LMFDB - Embedded newform 225.4.h.b.136.1

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			136.1
Character	$\chi$	$=$	225.136
Dual form			225.4.h.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.29718 + 3.12208i) q^{2} +(6.24620 - 19.2238i) q^{4} +(9.58545 - 5.75493i) q^{5} -9.63602 q^{7} +(20.0464 + 61.6963i) q^{8} +O(q^{10})$	\(q+(-4.29718 + 3.12208i) q^{2} +(6.24620 - 19.2238i) q^{4} +(9.58545 - 5.75493i) q^{5} -9.63602 q^{7} +(20.0464 + 61.6963i) q^{8} +(-23.2230 + 54.6565i) q^{10} +(-19.6877 + 14.3039i) q^{11} +(35.7572 + 25.9791i) q^{13} +(41.4077 - 30.0844i) q^{14} +(-147.942 - 107.486i) q^{16} +(-0.568894 - 1.75088i) q^{17} +(-22.1878 - 68.2870i) q^{19} +(-50.7592 - 220.216i) q^{20} +(39.9434 - 122.933i) q^{22} +(56.7348 - 41.2202i) q^{23} +(58.7616 - 110.327i) q^{25} -234.764 q^{26} +(-60.1885 + 185.241i) q^{28} +(31.0824 - 95.6617i) q^{29} +(-51.1943 - 157.560i) q^{31} +452.340 q^{32} +(7.91102 + 5.74769i) q^{34} +(-92.3655 + 55.4546i) q^{35} +(316.532 + 229.974i) q^{37} +(308.542 + 224.169i) q^{38} +(547.211 + 476.022i) q^{40} +(2.89600 + 2.10407i) q^{41} +9.64426 q^{43} +(152.003 + 467.818i) q^{44} +(-115.107 + 354.261i) q^{46} +(167.342 - 515.027i) q^{47} -250.147 q^{49} +(91.9413 + 657.554i) q^{50} +(722.765 - 525.119i) q^{52} +(-50.2766 + 154.735i) q^{53} +(-106.397 + 250.411i) q^{55} +(-193.167 - 594.507i) q^{56} +(165.097 + 508.117i) q^{58} +(134.417 + 97.6599i) q^{59} +(692.078 - 502.824i) q^{61} +(711.905 + 517.230i) q^{62} +(-760.253 + 552.356i) q^{64} +(492.256 + 43.2414i) q^{65} +(-218.322 - 671.926i) q^{67} -37.2120 q^{68} +(223.777 - 526.671i) q^{70} +(209.430 - 644.559i) q^{71} +(39.1313 - 28.4306i) q^{73} -2078.19 q^{74} -1451.33 q^{76} +(189.711 - 137.833i) q^{77} +(145.637 - 448.225i) q^{79} +(-2036.66 - 178.907i) q^{80} -19.0137 q^{82} +(185.987 + 572.410i) q^{83} +(-15.5293 - 13.5090i) q^{85} +(-41.4431 + 30.1102i) q^{86} +(-1277.17 - 927.915i) q^{88} +(558.915 - 406.075i) q^{89} +(-344.557 - 250.335i) q^{91} +(-438.034 - 1348.13i) q^{92} +(888.856 + 2735.62i) q^{94} +(-605.666 - 526.872i) q^{95} +(-190.279 + 585.617i) q^{97} +(1074.93 - 780.980i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.29718	+	3.12208i	−1.51928	+	1.10382i	−0.557440	+	0.830217i	$0.688216\pi$
$2$	−4.29718	+	3.12208i	−1.51928	+	1.10382i	−0.961842	+	0.273606i	$0.911784\pi$
$3$		0			0
$3$		0			0
$4$	6.24620	−	19.2238i	0.780775	−	2.40298i
$5$	9.58545	−	5.75493i	0.857348	−	0.514736i
$5$	9.58545	−	5.75493i	0.857348	−	0.514736i
$6$		0			0
$7$	−9.63602			−0.520296			−0.260148	−	0.965569i	$-0.583771\pi$
$7$	−9.63602			−0.520296			−0.260148	+	0.965569i	$0.583771\pi$
$8$	20.0464	+	61.6963i	0.885932	+	2.72662i
$9$		0			0
$10$	−23.2230	+	54.6565i	−0.734376	+	1.72839i
$11$	−19.6877	+	14.3039i	−0.539641	+	0.392072i	−0.823952	−	0.566660i	$-0.808235\pi$
$11$	−19.6877	+	14.3039i	−0.539641	+	0.392072i	0.284311	+	0.958732i	$0.408235\pi$
$12$		0			0
$13$	35.7572	+	25.9791i	0.762866	+	0.554255i	0.899788	−	0.436327i	$-0.143721\pi$
$13$	35.7572	+	25.9791i	0.762866	+	0.554255i	−0.136922	+	0.990582i	$0.543721\pi$
$14$	41.4077	−	30.0844i	0.790476	−	0.574315i
$15$		0			0
$16$	−147.942	−	107.486i	−2.31159	−	1.67947i
$17$	−0.568894	−	1.75088i	−0.00811630	−	0.0249794i	0.946916	−	0.321480i	$-0.104180\pi$
$17$	−0.568894	−	1.75088i	−0.00811630	−	0.0249794i	−0.955033	+	0.296501i	$0.904180\pi$
$18$		0			0
$19$	−22.1878	−	68.2870i	−0.267907	−	0.824532i	−0.991010	−	0.133791i	$-0.957285\pi$
$19$	−22.1878	−	68.2870i	−0.267907	−	0.824532i	0.723103	−	0.690740i	$-0.242715\pi$
$20$	−50.7592	−	220.216i	−0.567505	−	2.46208i
$21$		0			0
$22$	39.9434	−	122.933i	0.387089	−	1.19134i
$23$	56.7348	−	41.2202i	0.514349	−	0.373696i	−0.300122	−	0.953901i	$-0.597027\pi$
$23$	56.7348	−	41.2202i	0.514349	−	0.373696i	0.814471	+	0.580205i	$0.197027\pi$
$24$		0			0
$25$	58.7616	−	110.327i	0.470093	−	0.882617i
$26$	−234.764			−1.77081
$27$		0			0
$28$	−60.1885	+	185.241i	−0.406234	+	1.25026i
$29$	31.0824	−	95.6617i	0.199029	−	0.612549i	−0.800877	−	0.598830i	$-0.795633\pi$
$29$	31.0824	−	95.6617i	0.199029	−	0.612549i	0.999906	−	0.0137199i	$-0.00436731\pi$
$30$		0			0
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	−0.982678	−	0.185324i	$-0.940667\pi$
$31$	−51.1943	−	157.560i	−0.296605	−	0.912857i	0.686072	−	0.727533i	$-0.259333\pi$
$32$	452.340			2.49885
$33$		0			0
$34$	7.91102	+	5.74769i	0.0399038	+	0.0289918i
$35$	−92.3655	+	55.4546i	−0.446075	+	0.267815i
$36$		0			0
$37$	316.532	+	229.974i	1.40642	+	1.02182i	0.993831	+	0.110906i	$0.0353752\pi$
$37$	316.532	+	229.974i	1.40642	+	1.02182i	0.412588	+	0.910918i	$0.364625\pi$
$38$	308.542	+	224.169i	1.31716	+	0.956975i
$39$		0			0
$40$	547.211	+	476.022i	2.16304	+	1.88164i
$41$	2.89600	+	2.10407i	0.0110312	+	0.00801463i	0.593287	−	0.804991i	$-0.297830\pi$
$41$	2.89600	+	2.10407i	0.0110312	+	0.00801463i	−0.582256	+	0.813006i	$0.697830\pi$
$42$		0			0
$43$	9.64426			0.0342032			0.0171016	−	0.999854i	$-0.494556\pi$
$43$	9.64426			0.0342032			0.0171016	+	0.999854i	$0.494556\pi$
$44$	152.003	+	467.818i	0.520803	+	1.60287i
$45$		0			0
$46$	−115.107	+	354.261i	−0.368946	+	1.13550i
$47$	167.342	−	515.027i	0.519349	−	1.59839i	−0.255879	−	0.966709i	$-0.582365\pi$
$47$	167.342	−	515.027i	0.519349	−	1.59839i	0.775228	−	0.631682i	$-0.217635\pi$
$48$		0			0
$49$	−250.147			−0.729292
$50$	91.9413	+	657.554i	0.260049	+	1.85984i
$51$		0			0
$52$	722.765	−	525.119i	1.92749	−	1.40040i
$53$	−50.2766	+	154.735i	−0.130302	+	0.401029i	−0.994830	−	0.101556i	$-0.967618\pi$
$53$	−50.2766	+	154.735i	−0.130302	+	0.401029i	0.864528	+	0.502585i	$0.167618\pi$
$54$		0			0
$55$	−106.397	+	250.411i	−0.260847	+	0.613915i
$56$	−193.167	−	594.507i	−0.460947	−	1.41865i
$57$		0			0
$58$	165.097	+	508.117i	0.373764	+	1.15033i
$59$	134.417	+	97.6599i	0.296604	+	0.215496i	0.726127	−	0.687560i	$-0.241318\pi$
$59$	134.417	+	97.6599i	0.296604	+	0.215496i	−0.429523	+	0.903056i	$0.641318\pi$
$60$		0			0
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.467444	−	0.884023i	$-0.345175\pi$
$61$	692.078	−	502.824i	1.45265	−	1.05541i	0.985204	−	0.171387i	$-0.0548250\pi$
$62$	711.905	+	517.230i	1.45826	+	1.05949i
$63$		0			0
$64$	−760.253	+	552.356i	−1.48487	+	1.07882i
$65$	492.256	+	43.2414i	0.939337	+	0.0825144i
$66$		0			0
$67$	−218.322	−	671.926i	−0.398094	−	1.22521i	−0.926526	−	0.376231i	$-0.877220\pi$
$67$	−218.322	−	671.926i	−0.398094	−	1.22521i	0.528432	−	0.848975i	$-0.322780\pi$
$68$	−37.2120			−0.0663620
$69$		0			0
$70$	223.777	−	526.671i	0.382093	−	0.899275i
$71$	209.430	−	644.559i	0.350067	−	1.07740i	−0.608748	−	0.793364i	$-0.708328\pi$
$71$	209.430	−	644.559i	0.350067	−	1.07740i	0.958815	−	0.284032i	$-0.0916722\pi$
$72$		0			0
$73$	39.1313	−	28.4306i	0.0627394	−	0.0455829i	−0.555974	−	0.831200i	$-0.687654\pi$
$73$	39.1313	−	28.4306i	0.0627394	−	0.0455829i	0.618713	+	0.785617i	$0.287654\pi$
$74$	−2078.19			−3.26466
$75$		0			0
$76$	−1451.33			−2.19051
$77$	189.711	−	137.833i	0.280773	−	0.203994i
$78$		0			0
$79$	145.637	−	448.225i	0.207411	−	0.638345i	−0.792195	−	0.610268i	$-0.791062\pi$
$79$	145.637	−	448.225i	0.207411	−	0.638345i	0.999606	−	0.0280766i	$-0.00893822\pi$
$80$	−2036.66	−	178.907i	−2.84632	−	0.250030i
$81$		0			0
$82$	−19.0137			−0.0256062
$83$	185.987	+	572.410i	0.245961	+	0.756989i	0.995477	+	0.0950033i	$0.0302862\pi$
