LMFDB - Embedded newform 225.4.h.b.91.5

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			91.5
Character	$\chi$	$=$	225.91
Dual form			225.4.h.b.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51671 + 1.10196i) q^{2} +(-1.38603 - 4.26575i) q^{4} +(-2.00572 + 10.9990i) q^{5} -5.91678 q^{7} +(7.23313 - 22.2613i) q^{8} +O(q^{10})$	\(q+(1.51671 + 1.10196i) q^{2} +(-1.38603 - 4.26575i) q^{4} +(-2.00572 + 10.9990i) q^{5} -5.91678 q^{7} +(7.23313 - 22.2613i) q^{8} +(-15.1625 + 14.4720i) q^{10} +(-46.2426 - 33.5972i) q^{11} +(-23.8943 + 17.3602i) q^{13} +(-8.97406 - 6.52004i) q^{14} +(6.47220 - 4.70233i) q^{16} +(-16.1964 + 49.8475i) q^{17} +(28.8671 - 88.8439i) q^{19} +(49.6988 - 6.68896i) q^{20} +(-33.1141 - 101.915i) q^{22} +(-101.186 - 73.5160i) q^{23} +(-116.954 - 44.1216i) q^{25} -55.3710 q^{26} +(8.20082 + 25.2395i) q^{28} +(-42.2327 - 129.979i) q^{29} +(-22.0658 + 67.9115i) q^{31} -172.257 q^{32} +(-79.4951 + 57.7566i) q^{34} +(11.8674 - 65.0785i) q^{35} +(-149.002 + 108.256i) q^{37} +(141.685 - 102.940i) q^{38} +(230.343 + 124.207i) q^{40} +(28.3279 - 20.5814i) q^{41} +185.374 q^{43} +(-79.2239 + 243.826i) q^{44} +(-72.4588 - 223.005i) q^{46} +(-130.295 - 401.007i) q^{47} -307.992 q^{49} +(-128.766 - 195.798i) q^{50} +(107.173 + 77.8655i) q^{52} +(214.260 + 659.426i) q^{53} +(462.284 - 441.234i) q^{55} +(-42.7968 + 131.715i) q^{56} +(79.1762 - 243.679i) q^{58} +(466.375 - 338.841i) q^{59} +(29.5121 + 21.4418i) q^{61} +(-108.303 + 78.6867i) q^{62} +(-313.042 - 227.438i) q^{64} +(-143.019 - 297.633i) q^{65} +(-48.1248 + 148.113i) q^{67} +235.086 q^{68} +(89.7130 - 85.6279i) q^{70} +(-120.884 - 372.044i) q^{71} +(946.113 + 687.392i) q^{73} -345.287 q^{74} -418.997 q^{76} +(273.608 + 198.788i) q^{77} +(323.388 + 995.287i) q^{79} +(38.7393 + 80.6190i) q^{80} +65.6451 q^{82} +(-289.936 + 892.333i) q^{83} +(-515.785 - 278.124i) q^{85} +(281.159 + 204.274i) q^{86} +(-1082.40 + 786.407i) q^{88} +(378.143 + 274.737i) q^{89} +(141.378 - 102.717i) q^{91} +(-173.354 + 533.530i) q^{92} +(244.272 - 751.791i) q^{94} +(919.291 + 495.704i) q^{95} +(-529.272 - 1628.93i) q^{97} +(-467.135 - 339.393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.51671	+	1.10196i	0.536239	+	0.389600i	0.822686	−	0.568496i	$-0.192474\pi$
$2$	1.51671	+	1.10196i	0.536239	+	0.389600i	−0.286447	+	0.958096i	$0.592474\pi$
$3$		0			0
$3$		0			0
$4$	−1.38603	−	4.26575i	−0.173253	−	0.533219i
$5$	−2.00572	+	10.9990i	−0.179397	+	0.983777i
$5$	−2.00572	+	10.9990i	−0.179397	+	0.983777i
$6$		0			0
$7$	−5.91678			−0.319476			−0.159738	−	0.987159i	$-0.551065\pi$
$7$	−5.91678			−0.319476			−0.159738	+	0.987159i	$0.551065\pi$
$8$	7.23313	−	22.2613i	0.319662	−	0.983819i
$9$		0			0
$10$	−15.1625	+	14.4720i	−0.479479	+	0.457646i
$11$	−46.2426	−	33.5972i	−1.26752	−	0.920904i	−0.268415	−	0.963303i	$-0.586500\pi$
$11$	−46.2426	−	33.5972i	−1.26752	−	0.920904i	−0.999101	+	0.0423993i	$0.986500\pi$
$12$		0			0
$13$	−23.8943	+	17.3602i	−0.509777	+	0.370374i	−0.812739	−	0.582628i	$-0.802024\pi$
$13$	−23.8943	+	17.3602i	−0.509777	+	0.370374i	0.302962	+	0.953003i	$0.402024\pi$
$14$	−8.97406	−	6.52004i	−0.171316	−	0.124468i
$15$		0			0
$16$	6.47220	−	4.70233i	0.101128	−	0.0734739i
$17$	−16.1964	+	49.8475i	−0.231071	+	0.711165i	0.766547	+	0.642188i	$0.221973\pi$
$17$	−16.1964	+	49.8475i	−0.231071	+	0.711165i	−0.997618	+	0.0689764i	$0.978027\pi$
$18$		0			0
$19$	28.8671	−	88.8439i	0.348557	−	1.07275i	−0.611096	−	0.791557i	$-0.709271\pi$
$19$	28.8671	−	88.8439i	0.348557	−	1.07275i	0.959652	−	0.281190i	$-0.0907291\pi$
$20$	49.6988	−	6.68896i	0.555650	−	0.0747848i
$21$		0			0
$22$	−33.1141	−	101.915i	−0.320907	−	0.987649i
$23$	−101.186	−	73.5160i	−0.917338	−	0.666485i	0.0255223	−	0.999674i	$-0.491875\pi$
$23$	−101.186	−	73.5160i	−0.917338	−	0.666485i	−0.942860	+	0.333189i	$0.891875\pi$
$24$		0			0
$25$	−116.954	−	44.1216i	−0.935634	−	0.352973i
$26$	−55.3710			−0.417660
$27$		0			0
$28$	8.20082	+	25.2395i	0.0553503	+	0.170351i
$29$	−42.2327	−	129.979i	−0.270428	−	0.832293i	−0.990393	−	0.138282i	$-0.955842\pi$
$29$	−42.2327	−	129.979i	−0.270428	−	0.832293i	0.719965	−	0.694011i	$-0.244158\pi$
$30$		0			0
$31$	−22.0658	+	67.9115i	−0.127843	+	0.393460i	−0.994408	−	0.105603i	$-0.966323\pi$
$31$	−22.0658	+	67.9115i	−0.127843	+	0.393460i	0.866565	+	0.499064i	$0.166323\pi$
$32$	−172.257			−0.951594
$33$		0			0
$34$	−79.4951	+	57.7566i	−0.400979	+	0.291329i
$35$	11.8674	−	65.0785i	0.0573131	−	0.314293i
$36$		0			0
$37$	−149.002	+	108.256i	−0.662048	+	0.481006i	−0.867354	−	0.497692i	$-0.834181\pi$
$37$	−149.002	+	108.256i	−0.662048	+	0.481006i	0.205306	+	0.978698i	$0.434181\pi$
$38$	141.685	−	102.940i	0.604852	−	0.439451i
$39$		0			0
$40$	230.343	+	124.207i	0.910512	+	0.490970i
$41$	28.3279	−	20.5814i	0.107904	−	0.0783971i	−0.532525	−	0.846415i	$-0.678757\pi$
$41$	28.3279	−	20.5814i	0.107904	−	0.0783971i	0.640429	+	0.768017i	$0.278757\pi$
$42$		0			0
$43$	185.374			0.657425			0.328712	−	0.944430i	$-0.393385\pi$
$43$	185.374			0.657425			0.328712	+	0.944430i	$0.393385\pi$
$44$	−79.2239	+	243.826i	−0.271442	+	0.835413i
$45$		0			0
$46$	−72.4588	−	223.005i	−0.232249	−	0.714790i
$47$	−130.295	−	401.007i	−0.404372	−	1.24453i	−0.921419	−	0.388571i	$-0.872969\pi$
$47$	−130.295	−	401.007i	−0.404372	−	1.24453i	0.517047	−	0.855957i	$-0.327031\pi$
$48$		0			0
$49$	−307.992			−0.897935
$50$	−128.766	−	195.798i	−0.364205	−	0.553801i
$51$		0			0
$52$	107.173	+	77.8655i	0.285811	+	0.207654i
$53$	214.260	+	659.426i	0.555301	+	1.70904i	0.695148	+	0.718867i	$0.255339\pi$
$53$	214.260	+	659.426i	0.555301	+	1.70904i	−0.139847	+	0.990173i	$0.544661\pi$
$54$		0			0
$55$	462.284	−	441.234i	1.13335	−	1.08175i
$56$	−42.7968	+	131.715i	−0.102124	+	0.314307i
$57$		0			0
$58$	79.1762	−	243.679i	0.179247	−	0.551667i
$59$	466.375	−	338.841i	1.02910	−	0.747684i	0.0609711	−	0.998140i	$-0.480580\pi$
$59$	466.375	−	338.841i	1.02910	−	0.747684i	0.968128	+	0.250455i	$0.0805802\pi$
$60$		0			0
$61$	29.5121	+	21.4418i	0.0619448	+	0.0450056i	0.618327	−	0.785921i	$-0.287811\pi$
$61$	29.5121	+	21.4418i	0.0619448	+	0.0450056i	−0.556382	+	0.830927i	$0.687811\pi$
$62$	−108.303	+	78.6867i	−0.221847	+	0.161181i
$63$		0			0
$64$	−313.042	−	227.438i	−0.611410	−	0.444215i
$65$	−143.019	−	297.633i	−0.272913	−	0.567950i
$66$		0			0
$67$	−48.1248	+	148.113i	−0.0877519	+	0.270073i	−0.985297	−	0.170850i	$-0.945349\pi$
$67$	−48.1248	+	148.113i	−0.0877519	+	0.270073i	0.897545	+	0.440923i	$0.145349\pi$
$68$	235.086			0.419240
$69$		0			0
$70$	89.7130	−	85.6279i	0.153182	−	0.146207i
$71$	−120.884	−	372.044i	−0.202061	−	0.621880i	−0.999821	−	0.0189054i	$-0.993982\pi$
$71$	−120.884	−	372.044i	−0.202061	−	0.621880i	0.797760	−	0.602975i	$-0.206018\pi$
$72$		0			0
$73$	946.113	+	687.392i	1.51691	+	1.10210i	0.962994	+	0.269523i	$0.0868659\pi$
$73$	946.113	+	687.392i	1.51691	+	1.10210i	0.553913	+	0.832575i	$0.313134\pi$
$74$	−345.287			−0.542416
$75$		0			0
$76$	−418.997			−0.632397
$77$	273.608	+	198.788i	0.404941	+	0.294207i
$78$		0			0
$79$	323.388	+	995.287i	0.460557	+	1.41745i	0.864485	+	0.502659i	$0.167645\pi$
$79$	323.388	+	995.287i	0.460557	+	1.41745i	−0.403927	+	0.914791i	$0.632355\pi$
$80$	38.7393	+	80.6190i	0.0541398	+	0.112668i
$81$		0			0
$82$	65.6451			0.0884060
$83$	−289.936	+	892.333i	−0.383430	+	1.18007i	0.554184	+	0.832395i	$0.313031\pi$
