi$
$47$	9.62933	−	1.45139i	1.40458	−	0.211707i	0.807213	+	0.590260i	$0.200975\pi$
$48$	9.50867	−	1.17282i	1.37246	−	0.169281i
$49$	6.48076	−	2.64571i	0.925822	−	0.377959i
$50$	−0.216899	−	7.06738i	−0.0306741	−	0.999478i
$51$	−1.73073	−	11.4826i	−0.242350	−	1.60789i
$52$	2.71169	−	4.55432i	0.376044	−	0.631571i
$53$	−8.11554	+	2.50331i	−1.11475	+	0.343856i	−0.796796	−	0.604248i	$-0.793474\pi$
$53$	−8.11554	+	2.50331i	−1.11475	+	0.343856i	−0.317959	+	0.948105i	$0.602997\pi$
$54$	0.890364	+	0.0393078i	0.121163	+	0.00534911i
$55$	0.0256339	+	0.0123446i	0.00345647	+	0.00166455i
$56$	−5.01619	−	5.55318i	−0.670317	−	0.742075i
$57$	2.94730	−	1.41935i	0.390379	−	0.187997i
$58$	−2.84595	+	1.21898i	−0.373692	+	0.160060i
$59$	−0.462993	−	6.17821i	−0.0602765	−	0.804334i	−0.942650	−	0.333784i	$-0.891674\pi$
$59$	−0.462993	−	6.17821i	−0.0602765	−	0.804334i	0.882373	−	0.470550i	$-0.155945\pi$
$60$	0.0729033	+	0.0235652i	0.00941177	+	0.00304225i
$61$	2.72001	−	8.81806i	0.348262	−	1.12904i	−0.596867	−	0.802340i	$-0.703588\pi$
$61$	2.72001	−	8.81806i	0.348262	−	1.12904i	0.945129	−	0.326697i	$-0.105936\pi$
$62$	−10.6981	+	9.08207i	−1.35866	+	1.15342i
$63$	3.89409	+	6.10492i	0.490609	+	0.769147i
$64$	−3.75876	+	7.06199i	−0.469845	+	0.882749i
$65$	0.0350227	−	0.0238781i	0.00434403	−	0.00296171i
$66$	4.28927	−	4.23201i	0.527972	−	0.520924i
$67$	−4.78628	+	2.76336i	−0.584737	+	0.337598i	−0.763014	−	0.646382i	$-0.776281\pi$
$67$	−4.78628	+	2.76336i	−0.584737	+	0.337598i	0.178277	+	0.983980i	$0.442948\pi$
$68$	8.67884	+	4.32414i	1.05246	+	0.524379i
$69$	12.8876	−	2.94151i	1.55148	−	0.354116i
$70$	−0.0176438	−	0.0571842i	−0.00210883	−	0.00683482i
$71$	−13.9367	−	3.18096i	−1.65398	−	0.377510i	−0.709147	−	0.705061i	$-0.750920\pi$
$71$	−13.9367	−	3.18096i	−1.65398	−	0.377510i	−0.944834	+	0.327551i	$0.893777\pi$
$72$	4.72143	−	6.13454i	0.556426	−	0.722963i
$73$	−1.28303	+	8.51233i	−0.150167	+	0.996293i	0.779104	+	0.626895i	$0.215674\pi$
$73$	−1.28303	+	8.51233i	−0.150167	+	0.996293i	−0.929271	+	0.369399i	$0.879564\pi$
$74$	−0.312591	+	2.61620i	−0.0363379	+	0.304127i
$75$	−8.77851	−	8.14527i	−1.01365	−	0.940534i
$76$	−0.443375	+	2.69531i	−0.0508586	+	0.309173i
$77$	−4.63026	−	0.843540i	−0.527667	−	0.0961303i
$78$	−2.26514	−	8.68668i	−0.256477	−	0.983573i
$79$	0.651250	+	0.376000i	0.0732714	+	0.0423033i	0.536188	−	0.844099i	$-0.319864\pi$
$79$	0.651250	+	0.376000i	0.0732714	+	0.0423033i	−0.462917	+	0.886402i	$0.653197\pi$
$80$	−0.0510725	+	0.0385299i	−0.00571008	+	0.00430777i
$81$	7.12534	−	6.61135i	0.791704	−	0.734594i
$82$	4.71652	−	3.43224i	0.520853	−	0.379027i
$83$	−2.16800	+	2.71859i	−0.237969	+	0.298404i	−0.886447	−	0.462829i	$-0.846834\pi$
$83$	−2.16800	+	2.71859i	−0.237969	+	0.298404i	0.648478	+	0.761233i	$0.275406\pi$
$84$	−12.6618	−	0.558023i	−1.38152	−	0.0608853i
$85$	0.0483469	+	0.0606251i	0.00524396	+	0.00657572i
$86$	−12.6245	−	3.47380i	−1.36133	−	0.374589i
$87$	−1.91569	+	4.88111i	−0.205384	+	0.523309i
$88$	0.835561	+	4.96156i	0.0890711	+	0.528904i
$89$	1.89685	−	0.744461i	0.201066	−	0.0789127i	−0.262671	−	0.964885i	$-0.584603\pi$
$89$	1.89685	−	0.744461i	0.201066	−	0.0789127i	0.463737	+	0.885973i	$0.346508\pi$
$90$	0.0549249	−	0.0285582i	0.00578960	−	0.00301030i
$91$	−4.53754	+	5.34577i	−0.475663	+	0.560389i
$92$	−4.17036	+	10.2199i	−0.434790	+	1.06550i
$93$	−1.77615	+	23.7010i	−0.184178	+	2.45768i
$94$	4.46107	+	13.0292i	0.460124	+	1.34386i
$95$	−0.0123052	+	0.0180485i	−0.00126249	+	0.00185173i
$96$	4.04290	+	12.9320i	0.412627	+	1.31986i
$97$		−	12.1281i		−	1.23142i	−0.787973	−	0.615710i	$-0.788869\pi$
$97$		−	12.1281i		−	1.23142i	0.787973	−	0.615710i	$-0.211131\pi$
$98$	5.32433	+	8.34575i	0.537839	+	0.843048i
$99$		−	4.86859i		−	0.489312i
$100$	9.77780	−	2.09389i	0.977780	−	0.209389i
$101$	−6.66276	+	9.77248i	−0.662970	+	0.972398i	0.336558	+	0.941663i	$0.390737\pi$
$101$	−6.66276	+	9.77248i	−0.662970	+	0.972398i	−0.999528	+	0.0307352i	$0.990215\pi$
$102$	15.5368	−	5.31967i	1.53838	−	0.526726i
$103$	−0.411098	+	5.48572i	−0.0405067	+	0.540524i	0.939629	+	0.342195i	$0.111170\pi$
$103$	−0.411098	+	5.48572i	−0.0405067	+	0.540524i	−0.980136	+	0.198329i	$0.936449\pi$
$104$	7.02402	+	2.61789i	0.688762	+	0.256705i
$105$	−0.0899294	−	0.0467500i	−0.00877621	−	0.00456233i
$106$	−5.54075	−	10.6563i	−0.538165	−	1.03503i
$107$	−9.13170	+	3.58393i	−0.882794	+	0.346471i	−0.763055	−	0.646334i	$-0.776301\pi$
$107$	−9.13170	+	3.58393i	−0.882794	+	0.346471i	−0.119740	+	0.992805i	$0.538206\pi$
$108$	0.171086	+	1.24873i	0.0164628	+	0.120159i
$109$	−3.93663	+	10.0304i	−0.377061	+	0.960736i	0.608823	+	0.793306i	$0.291642\pi$
$109$	−3.93663	+	10.0304i	−0.377061	+	0.960736i	−0.985884	+	0.167430i	$0.946453\pi$
$110$	−0.0106749	+	0.0387946i	−0.00101781	+	0.00369892i
$111$	2.78228	+	3.48887i	0.264082	+	0.331149i
$112$	6.45412	−	8.38715i	0.609857	−	0.792511i
$113$	−8.16471	+	10.2382i	−0.768072	+	0.963131i	−0.999954	−	0.00961243i	$-0.996940\pi$
$113$	−8.16471	+	10.2382i	−0.768072	+	0.963131i	0.231882	+	0.972744i	$0.425512\pi$
$114$	2.72209	+	3.74065i	0.254947	+	0.350344i
$115$	−0.0647075	+	0.0600397i	−0.00603400	+	0.00559874i
$116$	−2.41762	−	3.65045i	−0.224471	−	0.338936i
$117$	−6.28165	−	3.62671i	−0.580738	−	0.335289i
$118$	8.47830	−	2.21080i	0.780491	−	0.203521i
$119$	−10.3722	−	7.54670i	−0.950820	−	0.691805i
$120$	−0.0142996	+	0.107405i	−0.00130537	+	0.00980473i
$121$	−5.74390	−	5.32956i	−0.522172	−	0.484505i
$122$	12.9582	+	1.54829i	1.17318	+	0.140176i
$123$	1.47244	−	9.76899i	0.132765	−	0.880840i
$124$	−15.3486	−	12.5812i	−1.37835	−	1.12983i
$125$	0.155926	+	0.0355892i	0.0139465	+	0.00318319i
$126$	−7.50629	+	6.96589i	−0.668713	+	0.620571i
$127$	6.66561	−	1.52138i	0.591477	−	0.135001i	0.0837027	−	0.996491i	$-0.473325\pi$
$127$	6.66561	−	1.52138i	0.591477	−	0.135001i	0.507775	+	0.861490i	$0.330468\pi$
$128$	−10.7784	−	3.43879i	−0.952688	−	0.303949i
$129$	−19.2050	+	11.0880i	−1.69091	+	0.976247i
$130$	0.0421023	+	0.0426720i	0.00369262	+	0.00374258i
$131$	−1.06471	+	0.725905i	−0.0930239	+	0.0634226i	−0.608939	−	0.793217i	$-0.708404\pi$
$131$	−1.06471	+	0.725905i	−0.0930239	+	0.0634226i	0.515915	+	0.856640i	$0.327452\pi$
$132$	6.97562	+	4.89450i	0.607150	+	0.426011i
$133$	1.17025	−	3.41873i	0.101474	−	0.296442i
$134$	−5.05833	−	5.95840i	−0.436973	−	0.514727i
$135$	−0.00297095	+	0.00963158i	−0.000255699	+	0.000828954i
$136$	−3.81540	+	13.1713i	−0.327168	+	1.12943i
$137$	−1.17209	−	15.6405i	−0.100138	−	1.33626i	−0.790354	−	0.612651i	$-0.790103\pi$
$137$	−1.17209	−	15.6405i	−0.100138	−	1.33626i	0.690215	−	0.723604i	$-0.257516\pi$
