LMFDB - Embedded newform 196.2.p.a.103.23

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			103.23
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14691 + 0.827407i) q^{2} +(0.330273 + 0.225176i) q^{3} +(0.630795 + 1.89792i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(0.192480 + 0.531527i) q^{6} +(1.62030 + 2.09156i) q^{7} +(-0.846889 + 2.69866i) q^{8} +(-1.03765 - 2.64388i) q^{9} +O(q^{10})$	\(q+(1.14691 + 0.827407i) q^{2} +(0.330273 + 0.225176i) q^{3} +(0.630795 + 1.89792i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(0.192480 + 0.531527i) q^{6} +(1.62030 + 2.09156i) q^{7} +(-0.846889 + 2.69866i) q^{8} +(-1.03765 - 2.64388i) q^{9} +(-0.210620 - 0.177316i) q^{10} +(-4.10220 - 1.61000i) q^{11} +(-0.219032 + 0.768872i) q^{12} +(2.89899 - 2.31187i) q^{13} +(0.127764 + 3.73948i) q^{14} +(-0.0608423 - 0.0485201i) q^{15} +(-3.20420 + 2.39439i) q^{16} +(4.17672 + 4.50144i) q^{17} +(0.997481 - 3.89085i) q^{18} +(2.69573 - 4.66913i) q^{19} +(-0.0948487 - 0.377634i) q^{20} +(0.0641719 + 1.05564i) q^{21} +(-3.37273 - 5.24071i) q^{22} +(-2.58949 + 2.79080i) q^{23} +(-0.887380 + 0.700596i) q^{24} +(-4.90668 - 0.739562i) q^{25} +(5.23773 - 0.252853i) q^{26} +(0.519478 - 2.27598i) q^{27} +(-2.94754 + 4.39455i) q^{28} +(-1.16681 - 5.11213i) q^{29} +(-0.0296346 - 0.105990i) q^{30} +(-4.63766 - 8.03266i) q^{31} +(-5.65606 + 0.0949747i) q^{32} +(-0.992315 - 1.45546i) q^{33} +(1.06579 + 8.61858i) q^{34} +(-0.284132 - 0.429623i) q^{35} +(4.36333 - 3.63712i) q^{36} +(10.0178 + 3.09008i) q^{37} +(6.95502 - 3.12460i) q^{38} +(1.47804 - 0.110764i) q^{39} +(0.203674 - 0.511590i) q^{40} +(-1.28140 - 2.66086i) q^{41} +(-0.799845 + 1.26382i) q^{42} +(-0.871772 + 1.81025i) q^{43} +(0.467995 - 8.80123i) q^{44} +(0.162981 + 0.528372i) q^{45} +(-5.27903 + 1.05823i) q^{46} +(-0.800046 + 0.120588i) q^{47} +(-1.59742 + 0.0692948i) q^{48} +(-1.74925 + 6.77791i) q^{49} +(-5.01559 - 4.90803i) q^{50} +(0.365842 + 2.42720i) q^{51} +(6.21641 + 4.04374i) q^{52} +(-5.82431 + 1.79656i) q^{53} +(2.47896 - 2.18052i) q^{54} +(0.772968 + 0.372242i) q^{55} +(-7.01663 + 2.60133i) q^{56} +(1.94170 - 0.935075i) q^{57} +(2.89159 - 6.82857i) q^{58} +(0.925691 + 12.3525i) q^{59} +(0.0537083 - 0.146080i) q^{60} +(2.27555 - 7.37716i) q^{61} +(1.32731 - 13.0500i) q^{62} +(3.84854 - 6.45419i) q^{63} +(-6.56556 - 4.57094i) q^{64} +(-0.596437 + 0.406644i) q^{65} +(0.0661633 - 2.49032i) q^{66} +(-1.40118 + 0.808972i) q^{67} +(-5.90871 + 10.7666i) q^{68} +(-1.48366 + 0.338636i) q^{69} +(0.0296004 - 0.727831i) q^{70} +(4.57108 + 1.04332i) q^{71} +(8.01372 - 0.561185i) q^{72} +(-2.28410 + 15.1540i) q^{73} +(8.93273 + 11.8328i) q^{74} +(-1.45401 - 1.34913i) q^{75} +(10.5621 + 2.17101i) q^{76} +(-3.27940 - 11.1887i) q^{77} +(1.78682 + 1.09590i) q^{78} +(2.58376 + 1.49174i) q^{79} +(0.656889 - 0.418225i) q^{80} +(-5.56201 + 5.16079i) q^{81} +(0.731965 - 4.11201i) q^{82} +(0.292327 - 0.366567i) q^{83} +(-1.96304 + 0.787685i) q^{84} +(-0.745368 - 0.934662i) q^{85} +(-2.49766 + 1.35488i) q^{86} +(0.765765 - 1.95114i) q^{87} +(7.81895 - 9.70698i) q^{88} +(-10.1900 + 3.99930i) q^{89} +(-0.250255 + 0.740846i) q^{90} +(9.53265 + 2.31749i) q^{91} +(-6.93015 - 3.15421i) q^{92} +(0.277072 - 3.69726i) q^{93} +(-1.01735 - 0.523661i) q^{94} +(-0.591270 + 0.867234i) q^{95} +(-1.88943 - 1.24224i) q^{96} +4.71195i q^{97} +(-7.61432 + 6.32630i) q^{98} +12.5164i 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 $

$2$	1.14691	+	0.827407i	0.810986	+	0.585065i
$2$	1.14691	+	0.827407i	0.810986	+	0.585065i
$3$	0.330273	+	0.225176i	0.190683	+	0.130006i	0.654899	−	0.755717i	$-0.272711\pi$
$3$	0.330273	+	0.225176i	0.190683	+	0.130006i	−0.464215	+	0.885722i	$0.653664\pi$
$4$	0.630795	+	1.89792i	0.315397	+	0.948960i
$5$	−0.194137	−	0.0145486i	−0.0868208	−	0.00650632i	0.0312488	−	0.999512i	$-0.490052\pi$
$5$	−0.194137	−	0.0145486i	−0.0868208	−	0.00650632i	−0.118070	+	0.993005i	$0.537671\pi$
$6$	0.192480	+	0.531527i	0.0785797	+	0.216995i
$7$	1.62030	+	2.09156i	0.612416	+	0.790535i
$7$	1.62030	+	2.09156i	0.612416	+	0.790535i
$8$	−0.846889	+	2.69866i	−0.299420	+	0.954121i
$9$	−1.03765	−	2.64388i	−0.345882	−	0.881294i
$10$	−0.210620	−	0.177316i	−0.0666039	−	0.0560724i
$11$	−4.10220	−	1.61000i	−1.23686	−	0.485432i	−0.345368	−	0.938467i	$-0.612246\pi$
$11$	−4.10220	−	1.61000i	−1.23686	−	0.485432i	−0.891493	+	0.453035i	$0.850341\pi$
$12$	−0.219032	+	0.768872i	−0.0632291	+	0.221954i
$13$	2.89899	−	2.31187i	0.804036	−	0.641197i	−0.132731	−	0.991152i	$-0.542375\pi$
$13$	2.89899	−	2.31187i	0.804036	−	0.641197i	0.936766	+	0.349955i	$0.113803\pi$
$14$	0.127764	+	3.73948i	0.0341463	+	0.999417i
$15$	−0.0608423	−	0.0485201i	−0.0157094	−	0.0125278i
$16$	−3.20420	+	2.39439i	−0.801049	+	0.598599i
$17$	4.17672	+	4.50144i	1.01300	+	1.09176i	0.995768	+	0.0919072i	$0.0292963\pi$
$17$	4.17672	+	4.50144i	1.01300	+	1.09176i	0.0172364	+	0.999851i	$0.494513\pi$
$18$	0.997481	−	3.89085i	0.235109	−	0.917081i
$19$	2.69573	−	4.66913i	0.618442	−	1.07117i	−0.371328	−	0.928502i	$-0.621098\pi$
$19$	2.69573	−	4.66913i	0.618442	−	1.07117i	0.989770	−	0.142671i	$-0.0455691\pi$
$20$	−0.0948487	−	0.377634i	−0.0212088	−	0.0844416i
$21$	0.0641719	+	1.05564i	0.0140034	+	0.230359i
$22$	−3.37273	−	5.24071i	−0.719068	−	1.11732i
$23$	−2.58949	+	2.79080i	−0.539945	+	0.581922i	−0.942807	−	0.333338i	$-0.891825\pi$
$23$	−2.58949	+	2.79080i	−0.539945	+	0.581922i	0.402862	+	0.915261i	$0.368015\pi$
$24$	−0.887380	+	0.700596i	−0.181136	+	0.143009i
$25$	−4.90668	−	0.739562i	−0.981335	−	0.147912i
$26$	5.23773	−	0.252853i	1.02720	−	0.0495886i
$27$	0.519478	−	2.27598i	0.0999736	−	0.438013i
$28$	−2.94754	+	4.39455i	−0.557032	+	0.830491i
$29$	−1.16681	−	5.11213i	−0.216671	−	0.949299i	−0.959918	−	0.280281i	$-0.909572\pi$
$29$	−1.16681	−	5.11213i	−0.216671	−	0.949299i	0.743247	−	0.669017i	$-0.233285\pi$
$30$	−0.0296346	−	0.105990i	−0.00541052	−	0.0193510i
$31$	−4.63766	−	8.03266i	−0.832948	−	1.44271i	−0.895690	−	0.444679i	$-0.853318\pi$
$31$	−4.63766	−	8.03266i	−0.832948	−	1.44271i	0.0627420	−	0.998030i	$-0.480015\pi$
$32$	−5.65606	+	0.0949747i	−0.999859	+	0.0167893i
$33$	−0.992315	−	1.45546i	−0.172740	−	0.253363i
$34$	1.06579	+	8.61858i	0.182782	+	1.47807i
$35$	−0.284132	−	0.429623i	−0.0480270	−	0.0726195i
$36$	4.36333	−	3.63712i	0.727222	−	0.606186i
$37$	10.0178	+	3.09008i	1.64691	+	0.508006i	0.973000	−	0.230804i	$-0.0741355\pi$
$37$	10.0178	+	3.09008i	1.64691	+	0.508006i	0.673914	+	0.738810i	$0.264612\pi$
$38$	6.95502	−	3.12460i	1.12825	−	0.506877i
$39$	1.47804	−	0.110764i	0.236675	−	0.0177364i
$40$	0.203674	−	0.511590i	0.0322038	−	0.0808895i
$41$	−1.28140	−	2.66086i	−0.200122	−	0.415557i	0.776622	−	0.629967i	$-0.216932\pi$
$41$	−1.28140	−	2.66086i	−0.200122	−	0.415557i	−0.976744	+	0.214410i	$0.931217\pi$
$42$	−0.799845	+	1.26382i	−0.123419	+	0.195011i
$43$	−0.871772	+	1.81025i	−0.132944	+	0.276061i	−0.956805	−	0.290731i	$-0.906101\pi$
$43$	−0.871772	+	1.81025i	−0.132944	+	0.276061i	0.823861	+	0.566792i	$0.191816\pi$
$44$	0.467995	−	8.80123i	0.0705529	−	1.32684i
$45$	0.162981	+	0.528372i	0.0242958	+	0.0787651i
$46$	−5.27903	+	1.05823i	−0.778351	+	0.156028i
$47$	−0.800046	+	0.120588i	−0.116699	+	0.0175895i	−0.207132	−	0.978313i	$-0.566413\pi$
$47$	−0.800046	+	0.120588i	−0.116699	+	0.0175895i	0.0904332	+	0.995903i	$0.471175\pi$
$48$	−1.59742	+	0.0692948i	−0.230568	+	0.0100018i
$49$	−1.74925	+	6.77791i	−0.249893	+	0.968274i
$50$	−5.01559	−	4.90803i	−0.709311	−	0.694100i
