LMFDB - Embedded newform 225.4.e.f.151.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(76,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [24,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			151.10
Character	$\chi$	$=$	225.151
Dual form			225.4.e.f.76.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81989 - 3.15215i) q^{2} +(5.18137 - 0.391700i) q^{3} +(-2.62402 - 4.54493i) q^{4} +(8.19483 - 17.0453i) q^{6} +(1.86027 - 3.22208i) q^{7} +10.0166 q^{8} +(26.6931 - 4.05909i) q^{9} +(14.0066 - 24.2602i) q^{11} +(-15.3762 - 22.5211i) q^{12} +(21.8210 + 37.7951i) q^{13} +(-6.77099 - 11.7277i) q^{14} +(39.2212 - 67.9331i) q^{16} -87.3128 q^{17} +(35.7838 - 91.5278i) q^{18} +38.5062 q^{19} +(8.37666 - 17.4235i) q^{21} +(-50.9811 - 88.3019i) q^{22} +(-57.9733 - 100.413i) q^{23} +(51.8995 - 3.92349i) q^{24} +158.848 q^{26} +(136.717 - 31.4873i) q^{27} -19.5255 q^{28} +(-98.0246 + 169.784i) q^{29} +(-86.7675 - 150.286i) q^{31} +(-102.690 - 177.865i) q^{32} +(63.0708 - 131.187i) q^{33} +(-158.900 + 275.223i) q^{34} +(-88.4915 - 110.667i) q^{36} +181.738 q^{37} +(70.0772 - 121.377i) q^{38} +(127.867 + 187.283i) q^{39} +(124.893 + 216.320i) q^{41} +(-39.6767 - 58.1133i) q^{42} +(-230.354 + 398.985i) q^{43} -147.015 q^{44} -422.021 q^{46} +(164.196 - 284.395i) q^{47} +(176.610 - 367.349i) q^{48} +(164.579 + 285.059i) q^{49} +(-452.400 + 34.2005i) q^{51} +(114.517 - 198.350i) q^{52} -667.821 q^{53} +(149.558 - 488.256i) q^{54} +(18.6335 - 32.2742i) q^{56} +(199.515 - 15.0829i) q^{57} +(356.788 + 617.976i) q^{58} +(-55.5587 - 96.2305i) q^{59} +(-218.973 + 379.272i) q^{61} -631.630 q^{62} +(36.5778 - 93.5586i) q^{63} -120.003 q^{64} +(-298.740 - 437.555i) q^{66} +(77.4225 + 134.100i) q^{67} +(229.110 + 396.831i) q^{68} +(-339.713 - 497.567i) q^{69} +912.989 q^{71} +(267.374 - 40.6581i) q^{72} -975.779 q^{73} +(330.743 - 572.863i) q^{74} +(-101.041 - 175.008i) q^{76} +(-52.1123 - 90.2611i) q^{77} +(823.048 - 62.2207i) q^{78} +(-428.020 + 741.352i) q^{79} +(696.048 - 216.700i) q^{81} +909.164 q^{82} +(34.2104 - 59.2542i) q^{83} +(-101.169 + 7.64816i) q^{84} +(838.439 + 1452.22i) q^{86} +(-441.397 + 918.107i) q^{87} +(140.298 - 243.004i) q^{88} +665.452 q^{89} +162.372 q^{91} +(-304.246 + 526.970i) q^{92} +(-508.441 - 744.699i) q^{93} +(-597.637 - 1035.14i) q^{94} +(-601.747 - 881.361i) q^{96} +(-701.837 + 1215.62i) q^{97} +1198.06 q^{98} +(275.407 - 704.435i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.81989	−	3.15215i	0.643429	−	1.11445i	−0.341233	−	0.939979i	$-0.610844\pi$
$2$	1.81989	−	3.15215i	0.643429	−	1.11445i	0.984662	−	0.174473i	$-0.0558222\pi$
$3$	5.18137	−	0.391700i	0.997155	−	0.0753828i
$3$	5.18137	−	0.391700i	0.997155	−	0.0753828i
$4$	−2.62402	−	4.54493i	−0.328002	−	0.568116i
$5$		0			0
$5$		0			0
$6$	8.19483	−	17.0453i	0.557588	−	1.15978i
$7$	1.86027	−	3.22208i	0.100445	−	0.173976i	−0.811423	−	0.584459i	$-0.801307\pi$
$7$	1.86027	−	3.22208i	0.100445	−	0.173976i	0.911868	+	0.410483i	$0.134640\pi$
$8$	10.0166			0.442674
$9$	26.6931	−	4.05909i	0.988635	−	0.150337i
$10$		0			0
$11$	14.0066	−	24.2602i	0.383923	−	0.664975i	−0.607696	−	0.794170i	$-0.707906\pi$
$11$	14.0066	−	24.2602i	0.383923	−	0.664975i	0.991619	+	0.129195i	$0.0412393\pi$
$12$	−15.3762	−	22.5211i	−0.369895	−	0.541774i
$13$	21.8210	+	37.7951i	0.465543	+	0.806344i	0.999226	−	0.0393404i	$-0.0125257\pi$
$13$	21.8210	+	37.7951i	0.465543	+	0.806344i	−0.533683	+	0.845685i	$0.679192\pi$
$14$	−6.77099	−	11.7277i	−0.129259	−	0.223883i
$15$		0			0
$16$	39.2212	−	67.9331i	0.612831	−	1.06146i
$17$	−87.3128			−1.24567			−0.622837	−	0.782351i	$-0.714020\pi$
$17$	−87.3128			−1.24567			−0.622837	+	0.782351i	$0.714020\pi$
$18$	35.7838	−	91.5278i	0.468574	−	1.19852i
$19$	38.5062			0.464944			0.232472	−	0.972603i	$-0.425319\pi$
$19$	38.5062			0.464944			0.232472	+	0.972603i	$0.425319\pi$
$20$		0			0
$21$	8.37666	−	17.4235i	0.0870446	−	0.181053i
$22$	−50.9811	−	88.3019i	−0.494055	−	0.855728i
$23$	−57.9733	−	100.413i	−0.525577	−	0.910327i	−0.999556	−	0.0297904i	$-0.990516\pi$
$23$	−57.9733	−	100.413i	−0.525577	−	0.910327i	0.473979	−	0.880536i	$-0.342817\pi$
$24$	51.8995	−	3.92349i	0.441414	−	0.0333700i
$25$		0			0
$26$	158.848			1.19818
$27$	136.717	−	31.4873i	0.974489	−	0.224435i
$28$	−19.5255			−0.131785
$29$	−98.0246	+	169.784i	−0.627679	+	1.08717i	0.360337	+	0.932822i	$0.382662\pi$
$29$	−98.0246	+	169.784i	−0.627679	+	1.08717i	−0.988016	+	0.154350i	$0.950672\pi$
$30$		0			0
$31$	−86.7675	−	150.286i	−0.502707	−	0.870713i	−0.999995	−	0.00312811i	$-0.999004\pi$
$31$	−86.7675	−	150.286i	−0.502707	−	0.870713i	0.497289	−	0.867585i	$-0.334329\pi$
$32$	−102.690	−	177.865i	−0.567290	−	0.982575i
$33$	63.0708	−	131.187i	0.332703	−	0.692024i
$34$	−158.900	+	275.223i	−0.801503	+	1.38824i
$35$		0			0
$36$	−88.4915	−	110.667i	−0.409683	−	0.512349i
$37$	181.738			0.807499			0.403749	−	0.914870i	$-0.367707\pi$
$37$	181.738			0.807499			0.403749	+	0.914870i	$0.367707\pi$
$38$	70.0772	−	121.377i	0.299159	−	0.518158i
$39$	127.867	+	187.283i	0.525003	+	0.768956i
$40$		0			0
$41$	124.893	+	216.320i	0.475730	+	0.823989i	0.999613	−	0.0278012i	$-0.00885054\pi$
$41$	124.893	+	216.320i	0.475730	+	0.823989i	−0.523883	+	0.851790i	$0.675517\pi$
$42$	−39.6767	−	58.1133i	−0.145768	−	0.213502i
$43$	−230.354	+	398.985i	−0.816945	+	1.41499i	0.0909774	+	0.995853i	$0.471001\pi$
$43$	−230.354	+	398.985i	−0.816945	+	1.41499i	−0.907923	+	0.419138i	$0.862332\pi$
$44$	−147.015			−0.503711
$45$		0			0
$46$	−422.021			−1.35269
$47$	164.196	−	284.395i	0.509583	−	0.882624i	−0.490355	−	0.871523i	$-0.663133\pi$
$47$	164.196	−	284.395i	0.509583	−	0.882624i	0.999938	−	0.0111016i	$-0.00353381\pi$
$48$	176.610	−	367.349i	0.531072	−	1.10463i
$49$	164.579	+	285.059i	0.479822	+	0.831075i
$50$		0			0
$51$	−452.400	+	34.2005i	−1.24213	+	0.0939024i
$52$	114.517	−	198.350i	0.305398	−	0.528965i
$53$	−667.821			−1.73080			−0.865399	−	0.501083i	$-0.832935\pi$
$53$	−667.821			−1.73080			−0.865399	+	0.501083i	$0.832935\pi$
$54$	149.558	−	488.256i	0.376893	−	1.23043i
$55$		0			0
$56$	18.6335	−	32.2742i	0.0444645	−	0.0770147i
$57$	199.515	−	15.0829i	0.463621	−	0.0350488i
$58$	356.788	+	617.976i	0.807735	+	1.39904i
$59$	−55.5587	−	96.2305i	−0.122595	−	0.212341i	0.798195	−	0.602399i	$-0.205788\pi$
$59$	−55.5587	−	96.2305i	−0.122595	−	0.212341i	−0.920790	+	0.390058i	$0.872455\pi$
$60$		0			0
$61$	−218.973	+	379.272i	−0.459617	+	0.796080i	−0.998941	−	0.0460189i	$-0.985347\pi$
$61$	−218.973	+	379.272i	−0.459617	+	0.796080i	0.539324	+	0.842098i	$0.318680\pi$
$62$	−631.630			−1.29382
$63$	36.5778	−	93.5586i	0.0731487	−	0.187100i
$64$	−120.003			−0.234381
$65$		0			0
$66$	−298.740	−	437.555i	−0.557156	−	0.816050i
$67$	77.4225	+	134.100i	0.141174	+	0.244521i	0.927939	−	0.372732i	$-0.121579\pi$
$67$	77.4225	+	134.100i	0.141174	+	0.244521i	−0.786765	+	0.617253i	$0.788246\pi$
$68$	229.110	+	396.831i	0.408584	+	0.707688i
$69$	−339.713	−	497.567i	−0.592705	−	0.868117i
$70$		0			0
$71$	912.989			1.52608			0.763041	−	0.646350i	$-0.223705\pi$
$71$	912.989			1.52608			0.763041	+	0.646350i	$0.223705\pi$
$72$	267.374	−	40.6581i	0.437643	−	0.0665501i
$73$	−975.779			−1.56447			−0.782234	−	0.622984i	$-0.785920\pi$
$73$	−975.779			−1.56447			−0.782234	+	0.622984i	$0.785920\pi$
$74$	330.743	−	572.863i	0.519568	−	0.899919i
$75$		0			0
$76$	−101.041	−	175.008i	−0.152503	−	0.264142i
$77$	−52.1123	−	90.2611i	−0.0771265	−	0.133587i
$78$	823.048	−	62.2207i	1.19477	−	0.0903218i
$79$	−428.020	+	741.352i	−0.609570	+	1.05581i	0.381742	+	0.924269i	$0.375324\pi$
$79$	−428.020	+	741.352i	−0.609570	+	1.05581i	−0.991311	+	0.131536i	$0.958009\pi$
$80$		0			0
$81$	696.048	−	216.700i	0.954798	−	0.297256i