$138$	7.36049	+	17.1845i	0.626566	+	1.46285i
$139$	14.2955	−	6.88434i	1.21253	−	0.583922i	0.285306	−	0.958437i	$-0.407905\pi$
$139$	14.2955	−	6.88434i	1.21253	−	0.583922i	0.927221	+	0.374515i	$0.122191\pi$
$140$	0.0750860	−	0.0390482i	0.00634592	−	0.00330018i
$141$	21.0146	+	10.1201i	1.76975	+	0.852268i
$142$	0.891641	−	20.1966i	0.0748249	−	1.69486i
$143$	4.50501	−	1.38961i	0.376728	−	0.116205i
$144$	9.73220	+	5.01333i	0.811016	+	0.417777i
$145$	−0.00521864	−	0.0346234i	−0.000433384	−	0.00287532i
$146$	−12.1685	+	0.373453i	−1.00707	+	0.0309072i
$147$	16.3951	+	3.50834i	1.35224	+	0.289363i
$148$	−3.71916	+	0.228498i	−0.305713	+	0.0187824i
$149$	−14.0126	+	2.11206i	−1.14796	+	0.173027i	−0.695343	−	0.718678i	$-0.744747\pi$
$149$	−14.0126	+	2.11206i	−1.14796	+	0.173027i	−0.452616	+	0.891705i	$0.649509\pi$
$150$	9.10644	−	14.2789i	0.743538	−	1.16587i
$151$	1.77169	+	5.74368i	0.144178	+	0.467414i	0.998642	−	0.0520968i	$-0.0165904\pi$
$151$	1.77169	+	5.74368i	0.144178	+	0.467414i	−0.854464	+	0.519511i	$0.826114\pi$
$152$	−3.86240	+	0.0666005i	−0.313282	+	0.00540201i
$153$	5.75721	−	11.9550i	0.465443	−	0.966501i
$154$	−0.000509202	−	6.65595i	−4.10327e−5	−	0.536352i
$155$	−0.0688616	−	0.142993i	−0.00553110	−	0.0114854i
$156$	11.5113	−	5.35421i	0.921645	−	0.428680i
$157$	23.1508	−	1.73491i	1.84763	−	0.138461i	0.895680	−	0.444700i	$-0.146690\pi$
$157$	23.1508	−	1.73491i	1.84763	−	0.138461i	0.951955	+	0.306238i	$0.0990705\pi$
$158$	−0.357985	+	1.00143i	−0.0284797	+	0.0796691i
$159$	−19.4382	−	5.99588i	−1.54155	−	0.475505i
$160$	−0.0665571	−	0.0612867i	−0.00526180	−	0.00484514i
$161$	7.68449	−	12.4163i	0.605623	−	0.978543i
$162$	11.0051	+	8.23696i	0.864646	+	0.647157i
$163$	9.13348	+	13.3964i	0.715390	+	1.04928i	0.995990	+	0.0894592i	$0.0285139\pi$
$163$	9.13348	+	13.3964i	0.715390	+	1.04928i	−0.280601	+	0.959825i	$0.590534\pi$
$164$	5.97125	+	5.69174i	0.466276	+	0.444450i
$165$	0.0340732	+	0.0590165i	0.00265260	+	0.00459443i
$166$	−4.33211	−	2.32696i	−0.336237	−	0.180607i
$167$	−0.311301	−	1.36390i	−0.0240892	−	0.105542i	0.961454	−	0.274965i	$-0.0886664\pi$
$167$	−0.311301	−	1.36390i	−0.0240892	−	0.105542i	−0.985543	+	0.169424i	$0.945809\pi$
$168$	−2.43436	−	17.7578i	−0.187815	−	1.37004i
$169$	−1.32983	+	5.82638i	−0.102295	+	0.448183i
$170$	−0.0720878	+	0.0826378i	−0.00552888	+	0.00633803i
$171$	3.69620	+	0.557113i	0.282656	+	0.0426035i
$172$	1.63182	−	18.4452i	0.124425	−	1.40643i
$173$	−1.13526	+	1.22352i	−0.0863122	+	0.0930225i	−0.774731	−	0.632291i	$-0.782115\pi$
$173$	−1.13526	+	1.22352i	−0.0863122	+	0.0930225i	0.688419	+	0.725313i	$0.258305\pi$
$174$	−7.27683	−	1.42756i	−0.551655	−	0.108223i
$175$	−13.2152	+	0.584436i	−0.998972	+	0.0441792i
$176$	−6.69112	+	2.42064i	−0.504362	+	0.182463i
$177$	7.41971	−	12.8513i	0.557699	−	0.965964i
$178$	1.51676	+	2.45031i	0.113686	+	0.183658i
$179$	13.2242	+	14.2523i	0.988424	+	1.06527i	0.997865	+	0.0653121i	$0.0208043\pi$
$179$	13.2242	+	14.2523i	0.988424	+	1.06527i	−0.00944103	+	0.999955i	$0.503005\pi$
$180$	0.0536605	+	0.0691751i	0.00399961	+	0.00515601i
$181$	6.08611	+	4.85351i	0.452377	+	0.360759i	0.823016	−	0.568018i	$-0.192290\pi$
$181$	6.08611	+	4.85351i	0.452377	+	0.360759i	−0.370639	+	0.928777i	$0.620861\pi$
$182$	−8.58814	−	4.95749i	−0.636596	−	0.367474i
$183$	17.2807	−	13.7809i	1.27742	−	1.01871i
$184$	−15.2764	−	3.21068i	−1.12619	−	0.236694i
$185$	−0.0277385	−	0.0108865i	−0.00203937	−	0.000800395i
$186$	−33.4255	+	3.53887i	−2.45088	+	0.259482i
$187$	3.15084	+	8.02820i	0.230412	+	0.587080i
$188$	−16.9962	+	9.51055i	−1.23958	+	0.693628i
$189$	0.0510193	−	1.66656i	0.00371111	−	0.121224i
$190$	−0.0282310	−	0.0125435i	−0.00204809	−	0.000910005i
$191$	18.0930	+	1.35588i	1.30916	+	0.0981081i	0.710957	−	0.703236i	$-0.248262\pi$
$191$	18.0930	+	1.35588i	1.30916	+	0.0981081i	0.598204	+	0.801344i	$0.295881\pi$
$192$	−16.9670	+	8.90409i	−1.22449	+	0.642598i
$193$	−19.9473	−	13.5998i	−1.43583	−	0.978936i	−0.996756	−	0.0804872i	$-0.974352\pi$
$193$	−19.9473	−	13.5998i	−1.43583	−	0.978936i	−0.439079	−	0.898448i	$-0.644695\pi$
$194$	16.8737	−	3.07539i	1.21146	−	0.220800i
$195$	0.101527			0.00727051
$196$	−10.2613	+	9.52399i	−0.732948	+	0.680285i
$197$	26.2360			1.86924			0.934620	−	0.355648i	$-0.115740\pi$
$197$	26.2360			1.86924			0.934620	+	0.355648i	$0.115740\pi$
$198$	6.77365	−	1.23456i	0.481382	−	0.0877362i
$199$	−17.6162	−	12.0105i	−1.24878	−	0.851402i	−0.255460	−	0.966820i	$-0.582227\pi$
$199$	−17.6162	−	12.0105i	−1.24878	−	0.851402i	−0.993317	+	0.115418i	$0.963179\pi$
$200$	5.39262	+	13.0728i	0.381316	+	0.924389i
$201$	−13.2005	−	0.989239i	−0.931090	−	0.0697755i
$202$	−15.2859	−	6.79180i	−1.07551	−	0.477869i
$203$	2.35225	+	5.29298i	0.165096	+	0.371495i
$204$	11.3410	+	20.2674i	0.794028	+	1.41900i
$205$	0.0241016	+	0.0614099i	0.00168333	+	0.00428905i
$206$	−7.73649	+	0.819087i	−0.539027	+	0.0570685i
$207$	14.0608	+	5.51845i	0.977292	+	0.383559i
$208$	−1.86114	+	10.4363i	−0.129047	+	0.723628i
$209$	−1.89948	+	1.51479i	−0.131390	+	0.104780i
$210$	0.0422391	−	0.136973i	0.00291477	−	0.00945203i
$211$	10.2851	+	8.20209i	0.708056	+	0.564655i	0.909933	−	0.414755i	$-0.136133\pi$
$211$	10.2851	+	8.20209i	0.708056	+	0.564655i	−0.201877	+	0.979411i	$0.564704\pi$
$212$	13.4211	−	10.4110i	0.921763	−	0.715030i
$213$	−23.2887	−	25.0992i	−1.59571	−	1.71977i
$214$	−7.30187	−	11.7961i	−0.499146	−	0.806363i
$215$	0.0740414	−	0.128243i	0.00504958	−	0.00874613i
$216$	−1.69396	+	0.554677i	−0.115259	+	0.0377410i
$217$	17.2599	+	19.7829i	1.17168	+	1.34295i
$218$	−14.9534	−	2.93355i	−1.01277	−	0.198685i
$219$	−14.0244	+	15.1147i	−0.947681	+	1.02136i
$220$	−0.0566816	−	0.00501453i	−0.00382147	−	0.000338079i
$221$	12.7054	+	1.91503i	0.854658	+	0.128819i
$222$	−4.14852	+	4.75566i	−0.278431	+	0.319179i
$223$	3.04308	−	13.3326i	0.203779	−	0.892816i	−0.764831	−	0.644231i	$-0.777177\pi$
$223$	3.04308	−	13.3326i	0.203779	−	0.892816i	0.968610	−	0.248585i	$-0.0799654\pi$
$224$	13.3056	+	6.85280i	0.889018	+	0.457872i
$225$	−3.04492	−	13.3407i	−0.202995	−	0.889378i
$226$	−16.3148	−	8.76335i	−1.08524	−	0.582930i
$227$	−10.8866	−	18.8562i	−0.722571	−	1.25153i	−0.959966	−	0.280116i	$-0.909627\pi$
$227$	−10.8866	−	18.8562i	−0.722571	−	1.25153i	0.237396	−	0.971413i	$-0.423706\pi$
$228$	−4.51409	+	4.73577i	−0.298953	+	0.313634i
$229$	−5.05667	−	7.41677i	−0.334154	−	0.490114i	0.621984	−	0.783030i	$-0.286327\pi$
$229$	−5.05667	−	7.41677i	−0.334154	−	0.490114i	−0.956138	+	0.292916i	$0.905374\pi$
$230$	−0.0999412	−	0.0748025i	−0.00658993	−	0.00493233i
$231$	−8.02509	−	7.91675i	−0.528012	−	0.520884i
$232$	4.46580	−	4.28929i	0.293194	−	0.281606i
