LMFDB - Embedded newform 225.4.h.b.136.5

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			136.5
Character	$\chi$	$=$	225.136
Dual form			225.4.h.b.91.5

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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	−0.286447	−	0.958096i	$-0.592474\pi$
$2$	1.51671	−	1.10196i	0.536239	−	0.389600i	0.822686	+	0.568496i	$0.192474\pi$
$3$		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	−0.999101	−	0.0423993i	$-0.986500\pi$
$11$	−46.2426	+	33.5972i	−1.26752	+	0.920904i	−0.268415	+	0.963303i	$0.586500\pi$
$12$		0			0
$13$	−23.8943	−	17.3602i	−0.509777	−	0.370374i	0.302962	−	0.953003i	$-0.402024\pi$
$13$	−23.8943	−	17.3602i	−0.509777	−	0.370374i	−0.812739	+	0.582628i	$0.802024\pi$
$14$	−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	−0.997618	−	0.0689764i	$-0.978027\pi$
$17$	−16.1964	−	49.8475i	−0.231071	−	0.711165i	0.766547	−	0.642188i	$-0.221973\pi$
$18$		0			0
$19$	28.8671	+	88.8439i	0.348557	+	1.07275i	0.959652	+	0.281190i	$0.0907291\pi$
$19$	28.8671	+	88.8439i	0.348557	+	1.07275i	−0.611096	+	0.791557i	$0.709271\pi$
$20$	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	−0.942860	−	0.333189i	$-0.891875\pi$
$23$	−101.186	+	73.5160i	−0.917338	+	0.666485i	0.0255223	+	0.999674i	$0.491875\pi$
$24$		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	0.719965	+	0.694011i	$0.244158\pi$
$29$	−42.2327	+	129.979i	−0.270428	+	0.832293i	−0.990393	+	0.138282i	$0.955842\pi$
$30$		0			0
$31$	−22.0658	−	67.9115i	−0.127843	−	0.393460i	0.866565	−	0.499064i	$-0.166323\pi$
$31$	−22.0658	−	67.9115i	−0.127843	−	0.393460i	−0.994408	+	0.105603i	$0.966323\pi$
$32$	−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	0.205306	−	0.978698i	$-0.434181\pi$
$37$	−149.002	−	108.256i	−0.662048	−	0.481006i	−0.867354	+	0.497692i	$0.834181\pi$
$38$	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	0.640429	−	0.768017i	$-0.278757\pi$
$41$	28.3279	+	20.5814i	0.107904	+	0.0783971i	−0.532525	+	0.846415i	$0.678757\pi$
$42$		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	0.517047	+	0.855957i	$0.327031\pi$
$47$	−130.295	+	401.007i	−0.404372	+	1.24453i	−0.921419	+	0.388571i	$0.872969\pi$
$48$		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	−0.139847	−	0.990173i	$-0.544661\pi$
$53$	214.260	−	659.426i	0.555301	−	1.70904i	0.695148	−	0.718867i	$-0.255339\pi$
$54$		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	0.968128	−	0.250455i	$-0.0805802\pi$
$59$	466.375	+	338.841i	1.02910	+	0.747684i	0.0609711	+	0.998140i	$0.480580\pi$
$60$		0			0
$61$	29.5121	−	21.4418i	0.0619448	−	0.0450056i	−0.556382	−	0.830927i	$-0.687811\pi$
$61$	29.5121	−	21.4418i	0.0619448	−	0.0450056i	0.618327	+	0.785921i	$0.287811\pi$
$62$	−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	0.897545	−	0.440923i	$-0.145349\pi$
$67$	−48.1248	−	148.113i	−0.0877519	−	0.270073i	−0.985297	+	0.170850i	$0.945349\pi$
$68$	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	0.797760	+	0.602975i	$0.206018\pi$
$71$	−120.884	+	372.044i	−0.202061	+	0.621880i	−0.999821	+	0.0189054i	$0.993982\pi$
$72$		0			0
$73$	946.113	−	687.392i	1.51691	−	1.10210i	0.553913	−	0.832575i	$-0.313134\pi$
$73$	946.113	−	687.392i	1.51691	−	1.10210i	0.962994	−	0.269523i	$-0.0868659\pi$
