LMFDB - Embedded newform 503.2.c.a.2.11

Newspace parameters

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.c (of order $251$, degree $250$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$10250$
Relative dimension:	$41$ over $\Q(\zeta_{251})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{251}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.11

$q$-expansion

$f(q)$	$=$	$q+(-0.968162 - 1.19202i) q^{2} +(0.996021 - 0.862065i) q^{3} +(-0.0734591 + 0.350630i) q^{4} +(-0.521680 - 1.64756i) q^{5} +(-1.99191 - 0.352655i) q^{6} +(0.222510 - 0.646070i) q^{7} +(-2.24135 + 1.15442i) q^{8} +(-0.181422 + 1.25171i) q^{9} +O(q^{10})$	\(q+(-0.968162 - 1.19202i) q^{2} +(0.996021 - 0.862065i) q^{3} +(-0.0734591 + 0.350630i) q^{4} +(-0.521680 - 1.64756i) q^{5} +(-1.99191 - 0.352655i) q^{6} +(0.222510 - 0.646070i) q^{7} +(-2.24135 + 1.15442i) q^{8} +(-0.181422 + 1.25171i) q^{9} +(-1.45885 + 2.21696i) q^{10} +(-5.46959 + 1.76961i) q^{11} +(0.229099 + 0.412561i) q^{12} +(-2.59529 + 0.875704i) q^{13} +(-0.985552 + 0.360264i) q^{14} +(-1.93991 - 1.19129i) q^{15} +(4.20231 + 1.84165i) q^{16} +(-2.39011 - 1.19343i) q^{17} +(1.66770 - 0.995597i) q^{18} +(-1.54810 - 3.47319i) q^{19} +(0.616008 - 0.0618881i) q^{20} +(-0.335330 - 0.835317i) q^{21} +(7.40486 + 4.80657i) q^{22} +(0.386888 - 1.33730i) q^{23} +(-1.23724 + 3.08201i) q^{24} +(1.64645 - 1.15884i) q^{25} +(3.55652 + 2.24581i) q^{26} +(3.02919 + 4.73125i) q^{27} +(0.210186 + 0.125478i) q^{28} +(0.334013 - 2.79582i) q^{29} +(0.458115 + 3.46576i) q^{30} +(-0.233659 - 2.86572i) q^{31} +(-0.532651 - 1.93136i) q^{32} +(-3.92230 + 6.47771i) q^{33} +(0.891424 + 4.00448i) q^{34} +(-1.18052 - 0.0295577i) q^{35} +(-0.425559 - 0.155561i) q^{36} +(-4.47868 - 5.65747i) q^{37} +(-2.64129 + 5.20797i) q^{38} +(-1.83005 + 3.10953i) q^{39} +(3.07125 + 3.09053i) q^{40} +(2.24137 - 11.4080i) q^{41} +(-0.671058 + 1.20844i) q^{42} +(0.279437 - 1.52277i) q^{43} +(-0.218688 - 2.04780i) q^{44} +(2.15691 - 0.354086i) q^{45} +(-1.96865 + 0.833544i) q^{46} +(-7.67646 + 0.288378i) q^{47} +(5.77321 - 1.78834i) q^{48} +(5.14758 + 4.02288i) q^{49} +(-2.97539 - 0.840655i) q^{50} +(-3.40941 + 0.871749i) q^{51} +(-0.116400 - 0.974317i) q^{52} +(-2.94975 + 6.61782i) q^{53} +(2.70698 - 8.19147i) q^{54} +(5.76892 + 8.08833i) q^{55} +(0.247113 + 1.70494i) q^{56} +(-4.53605 - 2.12480i) q^{57} +(-3.65605 + 2.30866i) q^{58} +(-1.21391 + 2.91772i) q^{59} +(0.560205 - 0.592681i) q^{60} +(-0.874408 - 1.44409i) q^{61} +(-3.18976 + 3.05300i) q^{62} +(0.768322 + 0.395729i) q^{63} +(3.54191 - 4.96595i) q^{64} +(2.79669 + 3.81907i) q^{65} +(11.5190 - 1.59602i) q^{66} +(8.52383 - 5.23442i) q^{67} +(0.594027 - 0.750375i) q^{68} +(-0.767490 - 1.66550i) q^{69} +(1.10770 + 1.43582i) q^{70} +(1.40371 + 8.89870i) q^{71} +(-1.03836 - 3.01495i) q^{72} +(-2.61101 - 2.49907i) q^{73} +(-2.40772 + 10.8160i) q^{74} +(0.640905 - 2.57358i) q^{75} +(1.33153 - 0.287673i) q^{76} +(-0.0737452 + 3.92749i) q^{77} +(5.47840 - 0.829076i) q^{78} +(-0.378289 - 6.70927i) q^{79} +(0.841981 - 7.88433i) q^{80} +(3.45757 + 1.02379i) q^{81} +(-15.7685 + 8.37302i) q^{82} +(-3.71862 - 7.11018i) q^{83} +(0.317520 - 0.0562151i) q^{84} +(-0.719377 + 4.56044i) q^{85} +(-2.08571 + 1.14119i) q^{86} +(-2.07750 - 3.07264i) q^{87} +(10.2164 - 10.2805i) q^{88} +(0.361321 + 1.37716i) q^{89} +(-2.51032 - 2.22826i) q^{90} +(-0.0117129 + 1.87159i) q^{91} +(0.440477 + 0.233891i) q^{92} +(-2.70316 - 2.65288i) q^{93} +(7.77581 + 8.87127i) q^{94} +(-4.91469 + 4.36249i) q^{95} +(-2.19549 - 1.46450i) q^{96} +(2.91483 + 12.3625i) q^{97} +(-0.188345 - 10.0308i) q^{98} +(-1.22273 - 7.16737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) $	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/503\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{101}{251}\right)$

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 $

$2$	−0.968162	−	1.19202i	−0.684594	−	0.842883i	0.309557	−	0.950881i	$-0.399819\pi$
$2$	−0.968162	−	1.19202i	−0.684594	−	0.842883i	−0.994151	+	0.107997i	$0.965556\pi$
$3$	0.996021	−	0.862065i	0.575053	−	0.497714i	−0.317742	−	0.948177i	$-0.602925\pi$
$3$	0.996021	−	0.862065i	0.575053	−	0.497714i	0.892795	+	0.450464i	$0.148741\pi$
$4$	−0.0734591	+	0.350630i	−0.0367296	+	0.175315i
$5$	−0.521680	−	1.64756i	−0.233302	−	0.736813i	−0.995943	−	0.0899900i	$-0.971316\pi$
$5$	−0.521680	−	1.64756i	−0.233302	−	0.736813i	0.762640	−	0.646823i	$-0.223903\pi$
$6$	−1.99191	−	0.352655i	−0.813192	−	0.143971i
$7$	0.222510	−	0.646070i	0.0841008	−	0.244191i	−0.895529	−	0.445003i	$-0.853203\pi$
$7$	0.222510	−	0.646070i	0.0841008	−	0.244191i	0.979630	+	0.200812i	$0.0643580\pi$
$8$	−2.24135	+	1.15442i	−0.792437	+	0.408149i
$9$	−0.181422	+	1.25171i	−0.0604741	+	0.417236i
$10$	−1.45885	+	2.21696i	−0.461330	+	0.701064i
$11$	−5.46959	+	1.76961i	−1.64914	+	0.533558i	−0.978149	−	0.207904i	$-0.933336\pi$
$11$	−5.46959	+	1.76961i	−1.64914	+	0.533558i	−0.670994	+	0.741462i	$0.734133\pi$
$12$	0.229099	+	0.412561i	0.0661353	+	0.119096i
$13$	−2.59529	+	0.875704i	−0.719805	+	0.242876i	−0.655652	−	0.755064i	$-0.727606\pi$
$13$	−2.59529	+	0.875704i	−0.719805	+	0.242876i	−0.0641533	+	0.997940i	$0.520435\pi$
$14$	−0.985552	+	0.360264i	−0.263400	+	0.0962847i
$15$	−1.93991	−	1.19129i	−0.500883	−	0.307589i
$16$	4.20231	+	1.84165i	1.05058	+	0.460413i
$17$	−2.39011	−	1.19343i	−0.579686	−	0.289449i	0.132791	−	0.991144i	$-0.457606\pi$
$17$	−2.39011	−	1.19343i	−0.579686	−	0.289449i	−0.712477	+	0.701695i	$0.752427\pi$
$18$	1.66770	−	0.995597i	0.393081	−	0.234664i
$19$	−1.54810	−	3.47319i	−0.355158	−	0.796804i	−0.999486	−	0.0320546i	$-0.989795\pi$
$19$	−1.54810	−	3.47319i	−0.355158	−	0.796804i	0.644328	−	0.764750i	$-0.277137\pi$
$20$	0.616008	−	0.0618881i	0.137743	−	0.0138386i
$21$	−0.335330	−	0.835317i	−0.0731749	−	0.182281i
$22$	7.40486	+	4.80657i	1.57872	+	1.02477i
$23$	0.386888	−	1.33730i	0.0806717	−	0.278846i	−0.910100	−	0.414389i	$-0.863995\pi$
$23$	0.386888	−	1.33730i	0.0806717	−	0.278846i	0.990771	+	0.135543i	$0.0432780\pi$
$24$	−1.23724	+	3.08201i	−0.252552	+	0.629114i
$25$	1.64645	−	1.15884i	0.329291	−	0.231768i
$26$	3.55652	+	2.24581i	0.697491	+	0.440440i
$27$	3.02919	+	4.73125i	0.582969	+	0.910530i
$28$	0.210186	+	0.125478i	0.0397214	+	0.0237132i
$29$	0.334013	−	2.79582i	0.0620246	−	0.519171i	−0.927394	−	0.374085i	$-0.877957\pi$
$29$	0.334013	−	2.79582i	0.0620246	−	0.519171i	0.989419	−	0.145086i	$-0.0463460\pi$
$30$	0.458115	+	3.46576i	0.0836401	+	0.632759i
$31$	−0.233659	−	2.86572i	−0.0419664	−	0.514698i	−0.983878	−	0.178838i	$-0.942766\pi$
$31$	−0.233659	−	2.86572i	−0.0419664	−	0.514698i	0.941912	−	0.335860i	$-0.109027\pi$
$32$	−0.532651	−	1.93136i	−0.0941603	−	0.341420i
$33$	−3.92230	+	6.47771i	−0.682786	+	1.12763i
$34$	0.891424	+	4.00448i	0.152878	+	0.686762i
$35$	−1.18052	−	0.0295577i	−0.199544	−	0.00499616i
$36$	−0.425559	−	0.155561i	−0.0709265	−	0.0259269i
$37$	−4.47868	−	5.65747i	−0.736290	−	0.930082i	0.263108	−	0.964766i	$-0.415252\pi$
$37$	−4.47868	−	5.65747i	−0.736290	−	0.930082i	−0.999398	+	0.0346840i	$0.988958\pi$
$38$	−2.64129	+	5.20797i	−0.428474	+	0.844844i
$39$	−1.83005	+	3.10953i	−0.293043	+	0.497923i
$40$	3.07125	+	3.09053i	0.485607	+	0.488655i
$41$	2.24137	−	11.4080i	0.350043	−	1.78163i	−0.236420	−	0.971651i	$-0.575974\pi$
$41$	2.24137	−	11.4080i	0.350043	−	1.78163i	0.586463	−	0.809976i	$-0.300520\pi$
$42$	−0.671058	+	1.20844i	−0.103547	+	0.186466i
$43$	0.279437	−	1.52277i	0.0426137	−	0.232220i	−0.955392	−	0.295340i	$-0.904567\pi$
$43$	0.279437	−	1.52277i	0.0426137	−	0.232220i	0.998006	+	0.0631197i	$0.0201050\pi$
