LMFDB - Embedded newform 225.4.e.f.76.2

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			76.2
Character	$\chi$	$=$	225.76
Dual form			225.4.e.f.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +O(q^{10})$	\(q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +(17.2761 + 29.9230i) q^{11} +(-47.5021 - 29.8427i) q^{12} +(3.77884 - 6.54514i) q^{13} +(-28.1837 + 48.8156i) q^{14} +(16.9062 + 29.2824i) q^{16} -82.0901 q^{17} +(50.8046 + 105.458i) q^{18} +146.406 q^{19} +(59.7265 - 31.5720i) q^{21} +(74.8995 - 129.730i) q^{22} +(93.9451 - 162.718i) q^{23} +(-2.35072 + 62.9468i) q^{24} -32.7659 q^{26} +(15.6778 - 139.417i) q^{27} +140.366 q^{28} +(-21.8589 - 37.8607i) q^{29} +(29.3391 - 50.8168i) q^{31} +(121.786 - 210.940i) q^{32} +(-158.726 + 83.9041i) q^{33} +(177.949 + 308.216i) q^{34} +(164.171 - 240.869i) q^{36} +329.358 q^{37} +(-317.368 - 549.697i) q^{38} +(33.2531 + 20.8909i) q^{39} +(86.4845 - 149.796i) q^{41} +(-248.011 - 155.811i) q^{42} +(78.3437 + 135.695i) q^{43} -373.030 q^{44} -814.589 q^{46} +(84.6230 + 146.571i) q^{47} +(-155.328 + 82.1077i) q^{48} +(86.9806 - 150.655i) q^{49} +(15.9183 - 426.255i) q^{51} +(40.7969 + 70.6623i) q^{52} -609.837 q^{53} +(-557.443 + 243.355i) q^{54} +(-78.8058 - 136.496i) q^{56} +(-28.3899 + 760.217i) q^{57} +(-94.7682 + 164.143i) q^{58} +(297.215 - 514.792i) q^{59} +(-162.538 - 281.525i) q^{61} -254.396 q^{62} +(152.357 + 316.254i) q^{63} -785.498 q^{64} +(659.102 + 414.075i) q^{66} +(344.191 - 596.156i) q^{67} +(443.128 - 767.521i) q^{68} +(826.700 + 519.366i) q^{69} -515.170 q^{71} +(-326.398 - 24.4124i) q^{72} +1088.37 q^{73} +(-713.959 - 1236.61i) q^{74} +(-790.310 + 1368.86i) q^{76} +(224.615 - 389.044i) q^{77} +(6.35373 - 170.138i) q^{78} +(262.896 + 455.349i) q^{79} +(720.889 + 108.442i) q^{81} -749.899 q^{82} +(179.006 + 310.048i) q^{83} +(-27.2188 + 728.855i) q^{84} +(339.655 - 588.300i) q^{86} +(200.832 - 106.161i) q^{87} +(209.430 + 362.744i) q^{88} +1517.67 q^{89} -98.2610 q^{91} +(1014.25 + 1756.72i) q^{92} +(258.179 + 162.198i) q^{93} +(366.879 - 635.453i) q^{94} +(1071.70 + 673.283i) q^{96} +(197.680 + 342.393i) q^{97} -754.200 q^{98} +(-404.896 - 840.462i) 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 $

$2$	−2.16773	−	3.75461i	−0.766407	−	1.32746i	−0.939500	−	0.342550i	$-0.888709\pi$
$2$	−2.16773	−	3.75461i	−0.766407	−	1.32746i	0.173093	−	0.984906i	$-0.444624\pi$
$3$	−0.193913	+	5.19253i	−0.0373185	+	0.999303i
$3$	−0.193913	+	5.19253i	−0.0373185	+	0.999303i
$4$	−5.39807	+	9.34974i	−0.674759	+	1.16872i
$5$		0			0
$5$		0			0
$6$	19.9163	−	10.5279i	1.35513	−	0.716334i
$7$	−6.50075	−	11.2596i	−0.351007	−	0.607963i	0.635419	−	0.772168i	$-0.280827\pi$
$7$	−6.50075	−	11.2596i	−0.351007	−	0.607963i	−0.986426	+	0.164205i	$0.947494\pi$
$8$	12.1226			0.535747
$9$	−26.9248	−	2.01380i	−0.997215	−	0.0745850i
$10$		0			0
$11$	17.2761	+	29.9230i	0.473539	+	0.820194i	0.999541	−	0.0302897i	$-0.00964297\pi$
$11$	17.2761	+	29.9230i	0.473539	+	0.820194i	−0.526002	+	0.850483i	$0.676310\pi$
$12$	−47.5021	−	29.8427i	−1.14272	−	0.717904i
$13$	3.77884	−	6.54514i	0.0806200	−	0.139638i	−0.822896	−	0.568191i	$-0.807643\pi$
$13$	3.77884	−	6.54514i	0.0806200	−	0.139638i	0.903516	+	0.428553i	$0.140977\pi$
$14$	−28.1837	+	48.8156i	−0.538029	+	0.931894i
$15$		0			0
$16$	16.9062	+	29.2824i	0.264159	+	0.457537i
$17$	−82.0901			−1.17116			−0.585581	−	0.810614i	$-0.699134\pi$
$17$	−82.0901			−1.17116			−0.585581	+	0.810614i	$0.699134\pi$
$18$	50.8046	+	105.458i	0.665264	+	1.38092i
$19$	146.406			1.76778			0.883890	−	0.467696i	$-0.154916\pi$
$19$	146.406			1.76778			0.883890	+	0.467696i	$0.154916\pi$
$20$		0			0
$21$	59.7265	−	31.5720i	0.620638	−	0.328075i
$22$	74.8995	−	129.730i	0.725847	−	1.25720i
$23$	93.9451	−	162.718i	0.851691	−	1.47517i	−0.0279894	−	0.999608i	$-0.508910\pi$
$23$	93.9451	−	162.718i	0.851691	−	1.47517i	0.879681	−	0.475565i	$-0.157756\pi$
$24$	−2.35072	+	62.9468i	−0.0199933	+	0.535374i
$25$		0			0
$26$	−32.7659			−0.247151
$27$	15.6778	−	139.417i	0.111748	−	0.993737i
$28$	140.366			0.947382
$29$	−21.8589	−	37.8607i	−0.139969	−	0.242433i	0.787516	−	0.616295i	$-0.211367\pi$
$29$	−21.8589	−	37.8607i	−0.139969	−	0.242433i	−0.927485	+	0.373861i	$0.878034\pi$
$30$		0			0
$31$	29.3391	−	50.8168i	0.169982	−	0.294418i	−0.768431	−	0.639933i	$-0.778962\pi$
$31$	29.3391	−	50.8168i	0.169982	−	0.294418i	0.938413	+	0.345514i	$0.112296\pi$
$32$	121.786	−	210.940i	0.672780	−	1.16529i
$33$	−158.726	+	83.9041i	−0.837294	+	0.442601i
$34$	177.949	+	308.216i	0.897587	+	1.55467i
$35$		0			0
$36$	164.171	−	240.869i	0.760049	−	1.11514i
$37$	329.358			1.46341			0.731705	−	0.681621i	$-0.238725\pi$
$37$	329.358			1.46341			0.731705	+	0.681621i	$0.238725\pi$
$38$	−317.368	−	549.697i	−1.35484	−	2.34665i
$39$	33.2531	+	20.8909i	0.136532	+	0.0857750i
$40$		0			0
$41$	86.4845	−	149.796i	0.329429	−	0.570588i	−0.652969	−	0.757384i	$-0.726477\pi$
$41$	86.4845	−	149.796i	0.329429	−	0.570588i	0.982399	+	0.186796i	$0.0598103\pi$
$42$	−248.011	−	155.811i	−0.911166	−	0.572431i
$43$	78.3437	+	135.695i	0.277844	+	0.481240i	0.970849	−	0.239693i	$-0.0770467\pi$
$43$	78.3437	+	135.695i	0.277844	+	0.481240i	−0.693004	+	0.720933i	$0.743713\pi$
$44$	−373.030			−1.27810
$45$		0			0
$46$	−814.589			−2.61097
$47$	84.6230	+	146.571i	0.262628	+	0.454886i	0.966940	−	0.255006i	$-0.0820774\pi$
$47$	84.6230	+	146.571i	0.262628	+	0.454886i	−0.704311	+	0.709891i	$0.748744\pi$
$48$	−155.328	+	82.1077i	−0.467076	+	0.246900i
$49$	86.9806	−	150.655i	0.253588	−	0.439227i
$50$		0			0
$51$	15.9183	−	426.255i	0.0437061	−	1.17035i
$52$	40.7969	+	70.6623i	0.108798	+	0.188444i
$53$	−609.837			−1.58052			−0.790259	−	0.612772i	$-0.790054\pi$
$53$	−609.837			−1.58052			−0.790259	+	0.612772i	$0.790054\pi$
$54$	−557.443	+	243.355i	−1.40479	+	0.613267i
$55$		0			0
$56$	−78.8058	−	136.496i	−0.188051	−	0.325714i
$57$	−28.3899	+	760.217i	−0.0659709	+	1.76655i
$58$	−94.7682	+	164.143i	−0.214546	+	0.371605i
$59$	297.215	−	514.792i	0.655833	−	1.13594i	−0.325852	−	0.945421i	$-0.605651\pi$
$59$	297.215	−	514.792i	0.655833	−	1.13594i	0.981684	−	0.190514i	$-0.0610156\pi$
$60$		0			0
$61$	−162.538	−	281.525i	−0.341163	−	0.590911i	0.643486	−	0.765458i	$-0.277487\pi$
$61$	−162.538	−	281.525i	−0.341163	−	0.590911i	−0.984649	+	0.174547i	$0.944154\pi$
$62$	−254.396			−0.521103
$63$	152.357	+	316.254i	0.304685	+	0.632449i
$64$	−785.498			−1.53418
$65$		0			0
$66$	659.102	+	414.075i	1.22924	+	0.772258i
$67$	344.191	−	596.156i	0.627606	−	1.08705i	−0.360425	−	0.932788i	$-0.617368\pi$
$67$	344.191	−	596.156i	0.627606	−	1.08705i	0.988031	−	0.154257i	$-0.0492985\pi$
$68$	443.128	−	767.521i	0.790253	−	1.36876i
$69$	826.700	+	519.366i	1.44236	+	0.906149i
$70$		0			0
$71$	−515.170			−0.861119			−0.430560	−	0.902562i	$-0.641684\pi$
$71$	−515.170			−0.861119			−0.430560	+	0.902562i	$0.641684\pi$
$72$	−326.398	−	24.4124i	−0.534255	−	0.0399587i
$73$	1088.37			1.74499			0.872497	−	0.488619i	$-0.162499\pi$
$73$	1088.37			1.74499			0.872497	+	0.488619i	$0.162499\pi$
$74$	−713.959	−	1236.61i	−1.12157	−	1.94261i
$75$		0			0
$76$	−790.310	+	1368.86i	−1.19283	+	2.06603i
$77$	224.615	−	389.044i	0.332431	−	0.575788i
$78$	6.35373	−	170.138i	0.00922331	−	0.246979i
$79$	262.896	+	455.349i	0.374406	+	0.648491i	0.990238	−	0.139387i	$-0.0445131\pi$
$79$	262.896	+	455.349i	0.374406	+	0.648491i	−0.615832	+	0.787878i	$0.711180\pi$
$80$		0			0
$81$	720.889	+	108.442i	0.988874	+	0.148755i
$82$	−749.899			−1.00991
$83$	179.006	+	310.048i	0.236729	+	0.410027i	0.959774	−	0.280775i	$-0.0905913\pi$
$83$	179.006	+	310.048i	0.236729	+	0.410027i	−0.723045	+	0.690801i	$0.757258\pi$
