LMFDB - Embedded newform 483.2.y.a.193.10

Newspace parameters

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			193.10
Character	$\chi$	$=$	483.193
Dual form			483.2.y.a.478.10

$q$-expansion

$f(q)$	$=$	$q+(0.275876 + 0.263047i) q^{2} +(-0.981929 + 0.189251i) q^{3} +(-0.0882501 - 1.85260i) q^{4} +(-3.33200 + 2.62031i) q^{5} +(-0.320672 - 0.206084i) q^{6} +(2.63533 + 0.234648i) q^{7} +(0.962219 - 1.11046i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})$	\(q+(0.275876 + 0.263047i) q^{2} +(-0.981929 + 0.189251i) q^{3} +(-0.0882501 - 1.85260i) q^{4} +(-3.33200 + 2.62031i) q^{5} +(-0.320672 - 0.206084i) q^{6} +(2.63533 + 0.234648i) q^{7} +(0.962219 - 1.11046i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-1.60848 - 0.153591i) q^{10} +(-0.117858 + 0.112378i) q^{11} +(0.437262 + 1.80242i) q^{12} +(-2.17377 - 4.75990i) q^{13} +(0.665299 + 0.757948i) q^{14} +(2.77589 - 3.20354i) q^{15} +(-3.13505 + 0.299361i) q^{16} +(-1.07257 + 0.552947i) q^{17} +(0.353879 + 0.141672i) q^{18} +(-7.46548 - 3.84872i) q^{19} +(5.14843 + 5.94161i) q^{20} +(-2.63211 + 0.268331i) q^{21} -0.0620749 q^{22} +(1.51901 - 4.54891i) q^{23} +(-0.734674 + 1.27249i) q^{24} +(3.05738 - 12.6027i) q^{25} +(0.652386 - 1.88495i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.202141 - 4.90291i) q^{28} +(-4.84295 - 3.11238i) q^{29} +(1.60848 - 0.153591i) q^{30} +(0.678487 + 1.96036i) q^{31} +(-3.25360 - 2.55866i) q^{32} +(0.0944609 - 0.132652i) q^{33} +(-0.441346 - 0.129591i) q^{34} +(-9.39575 + 6.12353i) q^{35} +(-0.770470 - 1.68709i) q^{36} +(-1.50396 + 0.602096i) q^{37} +(-1.04715 - 3.02554i) q^{38} +(3.03531 + 4.26249i) q^{39} +(-0.296360 + 6.22136i) q^{40} +(-0.616074 - 4.28489i) q^{41} +(-0.796719 - 0.618342i) q^{42} +(4.14596 + 4.78469i) q^{43} +(0.218592 + 0.208427i) q^{44} +(-2.11945 + 3.67099i) q^{45} +(1.61564 - 0.855365i) q^{46} +(0.923833 + 1.60013i) q^{47} +(3.02174 - 0.887262i) q^{48} +(6.88988 + 1.23675i) q^{49} +(4.15855 - 2.67254i) q^{50} +(0.948538 - 0.745939i) q^{51} +(-8.62635 + 4.44719i) q^{52} +(0.866331 + 1.21659i) q^{53} +(-0.374295 - 0.0721395i) q^{54} +(0.0982391 - 0.683268i) q^{55} +(2.79633 - 2.70064i) q^{56} +(8.05894 + 2.36632i) q^{57} +(-0.517352 - 2.13255i) q^{58} +(2.04871 + 0.195628i) q^{59} +(-6.17985 - 4.85989i) q^{60} +(0.139793 + 0.0269429i) q^{61} +(-0.328489 + 0.719290i) q^{62} +(2.53376 - 0.761612i) q^{63} +(0.671844 + 4.67278i) q^{64} +(19.7154 + 10.1640i) q^{65} +(0.0609531 - 0.0117478i) q^{66} +(-2.54832 + 10.5043i) q^{67} +(1.11904 + 1.93824i) q^{68} +(-0.630669 + 4.75418i) q^{69} +(-4.20283 - 0.782190i) q^{70} +(-11.4279 + 3.35554i) q^{71} +(0.480577 - 1.38854i) q^{72} +(-0.465136 - 9.76440i) q^{73} +(-0.573286 - 0.229509i) q^{74} +(-0.617053 + 12.9535i) q^{75} +(-6.47131 + 14.1702i) q^{76} +(-0.336964 + 0.268497i) q^{77} +(-0.283868 + 1.97435i) q^{78} +(7.11864 - 9.99673i) q^{79} +(9.66154 - 9.21226i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.957168 - 1.34415i) q^{82} +(1.72092 - 11.9692i) q^{83} +(0.729394 + 4.85256i) q^{84} +(2.12490 - 4.65287i) q^{85} +(-0.114829 + 2.41056i) q^{86} +(5.34445 + 2.13960i) q^{87} +(0.0113854 + 0.239009i) q^{88} +(-2.94191 + 8.50008i) q^{89} +(-1.55035 + 0.455223i) q^{90} +(-4.61170 - 13.0540i) q^{91} +(-8.56136 - 2.41267i) q^{92} +(-1.03723 - 1.79653i) q^{93} +(-0.166045 + 0.684447i) q^{94} +(34.9598 - 6.73795i) q^{95} +(3.67903 + 1.89667i) q^{96} +(0.197209 + 1.37162i) q^{97} +(1.57543 + 2.15355i) q^{98} +(-0.0676494 + 0.148131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.275876	+	0.263047i	0.195074	+	0.186002i	0.781320	−	0.624130i	$-0.214547\pi$
$2$	0.275876	+	0.263047i	0.195074	+	0.186002i	−0.586247	+	0.810133i	$0.699395\pi$
$3$	−0.981929	+	0.189251i	−0.566917	+	0.109264i
$3$	−0.981929	+	0.189251i	−0.566917	+	0.109264i
$4$	−0.0882501	−	1.85260i	−0.0441251	−	0.926299i
$5$	−3.33200	+	2.62031i	−1.49011	+	1.17184i	−0.548032	+	0.836458i	$0.684623\pi$
$5$	−3.33200	+	2.62031i	−1.49011	+	1.17184i	−0.942082	+	0.335381i	$0.891135\pi$
$6$	−0.320672	−	0.206084i	−0.130914	−	0.0841333i
$7$	2.63533	+	0.234648i	0.996059	+	0.0886886i
$7$	2.63533	+	0.234648i	0.996059	+	0.0886886i
$8$	0.962219	−	1.11046i	0.340196	−	0.392607i
$9$	0.928368	−	0.371662i	0.309456	−	0.123887i
$10$	−1.60848	−	0.153591i	−0.508647	−	0.0485699i
$11$	−0.117858	+	0.112378i	−0.0355356	+	0.0338832i	−0.707639	−	0.706574i	$-0.750240\pi$
$11$	−0.117858	+	0.112378i	−0.0355356	+	0.0338832i	0.672103	+	0.740457i	$0.265391\pi$
$12$	0.437262	+	1.80242i	0.126227	+	0.520313i
$13$	−2.17377	−	4.75990i	−0.602897	−	1.32016i	−0.927328	−	0.374250i	$-0.877900\pi$
$13$	−2.17377	−	4.75990i	−0.602897	−	1.32016i	0.324431	−	0.945909i	$-0.394827\pi$
$14$	0.665299	+	0.757948i	0.177809	+	0.202570i
$15$	2.77589	−	3.20354i	0.716731	−	0.827151i
$16$	−3.13505	+	0.299361i	−0.783761	+	0.0748401i
$17$	−1.07257	+	0.552947i	−0.260136	+	0.134109i	−0.583362	−	0.812213i	$-0.698263\pi$
$17$	−1.07257	+	0.552947i	−0.260136	+	0.134109i	0.323226	+	0.946322i	$0.395233\pi$
$18$	0.353879	+	0.141672i	0.0834100	+	0.0333923i
$19$	−7.46548	−	3.84872i	−1.71270	−	0.882957i	−0.979101	−	0.203372i	$-0.934810\pi$
$19$	−7.46548	−	3.84872i	−1.71270	−	0.882957i	−0.733597	−	0.679585i	$-0.762160\pi$
$20$	5.14843	+	5.94161i	1.15122	+	1.32858i
$21$	−2.63211	+	0.268331i	−0.574373	+	0.0585546i
$22$	−0.0620749			−0.0132344
$23$	1.51901	−	4.54891i	0.316735	−	0.948514i
$23$	1.51901	−	4.54891i	0.316735	−	0.948514i
$24$	−0.734674	+	1.27249i	−0.149965	+	0.259747i
$25$	3.05738	−	12.6027i	0.611475	−	2.52054i
$26$	0.652386	−	1.88495i	0.127943	−	0.369668i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.202141	−	4.90291i	0.0382010	−	0.926562i
$29$	−4.84295	−	3.11238i	−0.899313	−	0.577954i	0.00727325	−	0.999974i	$-0.497685\pi$
$29$	−4.84295	−	3.11238i	−0.899313	−	0.577954i	−0.906587	+	0.422020i	$0.861321\pi$
$30$	1.60848	−	0.153591i	0.293667	−	0.0280418i
$31$	0.678487	+	1.96036i	0.121860	+	0.352091i	0.989388	−	0.145297i	$-0.0464138\pi$
$31$	0.678487	+	1.96036i	0.121860	+	0.352091i	−0.867528	+	0.497388i	$0.834293\pi$
$32$	−3.25360	−	2.55866i	−0.575161	−	0.452312i
$33$	0.0944609	−	0.132652i	0.0164435	−	0.0230917i
$34$	−0.441346	−	0.129591i	−0.0756902	−	0.0222247i
$35$	−9.39575	+	6.12353i	−1.58817	+	1.03506i
$36$	−0.770470	−	1.68709i	−0.128412	−	0.281182i
$37$	−1.50396	+	0.602096i	−0.247250	+	0.0989840i	−0.491977	−	0.870608i	$-0.663726\pi$
$37$	−1.50396	+	0.602096i	−0.247250	+	0.0989840i	0.244727	+	0.969592i	$0.421302\pi$
$38$	−1.04715	−	3.02554i	−0.169870	−	0.490807i
$39$	3.03531	+	4.26249i	0.486038	+	0.682545i
$40$	−0.296360	+	6.22136i	−0.0468586	+	0.983684i
$41$	−0.616074	−	4.28489i	−0.0962146	−	0.669187i	−0.979662	−	0.200656i	$-0.935693\pi$
$41$	−0.616074	−	4.28489i	−0.0962146	−	0.669187i	0.883447	−	0.468531i	$-0.155217\pi$
$42$	−0.796719	−	0.618342i	−0.122936	−	0.0954123i
$43$	4.14596	+	4.78469i	0.632252	+	0.729658i	0.977985	−	0.208675i	$-0.0669150\pi$
$43$	4.14596	+	4.78469i	0.632252	+	0.729658i	−0.345733	+	0.938333i	$0.612370\pi$
$44$	0.218592	+	0.208427i	0.0329540	+	0.0314215i
$45$	−2.11945	+	3.67099i	−0.315949	+	0.547239i
$46$	1.61564	−	0.855365i	0.238212	−	0.126117i
$47$	0.923833	+	1.60013i	0.134755	+	0.233402i	0.925504	−	0.378738i	$-0.123642\pi$
$47$	0.923833	+	1.60013i	0.134755	+	0.233402i	−0.790749	+	0.612141i	$0.790309\pi$
$48$	3.02174	−	0.887262i	0.436150	−	0.128065i
$49$	6.88988	+	1.23675i	0.984269	+	0.176678i
$50$	4.15855	−	2.67254i	0.588108	−	0.377954i
$51$	0.948538	−	0.745939i	0.132822	−	0.104452i
