LMFDB - Embedded newform 225.4.e.f.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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			76.1
Character	$\chi$	$=$	225.76
Dual form			225.4.e.f.151.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42567 - 4.20138i) q^{2} +(4.79753 - 1.99591i) q^{3} +(-7.76772 + 13.4541i) q^{4} +(-20.0228 - 15.3148i) q^{6} +(8.11924 + 14.0629i) q^{7} +36.5569 q^{8} +(19.0327 - 19.1509i) q^{9} +O(q^{10})$	\(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	$-0.838620\pi$
$2$	−2.42567	−	4.20138i	−0.857603	−	1.48541i	0.0166066	−	0.999862i	$-0.494714\pi$
$3$	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	0.997566	−	0.0697271i	$-0.0222129\pi$
$7$	8.11924	+	14.0629i	0.438398	+	0.759327i	−0.559169	+	0.829054i	$0.688880\pi$
$8$	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	−0.684678	−	0.728846i	$-0.740057\pi$
$13$	13.5395	−	23.4511i	0.288860	−	0.500321i	0.973538	+	0.228525i	$0.0733903\pi$
$14$	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	$-0.690307\pi$
$17$	−78.9077			−1.12576			−0.562880	+	0.826538i	$0.690307\pi$
$18$	−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	−0.604055	−	0.796943i	$-0.706449\pi$
$23$	42.8140	−	74.1561i	0.388145	−	0.672288i	0.992200	+	0.124655i	$0.0397825\pi$
$24$	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	$-0.674156\pi$
$37$	−234.171			−1.04047			−0.520237	+	0.854022i	$0.674156\pi$
$38$	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	0.999543	−	0.0302295i	$-0.00962383\pi$
$43$	133.539	+	231.296i	0.473592	+	0.820285i	−0.525951	+	0.850515i	$0.676290\pi$
$44$	924.645			3.16808
$45$		0			0
$46$	−415.410			−1.33150
$47$	133.013	+	230.385i	0.412806	+	0.715001i	0.995195	−	0.0979088i	$-0.0312154\pi$
$47$	133.013	+	230.385i	0.412806	+	0.715001i	−0.582389	+	0.812910i	$0.697882\pi$
$48$	−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	$-0.214320\pi$
$53$	603.281			1.56353			0.781765	+	0.623574i	$0.214320\pi$
$54$	−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	−0.552959	−	0.833209i	$-0.686501\pi$
$67$	244.101	−	422.796i	0.445101	−	0.770937i	0.998059	+	0.0622718i	$0.0198346\pi$
$68$	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	$-0.529600\pi$
$73$	−115.831			−0.185712			−0.0928558	+	0.995680i	$0.529600\pi$
$74$	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	0.762209	−	0.647331i	$-0.224115\pi$
$83$	−135.732	−	235.095i	−0.179501	−	0.310904i	−0.941710	+	0.336427i	$0.890782\pi$
$84$	−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	$0.170507\pi$
$97$	833.050	+	1442.89i	0.871994	+	1.51034i	0.0120642	+	0.999927i	$0.496160\pi$
$98$	−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	−0.823610	−	0.567157i	$-0.808043\pi$
$103$	82.9660	−	143.701i	0.0793678	−	0.137469i	0.902977	+	0.429688i	$0.141377\pi$
$104$	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	$-0.565466\pi$
$107$	−452.071			−0.408443			−0.204221	+	0.978925i	$0.565466\pi$
$108$	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	−0.597691	−	0.801726i	$-0.703915\pi$
$113$	475.041	−	822.795i	0.395470	−	0.684974i	0.993161	+	0.116753i	$0.0372485\pi$