$82$	909.164			1.22439
$83$	34.2104	−	59.2542i	0.0452420	−	0.0783614i	−0.842518	−	0.538669i	$-0.818927\pi$
$83$	34.2104	−	59.2542i	0.0452420	−	0.0783614i	0.887760	+	0.460307i	$0.152261\pi$
$84$	−101.169	+	7.64816i	−0.131410	+	0.00993431i
$85$		0			0
$86$	838.439	+	1452.22i	1.05129	+	1.82089i
$87$	−441.397	+	918.107i	−0.543939	+	1.13140i
$88$	140.298	−	243.004i	0.169953	−	0.294367i
$89$	665.452			0.792559			0.396280	−	0.918130i	$-0.370301\pi$
$89$	665.452			0.792559			0.396280	+	0.918130i	$0.370301\pi$
$90$		0			0
$91$	162.372			0.187046
$92$	−304.246	+	526.970i	−0.344781	+	0.597178i
$93$	−508.441	−	744.699i	−0.566913	−	0.830340i
$94$	−597.637	−	1035.14i	−0.655762	−	1.13581i
$95$		0			0
$96$	−601.747	−	881.361i	−0.639745	−	0.937016i
$97$	−701.837	+	1215.62i	−0.734646	+	1.27245i	0.220232	+	0.975448i	$0.429319\pi$
$97$	−701.837	+	1215.62i	−0.734646	+	1.27245i	−0.954878	+	0.296997i	$0.904015\pi$
$98$	1198.06			1.23492
$99$	275.407	−	704.435i	0.279590	−	0.715135i
$100$		0			0
$101$	327.589	−	567.401i	0.322736	−	0.558995i	−0.658316	−	0.752742i	$-0.728731\pi$
$101$	327.589	−	567.401i	0.322736	−	0.558995i	0.981051	+	0.193747i	$0.0620641\pi$
$102$	−715.514	+	1488.27i	−0.694573	+	1.44471i
$103$	126.762	+	219.557i	0.121264	+	0.210035i	0.920266	−	0.391293i	$-0.127972\pi$
$103$	126.762	+	219.557i	0.121264	+	0.210035i	−0.799002	+	0.601328i	$0.794639\pi$
$104$	218.572	+	378.577i	0.206084	+	0.356948i
$105$		0			0
$106$	−1215.36	+	2105.07i	−1.11365	+	1.92889i
$107$	−1132.73			−1.02341			−0.511706	−	0.859161i	$-0.670986\pi$
$107$	−1132.73			−1.02341			−0.511706	+	0.859161i	$0.670986\pi$
$108$	−501.856	−	538.746i	−0.447140	−	0.480008i
$109$	1514.68			1.33101			0.665506	−	0.746392i	$-0.268216\pi$
$109$	1514.68			1.33101			0.665506	+	0.746392i	$0.268216\pi$
$110$		0			0
$111$	941.649	−	71.1866i	0.805201	−	0.0608715i
$112$	−145.924	−	252.748i	−0.123112	−	0.213236i
$113$	836.016	+	1448.02i	0.695980	+	1.20547i	0.969849	+	0.243706i	$0.0783633\pi$
$113$	836.016	+	1448.02i	0.695980	+	1.20547i	−0.273869	+	0.961767i	$0.588303\pi$
$114$	315.552	−	656.350i	0.259247	−	0.539235i
$115$		0			0
$116$	1028.87			0.823521
$117$	735.885	+	920.297i	0.581475	+	0.727192i
$118$	−404.443			−0.315526
$119$	−162.426	+	281.329i	−0.125122	+	0.216718i
$120$		0			0
$121$	273.129	+	473.073i	0.205206	+	0.355427i
$122$	797.015	+	1380.47i	0.591462	+	1.02444i
$123$	731.847	+	1071.91i	0.536491	+	0.785782i
$124$	−455.359	+	788.705i	−0.329778	+	0.571192i
$125$		0			0
$126$	−228.343	−	285.565i	−0.161447	−	0.201906i
$127$	547.016			0.382203			0.191102	−	0.981570i	$-0.438794\pi$
$127$	547.016			0.382203			0.191102	+	0.981570i	$0.438794\pi$
$128$	603.131	−	1044.65i	0.416482	−	0.721369i
$129$	−1037.27	+	2157.52i	−0.707955	+	1.47255i
$130$		0			0
$131$	−633.985	−	1098.09i	−0.422836	−	0.732374i	0.573379	−	0.819290i	$-0.305632\pi$
$131$	−633.985	−	1098.09i	−0.422836	−	0.732374i	−0.996216	+	0.0869161i	$0.972299\pi$
$132$	−761.736	+	57.5856i	−0.502277	+	0.0379711i
$133$	71.6321	−	124.070i	0.0467014	−	0.0808892i
$134$	563.602			0.363342
$135$		0			0
$136$	−874.575			−0.551428
$137$	465.222	−	805.788i	0.290121	−	0.502504i	−0.683717	−	0.729747i	$-0.739638\pi$
$137$	465.222	−	805.788i	0.290121	−	0.502504i	0.973838	+	0.227243i	$0.0729711\pi$
$138$	−2186.65	+	165.306i	−1.34884	+	0.101969i
$139$	−1565.13	−	2710.89i	−0.955057	−	1.65421i	−0.734238	−	0.678892i	$-0.762461\pi$
$139$	−1565.13	−	2710.89i	−0.955057	−	1.65421i	−0.220818	−	0.975315i	$-0.570873\pi$
$140$		0			0
$141$	739.361	−	1537.87i	0.441599	−	0.918527i
$142$	1661.54	−	2877.87i	0.981926	−	1.70075i
$143$	1222.56			0.714932
$144$	771.191	−	1972.55i	0.446291	−	1.14152i
$145$		0			0
$146$	−1775.81	+	3075.80i	−1.00662	+	1.74353i
$147$	964.401	+	1412.53i	0.541105	+	0.792540i
$148$	−476.882	−	825.984i	−0.264861	−	0.458753i
$149$	815.678	+	1412.80i	0.448476	+	0.776784i	0.998287	−	0.0585055i	$-0.0186335\pi$
$149$	815.678	+	1412.80i	0.448476	+	0.776784i	−0.549811	+	0.835289i	$0.685300\pi$
$150$		0			0
$151$	−910.818	+	1577.58i	−0.490870	+	0.850211i	−0.999945	−	0.0105108i	$-0.996654\pi$
$151$	−910.818	+	1577.58i	−0.490870	+	0.850211i	0.509075	+	0.860722i	$0.329988\pi$
$152$	385.700			0.205819
$153$	−2330.65	+	354.410i	−1.23152	+	0.187270i
$154$	−379.355			−0.198502
$155$		0			0
$156$	515.663	−	1072.58i	0.264654	−	0.550482i
$157$	−1417.59	−	2455.34i	−0.720612	−	1.24814i	−0.960755	−	0.277400i	$-0.910527\pi$
$157$	−1417.59	−	2455.34i	−0.720612	−	1.24814i	0.240142	−	0.970738i	$-0.422806\pi$
$158$	1557.90	+	2698.36i	0.784430	+	1.35867i
$159$	−3460.23	+	261.586i	−1.72587	+	0.130472i
$160$		0			0
$161$	−431.385			−0.211167
$162$	583.663	−	2588.41i	0.283067	−	1.25534i
$163$	−3048.62			−1.46495			−0.732473	−	0.680796i	$-0.761634\pi$
$163$	−3048.62			−1.46495			−0.732473	+	0.680796i	$0.761634\pi$
$164$	655.440	−	1135.26i	0.312081	−	0.540540i
$165$		0			0
$166$	−124.519	−	215.673i	−0.0582200	−	0.100840i
$167$	−1418.96	−	2457.71i	−0.657500	−	1.13882i	−0.981261	−	0.192685i	$-0.938281\pi$
$167$	−1418.96	−	2457.71i	−0.657500	−	1.13882i	0.323761	−	0.946139i	$-0.395053\pi$
$168$	83.9053	−	174.523i	0.0385324	−	0.0801474i
$169$	146.186	−	253.202i	0.0665391	−	0.115249i
$170$		0			0
$171$	1027.85	−	156.300i	0.459660	−	0.0698981i
$172$	2417.81			1.07184
$173$	255.267	−	442.135i	0.112183	−	0.194306i	−0.804467	−	0.593997i	$-0.797549\pi$
$173$	255.267	−	442.135i	0.112183	−	0.194306i	0.916650	+	0.399691i	$0.130883\pi$
$174$	2090.71	+	3062.20i	0.910900	+	1.33417i
$175$		0			0
$176$	−1098.71	−	1903.03i	−0.470561	−	0.815035i
$177$	−325.563	−	476.843i	−0.138253	−	0.202496i
$178$	1211.05	−	2097.60i	0.509956	−	0.883269i
$179$	−2274.36			−0.949687			−0.474843	−	0.880070i	$-0.657495\pi$
$179$	−2274.36			−0.949687			−0.474843	+	0.880070i	$0.657495\pi$
$180$		0			0
$181$	−975.489			−0.400594			−0.200297	−	0.979735i	$-0.564191\pi$
$181$	−975.489			−0.400594			−0.200297	+	0.979735i	$0.564191\pi$
$182$	295.500	−	511.820i	0.120351	−	0.208454i
$183$	−986.019	+	2050.92i	−0.398298	+	0.828462i
$184$	−580.694	−	1005.79i	−0.232659	−	0.402978i
$185$		0			0
$186$	−3272.71	+	247.410i	−1.29014	+	0.0975321i
$187$	−1222.96	+	2118.23i	−0.478244	+	0.828342i
$188$	−1723.41			−0.668578
$189$	152.876	−	499.089i	0.0588364	−	0.192081i
$190$		0			0
$191$	940.013	−	1628.15i	0.356110	−	0.616800i	−0.631198	−	0.775622i	$-0.717436\pi$
$191$	940.013	−	1628.15i	0.356110	−	0.616800i	0.987307	+	0.158822i	$0.0507696\pi$
$192$	−621.781	+	47.0053i	−0.233714	+	0.0176683i
$193$	−306.781	−	531.360i	−0.114418	−	0.198177i	0.803129	−	0.595805i	$-0.203167\pi$
$193$	−306.781	−	531.360i	−0.114418	−	0.198177i	−0.917547	+	0.397628i	$0.869834\pi$
$194$	2554.53	+	4424.58i	0.945386	+	1.63746i
$195$		0			0
$196$	863.715	−	1496.00i	0.314765	−	0.545189i
$197$	68.3454			0.0247178			0.0123589	−	0.999924i	$-0.496066\pi$
$197$	68.3454			0.0247178			0.0123589	+	0.999924i	$0.496066\pi$
$198$	−1719.27	−	2150.12i	−0.617087	−	0.771728i
$199$	2174.87			0.774736			0.387368	−	0.921925i	$-0.373384\pi$
$199$	2174.87			0.774736			0.387368	+	0.921925i	$0.373384\pi$
$200$		0			0
$201$	453.681	+	664.493i	0.159205	+	0.233183i
$202$	−1192.35	−	2065.22i	−0.415315	−	0.719347i
$203$	364.705	+	631.687i	0.126095	+	0.218403i
$204$	1342.54	+	1966.38i	0.460769	+	0.674874i
$205$		0			0
$206$	922.769			0.312099
$207$	−1955.08	−	2445.01i	−0.656459	−	0.820967i
$208$	3423.39			1.14120
$209$	539.343	−	934.169i	0.178503	−	0.309176i
$210$		0			0
$211$	237.521	+	411.398i	0.0774957	+	0.134227i	0.902169	−	0.431383i	$-0.141974\pi$
$211$	237.521	+	411.398i	0.0774957	+	0.134227i	−0.824673	+	0.565610i	$0.808641\pi$
$212$	1752.37	+	3035.20i	0.567705	+	0.983295i
$213$	4730.53	−	357.618i	1.52174	−	0.115040i