$44$	−0.218688	−	2.04780i	−0.0329685	−	0.308717i
$45$	2.15691	−	0.354086i	0.321533	−	0.0527840i
$46$	−1.96865	+	0.833544i	−0.290262	+	0.122899i
$47$	−7.67646	+	0.288378i	−1.11973	+	0.0420643i	−0.590958	−	0.806702i	$-0.701250\pi$
$47$	−7.67646	+	0.288378i	−1.11973	+	0.0420643i	−0.528768	+	0.848766i	$0.677346\pi$
$48$	5.77321	−	1.78834i	0.833292	−	0.258125i
$49$	5.14758	+	4.02288i	0.735369	+	0.574698i
$50$	−2.97539	−	0.840655i	−0.420784	−	0.118887i
$51$	−3.40941	+	0.871749i	−0.477413	+	0.122069i
$52$	−0.116400	−	0.974317i	−0.0161418	−	0.135113i
$53$	−2.94975	+	6.61782i	−0.405180	+	0.909028i	0.589668	+	0.807646i	$0.299259\pi$
$53$	−2.94975	+	6.61782i	−0.405180	+	0.909028i	−0.994848	+	0.101382i	$0.967674\pi$
$54$	2.70698	−	8.19147i	0.368374	−	1.11472i
$55$	5.76892	+	8.08833i	0.777881	+	1.09063i
$56$	0.247113	+	1.70494i	0.0330219	+	0.227832i
$57$	−4.53605	−	2.12480i	−0.600815	−	0.281437i
$58$	−3.65605	+	2.30866i	−0.480062	+	0.303142i
$59$	−1.21391	+	2.91772i	−0.158038	+	0.379855i	−0.982552	−	0.185986i	$-0.940452\pi$
$59$	−1.21391	+	2.91772i	−0.158038	+	0.379855i	0.824515	+	0.565840i	$0.191448\pi$
$60$	0.560205	−	0.592681i	0.0723221	−	0.0765147i
$61$	−0.874408	−	1.44409i	−0.111956	−	0.184897i	0.794419	−	0.607370i	$-0.207776\pi$
$61$	−0.874408	−	1.44409i	−0.111956	−	0.184897i	−0.906375	+	0.422473i	$0.861162\pi$
$62$	−3.18976	+	3.05300i	−0.405100	+	0.387732i
$63$	0.768322	+	0.395729i	0.0967994	+	0.0498571i
$64$	3.54191	−	4.96595i	0.442739	−	0.620743i
$65$	2.79669	+	3.81907i	0.346887	+	0.473698i
$66$	11.5190	−	1.59602i	1.41789	−	0.196457i
$67$	8.52383	−	5.23442i	1.04135	−	0.639486i	0.106422	−	0.994321i	$-0.466061\pi$
$67$	8.52383	−	5.23442i	1.04135	−	0.639486i	0.934929	+	0.354835i	$0.115463\pi$
$68$	0.594027	−	0.750375i	0.0720363	−	0.0909964i
$69$	−0.767490	−	1.66550i	−0.0923949	−	0.200503i
$70$	1.10770	+	1.43582i	0.132396	+	0.171613i
$71$	1.40371	+	8.89870i	0.166589	+	1.05608i	0.918097	+	0.396356i	$0.129725\pi$
$71$	1.40371	+	8.89870i	0.166589	+	1.05608i	−0.751507	+	0.659725i	$0.770673\pi$
$72$	−1.03836	−	3.01495i	−0.122372	−	0.355315i
$73$	−2.61101	−	2.49907i	−0.305596	−	0.292494i	0.523009	−	0.852327i	$-0.324809\pi$
$73$	−2.61101	−	2.49907i	−0.305596	−	0.292494i	−0.828605	+	0.559833i	$0.810865\pi$
$74$	−2.40772	+	10.8160i	−0.279891	+	1.25734i
$75$	0.640905	−	2.57358i	0.0740053	−	0.297171i
$76$	1.33153	−	0.287673i	0.152737	−	0.0329984i
$77$	−0.0737452	+	3.92749i	−0.00840405	+	0.447579i
$78$	5.47840	−	0.829076i	0.620307	−	0.0938744i
$79$	−0.378289	−	6.70927i	−0.0425608	−	0.754851i	−0.945608	−	0.325309i	$-0.894532\pi$
$79$	−0.378289	−	6.70927i	−0.0425608	−	0.754851i	0.903047	−	0.429542i	$-0.141325\pi$
$80$	0.841981	−	7.88433i	0.0941364	−	0.881494i
$81$	3.45757	+	1.02379i	0.384174	+	0.113754i
$82$	−15.7685	+	8.37302i	−1.74134	+	0.924645i
$83$	−3.71862	−	7.11018i	−0.408172	−	0.780444i	0.591493	−	0.806310i	$-0.298539\pi$
$83$	−3.71862	−	7.11018i	−0.408172	−	0.780444i	−0.999665	+	0.0258662i	$0.991766\pi$
$84$	0.317520	−	0.0562151i	0.0346443	−	0.00613357i
$85$	−0.719377	+	4.56044i	−0.0780274	+	0.494649i
$86$	−2.08571	+	1.14119i	−0.224908	+	0.123058i
$87$	−2.07750	−	3.07264i	−0.222731	−	0.329421i
$88$	10.2164	−	10.2805i	1.08907	−	1.09591i
$89$	0.361321	+	1.37716i	0.0383000	+	0.145978i	0.983655	−	0.180065i	$-0.0576309\pi$
$89$	0.361321	+	1.37716i	0.0383000	+	0.145978i	−0.945355	+	0.326044i	$0.894284\pi$
$90$	−2.51032	−	2.22826i	−0.264610	−	0.234880i
$91$	−0.0117129	+	1.87159i	−0.00122784	+	0.196196i
$92$	0.440477	+	0.233891i	0.0459229	+	0.0243849i
$93$	−2.70316	−	2.65288i	−0.280305	−	0.275091i
$94$	7.77581	+	8.87127i	0.802013	+	0.915002i
$95$	−4.91469	+	4.36249i	−0.504236	+	0.447582i
$96$	−2.19549	−	1.46450i	−0.224077	−	0.149470i
$97$	2.91483	+	12.3625i	0.295957	+	1.25522i	0.891914	+	0.452204i	$0.149362\pi$
$97$	2.91483	+	12.3625i	0.295957	+	1.25522i	−0.595958	+	0.803016i	$0.703227\pi$
$98$	−0.188345	−	10.0308i	−0.0190257	−	1.01326i
$99$	−1.22273	−	7.16737i	−0.122889	−	0.720348i
$100$	0.285377	+	0.662423i	0.0285377	+	0.0662423i
$101$	5.40288	−	2.12977i	0.537607	−	0.211920i	−0.0822830	−	0.996609i	$-0.526221\pi$
$101$	5.40288	−	2.12977i	0.537607	−	0.211920i	0.619890	+	0.784689i	$0.287177\pi$
$102$	4.34000	+	3.22008i	0.429724	+	0.318835i
$103$	−17.0024	+	3.45117i	−1.67529	+	0.340054i	−0.940903	−	0.338676i	$-0.890021\pi$
$103$	−17.0024	+	3.45117i	−1.67529	+	0.340054i	−0.734389	+	0.678729i	$0.762531\pi$
$104$	4.80603	−	4.95882i	0.471270	−	0.486252i
$105$	−1.20130	+	0.988245i	−0.117235	+	0.0964428i
$106$	10.7444	−	2.89097i	1.04359	−	0.280796i
$107$	6.47740	+	0.243334i	0.626194	+	0.0235239i	0.348747	−	0.937217i	$-0.386607\pi$
$107$	6.47740	+	0.243334i	0.626194	+	0.0235239i	0.277447	+	0.960741i	$0.410512\pi$
$108$	−1.88144	+	0.714573i	−0.181042	+	0.0687598i
$109$	−4.12760	−	4.36689i	−0.395353	−	0.418272i	0.498319	−	0.866994i	$-0.333951\pi$
$109$	−4.12760	−	4.36689i	−0.395353	−	0.418272i	−0.893671	+	0.448722i	$0.851879\pi$
$110$	4.05617	−	14.7075i	0.386741	−	1.40230i
$111$	−9.33796	−	1.77404i	−0.886320	−	0.168385i
$112$	2.12489	−	2.30520i	0.200783	−	0.217821i
$113$	−5.20397	−	10.5874i	−0.489548	−	0.995977i	−0.991381	−	0.131012i	$-0.958177\pi$
$113$	−5.20397	−	10.5874i	−0.489548	−	0.995977i	0.501833	−	0.864965i	$-0.332659\pi$
$114$	1.85883	+	7.46421i	0.174096	+	0.699087i
$115$	−2.40511	+	0.0602189i	−0.224278	+	0.00561544i
$116$	0.955763	+	0.322494i	0.0887404	+	0.0299428i
$117$	−0.625280	−	3.40742i	−0.0578072	−	0.315016i
$118$	4.65323	−	1.37782i	0.428365	−	0.126839i
$119$	−1.30286	+	1.27863i	−0.119433	+	0.117211i
$120$	5.72326	+	0.430614i	0.522460	+	0.0393095i
$121$	17.8695	−	12.9148i	1.62450	−	1.17407i
$122$	−0.874813	+	2.44042i	−0.0792018	+	0.220946i
$123$	−7.60197	−	13.2948i	−0.685447	−	1.19875i
$124$	1.02197	+	0.128585i	0.0917757	+	0.0115473i
$125$	−9.64264	−	7.34329i	−0.862464	−	0.656803i
$126$	−0.272145	−	1.29898i	−0.0242446	−	0.115723i
$127$	14.4343	−	8.13411i	1.28084	−	0.721785i	0.307584	−	0.951521i	$-0.400479\pi$
$127$	14.4343	−	8.13411i	1.28084	−	0.721785i	0.973253	+	0.229736i	$0.0737862\pi$
$128$	−13.3477	+	0.836414i	−1.17978	+	0.0739292i
$129$	−1.03440	−	1.75760i	−0.0910740	−	0.154748i
$130$	1.84475	−	7.03118i	0.161796	−	0.616676i
$131$	−4.06100	+	2.70888i	−0.354811	+	0.236676i	−0.719560	−	0.694430i	$-0.755657\pi$
$131$	−4.06100	+	2.70888i	−0.354811	+	0.236676i	0.364749	+	0.931106i	$0.381155\pi$
$132$	−1.98315	−	1.85113i	−0.172611	−	0.161120i
$133$	−2.58839	+	0.227362i	−0.224442	+	0.0197147i
$134$	−14.4920	−	5.09278i	−1.25191	−	0.439949i
$135$	6.21477	−	7.45899i	0.534882	−	0.641967i
$136$	6.73478	−	0.0842989i	0.577503	−	0.00722858i
$137$	0.547186	+	1.41400i	0.0467493	+	0.120806i	0.954022	−	0.299738i	$-0.0968992\pi$
$137$	0.547186	+	1.41400i	0.0467493	+	0.120806i	−0.907272	+	0.420544i	$0.861839\pi$
$138$	−1.24225	+	2.52733i	−0.105747	+	0.215141i
$139$	9.07840	+	1.96137i	0.770020	+	0.166361i	0.579113	−	0.815247i	$-0.303399\pi$
$139$	9.07840	+	1.96137i	0.770020	+	0.166361i	0.190907	+	0.981608i	$0.438857\pi$
$140$	0.0970837	−	0.411754i	0.00820507	−	0.0347996i
$141$	−7.39731	+	6.90484i	−0.622966	+	0.581492i
$142$	9.24838	−	10.2886i	0.776107	−	0.863402i
$143$	12.6455	−	9.38240i	1.05747	−	0.784596i
$144$	−3.06760	+	4.92594i	−0.255634	+	0.410495i
$145$	−4.78054	+	0.908217i	−0.397002	+	0.0754233i
$146$	−0.451047	+	5.53187i	−0.0373289	+	0.457821i
$147$	8.59508	−	0.430675i	0.708911	−	0.0355215i
$148$	2.31268	−	1.15477i	0.190101	−	0.0949212i
$149$	12.6237	−	19.7168i	1.03418	−	1.61526i	0.278361	−	0.960477i	$-0.410209\pi$
$149$	12.6237	−	19.7168i	1.03418	−	1.61526i	0.755814	−	0.654786i	$-0.227241\pi$
$150$	−3.68825	+	1.72767i	−0.301144	+	0.141064i