$114$	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	$-0.523416\pi$
$127$	−210.383			−0.146996			−0.0734979	+	0.997295i	$0.523416\pi$
$128$	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	$-0.960166\pi$
$137$	−968.837	−	1678.07i	−0.604185	−	1.04648i	0.387995	−	0.921661i	$-0.373168\pi$
$138$	−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	−0.700884	−	0.713275i	$-0.747211\pi$
$157$	525.779	−	910.676i	0.267272	−	0.462929i	0.968156	+	0.250346i	$0.0805444\pi$
$158$	−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	$-0.340553\pi$
$163$	1998.77			0.960463			0.480232	+	0.877142i	$0.340553\pi$
$164$	−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	$-0.638408\pi$
$167$	1240.51	−	2148.63i	0.574813	−	0.995606i	0.996062	−	0.0886604i	$-0.0282586\pi$
$168$	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	$-0.970873\pi$
$173$	−1313.04	−	2274.25i	−0.577042	−	0.999466i	0.418774	−	0.908090i	$-0.362460\pi$
$174$	−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	−0.970952	−	0.239274i	$-0.923091\pi$
$193$	−746.079	+	1292.25i	−0.278259	+	0.481958i	0.692693	+	0.721232i	$0.256424\pi$
$194$	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	$-0.295493\pi$
$197$	3313.50			1.19836			0.599181	+	0.800613i	$0.295493\pi$
$198$	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	0.952456	−	0.304675i	$-0.0985480\pi$
$223$	707.218	+	1224.94i	0.212371	+	0.367838i	−0.740085	+	0.672514i	$0.765215\pi$
$224$	568.561			0.169592
$225$		0			0
$226$	−4609.16			−1.35662
$227$	813.532	+	1409.08i	0.237868	+	0.411999i	0.960102	−	0.279649i	$-0.0902181\pi$
$227$	813.532	+	1409.08i	0.237868	+	0.411999i	−0.722234	+	0.691648i	$0.756885\pi$
$228$	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	$-0.413408\pi$
$233$	1911.28			0.537390			0.268695	+	0.963225i	$0.413408\pi$
$234$	−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	−0.992815	−	0.119659i	$-0.961820\pi$
$257$	−1618.26	+	2802.91i	−0.392780	+	0.680314i	0.600035	+	0.799973i	$0.295153\pi$
$258$	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	0.773614	−	0.633657i	$-0.218447\pi$
$263$	−690.768	−	1196.44i	−0.161956	−	0.280517i	−0.935570	+	0.353141i	$0.885114\pi$
$264$	−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	0.951459	−	0.307777i	$-0.0995850\pi$
$277$	964.393	+	1670.38i	0.209187	+	0.362322i	−0.742272	+	0.670099i	$0.766252\pi$
$278$	−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	$0.398760\pi$
$283$	−3171.79	+	5493.70i	−0.666231	+	1.15395i	−0.978950	+	0.204100i	$0.934573\pi$
$284$	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	−0.781085	−	0.624424i	$-0.785334\pi$
$293$	753.429	−	1304.98i	0.150225	−	0.260197i	0.931310	+	0.364228i	$0.118667\pi$
$294$	−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	$-0.222319\pi$
$307$	8239.13			1.53170			0.765850	+	0.643019i	$0.222319\pi$
$308$	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	0.622334	−	0.782752i	$-0.286185\pi$
$313$	−2030.70	−	3517.28i	−0.366716	−	0.635171i	−0.989050	+	0.147581i	$0.952851\pi$
$314$	−5101.46			−0.916853
$315$		0			0