$51$	0.365842	+	2.42720i	0.0512281	+	0.339876i
$52$	6.21641	+	4.04374i	0.862061	+	0.560766i
$53$	−5.82431	+	1.79656i	−0.800031	+	0.246777i	−0.667702	−	0.744429i	$-0.732722\pi$
$53$	−5.82431	+	1.79656i	−0.800031	+	0.246777i	−0.132329	+	0.991206i	$0.542246\pi$
$54$	2.47896	−	2.18052i	0.337343	−	0.296732i
$55$	0.772968	+	0.372242i	0.104227	+	0.0501931i
$56$	−7.01663	+	2.60133i	−0.937637	+	0.347617i
$57$	1.94170	−	0.935075i	0.257185	−	0.123854i
$58$	2.89159	−	6.82857i	0.379684	−	0.896635i
$59$	0.925691	+	12.3525i	0.120515	+	1.60816i	0.650065	+	0.759879i	$0.274742\pi$
$59$	0.925691	+	12.3525i	0.120515	+	1.60816i	−0.529550	+	0.848279i	$0.677639\pi$
$60$	0.0537083	−	0.146080i	0.00693371	−	0.0188589i
$61$	2.27555	−	7.37716i	0.291355	−	0.944549i	−0.685031	−	0.728514i	$-0.740211\pi$
$61$	2.27555	−	7.37716i	0.291355	−	0.944549i	0.976386	−	0.216035i	$-0.0693124\pi$
$62$	1.32731	−	13.0500i	0.168569	−	1.65735i
$63$	3.84854	−	6.45419i	0.484870	−	0.813151i
$64$	−6.56556	−	4.57094i	−0.820695	−	0.571367i
$65$	−0.596437	+	0.406644i	−0.0739789	+	0.0504380i
$66$	0.0661633	−	2.49032i	0.00814414	−	0.306538i
$67$	−1.40118	+	0.808972i	−0.171182	+	0.0988317i	−0.583143	−	0.812370i	$-0.698177\pi$
$67$	−1.40118	+	0.808972i	−0.171182	+	0.0988317i	0.411961	+	0.911201i	$0.364844\pi$
$68$	−5.90871	+	10.7666i	−0.716536	+	1.30564i
$69$	−1.48366	+	0.338636i	−0.178612	+	0.0407670i
$70$	0.0296004	−	0.727831i	0.00353792	−	0.0869924i
$71$	4.57108	+	1.04332i	0.542487	+	0.123819i	0.484979	−	0.874526i	$-0.338827\pi$
$71$	4.57108	+	1.04332i	0.542487	+	0.123819i	0.0575084	+	0.998345i	$0.481684\pi$
$72$	8.01372	−	0.561185i	0.944426	−	0.0661363i
$73$	−2.28410	+	15.1540i	−0.267333	+	1.77364i	0.303753	+	0.952751i	$0.401760\pi$
$73$	−2.28410	+	15.1540i	−0.267333	+	1.77364i	−0.571086	+	0.820890i	$0.693478\pi$
$74$	8.93273	+	11.8328i	1.03841	+	1.37554i
$75$	−1.45401	−	1.34913i	−0.167895	−	0.155784i
$76$	10.5621	+	2.17101i	1.21155	+	0.249031i
$77$	−3.27940	−	11.1887i	−0.373722	−	1.27507i
$78$	1.78682	+	1.09590i	0.202317	+	0.124087i
$79$	2.58376	+	1.49174i	0.290696	+	0.167834i	0.638256	−	0.769824i	$-0.279656\pi$
$79$	2.58376	+	1.49174i	0.290696	+	0.167834i	−0.347560	+	0.937658i	$0.612990\pi$
$80$	0.656889	−	0.418225i	0.0734424	−	0.0467590i
$81$	−5.56201	+	5.16079i	−0.618001	+	0.573421i
$82$	0.731965	−	4.11201i	0.0808320	−	0.454095i
$83$	0.292327	−	0.366567i	0.0320871	−	0.0402359i	−0.765529	−	0.643401i	$-0.777523\pi$
$83$	0.292327	−	0.366567i	0.0320871	−	0.0402359i	0.797616	+	0.603165i	$0.206094\pi$
$84$	−1.96304	+	0.787685i	−0.214185	+	0.0859435i
$85$	−0.745368	−	0.934662i	−0.0808465	−	0.101378i
$86$	−2.49766	+	1.35488i	−0.269329	+	0.146101i
$87$	0.765765	−	1.95114i	0.0820986	−	0.209184i
$88$	7.81895	−	9.70698i	0.833503	−	1.03477i
$89$	−10.1900	+	3.99930i	−1.08014	+	0.423924i	−0.837638	−	0.546226i	$-0.816064\pi$
$89$	−10.1900	+	3.99930i	−1.08014	+	0.423924i	−0.242504	+	0.970150i	$0.577969\pi$
$90$	−0.250255	+	0.740846i	−0.0263792	+	0.0780921i
$91$	9.53265	+	2.31749i	0.999294	+	0.242939i
$92$	−6.93015	−	3.15421i	−0.722518	−	0.328849i
$93$	0.277072	−	3.69726i	0.0287310	−	0.383388i
$94$	−1.01735	−	0.523661i	−0.104932	−	0.0540115i
$95$	−0.591270	+	0.867234i	−0.0606630	+	0.0889763i
$96$	−1.88943	−	1.24224i	−0.192839	−	0.126786i
$97$			4.71195i			0.478426i	0.970967	+	0.239213i	$0.0768894\pi$
$97$			4.71195i			0.478426i	−0.970967	+	0.239213i	$0.923111\pi$
$98$	−7.61432	+	6.32630i	−0.769163	+	0.639053i
$99$			12.5164i			1.25794i
$100$	−1.69148	−	9.77899i	−0.169148	−	0.977899i
$101$	−0.123474	+	0.181102i	−0.0122861	+	0.0180204i	−0.832333	−	0.554276i	$-0.812995\pi$
$101$	−0.123474	+	0.181102i	−0.0122861	+	0.0180204i	0.820047	+	0.572297i	$0.193947\pi$
$102$	−1.58870	+	3.08648i	−0.157305	+	0.305607i
$103$	−0.191758	+	2.55883i	−0.0188945	+	0.252129i	0.979756	+	0.200195i	$0.0641576\pi$
$103$	−0.191758	+	2.55883i	−0.0188945	+	0.252129i	−0.998651	+	0.0519340i	$0.983461\pi$
$104$	3.78383	+	9.78130i	0.371035	+	0.959135i
$105$	0.00289991	−	0.205873i	0.000283002	−	0.0200911i
$106$	−8.16644	−	2.75859i	−0.793195	−	0.267938i
$107$	−8.20581	+	3.22054i	−0.793286	+	0.311342i	−0.727159	−	0.686469i	$-0.759160\pi$
$107$	−8.20581	+	3.22054i	−0.793286	+	0.311342i	−0.0661272	+	0.997811i	$0.521064\pi$
$108$	4.64732	−	0.449750i	0.447188	−	0.0432772i
$109$	−2.12958	+	5.42609i	−0.203977	+	0.519725i	−0.995855	−	0.0909543i	$-0.971008\pi$
$109$	−2.12958	+	5.42609i	−0.203977	+	0.519725i	0.791878	+	0.610679i	$0.209104\pi$
$110$	0.578527	+	1.06649i	0.0551604	+	0.101685i
$111$	2.61279	+	3.27634i	0.247995	+	0.310976i
$112$	−10.1998	−	2.82213i	−0.963789	−	0.266666i
$113$	1.06011	−	1.32933i	0.0997265	−	0.125053i	−0.729464	−	0.684019i	$-0.760230\pi$
$113$	1.06011	−	1.32933i	0.0997265	−	0.125053i	0.829190	+	0.558966i	$0.188802\pi$
$114$	3.00064	+	0.534135i	0.281036	+	0.0500263i
$115$	0.543318	−	0.504125i	0.0506647	−	0.0470099i
$116$	8.96639	−	5.43922i	0.832509	−	0.505018i
$117$	−9.12044	−	5.26569i	−0.843185	−	0.486813i
$118$	−9.15886	+	14.9331i	−0.843141	+	1.37470i
$119$	−2.64748	+	16.0295i	−0.242694	+	1.46943i
$120$	0.182466	−	0.123102i	0.0166568	−	0.0112376i
$121$	6.17242	+	5.72717i	0.561129	+	0.520652i
$122$	8.71376	−	6.57811i	0.788907	−	0.595554i
$123$	0.175950	−	1.16735i	0.0158649	−	0.105257i
$124$	12.3199	−	13.8689i	1.10636	−	1.24546i
$125$	1.89081	+	0.431566i	0.169119	+	0.0386004i
$126$	9.75416	−	4.21805i	0.868969	−	0.375774i
$127$	4.30597	−	0.982809i	0.382093	−	0.0872102i	−0.0271602	−	0.999631i	$-0.508646\pi$
$127$	4.30597	−	0.982809i	0.382093	−	0.0872102i	0.409253	+	0.912421i	$0.365789\pi$
$128$	−3.74806	−	10.6748i	−0.331285	−	0.943531i
$129$	−0.695549	+	0.401575i	−0.0612397	+	0.0353567i
$130$	−1.02052	−	0.0271133i	−0.0895054	−	0.00237799i
$131$	6.19021	−	4.22042i	0.540841	−	0.368739i	−0.261874	−	0.965102i	$-0.584340\pi$
$131$	6.19021	−	4.22042i	0.540841	−	0.368739i	0.802715	+	0.596363i	$0.203388\pi$
$132$	2.13640	−	2.80143i	0.185949	−	0.243833i
$133$	14.1337	−	1.92713i	1.22554	−	0.167103i
$134$	−2.27637	−	0.231531i	−0.196649	−	0.0200012i
$135$	−0.133962	+	0.434296i	−0.0115297	+	0.0373782i
$136$	−15.6851	+	7.45935i	−1.34498	+	0.639634i
$137$	0.177227	+	2.36493i	0.0151415	+	0.202050i	0.999644	+	0.0266792i	$0.00849325\pi$
$137$	0.177227	+	2.36493i	0.0151415	+	0.202050i	−0.984503	+	0.175370i	$0.943888\pi$
$138$	−1.98181	−	0.839207i	−0.168703	−	0.0714381i
$139$	19.5010	−	9.39119i	1.65405	−	0.796550i	0.654887	−	0.755727i	$-0.272716\pi$
$139$	19.5010	−	9.39119i	1.65405	−	0.796550i	0.999166	−	0.0408233i	$-0.0129981\pi$
$140$	0.636161	−	0.810263i	0.0537654	−	0.0684797i
$141$	−0.291387	−	0.140325i	−0.0245392	−	0.0118175i
$142$	4.37936	+	4.97874i	0.367507	+	0.417806i
$143$	−15.6144	+	4.81639i	−1.30574	+	0.402767i
$144$	9.65532	+	5.98698i	0.804610	+	0.498915i
$145$	0.152147	+	1.00943i	0.0126351	+	0.0838286i
$146$	−15.1582	+	15.4904i	−1.25450	+	1.28199i
$147$	−2.10396	+	1.84467i	−0.173531	+	0.152146i
$148$	0.454447	+	20.9622i	0.0373553	+	1.72308i
$149$	11.9735	−	1.80472i	0.980911	−	0.147849i	0.361039	−	0.932551i	$-0.382422\pi$
$149$	11.9735	−	1.80472i	0.980911	−	0.147849i	0.619873	+	0.784702i	$0.287184\pi$
$150$	−0.551341	−	2.75038i	−0.0450168	−	0.224568i
$151$	−4.42620	−	14.3494i	−0.360199	−	1.16774i	−0.936550	−	0.350534i	$-0.886000\pi$
$151$	−4.42620	−	14.3494i	−0.360199	−	1.16774i	0.576351	−	0.817202i	$-0.304476\pi$
$152$	10.3174	+	11.2291i	0.836854	+	0.910799i
$153$	7.56730	−	15.7137i	0.611780	−	1.27037i
$154$	5.49643	−	15.5458i	0.442915	−	1.25272i
