LMFDB - Embedded newform 475.2.bc.a.6.17

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			6.17
Character	$\chi$	$=$	475.6
Dual form			475.2.bc.a.396.17

$q$-expansion

$f(q)$	$=$	$q+(-0.918651 - 0.574037i) q^{2} +(-1.08630 + 0.311492i) q^{3} +(-0.362341 - 0.742910i) q^{4} +(-0.569939 - 2.16221i) q^{5} +(1.17674 + 0.337424i) q^{6} +(-1.35582 + 2.34835i) q^{7} +(-0.320054 + 3.04511i) q^{8} +(-1.46112 + 0.913011i) q^{9} +O(q^{10})$	\(q+(-0.918651 - 0.574037i) q^{2} +(-1.08630 + 0.311492i) q^{3} +(-0.362341 - 0.742910i) q^{4} +(-0.569939 - 2.16221i) q^{5} +(1.17674 + 0.337424i) q^{6} +(-1.35582 + 2.34835i) q^{7} +(-0.320054 + 3.04511i) q^{8} +(-1.46112 + 0.913011i) q^{9} +(-0.717615 + 2.31348i) q^{10} +(0.234143 - 0.260042i) q^{11} +(0.625022 + 0.694157i) q^{12} +(0.0306491 + 0.877676i) q^{13} +(2.59356 - 1.37902i) q^{14} +(1.29264 + 2.17128i) q^{15} +(1.02426 - 1.31099i) q^{16} +(5.64801 - 0.394948i) q^{17} +1.86636 q^{18} +(4.32744 - 0.522754i) q^{19} +(-1.39982 + 1.20687i) q^{20} +(0.741336 - 2.97334i) q^{21} +(-0.364369 + 0.104481i) q^{22} +(-4.73422 + 0.665352i) q^{23} +(-0.600851 - 3.40760i) q^{24} +(-4.35034 + 2.46466i) q^{25} +(0.475662 - 0.823871i) q^{26} +(3.57133 - 3.96637i) q^{27} +(2.23588 + 0.156348i) q^{28} +(-3.35920 - 0.234898i) q^{29} +(0.0589145 - 2.73667i) q^{30} +(8.11144 - 3.61145i) q^{31} +(4.06097 - 1.47807i) q^{32} +(-0.173348 + 0.355417i) q^{33} +(-5.41527 - 2.87935i) q^{34} +(5.85036 + 1.59316i) q^{35} +(1.20771 + 0.754662i) q^{36} +(-2.08017 + 6.40210i) q^{37} +(-4.27548 - 2.00388i) q^{38} +(-0.306683 - 0.943873i) q^{39} +(6.76659 - 1.04350i) q^{40} +(3.28618 - 4.20612i) q^{41} +(-2.38783 + 2.30590i) q^{42} +(2.07113 + 11.7459i) q^{43} +(-0.278027 - 0.0797231i) q^{44} +(2.80688 + 2.63890i) q^{45} +(4.73103 + 2.10639i) q^{46} +(13.0163 + 0.910185i) q^{47} +(-0.704287 + 1.74317i) q^{48} +(-0.176490 - 0.305690i) q^{49} +(5.41125 + 0.233093i) q^{50} +(-6.01241 + 2.18834i) q^{51} +(0.640929 - 0.340788i) q^{52} +(1.97642 + 4.05225i) q^{53} +(-5.55764 + 1.59363i) q^{54} +(-0.695713 - 0.358059i) q^{55} +(-6.71704 - 4.88021i) q^{56} +(-4.53806 + 1.91583i) q^{57} +(2.95109 + 2.14409i) q^{58} +(0.641277 + 1.58722i) q^{59} +(1.14469 - 1.74706i) q^{60} +(-15.2276 + 2.14010i) q^{61} +(-9.52468 - 1.33861i) q^{62} +(-0.163049 - 4.66910i) q^{63} +(-7.83370 - 1.66510i) q^{64} +(1.88026 - 0.566492i) q^{65} +(0.363269 - 0.226996i) q^{66} +(1.09333 + 4.38511i) q^{67} +(-2.33992 - 4.05286i) q^{68} +(4.93553 - 2.19744i) q^{69} +(-4.45991 - 4.82188i) q^{70} +(9.87156 + 9.53285i) q^{71} +(-2.31258 - 4.74149i) q^{72} +(-0.239648 + 6.86261i) q^{73} +(5.58598 - 4.68720i) q^{74} +(3.95805 - 4.03245i) q^{75} +(-1.95637 - 3.02548i) q^{76} +(0.293213 + 0.902418i) q^{77} +(-0.260083 + 1.04314i) q^{78} +(-4.86932 + 1.39626i) q^{79} +(-3.41840 - 1.46748i) q^{80} +(-0.378206 + 0.775437i) q^{81} +(-5.43332 + 1.97757i) q^{82} +(0.0608704 - 0.0271012i) q^{83} +(-2.47754 + 0.526617i) q^{84} +(-4.07298 - 11.9871i) q^{85} +(4.83996 - 11.9793i) q^{86} +(3.72226 - 0.791192i) q^{87} +(0.716918 + 0.796218i) q^{88} +(-2.32289 - 2.97316i) q^{89} +(-1.06371 - 4.03548i) q^{90} +(-2.10264 - 1.11800i) q^{91} +(2.20970 + 3.27602i) q^{92} +(-7.68652 + 6.44976i) q^{93} +(-11.4349 - 8.30795i) q^{94} +(-3.59668 - 9.05891i) q^{95} +(-3.95102 + 2.87059i) q^{96} +(0.348191 - 1.39652i) q^{97} +(-0.0133444 + 0.382134i) q^{98} +(-0.104690 + 0.593728i) 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 $

$2$	−0.918651	−	0.574037i	−0.649584	−	0.405905i	0.164723	−	0.986340i	$-0.447327\pi$
$2$	−0.918651	−	0.574037i	−0.649584	−	0.405905i	−0.814307	+	0.580435i	$0.802883\pi$
$3$	−1.08630	+	0.311492i	−0.627176	+	0.179840i	−0.574146	−	0.818753i	$-0.694666\pi$
$3$	−1.08630	+	0.311492i	−0.627176	+	0.179840i	−0.0530300	+	0.998593i	$0.516888\pi$
$4$	−0.362341	−	0.742910i	−0.181171	−	0.371455i
$5$	−0.569939	−	2.16221i	−0.254884	−	0.966972i
$5$	−0.569939	−	2.16221i	−0.254884	−	0.966972i
$6$	1.17674	+	0.337424i	0.480401	+	0.137753i
$7$	−1.35582	+	2.34835i	−0.512451	+	0.887592i	0.487444	+	0.873154i	$0.337929\pi$
$7$	−1.35582	+	2.34835i	−0.512451	+	0.887592i	−0.999896	+	0.0144378i	$0.995404\pi$
$8$	−0.320054	+	3.04511i	−0.113156	+	1.07661i
$9$	−1.46112	+	0.913011i	−0.487041	+	0.304337i
$10$	−0.717615	+	2.31348i	−0.226930	+	0.731588i
$11$	0.234143	−	0.260042i	0.0705967	−	0.0784056i	−0.706812	−	0.707402i	$-0.749867\pi$
$11$	0.234143	−	0.260042i	0.0705967	−	0.0784056i	0.777408	+	0.628996i	$0.216534\pi$
$12$	0.625022	+	0.694157i	0.180428	+	0.200386i
$13$	0.0306491	+	0.877676i	0.00850054	+	0.243424i	0.996202	+	0.0870721i	$0.0277510\pi$
$13$	0.0306491	+	0.877676i	0.00850054	+	0.243424i	−0.987701	+	0.156352i	$0.950027\pi$
$14$	2.59356	−	1.37902i	0.693158	−	0.368559i
$15$	1.29264	+	2.17128i	0.333757	+	0.560623i
$16$	1.02426	−	1.31099i	0.256064	−	0.327747i
$17$	5.64801	−	0.394948i	1.36984	−	0.0957889i	0.634207	−	0.773164i	$-0.281327\pi$
$17$	5.64801	−	0.394948i	1.36984	−	0.0957889i	0.735638	+	0.677375i	$0.236882\pi$
$18$	1.86636			0.439906
$19$	4.32744	−	0.522754i	0.992783	−	0.119928i
$19$	4.32744	−	0.522754i	0.992783	−	0.119928i
$20$	−1.39982	+	1.20687i	−0.313009	+	0.269865i
$21$	0.741336	−	2.97334i	0.161773	−	0.648835i
$22$	−0.364369	+	0.104481i	−0.0776837	+	0.0222754i
$23$	−4.73422	+	0.665352i	−0.987154	+	0.138735i	−0.614230	−	0.789127i	$-0.710533\pi$
$23$	−4.73422	+	0.665352i	−0.987154	+	0.138735i	−0.372923	+	0.927862i	$0.621645\pi$
$24$	−0.600851	−	3.40760i	−0.122648	−	0.695573i
$25$	−4.35034	+	2.46466i	−0.870068	+	0.492932i
$26$	0.475662	−	0.823871i	0.0932851	−	0.161574i
$27$	3.57133	−	3.96637i	0.687303	−	0.763327i
$28$	2.23588	+	0.156348i	0.422542	+	0.0295470i
$29$	−3.35920	−	0.234898i	−0.623787	−	0.0436194i	−0.245634	−	0.969363i	$-0.578996\pi$
$29$	−3.35920	−	0.234898i	−0.623787	−	0.0436194i	−0.378153	+	0.925743i	$0.623441\pi$
$30$	0.0589145	−	2.73667i	0.0107563	−	0.499645i
$31$	8.11144	−	3.61145i	1.45686	−	0.648635i	0.482964	−	0.875640i	$-0.339560\pi$
$31$	8.11144	−	3.61145i	1.45686	−	0.648635i	0.973893	+	0.227005i	$0.0728935\pi$
$32$	4.06097	−	1.47807i	0.717885	−	0.261289i
$33$	−0.173348	+	0.355417i	−0.0301761	+	0.0618701i
$34$	−5.41527	−	2.87935i	−0.928710	−	0.493804i
$35$	5.85036	+	1.59316i	0.988892	+	0.269293i
$36$	1.20771	+	0.754662i	0.201285	+	0.125777i
$37$	−2.08017	+	6.40210i	−0.341977	+	1.05250i	0.621205	+	0.783648i	$0.286644\pi$
$37$	−2.08017	+	6.40210i	−0.341977	+	1.05250i	−0.963182	+	0.268850i	$0.913356\pi$
$38$	−4.27548	−	2.00388i	−0.693575	−	0.325072i
$39$	−0.306683	−	0.943873i	−0.0491086	−	0.151141i
$40$	6.76659	−	1.04350i	1.06989	−	0.164992i
$41$	3.28618	−	4.20612i	0.513215	−	0.656886i	−0.459693	−	0.888078i	$-0.652040\pi$
$41$	3.28618	−	4.20612i	0.513215	−	0.656886i	0.972908	+	0.231192i	$0.0742627\pi$
$42$	−2.38783	+	2.30590i	−0.368450	+	0.355808i
$43$	2.07113	+	11.7459i	0.315844	+	1.79124i	0.567449	+	0.823409i	$0.307930\pi$
$43$	2.07113	+	11.7459i	0.315844	+	1.79124i	−0.251605	+	0.967830i	$0.580958\pi$
$44$	−0.278027	−	0.0797231i	−0.0419142	−	0.0120187i
$45$	2.80688	+	2.63890i	0.418425	+	0.393384i
$46$	4.73103	+	2.10639i	0.697553	+	0.310570i
$47$	13.0163	+	0.910185i	1.89862	+	0.132764i	0.970741	−	0.240127i	$-0.0771892\pi$
$47$	13.0163	+	0.910185i	1.89862	+	0.132764i	0.927875	+	0.372892i	$0.121634\pi$
$48$	−0.704287	+	1.74317i	−0.101655	+	0.251605i
$49$	−0.176490	−	0.305690i	−0.0252129	−	0.0436700i
$50$	5.41125	+	0.233093i	0.765266	+	0.0329643i
$51$	−6.01241	+	2.18834i	−0.841906	+	0.306429i
