LMFDB - Embedded newform 225.4.p.b.68.2

Newspace parameters

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.2
Character	$\chi$	$=$	225.68
Dual form			225.4.p.b.182.2

$q$-expansion

$f(q)$	$=$	$q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +O(q^{10})$	\(q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +(-7.55654 + 4.36277i) q^{11} +(0.999152 - 61.3544i) q^{12} +(-73.7842 + 19.7704i) q^{13} +(-16.4389 + 28.4731i) q^{14} +(-9.50797 - 16.4683i) q^{16} +(5.92131 + 5.92131i) q^{17} +(-82.1614 - 87.6951i) q^{18} -106.718i q^{19} +(9.32953 + 37.2331i) q^{21} +(-10.0513 - 37.5120i) q^{22} +(-27.4553 - 102.465i) q^{23} +(84.7110 + 24.1833i) q^{24} -339.980i q^{26} +(-140.129 - 6.85080i) q^{27} +(-61.6846 - 61.6846i) q^{28} +(85.3380 + 147.810i) q^{29} +(-157.999 + 273.662i) q^{31} +(212.761 - 57.0093i) q^{32} +(-38.8906 - 23.3059i) q^{33} +(-32.2773 + 18.6353i) q^{34} +(281.176 - 150.349i) q^{36} +(31.7091 - 31.7091i) q^{37} +(458.791 + 122.933i) q^{38} +(-276.057 - 285.197i) q^{39} +(298.272 + 172.207i) q^{41} +(-170.816 - 2.78172i) q^{42} +(-115.545 + 431.220i) q^{43} +103.042 q^{44} +472.133 q^{46} +(60.9929 - 227.629i) q^{47} +(50.7917 - 84.7559i) q^{48} +(-249.789 - 144.216i) q^{49} +(-11.9448 + 41.8410i) q^{51} +(871.335 + 233.473i) q^{52} +(60.5508 - 60.5508i) q^{53} +(190.872 - 594.536i) q^{54} +(108.460 - 62.6197i) q^{56} +(484.682 - 269.405i) q^{57} +(-733.754 + 196.609i) q^{58} +(-25.4427 + 44.0680i) q^{59} +(-36.1174 - 62.5572i) q^{61} +(-994.494 - 994.494i) q^{62} +(-145.550 + 136.365i) q^{63} +828.227i q^{64} +(144.994 - 140.347i) q^{66} +(-4.59668 - 17.1550i) q^{67} +(-25.5947 - 95.5208i) q^{68} +(396.055 - 383.362i) q^{69} +109.592i q^{71} +(104.016 + 445.782i) q^{72} +(144.319 + 144.319i) q^{73} +(99.7935 + 172.847i) q^{74} +(-630.128 + 1091.41i) q^{76} +(-62.2595 + 16.6824i) q^{77} +(1544.09 - 858.266i) q^{78} +(-140.624 + 81.1891i) q^{79} +(-322.635 - 653.718i) q^{81} +(-1083.93 + 1083.93i) q^{82} +(-279.860 - 74.9883i) q^{83} +(124.433 - 435.873i) q^{84} +(-1720.76 - 993.479i) q^{86} +(-455.877 + 760.720i) q^{87} +(-38.2877 + 142.892i) q^{88} -1107.89 q^{89} -564.273 q^{91} +(-324.227 + 1210.03i) q^{92} +(-1641.75 - 26.7358i) q^{93} +(908.339 + 524.430i) q^{94} +(796.027 + 822.383i) q^{96} +(197.725 + 52.9802i) q^{97} +(907.741 - 907.741i) q^{98} +(7.67108 - 235.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) $	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.15194	+	4.29910i	−0.407272	+	1.51996i	0.392553	+	0.919729i	$0.371592\pi$
$2$	−1.15194	+	4.29910i	−0.407272	+	1.51996i	−0.799826	+	0.600232i	$0.795075\pi$
$3$	2.52446	+	4.54171i	0.485832	+	0.874052i
$3$	2.52446	+	4.54171i	0.485832	+	0.874052i
$4$	−10.2271	−	5.90461i	−1.27839	−	0.738077i
$5$		0			0
$5$		0			0
$6$	−22.4333	+	5.62113i	−1.52639	+	0.382469i
$7$	7.13532	+	1.91190i	0.385271	+	0.103233i	0.446255	−	0.894906i	$-0.352757\pi$
$7$	7.13532	+	1.91190i	0.385271	+	0.103233i	−0.0609842	+	0.998139i	$0.519424\pi$
$8$	11.9883	−	11.9883i	0.529811	−	0.529811i
$9$	−14.2542	+	22.9307i	−0.527934	+	0.849286i
$10$		0			0
$11$	−7.55654	+	4.36277i	−0.207126	+	0.119584i	−0.599975	−	0.800019i	$-0.704823\pi$
$11$	−7.55654	+	4.36277i	−0.207126	+	0.119584i	0.392849	+	0.919603i	$0.371489\pi$
$12$	0.999152	−	61.3544i	0.0240359	−	1.47596i
$13$	−73.7842	+	19.7704i	−1.57416	+	0.421794i	−0.937111	−	0.349030i	$-0.886511\pi$
$13$	−73.7842	+	19.7704i	−1.57416	+	0.421794i	−0.637047	+	0.770825i	$0.719844\pi$
$14$	−16.4389	+	28.4731i	−0.313821	+	0.543553i
$15$		0			0
$16$	−9.50797	−	16.4683i	−0.148562	−	0.257317i
$17$	5.92131	+	5.92131i	0.0844782	+	0.0844782i	0.748083	−	0.663605i	$-0.230974\pi$
$17$	5.92131	+	5.92131i	0.0844782	+	0.0844782i	−0.663605	+	0.748083i	$0.730974\pi$
$18$	−82.1614	−	87.6951i	−1.07587	−	1.14833i
$19$		−	106.718i		−	1.28857i	−0.764787	−	0.644284i	$-0.777156\pi$
$19$		−	106.718i		−	1.28857i	0.764787	−	0.644284i	$-0.222844\pi$
$20$		0			0
$21$	9.32953	+	37.2331i	0.0969462	+	0.386901i
$22$	−10.0513	−	37.5120i	−0.0974066	−	0.363526i
$23$	−27.4553	−	102.465i	−0.248906	−	0.928930i	−0.971380	−	0.237531i	$-0.923662\pi$
$23$	−27.4553	−	102.465i	−0.248906	−	0.928930i	0.722474	−	0.691398i	$-0.243005\pi$
$24$	84.7110	+	24.1833i	0.720482	+	0.205683i
$25$		0			0
$26$		−	339.980i		−	2.56445i
$27$	−140.129	−	6.85080i	−0.998807	−	0.0488310i
$28$	−61.6846	−	61.6846i	−0.416332	−	0.416332i
$29$	85.3380	+	147.810i	0.546444	+	0.946469i	0.998515	+	0.0544866i	$0.0173522\pi$
$29$	85.3380	+	147.810i	0.546444	+	0.946469i	−0.452070	+	0.891982i	$0.649314\pi$
$30$		0			0
$31$	−157.999	+	273.662i	−0.915400	+	1.58552i	−0.109085	+	0.994032i	$0.534792\pi$
$31$	−157.999	+	273.662i	−0.915400	+	1.58552i	−0.806315	+	0.591487i	$0.798541\pi$
$32$	212.761	−	57.0093i	1.17535	−	0.314935i
$33$	−38.8906	−	23.3059i	−0.205151	−	0.122941i
$34$	−32.2773	+	18.6353i	−0.162809	+	0.0939979i
$35$		0			0
$36$	281.176	−	150.349i	1.30174	−	0.696060i
$37$	31.7091	−	31.7091i	0.140890	−	0.140890i	−0.633144	−	0.774034i	$-0.718236\pi$
$37$	31.7091	−	31.7091i	0.140890	−	0.140890i	0.774034	+	0.633144i	$0.218236\pi$
$38$	458.791	+	122.933i	1.95857	+	0.524798i
$39$	−276.057	−	285.197i	−1.13345	−	1.17097i
$40$		0			0
$41$	298.272	+	172.207i	1.13615	+	0.655958i	0.945475	−	0.325695i	$-0.105598\pi$
$41$	298.272	+	172.207i	1.13615	+	0.655958i	0.190677	+	0.981653i	$0.438932\pi$
$42$	−170.816	−	2.78172i	−0.627558	−	0.0102197i
$43$	−115.545	+	431.220i	−0.409778	+	1.52931i	0.385292	+	0.922795i	$0.374101\pi$
$43$	−115.545	+	431.220i	−0.409778	+	1.52931i	−0.795070	+	0.606517i	$0.792566\pi$
$44$	103.042			0.353049
$45$		0			0
$46$	472.133			1.51331
$47$	60.9929	−	227.629i	0.189292	−	0.706448i	−0.804379	−	0.594117i	$-0.797502\pi$
$47$	60.9929	−	227.629i	0.189292	−	0.706448i	0.993671	−	0.112331i	$-0.0358317\pi$
$48$	50.7917	−	84.7559i	0.152732	−	0.254864i
$49$	−249.789	−	144.216i	−0.728249	−	0.420454i
$50$		0			0
$51$	−11.9448	+	41.8410i	−0.0327961	+	0.114881i
$52$	871.335	+	233.473i	2.32370	+	0.622633i
$53$	60.5508	−	60.5508i	0.156930	−	0.156930i	−0.624275	−	0.781205i	$-0.714605\pi$
$53$	60.5508	−	60.5508i	0.156930	−	0.156930i	0.781205	+	0.624275i	$0.214605\pi$
$54$	190.872	−	594.536i	0.481008	−	1.49826i
$55$		0			0
$56$	108.460	−	62.6197i	0.258815	−	0.149427i
$57$	484.682	−	269.405i	1.12627	−	0.626028i
$58$	−733.754	+	196.609i	−1.66115	+	0.445103i
