LMFDB - Embedded newform 225.4.h.b.91.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.7
Character	$\chi$	$=$	225.91
Dual form			225.4.h.b.136.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.11746 + 2.99151i) q^{2} +(5.53220 + 17.0263i) q^{4} +(10.3703 - 4.17822i) q^{5} -12.1888 q^{7} +(-15.5740 + 47.9320i) q^{8} +O(q^{10})$	\(q+(4.11746 + 2.99151i) q^{2} +(5.53220 + 17.0263i) q^{4} +(10.3703 - 4.17822i) q^{5} -12.1888 q^{7} +(-15.5740 + 47.9320i) q^{8} +(55.1983 + 13.8191i) q^{10} +(53.0773 + 38.5629i) q^{11} +(-24.5445 + 17.8326i) q^{13} +(-50.1870 - 36.4630i) q^{14} +(-91.6464 + 66.5850i) q^{16} +(-15.4803 + 47.6433i) q^{17} +(2.02724 - 6.23919i) q^{19} +(128.510 + 153.453i) q^{20} +(103.182 + 317.562i) q^{22} +(-48.1539 - 34.9858i) q^{23} +(90.0850 - 86.6585i) q^{25} -154.407 q^{26} +(-67.4311 - 207.532i) q^{28} +(-48.3877 - 148.922i) q^{29} +(87.6551 - 269.775i) q^{31} -173.351 q^{32} +(-206.265 + 149.860i) q^{34} +(-126.402 + 50.9276i) q^{35} +(-50.8593 + 36.9514i) q^{37} +(27.0116 - 19.6251i) q^{38} +(38.7631 + 562.139i) q^{40} +(199.228 - 144.748i) q^{41} -38.7316 q^{43} +(-362.951 + 1117.05i) q^{44} +(-93.6111 - 288.105i) q^{46} +(44.4855 + 136.912i) q^{47} -194.432 q^{49} +(630.161 - 87.3224i) q^{50} +(-439.410 - 319.250i) q^{52} +(-54.9578 - 169.143i) q^{53} +(711.550 + 178.139i) q^{55} +(189.830 - 584.235i) q^{56} +(246.267 - 757.932i) q^{58} +(-124.589 + 90.5195i) q^{59} +(-99.3211 - 72.1610i) q^{61} +(1167.95 - 848.564i) q^{62} +(19.4081 + 14.1008i) q^{64} +(-180.025 + 287.482i) q^{65} +(131.420 - 404.468i) q^{67} -896.831 q^{68} +(-672.804 - 168.439i) q^{70} +(-79.0054 - 243.154i) q^{71} +(267.322 + 194.221i) q^{73} -319.951 q^{74} +117.446 q^{76} +(-646.951 - 470.037i) q^{77} +(-225.825 - 695.018i) q^{79} +(-672.192 + 1073.42i) q^{80} +1253.33 q^{82} +(137.355 - 422.734i) q^{83} +(38.5297 + 558.754i) q^{85} +(-159.476 - 115.866i) q^{86} +(-2675.02 + 1943.52i) q^{88} +(838.773 + 609.404i) q^{89} +(299.169 - 217.359i) q^{91} +(329.284 - 1013.43i) q^{92} +(-226.407 + 696.810i) q^{94} +(-5.04570 - 73.1723i) q^{95} +(33.5699 + 103.318i) q^{97} +(-800.565 - 581.645i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8} - 25 q^{10} + 89 q^{11} + 33 q^{13} + 17 q^{14} - 207 q^{16} + 191 q^{17} - 115 q^{19} + 225 q^{20} + 808 q^{22} - 433 q^{23} + 90 q^{25} - 586 q^{26} - 13 q^{28} + 5 q^{29} - 639 q^{31} + 1386 q^{32} - 777 q^{34} + 1030 q^{35} + 699 q^{37} + 2355 q^{38} + 410 q^{40} - 341 q^{41} - 172 q^{43} - 548 q^{44} - 1239 q^{46} - 2319 q^{47} + 1344 q^{49} - 2335 q^{50} + 2344 q^{52} + 927 q^{53} + 1225 q^{55} + 2910 q^{56} + 2410 q^{58} + 1905 q^{59} + 1391 q^{61} + 3832 q^{62} - 3596 q^{64} - 1215 q^{65} - 3611 q^{67} - 3622 q^{68} + 560 q^{70} + 3719 q^{71} + 4593 q^{73} - 4848 q^{74} + 3520 q^{76} - 1368 q^{77} + 775 q^{79} - 9500 q^{80} - 6762 q^{82} + 2447 q^{83} - 8185 q^{85} - 3891 q^{86} - 10960 q^{88} + 5075 q^{89} + 376 q^{91} + 8456 q^{92} + 3573 q^{94} - 3265 q^{95} + 7439 q^{97} - 7082 q^{98}+O(q^{100}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8 - 25 * q^10 + 89 * q^11 + 33 * q^13 + 17 * q^14 - 207 * q^16 + 191 * q^17 - 115 * q^19 + 225 * q^20 + 808 * q^22 - 433 * q^23 + 90 * q^25 - 586 * q^26 - 13 * q^28 + 5 * q^29 - 639 * q^31 + 1386 * q^32 - 777 * q^34 + 1030 * q^35 + 699 * q^37 + 2355 * q^38 + 410 * q^40 - 341 * q^41 - 172 * q^43 - 548 * q^44 - 1239 * q^46 - 2319 * q^47 + 1344 * q^49 - 2335 * q^50 + 2344 * q^52 + 927 * q^53 + 1225 * q^55 + 2910 * q^56 + 2410 * q^58 + 1905 * q^59 + 1391 * q^61 + 3832 * q^62 - 3596 * q^64 - 1215 * q^65 - 3611 * q^67 - 3622 * q^68 + 560 * q^70 + 3719 * q^71 + 4593 * q^73 - 4848 * q^74 + 3520 * q^76 - 1368 * q^77 + 775 * q^79 - 9500 * q^80 - 6762 * q^82 + 2447 * q^83 - 8185 * q^85 - 3891 * q^86 - 10960 * q^88 + 5075 * q^89 + 376 * q^91 + 8456 * q^92 + 3573 * q^94 - 3265 * q^95 + 7439 * q^97 - 7082 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	4.11746	+	2.99151i	1.45574	+	1.05766i	0.984447	+	0.175681i	$0.0562127\pi$
$2$	4.11746	+	2.99151i	1.45574	+	1.05766i	0.471294	+	0.881976i	$0.343787\pi$
$3$		0			0
$3$		0			0
$4$	5.53220	+	17.0263i	0.691524	+	2.12829i
$5$	10.3703	−	4.17822i	0.927545	−	0.373711i
$5$	10.3703	−	4.17822i	0.927545	−	0.373711i
$6$		0			0
$7$	−12.1888			−0.658136			−0.329068	−	0.944306i	$-0.606735\pi$
$7$	−12.1888			−0.658136			−0.329068	+	0.944306i	$0.606735\pi$
$8$	−15.5740	+	47.9320i	−0.688282	+	2.11831i
$9$		0			0
$10$	55.1983	+	13.8191i	1.74552	+	0.436999i
$11$	53.0773	+	38.5629i	1.45485	+	1.05701i	0.984666	+	0.174448i	$0.0558140\pi$
$11$	53.0773	+	38.5629i	1.45485	+	1.05701i	0.470188	+	0.882566i	$0.344186\pi$
$12$		0			0
$13$	−24.5445	+	17.8326i	−0.523648	+	0.380453i	−0.817976	−	0.575252i	$-0.804904\pi$
$13$	−24.5445	+	17.8326i	−0.523648	+	0.380453i	0.294328	+	0.955704i	$0.404904\pi$
$14$	−50.1870	−	36.4630i	−0.958075	−	0.696082i
$15$		0			0
$16$	−91.6464	+	66.5850i	−1.43198	+	1.04039i
$17$	−15.4803	+	47.6433i	−0.220854	+	0.679718i	0.777832	+	0.628472i	$0.216319\pi$
$17$	−15.4803	+	47.6433i	−0.220854	+	0.679718i	−0.998686	+	0.0512459i	$0.983681\pi$
$18$		0			0
$19$	2.02724	−	6.23919i	0.0244779	−	0.0753352i	−0.938071	−	0.346442i	$-0.887390\pi$
$19$	2.02724	−	6.23919i	0.0244779	−	0.0753352i	0.962549	+	0.271107i	$0.0873897\pi$
$20$	128.510	+	153.453i	1.43679	+	1.71566i
$21$		0			0
$22$	103.182	+	317.562i	0.999933	+	3.07748i
$23$	−48.1539	−	34.9858i	−0.436555	−	0.317176i	0.347709	−	0.937602i	$-0.386960\pi$
$23$	−48.1539	−	34.9858i	−0.436555	−	0.317176i	−0.784265	+	0.620426i	$0.786960\pi$
$24$		0			0
$25$	90.0850	−	86.6585i	0.720680	−	0.693268i
$26$	−154.407			−1.16468
$27$		0			0
$28$	−67.4311	−	207.532i	−0.455117	−	1.40071i
$29$	−48.3877	−	148.922i	−0.309840	−	0.953590i	−0.977827	−	0.209417i	$-0.932844\pi$
$29$	−48.3877	−	148.922i	−0.309840	−	0.953590i	0.667986	−	0.744174i	$-0.267156\pi$
$30$		0			0
$31$	87.6551	−	269.775i	0.507849	−	1.56300i	−0.288079	−	0.957607i	$-0.593016\pi$
$31$	87.6551	−	269.775i	0.507849	−	1.56300i	0.795928	−	0.605392i	$-0.206984\pi$
$32$	−173.351			−0.957636
$33$		0			0
$34$	−206.265	+	149.860i	−1.04041	+	0.755905i
$35$	−126.402	+	50.9276i	−0.610451	+	0.245953i
$36$		0			0
$37$	−50.8593	+	36.9514i	−0.225979	+	0.164183i	−0.695014	−	0.718996i	$-0.744602\pi$
$37$	−50.8593	+	36.9514i	−0.225979	+	0.164183i	0.469035	+	0.883180i	$0.344602\pi$
$38$	27.0116	−	19.6251i	0.115312	−	0.0837792i
$39$		0			0
$40$	38.7631	+	562.139i	0.153225	+	2.22205i
