LMFDB - Embedded newform 225.4.e.g.76.5

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33753 - 2.31667i) q^{2} +(-0.694136 + 5.14958i) q^{3} +(0.422017 - 0.730954i) q^{4} +(12.8583 - 5.27964i) q^{6} +(7.70766 + 13.3501i) q^{7} -23.6584 q^{8} +(-26.0363 - 7.14902i) q^{9} +O(q^{10})$	\(q+(-1.33753 - 2.31667i) q^{2} +(-0.694136 + 5.14958i) q^{3} +(0.422017 - 0.730954i) q^{4} +(12.8583 - 5.27964i) q^{6} +(7.70766 + 13.3501i) q^{7} -23.6584 q^{8} +(-26.0363 - 7.14902i) q^{9} +(-22.2799 - 38.5899i) q^{11} +(3.47117 + 2.68059i) q^{12} +(14.0117 - 24.2689i) q^{13} +(20.6185 - 35.7123i) q^{14} +(28.2677 + 48.9610i) q^{16} +92.6615 q^{17} +(18.2625 + 69.8798i) q^{18} +49.5811 q^{19} +(-74.0974 + 30.4245i) q^{21} +(-59.6001 + 103.230i) q^{22} +(0.461404 - 0.799176i) q^{23} +(16.4221 - 121.831i) q^{24} -74.9642 q^{26} +(54.8872 - 129.114i) q^{27} +13.0110 q^{28} +(-94.9247 - 164.414i) q^{29} +(149.590 - 259.098i) q^{31} +(-19.0156 + 32.9360i) q^{32} +(214.187 - 87.9454i) q^{33} +(-123.938 - 214.666i) q^{34} +(-16.2134 + 16.0144i) q^{36} -57.8330 q^{37} +(-66.3163 - 114.863i) q^{38} +(115.249 + 89.0001i) q^{39} +(143.940 - 249.311i) q^{41} +(169.591 + 130.966i) q^{42} +(-0.295977 - 0.512647i) q^{43} -37.6099 q^{44} -2.46857 q^{46} +(-299.151 - 518.145i) q^{47} +(-271.750 + 111.581i) q^{48} +(52.6839 - 91.2513i) q^{49} +(-64.3197 + 477.168i) q^{51} +(-11.8263 - 20.4838i) q^{52} +146.339 q^{53} +(-372.528 + 45.5382i) q^{54} +(-182.351 - 315.840i) q^{56} +(-34.4160 + 255.322i) q^{57} +(-253.930 + 439.819i) q^{58} +(96.5330 - 167.200i) q^{59} +(283.076 + 490.303i) q^{61} -800.326 q^{62} +(-105.240 - 402.689i) q^{63} +554.019 q^{64} +(-490.223 - 378.571i) q^{66} +(-177.581 + 307.580i) q^{67} +(39.1047 - 67.7313i) q^{68} +(3.79514 + 2.93078i) q^{69} -320.703 q^{71} +(615.977 + 169.134i) q^{72} -636.782 q^{73} +(77.3535 + 133.980i) q^{74} +(20.9240 - 36.2415i) q^{76} +(343.452 - 594.875i) q^{77} +(52.0353 - 386.034i) q^{78} +(143.883 + 249.212i) q^{79} +(626.783 + 372.269i) q^{81} -770.097 q^{82} +(-142.529 - 246.867i) q^{83} +(-9.03144 + 67.0014i) q^{84} +(-0.791757 + 1.37136i) q^{86} +(912.556 - 374.696i) q^{87} +(527.105 + 912.973i) q^{88} -331.615 q^{89} +431.988 q^{91} +(-0.389441 - 0.674531i) q^{92} +(1230.41 + 950.175i) q^{93} +(-800.248 + 1386.07i) q^{94} +(-156.407 - 120.784i) q^{96} +(910.814 + 1577.58i) q^{97} -281.866 q^{98} +(304.207 + 1164.02i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * 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 $

$2$	−1.33753	−	2.31667i	−0.472889	−	0.819068i	0.526630	−	0.850095i	$-0.323455\pi$
$2$	−1.33753	−	2.31667i	−0.472889	−	0.819068i	−0.999519	+	0.0310272i	$0.990122\pi$
$3$	−0.694136	+	5.14958i	−0.133587	+	0.991037i
$3$	−0.694136	+	5.14958i	−0.133587	+	0.991037i
$4$	0.422017	−	0.730954i	0.0527521	−	0.0913693i
$5$		0			0
$5$		0			0
$6$	12.8583	−	5.27964i	0.874898	−	0.359234i
$7$	7.70766	+	13.3501i	0.416175	+	0.720835i	0.995551	−	0.0942246i	$-0.0300372\pi$
$7$	7.70766	+	13.3501i	0.416175	+	0.720835i	−0.579376	+	0.815060i	$0.696704\pi$
$8$	−23.6584			−1.04556
$9$	−26.0363	−	7.14902i	−0.964309	−	0.264779i
$10$		0			0
$11$	−22.2799	−	38.5899i	−0.610694	−	1.05775i	−0.991124	−	0.132944i	$-0.957557\pi$
$11$	−22.2799	−	38.5899i	−0.610694	−	1.05775i	0.380429	−	0.924810i	$-0.375776\pi$
$12$	3.47117	+	2.68059i	0.0835034	+	0.0644850i
$13$	14.0117	−	24.2689i	0.298933	−	0.517768i	−0.676959	−	0.736021i	$-0.736702\pi$
$13$	14.0117	−	24.2689i	0.298933	−	0.517768i	0.975892	+	0.218253i	$0.0700358\pi$
$14$	20.6185	−	35.7123i	0.393609	−	0.681750i
$15$		0			0
$16$	28.2677	+	48.9610i	0.441682	+	0.765016i
$17$	92.6615			1.32198			0.660991	−	0.750394i	$-0.270136\pi$
$17$	92.6615			1.32198			0.660991	+	0.750394i	$0.270136\pi$
$18$	18.2625	+	69.8798i	0.239140	+	0.915045i
$19$	49.5811			0.598667			0.299334	−	0.954149i	$-0.403236\pi$
$19$	49.5811			0.598667			0.299334	+	0.954149i	$0.403236\pi$
$20$		0			0
$21$	−74.0974	+	30.4245i	−0.769970	+	0.316150i
$22$	−59.6001	+	103.230i	−0.577581	+	1.00040i
$23$	0.461404	−	0.799176i	0.00418302	−	0.00724520i	−0.863926	−	0.503618i	$-0.832002\pi$
$23$	0.461404	−	0.799176i	0.00418302	−	0.00724520i	0.868109	+	0.496373i	$0.165335\pi$
$24$	16.4221	−	121.831i	0.139673	−	1.03619i
$25$		0			0
$26$	−74.9642			−0.565449
$27$	54.8872	−	129.114i	0.391224	−	0.920295i
$28$	13.0110			0.0878163
$29$	−94.9247	−	164.414i	−0.607830	−	1.05279i	−0.991597	−	0.129363i	$-0.958707\pi$
$29$	−94.9247	−	164.414i	−0.607830	−	1.05279i	0.383767	−	0.923430i	$-0.374627\pi$
$30$		0			0
$31$	149.590	−	259.098i	0.866683	−	1.50114i	0.00131648	−	0.999999i	$-0.499581\pi$
$31$	149.590	−	259.098i	0.866683	−	1.50114i	0.865366	−	0.501140i	$-0.167086\pi$
$32$	−19.0156	+	32.9360i	−0.105047	+	0.181947i
$33$	214.187	−	87.9454i	1.12985	−	0.463919i
$34$	−123.938	−	214.666i	−0.625151	−	1.08279i
$35$		0			0
$36$	−16.2134	+	16.0144i	−0.0750619	+	0.0741406i
$37$	−57.8330			−0.256965			−0.128482	−	0.991712i	$-0.541011\pi$
$37$	−57.8330			−0.256965			−0.128482	+	0.991712i	$0.541011\pi$
$38$	−66.3163	−	114.863i	−0.283103	−	0.490349i
$39$	115.249	+	89.0001i	0.473194	+	0.365421i
$40$		0			0
$41$	143.940	−	249.311i	0.548284	−	0.949656i	−0.450108	−	0.892974i	$-0.648615\pi$
$41$	143.940	−	249.311i	0.548284	−	0.949656i	0.998392	−	0.0566817i	$-0.0180520\pi$
$42$	169.591	+	130.966i	0.623059	+	0.481154i
$43$	−0.295977	−	0.512647i	−0.00104967	−	0.00181809i	0.865500	−	0.500909i	$-0.167001\pi$
$43$	−0.295977	−	0.512647i	−0.00104967	−	0.00181809i	−0.866550	+	0.499091i	$0.833667\pi$
$44$	−37.6099			−0.128862
$45$		0			0
$46$	−2.46857			−0.00791242
$47$	−299.151	−	518.145i	−0.928418	−	1.60807i	−0.785969	−	0.618266i	$-0.787836\pi$
$47$	−299.151	−	518.145i	−0.928418	−	1.60807i	−0.142449	−	0.989802i	$-0.545498\pi$
$48$	−271.750	+	111.581i	−0.817162	+	0.335528i
$49$	52.6839	−	91.2513i	0.153597	−	0.266039i
$50$		0			0
$51$	−64.3197	+	477.168i	−0.176599	+	1.31013i
$52$	−11.8263	−	20.4838i	−0.0315387	−	0.0546267i
$53$	146.339			0.379267			0.189634	−	0.981855i	$-0.439270\pi$
$53$	146.339			0.379267			0.189634	+	0.981855i	$0.439270\pi$
$54$	−372.528	+	45.5382i	−0.938790	+	0.114759i
$55$		0			0
$56$	−182.351	−	315.840i	−0.435136	−	0.753678i
$57$	−34.4160	+	255.322i	−0.0799739	+	0.593301i
$58$	−253.930	+	439.819i	−0.574873	+	0.995708i
$59$	96.5330	−	167.200i	0.213009	−	0.368942i	−0.739646	−	0.672996i	$-0.765007\pi$
$59$	96.5330	−	167.200i	0.213009	−	0.368942i	0.952655	+	0.304054i	$0.0983403\pi$
$60$		0			0
$61$	283.076	+	490.303i	0.594167	+	1.02913i	0.993664	+	0.112393i	$0.0358517\pi$
$61$	283.076	+	490.303i	0.594167	+	1.02913i	−0.399496	+	0.916735i	$0.630815\pi$
$62$	−800.326			−1.63938
$63$	−105.240	−	402.689i	−0.210459	−	0.805302i
$64$	554.019			1.08207
$65$		0			0
$66$	−490.223	−	378.571i	−0.914276	−	0.706044i
$67$	−177.581	+	307.580i	−0.323806	+	0.560849i	−0.981270	−	0.192637i	$-0.938296\pi$
$67$	−177.581	+	307.580i	−0.323806	+	0.560849i	0.657464	+	0.753486i	$0.271629\pi$
$68$	39.1047	−	67.7313i	0.0697373	−	0.120789i
$69$	3.79514	+	2.93078i	0.00662147	+	0.00511339i
$70$		0			0
$71$	−320.703			−0.536062			−0.268031	−	0.963410i	$-0.586373\pi$
$71$	−320.703			−0.536062			−0.268031	+	0.963410i	$0.586373\pi$
$72$	615.977	+	169.134i	1.00824	+	0.276842i
$73$	−636.782			−1.02095			−0.510477	−	0.859891i	$-0.670531\pi$
$73$	−636.782			−1.02095			−0.510477	+	0.859891i	$0.670531\pi$
$74$	77.3535	+	133.980i	0.121516	+	0.210471i
$75$		0			0
$76$	20.9240	−	36.2415i	0.0315809	−	0.0546998i
$77$	343.452	−	594.875i	0.508311	−	0.880420i
$78$	52.0353	−	386.034i	0.0755364	−	0.560381i
$79$	143.883	+	249.212i	0.204912	+	0.354918i	0.950105	−	0.311931i	$-0.100976\pi$
$79$	143.883	+	249.212i	0.204912	+	0.354918i	−0.745193	+	0.666849i	$0.767642\pi$
$80$		0			0
$81$	626.783	+	372.269i	0.859785	+	0.510657i
$82$	−770.097			−1.03711