$59$	−25.4427	+	44.0680i	−0.0561416	+	0.0972401i	−0.892730	−	0.450591i	$-0.851213\pi$
$59$	−25.4427	+	44.0680i	−0.0561416	+	0.0972401i	0.836589	+	0.547831i	$0.184546\pi$
$60$		0			0
$61$	−36.1174	−	62.5572i	−0.0758092	−	0.131305i	0.825629	−	0.564214i	$-0.190821\pi$
$61$	−36.1174	−	62.5572i	−0.0758092	−	0.131305i	−0.901438	+	0.432909i	$0.857487\pi$
$62$	−994.494	−	994.494i	−2.03711	−	2.03711i
$63$	−145.550	+	136.365i	−0.291072	+	0.272705i
$64$			828.227i			1.61763i
$65$		0			0
$66$	144.994	−	140.347i	0.270418	−	0.261751i
$67$	−4.59668	−	17.1550i	−0.00838169	−	0.0312809i	0.961608	−	0.274426i	$-0.0884877\pi$
$67$	−4.59668	−	17.1550i	−0.00838169	−	0.0312809i	−0.969990	+	0.243145i	$0.921821\pi$
$68$	−25.5947	−	95.5208i	−0.0456444	−	0.170347i
$69$	396.055	−	383.362i	0.691006	−	0.668861i
$70$		0			0
$71$			109.592i			0.183185i	0.995797	+	0.0915927i	$0.0291958\pi$
$71$			109.592i			0.183185i	−0.995797	+	0.0915927i	$0.970804\pi$
$72$	104.016	+	445.782i	0.170256	+	0.729666i
$73$	144.319	+	144.319i	0.231387	+	0.231387i	0.813271	−	0.581885i	$-0.197685\pi$
$73$	144.319	+	144.319i	0.231387	+	0.231387i	−0.581885	+	0.813271i	$0.697685\pi$
$74$	99.7935	+	172.847i	0.156767	+	0.271529i
$75$		0			0
$76$	−630.128	+	1091.41i	−0.951062	+	1.64729i
$77$	−62.2595	+	16.6824i	−0.0921446	+	0.0246901i
$78$	1544.09	−	858.266i	2.24146	−	1.24589i
$79$	−140.624	+	81.1891i	−0.200271	+	0.115626i	−0.596782	−	0.802404i	$-0.703554\pi$
$79$	−140.624	+	81.1891i	−0.200271	+	0.115626i	0.396511	+	0.918030i	$0.370221\pi$
$80$		0			0
$81$	−322.635	−	653.718i	−0.442572	−	0.896733i
$82$	−1083.93	+	1083.93i	−1.45975	+	1.45975i
$83$	−279.860	−	74.9883i	−0.370104	−	0.0991691i	0.0689728	−	0.997619i	$-0.478028\pi$
$83$	−279.860	−	74.9883i	−0.370104	−	0.0991691i	−0.439077	+	0.898449i	$0.644694\pi$
$84$	124.433	−	435.873i	0.161628	−	0.566163i
$85$		0			0
$86$	−1720.76	−	993.479i	−2.15760	−	1.24569i
$87$	−455.877	+	760.720i	−0.561783	+	0.937446i
$88$	−38.2877	+	142.892i	−0.0463805	+	0.173094i
$89$	−1107.89			−1.31950			−0.659751	−	0.751484i	$-0.729338\pi$
$89$	−1107.89			−1.31950			−0.659751	+	0.751484i	$0.729338\pi$
$90$		0			0
$91$	−564.273			−0.650021
$92$	−324.227	+	1210.03i	−0.367423	+	1.37124i
$93$	−1641.75	−	26.7358i	−1.83056	−	0.0298105i
$94$	908.339	+	524.430i	0.996681	+	0.575434i
$95$		0			0
$96$	796.027	+	822.383i	0.846294	+	0.874314i
$97$	197.725	+	52.9802i	0.206968	+	0.0554569i	0.360813	−	0.932638i	$-0.382499\pi$
$97$	197.725	+	52.9802i	0.206968	+	0.0554569i	−0.153845	+	0.988095i	$0.549166\pi$
$98$	907.741	−	907.741i	0.935670	−	0.935670i
$99$	7.67108	−	235.465i	0.00778760	−	0.239041i
$100$		0			0
$101$	−960.085	+	554.305i	−0.945862	+	0.546093i	−0.891793	−	0.452444i	$-0.850552\pi$
$101$	−960.085	+	554.305i	−0.945862	+	0.546093i	−0.0540686	+	0.998537i	$0.517219\pi$
$102$	−166.119	−	99.5500i	−0.161257	−	0.0966364i
$103$	276.457	−	74.0766i	0.264468	−	0.0708639i	−0.124148	−	0.992264i	$-0.539620\pi$
$103$	276.457	−	74.0766i	0.264468	−	0.0708639i	0.388616	+	0.921400i	$0.372953\pi$
$104$	−647.531	+	1121.56i	−0.610535	+	1.05748i
$105$		0			0
$106$	190.563	+	330.065i	0.174614	+	0.302441i
$107$	864.028	+	864.028i	0.780643	+	0.780643i	0.979939	−	0.199296i	$-0.0638656\pi$
$107$	864.028	+	864.028i	0.780643	+	0.780643i	−0.199296	+	0.979939i	$0.563866\pi$
$108$	1392.66	+	897.470i	1.24082	+	0.799621i
$109$			990.712i			0.870578i	0.900291	+	0.435289i	$0.143354\pi$
$109$			990.712i			0.870578i	−0.900291	+	0.435289i	$0.856646\pi$
$110$		0			0
$111$	224.062	+	63.9651i	0.191595	+	0.0546964i
$112$	−36.3567	−	135.685i	−0.0306730	−	0.114473i
$113$	−19.6119	−	73.1927i	−0.0163269	−	0.0609327i	0.957282	−	0.289157i	$-0.0933748\pi$
$113$	−19.6119	−	73.1927i	−0.0163269	−	0.0609327i	−0.973609	+	0.228224i	$0.926708\pi$
$114$	599.875	+	2394.03i	0.492837	+	1.96686i
$115$		0			0
$116$		−	2015.55i		−	1.61327i
$117$	598.386	−	1973.74i	0.472827	−	1.55959i
$118$	−160.144	−	160.144i	−0.124936	−	0.124936i
$119$	30.9295	+	53.5714i	0.0238261	+	0.0412679i
$120$		0			0
$121$	−627.432	+	1086.74i	−0.471399	+	0.816488i
$122$	310.545	−	83.2102i	0.230454	−	0.0617500i
$123$	−29.1401	+	1789.39i	−0.0213616	+	1.31174i
$124$	3231.73	−	1865.84i	2.34047	−	1.35127i
$125$		0			0
$126$	−418.584	−	782.818i	−0.295956	−	0.553484i
$127$	−1084.18	+	1084.18i	−0.757521	+	0.757521i	−0.975871	−	0.218350i	$-0.929933\pi$
$127$	−1084.18	+	1084.18i	−0.757521	+	0.757521i	0.218350	+	0.975871i	$0.429933\pi$
$128$	−1858.54	−	497.994i	−1.28338	−	0.343882i
$129$	−2250.16	+	563.825i	−1.53578	+	0.384822i
$130$		0			0
$131$	1415.36	+	817.157i	0.943972	+	0.545003i	0.891203	−	0.453604i	$-0.149862\pi$
$131$	1415.36	+	817.157i	0.943972	+	0.545003i	0.0527689	+	0.998607i	$0.483195\pi$
$132$	260.125	+	467.986i	0.171523	+	0.308583i
$133$	204.035	−	761.467i	0.133023	−	0.496448i
$134$	79.0463			0.0509594
$135$		0			0
$136$	141.972			0.0895149
$137$	−591.988	+	2209.33i	−0.369175	+	1.37778i	0.492497	+	0.870314i	$0.336084\pi$
$137$	−591.988	+	2209.33i	−0.369175	+	1.37778i	−0.861672	+	0.507465i	$0.830583\pi$
$138$	1191.88	+	2144.29i	0.735215	+	1.32271i
$139$	−1895.18	−	1094.18i	−1.15645	−	0.667678i	−0.206001	−	0.978552i	$-0.566045\pi$
$139$	−1895.18	−	1094.18i	−1.15645	−	0.667678i	−0.950451	+	0.310874i	$0.899378\pi$
$140$		0			0
$141$	1187.80	−	297.627i	0.709437	−	0.177764i
$142$	−471.146	−	126.243i	−0.278435	−	0.0746063i
$143$	471.299	−	471.299i	0.275609	−	0.275609i
$144$	513.158	+	16.7179i	0.296967	+	0.00967471i
$145$		0			0
$146$	−786.687	+	454.194i	−0.445936	+	0.257461i
$147$	24.4035	−	1498.54i	0.0136923	−	0.840797i
$148$	−511.522	+	137.062i	−0.284100	+	0.0761244i
$149$	311.430	−	539.412i	0.171230	−	0.296580i	−0.767620	−	0.640905i	$-0.778559\pi$
$149$	311.430	−	539.412i	0.171230	−	0.296580i	0.938850	+	0.344326i	$0.111892\pi$
$150$		0			0
$151$	−1009.02	−	1747.68i	−0.543795	−	0.941881i	−0.998682	−	0.0513314i	$-0.983654\pi$
$151$	−1009.02	−	1747.68i	−0.543795	−	0.941881i	0.454887	−	0.890549i	$-0.349680\pi$
$152$	−1279.36	−	1279.36i	−0.682697	−	0.682697i
$153$	−220.183	+	51.3763i	−0.116345	+	0.0271472i
$154$		−	286.877i		−	0.150112i
$155$		0			0
$156$	1139.28	+	4546.74i	0.584715	+	2.33353i
$157$	−182.444	−	680.891i	−0.0927428	−	0.346121i	0.903925	−	0.427692i	$-0.140673\pi$
$157$	−182.444	−	680.891i	−0.0927428	−	0.346121i	−0.996668	+	0.0815706i	$0.974006\pi$
$158$	−187.050	−	698.080i	−0.0941829	−	0.351495i