$151$	−1.85889	−	2.82487i	−0.151274	−	0.229885i	0.751778	−	0.659417i	$-0.229197\pi$
$151$	−1.85889	−	2.82487i	−0.151274	−	0.229885i	−0.903052	+	0.429532i	$0.858679\pi$
$152$	7.47935	+	5.99747i	0.606655	+	0.486459i
$153$	1.92744	−	2.77520i	0.155824	−	0.224362i
$154$	4.75304	−	3.71454i	0.383010	−	0.299326i
$155$	−4.59956	+	1.87995i	−0.369445	+	0.151002i
$156$	−0.955861	−	0.870095i	−0.0765302	−	0.0696633i
$157$	−1.47172	+	3.09133i	−0.117456	+	0.246715i	−0.953161	−	0.302464i	$-0.902191\pi$
$157$	−1.47172	+	3.09133i	−0.117456	+	0.246715i	0.835705	+	0.549179i	$0.185059\pi$
$158$	−7.63132	+	6.94658i	−0.607115	+	0.552640i
$159$	2.76698	+	9.13437i	0.219436	+	0.724403i
$160$	−2.90417	+	1.88513i	−0.229595	+	0.149033i
$161$	−0.777901	−	0.547518i	−0.0613072	−	0.0431505i
$162$	−2.12712	−	5.11267i	−0.167122	−	0.401689i
$163$	−5.01369	−	1.90420i	−0.392703	−	0.149149i	0.150784	−	0.988567i	$-0.451820\pi$
$163$	−5.01369	−	1.90420i	−0.392703	−	0.149149i	−0.543486	+	0.839418i	$0.682896\pi$
$164$	3.83533	+	1.62391i	0.299489	+	0.126806i
$165$	12.7186	+	3.08295i	0.990144	+	0.240008i
$166$	−4.87523	+	11.3165i	−0.378391	+	0.878328i
$167$	−0.300272	+	9.59306i	−0.0232358	+	0.742334i	0.916421	+	0.400215i	$0.131065\pi$
$167$	−0.300272	+	9.59306i	−0.0232358	+	0.742334i	−0.939657	+	0.342118i	$0.888856\pi$
$168$	1.71590	+	1.48512i	0.132384	+	0.114580i
$169$	−4.37372	+	3.33078i	−0.336440	+	0.256214i
$170$	6.13260	−	3.55773i	0.470349	−	0.272866i
$171$	4.62827	−	1.30765i	0.353933	−	0.0999988i
$172$	0.513402	+	0.209840i	0.0391465	+	0.0160002i
$173$	−7.98251	−	16.7672i	−0.606899	−	1.27478i	−0.942948	−	0.332940i	$-0.891959\pi$
$173$	−7.98251	−	16.7672i	−0.606899	−	1.27478i	0.336049	−	0.941845i	$-0.390909\pi$
$174$	−1.65128	+	5.45122i	−0.125183	+	0.413256i
$175$	−0.382340	−	1.32158i	−0.0289022	−	0.0999018i
$176$	−26.2439	−	2.63663i	−1.97821	−	0.198744i
$177$	1.30618	+	3.95258i	0.0981788	+	0.297094i
$178$	1.29178	−	1.76401i	0.0968229	−	0.132218i
$179$	2.75182	−	5.10499i	0.205681	−	0.381565i	−0.756493	−	0.654002i	$-0.773089\pi$
$179$	2.75182	−	5.10499i	0.205681	−	0.381565i	0.962174	+	0.272437i	$0.0878297\pi$
$180$	−0.0342917	+	0.782289i	−0.00255595	+	0.0583084i
$181$	1.61604	+	23.4384i	0.120120	+	1.74216i	0.546359	+	0.837551i	$0.316013\pi$
$181$	1.61604	+	23.4384i	0.120120	+	1.74216i	−0.426240	+	0.904610i	$0.640162\pi$
$182$	2.24231	−	1.79804i	0.166211	−	0.133280i
$183$	−2.11583	−	0.684548i	−0.156407	−	0.0506032i
$184$	0.676652	+	3.44398i	0.0498835	+	0.253894i
$185$	−6.98460	+	10.3303i	−0.513518	+	0.759498i
$186$	−0.545183	+	5.79064i	−0.0399748	+	0.424590i
$187$	15.1848	+	2.29800i	1.11042	+	0.168046i
$188$	0.462792	−	2.71278i	0.0337526	−	0.197850i
$189$	3.73074	−	0.904319i	0.271372	−	0.0657796i
$190$	9.95837	+	1.63480i	0.722456	+	0.118601i
$191$	0.276607	−	4.90586i	0.0200146	−	0.354975i	−0.972504	−	0.232885i	$-0.925184\pi$
$191$	0.276607	−	4.90586i	0.0200146	−	0.354975i	0.992519	−	0.122091i	$-0.0389599\pi$
$192$	−0.753149	−	7.99955i	−0.0543539	−	0.577318i
$193$	−1.50560	−	0.823786i	−0.108375	−	0.0592974i	0.424894	−	0.905243i	$-0.360311\pi$
$193$	−1.50560	−	0.823786i	−0.108375	−	0.0592974i	−0.533269	+	0.845946i	$0.679037\pi$
$194$	11.9143	−	15.4434i	0.855394	−	1.10877i
$195$	6.07785	+	1.39295i	0.435244	+	0.0997511i
$196$	−1.78868	+	1.50938i	−0.127763	+	0.107813i
$197$	−14.0646	+	1.05821i	−1.00206	+	0.0753945i	−0.565900	−	0.824474i	$-0.691471\pi$
$197$	−14.0646	+	1.05821i	−1.00206	+	0.0753945i	−0.436162	+	0.899868i	$0.643662\pi$
$198$	−7.35983	+	8.39669i	−0.523040	+	0.596727i
$199$	0.103483	+	16.5355i	0.00733574	+	1.17217i	0.813892	+	0.581016i	$0.197345\pi$
$199$	0.103483	+	16.5355i	0.00733574	+	1.17217i	−0.806556	+	0.591157i	$0.798671\pi$
$200$	−2.35249	+	4.49806i	−0.166346	+	0.318061i
$201$	3.97750	−	12.5617i	0.280551	−	0.886033i
$202$	−7.76959	−	4.37836i	−0.546666	−	0.308061i
$203$	−1.73197	−	0.837893i	−0.121561	−	0.0588086i
$204$	−0.0552094	−	1.25948i	−0.00386543	−	0.0881812i
$205$	−19.9646	+	2.25851i	−1.39439	+	0.157741i
$206$	20.5749	+	16.9258i	1.43352	+	1.17928i
$207$	1.60372	+	0.726886i	0.111466	+	0.0505221i
$208$	−12.5190	−	1.09965i	−0.868034	−	0.0762473i
$209$	14.6137	+	16.2574i	1.01085	+	1.12455i
$210$	2.34106	+	0.475192i	0.161548	+	0.0327914i
$211$	−15.2007	+	10.4168i	−1.04646	+	0.717124i	−0.960247	−	0.279153i	$-0.909946\pi$
$211$	−15.2007	+	10.4168i	−1.04646	+	0.717124i	−0.0862122	+	0.996277i	$0.527476\pi$
$212$	−2.10372	−	1.52041i	−0.144484	−	0.104422i
$213$	9.06938	+	7.65320i	0.621423	+	0.524389i
$214$	−5.98111	−	7.95675i	−0.408860	−	0.543913i
$215$	−2.65464	+	0.334008i	−0.181045	+	0.0227792i
$216$	−12.2513	−	7.10743i	−0.833598	−	0.483599i
$217$	−1.90344	−	0.486690i	−0.129214	−	0.0330387i
$218$	−1.20921	+	9.14803i	−0.0818983	+	0.619583i
$219$	−4.75498	−	0.238258i	−0.321312	−	0.0161000i
$220$	−3.25979	+	1.42860i	−0.219775	+	0.0963160i
$221$	7.24812	+	1.00427i	0.487561	+	0.0675545i
$222$	6.92597	+	12.8486i	0.464841	+	0.862340i
$223$	5.90963	−	2.85896i	0.395738	−	0.191450i	−0.226974	−	0.973901i	$-0.572883\pi$
$223$	5.90963	−	2.85896i	0.395738	−	0.191450i	0.622712	+	0.782451i	$0.286031\pi$
$224$	−1.36632	−	0.0856179i	−0.0912908	−	0.00572059i
$225$	1.15183	+	2.27112i	0.0767884	+	0.151408i
$226$	−7.58205	+	16.4535i	−0.504351	+	1.09447i
$227$	−17.2343	+	3.94983i	−1.14388	+	0.262160i	−0.752834	−	0.658211i	$-0.771314\pi$
$227$	−17.2343	+	3.94983i	−1.14388	+	0.262160i	−0.391048	+	0.920370i	$0.627887\pi$
$228$	1.07824	−	1.43439i	0.0714079	−	0.0949949i
$229$	11.3619	−	19.8704i	0.750817	−	1.31308i	−0.192538	−	0.981290i	$-0.561672\pi$
$229$	11.3619	−	19.8704i	0.750817	−	1.31308i	0.943355	−	0.331785i	$-0.107651\pi$
$230$	2.40032	+	2.80864i	0.158273	+	0.185196i
$231$	3.31230	+	3.97544i	0.217933	+	0.261565i
$232$	2.47891	+	6.65200i	0.162749	+	0.436725i
$233$	28.4949	+	0.356669i	1.86676	+	0.0233662i	0.937870	−	0.346988i	$-0.112796\pi$
$233$	28.4949	+	0.356669i	1.86676	+	0.0233662i	0.928891	+	0.370354i	$0.120764\pi$
$234$	−3.45633	+	4.04428i	−0.225947	+	0.264383i
$235$	4.47977	+	12.4970i	0.292228	+	0.815215i
$236$	−0.933868	−	0.639967i	−0.0607896	−	0.0416583i
$237$	−6.16061	−	6.35646i	−0.400175	−	0.412896i
$238$	2.78552	+	0.315114i	0.180559	+	0.0204258i
$239$	−0.563524	+	8.17310i	−0.0364513	+	0.528674i	0.943749	+	0.330664i	$0.107273\pi$
$239$	−0.563524	+	8.17310i	−0.0364513	+	0.528674i	−0.980200	+	0.198010i	$0.936552\pi$
$240$	−5.95817	−	8.57879i	−0.384598	−	0.553759i
$241$	11.5295	+	3.57145i	0.742682	+	0.230057i	0.643961	−	0.765058i	$-0.277290\pi$
$241$	11.5295	+	3.57145i	0.742682	+	0.230057i	0.0987211	+	0.995115i	$0.468525\pi$
$242$	−32.6952	−	8.79722i	−2.10173	−	0.565507i
$243$	−11.0241	+	4.99670i	−0.707198	+	0.320538i
$244$	0.570575	−	0.200512i	0.0365273	−	0.0128365i
$245$	3.94257	−	10.5796i	0.251881	−	0.675907i
$246$	−8.48768	+	21.9332i	−0.541155	+	1.39841i
$247$	7.05926	+	7.65827i	0.449170	+	0.487284i
$248$	3.83195	+	6.15333i	0.243329	+	0.390737i
$249$	−9.83326	−	3.87619i	−0.623158	−	0.245644i
$250$	0.582313	+	18.6037i	0.0368287	+	1.17660i
$251$	−6.88347	+	8.47504i	−0.434481	+	0.534940i	−0.945929	−	0.324374i	$-0.894846\pi$
$251$	−6.88347	+	8.47504i	−0.434481	+	0.534940i	0.511448	+	0.859314i	$0.329109\pi$
$252$	−0.195195	+	0.240327i	−0.0122961	+	0.0151392i
$253$	0.250380	+	7.99911i	0.0157413	+	0.502900i
$254$	−23.6707	−	9.33081i	−1.48523	−	0.585467i
$255$	3.21488	+	5.16244i	0.201324	+	0.323285i
$256$	5.65151	+	6.13107i	0.353219	+	0.383192i
$257$	−5.07416	+	13.1122i	−0.316517	+	0.817919i	0.679897	+	0.733308i	$0.262025\pi$
$257$	−5.07416	+	13.1122i	−0.316517	+	0.817919i	−0.996414	+	0.0846114i	$0.973035\pi$