$84$	−27.2188	+	728.855i	−0.0353549	+	0.946722i
$85$		0			0
$86$	339.655	−	588.300i	0.425884	−	0.737652i
$87$	200.832	−	106.161i	0.247488	−	0.130824i
$88$	209.430	+	362.744i	0.253697	+	0.439416i
$89$	1517.67			1.80756			0.903779	−	0.427999i	$-0.140781\pi$
$89$	1517.67			1.80756			0.903779	+	0.427999i	$0.140781\pi$
$90$		0			0
$91$	−98.2610			−0.113193
$92$	1014.25	+	1756.72i	1.14937	+	1.99077i
$93$	258.179	+	162.198i	0.287870	+	0.180851i
$94$	366.879	−	635.453i	0.402560	−	0.697255i
$95$		0			0
$96$	1071.70	+	673.283i	1.13937	+	0.715798i
$97$	197.680	+	342.393i	0.206922	+	0.358399i	0.950743	−	0.309979i	$-0.100322\pi$
$97$	197.680	+	342.393i	0.206922	+	0.358399i	−0.743822	+	0.668378i	$0.766989\pi$
$98$	−754.200			−0.777405
$99$	−404.896	−	840.462i	−0.411046	−	0.853228i
$100$		0			0
$101$	−166.629	−	288.610i	−0.164160	−	0.284334i	0.772197	−	0.635384i	$-0.219158\pi$
$101$	−166.629	−	288.610i	−0.164160	−	0.284334i	−0.936357	+	0.351050i	$0.885825\pi$
$102$	−1634.93	+	864.238i	−1.58708	+	0.838944i
$103$	−815.444	+	1412.39i	−0.780078	+	1.35114i	0.151817	+	0.988409i	$0.451487\pi$
$103$	−815.444	+	1412.39i	−0.780078	+	1.35114i	−0.931896	+	0.362727i	$0.881846\pi$
$104$	45.8092	−	79.3439i	0.0431919	−	0.0748106i
$105$		0			0
$106$	1321.96	+	2289.70i	1.21132	+	2.09807i
$107$	−688.472			−0.622029			−0.311015	−	0.950405i	$-0.600669\pi$
$107$	−688.472			−0.622029			−0.311015	+	0.950405i	$0.600669\pi$
$108$	1218.89	+	899.168i	1.08599	+	0.801134i
$109$	−1188.95			−1.04478			−0.522390	−	0.852707i	$-0.674959\pi$
$109$	−1188.95			−1.04478			−0.522390	+	0.852707i	$0.674959\pi$
$110$		0			0
$111$	−63.8668	+	1710.20i	−0.0546123	+	1.46239i
$112$	219.806	−	380.715i	0.185444	−	0.321198i
$113$	−134.208	+	232.455i	−0.111727	+	0.193518i	−0.916467	−	0.400111i	$-0.868972\pi$
$113$	−134.208	+	232.455i	−0.111727	+	0.193518i	0.804739	+	0.593628i	$0.202305\pi$
$114$	2915.86	−	1541.35i	2.39557	−	1.26632i
$115$		0			0
$116$	471.984			0.377781
$117$	−114.925	+	168.617i	−0.0908104	+	0.133236i
$118$	−2577.12			−2.01054
$119$	533.647	+	924.303i	0.411087	+	0.712023i
$120$		0			0
$121$	68.5754	−	118.776i	0.0515217	−	0.0892382i
$122$	−704.678	+	1220.54i	−0.522939	+	0.905756i
$123$	761.048	+	478.121i	0.557897	+	0.350493i
$124$	316.749	+	548.625i	0.229394	+	0.397323i
$125$		0			0
$126$	857.144	−	1257.59i	0.606036	−	0.889169i
$127$	−145.302			−0.101523			−0.0507616	−	0.998711i	$-0.516165\pi$
$127$	−145.302			−0.101523			−0.0507616	+	0.998711i	$0.516165\pi$
$128$	728.455	+	1261.72i	0.503023	+	0.871261i
$129$	−719.794	+	380.489i	−0.491274	+	0.259692i
$130$		0			0
$131$	134.659	−	233.237i	0.0898110	−	0.155557i	−0.817620	−	0.575758i	$-0.804707\pi$
$131$	134.659	−	233.237i	0.0898110	−	0.155557i	0.907431	+	0.420201i	$0.138040\pi$
$132$	72.3352	−	1936.97i	0.0476968	−	1.27721i
$133$	−951.747	−	1648.47i	−0.620504	−	1.07474i
$134$	−2984.45			−1.92401
$135$		0			0
$136$	−995.143			−0.627447
$137$	413.688	+	716.528i	0.257984	+	0.446841i	0.965702	−	0.259654i	$-0.0836086\pi$
$137$	413.688	+	716.528i	0.257984	+	0.446841i	−0.707718	+	0.706495i	$0.750275\pi$
$138$	157.959	−	4229.78i	0.0974375	−	2.60915i
$139$	84.9350	−	147.112i	0.0518280	−	0.0897687i	−0.838947	−	0.544212i	$-0.816829\pi$
$139$	84.9350	−	147.112i	0.0518280	−	0.0897687i	0.890775	+	0.454444i	$0.150162\pi$
$140$		0			0
$141$	−777.486	+	410.986i	−0.464370	+	0.245470i
$142$	1116.75	+	1934.26i	0.659968	+	1.14310i
$143$	261.134			0.152707
$144$	−396.227	−	822.467i	−0.229298	−	0.475965i
$145$		0			0
$146$	−2359.30	−	4086.42i	−1.33738	−	2.31640i
$147$	765.413	+	480.863i	0.429457	+	0.269802i
$148$	−1777.90	+	3079.41i	−0.987450	+	1.71031i
$149$	−873.174	+	1512.38i	−0.480089	+	0.831538i	−0.999739	−	0.0228410i	$-0.992729\pi$
$149$	−873.174	+	1512.38i	−0.480089	+	0.831538i	0.519650	+	0.854379i	$0.326062\pi$
$150$		0			0
$151$	−171.419	−	296.906i	−0.0923832	−	0.160012i	0.816130	−	0.577868i	$-0.196115\pi$
$151$	−171.419	−	296.906i	−0.0923832	−	0.160012i	−0.908513	+	0.417856i	$0.862782\pi$
$152$	1774.82			0.947082
$153$	2210.26	+	165.313i	1.16790	+	0.0873512i
$154$	−1947.61			−1.01911
$155$		0			0
$156$	−374.827	+	198.137i	−0.192373	+	0.101690i
$157$	1747.85	−	3027.36i	0.888494	−	1.53892i	0.0468373	−	0.998903i	$-0.485086\pi$
$157$	1747.85	−	3027.36i	0.888494	−	1.53892i	0.841656	−	0.540014i	$-0.181581\pi$
$158$	1139.77	−	1974.15i	0.573895	−	0.994016i
$159$	118.255	−	3166.60i	0.0589826	−	1.57942i
$160$		0			0
$161$	−2442.85			−1.19580
$162$	−1155.53	−	2941.73i	−0.560415	−	1.42669i
$163$	663.542			0.318851			0.159425	−	0.987210i	$-0.449036\pi$
$163$	663.542			0.318851			0.159425	+	0.987210i	$0.449036\pi$
$164$	933.699	+	1617.21i	0.444571	+	0.770020i
$165$		0			0
$166$	776.074	−	1344.20i	0.362862	−	0.628495i
$167$	−1229.82	+	2130.11i	−0.569858	+	0.987023i	0.426721	+	0.904383i	$0.359669\pi$
$167$	−1229.82	+	2130.11i	−0.569858	+	0.987023i	−0.996579	+	0.0826401i	$0.973665\pi$
$168$	724.039	−	382.733i	0.332505	−	0.175765i
$169$	1069.94	+	1853.19i	0.487001	+	0.843510i
$170$		0			0
$171$	−3941.95	−	294.831i	−1.76286	−	0.131850i
$172$	−1691.62			−0.749912
$173$	763.873	+	1323.07i	0.335701	+	0.581451i	0.983619	−	0.180259i	$-0.0576936\pi$
$173$	763.873	+	1323.07i	0.335701	+	0.581451i	−0.647918	+	0.761710i	$0.724360\pi$
$174$	−833.943	−	523.917i	−0.363339	−	0.228264i
$175$		0			0
$176$	−584.144	+	1011.77i	−0.250179	+	0.433323i
$177$	2615.44	+	1643.12i	1.11067	+	0.697767i
$178$	−3289.89	−	5698.26i	−1.38533	−	2.39945i
$179$	1006.17			0.420137			0.210069	−	0.977687i	$-0.432631\pi$
$179$	1006.17			0.420137			0.210069	+	0.977687i	$0.432631\pi$
$180$		0			0
$181$	591.861			0.243053			0.121527	−	0.992588i	$-0.461221\pi$
$181$	591.861			0.243053			0.121527	+	0.992588i	$0.461221\pi$
$182$	213.003	+	368.932i	0.0867518	+	0.150259i
$183$	1493.35	−	789.395i	0.603231	−	0.318873i
$184$	1138.86	−	1972.56i	0.456291	−	0.790319i
$185$		0			0
$186$	49.3307	−	1320.96i	0.0194468	−	0.520740i
$187$	−1418.19	−	2456.38i	−0.554591	−	0.960580i
$188$	−1827.20			−0.708843
$189$	−1671.70	+	729.792i	−0.643379	+	0.280870i
$190$		0			0
$191$	−1822.29	−	3156.29i	−0.690345	−	1.19571i	−0.971725	−	0.236117i	$-0.924125\pi$
$191$	−1822.29	−	3156.29i	−0.690345	−	1.19571i	0.281379	−	0.959597i	$-0.409208\pi$
$192$	152.318	−	4078.72i	0.0572531	−	1.53311i
$193$	−6.70078	+	11.6061i	−0.00249913	+	0.00432862i	−0.867272	−	0.497834i	$-0.834129\pi$
$193$	−6.70078	+	11.6061i	−0.00249913	+	0.00432862i	0.864773	+	0.502163i	$0.167462\pi$
$194$	857.034	−	1484.43i	0.317173	−	0.549359i
$195$		0			0
$196$	939.055	+	1626.49i	0.342221	+	0.592745i
$197$	−63.1983			−0.0228563			−0.0114281	−	0.999935i	$-0.503638\pi$
$197$	−63.1983			−0.0228563			−0.0114281	+	0.999935i	$0.503638\pi$
$198$	−2277.90	+	3342.12i	−0.817594	+	1.19957i
$199$	−4902.79			−1.74648			−0.873240	−	0.487291i	$-0.837985\pi$
$199$	−4902.79			−1.74648			−0.873240	+	0.487291i	$0.837985\pi$
$200$		0			0
$201$	3028.82	+	1902.82i	1.06287	+	0.667736i
$202$	−722.411	+	1251.25i	−0.251627	+	0.435831i
$203$	−284.198	+	492.246i	−0.0982602	+	0.170192i
$204$	3899.45	+	2449.79i	1.33831	+	0.840783i
$205$		0			0
$206$	7070.64			2.39143
$207$	−2857.13	+	4191.95i	−0.959345	+	1.40754i
$208$	255.543			0.0851861
$209$	2529.32	+	4380.90i	0.837112	+	1.44992i
$210$		0			0
$211$	1556.11	−	2695.26i	0.507711	−	0.879381i	−0.492249	−	0.870454i	$-0.663825\pi$
$211$	1556.11	−	2695.26i	0.507711	−	0.879381i	0.999960	−	0.00892670i	$-0.00284149\pi$
$212$	3291.94	−	5701.81i	1.06647	−	1.84718i
$213$	99.8980	−	2675.04i	0.0321357	−	0.860519i
$214$	1492.42	+	2584.95i	0.476728	+	0.825717i
$215$		0			0
$216$	190.055	−	1690.10i	0.0598685	−	0.532391i
$217$	−762.904			−0.238660