$83$	−142.529	−	246.867i	−0.188489	−	0.326472i	0.756258	−	0.654274i	$-0.227026\pi$
$83$	−142.529	−	246.867i	−0.188489	−	0.326472i	−0.944747	+	0.327801i	$0.893692\pi$
$84$	−9.03144	+	67.0014i	−0.0117311	+	0.0870292i
$85$		0			0
$86$	−0.791757	+	1.37136i	−0.000992759	+	0.00171951i
$87$	912.556	−	374.696i	1.12456	−	0.461743i
$88$	527.105	+	912.973i	0.638518	+	1.10595i
$89$	−331.615			−0.394957			−0.197478	−	0.980307i	$-0.563275\pi$
$89$	−331.615			−0.394957			−0.197478	+	0.980307i	$0.563275\pi$
$90$		0			0
$91$	431.988			0.497634
$92$	−0.389441	−	0.674531i	−0.000441326	−	0.000764399i
$93$	1230.41	+	950.175i	1.37191	+	1.05945i
$94$	−800.248	+	1386.07i	−0.878078	+	1.52088i
$95$		0			0
$96$	−156.407	−	120.784i	−0.166284	−	0.128411i
$97$	910.814	+	1577.58i	0.953393	+	1.65133i	0.738003	+	0.674798i	$0.235769\pi$
$97$	910.814	+	1577.58i	0.953393	+	1.65133i	0.215391	+	0.976528i	$0.430898\pi$
$98$	−281.866			−0.290538
$99$	304.207	+	1164.02i	0.308828	+	1.18170i
$100$		0			0
$101$	573.683	+	993.648i	0.565184	+	0.978927i	0.997033	+	0.0769812i	$0.0245281\pi$
$101$	573.683	+	993.648i	0.565184	+	0.978927i	−0.431849	+	0.901946i	$0.642139\pi$
$102$	1191.47	−	489.219i	1.15660	−	0.474901i
$103$	791.272	−	1370.52i	0.756955	−	1.31108i	−0.187442	−	0.982276i	$-0.560020\pi$
$103$	791.272	−	1370.52i	0.756955	−	1.31108i	0.944397	−	0.328808i	$-0.106647\pi$
$104$	−331.493	+	574.162i	−0.312553	+	0.541358i
$105$		0			0
$106$	−195.733	−	339.019i	−0.179351	−	0.310646i
$107$	385.387			0.348194			0.174097	−	0.984728i	$-0.444299\pi$
$107$	385.387			0.348194			0.174097	+	0.984728i	$0.444299\pi$
$108$	−71.2130	−	94.6082i	−0.0634488	−	0.0842934i
$109$	−203.502			−0.178825			−0.0894126	−	0.995995i	$-0.528499\pi$
$109$	−203.502			−0.178825			−0.0894126	+	0.995995i	$0.528499\pi$
$110$		0			0
$111$	40.1440	−	297.816i	0.0343270	−	0.254661i
$112$	−435.755	+	754.750i	−0.367634	+	0.636761i
$113$	33.0075	−	57.1707i	0.0274786	−	0.0475944i	−0.851959	−	0.523608i	$-0.824586\pi$
$113$	33.0075	−	57.1707i	0.0274786	−	0.0475944i	0.879438	+	0.476014i	$0.157919\pi$
$114$	637.529	−	261.770i	0.523773	−	0.215062i
$115$		0			0
$116$	−160.239			−0.128257
$117$	−538.311	+	531.704i	−0.425358	+	0.420137i
$118$	−516.464			−0.402918
$119$	714.203	+	1237.04i	0.550175	+	0.952932i
$120$		0			0
$121$	−327.286	+	566.876i	−0.245895	+	0.425903i
$122$	757.247	−	1311.59i	0.561950	−	0.973327i
$123$	1183.93	+	914.286i	0.867901	+	0.670231i
$124$	−126.259	−	218.687i	−0.0914386	−	0.158376i
$125$		0			0
$126$	−792.138	+	782.415i	−0.560073	+	0.553199i
$127$	−1821.52			−1.27270			−0.636352	−	0.771399i	$-0.719557\pi$
$127$	−1821.52			−1.27270			−0.636352	+	0.771399i	$0.719557\pi$
$128$	−588.893	−	1019.99i	−0.406650	−	0.704339i
$129$	2.84536	−	1.16831i	0.00194202	−	0.000797394i
$130$		0			0
$131$	−119.129	+	206.337i	−0.0794530	+	0.137617i	−0.903014	−	0.429611i	$-0.858651\pi$
$131$	−119.129	+	206.337i	−0.0794530	+	0.137617i	0.823561	+	0.567228i	$0.191984\pi$
$132$	26.1064	−	193.675i	0.0172142	−	0.127707i
$133$	382.154	+	661.910i	0.249150	+	0.431541i
$134$	950.083			0.612498
$135$		0			0
$136$	−2192.22			−1.38221
$137$	−1023.74	−	1773.17i	−0.638424	−	1.10578i	−0.985779	−	0.168048i	$-0.946253\pi$
$137$	−1023.74	−	1773.17i	−0.638424	−	1.10578i	0.347355	−	0.937734i	$-0.387080\pi$
$138$	1.71353	−	12.7121i	0.00105699	−	0.00784150i
$139$	1089.68	−	1887.39i	0.664934	−	1.15170i	−0.314369	−	0.949301i	$-0.601793\pi$
$139$	1089.68	−	1887.39i	0.664934	−	1.15170i	0.979303	−	0.202399i	$-0.0648737\pi$
$140$		0			0
$141$	2875.88	−	1180.84i	1.71768	−	0.705281i
$142$	428.950	+	742.964i	0.253498	+	0.439071i
$143$	−1248.71			−0.730228
$144$	−385.964	−	1476.85i	−0.223359	−	0.854660i
$145$		0			0
$146$	851.716	+	1475.22i	0.482798	+	0.836231i
$147$	433.336	+	334.641i	0.243136	+	0.187760i
$148$	−24.4065	+	42.2733i	−0.0135554	+	0.0234787i
$149$	−77.9741	+	135.055i	−0.0428717	+	0.0742560i	−0.886665	−	0.462412i	$-0.846984\pi$
$149$	−77.9741	+	135.055i	−0.0428717	+	0.0742560i	0.843793	+	0.536668i	$0.180317\pi$
$150$		0			0
$151$	−807.071	−	1397.89i	−0.434957	−	0.753368i	0.562335	−	0.826909i	$-0.309903\pi$
$151$	−807.071	−	1397.89i	−0.434957	−	0.753368i	−0.997292	+	0.0735418i	$0.976570\pi$
$152$	−1173.01			−0.625943
$153$	−2412.57	−	662.439i	−1.27480	−	0.350033i
$154$	−1837.51			−0.961498
$155$		0			0
$156$	113.692	−	46.6820i	0.0583502	−	0.0239587i
$157$	−494.254	+	856.073i	−0.251247	+	0.435172i	−0.963869	−	0.266375i	$-0.914174\pi$
$157$	−494.254	+	856.073i	−0.251247	+	0.435172i	0.712623	+	0.701548i	$0.247507\pi$
$158$	384.895	−	666.658i	0.193801	−	0.335674i
$159$	−101.579	+	753.583i	−0.0506650	+	0.375868i
$160$		0			0
$161$	14.2254			0.00696347
$162$	24.0828	−	1949.97i	0.0116798	−	0.945706i
$163$	−2974.11			−1.42914			−0.714570	−	0.699564i	$-0.753378\pi$
$163$	−2974.11			−1.42914			−0.714570	+	0.699564i	$0.753378\pi$
$164$	−121.490	−	210.427i	−0.0578462	−	0.100193i
$165$		0			0
$166$	−381.274	+	660.386i	−0.178269	+	0.308770i
$167$	−1219.48	+	2112.20i	−0.565067	+	0.978724i	0.431977	+	0.901885i	$0.357816\pi$
$167$	−1219.48	+	2112.20i	−0.565067	+	0.978724i	−0.997043	+	0.0768396i	$0.975517\pi$
$168$	1753.02	−	719.793i	0.805051	−	0.330555i
$169$	705.847	+	1222.56i	0.321278	+	0.556469i
$170$		0			0
$171$	−1290.91	−	354.456i	−0.577300	−	0.158514i
$172$	−0.499628			−0.000221490
$173$	1326.79	+	2298.08i	0.583089	+	1.00994i	0.995111	+	0.0987652i	$0.0314893\pi$
$173$	1326.79	+	2298.08i	0.583089	+	1.00994i	−0.412022	+	0.911174i	$0.635177\pi$
$174$	−2088.62	−	1612.93i	−0.909989	−	0.702733i
$175$		0			0
$176$	1259.60	−	2181.69i	0.539466	−	0.934382i
$177$	794.003	+	613.164i	0.337180	+	0.260385i
$178$	443.546	+	768.244i	0.186771	+	0.323496i
$179$	−2102.30			−0.877841			−0.438921	−	0.898526i	$-0.644639\pi$
$179$	−2102.30			−0.877841			−0.438921	+	0.898526i	$0.644639\pi$
$180$		0			0
$181$	1597.36			0.655973			0.327987	−	0.944682i	$-0.393630\pi$
$181$	1597.36			0.655973			0.327987	+	0.944682i	$0.393630\pi$
$182$	−577.798	−	1000.78i	−0.235326	−	0.407596i
$183$	−2721.35	+	1117.39i	−1.09928	+	0.451364i
$184$	−10.9161	+	18.9072i	−0.00437360	+	0.00757531i
$185$		0			0
$186$	555.535	−	4121.34i	0.218999	−	1.62469i
$187$	−2064.49	−	3575.79i	−0.807327	−	1.39833i
$188$	−504.987			−0.195904
$189$	2146.73	−	262.418i	0.826199	−	0.100995i
$190$		0			0
$191$	1703.71	+	2950.92i	0.645426	+	1.11791i	0.984203	+	0.177044i	$0.0566535\pi$
$191$	1703.71	+	2950.92i	0.645426	+	1.11791i	−0.338777	+	0.940867i	$0.610013\pi$
$192$	−384.564	+	2852.96i	−0.144550	+	1.07237i
$193$	−409.565	+	709.387i	−0.152752	+	0.264574i	−0.932238	−	0.361845i	$-0.882147\pi$
$193$	−409.565	+	709.387i	−0.152752	+	0.264574i	0.779486	+	0.626419i	$0.215480\pi$
$194$	2436.49	−	4220.12i	0.901698	−	1.56179i
$195$		0			0
$196$	−44.4670	−	77.0191i	−0.0162052	−	0.0280682i
$197$	359.979			0.130190			0.0650950	−	0.997879i	$-0.479265\pi$
$197$	359.979			0.130190			0.0650950	+	0.997879i	$0.479265\pi$
$198$	2289.77	−	2261.66i	0.821851	−	0.811764i
$199$	−1338.34			−0.476745			−0.238372	−	0.971174i	$-0.576614\pi$
$199$	−1338.34			−0.476745			−0.238372	+	0.971174i	$0.576614\pi$
$200$		0			0
$201$	−1460.64	−	1127.97i	−0.512566	−	0.395826i
$202$	1534.64	−	2658.07i	0.534538	−	0.925848i
$203$	1463.30	−	2534.50i	0.505927	−	0.876291i
$204$	321.644	+	248.387i	0.110390	+	0.0852480i
$205$		0			0
$206$	−4233.41			−1.43182
$207$	−17.7266	+	17.5090i	−0.00595210	+	0.00587904i
$208$	1584.31			0.528135
$209$	−1104.66	−	1913.33i	−0.365603	−	0.633242i
$210$		0			0
$211$	−534.114	+	925.113i	−0.174265	+	0.301836i	−0.939907	−	0.341431i	$-0.889088\pi$
$211$	−534.114	+	925.113i	−0.174265	+	0.301836i	0.765642	+	0.643267i	$0.222422\pi$
$212$	61.7574	−	106.967i	0.0200071	−	0.0346534i
$213$	222.611	−	1651.49i	0.0716107	−	0.531258i
$214$	−515.468	−	892.816i	−0.164657	−	0.285195i
$215$		0			0
$216$	−1298.54	+	3054.62i	−0.409049	+	0.962225i
