LMFDB - Embedded newform 225.4.h.b.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	225.91
Dual form			225.4.h.b.136.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81638 + 2.04622i) q^{2} +(1.27284 + 3.91740i) q^{4} +(-9.28856 - 6.22275i) q^{5} +12.5082 q^{7} +(4.17503 - 12.8494i) q^{8} +O(q^{10})$	\(q+(2.81638 + 2.04622i) q^{2} +(1.27284 + 3.91740i) q^{4} +(-9.28856 - 6.22275i) q^{5} +12.5082 q^{7} +(4.17503 - 12.8494i) q^{8} +(-13.4270 - 36.5321i) q^{10} +(30.5650 + 22.2068i) q^{11} +(25.8465 - 18.7786i) q^{13} +(35.2278 + 25.5945i) q^{14} +(64.7099 - 47.0145i) q^{16} +(5.81584 - 17.8993i) q^{17} +(49.5522 - 152.506i) q^{19} +(12.5542 - 44.3076i) q^{20} +(40.6427 + 125.085i) q^{22} +(86.4266 + 62.7926i) q^{23} +(47.5547 + 115.601i) q^{25} +111.218 q^{26} +(15.9210 + 48.9997i) q^{28} +(-33.1890 - 102.145i) q^{29} +(-2.18936 + 6.73816i) q^{31} +170.364 q^{32} +(53.0055 - 38.5108i) q^{34} +(-116.183 - 77.8354i) q^{35} +(-52.3230 + 38.0149i) q^{37} +(451.619 - 328.120i) q^{38} +(-118.739 + 93.3724i) q^{40} +(-305.782 + 222.164i) q^{41} -234.897 q^{43} +(-48.0885 + 148.001i) q^{44} +(114.923 + 353.696i) q^{46} +(-32.9933 - 101.543i) q^{47} -186.545 q^{49} +(-102.612 + 422.883i) q^{50} +(106.462 + 77.3489i) q^{52} +(64.0024 + 196.979i) q^{53} +(-145.718 - 396.467i) q^{55} +(52.2221 - 160.723i) q^{56} +(115.539 - 355.591i) q^{58} +(261.882 - 190.269i) q^{59} +(221.781 + 161.134i) q^{61} +(-19.9538 + 14.4973i) q^{62} +(-37.8690 - 27.5134i) q^{64} +(-356.931 + 13.5896i) q^{65} +(-43.7313 + 134.591i) q^{67} +77.5215 q^{68} +(-167.948 - 456.950i) q^{70} +(185.509 + 570.937i) q^{71} +(116.952 + 84.9707i) q^{73} -225.148 q^{74} +660.500 q^{76} +(382.313 + 277.767i) q^{77} +(98.8328 + 304.176i) q^{79} +(-893.621 + 34.0233i) q^{80} -1315.80 q^{82} +(344.182 - 1059.28i) q^{83} +(-165.404 + 130.068i) q^{85} +(-661.558 - 480.650i) q^{86} +(412.954 - 300.028i) q^{88} +(-43.7671 - 31.7986i) q^{89} +(323.293 - 234.886i) q^{91} +(-135.977 + 418.493i) q^{92} +(114.857 - 353.495i) q^{94} +(-1409.28 + 1108.21i) q^{95} +(406.468 + 1250.98i) q^{97} +(-525.381 - 381.712i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8} - 25 q^{10} + 89 q^{11} + 33 q^{13} + 17 q^{14} - 207 q^{16} + 191 q^{17} - 115 q^{19} + 225 q^{20} + 808 q^{22} - 433 q^{23} + 90 q^{25} - 586 q^{26} - 13 q^{28} + 5 q^{29} - 639 q^{31} + 1386 q^{32} - 777 q^{34} + 1030 q^{35} + 699 q^{37} + 2355 q^{38} + 410 q^{40} - 341 q^{41} - 172 q^{43} - 548 q^{44} - 1239 q^{46} - 2319 q^{47} + 1344 q^{49} - 2335 q^{50} + 2344 q^{52} + 927 q^{53} + 1225 q^{55} + 2910 q^{56} + 2410 q^{58} + 1905 q^{59} + 1391 q^{61} + 3832 q^{62} - 3596 q^{64} - 1215 q^{65} - 3611 q^{67} - 3622 q^{68} + 560 q^{70} + 3719 q^{71} + 4593 q^{73} - 4848 q^{74} + 3520 q^{76} - 1368 q^{77} + 775 q^{79} - 9500 q^{80} - 6762 q^{82} + 2447 q^{83} - 8185 q^{85} - 3891 q^{86} - 10960 q^{88} + 5075 q^{89} + 376 q^{91} + 8456 q^{92} + 3573 q^{94} - 3265 q^{95} + 7439 q^{97} - 7082 q^{98}+O(q^{100}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8 - 25 * q^10 + 89 * q^11 + 33 * q^13 + 17 * q^14 - 207 * q^16 + 191 * q^17 - 115 * q^19 + 225 * q^20 + 808 * q^22 - 433 * q^23 + 90 * q^25 - 586 * q^26 - 13 * q^28 + 5 * q^29 - 639 * q^31 + 1386 * q^32 - 777 * q^34 + 1030 * q^35 + 699 * q^37 + 2355 * q^38 + 410 * q^40 - 341 * q^41 - 172 * q^43 - 548 * q^44 - 1239 * q^46 - 2319 * q^47 + 1344 * q^49 - 2335 * q^50 + 2344 * q^52 + 927 * q^53 + 1225 * q^55 + 2910 * q^56 + 2410 * q^58 + 1905 * q^59 + 1391 * q^61 + 3832 * q^62 - 3596 * q^64 - 1215 * q^65 - 3611 * q^67 - 3622 * q^68 + 560 * q^70 + 3719 * q^71 + 4593 * q^73 - 4848 * q^74 + 3520 * q^76 - 1368 * q^77 + 775 * q^79 - 9500 * q^80 - 6762 * q^82 + 2447 * q^83 - 8185 * q^85 - 3891 * q^86 - 10960 * q^88 + 5075 * q^89 + 376 * q^91 + 8456 * q^92 + 3573 * q^94 - 3265 * q^95 + 7439 * q^97 - 7082 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.81638	+	2.04622i	0.995740	+	0.723448i	0.961171	−	0.275955i	$-0.0889939\pi$
$2$	2.81638	+	2.04622i	0.995740	+	0.723448i	0.0345696	+	0.999402i	$0.488994\pi$
$3$		0			0
$3$		0			0
$4$	1.27284	+	3.91740i	0.159105	+	0.489676i
$5$	−9.28856	−	6.22275i	−0.830794	−	0.556580i
$5$	−9.28856	−	6.22275i	−0.830794	−	0.556580i
$6$		0			0
$7$	12.5082			0.675379			0.337690	−	0.941258i	$-0.390355\pi$
$7$	12.5082			0.675379			0.337690	+	0.941258i	$0.390355\pi$
$8$	4.17503	−	12.8494i	0.184512	−	0.567869i
$9$		0			0
$10$	−13.4270	−	36.5321i	−0.424599	−	1.15525i
$11$	30.5650	+	22.2068i	0.837791	+	0.608691i	0.921753	−	0.387778i	$-0.126757\pi$
$11$	30.5650	+	22.2068i	0.837791	+	0.608691i	−0.0839620	+	0.996469i	$0.526757\pi$
$12$		0			0
$13$	25.8465	−	18.7786i	0.551424	−	0.400633i	−0.276886	−	0.960903i	$-0.589302\pi$
$13$	25.8465	−	18.7786i	0.551424	−	0.400633i	0.828310	+	0.560269i	$0.189302\pi$
$14$	35.2278	+	25.5945i	0.672502	+	0.488602i
$15$		0			0
$16$	64.7099	−	47.0145i	1.01109	−	0.734602i
$17$	5.81584	−	17.8993i	0.0829735	−	0.255366i	−0.900960	−	0.433902i	$-0.857136\pi$
$17$	5.81584	−	17.8993i	0.0829735	−	0.255366i	0.983933	+	0.178536i	$0.0571362\pi$
$18$		0			0
$19$	49.5522	−	152.506i	0.598319	−	1.84144i	0.0608593	−	0.998146i	$-0.480616\pi$
$19$	49.5522	−	152.506i	0.598319	−	1.84144i	0.537459	−	0.843290i	$-0.319384\pi$
$20$	12.5542	−	44.3076i	0.140360	−	0.495374i
$21$		0			0
$22$	40.6427	+	125.085i	0.393866	+	1.21220i
$23$	86.4266	+	62.7926i	0.783530	+	0.569268i	0.906036	−	0.423200i	$-0.139093\pi$
$23$	86.4266	+	62.7926i	0.783530	+	0.569268i	−0.122506	+	0.992468i	$0.539093\pi$
$24$		0			0
$25$	47.5547	+	115.601i	0.380438	+	0.924807i
$26$	111.218			0.838913
$27$		0			0
$28$	15.9210	+	48.9997i	0.107456	+	0.330717i
$29$	−33.1890	−	102.145i	−0.212519	−	0.654065i	−0.999320	−	0.0368592i	$-0.988265\pi$
$29$	−33.1890	−	102.145i	−0.212519	−	0.654065i	0.786802	−	0.617206i	$-0.211735\pi$
$30$		0			0
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	−0.957198	−	0.289432i	$-0.906533\pi$
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	0.944514	+	0.328471i	$0.106533\pi$
$32$	170.364			0.941138
$33$		0			0
$34$	53.0055	−	38.5108i	0.267364	−	0.194251i
$35$	−116.183	−	77.8354i	−0.561101	−	0.375903i
$36$		0			0
$37$	−52.3230	+	38.0149i	−0.232482	+	0.168908i	−0.697928	−	0.716168i	$-0.745894\pi$
$37$	−52.3230	+	38.0149i	−0.232482	+	0.168908i	0.465445	+	0.885077i	$0.345894\pi$
$38$	451.619	−	328.120i	1.92795	−	1.40074i
$39$		0			0
$40$	−118.739	+	93.3724i	−0.469356	+	0.369087i
$41$	−305.782	+	222.164i	−1.16476	+	0.846248i	−0.990372	−	0.138429i	$-0.955795\pi$
$41$	−305.782	+	222.164i	−1.16476	+	0.846248i	−0.174388	+	0.984677i	$0.555795\pi$
$42$		0			0
$43$	−234.897			−0.833056			−0.416528	−	0.909123i	$-0.636753\pi$
$43$	−234.897			−0.833056			−0.416528	+	0.909123i	$0.636753\pi$
$44$	−48.0885	+	148.001i	−0.164764	+	0.507091i
$45$		0			0
$46$	114.923	+	353.696i	0.368357	+	1.13369i
$47$	−32.9933	−	101.543i	−0.102395	−	0.315139i	0.886715	−	0.462316i	$-0.152981\pi$
$47$	−32.9933	−	101.543i	−0.102395	−	0.315139i	−0.989110	+	0.147177i	$0.952981\pi$
$48$		0			0
$49$	−186.545			−0.543863
$50$	−102.612	+	422.883i	−0.290232	+	1.19609i
$51$		0			0
$52$	106.462	+	77.3489i	0.283915	+	0.206276i
$53$	64.0024	+	196.979i	0.165876	+	0.510512i	0.999100	−	0.0424228i	$-0.0135077\pi$
$53$	64.0024	+	196.979i	0.165876	+	0.510512i	−0.833224	+	0.552935i	$0.813508\pi$
$54$		0			0
$55$	−145.718	−	396.467i	−0.357247	−	0.971994i
$56$	52.2221	−	160.723i	0.124615	−	0.383527i
$57$		0			0
$58$	115.539	−	355.591i	0.261568	−	0.805025i
$59$	261.882	−	190.269i	0.577868	−	0.419845i	−0.260087	−	0.965585i	$-0.583751\pi$
$59$	261.882	−	190.269i	0.577868	−	0.419845i	0.837955	+	0.545740i	$0.183751\pi$
$60$		0			0
$61$	221.781	+	161.134i	0.465511	+	0.338214i	0.795689	−	0.605705i	$-0.207109\pi$