$83$	−289.936	+	892.333i	−0.383430	+	1.18007i	−0.937613	+	0.347680i	$0.886969\pi$
$84$		0			0
$85$	−515.785	−	278.124i	−0.658174	−	0.354903i
$86$	281.159	+	204.274i	0.352537	+	0.256133i
$87$		0			0
$88$	−1082.40	+	786.407i	−1.31118	+	0.952628i
$89$	378.143	+	274.737i	0.450371	+	0.327214i	0.789742	−	0.613439i	$-0.210214\pi$
$89$	378.143	+	274.737i	0.450371	+	0.327214i	−0.339371	+	0.940653i	$0.610214\pi$
$90$		0			0
$91$	141.378	−	102.717i	0.162862	−	0.118326i
$92$	−173.354	+	533.530i	−0.196451	+	0.604613i
$93$		0			0
$94$	244.272	−	751.791i	0.268029	−	0.824908i
$95$	919.291	+	495.704i	0.992813	+	0.535349i
$96$		0			0
$97$	−529.272	−	1628.93i	−0.554014	−	1.70508i	−0.698532	−	0.715579i	$-0.746163\pi$
$97$	−529.272	−	1628.93i	−0.554014	−	1.70508i	0.144518	−	0.989502i	$-0.453837\pi$
$98$	−467.135	−	339.393i	−0.481508	−	0.349836i
$99$		0			0
$100$	−26.1103	+	560.051i	−0.0261103	+	0.560051i
$101$	−1054.59			−1.03896			−0.519482	−	0.854482i	$-0.673875\pi$
$101$	−1054.59			−1.03896			−0.519482	+	0.854482i	$0.673875\pi$
$102$		0			0
$103$	28.4548	+	87.5749i	0.0272207	+	0.0837768i	0.963744	−	0.266829i	$-0.0859758\pi$
$103$	28.4548	+	87.5749i	0.0272207	+	0.0837768i	−0.936523	+	0.350606i	$0.885976\pi$
$104$	213.631	+	657.487i	0.201425	+	0.619922i
$105$		0			0
$106$	−401.687	+	1236.26i	−0.368069	+	1.13280i
$107$	66.9507			0.0604894			0.0302447	−	0.999543i	$-0.490371\pi$
$107$	66.9507			0.0604894			0.0302447	+	0.999543i	$0.490371\pi$
$108$		0			0
$109$	−160.237	+	116.419i	−0.140806	+	0.102302i	−0.655958	−	0.754797i	$-0.727735\pi$
$109$	−160.237	+	116.419i	−0.140806	+	0.102302i	0.515152	+	0.857099i	$0.327735\pi$
$110$	1187.37	−	159.808i	1.02920	−	0.138519i
$111$		0			0
$112$	−38.2946	+	27.8227i	−0.0323080	+	0.0234732i
$113$	1326.05	−	963.435i	1.10394	−	0.802056i	0.122237	−	0.992501i	$-0.460993\pi$
$113$	1326.05	−	963.435i	1.10394	−	0.802056i	0.981698	+	0.190445i	$0.0609931\pi$
$114$		0			0
$115$	1011.55	−	965.490i	0.820240	−	0.782890i
$116$	−495.922	+	360.309i	−0.396942	+	0.288395i
$117$		0			0
$118$	1080.74			0.843141
$119$	95.8308	−	294.937i	0.0738218	−	0.227200i
$120$		0			0
$121$	598.304	+	1841.39i	0.449515	+	1.38346i
$122$	21.1334	+	65.0420i	0.0156830	+	0.0482675i
$123$		0			0
$124$	320.277			0.231950
$125$	719.869	−	1197.88i	0.515096	−	0.857132i
$126$		0			0
$127$	−404.153	−	293.635i	−0.282384	−	0.205164i	0.437572	−	0.899183i	$-0.355838\pi$
$127$	−404.153	−	293.635i	−0.282384	−	0.205164i	−0.719957	+	0.694019i	$0.755838\pi$
$128$	201.675	+	620.692i	0.139263	+	0.428609i
$129$		0			0
$130$	111.059	−	609.024i	0.0749269	−	0.410884i
$131$	−80.0952	+	246.508i	−0.0534195	+	0.164408i	−0.974207	−	0.225656i	$-0.927547\pi$
$131$	−80.0952	+	246.508i	−0.0534195	+	0.164408i	0.920787	+	0.390065i	$0.127547\pi$
$132$		0			0
$133$	−170.801	+	525.670i	−0.111356	+	0.342717i
$134$	−236.205	+	171.613i	−0.152276	+	0.110635i
$135$		0			0
$136$	992.519	+	721.107i	0.625792	+	0.454665i
$137$	−123.196	+	89.5073i	−0.0768275	+	0.0558184i	−0.625536	−	0.780195i	$-0.715120\pi$
$137$	−123.196	+	89.5073i	−0.0768275	+	0.0558184i	0.548709	+	0.836014i	$0.315120\pi$
$138$		0			0
$139$	−1835.62	−	1333.66i	−1.12011	−	0.813809i	−0.135885	−	0.990725i	$-0.543388\pi$
$139$	−1835.62	−	1333.66i	−1.12011	−	0.813809i	−0.984226	+	0.176916i	$0.943388\pi$
$140$	−294.057	+	39.5771i	−0.177517	+	0.0238920i
$141$		0			0
$142$	226.629	−	697.493i	0.133932	−	0.412200i
$143$	1688.19			0.987229
$144$		0			0
$145$	1514.34	−	203.815i	0.867304	−	0.116730i
$146$	677.506	+	2085.15i	0.384047	+	1.18197i
$147$		0			0
$148$	668.315	+	485.559i	0.371184	+	0.269681i
$149$	−1563.68			−0.859744			−0.429872	−	0.902890i	$-0.641441\pi$
$149$	−1563.68			−0.859744			−0.429872	+	0.902890i	$0.641441\pi$
$150$		0			0
$151$	−2328.94			−1.25514			−0.627571	−	0.778559i	$-0.715951\pi$
$151$	−2328.94			−1.25514			−0.627571	+	0.778559i	$0.715951\pi$
$152$	−1768.98	−	1285.24i	−0.943968	−	0.685833i
$153$		0			0
$154$	195.929	+	603.007i	0.102522	+	0.315530i
$155$	−702.698	−	378.912i	−0.364142	−	0.196354i
$156$		0			0
$157$	−290.519			−0.147681			−0.0738406	−	0.997270i	$-0.523526\pi$
$157$	−290.519			−0.147681			−0.0738406	+	0.997270i	$0.523526\pi$
$158$	−606.275	+	1865.92i	−0.305270	+	0.939525i
$159$		0			0
$160$	345.499	−	1894.65i	0.170713	−	0.936156i
$161$	598.696	+	434.978i	0.293068	+	0.212926i
$162$		0			0
$163$	1590.13	−	1155.30i	0.764102	−	0.555153i	−0.136064	−	0.990700i	$-0.543445\pi$
$163$	1590.13	−	1155.30i	0.764102	−	0.555153i	0.900166	+	0.435547i	$0.143445\pi$
$164$	−127.059	−	92.3135i	−0.0604976	−	0.0439541i
$165$		0			0
$166$	−1423.06	+	1033.91i	−0.665367	+	0.483418i
$167$	634.745	−	1953.54i	0.294120	−	0.905208i	−0.689396	−	0.724385i	$-0.742124\pi$
$167$	634.745	−	1953.54i	0.294120	−	0.905208i	0.983516	−	0.180823i	$-0.0578761\pi$
$168$		0			0
$169$	−409.350	+	1259.85i	−0.186322	+	0.573440i
$170$	−475.817	−	990.207i	−0.214668	−	0.446738i
$171$		0			0
$172$	−256.933	−	790.759i	−0.113901	−	0.350551i
$173$	−1034.32	−	751.479i	−0.454555	−	0.330254i	0.336836	−	0.941563i	$-0.390643\pi$
$173$	−1034.32	−	751.479i	−0.454555	−	0.330254i	−0.791392	+	0.611310i	$0.790643\pi$
$174$		0			0
$175$	691.993	+	261.058i	0.298913	+	0.112767i
$176$	−457.276			−0.195844
$177$		0			0
$178$	270.786	+	833.393i	0.114024	+	0.350930i
$179$	−144.118	−	443.549i	−0.0601781	−	0.185209i	0.916448	−	0.400153i	$-0.131043\pi$
$179$	−144.118	−	443.549i	−0.0601781	−	0.185209i	−0.976626	+	0.214944i	$0.931043\pi$
$180$		0			0
$181$	360.349	−	1109.04i	0.147981	−	0.455439i	−0.849401	−	0.527748i	$-0.823037\pi$
$181$	360.349	−	1109.04i	0.147981	−	0.455439i	0.997382	+	0.0723088i	$0.0230367\pi$
$182$	327.619			0.133432
$183$		0			0
$184$	−2368.45	+	1720.78i	−0.948938	+	0.689444i
$185$	−891.850	−	1856.00i	−0.354433	−	0.737598i
$186$		0			0
$187$	2423.70	−	1760.92i	0.947801	−	0.688618i
$188$	−1530.00	+	1111.61i	−0.593547	+	0.431237i
$189$		0			0
$190$	848.056	+	1764.86i	0.323813	+	0.673875i
$191$	1809.34	−	1314.56i	0.685440	−	0.498001i	−0.189718	−	0.981839i	$-0.560757\pi$
$191$	1809.34	−	1314.56i	0.685440	−	0.498001i	0.875158	+	0.483837i	$0.160757\pi$
$192$		0			0
$193$	1902.42			0.709530			0.354765	−	0.934956i	$-0.384561\pi$
$193$	1902.42			0.709530			0.354765	+	0.934956i	$0.384561\pi$
$194$	992.257	−	3053.85i	0.367216	−	1.13017i
$195$		0			0
$196$	426.885	+	1313.82i	0.155570	+	0.478796i
$197$	−559.983	−	1723.45i	−0.202524	−	0.623304i	−0.999806	−	0.0196971i	$-0.993730\pi$
$197$	−559.983	−	1723.45i	−0.202524	−	0.623304i	0.797282	−	0.603607i	$-0.206270\pi$
$198$		0			0
$199$	−3011.24			−1.07267			−0.536335	−	0.844005i	$-0.680192\pi$
$199$	−3011.24			−1.07267			−0.536335	+	0.844005i	$0.680192\pi$
$200$	−1828.15	+	2284.41i	−0.646348	+	0.807662i
$201$		0			0
$202$	−1599.50	−	1162.11i	−0.557132	−	0.404780i
$203$	249.882	+	769.058i	0.0863954	+	0.265898i
$204$		0			0
$205$	169.557	+	352.858i	0.0577675	+	0.120218i
$206$	−53.3459	+	164.182i	−0.0180427	+	0.0555296i
$207$		0			0
$208$	−73.0153	+	224.718i	−0.0243399	+	0.0749105i
$209$	−4319.80	+	3138.52i	−1.42970	+	1.03874i
$210$		0			0
$211$	−3153.40	−	2291.08i	−1.02886	−	0.747509i	−0.0607784	−	0.998151i	$-0.519358\pi$
$211$	−3153.40	−	2291.08i	−1.02886	−	0.747509i	−0.968080	+	0.250642i	$0.919358\pi$
$212$	2515.98	−	1827.96i	0.815085	−	0.592194i
$213$		0			0
$214$	101.545	+	73.7767i	0.0324368	+	0.0235667i