$52$	0.640929	−	0.340788i	0.0888809	−	0.0472588i
$53$	1.97642	+	4.05225i	0.271482	+	0.556620i	0.990360	−	0.138516i	$-0.0442332\pi$
$53$	1.97642	+	4.05225i	0.271482	+	0.556620i	−0.718879	+	0.695136i	$0.755344\pi$
$54$	−5.55764	+	1.59363i	−0.756300	+	0.216865i
$55$	−0.695713	−	0.358059i	−0.0938099	−	0.0482806i
$56$	−6.71704	−	4.88021i	−0.897602	−	0.652146i
$57$	−4.53806	+	1.91583i	−0.601081	+	0.253758i
$58$	2.95109	+	2.14409i	0.387497	+	0.281533i
$59$	0.641277	+	1.58722i	0.0834871	+	0.206638i	0.963153	−	0.268955i	$-0.0866782\pi$
$59$	0.641277	+	1.58722i	0.0834871	+	0.206638i	−0.879666	+	0.475592i	$0.842234\pi$
$60$	1.14469	−	1.74706i	0.147779	−	0.225544i
$61$	−15.2276	+	2.14010i	−1.94970	+	0.274012i	−0.999313	−	0.0370670i	$-0.988199\pi$
$61$	−15.2276	+	2.14010i	−1.94970	+	0.274012i	−0.950384	+	0.311079i	$0.899310\pi$
$62$	−9.52468	−	1.33861i	−1.20964	−	0.170003i
$63$	−0.163049	−	4.66910i	−0.0205422	−	0.588252i
$64$	−7.83370	−	1.66510i	−0.979213	−	0.208138i
$65$	1.88026	−	0.566492i	0.233217	−	0.0702647i
$66$	0.363269	−	0.226996i	0.0447153	−	0.0279412i
$67$	1.09333	+	4.38511i	0.133572	+	0.535726i	0.999375	+	0.0353425i	$0.0112522\pi$
$67$	1.09333	+	4.38511i	0.133572	+	0.535726i	−0.865804	+	0.500384i	$0.833192\pi$
$68$	−2.33992	−	4.05286i	−0.283757	−	0.491482i
$69$	4.93553	−	2.19744i	0.594169	−	0.264541i
$70$	−4.45991	−	4.82188i	−0.533061	−	0.576324i
$71$	9.87156	+	9.53285i	1.17154	+	1.13134i	0.988965	+	0.148149i	$0.0473315\pi$
$71$	9.87156	+	9.53285i	1.17154	+	1.13134i	0.182573	+	0.983192i	$0.441557\pi$
$72$	−2.31258	−	4.74149i	−0.272540	−	0.558790i
$73$	−0.239648	+	6.86261i	−0.0280487	+	0.803208i	0.901124	+	0.433562i	$0.142743\pi$
$73$	−0.239648	+	6.86261i	−0.0280487	+	0.803208i	−0.929172	+	0.369646i	$0.879479\pi$
$74$	5.58598	−	4.68720i	0.649357	−	0.544876i
$75$	3.95805	−	4.03245i	0.457037	−	0.465628i
$76$	−1.95637	−	3.02548i	−0.224411	−	0.347047i
$77$	0.293213	+	0.902418i	0.0334148	+	0.102840i
$78$	−0.260083	+	1.04314i	−0.0294486	+	0.118112i
$79$	−4.86932	+	1.39626i	−0.547842	+	0.157091i	−0.538130	−	0.842862i	$-0.680869\pi$
$79$	−4.86932	+	1.39626i	−0.547842	+	0.157091i	−0.00971156	+	0.999953i	$0.503091\pi$
$80$	−3.41840	−	1.46748i	−0.382188	−	0.164069i
$81$	−0.378206	+	0.775437i	−0.0420229	+	0.0861596i
$82$	−5.43332	+	1.97757i	−0.600010	+	0.218386i
$83$	0.0608704	−	0.0271012i	0.00668139	−	0.00297475i	−0.403393	−	0.915027i	$-0.632169\pi$
$83$	0.0608704	−	0.0271012i	0.00668139	−	0.00297475i	0.410075	+	0.912052i	$0.365503\pi$
$84$	−2.47754	+	0.526617i	−0.270322	+	0.0574586i
$85$	−4.07298	−	11.9871i	−0.441777	−	1.30019i
$86$	4.83996	−	11.9793i	0.521906	−	1.29176i
$87$	3.72226	−	0.791192i	0.399069	−	0.0848247i
$88$	0.716918	+	0.796218i	0.0764237	+	0.0848771i
$89$	−2.32289	−	2.97316i	−0.246226	−	0.315154i	0.648982	−	0.760804i	$-0.275195\pi$
$89$	−2.32289	−	2.97316i	−0.246226	−	0.315154i	−0.895208	+	0.445649i	$0.852973\pi$
$90$	−1.06371	−	4.03548i	−0.112125	−	0.425377i
$91$	−2.10264	−	1.11800i	−0.220417	−	0.117198i
$92$	2.20970	+	3.27602i	0.230377	+	0.341548i
$93$	−7.68652	+	6.44976i	−0.797055	+	0.668809i
$94$	−11.4349	−	8.30795i	−1.17942	−	0.856900i
$95$	−3.59668	−	9.05891i	−0.369012	−	0.929425i
$96$	−3.95102	+	2.87059i	−0.403250	+	0.292978i
$97$	0.348191	−	1.39652i	0.0353534	−	0.141795i	−0.950025	−	0.312173i	$-0.898943\pi$
$97$	0.348191	−	1.39652i	0.0353534	−	0.141795i	0.985379	+	0.170378i	$0.0544988\pi$
$98$	−0.0133444	+	0.382134i	−0.00134799	+	0.0386014i
$99$	−0.104690	+	0.593728i	−0.0105218	+	0.0596719i
$100$	3.40733	+	2.33886i	0.340733	+	0.233886i
$101$	−2.35373	+	0.856688i	−0.234205	+	0.0852436i	−0.456456	−	0.889746i	$-0.650882\pi$
$101$	−2.35373	+	0.856688i	−0.234205	+	0.0852436i	0.222252	+	0.974989i	$0.428659\pi$
$102$	6.77950	+	1.44103i	0.671270	+	0.142683i
$103$	−11.0088	−	4.90145i	−1.08473	−	0.482955i	−0.215070	−	0.976599i	$-0.568998\pi$
$103$	−11.0088	−	4.90145i	−1.08473	−	0.482955i	−0.869664	+	0.493644i	$0.835665\pi$
$104$	−2.68243	−	0.187574i	−0.263034	−	0.0183931i
$105$	−6.85150	+	0.0916929i	−0.668638	+	0.00894831i
$106$	0.510506	−	4.85714i	0.0495847	−	0.471767i
$107$	−0.433806	+	0.751375i	−0.0419376	+	0.0726381i	−0.886232	−	0.463241i	$-0.846686\pi$
$107$	−0.433806	+	0.751375i	−0.0419376	+	0.0726381i	0.844295	+	0.535879i	$0.180020\pi$
$108$	−4.24069	−	1.21600i	−0.408061	−	0.117010i
$109$	−3.70892	−	0.521254i	−0.355250	−	0.0499271i	−0.0407090	−	0.999171i	$-0.512962\pi$
$109$	−3.70892	−	0.521254i	−0.355250	−	0.0499271i	−0.314541	+	0.949244i	$0.601851\pi$
$110$	0.433578	+	0.728296i	0.0413401	+	0.0694403i
$111$	0.265487	−	7.60255i	0.0251989	−	0.721602i
$112$	1.68995	+	4.18277i	0.159685	+	0.395234i
$113$	2.73392	−	8.41414i	0.257185	−	0.791535i	−0.736206	−	0.676758i	$-0.763384\pi$
$113$	2.73392	−	8.41414i	0.257185	−	0.791535i	0.993391	−	0.114778i	$-0.0366156\pi$
$114$	5.26865	+	0.845038i	0.493454	+	0.0791451i
$115$	4.13685	+	9.85719i	0.385763	+	0.919188i
$116$	1.04267	+	2.58069i	0.0968093	+	0.239611i
$117$	−0.846111	−	1.25441i	−0.0782229	−	0.115970i
$118$	0.322011	−	1.82621i	0.0296435	−	0.168116i
$119$	−6.73021	+	13.7990i	−0.616957	+	1.26495i
$120$	−7.02550	+	3.24129i	−0.641338	+	0.295888i
$121$	1.13701	+	10.8180i	0.103365	+	0.983452i
$122$	15.2174	+	6.77520i	1.37771	+	0.613398i
$123$	−2.25961	+	5.59273i	−0.203742	+	0.504279i
$124$	−5.62209	−	4.71749i	−0.504879	−	0.423643i
$125$	7.80855	+	8.00166i	0.698418	+	0.715690i
$126$	−2.53045	+	4.38287i	−0.225431	+	0.390457i
$127$	−9.95591	−	12.7430i	−0.883444	−	1.13076i	−0.990637	−	0.136519i	$-0.956409\pi$
$127$	−9.95591	−	12.7430i	−0.883444	−	1.13076i	0.107193	−	0.994238i	$-0.465814\pi$
$128$	0.0232146	+	0.0224181i	0.00205190	+	0.00198150i
$129$	−5.90862	−	12.1145i	−0.520225	−	1.06662i
$130$	−2.05248	−	0.558928i	−0.180015	−	0.0490212i
$131$	12.0316	−	0.841329i	1.05120	−	0.0735072i	0.466313	−	0.884620i	$-0.345582\pi$
$131$	12.0316	−	0.841329i	1.05120	−	0.0735072i	0.584890	+	0.811113i	$0.301138\pi$
$132$	0.326854			0.0284490
$133$	−4.63962	+	10.8711i	−0.402306	+	0.942643i
$134$	1.51282	−	4.65599i	0.130688	−	0.402217i
$135$	−10.6116	−	5.46140i	−0.913299	−	0.470042i
$136$	−0.605010	+	17.3252i	−0.0518792	+	1.48563i
$137$	8.05250	+	4.28159i	0.687972	+	0.365801i	0.776364	−	0.630285i	$-0.217062\pi$
$137$	8.05250	+	4.28159i	0.687972	+	0.365801i	−0.0883925	+	0.996086i	$0.528173\pi$
$138$	−5.79544	−	0.814496i	−0.493341	−	0.0693345i
$139$	11.4829	+	14.6974i	0.973964	+	1.24662i	0.969110	+	0.246629i	$0.0793230\pi$
$139$	11.4829	+	14.6974i	0.973964	+	1.24662i	0.00485436	+	0.999988i	$0.498455\pi$
$140$	−0.936258	−	4.92356i	−0.0791282	−	0.416117i
$141$	−14.4231	+	3.06572i	−1.21464	+	0.258180i
$142$	−3.59630	−	14.4240i	−0.301795	−	1.21043i
$143$	0.235409	+	0.197531i	0.0196859	+	0.0165184i
$144$	−0.299618	+	2.85067i	−0.0249681	+	0.237556i
$145$	1.40664	+	7.39718i	0.116815	+	0.614302i
$146$	4.15954	−	6.16678i	0.344246	−	0.510366i
$147$	0.286941	+	0.277096i	0.0236665	+	0.0228545i
$148$	5.50991	−	0.774368i	0.452912	−	0.0636526i
$149$	−6.98703	−	2.54307i	−0.572400	−	0.208336i	0.0395713	−	0.999217i	$-0.487401\pi$
$149$	−6.98703	−	2.54307i	−0.572400	−	0.208336i	−0.611971	+	0.790880i	$0.709623\pi$
$150$	−5.95084	+	1.43235i	−0.485884	+	0.116951i
$151$	22.1931			1.80605			0.903025	−	0.429589i	$-0.141341\pi$
$151$	22.1931			1.80605			0.903025	+	0.429589i	$0.141341\pi$
$152$	0.206829	+	13.3448i	0.0167760	+	1.08241i
$153$	−7.89185	+	5.73377i	−0.638019	+	0.463548i
$154$	0.248660	−	0.997322i	0.0200376	−	0.0803665i
$155$	−12.4317	−	15.4804i	−0.998542	−	1.24341i
$156$	−0.590089	+	0.569842i	−0.0472449	+	0.0456239i
