LMFDB - Embedded newform 196.2.p.a.103.20

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			103.20
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.852071 - 1.12870i) q^{2} +(-0.330273 - 0.225176i) q^{3} +(-0.547949 - 1.92347i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(-0.535574 + 0.180915i) q^{6} +(-1.62030 - 2.09156i) q^{7} +(-2.63793 - 1.02046i) q^{8} +(-1.03765 - 2.64388i) q^{9} +O(q^{10})$	\(q+(0.852071 - 1.12870i) q^{2} +(-0.330273 - 0.225176i) q^{3} +(-0.547949 - 1.92347i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(-0.535574 + 0.180915i) q^{6} +(-1.62030 - 2.09156i) q^{7} +(-2.63793 - 1.02046i) q^{8} +(-1.03765 - 2.64388i) q^{9} +(-0.181840 + 0.206727i) q^{10} +(4.10220 + 1.61000i) q^{11} +(-0.252148 + 0.758657i) q^{12} +(2.89899 - 2.31187i) q^{13} +(-3.74137 + 0.0466832i) q^{14} +(0.0608423 + 0.0485201i) q^{15} +(-3.39950 + 2.10793i) q^{16} +(4.17672 + 4.50144i) q^{17} +(-3.86831 - 1.08158i) q^{18} +(-2.69573 + 4.66913i) q^{19} +(0.0783936 + 0.381390i) q^{20} +(0.0641719 + 1.05564i) q^{21} +(5.31258 - 3.25835i) q^{22} +(2.58949 - 2.79080i) q^{23} +(0.641452 + 0.931030i) q^{24} +(-4.90668 - 0.739562i) q^{25} +(-0.139270 - 5.24198i) q^{26} +(-0.519478 + 2.27598i) q^{27} +(-3.13522 + 4.26268i) q^{28} +(-1.16681 - 5.11213i) q^{29} +(0.106607 - 0.0273304i) q^{30} +(4.63766 + 8.03266i) q^{31} +(-0.517387 + 5.63314i) q^{32} +(-0.992315 - 1.45546i) q^{33} +(8.63966 - 0.878742i) q^{34} +(0.284132 + 0.429623i) q^{35} +(-4.51686 + 3.44460i) q^{36} +(10.0178 + 3.09008i) q^{37} +(2.97312 + 7.02111i) q^{38} +(-1.47804 + 0.110764i) q^{39} +(0.497274 + 0.236488i) q^{40} +(-1.28140 - 2.66086i) q^{41} +(1.24618 + 0.827049i) q^{42} +(0.871772 - 1.81025i) q^{43} +(0.848987 - 8.77268i) q^{44} +(0.162981 + 0.528372i) q^{45} +(-0.943565 - 5.30073i) 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} +(-6.03532 - 4.30935i) q^{52} +(-5.82431 + 1.79656i) q^{53} +(2.12628 + 2.52564i) q^{54} +(-0.772968 - 0.372242i) q^{55} +(2.13987 + 7.17084i) q^{56} +(1.94170 - 0.935075i) q^{57} +(-6.76429 - 3.03891i) q^{58} +(-0.925691 - 12.3525i) q^{59} +(0.0599887 - 0.143615i) q^{60} +(2.27555 - 7.37716i) q^{61} +(13.0181 + 1.60985i) q^{62} +(-3.84854 + 6.45419i) q^{63} +(5.91731 + 5.38382i) q^{64} +(-0.596437 + 0.406644i) q^{65} +(-2.48831 - 0.120124i) q^{66} +(1.40118 - 0.808972i) q^{67} +(6.36976 - 10.5004i) q^{68} +(-1.48366 + 0.338636i) q^{69} +(0.727018 + 0.0453686i) q^{70} +(-4.57108 - 1.04332i) q^{71} +(0.0392500 + 8.03325i) q^{72} +(-2.28410 + 15.1540i) q^{73} +(12.0237 - 8.67416i) q^{74} +(1.45401 + 1.34913i) q^{75} +(10.4581 + 2.62671i) q^{76} +(-3.27940 - 11.1887i) q^{77} +(-1.13437 + 1.76265i) q^{78} +(-2.58376 - 1.49174i) q^{79} +(0.690638 - 0.359770i) q^{80} +(-5.56201 + 5.16079i) q^{81} +(-4.09518 - 0.820918i) q^{82} +(-0.292327 + 0.366567i) q^{83} +(1.99533 - 0.701870i) q^{84} +(-0.745368 - 0.934662i) q^{85} +(-1.30043 - 2.52644i) q^{86} +(-0.765765 + 1.95114i) q^{87} +(-9.17837 - 8.43320i) q^{88} +(-10.1900 + 3.99930i) q^{89} +(0.735248 + 0.266253i) q^{90} +(-9.53265 - 2.31749i) q^{91} +(-6.78694 - 3.45159i) q^{92} +(0.277072 - 3.69726i) q^{93} +(0.545589 - 1.00577i) q^{94} +(0.591270 - 0.867234i) q^{95} +(1.43933 - 1.74397i) q^{96} +4.71195i q^{97} +(6.15978 + 7.74965i) 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 $

$2$	0.852071	−	1.12870i	0.602505	−	0.798115i
$2$	0.852071	−	1.12870i	0.602505	−	0.798115i
$3$	−0.330273	−	0.225176i	−0.190683	−	0.130006i	0.464215	−	0.885722i	$-0.346336\pi$
$3$	−0.330273	−	0.225176i	−0.190683	−	0.130006i	−0.654899	+	0.755717i	$0.727289\pi$
$4$	−0.547949	−	1.92347i	−0.273975	−	0.961737i
$5$	−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	$0.537671\pi$
$6$	−0.535574	+	0.180915i	−0.218647	+	0.0738580i
$7$	−1.62030	−	2.09156i	−0.612416	−	0.790535i
$7$	−1.62030	−	2.09156i	−0.612416	−	0.790535i
$8$	−2.63793	−	1.02046i	−0.932648	−	0.360789i
$9$	−1.03765	−	2.64388i	−0.345882	−	0.881294i
$10$	−0.181840	+	0.206727i	−0.0575028	+	0.0653729i
$11$	4.10220	+	1.61000i	1.23686	+	0.485432i	0.891493	−	0.453035i	$-0.149659\pi$
$11$	4.10220	+	1.61000i	1.23686	+	0.485432i	0.345368	+	0.938467i	$0.387754\pi$
$12$	−0.252148	+	0.758657i	−0.0727889	+	0.219005i
$13$	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	$0.113803\pi$
$14$	−3.74137	+	0.0466832i	−0.999922	+	0.0124766i
$15$	0.0608423	+	0.0485201i	0.0157094	+	0.0125278i
$16$	−3.39950	+	2.10793i	−0.849876	+	0.526983i
$17$	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	$0.494513\pi$
$18$	−3.86831	−	1.08158i	−0.911770	−	0.254930i
$19$	−2.69573	+	4.66913i	−0.618442	+	1.07117i	0.371328	+	0.928502i	$0.378902\pi$
$19$	−2.69573	+	4.66913i	−0.618442	+	1.07117i	−0.989770	+	0.142671i	$0.954431\pi$
$20$	0.0783936	+	0.381390i	0.0175293	+	0.0852814i
$21$	0.0641719	+	1.05564i	0.0140034	+	0.230359i
$22$	5.31258	−	3.25835i	1.13265	−	0.694682i
$23$	2.58949	−	2.79080i	0.539945	−	0.581922i	−0.402862	−	0.915261i	$-0.631985\pi$
$23$	2.58949	−	2.79080i	0.539945	−	0.581922i	0.942807	+	0.333338i	$0.108175\pi$
$24$	0.641452	+	0.931030i	0.130936	+	0.190046i
$25$	−4.90668	−	0.739562i	−0.981335	−	0.147912i
$26$	−0.139270	−	5.24198i	−0.0273131	−	1.02804i
$27$	−0.519478	+	2.27598i	−0.0999736	+	0.438013i
$28$	−3.13522	+	4.26268i	−0.592501	+	0.805570i
$29$	−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	$-0.233285\pi$
$30$	0.106607	−	0.0273304i	0.0194637	−	0.00498983i
$31$	4.63766	+	8.03266i	0.832948	+	1.44271i	0.895690	+	0.444679i	$0.146682\pi$
$31$	4.63766	+	8.03266i	0.832948	+	1.44271i	−0.0627420	+	0.998030i	$0.519985\pi$
$32$	−0.517387	+	5.63314i	−0.0914619	+	0.995809i
$33$	−0.992315	−	1.45546i	−0.172740	−	0.253363i
$34$	8.63966	−	0.878742i	1.48169	−	0.150703i
$35$	0.284132	+	0.429623i	0.0480270	+	0.0726195i
$36$	−4.51686	+	3.44460i	−0.752810	+	0.574100i
$37$	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	$0.264612\pi$
$38$	2.97312	+	7.02111i	0.482304	+	1.13897i
$39$	−1.47804	+	0.110764i	−0.236675	+	0.0177364i
$40$	0.497274	+	0.236488i	0.0786259	+	0.0373921i
$41$	−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	$0.931217\pi$
$42$	1.24618	+	0.827049i	0.192290	+	0.127616i
$43$	0.871772	−	1.81025i	0.132944	−	0.276061i	−0.823861	−	0.566792i	$-0.808184\pi$
$43$	0.871772	−	1.81025i	0.132944	−	0.276061i	0.956805	+	0.290731i	$0.0938986\pi$
$44$	0.848987	−	8.77268i	0.127990	−	1.32253i
$45$	0.162981	+	0.528372i	0.0242958	+	0.0787651i
$46$	−0.943565	−	5.30073i	−0.139121	−	0.781550i
$47$	0.800046	−	0.120588i	0.116699	−	0.0175895i	−0.0904332	−	0.995903i	$-0.528825\pi$