$217$	4611.96			1.44277
$218$	272.190	+	471.448i	0.0845645	+	0.146470i
$219$	442.013	−	3279.16i	0.136386	−	1.01180i
$220$		0			0
$221$	1298.34	−	2248.79i	0.395185	−	0.684480i
$222$	−743.635	+	305.337i	−0.224818	+	0.0923104i
$223$	759.415	+	1315.35i	0.228046	+	0.394987i	0.957229	−	0.289332i	$-0.0934331\pi$
$223$	759.415	+	1315.35i	0.228046	+	0.394987i	−0.729183	+	0.684319i	$0.760100\pi$
$224$	−586.263			−0.174872
$225$		0			0
$226$	−176.594			−0.0519774
$227$	2117.56	+	3667.72i	0.619152	+	1.07240i	0.989641	+	0.143566i	$0.0458569\pi$
$227$	2117.56	+	3667.72i	0.619152	+	1.07240i	−0.370489	+	0.928837i	$0.620810\pi$
$228$	172.104	+	132.907i	0.0499907	+	0.0386050i
$229$	2768.26	−	4794.77i	0.798829	−	1.38361i	−0.121550	−	0.992585i	$-0.538787\pi$
$229$	2768.26	−	4794.77i	0.798829	−	1.38361i	0.920379	−	0.391027i	$-0.127880\pi$
$230$		0			0
$231$	2824.96	+	2181.56i	0.804626	+	0.621367i
$232$	2245.76	+	3889.78i	0.635524	+	1.10076i
$233$	6337.30			1.78185			0.890923	−	0.454154i	$-0.150059\pi$
$233$	6337.30			1.78185			0.890923	+	0.454154i	$0.150059\pi$
$234$	1951.79	+	535.920i	0.545268	+	0.149719i
$235$		0			0
$236$	−81.4771	−	141.122i	−0.0224733	−	0.0389249i
$237$	−1383.21	+	567.948i	−0.379111	+	0.155663i
$238$	1910.54	−	3309.15i	0.520344	−	0.901262i
$239$	−1271.43	+	2202.19i	−0.344110	+	0.596016i	−0.985192	−	0.171457i	$-0.945153\pi$
$239$	−1271.43	+	2202.19i	−0.344110	+	0.596016i	0.641082	+	0.767473i	$0.278486\pi$
$240$		0			0
$241$	−1025.71	−	1776.58i	−0.274157	−	0.474854i	0.695765	−	0.718269i	$-0.255065\pi$
$241$	−1025.71	−	1776.58i	−0.274157	−	0.474854i	−0.969922	+	0.243415i	$0.921732\pi$
$242$	1751.02			0.465124
$243$	−2352.10	+	2969.26i	−0.620935	+	0.783862i
$244$	477.852			0.125374
$245$		0			0
$246$	534.552	−	3965.68i	0.138544	−	1.02781i
$247$	694.713	−	1203.28i	0.178962	−	0.309971i
$248$	−3539.05	+	6129.82i	−0.906170	+	1.56953i
$249$	1370.20	−	562.605i	0.348726	−	0.143187i
$250$		0			0
$251$	−2770.89			−0.696801			−0.348401	−	0.937346i	$-0.613275\pi$
$251$	−2770.89			−0.696801			−0.348401	+	0.937346i	$0.613275\pi$
$252$	−338.760	−	93.0162i	−0.0846821	−	0.0232519i
$253$	−41.1201			−0.0102182
$254$	2436.34	+	4219.86i	0.601848	+	1.04243i
$255$		0			0
$256$	640.748	−	1109.81i	0.156433	−	0.270949i
$257$	213.378	−	369.581i	0.0517904	−	0.0897036i	−0.838968	−	0.544181i	$-0.816841\pi$
$257$	213.378	−	369.581i	0.0517904	−	0.0897036i	0.890758	+	0.454477i	$0.150174\pi$
$258$	−6.51235	−	5.02913i	−0.00157148	−	0.00121356i
$259$	−445.757	−	772.074i	−0.106942	−	0.185229i
$260$		0			0
$261$	1296.09	+	4959.37i	0.307379	+	1.17616i
$262$	637.355			0.150290
$263$	−1881.19	−	3258.32i	−0.441063	−	0.763943i	0.556706	−	0.830710i	$-0.312065\pi$
$263$	−1881.19	−	3258.32i	−0.441063	−	0.763943i	−0.997769	+	0.0667669i	$0.978732\pi$
$264$	−5067.31	+	2080.64i	−1.18133	+	0.485056i
$265$		0			0
$266$	1022.29	−	1770.65i	0.235641	−	0.408142i
$267$	230.186	−	1707.68i	0.0527609	−	0.391417i
$268$	149.885	+	259.608i	0.0341629	+	0.0591719i
$269$	−1980.25			−0.448839			−0.224420	−	0.974493i	$-0.572049\pi$
$269$	−1980.25			−0.448839			−0.224420	+	0.974493i	$0.572049\pi$
$270$		0			0
$271$	5659.70			1.26864			0.634321	−	0.773070i	$-0.281280\pi$
$271$	5659.70			1.26864			0.634321	+	0.773070i	$0.281280\pi$
$272$	2619.32	+	4536.80i	0.583896	+	1.01134i
$273$	−299.859	+	2224.56i	−0.0664772	+	0.493174i
$274$	−2738.57	+	4743.34i	−0.603807	+	1.04582i
$275$		0			0
$276$	3.74388	−	1.53724i	0.000816503	−	0.000335257i
$277$	−3084.78	−	5343.00i	−0.669121	−	1.15895i	−0.978150	−	0.207900i	$-0.933337\pi$
$277$	−3084.78	−	5343.00i	−0.669121	−	1.15895i	0.309029	−	0.951053i	$-0.399996\pi$
$278$	−5829.95			−1.25776
$279$	−5747.07	+	5676.53i	−1.23322	+	1.21808i
$280$		0			0
$281$	−1671.73	−	2895.52i	−0.354900	−	0.614705i	0.632201	−	0.774805i	$-0.282152\pi$
$281$	−1671.73	−	2895.52i	−0.354900	−	0.614705i	−0.987101	+	0.160100i	$0.948818\pi$
$282$	−6582.20	−	5083.06i	−1.38994	−	1.07338i
$283$	2551.66	−	4419.60i	0.535973	−	0.928333i	−0.463142	−	0.886284i	$-0.653278\pi$
$283$	2551.66	−	4419.60i	0.535973	−	0.928333i	0.999116	−	0.0420490i	$-0.0133886\pi$
$284$	−135.342	+	234.419i	−0.0282784	+	0.0489796i
$285$		0			0
$286$	1670.19	+	2892.86i	0.345317	+	0.598106i
$287$	4437.76			0.912727
$288$	730.556	−	721.590i	0.149474	−	0.147639i
$289$	3673.14			0.747638
$290$		0			0
$291$	−8756.08	+	3595.26i	−1.76389	+	0.724253i
$292$	−268.733	+	465.458i	−0.0538575	+	0.0932839i
$293$	−2065.14	+	3576.93i	−0.411764	+	0.713195i	−0.995083	−	0.0990477i	$-0.968420\pi$
$293$	−2065.14	+	3576.93i	−0.411764	+	0.713195i	0.583319	+	0.812243i	$0.301754\pi$
$294$	195.653	−	1451.49i	0.0388120	−	0.287934i
$295$		0			0
$296$	1368.23			0.268672
$297$	−6205.37	+	758.550i	−1.21236	+	0.148200i
$298$	417.172			0.0810943
$299$	−12.9301	−	22.3956i	−0.00250089	−	0.00433167i
$300$		0			0
$301$	4.56258	−	7.90261i	0.000873696	−	0.00151329i
$302$	−2158.97	+	3739.44i	−0.411373	+	0.712519i
$303$	−5515.08	+	2264.50i	−1.04565	+	0.429347i
$304$	1401.54	+	2427.54i	0.264421	+	0.457990i
$305$		0			0
$306$	1692.23	+	6475.16i	0.316138	+	1.20967i
$307$	−3382.52			−0.628830			−0.314415	−	0.949286i	$-0.601808\pi$
$307$	−3382.52			−0.628830			−0.314415	+	0.949286i	$0.601808\pi$
$308$	−289.884	−	502.095i	−0.0536289	−	0.0928880i
$309$	6508.37	+	5026.05i	1.19821	+	0.925313i
$310$		0			0
$311$	3010.61	−	5214.53i	0.548926	−	0.950767i	−0.449423	−	0.893319i	$-0.648370\pi$
$311$	3010.61	−	5214.53i	0.548926	−	0.950767i	0.998348	−	0.0574482i	$-0.0182964\pi$
$312$	−2726.59	−	2105.60i	−0.494753	−	0.382070i
$313$	−5096.47	−	8827.35i	−0.920350	−	1.59409i	−0.798874	−	0.601499i	$-0.794571\pi$
$313$	−5096.47	−	8827.35i	−0.920350	−	1.59409i	−0.121476	−	0.992594i	$-0.538763\pi$
$314$	2644.32			0.475247
$315$		0			0
$316$	242.884			0.0432382
$317$	2700.30	+	4677.05i	0.478435	+	0.828673i	0.999694	−	0.0247250i	$-0.00787101\pi$
$317$	2700.30	+	4677.05i	0.478435	+	0.828673i	−0.521260	+	0.853398i	$0.674538\pi$
$318$	1881.67	−	772.616i	0.331820	−	0.136246i
$319$	−4229.82	+	7326.27i	−0.742397	+	1.28587i
$320$		0			0
$321$	−267.511	+	1984.58i	−0.0465141	+	0.345074i
$322$	−19.0269	−	32.9556i	−0.00329295	−	0.00570355i
$323$	4594.25			0.791428
$324$	536.624	−	301.046i	0.0920138	−	0.0516197i
$325$		0			0
$326$	3977.96	+	6890.03i	0.675825	+	1.17056i
$327$	141.258	−	1047.95i	0.0238887	−	0.177222i
$328$	−3405.38	+	5898.29i	−0.573265	+	0.992923i
$329$	4611.51	−	7987.37i	0.772768	−	1.33847i
$330$		0			0
$331$	1151.45	+	1994.37i	0.191206	+	0.331179i	0.945650	−	0.325185i	$-0.105427\pi$
$331$	1151.45	+	1994.37i	0.191206	+	0.331179i	−0.754444	+	0.656365i	$0.772093\pi$
$332$	−240.598			−0.0397727
$333$	1505.76	+	413.449i	0.247793	+	0.0680387i
$334$	6524.37			1.06886
$335$		0			0
$336$	−3584.17	−	2767.86i	−0.581942	−	0.449402i
$337$	4783.16	−	8284.68i	0.773162	−	1.33916i	−0.162660	−	0.986682i	$-0.552007\pi$
$337$	4783.16	−	8284.68i	0.773162	−	1.33916i	0.935822	−	0.352473i	$-0.114659\pi$
$338$	1888.19	−	3270.43i	0.303857	−	0.526296i
$339$	271.493	+	209.659i	0.0434970	+	0.0335903i
$340$		0			0
$341$	−13331.4			−2.11711
$342$	905.475	+	3464.71i	0.143165	+	0.547808i
$343$	6911.73			1.08804
$344$	7.00232	+	12.1284i	0.00109750	+	0.00190092i
$345$		0			0
$346$	3549.26	−	6147.50i	0.551472	−	0.955178i
$347$	−40.7609	+	70.5999i	−0.00630593	+	0.0109222i	−0.869161	−	0.494529i	$-0.835341\pi$
$347$	−40.7609	+	70.5999i	−0.00630593	+	0.0109222i	0.862855	+	0.505451i	$0.168674\pi$
$348$	111.228	−	825.165i	0.0171334	−	0.127108i
$349$	−46.7859	−	81.0356i	−0.00717591	−	0.0124290i	0.862415	−	0.506202i	$-0.168951\pi$
$349$	−46.7859	−	81.0356i	−0.00717591	−	0.0124290i	−0.869591	+	0.493773i	$0.835618\pi$
$350$		0			0
$351$	−2364.39	−	3141.15i	−0.359549	−	0.477670i
$352$	1694.66			0.256607
$353$	3337.71	+	5781.08i	0.503253	+	0.871659i	0.999993	+	0.00376007i	$0.00119687\pi$