$258$	−1.09362	+	2.93467i	−0.0680861	+	0.182704i
$259$	−4.65167	+	1.63469i	−0.289041	+	0.101575i
$260$	−1.54452	+	0.700058i	−0.0957874	+	0.0434157i
$261$	3.43895	+	0.925310i	0.212866	+	0.0572753i
$262$	7.16073	+	2.21815i	0.442392	+	0.137037i
$263$	−9.62191	−	13.8540i	−0.593313	−	0.854273i	0.404880	−	0.914370i	$-0.367313\pi$
$263$	−9.62191	−	13.8540i	−0.593313	−	0.854273i	−0.998193	+	0.0600965i	$0.980859\pi$
$264$	1.31325	−	19.0468i	0.0808250	−	1.17225i
$265$	12.4421	+	1.40752i	0.764313	+	0.0864634i
$266$	2.77700	+	2.86528i	0.170269	+	0.175682i
$267$	1.54708	+	1.06019i	0.0946799	+	0.0648829i
$268$	1.20919	+	3.37323i	0.0738632	+	0.206053i
$269$	15.4820	−	18.1156i	0.943952	−	1.10453i	−0.0504350	−	0.998727i	$-0.516061\pi$
$269$	15.4820	−	18.1156i	0.943952	−	1.10453i	0.994388	−	0.105799i	$-0.0337400\pi$
$270$	−14.9081	−	0.186605i	−0.907281	−	0.0113564i
$271$	2.96259	+	7.94992i	0.179965	+	0.482923i	0.995387	−	0.0959435i	$-0.0305868\pi$
$271$	2.96259	+	7.94992i	0.179965	+	0.482923i	−0.815422	+	0.578867i	$0.803495\pi$
$272$	−7.84609	−	9.41690i	−0.475739	−	0.570983i
$273$	1.60177	+	1.87424i	0.0969434	+	0.113434i
$274$	1.15574	−	2.02123i	0.0698210	−	0.122107i
$275$	−6.95472	+	9.25197i	−0.419386	+	0.557915i
$276$	0.640353	−	0.146759i	0.0385447	−	0.00883385i
$277$	−2.06718	+	4.48590i	−0.124205	+	0.269532i	−0.960257	−	0.279119i	$-0.909958\pi$
$277$	−2.06718	+	4.48590i	−0.124205	+	0.269532i	0.836052	+	0.548650i	$0.184858\pi$
$278$	−6.45138	−	12.7205i	−0.386928	−	0.762927i
$279$	3.62943	+	0.227432i	0.217288	+	0.0136160i
$280$	2.68008	−	1.29657i	0.160165	−	0.0774846i
$281$	3.65824	+	6.78651i	0.218232	+	0.404849i	0.965781	−	0.259357i	$-0.0835107\pi$
$281$	3.65824	+	6.78651i	0.218232	+	0.404849i	−0.747549	+	0.664206i	$0.768770\pi$
$282$	15.3925	+	2.13272i	0.916609	+	0.127002i
$283$	−22.6549	+	9.92846i	−1.34669	+	0.590186i	−0.945444	−	0.325783i	$-0.894372\pi$
$283$	−22.6549	+	9.92846i	−1.34669	+	0.590186i	−0.401249	+	0.915969i	$0.631424\pi$
$284$	−3.22327	−	0.161509i	−0.191266	−	0.00958377i
$285$	−1.13438	+	8.58191i	−0.0671950	+	0.508348i
$286$	−23.4269	−	5.99001i	−1.38526	−	0.354197i
$287$	−6.87162	−	3.98647i	−0.405619	−	0.235314i
$288$	2.51414	−	0.316331i	0.148147	−	0.0186400i
$289$	−5.92646	−	7.88405i	−0.348615	−	0.463768i
$290$	5.71095	+	4.81919i	0.335359	+	0.282992i
$291$	13.5605	+	9.80051i	0.794931	+	0.574516i
$292$	1.06805	−	0.731921i	0.0625030	−	0.0428324i
$293$	16.4589	+	3.34085i	0.961539	+	0.195175i	0.654113	−	0.756397i	$-0.273042\pi$
$293$	16.4589	+	3.34085i	0.961539	+	0.195175i	0.307426	+	0.951572i	$0.400532\pi$
$294$	−8.83481	−	9.82853i	−0.515256	−	0.573211i
$295$	5.44040	+	0.477879i	0.316752	+	0.0278232i
$296$	16.5694	+	7.51009i	0.963075	+	0.436515i
$297$	−24.9409	−	20.5175i	−1.44722	−	1.19055i
$298$	−35.7246	+	4.04136i	−2.06947	+	0.234110i
$299$	0.166989	+	3.80948i	0.00965722	+	0.220308i
$300$	0.855294	+	0.413773i	0.0493804	+	0.0238892i
$301$	−0.921638	−	0.519367i	−0.0531223	−	0.0299358i
$302$	−1.56759	+	4.95076i	−0.0902049	+	0.284884i
$303$	3.54538	−	6.77893i	0.203677	−	0.389439i
$304$	−0.109184	−	17.4465i	−0.00626214	−	1.00062i
$305$	−1.92307	+	2.19400i	−0.110115	+	0.125628i
$306$	−5.17416	+	0.389300i	−0.295787	+	0.0222548i
$307$	10.5550	−	8.90686i	0.602407	−	0.508341i	−0.291514	−	0.956567i	$-0.594159\pi$
$307$	10.5550	−	8.90686i	0.602407	−	0.508341i	0.893921	+	0.448225i	$0.147944\pi$
$308$	−1.37168	−	0.314367i	−0.0781587	−	0.0179127i
$309$	−13.9596	+	18.0946i	−0.794132	+	1.02936i
$310$	6.69405	+	3.66265i	0.380197	+	0.208024i
$311$	2.29577	+	24.3844i	0.130181	+	1.38271i	0.781498	+	0.623907i	$0.214456\pi$
$311$	2.29577	+	24.3844i	0.130181	+	1.38271i	−0.651317	+	0.758806i	$0.725783\pi$
$312$	0.512081	−	9.08219i	0.0289909	−	0.514178i
$313$	10.4888	+	1.72188i	0.592865	+	0.0973266i	0.450945	−	0.892552i	$-0.351087\pi$
$313$	10.4888	+	1.72188i	0.592865	+	0.0973266i	0.141919	+	0.989878i	$0.454673\pi$
$314$	5.10978	−	1.23859i	0.288361	−	0.0698978i
$315$	0.251170	−	1.47230i	0.0141518	−	0.0829548i
$316$	2.38026	+	0.360217i	0.133900	+	0.0202638i
$317$	2.39095	−	25.3954i	0.134289	−	1.42635i	−0.627548	−	0.778578i	$-0.715941\pi$
$317$	2.39095	−	25.3954i	0.134289	−	1.42635i	0.761837	−	0.647769i	$-0.224298\pi$
$318$	8.20944	−	12.1418i	0.460363	−	0.680880i
$319$	3.12061	+	15.8831i	0.174721	+	0.889282i
$320$	−10.0295	−	3.24490i	−0.560664	−	0.181395i
$321$	6.66139	−	5.34157i	0.371803	−	0.298138i
$322$	0.100483	+	1.45736i	0.00559969	+	0.0812154i
$323$	−0.444875	+	10.1488i	−0.0247535	+	0.564696i
$324$	−0.612960	+	1.13712i	−0.0340534	+	0.0631734i
$325$	−3.25823	+	4.44934i	−0.180734	+	0.246805i
$326$	2.58422	+	7.81998i	0.143127	+	0.433109i
$327$	−7.87572	−	0.791245i	−0.435528	−	0.0437560i
$328$	8.14591	+	28.1567i	0.449782	+	1.55470i
$329$	−1.52178	+	5.02369i	−0.0838982	+	0.276965i
$330$	−8.63876	−	18.1456i	−0.475548	−	0.998884i
$331$	−0.660682	−	0.270038i	−0.0363144	−	0.0148426i	0.360113	−	0.932909i	$-0.382738\pi$
$331$	−0.660682	−	0.270038i	−0.0363144	−	0.0148426i	−0.396427	+	0.918066i	$0.629750\pi$
$332$	2.76621	−	0.781554i	0.151816	−	0.0428933i
$333$	7.89403	−	4.57960i	0.432590	−	0.250961i
$334$	11.7258	−	8.92971i	0.641608	−	0.488612i
$335$	−13.0707	−	11.3129i	−0.714131	−	0.618087i
$336$	0.129205	−	4.12782i	0.00704870	−	0.225191i
$337$	−0.776730	+	1.80296i	−0.0423112	+	0.0982135i	−0.938241	−	0.345981i	$-0.887546\pi$
$337$	−0.776730	+	1.80296i	−0.0423112	+	0.0982135i	0.895930	+	0.444195i	$0.146510\pi$
$338$	8.20482	+	1.98882i	0.446283	+	0.108178i
$339$	−14.3103	−	6.05909i	−0.777227	−	0.329085i
$340$	−1.54618	−	0.587241i	−0.0838535	−	0.0318476i
$341$	6.34923	+	15.2608i	0.343830	+	0.826419i
$342$	−6.03967	−	4.25096i	−0.326588	−	0.229866i
$343$	7.75651	−	5.03484i	0.418812	−	0.271856i
$344$	1.13160	+	3.73564i	0.0610118	+	0.201412i
$345$	−2.34363	+	2.13335i	−0.126177	+	0.114855i
$346$	−12.2584	+	25.7486i	−0.659016	+	1.38425i
$347$	−6.39621	−	5.82230i	−0.343366	−	0.312557i	0.483076	−	0.875578i	$-0.339519\pi$
$347$	−6.39621	−	5.82230i	−0.343366	−	0.312557i	−0.826442	+	0.563021i	$0.809639\pi$
$348$	1.22997	−	0.502720i	0.0659333	−	0.0269486i
$349$	9.58641	−	7.49187i	0.513149	−	0.401031i	−0.325635	−	0.945496i	$-0.605578\pi$
$349$	9.58641	−	7.49187i	0.513149	−	0.401031i	0.838784	+	0.544465i	$0.183267\pi$
$350$	−1.20518	+	1.73526i	−0.0644193	+	0.0927533i
$351$	−12.0048	−	9.62631i	−0.640770	−	0.513815i
$352$	6.33115	+	9.62119i	0.337451	+	0.512811i
$353$	17.0624	−	7.99248i	0.908141	−	0.425397i	0.0870567	−	0.996203i	$-0.472254\pi$
$353$	17.0624	−	7.99248i	0.908141	−	0.425397i	0.821085	+	0.570807i	$0.193369\pi$
$354$	3.44694	−	5.38373i	0.183203	−	0.286142i
$355$	13.9289	−	6.95497i	0.739268	−	0.369131i
$356$	−0.509415	+	0.0255253i	−0.0269990	+	0.00135284i
$357$	−0.195416	+	2.39669i	−0.0103425	+	0.126846i
$358$	−8.74944	+	1.66224i	−0.462423	+	0.0878520i
$359$	10.7055	−	17.1908i	0.565015	−	0.907298i	−0.434962	−	0.900449i	$-0.643238\pi$
$359$	10.7055	−	17.1908i	0.565015	−	0.907298i	0.999977	−	0.00684920i	$-0.00218019\pi$
$360$	−4.42563	+	3.28361i	−0.233251	+	0.173061i
$361$	3.03527	−	3.37667i	0.159751	−	0.177719i
$362$	26.3744	−	24.6185i	1.38621	−	1.29392i
$363$	6.66507	−	28.2681i	0.349825	−	1.48369i
$364$	−0.655376	−	0.141592i	−0.0343511	−	0.00742146i
$365$	−2.75526	+	5.60552i	−0.144217	+	0.293407i
$366$	1.23247	+	3.18486i	0.0644224	+	0.166475i
$367$	−14.3747	+	0.179928i	−0.750355	+	0.00939217i	−0.386779	−	0.922172i	$-0.626412\pi$
$367$	−14.3747	+	0.179928i	−0.750355	+	0.00939217i	−0.363576	+	0.931564i	$0.618444\pi$
$368$	4.08866	−	4.90723i	0.213136	−	0.255807i
$369$	13.8728	+	4.87520i	0.722190	+	0.253793i
$370$	19.0761	−	1.67563i	0.991720	−	0.0871117i
