LMFDB - Embedded newform 475.2.bc.a.6.13

Newspace parameters

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bc (of order $45$, degree $24$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$1152$
Relative dimension:	$48$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			6.13
Character	$\chi$	$=$	475.6
Dual form			475.2.bc.a.396.13

$q$-expansion

$f(q)$	$=$	$q+(-1.30322 - 0.814342i) q^{2} +(1.85231 - 0.531140i) q^{3} +(0.158485 + 0.324943i) q^{4} +(-0.982153 - 2.00882i) q^{5} +(-2.84649 - 0.816218i) q^{6} +(0.367774 - 0.637004i) q^{7} +(-0.263190 + 2.50409i) q^{8} +(0.604785 - 0.377912i) q^{9} +O(q^{10})$	\(q+(-1.30322 - 0.814342i) q^{2} +(1.85231 - 0.531140i) q^{3} +(0.158485 + 0.324943i) q^{4} +(-0.982153 - 2.00882i) q^{5} +(-2.84649 - 0.816218i) q^{6} +(0.367774 - 0.637004i) q^{7} +(-0.263190 + 2.50409i) q^{8} +(0.604785 - 0.377912i) q^{9} +(-0.355909 + 3.41775i) q^{10} +(1.34614 - 1.49504i) q^{11} +(0.466154 + 0.517716i) q^{12} +(-0.168125 - 4.81446i) q^{13} +(-0.998029 + 0.530661i) q^{14} +(-2.88622 - 3.19930i) q^{15} +(2.82734 - 3.61883i) q^{16} +(-1.55778 + 0.108930i) q^{17} -1.09592 q^{18} +(-4.25336 - 0.953362i) q^{19} +(0.497097 - 0.637513i) q^{20} +(0.342892 - 1.37527i) q^{21} +(-2.97179 + 0.852148i) q^{22} +(0.267146 - 0.0375450i) q^{23} +(0.842512 + 4.77812i) q^{24} +(-3.07075 + 3.94595i) q^{25} +(-3.70151 + 6.41121i) q^{26} +(-2.94863 + 3.27478i) q^{27} +(0.265277 + 0.0185500i) q^{28} +(-2.78965 - 0.195072i) q^{29} +(1.15605 + 6.51975i) q^{30} +(8.77582 - 3.90724i) q^{31} +(-1.89954 + 0.691376i) q^{32} +(1.69939 - 3.48426i) q^{33} +(2.11883 + 1.12660i) q^{34} +(-1.64084 - 0.113159i) q^{35} +(0.218649 + 0.136627i) q^{36} +(0.0553274 - 0.170280i) q^{37} +(4.76670 + 4.70613i) q^{38} +(-2.86857 - 8.82856i) q^{39} +(5.28876 - 1.93069i) q^{40} +(-1.24163 + 1.58921i) q^{41} +(-1.56680 + 1.51304i) q^{42} +(-1.18807 - 6.73786i) q^{43} +(0.699147 + 0.200477i) q^{44} +(-1.35315 - 0.843740i) q^{45} +(-0.378725 - 0.168619i) q^{46} +(-7.58492 - 0.530389i) q^{47} +(3.31499 - 8.20489i) q^{48} +(3.22948 + 5.59363i) q^{49} +(7.21521 - 2.64179i) q^{50} +(-2.82762 + 1.02917i) q^{51} +(1.53778 - 0.817653i) q^{52} +(0.654382 + 1.34168i) q^{53} +(6.50950 - 1.86657i) q^{54} +(-4.32539 - 1.23580i) q^{55} +(1.49832 + 1.08859i) q^{56} +(-8.38490 + 0.493214i) q^{57} +(3.47667 + 2.52595i) q^{58} +(5.18420 + 12.8313i) q^{59} +(0.582167 - 1.44490i) q^{60} +(5.15595 - 0.724621i) q^{61} +(-14.6186 - 2.05452i) q^{62} +(-0.0183067 - 0.524236i) q^{63} +(-5.94548 - 1.26375i) q^{64} +(-9.50629 + 5.06627i) q^{65} +(-5.05206 + 3.15688i) q^{66} +(-2.81032 - 11.2716i) q^{67} +(-0.282281 - 0.488925i) q^{68} +(0.474895 - 0.211437i) q^{69} +(2.04622 + 1.48367i) q^{70} +(0.224448 + 0.216747i) q^{71} +(0.787150 + 1.61390i) q^{72} +(0.397608 - 11.3860i) q^{73} +(-0.210770 + 0.176857i) q^{74} +(-3.59212 + 8.94010i) q^{75} +(-0.364307 - 1.53320i) q^{76} +(-0.457271 - 1.40733i) q^{77} +(-3.45109 + 13.8416i) q^{78} +(15.7669 - 4.52109i) q^{79} +(-10.0465 - 2.12538i) q^{80} +(-4.66026 + 9.55496i) q^{81} +(2.91228 - 1.05998i) q^{82} +(5.48069 - 2.44016i) q^{83} +(0.501226 - 0.106539i) q^{84} +(1.74880 + 3.02231i) q^{85} +(-3.93861 + 9.74840i) q^{86} +(-5.27090 + 1.12036i) q^{87} +(3.38942 + 3.76433i) q^{88} +(-5.66697 - 7.25339i) q^{89} +(1.07636 + 2.20150i) q^{90} +(-3.12866 - 1.66354i) q^{91} +(0.0545388 + 0.0808571i) q^{92} +(14.1802 - 11.8986i) q^{93} +(9.45289 + 6.86793i) q^{94} +(2.26232 + 9.48061i) q^{95} +(-3.15131 + 2.28956i) q^{96} +(0.373123 - 1.49651i) q^{97} +(0.346401 - 9.91963i) q^{98} +(0.249133 - 1.41290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.30322	−	0.814342i	−0.921515	−	0.575827i	−0.0158751	−	0.999874i	$-0.505053\pi$
$2$	−1.30322	−	0.814342i	−0.921515	−	0.575827i	−0.905640	+	0.424047i	$0.860609\pi$
$3$	1.85231	−	0.531140i	1.06943	−	0.306654i	0.305659	−	0.952141i	$-0.401123\pi$
$3$	1.85231	−	0.531140i	1.06943	−	0.306654i	0.763771	+	0.645487i	$0.223346\pi$
$4$	0.158485	+	0.324943i	0.0792427	+	0.162472i
$5$	−0.982153	−	2.00882i	−0.439232	−	0.898374i
$5$	−0.982153	−	2.00882i	−0.439232	−	0.898374i
$6$	−2.84649	−	0.816218i	−1.16208	−	0.333220i
$7$	0.367774	−	0.637004i	0.139006	−	0.240765i	−0.788115	−	0.615528i	$-0.788943\pi$
$7$	0.367774	−	0.637004i	0.139006	−	0.240765i	0.927120	+	0.374763i	$0.122276\pi$
$8$	−0.263190	+	2.50409i	−0.0930517	+	0.885328i
$9$	0.604785	−	0.377912i	0.201595	−	0.125971i
$10$	−0.355909	+	3.41775i	−0.112548	+	1.08079i
$11$	1.34614	−	1.49504i	0.405877	−	0.450772i	−0.505204	−	0.863000i	$-0.668583\pi$
$11$	1.34614	−	1.49504i	0.405877	−	0.450772i	0.911081	+	0.412228i	$0.135249\pi$
$12$	0.466154	+	0.517716i	0.134567	+	0.149452i
$13$	−0.168125	−	4.81446i	−0.0466294	−	1.33529i	−0.766975	−	0.641677i	$-0.778239\pi$
$13$	−0.168125	−	4.81446i	−0.0466294	−	1.33529i	0.720346	−	0.693615i	$-0.243983\pi$
$14$	−0.998029	+	0.530661i	−0.266734	+	0.141825i
$15$	−2.88622	−	3.19930i	−0.745218	−	0.826055i
$16$	2.82734	−	3.61883i	0.706835	−	0.904707i
$17$	−1.55778	+	0.108930i	−0.377816	+	0.0264195i	−0.257402	−	0.966304i	$-0.582867\pi$
$17$	−1.55778	+	0.108930i	−0.377816	+	0.0264195i	−0.120414	+	0.992724i	$0.538422\pi$
$18$	−1.09592			−0.258310
$19$	−4.25336	−	0.953362i	−0.975789	−	0.218716i
$19$	−4.25336	−	0.953362i	−0.975789	−	0.218716i
$20$	0.497097	−	0.637513i	0.111154	−	0.142552i
$21$	0.342892	−	1.37527i	0.0748252	−	0.300108i
$22$	−2.97179	+	0.852148i	−0.633588	+	0.181678i
$23$	0.267146	−	0.0375450i	0.0557039	−	0.00782867i	−0.111266	−	0.993791i	$-0.535491\pi$
$23$	0.267146	−	0.0375450i	0.0557039	−	0.00782867i	0.166970	+	0.985962i	$0.446602\pi$
$24$	0.842512	+	4.77812i	0.171977	+	0.975331i
$25$	−3.07075	+	3.94595i	−0.614150	+	0.789189i
$26$	−3.70151	+	6.41121i	−0.725927	+	1.25734i
$27$	−2.94863	+	3.27478i	−0.567464	+	0.630232i
$28$	0.265277	+	0.0185500i	0.0501326	+	0.00350561i
$29$	−2.78965	−	0.195072i	−0.518026	−	0.0362239i	−0.191649	−	0.981464i	$-0.561383\pi$
$29$	−2.78965	−	0.195072i	−0.518026	−	0.0362239i	−0.326377	+	0.945240i	$0.605828\pi$
$30$	1.15605	+	6.51975i	0.211065	+	1.19034i
$31$	8.77582	−	3.90724i	1.57618	−	0.701762i	0.582380	−	0.812917i	$-0.302122\pi$
$31$	8.77582	−	3.90724i	1.57618	−	0.701762i	0.993803	+	0.111155i	$0.0354550\pi$
$32$	−1.89954	+	0.691376i	−0.335794	+	0.122219i
$33$	1.69939	−	3.48426i	0.295826	−	0.606533i
$34$	2.11883	+	1.12660i	0.363377	+	0.193211i
$35$	−1.64084	−	0.113159i	−0.277352	−	0.0191273i
$36$	0.218649	+	0.136627i	0.0364416	+	0.0227712i
$37$	0.0553274	−	0.170280i	0.00909576	−	0.0279939i	−0.946406	−	0.322980i	$-0.895315\pi$
$37$	0.0553274	−	0.170280i	0.00909576	−	0.0279939i	0.955501	+	0.294987i	$0.0953152\pi$
$38$	4.76670	+	4.70613i	0.773261	+	0.763435i
$39$	−2.86857	−	8.82856i	−0.459339	−	1.41370i
$40$	5.28876	−	1.93069i	0.836227	−	0.305269i
$41$	−1.24163	+	1.58921i	−0.193910	+	0.248193i	−0.875133	−	0.483883i	$-0.839226\pi$
$41$	−1.24163	+	1.58921i	−0.193910	+	0.248193i	0.681223	+	0.732076i	$0.261448\pi$
$42$	−1.56680	+	1.51304i	−0.241762	+	0.233467i
$43$	−1.18807	−	6.73786i	−0.181178	−	1.02751i	−0.930768	−	0.365611i	$-0.880860\pi$
$43$	−1.18807	−	6.73786i	−0.181178	−	1.02751i	0.749589	−	0.661903i	$-0.230251\pi$
$44$	0.699147	+	0.200477i	0.105400	+	0.0302231i
$45$	−1.35315	−	0.843740i	−0.201716	−	0.125777i
$46$	−0.378725	−	0.168619i	−0.0558399	−	0.0248615i
$47$	−7.58492	−	0.530389i	−1.10637	−	0.0773652i	−0.495138	−	0.868814i	$-0.664883\pi$
$47$	−7.58492	−	0.530389i	−1.10637	−	0.0773652i	−0.611235	+	0.791449i	$0.709327\pi$
$48$	3.31499	−	8.20489i	0.478478	−	1.18427i
