LMFDB - Embedded newform 225.4.h.b.46.2

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			46.2
Character	$\chi$	$=$	225.46
Dual form			225.4.h.b.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906232 + 2.78910i) q^{2} +(-0.485661 - 0.352853i) q^{4} +(10.1222 + 4.74784i) q^{5} -23.0864 q^{7} +(-17.5561 + 12.7553i) q^{8} +O(q^{10})$	\(q+(-0.906232 + 2.78910i) q^{2} +(-0.485661 - 0.352853i) q^{4} +(10.1222 + 4.74784i) q^{5} -23.0864 q^{7} +(-17.5561 + 12.7553i) q^{8} +(-22.4152 + 23.9290i) q^{10} +(10.1957 - 31.3790i) q^{11} +(6.98730 + 21.5047i) q^{13} +(20.9216 - 64.3901i) q^{14} +(-21.1498 - 65.0923i) q^{16} +(-103.416 + 75.1358i) q^{17} +(-64.4944 + 46.8579i) q^{19} +(-3.24065 - 5.87748i) q^{20} +(78.2794 + 56.8733i) q^{22} +(-3.36642 + 10.3608i) q^{23} +(79.9161 + 96.1167i) q^{25} -66.3107 q^{26} +(11.2122 + 8.14611i) q^{28} +(-3.28945 - 2.38992i) q^{29} +(-44.1789 + 32.0979i) q^{31} +27.1110 q^{32} +(-115.842 - 356.526i) q^{34} +(-233.684 - 109.610i) q^{35} +(-80.2988 - 247.134i) q^{37} +(-72.2443 - 222.345i) q^{38} +(-238.266 + 45.7571i) q^{40} +(-33.2460 - 102.321i) q^{41} +124.154 q^{43} +(-16.0238 + 11.6420i) q^{44} +(-25.8465 - 18.7786i) q^{46} +(-368.812 - 267.958i) q^{47} +189.981 q^{49} +(-340.501 + 135.789i) q^{50} +(4.19455 - 12.9095i) q^{52} +(559.680 + 406.631i) q^{53} +(252.184 - 269.216i) q^{55} +(405.307 - 294.473i) q^{56} +(9.64673 - 7.00876i) q^{58} +(-130.566 - 401.842i) q^{59} +(-125.372 + 385.857i) q^{61} +(-49.4877 - 152.307i) q^{62} +(144.629 - 445.123i) q^{64} +(-31.3743 + 250.848i) q^{65} +(-484.733 + 352.179i) q^{67} +76.7368 q^{68} +(517.486 - 552.434i) q^{70} +(734.084 + 533.343i) q^{71} +(-218.714 + 673.134i) q^{73} +762.051 q^{74} +47.8564 q^{76} +(-235.381 + 724.427i) q^{77} +(69.9257 + 50.8040i) q^{79} +(94.9665 - 759.290i) q^{80} +315.511 q^{82} +(40.4126 - 29.3615i) q^{83} +(-1403.52 + 269.536i) q^{85} +(-112.512 + 346.278i) q^{86} +(221.251 + 680.941i) q^{88} +(-202.969 + 624.673i) q^{89} +(-161.311 - 496.465i) q^{91} +(5.29078 - 3.84398i) q^{92} +(1081.59 - 785.820i) q^{94} +(-875.296 + 168.094i) q^{95} +(43.2567 + 31.4278i) q^{97} +(-172.167 + 529.875i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.906232	+	2.78910i	−0.320401	+	0.986094i	0.653072	+	0.757296i	$0.273480\pi$
$2$	−0.906232	+	2.78910i	−0.320401	+	0.986094i	−0.973474	+	0.228799i	$0.926520\pi$
$3$		0			0
$3$		0			0
$4$	−0.485661	−	0.352853i	−0.0607076	−	0.0441067i
$5$	10.1222	+	4.74784i	0.905353	+	0.424660i
$5$	10.1222	+	4.74784i	0.905353	+	0.424660i
$6$		0			0
$7$	−23.0864			−1.24655			−0.623274	−	0.782004i	$-0.714198\pi$
$7$	−23.0864			−1.24655			−0.623274	+	0.782004i	$0.714198\pi$
$8$	−17.5561	+	12.7553i	−0.775878	+	0.563708i
$9$		0			0
$10$	−22.4152	+	23.9290i	−0.708831	+	0.756702i
$11$	10.1957	−	31.3790i	0.279464	−	0.860102i	−0.708539	−	0.705671i	$-0.750646\pi$
$11$	10.1957	−	31.3790i	0.279464	−	0.860102i	0.988004	−	0.154431i	$-0.0493544\pi$
$12$		0			0
$13$	6.98730	+	21.5047i	0.149071	+	0.458794i	0.997512	−	0.0704960i	$-0.0224582\pi$
$13$	6.98730	+	21.5047i	0.149071	+	0.458794i	−0.848441	+	0.529290i	$0.822458\pi$
$14$	20.9216	−	64.3901i	0.399396	−	1.22921i
$15$		0			0
$16$	−21.1498	−	65.0923i	−0.330465	−	1.01707i
$17$	−103.416	+	75.1358i	−1.47541	+	1.07195i	−0.496408	+	0.868089i	$0.665348\pi$
$17$	−103.416	+	75.1358i	−1.47541	+	1.07195i	−0.979000	+	0.203858i	$0.934652\pi$
$18$		0			0
$19$	−64.4944	+	46.8579i	−0.778738	+	0.565786i	−0.904600	−	0.426261i	$-0.859830\pi$
$19$	−64.4944	+	46.8579i	−0.778738	+	0.565786i	0.125862	+	0.992048i	$0.459830\pi$
$20$	−3.24065	−	5.87748i	−0.0362315	−	0.0657122i
$21$		0			0
$22$	78.2794	+	56.8733i	0.758601	+	0.551156i
$23$	−3.36642	+	10.3608i	−0.0305195	+	0.0939293i	−0.965156	−	0.261675i	$-0.915725\pi$
$23$	−3.36642	+	10.3608i	−0.0305195	+	0.0939293i	0.934636	+	0.355605i	$0.115725\pi$
$24$		0			0
$25$	79.9161	+	96.1167i	0.639328	+	0.768934i
$26$	−66.3107			−0.500177
$27$		0			0
$28$	11.2122	+	8.14611i	0.0756750	+	0.0549811i
$29$	−3.28945	−	2.38992i	−0.0210633	−	0.0153034i	0.577204	−	0.816600i	$-0.304144\pi$
$29$	−3.28945	−	2.38992i	−0.0210633	−	0.0153034i	−0.598267	+	0.801297i	$0.704144\pi$
$30$		0			0
$31$	−44.1789	+	32.0979i	−0.255960	+	0.185966i	−0.708364	−	0.705847i	$-0.750567\pi$
$31$	−44.1789	+	32.0979i	−0.255960	+	0.185966i	0.452404	+	0.891813i	$0.350567\pi$
$32$	27.1110			0.149768
$33$		0			0
$34$	−115.842	−	356.526i	−0.584318	−	1.79835i
$35$	−233.684	−	109.610i	−1.12857	−	0.529358i
$36$		0			0
$37$	−80.2988	−	247.134i	−0.356785	−	1.09807i	−0.954967	−	0.296711i	$-0.904110\pi$
$37$	−80.2988	−	247.134i	−0.356785	−	1.09807i	0.598182	−	0.801360i	$-0.295890\pi$
$38$	−72.2443	−	222.345i	−0.308410	−	0.949188i
$39$		0			0
$40$	−238.266	+	45.7571i	−0.941827	+	0.180871i
$41$	−33.2460	−	102.321i	−0.126638	−	0.389751i	0.867558	−	0.497336i	$-0.165688\pi$
$41$	−33.2460	−	102.321i	−0.126638	−	0.389751i	−0.994196	+	0.107585i	$0.965688\pi$
$42$		0			0
$43$	124.154			0.440310			0.220155	−	0.975465i	$-0.429344\pi$
$43$	124.154			0.440310			0.220155	+	0.975465i	$0.429344\pi$
$44$	−16.0238	+	11.6420i	−0.0549019	+	0.0398885i
$45$		0			0
$46$	−25.8465	−	18.7786i	−0.0828446	−	0.0601901i
$47$	−368.812	−	267.958i	−1.14461	−	0.831609i	−0.156857	−	0.987621i	$-0.550136\pi$
$47$	−368.812	−	267.958i	−1.14461	−	0.831609i	−0.987755	+	0.156012i	$0.950136\pi$
$48$		0			0
$49$	189.981			0.553881
$50$	−340.501	+	135.789i	−0.963083	+	0.384071i
$51$		0			0
$52$	4.19455	−	12.9095i	0.0111861	−	0.0344274i
$53$	559.680	+	406.631i	1.45053	+	1.05387i	0.985708	+	0.168463i	$0.0538805\pi$
$53$	559.680	+	406.631i	1.45053	+	1.05387i	0.464819	+	0.885406i	$0.346119\pi$
$54$		0			0
$55$	252.184	−	269.216i	0.618264	−	0.660019i
$56$	405.307	−	294.473i	0.967168	−	0.702689i
$57$		0			0
$58$	9.64673	−	7.00876i	0.0218393	−	0.0158672i
$59$	−130.566	−	401.842i	−0.288107	−	0.886701i	−0.985450	−	0.169964i	$-0.945635\pi$
$59$	−130.566	−	401.842i	−0.288107	−	0.886701i	0.697344	−	0.716737i	$-0.254365\pi$
$60$		0			0
$61$	−125.372	+	385.857i	−0.263152	+	0.809900i	0.728961	+	0.684555i	$0.240004\pi$
$61$	−125.372	+	385.857i	−0.263152	+	0.809900i	−0.992113	+	0.125344i	$0.959996\pi$
$62$	−49.4877	−	152.307i	−0.101370	−	0.311985i
$63$		0			0
$64$	144.629	−	445.123i	0.282479	−	0.869382i
$65$	−31.3743	+	250.848i	−0.0598693	+	0.478676i
$66$		0			0
$67$	−484.733	+	352.179i	−0.883873	+	0.642172i	−0.934273	−	0.356558i	$-0.883950\pi$
$67$	−484.733	+	352.179i	−0.883873	+	0.642172i	0.0504000	+	0.998729i	$0.483950\pi$
$68$	76.7368			0.136849
$69$		0			0
$70$	517.486	−	552.434i	0.883591	−	0.943265i
$71$	734.084	+	533.343i	1.22704	+	0.891496i	0.996665	−	0.0816063i	$-0.0260050\pi$
$71$	734.084	+	533.343i	1.22704	+	0.891496i	0.230374	+	0.973102i	$0.426005\pi$
$72$		0			0
$73$	−218.714	+	673.134i	−0.350666	+	1.07924i	0.607815	+	0.794079i	$0.292046\pi$
$73$	−218.714	+	673.134i	−0.350666	+	1.07924i	−0.958480	+	0.285159i	$0.907954\pi$
$74$	762.051			1.19712
$75$		0			0
$76$	47.8564			0.0722303
$77$	−235.381	+	724.427i	−0.348365	+	1.07216i
$78$		0			0
$79$	69.9257	+	50.8040i	0.0995856	+	0.0723532i	0.636464	−	0.771307i	$-0.280397\pi$
$79$	69.9257	+	50.8040i	0.0995856	+	0.0723532i	−0.536878	+	0.843660i	$0.680397\pi$
$80$	94.9665	−	759.290i	0.132720	−	1.06114i
$81$		0			0
$82$	315.511			0.424906
$83$	40.4126	−	29.3615i	0.0534441	−	0.0388294i	−0.560742	−	0.827990i	$-0.689484\pi$