$316$	12160.2			2.16477
$317$	−503.804	−	872.615i	−0.0892633	−	0.154609i	0.817937	−	0.575308i	$-0.195118\pi$
$317$	−503.804	−	872.615i	−0.0892633	−	0.154609i	−0.907200	+	0.420700i	$0.861785\pi$
$318$	−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	−0.695550	−	0.718478i	$-0.744839\pi$
$337$	1697.85	−	2940.77i	0.274445	−	0.475352i	0.969995	+	0.243125i	$0.0781726\pi$
$338$	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	$-0.615464\pi$
$347$	4086.81	−	7078.56i	0.632252	−	1.09509i	0.987090	−	0.160165i	$-0.0512026\pi$
$348$	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	0.961578	−	0.274532i	$-0.0885230\pi$
$353$	1611.89	+	2791.87i	0.243037	+	0.420953i	−0.718541	+	0.695485i	$0.755190\pi$
$354$	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	0.922024	−	0.387132i	$-0.126534\pi$
$367$	884.083	+	1531.28i	0.125746	+	0.217798i	−0.796278	+	0.604930i	$0.793201\pi$
$368$	−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	−0.951799	−	0.306723i	$-0.900767\pi$
$373$	−1514.74	+	2623.61i	−0.210269	+	0.364197i	0.741529	+	0.670920i	$0.234101\pi$
$374$	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	$0.390631\pi$
$383$	−4849.33	+	8399.29i	−0.646969	+	1.12058i	−0.983843	+	0.179034i	$0.942703\pi$
$384$	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	$-0.849682\pi$
$397$	−14088.8			−1.78111			−0.890553	+	0.454879i	$0.849682\pi$
$398$	−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	$-0.419940\pi$
$433$	4484.74			0.497744			0.248872	+	0.968536i	$0.419940\pi$
$434$	−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	0.993341	−	0.115212i	$-0.0367549\pi$
$443$	3700.66	+	6409.74i	0.396894	+	0.687440i	−0.596447	+	0.802652i	$0.703422\pi$
$444$	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	0.734503	−	0.678605i	$-0.237415\pi$
$457$	−2153.58	−	3730.11i	−0.220438	−	0.381810i	−0.954941	+	0.296795i	$0.904082\pi$
$458$	−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	−0.996792	−	0.0800354i	$-0.974497\pi$
$463$	−4274.77	+	7404.13i	−0.429083	+	0.743194i	0.567709	+	0.823230i	$0.307830\pi$
$464$	−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	$-0.716749\pi$
$467$	−12706.2			−1.25904			−0.629522	+	0.776983i	$0.716749\pi$
$468$	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	$-0.250073\pi$
$487$	15195.3			1.41389			0.706945	+	0.707268i	$0.250073\pi$
$488$	−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	$-0.665403\pi$
$503$	−11203.5			−0.993119			−0.496559	+	0.868003i	$0.665403\pi$
$504$	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	$-0.701526\pi$
$523$	−14153.1			−1.18331			−0.591656	+	0.806190i	$0.701526\pi$
$524$	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	0.841216	−	0.540699i	$-0.181840\pi$
$547$	−609.617	−	1055.89i	−0.0476515	−	0.0825348i	−0.888867	+	0.458165i	$0.848507\pi$
$548$	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	$-0.660089\pi$
$557$	−12672.4			−0.963995			−0.481998	+	0.876172i	$0.660089\pi$
$558$	−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	−0.669788	−	0.742552i	$-0.733615\pi$