$353$	3337.71	+	5781.08i	0.503253	+	0.871659i	−0.496740	+	0.867899i	$0.665470\pi$
$354$	358.496	−	2659.57i	0.0538245	−	0.399307i
$355$		0			0
$356$	−139.947	+	242.396i	−0.0208348	+	0.0360869i
$357$	−6865.97	+	2819.17i	−1.01789	+	0.417945i
$358$	2811.90	+	4870.35i	0.415122	+	0.719012i
$359$	−8334.50			−1.22529			−0.612644	−	0.790359i	$-0.709894\pi$
$359$	−8334.50			−1.22529			−0.612644	+	0.790359i	$0.709894\pi$
$360$		0			0
$361$	−4400.72			−0.641598
$362$	−2136.53	−	3700.57i	−0.310203	−	0.537287i
$363$	−2691.99	−	2078.88i	−0.389237	−	0.300586i
$364$	182.306	−	315.764i	0.0262512	−	0.0454685i
$365$		0			0
$366$	6228.51	+	4809.93i	0.889534	+	0.686937i
$367$	62.8805	+	108.912i	0.00894369	+	0.0154909i	0.870463	−	0.492235i	$-0.163820\pi$
$367$	62.8805	+	108.912i	0.00894369	+	0.0154909i	−0.861519	+	0.507725i	$0.830486\pi$
$368$	52.1713			0.00739026
$369$	−5530.00	+	5462.13i	−0.780164	+	0.770588i
$370$		0			0
$371$	1127.93	+	1953.63i	0.157841	+	0.273389i
$372$	1213.79	−	498.382i	0.169172	−	0.0694621i
$373$	−717.879	+	1243.40i	−0.0996525	+	0.172603i	−0.911541	−	0.411210i	$-0.865106\pi$
$373$	−717.879	+	1243.40i	−0.0996525	+	0.172603i	0.811888	+	0.583813i	$0.198440\pi$
$374$	−5522.63	+	9565.48i	−0.763552	+	1.32251i
$375$		0			0
$376$	7077.42	+	12258.5i	0.970718	+	1.68133i
$377$	−5320.21			−0.726803
$378$	−3479.26	−	4622.28i	−0.473422	−	0.628953i
$379$	−2125.04			−0.288010			−0.144005	−	0.989577i	$-0.545998\pi$
$379$	−2125.04			−0.288010			−0.144005	+	0.989577i	$0.545998\pi$
$380$		0			0
$381$	1264.38	−	9380.05i	0.170016	−	1.26130i
$382$	4557.54	−	7893.90i	0.610430	−	1.05730i
$383$	3530.38	−	6114.80i	0.471002	−	0.815800i	−0.528447	−	0.848966i	$-0.677226\pi$
$383$	3530.38	−	6114.80i	0.471002	−	0.815800i	0.999450	+	0.0331659i	$0.0105590\pi$
$384$	5661.30	−	2324.54i	0.752349	−	0.308915i
$385$		0			0
$386$	2191.22			0.288939
$387$	4.04123	+	15.4634i	0.000530820	+	0.00203113i
$388$	1537.51			0.201174
$389$	4909.56	+	8503.61i	0.639909	+	1.10836i	0.985452	+	0.169952i	$0.0543614\pi$
$389$	4909.56	+	8503.61i	0.639909	+	1.10836i	−0.345543	+	0.938403i	$0.612305\pi$
$390$		0			0
$391$	42.7544	−	74.0528i	0.00552988	−	0.00957803i
$392$	−1246.42	+	2158.85i	−0.160596	+	0.278160i
$393$	−979.859	−	756.691i	−0.125769	−	0.0971247i
$394$	−481.483	−	833.954i	−0.0615654	−	0.106634i
$395$		0			0
$396$	979.225	+	268.874i	0.124262	+	0.0341198i
$397$	10995.5			1.39005			0.695023	−	0.718987i	$-0.255394\pi$
$397$	10995.5			1.39005			0.695023	+	0.718987i	$0.255394\pi$
$398$	1790.07	+	3100.49i	0.225447	+	0.390486i
$399$	−3673.83	+	1508.48i	−0.460956	+	0.189269i
$400$		0			0
$401$	3265.90	−	5656.71i	0.406712	−	0.704446i	−0.587807	−	0.809001i	$-0.700009\pi$
$401$	3265.90	−	5656.71i	0.406712	−	0.704446i	0.994519	+	0.104555i	$0.0333419\pi$
$402$	−659.487	+	4892.53i	−0.0818215	+	0.607008i
$403$	−4192.01	−	7260.77i	−0.518161	−	0.897481i
$404$	968.415			0.119259
$405$		0			0
$406$	−7828.82			−0.956989
$407$	1288.51	+	2231.77i	0.156927	+	0.271805i
$408$	1521.70	−	11289.0i	0.184645	−	1.36983i
$409$	2502.67	−	4334.75i	0.302565	−	0.524058i	−0.674151	−	0.738593i	$-0.735490\pi$
$409$	2502.67	−	4334.75i	0.302565	−	0.524058i	0.976716	+	0.214535i	$0.0688238\pi$
$410$		0			0
$411$	9841.70	−	4041.01i	1.18116	−	0.484984i
$412$	−667.860	−	1156.77i	−0.0798619	−	0.138325i
$413$	2976.17			0.354596
$414$	64.2726	+	17.6479i	0.00763002	+	0.00209504i
$415$		0			0
$416$	532.880	+	922.975i	0.0628043	+	0.108780i
$417$	8962.87	+	6921.52i	1.05255	+	0.812826i
$418$	−2955.04	+	5118.27i	−0.345779	+	0.598907i
$419$	36.7472	−	63.6481i	0.00428453	−	0.00742103i	−0.863875	−	0.503706i	$-0.831970\pi$
$419$	36.7472	−	63.6481i	0.00428453	−	0.00742103i	0.868160	+	0.496285i	$0.165303\pi$
$420$		0			0
$421$	−2515.40	−	4356.81i	−0.291195	−	0.504365i	0.682897	−	0.730514i	$-0.260720\pi$
$421$	−2515.40	−	4356.81i	−0.291195	−	0.504365i	−0.974093	+	0.226149i	$0.927386\pi$
$422$	2857.58			0.329632
$423$	4084.57	+	15629.2i	0.469501	+	1.79650i
$424$	−3462.13			−0.396547
$425$		0			0
$426$	−4123.70	+	1693.20i	−0.469000	+	0.192572i
$427$	−4363.71	+	7558.17i	−0.494555	+	0.856594i
$428$	162.640	−	281.700i	0.0183680	−	0.0318143i
$429$	866.776	−	6430.34i	0.0975486	−	0.723683i
$430$		0			0
$431$	−1951.29			−0.218075			−0.109037	−	0.994038i	$-0.534777\pi$
$431$	−1951.29			−0.218075			−0.109037	+	0.994038i	$0.534777\pi$
$432$	7873.08	−	962.413i	0.876838	−	0.107185i
$433$	−3805.50			−0.422357			−0.211178	−	0.977448i	$-0.567730\pi$
$433$	−3805.50			−0.422357			−0.211178	+	0.977448i	$0.567730\pi$
$434$	−6168.64	−	10684.4i	−0.682268	−	1.18172i
$435$		0			0
$436$	−85.8812	+	148.751i	−0.00943340	+	0.0163391i
$437$	22.8769	−	39.6240i	0.00250424	−	0.00433747i
$438$	−8187.95	+	3361.98i	−0.893231	+	0.366762i
$439$	−5952.18	−	10309.5i	−0.647111	−	1.12083i	−0.983810	−	0.179217i	$-0.942644\pi$
$439$	−5952.18	−	10309.5i	−0.647111	−	1.12083i	0.336698	−	0.941613i	$-0.390690\pi$
$440$		0			0
$441$	−2024.05	+	1999.21i	−0.218557	+	0.215874i
$442$	−6946.29			−0.747514
$443$	4534.23	+	7853.51i	0.486292	+	0.842283i	0.999876	−	0.0157565i	$-0.00501565\pi$
$443$	4534.23	+	7853.51i	0.486292	+	0.842283i	−0.513583	+	0.858040i	$0.671682\pi$
$444$	−200.748	−	155.027i	−0.0214574	−	0.0165704i
$445$		0			0
$446$	2031.48	−	3518.63i	0.215681	−	0.373570i
$447$	−641.353	−	495.281i	−0.0678634	−	0.0524071i
$448$	4270.19	+	7396.18i	0.450329	+	0.779993i
$449$	7332.48			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$449$	7332.48			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$450$		0			0
$451$	−12827.9			−1.33934
$452$	−27.8594	−	48.2539i	−0.00289911	−	0.00502140i
$453$	7758.75	−	3185.75i	0.804720	−	0.330419i
$454$	5664.61	−	9811.40i	0.585580	−	1.01425i
$455$		0			0
$456$	814.226	−	6040.49i	0.0836176	−	0.620333i
$457$	−585.214	−	1013.62i	−0.0599019	−	0.103753i	0.834519	−	0.550979i	$-0.185745\pi$
$457$	−585.214	−	1013.62i	−0.0599019	−	0.103753i	−0.894421	+	0.447226i	$0.852412\pi$
$458$	−14810.5			−1.51103
$459$	5085.93	−	11963.9i	0.517191	−	1.21661i
$460$		0			0
$461$	7373.89	+	12771.9i	0.744981	+	1.29034i	0.950204	+	0.311629i	$0.100875\pi$
$461$	7373.89	+	12771.9i	0.744981	+	1.29034i	−0.205223	+	0.978715i	$0.565792\pi$
$462$	1275.48	−	9462.40i	0.128443	−	0.952881i
$463$	−1042.75	+	1806.10i	−0.104667	+	0.181289i	−0.913602	−	0.406609i	$-0.866711\pi$
$463$	−1042.75	+	1806.10i	−0.104667	+	0.181289i	0.808935	+	0.587898i	$0.200044\pi$
$464$	5366.60	−	9295.23i	0.536936	−	0.930000i
$465$		0			0
$466$	−8476.34	−	14681.4i	−0.842615	−	1.45945i
$467$	9943.76			0.985315			0.492658	−	0.870223i	$-0.336025\pi$
$467$	9943.76			0.985315			0.492658	+	0.870223i	$0.336025\pi$
$468$	161.475	+	617.869i	0.0159491	+	0.0610278i
$469$	−5474.95			−0.539040
$470$		0			0
$471$	−4065.34	−	3139.43i	−0.397709	−	0.307128i
$472$	−2283.81	+	3955.68i	−0.222714	+	0.385752i
$473$	−13.1887	+	22.8434i	−0.00128206	+	0.00222059i
$474$	3165.84	+	2444.80i	0.306776	+	0.236906i
$475$		0			0
$476$	1205.62			0.116092
$477$	−3810.13	−	1046.18i	−0.365731	−	0.100422i
$478$	6802.34			0.650903
$479$	1332.10	+	2307.26i	0.127067	+	0.220087i	0.922539	−	0.385904i	$-0.126110\pi$
$479$	1332.10	+	2307.26i	0.127067	+	0.220087i	−0.795472	+	0.605990i	$0.792777\pi$
$480$		0			0
$481$	−810.336	+	1403.54i	−0.0768153	+	0.133048i
$482$	−2743.84	+	4752.47i	−0.259292	+	0.449106i
$483$	−9.87436	+	73.2548i	−0.000930226	+	0.00690105i
$484$	276.240	+	478.463i	0.0259429	+	0.0449345i
$485$		0			0
$486$	10024.8	+	1477.56i	0.935669	+	0.137909i
$487$	−3071.50			−0.285797			−0.142898	−	0.989737i	$-0.545642\pi$
$487$	−3071.50			−0.285797			−0.142898	+	0.989737i	$0.545642\pi$
$488$	−6697.12	−	11599.8i	−0.621239	−	1.07602i
$489$	2064.43	−	15315.4i	0.190914	−	1.41633i
$490$		0			0
$491$	−8044.80	+	13934.0i	−0.739423	+	1.28072i	0.213332	+	0.976980i	$0.431568\pi$