$83$	185.987	+	572.410i	0.245961	+	0.756989i	−0.749516	+	0.661986i	$0.769714\pi$
$84$		0			0
$85$	−15.5293	−	13.5090i	−0.0198163	−	0.0172383i
$86$	−41.4431	+	30.1102i	−0.0519643	+	0.0377542i
$87$		0			0
$88$	−1277.17	−	927.915i	−1.54712	−	1.12405i
$89$	558.915	−	406.075i	0.665672	−	0.483639i	−0.202902	−	0.979199i	$-0.565037\pi$
$89$	558.915	−	406.075i	0.665672	−	0.483639i	0.868574	+	0.495560i	$0.165037\pi$
$90$		0			0
$91$	−344.557	−	250.335i	−0.396916	−	0.288376i
$92$	−438.034	−	1348.13i	−0.496394	−	1.52774i
$93$		0			0
$94$	888.856	+	2735.62i	0.975303	+	3.00168i
$95$	−605.666	−	526.872i	−0.654106	−	0.569010i
$96$		0			0
$97$	−190.279	+	585.617i	−0.199174	+	0.612994i	0.800729	+	0.599027i	$0.204446\pi$
$97$	−190.279	+	585.617i	−0.199174	+	0.612994i	−0.999902	+	0.0139669i	$0.995554\pi$
$98$	1074.93	−	780.980i	1.10800	−	0.805009i
$99$		0			0
$100$	−1753.87	−	1818.75i	−1.75387	−	1.81875i
$101$	−626.998			−0.617709			−0.308855	−	0.951109i	$-0.599946\pi$
$101$	−626.998			−0.617709			−0.308855	+	0.951109i	$0.599946\pi$
$102$		0			0
$103$	470.599	−	1448.36i	0.450189	−	1.38554i	−0.426502	−	0.904487i	$-0.640254\pi$
$103$	470.599	−	1448.36i	0.450189	−	1.38554i	0.876691	−	0.481054i	$-0.159746\pi$
$104$	−886.015	+	2726.87i	−0.835393	+	2.57108i
$105$		0			0
$106$	−267.049	−	821.893i	−0.244699	−	0.753107i
$107$	435.652			0.393608			0.196804	−	0.980443i	$-0.436944\pi$
$107$	435.652			0.393608			0.196804	+	0.980443i	$0.436944\pi$
$108$		0			0
$109$	1426.54	+	1036.44i	1.25356	+	0.910764i	0.998423	−	0.0561410i	$-0.0178796\pi$
$109$	1426.54	+	1036.44i	1.25356	+	0.910764i	0.255136	+	0.966905i	$0.417880\pi$
$110$	−324.596	−	1408.24i	−0.281354	−	1.22064i
$111$		0			0
$112$	1425.57	+	1035.74i	1.20271	+	0.873820i
$113$	744.284	+	540.754i	0.619614	+	0.450176i	0.852786	−	0.522260i	$-0.174911\pi$
$113$	744.284	+	540.754i	0.619614	+	0.450176i	−0.233173	+	0.972435i	$0.574911\pi$
$114$		0			0
$115$	306.609	−	721.619i	0.248621	−	0.585142i
$116$	−1644.84	−	1195.04i	−1.31655	−	0.956527i
$117$		0			0
$118$	−882.517			−0.688494
$119$	5.48187	+	16.8715i	0.00422288	+	0.0129967i
$120$		0			0
$121$	−228.300	+	702.635i	−0.171525	+	0.527900i
$122$	−1404.12	+	4321.45i	−1.04200	+	3.20693i
$123$		0			0
$124$	−3348.67			−2.42516
$125$	−71.6685	−	1395.70i	−0.0512818	−	0.998684i
$126$		0			0
$127$	−833.392	+	605.495i	−0.582296	+	0.423063i	−0.839551	−	0.543281i	$-0.817182\pi$
$127$	−833.392	+	605.495i	−0.582296	+	0.423063i	0.257255	+	0.966344i	$0.417182\pi$
$128$	424.196	−	1305.54i	0.292922	−	0.901520i
$129$		0			0
$130$	−2250.32	+	1351.05i	−1.51820	+	0.911499i
$131$	−94.1854	−	289.873i	−0.0628169	−	0.193331i	0.914723	−	0.404082i	$-0.132409\pi$
$131$	−94.1854	−	289.873i	−0.0628169	−	0.193331i	−0.977540	+	0.210751i	$0.932409\pi$
$132$		0			0
$133$	213.802	+	658.014i	0.139391	+	0.429001i
$134$	3035.98	+	2205.77i	1.95723	+	1.42201i
$135$		0			0
$136$	96.6184	−	70.1974i	0.0609188	−	0.0442601i
$137$	−1466.78	−	1065.68i	−0.914712	−	0.664577i	0.0274903	−	0.999622i	$-0.491248\pi$
$137$	−1466.78	−	1065.68i	−0.914712	−	0.664577i	−0.942202	+	0.335045i	$0.891248\pi$
$138$		0			0
$139$	579.242	−	420.844i	0.353458	−	0.256802i	−0.396860	−	0.917879i	$-0.629900\pi$
$139$	579.242	−	420.844i	0.353458	−	0.256802i	0.750318	+	0.661077i	$0.229900\pi$
$140$	489.116	+	2122.00i	0.295270	+	1.28101i
$141$		0			0
$142$	1112.41	+	3423.64i	0.657404	+	2.02328i
$143$	−1075.58			−0.628982
$144$		0			0
$145$	−252.588	−	1095.84i	−0.144664	−	0.627616i
$146$	−79.3917	+	244.343i	−0.0450035	+	0.138506i
$147$		0			0
$148$	6398.10	−	4648.49i	3.55352	−	2.58178i
$149$	−725.618			−0.398959			−0.199480	−	0.979902i	$-0.563925\pi$
$149$	−725.618			−0.398959			−0.199480	+	0.979902i	$0.563925\pi$
$150$		0			0
$151$	3051.31			1.64445			0.822227	−	0.569160i	$-0.192732\pi$
$151$	3051.31			1.64445			0.822227	+	0.569160i	$0.192732\pi$
$152$	3768.27	−	2737.81i	2.01084	−	1.46096i
$153$		0			0
$154$	−384.895	+	1184.58i	−0.201401	+	0.619848i
$155$	−1397.46	−	1215.66i	−0.724175	−	0.629963i
$156$		0			0
$157$	−2166.76			−1.10144			−0.550722	−	0.834689i	$-0.685647\pi$
$157$	−2166.76			−1.10144			−0.550722	+	0.834689i	$0.685647\pi$
$158$	773.566	+	2380.79i	0.389504	+	1.19877i
$159$		0			0
$160$	4335.88	−	2603.19i	2.14239	−	1.28625i
$161$	−546.698	+	397.199i	−0.267614	+	0.194433i
$162$		0			0
$163$	62.9438	+	45.7313i	0.0302463	+	0.0219752i	0.602806	−	0.797888i	$-0.294049\pi$
$163$	62.9438	+	45.7313i	0.0302463	+	0.0219752i	−0.572559	+	0.819863i	$0.694049\pi$
$164$	58.5372	−	42.5298i	0.0278719	−	0.0202501i
$165$		0			0
$166$	−2586.33	−	1879.08i	−1.20927	−	0.878583i
$167$	39.0563	+	120.203i	0.0180974	+	0.0556981i	0.959697	−	0.281035i	$-0.0906778\pi$
$167$	39.0563	+	120.203i	0.0180974	+	0.0556981i	−0.941600	+	0.336734i	$0.890678\pi$
$168$		0			0
$169$	−75.2487	−	231.592i	−0.0342506	−	0.105413i
$170$	108.908	+	9.56685i	0.0491346	+	0.00431614i
$171$		0			0
$172$	60.2400	−	185.400i	0.0267050	−	0.0821895i
$173$	2620.45	−	1903.87i	1.15161	−	0.836697i	0.162919	−	0.986639i	$-0.447909\pi$
$173$	2620.45	−	1903.87i	1.15161	−	0.836697i	0.988695	+	0.149943i	$0.0479090\pi$
$174$		0			0
$175$	−566.228	+	1063.11i	−0.244587	+	0.459222i
$176$	4450.09			1.90590
$177$		0			0
$178$	−1133.96	+	3489.95i	−0.477492	+	1.46957i
$179$	−438.802	+	1350.49i	−0.183227	+	0.563914i	−0.999913	−	0.0131674i	$-0.995809\pi$
$179$	−438.802	+	1350.49i	−0.183227	+	0.563914i	0.816686	+	0.577082i	$0.195809\pi$
$180$		0			0
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	0.920383	−	0.391018i	$-0.127877\pi$
$181$	−131.635	−	405.129i	−0.0540570	−	0.166370i	−0.974440	+	0.224648i	$0.927877\pi$
$182$	2262.19			0.921344
$183$		0			0
$184$	3680.46	+	2674.01i	1.47461	+	1.07136i
$185$	4357.58	+	382.784i	1.73176	+	0.152123i
$186$		0			0
$187$	36.2446	+	26.3332i	0.0141736	+	0.0102977i
$188$	−8855.54	−	6433.92i	−3.43541	−	2.49597i
$189$		0			0
$190$	4247.59	+	373.122i	1.62186	+	0.142469i
$191$	−1193.36	−	867.030i	−0.452088	−	0.328461i	0.338331	−	0.941027i	$-0.390138\pi$
$191$	−1193.36	−	867.030i	−0.452088	−	0.328461i	−0.790420	+	0.612566i	$0.790138\pi$
$192$		0			0
$193$	−1535.93			−0.572841			−0.286421	−	0.958104i	$-0.592465\pi$
$193$	−1535.93			−0.572841			−0.286421	+	0.958104i	$0.592465\pi$
$194$	−1010.68	−	3110.57i	−0.374036	−	1.15116i
$195$		0			0
$196$	−1562.47	+	4808.79i	−0.569413	+	1.75247i
$197$	96.3752	−	296.613i	0.0348551	−	0.107273i	−0.932115	−	0.362162i	$-0.882039\pi$
$197$	96.3752	−	296.613i	0.0348551	−	0.107273i	0.966970	+	0.254889i	$0.0820388\pi$
$198$		0			0
$199$	−1453.74			−0.517855			−0.258927	−	0.965897i	$-0.583369\pi$
$199$	−1453.74			−0.517855			−0.258927	+	0.965897i	$0.583369\pi$
$200$	7984.73	+	1413.72i	2.82303	+	0.499825i
$201$		0			0
$202$	2694.32	−	1957.54i	0.938474	−	0.681842i
$203$	−299.510	+	921.798i	−0.103554	+	0.318707i
$204$		0			0
$205$	39.8682	+	3.50215i	0.0135830	+	0.00119317i
$206$	2499.64	+	7693.09i	0.845427	+	2.60196i
$207$		0			0
$208$	−2497.59	−	7686.78i	−0.832579	−	2.56242i
$209$	1413.60	+	1027.04i	0.467849	+	0.339912i
$210$		0			0
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	−0.878437	−	0.477858i	$-0.841413\pi$
$211$	−2131.43	+	1548.57i	−0.695420	+	0.505252i	0.183018	+	0.983110i	$0.441413\pi$
$212$	2660.57	+	1933.02i	0.861928	+	0.626227i
$213$		0			0
