LMFDB - Embedded newform 475.2.bc.a.6.14

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label			6.14
Character	$\chi$	$=$	475.6
Dual form			475.2.bc.a.396.14

$q$-expansion

$f(q)$	$=$	$q+(-1.05096 - 0.656713i) q^{2} +(3.06632 - 0.879252i) q^{3} +(-0.203496 - 0.417228i) q^{4} +(1.91224 - 1.15903i) q^{5} +(-3.79999 - 1.08963i) q^{6} +(-0.887411 + 1.53704i) q^{7} +(-0.319211 + 3.03709i) q^{8} +(6.08506 - 3.80237i) q^{9} +O(q^{10})$	\(q+(-1.05096 - 0.656713i) q^{2} +(3.06632 - 0.879252i) q^{3} +(-0.203496 - 0.417228i) q^{4} +(1.91224 - 1.15903i) q^{5} +(-3.79999 - 1.08963i) q^{6} +(-0.887411 + 1.53704i) q^{7} +(-0.319211 + 3.03709i) q^{8} +(6.08506 - 3.80237i) q^{9} +(-2.77084 - 0.0377008i) q^{10} +(0.0524015 - 0.0581978i) q^{11} +(-0.990830 - 1.10043i) q^{12} +(0.0328451 + 0.940560i) q^{13} +(1.94203 - 1.03260i) q^{14} +(4.84445 - 5.23528i) q^{15} +(1.75839 - 2.25063i) q^{16} +(4.15450 - 0.290511i) q^{17} -8.89223 q^{18} +(2.38968 - 3.64546i) q^{19} +(-0.872710 - 0.561982i) q^{20} +(-1.36964 + 5.49331i) q^{21} +(-0.0932912 + 0.0267508i) q^{22} +(-8.82381 + 1.24011i) q^{23} +(1.69157 + 9.59335i) q^{24} +(2.31331 - 4.43267i) q^{25} +(0.583159 - 1.01006i) q^{26} +(8.91213 - 9.89793i) q^{27} +(0.821880 + 0.0574714i) q^{28} +(-0.853856 - 0.0597074i) q^{29} +(-8.52941 + 2.32066i) q^{30} +(-9.29246 + 4.13727i) q^{31} +(2.41329 - 0.878365i) q^{32} +(0.109509 - 0.224527i) q^{33} +(-4.55700 - 2.42300i) q^{34} +(0.0845297 + 3.96772i) q^{35} +(-2.82474 - 1.76509i) q^{36} +(-2.21694 + 6.82305i) q^{37} +(-4.90549 + 2.26190i) q^{38} +(0.927702 + 2.85517i) q^{39} +(2.90966 + 6.17762i) q^{40} +(-6.03769 + 7.72789i) q^{41} +(5.04696 - 4.87380i) q^{42} +(-0.458745 - 2.60167i) q^{43} +(-0.0349452 - 0.0100204i) q^{44} +(7.22905 - 14.3238i) q^{45} +(10.0879 + 4.49141i) q^{46} +(0.397653 + 0.0278066i) q^{47} +(3.41290 - 8.44722i) q^{48} +(1.92500 + 3.33421i) q^{49} +(-5.34220 + 3.13938i) q^{50} +(12.4836 - 4.54365i) q^{51} +(0.385744 - 0.205104i) q^{52} +(0.385363 + 0.790112i) q^{53} +(-15.8664 + 4.54962i) q^{54} +(0.0327514 - 0.172023i) q^{55} +(-4.38486 - 3.18579i) q^{56} +(4.12224 - 13.2793i) q^{57} +(0.858159 + 0.623489i) q^{58} +(-3.01749 - 7.46855i) q^{59} +(-3.17013 - 0.955883i) q^{60} +(7.01217 - 0.985496i) q^{61} +(12.4830 + 1.75437i) q^{62} +(0.444445 + 12.7273i) q^{63} +(-8.70047 - 1.84934i) q^{64} +(1.15294 + 1.76051i) q^{65} +(-0.262540 + 0.164053i) q^{66} +(-0.208176 - 0.834948i) q^{67} +(-0.966632 - 1.67426i) q^{68} +(-25.9662 + 11.5609i) q^{69} +(2.51682 - 4.22543i) q^{70} +(-9.31522 - 8.99560i) q^{71} +(9.60573 + 19.6947i) q^{72} +(-0.430714 + 12.3340i) q^{73} +(6.81071 - 5.71487i) q^{74} +(3.19592 - 15.6260i) q^{75} +(-2.00728 - 0.255207i) q^{76} +(0.0429507 + 0.132189i) q^{77} +(0.900052 - 3.60991i) q^{78} +(8.18566 - 2.34720i) q^{79} +(0.753912 - 6.34176i) q^{80} +(9.18821 - 18.8386i) q^{81} +(11.4204 - 4.15668i) q^{82} +(8.73888 - 3.89080i) q^{83} +(2.57068 - 0.546414i) q^{84} +(7.60769 - 5.37070i) q^{85} +(-1.22643 + 3.03552i) q^{86} +(-2.67069 + 0.567673i) q^{87} +(0.160025 + 0.177726i) q^{88} +(-0.713941 - 0.913803i) q^{89} +(-17.0041 + 10.3063i) q^{90} +(-1.47483 - 0.784179i) q^{91} +(2.31301 + 3.42918i) q^{92} +(-24.8559 + 20.8566i) q^{93} +(-0.399657 - 0.290368i) q^{94} +(0.344457 - 9.74071i) q^{95} +(6.62760 - 4.81523i) q^{96} +(-1.30205 + 5.22223i) q^{97} +(0.166513 - 4.76830i) q^{98} +(0.0975771 - 0.553387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05096	−	0.656713i	−0.743142	−	0.464366i	0.104775	−	0.994496i	$-0.466588\pi$
$2$	−1.05096	−	0.656713i	−0.743142	−	0.464366i	−0.847917	+	0.530129i	$0.822143\pi$
$3$	3.06632	−	0.879252i	1.77034	−	0.507636i	0.777687	−	0.628651i	$-0.216393\pi$
$3$	3.06632	−	0.879252i	1.77034	−	0.507636i	0.992651	+	0.121015i	$0.0386148\pi$
$4$	−0.203496	−	0.417228i	−0.101748	−	0.208614i
$5$	1.91224	−	1.15903i	0.855179	−	0.518332i
$5$	1.91224	−	1.15903i	0.855179	−	0.518332i
$6$	−3.79999	−	1.08963i	−1.55134	−	0.444840i
$7$	−0.887411	+	1.53704i	−0.335410	+	0.580947i	−0.983563	−	0.180563i	$-0.942208\pi$
$7$	−0.887411	+	1.53704i	−0.335410	+	0.580947i	0.648154	+	0.761510i	$0.275541\pi$
$8$	−0.319211	+	3.03709i	−0.112858	+	1.07377i
$9$	6.08506	−	3.80237i	2.02835	−	1.26746i
$10$	−2.77084	−	0.0377008i	−0.876216	−	0.0119221i
$11$	0.0524015	−	0.0581978i	0.0157997	−	0.0175473i	−0.735193	−	0.677858i	$-0.762909\pi$
$11$	0.0524015	−	0.0581978i	0.0157997	−	0.0175473i	0.750993	+	0.660310i	$0.229575\pi$
$12$	−0.990830	−	1.10043i	−0.286028	−	0.317666i
$13$	0.0328451	+	0.940560i	0.00910958	+	0.260864i	0.995398	+	0.0958312i	$0.0305509\pi$
$13$	0.0328451	+	0.940560i	0.00910958	+	0.260864i	−0.986288	+	0.165033i	$0.947227\pi$
$14$	1.94203	−	1.03260i	0.519029	−	0.275973i
$15$	4.84445	−	5.23528i	1.25083	−	1.35174i
$16$	1.75839	−	2.25063i	0.439597	−	0.562658i
$17$	4.15450	−	0.290511i	1.00761	−	0.0704593i	0.443601	−	0.896225i	$-0.353701\pi$
$17$	4.15450	−	0.290511i	1.00761	−	0.0704593i	0.564014	+	0.825765i	$0.309256\pi$
$18$	−8.89223			−2.09592
$19$	2.38968	−	3.64546i	0.548231	−	0.836327i
$19$	2.38968	−	3.64546i	0.548231	−	0.836327i
$20$	−0.872710	−	0.561982i	−0.195144	−	0.125663i
$21$	−1.36964	+	5.49331i	−0.298879	+	1.19874i
$22$	−0.0932912	+	0.0267508i	−0.0198898	+	0.00570330i
$23$	−8.82381	+	1.24011i	−1.83989	+	0.258580i	−0.971455	−	0.237223i	$-0.923763\pi$
$23$	−8.82381	+	1.24011i	−1.83989	+	0.258580i	−0.868435	+	0.495802i	$0.834874\pi$
$24$	1.69157	+	9.59335i	0.345290	+	1.95823i
$25$	2.31331	−	4.43267i	0.462663	−	0.886534i
$26$	0.583159	−	1.01006i	0.114367	−	0.198089i
$27$	8.91213	−	9.89793i	1.71514	−	1.90486i
$28$	0.821880	+	0.0574714i	0.155321	+	0.0108611i
$29$	−0.853856	−	0.0597074i	−0.158557	−	0.0110874i	−0.00974268	−	0.999953i	$-0.503101\pi$
$29$	−0.853856	−	0.0597074i	−0.158557	−	0.0110874i	−0.148814	+	0.988865i	$0.547546\pi$
$30$	−8.52941	+	2.32066i	−1.55725	+	0.423693i
$31$	−9.29246	+	4.13727i	−1.66898	+	0.743076i	−1.00000		0.000208606i	$-0.999934\pi$
$31$	−9.29246	+	4.13727i	−1.66898	+	0.743076i	−0.668976	+	0.743284i	$0.733267\pi$
$32$	2.41329	−	0.878365i	0.426613	−	0.155275i
$33$	0.109509	−	0.224527i	0.0190631	−	0.0390851i
$34$	−4.55700	−	2.42300i	−0.781519	−	0.415541i
$35$	0.0845297	+	3.96772i	0.0142881	+	0.670667i
$36$	−2.82474	−	1.76509i	−0.470790	−	0.294182i
$37$	−2.21694	+	6.82305i	−0.364463	+	1.12170i	0.585853	+	0.810417i	$0.300760\pi$
$37$	−2.21694	+	6.82305i	−0.364463	+	1.12170i	−0.950316	+	0.311286i	$0.899240\pi$
$38$	−4.90549	+	2.26190i	−0.795776	+	0.366929i
$39$	0.927702	+	2.85517i	0.148551	+	0.457194i
$40$	2.90966	+	6.17762i	0.460058	+	0.976767i
$41$	−6.03769	+	7.72789i	−0.942929	+	1.20689i	0.0353024	+	0.999377i	$0.488761\pi$
$41$	−6.03769	+	7.72789i	−0.942929	+	1.20689i	−0.978231	+	0.207517i	$0.933462\pi$
$42$	5.04696	−	4.87380i	0.778763	−	0.752043i
$43$	−0.458745	−	2.60167i	−0.0699579	−	0.396751i	−0.999600	−	0.0282868i	$-0.990995\pi$
$43$	−0.458745	−	2.60167i	−0.0699579	−	0.396751i	0.929642	−	0.368464i	$-0.120116\pi$
$44$	−0.0349452	−	0.0100204i	−0.00526819	−	0.00151063i
$45$	7.22905	−	14.3238i	1.07764	−	2.13526i
$46$	10.0879	+	4.49141i	1.48738	+	0.662222i
$47$	0.397653	+	0.0278066i	0.0580037	+	0.00405601i	0.0987288	−	0.995114i	$-0.468522\pi$
$47$	0.397653	+	0.0278066i	0.0580037	+	0.00405601i	−0.0407252	+	0.999170i	$0.512967\pi$
$48$	3.41290	−	8.44722i	0.492609	−	1.21925i
$49$	1.92500	+	3.33421i	0.275001	+	0.476315i
$50$	−5.34220	+	3.13938i	−0.755501	+	0.443976i
$51$	12.4836	−	4.54365i	1.74805	−	0.636238i