$52$	−8.62635	+	4.44719i	−1.19626	+	0.616715i
$53$	0.866331	+	1.21659i	0.119000	+	0.167112i	0.869779	−	0.493441i	$-0.164261\pi$
$53$	0.866331	+	1.21659i	0.119000	+	0.167112i	−0.750779	+	0.660553i	$0.770322\pi$
$54$	−0.374295	−	0.0721395i	−0.0509351	−	0.00981695i
$55$	0.0982391	−	0.683268i	0.0132466	−	0.0921318i
$56$	2.79633	−	2.70064i	0.373675	−	0.360888i
$57$	8.05894	+	2.36632i	1.06743	+	0.313427i
$58$	−0.517352	−	2.13255i	−0.0679316	−	0.280018i
$59$	2.04871	+	0.195628i	0.266719	+	0.0254686i	0.227559	−	0.973764i	$-0.426926\pi$
$59$	2.04871	+	0.195628i	0.266719	+	0.0254686i	0.0391605	+	0.999233i	$0.487532\pi$
$60$	−6.17985	−	4.85989i	−0.797815	−	0.627409i
$61$	0.139793	+	0.0269429i	0.0178987	+	0.00344969i	0.198193	−	0.980163i	$-0.436493\pi$
$61$	0.139793	+	0.0269429i	0.0178987	+	0.00344969i	−0.180294	+	0.983613i	$0.557705\pi$
$62$	−0.328489	+	0.719290i	−0.0417181	+	0.0913499i
$63$	2.53376	−	0.761612i	0.319224	−	0.0959541i
$64$	0.671844	+	4.67278i	0.0839805	+	0.584097i
$65$	19.7154	+	10.1640i	2.44540	+	1.26069i
$66$	0.0609531	−	0.0117478i	0.00750281	−	0.00144605i
$67$	−2.54832	+	10.5043i	−0.311327	+	1.28331i	0.574197	+	0.818717i	$0.305314\pi$
$67$	−2.54832	+	10.5043i	−0.311327	+	1.28331i	−0.885525	+	0.464592i	$0.846201\pi$
$68$	1.11904	+	1.93824i	0.135704	+	0.235046i
$69$	−0.630669	+	4.75418i	−0.0759236	+	0.572336i
$70$	−4.20283	−	0.782190i	−0.502335	−	0.0934896i
$71$	−11.4279	+	3.35554i	−1.35625	+	0.398230i	−0.877438	−	0.479690i	$-0.840749\pi$
$71$	−11.4279	+	3.35554i	−1.35625	+	0.398230i	−0.478808	+	0.877920i	$0.658931\pi$
$72$	0.480577	−	1.38854i	0.0566365	−	0.163641i
$73$	−0.465136	−	9.76440i	−0.0544400	−	1.14284i	−0.846498	−	0.532391i	$-0.821294\pi$
$73$	−0.465136	−	9.76440i	−0.0544400	−	1.14284i	0.792058	−	0.610445i	$-0.209010\pi$
$74$	−0.573286	−	0.229509i	−0.0666432	−	0.0266799i
$75$	−0.617053	+	12.9535i	−0.0712512	+	1.49575i
$76$	−6.47131	+	14.1702i	−0.742310	+	1.62543i
$77$	−0.336964	+	0.268497i	−0.0384007	+	0.0305980i
$78$	−0.283868	+	1.97435i	−0.0321418	+	0.223551i
$79$	7.11864	−	9.99673i	0.800910	−	1.12472i	−0.188854	−	0.982005i	$-0.560477\pi$
$79$	7.11864	−	9.99673i	0.800910	−	1.12472i	0.989764	−	0.142715i	$-0.0455832\pi$
$80$	9.66154	−	9.21226i	1.08019	−	1.02996i
$81$	0.723734	−	0.690079i	0.0804149	−	0.0766754i
$82$	0.957168	−	1.34415i	0.105701	−	0.148437i
$83$	1.72092	−	11.9692i	0.188895	−	1.31380i	−0.645979	−	0.763355i	$-0.723551\pi$
$83$	1.72092	−	11.9692i	0.188895	−	1.31380i	0.834874	−	0.550441i	$-0.185540\pi$
$84$	0.729394	+	4.85256i	0.0795834	+	0.529458i
$85$	2.12490	−	4.65287i	0.230477	−	0.504675i
$86$	−0.114829	+	2.41056i	−0.0123823	+	0.259937i
$87$	5.34445	+	2.13960i	0.572985	+	0.229389i
$88$	0.0113854	+	0.239009i	0.00121369	+	0.0254784i
$89$	−2.94191	+	8.50008i	−0.311842	+	0.901007i	0.674786	+	0.738014i	$0.264236\pi$
$89$	−2.94191	+	8.50008i	−0.311842	+	0.901007i	−0.986627	+	0.162993i	$0.947885\pi$
$90$	−1.55035	+	0.455223i	−0.163421	+	0.0479847i
$91$	−4.61170	−	13.0540i	−0.483438	−	1.36843i
$92$	−8.56136	−	2.41267i	−0.892584	−	0.251538i
$93$	−1.03723	−	1.79653i	−0.107555	−	0.186291i
$94$	−0.166045	+	0.684447i	−0.0171262	+	0.0705953i
$95$	34.9598	−	6.73795i	3.58680	−	0.691299i
$96$	3.67903	+	1.89667i	0.375490	+	0.193578i
$97$	0.197209	+	1.37162i	0.0200235	+	0.139267i	0.997381	−	0.0723289i	$-0.0230431\pi$
$97$	0.197209	+	1.37162i	0.0200235	+	0.139267i	−0.977357	+	0.211596i	$0.932134\pi$
$98$	1.57543	+	2.15355i	0.159142	+	0.217541i
$99$	−0.0676494	+	0.148131i	−0.00679902	+	0.0148878i
$100$	−23.6175	−	4.55190i	−2.36175	−	0.455190i
$101$	−1.06045	−	0.833945i	−0.105518	−	0.0829806i	0.564006	−	0.825771i	$-0.309260\pi$
$101$	−1.06045	−	0.833945i	−0.105518	−	0.0829806i	−0.669524	+	0.742790i	$0.733502\pi$
$102$	0.457896	+	0.0437237i	0.0453384	+	0.00432929i
$103$	1.46562	+	6.04136i	0.144412	+	0.595273i	0.997317	+	0.0732068i	$0.0233233\pi$
$103$	1.46562	+	6.04136i	0.144412	+	0.595273i	−0.852905	+	0.522066i	$0.825162\pi$
$104$	−7.37733	−	2.16618i	−0.723406	−	0.212411i
$105$	8.06707	−	7.79102i	0.787265	−	0.760326i
$106$	−0.0810211	+	0.563514i	−0.00786946	+	0.0547333i
$107$	−14.1991	−	2.73665i	−1.37268	−	0.264562i	−0.550994	−	0.834509i	$-0.685751\pi$
$107$	−14.1991	−	2.73665i	−1.37268	−	0.264562i	−0.821681	+	0.569947i	$0.806964\pi$
$108$	1.07583	+	1.51079i	0.103522	+	0.145376i
$109$	9.66983	−	4.98515i	0.926202	−	0.477490i	0.0719843	−	0.997406i	$-0.477067\pi$
$109$	9.66983	−	4.98515i	0.926202	−	0.477490i	0.854218	+	0.519915i	$0.174037\pi$
$110$	0.206833	−	0.162656i	0.0197208	−	0.0155086i
$111$	1.36284	−	0.875842i	0.129355	−	0.0831313i
$112$	−8.33211	+	0.0532805i	−0.787310	+	0.00503454i
$113$	−8.58625	+	2.52115i	−0.807726	+	0.237170i	−0.659423	−	0.751772i	$-0.729199\pi$
$113$	−8.58625	+	2.52115i	−0.807726	+	0.237170i	−0.148303	+	0.988942i	$0.547381\pi$
$114$	1.60081	+	2.77269i	0.149930	+	0.259686i
$115$	6.85824	+	19.1372i	0.639535	+	1.78456i
$116$	−5.33859	+	9.24671i	−0.495676	+	0.858535i
$117$	−3.78714	−	3.61103i	−0.350121	−	0.333840i
$118$	0.513730	+	0.592876i	0.0472927	+	0.0545787i
$119$	−2.95631	+	1.20552i	−0.271004	+	0.110510i
$120$	−0.886396	−	6.16502i	−0.0809165	−	0.562787i
$121$	−0.522139	+	10.9611i	−0.0474672	+	0.996459i
$122$	0.0314783	+	0.0442050i	0.00284991	+	0.00400214i
$123$	1.41586	+	4.09086i	0.127664	+	0.368861i
$124$	3.57188	−	1.42997i	0.320765	−	0.128415i
$125$	14.0313	+	30.7242i	1.25499	+	2.74805i
$126$	0.899343	+	0.456388i	0.0801198	+	0.0406583i
$127$	−16.3167	−	4.79103i	−1.44788	−	0.425135i	−0.539037	−	0.842282i	$-0.681212\pi$
$127$	−16.3167	−	4.79103i	−1.44788	−	0.425135i	−0.908839	+	0.417147i	$0.863030\pi$
$128$	−5.84571	+	8.20916i	−0.516693	+	0.725594i
$129$	−4.97654	−	3.91360i	−0.438160	−	0.344573i
$130$	2.76540	+	7.99009i	0.242541	+	0.700777i
$131$	11.5518	−	1.10306i	1.00929	−	0.0963752i	0.422707	−	0.906267i	$-0.361080\pi$
$131$	11.5518	−	1.10306i	1.00929	−	0.0963752i	0.586580	+	0.809891i	$0.300474\pi$
$132$	−0.254087	−	0.163292i	−0.0221154	−	0.0142127i
$133$	−18.7709	−	11.8944i	−1.62764	−	1.03137i
$134$	−3.46615	+	2.22756i	−0.299430	+	0.192432i
$135$	1.38641	−	4.00576i	0.119323	−	0.344761i
$136$	−0.418019	+	1.72310i	−0.0358448	+	0.147754i
$137$	0.156764	−	0.271523i	0.0133932	−	0.0231977i	−0.859251	−	0.511554i	$-0.829070\pi$
$137$	0.156764	−	0.271523i	0.0133932	−	0.0231977i	0.872644	+	0.488356i	$0.162403\pi$
$138$	−1.42456	+	1.14567i	−0.121267	+	0.0975258i
$139$	11.4853			0.974174			0.487087	−	0.873353i	$-0.338059\pi$
$139$	11.4853			0.974174			0.487087	+	0.873353i	$0.338059\pi$
$140$	12.1736	+	16.8661i	1.02886	+	1.42545i
$141$	−1.20996	−	1.39637i	−0.101897	−	0.117596i
$142$	−4.03535	−	2.08037i	−0.338639	−	0.174581i
$143$	0.791104	+	0.316710i	0.0661555	+	0.0264847i
$144$	−2.79921	+	1.44310i	−0.233268	+	0.120258i
$145$	24.2921	−	2.31961i	2.01735	−	0.192633i
$146$	2.44018	−	2.81611i	0.201950	−	0.233063i
$147$	−6.99943	+	0.0895208i	−0.577303	+	0.00738355i
$148$	1.24817	+	2.73310i	0.102599	+	0.224660i
$149$	4.47557	+	18.4485i	0.366653	+	1.51136i	0.794361	+	0.607446i	$0.207806\pi$
$149$	4.47557	+	18.4485i	0.366653	+	1.51136i	−0.427708	+	0.903917i	$0.640679\pi$
$150$	−3.57762	+	3.41125i	−0.292112	+	0.278528i
$151$	−2.26907	−	0.216670i	−0.184655	−	0.0176324i	0.00231907	−	0.999997i	$-0.499262\pi$
$151$	−2.26907	−	0.216670i	−0.184655	−	0.0176324i	−0.186974	+	0.982365i	$0.559868\pi$
$152$	−11.4573	+	4.58680i	−0.929308	+	0.372039i
$153$	−0.790227	+	0.911971i	−0.0638861	+	0.0737285i
$154$	−0.163588	−	0.0145657i	−0.0131823	−	0.00117374i
$155$	−7.39747	−	4.75407i	−0.594179	−	0.381856i