$214$	−2061.44	+	3570.53i	−0.658493	+	1.14054i
$215$		0			0
$216$	1369.44	−	315.395i	0.431381	−	0.0993514i
$217$	−645.644			−0.201978
$218$	2756.56	−	4774.50i	0.856412	−	1.48335i
$219$	−5055.87	+	382.213i	−1.56002	+	0.117934i
$220$		0			0
$221$	−1905.25	−	3300.00i	−0.579915	−	1.00444i
$222$	1489.31	−	3097.77i	0.450252	−	0.936525i
$223$	1483.17	−	2568.93i	0.445384	−	0.771427i	−0.552695	−	0.833384i	$-0.686401\pi$
$223$	1483.17	−	2568.93i	0.445384	−	0.771427i	0.998079	+	0.0619561i	$0.0197339\pi$
$224$	−764.129			−0.227926
$225$		0			0
$226$	6085.84			1.79126
$227$	1416.11	−	2452.78i	0.414056	−	0.717167i	−0.581273	−	0.813709i	$-0.697445\pi$
$227$	1416.11	−	2452.78i	0.414056	−	0.717167i	0.995329	+	0.0965423i	$0.0307783\pi$
$228$	−592.081	−	867.204i	−0.171980	−	0.251895i
$229$	2146.22	+	3717.37i	0.619330	+	1.07271i	0.989608	+	0.143790i	$0.0459289\pi$
$229$	2146.22	+	3717.37i	0.619330	+	1.07271i	−0.370278	+	0.928921i	$0.620738\pi$
$230$		0			0
$231$	−305.368	−	447.263i	−0.0869772	−	0.127393i
$232$	−981.870	+	1700.65i	−0.277857	+	0.481263i
$233$	−4267.52			−1.19989			−0.599945	−	0.800041i	$-0.704811\pi$
$233$	−4267.52			−1.19989			−0.599945	+	0.800041i	$0.704811\pi$
$234$	4240.14	−	644.776i	1.18456	−	0.180130i
$235$		0			0
$236$	−291.574	+	505.021i	−0.0804231	+	0.139297i
$237$	−1927.34	+	4008.87i	−0.528246	+	1.09875i
$238$	591.194	+	1023.98i	0.161014	+	0.278885i
$239$	−1292.52	−	2238.70i	−0.349816	−	0.605898i	0.636401	−	0.771358i	$-0.280422\pi$
$239$	−1292.52	−	2238.70i	−0.349816	−	0.605898i	−0.986216	+	0.165460i	$0.947089\pi$
$240$		0			0
$241$	1952.49	−	3381.82i	0.521872	−	0.903909i	−0.477804	−	0.878466i	$-0.658567\pi$
$241$	1952.49	−	3381.82i	0.521872	−	0.903909i	0.999676	−	0.0254427i	$-0.00809954\pi$
$242$	1988.26			0.528141
$243$	3521.60	−	1395.44i	0.929673	−	0.368385i
$244$	2298.36			0.603021
$245$		0			0
$246$	4710.71	−	356.120i	1.22091	−	0.0922983i
$247$	840.245	+	1455.35i	0.216452	+	0.374905i
$248$	−869.112	−	1505.35i	−0.222535	−	0.385442i
$249$	154.047	−	320.418i	0.0392062	−	0.0815489i
$250$		0			0
$251$	1466.63			0.368815			0.184408	−	0.982850i	$-0.440963\pi$
$251$	1466.63			0.368815			0.184408	+	0.982850i	$0.440963\pi$
$252$	−521.198	+	79.2558i	−0.130287	+	0.0198121i
$253$	−3248.04			−0.807126
$254$	995.510	−	1724.27i	0.245921	−	0.425947i
$255$		0			0
$256$	−2675.28	−	4633.72i	−0.653144	−	1.13128i
$257$	−2223.67	−	3851.51i	−0.539723	−	0.934828i	−0.998919	−	0.0464928i	$-0.985196\pi$
$257$	−2223.67	−	3851.51i	−0.539723	−	0.934828i	0.459195	−	0.888335i	$-0.348138\pi$
$258$	4913.09	+	7196.06i	1.18557	+	1.73646i
$259$	338.081	−	585.574i	0.0811094	−	0.140486i
$260$		0			0
$261$	−1927.42	+	4929.95i	−0.457104	+	1.16918i
$262$	−4615.14			−1.08826
$263$	−877.572	+	1520.00i	−0.205754	+	0.356377i	−0.950373	−	0.311113i	$-0.899298\pi$
$263$	−877.572	+	1520.00i	−0.205754	+	0.356377i	0.744618	+	0.667490i	$0.232631\pi$
$264$	631.752	−	1314.05i	0.147279	−	0.306341i
$265$		0			0
$266$	−260.725	−	451.589i	−0.0600981	−	0.104093i
$267$	3447.95	−	260.658i	0.790304	−	0.0597453i
$268$	406.316	−	703.760i	0.0926108	−	0.160407i
$269$	−3412.93			−0.773569			−0.386785	−	0.922170i	$-0.626414\pi$
$269$	−3412.93			−0.773569			−0.386785	+	0.922170i	$0.626414\pi$
$270$		0			0
$271$	206.271			0.0462365			0.0231183	−	0.999733i	$-0.492641\pi$
$271$	206.271			0.0462365			0.0231183	+	0.999733i	$0.492641\pi$
$272$	−3424.51	+	5931.43i	−0.763388	+	1.32223i
$273$	841.309	−	63.6012i	0.186514	−	0.0141001i
$274$	−1693.31	−	2932.89i	−0.373345	−	0.646652i
$275$		0			0
$276$	−1370.00	+	2849.60i	−0.298783	+	0.621469i
$277$	−2651.82	+	4593.09i	−0.575208	+	0.996289i	0.420811	+	0.907148i	$0.361746\pi$
$277$	−2651.82	+	4593.09i	−0.575208	+	0.996289i	−0.996019	+	0.0891411i	$0.971588\pi$
$278$	−11393.5			−2.45805
$279$	−2926.12	−	3659.40i	−0.627893	−	0.785242i
$280$		0			0
$281$	−1424.58	+	2467.44i	−0.302431	+	0.523825i	−0.976686	−	0.214673i	$-0.931131\pi$
$281$	−1424.58	+	2467.44i	−0.302431	+	0.523825i	0.674255	+	0.738498i	$0.264465\pi$
$282$	−3502.04	−	5129.34i	−0.739516	−	1.08315i
$283$	4037.52	+	6993.19i	0.848077	+	1.46891i	0.882922	+	0.469520i	$0.155573\pi$
$283$	4037.52	+	6993.19i	0.848077	+	1.46891i	−0.0348448	+	0.999393i	$0.511094\pi$
$284$	−2395.70	−	4149.47i	−0.500558	−	0.866992i
$285$		0			0
$286$	2224.92	−	3853.67i	0.460008	−	0.796757i
$287$	929.336			0.191139
$288$	−3463.10	−	4330.95i	−0.708560	−	0.886124i
$289$	2710.53			0.551705
$290$		0			0
$291$	−3160.32	+	6573.47i	−0.636636	+	1.32420i
$292$	2560.46	+	4434.85i	0.513149	+	0.888800i
$293$	−1311.43	−	2271.46i	−0.261482	−	0.452900i	0.705154	−	0.709054i	$-0.250878\pi$
$293$	−1311.43	−	2271.46i	−0.261482	−	0.452900i	−0.966636	+	0.256154i	$0.917545\pi$
$294$	6207.60	−	469.282i	1.23141	−	0.0930920i
$295$		0			0
$296$	1820.39			0.357459
$297$	1151.06	−	3757.81i	0.224886	−	0.734176i
$298$	5937.79			1.15425
$299$	2530.07	−	4382.22i	0.489358	−	0.847593i
$300$		0			0
$301$	857.042	+	1484.44i	0.164116	+	0.284258i
$302$	3315.18	+	5742.06i	0.631680	+	1.09410i
$303$	1475.11	−	3068.23i	0.279679	−	0.581733i
$304$	1510.26	−	2615.85i	0.284932	−	0.493517i
$305$		0			0
$306$	−3124.39	+	7991.55i	−0.583690	+	1.49296i
$307$	1699.16			0.315883			0.157941	−	0.987448i	$-0.449514\pi$
$307$	1699.16			0.315883			0.157941	+	0.987448i	$0.449514\pi$
$308$	−273.487	+	473.693i	−0.0505953	+	0.0876337i
$309$	742.799	+	1087.96i	0.136752	+	0.200296i
$310$		0			0
$311$	−2409.47	−	4173.32i	−0.439319	−	0.760924i	0.558318	−	0.829627i	$-0.311447\pi$
$311$	−2409.47	−	4173.32i	−0.439319	−	0.760924i	−0.997637	+	0.0687036i	$0.978114\pi$
$312$	1280.79	+	1875.93i	0.232405	+	0.340397i
$313$	−3008.23	+	5210.40i	−0.543243	+	0.940925i	0.455472	+	0.890250i	$0.349471\pi$
$313$	−3008.23	+	5210.40i	−0.543243	+	0.940925i	−0.998715	+	0.0506747i	$0.983863\pi$
$314$	−10319.5			−1.85465
$315$		0			0
$316$	4492.52			0.799760
$317$	3638.36	−	6301.82i	0.644639	−	1.11655i	−0.339746	−	0.940517i	$-0.610341\pi$
$317$	3638.36	−	6301.82i	0.644639	−	1.11655i	0.984385	−	0.176030i	$-0.0563256\pi$
$318$	−5472.69	+	11383.2i	−0.965072	+	2.00735i
$319$	2745.99	+	4756.19i	0.481962	+	0.834782i
$320$		0			0
$321$	−5869.08	+	443.690i	−1.02050	+	0.0771476i
$322$	−785.074	+	1359.79i	−0.135871	+	0.235335i
$323$	−3362.09			−0.579169
$324$	−2811.33	−	2594.86i	−0.482052	−	0.444936i
$325$		0			0
$326$	−5548.16	+	9609.69i	−0.942589	+	1.63261i
$327$	7848.13	−	593.302i	1.32723	−	0.100335i
$328$	1250.99	+	2166.79i	0.210593	+	0.364758i
$329$	−610.898	−	1058.11i	−0.102370	−	0.177311i
$330$		0			0
$331$	797.088	−	1380.60i	0.132362	−	0.229258i	−0.792224	−	0.610230i	$-0.791077\pi$
$331$	797.088	−	1380.60i	0.132362	−	0.229258i	0.924587	+	0.380972i	$0.124410\pi$
$332$	−359.075			−0.0593579
$333$	4851.15	−	737.688i	0.798322	−	0.121397i
$334$	−10329.4			−1.69222
$335$		0			0
$336$	−855.088	−	1252.42i	−0.138836	−	0.203349i
$337$	4198.47	+	7271.96i	0.678650	+	1.17546i	0.975388	+	0.220497i	$0.0707679\pi$
$337$	4198.47	+	7271.96i	0.678650	+	1.17546i	−0.296738	+	0.954959i	$0.595899\pi$
$338$	−532.087	−	921.602i	−0.0856264	−	0.148309i
$339$	4898.90	+	7175.27i	0.784872	+	1.14958i
$340$		0			0
$341$	−4861.28			−0.772003
$342$	1377.90	−	3524.39i	0.217861	−	0.557243i
$343$	2500.79			0.393673
$344$	−2307.36	+	3996.46i	−0.361640	+	0.626379i
$345$		0			0
$346$	−929.117	−	1609.28i	−0.144363	−	0.250044i
$347$	5210.44	+	9024.74i	0.806083	+	1.39618i	0.915557	+	0.402188i	$0.131750\pi$
$347$	5210.44	+	9024.74i	0.806083	+	1.39618i	−0.109474	+	0.993990i	$0.534917\pi$
$348$	5330.97	−	403.010i	0.821178	−	0.0620793i
$349$	3953.71	−	6848.03i	0.606411	−	1.05033i	−0.385416	−	0.922743i	$-0.625942\pi$
$349$	3953.71	−	6848.03i	0.606411	−	1.05033i	0.991827	−	0.127591i	$-0.0407245\pi$