$61$	221.781	+	161.134i	0.465511	+	0.338214i	−0.330178	+	0.943919i	$0.607109\pi$
$62$	−19.9538	+	14.4973i	−0.0408732	+	0.0296961i
$63$		0			0
$64$	−37.8690	−	27.5134i	−0.0739629	−	0.0537372i
$65$	−356.931	+	13.5896i	−0.681105	+	0.0259321i
$66$		0			0
$67$	−43.7313	+	134.591i	−0.0797407	+	0.245417i	−0.982978	−	0.183726i	$-0.941184\pi$
$67$	−43.7313	+	134.591i	−0.0797407	+	0.245417i	0.903237	+	0.429142i	$0.141184\pi$
$68$	77.5215			0.138248
$69$		0			0
$70$	−167.948	−	456.950i	−0.286765	−	0.780229i
$71$	185.509	+	570.937i	0.310082	+	0.954334i	0.977732	+	0.209859i	$0.0673003\pi$
$71$	185.509	+	570.937i	0.310082	+	0.954334i	−0.667650	+	0.744475i	$0.732700\pi$
$72$		0			0
$73$	116.952	+	84.9707i	0.187510	+	0.136234i	0.677580	−	0.735449i	$-0.263029\pi$
$73$	116.952	+	84.9707i	0.187510	+	0.136234i	−0.490070	+	0.871683i	$0.663029\pi$
$74$	−225.148			−0.353688
$75$		0			0
$76$	660.500			0.996902
$77$	382.313	+	277.767i	0.565826	+	0.411097i
$78$		0			0
$79$	98.8328	+	304.176i	0.140754	+	0.433196i	0.996441	−	0.0842982i	$-0.0268648\pi$
$79$	98.8328	+	304.176i	0.140754	+	0.433196i	−0.855687	+	0.517494i	$0.826865\pi$
$80$	−893.621	+	34.0233i	−1.24887	+	0.0475491i
$81$		0			0
$82$	−1315.80			−1.77202
$83$	344.182	−	1059.28i	0.455167	−	1.40086i	−0.415773	−	0.909469i	$-0.636489\pi$
$83$	344.182	−	1059.28i	0.455167	−	1.40086i	0.870939	−	0.491390i	$-0.163511\pi$
$84$		0			0
$85$	−165.404	+	130.068i	−0.211065	+	0.165975i
$86$	−661.558	−	480.650i	−0.829507	−	0.602672i
$87$		0			0
$88$	412.954	−	300.028i	0.500239	−	0.363445i
$89$	−43.7671	−	31.7986i	−0.0521270	−	0.0378725i	0.561417	−	0.827533i	$-0.310257\pi$
$89$	−43.7671	−	31.7986i	−0.0521270	−	0.0378725i	−0.613544	+	0.789661i	$0.710257\pi$
$90$		0			0
$91$	323.293	−	234.886i	0.372421	−	0.270579i
$92$	−135.977	+	418.493i	−0.154093	+	0.474249i
$93$		0			0
$94$	114.857	−	353.495i	0.126028	−	0.387874i
$95$	−1409.28	+	1108.21i	−1.52199	+	1.19684i
$96$		0			0
$97$	406.468	+	1250.98i	0.425470	+	1.30946i	0.902543	+	0.430599i	$0.141698\pi$
$97$	406.468	+	1250.98i	0.425470	+	1.30946i	−0.477073	+	0.878863i	$0.658302\pi$
$98$	−525.381	−	381.712i	−0.541546	−	0.393456i
$99$		0			0
$100$	−392.325	+	333.433i	−0.392325	+	0.333433i
$101$	345.232			0.340117			0.170059	−	0.985434i	$-0.445604\pi$
$101$	345.232			0.340117			0.170059	+	0.985434i	$0.445604\pi$
$102$		0			0
$103$	−450.899	−	1387.73i	−0.431344	−	1.32754i	−0.896787	−	0.442463i	$-0.854105\pi$
$103$	−450.899	−	1387.73i	−0.431344	−	1.32754i	0.465443	−	0.885078i	$-0.345895\pi$
$104$	−133.384	−	410.513i	−0.125763	−	0.387058i
$105$		0			0
$106$	−222.807	+	685.731i	−0.204160	+	0.628340i
$107$	1081.01			0.976683			0.488342	−	0.872653i	$-0.337602\pi$
$107$	1081.01			0.976683			0.488342	+	0.872653i	$0.337602\pi$
$108$		0			0
$109$	−1031.20	+	749.212i	−0.906158	+	0.658362i	−0.940040	−	0.341064i	$-0.889213\pi$
$109$	−1031.20	+	749.212i	−0.906158	+	0.658362i	0.0338823	+	0.999426i	$0.489213\pi$
$110$	400.863	−	1414.77i	0.347462	−	1.22630i
$111$		0			0
$112$	809.404	−	588.067i	0.682871	−	0.496135i
$113$	−227.388	+	165.207i	−0.189300	+	0.137535i	−0.678399	−	0.734694i	$-0.737326\pi$
$113$	−227.388	+	165.207i	−0.189300	+	0.137535i	0.489099	+	0.872228i	$0.337326\pi$
$114$		0			0
$115$	−412.036	−	1121.06i	−0.334109	−	0.909042i
$116$	357.900	−	260.029i	0.286467	−	0.208130i
$117$		0			0
$118$	1126.89			0.879142
$119$	72.7457	−	223.888i	0.0560386	−	0.172469i
$120$		0			0
$121$	29.7771	+	91.6445i	0.0223720	+	0.0688539i
$122$	294.906	+	907.627i	0.218848	+	0.673546i
$123$		0			0
$124$	−29.1828			−0.0211346
$125$	277.640	−	1369.69i	0.198663	−	0.980068i
$126$		0			0
$127$	157.590	+	114.496i	0.110109	+	0.0799990i	0.641477	−	0.767142i	$-0.278322\pi$
$127$	157.590	+	114.496i	0.110109	+	0.0799990i	−0.531368	+	0.847141i	$0.678322\pi$
$128$	−471.518	−	1451.18i	−0.325600	−	1.00209i
$129$		0			0
$130$	−1033.06	−	692.085i	−0.696964	−	0.466922i
$131$	−766.106	+	2357.83i	−0.510954	+	1.57256i	0.279570	+	0.960125i	$0.409808\pi$
$131$	−766.106	+	2357.83i	−0.510954	+	1.57256i	−0.790524	+	0.612431i	$0.790192\pi$
$132$		0			0
$133$	619.809	−	1907.58i	0.404092	−	1.24367i
$134$	−398.567	+	289.576i	−0.256947	+	0.186683i
$135$		0			0
$136$	−205.714	−	149.460i	−0.129705	−	0.0942361i
$137$	−1428.80	+	1038.08i	−0.891027	+	0.647369i	−0.936145	−	0.351613i	$-0.885633\pi$
$137$	−1428.80	+	1038.08i	−0.891027	+	0.647369i	0.0451188	+	0.998982i	$0.485633\pi$
$138$		0			0
$139$	1897.81	+	1378.84i	1.15806	+	0.841379i	0.989531	−	0.144318i	$-0.0460987\pi$
$139$	1897.81	+	1378.84i	1.15806	+	0.841379i	0.168528	+	0.985697i	$0.446099\pi$
$140$	157.030	−	554.209i	0.0947961	−	0.334566i
$141$		0			0
$142$	−645.799	+	1987.56i	−0.381650	+	1.17460i
$143$	1207.01			0.705840
$144$		0			0
$145$	−327.346	+	1155.31i	−0.187480	+	0.661677i
$146$	155.513	+	478.620i	0.0881530	+	0.271307i
$147$		0			0
$148$	−215.519	−	156.583i	−0.119699	−	0.0869667i
$149$	−222.823			−0.122513			−0.0612563	−	0.998122i	$-0.519511\pi$
$149$	−222.823			−0.122513			−0.0612563	+	0.998122i	$0.519511\pi$
$150$		0			0
$151$	−1320.15			−0.711471			−0.355735	−	0.934587i	$-0.615770\pi$
$151$	−1320.15			−0.711471			−0.355735	+	0.934587i	$0.615770\pi$
$152$	−1752.73	−	1273.43i	−0.935297	−	0.679533i
$153$		0			0
$154$	508.367	+	1564.59i	0.266009	+	0.818692i
$155$	62.2659	−	48.9640i	0.0322666	−	0.0253734i
$156$		0			0
$157$	−1708.75			−0.868620			−0.434310	−	0.900763i	$-0.643008\pi$
$157$	−1708.75			−0.868620			−0.434310	+	0.900763i	$0.643008\pi$
$158$	−344.060	+	1058.91i	−0.173240	+	0.533179i
$159$		0			0
$160$	−1582.44	−	1060.13i	−0.781892	−	0.523819i
$161$	1081.04	+	785.423i	0.529180	+	0.384472i
$162$		0			0
$163$	−1100.74	+	799.735i	−0.528937	+	0.384295i	−0.819960	−	0.572421i	$-0.806004\pi$
$163$	−1100.74	+	799.735i	−0.528937	+	0.384295i	0.291023	+	0.956716i	$0.406004\pi$
$164$	−1259.52	−	915.094i	−0.599707	−	0.435712i
$165$		0			0
$166$	3136.87	−	2279.07i	1.46668	−	1.06560i
$167$	−901.420	+	2774.28i	−0.417688	+	1.28551i	0.492136	+	0.870518i	$0.336216\pi$
$167$	−901.420	+	2774.28i	−0.417688	+	1.28551i	−0.909824	+	0.414994i	$0.863784\pi$
$168$		0			0
$169$	−363.505	+	1118.75i	−0.165455	+	0.509218i
$170$	−731.988	+	27.8694i	−0.330241	+	0.0125734i
$171$		0			0
$172$	−298.986	−	920.185i	−0.132544	−	0.407927i
$173$	1432.40	+	1040.70i	0.629499	+	0.457357i	0.856226	−	0.516601i	$-0.172803\pi$
$173$	1432.40	+	1040.70i	0.629499	+	0.457357i	−0.226728	+	0.973958i	$0.572803\pi$
$174$		0			0
$175$	594.824	+	1445.96i	0.256940	+	0.624595i
$176$	3021.90			1.29423
$177$		0			0
$178$	−58.1977	−	179.114i	−0.0245062	−	0.0754223i
$179$	644.168	+	1982.55i	0.268980	+	0.827835i	0.990750	+	0.135702i	$0.0433289\pi$
$179$	644.168	+	1982.55i	0.268980	+	0.827835i	−0.721770	+	0.692133i	$0.756671\pi$
$180$		0			0
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	−0.978906	−	0.204310i	$-0.934505\pi$
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	0.912042	+	0.410096i	$0.134505\pi$
$182$	1391.14			0.566584
$183$		0			0
$184$	1167.68	−	848.370i	0.467840	−	0.339906i
$185$	722.562	−	27.5105i	0.287156	−	0.0109330i
$186$		0			0
$187$	575.247	−	417.942i	0.224953	−	0.163438i
$188$	355.789	−	258.496i	0.138024	−	0.100281i
$189$		0			0
$190$	−6236.70	+	237.453i	−2.38136	+	0.0906667i
$191$	1872.83	−	1360.69i	0.709494	−	0.515478i	−0.173516	−	0.984831i	$-0.555513\pi$
$191$	1872.83	−	1360.69i	0.709494	−	0.515478i	0.883011	+	0.469353i	$0.155513\pi$
$192$		0			0
$193$	2028.97			0.756727			0.378363	−	0.925657i	$-0.376487\pi$
$193$	2028.97			0.756727			0.378363	+	0.925657i	$0.376487\pi$
$194$	−1415.01	+	4354.96i	−0.523670	+	1.61169i
$195$		0			0
$196$	−237.442	−	730.772i	−0.0865314	−	0.266316i
$197$	−815.098	−	2508.61i	−0.294788	−	0.907265i	−0.983292	−	0.182033i	$-0.941732\pi$