$156$	7.62882	−	5.99937i	0.610795	−	0.480334i
$157$	−0.219236	−	4.60233i	−0.0174969	−	0.367306i	−0.990587	−	0.136882i	$-0.956292\pi$
$157$	−0.219236	−	4.60233i	−0.0174969	−	0.367306i	0.973090	−	0.230424i	$-0.0740112\pi$
$158$	4.59347	−	0.885319i	0.365437	−	0.0704322i
$159$	−1.08092	−	1.03065i	−0.0857223	−	0.0817361i
$160$	17.5455			1.38709
$161$	5.07047	−	11.6314i	0.399609	−	0.916686i
$162$	0.381184			0.0299486
$163$	−16.0339	−	15.2883i	−1.25587	−	1.19747i	−0.971047	−	0.238888i	$-0.923217\pi$
$163$	−16.0339	−	15.2883i	−1.25587	−	1.19747i	−0.284821	−	0.958581i	$-0.591934\pi$
$164$	−7.88381	+	1.51948i	−0.615622	+	0.118651i
$165$	0.0328455	+	0.689512i	0.00255702	+	0.0536785i
$166$	3.62323	−	2.84934i	0.281218	−	0.221152i
$167$	−10.5050	−	6.75118i	−0.812904	−	0.522422i	0.0668990	−	0.997760i	$-0.478689\pi$
$167$	−10.5050	−	6.75118i	−0.812904	−	0.522422i	−0.879803	+	0.475338i	$0.842326\pi$
$168$	−2.23469	+	3.18104i	−0.172410	+	0.245423i
$169$	−9.41818	+	10.8692i	−0.724475	+	0.836089i
$170$	1.81013	−	0.724668i	0.138831	−	0.0555795i
$171$	−8.36114	−	0.798392i	−0.639392	−	0.0610545i
$172$	8.49823	−	8.10304i	0.647984	−	0.617851i
$173$	2.16337	+	8.91754i	0.164478	+	0.677988i	0.993008	+	0.118044i	$0.0376623\pi$
$173$	2.16337	+	8.91754i	0.164478	+	0.677988i	−0.828530	+	0.559944i	$0.810823\pi$
$174$	0.911590	+	1.99610i	0.0691075	+	0.151324i
$175$	11.0144	−	32.4948i	0.832609	−	2.45637i
$176$	0.335850	−	0.387591i	0.0253156	−	0.0292158i
$177$	−2.04871	+	0.195628i	−0.153990	+	0.0147043i
$178$	−3.04752	+	1.57111i	−0.228421	+	0.117759i
$179$	4.53150	+	1.81414i	0.338700	+	0.135595i	0.534776	−	0.844994i	$-0.320396\pi$
$179$	4.53150	+	1.81414i	0.338700	+	0.135595i	−0.196076	+	0.980589i	$0.562820\pi$
$180$	6.98791	+	3.60252i	0.520848	+	0.268516i
$181$	3.56947	+	4.11939i	0.265317	+	0.306192i	0.872739	−	0.488188i	$-0.162342\pi$
$181$	3.56947	+	4.11939i	0.265317	+	0.306192i	−0.607422	+	0.794379i	$0.707796\pi$
$182$	2.16155	−	4.81437i	0.160225	−	0.356865i
$183$	−0.142366			−0.0105240
$184$	−3.58977	−	6.06385i	−0.264641	−	0.447033i
$185$	3.43352	−	5.94703i	0.252437	−	0.437235i
$186$	0.186426	−	0.768458i	0.0136694	−	0.0563461i
$187$	0.0642721	−	0.185702i	0.00470004	−	0.0135799i
$188$	2.88286	−	1.85270i	0.210254	−	0.135122i
$189$	−2.34384	+	1.22737i	−0.170489	+	0.0892777i
$190$	11.4170	+	7.33723i	0.828273	+	0.532299i
$191$	10.6953	−	1.02127i	0.773882	−	0.0738968i	0.299360	−	0.954140i	$-0.403227\pi$
$191$	10.6953	−	1.02127i	0.773882	−	0.0738968i	0.474522	+	0.880243i	$0.342621\pi$
$192$	−1.54403	−	4.46119i	−0.111431	−	0.321958i
$193$	15.6643	+	12.3186i	1.12754	+	0.886710i	0.994535	−	0.104405i	$-0.0332938\pi$
$193$	15.6643	+	12.3186i	1.12754	+	0.886710i	0.133009	+	0.991115i	$0.457536\pi$
$194$	−0.306395	+	0.430271i	−0.0219979	+	0.0308917i
$195$	−21.2827	−	6.24916i	−1.52409	−	0.447512i
$196$	1.68316	−	12.8733i	0.120226	−	0.919523i
$197$	−6.13495	−	13.4337i	−0.437097	−	0.957110i	−0.992122	−	0.125276i	$-0.960018\pi$
$197$	−6.13495	−	13.4337i	−0.437097	−	0.957110i	0.555025	−	0.831834i	$-0.312709\pi$
$198$	−0.0576283	+	0.0230709i	−0.00409547	+	0.00163958i
$199$	−3.83305	−	11.0749i	−0.271717	−	0.785076i	−0.995475	−	0.0950218i	$-0.969708\pi$
$199$	−3.83305	−	11.0749i	−0.271717	−	0.785076i	0.723758	−	0.690054i	$-0.242413\pi$
$200$	−11.0529	−	15.5216i	−0.781558	−	1.09755i
$201$	0.514314	−	10.7968i	0.0362769	−	0.761546i
$202$	−0.0731850	−	0.509013i	−0.00514928	−	0.0358140i
$203$	−12.0324	−	9.33851i	−0.844512	−	0.655435i
$204$	−1.46563	−	1.69143i	−0.102615	−	0.118424i
$205$	13.2805	+	12.6629i	0.927551	+	0.884418i
$206$	−1.18483	+	2.05219i	−0.0825512	+	0.142983i
$207$	−0.280463	−	4.78762i	−0.0194936	−	0.332763i
$208$	8.23981	+	14.2718i	0.571328	+	0.989569i
$209$	1.31238	−	0.385349i	0.0907792	−	0.0266552i
$210$	4.27491	−	0.0273364i	0.294997	−	0.00188639i
$211$	−0.765138	+	0.491724i	−0.0526742	+	0.0338517i	−0.566713	−	0.823915i	$-0.691785\pi$
$211$	−0.765138	+	0.491724i	−0.0526742	+	0.0338517i	0.514039	+	0.857767i	$0.328149\pi$
$212$	2.17740	−	1.71233i	0.149545	−	0.117603i
$213$	10.5864	−	5.45765i	0.725366	−	0.373952i
$214$	−3.19731	−	4.49000i	−0.218564	−	0.306930i
$215$	−26.3517	−	5.07887i	−1.79717	−	0.346376i
$216$	−0.209110	+	1.45439i	−0.0142281	+	0.0989589i
$217$	1.32804	+	5.32539i	0.0901532	+	0.361511i
$218$	3.97900	+	1.16834i	0.269492	+	0.0791299i
$219$	2.30466	+	9.49992i	0.155734	+	0.641945i
$220$	−1.27449	−	0.121699i	−0.0859261	−	0.00820495i
$221$	4.96349	+	3.90333i	0.333880	+	0.262566i
$222$	0.606361	+	0.116867i	0.0406963	+	0.00784357i
$223$	0.685100	−	1.50016i	0.0458777	−	0.100458i	−0.885305	−	0.465010i	$-0.846051\pi$
$223$	0.685100	−	1.50016i	0.0458777	−	0.100458i	0.931183	+	0.364552i	$0.118778\pi$
$224$	−7.97391	−	7.50635i	−0.532780	−	0.501539i
$225$	−1.84557	−	12.8362i	−0.123038	−	0.855749i
$226$	−3.03192	−	1.56306i	−0.201680	−	0.103973i
$227$	−0.706694	+	0.136204i	−0.0469049	+	0.00904019i	−0.212650	−	0.977128i	$-0.568209\pi$
$227$	−0.706694	+	0.136204i	−0.0469049	+	0.00904019i	0.165745	+	0.986169i	$0.446997\pi$
$228$	3.67264	−	15.1388i	0.243226	−	1.00259i
$229$	0.0400333	+	0.0693397i	0.00264548	+	0.00458210i	0.867345	−	0.497707i	$-0.165825\pi$
$229$	0.0400333	+	0.0693397i	0.00264548	+	0.00458210i	−0.864700	+	0.502289i	$0.832491\pi$
$230$	−3.14197	+	7.08354i	−0.207175	+	0.467075i
$231$	0.280062	−	0.327416i	0.0184267	−	0.0215424i
$232$	−8.11615	+	2.38312i	−0.532851	+	0.156459i
$233$	8.26561	−	23.8819i	0.541498	−	1.56456i	−0.259409	−	0.965768i	$-0.583528\pi$
$233$	8.26561	−	23.8819i	0.541498	−	1.56456i	0.800907	−	0.598788i	$-0.204351\pi$
$234$	−0.0949093	−	1.99239i	−0.00620441	−	0.130247i
$235$	−7.27104	−	2.91088i	−0.474310	−	0.189885i
$236$	0.181621	−	3.81270i	0.0118225	−	0.248186i
$237$	−5.09810	+	11.1633i	−0.331157	+	0.725134i
$238$	−1.13268	−	0.445075i	−0.0734209	−	0.0288499i
$239$	0.739756	−	5.14512i	0.0478508	−	0.332810i	−0.951808	−	0.306694i	$-0.900777\pi$
$239$	0.739756	−	5.14512i	0.0478508	−	0.332810i	0.999659	−	0.0261156i	$-0.00831380\pi$
$240$	−7.74351	+	10.8742i	−0.499842	+	0.701929i
$241$	−0.865744	+	0.825486i	−0.0557675	+	0.0531742i	−0.717450	−	0.696610i	$-0.754691\pi$
$241$	−0.865744	+	0.825486i	−0.0557675	+	0.0531742i	0.661683	+	0.749784i	$0.269843\pi$
$242$	−3.02732	+	2.88654i	−0.194603	+	0.185554i
$243$	−0.580057	+	0.814576i	−0.0372107	+	0.0522551i
$244$	0.0375776	−	0.261358i	0.00240566	−	0.0167317i
$245$	−26.1977	+	13.9328i	−1.67371	+	0.890134i
$246$	−0.685488	+	1.50101i	−0.0437051	+	0.0957008i
$247$	−2.09127	+	43.9012i	−0.133064	+	2.79337i
$248$	2.82975	+	1.13286i	0.179690	+	0.0719369i
$249$	0.575376	+	12.0786i	0.0364630	+	0.765452i
$250$	−4.21102	+	12.1669i	−0.266328	+	0.769505i
$251$	22.5191	−	6.61220i	1.42139	−	0.417358i	0.521418	−	0.853302i	$-0.325403\pi$
$251$	22.5191	−	6.61220i	1.42139	−	0.417358i	0.899974	+	0.435943i	$0.143585\pi$
$252$	−1.63457	−	4.62683i	−0.102968	−	0.291463i
$253$	0.332169	+	0.706830i	0.0208833	+	0.0444380i
$254$	−3.24113	−	5.61380i	−0.203366	−	0.352241i
$255$	−1.20593	+	4.97093i	−0.0755186	+	0.311292i
$256$	5.49895	−	1.05984i	0.343684	−	0.0662397i
$257$	13.4388	+	6.92821i	0.838292	+	0.432170i	0.823224	−	0.567717i	$-0.192173\pi$
$257$	13.4388	+	6.92821i	0.838292	+	0.432170i	0.0150683	+	0.999886i	$0.495203\pi$
$258$	−0.343448	−	2.38873i	−0.0213821	−	0.148716i
$259$	−4.10471	+	1.23382i	−0.255054	+	0.0766657i
$260$	17.0899	−	37.4217i	1.05987	−	2.32080i
$261$	−5.65279	−	1.08949i	−0.349899	−	0.0674375i
$262$	3.47702	+	2.73436i	0.214811	+	0.168929i
$263$	−25.2713	−	2.41312i	−1.55830	−	0.148799i	−0.719984	−	0.693991i	$-0.755851\pi$