$49$	3.22948	+	5.59363i	0.461355	+	0.799090i
$50$	7.21521	−	2.64179i	1.02038	−	0.373606i
$51$	−2.82762	+	1.02917i	−0.395946	+	0.144113i
$52$	1.53778	−	0.817653i	0.213252	−	0.113388i
$53$	0.654382	+	1.34168i	0.0898863	+	0.184294i	0.939001	−	0.343914i	$-0.111753\pi$
$53$	0.654382	+	1.34168i	0.0898863	+	0.184294i	−0.849115	+	0.528208i	$0.822864\pi$
$54$	6.50950	−	1.86657i	0.885831	−	0.254008i
$55$	−4.32539	−	1.23580i	−0.583236	−	0.166636i
$56$	1.49832	+	1.08859i	0.200221	+	0.145469i
$57$	−8.38490	+	0.493214i	−1.11061	+	0.0653278i
$58$	3.47667	+	2.52595i	0.456510	+	0.331674i
$59$	5.18420	+	12.8313i	0.674925	+	1.67050i	0.739990	+	0.672618i	$0.234830\pi$
$59$	5.18420	+	12.8313i	0.674925	+	1.67050i	−0.0650651	+	0.997881i	$0.520726\pi$
$60$	0.582167	−	1.44490i	0.0751574	−	0.186536i
$61$	5.15595	−	0.724621i	0.660151	−	0.0927782i	0.198861	−	0.980028i	$-0.436276\pi$
$61$	5.15595	−	0.724621i	0.660151	−	0.0927782i	0.461290	+	0.887249i	$0.347387\pi$
$62$	−14.6186	−	2.05452i	−1.85657	−	0.260924i
$63$	−0.0183067	−	0.524236i	−0.00230643	−	0.0660476i
$64$	−5.94548	−	1.26375i	−0.743185	−	0.157969i
$65$	−9.50629	+	5.06627i	−1.17911	+	0.628394i
$66$	−5.05206	+	3.15688i	−0.621865	+	0.388585i
$67$	−2.81032	−	11.2716i	−0.343335	−	1.37704i	−0.855344	−	0.518061i	$-0.826654\pi$
$67$	−2.81032	−	11.2716i	−0.343335	−	1.37704i	0.512009	−	0.858980i	$-0.328901\pi$
$68$	−0.282281	−	0.488925i	−0.0342316	−	0.0592909i
$69$	0.474895	−	0.211437i	0.0571707	−	0.0254540i
$70$	2.04622	+	1.48367i	0.244570	+	0.177333i
$71$	0.224448	+	0.216747i	0.0266371	+	0.0257231i	0.707858	−	0.706355i	$-0.249662\pi$
$71$	0.224448	+	0.216747i	0.0266371	+	0.0257231i	−0.681221	+	0.732078i	$0.738551\pi$
$72$	0.787150	+	1.61390i	0.0927665	+	0.190199i
$73$	0.397608	−	11.3860i	0.0465365	−	1.33263i	−0.721585	−	0.692326i	$-0.756586\pi$
$73$	0.397608	−	11.3860i	0.0465365	−	1.33263i	0.768122	−	0.640304i	$-0.221192\pi$
$74$	−0.210770	+	0.176857i	−0.0245015	+	0.0205592i
$75$	−3.59212	+	8.94010i	−0.414782	+	1.03231i
$76$	−0.364307	−	1.53320i	−0.0417889	−	0.175870i
$77$	−0.457271	−	1.40733i	−0.0521108	−	0.160381i
$78$	−3.45109	+	13.8416i	−0.390759	+	1.56725i
$79$	15.7669	−	4.52109i	1.77392	−	0.508662i	0.780696	−	0.624911i	$-0.214865\pi$
$79$	15.7669	−	4.52109i	1.77392	−	0.508662i	0.993220	+	0.116249i	$0.0370871\pi$
$80$	−10.0465	−	2.12538i	−1.12323	−	0.237625i
$81$	−4.66026	+	9.55496i	−0.517807	+	1.06166i
$82$	2.91228	−	1.05998i	0.321607	−	0.117055i
$83$	5.48069	−	2.44016i	0.601584	−	0.267842i	−0.0832652	−	0.996527i	$-0.526535\pi$
$83$	5.48069	−	2.44016i	0.601584	−	0.267842i	0.684849	+	0.728685i	$0.259868\pi$
$84$	0.501226	−	0.106539i	0.0546883	−	0.0116244i
$85$	1.74880	+	3.02231i	0.189684	+	0.327816i
$86$	−3.93861	+	9.74840i	−0.424711	+	1.05120i
$87$	−5.27090	+	1.12036i	−0.565100	+	0.120116i
$88$	3.38942	+	3.76433i	0.361313	+	0.401279i
$89$	−5.66697	−	7.25339i	−0.600697	−	0.768857i	0.387529	−	0.921858i	$-0.373329\pi$
$89$	−5.66697	−	7.25339i	−0.600697	−	0.768857i	−0.988226	+	0.153000i	$0.951106\pi$
$90$	1.07636	+	2.20150i	0.113458	+	0.232059i
$91$	−3.12866	−	1.66354i	−0.327973	−	0.174386i
$92$	0.0545388	+	0.0808571i	0.00568606	+	0.00842993i
$93$	14.1802	−	11.8986i	1.47042	−	1.23383i
$94$	9.45289	+	6.86793i	0.974991	+	0.708372i
$95$	2.26232	+	9.48061i	0.232109	+	0.972690i
$96$	−3.15131	+	2.28956i	−0.321629	+	0.233677i
$97$	0.373123	−	1.49651i	0.0378849	−	0.151948i	−0.948374	−	0.317153i	$-0.897273\pi$
$97$	0.373123	−	1.49651i	0.0378849	−	0.151948i	0.986259	+	0.165205i	$0.0528286\pi$
$98$	0.346401	−	9.91963i	0.0349918	−	1.00203i
$99$	0.249133	−	1.41290i	0.0250388	−	0.142002i
$100$	−1.76888	−	0.372445i	−0.176888	−	0.0372445i
$101$	1.71236	−	0.623247i	0.170386	−	0.0620154i	−0.255419	−	0.966831i	$-0.582213\pi$
$101$	1.71236	−	0.623247i	0.170386	−	0.0620154i	0.425805	+	0.904815i	$0.359991\pi$
$102$	4.52311	+	0.961416i	0.447854	+	0.0951944i
$103$	−0.424940	−	0.189195i	−0.0418705	−	0.0186420i	0.385695	−	0.922627i	$-0.373962\pi$
$103$	−0.424940	−	0.189195i	−0.0418705	−	0.0186420i	−0.427565	+	0.903985i	$0.640629\pi$
$104$	12.1001	+	0.846120i	1.18651	+	0.0829689i
$105$	−3.09944	+	0.661911i	−0.302474	+	0.0645959i
$106$	0.239784	−	2.28140i	0.0232899	−	0.221589i
$107$	9.40351	−	16.2874i	0.909071	−	1.57456i	0.0937143	−	0.995599i	$-0.470126\pi$
$107$	9.40351	−	16.2874i	0.909071	−	1.57456i	0.815357	−	0.578959i	$-0.196541\pi$
$108$	−1.53143	−	0.439131i	−0.147362	−	0.0422554i
$109$	11.2709	+	1.58402i	1.07955	+	0.151721i	0.656457	−	0.754363i	$-0.272054\pi$
$109$	11.2709	+	1.58402i	1.07955	+	0.151721i	0.423096	+	0.906085i	$0.360943\pi$
$110$	4.63057	+	5.13287i	0.441507	+	0.489400i
$111$	0.0120406	−	0.344798i	0.00114284	−	0.0327267i
$112$	−1.26538	−	3.13194i	−0.119568	−	0.295940i
$113$	0.340527	−	1.04803i	0.0320341	−	0.0985908i	−0.933761	−	0.357897i	$-0.883494\pi$
$113$	0.340527	−	1.04803i	0.0320341	−	0.0985908i	0.965795	+	0.259306i	$0.0834939\pi$
$114$	11.3290	+	6.18541i	1.06106	+	0.579317i
$115$	−0.337800	−	0.499775i	−0.0315000	−	0.0466043i
$116$	−0.378732	−	0.937394i	−0.0351644	−	0.0870349i
$117$	−1.92112	−	2.84818i	−0.177608	−	0.263314i
$118$	3.69295	−	20.9438i	0.339964	−	1.92803i
$119$	−0.503521	+	1.03237i	−0.0461577	+	0.0946373i
$120$	8.77094	−	6.38531i	0.800673	−	0.582896i
$121$	0.726761	+	6.91467i	0.0660692	+	0.628606i
$122$	−7.30942	−	3.25436i	−0.661764	−	0.294636i
$123$	−1.45578	+	3.60319i	−0.131263	+	0.324888i
$124$	2.66047	+	2.23240i	0.238917	+	0.200475i
$125$	10.9427	+	2.29308i	0.978741	+	0.205099i
$126$	−0.403050	+	0.698103i	−0.0359065	+	0.0621919i
$127$	4.85179	+	6.21000i	0.430526	+	0.551049i	0.953536	−	0.301278i	$-0.0974132\pi$
$127$	4.85179	+	6.21000i	0.430526	+	0.551049i	−0.523010	+	0.852327i	$0.675191\pi$
$128$	9.62735	+	9.29702i	0.850946	+	0.821749i
$129$	−5.77941	−	11.8495i	−0.508849	−	1.04329i
$130$	16.5144	+	1.13890i	1.44841	+	0.0998883i
$131$	15.9277	−	1.11378i	1.39161	−	0.0973111i	0.645821	−	0.763489i	$-0.276515\pi$
$131$	15.9277	−	1.11378i	1.39161	−	0.0973111i	0.745793	+	0.666178i	$0.232071\pi$
$132$	1.40152			0.121986
$133$	−2.17157	+	2.35879i	−0.188299	+	0.204533i
$134$	−5.51645	+	16.9779i	−0.476548	+	1.46666i
$135$	9.47447	+	2.70694i	0.815432	+	0.232976i
$136$	0.137220	−	3.92948i	0.0117665	−	0.336950i
$137$	10.8352	+	5.76120i	0.925718	+	0.492213i	0.862653	−	0.505797i	$-0.168801\pi$
$137$	10.8352	+	5.76120i	0.925718	+	0.492213i	0.0630649	+	0.998009i	$0.479912\pi$
$138$	−0.791075	−	0.111178i	−0.0673408	−	0.00946413i
$139$	−2.41494	−	3.09098i	−0.204832	−	0.262173i	0.674615	−	0.738170i	$-0.264310\pi$
$139$	−2.41494	−	3.09098i	−0.204832	−	0.262173i	−0.879447	+	0.475997i	$0.842087\pi$
$140$	−0.223279	−	0.551113i	−0.0188705	−	0.0465776i
$141$	−14.3313	+	3.04621i	−1.20691	+	0.256537i
$142$	−0.115999	−	0.465246i	−0.00973440	−	0.0390426i
$143$	−7.42414	−	6.22959i	−0.620838	−	0.520945i
$144$	0.342335	−	3.25710i	0.0285279	−	0.271425i
$145$	2.34800	+	5.79551i	0.194991	+	0.481291i
$146$	−9.79026	+	14.5147i	−0.810248	+	1.20124i
$147$	8.95300	+	8.64581i	0.738431	+	0.713094i
$148$	0.0640999	−	0.00900866i	0.00526898	−	0.000740507i
$149$	7.70214	+	2.80335i	0.630984	+	0.229659i	0.637659	−	0.770318i	$-0.279903\pi$
$149$	7.70214	+	2.80335i	0.630984	+	0.229659i	−0.00667562	+	0.999978i	$0.502125\pi$
$150$	11.9616	−	8.72570i	0.976662	−	0.712450i
$151$	13.5642			1.10384			0.551921	−	0.833896i	$-0.313895\pi$
$151$	13.5642			1.10384			0.551921	+	0.833896i	$0.313895\pi$
$152$	3.50674	−	10.3999i	0.284434	−	0.843541i
$153$	−0.900954	+	0.654581i	−0.0728378	+	0.0529198i
$154$	−0.550127	+	2.20644i	−0.0443305	+	0.177800i