$563$	4116.80	−	7130.50i	0.308175	−	0.533774i	0.977963	+	0.208778i	$0.0669486\pi$
$564$	−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	$-0.737071\pi$
$577$	−18788.9			−1.35562			−0.677810	+	0.735237i	$0.737071\pi$
$578$	−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	0.932949	−	0.360008i	$-0.117226\pi$
$587$	2200.11	+	3810.70i	0.154699	+	0.267946i	−0.778251	+	0.627954i	$0.783893\pi$
$588$	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	$-0.652473\pi$
$593$	−13311.2			−0.921798			−0.460899	+	0.887453i	$0.652473\pi$
$594$	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	−0.655676	−	0.755042i	$-0.727616\pi$
$607$	4876.00	−	8445.49i	0.326048	−	0.564731i	0.981724	+	0.190311i	$0.0609497\pi$
$608$	−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	$-0.791574\pi$
$613$	−24076.3			−1.58635			−0.793176	+	0.608992i	$0.791574\pi$
$614$	−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	−0.953860	−	0.300253i	$-0.902929\pi$
$617$	−3324.25	+	5757.76i	−0.216903	+	0.375687i	0.736957	+	0.675940i	$0.236262\pi$
$618$	−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	−0.572958	−	0.819585i	$-0.694204\pi$
$643$	6901.87	−	11954.4i	0.423302	−	0.733180i	0.996260	+	0.0864042i	$0.0275376\pi$
$644$	−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	$-0.236254\pi$
$647$	24257.1			1.47395			0.736974	+	0.675921i	$0.236254\pi$
$648$	−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	−0.946806	−	0.321804i	$-0.895711\pi$
$653$	−3249.10	+	5627.61i	−0.194712	+	0.337252i	0.752094	+	0.659056i	$0.229044\pi$
$654$	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	0.835447	−	0.549572i	$-0.185209\pi$
$673$	−1016.47	−	1760.57i	−0.0582198	−	0.100840i	−0.893666	+	0.448732i	$0.851876\pi$
$674$	−16473.7			−0.941458
$675$		0			0
$676$	−22739.6			−1.29379
$677$	4499.50	+	7793.36i	0.255435	+	0.442427i	0.965014	−	0.262199i	$-0.0844478\pi$
$677$	4499.50	+	7793.36i	0.255435	+	0.442427i	−0.709578	+	0.704627i	$0.751114\pi$
$678$	−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	$-0.267404\pi$
$683$	23826.0			1.33481			0.667407	+	0.744693i	$0.267404\pi$
$684$	−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	$0.270716\pi$
$727$	19224.0	+	33296.9i	0.980713	+	1.69865i	0.321090	+	0.947049i	$0.395951\pi$
$728$	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	$0.501101\pi$
$733$	−17220.7	+	29827.1i	−0.867750	+	1.50299i	−0.864290	+	0.502993i	$0.832232\pi$
$734$	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	−0.873253	−	0.487266i	$-0.837994\pi$
$743$	−296.537	+	513.617i	−0.0146418	+	0.0253604i	0.858612	+	0.512627i	$0.171327\pi$
$744$	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	$-0.428099\pi$
$757$	9329.48			0.447934			0.223967	+	0.974597i	$0.428099\pi$
$758$	−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	$-0.581010\pi$
$773$	−10821.5			−0.503523			−0.251762	+	0.967789i	$0.581010\pi$
$774$	−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
$781$	2179.82	+	3775.57i	0.0998723	+	0.172984i
$782$	32779.1			1.49895
$783$	−31417.3	+	4284.71i	−1.43393	+	0.195560i
$784$	−4208.79			−0.191727
$785$		0			0