$52$	0.385744	−	0.205104i	0.0534930	−	0.0284427i
$53$	0.385363	+	0.790112i	0.0529337	+	0.108530i	0.923621	−	0.383306i	$-0.125215\pi$
$53$	0.385363	+	0.790112i	0.0529337	+	0.108530i	−0.870688	+	0.491837i	$0.836326\pi$
$54$	−15.8664	+	4.54962i	−2.15914	+	0.619125i
$55$	0.0327514	−	0.172023i	0.00441620	−	0.0231956i
$56$	−4.38486	−	3.18579i	−0.585952	−	0.425719i
$57$	4.12224	−	13.2793i	0.546005	−	1.75888i
$58$	0.858159	+	0.623489i	0.112682	+	0.0818681i
$59$	−3.01749	−	7.46855i	−0.392844	−	0.972323i	−0.985926	−	0.167181i	$-0.946534\pi$
$59$	−3.01749	−	7.46855i	−0.392844	−	0.972323i	0.593082	−	0.805142i	$-0.297911\pi$
$60$	−3.17013	−	0.955883i	−0.409262	−	0.123404i
$61$	7.01217	−	0.985496i	0.897816	−	0.126180i	0.324856	−	0.945763i	$-0.394684\pi$
$61$	7.01217	−	0.985496i	0.897816	−	0.126180i	0.572960	+	0.819584i	$0.305795\pi$
$62$	12.4830	+	1.75437i	1.58534	+	0.222806i
$63$	0.444445	+	12.7273i	0.0559949	+	1.60348i
$64$	−8.70047	−	1.84934i	−1.08756	−	0.231168i
$65$	1.15294	+	1.76051i	0.143005	+	0.218364i
$66$	−0.262540	+	0.164053i	−0.0323164	+	0.0201935i
$67$	−0.208176	−	0.834948i	−0.0254327	−	0.102005i	0.956238	−	0.292590i	$-0.0945171\pi$
$67$	−0.208176	−	0.834948i	−0.0254327	−	0.102005i	−0.981671	+	0.190585i	$0.938962\pi$
$68$	−0.966632	−	1.67426i	−0.117221	−	0.203033i
$69$	−25.9662	+	11.5609i	−3.12596	+	1.39177i
$70$	2.51682	−	4.22543i	0.300817	−	0.505036i
$71$	−9.31522	−	8.99560i	−1.10551	−	1.06758i	−0.997299	−	0.0734541i	$-0.976598\pi$
$71$	−9.31522	−	8.99560i	−1.10551	−	1.06758i	−0.108215	−	0.994128i	$-0.534513\pi$
$72$	9.60573	+	19.6947i	1.13205	+	2.32104i
$73$	−0.430714	+	12.3340i	−0.0504112	+	1.44359i	0.666022	+	0.745932i	$0.267996\pi$
$73$	−0.430714	+	12.3340i	−0.0504112	+	1.44359i	−0.716433	+	0.697656i	$0.754226\pi$
$74$	6.81071	−	5.71487i	0.791729	−	0.664340i
$75$	3.19592	−	15.6260i	0.369033	−	1.80433i
$76$	−2.00728	−	0.255207i	−0.230251	−	0.0292742i
$77$	0.0429507	+	0.132189i	0.00489468	+	0.0150643i
$78$	0.900052	−	3.60991i	0.101911	−	0.408742i
$79$	8.18566	−	2.34720i	0.920958	−	0.264081i	0.218526	−	0.975831i	$-0.429875\pi$
$79$	8.18566	−	2.34720i	0.920958	−	0.264081i	0.702432	+	0.711751i	$0.252097\pi$
$80$	0.753912	−	6.34176i	0.0842900	−	0.709031i
$81$	9.18821	−	18.8386i	1.02091	−	2.09318i
$82$	11.4204	−	4.15668i	1.26117	−	0.459029i
$83$	8.73888	−	3.89080i	0.959216	−	0.427071i	0.133433	−	0.991058i	$-0.457400\pi$
$83$	8.73888	−	3.89080i	0.959216	−	0.427071i	0.825783	+	0.563987i	$0.190733\pi$
$84$	2.57068	−	0.546414i	0.280484	−	0.0596186i
$85$	7.60769	−	5.37070i	0.825170	−	0.582535i
$86$	−1.22643	+	3.03552i	−0.132249	+	0.327328i
$87$	−2.67069	+	0.567673i	−0.286328	+	0.0608609i
$88$	0.160025	+	0.177726i	0.0170587	+	0.0189456i
$89$	−0.713941	−	0.913803i	−0.0756776	−	0.0968629i	0.748682	−	0.662929i	$-0.230687\pi$
$89$	−0.713941	−	0.913803i	−0.0756776	−	0.0968629i	−0.824360	+	0.566066i	$0.808465\pi$
$90$	−17.0041	+	10.3063i	−1.79239	+	1.08638i
$91$	−1.47483	−	0.784179i	−0.154604	−	0.0822043i
$92$	2.31301	+	3.42918i	0.241148	+	0.357517i
$93$	−24.8559	+	20.8566i	−2.57744	+	2.16273i
$94$	−0.399657	−	0.290368i	−0.0412215	−	0.0299491i
$95$	0.344457	−	9.74071i	0.0353405	−	0.999375i
$96$	6.62760	−	4.81523i	0.676427	−	0.491453i
$97$	−1.30205	+	5.22223i	−0.132203	+	0.530237i	0.867272	+	0.497835i	$0.165871\pi$
$97$	−1.30205	+	5.22223i	−0.132203	+	0.530237i	−0.999475	+	0.0324024i	$0.989684\pi$
$98$	0.166513	−	4.76830i	0.0168203	−	0.481671i
$99$	0.0975771	−	0.553387i	0.00980687	−	0.0556175i
$100$	−2.32018	−	0.0631499i	−0.232018	−	0.00631499i
$101$	−3.40492	+	1.23929i	−0.338803	+	0.123314i	−0.505818	−	0.862640i	$-0.668809\pi$
$101$	−3.40492	+	1.23929i	−0.338803	+	0.123314i	0.167015	+	0.985954i	$0.446587\pi$
$102$	−16.1036	−	3.42293i	−1.59450	−	0.338921i
$103$	17.9226	+	7.97964i	1.76596	+	0.786257i	0.987310	+	0.158802i	$0.0507631\pi$
$103$	17.9226	+	7.97964i	1.76596	+	0.786257i	0.778652	+	0.627456i	$0.215904\pi$
$104$	−2.86705	−	0.200484i	−0.281137	−	0.0196590i
$105$	3.74782	+	12.0920i	0.365750	+	1.18005i
$106$	0.113875	−	1.08345i	0.0110605	−	0.105234i
$107$	0.907607	−	1.57202i	0.0877416	−	0.151973i	−0.818815	−	0.574058i	$-0.805368\pi$
$107$	0.907607	−	1.57202i	0.0877416	−	0.151973i	0.906556	+	0.422085i	$0.138702\pi$
$108$	−5.94327	−	1.70420i	−0.571891	−	0.163987i
$109$	10.6420	+	1.49563i	1.01932	+	0.143256i	0.628984	−	0.777418i	$-0.283471\pi$
$109$	10.6420	+	1.49563i	1.01932	+	0.143256i	0.390333	+	0.920674i	$0.372360\pi$
$110$	−0.147390	+	0.159281i	−0.0140531	+	0.0151868i
$111$	−0.798669	+	22.8709i	−0.0758063	+	2.17081i
$112$	1.89890	+	4.69995i	0.179429	+	0.444103i
$113$	−0.106058	+	0.326413i	−0.00997711	+	0.0307064i	−0.955921	−	0.293624i	$-0.905139\pi$
$113$	−0.106058	+	0.326413i	−0.00997711	+	0.0307064i	0.945944	+	0.324330i	$0.105139\pi$
$114$	−13.0530	+	11.2489i	−1.22253	+	1.05355i
$115$	−15.4359	+	12.5984i	−1.43941	+	1.17481i
$116$	0.148844	+	0.368402i	0.0138198	+	0.0342053i
$117$	3.77622	+	5.59848i	0.349112	+	0.517579i
$118$	−1.73343	+	9.83079i	−0.159575	+	0.904997i
$119$	−3.24022	+	6.64344i	−0.297031	+	0.609003i
$120$	14.3536	+	16.3842i	1.31030	+	1.49567i
$121$	1.14917	+	10.9336i	0.104470	+	0.993967i
$122$	−8.01670	−	3.56927i	−0.725798	−	0.323146i
$123$	−11.7187	+	29.0048i	−1.05664	+	2.61528i
$124$	3.61716	+	3.03516i	0.324830	+	0.272565i
$125$	−0.713975	−	11.1575i	−0.0638599	−	0.997959i
$126$	7.89106	−	13.6677i	0.702992	−	1.21762i
$127$	7.32016	+	9.36938i	0.649560	+	0.831398i	0.994224	−	0.107328i	$-0.0342294\pi$
$127$	7.32016	+	9.36938i	0.649560	+	0.831398i	−0.344664	+	0.938726i	$0.612007\pi$
$128$	4.23460	+	4.08930i	0.374289	+	0.361447i
$129$	−3.69418	−	7.57419i	−0.325254	−	0.666870i
$130$	−0.0555484	−	2.60738i	−0.00487192	−	0.228682i
$131$	2.39096	−	0.167192i	0.208899	−	0.0146076i	0.0350764	−	0.999385i	$-0.488833\pi$
$131$	2.39096	−	0.167192i	0.208899	−	0.0146076i	0.173823	+	0.984777i	$0.444388\pi$
$132$	−0.115963			−0.0100933
$133$	3.48259	+	6.90807i	0.301979	+	0.599005i
$134$	−0.329537	+	1.01421i	−0.0284676	+	0.0876144i
$135$	5.57017	−	29.2566i	0.479404	−	2.51801i
$136$	−0.443855	+	12.7103i	−0.0380602	+	1.08990i
$137$	−7.43960	−	3.95571i	−0.635608	−	0.337959i	0.120202	−	0.992749i	$-0.461646\pi$
$137$	−7.43960	−	3.95571i	−0.635608	−	0.337959i	−0.755810	+	0.654791i	$0.772757\pi$
$138$	34.8817	+	4.90230i	2.96933	+	0.417311i
$139$	−3.01671	−	3.86121i	−0.255874	−	0.327503i	0.642872	−	0.765974i	$-0.277743\pi$
$139$	−3.01671	−	3.86121i	−0.255874	−	0.327503i	−0.898746	+	0.438470i	$0.855520\pi$
$140$	1.63824	−	0.842682i	0.138457	−	0.0712196i
$141$	1.24378	−	0.264373i	0.104745	−	0.0222643i
$142$	3.88240	+	15.5715i	0.325804	+	1.30673i
$143$	0.0564596	+	0.0473752i	0.00472139	+	0.00396172i
$144$	2.14216	−	20.3813i	0.178513	−	1.69844i
$145$	−1.70198	+	0.875467i	−0.141342	+	0.0727036i
$146$	8.55258	−	12.6797i	0.707817	−	1.04938i
$147$	8.83428	+	8.53116i	0.728639	+	0.703638i
$148$	3.29790	−	0.463490i	0.271086	−	0.0380987i
$149$	−11.8933	−	4.32881i	−0.974339	−	0.354630i	−0.194702	−	0.980862i	$-0.562374\pi$
$149$	−11.8933	−	4.32881i	−0.974339	−	0.354630i	−0.779637	+	0.626232i	$0.784596\pi$
$150$	−13.6206	+	14.3235i	−1.11211	+	1.16951i
$151$	−12.5001			−1.01724			−0.508622	−	0.860990i	$-0.669845\pi$
$151$	−12.5001			−1.01724			−0.508622	+	0.860990i	$0.669845\pi$
$152$	10.3088	+	8.42136i	0.836154	+	0.683063i
$153$	24.1758	−	17.5647i	1.95450	−	1.42002i
$154$	0.0416705	−	0.167131i	0.00335791	−	0.0134678i
$155$	−12.9742	+	18.6817i	−1.04211	+	1.50055i
$156$	1.00247	−	0.968078i	0.0802622	−	0.0775083i
