LMFDB - Embedded newform 225.4.e.e.76.12

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.12
Character	$\chi$	$=$	225.76
Dual form			225.4.e.e.151.12

$q$-expansion

$f(q)$	$=$	$q+(2.42567 + 4.20138i) q^{2} +(-4.79753 + 1.99591i) q^{3} +(-7.76772 + 13.4541i) q^{4} +(-20.0228 - 15.3148i) q^{6} +(-8.11924 - 14.0629i) q^{7} -36.5569 q^{8} +(19.0327 - 19.1509i) q^{9} +O(q^{10})$	\(q+(2.42567 + 4.20138i) q^{2} +(-4.79753 + 1.99591i) q^{3} +(-7.76772 + 13.4541i) q^{4} +(-20.0228 - 15.3148i) q^{6} +(-8.11924 - 14.0629i) q^{7} -36.5569 q^{8} +(19.0327 - 19.1509i) q^{9} +(-29.7592 - 51.5445i) q^{11} +(10.4127 - 80.0501i) q^{12} +(-13.5395 + 23.4511i) q^{13} +(39.3891 - 68.2240i) q^{14} +(-26.5331 - 45.9567i) q^{16} +78.9077 q^{17} +(126.627 + 33.5097i) q^{18} -142.290 q^{19} +(67.0207 + 51.2621i) q^{21} +(144.372 - 250.060i) q^{22} +(-42.8140 + 74.1561i) q^{23} +(175.383 - 72.9643i) q^{24} -131.369 q^{26} +(-53.0864 + 129.865i) q^{27} +252.272 q^{28} +(-113.004 - 195.729i) q^{29} +(75.3561 - 130.521i) q^{31} +(-17.5066 + 30.3223i) q^{32} +(245.649 + 187.890i) q^{33} +(191.404 + 331.521i) q^{34} +(109.817 + 404.826i) q^{36} +234.171 q^{37} +(-345.149 - 597.816i) q^{38} +(18.1499 - 139.531i) q^{39} +(-36.9290 + 63.9629i) q^{41} +(-52.8017 + 405.924i) q^{42} +(-133.539 - 231.296i) q^{43} +924.645 q^{44} -415.410 q^{46} +(-133.013 - 230.385i) q^{47} +(219.019 + 167.521i) q^{48} +(39.6560 - 68.6862i) q^{49} +(-378.563 + 157.493i) q^{51} +(-210.342 - 364.323i) q^{52} -603.281 q^{53} +(-674.380 + 91.9724i) q^{54} +(296.814 + 514.097i) q^{56} +(682.643 - 283.999i) q^{57} +(548.222 - 949.548i) q^{58} +(-254.360 + 440.565i) q^{59} +(-39.1519 - 67.8131i) q^{61} +731.155 q^{62} +(-423.849 - 112.164i) q^{63} -594.391 q^{64} +(-193.533 + 1487.82i) q^{66} +(-244.101 + 422.796i) q^{67} +(-612.933 + 1061.63i) q^{68} +(57.3928 - 441.219i) q^{69} -73.2487 q^{71} +(-695.776 + 700.098i) q^{72} +115.831 q^{73} +(568.021 + 983.842i) q^{74} +(1105.27 - 1914.39i) q^{76} +(-483.244 + 837.004i) q^{77} +(630.249 - 262.202i) q^{78} +(-391.371 - 677.875i) q^{79} +(-4.51465 - 728.986i) q^{81} -358.310 q^{82} +(135.732 + 235.095i) q^{83} +(-1210.28 + 503.512i) q^{84} +(647.840 - 1122.09i) q^{86} +(932.801 + 713.471i) q^{87} +(1087.91 + 1884.31i) q^{88} +211.511 q^{89} +439.722 q^{91} +(-665.135 - 1152.05i) q^{92} +(-101.016 + 776.581i) q^{93} +(645.289 - 1117.67i) q^{94} +(23.4678 - 180.414i) q^{96} +(-833.050 - 1442.89i) q^{97} +384.769 q^{98} +(-1553.52 - 411.113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9 - 29 * q^11 - 77 * q^12 + 24 * q^13 + 69 * q^14 - 192 * q^16 + 158 * q^17 + 125 * q^18 - 150 * q^19 - 60 * q^21 - 18 * q^22 - 318 * q^23 + 342 * q^24 - 308 * q^26 - 394 * q^27 - 192 * q^28 - 106 * q^29 - 60 * q^31 - 914 * q^32 - 80 * q^33 + 108 * q^34 + 1303 * q^36 + 168 * q^37 - 640 * q^38 - 410 * q^39 + 353 * q^41 + 1521 * q^42 - 426 * q^43 + 1142 * q^44 + 540 * q^46 - 1210 * q^47 + 2680 * q^48 - 666 * q^49 - 1369 * q^51 - 75 * q^52 + 896 * q^53 - 2128 * q^54 + 570 * q^56 + 1544 * q^57 + 594 * q^58 - 482 * q^59 - 402 * q^61 + 5088 * q^62 - 1038 * q^63 + 1950 * q^64 + 2041 * q^66 - 201 * q^67 - 3437 * q^68 + 2856 * q^69 - 1888 * q^71 - 5493 * q^72 + 906 * q^73 - 10 * q^74 + 462 * q^76 - 2652 * q^77 - 4589 * q^78 - 258 * q^79 + 3071 * q^81 - 1746 * q^82 - 3012 * q^83 - 2703 * q^84 - 1952 * q^86 + 2708 * q^87 - 216 * q^88 - 1476 * q^89 - 1236 * q^91 - 5232 * q^92 + 3024 * q^93 - 63 * q^94 - 10424 * q^96 - 318 * q^97 + 15022 * q^98 - 1697 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.42567	+	4.20138i	0.857603	+	1.48541i	0.874209	+	0.485549i	$0.161380\pi$
$2$	2.42567	+	4.20138i	0.857603	+	1.48541i	−0.0166066	+	0.999862i	$0.505286\pi$
$3$	−4.79753	+	1.99591i	−0.923286	+	0.384113i
$3$	−4.79753	+	1.99591i	−0.923286	+	0.384113i
$4$	−7.76772	+	13.4541i	−0.970965	+	1.68176i
$5$		0			0
$5$		0			0
$6$	−20.0228	−	15.3148i	−1.36238	−	1.04204i
$7$	−8.11924	−	14.0629i	−0.438398	−	0.759327i	0.559169	−	0.829054i	$-0.311120\pi$
$7$	−8.11924	−	14.0629i	−0.438398	−	0.759327i	−0.997566	+	0.0697271i	$0.977787\pi$
$8$	−36.5569			−1.61560
$9$	19.0327	−	19.1509i	0.704914	−	0.709293i
$10$		0			0
$11$	−29.7592	−	51.5445i	−0.815704	−	1.41284i	−0.908821	−	0.417186i	$-0.863016\pi$
$11$	−29.7592	−	51.5445i	−0.815704	−	1.41284i	0.0931172	−	0.995655i	$-0.470317\pi$
$12$	10.4127	−	80.0501i	0.250491	−	1.92571i
$13$	−13.5395	+	23.4511i	−0.288860	+	0.500321i	−0.973538	−	0.228525i	$-0.926610\pi$
$13$	−13.5395	+	23.4511i	−0.288860	+	0.500321i	0.684678	+	0.728846i	$0.259943\pi$
$14$	39.3891	−	68.2240i	0.751942	−	1.30240i
$15$		0			0
$16$	−26.5331	−	45.9567i	−0.414580	−	0.718074i
$17$	78.9077			1.12576			0.562880	−	0.826538i	$-0.309693\pi$
$17$	78.9077			1.12576			0.562880	+	0.826538i	$0.309693\pi$
$18$	126.627	+	33.5097i	1.65813	+	0.438796i
$19$	−142.290			−1.71809			−0.859044	−	0.511902i	$-0.828941\pi$
$19$	−142.290			−1.71809			−0.859044	+	0.511902i	$0.828941\pi$
$20$		0			0
$21$	67.0207	+	51.2621i	0.696434	+	0.532681i
$22$	144.372	−	250.060i	1.39910	−	2.42331i
$23$	−42.8140	+	74.1561i	−0.388145	+	0.672288i	−0.992200	−	0.124655i	$-0.960217\pi$
$23$	−42.8140	+	74.1561i	−0.388145	+	0.672288i	0.604055	+	0.796943i	$0.293551\pi$
$24$	175.383	−	72.9643i	1.49166	−	0.620574i
$25$		0			0
$26$	−131.369			−0.990910
$27$	−53.0864	+	129.865i	−0.378388	+	0.925647i
$28$	252.272			1.70267
$29$	−113.004	−	195.729i	−0.723600	−	1.25331i	−0.959548	−	0.281546i	$-0.909153\pi$
$29$	−113.004	−	195.729i	−0.723600	−	1.25331i	0.235948	−	0.971766i	$-0.424180\pi$
$30$		0			0
$31$	75.3561	−	130.521i	0.436592	−	0.756200i	−0.560832	−	0.827930i	$-0.689519\pi$
$31$	75.3561	−	130.521i	0.436592	−	0.756200i	0.997424	+	0.0717300i	$0.0228520\pi$
$32$	−17.5066	+	30.3223i	−0.0967112	+	0.167509i
$33$	245.649	+	187.890i	1.29582	+	0.991133i
$34$	191.404	+	331.521i	0.965455	+	1.67222i
$35$		0			0
$36$	109.817	+	404.826i	0.508414	+	1.87419i
$37$	234.171			1.04047			0.520237	−	0.854022i	$-0.325844\pi$
$37$	234.171			1.04047			0.520237	+	0.854022i	$0.325844\pi$
$38$	−345.149	−	597.816i	−1.47344	−	2.55207i
$39$	18.1499	−	139.531i	0.0745208	−	0.572894i
$40$		0			0
$41$	−36.9290	+	63.9629i	−0.140667	+	0.243642i	−0.927748	−	0.373207i	$-0.878258\pi$
$41$	−36.9290	+	63.9629i	−0.140667	+	0.243642i	0.787081	+	0.616850i	$0.211591\pi$
$42$	−52.8017	+	405.924i	−0.193988	+	1.49132i
$43$	−133.539	−	231.296i	−0.473592	−	0.820285i	0.525951	−	0.850515i	$-0.323710\pi$
$43$	−133.539	−	231.296i	−0.473592	−	0.820285i	−0.999543	+	0.0302295i	$0.990376\pi$