$197$	−815.098	−	2508.61i	−0.294788	−	0.907265i	0.688504	−	0.725232i	$-0.258268\pi$
$198$		0			0
$199$	594.340			0.211717			0.105858	−	0.994381i	$-0.466241\pi$
$199$	594.340			0.211717			0.105858	+	0.994381i	$0.466241\pi$
$200$	1683.94	−	128.414i	0.595364	−	0.0454011i
$201$		0			0
$202$	972.304	+	706.420i	0.338669	+	0.246057i
$203$	−415.134	−	1277.65i	−0.143531	−	0.441742i
$204$		0			0
$205$	4222.75	−	160.775i	1.43868	−	0.0547757i
$206$	1569.69	−	4831.00i	0.530899	−	1.63394i
$207$		0			0
$208$	789.658	−	2430.32i	0.263235	−	0.810154i
$209$	4901.23	−	3560.95i	1.62213	−	1.17855i
$210$		0			0
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	0.808461	−	0.588550i	$-0.200301\pi$
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	−0.309916	+	0.950764i	$0.600301\pi$
$212$	−690.182	+	501.446i	−0.223594	+	0.162450i
$213$		0			0
$214$	3044.53	+	2211.98i	0.972523	+	0.706579i
$215$	2181.85	+	1461.70i	0.692098	+	0.463662i
$216$		0			0
$217$	−27.3850	+	84.2823i	−0.00856688	+	0.0263661i
$218$	−4437.31			−1.37859
$219$		0			0
$220$	1367.65	−	1075.48i	0.419122	−	0.329584i
$221$	−185.804	−	571.847i	−0.0565546	−	0.174057i
$222$		0			0
$223$	−1810.08	−	1315.10i	−0.543553	−	0.394914i	0.281850	−	0.959458i	$-0.409052\pi$
$223$	−1810.08	−	1315.10i	−0.543553	−	0.394914i	−0.825403	+	0.564544i	$0.809052\pi$
$224$	2130.95			0.635625
$225$		0			0
$226$	−978.462			−0.287993
$227$	−1359.84	−	987.983i	−0.397603	−	0.288875i	0.370961	−	0.928648i	$-0.379028\pi$
$227$	−1359.84	−	987.983i	−0.397603	−	0.288875i	−0.768564	+	0.639773i	$0.779028\pi$
$228$		0			0
$229$	1280.57	+	3941.19i	0.369531	+	1.13730i	0.947095	+	0.320953i	$0.104003\pi$
$229$	1280.57	+	3941.19i	0.369531	+	1.13730i	−0.577564	+	0.816345i	$0.695997\pi$
$230$	1133.49	−	4000.46i	0.324958	−	1.14688i
$231$		0			0
$232$	−1451.07			−0.410635
$233$	1435.29	−	4417.38i	0.403559	−	1.24203i	−0.518534	−	0.855057i	$-0.673522\pi$
$233$	1435.29	−	4417.38i	0.403559	−	1.24203i	0.922093	−	0.386969i	$-0.126478\pi$
$234$		0			0
$235$	−325.416	+	1148.50i	−0.0903310	+	0.318807i
$236$	1078.69	+	783.717i	0.297530	+	0.216168i
$237$		0			0
$238$	663.004	−	481.701i	0.180572	−	0.131193i
$239$	2707.72	+	1967.27i	0.732835	+	0.532436i	0.890459	−	0.455063i	$-0.150383\pi$
$239$	2707.72	+	1967.27i	0.732835	+	0.532436i	−0.157624	+	0.987499i	$0.550383\pi$
$240$		0			0
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.629222	−	0.777226i	$-0.283374\pi$
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.933626	−	0.358250i	$-0.116626\pi$
$242$	−103.661	+	319.036i	−0.0275355	+	0.0847455i
$243$		0			0
$244$	−348.933	+	1073.90i	−0.0915497	+	0.281761i
$245$	1732.73	+	1160.82i	0.451838	+	0.302703i
$246$		0			0
$247$	−1583.09	−	4872.26i	−0.407813	−	1.25512i
$248$	77.4408	+	56.2640i	0.0198286	+	0.0144063i
$249$		0			0
$250$	3584.62	−	3289.44i	0.906845	−	0.832171i
$251$	−5546.43			−1.39477			−0.697386	−	0.716696i	$-0.745654\pi$
$251$	−5546.43			−1.39477			−0.697386	+	0.716696i	$0.745654\pi$
$252$		0			0
$253$	1247.21	+	3838.51i	0.309926	+	0.953855i
$254$	209.550	+	644.928i	0.0517651	+	0.159317i
$255$		0			0
$256$	1525.75	−	4695.77i	0.372497	−	1.14643i
$257$	56.6174			0.0137420			0.00687100	−	0.999976i	$-0.497813\pi$
$257$	56.6174			0.0137420			0.00687100	+	0.999976i	$0.497813\pi$
$258$		0			0
$259$	−654.466	+	475.498i	−0.157014	+	0.114077i
$260$	−507.552	−	1380.94i	−0.121066	−	0.329394i
$261$		0			0
$262$	−6982.29	+	5072.93i	−1.64644	+	1.19621i
$263$	−5389.55	+	3915.74i	−1.26363	+	0.918079i	−0.998930	−	0.0462529i	$-0.985272\pi$
$263$	−5389.55	+	3915.74i	−1.26363	+	0.918079i	−0.264697	+	0.964332i	$0.585272\pi$
$264$		0			0
$265$	631.262	−	2227.92i	0.146333	−	0.516454i
$266$	5648.94	−	4104.19i	1.30210	−	0.946031i
$267$		0			0
$268$	−582.911			−0.132862
$269$	−1574.21	+	4844.92i	−0.356807	+	1.09814i	0.598147	+	0.801387i	$0.295904\pi$
$269$	−1574.21	+	4844.92i	−0.356807	+	1.09814i	−0.954954	+	0.296754i	$0.904096\pi$
$270$		0			0
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	0.961994	+	0.273072i	$0.0880396\pi$
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	−0.617762	+	0.786365i	$0.711960\pi$
$272$	−465.185	−	1431.69i	−0.103698	−	0.319151i
$273$		0			0
$274$	−6148.19			−1.35557
$275$	−1113.61	+	4589.38i	−0.244194	+	1.00636i
$276$		0			0
$277$	−4137.40	−	3006.00i	−0.897445	−	0.652032i	0.0403637	−	0.999185i	$-0.487148\pi$
$277$	−4137.40	−	3006.00i	−0.897445	−	0.652032i	−0.937808	+	0.347153i	$0.887148\pi$
$278$	2523.55	+	7766.67i	0.544432	+	1.67559i
$279$		0			0
$280$	−1485.21	+	1167.92i	−0.316993	+	0.249273i
$281$	−208.142	+	640.597i	−0.0441877	+	0.135996i	−0.970716	−	0.240228i	$-0.922778\pi$
$281$	−208.142	+	640.597i	−0.0441877	+	0.135996i	0.926529	+	0.376224i	$0.122778\pi$
$282$		0			0
$283$	879.284	−	2706.16i	0.184693	−	0.568425i	−0.815250	−	0.579109i	$-0.803401\pi$
$283$	879.284	−	2706.16i	0.184693	−	0.568425i	0.999943	+	0.0106833i	$0.00340066\pi$
$284$	−2000.47	+	1453.42i	−0.417978	+	0.303679i
$285$		0			0
$286$	3399.39	+	2469.80i	0.702833	+	0.510638i
$287$	−3824.79	+	2778.87i	−0.786655	+	0.571538i
$288$		0			0
$289$	3688.14	+	2679.59i	0.750690	+	0.545408i
$290$	−3285.94	+	2583.96i	−0.665370	+	0.523226i
$291$		0			0
$292$	−184.003	+	566.303i	−0.0368766	+	0.113495i
$293$	−208.321			−0.0415367			−0.0207684	−	0.999784i	$-0.506611\pi$
$293$	−208.321			−0.0415367			−0.0207684	+	0.999784i	$0.506611\pi$
$294$		0			0
$295$	−3616.51	+	137.693i	−0.713766	+	0.0271756i
$296$	270.019	+	831.032i	0.0530220	+	0.163185i
$297$		0			0
$298$	−627.554	−	455.945i	−0.121991	−	0.0886314i
$299$	3412.98			0.660126
$300$		0			0
$301$	−2938.13			−0.562629
$302$	−3718.04	−	2701.31i	−0.708440	−	0.514712i
$303$		0			0
$304$	−3963.48	−	12198.3i	−0.747766	−	2.30139i
$305$	−1057.34	−	2876.79i	−0.198501	−	0.540080i
$306$		0			0
$307$	661.860			0.123044			0.0615218	−	0.998106i	$-0.480405\pi$
$307$	661.860			0.123044			0.0615218	+	0.998106i	$0.480405\pi$
$308$	−601.501	+	1851.23i	−0.111278	+	0.342479i
$309$		0			0
$310$	275.555	−	10.4914i	0.0504855	−	0.00192216i
$311$	−7024.85	−	5103.86i	−1.28085	−	0.930589i	−0.281267	−	0.959629i	$-0.590755\pi$
$311$	−7024.85	−	5103.86i	−1.28085	−	0.930589i	−0.999578	+	0.0290408i	$0.990755\pi$
$312$		0			0
$313$	−3033.40	+	2203.89i	−0.547788	+	0.397992i	−0.826969	−	0.562247i	$-0.809937\pi$
$313$	−3033.40	+	2203.89i	−0.547788	+	0.397992i	0.279181	+	0.960238i	$0.409937\pi$
$314$	−4812.50	−	3496.48i	−0.864920	−	0.628401i
$315$		0			0
$316$	−1065.78	+	774.336i	−0.189731	+	0.137848i
$317$	1932.02	−	5946.15i	0.342313	−	1.05353i	−0.620694	−	0.784053i	$-0.713149\pi$
$317$	1932.02	−	5946.15i	0.342313	−	1.05353i	0.963007	−	0.269477i	$-0.0868509\pi$
$318$		0			0
$319$	1253.89	−	3859.09i	0.220077	−	0.677327i
$320$	180.539	+	491.210i	0.0315389	+	0.0858108i
$321$		0			0
$322$	1437.48	+	4424.10i	0.248781	+	0.765668i
$323$	−2441.57	−	1773.90i	−0.420596	−	0.305581i
$324$		0			0
$325$	3399.94	+	2094.86i	0.580291	+	0.357545i
$326$	−4736.54			−0.804701
$327$		0			0
$328$	1578.03	+	4856.66i	0.265646	+	0.817574i
$329$	−412.686	−	1270.12i	−0.0691554	−	0.212839i
$330$		0			0
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	0.730553	+	0.682856i	$0.239262\pi$
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	−0.992402	+	0.123034i	$0.960738\pi$
$332$	4587.72			0.758386
$333$		0			0
$334$	−8215.53	+	5968.93i	−1.34591	+	0.977861i
$335$	1243.73	−	978.028i	0.202842	−	0.159509i
$336$		0			0
$337$	4227.20	−	3071.24i	0.683294	−	0.496442i	−0.191155	−	0.981560i	$-0.561223\pi$
$337$	4227.20	−	3071.24i	0.683294	−	0.496442i	0.874449	+	0.485118i	$0.161223\pi$
$338$	−3312.98	+	2407.02i	−0.533143	+	0.387351i
$339$		0			0
$340$	−720.063	−	482.397i	−0.114856	−	0.0769461i
$341$	−216.551	+	157.333i	−0.0343897	+	0.0249856i
$342$		0			0
$343$	−6623.65			−1.04269