$157$	3.44780	+	19.5535i	0.275165	+	1.56054i	0.738438	+	0.674321i	$0.235564\pi$
$157$	3.44780	+	19.5535i	0.275165	+	1.56054i	−0.463274	+	0.886215i	$0.653325\pi$
$158$	5.27471	+	1.51250i	0.419633	+	0.120328i
$159$	−3.40922	−	3.78633i	−0.270369	−	0.300275i
$160$	−5.51041	−	7.93828i	−0.435636	−	0.627576i
$161$	4.85627	−	12.0197i	0.382728	−	0.947285i
$162$	0.792568	−	0.495251i	0.0622700	−	0.0389106i
$163$	−15.6333	+	3.32297i	−1.22450	+	0.260275i	−0.774396	−	0.632702i	$-0.781946\pi$
$163$	−15.6333	+	3.32297i	−1.22450	+	0.260275i	−0.450103	+	0.892977i	$0.648613\pi$
$164$	−4.31549	−	0.917286i	−0.336983	−	0.0716280i
$165$	0.867285	+	0.172250i	0.0675181	+	0.0134097i
$166$	−0.0714757	−	0.0100453i	−0.00554759	−	0.000779663i
$167$	−11.0720	+	10.6921i	−0.856776	+	0.827379i	−0.986430	−	0.164180i	$-0.947502\pi$
$167$	−11.0720	+	10.6921i	−0.856776	+	0.827379i	0.129654	+	0.991559i	$0.458613\pi$
$168$	8.81687	+	3.20908i	0.680236	+	0.247586i
$169$	12.1990	−	0.853034i	0.938381	−	0.0656180i
$170$	−3.13940	+	13.3500i	−0.240781	+	1.02390i
$171$	−5.84564	+	4.71481i	−0.447027	+	0.360550i
$172$	7.97572	−	5.79470i	0.608143	−	0.441842i
$173$	0.360195	+	0.225075i	0.0273851	+	0.0171121i	0.543543	−	0.839381i	$-0.317083\pi$
$173$	0.360195	+	0.225075i	0.0273851	+	0.0171121i	−0.516158	+	0.856494i	$0.672638\pi$
$174$	−3.87363	−	1.40989i	−0.293659	−	0.106883i
$175$	0.110395	−	13.5577i	0.00834508	−	1.02487i
$176$	−0.101090	−	0.573307i	−0.00761991	−	0.0432147i
$177$	−1.19102	−	1.52444i	−0.0895228	−	0.114584i
$178$	0.427219	+	4.06472i	0.0320214	+	0.304664i
$179$	14.1310	+	6.29152i	1.05620	+	0.470250i	0.859990	−	0.510312i	$-0.170470\pi$
$179$	14.1310	+	6.29152i	1.05620	+	0.470250i	0.196210	+	0.980562i	$0.437137\pi$
$180$	0.943418	−	3.04144i	0.0703183	−	0.226696i
$181$	−2.45636	−	9.85192i	−0.182580	−	0.732287i	−0.989851	−	0.142107i	$-0.954612\pi$
$181$	−2.45636	−	9.85192i	−0.182580	−	0.732287i	0.807272	−	0.590180i	$-0.200943\pi$
$182$	1.28982	+	2.23404i	0.0956081	+	0.165598i
$183$	15.8751	−	7.06807i	1.17352	−	0.522487i
$184$	−0.510862	−	14.6292i	−0.0376612	−	1.07848i
$185$	15.0283	+	0.848963i	1.10490	+	0.0624170i
$186$	10.7636	−	1.51273i	0.789227	−	0.110919i
$187$	1.21974	−	1.56119i	0.0891961	−	0.114166i
$188$	−4.04014	−	9.99971i	−0.294658	−	0.729304i
$189$	4.47232	+	13.7644i	0.325314	+	1.00121i
$190$	−1.89605	+	10.3866i	−0.137554	+	0.753523i
$191$	4.06165	−	12.5005i	0.293890	−	0.904502i	−0.689701	−	0.724094i	$-0.742258\pi$
$191$	4.06165	−	12.5005i	0.293890	−	0.904502i	0.983592	−	0.180408i	$-0.0577418\pi$
$192$	9.02842	−	0.631328i	0.651570	−	0.0455622i
$193$	−17.7644	−	6.46573i	−1.27871	−	0.465413i	−0.388706	−	0.921362i	$-0.627078\pi$
$193$	−17.7644	−	6.46573i	−1.27871	−	0.465413i	−0.890006	+	0.455949i	$0.849300\pi$
$194$	−1.12152	+	1.08304i	−0.0805203	+	0.0777575i
$195$	−1.86606	+	1.20106i	−0.133632	+	0.0860100i
$196$	−0.163151	+	0.241881i	−0.0116536	+	0.0172772i
$197$	0.371044	+	3.53025i	0.0264358	+	0.251520i	0.999756	+	0.0220705i	$0.00702584\pi$
$197$	0.371044	+	3.53025i	0.0264358	+	0.251520i	−0.973321	+	0.229449i	$0.926307\pi$
$198$	0.436995	−	0.485333i	0.0310559	−	0.0344911i
$199$	7.27402	+	6.10362i	0.515641	+	0.432674i	0.863109	−	0.505017i	$-0.168514\pi$
$199$	7.27402	+	6.10362i	0.515641	+	0.432674i	−0.347468	+	0.937692i	$0.612958\pi$
$200$	−6.11282	−	14.0361i	−0.432241	−	0.992501i
$201$	−2.55361	−	4.42298i	−0.180118	−	0.311973i
$202$	2.65402	+	0.564130i	0.186737	+	0.0396921i
$203$	5.10608	−	7.57008i	0.358377	−	0.531316i
$204$	3.80429	+	3.67376i	0.266353	+	0.257214i
$205$	−10.9675	−	4.70820i	−0.766000	−	0.328835i
$206$	7.29967	+	10.8222i	0.508592	+	0.754018i
$207$	6.30981	−	5.29456i	0.438562	−	0.367997i
$208$	1.18201	+	0.858784i	0.0819580	+	0.0595460i
$209$	0.877300	−	1.24771i	0.0606841	−	0.0863062i
$210$	6.34677	+	3.84878i	0.437969	+	0.265591i
$211$	3.48929	+	2.18035i	0.240213	+	0.150102i	0.644684	−	0.764449i	$-0.276989\pi$
$211$	3.48929	+	2.18035i	0.240213	+	0.150102i	−0.404471	+	0.914551i	$0.632544\pi$
$212$	2.29432	−	2.93660i	0.157575	−	0.201686i
$213$	−13.6929	−	7.28063i	−0.938220	−	0.498861i
$214$	0.829833	−	0.441230i	0.0567262	−	0.0301619i
$215$	24.2168	−	11.1727i	1.65157	−	0.761971i
$216$	10.9350	+	12.1445i	0.744032	+	0.826332i
$217$	−2.51672	+	23.9449i	−0.170846	+	1.62549i
$218$	3.10798	+	2.60790i	0.210499	+	0.176630i
$219$	−1.87732	−	7.52951i	−0.126857	−	0.508797i
$220$	−0.0139197	+	0.646592i	−0.000938467	+	0.0435932i
$221$	0.519743	+	4.94502i	0.0349617	+	0.332638i
$222$	−4.60803	+	6.83169i	−0.309271	+	0.458513i
$223$	20.0504	−	10.6610i	1.34267	−	0.713912i	0.366400	−	0.930457i	$-0.380590\pi$
$223$	20.0504	−	10.6610i	1.34267	−	0.713912i	0.976272	+	0.216546i	$0.0694791\pi$
$224$	−2.03491	+	11.5406i	−0.135963	+	0.771087i
$225$	4.10612	−	7.57308i	0.273741	−	0.504872i
$226$	−7.34154	+	6.16028i	−0.488352	+	0.409776i
$227$	−1.83761	−	5.65557i	−0.121966	−	0.375373i	0.871370	−	0.490626i	$-0.163232\pi$
$227$	−1.83761	−	5.65557i	−0.121966	−	0.375373i	−0.993336	+	0.115253i	$0.963232\pi$
$228$	3.06762	+	2.67719i	0.203158	+	0.177301i
$229$	−7.43029	+	5.39842i	−0.491008	+	0.356738i	−0.805572	−	0.592498i	$-0.798142\pi$
$229$	−7.43029	+	5.39842i	−0.491008	+	0.356738i	0.314564	+	0.949236i	$0.398142\pi$
$230$	1.85807	−	11.4300i	0.122517	−	0.753673i
$231$	−0.599613	−	0.888963i	−0.0394517	−	0.0584895i
$232$	1.79041	−	10.1539i	0.117546	−	0.666639i
$233$	0.436256	−	0.894457i	0.0285801	−	0.0585978i	−0.884026	−	0.467437i	$-0.845177\pi$
$233$	0.436256	−	0.894457i	0.0285801	−	0.0585978i	0.912606	+	0.408839i	$0.134066\pi$
$234$	0.0572024	+	1.63806i	0.00373944	+	0.107084i
$235$	−5.45046	−	28.6627i	−0.355549	−	1.86975i
$236$	0.946797	−	1.05152i	0.0616313	−	0.0684484i
$237$	4.85462	−	3.03351i	0.315342	−	0.197047i
$238$	14.1038	−	8.81305i	0.914215	−	0.571265i
$239$	−7.05142	+	7.83139i	−0.456118	+	0.506571i	−0.926708	−	0.375781i	$-0.877374\pi$
$239$	−7.05142	+	7.83139i	−0.456118	+	0.506571i	0.470590	+	0.882352i	$0.344041\pi$
$240$	4.17051	+	0.529318i	0.269205	+	0.0341673i
$241$	−0.0895964	−	2.56570i	−0.00577141	−	0.165272i	−0.998854	−	0.0478558i	$-0.984761\pi$
$241$	−0.0895964	−	2.56570i	−0.00577141	−	0.165272i	0.993083	−	0.117416i	$-0.0374610\pi$
$242$	5.16539	−	10.5906i	0.332044	−	0.680791i
$243$	−2.61112	+	14.8084i	−0.167503	+	0.949959i
$244$	7.10750	+	10.5373i	0.455011	+	0.674582i
$245$	−0.560379	+	0.555834i	−0.0358013	+	0.0355110i
$246$	5.28622	−	3.84066i	0.337037	−	0.244872i
$247$	0.591441	+	3.78207i	0.0376325	+	0.240647i
$248$	8.40115	+	25.8561i	0.533473	+	1.64186i
$249$	−0.0576817	+	0.0484007i	−0.00365543	+	0.00306727i
$250$	−2.58008	−	11.8331i	−0.163179	−	0.748392i
$251$	2.48658	−	14.1021i	0.156952	−	0.890118i	−0.800028	−	0.599963i	$-0.795182\pi$
$251$	2.48658	−	14.1021i	0.156952	−	0.890118i	0.956980	−	0.290155i	$-0.0937068\pi$
$252$	−3.40965	+	1.81294i	−0.214787	+	0.114205i
$253$	−0.935464	+	1.38688i	−0.0588121	+	0.0871926i
$254$	1.83106	+	17.4214i	0.114891	+	1.09312i
$255$	8.15837	+	11.7529i	0.510897	+	0.735996i
$256$	3.86651	+	15.5077i	0.241657	+	0.969232i
$257$	−11.6567	−	9.78112i	−0.727124	−	0.610129i	0.202222	−	0.979340i	$-0.435184\pi$
$257$	−11.6567	−	9.78112i	−0.727124	−	0.610129i	−0.929346	+	0.369210i	$0.879628\pi$
$258$	−1.52619	+	14.5207i	−0.0950165	+	0.904021i
$259$	−12.2140	−	13.5650i	−0.758942	−	0.842891i
$260$	−1.10215	−	1.19160i	−0.0683523	−	0.0738997i
$261$	5.12267	−	2.72377i	0.317085	−	0.168597i
$262$	−11.5358	−	6.13367i	−0.712681	−	0.378939i
$263$	8.01688	−	10.2611i	0.494342	−	0.632729i	−0.474545	−	0.880231i	$-0.657388\pi$