$218$	2577.32	+	4464.06i	0.800727	+	1.38690i
$219$	−211.050	+	5651.42i	−0.0651206	+	1.74378i
$220$		0			0
$221$	−310.205	+	537.291i	−0.0944192	+	0.163539i
$222$	6559.60	−	3467.46i	1.98311	−	1.04829i
$223$	2434.71	+	4217.05i	0.731123	+	1.26634i	0.956404	+	0.292048i	$0.0943368\pi$
$223$	2434.71	+	4217.05i	0.731123	+	1.26634i	−0.225281	+	0.974294i	$0.572330\pi$
$224$	−3166.81			−0.944603
$225$		0			0
$226$	1163.70			0.342515
$227$	−3293.59	−	5704.67i	−0.963011	−	1.66798i	−0.714867	−	0.699260i	$-0.753513\pi$
$227$	−3293.59	−	5704.67i	−0.963011	−	1.66798i	−0.248144	−	0.968723i	$-0.579820\pi$
$228$	−6954.58	−	4369.15i	−2.02008	−	1.26910i
$229$	−8.21503	+	14.2288i	−0.00237059	+	0.00410598i	−0.867208	−	0.497946i	$-0.834088\pi$
$229$	−8.21503	+	14.2288i	−0.00237059	+	0.00410598i	0.864838	+	0.502052i	$0.167421\pi$
$230$		0			0
$231$	1976.57	+	1241.76i	0.562981	+	0.353687i
$232$	−264.986	−	458.969i	−0.0749879	−	0.129883i
$233$	−707.542			−0.198938			−0.0994692	−	0.995041i	$-0.531714\pi$
$233$	−707.542			−0.198938			−0.0994692	+	0.995041i	$0.531714\pi$
$234$	882.216	+	65.9839i	0.246463	+	0.0184338i
$235$		0			0
$236$	3208.78	+	5557.77i	0.885058	+	1.53297i
$237$	−2415.39	+	1276.80i	−0.662012	+	0.349945i
$238$	2313.60	−	4007.27i	0.630120	−	1.09140i
$239$	3056.02	−	5293.18i	0.827102	−	1.43258i	−0.0731999	−	0.997317i	$-0.523321\pi$
$239$	3056.02	−	5293.18i	0.827102	−	1.43258i	0.900302	−	0.435266i	$-0.143346\pi$
$240$		0			0
$241$	−1544.12	−	2674.49i	−0.412719	−	0.714850i	0.582467	−	0.812854i	$-0.302087\pi$
$241$	−1544.12	−	2674.49i	−0.412719	−	0.714850i	−0.995186	+	0.0980044i	$0.968754\pi$
$242$	−594.611			−0.157946
$243$	−702.879	+	3722.21i	−0.185554	+	0.982634i
$244$	3509.58			0.920810
$245$		0			0
$246$	145.415	−	3893.87i	0.0376883	−	1.00920i
$247$	553.244	−	958.246i	0.142518	−	0.246849i
$248$	355.665	−	616.030i	0.0910676	−	0.157734i
$249$	−1644.65	+	869.375i	−0.418575	+	0.221263i
$250$		0			0
$251$	2743.28			0.689859			0.344929	−	0.938629i	$-0.387903\pi$
$251$	2743.28			0.689859			0.344929	+	0.938629i	$0.387903\pi$
$252$	−3779.33	−	282.669i	−0.944743	−	0.0706605i
$253$	6492.00			1.61324
$254$	314.974	+	545.552i	0.0778081	+	0.134768i
$255$		0			0
$256$	16.1888	−	28.0399i	0.00395235	−	0.00684568i
$257$	360.023	−	623.578i	0.0873838	−	0.151353i	−0.819021	−	0.573764i	$-0.805483\pi$
$257$	360.023	−	623.578i	0.0873838	−	0.151353i	0.906404	+	0.422411i	$0.138816\pi$
$258$	2988.91	+	1877.75i	0.721245	+	0.453115i
$259$	−2141.08	−	3708.45i	−0.513668	−	0.889699i
$260$		0			0
$261$	512.303	+	1063.41i	0.121497	+	0.252197i
$262$	−1167.62			−0.275327
$263$	−2614.08	−	4527.72i	−0.612894	−	1.06156i	−0.990750	−	0.135699i	$-0.956672\pi$
$263$	−2614.08	−	4527.72i	−0.612894	−	1.06156i	0.377857	−	0.925864i	$-0.376661\pi$
$264$	−1924.17	+	1017.13i	−0.448578	+	0.237122i
$265$		0			0
$266$	−4126.26	+	7146.88i	−0.951116	+	1.64738i
$267$	−294.295	+	7880.55i	−0.0674554	+	1.80630i
$268$	3715.94	+	6436.19i	0.846966	+	1.46699i
$269$	320.400			0.0726213			0.0363107	−	0.999341i	$-0.488439\pi$
$269$	320.400			0.0726213			0.0363107	+	0.999341i	$0.488439\pi$
$270$		0			0
$271$	−1044.06			−0.234029			−0.117014	−	0.993130i	$-0.537332\pi$
$271$	−1044.06			−0.234029			−0.117014	+	0.993130i	$0.537332\pi$
$272$	−1387.83	−	2403.79i	−0.309373	−	0.535850i
$273$	19.0541	−	510.224i	0.00422419	−	0.113114i
$274$	1793.52	−	3106.48i	0.395441	−	0.684923i
$275$		0			0
$276$	−9318.52	+	4925.85i	−2.03228	+	1.07428i
$277$	1665.66	+	2885.01i	0.361299	+	0.625789i	0.988175	−	0.153330i	$-0.0489999\pi$
$277$	1665.66	+	2885.01i	0.361299	+	0.625789i	−0.626876	+	0.779119i	$0.715667\pi$
$278$	−736.463			−0.158885
$279$	−892.283	+	1309.15i	−0.191468	+	0.280920i
$280$		0			0
$281$	2800.64	+	4850.86i	0.594563	+	1.02981i	0.993608	+	0.112883i	$0.0360084\pi$
$281$	2800.64	+	4850.86i	0.594563	+	1.02981i	−0.399045	+	0.916931i	$0.630658\pi$
$282$	3228.47	+	2028.25i	0.681746	+	0.428300i
$283$	3133.92	−	5428.11i	0.658277	−	1.14017i	−0.322785	−	0.946472i	$-0.604619\pi$
$283$	3133.92	−	5428.11i	0.658277	−	1.14017i	0.981062	−	0.193696i	$-0.0620476\pi$
$284$	2780.93	−	4816.71i	0.581048	−	1.00640i
$285$		0			0
$286$	−566.066	−	980.455i	−0.117036	−	0.202712i
$287$	−2248.85			−0.462529
$288$	−3703.86	+	5434.26i	−0.757819	+	1.11186i
$289$	1825.78			0.371622
$290$		0			0
$291$	−1816.22	+	960.068i	−0.365871	+	0.193403i
$292$	−5875.12	+	10176.0i	−1.17745	+	2.03940i
$293$	1051.43	−	1821.13i	0.209642	−	0.363111i	−0.741960	−	0.670445i	$-0.766103\pi$
$293$	1051.43	−	1821.13i	0.209642	−	0.363111i	0.951602	+	0.307334i	$0.0994368\pi$
$294$	146.249	−	3916.21i	0.0290116	−	0.776864i
$295$		0			0
$296$	3992.67			0.784018
$297$	4442.64	−	1939.46i	0.867973	−	0.378918i
$298$	7571.21			1.47177
$299$	−710.006	−	1229.77i	−0.137327	−	0.237857i
$300$		0			0
$301$	1018.59	−	1764.24i	0.195051	−	0.337838i
$302$	−743.178	+	1287.22i	−0.141606	+	0.245269i
$303$	1530.93	−	809.260i	0.290262	−	0.153435i
$304$	2475.16	+	4287.11i	0.466975	+	0.808824i
$305$		0			0
$306$	−4170.55	−	8657.02i	−0.779132	−	1.61728i
$307$	−2020.07			−0.375543			−0.187771	−	0.982213i	$-0.560126\pi$
$307$	−2020.07			−0.375543			−0.187771	+	0.982213i	$0.560126\pi$
$308$	2424.97	+	4200.18i	0.448622	+	0.777037i
$309$	−7175.76	−	4508.10i	−1.32108	−	0.829957i
$310$		0			0
$311$	−2696.66	+	4670.75i	−0.491684	+	0.851621i	−0.999954	−	0.00957637i	$-0.996952\pi$
$311$	−2696.66	+	4670.75i	−0.491684	+	0.851621i	0.508270	+	0.861198i	$0.330285\pi$
$312$	403.113	+	253.252i	0.0731467	+	0.0459537i
$313$	−1555.89	−	2694.87i	−0.280971	−	0.486656i	0.690653	−	0.723186i	$-0.257323\pi$
$313$	−1555.89	−	2694.87i	−0.280971	−	0.486656i	−0.971624	+	0.236530i	$0.923990\pi$
$314$	−15155.4			−2.72379
$315$		0			0
$316$	−5676.53			−1.01054
$317$	2466.79	+	4272.60i	0.437062	+	0.757013i	0.997461	−	0.0712090i	$-0.0226857\pi$
$317$	2466.79	+	4272.60i	0.437062	+	0.757013i	−0.560399	+	0.828222i	$0.689352\pi$
$318$	−12145.7	+	6420.31i	−2.14181	+	1.13218i
$319$	755.271	−	1308.17i	0.132561	−	0.229603i
$320$		0			0
$321$	133.504	−	3574.92i	0.0232132	−	0.621596i
$322$	5295.44	+	9171.96i	0.916469	+	1.58737i
$323$	−12018.5			−2.07036
$324$	−4905.32	+	6154.75i	−0.841104	+	1.05534i
$325$		0			0
$326$	−1438.38	−	2491.34i	−0.244369	−	0.423260i
$327$	230.553	−	6173.68i	0.0389896	−	1.04405i
$328$	1048.41	−	1815.91i	0.176491	−	0.305691i
$329$	1100.23	−	1905.65i	0.184369	−	0.319336i
$330$		0			0
$331$	−4386.39	−	7597.45i	−0.728392	−	1.26161i	−0.957563	−	0.288226i	$-0.906935\pi$
$331$	−4386.39	−	7597.45i	−0.728392	−	1.26161i	0.229171	−	0.973386i	$-0.426399\pi$
$332$	−3865.16			−0.638940
$333$	−8867.91	−	663.260i	−1.45933	−	0.109148i
$334$	10663.7			1.74697
$335$		0			0
$336$	1934.25	+	1215.17i	0.314053	+	0.197301i
$337$	5171.06	−	8956.54i	0.835863	−	1.44776i	−0.0574635	−	0.998348i	$-0.518301\pi$
$337$	5171.06	−	8956.54i	0.835863	−	1.44776i	0.893326	−	0.449409i	$-0.148365\pi$
$338$	4638.68	−	8034.43i	0.746482	−	1.29294i
$339$	−1181.00	−	741.954i	−0.189213	−	0.118871i
$340$		0			0
$341$	2027.46			0.321973
$342$	7438.09	+	15439.6i	1.17604	+	2.44116i
$343$	−6721.27			−1.05806
$344$	949.727	+	1644.98i	0.148854	+	0.257823i
$345$		0			0
$346$	3311.74	−	5736.10i	0.514567	−	0.891256i
$347$	−669.161	+	1159.02i	−0.103523	+	0.179307i	−0.913134	−	0.407660i	$-0.866345\pi$
$347$	−669.161	+	1159.02i	−0.103523	+	0.179307i	0.809611	+	0.586967i	$0.199678\pi$
$348$	−91.5236	+	2450.79i	−0.0140982	+	0.377518i
$349$	−5056.17	−	8757.55i	−0.775503	−	1.34321i	−0.934511	−	0.355934i	$-0.884163\pi$
$349$	−5056.17	−	8757.55i	−0.775503	−	1.34321i	0.159008	−	0.987277i	$-0.449170\pi$
$350$		0			0
$351$	−853.262	−	629.448i	−0.129754	−	0.0957193i