$44$	924.645			3.16808
$45$		0			0
$46$	−415.410			−1.33150
$47$	−133.013	−	230.385i	−0.412806	−	0.715001i	0.582389	−	0.812910i	$-0.302118\pi$
$47$	−133.013	−	230.385i	−0.412806	−	0.715001i	−0.995195	+	0.0979088i	$0.968785\pi$
$48$	219.019	+	167.521i	0.658598	+	0.503742i
$49$	39.6560	−	68.6862i	0.115615	−	0.200251i
$50$		0			0
$51$	−378.563	+	157.493i	−1.03940	+	0.432420i
$52$	−210.342	−	364.323i	−0.560946	−	0.971588i
$53$	−603.281			−1.56353			−0.781765	−	0.623574i	$-0.785680\pi$
$53$	−603.281			−1.56353			−0.781765	+	0.623574i	$0.785680\pi$
$54$	−674.380	+	91.9724i	−1.69947	+	0.231775i
$55$		0			0
$56$	296.814	+	514.097i	0.708276	+	1.22677i
$57$	682.643	−	283.999i	1.58629	−	0.659940i
$58$	548.222	−	949.548i	1.24112	−	2.14969i
$59$	−254.360	+	440.565i	−0.561270	+	0.972148i	0.436116	+	0.899890i	$0.356354\pi$
$59$	−254.360	+	440.565i	−0.561270	+	0.972148i	−0.997386	+	0.0722573i	$0.976980\pi$
$60$		0			0
$61$	−39.1519	−	67.8131i	−0.0821786	−	0.142337i	0.822007	−	0.569478i	$-0.192854\pi$
$61$	−39.1519	−	67.8131i	−0.0821786	−	0.142337i	−0.904185	+	0.427140i	$0.859521\pi$
$62$	731.155			1.49769
$63$	−423.849	−	112.164i	−0.847618	−	0.224308i
$64$	−594.391			−1.16092
$65$		0			0
$66$	−193.533	+	1487.82i	−0.360943	+	2.77482i
$67$	−244.101	+	422.796i	−0.445101	+	0.770937i	−0.998059	−	0.0622718i	$-0.980165\pi$
$67$	−244.101	+	422.796i	−0.445101	+	0.770937i	0.552959	+	0.833209i	$0.313499\pi$
$68$	−612.933	+	1061.63i	−1.09307	+	1.89326i
$69$	57.3928	−	441.219i	0.100135	−	0.769805i
$70$		0			0
$71$	−73.2487			−0.122437			−0.0612184	−	0.998124i	$-0.519499\pi$
$71$	−73.2487			−0.122437			−0.0612184	+	0.998124i	$0.519499\pi$
$72$	−695.776	+	700.098i	−1.13886	+	1.14594i
$73$	115.831			0.185712			0.0928558	−	0.995680i	$-0.470400\pi$
$73$	115.831			0.185712			0.0928558	+	0.995680i	$0.470400\pi$
$74$	568.021	+	983.842i	0.892313	+	1.54553i
$75$		0			0
$76$	1105.27	−	1914.39i	1.66820	−	2.88941i
$77$	−483.244	+	837.004i	−0.715205	+	1.23877i
$78$	630.249	−	262.202i	0.914893	−	0.380622i
$79$	−391.371	−	677.875i	−0.557376	−	0.965404i	−0.997714	−	0.0675718i	$-0.978475\pi$
$79$	−391.371	−	677.875i	−0.557376	−	0.965404i	0.440338	−	0.897832i	$-0.354859\pi$
$80$		0			0
$81$	−4.51465	−	728.986i	−0.00619293	−	0.999981i
$82$	−358.310			−0.482545
$83$	135.732	+	235.095i	0.179501	+	0.310904i	0.941710	−	0.336427i	$-0.109218\pi$
$83$	135.732	+	235.095i	0.179501	+	0.310904i	−0.762209	+	0.647331i	$0.775885\pi$
$84$	−1210.28	+	503.512i	−1.57206	+	0.654020i
$85$		0			0
$86$	647.840	−	1122.09i	0.812307	−	1.40696i
$87$	932.801	+	713.471i	1.14950	+	0.879220i
$88$	1087.91	+	1884.31i	1.31785	+	2.28259i
$89$	211.511			0.251911			0.125955	−	0.992036i	$-0.459800\pi$
$89$	211.511			0.251911			0.125955	+	0.992036i	$0.459800\pi$
$90$		0			0
$91$	439.722			0.506543
$92$	−665.135	−	1152.05i	−0.753751	−	1.30553i
$93$	−101.016	+	776.581i	−0.112633	+	0.865889i
$94$	645.289	−	1117.67i	0.708047	−	1.22637i
$95$		0			0
$96$	23.4678	−	180.414i	0.0249498	−	0.191806i
$97$	−833.050	−	1442.89i	−0.871994	−	1.51034i	−0.859930	−	0.510411i	$-0.829493\pi$
$97$	−833.050	−	1442.89i	−0.871994	−	1.51034i	−0.0120642	−	0.999927i	$-0.503840\pi$
$98$	384.769			0.396607
$99$	−1553.52	−	411.113i	−1.57712	−	0.417358i
$100$		0			0
$101$	228.292	+	395.413i	0.224910	+	0.389555i	0.956292	−	0.292412i	$-0.0944580\pi$
$101$	228.292	+	395.413i	0.224910	+	0.389555i	−0.731383	+	0.681967i	$0.761125\pi$
$102$	−1579.95	−	1208.46i	−1.53371	−	1.17309i
$103$	−82.9660	+	143.701i	−0.0793678	+	0.137469i	−0.902977	−	0.429688i	$-0.858623\pi$
$103$	−82.9660	+	143.701i	−0.0793678	+	0.137469i	0.823610	+	0.567157i	$0.191957\pi$
$104$	494.963	−	857.300i	0.466683	−	0.808319i
$105$		0			0
$106$	−1463.36	−	2534.61i	−1.34089	−	2.32248i
$107$	452.071			0.408443			0.204221	−	0.978925i	$-0.434534\pi$
$107$	452.071			0.408443			0.204221	+	0.978925i	$0.434534\pi$
$108$	−1334.85	−	1722.98i	−1.18931	−	1.53513i
$109$	−463.243			−0.407070			−0.203535	−	0.979068i	$-0.565243\pi$
$109$	−463.243			−0.407070			−0.203535	+	0.979068i	$0.565243\pi$
$110$		0			0
$111$	−1123.44	+	467.385i	−0.960655	+	0.399660i
$112$	−430.857	+	746.267i	−0.363502	+	0.629604i
$113$	−475.041	+	822.795i	−0.395470	+	0.684974i	−0.993161	−	0.116753i	$-0.962752\pi$
$113$	−475.041	+	822.795i	−0.395470	+	0.684974i	0.597691	+	0.801726i	$0.296085\pi$
$114$	2849.05	+	2179.15i	2.34069	+	1.79032i
$115$		0			0
$116$	3511.14			2.81036
$117$	191.417	+	705.632i	0.151252	+	0.557570i
$118$	−2467.97			−1.92539
$119$	−640.670	−	1109.67i	−0.493531	−	0.854820i
$120$		0			0
$121$	−1105.72	+	1915.17i	−0.830746	+	1.43889i
$122$	189.939	−	328.984i	0.140953	−	0.244138i
$123$	49.5038	−	380.571i	0.0362895	−	0.278983i
$124$	1170.69	+	2027.69i	0.847831	+	1.46849i
$125$		0			0
$126$	−556.871	−	2052.82i	−0.393730	−	1.45143i
$127$	210.383			0.146996			0.0734979	−	0.997295i	$-0.476584\pi$
$127$	210.383			0.146996			0.0734979	+	0.997295i	$0.476584\pi$
$128$	−1301.74	−	2254.68i	−0.898896	−	1.55693i
$129$	1102.30	+	843.118i	0.752343	+	0.575445i
$130$		0			0
$131$	462.388	−	800.879i	0.308389	−	0.534146i	−0.669621	−	0.742703i	$-0.733543\pi$
$131$	462.388	−	800.879i	0.308389	−	0.534146i	0.978010	+	0.208557i	$0.0668767\pi$
$132$	−4436.02	+	1845.51i	−2.92504	+	1.21690i
$133$	1155.29	+	2001.02i	0.753205	+	1.30459i
$134$	−2368.44			−1.52688
$135$		0			0
$136$	−2884.62			−1.81878
$137$	968.837	+	1678.07i	0.604185	+	1.04648i	0.992180	+	0.124817i	$0.0398344\pi$
$137$	968.837	+	1678.07i	0.604185	+	1.04648i	−0.387995	+	0.921661i	$0.626832\pi$
$138$	1992.95	−	829.122i	1.22935	−	0.511446i
$139$	985.256	−	1706.51i	0.601211	−	1.04133i	−0.391427	−	0.920209i	$-0.628019\pi$
$139$	985.256	−	1706.51i	0.601211	−	1.04133i	0.992638	−	0.121119i	$-0.0386481\pi$
$140$		0			0
$141$	1097.96	+	839.797i	0.655780	+	0.501586i
$142$	−177.677	−	307.745i	−0.105002	−	0.181869i
$143$	1611.70			0.942498
$144$	−1385.11	−	366.546i	−0.801568	−	0.212121i
$145$		0			0
$146$	280.966	+	486.648i	0.159267	+	0.275858i
$147$	−53.1594	+	408.674i	−0.0298266	+	0.229298i
$148$	−1818.98	+	3150.56i	−1.01026	+	1.74983i
$149$	−798.166	+	1382.46i	−0.438848	+	0.760106i	−0.997601	−	0.0692276i	$-0.977947\pi$
$149$	−798.166	+	1382.46i	−0.438848	+	0.760106i	0.558753	+	0.829334i	$0.311280\pi$
$150$		0			0
$151$	1836.48	+	3180.88i	0.989741	+	1.71428i	0.618600	+	0.785706i	$0.287700\pi$
$151$	1836.48	+	3180.88i	0.989741	+	1.71428i	0.371141	+	0.928576i	$0.378967\pi$
$152$	5201.70			2.77575
$153$	1501.82	−	1511.15i	0.793564	−	0.798494i
$154$	−4688.76			−2.45345