$155$	−16.4682	−	13.7916i	−1.32275	−	1.10776i
$156$	2.41415	−	2.33132i	0.193287	−	0.186655i
$157$	1.43144	+	8.11809i	0.114241	+	0.647894i	0.987123	+	0.159963i	$0.0511373\pi$
$157$	1.43144	+	8.11809i	0.114241	+	0.647894i	−0.872882	+	0.487932i	$0.837752\pi$
$158$	−24.2294	−	6.94768i	−1.92759	−	0.552728i
$159$	1.92474	+	2.13764i	0.152642	+	0.169526i
$160$	3.25449	+	3.13681i	0.257290	+	0.247986i
$161$	0.0743333	−	0.183981i	0.00585828	−	0.0144998i
$162$	13.8543	−	8.65716i	1.08850	−	0.680171i
$163$	1.52885	−	0.324968i	0.119749	−	0.0254534i	−0.147647	−	0.989040i	$-0.547170\pi$
$163$	1.52885	−	0.324968i	0.119749	−	0.0254534i	0.267396	+	0.963587i	$0.413837\pi$
$164$	−0.713183	−	0.151592i	−0.0556903	−	0.0118373i
$165$	−8.66834	+	0.00830646i	−0.674829	+	0.000646657i
$166$	−9.12966	−	1.28309i	−0.708599	−	0.0995871i
$167$	−6.90661	+	6.66964i	−0.534450	+	0.516112i	−0.912172	−	0.409807i	$-0.865596\pi$
$167$	−6.90661	+	6.66964i	−0.534450	+	0.516112i	0.377723	+	0.925919i	$0.376707\pi$
$168$	3.35354	+	1.22059i	0.258731	+	0.0941704i
$169$	−10.1825	+	0.712026i	−0.783266	+	0.0547713i
$170$	0.182130	−	5.36286i	0.0139687	−	0.411312i
$171$	−2.93266	+	1.03082i	−0.224266	+	0.0788285i
$172$	2.00113	−	1.45391i	0.152585	−	0.110859i
$173$	−8.93864	−	5.58548i	−0.679592	−	0.424656i	0.145725	−	0.989325i	$-0.453448\pi$
$173$	−8.93864	−	5.58548i	−0.679592	−	0.424656i	−0.825318	+	0.564669i	$0.809004\pi$
$174$	7.78150	+	2.83223i	0.589914	+	0.214711i
$175$	1.38424	+	3.40730i	0.104639	+	0.257567i
$176$	−1.60430	−	9.09844i	−0.120929	−	0.685821i
$177$	16.4180	+	21.0140i	1.23405	+	1.57951i
$178$	1.47856	+	14.0676i	0.110823	+	1.05441i
$179$	−13.4441	−	5.98571i	−1.00486	−	0.447393i	−0.162733	−	0.986670i	$-0.552031\pi$
$179$	−13.4441	−	5.98571i	−1.00486	−	0.447393i	−0.842129	+	0.539277i	$0.818698\pi$
$180$	0.0597131	−	0.573417i	0.00445075	−	0.0427400i
$181$	−2.59061	−	10.3904i	−0.192559	−	0.772311i	−0.986424	−	0.164217i	$-0.947490\pi$
$181$	−2.59061	−	10.3904i	−0.192559	−	0.772311i	0.793866	−	0.608093i	$-0.208065\pi$
$182$	2.72264	+	4.71576i	0.201816	+	0.349555i
$183$	9.16552	−	4.08075i	0.677535	−	0.301658i
$184$	0.0237056	+	0.678839i	0.00174760	+	0.0500447i
$185$	−0.396403	+	0.0560982i	−0.0291441	+	0.00412442i
$186$	−28.1694	+	3.95896i	−2.06548	+	0.290285i
$187$	−1.93413	+	2.47558i	−0.141438	+	0.181032i
$188$	−1.02975	−	2.54872i	−0.0751024	−	0.185885i
$189$	1.00162	+	3.08267i	0.0728571	+	0.224231i
$190$	4.77216	−	14.1976i	0.346209	−	1.03000i
$191$	−7.56681	+	23.2883i	−0.547515	+	1.68508i	0.167417	+	0.985886i	$0.446457\pi$
$191$	−7.56681	+	23.2883i	−0.547515	+	1.68508i	−0.714933	+	0.699193i	$0.753543\pi$
$192$	−11.6841	+	0.817030i	−0.843225	+	0.0589641i
$193$	14.5011	+	5.27796i	1.04381	+	0.379916i	0.806324	−	0.591474i	$-0.201454\pi$
$193$	14.5011	+	5.27796i	1.04381	+	0.379916i	0.237487	+	0.971391i	$0.423676\pi$
$194$	−1.70494	+	1.64644i	−0.122407	+	0.118207i
$195$	−14.9177	+	14.4335i	−1.06828	+	1.03360i
$196$	−1.30579	+	1.93591i	−0.0932704	+	0.138279i
$197$	−0.880078	−	8.37338i	−0.0627029	−	0.596578i	−0.980086	−	0.198573i	$-0.936369\pi$
$197$	−0.880078	−	8.37338i	−0.0627029	−	0.596578i	0.917383	−	0.398005i	$-0.130297\pi$
$198$	−1.47526	+	1.63844i	−0.104842	+	0.116439i
$199$	6.08967	+	5.10984i	0.431685	+	0.362227i	0.832587	−	0.553894i	$-0.186859\pi$
$199$	6.08967	+	5.10984i	0.431685	+	0.362227i	−0.400902	+	0.916121i	$0.631303\pi$
$200$	−9.07280	−	8.72796i	−0.641544	−	0.617160i
$201$	−11.1923	−	19.3857i	−0.789447	−	1.36736i
$202$	−2.73911	−	0.582216i	−0.192723	−	0.0409646i
$203$	−1.15022	+	1.70528i	−0.0807299	+	0.119687i
$204$	−0.782559	−	0.755708i	−0.0547901	−	0.0529101i
$205$	4.41192	+	0.933364i	0.308142	+	0.0651890i
$206$	0.399720	+	0.592609i	0.0278498	+	0.0412890i
$207$	0.147377	−	0.123664i	0.0102434	−	0.00859527i
$208$	−17.8981	−	13.0037i	−1.24101	−	0.901644i
$209$	−7.15094	+	5.07559i	−0.494641	+	0.351086i
$210$	4.57827	+	1.66139i	0.315931	+	0.114647i
$211$	−5.42134	−	3.38763i	−0.373220	−	0.233214i	0.330320	−	0.943869i	$-0.392843\pi$
$211$	−5.42134	−	3.38763i	−0.373220	−	0.233214i	−0.703541	+	0.710655i	$0.748399\pi$
$212$	−0.332260	+	0.425274i	−0.0228197	+	0.0292079i
$213$	0.530869	+	0.282268i	0.0363746	+	0.0193407i
$214$	−25.5183	+	13.5683i	−1.74439	+	0.927511i
$215$	−12.3683	+	9.00423i	−0.843512	+	0.614083i
$216$	−7.42429	−	8.24551i	−0.505159	−	0.561036i
$217$	0.738590	−	7.02721i	0.0501387	−	0.477038i
$218$	−13.3985	−	11.2427i	−0.907459	−	0.761449i
$219$	−5.31107	−	21.3015i	−0.358889	−	1.43942i
$220$	−0.283946	−	1.60136i	−0.0191436	−	0.107964i
$221$	0.786342	+	7.48154i	0.0528951	+	0.503263i
$222$	−0.296475	+	0.439542i	−0.0198981	+	0.0295001i
$223$	−18.9347	+	10.0677i	−1.26796	+	0.674186i	−0.960739	−	0.277453i	$-0.910510\pi$
$223$	−18.9347	+	10.0677i	−1.26796	+	0.674186i	−0.307220	+	0.951639i	$0.599399\pi$
$224$	−0.258193	+	1.46428i	−0.0172512	+	0.0978366i
$225$	−0.365925	+	3.54692i	−0.0243950	+	0.236461i
$226$	−1.29724	+	1.08851i	−0.0862911	+	0.0724068i
$227$	−4.30738	−	13.2568i	−0.285891	−	0.879882i	−0.986130	−	0.165974i	$-0.946923\pi$
$227$	−4.30738	−	13.2568i	−0.285891	−	0.879882i	0.700239	−	0.713908i	$-0.253077\pi$
$228$	−1.48915	−	2.64645i	−0.0986214	−	0.175265i
$229$	13.1425	−	9.54856i	0.868478	−	0.630986i	−0.0617000	−	0.998095i	$-0.519652\pi$
$229$	13.1425	−	9.54856i	0.868478	−	0.630986i	0.930178	+	0.367108i	$0.119652\pi$
$230$	0.0332395	+	0.926401i	0.00219175	+	0.0610851i
$231$	−1.59450	−	2.36394i	−0.104910	−	0.155536i
$232$	1.22268	−	6.93419i	0.0802732	−	0.455252i
$233$	−8.59909	+	17.6307i	−0.563345	+	1.15503i	0.407028	+	0.913416i	$0.366565\pi$
$233$	−8.59909	+	17.6307i	−0.563345	+	1.15503i	−0.970373	+	0.241613i	$0.922324\pi$
$234$	0.184251	+	5.27625i	0.0120448	+	0.344919i
$235$	6.38409	+	15.7577i	0.416452	+	1.02792i
$236$	−3.34784	+	3.71815i	−0.217926	+	0.242031i
$237$	26.8038	−	16.7489i	1.74109	−	1.08796i
$238$	1.49690	−	0.935368i	0.0970297	−	0.0606309i
$239$	5.94886	−	6.60688i	0.384800	−	0.427364i	−0.519361	−	0.854555i	$-0.673830\pi$
$239$	5.94886	−	6.60688i	0.384800	−	0.427364i	0.904161	+	0.427191i	$0.140497\pi$
$240$	−19.7380	+	1.39922i	−1.27408	+	0.0903195i
$241$	−0.603910	−	17.2937i	−0.0389012	−	1.11399i	−0.849234	−	0.528016i	$-0.822936\pi$
$241$	−0.603910	−	17.2937i	−0.0389012	−	1.11399i	0.810333	−	0.585969i	$-0.199286\pi$
$242$	4.68377	−	9.60316i	0.301084	−	0.617314i
$243$	−1.26159	+	7.15484i	−0.0809312	+	0.458983i
$244$	1.05260	+	1.56055i	0.0673860	+	0.0999038i
$245$	8.06477	−	11.9813i	0.515240	−	0.765455i
$246$	4.83143	−	3.51024i	0.308041	−	0.223805i
$247$	−3.87483	+	20.6379i	−0.246550	+	1.31316i
$248$	7.47437	+	23.0037i	0.474623	+	1.46074i
$249$	8.85585	−	7.43094i	0.561216	−	0.470917i
$250$	−12.3933	−	11.8994i	−0.783823	−	0.752587i
$251$	−3.47820	+	19.7258i	−0.219542	+	1.24508i	0.653307	+	0.757093i	$0.273381\pi$
$251$	−3.47820	+	19.7258i	−0.219542	+	1.24508i	−0.872849	+	0.487991i	$0.837730\pi$
$252$	0.167446	−	0.0890324i	0.0105481	−	0.00560852i
$253$	0.303486	−	0.449936i	0.0190800	−	0.0282872i
$254$	−1.26588	−	12.0440i	−0.0794281	−	0.755708i
$255$	4.84458	+	4.66939i	0.303379	+	0.292409i
$256$	−2.03464	−	8.16051i	−0.127165	−	0.510032i
$257$	−10.8260	−	9.08406i	−0.675305	−	0.566648i	0.239325	−	0.970939i	$-0.423074\pi$
$257$	−10.8260	−	9.08406i	−0.675305	−	0.566648i	−0.914630	+	0.404291i	$0.867518\pi$
$258$	−2.11774	+	20.1490i	−0.131845	+	1.25442i
$259$	−0.0881211	−	0.0978684i	−0.00547558	−	0.00608125i
$260$	−3.15286	−	2.28607i	−0.195532	−	0.141776i
$261$	−1.76086	+	0.936266i	−0.108994	+	0.0579534i