$491$	−8044.80	+	13934.0i	−0.739423	+	1.28072i	−0.952755	+	0.303739i	$0.901765\pi$
$492$	1167.94	−	479.558i	0.107022	−	0.0439434i
$493$	−8795.86	−	15234.9i	−0.803541	−	1.39177i
$494$	−3716.80			−0.338516
$495$		0			0
$496$	16914.3			1.53119
$497$	−2471.87	−	4281.40i	−0.223096	−	0.386413i
$498$	−3136.05	−	2421.80i	−0.282189	−	0.217918i
$499$	−6030.29	+	10444.8i	−0.540987	+	0.937018i	0.457860	+	0.889024i	$0.348616\pi$
$499$	−6030.29	+	10444.8i	−0.540987	+	0.937018i	−0.998848	+	0.0479936i	$0.984717\pi$
$500$		0			0
$501$	−10030.5	−	7745.96i	−0.894467	−	0.690747i
$502$	3706.16	+	6419.25i	0.329510	+	0.570727i
$503$	1324.90			0.117444			0.0587222	−	0.998274i	$-0.481297\pi$
$503$	1324.90			0.117444			0.0587222	+	0.998274i	$0.481297\pi$
$504$	2489.79	+	9526.96i	0.220048	+	0.841993i
$505$		0			0
$506$	54.9995	+	95.2619i	0.00483207	+	0.00836939i
$507$	−6785.64	+	2786.19i	−0.594400	+	0.244061i
$508$	−768.710	+	1331.45i	−0.0671378	+	0.116286i
$509$	6060.53	−	10497.2i	0.527757	−	0.914102i	−0.471719	−	0.881749i	$-0.656366\pi$
$509$	6060.53	−	10497.2i	0.527757	−	0.914102i	0.999476	−	0.0323536i	$-0.0103003\pi$
$510$		0			0
$511$	−4908.10	−	8501.08i	−0.424895	−	0.735940i
$512$	−12850.4			−1.10920
$513$	2721.37	−	6401.60i	0.234213	−	0.550951i
$514$	−1141.60			−0.0979644
$515$		0			0
$516$	0.346810	−	2.57288i	2.95881e−5	−	0.000219505i
$517$	−13330.1	+	23088.4i	−1.13396	+	1.96408i
$518$	−1192.43	+	2065.35i	−0.101143	+	0.175186i
$519$	−12755.1	+	5237.26i	−1.07878	+	0.442948i
$520$		0			0
$521$	17997.6			1.51342			0.756708	−	0.653753i	$-0.226807\pi$
$521$	17997.6			1.51342			0.756708	+	0.653753i	$0.226807\pi$
$522$	9755.68	−	9635.94i	0.817997	−	0.807957i
$523$	6451.03			0.539357			0.269679	−	0.962950i	$-0.413083\pi$
$523$	6451.03			0.539357			0.269679	+	0.962950i	$0.413083\pi$
$524$	100.549	+	174.156i	0.00838263	+	0.0145191i
$525$		0			0
$526$	−5032.32	+	8716.23i	−0.417147	+	0.722520i
$527$	13861.2	−	24008.4i	1.14574	−	1.98448i
$528$	10360.5	+	8000.81i	0.853942	+	0.659452i
$529$	6083.07	+	10536.2i	0.499965	+	0.865965i
$530$		0			0
$531$	−3708.68	+	3663.16i	−0.303094	+	0.299374i
$532$	645.101			0.0525727
$533$	−4033.67	−	6986.53i	−0.327801	−	0.567768i
$534$	−4264.02	+	1750.81i	−0.345547	+	0.141882i
$535$		0			0
$536$	4201.28	−	7276.84i	0.338559	−	0.586402i
$537$	1459.29	−	10826.0i	0.117268	−	0.869973i
$538$	2648.64	+	4587.59i	0.212251	+	0.367630i
$539$	−4695.17			−0.375204
$540$		0			0
$541$	−520.899			−0.0413959			−0.0206980	−	0.999786i	$-0.506589\pi$
$541$	−520.899			−0.0413959			−0.0206980	+	0.999786i	$0.506589\pi$
$542$	−7570.03	−	13111.7i	−0.599927	−	1.03910i
$543$	−1108.79	+	8225.76i	−0.0876292	+	0.650094i
$544$	−1762.01	+	3051.89i	−0.138871	+	0.240531i
$545$		0			0
$546$	5554.65	−	2280.74i	0.435379	−	0.178767i
$547$	−4049.16	−	7013.36i	−0.316508	−	0.548207i	0.663249	−	0.748399i	$-0.269177\pi$
$547$	−4049.16	−	7013.36i	−0.316508	−	0.548207i	−0.979757	+	0.200191i	$0.935844\pi$
$548$	−1728.14			−0.134713
$549$	−3865.09	−	14789.4i	−0.300470	−	1.14972i
$550$		0			0
$551$	−4706.47	−	8151.84i	−0.363888	−	0.630273i
$552$	−89.7868	−	69.3373i	−0.00692315	−	0.00534636i
$553$	−2218.00	+	3841.68i	−0.170559	+	0.295416i
$554$	−8251.99	+	14292.9i	−0.632840	+	1.09611i
$555$		0			0
$556$	−919.730	−	1593.02i	−0.0701533	−	0.121509i
$557$	−6687.22			−0.508701			−0.254351	−	0.967112i	$-0.581862\pi$
$557$	−6687.22			−0.508701			−0.254351	+	0.967112i	$0.581862\pi$
$558$	20837.6	+	5721.55i	1.58087	+	0.434072i
$559$	−16.5885			−0.00125513
$560$		0			0
$561$	19846.9	−	8149.15i	1.49365	−	0.613293i
$562$	−4471.98	+	7745.69i	−0.335657	+	0.581374i
$563$	−1213.77	+	2102.31i	−0.0908602	+	0.157375i	−0.907873	−	0.419245i	$-0.862295\pi$
$563$	−1213.77	+	2102.31i	−0.0908602	+	0.157375i	0.817013	+	0.576619i	$0.195628\pi$
$564$	350.530	−	2600.47i	0.0261701	−	0.194148i
$565$		0			0
$566$	−13651.7			−1.01382
$567$	−138.779	+	11236.9i	−0.0102790	+	0.832286i
$568$	7587.30			0.560486
$569$	−1276.83	−	2211.53i	−0.0940727	−	0.162939i	0.815149	−	0.579252i	$-0.196655\pi$
$569$	−1276.83	−	2211.53i	−0.0940727	−	0.162939i	−0.909221	+	0.416313i	$0.863322\pi$
$570$		0			0
$571$	−4518.07	+	7825.53i	−0.331130	+	0.573535i	−0.982734	−	0.185025i	$-0.940763\pi$
$571$	−4518.07	+	7825.53i	−0.331130	+	0.573535i	0.651603	+	0.758560i	$0.274097\pi$
$572$	−526.977	+	912.752i	−0.0385210	+	0.0667204i
$573$	−16378.6	+	6725.07i	−1.19411	+	0.490303i
$574$	−5935.65	−	10280.8i	−0.431619	−	0.747585i
$575$		0			0
$576$	−14424.6	−	3960.69i	−1.04345	−	0.286508i
$577$	5427.02			0.391560			0.195780	−	0.980648i	$-0.437276\pi$
$577$	5427.02			0.391560			0.195780	+	0.980648i	$0.437276\pi$
$578$	−4912.95	−	8509.48i	−0.353550	−	0.612366i
$579$	−3368.75	−	2601.50i	−0.241797	−	0.186726i
$580$		0			0
$581$	2197.13	−	3805.54i	0.156889	−	0.271739i
$582$	20040.6	+	15476.2i	1.42733	+	1.10225i
$583$	−3260.41	−	5647.20i	−0.231616	−	0.401171i
$584$	15065.2			1.06747
$585$		0			0
$586$	11048.8			0.778874
$587$	−2669.69	−	4624.04i	−0.187717	−	0.325136i	0.756772	−	0.653679i	$-0.226776\pi$
$587$	−2669.69	−	4624.04i	−0.187717	−	0.325136i	−0.944489	+	0.328544i	$0.893442\pi$
$588$	427.482	−	175.525i	0.0299814	−	0.0123104i
$589$	7416.84	−	12846.3i	0.518855	−	0.898683i
$590$		0			0
$591$	−249.874	+	1853.74i	−0.0173916	+	0.129023i
$592$	−1634.80	−	2831.56i	−0.113497	−	0.196582i
$593$	4617.67			0.319772			0.159886	−	0.987135i	$-0.448887\pi$
$593$	4617.67			0.319772			0.159886	+	0.987135i	$0.448887\pi$
$594$	10057.2	+	13361.2i	0.694700	+	0.922926i
$595$		0			0
$596$	65.8128	+	113.991i	0.00452315	+	0.00783432i
$597$	928.988	−	6891.87i	0.0636867	−	0.472472i
$598$	−34.5888	+	59.9095i	−0.00236529	+	0.00409680i
$599$	−5444.19	+	9429.61i	−0.371358	+	0.643211i	−0.989775	−	0.142639i	$-0.954441\pi$
$599$	−5444.19	+	9429.61i	−0.371358	+	0.643211i	0.618417	+	0.785850i	$0.287774\pi$
$600$		0			0
$601$	5636.61	+	9762.89i	0.382566	+	0.662623i	0.991428	−	0.130653i	$-0.0417072\pi$
$601$	5636.61	+	9762.89i	0.382566	+	0.662623i	−0.608863	+	0.793276i	$0.708374\pi$
$602$	−24.4104			−0.00165264
$603$	6822.47	−	6738.73i	0.460750	−	0.455095i
$604$	−1362.39			−0.0917795
$605$		0			0
$606$	12622.7	+	9747.81i	0.846142	+	0.653428i
$607$	−5112.34	+	8854.84i	−0.341851	+	0.592103i	−0.984776	−	0.173825i	$-0.944387\pi$
$607$	−5112.34	+	8854.84i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$608$	−942.813	+	1633.00i	−0.0628884	+	0.108926i
$609$	12035.9	+	9294.65i	0.800852	+	0.618453i
$610$		0			0
$611$	−16766.4			−1.11014
$612$	−1502.36	+	1483.92i	−0.0992306	+	0.0980126i
$613$	−7119.74			−0.469109			−0.234554	−	0.972103i	$-0.575363\pi$
$613$	−7119.74			−0.469109			−0.234554	+	0.972103i	$0.575363\pi$
$614$	4524.23	+	7836.20i	0.297367	+	0.515054i
$615$		0			0
$616$	−8125.50	+	14073.8i	−0.531470	+	0.920533i
$617$	−2679.48	+	4640.99i	−0.174832	+	0.302819i	−0.940103	−	0.340890i	$-0.889272\pi$
$617$	−2679.48	+	4640.99i	−0.174832	+	0.302819i	0.765271	+	0.643708i	$0.222605\pi$
$618$	2938.56	−	21800.3i	0.191272	−	1.41899i
$619$	10798.6	+	18703.7i	0.701183	+	1.21448i	0.968051	+	0.250752i	$0.0806777\pi$
$619$	10798.6	+	18703.7i	0.701183	+	1.21448i	−0.266869	+	0.963733i	$0.585989\pi$
$620$		0			0
$621$	−77.8595	−	103.438i	−0.00503123	−	0.00668411i
$622$	−16107.1			−1.03832
$623$	−2555.98	−	4427.08i	−0.164371	−	0.284699i
$624$	−1099.73	+	8158.52i	−0.0705517	+	0.523401i
$625$		0			0
$626$	−13633.4	+	23613.7i	−0.870447	+	1.50766i
$627$	10619.6	−	4360.43i	0.676406	−	0.277733i
$628$	417.167	+	722.554i	0.0265076	+	0.0459125i
$629$	−5358.89			−0.339703
$630$		0			0
$631$	−1384.23			−0.0873305			−0.0436652	−	0.999046i	$-0.513903\pi$
$631$	−1384.23			−0.0873305			−0.0436652	+	0.999046i	$0.513903\pi$
$632$	−3404.03	−	5895.95i	−0.214248	−	0.371089i
$633$	−4393.20	−	3392.62i	−0.275851	−	0.213025i
$634$	7223.47	−	12511.4i	0.452493	−	0.783741i
$635$		0			0
$636$	507.967	+	392.274i	0.0316701	+	0.0244571i