$47$	0.800046	−	0.120588i	0.116699	−	0.0175895i	0.207132	+	0.978313i	$0.433587\pi$
$48$	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
$52$	−6.03532	−	4.30935i	−0.836948	−	0.597599i
$53$	−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	$0.542246\pi$
$54$	2.12628	+	2.52564i	0.289350	+	0.343696i
$55$	−0.772968	−	0.372242i	−0.104227	−	0.0501931i
$56$	2.13987	+	7.17084i	0.285952	+	0.958244i
$57$	1.94170	−	0.935075i	0.257185	−	0.123854i
$58$	−6.76429	−	3.03891i	−0.888195	−	0.399029i
$59$	−0.925691	−	12.3525i	−0.120515	−	1.60816i	−0.650065	−	0.759879i	$-0.725258\pi$
$59$	−0.925691	−	12.3525i	−0.120515	−	1.60816i	0.529550	−	0.848279i	$-0.322361\pi$
$60$	0.0599887	−	0.143615i	0.00774451	−	0.0185406i
$61$	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	$-0.0693124\pi$
$62$	13.0181	+	1.60985i	1.65330	+	0.204451i
$63$	−3.84854	+	6.45419i	−0.484870	+	0.813151i
$64$	5.91731	+	5.38382i	0.739663	+	0.672977i
$65$	−0.596437	+	0.406644i	−0.0739789	+	0.0504380i
$66$	−2.48831	−	0.120124i	−0.306289	−	0.0147862i
$67$	1.40118	−	0.808972i	0.171182	−	0.0988317i	−0.411961	−	0.911201i	$-0.635156\pi$
$67$	1.40118	−	0.808972i	0.171182	−	0.0988317i	0.583143	+	0.812370i	$0.301823\pi$
$68$	6.36976	−	10.5004i	0.772447	−	1.27336i
$69$	−1.48366	+	0.338636i	−0.178612	+	0.0407670i
$70$	0.727018	+	0.0453686i	0.0868953	+	0.00542259i
$71$	−4.57108	−	1.04332i	−0.542487	−	0.123819i	−0.0575084	−	0.998345i	$-0.518316\pi$
$71$	−4.57108	−	1.04332i	−0.542487	−	0.123819i	−0.484979	+	0.874526i	$0.661173\pi$
$72$	0.0392500	+	8.03325i	0.00462566	+	0.946727i
$73$	−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	$0.693478\pi$
$74$	12.0237	−	8.67416i	1.39772	−	1.00835i
$75$	1.45401	+	1.34913i	0.167895	+	0.155784i
$76$	10.4581	+	2.62671i	1.19962	+	0.301304i
$77$	−3.27940	−	11.1887i	−0.373722	−	1.27507i
$78$	−1.13437	+	1.76265i	−0.128443	+	0.199580i
$79$	−2.58376	−	1.49174i	−0.290696	−	0.167834i	0.347560	−	0.937658i	$-0.387010\pi$
$79$	−2.58376	−	1.49174i	−0.290696	−	0.167834i	−0.638256	+	0.769824i	$0.720344\pi$
$80$	0.690638	−	0.359770i	0.0772157	−	0.0402235i
$81$	−5.56201	+	5.16079i	−0.618001	+	0.573421i
$82$	−4.09518	−	0.820918i	−0.452237	−	0.0906553i
$83$	−0.292327	+	0.366567i	−0.0320871	+	0.0402359i	−0.797616	−	0.603165i	$-0.793906\pi$
$83$	−0.292327	+	0.366567i	−0.0320871	+	0.0402359i	0.765529	+	0.643401i	$0.222477\pi$
$84$	1.99533	−	0.701870i	0.217709	−	0.0765803i
$85$	−0.745368	−	0.934662i	−0.0808465	−	0.101378i
$86$	−1.30043	−	2.52644i	−0.140229	−	0.272433i
$87$	−0.765765	+	1.95114i	−0.0820986	+	0.209184i
$88$	−9.17837	−	8.43320i	−0.978417	−	0.898983i
$89$	−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	$0.577969\pi$
$90$	0.735248	+	0.266253i	0.0775020	+	0.0280655i
$91$	−9.53265	−	2.31749i	−0.999294	−	0.242939i
$92$	−6.78694	−	3.45159i	−0.707587	−	0.359853i
$93$	0.277072	−	3.69726i	0.0287310	−	0.383388i
$94$	0.545589	−	1.00577i	0.0562732	−	0.103737i
$95$	0.591270	−	0.867234i	0.0606630	−	0.0889763i
$96$	1.43933	−	1.74397i	0.146901	−	0.177993i
$97$			4.71195i			0.478426i	0.970967	+	0.239213i	$0.0768894\pi$
$97$			4.71195i			0.478426i	−0.970967	+	0.239213i	$0.923111\pi$
$98$	6.15978	+	7.74965i	0.622232	+	0.782833i
$99$		−	12.5164i		−	1.25794i
$100$	1.26608	+	9.84311i	0.126608	+	0.984311i
$101$	−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	$0.193947\pi$
$102$	−3.05132	−	1.65522i	−0.302126	−	0.163891i
$103$	0.191758	−	2.55883i	0.0188945	−	0.252129i	−0.979756	−	0.200195i	$-0.935842\pi$
$103$	0.191758	−	2.55883i	0.0188945	−	0.252129i	0.998651	−	0.0519340i	$-0.0165385\pi$
$104$	−10.0065	+	3.14022i	−0.981219	+	0.307924i
$105$	0.00289991	−	0.205873i	0.000283002	−	0.0200911i
$106$	−2.93494	+	8.10473i	−0.285067	+	0.787201i
$107$	8.20581	−	3.22054i	0.793286	−	0.311342i	0.0661272	−	0.997811i	$-0.478936\pi$
$107$	8.20581	−	3.22054i	0.793286	−	0.311342i	0.727159	+	0.686469i	$0.240840\pi$
$108$	4.66244	−	0.247920i	0.448644	−	0.0238561i
$109$	−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	$0.209104\pi$
$110$	−1.07877	+	0.555276i	−0.102857	+	0.0529435i
$111$	−2.61279	−	3.27634i	−0.247995	−	0.310976i
$112$	9.91709	+	3.69478i	0.937076	+	0.349124i
$113$	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	$0.188802\pi$
$114$	0.599046	−	2.98836i	0.0561058	−	0.279886i
$115$	−0.543318	+	0.504125i	−0.0506647	+	0.0470099i
$116$	−9.19369	+	5.04552i	−0.853613	+	0.468464i
$117$	−9.12044	−	5.26569i	−0.843185	−	0.486813i
$118$	−14.7311	−	9.48037i	−1.35610	−	0.872739i
$119$	2.64748	−	16.0295i	0.242694	−	1.46943i
$120$	−0.110985	−	0.190080i	−0.0101315	−	0.0173518i
$121$	6.17242	+	5.72717i	0.561129	+	0.520652i
$122$	−6.38770	−	8.85429i	−0.578316	−	0.801630i
$123$	−0.175950	+	1.16735i	−0.0158649	+	0.105257i
$124$	12.9094	−	13.3219i	1.15930	−	1.19634i
$125$	1.89081	+	0.431566i	0.169119	+	0.0386004i
$126$	4.00564	+	9.84329i	0.356851	+	0.876910i
$127$	−4.30597	+	0.982809i	−0.382093	+	0.0872102i	−0.409253	−	0.912421i	$-0.634211\pi$
$127$	−4.30597	+	0.982809i	−0.382093	+	0.0872102i	0.0271602	+	0.999631i	$0.491354\pi$
$128$	11.1187	−	2.09150i	0.982764	−	0.184864i
$129$	−0.695549	+	0.401575i	−0.0612397	+	0.0353567i
$130$	−0.0492259	+	1.01969i	−0.00431740	+	0.0894328i
$131$	−6.19021	+	4.22042i	−0.540841	+	0.368739i	−0.802715	−	0.596363i	$-0.796612\pi$
$131$	−6.19021	+	4.22042i	−0.540841	+	0.368739i	0.261874	+	0.965102i	$0.415660\pi$
$132$	−2.25580	+	2.70621i	−0.196342	+	0.235545i
$133$	14.1337	−	1.92713i	1.22554	−	0.167103i
$134$	0.280815	−	2.27082i	0.0242587	−	0.196169i
$135$	0.133962	−	0.434296i	0.0115297	−	0.0373782i
$136$	−6.42433	−	16.1366i	−0.550882	−	1.38371i
$137$	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	$0.943888\pi$
$138$	−0.881964	+	1.96316i	−0.0750778	+	0.167115i
$139$	−19.5010	+	9.39119i	−1.65405	+	0.796550i	−0.654887	+	0.755727i	$0.727284\pi$
$139$	−19.5010	+	9.39119i	−1.65405	+	0.796550i	−0.999166	+	0.0408233i	$0.987002\pi$
$140$	0.670679	−	0.781931i	0.0566827	−	0.0660853i
$141$	−0.291387	−	0.140325i	−0.0245392	−	0.0118175i
$142$	−5.07249	+	4.27042i	−0.425673	+	0.358365i
$143$	15.6144	−	4.81639i	1.30574	−	0.402767i
$144$	9.10061	+	6.80060i	0.758384	+	0.566716i
$145$	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	$0.287184\pi$
$150$	2.76169	−	0.491599i	0.225491	−	0.0401389i
$151$	4.42620	+	14.3494i	0.360199	+	1.16774i	0.936550	+	0.350534i	$0.114000\pi$
$151$	4.42620	+	14.3494i	0.360199	+	1.16774i	−0.576351	+	0.817202i	$0.695524\pi$
$152$	11.8758	−	9.56594i	0.963255	−	0.775900i
$153$	7.56730	−	15.7137i	0.611780	−	1.27037i
$154$	−15.4230	−	5.83208i	−1.24282	−	0.469963i