$83$	40.4126	−	29.3615i	0.0534441	−	0.0388294i	0.614187	+	0.789161i	$0.289484\pi$
$84$		0			0
$85$	−1403.52	+	269.536i	−1.79098	+	0.343944i
$86$	−112.512	+	346.278i	−0.141076	+	0.434187i
$87$		0			0
$88$	221.251	+	680.941i	0.268017	+	0.824870i
$89$	−202.969	+	624.673i	−0.241737	+	0.743991i	0.754418	+	0.656394i	$0.227919\pi$
$89$	−202.969	+	624.673i	−0.241737	+	0.743991i	−0.996156	+	0.0875977i	$0.972081\pi$
$90$		0			0
$91$	−161.311	−	496.465i	−0.185825	−	0.571909i
$92$	5.29078	−	3.84398i	0.00599567	−	0.00435611i
$93$		0			0
$94$	1081.59	−	785.820i	1.18678	−	0.862247i
$95$	−875.296	+	168.094i	−0.945300	+	0.181538i
$96$		0			0
$97$	43.2567	+	31.4278i	0.0452789	+	0.0328970i	0.610195	−	0.792252i	$-0.291091\pi$
$97$	43.2567	+	31.4278i	0.0452789	+	0.0328970i	−0.564916	+	0.825149i	$0.691091\pi$
$98$	−172.167	+	529.875i	−0.177464	+	0.546178i
$99$		0			0
$100$	−4.89700	−	74.8788i	−0.00489700	−	0.0748788i
$101$	97.8634			0.0964136			0.0482068	−	0.998837i	$-0.484649\pi$
$101$	97.8634			0.0964136			0.0482068	+	0.998837i	$0.484649\pi$
$102$		0			0
$103$	1108.95	+	805.697i	1.06085	+	0.770754i	0.974246	−	0.225489i	$-0.0723979\pi$
$103$	1108.95	+	805.697i	1.06085	+	0.770754i	0.0866060	+	0.996243i	$0.472398\pi$
$104$	−396.968	−	288.414i	−0.374287	−	0.271936i
$105$		0			0
$106$	−1641.33	+	1192.50i	−1.50397	+	1.09269i
$107$	157.443			0.142249			0.0711244	−	0.997467i	$-0.477341\pi$
$107$	157.443			0.142249			0.0711244	+	0.997467i	$0.477341\pi$
$108$		0			0
$109$	248.352	+	764.348i	0.218236	+	0.671663i	0.998908	+	0.0467211i	$0.0148772\pi$
$109$	248.352	+	764.348i	0.218236	+	0.671663i	−0.780672	+	0.624942i	$0.785123\pi$
$110$	522.331	+	947.338i	0.452748	+	0.821138i
$111$		0			0
$112$	488.272	+	1502.75i	0.411941	+	1.26782i
$113$	206.016	+	634.054i	0.171508	+	0.527847i	0.999457	−	0.0329564i	$-0.0104923\pi$
$113$	206.016	+	634.054i	0.171508	+	0.527847i	−0.827949	+	0.560804i	$0.810492\pi$
$114$		0			0
$115$	−83.2668	+	88.8903i	−0.0675189	+	0.0720788i
$116$	0.754264	+	2.32139i	0.000603721	+	0.00185806i
$117$		0			0
$118$	1239.10			0.966681
$119$	2387.49	−	1734.61i	1.83917	−	1.33623i
$120$		0			0
$121$	196.112	+	142.483i	0.147342	+	0.107050i
$122$	−962.575	−	699.351i	−0.714323	−	0.518986i
$123$		0			0
$124$	32.7818			0.0237411
$125$	352.576	+	1352.34i	0.252283	+	0.967654i
$126$		0			0
$127$	123.294	−	379.461i	0.0861465	−	0.265132i	−0.898699	−	0.438566i	$-0.855486\pi$
$127$	123.294	−	379.461i	0.0861465	−	0.265132i	0.984845	+	0.173435i	$0.0554865\pi$
$128$	1285.89	+	934.254i	0.887951	+	0.645134i
$129$		0			0
$130$	−671.208	−	314.833i	−0.452837	−	0.212405i
$131$	80.7018	−	58.6333i	0.0538241	−	0.0391055i	−0.560548	−	0.828122i	$-0.689409\pi$
$131$	80.7018	−	58.6333i	0.0538241	−	0.0391055i	0.614372	+	0.789017i	$0.289409\pi$
$132$		0			0
$133$	1488.94	−	1081.78i	0.970734	−	0.705280i
$134$	−542.980	−	1671.12i	−0.350047	−	1.07734i
$135$		0			0
$136$	857.198	−	2638.18i	0.540471	−	1.66340i
$137$	888.714	+	2735.18i	0.554219	+	1.70571i	0.697998	+	0.716099i	$0.254074\pi$
$137$	888.714	+	2735.18i	0.554219	+	1.70571i	−0.143780	+	0.989610i	$0.545926\pi$
$138$		0			0
$139$	331.520	−	1020.32i	0.202296	−	0.622604i	−0.797517	−	0.603296i	$-0.793854\pi$
$139$	331.520	−	1020.32i	0.202296	−	0.622604i	0.999814	−	0.0193081i	$-0.00614633\pi$
$140$	74.8148	+	135.690i	0.0451643	+	0.0819134i
$141$		0			0
$142$	−2152.80	+	1564.10i	−1.27224	+	0.924339i
$143$	746.036			0.436270
$144$		0			0
$145$	−21.9493	−	39.8089i	−0.0125710	−	0.0227997i
$146$	−1679.23	−	1220.03i	−0.951876	−	0.691579i
$147$		0			0
$148$	−48.2042	+	148.357i	−0.0267727	+	0.0823979i
$149$	−1542.11			−0.847884			−0.423942	−	0.905689i	$-0.639354\pi$
$149$	−1542.11			−0.847884			−0.423942	+	0.905689i	$0.639354\pi$
$150$		0			0
$151$	269.554			0.145271			0.0726357	−	0.997359i	$-0.476859\pi$
$151$	269.554			0.145271			0.0726357	+	0.997359i	$0.476859\pi$
$152$	534.586	−	1645.29i	0.285267	−	0.877962i
$153$		0			0
$154$	−1807.19	−	1313.00i	−0.945632	−	0.687042i
$155$	−599.581	+	115.145i	−0.310707	+	0.0596689i
$156$		0			0
$157$	−746.763			−0.379606			−0.189803	−	0.981822i	$-0.560785\pi$
$157$	−746.763			−0.379606			−0.189803	+	0.981822i	$0.560785\pi$
$158$	−205.066	+	148.989i	−0.103254	+	0.0750187i
$159$		0			0
$160$	274.421	+	128.718i	0.135593	+	0.0636005i
$161$	77.7185	−	239.193i	0.0380440	−	0.117087i
$162$		0			0
$163$	−95.3713	−	293.523i	−0.0458285	−	0.141046i	0.925524	−	0.378689i	$-0.123625\pi$
$163$	−95.3713	−	293.523i	−0.0458285	−	0.141046i	−0.971352	+	0.237643i	$0.923625\pi$
$164$	−19.9579	+	61.4241i	−0.00950275	+	0.0292465i
$165$		0			0
$166$	45.2688	+	139.323i	0.0211659	+	0.0651419i
$167$	−1076.45	+	782.086i	−0.498791	+	0.362393i	−0.808555	−	0.588421i	$-0.799750\pi$
$167$	−1076.45	+	782.086i	−0.498791	+	0.362393i	0.309764	+	0.950813i	$0.399750\pi$
$168$		0			0
$169$	1363.78	−	990.845i	0.620747	−	0.450999i
$170$	520.154	−	4158.82i	0.234671	−	1.87627i
$171$		0			0
$172$	−60.2968	−	43.8082i	−0.0267302	−	0.0194206i
$173$	181.390	−	558.261i	0.0797157	−	0.245340i	−0.903254	−	0.429106i	$-0.858829\pi$
$173$	181.390	−	558.261i	0.0797157	−	0.245340i	0.982970	+	0.183766i	$0.0588288\pi$
$174$		0			0
$175$	−1844.97	−	2218.99i	−0.796953	−	0.958512i
$176$	−2258.17			−0.967135
$177$		0			0
$178$	−1558.34	−	1132.20i	−0.656193	−	0.476752i
$179$	318.972	+	231.747i	0.133191	+	0.0967686i	0.652386	−	0.757887i	$-0.273768\pi$
$179$	318.972	+	231.747i	0.133191	+	0.0967686i	−0.519195	+	0.854656i	$0.673768\pi$
$180$		0			0
$181$	−1828.34	+	1328.37i	−0.750826	+	0.545507i	−0.896083	−	0.443887i	$-0.853599\pi$
$181$	−1828.34	+	1328.37i	−0.750826	+	0.545507i	0.145257	+	0.989394i	$0.453599\pi$
$182$	1530.88			0.623495
$183$		0			0
$184$	−73.0532	−	224.835i	−0.0292693	−	0.0900817i
$185$	360.557	−	2882.78i	0.143290	−	1.14565i
$186$		0			0
$187$	1303.30	+	4011.13i	0.509660	+	1.56857i
$188$	84.5679	+	260.273i	0.0328072	+	0.100970i
$189$		0			0
$190$	324.391	−	2593.62i	0.123862	−	0.990319i
$191$	179.253	+	551.684i	0.0679073	+	0.208997i	0.979252	−	0.202647i	$-0.0649545\pi$
$191$	179.253	+	551.684i	0.0679073	+	0.208997i	−0.911344	+	0.411645i	$0.864955\pi$
$192$		0			0
$193$	−484.411			−0.180667			−0.0903333	−	0.995912i	$-0.528793\pi$
$193$	−484.411			−0.180667			−0.0903333	+	0.995912i	$0.528793\pi$
$194$	−126.856	+	92.1661i	−0.0469470	+	0.0341090i
$195$		0			0
$196$	−92.2664	−	67.0355i	−0.0336248	−	0.0244298i
$197$	−718.404	−	521.951i	−0.259818	−	0.188769i	0.450249	−	0.892903i	$-0.351335\pi$
$197$	−718.404	−	521.951i	−0.259818	−	0.188769i	−0.710067	+	0.704134i	$0.751335\pi$
$198$		0			0
$199$	2561.69			0.912530			0.456265	−	0.889844i	$-0.349187\pi$
$199$	2561.69			0.912530			0.456265	+	0.889844i	$0.349187\pi$
$200$	−2629.01	−	668.085i	−0.929495	−	0.236204i
$201$		0			0
$202$	−88.6870	+	272.950i	−0.0308911	+	0.0950729i
$203$	75.9414	+	55.1747i	0.0262564	+	0.0190764i
$204$		0			0
$205$	149.281	−	1193.55i	0.0508596	−	0.406641i
$206$	−3252.13	+	2362.81i	−1.09993	+	0.799149i
$207$		0			0
$208$	1252.01	−	909.639i	0.417362	−	0.303231i
$209$	812.792	+	2501.52i	0.269005	+	0.827911i
$210$		0			0
$211$	−1834.57	+	5646.23i	−0.598565	+	1.84219i	−0.0624487	+	0.998048i	$0.519891\pi$
$211$	−1834.57	+	5646.23i	−0.598565	+	1.84219i	−0.536116	+	0.844144i	$0.680109\pi$
$212$	−128.333	−	394.970i	−0.0415754	−	0.127956i
$213$		0			0