$344$	−980.700	+	3018.28i	−0.153709	+	0.473067i
$345$		0			0
$346$	1904.68	+	5862.00i	0.295943	+	0.910818i
$347$	243.163	+	748.379i	0.0376187	+	0.115778i	0.968102	−	0.250555i	$-0.0806130\pi$
$347$	243.163	+	748.379i	0.0376187	+	0.115778i	−0.930484	+	0.366333i	$0.880613\pi$
$348$		0			0
$349$	4031.08			0.618277			0.309138	−	0.951017i	$-0.399959\pi$
$349$	4031.08			0.618277			0.309138	+	0.951017i	$0.399959\pi$
$350$	−1283.50	+	5289.51i	−0.196017	+	0.807817i
$351$		0			0
$352$	5207.18	+	3783.24i	0.788477	+	0.572862i
$353$	−730.568	−	2248.46i	−0.110154	−	0.339018i	0.880752	−	0.473578i	$-0.157038\pi$
$353$	−730.568	−	2248.46i	−0.110154	−	0.339018i	−0.990905	+	0.134560i	$0.957038\pi$
$354$		0			0
$355$	1829.69	−	6457.55i	0.273549	−	0.965440i
$356$	68.8596	−	211.928i	0.0102515	−	0.0315510i
$357$		0			0
$358$	−2242.50	+	6901.71i	−0.331061	+	1.01890i
$359$	−3962.13	+	2878.66i	−0.582488	+	0.423202i	−0.839620	−	0.543174i	$-0.817222\pi$
$359$	−3962.13	+	2878.66i	−0.582488	+	0.423202i	0.257132	+	0.966376i	$0.417222\pi$
$360$		0			0
$361$	−15253.6	−	11082.4i	−2.22388	−	1.61575i
$362$	−1483.95	+	1078.15i	−0.215455	+	0.156537i
$363$		0			0
$364$	1331.64	+	967.496i	0.191750	+	0.139315i
$365$	−557.566	−	1517.02i	−0.0799571	−	0.217547i
$366$		0			0
$367$	−3638.89	+	11199.3i	−0.517570	+	1.59292i	0.260986	+	0.965343i	$0.415952\pi$
$367$	−3638.89	+	11199.3i	−0.517570	+	1.59292i	−0.778556	+	0.627575i	$0.784048\pi$
$368$	8544.82			1.21041
$369$		0			0
$370$	2091.30	+	1401.04i	0.293842	+	0.196856i
$371$	800.555	+	2463.85i	0.112029	+	0.344790i
$372$		0			0
$373$	−10144.8	−	7370.66i	−1.40826	−	1.02316i	−0.993573	−	0.113193i	$-0.963892\pi$
$373$	−10144.8	−	7370.66i	−1.40826	−	1.02316i	−0.414684	−	0.909966i	$-0.636108\pi$
$374$	2475.32			0.342234
$375$		0			0
$376$	−1442.51			−0.197851
$377$	−2775.96	−	2016.85i	−0.379228	−	0.275525i
$378$		0			0
$379$	1673.08	+	5149.21i	0.226755	+	0.697881i	0.998109	+	0.0614740i	$0.0195801\pi$
$379$	1673.08	+	5149.21i	0.226755	+	0.697881i	−0.771353	+	0.636407i	$0.780420\pi$
$380$	−6135.09	−	4110.13i	−0.828220	−	0.554855i
$381$		0			0
$382$	8058.88			1.07939
$383$	4385.52	−	13497.2i	0.585090	−	1.80072i	−0.0138191	−	0.999905i	$-0.504399\pi$
$383$	4385.52	−	13497.2i	0.585090	−	1.80072i	0.598909	−	0.800817i	$-0.295601\pi$
$384$		0			0
$385$	−1822.67	−	4959.09i	−0.241277	−	0.656465i
$386$	5714.34	+	4151.71i	0.753503	+	0.547452i
$387$		0			0
$388$	−4383.23	+	3184.60i	−0.573517	+	0.416685i
$389$	191.659	+	139.248i	0.0249807	+	0.0181495i	0.600206	−	0.799846i	$-0.295085\pi$
$389$	191.659	+	139.248i	0.0249807	+	0.0181495i	−0.575225	+	0.817995i	$0.695085\pi$
$390$		0			0
$391$	1626.59	−	1181.79i	0.210384	−	0.152853i
$392$	−778.830	+	2396.99i	−0.100349	+	0.308843i
$393$		0			0
$394$	2837.55	−	8733.07i	0.362826	−	1.11666i
$395$	974.798	−	3440.37i	0.124171	−	0.438238i
$396$		0			0
$397$	−3538.88	−	10891.6i	−0.447384	−	1.37691i	−0.879848	−	0.475255i	$-0.842356\pi$
$397$	−3538.88	−	10891.6i	−0.447384	−	1.37691i	0.432464	−	0.901651i	$-0.357644\pi$
$398$	1673.89	+	1216.15i	0.210815	+	0.153166i
$399$		0			0
$400$	8512.18	+	5244.76i	1.06402	+	0.655595i
$401$	−13344.5			−1.66183			−0.830915	−	0.556399i	$-0.812182\pi$
$401$	−13344.5			−1.66183			−0.830915	+	0.556399i	$0.812182\pi$
$402$		0			0
$403$	69.9457	+	215.271i	0.00864576	+	0.0266089i
$404$	439.426	+	1352.41i	0.0541145	+	0.166547i
$405$		0			0
$406$	1445.18	−	4447.81i	0.176658	−	0.543697i
$407$	−2443.44			−0.297584
$408$		0			0
$409$	6080.01	−	4417.39i	0.735055	−	0.534048i	−0.156104	−	0.987741i	$-0.549893\pi$
$409$	6080.01	−	4417.39i	0.735055	−	0.534048i	0.891158	+	0.453692i	$0.149893\pi$
$410$	12221.8	+	8187.87i	1.47218	+	0.986268i
$411$		0			0
$412$	4862.36	−	3532.71i	0.581435	−	0.422437i
$413$	3275.68	−	2379.92i	0.390280	−	0.283555i
$414$		0			0
$415$	−9788.60	+	7697.45i	−1.15784	+	0.910489i
$416$	4403.31	−	3199.19i	0.518967	−	0.377051i
$417$		0			0
$418$	21090.2			2.46784
$419$	1980.00	−	6093.82i	0.230858	−	0.710507i	−0.766786	−	0.641903i	$-0.778145\pi$
$419$	1980.00	−	6093.82i	0.230858	−	0.710507i	0.997644	−	0.0686047i	$-0.0218547\pi$
$420$		0			0
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	0.728924	+	0.684594i	$0.240021\pi$
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	−0.187318	+	0.982299i	$0.559979\pi$
$422$	2031.83	+	6253.32i	0.234378	+	0.721343i
$423$		0			0
$424$	2798.28			0.320510
$425$	2345.75	−	178.881i	0.267730	−	0.0204165i
$426$		0			0
$427$	2774.09	+	2015.49i	0.314397	+	0.228423i
$428$	1375.95	+	4234.75i	0.155395	+	0.478258i
$429$		0			0
$430$	3153.96	+	8581.26i	0.353715	+	0.962384i
$431$	−3787.43	+	11656.5i	−0.423281	+	1.30272i	0.481350	+	0.876528i	$0.340147\pi$
$431$	−3787.43	+	11656.5i	−0.423281	+	1.30272i	−0.904631	+	0.426196i	$0.859853\pi$
$432$		0			0
$433$	3856.48	−	11869.0i	0.428016	−	1.31730i	−0.472061	−	0.881566i	$-0.656490\pi$
$433$	3856.48	−	11869.0i	0.428016	−	1.31730i	0.900077	−	0.435731i	$-0.143510\pi$
$434$	−249.586	+	181.335i	−0.0276049	+	0.0200561i
$435$		0			0
$436$	−4247.52	−	3086.01i	−0.466558	−	0.338974i
$437$	13858.9	−	10069.1i	1.51707	−	1.10222i
$438$		0			0
$439$	−13041.9	−	9475.47i	−1.41789	−	1.03016i	−0.992115	−	0.125330i	$-0.960001\pi$
$439$	−13041.9	−	9475.47i	−1.41789	−	1.03016i	−0.425776	−	0.904828i	$-0.639999\pi$
$440$	−5702.75	+	217.124i	−0.617881	+	0.0235249i
$441$		0			0
$442$	646.829	−	1990.73i	0.0696075	−	0.214230i
$443$	11988.6			1.28577			0.642885	−	0.765963i	$-0.277737\pi$
$443$	11988.6			1.28577			0.642885	+	0.765963i	$0.277737\pi$
$444$		0			0
$445$	208.658	+	567.715i	0.0222277	+	0.0604770i
$446$	−2406.89	−	7407.66i	−0.255538	−	0.786464i
$447$		0			0
$448$	−473.673	−	344.144i	−0.0499530	−	0.0362930i
$449$	−768.211			−0.0807442			−0.0403721	−	0.999185i	$-0.512854\pi$
$449$	−768.211			−0.0807442			−0.0403721	+	0.999185i	$0.512854\pi$
$450$		0			0
$451$	−14279.8			−1.49093
$452$	−936.613	−	680.490i	−0.0974659	−	0.0708131i
$453$		0			0
$454$	−1808.20	−	5565.07i	−0.186923	−	0.575290i
$455$	−4464.56	+	169.982i	−0.460004	+	0.0175140i
$456$		0			0
$457$	13017.8			1.33249			0.666246	−	0.745732i	$-0.267900\pi$
$457$	13017.8			1.33249			0.666246	+	0.745732i	$0.267900\pi$
$458$	−4457.97	+	13720.2i	−0.454819	+	1.39979i
$459$		0			0
$460$	3867.21	−	3041.05i	0.391977	−	0.308238i
$461$	12600.2	+	9154.58i	1.27299	+	0.924883i	0.999318	−	0.0369393i	$-0.0117608\pi$
$461$	12600.2	+	9154.58i	1.27299	+	0.924883i	0.273675	+	0.961822i	$0.411761\pi$
$462$		0			0
$463$	−3292.54	+	2392.17i	−0.330491	+	0.240116i	−0.740639	−	0.671903i	$-0.765477\pi$
$463$	−3292.54	+	2392.17i	−0.330491	+	0.240116i	0.410148	+	0.912019i	$0.365477\pi$
$464$	−6949.96	−	5049.44i	−0.695353	−	0.505203i
$465$		0			0
$466$	13081.3	−	9504.09i	1.30038	−	0.944782i
$467$	−153.591	+	472.706i	−0.0152192	+	0.0468399i	−0.958378	−	0.285503i	$-0.907839\pi$
$467$	−153.591	+	472.706i	−0.0152192	+	0.0468399i	0.943159	+	0.332343i	$0.107839\pi$
$468$		0			0
$469$	−547.000	+	1683.49i	−0.0538552	+	0.165749i
$470$	−3266.57	+	2568.73i	−0.320586	+	0.252099i
$471$		0			0
$472$	−1351.47	−	4159.41i	−0.131794	−	0.405619i
$473$	−7179.62	−	5216.30i	−0.697926	−	0.507073i
$474$		0			0
$475$	19986.3	−	1524.11i	1.93060	−	0.147223i
$476$	969.655			0.0933698
$477$		0			0
$478$	3600.49	+	11081.2i	0.344524	+	1.06034i
$479$	−1404.36	−	4322.18i	−0.133960	−	0.412287i	0.861467	−	0.507814i	$-0.169546\pi$
$479$	−1404.36	−	4322.18i	−0.133960	−	0.412287i	−0.995427	+	0.0955270i	$0.969546\pi$
$480$		0			0
$481$	−638.500	+	1965.10i	−0.0605261	+	0.186280i
$482$	25160.4			2.37765
$483$		0			0
$484$	−321.107	+	233.298i	−0.0301566	+	0.0219100i
$485$	4009.04	−	14149.2i	0.375342	−	1.32470i
$486$		0			0
$487$	13359.2	−	9706.02i	1.24304	−	0.903125i	0.245247	−	0.969461i	$-0.421131\pi$