$214$	−1872.07	+	1360.14i	−0.598001	+	0.434473i
$215$	92.4446	−	55.5020i	0.0293240	−	0.0176056i
$216$		0			0
$217$	493.309	+	1518.25i	0.154323	+	0.474956i
$218$	−9365.97			−2.90983
$219$		0			0
$220$	4149.27	+	3609.47i	1.27156	+	1.10614i
$221$	25.1442	−	77.3858i	0.00765330	−	0.0235544i
$222$		0			0
$223$	−2828.58	+	2055.08i	−0.849396	+	0.617123i	−0.924980	−	0.380017i	$-0.875918\pi$
$223$	−2828.58	+	2055.08i	−0.849396	+	0.617123i	0.0755831	+	0.997140i	$0.475918\pi$
$224$	−4358.76			−1.30014
$225$		0			0
$226$	−4886.60			−1.43828
$227$	−4348.31	+	3159.23i	−1.27140	+	0.923724i	−0.999257	−	0.0385335i	$-0.987731\pi$
$227$	−4348.31	+	3159.23i	−1.27140	+	0.923724i	−0.272140	+	0.962258i	$0.587731\pi$
$228$		0			0
$229$	−207.178	+	637.627i	−0.0597846	+	0.183998i	−0.976489	−	0.215569i	$-0.930839\pi$
$229$	−207.178	+	637.627i	−0.0597846	+	0.183998i	0.916704	+	0.399567i	$0.130839\pi$
$230$	935.402	+	4058.18i	0.268168	+	1.16343i
$231$		0			0
$232$	6525.06			1.84651
$233$	1442.14	+	4438.46i	0.405485	+	1.24795i	0.920490	+	0.390767i	$0.127790\pi$
$233$	1442.14	+	4438.46i	0.405485	+	1.24795i	−0.515005	+	0.857187i	$0.672210\pi$
$234$		0			0
$235$	−1359.89	−	5899.80i	−0.377487	−	1.63771i
$236$	2717.00	−	1974.01i	0.749413	−	0.544480i
$237$		0			0
$238$	−76.2307	−	55.3849i	−0.0207618	−	0.0150843i
$239$	5138.90	−	3733.63i	1.39083	−	1.01050i	0.395054	−	0.918658i	$-0.370726\pi$
$239$	5138.90	−	3733.63i	1.39083	−	1.01050i	0.995774	−	0.0918383i	$-0.0292743\pi$
$240$		0			0
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	0.447938	−	0.894064i	$-0.352158\pi$
$241$	−987.511	−	717.469i	−0.263947	−	0.191769i	−0.711885	+	0.702296i	$0.752158\pi$
$242$	−1212.64	−	3732.12i	−0.322113	−	0.991362i
$243$		0			0
$244$	−5343.35	−	16445.1i	−1.40194	−	4.31472i
$245$	−2397.77	+	1439.58i	−0.625257	+	0.375393i
$246$		0			0
$247$	980.662	−	3018.17i	0.252624	−	0.777496i
$248$	8694.60	−	6317.00i	2.22624	−	1.61746i
$249$		0			0
$250$	4665.47	+	5773.83i	1.18028	+	1.46068i
$251$	−5225.08			−1.31396			−0.656980	−	0.753908i	$-0.728166\pi$
$251$	−5225.08			−1.31396			−0.656980	+	0.753908i	$0.728166\pi$
$252$		0			0
$253$	−527.364	+	1623.06i	−0.131048	+	0.403324i
$254$	1690.83	−	5203.84i	0.417685	−	1.28550i
$255$		0			0
$256$	−69.9686	−	215.341i	−0.0170822	−	0.0525735i
$257$	−5648.44			−1.37097			−0.685487	−	0.728085i	$-0.740411\pi$
$257$	−5648.44			−1.37097			−0.685487	+	0.728085i	$0.740411\pi$
$258$		0			0
$259$	−3050.11	−	2216.03i	−0.731754	−	0.531651i
$260$	3906.00	−	9192.96i	0.931692	−	2.19278i
$261$		0			0
$262$	1309.74	+	951.580i	0.308839	+	0.224385i
$263$	215.671	+	156.694i	0.0505660	+	0.0367383i	0.612781	−	0.790253i	$-0.290051\pi$
$263$	215.671	+	156.694i	0.0505660	+	0.0367383i	−0.562215	+	0.826991i	$0.690051\pi$
$264$		0			0
$265$	408.568	+	1772.55i	0.0947099	+	0.410893i
$266$	−2973.12	−	2160.10i	−0.685314	−	0.497910i
$267$		0			0
$268$	−14280.7			−3.25497
$269$	20.8315	+	64.1126i	0.00472162	+	0.0145317i	0.953390	−	0.301742i	$-0.0975682\pi$
$269$	20.8315	+	64.1126i	0.00472162	+	0.0145317i	−0.948668	+	0.316274i	$0.897568\pi$
$270$		0			0
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	0.689810	+	0.723990i	$0.257694\pi$
$271$	−1310.75	+	4034.06i	−0.293809	+	0.904250i	−0.983619	+	0.180260i	$0.942306\pi$
$272$	−104.031	+	320.175i	−0.0231905	+	0.0713731i
$273$		0			0
$274$	9630.15			2.12328
$275$	421.232	+	3012.60i	0.0923682	+	0.660607i
$276$		0			0
$277$	−7067.18	+	5134.61i	−1.53295	+	1.11375i	−0.578373	+	0.815773i	$0.696312\pi$
$277$	−7067.18	+	5134.61i	−1.53295	+	1.11375i	−0.954573	+	0.297977i	$0.903688\pi$
$278$	−1175.20	+	3616.88i	−0.253538	+	0.780310i
$279$		0			0
$280$	−5272.94	−	4586.95i	−1.12542	−	0.979010i
$281$	−2157.19	−	6639.13i	−0.457960	−	1.40946i	−0.867624	−	0.497221i	$-0.834354\pi$
$281$	−2157.19	−	6639.13i	−0.457960	−	1.40946i	0.409664	−	0.912237i	$-0.365646\pi$
$282$		0			0
$283$	2061.43	+	6344.42i	0.433000	+	1.33264i	0.895122	+	0.445821i	$0.147088\pi$
$283$	2061.43	+	6344.42i	0.433000	+	1.33264i	−0.462122	+	0.886817i	$0.652912\pi$
$284$	−11082.8	−	8052.10i	−2.31564	−	1.68241i
$285$		0			0
$286$	4621.95	−	3358.04i	0.955600	−	0.694284i
$287$	−27.9059	−	20.2748i	−0.00573949	−	0.00416998i
$288$		0			0
$289$	3971.96	−	2885.80i	0.808459	−	0.587380i
$290$	4506.71	+	3920.41i	0.912562	+	0.793842i
$291$		0			0
$292$	−302.123	−	929.838i	−0.0605493	−	0.186351i
$293$	4204.23			0.838272			0.419136	−	0.907923i	$-0.362333\pi$
$293$	4204.23			0.838272			0.419136	+	0.907923i	$0.362333\pi$
$294$		0			0
$295$	1850.48	+	162.552i	0.365216	+	0.0320818i
$296$	−7843.23	+	24139.0i	−1.54013	+	4.74003i
$297$		0			0
$298$	3118.11	−	2265.44i	0.606132	−	0.440380i
$299$	3099.54			0.599502
$300$		0			0
$301$	−92.9323			−0.0177958
$302$	−13112.0	+	9526.46i	−2.49839	+	1.81519i
$303$		0			0
$304$	−4057.39	+	12487.4i	−0.765484	+	2.35592i
$305$	3740.16	−	8802.65i	0.702167	−	1.65258i
$306$		0			0
$307$	1361.03			0.253024			0.126512	−	0.991965i	$-0.459622\pi$
$307$	1361.03			0.253024			0.126512	+	0.991965i	$0.459622\pi$
$308$	−1464.70	−	4507.90i	−0.270972	−	0.833965i
$309$		0			0
$310$	9800.55	+	860.912i	1.79559	+	0.157731i
$311$	1990.40	−	1446.11i	0.362911	−	0.263670i	−0.391354	−	0.920240i	$-0.627993\pi$
$311$	1990.40	−	1446.11i	0.362911	−	0.263670i	0.754265	+	0.656570i	$0.227993\pi$
$312$		0			0
$313$	2333.11	+	1695.11i	0.421327	+	0.306112i	0.778171	−	0.628052i	$-0.216147\pi$
$313$	2333.11	+	1695.11i	0.421327	+	0.306112i	−0.356845	+	0.934164i	$0.616147\pi$
$314$	9310.97	−	6764.82i	1.67340	−	1.21580i
$315$		0			0
$316$	−7706.92	−	5599.40i	−1.37199	−	0.996807i
$317$	2319.10	+	7137.47i	0.410896	+	1.26461i	0.915871	+	0.401473i	$0.131502\pi$
$317$	2319.10	+	7137.47i	0.410896	+	1.26461i	−0.504975	+	0.863134i	$0.668498\pi$
$318$		0			0
$319$	756.398	+	2327.96i	0.132759	+	0.408591i
$320$	−4108.60	+	9669.79i	−0.717742	+	1.68924i
$321$		0			0
$322$	1109.17	−	3413.67i	0.191961	−	0.590796i
$323$	−106.939	+	77.6961i	−0.0184219	+	0.0133843i
$324$		0			0
$325$	4967.35	−	2418.41i	0.847812	−	0.412767i
$326$	−413.258			−0.0702093
$327$		0			0
$328$	−71.7589	+	220.851i	−0.0120800	+	0.0371783i
$329$	−1612.51	+	4962.81i	−0.270215	+	0.831636i
$330$		0			0
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	0.920960	−	0.389658i	$-0.127407\pi$
$331$	−320.055	−	985.027i	−0.0531474	−	0.163571i	−0.974107	+	0.226087i	$0.927407\pi$
$332$	12165.6			2.01107
$333$		0			0
$334$	−543.116	−	394.597i	−0.0889760	−	0.0646448i
$335$	−5959.60	−	5184.28i	−0.971963	−	0.845515i
$336$		0			0
$337$	−1057.22	−	768.117i	−0.170892	−	0.124160i	0.499052	−	0.866572i	$-0.333682\pi$
$337$	−1057.22	−	768.117i	−0.170892	−	0.124160i	−0.669944	+	0.742412i	$0.733682\pi$
$338$	1046.40	+	760.258i	0.168393	+	0.122345i
$339$		0			0
$340$	−356.694	+	214.152i	−0.0568954	+	0.0341589i
$341$	3261.62	+	2369.70i	0.517966	+	0.376325i
$342$		0			0
$343$	5715.58			0.899744
$344$	193.332	+	595.016i	0.0303017	+	0.0932590i
$345$		0			0
$346$	−5316.51	+	16362.5i	−0.826061	+	2.54236i
$347$	−1032.43	+	3177.49i	−0.159723	+	0.491576i	−0.998609	−	0.0527312i	$-0.983207\pi$
$347$	−1032.43	+	3177.49i	−0.159723	+	0.491576i	0.838886	+	0.544307i	$0.183207\pi$
$348$		0			0
$349$	10728.2			1.64546			0.822732	−	0.568429i	$-0.192449\pi$
$349$	10728.2			1.64546			0.822732	+	0.568429i	$0.192449\pi$
$350$	−885.949	−	6336.20i	−0.135303	−	0.967669i