$214$	−142.680	+	439.124i	−0.0455767	+	0.140271i
$215$	1256.71	+	589.464i	0.398636	+	0.186982i
$216$		0			0
$217$	1019.93	−	741.024i	0.319067	−	0.231815i
$218$	−2356.90			−0.732246
$219$		0			0
$220$	−217.470	+	41.7635i	−0.0666446	+	0.0127986i
$221$	−2338.37	−	1698.92i	−0.711745	−	0.517113i
$222$		0			0
$223$	1254.79	−	3861.86i	0.376803	−	1.15968i	−0.565451	−	0.824782i	$-0.691298\pi$
$223$	1254.79	−	3861.86i	0.376803	−	1.15968i	0.942254	−	0.334899i	$-0.108702\pi$
$224$	−625.894			−0.186693
$225$		0			0
$226$	−1955.13			−0.575458
$227$	104.511	−	321.653i	0.0305580	−	0.0940479i	−0.934614	−	0.355663i	$-0.884255\pi$
$227$	104.511	−	321.653i	0.0305580	−	0.0940479i	0.965172	+	0.261615i	$0.0842551\pi$
$228$		0			0
$229$	3014.84	+	2190.41i	0.869983	+	0.632079i	0.930582	−	0.366083i	$-0.119301\pi$
$229$	3014.84	+	2190.41i	0.869983	+	0.632079i	−0.0605996	+	0.998162i	$0.519301\pi$
$230$	−172.464	−	312.794i	−0.0494433	−	0.0896741i
$231$		0			0
$232$	88.2340			0.0249692
$233$	539.192	−	391.746i	0.151604	−	0.110147i	−0.509398	−	0.860531i	$-0.670132\pi$
$233$	539.192	−	391.746i	0.151604	−	0.110147i	0.661001	+	0.750385i	$0.270132\pi$
$234$		0			0
$235$	−2460.95	−	4463.37i	−0.683127	−	1.23897i
$236$	−78.3803	+	241.230i	−0.0216192	+	0.0665370i
$237$		0			0
$238$	2674.38	+	8230.90i	0.728380	+	2.24172i
$239$	104.814	−	322.586i	0.0283677	−	0.0873068i	−0.935870	−	0.352345i	$-0.885384\pi$
$239$	104.814	−	322.586i	0.0283677	−	0.0873068i	0.964238	+	0.265038i	$0.0853845\pi$
$240$		0			0
$241$	−1482.91	−	4563.93i	−0.396360	−	1.21987i	−0.927898	−	0.372835i	$-0.878386\pi$
$241$	−1482.91	−	4563.93i	−0.396360	−	1.21987i	0.531538	−	0.847034i	$-0.321614\pi$
$242$	−575.122	+	417.851i	−0.152770	+	0.110994i
$243$		0			0
$244$	197.039	−	143.157i	0.0516974	−	0.0375603i
$245$	1923.02	+	901.999i	0.501458	+	0.235211i
$246$		0			0
$247$	−1458.31	−	1059.52i	−0.375667	−	0.272938i
$248$	366.193	−	1127.03i	0.0937633	−	0.288574i
$249$		0			0
$250$	−4091.31	−	242.163i	−1.03503	−	0.0612629i
$251$	−5089.00			−1.27974			−0.639870	−	0.768483i	$-0.721012\pi$
$251$	−5089.00			−1.27974			−0.639870	+	0.768483i	$0.721012\pi$
$252$		0			0
$253$	290.788	+	211.270i	0.0722597	+	0.0524997i
$254$	946.620	+	687.759i	0.233843	+	0.169897i
$255$		0			0
$256$	−741.880	+	539.007i	−0.181123	+	0.131594i
$257$	−196.116			−0.0476007			−0.0238003	−	0.999717i	$-0.507577\pi$
$257$	−196.116			−0.0476007			−0.0238003	+	0.999717i	$0.507577\pi$
$258$		0			0
$259$	1853.81	+	5705.44i	0.444749	+	1.36880i
$260$	103.750	−	110.757i	0.0247473	−	0.0264186i
$261$		0			0
$262$	90.3993	+	278.221i	0.0213164	+	0.0656051i
$263$	−1766.86	−	5437.83i	−0.414255	−	1.27495i	−0.912915	−	0.408149i	$-0.866174\pi$
$263$	−1766.86	−	5437.83i	−0.414255	−	1.27495i	0.498660	−	0.866798i	$-0.333826\pi$
$264$		0			0
$265$	3734.55	+	6773.25i	0.865703	+	1.57010i
$266$	1667.86	+	5133.14i	0.384448	+	1.18321i
$267$		0			0
$268$	359.683			0.0819819
$269$	−1561.66	+	1134.61i	−0.353963	+	0.257169i	−0.750530	−	0.660837i	$-0.770202\pi$
$269$	−1561.66	+	1134.61i	−0.353963	+	0.257169i	0.396567	+	0.918006i	$0.370202\pi$
$270$		0			0
$271$	−2609.72	−	1896.08i	−0.584980	−	0.425013i	0.255536	−	0.966799i	$-0.417748\pi$
$271$	−2609.72	−	1896.08i	−0.584980	−	0.425013i	−0.840516	+	0.541787i	$0.817748\pi$
$272$	7077.98	+	5142.45i	1.57781	+	1.14635i
$273$		0			0
$274$	−8434.06			−1.85956
$275$	3830.84	−	1527.71i	0.840031	−	0.334998i
$276$		0			0
$277$	−1076.72	+	3313.79i	−0.233551	+	0.718795i	0.763760	+	0.645501i	$0.223351\pi$
$277$	−1076.72	+	3313.79i	−0.233551	+	0.718795i	−0.997310	+	0.0732945i	$0.976649\pi$
$278$	2545.32	+	1849.28i	0.549130	+	0.398967i
$279$		0			0
$280$	5500.69	−	1056.37i	1.17403	−	0.225464i
$281$	5479.65	−	3981.20i	1.16330	−	0.845190i	0.173112	−	0.984902i	$-0.444618\pi$
$281$	5479.65	−	3981.20i	1.16330	−	0.845190i	0.990192	+	0.139712i	$0.0446178\pi$
$282$		0			0
$283$	−5888.07	+	4277.94i	−1.23678	+	0.898576i	−0.997380	−	0.0723447i	$-0.976952\pi$
$283$	−5888.07	+	4277.94i	−1.23678	+	0.898576i	−0.239403	+	0.970920i	$0.576952\pi$
$284$	−168.324	−	518.048i	−0.0351697	−	0.108241i
$285$		0			0
$286$	−676.081	+	2080.76i	−0.139782	+	0.430203i
$287$	767.530	+	2362.21i	0.157860	+	0.485844i
$288$		0			0
$289$	3531.19	−	10867.9i	0.718743	−	2.21206i
$290$	130.922	−	25.1426i	0.0265104	−	0.00509112i
$291$		0			0
$292$	343.739	−	249.741i	0.0688897	−	0.0500513i
$293$	−7447.74			−1.48499			−0.742494	−	0.669853i	$-0.766357\pi$
$293$	−7447.74			−1.48499			−0.742494	+	0.669853i	$0.766357\pi$
$294$		0			0
$295$	586.268	−	4687.42i	0.115708	−	0.925125i
$296$	4562.00	+	3314.48i	0.895813	+	0.650846i
$297$		0			0
$298$	1397.51	−	4301.10i	0.271663	−	0.836093i
$299$	−246.328			−0.0476438
$300$		0			0
$301$	−2866.27			−0.548867
$302$	−244.278	+	751.812i	−0.0465452	+	0.143251i
$303$		0			0
$304$	4414.13	+	3207.05i	0.832789	+	0.605057i
$305$	−3101.02	+	3310.45i	−0.582177	+	0.621495i
$306$		0			0
$307$	10393.1			1.93214			0.966068	−	0.258290i	$-0.0831589\pi$
$307$	10393.1			1.93214			0.966068	+	0.258290i	$0.0831589\pi$
$308$	369.932	−	268.771i	0.0684378	−	0.0497230i
$309$		0			0
$310$	222.209	−	1776.64i	0.0407117	−	0.325504i
$311$	554.724	−	1707.26i	0.101143	−	0.311286i	−0.887663	−	0.460494i	$-0.847672\pi$
$311$	554.724	−	1707.26i	0.101143	−	0.311286i	0.988806	+	0.149208i	$0.0476723\pi$
$312$		0			0
$313$	−1045.63	−	3218.13i	−0.188826	−	0.581148i	0.811167	−	0.584815i	$-0.198833\pi$
$313$	−1045.63	−	3218.13i	−0.188826	−	0.581148i	−0.999993	+	0.00366673i	$0.998833\pi$
$314$	676.740	−	2082.79i	0.121626	−	0.374327i
$315$		0			0
$316$	−16.0338	−	49.3471i	−0.00285435	−	0.00878478i
$317$	116.264	−	84.4709i	0.0205995	−	0.0149664i	−0.577438	−	0.816435i	$-0.695947\pi$
$317$	116.264	−	84.4709i	0.0205995	−	0.0149664i	0.598037	+	0.801468i	$0.295947\pi$
$318$		0			0
$319$	−108.531	+	78.8527i	−0.0190489	+	0.0138398i
$320$	3577.34	−	3818.93i	0.624935	−	0.667140i
$321$		0			0
$322$	596.701	+	433.529i	0.103270	+	0.0750299i
$323$	3149.02	−	9691.67i	0.542464	−	1.66953i
$324$		0			0
$325$	−1508.56	+	2390.17i	−0.257477	+	0.407946i
$326$	905.091			0.153768
$327$		0			0
$328$	1888.80	+	1372.29i	0.317961	+	0.231013i
$329$	8514.54	+	6186.17i	1.42681	+	1.03664i
$330$		0			0
$331$	3825.63	−	2779.48i	0.635273	−	0.461553i	−0.222950	−	0.974830i	$-0.571569\pi$
$331$	3825.63	−	2779.48i	0.635273	−	0.461553i	0.858223	+	0.513277i	$0.171569\pi$
$332$	−29.9871			−0.00495710
$333$		0			0
$334$	−1205.80	−	3711.07i	−0.197540	−	0.607966i
$335$	−6578.63	+	1263.38i	−1.07292	+	0.206047i
$336$		0			0
$337$	−669.211	−	2059.62i	−0.108173	−	0.332922i	0.882289	−	0.470708i	$-0.156001\pi$
$337$	−669.211	−	2059.62i	−0.108173	−	0.332922i	−0.990462	+	0.137786i	$0.956001\pi$
$338$	1527.66	+	4701.65i	0.245839	+	0.756616i
$339$		0			0
$340$	776.742	+	364.334i	0.123896	+	0.0581141i
$341$	556.766	+	1713.55i	0.0884181	+	0.272123i
$342$		0			0
$343$	3532.65			0.556109
$344$	−2179.66	+	1583.62i	−0.341627	+	0.248206i
$345$		0			0
$346$	1392.66	+	1011.83i	0.216387	+	0.157214i
$347$	4639.89	+	3371.08i	0.717817	+	0.521525i	0.885686	−	0.464285i	$-0.153689\pi$
$347$	4639.89	+	3371.08i	0.717817	+	0.521525i	−0.167869	+	0.985809i	$0.553689\pi$
$348$		0			0
$349$	−8077.21			−1.23886			−0.619431	−	0.785051i	$-0.712637\pi$
$349$	−8077.21			−1.23886			−0.619431	+	0.785051i	$0.712637\pi$
$350$	7860.94	−	3134.89i	1.20053	−	0.478762i
