LMFDB - Embedded newform 225.3.r.b.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(28,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.r (of order $20$, degree $8$, 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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	225.37
Dual form			225.3.r.b.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.202100 + 1.27601i) q^{2} +(2.21687 - 0.720305i) q^{4} +(-1.23939 - 4.84396i) q^{5} +(1.27981 + 1.27981i) q^{7} +(3.71321 + 7.28759i) q^{8} +O(q^{10})$	\(q+(0.202100 + 1.27601i) q^{2} +(2.21687 - 0.720305i) q^{4} +(-1.23939 - 4.84396i) q^{5} +(1.27981 + 1.27981i) q^{7} +(3.71321 + 7.28759i) q^{8} +(5.93045 - 2.56044i) q^{10} +(2.26637 + 1.64661i) q^{11} +(2.80131 - 17.6867i) q^{13} +(-1.37440 + 1.89170i) q^{14} +(-1.00546 + 0.730511i) q^{16} +(24.2628 - 12.3625i) q^{17} +(8.64024 + 2.80738i) q^{19} +(-6.23670 - 9.84568i) q^{20} +(-1.64306 + 3.22469i) q^{22} +(24.8036 - 3.92850i) q^{23} +(-21.9278 + 12.0071i) q^{25} +23.1346 q^{26} +(3.75903 + 1.91532i) q^{28} +(-27.5633 + 8.95587i) q^{29} +(-14.3903 + 44.2887i) q^{31} +(21.9985 + 21.9985i) q^{32} +(20.6782 + 28.4611i) q^{34} +(4.61315 - 7.78553i) q^{35} +(-31.3477 - 4.96498i) q^{37} +(-1.83606 + 11.5924i) q^{38} +(30.6986 - 27.0188i) q^{40} +(-11.2150 + 8.14820i) q^{41} +(27.8178 - 27.8178i) q^{43} +(6.21031 + 2.01785i) q^{44} +(10.0256 + 30.8556i) q^{46} +(-18.8125 + 36.9215i) q^{47} -45.7242i q^{49} +(-19.7528 - 25.5534i) q^{50} +(-6.52972 - 41.2270i) q^{52} +(-28.1946 - 14.3659i) q^{53} +(5.16720 - 13.0190i) q^{55} +(-4.57452 + 14.0789i) q^{56} +(-16.9983 - 33.3611i) q^{58} +(-18.6844 - 25.7169i) q^{59} +(36.7017 + 26.6654i) q^{61} +(-59.4210 - 9.41137i) q^{62} +(-26.5465 + 36.5381i) q^{64} +(-89.1457 + 8.35144i) q^{65} +(-86.9965 + 44.3269i) q^{67} +(44.8827 - 44.8827i) q^{68} +(10.8667 + 4.31297i) q^{70} +(1.13108 + 3.48112i) q^{71} +(76.0348 - 12.0427i) q^{73} -41.0033i q^{74} +21.1765 q^{76} +(0.793169 + 5.00787i) q^{77} +(-133.301 + 43.3122i) q^{79} +(4.78473 + 3.96502i) q^{80} +(-12.6637 - 12.6637i) q^{82} +(-9.52910 - 18.7019i) q^{83} +(-89.9546 - 102.206i) q^{85} +(41.1177 + 29.8738i) q^{86} +(-3.58433 + 22.6306i) q^{88} +(-98.0657 + 134.976i) q^{89} +(26.2208 - 19.0505i) q^{91} +(52.1566 - 26.5751i) q^{92} +(-50.9142 - 16.5430i) q^{94} +(2.89019 - 45.3324i) q^{95} +(16.0242 - 31.4493i) q^{97} +(58.3445 - 9.24086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{20}\right)$

Coefficient data

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

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

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

$2$	0.202100	+	1.27601i	0.101050	+	0.638005i	0.985279	+	0.170952i	$0.0546842\pi$
$2$	0.202100	+	1.27601i	0.101050	+	0.638005i	−0.884229	+	0.467053i	$0.845316\pi$
$3$		0			0
$3$		0			0
$4$	2.21687	−	0.720305i	0.554218	−	0.180076i
$5$	−1.23939	−	4.84396i	−0.247879	−	0.968791i
$5$	−1.23939	−	4.84396i	−0.247879	−	0.968791i
$6$		0			0
$7$	1.27981	+	1.27981i	0.182830	+	0.182830i	0.792588	−	0.609758i	$-0.208733\pi$
$7$	1.27981	+	1.27981i	0.182830	+	0.182830i	−0.609758	+	0.792588i	$0.708733\pi$
$8$	3.71321	+	7.28759i	0.464152	+	0.910949i
$9$		0			0
$10$	5.93045	−	2.56044i	0.593045	−	0.256044i
$11$	2.26637	+	1.64661i	0.206033	+	0.149692i	0.686017	−	0.727585i	$-0.259357\pi$
$11$	2.26637	+	1.64661i	0.206033	+	0.149692i	−0.479984	+	0.877277i	$0.659357\pi$
$12$		0			0
$13$	2.80131	−	17.6867i	0.215485	−	1.36052i	−0.608341	−	0.793676i	$-0.708165\pi$
$13$	2.80131	−	17.6867i	0.215485	−	1.36052i	0.823826	−	0.566843i	$-0.191835\pi$
$14$	−1.37440	+	1.89170i	−0.0981714	+	0.135121i
$15$		0			0
$16$	−1.00546	+	0.730511i	−0.0628414	+	0.0456569i
$17$	24.2628	−	12.3625i	1.42722	−	0.727206i	0.441766	−	0.897131i	$-0.354352\pi$
$17$	24.2628	−	12.3625i	1.42722	−	0.727206i	0.985457	+	0.169924i	$0.0543523\pi$
$18$		0			0
$19$	8.64024	+	2.80738i	0.454749	+	0.147757i	0.527430	−	0.849598i	$-0.323156\pi$
$19$	8.64024	+	2.80738i	0.454749	+	0.147757i	−0.0726811	+	0.997355i	$0.523156\pi$
$20$	−6.23670	−	9.84568i	−0.311835	−	0.492284i
$21$		0			0
$22$	−1.64306	+	3.22469i	−0.0746846	+	0.146577i
$23$	24.8036	−	3.92850i	1.07842	−	0.170804i	0.408142	−	0.912918i	$-0.366177\pi$
$23$	24.8036	−	3.92850i	1.07842	−	0.170804i	0.670274	+	0.742114i	$0.266177\pi$
$24$		0			0
$25$	−21.9278	+	12.0071i	−0.877112	+	0.480285i
$26$	23.1346			0.889792
$27$		0			0
$28$	3.75903	+	1.91532i	0.134251	+	0.0684043i
$29$	−27.5633	+	8.95587i	−0.950459	+	0.308823i	−0.742902	−	0.669400i	$-0.766551\pi$
$29$	−27.5633	+	8.95587i	−0.950459	+	0.308823i	−0.207557	+	0.978223i	$0.566551\pi$
$30$		0			0
$31$	−14.3903	+	44.2887i	−0.464202	+	1.42867i	0.395781	+	0.918345i	$0.370474\pi$
$31$	−14.3903	+	44.2887i	−0.464202	+	1.42867i	−0.859983	+	0.510322i	$0.829526\pi$
$32$	21.9985	+	21.9985i	0.687454	+	0.687454i
$33$		0			0
$34$	20.6782	+	28.4611i	0.608182	+	0.837090i
$35$	4.61315	−	7.78553i	0.131804	−	0.222444i
$36$		0			0
$37$	−31.3477	−	4.96498i	−0.847234	−	0.134189i	−0.282302	−	0.959326i	$-0.591098\pi$
$37$	−31.3477	−	4.96498i	−0.847234	−	0.134189i	−0.564933	+	0.825137i	$0.691098\pi$
$38$	−1.83606	+	11.5924i	−0.0483172	+	0.305063i
$39$		0			0
$40$	30.6986	−	27.0188i	0.767466	−	0.675471i
$41$	−11.2150	+	8.14820i	−0.273537	+	0.198737i	−0.716094	−	0.698004i	$-0.754072\pi$
$41$	−11.2150	+	8.14820i	−0.273537	+	0.198737i	0.442556	+	0.896741i	$0.354072\pi$
$42$		0			0
$43$	27.8178	−	27.8178i	0.646925	−	0.646925i	−0.305324	−	0.952249i	$-0.598765\pi$
$43$	27.8178	−	27.8178i	0.646925	−	0.646925i	0.952249	+	0.305324i	$0.0987647\pi$
$44$	6.21031	+	2.01785i	0.141143	+	0.0458603i
$45$		0			0
$46$	10.0256	+	30.8556i	0.217948	+	0.670774i
$47$	−18.8125	+	36.9215i	−0.400265	+	0.785564i	−0.999892	−	0.0147156i	$-0.995316\pi$
$47$	−18.8125	+	36.9215i	−0.400265	+	0.785564i	0.599627	+	0.800280i	$0.295316\pi$
$48$		0			0
$49$		−	45.7242i		−	0.933146i
$50$	−19.7528	−	25.5534i	−0.395056	−	0.511069i
$51$		0			0
$52$	−6.52972	−	41.2270i	−0.125572	−	0.792828i
$53$	−28.1946	−	14.3659i	−0.531974	−	0.271054i	0.167302	−	0.985906i	$-0.446494\pi$
$53$	−28.1946	−	14.3659i	−0.531974	−	0.271054i	−0.699277	+	0.714851i	$0.746494\pi$
$54$		0			0
$55$	5.16720	−	13.0190i	0.0939490	−	0.236709i
$56$	−4.57452	+	14.0789i	−0.0816879	+	0.251410i
$57$		0			0
$58$	−16.9983	−	33.3611i	−0.293074	−	0.575191i
$59$	−18.6844	−	25.7169i	−0.316685	−	0.435879i	0.620767	−	0.783995i	$-0.286821\pi$
$59$	−18.6844	−	25.7169i	−0.316685	−	0.435879i	−0.937451	+	0.348116i	$0.886821\pi$
$60$		0			0
$61$	36.7017	+	26.6654i	0.601667	+	0.437137i	0.846470	−	0.532436i	$-0.178723\pi$
$61$	36.7017	+	26.6654i	0.601667	+	0.437137i	−0.244803	+	0.969573i	$0.578723\pi$
$62$	−59.4210	−	9.41137i	−0.958404	−	0.151796i
$63$		0			0
$64$	−26.5465	+	36.5381i	−0.414788	+	0.570907i
$65$	−89.1457	+	8.35144i	−1.37147	+	0.128484i
$66$		0			0
$67$	−86.9965	+	44.3269i	−1.29846	+	0.661596i	−0.960162	−	0.279444i	$-0.909850\pi$
$67$	−86.9965	+	44.3269i	−1.29846	+	0.661596i	−0.338294	+	0.941041i	$0.609850\pi$
$68$	44.8827	−	44.8827i	0.660040	−	0.660040i
$69$		0			0
$70$	10.8667	+	4.31297i	0.155239	+	0.0616139i
$71$	1.13108	+	3.48112i	0.0159308	+	0.0490299i	0.958706	−	0.284399i	$-0.0917942\pi$
$71$	1.13108	+	3.48112i	0.0159308	+	0.0490299i	−0.942775	+	0.333429i	$0.891794\pi$
$72$		0			0
$73$	76.0348	−	12.0427i	1.04157	−	0.164969i	0.387865	−	0.921716i	$-0.373213\pi$
$73$	76.0348	−	12.0427i	1.04157	−	0.164969i	0.653707	+	0.756747i	$0.273213\pi$
$74$		−	41.0033i		−	0.554099i
$75$		0			0
$76$	21.1765			0.278638
$77$	0.793169	+	5.00787i	0.0103009	+	0.0650373i