$74$	−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	−0.403927	−	0.914791i	$-0.632355\pi$
$79$	323.388	−	995.287i	0.460557	−	1.41745i	0.864485	−	0.502659i	$-0.167645\pi$
$80$	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	−0.937613	−	0.347680i	$-0.886969\pi$
$83$	−289.936	−	892.333i	−0.383430	−	1.18007i	0.554184	−	0.832395i	$-0.313031\pi$
$84$		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	−0.339371	−	0.940653i	$-0.610214\pi$
$89$	378.143	−	274.737i	0.450371	−	0.327214i	0.789742	+	0.613439i	$0.210214\pi$
$90$		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	0.144518	+	0.989502i	$0.453837\pi$
$97$	−529.272	+	1628.93i	−0.554014	+	1.70508i	−0.698532	+	0.715579i	$0.746163\pi$
$98$	−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	−0.936523	−	0.350606i	$-0.885976\pi$
$103$	28.4548	−	87.5749i	0.0272207	−	0.0837768i	0.963744	+	0.266829i	$0.0859758\pi$
$104$	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	0.515152	−	0.857099i	$-0.327735\pi$
$109$	−160.237	−	116.419i	−0.140806	−	0.102302i	−0.655958	+	0.754797i	$0.727735\pi$
$110$	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	0.981698	−	0.190445i	$-0.0609931\pi$
$113$	1326.05	+	963.435i	1.10394	+	0.802056i	0.122237	+	0.992501i	$0.460993\pi$
$114$		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	−0.719957	−	0.694019i	$-0.755838\pi$
$127$	−404.153	+	293.635i	−0.282384	+	0.205164i	0.437572	+	0.899183i	$0.355838\pi$
$128$	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	0.920787	−	0.390065i	$-0.127547\pi$
$131$	−80.0952	−	246.508i	−0.0534195	−	0.164408i	−0.974207	+	0.225656i	$0.927547\pi$
$132$		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	0.548709	−	0.836014i	$-0.315120\pi$
$137$	−123.196	−	89.5073i	−0.0768275	−	0.0558184i	−0.625536	+	0.780195i	$0.715120\pi$
$138$		0			0
$139$	−1835.62	+	1333.66i	−1.12011	+	0.813809i	−0.984226	−	0.176916i	$-0.943388\pi$
$139$	−1835.62	+	1333.66i	−1.12011	+	0.813809i	−0.135885	+	0.990725i	$0.543388\pi$
$140$	−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	0.900166	−	0.435547i	$-0.143445\pi$
$163$	1590.13	+	1155.30i	0.764102	+	0.555153i	−0.136064	+	0.990700i	$0.543445\pi$
$164$	−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	0.983516	+	0.180823i	$0.0578761\pi$
$167$	634.745	+	1953.54i	0.294120	+	0.905208i	−0.689396	+	0.724385i	$0.742124\pi$
$168$		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	−0.791392	−	0.611310i	$-0.790643\pi$
$173$	−1034.32	+	751.479i	−0.454555	+	0.330254i	0.336836	+	0.941563i	$0.390643\pi$
$174$		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	−0.976626	−	0.214944i	$-0.931043\pi$
$179$	−144.118	+	443.549i	−0.0601781	+	0.185209i	0.916448	+	0.400153i	$0.131043\pi$
$180$		0			0
$181$	360.349	+	1109.04i	0.147981	+	0.455439i	0.997382	−	0.0723088i	$-0.0230367\pi$
$181$	360.349	+	1109.04i	0.147981	+	0.455439i	−0.849401	+	0.527748i	$0.823037\pi$
$182$	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	0.875158	−	0.483837i	$-0.160757\pi$
$191$	1809.34	+	1314.56i	0.685440	+	0.498001i	−0.189718	+	0.981839i	$0.560757\pi$
$192$		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	0.797282	+	0.603607i	$0.206270\pi$