$41$	199.228	−	144.748i	0.758882	−	0.551360i	−0.139685	−	0.990196i	$-0.544609\pi$
$41$	199.228	−	144.748i	0.758882	−	0.551360i	0.898567	+	0.438836i	$0.144609\pi$
$42$		0			0
$43$	−38.7316			−0.137361			−0.0686804	−	0.997639i	$-0.521879\pi$
$43$	−38.7316			−0.137361			−0.0686804	+	0.997639i	$0.521879\pi$
$44$	−362.951	+	1117.05i	−1.24357	+	3.82731i
$45$		0			0
$46$	−93.6111	−	288.105i	−0.300048	−	0.923452i
$47$	44.4855	+	136.912i	0.138061	+	0.424909i	0.996054	−	0.0887535i	$-0.0282883\pi$
$47$	44.4855	+	136.912i	0.138061	+	0.424909i	−0.857992	+	0.513663i	$0.828288\pi$
$48$		0			0
$49$	−194.432			−0.566857
$50$	630.161	−	87.3224i	1.78236	−	0.246985i
$51$		0			0
$52$	−439.410	−	319.250i	−1.17183	−	0.851385i
$53$	−54.9578	−	169.143i	−0.142435	−	0.438368i	0.854238	−	0.519883i	$-0.174024\pi$
$53$	−54.9578	−	169.143i	−0.142435	−	0.438368i	−0.996672	+	0.0815143i	$0.974024\pi$
$54$		0			0
$55$	711.550	+	178.139i	1.74446	+	0.436733i
$56$	189.830	−	584.235i	0.452983	−	1.39414i
$57$		0			0
$58$	246.267	−	757.932i	0.557525	−	1.71588i
$59$	−124.589	+	90.5195i	−0.274918	+	0.199740i	−0.716698	−	0.697384i	$-0.754347\pi$
$59$	−124.589	+	90.5195i	−0.274918	+	0.199740i	0.441780	+	0.897124i	$0.354347\pi$
$60$		0			0
$61$	−99.3211	−	72.1610i	−0.208472	−	0.151463i	0.478650	−	0.878006i	$-0.341126\pi$
$61$	−99.3211	−	72.1610i	−0.208472	−	0.151463i	−0.687122	+	0.726542i	$0.741126\pi$
$62$	1167.95	−	848.564i	2.39241	−	1.73819i
$63$		0			0
$64$	19.4081	+	14.1008i	0.0379064	+	0.0275406i
$65$	−180.025	+	287.482i	−0.343528	+	0.548580i
$66$		0			0
$67$	131.420	−	404.468i	0.239634	−	0.737517i	−0.756839	−	0.653601i	$-0.773257\pi$
$67$	131.420	−	404.468i	0.239634	−	0.737517i	0.996473	−	0.0839158i	$-0.0267427\pi$
$68$	−896.831			−1.59936
$69$		0			0
$70$	−672.804	−	168.439i	−1.14879	−	0.287605i
$71$	−79.0054	−	243.154i	−0.132059	−	0.406437i	0.863062	−	0.505099i	$-0.168544\pi$
$71$	−79.0054	−	243.154i	−0.132059	−	0.406437i	−0.995121	+	0.0986615i	$0.968544\pi$
$72$		0			0
$73$	267.322	+	194.221i	0.428598	+	0.311395i	0.781088	−	0.624421i	$-0.214665\pi$
$73$	267.322	+	194.221i	0.428598	+	0.311395i	−0.352490	+	0.935816i	$0.614665\pi$
$74$	−319.951			−0.502616
$75$		0			0
$76$	117.446			0.177262
$77$	−646.951	−	470.037i	−0.957492	−	0.695659i
$78$		0			0
$79$	−225.825	−	695.018i	−0.321611	−	0.989818i	−0.972947	−	0.231029i	$-0.925791\pi$
$79$	−225.825	−	695.018i	−0.321611	−	0.989818i	0.651335	−	0.758790i	$-0.274209\pi$
$80$	−672.192	+	1073.42i	−0.939416	+	1.50015i
$81$		0			0
$82$	1253.33			1.68789
$83$	137.355	−	422.734i	0.181646	−	0.559049i	−0.818228	−	0.574893i	$-0.805043\pi$
$83$	137.355	−	422.734i	0.181646	−	0.559049i	0.999874	+	0.0158440i	$0.00504350\pi$
$84$		0			0
$85$	38.5297	+	558.754i	0.0491662	+	0.713004i
$86$	−159.476	−	115.866i	−0.199962	−	0.145281i
$87$		0			0
$88$	−2675.02	+	1943.52i	−3.24044	+	2.35432i
$89$	838.773	+	609.404i	0.998986	+	0.725805i	0.961870	−	0.273506i	$-0.0881832\pi$
$89$	838.773	+	609.404i	0.998986	+	0.725805i	0.0371151	+	0.999311i	$0.488183\pi$
$90$		0			0
$91$	299.169	−	217.359i	0.344632	−	0.250390i
$92$	329.284	−	1013.43i	0.373155	−	1.14845i
$93$		0			0
$94$	−226.407	+	696.810i	−0.248427	+	0.764579i
$95$	−5.04570	−	73.1723i	−0.00544924	−	0.0790244i
$96$		0			0
$97$	33.5699	+	103.318i	0.0351393	+	0.108148i	0.967088	−	0.254443i	$-0.0818922\pi$
$97$	33.5699	+	103.318i	0.0351393	+	0.108148i	−0.931948	+	0.362591i	$0.881892\pi$
$98$	−800.565	−	581.645i	−0.825197	−	0.599541i
$99$		0			0
$100$	1973.85	+	1054.41i	1.97385	+	1.05441i
$101$	1356.67			1.33657			0.668285	−	0.743905i	$-0.267028\pi$
$101$	1356.67			1.33657			0.668285	+	0.743905i	$0.267028\pi$
$102$		0			0
$103$	−166.019	−	510.955i	−0.158819	−	0.488796i	0.839709	−	0.543037i	$-0.182726\pi$
$103$	−166.019	−	510.955i	−0.158819	−	0.488796i	−0.998528	+	0.0542418i	$0.982726\pi$
$104$	−472.496	−	1454.19i	−0.445501	−	1.37111i
$105$		0			0
$106$	279.705	−	860.844i	0.256296	−	0.788798i
$107$	419.322			0.378854			0.189427	−	0.981895i	$-0.439337\pi$
$107$	419.322			0.378854			0.189427	+	0.981895i	$0.439337\pi$
$108$		0			0
$109$	303.560	−	220.549i	0.266750	−	0.193805i	−0.446367	−	0.894850i	$-0.647283\pi$
$109$	303.560	−	220.549i	0.266750	−	0.193805i	0.713118	+	0.701044i	$0.247283\pi$
$110$	2396.87	+	2862.09i	2.07757	+	2.48081i
$111$		0			0
$112$	1117.06	−	811.595i	0.942434	−	0.684719i
$113$	−1883.17	+	1368.21i	−1.56774	+	1.13903i	−0.638451	+	0.769662i	$0.720425\pi$
$113$	−1883.17	+	1368.21i	−1.56774	+	1.13903i	−0.929285	+	0.369364i	$0.879575\pi$
$114$		0			0
$115$	−645.547	−	161.615i	−0.523457	−	0.131050i
$116$	2267.91	−	1647.73i	1.81526	−	1.31886i
$117$		0			0
$118$	−783.781			−0.611465
$119$	188.686	−	580.717i	0.145352	−	0.447347i
$120$		0			0
$121$	918.799	+	2827.77i	0.690307	+	2.12455i
$122$	−193.080	−	594.240i	−0.143284	−	0.440983i
$123$		0			0
$124$	5078.20			3.67771
$125$	572.128	−	1275.07i	0.409382	−	0.912363i
$126$		0			0
$127$	−711.115	−	516.655i	−0.496860	−	0.360990i	0.310956	−	0.950424i	$-0.399351\pi$
$127$	−711.115	−	516.655i	−0.496860	−	0.360990i	−0.807816	+	0.589434i	$0.799351\pi$
$128$	466.275	+	1435.05i	0.321979	+	0.990950i
$129$		0			0
$130$	−1601.25	+	645.148i	−1.08030	+	0.435255i
$131$	−291.806	+	898.086i	−0.194620	+	0.598978i	0.805361	+	0.592785i	$0.201971\pi$
$131$	−291.806	+	898.086i	−0.194620	+	0.598978i	−0.999981	+	0.00619352i	$0.998029\pi$
$132$		0			0
$133$	−24.7097	+	76.0485i	−0.0161098	+	0.0495808i
$134$	1751.08	−	1272.24i	1.12889	−	0.820183i
$135$		0			0
$136$	−2042.55	−	1484.00i	−1.28785	−	0.935675i
$137$	−2447.22	+	1778.01i	−1.52613	+	1.10880i	−0.567789	+	0.823174i	$0.692201\pi$
$137$	−2447.22	+	1778.01i	−1.52613	+	1.10880i	−0.958342	+	0.285624i	$0.907799\pi$
$138$		0			0
$139$	−1171.98	−	851.495i	−0.715153	−	0.519589i	0.169679	−	0.985499i	$-0.445727\pi$
$139$	−1171.98	−	851.495i	−0.715153	−	0.519589i	−0.884832	+	0.465910i	$0.845727\pi$
$140$	−1566.39	−	1870.42i	−0.945601	−	1.12914i
$141$		0			0
$142$	402.095	−	1237.52i	0.237627	−	0.731341i
$143$	−1990.44			−1.16398
$144$		0			0
$145$	−1124.02	−	1342.19i	−0.643758	−	0.768707i
$146$	519.673	+	1599.39i	0.294579	+	0.906620i
$147$		0			0
$148$	−910.511	−	661.525i	−0.505700	−	0.367412i
$149$	−2781.89			−1.52954			−0.764770	−	0.644303i	$-0.777148\pi$
$149$	−2781.89			−1.52954			−0.764770	+	0.644303i	$0.777148\pi$
$150$		0			0
$151$	−397.000			−0.213957			−0.106978	−	0.994261i	$-0.534118\pi$
$151$	−397.000			−0.213957			−0.106978	+	0.994261i	$0.534118\pi$