$262$	−21.6643	−	11.5191i	−1.33843	−	0.711654i
$263$	−2.75920	+	3.53161i	−0.170139	+	0.217769i	−0.865522	−	0.500872i	$-0.833013\pi$
$263$	−2.75920	+	3.53161i	−0.170139	+	0.217769i	0.695382	+	0.718640i	$0.255235\pi$
$264$	8.27764	+	5.17244i	0.509453	+	0.318342i
$265$	2.05250	−	2.63228i	0.126084	−	0.161699i
$266$	4.75089	−	1.30561i	0.291296	−	0.0800523i
$267$	−14.3495	−	10.4255i	−0.878177	−	0.638033i
$268$	3.21722	−	2.69957i	0.196523	−	0.164903i
$269$	−7.61087	−	11.2836i	−0.464043	−	0.687972i	0.522284	−	0.852771i	$-0.325080\pi$
$269$	−7.61087	−	11.2836i	−0.464043	−	0.687972i	−0.986327	+	0.164800i	$0.947302\pi$
$270$	−10.1429	−	11.2432i	−0.617279	−	0.684238i
$271$	11.8934	+	11.4854i	0.722475	+	0.697686i	0.961953	−	0.273216i	$-0.0880874\pi$
$271$	11.8934	+	11.4854i	0.722475	+	0.697686i	−0.239478	+	0.970902i	$0.576976\pi$
$272$	−4.01016	+	5.94531i	−0.243152	+	0.360487i
$273$	−6.67881	−	1.41963i	−0.404220	−	0.0859197i
$274$	−9.42911	−	16.3317i	−0.569634	−	0.986634i
$275$	1.76569	+	9.90270i	0.106475	+	0.597155i
$276$	0.143969	+	0.120804i	0.00866591	+	0.00727156i
$277$	−6.60952	+	7.34062i	−0.397128	+	0.441055i	−0.908234	−	0.418462i	$-0.862569\pi$
$277$	−6.60952	+	7.34062i	−0.397128	+	0.441055i	0.511106	+	0.859517i	$0.329236\pi$
$278$	0.630079	+	5.99481i	0.0377897	+	0.359545i
$279$	3.83089	−	5.67952i	0.229349	−	0.340024i
$280$	0.715212	−	4.07902i	0.0427421	−	0.243768i
$281$	17.0841	−	16.4979i	1.01915	−	0.984185i	0.0192752	−	0.999814i	$-0.493864\pi$
$281$	17.0841	−	16.4979i	1.01915	−	0.984185i	0.999878	+	0.0156295i	$0.00497523\pi$
$282$	21.1575	+	7.70069i	1.25991	+	0.458570i
$283$	−15.6343	+	1.09326i	−0.929361	+	0.0649873i	−0.526407	−	0.850233i	$-0.676461\pi$
$283$	−15.6343	+	1.09326i	−0.929361	+	0.0649873i	−0.402954	+	0.915220i	$0.632017\pi$
$284$	−0.0348587	+	0.107284i	−0.00206848	+	0.00636613i
$285$	9.22604	+	16.3594i	0.546503	+	0.969046i
$286$	4.60226	+	14.1643i	0.272138	+	0.837553i
$287$	0.555695	+	1.37539i	0.0328016	+	0.0811869i
$288$	−0.887534	+	1.13599i	−0.0522985	+	0.0669390i
$289$	−14.4198	+	2.02656i	−0.848221	+	0.119210i
$290$	1.65957	−	9.46490i	0.0974531	−	0.555798i
$291$	−0.103721	−	2.97018i	−0.00608024	−	0.174115i
$292$	3.76281	−	1.67531i	0.220202	−	0.0980403i
$293$	5.65305	+	9.79137i	0.330255	+	0.572018i	0.982562	−	0.185937i	$-0.0595320\pi$
$293$	5.65305	+	9.79137i	0.330255	+	0.572018i	−0.652307	+	0.757955i	$0.726199\pi$
$294$	−4.62707	−	18.5582i	−0.269856	−	1.08234i
$295$	20.6842	−	23.0165i	1.20428	−	1.34007i
$296$	0.411834	+	0.183361i	0.0239374	+	0.0106576i
$297$	0.926666	+	8.81664i	0.0537706	+	0.511593i
$298$	−7.75469	−	9.92555i	−0.449217	−	0.574972i
$299$	−0.225673	−	1.27985i	−0.0130510	−	0.0740159i
$300$	−3.47432	+	0.249640i	−0.200590	+	0.0144130i
$301$	−4.72898	−	1.72121i	−0.272574	−	0.0992088i
$302$	−17.6772	−	11.0459i	−1.01721	−	0.635622i
$303$	2.84078	−	2.06395i	0.163198	−	0.118571i
$304$	−15.4758	+	12.6967i	−0.887595	+	0.728207i
$305$	−6.51957	−	9.64570i	−0.373309	−	0.552311i
$306$	1.70719	−	0.119379i	0.0975937	−	0.00682442i
$307$	−14.7667	−	5.37462i	−0.842778	−	0.306746i	−0.115685	−	0.993286i	$-0.536906\pi$
$307$	−14.7667	−	5.37462i	−0.842778	−	0.306746i	−0.727092	+	0.686540i	$0.759129\pi$
$308$	0.384833	−	0.371629i	0.0219279	−	0.0211755i
$309$	−0.887608	−	0.124745i	−0.0504942	−	0.00709650i
$310$	10.2306	+	31.3841i	0.581058	+	1.78250i
$311$	−21.0865	−	4.48208i	−1.19571	−	0.254155i	−0.433298	−	0.901251i	$-0.642650\pi$
$311$	−21.0865	−	4.48208i	−1.19571	−	0.254155i	−0.762409	+	0.647095i	$0.775984\pi$
$312$	22.8625	−	4.85957i	1.29433	−	0.275119i
$313$	−6.86096	+	4.28720i	−0.387804	+	0.242327i	−0.709784	−	0.704420i	$-0.751207\pi$
$313$	−6.86096	+	4.28720i	−0.387804	+	0.242327i	0.321979	+	0.946747i	$0.395652\pi$
$314$	4.74542	−	11.7453i	0.267800	−	0.662827i
$315$	−1.03512	+	0.551655i	−0.0583223	+	0.0310823i
$316$	3.96792	+	4.40682i	0.223213	+	0.247903i
$317$	26.2488	+	7.52673i	1.47428	+	0.422743i	0.914053	−	0.405595i	$-0.132936\pi$
$317$	26.2488	+	7.52673i	1.47428	+	0.422743i	0.560228	+	0.828338i	$0.310714\pi$
$318$	−0.767587	−	4.35320i	−0.0430442	−	0.244116i
$319$	−4.04691	+	3.90805i	−0.226583	+	0.218809i
$320$	3.30072	+	13.1846i	0.184516	+	0.737042i
$321$	8.76731	−	35.1637i	0.489343	−	1.96265i
$322$	−0.246696	+	0.179235i	−0.0137478	+	0.00998839i
$323$	6.72964	+	1.02180i	0.374447	+	0.0568547i
$324$	−3.84340			−0.213522
$325$	19.5139	+	14.1206i	1.08244	+	0.783270i
$326$	−2.25707	−	0.821505i	−0.125007	−	0.0454989i
$327$	21.7184	−	3.05233i	1.20103	−	0.168794i
$328$	−3.65274	−	3.52741i	−0.201689	−	0.194769i
$329$	−3.12740	+	4.63656i	−0.172419	+	0.255622i
$330$	11.3035	+	7.04816i	0.622238	+	0.387989i
$331$	−2.31328	+	22.0094i	−0.127149	+	1.20974i	0.725858	+	0.687845i	$0.241443\pi$
$331$	−2.31328	+	22.0094i	−0.127149	+	1.20974i	−0.853007	+	0.521900i	$0.825224\pi$
$332$	1.66152	+	1.39418i	0.0911879	+	0.0765157i
$333$	−0.0308897	−	0.123892i	−0.00169274	−	0.00678922i
$334$	14.4322	−	3.06766i	0.789694	−	0.167855i
$335$	−19.8824	+	16.7158i	−1.08629	+	0.913283i
$336$	−4.00738	−	5.12921i	−0.218620	−	0.279821i
$337$	−22.9978	−	3.23213i	−1.25277	−	0.176065i	−0.518591	−	0.855022i	$-0.673543\pi$
$337$	−22.9978	−	3.23213i	−1.25277	−	0.176065i	−0.734178	+	0.678957i	$0.762432\pi$
$338$	13.8498	+	7.36407i	0.753330	+	0.400553i
$339$	0.0741071	−	2.12215i	0.00402494	−	0.115259i
$340$	−0.704921	+	1.04725i	−0.0382297	+	0.0567952i
$341$	5.97200	−	18.3799i	0.323402	−	0.995328i
$342$	4.66133	+	1.04481i	0.252056	+	0.0564966i
$343$	9.89972			0.534535
$344$	17.1849	−	1.20168i	0.926546	−	0.0647904i
$345$	−0.891160	−	0.746318i	−0.0479784	−	0.0401804i
$346$	7.10052	+	14.5582i	0.381726	+	0.782654i
$347$	−8.04817	−	7.77203i	−0.432048	−	0.417224i	0.446570	−	0.894749i	$-0.352645\pi$
$347$	−8.04817	−	7.77203i	−0.432048	−	0.417224i	−0.878619	+	0.477524i	$0.841534\pi$
$348$	−1.19942	−	1.53518i	−0.0642954	−	0.0822944i
$349$	−6.65011	+	11.5183i	−0.355972	+	0.616562i	−0.987284	−	0.158967i	$-0.949184\pi$
$349$	−6.65011	+	11.5183i	−0.355972	+	0.616562i	0.631311	+	0.775529i	$0.282517\pi$
$350$	0.970737	−	5.56770i	0.0518881	−	0.297606i
$351$	16.2621	+	13.6455i	0.868004	+	0.728342i
$352$	−1.52341	+	3.77058i	−0.0811982	+	0.200973i
$353$	7.00148	+	3.11726i	0.372651	+	0.165915i	0.584512	−	0.811385i	$-0.301286\pi$
$353$	7.00148	+	3.11726i	0.372651	+	0.165915i	−0.211861	+	0.977300i	$0.567952\pi$
$354$	−4.28360	−	40.7557i	−0.227671	−	2.16614i
$355$	0.214964	−	0.663755i	0.0114091	−	0.0352284i
$356$	1.45881	−	2.99100i	0.0773166	−	0.158523i
$357$	−0.384341	+	2.17971i	−0.0203415	+	0.115362i
$358$	12.6462	+	18.7488i	0.668374	+	0.990906i
$359$	11.2571	+	27.8624i	0.594128	+	1.47052i	0.861921	+	0.507043i	$0.169261\pi$
$359$	11.2571	+	27.8624i	0.594128	+	1.47052i	−0.267792	+	0.963477i	$0.586294\pi$
$360$	2.46893	−	3.16634i	0.130124	−	0.166881i
$361$	17.1822	+	8.10999i	0.904326	+	0.426842i
$362$	−5.08518	+	15.6506i	−0.267271	+	0.822576i
$363$	5.01884	+	12.4221i	0.263421	+	0.651990i
$364$	0.0447085	−	1.28028i	0.00234336	−	0.0671051i
$365$	−23.2630	+	10.3841i	−1.21764	+	0.543527i
$366$	−15.2678	−	2.14575i	−0.798061	−	0.112160i
$367$	−1.32040	−	0.378619i	−0.0689243	−	0.0197637i	0.240998	−	0.970526i	$-0.422525\pi$
$367$	−1.32040	−	0.378619i	−0.0689243	−	0.0197637i	−0.309922	+	0.950762i	$0.600303\pi$
$368$	0.619445	−	1.07291i	0.0322908	−	0.0559293i
$369$	−0.150337	+	1.43036i	−0.00782621	+	0.0744614i
$370$	0.562283	+	0.249699i	0.0292317	+	0.0129812i
$371$	1.09532	+	0.0765923i	0.0568662	+	0.00397647i
$372$	6.11372	+	2.72201i	0.316982	+	0.141129i