$197$	−559.983	+	1723.45i	−0.202524	+	0.623304i	−0.999806	+	0.0196971i	$0.993730\pi$
$198$		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	−0.968080	−	0.250642i	$-0.919358\pi$
$211$	−3153.40	+	2291.08i	−1.02886	+	0.747509i	−0.0607784	+	0.998151i	$0.519358\pi$
$212$	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	−0.934150	−	0.356880i	$-0.883841\pi$
$223$	−2941.83	+	2137.36i	−0.883406	+	0.641832i	0.0507445	+	0.998712i	$0.483841\pi$
$224$	1019.21			0.304012
$225$		0			0
$226$	3072.90			0.904454
$227$	562.815	−	408.909i	0.164561	−	0.119561i	−0.502457	−	0.864602i	$-0.667570\pi$
$227$	562.815	−	408.909i	0.164561	−	0.119561i	0.667018	+	0.745042i	$0.267570\pi$
$228$		0			0
$229$	−1706.92	+	5253.37i	−0.492562	+	1.51595i	0.328160	+	0.944622i	$0.393572\pi$
$229$	−1706.92	+	5253.37i	−0.492562	+	1.51595i	−0.820722	+	0.571328i	$0.806428\pi$
$230$	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	0.858985	+	0.512001i	$0.171096\pi$
$233$	1653.81	+	5089.90i	0.464998	+	1.43112i	−0.393986	+	0.919116i	$0.628904\pi$
$234$		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	−0.979535	−	0.201273i	$-0.935492\pi$
$239$	−4030.36	+	2928.23i	−1.09081	+	0.792517i	−0.111271	+	0.993790i	$0.535492\pi$
$240$		0			0
$241$	1105.03	+	802.852i	0.295358	+	0.214590i	0.725588	−	0.688129i	$-0.241568\pi$
$241$	1105.03	+	802.852i	0.295358	+	0.214590i	−0.430230	+	0.902719i	$0.641568\pi$
$242$	−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	0.541341	−	0.840803i	$-0.317917\pi$
$263$	−388.238	−	282.072i	−0.0910258	−	0.0661341i	−0.632367	+	0.774669i	$0.717917\pi$
$264$		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	−0.964703	−	0.263342i	$-0.915175\pi$
$269$	−1495.78	−	4603.53i	−0.339030	−	1.04343i	0.625673	−	0.780086i	$-0.284825\pi$
$270$		0			0
$271$	1441.77	−	4437.32i	0.323179	−	0.994643i	−0.649077	−	0.760723i	$-0.724845\pi$
$271$	1441.77	−	4437.32i	0.323179	−	0.994643i	0.972256	−	0.233920i	$-0.0751553\pi$
$272$	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	−0.485221	+	0.874392i	$0.661261\pi$
$277$	−6762.05	+	4912.91i	−1.46676	+	1.06566i	−0.981537	+	0.191271i	$0.938739\pi$
$278$	−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	−0.951447	−	0.307813i	$-0.900403\pi$
$281$	−1708.18	−	5257.23i	−0.362638	−	1.11609i	0.588809	−	0.808272i	$-0.299597\pi$
$282$		0			0
$283$	−161.101	−	495.817i	−0.0338390	−	0.104146i	0.932710	−	0.360626i	$-0.117437\pi$
$283$	−161.101	−	495.817i	−0.0338390	−	0.104146i	−0.966549	+	0.256481i	$0.917437\pi$
$284$	−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	−0.0967289	−	0.995311i	$-0.530838\pi$
$311$	4497.20	−	3267.41i	0.819977	−	0.595748i	0.916706	+	0.399563i	$0.130838\pi$
$312$		0			0
$313$	4746.67	+	3448.66i	0.857180	+	0.622778i	0.927116	−	0.374773i	$-0.122279\pi$
$313$	4746.67	+	3448.66i	0.857180	+	0.622778i	−0.0699360	+	0.997551i	$0.522279\pi$
$314$	−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	0.959410	−	0.282013i	$-0.0910022\pi$
$317$	98.5888	+	303.425i	0.0174678	+	0.0537604i	−0.941943	+	0.335774i	$0.891002\pi$
$318$		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	0.997652	−	0.0684939i	$-0.0218194\pi$
$331$	904.957	+	2785.17i	0.150275	+	0.462498i	−0.847377	+	0.530992i	$0.821819\pi$