$351$		0			0
$352$	276.414	−	850.714i	0.0418549	−	0.128816i
$353$	3016.92	+	2191.92i	0.454885	+	0.330493i	0.791521	−	0.611142i	$-0.209289\pi$
$353$	3016.92	+	2191.92i	0.454885	+	0.330493i	−0.336637	+	0.941635i	$0.609289\pi$
$354$		0			0
$355$	4898.28	+	8883.90i	0.732321	+	1.32819i
$356$	318.992	−	231.761i	0.0474903	−	0.0345037i
$357$		0			0
$358$	−935.428	+	679.628i	−0.138097	+	0.100334i
$359$	2778.12	+	8550.19i	0.408423	+	1.25700i	0.918003	+	0.396573i	$0.129801\pi$
$359$	2778.12	+	8550.19i	0.408423	+	1.25700i	−0.509580	+	0.860423i	$0.670199\pi$
$360$		0			0
$361$	−155.686	+	479.152i	−0.0226981	+	0.0698575i
$362$	−2048.04	−	6303.22i	−0.297355	−	0.915166i
$363$		0			0
$364$	−96.8369	+	298.033i	−0.0139440	+	0.0429154i
$365$	−5409.79	+	5775.14i	−0.775785	+	0.828178i
$366$		0			0
$367$	−2587.97	+	1880.27i	−0.368096	+	0.267437i	−0.756421	−	0.654085i	$-0.773054\pi$
$367$	−2587.97	+	1880.27i	−0.368096	+	0.267437i	0.388325	+	0.921522i	$0.373054\pi$
$368$	745.607			0.105618
$369$		0			0
$370$	7713.59	+	3618.09i	1.08381	+	0.508367i
$371$	−12921.0	−	9387.64i	−1.80815	−	1.31370i
$372$		0			0
$373$	1508.05	−	4641.29i	0.209340	−	0.644282i	−0.790167	−	0.612891i	$-0.790006\pi$
$373$	1508.05	−	4641.29i	0.209340	−	0.644282i	0.999507	−	0.0313905i	$-0.00999356\pi$
$374$	−12368.5			−1.71006
$375$		0			0
$376$	9892.77			1.35686
$377$	28.4102	−	87.4376i	0.00388117	−	0.0119450i
$378$		0			0
$379$	−1685.85	−	1224.84i	−0.228486	−	0.166005i	0.467652	−	0.883912i	$-0.345100\pi$
$379$	−1685.85	−	1224.84i	−0.228486	−	0.166005i	−0.696138	+	0.717908i	$0.745100\pi$
$380$	484.410	+	227.214i	0.0653940	+	0.0306733i
$381$		0			0
$382$	−1701.14			−0.227849
$383$	6355.68	−	4617.67i	0.847938	−	0.616063i	−0.0766388	−	0.997059i	$-0.524419\pi$
$383$	6355.68	−	4617.67i	0.847938	−	0.616063i	0.924577	+	0.380996i	$0.124419\pi$
$384$		0			0
$385$	−5822.03	+	6215.22i	−0.770696	+	0.822745i
$386$	438.989	−	1351.07i	0.0578858	−	0.178154i
$387$		0			0
$388$	−9.91868	−	30.5266i	−0.00129780	−	0.00399420i
$389$	1411.80	−	4345.07i	0.184013	−	0.566333i	−0.815917	−	0.578169i	$-0.803768\pi$
$389$	1411.80	−	4345.07i	0.184013	−	0.566333i	0.999930	+	0.0118357i	$0.00376752\pi$
$390$		0			0
$391$	−430.325	−	1324.41i	−0.0556585	−	0.171299i
$392$	−3335.33	+	2423.26i	−0.429744	+	0.312227i
$393$		0			0
$394$	2106.81	−	1530.69i	0.269390	−	0.195723i
$395$	466.590	+	846.242i	0.0594346	+	0.107795i
$396$		0			0
$397$	−11428.8	−	8303.49i	−1.44482	−	1.04972i	−0.987007	−	0.160676i	$-0.948633\pi$
$397$	−11428.8	−	8303.49i	−1.44482	−	1.04972i	−0.457814	−	0.889048i	$-0.651367\pi$
$398$	−2321.49	+	7144.80i	−0.292376	+	0.899841i
$399$		0			0
$400$	4566.25	−	7234.77i	0.570782	−	0.904346i
$401$	8967.23			1.11671			0.558357	−	0.829601i	$-0.311432\pi$
$401$	8967.23			1.11671			0.558357	+	0.829601i	$0.311432\pi$
$402$		0			0
$403$	−998.946	−	725.777i	−0.123477	−	0.0897110i
$404$	−47.5285	−	34.5315i	−0.00585304	−	0.00425249i
$405$		0			0
$406$	−222.708	+	161.807i	−0.0272237	+	0.0197792i
$407$	−8573.53			−1.04416
$408$		0			0
$409$	3544.85	+	10909.9i	0.428561	+	1.31898i	0.899543	+	0.436832i	$0.143900\pi$
$409$	3544.85	+	10909.9i	0.428561	+	1.31898i	−0.470982	+	0.882143i	$0.656100\pi$
$410$	3193.65	+	1497.99i	0.384690	+	0.180441i
$411$		0			0
$412$	−254.279	−	782.591i	−0.0304064	−	0.0935813i
$413$	3014.31	+	9277.08i	0.359139	+	1.10532i
$414$		0			0
$415$	548.466	−	105.329i	0.0648750	−	0.0124588i
$416$	189.432	+	583.013i	0.0223262	+	0.0687128i
$417$		0			0
$418$	−7713.55			−0.902588
$419$	12212.5	−	8872.89i	1.42391	−	1.03453i	0.432801	−	0.901489i	$-0.357525\pi$
$419$	12212.5	−	8872.89i	1.42391	−	1.03453i	0.991110	−	0.133043i	$-0.0424749\pi$
$420$		0			0
$421$	6550.68	+	4759.35i	0.758339	+	0.550966i	0.898400	−	0.439177i	$-0.144730\pi$
$421$	6550.68	+	4759.35i	0.758339	+	0.550966i	−0.140061	+	0.990143i	$0.544730\pi$
$422$	−14085.3	−	10233.6i	−1.62479	−	1.18048i
$423$		0			0
$424$	−15012.5			−1.71951
$425$	−15486.4	−	3935.41i	−1.76753	−	0.449165i
$426$		0			0
$427$	2894.40	−	8908.03i	0.328032	−	1.00958i
$428$	−76.4641	−	55.5544i	−0.00863559	−	0.00627412i
$429$		0			0
$430$	−2782.94	+	2970.89i	−0.312105	+	0.333183i
$431$	8532.88	−	6199.50i	0.953629	−	0.692852i	0.00196669	−	0.999998i	$-0.499374\pi$
$431$	8532.88	−	6199.50i	0.953629	−	0.692852i	0.951662	+	0.307146i	$0.0993740\pi$
$432$		0			0
$433$	−9807.46	+	7125.54i	−1.08849	+	0.790835i	−0.979144	−	0.203169i	$-0.934876\pi$
$433$	−9807.46	+	7125.54i	−1.08849	+	0.790835i	−0.109347	+	0.994004i	$0.534876\pi$
$434$	1142.49	+	3516.23i	0.126362	+	0.388904i
$435$		0			0
$436$	149.088	−	458.846i	0.0163762	−	0.0504007i
$437$	−268.369	−	825.956i	−0.0293772	−	0.0904138i
$438$		0			0
$439$	−4264.20	+	13123.9i	−0.463598	+	1.42681i	0.397140	+	0.917758i	$0.370003\pi$
$439$	−4264.20	+	13123.9i	−0.463598	+	1.42681i	−0.860738	+	0.509049i	$0.829997\pi$
$440$	−993.460	+	7943.06i	−0.107639	+	0.860615i
$441$		0			0
$442$	6857.56	−	4982.31i	0.737966	−	0.536164i
$443$	−4540.71			−0.486988			−0.243494	−	0.969902i	$-0.578294\pi$
$443$	−4540.71			−0.486988			−0.243494	+	0.969902i	$0.578294\pi$
$444$		0			0
$445$	−5020.33	+	5359.38i	−0.534801	+	0.570919i
$446$	9633.95	+	6999.47i	1.02283	+	0.743127i
$447$		0			0
$448$	−3338.97	+	10276.3i	−0.352124	+	1.08373i
$449$	−17013.4			−1.78822			−0.894110	−	0.447848i	$-0.852191\pi$
$449$	−17013.4			−1.78822			−0.894110	+	0.447848i	$0.852191\pi$
$450$		0			0
$451$	−3549.68			−0.370617
$452$	123.674	−	380.629i	0.0128697	−	0.0396090i
$453$		0			0
$454$	802.410	+	582.985i	0.0829493	+	0.0602662i
$455$	724.319	−	5791.18i	0.0746299	−	0.596692i
$456$		0			0
$457$	260.393			0.0266535			0.0133268	−	0.999911i	$-0.495758\pi$
$457$	260.393			0.0266535			0.0133268	+	0.999911i	$0.495758\pi$
$458$	−8841.40	+	6423.65i	−0.902034	+	0.655366i
$459$		0			0
$460$	71.8047	−	13.7896i	0.00727807	−	0.00139770i
$461$	−3313.69	+	10198.5i	−0.334781	+	1.03035i	0.632049	+	0.774928i	$0.282214\pi$
$461$	−3313.69	+	10198.5i	−0.334781	+	1.03035i	−0.966830	+	0.255421i	$0.917786\pi$
$462$		0			0
$463$	−4017.07	−	12363.3i	−0.403216	−	1.24097i	−0.922375	−	0.386295i	$-0.873755\pi$
$463$	−4017.07	−	12363.3i	−0.403216	−	1.24097i	0.519159	−	0.854678i	$-0.326245\pi$
$464$	−85.9946	+	264.664i	−0.00860387	+	0.0264800i
$465$		0			0
$466$	603.984	+	1858.87i	0.0600408	+	0.184787i
$467$	6068.69	−	4409.16i	0.601340	−	0.436899i	−0.245014	−	0.969519i	$-0.578793\pi$
$467$	6068.69	−	4409.16i	0.601340	−	0.436899i	0.846354	+	0.532621i	$0.178793\pi$
$468$		0			0
$469$	11190.7	−	8130.54i	1.10179	−	0.800497i
$470$	14679.0	−	2818.99i	1.44062	−	0.276660i
$471$		0			0
$472$	7417.84	+	5389.37i	0.723376	+	0.525564i
$473$	1265.83	−	3895.83i	0.123051	−	0.378712i
$474$		0			0
$475$	−9657.97	−	2454.29i	−0.932922	−	0.237075i
$476$	−1771.58			−0.170588
$477$		0			0
$478$	804.736	+	584.675i	0.0770037	+	0.0559464i
$479$	−2637.83	−	1916.49i	−0.251619	−	0.182812i	0.454825	−	0.890581i	$-0.349702\pi$
$479$	−2637.83	−	1916.49i	−0.251619	−	0.182812i	−0.706444	+	0.707769i	$0.749702\pi$
$480$		0			0
$481$	4753.48	−	3453.60i	0.450603	−	0.327382i
$482$	14073.1			1.32990
$483$		0			0
$484$	−44.9680	−	138.397i	−0.00422314	−	0.0129975i
$485$	288.637	+	523.493i	0.0270233	+	0.0490115i
$486$		0			0
$487$	−2679.05	−	8245.28i	−0.249280	−	0.767206i	−0.994903	−	0.100837i	$-0.967848\pi$
$487$	−2679.05	−	8245.28i	−0.249280	−	0.767206i	0.745623	−	0.666368i	$-0.232152\pi$