$155$	0.783479	+	1.62691i	0.0629305	+	0.130677i
$156$	1.14256	+	2.73533i	0.0914779	+	0.219001i
$157$	2.73440	−	0.204915i	0.218229	−	0.0163540i	0.0348332	−	0.999393i	$-0.488910\pi$
$157$	2.73440	−	0.204915i	0.218229	−	0.0163540i	0.183396	+	0.983039i	$0.441291\pi$
$158$	1.72907	+	3.84871i	0.137557	+	0.306187i
$159$	−2.32816	−	0.718141i	−0.184635	−	0.0569523i
$160$	1.09943	+	0.0638495i	0.0869178	+	0.00504774i
$161$	−10.0329	−	0.894126i	−0.790701	−	0.0704670i
$162$	−10.6492	+	1.31690i	−0.836679	+	0.103466i
$163$	1.69172	+	2.48130i	0.132506	+	0.194350i	0.886757	−	0.462235i	$-0.152952\pi$
$163$	1.69172	+	2.48130i	0.132506	+	0.194350i	−0.754252	+	0.656586i	$0.772000\pi$
$164$	4.24180	−	4.11046i	0.331229	−	0.320973i
$165$	0.171470	+	0.296996i	0.0133490	+	0.0231211i
$166$	0.638572	−	0.178545i	0.0495628	−	0.0138577i
$167$	−0.423853	−	1.85702i	−0.0327987	−	0.143701i	0.955877	−	0.293766i	$-0.0949087\pi$
$167$	−0.423853	−	1.85702i	−0.0327987	−	0.143701i	−0.988676	+	0.150065i	$0.952052\pi$
$168$	−2.90316	−	0.720831i	−0.223984	−	0.0556134i
$169$	0.166644	−	0.730116i	0.0128188	−	0.0561627i
$170$	−0.0815223	−	1.68869i	−0.00625248	−	0.129517i
$171$	−15.1418	−	2.28227i	−1.15793	−	0.174529i
$172$	−3.98562	−	0.512655i	−0.303901	−	0.0390896i
$173$	2.19697	−	2.36777i	0.167032	−	0.180018i	−0.643989	−	0.765035i	$-0.722722\pi$
$173$	2.19697	−	2.36777i	0.167032	−	0.180018i	0.811021	+	0.585017i	$0.198912\pi$
$174$	2.49265	−	1.60417i	0.188967	−	0.121612i
$175$	−6.40345	−	11.4609i	−0.484056	−	0.866364i
$176$	16.9992	−	4.66355i	1.28137	−	0.351528i
$177$	−2.47576	+	4.28814i	−0.186089	+	0.322316i
$178$	−14.9961	−	3.84449i	−1.12400	−	0.288157i
$179$	−11.4196	−	12.3074i	−0.853539	−	0.919897i	0.144030	−	0.989573i	$-0.453994\pi$
$179$	−11.4196	−	12.3074i	−0.853539	−	0.919897i	−0.997570	+	0.0696766i	$0.977803\pi$
$180$	−0.900001	+	0.642620i	−0.0670821	+	0.0478981i
$181$	−8.10171	−	6.46089i	−0.602195	−	0.480235i	0.274301	−	0.961644i	$-0.411554\pi$
$181$	−8.10171	−	6.46089i	−0.602195	−	0.480235i	−0.876496	+	0.481409i	$0.840125\pi$
$182$	9.01556	+	10.5453i	0.668278	+	0.781672i
$183$	2.41272	−	1.92408i	0.178353	−	0.142232i
$184$	−5.33842	−	9.35165i	−0.393554	−	0.689413i
$185$	−1.89987	−	0.745644i	−0.139681	−	0.0548209i
$186$	3.37692	−	4.01117i	0.247608	−	0.294113i
$187$	−9.88647	−	25.1903i	−0.722970	−	1.84210i
$188$	−0.733530	−	1.44236i	−0.0534982	−	0.105195i
$189$	5.60207	−	2.60126i	0.407490	−	0.189214i
$190$	−1.39569	+	0.505416i	−0.101254	+	0.0366667i
$191$	−6.21485	−	0.465739i	−0.449691	−	0.0336997i	−0.152040	−	0.988374i	$-0.548584\pi$
$191$	−6.21485	−	0.465739i	−0.449691	−	0.0336997i	−0.297651	+	0.954675i	$0.596203\pi$
$192$	−1.13916	−	2.98807i	−0.0822118	−	0.215645i
$193$	1.49459	+	1.01899i	0.107583	+	0.0733488i	0.615916	−	0.787811i	$-0.288786\pi$
$193$	1.49459	+	1.01899i	0.107583	+	0.0733488i	−0.508333	+	0.861160i	$0.669738\pi$
$194$	−3.89870	+	5.40417i	−0.279910	+	0.387997i
$195$	−0.288554			−0.0206638
$196$	−13.9674	+	0.955539i	−0.997668	+	0.0682528i
$197$	9.35286			0.666364			0.333182	−	0.942863i	$-0.391878\pi$
$197$	9.35286			0.666364			0.333182	+	0.942863i	$0.391878\pi$
$198$	−10.3561	+	14.3551i	−0.735977	+	1.02017i
$199$	13.4363	+	9.16071i	0.952474	+	0.649386i	0.936567	−	0.350488i	$-0.113984\pi$
$199$	13.4363	+	9.16071i	0.952474	+	0.649386i	0.0159065	+	0.999873i	$0.494937\pi$
$200$	6.15124	−	12.6151i	0.434958	−	0.892025i
$201$	−0.644934	−	0.0483311i	−0.0454901	−	0.00340901i
$202$	−0.291458	+	0.105545i	−0.0205069	+	0.00742611i
$203$	8.80174	−	10.7236i	0.617761	−	0.752652i
$204$	−4.37586	+	2.22540i	−0.306372	+	0.155809i
$205$	0.210057	+	0.535216i	0.0146710	+	0.0373811i
$206$	−2.33712	+	2.77608i	−0.162835	+	0.193419i
$207$	10.0655	+	3.95043i	0.699602	+	0.274574i
$208$	−3.75341	+	14.3490i	−0.260252	+	0.994925i
$209$	−18.5757	+	14.8136i	−1.28491	+	1.02468i
$210$	0.173666	−	0.233718i	0.0119841	−	0.0161280i
$211$	−5.84824	−	4.66382i	−0.402609	−	0.321070i	0.401164	−	0.916006i	$-0.368606\pi$
$211$	−5.84824	−	4.66382i	−0.402609	−	0.321070i	−0.803773	+	0.594936i	$0.797177\pi$
$212$	−7.08368	−	9.92081i	−0.486509	−	0.681364i
$213$	1.27477	+	1.37388i	0.0873461	+	0.0941367i
$214$	−12.0760	−	3.09588i	−0.825499	−	0.211630i
$215$	0.195580	−	0.338754i	0.0133384	−	0.0231029i
$216$	5.70217	+	3.32940i	0.387983	+	0.226537i
$217$	9.28639	−	22.7153i	0.630401	−	1.54201i
$218$	−6.93202	+	4.46119i	−0.469496	+	0.302150i
$219$	−4.16670	+	4.49063i	−0.281559	+	0.303449i
$220$	−0.218901	+	1.70184i	−0.0147583	+	0.114738i
$221$	22.5150	+	3.39359i	1.51452	+	0.228278i
$222$	0.285766	+	5.91950i	0.0191794	+	0.397291i
$223$	2.47878	−	10.8603i	0.165992	−	0.727257i	−0.821581	−	0.570092i	$-0.806907\pi$
$223$	2.47878	−	10.8603i	0.165992	−	0.727257i	0.987572	−	0.157165i	$-0.0502354\pi$
$224$	−9.36316	−	11.6761i	−0.625602	−	0.780142i
$225$	3.13608	+	13.7401i	0.209072	+	0.916005i
$226$	2.31575	−	0.647481i	0.154041	−	0.0430698i
$227$	−8.60483	−	14.9040i	−0.571123	−	0.989214i	−0.996451	−	0.0841746i	$-0.973175\pi$
$227$	−8.60483	−	14.9040i	−0.571123	−	0.989214i	0.425328	−	0.905039i	$-0.360159\pi$
$228$	2.99951	+	3.09536i	0.198648	+	0.204995i
$229$	−4.84690	−	7.10909i	−0.320292	−	0.469782i	0.632001	−	0.774968i	$-0.282234\pi$
$229$	−4.84690	−	7.10909i	−0.320292	−	0.469782i	−0.952293	+	0.305186i	$0.901281\pi$
$230$	1.04025	−	0.128640i	0.0685922	−	0.00848228i
$231$	1.43633	−	4.43377i	0.0945036	−	0.291720i
$232$	14.7841	+	1.18058i	0.970622	+	0.0775088i
$233$	0.870386	+	0.268478i	0.0570209	+	0.0175886i	0.323134	−	0.946353i	$-0.395263\pi$
$233$	0.870386	+	0.268478i	0.0570209	+	0.0175886i	−0.266114	+	0.963942i	$0.585740\pi$
$234$	−6.10343	−	13.5856i	−0.398994	−	0.888117i
$235$	0.157073	−	0.0117710i	0.0102463	−	0.000767856i
$236$	−22.8601	+	9.54877i	−1.48807	+	0.621572i
$237$	0.517444	+	1.07448i	0.0336116	+	0.0697952i
$238$	−16.2994	+	16.1939i	−1.05653	+	1.04969i
$239$	−10.0439	+	20.8563i	−0.649683	+	1.34908i	0.272435	+	0.962174i	$0.412171\pi$
$239$	−10.0439	+	20.8563i	−0.649683	+	1.34908i	−0.922119	+	0.386907i	$0.873543\pi$
$240$	0.311127	+	0.00978750i	0.0200832	+	0.000631780i
$241$	−4.79813	−	15.5552i	−0.309075	−	1.00200i	−0.968245	−	0.250003i	$-0.919568\pi$
$241$	−4.79813	−	15.5552i	−0.309075	−	1.00200i	0.659170	−	0.751994i	$-0.270908\pi$
$242$	2.34050	+	11.6756i	0.150453	+	0.750539i
$243$	−9.92439	+	1.49586i	−0.636650	+	0.0959595i
$244$	15.4367	−	0.334658i	0.988231	−	0.0214243i
$245$	0.438204	−	1.29040i	0.0279958	−	0.0824404i
$246$	1.16768	−	1.19326i	0.0744483	−	0.0760798i
$247$	−2.97954	−	19.7679i	−0.189583	−	1.25780i
$248$	25.6050	−	5.71270i	1.62592	−	0.362757i
$249$	0.179090	−	0.0552419i	0.0113494	−	0.00350082i
$250$	1.81151	+	2.05944i	0.114570	+	0.130250i
$251$	0.769700	+	0.370668i	0.0485830	+	0.0233964i	0.458018	−	0.888943i	$-0.348560\pi$
$251$	0.769700	+	0.370668i	0.0485830	+	0.0233964i	−0.409434	+	0.912340i	$0.634274\pi$
$252$	14.6772	+	3.23295i	0.924574	+	0.203657i
$253$	15.1158	−	7.27938i	0.950321	−	0.457650i
$254$	5.75173	+	2.43560i	0.360896	+	0.152823i
$255$	−0.0357112	−	0.476533i	−0.00223632	−	0.0298417i
$256$	4.53375	−	15.3442i	0.283359	−	0.959014i
$257$	−3.63630	+	11.7886i	−0.226826	+	0.735353i	0.768592	+	0.639739i	$0.220958\pi$
$257$	−3.63630	+	11.7886i	−0.226826	+	0.735353i	−0.995419	+	0.0956137i	$0.969519\pi$
$258$	−1.13000	−	0.114932i	−0.0703505	−	0.00715537i
$259$	9.76875	+	25.9597i	0.607001	+	1.61306i
$260$	−1.14801	−	0.875481i	−0.0711963	−	0.0542950i
$261$	−12.3051	+	8.38949i	−0.761668	+	0.519297i