$352$	8415.95			1.27435
$353$	−822.140	−	1423.99i	−0.123961	−	0.214706i	0.797366	−	0.603497i	$-0.206226\pi$
$353$	−822.140	−	1423.99i	−0.123961	−	0.214706i	−0.921326	+	0.388791i	$0.872893\pi$
$354$	499.737	−	13381.8i	0.0750303	−	2.00914i
$355$		0			0
$356$	−8192.50	+	14189.8i	−1.21967	+	2.11253i
$357$	−4902.96	+	2591.74i	−0.726868	+	0.384229i
$358$	−2181.10	−	3777.77i	−0.321996	−	0.557714i
$359$	11283.0			1.65876			0.829379	−	0.558686i	$-0.188694\pi$
$359$	11283.0			1.65876			0.829379	+	0.558686i	$0.188694\pi$
$360$		0			0
$361$	14575.7			2.12504
$362$	−1282.99	−	2222.21i	−0.186278	−	0.322643i
$363$	603.451	+	379.112i	0.0872533	+	0.0548160i
$364$	530.420	−	918.715i	0.0763780	−	0.132291i
$365$		0			0
$366$	−6201.04	−	3895.74i	−0.885610	−	0.556376i
$367$	139.011	+	240.774i	0.0197720	+	0.0342461i	0.875742	−	0.482779i	$-0.160373\pi$
$367$	139.011	+	240.774i	0.0197720	+	0.0342461i	−0.855970	+	0.517025i	$0.827039\pi$
$368$	6353.01			0.899928
$369$	−2630.23	+	3859.05i	−0.371069	+	0.544429i
$370$		0			0
$371$	3964.39	+	6866.53i	0.554774	+	0.960896i
$372$	−2910.18	+	1538.34i	−0.405607	+	0.214407i
$373$	−4916.70	+	8515.98i	−0.682513	+	1.18215i	0.291699	+	0.956510i	$0.405780\pi$
$373$	−4916.70	+	8515.98i	−0.682513	+	1.18215i	−0.974212	+	0.225637i	$0.927554\pi$
$374$	−6148.51	+	10649.5i	−0.850085	+	1.47239i
$375$		0			0
$376$	1025.85	+	1776.82i	0.140702	+	0.243704i
$377$	−330.405			−0.0451372
$378$	6363.88	+	4694.61i	0.865933	+	0.638796i
$379$	13511.9			1.83129			0.915644	−	0.401990i	$-0.131681\pi$
$379$	13511.9			1.83129			0.915644	+	0.401990i	$0.131681\pi$
$380$		0			0
$381$	28.1758	−	754.484i	0.00378869	−	0.101452i
$382$	−7900.43	+	13683.9i	−1.05817	+	1.83281i
$383$	694.822	−	1203.47i	0.0926991	−	0.160559i	−0.815947	−	0.578127i	$-0.803784\pi$
$383$	694.822	−	1203.47i	0.0926991	−	0.160559i	0.908646	+	0.417567i	$0.137117\pi$
$384$	−6692.78	+	3537.86i	−0.889426	+	0.470158i
$385$		0			0
$386$	58.1018			0.00766141
$387$	−1836.13	−	3811.34i	−0.241177	−	0.500623i
$388$	−4268.38			−0.558490
$389$	453.369	+	785.258i	0.0590918	+	0.102350i	0.894058	−	0.447951i	$-0.147846\pi$
$389$	453.369	+	785.258i	0.0590918	+	0.102350i	−0.834966	+	0.550301i	$0.814513\pi$
$390$		0			0
$391$	−7711.96	+	13357.5i	−0.997469	+	1.72767i
$392$	1054.43	−	1826.32i	0.135859	−	0.235314i
$393$	1184.98	+	744.450i	0.152097	+	0.0955536i
$394$	136.997	+	237.285i	0.0175172	+	0.0303407i
$395$		0			0
$396$	10043.8	+	751.206i	1.27454	+	0.0953271i
$397$	1904.52			0.240769			0.120384	−	0.992727i	$-0.461587\pi$
$397$	1904.52			0.240769			0.120384	+	0.992727i	$0.461587\pi$
$398$	10627.9	+	18408.1i	1.33851	+	2.31837i
$399$	8744.32	−	4622.32i	1.09715	−	0.579963i
$400$		0			0
$401$	5206.91	−	9018.64i	0.648431	−	1.12312i	−0.335067	−	0.942194i	$-0.608759\pi$
$401$	5206.91	−	9018.64i	0.648431	−	1.12312i	0.983498	−	0.180921i	$-0.0579078\pi$
$402$	578.722	−	15496.8i	0.0718011	−	1.92267i
$403$	−221.735	−	384.057i	−0.0274080	−	0.0474720i
$404$	3597.90			0.443075
$405$		0			0
$406$	2464.26			0.301229
$407$	5690.02	+	9855.40i	0.692982	+	1.20028i
$408$	192.971	−	5167.31i	0.0234154	−	0.627010i
$409$	−3124.74	+	5412.21i	−0.377771	+	0.654319i	−0.990738	−	0.135790i	$-0.956643\pi$
$409$	−3124.74	+	5412.21i	−0.377771	+	0.654319i	0.612966	+	0.790109i	$0.289976\pi$
$410$		0			0
$411$	−3800.82	+	2009.14i	−0.456157	+	0.241128i
$412$	−8803.65	−	15248.4i	−1.05273	−	1.82338i
$413$	−7728.48			−0.920808
$414$	21932.6	+	1640.42i	2.60370	+	0.194739i
$415$		0			0
$416$	−920.420	−	1594.21i	−0.108479	−	0.187891i
$417$	747.413	+	469.555i	0.0877721	+	0.0551419i
$418$	10965.7	−	18993.2i	1.28314	−	2.22246i
$419$	−1495.14	+	2589.65i	−0.174325	+	0.301940i	−0.939927	−	0.341374i	$-0.889108\pi$
$419$	−1495.14	+	2589.65i	−0.174325	+	0.301940i	0.765602	+	0.643314i	$0.222441\pi$
$420$		0			0
$421$	2346.32	+	4063.95i	0.271622	+	0.470463i	0.969277	−	0.245971i	$-0.0791067\pi$
$421$	2346.32	+	4063.95i	0.271622	+	0.470463i	−0.697656	+	0.716433i	$0.745773\pi$
$422$	−13492.9			−1.55645
$423$	−1983.29	−	4116.82i	−0.227969	−	0.473207i
$424$	−7392.79			−0.846758
$425$		0			0
$426$	−10260.3	+	5423.67i	−1.16693	+	0.616849i
$427$	−2113.24	+	3660.24i	−0.239501	+	0.414828i
$428$	3716.43	−	6437.04i	0.419720	−	0.726977i
$429$	−50.6371	+	1355.94i	−0.00569879	+	0.152601i
$430$		0			0
$431$	817.709			0.0913866			0.0456933	−	0.998956i	$-0.485450\pi$
$431$	817.709			0.0913866			0.0456933	+	0.998956i	$0.485450\pi$
$432$	4347.52	−	1897.93i	0.484190	−	0.211376i
$433$	5547.29			0.615671			0.307836	−	0.951440i	$-0.400395\pi$
$433$	5547.29			0.615671			0.307836	+	0.951440i	$0.400395\pi$
$434$	1653.77	+	2864.41i	0.182911	+	0.316811i
$435$		0			0
$436$	6418.06	−	11116.4i	0.704975	−	1.22105i
$437$	13754.1	−	23822.8i	1.50560	−	2.60778i
$438$	21676.4	−	11458.3i	2.36470	−	1.25000i
$439$	−6690.82	−	11588.8i	−0.727416	−	1.25992i	−0.957972	−	0.286862i	$-0.907388\pi$
$439$	−6690.82	−	11588.8i	−0.727416	−	1.25992i	0.230556	−	0.973059i	$-0.425946\pi$
$440$		0			0
$441$	−2645.32	+	3881.19i	−0.285641	+	0.419089i
$442$	2689.76			0.289454
$443$	5418.44	+	9385.00i	0.581123	+	1.00654i	0.995347	+	0.0963598i	$0.0307199\pi$
$443$	5418.44	+	9385.00i	0.581123	+	1.00654i	−0.414223	+	0.910175i	$0.635947\pi$
$444$	−15645.2	−	9828.95i	−1.67227	−	1.05059i
$445$		0			0
$446$	10555.6	−	18282.8i	1.12068	−	1.94107i
$447$	−7683.77	−	4827.26i	−0.813043	−	0.510786i
$448$	5106.32	+	8844.41i	0.538507	+	0.932721i
$449$	2970.62			0.312232			0.156116	−	0.987739i	$-0.450103\pi$
$449$	2970.62			0.312232			0.156116	+	0.987739i	$0.450103\pi$
$450$		0			0
$451$	5976.44			0.623991
$452$	−1448.93	−	2509.61i	−0.150778	−	0.261155i
$453$	1574.94	−	832.524i	0.163349	−	0.0863475i
$454$	−14279.2	+	24732.3i	−1.47612	+	2.55671i
$455$		0			0
$456$	−344.159	+	9215.79i	−0.0353437	+	0.946423i
$457$	−8088.16	−	14009.1i	−0.827896	−	1.43396i	−0.899686	−	0.436538i	$-0.856204\pi$
$457$	−8088.16	−	14009.1i	−0.827896	−	1.43396i	0.0717901	−	0.997420i	$-0.477129\pi$
$458$	71.2317			0.00726733
$459$	−1286.99	+	11444.8i	−0.130875	+	1.16383i
$460$		0			0
$461$	−2865.91	−	4963.90i	−0.289541	−	0.501500i	0.684159	−	0.729333i	$-0.260169\pi$
$461$	−2865.91	−	4963.90i	−0.289541	−	0.501500i	−0.973700	+	0.227833i	$0.926836\pi$
$462$	377.667	−	10113.0i	0.0380317	−	1.01840i
$463$	−7020.03	+	12159.1i	−0.704641	+	1.22047i	0.262181	+	0.965019i	$0.415558\pi$
$463$	−7020.03	+	12159.1i	−0.704641	+	1.22047i	−0.966821	+	0.255454i	$0.917775\pi$
$464$	739.101	−	1280.16i	0.0739481	−	0.128082i
$465$		0			0
$466$	1533.76	+	2656.55i	0.152468	+	0.264082i
$467$	3.48921			0.000345742			0.000172871	−	1.00000i	$-0.499945\pi$
$467$	3.48921			0.000345742			0.000172871		1.00000i	$0.499945\pi$
$468$	−956.148	−	1984.72i	−0.0944401	−	0.196034i
$469$	−8949.99			−0.881177
$470$		0			0
$471$	15380.7	+	9662.80i	1.50469	+	0.945305i
$472$	3603.01	−	6240.60i	0.351360	−	0.608574i
$473$	−2706.94	+	4688.56i	−0.263140	+	0.455772i
$474$	10029.8	+	6301.12i	0.971907	+	0.610591i
$475$		0			0
$476$	−11522.7			−1.10954
$477$	16419.7	+	1228.09i	1.57612	+	0.117883i
$478$	−26498.4			−2.53559
$479$	1825.54	+	3161.93i	0.174136	+	0.301612i	0.939862	−	0.341555i	$-0.110954\pi$
$479$	1825.54	+	3161.93i	0.174136	+	0.301612i	−0.765726	+	0.643167i	$0.777620\pi$
$480$		0			0
$481$	1244.59	−	2155.69i	0.117980	−	0.204348i
$482$	−6694.44	+	11595.1i	−0.632621	+	1.09573i
$483$	473.700	−	12684.6i	0.0446255	−	1.19497i
$484$	740.350	+	1282.32i	0.0695295	+	0.120429i
$485$		0			0
$486$	15499.1	−	5429.70i	1.44661	−	0.506782i
$487$	−13646.8			−1.26981			−0.634903	−	0.772592i	$-0.718960\pi$
$487$	−13646.8			−1.26981			−0.634903	+	0.772592i	$0.718960\pi$