$152$	267.484	+	194.339i	0.142736	+	0.103704i
$153$		0			0
$154$	−1257.67	−	3870.72i	−0.658091	−	2.02540i
$155$	−218.170	−	3163.88i	−0.113057	−	1.63954i
$156$		0			0
$157$	1290.51			0.656010			0.328005	−	0.944676i	$-0.393624\pi$
$157$	1290.51			0.656010			0.328005	+	0.944676i	$0.393624\pi$
$158$	1149.33	−	3537.26i	0.578706	−	1.78107i
$159$		0			0
$160$	−1797.69	+	724.296i	−0.888250	+	0.357879i
$161$	586.940	+	426.437i	0.287313	+	0.208745i
$162$		0			0
$163$	−1184.62	+	860.677i	−0.569243	+	0.413579i	−0.834830	−	0.550508i	$-0.814434\pi$
$163$	−1184.62	+	860.677i	−0.569243	+	0.413579i	0.265587	+	0.964087i	$0.414434\pi$
$164$	3566.69	+	2591.35i	1.69824	+	1.23385i
$165$		0			0
$166$	1830.16	−	1329.69i	0.855713	−	0.621712i
$167$	1079.89	−	3323.56i	0.500386	−	1.54003i	−0.308006	−	0.951384i	$-0.599662\pi$
$167$	1079.89	−	3323.56i	0.500386	−	1.54003i	0.808392	−	0.588645i	$-0.200338\pi$
$168$		0			0
$169$	−394.480	+	1214.08i	−0.179554	+	0.552610i
$170$	−1512.87	+	2415.91i	−0.682541	+	1.08995i
$171$		0			0
$172$	−214.271	−	659.458i	−0.0949884	−	0.292344i
$173$	1359.19	+	987.509i	0.597325	+	0.433982i	0.844929	−	0.534879i	$-0.179643\pi$
$173$	1359.19	+	987.509i	0.597325	+	0.433982i	−0.247603	+	0.968862i	$0.579643\pi$
$174$		0			0
$175$	−1098.03	+	1056.27i	−0.474305	+	0.456264i
$176$	−7432.06			−3.18302
$177$		0			0
$178$	1630.57	+	5018.39i	0.686610	+	2.11317i
$179$	−527.771	−	1624.31i	−0.220377	−	0.678250i	−0.998728	−	0.0504208i	$-0.983944\pi$
$179$	−527.771	−	1624.31i	−0.220377	−	0.678250i	0.778351	−	0.627829i	$-0.216056\pi$
$180$		0			0
$181$	794.795	−	2446.13i	0.326390	−	1.00453i	−0.644419	−	0.764673i	$-0.722901\pi$
$181$	794.795	−	2446.13i	0.326390	−	1.00453i	0.970809	−	0.239853i	$-0.0770994\pi$
$182$	1882.05			0.766521
$183$		0			0
$184$	2426.89	−	1763.24i	0.972351	−	0.706455i
$185$	−373.033	+	595.697i	−0.148248	+	0.236738i
$186$		0			0
$187$	−2658.91	+	1931.81i	−1.03978	+	0.755445i
$188$	−2085.02	+	1514.85i	−0.808858	+	0.587670i
$189$		0			0
$190$	198.120	−	316.378i	0.0756481	−	0.120802i
$191$	−3046.87	+	2213.68i	−1.15426	+	0.838619i	−0.989041	−	0.147638i	$-0.952833\pi$
$191$	−3046.87	+	2213.68i	−1.15426	+	0.838619i	−0.165219	+	0.986257i	$0.552833\pi$
$192$		0			0
$193$	−3986.49			−1.48681			−0.743403	−	0.668844i	$-0.766789\pi$
$193$	−3986.49			−1.48681			−0.743403	+	0.668844i	$0.766789\pi$
$194$	−170.853	+	525.830i	−0.0632294	+	0.194600i
$195$		0			0
$196$	−1075.64	−	3310.47i	−0.391996	−	1.20644i
$197$	1385.47	+	4264.02i	0.501068	+	1.54213i	0.807283	+	0.590165i	$0.200937\pi$
$197$	1385.47	+	4264.02i	0.501068	+	1.54213i	−0.306215	+	0.951962i	$0.599063\pi$
$198$		0			0
$199$	−2104.92			−0.749816			−0.374908	−	0.927062i	$-0.622326\pi$
$199$	−2104.92			−0.749816			−0.374908	+	0.927062i	$0.622326\pi$
$200$	2750.72	+	5667.57i	0.972527	+	2.00379i
$201$		0			0
$202$	5586.03	+	4058.49i	1.94570	+	1.41363i
$203$	589.790	+	1815.19i	0.203917	+	0.627592i
$204$		0			0
$205$	1461.26	−	2333.49i	0.497848	−	0.795014i
$206$	844.949	−	2600.49i	0.285779	−	0.879536i
$207$		0			0
$208$	1062.03	−	3268.60i	0.354032	−	1.08960i
$209$	348.201	−	252.983i	0.115242	−	0.0837283i
$210$		0			0
$211$	−849.278	−	617.037i	−0.277094	−	0.201320i	0.440555	−	0.897726i	$-0.354782\pi$
$211$	−849.278	−	617.037i	−0.277094	−	0.201320i	−0.717649	+	0.696405i	$0.754782\pi$
$212$	2575.84	−	1871.46i	0.834480	−	0.606285i
$213$		0			0
$214$	1726.54	+	1254.40i	0.551513	+	0.400697i
$215$	−401.657	+	161.829i	−0.127408	+	0.0513332i
$216$		0			0
$217$	−1068.41	+	3288.24i	−0.334234	+	1.02867i
$218$	1909.67			0.593299
$219$		0			0
$220$	903.370	+	13100.6i	0.276842	+	4.01474i
$221$	−469.651	−	1445.44i	−0.142951	−	0.439957i
$222$		0			0
$223$	3954.03	+	2872.77i	1.18736	+	0.862669i	0.992983	−	0.118258i	$-0.0377310\pi$
$223$	3954.03	+	2872.77i	1.18736	+	0.862669i	0.194379	+	0.980927i	$0.437731\pi$
$224$	2112.94			0.630254
$225$		0			0
$226$	−11846.9			−3.48692
$227$	4196.25	+	3048.75i	1.22694	+	0.891422i	0.996657	−	0.0817020i	$-0.0260356\pi$
$227$	4196.25	+	3048.75i	1.22694	+	0.891422i	0.230281	+	0.973124i	$0.426036\pi$
$228$		0			0
$229$	876.848	+	2698.66i	0.253030	+	0.778745i	0.994211	+	0.107441i	$0.0342656\pi$
$229$	876.848	+	2698.66i	0.253030	+	0.778745i	−0.741182	+	0.671304i	$0.765734\pi$
$230$	−2174.54	−	2596.60i	−0.623412	−	0.744412i
$231$		0			0
$232$	7891.71			2.23326
$233$	1121.13	−	3450.49i	0.315227	−	0.970169i	−0.660434	−	0.750884i	$-0.729628\pi$
$233$	1121.13	−	3450.49i	0.315227	−	0.970169i	0.975661	−	0.219285i	$-0.0703724\pi$
$234$		0			0
$235$	1033.38	+	1233.95i	0.286851	+	0.342527i
$236$	−2230.47	−	1620.53i	−0.615217	−	0.446981i
$237$		0			0
$238$	2514.13	−	1826.62i	0.684734	−	0.497488i
$239$	−3191.25	−	2318.58i	−0.863703	−	0.627517i	0.0651870	−	0.997873i	$-0.479236\pi$
$239$	−3191.25	−	2318.58i	−0.863703	−	0.627517i	−0.928890	+	0.370356i	$0.879236\pi$
$240$		0			0
$241$	2251.07	−	1635.50i	0.601678	−	0.437144i	−0.244796	−	0.969575i	$-0.578721\pi$
$241$	2251.07	−	1635.50i	0.601678	−	0.437144i	0.846474	+	0.532430i	$0.178721\pi$
$242$	−4676.19	+	14391.8i	−1.24213	+	3.82290i
$243$		0			0
$244$	679.175	−	2090.28i	0.178195	−	0.548429i
$245$	−2016.31	+	812.379i	−0.525786	+	0.211841i
$246$		0			0
$247$	61.5037	+	189.289i	0.0158437	+	0.0487618i
$248$	11565.7	+	8402.96i	2.96138	+	2.15157i
$249$		0			0
$250$	6170.08	−	3538.50i	1.56092	−	0.895179i
$251$	−273.252			−0.0687153			−0.0343576	−	0.999410i	$-0.510939\pi$
$251$	−273.252			−0.0687153			−0.0343576	+	0.999410i	$0.510939\pi$
$252$		0			0
$253$	−1206.72	−	3713.91i	−0.299865	−	0.922890i
$254$	−1382.41	−	4254.61i	−0.341496	−	1.05102i
$255$		0			0
$256$	−2313.78	+	7121.09i	−0.564888	+	1.73855i
$257$	−2577.85			−0.625687			−0.312844	−	0.949805i	$-0.601282\pi$
$257$	−2577.85			−0.625687			−0.312844	+	0.949805i	$0.601282\pi$
$258$		0			0
$259$	619.916	−	450.395i	0.148725	−	0.108055i
$260$	−5890.69	−	1474.76i	−1.40510	−	0.351772i
$261$		0			0
$262$	−3888.13	+	2824.89i	−0.916830	+	0.666116i
$263$	−4005.56	+	2910.21i	−0.939138	+	0.682324i	−0.948213	−	0.317635i	$-0.897111\pi$
$263$	−4005.56	+	2910.21i	−0.939138	+	0.682324i	0.00907517	+	0.999959i	$0.497111\pi$
$264$		0			0
$265$	−1276.64	−	1524.43i	−0.295938	−	0.353377i
$266$	−329.241	+	239.207i	−0.0758911	+	0.0551381i
$267$		0			0
$268$	7613.66			1.73537
$269$	1187.86	−	3655.85i	0.269238	−	0.828629i	−0.721449	−	0.692468i	$-0.756523\pi$
$269$	1187.86	−	3655.85i	0.269238	−	0.828629i	0.990687	−	0.136161i	$-0.0434765\pi$