$159$	427.862	+	122.146i	0.213407	+	0.0609233i
$160$		0			0
$161$		−	783.611i		−	0.383585i
$162$	3182.06	−	633.996i	1.54325	−	0.307478i
$163$	426.426	+	426.426i	0.204909	+	0.204909i	0.802100	−	0.597190i	$-0.203716\pi$
$163$	426.426	+	426.426i	0.204909	+	0.204909i	−0.597190	+	0.802100i	$0.703716\pi$
$164$	−2033.64	−	3522.36i	−0.968294	−	1.67714i
$165$		0			0
$166$	644.765	−	1116.77i	0.301467	−	0.522155i
$167$	−613.477	+	164.381i	−0.284265	+	0.0761686i	−0.398134	−	0.917327i	$-0.630342\pi$
$167$	−613.477	+	164.381i	−0.284265	+	0.0761686i	0.113869	+	0.993496i	$0.463676\pi$
$168$	558.204	+	334.515i	0.256348	+	0.153621i
$169$	3150.58	−	1818.99i	1.43404	−	0.827943i
$170$		0			0
$171$	2447.12	+	1521.18i	1.09436	+	0.680278i
$172$	3727.88	−	3727.88i	1.65260	−	1.65260i
$173$	−686.713	−	184.004i	−0.301791	−	0.0808646i	0.104746	−	0.994499i	$-0.466597\pi$
$173$	−686.713	−	184.004i	−0.301791	−	0.0808646i	−0.406537	+	0.913634i	$0.633264\pi$
$174$	−2745.27	−	2836.16i	−1.19608	−	1.23568i
$175$		0			0
$176$	143.695	+	82.9622i	0.0615420	+	0.0355313i
$177$	−264.373	−	4.30529i	−0.112268	−	0.00182828i
$178$	1276.22	−	4762.91i	0.537397	−	2.00559i
$179$	2690.52			1.12346			0.561730	−	0.827321i	$-0.310136\pi$
$179$	2690.52			1.12346			0.561730	+	0.827321i	$0.310136\pi$
$180$		0			0
$181$	197.441			0.0810810			0.0405405	−	0.999178i	$-0.487092\pi$
$181$	197.441			0.0810810			0.0405405	+	0.999178i	$0.487092\pi$
$182$	650.009	−	2425.87i	0.264736	−	0.988007i
$183$	192.939	−	321.958i	0.0779371	−	0.130054i
$184$	−1557.52	−	899.232i	−0.624030	−	0.360284i
$185$		0			0
$186$	2006.14	−	7027.26i	0.790846	−	2.77023i
$187$	−70.5779	−	18.9113i	−0.0275998	−	0.00739535i
$188$	−1967.84	+	1967.84i	−0.763402	+	0.763402i
$189$	−986.766	−	316.795i	−0.379771	−	0.121923i
$190$		0			0
$191$	306.085	−	176.718i	0.115956	−	0.0669470i	−0.440900	−	0.897556i	$-0.645341\pi$
$191$	306.085	−	176.718i	0.115956	−	0.0669470i	0.556856	+	0.830609i	$0.312007\pi$
$192$	−3761.56	+	2090.82i	−1.41389	+	0.785897i
$193$	−1387.59	+	371.803i	−0.517517	+	0.138668i	−0.508118	−	0.861287i	$-0.669659\pi$
$193$	−1387.59	+	371.803i	−0.517517	+	0.138668i	−0.00939936	+	0.999956i	$0.502992\pi$
$194$	−455.534	+	789.008i	−0.168585	+	0.291997i
$195$		0			0
$196$	1703.08	+	2949.82i	0.620655	+	1.07501i
$197$	2647.40	+	2647.40i	0.957458	+	0.957458i	0.999131	−	0.0416736i	$-0.0132690\pi$
$197$	2647.40	+	2647.40i	0.957458	+	0.957458i	−0.0416736	+	0.999131i	$0.513269\pi$
$198$	1003.45	+	304.220i	0.360162	+	0.109192i
$199$			3785.65i			1.34853i	0.738488	+	0.674266i	$0.235540\pi$
$199$			3785.65i			1.34853i	−0.738488	+	0.674266i	$0.764460\pi$
$200$		0			0
$201$	66.3090	−	64.1839i	0.0232690	−	0.0225233i
$202$	−1277.05	−	4766.03i	−0.444818	−	1.66008i
$203$	326.316	+	1217.83i	0.112822	+	0.421058i
$204$	369.215	−	357.382i	0.126717	−	0.122656i
$205$		0			0
$206$			1273.85i			0.430842i
$207$	2740.94	+	830.983i	0.920332	+	0.279021i
$208$	1027.12	+	1027.12i	0.342395	+	0.342395i
$209$	465.586	+	806.418i	0.154092	+	0.266895i
$210$		0			0
$211$	676.890	−	1172.41i	0.220849	−	0.382521i	−0.734217	−	0.678915i	$-0.762451\pi$
$211$	676.890	−	1172.41i	0.220849	−	0.382521i	0.955066	+	0.296394i	$0.0957840\pi$
$212$	−976.788	+	261.730i	−0.316444	+	0.0847908i
$213$	−497.734	+	276.660i	−0.160114	+	0.0889974i
$214$	−4709.85	+	2719.24i	−1.50448	+	0.868613i
$215$		0			0
$216$	−1762.03	+	1597.77i	−0.555050	+	0.503308i
$217$	−1650.59	+	1650.59i	−0.516355	+	0.516355i
$218$	−4259.17	−	1141.24i	−1.32325	−	0.354563i
$219$	−291.126	+	1019.78i	−0.0898288	+	0.314659i
$220$		0			0
$221$	−553.966	−	319.832i	−0.168614	−	0.0973496i
$222$	−533.098	+	889.579i	−0.161168	+	0.268940i
$223$	−508.185	+	1896.57i	−0.152604	+	0.569525i	0.846695	+	0.532079i	$0.178589\pi$
$223$	−508.185	+	1896.57i	−0.152604	+	0.569525i	−0.999299	+	0.0374461i	$0.988078\pi$
$224$	1627.12			0.485341
$225$		0			0
$226$	337.255			0.0992648
$227$	816.800	−	3048.34i	0.238823	−	0.891301i	−0.737564	−	0.675277i	$-0.764024\pi$
$227$	816.800	−	3048.34i	0.238823	−	0.891301i	0.976388	−	0.216025i	$-0.0693092\pi$
$228$	−6547.62	−	106.627i	−1.90187	−	0.0309718i
$229$	3455.23	+	1994.88i	0.997066	+	0.575656i	0.907379	−	0.420314i	$-0.138080\pi$
$229$	3455.23	+	1994.88i	0.997066	+	0.575656i	0.0896872	+	0.995970i	$0.471413\pi$
$230$		0			0
$231$	−232.938	−	240.651i	−0.0663472	−	0.0685439i
$232$	2795.04	+	748.928i	0.790962	+	0.211937i
$233$	2166.38	−	2166.38i	0.609118	−	0.609118i	−0.333598	−	0.942715i	$-0.608263\pi$
$233$	2166.38	−	2166.38i	0.609118	−	0.609118i	0.942715	+	0.333598i	$0.108263\pi$
$234$	7795.98	+	4846.15i	2.17795	+	1.35386i
$235$		0			0
$236$	520.409	−	300.458i	0.143541	−	0.0828736i
$237$	−723.736	−	433.713i	−0.198362	−	0.118872i
$238$	−265.938	+	71.2579i	−0.0724294	+	0.0194074i
$239$	−1946.01	+	3370.59i	−0.526682	+	0.912239i	0.472835	+	0.881151i	$0.343231\pi$
$239$	−1946.01	+	3370.59i	−0.526682	+	0.912239i	−0.999517	+	0.0310884i	$0.990103\pi$
$240$		0			0
$241$	−3291.66	−	5701.33i	−0.879812	−	1.52388i	−0.851547	−	0.524278i	$-0.824335\pi$
$241$	−3291.66	−	5701.33i	−0.879812	−	1.52388i	−0.0282647	−	0.999600i	$-0.508998\pi$
$242$	−3949.26	−	3949.26i	−1.04904	−	1.04904i
$243$	2154.52	−	3115.60i	0.568775	−	0.822493i
$244$			853.037i			0.223812i
$245$		0			0
$246$	−7659.22	−	2186.55i	−1.98510	−	0.566705i
$247$	2109.86	+	7874.10i	0.543511	+	2.02841i
$248$	1386.60	+	5174.85i	0.355036	+	1.32501i
$249$	−365.921	−	1460.35i	−0.0931297	−	0.371670i
$250$		0			0
$251$			6323.18i			1.59010i	0.606543	+	0.795051i	$0.292556\pi$
$251$			6323.18i			1.59010i	−0.606543	+	0.795051i	$0.707444\pi$
$252$	2293.74	−	535.206i	0.573380	−	0.133789i
$253$	654.497	+	654.497i	0.162640	+	0.162640i
$254$	−3412.08	−	5909.89i	−0.842885	−	1.45992i
$255$		0			0
$256$	968.943	−	1678.26i	0.236558	−	0.409731i
$257$	1363.16	−	365.257i	0.330861	−	0.0886541i	−0.0895642	−	0.995981i	$-0.528547\pi$
$257$	1363.16	−	365.257i	0.330861	−	0.0886541i	0.420426	+	0.907327i	$0.361881\pi$
$258$	168.112	−	10323.2i	0.0405666	−	2.49106i
$259$	286.879	−	165.630i	0.0688255	−	0.0397364i
$260$		0			0
$261$	−4605.81	−	150.050i	−1.09231	−	0.0355857i
$262$	−5143.45	+	5143.45i	−1.21284	+	1.21284i
$263$	−317.317	−	85.0248i	−0.0743977	−	0.0199348i	0.221428	−	0.975177i	$-0.428928\pi$
$263$	−317.317	−	85.0248i	−0.0743977	−	0.0199348i	−0.295826	+	0.955242i	$0.595595\pi$
$264$	−745.628	+	186.833i	−0.173827	+	0.0435559i
$265$		0			0