$786$	−21523.6	+	8954.45i	−0.976746	+	0.406354i
$787$	6993.16	−	12112.5i	0.316746	−	0.548620i	−0.663061	−	0.748565i	$-0.730743\pi$
$787$	6993.16	−	12112.5i	0.316746	−	0.548620i	0.979807	+	0.199945i	$0.0640763\pi$
$788$	−25738.4	+	44580.2i	−1.16357	+	2.01536i
$789$	−5701.98	−	4361.27i	−0.257282	−	0.196788i
$790$		0			0
$791$	15427.9			0.693492
$792$	−56791.9	−	15029.0i	−2.54800	−	0.674284i
$793$	−2120.39			−0.0949525
$794$	34174.9	+	59192.6i	1.52748	+	2.64568i
$795$		0			0
$796$	−16818.4	+	29130.3i	−0.748885	+	1.29711i
$797$	10069.6	−	17441.0i	0.447532	−	0.775148i	−0.550693	−	0.834708i	$-0.685636\pi$
$797$	10069.6	−	17441.0i	0.447532	−	0.775148i	0.998225	+	0.0595602i	$0.0189698\pi$
$798$	−7513.17	+	57759.1i	−0.333288	+	2.56222i
$799$	−10495.7	−	18179.1i	−0.464721	−	0.804920i
$800$		0			0
$801$	4025.61	−	4050.62i	0.177575	−	0.178679i
$802$	−34761.1			−1.53050
$803$	3447.03	+	5970.43i	0.151486	+	0.262381i
$804$	31303.1	+	23942.8i	1.37310	+	1.05025i
$805$		0			0
$806$	−9899.48	+	17146.4i	−0.432623	+	0.749326i
$807$	3459.33	−	1439.18i	0.150897	−	0.0627775i
$808$	8345.64	+	14455.1i	0.363364	+	0.629366i
$809$	4443.65			0.193115			0.0965576	−	0.995327i	$-0.469217\pi$
$809$	4443.65			0.193115			0.0965576	+	0.995327i	$0.469217\pi$
$810$		0			0
$811$	3871.68			0.167636			0.0838181	−	0.996481i	$-0.473289\pi$
$811$	3871.68			0.167636			0.0838181	+	0.996481i	$0.473289\pi$
$812$	28507.8	+	49377.0i	1.23205	+	2.13398i
$813$	18311.3	−	7618.03i	0.789921	−	0.328630i
$814$	33807.8	−	58556.8i	1.45573	−	2.52139i
$815$		0			0
$816$	17282.3	+	13218.7i	0.741423	+	0.567093i
$817$	−19001.3	−	32911.2i	−0.813672	−	1.40932i
$818$	9895.00			0.422947
$819$	8369.09	−	8421.08i	0.357069	−	0.359287i
$820$		0			0
$821$	16596.6	+	28746.2i	0.705513	+	1.22198i	0.966506	+	0.256643i	$0.0826165\pi$
$821$	16596.6	+	28746.2i	0.705513	+	1.22198i	−0.260994	+	0.965341i	$0.584050\pi$
$822$	−6300.62	+	48437.3i	−0.267347	+	2.05529i
$823$	−3072.38	+	5321.52i	−0.130129	+	0.225391i	−0.923726	−	0.383053i	$-0.874873\pi$
$823$	−3072.38	+	5321.52i	−0.130129	+	0.225391i	0.793597	+	0.608444i	$0.208206\pi$
$824$	3032.98	−	5253.28i	0.128227	−	0.222095i
$825$		0			0
$826$	20038.1	+	34707.0i	0.844084	+	1.46200i
$827$	138.554			0.00582585			0.00291293	−	0.999996i	$-0.499073\pi$
$827$	138.554			0.00582585			0.00291293	+	0.999996i	$0.499073\pi$
$828$	34722.0	+	9188.60i	1.45734	+	0.385659i
$829$	−21615.2			−0.905580			−0.452790	−	0.891617i	$-0.649571\pi$
$829$	−21615.2			−0.905580			−0.452790	+	0.891617i	$0.649571\pi$
$830$		0			0
$831$	7960.63	+	6088.85i	0.332312	+	0.254176i
$832$	−8047.76	+	13939.1i	−0.335344	+	0.580832i
$833$	−3129.16	+	5419.87i	−0.130155	+	0.225435i
$834$	−45862.6	+	19080.1i	−1.90418	+	0.792195i
$835$		0			0
$836$	−131568.			−5.44304
$837$	−12949.6	−	16715.0i	−0.534773	−	0.690267i
$838$	64006.8			2.63852
$839$	−6484.88	−	11232.1i	−0.266845	−	0.462189i	0.701200	−	0.712964i	$-0.252648\pi$
$839$	−6484.88	−	11232.1i	−0.266845	−	0.462189i	−0.968045	+	0.250775i	$0.919315\pi$
$840$		0			0
$841$	−13345.5	+	23115.0i	−0.547193	+	0.947765i
$842$	−27269.7	+	47232.6i	−1.11612	+	1.93318i