$488$	−1970.38	−	3412.80i	−0.182777	−	0.316579i
$489$	−128.669	+	3445.46i	−0.0118990	+	0.318628i
$490$		0			0
$491$	−20.8492	+	36.1118i	−0.00191631	+	0.00331915i	−0.866982	−	0.498340i	$-0.833943\pi$
$491$	−20.8492	+	36.1118i	−0.00191631	+	0.00331915i	0.865066	+	0.501659i	$0.167277\pi$
$492$	−8578.50	+	4534.67i	−0.786074	+	0.415525i
$493$	1794.40	+	3107.99i	0.163926	+	0.283929i
$494$	−4797.12			−0.436908
$495$		0			0
$496$	1984.05			0.179610
$497$	3348.99	+	5800.62i	0.302259	+	0.523528i
$498$	6829.31	+	4290.45i	0.614515	+	0.386063i
$499$	1196.47	−	2072.34i	0.107337	−	0.185913i	−0.807354	−	0.590068i	$-0.799101\pi$
$499$	1196.47	−	2072.34i	0.107337	−	0.185913i	0.914691	+	0.404155i	$0.132434\pi$
$500$		0			0
$501$	−10822.2	−	6798.94i	−0.965070	−	0.606295i
$502$	−5946.69	−	10300.0i	−0.528713	−	0.915757i
$503$	−1254.89			−0.111238			−0.0556190	−	0.998452i	$-0.517713\pi$
$503$	−1254.89			−0.111238			−0.0556190	+	0.998452i	$0.517713\pi$
$504$	1846.95	+	3833.81i	0.163234	+	0.338833i
$505$		0			0
$506$	−14072.9	−	24375.0i	−1.23640	−	2.14150i
$507$	−9830.23	+	5196.35i	−0.861097	+	0.455183i
$508$	784.349	−	1358.53i	0.0685037	−	0.118652i
$509$	−273.965	+	474.521i	−0.0238571	+	0.0413217i	−0.877707	−	0.479197i	$-0.840928\pi$
$509$	−273.965	+	474.521i	−0.0238571	+	0.0413217i	0.853850	+	0.520519i	$0.174261\pi$
$510$		0			0
$511$	−7075.25	−	12254.7i	−0.612506	−	1.06089i
$512$	11514.9			0.993929
$513$	2295.32	−	20411.5i	0.197545	−	1.75671i
$514$	−3121.73			−0.267886
$515$		0			0
$516$	328.027	−	8783.80i	0.0279856	−	0.749390i
$517$	−2923.90	+	5064.35i	−0.248729	+	0.430812i
$518$	−9282.53	+	16077.8i	−0.787357	+	1.36374i
$519$	−7018.20	+	3709.88i	−0.593573	+	0.313768i
$520$		0			0
$521$	12151.4			1.02181			0.510903	−	0.859638i	$-0.329311\pi$
$521$	12151.4			1.02181			0.510903	+	0.859638i	$0.329311\pi$
$522$	2882.17	−	4228.68i	0.241665	−	0.354568i
$523$	−18913.8			−1.58134			−0.790672	−	0.612241i	$-0.790268\pi$
$523$	−18913.8			−1.58134			−0.790672	+	0.612241i	$0.790268\pi$
$524$	1453.80	+	2518.06i	0.121202	+	0.209927i
$525$		0			0
$526$	−11333.2	+	19629.7i	−0.939452	+	1.62718i
$527$	−2408.45	+	4171.55i	−0.199077	+	0.344812i
$528$	−5140.37	−	3229.38i	−0.423685	−	0.266176i
$529$	−11567.9	−	20036.1i	−0.950757	−	1.64676i
$530$		0			0
$531$	−9039.14	+	13262.1i	−0.738730	+	1.08386i
$532$	20550.4			1.67476
$533$	−653.621	−	1132.11i	−0.0531172	−	0.0920017i
$534$	30226.4	−	15977.9i	2.44948	−	1.29482i
$535$		0			0
$536$	4172.48	−	7226.94i	0.336238	−	0.582381i
$537$	−195.109	+	5224.56i	−0.0156789	+	0.419845i
$538$	−694.540	−	1202.98i	−0.0556575	−	0.0964016i
$539$	6010.73			0.480335
$540$		0			0
$541$	−9936.16			−0.789628			−0.394814	−	0.918761i	$-0.629191\pi$
$541$	−9936.16			−0.789628			−0.394814	+	0.918761i	$0.629191\pi$
$542$	2263.23	+	3920.02i	0.179361	+	0.310663i
$543$	−114.769	+	3073.26i	−0.00907039	+	0.242884i
$544$	−9997.44	+	17316.1i	−0.787935	+	1.36474i
$545$		0			0
$546$	−1957.00	+	1034.48i	−0.153391	+	0.0810840i
$547$	6359.84	+	11015.6i	0.497125	+	0.861045i	0.999994	−	0.00331677i	$-0.00105576\pi$
$547$	6359.84	+	11015.6i	0.497125	+	0.861045i	−0.502870	+	0.864362i	$0.667722\pi$
$548$	−8932.47			−0.696307
$549$	3809.38	+	7907.32i	0.296139	+	0.614711i
$550$		0			0
$551$	−3200.27	−	5543.03i	−0.247434	−	0.428568i
$552$	10021.7	+	6296.05i	0.772741	+	0.485467i
$553$	3418.04	−	5920.22i	0.262839	−	0.455250i
$554$	7221.40	−	12507.8i	0.553805	−	0.959218i
$555$		0			0
$556$	916.971	+	1588.24i	0.0699429	+	0.121145i
$557$	16006.5			1.21763			0.608813	−	0.793314i	$-0.291646\pi$
$557$	16006.5			1.21763			0.608813	+	0.793314i	$0.291646\pi$
$558$	6849.57	+	512.302i	0.519651	+	0.0388665i
$559$	1184.19			0.0895993
$560$		0			0
$561$	13029.9	−	6887.69i	0.980608	−	0.518358i
$562$	12142.1	−	21030.7i	0.911355	−	1.57851i
$563$	2313.29	−	4006.74i	0.173168	−	0.299936i	−0.766358	−	0.642414i	$-0.777933\pi$
$563$	2313.29	−	4006.74i	0.173168	−	0.299936i	0.939526	+	0.342478i	$0.111266\pi$
$564$	354.318	−	9487.82i	0.0264530	−	0.708350i
$565$		0			0
$566$	−27173.9			−2.01803
$567$	−3465.30	−	8821.90i	−0.256665	−	0.653412i
$568$	−6245.19			−0.461342
$569$	−8429.52	−	14600.4i	−0.621061	−	1.07571i	−0.989288	−	0.145974i	$-0.953369\pi$
$569$	−8429.52	−	14600.4i	−0.621061	−	1.07571i	0.368227	−	0.929736i	$-0.379965\pi$
$570$		0			0
$571$	−8074.57	+	13985.6i	−0.591787	+	1.02501i	0.402205	+	0.915550i	$0.368244\pi$
$571$	−8074.57	+	13985.6i	−0.591787	+	1.02501i	−0.993992	+	0.109455i	$0.965089\pi$
$572$	−1409.62	+	2441.53i	−0.103040	+	0.178471i
$573$	16742.5	−	8850.23i	1.22064	−	0.645242i
$574$	4874.90	+	8443.58i	0.354485	+	0.613986i
$575$		0			0
$576$	21149.4	+	1581.83i	1.52990	+	0.114427i
$577$	−7430.10			−0.536082			−0.268041	−	0.963408i	$-0.586376\pi$
$577$	−7430.10			−0.536082			−0.268041	+	0.963408i	$0.586376\pi$
$578$	−3957.79	−	6855.10i	−0.284814	−	0.493312i
$579$	−58.9656	−	37.0446i	−0.00423234	−	0.00265893i
$580$		0			0
$581$	2327.35	−	4031.09i	0.166187	−	0.287845i
$582$	7541.75	+	4738.03i	0.537140	+	0.337453i
$583$	−10535.6	−	18248.2i	−0.748437	−	1.29633i
$584$	13193.9			0.934875
$585$		0			0
$586$	−9116.84			−0.642685
$587$	8576.06	+	14854.2i	0.603019	+	1.04446i	0.992361	+	0.123366i	$0.0393689\pi$
$587$	8576.06	+	14854.2i	0.603019	+	1.04446i	−0.389343	+	0.921093i	$0.627298\pi$
$588$	−8627.70	+	4560.68i	−0.605103	+	0.319863i
$589$	4295.41	−	7439.87i	0.300491	−	0.520466i
$590$		0			0
$591$	12.2549	−	328.159i	0.000852963	−	0.0228404i
$592$	5568.19	+	9644.39i	0.386573	+	0.669564i
$593$	15477.7			1.07183			0.535913	−	0.844273i	$-0.319967\pi$
$593$	15477.7			1.07183			0.535913	+	0.844273i	$0.319967\pi$
$594$	−16912.3	−	12476.2i	−1.16822	−	0.861790i
$595$		0			0
$596$	−9426.92	−	16327.9i	−0.647889	−	1.12218i
$597$	950.713	−	25457.9i	0.0651760	−	1.74526i
$598$	−3078.20	+	5331.59i	−0.210496	+	0.364590i
$599$	−9479.61	+	16419.2i	−0.646622	+	1.11998i	0.337302	+	0.941396i	$0.390486\pi$
$599$	−9479.61	+	16419.2i	−0.646622	+	1.11998i	−0.983924	+	0.178586i	$0.942848\pi$
$600$		0			0
$601$	1046.80	+	1813.12i	0.0710482	+	0.123059i	0.899361	−	0.437207i	$-0.144032\pi$
$601$	1046.80	+	1813.12i	0.0710482	+	0.123059i	−0.828313	+	0.560266i	$0.810699\pi$
$602$	−8832.06			−0.597953
$603$	−10467.8	+	15358.3i	−0.706935	+	1.03721i
$604$	3701.33			0.249346
$605$		0			0
$606$	−6357.09	−	3993.78i	−0.426137	−	0.267716i
$607$	−3067.63	+	5313.28i	−0.205125	+	0.355288i	−0.950173	−	0.311724i	$-0.899094\pi$
$607$	−3067.63	+	5313.28i	−0.205125	+	0.355288i	0.745047	+	0.667012i	$0.232427\pi$
$608$	17830.2	−	30882.8i	1.18933	−	2.05997i
$609$	−2500.89	−	1571.16i	−0.166406	−	0.104543i
$610$		0			0
$611$	1279.11			0.0846924
$612$	−13476.8	+	19773.0i	−0.890141	+	1.30600i
$613$	12762.8			0.840922			0.420461	−	0.907311i	$-0.361868\pi$
$613$	12762.8			0.840922			0.420461	+	0.907311i	$0.361868\pi$
$614$	4378.96	+	7584.59i	0.287819	+	0.498516i
$615$		0			0
$616$	2722.91	−	4716.21i	0.178099	−	0.308477i
$617$	367.040	−	635.732i	0.0239489	−	0.0414807i	−0.853803	−	0.520597i	$-0.825709\pi$
$617$	367.040	−	635.732i	0.0239489	−	0.0414807i	0.877751	+	0.479116i	$0.159043\pi$
$618$	−1371.09	+	36714.5i	−0.0892446	+	2.38976i
$619$	5324.85	+	9222.91i	0.345757	+	0.598869i	0.985491	−	0.169727i	$-0.0542887\pi$
$619$	5324.85	+	9222.91i	0.345757	+	0.598869i	−0.639734	+	0.768597i	$0.720955\pi$
$620$		0			0
$621$	−21212.8	−	15648.6i	−1.37076	−	1.01120i
$622$	23382.5			1.50732
$623$	−9865.99	−	17088.4i	−0.634466	−	1.09893i
$624$	−49.5530	+	1326.91i	−0.00317902	+	0.0851267i
$625$		0			0
$626$	−6745.47	+	11683.5i	−0.430676	+	0.745952i
$627$	−23238.5	+	12284.0i	−1.48015	+	0.782420i
$628$	18870.0	+	32683.9i	1.19904	+	2.07680i
$629$	−27037.1			−1.71389