$266$	3038.59	+	1754.33i	0.700405	+	0.404379i
$267$	−2796.81	−	5031.70i	−0.641057	−	1.15331i
$268$	−54.2832	+	202.588i	−0.0123727	+	0.0461754i
$269$	764.226			0.173218			0.0866091	−	0.996242i	$-0.472397\pi$
$269$	764.226			0.173218			0.0866091	+	0.996242i	$0.472397\pi$
$270$		0			0
$271$	4645.09			1.04121			0.520607	−	0.853797i	$-0.325706\pi$
$271$	4645.09			1.04121			0.520607	+	0.853797i	$0.325706\pi$
$272$	41.2142	−	153.813i	0.00918742	−	0.0342879i
$273$	−1424.49	−	2562.76i	−0.315801	−	0.568152i
$274$	−8816.19	−	5090.03i	−1.94382	−	1.12226i
$275$		0			0
$276$	−6314.10	+	1582.13i	−1.37704	+	0.345047i
$277$	−5783.77	−	1549.76i	−1.25456	−	0.336158i	−0.430463	−	0.902608i	$-0.641650\pi$
$277$	−5783.77	−	1549.76i	−1.25456	−	0.336158i	−0.824096	+	0.566450i	$0.808316\pi$
$278$	6887.13	−	6887.13i	1.48584	−	1.48584i
$279$	−4023.11	−	7523.85i	−0.863288	−	1.61448i
$280$		0			0
$281$	4201.11	−	2425.51i	0.891877	−	0.514925i	0.0173209	−	0.999850i	$-0.494486\pi$
$281$	4201.11	−	2425.51i	0.891877	−	0.514925i	0.874556	+	0.484925i	$0.161153\pi$
$282$	−88.7415	+	5449.31i	−0.0187393	+	1.15071i
$283$	345.530	−	92.5845i	0.0725782	−	0.0194473i	−0.222347	−	0.974968i	$-0.571372\pi$
$283$	345.530	−	92.5845i	0.0725782	−	0.0194473i	0.294925	+	0.955520i	$0.404705\pi$
$284$	647.098	−	1120.81i	0.135205	−	0.234182i
$285$		0			0
$286$	1483.25	+	2569.07i	0.306667	+	0.531162i
$287$	1799.02	+	1799.02i	0.370010	+	0.370010i
$288$	−1725.48	+	5691.39i	−0.353039	+	1.16447i
$289$		−	4842.88i		−	0.985727i
$290$		0			0
$291$	258.528	+	1031.75i	0.0520796	+	0.207844i
$292$	−623.814	−	2328.11i	−0.125020	−	0.466582i
$293$	2206.15	+	8233.45i	0.439879	+	1.64165i	0.729114	+	0.684392i	$0.239932\pi$
$293$	2206.15	+	8233.45i	0.439879	+	1.64165i	−0.289236	+	0.957258i	$0.593401\pi$
$294$	6414.25	+	1831.14i	1.27240	+	0.363245i
$295$		0			0
$296$		−	760.273i		−	0.149290i
$297$	1088.78	−	559.581i	0.212718	−	0.109327i
$298$	1960.24	+	1960.24i	0.381052	+	0.381052i
$299$	4051.54	+	7017.48i	0.783635	+	1.35730i
$300$		0			0
$301$	−1648.90	+	2855.98i	−0.315751	+	0.546897i
$302$	8675.77	−	2324.67i	1.65310	−	0.442946i
$303$	−4941.19	−	2961.10i	−0.936844	−	0.561422i
$304$	−1757.46	+	1014.67i	−0.331570	+	0.191432i
$305$		0			0
$306$	32.7665	−	1005.77i	0.00612137	−	0.187896i
$307$	6239.03	−	6239.03i	1.15987	−	1.15987i	0.175367	−	0.984503i	$-0.443889\pi$
$307$	6239.03	−	6239.03i	1.15987	−	1.15987i	0.984503	−	0.175367i	$-0.0561111\pi$
$308$	735.237	+	197.006i	0.136020	+	0.0364463i
$309$	1034.34	+	1068.59i	0.190426	+	0.196730i
$310$		0			0
$311$	−1983.11	−	1144.95i	−0.361582	−	0.208760i	0.308192	−	0.951324i	$-0.400276\pi$
$311$	−1983.11	−	1144.95i	−0.361582	−	0.208760i	−0.669775	+	0.742565i	$0.733609\pi$
$312$	−6728.45	−	109.572i	−1.22091	−	0.0198824i
$313$	−1583.94	+	5911.34i	−0.286037	+	1.06750i	0.662042	+	0.749467i	$0.269690\pi$
$313$	−1583.94	+	5911.34i	−0.286037	+	1.06750i	−0.948079	+	0.318036i	$0.896977\pi$
$314$	3137.38			0.563862
$315$		0			0
$316$	1917.56			0.341365
$317$	−2327.37	+	8685.87i	−0.412361	+	1.53895i	0.377704	+	0.925927i	$0.376714\pi$
$317$	−2327.37	+	8685.87i	−0.412361	+	1.53895i	−0.790064	+	0.613024i	$0.789953\pi$
$318$	−1017.99	+	1698.72i	−0.179516	+	0.299558i
$319$	−1289.72	−	744.620i	−0.226365	−	0.130692i
$320$		0			0
$321$	−1742.96	+	6105.37i	−0.303061	+	1.06158i
$322$	3368.82	+	902.673i	0.583035	+	0.156224i
$323$	631.910	−	631.910i	0.108856	−	0.108856i
$324$	−560.337	+	8590.67i	−0.0960797	+	1.47302i
$325$		0			0
$326$	−2324.46	+	1342.03i	−0.394909	+	0.228001i
$327$	−4499.53	+	2501.01i	−0.760931	+	0.422955i
$328$	5640.22	−	1511.29i	0.949479	−	0.254412i
$329$	870.409	−	1507.59i	0.145858	−	0.252633i
$330$		0			0
$331$	368.018	+	637.425i	0.0611120	+	0.105849i	0.894963	−	0.446141i	$-0.147202\pi$
$331$	368.018	+	637.425i	0.0611120	+	0.105849i	−0.833851	+	0.551990i	$0.813869\pi$
$332$	2419.38	+	2419.38i	0.399942	+	0.399942i
$333$	275.124	+	1179.10i	0.0452754	+	0.194037i
$334$		−	2826.75i		−	0.463093i
$335$		0			0
$336$	524.460	−	507.652i	0.0851537	−	0.0824247i
$337$	−1168.46	−	4360.75i	−0.188873	−	0.704883i	−0.993768	−	0.111466i	$-0.964445\pi$
$337$	−1168.46	−	4360.75i	−0.188873	−	0.704883i	0.804896	−	0.593417i	$-0.202221\pi$
$338$	4190.74	+	15640.0i	0.674396	+	2.51688i
$339$	282.910	−	273.844i	0.0453262	−	0.0438736i
$340$		0			0
$341$		−	2757.25i		−	0.437869i
$342$	−9358.64	+	8768.10i	−1.47970	+	1.38633i
$343$	−3298.23	−	3298.23i	−0.519207	−	0.519207i
$344$	3784.39	+	6554.76i	0.593141	+	1.02735i
$345$		0			0
$346$	1582.11	−	2740.29i	0.245822	−	0.425777i
$347$	3929.82	−	1052.99i	0.607964	−	0.162904i	0.0583140	−	0.998298i	$-0.481428\pi$
$347$	3929.82	−	1052.99i	0.607964	−	0.162904i	0.549651	+	0.835395i	$0.314761\pi$
$348$	9154.05	−	5088.18i	1.41008	−	0.783779i
$349$	−2120.49	+	1224.26i	−0.325235	+	0.187775i	−0.653724	−	0.756733i	$-0.726794\pi$
$349$	−2120.49	+	1224.26i	−0.325235	+	0.187775i	0.328489	+	0.944508i	$0.393461\pi$
$350$		0			0
$351$	10474.7	−	2264.92i	1.59288	−	0.344424i
$352$	−1359.02	+	1359.02i	−0.205784	+	0.205784i
$353$	10497.9	+	2812.90i	1.58285	+	0.424123i	0.939807	−	0.341707i	$-0.111005\pi$
$353$	10497.9	+	2812.90i	1.58285	+	0.424123i	0.643043	+	0.765830i	$0.277672\pi$
$354$	323.051	−	1131.61i	0.0485027	−	0.169899i
$355$		0			0
$356$	11330.5	+	6541.64i	1.68683	+	0.973894i
$357$	−165.226	+	275.712i	−0.0244949	+	0.0408745i
$358$	−3099.32	+	11566.8i	−0.457554	+	1.70762i
$359$	6928.63			1.01861			0.509303	−	0.860587i	$-0.329903\pi$
$359$	6928.63			1.01861			0.509303	+	0.860587i	$0.329903\pi$
$360$		0			0
$361$	−4529.72			−0.660406
$362$	−227.440	+	848.818i	−0.0330221	+	0.123240i
$363$	−6519.61	−	106.171i	−0.942674	−	0.0153514i
$364$	5770.88	+	3331.82i	0.830978	+	0.479766i
$365$		0			0
$366$	1161.87	+	1200.34i	0.165935	+	0.171429i
$367$	9084.65	+	2434.22i	1.29214	+	0.346227i	0.838472	−	0.544944i	$-0.183449\pi$
$367$	9084.65	+	2434.22i	1.29214	+	0.346227i	0.453666	+	0.891172i	$0.350116\pi$
$368$	−1426.37	+	1426.37i	−0.202051	+	0.202051i
$369$	−8200.47	+	4384.91i	−1.15691	+	0.618615i
$370$		0			0
$371$	547.817	−	316.282i	0.0766610	−	0.0442603i
$372$	16632.5	+	9967.34i	2.31816	+	1.38920i
$373$	5601.71	−	1500.97i	0.777602	−	0.208358i	0.151875	−	0.988400i	$-0.451469\pi$
$373$	5601.71	−	1500.97i	0.777602	−	0.208358i	0.625727	+	0.780042i	$0.284802\pi$
$374$	162.603	−	281.637i	0.0224813	−	0.0389388i
$375$		0			0