$262$	10.5916	+	0.281399i	0.654352	+	0.0173849i
$263$	4.28173	−	2.47206i	0.264023	−	0.152434i	−0.362145	−	0.932122i	$-0.617956\pi$
$263$	4.28173	−	2.47206i	0.264023	−	0.152434i	0.626168	+	0.779688i	$0.284622\pi$
$264$	4.76817	−	1.44531i	0.293461	−	0.0889527i
$265$	1.15685	−	0.264044i	0.0710650	−	0.0162201i
$266$	17.8045	+	9.48405i	1.09167	+	0.581505i
$267$	−4.26604	−	0.973696i	−0.261078	−	0.0595893i
$268$	−2.41922	−	2.14903i	−0.147777	−	0.131273i
$269$	2.93531	−	19.4745i	0.178969	−	1.18738i	−0.701286	−	0.712880i	$-0.747391\pi$
$269$	2.93531	−	19.4745i	0.178969	−	1.18738i	0.880255	−	0.474501i	$-0.157371\pi$
$270$	−0.512982	+	0.387255i	−0.0312191	+	0.0235676i
$271$	18.1498	+	16.8406i	1.10252	+	1.02299i	0.999599	+	0.0283020i	$0.00901002\pi$
$271$	18.1498	+	16.8406i	1.10252	+	1.02299i	0.102923	+	0.994689i	$0.467180\pi$
$272$	−24.1613	−	4.42276i	−1.46499	−	0.268169i
$273$	2.62653	+	2.91193i	0.158965	+	0.176238i
$274$	−1.75350	+	2.85899i	−0.105933	+	0.172718i
$275$	18.9375	+	10.9336i	1.14197	+	0.659319i
$276$	−1.57859	−	2.60226i	−0.0950198	−	0.156638i
$277$	−2.99811	+	2.78184i	−0.180139	+	0.167144i	−0.765088	−	0.643925i	$-0.777305\pi$
$277$	−2.99811	+	2.78184i	−0.180139	+	0.167144i	0.584950	+	0.811070i	$0.301114\pi$
$278$	30.1362	+	5.36444i	1.80745	+	0.321738i
$279$	−16.4252	+	20.5965i	−0.983348	+	1.23308i
$280$	1.40004	−	0.402932i	0.0836681	−	0.0240798i
$281$	1.54521	+	1.93763i	0.0921794	+	0.115589i	0.825782	−	0.563989i	$-0.190734\pi$
$281$	1.54521	+	1.93763i	0.0921794	+	0.115589i	−0.733603	+	0.679579i	$0.762163\pi$
$282$	−0.218089	−	0.402035i	−0.0129870	−	0.0239409i
$283$	−3.96822	+	10.1109i	−0.235886	+	0.601028i	−0.998975	−	0.0452654i	$-0.985587\pi$
$283$	−3.96822	+	10.1109i	−0.235886	+	0.601028i	0.763089	+	0.646294i	$0.223682\pi$
$284$	0.903277	+	9.33366i	0.0535996	+	0.553851i
$285$	−0.390561	+	0.153284i	−0.0231349	+	0.00907976i
$286$	−21.8933	−	7.39548i	−1.29458	−	0.437304i
$287$	3.48910	−	6.99154i	0.205955	−	0.412697i
$288$	6.12009	+	14.8554i	0.360630	+	0.875363i
$289$	−1.54751	+	20.6500i	−0.0910298	+	1.21471i
$290$	−0.660711	+	1.28361i	−0.0387983	+	0.0753763i
$291$	−1.06102	+	1.55623i	−0.0621980	+	0.0912278i
$292$	−30.2019	+	5.22403i	−1.76743	+	0.305713i
$293$		−	17.6595i		−	1.03168i	−0.856686	−	0.515838i	$-0.827480\pi$
$293$		−	17.6595i		−	1.03168i	0.856686	−	0.515838i	$-0.172520\pi$
$294$	−3.93934	+	0.374842i	−0.229747	+	0.0218612i
$295$		−	2.41155i		−	0.140406i
$296$	−16.8230	+	24.4177i	−0.977819	+	1.41925i
$297$	−5.79533	+	8.50019i	−0.336279	+	0.493231i
$298$	15.2258	+	7.83715i	0.882007	+	0.453994i
$299$	−1.05493	+	14.0771i	−0.0610082	+	0.814098i
$300$	1.64335	−	3.61062i	0.0948788	−	0.208459i
$301$	−5.19878	+	1.10979i	−0.299653	+	0.0639673i
$302$	6.79635	−	20.1197i	0.391086	−	1.15776i
$303$	−0.0815600	+	0.0320099i	−0.00468550	+	0.00183892i
$304$	2.54211	+	21.4154i	0.145800	+	1.22826i
$305$	−0.549097	+	1.39908i	−0.0314412	+	0.0801109i
$306$	21.6806	−	11.7609i	1.23940	−	0.672325i
$307$	−4.68520	−	5.87506i	−0.267399	−	0.335307i	0.629945	−	0.776640i	$-0.283077\pi$
$307$	−4.68520	−	5.87506i	−0.267399	−	0.335307i	−0.897344	+	0.441332i	$0.854506\pi$
$308$	19.1666	−	13.2818i	1.09212	−	0.756801i
$309$	−0.639521	+	0.801933i	−0.0363811	+	0.0456204i
$310$	−0.447540	+	2.51417i	−0.0254185	+	0.142795i
$311$	19.4112	−	18.0110i	1.10071	−	1.02131i	0.101060	−	0.994880i	$-0.467777\pi$
$311$	19.4112	−	18.0110i	1.10071	−	1.02131i	0.999651	−	0.0264294i	$-0.00841373\pi$
$312$	−0.952820	+	4.08253i	−0.0539428	+	0.231128i
$313$	24.3382	+	14.0516i	1.37567	+	0.794246i	0.991635	−	0.129071i	$-0.0411996\pi$
$313$	24.3382	+	14.0516i	1.37567	+	0.794246i	0.384039	+	0.923317i	$0.374533\pi$
$314$	3.30566	+	2.02745i	0.186549	+	0.114415i
$315$	−0.841044	+	1.19701i	−0.0473875	+	0.0674437i
$316$	−1.20137	+	5.84476i	−0.0675825	+	0.328793i
$317$	−18.3666	−	17.0418i	−1.03157	−	0.957160i	−0.0324689	−	0.999473i	$-0.510337\pi$
$317$	−18.3666	−	17.0418i	−1.03157	−	0.957160i	−0.999104	+	0.0423126i	$0.986527\pi$
$318$	−2.07599	−	2.74998i	−0.116416	−	0.154211i
$319$	−3.44402	+	22.8496i	−0.192828	+	1.27933i
$320$	1.20812	+	0.982909i	0.0675359	+	0.0549463i
$321$	−3.43535	−	0.784096i	−0.191743	−	0.0437640i
$322$	−10.7670	−	9.32675i	−0.600020	−	0.519760i
$323$	32.2771	−	7.36704i	1.79595	−	0.409913i
$324$	−13.3032	−	7.30084i	−0.739069	−	0.405602i
$325$	−15.9342	+	9.19961i	−0.883870	+	0.510302i
$326$	−0.112797	+	4.24556i	−0.00624723	+	0.235140i
$327$	−1.92517	+	1.31256i	−0.106462	+	0.0725847i
$328$	8.26598	−	1.20462i	0.456412	−	0.0665141i
$329$	−1.54853	−	1.47796i	−0.0853733	−	0.0814824i
$330$	−0.0490755	+	0.482502i	−0.00270152	+	0.0265609i
$331$	−3.22837	+	10.4661i	−0.177447	+	0.575270i	0.822531	+	0.568720i	$0.192561\pi$
$331$	−3.22837	+	10.4661i	−0.177447	+	0.575270i	−0.999979	+	0.00655005i	$0.997915\pi$
$332$	0.880112	+	0.323585i	0.0483024	+	0.0177590i
$333$	−2.22513	−	29.6923i	−0.121936	−	1.62713i
$334$	1.05039	−	2.48053i	0.0574749	−	0.135729i
$335$	0.283791	−	0.136667i	0.0155052	−	0.00746689i
$336$	−2.73324	−	3.22882i	−0.149110	−	0.176147i
$337$	3.01180	+	1.45040i	0.164063	+	0.0790086i	0.514113	−	0.857722i	$-0.328121\pi$
$337$	3.01180	+	1.45040i	0.164063	+	0.0790086i	−0.350050	+	0.936731i	$0.613835\pi$
$338$	0.795228	−	0.699493i	0.0432547	−	0.0380474i
$339$	0.649459	−	0.200332i	0.0352738	−	0.0108805i
$340$	1.30374	−	2.00423i	0.0707052	−	0.108695i
$341$	6.09207	+	40.4182i	0.329904	+	2.18877i
$342$	−15.4779	−	15.1460i	−0.836951	−	0.819003i
$343$	−17.0107	+	7.32360i	−0.918493	+	0.395437i
$344$	−4.14697	−	3.88570i	−0.223589	−	0.209503i
$345$	0.292960	−	0.0441567i	0.0157725	−	0.00237732i
$346$	4.47883	−	0.897824i	0.240783	−	0.0482673i
$347$	6.69590	+	21.7076i	0.359455	+	1.16532i	0.937107	+	0.349041i	$0.113493\pi$
$347$	6.69590	+	21.7076i	0.359455	+	1.16532i	−0.577653	+	0.816283i	$0.696031\pi$
$348$	4.18614	+	0.222593i	0.224401	+	0.0119323i
$349$	−4.52558	+	9.39746i	−0.242249	+	0.503035i	−0.986274	−	0.165117i	$-0.947200\pi$
$349$	−4.52558	+	9.39746i	−0.242249	+	0.503035i	0.744025	+	0.668151i	$0.232914\pi$
$350$	2.13868	−	18.4429i	0.114317	−	0.985814i
$351$	−3.75581	−	7.79902i	−0.200470	−	0.416281i
$352$	23.3552	+	8.71663i	1.24484	+	0.464598i
$353$	18.8128	−	1.40983i	1.00130	−	0.0750374i	0.436023	−	0.899935i	$-0.356387\pi$
$353$	18.8128	−	1.40983i	1.00130	−	0.0750374i	0.565282	+	0.824898i	$0.308768\pi$
$354$	−6.38750	+	2.86964i	−0.339492	+	0.152520i
$355$	−0.872238	−	0.269050i	−0.0462936	−	0.0142797i
$356$	−14.0182	−	16.8171i	−0.742961	−	0.891307i
$357$	−4.48387	+	4.69798i	−0.237311	+	0.248643i
$358$	−2.91399	−	23.5641i	−0.154009	−	1.24540i
$359$	3.74259	+	5.48938i	0.197527	+	0.289718i	0.912204	−	0.409736i	$-0.134379\pi$
$359$	3.74259	+	5.48938i	0.197527	+	0.289718i	−0.714678	+	0.699454i	$0.753427\pi$
$360$	−1.56393	−	0.00764126i	−0.0824261	−	0.000402730i
$361$	−5.03387	−	8.71891i	−0.264940	−	0.458890i
$362$	−3.94612	−	14.1135i	−0.207403	−	0.741787i
$363$	0.748961	+	3.28141i	0.0393103	+	0.172230i
$364$	1.61473	+	19.5541i	0.0846349	+	1.02491i
$365$	0.663898	−	2.90873i	0.0347500	−	0.152250i
$366$	4.35916	−	0.210440i	0.227857	−	0.0109999i
$367$	21.3368	+	3.21600i	1.11377	+	0.167874i	0.680045	−	0.733171i	$-0.261960\pi$
$367$	21.3368	+	3.21600i	1.11377	+	0.167874i	0.433727	+	0.901045i	$0.357198\pi$
$368$	1.61494	−	15.1425i	0.0841845	−	0.789359i
$369$	−5.70536	+	6.14892i	−0.297009	+	0.320100i
$370$	−1.56202	−	2.42715i	−0.0812058	−	0.126182i
$371$	−13.1948	−	9.27093i	−0.685038	−	0.481323i