$488$	−2720.65	−	8373.30i	−0.252373	−	0.776724i
$489$		0			0
$490$	−4258.46	+	4546.06i	−0.392608	+	0.419122i
$491$	730.668	+	2248.76i	0.0671580	+	0.206691i	0.979004	−	0.203842i	$-0.0653428\pi$
$491$	730.668	+	2248.76i	0.0671580	+	0.206691i	−0.911846	+	0.410533i	$0.865343\pi$
$492$		0			0
$493$	519.749			0.0474813
$494$	4276.67	−	3107.18i	0.389507	−	0.282993i
$495$		0			0
$496$	3023.70	+	2196.85i	0.273726	+	0.198874i
$497$	−16947.3	−	12313.0i	−1.52956	−	1.11129i
$498$		0			0
$499$	−8407.18			−0.754223			−0.377111	−	0.926168i	$-0.623083\pi$
$499$	−8407.18			−0.754223			−0.377111	+	0.926168i	$0.623083\pi$
$500$	305.944	−	781.185i	0.0273645	−	0.0698713i
$501$		0			0
$502$	4611.81	−	14193.7i	0.410030	−	1.26194i
$503$	−11463.0	−	8328.32i	−1.01612	−	0.738254i	−0.0506352	−	0.998717i	$-0.516125\pi$
$503$	−11463.0	−	8328.32i	−1.01612	−	0.738254i	−0.965484	+	0.260464i	$0.916125\pi$
$504$		0			0
$505$	990.589	+	464.640i	0.0872884	+	0.0409430i
$506$	−852.774	+	619.576i	−0.0749218	+	0.0544339i
$507$		0			0
$508$	−193.773	+	140.785i	−0.0169238	+	0.0122959i
$509$	−5208.73	−	16030.8i	−0.453581	−	1.39598i	−0.872793	−	0.488090i	$-0.837694\pi$
$509$	−5208.73	−	16030.8i	−0.453581	−	1.39598i	0.419212	−	0.907888i	$-0.362306\pi$
$510$		0			0
$511$	5049.32	−	15540.2i	0.437121	−	1.34532i
$512$	3098.30	+	9535.59i	0.267435	+	0.823081i
$513$		0			0
$514$	177.727	−	546.986i	0.0152513	−	0.0469387i
$515$	7399.61	+	13420.5i	0.633137	+	1.14831i
$516$		0			0
$517$	−12168.5	+	8840.95i	−1.03515	+	0.752078i
$518$	−17593.0			−1.49226
$519$		0			0
$520$	−2648.83	−	4804.11i	−0.223382	−	0.405142i
$521$	7388.51	+	5368.07i	0.621298	+	0.451400i	0.853375	−	0.521298i	$-0.174552\pi$
$521$	7388.51	+	5368.07i	0.621298	+	0.451400i	−0.232076	+	0.972698i	$0.574552\pi$
$522$		0			0
$523$	4037.14	−	12425.0i	0.337537	−	1.03883i	−0.627922	−	0.778276i	$-0.716094\pi$
$523$	4037.14	−	12425.0i	0.337537	−	1.03883i	0.965459	−	0.260555i	$-0.0839056\pi$
$524$	−59.8827			−0.00499235
$525$		0			0
$526$	16767.8			1.38995
$527$	2157.09	−	6638.84i	0.178300	−	0.548752i
$528$		0			0
$529$	9747.30	+	7081.83i	0.801126	+	0.582052i
$530$	−22275.6	+	4277.87i	−1.82564	+	0.350601i
$531$		0			0
$532$	−1104.83			−0.0900385
$533$	1968.07	−	1429.89i	0.159938	−	0.116202i
$534$		0			0
$535$	1593.67	+	747.515i	0.128785	+	0.0604073i
$536$	4017.89	−	12365.8i	0.323780	−	0.996493i
$537$		0			0
$538$	−1749.32	−	5383.84i	−0.140183	−	0.431439i
$539$	1936.98	−	5961.41i	0.154790	−	0.476394i
$540$		0			0
$541$	4049.31	+	12462.5i	0.321799	+	0.990396i	0.972865	+	0.231374i	$0.0743222\pi$
$541$	4049.31	+	12462.5i	0.321799	+	0.990396i	−0.651066	+	0.759021i	$0.725678\pi$
$542$	7653.35	−	5560.49i	0.606531	−	0.440670i
$543$		0			0
$544$	−2803.69	+	2037.00i	−0.220969	+	0.160544i
$545$	−1115.15	+	8915.98i	−0.0876470	+	0.700768i
$546$		0			0
$547$	−13874.1	−	10080.1i	−1.08448	−	0.787923i	−0.106024	−	0.994364i	$-0.533812\pi$
$547$	−13874.1	−	10080.1i	−1.08448	−	0.787923i	−0.978459	+	0.206441i	$0.933812\pi$
$548$	533.504	−	1641.96i	0.0415879	−	0.127994i
$549$		0			0
$550$	789.304	+	12069.0i	0.0611928	+	0.935684i
$551$	324.138			0.0250612
$552$		0			0
$553$	−1614.33	−	1172.88i	−0.124138	−	0.0901916i
$554$	−8266.72	−	6006.12i	−0.633970	−	0.460606i
$555$		0			0
$556$	−521.028	+	378.549i	−0.0397419	+	0.0288742i
$557$	2642.14			0.200990			0.100495	−	0.994938i	$-0.467957\pi$
$557$	2642.14			0.200990			0.100495	+	0.994938i	$0.467957\pi$
$558$		0			0
$559$	867.502	+	2669.90i	0.0656376	+	0.202012i
$560$	−2192.43	+	17529.3i	−0.165441	+	1.32276i
$561$		0			0
$562$	6138.11	+	18891.2i	0.460713	+	1.41793i
$563$	6044.68	+	18603.6i	0.452491	+	1.39263i	0.874055	+	0.485827i	$0.161481\pi$
$563$	6044.68	+	18603.6i	0.452491	+	1.39263i	−0.421564	+	0.906799i	$0.638519\pi$
$564$		0			0
$565$	−925.053	+	7396.12i	−0.0688801	+	0.550721i
$566$	−6595.61	−	20299.2i	−0.489813	−	1.50749i
$567$		0			0
$568$	−19690.6			−1.45458
$569$	−4013.66	+	2916.09i	−0.295714	+	0.214849i	−0.725742	−	0.687967i	$-0.758504\pi$
$569$	−4013.66	+	2916.09i	−0.295714	+	0.214849i	0.430028	+	0.902815i	$0.358504\pi$
$570$		0			0
$571$	−8114.55	−	5895.57i	−0.594717	−	0.432087i	0.249283	−	0.968431i	$-0.419805\pi$
$571$	−8114.55	−	5895.57i	−0.594717	−	0.432087i	−0.844000	+	0.536344i	$0.819805\pi$
$572$	−362.321	−	263.241i	−0.0264849	−	0.0192424i
$573$		0			0
$574$	−7284.00			−0.529666
$575$	−1264.88	+	504.424i	−0.0917374	+	0.0365842i
$576$		0			0
$577$	6944.95	−	21374.3i	0.501078	−	1.54216i	−0.306188	−	0.951971i	$-0.599054\pi$
$577$	6944.95	−	21374.3i	0.501078	−	1.54216i	0.807266	−	0.590188i	$-0.200946\pi$
$578$	27111.5	+	19697.6i	1.95102	+	1.41750i
$579$		0			0
$580$	−3.38679	+	27.0786i	−0.000242463	+	0.00193858i
$581$	−932.981	+	677.850i	−0.0666206	+	0.0484027i
$582$		0			0
$583$	18466.0	−	13416.3i	1.31181	−	0.953082i
$584$	−4746.22	−	14607.4i	−0.336301	−	1.03503i
$585$		0			0
$586$	6749.38	−	20772.5i	0.475792	−	1.46434i
$587$	−6336.07	−	19500.4i	−0.445515	−	1.37115i	−0.881918	−	0.471403i	$-0.843748\pi$
$587$	−6336.07	−	19500.4i	−0.445515	−	1.37115i	0.436403	−	0.899751i	$-0.356252\pi$
$588$		0			0
$589$	1345.25	−	4140.26i	0.0941090	−	0.289638i
$590$	12542.4	+	5883.04i	0.875187	+	0.410510i
$591$		0			0
$592$	−14388.2	+	10453.7i	−0.998907	+	0.725749i
$593$	373.656			0.0258756			0.0129378	−	0.999916i	$-0.495882\pi$
$593$	373.656			0.0258756			0.0129378	+	0.999916i	$0.495882\pi$
$594$		0			0
$595$	32402.2	−	6222.61i	2.23254	−	0.428743i
$596$	748.944	+	544.139i	0.0514730	+	0.0373973i
$597$		0			0
$598$	223.230	−	687.031i	0.0152651	−	0.0469813i
$599$	2173.18			0.148236			0.0741182	−	0.997249i	$-0.476386\pi$
$599$	2173.18			0.148236			0.0741182	+	0.997249i	$0.476386\pi$
$600$		0			0
$601$	14405.7			0.977739			0.488869	−	0.872357i	$-0.337409\pi$
$601$	14405.7			0.977739			0.488869	+	0.872357i	$0.337409\pi$
$602$	2597.51	−	7994.30i	0.175858	−	0.541235i
$603$		0			0
$604$	−130.912	−	95.1131i	−0.00881909	−	0.00640744i
$605$	1308.58	+	2373.35i	0.0879364	+	0.159488i
$606$		0			0
$607$	−5142.91			−0.343895			−0.171948	−	0.985106i	$-0.555006\pi$
$607$	−5142.91			−0.343895			−0.171948	+	0.985106i	$0.555006\pi$
$608$	−1748.50	+	1270.36i	−0.116630	+	0.0847369i
$609$		0			0
$610$	−6422.92	−	11649.1i	−0.426322	−	0.773210i
$611$	3185.35	−	9803.49i	0.210909	−	0.649111i
$612$		0			0
$613$	7778.26	+	23939.0i	0.512497	+	1.57730i	0.787790	+	0.615944i	$0.211225\pi$
$613$	7778.26	+	23939.0i	0.512497	+	1.57730i	−0.275293	+	0.961360i	$0.588775\pi$
$614$	−9418.56	+	28987.3i	−0.619059	+	1.90527i
$615$		0			0
$616$	−5107.89	−	15720.5i	−0.334095	−	1.02824i
$617$	−15687.9	+	11397.9i	−1.02362	+	0.743701i	−0.967021	−	0.254697i	$-0.918024\pi$
$617$	−15687.9	+	11397.9i	−1.02362	+	0.743701i	−0.0565950	+	0.998397i	$0.518024\pi$
$618$		0			0
$619$	4465.49	−	3244.37i	0.289957	−	0.210666i	−0.433292	−	0.901254i	$-0.642648\pi$
$619$	4465.49	−	3244.37i	0.289957	−	0.210666i	0.723249	+	0.690588i	$0.242648\pi$
$620$	331.823	+	155.643i	0.0214941	+	0.0100819i
$621$		0			0
$622$	4259.01	+	3094.35i	0.274551	+	0.199473i
$623$	4685.81	−	14421.4i	0.301337	−	0.927421i
$624$		0			0
$625$	−2851.85	+	15362.5i	−0.182518	+	0.983202i
$626$	9923.25			0.633567
$627$		0			0
$628$	362.674	+	263.498i	0.0230450	+	0.0167432i
$629$	26872.8	+	19524.2i	1.70348	+	1.23765i
$630$		0			0
$631$	−5841.61	+	4244.18i	−0.368544	+	0.267763i	−0.756607	−	0.653870i	$-0.773144\pi$