$157$	−1.08742	−	6.16705i	−0.0867853	−	0.492184i	−0.996957	−	0.0779529i	$-0.975162\pi$
$157$	−1.08742	−	6.16705i	−0.0867853	−	0.492184i	0.910172	−	0.414231i	$-0.135949\pi$
$158$	−10.1442	−	2.90881i	−0.807033	−	0.231413i
$159$	1.87635	+	2.08390i	0.148804	+	0.165264i
$160$	3.59674	−	4.47671i	0.284347	−	0.353915i
$161$	5.92425	−	14.6630i	0.466896	−	1.15561i
$162$	−22.0280	+	13.7646i	−1.73069	+	1.08145i
$163$	5.49904	−	1.16886i	0.430718	−	0.0915520i	0.0125494	−	0.999921i	$-0.496005\pi$
$163$	5.49904	−	1.16886i	0.430718	−	0.0915520i	0.418169	+	0.908369i	$0.362672\pi$
$164$	4.45293	+	0.946500i	0.347716	+	0.0739093i
$165$	−0.0508251	−	0.556273i	−0.00395673	−	0.0433058i
$166$	−11.7394	−	1.64986i	−0.911151	−	0.128054i
$167$	−6.19088	+	5.97847i	−0.479065	+	0.462628i	−0.894547	−	0.446974i	$-0.852502\pi$
$167$	−6.19088	+	5.97847i	−0.479065	+	0.462628i	0.415482	+	0.909601i	$0.363613\pi$
$168$	−16.2465	−	5.91324i	−1.25344	−	0.456216i
$169$	12.0848	−	0.845049i	0.929597	−	0.0650037i
$170$	−11.5224	+	0.648330i	−0.883728	+	0.0497247i
$171$	0.679978	−	31.2693i	0.0519992	−	2.39123i
$172$	−0.992136	+	0.720829i	−0.0756497	+	0.0549627i
$173$	0.265835	+	0.166112i	0.0202110	+	0.0126293i	0.539987	−	0.841673i	$-0.318429\pi$
$173$	0.265835	+	0.166112i	0.0202110	+	0.0126293i	−0.519776	+	0.854303i	$0.673985\pi$
$174$	3.17959	+	1.15728i	0.241044	+	0.0877328i
$175$	4.76034	+	7.48926i	0.359848	+	0.566135i
$176$	−0.0388397	−	0.220271i	−0.00292765	−	0.0166035i
$177$	−15.8193	−	20.2478i	−1.18905	−	1.52192i
$178$	0.150218	+	1.42923i	0.0112593	+	0.107125i
$179$	−6.70190	−	2.98388i	−0.500923	−	0.223025i	0.140690	−	0.990054i	$-0.455068\pi$
$179$	−6.70190	−	2.98388i	−0.500923	−	0.223025i	−0.641613	+	0.767028i	$0.721735\pi$
$180$	−7.44736	−	0.101331i	−0.555093	−	0.00755277i
$181$	−1.40553	−	5.63727i	−0.104472	−	0.419015i	0.895171	−	0.445722i	$-0.147053\pi$
$181$	−1.40553	−	5.63727i	−0.104472	−	0.419015i	−0.999643	+	0.0267078i	$0.991498\pi$
$182$	1.03500	+	1.79268i	0.0767196	+	0.132882i
$183$	20.6350	−	9.18730i	1.52538	−	0.679145i
$184$	−0.949655	−	27.1946i	−0.0700095	−	2.00481i
$185$	3.66877	+	15.6168i	0.269734	+	1.14817i
$186$	39.8194	−	5.59625i	2.91970	−	0.410337i
$187$	0.200795	−	0.257006i	0.0146836	−	0.0187941i
$188$	−0.0693189	−	0.171570i	−0.00505560	−	0.0125131i
$189$	7.30479	+	22.4818i	0.531345	+	1.63531i
$190$	−6.75886	+	10.0109i	−0.490339	+	0.726267i
$191$	−1.10425	+	3.39853i	−0.0799007	+	0.245909i	−0.983025	−	0.183469i	$-0.941267\pi$
$191$	−1.10425	+	3.39853i	−0.0799007	+	0.245909i	0.903125	+	0.429378i	$0.141267\pi$
$192$	−28.3044	+	1.97924i	−2.04270	+	0.142839i
$193$	−0.691763	−	0.251781i	−0.0497942	−	0.0181236i	0.317003	−	0.948425i	$-0.397323\pi$
$193$	−0.691763	−	0.251781i	−0.0497942	−	0.0181236i	−0.366797	+	0.930301i	$0.619546\pi$
$194$	4.79791	−	4.63329i	0.344470	−	0.332651i
$195$	5.08321	+	4.38454i	0.364016	+	0.313984i
$196$	0.999393	−	1.48166i	0.0713852	−	0.105833i
$197$	−0.658031	−	6.26075i	−0.0468828	−	0.446060i	−0.992633	−	0.121164i	$-0.961337\pi$
$197$	−0.658031	−	6.26075i	−0.0468828	−	0.446060i	0.945750	−	0.324896i	$-0.105329\pi$
$198$	−0.465966	+	0.517508i	−0.0331148	+	0.0367777i
$199$	−19.6912	−	16.5229i	−1.39587	−	1.17127i	−0.962897	−	0.269868i	$-0.913020\pi$
$199$	−19.6912	−	16.5229i	−1.39587	−	1.17127i	−0.432973	−	0.901407i	$-0.642535\pi$
$200$	12.7240	+	8.44071i	0.899722	+	0.596848i
$201$	−1.37246	−	2.37718i	−0.0968061	−	0.167673i
$202$	4.39230	+	0.933613i	0.309041	+	0.0656888i
$203$	0.849494	−	1.25943i	0.0596228	−	0.0883944i
$204$	−4.43609	−	4.28388i	−0.310588	−	0.299932i
$205$	−2.58867	+	21.7754i	−0.180801	+	1.52086i
$206$	−13.5956	−	20.1563i	−0.947249	−	1.40435i
$207$	−48.9781	+	41.0975i	−3.40421	+	2.85647i
$208$	2.17461	+	1.57995i	0.150782	+	0.109550i
$209$	−0.0869348	−	0.330102i	−0.00601341	−	0.0228336i
$210$	4.00214	−	15.1694i	0.276174	−	1.04679i
$211$	−11.9357	−	7.45825i	−0.821687	−	0.513447i	0.0527378	−	0.998608i	$-0.483205\pi$
$211$	−11.9357	−	7.45825i	−0.821687	−	0.513447i	−0.874425	+	0.485161i	$0.838761\pi$
$212$	0.251237	−	0.321568i	0.0172550	−	0.0220854i
$213$	−36.4728	−	19.3929i	−2.49908	−	1.32878i
$214$	−1.98623	+	1.05610i	−0.135776	+	0.0721932i
$215$	−3.89263	−	4.44332i	−0.265475	−	0.303032i
$216$	27.2161	+	30.2265i	1.85182	+	2.05665i
$217$	1.88708	−	17.9544i	0.128103	−	1.21882i
$218$	−10.2021	−	8.56059i	−0.690974	−	0.579796i
$219$	9.52401	+	38.1987i	0.643573	+	2.58123i
$220$	−0.0784374	+	0.0213411i	−0.00528825	+	0.00143881i
$221$	0.409698	+	3.89801i	0.0275593	+	0.262209i
$222$	15.8590	−	23.5119i	1.06439	−	1.57802i
$223$	17.6420	−	9.38041i	1.18139	−	0.628159i	0.241759	−	0.970336i	$-0.422276\pi$
$223$	17.6420	−	9.38041i	1.18139	−	0.628159i	0.939635	+	0.342178i	$0.111164\pi$
$224$	−0.791495	+	4.48879i	−0.0528840	+	0.299920i
$225$	−2.77799	−	35.7692i	−0.185199	−	2.38461i
$226$	0.325823	−	0.273398i	0.0216734	−	0.0181862i
$227$	5.10530	+	15.7125i	0.338851	+	1.04288i	0.964794	+	0.263007i	$0.0847142\pi$
$227$	5.10530	+	15.7125i	0.338851	+	1.04288i	−0.625943	+	0.779869i	$0.715286\pi$
$228$	−6.37934	+	0.982359i	−0.422482	+	0.0650583i
$229$	5.80704	−	4.21906i	0.383740	−	0.278803i	−0.379145	−	0.925337i	$-0.623782\pi$
$229$	5.80704	−	4.21906i	0.383740	−	0.278803i	0.762885	+	0.646534i	$0.223782\pi$
$230$	24.4961	−	3.10346i	1.61522	−	0.204636i
$231$	0.247927	+	0.367567i	0.0163124	+	0.0241842i
$232$	0.453897	−	2.57418i	0.0297998	−	0.169003i
$233$	−1.45598	+	2.98520i	−0.0953843	+	0.195567i	−0.941151	−	0.337986i	$-0.890254\pi$
$233$	−1.45598	+	2.98520i	−0.0953843	+	0.195567i	0.845767	+	0.533553i	$0.179143\pi$
$234$	−0.292066	−	8.36368i	−0.0190929	−	0.546751i
$235$	0.792636	−	0.407718i	0.0517059	−	0.0265966i
$236$	−2.50204	+	2.77880i	−0.162869	+	0.180884i
$237$	23.0360	−	14.3945i	1.49635	−	0.935024i
$238$	7.76818	−	4.85410i	0.503536	−	0.314645i
$239$	−8.76875	+	9.73868i	−0.567203	+	0.629943i	−0.956697	−	0.291086i	$-0.905983\pi$
$239$	−8.76875	+	9.73868i	−0.567203	+	0.629943i	0.389494	+	0.921029i	$0.372650\pi$
$240$	−3.26428	−	20.1087i	−0.210708	−	1.29801i
$241$	0.776442	+	22.2344i	0.0500150	+	1.43224i	0.722110	+	0.691778i	$0.243172\pi$
$241$	0.776442	+	22.2344i	0.0500150	+	1.43224i	−0.672095	+	0.740465i	$0.734605\pi$
$242$	5.97253	−	12.2455i	0.383929	−	0.787171i
$243$	4.67161	−	26.4940i	0.299684	−	1.69959i
$244$	−1.83812	−	2.72513i	−0.117674	−	0.174458i
$245$	7.54550	+	4.14467i	0.482064	+	0.264793i
$246$	31.3637	−	22.7871i	1.99968	−	1.45285i
$247$	3.50727	+	2.12791i	0.223162	+	0.135395i
$248$	−9.59901	−	29.5427i	−0.609538	−	1.87596i
$249$	23.3752	−	19.6141i	1.48134	−	1.24299i
$250$	−6.57693	+	12.1950i	−0.415962	+	0.771279i
$251$	2.93106	−	16.6228i	0.185007	−	1.04922i	−0.740940	−	0.671571i	$-0.765620\pi$
$251$	2.93106	−	16.6228i	0.185007	−	1.04922i	0.925947	−	0.377654i	$-0.123269\pi$
$252$	5.21972	−	2.77537i	0.328811	−	0.174832i
$253$	−0.390209	+	0.578509i	−0.0245323	+	0.0363706i
$254$	−1.54021	−	14.6541i	−0.0966413	−	0.919480i
$255$	18.6054	−	23.1573i	1.16511	−	1.45017i
$256$	2.53882	+	10.1826i	0.158676	+	0.636415i
$257$	−6.66224	−	5.59028i	−0.415579	−	0.348712i	0.410899	−	0.911681i	$-0.365215\pi$
$257$	−6.66224	−	5.59028i	−0.415579	−	0.348712i	−0.826478	+	0.562969i	$0.809659\pi$
$258$	−1.09163	+	10.3862i	−0.0679621	+	0.646616i
$259$	−8.51997	−	9.46238i	−0.529405	−	0.587964i
$260$	0.499914	−	0.839294i	0.0310033	−	0.0520508i
$261$	−5.42280	+	2.88335i	−0.335663	+	0.178475i
$262$	−2.62260	−	1.39446i	−0.162025	−	0.0861501i
$263$	16.4822	−	21.0962i	1.01633	−	1.30085i	0.0632956	−	0.997995i	$-0.479839\pi$