$155$		0			0
$156$	1736.28	+	1328.03i	0.891114	+	0.681586i
$157$	−525.779	+	910.676i	−0.267272	+	0.462929i	−0.968156	−	0.250346i	$-0.919456\pi$
$157$	−525.779	+	910.676i	−0.267272	+	0.462929i	0.700884	+	0.713275i	$0.252789\pi$
$158$	1898.67	−	3288.60i	0.956014	−	1.65587i
$159$	2894.26	−	1204.10i	1.44358	−	0.600573i
$160$		0			0
$161$	1390.47			0.680648
$162$	3051.79	−	1787.24i	1.48007	−	0.866785i
$163$	−1998.77			−0.960463			−0.480232	−	0.877142i	$-0.659447\pi$
$163$	−1998.77			−0.960463			−0.480232	+	0.877142i	$0.659447\pi$
$164$	−573.708	−	993.691i	−0.273165	−	0.473136i
$165$		0			0
$166$	−658.483	+	1140.53i	−0.307881	+	0.533265i
$167$	−1240.51	+	2148.63i	−0.574813	+	0.995606i	0.421249	+	0.906945i	$0.361592\pi$
$167$	−1240.51	+	2148.63i	−0.574813	+	0.995606i	−0.996062	+	0.0886604i	$0.971741\pi$
$168$	−2450.07	−	1873.98i	−1.12516	−	0.860601i
$169$	731.863	+	1267.62i	0.333119	+	0.576980i
$170$		0			0
$171$	−2708.17	+	2724.99i	−1.21110	+	1.21863i
$172$	4149.16			1.83936
$173$	1313.04	+	2274.25i	0.577042	+	0.999466i	0.995816	+	0.0913761i	$0.0291265\pi$
$173$	1313.04	+	2274.25i	0.577042	+	0.999466i	−0.418774	+	0.908090i	$0.637540\pi$
$174$	−734.899	+	5649.69i	−0.320187	+	2.46151i
$175$		0			0
$176$	−1579.21	+	2735.27i	−0.676349	+	1.17147i
$177$	340.974	−	2621.31i	0.144798	−	1.11316i
$178$	513.054	+	888.636i	0.216039	+	0.374191i
$179$	−3231.72			−1.34944			−0.674720	−	0.738074i	$-0.735736\pi$
$179$	−3231.72			−1.34944			−0.674720	+	0.738074i	$0.735736\pi$
$180$		0			0
$181$	337.854			0.138743			0.0693714	−	0.997591i	$-0.477901\pi$
$181$	337.854			0.138743			0.0693714	+	0.997591i	$0.477901\pi$
$182$	1066.62	+	1847.44i	0.434412	+	0.752424i
$183$	323.182	+	247.192i	0.130548	+	0.0998523i
$184$	1565.15	−	2710.92i	0.627088	−	1.08615i
$185$		0			0
$186$	−3507.74	+	1459.32i	−1.38280	+	0.575283i
$187$	−2348.23	−	4067.26i	−0.918288	−	1.59052i
$188$	4132.82			1.60328
$189$	2257.30	−	307.852i	0.868753	−	0.118481i
$190$		0			0
$191$	−505.253	−	875.124i	−0.191407	−	0.331527i	0.754309	−	0.656519i	$-0.227972\pi$
$191$	−505.253	−	875.124i	−0.191407	−	0.331527i	−0.945717	+	0.324992i	$0.894639\pi$
$192$	2851.61	−	1186.35i	1.07186	−	0.445925i
$193$	746.079	−	1292.25i	0.278259	−	0.481958i	−0.692693	−	0.721232i	$-0.743576\pi$
$193$	746.079	−	1292.25i	0.278259	−	0.481958i	0.970952	+	0.239274i	$0.0769094\pi$
$194$	4041.41	−	6999.92i	1.49565	−	2.59054i
$195$		0			0
$196$	616.073	+	1067.07i	0.224516	+	0.388874i
$197$	−3313.50			−1.19836			−0.599181	−	0.800613i	$-0.704507\pi$
$197$	−3313.50			−1.19836			−0.599181	+	0.800613i	$0.704507\pi$
$198$	−2041.08	−	7524.15i	−0.732593	−	2.70060i
$199$	2165.17			0.771279			0.385640	−	0.922649i	$-0.373981\pi$
$199$	2165.17			0.771279			0.385640	+	0.922649i	$0.373981\pi$
$200$		0			0
$201$	327.222	−	2515.58i	0.114828	−	0.882764i
$202$	−1107.52	+	1918.28i	−0.385766	+	0.668167i
$203$	−1835.02	+	3178.35i	−0.634449	+	1.09890i
$204$	821.645	−	6316.57i	0.281993	−	2.16788i
$205$		0			0
$206$	−804.991			−0.272264
$207$	605.291	+	2231.32i	0.203240	+	0.749214i
$208$	1436.98			0.479023
$209$	4234.45	+	7334.29i	1.40145	+	2.42738i
$210$		0			0
$211$	1279.85	−	2216.77i	0.417576	−	0.723263i	−0.578119	−	0.815952i	$-0.696213\pi$
$211$	1279.85	−	2216.77i	0.417576	−	0.723263i	0.995695	+	0.0926897i	$0.0295464\pi$
$212$	4686.12	−	8116.59i	1.51813	−	2.62948i
$213$	351.413	−	146.198i	0.113044	−	0.0470296i
$214$	1096.57	+	1899.32i	0.350282	+	0.606706i
$215$		0			0
$216$	1940.67	−	4747.45i	0.611325	−	1.49548i
$217$	−2447.34			−0.765604
$218$	−1123.67	−	1946.26i	−0.349104	−	0.604666i
$219$	−555.701	+	231.188i	−0.171465	+	0.0713343i
$220$		0			0
$221$	−1068.37	+	1850.47i	−0.325188	+	0.563242i
$222$	−4688.76	−	3586.30i	−1.41752	−	1.08422i
$223$	−707.218	−	1224.94i	−0.212371	−	0.367838i	0.740085	−	0.672514i	$-0.234785\pi$
$223$	−707.218	−	1224.94i	−0.212371	−	0.367838i	−0.952456	+	0.304675i	$0.901452\pi$
$224$	568.561			0.169592
$225$		0			0
$226$	−4609.16			−1.35662
$227$	−813.532	−	1409.08i	−0.237868	−	0.411999i	0.722234	−	0.691648i	$-0.243115\pi$
$227$	−813.532	−	1409.08i	−0.237868	−	0.411999i	−0.960102	+	0.279649i	$0.909782\pi$
$228$	−1481.63	+	11390.4i	−0.430366	+	3.30853i
$229$	3309.78	−	5732.71i	0.955093	−	1.65427i	0.220939	−	0.975288i	$-0.429088\pi$
$229$	3309.78	−	5732.71i	0.955093	−	1.65427i	0.734154	−	0.678983i	$-0.237579\pi$
$230$		0			0
$231$	647.796	−	4980.07i	0.184510	−	1.41846i
$232$	4131.09	+	7155.26i	1.16905	+	2.02485i
$233$	−1911.28			−0.537390			−0.268695	−	0.963225i	$-0.586592\pi$
$233$	−1911.28			−0.537390			−0.268695	+	0.963225i	$0.586592\pi$
$234$	−2500.31	+	2515.84i	−0.698506	+	0.702845i
$235$		0			0
$236$	−3951.60	−	6844.37i	−1.08995	−	1.88784i
$237$	3230.60	+	2470.99i	0.885442	+	0.677248i
$238$	3108.11	−	5383.40i	0.846507	−	1.46619i
$239$	−1443.35	+	2499.95i	−0.390637	+	0.676603i	−0.992534	−	0.121971i	$-0.961079\pi$
$239$	−1443.35	+	2499.95i	−0.390637	+	0.676603i	0.601897	+	0.798574i	$0.294412\pi$
$240$		0			0
$241$	644.326	+	1116.01i	0.172219	+	0.298291i	0.939195	−	0.343384i	$-0.111573\pi$
$241$	644.326	+	1116.01i	0.172219	+	0.298291i	−0.766977	+	0.641675i	$0.778240\pi$
$242$	−10728.5			−2.84980
$243$	1476.65	+	3488.32i	0.389824	+	0.920889i
$244$	1216.48			0.319170
$245$		0			0
$246$	1719.00	−	715.154i	0.445527	−	0.185352i
$247$	1926.54	−	3336.87i	0.496287	−	0.859595i
$248$	−2754.79	+	4771.43i	−0.705359	+	1.22172i
$249$	−1120.41	−	856.968i	−0.285153	−	0.218105i
$250$		0			0
$251$	4356.21			1.09546			0.547732	−	0.836654i	$-0.315491\pi$
$251$	4356.21			1.09546			0.547732	+	0.836654i	$0.315491\pi$
$252$	4801.41	−	4831.23i	1.20024	−	1.20769i
$253$	5096.45			1.26645
$254$	510.319	+	883.898i	0.126064	+	0.218349i
$255$		0			0
$256$	3937.62	−	6820.15i	0.961332	−	1.66508i
$257$	1618.26	−	2802.91i	0.392780	−	0.680314i	−0.600035	−	0.799973i	$-0.704847\pi$
$257$	1618.26	−	2802.91i	0.392780	−	0.680314i	0.992815	+	0.119659i	$0.0381802\pi$
$258$	−868.439	+	6676.31i	−0.209561	+	1.61104i
$259$	−1901.29	−	3293.13i	−0.456141	−	0.790060i
$260$		0			0
$261$	−5899.17	−	1561.12i	−1.39904	−	0.370232i
$262$	4486.40			1.05790
$263$	690.768	+	1196.44i	0.161956	+	0.280517i	0.935570	−	0.353141i	$-0.114886\pi$
$263$	690.768	+	1196.44i	0.161956	+	0.280517i	−0.773614	+	0.633657i	$0.781553\pi$
$264$	−8980.17	−	6868.67i	−2.09353	−	1.60128i
$265$		0			0
$266$	−5604.70	+	9707.62i	−1.29190	+	2.23764i
$267$	−1014.73	+	422.156i	−0.232586	+	0.0967623i
$268$	−3792.22	−	6568.32i	−0.864354	−	1.49710i
$269$	721.063			0.163435			0.0817175	−	0.996656i	$-0.473959\pi$