$631$	−5841.61	+	4244.18i	−0.368544	+	0.267763i	0.388063	+	0.921633i	$0.373144\pi$
$632$	−1875.64			−0.118052
$633$		0			0
$634$	130.235	+	400.822i	0.00815820	+	0.0251083i
$635$	3049.62	−	3255.58i	0.190584	−	0.203455i
$636$		0			0
$637$	1327.45	+	4085.48i	0.0825677	+	0.254117i
$638$	−121.573	−	374.163i	−0.00754408	−	0.0232183i
$639$		0			0
$640$	8580.29	+	15561.9i	0.529947	+	0.961151i
$641$	3909.89	+	12033.4i	0.240923	+	0.741483i	0.996280	+	0.0861709i	$0.0274631\pi$
$641$	3909.89	+	12033.4i	0.240923	+	0.741483i	−0.755358	+	0.655313i	$0.772537\pi$
$642$		0			0
$643$	−2621.20			−0.160762			−0.0803810	−	0.996764i	$-0.525614\pi$
$643$	−2621.20			−0.160762			−0.0803810	+	0.996764i	$0.525614\pi$
$644$	−122.145	+	88.7435i	−0.00747389	+	0.00543010i
$645$		0			0
$646$	24177.3	+	17565.8i	1.47251	+	1.06984i
$647$	18737.8	+	13613.8i	1.13858	+	0.827225i	0.986920	−	0.161209i	$-0.0515392\pi$
$647$	18737.8	+	13613.8i	1.13858	+	0.827225i	0.151657	+	0.988433i	$0.451539\pi$
$648$		0			0
$649$	−13940.6			−0.843169
$650$	−5299.29	−	6373.57i	−0.319778	−	0.384603i
$651$		0			0
$652$	−57.2523	+	176.205i	−0.00343892	+	0.0105839i
$653$	2605.80	+	1893.23i	0.156161	+	0.113457i	0.663122	−	0.748512i	$-0.269231\pi$
$653$	2605.80	+	1893.23i	0.156161	+	0.113457i	−0.506961	+	0.861969i	$0.669231\pi$
$654$		0			0
$655$	1095.26	−	210.336i	0.0653363	−	0.0125474i
$656$	−5957.14	+	4328.12i	−0.354554	+	0.257599i
$657$		0			0
$658$	−24970.0	+	18141.7i	−1.47938	+	1.07483i
$659$	3369.76	+	10371.1i	0.199192	+	0.613048i	0.999902	+	0.0139970i	$0.00445553\pi$
$659$	3369.76	+	10371.1i	0.199192	+	0.613048i	−0.800711	+	0.599051i	$0.795544\pi$
$660$		0			0
$661$	−7834.53	+	24112.2i	−0.461010	+	1.41884i	0.402921	+	0.915235i	$0.367995\pi$
$661$	−7834.53	+	24112.2i	−0.461010	+	1.41884i	−0.863932	+	0.503609i	$0.832005\pi$
$662$	4285.33	+	13188.9i	0.251592	+	0.774321i
$663$		0			0
$664$	−334.975	+	1030.95i	−0.0195776	+	0.0602537i
$665$	20207.4	−	3880.69i	1.17836	−	0.226296i
$666$		0			0
$667$	35.8352	−	26.0358i	0.00208027	−	0.00151141i
$668$	798.751			0.0462644
$669$		0			0
$670$	2438.08	−	19493.3i	0.140584	−	1.12402i
$671$	10829.5	+	7868.12i	0.623055	+	0.452676i
$672$		0			0
$673$	5668.36	−	17445.4i	0.324664	−	0.999215i	−0.646927	−	0.762552i	$-0.723946\pi$
$673$	5668.36	−	17445.4i	0.324664	−	0.999215i	0.971592	−	0.236663i	$-0.0760537\pi$
$674$	6350.94			0.362951
$675$		0			0
$676$	−1011.96			−0.0575762
$677$	2357.65	−	7256.09i	0.133843	−	0.411926i	−0.861565	−	0.507647i	$-0.830516\pi$
$677$	2357.65	−	7256.09i	0.133843	−	0.411926i	0.995408	+	0.0957206i	$0.0305155\pi$
$678$		0			0
$679$	−998.641	−	725.555i	−0.0564423	−	0.0410077i
$680$	21202.4	−	22634.3i	1.19570	−	1.27645i
$681$		0			0
$682$	−5283.81			−0.296668
$683$	−11840.9	+	8602.91i	−0.663366	+	0.481963i	−0.867798	−	0.496917i	$-0.834465\pi$
$683$	−11840.9	+	8602.91i	−0.663366	+	0.481963i	0.204432	+	0.978881i	$0.434465\pi$
$684$		0			0
$685$	−3990.49	+	31905.4i	−0.222582	+	1.77962i
$686$	−3201.40	+	9852.91i	−0.178178	+	0.548376i
$687$		0			0
$688$	−2625.83	−	8081.48i	−0.145507	−	0.447825i
$689$	−4833.83	+	14877.0i	−0.267277	+	0.822595i
$690$		0			0
$691$	2186.27	+	6728.66i	0.120361	+	0.370434i	0.993027	−	0.117883i	$-0.0376108\pi$
$691$	2186.27	+	6728.66i	0.120361	+	0.370434i	−0.872666	+	0.488318i	$0.837611\pi$
$692$	−285.078	+	207.122i	−0.0156605	+	0.0113780i
$693$		0			0
$694$	−13607.1	+	9886.13i	−0.744262	+	0.540738i
$695$	8199.99	−	8753.78i	0.447545	−	0.477770i
$696$		0			0
$697$	11126.1	+	8083.58i	0.604635	+	0.439293i
$698$	7319.82	−	22528.1i	0.396933	−	1.22163i
$699$		0			0
$700$	113.054	+	1728.68i	0.00610435	+	0.0933400i
$701$	−12304.1			−0.662937			−0.331468	−	0.943466i	$-0.607544\pi$
$701$	−12304.1			−0.662937			−0.331468	+	0.943466i	$0.607544\pi$
$702$		0			0
$703$	16759.0	+	12176.1i	0.899116	+	0.653246i
$704$	−12492.9	−	9076.65i	−0.668814	−	0.485922i
$705$		0			0
$706$	−8847.49	+	6428.08i	−0.471643	+	0.342669i
$707$	−2259.31			−0.120184
$708$		0			0
$709$	2825.10	+	8694.77i	0.149646	+	0.460562i	0.997579	−	0.0695404i	$-0.0221533\pi$
$709$	2825.10	+	8694.77i	0.149646	+	0.460562i	−0.847933	+	0.530103i	$0.822153\pi$
$710$	−29217.0	+	5610.91i	−1.54436	+	0.296583i
$711$		0			0
$712$	−4404.53	−	13555.7i	−0.231835	−	0.713516i
$713$	−183.834	−	565.783i	−0.00965588	−	0.0297177i
$714$		0			0
$715$	7551.49	+	3542.06i	0.394979	+	0.185266i
$716$	−73.1398	−	225.101i	−0.00381754	−	0.0117492i
$717$		0			0
$718$	−26364.9			−1.37038
$719$	2907.80	−	2112.64i	0.150824	−	0.109580i	−0.509814	−	0.860285i	$-0.670286\pi$
$719$	2907.80	−	2112.64i	0.150824	−	0.109580i	0.660638	+	0.750704i	$0.270286\pi$
$720$		0			0
$721$	−25601.6	−	18600.6i	−1.32240	−	0.960781i
$722$	−1195.31	−	868.447i	−0.0616136	−	0.0447649i
$723$		0			0
$724$	1356.67			0.0696413
$725$	−33.1681	−	507.164i	−0.00169908	−	0.0259801i
$726$		0			0
$727$	−5718.08	+	17598.5i	−0.291708	+	0.897786i	0.692599	+	0.721323i	$0.256466\pi$
$727$	−5718.08	+	17598.5i	−0.291708	+	0.897786i	−0.984307	+	0.176463i	$0.943534\pi$
$728$	9164.55	+	6658.43i	0.466567	+	0.338981i
$729$		0			0
$730$	−11204.9	−	20322.0i	−0.568099	−	1.03035i
$731$	−12839.5	+	9328.42i	−0.649637	+	0.471989i
$732$		0			0
$733$	28255.0	−	20528.5i	1.42377	−	1.03443i	0.432634	−	0.901570i	$-0.357584\pi$
$733$	28255.0	−	20528.5i	1.42377	−	1.03443i	0.991135	−	0.132858i	$-0.0424156\pi$
$734$	−2898.96	−	8922.07i	−0.145780	−	0.448664i
$735$		0			0
$736$	−91.2669	+	280.891i	−0.00457085	+	0.0140676i
$737$	6108.85	+	18801.1i	0.305322	+	0.939685i
$738$		0			0
$739$	−6001.98	+	18472.2i	−0.298764	+	0.919500i	0.683168	+	0.730262i	$0.260602\pi$
$739$	−6001.98	+	18472.2i	−0.298764	+	0.919500i	−0.981931	+	0.189238i	$0.939398\pi$
$740$	−1192.31	+	1272.83i	−0.0592298	+	0.0632299i
$741$		0			0
$742$	37892.4	−	27530.5i	1.87476	−	1.36210i
$743$	−39704.0			−1.96043			−0.980214	−	0.197943i	$-0.936574\pi$
$743$	−39704.0			−1.96043			−0.980214	+	0.197943i	$0.936574\pi$
$744$		0			0
$745$	−15609.5	−	7321.70i	−0.767634	−	0.360062i
$746$	11578.4	+	8412.18i	0.568250	+	0.412857i
$747$		0			0
$748$	782.382	−	2407.92i	0.0382443	−	0.117704i
$749$	−3634.80			−0.177320
$750$		0			0
$751$	−18656.7			−0.906515			−0.453258	−	0.891380i	$-0.649738\pi$
$751$	−18656.7			−0.906515			−0.453258	+	0.891380i	$0.649738\pi$
$752$	−9641.69	+	29674.1i	−0.467548	+	1.43897i
$753$		0			0
$754$	218.126	+	158.478i	0.0105354	+	0.00765440i
$755$	2728.47	+	1279.80i	0.131522	+	0.0616909i
$756$		0			0
$757$	34418.7			1.65253			0.826267	−	0.563279i	$-0.190460\pi$
$757$	34418.7			1.65253			0.826267	+	0.563279i	$0.190460\pi$
$758$	4943.96	−	3592.00i	0.236903	−	0.172120i
$759$		0			0
$760$	13222.7	−	14115.7i	0.631103	−	0.673724i
$761$	−2868.97	+	8829.77i	−0.136662	+	0.420603i	−0.995845	−	0.0910659i	$-0.970973\pi$
$761$	−2868.97	+	8829.77i	−0.136662	+	0.420603i	0.859183	+	0.511669i	$0.170973\pi$
$762$		0			0
$763$	−5733.54	−	17646.0i	−0.272042	−	0.837259i
$764$	107.607	−	331.182i	0.00509568	−	0.0156829i
$765$		0			0
$766$	7119.41	+	21911.3i	0.335816	+	1.03353i
$767$	7729.18	−	5615.58i	0.363865	−	0.264363i
$768$		0			0
$769$	−7267.60	+	5280.22i	−0.340802	+	0.247607i	−0.745000	−	0.667064i	$-0.767551\pi$
$769$	−7267.60	+	5280.22i	−0.340802	+	0.247607i	0.404198	+	0.914671i	$0.367551\pi$
$770$	−12058.7	−	21870.6i	−0.564372	−	1.02359i
$771$		0			0