$263$	16.4822	−	21.0962i	1.01633	−	1.30085i	0.953038	−	0.302852i	$-0.0979389\pi$
$264$	0.646952	+	0.404261i	0.0398172	+	0.0248805i
$265$	1.65267	+	1.06424i	0.101523	+	0.0653755i
$266$	0.876548	−	9.54717i	0.0537446	−	0.585375i
$267$	−2.99263	−	2.17427i	−0.183146	−	0.133063i
$268$	−0.306001	+	0.256765i	−0.0186920	+	0.0156844i
$269$	−11.9708	−	17.7474i	−0.729872	−	1.08208i	−0.993091	−	0.117344i	$-0.962562\pi$
$269$	−11.9708	−	17.7474i	−0.729872	−	1.08208i	0.263219	−	0.964736i	$-0.415216\pi$
$270$	−25.0672	+	27.0895i	−1.52554	+	1.64862i
$271$	11.0348	+	10.6562i	0.670316	+	0.647317i	0.949809	−	0.312831i	$-0.101277\pi$
$271$	11.0348	+	10.6562i	0.670316	+	0.647317i	−0.279492	+	0.960148i	$0.590166\pi$
$272$	6.65139	−	9.86109i	0.403300	−	0.597916i
$273$	−5.21177	−	1.10780i	−0.315431	−	0.0670469i
$274$	5.22097	+	9.04298i	0.315410	+	0.546306i
$275$	−0.136750	−	0.366908i	−0.00824636	−	0.0221254i
$276$	10.1075	+	8.48123i	0.608402	+	0.510510i
$277$	5.25404	−	5.83520i	0.315684	−	0.350603i	−0.564331	−	0.825549i	$-0.690866\pi$
$277$	5.25404	−	5.83520i	0.315684	−	0.350603i	0.880015	+	0.474946i	$0.157532\pi$
$278$	0.634734	+	6.03909i	0.0380688	+	0.362201i
$279$	−40.8138	+	60.5089i	−2.44346	+	3.62258i
$280$	−12.0773	−	1.00982i	−0.721758	−	0.0603481i
$281$	−13.7169	+	13.2462i	−0.818281	+	0.790205i	−0.980494	−	0.196551i	$-0.937026\pi$
$281$	−13.7169	+	13.2462i	−0.818281	+	0.790205i	0.162213	+	0.986756i	$0.448137\pi$
$282$	−1.48078	−	0.538960i	−0.0881792	−	0.0320946i
$283$	11.4542	−	0.800957i	0.680883	−	0.0476120i	0.274873	−	0.961481i	$-0.411364\pi$
$283$	11.4542	−	0.800957i	0.680883	−	0.0476120i	0.406010	+	0.913869i	$0.366920\pi$
$284$	−1.85761	+	5.71713i	−0.110229	+	0.339249i
$285$	−7.50832	−	30.1709i	−0.444755	−	1.78717i
$286$	−0.0282249	−	0.0868673i	−0.00166897	−	0.00513657i
$287$	−6.52017	−	16.1380i	−0.384874	−	0.952595i
$288$	11.3451	−	14.5211i	0.668519	−	0.855666i
$289$	0.340927	−	0.0479141i	0.0200545	−	0.00281848i
$290$	2.36364	+	0.197631i	0.138798	+	0.0116053i
$291$	0.599165	+	17.1578i	0.0351237	+	1.00581i
$292$	5.23374	−	2.33021i	0.306282	−	0.136365i
$293$	−5.65361	−	9.79235i	−0.330288	−	0.572075i	0.652280	−	0.757978i	$-0.273812\pi$
$293$	−5.65361	−	9.79235i	−0.330288	−	0.572075i	−0.982568	+	0.185903i	$0.940479\pi$
$294$	−3.68195	−	14.7675i	−0.214736	−	0.861259i
$295$	−14.4264	−	10.7843i	−0.839938	−	0.627886i
$296$	−20.0146	−	8.91106i	−1.16332	−	0.517945i
$297$	−0.109028	−	1.03733i	−0.00632645	−	0.0601921i
$298$	9.65663	+	12.3599i	0.559393	+	0.715991i
$299$	−1.45621	−	8.25858i	−0.0842149	−	0.477606i
$300$	−7.16994	+	1.84639i	−0.413956	+	0.106601i
$301$	4.40597	+	1.60364i	0.253956	+	0.0924323i
$302$	13.1371	+	8.20899i	0.755956	+	0.472374i
$303$	−9.35092	+	6.79384i	−0.537197	+	0.390296i
$304$	−4.00261	−	11.7884i	−0.229566	−	0.676113i
$305$	12.2667	−	10.0118i	0.702390	−	0.573274i
$306$	−36.9428	+	2.58329i	−2.11188	+	0.147677i
$307$	−11.4447	−	4.16552i	−0.653182	−	0.237739i	−0.00589173	−	0.999983i	$-0.501875\pi$
$307$	−11.4447	−	4.16552i	−0.653182	−	0.237739i	−0.647290	+	0.762244i	$0.724098\pi$
$308$	0.0464125	−	0.0448200i	0.00264460	−	0.00255386i
$309$	61.9724	+	8.70965i	3.52548	+	0.495474i
$310$	25.9039	−	11.1134i	1.47124	−	0.631197i
$311$	3.23905	+	0.688482i	0.183670	+	0.0390402i	0.298828	−	0.954307i	$-0.403404\pi$
$311$	3.23905	+	0.688482i	0.183670	+	0.0390402i	−0.115158	+	0.993347i	$0.536738\pi$
$312$	−8.96756	+	1.90611i	−0.507688	+	0.107912i
$313$	−23.5052	+	14.6877i	−1.32859	+	0.830198i	−0.993702	−	0.112059i	$-0.964255\pi$
$313$	−23.5052	+	14.6877i	−1.32859	+	0.830198i	−0.334892	+	0.942256i	$0.608700\pi$
$314$	−2.90715	+	7.19545i	−0.164060	+	0.406063i
$315$	15.6011	+	23.8224i	0.879023	+	1.34224i
$316$	−2.64506	−	2.93764i	−0.148796	−	0.165255i
$317$	24.2454	+	6.95225i	1.36176	+	0.390477i	0.875449	−	0.483311i	$-0.160566\pi$
$317$	24.2454	+	6.95225i	1.36176	+	0.390477i	0.486307	+	0.873788i	$0.338344\pi$
$318$	−0.603448	−	3.42232i	−0.0338397	−	0.191914i
$319$	−0.0482182	+	0.0465638i	−0.00269970	+	0.00260707i
$320$	−18.7808	+	6.54769i	−1.04988	+	0.366027i
$321$	1.40081	−	5.61833i	0.0781854	−	0.313584i
$322$	−15.8556	+	11.5197i	−0.883596	+	0.641970i
$323$	8.86890	−	15.8393i	0.493479	−	0.881323i
$324$	−9.72975			−0.540542
$325$	4.24517	+	2.03022i	0.235480	+	0.112616i
$326$	−6.54689	−	2.38287i	−0.362598	−	0.131975i
$327$	33.9467	−	4.77090i	1.87726	−	0.263831i
$328$	−21.5430	−	20.8039i	−1.18951	−	1.14870i
$329$	−0.395621	+	0.586533i	−0.0218113	+	0.0323366i
$330$	−0.311897	+	0.617999i	−0.0171693	+	0.0340197i
$331$	0.270488	−	2.57352i	0.0148674	−	0.141454i	−0.984570	−	0.174991i	$-0.944011\pi$
$331$	0.270488	−	2.57352i	0.0148674	−	0.141454i	0.999437	+	0.0335370i	$0.0106772\pi$
$332$	−3.40167	−	2.85434i	−0.186691	−	0.156652i
$333$	12.4535	+	49.9484i	0.682449	+	2.73715i
$334$	10.4325	−	2.21750i	0.570842	−	0.121336i
$335$	−1.36581	−	1.35534i	−0.0746222	−	0.0740501i
$336$	9.95507	+	12.7419i	0.543094	+	0.695128i
$337$	3.59217	+	0.504846i	0.195678	+	0.0275007i	0.236331	−	0.971673i	$-0.424055\pi$
$337$	3.59217	+	0.504846i	0.195678	+	0.0275007i	−0.0406532	+	0.999173i	$0.512944\pi$
$338$	−13.2556	−	7.04811i	−0.721008	−	0.383367i
$339$	−0.0382082	+	1.09414i	−0.00207518	+	0.0594254i
$340$	−3.78894	−	2.08122i	−0.205484	−	0.112870i
$341$	−0.246159	+	0.757600i	−0.0133303	+	0.0410263i
$342$	−21.2496	+	32.4163i	−1.14905	+	1.75287i
$343$	−19.2568			−1.03977
$344$	8.04795	−	0.562767i	0.433916	−	0.0303424i
$345$	−36.2542	+	52.2027i	−1.95186	+	2.81050i
$346$	−0.170294	−	0.349155i	−0.00915507	−	0.0187707i
$347$	−6.25989	−	6.04510i	−0.336048	−	0.324518i	0.507418	−	0.861700i	$-0.330600\pi$
$347$	−6.25989	−	6.04510i	−0.336048	−	0.324518i	−0.843466	+	0.537182i	$0.819489\pi$
$348$	0.780322	+	0.998767i	0.0418297	+	0.0535395i
$349$	−1.36030	+	2.35612i	−0.0728154	+	0.126120i	−0.900134	−	0.435613i	$-0.856532\pi$
$349$	−1.36030	+	2.35612i	−0.0728154	+	0.126120i	0.827319	+	0.561733i	$0.189865\pi$
$350$	−0.0846316	−	10.9971i	−0.00452375	−	0.587819i
$351$	9.60231	+	8.05730i	0.512533	+	0.430067i
$352$	0.0753411	−	0.186476i	0.00401569	−	0.00993919i
$353$	3.35978	+	1.49587i	0.178823	+	0.0796172i	0.494195	−	0.869351i	$-0.335463\pi$
$353$	3.35978	+	1.49587i	0.178823	+	0.0796172i	−0.315372	+	0.948968i	$0.602129\pi$
$354$	3.32848	+	31.6684i	0.176907	+	1.68316i
$355$	−28.2391	−	6.40515i	−1.49877	−	0.339950i
$356$	−0.235980	+	0.483831i	−0.0125069	+	0.0256430i
$357$	−4.09429	+	23.2199i	−0.216693	+	1.22892i
$358$	5.08388	+	7.53717i	0.268692	+	0.398352i
$359$	7.96997	+	19.7264i	0.420639	+	1.04112i	0.977580	+	0.210566i	$0.0675307\pi$
$359$	7.96997	+	19.7264i	0.420639	+	1.04112i	−0.556941	+	0.830552i	$0.688025\pi$
$360$	41.1951	+	26.5276i	2.17117	+	1.39813i
$361$	−7.57882	−	17.4230i	−0.398885	−	0.917001i
$362$	−2.22491	+	6.84758i	−0.116939	+	0.359901i
$363$	13.1371	+	32.5156i	0.689521	+	1.70663i
$364$	−0.0270606	+	0.774915i	−0.00141836	+	0.0406166i
$365$	13.4718	+	24.0848i	0.705148	+	1.26066i
$366$	−27.7200	−	3.89580i	−1.44895	−	0.203637i
$367$	4.63440	+	1.32889i	0.241914	+	0.0693677i	0.394403	−	0.918937i	$-0.370951\pi$
$367$	4.63440	+	1.32889i	0.241914	+	0.0693677i	−0.152490	+	0.988305i	$0.548729\pi$
$368$	−12.7246	+	22.0397i	−0.663318	+	1.14890i
$369$	−7.35543	+	69.9822i	−0.382908	+	3.64313i
$370$	6.40003	−	18.8220i	0.332722	−	0.978509i
$371$	−1.55641	−	0.108835i	−0.0808047	−	0.00565042i
$372$	13.7600	+	6.12635i	0.713424	+	0.317637i
$373$	−13.9274	−	2.96036i	−0.721134	−	0.153282i	−0.167296	−	0.985907i	$-0.553504\pi$