$373$	20.2474	+	4.30372i	1.04837	+	0.222838i	0.699722	−	0.714415i	$-0.253307\pi$
$373$	20.2474	+	4.30372i	1.04837	+	0.222838i	0.348649	+	0.937253i	$0.386640\pi$
$374$	4.53656	−	1.65117i	0.234580	−	0.0853802i
$375$	21.4871	−	1.56461i	1.10959	−	0.0807961i
$376$	3.32441	−	18.8537i	0.171444	−	0.972305i
$377$	−0.470155	+	13.4635i	−0.0242142	+	0.693404i
$378$	1.20501	−	4.83305i	0.0619793	−	0.248585i
$379$	−0.379083	+	0.275420i	−0.0194722	+	0.0141474i	−0.597479	−	0.801885i	$-0.703831\pi$
$379$	−0.379083	+	0.275420i	−0.0194722	+	0.0141474i	0.578007	+	0.816032i	$0.303831\pi$
$380$	−2.72211	+	2.23766i	−0.139642	+	0.114790i
$381$	12.2854	+	8.92585i	0.629399	+	0.457285i
$382$	28.8258	−	24.1877i	1.47486	−	1.23755i
$383$	3.87853	+	5.75016i	0.198184	+	0.293819i	0.915009	−	0.403433i	$-0.132183\pi$
$383$	3.87853	+	5.75016i	0.198184	+	0.293819i	−0.716825	+	0.697253i	$0.754405\pi$
$384$	22.7708	+	12.1075i	1.16202	+	0.617856i
$385$	−2.37798	+	2.30079i	−0.121193	+	0.117259i
$386$	−14.6000	−	18.6872i	−0.743122	−	0.951153i
$387$	−3.26484	−	3.62597i	−0.165961	−	0.184318i
$388$	0.545417	−	0.115932i	0.0276893	−	0.00588555i
$389$	6.96994	−	17.2512i	0.353390	−	0.874671i	−0.640867	−	0.767652i	$-0.721425\pi$
$389$	6.96994	−	17.2512i	0.353390	−	0.874671i	0.994257	−	0.107019i	$-0.0341306\pi$
$390$	31.1947	−	6.66190i	1.57961	−	0.337338i
$391$	−0.412065	+	0.0875871i	−0.0208390	+	0.00442947i
$392$	−14.8569	+	6.61472i	−0.750387	+	0.334094i
$393$	28.9115	−	10.5229i	1.45839	−	0.530811i
$394$	−5.67186	+	11.6290i	−0.285744	+	0.585862i
$395$	−24.5676	−	27.2326i	−1.23613	−	1.37022i
$396$	0.498596	−	0.142970i	0.0250554	−	0.00718452i
$397$	0.689885	−	2.76698i	0.0346243	−	0.138871i	−0.950496	−	0.310737i	$-0.899424\pi$
$397$	0.689885	−	2.76698i	0.0346243	−	0.138871i	0.985120	+	0.171866i	$0.0549797\pi$
$398$	−3.77502	−	11.6183i	−0.189225	−	0.582373i
$399$	−2.76957	+	5.52260i	−0.138652	+	0.276476i
$400$	5.59765	+	22.2690i	0.279883	+	1.11345i
$401$	−6.94365	+	5.82641i	−0.346749	+	0.290957i	−0.799483	−	0.600689i	$-0.794893\pi$
$401$	−6.94365	+	5.82641i	−0.346749	+	0.290957i	0.452734	+	0.891646i	$0.350449\pi$
$402$	−1.20051	+	34.3782i	−0.0598762	+	1.71463i
$403$	−20.2867	−	41.5939i	−1.01055	−	2.07194i
$404$	0.473903	+	0.457643i	0.0235776	+	0.0227686i
$405$	23.7713	−	0.0227789i	1.18121	−	0.00113189i
$406$	2.88767	−	1.28567i	0.143313	−	0.0638069i
$407$	−0.180097	−	0.311938i	−0.00892710	−	0.0154622i
$408$	−1.83293	−	7.35148i	−0.0907435	−	0.363952i
$409$	−18.7112	+	11.6921i	−0.925209	+	0.578135i	−0.906738	−	0.421695i	$-0.861435\pi$
$409$	−18.7112	+	11.6921i	−0.925209	+	0.578135i	−0.0184712	+	0.999829i	$0.505880\pi$
$410$	−4.98962	−	4.80919i	−0.246420	−	0.237509i
$411$	23.1302	+	4.91648i	1.14093	+	0.242512i
$412$	−0.00586899	−	0.168066i	−0.000289144	−	0.00828001i
$413$	10.0802	+	1.41668i	0.496016	+	0.0697104i
$414$	−0.292770	+	0.0411462i	−0.0143889	+	0.00202222i
$415$	−10.2847	−	8.61313i	−0.504857	−	0.422802i
$416$	3.64796	+	9.02903i	0.178856	+	0.442684i
$417$	−6.11495	−	4.44277i	−0.299450	−	0.217563i
$418$	13.4525	−	0.791300i	0.657984	−	0.0387037i
$419$	−2.28563	−	1.66061i	−0.111660	−	0.0811259i	0.530554	−	0.847651i	$-0.321984\pi$
$419$	−2.28563	−	1.66061i	−0.111660	−	0.0811259i	−0.642214	+	0.766525i	$0.721984\pi$
$420$	−0.706299	−	0.902238i	−0.0344639	−	0.0440247i
$421$	−9.16927	+	2.62925i	−0.446883	+	0.128142i	−0.491529	−	0.870861i	$-0.663562\pi$
$421$	−9.16927	+	2.62925i	−0.446883	+	0.128142i	0.0446461	+	0.999003i	$0.485784\pi$
$422$	4.30650	+	8.82964i	0.209637	+	0.429820i
$423$	−4.78768	+	2.54566i	−0.232785	+	0.123774i
$424$	−3.53191	+	1.28551i	−0.171525	+	0.0624299i
$425$	4.35371	−	6.48140i	0.211186	−	0.314394i
$426$	−0.461976	−	0.800166i	−0.0223828	−	0.0387682i
$427$	1.43464	−	3.55085i	0.0694270	−	0.171838i
$428$	6.78278	+	0.474298i	0.327858	+	0.0229261i
$429$	−17.0606	−	7.59586i	−0.823692	−	0.366731i
$430$	23.4511	−	1.66245i	1.13091	−	0.0801703i
$431$	−37.1839	−	10.6623i	−1.79108	−	0.513585i	−0.795374	−	0.606119i	$-0.792726\pi$
$431$	−37.1839	−	10.6623i	−1.79108	−	0.513585i	−0.995710	+	0.0925338i	$0.970503\pi$
$432$	3.51411	+	19.9295i	0.169073	+	0.958858i
$433$	0.781935	−	0.755105i	0.0375774	−	0.0362881i	−0.675633	−	0.737238i	$-0.736129\pi$
$433$	0.781935	−	0.755105i	0.0375774	−	0.0362881i	0.713210	+	0.700950i	$0.247241\pi$
$434$	−6.68509	+	8.55653i	−0.320895	+	0.410727i
$435$	7.42745	+	9.48795i	0.356119	+	0.454912i
$436$	1.27155	+	3.91343i	0.0608963	+	0.187419i
$437$	−1.17206	−	0.0949948i	−0.0560675	−	0.00454422i
$438$	−10.4252	+	32.0856i	−0.498137	+	1.53311i
$439$	−26.2366	−	16.3945i	−1.25221	−	0.782465i	−0.268679	−	0.963230i	$-0.586587\pi$
$439$	−26.2366	−	16.3945i	−1.25221	−	0.782465i	−0.983526	+	0.180765i	$0.942143\pi$
$440$	4.23295	−	10.5059i	0.201798	−	0.500849i
$441$	4.06704	+	2.16248i	0.193669	+	0.102975i
$442$	5.06776	−	10.3904i	0.241049	−	0.494223i
$443$	−4.20159	+	1.52925i	−0.199623	+	0.0726570i	−0.439897	−	0.898048i	$-0.644985\pi$
$443$	−4.20159	+	1.52925i	−0.199623	+	0.0726570i	0.240274	+	0.970705i	$0.422763\pi$
$444$	0.113948	−	0.0507329i	0.00540773	−	0.00240767i
$445$	−9.00495	+	18.5079i	−0.426876	+	0.877357i
$446$	32.8746	+	2.29882i	1.55666	+	0.108852i
$447$	15.7557	+	1.10175i	0.745219	+	0.0521108i
$448$	−2.99161	+	3.32252i	−0.141340	+	0.156974i
$449$	19.6470	−	34.0296i	0.927198	−	1.60595i	0.139211	−	0.990263i	$-0.455544\pi$
$449$	19.6470	−	34.0296i	0.927198	−	1.60595i	0.787987	−	0.615691i	$-0.211123\pi$
$450$	3.36529	−	4.32443i	0.158641	−	0.203855i
$451$	0.704530	+	3.99559i	0.0331750	+	0.188145i
$452$	0.394520	−	0.0554462i	0.0185567	−	0.00260797i
$453$	25.1251	−	7.20452i	1.18048	−	0.338498i
$454$	−5.18207	+	20.7841i	−0.243207	+	0.975448i
$455$	−0.268933	+	7.91878i	−0.0126078	+	0.371238i
$456$	0.971771	−	21.1263i	0.0455074	−	0.989331i
$457$	15.6753			0.733257			0.366629	−	0.930367i	$-0.380512\pi$
$457$	15.6753			0.733257			0.366629	+	0.930367i	$0.380512\pi$
$458$	−24.9033	+	1.74141i	−1.16365	+	0.0813706i
$459$	4.23658	−	5.42258i	0.197747	−	0.253104i
$460$	0.108862	−	0.188973i	0.00507573	−	0.00881090i
$461$	28.3117	−	15.0536i	1.31861	−	0.701116i	0.347033	−	0.937853i	$-0.387189\pi$
$461$	28.3117	−	15.0536i	1.31861	−	0.701116i	0.971574	+	0.236737i	$0.0760779\pi$
$462$	0.152925	+	4.37920i	0.00711471	+	0.203739i
$463$	2.08799	+	2.31895i	0.0970370	+	0.107771i	0.789707	−	0.613484i	$-0.210232\pi$
$463$	2.08799	+	2.31895i	0.0970370	+	0.107771i	−0.692670	+	0.721255i	$0.743566\pi$
$464$	−8.59322	+	9.54374i	−0.398930	+	0.443057i
$465$	−37.8293	−	16.7993i	−1.75429	−	0.779048i
$466$	25.5640	−	15.9741i	1.18423	−	0.739987i
$467$	−3.36807	+	32.0450i	−0.155856	+	1.48287i	0.584907	+	0.811101i	$0.301131\pi$
$467$	−3.36807	+	32.0450i	−0.155856	+	1.48287i	−0.740762	+	0.671767i	$0.765536\pi$
$468$	0.621026	−	1.07565i	0.0287070	−	0.0497219i
$469$	−8.21359	−	2.35521i	−0.379268	−	0.108753i
$470$	4.51227	−	25.7345i	0.208136	−	1.18705i
$471$	6.96331	+	14.2769i	0.320852	+	0.657845i
$472$	−33.4952	+	9.60460i	−1.54174	+	0.442087i
$473$	−11.6727	−	7.29390i	−0.536711	−	0.335374i
$474$	−48.5706			−2.23092
$475$	16.8229	−	13.8560i	0.771889	−	0.635757i
$476$	−0.415263			−0.0190335
$477$	0.902797	+	0.564130i	0.0413363	+	0.0258298i
$478$	−13.1329	+	3.76581i	−0.600686	+	0.172244i
$479$	1.67217	+	3.42845i	0.0764034	+	0.156650i	0.933576	−	0.358378i	$-0.116670\pi$
$479$	1.67217	+	3.42845i	0.0764034	+	0.156650i	−0.857173	+	0.515028i	$0.827781\pi$
$480$	7.69440	+	4.08173i	0.351200	+	0.186305i
$481$	−0.829109	−	0.237743i	−0.0378041	−	0.0108402i
$482$	−13.2960	+	23.0293i	−0.605614	+	1.04895i