$233$	23.3834	+	7.21284i	1.53190	+	0.472529i	0.942188	−	0.335085i	$-0.108765\pi$
$233$	23.3834	+	7.21284i	1.53190	+	0.472529i	0.589712	+	0.807614i	$0.299241\pi$
$234$	3.45295	−	9.65926i	0.225726	−	0.631446i
$235$	−0.155316	+	0.0116393i	−0.0101317	+	0.000759266i
$236$	5.22577	+	11.2352i	0.340169	+	0.731349i
$237$	0.781500	+	1.62280i	0.0507639	+	0.105412i
$238$	7.86954	−	16.3445i	0.510107	−	1.05945i
$239$	2.20801	−	4.58497i	0.142824	−	0.296577i	−0.817270	−	0.576255i	$-0.804513\pi$
$239$	2.20801	−	4.58497i	0.142824	−	0.296577i	0.960094	+	0.279678i	$0.0902277\pi$
$240$	−0.153059	+	0.00734051i	−0.00987989	+	0.000473828i
$241$	1.50596	+	4.88220i	0.0970073	+	0.314490i	0.991050	−	0.133492i	$-0.0426191\pi$
$241$	1.50596	+	4.88220i	0.0970073	+	0.314490i	−0.894043	+	0.447982i	$0.852143\pi$
$242$	5.95847	−	9.34289i	0.383025	−	0.600584i
$243$	21.1519	−	3.18814i	1.35689	−	0.204519i
$244$	1.13177	+	18.4213i	0.0724543	+	1.17931i
$245$	−0.106526	+	0.0344513i	−0.00680569	+	0.00220101i
$246$	13.9649	−	0.428585i	0.890370	−	0.0273256i
$247$	0.539475	+	3.57918i	0.0343260	+	0.227738i
$248$	13.6122	−	24.5447i	0.864374	−	1.55859i
$249$	−7.95852	+	2.45488i	−0.504351	+	0.155572i
$250$	−0.00997586	+	0.225964i	−0.000630929	+	0.0142912i
$251$	−7.64898	−	3.68355i	−0.482799	−	0.232504i	0.176620	−	0.984279i	$-0.443484\pi$
$251$	−7.64898	−	3.68355i	−0.482799	−	0.232504i	−0.659419	+	0.751775i	$0.729198\pi$
$252$	−11.5950	−	8.67708i	−0.730417	−	0.546604i
$253$	−8.84540	+	4.25972i	−0.556105	+	0.267806i
$254$	3.80693	+	8.88804i	0.238868	+	0.557685i
$255$	0.0138795	+	0.185209i	0.000869167	+	0.0115982i
$256$	2.05122	−	15.8680i	0.128202	−	0.991748i
$257$	−1.56299	+	5.06709i	−0.0974967	+	0.316077i	−0.991162	−	0.132658i	$-0.957649\pi$
$257$	−1.56299	+	5.06709i	−0.0974967	+	0.316077i	0.893665	+	0.448734i	$0.148125\pi$
$258$	−20.2966	−	23.9082i	−1.26361	−	1.48846i
$259$	4.90191	+	0.518602i	0.304590	+	0.0322244i
$260$	−0.0486931	+	0.0693973i	−0.00301982	+	0.00430384i
$261$	−4.95053	+	3.37522i	−0.306430	+	0.208921i
$262$	−1.27993	−	1.29725i	−0.0790745	−	0.0801443i
$263$	−0.775770	+	0.447891i	−0.0478360	+	0.0276182i	−0.523727	−	0.851886i	$-0.675459\pi$
$263$	−0.775770	+	0.447891i	−0.0478360	+	0.0276182i	0.475891	+	0.879504i	$0.342126\pi$
$264$	−5.04084	+	10.9463i	−0.310242	+	0.673696i
$265$	0.132429	−	0.0302261i	0.00813507	−	0.00185678i
$266$	5.05321	+	0.761254i	0.309832	+	0.0466754i
$267$	4.75832	+	1.08606i	0.291205	+	0.0664656i
$268$	7.00722	−	8.54853i	0.428034	−	0.522185i
$269$	−1.46427	+	9.71481i	−0.0892783	+	0.592323i	0.898799	+	0.438362i	$0.144441\pi$
$269$	−1.46427	+	9.71481i	−0.0892783	+	0.592323i	−0.988077	+	0.153961i	$0.950797\pi$
$270$	−0.0141537	−	0.00169113i	−0.000861368	−	0.000102919i
$271$	0.444104	+	0.412069i	0.0269774	+	0.0250314i	0.693546	−	0.720412i	$-0.256047\pi$
$271$	0.444104	+	0.412069i	0.0269774	+	0.0250314i	−0.666569	+	0.745443i	$0.732238\pi$
$272$	−19.2927	−	1.96842i	−1.16979	−	0.119353i
$273$	−16.1925	+	4.45694i	−0.980017	+	0.269746i
$274$	21.4633	−	5.59677i	1.29664	−	0.338113i
$275$	7.70238	+	4.44697i	0.464471	+	0.268162i
$276$	−22.0423	+	14.5982i	−1.32679	+	0.878708i
$277$	−11.8402	+	10.9861i	−0.711411	+	0.660093i	−0.950436	−	0.310921i	$-0.899363\pi$
$277$	−11.8402	+	10.9861i	−0.711411	+	0.660093i	0.239025	+	0.971013i	$0.423172\pi$
$278$	13.2031	+	18.1435i	0.791871	+	1.08818i
$279$	−16.9329	+	21.2332i	−1.01375	+	1.27120i
$280$	0.0733675	+	0.0945650i	0.00438455	+	0.00565134i
$281$	−2.78044	−	3.48656i	−0.165867	−	0.207991i	0.691951	−	0.721945i	$-0.256752\pi$
$281$	−2.78044	−	3.48656i	−0.165867	−	0.207991i	−0.857818	+	0.513954i	$0.828180\pi$
$282$	−8.75126	+	31.8038i	−0.521130	+	1.89389i
$283$	−1.35965	+	3.46433i	−0.0808227	+	0.205933i	−0.965573	−	0.260133i	$-0.916234\pi$
$283$	−1.35965	+	3.46433i	−0.0808227	+	0.205933i	0.884750	+	0.466066i	$0.154329\pi$
$284$	28.3256	−	3.88084i	1.68081	−	0.230286i
$285$	−0.0487039	+	0.0191149i	−0.00288497	+	0.00113227i
$286$	3.07572	+	5.91542i	0.181871	+	0.349786i
$287$	−6.53979	−	8.73622i	−0.386032	−	0.515683i
$288$	−4.50716	+	14.8116i	−0.265587	+	0.872782i
$289$	−0.486127	+	6.48691i	−0.0285957	+	0.381583i
$290$	0.0468480	−	0.0160403i	0.00275101	−	0.000941919i
$291$	16.3639	−	24.0014i	0.959266	−	1.40698i
$292$	−3.60522	−	16.8353i	−0.210980	−	0.985210i
$293$			24.3816i			1.42439i	0.701982	+	0.712195i	$0.252299\pi$
$293$			24.3816i			1.42439i	−0.701982	+	0.712195i	$0.747701\pi$
$294$	−0.723727	+	23.7000i	−0.0422086	+	1.38221i
$295$			0.0990916i			0.00576934i
$296$	−1.26100	−	5.11651i	−0.0732940	−	0.297391i
$297$	−0.631505	+	0.926248i	−0.0366436	+	0.0537463i
$298$	−6.49176	−	18.9601i	−0.376058	−	1.09833i
$299$	−1.09306	+	14.5858i	−0.0632130	+	0.843519i
$300$	22.1754	+	9.04895i	1.28030	+	0.522441i
$301$	−6.17909	+	23.7039i	−0.356157	+	1.36627i
$302$	−7.54189	+	3.92140i	−0.433987	+	0.225651i
$303$	−26.3711	+	10.3499i	−1.51498	+	0.594586i
$304$	−1.07207	−	5.35684i	−0.0614875	−	0.307236i
$305$	−0.0539220	+	0.137391i	−0.00308757	+	0.00786699i
$306$	18.0928	+	4.97848i	1.03429	+	0.284601i
$307$	13.1605	+	16.5027i	0.751109	+	0.941860i	0.999642	−	0.0267631i	$-0.00851996\pi$
$307$	13.1605	+	16.5027i	0.751109	+	0.941860i	−0.248533	+	0.968623i	$0.579949\pi$
$308$	9.26026	−	1.68850i	0.527652	−	0.0962111i
$309$	−8.21518	+	10.3015i	−0.467345	+	0.586033i
$310$	0.181483	−	0.132066i	0.0103075	−	0.00750085i
$311$	16.4397	−	15.2538i	0.932211	−	0.864965i	−0.0588647	−	0.998266i	$-0.518748\pi$
$311$	16.4397	−	15.2538i	0.932211	−	0.864965i	0.991076	+	0.133301i	$0.0425576\pi$
$312$	10.3683	+	14.6580i	0.586988	+	0.829844i
$313$	15.4240	+	8.90503i	0.871814	+	0.503342i	0.867951	−	0.496650i	$-0.165437\pi$
$313$	15.4240	+	8.90503i	0.871814	+	0.503342i	0.00386363	+	0.999993i	$0.498770\pi$
$314$	8.28425	+	31.7696i	0.467508	+	1.79286i
$315$	−0.0548113	−	0.102024i	−0.00308827	−	0.00574838i
$316$	−1.48405	−	0.244125i	−0.0834845	−	0.0137331i
$317$	−7.86770	−	7.30016i	−0.441894	−	0.410018i	0.427595	−	0.903971i	$-0.359361\pi$
$317$	−7.86770	−	7.30016i	−0.441894	−	0.410018i	−0.869489	+	0.493953i	$0.835552\pi$
$318$	3.41299	−	28.5646i	0.191391	−	1.60183i
$319$	0.580423	−	3.85086i	0.0324975	−	0.215607i
$320$	0.0683905	−	0.108141i	0.00382314	−	0.00604529i
$321$	−22.9072	−	5.22841i	−1.27855	−	0.291822i
$322$	19.2234	+	7.54291i	1.07128	+	0.420350i
$323$	−6.45550	+	1.47343i	−0.359194	+	0.0819836i
$324$	−8.66940	+	17.4001i	−0.481633	+	0.966672i
$325$	11.4753	−	6.62526i	0.636535	−	0.367504i
$326$	−16.3222	+	16.1044i	−0.904006	+	0.891938i
$327$	−21.3241	+	14.5385i	−1.17922	+	0.803981i
$328$	−6.40472	+	9.75105i	−0.353641	+	0.538412i