$269$	721.063			0.163435			0.0817175	+	0.996656i	$0.473959\pi$
$270$		0			0
$271$	3816.82			0.855554			0.427777	−	0.903884i	$-0.359297\pi$
$271$	3816.82			0.855554			0.427777	+	0.903884i	$0.359297\pi$
$272$	−2093.67	−	3626.34i	−0.466718	−	0.808379i
$273$	−2109.58	+	877.646i	−0.467684	+	0.194570i
$274$	−4700.15	+	8140.90i	−1.03630	+	1.79493i
$275$		0			0
$276$	5490.39	+	4199.44i	1.19740	+	0.915856i
$277$	−964.393	−	1670.38i	−0.209187	−	0.362322i	0.742272	−	0.670099i	$-0.233748\pi$
$277$	−964.393	−	1670.38i	−0.209187	−	0.362322i	−0.951459	+	0.307777i	$0.900415\pi$
$278$	9559.61			2.06240
$279$	−1065.36	−	3927.29i	−0.228607	−	0.842727i
$280$		0			0
$281$	−2471.93	−	4281.50i	−0.524778	−	0.908943i	−0.999584	−	0.0288518i	$-0.990815\pi$
$281$	−2471.93	−	4281.50i	−0.524778	−	0.908943i	0.474805	−	0.880091i	$-0.342518\pi$
$282$	−865.019	+	6650.01i	−0.182664	+	1.40426i
$283$	3171.79	−	5493.70i	0.666231	−	1.15395i	−0.312719	−	0.949846i	$-0.601240\pi$
$283$	3171.79	−	5493.70i	0.666231	−	1.15395i	0.978950	−	0.204100i	$-0.0654268\pi$
$284$	568.975	−	985.494i	0.118882	−	0.205909i
$285$		0			0
$286$	3909.45	+	6771.37i	0.808289	+	1.40000i
$287$	1199.34			0.246672
$288$	247.503	+	912.382i	0.0506397	+	0.186676i
$289$	1313.43			0.267337
$290$		0			0
$291$	6876.46	+	5259.60i	1.38524	+	1.05953i
$292$	−899.739	+	1558.39i	−0.180319	+	0.312322i
$293$	−753.429	+	1304.98i	−0.150225	+	0.260197i	−0.931310	−	0.364228i	$-0.881333\pi$
$293$	−753.429	+	1304.98i	−0.150225	+	0.260197i	0.781085	+	0.624424i	$0.214666\pi$
$294$	−1845.94	+	767.964i	−0.366182	+	0.152342i
$295$		0			0
$296$	−8560.58			−1.68099
$297$	8273.62	−	1128.36i	1.61644	−	0.220452i
$298$	−7744.34			−1.50543
$299$	−1159.36	−	2008.07i	−0.224240	−	0.388394i
$300$		0			0
$301$	−2168.46	+	3755.89i	−0.415243	+	0.719222i
$302$	−8909.40	+	15431.5i	−1.69761	+	2.94035i
$303$	−1884.45	−	1441.36i	−0.357289	−	0.273280i
$304$	3775.41	+	6539.20i	0.712285	+	1.23371i
$305$		0			0
$306$	9991.86	+	2644.18i	1.86666	+	0.493979i
$307$	−8239.13			−1.53170			−0.765850	−	0.643019i	$-0.777681\pi$
$307$	−8239.13			−1.53170			−0.765850	+	0.643019i	$0.777681\pi$
$308$	−7507.41	−	13003.2i	−1.38888	−	2.40561i
$309$	111.217	−	855.005i	0.0204755	−	0.157409i
$310$		0			0
$311$	402.948	−	697.927i	0.0734698	−	0.127253i	−0.826950	−	0.562275i	$-0.809926\pi$
$311$	402.948	−	697.927i	0.0734698	−	0.127253i	0.900420	+	0.435022i	$0.143259\pi$
$312$	−663.504	+	5100.83i	−0.120396	+	0.925569i
$313$	2030.70	+	3517.28i	0.366716	+	0.635171i	0.989050	−	0.147581i	$-0.0471487\pi$
$313$	2030.70	+	3517.28i	0.366716	+	0.635171i	−0.622334	+	0.782752i	$0.713815\pi$
$314$	−5101.46			−0.916853
$315$		0			0
$316$	12160.2			2.16477
$317$	503.804	+	872.615i	0.0892633	+	0.154609i	0.907200	−	0.420700i	$-0.138215\pi$
$317$	503.804	+	872.615i	0.0892633	+	0.154609i	−0.817937	+	0.575308i	$0.804882\pi$
$318$	12079.4	+	9239.16i	2.13012	+	1.62926i
$319$	−6725.85	+	11649.5i	−1.18049	+	2.04466i
$320$		0			0
$321$	−2168.83	+	902.295i	−0.377110	+	0.156888i
$322$	3372.81	+	5841.89i	0.583726	+	1.01104i
$323$	−11227.8			−1.93416
$324$	9842.91	+	5601.82i	1.68774	+	0.960531i
$325$		0			0
$326$	−4848.34	−	8397.57i	−0.823696	−	1.42668i
$327$	2222.42	−	924.591i	0.375842	−	0.156361i
$328$	1350.01	−	2338.29i	0.227262	−	0.393629i
$329$	−2159.92	+	3741.10i	−0.361946	+	0.626910i
$330$		0			0
$331$	−4647.21	−	8049.20i	−0.771702	−	1.33663i	−0.936629	−	0.350322i	$-0.886072\pi$
$331$	−4647.21	−	8049.20i	−0.771702	−	1.33663i	0.164927	−	0.986306i	$-0.447261\pi$
$332$	−4217.32			−0.697155
$333$	4456.91	−	4484.59i	0.733444	−	0.738001i
$334$	−12036.3			−1.97185
$335$		0			0
$336$	577.570	−	4440.19i	0.0937769	−	0.720930i
$337$	−1697.85	+	2940.77i	−0.274445	+	0.475352i	−0.969995	−	0.243125i	$-0.921827\pi$
$337$	−1697.85	+	2940.77i	−0.274445	+	0.475352i	0.695550	+	0.718478i	$0.255161\pi$
$338$	−3550.51	+	6149.67i	−0.571368	+	0.989639i
$339$	636.799	−	4895.53i	0.102024	−	0.784332i
$340$		0			0
$341$	−8970.16			−1.42452
$342$	−18017.8	−	4768.11i	−2.84881	−	0.753889i
$343$	−6857.70			−1.07954
$344$	4881.76	+	8455.46i	0.765136	+	1.32525i
$345$		0			0
$346$	−6369.98	+	11033.1i	−0.989746	+	1.71429i
$347$	−4086.81	+	7078.56i	−0.632252	+	1.09509i	0.354838	+	0.934928i	$0.384536\pi$
$347$	−4086.81	+	7078.56i	−0.632252	+	1.09509i	−0.987090	+	0.160165i	$0.948797\pi$
$348$	−16844.8	+	7007.93i	−2.59476	+	1.07950i
$349$	2787.95	+	4828.88i	0.427609	+	0.740641i	0.996660	−	0.0816612i	$-0.0260225\pi$
$349$	2787.95	+	4828.88i	0.427609	+	0.740641i	−0.569051	+	0.822302i	$0.692689\pi$
$350$		0			0
$351$	−2326.71	−	3003.24i	−0.353819	−	0.456698i
$352$	2083.93			0.315551
$353$	−1611.89	−	2791.87i	−0.243037	−	0.420953i	0.718541	−	0.695485i	$-0.244810\pi$
$353$	−1611.89	−	2791.87i	−0.243037	−	0.420953i	−0.961578	+	0.274532i	$0.911477\pi$
$354$	11840.2	−	4925.86i	1.77768	−	0.739566i
$355$		0			0
$356$	−1642.95	+	2845.68i	−0.244597	+	0.423654i
$357$	5288.45	+	4044.98i	0.784018	+	0.599672i
$358$	−7839.07	−	13577.7i	−1.15728	−	2.00447i
$359$	−2593.48			−0.381278			−0.190639	−	0.981660i	$-0.561056\pi$
$359$	−2593.48			−0.381278			−0.190639	+	0.981660i	$0.561056\pi$
$360$		0			0
$361$	13387.6			1.95182
$362$	819.520	+	1419.45i	0.118986	+	0.206090i
$363$	1482.24	−	11395.0i	0.214318	−	1.64761i
$364$	−3415.64	+	5916.06i	−0.491835	+	0.851883i
$365$		0			0
$366$	−254.616	+	1957.41i	−0.0363634	+	0.279551i
$367$	−884.083	−	1531.28i	−0.125746	−	0.217798i	0.796278	−	0.604930i	$-0.206799\pi$
$367$	−884.083	−	1531.28i	−0.125746	−	0.217798i	−0.922024	+	0.387132i	$0.873466\pi$
$368$	4543.96			0.643669
$369$	522.090	+	1924.61i	0.0736556	+	0.271521i
$370$		0			0
$371$	4898.18	+	8483.90i	0.685447	+	1.18723i
$372$	−9663.52	−	7391.34i	−1.34686	−	1.03017i
$373$	1514.74	−	2623.61i	0.210269	−	0.364197i	−0.741529	−	0.670920i	$-0.765899\pi$
$373$	1514.74	−	2623.61i	0.210269	−	0.364197i	0.951799	+	0.306723i	$0.0992326\pi$
$374$	11392.1	−	19731.6i	1.57505	−	2.72807i
$375$		0			0
$376$	4862.53	+	8422.15i	0.666931	+	1.15516i
$377$	6120.10			0.836077
$378$	6768.86	+	8737.02i	0.921038	+	1.18885i
$379$	9435.84			1.27886			0.639428	−	0.768851i	$-0.279171\pi$
$379$	9435.84			1.27886			0.639428	+	0.768851i	$0.279171\pi$
$380$		0			0
$381$	−1009.32	+	419.906i	−0.135719	+	0.0564630i
$382$	2451.15	−	4245.52i	0.328303	−	0.568638i
$383$	4849.33	−	8399.29i	0.646969	−	1.12058i	−0.336874	−	0.941550i	$-0.609369\pi$
$383$	4849.33	−	8399.29i	0.646969	−	1.12058i	0.983843	−	0.179034i	$-0.0572972\pi$
$384$	10745.3	+	8218.75i	1.42798	+	1.09222i
$385$		0			0