$376$	−1997.67	−	3460.07i	−0.273995	−	0.474573i
$377$	−9218.86	−	9218.86i	−1.25940	−	1.25940i
$378$	2498.63	−	3877.28i	0.339989	−	0.527581i
$379$		−	6617.31i		−	0.896856i	−0.893819	−	0.448428i	$-0.851984\pi$
$379$		−	6617.31i		−	0.896856i	0.893819	−	0.448428i	$-0.148016\pi$
$380$		0			0
$381$	−7660.97	−	2187.05i	−1.03014	−	0.294084i
$382$	407.137	+	1519.46i	0.0545313	+	0.203514i
$383$	−3218.73	−	12012.4i	−0.429423	−	1.60263i	−0.754070	−	0.656795i	$-0.771912\pi$
$383$	−3218.73	−	12012.4i	−0.429423	−	1.60263i	0.324646	−	0.945836i	$-0.394755\pi$
$384$	−2430.06	−	9698.10i	−0.322939	−	1.28881i
$385$		0			0
$386$		−	6393.68i		−	0.843082i
$387$	−8241.18	−	8796.23i	−1.08249	−	1.15539i
$388$	−1709.32	−	1709.32i	−0.223654	−	0.223654i
$389$	−4995.39	−	8652.28i	−0.651096	−	1.12773i	−0.982857	−	0.184369i	$-0.940976\pi$
$389$	−4995.39	−	8652.28i	−0.651096	−	1.12773i	0.331761	−	0.943364i	$-0.392357\pi$
$390$		0			0
$391$	444.154	−	769.297i	0.0574471	−	0.0995014i
$392$	−4723.43	+	1265.64i	−0.608595	+	0.163073i
$393$	−138.276	+	8491.02i	−0.0177483	+	1.08986i
$394$	−14431.1	+	8331.78i	−1.84524	+	1.06535i
$395$		0			0
$396$	−1468.78	+	2362.82i	−0.186386	+	0.299839i
$397$	−1248.70	+	1248.70i	−0.157860	+	0.157860i	−0.781618	−	0.623758i	$-0.785605\pi$
$397$	−1248.70	+	1248.70i	−0.157860	+	0.157860i	0.623758	+	0.781618i	$0.285605\pi$
$398$	−16274.9	−	4360.85i	−2.04972	−	0.549220i
$399$	3973.44	−	995.628i	0.498548	−	0.124922i
$400$		0			0
$401$	7999.65	+	4618.60i	0.996218	+	0.575166i	0.907127	−	0.420857i	$-0.138271\pi$
$401$	7999.65	+	4618.60i	0.996218	+	0.575166i	0.0890905	+	0.996024i	$0.471604\pi$
$402$	199.549	+	359.005i	0.0247577	+	0.0445412i
$403$	6247.40	−	23315.6i	0.772221	−	2.88197i
$404$	13091.8			1.61224
$405$		0			0
$406$	−5611.47			−0.685942
$407$	−101.271	+	377.950i	−0.0123338	+	0.0460302i
$408$	358.403	+	644.797i	0.0434892	+	0.0782407i
$409$	2817.50	+	1626.68i	0.340626	+	0.196661i	0.660549	−	0.750783i	$-0.270324\pi$
$409$	2817.50	+	1626.68i	0.340626	+	0.196661i	−0.319923	+	0.947444i	$0.603657\pi$
$410$		0			0
$411$	−11528.6	+	2888.73i	−1.38361	+	0.346692i
$412$	−3264.75	−	874.787i	−0.390395	−	0.104606i
$413$	−265.796	+	265.796i	−0.0316681	+	0.0316681i
$414$	−6729.89	+	10826.3i	−0.798927	+	1.28523i
$415$		0			0
$416$	−14571.3	+	8412.77i	−1.71735	+	0.991514i
$417$	185.152	−	11369.6i	0.0217433	−	1.33518i
$418$	−4003.20	+	1072.65i	−0.468428	+	0.125515i
$419$	−1840.03	+	3187.02i	−0.214537	+	0.371590i	−0.953129	−	0.302563i	$-0.902158\pi$
$419$	−1840.03	+	3187.02i	−0.214537	+	0.371590i	0.738592	+	0.674153i	$0.235491\pi$
$420$		0			0
$421$	−3430.26	−	5941.39i	−0.397104	−	0.687804i	0.596263	−	0.802789i	$-0.296651\pi$
$421$	−3430.26	−	5941.39i	−0.397104	−	0.687804i	−0.993367	+	0.114985i	$0.963318\pi$
$422$	4260.56	+	4260.56i	0.491472	+	0.491472i
$423$	4350.28	+	4643.28i	0.500043	+	0.533721i
$424$		−	1451.80i		−	0.166287i
$425$		0			0
$426$	−616.030	−	2458.50i	−0.0700628	−	0.279613i
$427$	−138.106	−	515.419i	−0.0156520	−	0.0584142i
$428$	−3734.74	−	13938.3i	−0.421789	−	1.57414i
$429$	3330.28	+	950.728i	0.374796	+	0.106997i
$430$		0			0
$431$			3116.28i			0.348273i	0.984722	+	0.174137i	$0.0557134\pi$
$431$			3116.28i			0.348273i	−0.984722	+	0.174137i	$0.944287\pi$
$432$	1219.52	+	2372.82i	0.135820	+	0.264264i
$433$	−526.507	−	526.507i	−0.0584349	−	0.0584349i	0.677285	−	0.735720i	$-0.263156\pi$
$433$	−526.507	−	526.507i	−0.0584349	−	0.0584349i	−0.735720	+	0.677285i	$0.763156\pi$
$434$	−5194.66	−	8997.41i	−0.574543	−	0.995137i
$435$		0			0
$436$	5849.77	−	10132.1i	0.642554	−	1.11294i
$437$	−10934.8	+	2929.98i	−1.19699	+	0.320732i
$438$	−4048.77	−	2426.31i	−0.441685	−	0.264688i
$439$	3213.40	−	1855.26i	0.349356	−	0.201701i	−0.315046	−	0.949076i	$-0.602020\pi$
$439$	3213.40	−	1855.26i	0.349356	−	0.201701i	0.664401	+	0.747376i	$0.268687\pi$
$440$		0			0
$441$	6867.52	−	3672.16i	0.741553	−	0.396519i
$442$	2013.13	−	2013.13i	0.216640	−	0.216640i
$443$	1898.77	+	508.773i	0.203641	+	0.0545655i	0.359198	−	0.933261i	$-0.383050\pi$
$443$	1898.77	+	508.773i	0.203641	+	0.0545655i	−0.155556	+	0.987827i	$0.549717\pi$
$444$	−1913.81	−	1977.17i	−0.204562	−	0.211335i
$445$		0			0
$446$	−7568.16	−	4369.48i	−0.803504	−	0.463903i
$447$	3236.05	+	52.6987i	0.342415	+	0.00557621i
$448$	−1583.49	+	5909.67i	−0.166993	+	0.623226i
$449$	−6556.48			−0.689131			−0.344565	−	0.938762i	$-0.611974\pi$
$449$	−6556.48			−0.689131			−0.344565	+	0.938762i	$0.611974\pi$
$450$		0			0
$451$	−3005.20			−0.313768
$452$	−231.602	+	864.350i	−0.0241010	+	0.0899460i
$453$	5390.20	−	8994.62i	0.559059	−	0.932901i
$454$	12164.2	+	7023.01i	1.25748	+	0.726005i
$455$		0			0
$456$	2580.79	−	9040.18i	0.265036	−	0.928389i
$457$	−12355.7	−	3310.69i	−1.26471	−	0.338879i	−0.436710	−	0.899603i	$-0.643856\pi$
$457$	−12355.7	−	3310.69i	−1.26471	−	0.338879i	−0.828003	+	0.560724i	$0.810523\pi$
$458$	−12556.4	+	12556.4i	−1.28105	+	1.28105i
$459$	−789.180	−	870.311i	−0.0802522	−	0.0885025i
$460$		0			0
$461$	−1996.02	+	1152.40i	−0.201657	+	0.116427i	−0.597428	−	0.801922i	$-0.703811\pi$
$461$	−1996.02	+	1152.40i	−0.201657	+	0.116427i	0.395771	+	0.918349i	$0.370477\pi$
$462$	1302.91	−	724.210i	0.131206	−	0.0729292i
$463$	1195.40	−	320.306i	0.119989	−	0.0321509i	−0.198325	−	0.980136i	$-0.563550\pi$
$463$	1195.40	−	320.306i	0.119989	−	0.0321509i	0.318314	+	0.947985i	$0.396883\pi$
$464$	1622.78	−	2810.74i	0.162362	−	0.281219i
$465$		0			0
$466$	6817.95	+	11809.0i	0.677759	+	1.17391i
$467$	−3769.54	−	3769.54i	−0.373519	−	0.373519i	0.495238	−	0.868757i	$-0.335081\pi$
$467$	−3769.54	−	3769.54i	−0.373519	−	0.373519i	−0.868757	+	0.495238i	$0.835081\pi$
$468$	−17773.9	+	16652.3i	−1.75555	+	1.64478i
$469$		−	131.195i		−	0.0129169i
$470$		0			0
$471$	2631.83	−	2547.49i	0.257470	−	0.249219i
$472$	223.285	+	833.312i	0.0217744	+	0.0812633i
$473$	−1008.19	−	3762.63i	−0.0980058	−	0.365763i
$474$	2698.28	−	2611.80i	0.261468	−	0.253089i
$475$		0			0
$476$		−	730.507i		−	0.0703419i
$477$	525.369	+	2251.58i	0.0504298	+	0.216127i
$478$	−12248.8	−	12248.8i	−1.17207	−	1.17207i
$479$	−1205.53	−	2088.04i	−0.114994	−	0.199175i	0.802783	−	0.596271i	$-0.203352\pi$
$479$	−1205.53	−	2088.04i	−0.114994	−	0.199175i	−0.917777	+	0.397096i	$0.870018\pi$
$480$		0			0
$481$	−1712.73	+	2966.53i	−0.162357	+	0.281210i
$482$	28302.4	−	7583.60i	2.67456	−	0.716646i
$483$	3558.93	−	1978.19i	0.335273	−	0.186358i