$373$	−13.9274	−	2.96036i	−0.721134	−	0.153282i	−0.553837	+	0.832625i	$0.686837\pi$
$374$	−0.379807	+	0.138238i	−0.0196394	+	0.00714814i
$375$	−11.9995	−	33.5847i	−0.619654	−	1.73431i
$376$	−0.211387	+	1.19883i	−0.0109014	+	0.0618251i
$377$	0.0281134	−	0.805063i	0.00144792	−	0.0414629i
$378$	7.08707	−	28.4247i	0.364520	−	1.46201i
$379$	23.9714	−	17.4162i	1.23133	−	0.894611i	0.234337	−	0.972155i	$-0.424708\pi$
$379$	23.9714	−	17.4162i	1.23133	−	0.894611i	0.996989	+	0.0775443i	$0.0247079\pi$
$380$	−4.13419	+	1.83847i	−0.212079	+	0.0943117i
$381$	30.6840	+	22.2932i	1.57199	+	1.14212i
$382$	3.39239	−	2.84655i	0.173570	−	0.145642i
$383$	3.18952	+	4.72865i	0.162977	+	0.241623i	0.901676	−	0.432412i	$-0.142337\pi$
$383$	3.18952	+	4.72865i	0.162977	+	0.241623i	−0.738699	+	0.674035i	$0.764560\pi$
$384$	16.5801	+	8.81581i	0.846102	+	0.449880i
$385$	0.235342	+	0.202995i	0.0119941	+	0.0103456i
$386$	0.561668	+	0.718902i	0.0285881	+	0.0365912i
$387$	−12.6840	−	14.0870i	−0.644764	−	0.716083i
$388$	2.44382	−	0.519450i	0.124066	−	0.0263711i
$389$	2.25690	−	5.58602i	0.114429	−	0.283223i	−0.859091	−	0.511823i	$-0.828970\pi$
$389$	2.25690	−	5.58602i	0.114429	−	0.283223i	0.973520	+	0.228600i	$0.0734149\pi$
$390$	−2.46287	−	7.94620i	−0.124712	−	0.402371i
$391$	−36.2982	+	7.71543i	−1.83568	+	0.390186i
$392$	−10.7408	+	4.78210i	−0.542491	+	0.241532i
$393$	7.18443	−	2.61492i	0.362406	−	0.131905i
$394$	−3.41995	+	7.01194i	−0.172295	+	0.353257i
$395$	12.9325	−	13.9758i	0.650703	−	0.703199i
$396$	−0.250745	+	0.0718999i	−0.0126004	+	0.00361311i
$397$	5.98670	−	24.0113i	0.300464	−	1.20509i	−0.610301	−	0.792169i	$-0.708952\pi$
$397$	5.98670	−	24.0113i	0.300464	−	1.20509i	0.910765	−	0.412925i	$-0.135493\pi$
$398$	9.84388	+	30.2963i	0.493429	+	1.51862i
$399$	16.7527	+	18.1202i	0.838682	+	0.907146i
$400$	−5.90861	−	13.0008i	−0.295431	−	0.650039i
$401$	−23.2631	+	19.5201i	−1.16170	+	0.974786i	−0.999927	−	0.0120414i	$-0.996167\pi$
$401$	−23.2631	+	19.5201i	−1.16170	+	0.974786i	−0.161777	+	0.986827i	$0.551723\pi$
$402$	−0.118718	+	3.39963i	−0.00592111	+	0.169558i
$403$	−4.19656	−	8.60423i	−0.209046	−	0.428607i
$404$	1.20995	+	1.16844i	0.0601974	+	0.0581320i
$405$	−4.26441	−	46.6733i	−0.211900	−	2.31922i
$406$	−1.71987	+	0.765734i	−0.0853555	+	0.0380027i
$407$	0.280915	+	0.486560i	0.0139245	+	0.0241179i
$408$	9.81459	+	39.3642i	0.485895	+	1.94882i
$409$	−17.0026	+	10.6244i	−0.840727	+	0.525344i	−0.880600	−	0.473860i	$-0.842860\pi$
$409$	−17.0026	+	10.6244i	−0.840727	+	0.525344i	0.0398732	+	0.999205i	$0.487305\pi$
$410$	17.0208	−	21.1851i	0.840598	−	1.04626i
$411$	−26.2902	−	5.58816i	−1.29680	−	0.275644i
$412$	−0.317835	−	9.10161i	−0.0156586	−	0.448404i
$413$	14.1572	+	1.98967i	0.696631	+	0.0979052i
$414$	78.4633	−	11.0273i	3.85626	−	0.541962i
$415$	12.2013	−	17.5687i	0.598937	−	0.862415i
$416$	0.905420	+	2.24099i	0.0443919	+	0.109874i
$417$	−12.6451	−	9.18724i	−0.619236	−	0.449901i
$418$	−0.125417	+	0.404016i	−0.00613436	+	0.0197611i
$419$	−28.1503	−	20.4524i	−1.37523	−	0.999166i	−0.997308	−	0.0733305i	$-0.976637\pi$
$419$	−28.1503	−	20.4524i	−1.37523	−	0.999166i	−0.377926	−	0.925836i	$-0.623363\pi$
$420$	4.28244	−	4.02436i	0.208962	−	0.196368i
$421$	31.0225	−	8.89557i	1.51195	−	0.433544i	0.585721	−	0.810513i	$-0.300812\pi$
$421$	31.0225	−	8.89557i	1.51195	−	0.433544i	0.926226	+	0.376969i	$0.123034\pi$
$422$	7.64602	+	15.6767i	0.372202	+	0.763128i
$423$	2.52548	−	1.34282i	0.122793	−	0.0652901i
$424$	−2.52265	+	0.918171i	−0.122511	+	0.0445903i
$425$	8.32293	−	19.0876i	0.403721	−	0.925884i
$426$	25.5959	+	44.3334i	1.24013	+	2.14796i
$427$	−4.70793	+	11.6525i	−0.227832	+	0.563905i
$428$	−0.840584	−	0.0587794i	−0.0406312	−	0.00284121i
$429$	0.214778	+	0.0956252i	0.0103696	+	0.00461683i
$430$	1.17302	+	7.22610i	0.0565681	+	0.348473i
$431$	−23.4077	−	6.71205i	−1.12751	−	0.323308i	−0.340497	−	0.940245i	$-0.610595\pi$
$431$	−23.4077	−	6.71205i	−1.12751	−	0.323308i	−0.787012	+	0.616937i	$0.788373\pi$
$432$	−6.60562	−	37.4623i	−0.317813	−	1.80241i
$433$	−19.1765	+	18.5185i	−0.921563	+	0.889943i	−0.994214	−	0.107415i	$-0.965743\pi$
$433$	−19.1765	+	18.5185i	−0.921563	+	0.889943i	0.0726516	+	0.997357i	$0.476854\pi$
$434$	−13.7741	+	17.6301i	−0.661178	+	0.846270i
$435$	−4.44905	+	4.18093i	−0.213316	+	0.200460i
$436$	−1.54158	−	4.74449i	−0.0738281	−	0.227220i
$437$	−16.5654	+	35.1303i	−0.792428	+	1.68051i
$438$	15.0762	−	46.3999i	0.720371	−	2.21707i
$439$	−20.5092	−	12.8156i	−0.978852	−	0.611655i	−0.0566628	−	0.998393i	$-0.518046\pi$
$439$	−20.5092	−	12.8156i	−0.978852	−	0.611655i	−0.922189	+	0.386739i	$0.873602\pi$
$440$	0.511994	+	0.154381i	0.0244084	+	0.00735981i
$441$	24.3917	+	12.9693i	1.16151	+	0.617584i
$442$	2.12930	−	4.36572i	0.101281	−	0.207656i
$443$	10.5309	−	3.83294i	0.500339	−	0.182108i	−0.0795076	−	0.996834i	$-0.525335\pi$
$443$	10.5309	−	3.83294i	0.500339	−	0.182108i	0.579846	+	0.814726i	$0.303113\pi$
$444$	9.70489	−	4.32090i	0.460574	−	0.205061i
$445$	−2.42435	−	0.919932i	−0.114925	−	0.0436090i
$446$	−24.7013	−	1.72728i	−1.16964	−	0.0817891i
$447$	−40.2748	−	2.81629i	−1.90493	−	0.133206i
$448$	10.5634	−	11.7318i	0.499074	−	0.554278i
$449$	8.92838	−	15.4644i	0.421356	−	0.729811i	−0.574716	−	0.818353i	$-0.694887\pi$
$449$	8.92838	−	15.4644i	0.421356	−	0.729811i	0.996072	+	0.0885422i	$0.0282208\pi$
$450$	−20.5705	+	39.4163i	−0.969704	+	1.85810i
$451$	0.133362	+	0.756333i	0.00627977	+	0.0356144i
$452$	0.157771	−	0.0221733i	0.00742093	−	0.00104294i
$453$	−38.3293	+	10.9907i	−1.80087	+	0.516390i
$454$	4.95314	−	19.8660i	0.232462	−	0.932355i
$455$	−3.72910	+	0.209825i	−0.174823	+	0.00983676i
$456$	39.0145	+	16.7585i	1.82702	+	0.784790i
$457$	6.25501			0.292597			0.146299	−	0.989240i	$-0.453264\pi$
$457$	6.25501			0.292597			0.146299	+	0.989240i	$0.453264\pi$
$458$	−8.87369	+	0.620509i	−0.414640	+	0.0289945i
$459$	34.1500	−	43.7100i	1.59399	−	2.04021i
$460$	8.39754	+	3.87657i	0.391537	+	0.180746i
$461$	−11.1359	+	5.92106i	−0.518651	+	0.275771i	−0.708091	−	0.706121i	$-0.750444\pi$
$461$	−11.1359	+	5.92106i	−0.518651	+	0.275771i	0.189441	+	0.981892i	$0.439332\pi$
$462$	−0.0191756	−	0.549116i	−0.000892128	−	0.0255472i
$463$	−25.8356	−	28.6934i	−1.20068	−	1.33349i	−0.928538	−	0.371238i	$-0.878934\pi$
$463$	−25.8356	−	28.6934i	−1.20068	−	1.33349i	−0.272145	−	0.962256i	$-0.587733\pi$
$464$	−1.63579	+	1.81673i	−0.0759396	+	0.0843394i
$465$	−23.3571	+	68.6915i	−1.08316	+	3.18549i
$466$	3.49060	−	2.18117i	0.161699	−	0.101041i
$467$	1.63425	−	15.5488i	0.0756239	−	0.719513i	−0.889361	−	0.457206i	$-0.848850\pi$
$467$	1.63425	−	15.5488i	0.0756239	−	0.719513i	0.964984	−	0.262307i	$-0.0844833\pi$
$468$	1.56740	−	2.71481i	0.0724529	−	0.125492i
$469$	1.46809	+	0.420967i	0.0677900	+	0.0194385i
$470$	−1.10078	−	0.0920394i	−0.0507754	−	0.00424546i
$471$	−8.75675	−	17.9540i	−0.403490	−	0.827277i
$472$	23.6459	−	6.78035i	1.08839	−	0.312091i
$473$	−0.175450	−	0.109634i	−0.00806722	−	0.00504096i
$474$	−33.6630			−1.54619
$475$	−10.6311	−	19.0258i	−0.487786	−	0.872963i
$476$	3.43120			0.157269
$477$	5.34926	+	3.34259i	0.244926	+	0.153047i
$478$	15.6111	−	4.47642i	0.714037	−	0.204747i
$479$	6.32365	+	12.9654i	0.288935	+	0.592405i	0.993052	−	0.117680i	$-0.0375456\pi$
$479$	6.32365	+	12.9654i	0.288935	+	0.592405i	−0.704117	+	0.710084i	$0.748657\pi$
$480$	7.09257	−	16.8894i	0.323730	−	0.770894i
$481$	−6.49030	−	1.86106i	−0.295932	−	0.0848573i
$482$	13.7856	−	23.8774i	0.627917	−	1.08758i
$483$	5.27312	−	50.1704i	0.239935	−	2.28283i