$329$	24.2604	−	8.67457i	1.33752	−	0.478245i
$330$	−0.0734692	+	0.0623710i	−0.00404435	+	0.00343341i
$331$	1.29386	−	4.19458i	0.0711168	−	0.230555i	−0.913036	−	0.407880i	$-0.866268\pi$
$331$	1.29386	−	4.19458i	0.0711168	−	0.230555i	0.984152	+	0.177325i	$0.0567444\pi$
$332$	2.13897	−	6.61730i	0.117391	−	0.363172i
$333$	0.381054	+	5.08481i	0.0208816	+	0.278646i
$334$	1.81864	−	0.778962i	0.0995118	−	0.0426229i
$335$	0.0796408	−	0.0383530i	0.00435124	−	0.00209545i
$336$	24.0890	−	7.88985i	1.31416	−	0.430427i
$337$	−19.0708	−	9.18402i	−1.03885	−	0.500286i	−0.164908	−	0.986309i	$-0.552733\pi$
$337$	−19.0708	−	9.18402i	−1.03885	−	0.500286i	−0.873946	+	0.486023i	$0.838447\pi$
$338$	−8.44343	−	0.372760i	−0.459262	−	0.0202755i
$339$	−29.9719	+	9.24509i	−1.62785	+	0.502125i
$340$	−0.133253	−	0.0793403i	−0.00722667	−	0.00430283i
$341$	−2.63088	−	17.4547i	−0.142470	−	0.945228i
$342$	0.162160	+	5.28377i	0.00876859	+	0.285714i
$343$	15.4774	−	10.1710i	0.835702	−	0.549183i
$344$	26.0765	−	2.40692i	1.40595	−	0.129772i
$345$	−0.209064	+	0.0315114i	−0.0112556	+	0.00169652i
$346$	−1.99015	−	1.26923i	−0.106991	−	0.0682340i
$347$	−4.10622	−	13.3120i	−0.220433	−	0.714627i	−0.996471	−	0.0839405i	$-0.973249\pi$
$347$	−4.10622	−	13.3120i	−0.220433	−	0.714627i	0.776037	−	0.630687i	$-0.217227\pi$
$348$	0.140931	−	10.4862i	0.00755471	−	0.562119i
$349$	3.28486	−	6.82108i	0.175835	−	0.365124i	−0.794362	−	0.607445i	$-0.792194\pi$
$349$	3.28486	−	6.82108i	0.175835	−	0.365124i	0.970196	+	0.242321i	$0.0779087\pi$
$350$	−4.16417	−	18.2380i	−0.222584	−	0.974861i
$351$	0.724660	+	1.50477i	0.0386795	+	0.0803188i
$352$	−5.06453	−	8.69549i	−0.269940	−	0.463471i
$353$	24.1002	−	1.80606i	1.28272	−	0.0961267i	0.584138	−	0.811655i	$-0.301433\pi$
$353$	24.1002	−	1.80606i	1.28272	−	0.0961267i	0.698584	+	0.715528i	$0.253814\pi$
$354$	19.7614	+	7.06421i	1.05031	+	0.375459i
$355$	0.218479	+	0.0673918i	0.0115956	+	0.00357678i
$356$	−3.02448	+	2.73160i	−0.160297	+	0.144774i
$357$	−10.3441	−	28.9296i	−0.547469	−	1.53112i
$358$	−16.4758	+	22.0128i	−0.870774	+	1.16341i
$359$	−8.07426	−	11.8428i	−0.426143	−	0.625037i	0.551783	−	0.833988i	$-0.313948\pi$
$359$	−8.07426	−	11.8428i	−0.426143	−	0.625037i	−0.977926	+	0.208951i	$0.932995\pi$
$360$	−0.0826359	+	0.0921986i	−0.00435529	+	0.00485929i
$361$	8.56734	+	14.8391i	0.450913	+	0.781004i
$362$	−5.20937	+	9.69831i	−0.273799	+	0.509732i
$363$	−4.17620	−	18.2971i	−0.219193	−	0.960349i
$364$	4.71958	−	13.2057i	0.247373	−	0.692168i
$365$	0.0306377	−	0.134232i	0.00160365	−	0.00702605i
$366$	23.5552	+	20.5480i	1.23125	+	1.07406i
$367$	6.78258	+	1.02231i	0.354048	+	0.0533641i	0.323658	−	0.946174i	$-0.395087\pi$
$367$	6.78258	+	1.02231i	0.354048	+	0.0533641i	0.0303895	+	0.999538i	$0.490325\pi$
$368$	0.593283	−	22.0681i	0.0309270	−	1.15038i
$369$	7.67832	−	8.27526i	0.399717	−	0.430793i
$370$	0.00811258	−	0.0413529i	0.000421753	−	0.00214984i
$371$	−19.7942	+	10.6343i	−1.02767	+	0.552104i
$372$	−13.3995	−	45.6073i	−0.694732	−	2.36463i
$373$	3.50987	−	6.07927i	0.181734	−	0.314773i	−0.760737	−	0.649060i	$-0.775162\pi$
$373$	3.50987	−	6.07927i	0.181734	−	0.314773i	0.942471	+	0.334288i	$0.108496\pi$
$374$	−10.3706	+	6.41950i	−0.536251	+	0.331944i
$375$	0.260558	+	0.280815i	0.0134552	+	0.0145012i
$376$	−17.5418	−	21.2351i	−0.904649	−	1.09512i
$377$	−4.53615	−	3.61746i	−0.233624	−	0.186309i
$378$	2.33161	−	0.351616i	0.119925	−	0.0180852i
$379$	−17.7291	+	14.1385i	−0.910683	+	0.726246i	−0.962176	−	0.272428i	$-0.912173\pi$
$379$	−17.7291	+	14.1385i	−0.910683	+	0.726246i	0.0514928	+	0.998673i	$0.483602\pi$
$380$	0.0102931	−	0.0424584i	0.000528023	−	0.00217807i
$381$	15.2439	+	5.98280i	0.780970	+	0.306508i
$382$	2.70151	+	25.5165i	0.138221	+	1.30554i
$383$	6.38262	+	16.2627i	0.326137	+	0.830983i	0.996071	+	0.0885623i	$0.0282272\pi$
$383$	6.38262	+	16.2627i	0.326137	+	0.830983i	−0.669934	+	0.742421i	$0.733678\pi$
$384$	−16.6906	−	21.3482i	−0.851740	−	1.08942i
$385$	0.0728413	+	0.0189882i	0.00371234	+	0.000967726i
$386$	13.8632	−	31.2011i	0.705618	−	1.58809i
$387$	−25.2690	−	1.89365i	−1.28449	−	0.0962595i
$388$	8.55754	+	22.6965i	0.434443	+	1.15224i
$389$	6.71120	+	4.57562i	0.340271	+	0.231993i	0.721384	−	0.692536i	$-0.243506\pi$
$389$	6.71120	+	4.57562i	0.340271	+	0.231993i	−0.381112	+	0.924529i	$0.624459\pi$
$390$	0.0257448	+	0.141254i	0.00130364	+	0.00715268i
$391$	−26.7573			−1.35317
$392$	−15.8527	−	11.8614i	−0.800681	−	0.599091i
$393$	−3.08648			−0.155692
$394$	6.65282	+	36.5020i	0.335164	+	1.83895i
$395$	−0.00993760	−	0.00677534i	−0.000500015	−	0.000340904i
$396$	3.43527	+	9.11108i	0.172629	+	0.457849i
$397$	20.7211	+	1.55283i	1.03996	+	0.0779342i	0.583746	−	0.811936i	$-0.301586\pi$
$397$	20.7211	+	1.55283i	1.03996	+	0.0779342i	0.456214	+	0.889870i	$0.349205\pi$
$398$	12.2431	−	27.5549i	0.613692	−	1.38120i
$399$	6.92865	−	5.18668i	0.346866	−	0.259659i
$400$	−16.8207	+	10.8177i	−0.841036	+	0.540884i
$401$	−3.07366	−	7.83157i	−0.153491	−	0.391090i	0.833358	−	0.552734i	$-0.186415\pi$
$401$	−3.07366	−	7.83157i	−0.153491	−	0.391090i	−0.986849	+	0.161644i	$0.948320\pi$
$402$	−1.97100	−	18.6166i	−0.0983045	−	0.928511i
$403$	−24.4806	−	9.60792i	−1.21946	−	0.478604i
$404$	5.57325	−	22.9894i	0.277280	−	1.14377i
$405$	−0.121546	+	0.0969301i	−0.00603969	+	0.00481649i
$406$	−6.76762	+	4.61485i	−0.335871	+	0.229031i
$407$	−2.59115	−	2.06637i	−0.128439	−	0.102426i
$408$	−25.3221	+	20.9180i	−1.25363	+	1.03559i
$409$	−21.3546	−	23.0148i	−1.05592	−	1.13801i	−0.990126	−	0.140177i	$-0.955233\pi$
$409$	−21.3546	−	23.0148i	−1.05592	−	1.13801i	−0.0657930	−	0.997833i	$-0.520958\pi$
$410$	−0.0793277	+	0.0491045i	−0.00391771	+	0.00242510i
$411$	18.7834	−	32.5338i	0.926516	−	1.60477i
$412$	−3.10138	−	10.5560i	−0.152794	−	0.520058i
$413$	−4.35002	−	15.8041i	−0.214051	−	0.777669i
$414$	−4.11231	+	20.9620i	−0.202109	+	1.03023i
$415$	0.0378275	−	0.0407684i	0.00185688	−	0.00200124i
$416$	−14.9919	+	0.0570104i	−0.735039	+	0.00279516i
$417$	37.5793	+	5.66417i	1.84027	+	0.277376i
$418$	−2.58918	−	2.25863i	−0.126641	−	0.110473i
$419$	−3.56358	+	15.6130i	−0.174092	+	0.762747i	0.810193	+	0.586163i	$0.199362\pi$
$419$	−3.56358	+	15.6130i	−0.174092	+	0.762747i	−0.984285	+	0.176585i	$0.943495\pi$
$420$	0.201280	+	0.0240340i	0.00982148	+	0.00117274i
$421$	−7.33975	−	32.1576i	−0.357718	−	1.56726i	−0.758864	−	0.651249i	$-0.774245\pi$
$421$	−7.33975	−	32.1576i	−0.357718	−	1.56726i	0.401146	−	0.916014i	$-0.368612\pi$
$422$	−8.80347	+	16.3895i	−0.428546	+	0.797826i
$423$	13.3260	+	23.0814i	0.647935	+	1.12226i
$424$	17.8880	+	16.0327i	0.868719	+	0.778616i