$263$	8.01688	−	10.2611i	0.494342	−	0.632729i	0.968887	+	0.247502i	$0.0796098\pi$
$264$	−1.02680	−	0.641617i	−0.0631953	−	0.0394888i
$265$	7.63540	−	6.58297i	0.469039	−	0.404389i
$266$	10.5026	−	7.32342i	0.643955	−	0.449028i
$267$	3.44947	+	2.50619i	0.211104	+	0.153376i
$268$	2.86158	−	2.40115i	0.174799	−	0.146674i
$269$	14.3963	+	21.3434i	0.877760	+	1.30133i	0.952628	+	0.304139i	$0.0983687\pi$
$269$	14.3963	+	21.3434i	0.877760	+	1.30133i	−0.0748678	+	0.997193i	$0.523853\pi$
$270$	6.61328	+	11.1085i	0.402472	+	0.676044i
$271$	8.31505	+	8.02975i	0.505103	+	0.487773i	0.902990	−	0.429662i	$-0.141367\pi$
$271$	8.31505	+	8.02975i	0.505103	+	0.487773i	−0.397886	+	0.917435i	$0.630256\pi$
$272$	5.26724	−	7.80900i	0.319373	−	0.473490i
$273$	2.63235	+	0.559523i	0.159317	+	0.0338639i
$274$	−4.93964	−	8.55571i	−0.298415	−	0.516870i
$275$	−0.377686	+	1.70835i	−0.0227753	+	0.103018i
$276$	−3.42085	−	2.87043i	−0.205911	−	0.172780i
$277$	−16.3428	+	18.1505i	−0.981944	+	1.09056i	0.0139385	+	0.999903i	$0.495563\pi$
$277$	−16.3428	+	18.1505i	−0.981944	+	1.09056i	−0.995882	+	0.0906561i	$0.971104\pi$
$278$	−2.11190	−	20.0934i	−0.126663	−	1.20512i
$279$	−8.55452	+	12.6826i	−0.512146	+	0.759288i
$280$	−6.72377	+	17.3051i	−0.401822	+	1.03418i
$281$	−8.24741	+	7.96443i	−0.491999	+	0.475118i	−0.898775	−	0.438410i	$-0.855542\pi$
$281$	−8.24741	+	7.96443i	−0.491999	+	0.475118i	0.406776	+	0.913528i	$0.366653\pi$
$282$	15.0096	+	5.46305i	0.893809	+	0.325320i
$283$	−0.740404	+	0.0517741i	−0.0440124	+	0.00307765i	−0.0917457	−	0.995782i	$-0.529245\pi$
$283$	−0.740404	+	0.0517741i	−0.0440124	+	0.00307765i	0.0477333	+	0.998860i	$0.484800\pi$
$284$	3.50518	−	10.7878i	0.207994	−	0.640140i
$285$	6.72885	+	8.72036i	0.398583	+	0.516550i
$286$	−0.102868	−	0.316596i	−0.00608272	−	0.0187207i
$287$	5.42196	+	13.4198i	0.320048	+	0.792148i
$288$	−4.58408	+	5.86736i	−0.270120	+	0.345737i
$289$	14.9095	−	2.09540i	0.877031	−	0.123259i
$290$	2.95404	−	7.60288i	0.173467	−	0.446457i
$291$	0.0567636	+	1.62550i	0.00332754	+	0.0952882i
$292$	5.18514	−	2.30857i	0.303437	−	0.135099i
$293$	−15.5290	−	26.8970i	−0.907213	−	1.57134i	−0.817918	−	0.575335i	$-0.804872\pi$
$293$	−15.5290	−	26.8970i	−0.907213	−	1.57134i	−0.0892954	−	0.996005i	$-0.528462\pi$
$294$	−0.104536	−	0.419269i	−0.00609664	−	0.0244523i
$295$	3.06641	−	2.29119i	0.178533	−	0.133398i
$296$	−18.8293	−	8.38335i	−1.09443	−	0.487273i
$297$	−0.195220	−	1.85739i	−0.0113278	−	0.107777i
$298$	4.95882	+	6.34700i	0.287257	+	0.367672i
$299$	−0.729063	−	4.13472i	−0.0421628	−	0.239117i
$300$	−4.42992	−	1.47935i	−0.255761	−	0.0854105i
$301$	−30.3916	−	11.0616i	−1.75174	−	0.637582i
$302$	−20.3877	−	12.7397i	−1.17318	−	0.733085i
$303$	2.29001	−	1.66379i	0.131557	−	0.0955820i
$304$	3.74708	−	6.20865i	0.214910	−	0.356091i
$305$	13.3062	+	31.7056i	0.761909	+	1.81546i
$306$	10.5412	−	0.737116i	0.602603	−	0.0421381i
$307$	−17.6106	−	6.40974i	−1.00509	−	0.365823i	−0.213545	−	0.976933i	$-0.568501\pi$
$307$	−17.6106	−	6.40974i	−1.00509	−	0.365823i	−0.791546	+	0.611110i	$0.790723\pi$
$308$	0.564172	−	0.544815i	0.0321467	−	0.0310437i
$309$	13.4857	+	1.89529i	0.767173	+	0.107819i
$310$	2.53413	+	21.3573i	0.143929	+	1.21301i
$311$	−7.99473	−	1.69933i	−0.453339	−	0.0963603i	−0.0244175	−	0.999702i	$-0.507773\pi$
$311$	−7.99473	−	1.69933i	−0.453339	−	0.0963603i	−0.428922	+	0.903342i	$0.641106\pi$
$312$	2.97235	−	0.631793i	0.168276	−	0.0357682i
$313$	1.44298	−	0.901672i	0.0815618	−	0.0509655i	−0.488525	−	0.872550i	$-0.662465\pi$
$313$	1.44298	−	0.901672i	0.0815618	−	0.0509655i	0.570087	+	0.821584i	$0.306909\pi$
$314$	8.05708	−	19.9420i	0.454687	−	1.12539i
$315$	−10.0027	+	3.01365i	−0.563587	+	0.169800i
$316$	2.80165	+	3.11155i	0.157605	+	0.175038i
$317$	1.94826	+	0.558656i	0.109425	+	0.0313772i	0.329903	−	0.944015i	$-0.392984\pi$
$317$	1.94826	+	0.558656i	0.109425	+	0.0313772i	−0.220478	+	0.975392i	$0.570762\pi$
$318$	0.958395	+	5.43533i	0.0537441	+	0.304798i
$319$	−0.847615	+	0.818532i	−0.0474573	+	0.0458290i
$320$	0.864419	+	17.8871i	0.0483225	+	0.999922i
$321$	0.237197	−	0.951345i	0.0132390	−	0.0530989i
$322$	−11.3610	+	8.25422i	−0.633122	+	0.459990i
$323$	24.2350	−	4.66163i	1.34847	−	0.259380i
$324$	0.713119			0.0396177
$325$	−2.29651	−	3.74265i	−0.127387	−	0.207605i
$326$	16.2691	+	5.92146i	0.901062	+	0.327960i
$327$	4.19136	−	0.589058i	0.231783	−	0.0325750i
$328$	11.7563	+	11.3530i	0.649135	+	0.626863i
$329$	−19.7851	+	29.3326i	−1.09079	+	1.61716i
$330$	−0.697854	−	0.656092i	−0.0384156	−	0.0361166i
$331$	0.588808	−	5.60213i	0.0323638	−	0.307921i	−0.966351	−	0.257229i	$-0.917191\pi$
$331$	0.588808	−	5.60213i	0.0323638	−	0.307921i	0.998714	−	0.0506922i	$-0.0161428\pi$
$332$	−0.0421896	−	0.0354013i	−0.00231546	−	0.00194290i
$333$	−2.80581	−	11.2535i	−0.153757	−	0.616686i
$334$	16.3089	−	3.46657i	0.892385	−	0.189682i
$335$	8.85841	−	4.86326i	0.483987	−	0.265708i
$336$	−3.13869	−	4.01734i	−0.171229	−	0.219164i
$337$	−11.2256	−	1.57765i	−0.611496	−	0.0859402i	−0.173375	−	0.984856i	$-0.555467\pi$
$337$	−11.2256	−	1.57765i	−0.611496	−	0.0859402i	−0.438122	+	0.898916i	$0.644356\pi$
$338$	−11.6963	−	6.21901i	−0.636192	−	0.338269i
$339$	−0.348924	+	9.99187i	−0.0189509	+	0.542684i
$340$	−7.42954	+	7.36929i	−0.402923	+	0.399656i
$341$	0.960108	−	2.95491i	0.0519927	−	0.160017i
$342$	8.07658	−	0.975649i	0.436731	−	0.0527570i
$343$	−18.0243			−0.973221
$344$	−36.4305	+	2.54747i	−1.96420	+	0.137350i
$345$	−7.56429	−	9.41927i	−0.407248	−	0.507117i
$346$	−0.201692	−	0.413530i	−0.0108430	−	0.0222315i
$347$	−21.6033	−	20.8620i	−1.15972	−	1.11993i	−0.990944	−	0.134279i	$-0.957128\pi$
$347$	−21.6033	−	20.8620i	−1.15972	−	1.11993i	−0.168781	−	0.985654i	$-0.553983\pi$
$348$	−1.93652	−	2.47863i	−0.103808	−	0.132868i
$349$	4.68922	−	8.12196i	0.251008	−	0.434759i	−0.712796	−	0.701372i	$-0.752571\pi$
$349$	4.68922	−	8.12196i	0.251008	−	0.434759i	0.963804	+	0.266613i	$0.0859046\pi$
$350$	−7.88405	+	12.3915i	−0.421420	+	0.662351i
$351$	3.59064	+	3.01291i	0.191654	+	0.160817i
$352$	0.566486	−	1.40210i	0.0301938	−	0.0747323i
$353$	29.4969	+	13.1328i	1.56996	+	0.698991i	0.993036	−	0.117808i	$-0.0375867\pi$
$353$	29.4969	+	13.1328i	1.56996	+	0.698991i	0.576923	+	0.816799i	$0.304253\pi$
$354$	0.219050	+	2.08412i	0.0116424	+	0.110770i
$355$	14.9859	−	26.7776i	0.795368	−	1.42121i
$356$	−1.36711	+	2.80300i	−0.0724568	+	0.148559i
$357$	3.01276	−	17.0862i	0.159452	−	0.904299i
$358$	−9.36987	−	13.8914i	−0.495213	−	0.734184i
$359$	−3.72749	−	9.22587i	−0.196730	−	0.486923i	0.796284	−	0.604923i	$-0.206796\pi$
$359$	−3.72749	−	9.22587i	−0.196730	−	0.486923i	−0.993014	+	0.118000i	$0.962352\pi$
$360$	−8.93409	+	7.70266i	−0.470868	+	0.405966i
$361$	18.4535	−	4.52437i	0.971235	−	0.238125i
$362$	−3.39883	+	10.4605i	−0.178638	+	0.549792i
$363$	−4.60484	−	11.3974i	−0.241692	−	0.598208i
$364$	−0.0686951	+	1.96717i	−0.00360060	+	0.103108i
$365$	14.9750	−	3.39310i	0.783829	−	0.177603i
$366$	−18.6410	−	2.61983i	−0.974382	−	0.136941i
$367$	−2.89268	−	0.829463i	−0.150997	−	0.0432976i	0.199287	−	0.979941i	$-0.436137\pi$
$367$	−2.89268	−	0.829463i	−0.150997	−	0.0432976i	−0.350284	+	0.936643i	$0.613915\pi$
$368$	−3.97679	+	6.88799i	−0.207304	+	0.359062i
$369$	−0.961281	+	9.14598i	−0.0500423	+	0.476121i
$370$	−13.3184	−	9.40668i	−0.692390	−	0.489030i
$371$	−12.1958	−	0.852811i	−0.633172	−	0.0442757i
$372$	7.57674	+	3.37338i	0.392835	+	0.174902i
$373$	33.1113	+	7.03803i	1.71444	+	0.364416i	0.957358	−	0.288904i	$-0.0932909\pi$