$270$		0			0
$271$	1772.57	+	5455.41i	0.397328	+	1.22285i	0.927133	+	0.374731i	$0.122265\pi$
$271$	1772.57	+	5455.41i	0.397328	+	1.22285i	−0.529805	+	0.848119i	$0.677735\pi$
$272$	−1753.62	−	5397.09i	−0.390915	−	1.20311i
$273$		0			0
$274$	−15395.2			−3.39438
$275$	8123.27	−	1125.66i	1.78128	−	0.246835i
$276$		0			0
$277$	−772.261	−	561.081i	−0.167512	−	0.121704i	0.500871	−	0.865522i	$-0.333013\pi$
$277$	−772.261	−	561.081i	−0.167512	−	0.121704i	−0.668383	+	0.743818i	$0.733013\pi$
$278$	−2278.33	−	7011.99i	−0.491530	−	1.51277i
$279$		0			0
$280$	−472.477	−	6851.83i	−0.100843	−	1.46241i
$281$	−1001.45	+	3082.16i	−0.212604	+	0.654327i	0.786711	+	0.617321i	$0.211782\pi$
$281$	−1001.45	+	3082.16i	−0.212604	+	0.654327i	−0.999315	+	0.0370061i	$0.988218\pi$
$282$		0			0
$283$	1050.05	−	3231.71i	0.220561	−	0.678817i	−0.778151	−	0.628077i	$-0.783842\pi$
$283$	1050.05	−	3231.71i	0.220561	−	0.678817i	0.998712	−	0.0507397i	$-0.0161579\pi$
$284$	3702.95	−	2690.35i	0.773695	−	0.562122i
$285$		0			0
$286$	−8195.53	−	5954.40i	−1.69445	−	1.23109i
$287$	−2428.36	+	1764.31i	−0.499448	+	0.362870i
$288$		0			0
$289$	1944.45	+	1412.73i	0.395777	+	0.287549i
$290$	−612.948	−	8888.91i	−0.124116	−	1.79991i
$291$		0			0
$292$	−1827.99	+	5625.98i	−0.366353	+	1.12752i
$293$	−1329.67			−0.265120			−0.132560	−	0.991175i	$-0.542320\pi$
$293$	−1329.67			−0.265120			−0.132560	+	0.991175i	$0.542320\pi$
$294$		0			0
$295$	−913.816	+	1459.27i	−0.180354	+	0.288007i
$296$	−979.070	−	3013.27i	−0.192254	−	0.591698i
$297$		0			0
$298$	−11454.3	−	8322.05i	−2.22661	−	1.61773i
$299$	1805.80			0.349272
$300$		0			0
$301$	472.094			0.0904021
$302$	−1634.63	−	1187.63i	−0.311465	−	0.226293i
$303$		0			0
$304$	229.648	+	706.783i	0.0433263	+	0.133345i
$305$	−1331.49	−	333.344i	−0.249970	−	0.0625811i
$306$		0			0
$307$	−2796.37			−0.519861			−0.259930	−	0.965627i	$-0.583700\pi$
$307$	−2796.37			−0.519861			−0.259930	+	0.965627i	$0.583700\pi$
$308$	4423.96	−	13615.5i	0.818437	−	2.51889i
$309$		0			0
$310$	8566.46	−	13679.8i	1.56949	−	2.50632i
$311$	3567.13	+	2591.67i	0.650397	+	0.472541i	0.863406	−	0.504509i	$-0.168327\pi$
$311$	3567.13	+	2591.67i	0.650397	+	0.472541i	−0.213010	+	0.977050i	$0.568327\pi$
$312$		0			0
$313$	−6799.15	+	4939.87i	−1.22783	+	0.892071i	−0.996726	−	0.0808578i	$-0.974234\pi$
$313$	−6799.15	+	4939.87i	−1.22783	+	0.892071i	−0.231105	+	0.972929i	$0.574234\pi$
$314$	5313.60	+	3860.56i	0.954981	+	0.693834i
$315$		0			0
$316$	10584.3	−	7689.95i	1.88422	−	1.36897i
$317$	−2370.03	+	7294.20i	−0.419918	+	1.29238i	0.487859	+	0.872923i	$0.337778\pi$
$317$	−2370.03	+	7294.20i	−0.419918	+	1.29238i	−0.907777	+	0.419453i	$0.862222\pi$
$318$		0			0
$319$	3174.58	−	9770.34i	0.557186	−	1.71484i
$320$	260.183	+	65.1380i	0.0454522	+	0.0113791i
$321$		0			0
$322$	1141.01	+	3511.67i	0.197472	+	0.607757i
$323$	265.874	+	193.168i	0.0458006	+	0.0332761i
$324$		0			0
$325$	−665.745	+	3733.44i	−0.113627	+	0.637213i
$326$	−7452.34			−1.26610
$327$		0			0
$328$	3835.25	+	11803.7i	0.645629	+	1.98704i
$329$	−542.227	−	1668.80i	−0.0908631	−	0.279648i
$330$		0			0
$331$	1072.59	−	3301.09i	0.178111	−	0.548170i	−0.821651	−	0.569991i	$-0.806947\pi$
$331$	1072.59	−	3301.09i	0.178111	−	0.548170i	0.999762	+	0.0218216i	$0.00694658\pi$
$332$	7957.49			1.31543
$333$		0			0
$334$	14388.9	−	10454.1i	2.35726	−	1.71265i
$335$	−327.098	−	4743.54i	−0.0533471	−	0.773634i
$336$		0			0
$337$	9068.59	−	6588.72i	1.46587	−	1.06502i	0.484084	−	0.875022i	$-0.339153\pi$
$337$	9068.59	−	6588.72i	1.46587	−	1.06502i	0.981785	−	0.189994i	$-0.0608469\pi$
$338$	−5256.19	+	3818.85i	−0.845856	+	0.614550i
$339$		0			0
$340$	−9300.38	+	3747.16i	−1.48348	+	0.597700i
$341$	15055.8	−	10938.7i	2.39096	−	1.73713i
$342$		0			0
$343$	6550.68			1.03120
$344$	603.208	−	1856.48i	0.0945430	−	0.290973i
$345$		0			0
$346$	2642.26	+	8132.05i	0.410546	+	1.26353i
$347$	−2009.92	−	6185.89i	−0.310946	−	0.956992i	−0.977391	−	0.211438i	$-0.932185\pi$
$347$	−2009.92	−	6185.89i	−0.310946	−	0.956992i	0.666446	−	0.745553i	$-0.267815\pi$
$348$		0			0
$349$	256.654			0.0393650			0.0196825	−	0.999806i	$-0.493734\pi$
$349$	256.654			0.0393650			0.0196825	+	0.999806i	$0.493734\pi$
$350$	−7680.93	+	1064.36i	−1.17304	+	0.162550i
$351$		0			0
$352$	−9200.98	−	6684.90i	−1.39322	−	1.01223i
$353$	2829.51	+	8708.32i	0.426627	+	1.31302i	0.901428	+	0.432930i	$0.142520\pi$
$353$	2829.51	+	8708.32i	0.426627	+	1.31302i	−0.474800	+	0.880094i	$0.657480\pi$
$354$		0			0
$355$	−1835.26	−	2191.47i	−0.274381	−	0.327637i
$356$	−5735.67	+	17652.6i	−0.853904	+	2.62805i
$357$		0			0
$358$	2686.06	−	8266.86i	0.396545	−	1.22044i
$359$	5196.70	−	3775.62i	0.763987	−	0.555069i	−0.136144	−	0.990689i	$-0.543471\pi$
$359$	5196.70	−	3775.62i	0.763987	−	0.555069i	0.900130	+	0.435620i	$0.143471\pi$
$360$		0			0
$361$	5514.23	+	4006.32i	0.803941	+	0.584097i
$362$	10590.1	−	7694.19i	1.53758	−	1.11712i
$363$		0			0
$364$	5355.90	+	3891.29i	0.771224	+	0.560327i
$365$	3583.70	+	897.193i	0.513916	+	0.128661i
$366$		0			0
$367$	561.620	−	1728.49i	0.0798810	−	0.245848i	−0.903139	−	0.429349i	$-0.858743\pi$
$367$	561.620	−	1728.49i	0.0798810	−	0.245848i	0.983020	+	0.183501i	$0.0587430\pi$
$368$	6742.66			0.955124
$369$		0			0
$370$	−3317.98	+	1336.83i	−0.466199	+	0.187833i
$371$	669.872	+	2061.65i	0.0937413	+	0.288506i
$372$		0			0
$373$	1181.35	+	858.298i	0.163989	+	0.119145i	0.666753	−	0.745279i	$-0.267684\pi$
$373$	1181.35	+	858.298i	0.163989	+	0.119145i	−0.502764	+	0.864424i	$0.667684\pi$
$374$	−16727.0			−2.31265
$375$		0			0
$376$	−7255.30			−0.995116
$377$	3843.32	+	2792.34i	0.525043	+	0.381466i
$378$		0			0
$379$	−1646.02	−	5065.94i	−0.223089	−	0.686596i	−0.998480	−	0.0551151i	$-0.982447\pi$
$379$	−1646.02	−	5065.94i	−0.223089	−	0.686596i	0.775391	−	0.631481i	$-0.217553\pi$
$380$	1217.94	−	490.713i	0.164419	−	0.0662449i
$381$		0			0
$382$	−19167.6			−2.56728
$383$	−1998.12	+	6149.57i	−0.266577	+	0.820439i	0.724749	+	0.689013i	$0.241956\pi$
$383$	−1998.12	+	6149.57i	−0.266577	+	0.820439i	−0.991326	+	0.131426i	$0.958044\pi$
$384$		0			0
$385$	−8672.97	−	2171.31i	−1.14809	−	0.287430i
$386$	−16414.2	−	11925.6i	−2.16440	−	1.57253i
$387$		0			0
$388$	−1573.41	+	1143.15i	−0.205870	+	0.149573i
$389$	−6836.98	−	4967.36i	−0.891128	−	0.647442i	0.0450438	−	0.998985i	$-0.485657\pi$
$389$	−6836.98	−	4967.36i	−0.891128	−	0.647442i	−0.936172	+	0.351543i	$0.885657\pi$
$390$		0			0