$332$	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	0.196797	−	0.980444i	$-0.436946\pi$
$337$	−4174.94	−	3033.27i	−0.674848	−	0.490306i	−0.871644	+	0.490139i	$0.836946\pi$
$338$	−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	−0.984126	−	0.177470i	$-0.943209\pi$
$347$	−540.620	+	1663.86i	−0.0836369	+	0.257408i	0.900489	+	0.434878i	$0.143209\pi$
$348$		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	−0.958450	−	0.285260i	$-0.907920\pi$
$353$	−101.976	+	313.851i	−0.0153758	+	0.0473218i	0.943074	+	0.332582i	$0.107920\pi$
$354$		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	0.808872	−	0.587985i	$-0.200079\pi$
$359$	3398.46	+	2469.12i	0.499620	+	0.362995i	−0.309252	+	0.950980i	$0.600079\pi$
$360$		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	−0.812700	−	0.582682i	$-0.802003\pi$
$367$	−3499.21	−	10769.5i	−0.497704	−	1.53177i	0.314997	−	0.949093i	$-0.397997\pi$
$368$	−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	−0.939934	−	0.341357i	$-0.889114\pi$
$373$	−6524.79	+	4740.54i	−0.905740	+	0.658059i	0.0341938	+	0.999415i	$0.489114\pi$
$374$	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	−0.881624	−	0.471952i	$-0.843550\pi$
$379$	804.469	−	2475.90i	0.109031	−	0.335563i	0.990655	+	0.136389i	$0.0435496\pi$
$380$	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	−0.930984	−	0.365061i	$-0.881048\pi$
$383$	−2941.06	−	9051.66i	−0.392380	−	1.20762i	0.538604	−	0.842559i	$-0.318952\pi$
$384$		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	−0.300164	−	0.953888i	$-0.597041\pi$
$389$	3945.71	−	2866.72i	0.514281	−	0.373647i	0.814445	+	0.580241i	$0.197041\pi$
$390$		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	−0.935441	−	0.353483i	$-0.884997\pi$
$397$	230.334	−	708.897i	0.0291188	−	0.0896184i	0.964560	+	0.263865i	$0.0849972\pi$
$398$	−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	0.516850	−	0.856076i	$-0.327105\pi$
$409$	−1138.26	−	826.991i	−0.137612	−	0.0999807i	−0.654461	+	0.756095i	$0.727105\pi$
$410$	−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	0.999461	−	0.0328318i	$-0.0104526\pi$
$419$	1471.61	+	4529.15i	0.171582	+	0.528075i	−0.827879	+	0.560907i	$0.810453\pi$
$420$		0			0
$421$	−1185.64	+	3649.02i	−0.137255	+	0.422429i	−0.995934	−	0.0900856i	$-0.971286\pi$
$421$	−1185.64	+	3649.02i	−0.137255	+	0.422429i	0.858679	+	0.512515i	$0.171286\pi$
$422$	−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	0.988708	−	0.149853i	$-0.0478800\pi$
$431$	901.448	+	2774.37i	0.100745	+	0.310062i	−0.887963	+	0.459915i	$0.847880\pi$
$432$		0			0
$433$	648.396	+	1995.56i	0.0719629	+	0.221479i	0.980569	−	0.196175i	$-0.0628522\pi$
$433$	648.396	+	1995.56i	0.0719629	+	0.221479i	−0.908606	+	0.417655i	$0.862852\pi$
$434$	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	−0.582735	−	0.812662i	$-0.698018\pi$
$439$	92.6878	−	67.3416i	0.0100769	−	0.00732127i	0.592812	+	0.805341i	$0.298018\pi$
$440$	−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	−0.961230	−	0.275747i	$-0.911075\pi$
$461$	−9858.66	+	7162.73i	−0.996016	+	0.723648i	−0.0347857	+	0.999395i	$0.511075\pi$
$462$		0			0
$463$	−8431.33	−	6125.72i	−0.846301	−	0.614873i	0.0778229	−	0.996967i	$-0.475203\pi$
$463$	−8431.33	−	6125.72i	−0.846301	−	0.614873i	−0.924124	+	0.382094i	$0.875203\pi$