$386$	7238.96			0.954542
$387$	−6971.12	−	1844.79i	−0.915664	−	0.242315i
$388$	25883.6			3.38670
$389$	−6379.36	−	11049.4i	−0.831481	−	1.44017i	−0.896863	−	0.442308i	$-0.854160\pi$
$389$	−6379.36	−	11049.4i	−0.831481	−	1.44017i	0.0653822	−	0.997860i	$-0.479173\pi$
$390$		0			0
$391$	−3378.36	+	5851.49i	−0.436959	+	0.756835i
$392$	−1449.70	+	2510.95i	−0.186788	+	0.323526i
$393$	−619.838	+	4765.13i	−0.0795590	+	0.611626i
$394$	−8037.46	−	13921.3i	−1.02772	−	1.78006i
$395$		0			0
$396$	17598.5	−	17707.8i	2.23322	−	2.24710i
$397$	14088.8			1.78111			0.890553	−	0.454879i	$-0.150318\pi$
$397$	14088.8			1.78111			0.890553	+	0.454879i	$0.150318\pi$
$398$	5251.97	+	9096.68i	0.661451	+	1.14567i
$399$	−9536.40	−	7294.11i	−1.19653	−	0.915193i
$400$		0			0
$401$	3582.63	−	6205.30i	0.446155	−	0.772763i	−0.551977	−	0.833860i	$-0.686126\pi$
$401$	3582.63	−	6205.30i	0.446155	−	0.772763i	0.998132	+	0.0610961i	$0.0194596\pi$
$402$	11362.6	−	4727.19i	1.40974	−	0.586494i
$403$	2040.57	+	3534.37i	0.252228	+	0.436872i
$404$	−7093.22			−0.873517
$405$		0			0
$406$	−17804.6			−2.17642
$407$	−6968.76	−	12070.2i	−0.848719	−	1.47002i
$408$	13839.1	−	5757.45i	1.67926	−	0.698618i
$409$	−1019.82	+	1766.39i	−0.123293	+	0.213550i	−0.921065	−	0.389410i	$-0.872679\pi$
$409$	−1019.82	+	1766.39i	−0.123293	+	0.213550i	0.797771	+	0.602960i	$0.206012\pi$
$410$		0			0
$411$	−7997.31	−	6116.91i	−0.959802	−	0.734123i
$412$	−1288.91	−	2232.46i	−0.154127	−	0.266955i
$413$	8260.85			0.984237
$414$	−7906.37	+	7955.49i	−0.938591	+	0.944422i
$415$		0			0
$416$	−474.061	−	821.099i	−0.0558721	−	0.0967732i
$417$	−1320.75	+	10153.5i	−0.155102	+	1.19238i
$418$	−20542.7	+	35581.1i	−2.40378	+	4.16346i
$419$	−6596.83	+	11426.0i	−0.769156	+	1.33222i	0.168865	+	0.985639i	$0.445990\pi$
$419$	−6596.83	+	11426.0i	−0.769156	+	1.33222i	−0.938021	+	0.346578i	$0.887344\pi$
$420$		0			0
$421$	−5621.08	−	9735.99i	−0.650724	−	1.12709i	−0.982948	−	0.183886i	$-0.941132\pi$
$421$	−5621.08	−	9735.99i	−0.650724	−	1.12709i	0.332224	−	0.943201i	$-0.392201\pi$
$422$	12418.0			1.43246
$423$	−6943.66	−	1837.52i	−0.798138	−	0.211214i
$424$	22054.1			2.52604
$425$		0			0
$426$	1466.64	+	1121.79i	0.166805	+	0.127584i
$427$	−635.768	+	1101.18i	−0.0720538	+	0.124801i
$428$	−3511.56	+	6082.21i	−0.396584	+	0.686903i
$429$	−7732.19	+	3216.81i	−0.870195	+	0.362026i
$430$		0			0
$431$	−5546.88			−0.619916			−0.309958	−	0.950750i	$-0.600315\pi$
$431$	−5546.88			−0.619916			−0.309958	+	0.950750i	$0.600315\pi$
$432$	7376.70	−	1006.04i	0.821555	−	0.112044i
$433$	−4484.74			−0.497744			−0.248872	−	0.968536i	$-0.580060\pi$
$433$	−4484.74			−0.497744			−0.248872	+	0.968536i	$0.580060\pi$
$434$	−5936.42	−	10282.2i	−0.656584	−	1.13724i
$435$		0			0
$436$	3598.34	−	6232.50i	0.395250	−	0.684594i
$437$	6092.03	−	10551.7i	0.666868	−	1.15505i
$438$	−2319.25	−	1773.93i	−0.253009	−	0.193519i
$439$	−2634.86	−	4563.71i	−0.286458	−	0.496159i	0.686504	−	0.727126i	$-0.259144\pi$
$439$	−2634.86	−	4563.71i	−0.286458	−	0.496159i	−0.972962	+	0.230967i	$0.925811\pi$
$440$		0			0
$441$	−560.643	−	2066.73i	−0.0605381	−	0.223165i
$442$	−10366.1			−1.11553
$443$	−3700.66	−	6409.74i	−0.396894	−	0.687440i	0.596447	−	0.802652i	$-0.296578\pi$
$443$	−3700.66	−	6409.74i	−0.396894	−	0.687440i	−0.993341	+	0.115212i	$0.963245\pi$
$444$	2438.36	−	18745.4i	0.260630	−	2.00365i
$445$		0			0
$446$	3430.95	−	5942.58i	0.364261	−	0.630918i
$447$	1069.95	−	8225.49i	0.113215	−	0.870363i
$448$	4826.00	+	8358.87i	0.508944	+	0.881517i
$449$	−938.733			−0.0986672			−0.0493336	−	0.998782i	$-0.515710\pi$
$449$	−938.733			−0.0986672			−0.0493336	+	0.998782i	$0.515710\pi$
$450$		0			0
$451$	4395.91			0.458970
$452$	−7379.97	−	12782.5i	−0.767974	−	1.33017i
$453$	−15159.4	−	11594.9i	−1.57229	−	1.20260i
$454$	3946.71	−	6835.91i	0.407992	−	0.706663i
$455$		0			0
$456$	−24955.3	+	10382.1i	−2.56281	+	1.06620i
$457$	2153.58	+	3730.11i	0.220438	+	0.381810i	0.954941	−	0.296795i	$-0.0959180\pi$
$457$	2153.58	+	3730.11i	0.220438	+	0.381810i	−0.734503	+	0.678605i	$0.762585\pi$
$458$	32113.7			3.27636
$459$	−4188.93	+	10247.3i	−0.425975	+	1.04206i
$460$		0			0
$461$	−2621.39	−	4540.38i	−0.264838	−	0.458713i	0.702683	−	0.711503i	$-0.251985\pi$
$461$	−2621.39	−	4540.38i	−0.264838	−	0.458713i	−0.967521	+	0.252790i	$0.918652\pi$
$462$	22494.5	−	9358.35i	2.26523	−	0.942402i
$463$	4274.77	−	7404.13i	0.429083	−	0.743194i	−0.567709	−	0.823230i	$-0.692170\pi$
$463$	4274.77	−	7404.13i	0.429083	−	0.743194i	0.996792	+	0.0800354i	$0.0255033\pi$
$464$	−5996.72	+	10386.6i	−0.599980	+	1.03920i
$465$		0			0
$466$	−4636.12	−	8029.99i	−0.460867	−	0.798245i
$467$	12706.2			1.25904			0.629522	−	0.776983i	$-0.283251\pi$
$467$	12706.2			1.25904			0.629522	+	0.776983i	$0.283251\pi$
$468$	−10980.5	−	2905.80i	−1.08456	−	0.287010i
$469$	7927.67			0.780524
$470$		0			0
$471$	704.814	−	5418.41i	0.0689514	−	0.530079i
$472$	9298.63	−	16105.7i	0.906788	−	1.57060i
$473$	−7948.01	+	13766.4i	−0.772622	+	1.33822i
$474$	−2545.20	+	19566.7i	−0.246635	+	1.89606i
$475$		0			0
$476$	19906.2			1.91680
$477$	−11482.1	+	11553.4i	−1.10215	+	1.10900i
$478$	−14004.3			−1.34005
$479$	9178.08	+	15896.9i	0.875485	+	1.51638i	0.856246	+	0.516569i	$0.172791\pi$
$479$	9178.08	+	15896.9i	0.875485	+	1.51638i	0.0192388	+	0.999815i	$0.493876\pi$
$480$		0			0
$481$	−3170.57	+	5491.58i	−0.300552	+	0.520571i
$482$	−3125.84	+	5414.11i	−0.295390	+	0.511631i
$483$	−6670.82	+	2775.25i	−0.628433	+	0.261446i
$484$	−17177.9	−	29753.0i	−1.61325	−	2.79423i
$485$		0			0
$486$	−11073.9	+	14665.5i	−1.03359	+	1.36881i
$487$	−15195.3			−1.41389			−0.706945	−	0.707268i	$-0.749927\pi$
$487$	−15195.3			−1.41389			−0.706945	+	0.707268i	$0.749927\pi$
$488$	1431.27	+	2479.04i	0.132768	+	0.229961i
$489$	9589.15	−	3989.36i	0.886782	−	0.368927i
$490$		0			0
$491$	−3971.95	+	6879.62i	−0.365075	+	0.632328i	−0.988788	−	0.149325i	$-0.952290\pi$
$491$	−3971.95	+	6879.62i	−0.365075	+	0.632328i	0.623713	+	0.781653i	$0.285623\pi$
$492$	4735.70	+	3622.20i	0.433947	+	0.331913i
$493$	−8916.92	−	15444.6i	−0.814600	−	1.41093i
$494$	18692.6			1.70247
$495$		0			0
$496$	−7997.73			−0.724009
$497$	594.723	+	1030.09i	0.0536760	+	0.0929696i
$498$	882.705	−	6785.98i	0.0794277	−	0.610617i
$499$	9578.93	−	16591.2i	0.859343	−	1.48843i	−0.0132143	−	0.999913i	$-0.504206\pi$
$499$	9578.93	−	16591.2i	0.859343	−	1.48843i	0.872557	−	0.488512i	$-0.162460\pi$
$500$		0			0
$501$	1662.93	−	12784.1i	0.148291	−	1.14002i
$502$	10566.7	+	18302.1i	0.939474	+	1.62722i
$503$	11203.5			0.993119			0.496559	−	0.868003i	$-0.334597\pi$