$78$		0			0
$79$	−133.301	+	43.3122i	−1.68736	+	0.548256i	−0.986316	−	0.164864i	$-0.947281\pi$
$79$	−133.301	+	43.3122i	−1.68736	+	0.548256i	−0.701042	+	0.713120i	$0.747281\pi$
$80$	4.78473	+	3.96502i	0.0598091	+	0.0495628i
$81$		0			0
$82$	−12.6637	−	12.6637i	−0.154436	−	0.154436i
$83$	−9.52910	−	18.7019i	−0.114808	−	0.225324i	0.826451	−	0.563009i	$-0.190356\pi$
$83$	−9.52910	−	18.7019i	−0.114808	−	0.225324i	−0.941259	+	0.337685i	$0.890356\pi$
$84$		0			0
$85$	−89.9546	−	102.206i	−1.05829	−	1.20242i
$86$	41.1177	+	29.8738i	0.478113	+	0.347369i
$87$		0			0
$88$	−3.58433	+	22.6306i	−0.0407311	+	0.257166i
$89$	−98.0657	+	134.976i	−1.10186	+	1.51658i	−0.268967	+	0.963149i	$0.586682\pi$
$89$	−98.0657	+	134.976i	−1.10186	+	1.51658i	−0.832894	+	0.553433i	$0.813318\pi$
$90$		0			0
$91$	26.2208	−	19.0505i	0.288141	−	0.209347i
$92$	52.1566	−	26.5751i	0.566919	−	0.288860i
$93$		0			0
$94$	−50.9142	−	16.5430i	−0.541640	−	0.175990i
$95$	2.89019	−	45.3324i	0.0304230	−	0.477183i
$96$		0			0
$97$	16.0242	−	31.4493i	0.165198	−	0.324220i	−0.793536	−	0.608523i	$-0.791762\pi$
$97$	16.0242	−	31.4493i	0.165198	−	0.324220i	0.958734	+	0.284303i	$0.0917623\pi$
$98$	58.3445	−	9.24086i	0.595352	−	0.0942944i
$99$		0			0
$100$	−39.9623	+	42.4130i	−0.399623	+	0.424130i
$101$	−8.47158			−0.0838770			−0.0419385	−	0.999120i	$-0.513353\pi$
$101$	−8.47158			−0.0838770			−0.0419385	+	0.999120i	$0.513353\pi$
$102$		0			0
$103$	132.641	+	67.5842i	1.28778	+	0.656157i	0.957693	−	0.287793i	$-0.0929215\pi$
$103$	132.641	+	67.5842i	1.28778	+	0.656157i	0.330088	+	0.943950i	$0.392921\pi$
$104$	139.296	−	45.2599i	1.33938	−	0.435191i
$105$		0			0
$106$	12.6329	−	38.8800i	0.119178	−	0.366792i
$107$	−107.492	−	107.492i	−1.00460	−	1.00460i	−0.999989	−	0.00460610i	$-0.998534\pi$
$107$	−107.492	−	107.492i	−1.00460	−	1.00460i	−0.00460610	−	0.999989i	$-0.501466\pi$
$108$		0			0
$109$	65.8481	+	90.6322i	0.604111	+	0.831488i	0.996077	−	0.0884922i	$-0.0282048\pi$
$109$	65.8481	+	90.6322i	0.604111	+	0.831488i	−0.391966	+	0.919980i	$0.628205\pi$
$110$	17.6566	+	3.96225i	0.160515	+	0.0360205i
$111$		0			0
$112$	−2.22172	−	0.351885i	−0.0198367	−	0.00314183i
$113$	−1.99324	+	12.5848i	−0.0176393	+	0.111370i	−0.994937	−	0.100501i	$-0.967956\pi$
$113$	−1.99324	+	12.5848i	−0.0176393	+	0.111370i	0.977298	+	0.211871i	$0.0679556\pi$
$114$		0			0
$115$	−49.7708	−	115.278i	−0.432790	−	1.00242i
$116$	−54.6534	+	39.7080i	−0.471150	+	0.342310i
$117$		0			0
$118$	29.0388	−	29.0388i	0.246092	−	0.246092i
$119$	46.8734	+	15.2301i	0.393894	+	0.127984i
$120$		0			0
$121$	−34.9660	−	107.614i	−0.288975	−	0.889373i
$122$	−26.6078	+	52.2208i	−0.218097	+	0.428039i
$123$		0			0
$124$			108.548i			0.875384i
$125$	85.3392	+	91.3358i	0.682714	+	0.730686i
$126$		0			0
$127$	26.8016	+	169.219i	0.211036	+	1.33243i	0.834686	+	0.550727i	$0.185649\pi$
$127$	26.8016	+	169.219i	0.211036	+	1.33243i	−0.623649	+	0.781704i	$0.714351\pi$
$128$	58.8911	+	30.0065i	0.460086	+	0.234426i
$129$		0			0
$130$	−28.6729	−	112.063i	−0.220561	−	0.862023i
$131$	−8.07464	+	24.8512i	−0.0616385	+	0.189704i	−0.977134	−	0.212624i	$-0.931799\pi$
$131$	−8.07464	+	24.8512i	−0.0616385	+	0.189704i	0.915495	+	0.402328i	$0.131799\pi$
$132$		0			0
$133$	7.46494	+	14.6508i	0.0561274	+	0.110156i
$134$	−74.1436	−	102.050i	−0.553310	−	0.761566i
$135$		0			0
$136$	180.186	+	130.913i	1.32490	+	0.962593i
$137$	−209.827	−	33.2334i	−1.53159	−	0.242579i	−0.666997	−	0.745060i	$-0.732421\pi$
$137$	−209.827	−	33.2334i	−1.53159	−	0.242579i	−0.864588	+	0.502481i	$0.832421\pi$
$138$		0			0
$139$	23.5058	−	32.3529i	0.169106	−	0.232755i	−0.716050	−	0.698049i	$-0.754052\pi$
$139$	23.5058	−	32.3529i	0.169106	−	0.232755i	0.885156	+	0.465295i	$0.154052\pi$
$140$	4.61881	−	20.5824i	0.0329915	−	0.147017i
$141$		0			0
$142$	−4.21335	+	2.14681i	−0.0296715	+	0.0151184i
$143$	35.4720	−	35.4720i	0.248056	−	0.248056i
$144$		0			0
$145$	77.5436	+	122.416i	0.534784	+	0.844246i
$146$	30.7333	+	94.5873i	0.210502	+	0.647858i
$147$		0			0
$148$	−73.0700	+	11.5732i	−0.493717	+	0.0781970i
$149$			196.500i			1.31879i	0.751797	+	0.659394i	$0.229187\pi$
$149$			196.500i			1.31879i	−0.751797	+	0.659394i	$0.770813\pi$
$150$		0			0
$151$	171.438			1.13535			0.567677	−	0.823251i	$-0.307842\pi$
$151$	171.438			1.13535			0.567677	+	0.823251i	$0.307842\pi$
$152$	11.6240	+	73.3910i	0.0764736	+	0.482835i
$153$		0			0
$154$	−6.22979	+	2.02418i	−0.0404532	+	0.0131440i
$155$	232.368	+	14.8147i	1.49915	+	0.0955787i
$156$		0			0
$157$	−120.559	−	120.559i	−0.767894	−	0.767894i	0.209841	−	0.977735i	$-0.432705\pi$
$157$	−120.559	−	120.559i	−0.767894	−	0.767894i	−0.977735	+	0.209841i	$0.932705\pi$
$158$	−82.2070	−	161.340i	−0.520297	−	1.02114i
$159$		0			0
$160$	79.2950	−	133.825i	0.495594	−	0.836404i
$161$	36.7716	+	26.7161i	0.228395	+	0.165939i
$162$		0			0
$163$	−11.0686	+	69.8841i	−0.0679053	+	0.428737i	0.930192	+	0.367074i	$0.119640\pi$
$163$	−11.0686	+	69.8841i	−0.0679053	+	0.428737i	−0.998097	+	0.0616630i	$0.980360\pi$
$164$	−18.9931	+	26.1418i	−0.115812	+	0.159401i
$165$		0			0
$166$	21.9380	−	15.9389i	0.132157	−	0.0960173i
$167$	104.454	−	53.2219i	0.625473	−	0.318694i	−0.112371	−	0.993666i	$-0.535844\pi$
$167$	104.454	−	53.2219i	0.625473	−	0.318694i	0.737843	+	0.674972i	$0.235844\pi$
$168$		0			0
$169$	−144.245	−	46.8681i	−0.853522	−	0.277326i
$170$	112.236	−	135.439i	0.660210	−	0.796698i
$171$		0			0
$172$	41.6311	−	81.7057i	0.242041	−	0.475033i
$173$	22.3007	−	3.53209i	0.128906	−	0.0204167i	−0.0916480	−	0.995791i	$-0.529213\pi$
$173$	22.3007	−	3.53209i	0.128906	−	0.0204167i	0.220554	+	0.975375i	$0.429213\pi$
$174$		0			0
$175$	−43.4303	−	12.6966i	−0.248173	−	0.0725518i
$176$	−3.48162			−0.0197819
$177$		0			0
$178$	−192.049	−	97.8541i	−1.07893	−	0.549742i
$179$	239.985	−	77.9757i	1.34070	−	0.435619i	0.451144	−	0.892451i	$-0.351016\pi$
$179$	239.985	−	77.9757i	1.34070	−	0.435619i	0.889553	+	0.456833i	$0.151016\pi$
$180$		0			0
$181$	−81.2286	+	249.996i	−0.448777	+	1.38119i	0.429512	+	0.903061i	$0.358686\pi$
$181$	−81.2286	+	249.996i	−0.448777	+	1.38119i	−0.878288	+	0.478131i	$0.841314\pi$
$182$	29.6079	+	29.6079i	0.162681	+	0.162681i
$183$		0			0
$184$	120.730	+	166.171i	0.656142	+	0.903103i
$185$	14.8019	+	158.000i	0.0800105	+	0.854056i
$186$		0			0
$187$	75.3447	+	11.9334i	0.402913	+	0.0638151i
$188$	−15.1100	+	95.4009i	−0.0803725	+	0.507452i
$189$		0			0
$190$	58.4286	−	5.47377i	0.307519	−	0.0288093i
$191$	285.982	−	207.778i	1.49729	−	1.08784i	0.525844	−	0.850581i	$-0.323749\pi$
$191$	285.982	−	207.778i	1.49729	−	1.08784i	0.971445	−	0.237264i	$-0.0762505\pi$
$192$		0			0
$193$	123.500	−	123.500i	0.639896	−	0.639896i	−0.310633	−	0.950530i	$-0.600541\pi$
$193$	123.500	−	123.500i	0.639896	−	0.639896i	0.950530	+	0.310633i	$0.100541\pi$
$194$	43.3681	+	14.0912i	0.223547	+	0.0726348i
$195$		0			0
$196$	−32.9354	−	101.365i	−0.168038	−	0.517166i
$197$	35.4963	−	69.6653i	0.180184	−	0.353631i	−0.783194	−	0.621777i	$-0.786411\pi$
$197$	35.4963	−	69.6653i	0.180184	−	0.353631i	0.963378	+	0.268146i	$0.0864110\pi$
$198$		0			0
$199$			123.408i			0.620143i	0.950713	+	0.310071i	$0.100353\pi$
$199$			123.408i			0.620143i	−0.950713	+	0.310071i	$0.899647\pi$
$200$	−168.926	−	115.216i	−0.844629	−	0.576079i
$201$		0			0
$202$	−1.71211	−	10.8098i	−0.00847577	−	0.0535139i
$203$	−46.7376	−	23.8140i	−0.230235	−	0.117310i
$204$		0			0
$205$	53.3694	+	44.2263i	0.260338	+	0.215738i
$206$	−59.4312	+	182.910i	−0.288501	+	0.887915i
$207$		0			0
$208$	10.1038	+	19.8297i	0.0485758	+	0.0953353i
$209$	14.9593	+	20.5897i	0.0715755	+	0.0985153i