$215$	−371.808	+	2038.92i	−0.117940	+	0.646759i
$216$		0			0
$217$	130.558	−	401.818i	0.0408428	−	0.125701i
$218$	−371.321			−0.115362
$219$		0			0
$220$	−2522.93	−	1360.43i	−0.773164	−	0.416909i
$221$	−478.362	−	1472.25i	−0.145602	−	0.448118i
$222$		0			0
$223$	−2941.83	−	2137.36i	−0.883406	−	0.641832i	0.0507445	−	0.998712i	$-0.483841\pi$
$223$	−2941.83	−	2137.36i	−0.883406	−	0.641832i	−0.934150	+	0.356880i	$0.883841\pi$
$224$	1019.21			0.304012
$225$		0			0
$226$	3072.90			0.904454
$227$	562.815	+	408.909i	0.164561	+	0.119561i	0.667018	−	0.745042i	$-0.267570\pi$
$227$	562.815	+	408.909i	0.164561	+	0.119561i	−0.502457	+	0.864602i	$0.667570\pi$
$228$		0			0
$229$	−1706.92	−	5253.37i	−0.492562	−	1.51595i	−0.820722	−	0.571328i	$-0.806428\pi$
$229$	−1706.92	−	5253.37i	−0.492562	−	1.51595i	0.328160	−	0.944622i	$-0.393572\pi$
$230$	2598.16	−	349.686i	0.744859	−	0.100250i
$231$		0			0
$232$	−3198.97			−0.905271
$233$	1653.81	−	5089.90i	0.464998	−	1.43112i	−0.393986	−	0.919116i	$-0.628904\pi$
$233$	1653.81	−	5089.90i	0.464998	−	1.43112i	0.858985	−	0.512001i	$-0.171096\pi$
$234$		0			0
$235$	4671.99	−	628.802i	1.29688	−	0.174547i
$236$	−2091.82	−	1519.80i	−0.576974	−	0.419196i
$237$		0			0
$238$	470.355	−	341.733i	0.128103	−	0.0930726i
$239$	−4030.36	−	2928.23i	−1.09081	−	0.792517i	−0.111271	−	0.993790i	$-0.535492\pi$
$239$	−4030.36	−	2928.23i	−1.09081	−	0.792517i	−0.979535	+	0.201273i	$0.935492\pi$
$240$		0			0
$241$	1105.03	−	802.852i	0.295358	−	0.214590i	−0.430230	−	0.902719i	$-0.641568\pi$
$241$	1105.03	−	802.852i	0.295358	−	0.214590i	0.725588	+	0.688129i	$0.241568\pi$
$242$	−1121.68	+	3452.17i	−0.297951	+	0.916998i
$243$		0			0
$244$	50.5608	−	155.610i	0.0132657	−	0.0408275i
$245$	617.745	−	3387.59i	0.161087	−	0.883368i
$246$		0			0
$247$	852.591	+	2624.01i	0.219632	+	0.675957i
$248$	1352.19	+	982.425i	0.346227	+	0.251549i
$249$		0			0
$250$	2411.84	−	1023.57i	0.610154	−	0.258946i
$251$	56.3223			0.0141635			0.00708174	−	0.999975i	$-0.497746\pi$
$251$	56.3223			0.0141635			0.00708174	+	0.999975i	$0.497746\pi$
$252$		0			0
$253$	2209.18	+	6799.15i	0.548971	+	1.68956i
$254$	−289.412	−	890.719i	−0.0714934	−	0.220034i
$255$		0			0
$256$	−1334.66	+	4107.67i	−0.325845	+	1.00285i
$257$	587.079			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$257$	587.079			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$258$		0			0
$259$	881.612	−	640.529i	0.211509	−	0.153670i
$260$	−1071.40	+	1022.61i	−0.255559	+	0.243922i
$261$		0			0
$262$	−393.122	+	285.620i	−0.0926991	+	0.0673498i
$263$	−388.238	+	282.072i	−0.0910258	+	0.0661341i	−0.632367	−	0.774669i	$-0.717917\pi$
$263$	−388.238	+	282.072i	−0.0910258	+	0.0661341i	0.541341	+	0.840803i	$0.317917\pi$
$264$		0			0
$265$	−7682.74	+	1034.02i	−1.78093	+	0.239696i
$266$	−838.321	+	609.076i	−0.193236	+	0.140394i
$267$		0			0
$268$	698.515			0.159211
$269$	−1495.78	+	4603.53i	−0.339030	+	1.04343i	0.625673	+	0.780086i	$0.284825\pi$
$269$	−1495.78	+	4603.53i	−0.339030	+	1.04343i	−0.964703	+	0.263342i	$0.915175\pi$
$270$		0			0
$271$	1441.77	+	4437.32i	0.323179	+	0.994643i	0.972256	+	0.233920i	$0.0751553\pi$
$271$	1441.77	+	4437.32i	0.323179	+	0.994643i	−0.649077	+	0.760723i	$0.724845\pi$
$272$	129.573	+	398.784i	0.0288842	+	0.0888964i
$273$		0			0
$274$	−285.486			−0.0629448
$275$	3925.90	+	5969.64i	0.860876	+	1.30903i
$276$		0			0
$277$	−6762.05	−	4912.91i	−1.46676	−	1.06566i	−0.981537	−	0.191271i	$-0.938739\pi$
$277$	−6762.05	−	4912.91i	−1.46676	−	1.06566i	−0.485221	−	0.874392i	$-0.661261\pi$
$278$	−1314.48	−	4045.55i	−0.283587	−	0.872791i
$279$		0			0
$280$	−1362.89	−	734.904i	−0.290887	−	0.156853i
$281$	−1708.18	+	5257.23i	−0.362638	+	1.11609i	0.588809	+	0.808272i	$0.299597\pi$
$281$	−1708.18	+	5257.23i	−0.362638	+	1.11609i	−0.951447	+	0.307813i	$0.900403\pi$
$282$		0			0
$283$	−161.101	+	495.817i	−0.0338390	+	0.104146i	−0.966549	−	0.256481i	$-0.917437\pi$
$283$	−161.101	+	495.817i	−0.0338390	+	0.104146i	0.932710	+	0.360626i	$0.117437\pi$
$284$	−1419.50	+	1031.33i	−0.296591	+	0.215486i
$285$		0			0
$286$	2560.50	+	1860.31i	0.529390	+	0.384625i
$287$	−167.610	+	121.776i	−0.0344729	+	0.0250460i
$288$		0			0
$289$	1752.25	+	1273.08i	0.356656	+	0.259126i
$290$	2521.41	+	1359.61i	0.510560	+	0.275307i
$291$		0			0
$292$	1620.90	−	4988.63i	0.324850	−	0.999786i
$293$	2209.70			0.440587			0.220294	−	0.975434i	$-0.429298\pi$
$293$	2209.70			0.440587			0.220294	+	0.975434i	$0.429298\pi$
$294$		0			0
$295$	2791.48	+	5809.26i	0.550937	+	1.14654i
$296$	1332.17	+	4100.01i	0.261591	+	0.805094i
$297$		0			0
$298$	−2371.66	−	1723.11i	−0.461028	−	0.334957i
$299$	3694.03			0.714486
$300$		0			0
$301$	−1096.82			−0.210032
$302$	−3532.33	−	2566.39i	−0.673056	−	0.489004i
$303$		0			0
$304$	−230.939	−	710.758i	−0.0435700	−	0.134095i
$305$	−295.030	+	281.596i	−0.0553881	+	0.0528660i
$306$		0			0
$307$	10095.6			1.87683			0.938413	−	0.345516i	$-0.112296\pi$
$307$	10095.6			1.87683			0.938413	+	0.345516i	$0.112296\pi$
$308$	468.751	−	1442.67i	0.0867193	−	0.266895i
$309$		0			0
$310$	−648.246	−	1349.04i	−0.118767	−	0.247163i
$311$	4497.20	+	3267.41i	0.819977	+	0.595748i	0.916706	−	0.399563i	$-0.130838\pi$
$311$	4497.20	+	3267.41i	0.819977	+	0.595748i	−0.0967289	+	0.995311i	$0.530838\pi$
$312$		0			0
$313$	4746.67	−	3448.66i	0.857180	−	0.622778i	−0.0699360	−	0.997551i	$-0.522279\pi$
$313$	4746.67	−	3448.66i	0.857180	−	0.622778i	0.927116	+	0.374773i	$0.122279\pi$
$314$	−440.634	−	320.139i	−0.0791923	−	0.0575366i
$315$		0			0
$316$	3797.42	−	2758.99i	0.676018	−	0.491156i
$317$	98.5888	−	303.425i	0.0174678	−	0.0537604i	−0.941943	−	0.335774i	$-0.891002\pi$
$317$	98.5888	−	303.425i	0.0174678	−	0.0537604i	0.959410	+	0.282013i	$0.0910022\pi$
$318$		0			0
$319$	−2413.98	+	7429.47i	−0.423690	+	1.30398i
$320$	3129.46	−	2986.96i	0.546694	−	0.521800i
$321$		0			0
$322$	428.723	+	1319.47i	0.0741982	+	0.228358i
$323$	3961.10	+	2877.91i	0.682358	+	0.495762i
$324$		0			0
$325$	3560.50	−	976.097i	0.607696	−	0.166597i
$326$	3684.86			0.626029
$327$		0			0
$328$	−253.270	−	779.484i	−0.0426356	−	0.131219i
$329$	770.927	+	2372.67i	0.129187	+	0.397597i
$330$		0			0
$331$	904.957	−	2785.17i	0.150275	−	0.462498i	−0.847377	−	0.530992i	$-0.821819\pi$
$331$	904.957	−	2785.17i	0.150275	−	0.462498i	0.997652	+	0.0684939i	$0.0218194\pi$
$332$	4208.33			0.695669
$333$		0			0
$334$	3115.44	−	2263.50i	0.510388	−	0.370818i
$335$	−1532.56	−	826.395i	−0.249949	−	0.134779i
$336$		0			0
$337$	−4174.94	+	3033.27i	−0.674848	+	0.490306i	−0.871644	−	0.490139i	$-0.836946\pi$
$337$	−4174.94	+	3033.27i	−0.674848	+	0.490306i	0.196797	+	0.980444i	$0.436946\pi$
$338$	−2009.16	+	1459.74i	−0.323326	+	0.234910i
$339$		0			0
$340$	−471.516	+	2585.70i	−0.0752104	+	0.412439i
$341$	3302.02	−	2399.06i	0.524382	−	0.380986i
$342$		0			0
$343$	3851.78			0.606345
$344$	1340.83	−	4126.66i	0.210154	−	0.646787i
$345$		0			0
$346$	−740.672	−	2279.55i	−0.115083	−	0.354190i
$347$	−540.620	−	1663.86i	−0.0836369	−	0.257408i	0.900489	−	0.434878i	$-0.143209\pi$
$347$	−540.620	−	1663.86i	−0.0836369	−	0.257408i	−0.984126	+	0.177470i	$0.943209\pi$
$348$		0			0
$349$	−1775.11			−0.272262			−0.136131	−	0.990691i	$-0.543467\pi$
$349$	−1775.11			−0.272262			−0.136131	+	0.990691i	$0.543467\pi$
$350$	761.879	+	1158.50i	0.116355	+	0.176926i
$351$		0			0