$350$		0			0
$351$	4173.37	+	4480.15i	0.634639	+	0.681290i
$352$	−5753.39			−0.871184
$353$	2501.98	−	4333.56i	0.377244	−	0.653406i	−0.613416	−	0.789760i	$-0.710205\pi$
$353$	2501.98	−	4333.56i	0.377244	−	0.653406i	0.990660	+	0.136354i	$0.0435384\pi$
$354$	−2095.57	+	158.421i	−0.314628	+	0.0237852i
$355$		0			0
$356$	−1746.16	−	3024.43i	−0.259961	−	0.450266i
$357$	−731.390	+	1521.29i	−0.108429	+	0.225533i
$358$	−4139.10	+	7169.13i	−0.611056	+	1.05838i
$359$	−2385.12			−0.350646			−0.175323	−	0.984511i	$-0.556097\pi$
$359$	−2385.12			−0.350646			−0.175323	+	0.984511i	$0.556097\pi$
$360$		0			0
$361$	−5376.27			−0.783827
$362$	−1775.28	+	3074.88i	−0.257754	+	0.446443i
$363$	1600.48	+	2344.18i	0.231415	+	0.338946i
$364$	−426.067	−	737.970i	−0.0613516	−	0.106264i
$365$		0			0
$366$	4670.36	+	6840.53i	0.667004	+	0.976941i
$367$	904.006	−	1565.78i	0.128580	−	0.222706i	−0.794547	−	0.607203i	$-0.792292\pi$
$367$	904.006	−	1565.78i	0.128580	−	0.222706i	0.923126	+	0.384496i	$0.125625\pi$
$368$	−9095.14			−1.28836
$369$	4211.84	+	5267.32i	0.594199	+	0.743104i
$370$		0			0
$371$	−1242.33	+	2151.78i	−0.173850	+	0.301118i
$372$	−2050.45	+	4264.93i	−0.285781	+	0.594426i
$373$	−6266.85	−	10854.5i	−0.869933	−	1.50677i	−0.862064	−	0.506799i	$-0.830829\pi$
$373$	−6266.85	−	10854.5i	−0.869933	−	1.50677i	−0.00786860	−	0.999969i	$-0.502505\pi$
$374$	4451.30	+	7709.89i	0.615432	+	1.06596i
$375$		0			0
$376$	1644.68	−	2848.67i	0.225579	−	0.390715i
$377$	−8555.98			−1.16885
$378$	−1294.98	−	1390.18i	−0.176208	−	0.189161i
$379$	5221.98			0.707745			0.353872	−	0.935294i	$-0.384865\pi$
$379$	5221.98			0.707745			0.353872	+	0.935294i	$0.384865\pi$
$380$		0			0
$381$	2834.29	−	214.266i	0.381116	−	0.0288115i
$382$	−3421.44	−	5926.12i	−0.458263	−	0.793734i
$383$	4278.85	+	7411.18i	0.570859	+	0.988756i	0.996478	+	0.0838538i	$0.0267229\pi$
$383$	4278.85	+	7411.18i	0.570859	+	0.988756i	−0.425619	+	0.904902i	$0.639944\pi$
$384$	2715.85	−	5648.98i	0.360919	−	0.750712i
$385$		0			0
$386$	−2233.23			−0.294478
$387$	−4529.36	+	11585.2i	−0.594936	+	1.52173i
$388$	7366.52			0.963862
$389$	2730.66	−	4729.65i	0.355913	−	0.616459i	−0.631361	−	0.775489i	$-0.717503\pi$
$389$	2730.66	−	4729.65i	0.355913	−	0.616459i	0.987274	+	0.159030i	$0.0508366\pi$
$390$		0			0
$391$	5061.82	+	8767.32i	0.654698	+	1.13397i
$392$	1648.51	+	2855.31i	0.212404	+	0.367895i
$393$	−3715.04	−	5441.30i	−0.476842	−	0.698416i
$394$	124.381	−	215.435i	0.0159042	−	0.0275468i
$395$		0			0
$396$	−3924.28	+	596.745i	−0.497986	+	0.0757261i
$397$	−1998.55			−0.252656			−0.126328	−	0.991989i	$-0.540319\pi$
$397$	−1998.55			−0.252656			−0.126328	+	0.991989i	$0.540319\pi$
$398$	3958.03	−	6855.51i	0.498488	−	0.863406i
$399$	322.554	−	670.912i	0.0404709	−	0.0841795i
$400$		0			0
$401$	246.083	+	426.228i	0.0306454	+	0.0530793i	0.880941	−	0.473225i	$-0.156910\pi$
$401$	246.083	+	426.228i	0.0306454	+	0.0530793i	−0.850296	+	0.526305i	$0.823577\pi$
$402$	2920.23	−	220.763i	0.362308	−	0.0273897i
$403$	3786.71	−	6558.78i	0.468063	−	0.810709i
$404$	−3438.40			−0.423432
$405$		0			0
$406$	2654.89			0.324532
$407$	2545.53	−	4408.99i	0.310018	−	0.536966i
$408$	−4531.49	+	342.571i	−0.549859	+	0.0415681i
$409$	4000.23	+	6928.60i	0.483615	+	0.837646i	0.999823	−	0.0188177i	$-0.00599021\pi$
$409$	4000.23	+	6928.60i	0.483615	+	0.837646i	−0.516208	+	0.856463i	$0.672657\pi$
$410$		0			0
$411$	2094.86	−	4357.31i	0.251415	−	0.522945i
$412$	665.249	−	1152.24i	0.0795496	−	0.137784i
$413$	−413.417			−0.0492565
$414$	−11265.1	+	1713.02i	−1.33731	+	0.203358i
$415$		0			0
$416$	4481.62	−	7762.40i	0.528196	−	0.914863i
$417$	−9171.39	−	13433.1i	−1.07704	−	1.57751i
$418$	−1963.09	−	3400.17i	−0.229708	−	0.397866i
$419$	−2752.47	−	4767.41i	−0.320923	−	0.555855i	0.659756	−	0.751480i	$-0.270660\pi$
$419$	−2752.47	−	4767.41i	−0.320923	−	0.555855i	−0.980679	+	0.195625i	$0.937326\pi$
$420$		0			0
$421$	5202.28	−	9010.61i	0.602241	−	1.04311i	−0.390240	−	0.920713i	$-0.627608\pi$
$421$	5202.28	−	9010.61i	0.602241	−	1.04311i	0.992481	−	0.122399i	$-0.0390588\pi$
$422$	1729.05			0.199452
$423$	3228.52	−	8257.89i	0.371101	−	0.949202i
$424$	−6689.28			−0.766179
$425$		0			0
$426$	7481.79	−	15562.1i	0.850925	−	1.76993i
$427$	814.698	+	1411.10i	0.0923326	+	0.159925i
$428$	2972.30	+	5148.17i	0.335681	+	0.581417i
$429$	6334.51	−	478.875i	0.712897	−	0.0538935i
$430$		0			0
$431$	6446.05			0.720406			0.360203	−	0.932874i	$-0.382707\pi$
$431$	6446.05			0.720406			0.360203	+	0.932874i	$0.382707\pi$
$432$	3223.17	−	10522.6i	0.358970	−	1.17192i
$433$	6307.26			0.700018			0.350009	−	0.936746i	$-0.386179\pi$
$433$	6307.26			0.700018			0.350009	+	0.936746i	$0.386179\pi$
$434$	−1175.00	+	2035.17i	−0.129958	+	0.225095i
$435$		0			0
$436$	−3974.56	−	6884.13i	−0.436575	−	0.756170i
$437$	−2232.34	−	3866.52i	−0.244364	−	0.423251i
$438$	−7996.34	+	16632.4i	−0.872329	+	1.81445i
$439$	3947.14	−	6836.64i	0.429127	−	0.743269i	−0.567669	−	0.823257i	$-0.692155\pi$
$439$	3947.14	−	6836.64i	0.429127	−	0.743269i	0.996796	+	0.0799877i	$0.0254881\pi$
$440$		0			0
$441$	5550.20	+	6941.08i	0.599309	+	0.749495i
$442$	−13869.4			−1.49254
$443$	4389.59	−	7602.99i	0.470780	−	0.815415i	−0.528661	−	0.848833i	$-0.677306\pi$
$443$	4389.59	−	7602.99i	0.470780	−	0.815415i	0.999441	+	0.0334178i	$0.0106392\pi$
$444$	−2794.44	−	4092.93i	−0.298690	−	0.437482i
$445$		0			0
$446$	−5398.43	−	9350.36i	−0.573146	−	0.992718i
$447$	4779.72	+	7000.71i	0.505756	+	0.740766i
$448$	−223.239	+	386.661i	−0.0235425	+	0.0407768i
$449$	16514.2			1.73575			0.867874	−	0.496784i	$-0.165486\pi$
$449$	16514.2			1.73575			0.867874	+	0.496784i	$0.165486\pi$
$450$		0			0
$451$	6997.29			0.730576
$452$	4387.44	−	7599.27i	0.456566	−	0.790796i
$453$	−4101.34	+	8530.81i	−0.425382	+	0.884795i
$454$	−5154.35	−	8927.60i	−0.532832	−	0.922892i
$455$		0			0
$456$	1998.46	−	151.079i	0.205233	−	0.0155152i
$457$	7748.44	−	13420.7i	0.793121	−	1.37373i	−0.130904	−	0.991395i	$-0.541788\pi$
$457$	7748.44	−	13420.7i	0.793121	−	1.37373i	0.924025	−	0.382332i	$-0.124879\pi$
$458$	15623.6			1.59398
$459$	−11937.1	+	2749.25i	−1.21390	+	0.279573i
$460$		0			0
$461$	7641.45	−	13235.4i	0.772012	−	1.33716i	−0.164446	−	0.986386i	$-0.552584\pi$
$461$	7641.45	−	13235.4i	0.772012	−	1.33716i	0.936459	−	0.350778i	$-0.114083\pi$
$462$	−1965.58	+	148.593i	−0.197937	+	0.0149636i
$463$	−6824.87	−	11821.0i	−0.685051	−	1.18654i	−0.973421	−	0.229025i	$-0.926446\pi$
$463$	−6824.87	−	11821.0i	−0.685051	−	1.18654i	0.288369	−	0.957519i	$-0.406887\pi$
$464$	7689.28	+	13318.2i	0.769323	+	1.33251i
$465$		0			0
$466$	−7766.42	+	13451.8i	−0.772044	+	1.33722i
$467$	6841.24			0.677891			0.338945	−	0.940806i	$-0.389930\pi$
$467$	6841.24			0.677891			0.338945	+	0.940806i	$0.389930\pi$
$468$	2251.71	−	5759.42i	0.222405	−	0.568866i
$469$	576.107			0.0567210
$470$		0			0
$471$	−8306.82	−	12166.8i	−0.812650	−	1.19026i
$472$	−556.507	−	963.899i	−0.0542698	−	0.0939980i
$473$	6452.96	+	11176.9i	0.627289	+	1.08650i
$474$	9129.00	+	13371.0i	0.884618	+	1.29567i
$475$		0			0
$476$	1704.83			0.164161
$477$	−17826.2	+	2710.74i	−1.71113	+	0.260202i
$478$	−9408.96			−0.900326
$479$	2888.63	−	5003.25i	0.275542	−	0.477254i	−0.694729	−	0.719271i	$-0.744476\pi$
$479$	2888.63	−	5003.25i	0.275542	−	0.477254i	0.970272	+	0.242018i	$0.0778092\pi$
$480$		0			0
$481$	3965.70	+	6868.79i	0.375926	+	0.651122i
$482$	−7106.66	−	12309.1i	−0.671576	−	1.16320i
$483$	−2235.16	+	168.974i	−0.210566	+	0.0159183i
$484$	1433.39	−	2482.70i	0.134616	−	0.233161i
$485$		0			0
$486$	2010.29	−	13640.1i	0.187631	−	1.27311i
$487$	17699.8			1.64693			0.823463	−	0.567370i	$-0.192039\pi$
$487$	17699.8			1.64693			0.823463	+	0.567370i	$0.192039\pi$