$210$		0			0
$211$	−302.644	−	219.884i	−1.43433	−	1.04210i	−0.989190	−	0.146641i	$-0.953154\pi$
$211$	−302.644	−	219.884i	−1.43433	−	1.04210i	−0.445141	−	0.895461i	$-0.646846\pi$
$212$	−72.8517	−	11.5386i	−0.343640	−	0.0544272i
$213$		0			0
$214$	115.436	−	158.885i	0.539422	−	0.742451i
$215$	−169.225	−	100.271i	−0.787094	−	0.466376i
$216$		0			0
$217$	−75.0979	+	38.2643i	−0.346073	+	0.176333i
$218$	−102.340	+	102.340i	−0.469448	+	0.469448i
$219$		0			0
$220$	2.07737	−	32.5834i	0.00944258	−	0.148106i
$221$	−150.685	−	463.761i	−0.681833	−	2.09847i
$222$		0			0
$223$	99.0917	−	15.6946i	0.444357	−	0.0703793i	0.0697536	−	0.997564i	$-0.477779\pi$
$223$	99.0917	−	15.6946i	0.444357	−	0.0703793i	0.374604	+	0.927185i	$0.377779\pi$
$224$			56.3078i			0.251374i
$225$		0			0
$226$	−16.4612			−0.0728371
$227$	−3.69131	−	23.3060i	−0.0162613	−	0.102670i	0.978223	−	0.207558i	$-0.0665515\pi$
$227$	−3.69131	−	23.3060i	−0.0162613	−	0.102670i	−0.994484	+	0.104888i	$0.966552\pi$
$228$		0			0
$229$	−67.7925	+	22.0271i	−0.296037	+	0.0961883i	−0.453270	−	0.891373i	$-0.649743\pi$
$229$	−67.7925	+	22.0271i	−0.296037	+	0.0961883i	0.157233	+	0.987562i	$0.449743\pi$
$230$	137.038	−	86.8058i	0.595816	−	0.377417i
$231$		0			0
$232$	−167.615	−	167.615i	−0.722479	−	0.722479i
$233$	104.284	+	204.669i	0.447571	+	0.878407i	0.999023	+	0.0442006i	$0.0140741\pi$
$233$	104.284	+	204.669i	0.447571	+	0.878407i	−0.551452	+	0.834207i	$0.685926\pi$
$234$		0			0
$235$	202.162	+	45.3664i	0.860265	+	0.193048i
$236$	−59.9449	−	43.5525i	−0.254004	−	0.184544i
$237$		0			0
$238$	−9.96062	+	62.8889i	−0.0418514	+	0.264239i
$239$	−178.631	+	245.864i	−0.747410	+	1.02872i	0.250748	+	0.968052i	$0.419323\pi$
$239$	−178.631	+	245.864i	−0.747410	+	1.02872i	−0.998158	+	0.0606692i	$0.980677\pi$
$240$		0			0
$241$	−62.1539	+	45.1575i	−0.257900	+	0.187375i	−0.709221	−	0.704986i	$-0.750953\pi$
$241$	−62.1539	+	45.1575i	−0.257900	+	0.187375i	0.451321	+	0.892362i	$0.350953\pi$
$242$	130.250	−	66.3657i	0.538223	−	0.274239i
$243$		0			0
$244$	100.570	+	32.6772i	0.412173	+	0.133923i
$245$	−221.486	+	56.6702i	−0.904024	+	0.231307i
$246$		0			0
$247$	73.8574	−	144.953i	0.299018	−	0.586856i
$248$	−376.192	+	59.5830i	−1.51690	+	0.240254i
$249$		0			0
$250$	−99.2982	+	127.353i	−0.397193	+	0.509410i
$251$	3.29750			0.0131375			0.00656873	−	0.999978i	$-0.497909\pi$
$251$	3.29750			0.0131375			0.00656873	+	0.999978i	$0.497909\pi$
$252$		0			0
$253$	62.6827	+	31.9384i	0.247758	+	0.126239i
$254$	−210.508	+	68.3982i	−0.828772	+	0.269284i
$255$		0			0
$256$	−82.2119	+	253.022i	−0.321140	+	0.988368i
$257$	168.641	+	168.641i	0.656192	+	0.656192i	0.954477	−	0.298285i	$-0.0964146\pi$
$257$	168.641	+	168.641i	0.656192	+	0.656192i	−0.298285	+	0.954477i	$0.596415\pi$
$258$		0			0
$259$	−33.7648	−	46.4733i	−0.130366	−	0.179434i
$260$	−191.609	+	82.7262i	−0.736958	+	0.318178i
$261$		0			0
$262$	−33.3422	−	5.28089i	−0.127260	−	0.0201561i
$263$	−16.3632	+	103.313i	−0.0622174	+	0.392825i	0.936853	+	0.349723i	$0.113724\pi$
$263$	−16.3632	+	103.313i	−0.0622174	+	0.392825i	−0.999071	+	0.0431023i	$0.986276\pi$
$264$		0			0
$265$	−34.6434	+	154.379i	−0.130730	+	0.582560i
$266$	−17.1859	+	12.4863i	−0.0646085	+	0.0469408i
$267$		0			0
$268$	−160.931	+	160.931i	−0.600489	+	0.600489i
$269$	−315.804	−	102.611i	−1.17399	−	0.381453i	−0.343860	−	0.939021i	$-0.611735\pi$
$269$	−315.804	−	102.611i	−1.17399	−	0.381453i	−0.830131	+	0.557568i	$0.811735\pi$
$270$		0			0
$271$	−48.6583	−	149.755i	−0.179551	−	0.552601i	0.820261	−	0.571989i	$-0.193828\pi$
$271$	−48.6583	−	149.755i	−0.179551	−	0.552601i	−0.999812	+	0.0193883i	$0.993828\pi$
$272$	−15.3644	+	30.1543i	−0.0564866	+	0.110861i
$273$		0			0
$274$		−	274.458i		−	1.00167i
$275$	−69.4676	−	8.89402i	−0.252609	−	0.0323419i
$276$		0			0
$277$	78.0548	+	492.819i	0.281786	+	1.77913i	0.570082	+	0.821588i	$0.306911\pi$
$277$	78.0548	+	492.819i	0.281786	+	1.77913i	−0.288295	+	0.957541i	$0.593089\pi$
$278$	46.0331	+	23.4551i	0.165587	+	0.0843707i
$279$		0			0
$280$	73.8674	+	4.70945i	0.263812	+	0.0168195i
$281$	−11.1228	+	34.2324i	−0.0395828	+	0.121823i	−0.968895	−	0.247471i	$-0.920401\pi$
$281$	−11.1228	+	34.2324i	−0.0395828	+	0.121823i	0.929313	+	0.369294i	$0.120401\pi$
$282$		0			0
$283$	−193.095	−	378.969i	−0.682313	−	1.33911i	−0.929022	−	0.370025i	$-0.879349\pi$
$283$	−193.095	−	378.969i	−0.682313	−	1.33911i	0.246709	−	0.969090i	$-0.420651\pi$
$284$	5.01494	+	6.90247i	0.0176582	+	0.0243045i
$285$		0			0
$286$	52.4315	+	38.0937i	0.183327	+	0.133195i
$287$	−24.7813	−	3.92497i	−0.0863458	−	0.0136758i
$288$		0			0
$289$	265.981	−	366.092i	0.920350	−	1.26675i
$290$	−140.532	+	123.687i	−0.484593	+	0.426505i
$291$		0			0
$292$	159.885	−	81.4654i	0.547551	−	0.278991i
$293$	−14.8732	+	14.8732i	−0.0507618	+	0.0507618i	−0.732032	−	0.681270i	$-0.761428\pi$
$293$	−14.8732	+	14.8732i	−0.0507618	+	0.0507618i	0.681270	+	0.732032i	$0.261428\pi$
$294$		0			0
$295$	−101.414	+	122.380i	−0.343776	+	0.414846i
$296$	−80.2178	−	246.885i	−0.271006	−	0.834071i
$297$		0			0
$298$	−250.735	+	39.7126i	−0.841393	+	0.133264i
$299$		−	449.699i		−	1.50401i
$300$		0			0
$301$	71.2029			0.236554
$302$	34.6477	+	218.757i	0.114728	+	0.724361i
$303$		0			0
$304$	−10.7383	+	3.48907i	−0.0353232	+	0.0114772i
$305$	83.6779	−	210.830i	0.274354	−	0.691247i
$306$		0			0
$307$	−53.7073	−	53.7073i	−0.174942	−	0.174942i	0.614205	−	0.789147i	$-0.289477\pi$
$307$	−53.7073	−	53.7073i	−0.174942	−	0.174942i	−0.789147	+	0.614205i	$0.789477\pi$
$308$	5.36555	+	10.5305i	0.0174206	+	0.0341899i
$309$		0			0
$310$	28.0578	+	299.497i	0.0905090	+	0.966120i
$311$	161.560	+	117.380i	0.519485	+	0.377428i	0.816410	−	0.577473i	$-0.195961\pi$
$311$	161.560	+	117.380i	0.519485	+	0.377428i	−0.296925	+	0.954901i	$0.595961\pi$
$312$		0			0
$313$	−26.3462	+	166.343i	−0.0841730	+	0.531447i	0.909186	+	0.416390i	$0.136705\pi$
$313$	−26.3462	+	166.343i	−0.0841730	+	0.531447i	−0.993359	+	0.115057i	$0.963295\pi$
$314$	129.470	−	178.200i	0.412324	−	0.567516i
$315$		0			0
$316$	−264.314	+	192.035i	−0.836436	+	0.607706i
$317$	270.200	−	137.674i	0.852366	−	0.434302i	0.0274941	−	0.999622i	$-0.491247\pi$
$317$	270.200	−	137.674i	0.852366	−	0.434302i	0.824872	+	0.565320i	$0.191247\pi$
$318$		0			0
$319$	−77.2155	−	25.0888i	−0.242055	−	0.0786484i
$320$	209.890	+	83.3048i	0.655907	+	0.260328i
$321$		0			0
$322$	−26.6585	+	52.3202i	−0.0827903	+	0.162485i
$323$	244.343	−	38.7001i	0.756478	−	0.119814i
$324$		0			0
$325$	150.941	+	421.467i	0.464433	+	1.29682i
$326$	−91.4098			−0.280398
$327$		0			0
$328$	−101.025	−	51.4746i	−0.308002	−	0.156935i
$329$	−71.3289	+	23.1762i	−0.216805	+	0.0704442i
$330$		0			0
$331$	134.681	−	414.505i	0.406890	−	1.25228i	−0.512416	−	0.858737i	$-0.671249\pi$
$331$	134.681	−	414.505i	0.406890	−	1.25228i	0.919306	−	0.393543i	$-0.128751\pi$
$332$	−34.5959	−	34.5959i	−0.104204	−	0.104204i
$333$		0			0
$334$	89.0218	+	122.528i	0.266532	+	0.366850i
$335$	322.541	+	366.469i	0.962808	+	1.09394i
$336$		0			0
$337$	−166.306	−	26.3402i	−0.493488	−	0.0781609i	−0.0952699	−	0.995451i	$-0.530371\pi$
$337$	−166.306	−	26.3402i	−0.493488	−	0.0781609i	−0.398218	+	0.917291i	$0.630371\pi$
$338$	30.6522	−	193.530i	0.0906869	−	0.572575i
$339$		0			0
$340$	−273.037	−	161.782i	−0.803050	−	0.475831i
$341$	−105.540	+	76.6793i	−0.309501	+	0.224866i
$342$		0			0
$343$	121.229	−	121.229i	0.353437	−	0.353437i
$344$	306.018	+	99.4312i	0.889587	+	0.289044i
$345$		0			0
$346$	9.01396	+	27.7421i	0.0260519	+	0.0801795i
$347$	17.6279	−	34.5967i	0.0508008	−	0.0997022i	−0.864210	−	0.503131i	$-0.832182\pi$