$352$	7965.61	+	5787.35i	1.20616	+	0.876327i
$353$	−101.976	−	313.851i	−0.0153758	−	0.0473218i	0.943074	−	0.332582i	$-0.107920\pi$
$353$	−101.976	−	313.851i	−0.0153758	−	0.0473218i	−0.958450	+	0.285260i	$0.907920\pi$
$354$		0			0
$355$	4334.56	−	583.388i	0.648041	−	0.0872197i
$356$	647.843	−	1993.86i	0.0964484	−	0.296838i
$357$		0			0
$358$	270.186	−	831.548i	0.0398877	−	0.122762i
$359$	3398.46	−	2469.12i	0.499620	−	0.362995i	−0.309252	−	0.950980i	$-0.600079\pi$
$359$	3398.46	−	2469.12i	0.499620	−	0.362995i	0.808872	+	0.587985i	$0.200079\pi$
$360$		0			0
$361$	−1510.88	−	1097.72i	−0.220277	−	0.160040i
$362$	1768.66	−	1285.01i	0.256792	−	0.186570i
$363$		0			0
$364$	−634.118	−	460.713i	−0.0913099	−	0.0663405i
$365$	−9458.23	+	9027.55i	−1.35635	+	1.29458i
$366$		0			0
$367$	−3499.21	+	10769.5i	−0.497704	+	1.53177i	0.314997	+	0.949093i	$0.397997\pi$
$367$	−3499.21	+	10769.5i	−0.497704	+	1.53177i	−0.812700	+	0.582682i	$0.802003\pi$
$368$	−1000.59			−0.141738
$369$		0			0
$370$	692.548	−	3797.79i	0.0973077	−	0.533616i
$371$	−1267.73	−	3901.68i	−0.177405	−	0.545998i
$372$		0			0
$373$	−6524.79	−	4740.54i	−0.905740	−	0.658059i	0.0341938	−	0.999415i	$-0.489114\pi$
$373$	−6524.79	−	4740.54i	−0.905740	−	0.658059i	−0.939934	+	0.341357i	$0.889114\pi$
$374$	5616.52			0.776533
$375$		0			0
$376$	−9869.36			−1.35365
$377$	3265.59	+	2372.59i	0.446118	+	0.324124i
$378$		0			0
$379$	804.469	+	2475.90i	0.109031	+	0.335563i	0.990655	−	0.136389i	$-0.0435496\pi$
$379$	804.469	+	2475.90i	0.109031	+	0.335563i	−0.881624	+	0.471952i	$0.843550\pi$
$380$	840.389	−	4608.53i	0.113450	−	0.622138i
$381$		0			0
$382$	4192.83			0.561581
$383$	−2941.06	+	9051.66i	−0.392380	+	1.20762i	0.538604	+	0.842559i	$0.318952\pi$
$383$	−2941.06	+	9051.66i	−0.392380	+	1.20762i	−0.930984	+	0.365061i	$0.881048\pi$
$384$		0			0
$385$	−2735.24	+	2610.69i	−0.362079	+	0.345592i
$386$	2885.42	+	2096.38i	0.380477	+	0.276433i
$387$		0			0
$388$	−6215.03	+	4515.48i	−0.813197	+	0.590822i
$389$	3945.71	+	2866.72i	0.514281	+	0.373647i	0.814445	−	0.580241i	$-0.197041\pi$
$389$	3945.71	+	2866.72i	0.514281	+	0.373647i	−0.300164	+	0.953888i	$0.597041\pi$
$390$		0			0
$391$	5303.45	−	3853.18i	0.685951	−	0.498373i
$392$	−2227.74	+	6856.29i	−0.287036	+	0.883405i
$393$		0			0
$394$	1049.83	−	3231.06i	0.134238	−	0.413143i
$395$	−11595.7	+	1560.67i	−1.47708	+	0.198800i
$396$		0			0
$397$	230.334	+	708.897i	0.0291188	+	0.0896184i	0.964560	−	0.263865i	$-0.0849972\pi$
$397$	230.334	+	708.897i	0.0291188	+	0.0896184i	−0.935441	+	0.353483i	$0.884997\pi$
$398$	−4567.19	−	3318.26i	−0.575207	−	0.417912i
$399$		0			0
$400$	−964.425	+	264.393i	−0.120553	+	0.0330491i
$401$	−14597.9			−1.81792			−0.908960	−	0.416883i	$-0.863122\pi$
$401$	−14597.9			−1.81792			−0.908960	+	0.416883i	$0.863122\pi$
$402$		0			0
$403$	−651.713	−	2005.77i	−0.0805562	−	0.247926i
$404$	1461.69	+	4498.60i	0.180004	+	0.553995i
$405$		0			0
$406$	−468.469	+	1441.80i	−0.0572653	+	0.176244i
$407$	10527.4			1.28212
$408$		0			0
$409$	−1138.26	+	826.991i	−0.137612	+	0.0999807i	−0.654461	−	0.756095i	$-0.727105\pi$
$409$	−1138.26	+	826.991i	−0.137612	+	0.0999807i	0.516850	+	0.856076i	$0.327105\pi$
$410$	−131.666	+	722.028i	−0.0158598	+	0.0869718i
$411$		0			0
$412$	334.134	−	242.762i	0.0399553	−	0.0290292i
$413$	−2759.44	+	2004.85i	−0.328773	+	0.238867i
$414$		0			0
$415$	−9233.20	−	4978.77i	−1.09214	−	0.588911i
$416$	4115.96	−	2990.42i	0.485100	−	0.352446i
$417$		0			0
$418$	−10010.4			−1.17135
$419$	1471.61	−	4529.15i	0.171582	−	0.528075i	−0.827879	−	0.560907i	$-0.810453\pi$
$419$	1471.61	−	4529.15i	0.171582	−	0.528075i	0.999461	+	0.0328318i	$0.0104526\pi$
$420$		0			0
$421$	−1185.64	−	3649.02i	−0.137255	−	0.422429i	0.858679	−	0.512515i	$-0.171286\pi$
$421$	−1185.64	−	3649.02i	−0.137255	−	0.422429i	−0.995934	+	0.0900856i	$0.971286\pi$
$422$	−2258.13	−	6949.82i	−0.260484	−	0.801687i
$423$		0			0
$424$	16229.4			1.85889
$425$	4093.60	−	5115.26i	0.467220	−	0.583828i
$426$		0			0
$427$	−174.617	−	126.866i	−0.0197899	−	0.0143782i
$428$	−92.7955	−	285.595i	−0.0104800	−	0.0322541i
$429$		0			0
$430$	−2810.73	+	2682.74i	−0.315222	+	0.300868i
$431$	901.448	−	2774.37i	0.100745	−	0.310062i	−0.887963	−	0.459915i	$-0.847880\pi$
$431$	901.448	−	2774.37i	0.100745	−	0.310062i	0.988708	+	0.149853i	$0.0478800\pi$
$432$		0			0
$433$	648.396	−	1995.56i	0.0719629	−	0.221479i	−0.908606	−	0.417655i	$-0.862852\pi$
$433$	648.396	−	1995.56i	0.0719629	−	0.221479i	0.980569	+	0.196175i	$0.0628522\pi$
$434$	640.805	−	465.572i	0.0708747	−	0.0514935i
$435$		0			0
$436$	718.705	+	522.170i	0.0789443	+	0.0573564i
$437$	−9452.40	+	6867.57i	−1.03471	+	0.751763i
$438$		0			0
$439$	92.6878	+	67.3416i	0.0100769	+	0.00732127i	0.592812	−	0.805341i	$-0.298018\pi$
$439$	92.6878	+	67.3416i	0.0100769	+	0.00732127i	−0.582735	+	0.812662i	$0.698018\pi$
$440$	−6478.67	−	13482.5i	−0.701951	−	1.46081i
$441$		0			0
$442$	896.814	−	2760.11i	0.0965093	−	0.297025i
$443$	−251.202			−0.0269413			−0.0134706	−	0.999909i	$-0.504288\pi$
$443$	−251.202			−0.0269413			−0.0134706	+	0.999909i	$0.504288\pi$
$444$		0			0
$445$	−3780.27	+	3608.13i	−0.402701	+	0.384364i
$446$	−2106.63	−	6483.53i	−0.223659	−	0.688350i
$447$		0			0
$448$	1852.20	+	1345.70i	0.195331	+	0.141916i
$449$	−9890.92			−1.03960			−0.519801	−	0.854287i	$-0.673994\pi$
$449$	−9890.92			−1.03960			−0.519801	+	0.854287i	$0.673994\pi$
$450$		0			0
$451$	−2001.44			−0.208967
$452$	−5947.72	−	4321.27i	−0.618932	−	0.449680i
$453$		0			0
$454$	403.029	+	1240.39i	0.0416632	+	0.128226i
$455$	846.215	+	1761.03i	0.0871893	+	0.181447i
$456$		0			0
$457$	−3340.55			−0.341935			−0.170967	−	0.985277i	$-0.554689\pi$
$457$	−3340.55			−0.341935			−0.170967	+	0.985277i	$0.554689\pi$
$458$	3200.07	−	9848.81i	0.326484	−	1.00481i
$459$		0			0
$460$	−5520.58	−	2976.83i	−0.559561	−	0.301729i
$461$	−9858.66	−	7162.73i	−0.996016	−	0.723648i	−0.0347857	−	0.999395i	$-0.511075\pi$
$461$	−9858.66	−	7162.73i	−0.996016	−	0.723648i	−0.961230	+	0.275747i	$0.911075\pi$
$462$		0			0
$463$	−8431.33	+	6125.72i	−0.846301	+	0.614873i	−0.924124	−	0.382094i	$-0.875203\pi$
$463$	−8431.33	+	6125.72i	−0.846301	+	0.614873i	0.0778229	+	0.996967i	$0.475203\pi$
$464$	−884.542	−	642.658i	−0.0884997	−	0.0642988i
$465$		0			0
$466$	8117.20	−	5897.49i	0.806914	−	0.586257i
$467$	−4094.04	+	12600.2i	−0.405673	+	1.24853i	0.514658	+	0.857395i	$0.327919\pi$
$467$	−4094.04	+	12600.2i	−0.405673	+	1.24853i	−0.920332	+	0.391139i	$0.872081\pi$
$468$		0			0
$469$	284.744	−	876.352i	0.0280347	−	0.0862818i
$470$	7778.98	+	4194.61i	0.763441	+	0.411666i
$471$		0			0
$472$	−4169.69	−	12833.0i	−0.406622	−	1.25145i
$473$	−8572.18	−	6228.05i	−0.833296	−	0.605425i
$474$		0			0
$475$	−7296.07	+	9117.00i	−0.704772	+	0.880667i
$476$	−1390.95			−0.133937
$477$		0			0
$478$	−2886.12	−	8882.57i	−0.276168	−	0.849957i
$479$	−232.883	−	716.739i	−0.0222144	−	0.0683688i	0.939335	−	0.343002i	$-0.111444\pi$
$479$	−232.883	−	716.739i	−0.0222144	−	0.0683688i	−0.961549	+	0.274633i	$0.911444\pi$
$480$		0			0
$481$	1680.95	−	5173.42i	0.159344	−	0.490411i
$482$	2560.72			0.241987
$483$		0			0
$484$	7025.65	−	5104.43i	0.659810	−	0.479380i
$485$	18978.1	−	2554.26i	1.77681	−	0.239140i
$486$		0			0
$487$	−1593.20	+	1157.53i	−0.148244	+	0.107705i	−0.659435	−	0.751762i	$-0.729204\pi$