$425$	13.6548	+	20.0279i	0.662353	+	0.971494i
$426$	29.0149	−	38.7659i	1.40578	−	1.87822i
$427$	2.56868	−	24.2796i	0.124307	−	1.17497i
$428$	14.5602	−	13.1503i	0.703796	−	0.635641i
$429$	10.7903	+	3.32837i	0.520961	+	0.160695i
$430$	0.197200	+	0.0704939i	0.00950980	+	0.00339952i
$431$	−6.81769	+	0.510915i	−0.328396	+	0.0246099i	−0.237908	−	0.971288i	$-0.576462\pi$
$431$	−6.81769	+	0.510915i	−0.328396	+	0.0246099i	−0.0904881	+	0.995898i	$0.528843\pi$
$432$	−1.20127	−	2.21615i	−0.0577960	−	0.106624i
$433$	−7.81590	−	16.2299i	−0.375608	−	0.779959i	0.624391	−	0.781112i	$-0.285347\pi$
$433$	−7.81590	−	16.2299i	−0.375608	−	0.779959i	−0.999999	+	0.00115329i	$0.999633\pi$
$434$	−23.1471	+	29.0301i	−1.11110	+	1.39349i
$435$	0.0363881	−	0.0755606i	0.00174468	−	0.00362286i
$436$	0.289605	−	21.5485i	0.0138696	−	1.03199i
$437$	−2.22177	−	7.20280i	−0.106282	−	0.344557i
$438$	−24.5852	−	15.6793i	−1.17473	−	0.749188i
$439$	6.08892	−	0.917757i	0.290608	−	0.0438021i	−0.00212023	−	0.999998i	$-0.500675\pi$
$439$	6.08892	−	0.917757i	0.290608	−	0.0438021i	0.292728	+	0.956196i	$0.405437\pi$
$440$	−0.00739639	−	0.0801323i	−0.000352609	−	0.00382016i
$441$	13.2206	+	13.8656i	0.629551	+	0.660265i
$442$	0.557411	+	18.1626i	0.0265133	+	0.863905i
$443$	−4.50741	−	29.9047i	−0.214154	−	1.42082i	−0.794904	−	0.606735i	$-0.792479\pi$
$443$	−4.50741	−	29.9047i	−0.214154	−	1.42082i	0.580751	−	0.814082i	$-0.302759\pi$
$444$	−7.66849	−	4.56590i	−0.363931	−	0.216688i
$445$	−0.0311434	+	0.00960645i	−0.00147634	+	0.000455390i
$446$	19.3212	+	0.852992i	0.914885	+	0.0403904i
$447$	−30.5806	−	14.7268i	−1.44641	−	0.696555i
$448$	−6.16028	+	20.2497i	−0.291046	+	0.956709i
$449$	−9.58460	+	4.61570i	−0.452325	+	0.217828i	−0.646154	−	0.763207i	$-0.723624\pi$
$449$	−9.58460	+	4.61570i	−0.452325	+	0.217828i	0.193829	+	0.981035i	$0.437909\pi$
$450$	17.7887	−	7.61925i	0.838566	−	0.359175i
$451$	0.548316	+	7.31677i	0.0258192	+	0.344533i
$452$	8.05537	−	24.9208i	0.378893	−	1.17218i
$453$	−4.24352	+	13.7571i	−0.199378	+	0.646367i
$454$	23.4739	−	19.9280i	1.10169	−	0.935266i
$455$	0.0787601	−	0.0798379i	0.00369233	−	0.00374286i
$456$	−7.73351	−	5.07955i	−0.362155	−	0.237872i
$457$	−10.9773	+	7.48419i	−0.513496	+	0.350096i	−0.792180	−	0.610287i	$-0.791054\pi$
$457$	−10.9773	+	7.48419i	−0.513496	+	0.350096i	0.278684	+	0.960383i	$0.410102\pi$
$458$	9.03666	−	8.91603i	0.422255	−	0.416618i
$459$	−2.64598	+	1.52766i	−0.123504	+	0.0713050i
$460$	0.0787296	−	0.158016i	0.00367079	−	0.00736752i
$461$	0.584631	−	0.133438i	0.0272290	−	0.00621484i	−0.208885	−	0.977940i	$-0.566983\pi$
$461$	0.584631	−	0.133438i	0.0272290	−	0.00621484i	0.236114	+	0.971725i	$0.424126\pi$
$462$	8.97956	−	13.1728i	0.417767	−	0.612852i
$463$	29.5541	+	6.74552i	1.37349	+	0.313491i	0.844691	−	0.535254i	$-0.179784\pi$
$463$	29.5541	+	6.74552i	1.37349	+	0.313491i	0.528803	+	0.848745i	$0.322641\pi$
$464$	7.10009	+	5.12559i	0.329613	+	0.237949i
$465$	0.0566567	−	0.375893i	0.00262739	−	0.0174316i
$466$	−4.10570	+	34.3622i	−0.190193	+	1.59180i
$467$	25.2631	+	23.4408i	1.16904	+	1.08471i	0.994990	+	0.0999718i	$0.0318753\pi$
$467$	25.2631	+	23.4408i	1.16904	+	1.08471i	0.174048	+	0.984737i	$0.444315\pi$
$468$	14.3145	+	2.35471i	0.661686	+	0.108846i
$469$	−11.0182	+	9.61306i	−0.508775	+	0.443890i
$470$	−0.0555781	−	0.213139i	−0.00256363	−	0.00983136i
$471$	48.1561	+	27.8029i	2.21891	+	1.28109i
$472$	−14.3063	+	10.1196i	−0.658503	+	0.465790i
$473$	12.0733	−	11.2024i	0.555133	−	0.515088i
$474$	−2.05962	+	1.49880i	−0.0946017	+	0.0688421i
$475$	−4.25749	+	5.33872i	−0.195347	+	0.244957i
$476$	24.7355	+	6.80428i	1.13375	+	0.311874i
$477$	−14.4924	−	18.1729i	−0.663561	−	0.832080i
$478$	6.93894	+	1.90935i	0.317380	+	0.0873316i
$479$	2.26375	−	5.76795i	0.103434	−	0.263544i	−0.869783	−	0.493434i	$-0.835741\pi$
$479$	2.26375	−	5.76795i	0.103434	−	0.263544i	0.973217	+	0.229890i	$0.0738366\pi$
$480$	−0.0490248	−	0.211088i	−0.00223766	−	0.00963481i
$481$	−4.59631	+	1.80392i	−0.209574	+	0.0822517i
$482$	−6.41070	+	3.33324i	−0.291999	+	0.151825i
$483$	31.9603	−	14.2035i	1.45424	−	0.646280i
$484$	14.5096	+	5.92085i	0.659529	+	0.269129i
$485$	−0.0144959	+	0.193435i	−0.000658226	+	0.00878342i
$486$	9.79924	+	28.6201i	0.444503	+	1.29823i
$487$	−14.0665	+	20.6317i	−0.637412	+	0.934911i	0.362584	+	0.931951i	$0.381895\pi$
$487$	−14.0665	+	20.6317i	−0.637412	+	0.934911i	−0.999996	+	0.00296028i	$0.999058\pi$
$488$	−25.3425	+	6.24583i	−1.14720	+	0.282736i
$489$			38.8347i			1.75616i
$490$	−0.0749443	−	0.139473i	−0.00338564	−	0.00630074i
$491$			18.3343i			0.827414i	0.910410	+	0.413707i	$0.135766\pi$
$491$			18.3343i			0.827414i	−0.910410	+	0.413707i	$0.864234\pi$
$492$	4.13745	+	19.3206i	0.186531	+	0.871041i
$493$	5.97896	−	8.76952i	0.269279	−	0.394959i
$494$	−4.84290	+	1.65816i	−0.217892	+	0.0746042i
$495$	−0.00581912	+	0.0776508i	−0.000261550	+	0.00349014i
$496$	37.6007	+	12.7146i	1.68832	+	0.570901i
$497$	−37.8036	−	1.15730i	−1.69572	−	0.0519120i
$498$	−5.43355	−	10.4501i	−0.243483	−	0.468282i
$499$	1.37167	−	0.538342i	0.0614045	−	0.0240995i	−0.334440	−	0.942417i	$-0.608547\pi$
$499$	1.37167	−	0.538342i	0.0614045	−	0.0240995i	0.395845	+	0.918318i	$0.370452\pi$
$500$	−0.316912	+	0.0434197i	−0.0141727	+	0.00194179i
$501$	1.22418	−	3.11916i	0.0546924	−	0.139354i
$502$	3.18531	−	11.5760i	0.142167	−	0.516664i
$503$	9.18796	+	11.5213i	0.409671	+	0.513711i	0.943270	−	0.332027i	$-0.107732\pi$
$503$	9.18796	+	11.5213i	0.409671	+	0.513711i	−0.533599	+	0.845737i	$0.679161\pi$
$504$	9.13215	−	18.3324i	0.406778	−	0.816588i
$505$	0.117947	−	0.147901i	0.00524857	−	0.00658150i
$506$	−8.16950	−	11.2264i	−0.363179	−	0.499074i
$507$	−10.4930	+	9.73608i	−0.466010	+	0.432394i
$508$	−11.4005	+	7.55035i	−0.505817	+	0.334993i
$509$	−11.0515	−	6.38058i	−0.489849	−	0.282814i	0.234663	−	0.972077i	$-0.424601\pi$
$509$	−11.0515	−	6.38058i	−0.489849	−	0.282814i	−0.724512	+	0.689262i	$0.757935\pi$
$510$	−0.254160	+	0.0662749i	−0.0112544	+	0.00293470i
$511$	1.00627	+	22.7537i	0.0445149	+	1.00656i
$512$	22.5972	−	1.16988i	0.998663	−	0.0517017i
$513$	−0.630938	−	0.585424i	−0.0278566	−	0.0258471i
$514$	−7.44616	−	0.889689i	−0.328436	−	0.0392425i
$515$	0.0131135	−	0.0870021i	0.000577848	−	0.00383377i
$516$	28.1166	−	34.3012i	1.23776	−	1.51002i
$517$	−16.8886	−	3.85470i	−0.742758	−	0.169530i
$518$	0.521478	+	6.95150i	0.0229124	+	0.305432i
$519$	−3.89751	+	0.889581i	−0.171082	+	0.0390483i
$520$	−0.108899	−	0.0501490i	−0.00477555	−	0.00219918i
$521$	−23.8562	+	13.7734i	−1.04516	+	0.603422i	−0.921290	−	0.388877i	$-0.872863\pi$
$521$	−23.8562	+	13.7734i	−1.04516	+	0.603422i	−0.123868	+	0.992299i	$0.539530\pi$