$371$	3.61923	+	3.37828i	0.187901	+	0.175391i
$372$	1.12875	−	0.752932i	0.0585231	−	0.0390377i
$373$	7.43361	−	28.3328i	0.384898	−	1.46702i	−0.438076	−	0.898938i	$-0.644340\pi$
$373$	7.43361	−	28.3328i	0.384898	−	1.46702i	0.822973	−	0.568080i	$-0.192314\pi$
$374$	−11.9621	−	20.3254i	−0.618545	−	1.05100i
$375$	−15.9347	+	0.998519i	−0.822862	+	0.0515633i
$376$	16.8727	−	9.50821i	0.870144	−	0.490349i
$377$	1.58145	+	7.54848i	0.0814489	+	0.388766i
$378$	−4.68993	−	3.57158i	−0.241224	−	0.183702i
$379$	−8.73064	−	1.09850i	−0.448463	−	0.0564259i	−0.102625	−	0.994720i	$-0.532724\pi$
$379$	−8.73064	−	1.09850i	−0.448463	−	0.0564259i	−0.345838	+	0.938294i	$0.612405\pi$
$380$	−1.16859	−	2.04370i	−0.0599474	−	0.104840i
$381$	7.36474	−	20.5450i	0.377307	−	1.05255i
$382$	−6.11566	+	4.41994i	−0.312905	+	0.226144i
$383$	−8.79852	−	0.661995i	−0.449584	−	0.0338264i	−0.151696	−	0.988427i	$-0.548473\pi$
$383$	−8.79852	−	0.661995i	−0.449584	−	0.0338264i	−0.297888	+	0.954601i	$0.596282\pi$
$384$	−12.5736	+	12.3397i	−0.641643	+	0.629708i
$385$	6.50926	−	1.92739i	0.331743	−	0.0982291i
$386$	0.475693	+	2.59226i	0.0242122	+	0.131942i
$387$	1.85537	+	0.626037i	0.0943135	+	0.0318233i
$388$	−4.54878	+	0.113892i	−0.230929	+	0.00578197i
$389$	−6.23838	−	25.0505i	−0.316298	−	1.27011i	−0.891846	−	0.452340i	$-0.850589\pi$
$389$	−6.23838	−	25.0505i	−0.316298	−	1.27011i	0.575547	−	0.817769i	$-0.304789\pi$
$390$	−4.22393	−	8.59350i	−0.213887	−	0.435149i
$391$	−2.52067	+	2.73456i	−0.127476	+	0.138293i
$392$	−16.1816	−	3.07422i	−0.817295	−	0.155271i
$393$	−1.70961	+	6.19894i	−0.0862383	+	0.312695i
$394$	14.8782	+	15.7407i	0.749554	+	0.793007i
$395$	−10.8566	+	4.12334i	−0.546255	+	0.207468i
$396$	2.60292	+	0.0977827i	0.130802	+	0.00491376i
$397$	−29.6140	+	7.96816i	−1.48628	+	0.399911i	−0.909057	−	0.416673i	$-0.863196\pi$
$397$	−29.6140	+	7.96816i	−1.48628	+	0.399911i	−0.577227	+	0.816583i	$0.695865\pi$
$398$	19.6105	−	16.1324i	0.982984	−	0.808646i
$399$	−2.38209	+	2.45782i	−0.119254	+	0.123045i
$400$	9.05309	−	1.83761i	0.452654	−	0.0918805i
$401$	22.2937	+	16.5409i	1.11330	+	0.826013i	0.986148	−	0.165870i	$-0.0530433\pi$
$401$	22.2937	+	16.5409i	1.11330	+	0.826013i	0.127147	+	0.991884i	$0.459418\pi$
$402$	−18.8246	+	7.42050i	−0.938886	+	0.370101i
$403$	3.11593	+	7.23276i	0.155216	+	0.360289i
$404$	0.349871	+	2.05086i	0.0174067	+	0.102034i
$405$	−0.116991	−	6.23065i	−0.00581332	−	0.309604i
$406$	0.678049	+	2.87576i	0.0336510	+	0.142722i
$407$	34.5081	+	23.0185i	1.71050	+	1.14099i
$408$	6.63531	−	5.88978i	0.328497	−	0.291588i
$409$	15.3654	+	17.5301i	0.759768	+	0.866806i	0.994444	−	0.105268i	$-0.0335701\pi$
$409$	15.3654	+	17.5301i	0.759768	+	0.866806i	−0.234676	+	0.972074i	$0.575403\pi$
$410$	22.0212	+	21.6116i	1.08755	+	1.06732i
$411$	1.76397	+	0.936659i	0.0870100	+	0.0462020i
$412$	0.0388953	−	6.21506i	0.00191623	−	0.306194i
$413$	1.61494	+	1.43349i	0.0794661	+	0.0705375i
$414$	−0.686195	−	2.61540i	−0.0337247	−	0.128540i
$415$	−9.77454	+	9.83590i	−0.479813	+	0.482826i
$416$	3.07369	+	4.54601i	0.150700	+	0.222887i
$417$	10.7331	−	5.87261i	0.525602	−	0.287583i
$418$	5.23068	−	33.1595i	0.255841	−	1.62189i
$419$	−19.6067	+	3.47125i	−0.957849	+	0.169581i	−0.631248	−	0.775581i	$-0.717457\pi$
$419$	−19.6067	+	3.47125i	−0.957849	+	0.169581i	−0.326601	+	0.945162i	$0.605903\pi$
$420$	−0.258262	−	0.493808i	−0.0126019	−	0.0240954i
$421$	−21.0870	+	11.1971i	−1.02772	+	0.545715i	−0.895293	−	0.445478i	$-0.853034\pi$
$421$	−21.0870	+	11.1971i	−1.02772	+	0.545715i	−0.132426	+	0.991193i	$0.542277\pi$
$422$	27.1338	+	8.03431i	1.32085	+	0.391104i
$423$	1.03172	−	9.66100i	0.0501637	−	0.469734i
$424$	−1.02832	−	18.2381i	−0.0499396	−	0.885721i
$425$	−5.31819	+	0.804830i	−0.257970	+	0.0390400i
$426$	0.342118	−	18.2204i	0.0165757	−	0.882781i
$427$	−1.12755	+	0.243604i	−0.0545659	+	0.0117888i
$428$	−0.561144	+	2.25330i	−0.0271239	+	0.108917i
$429$	4.50697	−	20.2463i	0.217599	−	0.977503i
$430$	2.96826	+	2.84100i	0.143142	+	0.137005i
$431$	7.71586	+	22.4034i	0.371660	+	1.07914i	0.962251	+	0.272164i	$0.0877393\pi$
$431$	7.71586	+	22.4034i	0.371660	+	1.07914i	−0.590591	+	0.806971i	$0.701105\pi$
$432$	4.01628	+	25.4609i	0.193233	+	1.22499i
$433$	−19.5850	−	25.3863i	−0.941194	−	1.21999i	−0.975371	−	0.220573i	$-0.929207\pi$
$433$	−19.5850	−	25.3863i	−0.941194	−	1.21999i	0.0341762	−	0.999416i	$-0.489119\pi$
$434$	1.26270	+	2.74013i	0.0606115	+	0.131531i
$435$	−3.97858	+	5.02574i	−0.190758	+	0.240966i
$436$	1.83437	−	1.12647i	0.0878505	−	0.0539484i
$437$	−5.24363	+	0.726536i	−0.250837	+	0.0347549i
$438$	4.31959	+	5.89869i	0.206398	+	0.281850i
$439$	19.4879	−	27.3230i	0.930106	−	1.30406i	−0.0224680	−	0.999748i	$-0.507152\pi$
$439$	19.4879	−	27.3230i	0.930106	−	1.30406i	0.952574	−	0.304308i	$-0.0984253\pi$
$440$	−22.2675	−	11.4690i	−1.06156	−	0.546763i
$441$	−5.96936	+	5.71342i	−0.284255	+	0.272068i
$442$	−5.82024	−	9.61217i	−0.276841	−	0.457205i
$443$	6.83382	−	7.22999i	0.324685	−	0.343507i	−0.543807	−	0.839210i	$-0.683018\pi$
$443$	6.83382	−	7.22999i	0.324685	−	0.343507i	0.868492	+	0.495703i	$0.165090\pi$
$444$	1.30799	−	3.14385i	0.0620746	−	0.149201i
$445$	2.08046	−	1.31373i	0.0986233	−	0.0622770i
$446$	−9.12941	−	4.27645i	−0.432290	−	0.202496i
$447$	−4.42368	−	30.5208i	−0.209233	−	1.44358i
$448$	−2.42024	−	3.39330i	−0.114345	−	0.160318i
$449$	2.92945	−	8.86465i	0.138249	−	0.418349i	−0.857046	−	0.515240i	$-0.827703\pi$
$449$	2.92945	−	8.86465i	0.138249	−	0.418349i	0.995295	+	0.0968914i	$0.0308900\pi$
$450$	1.59206	−	3.57180i	0.0750502	−	0.168376i
$451$	7.92833	+	66.3633i	0.373330	+	3.12493i
$452$	4.09453	−	1.04693i	0.192591	−	0.0492434i
$453$	−4.28671	−	1.21115i	−0.201407	−	0.0569048i
$454$	21.3939	+	16.7195i	1.00406	+	0.784686i
$455$	3.08968	−	0.957074i	0.144846	−	0.0448683i
$456$	12.6198	−	0.474083i	0.590976	−	0.0222010i
$457$	30.9605	−	13.1089i	1.44827	−	0.613210i	0.483274	−	0.875469i	$-0.339448\pi$
$457$	30.9605	−	13.1089i	1.44827	−	0.613210i	0.964998	+	0.262259i	$0.0844674\pi$
$458$	−34.6861	+	5.69418i	−1.62077	+	0.266072i
$459$	−1.59369	−	14.9233i	−0.0743870	−	0.696561i
$460$	0.155563	−	0.847729i	0.00725317	−	0.0395256i
$461$	6.84017	−	12.3178i	0.318579	−	0.573696i	−0.666561	−	0.745450i	$-0.732234\pi$
$461$	6.84017	−	12.3178i	0.318579	−	0.573696i	0.985140	+	0.171755i	$0.0549436\pi$
$462$	1.53194	−	7.79719i	0.0712725	−	0.362758i
$463$	−29.5573	−	29.7428i	−1.37364	−	1.38227i	−0.846394	−	0.532557i	$-0.821231\pi$
$463$	−29.5573	−	29.7428i	−1.37364	−	1.38227i	−0.527249	−	0.849711i	$-0.676777\pi$
$464$	6.55256	−	11.1338i	0.304195	−	0.516873i
$465$	−2.96061	+	5.83759i	−0.137295	+	0.270712i
$466$	−27.1625	−	34.3117i	−1.25828	−	1.58946i
$467$	1.36183	+	0.497810i	0.0630178	+	0.0230359i	0.374642	−	0.927169i	$-0.377766\pi$
$467$	1.36183	+	0.497810i	0.0630178	+	0.0230359i	−0.311625	+	0.950205i	$0.600873\pi$
$468$	1.24068	+	0.0310639i	0.0573503	+	0.00143593i
$469$	−1.48516	−	6.67169i	−0.0685785	−	0.308070i
$470$	10.5595	−	17.4391i	0.487074	−	0.804406i
$471$	1.19906	+	4.34774i	0.0552500	+	0.200333i
$472$	−0.647476	−	7.94099i	−0.0298025	−	0.365514i
$473$	1.16631	+	8.82342i	0.0536268	+	0.405701i
$474$	−1.61254	+	13.4976i	−0.0740665	+	0.619967i
$475$	−6.57375	−	3.92444i	−0.301624	−	0.180066i
$476$	−0.352618	−	0.550748i	−0.0161622	−	0.0252435i
$477$	−7.74843	−	4.89285i	−0.354776	−	0.224028i
$478$	10.2881	−	7.24116i	0.470565	−	0.331203i
$479$	−4.35163	+	10.8400i	−0.198831	+	0.495294i	−0.993777	−	0.111386i	$-0.964471\pi$
$479$	−4.35163	+	10.8400i	−0.198831	+	0.495294i	0.794946	+	0.606680i	$0.207499\pi$
$480$	−1.26751	+	4.38121i	−0.0578537	+	0.199974i