$484$	12833.6	−	7409.49i	1.20526	−	0.695858i
$485$		0			0
$486$	10912.4	+	12851.5i	1.01851	+	1.19950i
$487$	13278.0	−	13278.0i	1.23549	−	1.23549i	0.273666	−	0.961825i	$-0.411764\pi$
$487$	13278.0	−	13278.0i	1.23549	−	1.23549i	0.961825	−	0.273666i	$-0.0882362\pi$
$488$	−1182.94	−	316.967i	−0.109732	−	0.0294025i
$489$	−860.207	+	3013.20i	−0.0795499	+	0.278653i
$490$		0			0
$491$	−4882.30	−	2818.80i	−0.448748	−	0.259085i	0.258553	−	0.965997i	$-0.416754\pi$
$491$	−4882.30	−	2818.80i	−0.448748	−	0.259085i	−0.707301	+	0.706912i	$0.750088\pi$
$492$	10863.7	−	18128.2i	0.995474	−	1.66115i
$493$	−369.915	+	1380.54i	−0.0337934	+	0.126119i
$494$	−36282.0			−3.30446
$495$		0			0
$496$	6008.99			0.543975
$497$	−209.529	+	781.973i	−0.0189108	+	0.0705760i
$498$	6699.70	+	109.104i	0.602853	+	0.00981741i
$499$	5518.24	+	3185.96i	0.495051	+	0.285818i	0.726667	−	0.686990i	$-0.241068\pi$
$499$	5518.24	+	3185.96i	0.495051	+	0.285818i	−0.231617	+	0.972807i	$0.574402\pi$
$500$		0			0
$501$	−2295.27	−	2371.26i	−0.204680	−	0.211457i
$502$	−27184.0	−	7283.92i	−2.41689	−	0.647604i
$503$	−5861.56	+	5861.56i	−0.519591	+	0.519591i	−0.917448	−	0.397857i	$-0.869754\pi$
$503$	−5861.56	+	5861.56i	−0.519591	+	0.519591i	0.397857	+	0.917448i	$0.369754\pi$
$504$	−110.104	+	3379.67i	−0.00973104	+	0.298695i
$505$		0			0
$506$	−3567.69	+	2059.81i	−0.313445	+	0.180968i
$507$	16214.8	+	9717.06i	1.42037	+	0.851183i
$508$	17489.6	−	4686.33i	1.52751	−	0.409296i
$509$	−10716.8	+	18562.0i	−0.933228	+	1.61640i	−0.155465	+	0.987841i	$0.549688\pi$
$509$	−10716.8	+	18562.0i	−0.933228	+	1.61640i	−0.777763	+	0.628557i	$0.783646\pi$
$510$		0			0
$511$	753.837	+	1305.68i	0.0652598	+	0.113033i
$512$	−4785.52	−	4785.52i	−0.413070	−	0.413070i
$513$	−731.103	+	14954.3i	−0.0629220	+	1.28703i
$514$			6281.10i			0.539003i
$515$		0			0
$516$	26341.8	+	7520.05i	2.24735	+	0.641573i
$517$	532.196	+	1986.18i	0.0452727	+	0.168960i
$518$	381.591	+	1424.12i	0.0323671	+	0.120796i
$519$	−897.886	−	3583.36i	−0.0759399	−	0.303068i
$520$		0			0
$521$		−	18398.8i		−	1.54715i	−0.633703	−	0.773577i	$-0.718466\pi$
$521$		−	18398.8i		−	1.54715i	0.633703	−	0.773577i	$-0.281534\pi$
$522$	5950.70	−	19628.0i	0.498956	−	1.64577i
$523$	12039.3	+	12039.3i	1.00658	+	1.00658i	0.999978	+	0.00659910i	$0.00210057\pi$
$523$	12039.3	+	12039.3i	1.00658	+	1.00658i	0.00659910	+	0.999978i	$0.497899\pi$
$524$	−9649.99	−	16714.3i	−0.804508	−	1.39345i
$525$		0			0
$526$	731.060	−	1266.23i	0.0606003	−	0.104963i
$527$	−2555.99	+	684.877i	−0.211273	+	0.0566104i
$528$	−14.0385	+	862.054i	−0.00115709	+	0.0710532i
$529$	791.700	−	457.088i	0.0650695	−	0.0375679i
$530$		0			0
$531$	−647.846	−	1211.57i	−0.0529456	−	0.0990166i
$532$	−6582.85	+	6582.85i	−0.536471	+	0.536471i
$533$	−25412.4	−	6809.22i	−2.06516	−	0.553359i
$534$	24853.5	−	6227.57i	2.01408	−	0.504669i
$535$		0			0
$536$	−260.765	−	150.553i	−0.0210137	−	0.0121322i
$537$	6792.12	+	12219.6i	0.545813	+	0.981962i
$538$	−880.343	+	3285.49i	−0.0705470	+	0.263285i
$539$	2516.72			0.201119
$540$		0			0
$541$	11737.9			0.932811			0.466405	−	0.884571i	$-0.345549\pi$
$541$	11737.9			0.932811			0.466405	+	0.884571i	$0.345549\pi$
$542$	−5350.86	+	19969.7i	−0.424058	+	1.58260i
$543$	498.431	+	896.719i	0.0393918	+	0.0708690i
$544$	1597.40	+	922.257i	0.125897	+	0.0726865i
$545$		0			0
$546$	12658.5	−	3171.85i	0.992187	−	0.248613i
$547$	8392.40	+	2248.74i	0.656002	+	0.175775i	0.571441	−	0.820643i	$-0.306385\pi$
$547$	8392.40	+	2248.74i	0.656002	+	0.175775i	0.0845610	+	0.996418i	$0.473051\pi$
$548$	19099.6	−	19099.6i	1.48886	−	1.48886i
$549$	1949.31	+	63.5054i	0.151538	+	0.00493687i
$550$		0			0
$551$	15774.0	−	9107.10i	1.21959	−	0.704130i
$552$	152.164	−	9343.85i	0.0117328	−	0.720472i
$553$	−1158.62	+	310.452i	−0.0890951	+	0.0238730i
$554$	13325.1	−	23079.8i	1.02189	−	1.76997i
$555$		0			0
$556$	12921.4	+	22380.6i	0.985595	+	1.70710i
$557$	3736.22	+	3736.22i	0.284217	+	0.284217i	0.834788	−	0.550571i	$-0.185590\pi$
$557$	3736.22	+	3736.22i	0.284217	+	0.284217i	−0.550571	+	0.834788i	$0.685590\pi$
$558$	36980.2	−	8628.73i	2.80555	−	0.654629i
$559$		−	34101.6i		−	2.58022i
$560$		0			0
$561$	−92.2815	−	368.285i	−0.00694497	−	0.0277166i
$562$	5588.10	+	20855.1i	0.419430	+	1.56533i
$563$	2537.76	+	9471.07i	0.189972	+	0.708984i	0.993511	+	0.113733i	$0.0362807\pi$
$563$	2537.76	+	9471.07i	0.189972	+	0.708984i	−0.803540	+	0.595251i	$0.797053\pi$
$564$	−13905.1	−	3969.62i	−1.03814	−	0.296367i
$565$		0			0
$566$			1592.12i			0.118236i
$567$	−1052.26	−	5281.34i	−0.0779377	−	0.391174i
$568$	1313.81	+	1313.81i	0.0970536	+	0.0970536i
$569$	5188.49	+	8986.72i	0.382272	+	0.662114i	0.991387	−	0.130968i	$-0.0418084\pi$
$569$	5188.49	+	8986.72i	0.382272	+	0.662114i	−0.609115	+	0.793082i	$0.708475\pi$
$570$		0			0
$571$	2372.48	−	4109.26i	0.173880	−	0.301168i	−0.765893	−	0.642968i	$-0.777703\pi$
$571$	2372.48	−	4109.26i	0.173880	−	0.301168i	0.939773	+	0.341799i	$0.111036\pi$
$572$	−7602.86	+	2037.18i	−0.555755	+	0.148914i
$573$	1575.30	+	944.030i	0.114850	+	0.0688262i
$574$	−9806.54	+	5661.81i	−0.713096	+	0.411706i
$575$		0			0
$576$	−18991.8	−	11805.7i	−1.37383	−	0.854002i
$577$	−2575.02	+	2575.02i	−0.185788	+	0.185788i	−0.793872	−	0.608085i	$-0.791938\pi$
$577$	−2575.02	+	2575.02i	−0.185788	+	0.185788i	0.608085	+	0.793872i	$0.291938\pi$
$578$	20820.0	+	5578.70i	1.49827	+	0.401459i
$579$	−5191.53	−	5363.42i	−0.372630	−	0.384967i
$580$		0			0
$581$	−1853.52	−	1070.13i	−0.132353	−	0.0764140i
$582$	−4733.42	−	77.0834i	−0.337125	−	0.00549005i
$583$	−193.385	+	721.724i	−0.0137379	+	0.0512706i
$584$	3460.26			0.245182
$585$		0			0
$586$	−37937.8			−2.67439
$587$	2355.29	−	8790.07i	0.165610	−	0.618067i	−0.832351	−	0.554249i	$-0.813006\pi$
$587$	2355.29	−	8790.07i	0.165610	−	0.618067i	0.997962	−	0.0638179i	$-0.0203277\pi$
$588$	−9097.86	+	15181.6i	−0.638077	+	1.06476i
$589$	29204.6	+	16861.3i	2.04305	+	1.17955i
$590$		0			0
$591$	−5340.45	+	18706.9i	−0.371704	+	1.30203i
$592$	−823.683	−	220.705i	−0.0571844	−	0.0153225i
$593$	9619.29	−	9619.29i	0.666133	−	0.666133i	−0.290686	−	0.956819i	$-0.593883\pi$
$593$	9619.29	−	9619.29i	0.666133	−	0.666133i	0.956819	+	0.290686i	$0.0938833\pi$
$594$	1151.49	+	5325.36i	0.0795390	+	0.367849i
$595$		0			0
$596$	−6370.05	+	3677.75i	−0.437797	+	0.252762i
$597$	−17193.3	+	9556.73i	−1.17869	+	0.655161i
$598$	−34836.0	+	9334.27i	−2.38219	+	0.638306i