$155$	−0.783479	−	1.62691i	−0.0629305	−	0.130677i
$156$	1.02294	+	2.78227i	0.0819008	+	0.222760i
$157$	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	$0.441291\pi$
$158$	−3.88528	+	1.64524i	−0.309096	+	0.130888i
$159$	2.32816	+	0.718141i	0.184635	+	0.0569523i
$160$	0.182398	−	1.08608i	0.0144199	−	0.0858619i
$161$	−10.0329	−	0.894126i	−0.790701	−	0.0704670i
$162$	1.08578	+	10.6752i	0.0853070	+	0.838725i
$163$	−1.69172	−	2.48130i	−0.132506	−	0.194350i	0.754252	−	0.656586i	$-0.228000\pi$
$163$	−1.69172	−	2.48130i	−0.132506	−	0.194350i	−0.886757	+	0.462235i	$0.847048\pi$
$164$	−4.41596	+	3.92277i	−0.344828	+	0.306317i
$165$	0.171470	+	0.296996i	0.0133490	+	0.0231211i
$166$	0.164662	+	0.642292i	0.0127802	+	0.0498515i
$167$	0.423853	+	1.85702i	0.0327987	+	0.143701i	0.988676	−	0.150065i	$-0.0479484\pi$
$167$	0.423853	+	1.85702i	0.0327987	+	0.143701i	−0.955877	+	0.293766i	$0.905091\pi$
$168$	0.907962	−	2.85018i	0.0700508	−	0.219896i
$169$	0.166644	−	0.730116i	0.0128188	−	0.0561627i
$170$	−1.69006	+	0.0449019i	−0.129622	+	0.00344382i
$171$	15.1418	+	2.28227i	1.15793	+	0.174529i
$172$	−3.95966	−	0.684904i	−0.301921	−	0.0522234i
$173$	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	$0.198912\pi$
$174$	1.54977	+	2.52683i	0.117488	+	0.191558i
$175$	6.40345	+	11.4609i	0.484056	+	0.866364i
$176$	−17.3392	+	3.17398i	−1.30699	+	0.239248i
$177$	−2.47576	+	4.28814i	−0.186089	+	0.322316i
$178$	−4.16862	+	14.9092i	−0.312451	+	1.11749i
$179$	11.4196	+	12.3074i	0.853539	+	0.919897i	0.997570	−	0.0696766i	$-0.0221967\pi$
$179$	11.4196	+	12.3074i	0.853539	+	0.919897i	−0.144030	+	0.989573i	$0.546006\pi$
$180$	0.927005	−	0.603011i	0.0690949	−	0.0449458i
$181$	−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	$0.840125\pi$
$182$	−10.7383	+	8.78488i	−0.795973	+	0.651179i
$183$	−2.41272	+	1.92408i	−0.178353	+	0.142232i
$184$	−9.67878	+	4.71945i	−0.713529	+	0.347923i
$185$	−1.89987	−	0.745644i	−0.139681	−	0.0548209i
$186$	−3.93703	−	3.46306i	−0.288677	−	0.253924i
$187$	9.88647	+	25.1903i	0.722970	+	1.84210i
$188$	−0.670332	−	1.47279i	−0.0488890	−	0.107414i
$189$	5.60207	−	2.60126i	0.407490	−	0.189214i
$190$	−0.475047	−	1.40631i	−0.0344635	−	0.102025i
$191$	6.21485	+	0.465739i	0.449691	+	0.0336997i	0.297651	−	0.954675i	$-0.403797\pi$
$191$	6.21485	+	0.465739i	0.449691	+	0.0336997i	0.152040	+	0.988374i	$0.451416\pi$
$192$	−0.742019	−	3.11057i	−0.0535506	−	0.224486i
$193$	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	$0.669738\pi$
$194$	5.31840	+	4.01491i	0.381839	+	0.288254i
$195$	0.288554			0.0206638
$196$	13.9956	−	0.349318i	0.999689	−	0.0249513i
$197$	9.35286			0.666364			0.333182	−	0.942863i	$-0.391878\pi$
$197$	9.35286			0.666364			0.333182	+	0.942863i	$0.391878\pi$
$198$	−14.1273	−	10.6648i	−1.00398	−	0.757916i
$199$	−13.4363	−	9.16071i	−0.952474	−	0.649386i	−0.0159065	−	0.999873i	$-0.505063\pi$
$199$	−13.4363	−	9.16071i	−0.952474	−	0.649386i	−0.936567	+	0.350488i	$0.886016\pi$
$200$	12.1888	+	6.95800i	0.861875	+	0.492005i
$201$	−0.644934	−	0.0483311i	−0.0454901	−	0.00340901i
$202$	0.0992029	+	0.293677i	0.00697989	+	0.0206631i
$203$	−8.80174	+	10.7236i	−0.617761	+	0.752652i
$204$	−4.46820	+	2.03367i	−0.312836	+	0.142385i
$205$	0.210057	+	0.535216i	0.0146710	+	0.0373811i
$206$	−2.72477	−	2.39674i	−0.189844	−	0.166989i
$207$	−10.0655	−	3.95043i	−0.699602	−	0.274574i
$208$	−4.98187	+	13.9701i	−0.345431	+	0.968651i
$209$	−18.5757	+	14.8136i	−1.28491	+	1.02468i
$210$	−0.229899	−	0.178691i	−0.0158645	−	0.0123309i
$211$	5.84824	+	4.66382i	0.402609	+	0.321070i	0.803773	−	0.594936i	$-0.202823\pi$
$211$	5.84824	+	4.66382i	0.402609	+	0.321070i	−0.401164	+	0.916006i	$0.631394\pi$
$212$	6.64707	+	10.2185i	0.456522	+	0.701809i
$213$	1.27477	+	1.37388i	0.0873461	+	0.0941367i
$214$	3.35689	−	12.0061i	0.229473	−	0.820718i
$215$	−0.195580	+	0.338754i	−0.0133384	+	0.0231029i
$216$	3.69290	−	5.47377i	0.251270	−	0.372443i
$217$	9.28639	−	22.7153i	0.630401	−	1.54201i
$218$	4.30990	+	7.02708i	0.291903	+	0.475934i
$219$	4.16670	−	4.49063i	0.281559	−	0.303449i
$220$	−0.292450	+	1.69075i	−0.0197170	+	0.113991i
$221$	22.5150	+	3.39359i	1.51452	+	0.228278i
$222$	−5.92431	+	0.157398i	−0.397613	+	0.0105639i
$223$	−2.47878	+	10.8603i	−0.165992	+	0.727257i	0.821581	+	0.570092i	$0.193093\pi$
$223$	−2.47878	+	10.8603i	−0.165992	+	0.727257i	−0.987572	+	0.157165i	$0.949765\pi$
$224$	12.6204	−	8.04524i	0.843235	−	0.537545i
$225$	3.13608	+	13.7401i	0.209072	+	0.916005i
$226$	−0.597137	−	2.32923i	−0.0397210	−	0.154938i
$227$	8.60483	+	14.9040i	0.571123	+	0.989214i	0.996451	+	0.0841746i	$0.0268253\pi$
$227$	8.60483	+	14.9040i	0.571123	+	0.989214i	−0.425328	+	0.905039i	$0.639841\pi$
$228$	−2.86255	−	3.22244i	−0.189577	−	0.213412i
$229$	−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	$0.901281\pi$
$230$	0.106063	+	1.04280i	0.00699360	+	0.0687600i
$231$	−1.43633	+	4.43377i	−0.0945036	+	0.291720i
$232$	−2.13879	+	14.6761i	−0.140418	+	0.963534i
$233$	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	$0.585740\pi$
$234$	−13.7147	+	5.80754i	−0.896556	+	0.379651i
$235$	−0.157073	+	0.0117710i	−0.0102463	+	0.000767856i
$236$	−23.2525	+	8.54908i	−1.51361	+	0.556498i
$237$	0.517444	+	1.07448i	0.0336116	+	0.0697952i
$238$	−15.8368	−	16.6465i	−1.02655	−	1.07903i
$239$	10.0439	−	20.8563i	0.649683	−	1.34908i	−0.272435	−	0.962174i	$-0.587829\pi$
$239$	10.0439	−	20.8563i	0.649683	−	1.34908i	0.922119	−	0.386907i	$-0.126457\pi$
$240$	−0.309111	−	0.0366929i	−0.0199530	−	0.00236852i
$241$	−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	$-0.270908\pi$
$242$	11.7236	−	2.08688i	0.753623	−	0.134150i
$243$	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
$248$	−4.03676	−	25.9221i	−0.256334	−	1.64606i
$249$	0.179090	−	0.0552419i	0.0113494	−	0.00350082i
$250$	2.09822	−	1.76644i	0.132703	−	0.111720i
$251$	−0.769700	−	0.370668i	−0.0485830	−	0.0233964i	0.409434	−	0.912340i	$-0.365726\pi$
$251$	−0.769700	−	0.370668i	−0.0485830	−	0.0233964i	−0.458018	+	0.888943i	$0.651440\pi$
$252$	14.5233	+	3.86600i	0.914879	+	0.243535i
$253$	15.1158	−	7.27938i	0.950321	−	0.457650i
$254$	−2.55969	+	5.69759i	−0.160609	+	0.357499i
$255$	0.0357112	+	0.476533i	0.00223632	+	0.0298417i
$256$	7.11325	−	14.3318i	0.444578	−	0.895740i
$257$	−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	$0.969519\pi$
$258$	−0.139397	+	1.12724i	−0.00867849	+	0.0701789i
$259$	−9.76875	−	25.9597i	−0.607001	−	1.61306i
$260$	1.10899	+	0.924411i	0.0687764	+	0.0573295i
$261$	−12.3051	+	8.38949i	−0.761668	+	0.519297i
$262$	−0.510899	+	10.5830i	−0.0315635	+	0.653821i