$464$	−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	−0.920332	−	0.391139i	$-0.872081\pi$
$467$	−4094.04	−	12600.2i	−0.405673	−	1.24853i	0.514658	−	0.857395i	$-0.327919\pi$
$468$		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	−0.961549	−	0.274633i	$-0.911444\pi$
$479$	−232.883	+	716.739i	−0.0222144	+	0.0683688i	0.939335	+	0.343002i	$0.111444\pi$
$480$		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	0.511191	−	0.859467i	$-0.329204\pi$
$487$	−1593.20	−	1157.53i	−0.148244	−	0.107705i	−0.659435	+	0.751762i	$0.729204\pi$
$488$	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	0.985022	−	0.172429i	$-0.0551617\pi$
$491$	12244.4	+	8896.07i	1.12542	+	0.817666i	0.140398	+	0.990095i	$0.455162\pi$
$492$		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	−0.826565	−	0.562842i	$-0.809708\pi$
$503$	1951.30	−	6005.48i	0.172970	−	0.532348i	0.999535	+	0.0304937i	$0.00970794\pi$
$504$		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	0.660593	−	0.750744i	$-0.270305\pi$
$509$	1730.89	+	1257.57i	0.150728	+	0.109510i	−0.509865	+	0.860254i	$0.670305\pi$
$510$		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	0.645345	+	0.763891i	$0.276714\pi$
$521$	−3873.88	+	11922.6i	−0.325754	+	1.00257i	−0.971099	+	0.238677i	$0.923286\pi$
$522$		0			0
$523$	4612.96	−	3351.51i	0.385680	−	0.280213i	−0.378003	−	0.925804i	$-0.623389\pi$
$523$	4612.96	−	3351.51i	0.385680	−	0.280213i	0.763683	+	0.645591i	$0.223389\pi$
$524$	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	0.980438	−	0.196827i	$-0.0630638\pi$
$541$	13794.1	+	10022.0i	1.09622	+	0.796448i	0.115778	+	0.993275i	$0.463064\pi$
$542$	−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	−0.838825	−	0.544401i	$-0.816757\pi$
$547$	2044.23	−	6291.50i	0.159790	−	0.491783i	0.998615	+	0.0526188i	$0.0167568\pi$
$548$	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	0.965197	−	0.261526i	$-0.0842256\pi$
$563$	13555.5	+	9848.62i	1.01473	+	0.737247i	0.0495366	+	0.998772i	$0.484226\pi$
$564$		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	0.857038	−	0.515254i	$-0.172302\pi$
$569$	−1889.04	−	5813.88i	−0.139179	−	0.428349i	−0.996217	+	0.0869048i	$0.972302\pi$
$570$		0			0
$571$	−3930.14	+	12095.7i	−0.288041	+	0.886499i	0.697430	+	0.716653i	$0.254327\pi$
$571$	−3930.14	+	12095.7i	−0.288041	+	0.886499i	−0.985471	+	0.169846i	$0.945673\pi$
$572$	−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	−0.216674	−	0.976244i	$-0.569521\pi$
$577$	8937.40	−	6493.40i	0.644833	−	0.468499i	0.861507	+	0.507745i	$0.169521\pi$
$578$	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	0.789900	−	0.613236i	$-0.210132\pi$
$587$	6410.81	+	4657.73i	0.450771	+	0.327504i	−0.339129	+	0.940740i	$0.610132\pi$
$588$		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	0.324306	−	0.945952i	$-0.394869\pi$
$613$	−7211.16	−	5239.22i	−0.475132	−	0.345204i	−0.799438	+	0.600749i	$0.794869\pi$
$614$	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	−0.945409	−	0.325885i	$-0.894338\pi$
$617$	−5702.91	−	17551.7i	−0.372108	−	1.14523i	0.573302	−	0.819344i	$-0.305662\pi$
$618$		0			0
$619$	5256.38	+	16177.5i	0.341312	+	1.05045i	0.963529	+	0.267605i	$0.0862321\pi$