$503$	11203.5			0.993119			0.496559	+	0.868003i	$0.334597\pi$
$504$	15494.6	+	4100.38i	1.36941	+	0.362392i
$505$		0			0
$506$	12362.3	+	21412.1i	1.08611	+	1.88119i
$507$	−6041.20	−	4620.74i	−0.529190	−	0.404762i
$508$	−1634.19	+	2830.51i	−0.142728	+	0.247212i
$509$	−3544.02	+	6138.42i	−0.308617	+	0.534540i	−0.978060	−	0.208323i	$-0.933199\pi$
$509$	−3544.02	+	6138.42i	−0.308617	+	0.534540i	0.669443	+	0.742863i	$0.266533\pi$
$510$		0			0
$511$	−940.456	−	1628.92i	−0.0814155	−	0.141016i
$512$	17377.5			1.49997
$513$	7553.68	−	18478.5i	0.650104	−	1.59034i
$514$	15701.5			1.34740
$515$		0			0
$516$	−19905.7	+	8281.36i	−1.69826	+	0.706524i
$517$	−7916.71	+	13712.1i	−0.673455	+	1.16646i
$518$	9223.80	−	15976.1i	0.782376	−	1.35511i
$519$	−10838.5	−	8290.07i	−0.916683	−	0.701144i
$520$		0			0
$521$	−9739.55			−0.818997			−0.409499	−	0.912311i	$-0.634296\pi$
$521$	−9739.55			−0.818997			−0.409499	+	0.912311i	$0.634296\pi$
$522$	−7750.58	−	28571.4i	−0.649873	−	2.39566i
$523$	14153.1			1.18331			0.591656	−	0.806190i	$-0.298474\pi$
$523$	14153.1			1.18331			0.591656	+	0.806190i	$0.298474\pi$
$524$	7183.40	+	12442.0i	0.598871	+	1.03727i
$525$		0			0
$526$	−3351.14	+	5804.35i	−0.277789	+	0.481144i
$527$	5946.18	−	10299.1i	0.491498	−	0.851300i
$528$	2116.95	−	16274.5i	0.174486	−	1.34140i
$529$	2417.42	+	4187.09i	0.198686	+	0.344135i
$530$		0			0
$531$	3596.07	+	13256.4i	0.293891	+	1.08338i
$532$	−35895.9			−2.92534
$533$	−1000.00	−	1732.05i	−0.0812661	−	0.140757i
$534$	−4235.03	−	3239.25i	−0.343198	−	0.262502i
$535$		0			0
$536$	8923.59	−	15456.1i	0.719106	−	1.24553i
$537$	15504.3	−	6450.22i	1.24592	−	0.518338i
$538$	1749.06	+	3029.46i	0.140162	+	0.242768i
$539$	−4720.52			−0.377231
$540$		0			0
$541$	−12175.5			−0.967592			−0.483796	−	0.875181i	$-0.660742\pi$
$541$	−12175.5			−0.967592			−0.483796	+	0.875181i	$0.660742\pi$
$542$	9258.33	+	16035.9i	0.733725	+	1.27085i
$543$	−1620.86	+	674.326i	−0.128099	+	0.0532930i
$544$	−1381.41	+	2392.66i	−0.108874	+	0.188575i
$545$		0			0
$546$	−8804.47	−	6734.27i	−0.690103	−	0.527839i
$547$	609.617	+	1055.89i	0.0476515	+	0.0825348i	0.888867	−	0.458165i	$-0.151493\pi$
$547$	609.617	+	1055.89i	0.0476515	+	0.0825348i	−0.841216	+	0.540699i	$0.818160\pi$
$548$	−30102.6			−2.34657
$549$	−2043.85	−	540.870i	−0.158888	−	0.0420470i
$550$		0			0
$551$	16079.4	+	27850.4i	1.24321	+	2.15330i
$552$	−2098.10	+	16129.6i	−0.161778	+	1.24370i
$553$	−6355.27	+	11007.7i	−0.488705	+	0.846461i
$554$	4678.59	−	8103.56i	0.358798	−	0.621457i
$555$		0			0
$556$	15306.4	+	26511.4i	1.16751	+	2.02218i
$557$	12672.4			0.963995			0.481998	−	0.876172i	$-0.339911\pi$
$557$	12672.4			0.963995			0.481998	+	0.876172i	$0.339911\pi$
$558$	13915.8	−	14002.3i	1.05574	−	1.06230i
$559$	7232.19			0.547208
$560$		0			0
$561$	19383.6	+	14825.9i	1.45878	+	1.11578i
$562$	11992.1	−	20771.0i	0.900102	−	1.55902i
$563$	−4116.80	+	7130.50i	−0.308175	+	0.533774i	−0.977963	−	0.208778i	$-0.933051\pi$
$563$	−4116.80	+	7130.50i	−0.308175	+	0.533774i	0.669788	+	0.742552i	$0.266385\pi$
$564$	−19827.3	+	8248.74i	−1.48029	+	0.615842i
$565$		0			0
$566$	30774.8			2.28545
$567$	−10215.0	+	5982.30i	−0.756597	+	0.443092i
$568$	2677.75			0.197809
$569$	−1974.55	−	3420.02i	−0.145479	−	0.251977i	0.784073	−	0.620669i	$-0.213139\pi$
$569$	−1974.55	−	3420.02i	−0.145479	−	0.251977i	−0.929552	+	0.368692i	$0.879806\pi$
$570$		0			0
$571$	1955.13	−	3386.38i	0.143292	−	0.248189i	−0.785442	−	0.618935i	$-0.787565\pi$
$571$	1955.13	−	3386.38i	0.143292	−	0.248189i	0.928734	+	0.370746i	$0.120898\pi$
$572$	−12519.2	+	21684.0i	−0.915133	+	1.58506i
$573$	4170.64	+	3190.00i	0.304068	+	0.232572i
$574$	2909.20	+	5038.88i	0.211547	+	0.366409i
$575$		0			0
$576$	−11312.8	+	11383.1i	−0.818348	+	0.823432i
$577$	18788.9			1.35562			0.677810	−	0.735237i	$-0.262929\pi$
$577$	18788.9			1.35562			0.677810	+	0.735237i	$0.262929\pi$
$578$	3185.94	+	5518.21i	0.229269	+	0.397106i
$579$	−1000.13	+	7688.71i	−0.0717858	+	0.551868i
$580$		0			0
$581$	2204.09	−	3817.59i	0.157385	−	0.272599i
$582$	−5417.56	+	41648.6i	−0.385851	+	2.96631i
$583$	17953.2	+	31095.8i	1.27538	+	2.20902i
$584$	−4234.41			−0.300036
$585$		0			0
$586$	−7310.27			−0.515332
$587$	−2200.11	−	3810.70i	−0.154699	−	0.267946i	0.778251	−	0.627954i	$-0.216107\pi$
$587$	−2200.11	−	3810.70i	−0.154699	−	0.267946i	−0.932949	+	0.360008i	$0.882774\pi$
$588$	−5085.41	−	3889.68i	−0.356664	−	0.272802i
$589$	−10722.4	+	18571.8i	−0.750103	+	1.29922i
$590$		0			0
$591$	15896.7	−	6613.46i	1.10643	−	0.460307i
$592$	−6213.30	−	10761.7i	−0.431360	−	0.747137i
$593$	13311.2			0.921798			0.460899	−	0.887453i	$-0.347527\pi$
$593$	13311.2			0.921798			0.460899	+	0.887453i	$0.347527\pi$
$594$	24809.7	+	32023.6i	1.71373	+	2.21203i
$595$		0			0
$596$	−12399.9	−	21477.2i	−0.852211	−	1.47607i
$597$	−10387.5	+	4321.48i	−0.712111	+	0.296259i
$598$	5624.45	−	9741.84i	0.384617	−	0.666176i
$599$	7966.01	−	13797.5i	0.543377	−	0.941156i	−0.455331	−	0.890322i	$-0.650479\pi$
$599$	7966.01	−	13797.5i	0.543377	−	0.941156i	0.998707	−	0.0508333i	$-0.0161877\pi$
$600$		0			0
$601$	−11754.9	−	20360.2i	−0.797828	−	1.38188i	−0.921028	−	0.389496i	$-0.872649\pi$
$601$	−11754.9	−	20360.2i	−0.797828	−	1.38188i	0.123201	−	0.992382i	$-0.460684\pi$
$602$	−21039.9			−1.42445
$603$	3451.03	+	12721.7i	0.233062	+	0.859151i
$604$	−57061.2			−3.84402
$605$		0			0
$606$	1484.65	−	11413.5i	0.0995208	−	0.765087i
$607$	−4876.00	+	8445.49i	−0.326048	+	0.564731i	−0.981724	−	0.190311i	$-0.939050\pi$
$607$	−4876.00	+	8445.49i	−0.326048	+	0.564731i	0.655676	+	0.755042i	$0.272384\pi$
$608$	2491.02	−	4314.57i	0.166158	−	0.287795i
$609$	2459.87	−	18910.8i	0.163676	−	1.25830i
$610$		0			0
$611$	7203.71			0.476973
$612$	8665.44	+	31943.9i	0.572353	+	2.10989i
$613$	24076.3			1.58635			0.793176	−	0.608992i	$-0.208426\pi$
$613$	24076.3			1.58635			0.793176	+	0.608992i	$0.208426\pi$
$614$	−19985.4	−	34615.7i	−1.31359	−	2.27520i
$615$		0			0
$616$	17665.9	−	30598.3i	1.15549	−	2.00136i
$617$	3324.25	−	5757.76i	0.216903	−	0.375687i	−0.736957	−	0.675940i	$-0.763738\pi$
$617$	3324.25	−	5757.76i	0.216903	−	0.375687i	0.953860	+	0.300253i	$0.0970712\pi$
$618$	3861.97	−	1606.69i	0.251378	−	0.104580i
$619$	4100.83	+	7102.85i	0.266278	+	0.461208i	0.967898	−	0.251344i	$-0.0808726\pi$
$619$	4100.83	+	7102.85i	0.266278	+	0.461208i	−0.701619	+	0.712552i	$0.747539\pi$
$620$		0			0
$621$	−7357.41	−	9496.71i	−0.475431	−	0.613671i
$622$	3909.67			0.252031
$623$	−1717.30	−	2974.46i	−0.110437	−	0.191283i