$487$	13359.2	−	9706.02i	1.24304	−	0.903125i	0.997797	+	0.0663359i	$0.0211309\pi$
$488$	2996.41	−	2177.02i	0.277954	−	0.201945i
$489$		0			0
$490$	2504.74	+	6814.87i	0.230923	+	0.628295i
$491$	−1292.08	+	938.748i	−0.118759	+	0.0862833i	−0.645579	−	0.763693i	$-0.723384\pi$
$491$	−1292.08	+	938.748i	−0.118759	+	0.0862833i	0.526821	+	0.849977i	$0.323384\pi$
$492$		0			0
$493$	−2021.35			−0.184659
$494$	5511.12	−	16961.5i	0.501937	−	1.54480i
$495$		0			0
$496$	175.118	+	538.958i	0.0158529	+	0.0487901i
$497$	2320.38	+	7141.39i	0.209423	+	0.644537i
$498$		0			0
$499$	−3319.59			−0.297806			−0.148903	−	0.988852i	$-0.547574\pi$
$499$	−3319.59			−0.297806			−0.148903	+	0.988852i	$0.547574\pi$
$500$	5719.01	−	655.765i	0.511524	−	0.0586534i
$501$		0			0
$502$	−15620.9	−	11349.2i	−1.38883	−	1.00904i
$503$	−2028.57	−	6243.29i	−0.179820	−	0.553429i	0.820001	−	0.572362i	$-0.193973\pi$
$503$	−2028.57	−	6243.29i	−0.179820	−	0.553429i	−0.999821	+	0.0189337i	$0.993973\pi$
$504$		0			0
$505$	−3206.71	−	2148.29i	−0.282568	−	0.189302i
$506$	−4341.83	+	13362.8i	−0.381458	+	1.17401i
$507$		0			0
$508$	−247.940	+	763.080i	−0.0216546	+	0.0666461i
$509$	12497.0	−	9079.59i	1.08825	−	0.790660i	0.109147	−	0.994026i	$-0.465188\pi$
$509$	12497.0	−	9079.59i	1.08825	−	0.790660i	0.979103	+	0.203366i	$0.0651880\pi$
$510$		0			0
$511$	1462.86	+	1062.83i	0.126640	+	0.0920095i
$512$	4030.06	−	2928.01i	0.347862	−	0.252736i
$513$		0			0
$514$	159.456	+	115.852i	0.0136835	+	0.00994162i
$515$	−4447.27	+	15695.8i	−0.380524	+	1.34299i
$516$		0			0
$517$	1246.50	−	3836.33i	0.106037	−	0.326348i
$518$	−2816.20			−0.238874
$519$		0			0
$520$	−1315.58	+	4643.08i	−0.110946	+	0.391563i
$521$	2533.05	+	7795.93i	0.213004	+	0.655559i	0.999289	+	0.0376951i	$0.0120016\pi$
$521$	2533.05	+	7795.93i	0.213004	+	0.655559i	−0.786285	+	0.617863i	$0.787998\pi$
$522$		0			0
$523$	13281.5	+	9649.57i	1.11044	+	0.806781i	0.982733	−	0.185031i	$-0.0592387\pi$
$523$	13281.5	+	9649.57i	1.11044	+	0.806781i	0.127706	+	0.991812i	$0.459239\pi$
$524$	−10211.7			−0.851338
$525$		0			0
$526$	−23191.5			−1.92243
$527$	107.876	+	78.3762i	0.00891676	+	0.00647841i
$528$		0			0
$529$	−233.162	−	717.598i	−0.0191635	−	0.0589790i
$530$	6336.69	−	4982.98i	0.519336	−	0.408390i
$531$		0			0
$532$	8261.66			0.673287
$533$	−3731.48	+	11484.3i	−0.303242	+	0.933284i
$534$		0			0
$535$	−10041.0	−	6726.85i	−0.811423	−	0.543602i
$536$	1546.84	+	1123.84i	0.124651	+	0.0905646i
$537$		0			0
$538$	−14347.3	+	10423.9i	−1.14973	+	0.835331i
$539$	−5701.75	−	4142.56i	−0.455643	−	0.331044i
$540$		0			0
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.994468	−	0.105043i	$-0.966502\pi$
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.207406	+	0.978255i	$0.566502\pi$
$542$	−5346.12	+	16453.7i	−0.423682	+	1.30396i
$543$		0			0
$544$	990.811	−	3049.40i	0.0780895	−	0.240335i
$545$	14240.5	−	542.188i	1.11926	−	0.0426143i
$546$		0			0
$547$	3698.27	+	11382.1i	0.289080	+	0.889695i	0.985146	+	0.171718i	$0.0549319\pi$
$547$	3698.27	+	11382.1i	0.289080	+	0.889695i	−0.696067	+	0.717977i	$0.745068\pi$
$548$	−5885.23	−	4275.87i	−0.458768	−	0.333314i
$549$		0			0
$550$	−12527.2	+	10646.7i	−0.971205	+	0.825415i
$551$	−17222.3			−1.33157
$552$		0			0
$553$	1236.22	+	3804.70i	0.0950623	+	0.292572i
$554$	−5501.56	−	16932.0i	−0.421911	−	1.29851i
$555$		0			0
$556$	−2985.86	+	9189.54i	−0.227750	+	0.700941i
$557$	1182.53			0.0899558			0.0449779	−	0.998988i	$-0.485678\pi$
$557$	1182.53			0.0899558			0.0449779	+	0.998988i	$0.485678\pi$
$558$		0			0
$559$	−6071.25	+	4411.02i	−0.459367	+	0.333750i
$560$	−11177.6	+	425.571i	−0.843464	+	0.0321137i
$561$		0			0
$562$	−1897.01	+	1378.26i	−0.142385	+	0.103449i
$563$	−6830.40	+	4962.58i	−0.511310	+	0.371488i	−0.813320	−	0.581816i	$-0.802342\pi$
$563$	−6830.40	+	4962.58i	−0.511310	+	0.371488i	0.302011	+	0.953305i	$0.402342\pi$
$564$		0			0
$565$	3140.16	−	119.557i	0.233818	−	0.00890229i
$566$	8013.79	−	5822.36i	0.595132	−	0.432389i
$567$		0			0
$568$	8110.70			0.599150
$569$	−1206.03	+	3711.79i	−0.0888568	+	0.273473i	−0.985604	−	0.169070i	$-0.945924\pi$
$569$	−1206.03	+	3711.79i	−0.0888568	+	0.273473i	0.896747	+	0.442543i	$0.145924\pi$
$570$		0			0
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	0.971880	−	0.235478i	$-0.0756656\pi$
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	−0.924678	+	0.380751i	$0.875666\pi$
$572$	1536.33	+	4728.34i	0.112303	+	0.345633i
$573$		0			0
$574$	−16458.2			−1.19678
$575$	−3148.88	+	12977.1i	−0.228378	+	0.941185i
$576$		0			0
$577$	5851.58	+	4251.42i	0.422192	+	0.306740i	0.778519	−	0.627621i	$-0.215971\pi$
$577$	5851.58	+	4251.42i	0.422192	+	0.306740i	−0.356327	+	0.934361i	$0.615971\pi$
$578$	4904.17	+	15093.5i	0.352918	+	1.08617i
$579$		0			0
$580$	−4942.47	+	188.177i	−0.353836	+	0.0134718i
$581$	4305.09	−	13249.7i	0.307410	−	0.946111i
$582$		0			0
$583$	−2418.04	+	7441.95i	−0.171775	+	0.528669i
$584$	1580.10	−	1148.01i	0.111961	−	0.0813443i
$585$		0			0
$586$	−586.712	−	426.271i	−0.0413598	−	0.0300497i
$587$	8558.36	−	6218.01i	0.601774	−	0.437214i	−0.244734	−	0.969590i	$-0.578701\pi$
$587$	8558.36	−	6218.01i	0.601774	−	0.437214i	0.846508	+	0.532376i	$0.178701\pi$
$588$		0			0
$589$	919.123	+	667.782i	0.0642985	+	0.0467156i
$590$	−10467.2	−	7012.37i	−0.730386	−	0.489313i
$591$		0			0
$592$	−1598.57	+	4919.88i	−0.110981	+	0.341564i
$593$	−7485.02			−0.518335			−0.259168	−	0.965832i	$-0.583448\pi$
$593$	−7485.02			−0.518335			−0.259168	+	0.965832i	$0.583448\pi$
$594$		0			0
$595$	−2068.90	+	1626.92i	−0.142549	+	0.112096i
$596$	−283.618	−	872.888i	−0.0194924	−	0.0599914i
$597$		0			0
$598$	9612.24	+	6983.70i	0.657314	+	0.477566i
$599$	−16860.4			−1.15008			−0.575039	−	0.818126i	$-0.695013\pi$
$599$	−16860.4			−1.15008			−0.575039	+	0.818126i	$0.695013\pi$
$600$		0			0
$601$	11032.4			0.748788			0.374394	−	0.927270i	$-0.377851\pi$
$601$	11032.4			0.748788			0.374394	+	0.927270i	$0.377851\pi$
$602$	−8274.90	−	6012.07i	−0.560232	−	0.407032i
$603$		0			0
$604$	−1680.34	−	5171.55i	−0.113199	−	0.348390i
$605$	293.694	−	1036.54i	0.0197362	−	0.0696552i
$606$		0			0
$607$	937.076			0.0626602			0.0313301	−	0.999509i	$-0.490026\pi$
$607$	937.076			0.0626602			0.0313301	+	0.999509i	$0.490026\pi$
$608$	8441.92	−	25981.6i	0.563101	−	1.73305i
$609$		0			0
$610$	2908.68	−	10265.7i	0.193064	−	0.681385i
$611$	−2759.59	−	2004.96i	−0.182718	−	0.132753i
$612$		0			0
$613$	17272.2	−	12549.0i	1.13804	−	0.826835i	0.151196	−	0.988504i	$-0.451688\pi$
$613$	17272.2	−	12549.0i	1.13804	−	0.826835i	0.986845	+	0.161669i	$0.0516876\pi$
$614$	1864.05	+	1354.31i	0.122519	+	0.0890156i
$615$		0			0
$616$	5165.31	−	3752.82i	0.337851	−	0.245463i
$617$	−8530.27	+	26253.5i	−0.556590	+	1.71301i	0.135119	+	0.990829i	$0.456858\pi$
$617$	−8530.27	+	26253.5i	−0.556590	+	1.71301i	−0.691708	+	0.722177i	$0.743142\pi$
$618$		0			0
$619$	3030.03	−	9325.47i	0.196748	−	0.605529i	−0.803204	−	0.595705i	$-0.796873\pi$
$619$	3030.03	−	9325.47i	0.196748	−	0.605529i	0.999952	−	0.00982399i	$-0.00312712\pi$
$620$	271.066	+	181.597i	0.0175585	+	0.0117631i
$621$		0			0
$622$	−9341.05	−	28748.8i	−0.602157	−	1.85325i
$623$	−547.447	−	397.744i	−0.0352055	−	0.0255783i
$624$		0			0
$625$	−11102.1	+	10994.7i	−0.710534	+	0.703663i
$626$	−13052.8			−0.833381
$627$		0			0
$628$	−2174.97	−	6693.88i	−0.138202	−	0.425342i
$629$	376.138	+	1157.63i	0.0238436	+	0.0733830i
$630$		0			0
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	−1.00000		0.000497352i	$-0.999842\pi$
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	0.809309	+	0.587383i	$0.199842\pi$
$632$	4321.11			0.271969
$633$		0			0
$634$	17608.4	−	12793.3i	1.10303	−	0.801397i
$635$	−751.306	−	2044.15i	−0.0469523	−	0.127747i
$636$		0			0
$637$	−4821.53	+	3503.04i	−0.299899	+	0.217890i