$488$	−2193.36	+	3799.01i	−0.203460	+	0.352404i
$489$	−15796.0	+	1194.15i	−1.46078	+	0.110432i
$490$		0			0
$491$	6045.50	+	10471.1i	0.555661	+	0.962433i	0.997852	+	0.0655120i	$0.0208681\pi$
$491$	6045.50	+	10471.1i	0.555661	+	0.962433i	−0.442191	+	0.896921i	$0.645799\pi$
$492$	2951.40	−	6138.91i	0.270446	−	0.562528i
$493$	8558.80	−	14824.3i	0.781884	−	1.35426i
$494$	6116.63			0.557085
$495$		0			0
$496$	−13612.5			−1.23230
$497$	1698.41	−	2941.73i	0.153288	−	0.265502i
$498$	−729.656	−	1068.71i	−0.0656560	−	0.0961643i
$499$	8153.68	+	14122.6i	0.731481	+	1.26696i	0.956250	+	0.292550i	$0.0945039\pi$
$499$	8153.68	+	14122.6i	0.731481	+	1.26696i	−0.224769	+	0.974412i	$0.572163\pi$
$500$		0			0
$501$	−8314.85	−	12178.5i	−0.741477	−	1.08602i
$502$	2669.10	−	4623.02i	0.237307	−	0.411027i
$503$	8574.88			0.760109			0.380054	−	0.924964i	$-0.375905\pi$
$503$	8574.88			0.760109			0.380054	+	0.924964i	$0.375905\pi$
$504$	366.384	−	937.135i	0.0323810	−	0.0828241i
$505$		0			0
$506$	−5911.09	+	10238.3i	−0.519328	+	0.899503i
$507$	658.266	−	1369.20i	0.0576620	−	0.119937i
$508$	−1435.38	−	2486.15i	−0.125364	−	0.217136i
$509$	−2027.21	−	3511.23i	−0.176532	−	0.305762i	0.764159	−	0.645028i	$-0.223154\pi$
$509$	−2027.21	−	3511.23i	−0.176532	−	0.305762i	−0.940690	+	0.339267i	$0.889821\pi$
$510$		0			0
$511$	−1815.21	+	3144.04i	−0.157143	+	0.272180i
$512$	−9824.79			−0.848044
$513$	5264.46	−	1212.46i	0.453083	−	0.104350i
$514$	−16187.4			−1.38909
$515$		0			0
$516$	12527.6	−	947.057i	1.06879	−	0.0807982i
$517$	−4599.66	−	7966.84i	−0.391282	−	0.677720i
$518$	−1230.54	−	2131.36i	−0.104376	−	0.180785i
$519$	1149.45	−	2390.85i	0.0972161	−	0.202210i
$520$		0			0
$521$	−22757.9			−1.91371			−0.956854	−	0.290570i	$-0.906155\pi$
$521$	−22757.9			−1.91371			−0.956854	+	0.290570i	$0.906155\pi$
$522$	12032.2	+	15047.5i	1.00888	+	1.26170i
$523$	−12468.0			−1.04242			−0.521211	−	0.853428i	$-0.674520\pi$
$523$	−12468.0			−1.04242			−0.521211	+	0.853428i	$0.674520\pi$
$524$	−3327.18	+	5762.84i	−0.277382	+	0.480440i
$525$		0			0
$526$	3194.17	+	5532.47i	0.264777	+	0.458607i
$527$	7575.92	+	13121.9i	0.626209	+	1.08463i
$528$	−6438.26	−	9429.92i	−0.530661	−	0.777244i
$529$	−638.318	+	1105.60i	−0.0524631	+	0.0908687i
$530$		0			0
$531$	−1873.64	−	2343.18i	−0.153125	−	0.191498i
$532$	−751.855			−0.0612726
$533$	−5450.56	+	9440.65i	−0.442946	+	0.767205i
$534$	5453.27	−	11342.8i	0.441921	−	0.919198i
$535$		0			0
$536$	775.507	+	1343.22i	0.0624941	+	0.108243i
$537$	−11784.3	+	890.869i	−0.946985	+	0.0715900i
$538$	−6211.17	+	10758.1i	−0.497737	+	0.862106i
$539$	9220.77			0.736859
$540$		0			0
$541$	−22965.1			−1.82504			−0.912519	−	0.409034i	$-0.865866\pi$
$541$	−22965.1			−1.82504			−0.912519	+	0.409034i	$0.865866\pi$
$542$	375.392	−	650.198i	0.0297499	−	0.0515284i
$543$	−5054.37	+	382.099i	−0.399454	+	0.0301979i
$544$	8966.20	+	15529.9i	0.706659	+	1.22397i
$545$		0			0
$546$	1330.61	−	2767.68i	0.104295	−	0.216933i
$547$	5091.50	−	8818.73i	0.397983	−	0.689327i	−0.595494	−	0.803360i	$-0.703044\pi$
$547$	5091.50	−	8818.73i	0.397983	−	0.689327i	0.993477	+	0.114033i	$0.0363770\pi$
$548$	−4883.00			−0.380641
$549$	−4305.58	+	11012.8i	−0.334713	+	0.856129i
$550$		0			0
$551$	−3774.56	+	6537.73i	−0.291836	+	0.505475i
$552$	−3402.76	−	4983.92i	−0.262375	−	0.384293i
$553$	1592.47	+	2758.23i	0.122457	+	0.212101i
$554$	9652.07	+	16717.9i	0.740211	+	1.28208i
$555$		0			0
$556$	−8213.87	+	14226.8i	−0.626521	+	1.08517i
$557$	−4498.86			−0.342231			−0.171116	−	0.985251i	$-0.554737\pi$
$557$	−4498.86			−0.342231			−0.171116	+	0.985251i	$0.554737\pi$
$558$	−16860.2	+	2563.84i	−1.27912	+	0.194509i
$559$	−20106.2			−1.52129
$560$		0			0
$561$	−5506.89	+	11454.3i	−0.414440	+	0.862037i
$562$	5185.15	+	8980.94i	0.389186	+	0.674089i
$563$	6021.09	+	10428.8i	0.450726	+	0.780680i	0.998431	−	0.0559910i	$-0.0178318\pi$
$563$	6021.09	+	10428.8i	0.450726	+	0.780680i	−0.547705	+	0.836671i	$0.684498\pi$
$564$	−8929.62	+	675.060i	−0.666675	+	0.0503992i
$565$		0			0
$566$	29391.4			2.18271
$567$	596.613	−	2645.84i	0.0441894	−	0.195970i
$568$	9145.01			0.675557
$569$	−1745.67	+	3023.58i	−0.128615	+	0.222768i	−0.923140	−	0.384463i	$-0.874387\pi$
$569$	−1745.67	+	3023.58i	−0.128615	+	0.222768i	0.794525	+	0.607231i	$0.207720\pi$
$570$		0			0
$571$	8050.10	+	13943.2i	0.589993	+	1.02190i	0.994233	+	0.107245i	$0.0342029\pi$
$571$	8050.10	+	13943.2i	0.589993	+	1.02190i	−0.404239	+	0.914653i	$0.632464\pi$
$572$	−3208.01	−	5556.43i	−0.234499	−	0.406164i
$573$	4232.81	−	8804.25i	0.308600	−	0.641890i
$574$	1691.29	−	2929.40i	0.122985	−	0.213016i
$575$		0			0
$576$	−3203.26	+	487.104i	−0.231718	+	0.0352361i
$577$	5196.41			0.374921			0.187460	−	0.982272i	$-0.439974\pi$
$577$	5196.41			0.374921			0.187460	+	0.982272i	$0.439974\pi$
$578$	4932.87	−	8543.98i	0.354983	−	0.614849i
$579$	−1797.68	−	2633.01i	−0.129031	−	0.188988i
$580$		0			0
$581$	−127.281	−	220.458i	−0.00908868	−	0.0157421i
$582$	14969.1	+	21924.8i	1.06613	+	1.56153i
$583$	−9353.92	+	16201.5i	−0.664494	+	1.15094i
$584$	−9773.95			−0.692550
$585$		0			0
$586$	−9546.61			−0.672981
$587$	−1948.60	+	3375.07i	−0.137014	+	0.237315i	−0.926365	−	0.376627i	$-0.877084\pi$
$587$	−1948.60	+	3375.07i	−0.137014	+	0.237315i	0.789351	+	0.613942i	$0.210417\pi$
$588$	3889.24	−	8089.63i	0.272771	−	0.567365i
$589$	−3341.09	−	5786.94i	−0.233730	−	0.404833i
$590$		0			0
$591$	354.123	−	26.7709i	0.0246475	−	0.00186330i
$592$	7127.96	−	12346.0i	0.494861	−	0.857124i
$593$	3023.70			0.209390			0.104695	−	0.994504i	$-0.466613\pi$
$593$	3023.70			0.209390			0.104695	+	0.994504i	$0.466613\pi$
$594$	−9750.38	−	10467.1i	−0.673506	−	0.723015i
$595$		0			0
$596$	4280.71	−	7414.40i	0.294202	−	0.509573i
$597$	11268.8	−	851.897i	0.772532	−	0.0584017i
$598$	−9208.93	−	15950.3i	−0.629734	−	1.09073i
$599$	−8314.74	−	14401.6i	−0.567164	−	0.982356i	−0.996845	−	0.0793757i	$-0.974707\pi$
$599$	−8314.74	−	14401.6i	−0.567164	−	0.982356i	0.429681	−	0.902981i	$-0.358626\pi$
$600$		0			0
$601$	1479.34	−	2562.29i	0.100405	−	0.173907i	−0.811446	−	0.584427i	$-0.801319\pi$
$601$	1479.34	−	2562.29i	0.100405	−	0.173907i	0.911852	+	0.410520i	$0.134653\pi$
$602$	6238.89			0.422389
$603$	2610.97	+	3265.28i	0.176330	+	0.220518i
$604$	9560.01			0.644025
$605$		0			0
$606$	−6986.97	−	10233.6i	−0.468360	−	0.685993i
$607$	3506.18	+	6072.88i	0.234451	+	0.406080i	0.959113	−	0.283024i	$-0.0913376\pi$
$607$	3506.18	+	6072.88i	0.234451	+	0.406080i	−0.724662	+	0.689104i	$0.758004\pi$
$608$	−3954.22	−	6848.92i	−0.263758	−	0.456843i
$609$	2137.10	+	3130.15i	0.142200	+	0.208276i
$610$		0			0
$611$	14331.7			0.948932
$612$	7726.44	+	9662.68i	0.510332	+	0.638220i
$613$	−8462.75			−0.557597			−0.278799	−	0.960350i	$-0.589936\pi$
$613$	−8462.75			−0.557597			−0.278799	+	0.960350i	$0.589936\pi$
$614$	3092.28	−	5355.99i	0.203248	−	0.352036i
$615$		0			0
$616$	−521.986	−	904.106i	−0.0341419	−	0.0591355i
$617$	−4206.71	−	7286.24i	−0.274483	−	0.475418i	0.695522	−	0.718505i	$-0.255173\pi$
$617$	−4206.71	−	7286.24i	−0.274483	−	0.475418i	−0.970005	+	0.243087i	$0.921840\pi$
$618$	4781.21	−	361.449i	0.311211	−	0.0235269i
$619$	560.233	−	970.351i	0.0363775	−	0.0630076i	−0.847263	−	0.531173i	$-0.821751\pi$
$619$	560.233	−	970.351i	0.0363775	−	0.0630076i	0.883641	+	0.468165i	$0.155085\pi$
$620$		0			0
$621$	−11087.7	−	11902.7i	−0.716478	−	0.769146i
$622$	−17539.9			−1.13068
$623$	1237.92	−	2144.14i	0.0796088	−	0.137886i
$624$	17737.8	−	1340.94i	1.13795	−	0.0860266i
$625$		0			0
$626$	10949.3	+	18964.7i	0.699077	+	1.21084i
$627$	2428.62	−	5051.53i	0.154688	−	0.321752i
$628$	−7439.57	+	12885.7i	−0.472725	+	0.818783i
$629$	−15868.0			−1.00588
$630$		0			0