$624$	−6893.97	+	2868.09i	−0.442275	+	0.183999i
$625$		0			0
$626$	−9851.62	+	17063.5i	−0.628994	+	1.08945i
$627$	−34953.5	−	26734.9i	−2.22633	−	1.70285i
$628$	−8168.21	−	14147.7i	−0.519024	−	0.898975i
$629$	18477.9			1.17132
$630$		0			0
$631$	28159.1			1.77654			0.888269	−	0.459323i	$-0.151908\pi$
$631$	28159.1			1.77654			0.888269	+	0.459323i	$0.151908\pi$
$632$	14307.3	+	24781.0i	0.900498	+	1.55971i
$633$	−1715.66	+	13189.5i	−0.107727	+	0.828175i
$634$	−2444.12	+	4233.35i	−0.153105	+	0.265186i
$635$		0			0
$636$	−6281.81	+	48292.7i	−0.391651	+	3.01090i
$637$	1073.85	+	1859.95i	0.0667932	+	0.115689i
$638$	−65258.6			−4.04955
$639$	−1394.12	+	1402.78i	−0.0863075	+	0.0868436i
$640$		0			0
$641$	−5777.99	−	10007.8i	−0.356032	−	0.616666i	0.631262	−	0.775570i	$-0.282537\pi$
$641$	−5777.99	−	10007.8i	−0.356032	−	0.616666i	−0.987294	+	0.158904i	$0.949204\pi$
$642$	−9051.74	−	6923.40i	−0.556454	−	0.425615i
$643$	−6901.87	+	11954.4i	−0.423302	+	0.733180i	−0.996260	−	0.0864042i	$-0.972462\pi$
$643$	−6901.87	+	11954.4i	−0.423302	+	0.733180i	0.572958	+	0.819585i	$0.305796\pi$
$644$	−10800.8	+	18707.5i	−0.660885	+	1.14469i
$645$		0			0
$646$	−27234.9	−	47172.3i	−1.65874	−	2.87302i
$647$	−24257.1			−1.47395			−0.736974	−	0.675921i	$-0.763746\pi$
$647$	−24257.1			−1.47395			−0.736974	+	0.675921i	$0.763746\pi$
$648$	165.041	+	26649.5i	0.0100053	+	1.61557i
$649$	30278.3			1.83132
$650$		0			0
$651$	11741.2	−	4884.67i	0.706871	−	0.294079i
$652$	15525.9	−	26891.6i	0.932576	−	1.61527i
$653$	3249.10	−	5627.61i	0.194712	−	0.337252i	−0.752094	−	0.659056i	$-0.770956\pi$
$653$	3249.10	−	5627.61i	0.194712	−	0.337252i	0.946806	+	0.321804i	$0.104289\pi$
$654$	9275.41	+	7094.49i	0.554583	+	0.424184i
$655$		0			0
$656$	3919.37			0.233271
$657$	2204.57	−	2218.26i	0.130911	−	0.131724i
$658$	−20957.0			−1.24162
$659$	−1901.37	−	3293.26i	−0.112393	−	0.194670i	0.804342	−	0.594167i	$-0.202518\pi$
$659$	−1901.37	−	3293.26i	−0.112393	−	0.194670i	−0.916734	+	0.399497i	$0.869185\pi$
$660$		0			0
$661$	−4837.05	+	8378.01i	−0.284628	+	0.492991i	−0.972519	−	0.232824i	$-0.925204\pi$
$661$	−4837.05	+	8378.01i	−0.284628	+	0.492991i	0.687891	+	0.725814i	$0.258537\pi$
$662$	22545.1	−	39049.3i	1.32363	−	2.29259i
$663$	1432.17	−	11010.1i	0.0838926	−	0.644942i
$664$	−4961.95	−	8594.35i	−0.290002	−	0.502298i
$665$		0			0
$666$	29652.4	+	7847.02i	1.72524	+	0.456555i
$667$	19352.7			1.12345
$668$	−19271.9	−	33379.9i	−1.11625	−	1.93340i
$669$	5837.77	+	4465.14i	0.337371	+	0.258045i
$670$		0			0
$671$	−2330.26	+	4036.13i	−0.134067	+	0.232210i
$672$	−2727.69	+	1134.80i	−0.156582	+	0.0651425i
$673$	1016.47	+	1760.57i	0.0582198	+	0.100840i	0.893666	−	0.448732i	$-0.148124\pi$
$673$	1016.47	+	1760.57i	0.0582198	+	0.100840i	−0.835447	+	0.549572i	$0.814791\pi$
$674$	−16473.7			−0.941458
$675$		0			0
$676$	−22739.6			−1.29379
$677$	−4499.50	−	7793.36i	−0.255435	−	0.442427i	0.709578	−	0.704627i	$-0.248886\pi$
$677$	−4499.50	−	7793.36i	−0.255435	−	0.442427i	−0.965014	+	0.262199i	$0.915552\pi$
$678$	22112.6	−	9199.48i	1.25255	−	0.521097i
$679$	−13527.5	+	23430.3i	−0.764561	+	1.32426i
$680$		0			0
$681$	6715.34	+	5136.37i	0.377875	+	0.289025i
$682$	−21758.6	−	37687.0i	−1.22167	−	2.11600i
$683$	−23826.0			−1.33481			−0.667407	−	0.744693i	$-0.732596\pi$
$683$	−23826.0			−1.33481			−0.667407	+	0.744693i	$0.732596\pi$
$684$	−15626.0	−	57602.9i	−0.873500	−	3.22003i
$685$		0			0
$686$	−16634.5	−	28811.8i	−0.925814	−	1.60356i
$687$	−4436.81	+	34108.9i	−0.246397	+	1.89423i
$688$	−7086.39	+	12274.0i	−0.392684	+	0.680148i
$689$	8168.13	−	14147.6i	0.451642	−	0.782266i
$690$		0			0
$691$	2939.49	+	5091.35i	0.161828	+	0.280295i	0.935524	−	0.353262i	$-0.114928\pi$
$691$	2939.49	+	5091.35i	0.161828	+	0.280295i	−0.773696	+	0.633557i	$0.781594\pi$
$692$	−40797.2			−2.24115
$693$	6831.95	+	25185.0i	0.374494	+	1.38052i
$694$	−39653.0			−2.16888
$695$		0			0
$696$	−34100.3	−	26082.3i	−1.85714	−	1.42047i
$697$	−2913.98	+	5047.17i	−0.158357	+	0.274283i
$698$	−13525.3	+	23426.5i	−0.733438	+	1.27035i
$699$	9169.41	−	3814.74i	0.496164	−	0.206419i
$700$		0			0
$701$	−24961.0			−1.34489			−0.672443	−	0.740148i	$-0.734755\pi$
$701$	−24961.0			−1.34489			−0.672443	+	0.740148i	$0.734755\pi$
$702$	6973.93	−	17060.2i	0.374949	−	0.917233i
$703$	−33320.3			−1.78762
$704$	17688.6	+	30637.6i	0.946966	+	1.64019i
$705$		0			0
$706$	7819.80	−	13544.3i	0.416859	−	0.722020i
$707$	3707.11	−	6420.90i	0.197200	−	0.341560i
$708$	32618.7	+	24949.1i	1.73148	+	1.32436i
$709$	5754.43	+	9966.96i	0.304813	+	0.527951i	0.977220	−	0.212231i	$-0.0680728\pi$
$709$	5754.43	+	9966.96i	0.304813	+	0.527951i	−0.672407	+	0.740182i	$0.734739\pi$
$710$		0			0
$711$	−20430.8	−	5406.66i	−1.07766	−	0.285184i
$712$	−7732.17			−0.406988
$713$	6452.60	+	11176.2i	0.338922	+	0.587031i
$714$	−4166.46	+	32030.5i	−0.218384	+	1.67887i
$715$		0			0
$716$	25103.1	−	43479.8i	1.31026	−	2.26943i
$717$	1934.83	−	14874.4i	0.100777	−	0.774747i
$718$	−6290.92	−	10896.2i	−0.326985	−	0.566355i
$719$	16503.6			0.856022			0.428011	−	0.903773i	$-0.359214\pi$
$719$	16503.6			0.856022			0.428011	+	0.903773i	$0.359214\pi$
$720$		0			0
$721$	2694.48			0.139179
$722$	32473.8	+	56246.2i	1.67389	+	2.89926i
$723$	−5318.62	−	4068.06i	−0.273585	−	0.209257i
$724$	−2624.35	+	4545.51i	−0.134714	+	0.233332i
$725$		0			0
$726$	51470.2	−	21413.1i	2.63118	−	1.09465i
$727$	−19224.0	−	33296.9i	−0.980713	−	1.69865i	−0.659623	−	0.751597i	$-0.729284\pi$
$727$	−19224.0	−	33296.9i	−0.980713	−	1.69865i	−0.321090	−	0.947049i	$-0.604049\pi$
$728$	−16074.9			−0.818372
$729$	−14046.7	−	13788.1i	−0.713645	−	0.700508i
$730$		0			0
$731$	−10537.2	−	18251.0i	−0.533151	−	0.923445i
$732$	−5836.13	+	2428.00i	−0.294685	+	0.122597i
$733$	17220.7	−	29827.1i	0.867750	−	1.50299i	0.00345985	−	0.999994i	$-0.498899\pi$
$733$	17220.7	−	29827.1i	0.867750	−	1.50299i	0.864290	−	0.502993i	$-0.167768\pi$
$734$	4288.98	−	7428.73i	0.215680	−	0.373569i
$735$		0			0
$736$	−1499.06	−	2596.44i	−0.0750760	−	0.130035i
$737$	29057.1			1.45228
$738$	−6819.59	+	6861.96i	−0.340153	+	0.342266i
$739$	4619.83			0.229964			0.114982	−	0.993368i	$-0.463319\pi$
$739$	4619.83			0.229964			0.114982	+	0.993368i	$0.463319\pi$
$740$		0			0
$741$	−2582.56	+	19854.0i	−0.128033	+	0.984283i
$742$	−23762.7	+	41158.2i	−1.17568	+	2.03634i
$743$	296.537	−	513.617i	0.0146418	−	0.0253604i	−0.858612	−	0.512627i	$-0.828673\pi$
$743$	296.537	−	513.617i	0.0146418	−	0.0253604i	0.873253	+	0.487266i	$0.162006\pi$
$744$	3692.83	−	28389.4i	0.181970	−	1.39893i