$263$	−25.2713	−	2.41312i	−1.55830	−	0.148799i	−0.838312	+	0.545192i	$0.816457\pi$
$264$	−0.0564124	−	0.232535i	−0.00347194	−	0.0143115i
$265$	−6.07446	−	1.78362i	−0.373151	−	0.109567i
$266$	−2.04964	−	8.21900i	−0.125672	−	0.503939i
$267$	1.28009	−	8.90324i	0.0783404	−	0.544869i
$268$	19.6852	+	3.79401i	1.20247	+	0.231756i
$269$	1.26808	+	1.78076i	0.0773159	+	0.108575i	0.851423	−	0.524480i	$-0.175740\pi$
$269$	1.26808	+	1.78076i	0.0773159	+	0.108575i	−0.774107	+	0.633055i	$0.781801\pi$
$270$	1.43618	−	0.740402i	0.0874031	−	0.0450594i
$271$	2.17056	−	1.70694i	0.131852	−	0.103689i	−0.550055	−	0.835128i	$-0.685393\pi$
$271$	2.17056	−	1.70694i	0.131852	−	0.103689i	0.681907	+	0.731439i	$0.261151\pi$
$272$	3.19701	−	2.05460i	0.193847	−	0.124578i
$273$	6.99884	+	11.9453i	0.423589	+	0.722962i
$274$	0.114670	−	0.0336703i	0.00692750	−	0.00203410i
$275$	1.05592	+	1.82891i	0.0636746	+	0.110288i
$276$	8.86325	+	0.748818i	0.533505	+	0.0450736i
$277$	4.37380	−	7.57564i	0.262796	−	0.455176i	−0.704188	−	0.710014i	$-0.748689\pi$
$277$	4.37380	−	7.57564i	0.262796	−	0.455176i	0.966984	+	0.254838i	$0.0820220\pi$
$278$	3.16853	+	3.02118i	0.190036	+	0.181199i
$279$	1.35848	+	1.56777i	0.0813299	+	0.0938598i
$280$	−2.24083	+	16.3258i	−0.133915	+	0.975652i
$281$	−1.24337	−	8.64785i	−0.0741734	−	0.515888i	−0.992708	−	0.120546i	$-0.961535\pi$
$281$	−1.24337	−	8.64785i	−0.0741734	−	0.515888i	0.918534	−	0.395341i	$-0.129374\pi$
$282$	0.0335120	−	0.703503i	0.00199561	−	0.0418930i
$283$	−14.2191	−	19.9679i	−0.845238	−	1.18697i	−0.980570	−	0.196171i	$-0.937149\pi$
$283$	−14.2191	−	19.9679i	−0.845238	−	1.18697i	0.135332	−	0.990800i	$-0.456790\pi$
$284$	7.22499	+	20.8752i	0.428724	+	1.23872i
$285$	−33.0529	+	13.2324i	−1.95788	+	0.783818i
$286$	0.134937	+	0.295470i	0.00797898	+	0.0174715i
$287$	−0.618115	−	11.4366i	−0.0364862	−	0.675084i
$288$	−3.97150	−	1.16614i	−0.234023	−	0.0687153i
$289$	−9.01632	+	12.6616i	−0.530372	+	0.744803i
$290$	7.31176	+	5.75003i	0.429362	+	0.337654i
$291$	−0.453225	−	1.30951i	−0.0265685	−	0.0767648i
$292$	−18.0485	+	1.72342i	−1.05621	+	0.100855i
$293$	−2.77762	−	1.78507i	−0.162270	−	0.104285i	0.456985	−	0.889474i	$-0.348929\pi$
$293$	−2.77762	−	1.78507i	−0.162270	−	0.104285i	−0.619256	+	0.785189i	$0.712566\pi$
$294$	−1.95452	−	1.81648i	−0.113990	−	0.105939i
$295$	−7.33890	+	4.71643i	−0.427287	+	0.274601i
$296$	−0.778538	+	2.24944i	−0.0452516	+	0.130746i
$297$	0.0383928	−	0.158257i	0.00222778	−	0.00918302i
$298$	−3.61813	+	6.26679i	−0.209593	+	0.363025i
$299$	−24.9544	+	2.65799i	−1.44315	+	0.153715i
$300$	24.0522			1.38865
$301$	9.80323	+	13.5821i	0.565049	+	0.782857i
$302$	−0.568988	−	0.656647i	−0.0327416	−	0.0377858i
$303$	1.19911	+	0.618184i	0.0688870	+	0.0355137i
$304$	24.5568	+	9.83105i	1.40843	+	0.563849i
$305$	−0.536389	+	0.276528i	−0.0307135	+	0.0158339i
$306$	−0.457896	+	0.0437237i	−0.0261761	+	0.00249952i
$307$	6.50966	−	7.51255i	0.371526	−	0.428764i	−0.538942	−	0.842343i	$-0.681176\pi$
$307$	6.50966	−	7.51255i	0.371526	−	0.428764i	0.910468	+	0.413579i	$0.135721\pi$
$308$	0.527154	+	0.600565i	0.0300374	+	0.0342204i
$309$	−2.58247	−	5.65481i	−0.146911	−	0.321691i
$310$	−0.790240	−	3.25741i	−0.0448826	−	0.185009i
$311$	9.49693	−	9.05530i	0.538521	−	0.513479i	−0.371281	−	0.928520i	$-0.621081\pi$
$311$	9.49693	−	9.05530i	0.538521	−	0.513479i	0.909802	+	0.415041i	$0.136233\pi$
$312$	7.65396	+	0.730865i	0.433320	+	0.0413771i
$313$	14.6295	−	5.85679i	0.826911	−	0.331045i	0.0806864	−	0.996740i	$-0.474289\pi$
$313$	14.6295	−	5.85679i	0.826911	−	0.331045i	0.746224	+	0.665694i	$0.231865\pi$
$314$	1.15015	−	1.32734i	0.0649065	−	0.0749061i
$315$	−6.44682	+	9.17693i	−0.363237	+	0.517062i
$316$	−19.1481	−	12.3058i	−1.07717	−	0.692253i
$317$	−15.0723	+	11.8530i	−0.846547	+	0.665732i	−0.944158	−	0.329492i	$-0.893122\pi$
$317$	−15.0723	+	11.8530i	−0.846547	+	0.665732i	0.0976108	+	0.995225i	$0.468880\pi$
$318$	−0.0270888	−	0.568664i	−0.00151906	−	0.0318891i
$319$	0.920544	−	0.177420i	0.0515406	−	0.00993363i
$320$	−14.4827	−	13.8092i	−0.809608	−	0.771960i
$321$	14.4604			0.807100
$322$	4.45843	−	1.87506i	0.248459	−	0.104493i
$323$	10.1354			0.563947
$324$	−1.34231	−	1.27989i	−0.0745727	−	0.0711049i
$325$	−66.6336	+	12.8426i	−3.69616	+	0.712377i
$326$	−0.401824	−	8.43532i	−0.0222550	−	0.467189i
$327$	−8.55164	+	6.72508i	−0.472907	+	0.371898i
$328$	−5.35100	−	3.43888i	−0.295459	−	0.189880i
$329$	2.05913	+	4.43363i	0.113524	+	0.244434i
$330$	−0.172313	+	0.198860i	−0.00948551	+	0.0109469i
$331$	18.8340	−	7.53998i	1.03521	−	0.414435i	0.209069	−	0.977901i	$-0.432957\pi$
$331$	18.8340	−	7.53998i	1.03521	−	0.414435i	0.826139	+	0.563466i	$0.190532\pi$
$332$	−22.3261	−	2.13188i	−1.22530	−	0.117002i
$333$	−1.17245	+	1.11793i	−0.0642501	+	0.0612624i
$334$	−1.12221	−	4.62580i	−0.0614045	−	0.253113i
$335$	−19.0336	−	41.6778i	−1.03992	−	2.27710i
$336$	8.17145	−	1.62918i	0.445789	−	0.0888790i
$337$	9.50193	−	10.9658i	0.517603	−	0.597346i	−0.435426	−	0.900225i	$-0.643402\pi$
$337$	9.50193	−	10.9658i	0.517603	−	0.597346i	0.953029	+	0.302879i	$0.0979476\pi$
$338$	−5.45735	+	0.521113i	−0.296841	+	0.0283448i
$339$	7.95395	−	4.10055i	0.431999	−	0.222711i
$340$	−8.80743	−	3.52596i	−0.477650	−	0.191222i
$341$	−0.300266	−	0.154798i	−0.0162603	−	0.00838278i
$342$	−2.09662	−	2.41963i	−0.113372	−	0.130839i
$343$	17.8669	+	4.87593i	0.964721	+	0.263275i
$344$	9.30252			0.501558
$345$	−10.3561	−	17.4935i	−0.557551	−	0.941817i
$346$	−1.74891	+	3.02920i	−0.0940220	+	0.162851i
$347$	7.65839	−	31.5683i	0.411124	−	1.69468i	−0.270291	−	0.962779i	$-0.587120\pi$
$347$	7.65839	−	31.5683i	0.411124	−	1.69468i	0.681415	−	0.731897i	$-0.261365\pi$
$348$	3.49216	−	10.0899i	0.187200	−	0.540878i
$349$	−4.83512	+	3.10735i	−0.258818	+	0.166332i	−0.663615	−	0.748074i	$-0.730979\pi$
$349$	−4.83512	+	3.10735i	−0.258818	+	0.166332i	0.404797	+	0.914407i	$0.367342\pi$
$350$	11.5862	−	6.06722i	0.619311	−	0.324306i
$351$	4.40209	+	2.82905i	0.234966	+	0.151004i
$352$	0.671001	−	0.0640728i	0.0357645	−	0.00341509i
$353$	6.84670	+	19.7822i	0.364413	+	1.05290i	0.966984	+	0.254837i	$0.0820219\pi$
$353$	6.84670	+	19.7822i	0.364413	+	1.05290i	−0.602571	+	0.798065i	$0.705857\pi$
$354$	−0.616649	−	0.484938i	−0.0327745	−	0.0257742i
$355$	29.2853	−	41.1254i	1.55430	−	2.18271i
$356$	16.0069	+	4.70004i	0.848362	+	0.249102i
$357$	2.67474	−	1.74322i	0.141562	−	0.0922609i
$358$	0.772927	+	1.69247i	0.0408505	+	0.0894500i
$359$	−1.45609	+	0.582932i	−0.0768496	+	0.0307660i	−0.409769	−	0.912189i	$-0.634391\pi$
$359$	−1.45609	+	0.582932i	−0.0768496	+	0.0307660i	0.332919	+	0.942955i	$0.391966\pi$
$360$	2.03712	+	5.88586i	0.107365	+	0.310212i
$361$	29.8996	+	41.9882i	1.57366	+	2.20990i
$362$	−0.0988624	+	2.07538i	−0.00519609	+	0.109079i
$363$	−1.56169	−	10.8618i	−0.0819674	−	0.570096i
$364$	−23.7768	+	9.69564i	−1.24624	+	0.508190i
$365$	27.1356	+	31.3162i	1.42034	+	1.63916i
$366$	−0.0392753	−	0.0374489i	−0.00205295	−	0.00195749i
$367$	4.24321	−	7.34946i	0.221494	−	0.383639i	−0.733768	−	0.679400i	$-0.762240\pi$
$367$	4.24321	−	7.34946i	0.221494	−	0.383639i	0.955262	+	0.295761i	$0.0955734\pi$
$368$	−3.40039	+	14.7158i	−0.177258	+	0.767113i
$369$	−2.16448	−	3.74898i	−0.112678	−	0.195164i
$370$	2.51157	−	0.737465i	0.130571	−	0.0383390i
$371$	1.99759	+	3.40940i	0.103710	+	0.177007i
$372$	−3.23671	+	2.08011i	−0.167816	+	0.107849i
$373$	9.36239	−	7.36266i	0.484766	−	0.381224i	−0.345654	−	0.938362i	$-0.612343\pi$
$373$	9.36239	−	7.36266i	0.484766	−	0.381224i	0.830420	+	0.557138i	$0.188100\pi$