$351$		0			0
$352$	−8905.52	+	6470.24i	−1.34848	+	0.979730i
$353$	−2579.99	+	7940.38i	−0.389005	+	1.19723i	0.544528	+	0.838743i	$0.316709\pi$
$353$	−2579.99	+	7940.38i	−0.389005	+	1.19723i	−0.933533	+	0.358491i	$0.883291\pi$
$354$		0			0
$355$	−1701.91	−	7383.64i	−0.254445	−	1.10390i
$356$	−4315.23	−	13280.9i	−0.642435	−	1.97721i
$357$		0			0
$358$	−2330.74	−	7173.29i	−0.344088	−	1.05899i
$359$	8253.90	+	5996.81i	1.21344	+	0.881614i	0.995538	−	0.0943571i	$-0.0300795\pi$
$359$	8253.90	+	5996.81i	1.21344	+	0.881614i	0.217899	+	0.975971i	$0.430080\pi$
$360$		0			0
$361$	1378.24	−	1001.35i	0.200939	−	0.145990i
$362$	1830.50	+	1329.94i	0.265771	+	0.193094i
$363$		0			0
$364$	−6964.57	+	5060.06i	−1.00287	+	0.728624i
$365$	211.475	−	497.718i	0.0303264	−	0.0713746i
$366$		0			0
$367$	−2307.74	−	7102.49i	−0.328237	−	1.01021i	−0.969958	−	0.243272i	$-0.921779\pi$
$367$	−2307.74	−	7102.49i	−0.328237	−	1.01021i	0.641721	−	0.766938i	$-0.278221\pi$
$368$	−12824.0			−1.81657
$369$		0			0
$370$	−19920.4	+	11959.8i	−2.79895	+	1.68044i
$371$	484.466	−	1491.03i	0.0677958	−	0.208654i
$372$		0			0
$373$	4675.25	−	3396.77i	0.648995	−	0.471523i	−0.213934	−	0.976848i	$-0.568628\pi$
$373$	4675.25	−	3396.77i	0.648995	−	0.471523i	0.862929	+	0.505326i	$0.168628\pi$
$374$	−237.964			−0.0329006
$375$		0			0
$376$	35129.9			4.81831
$377$	3596.62	−	2613.10i	0.491341	−	0.356980i
$378$		0			0
$379$	−2500.18	+	7694.77i	−0.338854	+	1.04289i	0.625938	+	0.779873i	$0.284716\pi$
$379$	−2500.18	+	7694.77i	−0.338854	+	1.04289i	−0.964792	+	0.263013i	$0.915284\pi$
$380$	−13911.6	+	8352.28i	−1.87803	+	1.12753i
$381$		0			0
$382$	7835.04			1.04941
$383$	−653.851	−	2012.35i	−0.0872330	−	0.268475i	0.897919	−	0.440161i	$-0.145079\pi$
$383$	−653.851	−	2012.35i	−0.0872330	−	0.268475i	−0.985152	+	0.171686i	$0.945079\pi$
$384$		0			0
$385$	1025.24	−	2412.96i	0.135717	−	0.319418i
$386$	6600.15	−	4795.29i	0.870307	−	0.632315i
$387$		0			0
$388$	10069.3	+	7315.77i	1.31750	+	0.957222i
$389$	−5428.83	+	3944.27i	−0.707590	+	0.514094i	−0.882395	−	0.470509i	$-0.844070\pi$
$389$	−5428.83	+	3944.27i	−0.707590	+	0.514094i	0.174805	+	0.984603i	$0.444070\pi$
$390$		0			0
$391$	−104.448	−	75.8857i	−0.0135093	−	0.00981510i
$392$	−5014.54	−	15433.2i	−0.646103	−	1.98850i
$393$		0			0
$394$	511.907	+	1575.49i	0.0654556	+	0.201452i
$395$	−1183.50	−	5134.56i	−0.150756	−	0.654046i
$396$		0			0
$397$	−2029.26	+	6245.42i	−0.256538	+	0.789544i	0.736984	+	0.675910i	$0.236249\pi$
$397$	−2029.26	+	6245.42i	−0.256538	+	0.789544i	−0.993523	+	0.113634i	$0.963751\pi$
$398$	6246.99	−	4538.70i	0.786767	−	0.571620i
$399$		0			0
$400$	−20551.9	+	10005.9i	−2.56899	+	1.25074i
$401$	10290.4			1.28149			0.640744	−	0.767754i	$-0.278626\pi$
$401$	10290.4			1.28149			0.640744	+	0.767754i	$0.278626\pi$
$402$		0			0
$403$	2262.70	−	6963.87i	0.279685	−	0.860782i
$404$	−3916.36	+	12053.3i	−0.482292	+	1.48434i
$405$		0			0
$406$	−1590.88	−	4896.23i	−0.194468	−	0.598511i
$407$	−9521.30			−1.15959
$408$		0			0
$409$	−5384.48	−	3912.06i	−0.650967	−	0.472955i	0.212633	−	0.977132i	$-0.431796\pi$
$409$	−5384.48	−	3912.06i	−0.650967	−	0.472955i	−0.863600	+	0.504177i	$0.831796\pi$
$410$	−182.255	+	109.422i	−0.0219535	+	0.0131805i
$411$		0			0
$412$	−24903.5	−	18093.4i	−2.97793	−	2.16359i
$413$	−1295.25	−	941.053i	−0.154322	−	0.112121i
$414$		0			0
$415$	5076.95	+	4416.46i	0.600524	+	0.522399i
$416$	16174.4	+	11751.4i	1.90629	+	1.38500i
$417$		0			0
$418$	−9280.97			−1.08600
$419$	−1348.17	−	4149.23i	−0.157189	−	0.483778i	0.841187	−	0.540744i	$-0.181857\pi$
$419$	−1348.17	−	4149.23i	−0.157189	−	0.483778i	−0.998376	+	0.0569662i	$0.981857\pi$
$420$		0			0
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	−0.678395	−	0.734697i	$-0.737324\pi$
$421$	2611.17	−	8036.36i	0.302282	−	0.930329i	0.980677	−	0.195632i	$-0.0626757\pi$
$422$	4324.35	−	13309.0i	0.498830	−	1.53524i
$423$		0			0
$424$	−10554.5			−1.20889
$425$	−226.598	−	40.1198i	−0.0258627	−	0.00457905i
$426$		0			0
$427$	−6668.88	+	4845.22i	−0.755807	+	0.549126i
$428$	2721.17	−	8374.90i	0.307319	−	0.945832i
$429$		0			0
$430$	−223.969	+	527.122i	−0.0251180	+	0.0591164i
$431$	123.883	+	381.273i	0.0138451	+	0.0426109i	0.957740	−	0.287634i	$-0.0928687\pi$
$431$	123.883	+	381.273i	0.0138451	+	0.0426109i	−0.943895	+	0.330245i	$0.892869\pi$
$432$		0			0
$433$	−3996.84	−	12301.0i	−0.443594	−	1.36524i	−0.884019	−	0.467451i	$-0.845172\pi$
$433$	−3996.84	−	12301.0i	−0.443594	−	1.36524i	0.440425	−	0.897789i	$-0.354828\pi$
$434$	−6859.93	−	4984.03i	−0.758727	−	0.551247i
$435$		0			0
$436$	28834.9	−	20949.8i	3.16730	−	2.30118i
$437$	−4073.62	−	2959.66i	−0.445922	−	0.323981i
$438$		0			0
$439$	−4561.58	+	3314.18i	−0.495928	+	0.360313i	−0.807460	−	0.589923i	$-0.799158\pi$
$439$	−4561.58	+	3314.18i	−0.495928	+	0.360313i	0.311531	+	0.950236i	$0.399158\pi$
$440$	−17582.3	−	1544.48i	−1.90501	−	0.167342i
$441$		0			0
$442$	133.556	+	411.042i	0.0143724	+	0.0442337i
$443$	2827.26			0.303221			0.151611	−	0.988440i	$-0.451554\pi$
$443$	2827.26			0.303221			0.151611	+	0.988440i	$0.451554\pi$
$444$		0			0
$445$	3020.51	−	7108.93i	0.321766	−	0.757293i
$446$	5738.76	−	17662.1i	0.609278	−	1.87517i
$447$		0			0
$448$	7325.82	−	5322.52i	0.772572	−	0.561306i
$449$	14913.8			1.56754			0.783769	−	0.621052i	$-0.213294\pi$
$449$	14913.8			1.56754			0.783769	+	0.621052i	$0.213294\pi$
$450$		0			0
$451$	−87.1118			−0.00909520
$452$	15044.3	−	10930.3i	1.56554	−	1.13743i
$453$		0			0
$454$	8822.07	−	27151.5i	0.911983	−	2.80679i
$455$	−4743.39	−	416.675i	−0.488733	−	0.0429319i
$456$		0			0
$457$	6570.60			0.672559			0.336280	−	0.941762i	$-0.390831\pi$
$457$	6570.60			0.672559			0.336280	+	0.941762i	$0.390831\pi$
$458$	−1100.45	−	3386.82i	−0.112272	−	0.345537i
$459$		0			0
$460$	−11957.1	−	10401.6i	−1.21197	−	1.05430i
$461$	−11261.5	+	8181.99i	−1.13775	+	0.826623i	−0.986804	−	0.161919i	$-0.948232\pi$
$461$	−11261.5	+	8181.99i	−1.13775	+	0.826623i	−0.150945	+	0.988542i	$0.548232\pi$
$462$		0			0
$463$	9396.58	+	6827.02i	0.943188	+	0.685266i	0.949186	−	0.314716i	$-0.101909\pi$
$463$	9396.58	+	6827.02i	0.943188	+	0.685266i	−0.00599770	+	0.999982i	$0.501909\pi$
$464$	−14880.7	+	10811.4i	−1.48883	+	1.08170i
$465$		0			0
$466$	−20054.4	−	14570.4i	−1.99357	−	1.44841i
$467$	1752.46	+	5393.52i	0.173649	+	0.534437i	0.999569	−	0.0293500i	$-0.00934375\pi$
$467$	1752.46	+	5393.52i	0.173649	+	0.534437i	−0.825920	+	0.563787i	$0.809344\pi$
$468$		0			0
$469$	2103.75	+	6474.69i	0.207127	+	0.637470i
$470$	24263.4	+	21106.8i	2.38125	+	2.07146i
$471$		0			0
$472$	−3330.68	+	10250.8i	−0.324803	+	0.999641i
$473$	−189.873	+	137.951i	−0.0184574	+	0.0134101i
$474$		0			0
$475$	−8837.69	−	1564.74i	−0.853687	−	0.151147i
$476$	358.575			0.0345279
$477$		0			0
$478$	−10426.1	+	32088.2i	−0.997652	+	3.07046i
$479$	−2337.30	+	7193.47i	−0.222952	+	0.686175i	0.775541	+	0.631297i	$0.217477\pi$
$479$	−2337.30	+	7193.47i	−0.222952	+	0.686175i	−0.998493	+	0.0548782i	$0.982523\pi$
$480$		0			0
$481$	5343.77	+	16446.4i	0.506559	+	1.55903i
$482$	6483.51			0.612688
$483$		0			0
$484$	12081.3	+	8777.60i	1.13461	+	0.824342i
$485$	1546.28	+	6708.44i	0.144769	+	0.628072i
$486$		0			0
$487$	−3743.14	−	2719.55i	−0.348291	−	0.253049i	0.399860	−	0.916576i	$-0.369059\pi$
$487$	−3743.14	−	2719.55i	−0.348291	−	0.253049i	−0.748152	+	0.663527i	$0.769059\pi$