$745$		0			0
$746$	14697.1			0.721310
$747$	7085.64	+	1875.09i	0.347055	+	0.0918422i
$748$	72961.6			3.56650
$749$	−3670.48	−	6357.45i	−0.179060	−	0.310142i
$750$		0			0
$751$	11099.8	−	19225.4i	0.539331	−	0.934150i	−0.459609	−	0.888122i	$-0.652010\pi$
$751$	11099.8	−	19225.4i	0.539331	−	0.934150i	0.998940	−	0.0460280i	$-0.0146563\pi$
$752$	−7058.48	+	12225.6i	−0.342282	+	0.592850i
$753$	−20899.1	+	8694.61i	−1.01143	+	0.420783i
$754$	14845.3	+	25712.8i	0.717022	+	1.24192i
$755$		0			0
$756$	−13392.2	+	32761.2i	−0.644272	+	1.57608i
$757$	−9329.48			−0.447934			−0.223967	−	0.974597i	$-0.571901\pi$
$757$	−9329.48			−0.447934			−0.223967	+	0.974597i	$0.571901\pi$
$758$	22888.2	+	39643.5i	1.09675	+	1.89963i
$759$	−24450.4	+	10172.1i	−1.16929	+	0.486459i
$760$		0			0
$761$	−11435.9	+	19807.5i	−0.544745	+	0.943526i	0.453878	+	0.891064i	$0.350040\pi$
$761$	−11435.9	+	19807.5i	−0.544745	+	0.943526i	−0.998623	+	0.0524619i	$0.983293\pi$
$762$	−4212.45	−	3221.98i	−0.200264	−	0.153176i
$763$	3761.18	+	6514.55i	0.178458	+	0.309099i
$764$	15698.7			0.743400
$765$		0			0
$766$	47051.4			2.21937
$767$	−6887.83	−	11930.1i	−0.324257	−	0.561630i
$768$	−5278.43	+	40579.0i	−0.248006	+	1.90660i
$769$	6416.15	−	11113.1i	0.300874	−	0.521130i	−0.675460	−	0.737397i	$-0.736055\pi$
$769$	6416.15	−	11113.1i	0.300874	−	0.521130i	0.976334	+	0.216267i	$0.0693882\pi$
$770$		0			0
$771$	−2169.30	+	16677.0i	−0.101330	+	0.778997i
$772$	11590.7	+	20075.6i	0.540359	+	0.935929i
$773$	10821.5			0.503523			0.251762	−	0.967789i	$-0.418990\pi$
$773$	10821.5			0.503523			0.251762	+	0.967789i	$0.418990\pi$
$774$	−9158.96	−	33763.2i	−0.425338	−	1.56795i
$775$		0			0
$776$	30453.7	+	52747.4i	1.40880	+	2.44011i
$777$	15694.3	+	12004.1i	0.724621	+	0.554241i
$778$	30948.4	−	53604.2i	1.42616	−	2.47018i
$779$	5254.64	−	9101.31i	0.241678	−	0.418598i
$780$		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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42567 + 4.20138i) q^{2} +(-4.79753 + 1.99591i) q^{3} +(-7.76772 + 13.4541i) q^{4} +(-20.0228 - 15.3148i) q^{6} +(-8.11924 - 14.0629i) q^{7} -36.5569 q^{8} +(19.0327 - 19.1509i) q^{9} +O(q^{10})\)	\(q+(2.42567 + 4.20138i) q^{2} +(-4.79753 + 1.99591i) q^{3} +(-7.76772 + 13.4541i) q^{4} +(-20.0228 - 15.3148i) q^{6} +(-8.11924 - 14.0629i) q^{7} -36.5569 q^{8} +(19.0327 - 19.1509i) q^{9} +(-29.7592 - 51.5445i) q^{11} +(10.4127 - 80.0501i) q^{12} +(-13.5395 + 23.4511i) q^{13} +(39.3891 - 68.2240i) q^{14} +(-26.5331 - 45.9567i) q^{16} +78.9077 q^{17} +(126.627 + 33.5097i) q^{18} -142.290 q^{19} +(67.0207 + 51.2621i) q^{21} +(144.372 - 250.060i) q^{22} +(-42.8140 + 74.1561i) q^{23} +(175.383 - 72.9643i) q^{24} -131.369 q^{26} +(-53.0864 + 129.865i) q^{27} +252.272 q^{28} +(-113.004 - 195.729i) q^{29} +(75.3561 - 130.521i) q^{31} +(-17.5066 + 30.3223i) q^{32} +(245.649 + 187.890i) q^{33} +(191.404 + 331.521i) q^{34} +(109.817 + 404.826i) q^{36} +234.171 q^{37} +(-345.149 - 597.816i) q^{38} +(18.1499 - 139.531i) q^{39} +(-36.9290 + 63.9629i) q^{41} +(-52.8017 + 405.924i) q^{42} +(-133.539 - 231.296i) q^{43} +924.645 q^{44} -415.410 q^{46} +(-133.013 - 230.385i) q^{47} +(219.019 + 167.521i) q^{48} +(39.6560 - 68.6862i) q^{49} +(-378.563 + 157.493i) q^{51} +(-210.342 - 364.323i) q^{52} -603.281 q^{53} +(-674.380 + 91.9724i) q^{54} +(296.814 + 514.097i) q^{56} +(682.643 - 283.999i) q^{57} +(548.222 - 949.548i) q^{58} +(-254.360 + 440.565i) q^{59} +(-39.1519 - 67.8131i) q^{61} +731.155 q^{62} +(-423.849 - 112.164i) q^{63} -594.391 q^{64} +(-193.533 + 1487.82i) q^{66} +(-244.101 + 422.796i) q^{67} +(-612.933 + 1061.63i) q^{68} +(57.3928 - 441.219i) q^{69} -73.2487 q^{71} +(-695.776 + 700.098i) q^{72} +115.831 q^{73} +(568.021 + 983.842i) q^{74} +(1105.27 - 1914.39i) q^{76} +(-483.244 + 837.004i) q^{77} +(630.249 - 262.202i) q^{78} +(-391.371 - 677.875i) q^{79} +(-4.51465 - 728.986i) q^{81} -358.310 q^{82} +(135.732 + 235.095i) q^{83} +(-1210.28 + 503.512i) q^{84} +(647.840 - 1122.09i) q^{86} +(932.801 + 713.471i) q^{87} +(1087.91 + 1884.31i) q^{88} +211.511 q^{89} +439.722 q^{91} +(-665.135 - 1152.05i) q^{92} +(-101.016 + 776.581i) q^{93} +(645.289 - 1117.67i) q^{94} +(23.4678 - 180.414i) q^{96} +(-833.050 - 1442.89i) q^{97} +384.769 q^{98} +(-1553.52 - 411.113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9	\( 24 q - 4 q^{2} - q^{3} - 48 q^{4} - 13 q^{6} + 6 q^{7} + 90 q^{8} - 61 q^{9} - 29 q^{11} - 77 q^{12} + 24 q^{13} + 69 q^{14} - 192 q^{16} + 158 q^{17} + 125 q^{18} - 150 q^{19} - 60 q^{21} - 18 q^{22} - 318 q^{23} + 342 q^{24} - 308 q^{26} - 394 q^{27} - 192 q^{28} - 106 q^{29} - 60 q^{31} - 914 q^{32} - 80 q^{33} + 108 q^{34} + 1303 q^{36} + 168 q^{37} - 640 q^{38} - 410 q^{39} + 353 q^{41} + 1521 q^{42} - 426 q^{43} + 1142 q^{44} + 540 q^{46} - 1210 q^{47} + 2680 q^{48} - 666 q^{49} - 1369 q^{51} - 75 q^{52} + 896 q^{53} - 2128 q^{54} + 570 q^{56} + 1544 q^{57} + 594 q^{58} - 482 q^{59} - 402 q^{61} + 5088 q^{62} - 1038 q^{63} + 1950 q^{64} + 2041 q^{66} - 201 q^{67} - 3437 q^{68} + 2856 q^{69} - 1888 q^{71} - 5493 q^{72} + 906 q^{73} - 10 q^{74} + 462 q^{76} - 2652 q^{77} - 4589 q^{78} - 258 q^{79} + 3071 q^{81} - 1746 q^{82} - 3012 q^{83} - 2703 q^{84} - 1952 q^{86} + 2708 q^{87} - 216 q^{88} - 1476 q^{89} - 1236 q^{91} - 5232 q^{92} + 3024 q^{93} - 63 q^{94} - 10424 q^{96} - 318 q^{97} + 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - q^3 - 48 * q^4 - 13 * q^6 + 6 * q^7 + 90 * q^8 - 61 * q^9 - 29 * q^11 - 77 * q^12 + 24 * q^13 + 69 * q^14 - 192 * q^16 + 158 * q^17 + 125 * q^18 - 150 * q^19 - 60 * q^21 - 18 * q^22 - 318 * q^23 + 342 * q^24 - 308 * q^26 - 394 * q^27 - 192 * q^28 - 106 * q^29 - 60 * q^31 - 914 * q^32 - 80 * q^33 + 108 * q^34 + 1303 * q^36 + 168 * q^37 - 640 * q^38 - 410 * q^39 + 353 * q^41 + 1521 * q^42 - 426 * q^43 + 1142 * q^44 + 540 * q^46 - 1210 * q^47 + 2680 * q^48 - 666 * q^49 - 1369 * q^51 - 75 * q^52 + 896 * q^53 - 2128 * q^54 + 570 * q^56 + 1544 * q^57 + 594 * q^58 - 482 * q^59 - 402 * q^61 + 5088 * q^62 - 1038 * q^63 + 1950 * q^64 + 2041 * q^66 - 201 * q^67 - 3437 * q^68 + 2856 * q^69 - 1888 * q^71 - 5493 * q^72 + 906 * q^73 - 10 * q^74 + 462 * q^76 - 2652 * q^77 - 4589 * q^78 - 258 * q^79 + 3071 * q^81 - 1746 * q^82 - 3012 * q^83 - 2703 * q^84 - 1952 * q^86 + 2708 * q^87 - 216 * q^88 - 1476 * q^89 - 1236 * q^91 - 5232 * q^92 + 3024 * q^93 - 63 * q^94 - 10424 * q^96 - 318 * q^97 + 15022 * q^98 - 1697 * q^99

Introduction

L-functions

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