$631$	7709.69			0.486399			0.243200	−	0.969976i	$-0.421803\pi$
$631$	7709.69			0.486399			0.243200	+	0.969976i	$0.421803\pi$
$632$	−4287.29	+	7425.80i	−0.269840	+	0.467377i
$633$	1391.83	+	2038.57i	0.0873936	+	0.128003i
$634$	−13242.8	−	22937.3i	−0.829559	−	1.43684i
$635$		0			0
$636$	10268.6	+	15040.1i	0.640214	+	0.937702i
$637$	−7182.55	+	12440.5i	−0.446755	+	0.773803i
$638$	19989.6			1.24043
$639$	24370.5	−	3705.90i	1.50874	−	0.229426i
$640$		0			0
$641$	−10149.8	+	17580.0i	−0.625419	+	1.08326i	0.363041	+	0.931773i	$0.381739\pi$
$641$	−10149.8	+	17580.0i	−0.625419	+	1.08326i	−0.988460	+	0.151484i	$0.951595\pi$
$642$	−9282.53	+	19307.7i	−0.570642	+	1.18694i
$643$	15932.6	+	27596.1i	0.977169	+	1.69251i	0.672582	+	0.740023i	$0.265185\pi$
$643$	15932.6	+	27596.1i	0.977169	+	1.69251i	0.304587	+	0.952484i	$0.401481\pi$
$644$	1131.96	+	1960.61i	0.0692632	+	0.119967i
$645$		0			0
$646$	−6118.64	+	10597.8i	−0.372654	+	0.645456i
$647$	−22400.4			−1.36113			−0.680563	−	0.732689i	$-0.738265\pi$
$647$	−22400.4			−1.36113			−0.680563	+	0.732689i	$0.738265\pi$
$648$	6972.01	−	2170.59i	0.422664	−	0.131587i
$649$	−3112.76			−0.188269
$650$		0			0
$651$	−3345.32	+	252.899i	−0.201403	+	0.0152257i
$652$	7999.63	+	13855.8i	0.480506	+	0.832260i
$653$	5171.12	+	8956.65i	0.309895	+	0.536755i	0.978339	−	0.207008i	$-0.0663726\pi$
$653$	5171.12	+	8956.65i	0.309895	+	0.536755i	−0.668444	+	0.743763i	$0.733039\pi$
$654$	12412.6	−	25818.2i	0.742157	−	1.54369i
$655$		0			0
$656$	19593.7			1.16617
$657$	−26046.6	+	3960.77i	−1.54669	+	0.235197i
$658$	−4447.07			−0.263472
$659$	−118.705	+	205.603i	−0.00701682	+	0.0121535i	−0.869512	−	0.493911i	$-0.835567\pi$
$659$	−118.705	+	205.603i	−0.00701682	+	0.0121535i	0.862496	+	0.506064i	$0.168900\pi$
$660$		0			0
$661$	−14411.8	−	24962.0i	−0.848042	−	1.46885i	−0.882953	−	0.469461i	$-0.844448\pi$
$661$	−14411.8	−	24962.0i	−0.848042	−	1.46885i	0.0349116	−	0.999390i	$-0.488885\pi$
$662$	−2901.23	−	5025.08i	−0.170332	−	0.295023i
$663$	−11164.4	−	16352.2i	−0.653983	−	0.957869i
$664$	342.671	−	593.524i	0.0200274	−	0.0346885i
$665$		0			0
$666$	6503.26	−	16634.0i	0.378373	−	0.967801i
$667$	22731.2			1.31958
$668$	−7446.76	+	12898.2i	−0.431323	+	0.747073i
$669$	6678.61	−	13891.5i	0.385964	−	0.802807i
$670$		0			0
$671$	6134.15	+	10624.7i	0.352915	+	0.611267i
$672$	−3959.23	+	299.309i	−0.227278	+	0.0171817i
$673$	−3880.42	+	6721.08i	−0.222257	+	0.384961i	−0.955493	−	0.295014i	$-0.904676\pi$
$673$	−3880.42	+	6721.08i	−0.222257	+	0.384961i	0.733236	+	0.679974i	$0.238009\pi$
$674$	30563.0			1.74665
$675$		0			0
$676$	−1534.38			−0.0872998
$677$	−11796.7	+	20432.4i	−0.669693	+	1.15994i	0.308296	+	0.951290i	$0.400241\pi$
$677$	−11796.7	+	20432.4i	−0.669693	+	1.15994i	−0.977990	+	0.208653i	$0.933092\pi$
$678$	31533.0	−	2383.82i	1.78616	−	0.135030i
$679$	2611.21	+	4522.75i	0.147583	+	0.255622i
$680$		0			0
$681$	6376.65	−	13263.5i	0.358816	−	0.746339i
$682$	−8847.01	+	15323.5i	−0.496729	+	0.860361i
$683$	−4383.39			−0.245572			−0.122786	−	0.992433i	$-0.539183\pi$
$683$	−4383.39			−0.245572			−0.122786	+	0.992433i	$0.539183\pi$
$684$	−3407.48	−	4261.38i	−0.190480	−	0.238214i
$685$		0			0
$686$	4551.17	−	7882.86i	0.253301	−	0.438730i
$687$	12576.5	+	18420.4i	0.698432	+	1.02297i
$688$	18069.5	+	31297.3i	1.00130	+	1.73430i
$689$	−14572.5	−	25240.4i	−0.805761	−	1.39562i
$690$		0			0
$691$	8876.26	−	15374.1i	0.488667	−	0.846396i	−0.511248	−	0.859433i	$-0.670817\pi$
$691$	8876.26	−	15374.1i	0.488667	−	0.846396i	0.999915	+	0.0130375i	$0.00415008\pi$
$692$	−2679.30			−0.147185
$693$	−1757.42	−	2197.82i	−0.0963330	−	0.120474i
$694$	37929.7			2.07463
$695$		0			0
$696$	−4421.28	+	9196.28i	−0.240788	+	0.500839i
$697$	−10904.7	−	18887.5i	−0.592605	−	1.02642i
$698$	−14390.7	−	24925.3i	−0.780364	−	1.35163i
$699$	−22111.6	+	1671.59i	−1.19648	+	0.0904510i
$700$		0			0
$701$	15650.2			0.843223			0.421611	−	0.906777i	$-0.361465\pi$
$701$	15650.2			0.843223			0.421611	+	0.906777i	$0.361465\pi$
$702$	21717.2	−	5001.69i	1.16761	−	0.268912i
$703$	6998.03			0.375442
$704$	−1680.84	+	2911.30i	−0.0899845	+	0.155858i
$705$		0			0
$706$	−9106.68	−	15773.2i	−0.485460	−	0.840841i
$707$	−1218.81	−	2111.04i	−0.0648345	−	0.112297i
$708$	−1312.93	+	2730.91i	−0.0696936	+	0.144963i
$709$	−6608.80	+	11446.8i	−0.350069	+	0.606337i	−0.986261	−	0.165194i	$-0.947175\pi$
$709$	−6608.80	+	11446.8i	−0.350069	+	0.606337i	0.636192	+	0.771530i	$0.280508\pi$
$710$		0			0
$711$	−8415.98	+	21526.4i	−0.443916	+	1.13545i
$712$	6665.54			0.350845
$713$	−10060.4	+	17425.1i	−0.528422	+	0.915254i
$714$	3464.29	+	5074.04i	0.181579	+	0.265954i
$715$		0			0
$716$	5967.97	+	10336.8i	0.311499	+	0.539533i
$717$	−7573.90	−	11093.3i	−0.394495	−	0.577804i
$718$	−4340.67	+	7518.26i	−0.225616	+	0.390779i
$719$	−14824.5			−0.768932			−0.384466	−	0.923139i	$-0.625614\pi$
$719$	−14824.5			−0.768932			−0.384466	+	0.923139i	$0.625614\pi$
$720$		0			0
$721$	943.243			0.0487215
$722$	−9784.23	+	16946.8i	−0.504337	+	0.873537i
$723$	8791.93	−	18287.2i	0.452248	−	0.940677i
$724$	2559.70	+	4433.53i	0.131396	+	0.227584i
$725$		0			0
$726$	10301.9	−	778.802i	0.526639	−	0.0398127i
$727$	−3610.05	+	6252.78i	−0.184167	+	0.318986i	−0.943295	−	0.331954i	$-0.892292\pi$
$727$	−3610.05	+	6252.78i	−0.184167	+	0.318986i	0.759129	+	0.650941i	$0.225625\pi$
$728$	1626.41			0.0828005
$729$	17700.1	−	8609.71i	0.899258	−	0.437419i
$730$		0			0
$731$	20112.9	−	34836.5i	1.01765	−	1.76262i
$732$	11908.6	−	900.267i	0.601305	−	0.0454574i
$733$	−930.981	−	1612.51i	−0.0469121	−	0.0812542i	0.841616	−	0.540077i	$-0.181605\pi$
$733$	−930.981	−	1612.51i	−0.0469121	−	0.0812542i	−0.888528	+	0.458822i	$0.848271\pi$
$734$	−3290.39	−	5699.12i	−0.165464	−	0.286592i
$735$		0			0
$736$	−11906.6	+	20622.9i	−0.596310	+	1.03284i
$737$	4337.71			0.216800
$738$	24268.4	−	3690.38i	1.21048	−	0.184071i
$739$	−29412.7			−1.46409			−0.732046	−	0.681255i	$-0.761434\pi$
$739$	−29412.7			−1.46409			−0.732046	+	0.681255i	$0.761434\pi$
$740$		0			0
$741$	4923.68	+	7211.57i	0.244097	+	0.357522i
$742$	4521.81	+	7832.00i	0.223721	+	0.387496i
$743$	−17211.1	−	29810.5i	−0.849816	−	1.47192i	−0.881373	−	0.472422i	$-0.843380\pi$
$743$	−17211.1	−	29810.5i	−0.849816	−	1.47192i	0.0315568	−	0.999502i	$-0.489953\pi$
$744$	−5092.84	−	7459.32i	−0.250958	−	0.367570i
$745$		0			0
$746$	−45619.9			−2.23896
$747$	672.666	−	1720.54i	0.0329472	−	0.0842724i
$748$	12836.3			0.627460
$749$	−2107.18	+	3649.75i	−0.102797	+	0.178049i
$750$		0			0
$751$	14688.2	+	25440.7i	0.713689	+	1.23615i	0.963463	+	0.267842i	$0.0863105\pi$
$751$	14688.2	+	25440.7i	0.713689	+	1.23615i	−0.249773	+	0.968304i	$0.580356\pi$
$752$	−12879.9	−	22308.7i	−0.624577	−	1.08180i
$753$	7599.13	−	574.478i	0.367766	−	0.0278023i
$754$	−15571.0	+	26969.7i	−0.752071	+	1.30262i
$755$		0			0
$756$	−2669.47	+	614.807i	−0.128423	+	0.0295771i
$757$	6235.27			0.299372			0.149686	−	0.988734i	$-0.452174\pi$
$757$	6235.27			0.299372			0.149686	+	0.988734i	$0.452174\pi$
$758$	9503.45	−	16460.5i	0.455384	−	0.788748i
$759$	−16829.3	+	1272.26i	−0.804829	+	0.0608434i
$760$		0			0
$761$	13985.1	+	24222.9i	0.666176	+	1.15385i	0.978965	+	0.204028i	$0.0654034\pi$
$761$	13985.1	+	24222.9i	0.666176	+	1.15385i	−0.312789	+	0.949823i	$0.601263\pi$
$762$	4482.71	−	9324.04i	0.213112	−	0.443274i
$763$	2817.72	−	4880.44i	0.133694	−	0.231565i
$764$	−9866.44			−0.467219
$765$		0			0
$766$	31148.2			1.46923
$767$	2424.69	−	4199.69i	0.114147	−	0.197708i
$768$	−15676.6	−	22961.1i	−0.736565	−	1.07882i
$769$	4534.05	+	7853.21i	0.212616	+	0.368263i	0.952533	−	0.304437i	$-0.0984682\pi$
$769$	4534.05	+	7853.21i	0.212616	+	0.368263i	−0.739916	+	0.672699i	$0.765135\pi$
$770$		0			0
$771$	−13030.3	−	19085.1i	−0.608658	−	0.891482i