$391$	2412.27	−	1752.62i	0.312005	−	0.226685i
$392$	3028.09	−	9319.51i	0.390158	−	1.20078i
$393$		0			0
$394$	−7051.26	+	21701.6i	−0.901618	+	2.77490i
$395$	−5245.80	−	6263.98i	−0.668215	−	0.797912i
$396$		0			0
$397$	−2246.56	−	6914.21i	−0.284009	−	0.874091i	−0.986694	−	0.162589i	$-0.948015\pi$
$397$	−2246.56	−	6914.21i	−0.284009	−	0.874091i	0.702684	−	0.711502i	$-0.251985\pi$
$398$	−8666.90	−	6296.87i	−1.09154	−	0.793049i
$399$		0			0
$400$	−2485.81	+	13940.3i	−0.310727	+	1.74253i
$401$	5597.79			0.697108			0.348554	−	0.937289i	$-0.386673\pi$
$401$	5597.79			0.697108			0.348554	+	0.937289i	$0.386673\pi$
$402$		0			0
$403$	2659.34	+	8184.61i	0.328713	+	1.01167i
$404$	7505.36	+	23099.1i	0.924272	+	2.84462i
$405$		0			0
$406$	−3001.71	+	9238.31i	−0.366927	+	1.12929i
$407$	−4124.43			−0.502310
$408$		0			0
$409$	4310.85	−	3132.02i	0.521168	−	0.378651i	−0.295876	−	0.955226i	$-0.595611\pi$
$409$	4310.85	−	3132.02i	0.521168	−	0.378651i	0.817044	+	0.576576i	$0.195611\pi$
$410$	12997.3	−	5236.67i	1.56559	−	0.630782i
$411$		0			0
$412$	7781.25	−	5653.41i	0.930473	−	0.676028i
$413$	1518.60	−	1103.33i	0.180933	−	0.131456i
$414$		0			0
$415$	−341.870	−	4957.77i	−0.0404379	−	0.586427i
$416$	4254.81	−	3091.30i	0.501464	−	0.364335i
$417$		0			0
$418$	2190.50			0.256318
$419$	−1244.35	+	3829.71i	−0.145084	+	0.446524i	−0.997022	−	0.0771198i	$-0.975428\pi$
$419$	−1244.35	+	3829.71i	−0.145084	+	0.446524i	0.851937	+	0.523644i	$0.175428\pi$
$420$		0			0
$421$	2566.47	+	7898.79i	0.297108	+	0.914403i	0.982505	+	0.186234i	$0.0596283\pi$
$421$	2566.47	+	7898.79i	0.297108	+	0.914403i	−0.685398	+	0.728169i	$0.740372\pi$
$422$	−1651.00	−	5081.24i	−0.190448	−	0.586140i
$423$		0			0
$424$	8963.25			1.02664
$425$	2734.16	+	5633.44i	0.312061	+	0.642970i
$426$		0			0
$427$	1210.61	+	879.559i	0.137203	+	0.0996835i
$428$	2319.77	+	7139.51i	0.261987	+	0.806312i
$429$		0			0
$430$	−2137.92	−	535.237i	−0.239767	−	0.0600265i
$431$	3040.84	−	9358.73i	0.339842	−	1.04593i	−0.624445	−	0.781068i	$-0.714675\pi$
$431$	3040.84	−	9358.73i	0.339842	−	1.04593i	0.964287	−	0.264858i	$-0.0853251\pi$
$432$		0			0
$433$	−2706.83	+	8330.75i	−0.300420	+	0.924597i	0.680927	+	0.732351i	$0.261577\pi$
$433$	−2706.83	+	8330.75i	−0.300420	+	0.924597i	−0.981347	+	0.192246i	$0.938423\pi$
$434$	−14235.9	+	10343.0i	−1.57453	+	1.14397i
$435$		0			0
$436$	5434.50	+	3948.40i	0.596939	+	0.433702i
$437$	−315.902	+	229.516i	−0.0345805	+	0.0251242i
$438$		0			0
$439$	−12503.7	−	9084.45i	−1.35938	−	0.987647i	−0.998484	−	0.0550403i	$-0.982471\pi$
$439$	−12503.7	−	9084.45i	−1.35938	−	0.987647i	−0.360895	−	0.932606i	$-0.617529\pi$
$440$	−19620.3	+	31331.6i	−2.12582	+	3.39472i
$441$		0			0
$442$	2390.27	−	7356.48i	0.257225	−	0.791657i
$443$	−1298.99			−0.139316			−0.0696579	−	0.997571i	$-0.522191\pi$
$443$	−1298.99			−0.139316			−0.0696579	+	0.997571i	$0.522191\pi$
$444$		0			0
$445$	11244.5	+	2815.11i	1.19785	+	0.299885i
$446$	7686.64	+	23657.0i	0.816082	+	2.51164i
$447$		0			0
$448$	−236.562	−	171.873i	−0.0249476	−	0.0181255i
$449$	10414.4			1.09462			0.547310	−	0.836930i	$-0.315652\pi$
$449$	10414.4			1.09462			0.547310	+	0.836930i	$0.315652\pi$
$450$		0			0
$451$	16156.4			1.68686
$452$	−33713.6	−	24494.4i	−3.50831	−	2.54894i
$453$		0			0
$454$	8157.50	+	25106.2i	0.843283	+	2.59536i
$455$	2194.29	−	3504.07i	0.226088	−	0.361040i
$456$		0			0
$457$	7437.70			0.761315			0.380658	−	0.924716i	$-0.375698\pi$
$457$	7437.70			0.761315			0.380658	+	0.924716i	$0.375698\pi$
$458$	−4462.68	+	13734.7i	−0.455300	+	1.40127i
$459$		0			0
$460$	−819.574	−	11885.4i	−0.0830714	−	1.20469i
$461$	9362.27	+	6802.09i	0.945867	+	0.687212i	0.949826	−	0.312780i	$-0.101260\pi$
$461$	9362.27	+	6802.09i	0.945867	+	0.687212i	−0.00395912	+	0.999992i	$0.501260\pi$
$462$		0			0
$463$	−13343.9	+	9694.92i	−1.33940	+	0.973134i	−0.339939	+	0.940448i	$0.610406\pi$
$463$	−13343.9	+	9694.92i	−1.33940	+	0.973134i	−0.999466	+	0.0326869i	$0.989594\pi$
$464$	14350.5	+	10426.3i	1.43579	+	1.04316i
$465$		0			0
$466$	14938.4	−	10853.4i	1.48500	−	1.07891i
$467$	1771.15	−	5451.05i	0.175501	−	0.540138i	−0.824155	−	0.566365i	$-0.808349\pi$
$467$	1771.15	−	5451.05i	0.175501	−	0.540138i	0.999656	+	0.0262270i	$0.00834927\pi$
$468$		0			0
$469$	−1601.85	+	4930.00i	−0.157712	+	0.485386i
$470$	563.517	+	8172.08i	0.0553045	+	0.802021i
$471$		0			0
$472$	−2398.42	−	7381.57i	−0.233890	−	0.719840i
$473$	−2055.77	−	1493.60i	−0.199840	−	0.145192i
$474$		0			0
$475$	−358.055	−	737.734i	−0.0345867	−	0.0712623i
$476$	10931.3			1.05260
$477$		0			0
$478$	−6203.79	−	19093.3i	−0.593629	−	1.82700i
$479$	−1410.27	−	4340.36i	−0.134524	−	0.414021i	0.860992	−	0.508618i	$-0.169844\pi$
$479$	−1410.27	−	4340.36i	−0.134524	−	0.414021i	−0.995516	+	0.0945975i	$0.969844\pi$
$480$		0			0
$481$	589.375	−	1813.91i	0.0558694	−	0.171948i
$482$	14161.3			1.33824
$483$		0			0
$484$	−43063.7	+	31287.6i	−4.04430	+	2.93835i
$485$	779.813	+	931.169i	0.0730092	+	0.0871798i
$486$		0			0
$487$	−3999.99	+	2906.16i	−0.372191	+	0.270412i	−0.758119	−	0.652117i	$-0.773881\pi$
$487$	−3999.99	+	2906.16i	−0.372191	+	0.270412i	0.385928	+	0.922529i	$0.373881\pi$
$488$	5005.65	−	3636.82i	0.464334	−	0.337359i
$489$		0			0
$490$	−10732.3	−	2686.88i	−0.989463	−	0.247716i
$491$	1483.55	−	1077.86i	0.136358	−	0.0990700i	−0.517515	−	0.855674i	$-0.673143\pi$
$491$	1483.55	−	1077.86i	0.136358	−	0.0990700i	0.653873	+	0.756604i	$0.273143\pi$
$492$		0			0
$493$	7844.19			0.716602
$494$	−313.020	+	963.377i	−0.0285090	+	0.0877417i
$495$		0			0
$496$	9929.67	+	30560.4i	0.898902	+	2.76654i
$497$	962.985	+	2963.76i	0.0869130	+	0.267491i
$498$		0			0
$499$	21592.7			1.93712			0.968561	−	0.248775i	$-0.0800280\pi$
$499$	21592.7			1.93712			0.968561	+	0.248775i	$0.0800280\pi$
$500$	24874.8	+	2687.34i	2.22487	+	0.240363i
$501$		0			0
$502$	−1125.10	−	817.436i	−0.100032	−	0.0726772i
$503$	−6453.77	−	19862.7i	−0.572086	−	1.76070i	−0.645894	−	0.763427i	$-0.723515\pi$
$503$	−6453.77	−	19862.7i	−0.572086	−	1.76070i	0.0738083	−	0.997272i	$-0.476485\pi$
$504$		0			0
$505$	14069.0	−	5668.46i	1.23973	−	0.499491i
$506$	6141.55	−	18901.8i	0.539576	−	1.66064i
$507$		0			0
$508$	4862.73	−	14965.9i	0.424702	−	1.30710i
$509$	−7139.02	+	5186.80i	−0.621673	+	0.451672i	−0.853506	−	0.521084i	$-0.825528\pi$
$509$	−7139.02	+	5186.80i	−0.621673	+	0.451672i	0.231832	+	0.972756i	$0.425528\pi$
$510$		0			0
$511$	−3258.34	−	2367.33i	−0.282076	−	0.204940i
$512$	−21063.9	+	15303.8i	−1.81817	+	1.32098i