$599$	339.119	−	587.372i	0.0231320	−	0.0400657i	−0.854228	−	0.519899i	$-0.825970\pi$
$599$	339.119	−	587.372i	0.0231320	−	0.0400657i	0.877360	+	0.479833i	$0.159303\pi$
$600$		0			0
$601$	−4560.19	−	7898.48i	−0.309508	−	0.536083i	0.668747	−	0.743490i	$-0.266831\pi$
$601$	−4560.19	−	7898.48i	−0.309508	−	0.536083i	−0.978255	+	0.207407i	$0.933498\pi$
$602$	−10378.7	−	10378.7i	−0.702666	−	0.702666i
$603$	458.899	+	139.126i	0.0309914	+	0.00939579i
$604$			23831.5i			1.60545i
$605$		0			0
$606$	18422.0	−	17831.6i	1.23489	−	1.19532i
$607$	3566.69	+	13311.1i	0.238497	+	0.890082i	0.976541	+	0.215330i	$0.0690827\pi$
$607$	3566.69	+	13311.1i	0.238497	+	0.890082i	−0.738045	+	0.674752i	$0.764251\pi$
$608$	−6083.91	−	22705.5i	−0.405815	−	1.51452i
$609$	−4707.25	+	4556.39i	−0.313214	+	0.303176i
$610$		0			0
$611$			18001.3i			1.19190i
$612$	2555.19	+	774.669i	0.168771	+	0.0511669i
$613$	−7501.39	−	7501.39i	−0.494255	−	0.494255i	0.415389	−	0.909644i	$-0.363645\pi$
$613$	−7501.39	−	7501.39i	−0.494255	−	0.494255i	−0.909644	+	0.415389i	$0.863645\pi$
$614$	19635.2	+	34009.2i	1.29057	+	2.23534i
$615$		0			0
$616$	−546.390	+	946.376i	−0.0357381	+	0.0619003i
$617$	−21447.4	+	5746.81i	−1.39942	+	0.374972i	−0.878135	−	0.478413i	$-0.841212\pi$
$617$	−21447.4	+	5746.81i	−1.39942	+	0.374972i	−0.521281	+	0.853385i	$0.674546\pi$
$618$	−5785.46	+	3215.78i	−0.376578	+	0.209317i
$619$	6003.77	−	3466.28i	0.389841	−	0.225075i	−0.292250	−	0.956342i	$-0.594404\pi$
$619$	6003.77	−	3466.28i	0.389841	−	0.225075i	0.682091	+	0.731267i	$0.261071\pi$
$620$		0			0
$621$	3145.32	+	14546.3i	0.203248	+	0.939976i
$622$	7206.69	−	7206.69i	0.464569	−	0.464569i
$623$	−7905.13	−	2118.17i	−0.508366	−	0.136216i
$624$	−2071.96	+	7257.82i	−0.132924	+	0.465618i
$625$		0			0
$626$	−23588.8	−	13619.0i	−1.50607	−	0.869529i
$627$	−2487.16	+	4150.33i	−0.158417	+	0.264351i
$628$	−2154.52	+	8040.79i	−0.136903	+	0.510928i
$629$	375.519			0.0238043
$630$		0			0
$631$	5174.87			0.326479			0.163239	−	0.986586i	$-0.447806\pi$
$631$	5174.87			0.326479			0.163239	+	0.986586i	$0.447806\pi$
$632$	−712.516	+	2659.15i	−0.0448455	+	0.167366i
$633$	7033.52	+	114.540i	0.441639	+	0.00719205i
$634$	−34660.5	−	20011.2i	−2.17120	−	1.25354i
$635$		0			0
$636$	−3654.56	−	3775.56i	−0.227850	−	0.235394i
$637$	21281.7	+	5702.42i	1.32372	+	0.354691i
$638$	4686.88	−	4686.88i	0.290839	−	0.290839i
$639$	−2513.02	−	1562.15i	−0.155577	−	0.0967097i
$640$		0			0
$641$	1800.01	−	1039.24i	0.110914	−	0.0640365i	−0.443517	−	0.896266i	$-0.646269\pi$
$641$	1800.01	−	1039.24i	0.110914	−	0.0640365i	0.554431	+	0.832230i	$0.312936\pi$
$642$	−24239.8	−	14526.2i	−1.49014	−	0.892995i
$643$	−8982.29	+	2406.80i	−0.550898	+	0.147613i	−0.523521	−	0.852013i	$-0.675382\pi$
$643$	−8982.29	+	2406.80i	−0.550898	+	0.147613i	−0.0273763	+	0.999625i	$0.508715\pi$
$644$	−4626.92	+	8014.06i	−0.283115	+	0.490370i
$645$		0			0
$646$	1988.72	+	3444.57i	0.121123	+	0.209791i
$647$	12361.4	+	12361.4i	0.751125	+	0.751125i	0.974689	−	0.223564i	$-0.0717691\pi$
$647$	12361.4	+	12361.4i	0.751125	+	0.751125i	−0.223564	+	0.974689i	$0.571769\pi$
$648$	−11704.8	−	3969.11i	−0.709578	−	0.240619i
$649$		−	444.002i		−	0.0268546i
$650$		0			0
$651$	−11663.3	−	3329.64i	−0.702184	−	0.200459i
$652$	−1843.22	−	6878.98i	−0.110715	−	0.413192i
$653$	7383.03	+	27553.8i	0.442450	+	1.65125i	0.722581	+	0.691286i	$0.242955\pi$
$653$	7383.03	+	27553.8i	0.442450	+	1.65125i	−0.280131	+	0.959962i	$0.590378\pi$
$654$	−5568.92	−	22224.9i	−0.332969	−	1.32884i
$655$		0			0
$656$		−	6549.37i		−	0.389802i
$657$	−5366.48	+	1252.18i	−0.318670	+	0.0743565i
$658$	5478.63	+	5478.63i	0.324589	+	0.324589i
$659$	5594.17	+	9689.39i	0.330680	+	0.572754i	0.982645	−	0.185494i	$-0.0593887\pi$
$659$	5594.17	+	9689.39i	0.330680	+	0.572754i	−0.651966	+	0.758249i	$0.726055\pi$
$660$		0			0
$661$	−12520.6	+	21686.4i	−0.736757	+	1.27610i	0.217190	+	0.976129i	$0.430311\pi$
$661$	−12520.6	+	21686.4i	−0.736757	+	1.27610i	−0.953948	+	0.299972i	$0.903023\pi$
$662$	−3164.29	+	847.869i	−0.185776	+	0.0497785i
$663$	54.1206	−	3323.36i	0.00317024	−	0.194673i
$664$	−4254.01	+	2456.06i	−0.248626	+	0.143544i
$665$		0			0
$666$	−5385.99	−	175.467i	−0.313368	−	0.0102090i
$667$	12802.3	−	12802.3i	0.743190	−	0.743190i
$668$	7244.69	+	1941.21i	0.419619	+	0.112437i
$669$	−9896.58	+	2479.79i	−0.571934	+	0.143310i
$670$		0			0
$671$	545.845	+	315.144i	0.0314040	+	0.0181311i
$672$	4107.59	+	7389.90i	0.235794	+	0.424213i
$673$	4660.65	−	17393.8i	0.266946	−	0.996257i	−0.694102	−	0.719877i	$-0.744198\pi$
$673$	4660.65	−	17393.8i	0.266946	−	0.996257i	0.961048	−	0.276381i	$-0.0891350\pi$
$674$	20093.3			1.14832
$675$		0			0
$676$	−42961.7			−2.44434
$677$	5566.38	−	20774.0i	0.316002	−	1.17934i	−0.607051	−	0.794663i	$-0.707648\pi$
$677$	5566.38	−	20774.0i	0.316002	−	1.17934i	0.923053	−	0.384673i	$-0.125686\pi$
$678$	851.386	+	1531.71i	0.0482261	+	0.0867626i
$679$	1309.54	+	756.062i	0.0740139	+	0.0427319i
$680$		0			0
$681$	15906.6	−	3985.74i	0.895072	−	0.224279i
$682$	11853.7	+	3176.18i	0.665544	+	0.178332i
$683$	4348.95	−	4348.95i	0.243643	−	0.243643i	−0.574713	−	0.818355i	$-0.694886\pi$
$683$	4348.95	−	4348.95i	0.243643	−	0.243643i	0.818355	+	0.574713i	$0.194886\pi$
$684$	−16044.9	−	30006.5i	−0.896920	−	1.67738i
$685$		0			0
$686$	17978.8	−	10380.1i	1.00063	−	0.577715i
$687$	−337.564	+	20728.6i	−0.0187465	+	1.15116i
$688$	8200.05	−	2197.20i	0.454395	−	0.121755i
$689$	−3270.58	+	5664.81i	−0.180841	+	0.313225i
$690$		0			0
$691$	7927.92	+	13731.6i	0.436458	+	0.755967i	0.997413	−	0.0718787i	$-0.0228994\pi$
$691$	7927.92	+	13731.6i	0.436458	+	0.755967i	−0.560955	+	0.827846i	$0.689566\pi$
$692$	5936.61	+	5936.61i	0.326121	+	0.326121i
$693$	504.921	−	1665.45i	0.0276773	−	0.0912918i
$694$			18107.7i			0.990429i
$695$		0			0
$696$	3654.54	+	14584.9i	0.199030	+	0.794308i
$697$	746.467	+	2785.85i	0.0405659	+	0.151394i
$698$	−2820.56	−	10526.5i	−0.152951	−	0.570820i
$699$	15308.0	+	4370.13i	0.828330	+	0.236471i
$700$		0			0
$701$		−	21918.5i		−	1.18096i	−0.807054	−	0.590478i	$-0.798939\pi$
$701$		−	21918.5i		−	1.18096i	0.807054	−	0.590478i	$-0.201061\pi$
$702$	−2329.14	+	47641.0i	−0.125224	+	2.56139i
$703$	−3383.93	−	3383.93i	−0.181547	−	0.181547i
$704$	−3613.36	−	6258.53i	−0.193443	−	0.335053i
$705$		0			0
$706$	−24185.9	+	41891.2i	−1.28930	+	2.23314i
$707$	−7910.29	+	2119.56i	−0.420788	+	0.112750i