$372$	7.19188	−	1.80635i	0.372882	−	0.0936551i
$373$	−14.3264	+	24.8140i	−0.741792	+	1.28482i	0.209886	+	0.977726i	$0.432691\pi$
$373$	−14.3264	+	24.8140i	−0.741792	+	1.28482i	−0.951679	+	0.307096i	$0.900643\pi$
$374$	9.50378	−	37.0711i	0.491429	−	1.91690i
$375$	0.527306	+	0.568301i	0.0272300	+	0.0293469i
$376$	0.352125	−	2.26118i	0.0181595	−	0.116611i
$377$	−15.2011	−	12.1225i	−0.782899	−	0.624341i
$378$	8.57735	+	1.65179i	0.441171	+	0.0849588i
$379$	16.2053	−	12.9233i	0.832408	−	0.663823i	−0.111597	−	0.993754i	$-0.535597\pi$
$379$	16.2053	−	12.9233i	0.832408	−	0.663823i	0.944005	+	0.329930i	$0.107025\pi$
$380$	−2.01891	−	0.575137i	−0.103568	−	0.0295039i
$381$	1.64345	+	0.645007i	0.0841966	+	0.0330447i
$382$	−6.74250	−	5.67637i	−0.344976	−	0.290428i
$383$	0.540532	+	1.37725i	0.0276199	+	0.0703744i	0.944018	−	0.329893i	$-0.107013\pi$
$383$	0.540532	+	1.37725i	0.0276199	+	0.0703744i	−0.916399	+	0.400267i	$0.868917\pi$
$384$	1.16583	−	4.36959i	0.0594938	−	0.222984i
$385$	0.473875	+	2.21985i	0.0241509	+	0.113134i
$386$	0.871034	+	2.40533i	0.0443344	+	0.122428i
$387$	5.69068	+	0.426458i	0.289274	+	0.0216781i
$388$	−8.94289	+	2.97227i	−0.454007	+	0.150894i
$389$	9.22428	+	6.28901i	0.467690	+	0.318865i	0.774132	−	0.633024i	$-0.218186\pi$
$389$	9.22428	+	6.28901i	0.467690	+	0.318865i	−0.306443	+	0.951889i	$0.599139\pi$
$390$	−0.330944	−	0.238751i	−0.0167580	−	0.0120896i
$391$	−23.3782			−1.18229
$392$	−16.8099	−	10.4608i	−0.849027	−	0.528349i
$393$	2.99480			0.151068
$394$	10.7269	+	7.73862i	0.540412	+	0.389866i
$395$	−0.479902	−	0.327192i	−0.0241465	−	0.0164628i
$396$	−23.7550	+	7.89525i	−1.19374	+	0.396751i
$397$	−15.4021	−	1.15423i	−0.773010	−	0.0579291i	−0.317616	−	0.948219i	$-0.602882\pi$
$397$	−15.4021	−	1.15423i	−0.773010	−	0.0579291i	−0.455394	+	0.890290i	$0.650501\pi$
$398$	7.83055	+	21.6238i	0.392510	+	1.08390i
$399$	5.10191	+	2.54609i	0.255415	+	0.127464i
$400$	17.4928	−	9.37882i	0.874638	−	0.468941i
$401$	−12.8979	−	32.8634i	−0.644092	−	1.64112i	−0.761599	−	0.648048i	$-0.775585\pi$
$401$	−12.8979	−	32.8634i	−0.644092	−	1.64112i	0.117507	−	0.993072i	$-0.462510\pi$
$402$	−0.699690	−	0.589054i	−0.0348974	−	0.0293794i
$403$	−32.0150	−	12.5650i	−1.59478	−	0.625905i
$404$	−0.421604	−	0.120104i	−0.0209756	−	0.00597542i
$405$	1.15488	−	0.920982i	0.0573862	−	0.0457640i
$406$	18.9676	−	5.01640i	0.941346	−	0.248960i
$407$	−36.1200	−	28.8047i	−1.79040	−	1.42780i
$408$	−6.86003	−	1.06829i	−0.339622	−	0.0528881i
$409$	−15.8079	−	17.0369i	−0.781652	−	0.842420i	0.209130	−	0.977888i	$-0.432937\pi$
$409$	−15.8079	−	17.0369i	−0.781652	−	0.842420i	−0.990782	+	0.135468i	$0.956746\pi$
$410$	−0.201926	+	0.787645i	−0.00997240	+	0.0388990i
$411$	−0.473993	+	0.820980i	−0.0233803	+	0.0404959i
$412$	−4.97741	+	1.25016i	−0.245220	+	0.0615907i
$413$	−24.3361	+	21.9509i	−1.19750	+	1.08013i
$414$	8.27561	+	12.8591i	0.406724	+	0.631988i
$415$	−0.0620846	+	0.0669113i	−0.00304762	+	0.00328455i
$416$	−16.1773	+	13.3514i	−0.793157	+	0.654606i
$417$	8.55533	+	1.28951i	0.418956	+	0.0631475i
$418$	−33.5615	+	1.62019i	−1.64155	+	0.0792463i
$419$	3.42751	−	15.0169i	0.167445	−	0.733623i	−0.819568	−	0.572982i	$-0.805787\pi$
$419$	3.42751	−	15.0169i	0.167445	−	0.733623i	0.987013	−	0.160641i	$-0.0513563\pi$
$420$	0.392559	−	0.124360i	0.0191549	−	0.00606813i
$421$	1.28026	+	5.60919i	0.0623961	+	0.273375i	0.996496	−	0.0836356i	$-0.0266532\pi$
$421$	1.28026	+	5.60919i	0.0623961	+	0.273375i	−0.934100	+	0.357011i	$0.883796\pi$
$422$	−2.84852	−	10.1878i	−0.138664	−	0.495936i
$423$	1.14898	+	1.99010i	0.0558656	+	0.0967620i
$424$	0.0842305	−	17.2393i	0.00409059	−	0.837216i
$425$	−17.1647	−	25.1760i	−0.832612	−	1.22122i
$426$	0.325290	+	2.63047i	0.0157604	+	0.127447i
$427$	19.1169	−	7.19377i	0.925130	−	0.348131i
$428$	−11.2885	−	13.5425i	−0.545651	−	0.654600i
$429$	−6.24154	−	1.92526i	−0.301344	−	0.0929524i
$430$	0.504600	−	0.226696i	0.0243340	−	0.0109322i
$431$	28.3932	−	2.12777i	1.36765	−	0.102491i	0.629433	−	0.777054i	$-0.283287\pi$
$431$	28.3932	−	2.12777i	1.36765	−	0.102491i	0.738217	+	0.674563i	$0.235668\pi$
$432$	3.78509	+	8.53653i	0.182110	+	0.410714i
$433$	12.2009	+	25.3353i	0.586336	+	1.21754i	0.957355	+	0.288914i	$0.0932942\pi$
$433$	12.2009	+	25.3353i	0.586336	+	1.21754i	−0.371019	+	0.928625i	$0.620992\pi$
$434$	29.4454	−	18.3687i	1.41343	−	0.881726i
$435$	−0.177050	+	0.367648i	−0.00848889	+	0.0176274i
$436$	−11.6416	−	0.619029i	−0.557532	−	0.0296461i
$437$	6.05008	+	19.6139i	0.289415	+	0.938259i
$438$	−8.49440	+	1.70279i	−0.405878	+	0.0813622i
$439$	30.6784	−	4.62403i	1.46420	−	0.220693i	0.631915	−	0.775038i	$-0.282269\pi$
$439$	30.6784	−	4.62403i	1.46420	−	0.220693i	0.832287	+	0.554345i	$0.187031\pi$
$440$	−1.65917	+	1.77073i	−0.0790979	+	0.0844163i
$441$	19.7351	−	2.40828i	0.939767	−	0.114680i
$442$	23.0148	+	22.5212i	1.09470	+	1.07123i
$443$	−2.25301	−	14.9477i	−0.107044	−	0.710188i	−0.976395	−	0.215993i	$-0.930701\pi$
$443$	−2.25301	−	14.9477i	−0.107044	−	0.710188i	0.869351	−	0.494195i	$-0.164537\pi$
$444$	−4.57009	+	7.02557i	−0.216887	+	0.333419i
$445$	2.03645	−	0.628162i	0.0965370	−	0.0297777i
$446$	11.8288	−	10.4048i	0.560110	−	0.492680i
$447$	4.36092	+	2.10011i	0.206265	+	0.0993318i
$448$	−1.07779	−	21.1386i	−0.0509210	−	0.998703i
$449$	−37.6374	+	18.1252i	−1.77622	+	0.855383i	−0.815068	+	0.579366i	$0.803300\pi$
$449$	−37.6374	+	18.1252i	−1.77622	+	0.855383i	−0.961153	+	0.276017i	$0.910985\pi$
$450$	−7.77184	+	18.3534i	−0.366368	+	0.865188i
$451$	0.972601	+	12.9785i	0.0457980	+	0.611132i
$452$	3.19168	+	1.17346i	0.150124	+	0.0551950i
$453$	1.76929	−	5.73589i	0.0831284	−	0.269496i
$454$	2.46273	−	24.2132i	0.115582	−	1.13638i
$455$	−1.81693	−	0.588598i	−0.0851789	−	0.0275939i
$456$	0.879045	+	6.03191i	0.0411651	+	0.282470i
$457$	6.38832	−	4.35548i	0.298833	−	0.203741i	−0.404616	−	0.914487i	$-0.632595\pi$
$457$	6.38832	−	4.35548i	0.298833	−	0.203741i	0.703449	+	0.710746i	$0.251642\pi$
$458$	0.323170	−	12.1638i	0.0151008	−	0.568378i
$459$	12.4149	−	7.16775i	0.579478	−	0.334562i
$460$	1.29951	+	0.713174i	0.0605900	+	0.0332519i
$461$	17.1104	−	3.90534i	0.796911	−	0.181890i	0.195368	−	0.980730i	$-0.437410\pi$
$461$	17.1104	−	3.90534i	0.796911	−	0.181890i	0.601543	+	0.798840i	$0.294553\pi$
$462$	5.31587	−	3.89669i	0.247317	−	0.181290i
$463$	−26.7014	−	6.09441i	−1.24092	−	0.283231i	−0.448818	−	0.893623i	$-0.648155\pi$
$463$	−26.7014	−	6.09441i	−1.24092	−	0.283231i	−0.792099	+	0.610392i	$0.791012\pi$
$464$	15.9791	+	13.5865i	0.741813	+	0.630736i
$465$	−0.107580	+	0.713746i	−0.00498890	+	0.0330992i
$466$	0.776111	+	1.02808i	0.0359526	+	0.0476250i
$467$	1.40072	+	1.29968i	0.0648175	+	0.0601419i	0.711916	−	0.702264i	$-0.247827\pi$
$467$	1.40072	+	1.29968i	0.0648175	+	0.0601419i	−0.647099	+	0.762406i	$0.724018\pi$
$468$	4.24073	−	20.6314i	0.196028	−	0.953688i
$469$	−3.96235	−	1.61988i	−0.182964	−	0.0747989i
$470$	0.189888	+	0.116463i	0.00875888	+	0.00537205i
$471$	0.949242	+	0.548045i	0.0437388	+	0.0252526i
$472$	−34.1192	−	7.96306i	−1.57046	−	0.366530i
$473$	6.49068	−	6.02248i	0.298442	−	0.276914i
$474$	−0.295575	+	1.66047i	−0.0135762	+	0.0762679i
$475$	−16.6802	+	20.9163i	−0.765339	+	0.959704i
$476$	−32.0928	+	5.08665i	−1.47097	+	0.233146i
$477$	10.7935	+	13.5346i	0.494199	+	0.619707i
$478$	−28.7760	+	15.6099i	−1.31618	+	0.713979i
$479$	2.51807	−	6.41594i	0.115054	−	0.293152i	−0.861735	−	0.507359i	$-0.830622\pi$
$479$	2.51807	−	6.41594i	0.115054	−	0.293152i	0.976788	+	0.214208i	$0.0687169\pi$