$484$	4.32797	−	2.70441i	0.196726	−	0.122928i
$485$	3.56288	+	11.4953i	0.161782	+	0.521973i
$486$	−22.3087	+	24.7763i	−1.01194	+	1.12388i
$487$	19.1557	+	21.2745i	0.868027	+	0.964041i	0.999628	−	0.0272613i	$-0.00867863\pi$
$487$	19.1557	+	21.2745i	0.868027	+	0.964041i	−0.131602	+	0.991303i	$0.542012\pi$
$488$	0.754679	+	21.6112i	0.0341627	+	0.978292i
$489$	15.8341	−	8.41913i	0.716042	−	0.380726i
$490$	−5.20817	−	9.31111i	−0.235281	−	0.420633i
$491$	25.0378	−	32.0469i	1.12994	−	1.44626i	0.251844	−	0.967768i	$-0.418963\pi$
$491$	25.0378	−	32.0469i	1.12994	−	1.44626i	0.878094	−	0.478488i	$-0.158815\pi$
$492$	14.4863	−	1.01298i	0.653093	−	0.0456687i
$493$	−3.56469			−0.160546
$494$	−2.28858	−	4.53961i	−0.102968	−	0.204247i
$495$	−0.454800	−	1.17130i	−0.0204417	−	0.0526461i
$496$	−7.02827	+	28.1888i	−0.315579	+	1.26572i
$497$	22.0930	−	6.33507i	0.991008	−	0.284167i
$498$	−37.4472	+	5.26286i	−1.67805	+	0.235835i
$499$	−6.87356	−	38.9819i	−0.307703	−	1.74507i	−0.610501	−	0.792015i	$-0.709032\pi$
$499$	−6.87356	−	38.9819i	−0.307703	−	1.74507i	0.302798	−	0.953055i	$-0.402079\pi$
$500$	−4.50994	+	2.56840i	−0.201690	+	0.114862i
$501$	−13.7266	+	23.7752i	−0.613260	+	1.06220i
$502$	−13.9969	+	15.5451i	−0.624711	+	0.693812i
$503$	−29.1298	−	2.03695i	−1.29883	−	0.0908233i	−0.596467	−	0.802638i	$-0.703429\pi$
$503$	−29.1298	−	2.03695i	−1.29883	−	0.0908233i	−0.702367	+	0.711815i	$0.747874\pi$
$504$	−38.7957	−	2.71286i	−1.72810	−	0.120840i
$505$	−5.07466	+	6.31622i	−0.225819	+	0.281068i
$506$	0.790010	−	0.351735i	0.0351202	−	0.0156365i
$507$	36.3127	−	13.2167i	1.61270	−	0.586976i
$508$	2.41955	−	4.96080i	0.107350	−	0.220100i
$509$	11.5900	+	6.16252i	0.513719	+	0.273149i	0.706026	−	0.708186i	$-0.250486\pi$
$509$	11.5900	+	6.16252i	0.513719	+	0.273149i	−0.192308	+	0.981335i	$0.561597\pi$
$510$	−34.7613	+	12.1191i	−1.53925	+	0.536642i
$511$	−18.5757	−	11.6074i	−0.821739	−	0.513480i
$512$	7.65711	−	23.5662i	0.338400	−	1.04149i
$513$	−14.7854	−	56.1418i	−0.652789	−	2.47872i
$514$	3.33054	+	10.2504i	0.146904	+	0.452124i
$515$	43.5208	−	5.51375i	1.91776	−	0.242965i
$516$	−2.40841	+	3.08263i	−0.106024	+	0.135705i
$517$	0.0224559	−	0.0216854i	0.000987610	−	0.000953724i
$518$	2.74008	+	15.5398i	0.120392	+	0.682779i
$519$	0.961188	+	0.275616i	0.0421915	+	0.0120982i
$520$	−5.71485	+	2.93962i	−0.250613	+	0.128911i
$521$	28.5840	+	12.7264i	1.25229	+	0.557555i	0.922316	−	0.386436i	$-0.126294\pi$
$521$	28.5840	+	12.7264i	1.25229	+	0.557555i	0.329972	+	0.943991i	$0.392961\pi$
$522$	7.59268	+	0.530932i	0.332323	+	0.0232383i
$523$	−10.6568	+	26.3764i	−0.465987	+	1.15336i	0.493030	+	0.870012i	$0.335889\pi$
$523$	−10.6568	+	26.3764i	−0.465987	+	1.15336i	−0.959018	+	0.283347i	$0.908555\pi$
$524$	−0.556306	−	0.963551i	−0.0243024	−	0.0420929i
$525$	21.1816	+	18.7789i	0.924442	+	0.819578i
$526$	−31.1763	+	11.3472i	−1.35935	+	0.494763i
$527$	−37.4036	+	19.8879i	−1.62933	+	0.866329i
$528$	−0.312768	−	0.641270i	−0.0136115	−	0.0279077i
$529$	54.2127	−	15.5452i	2.35707	−	0.675880i
$530$	−1.03799	−	2.20380i	−0.0450874	−	0.0957269i
$531$	−46.7598	−	33.9730i	−2.02920	−	1.47430i
$532$	2.17354	−	2.85880i	0.0942351	−	0.123944i
$533$	−7.46685	−	5.42499i	−0.323425	−	0.234982i
$534$	1.71726	+	4.25038i	0.0743133	+	0.183932i
$535$	−0.0864535	−	4.05802i	−0.00373771	−	0.175443i
$536$	2.60227	−	0.365725i	0.112401	−	0.0157969i
$537$	−23.1737	−	3.25685i	−1.00002	−	0.140544i
$538$	0.925863	+	26.5132i	0.0399168	+	1.14307i
$539$	0.294916	+	0.0626864i	0.0127030	+	0.00270010i
$540$	−13.3402	+	3.62956i	−0.574069	+	0.156191i
$541$	25.9897	−	16.2401i	1.11738	−	0.698218i	0.160022	−	0.987113i	$-0.448843\pi$
$541$	25.9897	−	16.2401i	1.11738	−	0.698218i	0.957361	+	0.288895i	$0.0932879\pi$
$542$	−4.59909	−	18.4459i	−0.197548	−	0.792321i
$543$	−9.26637	−	16.0498i	−0.397658	−	0.688764i
$544$	9.77084	−	4.35026i	0.418921	−	0.186516i
$545$	22.0835	−	9.47434i	0.945953	−	0.405836i
$546$	4.74986	+	4.58689i	0.203275	+	0.196301i
$547$	8.95012	+	18.3505i	0.382679	+	0.784609i	0.999998	−	0.00210430i	$-0.000669819\pi$
$547$	8.95012	+	18.3505i	0.382679	+	0.784609i	−0.617318	+	0.786713i	$0.711781\pi$
$548$	−0.136504	+	3.90898i	−0.00583118	+	0.166983i
$549$	38.9223	−	32.6597i	1.66116	−	1.39388i
$550$	−0.0972343	+	0.475412i	−0.00414608	+	0.0202717i
$551$	−2.25811	+	2.97002i	−0.0961986	+	0.126527i
$552$	−26.8228	−	82.5521i	−1.14165	−	3.51365i
$553$	−3.65630	+	14.6646i	−0.155482	+	0.623603i
$554$	−9.35384	+	2.68217i	−0.397407	+	0.113955i
$555$	24.9807	+	44.6603i	1.06037	+	1.89572i
$556$	−0.997117	+	2.04439i	−0.0422872	+	0.0867015i
$557$	13.1014	−	4.76851i	0.555123	−	0.202048i	−0.0491984	−	0.998789i	$-0.515667\pi$
$557$	13.1014	−	4.76851i	0.555123	−	0.202048i	0.604321	+	0.796741i	$0.293444\pi$
$558$	82.6307	−	36.7896i	3.49804	−	1.55743i
$559$	2.43196	−	0.516929i	0.102861	−	0.0218638i
$560$	9.07852	+	6.78654i	0.383637	+	0.286784i
$561$	0.389728	−	0.964611i	0.0164543	−	0.0407259i
$562$	23.1149	−	4.91322i	0.975043	−	0.207252i
$563$	−9.61569	−	10.6793i	−0.405253	−	0.450079i	0.505626	−	0.862753i	$-0.331262\pi$
$563$	−9.61569	−	10.6793i	−0.405253	−	0.450079i	−0.910879	+	0.412674i	$0.864595\pi$
$564$	−0.363407	−	0.465140i	−0.0153022	−	0.0195859i
$565$	0.175513	+	0.747105i	0.00738390	+	0.0314309i
$566$	−12.5639	−	6.68037i	−0.528102	−	0.280797i
$567$	20.8020	+	30.8402i	0.873602	+	1.29517i
$568$	30.2940	−	25.4197i	1.27111	−	1.06659i
$569$	26.7373	+	19.4258i	1.12089	+	0.814373i	0.984343	−	0.176261i	$-0.0564004\pi$
$569$	26.7373	+	19.4258i	1.12089	+	0.814373i	0.136544	+	0.990634i	$0.456400\pi$
$570$	−11.9227	+	36.6393i	−0.499387	+	1.53465i
$571$	−5.40166	+	3.92454i	−0.226052	+	0.164237i	−0.695047	−	0.718964i	$-0.744616\pi$
$571$	−5.40166	+	3.92454i	−0.226052	+	0.164237i	0.468994	+	0.883201i	$0.344616\pi$
$572$	0.00827698	−	0.0331972i	0.000346078	−	0.00138804i
$573$	−0.397814	+	11.3919i	−0.0166189	+	0.475903i
$574$	−3.74559	+	21.2423i	−0.156338	+	0.886636i
$575$	−14.9153	+	41.9818i	−0.622009	+	1.75076i
$576$	−59.9748	+	21.8290i	−2.49895	+	0.909543i
$577$	−10.0842	−	2.14347i	−0.419811	−	0.0892336i	−0.00683760	−	0.999977i	$-0.502176\pi$
$577$	−10.0842	−	2.14347i	−0.419811	−	0.0892336i	−0.412974	+	0.910743i	$0.635510\pi$
$578$	−0.389766	−	0.173535i	−0.0162121	−	0.00721811i
$579$	−2.34254	−	0.163807i	−0.0973527	−	0.00680757i
$580$	0.711614	+	0.531959i	0.0295482	+	0.0220884i
$581$	−1.77466	+	16.8847i	−0.0736252	+	0.700497i
$582$	10.6381	−	18.4257i	0.440963	−	0.763769i
$583$	0.0661764	+	0.0189758i	0.00274075	+	0.000785896i
$584$	−37.3221	−	5.24528i	−1.54440	−	0.217051i
$585$	13.7098	+	6.32888i	0.566831	+	0.261667i
$586$	−0.489037	+	14.0042i	−0.0202019	+	0.578507i
$587$	−2.25379	−	5.57832i	−0.0930238	−	0.230242i	0.873497	−	0.486829i	$-0.161846\pi$
$587$	−2.25379	−	5.57832i	−0.0930238	−	0.230242i	−0.966521	+	0.256587i	$0.917402\pi$
$588$	1.76170	−	5.42196i	0.0726513	−	0.223598i
$589$	−7.12378	+	43.7621i	−0.293530	+	1.80319i
$590$	8.07941	+	20.8079i	0.332624	+	0.856648i
$591$	−7.52251	−	18.6189i	−0.309435	−	0.765878i
$592$	11.4579	+	16.9871i	0.470918	+	0.698165i
$593$	−2.02623	+	11.4913i	−0.0832072	+	0.471891i	0.914522	+	0.404536i	$0.132567\pi$
$593$	−2.02623	+	11.4913i	−0.0832072	+	0.471891i	−0.997729	+	0.0673549i	$0.978544\pi$
$594$	−0.566646	+	1.16180i	−0.0232498	+	0.0476691i
$595$	1.50385	+	16.4593i	0.0616517	+	0.674767i
$596$	0.614136	+	5.84312i	0.0251560	+	0.239343i
$597$	−74.9071	−	33.3508i	−3.06574	−	1.36496i
$598$	−3.89310	+	9.63576i	−0.159201	+	0.394036i