$708$	2678.35	+	1605.05i	0.142173	+	0.0851999i
$709$	−25661.5	+	14815.7i	−1.35929	+	0.784787i	−0.989528	−	0.144338i	$-0.953895\pi$
$709$	−25661.5	+	14815.7i	−1.35929	+	0.784787i	−0.369763	+	0.929126i	$0.620561\pi$
$710$		0			0
$711$	142.755	−	4381.89i	0.00752987	−	0.231130i
$712$	−13281.6	+	13281.6i	−0.699087	+	0.699087i
$713$	32378.6	+	8675.82i	1.70068	+	0.455697i
$714$	−994.982	−	1027.92i	−0.0521516	−	0.0538783i
$715$		0			0
$716$	−27516.2	−	15886.5i	−1.43622	−	0.829199i
$717$	−20220.8	−	329.295i	−1.05322	−	0.0171517i
$718$	−7981.37	+	29786.9i	−0.414850	+	1.54824i
$719$	5855.14			0.303700			0.151850	−	0.988404i	$-0.451477\pi$
$719$	5855.14			0.303700			0.151850	+	0.988404i	$0.451477\pi$
$720$		0			0
$721$	2114.24			0.109207
$722$	5217.97	−	19473.7i	0.268965	−	1.00379i
$723$	17584.1	−	29342.5i	0.904508	−	1.50935i
$724$	−2019.25	−	1165.81i	−0.103653	−	0.0598440i
$725$		0			0
$726$	7966.64	−	27906.1i	0.407258	−	1.42658i
$727$	−17456.9	−	4677.55i	−0.890563	−	0.238626i	−0.215604	−	0.976481i	$-0.569172\pi$
$727$	−17456.9	−	4677.55i	−0.890563	−	0.238626i	−0.674959	+	0.737855i	$0.735839\pi$
$728$	−6764.65	+	6764.65i	−0.344388	+	0.344388i
$729$	19589.1	+	1919.99i	0.995231	+	0.0975455i
$730$		0			0
$731$	−3237.56	+	1869.21i	−0.163811	+	0.0945762i
$732$	−3874.25	+	2153.46i	−0.195623	+	0.108735i
$733$	−35884.0	+	9615.09i	−1.80819	+	0.484504i	−0.995208	−	0.0977795i	$-0.968826\pi$
$733$	−35884.0	+	9615.09i	−1.80819	+	0.484504i	−0.812986	+	0.582284i	$0.802159\pi$
$734$	−20929.9	+	36251.7i	−1.05250	+	1.82299i
$735$		0			0
$736$	−11682.9	−	20235.3i	−0.585104	−	1.01343i
$737$	109.578	+	109.578i	0.00547676	+	0.00547676i
$738$	−9404.70	−	40305.8i	−0.469095	−	2.01040i
$739$			16862.4i			0.839371i	0.907670	+	0.419686i	$0.137860\pi$
$739$			16862.4i			0.839371i	−0.907670	+	0.419686i	$0.862140\pi$
$740$		0			0
$741$	−30435.6	+	29460.2i	−1.50888	+	1.46052i
$742$	728.677	+	2719.46i	0.0360520	+	0.134548i
$743$	2026.03	+	7561.26i	0.100038	+	0.373345i	0.997735	−	0.0672671i	$-0.0214280\pi$
$743$	2026.03	+	7561.26i	0.100038	+	0.373345i	−0.897697	+	0.440613i	$0.854761\pi$
$744$	−20002.3	+	19361.2i	−0.985643	+	0.954055i
$745$		0			0
$746$			25811.4i			1.26678i
$747$	5708.72	−	5348.49i	0.279613	−	0.261969i
$748$	610.143	+	610.143i	0.0298249	+	0.0298249i
$749$	4513.18	+	7817.06i	0.220171	+	0.381347i
$750$		0			0
$751$	9768.62	−	16919.7i	0.474650	−	0.822117i	−0.524929	−	0.851146i	$-0.675908\pi$
$751$	9768.62	−	16919.7i	0.474650	−	0.822117i	0.999579	+	0.0290288i	$0.00924145\pi$
$752$	−4328.57	+	1159.84i	−0.209903	+	0.0562433i
$753$	−28718.0	+	15962.6i	−1.38983	+	0.772523i
$754$	50252.4	−	29013.2i	2.42717	−	1.40133i
$755$		0			0
$756$	8221.19	+	9066.37i	0.395505	+	0.436165i
$757$	−10039.5	+	10039.5i	−0.482024	+	0.482024i	−0.905777	−	0.423754i	$-0.860712\pi$
$757$	−10039.5	+	10039.5i	−0.482024	+	0.482024i	0.423754	+	0.905777i	$0.360712\pi$
$758$	28448.5	+	7622.74i	1.36319	+	0.365265i
$759$	−1320.28	+	4624.79i	−0.0631400	+	0.221172i
$760$		0			0
$761$	−20084.8	−	11595.9i	−0.956731	−	0.552369i	−0.0615654	−	0.998103i	$-0.519609\pi$
$761$	−20084.8	−	11595.9i	−0.956731	−	0.552369i	−0.895165	+	0.445734i	$0.852943\pi$
$762$	18227.3	−	30415.9i	0.866545	−	1.44600i
$763$	−1894.15	+	7069.05i	−0.0898725	+	0.335409i
$764$	−4173.81			−0.197648
$765$		0			0
$766$	55350.5			2.61083
$767$	1006.02	−	3754.54i	0.0473604	−	0.176752i
$768$	10068.2	+	163.960i	0.473054	+	0.00770364i
$769$	−30950.8	−	17869.4i	−1.45138	−	0.837956i	−0.452822	−	0.891601i	$-0.649583\pi$
$769$	−30950.8	−	17869.4i	−1.45138	−	0.837956i	−0.998560	+	0.0536450i	$0.982916\pi$
$770$		0			0
$771$	5100.12	+	5268.98i	0.238231	+	0.246119i
$772$	16386.4	+	4390.71i	0.763935	+	0.204696i
$773$	−7858.61	+	7858.61i	−0.365659	+	0.365659i	−0.865891	−	0.500232i	$-0.833248\pi$
$773$	−7858.61	+	7858.61i	−0.365659	+	0.365659i	0.500232	+	0.865891i	$0.333248\pi$
$774$	47309.2	−	25296.9i	2.19702	−	1.17478i
$775$		0			0
$776$	3005.51	−	1735.23i	0.139036	−	0.0802723i
$777$	1476.46	+	884.796i	0.0681694	+	0.0408518i
$778$	42951.4	−	11508.8i	1.97928	−	0.530347i
$779$	18377.6	−	31831.0i	0.845246	−	1.46401i
$780$		0			0

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +O(q^{10})\)	\(q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +(-7.55654 + 4.36277i) q^{11} +(0.999152 - 61.3544i) q^{12} +(-73.7842 + 19.7704i) q^{13} +(-16.4389 + 28.4731i) q^{14} +(-9.50797 - 16.4683i) q^{16} +(5.92131 + 5.92131i) q^{17} +(-82.1614 - 87.6951i) q^{18} -106.718i q^{19} +(9.32953 + 37.2331i) q^{21} +(-10.0513 - 37.5120i) q^{22} +(-27.4553 - 102.465i) q^{23} +(84.7110 + 24.1833i) q^{24} -339.980i q^{26} +(-140.129 - 6.85080i) q^{27} +(-61.6846 - 61.6846i) q^{28} +(85.3380 + 147.810i) q^{29} +(-157.999 + 273.662i) q^{31} +(212.761 - 57.0093i) q^{32} +(-38.8906 - 23.3059i) q^{33} +(-32.2773 + 18.6353i) q^{34} +(281.176 - 150.349i) q^{36} +(31.7091 - 31.7091i) q^{37} +(458.791 + 122.933i) q^{38} +(-276.057 - 285.197i) q^{39} +(298.272 + 172.207i) q^{41} +(-170.816 - 2.78172i) q^{42} +(-115.545 + 431.220i) q^{43} +103.042 q^{44} +472.133 q^{46} +(60.9929 - 227.629i) q^{47} +(50.7917 - 84.7559i) q^{48} +(-249.789 - 144.216i) q^{49} +(-11.9448 + 41.8410i) q^{51} +(871.335 + 233.473i) q^{52} +(60.5508 - 60.5508i) q^{53} +(190.872 - 594.536i) q^{54} +(108.460 - 62.6197i) q^{56} +(484.682 - 269.405i) q^{57} +(-733.754 + 196.609i) q^{58} +(-25.4427 + 44.0680i) q^{59} +(-36.1174 - 62.5572i) q^{61} +(-994.494 - 994.494i) q^{62} +(-145.550 + 136.365i) q^{63} +828.227i q^{64} +(144.994 - 140.347i) q^{66} +(-4.59668 - 17.1550i) q^{67} +(-25.5947 - 95.5208i) q^{68} +(396.055 - 383.362i) q^{69} +109.592i q^{71} +(104.016 + 445.782i) q^{72} +(144.319 + 144.319i) q^{73} +(99.7935 + 172.847i) q^{74} +(-630.128 + 1091.41i) q^{76} +(-62.2595 + 16.6824i) q^{77} +(1544.09 - 858.266i) q^{78} +(-140.624 + 81.1891i) q^{79} +(-322.635 - 653.718i) q^{81} +(-1083.93 + 1083.93i) q^{82} +(-279.860 - 74.9883i) q^{83} +(124.433 - 435.873i) q^{84} +(-1720.76 - 993.479i) q^{86} +(-455.877 + 760.720i) q^{87} +(-38.2877 + 142.892i) q^{88} -1107.89 q^{89} -564.273 q^{91} +(-324.227 + 1210.03i) q^{92} +(-1641.75 - 26.7358i) q^{93} +(908.339 + 524.430i) q^{94} +(796.027 + 822.383i) q^{96} +(197.725 + 52.9802i) q^{97} +(907.741 - 907.741i) q^{98} +(7.67108 - 235.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more