$373$	33.1113	+	7.03803i	1.71444	+	0.364416i	0.757082	+	0.653320i	$0.226624\pi$
$374$	−2.01670	+	0.734017i	−0.104281	+	0.0379551i
$375$	−10.9749	−	6.25991i	−0.566740	−	0.323260i
$376$	−6.93752	+	39.3446i	−0.357775	+	2.02904i
$377$	0.103208	−	2.95549i	0.00531548	−	0.152215i
$378$	3.79277	−	15.2119i	0.195079	−	0.782418i
$379$	−4.52759	+	3.28948i	−0.232567	+	0.168969i	−0.697965	−	0.716132i	$-0.745911\pi$
$379$	−4.52759	+	3.28948i	−0.232567	+	0.168969i	0.465399	+	0.885101i	$0.345911\pi$
$380$	−5.42673	+	5.95443i	−0.278385	+	0.305456i
$381$	14.7844	+	10.7415i	0.757430	+	0.550305i
$382$	−10.9070	+	9.15202i	−0.558048	+	0.468258i
$383$	3.43222	+	5.08847i	0.175378	+	0.260009i	0.906470	−	0.422270i	$-0.138767\pi$
$383$	3.43222	+	5.08847i	0.175378	+	0.260009i	−0.731092	+	0.682279i	$0.760989\pi$
$384$	−0.0322011	−	0.0171216i	−0.00164326	−	0.000873734i
$385$	1.78411	−	1.14831i	0.0909265	−	0.0585235i
$386$	12.6077	+	16.1372i	0.641717	+	0.821361i
$387$	−13.7503	−	15.2713i	−0.698969	−	0.776284i
$388$	−1.16365	+	0.247342i	−0.0590754	+	0.0125569i
$389$	−1.92509	+	4.76476i	−0.0976058	+	0.241583i	−0.968085	−	0.250623i	$-0.919365\pi$
$389$	−1.92509	+	4.76476i	−0.0976058	+	0.241583i	0.870479	+	0.492205i	$0.163809\pi$
$390$	2.40372	−	0.0321687i	0.121717	−	0.00162892i
$391$	−26.4762	+	5.62768i	−1.33896	+	0.284604i
$392$	0.987346	−	0.439595i	0.0498685	−	0.0222029i
$393$	−12.8078	+	4.66167i	−0.646069	+	0.235150i
$394$	1.68563	−	3.45606i	0.0849209	−	0.174114i
$395$	5.79422	+	9.73274i	0.291539	+	0.489707i
$396$	0.479020	−	0.137357i	0.0240717	−	0.00690244i
$397$	2.95846	−	11.8658i	0.148481	−	0.595525i	−0.849237	−	0.528011i	$-0.822938\pi$
$397$	2.95846	−	11.8658i	0.148481	−	0.595525i	0.997718	−	0.0675136i	$-0.0215066\pi$
$398$	−3.17858	−	9.78265i	−0.159328	−	0.490360i
$399$	1.65376	−	13.2545i	0.0827917	−	0.663553i
$400$	−1.22472	+	8.22768i	−0.0612361	+	0.411384i
$401$	6.33930	−	5.31931i	0.316570	−	0.265634i	−0.470631	−	0.882330i	$-0.655974\pi$
$401$	6.33930	−	5.31931i	0.316570	−	0.265634i	0.787201	+	0.616696i	$0.211529\pi$
$402$	−0.193078	+	5.52904i	−0.00962987	+	0.275763i
$403$	3.41829	+	7.00853i	0.170277	+	0.349120i
$404$	1.48930	+	1.43820i	0.0740952	+	0.0715529i
$405$	1.89221	+	0.375810i	0.0940249	+	0.0186742i
$406$	−9.03621	+	4.02318i	−0.448460	+	0.199667i
$407$	1.17776	+	2.03993i	0.0583792	+	0.101116i
$408$	−4.73944	−	19.0088i	−0.234637	−	0.941078i
$409$	28.7626	−	17.9728i	1.42222	−	0.888700i	0.422374	−	0.906422i	$-0.361197\pi$
$409$	28.7626	−	17.9728i	1.42222	−	0.888700i	0.999843	+	0.0177215i	$0.00564123\pi$
$410$	7.37258	+	10.6209i	0.364106	+	0.524529i
$411$	−10.0811	−	2.14281i	−0.497264	−	0.105697i
$412$	0.347622	+	9.95458i	0.0171261	+	0.490427i
$413$	−4.59679	−	0.646036i	−0.226193	−	0.0317894i
$414$	−8.83578	+	1.24179i	−0.434255	+	0.0610306i
$415$	−0.0932910	−	0.116169i	−0.00457948	−	0.00570250i
$416$	1.42173	+	3.51892i	0.0697062	+	0.172529i
$417$	−17.0520	−	12.3890i	−0.835038	−	0.606691i
$418$	−1.52217	+	0.642611i	−0.0744516	+	0.0314311i
$419$	−1.99159	−	1.44698i	−0.0972956	−	0.0706894i	0.538074	−	0.842898i	$-0.319152\pi$
$419$	−1.99159	−	1.44698i	−0.0972956	−	0.0706894i	−0.635369	+	0.772208i	$0.719152\pi$
$420$	2.55070	+	5.05683i	0.124462	+	0.246748i
$421$	17.8061	−	5.10581i	0.867815	−	0.248842i	0.187950	−	0.982179i	$-0.439816\pi$
$421$	17.8061	−	5.10581i	0.867815	−	0.248842i	0.679866	+	0.733337i	$0.262038\pi$
$422$	−1.95384	−	4.00596i	−0.0951113	−	0.195007i
$423$	−19.8494	+	10.5541i	−0.965109	+	0.513158i
$424$	−12.9721	+	4.72146i	−0.629982	+	0.229295i
$425$	−23.5974	+	15.6386i	−1.14464	+	0.758583i
$426$	8.39962	+	14.5486i	0.406963	+	0.704880i
$427$	15.6202	−	38.6613i	0.755914	−	1.87095i
$428$	0.715390	+	0.0500249i	0.0345797	+	0.00241805i
$429$	−0.317254	−	0.141251i	−0.0153172	−	0.00681964i
$430$	−28.6603	−	3.63755i	−1.38212	−	0.175418i
$431$	−22.0776	−	6.33065i	−1.06344	−	0.304937i	−0.302092	−	0.953279i	$-0.597685\pi$
$431$	−22.0776	−	6.33065i	−1.06344	−	0.304937i	−0.761349	+	0.648342i	$0.775463\pi$
$432$	−1.54190	−	8.74454i	−0.0741846	−	0.420722i
$433$	9.10120	−	8.78893i	0.437376	−	0.422369i	−0.443091	−	0.896477i	$-0.646118\pi$
$433$	9.10120	−	8.78893i	0.437376	−	0.422369i	0.880467	+	0.474108i	$0.157229\pi$
$434$	16.0573	−	20.5523i	0.770773	−	0.986544i
$435$	−3.83219	−	7.59740i	−0.183739	−	0.364267i
$436$	0.956650	+	2.94426i	0.0458152	+	0.141005i
$437$	−20.1392	+	5.35410i	−0.963391	+	0.256121i
$438$	−2.59761	+	7.99463i	−0.124119	+	0.381998i
$439$	24.4118	+	15.2542i	1.16511	+	0.728041i	0.967657	−	0.252271i	$-0.0811775\pi$
$439$	24.4118	+	15.2542i	1.16511	+	0.728041i	0.197453	+	0.980312i	$0.436733\pi$
$440$	1.31299	−	2.00392i	0.0625945	−	0.0955334i
$441$	0.536973	+	0.285513i	0.0255701	+	0.0135959i
$442$	2.36116	−	4.84110i	0.112309	−	0.230268i
$443$	6.18197	−	2.25005i	0.293714	−	0.106903i	−0.190960	−	0.981598i	$-0.561160\pi$
$443$	6.18197	−	2.25005i	0.293714	−	0.106903i	0.484675	+	0.874694i	$0.338938\pi$
$444$	−5.74421	+	2.55749i	−0.272608	+	0.121373i
$445$	−5.10471	+	6.71710i	−0.241986	+	0.318421i
$446$	−24.5391	−	1.71594i	−1.16196	−	0.0812521i
$447$	8.38215	+	0.586137i	0.396462	+	0.0277233i
$448$	14.5313	−	16.1387i	0.686541	−	0.762481i
$449$	4.91717	−	8.51679i	0.232056	−	0.401932i	−0.726357	−	0.687317i	$-0.758788\pi$
$449$	4.91717	−	8.51679i	0.232056	−	0.401932i	0.958413	+	0.285385i	$0.0921215\pi$
$450$	−8.11932	+	4.59995i	−0.382748	+	0.216844i
$451$	−0.324332	−	1.83938i	−0.0152722	−	0.0866129i
$452$	−7.24156	+	1.01773i	−0.340614	+	0.0478702i
$453$	−24.1084	+	6.91296i	−1.13271	+	0.324799i
$454$	−1.55839	+	6.25034i	−0.0731387	+	0.293343i
$455$	−1.21897	+	5.18355i	−0.0571461	+	0.243009i
$456$	−4.38148	−	14.4321i	−0.205182	−	0.675844i
$457$	−15.1242			−0.707479			−0.353739	−	0.935344i	$-0.615090\pi$
$457$	−15.1242			−0.707479			−0.353739	+	0.935344i	$0.615090\pi$
$458$	9.92474	−	0.694005i	0.463752	−	0.0324287i
$459$	18.6044	−	23.8126i	0.868380	−	1.11148i
$460$	5.82406	−	6.64498i	0.271548	−	0.309824i
$461$	−26.5284	+	14.1054i	−1.23555	+	0.656954i	−0.953195	−	0.302355i	$-0.902227\pi$
$461$	−26.5284	+	14.1054i	−1.23555	+	0.656954i	−0.282356	+	0.959310i	$0.591116\pi$
$462$	0.0405377	+	1.16085i	0.00188598	+	0.0540075i
$463$	13.4638	+	14.9531i	0.625718	+	0.694930i	0.969770	−	0.244020i	$-0.0784664\pi$
$463$	13.4638	+	14.9531i	0.625718	+	0.694930i	−0.344052	+	0.938951i	$0.611800\pi$
$464$	−3.74862	+	4.16327i	−0.174025	+	0.193275i
$465$	18.3266	+	12.9439i	0.849876	+	0.600261i
$466$	−0.914217	+	0.571266i	−0.0423503	+	0.0264634i
$467$	1.04805	−	9.97149i	0.0484978	−	0.461425i	−0.943142	−	0.332390i	$-0.892145\pi$
$467$	1.04805	−	9.97149i	0.0484978	−	0.461425i	0.991640	−	0.129036i	$-0.0411882\pi$
$468$	−0.625333	+	1.08311i	−0.0289060	+	0.0500667i
$469$	−11.7801	−	3.37789i	−0.543955	−	0.155977i
$470$	−11.4464	+	29.4598i	−0.527981	+	1.35888i
$471$	−9.83609	−	20.1670i	−0.453223	−	0.929245i
$472$	−5.03849	+	1.44476i	−0.231915	+	0.0665006i
$473$	3.53937	+	2.21165i	0.162741	+	0.101692i
$474$	−6.20105			−0.284823
$475$	−17.5374	+	12.9398i	−0.804672	+	0.593720i
$476$	12.6900			0.581647
$477$	−6.58754	−	4.11635i	−0.301623	−	0.188475i
$478$	10.9733	−	3.14654i	0.501907	−	0.143919i
$479$	2.58244	+	5.29478i	0.117995	+	0.241925i	0.949614	−	0.313421i	$-0.101475\pi$
$479$	2.58244	+	5.29478i	0.117995	+	0.241925i	−0.831620	+	0.555345i	$0.812586\pi$
$480$	8.45867	+	6.90690i	0.386084	+	0.315255i
$481$	−5.68272	−	1.62949i	−0.259110	−	0.0742986i
$482$	−1.39050	+	2.40842i	−0.0633355	+	0.109700i
$483$	−1.53134	+	14.5697i	−0.0696782	+	0.662944i