$347$	17.6279	−	34.5967i	0.0508008	−	0.0997022i	0.915011	+	0.403428i	$0.132182\pi$
$348$		0			0
$349$		−	220.279i		−	0.631173i	−0.948897	−	0.315586i	$-0.897799\pi$
$349$		−	220.279i		−	0.631173i	0.948897	−	0.315586i	$-0.102201\pi$
$350$	7.42369	−	57.9834i	0.0212105	−	0.165667i
$351$		0			0
$352$	13.6337	+	86.0798i	0.0387321	+	0.244545i
$353$	268.455	+	136.785i	0.760495	+	0.387492i	0.790820	−	0.612048i	$-0.209654\pi$
$353$	268.455	+	136.785i	0.760495	+	0.387492i	−0.0303249	+	0.999540i	$0.509654\pi$
$354$		0			0
$355$	15.4605	−	9.79340i	0.0435508	−	0.0275870i
$356$	−120.175	+	369.861i	−0.337571	+	1.03894i
$357$		0			0
$358$	147.999	+	290.464i	0.413404	+	0.811351i
$359$	−140.056	−	192.770i	−0.390127	−	0.536964i	0.568105	−	0.822956i	$-0.307677\pi$
$359$	−140.056	−	192.770i	−0.390127	−	0.536964i	−0.958232	+	0.285992i	$0.907677\pi$
$360$		0			0
$361$	−225.283	−	163.678i	−0.624052	−	0.453400i
$362$	−335.413	−	53.1243i	−0.926556	−	0.146752i
$363$		0			0
$364$	44.4060	−	61.1196i	0.121994	−	0.167911i
$365$	−152.571	−	353.383i	−0.418004	−	0.968174i
$366$		0			0
$367$	624.401	−	318.148i	1.70136	−	0.866888i	0.715650	−	0.698459i	$-0.246130\pi$
$367$	624.401	−	318.148i	1.70136	−	0.866888i	0.985714	−	0.168430i	$-0.0538696\pi$
$368$	−22.0692	+	22.0692i	−0.0599707	+	0.0599707i
$369$		0			0
$370$	−198.618	+	50.8193i	−0.536806	+	0.137349i
$371$	−17.6982	−	54.4693i	−0.0477039	−	0.146818i
$372$		0			0
$373$	−544.089	+	86.1752i	−1.45868	+	0.231033i	−0.834830	−	0.550508i	$-0.814434\pi$
$373$	−544.089	+	86.1752i	−1.45868	+	0.231033i	−0.623854	+	0.781541i	$0.714434\pi$
$374$			98.5522i			0.263509i
$375$		0			0
$376$	−338.924			−0.901393
$377$	81.1869	+	512.594i	0.215350	+	1.35966i
$378$		0			0
$379$	322.888	−	104.913i	0.851946	−	0.276814i	0.149685	−	0.988734i	$-0.452174\pi$
$379$	322.888	−	104.913i	0.851946	−	0.276814i	0.702261	+	0.711920i	$0.252174\pi$
$380$	−26.2460	−	102.578i	−0.0690684	−	0.269942i
$381$		0			0
$382$	322.924	+	322.924i	0.845351	+	0.845351i
$383$	−107.231	−	210.453i	−0.279977	−	0.549486i	0.707601	−	0.706612i	$-0.249777\pi$
$383$	−107.231	−	210.453i	−0.279977	−	0.549486i	−0.987579	+	0.157126i	$0.949777\pi$
$384$		0			0
$385$	23.2749	−	10.0488i	0.0604542	−	0.0261008i
$386$	182.547	+	132.628i	0.472918	+	0.343595i
$387$		0			0
$388$	12.8705	−	81.2614i	0.0331715	−	0.209437i
$389$	415.555	−	571.963i	1.06827	−	1.47034i	0.196446	−	0.980515i	$-0.437060\pi$
$389$	415.555	−	571.963i	1.06827	−	1.47034i	0.871820	−	0.489827i	$-0.162940\pi$
$390$		0			0
$391$	553.237	−	401.950i	1.41493	−	1.02801i
$392$	333.219	−	169.784i	0.850049	−	0.433122i
$393$		0			0
$394$	96.0674	+	31.2142i	0.243826	+	0.0792238i
$395$	375.015	+	592.025i	0.949405	+	1.49880i
$396$		0			0
$397$	−83.9994	+	164.858i	−0.211585	+	0.415260i	−0.972270	−	0.233862i	$-0.924864\pi$
$397$	−83.9994	+	164.858i	−0.211585	+	0.415260i	0.760684	+	0.649122i	$0.224864\pi$
$398$	−157.470	+	24.9408i	−0.395654	+	0.0626654i
$399$		0			0
$400$	13.2762	−	28.0912i	0.0331906	−	0.0702281i
$401$	−652.180			−1.62639			−0.813193	−	0.581995i	$-0.802272\pi$
$401$	−652.180			−1.62639			−0.813193	+	0.581995i	$0.802272\pi$
$402$		0			0
$403$	743.011	+	378.583i	1.84370	+	0.939412i
$404$	−18.7804	+	6.10212i	−0.0464861	+	0.0151043i
$405$		0			0
$406$	20.9412	−	64.4504i	0.0515793	−	0.158745i
$407$	−62.8700	−	62.8700i	−0.154472	−	0.154472i
$408$		0			0
$409$	−355.310	−	489.043i	−0.868730	−	1.19570i	−0.979417	−	0.201849i	$-0.935305\pi$
$409$	−355.310	−	489.043i	−0.868730	−	1.19570i	0.110687	−	0.993855i	$-0.464695\pi$
$410$	−45.6472	+	77.0379i	−0.111335	+	0.187897i
$411$		0			0
$412$	342.730	+	54.2831i	0.831869	+	0.131755i
$413$	9.00022	−	56.8251i	0.0217923	−	0.137591i
$414$		0			0
$415$	−78.7809	+	69.3376i	−0.189834	+	0.167078i
$416$	450.707	−	327.458i	1.08343	−	0.787158i
$417$		0			0
$418$	−23.2494	+	23.2494i	−0.0556205	+	0.0556205i
$419$	282.385	+	91.7525i	0.673950	+	0.218980i	0.625945	−	0.779867i	$-0.284714\pi$
$419$	282.385	+	91.7525i	0.673950	+	0.218980i	0.0480053	+	0.998847i	$0.484714\pi$
$420$		0			0
$421$	−170.801	−	525.672i	−0.405704	−	1.24863i	−0.920306	−	0.391199i	$-0.872060\pi$
$421$	−170.801	−	525.672i	−0.405704	−	1.24863i	0.514602	−	0.857429i	$-0.327940\pi$
$422$	219.409	−	430.615i	0.519927	−	1.02041i
$423$		0			0
$424$		−	258.815i		−	0.610412i
$425$	−383.591	+	562.409i	−0.902568	+	1.32332i
$426$		0			0
$427$	12.8446	+	81.0978i	0.0300811	+	0.189925i
$428$	−315.722	−	160.868i	−0.737668	−	0.375861i
$429$		0			0
$430$	93.7461	−	236.198i	0.218014	−	0.549297i
$431$	−69.6929	+	214.493i	−0.161700	+	0.497663i	−0.998778	−	0.0494214i	$-0.984262\pi$
$431$	−69.6929	+	214.493i	−0.161700	+	0.497663i	0.837078	+	0.547084i	$0.184262\pi$
$432$		0			0
$433$	−87.9085	−	172.530i	−0.203022	−	0.398453i	0.766937	−	0.641723i	$-0.221780\pi$
$433$	−87.9085	−	172.530i	−0.203022	−	0.398453i	−0.969959	+	0.243270i	$0.921780\pi$
$434$	−64.0028	−	88.0924i	−0.147472	−	0.202978i
$435$		0			0
$436$	211.260	+	153.489i	0.484540	+	0.352039i
$437$	225.337	+	35.6899i	0.515646	+	0.0816704i
$438$		0			0
$439$	−424.325	+	584.033i	−0.966571	+	1.33037i	−0.0228109	+	0.999740i	$0.507262\pi$
$439$	−424.325	+	584.033i	−0.966571	+	1.33037i	−0.943760	+	0.330631i	$0.892738\pi$
$440$	114.064	−	10.6859i	0.259236	−	0.0242860i
$441$		0			0
$442$	561.310	−	286.002i	1.26993	−	0.647063i
$443$	324.984	−	324.984i	0.733599	−	0.733599i	−0.237732	−	0.971331i	$-0.576404\pi$
$443$	324.984	−	324.984i	0.733599	−	0.733599i	0.971331	+	0.237732i	$0.0764040\pi$
$444$		0			0
$445$	775.359	+	307.738i	1.74238	+	0.691545i
$446$	40.0529	+	123.270i	0.0898046	+	0.276390i
$447$		0			0
$448$	−80.7362	+	12.7874i	−0.180215	+	0.0285432i
$449$			76.3546i			0.170055i	0.996379	+	0.0850274i	$0.0270978\pi$
$449$			76.3546i			0.170055i	−0.996379	+	0.0850274i	$0.972902\pi$
$450$		0			0
$451$	−38.8343			−0.0861072
$452$	4.64615	+	29.3347i	0.0102791	+	0.0648997i
$453$		0			0
$454$	28.9927	−	9.42030i	0.0638606	−	0.0207496i
$455$	−124.778	−	103.401i	−0.274237	−	0.227256i
$456$		0			0
$457$	307.229	+	307.229i	0.672273	+	0.672273i	0.958240	−	0.285967i	$-0.0923147\pi$
$457$	307.229	+	307.229i	0.672273	+	0.672273i	−0.285967	+	0.958240i	$0.592315\pi$
$458$	−41.8077	−	82.0522i	−0.0912831	−	0.179153i
$459$		0			0
$460$	−193.371	−	219.707i	−0.420372	−	0.477624i
$461$	338.793	+	246.148i	0.734909	+	0.533943i	0.891113	−	0.453782i	$-0.149926\pi$
$461$	338.793	+	246.148i	0.734909	+	0.533943i	−0.156204	+	0.987725i	$0.549926\pi$
$462$		0			0
$463$	−53.8967	+	340.290i	−0.116408	+	0.734969i	0.858575	+	0.512688i	$0.171350\pi$
$463$	−53.8967	+	340.290i	−0.116408	+	0.734969i	−0.974983	+	0.222281i	$0.928650\pi$
$464$	21.1715	−	29.1401i	0.0456283	−	0.0628019i
$465$		0			0
$466$	−240.084	+	174.431i	−0.515201	+	0.374315i
$467$	−157.765	+	80.3853i	−0.337827	+	0.172131i	−0.614671	−	0.788783i	$-0.710711\pi$
$467$	−157.765	+	80.3853i	−0.337827	+	0.172131i	0.276845	+	0.960915i	$0.410711\pi$
$468$		0			0
$469$	−168.069	−	54.6089i	−0.358356	−	0.116437i
$470$	−17.0309	+	267.129i	−0.0362361	+	0.568360i
$471$		0			0
$472$	118.035	−	231.656i	0.250074	−	0.490797i
$473$	108.850	−	17.2402i	0.230128	−	0.0364486i
$474$		0			0
$475$	−223.170	+	42.1847i	−0.469832	+	0.0888100i
$476$	114.883			0.241350
$477$		0			0
$478$	−349.827	−	178.246i	−0.731855	−	0.372899i
$479$	342.771	−	111.373i	0.715597	−	0.232512i	0.0714837	−	0.997442i	$-0.477227\pi$
$479$	342.771	−	111.373i	0.715597	−	0.232512i	0.644113	+	0.764930i	$0.277227\pi$
$480$		0			0
$481$	−175.629	+	540.530i	−0.365133	+	1.12376i
$482$	−70.1827	−	70.1827i	−0.145607	−	0.145607i