$263$	−4.28173	+	2.47206i	−0.264023	+	0.152434i	−0.626168	−	0.779688i	$-0.715378\pi$
$263$	−4.28173	+	2.47206i	−0.264023	+	0.152434i	0.362145	+	0.932122i	$0.382044\pi$
$264$	1.13241	+	4.85201i	0.0696950	+	0.298621i
$265$	1.15685	−	0.264044i	0.0710650	−	0.0162201i
$266$	9.86772	−	17.5948i	0.605029	−	1.07881i
$267$	4.26604	+	0.973696i	0.261078	+	0.0595893i
$268$	−2.32381	−	2.25186i	−0.141949	−	0.137554i
$269$	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	$-0.157371\pi$
$270$	−0.376046	−	0.521255i	−0.0228854	−	0.0317226i
$271$	−18.1498	−	16.8406i	−1.10252	−	1.02299i	−0.999599	−	0.0283020i	$-0.990990\pi$
$271$	−18.1498	−	16.8406i	−1.10252	−	1.02299i	−0.102923	−	0.994689i	$-0.532820\pi$
$272$	−23.6875	−	6.49840i	−1.43627	−	0.394024i
$273$	2.62653	+	2.91193i	0.158965	+	0.176238i
$274$	2.82032	+	1.81505i	0.170382	+	0.109651i
$275$	−18.9375	−	10.9336i	−1.14197	−	0.659319i
$276$	1.46433	+	2.66823i	0.0881421	+	0.160608i
$277$	−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	$0.301114\pi$
$278$	−6.01636	+	30.0128i	−0.360838	+	1.80005i
$279$	16.4252	−	20.5965i	0.983348	−	1.23308i
$280$	−0.311103	−	1.42326i	−0.0185920	−	0.0850560i
$281$	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	$0.762163\pi$
$282$	−0.406668	+	0.209324i	−0.0242167	+	0.0124650i
$283$	3.96822	−	10.1109i	0.235886	−	0.601028i	−0.763089	−	0.646294i	$-0.776318\pi$
$283$	3.96822	−	10.1109i	0.235886	−	0.601028i	0.998975	+	0.0452654i	$0.0144133\pi$
$284$	0.497922	+	9.36404i	0.0295462	+	0.555653i
$285$	−0.390561	+	0.153284i	−0.0231349	+	0.00907976i
$286$	7.86826	−	21.7279i	0.465260	−	1.28480i
$287$	−3.48910	+	6.99154i	−0.205955	+	0.412697i
$288$	15.4302	−	4.47731i	0.909235	−	0.263828i
$289$	−1.54751	+	20.6500i	−0.0910298	+	1.21471i
$290$	1.26899	+	0.688377i	0.0745176	+	0.0404229i
$291$	1.06102	−	1.55623i	0.0621980	−	0.0912278i
$292$	30.3999	−	3.91022i	1.77902	−	0.228828i
$293$		−	17.6595i		−	1.03168i	−0.856686	−	0.515838i	$-0.827480\pi$
$293$		−	17.6595i		−	1.03168i	0.856686	−	0.515838i	$-0.172520\pi$
$294$	−0.289371	−	3.94654i	−0.0168765	−	0.230167i
$295$			2.41155i			0.140406i
$296$	−23.2729	−	18.3742i	−1.35271	−	1.06798i
$297$	−5.79533	+	8.50019i	−0.336279	+	0.493231i
$298$	8.16532	−	15.0524i	0.473004	−	0.871960i
$299$	1.05493	−	14.0771i	0.0610082	−	0.814098i
$300$	1.79828	−	3.53600i	0.103824	−	0.204151i
$301$	−5.19878	+	1.10979i	−0.299653	+	0.0639673i
$302$	19.9677	+	7.23083i	1.14901	+	0.416087i
$303$	0.0815600	−	0.0320099i	0.00468550	−	0.00183892i
$304$	−0.678086	−	21.5551i	−0.0388909	−	1.23627i
$305$	−0.549097	+	1.39908i	−0.0314412	+	0.0801109i
$306$	−11.2882	−	21.9304i	−0.645304	−	1.25368i
$307$	4.68520	+	5.87506i	0.267399	+	0.335307i	0.897344	−	0.441332i	$-0.145494\pi$
$307$	4.68520	+	5.87506i	0.267399	+	0.335307i	−0.629945	+	0.776640i	$0.716923\pi$
$308$	−19.7242	+	12.4387i	−1.12389	+	0.708759i
$309$	−0.639521	+	0.801933i	−0.0363811	+	0.0456204i
$310$	−2.50388	−	0.501927i	−0.142211	−	0.0285076i
$311$	−19.4112	+	18.0110i	−1.10071	+	1.02131i	−0.101060	+	0.994880i	$0.532223\pi$
$311$	−19.4112	+	18.0110i	−1.10071	+	1.02131i	−0.999651	+	0.0264294i	$0.991586\pi$
$312$	4.01198	+	1.21610i	0.227134	+	0.0688480i
$313$	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	$0.374533\pi$
$314$	2.09862	−	3.26094i	0.118432	−	0.184025i
$315$	0.841044	−	1.19701i	0.0473875	−	0.0674437i
$316$	−1.45355	+	5.78720i	−0.0817683	+	0.325555i
$317$	−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	$0.986527\pi$
$318$	2.79433	−	2.01589i	0.156698	−	0.113046i
$319$	3.44402	−	22.8496i	0.192828	−	1.27933i
$320$	−1.07044	−	1.13129i	−0.0598396	−	0.0632409i
$321$	−3.43535	−	0.784096i	−0.191743	−	0.0437640i
$322$	−9.55793	+	10.5623i	−0.532643	+	0.588614i
$323$	−32.2771	+	7.36704i	−1.79595	+	0.409913i
$324$	12.9743	+	7.87053i	0.720797	+	0.437252i
$325$	−15.9342	+	9.19961i	−0.883870	+	0.510302i
$326$	−4.24212	−	0.204790i	−0.234949	−	0.0113423i
$327$	1.92517	−	1.31256i	0.106462	−	0.0725847i
$328$	0.664934	+	8.32679i	0.0367149	+	0.459770i
$329$	−1.54853	−	1.47796i	−0.0853733	−	0.0814824i
$330$	0.481325	+	0.0595218i	0.0264961	+	0.00327657i
$331$	3.22837	−	10.4661i	0.177447	−	0.575270i	−0.822531	−	0.568720i	$-0.807439\pi$
$331$	3.22837	−	10.4661i	0.177447	−	0.575270i	0.999979	−	0.00655005i	$-0.00208496\pi$
$332$	0.865262	+	0.361424i	0.0474874	+	0.0198357i
$333$	−2.22513	−	29.6923i	−0.121936	−	1.62713i
$334$	2.45718	+	1.10391i	0.134451	+	0.0604033i
$335$	−0.283791	+	0.136667i	−0.0155052	+	0.00746689i
$336$	−2.44337	−	3.45338i	−0.133297	−	0.188397i
$337$	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	$0.613835\pi$
$338$	−0.682092	−	0.810202i	−0.0371009	−	0.0440692i
$339$	−0.649459	+	0.200332i	−0.0352738	+	0.0108805i
$340$	−1.38937	+	1.94584i	−0.0753494	+	0.105528i
$341$	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
$346$	−0.800538	−	4.49723i	−0.0430372	−	0.241773i
$347$	−6.69590	−	21.7076i	−0.359455	−	1.16532i	−0.937107	−	0.349041i	$-0.886507\pi$
$347$	−6.69590	−	21.7076i	−0.359455	−	1.16532i	0.577653	−	0.816283i	$-0.303969\pi$
$348$	4.17256	+	0.403805i	0.223673	+	0.0216462i
$349$	−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	$0.232914\pi$
$350$	18.3922	+	2.53791i	0.983104	+	0.135657i
$351$	3.75581	+	7.79902i	0.200470	+	0.416281i
$352$	−11.1918	+	22.2753i	−0.596523	+	1.18728i
$353$	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	$0.308768\pi$
$354$	2.73052	+	6.44820i	0.145126	+	0.342718i
$355$	0.872238	+	0.269050i	0.0462936	+	0.0142797i
$356$	13.2762	+	17.4089i	0.703635	+	0.922668i
$357$	−4.48387	+	4.69798i	−0.237311	+	0.248643i
$358$	23.6217	−	2.40257i	1.24845	−	0.126980i
$359$	−3.74259	−	5.48938i	−0.197527	−	0.289718i	0.714678	−	0.699454i	$-0.246573\pi$
$359$	−3.74259	−	5.48938i	−0.197527	−	0.289718i	−0.912204	+	0.409736i	$0.865621\pi$
$360$	0.109252	−	1.56012i	0.00575811	−	0.0822257i
$361$	−5.03387	−	8.71891i	−0.264940	−	0.458890i
$362$	−14.1957	+	3.63929i	−0.746108	+	0.191277i
$363$	−0.748961	−	3.28141i	−0.0393103	−	0.172230i
$364$	0.765772	+	19.6057i	0.0401374	+	1.02762i
$365$	0.663898	−	2.90873i	0.0347500	−	0.152250i
$366$	0.115909	+	4.36270i	0.00605865	+	0.228042i
$367$	−21.3368	−	3.21600i	−1.11377	−	0.167874i	−0.433727	−	0.901045i	$-0.642802\pi$
$367$	−21.3368	−	3.21600i	−1.11377	−	0.167874i	−0.680045	+	0.733171i	$0.738040\pi$
$368$	−2.92015	+	14.9458i	−0.152223	+	0.779104i
$369$	−5.70536	+	6.14892i	−0.297009	+	0.320100i
$370$	−2.46044	+	1.50905i	−0.127912	+	0.0784518i
$371$	13.1948	+	9.27093i	0.685038	+	0.481323i
$372$	−7.26341	+	1.49297i	−0.376590	+	0.0774070i