$843$	−20404.6	−	15606.9i	−0.833657	−	0.637640i
$844$	19883.0	+	34438.4i	0.810903	+	1.40453i
$845$		0			0
$846$	−9122.88	−	33630.2i	−0.370746	−	1.36670i
$847$	−35910.5			−1.45679
$848$	−16006.9	−	27724.8i	−0.648208	−	1.12273i
$849$	−4251.83	+	32686.8i	−0.171876	+	1.32133i
$850$		0			0
$851$	−10025.8	+	17365.2i	−0.403855	+	0.699497i
$852$	762.719	−	5863.56i	0.0306694	−	0.235777i
$853$	−19772.3	−	34246.6i	−0.793658	−	1.37466i	−0.923688	−	0.383146i	$-0.874841\pi$
$853$	−19772.3	−	34246.6i	−0.793658	−	1.37466i	0.130030	−	0.991510i	$-0.458493\pi$
$854$	−6168.64			−0.247174
$855$		0			0
$856$	−16526.3			−0.659881
$857$	7419.10	+	12850.3i	0.295719	+	0.512201i	0.975152	−	0.221537i	$-0.0711073\pi$
$857$	7419.10	+	12850.3i	0.295719	+	0.512201i	−0.679433	+	0.733738i	$0.737774\pi$
$858$	32270.8	+	24683.0i	1.28404	+	0.982124i
$859$	12244.8	−	21208.7i	0.486366	−	0.842411i	−0.513511	−	0.858083i	$-0.671655\pi$
$859$	12244.8	−	21208.7i	0.486366	−	0.842411i	0.999877	+	0.0156718i	$0.00498870\pi$
$860$		0			0
$861$	−5753.88	+	2393.78i	−0.227749	+	0.0947500i
$862$	13454.9	+	23304.6i	0.531642	+	0.920831i
$863$	10016.3			0.395084			0.197542	−	0.980294i	$-0.436704\pi$
$863$	10016.3			0.395084			0.197542	+	0.980294i	$0.436704\pi$
$864$	−3008.44	−	3883.19i	−0.118460	−	0.152904i
$865$		0			0
$866$	−10878.5	−	18842.1i	−0.426866	−	0.739354i
$867$	6301.22	−	2621.49i	0.246829	−	0.102688i
$868$	−19010.2	+	32926.7i	−0.743374	+	1.28756i
$869$	−23293.8	+	40346.1i	−0.909308	+	1.57497i
$870$		0			0
$871$	−6610.03	−	11448.9i	−0.257144	−	0.445386i
$872$	−16934.7			−0.657663
$873$	43487.8	+	11508.3i	1.68595	+	0.446159i
$874$	59108.9			2.28763
$875$		0			0
$876$	1206.11	−	9272.25i	0.0465192	−	0.357626i
$877$	16957.1	−	29370.5i	0.652907	−	1.13087i	−0.329507	−	0.944153i	$-0.606883\pi$
$877$	16957.1	−	29370.5i	0.652907	−	1.13087i	0.982414	−	0.186715i	$-0.0597841\pi$
$878$	−12782.6	+	22140.1i	−0.491334	+	0.851015i
$879$	1009.98	−	7764.45i	0.0387552	−	0.297939i
$880$		0			0
$881$	37237.1			1.42401			0.712004	−	0.702176i	$-0.247788\pi$
$881$	37237.1			1.42401			0.712004	+	0.702176i	$0.247788\pi$
$882$	−7323.18	+	7368.67i	−0.279574	+	0.281311i
$883$	36907.3			1.40660			0.703302	−	0.710892i	$-0.251708\pi$
$883$	36907.3			1.40660			0.703302	+	0.710892i	$0.251708\pi$
$884$	−16597.6	−	28747.9i	−0.631492	−	1.09378i
$885$		0			0
$886$	17953.2	−	31095.8i	0.680754	−	1.17910i
$887$	7791.52	−	13495.3i	0.294942	−	0.510855i	−0.680029	−	0.733185i	$-0.738033\pi$
$887$	7791.52	−	13495.3i	0.294942	−	0.510855i	0.974971	+	0.222330i	$0.0713663\pi$
$888$	−41069.7	+	17086.2i	−1.55204	+	0.645691i
$889$	−1708.15	−	2958.60i	−0.0644426	−	0.111618i
$890$		0			0
$891$	−37440.9	+	21926.8i	−1.40776	+	0.824438i
$892$	−21973.9			−0.824820
$893$	−18926.4	−	32781.5i	−0.709237	−	1.22843i
$894$	37153.7	−	15457.0i	1.38994	−	0.578255i
$895$		0			0
$896$	−21138.3	+	36612.6i	−0.788148	+	1.36511i
$897$	−9570.02	−	7319.82i	−0.356225	−	0.272466i
$898$	2277.05	+	3943.97i	0.0846172	+	0.146561i
$899$	−34062.3			−1.26367
$900$		0			0
$901$	−47603.5			−1.76016
$902$	−10663.0	−	18468.9i	−0.393614	−	0.681759i