$772$	−1610.00	+	2788.60i	−0.0750584	+	0.130005i
$773$	−31339.8			−1.45823			−0.729117	−	0.684389i	$-0.760069\pi$
$773$	−31339.8			−1.45823			−0.729117	+	0.684389i	$0.760069\pi$
$774$	28275.2	+	35361.0i	1.31309	+	1.64215i
$775$		0			0
$776$	−7029.99	+	12176.3i	−0.325209	+	0.563278i
$777$	1522.35	−	3166.50i	0.0702884	−	0.146200i
$778$	−9939.03	−	17214.9i	−0.458010	−	0.793296i
$779$	4809.14	+	8329.68i	0.221188	+	0.383109i
$780$		0			0
$781$	12787.9	−	22149.3i	0.585899	−	1.01481i
$782$	36847.8			1.68501
$783$	−8055.60	+	26298.8i	−0.367667	+	1.20031i
$784$	25819.9			1.17620
$785$		0			0
$786$	−23912.7	+	1807.75i	−1.08516	+	0.0820361i
$787$	−5039.70	−	8729.01i	−0.228267	−	0.395369i	0.729028	−	0.684484i	$-0.239972\pi$
$787$	−5039.70	−	8729.01i	−0.228267	−	0.395369i	−0.957294	+	0.289115i	$0.906639\pi$
$788$	−179.340	−	310.625i	−0.00810750	−	0.0140426i
$789$	−3951.64	+	8219.42i	−0.178304	+	0.370873i
$790$		0			0
$791$	6220.87			0.279632
$792$	2758.63	−	7056.02i	0.123767	−	0.316572i
$793$	−19112.9			−0.855886
$794$	−3637.15	+	6299.72i	−0.162566	+	0.281573i
$795$		0			0
$796$	−5706.90	−	9884.63i	−0.254115	−	0.440140i
$797$	3815.40	+	6608.47i	0.169571	+	0.293706i	0.938269	−	0.345906i	$-0.112428\pi$
$797$	3815.40	+	6608.47i	0.169571	+	0.293706i	−0.768698	+	0.639612i	$0.779095\pi$
$798$	−1527.80	−	2237.72i	−0.0677739	−	0.0992664i
$799$	−14336.4	+	24831.4i	−0.634775	+	1.09946i
$800$		0			0
$801$	17763.0	−	2701.13i	0.783552	−	0.119151i
$802$	1791.38			0.0788725
$803$	−13667.4	+	23672.6i	−0.600636	+	1.04033i
$804$	1829.61	−	3805.59i	0.0802554	−	0.166931i
$805$		0			0
$806$	−13782.8	−	23872.5i	−0.602331	−	1.04327i
$807$	−17683.7	+	1336.85i	−0.771368	+	0.0583138i
$808$	3281.32	−	5683.41i	0.142867	−	0.247452i
$809$	−2066.39			−0.0898028			−0.0449014	−	0.998991i	$-0.514297\pi$
$809$	−2066.39			−0.0898028			−0.0449014	+	0.998991i	$0.514297\pi$
$810$		0			0
$811$	−27700.4			−1.19937			−0.599687	−	0.800235i	$-0.704708\pi$
$811$	−27700.4			−1.19937			−0.599687	+	0.800235i	$0.704708\pi$
$812$	1913.98	−	3315.11i	0.0827187	−	0.143273i
$813$	1068.77	−	80.7966i	0.0461049	−	0.00348544i
$814$	−9265.18	−	16047.8i	−0.398949	−	0.691000i
$815$		0			0
$816$	−15420.3	+	32074.3i	−0.661543	+	1.37601i
$817$	−8870.06	+	15363.4i	−0.379834	+	0.657892i
$818$	29119.9			1.24469
$819$	4334.22	−	659.082i	0.184921	−	0.0281199i
$820$		0			0
$821$	−8551.54	+	14811.7i	−0.363521	+	0.629637i	−0.988538	−	0.150974i	$-0.951759\pi$
$821$	−8551.54	+	14811.7i	−0.363521	+	0.629637i	0.625017	+	0.780612i	$0.285092\pi$
$822$	−9922.46	−	14533.1i	−0.421029	−	0.616668i
$823$	4595.08	+	7958.91i	0.194623	+	0.337096i	0.946777	−	0.321891i	$-0.104318\pi$
$823$	4595.08	+	7958.91i	0.194623	+	0.337096i	−0.752154	+	0.658987i	$0.770985\pi$
$824$	1269.72	+	2199.21i	0.0536804	+	0.0929771i
$825$		0			0
$826$	−752.374	+	1303.15i	−0.0316930	+	0.0548940i
$827$	9902.35			0.416371			0.208185	−	0.978089i	$-0.433244\pi$
$827$	9902.35			0.416371			0.208185	+	0.978089i	$0.433244\pi$
$828$	−5982.27	+	15301.4i	−0.251085	+	0.642224i
$829$	26858.5			1.12525			0.562626	−	0.826711i	$-0.309791\pi$
$829$	26858.5			1.12525			0.562626	+	0.826711i	$0.309791\pi$
$830$		0			0
$831$	−11941.0	+	24837.2i	−0.498468	+	1.03682i
$832$	−2618.59	−	4535.54i	−0.109115	−	0.188992i
$833$	−14369.8	−	24889.3i	−0.597701	−	1.03525i
$834$	−59033.9	+	4462.84i	−2.45105	+	0.185294i
$835$		0			0
$836$	−5660.98			−0.234197
$837$	−16594.7	−	17814.5i	−0.685300	−	0.735676i
$838$	−20036.8			−0.825965
$839$	4650.27	−	8054.51i	0.191353	−	0.331433i	−0.754346	−	0.656477i	$-0.772046\pi$
$839$	4650.27	−	8054.51i	0.191353	−	0.331433i	0.945699	+	0.325044i	$0.105379\pi$
$840$		0			0
$841$	−7023.13	−	12164.4i	−0.287963	−	0.498767i
$842$	−18935.2	−	32796.7i	−0.774999	−	1.34234i
$843$	−6414.75	+	13342.7i	−0.262083	+	0.545133i
$844$	1246.52	−	2159.03i	0.0508375	−	0.0880532i
$845$		0			0
$846$	−20154.5	−	25205.2i	−0.819063	−	1.02432i
$847$	2032.37			0.0824477
$848$	−26192.8	+	45367.2i	−1.06069	+	1.83716i
$849$	23659.1	+	34652.8i	0.956395	+	1.40080i
$850$		0			0
$851$	−10535.9	−	18248.8i	−0.424403	−	0.735088i
$852$	−14038.3	−	20561.5i	−0.564490	−	0.826792i
$853$	11107.3	−	19238.4i	0.445845	−	0.772227i	−0.552265	−	0.833668i	$-0.686236\pi$
$853$	11107.3	−	19238.4i	0.445845	−	0.772227i	0.998111	+	0.0614415i	$0.0195698\pi$
$854$	5930.65			0.237638
$855$		0			0
$856$	−11346.1			−0.453037
$857$	17174.0	−	29746.2i	0.684541	−	1.18566i	−0.289040	−	0.957317i	$-0.593336\pi$
$857$	17174.0	−	29746.2i	0.684541	−	1.18566i	0.973581	−	0.228343i	$-0.0733306\pi$
$858$	10018.6	−	20838.8i	0.398637	−	0.829167i
$859$	−5589.12	−	9680.65i	−0.222001	−	0.384516i	0.733415	−	0.679781i	$-0.237925\pi$
$859$	−5589.12	−	9680.65i	−0.222001	−	0.384516i	−0.955415	+	0.295265i	$0.904592\pi$
$860$		0			0
$861$	4815.23	−	364.021i	0.190595	−	0.0144086i
$862$	11731.1	−	20318.9i	0.463531	−	0.802858i
$863$	33684.0			1.32864			0.664321	−	0.747448i	$-0.268721\pi$
$863$	33684.0			1.32864			0.664321	+	0.747448i	$0.268721\pi$
$864$	−19640.0	−	21083.7i	−0.773342	−	0.830189i
$865$		0			0
$866$	11478.5	−	19881.4i	0.450412	−	0.780136i
$867$	14044.2	−	1061.71i	0.550135	−	0.0415891i
$868$	1694.18	+	2934.41i	0.0662492	+	0.114747i
$869$	11990.2	+	20767.7i	0.468056	+	0.810697i
$870$		0			0
$871$	−3378.87	+	5852.38i	−0.131445	+	0.227670i
$872$	15171.9			0.589204
$873$	−13799.9	+	35297.4i	−0.535002	+	1.36843i
$874$	−16250.4			−0.628924
$875$		0			0
$876$	15003.8	+	21975.6i	0.578689	+	0.847589i
$877$	2704.66	+	4684.60i	0.104139	+	0.180374i	0.913386	−	0.407095i	$-0.133458\pi$
$877$	2704.66	+	4684.60i	0.104139	+	0.180374i	−0.809247	+	0.587468i	$0.800125\pi$
$878$	−14366.7	−	24883.9i	−0.552225	−	0.956482i
$879$	−7684.71	−	11255.6i	−0.294879	−	0.431901i
$880$		0			0
$881$	−41501.3			−1.58708			−0.793538	−	0.608520i	$-0.791763\pi$
$881$	−41501.3			−1.58708			−0.793538	+	0.608520i	$0.791763\pi$
$882$	31980.1	−	4863.04i	1.22089	−	0.185654i
$883$	−10532.8			−0.401423			−0.200711	−	0.979650i	$-0.564325\pi$
$883$	−10532.8			−0.401423			−0.200711	+	0.979650i	$0.564325\pi$
$884$	−9998.84	+	17318.5i	−0.380427	+	0.658919i
$885$		0			0
$886$	−15977.2	−	27673.2i	−0.605827	−	1.04932i
$887$	15001.2	+	25982.9i	0.567861	+	0.983564i	0.996777	+	0.0802195i	$0.0255621\pi$
$887$	15001.2	+	25982.9i	0.567861	+	0.983564i	−0.428916	+	0.903344i	$0.641105\pi$
$888$	9432.09	−	713.046i	0.356442	−	0.0269462i
$889$	1017.60	−	1762.53i	0.0383905	−	0.0664943i
$890$		0			0
$891$	4492.11	−	19921.5i	0.168902	−	0.749040i
$892$	−15567.5			−0.584347
$893$	6322.56	−	10951.0i	0.236928	−	0.410371i
$894$	30765.9	−	2325.83i	1.15097	−	0.0870106i
$895$		0			0
$896$	−2243.97	−	3886.68i	−0.0836673	−	0.144916i
$897$	11392.7	−	23696.9i	0.424072	−	0.882070i
$898$	30054.0	−	52055.0i	1.11683	−	1.93441i
$899$	34021.4			1.26215
$900$		0			0
$901$	58309.4			2.15601
$902$	12734.3	−	22056.5i	0.470074	−	0.814192i
$903$	5022.10	+	7355.72i	0.185078	+	0.271078i
$904$	8374.01	+	14504.2i	0.308092	+	0.533632i
$905$		0			0
$906$	19426.3	+	28453.2i	0.712359	+	1.04337i
$907$	549.175	−	951.200i	0.0201048	−	0.0348226i	−0.855798	−	0.517310i	$-0.826933\pi$
$907$	549.175	−	951.200i	0.0201048	−	0.0348226i	0.875903	+	0.482488i	$0.160267\pi$
$908$	−14863.6			−0.543245
$909$	6441.25	−	16475.4i	0.235031	−	0.601161i
$910$		0			0
$911$	18420.8	−	31905.7i	0.669931	−	1.16036i	−0.307992	−	0.951389i	$-0.599657\pi$
$911$	18420.8	−	31905.7i	0.669931	−	1.16036i	0.977923	−	0.208966i	$-0.0670098\pi$
$912$	6800.59	−	14145.2i	0.246919	−	0.513592i
$913$	−958.346	−	1659.90i	−0.0347389	−	0.0601696i
$914$	−28202.6	−	48848.4i	−1.02063	−	1.76779i
$915$		0			0
$916$	11263.5	−	19508.9i	0.406283	−	0.703703i
$917$	−4717.54			−0.169888