$487$	−1593.20	+	1157.53i	−0.148244	+	0.107705i	0.511191	+	0.859467i	$0.329204\pi$
$488$	690.786	−	501.886i	0.0640787	−	0.0465559i
$489$		0			0
$490$	4669.91	−	4457.27i	0.430541	−	0.410936i
$491$	12244.4	−	8896.07i	1.12542	−	0.817666i	0.140398	−	0.990095i	$-0.455162\pi$
$491$	12244.4	−	8896.07i	1.12542	−	0.817666i	0.985022	+	0.172429i	$0.0551617\pi$
$492$		0			0
$493$	7163.15			0.654386
$494$	−1598.40	+	4919.38i	−0.145578	+	0.448043i
$495$		0			0
$496$	176.528	+	543.297i	0.0159805	+	0.0491830i
$497$	715.247	+	2201.30i	0.0645538	+	0.198676i
$498$		0			0
$499$	12081.3			1.08384			0.541918	−	0.840431i	$-0.317698\pi$
$499$	12081.3			1.08384			0.541918	+	0.840431i	$0.317698\pi$
$500$	−6107.61	−	1410.49i	−0.546281	−	0.126158i
$501$		0			0
$502$	85.4248	+	62.0647i	0.00759501	+	0.00551810i
$503$	1951.30	+	6005.48i	0.172970	+	0.532348i	0.999535	−	0.0304937i	$-0.00970794\pi$
$503$	1951.30	+	6005.48i	0.172970	+	0.532348i	−0.826565	+	0.562842i	$0.809708\pi$
$504$		0			0
$505$	2115.20	−	11599.4i	0.186387	−	1.02211i
$506$	−4141.67	+	12746.8i	−0.363873	+	1.11989i
$507$		0			0
$508$	−692.405	+	2131.00i	−0.0604734	+	0.186118i
$509$	1730.89	−	1257.57i	0.150728	−	0.109510i	−0.509865	−	0.860254i	$-0.670305\pi$
$509$	1730.89	−	1257.57i	0.150728	−	0.109510i	0.660593	+	0.750744i	$0.270305\pi$
$510$		0			0
$511$	−5597.95	−	4067.15i	−0.484616	−	0.352094i
$512$	−2326.83	+	1690.54i	−0.200845	+	0.145922i
$513$		0			0
$514$	890.430	+	646.935i	0.0764108	+	0.0555157i
$515$	−1020.30	+	137.323i	−0.0873010	+	0.0117498i
$516$		0			0
$517$	−7447.53	+	22921.1i	−0.633544	+	1.94985i
$518$	2042.99			0.173289
$519$		0			0
$520$	−7660.16	+	1030.98i	−0.646000	+	0.0869451i
$521$	−3873.88	−	11922.6i	−0.325754	−	1.00257i	−0.971099	−	0.238677i	$-0.923286\pi$
$521$	−3873.88	−	11922.6i	−0.325754	−	1.00257i	0.645345	−	0.763891i	$-0.276714\pi$
$522$		0			0
$523$	4612.96	+	3351.51i	0.385680	+	0.280213i	0.763683	−	0.645591i	$-0.223389\pi$
$523$	4612.96	+	3351.51i	0.385680	+	0.280213i	−0.378003	+	0.925804i	$0.623389\pi$
$524$	1162.56			0.0969207
$525$		0			0
$526$	−899.676			−0.0745774
$527$	−3027.83	−	2199.85i	−0.250274	−	0.181835i
$528$		0			0
$529$	1074.22	+	3306.10i	0.0882893	+	0.271727i
$530$	−12792.0	−	6897.74i	−1.04839	−	0.565318i
$531$		0			0
$532$	2479.11			0.202036
$533$	−319.578	+	983.559i	−0.0259708	+	0.0799300i
$534$		0			0
$535$	−134.284	+	736.388i	−0.0108516	+	0.0595081i
$536$	2949.09	+	2142.64i	0.237652	+	0.172664i
$537$		0			0
$538$	−7341.55	+	5333.95i	−0.588321	+	0.427440i
$539$	14242.3	+	10347.7i	1.13815	+	0.826912i
$540$		0			0
$541$	13794.1	−	10022.0i	1.09622	−	0.796448i	0.115778	−	0.993275i	$-0.463064\pi$
$541$	13794.1	−	10022.0i	1.09622	−	0.796448i	0.980438	+	0.196827i	$0.0630638\pi$
$542$	−2702.98	+	8318.91i	−0.214212	+	0.659276i
$543$		0			0
$544$	2789.95	−	8586.58i	0.219886	−	0.676740i
$545$	−959.094	−	1995.94i	−0.0753818	−	0.156874i
$546$		0			0
$547$	2044.23	+	6291.50i	0.159790	+	0.491783i	0.998615	−	0.0526188i	$-0.0167568\pi$
$547$	2044.23	+	6291.50i	0.159790	+	0.491783i	−0.838825	+	0.544401i	$0.816757\pi$
$548$	552.569	+	401.465i	0.0430741	+	0.0312951i
$549$		0			0
$550$	−623.810	+	13380.4i	−0.0483624	+	1.03735i
$551$	−12767.0			−0.987099
$552$		0			0
$553$	−1913.42	−	5888.90i	−0.147137	−	0.452842i
$554$	−4842.26	−	14903.0i	−0.371350	−	1.14290i
$555$		0			0
$556$	−3144.83	+	9678.80i	−0.239875	+	0.738260i
$557$	−567.016			−0.0431333			−0.0215667	−	0.999767i	$-0.506865\pi$
$557$	−567.016			−0.0431333			−0.0215667	+	0.999767i	$0.506865\pi$
$558$		0			0
$559$	−4429.39	+	3218.14i	−0.335140	+	0.243493i
$560$	−229.212	−	477.005i	−0.0172964	−	0.0359949i
$561$		0			0
$562$	−8384.05	+	6091.37i	−0.629288	+	0.457204i
$563$	13555.5	−	9848.62i	1.01473	−	0.737247i	0.0495366	−	0.998772i	$-0.484226\pi$
$563$	13555.5	−	9848.62i	1.01473	−	0.737247i	0.965197	+	0.261526i	$0.0842256\pi$
$564$		0			0
$565$	7937.09	+	16517.6i	0.591001	+	1.22991i
$566$	−790.712	+	574.486i	−0.0587210	+	0.0426633i
$567$		0			0
$568$	−9156.55			−0.676409
$569$	−1889.04	+	5813.88i	−0.139179	+	0.428349i	−0.996217	−	0.0869048i	$-0.972302\pi$
$569$	−1889.04	+	5813.88i	−0.139179	+	0.428349i	0.857038	+	0.515254i	$0.172302\pi$
$570$		0			0
$571$	−3930.14	−	12095.7i	−0.288041	−	0.886499i	−0.985471	−	0.169846i	$-0.945673\pi$
$571$	−3930.14	−	12095.7i	−0.288041	−	0.886499i	0.697430	−	0.716653i	$-0.254327\pi$
$572$	−2339.88	−	7201.41i	−0.171041	−	0.526409i
$573$		0			0
$574$	−388.408			−0.0282436
$575$	8590.49	+	13062.5i	0.623041	+	0.947381i
$576$		0			0
$577$	8937.40	+	6493.40i	0.644833	+	0.468499i	0.861507	−	0.507745i	$-0.169521\pi$
$577$	8937.40	+	6493.40i	0.644833	+	0.468499i	−0.216674	+	0.976244i	$0.569521\pi$
$578$	1254.78	+	3861.80i	0.0902972	+	0.277906i
$579$		0			0
$580$	−2968.34	−	6177.31i	−0.212506	−	0.442239i
$581$	1715.49	−	5279.74i	0.122497	−	0.377006i
$582$		0			0
$583$	12246.9	−	37692.1i	0.870009	−	2.67761i
$584$	22145.6	−	16089.7i	1.56916	−	1.14006i
$585$		0			0
$586$	3351.48	+	2434.99i	0.236260	+	0.171653i
$587$	6410.81	−	4657.73i	0.450771	−	0.327504i	−0.339129	−	0.940740i	$-0.610132\pi$
$587$	6410.81	−	4657.73i	0.450771	−	0.327504i	0.789900	+	0.613236i	$0.210132\pi$
$588$		0			0
$589$	5396.55	+	3920.82i	0.377523	+	0.274286i
$590$	−2167.67	+	11887.1i	−0.151257	+	0.829463i
$591$		0			0
$592$	−455.314	+	1401.31i	−0.0316103	+	0.0972864i
$593$	−14752.2			−1.02158			−0.510792	−	0.859704i	$-0.670648\pi$
$593$	−14752.2			−1.02158			−0.510792	+	0.859704i	$0.670648\pi$
$594$		0			0
$595$	3051.79	+	1645.60i	0.210271	+	0.113383i
$596$	2167.31	+	6670.28i	0.148954	+	0.458432i
$597$		0			0
$598$	5602.78	+	4070.66i	0.383135	+	0.278364i
$599$	610.057			0.0416131			0.0208065	−	0.999784i	$-0.493377\pi$
$599$	610.057			0.0416131			0.0208065	+	0.999784i	$0.493377\pi$
$600$		0			0
$601$	−16775.8			−1.13860			−0.569300	−	0.822130i	$-0.692786\pi$
$601$	−16775.8			−1.13860			−0.569300	+	0.822130i	$0.692786\pi$
$602$	−1663.56	−	1208.64i	−0.112627	−	0.0818284i
$603$		0			0
$604$	3227.97	+	9934.68i	0.217458	+	0.669266i
$605$	−21453.4	+	2887.41i	−1.44166	+	0.194033i
$606$		0			0
$607$	10205.9			0.682445			0.341222	−	0.939983i	$-0.389159\pi$
$607$	10205.9			0.682445			0.341222	+	0.939983i	$0.389159\pi$
$608$	−4972.56	+	15304.0i	−0.331684	+	1.02082i
$609$		0			0
$610$	−757.782	+	101.990i	−0.0502979	+	0.00676959i
$611$	10074.9	+	7319.83i	0.667080	+	0.484662i
$612$		0			0
$613$	−7211.16	+	5239.22i	−0.475132	+	0.345204i	−0.799438	−	0.600749i	$-0.794869\pi$
$613$	−7211.16	+	5239.22i	−0.475132	+	0.345204i	0.324306	+	0.945952i	$0.394869\pi$
$614$	15312.1	+	11124.9i	1.00643	+	0.731212i
$615$		0			0
$616$	6404.30	−	4653.00i	0.418891	−	0.304342i
$617$	−5702.91	+	17551.7i	−0.372108	+	1.14523i	0.573302	+	0.819344i	$0.305662\pi$
$617$	−5702.91	+	17551.7i	−0.372108	+	1.14523i	−0.945409	+	0.325885i	$0.894338\pi$
$618$		0			0
$619$	5256.38	−	16177.5i	0.341312	−	1.05045i	−0.622217	−	0.782845i	$-0.713768\pi$
$619$	5256.38	−	16177.5i	0.341312	−	1.05045i	0.963529	−	0.267605i	$-0.0862321\pi$
$620$	−642.386	+	3522.72i	−0.0416110	+	0.228187i
$621$		0			0
$622$	3220.42	+	9911.43i	0.207600	+	0.638927i
$623$	−2237.39	−	1625.56i	−0.143883	−	0.104537i
$624$		0			0
$625$	11731.6	+	10320.4i	0.750820	+	0.660507i
$626$	10999.6			0.702288
$627$		0			0
$628$	402.667	+	1239.28i	0.0255862	+	0.0787464i
$629$	−2983.01	−	9180.75i	−0.189094	−	0.581972i
$630$		0			0