$903$	−2906.86	+	22347.1i	−0.107125	+	0.823548i
$904$	17366.0	−	30078.8i	0.638922	−	1.10665i
$905$		0			0
$906$	11943.2	−	91815.6i	0.437953	−	3.36685i
$907$	−13559.3	−	23485.4i	−0.496394	−	0.859779i	0.503598	−	0.863938i	$-0.332009\pi$
$907$	−13559.3	−	23485.4i	−0.496394	−	0.859779i	−0.999991	+	0.00415907i	$0.998676\pi$
$908$	−25277.1			−0.923845
$909$	11917.5	+	3153.77i	0.434850	+	0.115076i
$910$		0			0
$911$	10366.8	+	17955.8i	0.377021	+	0.653020i	0.990627	−	0.136593i	$-0.0436151\pi$
$911$	10366.8	+	17955.8i	0.377021	+	0.653020i	−0.613606	+	0.789612i	$0.710282\pi$
$912$	31164.3	+	23836.7i	1.13153	+	0.865472i
$913$	−8078.58	+	13992.5i	−0.292839	+	0.507212i
$914$	−10447.7	+	18096.0i	−0.378097	+	0.654883i
$915$		0			0
$916$	51418.9	+	89060.1i	1.85472	+	3.21248i
$917$	15016.9			0.540789
$918$	53213.8	−	7257.34i	1.91320	−	0.260924i
$919$	−48056.4			−1.72495			−0.862477	−	0.506096i	$-0.831088\pi$
$919$	−48056.4			−1.72495			−0.862477	+	0.506096i	$0.831088\pi$
$920$		0			0
$921$	39527.5	−	16444.6i	1.41420	−	0.588346i
$922$	−12717.2	+	22026.9i	−0.454251	+	0.786786i
$923$	−991.751	+	1717.76i	−0.0353672	+	0.0612577i
$924$	61970.3	+	47399.3i	2.20636	+	1.68758i
$925$		0			0
$926$	41476.7			1.47193
$927$	−1172.95	−	4323.90i	−0.0415584	−	0.153199i
$928$	−7913.29			−0.279921
$929$	−17838.8	−	30897.6i	−0.630001	−	1.09119i	−0.987551	−	0.157299i	$-0.949721\pi$
$929$	−17838.8	−	30897.6i	−0.630001	−	1.09119i	0.357550	−	0.933894i	$-0.383612\pi$
$930$		0			0
$931$	−5642.67	+	9773.38i	−0.198637	+	0.344049i
$932$	−14846.2	+	25714.4i	−0.521786	+	0.903760i
$933$	540.158	−	4152.58i	0.0189539	−	0.145712i
$934$	30821.0	+	53383.6i	1.07976	+	1.87020i
$935$		0			0
$936$	−6997.62	−	25795.7i	−0.244364	−	0.900811i
$937$	33519.2			1.16865			0.584324	−	0.811520i	$-0.301360\pi$
$937$	33519.2			1.16865			0.584324	+	0.811520i	$0.301360\pi$
$938$	−19229.9	−	33307.1i	−0.669380	−	1.15940i
$939$	−16762.6	−	12821.2i	−0.582562	−	0.445584i
$940$		0			0
$941$	26137.5	−	45271.5i	0.905482	−	1.56834i	0.0852134	−	0.996363i	$-0.472843\pi$
$941$	26137.5	−	45271.5i	0.905482	−	1.56834i	0.820269	−	0.571978i	$-0.193824\pi$
$942$	−24474.4	+	10182.1i	−0.846518	+	0.352176i
$943$	3162.16	+	5477.02i	0.109198	+	0.189137i
$944$	26995.9			0.930765
$945$		0			0
$946$	−77116.9			−2.65041
$947$	−14234.3	−	24654.6i	−0.488440	−	0.846004i	0.511471	−	0.859300i	$-0.329101\pi$
$947$	−14234.3	−	24654.6i	−0.488440	−	0.846004i	−0.999912	+	0.0132968i	$0.995767\pi$
$948$	58339.2	−	24270.8i	1.99870	−	0.831517i
$949$	−1568.29	+	2716.36i	−0.0536447	+	0.0929154i
$950$		0			0
$951$	−4158.68	−	3180.85i	−0.141803	−	0.108461i
$952$	−23420.9	−	40566.2i	−0.797349	−	1.38105i
$953$	−492.737			−0.0167485			−0.00837424	−	0.999965i	$-0.502666\pi$
$953$	−492.737			−0.0167485			−0.00837424	+	0.999965i	$0.502666\pi$
$954$	−76391.8	−	20215.8i	−2.59253	−	0.686070i
$955$		0			0
$956$	−22423.0	−	38837.8i	−0.758590	−	1.31392i
$957$	−9016.09	+	69313.1i	−0.304544	+	2.34125i
$958$	44525.9	−	77121.1i	1.50164	−	2.60091i
$959$	15732.4	−	27249.4i	0.529746	−	0.917547i
$960$		0			0