$513$		0			0
$514$	−10614.2	−	7711.65i	−0.910839	−	0.661763i
$515$	−3856.55	−	4605.08i	−0.329980	−	0.394027i
$516$		0			0
$517$	−2918.57	+	8982.43i	−0.248276	+	0.764114i
$518$	3899.84			0.330789
$519$		0			0
$520$	−10975.8	−	13106.2i	−0.925621	−	1.10528i
$521$	6129.99	+	18866.2i	0.515470	+	1.58645i	0.782425	+	0.622744i	$0.213982\pi$
$521$	6129.99	+	18866.2i	0.515470	+	1.58645i	−0.266955	+	0.963709i	$0.586018\pi$
$522$		0			0
$523$	−10511.2	−	7636.84i	−0.878820	−	0.638500i	0.0541191	−	0.998534i	$-0.482765\pi$
$523$	−10511.2	−	7636.84i	−0.878820	−	0.638500i	−0.932939	+	0.360034i	$0.882765\pi$
$524$	−16905.5			−1.40939
$525$		0			0
$526$	−25198.6			−2.08881
$527$	11496.0	+	8352.36i	0.950237	+	0.690388i
$528$		0			0
$529$	−2665.02	−	8202.10i	−0.219037	−	0.674127i
$530$	−696.174	−	10095.9i	−0.0570563	−	0.827426i
$531$		0			0
$532$	−1431.53			−0.116663
$533$	−2308.72	+	7105.52i	−0.187621	+	0.577438i
$534$		0			0
$535$	4348.48	−	1752.02i	0.351404	−	0.141582i
$536$	17340.2	+	12598.4i	1.39736	+	1.01524i
$537$		0			0
$538$	15827.5	−	11499.3i	1.26835	−	0.921508i
$539$	−10319.9	−	7497.86i	−0.824695	−	0.599176i
$540$		0			0
$541$	−6536.17	+	4748.81i	−0.519431	+	0.377389i	−0.816389	−	0.577502i	$-0.804028\pi$
$541$	−6536.17	+	4748.81i	−0.519431	+	0.377389i	0.296959	+	0.954890i	$0.404028\pi$
$542$	−9021.42	+	27765.1i	−0.714950	+	2.20039i
$543$		0			0
$544$	2683.51	−	8259.00i	0.211497	−	0.650922i
$545$	2226.50	−	3555.50i	0.174996	−	0.279451i
$546$		0			0
$547$	72.1473	+	222.046i	0.00563948	+	0.0173565i	0.953837	−	0.300326i	$-0.0970954\pi$
$547$	72.1473	+	222.046i	0.00563948	+	0.0173565i	−0.948197	+	0.317682i	$0.897095\pi$
$548$	−43811.5	−	31830.9i	−3.41521	−	2.48129i
$549$		0			0
$550$	36814.6	+	19666.0i	2.85415	+	1.52466i
$551$	−1027.25			−0.0794231
$552$		0			0
$553$	2752.55	+	8471.47i	0.211664	+	0.651435i
$554$	−1501.28	−	4620.45i	−0.115132	−	0.354340i
$555$		0			0
$556$	8014.22	−	24665.2i	0.611292	−	1.88136i
$557$	−290.431			−0.0220932			−0.0110466	−	0.999939i	$-0.503516\pi$
$557$	−290.431			−0.0220932			−0.0110466	+	0.999939i	$0.503516\pi$
$558$		0			0
$559$	950.649	−	690.687i	0.0719287	−	0.0522593i
$560$	8193.24	−	13083.8i	0.618264	−	0.987305i
$561$		0			0
$562$	−13343.7	+	9694.79i	−1.00155	+	0.727669i
$563$	11881.7	−	8632.59i	0.889442	−	0.646217i	−0.0462906	−	0.998928i	$-0.514740\pi$
$563$	11881.7	−	8632.59i	0.889442	−	0.646217i	0.935732	+	0.352711i	$0.114740\pi$
$564$		0			0
$565$	−13812.4	+	22057.0i	−1.02848	+	1.64238i
$566$	13991.2	−	10165.2i	1.03904	−	0.754904i
$567$		0			0
$568$	12885.3			0.951855
$569$	−1838.96	+	5659.74i	−0.135489	+	0.416993i	−0.995666	−	0.0930035i	$-0.970353\pi$
$569$	−1838.96	+	5659.74i	−0.135489	+	0.416993i	0.860177	+	0.509996i	$0.170353\pi$
$570$		0			0
$571$	−3758.44	−	11567.3i	−0.275457	−	0.847769i	−0.989098	−	0.147257i	$-0.952955\pi$
$571$	−3758.44	−	11567.3i	−0.275457	−	0.847769i	0.713641	−	0.700511i	$-0.247045\pi$
$572$	−11011.5	−	33889.8i	−0.804918	−	2.47728i
$573$		0			0
$574$	−15276.6			−1.11086
$575$	−7369.76	+	1021.24i	−0.534505	+	0.0740672i
$576$		0			0
$577$	−17874.4	−	12986.5i	−1.28964	−	0.936975i	−0.289838	−	0.957076i	$-0.593601\pi$
$577$	−17874.4	−	12986.5i	−1.28964	−	0.936975i	−0.999798	+	0.0201004i	$0.993601\pi$
$578$	3780.02	+	11633.7i	0.272021	+	0.837193i
$579$		0			0
$580$	16634.2	−	26563.2i	1.19086	−	1.90169i
$581$	−1674.19	+	5152.64i	−0.119548	+	0.367930i
$582$		0			0
$583$	3605.62	−	11097.0i	0.256140	−	0.788318i
$584$	−13472.7	+	9788.46i	−0.954628	+	0.693578i
$585$		0			0
$586$	−5474.85	−	3977.71i	−0.385946	−	0.280406i
$587$	−1700.21	+	1235.28i	−0.119549	+	0.0868576i	−0.645953	−	0.763377i	$-0.723540\pi$
$587$	−1700.21	+	1235.28i	−0.119549	+	0.0868576i	0.526404	+	0.850235i	$0.323540\pi$
$588$		0			0
$589$	−1505.48	−	1093.79i	−0.105318	−	0.0765178i
$590$	−8128.02	+	3274.81i	−0.567162	+	0.228511i
$591$		0			0
$592$	2200.66	−	6772.93i	0.152781	−	0.470212i
$593$	−17313.9			−1.19898			−0.599491	−	0.800382i	$-0.704630\pi$
$593$	−17313.9			−1.19898			−0.599491	+	0.800382i	$0.704630\pi$
$594$		0			0
$595$	−469.632	−	6810.56i	−0.0323581	−	0.469254i
$596$	−15390.0	−	47365.5i	−1.05771	−	3.25531i
$597$		0			0
$598$	7435.32	+	5402.07i	0.508449	+	0.369410i
$599$	15628.8			1.06607			0.533035	−	0.846093i	$-0.321051\pi$
$599$	15628.8			1.06607			0.533035	+	0.846093i	$0.321051\pi$
$600$		0			0
$601$	−2308.10			−0.156655			−0.0783274	−	0.996928i	$-0.524958\pi$
$601$	−2308.10			−0.156655			−0.0783274	+	0.996928i	$0.524958\pi$
$602$	1943.82	+	1412.27i	0.131602	+	0.0956144i
$603$		0			0
$604$	−2196.28	−	6759.47i	−0.147956	−	0.455362i
$605$	21343.2	+	25485.8i	1.43426	+	1.71264i
$606$		0			0
$607$	−17662.5			−1.18105			−0.590527	−	0.807018i	$-0.701080\pi$
$607$	−17662.5			−1.18105			−0.590527	+	0.807018i	$0.701080\pi$
$608$	−351.422	+	1081.57i	−0.0234409	+	0.0721436i
$609$		0			0
$610$	−4485.15	−	5355.69i	−0.297703	−	0.355485i
$611$	−3533.39	−	2567.15i	−0.233953	−	0.169977i
$612$		0			0
$613$	3294.96	−	2393.93i	0.217100	−	0.157732i	−0.473920	−	0.880568i	$-0.657161\pi$
$613$	3294.96	−	2393.93i	0.217100	−	0.157732i	0.691020	+	0.722835i	$0.257161\pi$
$614$	−11513.9	−	8365.36i	−0.756782	−	0.549834i
$615$		0			0
$616$	32605.4	−	23689.2i	2.13265	−	1.54946i
$617$	2467.97	−	7595.62i	0.161032	−	0.495605i	−0.837690	−	0.546146i	$-0.816094\pi$
$617$	2467.97	−	7595.62i	0.161032	−	0.495605i	0.998722	+	0.0505408i	$0.0160945\pi$
$618$		0			0
$619$	−4488.98	+	13815.7i	−0.291482	+	0.897089i	0.692898	+	0.721035i	$0.256333\pi$
$619$	−4488.98	+	13815.7i	−0.291482	+	0.897089i	−0.984380	+	0.176054i	$0.943667\pi$
$620$	52662.3	−	21217.8i	3.41124	−	1.37440i
$621$		0			0
$622$	6934.50	+	21342.2i	0.447023	+	1.37579i
$623$	−10223.7	−	7427.93i	−0.657468	−	0.477679i
$624$		0			0
$625$	605.622	−	15613.3i	0.0387598	−	0.999249i
$626$	−42772.9			−2.73091
$627$		0			0
$628$	7139.34	+	21972.6i	0.453647	+	1.39618i
$629$	−973.174	−	2995.12i	−0.0616900	−	0.189862i
$630$		0			0
$631$	−5214.35	+	16048.1i	−0.328970	+	1.01247i	0.640647	+	0.767836i	$0.278666\pi$
$631$	−5214.35	+	16048.1i	−0.328970	+	1.01247i	−0.969617	+	0.244630i	$0.921334\pi$
$632$	36830.6			2.31811
$633$		0			0
$634$	−31579.1	+	22943.6i	−1.97818	+	1.43723i
$635$	−9533.15	−	2386.66i	−0.595766	−	0.149153i
$636$		0			0
$637$	4772.24	−	3467.24i	0.296834	−	0.215662i
$638$	42299.2	−	30732.2i	2.62483	−	1.90705i
$639$		0			0
$640$	10831.3	+	12933.6i	0.668979	+	0.798823i
$641$	−10979.0	+	7976.68i	−0.676510	+	0.491513i	−0.872198	−	0.489153i	$-0.837306\pi$