$488$	44896.0	+	32618.9i	4.16465	+	3.02579i
$489$		0			0
$490$	5809.17	−	13672.2i	0.535575	−	1.26050i
$491$	−14224.2	−	10334.5i	−1.30739	−	0.949874i	−0.307391	−	0.951583i	$-0.599456\pi$
$491$	−14224.2	−	10334.5i	−1.30739	−	0.949874i	−0.999999	+	0.00170911i	$0.999456\pi$
$492$		0			0
$493$	−185.174			−0.0169165
$494$	5208.89	+	16031.3i	0.474411	+	1.46009i
$495$		0			0
$496$	−9361.68	+	28812.3i	−0.847484	+	2.60829i
$497$	−2018.07	+	6210.99i	−0.182139	+	0.560565i
$498$		0			0
$499$	−2983.65			−0.267669			−0.133834	−	0.991004i	$-0.542729\pi$
$499$	−2983.65			−0.267669			−0.133834	+	0.991004i	$0.542729\pi$
$500$	−27278.4	−	7340.10i	−2.43986	−	0.656519i
$501$		0			0
$502$	22453.1	−	16313.1i	1.99628	−	1.45038i
$503$	−1756.75	+	5406.72i	−0.155725	+	0.479272i	−0.998234	−	0.0594106i	$-0.981078\pi$
$503$	−1756.75	+	5406.72i	−0.155725	+	0.479272i	0.842509	+	0.538683i	$0.181078\pi$
$504$		0			0
$505$	−6010.06	+	3608.33i	−0.529592	+	0.317957i
$506$	−2801.15	−	8621.05i	−0.246099	−	0.757416i
$507$		0			0
$508$	6434.40	+	19803.0i	0.561969	+	1.72956i
$509$	4078.11	+	2962.92i	0.355126	+	0.258014i	0.751016	−	0.660284i	$-0.229564\pi$
$509$	4078.11	+	2962.92i	0.355126	+	0.258014i	−0.395890	+	0.918298i	$0.629564\pi$
$510$		0			0
$511$	−377.070	+	273.958i	−0.0326431	+	0.0237166i
$512$	9857.45	+	7161.86i	0.850863	+	0.618188i
$513$		0			0
$514$	24272.4	−	17634.9i	2.08290	−	1.51331i
$515$	−3824.28	−	16591.4i	−0.327219	−	1.41962i
$516$		0			0
$517$	4072.32	+	12533.3i	0.346423	+	1.06618i
$518$	20025.5			1.69859
$519$		0			0
$520$	7200.11	+	31237.2i	0.607203	+	2.63432i
$521$	−5057.33	+	15564.9i	−0.425270	+	1.30885i	0.477466	+	0.878650i	$0.341555\pi$
$521$	−5057.33	+	15564.9i	−0.425270	+	1.30885i	−0.902736	+	0.430196i	$0.858445\pi$
$522$		0			0
$523$	−2132.73	+	1549.52i	−0.178313	+	0.129552i	−0.673362	−	0.739313i	$-0.735150\pi$
$523$	−2132.73	+	1549.52i	−0.178313	+	0.129552i	0.495048	+	0.868865i	$0.335150\pi$
$524$	−6160.77			−0.513615
$525$		0			0
$526$	−1415.99			−0.117377
$527$	−246.743	+	179.270i	−0.0203953	+	0.0148180i
$528$		0			0
$529$	−2240.08	+	6894.26i	−0.184111	+	0.566636i
$530$	−7289.72	−	6341.37i	−0.597444	−	0.519719i
$531$		0			0
$532$	13985.0			1.13971
$533$	48.8910	+	150.471i	0.00397318	+	0.0122282i
$534$		0			0
$535$	4175.92	−	2507.15i	0.337459	−	0.202604i
$536$	37078.8	−	26939.3i	2.98799	−	2.17090i
$537$		0			0
$538$	−289.681	−	210.466i	−0.0232138	−	0.0168658i
$539$	4924.81	−	3578.09i	0.393556	−	0.285935i
$540$		0			0
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	0.149573	−	0.988751i	$-0.452210\pi$
$541$	−9369.11	−	6807.06i	−0.744565	−	0.540958i	−0.894137	+	0.447793i	$0.852210\pi$
$542$	−6962.16	−	21427.3i	−0.551754	−	1.69812i
$543$		0			0
$544$	−257.334	−	791.992i	−0.0202814	−	0.0624198i
$545$	19638.7	+	1725.13i	1.54354	+	0.135590i
$546$		0			0
$547$	1752.01	−	5392.13i	0.136948	−	0.421483i	−0.858940	−	0.512076i	$-0.828876\pi$
$547$	1752.01	−	5392.13i	0.136948	−	0.421483i	0.995888	+	0.0905938i	$0.0288765\pi$
$548$	−29648.2	+	21540.7i	−2.31115	+	1.67915i
$549$		0			0
$550$	−11215.7	−	11630.6i	−0.869526	−	0.901690i
$551$	−7222.10			−0.558388
$552$		0			0
$553$	−1403.36	+	4319.10i	−0.107915	+	0.332128i
$554$	14338.3	−	44128.7i	1.09959	−	3.38420i
$555$		0			0
$556$	−4472.17	−	13763.9i	−0.341119	−	1.04986i
$557$	4968.53			0.377959			0.188980	−	0.981981i	$-0.439482\pi$
$557$	4968.53			0.377959			0.188980	+	0.981981i	$0.439482\pi$
$558$		0			0
$559$	344.852	+	250.549i	0.0260924	+	0.0189573i
$560$	19625.3	+	1723.95i	1.48093	+	0.130090i
$561$		0			0
$562$	29997.7	+	21794.6i	2.25156	+	1.63586i
$563$	8731.04	+	6343.47i	0.653587	+	0.474859i	0.864491	−	0.502648i	$-0.167641\pi$
$563$	8731.04	+	6343.47i	0.653587	+	0.474859i	−0.210904	+	0.977507i	$0.567641\pi$
$564$		0			0
$565$	10246.3	+	900.067i	0.762946	+	0.0670197i
$566$	−28666.1	−	20827.1i	−2.12885	−	1.54670i
$567$		0			0
$568$	43965.3			3.24778
$569$	876.580	+	2697.84i	0.0645838	+	0.198768i	0.978141	−	0.207941i	$-0.0666762\pi$
$569$	876.580	+	2697.84i	0.0645838	+	0.198768i	−0.913558	+	0.406709i	$0.866676\pi$
$570$		0			0
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	−0.849258	−	0.527978i	$-0.822950\pi$
$571$	2021.34	−	6221.03i	0.148144	−	0.455941i	0.997402	+	0.0720377i	$0.0229502\pi$
$572$	−6718.28	+	20676.7i	−0.491093	+	1.51143i
$573$		0			0
$574$	183.216			0.0133228
$575$	−1213.88	−	8681.55i	−0.0880390	−	0.629645i
$576$		0			0
$577$	4388.86	−	3188.69i	0.316656	−	0.230064i	−0.418091	−	0.908405i	$-0.637301\pi$
$577$	4388.86	−	3188.69i	0.316656	−	0.230064i	0.734747	+	0.678341i	$0.237301\pi$
$578$	−8058.52	+	24801.6i	−0.579914	+	1.78479i
$579$		0			0
$580$	−22643.9	−	1989.11i	−1.62110	−	0.142403i
$581$	−1792.18	−	5515.75i	−0.127972	−	0.393859i
$582$		0			0
$583$	−1223.50	−	3765.53i	−0.0869159	−	0.267500i
$584$	2538.50	+	1844.33i	0.179870	+	0.130683i
$585$		0			0
$586$	−18066.3	+	13126.0i	−1.27357	+	0.925304i
$587$	−16859.9	−	12249.4i	−1.18549	−	0.861310i	−0.192711	−	0.981256i	$-0.561728\pi$
$587$	−16859.9	−	12249.4i	−1.18549	−	0.861310i	−0.992780	+	0.119946i	$0.961728\pi$
$588$		0			0
$589$	−9623.39	+	6991.80i	−0.673217	+	0.489121i
$590$	−8459.32	+	5078.82i	−0.590279	+	0.354393i
$591$		0			0
$592$	−22109.3	−	68045.4i	−1.53494	−	4.72407i
$593$	8301.64			0.574886			0.287443	−	0.957798i	$-0.407195\pi$
$593$	8301.64			0.574886			0.287443	+	0.957798i	$0.407195\pi$
$594$		0			0
$595$	149.640	+	130.173i	0.0103103	+	0.00896902i
$596$	−4532.36	+	13949.2i	−0.311498	+	0.958691i
$597$		0			0
$598$	−13319.3	+	9677.03i	−0.910813	+	0.661744i
$599$	−22052.7			−1.50426			−0.752129	−	0.659016i	$-0.770973\pi$
$599$	−22052.7			−1.50426			−0.752129	+	0.659016i	$0.770973\pi$
$600$		0			0
$601$	−4849.47			−0.329141			−0.164571	−	0.986365i	$-0.552624\pi$
$601$	−4849.47			−0.329141			−0.164571	+	0.986365i	$0.552624\pi$
$602$	399.347	−	290.142i	0.0270368	−	0.0196434i
$603$		0			0
$604$	19059.1	−	58658.0i	1.28395	−	3.95159i
$605$	1855.26	+	8048.92i	0.124673	+	0.540884i
$606$		0			0
$607$	−23938.2			−1.60070			−0.800348	−	0.599536i	$-0.795352\pi$
$607$	−23938.2			−1.60070			−0.800348	+	0.599536i	$0.795352\pi$
$608$	−10036.4	−	30888.9i	−0.669458	−	2.06038i
$609$		0			0
$610$	11410.5	+	49503.7i	0.757371	+	3.28581i
$611$	19363.6	−	14068.5i	1.28211	−	0.931507i
$612$		0			0
$613$	19265.9	+	13997.5i	1.26940	+	0.922275i	0.999179	−	0.0405223i	$-0.0129022\pi$
$613$	19265.9	+	13997.5i	1.26940	+	0.922275i	0.270224	+	0.962797i	$0.412902\pi$
$614$	−5848.60	+	4249.26i	−0.384414	+	0.279293i
$615$		0			0
$616$	12306.8	+	8941.40i	0.804959	+	0.584837i
$617$	−8.51935	−	26.2199i	−0.000555877	−	0.00171081i	0.950778	−	0.309872i	$-0.100286\pi$
$617$	−8.51935	−	26.2199i	−0.000555877	−	0.00171081i	−0.951334	+	0.308161i	$0.900286\pi$
$618$		0			0
$619$	7240.90	+	22285.2i	0.470172	+	1.44704i	0.852360	+	0.522956i	$0.175171\pi$
$619$	7240.90	+	22285.2i	0.470172	+	1.44704i	−0.382188	+	0.924085i	$0.624829\pi$
$620$	−32098.5	+	19271.4i	−2.07921	+	1.24832i
$621$		0			0
$622$	−4038.23	+	12428.4i	−0.260319	+	0.801179i
$623$	−5385.71	+	3912.95i	−0.346347	+	0.251636i
$624$		0			0
$625$	−8719.15	−	12966.0i	−0.558026	−	0.829824i
$626$	−15318.1			−0.978007
$627$		0			0
$628$	−13534.0	+	41653.5i	−0.859980	+	2.64675i
$629$	222.583	−	685.039i	0.0141096	−	0.0434249i