$483$		0			0
$484$	−155.030	−	213.381i	−0.320310	−	0.440869i
$485$	−172.199	−	38.6426i	−0.355050	−	0.0796754i
$486$		0			0
$487$	−432.824	−	68.5526i	−0.888756	−	0.140765i	−0.304671	−	0.952458i	$-0.598547\pi$
$487$	−432.824	−	68.5526i	−0.888756	−	0.140765i	−0.584085	+	0.811692i	$0.698547\pi$
$488$	−58.0449	+	366.481i	−0.118945	+	0.750986i
$489$		0			0
$490$	−117.074	−	271.165i	−0.238927	−	0.553398i
$491$	−480.359	+	349.001i	−0.978328	+	0.710797i	−0.957334	−	0.288983i	$-0.906683\pi$
$491$	−480.359	+	349.001i	−0.978328	+	0.710797i	−0.0209938	+	0.999780i	$0.506683\pi$
$492$		0			0
$493$	−558.046	+	558.046i	−1.13194	+	1.13194i
$494$	199.888	+	64.9477i	0.404632	+	0.131473i
$495$		0			0
$496$	−17.8845	−	55.0428i	−0.0360575	−	0.110973i
$497$	−3.00760	+	5.90274i	−0.00605151	+	0.0118767i
$498$		0			0
$499$			471.200i			0.944289i	0.881521	+	0.472145i	$0.156520\pi$
$499$			471.200i			0.944289i	−0.881521	+	0.472145i	$0.843480\pi$
$500$	254.976	+	141.009i	0.509951	+	0.282019i
$501$		0			0
$502$	0.666426	+	4.20765i	0.00132754	+	0.00838177i
$503$	−245.179	−	124.925i	−0.487434	−	0.248360i	0.192960	−	0.981207i	$-0.438191\pi$
$503$	−245.179	−	124.925i	−0.487434	−	0.248360i	−0.680394	+	0.732847i	$0.738191\pi$
$504$		0			0
$505$	10.4996	+	41.0360i	0.0207913	+	0.0812593i
$506$	−28.0856	+	86.4385i	−0.0555051	+	0.170827i
$507$		0			0
$508$	181.305	+	355.831i	0.356899	+	0.700454i
$509$	99.5633	+	137.037i	0.195606	+	0.269228i	0.895542	−	0.444977i	$-0.146788\pi$
$509$	99.5633	+	137.037i	0.195606	+	0.269228i	−0.699936	+	0.714205i	$0.746788\pi$
$510$		0			0
$511$	112.722	+	81.8977i	0.220592	+	0.160269i
$512$	−78.3486	−	12.4092i	−0.153025	−	0.0242367i
$513$		0			0
$514$	−181.105	+	249.270i	−0.352345	+	0.484961i
$515$	162.980	−	726.273i	0.316466	−	1.41024i
$516$		0			0
$517$	−103.431	+	52.7009i	−0.200061	+	0.101936i
$518$	52.4765	−	52.4765i	0.101306	−	0.101306i
$519$		0			0
$520$	−391.879	−	618.647i	−0.753614	−	1.18971i
$521$	−222.241	−	683.987i	−0.426566	−	1.31284i	−0.901487	−	0.432807i	$-0.857523\pi$
$521$	−222.241	−	683.987i	−0.426566	−	1.31284i	0.474920	−	0.880029i	$-0.342477\pi$
$522$		0			0
$523$	154.804	−	24.5185i	0.295991	−	0.0468804i	−0.00667264	−	0.999978i	$-0.502124\pi$
$523$	154.804	−	24.5185i	0.295991	−	0.0468804i	0.302664	+	0.953097i	$0.402124\pi$
$524$			60.9081i			0.116237i
$525$		0			0
$526$	−135.135			−0.256911
$527$	198.371	+	1252.47i	0.376416	+	2.37660i
$528$		0			0
$529$	96.6746	−	31.4115i	0.182750	−	0.0593790i
$530$	−203.990	−	13.0055i	−0.384886	−	0.0245386i
$531$		0			0
$532$	27.1018	+	27.1018i	0.0509433	+	0.0509433i
$533$	112.698	+	221.183i	0.211442	+	0.414978i
$534$		0			0
$535$	−387.461	+	653.910i	−0.724225	+	1.22226i
$536$	−646.073	−	469.400i	−1.20536	−	0.875746i
$537$		0			0
$538$	67.1084	−	423.706i	0.124737	−	0.787558i
$539$	75.2900	−	103.628i	0.139685	−	0.192259i
$540$		0			0
$541$	−16.6570	+	12.1020i	−0.0307893	+	0.0223698i	−0.603073	−	0.797686i	$-0.706057\pi$
$541$	−16.6570	+	12.1020i	−0.0307893	+	0.0223698i	0.572284	+	0.820055i	$0.306057\pi$
$542$	181.255	−	92.3539i	0.334418	−	0.170395i
$543$		0			0
$544$	805.702	+	261.789i	1.48107	+	0.481229i
$545$	357.406	−	431.294i	0.655792	−	0.791366i
$546$		0			0
$547$	−114.427	+	224.575i	−0.209190	+	0.410558i	−0.971632	−	0.236499i	$-0.924000\pi$
$547$	−114.427	+	224.575i	−0.209190	+	0.410558i	0.762442	+	0.647056i	$0.224000\pi$
$548$	−489.098	+	77.4655i	−0.892515	+	0.141360i
$549$		0			0
$550$	−2.69054	−	90.4388i	−0.00489190	−	0.164434i
$551$	−263.296			−0.477852
$552$		0			0
$553$	−226.032	−	115.169i	−0.408737	−	0.208262i
$554$	−613.067	+	199.197i	−1.10662	+	0.359562i
$555$		0			0
$556$	28.8053	−	88.6536i	0.0518081	−	0.159449i
$557$	−587.229	−	587.229i	−1.05427	−	1.05427i	−0.998440	−	0.0558301i	$-0.982219\pi$
$557$	−587.229	−	587.229i	−1.05427	−	1.05427i	−0.0558301	−	0.998440i	$-0.517781\pi$
$558$		0			0
$559$	−414.080	−	569.932i	−0.740751	−	1.01956i
$560$	1.04906	+	11.1980i	0.00187333	+	0.0199965i
$561$		0			0
$562$	−45.9287	−	7.27440i	−0.0817237	−	0.0129438i
$563$	142.523	−	899.852i	0.253148	−	1.59832i	−0.453835	−	0.891086i	$-0.649944\pi$
$563$	142.523	−	899.852i	0.253148	−	1.59832i	0.706983	−	0.707230i	$-0.250056\pi$
$564$		0			0
$565$	63.4307	−	5.94238i	0.112267	−	0.0105175i
$566$	444.544	−	322.980i	0.785414	−	0.570636i
$567$		0			0
$568$	−21.1690	+	21.1690i	−0.0372694	+	0.0372694i
$569$	−882.800	−	286.839i	−1.55149	−	0.504111i	−0.596974	−	0.802260i	$-0.703631\pi$
$569$	−882.800	−	286.839i	−1.55149	−	0.504111i	−0.954519	+	0.298150i	$0.903631\pi$
$570$		0			0
$571$	−93.5955	−	288.057i	−0.163915	−	0.504479i	0.835040	−	0.550190i	$-0.185445\pi$
$571$	−93.5955	−	288.057i	−0.163915	−	0.504479i	−0.998955	+	0.0457110i	$0.985445\pi$
$572$	53.0862	−	104.188i	0.0928081	−	0.182146i
$573$		0			0
$574$		−	32.4143i		−	0.0564710i
$575$	−496.718	+	383.963i	−0.863857	+	0.667762i
$576$		0			0
$577$	−96.9341	−	612.018i	−0.167997	−	1.06069i	−0.917223	−	0.398375i	$-0.869574\pi$
$577$	−96.9341	−	612.018i	−0.167997	−	1.06069i	0.749226	−	0.662314i	$-0.230426\pi$
$578$	520.891	+	265.407i	0.901196	+	0.459182i
$579$		0			0
$580$	260.081	+	215.525i	0.448415	+	0.371594i
$581$	11.7395	−	36.1303i	0.0202056	−	0.0621864i
$582$		0			0
$583$	−40.2444	−	78.9840i	−0.0690298	−	0.135479i
$584$	370.096	+	509.393i	0.633726	+	0.872249i
$585$		0			0
$586$	−21.9842	−	15.9725i	−0.0375157	−	0.0272568i
$587$	−1039.32	−	164.612i	−1.77056	−	0.280429i	−0.815915	−	0.578173i	$-0.803766\pi$
$587$	−1039.32	−	164.612i	−1.77056	−	0.280429i	−0.954646	+	0.297743i	$0.903766\pi$
$588$		0			0
$589$	−248.671	+	342.266i	−0.422191	+	0.581096i
$590$	−176.653	−	104.672i	−0.299412	−	0.177411i
$591$		0			0
$592$	35.1459	−	17.9077i	0.0593680	−	0.0302495i
$593$	−707.610	+	707.610i	−1.19327	+	1.19327i	−0.217129	+	0.976143i	$0.569669\pi$
$593$	−707.610	+	707.610i	−1.19327	+	1.19327i	−0.976143	+	0.217129i	$0.930331\pi$
$594$		0			0
$595$	15.6793	−	245.929i	0.0263517	−	0.413326i
$596$	141.540	+	435.614i	0.237483	+	0.730896i
$597$		0			0
$598$	573.820	−	90.8842i	0.959566	−	0.151980i
$599$			170.870i			0.285259i	0.989776	+	0.142630i	$0.0455558\pi$
$599$			170.870i			0.285259i	−0.989776	+	0.142630i	$0.954444\pi$
$600$		0			0
$601$	236.135			0.392903			0.196452	−	0.980513i	$-0.437058\pi$
$601$	236.135			0.392903			0.196452	+	0.980513i	$0.437058\pi$
$602$	14.3901	+	90.8555i	0.0239038	+	0.150923i
$603$		0			0
$604$	380.057	−	123.488i	0.629233	−	0.204450i
$605$	−477.942	+	302.750i	−0.789986	+	0.500413i
$606$		0			0
$607$	−295.001	−	295.001i	−0.485998	−	0.485998i	0.421042	−	0.907041i	$-0.361664\pi$
$607$	−295.001	−	295.001i	−0.485998	−	0.485998i	−0.907041	+	0.421042i	$0.861664\pi$
$608$	128.314	+	251.831i	0.211043	+	0.414195i
$609$		0			0
$610$	285.933	+	64.1650i	0.468742	+	0.105189i
$611$	600.322	+	436.160i	0.982524	+	0.713845i
$612$		0			0
$613$	112.568	−	710.725i	0.183634	−	1.15942i	−0.707848	−	0.706365i	$-0.750334\pi$
$613$	112.568	−	710.725i	0.183634	−	1.15942i	0.891482	−	0.453056i	$-0.149666\pi$
$614$	57.6768	−	79.3852i	0.0939361	−	0.129292i
$615$		0			0
$616$	−33.5501	+	24.3756i	−0.0544645	+	0.0395708i
$617$	732.469	−	373.211i	1.18715	−	0.604881i	0.254992	−	0.966943i	$-0.417927\pi$
$617$	732.469	−	373.211i	1.18715	−	0.604881i	0.932154	+	0.362062i	$0.117927\pi$
$618$		0			0
$619$	360.303	+	117.070i	0.582073	+	0.189127i	0.585229	−	0.810868i	$-0.301005\pi$
$619$	360.303	+	117.070i	0.582073	+	0.189127i	−0.00315628	+	0.999995i	$0.501005\pi$
$620$	525.800	−	134.533i	0.848065	−	0.216989i
$621$		0			0
$622$	−117.127	+	229.874i	−0.188307	+	0.369573i