$480$	0.348736	+	0.268654i	0.0159175	+	0.0122623i
$481$	36.1853	−	14.2017i	1.64991	−	0.647542i
$482$	7.36744	−	21.8104i	0.335578	−	0.993434i
$483$	−3.11225	−	2.55447i	−0.141612	−	0.116233i
$484$	−6.97618	+	15.3274i	−0.317099	+	0.696701i
$485$	0.0685521	−	0.914765i	0.00311279	−	0.0415373i
$486$	−12.6200	−	6.49590i	−0.572457	−	0.294660i
$487$	−8.50254	+	12.4709i	−0.385287	+	0.565112i	−0.969066	−	0.246800i	$-0.920621\pi$
$487$	−8.50254	+	12.4709i	−0.385287	+	0.565112i	0.583779	+	0.811912i	$0.301573\pi$
$488$	17.9813	+	12.3886i	0.813976	+	0.560805i
$489$			1.20044i			0.0542858i
$490$	1.57026	−	1.11739i	0.0709372	−	0.0504787i
$491$			41.7664i			1.88489i	0.334359	+	0.942446i	$0.391480\pi$
$491$			41.7664i			1.88489i	−0.334359	+	0.942446i	$0.608520\pi$
$492$	2.32653	−	0.402421i	0.104888	−	0.0181425i
$493$	18.1385	−	26.6043i	0.816916	−	1.19820i
$494$	12.9389	−	25.1373i	0.582148	−	1.13098i
$495$	0.182095	−	2.42989i	0.00818457	−	0.109215i
$496$	34.0933	+	14.6338i	1.53084	+	0.657079i
$497$	5.22436	+	11.2512i	0.234345	+	0.504684i
$498$	0.251107	+	0.0848229i	0.0112524	+	0.00380101i
$499$	−29.2093	+	11.4638i	−1.30759	+	0.513191i	−0.913858	−	0.406035i	$-0.866911\pi$
$499$	−29.2093	+	11.4638i	−1.30759	+	0.513191i	−0.393731	+	0.919226i	$0.628816\pi$
$500$	0.373638	+	3.86084i	0.0167096	+	0.172662i
$501$	0.278170	−	0.708766i	0.0124277	−	0.0316653i
$502$	0.576082	+	1.06198i	0.0257118	+	0.0473984i
$503$	15.6121	+	19.5770i	0.696111	+	0.872896i	0.996726	−	0.0808497i	$-0.0257634\pi$
$503$	15.6121	+	19.5770i	0.696111	+	0.872896i	−0.300615	+	0.953746i	$0.597192\pi$
$504$	14.1584	+	15.8519i	0.630665	+	0.706099i
$505$	0.0266056	−	0.0333624i	0.00118393	−	0.00148461i
$506$	23.3594	+	4.15813i	1.03845	+	0.184852i
$507$	0.219443	−	0.203613i	0.00974580	−	0.00904278i
$508$	4.58147	+	7.55243i	0.203270	+	0.335085i
$509$	25.2495	+	14.5778i	1.11916	+	0.646149i	0.941187	−	0.337886i	$-0.109712\pi$
$509$	25.2495	+	14.5778i	1.11916	+	0.646149i	0.177976	+	0.984035i	$0.443045\pi$
$510$	0.353329	−	0.576087i	0.0156457	−	0.0255096i
$511$	−35.3964	+	19.7767i	−1.56585	+	0.874870i
$512$	17.8957	−	13.8472i	0.790886	−	0.611963i
$513$	−9.22650	−	8.56094i	−0.407360	−	0.377975i
$514$	−13.9245	+	10.5117i	−0.614182	+	0.463653i
$515$	0.0744547	−	0.493975i	0.00328087	−	0.0217671i
$516$	−1.20091	−	1.06678i	−0.0528669	−	0.0469625i
$517$	3.47610	+	0.793397i	0.152879	+	0.0348936i
$518$	−10.2754	+	37.8561i	−0.451474	+	1.66330i
$519$	1.25876	−	0.287305i	0.0552536	−	0.0126113i
$520$	−0.592279	−	1.95396i	−0.0259731	−	0.0856870i
$521$	28.9879	−	16.7362i	1.26998	−	0.733225i	0.294998	−	0.955498i	$-0.404681\pi$
$521$	28.9879	−	16.7362i	1.26998	−	0.733225i	0.974985	+	0.222273i	$0.0713476\pi$
$522$	−21.0544	−	0.559376i	−0.921525	−	0.0244832i
$523$	−10.4464	+	7.12227i	−0.456791	+	0.311435i	−0.769766	−	0.638327i	$-0.779627\pi$
$523$	−10.4464	+	7.12227i	−0.456791	+	0.311435i	0.312975	+	0.949762i	$0.398675\pi$
$524$	11.9148	+	9.08631i	0.520499	+	0.396937i
$525$	0.465841	−	5.22714i	0.0203310	−	0.228131i
$526$	6.95615	+	0.707512i	0.303303	+	0.0308490i
$527$	16.7883	−	54.4263i	0.731310	−	2.37085i
$528$	6.66451	+	2.28758i	0.290036	+	0.0995542i
$529$	0.635653	+	8.48221i	0.0276371	+	0.368792i
$530$	1.54528	+	0.654355i	0.0671225	+	0.0284234i
$531$	31.6980	−	15.2649i	1.37558	−	0.662442i
$532$	12.5730	+	25.6089i	0.545107	+	1.11029i
$533$	−9.86635	−	4.75138i	−0.427359	−	0.205805i
$534$	−4.08711	−	4.64649i	−0.176867	−	0.201073i
$535$	1.63991	−	0.505845i	0.0708994	−	0.0218696i
$536$	−0.996498	−	4.46642i	−0.0430422	−	0.192920i
$537$	−1.00025	−	6.63622i	−0.0431639	−	0.286374i
$538$	19.4799	−	19.9067i	0.839836	−	0.858241i
$539$	18.0882	−	24.9881i	0.779114	−	1.07631i
$540$	−0.908761	+	0.0197014i	−0.0391068	+	0.000847813i
$541$	18.5357	−	2.79381i	0.796912	−	0.120115i	0.262050	−	0.965054i	$-0.415602\pi$
$541$	18.5357	−	2.79381i	0.796912	−	0.120115i	0.534862	+	0.844939i	$0.320363\pi$
$542$	6.88215	+	34.3319i	0.295614	+	1.47468i
$543$	−1.22093	−	3.95817i	−0.0523953	−	0.169861i
$544$	−24.0513	−	25.0637i	−1.03119	−	1.07460i
$545$	0.492373	−	1.02242i	0.0210910	−	0.0437958i
$546$	0.603037	+	5.51293i	0.0258076	+	0.235932i
$547$	1.22035	+	2.53409i	0.0521784	+	0.108350i	0.925428	−	0.378924i	$-0.123706\pi$
$547$	1.22035	+	2.53409i	0.0521784	+	0.108350i	−0.873249	+	0.487273i	$0.837991\pi$
$548$	−4.37665	+	1.82815i	−0.186961	+	0.0780946i
$549$	−21.8656	+	1.63860i	−0.933199	+	0.0699336i
$550$	12.6730	+	28.2088i	0.540381	+	1.20283i
$551$	−27.0146	−	8.33290i	−1.15086	−	0.354994i
$552$	0.342632	−	4.29068i	0.0145834	−	0.182624i
$553$	1.06642	+	7.82116i	0.0453487	+	0.332590i
$554$	−5.74026	+	0.709855i	−0.243880	+	0.0301588i
$555$	−0.459575	−	0.674072i	−0.0195079	−	0.0286128i
$556$	30.1248	+	31.0874i	1.27758	+	1.31840i
$557$	−2.95318	−	5.11505i	−0.125130	−	0.216732i	0.796654	−	0.604436i	$-0.206601\pi$
$557$	−2.95318	−	5.11505i	−0.125130	−	0.216732i	−0.921784	+	0.387704i	$0.873268\pi$
$558$	−35.8798	+	10.0320i	−1.51891	+	0.424688i
$559$	1.65781	+	7.26333i	0.0701178	+	0.307206i
$560$	1.93910	+	0.696273i	0.0819420	+	0.0294229i
$561$	2.40703	−	10.5459i	0.101625	−	0.445248i
$562$	0.169002	+	3.50080i	0.00712894	+	0.147672i
$563$	1.71325	+	0.258230i	0.0722048	+	0.0108831i	0.185045	−	0.982730i	$-0.440757\pi$
$563$	1.71325	+	0.258230i	0.0722048	+	0.0108831i	−0.112841	+	0.993613i	$0.535995\pi$
$564$	0.0825195	−	0.641546i	0.00347470	−	0.0270139i
$565$	−0.225146	+	0.242650i	−0.00947198	+	0.0102084i
$566$	−12.9170	+	8.31289i	−0.542941	+	0.349417i
$567$	−19.8062	−	3.27124i	−0.831783	−	0.137379i
$568$	−6.68676	+	11.4522i	−0.280570	+	0.480525i
$569$	4.44875	−	7.70545i	0.186501	−	0.323029i	−0.757580	−	0.652742i	$-0.773619\pi$
$569$	4.44875	−	7.70545i	0.186501	−	0.323029i	0.944081	+	0.329713i	$0.106952\pi$
$570$	−0.574766	−	0.147351i	−0.0240743	−	0.00617184i
$571$	3.16463	+	3.41066i	0.132436	+	0.142732i	0.795788	−	0.605576i	$-0.207057\pi$
$571$	3.16463	+	3.41066i	0.132436	+	0.142732i	−0.663352	+	0.748308i	$0.730867\pi$
$572$	−18.9906	−	26.5966i	−0.794036	−	1.11206i
$573$	−1.94772	−	1.55326i	−0.0813673	−	0.0648883i
$574$	9.78652	−	5.13174i	0.408481	−	0.214195i
$575$	14.7697	−	11.7785i	0.615941	−	0.491196i
$576$	−5.27228	+	22.1016i	−0.219678	+	0.920899i
$577$	−21.2859	−	8.35411i	−0.886145	−	0.347786i	−0.121770	−	0.992558i	$-0.538857\pi$
$577$	−21.2859	−	8.35411i	−0.886145	−	0.347786i	−0.764375	+	0.644772i	$0.776952\pi$
$578$	−18.8608	+	22.4033i	−0.784507	+	0.931853i
$579$	0.264169	+	0.673093i	0.0109785	+	0.0279728i
$580$	−1.81984	+	0.925506i	−0.0755649	+	0.0384296i
$581$	1.24035	+	0.0174715i	0.0514586	+	0.000724841i
$582$	−2.50453	+	0.906956i	−0.103816	+	0.0375945i
$583$	26.7850	+	2.00726i	1.10932	+	0.0831321i
$584$	−38.9611	−	18.9978i	−1.61222	−	0.786133i
$585$	1.69401	+	1.15496i	0.0700387	+	0.0477516i
$586$	14.6116	−	20.2538i	0.603598	−	0.836676i
$587$	−28.2761			−1.16708			−0.583539	−	0.812085i	$-0.698332\pi$
$587$	−28.2761			−1.16708			−0.583539	+	0.812085i	$0.698332\pi$
$588$	−4.82821	−	2.82953i	−0.199112	−	0.116688i
$589$	−50.0074			−2.06052
$590$	1.99533	−	2.76582i	0.0821465	−	0.113867i
$591$	3.08900	+	2.10604i	0.127064	+	0.0866310i
$592$	−39.4978	+	14.0853i	−1.62335	+	0.578903i
$593$	−0.991362	−	0.0742923i	−0.0407103	−	0.00305082i	0.0543594	−	0.998521i	$-0.482688\pi$
$593$	−0.991362	−	0.0742923i	−0.0407103	−	0.00305082i	−0.0950697	+	0.995471i	$0.530307\pi$
$594$	−13.6798	+	4.95383i	−0.561290	+	0.203258i
$595$	0.747181	−	3.07342i	0.0306314	−	0.125998i
$596$	10.9781	+	21.5864i	0.449679	+	0.884214i