$483$	0.0399681	−	0.380271i	0.00181861	−	0.0173029i
$484$	−2.13169	+	1.33203i	−0.0968951	+	0.0605468i
$485$	−3.37270	+	0.720268i	−0.153146	+	0.0327057i
$486$	7.47062	−	8.29696i	0.338874	−	0.376358i
$487$	17.8783	+	19.8559i	0.810144	+	0.899756i	0.996573	−	0.0827127i	$-0.0263584\pi$
$487$	17.8783	+	19.8559i	0.810144	+	0.899756i	−0.186430	+	0.982468i	$0.559692\pi$
$488$	0.457520	+	13.1016i	0.0207109	+	0.593084i
$489$	2.65930	−	1.41398i	0.120258	−	0.0639422i
$490$	−20.2670	+	9.04674i	−0.915570	+	0.408690i
$491$	−5.83556	+	7.46918i	−0.263355	+	0.337079i	−0.901454	−	0.432875i	$-0.857499\pi$
$491$	−5.83556	+	7.46918i	−0.263355	+	0.337079i	0.638098	+	0.769955i	$0.279721\pi$
$492$	−1.40155	+	0.0980060i	−0.0631868	+	0.00441845i
$493$	4.36691			0.196676
$494$	21.8561	−	23.7403i	0.983352	−	1.06813i
$495$	−3.08296	+	0.887221i	−0.138569	+	0.0398776i
$496$	10.6726	−	42.8053i	0.479212	−	1.92201i
$497$	0.220615	−	0.0632602i	0.00989592	−	0.00283761i
$498$	−17.5924	+	2.47245i	−0.788336	+	0.110793i
$499$	3.44894	+	19.5599i	0.154396	+	0.875622i	0.959336	+	0.282266i	$0.0910862\pi$
$499$	3.44894	+	19.5599i	0.154396	+	0.875622i	−0.804940	+	0.593356i	$0.797803\pi$
$500$	0.989132	+	3.91916i	0.0442353	+	0.175270i
$501$	−9.25065	+	16.0226i	−0.413289	+	0.715837i
$502$	20.5964	−	22.8746i	0.919264	−	1.02095i
$503$	−15.1190	−	1.05723i	−0.674124	−	0.0471393i	−0.271408	−	0.962464i	$-0.587489\pi$
$503$	−15.1190	−	1.05723i	−0.674124	−	0.0471393i	−0.402716	+	0.915325i	$0.631934\pi$
$504$	1.31755	+	0.0921321i	0.0586884	+	0.00410389i
$505$	−2.93379	−	2.82770i	−0.130552	−	0.125831i
$506$	−0.761910	+	0.339224i	−0.0338710	+	0.0150803i
$507$	−18.4828	+	6.72720i	−0.820852	+	0.298766i
$508$	−1.24896	+	2.56075i	−0.0554137	+	0.113615i
$509$	−22.9126	−	12.1829i	−1.01558	−	0.539996i	−0.123729	−	0.992316i	$-0.539485\pi$
$509$	−22.9126	−	12.1829i	−1.01558	−	0.539996i	−0.891856	+	0.452320i	$0.850596\pi$
$510$	−2.51107	−	10.0304i	−0.111192	−	0.444153i
$511$	−7.10669	−	4.44075i	−0.314381	−	0.196447i
$512$	4.27766	−	13.1653i	0.189048	−	0.581829i
$513$	15.6636	−	11.1177i	0.691567	−	0.490860i
$514$	6.71107	+	20.6546i	0.296013	+	0.911034i
$515$	0.0372956	+	1.03945i	0.00164344	+	0.0458035i
$516$	2.93448	−	3.75596i	0.129183	−	0.165347i
$517$	−11.0033	+	10.6258i	−0.483926	+	0.467321i
$518$	0.0351428	+	0.199305i	0.00154409	+	0.00875694i
$519$	−19.5238	−	5.59835i	−0.856999	−	0.245740i
$520$	−10.1844	−	25.1379i	−0.446616	−	1.10237i
$521$	6.44335	+	2.86877i	0.282288	+	0.125683i	0.542997	−	0.839735i	$-0.317290\pi$
$521$	6.44335	+	2.86877i	0.282288	+	0.125683i	−0.260709	+	0.965418i	$0.583956\pi$
$522$	3.05723	+	0.213782i	0.133811	+	0.00935699i
$523$	−12.3645	+	30.6032i	−0.540662	+	1.33818i	0.371530	+	0.928421i	$0.378833\pi$
$523$	−12.3645	+	30.6032i	−0.540662	+	1.33818i	−0.912192	+	0.409764i	$0.865611\pi$
$524$	2.88623	+	4.99909i	0.126085	+	0.218386i
$525$	4.37379	+	5.57613i	0.190888	+	0.243362i
$526$	6.47178	−	2.35553i	0.282183	−	0.102706i
$527$	−13.2451	+	7.04257i	−0.576968	+	0.306779i
$528$	−7.80421	−	16.0010i	−0.339635	−	0.696354i
$529$	−22.0391	+	6.31960i	−0.958220	+	0.274765i
$530$	−4.81843	+	1.75900i	−0.209299	+	0.0764059i
$531$	7.98444	+	5.80103i	0.346495	+	0.251743i
$532$	−1.11063	−	0.331804i	−0.0481521	−	0.0143855i
$533$	7.85995	+	5.71059i	0.340452	+	0.247353i
$534$	10.2106	+	25.2722i	0.441857	+	1.09363i
$535$	−41.9541	−	2.89332i	−1.81383	−	0.125089i
$536$	28.9646	−	4.07071i	1.25108	−	0.175828i
$537$	−28.0819	−	3.94665i	−1.21182	−	0.170311i
$538$	0.729942	+	20.9028i	0.0314701	+	0.901184i
$539$	12.7101	+	2.70160i	0.547461	+	0.116366i
$540$	0.621964	+	3.50767i	0.0267651	+	0.150946i
$541$	31.9075	−	19.9380i	1.37181	−	0.857203i	0.374273	−	0.927319i	$-0.377892\pi$
$541$	31.9075	−	19.9380i	1.37181	−	0.857203i	0.997539	+	0.0701154i	$0.0223368\pi$
$542$	−6.14675	−	24.6533i	−0.264025	−	1.05895i
$543$	−10.3174	−	17.8702i	−0.442760	−	0.766883i
$544$	2.88375	−	1.28393i	0.123640	−	0.0550479i
$545$	−7.88770	−	24.1969i	−0.337872	−	1.03648i
$546$	7.54790	+	7.28892i	0.323020	+	0.311937i
$547$	−9.83475	−	20.1642i	−0.420503	−	0.862160i	−0.998922	−	0.0464196i	$-0.985219\pi$
$547$	−9.83475	−	20.1642i	−0.420503	−	0.862160i	0.578419	−	0.815740i	$-0.303670\pi$
$548$	−0.154835	+	4.43391i	−0.00661424	+	0.189407i
$549$	2.84440	−	2.38673i	0.121396	−	0.101863i
$550$	5.76310	−	14.3433i	0.245740	−	0.611599i
$551$	11.6794	+	3.48926i	0.497561	+	0.148647i
$552$	0.404469	+	1.24483i	0.0172153	+	0.0529833i
$553$	2.91871	−	11.7063i	0.124116	−	0.497803i
$554$	14.5914	−	4.18402i	0.619930	−	0.177762i
$555$	−0.704464	+	0.314457i	−0.0299028	+	0.0133479i
$556$	0.621660	−	1.27459i	0.0263643	−	0.0540547i
$557$	43.7143	−	15.9107i	1.85224	−	0.674159i	0.868192	−	0.496228i	$-0.165282\pi$
$557$	43.7143	−	15.9107i	1.85224	−	0.674159i	0.984043	−	0.177931i	$-0.0569403\pi$
$558$	−9.61756	+	4.28201i	−0.407144	+	0.181272i
$559$	−32.2394	+	6.85270i	−1.36358	+	0.289838i
$560$	−5.04871	+	5.61798i	−0.213347	+	0.237403i
$561$	−2.26773	+	5.61282i	−0.0957435	+	0.236974i
$562$	−35.6993	+	7.58812i	−1.50588	+	0.320086i
$563$	28.5750	+	31.7358i	1.20429	+	1.33750i	0.926239	+	0.376937i	$0.123023\pi$
$563$	28.5750	+	31.7358i	1.20429	+	1.33750i	0.278054	+	0.960566i	$0.410311\pi$
$564$	−3.26115	−	4.17408i	−0.137319	−	0.175760i
$565$	−2.43977	+	0.345271i	−0.102642	+	0.0145257i
$566$	21.2652	+	11.3069i	0.893842	+	0.475264i
$567$	4.37262	+	6.48267i	0.183633	+	0.272247i
$568$	−0.601825	+	0.504991i	−0.0252520	+	0.0211890i
$569$	10.0683	+	7.31506i	0.422086	+	0.306663i	0.778476	−	0.627674i	$-0.215993\pi$
$569$	10.0683	+	7.31506i	0.422086	+	0.306663i	−0.356391	+	0.934337i	$0.615993\pi$
$570$	1.29858	−	28.8330i	0.0543915	−	1.20768i
$571$	−28.0876	+	20.4069i	−1.17543	+	0.854000i	−0.991649	−	0.128967i	$-0.958834\pi$
$571$	−28.0876	+	20.4069i	−1.17543	+	0.854000i	−0.183782	+	0.982967i	$0.558834\pi$
$572$	0.847646	−	3.39972i	0.0354419	−	0.142150i
$573$	−1.64673	+	47.1560i	−0.0687929	+	1.96997i
$574$	0.395848	−	2.24496i	0.0165224	−	0.0937030i
$575$	−0.672190	+	1.16944i	−0.0280322	+	0.0487689i
$576$	−4.07332	+	1.48257i	−0.169722	+	0.0617736i
$577$	18.4954	+	3.93131i	0.769972	+	0.163663i	0.576117	−	0.817367i	$-0.304567\pi$
$577$	18.4954	+	3.93131i	0.769972	+	0.163663i	0.193856	+	0.981030i	$0.437901\pi$
$578$	20.4424	+	9.10155i	0.850292	+	0.378575i
$579$	29.6638	+	2.07429i	1.23279	+	0.0862047i
$580$	−1.51109	+	1.68147i	−0.0627445	+	0.0698193i
$581$	0.461265	−	4.38865i	0.0191365	−	0.182072i
$582$	−2.28357	+	3.95527i	−0.0946572	+	0.163951i
$583$	2.88676	+	0.827765i	0.119557	+	0.0342825i
$584$	28.4069	+	3.99232i	1.17548	+	0.165203i
$585$	−3.83466	+	6.65654i	−0.158543	+	0.275214i
$586$	0.606358	−	17.3638i	0.0250484	−	0.717293i
$587$	3.79799	+	9.40036i	0.156760	+	0.387994i	0.985041	−	0.172318i	$-0.0551256\pi$
$587$	3.79799	+	9.40036i	0.156760	+	0.387994i	−0.828282	+	0.560312i	$0.810681\pi$
$588$	−1.39048	+	4.27945i	−0.0573423	+	0.176481i
$589$	−41.0518	+	8.25240i	−1.69151	+	0.340034i
$590$	−45.6994	+	13.1515i	−1.88141	+	0.541438i
$591$	−6.07761	−	15.0426i	−0.250000	−	0.618771i
$592$	−0.459785	−	0.681660i	−0.0188971	−	0.0280160i
$593$	4.03854	−	22.9037i	0.165843	−	0.940543i	−0.782348	−	0.622842i	$-0.785978\pi$
$593$	4.03854	−	22.9037i	0.165843	−	0.940543i	0.948191	−	0.317701i	$-0.102911\pi$
$594$	5.97211	−	12.2446i	0.245039	−	0.502404i
$595$	2.56839	−	0.00246116i	0.105294	−	0.000100898i
$596$	0.309747	+	2.94705i	0.0126877	+	0.120716i
$597$	13.9940	+	6.23052i	0.572735	+	0.254998i
$598$	−0.748137	+	1.85171i	−0.0305936	+	0.0757219i