$623$	−298.249	+	47.2379i	−0.478730	+	0.0758234i
$624$		0			0
$625$	336.657	−	526.580i	0.538652	−	0.842528i
$626$	−217.580			−0.347572
$627$		0			0
$628$	−354.104	−	180.425i	−0.563860	−	0.287301i
$629$	−821.961	+	267.071i	−1.30678	+	0.424597i
$630$		0			0
$631$	−102.961	+	316.882i	−0.163171	+	0.502190i	−0.998897	−	0.0469574i	$-0.985048\pi$
$631$	−102.961	+	316.882i	−0.163171	+	0.502190i	0.835725	+	0.549148i	$0.185048\pi$
$632$	−810.618	−	810.618i	−1.28262	−	1.28262i
$633$		0			0
$634$	230.280	+	316.954i	0.363218	+	0.499927i
$635$	786.470	−	339.554i	1.23854	−	0.534731i
$636$		0			0
$637$	−808.712	−	128.087i	−1.26956	−	0.201079i
$638$	16.4083	−	103.598i	0.0257184	−	0.162380i
$639$		0			0
$640$	72.3609	−	322.456i	0.113064	−	0.503837i
$641$	340.793	−	247.601i	0.531659	−	0.386273i	−0.289319	−	0.957233i	$-0.593429\pi$
$641$	340.793	−	247.601i	0.531659	−	0.386273i	0.820978	+	0.570960i	$0.193429\pi$
$642$		0			0
$643$	456.781	−	456.781i	0.710391	−	0.710391i	−0.256226	−	0.966617i	$-0.582479\pi$
$643$	456.781	−	456.781i	0.710391	−	0.710391i	0.966617	+	0.256226i	$0.0824792\pi$
$644$	100.762	+	32.7394i	0.156462	+	0.0508376i
$645$		0			0
$646$	98.7633	+	303.962i	0.152884	+	0.470530i
$647$	19.6573	−	38.5797i	0.0303823	−	0.0596286i	−0.875316	−	0.483551i	$-0.839347\pi$
$647$	19.6573	−	38.5797i	0.0303823	−	0.0596286i	0.905699	+	0.423922i	$0.139347\pi$
$648$		0			0
$649$		−	89.0498i		−	0.137211i
$650$	−507.291	+	277.780i	−0.780448	+	0.427354i
$651$		0			0
$652$	25.8003	+	162.897i	0.0395710	+	0.249842i
$653$	−41.4282	−	21.1087i	−0.0634428	−	0.0323257i	0.421981	−	0.906605i	$-0.361335\pi$
$653$	−41.4282	−	21.1087i	−0.0634428	−	0.0323257i	−0.485424	+	0.874279i	$0.661335\pi$
$654$		0			0
$655$	130.386	+	8.31280i	0.199062	+	0.0126913i
$656$	5.32394	−	16.3854i	0.00811577	−	0.0249778i
$657$		0			0
$658$	−43.9886	−	86.3324i	−0.0668519	−	0.131204i
$659$	92.1880	+	126.886i	0.139891	+	0.192543i	0.873214	−	0.487337i	$-0.162032\pi$
$659$	92.1880	+	126.886i	0.139891	+	0.192543i	−0.733323	+	0.679880i	$0.762032\pi$
$660$		0			0
$661$	397.805	+	289.023i	0.601824	+	0.437251i	0.846526	−	0.532348i	$-0.178690\pi$
$661$	397.805	+	289.023i	0.601824	+	0.437251i	−0.244702	+	0.969598i	$0.578690\pi$
$662$	556.131	+	88.0825i	0.840077	+	0.133055i
$663$		0			0
$664$	100.908	−	138.888i	0.151970	−	0.209169i
$665$	61.7157	−	54.3179i	0.0928056	−	0.0816811i
$666$		0			0
$667$	−648.485	+	330.420i	−0.972242	+	0.495382i
$668$	193.225	−	193.225i	0.289259	−	0.289259i
$669$		0			0
$670$	−402.432	+	485.628i	−0.600645	+	0.724818i
$671$	39.2721	+	120.867i	0.0585277	+	0.180130i
$672$		0			0
$673$	135.747	−	21.5002i	0.201705	−	0.0319469i	−0.0547645	−	0.998499i	$-0.517441\pi$
$673$	135.747	−	21.5002i	0.201705	−	0.0319469i	0.256469	+	0.966552i	$0.417441\pi$
$674$		−	217.531i		−	0.322746i
$675$		0			0
$676$	−353.532			−0.522977
$677$	116.940	+	738.328i	0.172732	+	1.09059i	0.909885	+	0.414861i	$0.136170\pi$
$677$	116.940	+	738.328i	0.172732	+	1.09059i	−0.737153	+	0.675726i	$0.763830\pi$
$678$		0			0
$679$	60.7571	−	19.7412i	0.0894803	−	0.0290739i
$680$	410.814	−	1035.06i	0.604138	−	1.52215i
$681$		0			0
$682$	−119.173	−	119.173i	−0.174741	−	0.174741i
$683$	76.7144	+	150.561i	0.112320	+	0.220440i	0.940323	−	0.340284i	$-0.110523\pi$
$683$	76.7144	+	150.561i	0.112320	+	0.220440i	−0.828003	+	0.560724i	$0.810523\pi$
$684$		0			0
$685$	99.0776	+	1057.58i	0.144639	+	1.54392i
$686$	179.190	+	130.189i	0.261209	+	0.189780i
$687$		0			0
$688$	−7.64853	+	48.2909i	−0.0111170	+	0.0701903i
$689$	−333.068	+	458.428i	−0.483407	+	0.665353i
$690$		0			0
$691$	805.662	−	585.348i	1.16594	−	0.847103i	0.175420	−	0.984494i	$-0.443872\pi$
$691$	805.662	−	585.348i	1.16594	−	0.847103i	0.990517	+	0.137391i	$0.0438717\pi$
$692$	46.8937	−	23.8935i	0.0677655	−	0.0345282i
$693$		0			0
$694$	47.7083	+	15.5014i	0.0687439	+	0.0223363i
$695$	−185.849	−	73.7629i	−0.267409	−	0.106134i
$696$		0			0
$697$	−171.376	+	336.344i	−0.245876	+	0.482560i
$698$	281.078	−	44.5185i	0.402691	−	0.0637800i
$699$		0			0
$700$	−105.425	+	3.13637i	−0.150607	+	0.00448053i
$701$	444.962			0.634753			0.317376	−	0.948300i	$-0.397198\pi$
$701$	444.962			0.634753			0.317376	+	0.948300i	$0.397198\pi$
$702$		0			0
$703$	−256.913	−	130.904i	−0.365452	−	0.186207i
$704$	−120.328	+	39.0970i	−0.170921	+	0.0555355i
$705$		0			0
$706$	−120.284	+	370.195i	−0.170373	+	0.524356i
$707$	−10.8420	−	10.8420i	−0.0153352	−	0.0153352i
$708$		0			0
$709$	−110.671	−	152.325i	−0.156094	−	0.214845i	0.723806	−	0.690003i	$-0.242391\pi$
$709$	−110.671	−	152.325i	−0.156094	−	0.214845i	−0.879900	+	0.475158i	$0.842391\pi$
$710$	15.6210	+	17.7485i	0.0220015	+	0.0249979i
$711$		0			0
$712$	−1347.79	−	213.469i	−1.89296	−	0.299815i
$713$	−182.942	+	1155.05i	−0.256580	+	1.61998i
$714$		0			0
$715$	−215.789	−	127.861i	−0.301802	−	0.178827i
$716$	475.849	−	345.724i	0.664593	−	0.482855i
$717$		0			0
$718$	217.671	−	217.671i	0.303163	−	0.303163i
$719$	−40.6847	−	13.2193i	−0.0565852	−	0.0183856i	0.280588	−	0.959828i	$-0.409471\pi$
$719$	−40.6847	−	13.2193i	−0.0565852	−	0.0183856i	−0.337173	+	0.941443i	$0.609471\pi$
$720$		0			0
$721$	83.2609	+	256.251i	0.115480	+	0.355410i
$722$	163.324	−	320.542i	0.226211	−	0.443964i
$723$		0			0
$724$			612.718i			0.846296i
$725$	496.869	−	527.339i	0.685336	−	0.727364i
$726$		0			0
$727$	59.7654	+	377.344i	0.0822082	+	0.519042i	0.994087	+	0.108583i	$0.0346314\pi$
$727$	59.7654	+	377.344i	0.0822082	+	0.519042i	−0.911879	+	0.410459i	$0.865369\pi$
$728$	236.196	+	120.348i	0.324445	+	0.165313i
$729$		0			0
$730$	420.086	−	266.101i	0.575460	−	0.364522i
$731$	331.039	−	1018.83i	0.452858	−	1.39375i
$732$		0			0
$733$	119.985	+	235.483i	0.163690	+	0.321260i	0.958253	−	0.285922i	$-0.0922999\pi$
$733$	119.985	+	235.483i	0.163690	+	0.321260i	−0.794563	+	0.607182i	$0.792300\pi$
$734$	532.151	+	732.443i	0.725002	+	0.997879i
$735$		0			0
$736$	632.063	+	459.220i	0.858781	+	0.623941i
$737$	−270.155	−	42.7884i	−0.366561	−	0.0580576i
$738$		0			0
$739$	−283.341	+	389.986i	−0.383412	+	0.527721i	−0.956484	−	0.291784i	$-0.905751\pi$
$739$	−283.341	+	389.986i	−0.383412	+	0.527721i	0.573073	+	0.819505i	$0.305751\pi$
$740$	146.622	+	339.604i	0.198138	+	0.458925i
$741$		0			0
$742$	65.9266	−	33.5913i	0.0888499	−	0.0452713i
$743$	−265.405	+	265.405i	−0.357207	+	0.357207i	−0.862783	−	0.505575i	$-0.831280\pi$
$743$	−265.405	+	265.405i	−0.357207	+	0.357207i	0.505575	+	0.862783i	$0.331280\pi$
$744$		0			0
$745$	951.835	−	243.540i	1.27763	−	0.326900i
$746$	−219.921	−	676.847i	−0.294800	−	0.907301i
$747$		0			0
$748$	175.625	−	27.8163i	0.234793	−	0.0371875i
$749$		−	275.138i		−	0.367340i
$750$		0			0
$751$	−518.509			−0.690425			−0.345213	−	0.938525i	$-0.612193\pi$
$751$	−518.509			−0.690425			−0.345213	+	0.938525i	$0.612193\pi$
$752$	−8.05637	−	50.8659i	−0.0107133	−	0.0676408i
$753$		0			0
$754$	−637.666	+	207.190i	−0.845711	+	0.274788i
$755$	−212.480	−	830.440i	−0.281430	−	1.09992i
$756$		0			0
$757$	−378.952	−	378.952i	−0.500598	−	0.500598i	0.411026	−	0.911624i	$-0.365171\pi$
$757$	−378.952	−	378.952i	−0.500598	−	0.500598i	−0.911624	+	0.411026i	$0.865171\pi$
$758$	199.125	+	390.805i	0.262698	+	0.515574i
$759$		0			0
$760$	341.096	−	147.266i	0.448810	−	0.193771i
$761$	280.723	+	203.957i	0.368886	+	0.268012i	0.756749	−	0.653706i	$-0.226786\pi$
$761$	280.723	+	203.957i	0.368886	+	0.268012i	−0.387863	+	0.921717i	$0.626786\pi$
$762$		0			0
$763$	−31.7189	+	200.265i	−0.0415712	+	0.262470i
$764$	484.322	−	666.612i	0.633929	−	0.872529i
$765$		0			0
$766$	246.869	−	179.361i	0.322283	−	0.234152i