$373$	−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	$0.900643\pi$
$374$	36.8564	+	10.3050i	1.90580	+	0.532861i
$375$	−0.527306	−	0.568301i	−0.0272300	−	0.0293469i
$376$	−2.23352	−	0.498317i	−0.115185	−	0.0256988i
$377$	−15.2011	−	12.1225i	−0.782899	−	0.624341i
$378$	1.83731	−	8.53954i	0.0945009	−	0.439226i
$379$	−16.2053	+	12.9233i	−0.832408	+	0.663823i	−0.944005	−	0.329930i	$-0.892975\pi$
$379$	−16.2053	+	12.9233i	−0.832408	+	0.663823i	0.111597	+	0.993754i	$0.464403\pi$
$380$	−1.99209	−	0.662093i	−0.102192	−	0.0339646i
$381$	1.64345	+	0.645007i	0.0841966	+	0.0330447i
$382$	5.82118	−	6.61789i	0.297837	−	0.338601i
$383$	−0.540532	−	1.37725i	−0.0276199	−	0.0703744i	0.916399	−	0.400267i	$-0.131083\pi$
$383$	−0.540532	−	1.37725i	−0.0276199	−	0.0703744i	−0.944018	+	0.329893i	$0.892987\pi$
$384$	−4.14317	−	1.81291i	−0.211430	−	0.0925144i
$385$	0.473875	+	2.21985i	0.0241509	+	0.113134i
$386$	2.42364	−	0.818695i	0.123360	−	0.0416705i
$387$	−5.69068	−	0.426458i	−0.289274	−	0.0216781i
$388$	9.06330	−	2.58191i	0.460120	−	0.131076i
$389$	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	$0.599139\pi$
$390$	0.245868	−	0.325692i	0.0124500	−	0.0164921i
$391$	23.3782			1.18229
$392$	11.5310	−	16.0946i	0.582404	−	0.812900i
$393$	2.99480			0.151068
$394$	7.96930	−	10.5566i	0.401488	−	0.531835i
$395$	0.479902	+	0.327192i	0.0241465	+	0.0164628i
$396$	−24.0749	+	6.85832i	−1.20981	+	0.344644i
$397$	−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	$0.650501\pi$
$398$	−21.7884	+	7.36003i	−1.09215	+	0.368925i
$399$	−5.10191	−	2.54609i	−0.255415	−	0.127464i
$400$	18.2392	−	7.82879i	0.911961	−	0.391440i
$401$	−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	$-0.462510\pi$
$402$	−0.604081	+	0.686758i	−0.0301288	+	0.0342524i
$403$	32.0150	+	12.5650i	1.59478	+	0.625905i
$404$	0.416003	+	0.138263i	0.0206969	+	0.00687885i
$405$	1.15488	−	0.920982i	0.0573862	−	0.0457640i
$406$	4.60411	+	19.0719i	0.228498	+	0.946521i
$407$	36.1200	+	28.8047i	1.79040	+	1.42780i
$408$	−1.51181	+	6.77611i	−0.0748457	+	0.335467i
$409$	−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	$0.956746\pi$
$410$	0.783084	+	0.218950i	0.0386737	+	0.0108132i
$411$	0.473993	−	0.820980i	0.0233803	−	0.0404959i
$412$	−5.02692	+	1.03327i	−0.247658	+	0.0509054i
$413$	−24.3361	+	21.9509i	−1.19750	+	1.08013i
$414$	−13.0354	+	7.99496i	−0.640655	+	0.392931i
$415$	0.0620846	−	0.0669113i	0.00304762	−	0.00328455i
$416$	11.5232	+	17.5266i	0.564971	+	0.859311i
$417$	8.55533	+	1.28951i	0.418956	+	0.0631475i
$418$	0.892391	+	33.5888i	0.0436483	+	1.64288i
$419$	−3.42751	+	15.0169i	−0.167445	+	0.733623i	0.819568	+	0.572982i	$0.194213\pi$
$419$	−3.42751	+	15.0169i	−0.167445	+	0.733623i	−0.987013	+	0.160641i	$0.948644\pi$
$420$	−0.397580	+	0.107230i	−0.0193999	+	0.00523228i
$421$	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	$0.883796\pi$
$422$	10.2472	−	2.62703i	0.498825	−	0.127882i
$423$	−1.14898	−	1.99010i	−0.0558656	−	0.0967620i
$424$	17.1974	+	1.20430i	0.835181	+	0.0584861i
$425$	−17.1647	−	25.1760i	−0.832612	−	1.22122i
$426$	2.63690	−	0.268200i	0.127758	−	0.0129943i
$427$	−19.1169	+	7.19377i	−0.925130	+	0.348131i
$428$	−10.6910	−	14.0190i	−0.516769	−	0.677633i
$429$	−6.24154	−	1.92526i	−0.301344	−	0.0929524i
$430$	0.215706	+	0.509395i	0.0104023	+	0.0245652i
$431$	−28.3932	+	2.12777i	−1.36765	+	0.102491i	−0.738217	−	0.674563i	$-0.764332\pi$
$431$	−28.3932	+	2.12777i	−1.36765	+	0.102491i	−0.629433	+	0.777054i	$0.716713\pi$
$432$	−3.03165	−	8.83224i	−0.145860	−	0.424941i
$433$	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	$0.620992\pi$
$434$	−17.7262	−	29.8366i	−0.850883	−	1.43220i
$435$	0.177050	−	0.367648i	0.00848889	−	0.0176274i
$436$	11.6038	+	1.12298i	0.555723	+	0.0537808i
$437$	6.05008	+	19.6139i	0.289415	+	0.938259i
$438$	−1.51827	−	8.52931i	−0.0725460	−	0.407546i
$439$	−30.6784	+	4.62403i	−1.46420	+	0.220693i	−0.832287	−	0.554345i	$-0.812969\pi$
$439$	−30.6784	+	4.62403i	−1.46420	+	0.220693i	−0.631915	+	0.775038i	$0.717731\pi$
$440$	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	$0.0692990\pi$
$443$	2.25301	+	14.9477i	0.107044	+	0.710188i	−0.869351	+	0.494195i	$0.835463\pi$
$444$	−4.87028	+	6.82091i	−0.231133	+	0.323706i
$445$	2.03645	−	0.628162i	0.0965370	−	0.0297777i
$446$	10.1459	+	12.0515i	0.480424	+	0.570657i
$447$	−4.36092	−	2.10011i	−0.206265	−	0.0993318i
$448$	1.67276	−	21.0998i	0.0790305	−	0.996872i
$449$	−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	$0.910985\pi$
$450$	18.1807	+	8.16781i	0.857044	+	0.385034i
$451$	−0.972601	−	12.9785i	−0.0457980	−	0.611132i
$452$	−3.13782	−	1.31068i	−0.147591	−	0.0616493i
$453$	1.76929	−	5.73589i	0.0831284	−	0.269496i
$454$	24.1542	+	2.98696i	1.13361	+	0.140185i
$455$	1.81693	+	0.588598i	0.0851789	+	0.0275939i
$456$	−6.07628	+	0.485220i	−0.284548	+	0.0227225i
$457$	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	$0.251642\pi$
$458$	−12.1540	−	0.586737i	−0.567917	−	0.0274164i
$459$	−12.4149	+	7.16775i	−0.579478	+	0.334562i
$460$	1.26738	+	0.768823i	0.0590920	+	0.0358466i
$461$	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	$0.294553\pi$
$462$	3.78056	+	5.39908i	0.175887	+	0.251188i
$463$	26.7014	+	6.09441i	1.24092	+	0.283231i	0.792099	−	0.610392i	$-0.208988\pi$
$463$	26.7014	+	6.09441i	1.24092	+	0.283231i	0.448818	+	0.893623i	$0.351845\pi$
$464$	14.7426	+	14.9191i	0.684408	+	0.692604i
$465$	−0.107580	+	0.713746i	−0.00498890	+	0.0330992i
$466$	1.04466	−	0.753646i	0.0483931	−	0.0349120i
$467$	−1.40072	−	1.29968i	−0.0648175	−	0.0601419i	0.647099	−	0.762406i	$-0.275982\pi$
$467$	−1.40072	−	1.29968i	−0.0648175	−	0.0601419i	−0.711916	+	0.702264i	$0.752173\pi$
$468$	−5.13088	+	20.4283i	−0.237175	+	0.944296i
$469$	−3.96235	−	1.61988i	−0.182964	−	0.0747989i
$470$	−0.120552	+	0.187319i	−0.00556063	+	0.00864038i
$471$	−0.949242	−	0.548045i	−0.0437388	−	0.0252526i
$472$	−10.1634	+	33.5296i	−0.467807	+	1.54332i
$473$	6.49068	−	6.02248i	0.298442	−	0.276914i
$474$	1.65367	+	0.331495i	0.0759557	+	0.0152261i
$475$	16.6802	−	20.9163i	0.765339	−	0.959704i
$476$	−32.2831	+	3.69102i	−1.47969	+	0.169178i
$477$	10.7935	+	13.5346i	0.494199	+	0.619707i
$478$	−14.9825	−	29.1076i	−0.685284	−	1.33135i
$479$	−2.51807	+	6.41594i	−0.115054	+	0.293152i	−0.976788	−	0.214208i	$-0.931283\pi$
$479$	−2.51807	+	6.41594i	−0.115054	+	0.293152i	0.861735	+	0.507359i	$0.169378\pi$
$480$	−0.304800	+	0.317630i	−0.0139122	+	0.0144978i
$481$	36.1853	−	14.2017i	1.64991	−	0.647542i
$482$	−21.6455	−	7.83844i	−0.985928	−	0.357031i
$483$	3.11225	+	2.55447i	0.141612	+	0.116233i