$619$	5256.38	+	16177.5i	0.341312	+	1.05045i	−0.622217	+	0.782845i	$0.713768\pi$
$620$	−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	0.928414	+	0.371547i	$0.121172\pi$
$631$	6272.07	+	19303.5i	0.395701	+	1.21784i	−0.532713	+	0.846296i	$0.678828\pi$
$632$	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	0.927714	−	0.373292i	$-0.121771\pi$
$641$	13946.6	+	10132.8i	0.859371	+	0.624370i	−0.0683428	+	0.997662i	$0.521771\pi$
$642$		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	−0.883611	−	0.468223i	$-0.844895\pi$
$647$	1752.03	−	5392.20i	0.106460	−	0.327649i	0.990070	+	0.140573i	$0.0448945\pi$
$648$		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	−0.412835	−	0.910806i	$-0.635461\pi$
$653$	7617.70	−	23444.9i	0.456514	−	1.40501i	0.869349	−	0.494199i	$-0.164539\pi$
$654$		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	0.554926	−	0.831900i	$-0.312747\pi$
$659$	−1095.83	−	796.169i	−0.0647763	−	0.0470627i	−0.619702	+	0.784837i	$0.712747\pi$
$660$		0			0
$661$	−7325.16	+	5322.04i	−0.431037	+	0.313167i	−0.782064	−	0.623199i	$-0.785833\pi$
$661$	−7325.16	+	5322.04i	−0.431037	+	0.313167i	0.351026	+	0.936366i	$0.385833\pi$
$662$	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	−0.769171	−	0.639044i	$-0.779330\pi$
$673$	−6967.78	+	5062.39i	−0.399091	+	0.289956i	0.370080	+	0.929000i	$0.379330\pi$
$674$	−9674.72			−0.552903
$675$		0			0
$676$	5941.57			0.338050
$677$	−6541.98	+	4753.03i	−0.371387	+	0.269828i	−0.757786	−	0.652503i	$-0.773719\pi$
$677$	−6541.98	+	4753.03i	−0.371387	+	0.269828i	0.386399	+	0.922332i	$0.373719\pi$
$678$		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	0.561064	+	0.827773i	$0.310392\pi$
$683$	10597.5	+	32615.7i	0.593706	+	1.82724i	0.0326425	+	0.999467i	$0.489608\pi$
$684$		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	0.342802	−	0.939408i	$-0.388624\pi$
$691$	−8077.57	−	5868.70i	−0.444697	−	0.323091i	−0.787498	+	0.616317i	$0.788624\pi$
$692$	−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	0.845368	−	0.534184i	$-0.179381\pi$
$709$	11300.0	+	8209.94i	0.598563	+	0.434881i	−0.246806	+	0.969065i	$0.579381\pi$
$710$	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	−0.903394	−	0.428811i	$-0.858933\pi$
$719$	−8185.68	−	25192.9i	−0.424582	−	1.30673i	0.478812	−	0.877917i	$-0.341067\pi$
$720$		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	−0.882946	−	0.469474i	$-0.844444\pi$
$727$	−13903.6	+	10101.6i	−0.709295	+	0.515333i	0.173651	+	0.984807i	$0.444444\pi$
$728$	−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	0.821306	−	0.570488i	$-0.193246\pi$
$733$	−3541.75	−	10900.4i	−0.178469	−	0.549270i	−0.999775	+	0.0212175i	$0.993246\pi$
$734$	−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	−0.556760	+	0.830673i	$0.687956\pi$
$739$	−30512.3	+	22168.5i	−1.51883	+	1.10349i	−0.962066	+	0.272818i	$0.912044\pi$
$740$	−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	−0.340238	−	0.940339i	$-0.610508\pi$
$761$	9424.61	−	6847.38i	0.448938	−	0.326173i	0.789176	+	0.614167i	$0.210508\pi$
$762$		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	0.826318	−	0.563203i	$-0.190431\pi$
$769$	−3694.13	−	11369.4i	−0.173230	−	0.533147i	−0.999548	+	0.0300565i	$0.990431\pi$