$374$	0.0665795	−	0.0343241i	0.00344274	−	0.00177486i
$375$	−19.5923	−	27.5135i	−1.01174	−	1.42079i
$376$	2.66580	+	0.513792i	0.137478	+	0.0264968i
$377$	−4.28712	+	29.8176i	−0.220798	+	1.53568i
$378$	−0.969463	−	0.277939i	−0.0498638	−	0.0142956i
$379$	15.0723	+	4.42561i	0.774210	+	0.227328i	0.644891	−	0.764275i	$-0.276903\pi$
$379$	15.0723	+	4.42561i	0.774210	+	0.227328i	0.129319	+	0.991603i	$0.458721\pi$
$380$	−15.5679	−	64.1718i	−0.798617	−	3.29195i
$381$	16.9286	+	1.61648i	0.867278	+	0.0828150i
$382$	3.21921	+	2.53161i	0.164709	+	0.129529i
$383$	−34.9345	−	6.73307i	−1.78507	−	0.344044i	−0.813639	−	0.581371i	$-0.802517\pi$
$383$	−34.9345	−	6.73307i	−1.78507	−	0.344044i	−0.971430	+	0.237327i	$0.923729\pi$
$384$	4.18648	−	9.16712i	0.213640	−	0.467807i
$385$	0.419219	−	1.77758i	0.0213654	−	0.0905939i
$386$	1.08105	+	7.51885i	0.0550239	+	0.382699i
$387$	5.62726	+	2.90106i	0.286050	+	0.147469i
$388$	2.52365	−	0.486394i	0.128119	−	0.0246929i
$389$	6.01046	−	24.7754i	0.304742	−	1.25616i	−0.589202	−	0.807986i	$-0.700558\pi$
$389$	6.01046	−	24.7754i	0.304742	−	1.25616i	0.893944	−	0.448179i	$-0.147927\pi$
$390$	−4.22756	−	7.32234i	−0.214071	−	0.370781i
$391$	0.886070	+	5.71894i	0.0448105	+	0.289219i
$392$	8.00293	−	6.46091i	0.404209	−	0.326325i
$393$	−11.1343	+	3.26933i	−0.561651	+	0.164916i
$394$	1.84120	−	5.31981i	0.0927584	−	0.268008i
$395$	2.47526	+	51.9621i	0.124544	+	2.61450i
$396$	0.280398	+	0.112254i	0.0140905	+	0.00564100i
$397$	−0.00340927	+	0.0715694i	−0.000171106	+	0.00359197i	−0.998951	−	0.0457859i	$-0.985421\pi$
$397$	−0.00340927	+	0.0715694i	−0.000171106	+	0.00359197i	0.998780	+	0.0493778i	$0.0157238\pi$
$398$	1.85576	−	4.06356i	0.0930210	−	0.203688i
$399$	20.6827	+	8.12704i	1.03543	+	0.406861i
$400$	−5.81227	+	40.4252i	−0.290614	+	2.02126i
$401$	3.44028	−	4.83119i	0.171799	−	0.241258i	−0.719695	−	0.694290i	$-0.755718\pi$
$401$	3.44028	−	4.83119i	0.171799	−	0.241258i	0.891494	+	0.453032i	$0.149658\pi$
$402$	2.98195	−	2.84328i	0.148726	−	0.141810i
$403$	7.85624	−	7.49091i	0.391347	−	0.373149i
$404$	−1.45138	+	2.03818i	−0.0722089	+	0.101403i
$405$	−0.603258	+	4.19575i	−0.0299761	+	0.208488i
$406$	−0.862991	−	5.74136i	−0.0428295	−	0.284939i
$407$	0.109592	−	0.239974i	0.00543230	−	0.0118951i
$408$	0.0843665	−	1.77107i	0.00417676	−	0.0876810i
$409$	−17.0533	−	6.82709i	−0.843229	−	0.337578i	−0.0904903	−	0.995897i	$-0.528843\pi$
$409$	−17.0533	−	6.82709i	−0.843229	−	0.337578i	−0.752739	+	0.658319i	$0.771268\pi$
$410$	0.332822	+	6.98679i	0.0164369	+	0.345053i
$411$	−0.102545	+	0.296284i	−0.00505816	+	0.0146146i
$412$	11.0629	−	3.24835i	0.545028	−	0.160035i
$413$	5.35311	+	0.996269i	0.263409	+	0.0490232i
$414$	1.18200	−	1.39456i	0.0580920	−	0.0685391i
$415$	25.6291	+	44.3908i	1.25808	+	2.17906i
$416$	−5.10638	+	21.0488i	−0.250361	+	1.03200i
$417$	−11.2778	+	2.17362i	−0.552276	+	0.106442i
$418$	0.463419	+	0.238909i	0.0226666	+	0.0116854i
$419$	−2.15524	−	14.9900i	−0.105290	−	0.732310i	−0.972252	−	0.233935i	$-0.924840\pi$
$419$	−2.15524	−	14.9900i	−0.105290	−	0.732310i	0.866962	−	0.498374i	$-0.166070\pi$
$420$	−15.1456	−	14.2575i	−0.739027	−	0.695694i
$421$	4.17586	−	9.14385i	0.203519	−	0.445644i	−0.780159	−	0.625581i	$-0.784862\pi$
$421$	4.17586	−	9.14385i	0.203519	−	0.445644i	0.983678	+	0.179937i	$0.0575893\pi$
$422$	−0.340429	−	0.0656124i	−0.0165718	−	0.00319396i
$423$	1.45236	+	1.14215i	0.0706163	+	0.0555333i
$424$	2.18458	+	0.208602i	0.106092	+	0.0101306i
$425$	3.68937	+	15.2078i	0.178961	+	0.737686i
$426$	4.35614	+	1.27908i	0.211056	+	0.0619716i
$427$	0.362078	+	0.103805i	0.0175222	+	0.00502350i
$428$	−3.81684	+	26.5467i	−0.184494	+	1.28318i
$429$	−0.836746	−	0.161270i	−0.0403985	−	0.00778617i
$430$	−5.93381	−	8.33287i	−0.286154	−	0.401847i
$431$	−5.03233	+	2.59434i	−0.242399	+	0.124965i	−0.575146	−	0.818051i	$-0.695055\pi$
$431$	−5.03233	+	2.59434i	−0.242399	+	0.124965i	0.332747	+	0.943016i	$0.392024\pi$
$432$	2.47552	−	1.94677i	0.119104	−	0.0936641i
$433$	8.60220	−	5.52830i	0.413395	−	0.265673i	−0.317370	−	0.948302i	$-0.602800\pi$
$433$	8.60220	−	5.52830i	0.413395	−	0.265673i	0.730765	+	0.682629i	$0.239163\pi$
$434$	−1.03445	+	1.81848i	−0.0496554	+	0.0872900i
$435$	−23.4141	+	6.87500i	−1.12262	+	0.329631i
$436$	−10.0888	−	17.4744i	−0.483168	−	0.836871i
$437$	−28.8476	+	28.1136i	−1.37997	+	1.34486i
$438$	−1.86313	+	3.22703i	−0.0890236	+	0.154193i
$439$	−4.08108	−	3.89130i	−0.194779	−	0.185722i	0.586413	−	0.810012i	$-0.300540\pi$
$439$	−4.08108	−	3.89130i	−0.194779	−	0.185722i	−0.781192	+	0.624291i	$0.785388\pi$
$440$	−0.664214	−	0.766544i	−0.0316652	−	0.0365435i
$441$	6.85600	−	1.41255i	0.326476	−	0.0672644i
$442$	0.342547	+	2.38246i	0.0162933	+	0.113322i
$443$	−1.14597	+	24.0569i	−0.0544468	+	1.14298i	0.792005	+	0.610514i	$0.209037\pi$
$443$	−1.14597	+	24.0569i	−0.0544468	+	1.14298i	−0.846452	+	0.532465i	$0.821266\pi$
$444$	−1.74285	−	2.44750i	−0.0827122	−	0.116153i
$445$	−12.4704	−	36.0310i	−0.591155	−	1.70803i
$446$	0.583615	−	0.233644i	0.0276350	−	0.0110634i
$447$	−7.88610	−	17.2681i	−0.373000	−	0.816755i
$448$	0.674070	+	12.4719i	0.0318468	+	0.589244i
$449$	26.2878	+	7.71880i	1.24060	+	0.364273i	0.835240	−	0.549885i	$-0.185329\pi$
$449$	26.2878	+	7.71880i	1.24060	+	0.364273i	0.405358	+	0.914158i	$0.367147\pi$
$450$	2.86738	−	4.02668i	0.135170	−	0.189819i
$451$	0.554136	+	0.435777i	0.0260932	+	0.0205199i
$452$	5.42841	+	15.6844i	0.255331	+	0.737731i
$453$	2.26907	−	0.216670i	0.106610	−	0.0101801i
$454$	−0.230788	−	0.148318i	−0.0108314	−	0.00696093i
$455$	49.5716	+	31.4117i	2.32395	+	1.47260i
$456$	10.3822	−	6.67222i	0.486190	−	0.312455i
$457$	−10.3007	+	29.7618i	−0.481845	+	1.39220i	0.398196	+	0.917300i	$0.369636\pi$
$457$	−10.3007	+	29.7618i	−0.481845	+	1.39220i	−0.880041	+	0.474898i	$0.842485\pi$
$458$	−0.00719539	+	0.0296598i	−0.000336218	+	0.00138591i
$459$	0.603355	−	1.04504i	0.0281622	−	0.0487784i
$460$	34.8484	−	14.3944i	1.62481	−	0.671144i
$461$	−21.5026			−1.00148			−0.500738	−	0.865599i	$-0.666938\pi$
$461$	−21.5026			−1.00148			−0.500738	+	0.865599i	$0.666938\pi$
$462$	0.163388	−	0.0166566i	0.00760149	−	0.000774936i
$463$	5.00323	+	5.77403i	0.232520	+	0.268342i	0.860004	−	0.510287i	$-0.170461\pi$
$463$	5.00323	+	5.77403i	0.232520	+	0.268342i	−0.627484	+	0.778629i	$0.715915\pi$
$464$	16.1146	+	8.30765i	0.748101	+	0.385673i
$465$	8.16350	+	3.26817i	0.378573	+	0.151558i
$466$	8.56235	−	4.41420i	0.396643	−	0.204484i
$467$	−0.142973	+	0.0136522i	−0.00661599	+	0.000631751i	−0.0983635	−	0.995151i	$-0.531361\pi$
$467$	−0.142973	+	0.0136522i	−0.00661599	+	0.000631751i	0.0917475	+	0.995782i	$0.470755\pi$
$468$	−6.35557	+	7.33472i	−0.293786	+	0.339048i
$469$	−9.18049	+	27.0844i	−0.423915	+	1.25064i
$470$	−1.24020	−	2.71567i	−0.0572063	−	0.125264i
$471$	1.08627	+	4.47766i	0.0500527	+	0.206320i
$472$	2.18854	−	2.08677i	0.100736	−	0.0960515i
$473$	−1.02633	−	0.0980025i	−0.0471906	−	0.00450616i
$474$	−4.34291	+	1.73864i	−0.199477	+	0.0798584i
$475$	−71.3290	+	82.3180i	−3.27280	+	3.77701i
$476$	2.49424	+	5.37047i	0.114323	+	0.246155i
$477$	1.25644	+	0.807462i	0.0575282	+	0.0369712i
$478$	1.55749	−	1.22482i	0.0712378	−	0.0560220i
$479$	−1.36003	−	28.5506i	−0.0621414	−	1.30451i	−0.787576	−	0.616218i	$-0.788664\pi$
$479$	−1.36003	−	28.5506i	−0.0621414	−	1.30451i	0.725435	−	0.688291i	$-0.241639\pi$
$480$	−17.2284	+	3.32050i	−0.786366	+	0.151560i
$481$	6.13519	+	5.84989i	0.279741	+	0.266732i
$482$	−0.455979			−0.0207693
$483$	−2.77758	+	12.3808i	−0.126384	+	0.563347i
$484$	20.3525			0.925114