$637$	−1476.38	−	2557.16i	−0.0918309	−	0.159056i
$638$	22630.1			1.40429
$639$	8349.93	+	2292.71i	0.516930	+	0.141938i
$640$		0			0
$641$	811.571	+	1405.68i	0.0500080	+	0.0866164i	0.889946	−	0.456066i	$-0.150742\pi$
$641$	811.571	+	1405.68i	0.0500080	+	0.0866164i	−0.839938	+	0.542683i	$0.817409\pi$
$642$	4955.43	−	2034.71i	0.304635	−	0.125083i
$643$	−14085.4	+	24396.6i	−0.863879	+	1.49628i	0.00427672	+	0.999991i	$0.498639\pi$
$643$	−14085.4	+	24396.6i	−0.863879	+	1.49628i	−0.868156	+	0.496292i	$0.834695\pi$
$644$	6.00335	−	10.3981i	0.000367337	−	0.000636247i
$645$		0			0
$646$	−6144.96	−	10643.4i	−0.374257	−	0.648233i
$647$	−16695.3			−1.01447			−0.507235	−	0.861808i	$-0.669332\pi$
$647$	−16695.3			−1.01447			−0.507235	+	0.861808i	$0.669332\pi$
$648$	−14828.7	−	8807.27i	−0.898958	−	0.533923i
$649$	−8602.97			−0.520333
$650$		0			0
$651$	−3201.33	+	23749.6i	−0.192734	+	1.42983i
$652$	−1255.12	+	2173.93i	−0.0753901	+	0.130580i
$653$	−2244.98	+	3888.42i	−0.134537	+	0.233025i	−0.925421	−	0.378942i	$-0.876288\pi$
$653$	−2244.98	+	3888.42i	−0.134537	+	0.233025i	0.790883	+	0.611967i	$0.209621\pi$
$654$	−2616.69	+	1074.42i	−0.156454	+	0.0642401i
$655$		0			0
$656$	16275.4			0.968669
$657$	16579.5	+	4552.37i	0.984516	+	0.270327i
$658$	−24672.2			−1.46173
$659$	7650.45	+	13251.0i	0.452229	+	0.783284i	0.998524	−	0.0543086i	$-0.0172955\pi$
$659$	7650.45	+	13251.0i	0.452229	+	0.783284i	−0.546295	+	0.837593i	$0.683962\pi$
$660$		0			0
$661$	10317.4	−	17870.3i	0.607113	−	1.05155i	−0.384600	−	0.923083i	$-0.625661\pi$
$661$	10317.4	−	17870.3i	0.607113	−	1.05155i	0.991714	−	0.128468i	$-0.0410059\pi$
$662$	3080.20	−	5335.06i	0.180839	−	0.313222i
$663$	10679.1	+	8246.88i	0.625554	+	0.483080i
$664$	3372.00	+	5840.47i	0.197077	+	0.341347i
$665$		0			0
$666$	−1056.18	−	4041.36i	−0.0614504	−	0.235134i
$667$	−175.195			−0.0101703
$668$	1029.28	+	1782.77i	0.0596169	+	0.103259i
$669$	−7300.61	+	2997.64i	−0.421910	+	0.173237i
$670$		0			0
$671$	12613.8	−	21847.8i	0.725709	−	1.25697i
$672$	406.946	−	3019.01i	0.0233606	−	0.173305i
$673$	8776.92	+	15202.1i	0.502712	+	0.870723i	0.999995	+	0.00313453i	$0.000997755\pi$
$673$	8776.92	+	15202.1i	0.502712	+	0.870723i	−0.497283	+	0.867588i	$0.665669\pi$
$674$	−25590.5			−1.46248
$675$		0			0
$676$	1191.52			0.0677922
$677$	−7591.32	−	13148.6i	−0.430958	−	0.746440i	0.565998	−	0.824406i	$-0.308491\pi$
$677$	−7591.32	−	13148.6i	−0.430958	−	0.746440i	−0.996956	+	0.0779659i	$0.975157\pi$
$678$	122.581	−	909.387i	0.00694348	−	0.0515115i
$679$	−14040.5	+	24318.8i	−0.793556	+	1.37448i
$680$		0			0
$681$	−20357.1	+	8358.65i	−1.14550	+	0.470344i
$682$	17831.2	+	30884.5i	1.00116	+	1.73406i
$683$	1735.90			0.0972510			0.0486255	−	0.998817i	$-0.484516\pi$
$683$	1735.90			0.0972510			0.0486255	+	0.998817i	$0.484516\pi$
$684$	−803.877	+	794.010i	−0.0449371	+	0.0443856i
$685$		0			0
$686$	−9244.67	−	16012.2i	−0.514523	−	0.891181i
$687$	22769.5	+	17583.6i	1.26450	+	0.976501i
$688$	16.7331	−	28.9827i	0.000927246	−	0.00160604i
$689$	2050.45	−	3551.48i	0.113376	−	0.196373i
$690$		0			0
$691$	13824.0	+	23943.8i	0.761055	+	1.31819i	0.942307	+	0.334750i	$0.108652\pi$
$691$	13824.0	+	23943.8i	0.761055	+	1.31819i	−0.181252	+	0.983437i	$0.558015\pi$
$692$	2239.72			0.123037
$693$	−13195.0	+	13033.0i	−0.723285	+	0.714408i
$694$	218.076			0.0119280
$695$		0			0
$696$	−21589.6	+	8864.70i	−1.17579	+	0.482781i
$697$	13337.7	−	23101.5i	0.724822	−	1.25543i
$698$	−125.155	+	216.775i	−0.00678682	+	0.0117551i
$699$	−4398.95	+	32634.4i	−0.238031	+	1.76588i
$700$		0			0
$701$	19116.9			1.03001			0.515005	−	0.857187i	$-0.327790\pi$
$701$	19116.9			1.03001			0.515005	+	0.857187i	$0.327790\pi$
$702$	−4114.57	+	9678.91i	−0.221217	+	0.520380i
$703$	−2867.42			−0.153836
$704$	−12343.5	−	21379.5i	−0.660812	−	1.14456i
$705$		0			0
$706$	8928.58	−	15464.8i	0.475965	−	0.824396i
$707$	−8843.51	+	15317.4i	−0.470430	+	0.814809i
$708$	783.277	−	321.614i	0.0415782	−	0.0170720i
$709$	5022.64	+	8699.47i	0.266050	+	0.460812i	0.967838	−	0.251574i	$-0.0809481\pi$
$709$	5022.64	+	8699.47i	0.266050	+	0.460812i	−0.701788	+	0.712385i	$0.747615\pi$
$710$		0			0
$711$	−1964.56	−	7517.19i	−0.103624	−	0.396507i
$712$	7845.47			0.412952
$713$	−138.043	−	239.098i	−0.00725070	−	0.0125586i
$714$	15714.6	+	12135.5i	0.823673	+	0.636077i
$715$		0			0
$716$	−887.207	+	1536.69i	−0.0463080	+	0.0802077i
$717$	−10457.8	−	8075.97i	−0.544705	−	0.420645i
$718$	11147.7	+	19308.3i	0.579425	+	1.00359i
$719$	22559.7			1.17014			0.585072	−	0.810981i	$-0.301066\pi$
$719$	22559.7			1.17014			0.585072	+	0.810981i	$0.301066\pi$
$720$		0			0
$721$	24395.4			1.26010
$722$	5886.10	+	10195.0i	0.303404	+	0.525512i
$723$	9860.64	−	4048.79i	0.507222	−	0.208266i
$724$	674.114	−	1167.60i	0.0346040	−	0.0599358i
$725$		0			0
$726$	−1215.45	+	9017.03i	−0.0621343	+	0.460955i
$727$	−1834.04	−	3176.64i	−0.0935635	−	0.162057i	0.815445	−	0.578835i	$-0.196492\pi$
$727$	−1834.04	−	3176.64i	−0.0935635	−	0.162057i	−0.909008	+	0.416778i	$0.863159\pi$
$728$	−10220.1			−0.520307
$729$	−13657.8	−	14173.4i	−0.693887	−	0.720084i
$730$		0			0
$731$	−27.4256	−	47.5026i	−0.00138765	−	0.00240348i
$732$	−331.694	+	2460.74i	−0.0167483	+	0.124251i
$733$	15714.2	−	27217.8i	0.791838	−	1.37150i	−0.132989	−	0.991117i	$-0.542458\pi$
$733$	15714.2	−	27217.8i	0.791838	−	1.37150i	0.924828	−	0.380387i	$-0.124209\pi$
$734$	168.209	−	291.347i	0.00845875	−	0.0146510i
$735$		0			0
$736$	17.5478	+	30.3936i	0.000878830	+	0.00152218i
$737$	15826.0			0.790987
$738$	20050.5	+	5505.44i	1.00009	+	0.274604i
$739$	17467.0			0.869465			0.434732	−	0.900560i	$-0.356843\pi$
$739$	17467.0			0.869465			0.434732	+	0.900560i	$0.356843\pi$
$740$		0			0
$741$	5714.15	+	4412.72i	0.283286	+	0.218766i
$742$	3017.28	−	5226.09i	0.149283	−	0.258566i
$743$	12496.7	−	21644.9i	0.617038	−	1.06874i	−0.372985	−	0.927837i	$-0.621666\pi$
$743$	12496.7	−	21644.9i	0.617038	−	1.06874i	0.990023	−	0.140904i	$-0.0450010\pi$
$744$	−29109.4	−	22479.6i	−1.43441	−	1.10772i
$745$		0			0
$746$	3840.74			0.188498
$747$	1946.07	+	7446.47i	0.0953187	+	0.364728i
$748$	−3484.99			−0.170353
$749$	2970.43	+	5144.94i	0.144910	+	0.250991i
$750$		0			0
$751$	4674.02	−	8095.64i	0.227107	−	0.393361i	−0.729842	−	0.683615i	$-0.760407\pi$
$751$	4674.02	−	8095.64i	0.227107	−	0.393361i	0.956950	+	0.290254i	$0.0937399\pi$
$752$	16912.6	−	29293.5i	0.820132	−	1.42051i
$753$	1923.38	−	14268.9i	0.0930833	−	0.690556i
$754$	7115.95	+	12325.2i	0.343697	+	0.595301i
$755$		0			0
$756$	714.140	−	1679.91i	0.0343558	−	0.0808169i
$757$	−11708.4			−0.562153			−0.281076	−	0.959685i	$-0.590691\pi$
$757$	−11708.4			−0.562153			−0.281076	+	0.959685i	$0.590691\pi$
$758$	2842.31	+	4923.02i	0.136197	+	0.235900i
$759$	28.5430	−	211.751i	0.00136501	−	0.0101266i
$760$		0			0
$761$	−9705.34	+	16810.1i	−0.462310	+	0.800745i	−0.999076	−	0.0429866i	$-0.986313\pi$
$761$	−9705.34	+	16810.1i	−0.462310	+	0.800745i	0.536765	+	0.843732i	$0.319646\pi$
$762$	−23421.6	+	9616.95i	−1.11349	+	0.457199i
$763$	−1568.52	−	2716.76i	−0.0744225	−	0.128904i
$764$	2875.98			0.136190
$765$		0			0
$766$	−18888.0			−0.890927
$767$	−2705.17	−	4685.50i	−0.127351	−	0.220578i
$768$	5270.28	+	4069.94i	0.247624	+	0.191226i
$769$	4928.83	−	8536.98i	0.231129	−	0.400327i	−0.727012	−	0.686625i	$-0.759091\pi$
$769$	4928.83	−	8536.98i	0.231129	−	0.400327i	0.958141	+	0.286298i	$0.0924247\pi$
$770$		0			0
$771$	1755.07	+	1355.34i	0.0819811	+	0.0633094i
$772$	345.686	+	598.746i	0.0161160	+	0.0279137i
$773$	−27574.5			−1.28303			−0.641517	−	0.767108i	$-0.721695\pi$
$773$	−27574.5			−1.28303			−0.641517	+	0.767108i	$0.721695\pi$
$774$	30.4183	−	30.0450i	0.00141262	−	0.00139528i
$775$		0			0
$776$	−21548.4	−	37322.9i	−0.996831	−	1.72656i
$777$	4285.27	−	1759.54i	0.197855	−	0.0812395i
$778$	13133.4	−	22747.7i	0.605212	−	1.04826i