$599$	9.09523	+	7.63181i	0.371621	+	0.311827i	0.809403	−	0.587254i	$-0.199791\pi$
$599$	9.09523	+	7.63181i	0.371621	+	0.311827i	−0.437781	+	0.899081i	$0.644236\pi$
$600$	−21.4414	−	11.3479i	−0.875340	−	0.463277i
$601$	−5.78715	+	10.0236i	−0.236063	+	0.408873i	−0.959581	−	0.281433i	$-0.909190\pi$
$601$	−5.78715	+	10.0236i	−0.236063	+	0.408873i	0.723518	+	0.690305i	$0.242524\pi$
$602$	4.76125	+	6.09412i	0.194054	+	0.248378i
$603$	−5.95929	−	5.75482i	−0.242681	−	0.234354i
$604$	2.14973	+	4.40761i	0.0874715	+	0.179343i
$605$	13.1766	−	8.25120i	0.535703	−	0.335459i
$606$	−5.38291	+	0.376410i	−0.218666	+	0.0152906i
$607$	20.8495			0.846256			0.423128	−	0.906070i	$-0.360932\pi$
$607$	20.8495			0.846256			0.423128	+	0.906070i	$0.360932\pi$
$608$	8.73857	−	1.12972i	0.354396	−	0.0458164i
$609$	−1.22483	+	3.76962i	−0.0496324	+	0.152753i
$610$	0.641525	+	17.8796i	0.0259746	+	0.723925i
$611$	−1.27833	+	36.6065i	−0.0517155	+	1.48094i
$612$	−0.355490	−	0.189017i	−0.0143698	−	0.00764057i
$613$	14.0176	+	1.97005i	0.566166	+	0.0795694i	0.416448	−	0.909159i	$-0.363275\pi$
$613$	14.0176	+	1.97005i	0.566166	+	0.0795694i	0.149718	+	0.988729i	$0.452164\pi$
$614$	14.8674	+	19.0294i	0.600000	+	0.767965i
$615$	8.66797	−	0.614471i	0.349526	−	0.0247779i
$616$	3.64444	−	0.774649i	0.146838	−	0.0312115i
$617$	10.3624	+	41.5615i	0.417176	+	1.67320i	0.700088	+	0.714056i	$0.253144\pi$
$617$	10.3624	+	41.5615i	0.417176	+	1.67320i	−0.282912	+	0.959146i	$0.591300\pi$
$618$	1.05516	+	0.885386i	0.0424448	+	0.0356154i
$619$	0.754809	−	7.18152i	0.0303383	−	0.288650i	−0.968825	−	0.247747i	$-0.920310\pi$
$619$	0.754809	−	7.18152i	0.0303383	−	0.288650i	0.999163	−	0.0409030i	$-0.0130235\pi$
$620$	1.87151	−	7.53698i	0.0751616	−	0.302692i
$621$	−0.664764	+	0.985553i	−0.0266760	+	0.0395489i
$622$	23.8304	+	23.0128i	0.955513	+	0.922728i
$623$	−6.70460	+	0.942270i	−0.268614	+	0.0377512i
$624$	−40.0595	−	14.5805i	−1.60366	−	0.583685i
$625$	−6.14098	−	24.2340i	−0.245639	−	0.969361i
$626$	12.4326			0.496906
$627$	−10.5499	+	13.1997i	−0.421322	+	0.527146i
$628$	−2.41106	+	1.75173i	−0.0962116	+	0.0699018i
$629$	−0.0676390	+	0.271285i	−0.00269694	+	0.0108169i
$630$	1.79822	+	0.124012i	0.0716429	+	0.00494078i
$631$	−27.6645	+	26.7153i	−1.10131	+	1.06352i	−0.103685	+	0.994610i	$0.533063\pi$
$631$	−27.6645	+	26.7153i	−1.10131	+	1.06352i	−0.997623	+	0.0689104i	$0.978048\pi$
$632$	7.17150	+	40.6716i	0.285267	+	1.61783i
$633$	−11.8413	−	3.39543i	−0.470649	−	0.134956i
$634$	−28.0786	−	31.1845i	−1.11515	−	1.23849i
$635$	7.70961	−	15.8456i	0.305946	−	0.628812i
$636$	−0.389568	+	0.964214i	−0.0154474	+	0.0382336i
$637$	26.3874	−	16.4887i	1.04551	−	0.653304i
$638$	8.45650	−	1.79748i	0.334796	−	0.0711631i
$639$	0.217654	+	0.0462637i	0.00861025	+	0.00183017i
$640$	9.22056	−	28.4708i	0.364475	−	1.12541i
$641$	36.1353	+	5.07848i	1.42726	+	0.200588i	0.810118	−	0.586267i	$-0.199403\pi$
$641$	36.1353	+	5.07848i	1.42726	+	0.200588i	0.617139	+	0.786854i	$0.288292\pi$
$642$	−40.0610	+	38.6865i	−1.58108	+	1.52683i
$643$	−19.0502	−	6.93369i	−0.751265	−	0.273438i	−0.0621270	−	0.998068i	$-0.519788\pi$
$643$	−19.0502	−	6.93369i	−0.751265	−	0.273438i	−0.689138	+	0.724630i	$0.742011\pi$
$644$	0.0715642	−	0.00500426i	0.00282002	−	0.000197195i
$645$	−18.1274	+	23.2479i	−0.713766	+	0.915385i
$646$	−7.93810	−	6.81186i	−0.312320	−	0.268009i
$647$	18.1204	−	13.1652i	0.712384	−	0.517578i	−0.171558	−	0.985174i	$-0.554880\pi$
$647$	18.1204	−	13.1652i	0.712384	−	0.517578i	0.883942	+	0.467596i	$0.154880\pi$
$648$	−22.6999	−	14.1845i	−0.891736	−	0.557219i
$649$	26.1621	+	9.52221i	1.02695	+	0.373779i
$650$	−13.9319	−	34.2932i	−0.546453	−	1.34509i
$651$	−2.36434	−	13.4088i	−0.0926658	−	0.525534i
$652$	0.347897	+	0.445288i	0.0136247	+	0.0174388i
$653$	−0.281069	−	2.67419i	−0.0109991	−	0.104649i	0.987645	−	0.156708i	$-0.0500883\pi$
$653$	−0.281069	−	2.67419i	−0.0109991	−	0.104649i	−0.998644	+	0.0520590i	$0.983422\pi$
$654$	−30.7895	−	13.7084i	−1.20397	−	0.536040i
$655$	−17.8809	−	30.9021i	−0.698663	−	1.20745i
$656$	2.24058	+	8.98648i	0.0874800	+	0.350863i
$657$	−4.06243	−	7.03634i	−0.158491	−	0.274514i
$658$	7.85142	−	3.49568i	0.306080	−	0.136276i
$659$	−1.44097	−	41.2641i	−0.0561324	−	1.60742i	−0.622062	−	0.782968i	$-0.713705\pi$
$659$	−1.44097	−	41.2641i	−0.0561324	−	1.60742i	0.565930	−	0.824454i	$-0.308517\pi$
$660$	−1.37650	−	2.81540i	−0.0535803	−	0.109589i
$661$	46.7640	−	6.57226i	1.81891	−	0.255631i	0.854389	−	0.519634i	$-0.173932\pi$
$661$	46.7640	−	6.57226i	1.81891	−	0.255631i	0.964522	+	0.264003i	$0.0850430\pi$
$662$	20.9379	−	26.7992i	0.813773	−	1.04158i
$663$	5.43030	+	13.4405i	0.210895	+	0.521984i
$664$	4.66791	+	14.3663i	0.181150	+	0.557522i
$665$	6.87120	+	2.04562i	0.266454	+	0.0793257i
$666$	−0.0606342	+	0.186613i	−0.00234953	+	0.00723110i
$667$	−0.752570	+	0.0526248i	−0.0291396	+	0.00203764i
$668$	−3.26185	−	1.18722i	−0.126205	−	0.0459348i
$669$	−29.7254	+	28.7055i	−1.14925	+	1.10982i
$670$	39.5236	−	5.59330i	1.52693	−	0.216088i
$671$	5.85729	−	8.68380i	0.226118	−	0.335234i
$672$	0.299488	+	2.84944i	0.0115530	+	0.109920i
$673$	−2.61712	+	2.90661i	−0.100883	+	0.112042i	−0.791472	−	0.611206i	$-0.790685\pi$
$673$	−2.61712	+	2.90661i	−0.100883	+	0.112042i	0.690589	+	0.723247i	$0.257351\pi$
$674$	27.3391	+	22.9402i	1.05306	+	0.883625i
$675$	−3.86762	−	21.6912i	−0.148865	−	0.834893i
$676$	−1.84514	−	3.19587i	−0.0709668	−	0.122918i
$677$	−28.4911	−	6.05598i	−1.09500	−	0.232750i	−0.375211	−	0.926939i	$-0.622430\pi$
$677$	−28.4911	−	6.05598i	−1.09500	−	0.232750i	−0.719793	+	0.694189i	$0.755763\pi$
$678$	−1.82473	+	2.70528i	−0.0700784	+	0.103896i
$679$	−0.816060	−	0.788060i	−0.0313175	−	0.0302430i
$680$	−8.02840	+	3.58370i	−0.307875	+	0.137428i
$681$	−15.0198	−	22.2678i	−0.575560	−	0.853302i
$682$	−22.7503	+	19.0898i	−0.871156	+	0.730986i
$683$	6.81327	+	4.95013i	0.260703	+	0.189411i	0.710457	−	0.703741i	$-0.248488\pi$
$683$	6.81327	+	4.95013i	0.260703	+	0.189411i	−0.449754	+	0.893152i	$0.648488\pi$
$684$	−0.799740	−	0.789577i	−0.0305788	−	0.0301902i
$685$	0.931374	−	27.4245i	0.0355860	−	1.04784i
$686$	−12.9015	−	8.06176i	−0.492582	−	0.307799i
$687$	19.2722	−	24.6673i	0.735282	−	0.941118i
$688$	−27.7422	−	14.7508i	−1.05766	−	0.562369i
$689$	6.34946	−	3.37607i	0.241895	−	0.128618i
$690$	0.553619	+	1.69832i	0.0210759	+	0.0646541i
$691$	19.7404	+	21.9240i	0.750961	+	0.834026i	0.990594	−	0.136837i	$-0.0436937\pi$
$691$	19.7404	+	21.9240i	0.750961	+	0.834026i	−0.239633	+	0.970864i	$0.577027\pi$
$692$	0.398320	−	3.78977i	0.0151419	−	0.144065i
$693$	−0.808398	−	0.678327i	−0.0307085	−	0.0257675i
$694$	4.15944	+	16.6826i	0.157890	+	0.633264i
$695$	−3.83739	+	7.88700i	−0.145561	+	0.299171i
$696$	−1.41824	−	13.4937i	−0.0537583	−	0.511476i
$697$	1.76107	−	2.61089i	0.0667052	−	0.0988945i
$698$	18.0464	−	9.59545i	0.683067	−	0.363193i
$699$	−6.56375	+	37.2249i	−0.248264	+	1.40797i
$700$	−0.887796	+	0.989805i	−0.0335555	+	0.0374111i
$701$	−13.8030	+	11.5821i	−0.521332	+	0.437449i	−0.865096	−	0.501607i	$-0.832742\pi$
$701$	−13.8030	+	11.5821i	−0.521332	+	0.437449i	0.343764	+	0.939056i	$0.388298\pi$
$702$	−10.0809	−	31.0259i	−0.380480	−	1.17100i
$703$	−0.397666	+	0.671516i	−0.0149983	+	0.0253267i
$704$	−9.89281	+	7.18755i	−0.372849	+	0.270891i
$705$	20.1948	+	25.7972i	0.760581	+	0.971579i
$706$	−6.58595	−	9.76407i	−0.247865	−	0.367476i
$707$	0.232750	−	1.31999i	0.00875347	−	0.0496434i
$708$	−4.22636	+	8.66532i	−0.158836	+	0.325663i
$709$	1.58815	+	45.4788i	0.0596444	+	1.70799i	0.548930	+	0.835868i	$0.315035\pi$
$709$	1.58815	+	45.4788i	0.0596444	+	1.70799i	−0.489286	+	0.872123i	$0.662743\pi$