$630$		0			0
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	0.969774	−	0.244005i	$-0.0784614\pi$
$631$	662.358	+	2038.53i	0.0417877	+	0.128609i	−0.927986	+	0.372614i	$0.878461\pi$
$632$	30573.3			1.92427
$633$		0			0
$634$	−32249.4	−	23430.5i	−2.02017	−	1.46774i
$635$	−4503.86	+	10600.1i	−0.281465	+	0.662441i
$636$		0			0
$637$	−8944.56	−	6498.60i	−0.556352	−	0.404213i
$638$	−10518.4	−	7642.10i	−0.652710	−	0.474222i
$639$		0			0
$640$	−3447.18	−	14955.4i	−0.212909	−	0.923694i
$641$	16852.6	+	12244.1i	1.03844	+	0.754469i	0.969980	−	0.243185i	$-0.0781923\pi$
$641$	16852.6	+	12244.1i	1.03844	+	0.754469i	0.0684575	+	0.997654i	$0.478192\pi$
$642$		0			0
$643$	−29336.6			−1.79926			−0.899628	−	0.436657i	$-0.856162\pi$
$643$	−29336.6			−1.79926			−0.899628	+	0.436657i	$0.856162\pi$
$644$	4220.91	+	12990.6i	0.258272	+	0.794879i
$645$		0			0
$646$	216.964	−	667.748i	0.0132142	−	0.0406690i
$647$	2452.54	−	7548.13i	0.149025	−	0.458652i	−0.848482	−	0.529225i	$-0.822483\pi$
$647$	2452.54	−	7548.13i	0.149025	−	0.458652i	0.997507	+	0.0705732i	$0.0224828\pi$
$648$		0			0
$649$	−4043.28			−0.244550
$650$	−13795.1	+	25900.8i	−0.832444	+	1.56294i
$651$		0			0
$652$	1272.29	−	924.374i	0.0764215	−	0.0555234i
$653$	3363.18	−	10350.8i	0.201549	−	0.620304i	−0.798288	−	0.602275i	$-0.794261\pi$
$653$	3363.18	−	10350.8i	0.201549	−	0.620304i	0.999837	−	0.0180290i	$-0.00573912\pi$
$654$		0			0
$655$	−2571.01	−	2236.53i	−0.153370	−	0.133417i
$656$	−202.281	−	622.558i	−0.0120393	−	0.0370530i
$657$		0			0
$658$	−8565.03	−	26360.5i	−0.507447	−	1.56176i
$659$	−23268.1	−	16905.3i	−1.37541	−	0.999295i	−0.997292	−	0.0735377i	$-0.976571\pi$
$659$	−23268.1	−	16905.3i	−1.37541	−	0.999295i	−0.378119	−	0.925757i	$-0.623429\pi$
$660$		0			0
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	−0.447823	−	0.894122i	$-0.647801\pi$
$661$	4489.07	−	3261.50i	0.264152	−	0.191918i	0.711976	+	0.702204i	$0.247801\pi$
$662$	4450.67	+	3233.60i	0.261299	+	0.189845i
$663$		0			0
$664$	−31587.2	+	22949.4i	−1.84612	+	1.34128i
$665$	5836.21	+	5076.95i	0.340329	+	0.296053i
$666$		0			0
$667$	−2179.75	−	6708.57i	−0.126537	−	0.389441i
$668$	2554.72			0.147972
$669$		0			0
$670$	41795.2	+	3671.43i	2.40999	+	0.211701i
$671$	−6433.04	+	19798.9i	−0.370111	+	1.13909i
$672$		0			0
$673$	8913.64	−	6476.14i	0.510543	−	0.370931i	−0.302487	−	0.953154i	$-0.597817\pi$
$673$	8913.64	−	6476.14i	0.510543	−	0.370931i	0.813030	+	0.582222i	$0.197817\pi$
$674$	6941.20			0.396684
$675$		0			0
$676$	−4922.10			−0.280047
$677$	−3876.03	+	2816.10i	−0.220041	+	0.159869i	−0.692345	−	0.721566i	$-0.743422\pi$
$677$	−3876.03	+	2816.10i	−0.220041	+	0.159869i	0.472304	+	0.881436i	$0.343422\pi$
$678$		0			0
$679$	1833.53	−	5643.02i	0.103629	−	0.318938i
$680$	522.150	−	1228.90i	0.0294464	−	0.0693035i
$681$		0			0
$682$	−21414.2			−1.20233
$683$	−3369.89	−	10371.5i	−0.188793	−	0.581044i	0.811200	−	0.584768i	$-0.198815\pi$
$683$	−3369.89	−	10371.5i	−0.188793	−	0.581044i	−0.999993	+	0.00372404i	$0.998815\pi$
$684$		0			0
$685$	−20192.7	−	1773.79i	−1.12631	−	0.0989386i
$686$	−24560.9	+	17844.5i	−1.36696	+	0.993158i
$687$		0			0
$688$	−1426.79	−	1036.62i	−0.0790636	−	0.0574431i
$689$	−5817.64	+	4226.76i	−0.321675	+	0.233711i
$690$		0			0
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.960029	−	0.279900i	$-0.0903012\pi$
$691$	17991.6	+	13071.6i	0.990494	+	0.719636i	0.0304648	+	0.999536i	$0.490301\pi$
$692$	−20231.8	−	62267.1i	−1.11141	−	3.42058i
$693$		0			0
$694$	−5483.86	−	16877.6i	−0.299949	−	0.923148i
$695$	3130.37	−	7367.48i	0.170851	−	0.402107i
$696$		0			0
$697$	2.03644	−	6.26753i	0.000110668	−	0.000340602i
$698$	−46101.0	+	33494.3i	−2.49992	+	1.81630i
$699$		0			0
$700$	16900.4	+	17525.5i	0.912534	+	0.946288i
$701$	23186.1			1.24925			0.624626	−	0.780924i	$-0.285251\pi$
$701$	23186.1			1.24925			0.624626	+	0.780924i	$0.285251\pi$
$702$		0			0
$703$	8681.07	−	26717.6i	0.465737	−	1.43339i
$704$	7066.75	−	21749.2i	0.378321	−	1.16435i
$705$		0			0
$706$	−13703.9	−	42176.1i	−0.730526	−	2.24833i
$707$	6041.76			0.321392
$708$		0			0
$709$	6798.49	+	4939.39i	0.360117	+	0.261640i	0.753101	−	0.657905i	$-0.228557\pi$
$709$	6798.49	+	4939.39i	0.360117	+	0.261640i	−0.392984	+	0.919545i	$0.628557\pi$
$710$	30365.8	+	26415.3i	1.60508	+	1.39627i
$711$		0			0
$712$	36257.5	+	26342.6i	1.90844	+	1.38656i
$713$	−9399.15	−	6828.88i	−0.493690	−	0.358687i
$714$		0			0
$715$	−10309.9	+	6189.88i	−0.539256	+	0.323760i
$716$	23220.8	+	16870.9i	1.21202	+	0.880581i
$717$		0			0
$718$	−54191.0			−2.81670
$719$	2318.10	+	7134.38i	0.120237	+	0.370052i	0.993003	−	0.118087i	$-0.0376760\pi$
$719$	2318.10	+	7134.38i	0.120237	+	0.370052i	−0.872766	+	0.488139i	$0.837676\pi$
$720$		0			0
$721$	−4534.70	+	13956.4i	−0.234232	+	0.720891i
$722$	−2796.24	+	8605.94i	−0.144135	+	0.443601i
$723$		0			0
$724$	−8610.36			−0.441991
$725$	−8727.63	−	9050.46i	−0.447084	−	0.463622i
$726$		0			0
$727$	−2031.25	+	1475.79i	−0.103624	+	0.0752876i	−0.638391	−	0.769712i	$-0.720400\pi$
$727$	−2031.25	+	1475.79i	−0.103624	+	0.0752876i	0.534766	+	0.845000i	$0.320400\pi$
$728$	8537.65	−	26276.2i	0.434652	−	1.33772i
$729$		0			0
$730$	645.169	+	2799.03i	0.0327106	+	0.141913i
$731$	−5.48656	−	16.8859i	−0.000277603	−	0.000854375i
$732$		0			0
$733$	−688.054	−	2117.61i	−0.0346710	−	0.106706i	0.932223	−	0.361884i	$-0.117866\pi$
$733$	−688.054	−	2117.61i	−0.0346710	−	0.106706i	−0.966894	+	0.255177i	$0.917866\pi$
$734$	32091.3	+	23315.7i	1.61378	+	1.17248i
$735$		0			0
$736$	25663.4	−	18645.6i	1.28528	−	0.933811i
$737$	13909.4	+	10105.8i	0.695197	+	0.505090i
$738$		0			0
$739$	6654.13	−	4834.51i	0.331226	−	0.240650i	−0.409724	−	0.912209i	$-0.634375\pi$
$739$	6654.13	−	4834.51i	0.331226	−	0.240650i	0.740951	+	0.671559i	$0.234375\pi$
$740$	34576.9	−	81378.5i	1.71767	−	4.04261i
$741$		0			0
$742$	2573.29	+	7919.78i	0.127316	+	0.391839i
$743$	449.577			0.0221984			0.0110992	−	0.999938i	$-0.496467\pi$
$743$	449.577			0.0221984			0.0110992	+	0.999938i	$0.496467\pi$
$744$		0			0
$745$	−6955.37	+	4175.88i	−0.342047	+	0.205359i
$746$	−9485.39	+	29193.0i	−0.465529	+	1.43275i
$747$		0			0
$748$	732.617	−	532.277i	0.0358117	−	0.0260187i
$749$	−4197.95			−0.204793
$750$		0			0
$751$	4588.83			0.222968			0.111484	−	0.993766i	$-0.464440\pi$
$751$	4588.83			0.222968			0.111484	+	0.993766i	$0.464440\pi$
$752$	−80115.0	+	58206.9i	−3.88496	+	2.82259i
$753$		0			0
$754$	−7297.02	+	22457.9i	−0.352443	+	1.08471i
$755$	29248.2	−	17560.1i	1.40987	−	0.846460i
$756$		0			0
$757$	3857.39			0.185204			0.0926019	−	0.995703i	$-0.470482\pi$
$757$	3857.39			0.185204			0.0926019	+	0.995703i	$0.470482\pi$
$758$	−13280.0	−	40871.6i	−0.636346	−	1.95847i
$759$		0			0
$760$	20364.7	−	47929.2i	0.971979	−	2.28760i
$761$	−1652.00	+	1200.25i	−0.0786924	+	0.0571734i	−0.626436	−	0.779473i	$-0.715487\pi$
$761$	−1652.00	+	1200.25i	−0.0786924	+	0.0571734i	0.547743	+	0.836646i	$0.315487\pi$
$762$		0			0
$763$	−13746.2	−	9987.19i	−0.652222	−	0.473867i
$764$	−24121.7	+	17525.4i	−1.14227	+	0.829904i
$765$		0			0
$766$	9092.43	+	6606.03i	0.428881	+	0.311600i
$767$	2269.27	+	6984.08i	0.106830	+	0.328788i
$768$		0			0
$769$	2316.48	+	7129.41i	0.108628	+	0.334321i	0.990565	−	0.137046i	$-0.0437607\pi$
$769$	2316.48	+	7129.41i	0.108628	+	0.334321i	−0.881937	+	0.471367i	$0.843761\pi$