$484$	7.63389	−	15.0107i	0.346995	−	0.682304i
$485$	0.0685521	−	0.914765i	0.00311279	−	0.0415373i
$486$	6.76790	−	12.4763i	0.306998	−	0.565936i
$487$	8.50254	−	12.4709i	0.385287	−	0.565112i	−0.583779	−	0.811912i	$-0.698427\pi$
$487$	8.50254	−	12.4709i	0.385287	−	0.565112i	0.969066	+	0.246800i	$0.0793791\pi$
$488$	−13.5309	+	17.1383i	−0.612514	+	0.775814i
$489$			1.20044i			0.0542858i
$490$	−1.08310	−	1.59411i	−0.0489293	−	0.0720147i
$491$		−	41.7664i		−	1.88489i	−0.334359	−	0.942446i	$-0.608520\pi$
$491$		−	41.7664i		−	1.88489i	0.334359	−	0.942446i	$-0.391480\pi$
$492$	2.34179	−	0.301215i	0.105576	−	0.0135798i
$493$	18.1385	−	26.6043i	0.816916	−	1.19820i
$494$	24.8509	+	13.4807i	1.11810	+	0.606524i
$495$	−0.182095	+	2.42989i	−0.00818457	+	0.109215i
$496$	−32.6980	−	17.5312i	−1.46819	−	0.787174i
$497$	5.22436	+	11.2512i	0.234345	+	0.504684i
$498$	0.0902456	−	0.249210i	0.00404400	−	0.0111674i
$499$	29.2093	−	11.4638i	1.30759	−	0.513191i	0.393731	−	0.919226i	$-0.371184\pi$
$499$	29.2093	−	11.4638i	1.30759	−	0.513191i	0.913858	+	0.406035i	$0.133089\pi$
$500$	−0.205964	−	3.87340i	−0.00921098	−	0.173224i
$501$	0.278170	−	0.708766i	0.0124277	−	0.0316653i
$502$	−1.07421	+	0.552929i	−0.0479445	+	0.0246784i
$503$	−15.6121	−	19.5770i	−0.696111	−	0.872896i	0.300615	−	0.953746i	$-0.402808\pi$
$503$	−15.6121	−	19.5770i	−0.696111	−	0.872896i	−0.996726	+	0.0808497i	$0.974237\pi$
$504$	16.7384	−	13.0984i	0.745589	−	0.583448i
$505$	0.0266056	−	0.0333624i	0.00118393	−	0.00148461i
$506$	4.66345	−	23.2638i	0.207316	−	1.03420i
$507$	−0.219443	+	0.203613i	−0.00974580	+	0.00904278i
$508$	4.24986	+	7.74389i	0.188557	+	0.343580i
$509$	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	$0.443045\pi$
$510$	0.568294	+	0.365733i	0.0251645	+	0.0161949i
$511$	35.3964	−	19.7767i	1.56585	−	0.874870i
$512$	−10.1154	−	20.2405i	−0.447043	−	0.894513i
$513$	−9.22650	−	8.56094i	−0.407360	−	0.377975i
$514$	10.2075	+	14.1490i	0.450232	+	0.624087i
$515$	−0.0744547	+	0.493975i	−0.00328087	+	0.0217671i
$516$	1.15354	+	1.11783i	0.0507820	+	0.0492096i
$517$	3.47610	+	0.793397i	0.152879	+	0.0348936i
$518$	−37.6245	−	11.0935i	−1.65312	−	0.487418i
$519$	−1.25876	+	0.287305i	−0.0552536	+	0.0126113i
$520$	1.98832	−	0.464054i	0.0871937	−	0.0203501i
$521$	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	$0.0713476\pi$
$522$	−1.01558	+	21.0373i	−0.0444509	+	0.920778i
$523$	10.4464	−	7.12227i	0.456791	−	0.311435i	−0.312975	−	0.949762i	$-0.601325\pi$
$523$	10.4464	−	7.12227i	0.456791	−	0.311435i	0.769766	+	0.638327i	$0.220373\pi$
$524$	11.5098	+	9.59414i	0.502807	+	0.419122i
$525$	0.465841	−	5.22714i	0.0203310	−	0.228131i
$526$	−0.858116	+	6.93918i	−0.0374156	+	0.302563i
$527$	−16.7883	+	54.4263i	−0.731310	+	2.37085i
$528$	6.44138	+	2.85610i	0.280325	+	0.124296i
$529$	0.635653	+	8.48221i	0.0276371	+	0.368792i
$530$	0.687694	−	1.53073i	0.0298715	−	0.0664907i
$531$	−31.6980	+	15.2649i	−1.37558	+	0.662442i
$532$	−11.4513	−	26.1298i	−0.496477	−	1.13287i
$533$	−9.86635	−	4.75138i	−0.427359	−	0.205805i
$534$	4.73399	−	3.98544i	0.204860	−	0.172467i
$535$	−1.63991	+	0.505845i	−0.0708994	+	0.0218696i
$536$	−4.52174	+	0.704154i	−0.195309	+	0.0304148i
$537$	−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	$0.320363\pi$
$542$	−34.4730	+	6.13642i	−1.48074	+	0.263582i
$543$	1.22093	+	3.95817i	0.0523953	+	0.169861i
$544$	−27.5182	+	21.1991i	−1.17983	+	0.908904i
$545$	0.492373	−	1.02242i	0.0210910	−	0.0437958i
$546$	5.52471	−	0.483407i	0.236436	−	0.0206879i
$547$	−1.22035	−	2.53409i	−0.0521784	−	0.108350i	0.873249	−	0.487273i	$-0.162009\pi$
$547$	−1.22035	−	2.53409i	−0.0521784	−	0.108350i	−0.925428	+	0.378924i	$0.876294\pi$
$548$	4.45177	−	1.63675i	0.190170	−	0.0699186i
$549$	−21.8656	+	1.63860i	−0.933199	+	0.0699336i
$550$	−28.4769	+	12.0587i	−1.21426	+	0.514183i
$551$	27.0146	+	8.33290i	1.15086	+	0.354994i
$552$	4.25935	+	0.620726i	0.181290	+	0.0264198i
$553$	1.06642	+	7.82116i	0.0453487	+	0.332590i
$554$	0.585272	+	5.75430i	0.0248658	+	0.244477i
$555$	0.459575	+	0.674072i	0.0195079	+	0.0286128i
$556$	28.7493	+	32.3638i	1.21924	+	1.37253i
$557$	−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	$0.873268\pi$
$558$	−9.25196	−	36.0888i	−0.391667	−	1.52776i
$559$	−1.65781	−	7.26333i	−0.0701178	−	0.307206i
$560$	−1.87152	−	0.861575i	−0.0790863	−	0.0364082i
$561$	2.40703	−	10.5459i	0.101625	−	0.445248i
$562$	3.50364	−	0.0930853i	0.147792	−	0.00392657i
$563$	−1.71325	−	0.258230i	−0.0722048	−	0.0108831i	0.112841	−	0.993613i	$-0.464005\pi$
$563$	−1.71325	−	0.258230i	−0.0722048	−	0.0108831i	−0.185045	+	0.982730i	$0.559243\pi$
$564$	−0.110246	+	0.637366i	−0.00464217	+	0.0268380i
$565$	−0.225146	+	0.242650i	−0.00947198	+	0.0102084i
$566$	−8.03097	−	13.0941i	−0.337567	−	0.550387i
$567$	19.8062	+	3.27124i	0.831783	+	0.137379i
$568$	10.9935	+	7.41682i	0.461277	+	0.311203i
$569$	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	$0.106952\pi$
$570$	−0.159774	+	0.571437i	−0.00669218	+	0.0239349i
$571$	−3.16463	−	3.41066i	−0.132436	−	0.142732i	0.663352	−	0.748308i	$-0.269133\pi$
$571$	−3.16463	−	3.41066i	−0.132436	−	0.142732i	−0.795788	+	0.605576i	$0.792943\pi$
$572$	−17.8201	−	27.3947i	−0.745095	−	1.14543i
$573$	−1.94772	−	1.55326i	−0.0813673	−	0.0648883i
$574$	4.91842	+	9.89545i	0.205291	+	0.413028i
$575$	−14.7697	+	11.7785i	−0.615941	+	0.491196i
$576$	8.09410	−	21.2312i	0.337254	−	0.884632i
$577$	−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	$0.776952\pi$
$578$	21.9892	+	19.3420i	0.914630	+	0.804520i
$579$	−0.264169	−	0.673093i	−0.0109785	−	0.0279728i
$580$	1.85824	−	0.845768i	0.0771594	−	0.0351186i
$581$	1.24035	+	0.0174715i	0.0514586	+	0.000724841i
$582$	−0.852459	−	2.52360i	−0.0353356	−	0.104606i
$583$	−26.7850	−	2.00726i	−1.10932	−	0.0831321i
$584$	21.4894	−	37.6443i	0.889237	−	1.55773i
$585$	1.69401	+	1.15496i	0.0700387	+	0.0477516i
$586$	−19.9323	−	15.0471i	−0.823397	−	0.621591i
$587$	28.2761			1.16708			0.583539	−	0.812085i	$-0.301668\pi$
$587$	28.2761			1.16708			0.583539	+	0.812085i	$0.301668\pi$
$588$	−4.70104	−	3.03612i	−0.193868	−	0.125207i
$589$	−50.0074			−2.06052
$590$	2.72192	+	2.05481i	0.112060	+	0.0845952i
$591$	−3.08900	−	2.10604i	−0.127064	−	0.0866310i
$592$	−40.5692	+	10.6121i	−1.66738	+	0.436154i
$593$	−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	$0.530307\pi$
$594$	4.65617	+	13.7840i	0.191045	+	0.565564i
$595$	−0.747181	+	3.07342i	−0.0306314	+	0.125998i
$596$	−10.0322	−	22.0419i	−0.410936	−	0.902872i
$597$	2.37487	+	6.05107i	0.0971970	+	0.247654i