$522$	−5.95126	−	6.03178i	−0.260479	−	0.264004i
$523$	−3.47822	+	2.37141i	−0.152092	+	0.103695i	−0.636975	−	0.770884i	$-0.719815\pi$
$523$	−3.47822	+	2.37141i	−0.152092	+	0.103695i	0.484883	+	0.874579i	$0.338862\pi$
$524$	1.48030	−	2.10971i	0.0646670	−	0.0921632i
$525$	−26.9412	−	16.6740i	−1.17581	−	0.727713i
$526$	−0.819865	−	0.965750i	−0.0357478	−	0.0421087i
$527$	14.1804	−	45.9716i	0.617707	−	2.00256i
$528$	−16.5077	−	4.23758i	−0.718406	−	0.184417i
$529$	−0.557448	−	7.43862i	−0.0242369	−	0.323418i
$530$	0.0756343	+	0.176584i	0.00328535	+	0.00767030i
$531$	15.2773	−	7.35714i	0.662977	−	0.319273i
$532$	0.222244	+	7.22354i	0.00963551	+	0.313180i
$533$	9.84883	+	4.74295i	0.426600	+	0.205440i
$534$	−0.304428	+	6.89563i	−0.0131739	+	0.298403i
$535$	0.149928	−	0.0462467i	0.00648195	−	0.00199942i
$536$	13.6704	+	7.58140i	0.590471	+	0.327467i
$537$	6.94062	+	46.0480i	0.299510	+	1.98712i
$538$	−13.8875	+	0.426208i	−0.598731	+	0.0183751i
$539$	−12.4510	+	0.169243i	−0.536302	+	0.00728981i
$540$	−0.00123618	−	0.0201208i	−5.31969e−5	−	0.000865862i
$541$	−19.0789	+	2.87568i	−0.820266	+	0.123635i	−0.545751	−	0.837947i	$-0.683756\pi$
$541$	−19.0789	+	2.87568i	−0.820266	+	0.123635i	−0.274515	+	0.961583i	$0.588517\pi$
$542$	−0.460694	+	0.722370i	−0.0197885	+	0.0310285i
$543$	5.49574	+	17.8168i	0.235845	+	0.764591i
$544$	−2.15350	−	27.3409i	−0.0923307	−	1.17223i
$545$	0.0747753	−	0.155273i	0.00320302	−	0.00665114i
$546$	−10.3069	−	21.3984i	−0.441097	−	0.915767i
$547$	−2.89015	−	6.00145i	−0.123574	−	0.256604i	0.830000	−	0.557764i	$-0.188340\pi$
$547$	−2.89015	−	6.00145i	−0.123574	−	0.256604i	−0.953574	+	0.301160i	$0.902626\pi$
$548$	13.2293	+	28.4425i	0.565128	+	1.21500i
$549$	25.1855	−	1.88739i	1.07489	−	0.0805520i
$550$	−4.23391	+	11.8439i	−0.180534	+	0.505026i
$551$	2.85713	+	0.881306i	0.121718	+	0.0375449i
$552$	−25.8998	−	26.9656i	−1.10237	−	1.14773i
$553$	1.88238	+	0.644347i	0.0800467	+	0.0274004i
$554$	−18.2873	−	13.6874i	−0.776955	−	0.581523i
$555$	−0.0402055	−	0.0589706i	−0.00170663	−	0.00250316i
$556$	−21.8950	+	22.9702i	−0.928554	+	0.974153i
$557$	11.6149	+	20.1176i	0.492139	+	0.852410i	0.999959	−	0.00905307i	$-0.00288172\pi$
$557$	11.6149	+	20.1176i	0.492139	+	0.852410i	−0.507820	+	0.861463i	$0.669548\pi$
$558$	−33.8354	−	18.1744i	−1.43237	−	0.769386i
$559$	−5.46013	−	23.9224i	−0.230939	−	1.01181i
$560$	−0.112964	+	0.126055i	−0.00477358	+	0.00532680i
$561$	−4.59660	+	20.1390i	−0.194068	+	0.850270i
$562$	4.14577	−	4.75251i	0.174879	−	0.200473i
$563$	5.68010	+	0.856137i	0.239388	+	0.0360819i	0.267640	−	0.963519i	$-0.413756\pi$
$563$	5.68010	+	0.856137i	0.239388	+	0.0360819i	−0.0282526	+	0.999601i	$0.508994\pi$
$564$	−46.4675	−	4.11091i	−1.95663	−	0.173100i
$565$	0.142459	−	0.153534i	0.00599329	−	0.00645923i
$566$	−5.16467	−	1.01320i	−0.217087	−	0.0425880i
$567$	15.1303	−	20.7951i	0.635412	−	0.873313i
$568$	12.5821	+	38.4251i	0.527932	+	1.61228i
$569$	13.3255	−	23.0804i	0.558633	−	0.967581i	−0.438978	−	0.898498i	$-0.644659\pi$
$569$	13.3255	−	23.0804i	0.558633	−	0.967581i	0.997611	−	0.0690828i	$-0.0220073\pi$
$570$	−0.0389445	−	0.0629144i	−0.00163121	−	0.00263519i
$571$	−19.0145	−	20.4927i	−0.795731	−	0.857594i	0.196691	−	0.980465i	$-0.436980\pi$
$571$	−19.0145	−	20.4927i	−0.795731	−	0.857594i	−0.992423	+	0.122871i	$0.960790\pi$
$572$	−7.45016	+	5.77924i	−0.311507	+	0.241642i
$573$	33.9764	+	27.0953i	1.41938	+	1.13192i
$574$	10.4963	−	11.3141i	0.438108	−	0.472240i
$575$	−21.5736	+	17.2044i	−0.899680	+	0.717471i
$576$	−21.7502	−	2.51493i	−0.906259	−	0.104789i
$577$	33.7461	+	13.2444i	1.40487	+	0.551370i	0.942167	−	0.335144i	$-0.108785\pi$
$577$	33.7461	+	13.2444i	1.40487	+	0.551370i	0.462702	+	0.886514i	$0.346880\pi$
$578$	−9.14847	+	0.968578i	−0.380526	+	0.0402875i
$579$	−21.1259	−	53.8278i	−0.877961	−	2.23701i
$580$	0.0341963	+	0.0611119i	0.00141992	+	0.00253753i
$581$	−4.24341	+	8.16273i	−0.176046	+	0.338647i
$582$	37.5424	+	16.6808i	1.55618	+	0.691440i
$583$	15.0655	+	1.12900i	0.623949	+	0.0467585i
$584$	22.5086	−	9.28494i	0.931413	−	0.384214i
$585$	0.0958532	+	0.0653516i	0.00396304	+	0.00270196i
$586$	−33.9220	+	6.18259i	−1.40131	+	0.255400i
$587$	28.8478			1.19068			0.595339	−	0.803475i	$-0.297018\pi$
$587$	28.8478			1.19068			0.595339	+	0.803475i	$0.297018\pi$
$588$	−33.1572	+	5.00284i	−1.36738	+	0.206314i
$589$	13.5526			0.558424
$590$	−0.137866	+	0.0251272i	−0.00567584	+	0.00103447i
$591$	51.9209	+	35.3990i	2.13574	+	1.45612i
$592$	6.79881	−	3.05184i	0.279429	−	0.125430i
$593$	7.48994	+	0.561293i	0.307575	+	0.0230496i	0.227624	−	0.973749i	$-0.426904\pi$
$593$	7.48994	+	0.561293i	0.307575	+	0.0230496i	0.0799514	+	0.996799i	$0.474523\pi$
$594$	−1.44882	−	0.643735i	−0.0594457	−	0.0264128i
$595$	0.156410	+	0.132762i	0.00641218	+	0.00544272i
$596$	24.7329	−	13.8398i	1.01310	−	0.566899i
$597$	−18.6570	−	47.5374i	−0.763582	−	1.94557i
$598$	−20.5703	+	2.17785i	−0.841183	+	0.0890588i
$599$	18.2262	+	7.15325i	0.744701	+	0.292274i	0.707191	−	0.707022i	$-0.249962\pi$
$599$	18.2262	+	7.15325i	0.744701	+	0.292274i	0.0375104	+	0.999296i	$0.488057\pi$
$600$	−6.96661	+	33.1470i	−0.284411	+	1.35322i
$601$	−15.7473	+	12.5581i	−0.642346	+	0.512254i	−0.889626	−	0.456690i	$-0.849035\pi$
$601$	−15.7473	+	12.5581i	−0.642346	+	0.512254i	0.247279	+	0.968944i	$0.420463\pi$
$602$	−34.5459	−	2.58620i	−1.40799	−	0.105406i
$603$	−11.8260	−	9.43092i	−0.481592	−	0.384057i
$604$	−7.36826	−	9.49861i	−0.299810	−	0.386493i
$605$	0.0852412	+	0.0918681i	0.00346555	+	0.00373497i
$606$	−21.0868	−	34.0655i	−0.856593	−	1.38382i
$607$	−4.51123	+	7.81368i	−0.183105	+	0.317147i	−0.942936	−	0.332973i	$-0.891948\pi$
$607$	−4.51123	+	7.81368i	−0.183105	+	0.317147i	0.759831	+	0.650120i	$0.225282\pi$
$608$	7.18109	−	2.84993i	0.291232	−	0.115580i
$609$	−2.48649	+	13.6485i	−0.100758	+	0.553067i
$610$	−0.204825	−	0.0401823i	−0.00829311	−	0.00162694i
$611$	−17.5541	+	18.9188i	−0.710163	+	0.765374i
$612$	−2.33864	+	26.4348i	−0.0945340	+	1.06856i
$613$	−20.0368	−	3.02006i	−0.809277	−	0.121979i	−0.268646	−	0.963239i	$-0.586576\pi$
$613$	−20.0368	−	3.02006i	−0.809277	−	0.121979i	−0.540631	+	0.841260i	$0.681814\pi$
$614$	−19.6230	+	22.4948i	−0.791918	+	0.907816i
$615$	−0.0351606	+	0.154049i	−0.00141781	+	0.00621185i
$616$	4.69737	+	12.4556i	0.189263	+	0.501850i
$617$	−2.25673	−	9.88738i	−0.0908525	−	0.398051i	0.908971	−	0.416860i	$-0.136870\pi$
$617$	−2.25673	−	9.88738i	−0.0908525	−	0.398051i	−0.999823	+	0.0188095i	$0.994012\pi$
$618$	−16.4156	−	8.81752i	−0.660332	−	0.354693i
$619$	−6.71696	−	11.6341i	−0.269977	−	0.467614i	0.698878	−	0.715241i	$-0.253683\pi$