$770$	3127.81	+	13569.8i	0.146388	+	0.635094i
$771$		0			0
$772$	−9593.70	+	29526.4i	−0.447260	+	1.37653i
$773$	9488.89	−	6894.08i	0.441516	−	0.320780i	−0.344721	−	0.938705i	$-0.612027\pi$
$773$	9488.89	−	6894.08i	0.441516	−	0.320780i	0.786237	+	0.617925i	$0.212027\pi$
$774$		0			0
$775$	−20391.4	−	3610.35i	−0.945135	−	0.167339i
$776$	−39944.8			−1.84786
$777$		0			0
$778$	11014.3	−	33898.5i	0.507560	−	1.56211i
$779$	79.4245	−	244.443i	0.00365299	−	0.0112427i
$780$		0			0
$781$	5096.54	+	15685.5i	0.233506	+	0.718659i
$782$	685.751			0.0313586
$783$		0			0
$784$	37007.2	+	26887.3i	1.68582	+	1.22482i
$785$	−20769.4	+	12469.6i	−0.944321	+	0.566953i
$786$		0			0
$787$	−6670.93	−	4846.71i	−0.302151	−	0.219526i	0.426370	−	0.904549i	$-0.359792\pi$
$787$	−6670.93	−	4846.71i	−0.302151	−	0.219526i	−0.728521	+	0.685023i	$0.759792\pi$
$788$	−5100.05	−	3705.40i	−0.230561	−	0.167512i
$789$		0			0
$790$	21116.3	+	18369.1i	0.950991	+	0.827272i
$791$	−7171.93	−	5210.71i	−0.322382	−	0.234225i
$792$		0			0
$793$	37809.7			1.69314
$794$	−10778.6	−	33173.2i	−0.481762	−	1.48271i
$795$		0			0
$796$	−9080.37	+	27946.5i	−0.404328	+	1.24439i
$797$	4254.84	−	13095.1i	0.189102	−	0.581996i	−0.810893	−	0.585194i	$-0.801018\pi$
$797$	4254.84	−	13095.1i	0.189102	−	0.581996i	0.999995	+	0.00319879i	$0.00101821\pi$
$798$		0			0
$799$	−996.948			−0.0441420
$800$	26580.2	−	49905.4i	1.17469	−	2.20553i
$801$		0			0
$802$	−44219.6	+	32127.4i	−1.94694	+	1.41454i
$803$	−363.736	+	1119.46i	−0.0159850	+	0.0491968i
$804$		0			0
$805$	−2954.49	+	6953.54i	−0.129357	+	0.304447i
$806$	12018.6	+	36989.3i	0.525231	+	1.61649i
$807$		0			0
$808$	−12569.0	−	38683.5i	−0.547248	−	1.68426i
$809$	−29901.2	−	21724.5i	−1.29947	−	0.944119i	−0.299518	−	0.954091i	$-0.596826\pi$
$809$	−29901.2	−	21724.5i	−1.29947	−	0.944119i	−0.999950	+	0.00997139i	$0.996826\pi$
$810$		0			0
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	−0.299562	−	0.954077i	$-0.596841\pi$
$811$	11900.0	−	8645.89i	0.515249	−	0.374351i	0.814811	+	0.579726i	$0.196841\pi$
$812$	15849.7	+	11515.5i	0.684994	+	0.497677i
$813$		0			0
$814$	40914.7	−	29726.3i	1.76174	−	1.27998i
$815$	866.525	+	76.1184i	0.0372430	+	0.00327155i
$816$		0			0
$817$	−213.985	−	658.577i	−0.00916325	−	0.0282016i
$818$	35351.8			1.51106
$819$		0			0
$820$	316.350	−	744.544i	0.0134724	−	0.0317081i
$821$	11760.0	−	36193.6i	0.499911	−	1.53857i	−0.309249	−	0.950981i	$-0.600078\pi$
$821$	11760.0	−	36193.6i	0.499911	−	1.53857i	0.809160	−	0.587588i	$-0.199922\pi$
$822$		0			0
$823$	3323.08	−	2414.36i	0.140748	−	0.102259i	−0.515183	−	0.857080i	$-0.672276\pi$
$823$	3323.08	−	2414.36i	0.140748	−	0.102259i	0.655931	+	0.754821i	$0.272276\pi$
$824$	98792.0			4.17668
$825$		0			0
$826$	8503.95			0.358221
$827$	−13578.9	+	9865.62i	−0.570959	+	0.414826i	−0.835453	−	0.549561i	$-0.814795\pi$
$827$	−13578.9	+	9865.62i	−0.570959	+	0.414826i	0.264494	+	0.964387i	$0.414795\pi$
$828$		0			0
$829$	−3997.64	+	12303.5i	−0.167483	+	0.515461i	−0.999211	−	0.0397237i	$-0.987352\pi$
$829$	−3997.64	+	12303.5i	−0.167483	+	0.515461i	0.831727	+	0.555184i	$0.187352\pi$
$830$	−35605.1	−	3127.67i	−1.48900	−	0.130799i
$831$		0			0
$832$	−41534.3			−1.73070
$833$	142.307	+	437.977i	0.00591915	+	0.0182173i
$834$		0			0
$835$	1066.13	+	927.433i	0.0441857	+	0.0384373i
$836$	28573.2	−	20759.7i	1.18209	−	0.858837i
$837$		0			0
$838$	18747.5	+	13620.9i	0.772819	+	0.561486i
$839$	34205.0	−	24851.4i	1.40750	−	1.02261i	0.413815	−	0.910361i	$-0.364196\pi$
$839$	34205.0	−	24851.4i	1.40750	−	1.02261i	0.993681	−	0.112244i	$-0.0358040\pi$
$840$		0			0
$841$	11546.1	+	8388.71i	0.473413	+	0.343955i
$842$	13869.5	+	42686.0i	0.567666	+	1.74710i
$843$		0			0
$844$	16456.2	+	50646.9i	0.671144	+	2.06557i
$845$	−2054.09	−	1786.86i	−0.0836245	−	0.0727453i
$846$		0			0
$847$	2199.90	−	6770.60i	0.0892438	−	0.274664i
$848$	24069.9	−	17487.8i	0.974720	−	0.708176i
$849$		0			0
$850$	1098.99	−	535.056i	0.0443471	−	0.0215909i
$851$	27437.9			1.10524
$852$		0			0
$853$	8807.70	−	27107.3i	0.353540	−	1.08809i	−0.603310	−	0.797506i	$-0.706152\pi$
$853$	8807.70	−	27107.3i	0.353540	−	1.08809i	0.956851	−	0.290579i	$-0.0938480\pi$
$854$	13530.2	−	41641.6i	0.542146	−	1.66855i
$855$		0			0
$856$	8733.23	+	26878.1i	0.348710	+	1.07322i
$857$	−4999.42			−0.199273			−0.0996366	−	0.995024i	$-0.531768\pi$
$857$	−4999.42			−0.199273			−0.0996366	+	0.995024i	$0.531768\pi$
$858$		0			0
$859$	−20283.7	−	14737.0i	−0.805669	−	0.585353i	0.106902	−	0.994270i	$-0.465907\pi$
$859$	−20283.7	−	14737.0i	−0.805669	−	0.585353i	−0.912572	+	0.408916i	$0.865907\pi$
$860$	−489.535	−	2123.82i	−0.0194105	−	0.0842111i
$861$		0			0
$862$	−1722.72	−	1251.63i	−0.0680695	−	0.0494554i
$863$	3644.26	+	2647.71i	0.143745	+	0.104437i	0.657334	−	0.753600i	$-0.271684\pi$
$863$	3644.26	+	2647.71i	0.143745	+	0.104437i	−0.513588	+	0.858037i	$0.671684\pi$
$864$		0			0
$865$	14161.6	−	33329.9i	0.556656	−	1.31012i
$866$	55579.9	+	40381.2i	2.18093	+	1.58454i
$867$		0			0
$868$	32267.9			1.26180
$869$	3544.12	+	10907.7i	0.138350	+	0.425797i
$870$		0			0
$871$	9649.46	−	29698.0i	0.375384	−	1.15531i
$872$	−35347.8	+	108789.i	−1.37274	+	4.22485i
$873$		0			0
$874$	26745.4			1.03510
$875$	690.599	+	13449.0i	0.0266817	+	0.519611i
$876$		0			0
$877$	−8221.02	+	5972.92i	−0.316538	+	0.229979i	−0.734697	−	0.678395i	$-0.762676\pi$
$877$	−8221.02	+	5972.92i	−0.316538	+	0.229979i	0.418159	+	0.908374i	$0.362676\pi$
$878$	9254.78	−	28483.3i	0.355733	−	1.09483i
$879$		0			0
$880$	42656.1	−	25610.0i	1.63402	−	0.981036i
$881$	10338.8	+	31819.5i	0.395372	+	1.21683i	0.928672	+	0.370903i	$0.120952\pi$
$881$	10338.8	+	31819.5i	0.395372	+	1.21683i	−0.533300	+	0.845926i	$0.679048\pi$
$882$		0			0
$883$	4567.13	+	14056.2i	0.174061	+	0.535706i	0.999589	−	0.0286552i	$-0.00912250\pi$
$883$	4567.13	+	14056.2i	0.174061	+	0.535706i	−0.825528	+	0.564361i	$0.809122\pi$
$884$	−1330.60	−	966.734i	−0.0506253	−	0.0367814i
$885$		0			0
$886$	−12149.2	+	8826.93i	−0.460678	+	0.334702i
$887$	−12478.8	−	9066.41i	−0.472377	−	0.343202i	0.325990	−	0.945373i	$-0.394302\pi$
$887$	−12478.8	−	9066.41i	−0.472377	−	0.343202i	−0.798367	+	0.602171i	$0.794302\pi$
$888$		0			0
$889$	8030.58	−	5834.56i	0.302966	−	0.220118i
$890$	9214.97	+	39978.6i	0.347064	+	1.50571i
$891$		0			0
$892$	21838.7	+	67212.5i	0.819745	+	2.52292i
$893$	−38882.6			−1.45706
$894$		0			0
$895$	3565.88	+	15470.4i	0.133178	+	0.577785i
$896$	−4087.56	+	12580.2i	−0.152406	+	0.469057i
$897$		0			0
$898$	−64087.2	+	46562.1i	−2.38153	+	1.73028i
$899$	−16663.7			−0.618203
$900$		0			0
$901$	299.525			0.0110750
$902$	374.335	−	271.970i	0.0138182	−	0.0100395i
$903$		0			0
$904$	−18442.3	+	56759.7i	−0.678521	+	2.08827i
$905$	−3593.27	−	3125.80i	−0.131983	−	0.114812i
$906$		0			0
$907$	43594.8			1.59596			0.797982	−	0.602681i	$-0.205901\pi$
$907$	43594.8			1.59596			0.797982	+	0.602681i	$0.205901\pi$
$908$	33572.1	+	103324.i	1.22701	+	3.77636i
$909$		0			0
$910$	21684.1	−	13018.7i	0.789913	−	0.474249i
$911$	−42130.2	+	30609.4i	−1.53220	+	1.11321i	−0.577205	+	0.816599i	$0.695857\pi$
$911$	−42130.2	+	30609.4i	−1.53220	+	1.11321i	−0.954998	+	0.296612i	$0.904143\pi$
$912$		0			0
$913$	−11849.4	−	8609.06i	−0.429525	−	0.312068i
$914$	−28235.0	+	20514.0i	−1.02181	+	0.742386i
$915$		0			0
$916$	10963.6	+	7965.50i	0.395466	+	0.287323i