$484$	7.62479	−	4.76450i	0.346581	−	0.216568i
$485$	−3.21802	+	0.0430664i	−0.146123	+	0.00195554i
$486$	10.8993	−	12.1049i	0.494401	−	0.549088i
$487$	15.9154	+	17.6758i	0.721195	+	0.800968i	0.986598	−	0.163170i	$-0.0521718\pi$
$487$	15.9154	+	17.6758i	0.721195	+	0.800968i	−0.265403	+	0.964137i	$0.585505\pi$
$488$	−1.64319	−	47.0547i	−0.0743836	−	2.13007i
$489$	15.9474	−	8.47940i	0.721168	−	0.383452i
$490$	0.833862	−	0.188940i	0.0376700	−	0.00853542i
$491$	20.3824	−	26.0882i	0.919843	−	1.17735i	−0.0639349	−	0.997954i	$-0.520365\pi$
$491$	20.3824	−	26.0882i	0.919843	−	1.17735i	0.983778	−	0.179391i	$-0.0574128\pi$
$492$	4.97364	−	0.347791i	0.224229	−	0.0156796i
$493$	−19.0656			−0.858670
$494$	1.62772	−	3.81391i	0.0732345	−	0.171596i
$495$	1.34343	−	0.112026i	0.0603829	−	0.00503519i
$496$	3.57363	−	14.3330i	0.160461	−	0.643572i
$497$	−35.7705	+	10.2570i	−1.60453	+	0.460090i
$498$	0.0807730	−	0.0113519i	0.00361953	−	0.000508691i
$499$	3.18281	+	18.0506i	0.142482	+	0.808057i	0.969354	+	0.245667i	$0.0790069\pi$
$499$	3.18281	+	18.0506i	0.142482	+	0.808057i	−0.826872	+	0.562390i	$0.809882\pi$
$500$	3.11515	−	8.70038i	0.139314	−	0.389093i
$501$	8.69700	−	15.0636i	0.388553	−	0.672994i
$502$	−10.3794	+	11.5275i	−0.463257	+	0.514499i
$503$	−11.9739	−	0.837296i	−0.533889	−	0.0373332i	−0.199732	−	0.979851i	$-0.564007\pi$
$503$	−11.9739	−	0.837296i	−0.533889	−	0.0373332i	−0.334157	+	0.942517i	$0.608452\pi$
$504$	14.2701	+	0.997864i	0.635641	+	0.0444484i
$505$	3.19382	+	4.60101i	0.142123	+	0.204742i
$506$	1.65549	−	0.737070i	0.0735954	−	0.0327668i
$507$	−12.9860	+	4.72652i	−0.576729	+	0.209912i
$508$	−5.85945	+	12.0137i	−0.259971	+	0.533020i
$509$	−32.1186	−	17.0778i	−1.42363	−	0.756959i	−0.434045	−	0.900891i	$-0.642914\pi$
$509$	−32.1186	−	17.0778i	−1.42363	−	0.756959i	−0.989587	+	0.143933i	$0.954025\pi$
$510$	−0.748091	−	15.4800i	−0.0331260	−	0.685467i
$511$	−15.7909	−	9.86724i	−0.698548	−	0.436501i
$512$	5.36997	−	16.5271i	0.237321	−	0.730400i
$513$	13.3813	−	19.0311i	0.590798	−	0.840245i
$514$	5.09370	+	15.6768i	0.224673	+	0.691473i
$515$	−4.32362	+	26.5970i	−0.190522	+	1.17200i
$516$	−6.85903	+	8.77915i	−0.301952	+	0.386481i
$517$	3.28435	−	3.17166i	0.144445	−	0.139489i
$518$	3.43358	+	19.4728i	0.150863	+	0.855587i
$519$	−0.461389	−	0.132301i	−0.0202527	−	0.00580737i
$520$	1.12325	+	5.90689i	0.0492576	+	0.259034i
$521$	0.251148	+	0.111818i	0.0110030	+	0.00489886i	0.412231	−	0.911079i	$-0.364750\pi$
$521$	0.251148	+	0.111818i	0.0110030	+	0.00489886i	−0.401228	+	0.915978i	$0.631416\pi$
$522$	−6.26948	−	0.438405i	−0.274408	−	0.0191885i
$523$	−3.68040	+	9.10930i	−0.160932	+	0.398322i	−0.986007	−	0.166701i	$-0.946688\pi$
$523$	−3.68040	+	9.10930i	−0.160932	+	0.398322i	0.825075	+	0.565023i	$0.191133\pi$
$524$	−4.98457	−	8.63352i	−0.217752	−	0.377157i
$525$	4.10320	+	14.7622i	0.179078	+	0.644274i
$526$	−13.2550	+	4.82442i	−0.577944	+	0.210355i
$527$	44.3872	−	23.6011i	1.93354	−	1.02808i
$528$	0.288394	+	0.591295i	0.0125507	+	0.0257328i
$529$	−0.138849	+	0.0398144i	−0.00603693	+	0.00173106i
$530$	−10.7931	+	1.66445i	−0.468824	+	0.0722991i
$531$	−2.38613	−	1.73363i	−0.103549	−	0.0752329i
$532$	9.75737	−	0.492229i	0.423036	−	0.0213408i
$533$	3.79233	+	2.75529i	0.164264	+	0.119345i
$534$	−1.73021	−	4.28243i	−0.0748737	−	0.185319i
$535$	1.87188	+	0.509744i	0.0809282	+	0.0220382i
$536$	−13.7031	+	1.92584i	−0.591882	+	0.0831836i
$537$	−17.3102	−	2.43280i	−0.746992	−	0.104983i
$538$	−0.973283	−	27.8712i	−0.0419612	−	1.20161i
$539$	−0.120816	−	0.0256803i	−0.00520392	−	0.00110613i
$540$	−0.212315	+	9.86233i	−0.00913656	+	0.424407i
$541$	−18.5408	+	11.5856i	−0.797130	+	0.498102i	−0.866313	−	0.499502i	$-0.833516\pi$
$541$	−18.5408	+	11.5856i	−0.797130	+	0.498102i	0.0691828	+	0.997604i	$0.477961\pi$
$542$	−3.02925	−	12.1497i	−0.130118	−	0.521873i
$543$	5.73713	+	9.93701i	0.246204	+	0.426438i
$544$	22.3527	−	9.95204i	0.958362	−	0.426690i
$545$	0.986793	+	8.31656i	0.0422696	+	0.356242i
$546$	−2.09702	−	2.02507i	−0.0897442	−	0.0866650i
$547$	4.70493	+	9.64653i	0.201168	+	0.412456i	0.975399	−	0.220448i	$-0.0707518\pi$
$547$	4.70493	+	9.64653i	0.201168	+	0.412456i	−0.774231	+	0.632904i	$0.781863\pi$
$548$	0.263082	−	7.53368i	0.0112383	−	0.321823i
$549$	20.2955	−	17.0299i	0.866191	−	0.726820i
$550$	1.32762	−	1.35257i	0.0566098	−	0.0576739i
$551$	−14.6595	+	0.739526i	−0.624516	+	0.0315049i
$552$	5.11181	+	15.7325i	0.217573	+	0.669621i
$553$	3.32303	−	13.3279i	0.141309	−	0.566761i
$554$	25.4324	−	7.29262i	1.08052	−	0.309834i
$555$	−16.5897	+	3.75895i	−0.704192	+	0.159559i
$556$	6.75813	−	13.8562i	0.286609	−	0.587635i
$557$	−12.5791	+	4.57841i	−0.532993	+	0.193994i	−0.594474	−	0.804115i	$-0.702640\pi$
$557$	−12.5791	+	4.57841i	−0.532993	+	0.193994i	0.0614813	+	0.998108i	$0.480418\pi$
$558$	15.1389	−	6.74027i	0.640881	−	0.285338i
$559$	−10.2457	+	2.17778i	−0.433345	+	0.0921103i
$560$	8.08087	−	6.03795i	0.341479	−	0.255150i
$561$	−0.838703	+	2.07586i	−0.0354101	+	0.0876430i
$562$	12.1484	−	2.58221i	0.512448	−	0.108924i
$563$	10.0269	+	11.1360i	0.422583	+	0.469325i	0.916414	−	0.400232i	$-0.131071\pi$
$563$	10.0269	+	11.1360i	0.422583	+	0.469325i	−0.493831	+	0.869558i	$0.664404\pi$
$564$	7.50363	+	9.60421i	0.315960	+	0.404410i
$565$	−19.7513	−	1.11577i	−0.830945	−	0.0469409i
$566$	0.709892	+	0.377456i	0.0298390	+	0.0158657i
$567$	−1.30822	−	1.93951i	−0.0549399	−	0.0814518i
$568$	−32.1880	+	27.0089i	−1.35058	+	1.13327i
$569$	2.78427	+	2.02289i	0.116723	+	0.0848039i	0.644615	−	0.764507i	$-0.277018\pi$
$569$	2.78427	+	2.02289i	0.116723	+	0.0848039i	−0.527893	+	0.849311i	$0.677018\pi$
$570$	−1.17566	−	11.8736i	−0.0492428	−	0.497329i
$571$	3.57635	−	2.59837i	0.149665	−	0.108738i	−0.510433	−	0.859918i	$-0.670515\pi$
$571$	3.57635	−	2.59837i	0.149665	−	0.108738i	0.660098	+	0.751179i	$0.270515\pi$
$572$	0.0614497	−	0.246461i	0.00256934	−	0.0103051i
$573$	−0.518379	+	14.8444i	−0.0216556	+	0.620135i
$574$	2.72258	−	15.4405i	0.113638	−	0.644476i
$575$	18.9556	−	14.5628i	0.790504	−	0.607309i
$576$	12.9663	−	4.71934i	0.540261	−	0.196639i
$577$	18.0559	+	3.83791i	0.751679	+	0.159774i	0.567791	−	0.823173i	$-0.307798\pi$
$577$	18.0559	+	3.83791i	0.751679	+	0.159774i	0.183888	+	0.982947i	$0.441132\pi$
$578$	−14.8995	−	6.63367i	−0.619736	−	0.275924i
$579$	21.3115	+	1.49025i	0.885677	+	0.0619326i
$580$	4.98576	−	3.72531i	0.207022	−	0.154685i
$581$	−0.0188861	+	0.179689i	−0.000783527	+	0.00745476i
$582$	0.880948	−	1.52585i	0.0365165	−	0.0632484i
$583$	1.51652	+	0.434855i	0.0628078	+	0.0180098i
$584$	−20.8207	−	2.92616i	−0.861567	−	0.121085i
$585$	−2.23007	+	2.54441i	−0.0922022	+	0.105198i
$586$	−1.17415	+	33.6232i	−0.0485035	+	1.38896i
$587$	3.37237	+	8.34690i	0.139192	+	0.344513i	0.980638	−	0.195828i	$-0.0627395\pi$
$587$	3.37237	+	8.34690i	0.139192	+	0.344513i	−0.841446	+	0.540342i	$0.818295\pi$
$588$	0.101887	−	0.313575i	0.00420174	−	0.0129316i
$589$	33.2139	−	19.8686i	1.36855	−	0.818671i
$590$	−4.13219	+	0.344574i	−0.170120	+	0.0141859i
$591$	−1.50271	−	3.71933i	−0.0618131	−	0.152993i
$592$	6.26244	+	9.28445i	0.257385	+	0.381589i
$593$	−5.64520	+	32.0155i	−0.231821	+	1.31472i	0.617386	+	0.786660i	$0.288192\pi$
$593$	−5.64520	+	32.0155i	−0.231821	+	1.31472i	−0.849207	+	0.528060i	$0.822920\pi$
$594$	−0.886872	+	1.81836i	−0.0363888	+	0.0746081i
$595$	33.6721	+	6.68758i	1.38042	+	0.274164i
$596$	0.642417	+	6.11219i	0.0263144	+	0.250365i
$597$	−9.80299	−	4.36457i	−0.401210	−	0.178630i
$598$	−1.70373	+	4.21687i	−0.0696706	+	0.172441i