$779$	7136.70	−	12361.1i	0.328240	−	0.568528i
$780$		0			0
$781$	7145.22	+	12375.9i	0.327370	+	0.567022i
$782$	−228.741			−0.0104601
$783$	−26438.3	+	3231.85i	−1.20668	+	0.147505i
$784$	5957.01			0.271365
$785$		0			0
$786$	−442.411	+	3282.11i	−0.0200767	+	0.148943i
$787$	−5888.51	+	10199.2i	−0.266712	+	0.461959i	−0.968011	−	0.250908i	$-0.919271\pi$
$787$	−5888.51	+	10199.2i	−0.266712	+	0.461959i	0.701298	+	0.712868i	$0.252604\pi$
$788$	151.917	−	263.128i	0.00686779	−	0.0118954i
$789$	18084.8	−	7425.64i	0.816016	−	0.335057i
$790$		0			0
$791$	1017.64			0.0457436
$792$	−7197.04	−	27538.8i	−0.322898	−	1.23554i
$793$	15865.5			0.710466
$794$	−14706.8	−	25473.0i	−0.657338	−	1.13854i
$795$		0			0
$796$	−564.800	+	978.263i	−0.0251493	+	0.0435598i
$797$	−12329.9	+	21356.0i	−0.547990	+	0.949146i	0.450422	+	0.892816i	$0.351273\pi$
$797$	−12329.9	+	21356.0i	−0.547990	+	0.949146i	−0.998412	+	0.0563307i	$0.982060\pi$
$798$	8408.51	+	6493.42i	0.373005	+	0.288051i
$799$	−27719.8	−	48012.1i	−1.22735	−	2.12584i
$800$		0			0
$801$	8634.05	+	2370.72i	0.380860	+	0.104576i
$802$	−17473.0			−0.769318
$803$	14187.4	+	24573.3i	0.623491	+	1.07992i
$804$	−1440.91	+	591.640i	−0.0632053	+	0.0259521i
$805$		0			0
$806$	−11213.9	+	19423.0i	−0.490065	+	0.848818i
$807$	1374.56	−	10197.4i	0.0599589	−	0.444817i
$808$	−13572.4	−	23508.1i	−0.590935	−	1.02353i
$809$	19263.0			0.837144			0.418572	−	0.908184i	$-0.362531\pi$
$809$	19263.0			0.837144			0.418572	+	0.908184i	$0.362531\pi$
$810$		0			0
$811$	−13597.4			−0.588741			−0.294370	−	0.955691i	$-0.595110\pi$
$811$	−13597.4			−0.588741			−0.294370	+	0.955691i	$0.595110\pi$
$812$	−1235.07	−	2139.20i	−0.0533774	−	0.0924524i
$813$	−3928.60	+	29145.1i	−0.169474	+	1.25727i
$814$	3446.85	−	5970.12i	0.148418	−	0.257067i
$815$		0			0
$816$	−25180.8	+	10339.3i	−1.08027	+	0.443562i
$817$	−14.6748	−	25.4176i	−0.000628406	−	0.00108843i
$818$	−13389.6			−0.572318
$819$	−11247.4	−	3088.29i	−0.479873	−	0.131763i
$820$		0			0
$821$	−14336.8	−	24832.1i	−0.609449	−	1.05560i	−0.991331	−	0.131386i	$-0.958057\pi$
$821$	−14336.8	−	24832.1i	−0.609449	−	1.05560i	0.381882	−	0.924211i	$-0.375276\pi$
$822$	−22525.3	−	17395.0i	−0.955790	−	0.738103i
$823$	4218.81	−	7307.19i	0.178686	−	0.309493i	−0.762745	−	0.646700i	$-0.776149\pi$
$823$	4218.81	−	7307.19i	0.178686	−	0.309493i	0.941431	+	0.337207i	$0.109482\pi$
$824$	−18720.2	+	32424.3i	−0.791443	+	1.37082i
$825$		0			0
$826$	−3980.73	−	6894.82i	−0.167684	−	0.290438i
$827$	11315.7			0.475799			0.237900	−	0.971290i	$-0.423541\pi$
$827$	11315.7			0.475799			0.237900	+	0.971290i	$0.423541\pi$
$828$	5.31738	+	20.3464i	0.000223178	+	0.000853971i
$829$	6773.57			0.283783			0.141891	−	0.989882i	$-0.454682\pi$
$829$	6773.57			0.283783			0.141891	+	0.989882i	$0.454682\pi$
$830$		0			0
$831$	29655.5	−	12176.6i	1.23795	−	0.508304i
$832$	7762.72	−	13445.4i	0.323466	−	0.560260i
$833$	4881.77	−	8455.47i	0.203053	−	0.351698i
$834$	4046.78	−	30021.8i	0.168020	−	1.24649i
$835$		0			0
$836$	−1864.74			−0.0771452
$837$	−25242.5	−	33535.3i	−1.04242	−	1.38489i
$838$	−196.602			−0.00810443
$839$	−4456.94	−	7719.65i	−0.183398	−	0.317654i	0.759638	−	0.650347i	$-0.225376\pi$
$839$	−4456.94	−	7719.65i	−0.183398	−	0.317654i	−0.943035	+	0.332692i	$0.892043\pi$
$840$		0			0
$841$	−5826.91	+	10092.5i	−0.238916	+	0.413814i
$842$	−6728.87	+	11654.7i	−0.275406	+	0.477018i
$843$	16071.1	−	6598.81i	0.656605	−	0.269603i
$844$	450.810	+	780.826i	0.0183857	+	0.0318450i
$845$		0			0
$846$	30744.6	−	30367.2i	1.24943	−	1.23410i
$847$	−10090.4			−0.409341
$848$	4136.66	+	7164.90i	0.167516	+	0.290146i
$849$	20987.9	+	16207.8i	0.848414	+	0.655182i
$850$		0			0
$851$	−26.6844	+	46.2187i	−0.00107489	+	0.00186176i
$852$	−1113.21	−	859.673i	−0.0447630	−	0.0345680i
$853$	15834.6	+	27426.4i	0.635600	+	1.10089i	0.986388	+	0.164437i	$0.0525806\pi$
$853$	15834.6	+	27426.4i	0.635600	+	1.10089i	−0.350787	+	0.936455i	$0.614086\pi$
$854$	23346.4			0.935478
$855$		0			0
$856$	−9117.63			−0.364059
$857$	22027.4	+	38152.6i	0.877995	+	1.52073i	0.853538	+	0.521031i	$0.174452\pi$
$857$	22027.4	+	38152.6i	0.877995	+	1.52073i	0.0244574	+	0.999701i	$0.492214\pi$
$858$	−16056.3	+	6592.75i	−0.638875	+	0.262323i
$859$	−9534.70	+	16514.6i	−0.378719	+	0.655961i	−0.990876	−	0.134775i	$-0.956969\pi$
$859$	−9534.70	+	16514.6i	−0.378719	+	0.655961i	0.612157	+	0.790736i	$0.290302\pi$
$860$		0			0
$861$	−3080.41	+	22852.6i	−0.121928	+	0.904547i
$862$	2609.91	+	4520.50i	0.103125	+	0.178618i
$863$	−6256.14			−0.246769			−0.123384	−	0.992359i	$-0.539375\pi$
$863$	−6256.14			−0.246769			−0.123384	+	0.992359i	$0.539375\pi$
$864$	3208.78	+	4262.94i	0.126348	+	0.167857i
$865$		0			0
$866$	5089.97	+	8816.09i	0.199728	+	0.345939i
$867$	−2549.66	+	18915.2i	−0.0998744	+	0.740937i
$868$	1946.32	−	3371.13i	0.0761089	−	0.131824i
$869$	6411.38	−	11104.8i	0.250277	−	0.433493i
$870$		0			0
$871$	4976.42	+	8619.41i	0.193593	+	0.335313i
$872$	4814.52			0.186973
$873$	−12436.1	−	47585.8i	−0.482130	−	1.84483i
$874$	−122.394			−0.00473690
$875$		0			0
$876$	−2210.38	−	1706.95i	−0.0852532	−	0.0658362i
$877$	−3478.73	+	6025.33i	−0.133943	+	0.231997i	−0.925193	−	0.379496i	$-0.876097\pi$
$877$	−3478.73	+	6025.33i	−0.133943	+	0.231997i	0.791250	+	0.611493i	$0.209431\pi$
$878$	−15922.5	+	27578.5i	−0.612024	+	1.06006i
$879$	−16986.2	−	13117.5i	−0.651797	−	0.503346i
$880$		0			0
$881$	10626.4			0.406371			0.203186	−	0.979140i	$-0.434871\pi$
$881$	10626.4			0.406371			0.203186	+	0.979140i	$0.434871\pi$
$882$	7338.76	+	2015.06i	0.280169	+	0.0769283i
$883$	−31013.5			−1.18198			−0.590990	−	0.806679i	$-0.701263\pi$
$883$	−31013.5			−1.18198			−0.590990	+	0.806679i	$0.701263\pi$
$884$	−1095.84	−	1898.06i	−0.0416936	−	0.0722155i
$885$		0			0
$886$	12129.3	−	21008.6i	0.459925	−	0.796613i
$887$	4698.69	−	8138.36i	0.177865	−	0.308072i	−0.763284	−	0.646063i	$-0.776414\pi$
$887$	4698.69	−	8138.36i	0.177865	−	0.308072i	0.941149	+	0.337992i	$0.109748\pi$
$888$	−949.740	+	7045.83i	−0.0358910	+	0.266264i
$889$	−14039.6	−	24317.4i	−0.529667	−	0.917410i
$890$		0			0
$891$	401.158	−	32481.6i	0.0150834	−	1.22130i
$892$	1281.94			0.0481195
$893$	−14832.2	−	25690.2i	−0.555814	−	0.962697i
$894$	−289.574	+	2148.26i	−0.0108331	+	0.0803675i
$895$		0			0
$896$	9077.97	−	15723.5i	0.338475	−	0.586256i
$897$	124.303	−	51.0389i	0.00462693	−	0.00189982i
$898$	−9807.42	−	16987.0i	−0.364452	−	0.631250i
$899$	−56799.2			−2.10718
$900$		0			0
$901$	13560.0			0.501385
$902$	17157.7	+	29718.0i	0.633357	+	1.09701i
$903$	37.5281	+	28.9808i	0.00138301	+	0.00106802i
$904$	−780.903	+	1352.56i	−0.0287306	+	0.0497628i
$905$		0			0
$906$	−17757.9	−	13713.5i	−0.651178	−	0.502869i
$907$	−13780.2	−	23868.1i	−0.504482	−	0.873788i	−0.999987	−	0.00518301i	$-0.998350\pi$
$907$	−13780.2	−	23868.1i	−0.504482	−	0.873788i	0.495505	−	0.868605i	$-0.334983\pi$
$908$	3574.58			0.130646
$909$	−7833.00	−	29972.2i	−0.285813	−	1.09364i
$910$		0			0
$911$	17935.0	+	31064.4i	0.652266	+	1.12976i	0.982572	+	0.185884i	$0.0595148\pi$
$911$	17935.0	+	31064.4i	0.652266	+	1.12976i	−0.330306	+	0.943874i	$0.607152\pi$
$912$	−13473.7	+	5532.31i	−0.489208	+	0.200869i
$913$	−6351.06	+	11000.4i	−0.230218	+	0.398750i
$914$	−1565.49	+	2711.50i	−0.0566539	+	0.0981274i
$915$		0			0
$916$	−2336.50	−	4046.94i	−0.0842798	−	0.145977i
$917$	−3672.82			−0.132265
$918$	−34519.0	+	4219.63i	−1.24106	+	0.151709i
$919$	3081.79			0.110619			0.0553095	−	0.998469i	$-0.482385\pi$
$919$	3081.79			0.110619			0.0553095	+	0.998469i	$0.482385\pi$
$920$		0			0
$921$	2347.93	−	17418.6i	0.0840032	−	0.623194i
$922$	19725.6	−	34165.8i	0.704586	−	1.22038i
$923$	−4493.58	+	7783.11i	−0.160247	+	0.277556i
$924$	2786.80	−	1144.26i	0.0992195	−	0.0407396i
$925$		0			0
$926$	5578.86			0.197984
$927$	−30399.7	+	30026.6i	−1.07709	+	1.06387i
$928$	7220.20			0.255404