$481$	16.5777	+	10.7608i	0.755880	+	0.490650i
$482$	−6.90523	−	17.2011i	−0.314525	−	0.783490i
$483$	−1.24680	+	0.125262i	−0.0567315	+	0.00569961i
$484$	3.21562	+	7.21431i	0.146165	+	0.327923i
$485$	18.8474	−	11.2516i	0.855815	−	0.510910i
$486$	16.6293	+	8.30334i	0.754320	+	0.376647i
$487$	−25.8486	−	11.3281i	−1.17131	−	0.513325i	−0.277044	−	0.960857i	$-0.589355\pi$
$487$	−25.8486	−	11.3281i	−1.17131	−	0.513325i	−0.894268	+	0.447532i	$0.852303\pi$
$488$	3.62694	+	2.22728i	0.164184	+	0.100824i
$489$	−6.63529	+	2.42550i	−0.300058	+	0.109685i
$490$	−16.4281	+	5.54318i	−0.742148	+	0.250415i
$491$	12.9835	+	23.3806i	0.585936	+	1.05515i	0.990086	+	0.140459i	$0.0448579\pi$
$491$	12.9835	+	23.3806i	0.585936	+	1.05515i	−0.404151	+	0.914692i	$0.632433\pi$
$492$	5.21999	−	1.68886i	0.235335	−	0.0761395i
$493$	−4.13494	+	6.28369i	−0.186228	+	0.283003i
$494$	2.29428	−	15.8292i	0.103225	−	0.712189i
$495$	−11.1708	+	5.75360i	−0.502091	+	0.258605i
$496$	4.29575	−	12.4730i	0.192885	−	0.560052i
$497$	6.06152	+	1.07316i	0.271896	+	0.0481376i
$498$	4.89971	+	15.4742i	0.219561	+	0.693415i
$499$	−8.34656	+	39.8392i	−0.373643	+	1.78345i	0.216639	+	0.976252i	$0.430491\pi$
$499$	−8.34656	+	39.8392i	−0.373643	+	1.78345i	−0.590282	+	0.807197i	$0.700983\pi$
$500$	3.28312	−	2.84157i	0.146825	−	0.127079i
$501$	7.97077	+	9.81374i	0.356108	+	0.438446i
$502$	16.7667			0.748335
$503$	−7.12663	−	21.2653i	−0.317761	−	0.948171i
$503$	−7.12663	−	21.2653i	−0.317761	−	0.948171i
$504$	−2.17891			−0.0970565
$505$	−6.32751	−	7.79053i	−0.281570	−	0.346674i
$506$	9.29267	−	8.04289i	0.413110	−	0.357550i
$507$	−1.48497	+	7.08796i	−0.0659499	+	0.314787i
$508$	1.79173	+	5.65863i	0.0794952	+	0.251061i
$509$	1.65554	+	0.293103i	0.0733804	+	0.0129916i	0.210902	−	0.977507i	$-0.432360\pi$
$509$	1.65554	+	0.293103i	0.0733804	+	0.0129916i	−0.137522	+	0.990499i	$0.543914\pi$
$510$	3.04119	−	8.83027i	0.134666	−	0.391011i
$511$	−2.19555	+	1.13083i	−0.0971253	+	0.0500250i
$512$	−1.99998	+	13.7987i	−0.0883873	+	0.609821i
$513$	11.7430	−	17.8454i	0.518468	−	0.787894i
$514$	20.5426	−	6.64629i	0.906097	−	0.293155i
$515$	14.5558	+	26.2121i	0.641405	+	1.15504i
$516$	0.692255	−	0.233580i	0.0304748	−	0.0102828i
$517$	41.4768	−	15.1617i	1.82415	−	0.666809i
$518$	6.45215	+	3.96222i	0.283491	+	0.174090i
$519$	−22.4051	−	9.81901i	−0.983477	−	0.431007i
$520$	−10.6772	−	5.33132i	−0.468225	−	0.233794i
$521$	−8.45705	+	5.04875i	−0.370510	+	0.221190i	−0.685774	−	0.727814i	$-0.740536\pi$
$521$	−8.45705	+	5.04875i	−0.370510	+	0.221190i	0.315264	+	0.949004i	$0.397907\pi$
$522$	−2.22648	−	4.99514i	−0.0974503	−	0.218631i
$523$	−23.5248	+	2.36345i	−1.02867	+	0.103347i	−0.599905	−	0.800071i	$-0.704795\pi$
$523$	−23.5248	+	2.36345i	−1.02867	+	0.103347i	−0.428762	+	0.903418i	$0.641050\pi$
$524$	−0.651497	−	1.62290i	−0.0284608	−	0.0708967i
$525$	−1.52010	−	0.986716i	−0.0663427	−	0.0430638i
$526$	−7.19862	+	24.8824i	−0.313875	+	1.08492i
$527$	−2.86156	+	7.12822i	−0.124651	+	0.310510i
$528$	−28.4124	+	19.9978i	−1.23649	+	0.870294i
$529$	17.8086	+	11.2455i	0.774286	+	0.488933i
$530$	−10.3682	−	16.1939i	−0.450365	−	0.703419i
$531$	−3.43190	−	2.04880i	−0.148932	−	0.0889103i
$532$	0.110421	−	0.924269i	0.00478736	−	0.0400721i
$533$	4.17300	+	31.5698i	0.180753	+	1.36744i
$534$	−0.234056	−	2.87059i	−0.0101286	−	0.124223i
$535$	−2.97822	−	10.7989i	−0.128760	−	0.466876i
$536$	−13.0622	+	21.5722i	−0.564199	+	0.931779i
$537$	−1.65996	−	7.45693i	−0.0716326	−	0.321790i
$538$	−36.5831	−	0.915963i	−1.57721	−	0.0394900i
$539$	−35.2741	−	12.8943i	−1.51936	−	0.555397i
$540$	2.15881	+	2.72702i	0.0929006	+	0.117352i
$541$	−5.94568	+	11.7234i	−0.255625	+	0.504029i	−0.983323	−	0.181868i	$-0.941785\pi$
$541$	−5.94568	+	11.7234i	−0.255625	+	0.504029i	0.727698	+	0.685898i	$0.240590\pi$
$542$	6.60817	−	11.2283i	0.283845	−	0.482295i
$543$	21.8150	+	21.9520i	0.936172	+	0.942050i
$544$	−1.03185	+	5.25185i	−0.0442402	+	0.225171i
$545$	−5.04143	+	9.07861i	−0.215951	+	0.388885i
$546$	0.683358	−	3.72391i	0.0292450	−	0.159368i
$547$	−1.59145	−	14.9024i	−0.0680457	−	0.637181i	−0.975949	−	0.218000i	$-0.930047\pi$
$547$	−1.59145	−	14.9024i	−0.0680457	−	0.637181i	0.907903	−	0.419180i	$-0.137682\pi$
$548$	−0.535986	+	0.0879891i	−0.0228962	+	0.00375871i
$549$	1.96622	−	0.832512i	0.0839161	−	0.0355308i
$550$	17.7618	−	0.667250i	0.757366	−	0.0284516i
$551$	−10.2275	+	3.16812i	−0.435706	+	0.134967i
$552$	3.64290	+	2.84696i	0.155052	+	0.121175i
$553$	−4.41883	−	1.24848i	−0.187908	−	0.0530906i
$554$	7.34864	−	1.87897i	0.312214	−	0.0798297i
$555$	1.94857	+	16.3104i	0.0827124	+	0.692337i
$556$	−1.35461	+	3.03908i	−0.0574481	+	0.128886i
$557$	−7.86547	+	23.8013i	−0.333271	+	1.00849i	0.637902	+	0.770117i	$0.279802\pi$
$557$	−7.86547	+	23.8013i	−0.333271	+	1.00849i	−0.971173	+	0.238376i	$0.923385\pi$
$558$	−3.24277	−	4.54653i	−0.137277	−	0.192470i
$559$	0.608274	+	4.19674i	0.0257273	+	0.177503i
$560$	−4.90647	−	2.29832i	−0.207336	−	0.0971217i
$561$	17.1054	−	10.8014i	0.722191	−	0.456037i
$562$	4.54787	−	10.9311i	0.191840	−	0.461101i
$563$	−17.5087	+	18.5237i	−0.737905	+	0.780682i	−0.981962	−	0.189079i	$-0.939450\pi$
$563$	−17.5087	+	18.5237i	−0.737905	+	0.780682i	0.244057	+	0.969761i	$0.421521\pi$
$564$	−1.87764	−	3.10094i	−0.0790631	−	0.130573i
$565$	−14.7286	+	14.0971i	−0.619636	+	0.593069i
$566$	33.7685	+	17.3927i	1.41940	+	0.731068i
$567$	1.43078	−	2.00603i	0.0600871	−	0.0842452i
$568$	−13.4190	−	18.3246i	−0.563050	−	0.768884i
$569$	16.5707	−	2.29597i	0.694679	−	0.0962520i	0.218809	−	0.975768i	$-0.429783\pi$
$569$	16.5707	−	2.29597i	0.694679	−	0.0962520i	0.475870	+	0.879516i	$0.342133\pi$
$570$	11.3280	−	6.95647i	0.474480	−	0.291375i
$571$	−0.761558	+	0.962000i	−0.0318702	+	0.0402585i	−0.799733	−	0.600356i	$-0.795026\pi$
$571$	−0.761558	+	0.962000i	−0.0318702	+	0.0402585i	0.767863	+	0.640615i	$0.221320\pi$
$572$	2.36082	+	5.12313i	0.0987110	+	0.214209i
$573$	−3.95366	−	5.12479i	−0.165167	−	0.214091i
$574$	1.90090	+	12.0506i	0.0793422	+	0.502984i
$575$	−0.912722	−	2.65014i	−0.0380632	−	0.110518i
$576$	5.57333	+	5.33437i	0.232222	+	0.222266i
$577$	−4.40283	+	19.7785i	−0.183292	+	0.823391i	0.793392	+	0.608711i	$0.208313\pi$
$577$	−4.40283	+	19.7785i	−0.183292	+	0.823391i	−0.976684	+	0.214680i	$0.931129\pi$
$578$	−3.66015	+	14.6975i	−0.152242	+	0.611335i
$579$	−2.20976	+	0.477414i	−0.0918346	+	0.0198406i
$580$	0.0327262	−	1.74292i	0.00135888	−	0.0723708i
$581$	−5.42110	+	0.820404i	−0.224905	+	0.0340361i
$582$	−1.44638	−	25.6528i	−0.0599545	−	1.06334i
$583$	4.42297	−	41.4167i	0.183181	−	1.71530i
$584$	8.73717	+	2.58708i	0.361546	+	0.107054i
$585$	−5.28774	+	2.80777i	−0.218621	+	0.116087i
$586$	−11.9525	−	22.8538i	−0.493754	−	0.944081i
$587$	44.1846	−	7.82262i	1.82369	−	0.322874i	0.846044	−	0.533113i	$-0.178978\pi$
$587$	44.1846	−	7.82262i	1.82369	−	0.322874i	0.977650	+	0.210238i	$0.0674240\pi$
$588$	−0.480380	+	3.04533i	−0.0198105	+	0.125587i
$589$	−9.59145	+	5.24796i	−0.395209	+	0.216238i
$590$	−4.69755	−	6.94772i	−0.193395	−	0.286033i
$591$	−13.0964	+	13.1786i	−0.538714	+	0.542096i
$592$	−8.40169	−	32.0226i	−0.345307	−	1.31612i
$593$	31.3745	+	27.8493i	1.28839	+	1.14363i	0.981411	+	0.191920i	$0.0614713\pi$
$593$	31.3745	+	27.8493i	1.28839	+	1.14363i	0.306984	+	0.951715i	$0.400680\pi$
$594$	−0.310373	+	49.5943i	−0.0127347	+	2.03488i
$595$	2.78629	+	1.47951i	0.114227	+	0.0606540i
$596$	5.98598	+	5.87463i	0.245195	+	0.240634i
$597$	14.3578	+	16.3805i	0.587625	+	0.670410i
$598$	4.37929	−	3.88725i	0.179083	−	0.158961i
$599$	22.7803	+	15.1956i	0.930779	+	0.620874i	0.925351	−	0.379111i	$-0.123770\pi$