$772$	235.260	+	170.926i	0.0109678	+	0.00796861i
$773$	12651.6	−	38937.5i	0.588674	−	1.81175i	0.00468915	−	0.999989i	$-0.498507\pi$
$773$	12651.6	−	38937.5i	0.588674	−	1.81175i	0.583985	−	0.811764i	$-0.301493\pi$
$774$		0			0
$775$	−6615.75	−	1681.20i	−0.306638	−	0.0779231i
$776$	−1160.29			−0.0536752
$777$		0			0
$778$	10839.4	+	7875.27i	0.499500	+	0.362908i
$779$	6938.71	+	5041.27i	0.319134	+	0.231864i
$780$		0			0
$781$	24220.2	−	17597.0i	1.10969	−	0.806238i
$782$	4083.87			0.186750
$783$		0			0
$784$	−4018.06	−	12366.3i	−0.183038	−	0.563334i
$785$	−7558.85	−	3545.51i	−0.343677	−	0.161203i
$786$		0			0
$787$	−9825.58	−	30240.0i	−0.445037	−	1.36968i	−0.882443	−	0.470418i	$-0.844103\pi$
$787$	−9825.58	−	30240.0i	−0.445037	−	1.36968i	0.437407	−	0.899264i	$-0.355897\pi$
$788$	164.729	+	506.983i	0.00744698	+	0.0229194i
$789$		0			0
$790$	−2783.09	+	534.472i	−0.125339	+	0.0240704i
$791$	−4756.18	−	14638.0i	−0.213793	−	0.657987i
$792$		0			0
$793$	−9173.74			−0.410806
$794$	33516.4	−	24351.1i	1.49805	−	1.08840i
$795$		0			0
$796$	−1244.11	−	903.902i	−0.0553976	−	0.0402487i
$797$	−3984.77	−	2895.11i	−0.177099	−	0.128670i	0.495704	−	0.868491i	$-0.334910\pi$
$797$	−3984.77	−	2895.11i	−0.177099	−	0.128670i	−0.672803	+	0.739821i	$0.734910\pi$
$798$		0			0
$799$	58274.1			2.58021
$800$	2166.60	+	2605.82i	0.0957511	+	0.115162i
$801$		0			0
$802$	−8126.39	+	25010.5i	−0.357796	+	1.10118i
$803$	18892.3	+	13726.1i	0.830256	+	0.603216i
$804$		0			0
$805$	1922.33	−	2052.15i	0.0841655	−	0.0898496i
$806$	2929.54	−	2128.43i	0.128026	−	0.0930160i
$807$		0			0
$808$	−1718.10	+	1248.27i	−0.0748052	+	0.0543491i
$809$	3212.47	+	9886.98i	0.139610	+	0.429676i	0.996279	−	0.0861917i	$-0.0274698\pi$
$809$	3212.47	+	9886.98i	0.139610	+	0.429676i	−0.856669	+	0.515867i	$0.827470\pi$
$810$		0			0
$811$	−5579.09	+	17170.7i	−0.241564	+	0.743458i	0.754618	+	0.656164i	$0.227822\pi$
$811$	−5579.09	+	17170.7i	−0.241564	+	0.743458i	−0.996183	+	0.0872941i	$0.972178\pi$
$812$	−17.4132	−	53.5924i	−0.000752567	−	0.00231616i
$813$		0			0
$814$	7769.60	−	23912.4i	0.334551	−	1.02964i
$815$	428.235	−	3423.89i	0.0184054	−	0.147158i
$816$		0			0
$817$	−8007.24	+	5817.60i	−0.342886	+	0.249121i
$818$	−33641.3			−1.43795
$819$		0			0
$820$	−493.649	+	526.988i	−0.0210231	+	0.0224429i
$821$	−23831.0	−	17314.2i	−1.01304	−	0.736018i	−0.0481966	−	0.998838i	$-0.515347\pi$
$821$	−23831.0	−	17314.2i	−1.01304	−	0.736018i	−0.964845	+	0.262820i	$0.915347\pi$
$822$		0			0
$823$	−10379.1	+	31943.7i	−0.439604	+	1.35296i	0.448690	+	0.893687i	$0.351891\pi$
$823$	−10379.1	+	31943.7i	−0.439604	+	1.35296i	−0.888294	+	0.459275i	$0.848109\pi$
$824$	−29745.6			−1.25757
$825$		0			0
$826$	−28606.3			−1.20501
$827$	5545.46	−	17067.2i	0.233174	−	0.717634i	−0.764185	−	0.644997i	$-0.776859\pi$
$827$	5545.46	−	17067.2i	0.233174	−	0.717634i	0.997358	−	0.0726371i	$-0.0231415\pi$
$828$		0			0
$829$	−10695.1	−	7770.43i	−0.448077	−	0.325547i	0.340759	−	0.940151i	$-0.389316\pi$
$829$	−10695.1	−	7770.43i	−0.448077	−	0.325547i	−0.788836	+	0.614604i	$0.789316\pi$
$830$	−203.265	+	1625.18i	−0.00850053	+	0.0679647i
$831$		0			0
$832$	10582.8			0.440977
$833$	−19647.0	+	14274.4i	−0.817200	+	0.593731i
$834$		0			0
$835$	−14609.2	+	2805.59i	−0.605476	+	0.116277i
$836$	487.927	−	1501.69i	0.0201858	−	0.0621255i
$837$		0			0
$838$	13680.0	+	42102.7i	0.563923	+	1.73558i
$839$	−10547.9	+	32463.0i	−0.434032	+	1.33581i	0.460043	+	0.887897i	$0.347834\pi$
$839$	−10547.9	+	32463.0i	−0.434032	+	1.33581i	−0.894075	+	0.447917i	$0.852166\pi$
$840$		0			0
$841$	−7531.51	−	23179.6i	−0.308808	−	0.950412i
$842$	−19210.7	+	13957.4i	−0.786277	+	0.571264i
$843$		0			0
$844$	2883.27	−	2094.82i	0.117590	−	0.0854345i
$845$	18508.8	−	3554.47i	0.753516	−	0.144707i
$846$		0			0
$847$	−4527.51	−	3289.43i	−0.183668	−	0.133443i
$848$	14631.5	−	45031.0i	0.592507	−	1.82355i
$849$		0			0
$850$	25010.5	−	39626.6i	1.00924	−	1.59904i
$851$	2830.83			0.114030
$852$		0			0
$853$	−8629.78	−	6269.90i	−0.346399	−	0.251673i	0.400958	−	0.916096i	$-0.368677\pi$
$853$	−8629.78	−	6269.90i	−0.346399	−	0.251673i	−0.747357	+	0.664423i	$0.768677\pi$
$854$	22222.4	+	16145.5i	0.890438	+	0.646941i
$855$		0			0
$856$	−2764.09	+	2008.23i	−0.110368	+	0.0801868i
$857$	36411.5			1.45133			0.725667	−	0.688046i	$-0.241531\pi$
$857$	36411.5			1.45133			0.725667	+	0.688046i	$0.241531\pi$
$858$		0			0
$859$	−10022.2	−	30845.3i	−0.398084	−	1.22518i	−0.926534	−	0.376212i	$-0.877226\pi$
$859$	−10022.2	−	30845.3i	−0.398084	−	1.22518i	0.528450	−	0.848965i	$-0.322774\pi$
$860$	−402.340	−	729.713i	−0.0159531	−	0.0289337i
$861$		0			0
$862$	9558.22	+	29417.2i	0.377673	+	1.16236i
$863$	−2892.80	−	8903.13i	−0.114104	−	0.351178i	0.877655	−	0.479293i	$-0.159107\pi$
$863$	−2892.80	−	8903.13i	−0.114104	−	0.351178i	−0.991759	+	0.128116i	$0.959107\pi$
$864$		0			0
$865$	4486.59	−	4789.59i	0.176357	−	0.188267i
$866$	−10986.0	−	33811.3i	−0.431084	−	1.32674i
$867$		0			0
$868$	−756.814			−0.0295944
$869$	2307.12	−	1676.22i	0.0900617	−	0.0654337i
$870$		0			0
$871$	−10960.5	−	7963.25i	−0.426385	−	0.309787i
$872$	−14109.5	−	10251.2i	−0.547946	−	0.398106i
$873$		0			0
$874$	2546.88			0.0985690
$875$	−8139.71	−	31220.6i	−0.314483	−	1.20623i
$876$		0			0
$877$	5449.81	−	16772.8i	0.209837	−	0.645812i	−0.789643	−	0.613567i	$-0.789734\pi$
$877$	5449.81	−	16772.8i	0.209837	−	0.645812i	0.999480	−	0.0322455i	$-0.0102659\pi$
$878$	−32739.4	−	23786.5i	−1.25843	−	0.914302i
$879$		0			0
$880$	−22857.5	−	10721.4i	−0.875599	−	0.410703i
$881$	−34441.7	+	25023.4i	−1.31711	+	0.956935i	−0.317144	+	0.948377i	$0.602724\pi$
$881$	−34441.7	+	25023.4i	−1.31711	+	0.956935i	−0.999963	+	0.00855755i	$0.997276\pi$
$882$		0			0
$883$	−477.880	+	347.200i	−0.0182129	+	0.0132324i	−0.596854	−	0.802350i	$-0.703583\pi$
$883$	−477.880	+	347.200i	−0.0182129	+	0.0132324i	0.578642	+	0.815582i	$0.303583\pi$
$884$	536.183	+	1650.20i	0.0204002	+	0.0627854i
$885$		0			0
$886$	4114.94	−	12664.5i	0.156032	−	0.480216i
$887$	−1272.22	−	3915.50i	−0.0481590	−	0.148218i	0.924085	−	0.382187i	$-0.124829\pi$
$887$	−1272.22	−	3915.50i	−0.0481590	−	0.148218i	−0.972244	+	0.233968i	$0.924829\pi$
$888$		0			0
$889$	−2846.42	+	8760.38i	−0.107386	+	0.330499i
$890$	−10398.2	−	18859.0i	−0.391629	−	0.710287i
$891$		0			0
$892$	−1972.07	+	1432.80i	−0.0740245	+	0.0537820i
$893$	36342.2			1.36187
$894$		0			0
$895$	2128.39	+	3860.21i	0.0794908	+	0.144170i
$896$	−29686.5	−	21568.5i	−1.10687	−	0.804190i
$897$		0			0
$898$	15418.1	−	47451.9i	0.572948	−	1.76335i
$899$	222.036			0.00823727
$900$		0			0
$901$	−88432.1			−3.26981
$902$	3216.84	−	9900.41i	0.118746	−	0.365463i
$903$		0			0
$904$	−11704.4	−	8503.72i	−0.430621	−	0.312864i
$905$	−24813.6	+	4765.27i	−0.911417	+	0.175031i
$906$		0			0
$907$	−16833.1			−0.616244			−0.308122	−	0.951347i	$-0.599700\pi$
$907$	−16833.1			−0.616244			−0.308122	+	0.951347i	$0.599700\pi$
$908$	−164.254	+	119.337i	−0.00600325	+	0.00436161i
$909$		0			0
$910$	15495.8	+	7268.35i	0.564483	+	0.264773i
$911$	−258.564	+	795.779i	−0.00940353	+	0.0289411i	−0.955648	−	0.294511i	$-0.904843\pi$
$911$	−258.564	+	795.779i	−0.00940353	+	0.0289411i	0.946245	+	0.323452i	$0.104843\pi$
$912$		0			0
$913$	−509.301	−	1567.47i	−0.0184615	−	0.0568188i
$914$	−235.976	+	726.261i	−0.00853983	+	0.0262829i
$915$		0			0
$916$	−691.296	−	2127.59i	−0.0249357	−	0.0767441i