$599$	14.5735	+	12.2286i	0.595458	+	0.499648i	0.889982	−	0.455996i	$-0.150717\pi$
$599$	14.5735	+	12.2286i	0.595458	+	0.499648i	−0.294524	+	0.955644i	$0.595161\pi$
$600$	46.4373	+	14.6943i	1.89579	+	0.599891i
$601$	−0.833549	+	1.44375i	−0.0340012	+	0.0588917i	−0.882525	−	0.470265i	$-0.844158\pi$
$601$	−0.833549	+	1.44375i	−0.0340012	+	0.0588917i	0.848524	+	0.529157i	$0.177492\pi$
$602$	−3.57737	−	4.57882i	−0.145803	−	0.186619i
$603$	−4.44155	−	4.28915i	−0.180874	−	0.174668i
$604$	2.54372	+	5.21539i	0.103502	+	0.212211i
$605$	14.8699	+	19.5758i	0.604546	+	0.795870i
$606$	14.2891	−	0.999189i	0.580454	−	0.0405893i
$607$	−33.6894			−1.36741			−0.683705	−	0.729758i	$-0.739633\pi$
$607$	−33.6894			−1.36741			−0.683705	+	0.729758i	$0.739633\pi$
$608$	2.56495	−	10.8966i	0.104022	−	0.441914i
$609$	1.49746	−	4.60872i	0.0606803	−	0.186755i
$610$	−19.4667	+	2.46628i	−0.788185	+	0.0998569i
$611$	−0.0130928	+	0.374930i	−0.000529679	+	0.0151680i
$612$	−12.2482	−	6.51246i	−0.495102	−	0.263251i
$613$	12.4716	+	1.75276i	0.503721	+	0.0707934i	0.386457	−	0.922307i	$-0.373699\pi$
$613$	12.4716	+	1.75276i	0.503721	+	0.0707934i	0.117264	+	0.993101i	$0.462588\pi$
$614$	9.29235	+	11.8937i	0.375009	+	0.479989i
$615$	11.2084	+	69.0464i	0.451966	+	2.78422i
$616$	−0.415179	+	0.0882491i	−0.0167280	+	0.00355566i
$617$	−6.27074	−	25.1506i	−0.252451	−	1.01252i	−0.953977	−	0.299880i	$-0.903053\pi$
$617$	−6.27074	−	25.1506i	−0.252451	−	1.01252i	0.701526	−	0.712644i	$-0.252502\pi$
$618$	−59.4108	−	49.8516i	−2.38985	−	2.00532i
$619$	4.27188	−	40.6443i	0.171702	−	1.63363i	−0.481499	−	0.876446i	$-0.659908\pi$
$619$	4.27188	−	40.6443i	0.171702	−	1.63363i	0.653201	−	0.757185i	$-0.273426\pi$
$620$	10.4347	+	1.61156i	0.419068	+	0.0647218i
$621$	−66.3645	+	98.3894i	−2.66311	+	3.94823i
$622$	−2.95198	−	2.85070i	−0.118364	−	0.114302i
$623$	2.03811	−	0.286438i	0.0816552	−	0.0114759i
$624$	8.05721	+	2.93258i	0.322546	+	0.117397i
$625$	−14.2972	−	20.5083i	−0.571886	−	0.820333i
$626$	34.3487			1.37285
$627$	−0.556813	−	0.935760i	−0.0222370	−	0.0373706i
$628$	−2.35178	+	1.70867i	−0.0938462	+	0.0681832i
$629$	−7.22813	+	28.9904i	−0.288204	+	1.15592i
$630$	−0.751658	−	35.2819i	−0.0299468	−	1.40566i
$631$	12.2177	−	11.7985i	0.486380	−	0.469691i	−0.410567	−	0.911831i	$-0.634669\pi$
$631$	12.2177	−	11.7985i	0.486380	−	0.469691i	0.896946	+	0.442139i	$0.145780\pi$
$632$	4.51571	+	25.6098i	0.179625	+	1.01870i
$633$	−43.1563	−	12.3749i	−1.71531	−	0.491857i
$634$	−20.9153	−	23.2288i	−0.830653	−	0.922533i
$635$	24.8573	+	9.43223i	0.986431	+	0.374307i
$636$	0.487632	−	1.20693i	0.0193359	−	0.0478579i
$637$	−3.07279	+	1.92009i	−0.121748	+	0.0760769i
$638$	0.0812545	−	0.0172712i	0.00321690	−	0.000683772i
$639$	−90.8883	−	19.3189i	−3.59549	−	0.764244i
$640$	12.8372	+	2.91171i	0.507434	+	0.115096i
$641$	9.04187	+	1.27075i	0.357132	+	0.0501917i	0.315458	−	0.948940i	$-0.397842\pi$
$641$	9.04187	+	1.27075i	0.357132	+	0.0501917i	0.0416745	+	0.999131i	$0.486731\pi$
$642$	−5.16182	+	4.98471i	−0.203721	+	0.196731i
$643$	9.35795	+	3.40602i	0.369042	+	0.134320i	0.519882	−	0.854238i	$-0.325976\pi$
$643$	9.35795	+	3.40602i	0.369042	+	0.134320i	−0.150841	+	0.988558i	$0.548198\pi$
$644$	−7.32338	+	0.512101i	−0.288582	+	0.0201796i
$645$	−15.8428	−	10.2020i	−0.623811	−	0.401704i
$646$	−19.7228	+	10.8222i	−0.775982	+	0.425793i
$647$	0.425697	−	0.309287i	0.0167359	−	0.0121593i	−0.579386	−	0.815053i	$-0.696708\pi$
$647$	0.425697	−	0.309287i	0.0167359	−	0.0121593i	0.596122	+	0.802894i	$0.296708\pi$
$648$	54.2816	+	33.9189i	2.13238	+	1.33246i
$649$	−0.592774	−	0.215752i	−0.0232684	−	0.00846901i
$650$	−3.12824	−	4.92154i	−0.122700	−	0.193039i
$651$	−10.0000	−	56.7129i	−0.391932	−	2.22275i
$652$	−1.60671	−	2.05650i	−0.0629237	−	0.0805386i
$653$	2.68811	+	25.5757i	0.105194	+	1.00085i	0.912042	+	0.410096i	$0.134505\pi$
$653$	2.68811	+	25.5757i	0.105194	+	1.00085i	−0.806848	+	0.590759i	$0.798829\pi$
$654$	−38.8098	−	17.2792i	−1.51758	−	0.675672i
$655$	4.37830	−	3.09089i	0.171074	−	0.120771i
$656$	6.77605	+	27.1773i	0.264560	+	1.06109i
$657$	44.2776	+	76.6910i	1.72743	+	2.99200i
$658$	0.800967	−	0.356613i	0.0312249	−	0.0139022i
$659$	−0.620364	−	17.7649i	−0.0241659	−	0.692022i	−0.949664	−	0.313270i	$-0.898576\pi$
$659$	−0.620364	−	17.7649i	−0.0241659	−	0.692022i	0.925498	−	0.378752i	$-0.123647\pi$
$660$	−0.221750	+	0.134405i	−0.00863160	+	0.00523170i
$661$	−2.51920	+	0.354050i	−0.0979854	+	0.0137709i	−0.187995	−	0.982170i	$-0.560199\pi$
$661$	−2.51920	+	0.354050i	−0.0979854	+	0.0137709i	0.0900100	+	0.995941i	$0.471310\pi$
$662$	−1.97434	+	2.52704i	−0.0767348	+	0.0982161i
$663$	4.68360	+	11.5923i	0.181896	+	0.450208i
$664$	9.02716	+	27.7828i	0.350322	+	1.07818i
$665$	14.6662	+	9.17345i	0.568730	+	0.355731i
$666$	19.7136	−	60.6722i	0.763886	−	2.35100i
$667$	7.60830	−	0.532024i	0.294595	−	0.0206001i
$668$	3.75420	+	1.36642i	0.145254	+	0.0528682i
$669$	45.8481	−	44.2750i	1.77259	−	1.71177i
$670$	0.545344	+	2.32135i	0.0210685	+	0.0896817i
$671$	0.310095	−	0.459734i	0.0119711	−	0.0177478i
$672$	1.51981	+	14.4600i	0.0586278	+	0.557806i
$673$	22.6285	−	25.1314i	0.872263	−	0.968746i	−0.127470	−	0.991842i	$-0.540686\pi$
$673$	22.6285	−	25.1314i	0.872263	−	0.968746i	0.999733	+	0.0230962i	$0.00735241\pi$
$674$	−3.44369	−	2.88960i	−0.132646	−	0.111303i
$675$	−23.2577	−	62.4016i	−0.895189	−	2.40184i
$676$	−2.81177	−	4.87013i	−0.108145	−	0.187313i
$677$	−43.6445	−	9.27693i	−1.67740	−	0.356541i	−0.731708	−	0.681618i	$-0.761276\pi$
$677$	−43.6445	−	9.27693i	−1.67740	−	0.356541i	−0.945688	+	0.325077i	$0.894610\pi$
$678$	0.758691	−	1.12480i	0.0291373	−	0.0431979i
$679$	−6.87133	−	6.63556i	−0.263697	−	0.254650i
$680$	13.8829	+	24.8196i	0.532383	+	0.951790i
$681$	29.4697	+	43.6907i	1.12928	+	1.67423i
$682$	0.756230	−	0.634552i	0.0289575	−	0.0242983i
$683$	−8.25663	−	5.99879i	−0.315931	−	0.229537i	0.418506	−	0.908214i	$-0.362554\pi$
$683$	−8.25663	−	5.99879i	−0.315931	−	0.229537i	−0.734437	+	0.678677i	$0.762554\pi$
$684$	−13.1848	+	6.07947i	−0.504134	+	0.232454i
$685$	−18.8111	+	1.05844i	−0.718734	+	0.0404410i
$686$	20.2382	+	12.6462i	0.772697	+	0.482835i
$687$	14.0966	−	18.0428i	0.537819	−	0.688377i
$688$	−6.66206	−	3.54228i	−0.253988	−	0.135048i
$689$	−0.730490	+	0.388408i	−0.0278295	+	0.0147972i
$690$	72.3840	−	31.0544i	2.75561	−	1.18222i
$691$	−29.2410	−	32.4755i	−1.11238	−	1.23542i	−0.969344	−	0.245707i	$-0.920980\pi$
$691$	−29.2410	−	32.4755i	−1.11238	−	1.23542i	−0.143037	−	0.989717i	$-0.545687\pi$
$692$	0.0152103	−	0.144717i	0.000578210	−	0.00550130i
$693$	0.763987	+	0.641062i	0.0290215	+	0.0243519i
$694$	2.60900	+	10.4641i	0.0990362	+	0.397213i
$695$	−10.2439	−	3.88711i	−0.388574	−	0.147446i
$696$	−0.871560	−	8.29234i	−0.0330364	−	0.314320i
$697$	−22.8386	+	33.8596i	−0.865072	+	1.28252i
$698$	2.97692	−	1.58286i	0.112678	−	0.0599120i
$699$	−1.83975	+	10.4337i	−0.0695857	+	0.394640i
$700$	2.15602	−	3.51017i	0.0814898	−	0.132672i
$701$	29.6144	−	24.8495i	1.11852	−	0.938551i	0.119993	−	0.992775i	$-0.461713\pi$
$701$	29.6144	−	24.8495i	1.11852	−	0.938551i	0.998529	+	0.0542232i	$0.0172683\pi$
$702$	−4.80032	−	14.7739i	−0.181176	−	0.557604i
$703$	19.5754	+	24.3867i	0.738300	+	0.919763i
$704$	−0.563545	+	0.409440i	−0.0212394	+	0.0154313i
$705$	2.07199	−	1.94712i	0.0780355	−	0.0733327i
$706$	−2.54864	−	3.77852i	−0.0959194	−	0.142206i
$707$	1.11673	−	6.33327i	0.0419988	−	0.238187i
$708$	−5.22878	+	10.7206i	−0.196510	+	0.402905i
$709$	−1.65606	−	47.4232i	−0.0621945	−	1.78102i	−0.484724	−	0.874667i	$-0.661080\pi$