$599$	17.8778	+	15.0013i	0.730468	+	0.612936i	0.930259	−	0.366903i	$-0.119582\pi$
$599$	17.8778	+	15.0013i	0.730468	+	0.612936i	−0.199791	+	0.979839i	$0.564026\pi$
$600$	11.0125	+	13.3433i	0.449582	+	0.544738i
$601$	11.6835	−	20.2364i	0.476579	−	0.825460i	−0.523060	−	0.852296i	$-0.675210\pi$
$601$	11.6835	−	20.2364i	0.476579	−	0.825460i	0.999640	+	0.0268359i	$0.00854315\pi$
$602$	21.5695	+	27.6077i	0.879106	+	1.12520i
$603$	−5.60115	−	5.40896i	−0.228096	−	0.220270i
$604$	−8.04148	−	16.4875i	−0.327203	−	0.670866i
$605$	22.7427	−	8.62405i	0.924624	−	0.350617i
$606$	−3.05879	+	0.213891i	−0.124255	+	0.00868874i
$607$	36.0108			1.46163			0.730817	−	0.682573i	$-0.239139\pi$
$607$	36.0108			1.46163			0.730817	+	0.682573i	$0.239139\pi$
$608$	16.8009	−	8.51915i	0.681368	−	0.345497i
$609$	−3.18872	+	9.81388i	−0.129214	+	0.397679i
$610$	5.97648	−	36.7646i	0.241980	−	1.48856i
$611$	−0.399911	+	11.4520i	−0.0161787	+	0.463297i
$612$	7.11922	+	3.78536i	0.287777	+	0.153014i
$613$	7.18106	+	1.00923i	0.290040	+	0.0407625i	0.282693	−	0.959211i	$-0.408772\pi$
$613$	7.18106	+	1.00923i	0.290040	+	0.0407625i	0.00734748	+	0.999973i	$0.497661\pi$
$614$	12.4986	+	15.9974i	0.504402	+	0.645604i
$615$	13.3805	+	1.69824i	0.539554	+	0.0684798i
$616$	−2.84181	+	0.604044i	−0.114500	+	0.0243376i
$617$	−0.503791	−	2.02060i	−0.0202819	−	0.0813461i	0.959302	−	0.282382i	$-0.0911247\pi$
$617$	−0.503791	−	2.02060i	−0.0202819	−	0.0813461i	−0.979584	+	0.201036i	$0.935569\pi$
$618$	−11.3007	−	9.48237i	−0.454579	−	0.381437i
$619$	1.78981	−	17.0289i	0.0719384	−	0.684448i	−0.897817	−	0.440369i	$-0.854848\pi$
$619$	1.78981	−	17.0289i	0.0719384	−	0.684448i	0.969755	−	0.244079i	$-0.0784857\pi$
$620$	−6.99598	+	14.8448i	−0.280965	+	0.596183i
$621$	−14.2684	+	21.1538i	−0.572573	+	0.848875i
$622$	6.36888	+	6.15036i	0.255369	+	0.246607i
$623$	10.1314	−	1.42388i	0.405907	−	0.0570465i
$624$	−1.55153	−	0.564710i	−0.0621108	−	0.0226065i
$625$	12.8509	−	21.4442i	0.514036	−	0.857769i
$626$	−1.84318			−0.0736684
$627$	−0.564359	+	1.62866i	−0.0225383	+	0.0650426i
$628$	13.2772	−	9.64644i	0.529817	−	0.384935i
$629$	−9.22032	+	36.9807i	−0.367638	+	1.47452i
$630$	10.9189	+	2.97341i	0.435020	+	0.118463i
$631$	−26.5751	+	25.6633i	−1.05794	+	1.02164i	−0.0582110	+	0.998304i	$0.518540\pi$
$631$	−26.5751	+	25.6633i	−1.05794	+	1.02164i	−0.999728	+	0.0233352i	$0.992572\pi$
$632$	−2.69331	−	15.2745i	−0.107134	−	0.607587i
$633$	−4.46958	−	1.28163i	−0.177650	−	0.0509403i
$634$	−1.46908	−	1.63158i	−0.0583448	−	0.0647985i
$635$	−21.8788	+	28.7895i	−0.868234	+	1.14248i
$636$	−1.57760	+	3.90469i	−0.0625558	+	0.154831i
$637$	0.262888	−	0.164270i	0.0104160	−	0.00650863i
$638$	1.24853	−	0.265383i	0.0494297	−	0.0105066i
$639$	−23.1272	−	4.91583i	−0.914896	−	0.194467i
$640$	0.0352418	−	0.0629719i	0.00139305	−	0.00248918i
$641$	2.62338	+	0.368692i	0.103617	+	0.0145625i	0.190791	−	0.981631i	$-0.438895\pi$
$641$	2.62338	+	0.368692i	0.103617	+	0.0145625i	−0.0871738	+	0.996193i	$0.527784\pi$
$642$	−0.764008	+	0.737794i	−0.0301530	+	0.0291184i
$643$	−1.98039	−	0.720803i	−0.0780990	−	0.0284257i	0.302675	−	0.953094i	$-0.402120\pi$
$643$	−1.98039	−	0.720803i	−0.0780990	−	0.0284257i	−0.380774	+	0.924668i	$0.624342\pi$
$644$	−10.6892	+	0.747460i	−0.421213	+	0.0294541i
$645$	−22.8265	+	19.6802i	−0.898794	+	0.774908i
$646$	−24.9394	−	9.62935i	−0.981228	−	0.378862i
$647$	4.84537	−	3.52037i	0.190491	−	0.138400i	−0.488452	−	0.872591i	$-0.662438\pi$
$647$	4.84537	−	3.52037i	0.190491	−	0.138400i	0.678943	+	0.734191i	$0.262438\pi$
$648$	−2.24024	−	1.39986i	−0.0880051	−	0.0549917i
$649$	0.562893	+	0.204876i	0.0220955	+	0.00804209i
$650$	−0.0387299	+	4.75647i	−0.00151911	+	0.186564i
$651$	−4.72474	−	26.7953i	−0.185177	−	1.05019i
$652$	8.13328	+	10.4101i	0.318524	+	0.407692i
$653$	−3.61262	−	34.3718i	−0.141373	−	1.34507i	−0.803331	−	0.595533i	$-0.796941\pi$
$653$	−3.61262	−	34.3718i	−0.141373	−	1.34507i	0.661958	−	0.749541i	$-0.269726\pi$
$654$	−4.18854	−	1.86486i	−0.163785	−	0.0729217i
$655$	−8.67639	−	25.5353i	−0.339015	−	0.997747i
$656$	−2.14828	−	8.61628i	−0.0838763	−	0.336409i
$657$	−5.91549	−	10.2459i	−0.230785	−	0.399732i
$658$	35.0136	−	15.5891i	1.36497	−	0.607725i
$659$	0.636851	+	18.2370i	0.0248082	+	0.710414i	0.946540	+	0.322586i	$0.104552\pi$
$659$	0.636851	+	18.2370i	0.0248082	+	0.710414i	−0.921732	+	0.387828i	$0.873226\pi$
$660$	−0.186287	−	0.706729i	−0.00725121	−	0.0275094i
$661$	−43.5632	+	6.12241i	−1.69441	+	0.238134i	−0.919263	−	0.393643i	$-0.871215\pi$
$661$	−43.5632	+	6.12241i	−1.69441	+	0.238134i	−0.775150	+	0.631777i	$0.782326\pi$
$662$	−3.75674	+	4.80841i	−0.146010	+	0.186884i
$663$	−2.10493	−	5.20988i	−0.0817487	−	0.202335i
$664$	0.0630444	+	0.194031i	0.00244660	+	0.00752985i
$665$	26.1499	+	3.83599i	1.01405	+	0.148753i
$666$	−3.88235	+	11.9486i	−0.150438	+	0.463000i
$667$	16.0595	−	1.12299i	0.621825	−	0.0434823i
$668$	11.9551	+	4.35130i	0.462557	+	0.168357i
$669$	−18.4599	+	17.8265i	−0.713702	+	0.689214i
$670$	−10.9295	−	0.617418i	−0.422242	−	0.0238529i
$671$	−3.00892	+	4.46091i	−0.116158	+	0.172211i
$672$	−1.38426	−	13.1704i	−0.0533991	−	0.508058i
$673$	23.5570	−	26.1627i	0.908057	−	1.00850i	−0.0918619	−	0.995772i	$-0.529282\pi$
$673$	23.5570	−	26.1627i	0.908057	−	1.00850i	0.999919	−	0.0127278i	$-0.00405151\pi$
$674$	9.40676	+	7.89321i	0.362335	+	0.304035i
$675$	−5.76076	+	26.0572i	−0.221732	+	1.00294i
$676$	−5.05392	−	8.75364i	−0.194381	−	0.336678i
$677$	−12.5620	−	2.67014i	−0.482798	−	0.102622i	−0.0399184	−	0.999203i	$-0.512710\pi$
$677$	−12.5620	−	2.67014i	−0.482798	−	0.102622i	−0.442880	+	0.896581i	$0.646043\pi$
$678$	6.05624	−	8.97874i	0.232588	−	0.344826i
$679$	2.80742	+	2.71110i	0.107739	+	0.104042i
$680$	37.8057	−	8.56616i	1.44978	−	0.328497i
$681$	3.75785	+	5.57124i	0.144001	+	0.213491i
$682$	−2.57823	+	2.16339i	−0.0987255	+	0.0828405i
$683$	−5.24860	−	3.81333i	−0.200832	−	0.145913i	0.482824	−	0.875717i	$-0.339611\pi$
$683$	−5.24860	−	3.81333i	−0.200832	−	0.145913i	−0.683656	+	0.729804i	$0.739611\pi$
$684$	5.62080	+	2.63442i	0.214917	+	0.100729i
$685$	4.66828	−	19.8515i	0.178366	−	0.758486i
$686$	16.5580	+	10.3466i	0.632189	+	0.395036i
$687$	6.38996	−	8.17878i	0.243792	−	0.312040i
$688$	17.5201	+	9.31562i	0.667949	+	0.355155i
$689$	−3.49599	+	1.85885i	−0.133187	+	0.0708166i
$690$	1.54193	+	12.9952i	0.0587004	+	0.494719i
$691$	15.0992	+	16.7694i	0.574402	+	0.637939i	0.958411	−	0.285391i	$-0.0921234\pi$
$691$	15.0992	+	16.7694i	0.574402	+	0.637939i	−0.384009	+	0.923329i	$0.625457\pi$
$692$	0.0366968	−	0.349146i	0.00139500	−	0.0132726i
$693$	−1.25234	−	1.05084i	−0.0475724	−	0.0399180i
$694$	7.87029	+	31.5660i	0.298752	+	1.19823i
$695$	25.2344	−	33.2050i	0.957195	−	1.25954i
$696$	1.21794	+	11.5879i	0.0461659	+	0.439239i
$697$	16.8992	−	25.0541i	0.640103	−	0.948992i
$698$	−8.97005	+	4.76946i	−0.339521	+	0.180527i
$699$	−0.195289	+	1.10754i	−0.00738650	+	0.0418909i
$700$	−10.1122	+	4.83052i	−0.382205	+	0.182576i
$701$	−14.2165	+	11.9291i	−0.536950	+	0.450555i	−0.870493	−	0.492180i	$-0.836200\pi$
$701$	−14.2165	+	11.9291i	−0.536950	+	0.450555i	0.333543	+	0.942735i	$0.391756\pi$
$702$	−1.56903	−	4.82897i	−0.0592191	−	0.182258i
$703$	−5.65508	+	28.7921i	−0.213285	+	1.08591i
$704$	−2.26720	+	1.64722i	−0.0854484	+	0.0620819i
$705$	14.8490	+	29.4385i	0.559246	+	1.10872i
$706$	−19.5586	−	28.9968i	−0.736096	−	1.09131i
$707$	1.17943	−	6.68889i	0.0443571	−	0.251562i
$708$	−0.700965	+	1.43719i	−0.0263439	+	0.0540129i
$709$	0.592178	+	16.9578i	0.0222397	+	0.636862i	0.958423	+	0.285350i	$0.0921100\pi$