$485$	−4.25117	−	4.05348i	−0.193035	−	0.184059i
$486$	−0.374295	+	0.0721395i	−0.0169784	+	0.00327232i
$487$	1.12976	+	23.7166i	0.0511944	+	1.07470i	0.867612	+	0.497242i	$0.165654\pi$
$487$	1.12976	+	23.7166i	0.0511944	+	1.07470i	−0.816418	+	0.577462i	$0.804043\pi$
$488$	0.164431	−	0.129310i	0.00744342	−	0.00585357i
$489$	18.6374	+	11.9775i	0.842814	+	0.541643i
$490$	−10.8923	−	3.04751i	−0.492064	−	0.137673i
$491$	−2.73896	+	3.16092i	−0.123607	+	0.142651i	−0.814180	−	0.580613i	$-0.802813\pi$
$491$	−2.73896	+	3.16092i	−0.123607	+	0.142651i	0.690573	+	0.723263i	$0.257359\pi$
$492$	7.45378	−	2.98404i	0.336042	−	0.134531i
$493$	6.91536	+	0.660337i	0.311452	+	0.0297401i
$494$	−12.1250	+	11.5612i	−0.545530	+	0.520162i
$495$	−0.162743	−	0.670836i	−0.00731475	−	0.0301518i
$496$	−2.71394	−	5.94270i	−0.121860	−	0.266835i
$497$	−30.9037	+	6.16141i	−1.38622	+	0.276377i
$498$	−3.01852	+	3.48355i	−0.135263	+	0.156102i
$499$	−4.98007	+	0.475539i	−0.222939	+	0.0212880i	−0.205927	−	0.978567i	$-0.566021\pi$
$499$	−4.98007	+	0.475539i	−0.222939	+	0.0212880i	−0.0170110	+	0.999855i	$0.505415\pi$
$500$	55.6813	−	28.7057i	2.49014	−	1.28376i
$501$	11.5929	+	4.64108i	0.517931	+	0.207348i
$502$	7.95179	+	4.09943i	0.354906	+	0.182967i
$503$	−20.7892	−	23.9920i	−0.926946	−	1.06975i	−0.997388	−	0.0722366i	$-0.976986\pi$
$503$	−20.7892	−	23.9920i	−0.926946	−	1.06975i	0.0704417	−	0.997516i	$-0.477559\pi$
$504$	1.59229	−	3.54648i	0.0709264	−	0.157973i
$505$	5.71860			0.254474
$506$	−0.0942922	+	0.282373i	−0.00419180	+	0.0125530i
$507$	7.19098	−	12.4551i	0.319363	−	0.553152i
$508$	−7.43589	+	30.6512i	−0.329914	+	1.35993i
$509$	−8.45357	+	24.4250i	−0.374698	+	1.08262i	0.587255	+	0.809402i	$0.300209\pi$
$509$	−8.45357	+	24.4250i	−0.374698	+	1.08262i	−0.961953	+	0.273216i	$0.911913\pi$
$510$	−1.64028	+	1.05414i	−0.0726327	+	0.0466782i
$511$	1.06541	−	25.8415i	0.0471311	−	1.14316i
$512$	18.7518	+	12.0511i	0.828722	+	0.532587i
$513$	8.36114	−	0.798392i	0.369153	−	0.0352499i
$514$	1.88501	+	5.44637i	0.0831441	+	0.240229i
$515$	−20.7137	−	16.2894i	−0.912753	−	0.717797i
$516$	−6.81114	+	9.56491i	−0.299844	+	0.421072i
$517$	−0.288700	−	0.0847700i	−0.0126970	−	0.00372818i
$518$	−1.45694	−	0.739352i	−0.0640144	−	0.0324853i
$519$	−3.81193	−	8.34697i	−0.167325	−	0.366391i
$520$	30.2573	−	12.1132i	1.32687	−	0.531199i
$521$	3.53567	+	10.2157i	0.154901	+	0.447556i	0.995573	−	0.0939874i	$-0.0299614\pi$
$521$	3.53567	+	10.2157i	0.154901	+	0.447556i	−0.840673	+	0.541544i	$0.817840\pi$
$522$	−1.27288	−	1.78751i	−0.0557125	−	0.0782373i
$523$	0.726665	−	15.2546i	0.0317749	−	0.667036i	−0.925655	−	0.378369i	$-0.876485\pi$
$523$	0.726665	−	15.2546i	0.0317749	−	0.667036i	0.957430	−	0.288667i	$-0.0932120\pi$
$524$	−3.06298	−	21.3035i	−0.133807	−	0.930649i
$525$	−4.66566	+	33.9920i	−0.203626	+	1.48353i
$526$	−6.33698	−	7.31326i	−0.276305	−	0.318873i
$527$	−1.81170	−	1.72745i	−0.0789188	−	0.0752489i
$528$	−0.256428	+	0.444147i	−0.0111596	+	0.0193290i
$529$	−18.3852	−	13.8197i	−0.799358	−	0.600855i
$530$	−1.20662	−	2.08993i	−0.0524122	−	0.0907807i
$531$	1.97466	−	0.579814i	0.0856931	−	0.0251618i
$532$	−20.3790	+	35.8246i	−0.883542	+	1.55319i
$533$	−19.0565	+	12.2468i	−0.825427	+	0.530469i
$534$	2.69512	−	2.11946i	0.116629	−	0.0917181i
$535$	54.4821	−	28.0875i	2.35547	−	1.21433i
$536$	9.21260	+	12.9373i	0.397924	+	0.558806i
$537$	−4.79294	−	0.923763i	−0.206830	−	0.0398633i
$538$	−0.118593	+	0.824833i	−0.00511291	+	0.0355611i
$539$	−0.951013	+	0.628508i	−0.0409630	+	0.0270718i
$540$	−7.54341	−	2.21495i	−0.324617	−	0.0953161i
$541$	−4.23970	−	17.4763i	−0.182279	−	0.751364i	−0.987399	−	0.158252i	$-0.949414\pi$
$541$	−4.23970	−	17.4763i	−0.182279	−	0.751364i	0.805120	−	0.593112i	$-0.202101\pi$
$542$	1.04781	+	0.100054i	0.0450073	+	0.00429768i
$543$	−4.28456	−	3.36942i	−0.183868	−	0.144596i
$544$	4.90451	+	0.945266i	0.210279	+	0.0405280i
$545$	−19.1572	+	41.9485i	−0.820605	+	1.79687i
$546$	−1.21136	+	5.13644i	−0.0518415	+	0.219819i
$547$	3.27268	+	22.7620i	0.139930	+	0.973233i	0.931911	+	0.362687i	$0.118141\pi$
$547$	3.27268	+	22.7620i	0.139930	+	0.973233i	−0.791981	+	0.610546i	$0.790950\pi$
$548$	−0.516857	−	0.266458i	−0.0220790	−	0.0113825i
$549$	0.139793	−	0.0269429i	0.00596622	−	0.00114990i
$550$	−0.189786	+	0.782310i	−0.00809252	+	0.0333578i
$551$	24.1763	+	41.8745i	1.02994	+	1.78392i
$552$	4.67249	+	5.27490i	0.198874	+	0.224515i
$553$	21.1056	−	24.6743i	0.897503	−	1.04926i
$554$	3.19937	−	0.939421i	0.135928	−	0.0399122i
$555$	−2.24599	+	6.48936i	−0.0953369	+	0.275458i
$556$	−1.01358	−	21.2777i	−0.0429855	−	0.902376i
$557$	−6.78795	−	2.71748i	−0.287614	−	0.115143i	0.223369	−	0.974734i	$-0.428294\pi$
$557$	−6.78795	−	2.71748i	−0.287614	−	0.115143i	−0.510984	+	0.859590i	$0.670719\pi$
$558$	−0.0376253	+	0.789852i	−0.00159281	+	0.0334371i
$559$	13.7623	−	30.1352i	0.582082	−	1.27458i
$560$	27.6229	−	22.0102i	1.16728	−	0.930103i
$561$	−0.0279663	+	0.194510i	−0.00118074	+	0.00821221i
$562$	1.93177	−	2.71280i	0.0814870	−	0.114432i
$563$	0.0420775	−	0.0401208i	0.00177335	−	0.00169089i	−0.689192	−	0.724579i	$-0.742034\pi$
$563$	0.0420775	−	0.0401208i	0.00177335	−	0.00169089i	0.690965	+	0.722888i	$0.257186\pi$
$564$	−2.48014	+	2.36481i	−0.104433	+	0.0995763i
$565$	22.0031	−	30.8991i	0.925679	−	1.29993i
$566$	1.32980	−	9.24896i	0.0558957	−	0.388763i
$567$	2.06920	−	1.64876i	0.0868982	−	0.0692414i
$568$	−7.26998	+	15.9190i	−0.305041	+	0.667948i
$569$	0.880288	−	18.4795i	0.0369036	−	0.774702i	−0.902252	−	0.431209i	$-0.858087\pi$
$569$	0.880288	−	18.4795i	0.0369036	−	0.774702i	0.939155	−	0.343492i	$-0.111610\pi$
$570$	−12.5992	−	5.04397i	−0.527723	−	0.211268i
$571$	0.403639	+	8.47343i	0.0168918	+	0.354602i	0.991452	+	0.130475i	$0.0416501\pi$
$571$	0.403639	+	8.47343i	0.0168918	+	0.354602i	−0.974560	+	0.224127i	$0.928047\pi$
$572$	0.516922	−	1.49355i	0.0216136	−	0.0624484i
$573$	−10.3087	+	3.02691i	−0.430653	+	0.126451i
$574$	2.83785	−	3.31769i	0.118450	−	0.138478i
$575$	−52.6843	−	33.0513i	−2.19709	−	1.37833i
$576$	2.36041	+	4.08836i	0.0983506	+	0.170348i
$577$	3.74596	−	15.4410i	0.155946	−	0.642819i	−0.839149	−	0.543901i	$-0.816947\pi$
$577$	3.74596	−	15.4410i	0.155946	−	0.642819i	0.995096	−	0.0989180i	$-0.0315381\pi$
$578$	−5.81799	+	1.12133i	−0.241997	+	0.0466410i
$579$	−17.7126	−	9.13146i	−0.736109	−	0.379491i
$580$	−6.44109	−	44.7988i	−0.267452	−	1.86017i
$581$	7.34374	−	31.1391i	0.304670	−	1.29187i
$582$	0.219428	−	0.480481i	0.00909560	−	0.0199166i
$583$	−0.238822	−	0.0460292i	−0.00989101	−	0.00190634i
$584$	−11.2905	−	8.87898i	−0.467206	−	0.367415i
$585$	22.0808	+	2.10846i	0.912927	+	0.0871740i
$586$	−0.296721	−	1.22310i	−0.0122574	−	0.0505258i
$587$	−18.8016	−	5.52066i	−0.776027	−	0.227862i	−0.130345	−	0.991469i	$-0.541609\pi$
$587$	−18.8016	−	5.52066i	−0.776027	−	0.227862i	−0.645682	+	0.763607i	$0.723427\pi$
$588$	0.783546	+	12.9592i	0.0323129	+	0.534429i
$589$	2.47965	−	17.2463i	0.102172	−	0.710623i
$590$	−3.26527	−	0.629328i	−0.134429	−	0.0259090i
$591$	8.56643	+	12.0299i	0.352376	+	0.494842i
$592$	4.53475	−	2.33783i	0.186377	−	0.0960840i
$593$	34.5015	−	27.1323i	1.41681	−	1.11419i	0.440511	−	0.897747i	$-0.354797\pi$
$593$	34.5015	−	27.1323i	1.41681	−	1.11419i	0.976296	−	0.216441i	$-0.0694450\pi$
$594$	0.0522207	−	0.0335602i	0.00214264	−	0.00137699i
$595$	6.69158	−	11.7632i	0.274328	−	0.482246i
$596$	33.7828	−	9.91952i	1.38380	−	0.406319i
$597$	5.85971	+	10.1493i	0.239822	+	0.415384i
$598$	−7.58348	−	5.83089i	−0.310112	−	0.238443i