$709$	−1.65606	−	47.4232i	−0.0621945	−	1.78102i	0.422529	−	0.906349i	$-0.361142\pi$
$710$	25.4718	+	25.2765i	0.955940	+	0.948612i
$711$	40.8853	−	45.4077i	1.53332	−	1.70292i
$712$	3.00320	−	1.87661i	0.112550	−	0.0703289i
$713$	76.8642	−	48.0301i	2.87859	−	1.79874i
$714$	19.5517	−	21.7144i	0.731705	−	0.812641i
$715$	0.162873	+	0.0251546i	0.00609112	+	0.000940728i
$716$	0.118850	+	3.40342i	0.00444164	+	0.127192i
$717$	−18.3250	+	37.5718i	−0.684359	+	1.40314i
$718$	4.57844	−	25.9656i	0.170866	−	0.969029i
$719$	3.59427	+	5.32872i	0.134044	+	0.198728i	0.890083	−	0.455798i	$-0.150646\pi$
$719$	3.59427	+	5.32872i	0.134044	+	0.198728i	−0.756040	+	0.654526i	$0.772868\pi$
$720$	−19.5261	−	41.4567i	−0.727696	−	1.54500i
$721$	−28.1697	+	20.4665i	−1.04909	+	0.762212i
$722$	−3.47688	+	23.2880i	−0.129396	+	0.866691i
$723$	21.9304	+	67.4950i	0.815602	+	2.51016i
$724$	−2.06600	+	1.73358i	−0.0767825	+	0.0644281i
$725$	−2.23990	+	3.64674i	−0.0831878	+	0.135437i
$726$	7.54679	−	42.8000i	0.280088	−	1.58846i
$727$	−23.8795	+	12.6969i	−0.885641	+	0.470904i	−0.848981	−	0.528424i	$-0.822783\pi$
$727$	−23.8795	+	12.6969i	−0.885641	+	0.470904i	−0.0366605	+	0.999328i	$0.511672\pi$
$728$	2.85240	−	4.22886i	0.105717	−	0.156732i
$729$	−2.39757	−	22.8114i	−0.0887990	−	0.844866i
$730$	1.65844	−	34.1593i	0.0613816	−	1.26429i
$731$	−2.66167	−	10.6754i	−0.0984454	−	0.394843i
$732$	−8.03233	−	6.73993i	−0.296883	−	0.249115i
$733$	−1.58786	+	15.1075i	−0.0586491	+	0.558009i	0.925259	+	0.379335i	$0.123847\pi$
$733$	−1.58786	+	15.1075i	−0.0586491	+	0.558009i	−0.983908	+	0.178674i	$0.942819\pi$
$734$	−3.99788	−	4.44009i	−0.147564	−	0.163887i
$735$	26.7811	+	6.07446i	0.987835	+	0.224060i
$736$	−20.2051	+	10.7433i	−0.744771	+	0.396002i
$737$	−0.0595009	−	0.0316372i	−0.00219174	−	0.00116537i
$738$	53.6886	−	68.7182i	1.97630	−	2.52955i
$739$	31.1654	+	19.4743i	1.14644	+	0.716374i	0.963753	−	0.266797i	$-0.0859654\pi$
$739$	31.1654	+	19.4743i	1.14644	+	0.716374i	0.182686	+	0.983171i	$0.441521\pi$
$740$	5.76918	−	4.70866i	0.212079	−	0.173094i
$741$	12.6253	+	3.44106i	0.463804	+	0.126410i
$742$	1.56425	+	1.13650i	0.0574255	+	0.0417221i
$743$	−20.8669	+	17.5094i	−0.765531	+	0.642357i	−0.939560	−	0.342384i	$-0.888766\pi$
$743$	−20.8669	+	17.5094i	−0.765531	+	0.642357i	0.174029	+	0.984741i	$0.444321\pi$
$744$	−55.4091	−	82.1474i	−2.03140	−	3.01167i
$745$	−27.7601	+	5.50695i	−1.01705	+	0.201759i
$746$	12.6930	+	12.2575i	0.464726	+	0.448780i
$747$	38.3824	−	56.9042i	1.40434	−	2.08202i
$748$	−0.148091	−	0.0314777i	−0.00541474	−	0.00115094i
$749$	1.61084	+	2.79006i	0.0588588	+	0.101946i
$750$	−9.44448	+	43.1765i	−0.344864	+	1.57658i
$751$	15.5069	+	13.0119i	0.565856	+	0.474809i	0.880268	−	0.474477i	$-0.157363\pi$
$751$	15.5069	+	13.0119i	0.565856	+	0.474809i	−0.314412	+	0.949287i	$0.601807\pi$
$752$	0.761810	−	0.846076i	0.0277804	−	0.0308532i
$753$	−5.62813	−	53.5480i	−0.205100	−	1.95140i
$754$	−0.558242	+	0.827628i	−0.0203300	+	0.0301404i
$755$	−23.9032	+	14.4880i	−0.869926	+	0.527271i
$756$	7.89355	−	7.62271i	0.287086	−	0.277235i
$757$	6.20241	+	2.25749i	0.225430	+	0.0820500i	0.452266	−	0.891883i	$-0.350616\pi$
$757$	6.20241	+	2.25749i	0.225430	+	0.0820500i	−0.226836	+	0.973933i	$0.572838\pi$
$758$	−36.6304	+	2.56145i	−1.33048	+	0.0930360i
$759$	−0.687850	+	2.11698i	−0.0249674	+	0.0768417i
$760$	29.4735	+	4.15549i	1.06911	+	0.150735i
$761$	−15.0316	−	46.2624i	−0.544894	−	1.67701i	−0.721242	−	0.692683i	$-0.756429\pi$
$761$	−15.0316	−	46.2624i	−0.544894	−	1.67701i	0.176349	−	0.984328i	$-0.443571\pi$
$762$	−17.6074	−	43.5799i	−0.637849	−	1.57873i
$763$	−11.7427	+	15.0299i	−0.425113	+	0.544120i
$764$	1.64267	−	0.230862i	0.0594298	−	0.00835231i
$765$	25.8719	−	61.6083i	0.935399	−	2.22745i
$766$	−0.246688	−	7.06423i	−0.00891321	−	0.255241i
$767$	6.92551	−	3.08344i	0.250066	−	0.111336i
$768$	16.7379	+	28.9909i	0.603978	+	1.04612i
$769$	−3.36562	−	13.4988i	−0.121367	−	0.486778i	−0.999958	−	0.00920154i	$-0.997071\pi$
$769$	−3.36562	−	13.4988i	−0.121367	−	0.486778i	0.878590	−	0.477576i	$-0.158485\pi$
$770$	−0.114026	−	0.367892i	−0.00410920

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.05096 - 0.656713i) q^{2} +(3.06632 - 0.879252i) q^{3} +(-0.203496 - 0.417228i) q^{4} +(1.91224 - 1.15903i) q^{5} +(-3.79999 - 1.08963i) q^{6} +(-0.887411 + 1.53704i) q^{7} +(-0.319211 + 3.03709i) q^{8} +(6.08506 - 3.80237i) q^{9} +O(q^{10})\)	\(q+(-1.05096 - 0.656713i) q^{2} +(3.06632 - 0.879252i) q^{3} +(-0.203496 - 0.417228i) q^{4} +(1.91224 - 1.15903i) q^{5} +(-3.79999 - 1.08963i) q^{6} +(-0.887411 + 1.53704i) q^{7} +(-0.319211 + 3.03709i) q^{8} +(6.08506 - 3.80237i) q^{9} +(-2.77084 - 0.0377008i) q^{10} +(0.0524015 - 0.0581978i) q^{11} +(-0.990830 - 1.10043i) q^{12} +(0.0328451 + 0.940560i) q^{13} +(1.94203 - 1.03260i) q^{14} +(4.84445 - 5.23528i) q^{15} +(1.75839 - 2.25063i) q^{16} +(4.15450 - 0.290511i) q^{17} -8.89223 q^{18} +(2.38968 - 3.64546i) q^{19} +(-0.872710 - 0.561982i) q^{20} +(-1.36964 + 5.49331i) q^{21} +(-0.0932912 + 0.0267508i) q^{22} +(-8.82381 + 1.24011i) q^{23} +(1.69157 + 9.59335i) q^{24} +(2.31331 - 4.43267i) q^{25} +(0.583159 - 1.01006i) q^{26} +(8.91213 - 9.89793i) q^{27} +(0.821880 + 0.0574714i) q^{28} +(-0.853856 - 0.0597074i) q^{29} +(-8.52941 + 2.32066i) q^{30} +(-9.29246 + 4.13727i) q^{31} +(2.41329 - 0.878365i) q^{32} +(0.109509 - 0.224527i) q^{33} +(-4.55700 - 2.42300i) q^{34} +(0.0845297 + 3.96772i) q^{35} +(-2.82474 - 1.76509i) q^{36} +(-2.21694 + 6.82305i) q^{37} +(-4.90549 + 2.26190i) q^{38} +(0.927702 + 2.85517i) q^{39} +(2.90966 + 6.17762i) q^{40} +(-6.03769 + 7.72789i) q^{41} +(5.04696 - 4.87380i) q^{42} +(-0.458745 - 2.60167i) q^{43} +(-0.0349452 - 0.0100204i) q^{44} +(7.22905 - 14.3238i) q^{45} +(10.0879 + 4.49141i) q^{46} +(0.397653 + 0.0278066i) q^{47} +(3.41290 - 8.44722i) q^{48} +(1.92500 + 3.33421i) q^{49} +(-5.34220 + 3.13938i) q^{50} +(12.4836 - 4.54365i) q^{51} +(0.385744 - 0.205104i) q^{52} +(0.385363 + 0.790112i) q^{53} +(-15.8664 + 4.54962i) q^{54} +(0.0327514 - 0.172023i) q^{55} +(-4.38486 - 3.18579i) q^{56} +(4.12224 - 13.2793i) q^{57} +(0.858159 + 0.623489i) q^{58} +(-3.01749 - 7.46855i) q^{59} +(-3.17013 - 0.955883i) q^{60} +(7.01217 - 0.985496i) q^{61} +(12.4830 + 1.75437i) q^{62} +(0.444445 + 12.7273i) q^{63} +(-8.70047 - 1.84934i) q^{64} +(1.15294 + 1.76051i) q^{65} +(-0.262540 + 0.164053i) q^{66} +(-0.208176 - 0.834948i) q^{67} +(-0.966632 - 1.67426i) q^{68} +(-25.9662 + 11.5609i) q^{69} +(2.51682 - 4.22543i) q^{70} +(-9.31522 - 8.99560i) q^{71} +(9.60573 + 19.6947i) q^{72} +(-0.430714 + 12.3340i) q^{73} +(6.81071 - 5.71487i) q^{74} +(3.19592 - 15.6260i) q^{75} +(-2.00728 - 0.255207i) q^{76} +(0.0429507 + 0.132189i) q^{77} +(0.900052 - 3.60991i) q^{78} +(8.18566 - 2.34720i) q^{79} +(0.753912 - 6.34176i) q^{80} +(9.18821 - 18.8386i) q^{81} +(11.4204 - 4.15668i) q^{82} +(8.73888 - 3.89080i) q^{83} +(2.57068 - 0.546414i) q^{84} +(7.60769 - 5.37070i) q^{85} +(-1.22643 + 3.03552i) q^{86} +(-2.67069 + 0.567673i) q^{87} +(0.160025 + 0.177726i) q^{88} +(-0.713941 - 0.913803i) q^{89} +(-17.0041 + 10.3063i) q^{90} +(-1.47483 - 0.784179i) q^{91} +(2.31301 + 3.42918i) q^{92} +(-24.8559 + 20.8566i) q^{93} +(-0.399657 - 0.290368i) q^{94} +(0.344457 - 9.74071i) q^{95} +(6.62760 - 4.81523i) q^{96} +(-1.30205 + 5.22223i) q^{97} +(0.166513 - 4.76830i) q^{98} +(0.0975771 - 0.553387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

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