$961$	3538.42	+	6128.72i	0.118775	+	0.205724i
$962$	30762.9			1.03102
$963$	−8604.13	+	8657.58i	−0.287917	+	0.289706i
$964$	−20019.8			−0.668873
$965$		0			0
$966$	−27841.1	−	21294.8i	−0.927300	−	0.709264i
$967$	−11603.2	+	20097.3i	−0.385866	+	0.668340i	−0.991889	−	0.127108i	$-0.959431\pi$
$967$	−11603.2	+	20097.3i	−0.385866	+	0.668340i	0.606023	+	0.795447i	$0.292764\pi$
$968$	−40421.8	+	70012.6i	−1.34216	+	2.32468i
$969$	53865.8	−	22409.7i	1.78578	−	0.742935i
$970$		0			0
$971$	−47923.0			−1.58385			−0.791927	−	0.610615i	$-0.790922\pi$
$971$	−47923.0			−1.58385			−0.791927	+	0.610615i	$0.790922\pi$
$972$	58402.4	+	7229.34i	1.92722	+	0.238561i
$973$	31998.1			1.05428
$974$	−36858.7	−	63841.2i	−1.21256	−	2.10021i
$975$		0			0
$976$	−2077.65	+	3598.59i	−0.0681392	+	0.118021i
$977$	12164.2	−	21069.1i	0.398330	−	0.689929i	−0.595190	−	0.803585i	$-0.702923\pi$
$977$	12164.2	−	21069.1i	0.398330	−	0.689929i	0.993520	+	0.113657i	$0.0362564\pi$
$978$	−40020.9	−	30610.8i	−1.30851	−	1.00084i
$979$	−6294.39	−	10902.2i	−0.205485	−	0.355910i
$980$		0			0
$981$	−8816.75	+	8871.52i	−0.286949	+	0.288732i
$982$	38538.5			1.25236
$983$	12686.3	+	21973.3i	0.411627	+	0.712958i	0.995068	−	0.0991972i	$-0.0316275\pi$
$983$	12686.3	+	21973.3i	0.411627	+	0.712958i	−0.583441	+	0.812155i	$0.698294\pi$
$984$	−1809.71	+	13912.5i	−0.0586294	+	0.450726i
$985$		0			0
$986$	43258.9	−	74926.7i	1.39721	−	2.42003i
$987$	−2895.41	+	22259.0i	−0.0933757	+	0.717845i
$988$	−29929.7	−	51839.7i	−0.963755	−	1.66927i
$989$	22869.3			0.735290
$990$		0			0
$991$	32297.1			1.03527			0.517635	−	0.855602i	$-0.326813\pi$
$991$	32297.1			1.03527			0.517635	+	0.855602i	$0.326813\pi$
$992$	−2638.46	−	4569.94i	−0.0844467	−	0.146266i
$993$	−38360.6	−	29340.9i	−1.22592	−	0.937668i
$994$	−2885.20	+	4997.32i	−0.0920654	+	0.159462i
$995$		0			0
$996$	20232.7	−	8417.40i	0.643674	−	0.267787i
$997$	12728.6	+	22046.6i	0.404332	+	0.700323i	0.994243	−	0.107145i	$-0.0341709\pi$
$997$	12728.6	+	22046.6i	0.404332	+	0.700323i	−0.589912	+	0.807468i	$0.700838\pi$
$998$	−92941.2			−2.94790
$999$	−12431.3	+	30410.6i	−0.393703	+	0.963111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.76.1	yes	24
5.2	odd	4		225.4.k.e.49.23		48
5.3	odd	4		225.4.k.e.49.2		48
5.4	even	2		225.4.e.e.76.12	✓	24
9.4	even	3		2025.4.a.bf.1.12		12
9.5	odd	6		2025.4.a.bj.1.1		12
9.7	even	3	inner	225.4.e.f.151.1	yes	24
45.4	even	6		2025.4.a.bi.1.1		12
45.7	odd	12		225.4.k.e.124.2		48
45.14	odd	6		2025.4.a.be.1.12		12
45.34	even	6		225.4.e.e.151.12	yes	24
45.43	odd	12		225.4.k.e.124.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.12	✓	24	5.4	even	2
225.4.e.e.151.12	yes	24	45.34	even	6
225.4.e.f.76.1	yes	24	1.1	even	1	trivial
225.4.e.f.151.1	yes	24	9.7	even	3	inner
225.4.k.e.49.2		48	5.3	odd	4
225.4.k.e.49.23		48	5.2	odd	4
225.4.k.e.124.2		48	45.7	odd	12
225.4.k.e.124.23		48	45.43	odd	12
2025.4.a.be.1.12		12	45.14	odd	6
2025.4.a.bf.1.12		12	9.4	even	3
2025.4.a.bi.1.1		12	45.4	even	6
2025.4.a.bj.1.1		12	9.5	odd	6

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

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