$597$	2.37487	+	6.05107i	0.0971970	+	0.247654i
$598$	−12.8574	+	15.2722i	−0.525777	+	0.624528i
$599$	34.0410	+	13.3601i	1.39088	+	0.545879i	0.938292	−	0.345843i	$-0.112407\pi$
$599$	34.0410	+	13.3601i	1.39088	+	0.545879i	0.452584	+	0.891722i	$0.350502\pi$
$600$	4.87222	−	2.78133i	0.198908	−	0.113547i
$601$	−18.2701	+	14.5699i	−0.745252	+	0.594319i	−0.920746	−	0.390162i	$-0.872419\pi$
$601$	−18.2701	+	14.5699i	−0.745252	+	0.594319i	0.175494	+	0.984480i	$0.443848\pi$
$602$	−6.88077	−	3.02868i	−0.280439	−	0.123440i
$603$	3.59276	+	2.86513i	0.146308	+	0.116677i
$604$	24.4420	−	17.4521i	0.994529	−	0.710116i
$605$	−1.11497	−	1.20166i	−0.0453302	−	0.0488543i
$606$	−0.120027	−	0.0307709i	−0.00487577	−	0.00124998i
$607$	−13.0059	+	22.5269i	−0.527894	+	0.914339i	0.471577	+	0.881825i	$0.343685\pi$
$607$	−13.0059	+	22.5269i	−0.527894	+	0.914339i	−0.999471	+	0.0325144i	$0.989649\pi$
$608$	−14.8037	+	26.6649i	−0.600370	+	1.08140i
$609$	5.32169	−	1.55979i	0.215646	−	0.0632057i
$610$	−1.78737	+	1.15028i	−0.0723685	+	0.0465737i
$611$	−2.04054	+	2.19918i	−0.0825516	+	0.0889695i
$612$	34.5967	+	4.45003i	1.39849	+	0.179882i
$613$	−26.5082	−	3.99546i	−1.07065	−	0.161375i	−0.410015	−	0.912079i	$-0.634477\pi$
$613$	−26.5082	−	3.99546i	−1.07065	−	0.161375i	−0.660639	+	0.750704i	$0.729715\pi$
$614$	−0.512430	−	10.6147i	−0.0206800	−	0.428375i
$615$	−0.0511419	+	0.224067i	−0.00206224	+	0.00903526i
$616$	32.9718	+	0.625579i	1.32847	+	0.0252053i
$617$	−7.57972	−	33.2089i	−0.305148	−	1.33694i	−0.862244	−	0.506493i	$-0.830942\pi$
$617$	−7.57972	−	33.2089i	−0.305148	−	1.33694i	0.557096	−	0.830448i	$-0.311915\pi$
$618$	−1.39700	+	0.390600i	−0.0561954	+	0.0157122i
$619$	−12.0083	−	20.7989i	−0.482653	−	0.835979i	0.517149	−	0.855895i	$-0.326993\pi$
$619$	−12.0083	−	20.7989i	−0.482653	−	0.835979i	−0.999802	+	0.0199165i	$0.993660\pi$
$620$	−2.59353	+	2.51323i	−0.104159	+	0.100934i
$621$	5.00664	+	7.34339i	0.200909	+	0.294680i
$622$	37.1653	−	4.59595i	1.49019	−	0.184281i
$623$	−24.8757	−	14.8330i	−0.996624	−	0.594272i
$624$	−4.47071	+	3.89391i	−0.178972	+	0.155881i
$625$	23.3474	+	7.20173i	0.933897	+	0.288069i
$626$	16.2872	+	36.2535i	0.650967	+	1.44898i
$627$	−9.47073	+	0.709733i	−0.378225	+	0.0283440i
$628$	2.11376	+	5.06042i	0.0843482	+	0.201933i
$629$	27.9317	+	58.0008i	1.11371	+	2.31265i
$630$	−1.95501	+	0.676971i	−0.0778896	+	0.0269712i
$631$	12.8293	−	26.6402i	0.510725	−	1.06053i	−0.473036	−	0.881043i	$-0.656842\pi$
$631$	12.8293	−	26.6402i	0.510725	−	1.06053i	0.983760	−	0.179487i	$-0.0574438\pi$
$632$	−6.21386	+	5.70937i	−0.247174	+	0.227107i
$633$	−0.881335	−	2.85722i	−0.0350299	−	0.113564i
$634$	−6.96437	−	34.7420i	−0.276591	−	1.37978i
$635$	−0.850248	+	0.128154i	−0.0337411	+	0.00508565i
$636$	−0.105615	−	4.87165i	−0.00418789	−	0.193174i
$637$	10.5986	+	23.6932i	0.419931	+	0.938757i
$638$	−22.8559	+	23.3567i	−0.904872	+	0.924702i
$639$	−1.98476	−	13.1680i	−0.0785157	−	0.520918i
$640$	0.572336	+	2.12691i	0.0226235	+	0.0840736i
$641$	26.5549	−	8.19111i	1.04886	−	0.323529i	0.278028	−	0.960573i	$-0.410319\pi$
$641$	26.5549	−	8.19111i	1.04886	−	0.323529i	0.770828	+	0.637044i	$0.219843\pi$
$642$	−3.29126	−	3.74172i	−0.129896	−	0.147674i
$643$	−22.3272	−	10.7522i	−0.880499	−	0.424026i	−0.0616919	−	0.998095i	$-0.519650\pi$
$643$	−22.3272	−	10.7522i	−0.880499	−	0.424026i	−0.818807	+	0.574069i	$0.805364\pi$
$644$	−4.63170	−	19.6056i	−0.182515	−	0.772569i
$645$	0.140874	−	0.0678415i	0.00554692	−	0.00267126i
$646$	43.1144	+	18.2570i	1.69631	+	0.718312i
$647$	1.45719	+	19.4448i	0.0572880	+	0.764456i	0.949685	+	0.313205i	$0.101403\pi$
$647$	1.45719	+	19.4448i	0.0572880	+	0.764456i	−0.892397	+	0.451250i	$0.850978\pi$
$648$	−9.21682	−	19.3806i	−0.362071	−	0.761342i
$649$	16.0901	−	52.1628i	0.631591	−	2.04757i
$650$	−25.8869	−	2.63296i	−1.01537	−	0.103273i
$651$	8.18199	−	5.41117i	0.320677	−	0.212080i
$652$	−3.64218	+	4.77594i	−0.142639	+	0.187040i
$653$	16.4595	−	11.2219i	0.644108	−	0.439146i	−0.196711	−	0.980462i	$-0.563026\pi$
$653$	16.4595	−	11.2219i	0.644108	−	0.439146i	0.840819	+	0.541316i	$0.182074\pi$
$654$	−3.29401	−	0.0875159i	−0.128806	−	0.00342214i
$655$	−1.26315	+	0.729281i	−0.0493555	+	0.0284954i
$656$	10.4770	+	5.45774i	0.409059	+	0.213089i
$657$	42.4355	−	9.68562i	1.65557	−	0.377872i
$658$	−0.553151	−	2.97635i	−0.0215641	−	0.116030i
$659$	3.79879	+	0.867049i	0.147980	+	0.0337754i	0.295869	−	0.955228i	$-0.404391\pi$
$659$	3.79879	+	0.867049i	0.147980	+	0.0337754i	−0.147889	+	0.989004i	$0.547248\pi$
$660$	−0.455511	+	0.512780i	−0.0177307	+	0.0199599i
$661$	−1.89468	+	12.5704i	−0.0736946	+	0.488932i	0.921288	+	0.388882i	$0.127138\pi$
$661$	−1.89468	+	12.5704i	−0.0736946	+	0.488932i	−0.994982	+	0.100050i	$0.968100\pi$
$662$	−12.3624	+	9.33250i	−0.480478	+	0.362718i
$663$	6.67195	+	6.19066i	0.259117	+	0.240425i
$664$	0.741671	+	1.09933i	0.0287824	+	0.0426624i
$665$	−2.77191	+	0.168503i	−0.107490	+	0.00653427i
$666$	22.0156	−	35.8954i	0.853086	−	1.39092i
$667$	17.2884	+	9.98145i	0.669409	+	0.386483i
$668$	3.25711	−	1.97584i	0.126022	−	0.0764475i
$669$	3.26415	−	3.02869i	0.126199	−	0.117096i
$670$	0.438561	+	0.0780668i	0.0169431	+	0.00301598i
$671$	−21.2120	+	26.5990i	−0.818880	+	1.02684i
$672$	−0.463219	−	5.96466i	−0.0178691	−	0.230092i
$673$	−15.0825	−	18.9129i	−0.581388	−	0.729038i	0.400961	−	0.916095i	$-0.368676\pi$
$673$	−15.0825	−	18.9129i	−0.581388	−	0.729038i	−0.982349	+	0.187058i	$0.940105\pi$
$674$	2.25418	+	4.15546i	0.0868276	+	0.160062i
$675$	−4.23214	+	10.7833i	−0.162895	+	0.415050i
$676$	1.49082	−	0.144276i	0.0573392	−	0.00554907i
$677$	9.04295	−	3.54910i	0.347549	−	0.136403i	−0.185144	−	0.982711i	$-0.559275\pi$
$677$	9.04295	−	3.54910i	0.347549	−	0.136403i	0.532693	+	0.846308i	$0.321180\pi$
$678$	0.910626	+	0.307605i	0.0349724	+	0.0118135i
$679$	−9.85532	+	7.63477i	−0.378212	+	0.292996i
$680$	3.15358	−	1.21994i	0.120934	−	0.0467826i
$681$	0.514086	−	6.86000i	0.0196998	−	0.262876i
$682$	−26.4553	+	51.3966i	−1.01303	+	1.96808i
$683$	13.2415	−	19.4217i	0.506670	−	0.743149i	−0.484637	−	0.874715i	$-0.661048\pi$
$683$	13.2415	−	19.4217i	0.506670	−	0.743149i	0.991307	+	0.131567i	$0.0420007\pi$
$684$	−5.21984	−	30.1776i	−0.199586	−	1.15387i
$685$		−	0.461699i		−	0.0176406i
$686$	−25.5693	−	5.67530i	−0.976242	−	0.216684i
$687$		−	3.43935i		−	0.131219i
$688$	−1.54113	−	7.88777i	−0.0587551	−	0.300718i
$689$	−12.7312	+	18.6733i	−0.485021	+	0.711395i
$690$	0.372534	+	0.191754i	0.0141821	+	0.00729995i
$691$	−1.12843	+	15.0579i	−0.0429277	+	0.572830i	0.933723	+	0.357996i	$0.116540\pi$
$691$	−1.12843	+	15.0579i	−0.0429277	+	0.572830i	−0.976651	+	0.214834i	$0.931079\pi$
$692$	5.87967	+	2.67609i	0.223511	+	0.101730i
$693$	−26.1787	+	20.2803i	−0.994447	+	0.770383i
$694$	−10.2814	+	30.4368i	−0.390278	+	1.15537i
$695$	−3.92250	+	1.53947i	−0.148789	+	0.0583954i
$696$	4.61694	+	3.71894i	0.175005	+	0.140966i
$697$	6.62564	−	16.8818i	0.250964	−	0.639446i
$698$	−12.9660	+	7.03353i	−0.490769	+	0.266223i
$699$	0.227010	+	0.284662i	0.00858631	+	0.0107669i
$700$	17.7126	−	19.3827i	0.669475	−	0.732598i
$701$	−1.23888	+	1.55350i	−0.0467918	+	0.0586751i	−0.804677	−	0.593713i	$-0.797661\pi$
$701$	−1.23888	+	1.55350i	−0.0467918	+	0.0586751i	0.757885	+	0.652388i	$0.226233\pi$
$702$	2.14540	−	12.0523i	0.0809728	−	0.454886i
$703$	41.4332	−	38.4444i	1.56268	−	1.44996i
$704$	19.5741	+	29.3214i	0.737726	+	1.10509i
$705$	0.0545276	+	0.0314815i	0.00205363	+	0.00118566i