$641$	−10979.0	+	7976.68i	−0.676510	+	0.491513i	0.195688	+	0.980666i	$0.437306\pi$
$642$		0			0
$643$	3996.76			0.245127			0.122564	−	0.992461i	$-0.460888\pi$
$643$	3996.76			0.245127			0.122564	+	0.992461i	$0.460888\pi$
$644$	−4013.59	+	12352.6i	−0.245587	+	0.755838i
$645$		0			0
$646$	516.858	+	1590.72i	0.0314791	+	0.0968827i
$647$	−94.3612	−	290.414i	−0.00573373	−	0.0176466i	0.948149	−	0.317827i	$-0.102953\pi$
$647$	−94.3612	−	290.414i	−0.00573373	−	0.0176466i	−0.953882	+	0.300180i	$0.902953\pi$
$648$		0			0
$649$	−10103.6			−0.611093
$650$	−13909.8	+	13380.7i	−0.839365	+	0.807438i
$651$		0			0
$652$	−21207.7	−	15408.3i	−1.27386	−	0.925516i
$653$	6842.36	+	21058.6i	0.410049	+	1.26200i	0.916605	+	0.399795i	$0.130919\pi$
$653$	6842.36	+	21058.6i	0.410049	+	1.26200i	−0.506555	+	0.862207i	$0.669081\pi$
$654$		0			0
$655$	726.292	+	10532.6i	0.0433261	+	0.628311i
$656$	−8620.51	+	26531.2i	−0.513071	+	1.57907i
$657$		0			0
$658$	2759.64	−	8493.30i	0.163499	−	0.503197i
$659$	−6034.69	+	4384.46i	−0.356719	+	0.259172i	−0.751682	−	0.659525i	$-0.770757\pi$
$659$	−6034.69	+	4384.46i	−0.356719	+	0.259172i	0.394963	+	0.918697i	$0.370757\pi$
$660$		0			0
$661$	−5736.86	−	4168.07i	−0.337576	−	0.245264i	0.406062	−	0.913845i	$-0.366902\pi$
$661$	−5736.86	−	4168.07i	−0.337576	−	0.245264i	−0.743639	+	0.668582i	$0.766902\pi$
$662$	14291.6	−	10383.4i	0.839059	−	0.609612i
$663$		0			0
$664$	18123.3	+	13167.4i	1.05922	+	0.769567i
$665$	61.5012	+	891.886i	0.00358634	+	0.0520088i
$666$		0			0
$667$	−2880.10	+	8864.05i	−0.167194	+	0.514569i
$668$	62562.3			3.62366
$669$		0			0
$670$	12843.5	−	20509.9i	0.740581	−	1.18263i
$671$	−2488.96	−	7660.22i	−0.143197	−	0.440715i
$672$		0			0
$673$	−2479.77	−	1801.66i	−0.142033	−	0.103193i	0.514500	−	0.857491i	$-0.327978\pi$
$673$	−2479.77	−	1801.66i	−0.142033	−	0.103193i	−0.656533	+	0.754297i	$0.727978\pi$
$674$	57049.7			3.26035
$675$		0			0
$676$	−22853.8			−1.30028
$677$	−17877.8	−	12989.0i	−1.01492	−	0.737383i	−0.0496847	−	0.998765i	$-0.515822\pi$
$677$	−17877.8	−	12989.0i	−1.01492	−	0.737383i	−0.965235	+	0.261382i	$0.915822\pi$
$678$		0			0
$679$	−409.179	−	1259.32i	−0.0231264	−	0.0711758i
$680$	−27382.2	−	6855.25i	−1.54421	−	0.386598i
$681$		0			0
$682$	94714.7			5.31791
$683$	−7085.23	+	21806.1i	−0.396938	+	1.22165i	0.530504	+	0.847683i	$0.322003\pi$
$683$	−7085.23	+	21806.1i	−0.396938	+	1.22165i	−0.927442	+	0.373967i	$0.877997\pi$
$684$		0			0
$685$	−17949.4	+	28663.4i	−1.00118	+	1.59879i
$686$	26972.1	+	19596.4i	1.50117	+	1.09066i
$687$		0			0
$688$	3549.61	−	2578.95i	0.196697	−	0.142909i
$689$	4365.17	+	3171.48i	0.241364	+	0.175361i
$690$		0			0
$691$	17372.5	−	12621.8i	0.956411	−	0.694874i	0.00409688	−	0.999992i	$-0.498696\pi$
$691$	17372.5	−	12621.8i	0.956411	−	0.694874i	0.952315	+	0.305118i	$0.0986959\pi$
$692$	−9294.37	+	28605.1i	−0.510577	+	1.57139i
$693$		0			0
$694$	10229.4	−	31482.8i	0.559514	−	1.72201i
$695$	−15711.5	−	3933.44i	−0.857513	−	0.214682i
$696$		0			0
$697$	3812.16	+	11732.6i	0.207167	+	0.637596i
$698$	1056.76	+	767.783i	0.0573052	+	0.0416347i
$699$		0			0
$700$	−24058.9	−	12852.0i	−1.29906	−	0.693943i
$701$	−14395.2			−0.775605			−0.387802	−	0.921743i	$-0.626766\pi$
$701$	−14395.2			−0.775605			−0.387802	+	0.921743i	$0.626766\pi$
$702$		0			0
$703$	127.443	+	392.230i	0.00683728	+	0.0210430i
$704$	486.361	+	1496.87i	0.0260375	+	0.0801353i
$705$		0			0
$706$	−14400.6	+	44320.6i	−0.767671	+	2.36265i
$707$	−16536.2			−0.879645
$708$		0			0
$709$	15777.6	−	11463.1i	0.835740	−	0.607201i	−0.0854373	−	0.996344i	$-0.527229\pi$
$709$	15777.6	−	11463.1i	0.835740	−	0.607201i	0.921177	+	0.389143i	$0.127229\pi$
$710$	−1000.80	−	14513.5i	−0.0529003	−	0.767155i
$711$		0			0
$712$	−42273.0	+	30713.1i	−2.22507	+	1.61661i
$713$	−13659.2	+	9924.00i	−0.717450	+	0.521258i
$714$		0			0
$715$	−20641.3	+	8316.47i	−1.07964	+	0.434991i
$716$	24736.3	−	17972.0i	1.29112	−	0.938052i
$717$		0			0
$718$	32692.0			1.69924
$719$	482.908	−	1486.24i	0.0250479	−	0.0770895i	−0.937751	−	0.347308i	$-0.887096\pi$
$719$	482.908	−	1486.24i	0.0250479	−	0.0770895i	0.962799	+	0.270218i	$0.0870959\pi$
$720$		0			0
$721$	2023.59	+	6227.96i	0.104525	+	0.321694i
$722$	10719.7	+	32991.7i	0.552555	+	1.70059i
$723$		0			0
$724$	46045.6			2.36363
$725$	−17264.4	−	9222.44i	−0.884389	−	0.472431i
$726$		0			0
$727$	9816.84	+	7132.35i	0.500807	+	0.363857i	0.809325	−	0.587361i	$-0.199833\pi$
$727$	9816.84	+	7132.35i	0.500807	+	0.363857i	−0.308518	+	0.951218i	$0.599833\pi$
$728$	5759.18	+	17724.9i	0.293200	+	0.902376i
$729$		0			0
$730$	12071.8	+	14414.8i	0.612049	+	0.730844i
$731$	599.575	−	1845.30i	0.0303366	−	0.0933666i
$732$		0			0
$733$	−5566.63	+	17132.3i	−0.280502	+	0.863298i	0.707208	+	0.707005i	$0.249954\pi$
$733$	−5566.63	+	17132.3i	−0.280502	+	0.863298i	−0.987711	+	0.156292i	$0.950046\pi$
$734$	7483.23	−	5436.89i	0.376309	−	0.273405i
$735$		0			0
$736$	8347.50	+	6064.81i	0.418061	+	0.303739i
$737$	22572.9	−	16400.1i	1.12820	−	0.819684i
$738$		0			0
$739$	2138.19	+	1553.48i	0.106434	+	0.0773286i	0.639729	−	0.768600i	$-0.279047\pi$
$739$	2138.19	+	1553.48i	0.106434	+	0.0773286i	−0.533295	+	0.845929i	$0.679047\pi$
$740$	−12206.2	−	3055.88i	−0.606365	−	0.151806i
$741$		0			0
$742$	−3409.28	+	10492.7i	−0.168678	+	0.519136i
$743$	12758.9			0.629987			0.314993	−	0.949094i	$-0.397998\pi$
$743$	12758.9			0.629987			0.314993	+	0.949094i	$0.397998\pi$
$744$		0			0
$745$	−28849.0	+	11623.3i	−1.41872	+	0.571606i
$746$	2296.53	+	7068.01i	0.112711	+	0.346888i
$747$		0			0
$748$	−47601.4	−	34584.4i	−2.32684	−	1.69055i
$749$	−5111.05			−0.249337
$750$		0			0
$751$	−3299.48			−0.160319			−0.0801597	−	0.996782i	$-0.525543\pi$
$751$	−3299.48			−0.160319			−0.0801597	+	0.996782i	$0.525543\pi$
$752$	−13193.3	−	9585.46i	−0.639772	−	0.464822i
$753$		0			0
$754$	7471.42	+	22994.7i	0.360866	+	1.11063i
$755$	−4117.00	+	1658.75i	−0.198454	+	0.0799579i
$756$		0			0
$757$	−13754.6			−0.660396			−0.330198	−	0.943912i	$-0.607115\pi$
$757$	−13754.6			−0.660396			−0.330198	+	0.943912i	$0.607115\pi$
$758$	8377.37	−	25782.9i	0.401424	−	1.23546i
$759$		0			0
$760$	3585.87	+	897.738i	0.171149	+	0.0428479i
$761$	−24964.0	−	18137.4i	−1.18915	−	0.863970i	−0.195978	−	0.980608i	$-0.562788\pi$
$761$	−24964.0	−	18137.4i	−1.18915	−	0.863970i	−0.993174	+	0.116638i	$0.962788\pi$
$762$		0			0
$763$	−3700.05	+	2688.24i	−0.175558	+	0.127550i
$764$	−54546.8	−	39630.5i	−2.58303	−	1.87668i