$917$	−1863.11	+	1353.63i	−0.0670943	+	0.0487468i
$918$		0			0
$919$	20095.6	−	14600.3i	0.721320	−	0.524069i	−0.165486	−	0.986212i	$-0.552919\pi$
$919$	20095.6	−	14600.3i	0.721320	−	0.524069i	0.886806	+	0.462143i	$0.152919\pi$
$920$	328.023	−	2622.66i	0.0117550	−	0.0939852i
$921$		0			0
$922$	−25441.6	−	18484.4i	−0.908757	−	0.660250i
$923$	−6340.12	+	19512.9i	−0.226097	+	0.695855i
$924$		0			0
$925$	17336.6	−	27468.1i	0.616241	−	0.976372i
$926$	38122.8			1.35291
$927$		0			0
$928$	−89.1801	−	64.7931i	−0.00315461	−	0.00229196i
$929$	1642.75	+	1193.53i	0.0580162	+	0.0421512i	0.616415	−	0.787421i	$-0.288584\pi$
$929$	1642.75	+	1193.53i	0.0580162	+	0.0421512i	−0.558399	+	0.829572i	$0.688584\pi$
$930$		0			0
$931$	−12252.7	+	8902.12i	−0.431328	+	0.313378i
$932$	−400.094			−0.0140617
$933$		0			0
$934$	6797.93	+	20921.9i	0.238153	+	0.732961i
$935$	−5852.05	+	46789.2i	−0.204687	+	1.63654i
$936$		0			0
$937$	16731.1	+	51493.0i	0.583331	+	1.79531i	0.605873	+	0.795561i	$0.292824\pi$
$937$	16731.1	+	51493.0i	0.583331	+	1.79531i	−0.0225425	+	0.999746i	$0.507176\pi$
$938$	12535.4	+	38580.1i	0.436351	+	1.34295i
$939$		0			0
$940$	−379.726	+	3036.04i	−0.0131758	+	0.105345i
$941$	12321.8	+	37922.8i	0.426866	+	1.31376i	0.901196	+	0.433411i	$0.142690\pi$
$941$	12321.8	+	37922.8i	0.426866	+	1.31376i	−0.474330	+	0.880347i	$0.657310\pi$
$942$		0			0
$943$	1172.04			0.0404740
$944$	−23395.4	+	16997.7i	−0.806626	+	0.586048i
$945$		0			0
$946$	9718.71	+	7061.06i	0.334020	+	0.242679i
$947$	32529.8	+	23634.3i	1.11624	+	0.810995i	0.983635	−	0.180175i	$-0.0576662\pi$
$947$	32529.8	+	23634.3i	1.11624	+	0.810995i	0.132604	+	0.991169i	$0.457666\pi$
$948$		0			0
$949$	−16003.8			−0.547422
$950$	15597.6	−	24712.8i	0.532687	−	0.843990i
$951$		0			0
$952$	−19789.6	+	60906.1i	−0.673723	+	2.07351i
$953$	32429.3	+	23561.3i	1.10230	+	0.800864i	0.981433	−	0.191805i	$-0.0614341\pi$
$953$	32429.3	+	23561.3i	1.10230	+	0.800864i	0.120862	+	0.992669i	$0.461434\pi$
$954$		0			0
$955$	−804.880	+	6435.30i	−0.0272726	+	0.218054i
$956$	−164.730	+	119.683i	−0.00557295	+	0.00404898i
$957$		0			0
$958$	7735.77	−	5620.36i	0.260889	−	0.189547i
$959$	−20517.2	−	63145.4i	−0.690860	−	2.12625i
$960$		0			0
$961$	−8284.42	+	25496.8i	−0.278085	+	0.855857i
$962$	5324.67	+	16387.7i	0.178456	+	0.549230i
$963$		0			0
$964$	−890.206	+	2739.77i	−0.0297423	+	0.0915375i
$965$	−4903.28	−	2299.90i	−0.163567	−	0.0767218i
$966$		0			0
$967$	−27925.3	+	20289.0i	−0.928664	+	0.674714i	−0.945665	−	0.325141i	$-0.894588\pi$
$967$	−27925.3	+	20289.0i	−0.928664	+	0.674714i	0.0170010	+	0.999855i	$0.494588\pi$
$968$	−5260.37			−0.174664
$969$		0			0
$970$	−1721.64	+	330.629i	−0.0569883	+	0.0109442i
$971$	−23202.4	−	16857.5i	−0.766838	−	0.557141i	0.134162	−	0.990959i	$-0.457166\pi$
$971$	−23202.4	−	16857.5i	−0.766838	−	0.557141i	−0.901000	+	0.433819i	$0.857166\pi$
$972$		0			0
$973$	−7653.61	+	23555.4i	−0.252172	+	0.776106i
$974$	25424.7			0.836407
$975$		0			0
$976$	27767.9			0.910685
$977$	−5681.83	+	17486.9i	−0.186057	+	0.572625i	−0.999965	−	0.00836916i	$-0.997336\pi$
$977$	−5681.83	+	17486.9i	−0.186057	+	0.572625i	0.813908	+	0.580994i	$0.197336\pi$
$978$		0			0
$979$	17532.2	+	12737.9i	0.572352	+	0.415838i
$980$	−615.661	−	1116.61i	−0.0200679	−	0.0363967i
$981$		0			0
$982$	−6934.17			−0.225334
$983$	−3855.47	+	2801.16i	−0.125097	+	0.0908883i	−0.648574	−	0.761151i	$-0.724634\pi$
$983$	−3855.47	+	2801.16i	−0.125097	+	0.0908883i	0.523477	+	0.852040i	$0.324634\pi$
$984$		0			0
$985$	−4793.66	−	8694.14i	−0.155065	−	0.281237i
$986$	−471.013	+	1449.63i	−0.0152131	+	0.0468211i
$987$		0			0
$988$	334.387	+	1029.14i	0.0107675	+	0.0331389i
$989$	−417.955	+	1286.33i	−0.0134380	+	0.0413580i
$990$		0			0
$991$	10828.5	+	33326.7i	0.347103	+	1.06827i	0.960448	+	0.278458i	$0.0898234\pi$
$991$	10828.5	+	33326.7i	0.347103	+	1.06827i	−0.613345	+	0.789815i	$0.710177\pi$
$992$	−1197.73	+	870.204i	−0.0383347	+	0.0278518i
$993$		0			0
$994$	49700.3	−	36109.4i	1.58591	−	1.15223i
$995$	25929.8	+	12162.5i	0.826162	+	0.387515i
$996$		0			0
$997$	10665.3	+	7748.82i	0.338791	+	0.246146i	0.744152	−	0.668011i	$-0.232854\pi$
$997$	10665.3	+	7748.82i	0.338791	+	0.246146i	−0.405361	+	0.914157i	$0.632854\pi$
$998$	7618.86	−	23448.4i	0.241654	−	0.743735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.46.2		28
3.2	odd	2		25.4.d.a.21.6	yes	28
15.2	even	4		125.4.e.b.24.11		56
15.8	even	4		125.4.e.b.24.4		56
15.14	odd	2		125.4.d.a.101.2		28
25.6	even	5	inner	225.4.h.b.181.2		28
75.8	even	20		125.4.e.b.99.11		56
75.17	even	20		125.4.e.b.99.4		56
75.41	odd	10		625.4.a.c.1.11		14
75.44	odd	10		125.4.d.a.26.2		28
75.56	odd	10		25.4.d.a.6.6	✓	28
75.59	odd	10		625.4.a.d.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.6.6	✓	28	75.56	odd	10
25.4.d.a.21.6	yes	28	3.2	odd	2
125.4.d.a.26.2		28	75.44	odd	10
125.4.d.a.101.2		28	15.14	odd	2
125.4.e.b.24.4		56	15.8	even	4
125.4.e.b.24.11		56	15.2	even	4
125.4.e.b.99.4		56	75.17	even	20
125.4.e.b.99.11		56	75.8	even	20
225.4.h.b.46.2		28	1.1	even	1	trivial
225.4.h.b.181.2		28	25.6	even	5	inner
625.4.a.c.1.11		14	75.41	odd	10
625.4.a.d.1.4		14	75.59	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)

\(f(q)\)	\(=\)	\(q+(-0.906232 + 2.78910i) q^{2} +(-0.485661 - 0.352853i) q^{4} +(10.1222 + 4.74784i) q^{5} -23.0864 q^{7} +(-17.5561 + 12.7553i) q^{8} +O(q^{10})\)	\(q+(-0.906232 + 2.78910i) q^{2} +(-0.485661 - 0.352853i) q^{4} +(10.1222 + 4.74784i) q^{5} -23.0864 q^{7} +(-17.5561 + 12.7553i) q^{8} +(-22.4152 + 23.9290i) q^{10} +(10.1957 - 31.3790i) q^{11} +(6.98730 + 21.5047i) q^{13} +(20.9216 - 64.3901i) q^{14} +(-21.1498 - 65.0923i) q^{16} +(-103.416 + 75.1358i) q^{17} +(-64.4944 + 46.8579i) q^{19} +(-3.24065 - 5.87748i) q^{20} +(78.2794 + 56.8733i) q^{22} +(-3.36642 + 10.3608i) q^{23} +(79.9161 + 96.1167i) q^{25} -66.3107 q^{26} +(11.2122 + 8.14611i) q^{28} +(-3.28945 - 2.38992i) q^{29} +(-44.1789 + 32.0979i) q^{31} +27.1110 q^{32} +(-115.842 - 356.526i) q^{34} +(-233.684 - 109.610i) q^{35} +(-80.2988 - 247.134i) q^{37} +(-72.2443 - 222.345i) q^{38} +(-238.266 + 45.7571i) q^{40} +(-33.2460 - 102.321i) q^{41} +124.154 q^{43} +(-16.0238 + 11.6420i) q^{44} +(-25.8465 - 18.7786i) q^{46} +(-368.812 - 267.958i) q^{47} +189.981 q^{49} +(-340.501 + 135.789i) q^{50} +(4.19455 - 12.9095i) q^{52} +(559.680 + 406.631i) q^{53} +(252.184 - 269.216i) q^{55} +(405.307 - 294.473i) q^{56} +(9.64673 - 7.00876i) q^{58} +(-130.566 - 401.842i) q^{59} +(-125.372 + 385.857i) q^{61} +(-49.4877 - 152.307i) q^{62} +(144.629 - 445.123i) q^{64} +(-31.3743 + 250.848i) q^{65} +(-484.733 + 352.179i) q^{67} +76.7368 q^{68} +(517.486 - 552.434i) q^{70} +(734.084 + 533.343i) q^{71} +(-218.714 + 673.134i) q^{73} +762.051 q^{74} +47.8564 q^{76} +(-235.381 + 724.427i) q^{77} +(69.9257 + 50.8040i) q^{79} +(94.9665 - 759.290i) q^{80} +315.511 q^{82} +(40.4126 - 29.3615i) q^{83} +(-1403.52 + 269.536i) q^{85} +(-112.512 + 346.278i) q^{86} +(221.251 + 680.941i) q^{88} +(-202.969 + 624.673i) q^{89} +(-161.311 - 496.465i) q^{91} +(5.29078 - 3.84398i) q^{92} +(1081.59 - 785.820i) q^{94} +(-875.296 + 168.094i) q^{95} +(43.2567 + 31.4278i) q^{97} +(-172.167 + 529.875i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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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