$770$	−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	−0.141877	−	0.989884i	$-0.545314\pi$
$773$	16241.6	−	11800.2i	0.755717	−	0.549061i	0.897594	+	0.440824i	$0.145314\pi$
$774$		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	0.967179	−	0.254096i	$-0.0817780\pi$
$787$	22616.7	+	16432.0i	1.02439	+	0.744266i	0.0572147	+	0.998362i	$0.481778\pi$
$788$	−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	0.488426	+	0.872605i	$0.337571\pi$
$797$	−9441.64	+	29058.4i	−0.419624	+	1.29147i	−0.908049	+	0.418863i	$0.862429\pi$
$798$		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	0.530983	−	0.847383i	$-0.321823\pi$
$809$	−2550.54	−	1853.08i	−0.110843	−	0.0805324i	−0.641826	+	0.766850i	$0.721823\pi$
$810$		0			0
$811$	−292.128	+	212.243i	−0.0126486	+	0.00918973i	−0.594092	−	0.804397i	$-0.702488\pi$
$811$	−292.128	+	212.243i	−0.0126486	+	0.00918973i	0.581443	+	0.813587i	$0.302488\pi$
$812$	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	−0.776490	−	0.630129i	$-0.783002\pi$
$821$	5224.35	−	16078.9i	0.222084	−	0.683505i	0.998574	−	0.0533758i	$-0.0169981\pi$
$822$		0			0
$823$	10939.7	−	7948.18i	0.463348	−	0.336642i	−0.331495	−	0.943457i	$-0.607553\pi$
$823$	10939.7	−	7948.18i	0.463348	−	0.336642i	0.794843	+	0.606815i	$0.207553\pi$
$824$	2155.35			0.0911226
$825$		0			0
$826$	−6394.53			−0.269364
$827$	−26154.0	+	19002.0i	−1.09971	+	0.798988i	−0.981013	−	0.193942i	$-0.937873\pi$
$827$	−26154.0	+	19002.0i	−1.09971	+	0.798988i	−0.118700	+	0.992930i	$0.537873\pi$
$828$		0			0
$829$	−8942.80	+	27523.1i	−0.374664	+	1.15310i	0.569042	+	0.822309i	$0.307314\pi$
$829$	−8942.80	+	27523.1i	−0.374664	+	1.15310i	−0.943705	+	0.330787i	$0.892686\pi$
$830$	−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	−0.877187	−	0.480150i	$-0.840582\pi$
$839$	−16807.4	+	12211.3i	−0.691603	+	0.502479i	0.185584	+	0.982628i	$0.440582\pi$
$840$		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	0.499375	+	0.866386i	$0.333563\pi$
$853$	−10310.8	+	31733.5i	−0.413877	+	1.27378i	−0.913252	+	0.407395i	$0.866437\pi$
$854$	−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	0.480050	−	0.877241i	$-0.340619\pi$
$859$	−5184.10	−	3766.47i	−0.205913	−	0.149604i	−0.685963	+	0.727637i	$0.740619\pi$
$860$	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	−0.947704	−	0.319149i	$-0.896603\pi$
$863$	−39146.1	−	28441.3i	−1.54409	−	1.12185i	−0.596386	−	0.802698i	$-0.703397\pi$
$864$		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	−0.0845052	−	0.996423i	$-0.526931\pi$
$877$	21739.2	−	15794.5i	0.837036	−	0.608142i	0.921541	+	0.388281i	$0.126931\pi$
$878$	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	−0.889970	−	0.456020i	$-0.849275\pi$
$881$	−11453.8	−	35251.1i	−0.438011	−	1.34806i	0.451959	−	0.892039i	$-0.350725\pi$
$882$		0			0
$883$	−656.803	−	2021.43i	−0.0250319	−	0.0770403i	0.937760	−	0.347284i	$-0.112896\pi$
$883$	−656.803	−	2021.43i	−0.0250319	−	0.0770403i	−0.962792	+	0.270243i	$0.912896\pi$
$884$	−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	0.554910	−	0.831910i	$-0.312753\pi$
$887$	−1712.00	−	1243.84i	−0.0648065	−	0.0470847i	−0.619717	+	0.784825i	$0.712753\pi$
$888$		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	−0.777161	−	0.629302i	$-0.783341\pi$