$767$	−507.188	+	258.425i	−0.661262	+	0.336930i
$768$		0			0
$769$	−359.323	−	116.751i	−0.467260	−	0.151822i	0.0659183	−	0.997825i	$-0.479002\pi$
$769$	−359.323	−	116.751i	−0.467260	−	0.151822i	−0.533178	+	0.846003i	$0.679002\pi$
$770$	17.5262	+	27.6681i	0.0227613	+	0.0359326i
$771$		0			0
$772$	184.826	−	362.741i	0.239412	−	0.469872i
$773$	1356.16	−	214.795i	1.75441	−	0.277871i	0.805313	−	0.592850i	$-0.201997\pi$
$773$	1356.16	−	214.795i	1.75441	−	0.277871i	0.949099	+	0.314979i	$0.101997\pi$
$774$		0			0
$775$	−216.233	−	1143.94i	−0.279011	−	1.47605i
$776$	288.691			0.372025
$777$		0			0
$778$	813.814	+	414.659i	1.04603	+	0.532980i
$779$	−119.776	+	38.9175i	−0.153756	+	0.0499583i
$780$		0			0
$781$	−3.16860	+	9.75196i	−0.00405711	+	0.0124865i
$782$	624.702	+	624.702i	0.798851	+	0.798851i
$783$		0			0
$784$	33.4020	+	45.9739i	0.0426046	+	0.0586402i
$785$	−434.564	+	733.405i	−0.553584	+	0.934274i
$786$		0			0
$787$	121.855	+	19.2999i	0.154835	+	0.0245234i	0.233370	−	0.972388i	$-0.425025\pi$
$787$	121.855	+	19.2999i	0.154835	+	0.0245234i	−0.0785359	+	0.996911i	$0.525025\pi$
$788$	28.5103	−	180.007i	0.0361806	−	0.228435i
$789$		0			0
$790$	−679.638	+	598.171i	−0.860302	+	0.757178i
$791$	−18.6571	+	13.5552i	−0.0235868	+	0.0171368i
$792$		0			0
$793$	574.436	−	574.436i	0.724383	−	0.724383i
$794$	−227.337	−	73.8662i	−0.286318	−	0.0930305i
$795$		0			0
$796$	88.8917	+	273.580i	0.111673	+	0.343694i
$797$	132.075	−	259.211i	0.165715	−	0.325234i	−0.793184	−	0.608982i	$-0.791578\pi$
$797$	132.075	−	259.211i	0.165715	−	0.325234i	0.958899	+	0.283748i	$0.0915781\pi$
$798$		0			0
$799$			1128.39i			1.41225i
$800$	−746.519	−	218.240i	−0.933148	−	0.272800i
$801$		0			0
$802$	−131.806	−	832.188i	−0.164346	−	1.03764i
$803$	192.153	+	97.9066i	0.239293	+	0.121926i
$804$		0			0
$805$	83.8372	−	211.232i	0.104146	−	0.262399i
$806$	−332.913	+	1024.60i	−0.413043	+	1.27122i
$807$		0			0
$808$	−31.4568	−	61.7374i	−0.0389317	−	0.0764077i
$809$	791.643	+	1089.60i	0.978545	+	1.34685i	0.937610	+	0.347689i	$0.113034\pi$
$809$	791.643	+	1089.60i	0.978545	+	1.34685i	0.0409347	+	0.999162i	$0.486966\pi$
$810$		0			0
$811$	351.764	+	255.572i	0.433742	+	0.315132i	0.783143	−	0.621841i	$-0.213615\pi$
$811$	351.764	+	255.572i	0.433742	+	0.315132i	−0.349402	+	0.936973i	$0.613615\pi$
$812$	−120.765	−	19.1272i	−0.148725	−	0.0235557i
$813$		0			0
$814$	67.5166	−	92.9287i	0.0829443	−	0.114163i
$815$	352.234	−	32.9983i	0.432189	−	0.0404888i
$816$		0			0
$817$	318.447	−	162.257i	0.389776	−	0.198601i
$818$	552.215	−	552.215i	0.675079	−	0.675079i
$819$		0			0
$820$	150.169	+	59.6018i	0.183133	+	0.0726851i
$821$	86.2266	+	265.378i	0.105026	+	0.323238i	0.989737	−	0.142903i	$-0.0456438\pi$
$821$	86.2266	+	265.378i	0.105026	+	0.323238i	−0.884710	+	0.466141i	$0.845644\pi$
$822$		0			0
$823$	821.134	−	130.055i	0.997733	−	0.158025i	0.363853	−	0.931457i	$-0.381461\pi$
$823$	821.134	−	130.055i	0.997733	−	0.158025i	0.633880	+	0.773431i	$0.281461\pi$
$824$			1217.59i			1.47766i
$825$		0			0
$826$	74.3284			0.0899859
$827$	76.1777	+	480.967i	0.0921133	+	0.581580i	0.989968	+	0.141289i	$0.0451248\pi$
$827$	76.1777	+	480.967i	0.0921133	+	0.581580i	−0.897855	+	0.440291i	$0.854875\pi$
$828$		0			0
$829$	718.878	−	233.578i	0.867163	−	0.281758i	0.158546	−	0.987352i	$-0.449319\pi$
$829$	718.878	−	233.578i	0.867163	−	0.281758i	0.708617	+	0.705593i	$0.249319\pi$
$830$	−104.397	−	86.5121i	−0.125780	−	0.104231i
$831$		0			0
$832$	571.875	+	571.875i	0.687350	+	0.687350i
$833$	−565.265	−	1109.40i	−0.678590	−	1.33181i
$834$		0			0
$835$	−387.264	−	440.007i	−0.463789	−	0.526955i
$836$	47.9937	+	34.8694i	0.0574087	+	0.0417099i
$837$		0			0
$838$	−60.0070	+	378.869i	−0.0716074	+	0.452111i
$839$	−170.239	+	234.314i	−0.202907	+	0.279278i	−0.898328	−	0.439325i	$-0.855218\pi$
$839$	−170.239	+	234.314i	−0.202907	+	0.279278i	0.695421	+	0.718602i	$0.255218\pi$
$840$		0			0
$841$	−0.854051	+	0.620504i	−0.00101552	+	0.000737817i
$842$	636.244	−	324.182i	0.755634	−	0.385015i
$843$		0			0
$844$	−829.305	−	269.458i	−0.982589	−	0.319263i
$845$	−48.2505	+	756.805i	−0.0571011	+	0.895628i
$846$		0			0
$847$	92.9759	−	182.475i	0.109771	−	0.215437i
$848$	38.8431	−	6.15214i	0.0458055	−	0.00725488i
$849$		0			0
$850$	−795.163	−	375.803i	−0.935486	−	0.442122i
$851$	−797.039			−0.936591
$852$		0			0
$853$	458.038	+	233.382i	0.536973	+	0.273601i	0.701375	−	0.712792i	$-0.252570\pi$
$853$	458.038	+	233.382i	0.536973	+	0.273601i	−0.164403	+	0.986393i	$0.552570\pi$
$854$	−100.886	+	32.7797i	−0.118133	+	0.0383837i
$855$		0			0
$856$	384.216	−	1182.50i	0.448851	−	1.38142i
$857$	−794.073	−	794.073i	−0.926572	−	0.926572i	0.0709103	−	0.997483i	$-0.477410\pi$
$857$	−794.073	−	794.073i	−0.926572	−	0.926572i	−0.997483	+	0.0709103i	$0.977410\pi$
$858$		0			0
$859$	439.811	+	605.348i	0.512004	+	0.704713i	0.984256	−	0.176751i	$-0.0565587\pi$
$859$	439.811	+	605.348i	0.512004	+	0.704713i	−0.472252	+	0.881464i	$0.656559\pi$
$860$	−447.376	−	100.394i	−0.520205	−	0.116737i
$861$		0			0
$862$	−287.780	−	45.5798i	−0.333851	−	0.0528768i
$863$	145.813	−	920.624i	0.168960	−	1.06677i	−0.746801	−	0.665048i	$-0.768411\pi$
$863$	145.813	−	920.624i	0.168960	−	1.06677i	0.915761	−	0.401724i	$-0.131589\pi$
$864$		0			0
$865$	−44.7487	−	103.646i	−0.0517326	−	0.119822i
$866$	202.384	−	147.040i	0.233700	−	0.169793i
$867$		0			0
$868$	−138.920	+	138.920i	−0.160046	+	0.160046i
$869$	−373.428	−	121.334i	−0.429722	−	0.139625i
$870$		0			0
$871$	540.296	+	1662.86i	0.620317	+	1.90914i
$872$	−415.982	+	816.411i	−0.477044	+	0.936251i
$873$		0			0
$874$			294.746i			0.337238i
$875$	−7.67444	+	226.110i	−0.00877079	+	0.258412i
$876$		0			0
$877$	−20.3449	−	128.453i	−0.0231983	−	0.146468i	0.973370	−	0.229238i	$-0.0736234\pi$
$877$	−20.3449	−	128.453i	−0.0231983	−	0.146468i	−0.996569	+	0.0827696i	$0.973623\pi$
$878$	−830.987	−	423.409i	−0.946455	−	0.482243i
$879$		0			0
$880$	4.31509	+	16.8648i	0.00490352	+	0.0191645i
$881$	51.9927	−	160.017i	0.0590155	−	0.181631i	−0.917203	−	0.398420i	$-0.869558\pi$
$881$	51.9927	−	160.017i	0.0590155	−	0.181631i	0.976218	+	0.216789i	$0.0695585\pi$
$882$		0			0
$883$	−1.80087	−	3.53441i	−0.00203949	−	0.00400272i	0.889985	−	0.455991i	$-0.150715\pi$
$883$	−1.80087	−	3.53441i	−0.00203949	−	0.00400272i	−0.892024	+	0.451988i	$0.850715\pi$
$884$	−668.099	−	919.559i	−0.755768	−	1.04023i
$885$		0			0
$886$	480.362	+	349.004i	0.542170	+	0.393909i
$887$	−702.101	−	111.202i	−0.791546	−	0.125369i	−0.252447	−	0.967611i	$-0.581235\pi$
$887$	−702.101	−	111.202i	−0.791546	−	0.125369i	−0.539099	+	0.842242i	$0.681235\pi$
$888$		0			0
$889$	−182.267	+	250.869i	−0.205024	+	0.282192i
$890$	−235.976	+	1051.56i	−0.265141	+	1.18153i
$891$		0			0
$892$	208.369	−	106.169i	0.233597	−	0.119024i
$893$	−266.197	+	266.197i	−0.298093	+	0.298093i
$894$		0			0
$895$	−675.147	−	1065.83i	−0.754354	−	1.19087i
$896$	36.9667	+	113.772i	0.0412575	+	0.126978i
$897$		0			0
$898$	−97.4292	+	15.4313i	−0.108496	+	0.0171840i
$899$		−	1349.62i		−	1.50125i
$900$		0			0
$901$	−861.679			−0.956358
$902$	−7.84842	−	49.5530i	−0.00870113	−	0.0549368i
$903$		0			0
$904$	−99.1143	+	32.2042i	−0.109640	+	0.0356241i
$905$	1311.64	+	83.6244i	1.44933	+	0.0924026i
$906$		0			0
$907$	−126.631	−	126.631i	−0.139615	−	0.139615i	0.633845	−	0.773460i	$-0.281476\pi$
$907$	−126.631	−	126.631i	−0.139615	−	0.139615i	−0.773460	+	0.633845i	$0.781476\pi$
$908$	−24.9706	−	49.0076i	−0.0275007	−	0.0539731i
$909$		0			0
$910$	106.723	−	180.115i	0.117279	−	0.197929i
$911$	877.720	+	637.701i	0.963469	+	0.700001i	0.953954	−	0.299954i	$-0.0969712\pi$