$599$	−5.19892	+	9.00479i	−0.212422	+	0.367926i	−0.952472	−	0.304626i	$-0.901469\pi$
$599$	−5.19892	+	9.00479i	−0.212422	+	0.367926i	0.740050	+	0.672552i	$0.234802\pi$
$600$	13.7907	+	13.1494i	0.563001	+	0.536820i
$601$	11.0771	+	12.7837i	0.451846	+	0.521458i	0.935273	−	0.353927i	$-0.115154\pi$
$601$	11.0771	+	12.7837i	0.451846	+	0.521458i	−0.483427	+	0.875384i	$0.660608\pi$
$602$	−0.868245	+	6.32567i	−0.0353870	+	0.257815i
$603$	1.53828	+	10.6990i	0.0626438	+	0.435697i
$604$	−0.201157	+	4.22280i	−0.00818495	+	0.171823i
$605$	−26.9816	−	37.8904i	−1.09696	−	1.54046i
$606$	0.168194	+	0.485964i	0.00683240	+	0.0197409i
$607$	−14.5564	+	5.82749i	−0.590825	+	0.236531i	−0.647756	−	0.761848i	$-0.724293\pi$
$607$	−14.5564	+	5.82749i	−0.590825	+	0.236531i	0.0569316	+	0.998378i	$0.481868\pi$
$608$	14.4421	+	31.6238i	0.585705	+	1.28252i
$609$	13.5823	+	6.89260i	0.550383	+	0.279302i
$610$	−0.220716	−	0.0648082i	−0.00893655	−	0.00262401i
$611$	5.60824	−	7.87567i	0.226885	−	0.318615i
$612$	1.75925	+	1.38349i	0.0711136	+	0.0559243i
$613$	−4.34355	−	12.5499i	−0.175435	−	0.506885i	0.822664	−	0.568528i	$-0.192487\pi$
$613$	−4.34355	−	12.5499i	−0.175435	−	0.506885i	−0.998098	+	0.0616436i	$0.980366\pi$
$614$	3.77201	−	0.360183i	0.152226	−	0.0145358i
$615$	−15.4370	−	9.92075i	−0.622479	−	0.400043i
$616$	−0.0260787	+	0.632538i	−0.00105074	+	0.0254857i
$617$	29.1450	−	18.7303i	1.17333	−	0.754054i	0.199183	−	0.979962i	$-0.436171\pi$
$617$	29.1450	−	18.7303i	1.17333	−	0.754054i	0.974149	+	0.225908i	$0.0725349\pi$
$618$	0.775042	−	2.23934i	0.0311767	−	0.0900793i
$619$	−3.03851	+	12.5249i	−0.122128	+	0.503418i	0.877584	+	0.479423i	$0.159154\pi$
$619$	−3.03851	+	12.5249i	−0.122128	+	0.503418i	−0.999712	+	0.0239954i	$0.992361\pi$
$620$	−8.15454	+	14.1241i	−0.327494	+	0.567237i
$621$	1.18146	+	4.64803i	0.0474103	+	0.186519i
$622$	5.00194			0.200560
$623$	−9.74741	+	21.7102i	−0.390522	+	0.869800i
$624$	−10.7919	−	12.4545i	−0.432020	−	0.498578i
$625$	−69.6259	−	35.8947i	−2.78504	−	1.43579i
$626$	5.57655	+	2.23251i	0.222884	+	0.0892291i
$627$	−1.21574	+	0.626755i	−0.0485518	+	0.0250302i
$628$	−8.50691	+	0.812312i	−0.339463	+	0.0324148i
$629$	1.28017	−	1.47740i	0.0510439	−	0.0589078i
$630$	−4.19249	+	0.835875i	−0.167033	+	0.0333021i
$631$	12.3254	+	26.9889i	0.490667	+	1.07441i	0.979391	+	0.201973i	$0.0647352\pi$
$631$	12.3254	+	26.9889i	0.490667	+	1.07441i	−0.488724	+	0.872438i	$0.662537\pi$
$632$	−4.25128	−	17.5240i	−0.169107	−	0.697068i
$633$	0.658251	−	0.627641i	0.0261631	−	0.0249465i
$634$	−7.27600	−	0.694774i	−0.288967	−	0.0275930i
$635$	66.9213	−	26.7912i	2.65569	−	1.06318i
$636$	−1.81399	+	2.09346i	−0.0719295	+	0.0830111i
$637$	−9.09025	−	35.4836i	−0.360169	−	1.40591i
$638$	0.300626	+	0.193200i	0.0119019	+	0.00764887i
$639$	−9.36220	+	7.36251i	−0.370363	+	0.291256i
$640$	−2.03265	−	42.6705i	−0.0803474	−	1.68670i
$641$	29.2044	−	5.62869i	1.15350	−	0.222320i	0.423588	−	0.905855i	$-0.360771\pi$
$641$	29.2044	−	5.62869i	1.15350	−	0.222320i	0.729917	+	0.683535i	$0.239558\pi$
$642$	3.98927	+	3.80376i	0.157444	+	0.150122i
$643$	5.62203			0.221711			0.110856	−	0.993837i	$-0.464641\pi$
$643$	5.62203			0.221711			0.110856	+	0.993837i	$0.464641\pi$
$644$	−21.9958	−	8.36707i	−0.866758	−	0.329709i
$645$	26.8367			1.05669
$646$	2.79610	+	2.66608i	0.110011	+	0.104895i
$647$	−31.9351	+	6.15498i	−1.25550	+	0.241977i	−0.773274	−	0.634072i	$-0.781382\pi$
$647$	−31.9351	+	6.15498i	−1.25550	+	0.241977i	−0.482222	+	0.876049i	$0.660170\pi$
$648$	−0.0699144	−	1.46768i	−0.00274650	−	0.0576561i
$649$	−0.263442	+	0.207173i	−0.0103410	+	0.00813225i
$650$	−21.7608	−	13.9848i	−0.853528	−	0.548529i
$651$	−2.31188	−	4.97782i	−0.0906096	−	0.195096i
$652$	−26.9080	+	31.0535i	−1.05380	+	1.21615i
$653$	26.0257	−	10.4191i	1.01847	−	0.407732i	0.198473	−	0.980106i	$-0.436402\pi$
$653$	26.0257	−	10.4191i	1.01847	−	0.407732i	0.819993	+	0.572374i	$0.193977\pi$
$654$	−4.12820	−	0.394196i	−0.161426	−	0.0154143i
$655$	−35.6002	+	33.9448i	−1.39102	+	1.32633i
$656$	3.21415	+	13.2489i	0.125491	+	0.517283i
$657$	−4.06088	−	8.89208i	−0.158430	−	0.346913i
$658$	−0.598187	+	1.76478i	−0.0233198	+	0.0687983i
$659$	8.24077	−	9.51036i	0.321015	−	0.370471i	−0.572190	−	0.820121i	$-0.693906\pi$
$659$	8.24077	−	9.51036i	0.321015	−	0.370471i	0.893205	+	0.449650i	$0.148451\pi$
$660$	1.27449	−	0.121699i	0.0496095	−	0.00473713i
$661$	−28.4193	+	14.6512i	−1.10538	+	0.569865i	−0.911558	−	0.411171i	$-0.865120\pi$
$661$	−28.4193	+	14.6512i	−1.10538	+	0.569865i	−0.193825	+	0.981036i	$0.562090\pi$
$662$	7.17920	+	2.87412i	0.279028	+	0.111706i
$663$	−5.61250	−	2.89345i	−0.217972	−	0.112372i
$664$	−11.6355	−	13.4280i	−0.451544	−	0.521109i
$665$	93.7115	−	9.55344i	3.63398	−	0.370467i
$666$	−0.617521			−0.0239284
$667$	−21.5144	+	17.3024i	−0.833041	+	0.669953i
$668$	−11.5801	+	20.0574i	−0.448049	+	0.776044i
$669$	−0.388812	+	1.60271i	−0.0150323	+	0.0619642i
$670$	5.71231	−	16.5046i	0.220686	−	0.637630i
$671$	−0.0195036	+	0.0125342i	−0.000752927	+	0.000483877i
$672$	9.25040	+	5.86163i	0.356842	+	0.226117i
$673$	4.80900	+	3.09056i	0.185374	+	0.119132i	0.630036	−	0.776566i	$-0.283040\pi$
$673$	4.80900	+	3.09056i	0.185374	+	0.119132i	−0.444663	+	0.895698i	$0.646676\pi$
$674$	5.50588	−	0.525748i	0.212078	−	0.0202510i
$675$	4.24149	+	12.2550i	0.163255	+	0.471695i
$676$	20.9673	+	16.4889i	0.806436	+	0.634188i
$677$	−12.4233	+	17.4461i	−0.477466	+	0.670507i	−0.981120	−	0.193398i	$-0.938049\pi$
$677$	−12.4233	+	17.4461i	−0.477466	+	0.670507i	0.503654	+	0.863905i	$0.331989\pi$
$678$	3.27294	+	0.961021i	0.125696	+	0.0369078i
$679$	0.197862	+	3.66093i	0.00759326	+	0.140494i
$680$	−3.12221	−	6.83670i	−0.119731	−	0.262175i
$681$	0.668147	−	0.267486i	0.0256034	−	0.0102501i
$682$	−0.0421170	−	0.121689i	−0.00161274	−	0.00465972i
$683$	−29.0455	−	40.7887i	−1.11140	−	1.56074i	−0.789277	−	0.614037i	$-0.789544\pi$
$683$	−29.0455	−	40.7887i	−1.11140	−	1.56074i	−0.322119	−	0.946699i	$-0.604395\pi$
$684$	−0.741228	+	15.5603i	−0.0283415	+	0.594962i
$685$	0.189138	+	1.31548i	0.00722658	+	0.0502620i
$686$	3.64644	+	6.04498i	0.139222	+	0.230798i
$687$	−0.0524325	−	0.0605103i	−0.00200042	−	0.00230861i
$688$	−14.4301	−	13.7591i	−0.550143	−	0.524560i
$689$	3.90765	−	6.76825i	0.148870	−	0.257850i
$690$	1.74462	−	7.55015i	0.0664166	−	0.287429i
$691$	−14.7278	−	25.5094i	−0.560273	−	0.970422i	−0.997472	−	0.0710568i	$-0.977363\pi$
$691$	−14.7278	−	25.5094i	−0.560273	−	0.970422i	0.437199	−	0.899365i	$-0.355971\pi$
$692$	16.3297	−	4.79483i	0.620762	−	0.182272i
$693$	−0.213037	+	0.374501i	−0.00809260	+	0.0142261i
$694$	10.4167	−	6.69442i	0.395413	−	0.254117i
$695$	−38.2691	+	30.0952i	−1.45163	+	1.14157i
$696$	7.51847	−	3.87604i	0.284987	−	0.146921i
$697$	3.03010	+	4.25517i	0.114773	+	0.161176i
$698$	−2.15127	−	0.414624i	−0.0814268	−	0.0156937i
$699$	−3.59656	+	25.0146i	−0.136034	+	0.946139i
$700$	−61.1717	−	17.5375i	−2.31207	−	0.662857i
$701$	−16.7696	−	4.92400i	−0.633379	−	0.185977i	−0.0507454	−	0.998712i	$-0.516160\pi$
$701$	−16.7696	−	4.92400i	−0.633379	−	0.185977i	−0.582634	+	0.812735i	$0.697978\pi$
$702$	0.470257	+	1.93842i	0.0177487	+	0.0731611i
$703$	13.5451	+	1.29340i	0.510863	+	0.0487815i
$704$	−0.604299	−	0.475226i	−0.0227754	−	0.0179107i
$705$	7.69053	+	1.48223i	0.289642	+	0.0558239i
$706$	−3.31482	+	7.25845i	−0.124755	+	0.273175i
$707$	−2.59894	−	2.44655i	−0.0977432	−	0.0920119i
$708$	0.543219	+	3.77817i	0.0204154	+	0.141992i
$709$	−34.9109	−	17.9978i	−1.31111	−	0.675922i	−0.346112	−	0.938193i	$-0.612498\pi$