$911$	−11515.9	+	8366.82i	−0.418815	+	0.304287i	0.358346	+	0.933589i	$0.383341\pi$
$912$		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	−0.954725	−	0.297491i	$-0.903850\pi$
$919$	−9951.33	−	30627.0i	−0.357197	−	1.09934i	0.597528	−	0.801848i	$-0.296150\pi$
$920$	−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	−0.827522	−	0.561434i	$-0.810250\pi$
$929$	4869.12	−	14985.6i	0.171960	−	0.529238i	0.999482	+	0.0321958i	$0.0102500\pi$
$930$		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	−0.116362	−	0.993207i	$-0.537123\pi$
$937$	−31461.7	−	22858.3i	−1.09692	−	0.796956i	−0.980554	+	0.196251i	$0.937123\pi$
$938$	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	0.987006	−	0.160684i	$-0.0513699\pi$
$941$	32883.6	+	23891.4i	1.13919	+	0.827669i	0.152182	+	0.988352i	$0.451370\pi$
$942$		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	0.780068	+	0.625695i	$0.215184\pi$
$947$	−6376.19	+	19623.9i	−0.218794	+	0.673380i	−0.998862	+	0.0476852i	$0.984816\pi$
$948$		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	−0.770906	−	0.636949i	$-0.780196\pi$
$953$	6682.98	−	20568.1i	0.227160	−	0.699125i	0.998065	−	0.0621759i	$-0.0198040\pi$
$954$		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	−0.977106	−	0.212752i	$-0.931757\pi$
$967$	−9371.85	−	28843.6i	−0.311663	−	0.959201i	0.665443	−	0.746449i	$-0.268243\pi$
$968$	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	0.595795	+	0.803137i	$0.296837\pi$
$971$	−10840.7	+	33364.3i	−0.358285	+	1.10269i	−0.954080	+	0.299552i	$0.903163\pi$
$972$		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	−0.993026	−	0.117899i	$-0.962384\pi$
$977$	−36271.9	+	26353.1i	−1.18776	+	0.862958i	−0.194733	+	0.980856i	$0.562384\pi$
$978$		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	−0.998262	−	0.0589243i	$-0.981233\pi$
$983$	−6943.28	−	21369.2i	−0.225286	−	0.693359i	0.772976	−	0.634435i	$-0.218767\pi$
$984$		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	0.930868	−	0.365355i	$-0.119052\pi$
$991$	27174.0	+	19743.1i	0.871049	+	0.632854i	−0.0598190	+	0.998209i	$0.519052\pi$
$992$	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	0.268285	+	0.963339i	$0.413543\pi$
$997$	−16212.5	+	49896.8i	−0.514999	+	1.58500i	−0.783284	+	0.621664i	$0.786457\pi$
$998$	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.136.5		28
3.2	odd	2		25.4.d.a.11.3	✓	28
15.2	even	4		125.4.e.b.74.6		56
15.8	even	4		125.4.e.b.74.9		56
15.14	odd	2		125.4.d.a.51.5		28
25.16	even	5	inner	225.4.h.b.91.5		28
75.29	odd	10		625.4.a.d.1.6		14
75.38	even	20		125.4.e.b.49.6		56
75.41	odd	10		25.4.d.a.16.3	yes	28
75.59	odd	10		125.4.d.a.76.5		28
75.62	even	20		125.4.e.b.49.9		56
75.71	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	3.2	odd	2
25.4.d.a.16.3	yes	28	75.41	odd	10
125.4.d.a.51.5		28	15.14	odd	2
125.4.d.a.76.5		28	75.59	odd	10
125.4.e.b.49.6		56	75.38	even	20
125.4.e.b.49.9		56	75.62	even	20
125.4.e.b.74.6		56	15.2	even	4
125.4.e.b.74.9		56	15.8	even	4
225.4.h.b.91.5		28	25.16	even	5	inner
225.4.h.b.136.5		28	1.1	even	1	trivial
625.4.a.c.1.9		14	75.71	odd	10
625.4.a.d.1.6		14	75.29	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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