$598$	−14.9900	−	13.1854i	−0.612986	−	0.539190i
$599$	−34.0410	−	13.3601i	−1.39088	−	0.545879i	−0.452584	−	0.891722i	$-0.649498\pi$
$599$	−34.0410	−	13.3601i	−1.39088	−	0.545879i	−0.938292	+	0.345843i	$0.887593\pi$
$600$	−2.45884	−	5.04266i	−0.100382	−	0.205866i
$601$	−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	$0.443848\pi$
$602$	−3.17711	+	6.81351i	−0.129489	+	0.277698i
$603$	−3.59276	−	2.86513i	−0.146308	−	0.116677i
$604$	25.1753	−	16.3764i	1.02437	−	0.666347i
$605$	−1.11497	−	1.20166i	−0.0453302	−	0.0488543i
$606$	0.0333652	−	0.119332i	0.00135537	−	0.00484753i
$607$	13.0059	−	22.5269i	0.527894	−	0.914339i	−0.471577	−	0.881825i	$-0.656315\pi$
$607$	13.0059	−	22.5269i	0.527894	−	0.914339i	0.999471	−	0.0325144i	$-0.0103515\pi$
$608$	−24.9072	−	17.6012i	−1.01012	−	0.713821i
$609$	5.32169	−	1.55979i	0.215646	−	0.0632057i
$610$	1.11127	+	1.81188i	0.0449942	+	0.0733609i
$611$	2.04054	−	2.19918i	0.0825516	−	0.0889695i
$612$	−34.3713	−	5.94522i	−1.38938	−	0.240321i
$613$	−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	$0.729715\pi$
$614$	10.6233	−	0.282242i	0.428723	−	0.0113904i
$615$	0.0511419	−	0.224067i	0.00206224	−	0.00903526i
$616$	−2.76684	+	32.8614i	−0.111479	+	1.32403i
$617$	−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	$-0.311915\pi$
$618$	0.360229	+	1.40513i	0.0144905	+	0.0565228i
$619$	12.0083	+	20.7989i	0.482653	+	0.835979i	0.999802	−	0.0199165i	$-0.00634004\pi$
$619$	12.0083	+	20.7989i	0.482653	+	0.835979i	−0.517149	+	0.855895i	$0.673007\pi$
$620$	−2.70001	+	2.39847i	−0.108435	+	0.0963247i
$621$	5.00664	+	7.34339i	0.200909	+	0.294680i
$622$	3.78934	+	37.2562i	0.151939	+	1.49384i
$623$	24.8757	+	14.8330i	0.996624	+	0.594272i
$624$	4.79111	−	3.49214i	0.191798	−	0.139798i
$625$	23.3474	+	7.20173i	0.933897	+	0.288069i
$626$	36.5980	−	15.4976i	1.46275	−	0.619408i
$627$	9.47073	−	0.709733i	0.378225	−	0.0283440i
$628$	−1.89246	−	5.14727i	−0.0755175	−	0.205399i
$629$	27.9317	+	58.0008i	1.11371	+	2.31265i
$630$	−0.634439	−	1.96923i	−0.0252766	−	0.0784559i
$631$	−12.8293	+	26.6402i	−0.510725	+	1.06053i	0.473036	+	0.881043i	$0.343158\pi$
$631$	−12.8293	+	26.6402i	−0.510725	+	1.06053i	−0.983760	+	0.179487i	$0.942556\pi$
$632$	5.29351	+	6.57173i	0.210565	+	0.261409i
$633$	−0.881335	−	2.85722i	−0.0350299	−	0.113564i
$634$	−34.8848	+	6.20973i	−1.38545	+	0.246620i
$635$	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
$640$	−2.18898	+	0.244276i	−0.0865272	+	0.00965586i
$641$	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	$0.219843\pi$
$642$	−3.81218	+	3.20939i	−0.150455	+	0.126665i
$643$	22.3272	+	10.7522i	0.880499	+	0.424026i	0.818807	−	0.574069i	$-0.194636\pi$
$643$	22.3272	+	10.7522i	0.880499	+	0.424026i	0.0616919	+	0.998095i	$0.480350\pi$
$644$	3.77768	+	19.7879i	0.148861	+	0.779753i
$645$	0.140874	−	0.0678415i	0.00554692	−	0.00267126i
$646$	−19.1872	+	42.7086i	−0.754909	+	1.68035i
$647$	−1.45719	−	19.4448i	−0.0572880	−	0.764456i	−0.949685	−	0.313205i	$-0.898597\pi$
$647$	−1.45719	−	19.4448i	−0.0572880	−	0.764456i	0.892397	−	0.451250i	$-0.149022\pi$
$648$	19.9386	−	7.93795i	0.783261	−	0.311832i
$649$	16.0901	−	52.1628i	0.631591	−	2.04757i
$650$	−3.19342	+	25.8237i	−0.125256	+	1.01289i
$651$	−8.18199	+	5.41117i	−0.320677	+	0.212080i
$652$	−3.84574	+	4.61361i	−0.150611	+	0.180683i
$653$	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	$0.182074\pi$
$654$	0.158891	−	3.29134i	0.00621312	−	0.128702i
$655$	1.26315	−	0.729281i	0.0493555	−	0.0284954i
$656$	9.96506	+	6.34450i	0.389070	+	0.247711i
$657$	42.4355	−	9.68562i	1.65557	−	0.377872i
$658$	−2.98764	+	0.488511i	−0.116470	+	0.0190441i
$659$	−3.79879	−	0.867049i	−0.147980	−	0.0337754i	0.147889	−	0.989004i	$-0.452752\pi$
$659$	−3.79879	−	0.867049i	−0.147980	−	0.0337754i	−0.295869	+	0.955228i	$0.595609\pi$
$660$	0.477306	−	0.492557i	0.0185791	−	0.0191728i
$661$	−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	$0.968100\pi$
$662$	−9.06236	−	12.5618i	−0.352219	−	0.488227i
$663$	−6.67195	−	6.19066i	−0.259117	−	0.240425i
$664$	1.14521	−	0.668666i	0.0444426	−	0.0259493i
$665$	−2.77191	+	0.168503i	−0.107490	+	0.00653427i
$666$	−35.4098	−	22.7884i	−1.37210	−	0.883033i
$667$	−17.2884	−	9.98145i	−0.669409	−	0.386483i
$668$	3.33968	−	1.83282i	0.129216	−	0.0709141i
$669$	3.26415	−	3.02869i	0.126199	−	0.117096i
$670$	−0.0875539	+	0.436766i	−0.00338250	+	0.0168737i
$671$	21.2120	−	26.5990i	0.818880	−	1.02684i
$672$	−5.97977	−	0.184685i	−0.230675	−	0.00712436i
$673$	−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	$0.940105\pi$
$674$	4.20334	−	2.16358i	0.161907	−	0.0833380i
$675$	4.23214	−	10.7833i	0.162895	−	0.415050i
$676$	−1.49567	+	0.0795306i	−0.0575258	+	0.00305887i
$677$	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	$0.321180\pi$
$678$	−0.327270	+	0.903745i	−0.0125687	+	0.0347081i
$679$	9.85532	−	7.63477i	0.378212	−	0.292996i
$680$	1.01244	+	3.22619i	0.0388252	+	0.123719i
$681$	0.514086	−	6.86000i	0.0196998	−	0.262876i
$682$	50.8111	+	27.5631i	1.94566	+	1.05544i
$683$	−13.2415	+	19.4217i	−0.506670	+	0.743149i	−0.991307	−	0.131567i	$-0.957999\pi$
$683$	−13.2415	+	19.4217i	−0.506670	+	0.743149i	0.484637	+	0.874715i	$0.338952\pi$
$684$	−3.90708	−	30.3755i	−0.149391	−	1.16144i
$685$		−	0.461699i		−	0.0176406i
$686$	6.22817	−	25.4403i	0.237792	−	0.971316i
$687$			3.43935i			0.131219i
$688$	0.852298	+	7.99159i	0.0324935	+	0.304677i
$689$	−12.7312	+	18.6733i	−0.485021	+	0.711395i
$690$	0.199783	−	0.368291i	0.00760562	−	0.0140206i
$691$	1.12843	−	15.0579i	0.0429277	−	0.572830i	−0.933723	−	0.357996i	$-0.883460\pi$
$691$	1.12843	−	15.0579i	0.0429277	−	0.572830i	0.976651	−	0.214834i	$-0.0689209\pi$
$692$	−5.75817	−	2.92839i	−0.218893	−	0.111321i
$693$	−26.1787	+	20.2803i	−0.994447	+	0.770383i
$694$	−30.2068	−	10.9387i	−1.14664	−	0.415228i
$695$	3.92250	−	1.53947i	0.148789	−	0.0583954i
$696$	4.01110	−	4.36552i	0.152040	−	0.165475i
$697$	6.62564	−	16.8818i	0.250964	−	0.639446i
$698$	6.75085	+	13.1154i	0.255523	+	0.496423i
$699$	−0.227010	−	0.284662i	−0.00858631	−	0.0107669i
$700$	18.5360	−	18.5969i	0.700596	−	0.702896i
$701$	−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	$0.226233\pi$
$702$	12.0030	+	2.40612i	0.453024	+	0.0908132i
$703$	−41.4332	+	38.4444i	−1.56268	+	1.44996i
$704$	15.6061	+	31.6124i	0.588176	+	1.19144i
$705$	0.0545276	+	0.0314815i	0.00205363	+	0.00118566i
$706$	14.4386	−	22.4354i	0.543403	−	0.844367i
$707$	0.578851	−	0.0351881i	0.0217699	−	0.00132338i
$708$	9.60471	+	2.41237i	0.360967	+	0.0906626i
$709$	−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	$-0.524989\pi$