$917$	907.572	+	2793.22i	0.0326834	+	0.100589i
$918$		0			0
$919$	4485.22	+	13804.1i	0.160994	+	0.495490i	0.998719	−	0.0506033i	$-0.0161144\pi$
$919$	4485.22	+	13804.1i	0.160994	+	0.495490i	−0.837724	+	0.546093i	$0.816114\pi$
$920$	50667.6	+	4450.81i	1.81572	+	0.159499i
$921$		0			0
$922$	22848.0	−	70318.9i	0.816116	−	2.51175i
$923$	24233.7	−	17606.8i	0.864206	−	0.627882i
$924$		0			0
$925$	43972.3	−	21408.4i	1.56303	−	0.760978i
$926$	−61693.3			−2.18938
$927$		0			0
$928$	14059.8	−	43271.6i	0.497345	−	1.53067i
$929$	−8814.66	+	27128.7i	−0.311302	+	0.958089i	0.665948	+	0.745998i	$0.268027\pi$
$929$	−8814.66	+	27128.7i	−0.311302	+	0.958089i	−0.977250	+	0.212091i	$0.931973\pi$
$930$		0			0
$931$	5550.21	+	17081.8i	0.195382	+	0.601324i
$932$	94332.2			3.31540
$933$		0			0
$934$	−24369.6	−	17705.6i	−0.853746	−	0.620283i
$935$	498.966	+	43.8308i	0.0174524	+	0.00153307i
$936$		0			0
$937$	−22316.8	−	16214.1i	−0.778077	−	0.565306i	0.126324	−	0.991989i	$-0.459682\pi$
$937$	−22316.8	−	16214.1i	−0.778077	−	0.565306i	−0.904401	+	0.426683i	$0.859682\pi$
$938$	−29254.7	−	21254.8i	−1.01834	−	0.739866i
$939$		0			0
$940$	−121911.	−	10709.1i	−4.23011	−	0.371586i
$941$	−2094.39	−	1521.66i	−0.0725560	−	0.0527150i	0.550916	−	0.834561i	$-0.314278\pi$
$941$	−2094.39	−	1521.66i	−0.0725560	−	0.0527150i	−0.623472	+	0.781846i	$0.714278\pi$
$942$		0			0
$943$	251.034			0.00866892
$944$	−9388.85	−	28895.9i	−0.323709	−	0.996273i
$945$		0			0
$946$	385.224	−	1185.60i	0.0132397	−	0.0407475i
$947$	7157.52	−	22028.6i	0.245605	−	0.755895i	−0.749931	−	0.661516i	$-0.769913\pi$
$947$	7157.52	−	22028.6i	0.245605	−	0.755895i	0.995536	−	0.0943789i	$-0.0300865\pi$
$948$		0			0
$949$	2137.83			0.0731263
$950$	42862.4	−	20868.1i	1.46383	−	0.712683i
$951$		0			0
$952$	−931.016	+	676.423i	−0.0316958	+	0.0230284i
$953$	13151.0	−	40474.6i	0.447012	−	1.37576i	−0.433250	−	0.901274i	$-0.642633\pi$
$953$	13151.0	−	40474.6i	0.447012	−	1.37576i	0.880262	−	0.474488i	$-0.157367\pi$
$954$		0			0
$955$	−16428.6	−	1443.14i	−0.556668	−	0.0488995i
$956$	−39676.1	−	122110.i	−1.34228	−	4.13110i
$957$		0			0
$958$	−12414.8	−	38208.8i	−0.418689	−	1.28859i
$959$	14133.9	+	10268.9i	0.475921	+	0.345777i
$960$		0			0
$961$	1897.20	−	1378.40i	0.0636838	−	0.0462690i
$962$	−74310.2	−	53989.6i	−2.49050	−	1.80945i
$963$		0			0
$964$	−19960.7	+	14502.3i	−0.666899	+	0.484531i
$965$	−14722.5	+	8839.14i	−0.491125	+	0.294862i
$966$		0			0
$967$	9275.49	+	28547.0i	0.308459	+	0.949339i	0.978364	+	0.206892i	$0.0663348\pi$
$967$	9275.49	+	28547.0i	0.308459	+	0.949339i	−0.669905	+	0.742447i	$0.733665\pi$
$968$	−47926.6			−1.59134
$969$		0			0
$970$	−27589.0	−	23999.8i	−0.913225	−	0.794419i
$971$	2208.86	−	6798.18i	0.0730028	−	0.224680i	−0.907897	−	0.419193i	$-0.862313\pi$
$971$	2208.86	−	6798.18i	0.0730028	−	0.224680i	0.980900	+	0.194514i	$0.0623129\pi$
$972$		0			0
$973$	−5581.59	+	4055.26i	−0.183903	+	0.133613i
$974$	24575.6			0.808474
$975$		0			0
$976$	−156434.			−5.13045
$977$	37940.6	−	27565.5i	1.24240	−	0.902658i	0.244646	−	0.969612i	$-0.421328\pi$
$977$	37940.6	−	27565.5i	1.24240	−	0.902658i	0.997756	+	0.0669543i	$0.0213282\pi$
$978$		0			0
$979$	−5195.25	+	15989.3i	−0.169603	+	0.521983i
$980$	12697.3	+	55086.3i	0.413877	+	1.79558i
$981$		0			0
$982$	93388.9			3.03479
$983$	−18941.8	−	58296.8i	−0.614597	−	1.89154i	−0.407456	−	0.913225i	$-0.633584\pi$
$983$	−18941.8	−	58296.8i	−0.614597	−	1.89154i	−0.207142	−	0.978311i	$-0.566416\pi$
$984$		0			0
$985$	−783.184	−	3397.80i	−0.0253343	−	0.109911i
$986$	795.727	−	578.130i	0.0257009	−	0.0186728i
$987$		0			0
$988$	−51895.3	−	37704.2i	−1.67106	−	1.21410i
$989$	547.165	−	397.539i	0.0175924	−	0.0127816i
$990$		0			0
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	0.369441	−	0.929254i	$-0.379549\pi$
$991$	−12484.0	−	9070.14i	−0.400168	−	0.290739i	−0.769609	+	0.638515i	$0.779549\pi$
$992$	−23157.2	−	71270.6i	−0.741172	−	2.28109i
$993$		0			0
$994$	−10719.2	−	32990.3i	−0.342045	−	1.05270i
$995$	−13934.8	+	8366.19i	−0.443982	+	0.266559i
$996$		0			0
$997$	6645.80	−	20453.7i	0.211108	−	0.649723i	−0.788299	−	0.615292i	$-0.789038\pi$
$997$	6645.80	−	20453.7i	0.211108	−	0.649723i	0.999407	−	0.0344311i	$-0.0109619\pi$
$998$	12821.3	−	9315.21i	0.406664	−	0.295459i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.136.1		28
3.2	odd	2		25.4.d.a.11.7	✓	28
15.2	even	4		125.4.e.b.74.14		56
15.8	even	4		125.4.e.b.74.1		56
15.14	odd	2		125.4.d.a.51.1		28
25.16	even	5	inner	225.4.h.b.91.1		28
75.29	odd	10		625.4.a.d.1.14		14
75.38	even	20		125.4.e.b.49.14		56
75.41	odd	10		25.4.d.a.16.7	yes	28
75.59	odd	10		125.4.d.a.76.1		28
75.62	even	20		125.4.e.b.49.1		56
75.71	odd	10		625.4.a.c.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.7	✓	28	3.2	odd	2
25.4.d.a.16.7	yes	28	75.41	odd	10
125.4.d.a.51.1		28	15.14	odd	2
125.4.d.a.76.1		28	75.59	odd	10
125.4.e.b.49.1		56	75.62	even	20
125.4.e.b.49.14		56	75.38	even	20
125.4.e.b.74.1		56	15.8	even	4
125.4.e.b.74.14		56	15.2	even	4
225.4.h.b.91.1		28	25.16	even	5	inner
225.4.h.b.136.1		28	1.1	even	1	trivial
625.4.a.c.1.1		14	75.71	odd	10
625.4.a.d.1.14		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)

\(f(q)\)	\(=\)	\(q+(-4.29718 + 3.12208i) q^{2} +(6.24620 - 19.2238i) q^{4} +(9.58545 - 5.75493i) q^{5} -9.63602 q^{7} +(20.0464 + 61.6963i) q^{8} +O(q^{10})\)	\(q+(-4.29718 + 3.12208i) q^{2} +(6.24620 - 19.2238i) q^{4} +(9.58545 - 5.75493i) q^{5} -9.63602 q^{7} +(20.0464 + 61.6963i) q^{8} +(-23.2230 + 54.6565i) q^{10} +(-19.6877 + 14.3039i) q^{11} +(35.7572 + 25.9791i) q^{13} +(41.4077 - 30.0844i) q^{14} +(-147.942 - 107.486i) q^{16} +(-0.568894 - 1.75088i) q^{17} +(-22.1878 - 68.2870i) q^{19} +(-50.7592 - 220.216i) q^{20} +(39.9434 - 122.933i) q^{22} +(56.7348 - 41.2202i) q^{23} +(58.7616 - 110.327i) q^{25} -234.764 q^{26} +(-60.1885 + 185.241i) q^{28} +(31.0824 - 95.6617i) q^{29} +(-51.1943 - 157.560i) q^{31} +452.340 q^{32} +(7.91102 + 5.74769i) q^{34} +(-92.3655 + 55.4546i) q^{35} +(316.532 + 229.974i) q^{37} +(308.542 + 224.169i) q^{38} +(547.211 + 476.022i) q^{40} +(2.89600 + 2.10407i) q^{41} +9.64426 q^{43} +(152.003 + 467.818i) q^{44} +(-115.107 + 354.261i) q^{46} +(167.342 - 515.027i) q^{47} -250.147 q^{49} +(91.9413 + 657.554i) q^{50} +(722.765 - 525.119i) q^{52} +(-50.2766 + 154.735i) q^{53} +(-106.397 + 250.411i) q^{55} +(-193.167 - 594.507i) q^{56} +(165.097 + 508.117i) q^{58} +(134.417 + 97.6599i) q^{59} +(692.078 - 502.824i) q^{61} +(711.905 + 517.230i) q^{62} +(-760.253 + 552.356i) q^{64} +(492.256 + 43.2414i) q^{65} +(-218.322 - 671.926i) q^{67} -37.2120 q^{68} +(223.777 - 526.671i) q^{70} +(209.430 - 644.559i) q^{71} +(39.1313 - 28.4306i) q^{73} -2078.19 q^{74} -1451.33 q^{76} +(189.711 - 137.833i) q^{77} +(145.637 - 448.225i) q^{79} +(-2036.66 - 178.907i) q^{80} -19.0137 q^{82} +(185.987 + 572.410i) q^{83} +(-15.5293 - 13.5090i) q^{85} +(-41.4431 + 30.1102i) q^{86} +(-1277.17 - 927.915i) q^{88} +(558.915 - 406.075i) q^{89} +(-344.557 - 250.335i) q^{91} +(-438.034 - 1348.13i) q^{92} +(888.856 + 2735.62i) q^{94} +(-605.666 - 526.872i) q^{95} +(-190.279 + 585.617i) q^{97} +(1074.93 - 780.980i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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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