$631$	6272.07	−	19303.5i	0.395701	−	1.21784i	−0.532713	−	0.846296i	$-0.678828\pi$
$631$	6272.07	−	19303.5i	0.395701	−	1.21784i	0.928414	−	0.371547i	$-0.121172\pi$
$632$	24495.5			1.54174
$633$		0			0
$634$	483.892	−	351.568i	0.0303120	−	0.0220230i
$635$	4040.29	−	3856.32i	0.252495	−	0.240997i
$636$		0			0
$637$	7359.25	−	5346.81i	0.457746	−	0.332572i
$638$	−11848.3	+	8608.27i	−0.735231	+	0.534177i
$639$		0			0
$640$	−7231.47	+	973.282i	−0.446639	+	0.0601131i
$641$	13946.6	−	10132.8i	0.859371	−	0.624370i	−0.0683428	−	0.997662i	$-0.521771\pi$
$641$	13946.6	−	10132.8i	0.859371	−	0.624370i	0.927714	+	0.373292i	$0.121771\pi$
$642$		0			0
$643$	1616.35			0.0991331			0.0495666	−	0.998771i	$-0.484216\pi$
$643$	1616.35			0.0991331			0.0495666	+	0.998771i	$0.484216\pi$
$644$	1025.70	−	3156.78i	0.0627613	−	0.193159i
$645$		0			0
$646$	2836.52	+	8729.92i	0.172758	+	0.531694i
$647$	1752.03	+	5392.20i	0.106460	+	0.327649i	0.990070	−	0.140573i	$-0.0448945\pi$
$647$	1752.03	+	5392.20i	0.106460	+	0.327649i	−0.883611	+	0.468223i	$0.844895\pi$
$648$		0			0
$649$	−32950.5			−1.99295
$650$	6475.88	+	2443.06i	0.390777	+	0.147423i
$651$		0			0
$652$	−7132.18	−	5181.83i	−0.428401	−	0.311252i
$653$	7617.70	+	23444.9i	0.456514	+	1.40501i	0.869349	+	0.494199i	$0.164539\pi$
$653$	7617.70	+	23444.9i	0.456514	+	1.40501i	−0.412835	+	0.910806i	$0.635461\pi$
$654$		0			0
$655$	−2550.68	−	1375.39i	−0.152158	−	0.0820472i
$656$	86.5632	−	266.414i	0.00515202	−	0.0158563i
$657$		0			0
$658$	−1445.30	+	4448.18i	−0.0856288	+	0.263538i
$659$	−1095.83	+	796.169i	−0.0647763	+	0.0470627i	−0.619702	−	0.784837i	$-0.712747\pi$
$659$	−1095.83	+	796.169i	−0.0647763	+	0.0470627i	0.554926	+	0.831900i	$0.312747\pi$
$660$		0			0
$661$	−7325.16	−	5322.04i	−0.431037	−	0.313167i	0.351026	−	0.936366i	$-0.385833\pi$
$661$	−7325.16	−	5322.04i	−0.431037	−	0.313167i	−0.782064	+	0.623199i	$0.785833\pi$
$662$	4441.70	−	3227.08i	0.260773	−	0.189462i
$663$		0			0
$664$	17767.3	+	12908.7i	1.03841	+	0.754450i
$665$	−5439.25	−	2932.97i	−0.317180	−	0.171031i
$666$		0			0
$667$	−5282.17	+	16256.9i	−0.306636	+	0.943730i
$668$	−9213.10			−0.533631
$669$		0			0
$670$	−1413.81	−	2942.22i	−0.0815225	−	0.169654i
$671$	−644.331	−	1983.05i	−0.0370703	−	0.114091i
$672$		0			0
$673$	−6967.78	−	5062.39i	−0.399091	−	0.289956i	0.370080	−	0.929000i	$-0.379330\pi$
$673$	−6967.78	−	5062.39i	−0.399091	−	0.289956i	−0.769171	+	0.639044i	$0.779330\pi$
$674$	−9674.72			−0.552903
$675$		0			0
$676$	5941.57			0.338050
$677$	−6541.98	−	4753.03i	−0.371387	−	0.269828i	0.386399	−	0.922332i	$-0.373719\pi$
$677$	−6541.98	−	4753.03i	−0.371387	−	0.269828i	−0.757786	+	0.652503i	$0.773719\pi$
$678$		0			0
$679$	3131.59	+	9638.03i	0.176994	+	0.544733i
$680$	−9922.14	+	9470.33i	−0.559554	+	0.534075i
$681$		0			0
$682$	7651.86			0.429626
$683$	10597.5	−	32615.7i	0.593706	−	1.82724i	0.0326425	−	0.999467i	$-0.489608\pi$
$683$	10597.5	−	32615.7i	0.593706	−	1.82724i	0.561064	−	0.827773i	$-0.310392\pi$
$684$		0			0
$685$	−737.390	−	1534.56i	−0.0411303	−	0.0855948i
$686$	5842.04	+	4244.49i	0.325146	+	0.236232i
$687$		0			0
$688$	1199.78	−	871.689i	0.0664841	−	0.0483035i
$689$	−16567.4	−	12036.9i	−0.916064	−	0.665559i
$690$		0			0
$691$	−8077.57	+	5868.70i	−0.444697	+	0.323091i	−0.787498	−	0.616317i	$-0.788624\pi$
$691$	−8077.57	+	5868.70i	−0.444697	+	0.323091i	0.342802	+	0.939408i	$0.388624\pi$
$692$	−1772.02	+	5453.73i	−0.0973443	+	0.299595i
$693$		0			0
$694$	1013.53	−	3119.33i	0.0554368	−	0.170617i
$695$	18350.6	−	17515.0i	1.00155	−	0.955945i
$696$		0			0
$697$	567.122	+	1745.42i	0.0308196	+	0.0948531i
$698$	−2692.33	−	1956.09i	−0.145997	−	0.106073i
$699$		0			0
$700$	154.489	−	3313.70i	0.00834161	−	0.178923i
$701$	−2668.87			−0.143797			−0.0718987	−	0.997412i	$-0.522906\pi$
$701$	−2668.87			−0.143797			−0.0718987	+	0.997412i	$0.522906\pi$
$702$		0			0
$703$	5316.65	+	16363.0i	0.285236	+	0.877867i
$704$	6834.58	+	21034.7i	0.365892	+	1.12610i
$705$		0			0
$706$	191.181	−	588.395i	0.0101915	−	0.0313662i
$707$	6239.76			0.331924
$708$		0			0
$709$	11300.0	−	8209.94i	0.598563	−	0.434881i	−0.246806	−	0.969065i	$-0.579381\pi$
$709$	11300.0	−	8209.94i	0.598563	−	0.434881i	0.845368	+	0.534184i	$0.179381\pi$
$710$	7217.14	+	3891.66i	0.381485	+	0.205706i
$711$		0			0
$712$	8851.15	−	6430.74i	0.465886	−	0.338486i
$713$	7225.33	−	5249.51i	0.379510	−	0.275730i
$714$		0			0
$715$	−3386.04	+	18568.4i	−0.177106	+	0.971213i
$716$	−1692.32	+	1229.54i	−0.0883310	+	0.0641762i
$717$		0			0
$718$	7875.35			0.409339
$719$	−8185.68	+	25192.9i	−0.424582	+	1.30673i	0.478812	+	0.877917i	$0.341067\pi$
$719$	−8185.68	+	25192.9i	−0.424582	+	1.30673i	−0.903394	+	0.428811i	$0.858933\pi$
$720$		0			0
$721$	−168.361	−	518.162i	−0.00869638	−	0.0267647i
$722$	−1081.93	−	3329.84i	−0.0557691	−	0.171640i
$723$		0			0
$724$	−5230.35			−0.268487
$725$	−795.589	+	17065.0i	−0.0407551	+	0.874175i
$726$		0			0
$727$	−13903.6	−	10101.6i	−0.709295	−	0.515333i	0.173651	−	0.984807i	$-0.444444\pi$
$727$	−13903.6	−	10101.6i	−0.709295	−	0.515333i	−0.882946	+	0.469474i	$0.844444\pi$
$728$	−1264.01	−	3890.21i	−0.0643505	−	0.198050i
$729$		0			0
$730$	−24293.4	+	3269.64i	−1.23170	+	0.165774i
$731$	−3002.40	+	9240.43i	−0.151912	+	0.467537i
$732$		0			0
$733$	−3541.75	+	10900.4i	−0.178469	+	0.549270i	−0.999775	−	0.0212175i	$-0.993246\pi$
$733$	−3541.75	+	10900.4i	−0.178469	+	0.549270i	0.821306	+	0.570488i	$0.193246\pi$
$734$	−17174.8	+	12478.2i	−0.863668	+	0.627491i
$735$		0			0
$736$	17430.0	+	12663.6i	0.872933	+	0.634223i
$737$	7201.60	−	5232.27i	0.359938	−	0.261510i
$738$		0			0
$739$	−30512.3	−	22168.5i	−1.51883	−	1.10349i	−0.962066	−	0.272818i	$-0.912044\pi$
$739$	−30512.3	−	22168.5i	−1.51883	−	1.10349i	−0.556760	−	0.830673i	$-0.687956\pi$
$740$	−6681.10	+	6376.87i	−0.331895	+	0.316782i
$741$		0			0
$742$	2376.69	−	7314.71i	0.117589	−	0.361902i
$743$	31924.8			1.57632			0.788160	−	0.615470i	$-0.211034\pi$
$743$	31924.8			1.57632			0.788160	+	0.615470i	$0.211034\pi$
$744$		0			0
$745$	3136.31	−	17198.9i	0.154235	−	0.845796i
$746$	−4672.37	−	14380.1i	−0.229313	−	0.705753i
$747$		0			0
$748$	−10871.0	−	7898.23i	−0.531394	−	0.386080i
$749$	−396.133			−0.0193249
$750$		0			0
$751$	26464.6			1.28589			0.642946	−	0.765911i	$-0.277712\pi$
$751$	26464.6			1.28589			0.642946	+	0.765911i	$0.277712\pi$
$752$	−2728.96	−	1982.70i	−0.132334	−	0.0961460i
$753$		0			0
$754$	2338.47	+	7197.07i	0.112947	+	0.347615i
$755$	4671.20	−	25615.9i	0.225169	−	1.23478i
$756$		0			0
$757$	−10652.8			−0.511470			−0.255735	−	0.966747i	$-0.582317\pi$
$757$	−10652.8			−0.511470			−0.255735	+	0.966747i	$0.582317\pi$
$758$	−1508.19	+	4641.72i	−0.0722688	+	0.222421i
$759$		0			0
$760$	17684.4	−	16879.1i	0.844051	−	0.805617i
$761$	9424.61	+	6847.38i	0.448938	+	0.326173i	0.789176	−	0.614167i	$-0.210508\pi$
$761$	9424.61	+	6847.38i	0.448938	+	0.326173i	−0.340238	+	0.940339i	$0.610508\pi$
$762$		0			0
$763$	948.085	−	688.824i	0.0449842	−	0.0326830i
$764$	−8115.38	−	5896.17i	−0.384299	−	0.279209i
$765$		0			0
$766$	−14435.3	+	10487.8i	−0.680898	+	0.494701i
$767$	−5261.35	+	16192.8i	−0.247688	+	0.762304i
$768$		0			0
$769$	−3694.13	+	11369.4i	−0.173230	+	0.533147i	−0.999548	−	0.0300565i	$-0.990431\pi$
$769$	−3694.13	+	11369.4i	−0.173230	+	0.533147i	0.826318	+	0.563203i	$0.190431\pi$