$619$	−6.71696	−	11.6341i	−0.269977	−	0.467614i	−0.968856	+	0.247626i	$0.920350\pi$
$620$	0.229763	+	0.219008i	0.00922749	+	0.00879555i
$621$	−1.95926	−	2.87370i	−0.0786223	−	0.115318i
$622$	25.3913	+	19.0045i	1.01810	+	0.762010i
$623$	4.54533	−	2.89929i	0.182105	−	0.116158i
$624$	−17.7644	+	18.1422i	−0.711145	+	0.726270i
$625$	23.8857	+	7.36775i	0.955426	+	0.294710i
$626$	−8.47838	+	23.7174i	−0.338864	+	0.947937i
$627$	−5.80290	+	0.434867i	−0.231745	+	0.0173669i
$628$	−42.1002	+	19.5818i	−1.67998	+	0.781401i
$629$	−3.91911	−	8.13812i	−0.156265	−	0.324488i
$630$	0.128046	−	0.102129i	0.00510148	−	0.00406893i
$631$	2.19768	−	4.56353i	0.0874883	−	0.181671i	−0.852634	−	0.522509i	$-0.824996\pi$
$631$	2.19768	−	4.56353i	0.0874883	−	0.181671i	0.940122	+	0.340837i	$0.110711\pi$
$632$	−0.0366706	−	2.12666i	−0.00145868	−	0.0845939i
$633$	9.28742	+	30.1091i	0.369142	+	1.19673i
$634$	8.16161	−	12.7974i	0.324139	−	0.508251i
$635$	−0.108130	+	0.0162980i	−0.00429102	+	0.000646768i
$636$	40.6073	−	2.49483i	1.61018	−	0.0989265i
$637$	−9.05662	+	16.1908i	−0.358837	+	0.641504i
$638$	5.50486	−	0.168945i	0.217939	−	0.00668858i
$639$	−5.83114	−	38.6871i	−0.230677	−	1.53044i
$640$	0.167799	+	0.0677292i	0.00663282	+	0.00267723i
$641$	16.1599	−	4.98467i	0.638278	−	0.196883i	0.0413080	−	0.999146i	$-0.486847\pi$
$641$	16.1599	−	4.98467i	0.638278	−	0.196883i	0.596970	+	0.802264i	$0.296371\pi$
$642$	1.46556	−	33.1964i	0.0578408	−	1.31016i
$643$	−0.547630	−	0.263725i	−0.0215964	−	0.0104003i	0.423054	−	0.906104i	$-0.360958\pi$
$643$	−0.547630	−	0.263725i	−0.0215964	−	0.0104003i	−0.444651	+	0.895704i	$0.646672\pi$
$644$	−5.61983	+	28.6580i	−0.221452	+	1.12928i
$645$	0.319560	−	0.153892i	0.0125827	−	0.00605950i
$646$	−3.68693	−	8.60787i	−0.145060	−	0.338672i
$647$	0.686199	+	9.15669i	0.0269773	+	0.359987i	0.994314	+	0.106491i	$0.0339614\pi$
$647$	0.686199	+	9.15669i	0.0269773	+	0.359987i	−0.967336	+	0.253496i	$0.918420\pi$
$648$	−26.4070	−	7.64945i	−1.03736	−	0.300499i
$649$	−3.24852	+	10.5315i	−0.127516	+	0.413396i
$650$	12.1275	+	14.2855i	0.475682	+	0.560324i
$651$	7.46515	+	62.4382i	0.292582	+	2.44715i
$652$	−26.5448	−	18.6254i	−1.03958	−	0.729426i
$653$	18.1920	−	12.4031i	0.711908	−	0.485371i	−0.152409	−	0.988317i	$-0.548703\pi$
$653$	18.1920	−	12.4031i	0.711908	−	0.485371i	0.864317	+	0.502947i	$0.167751\pi$
$654$	−25.6346	−	25.9815i	−1.00239	−	1.01596i
$655$	0.0178490	−	0.0103051i	0.000697418	−	0.000402654i
$656$	−15.1907	−	6.43821i	−0.593095	−	0.251370i
$657$	−22.9698	+	5.24270i	−0.896136	+	0.204537i
$658$	18.2207	+	31.5536i	0.710318	+	1.23009i
$659$	1.32496	+	0.302413i	0.0516131	+	0.0117804i	0.248250	−	0.968696i	$-0.420145\pi$
$659$	1.32496	+	0.302413i	0.0516131	+	0.0117804i	−0.196636	+	0.980476i	$0.563002\pi$
$660$	−0.105406	−	0.0864015i	−0.00410294	−	0.00336317i
$661$	4.85335	−	32.1998i	0.188773	−	1.25243i	−0.670886	−	0.741561i	$-0.734086\pi$
$661$	4.85335	−	32.1998i	0.188773	−	1.25243i	0.859659	−	0.510868i	$-0.170676\pi$
$662$	6.16398	+	0.736491i	0.239570	+	0.0286245i
$663$	22.5600	+	20.9326i	0.876159	+	0.812956i
$664$	9.74900	+	1.29795i	0.378335	+	0.0503701i
$665$	−0.0227509	+	0.0531278i	−0.000882242	+	0.00206021i
$666$	−6.97784	+	1.81954i	−0.270386	+	0.0705058i
$667$	10.4636	+	6.04116i	0.405152	+	0.233915i
$668$	1.54493	+	2.33274i	0.0597751	+	0.0902565i
$669$	24.0113	−	22.2792i	0.928329	−	0.861363i
$670$	0.0735553	+	0.101078i	0.00284169	+	0.00390500i
$671$	−10.2349	+	12.8342i	−0.395115	+	0.495459i
$672$	17.0855	+	31.5143i	0.659088	+	1.21569i
$673$	−16.2378	−	20.3616i	−0.625923	−	0.784883i	0.363241	−	0.931695i	$-0.381670\pi$
$673$	−16.2378	−	20.3616i	−0.625923	−	0.784883i	−0.989164	+	0.146812i	$0.953099\pi$
$674$	7.94178	−	28.8620i	0.305906	−	1.11172i
$675$	−1.15112	+	2.93301i	−0.0443067	+	0.112892i
$676$	−1.62243	−	11.8418i	−0.0624011	−	0.455454i
$677$	−25.4226	+	9.97763i	−0.977070	+	0.383472i	−0.799519	−	0.600640i	$-0.794912\pi$
$677$	−25.4226	+	9.97763i	−0.977070	+	0.383472i	−0.177550	+	0.984112i	$0.556817\pi$
$678$	−20.4628	−	39.3553i	−0.785868	−	1.51143i
$679$	−6.17964	−	31.4872i	−0.237153	−	1.20837i
$680$	0.0765959	−	0.205513i	0.00293732	−	0.00788107i
$681$	3.89724	−	52.0050i	0.149343	−	1.99284i
$682$	23.6176	−	8.08643i	0.904363	−	0.309645i
$683$	−1.00702	+	1.47703i	−0.0385326	+	0.0565170i	−0.845022	−	0.534732i	$-0.820413\pi$
$683$	−1.00702	+	1.47703i	−0.0385326	+	0.0565170i	0.806489	+	0.591249i	$0.201365\pi$
$684$	−7.31016	+	1.56545i	−0.279511	+	0.0598564i
$685$			0.250856i			0.00958471i
$686$	18.0756	+	18.9545i	0.690129	+	0.723687i
$687$		−	21.5004i		−	0.820293i
$688$	9.96110	+	35.6697i	0.379763	+	1.35990i
$689$	12.6793	−	18.5971i	0.483042	−	0.708492i
$690$	−0.0968552	−	0.282879i	−0.00368722	−	0.0107690i
$691$	2.29888	−	30.6764i	0.0874536	−	1.16699i	−0.764945	−	0.644095i	$-0.777234\pi$
$691$	2.29888	−	30.6764i	0.0874536	−	1.16699i	0.852399	−	0.522892i	$-0.175147\pi$
$692$	1.26121	−	3.09073i	0.0479441	−	0.117492i
$693$	−2.48070	−	12.6400i	−0.0942341	−	0.480152i
$694$	17.4797	−	9.08857i	0.663521	−	0.344997i
$695$	−0.236232	+	0.0927141i	−0.00896078	+	0.00351685i
$696$	14.6251	−	2.46297i	0.554364	−	0.0933586i
$697$	−7.30582	+	18.6149i	−0.276728	+	0.705090i
$698$	10.3231	+	2.84055i	0.390735	+	0.107516i
$699$	36.5437	+	45.8243i	1.38221	+	1.73323i
$700$	24.3185	−	10.4183i	0.919151	−	0.393774i
$701$	−13.4474	+	16.8625i	−0.507900	+	0.636886i	−0.967991	−	0.250986i	$-0.919245\pi$
$701$	−13.4474	+	16.8625i	−0.507900	+	0.636886i	0.460091	+	0.887872i	$0.347817\pi$
$702$	−1.90982	+	1.38979i	−0.0720816	+	0.0524542i
$703$	1.86528	−	1.73073i	0.0703504	−	0.0652756i
$704$	10.8137	−	9.25122i	0.407558	−	0.348668i
$705$	−0.323073	−	0.186527i	−0.0121676	−	0.00702500i
$706$	8.62397	+	33.0724i	0.324567	+	1.24470i
$707$	−12.3186	+	28.7664i	−0.463290	+	1.08187i
$708$	−4.81738	+	29.2852i	−0.181048	+	1.10061i
$709$	−1.77131	−	1.64354i	−0.0665231	−	0.0617244i	0.646211	−	0.763159i	$-0.276353\pi$
$709$	−1.77131	−	1.64354i	−0.0665231	−	0.0617244i	−0.712734	+	0.701435i	$0.752543\pi$
$710$	−0.0383608	+	0.321057i	−0.00143966	+	0.0120491i
$711$	−0.306750	+	2.03515i	−0.0115040	+	0.0763241i
$712$	−4.56739	−	3.51528i	−0.171170	−	0.131741i
$713$	53.3924	+	12.1865i	1.99956	+	0.456386i
$714$	37.6266	−	21.7276i	1.40814	−	0.813133i
$715$	−0.0735127	+	0.0167788i	−0.00274922	+	0.000627492i
$716$	−34.8042	−	17.3408i	−1.30069	−	0.648056i
$717$	10.5559	−	6.09446i	0.394218	−	0.227602i
$718$	14.4293	−	14.2367i	0.538498	−	0.531309i
$719$	−34.2294	+	23.3372i	−1.27654	+	0.870331i	−0.995986	−	0.0895071i	$-0.971471\pi$