$630$		0			0
$631$	−3465.43			−0.218632			−0.109316	−	0.994007i	$-0.534866\pi$
$631$	−3465.43			−0.218632			−0.109316	+	0.994007i	$0.534866\pi$
$632$	3186.98	+	5520.00i	0.200587	+	0.347427i
$633$	13693.5	+	8602.79i	0.859821	+	0.540174i
$634$	10694.6	−	18523.7i	0.669935	−	1.16036i
$635$		0			0
$636$	28968.5	+	18199.2i	1.80609	+	1.13466i
$637$	−657.371	−	1138.60i	−0.0408885	−	0.0708209i
$638$	−6548.89			−0.406384
$639$	13870.9	+	1037.45i	0.858721	+	0.0642266i
$640$		0			0
$641$	14605.0	+	25296.7i	0.899945	+	1.55875i	0.827563	+	0.561373i	$0.189727\pi$
$641$	14605.0	+	25296.7i	0.899945	+	1.55875i	0.0723819	+	0.997377i	$0.476940\pi$
$642$	−13711.8	+	7248.19i	−0.842932	+	0.445581i
$643$	−8512.87	+	14744.7i	−0.522107	+	0.904316i	0.477562	+	0.878598i	$0.341521\pi$
$643$	−8512.87	+	14744.7i	−0.522107	+	0.904316i	−0.999669	+	0.0257183i	$0.991813\pi$
$644$	13186.7	−	22840.0i	0.806877	−	1.39755i
$645$		0			0
$646$	26052.7	+	45124.7i	1.58674	+	2.74831i
$647$	−8673.26			−0.527019			−0.263509	−	0.964657i	$-0.584880\pi$
$647$	−8673.26			−0.527019			−0.263509	+	0.964657i	$0.584880\pi$
$648$	8739.03	+	1314.60i	0.529786	+	0.0796948i
$649$	20538.8			1.24225
$650$		0			0
$651$	147.937	−	3961.40i	0.00890645	−	0.238494i
$652$	−3581.85	+	6203.95i	−0.215147	+	0.372646i
$653$	−540.335	+	935.888i	−0.0323812	+	0.0560859i	−0.881762	−	0.471695i	$-0.843642\pi$
$653$	−540.335	+	935.888i	−0.0323812	+	0.0560859i	0.849381	+	0.527781i	$0.176976\pi$
$654$	−23679.5	+	12517.2i	−1.41582	+	0.748412i
$655$		0			0
$656$	5848.49			0.348087
$657$	−29304.3	−	2191.76i	−1.74013	−	0.130150i
$658$	−9539.95			−0.565206
$659$	−3484.81	−	6035.86i	−0.205992	−	0.356789i	0.744456	−	0.667671i	$-0.232709\pi$
$659$	−3484.81	−	6035.86i	−0.205992	−	0.356789i	−0.950448	+	0.310882i	$0.899375\pi$
$660$		0			0
$661$	−5448.66	+	9437.36i	−0.320618	+	0.555326i	−0.980616	−	0.195941i	$-0.937224\pi$
$661$	−5448.66	+	9437.36i	−0.320618	+	0.555326i	0.659998	+	0.751267i	$0.270557\pi$
$662$	−19017.0	+	32938.4i	−1.11649	+	1.93382i
$663$	−2729.75	−	1714.94i	−0.159901	−	0.100456i
$664$	2170.02	+	3758.58i	0.126827	+	0.219671i
$665$		0			0
$666$	16732.9	+	34733.3i	0.973554	+	2.02085i
$667$	−8214.14			−0.476841
$668$	−13277.3	−	22997.0i	−0.769034	−	1.33201i
$669$	−22369.3	+	11824.6i	−1.29274	+	0.683356i
$670$		0			0
$671$	5616.05	−	9727.28i	0.323108	−	0.559639i
$672$	614.084	−	16443.7i	0.0352512	−	0.943945i
$673$	14803.9	+	25641.2i	0.847919	+	1.46864i	0.883062	+	0.469257i	$0.155478\pi$
$673$	14803.9	+	25641.2i	0.847919	+	1.46864i	−0.0351426	+	0.999382i	$0.511189\pi$
$674$	−44837.8			−2.56244
$675$		0			0
$676$	−23102.5			−1.31443
$677$	3193.71	+	5531.66i	0.181306	+	0.314031i	0.942326	−	0.334698i	$-0.108634\pi$
$677$	3193.71	+	5531.66i	0.181306	+	0.314031i	−0.761020	+	0.648729i	$0.775301\pi$
$678$	−225.657	+	6042.56i	−0.0127821	+	0.342276i
$679$	2570.14	−	4451.62i	0.145262	−	0.251601i
$680$		0			0
$681$	30260.4	−	15995.9i	1.70276	−	0.900093i
$682$	−4394.97	−	7612.31i	−0.246762	−	0.427405i
$683$	19929.2			1.11650			0.558251	−	0.829672i	$-0.311473\pi$
$683$	19929.2			1.11650			0.558251	+	0.829672i	$0.311473\pi$
$684$	24035.5	−	35264.7i	1.34360	−	1.97131i
$685$		0			0
$686$	14569.9	+	25235.8i	0.810904	+	1.40453i
$687$	−72.2907	−	45.4159i	−0.00401465	−	0.00252216i
$688$	−2648.99	+	4588.18i	−0.146790	+	0.254248i
$689$	−2304.47	+	3991.46i	−0.127421	+	0.220700i
$690$		0			0
$691$	−6473.59	−	11212.6i	−0.356392	−	0.617289i	0.630963	−	0.775813i	$-0.282660\pi$
$691$	−6473.59	−	11212.6i	−0.356392	−	0.617289i	−0.987355	+	0.158524i	$0.949327\pi$
$692$	−16493.8			−0.906069
$693$	−6831.16	+	10022.6i	−0.374451	+	0.549390i
$694$	5802.23			0.317362
$695$		0			0
$696$	2434.60	−	1286.95i	0.132591	−	0.0700886i
$697$	−7099.52	+	12296.7i	−0.385815	+	0.668252i
$698$	−21920.8	+	37967.9i	−1.18870	+	2.05889i
$699$	137.201	−	3673.94i	0.00742408	−	0.198800i
$700$		0			0
$701$	−10692.9			−0.576125			−0.288063	−	0.957612i	$-0.593011\pi$
$701$	−10692.9			−0.576125			−0.288063	+	0.957612i	$0.593011\pi$
$702$	−513.696	+	4568.14i	−0.0276185	+	0.245603i
$703$	48220.0			2.58699
$704$	−13570.3	−	23504.5i	−0.726492	−	1.25832i
$705$		0			0
$706$	−3564.35	+	6173.63i	−0.190009	+	0.329104i
$707$	−2166.42	+	3752.35i	−0.115243	+	0.199607i
$708$	−29481.1	+	15584.0i	−1.56493	+	0.827234i
$709$	11786.7	+	20415.2i	0.624343	+	1.08139i	0.988668	+	0.150122i	$0.0479665\pi$
$709$	11786.7	+	20415.2i	0.624343	+	1.08139i	−0.364325	+	0.931272i	$0.618700\pi$
$710$		0			0
$711$	−6161.44	−	12789.6i	−0.324996	−	0.674610i
$712$	18398.1			0.968394
$713$	−5512.52	−	9547.97i	−0.289545	−	0.501507i
$714$	20359.3	+	12790.5i	1.06712	+	0.670410i
$715$		0			0
$716$	−5431.37	+	9407.41i	−0.283492	+	0.491022i
$717$	26892.4	+	16894.9i	1.40072	+	0.879988i
$718$	−24458.5	−	42363.3i	−1.27128	−	2.20193i
$719$	27013.2			1.40114			0.700572	−	0.713581i	$-0.252928\pi$
$719$	27013.2			1.40114			0.700572	+	0.713581i	$0.252928\pi$
$720$		0			0
$721$	21204.0			1.09525
$722$	−31596.1	−	54726.0i	−1.62865	−	2.82090i
$723$	14186.8	−	7499.25i	0.729754	−	0.385754i
$724$	−3194.91	+	5533.74i	−0.164003	+	0.284061i
$725$		0			0
$726$	115.303	−	3087.54i	0.00589432	−	0.157836i
$727$	8927.02	+	15462.1i	0.455412	+	0.788797i	0.998712	−	0.0507416i	$-0.0161585\pi$
$727$	8927.02	+	15462.1i	0.455412	+	0.788797i	−0.543299	+	0.839539i	$0.682825\pi$
$728$	−1191.18			−0.0606428
$729$	−19191.4	−	4371.50i	−0.975025	−	0.222095i
$730$		0			0
$731$	−6431.24	−	11139.2i	−0.325401	−	0.563611i
$732$	−680.552	+	18223.6i	−0.0343633	+	0.920169i
$733$	−4795.40	+	8305.88i	−0.241640	+	0.418533i	−0.961182	−	0.275916i	$-0.911019\pi$
$733$	−4795.40	+	8305.88i	−0.241640	+	0.418533i	0.719541	+	0.694449i	$0.244352\pi$
$734$	602.676	−	1043.87i	0.0303068	−	0.0524929i
$735$		0			0
$736$	−22882.4	−	39633.5i	−1.14600	−	1.98493i
$737$	23785.1			1.18878
$738$	20190.9	+	1510.14i	1.00710	+	0.0753240i
$739$	−6237.43			−0.310484			−0.155242	−	0.987876i	$-0.549616\pi$
$739$	−6237.43			−0.310484			−0.155242	+	0.987876i	$0.549616\pi$
$740$		0			0
$741$	4868.44	+	3058.55i	0.241359	+	0.151631i
$742$	17187.4	−	29769.5i	0.850365	−	1.47288i
$743$	8567.24	−	14838.9i	0.423017	−	0.732687i	−0.573216	−	0.819404i	$-0.694304\pi$
$743$	8567.24	−	14838.9i	0.423017	−	0.732687i	0.996233	+	0.0867173i	$0.0276377\pi$
$744$	3129.79	+	1966.26i	0.154225	+	0.0968905i
$745$		0			0
$746$	42632.3			2.09233
$747$	−4195.34	−	8708.47i	−0.205488	−	0.426541i
$748$	30622.1			1.49686
$749$	4475.59	+	7751.94i	0.218337	+	0.378171i
$750$		0			0
$751$	−19570.8	+	33897.7i	−0.950932	+	1.64706i	−0.207518	+	0.978231i	$0.566538\pi$
$751$	−19570.8	+	33897.7i	−0.950932	+	1.64706i	−0.743414	+	0.668831i	$0.766795\pi$
$752$	−2861.30	+	4955.92i	−0.138751	+	0.240324i
$753$	−531.958	+	14244.6i	−0.0257445	+	0.689378i
$754$	716.227	+	1240.54i	0.0345934	+	0.0599176i
$755$		0			0
$756$	2200.63	−	19569.5i	0.105868	−	0.941448i
$757$	3774.26			0.181212			0.0906062	−	0.995887i	$-0.471120\pi$
$757$	3774.26			0.181212			0.0906062	+	0.995887i	$0.471120\pi$
$758$	−29290.0	−	50731.8i	−1.40351	−	2.43095i
$759$	−1258.88	+	33709.9i	−0.0602036	+	1.61211i
$760$		0			0
$761$	−12998.9	+	22514.8i	−0.619200	+	1.07249i	0.370432	+	0.928860i	$0.379210\pi$
$761$	−12998.9	+	22514.8i	−0.619200	+	1.07249i	−0.989632	+	0.143627i	$0.954124\pi$
$762$	−2893.87	+	1529.73i	−0.137577	+	0.0727245i
$763$	7729.08	+	13387.2i	0.366725	+	0.635187i
$764$	39347.3			1.86327
$765$		0			0
$766$	−6024.73			−0.284181
$767$	−2246.25	−	3890.63i	−0.105746	−	0.183158i
$768$	142.459	+	89.4984i	0.00669341	+	0.00420507i
$769$	−7817.68	+	13540.6i	−0.366597	+	0.634964i	−0.989031	−	0.147708i	$-0.952810\pi$