$709$	−34.9109	−	17.9978i	−1.31111	−	0.675922i	−0.964994	+	0.262271i	$0.915529\pi$
$710$	18.8970	−	3.64210i	0.709192	−	0.136686i
$711$	2.89331	−	11.9264i	0.108508	−	0.447274i
$712$	6.60824	+	11.4458i	0.247654	+	0.428950i
$713$	9.94813	−	0.108580i	0.372561	−	0.00406634i
$714$	1.19644	+	0.222670i	0.0447758	+	0.00833323i
$715$	−3.46584	+	1.01766i	−0.129615	+	0.0380584i
$716$	2.96096	−	8.55514i	0.110656	−	0.319721i
$717$	0.247332	+	5.19214i	0.00923678	+	0.193904i
$718$	−0.555039	−	0.222204i	−0.0207139	−	0.00829258i
$719$	−0.148090	+	3.10878i	−0.00552281	+	0.115938i	0.994422	+	0.105471i	$0.0336349\pi$
$719$	−0.148090	+	3.10878i	−0.00552281	+	0.115938i	−0.999945	+	0.0104673i	$0.996668\pi$
$720$	5.54561	−	12.1432i	0.206673	−	0.452550i
$721$	2.44479	+	16.2648i	0.0910486	+	0.605735i
$722$	−2.79628	+	19.4485i	−0.104067	+	0.723799i
$723$	0.693875	−	0.974411i	0.0258055	−	0.0362387i
$724$	7.31656	−	6.97633i	0.271918	−	0.259273i
$725$	−54.0310	+	51.5184i	−2.00666	+	1.91335i
$726$	2.42633	−	3.40730i	0.0900495	−	0.126457i
$727$	−5.05459	+	35.1554i	−0.187464	+	1.30384i	0.651080	+	0.759009i	$0.274316\pi$
$727$	−5.05459	+	35.1554i	−0.187464	+	1.30384i	−0.838544	+	0.544833i	$0.816593\pi$
$728$	−18.9334	−	7.43966i	−0.701717	−	0.275732i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−0.751566	+	15.7773i	−0.0278167	+	0.583944i
$731$	−7.09249	−	2.83941i	−0.262325	−	0.105019i
$732$	0.0125638	+	0.263747i	0.000464371	+	0.00974836i
$733$	0.466393	−	1.34756i	0.0172266	−	0.0497731i	−0.936060	−	0.351841i	$-0.885556\pi$
$733$	0.466393	−	1.34756i	0.0172266	−	0.0497731i	0.953286	+	0.302068i	$0.0976770\pi$
$734$	3.10385	−	0.911374i	0.114565	−	0.0336394i
$735$	23.0875	−	18.6390i	0.851595	−	0.687508i
$736$	−16.5814	+	10.9137i	−0.611197	+	0.402285i
$737$	−0.880112	−	1.52440i	−0.0324193	−	0.0561520i
$738$	0.389032	−	1.60361i	0.0143205	−	0.0590298i
$739$	−12.0038	+	2.31354i	−0.441567	+	0.0851051i	−0.405189	−	0.914233i	$-0.632794\pi$
$739$	−12.0038	+	2.31354i	−0.441567	+	0.0851051i	−0.0363782	+	0.999338i	$0.511582\pi$
$740$	−11.3205	−	5.83611i	−0.416149	−	0.214540i
$741$	−6.25488	−	43.5036i	−0.229779	−	1.59815i
$742$	−0.345744	+	1.46603i	−0.0126927	+	0.0538197i
$743$	−17.1633	+	37.5824i	−0.629660	+	1.37876i	0.278620	+	0.960401i	$0.410123\pi$
$743$	−17.1633	+	37.5824i	−0.629660	+	1.37876i	−0.908280	+	0.418362i	$0.862604\pi$
$744$	−2.99301	−	0.576856i	−0.109729	−	0.0211486i
$745$	−63.2535	−	49.7431i	−2.31743	−	1.82245i
$746$	4.51958	+	0.431568i	0.165474	+	0.0158008i
$747$	−2.85088	−	11.7515i	−0.104308	−	0.429964i
$748$	−0.349703	−	0.102682i	−0.0127864	−	0.00375443i
$749$	−36.7770	−	10.5437i	−1.34380	−	0.385260i
$750$	1.83231	−	12.7440i	0.0669066	−	0.465345i
$751$	31.0234	+	5.97927i	1.13206	+	0.218187i	0.720674	−	0.693274i	$-0.243833\pi$
$751$	31.0234	+	5.97927i	1.13206	+	0.218187i	0.411386	+	0.911461i	$0.365045\pi$
$752$	−3.37527	−	4.73991i	−0.123084	−	0.172847i
$753$	−20.8608	+	10.7545i	−0.760209	+	0.391915i
$754$	−9.02613	+	7.09823i	−0.328712	+	0.258502i
$755$	8.12829	−	5.22373i	0.295819	−	0.190111i
$756$	2.48066	+	4.23387i	0.0902207	+	0.153984i
$757$	−17.3196	+	5.08549i	−0.629491	+	0.184835i	−0.580889	−	0.813983i	$-0.697295\pi$
$757$	−17.3196	+	5.08549i	−0.629491	+	0.184835i	−0.0486023	+	0.998818i	$0.515477\pi$
$758$	2.99392	+	5.18563i	0.108744	+	0.188351i
$759$	−0.459935	−	0.631193i	−0.0166946	−	0.0229109i
$760$	26.1568	−	45.3048i	0.948805	−	1.64338i
$761$	−33.5312	−	31.9720i	−1.21551	−	1.15898i	−0.982451	−	0.186519i	$-0.940279\pi$
$761$	−33.5312	−	31.9720i	−1.21551	−	1.15898i	−0.233055	−	0.972464i	$-0.574872\pi$
$762$	4.24497	+	4.89896i	0.153779	+	0.177471i
$763$	26.6529	−	10.8685i	0.964900	−	0.393465i
$764$	−2.83587	−	19.7239i	−0.102598	−	0.713586i
$765$	0.243387	−	5.10932i	0.00879968	−	0.184728i
$766$	−7.86646	−	11.0469i	−0.284227	−	0.399141i
$767$	−3.52226	−	10.1769i	−0.127182	−	0.367467i
$768$	−5.19900	+	2.08137i	−0.187603	+	0.0751048i
$769$	5.30892	+	11.6249i	0.191445	+	0.419205i	0.980876	−	0.194634i	$-0.0623518\pi$
$769$	5.30892	+	11.6249i	0.191445	+	0.419205i	−0.789431	+	0.613839i	$0.789624\pi$
$770$	0.583240	−	0.380117i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.275876 + 0.263047i) q^{2} +(-0.981929 + 0.189251i) q^{3} +(-0.0882501 - 1.85260i) q^{4} +(-3.33200 + 2.62031i) q^{5} +(-0.320672 - 0.206084i) q^{6} +(2.63533 + 0.234648i) q^{7} +(0.962219 - 1.11046i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\)	\(q+(0.275876 + 0.263047i) q^{2} +(-0.981929 + 0.189251i) q^{3} +(-0.0882501 - 1.85260i) q^{4} +(-3.33200 + 2.62031i) q^{5} +(-0.320672 - 0.206084i) q^{6} +(2.63533 + 0.234648i) q^{7} +(0.962219 - 1.11046i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-1.60848 - 0.153591i) q^{10} +(-0.117858 + 0.112378i) q^{11} +(0.437262 + 1.80242i) q^{12} +(-2.17377 - 4.75990i) q^{13} +(0.665299 + 0.757948i) q^{14} +(2.77589 - 3.20354i) q^{15} +(-3.13505 + 0.299361i) q^{16} +(-1.07257 + 0.552947i) q^{17} +(0.353879 + 0.141672i) q^{18} +(-7.46548 - 3.84872i) q^{19} +(5.14843 + 5.94161i) q^{20} +(-2.63211 + 0.268331i) q^{21} -0.0620749 q^{22} +(1.51901 - 4.54891i) q^{23} +(-0.734674 + 1.27249i) q^{24} +(3.05738 - 12.6027i) q^{25} +(0.652386 - 1.88495i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.202141 - 4.90291i) q^{28} +(-4.84295 - 3.11238i) q^{29} +(1.60848 - 0.153591i) q^{30} +(0.678487 + 1.96036i) q^{31} +(-3.25360 - 2.55866i) q^{32} +(0.0944609 - 0.132652i) q^{33} +(-0.441346 - 0.129591i) q^{34} +(-9.39575 + 6.12353i) q^{35} +(-0.770470 - 1.68709i) q^{36} +(-1.50396 + 0.602096i) q^{37} +(-1.04715 - 3.02554i) q^{38} +(3.03531 + 4.26249i) q^{39} +(-0.296360 + 6.22136i) q^{40} +(-0.616074 - 4.28489i) q^{41} +(-0.796719 - 0.618342i) q^{42} +(4.14596 + 4.78469i) q^{43} +(0.218592 + 0.208427i) q^{44} +(-2.11945 + 3.67099i) q^{45} +(1.61564 - 0.855365i) q^{46} +(0.923833 + 1.60013i) q^{47} +(3.02174 - 0.887262i) q^{48} +(6.88988 + 1.23675i) q^{49} +(4.15855 - 2.67254i) q^{50} +(0.948538 - 0.745939i) q^{51} +(-8.62635 + 4.44719i) q^{52} +(0.866331 + 1.21659i) q^{53} +(-0.374295 - 0.0721395i) q^{54} +(0.0982391 - 0.683268i) q^{55} +(2.79633 - 2.70064i) q^{56} +(8.05894 + 2.36632i) q^{57} +(-0.517352 - 2.13255i) q^{58} +(2.04871 + 0.195628i) q^{59} +(-6.17985 - 4.85989i) q^{60} +(0.139793 + 0.0269429i) q^{61} +(-0.328489 + 0.719290i) q^{62} +(2.53376 - 0.761612i) q^{63} +(0.671844 + 4.67278i) q^{64} +(19.7154 + 10.1640i) q^{65} +(0.0609531 - 0.0117478i) q^{66} +(-2.54832 + 10.5043i) q^{67} +(1.11904 + 1.93824i) q^{68} +(-0.630669 + 4.75418i) q^{69} +(-4.20283 - 0.782190i) q^{70} +(-11.4279 + 3.35554i) q^{71} +(0.480577 - 1.38854i) q^{72} +(-0.465136 - 9.76440i) q^{73} +(-0.573286 - 0.229509i) q^{74} +(-0.617053 + 12.9535i) q^{75} +(-6.47131 + 14.1702i) q^{76} +(-0.336964 + 0.268497i) q^{77} +(-0.283868 + 1.97435i) q^{78} +(7.11864 - 9.99673i) q^{79} +(9.66154 - 9.21226i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.957168 - 1.34415i) q^{82} +(1.72092 - 11.9692i) q^{83} +(0.729394 + 4.85256i) q^{84} +(2.12490 - 4.65287i) q^{85} +(-0.114829 + 2.41056i) q^{86} +(5.34445 + 2.13960i) q^{87} +(0.0113854 + 0.239009i) q^{88} +(-2.94191 + 8.50008i) q^{89} +(-1.55035 + 0.455223i) q^{90} +(-4.61170 - 13.0540i) q^{91} +(-8.56136 - 2.41267i) q^{92} +(-1.03723 - 1.79653i) q^{93} +(-0.166045 + 0.684447i) q^{94} +(34.9598 - 6.73795i) q^{95} +(3.67903 + 1.89667i) q^{96} +(0.197209 + 1.37162i) q^{97} +(1.57543 + 2.15355i) q^{98} +(-0.0676494 + 0.148131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

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