$638$	11428.0	−	8302.91i	0.709150	−	0.515228i
$639$		0			0
$640$	−4650.63	+	16413.6i	−0.287238	+	1.01375i
$641$	18210.1	−	13230.4i	1.12208	−	0.815242i	0.137561	−	0.990493i	$-0.456074\pi$
$641$	18210.1	−	13230.4i	1.12208	−	0.815242i	0.984524	+	0.175251i	$0.0560737\pi$
$642$		0			0
$643$	−649.245			−0.0398192			−0.0199096	−	0.999802i	$-0.506338\pi$
$643$	−649.245			−0.0398192			−0.0199096	+	0.999802i	$0.506338\pi$
$644$	−1700.82	+	5234.59i	−0.104071	+	0.320298i
$645$		0			0
$646$	−3246.58	−	9991.96i	−0.197732	−	0.608558i
$647$	−9808.83	−	30188.5i	−0.596020	−	1.83436i	−0.549584	−	0.835439i	$-0.685214\pi$
$647$	−9808.83	−	30188.5i	−0.596020	−	1.83436i	−0.0464360	−	0.998921i	$-0.514786\pi$
$648$		0			0
$649$	12229.7			0.739688
$650$	5288.96	+	12856.9i	0.319154	+	0.775832i
$651$		0			0
$652$	−4533.95	−	3294.11i	−0.272336	−	0.197864i
$653$	1670.26	+	5140.54i	0.100096	+	0.308062i	0.988548	−	0.150906i	$-0.0482191\pi$
$653$	1670.26	+	5140.54i	0.100096	+	0.308062i	−0.888453	+	0.458968i	$0.848219\pi$
$654$		0			0
$655$	21788.2	−	17133.6i	1.29975	−	1.02208i
$656$	−9342.22	+	28752.4i	−0.556025	+	1.71127i
$657$		0			0
$658$	1436.66	−	4421.58i	0.0851167	−	0.261962i
$659$	2971.87	−	2159.19i	0.175671	−	0.127633i	−0.496475	−	0.868051i	$-0.665373\pi$
$659$	2971.87	−	2159.19i	0.175671	−	0.127633i	0.672146	+	0.740418i	$0.265373\pi$
$660$		0			0
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	0.343698	−	0.939080i	$-0.388320\pi$
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	−0.786910	+	0.617068i	$0.788320\pi$
$662$	−14371.5	+	10441.5i	−0.843753	+	0.613023i
$663$		0			0
$664$	−12174.2	−	8845.06i	−0.711521	−	0.516950i
$665$	−17627.5	+	13861.7i	−1.02792	+	0.808322i
$666$		0			0
$667$	3545.55	−	10912.1i	0.205823	−	0.633460i
$668$	−12015.4			−0.695940
$669$		0			0
$670$	5504.07	−	209.559i	0.317374	−	0.0120836i
$671$	3200.49	+	9850.10i	0.184134	+	0.566705i
$672$		0			0
$673$	−25425.2	−	18472.5i	−1.45627	−	1.05804i	−0.984315	−	0.176422i	$-0.943548\pi$
$673$	−25425.2	−	18472.5i	−1.45627	−	1.05804i	−0.471958	−	0.881621i	$-0.656452\pi$
$674$	18189.8			1.03953
$675$		0			0
$676$	−4845.29			−0.275677
$677$	6007.13	+	4364.44i	0.341023	+	0.247768i	0.745094	−	0.666960i	$-0.232405\pi$
$677$	6007.13	+	4364.44i	0.341023	+	0.247768i	−0.404070	+	0.914728i	$0.632405\pi$
$678$		0			0
$679$	5084.19	+	15647.5i	0.287354	+	0.884384i
$680$	980.737	+	2668.38i	0.0553081	+	0.150482i
$681$		0			0
$682$	−931.827			−0.0523189
$683$	−6948.13	+	21384.1i	−0.389257	+	1.19801i	0.544087	+	0.839029i	$0.316876\pi$
$683$	−6948.13	+	21384.1i	−0.389257	+	1.19801i	−0.933344	+	0.358982i	$0.883124\pi$
$684$		0			0
$685$	19731.2	−	751.238i	1.10057	−	0.0419027i
$686$	−18654.7	−	13553.4i	−1.03825	−	0.754334i
$687$		0			0
$688$	−15200.1	+	11043.5i	−0.842296	+	0.611964i
$689$	5353.22	+	3889.34i	0.295996	+	0.215054i
$690$		0			0
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	−0.497794	−	0.867295i	$-0.665857\pi$
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	0.671020	+	0.741439i	$0.265857\pi$
$692$	−2253.62	+	6935.93i	−0.123800	+	0.381018i
$693$		0			0
$694$	−846.508	+	2605.28i	−0.0463012	+	0.142500i
$695$	−9047.75	−	24617.0i	−0.493814	−	1.34357i
$696$		0			0
$697$	2198.20	+	6765.37i	0.119459	+	0.367656i
$698$	11353.0	+	8248.47i	0.615643	+	0.447291i
$699$		0			0
$700$	−4907.29	+	4170.64i	−0.264969	+	0.225193i
$701$	12744.3			0.686655			0.343327	−	0.939216i	$-0.388446\pi$
$701$	12744.3			0.686655			0.343327	+	0.939216i	$0.388446\pi$
$702$		0			0
$703$	3204.78	+	9863.29i	0.171935	+	0.529162i
$704$	−546.482	−	1681.90i	−0.0292561	−	0.0900410i
$705$		0			0
$706$	2543.28	−	7827.41i	0.135577	−	0.417264i
$707$	4318.23			0.229708
$708$		0			0
$709$	12309.4	−	8943.33i	0.652032	−	0.473729i	−0.211931	−	0.977285i	$-0.567975\pi$
$709$	12309.4	−	8943.33i	0.652032	−	0.473729i	0.863963	+	0.503556i	$0.167975\pi$
$710$	18366.7	−	14443.0i	0.970829	−	0.763430i
$711$		0			0
$712$	−591.322	+	429.621i	−0.0311246	+	0.0226134i
$713$	−612.326	+	444.881i	−0.0321624	+	0.0233673i
$714$		0			0
$715$	−11211.4	−	7510.91i	−0.586408	−	0.392856i
$716$	−6946.51	+	5046.93i	−0.362574	+	0.263426i
$717$		0			0
$718$	−17049.2			−0.886172
$719$	−4155.65	+	12789.8i	−0.215549	+	0.663392i	0.783565	+	0.621310i	$0.213399\pi$
$719$	−4155.65	+	12789.8i	−0.215549	+	0.663392i	−0.999114	+	0.0420821i	$0.986601\pi$
$720$		0			0
$721$	−5639.94	−	17358.0i	−0.291321	−	0.896593i
$722$	−20282.9	−	62424.5i	−1.04550	−	3.21773i
$723$		0			0
$724$	−2170.30			−0.111407
$725$	10229.8	−	8694.16i	0.524033	−	0.445369i
$726$		0			0
$727$	23307.2	+	16933.7i	1.18902	+	0.863871i	0.993160	−	0.116761i	$-0.0372513\pi$
$727$	23307.2	+	16933.7i	1.18902	+	0.863871i	0.195857	+	0.980633i	$0.437251\pi$
$728$	−1668.39	−	5134.77i	−0.0849377	−	0.261411i
$729$		0			0
$730$	1533.84	−	5413.41i	0.0777671	−	0.274465i
$731$	−1366.12	+	4204.49i	−0.0691215	+	0.212734i
$732$		0			0
$733$	−4508.60	+	13876.0i	−0.227188	+	0.699213i	0.770874	+	0.636988i	$0.219820\pi$
$733$	−4508.60	+	13876.0i	−0.227188	+	0.699213i	−0.998062	+	0.0622256i	$0.980180\pi$
$734$	−33164.8	+	24095.6i	−1.66776	+	1.21170i
$735$		0			0
$736$	14724.0	+	10697.6i	0.737410	+	0.535760i
$737$	−4325.48	+	3142.65i	−0.216189	+	0.157070i
$738$		0			0
$739$	−836.136	−	607.488i	−0.0416208	−	0.0302393i	0.566780	−	0.823869i	$-0.308189\pi$
$739$	−836.136	−	607.488i	−0.0416208	−	0.0302393i	−0.608401	+	0.793630i	$0.708189\pi$
$740$	1027.48	+	2795.55i	0.0510416	+	0.138874i
$741$		0			0
$742$	−2786.92	+	8577.26i	−0.137885	+	0.424368i
$743$	3409.57			0.168351			0.0841756	−	0.996451i	$-0.473174\pi$
$743$	3409.57			0.168351			0.0841756	+	0.996451i	$0.473174\pi$
$744$		0			0
$745$	2069.71	+	1386.57i	0.101783	+	0.0681880i
$746$	−13489.7	−	41517.1i	−0.662056	−	2.03760i
$747$		0			0
$748$	2369.45	+	1721.50i	0.115823	+	0.0841503i
$749$	13521.5			0.659632
$750$		0			0
$751$	−19553.4			−0.950087			−0.475043	−	0.879962i	$-0.657568\pi$
$751$	−19553.4			−0.950087			−0.475043	+	0.879962i	$0.657568\pi$
$752$	−6908.98	−	5019.66i	−0.335032	−	0.243415i
$753$		0			0
$754$	−3691.23	−	11360.4i	−0.178285	−	0.548703i
$755$	12262.3	+	8214.95i	0.591086	+	0.395990i
$756$		0			0
$757$	12295.8			0.590353			0.295176	−	0.955443i	$-0.404622\pi$
$757$	12295.8			0.590353			0.295176	+	0.955443i	$0.404622\pi$
$758$	−5824.38	+	17925.6i	−0.279091	+	0.858954i
$759$		0			0
$760$	8356.08	+	22735.2i	0.398825	+	1.08512i
$761$	−1950.66	−	1417.24i	−0.0929190	−	0.0675096i	0.540356	−	0.841437i	$-0.318290\pi$
$761$	−1950.66	−	1417.24i	−0.0929190	−	0.0675096i	−0.633275	+	0.773927i	$0.718290\pi$
$762$		0			0
$763$	−12898.5	+	9371.29i	−0.612000	+	0.444644i
$764$	7714.20	+	5604.70i	0.365301	+	0.265407i
$765$		0			0
$766$	39969.6	−	29039.6i	1.88533	−	1.36977i
$767$	3195.76	−	9835.54i	0.150446	−	0.463026i
$768$		0			0
$769$	−8608.70	+	26494.8i	−0.403690	+	1.24243i	0.518294	+	0.855202i	$0.326567\pi$
$769$	−8608.70	+	26494.8i	−0.403690	+	1.24243i	−0.921984	+	0.387227i	$0.873433\pi$
$770$	5014.08	−	17696.3i	0.234669	−	0.828219i
$771$		0			0
$772$	2582.55	+	7948.28i	0.120399	+	0.370551i
$773$	−20165.3	−	14651.0i	−0.938287	−	0.681705i	0.00972064	−	0.999953i	$-0.496906\pi$
$773$	−20165.3	−	14651.0i	−0.938287	−	0.681705i	−0.948008	+	0.318247i	$0.896906\pi$
$774$		0			0
$775$	−883.051	+	67.3394i	−0.0409292	+	0.00312117i
$776$	17771.4			0.822107
$777$		0			0
$778$	254.851	+	784.352i	0.0117440	+	0.0361444i
$779$	18729.1	+	57642.4i	0.861414	+	2.65116i
$780$		0			0
$781$	−7008.59	+	21570.2i	−0.321110	+	0.988276i
$782$	6999.28			0.320069
$783$		0			0
$784$	−12071.3	+	8770.32i	−0.549895	+	0.399522i
$785$	15871.9	+	10633.1i	0.721644	+	0.483456i
$786$		0			0
$787$	−10460.2	+	7599.80i	−0.473782	+	0.344223i	−0.798913	−	0.601446i	$-0.794592\pi$
$787$	−10460.2	+	7599.80i	−0.473782	+	0.344223i	0.325131	+	0.945669i	$0.394592\pi$