$709$	0.592178	+	16.9578i	0.0222397	+	0.636862i	−0.936184	+	0.351512i	$0.885668\pi$
$710$	−29.1381	+	15.9968i	−1.09353	+	0.600348i
$711$	5.83989	−	6.48585i	0.219013	−	0.243238i
$712$	9.79705	−	6.12188i	0.367160	−	0.229427i
$713$	−35.9985	+	22.4943i	−1.34815	+	0.842420i
$714$	−12.5758	+	13.9668i	−0.470637	+	0.522696i
$715$	0.292937	−	0.621585i	0.0109552	−	0.0232460i
$716$	−0.446208	−	12.7777i	−0.0166756	−	0.477526i
$717$	5.22054	−	10.7037i	0.194965	−	0.399737i
$718$	−1.87172	+	10.6151i	−0.0698521	+	0.396151i
$719$	−10.0003	−	14.8261i	−0.372949	−	0.552920i	0.595109	−	0.803645i	$-0.297109\pi$
$719$	−10.0003	−	14.8261i	−0.372949	−	0.552920i	−0.968058	+	0.250725i	$0.919331\pi$
$720$	6.33452	−	0.976871i	0.236074	−	0.0364058i
$721$	26.4363	−	19.2071i	0.984540	−	0.715310i
$722$	−19.5494	−	6.43664i	−0.727555	−	0.239547i
$723$	0.896524	+	2.75922i	0.0333421	+	0.102616i
$724$	−6.42905	+	5.39461i	−0.238934	+	0.200489i
$725$	15.1926	−	7.25739i	0.564239	−	0.269533i
$726$	−2.31228	+	13.1136i	−0.0858166	+	0.486690i
$727$	−41.0357	+	21.8191i	−1.52193	+	0.809225i	−0.999067	−	0.0431910i	$-0.986248\pi$
$727$	−41.0357	+	21.8191i	−1.52193	+	0.809225i	−0.522864	+	0.852416i	$0.675136\pi$
$728$	4.07738	−	6.04496i	0.151118	−	0.224041i
$729$	−2.04678	−	19.4738i	−0.0758065	−	0.721251i
$730$	−15.7046	−	5.47914i	−0.581253	−	0.202792i
$731$	16.3368	+	65.5232i	0.604237	+	2.42346i
$732$	−11.0032	−	9.23275i	−0.406689	−	0.341252i
$733$	2.90169	−	27.6077i	0.107176	−	1.01972i	−0.800296	−	0.599604i	$-0.795325\pi$
$733$	2.90169	−	27.6077i	0.107176	−	1.01972i	0.907473	−	0.420111i	$-0.138009\pi$
$734$	2.18122	+	2.42249i	0.0805104	+	0.0894158i
$735$	0.435602	−	0.778356i	0.0160674	−	0.0287101i
$736$	−18.2421	+	9.69950i	−0.672413	+	0.357528i
$737$	1.39631	+	0.742430i	0.0514336	+	0.0273477i
$738$	6.13321	−	7.85015i	0.225767	−	0.288968i
$739$	−8.12655	−	5.07803i	−0.298940	−	0.186798i	0.372154	−	0.928171i	$-0.378619\pi$
$739$	−8.12655	−	5.07803i	−0.298940	−	0.186798i	−0.671093	+	0.741373i	$0.734175\pi$
$740$	−4.81466	−	11.4723i	−0.176991	−	0.421729i
$741$	−1.82056	−	3.92423i	−0.0668801	−	0.144160i
$742$	10.7141	+	7.78425i	0.393327	+	0.285769i
$743$	−33.6095	+	28.2017i	−1.23301	+	1.03462i	−0.234976	+	0.972001i	$0.575501\pi$
$743$	−33.6095	+	28.2017i	−1.23301	+	1.03462i	−0.998037	+	0.0626201i	$0.980054\pi$
$744$	−17.1801	−	25.4706i	−0.629854	−	0.933796i
$745$	−1.51648	+	16.5568i	−0.0555596	+	0.606596i
$746$	−26.3777	−	25.4726i	−0.965755	−	0.932619i
$747$	−0.0641954	+	0.0951736i	−0.00234879	+	0.00348222i
$748$	−1.60179	−	0.340471i	−0.0585672	−	0.0124488i
$749$	−1.17633	−	2.03746i	−0.0429820	−	0.0744470i
$750$	6.48866	+	12.0506i	0.236932	+	0.440027i
$751$	11.0683	+	9.28742i	0.403889	+	0.338903i	0.821994	−	0.569495i	$-0.192861\pi$
$751$	11.0683	+	9.28742i	0.403889	+	0.338903i	−0.418106	+	0.908398i	$0.637306\pi$
$752$	14.5252	−	16.1319i	0.529680	−	0.588269i
$753$	1.69151	+	16.0937i	0.0616422	+	0.586486i
$754$	−1.79137	+	2.65581i	−0.0652378	+	0.0967190i
$755$	−12.6487	−	47.9862i	−0.460334	−	1.74640i
$756$	8.60520	−	8.30995i	0.312968	−	0.302230i
$757$	−1.47568	−	0.537103i	−0.0536344	−	0.0195213i	0.315064	−	0.949071i	$-0.397974\pi$
$757$	−1.47568	−	0.537103i	−0.0536344	−	0.0195213i	−0.368698	+	0.929549i	$0.620196\pi$
$758$	6.04755	−	0.422886i	0.219657	−	0.0153599i
$759$	0.584193	−	1.79796i	0.0212049	−	0.0652618i
$760$	28.7365	−	8.05295i	1.04238	−	0.292111i
$761$	8.77848	+	27.0174i	0.318220	+	0.979379i	0.974409	+	0.224783i	$0.0721673\pi$
$761$	8.77848	+	27.0174i	0.318220	+	0.979379i	−0.656189	+	0.754596i	$0.727833\pi$
$762$	−7.41570	−	18.3545i	−0.268643	−	0.664914i
$763$	6.25271	−	8.00310i	0.226363	−	0.289732i
$764$	−10.7584	+	1.51200i	−0.389226	+	0.0547022i
$765$	16.8955	+	13.7960i	0.610858	+	0.498795i
$766$	−0.232040	−	6.64475i	−0.00838394	−	0.240084i
$767$	−1.37341	+	0.611480i	−0.0495908	+	0.0220793i
$768$	−9.03071	−	15.6416i	−0.325868	−	0.564419i
$769$	−7.79256	−	31.2542i	−0.281007	−	1.12706i	−0.930383	−	0.366589i	$-0.880525\pi$
$769$	−7.79256	−	31.2542i	−0.281007	−	1.12706i	0.649376	−	0.760467i	$-0.275030\pi$
$770$	−2.29814	+	0.0307558i

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)

\(f(q)\)	\(=\)	\(q+(-0.918651 - 0.574037i) q^{2} +(-1.08630 + 0.311492i) q^{3} +(-0.362341 - 0.742910i) q^{4} +(-0.569939 - 2.16221i) q^{5} +(1.17674 + 0.337424i) q^{6} +(-1.35582 + 2.34835i) q^{7} +(-0.320054 + 3.04511i) q^{8} +(-1.46112 + 0.913011i) q^{9} +O(q^{10})\)	\(q+(-0.918651 - 0.574037i) q^{2} +(-1.08630 + 0.311492i) q^{3} +(-0.362341 - 0.742910i) q^{4} +(-0.569939 - 2.16221i) q^{5} +(1.17674 + 0.337424i) q^{6} +(-1.35582 + 2.34835i) q^{7} +(-0.320054 + 3.04511i) q^{8} +(-1.46112 + 0.913011i) q^{9} +(-0.717615 + 2.31348i) q^{10} +(0.234143 - 0.260042i) q^{11} +(0.625022 + 0.694157i) q^{12} +(0.0306491 + 0.877676i) q^{13} +(2.59356 - 1.37902i) q^{14} +(1.29264 + 2.17128i) q^{15} +(1.02426 - 1.31099i) q^{16} +(5.64801 - 0.394948i) q^{17} +1.86636 q^{18} +(4.32744 - 0.522754i) q^{19} +(-1.39982 + 1.20687i) q^{20} +(0.741336 - 2.97334i) q^{21} +(-0.364369 + 0.104481i) q^{22} +(-4.73422 + 0.665352i) q^{23} +(-0.600851 - 3.40760i) q^{24} +(-4.35034 + 2.46466i) q^{25} +(0.475662 - 0.823871i) q^{26} +(3.57133 - 3.96637i) q^{27} +(2.23588 + 0.156348i) q^{28} +(-3.35920 - 0.234898i) q^{29} +(0.0589145 - 2.73667i) q^{30} +(8.11144 - 3.61145i) q^{31} +(4.06097 - 1.47807i) q^{32} +(-0.173348 + 0.355417i) q^{33} +(-5.41527 - 2.87935i) q^{34} +(5.85036 + 1.59316i) q^{35} +(1.20771 + 0.754662i) q^{36} +(-2.08017 + 6.40210i) q^{37} +(-4.27548 - 2.00388i) q^{38} +(-0.306683 - 0.943873i) q^{39} +(6.76659 - 1.04350i) q^{40} +(3.28618 - 4.20612i) q^{41} +(-2.38783 + 2.30590i) q^{42} +(2.07113 + 11.7459i) q^{43} +(-0.278027 - 0.0797231i) q^{44} +(2.80688 + 2.63890i) q^{45} +(4.73103 + 2.10639i) q^{46} +(13.0163 + 0.910185i) q^{47} +(-0.704287 + 1.74317i) q^{48} +(-0.176490 - 0.305690i) q^{49} +(5.41125 + 0.233093i) q^{50} +(-6.01241 + 2.18834i) q^{51} +(0.640929 - 0.340788i) q^{52} +(1.97642 + 4.05225i) q^{53} +(-5.55764 + 1.59363i) q^{54} +(-0.695713 - 0.358059i) q^{55} +(-6.71704 - 4.88021i) q^{56} +(-4.53806 + 1.91583i) q^{57} +(2.95109 + 2.14409i) q^{58} +(0.641277 + 1.58722i) q^{59} +(1.14469 - 1.74706i) q^{60} +(-15.2276 + 2.14010i) q^{61} +(-9.52468 - 1.33861i) q^{62} +(-0.163049 - 4.66910i) q^{63} +(-7.83370 - 1.66510i) q^{64} +(1.88026 - 0.566492i) q^{65} +(0.363269 - 0.226996i) q^{66} +(1.09333 + 4.38511i) q^{67} +(-2.33992 - 4.05286i) q^{68} +(4.93553 - 2.19744i) q^{69} +(-4.45991 - 4.82188i) q^{70} +(9.87156 + 9.53285i) q^{71} +(-2.31258 - 4.74149i) q^{72} +(-0.239648 + 6.86261i) q^{73} +(5.58598 - 4.68720i) q^{74} +(3.95805 - 4.03245i) q^{75} +(-1.95637 - 3.02548i) q^{76} +(0.293213 + 0.902418i) q^{77} +(-0.260083 + 1.04314i) q^{78} +(-4.86932 + 1.39626i) q^{79} +(-3.41840 - 1.46748i) q^{80} +(-0.378206 + 0.775437i) q^{81} +(-5.43332 + 1.97757i) q^{82} +(0.0608704 - 0.0271012i) q^{83} +(-2.47754 + 0.526617i) q^{84} +(-4.07298 - 11.9871i) q^{85} +(4.83996 - 11.9793i) q^{86} +(3.72226 - 0.791192i) q^{87} +(0.716918 + 0.796218i) q^{88} +(-2.32289 - 2.97316i) q^{89} +(-1.06371 - 4.03548i) q^{90} +(-2.10264 - 1.11800i) q^{91} +(2.20970 + 3.27602i) q^{92} +(-7.68652 + 6.44976i) q^{93} +(-11.4349 - 8.30795i) q^{94} +(-3.59668 - 9.05891i) q^{95} +(-3.95102 + 2.87059i) q^{96} +(0.348191 - 1.39652i) q^{97} +(-0.0133444 + 0.382134i) q^{98} +(-0.104690 + 0.593728i) 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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