$719$	−34.2294	+	23.3372i	−1.27654	+	0.870331i	−0.280555	+	0.959838i	$0.590518\pi$
$720$	−0.149230	−	0.0915915i	−0.00556147	−	0.00341341i
$721$	1.72784	+	14.4516i	0.0643482	+	0.538206i
$722$	−18.4730	+	15.6825i	−0.687495	+	0.583643i
$723$	−3.60704	+	11.6937i	−0.134147	+	0.434895i
$724$	−14.8142	−	4.78851i	−0.550564	−	0.177964i
$725$	−0.817961	−	10.9149i	−0.0303783	−	0.405370i
$726$	24.3977	−	10.4500i	0.905483	−	0.387837i
$727$	37.1888	−	17.9092i	1.37926	−	0.664215i	0.410416	−	0.911898i	$-0.365384\pi$
$727$	37.1888	−	17.9092i	1.37926	−	0.664215i	0.968841	+	0.247683i	$0.0796693\pi$
$728$	19.5698	+	3.21767i	0.725306	+	0.119255i
$729$	19.8885	+	9.57779i	0.736611	+	0.354733i
$730$	0.194526	+	0.00858793i	0.00719972	+	0.000317853i
$731$	42.8935	−	13.2309i	1.58647	−	0.489362i
$732$	−22.6153	+	37.9827i	−0.835885	+	1.40388i
$733$	−1.11455	−	7.39457i	−0.0411669	−	0.273125i	0.958772	−	0.284176i	$-0.0917201\pi$
$733$	−1.11455	−	7.39457i	−0.0411669	−	0.273125i	−0.999939	+	0.0110518i	$0.996482\pi$
$734$	0.297565	+	9.69580i	0.0109833	+	0.357878i
$735$	−0.257297	−	0.0755516i	−0.00949056	−	0.00278676i
$736$	30.8536	−	4.77050i	1.13728	−	0.175843i
$737$	9.72155	−	1.46529i	0.358098	−	0.0539746i
$738$	13.4603	+	8.58439i	0.495482	+	0.315996i
$739$	−2.35749	−	7.64279i	−0.0867217	−	0.281145i	0.901816	−	0.432121i	$-0.142235\pi$
$739$	−2.35749	−	7.64279i	−0.0867217	−	0.281145i	−0.988537	+	0.150976i	$0.951758\pi$
$740$	0.0595912		0.000800888i	0.00219062		2.94412e-5i
$741$	−3.76161	+	7.81106i	−0.138186	+	0.286946i
$742$	−19.8147	−	24.8430i	−0.727422	−	0.912015i
$743$	−9.02492	−	18.7404i	−0.331092	−	0.687520i	0.667265	−	0.744820i	$-0.267465\pi$
$743$	−9.02492	−	18.7404i	−0.331092	−	0.687520i	−0.998357	+	0.0573007i	$0.981751\pi$
$744$	60.0554	−	30.2076i	2.20174	−	1.10746i
$745$	0.226016	−	0.0169376i	0.00828060	−	0.000620545i
$746$	9.34807	+	3.34170i	0.342257	+	0.122348i
$747$	−9.09393	−	2.80511i	−0.332729	−	0.102633i
$748$	−11.5611	−	12.8007i	−0.422717	−	0.468041i
$749$	−21.8818	+	13.9576i	−0.799544	+	0.509998i
$750$	−0.324625	+	0.433721i	−0.0118536	+	0.0158373i
$751$	5.48368	+	8.04308i	0.200102	+	0.293496i	0.913154	−	0.407616i	$-0.133640\pi$
$751$	5.48368	+	8.04308i	0.200102	+	0.293496i	−0.713051	+	0.701112i	$0.752687\pi$
$752$	25.0961	−	29.7905i	0.915160	−	1.08635i
$753$	−10.1672	−	17.6101i	−0.370514	−	0.641749i
$754$	3.88269	−	7.22842i	0.141399	−	0.263244i
$755$	−0.0213922	−	0.0937254i	−0.000778542	−	0.00341102i
$756$	1.08044	+	3.15480i	0.0392953	+	0.114739i
$757$	9.91684	−	43.4485i	0.360434	−	1.57916i	−0.391662	−	0.920109i	$-0.628100\pi$
$757$	9.91684	−	43.4485i	0.360434	−	1.57916i	0.752096	−	0.659054i	$-0.229043\pi$
$758$	−24.1665	−	21.0812i	−0.877766	−	0.765705i
$759$	−23.2524	−	3.50474i	−0.844009	−	0.127214i
$760$	0.0616822	+	0.00355424i	0.00223745	+	0.000128926i
$761$	−21.9654	+	23.6731i	−0.796245	+	0.858148i	−0.992480	−	0.122409i	$-0.960938\pi$
$761$	−21.9654	+	23.6731i	−0.796245	+	0.858148i	0.196235	+	0.980557i	$0.437128\pi$
$762$	−4.45834	+	22.7259i	−0.161509	+	0.823271i
$763$	−5.10959	+	28.0469i	−0.184980	+	1.01537i
$764$	−34.8159	+	10.2289i	−1.25959	+	0.370070i
$765$	−0.106113	+	0.183792i	−0.00383651	+	0.00664503i
$766$	−21.0077	+	13.0039i	−0.759038

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.253576 + 1.39129i) q^{2} +(1.97899 + 1.34925i) q^{3} +(-1.87140 + 0.705597i) q^{4} +(-0.0159493 - 0.00119524i) q^{5} +(-1.37538 + 3.09550i) q^{6} +(2.59622 - 0.509531i) q^{7} +(-1.45623 - 2.42474i) q^{8} +(0.999898 + 2.54770i) q^{9} +O(q^{10})\)	\(q+(0.253576 + 1.39129i) q^{2} +(1.97899 + 1.34925i) q^{3} +(-1.87140 + 0.705597i) q^{4} +(-0.0159493 - 0.00119524i) q^{5} +(-1.37538 + 3.09550i) q^{6} +(2.59622 - 0.509531i) q^{7} +(-1.45623 - 2.42474i) q^{8} +(0.999898 + 2.54770i) q^{9} +(-0.00238144 - 0.0224933i) q^{10} +(-1.65591 - 0.649897i) q^{11} +(-4.65551 - 1.12862i) q^{12} +(-2.07204 + 1.65240i) q^{13} +(1.36725 + 3.48291i) q^{14} +(-0.0299509 - 0.0238850i) q^{15} +(3.00427 - 2.64091i) q^{16} +(-3.29762 - 3.55399i) q^{17} +(-3.29105 + 2.03719i) q^{18} +(0.682883 - 1.18279i) q^{19} +(0.0306909 - 0.00901703i) q^{20} +(5.82539 + 2.49461i) q^{21} +(0.484299 - 2.46866i) q^{22} +(3.75388 - 4.04572i) q^{23} +(0.389718 - 6.76337i) q^{24} +(-4.94390 - 0.745173i) q^{25} +(-2.82439 - 2.46381i) q^{26} +(0.140232 - 0.614395i) q^{27} +(-4.49905 + 2.78542i) q^{28} +(0.487147 + 2.13433i) q^{29} +(0.0256363 - 0.0477272i) q^{30} +(4.96153 + 8.59362i) q^{31} +(4.43609 + 3.51015i) q^{32} +(-2.40016 - 3.52038i) q^{33} +(4.10844 - 5.48916i) q^{34} +(-0.0420170 + 0.00502358i) q^{35} +(-3.66886 - 4.06224i) q^{36} +(1.78032 + 0.549155i) q^{37} +(1.81877 + 0.650165i) q^{38} +(-6.33006 + 0.474372i) q^{39} +(0.0203278 + 0.0404136i) q^{40} +(-1.78963 - 3.71620i) q^{41} +(-1.99355 + 8.73740i) q^{42} +(-4.01716 + 8.34173i) q^{43} +(3.55744 + 0.0478108i) q^{44} +(-0.0129026 - 0.0418292i) q^{45} +(6.58068 + 4.19686i) q^{46} +(9.62933 - 1.45139i) q^{47} +(9.50867 - 1.17282i) q^{48} +(6.48076 - 2.64571i) q^{49} +(-0.216899 - 7.06738i) q^{50} +(-1.73073 - 11.4826i) q^{51} +(2.71169 - 4.55432i) q^{52} +(-8.11554 + 2.50331i) q^{53} +(0.890364 + 0.0393078i) q^{54} +(0.0256339 + 0.0123446i) q^{55} +(-5.01619 - 5.55318i) q^{56} +(2.94730 - 1.41935i) q^{57} +(-2.84595 + 1.21898i) q^{58} +(-0.462993 - 6.17821i) q^{59} +(0.0729033 + 0.0235652i) q^{60} +(2.72001 - 8.81806i) q^{61} +(-10.6981 + 9.08207i) q^{62} +(3.89409 + 6.10492i) q^{63} +(-3.75876 + 7.06199i) q^{64} +(0.0350227 - 0.0238781i) q^{65} +(4.28927 - 4.23201i) q^{66} +(-4.78628 + 2.76336i) q^{67} +(8.67884 + 4.32414i) q^{68} +(12.8876 - 2.94151i) q^{69} +(-0.0176438 - 0.0571842i) q^{70} +(-13.9367 - 3.18096i) q^{71} +(4.72143 - 6.13454i) q^{72} +(-1.28303 + 8.51233i) q^{73} +(-0.312591 + 2.61620i) q^{74} +(-8.77851 - 8.14527i) q^{75} +(-0.443375 + 2.69531i) q^{76} +(-4.63026 - 0.843540i) q^{77} +(-2.26514 - 8.68668i) q^{78} +(0.651250 + 0.376000i) q^{79} +(-0.0510725 + 0.0385299i) q^{80} +(7.12534 - 6.61135i) q^{81} +(4.71652 - 3.43224i) q^{82} +(-2.16800 + 2.71859i) q^{83} +(-12.6618 - 0.558023i) q^{84} +(0.0483469 + 0.0606251i) q^{85} +(-12.6245 - 3.47380i) q^{86} +(-1.91569 + 4.88111i) q^{87} +(0.835561 + 4.96156i) q^{88} +(1.89685 - 0.744461i) q^{89} +(0.0549249 - 0.0285582i) q^{90} +(-4.53754 + 5.34577i) q^{91} +(-4.17036 + 10.2199i) q^{92} +(-1.77615 + 23.7010i) q^{93} +(4.46107 + 13.0292i) q^{94} +(-0.0123052 + 0.0180485i) q^{95} +(4.04290 + 12.9320i) q^{96} -12.1281i q^{97} +(5.32433 + 8.34575i) q^{98} -4.86859i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

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