$788$	8789.76	−	6386.13i	0.397363	−	0.288701i
$789$		0			0
$790$	9785.15	−	7694.74i	0.440684	−	0.346540i
$791$	−2844.22	+	2066.45i	−0.127849	+	0.0928880i
$792$		0			0
$793$	8758.12			0.392194
$794$	12319.7	−	37916.1i	0.550641	−	1.69470i
$795$		0			0
$796$	756.501	+	2328.27i	0.0336852	+	0.103673i
$797$	−4001.08	−	12314.1i	−0.177824	−	0.547285i	0.821927	−	0.569592i	$-0.192899\pi$
$797$	−4001.08	−	12314.1i	−0.177824	−	0.547285i	−0.999751	+	0.0223070i	$0.992899\pi$
$798$		0			0
$799$	−2009.43			−0.0889719
$800$	8101.62	+	19694.2i	0.358045	+	0.870371i
$801$		0			0
$802$	−37583.2	−	27305.8i	−1.65475	−	1.20225i
$803$	1687.72	+	5194.26i	0.0741697	+	0.228271i
$804$		0			0
$805$	−5153.83	−	14022.5i	−0.225650	−	0.613948i
$806$	−243.497	+	749.408i	−0.0106412	+	0.0327503i
$807$		0			0
$808$	1441.35	−	4436.03i	0.0627557	−	0.193142i
$809$	−7492.76	+	5443.81i	−0.325626	+	0.236581i	−0.738572	−	0.674174i	$-0.764500\pi$
$809$	−7492.76	+	5443.81i	−0.325626	+	0.236581i	0.412946	+	0.910755i	$0.364500\pi$
$810$		0			0
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	0.645545	−	0.763722i	$-0.276630\pi$
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	−0.526859	+	0.849953i	$0.676630\pi$
$812$	4476.68	−	3252.50i	0.193474	−	0.140567i
$813$		0			0
$814$	−6881.65	−	4999.81i	−0.296317	−	0.215287i
$815$	15200.8	−	578.750i	0.653328	−	0.0248745i
$816$		0			0
$817$	−11639.6	+	35823.2i	−0.498433	+	1.53402i
$818$	26162.6			1.11828
$819$		0			0
$820$	6004.71	+	16337.6i	0.255724	+	0.695772i
$821$	−3816.58	−	11746.2i	−0.162241	−	0.499325i	0.836582	−	0.547842i	$-0.184551\pi$
$821$	−3816.58	−	11746.2i	−0.162241	−	0.499325i	−0.998822	+	0.0485169i	$0.984551\pi$
$822$		0			0
$823$	−23545.0	−	17106.4i	−0.997239	−	0.724536i	−0.0357442	−	0.999361i	$-0.511380\pi$
$823$	−23545.0	−	17106.4i	−0.997239	−	0.724536i	−0.961494	+	0.274825i	$0.911380\pi$
$824$	−19714.0			−0.833457
$825$		0			0
$826$	14095.4			0.593754
$827$	−6507.78	−	4728.18i	−0.273637	−	0.198809i	0.442500	−	0.896768i	$-0.354092\pi$
$827$	−6507.78	−	4728.18i	−0.273637	−	0.198809i	−0.716137	+	0.697959i	$0.754092\pi$
$828$		0			0
$829$	7849.09	+	24157.0i	0.328842	+	1.01207i	0.969676	+	0.244393i	$0.0785886\pi$
$829$	7849.09	+	24157.0i	0.328842	+	1.01207i	−0.640834	+	0.767679i	$0.721411\pi$
$830$	−43319.1	+	1649.31i	−1.81160	+	0.0689740i
$831$		0			0
$832$	−1495.44			−0.0623139
$833$	−1084.92	+	3339.03i	−0.0451262	+	0.138884i
$834$		0			0
$835$	25636.6	−	20159.8i	1.06250	−	0.835519i
$836$	20188.2	+	14667.6i	0.835195	+	0.606805i
$837$		0			0
$838$	18045.7	−	13111.0i	0.743889	−	0.540467i
$839$	26598.5	+	19324.9i	1.09450	+	0.795198i	0.980153	−	0.198243i	$-0.0635236\pi$
$839$	26598.5	+	19324.9i	1.09450	+	0.795198i	0.114343	+	0.993441i	$0.463524\pi$
$840$		0			0
$841$	10399.0	−	7555.31i	0.426380	−	0.309784i
$842$	−16287.0	+	50126.2i	−0.666611	+	2.05162i
$843$		0			0
$844$	−2404.06	+	7398.93i	−0.0980463	+	0.301756i
$845$	10338.2	−	8129.60i	0.420880	−	0.330967i
$846$		0			0
$847$	372.458	+	1146.31i	0.0151096	+	0.0465025i
$848$	13402.5	+	9737.46i	0.542739	+	0.394323i
$849$		0			0
$850$	6972.54	+	4296.11i	0.281360	+	0.173359i
$851$	−6909.15			−0.278311
$852$		0			0
$853$	−2870.65	−	8834.96i	−0.115228	−	0.354635i	0.876767	−	0.480916i	$-0.159696\pi$
$853$	−2870.65	−	8834.96i	−0.115228	−	0.354635i	−0.991994	+	0.126281i	$0.959696\pi$
$854$	3688.74	+	11352.8i	0.147806	+	0.454899i
$855$		0			0
$856$	4513.24	−	13890.3i	0.180210	−	0.554628i
$857$	39874.7			1.58937			0.794687	−	0.607019i	$-0.207635\pi$
$857$	39874.7			1.58937			0.794687	+	0.607019i	$0.207635\pi$
$858$		0			0
$859$	−22161.6	+	16101.3i	−0.880261	+	0.639547i	−0.933321	−	0.359044i	$-0.883103\pi$
$859$	−22161.6	+	16101.3i	−0.880261	+	0.639547i	0.0530595	+	0.998591i	$0.483103\pi$
$860$	−2948.93	+	10407.7i	−0.116928	+	0.412674i
$861$		0			0
$862$	−34518.6	+	25079.2i	−1.36393	+	0.990953i
$863$	−26794.6	+	19467.4i	−1.05689	+	0.767879i	−0.973511	−	0.228639i	$-0.926572\pi$
$863$	−26794.6	+	19467.4i	−1.05689	+	0.767879i	−0.0833829	+	0.996518i	$0.526572\pi$
$864$		0			0
$865$	−6828.91	−	18580.1i	−0.268428	−	0.730336i
$866$	35148.0	−	25536.5i	1.37919	−	1.00204i
$867$		0			0
$868$	−365.024			−0.0142739
$869$	−3733.95	+	11491.9i	−0.145760	+	0.448603i
$870$		0			0
$871$	1397.13	+	4299.91i	0.0543511	+	0.167276i
$872$	5321.64	+	16378.3i	0.206667	+	0.636055i
$873$		0			0
$874$	59635.4			2.30801
$875$	3472.78	−	17132.3i	0.134173	−	0.661918i
$876$		0			0
$877$	−25574.8	−	18581.1i	−0.984719	−	0.715440i	−0.0259603	−	0.999663i	$-0.508264\pi$
$877$	−25574.8	−	18581.1i	−0.984719	−	0.715440i	−0.958758	+	0.284223i	$0.908264\pi$
$878$	−17342.0	−	53373.0i	−0.666586	−	2.05154i
$879$		0			0
$880$	−28069.1	−	18804.5i	−1.07524	−	0.720342i
$881$	13273.0	−	40850.2i	0.507583	−	1.56218i	−0.288803	−	0.957389i	$-0.593257\pi$
$881$	13273.0	−	40850.2i	0.507583	−	1.56218i	0.796385	−	0.604790i	$-0.206743\pi$
$882$		0			0
$883$	−633.110	+	1948.51i	−0.0241289	+	0.0742612i	−0.962396	−	0.271651i	$-0.912430\pi$
$883$	−633.110	+	1948.51i	−0.0241289	+	0.0742612i	0.938267	+	0.345912i	$0.112430\pi$
$884$	2003.66	−	1455.74i	0.0762333	−	0.0553868i
$885$		0			0
$886$	33764.5	+	24531.3i	1.28029	+	0.930187i
$887$	−9661.40	+	7019.42i	−0.365725	+	0.265715i	−0.755436	−	0.655222i	$-0.772575\pi$
$887$	−9661.40	+	7019.42i	−0.365725	+	0.265715i	0.389711	+	0.920937i	$0.372575\pi$
$888$		0			0
$889$	1971.17	+	1432.14i	0.0743655	+	0.0540297i
$890$	−574.010	+	2025.86i	−0.0216189	+	0.0763000i
$891$		0			0
$892$	2847.84	−	8764.75i	0.106898	−	0.328997i
$893$	−17120.8			−0.641574
$894$		0			0
$895$	6353.49	−	22423.5i	0.237289	−	0.837469i
$896$	−5897.85	−	18151.7i	−0.219903	−	0.676792i
$897$		0			0
$898$	−2163.57	−	1571.93i	−0.0804002	−	0.0584142i
$899$	760.933			0.0282297
$900$		0			0
$901$	3898.02			0.144131
$902$	−40217.3	−	29219.6i	−1.48458	−	1.07861i
$903$		0			0
$904$	1173.46	+	3611.55i	0.0431735	+	0.132874i
$905$	4630.66	−	3641.40i	0.170087	−	0.133751i
$906$		0			0
$907$	2447.01			0.0895827			0.0447913	−	0.998996i	$-0.485738\pi$
$907$	2447.01			0.0895827			0.0447913	+	0.998996i	$0.485738\pi$
$908$	2139.46	−	6584.59i	0.0781945	−	0.240658i
$909$		0			0
$910$	−12921.7	−	8656.74i	−0.470715	−	0.315349i
$911$	19395.7	+	14091.8i	0.705387	+	0.512493i	0.881682	−	0.471844i	$-0.156411\pi$
$911$	19395.7	+	14091.8i	0.705387	+	0.512493i	−0.176296	+	0.984337i	$0.556411\pi$
$912$		0			0
$913$	34043.2	−	24733.8i	1.23402	−	0.896571i
$914$	36663.2	+	26637.3i	1.32682	+	0.963988i
$915$		0			0
$916$	−13809.3	+	10033.0i	−0.498113	+	0.361900i
$917$	−9582.61	+	29492.2i	−0.345088	+	1.06207i
$918$		0			0
$919$	−6201.28	+	19085.6i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$919$	−6201.28	+	19085.6i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$920$	−16125.3	+	613.947i	−0.577864	+	0.0220013i
$921$		0			0
$922$	16754.6	+	51565.5i	0.598465	+	1.84189i
$923$	15516.1	+	11273.1i	0.553325	+	0.402014i
$924$		0			0
$925$	−6882.76	−	4240.79i	−0.244653	−	0.150742i
$926$	−14167.9			−0.502794
$927$		0			0
$928$	−5654.21	−	17401.9i	−0.200009	−	0.615565i
$929$	−4458.92	−	13723.2i	−0.157473	−	0.484653i	0.840930	−	0.541144i	$-0.182009\pi$
$929$	−4458.92	−	13723.2i	−0.157473	−	0.484653i	−0.998403	+	0.0564915i	$0.982009\pi$
$930$		0			0
$931$	−9243.71	+	28449.2i	−0.325403	+	1.00149i
$932$	19131.6			0.672398
$933$		0			0
$934$	−1399.83	+	1017.04i	−0.0490406	+	0.0356301i
$935$	−7943.97	+	302.455i	−0.277856	+	0.0105790i
$936$		0			0
$937$	30964.9	−	22497.3i	1.07959	−	0.784371i	0.101981	−	0.994786i	$-0.467482\pi$
$937$	30964.9	−	22497.3i	1.07959	−	0.784371i	0.977612	+	0.210416i	$0.0674818\pi$
$938$	−4985.35	+	3622.07i	−0.173537	+	0.126082i
$939$		0			0
$940$	−4913.32	+	187.068i	−0.170484	+	0.00649093i