$599$	22.7803	+	15.1956i	0.930779	+	0.620874i	0.00542791	+	0.999985i	$0.498272\pi$
$600$	1.53450	+	6.50816i	0.0626456	+	0.265695i
$601$	0.246555	+	13.1309i	0.0100572	+	0.535621i	0.968317	+	0.249723i	$0.0803396\pi$
$601$	0.246555	+	13.1309i	0.0100572	+	0.535621i	−0.958260	+	0.285898i	$0.907708\pi$
$602$	0.273200	+	1.60144i	0.0111348	+	0.0652698i
$603$	5.00555	+	11.6190i	0.203842	+	0.473161i
$604$	1.12704	−	0.444269i	0.0458585	−	0.0180770i
$605$	−30.6001	−	22.7038i	−1.24407	−	0.923042i
$606$	−11.5131	+	2.33695i	−0.467688	+	0.0949321i
$607$	20.5765	−	21.2307i	0.835175	−	0.861726i	−0.156869	−	0.987619i	$-0.550140\pi$
$607$	20.5765	−	21.2307i	0.835175	−	0.861726i	0.992044	+	0.125894i	$0.0401798\pi$
$608$	−5.88340	+	4.83994i	−0.238603	+	0.196286i
$609$	−2.44740	+	0.658516i	−0.0991737	+	0.0266844i
$610$	4.47712	+	0.168190i	0.181273	+	0.00680982i
$611$	19.6701	−	7.47073i	0.795768	−	0.302233i
$612$	0.831480	+	0.879682i	0.0336106	+	0.0355590i
$613$	−0.168600	+	0.611333i	−0.00680967	+	0.0246915i	−0.967336	−	0.253497i	$-0.918419\pi$
$613$	−0.168600	+	0.611333i	−0.00680967	+	0.0246915i	0.960527	+	0.278188i	$0.0897340\pi$
$614$	−20.8361	−	3.95848i	−0.840876	−	0.159751i
$615$	−17.9382	+	19.4604i	−0.723339	+	0.784717i
$616$	−4.36869	−	8.88801i	−0.176019	−	0.358108i
$617$	−8.26650	−	33.1944i	−0.332797	−	1.33636i	−0.870061	−	0.492944i	$-0.835921\pi$
$617$	−8.26650	−	33.1944i	−0.332797	−	1.33636i	0.537265	−	0.843414i	$-0.319458\pi$
$618$	35.0842	−	0.878432i	1.41129	−	0.0353357i
$619$	−9.59735	−	3.23834i	−0.385750	−	0.130160i	0.120142	−	0.992757i	$-0.461665\pi$
$619$	−9.59735	−	3.23834i	−0.385750	−	0.130160i	−0.505892	+	0.862597i	$0.668836\pi$
$620$	−0.321289	−	1.75084i	−0.0129033	−	0.0703155i
$621$	7.49905	−	2.22047i	0.300927	−	0.0891044i
$622$	26.8440	−	26.3447i	1.07634	−	1.05632i
$623$	0.970137	+	0.0729925i	0.0388677	+	0.00292438i
$624$	−13.4171	+	9.69689i	−0.537115	+	0.388186i
$625$	−3.67115	+	10.2412i	−0.146846	+	0.409650i
$626$	−8.10239	−	14.1699i	−0.323837	−	0.566345i
$627$	28.5704	+	3.59476i	1.14099	+	0.143561i
$628$	−0.975802	−	0.743115i	−0.0389387	−	0.0296535i
$629$	3.95274	+	18.8669i	0.157606	+	0.752274i
$630$	−1.99818	+	1.12603i	−0.0796095	+	0.0448620i
$631$	24.3646	−	1.52677i	0.969939	−	0.0607796i	0.430309	−	0.902682i	$-0.358405\pi$
$631$	24.3646	−	1.52677i	0.969939	−	0.0607796i	0.539630	+	0.841902i	$0.318564\pi$
$632$	8.59319	+	14.6011i	0.341819	+	0.580801i
$633$	−6.16022	+	23.4794i	−0.244847	+	0.933221i
$634$	−32.5866	+	21.7368i	−1.29418	+	0.863278i
$635$	−20.9315	−	19.5380i	−0.830643	−	0.775343i
$636$	−3.40605	+	0.299184i	−0.135058	+	0.0118634i
$637$	−16.8823	−	5.93281i	−0.668902	−	0.235066i
$638$	15.9116	−	19.0972i	0.629948	−	0.756066i
$639$	−11.3932	+	0.142609i	−0.450709	+	0.00564151i
$640$	8.34129	+	21.5549i	0.329718	+	0.852032i
$641$	16.1467	−	32.8502i	0.637756	−	1.29750i	−0.301231	−	0.953551i	$-0.597398\pi$
$641$	16.1467	−	32.8502i	0.637756	−	1.29750i	0.938987	−	0.343952i	$-0.111766\pi$
$642$	−12.8166	−	2.76898i	−0.505829	−	0.109283i
$643$	−3.71257	+	15.7459i	−0.146410	+	0.620957i	0.849259	+	0.527977i	$0.177049\pi$
$643$	−3.71257	+	15.7459i	−0.146410	+	0.620957i	−0.995668	+	0.0929792i	$0.970361\pi$
$644$	0.249120	−	0.232535i	0.00981672	−	0.00916318i
$645$	−2.35614	+	2.62115i	−0.0927727	+	0.103208i
$646$	12.5283	−	9.29542i	0.492919	−	0.365723i
$647$	−6.57998	+	10.5661i	−0.258686	+	0.415396i	−0.952399	−	0.304855i	$-0.901392\pi$
$647$	−6.57998	+	10.5661i	−0.258686	+	0.415396i	0.693713	+	0.720251i	$0.255974\pi$
$648$	−8.93150	+	1.69682i	−0.350862	+	0.0666575i
$649$	1.47636	−	18.1069i	0.0579523	−	0.710757i
$650$	8.45818	−	0.423815i	0.331757	−	0.0166234i
$651$	−2.31543	+	1.15614i	−0.0907488	+	0.0453127i
$652$	1.03597	−	1.61807i	0.0405718	−	0.0633685i
$653$	21.6267	−	10.1305i	0.846319	−	0.396437i	0.0481271	−	0.998841i	$-0.484675\pi$
$653$	21.6267	−	10.1305i	0.846319	−	0.396437i	0.798191	+	0.602404i	$0.205790\pi$
$654$	6.68179	+	10.1540i	0.261279	+	0.397055i
$655$	6.58159	+	5.27758i	0.257164	+	0.206212i
$656$	30.4285	−	43.8120i	1.18803	−	1.71057i
$657$	3.60180	−	2.81484i	0.140519	−	0.109817i
$658$	7.46165	−	3.04977i	0.290886	−	0.118892i
$659$	−11.6368	−	10.5927i	−0.453305	−	0.412632i	0.414102	−	0.910231i	$-0.364096\pi$
$659$	−11.6368	−	10.5927i	−0.453305	−	0.412632i	−0.867407	+	0.497599i	$0.834215\pi$
$660$	−2.01528	+	4.23306i	−0.0784445	+	0.164772i
$661$	2.89959	−	2.63941i	0.112781	−	0.102661i	−0.614801	−	0.788682i	$-0.710764\pi$
$661$	2.89959	−	2.63941i	0.112781	−	0.102661i	0.727582	+	0.686021i	$0.240644\pi$
$662$	0.317758	+	1.04898i	0.0123500	+	0.0407700i
$663$	8.08502	−	5.24808i	0.313996	−	0.203818i
$664$	16.5429	+	11.6435i	0.641988	+	0.451857i
$665$	1.72490	+	4.14593i	0.0668889	+	0.160772i
$666$	−13.1017	−	4.97602i	−0.507679	−	0.192817i
$667$	−3.60962	−	1.52834i	−0.139765	−	0.0591777i
$668$	−3.34156	−	0.809983i	−0.129289	−	0.0313392i
$669$	3.42151	−	7.94207i	0.132283	−	0.307058i
$670$	−0.830516	+	26.5332i	−0.0320856	+	1.02507i
$671$	7.33813	+	6.35122i	0.283286	+	0.245186i
$672$	−1.43469	+	1.09258i	−0.0553443	+	0.0421470i
$673$	24.8583	−	14.4212i	0.958217	−	0.555895i	0.0613121	−	0.998119i	$-0.480472\pi$
$673$	24.8583	−	14.4212i	0.958217	−	0.555895i	0.896905	+	0.442223i	$0.145810\pi$
$674$	2.90116	−	0.819682i	0.111749	−	0.0315730i
$675$	10.4702	+	4.27943i	0.402998	+	0.164715i
$676$	−0.846582	−	1.77824i	−0.0325608	−	0.0683937i
$677$	−6.24146	+	20.6043i	−0.239879	+	0.791889i	0.751370	+	0.659881i	$0.229393\pi$
$677$	−6.24146	+	20.6043i	−0.239879	+	0.791889i	−0.991249	+	0.132008i	$0.957858\pi$
$678$	6.63212	+	22.9243i	0.254705	+	0.880401i
$679$	8.63560	+	0.867588i	0.331404	+	0.0332950i
$680$	−3.65229	−	11.0520i	−0.140059	−	0.423825i
$681$	−13.7607	+	18.7912i	−0.527312	+	0.720081i
$682$	12.0441	−	22.3433i	0.461191	−	0.855570i
$683$	−0.353428	+	8.06268i	−0.0135236	+	0.308510i	0.980298	+	0.197523i	$0.0632896\pi$
$683$	−0.353428	+	8.06268i	−0.0135236	+	0.308510i	−0.993822	+	0.110987i	$0.964599\pi$
$684$	0.118514	+	1.71887i	0.00453149	+	0.0657227i
$685$	2.04419	−	1.63918i	0.0781046	−	0.0626298i
$686$	−13.5112	−	4.37136i	−0.515859	−	0.166899i
$687$	−5.81289	−	29.5861i	−0.221776	−	1.12878i
$688$	3.97869	−	5.88452i	0.151686	−	0.224345i
$689$	1.86022	−	19.7583i	0.0708689	−	0.752731i
$690$	4.81200	+	0.728226i	0.183190	+	0.0277231i
$691$	−0.472559	+	2.77004i	−0.0179770	+	0.105377i	−0.993338	−	0.115238i	$-0.963237\pi$
$691$	−0.472559	+	2.77004i	−0.0179770	+	0.105377i	0.975361	+	0.220615i	$0.0708066\pi$
$692$	6.46547	−	1.56721i	0.245780	−	0.0595763i
$693$	−4.90269	−	0.804842i	−0.186238	−	0.0305734i
$694$	−0.747713	+	13.2613i	−0.0283828	+	0.503393i
$695$	−1.50454	−	15.9804i	−0.0570706	−	0.606173i
$696$	8.20351	+	4.48855i	0.310953	+	0.170138i
$697$	−18.9717	+	24.5914i	−0.718605	+	0.931465i
$698$	−18.2116	−	4.17382i	−0.689321	−	0.157982i
$699$	28.6889	−	24.2092i	1.08512	−	0.915675i
$700$	0.491471	−	0.0369779i	0.0185759	−	0.00139763i
$701$	3.67539	−	4.19319i	0.138818	−	0.158375i	−0.678422	−	0.734672i	$-0.737336\pi$
$701$	3.67539	−	4.19319i	0.138818	−	0.158375i	0.817240	+	0.576298i	$0.195503\pi$
$702$	0.147881	+	23.6298i	0.00558140	+	0.891849i
$703$	−12.7160	+	24.3136i	−0.479594	+	0.917006i
$704$	−10.5850	+	33.4295i	−0.398938	+	1.25992i
$705$	15.2352	+	8.58542i	0.573790	+	0.323346i
$706$	−26.0464	−	12.6007i	−0.980268	−	0.474233i
$707$	−0.173786	−	3.96453i	−0.00653588	−	0.149102i
$708$	−1.48184	+	0.167635i	−0.0556911	+	0.00630010i
$709$	−30.5558	−	25.1365i	−1.14755	−	0.944022i	−0.148553	−	0.988904i	$-0.547462\pi$
$709$	−30.5558	−	25.1365i	−1.14755	−	0.944022i	−0.998992	+	0.0448823i	$0.985709\pi$
$710$	−21.7759	−	9.86993i	−0.817233	−	0.370412i