$710$	1.04689	−	0.755250i	0.0392890	−	0.0283440i
$711$	−1.26294	+	8.37906i	−0.0473640	+	0.314239i
$712$	30.9617	−	0.151277i	1.16034	−	0.00566935i
$713$	34.4267	+	7.85767i	1.28929	+	0.294272i
$714$	1.48206	+	9.06397i	0.0554646	+	0.339211i
$715$	−3.10140	+	0.707875i	−0.115986	+	0.0264730i
$716$	17.4156	−	28.7091i	0.650851	−	1.07291i
$717$	−8.01356	+	4.62663i	−0.299272	+	0.172785i
$718$	−9.38485	−	0.453057i	−0.350239	−	0.0169079i
$719$	34.0296	−	23.2010i	1.26909	−	0.865252i	0.273763	−	0.961797i	$-0.411732\pi$
$719$	34.0296	−	23.2010i	1.26909	−	0.865252i	0.995329	+	0.0965454i	$0.0307793\pi$
$720$	−1.66783	−	1.45265i	−0.0621563	−	0.0541371i
$721$	−5.66265	+	3.74500i	−0.210888	+	0.139471i
$722$	−14.1303	−	1.74739i	−0.525875	−	0.0650310i
$723$	−1.91796	+	6.21788i	−0.0713298	+	0.231245i
$724$	−7.98804	+	19.1237i	−0.296873	+	0.710725i
$725$	1.94442	+	25.9465i	0.0722140	+	0.963629i
$726$	−4.34192	−	1.95064i	−0.161144	−	0.0723951i
$727$	−7.55205	+	3.63687i	−0.280090	+	0.134884i	−0.568655	−	0.822576i	$-0.692536\pi$
$727$	−7.55205	+	3.63687i	−0.280090	+	0.134884i	0.288565	+	0.957460i	$0.406822\pi$
$728$	22.7815	+	15.8411i	0.844339	+	0.587110i
$729$	16.8936	+	8.13554i	0.625690	+	0.301316i
$730$	−2.71740	−	3.22779i	−0.100576	−	0.119466i
$731$	11.7899	−	3.63670i	0.436065	−	0.134508i
$732$	5.02296	+	3.58650i	0.185654	+	0.132561i
$733$	−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
$738$	2.07894	+	11.6790i	0.0765268	+	0.429910i
$739$	0.764853	+	2.47959i	0.0281356	+	0.0912133i	0.968552	−	0.248813i	$-0.0800403\pi$
$739$	0.764853	+	2.47959i	0.0281356	+	0.0912133i	−0.940416	+	0.340026i	$0.889564\pi$
$740$	−0.393195	+	4.06293i	−0.0144541	+	0.149356i
$741$	3.46721	−	7.19974i	0.127371	−	0.264489i
$742$	21.7070	−	6.99350i	0.796890	−	0.256739i
$743$	12.7510	+	26.4776i	0.467787	+	0.971370i	0.992745	+	0.120242i	$0.0383669\pi$
$743$	12.7510	+	26.4776i	0.467787	+	0.971370i	−0.524957	+	0.851128i	$0.675919\pi$
$744$	−4.50382	+	9.47037i	−0.165118	+	0.347200i
$745$	−2.35077	+	0.176166i	−0.0861255	+	0.00645421i
$746$	15.8006	+	37.3136i	0.578501	+	1.36615i
$747$	1.27249	+	0.392512i	0.0465580	+	0.0143612i
$748$	43.0356	−	32.8194i	1.57354	−	1.20000i
$749$	−20.0319	−	11.9447i	−0.731948	−	0.436450i
$750$	−1.09075	+	0.110940i	−0.0398284	+	0.00405096i
$751$	17.9660	+	26.3513i	0.655589	+	0.961573i	0.999743	+	0.0226595i	$0.00721337\pi$
$751$	17.9660	+	26.3513i	0.655589	+	0.961573i	−0.344154	+	0.938913i	$0.611834\pi$
$752$	−2.46557	+	2.09638i	−0.0899101	+	0.0764471i
$753$	0.170746	+	0.295740i	0.00622231	+	0.0107774i
$754$	−26.6352	+	6.82836i	−0.969997	+	0.248674i
$755$	−0.650528	−	2.85015i	−0.0236751	−	0.103727i
$756$	−8.07310	−	9.35007i	−0.293616	−	0.340059i
$757$	−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	$0.827388\pi$
$758$	0.778513	+	29.3025i	0.0282769	+	1.06431i
$759$	−6.63148	−	0.999535i	−0.240707	−	0.0362808i
$760$	−2.44471	+	1.68433i	−0.0886789	+	0.0610970i
$761$	−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	$0.432480\pi$
$762$	2.12836	−	1.30538i	0.0771024	−	0.0472889i
$763$	14.7996	−	4.33775i	0.535780	−	0.157037i
$764$	−2.50959	−	12.2093i	−0.0907936	−	0.441717i
$765$	−1.69771	+	2.94051i	−0.0613807	+	0.106315i
$766$	−2.01508	−	0.563417i	−0.0728080	−	0.0203571i

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)

\(f(q)\)	\(=\)	\(q+(0.852071 - 1.12870i) q^{2} +(-0.330273 - 0.225176i) q^{3} +(-0.547949 - 1.92347i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(-0.535574 + 0.180915i) q^{6} +(-1.62030 - 2.09156i) q^{7} +(-2.63793 - 1.02046i) q^{8} +(-1.03765 - 2.64388i) q^{9} +O(q^{10})\)	\(q+(0.852071 - 1.12870i) q^{2} +(-0.330273 - 0.225176i) q^{3} +(-0.547949 - 1.92347i) q^{4} +(-0.194137 - 0.0145486i) q^{5} +(-0.535574 + 0.180915i) q^{6} +(-1.62030 - 2.09156i) q^{7} +(-2.63793 - 1.02046i) q^{8} +(-1.03765 - 2.64388i) q^{9} +(-0.181840 + 0.206727i) q^{10} +(4.10220 + 1.61000i) q^{11} +(-0.252148 + 0.758657i) q^{12} +(2.89899 - 2.31187i) q^{13} +(-3.74137 + 0.0466832i) q^{14} +(0.0608423 + 0.0485201i) q^{15} +(-3.39950 + 2.10793i) q^{16} +(4.17672 + 4.50144i) q^{17} +(-3.86831 - 1.08158i) q^{18} +(-2.69573 + 4.66913i) q^{19} +(0.0783936 + 0.381390i) q^{20} +(0.0641719 + 1.05564i) q^{21} +(5.31258 - 3.25835i) q^{22} +(2.58949 - 2.79080i) q^{23} +(0.641452 + 0.931030i) q^{24} +(-4.90668 - 0.739562i) q^{25} +(-0.139270 - 5.24198i) q^{26} +(-0.519478 + 2.27598i) q^{27} +(-3.13522 + 4.26268i) q^{28} +(-1.16681 - 5.11213i) q^{29} +(0.106607 - 0.0273304i) q^{30} +(4.63766 + 8.03266i) q^{31} +(-0.517387 + 5.63314i) q^{32} +(-0.992315 - 1.45546i) q^{33} +(8.63966 - 0.878742i) q^{34} +(0.284132 + 0.429623i) q^{35} +(-4.51686 + 3.44460i) q^{36} +(10.0178 + 3.09008i) q^{37} +(2.97312 + 7.02111i) q^{38} +(-1.47804 + 0.110764i) q^{39} +(0.497274 + 0.236488i) q^{40} +(-1.28140 - 2.66086i) q^{41} +(1.24618 + 0.827049i) q^{42} +(0.871772 - 1.81025i) q^{43} +(0.848987 - 8.77268i) q^{44} +(0.162981 + 0.528372i) q^{45} +(-0.943565 - 5.30073i) 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} +(-6.03532 - 4.30935i) q^{52} +(-5.82431 + 1.79656i) q^{53} +(2.12628 + 2.52564i) q^{54} +(-0.772968 - 0.372242i) q^{55} +(2.13987 + 7.17084i) q^{56} +(1.94170 - 0.935075i) q^{57} +(-6.76429 - 3.03891i) q^{58} +(-0.925691 - 12.3525i) q^{59} +(0.0599887 - 0.143615i) q^{60} +(2.27555 - 7.37716i) q^{61} +(13.0181 + 1.60985i) q^{62} +(-3.84854 + 6.45419i) q^{63} +(5.91731 + 5.38382i) q^{64} +(-0.596437 + 0.406644i) q^{65} +(-2.48831 - 0.120124i) q^{66} +(1.40118 - 0.808972i) q^{67} +(6.36976 - 10.5004i) q^{68} +(-1.48366 + 0.338636i) q^{69} +(0.727018 + 0.0453686i) q^{70} +(-4.57108 - 1.04332i) q^{71} +(0.0392500 + 8.03325i) q^{72} +(-2.28410 + 15.1540i) q^{73} +(12.0237 - 8.67416i) q^{74} +(1.45401 + 1.34913i) q^{75} +(10.4581 + 2.62671i) q^{76} +(-3.27940 - 11.1887i) q^{77} +(-1.13437 + 1.76265i) q^{78} +(-2.58376 - 1.49174i) q^{79} +(0.690638 - 0.359770i) q^{80} +(-5.56201 + 5.16079i) q^{81} +(-4.09518 - 0.820918i) q^{82} +(-0.292327 + 0.366567i) q^{83} +(1.99533 - 0.701870i) q^{84} +(-0.745368 - 0.934662i) q^{85} +(-1.30043 - 2.52644i) q^{86} +(-0.765765 + 1.95114i) q^{87} +(-9.17837 - 8.43320i) q^{88} +(-10.1900 + 3.99930i) q^{89} +(0.735248 + 0.266253i) q^{90} +(-9.53265 - 2.31749i) q^{91} +(-6.78694 - 3.45159i) q^{92} +(0.277072 - 3.69726i) q^{93} +(0.545589 - 1.00577i) q^{94} +(0.591270 - 0.867234i) q^{95} +(1.43933 - 1.74397i) q^{96} +4.71195i q^{97} +(6.15978 + 7.74965i) 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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