$706$	22.7431	+	13.9489i	0.855946	+	0.524974i
$707$	−0.578851	+	0.0351881i	−0.0217699	+	0.00132338i
$708$	−9.70024	−	1.99385i	−0.364557	−	0.0749336i
$709$	−28.7151	−	26.6437i	−1.07842	−	1.00062i	−0.999993	−	0.00370477i	$-0.998821\pi$
$709$	−28.7151	−	26.6437i	−1.07842	−	1.00062i	−0.0784240	−	0.996920i	$-0.524989\pi$
$710$	−0.777763	−	1.03027i	−0.0291889	−	0.0386654i
$711$	1.26294	−	8.37906i	0.0473640	−	0.314239i
$712$	−2.16292	−	30.8864i	−0.0810587	−	1.15752i
$713$	34.4267	+	7.85767i	1.28929	+	0.294272i
$714$	−9.02972	+	1.67817i	−0.337929	+	0.0628038i
$715$	3.10140	−	0.707875i	0.115986	−	0.0264730i
$716$	16.1550	−	29.4369i	0.603741	−	1.10011i
$717$	−8.01356	+	4.62663i	−0.299272	+	0.172785i
$718$	−0.249540	+	9.39246i	−0.00931276	+	0.350523i
$719$	−34.0296	+	23.2010i	−1.26909	+	0.865252i	−0.995329	−	0.0965454i	$-0.969221\pi$
$719$	−34.0296	+	23.2010i	−1.26909	+	0.865252i	−0.273763	+	0.961797i	$0.588268\pi$
$720$	−1.78736	−	1.30277i	−0.0666108	−	0.0485513i
$721$	−5.66265	+	3.74500i	−0.210888	+	0.139471i
$722$	1.44071	−	14.1648i	0.0536177	−	0.527161i
$723$	1.91796	−	6.21788i	0.0713298	−	0.231245i
$724$	7.15175	−	19.4519i	0.265793	−	0.722923i
$725$	1.94442	+	25.9465i	0.0722140	+	0.963629i
$726$	−1.85608	+	4.38317i	−0.0688854	+	0.162675i
$727$	7.55205	−	3.63687i	0.280090	−	0.134884i	−0.288565	−	0.957460i	$-0.593178\pi$
$727$	7.55205	−	3.63687i	0.280090	−	0.134884i	0.568655	+	0.822576i	$0.307464\pi$
$728$	−14.3272	+	23.7628i	−0.531002	+	0.880706i
$729$	16.8936	+	8.13554i	0.625690	+	0.301316i
$730$	3.16813	−	2.78673i	0.117258	−	0.103141i
$731$	−11.7899	+	3.63670i	−0.436065	+	0.134508i
$732$	5.17367	+	3.36544i	0.191224	+	0.124390i
$733$	−4.83649	−	32.0880i	−0.178640	−	1.18520i	−0.880909	−	0.473286i	$-0.843068\pi$
$733$	−4.83649	−	32.0880i	−0.178640	−	1.18520i	0.702269	−	0.711911i	$-0.252170\pi$
$734$	21.8104	+	21.3427i	0.805036	+	0.787772i
$735$	0.435294	−	0.327510i	0.0160561	−	0.0120804i
$736$	14.3812	−	16.0309i	0.530099	−	0.590906i
$737$	7.05037	−	1.06267i	0.259704	−	0.0391441i
$738$	−11.6312	+	2.33158i	−0.428150	+	0.0858268i
$739$	−0.764853	−	2.47959i	−0.0281356	−	0.0912133i	0.940416	−	0.340026i	$-0.110436\pi$
$739$	−0.764853	−	2.47959i	−0.0281356	−	0.0912133i	−0.968552	+	0.248813i	$0.919960\pi$
$740$	0.216745	−	4.07615i	0.00796769	−	0.149842i
$741$	3.46721	−	7.19974i	0.127371	−	0.264489i
$742$	−7.46234	−	21.5503i	−0.273951	−	0.791138i
$743$	−12.7510	−	26.4776i	−0.467787	−	0.971370i	−0.992745	−	0.120242i	$-0.961633\pi$
$743$	−12.7510	−	26.4776i	−0.467787	−	0.971370i	0.524957	−	0.851128i	$-0.324081\pi$
$744$	9.74302	+	3.87889i	0.357196	+	0.142207i
$745$	−2.35077	+	0.176166i	−0.0861255	+	0.00645421i
$746$	−36.9623	+	16.6056i	−1.35329	+	0.607976i
$747$	−1.27249	−	0.392512i	−0.0465580	−	0.0143612i
$748$	41.5729	−	34.6536i	1.52005	−	1.26706i
$749$	−20.0319	−	11.9447i	−0.731948	−	0.436450i
$750$	0.134555	+	1.08809i	0.00491326	+	0.0397313i
$751$	−17.9660	−	26.3513i	−0.655589	−	0.961573i	−0.999743	−	0.0226595i	$-0.992787\pi$
$751$	−17.9660	−	26.3513i	−0.655589	−	0.961573i	0.344154	−	0.938913i	$-0.388166\pi$
$752$	2.27477	−	2.30201i	0.0829524	−	0.0839458i
$753$	0.170746	+	0.295740i	0.00622231	+	0.0107774i
$754$	−7.40406	−	26.4809i	−0.269640	−	0.964379i
$755$	0.650528	+	2.85015i	0.0236751	+	0.103727i
$756$	8.47073	+	8.99141i	0.308077	+	0.327014i
$757$	−8.49472	+	37.2178i	−0.308746	+	1.35270i	0.547789	+	0.836616i	$0.315469\pi$
$757$	−8.49472	+	37.2178i	−0.308746	+	1.35270i	−0.856535	+	0.516088i	$0.827388\pi$
$758$	29.2787	−	1.41344i	1.06345	−	0.0513385i
$759$	6.63148	+	0.999535i	0.240707	+	0.0362808i
$760$	−1.83963	−	2.33009i	−0.0667305	−	0.0845212i
$761$	−21.5187	+	23.1917i	−0.780054	+	0.840698i	−0.990586	−	0.136889i	$-0.956290\pi$
$761$	−21.5187	+	23.1917i	−0.780054	+	0.840698i	0.210533	+	0.977587i	$0.432480\pi$
$762$	1.35120	+	2.09957i	0.0489489	+	0.0760593i
$763$	−14.7996	+	4.33775i	−0.535780	+	0.157037i
$764$	−3.03636	−	12.0891i	−0.109852	−	0.437367i
$765$	−1.69771	+	2.94051i	−0.0613807	+	0.106315i
$766$	−0.519609	+	2.02682i	−0.0187742	+	0.0732321i

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)

\(f(q)\)	\(=\)	\(q+(1.14691 + 0.827407i) q^{2} +(0.330273 + 0.225176i) q^{3} +(0.630795 + 1.89792i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(0.192480 + 0.531527i) q^{6} +(1.62030 + 2.09156i) q^{7} +(-0.846889 + 2.69866i) q^{8} +(-1.03765 - 2.64388i) q^{9} +O(q^{10})\)	\(q+(1.14691 + 0.827407i) q^{2} +(0.330273 + 0.225176i) q^{3} +(0.630795 + 1.89792i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(0.192480 + 0.531527i) q^{6} +(1.62030 + 2.09156i) q^{7} +(-0.846889 + 2.69866i) q^{8} +(-1.03765 - 2.64388i) q^{9} +(-0.210620 - 0.177316i) q^{10} +(-4.10220 - 1.61000i) q^{11} +(-0.219032 + 0.768872i) q^{12} +(2.89899 - 2.31187i) q^{13} +(0.127764 + 3.73948i) q^{14} +(-0.0608423 - 0.0485201i) q^{15} +(-3.20420 + 2.39439i) q^{16} +(4.17672 + 4.50144i) q^{17} +(0.997481 - 3.89085i) q^{18} +(2.69573 - 4.66913i) q^{19} +(-0.0948487 - 0.377634i) q^{20} +(0.0641719 + 1.05564i) q^{21} +(-3.37273 - 5.24071i) q^{22} +(-2.58949 + 2.79080i) q^{23} +(-0.887380 + 0.700596i) q^{24} +(-4.90668 - 0.739562i) q^{25} +(5.23773 - 0.252853i) q^{26} +(0.519478 - 2.27598i) q^{27} +(-2.94754 + 4.39455i) q^{28} +(-1.16681 - 5.11213i) q^{29} +(-0.0296346 - 0.105990i) q^{30} +(-4.63766 - 8.03266i) q^{31} +(-5.65606 + 0.0949747i) q^{32} +(-0.992315 - 1.45546i) q^{33} +(1.06579 + 8.61858i) q^{34} +(-0.284132 - 0.429623i) q^{35} +(4.36333 - 3.63712i) q^{36} +(10.0178 + 3.09008i) q^{37} +(6.95502 - 3.12460i) q^{38} +(1.47804 - 0.110764i) q^{39} +(0.203674 - 0.511590i) q^{40} +(-1.28140 - 2.66086i) q^{41} +(-0.799845 + 1.26382i) q^{42} +(-0.871772 + 1.81025i) q^{43} +(0.467995 - 8.80123i) q^{44} +(0.162981 + 0.528372i) q^{45} +(-5.27903 + 1.05823i) q^{46} +(-0.800046 + 0.120588i) q^{47} +(-1.59742 + 0.0692948i) q^{48} +(-1.74925 + 6.77791i) q^{49} +(-5.01559 - 4.90803i) q^{50} +(0.365842 + 2.42720i) q^{51} +(6.21641 + 4.04374i) q^{52} +(-5.82431 + 1.79656i) q^{53} +(2.47896 - 2.18052i) q^{54} +(0.772968 + 0.372242i) q^{55} +(-7.01663 + 2.60133i) q^{56} +(1.94170 - 0.935075i) q^{57} +(2.89159 - 6.82857i) q^{58} +(0.925691 + 12.3525i) q^{59} +(0.0537083 - 0.146080i) q^{60} +(2.27555 - 7.37716i) q^{61} +(1.32731 - 13.0500i) q^{62} +(3.84854 - 6.45419i) q^{63} +(-6.56556 - 4.57094i) q^{64} +(-0.596437 + 0.406644i) q^{65} +(0.0661633 - 2.49032i) q^{66} +(-1.40118 + 0.808972i) q^{67} +(-5.90871 + 10.7666i) q^{68} +(-1.48366 + 0.338636i) q^{69} +(0.0296004 - 0.727831i) q^{70} +(4.57108 + 1.04332i) q^{71} +(8.01372 - 0.561185i) q^{72} +(-2.28410 + 15.1540i) q^{73} +(8.93273 + 11.8328i) q^{74} +(-1.45401 - 1.34913i) q^{75} +(10.5621 + 2.17101i) q^{76} +(-3.27940 - 11.1887i) q^{77} +(1.78682 + 1.09590i) q^{78} +(2.58376 + 1.49174i) q^{79} +(0.656889 - 0.418225i) q^{80} +(-5.56201 + 5.16079i) q^{81} +(0.731965 - 4.11201i) q^{82} +(0.292327 - 0.366567i) q^{83} +(-1.96304 + 0.787685i) q^{84} +(-0.745368 - 0.934662i) q^{85} +(-2.49766 + 1.35488i) q^{86} +(0.765765 - 1.95114i) q^{87} +(7.81895 - 9.70698i) q^{88} +(-10.1900 + 3.99930i) q^{89} +(-0.250255 + 0.740846i) q^{90} +(9.53265 + 2.31749i) q^{91} +(-6.93015 - 3.15421i) q^{92} +(0.277072 - 3.69726i) q^{93} +(-1.01735 - 0.523661i) q^{94} +(-0.591270 + 0.867234i) q^{95} +(-1.88943 - 1.24224i) q^{96} +4.71195i q^{97} +(-7.61432 + 6.32630i) q^{98} +12.5164i 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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