$911$	877.720	+	637.701i	0.963469	+	0.700001i	0.00951505	+	0.999955i	$0.496971\pi$
$912$		0			0
$913$	9.19836	−	58.0762i	0.0100749	−	0.0636102i
$914$	−329.936	+	454.118i	−0.360980	+	0.496846i
$915$		0			0
$916$	−134.421	+	97.6626i	−0.146748	+	0.106619i
$917$	−42.1388	+	21.4708i	−0.0459529	+	0.0234142i
$918$		0			0
$919$	−863.424	−	280.543i	−0.939526	−	0.305270i	−0.201073	−	0.979576i	$-0.564443\pi$
$919$	−863.424	−	280.543i	−0.939526	−	0.305270i	−0.738452	+	0.674306i	$0.764443\pi$
$920$	655.292	−	790.763i	0.712274	−	0.859525i
$921$		0			0
$922$	−245.617	+	482.050i	−0.266395	+	0.522830i
$923$	64.7382	−	10.2535i	0.0701389	−	0.0111089i
$924$		0			0
$925$	747.001	−	267.524i	0.807569	−	0.289216i
$926$	−445.106			−0.480676
$927$		0			0
$928$	−803.368	−	409.337i	−0.865698	−	0.441095i
$929$	1502.39	−	488.157i	1.61721	−	0.525465i	0.645932	−	0.763395i	$-0.276469\pi$
$929$	1502.39	−	488.157i	1.61721	−	0.525465i	0.971282	+	0.237930i	$0.0764690\pi$
$930$		0			0
$931$	128.365	−	395.068i	0.137879	−	0.424348i
$932$	378.608	+	378.608i	0.406232	+	0.406232i
$933$		0			0
$934$	−134.457	−	185.064i	−0.143958	−	0.198141i
$935$	−35.5767	−	379.756i	−0.0380500	−	0.406157i
$936$		0			0
$937$	1561.57	+	247.329i	1.66657	+	0.263959i	0.917268	−	0.398271i	$-0.130390\pi$
$937$	1561.57	+	247.329i	1.66657	+	0.263959i	0.749301	+	0.662230i	$0.230390\pi$
$938$	35.7148	−	225.494i	0.0380754	−	0.240399i
$939$		0			0
$940$	480.845	−	45.0470i	0.511537	−	0.0479224i
$941$	−911.873	+	662.515i	−0.969047	+	0.704054i	−0.955234	−	0.295851i	$-0.904397\pi$
$941$	−911.873	+	662.515i	−0.969047	+	0.704054i	−0.0138127	+	0.999905i	$0.504397\pi$
$942$		0			0
$943$	−246.163	+	246.163i	−0.261042	+	0.261042i
$944$	37.5729	+	12.2082i	0.0398018	+	0.0129324i
$945$		0			0
$946$	43.9973	+	135.410i	0.0465088	+	0.143139i
$947$	165.795	−	325.391i	0.175074	−	0.343602i	−0.786750	−	0.617272i	$-0.788238\pi$
$947$	165.795	−	325.391i	0.175074	−	0.343602i	0.961824	+	0.273670i	$0.0882377\pi$
$948$		0			0
$949$		−	1378.54i		−	1.45263i
$950$	−98.9308	−	276.242i	−0.104138	−	0.290781i
$951$		0			0
$952$	63.0603	+	398.147i	0.0662398	+	0.418221i
$953$	−444.297	−	226.381i	−0.466209	−	0.237545i	0.205074	−	0.978746i	$-0.434257\pi$
$953$	−444.297	−	226.381i	−0.466209	−	0.237545i	−0.671283	+	0.741201i	$0.734257\pi$
$954$		0			0
$955$	−1360.91	−	1127.77i	−1.42504	−	1.18091i
$956$	−218.904	+	673.719i	−0.228980	+	0.704727i
$957$		0			0
$958$	211.387	+	414.870i	0.220654	+	0.433059i
$959$	−226.007	−	311.071i	−0.235669	−	0.324370i
$960$		0			0
$961$	−976.942	−	709.790i	−1.01659	−	0.738595i
$962$	−725.216	−	114.863i	−0.753863	−	0.119400i
$963$		0			0
$964$	−105.260	+	144.878i	−0.109191	+	0.150288i
$965$	−751.294	−	445.163i	−0.778543	−	0.461309i
$966$		0			0
$967$	−1282.13	+	653.279i	−1.32589	+	0.675573i	−0.966271	−	0.257527i	$-0.917092\pi$
$967$	−1282.13	+	653.279i	−1.32589	+	0.675573i	−0.359616	+	0.933100i	$0.617092\pi$
$968$	654.412	−	654.412i	0.676046	−	0.676046i
$969$		0			0
$970$	14.5068	−	227.538i	0.0149554	−	0.234575i
$971$	415.272	+	1278.08i	0.427675	+	1.31625i	0.900410	+	0.435043i	$0.143267\pi$
$971$	415.272	+	1278.08i	0.427675	+	1.31625i	−0.472735	+	0.881204i	$0.656733\pi$
$972$		0			0
$973$	71.4885	−	11.3227i	0.0734722	−	0.0116369i
$974$		−	566.142i		−	0.581255i
$975$		0			0
$976$	−56.3815			−0.0577680
$977$	−147.737	−	932.776i	−0.151215	−	0.954735i	−0.940274	−	0.340418i	$-0.889432\pi$
$977$	−147.737	−	932.776i	−0.151215	−	0.954735i	0.789059	−	0.614317i	$-0.210568\pi$
$978$		0			0
$979$	−444.506	+	144.429i	−0.454041	+	0.147527i
$980$	−450.186	+	285.168i	−0.459373	+	0.290988i
$981$		0			0
$982$	−542.409	−	542.409i	−0.552352	−	0.552352i
$983$	0.210533	+	0.413194i	0.000214174	+	0.000420339i	0.891114	−	0.453780i	$-0.149925\pi$
$983$	0.210533	+	0.413194i	0.000214174	+	0.000420339i	−0.890899	+	0.454201i	$0.849925\pi$
$984$		0			0
$985$	−381.450	−	85.5995i	−0.387258	−	0.0869031i
$986$	−824.853	−	599.291i	−0.836565	−	0.607800i
$987$		0			0
$988$	59.3218	−	374.543i	0.0600423	−	0.379092i
$989$	580.698	−	799.262i	0.587156	−	0.808151i
$990$		0			0
$991$	293.072	−	212.929i	0.295734	−	0.214863i	−0.430017	−	0.902821i	$-0.641492\pi$
$991$	293.072	−	212.929i	0.295734	−	0.214863i	0.725751	+	0.687958i	$0.241492\pi$
$992$	−1290.85	+	657.721i	−1.30126	+	0.663025i
$993$		0			0
$994$	−8.13979	−	2.64478i	−0.00818892	−	0.00266074i
$995$	597.785	−	152.952i	0.600789	−	0.153720i
$996$		0			0
$997$	160.391	−	314.785i	0.160874	−	0.315732i	−0.796473	−	0.604674i	$-0.793303\pi$
$997$	160.391	−	314.785i	0.160874	−	0.315732i	0.957347	+	0.288942i	$0.0933034\pi$
$998$	−601.256	+	95.2296i	−0.602461	+	0.0954205i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.r.b.37.7		80
3.2	odd	2		75.3.k.a.37.4	✓	80
15.2	even	4		375.3.k.b.43.7		80
15.8	even	4		375.3.k.c.43.4		80
15.14	odd	2		375.3.k.a.82.7		80
25.23	odd	20	inner	225.3.r.b.73.7		80
75.2	even	20		375.3.k.a.343.7		80
75.11	odd	10		375.3.k.c.157.4		80
75.14	odd	10		375.3.k.b.157.7		80
75.23	even	20		75.3.k.a.73.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.37.4	✓	80	3.2	odd	2
75.3.k.a.73.4	yes	80	75.23	even	20
225.3.r.b.37.7		80	1.1	even	1	trivial
225.3.r.b.73.7		80	25.23	odd	20	inner
375.3.k.a.82.7		80	15.14	odd	2
375.3.k.a.343.7		80	75.2	even	20
375.3.k.b.43.7		80	15.2	even	4
375.3.k.b.157.7		80	75.14	odd	10
375.3.k.c.43.4		80	15.8	even	4
375.3.k.c.157.4		80	75.11	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.202100 + 1.27601i) q^{2} +(2.21687 - 0.720305i) q^{4} +(-1.23939 - 4.84396i) q^{5} +(1.27981 + 1.27981i) q^{7} +(3.71321 + 7.28759i) q^{8} +O(q^{10})\)	\(q+(0.202100 + 1.27601i) q^{2} +(2.21687 - 0.720305i) q^{4} +(-1.23939 - 4.84396i) q^{5} +(1.27981 + 1.27981i) q^{7} +(3.71321 + 7.28759i) q^{8} +(5.93045 - 2.56044i) q^{10} +(2.26637 + 1.64661i) q^{11} +(2.80131 - 17.6867i) q^{13} +(-1.37440 + 1.89170i) q^{14} +(-1.00546 + 0.730511i) q^{16} +(24.2628 - 12.3625i) q^{17} +(8.64024 + 2.80738i) q^{19} +(-6.23670 - 9.84568i) q^{20} +(-1.64306 + 3.22469i) q^{22} +(24.8036 - 3.92850i) q^{23} +(-21.9278 + 12.0071i) q^{25} +23.1346 q^{26} +(3.75903 + 1.91532i) q^{28} +(-27.5633 + 8.95587i) q^{29} +(-14.3903 + 44.2887i) q^{31} +(21.9985 + 21.9985i) q^{32} +(20.6782 + 28.4611i) q^{34} +(4.61315 - 7.78553i) q^{35} +(-31.3477 - 4.96498i) q^{37} +(-1.83606 + 11.5924i) q^{38} +(30.6986 - 27.0188i) q^{40} +(-11.2150 + 8.14820i) q^{41} +(27.8178 - 27.8178i) q^{43} +(6.21031 + 2.01785i) q^{44} +(10.0256 + 30.8556i) q^{46} +(-18.8125 + 36.9215i) q^{47} -45.7242i q^{49} +(-19.7528 - 25.5534i) q^{50} +(-6.52972 - 41.2270i) q^{52} +(-28.1946 - 14.3659i) q^{53} +(5.16720 - 13.0190i) q^{55} +(-4.57452 + 14.0789i) q^{56} +(-16.9983 - 33.3611i) q^{58} +(-18.6844 - 25.7169i) q^{59} +(36.7017 + 26.6654i) q^{61} +(-59.4210 - 9.41137i) q^{62} +(-26.5465 + 36.5381i) q^{64} +(-89.1457 + 8.35144i) q^{65} +(-86.9965 + 44.3269i) q^{67} +(44.8827 - 44.8827i) q^{68} +(10.8667 + 4.31297i) q^{70} +(1.13108 + 3.48112i) q^{71} +(76.0348 - 12.0427i) q^{73} -41.0033i q^{74} +21.1765 q^{76} +(0.793169 + 5.00787i) q^{77} +(-133.301 + 43.3122i) q^{79} +(4.78473 + 3.96502i) q^{80} +(-12.6637 - 12.6637i) q^{82} +(-9.52910 - 18.7019i) q^{83} +(-89.9546 - 102.206i) q^{85} +(41.1177 + 29.8738i) q^{86} +(-3.58433 + 22.6306i) q^{88} +(-98.0657 + 134.976i) q^{89} +(26.2208 - 19.0505i) q^{91} +(52.1566 - 26.5751i) q^{92} +(-50.9142 - 16.5430i) q^{94} +(2.89019 - 45.3324i) q^{95} +(16.0242 - 31.4493i) q^{97} +(58.3445 - 9.24086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

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