$710$	−0.820668	+	0.689964i	−0.0307991	+	0.0258939i
$711$	7.82702	−	8.69278i	0.293536	−	0.326005i
$712$	19.6546	−	12.2815i	0.736587	−	0.460271i
$713$	2.19773	−	1.37329i	0.0823056	−	0.0514303i
$714$	2.27591	−	2.52765i	0.0851737	−	0.0945950i
$715$	−5.22252	+	21.0322i	−0.195311	+	0.786560i
$716$	−0.185682	−	5.31723i	−0.00693925	−	0.198714i
$717$	7.50994	−	15.3977i	0.280464	−	0.575036i
$718$	8.01898	−	45.4779i	0.299266	−	1.69722i
$719$	−4.77953	−	7.08595i	−0.178247	−	0.264261i	0.729317	−	0.684176i	$-0.239838\pi$
$719$	−4.77953	−	7.08595i	−0.178247	−	0.264261i	−0.907564	+	0.419914i	$0.862060\pi$
$720$	−6.87916	+	2.51128i	−0.256371	+	0.0935898i
$721$	−0.276800	+	0.201107i	−0.0103086	+	0.00748961i
$722$	−15.7879	−	24.5613i	−0.587564	−	0.914076i
$723$	−10.3040	−	31.7125i	−0.383210	−	1.17940i
$724$	2.96571	−	2.48852i	0.110220	−	0.0924853i
$725$	9.33607	−	10.4088i	0.346733	−	0.386573i
$726$	3.57516	−	20.2757i	0.132687	−	0.752503i
$727$	−17.8305	+	9.48062i	−0.661295	+	0.351617i	−0.765958	−	0.642891i	$-0.777735\pi$
$727$	−17.8305	+	9.48062i	−0.661295	+	0.351617i	0.104663	+	0.994508i	$0.466624\pi$
$728$	4.98908	−	7.39661i	0.184907	−	0.274137i
$729$	−1.87031	−	17.7948i	−0.0692709	−	0.659068i
$730$	38.7729	+	5.41130i	1.43505	+	0.200281i
$731$	2.58470	+	10.3667i	0.0955986	+	0.383425i
$732$	2.77861	+	2.33153i	0.102700	+	0.0861759i
$733$	1.76498	−	16.7926i	0.0651909	−	0.620250i	−0.912336	−	0.409441i	$-0.865724\pi$
$733$	1.76498	−	16.7926i	0.0651909	−	0.620250i	0.977527	−	0.210809i	$-0.0676097\pi$
$734$	1.41245	+	1.56868i	0.0521343	+	0.0579011i
$735$	8.57470	−	26.4765i	0.316282	−	0.976601i
$736$	−0.481498	+	0.256017i	−0.0177482	+	0.00943690i
$737$	−20.6345	−	10.9716i	−0.760083	−	0.404143i
$738$	1.36072	−	1.74164i	0.0500888	−	0.0641108i
$739$	−25.1680	−	15.7267i	−0.925820	−	0.578517i	−0.0189011	−	0.999821i	$-0.506017\pi$
$739$	−25.1680	−	15.7267i	−0.925820	−	0.578517i	−0.906919	+	0.421305i	$0.861572\pi$
$740$	−0.0810528	−	0.119918i	−0.00297956	−	0.00440826i
$741$	3.78427	+	40.2859i	0.139019	+	1.47994i
$742$	−1.36507	−	0.991782i	−0.0501133	−	0.0364095i
$743$	−32.5455	+	27.3089i	−1.19398	+	1.00187i	−0.194196	+	0.980963i	$0.562210\pi$
$743$	−32.5455	+	27.3089i	−1.19398	+	1.00187i	−0.999782	+	0.0209034i	$0.993346\pi$
$744$	26.0630	+	38.6400i	0.955517	+	1.41661i
$745$	−1.93324	−	18.2256i	−0.0708286	−	0.667733i
$746$	−22.8821	−	22.0970i	−0.837774	−	0.809029i
$747$	2.39247	−	3.54699i	0.0875360	−	0.129777i
$748$	−1.11095	−	0.236140i	−0.0406205	−	0.00863415i
$749$	−6.91673	−	11.9801i	−0.252732	−	0.437745i
$750$	−29.2765	−	15.4588i	−1.06903	−	0.564476i
$751$	30.8572	+	25.8922i	1.12599	+	0.944821i	0.998892	−	0.0470685i	$-0.0149879\pi$
$751$	30.8572	+	25.8922i	1.12599	+	0.944821i	0.127102	+	0.991890i	$0.459432\pi$
$752$	−23.3645	+	25.9489i	−0.852016	+	0.946260i
$753$	4.03450	+	38.3857i	0.147025	+	1.39885i
$754$	11.5766	−	17.1630i	0.421594	−	0.625039i
$755$	−13.3222	−	27.2482i	−0.484843	−	0.991663i
$756$	−0.842949	+	0.814027i	−0.0306578	+	0.0296059i
$757$	−24.3313	−	8.85587i	−0.884336	−	0.321872i	−0.140378	−	0.990098i	$-0.544832\pi$
$757$	−24.3313	−	8.85587i	−0.884336	−	0.321872i	−0.743958	+	0.668226i	$0.767054\pi$
$758$	0.718314	−	0.0502294i	0.0260903	−	0.00182441i
$759$	0.323169	−	0.994612i	0.0117303	−	0.0361021i
$760$	−24.3357	+	3.16984i	−0.882748	+	0.114982i
$761$	−2.51329	−	7.73511i	−0.0911066	−	0.280397i	0.895113	−	0.445840i	$-0.147095\pi$
$761$	−2.51329	−	7.73511i	−0.0911066	−	0.280397i	−0.986219	+	0.165442i	$0.947095\pi$
$762$	−8.74185	−	21.6368i	−0.316684	−	0.783820i
$763$	5.15416	−	6.59702i	0.186593	−	0.238828i
$764$	−8.76659	+	1.23206i	−0.317164	+	0.0445745i
$765$	2.19981	+	1.16696i	0.0795344	+	0.0421915i
$766$	−0.371982	−	10.6522i	−0.0134403	−	0.384879i
$767$	60.9044	−	27.1164i	2.19913	−	0.979116i
$768$	−8.10316	−	14.0351i	−0.292398	−	0.506448i
$769$	4.43490	+	17.7874i	0.159927	+	0.641431i	0.995723	+	0.0923911i	$0.0294510\pi$
$769$	4.43490	+	17.7874i	0.159927	+	0.641431i	−0.835796	+	0.549040i	$0.814993\pi$
$770$	4.97266	−	1.06195i	0.179202	−	0.0382701i

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bc (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30322 - 0.814342i) q^{2} +(1.85231 - 0.531140i) q^{3} +(0.158485 + 0.324943i) q^{4} +(-0.982153 - 2.00882i) q^{5} +(-2.84649 - 0.816218i) q^{6} +(0.367774 - 0.637004i) q^{7} +(-0.263190 + 2.50409i) q^{8} +(0.604785 - 0.377912i) q^{9} +O(q^{10})\)	\(q+(-1.30322 - 0.814342i) q^{2} +(1.85231 - 0.531140i) q^{3} +(0.158485 + 0.324943i) q^{4} +(-0.982153 - 2.00882i) q^{5} +(-2.84649 - 0.816218i) q^{6} +(0.367774 - 0.637004i) q^{7} +(-0.263190 + 2.50409i) q^{8} +(0.604785 - 0.377912i) q^{9} +(-0.355909 + 3.41775i) q^{10} +(1.34614 - 1.49504i) q^{11} +(0.466154 + 0.517716i) q^{12} +(-0.168125 - 4.81446i) q^{13} +(-0.998029 + 0.530661i) q^{14} +(-2.88622 - 3.19930i) q^{15} +(2.82734 - 3.61883i) q^{16} +(-1.55778 + 0.108930i) q^{17} -1.09592 q^{18} +(-4.25336 - 0.953362i) q^{19} +(0.497097 - 0.637513i) q^{20} +(0.342892 - 1.37527i) q^{21} +(-2.97179 + 0.852148i) q^{22} +(0.267146 - 0.0375450i) q^{23} +(0.842512 + 4.77812i) q^{24} +(-3.07075 + 3.94595i) q^{25} +(-3.70151 + 6.41121i) q^{26} +(-2.94863 + 3.27478i) q^{27} +(0.265277 + 0.0185500i) q^{28} +(-2.78965 - 0.195072i) q^{29} +(1.15605 + 6.51975i) q^{30} +(8.77582 - 3.90724i) q^{31} +(-1.89954 + 0.691376i) q^{32} +(1.69939 - 3.48426i) q^{33} +(2.11883 + 1.12660i) q^{34} +(-1.64084 - 0.113159i) q^{35} +(0.218649 + 0.136627i) q^{36} +(0.0553274 - 0.170280i) q^{37} +(4.76670 + 4.70613i) q^{38} +(-2.86857 - 8.82856i) q^{39} +(5.28876 - 1.93069i) q^{40} +(-1.24163 + 1.58921i) q^{41} +(-1.56680 + 1.51304i) q^{42} +(-1.18807 - 6.73786i) q^{43} +(0.699147 + 0.200477i) q^{44} +(-1.35315 - 0.843740i) q^{45} +(-0.378725 - 0.168619i) q^{46} +(-7.58492 - 0.530389i) q^{47} +(3.31499 - 8.20489i) q^{48} +(3.22948 + 5.59363i) q^{49} +(7.21521 - 2.64179i) q^{50} +(-2.82762 + 1.02917i) q^{51} +(1.53778 - 0.817653i) q^{52} +(0.654382 + 1.34168i) q^{53} +(6.50950 - 1.86657i) q^{54} +(-4.32539 - 1.23580i) q^{55} +(1.49832 + 1.08859i) q^{56} +(-8.38490 + 0.493214i) q^{57} +(3.47667 + 2.52595i) q^{58} +(5.18420 + 12.8313i) q^{59} +(0.582167 - 1.44490i) q^{60} +(5.15595 - 0.724621i) q^{61} +(-14.6186 - 2.05452i) q^{62} +(-0.0183067 - 0.524236i) q^{63} +(-5.94548 - 1.26375i) q^{64} +(-9.50629 + 5.06627i) q^{65} +(-5.05206 + 3.15688i) q^{66} +(-2.81032 - 11.2716i) q^{67} +(-0.282281 - 0.488925i) q^{68} +(0.474895 - 0.211437i) q^{69} +(2.04622 + 1.48367i) q^{70} +(0.224448 + 0.216747i) q^{71} +(0.787150 + 1.61390i) q^{72} +(0.397608 - 11.3860i) q^{73} +(-0.210770 + 0.176857i) q^{74} +(-3.59212 + 8.94010i) q^{75} +(-0.364307 - 1.53320i) q^{76} +(-0.457271 - 1.40733i) q^{77} +(-3.45109 + 13.8416i) q^{78} +(15.7669 - 4.52109i) q^{79} +(-10.0465 - 2.12538i) q^{80} +(-4.66026 + 9.55496i) q^{81} +(2.91228 - 1.05998i) q^{82} +(5.48069 - 2.44016i) q^{83} +(0.501226 - 0.106539i) q^{84} +(1.74880 + 3.02231i) q^{85} +(-3.93861 + 9.74840i) q^{86} +(-5.27090 + 1.12036i) q^{87} +(3.38942 + 3.76433i) q^{88} +(-5.66697 - 7.25339i) q^{89} +(1.07636 + 2.20150i) q^{90} +(-3.12866 - 1.66354i) q^{91} +(0.0545388 + 0.0808571i) q^{92} +(14.1802 - 11.8986i) q^{93} +(9.45289 + 6.86793i) q^{94} +(2.26232 + 9.48061i) q^{95} +(-3.15131 + 2.28956i) q^{96} +(0.373123 - 1.49651i) q^{97} +(0.346401 - 9.91963i) q^{98} +(0.249133 - 1.41290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

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