$770$	−7025.43	+	945.551i	−0.328804	+	0.0442536i
$771$		0			0
$772$	−2636.81	−	8115.25i	−0.122928	−	0.378335i
$773$	16241.6	+	11800.2i	0.755717	+	0.549061i	0.897594	−	0.440824i	$-0.145314\pi$
$773$	16241.6	+	11800.2i	0.755717	+	0.549061i	−0.141877	+	0.989884i	$0.545314\pi$
$774$		0			0
$775$	5577.05	−	6968.96i	0.258495	−	0.323009i
$776$	−40090.4			−1.85459
$777$		0			0
$778$	2825.50	+	8695.99i	0.130204	+	0.400728i
$779$	−1010.79	−	3110.89i	−0.0464895	−	0.143080i
$780$		0			0
$781$	−6909.64	+	21265.7i	−0.316576	+	0.974322i
$782$	12289.8			0.562000
$783$		0			0
$784$	−1993.38	+	1448.28i	−0.0908064	+	0.0659747i
$785$	582.699	−	3195.41i	0.0264935	−	0.145285i
$786$		0			0
$787$	22616.7	−	16432.0i	1.02439	−	0.744266i	0.0572147	−	0.998362i	$-0.481778\pi$
$787$	22616.7	−	16432.0i	1.02439	−	0.744266i	0.967179	+	0.254096i	$0.0817780\pi$
$788$	−6575.66	+	4777.50i	−0.297269	+	0.215979i
$789$		0			0
$790$	−19307.2	−	10410.9i	−0.869518	−	0.468866i
$791$	−7845.98	+	5700.43i	−0.352681	+	0.256238i
$792$		0			0
$793$	−1077.41			−0.0482469
$794$	−431.822	+	1329.01i	−0.0193007	+	0.0594015i
$795$		0			0
$796$	4173.66	+	12845.2i	0.185844	+	0.571968i
$797$	−9441.64	−	29058.4i	−0.419624	−	1.29147i	−0.908049	−	0.418863i	$-0.862429\pi$
$797$	−9441.64	−	29058.4i	−0.419624	−	1.29147i	0.488426	−	0.872605i	$-0.337571\pi$
$798$		0			0
$799$	22099.5			0.978503
$800$	20146.2	+	7600.25i	0.890343	+	0.335887i
$801$		0			0
$802$	−22140.9	−	16086.3i	−0.974839	−	0.708262i
$803$	−20656.3	−	63573.6i	−0.907777	−	2.79385i
$804$		0			0
$805$	−5985.13	+	5712.59i	−0.262047	+	0.250115i
$806$	1221.81	−	3760.33i	0.0533949	−	0.164332i
$807$		0			0
$808$	−7627.96	+	23476.4i	−0.332117	+	1.02215i
$809$	−2550.54	+	1853.08i	−0.110843	+	0.0805324i	−0.641826	−	0.766850i	$-0.721823\pi$
$809$	−2550.54	+	1853.08i	−0.110843	+	0.0805324i	0.530983	+	0.847383i	$0.321823\pi$
$810$		0			0
$811$	−292.128	−	212.243i	−0.0126486	−	0.00918973i	0.581443	−	0.813587i	$-0.302488\pi$
$811$	−292.128	−	212.243i	−0.0126486	−	0.00918973i	−0.594092	+	0.804397i	$0.702488\pi$
$812$	2934.27	−	2131.87i	0.126813	−	0.0921354i
$813$		0			0
$814$	15967.0	+	11600.7i	0.687521	+	0.499513i
$815$	9517.72	+	19807.0i	0.409069	+	0.851299i
$816$		0			0
$817$	5351.21	−	16469.3i	0.229150	−	0.705250i
$818$	−2637.71			−0.112745
$819$		0			0
$820$	1270.20	−	1212.36i	0.0540941	−	0.0516309i
$821$	5224.35	+	16078.9i	0.222084	+	0.683505i	0.998574	+	0.0533758i	$0.0169981\pi$
$821$	5224.35	+	16078.9i	0.222084	+	0.683505i	−0.776490	+	0.630129i	$0.783002\pi$
$822$		0			0
$823$	10939.7	+	7948.18i	0.463348	+	0.336642i	0.794843	−	0.606815i	$-0.207553\pi$
$823$	10939.7	+	7948.18i	0.463348	+	0.336642i	−0.331495	+	0.943457i	$0.607553\pi$
$824$	2155.35			0.0911226
$825$		0			0
$826$	−6394.53			−0.269364
$827$	−26154.0	−	19002.0i	−1.09971	−	0.798988i	−0.118700	−	0.992930i	$-0.537873\pi$
$827$	−26154.0	−	19002.0i	−1.09971	−	0.798988i	−0.981013	+	0.193942i	$0.937873\pi$
$828$		0			0
$829$	−8942.80	−	27523.1i	−0.374664	−	1.15310i	−0.943705	−	0.330787i	$-0.892686\pi$
$829$	−8942.80	−	27523.1i	−0.374664	−	1.15310i	0.569042	−	0.822309i	$-0.307314\pi$
$830$	−8517.72	−	17725.9i	−0.356210	−	0.741297i
$831$		0			0
$832$	11428.3			0.476208
$833$	4988.37	−	15352.6i	0.207487	−	0.638580i
$834$		0			0
$835$	20213.8	+	10899.8i	0.837758	+	0.451740i
$836$	19375.5	+	14077.1i	0.801574	+	0.582377i
$837$		0			0
$838$	7222.93	−	5247.77i	0.297747	−	0.216326i
$839$	−16807.4	−	12211.3i	−0.691603	−	0.502479i	0.185584	−	0.982628i	$-0.440582\pi$
$839$	−16807.4	−	12211.3i	−0.691603	−	0.502479i	−0.877187	+	0.480150i	$0.840582\pi$
$840$		0			0
$841$	4620.18	−	3356.76i	0.189437	−	0.137634i
$842$	2222.79	−	6841.04i	0.0909767	−	0.279998i
$843$		0			0
$844$	−5402.48	+	16627.1i	−0.220333	+	0.678115i
$845$	−13036.0	−	7029.32i	−0.530712	−	0.286173i
$846$		0			0
$847$	−3540.04	−	10895.1i	−0.143609	−	0.441984i
$848$	4487.57	+	3260.41i	0.181726	+	0.132032i
$849$		0			0
$850$	11845.6	−	3247.42i	0.478001	−	0.131042i
$851$	23035.5			0.927905
$852$		0			0
$853$	−10310.8	−	31733.5i	−0.413877	−	1.27378i	−0.913252	−	0.407395i	$-0.866437\pi$
$853$	−10310.8	−	31733.5i	−0.413877	−	1.27378i	0.499375	−	0.866386i	$-0.333563\pi$
$854$	−125.042	−	384.840i	−0.00501036	−	0.0154203i
$855$		0			0
$856$	484.263	−	1490.41i	0.0193362	−	0.0595106i
$857$	25175.7			1.00348			0.501742	−	0.865017i	$-0.332693\pi$
$857$	25175.7			1.00348			0.501742	+	0.865017i	$0.332693\pi$
$858$		0			0
$859$	−5184.10	+	3766.47i	−0.205913	+	0.149604i	−0.685963	−	0.727637i	$-0.740619\pi$
$859$	−5184.10	+	3766.47i	−0.205913	+	0.149604i	0.480050	+	0.877241i	$0.340619\pi$
$860$	9212.87	−	1239.96i	0.365298	−	0.0491654i
$861$		0			0
$862$	4424.47	−	3214.57i	0.174824	−	0.127017i
$863$	−39146.1	+	28441.3i	−1.54409	+	1.12185i	−0.596386	+	0.802698i	$0.703397\pi$
$863$	−39146.1	+	28441.3i	−1.54409	+	1.12185i	−0.947704	+	0.319149i	$0.896603\pi$
$864$		0			0
$865$	10340.0	−	9869.21i	0.406442	−	0.387934i
$866$	3182.45	−	2312.18i	0.124878	−	0.0907289i
$867$		0			0
$868$	−1895.01			−0.0741024
$869$	18484.6	−	56889.6i	0.721572	−	2.22077i
$870$		0			0
$871$	−1421.37	−	4374.52i	−0.0552941	−	0.170178i
$872$	1432.62	+	4409.14i	0.0556359	+	0.171230i
$873$		0			0
$874$	−21904.3			−0.847741
$875$	−4259.31	+	7087.59i	−0.164561	+	0.273833i
$876$		0			0
$877$	21739.2	+	15794.5i	0.837036	+	0.608142i	0.921541	−	0.388281i	$-0.126931\pi$
$877$	21739.2	+	15794.5i	0.837036	+	0.608142i	−0.0845052	+	0.996423i	$0.526931\pi$
$878$	66.3732	+	204.276i	0.00255124	+	0.00785190i
$879$		0			0
$880$	917.168	−	5029.57i	0.0351338	−	0.192667i
$881$	−11453.8	+	35251.1i	−0.438011	+	1.34806i	0.451959	+	0.892039i	$0.350725\pi$
$881$	−11453.8	+	35251.1i	−0.438011	+	1.34806i	−0.889970	+	0.456020i	$0.849275\pi$
$882$		0			0
$883$	−656.803	+	2021.43i	−0.0250319	+	0.0770403i	−0.962792	−	0.270243i	$-0.912896\pi$
$883$	−656.803	+	2021.43i	−0.0250319	+	0.0770403i	0.937760	+	0.347284i	$0.112896\pi$
$884$	−5617.22	+	4081.15i	−0.213719	+	0.155276i
$885$		0			0
$886$	−381.001	−	276.814i	−0.0144469	−	0.0104963i
$887$	−1712.00	+	1243.84i	−0.0648065	+	0.0470847i	−0.619717	−	0.784825i	$-0.712753\pi$
$887$	−1712.00	+	1243.84i	−0.0648065	+	0.0470847i	0.554910	+	0.831910i	$0.312753\pi$
$888$		0			0
$889$	2391.29	+	1737.37i	0.0902151	+	0.0655451i
$890$	−9709.58	+	1306.81i	−0.365692	+	0.0492184i
$891$		0			0
$892$	−5040.01	+	15511.6i	−0.189184	+	0.582248i
$893$	−39388.2			−1.47601
$894$		0			0
$895$	5167.64	−	695.512i	0.193000	−	0.0259759i
$896$	−1193.27	−	3672.50i	−0.0444914	−	0.136930i
$897$		0			0
$898$	−15001.7	−	10899.4i	−0.557475	−	0.405029i
$899$	9758.97			0.362046
$900$		0			0
$901$	−36341.0			−1.34372
$902$	−3035.60	−	2205.49i	−0.112056	−	0.0814135i
$903$		0			0
$904$	−11855.8	−	36488.3i	−0.436191	−	1.34246i
$905$	11475.5	+	6187.89i	0.421503	+	0.227285i
$906$		0			0
$907$	−4188.50			−0.153337			−0.0766687	−	0.997057i	$-0.524428\pi$
$907$	−4188.50			−0.153337			−0.0766687	+	0.997057i	$0.524428\pi$
$908$	964.228	−	2967.59i	0.0352412	−	0.108461i
$909$		0			0
$910$	−657.110	+	3603.46i	−0.0239374	+	0.131268i
$911$	−11515.9	−	8366.82i	−0.418815	−	0.304287i	0.358346	−	0.933589i	$-0.383341\pi$
$911$	−11515.9	−	8366.82i	−0.418815	−	0.304287i	−0.777161	+	0.629302i	$0.783341\pi$
$912$		0			0
$913$	43387.3	−	31522.7i	1.57274	−	1.14266i
$914$	−5066.65	−	3681.14i	−0.183359	−	0.133218i
$915$		0			0