$929$	2135.02	+	3697.96i	0.0754011	+	0.130599i	0.901261	−	0.433277i	$-0.142643\pi$
$929$	2135.02	+	3697.96i	0.0754011	+	0.130599i	−0.825860	+	0.563876i	$0.809310\pi$
$930$		0			0
$931$	2612.13	−	4524.33i	0.0919538	−	0.159269i
$932$	2674.44	−	4632.27i	0.0939961	−	0.162806i
$933$	24762.9	+	19123.0i	0.868917	+	0.671016i
$934$	−13300.1	−	23036.4i	−0.465945	−	0.807040i
$935$		0			0
$936$	12735.6	−	12579.2i	0.444738	−	0.439279i
$937$	49225.3			1.71624			0.858122	−	0.513446i	$-0.171631\pi$
$937$	49225.3			1.71624			0.858122	+	0.513446i	$0.171631\pi$
$938$	7322.92	+	12683.7i	0.254906	+	0.441510i
$939$	48994.8	−	20117.3i	1.70275	−	0.699152i
$940$		0			0
$941$	−17284.9	+	29938.3i	−0.598800	+	1.03715i	0.394199	+	0.919025i	$0.371022\pi$
$941$	−17284.9	+	29938.3i	−0.598800	+	1.03715i	−0.992999	+	0.118127i	$0.962311\pi$
$942$	−1835.52	+	13617.1i	−0.0634867	+	0.470988i
$943$	−132.829	−	230.067i	−0.00458697	−	0.00794486i
$944$	10915.1			0.376329
$945$		0			0
$946$	70.5610			0.00242509
$947$	−13671.2	−	23679.2i	−0.469117	−	0.812534i	0.530260	−	0.847835i	$-0.322094\pi$
$947$	−13671.2	−	23679.2i	−0.469117	−	0.812534i	−0.999377	+	0.0353008i	$0.988761\pi$
$948$	−168.594	+	1250.75i	−0.00577604	+	0.0428506i
$949$	−8922.37	+	15454.0i	−0.305197	+	0.528618i
$950$		0			0
$951$	−25959.2	+	10658.9i	−0.885158	+	0.363447i
$952$	−16896.9	−	29266.2i	−0.575242	−	0.996349i
$953$	45941.5			1.56158			0.780792	−	0.624791i	$-0.214816\pi$
$953$	45941.5			1.56158			0.780792	+	0.624791i	$0.214816\pi$
$954$	2672.51	+	10226.1i	0.0906979	+	0.347047i
$955$		0			0
$956$	1073.13	+	1858.72i	0.0363050	+	0.0628822i
$957$	−34791.1	−	26867.2i	−1.17517	−	0.907518i
$958$	3563.45	−	6172.08i	0.120177	−	0.208153i
$959$	15781.3	−	27334.0i	0.531391	−	0.920397i
$960$		0			0
$961$	−29858.9	−	51717.1i	−1.00228	−	1.73600i
$962$	4335.40			0.145300
$963$	−10034.1	−	2755.14i	−0.335767	−	0.0921944i
$964$	−1731.47			−0.0578494
$965$		0			0
$966$	182.915	−	75.1050i	0.00609232	−	0.00250151i
$967$	23669.4	−	40996.6i	0.787132	−	1.36335i	−0.140585	−	0.990069i	$-0.544898\pi$
$967$	23669.4	−	40996.6i	0.787132	−	1.36335i	0.927717	−	0.373284i	$-0.121768\pi$
$968$	7743.05	−	13411.4i	0.257098	−	0.445307i
$969$	−3189.04	+	23658.5i	−0.105724	+	0.784334i
$970$		0			0
$971$	50168.3			1.65806			0.829031	−	0.559202i	$-0.188893\pi$
$971$	50168.3			1.65806			0.829031	+	0.559202i	$0.188893\pi$
$972$	1177.77	+	2972.36i	0.0388652	+	0.0980848i
$973$	33595.7			1.10691
$974$	4108.23	+	7115.66i	0.135150	+	0.234087i
$975$		0			0
$976$	−16003.8	+	27719.4i	−0.524867	+	0.909096i
$977$	−23821.0	+	41259.3i	−0.780044	+	1.35108i	0.151872	+	0.988400i	$0.451470\pi$
$977$	−23821.0	+	41259.3i	−0.780044	+	1.35108i	−0.931916	+	0.362675i	$0.881863\pi$
$978$	−38242.0	+	15702.2i	−1.25035	+	0.513396i
$979$	7388.35	+	12797.0i	0.241198	+	0.417767i
$980$		0			0
$981$	5298.45	+	1454.84i	0.172443	+	0.0473491i
$982$	43040.7			1.39866
$983$	5579.06	+	9663.22i	0.181022	+	0.313539i	0.942229	−	0.334970i	$-0.108726\pi$
$983$	5579.06	+	9663.22i	0.181022	+	0.313539i	−0.761207	+	0.648509i	$0.775393\pi$
$984$	−28009.9	−	21630.5i	−0.907443	−	0.700768i
$985$		0			0
$986$	−23529.5	+	40754.3i	−0.759971	+	1.31631i
$987$	37930.6	+	29291.7i	1.22325	+	0.944644i
$988$	−586.361	−	1015.61i	−0.0188812	−	0.0327032i
$989$	−0.546260			−1.75632e−5
$990$		0			0
$991$	−57670.7			−1.84861			−0.924304	−	0.381658i	$-0.875353\pi$
$991$	−57670.7			−1.84861			−0.924304	+	0.381658i	$0.875353\pi$
$992$	5689.09	+	9853.79i	0.182085	+	0.315381i
$993$	−11069.4	+	4545.11i	−0.353753	+	0.145252i
$994$	−6612.41	+	11453.0i	−0.210999	+	0.365461i
$995$		0			0
$996$	167.008	−	1238.98i	0.00531310	−	0.0394163i
$997$	25865.4	+	44800.2i	0.821630	+	1.42311i	0.904467	+	0.426543i	$0.140269\pi$
$997$	25865.4	+	44800.2i	0.821630	+	1.42311i	−0.0828370	+	0.996563i	$0.526398\pi$
$998$	32262.8			1.02331
$999$	−3174.29	+	7467.04i	−0.100531	+	0.236483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.5		32
5.2	odd	4		45.4.j.a.4.12	yes	32
5.3	odd	4		45.4.j.a.4.5	✓	32
5.4	even	2	inner	225.4.e.g.76.12		32
9.4	even	3		2025.4.a.bk.1.12		16
9.5	odd	6		2025.4.a.bl.1.5		16
9.7	even	3	inner	225.4.e.g.151.5		32
15.2	even	4		135.4.j.a.64.5		32
15.8	even	4		135.4.j.a.64.12		32
45.2	even	12		135.4.j.a.19.12		32
45.4	even	6		2025.4.a.bk.1.5		16
45.7	odd	12		45.4.j.a.34.5	yes	32
45.13	odd	12		405.4.b.e.244.5		16
45.14	odd	6		2025.4.a.bl.1.12		16
45.22	odd	12		405.4.b.e.244.12		16
45.23	even	12		405.4.b.f.244.12		16
45.32	even	12		405.4.b.f.244.5		16
45.34	even	6	inner	225.4.e.g.151.12		32
45.38	even	12		135.4.j.a.19.5		32
45.43	odd	12		45.4.j.a.34.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.5	✓	32	5.3	odd	4
45.4.j.a.4.12	yes	32	5.2	odd	4
45.4.j.a.34.5	yes	32	45.7	odd	12
45.4.j.a.34.12	yes	32	45.43	odd	12
135.4.j.a.19.5		32	45.38	even	12
135.4.j.a.19.12		32	45.2	even	12
135.4.j.a.64.5		32	15.2	even	4
135.4.j.a.64.12		32	15.8	even	4
225.4.e.g.76.5		32	1.1	even	1	trivial
225.4.e.g.76.12		32	5.4	even	2	inner
225.4.e.g.151.5		32	9.7	even	3	inner
225.4.e.g.151.12		32	45.34	even	6	inner
405.4.b.e.244.5		16	45.13	odd	12
405.4.b.e.244.12		16	45.22	odd	12
405.4.b.f.244.5		16	45.32	even	12
405.4.b.f.244.12		16	45.23	even	12
2025.4.a.bk.1.5		16	45.4	even	6
2025.4.a.bk.1.12		16	9.4	even	3
2025.4.a.bl.1.5		16	9.5	odd	6
2025.4.a.bl.1.12		16	45.14	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)

\(f(q)\)	\(=\)	\(q+(-1.33753 - 2.31667i) q^{2} +(-0.694136 + 5.14958i) q^{3} +(0.422017 - 0.730954i) q^{4} +(12.8583 - 5.27964i) q^{6} +(7.70766 + 13.3501i) q^{7} -23.6584 q^{8} +(-26.0363 - 7.14902i) q^{9} +O(q^{10})\)	\(q+(-1.33753 - 2.31667i) q^{2} +(-0.694136 + 5.14958i) q^{3} +(0.422017 - 0.730954i) q^{4} +(12.8583 - 5.27964i) q^{6} +(7.70766 + 13.3501i) q^{7} -23.6584 q^{8} +(-26.0363 - 7.14902i) q^{9} +(-22.2799 - 38.5899i) q^{11} +(3.47117 + 2.68059i) q^{12} +(14.0117 - 24.2689i) q^{13} +(20.6185 - 35.7123i) q^{14} +(28.2677 + 48.9610i) q^{16} +92.6615 q^{17} +(18.2625 + 69.8798i) q^{18} +49.5811 q^{19} +(-74.0974 + 30.4245i) q^{21} +(-59.6001 + 103.230i) q^{22} +(0.461404 - 0.799176i) q^{23} +(16.4221 - 121.831i) q^{24} -74.9642 q^{26} +(54.8872 - 129.114i) q^{27} +13.0110 q^{28} +(-94.9247 - 164.414i) q^{29} +(149.590 - 259.098i) q^{31} +(-19.0156 + 32.9360i) q^{32} +(214.187 - 87.9454i) q^{33} +(-123.938 - 214.666i) q^{34} +(-16.2134 + 16.0144i) q^{36} -57.8330 q^{37} +(-66.3163 - 114.863i) q^{38} +(115.249 + 89.0001i) q^{39} +(143.940 - 249.311i) q^{41} +(169.591 + 130.966i) q^{42} +(-0.295977 - 0.512647i) q^{43} -37.6099 q^{44} -2.46857 q^{46} +(-299.151 - 518.145i) q^{47} +(-271.750 + 111.581i) q^{48} +(52.6839 - 91.2513i) q^{49} +(-64.3197 + 477.168i) q^{51} +(-11.8263 - 20.4838i) q^{52} +146.339 q^{53} +(-372.528 + 45.5382i) q^{54} +(-182.351 - 315.840i) q^{56} +(-34.4160 + 255.322i) q^{57} +(-253.930 + 439.819i) q^{58} +(96.5330 - 167.200i) q^{59} +(283.076 + 490.303i) q^{61} -800.326 q^{62} +(-105.240 - 402.689i) q^{63} +554.019 q^{64} +(-490.223 - 378.571i) q^{66} +(-177.581 + 307.580i) q^{67} +(39.1047 - 67.7313i) q^{68} +(3.79514 + 2.93078i) q^{69} -320.703 q^{71} +(615.977 + 169.134i) q^{72} -636.782 q^{73} +(77.3535 + 133.980i) q^{74} +(20.9240 - 36.2415i) q^{76} +(343.452 - 594.875i) q^{77} +(52.0353 - 386.034i) q^{78} +(143.883 + 249.212i) q^{79} +(626.783 + 372.269i) q^{81} -770.097 q^{82} +(-142.529 - 246.867i) q^{83} +(-9.03144 + 67.0014i) q^{84} +(-0.791757 + 1.37136i) q^{86} +(912.556 - 374.696i) q^{87} +(527.105 + 912.973i) q^{88} -331.615 q^{89} +431.988 q^{91} +(-0.389441 - 0.674531i) q^{92} +(1230.41 + 950.175i) q^{93} +(-800.248 + 1386.07i) q^{94} +(-156.407 - 120.784i) q^{96} +(910.814 + 1577.58i) q^{97} -281.866 q^{98} +(304.207 + 1164.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

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