$918$	−13058.3	+	42631.0i	−0.469486	+	1.53271i
$919$	46004.8			1.65131			0.825657	−	0.564172i	$-0.190804\pi$
$919$	46004.8			1.65131			0.825657	+	0.564172i	$0.190804\pi$
$920$		0			0
$921$	8803.96	−	665.561i	0.314984	−	0.0238121i
$922$	−27813.2	−	48173.9i	−0.993470	−	1.72074i
$923$	19922.3	+	34506.5i	0.710457	+	1.23055i
$924$	−1231.49	+	2561.50i	−0.0438453	+	0.0911983i
$925$		0			0
$926$	−49682.1			−1.76313
$927$	4274.87	+	5346.14i	0.151462	+	0.189418i
$928$	40264.8			1.42431
$929$	−25451.4	+	44083.2i	−0.898853	+	1.55686i	−0.0698903	+	0.997555i	$0.522265\pi$
$929$	−25451.4	+	44083.2i	−0.898853	+	1.55686i	−0.828963	+	0.559304i	$0.811068\pi$
$930$		0			0
$931$	6337.31	+	10976.5i	0.223090	+	0.386404i
$932$	11198.0	+	19395.6i	0.393566	+	0.681677i
$933$	−14119.0	−	20679.7i	−0.495430	−	0.725641i
$934$	12450.3	−	21564.6i	0.436175	−	0.755477i
$935$		0			0
$936$	7371.04	+	9218.21i	0.257404	+	0.321909i
$937$	−26913.6			−0.938343			−0.469172	−	0.883107i	$-0.655447\pi$
$937$	−26913.6			−0.938343			−0.469172	+	0.883107i	$0.655447\pi$
$938$	1048.45	−	1815.97i	0.0364960	−	0.0632129i
$939$	−13545.8	+	28175.3i	−0.470768	+	0.979199i
$940$		0			0
$941$	−10780.5	−	18672.3i	−0.373468	−	0.646865i	0.616629	−	0.787254i	$-0.288498\pi$
$941$	−10780.5	−	18672.3i	−0.373468	−	0.646865i	−0.990096	+	0.140389i	$0.955165\pi$
$942$	−53468.9	+	4042.14i	−1.84938	+	0.139809i
$943$	14480.9	−	25081.6i	0.500066	−	0.866140i
$944$	−8716.32			−0.300521
$945$		0			0
$946$	46974.8			1.61446
$947$	−14284.5	+	24741.5i	−0.490163	+	0.848987i	−0.999936	−	0.0113221i	$-0.996396\pi$
$947$	−14284.5	+	24741.5i	−0.490163	+	0.848987i	0.509773	+	0.860309i	$0.329729\pi$
$948$	23277.4	−	1759.72i	0.797485	−	0.0602881i
$949$	−21292.5	−	36879.7i	−0.728328	−	1.26150i
$950$		0			0
$951$	16383.2	−	34077.2i	0.558636	−	1.16196i
$952$	−1626.95	+	2817.95i	−0.0553883	+	0.0959353i
$953$	−3807.33			−0.129414			−0.0647069	−	0.997904i	$-0.520611\pi$
$953$	−3807.33			−0.129414			−0.0647069	+	0.997904i	$0.520611\pi$
$954$	−23897.2	+	61124.2i	−0.811006	+	2.07439i
$955$		0			0
$956$	−6783.17	+	11748.8i	−0.229480	+	0.397472i
$957$	16091.0	+	23568.0i	0.543519	+	0.796075i
$958$	−10514.0	−	18210.8i	−0.354584	−	0.614158i
$959$	−1730.88	−	2997.97i	−0.0582825	−	0.100948i
$960$		0			0
$961$	−161.700	+	280.072i	−0.00542781	+	0.00940124i
$962$	28868.6			0.967526
$963$	−30236.1	+	4597.84i	−1.01178	+	0.153856i
$964$	−20493.5			−0.684701
$965$		0			0
$966$	−3535.13	+	7353.07i	−0.117744	+	0.244908i
$967$	−8952.67	−	15506.5i	−0.297723	−	0.515672i	0.677891	−	0.735162i	$-0.262894\pi$
$967$	−8952.67	−	15506.5i	−0.297723	−	0.515672i	−0.975615	+	0.219490i	$0.929561\pi$
$968$	2735.81	+	4738.57i	0.0908392	+	0.157338i
$969$	−17420.2	+	1316.93i	−0.577521	+	0.0436594i
$970$		0			0
$971$	−8567.95			−0.283170			−0.141585	−	0.989926i	$-0.545220\pi$
$971$	−8567.95			−0.283170			−0.141585	+	0.989926i	$0.545220\pi$
$972$	−15582.9	−	12343.8i	−0.514221	−	0.407331i
$973$	−11646.3			−0.383723
$974$	32211.7	−	55792.2i	1.05968	−	1.83542i
$975$		0			0
$976$	17176.8	+	29751.0i	0.563335	+	0.975725i
$977$	9810.17	+	16991.7i	0.321244	+	0.556411i	0.980745	−	0.195293i	$-0.0625657\pi$
$977$	9810.17	+	16991.7i	0.321244	+	0.556411i	−0.659501	+	0.751704i	$0.729232\pi$
$978$	−24982.9	+	51964.6i	−0.816837	+	1.69902i
$979$	9320.74	−	16144.0i	0.304282	−	0.527032i
$980$		0			0
$981$	40431.7	−	6148.23i	1.31589	−	0.200100i
$982$	44008.6			1.43011
$983$	23668.1	−	40994.4i	0.767951	−	1.33013i	−0.170721	−	0.985319i	$-0.554610\pi$
$983$	23668.1	−	40994.4i	0.767951	−	1.33013i	0.938672	−	0.344811i	$-0.112057\pi$
$984$	7330.59	+	10736.9i	0.237491	+	0.347845i
$985$		0			0
$986$	−31152.2	−	53957.2i	−1.00617	−	1.74275i
$987$	−3579.74	−	5243.14i	−0.115445	−	0.169089i
$988$	4409.64	−	7637.71i	0.141993	−	0.245939i
$989$	53417.6			1.71747
$990$		0			0
$991$	13735.8			0.440294			0.220147	−	0.975467i	$-0.429346\pi$
$991$	13735.8			0.440294			0.220147	+	0.975467i	$0.429346\pi$
$992$	−17820.4	+	30865.8i	−0.570361	+	0.987894i
$993$	3589.23	−	7465.60i	0.114704	−	0.238584i
$994$	−6181.84	−	10707.3i	−0.197259	−	0.341663i
$995$		0			0
$996$	−1860.50	+	140.650i	−0.0591890	+	0.00447456i
$997$	−17936.3	+	31066.6i	−0.569758	+	0.986850i	0.426831	+	0.904331i	$0.359630\pi$
$997$	−17936.3	+	31066.6i	−0.569758	+	0.986850i	−0.996590	+	0.0825187i	$0.973704\pi$
$998$	59355.3			1.88262
$999$	24846.6	−	5722.43i	0.786899	−	0.181231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.151.10	yes	24
5.2	odd	4		225.4.k.e.124.19		48
5.3	odd	4		225.4.k.e.124.6		48
5.4	even	2		225.4.e.e.151.3	yes	24
9.2	odd	6		2025.4.a.bj.1.10		12
9.4	even	3	inner	225.4.e.f.76.10	yes	24
9.7	even	3		2025.4.a.bf.1.3		12
45.4	even	6		225.4.e.e.76.3	✓	24
45.13	odd	12		225.4.k.e.49.19		48
45.22	odd	12		225.4.k.e.49.6		48
45.29	odd	6		2025.4.a.be.1.3		12
45.34	even	6		2025.4.a.bi.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.3	✓	24	45.4	even	6
225.4.e.e.151.3	yes	24	5.4	even	2
225.4.e.f.76.10	yes	24	9.4	even	3	inner
225.4.e.f.151.10	yes	24	1.1	even	1	trivial
225.4.k.e.49.6		48	45.22	odd	12
225.4.k.e.49.19		48	45.13	odd	12
225.4.k.e.124.6		48	5.3	odd	4
225.4.k.e.124.19		48	5.2	odd	4
2025.4.a.be.1.3		12	45.29	odd	6
2025.4.a.bf.1.3		12	9.7	even	3
2025.4.a.bi.1.10		12	45.34	even	6
2025.4.a.bj.1.10		12	9.2	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 $\F_{q}$
Belyi maps

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+(1.81989 - 3.15215i) q^{2} +(5.18137 - 0.391700i) q^{3} +(-2.62402 - 4.54493i) q^{4} +(8.19483 - 17.0453i) q^{6} +(1.86027 - 3.22208i) q^{7} +10.0166 q^{8} +(26.6931 - 4.05909i) q^{9} +(14.0066 - 24.2602i) q^{11} +(-15.3762 - 22.5211i) q^{12} +(21.8210 + 37.7951i) q^{13} +(-6.77099 - 11.7277i) q^{14} +(39.2212 - 67.9331i) q^{16} -87.3128 q^{17} +(35.7838 - 91.5278i) q^{18} +38.5062 q^{19} +(8.37666 - 17.4235i) q^{21} +(-50.9811 - 88.3019i) q^{22} +(-57.9733 - 100.413i) q^{23} +(51.8995 - 3.92349i) q^{24} +158.848 q^{26} +(136.717 - 31.4873i) q^{27} -19.5255 q^{28} +(-98.0246 + 169.784i) q^{29} +(-86.7675 - 150.286i) q^{31} +(-102.690 - 177.865i) q^{32} +(63.0708 - 131.187i) q^{33} +(-158.900 + 275.223i) q^{34} +(-88.4915 - 110.667i) q^{36} +181.738 q^{37} +(70.0772 - 121.377i) q^{38} +(127.867 + 187.283i) q^{39} +(124.893 + 216.320i) q^{41} +(-39.6767 - 58.1133i) q^{42} +(-230.354 + 398.985i) q^{43} -147.015 q^{44} -422.021 q^{46} +(164.196 - 284.395i) q^{47} +(176.610 - 367.349i) q^{48} +(164.579 + 285.059i) q^{49} +(-452.400 + 34.2005i) q^{51} +(114.517 - 198.350i) q^{52} -667.821 q^{53} +(149.558 - 488.256i) q^{54} +(18.6335 - 32.2742i) q^{56} +(199.515 - 15.0829i) q^{57} +(356.788 + 617.976i) q^{58} +(-55.5587 - 96.2305i) q^{59} +(-218.973 + 379.272i) q^{61} -631.630 q^{62} +(36.5778 - 93.5586i) q^{63} -120.003 q^{64} +(-298.740 - 437.555i) q^{66} +(77.4225 + 134.100i) q^{67} +(229.110 + 396.831i) q^{68} +(-339.713 - 497.567i) q^{69} +912.989 q^{71} +(267.374 - 40.6581i) q^{72} -975.779 q^{73} +(330.743 - 572.863i) q^{74} +(-101.041 - 175.008i) q^{76} +(-52.1123 - 90.2611i) q^{77} +(823.048 - 62.2207i) q^{78} +(-428.020 + 741.352i) q^{79} +(696.048 - 216.700i) q^{81} +909.164 q^{82} +(34.2104 - 59.2542i) q^{83} +(-101.169 + 7.64816i) q^{84} +(838.439 + 1452.22i) q^{86} +(-441.397 + 918.107i) q^{87} +(140.298 - 243.004i) q^{88} +665.452 q^{89} +162.372 q^{91} +(-304.246 + 526.970i) q^{92} +(-508.441 - 744.699i) q^{93} +(-597.637 - 1035.14i) q^{94} +(-601.747 - 881.361i) q^{96} +(-701.837 + 1215.62i) q^{97} +1198.06 q^{98} +(275.407 - 704.435i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22}+ \cdots - 1697 q^{99}+O(q^{100}) \) 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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