$769$	−7817.68	+	13540.6i	−0.366597	+	0.634964i	0.622434	+	0.782672i	$0.286144\pi$
$770$		0			0
$771$	3168.14	+	1990.35i	0.147987	+	0.0929712i
$772$	−72.3426	−	125.301i	−0.00337262	−	0.00584156i
$773$	−5936.28			−0.276213			−0.138107	−	0.990417i	$-0.544102\pi$
$773$	−5936.28			−0.276213			−0.138107	+	0.990417i	$0.544102\pi$
$774$	−10329.9	+	15155.9i	−0.479715	+	0.703833i
$775$		0			0
$776$	2396.40	+	4150.68i	0.110858	+	0.192011i
$777$	19671.4	−	10398.5i	0.908248	−	0.480108i
$778$	1965.56	−	3404.45i	0.0905767	−	0.156883i
$779$	12661.8	−	21930.9i	0.582358	−	1.00867i
$780$		0			0
$781$	−8900.11	−	15415.4i	−0.407773	−	0.706284i
$782$	66869.7			3.05787
$783$	−5621.14	+	2453.94i	−0.256556	+	0.112001i
$784$	5882.04			0.267950
$785$		0			0
$786$	226.416	−	6062.89i	0.0102748	−	0.275135i
$787$	5193.86	−	8996.04i	0.235249	−	0.407464i	−0.724096	−	0.689699i	$-0.757743\pi$
$787$	5193.86	−	8996.04i	0.235249	−	0.407464i	0.959345	+	0.282236i	$0.0910760\pi$
$788$	341.149	−	590.887i	0.0154225	−	0.0267126i
$789$	24017.2	−	12695.7i	1.08370	−	0.572851i
$790$		0			0
$791$	3489.80			0.156869
$792$	−4908.38	−	10188.6i	−0.220217	−	0.457114i
$793$	−2456.82			−0.110018
$794$	−4128.48	−	7150.73i	−0.184527	−	0.319610i
$795$		0			0
$796$	26465.6	−	45839.8i	1.17845	−	2.04114i
$797$	697.430	−	1207.98i	0.0309966	−	0.0536876i	−0.850111	−	0.526604i	$-0.823465\pi$
$797$	697.430	−	1207.98i	0.0309966	−	0.0536876i	0.881108	+	0.472916i	$0.156799\pi$
$798$	−36310.3	−	22811.6i	−1.61074	−	1.01193i
$799$	−6946.71	−	12032.0i	−0.307580	−	0.532745i
$800$		0			0
$801$	−40863.0	−	3056.28i	−1.80252	−	0.134817i
$802$	−45148.6			−1.98785
$803$	18802.8	+	32567.4i	0.826323	+	1.43123i
$804$	−34140.7	+	18047.1i	−1.49757	+	0.791630i
$805$		0			0
$806$	−961.322	+	1665.06i	−0.0420113	+	0.0727658i
$807$	−62.1296	+	1663.69i	−0.00271012	+	0.0725708i
$808$	−2019.97	−	3498.69i	−0.0879483	−	0.152331i
$809$	−7633.11			−0.331726			−0.165863	−	0.986149i	$-0.553041\pi$
$809$	−7633.11			−0.331726			−0.165863	+	0.986149i	$0.553041\pi$
$810$		0			0
$811$	−38117.1			−1.65040			−0.825199	−	0.564842i	$-0.808937\pi$
$811$	−38117.1			−1.65040			−0.825199	+	0.564842i	$0.808937\pi$
$812$	−3068.25	−	5314.36i	−0.132604	−	0.229677i
$813$	202.456	−	5421.29i	0.00873361	−	0.233866i
$814$	24668.8	−	42727.6i	1.06221	−	1.83981i
$815$		0			0
$816$	12750.9	−	6740.23i	0.547022	−	0.289161i
$817$	11470.0	+	19866.6i	0.491167	+	0.850727i
$818$	27094.3			1.15811
$819$	2645.66	+	197.878i	0.112878	+	0.00844250i
$820$		0			0
$821$	−1965.53	−	3404.41i	−0.0835537	−	0.144719i	0.821220	−	0.570611i	$-0.193294\pi$
$821$	−1965.53	−	3404.41i	−0.0835537	−	0.144719i	−0.904774	+	0.425892i	$0.859960\pi$
$822$	15782.7	+	9915.32i	0.669689	+	0.420726i
$823$	10749.1	−	18618.0i	0.455274	−	0.788558i	−0.543430	−	0.839455i	$-0.682875\pi$
$823$	10749.1	−	18618.0i	0.455274	−	0.788558i	0.998704	+	0.0508966i	$0.0162079\pi$
$824$	−9885.27	+	17121.8i	−0.417925	+	0.723867i
$825$		0			0
$826$	16753.2	+	29017.5i	0.705714	+	1.22233i
$827$	−5272.26			−0.221686			−0.110843	−	0.993838i	$-0.535355\pi$
$827$	−5272.26			−0.221686			−0.110843	+	0.993838i	$0.535355\pi$
$828$	−23770.7	−	49341.9i	−0.997690	−	2.07095i
$829$	−13595.1			−0.569573			−0.284786	−	0.958591i	$-0.591923\pi$
$829$	−13595.1			−0.569573			−0.284786	+	0.958591i	$0.591923\pi$
$830$		0			0
$831$	−15303.5	+	8089.57i	−0.638836	+	0.337694i
$832$	−2968.27	+	5141.19i	−0.123685	+	0.214229i
$833$	−7140.24	+	12367.3i	−0.296992	+	0.514406i
$834$	142.810	−	3824.11i	0.00592937	−	0.158775i
$835$		0			0
$836$	−54613.8			−2.25940
$837$	−6624.77	−	4887.07i	−0.273579	−	0.201818i
$838$	12964.2			0.534416
$839$	−7738.30	−	13403.1i	−0.318422	−	0.551522i	0.661737	−	0.749736i	$-0.269819\pi$
$839$	−7738.30	−	13403.1i	−0.318422	−	0.551522i	−0.980159	+	0.198213i	$0.936486\pi$
$840$		0			0
$841$	11238.9	−	19466.3i	0.460817	−	0.798159i
$842$	10172.4	−	17619.1i	0.416346	−	0.721132i
$843$	−25731.3	+	13601.8i	−1.05128	+	0.555718i
$844$	16800.0	+	29098.4i	0.685165	+	1.18674i
$845$		0			0
$846$	−11157.8	+	16370.6i	−0.453444	+	0.665288i
$847$	−1783.16			−0.0723380
$848$	−10310.0	−	17857.5i	−0.417508	−	0.723146i
$849$	27577.9	+	17325.6i	1.11481	+	0.700367i
$850$		0			0
$851$	30941.6	−	53592.4i	1.24637	−	2.15878i
$852$	24471.7	+	15374.1i	0.984020	+	0.618201i
$853$	−15155.0	−	26249.2i	−0.608320	−	1.05364i	−0.991517	−	0.129974i	$-0.958511\pi$
$853$	−15155.0	−	26249.2i	−0.608320	−	1.05364i	0.383198	−	0.923666i	$-0.374823\pi$
$854$	18323.7			0.734221
$855$		0			0
$856$	−8346.06			−0.333250
$857$	−15576.6	−	26979.5i	−0.620872	−	1.07538i	−0.989324	−	0.145734i	$-0.953446\pi$
$857$	−15576.6	−	26979.5i	−0.620872	−	1.07538i	0.368452	−	0.929647i	$-0.379888\pi$
$858$	5200.81	−	2749.19i	0.206938	−	0.109389i
$859$	8955.94	−	15512.1i	0.355731	−	0.616144i	−0.631512	−	0.775366i	$-0.717565\pi$
$859$	8955.94	−	15512.1i	0.355731	−	0.616144i	0.987243	+	0.159222i	$0.0508987\pi$
$860$		0			0
$861$	436.081	−	11677.3i	0.0172609	−	0.462206i
$862$	−1772.57	−	3070.18i	−0.0700394	−	0.121312i
$863$	−34410.6			−1.35730			−0.678649	−	0.734462i	$-0.737434\pi$
$863$	−34410.6			−1.35730			−0.678649	+	0.734462i	$0.737434\pi$
$864$	−27499.4	−	20286.2i	−1.08281	−	0.798785i
$865$		0			0
$866$	−12025.0	−	20827.9i	−0.471855	−	0.817276i
$867$	−354.042	+	9480.43i	−0.0138684	+	0.371364i
$868$	4118.21	−	7132.95i	0.161038	−	0.278926i
$869$	−9083.62	+	15733.3i	−0.354592	+	0.614172i
$870$		0			0
$871$	−2601.28	−	4505.55i	−0.101195	−	0.175275i
$872$	−14413.2			−0.559738
$873$	−4633.00	−	9616.94i	−0.179614	−	0.372834i
$874$	−119261.			−4.61562
$875$		0			0
$876$	−51700.0	−	32480.0i	−1.99404	−	1.25274i
$877$	14114.7	−	24447.3i	0.543464	−	0.941308i	−0.455237	−	0.890370i	$-0.650446\pi$
$877$	14114.7	−	24447.3i	0.543464	−	0.941308i	0.998702	−	0.0509378i	$-0.0162210\pi$
$878$	−29007.7	+	50242.9i	−1.11499	+	1.93122i
$879$	9252.39	+	5812.72i	0.355034	+	0.223047i
$880$		0			0
$881$	−20204.7			−0.772661			−0.386331	−	0.922360i	$-0.626258\pi$
$881$	−20204.7			−0.772661			−0.386331	+	0.922360i	$0.626258\pi$
$882$	20306.7	+	1518.81i	0.775240	+	0.0579828i
$883$	−19916.7			−0.759061			−0.379530	−	0.925179i	$-0.623914\pi$
$883$	−19916.7			−0.759061			−0.379530	+	0.925179i	$0.623914\pi$
$884$	−3349.02	−	5800.67i	−0.127420	−	0.220699i
$885$		0			0
$886$	23491.4	−	40688.2i	0.890754	−	1.54283i
$887$	3513.60	−	6085.74i	0.133005	−	0.230371i	−0.791829	−	0.610743i	$-0.790871\pi$
$887$	3513.60	−	6085.74i	0.133005	−	0.230371i	0.924834	+	0.380372i	$0.124204\pi$
$888$	−774.229	+	20732.1i	−0.0292584	+	0.783471i
$889$	944.570	+	1636.04i	0.0356354	+	0.0617223i
$890$		0			0
$891$	9209.21	+	23444.6i	0.346263	+	0.881509i
$892$	−52571.0			−1.97333
$893$	12389.3	+	21458.9i	0.464269	+	0.804137i
$894$	−1468.15	+	39313.8i	−0.0549244	+	1.47075i
$895$		0			0
$896$	9471.00	−	16404.3i	0.353129	−	0.611638i
$897$	6523.28	−	3448.26i	0.242816	−	0.128355i
$898$	−6439.49	−	11153.5i	−0.239297	−	0.414474i
$899$	−2565.28			−0.0951689
$900$		0			0
$901$	50061.5			1.85104
$902$	−12955.3	−	22439.2i	−0.478231	−	0.828320i
$903$	8963.37	+	5631.15i	0.330324	+	0.207523i
$904$	−1626.94	+	2817.95i	−0.0598576	+	0.103676i
$905$		0			0
$906$	−6539.83	−	4108.59i	−0.239814	−	0.150661i
$907$	−3186.11	−	5518.50i	−0.116641	−	0.202027i	0.801794	−	0.597601i	$-0.203879\pi$
$907$	−3186.11	−	5518.50i	−0.116641	−	0.202027i	−0.918434	+	0.395573i	$0.870546\pi$
$908$	71116.2			2.59920
$909$	3905.25	+	8106.31i	0.142496	+	0.295786i
$910$		0			0
$911$	17448.0	+	30220.8i	0.634553	+	1.09908i	0.986610	+	0.163099i	$0.0521491\pi$
$911$	17448.0	+	30220.8i	0.634553	+	1.09908i	−0.352057	+	0.935979i	$0.614518\pi$
$912$	−22740.9	+	12021.0i	−0.825688	+	0.436466i