$711$	8.46667	+	0.743704i	0.317525	+	0.0278911i
$712$	−2.39966	−	2.66957i	−0.0899312	−	0.100047i
$713$	−3.92272	−	0.796240i	−0.146907	−	0.0298194i
$714$	3.04609	−	2.08744i	0.113997	−	0.0781206i
$715$	−22.0550	−	15.9397i	−0.824811	−	0.596111i
$716$	1.58782	+	1.33988i	0.0593395	+	0.0500737i
$717$	6.48446	+	8.62637i	0.242167	+	0.322158i
$718$	−30.8564	+	3.88238i	−1.15155	+	0.144889i
$719$	−10.5414	−	6.11541i	−0.393126	−	0.228066i	0.292114	−	0.956384i	$-0.405641\pi$
$719$	−10.5414	−	6.11541i	−0.393126	−	0.228066i	−0.685240	+	0.728317i	$0.740303\pi$
$720$	9.71611	+	2.48431i	0.362098	+	0.0925846i
$721$	−1.55350	+	11.7526i	−0.0578553	+	0.437691i
$722$	−6.96368	−	0.348930i	−0.259161	−	0.0129858i
$723$	14.5625	−	6.38197i	0.541584	−	0.237348i
$724$	−8.33692	−	1.15513i	−0.309839	−	0.0429300i
$725$	−2.68998	−	4.99026i	−0.0999032	−	0.185333i
$726$	−40.1489	+	19.4232i	−1.49007	+	0.720863i
$727$	−40.7690	−	2.55472i	−1.51204	−	0.0947494i	−0.715191	−	0.698929i	$-0.753660\pi$
$727$	−40.7690	−	2.55472i	−1.51204	−	0.0947494i	−0.796848	+	0.604180i	$0.793501\pi$
$728$	−2.13435	−	4.20841i	−0.0791043	−	0.155974i
$729$	−11.2002	+	24.3052i	−0.414824	+	0.900193i
$730$	9.34942	−	2.14274i	0.346037	−	0.0793063i
$731$	−2.48520	+	3.30609i	−0.0919184	+	0.122280i
$732$	0.395450	−	0.691587i	0.0146163	−	0.0255618i
$733$	−21.5760	−	25.2463i	−0.796930	−	0.932494i	0.201970	−	0.979392i	$-0.435266\pi$
$733$	−21.5760	−	25.2463i	−0.796930	−	0.932494i	−0.998900	+	0.0468981i	$0.985066\pi$
$734$	14.1316	+	16.9607i	0.521605	+	0.626032i
$735$	−5.19345	−	13.9363i	−0.191563	−	0.514047i
$736$	−2.78889	−	0.0349084i	−0.102800	−	0.00128674i
$737$	−37.3589	+	43.7140i	−1.37613	+	1.61023i
$738$	−7.61981	−	21.2566i	−0.280489	−	0.782467i
$739$	−4.46217	−	3.05787i	−0.164144	−	0.112485i	0.480412	−	0.877043i	$-0.340487\pi$
$739$	−4.46217	−	3.05787i	−0.164144	−	0.112485i	−0.644555	+	0.764558i	$0.722957\pi$
$740$	−3.10903	−	3.20787i	−0.114290	−	0.117924i
$741$	13.6331	+	1.54225i	0.500824	+	0.0566561i
$742$	0.522968	−	7.58490i	0.0191988	−	0.278450i
$743$	19.8641	+	28.6010i	0.728743	+	1.04927i	0.996318	+	0.0857336i	$0.0273234\pi$
$743$	19.8641	+	28.6010i	0.728743	+	1.04927i	−0.267575	+	0.963537i	$0.586222\pi$
$744$	9.12128	+	2.82545i	0.334402	+	0.103586i
$745$	−39.0702	−	10.5125i	−1.43142	−	0.385149i
$746$	−40.9701	+	18.5698i	−1.50002	+	0.679888i
$747$	9.57450	−	3.36468i	0.350313	−	0.123107i
$748$	−1.92121	+	5.15544i	−0.0702464	+	0.188502i
$749$	1.59849	−	4.13070i	0.0584077	−	0.150933i
$750$	16.6176	+	18.0277i	0.606788	+	0.658277i
$751$	5.73929	+	9.21612i	0.209430	+	0.336301i	0.936751	−	0.349996i	$-0.113817\pi$
$751$	5.73929	+	9.21612i	0.209430	+	0.336301i	−0.727322	+	0.686297i	$0.759235\pi$
$752$	−32.7900	−	12.9255i	−1.19573	−	0.471345i
$753$	0.449961	+	14.3753i	0.0163975	+	0.523866i
$754$	7.46681	−	9.19326i	0.271925	−	0.334799i
$755$	−3.68441	+	4.53631i	−0.134090	+	0.165093i
$756$	0.0430245	+	1.37454i	0.00156479	+	0.0499916i
$757$	14.9909	+	5.90930i	0.544854	+	0.214777i	0.623079	−	0.782159i	$-0.285881\pi$
$757$	14.9909	+	5.90930i	0.544854	+	0.214777i	−0.0782249	+	0.996936i	$0.524925\pi$
$758$	7.14325	+	11.4706i	0.259454	+	0.416631i
$759$	7.14514	+	7.75144i	0.259352	+	0.281359i
$760$	5.97939	−	15.4515i	0.216895	−	0.560484i
$761$	3.49232	−	9.37142i	0.126597	−	0.339714i	−0.858227	−	0.513270i	$-0.828434\pi$
$761$	3.49232	−	9.37142i	0.126597	−	0.339714i	0.984824	+	0.173556i	$0.0555257\pi$
$762$	−31.6203	+	11.1120i	−1.14548	+	0.402547i
$763$	−3.73974	+	1.69504i	−0.135388	+	0.0613647i
$764$	1.69982	+	0.457367i	0.0614974	+	0.0165469i
$765$	−5.57782	−	1.72781i	−0.201667	−	0.0624693i
$766$	7.72929	+	11.1289i	0.279270	+	0.402104i
$767$	0.595397	−	8.63536i	0.0214985	−	0.311805i
$768$	10.9144	+	1.23470i	0.393839	+	0.0445533i
$769$	−17.8048	−	18.3709i	−0.642059	−	0.662470i	0.316094	−	0.948728i	$-0.397628\pi$
$769$	−17.8048	−	18.3709i	−0.642059	−	0.662470i	−0.958153	+	0.286258i	$0.907589\pi$
$770$	−8.59951	−	5.89313i	−0.309905	−	0.212373i
$771$	6.24964	+	17.4343i	0.225075	+	0.627882i
$772$	0.399444	−	0.467393i	0.0143763	−	0.0168218i

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\), degree \(250\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.968162 - 1.19202i) q^{2} +(0.996021 - 0.862065i) q^{3} +(-0.0734591 + 0.350630i) q^{4} +(-0.521680 - 1.64756i) q^{5} +(-1.99191 - 0.352655i) q^{6} +(0.222510 - 0.646070i) q^{7} +(-2.24135 + 1.15442i) q^{8} +(-0.181422 + 1.25171i) q^{9} +O(q^{10})\)	\(q+(-0.968162 - 1.19202i) q^{2} +(0.996021 - 0.862065i) q^{3} +(-0.0734591 + 0.350630i) q^{4} +(-0.521680 - 1.64756i) q^{5} +(-1.99191 - 0.352655i) q^{6} +(0.222510 - 0.646070i) q^{7} +(-2.24135 + 1.15442i) q^{8} +(-0.181422 + 1.25171i) q^{9} +(-1.45885 + 2.21696i) q^{10} +(-5.46959 + 1.76961i) q^{11} +(0.229099 + 0.412561i) q^{12} +(-2.59529 + 0.875704i) q^{13} +(-0.985552 + 0.360264i) q^{14} +(-1.93991 - 1.19129i) q^{15} +(4.20231 + 1.84165i) q^{16} +(-2.39011 - 1.19343i) q^{17} +(1.66770 - 0.995597i) q^{18} +(-1.54810 - 3.47319i) q^{19} +(0.616008 - 0.0618881i) q^{20} +(-0.335330 - 0.835317i) q^{21} +(7.40486 + 4.80657i) q^{22} +(0.386888 - 1.33730i) q^{23} +(-1.23724 + 3.08201i) q^{24} +(1.64645 - 1.15884i) q^{25} +(3.55652 + 2.24581i) q^{26} +(3.02919 + 4.73125i) q^{27} +(0.210186 + 0.125478i) q^{28} +(0.334013 - 2.79582i) q^{29} +(0.458115 + 3.46576i) q^{30} +(-0.233659 - 2.86572i) q^{31} +(-0.532651 - 1.93136i) q^{32} +(-3.92230 + 6.47771i) q^{33} +(0.891424 + 4.00448i) q^{34} +(-1.18052 - 0.0295577i) q^{35} +(-0.425559 - 0.155561i) q^{36} +(-4.47868 - 5.65747i) q^{37} +(-2.64129 + 5.20797i) q^{38} +(-1.83005 + 3.10953i) q^{39} +(3.07125 + 3.09053i) q^{40} +(2.24137 - 11.4080i) q^{41} +(-0.671058 + 1.20844i) q^{42} +(0.279437 - 1.52277i) q^{43} +(-0.218688 - 2.04780i) q^{44} +(2.15691 - 0.354086i) q^{45} +(-1.96865 + 0.833544i) q^{46} +(-7.67646 + 0.288378i) q^{47} +(5.77321 - 1.78834i) q^{48} +(5.14758 + 4.02288i) q^{49} +(-2.97539 - 0.840655i) q^{50} +(-3.40941 + 0.871749i) q^{51} +(-0.116400 - 0.974317i) q^{52} +(-2.94975 + 6.61782i) q^{53} +(2.70698 - 8.19147i) q^{54} +(5.76892 + 8.08833i) q^{55} +(0.247113 + 1.70494i) q^{56} +(-4.53605 - 2.12480i) q^{57} +(-3.65605 + 2.30866i) q^{58} +(-1.21391 + 2.91772i) q^{59} +(0.560205 - 0.592681i) q^{60} +(-0.874408 - 1.44409i) q^{61} +(-3.18976 + 3.05300i) q^{62} +(0.768322 + 0.395729i) q^{63} +(3.54191 - 4.96595i) q^{64} +(2.79669 + 3.81907i) q^{65} +(11.5190 - 1.59602i) q^{66} +(8.52383 - 5.23442i) q^{67} +(0.594027 - 0.750375i) q^{68} +(-0.767490 - 1.66550i) q^{69} +(1.10770 + 1.43582i) q^{70} +(1.40371 + 8.89870i) q^{71} +(-1.03836 - 3.01495i) q^{72} +(-2.61101 - 2.49907i) q^{73} +(-2.40772 + 10.8160i) q^{74} +(0.640905 - 2.57358i) q^{75} +(1.33153 - 0.287673i) q^{76} +(-0.0737452 + 3.92749i) q^{77} +(5.47840 - 0.829076i) q^{78} +(-0.378289 - 6.70927i) q^{79} +(0.841981 - 7.88433i) q^{80} +(3.45757 + 1.02379i) q^{81} +(-15.7685 + 8.37302i) q^{82} +(-3.71862 - 7.11018i) q^{83} +(0.317520 - 0.0562151i) q^{84} +(-0.719377 + 4.56044i) q^{85} +(-2.08571 + 1.14119i) q^{86} +(-2.07750 - 3.07264i) q^{87} +(10.2164 - 10.2805i) q^{88} +(0.361321 + 1.37716i) q^{89} +(-2.51032 - 2.22826i) q^{90} +(-0.0117129 + 1.87159i) q^{91} +(0.440477 + 0.233891i) q^{92} +(-2.70316 - 2.65288i) q^{93} +(7.77581 + 8.87127i) q^{94} +(-4.91469 + 4.36249i) q^{95} +(-2.19549 - 1.46450i) q^{96} +(2.91483 + 12.3625i) q^{97} +(-0.188345 - 10.0308i) q^{98} +(-1.22273 - 7.16737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) \)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

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