$941$	−13900.7	+	10099.5i	−0.481563	+	0.349876i	−0.801930	−	0.597417i	$-0.796194\pi$
$941$	−13900.7	+	10099.5i	−0.481563	+	0.349876i	0.320368	+	0.947293i	$0.396194\pi$
$942$		0			0
$943$	−40378.0			−1.39437
$944$	8001.00	−	24624.5i	0.275858	−	0.849005i
$945$		0			0
$946$	−9546.84	−	29382.1i	−0.328113	−	1.00983i
$947$	−5191.85	−	15978.9i	−0.178155	−	0.548304i	0.821609	−	0.570052i	$-0.193077\pi$
$947$	−5191.85	−	15978.9i	−0.178155	−	0.548304i	−0.999763	+	0.0217480i	$0.993077\pi$
$948$		0			0
$949$	4618.43			0.157977
$950$	59407.5	+	36603.8i	2.02888	+	1.25009i
$951$		0			0
$952$	−2573.12	−	1869.48i	−0.0876000	−	0.0636451i
$953$	5977.19	+	18395.9i	0.203169	+	0.625290i	0.999784	+	0.0208023i	$0.00662205\pi$
$953$	5977.19	+	18395.9i	0.203169	+	0.625290i	−0.796615	+	0.604487i	$0.793378\pi$
$954$		0			0
$955$	−25863.2	+	984.703i	−0.876348	+	0.0333657i
$956$	−4260.10	+	13111.2i	−0.144123	+	0.443565i
$957$		0			0
$958$	4888.92	−	15046.5i	0.164879	−	0.507444i
$959$	−17871.7	+	12984.6i	−0.601781	+	0.437219i
$960$		0			0
$961$	24060.8	+	17481.2i	0.807654	+	0.586795i
$962$	−5819.28	+	4227.96i	−0.195032	+	0.141699i
$963$		0			0
$964$	24084.3	+	17498.3i	0.804672	+	0.584628i
$965$	−18846.2	−	12625.8i	−0.628684	−	0.421179i
$966$		0			0
$967$	12275.5	−	37780.0i	0.408224	−	1.25638i	−0.509950	−	0.860204i	$-0.670336\pi$
$967$	12275.5	−	37780.0i	0.408224	−	1.25638i	0.918173	−	0.396179i	$-0.129664\pi$
$968$	1301.90			0.0432279
$969$		0			0
$970$	40243.2	−	31646.0i	1.33210	−	1.04752i
$971$	−3924.88	−	12079.5i	−0.129717	−	0.399229i	0.865014	−	0.501748i	$-0.167310\pi$
$971$	−3924.88	−	12079.5i	−0.129717	−	0.399229i	−0.994731	+	0.102520i	$0.967310\pi$
$972$		0			0
$973$	23738.2	+	17246.8i	0.782129	+	0.568250i
$974$	57485.2			1.89111
$975$		0			0
$976$	21927.1			0.719127
$977$	11761.8	+	8545.44i	0.385152	+	0.279829i	0.763466	−	0.645848i	$-0.223496\pi$
$977$	11761.8	+	8545.44i	0.385152	+	0.279829i	−0.378314	+	0.925677i	$0.623496\pi$
$978$		0			0
$979$	−631.596	−	1943.85i	−0.0206189	−	0.0634584i
$980$	−2341.92	+	8265.36i	−0.0763365	+	0.269416i
$981$		0			0
$982$	−5559.86			−0.180674
$983$	6980.26	−	21483.0i	0.226486	−	0.697053i	−0.771651	−	0.636046i	$-0.780569\pi$
$983$	6980.26	−	21483.0i	0.226486	−	0.697053i	0.998137	−	0.0610068i	$-0.0194311\pi$
$984$		0			0
$985$	−8039.39	+	28373.5i	−0.260057	+	0.917824i
$986$	−5692.89	−	4136.13i	−0.183873	−	0.133591i
$987$		0			0
$988$	17071.6	−	12403.2i	0.549716	−	0.399392i
$989$	−20301.3	−	14749.8i	−0.652724	−	0.474232i
$990$		0			0
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	−0.593791	−	0.804619i	$-0.702369\pi$
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	0.581747	+	0.813370i	$0.302369\pi$
$992$	−372.989	+	1147.94i	−0.0119379	+	0.0367411i
$993$		0			0
$994$	−8077.78	+	24860.9i	−0.257758	+	0.793298i
$995$	−5520.56	−	3698.43i	−0.175893	−	0.117837i
$996$		0			0
$997$	−6307.66	−	19413.0i	−0.200367	−	0.616666i	−0.999872	−	0.0160063i	$-0.994905\pi$
$997$	−6307.66	−	19413.0i	−0.200367	−	0.616666i	0.799505	−	0.600659i	$-0.205095\pi$
$998$	−9349.23	−	6792.62i	−0.296538	−	0.215447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.91.6		28
3.2	odd	2		25.4.d.a.16.2	yes	28
15.2	even	4		125.4.e.b.49.12		56
15.8	even	4		125.4.e.b.49.3		56
15.14	odd	2		125.4.d.a.76.6		28
25.11	even	5	inner	225.4.h.b.136.6		28
75.2	even	20		125.4.e.b.74.3		56
75.11	odd	10		25.4.d.a.11.2	✓	28
75.14	odd	10		125.4.d.a.51.6		28
75.23	even	20		125.4.e.b.74.12		56
75.44	odd	10		625.4.a.d.1.3		14
75.56	odd	10		625.4.a.c.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.2	✓	28	75.11	odd	10
25.4.d.a.16.2	yes	28	3.2	odd	2
125.4.d.a.51.6		28	75.14	odd	10
125.4.d.a.76.6		28	15.14	odd	2
125.4.e.b.49.3		56	15.8	even	4
125.4.e.b.49.12		56	15.2	even	4
125.4.e.b.74.3		56	75.2	even	20
125.4.e.b.74.12		56	75.23	even	20
225.4.h.b.91.6		28	1.1	even	1	trivial
225.4.h.b.136.6		28	25.11	even	5	inner
625.4.a.c.1.12		14	75.56	odd	10
625.4.a.d.1.3		14	75.44	odd	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81638 + 2.04622i) q^{2} +(1.27284 + 3.91740i) q^{4} +(-9.28856 - 6.22275i) q^{5} +12.5082 q^{7} +(4.17503 - 12.8494i) q^{8} +O(q^{10})\)	\(q+(2.81638 + 2.04622i) q^{2} +(1.27284 + 3.91740i) q^{4} +(-9.28856 - 6.22275i) q^{5} +12.5082 q^{7} +(4.17503 - 12.8494i) q^{8} +(-13.4270 - 36.5321i) q^{10} +(30.5650 + 22.2068i) q^{11} +(25.8465 - 18.7786i) q^{13} +(35.2278 + 25.5945i) q^{14} +(64.7099 - 47.0145i) q^{16} +(5.81584 - 17.8993i) q^{17} +(49.5522 - 152.506i) q^{19} +(12.5542 - 44.3076i) q^{20} +(40.6427 + 125.085i) q^{22} +(86.4266 + 62.7926i) q^{23} +(47.5547 + 115.601i) q^{25} +111.218 q^{26} +(15.9210 + 48.9997i) q^{28} +(-33.1890 - 102.145i) q^{29} +(-2.18936 + 6.73816i) q^{31} +170.364 q^{32} +(53.0055 - 38.5108i) q^{34} +(-116.183 - 77.8354i) q^{35} +(-52.3230 + 38.0149i) q^{37} +(451.619 - 328.120i) q^{38} +(-118.739 + 93.3724i) q^{40} +(-305.782 + 222.164i) q^{41} -234.897 q^{43} +(-48.0885 + 148.001i) q^{44} +(114.923 + 353.696i) q^{46} +(-32.9933 - 101.543i) q^{47} -186.545 q^{49} +(-102.612 + 422.883i) q^{50} +(106.462 + 77.3489i) q^{52} +(64.0024 + 196.979i) q^{53} +(-145.718 - 396.467i) q^{55} +(52.2221 - 160.723i) q^{56} +(115.539 - 355.591i) q^{58} +(261.882 - 190.269i) q^{59} +(221.781 + 161.134i) q^{61} +(-19.9538 + 14.4973i) q^{62} +(-37.8690 - 27.5134i) q^{64} +(-356.931 + 13.5896i) q^{65} +(-43.7313 + 134.591i) q^{67} +77.5215 q^{68} +(-167.948 - 456.950i) q^{70} +(185.509 + 570.937i) q^{71} +(116.952 + 84.9707i) q^{73} -225.148 q^{74} +660.500 q^{76} +(382.313 + 277.767i) q^{77} +(98.8328 + 304.176i) q^{79} +(-893.621 + 34.0233i) q^{80} -1315.80 q^{82} +(344.182 - 1059.28i) q^{83} +(-165.404 + 130.068i) q^{85} +(-661.558 - 480.650i) q^{86} +(412.954 - 300.028i) q^{88} +(-43.7671 - 31.7986i) q^{89} +(323.293 - 234.886i) q^{91} +(-135.977 + 418.493i) q^{92} +(114.857 - 353.495i) q^{94} +(-1409.28 + 1108.21i) q^{95} +(406.468 + 1250.98i) q^{97} +(-525.381 - 381.712i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8} - 25 q^{10} + 89 q^{11} + 33 q^{13} + 17 q^{14} - 207 q^{16} + 191 q^{17} - 115 q^{19} + 225 q^{20} + 808 q^{22} - 433 q^{23} + 90 q^{25} - 586 q^{26} - 13 q^{28} + 5 q^{29} - 639 q^{31} + 1386 q^{32} - 777 q^{34} + 1030 q^{35} + 699 q^{37} + 2355 q^{38} + 410 q^{40} - 341 q^{41} - 172 q^{43} - 548 q^{44} - 1239 q^{46} - 2319 q^{47} + 1344 q^{49} - 2335 q^{50} + 2344 q^{52} + 927 q^{53} + 1225 q^{55} + 2910 q^{56} + 2410 q^{58} + 1905 q^{59} + 1391 q^{61} + 3832 q^{62} - 3596 q^{64} - 1215 q^{65} - 3611 q^{67} - 3622 q^{68} + 560 q^{70} + 3719 q^{71} + 4593 q^{73} - 4848 q^{74} + 3520 q^{76} - 1368 q^{77} + 775 q^{79} - 9500 q^{80} - 6762 q^{82} + 2447 q^{83} - 8185 q^{85} - 3891 q^{86} - 10960 q^{88} + 5075 q^{89} + 376 q^{91} + 8456 q^{92} + 3573 q^{94} - 3265 q^{95} + 7439 q^{97} - 7082 q^{98}+O(q^{100}) \) 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8 - 25 * q^10 + 89 * q^11 + 33 * q^13 + 17 * q^14 - 207 * q^16 + 191 * q^17 - 115 * q^19 + 225 * q^20 + 808 * q^22 - 433 * q^23 + 90 * q^25 - 586 * q^26 - 13 * q^28 + 5 * q^29 - 639 * q^31 + 1386 * q^32 - 777 * q^34 + 1030 * q^35 + 699 * q^37 + 2355 * q^38 + 410 * q^40 - 341 * q^41 - 172 * q^43 - 548 * q^44 - 1239 * q^46 - 2319 * q^47 + 1344 * q^49 - 2335 * q^50 + 2344 * q^52 + 927 * q^53 + 1225 * q^55 + 2910 * q^56 + 2410 * q^58 + 1905 * q^59 + 1391 * q^61 + 3832 * q^62 - 3596 * q^64 - 1215 * q^65 - 3611 * q^67 - 3622 * q^68 + 560 * q^70 + 3719 * q^71 + 4593 * q^73 - 4848 * q^74 + 3520 * q^76 - 1368 * q^77 + 775 * q^79 - 9500 * q^80 - 6762 * q^82 + 2447 * q^83 - 8185 * q^85 - 3891 * q^86 - 10960 * q^88 + 5075 * q^89 + 376 * q^91 + 8456 * q^92 + 3573 * q^94 - 3265 * q^95 + 7439 * q^97 - 7082 * q^98

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