$913$	−6185.05	+	10712.8i	−0.224201	+	0.388327i
$914$	−35065.9	+	60735.8i	−1.26901	+	2.19799i
$915$		0			0
$916$	−88.6906	−	153.617i	−0.00319915	−	0.00554109i
$917$	−3501.54			−0.126097
$918$	45760.6	−	19977.0i	1.64523	−	0.718235i
$919$	−702.234			−0.0252063			−0.0126031	−	0.999921i	$-0.504012\pi$
$919$	−702.234			−0.0252063			−0.0126031	+	0.999921i	$0.504012\pi$
$920$		0			0
$921$	391.718	−	10489.3i	0.0140147	−	0.375281i
$922$	−12425.0	+	21520.7i	−0.443813	+	0.768707i
$923$	−1946.74	+	3371.86i	−0.0694235	+	0.120245i
$924$	−22279.8	+	11777.3i	−0.793237	+	0.419312i
$925$		0			0
$926$	60870.0			2.16017
$927$	24799.9	−	36386.2i	0.878680	−	1.28919i
$928$	−10648.5			−0.376673
$929$	15286.7	+	26477.3i	0.539871	+	0.935084i	0.998910	+	0.0466681i	$0.0148603\pi$
$929$	15286.7	+	26477.3i	0.539871	+	0.935084i	−0.459039	+	0.888416i	$0.651806\pi$
$930$		0			0
$931$	12734.5	−	22056.7i	0.448287	−	0.776456i
$932$	3819.37	−	6615.33i	0.134235	−	0.232503i
$933$	−23730.1	−	14908.2i	−0.832679	−	0.523122i
$934$	−7.56366	−	13.1006i	−0.000264979	−	0.000458957i
$935$		0			0
$936$	−1393.19	+	2044.07i	−0.0486514	+	0.0713808i
$937$	−13601.7			−0.474224			−0.237112	−	0.971482i	$-0.576201\pi$
$937$	−13601.7			−0.474224			−0.237112	+	0.971482i	$0.576201\pi$
$938$	19401.1	+	33603.7i	0.675341	+	1.16972i
$939$	14294.9	−	7556.42i	0.496802	−	0.262614i
$940$		0			0
$941$	−23803.1	+	41228.2i	−0.824611	+	1.42827i	0.0776049	+	0.996984i	$0.475273\pi$
$941$	−23803.1	+	41228.2i	−0.824611	+	1.42827i	−0.902216	+	0.431284i	$0.858061\pi$
$942$	2938.83	−	78695.1i	0.101648	−	2.72189i
$943$	−16249.6	−	28145.1i	−0.561144	−	0.971931i
$944$	20099.1			0.692976
$945$		0			0
$946$	23471.6			0.806690
$947$	24267.1	+	42031.9i	0.832710	+	1.44230i	0.895882	+	0.444293i	$0.146545\pi$
$947$	24267.1	+	42031.9i	0.832710	+	1.44230i	−0.0631720	+	0.998003i	$0.520122\pi$
$948$	1100.75	−	29475.6i	0.0377117	−	1.00983i
$949$	4112.79	−	7123.56i	0.140681	−	0.243667i
$950$		0			0
$951$	−22664.0	+	11980.4i	−0.772797	+	0.408507i
$952$	6469.17	+	11204.9i	0.220238	+	0.381464i
$953$	30379.5			1.03262			0.516312	−	0.856401i	$-0.327305\pi$
$953$	30379.5			1.03262			0.516312	+	0.856401i	$0.327305\pi$
$954$	−30982.5	−	64311.9i	−1.05146	−	2.18257i
$955$		0			0
$956$	32993.2	+	57146.0i	1.11619	+	1.93330i
$957$	6646.25	+	4175.44i	0.224496	+	0.141037i
$958$	7914.54	−	13708.4i	0.266918	−	0.462315i
$959$	5378.56	−	9315.94i	0.181108	−	0.313689i
$960$		0			0
$961$	13173.9	+	22817.9i	0.442212	+	0.765934i
$962$	−10791.7			−0.361683
$963$	18537.0	+	1386.44i	0.620297	+	0.0463941i
$964$	33341.0			1.11394
$965$		0			0
$966$	−48652.6	+	25718.2i	−1.62047	+	0.856593i
$967$	16161.9	−	27993.3i	0.537470	−	0.930925i	−0.461570	−	0.887104i	$-0.652714\pi$
$967$	16161.9	−	27993.3i	0.537470	−	0.930925i	0.999039	−	0.0438207i	$-0.0139530\pi$
$968$	831.310	−	1439.87i	0.0276026	−	0.0478091i
$969$	2330.53	−	62406.3i	0.0772627	−	2.06892i
$970$		0			0
$971$	−27461.7			−0.907609			−0.453805	−	0.891101i	$-0.649934\pi$
$971$	−27461.7			−0.907609			−0.453805	+	0.891101i	$0.649934\pi$
$972$	−31007.5	−	26664.5i	−1.02322	−	0.879902i
$973$	−2208.56			−0.0727681
$974$	29582.5	+	51238.4i	0.973188	+	1.68561i
$975$		0			0
$976$	5495.81	−	9519.02i	0.180242	−	0.312189i
$977$	21771.9	−	37710.1i	0.712943	−	1.23485i	−0.250804	−	0.968038i	$-0.580695\pi$
$977$	21771.9	−	37710.1i	0.712943	−	1.23485i	0.963747	−	0.266816i	$-0.0859716\pi$
$978$	13215.3	−	6985.72i	0.432085	−	0.228404i
$979$	26219.4	+	45413.3i	0.855949	+	1.48255i
$980$		0			0
$981$	32012.3	+	2394.31i	1.04187	+	0.0779249i
$982$	180.781			0.00587470
$983$	17184.5	+	29764.4i	0.557579	+	0.965756i	0.997698	+	0.0678161i	$0.0216031\pi$
$983$	17184.5	+	29764.4i	0.557579	+	0.965756i	−0.440118	+	0.897940i	$0.645064\pi$
$984$	9225.85	+	5796.05i	0.298892	+	0.187776i
$985$		0			0
$986$	7779.53	−	13474.5i	0.251268	−	0.435210i
$987$	9681.78	+	6082.48i	0.312234	+	0.196158i
$988$	5972.90	+	10345.4i	0.192331	+	0.333128i
$989$	29440.0			0.946550
$990$		0			0
$991$	4360.89			0.139786			0.0698931	−	0.997554i	$-0.477734\pi$
$991$	4360.89			0.139786			0.0698931	+	0.997554i	$0.477734\pi$
$992$	−7146.19	−	12377.6i	−0.228722	−	0.396157i
$993$	40300.6	−	21303.2i	1.28792	−	0.680803i
$994$	14519.4	−	25148.3i	0.463307	−	0.802471i
$995$		0			0
$996$	749.504	−	20070.0i	0.0238443	−	0.638495i
$997$	14677.3	+	25421.9i	0.466235	+	0.807543i	0.999256	−	0.0385591i	$-0.0122768\pi$
$997$	14677.3	+	25421.9i	0.466235	+	0.807543i	−0.533021	+	0.846102i	$0.678943\pi$
$998$	−10374.4			−0.329056
$999$	5163.60	−	45918.3i	0.163533	−	1.45424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.76.2	yes	24
5.2	odd	4		225.4.k.e.49.21		48
5.3	odd	4		225.4.k.e.49.4		48
5.4	even	2		225.4.e.e.76.11	✓	24
9.4	even	3		2025.4.a.bf.1.11		12
9.5	odd	6		2025.4.a.bj.1.2		12
9.7	even	3	inner	225.4.e.f.151.2	yes	24
45.4	even	6		2025.4.a.bi.1.2		12
45.7	odd	12		225.4.k.e.124.4		48
45.14	odd	6		2025.4.a.be.1.11		12
45.34	even	6		225.4.e.e.151.11	yes	24
45.43	odd	12		225.4.k.e.124.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.11	✓	24	5.4	even	2
225.4.e.e.151.11	yes	24	45.34	even	6
225.4.e.f.76.2	yes	24	1.1	even	1	trivial
225.4.e.f.151.2	yes	24	9.7	even	3	inner
225.4.k.e.49.4		48	5.3	odd	4
225.4.k.e.49.21		48	5.2	odd	4
225.4.k.e.124.4		48	45.7	odd	12
225.4.k.e.124.21		48	45.43	odd	12
2025.4.a.be.1.11		12	45.14	odd	6
2025.4.a.bf.1.11		12	9.4	even	3
2025.4.a.bi.1.2		12	45.4	even	6
2025.4.a.bj.1.2		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)

\(f(q)\)	\(=\)	\(q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +O(q^{10})\)	\(q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +(17.2761 + 29.9230i) q^{11} +(-47.5021 - 29.8427i) q^{12} +(3.77884 - 6.54514i) q^{13} +(-28.1837 + 48.8156i) q^{14} +(16.9062 + 29.2824i) q^{16} -82.0901 q^{17} +(50.8046 + 105.458i) q^{18} +146.406 q^{19} +(59.7265 - 31.5720i) q^{21} +(74.8995 - 129.730i) q^{22} +(93.9451 - 162.718i) q^{23} +(-2.35072 + 62.9468i) q^{24} -32.7659 q^{26} +(15.6778 - 139.417i) q^{27} +140.366 q^{28} +(-21.8589 - 37.8607i) q^{29} +(29.3391 - 50.8168i) q^{31} +(121.786 - 210.940i) q^{32} +(-158.726 + 83.9041i) q^{33} +(177.949 + 308.216i) q^{34} +(164.171 - 240.869i) q^{36} +329.358 q^{37} +(-317.368 - 549.697i) q^{38} +(33.2531 + 20.8909i) q^{39} +(86.4845 - 149.796i) q^{41} +(-248.011 - 155.811i) q^{42} +(78.3437 + 135.695i) q^{43} -373.030 q^{44} -814.589 q^{46} +(84.6230 + 146.571i) q^{47} +(-155.328 + 82.1077i) q^{48} +(86.9806 - 150.655i) q^{49} +(15.9183 - 426.255i) q^{51} +(40.7969 + 70.6623i) q^{52} -609.837 q^{53} +(-557.443 + 243.355i) q^{54} +(-78.8058 - 136.496i) q^{56} +(-28.3899 + 760.217i) q^{57} +(-94.7682 + 164.143i) q^{58} +(297.215 - 514.792i) q^{59} +(-162.538 - 281.525i) q^{61} -254.396 q^{62} +(152.357 + 316.254i) q^{63} -785.498 q^{64} +(659.102 + 414.075i) q^{66} +(344.191 - 596.156i) q^{67} +(443.128 - 767.521i) q^{68} +(826.700 + 519.366i) q^{69} -515.170 q^{71} +(-326.398 - 24.4124i) q^{72} +1088.37 q^{73} +(-713.959 - 1236.61i) q^{74} +(-790.310 + 1368.86i) q^{76} +(224.615 - 389.044i) q^{77} +(6.35373 - 170.138i) q^{78} +(262.896 + 455.349i) q^{79} +(720.889 + 108.442i) q^{81} -749.899 q^{82} +(179.006 + 310.048i) q^{83} +(-27.2188 + 728.855i) q^{84} +(339.655 - 588.300i) q^{86} +(200.832 - 106.161i) q^{87} +(209.430 + 362.744i) q^{88} +1517.67 q^{89} -98.2610 q^{91} +(1014.25 + 1756.72i) q^{92} +(258.179 + 162.198i) q^{93} +(366.879 - 635.453i) q^{94} +(1071.70 + 673.283i) q^{96} +(197.680 + 342.393i) q^{97} -754.200 q^{98} +(-404.896 - 840.462i) 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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