$916$	−20043.7	+	14562.6i	−0.722995	+	0.525287i
$917$	473.906	−	1458.53i	0.0170663	−	0.0525245i
$918$		0			0
$919$	−9951.33	+	30627.0i	−0.357197	+	1.09934i	0.597528	+	0.801848i	$0.296150\pi$
$919$	−9951.33	+	30627.0i	−0.357197	+	1.09934i	−0.954725	+	0.297491i	$0.903850\pi$
$920$	−14176.4	−	29501.9i	−0.508022	−	1.05723i
$921$		0			0
$922$	−7059.73	−	21727.6i	−0.252169	−	0.776096i
$923$	9347.23	+	6791.16i	0.333335	+	0.242182i
$924$		0			0
$925$	22202.8	−	6086.81i	0.789216	−	0.216360i
$926$	−19538.2			−0.693374
$927$		0			0
$928$	7274.88	+	22389.8i	0.257338	+	0.792005i
$929$	4869.12	+	14985.6i	0.171960	+	0.529238i	0.999482	−	0.0321958i	$-0.0102500\pi$
$929$	4869.12	+	14985.6i	0.171960	+	0.529238i	−0.827522	+	0.561434i	$0.810250\pi$
$930$		0			0
$931$	−8890.84	+	27363.2i	−0.312981	+	0.963257i
$932$	−24004.5			−0.843662
$933$		0			0
$934$	−20094.3	+	14599.4i	−0.703967	+	0.511462i
$935$	14507.1	+	30190.1i	0.507414	+	1.05596i
$936$		0			0
$937$	−31461.7	+	22858.3i	−1.09692	+	0.796956i	−0.980554	−	0.196251i	$-0.937123\pi$
$937$	−31461.7	+	22858.3i	−1.09692	+	0.796956i	−0.116362	+	0.993207i	$0.537123\pi$
$938$	1397.58	−	1015.40i	0.0486487	−	0.0353454i
$939$		0			0
$940$	−9157.82	−	19058.0i	−0.317761	−	0.661281i
$941$	32883.6	−	23891.4i	1.13919	−	0.827669i	0.152182	−	0.988352i	$-0.451370\pi$
$941$	32883.6	−	23891.4i	1.13919	−	0.827669i	0.987006	+	0.160684i	$0.0513699\pi$
$942$		0			0
$943$	−4379.46			−0.151235
$944$	1425.13	−	4386.10i	0.0491356	−	0.151224i
$945$		0			0
$946$	−6138.49	−	18892.3i	−0.210972	−	0.649305i
$947$	−6376.19	−	19623.9i	−0.218794	−	0.673380i	−0.998862	−	0.0476852i	$-0.984816\pi$
$947$	−6376.19	−	19623.9i	−0.218794	−	0.673380i	0.780068	−	0.625695i	$-0.215184\pi$
$948$		0			0
$949$	−34540.0			−1.18147
$950$	−21112.6	+	5787.92i	−0.721034	+	0.197668i
$951$		0			0
$952$	−5872.52	−	4266.63i	−0.199926	−	0.145255i
$953$	6682.98	+	20568.1i	0.227160	+	0.699125i	0.998065	+	0.0621759i	$0.0198040\pi$
$953$	6682.98	+	20568.1i	0.227160	+	0.699125i	−0.770906	+	0.636949i	$0.780196\pi$
$954$		0			0
$955$	10829.8	+	22537.5i	0.366956	+	0.763660i
$956$	−6904.91	+	21251.1i	−0.233599	+	0.718945i
$957$		0			0
$958$	436.599	−	1343.71i	0.0147243	−	0.0453167i
$959$	728.926	−	529.595i	0.0245446	−	0.0178327i
$960$		0			0
$961$	19976.4	+	14513.7i	0.670550	+	0.487183i
$962$	8250.40	−	5994.26i	0.276511	−	0.200897i
$963$		0			0
$964$	−4956.37	−	3601.01i	−0.165595	−	0.120312i
$965$	−3815.72	+	20924.6i	−0.127287	+	0.698019i
$966$		0			0
$967$	−9371.85	+	28843.6i	−0.311663	+	0.959201i	0.665443	+	0.746449i	$0.268243\pi$
$967$	−9371.85	+	28843.6i	−0.311663	+	0.959201i	−0.977106	+	0.212752i	$0.931757\pi$
$968$	45319.3			1.50477
$969$		0			0
$970$	31599.0	+	17039.0i	1.04596	+	0.564008i
$971$	−10840.7	−	33364.3i	−0.358285	−	1.10269i	−0.954080	−	0.299552i	$-0.903163\pi$
$971$	−10840.7	−	33364.3i	−0.358285	−	1.10269i	0.595795	−	0.803137i	$-0.296837\pi$
$972$		0			0
$973$	10861.0	+	7890.97i	0.357849	+	0.259993i
$974$	−3691.96			−0.121456
$975$		0			0
$976$	291.834			0.00957110
$977$	−36271.9	−	26353.1i	−1.18776	−	0.862958i	−0.194733	−	0.980856i	$-0.562384\pi$
$977$	−36271.9	−	26353.1i	−1.18776	−	0.862958i	−0.993026	+	0.117899i	$0.962384\pi$
$978$		0			0
$979$	−8255.92	−	25409.1i	−0.269520	−	0.829498i
$980$	−15306.8	+	2060.14i	−0.498937	+	0.0671519i
$981$		0			0
$982$	28374.3			0.922057
$983$	−6943.28	+	21369.2i	−0.225286	+	0.693359i	0.772976	+	0.634435i	$0.218767\pi$
$983$	−6943.28	+	21369.2i	−0.225286	+	0.693359i	−0.998262	+	0.0589243i	$0.981233\pi$
$984$		0			0
$985$	20079.3	−	2702.47i	0.649524	−	0.0874193i
$986$	10864.4	+	7893.48i	0.350907	+	0.254949i
$987$		0			0
$988$	10011.6	−	7273.88i	0.322381	−	0.234224i
$989$	−18757.3	−	13628.0i	−0.603081	−	0.438164i
$990$		0			0
$991$	27174.0	−	19743.1i	0.871049	−	0.632854i	−0.0598190	−	0.998209i	$-0.519052\pi$
$991$	27174.0	−	19743.1i	0.871049	−	0.632854i	0.930868	+	0.365355i	$0.119052\pi$
$992$	3800.98	−	11698.2i	0.121655	−	0.374414i
$993$		0			0
$994$	−1340.92	+	4126.92i	−0.0427880	+	0.131688i
$995$	6039.70	−	33120.5i	0.192434	−	1.05527i
$996$		0			0
$997$	−16212.5	−	49896.8i	−0.514999	−	1.58500i	−0.783284	−	0.621664i	$-0.786457\pi$
$997$	−16212.5	−	49896.8i	−0.514999	−	1.58500i	0.268285	−	0.963339i	$-0.413543\pi$
$998$	18323.9	+	13313.1i	0.581195	+	0.422263i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.91.5		28
3.2	odd	2		25.4.d.a.16.3	yes	28
15.2	even	4		125.4.e.b.49.9		56
15.8	even	4		125.4.e.b.49.6		56
15.14	odd	2		125.4.d.a.76.5		28
25.11	even	5	inner	225.4.h.b.136.5		28
75.2	even	20		125.4.e.b.74.6		56
75.11	odd	10		25.4.d.a.11.3	✓	28
75.14	odd	10		125.4.d.a.51.5		28
75.23	even	20		125.4.e.b.74.9		56
75.44	odd	10		625.4.a.d.1.6		14
75.56	odd	10		625.4.a.c.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.3	✓	28	75.11	odd	10
25.4.d.a.16.3	yes	28	3.2	odd	2
125.4.d.a.51.5		28	75.14	odd	10
125.4.d.a.76.5		28	15.14	odd	2
125.4.e.b.49.6		56	15.8	even	4
125.4.e.b.49.9		56	15.2	even	4
125.4.e.b.74.6		56	75.2	even	20
125.4.e.b.74.9		56	75.23	even	20
225.4.h.b.91.5		28	1.1	even	1	trivial
225.4.h.b.136.5		28	25.11	even	5	inner
625.4.a.c.1.9		14	75.56	odd	10
625.4.a.d.1.6		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)

\(f(q)\)	\(=\)	\(q+(1.51671 + 1.10196i) q^{2} +(-1.38603 - 4.26575i) q^{4} +(-2.00572 + 10.9990i) q^{5} -5.91678 q^{7} +(7.23313 - 22.2613i) q^{8} +O(q^{10})\)	\(q+(1.51671 + 1.10196i) q^{2} +(-1.38603 - 4.26575i) q^{4} +(-2.00572 + 10.9990i) q^{5} -5.91678 q^{7} +(7.23313 - 22.2613i) q^{8} +(-15.1625 + 14.4720i) q^{10} +(-46.2426 - 33.5972i) q^{11} +(-23.8943 + 17.3602i) q^{13} +(-8.97406 - 6.52004i) q^{14} +(6.47220 - 4.70233i) q^{16} +(-16.1964 + 49.8475i) q^{17} +(28.8671 - 88.8439i) q^{19} +(49.6988 - 6.68896i) q^{20} +(-33.1141 - 101.915i) q^{22} +(-101.186 - 73.5160i) q^{23} +(-116.954 - 44.1216i) q^{25} -55.3710 q^{26} +(8.20082 + 25.2395i) q^{28} +(-42.2327 - 129.979i) q^{29} +(-22.0658 + 67.9115i) q^{31} -172.257 q^{32} +(-79.4951 + 57.7566i) q^{34} +(11.8674 - 65.0785i) q^{35} +(-149.002 + 108.256i) q^{37} +(141.685 - 102.940i) q^{38} +(230.343 + 124.207i) q^{40} +(28.3279 - 20.5814i) q^{41} +185.374 q^{43} +(-79.2239 + 243.826i) q^{44} +(-72.4588 - 223.005i) q^{46} +(-130.295 - 401.007i) q^{47} -307.992 q^{49} +(-128.766 - 195.798i) q^{50} +(107.173 + 77.8655i) q^{52} +(214.260 + 659.426i) q^{53} +(462.284 - 441.234i) q^{55} +(-42.7968 + 131.715i) q^{56} +(79.1762 - 243.679i) q^{58} +(466.375 - 338.841i) q^{59} +(29.5121 + 21.4418i) q^{61} +(-108.303 + 78.6867i) q^{62} +(-313.042 - 227.438i) q^{64} +(-143.019 - 297.633i) q^{65} +(-48.1248 + 148.113i) q^{67} +235.086 q^{68} +(89.7130 - 85.6279i) q^{70} +(-120.884 - 372.044i) q^{71} +(946.113 + 687.392i) q^{73} -345.287 q^{74} -418.997 q^{76} +(273.608 + 198.788i) q^{77} +(323.388 + 995.287i) q^{79} +(38.7393 + 80.6190i) q^{80} +65.6451 q^{82} +(-289.936 + 892.333i) q^{83} +(-515.785 - 278.124i) q^{85} +(281.159 + 204.274i) q^{86} +(-1082.40 + 786.407i) q^{88} +(378.143 + 274.737i) q^{89} +(141.378 - 102.717i) q^{91} +(-173.354 + 533.530i) q^{92} +(244.272 - 751.791i) q^{94} +(919.291 + 495.704i) q^{95} +(-529.272 - 1628.93i) q^{97} +(-467.135 - 339.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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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