$765$		0			0
$766$	−26623.6	+	19343.2i	−1.25581	+	0.912400i
$767$	1443.79	−	4443.52i	0.0679688	−	0.209187i
$768$		0			0
$769$	2119.16	−	6522.09i	0.0993741	−	0.305842i	−0.888995	−	0.457917i	$-0.848596\pi$
$769$	2119.16	−	6522.09i	0.0993741	−	0.305842i	0.988369	+	0.152075i	$0.0485956\pi$
$770$	−29215.1	−	34885.5i	−1.36732	−	1.63271i
$771$		0			0
$772$	−22054.0	−	67875.3i	−1.02816	−	3.16436i
$773$	1941.17	+	1410.35i	0.0903224	+	0.0656230i	0.632030	−	0.774944i	$-0.282222\pi$
$773$	1941.17	+	1410.35i	0.0903224	+	0.0656230i	−0.541708	+	0.840567i	$0.682222\pi$
$774$		0			0
$775$	−15481.8	−	31898.7i	−0.717580	−	1.47850i
$776$	−5475.04			−0.253276
$777$		0			0
$778$	−13291.1	−	40905.8i	−0.612479	−	1.88502i
$779$	−499.226	−	1536.46i	−0.0229610	−	0.0706667i
$780$		0			0
$781$	5183.32	−	15952.6i	0.237482	−	0.730896i
$782$	15175.4			0.693953
$783$		0			0
$784$	17819.0	−	12946.3i	0.811726	−	0.589753i
$785$	13382.9	−	5392.02i	0.608479	−	0.245158i
$786$		0			0
$787$	4368.91	−	3174.20i	0.197884	−	0.143771i	−0.484431	−	0.874830i	$-0.660973\pi$
$787$	4368.91	−	3174.20i	0.197884	−	0.143771i	0.682315	+	0.731058i	$0.260973\pi$
$788$	−64936.1	+	47178.8i	−2.93560	+	2.13284i
$789$		0			0
$790$	−2860.62	−	41484.5i	−0.128831	−	1.86830i
$791$	22953.7	−	16676.9i	1.03178	−	0.749634i
$792$		0			0
$793$	3724.61			0.166790
$794$	11433.8	−	35189.6i	0.511045	−	1.57283i
$795$		0			0
$796$	−11644.8	−	35839.0i	−0.518516	−	1.59583i
$797$	1421.94	+	4376.29i	0.0631967	+	0.194499i	0.977670	−	0.210147i	$-0.0673944\pi$
$797$	1421.94	+	4376.29i	0.0631967	+	0.194499i	−0.914473	+	0.404647i	$0.867394\pi$
$798$		0			0
$799$	−7211.61			−0.319310
$800$	−15616.3	+	15022.3i	−0.690149	+	0.663898i
$801$		0			0
$802$	23048.6	+	16745.8i	1.01481	+	0.737301i
$803$	6699.00	+	20617.4i	0.294399	+	0.906068i
$804$		0			0
$805$	7868.47	+	1969.90i	0.344506	+	0.0862484i
$806$	−13534.6	+	41655.2i	−0.591484	+	1.82040i
$807$		0			0
$808$	−21128.8	+	65027.8i	−0.919937	+	2.83128i
$809$	10529.0	−	7649.76i	0.457577	−	0.332449i	−0.335003	−	0.942217i	$-0.608737\pi$
$809$	10529.0	−	7649.76i	0.457577	−	0.332449i	0.792580	+	0.609768i	$0.208737\pi$
$810$		0			0
$811$	28816.4	+	20936.3i	1.24770	+	0.906504i	0.998086	−	0.0618426i	$-0.0196977\pi$
$811$	28816.4	+	20936.3i	1.24770	+	0.906504i	0.249610	+	0.968347i	$0.419698\pi$
$812$	−27643.2	+	20083.9i	−1.19469	+	0.867990i
$813$		0			0
$814$	−16982.1	−	12338.2i	−0.731233	−	0.531272i
$815$	−8688.74	+	13875.1i	−0.373439	+	0.596346i
$816$		0			0
$817$	−78.5181	+	241.654i	−0.00336230	+	0.0103481i
$818$	27119.2			1.15917
$819$		0			0
$820$	47814.8	+	11970.6i	2.03630	+	0.509795i
$821$	835.424	+	2571.17i	0.0355134	+	0.109299i	0.967242	−	0.253857i	$-0.0816992\pi$
$821$	835.424	+	2571.17i	0.0355134	+	0.109299i	−0.931728	+	0.363156i	$0.881699\pi$
$822$		0			0
$823$	6927.33	+	5033.00i	0.293404	+	0.213171i	0.724743	−	0.689020i	$-0.241959\pi$
$823$	6927.33	+	5033.00i	0.293404	+	0.213171i	−0.431339	+	0.902190i	$0.641959\pi$
$824$	27076.7			1.14473
$825$		0			0
$826$	9553.39			0.402427
$827$	−30800.4	−	22377.8i	−1.29509	−	0.940935i	−0.295191	−	0.955438i	$-0.595383\pi$
$827$	−30800.4	−	22377.8i	−1.29509	−	0.940935i	−0.999895	+	0.0145034i	$0.995383\pi$
$828$		0			0
$829$	−2638.96	−	8121.89i	−0.110561	−	0.340271i	0.880434	−	0.474168i	$-0.157251\pi$
$829$	−2638.96	−	8121.89i	−0.110561	−	0.340271i	−0.990995	+	0.133896i	$0.957251\pi$
$830$	13423.6	−	21436.1i	0.561372	−	0.896455i
$831$		0			0
$832$	−727.817			−0.0303276
$833$	3009.86	−	9263.39i	0.125193	−	0.385303i
$834$		0			0
$835$	−2687.80	−	38978.2i	−0.111395	−	1.61545i
$836$	6233.70	+	4529.05i	0.257891	+	0.187369i
$837$		0			0
$838$	−16580.1	+	12046.2i	−0.683474	+	0.496573i
$839$	18210.5	+	13230.7i	0.749342	+	0.544429i	0.895623	−	0.444814i	$-0.146730\pi$
$839$	18210.5	+	13230.7i	0.749342	+	0.544429i	−0.146281	+	0.989243i	$0.546730\pi$
$840$		0			0
$841$	−105.272	+	76.4848i	−0.00431638	+	0.00313604i
$842$	−13062.0	+	40200.6i	−0.534614	+	1.64537i
$843$		0			0
$844$	5807.51	−	17873.7i	0.236852	−	0.728954i
$845$	981.843	+	14238.6i	0.0399721	+	0.579672i
$846$		0			0
$847$	−11199.1	−	34467.3i	−0.454316	−	1.39824i
$848$	16299.1	+	11842.0i	0.660037	+	0.479545i
$849$		0			0
$850$	−5594.71	+	31374.7i	−0.225761	+	1.26605i
$851$	3741.85			0.150727
$852$		0			0
$853$	12201.6	+	37552.5i	0.489770	+	1.50736i	0.824952	+	0.565202i	$0.191202\pi$
$853$	12201.6	+	37552.5i	0.489770	+	1.50736i	−0.335183	+	0.942153i	$0.608798\pi$
$854$	2353.42	+	7243.09i	0.0943004	+	0.290227i
$855$		0			0
$856$	−6530.53	+	20098.9i	−0.260758	+	0.802531i
$857$	19669.0			0.783989			0.391995	−	0.919968i	$-0.371785\pi$
$857$	19669.0			0.783989			0.391995	+	0.919968i	$0.371785\pi$
$858$		0			0
$859$	36059.4	−	26198.7i	1.43228	−	1.04061i	0.442696	−	0.896672i	$-0.354022\pi$
$859$	36059.4	−	26198.7i	1.43228	−	1.04061i	0.989586	−	0.143942i	$-0.0459778\pi$
$860$	−4977.40	−	5943.49i	−0.197358	−	0.235664i
$861$		0			0
$862$	40517.2	−	29437.5i	1.60095	−	1.16316i
$863$	36666.4	−	26639.7i	1.44628	−	1.05078i	0.459594	−	0.888129i	$-0.347995\pi$
$863$	36666.4	−	26639.7i	1.44628	−	1.05078i	0.986683	−	0.162653i	$-0.0520051\pi$
$864$		0			0
$865$	18221.2	+	4561.75i	0.716230	+	0.179311i
$866$	−36066.7	+	26204.0i	−1.41524	+	1.02823i
$867$		0			0
$868$	−61897.4			−2.42043
$869$	14815.7	−	45598.1i	0.578354	−	1.77999i
$870$		0			0
$871$	3987.10	+	12271.0i	0.155107	+	0.477369i
$872$	5843.70	+	17985.1i	0.226941	+	0.698453i
$873$		0			0
$874$	−1987.31			−0.0769129
$875$	−6973.58	+	15541.6i	−0.269429	+	0.600459i
$876$		0			0
$877$	−1081.10	−	785.468i	−0.0416263	−	0.0302433i	0.566778	−	0.823871i	$-0.308190\pi$
$877$	−1081.10	−	785.468i	−0.0416263	−	0.0302433i	−0.608404	+	0.793628i	$0.708190\pi$
$878$	−24307.1	−	74809.6i	−0.934311	−	2.87552i
$879$		0			0
$880$	−77072.4	+	31052.7i	−2.95240	+	1.18953i
$881$	−13573.0	+	41773.5i	−0.519055	+	1.59749i	0.256725	+	0.966484i	$0.417356\pi$
$881$	−13573.0	+	41773.5i	−0.519055	+	1.59749i	−0.775780	+	0.631003i	$0.782644\pi$
$882$		0			0
$883$	2980.74	−	9173.79i	0.113601	−	0.349629i	−0.878051	−	0.478566i	$-0.841157\pi$
$883$	2980.74	−	9173.79i	0.113601	−	0.349629i	0.991653	+	0.128937i	$0.0411566\pi$
$884$	22012.3	−	15992.9i	0.837504	−	0.608482i
$885$		0			0
$886$	−5348.54	−	3885.94i	−0.202808	−	0.147348i
$887$	−19694.3	+	14308.7i	−0.745513	+	0.541647i	−0.894433	−	0.447202i	$-0.852420\pi$
$887$	−19694.3	+	14308.7i	−0.745513	+	0.541647i	0.148920	+	0.988849i	$0.452420\pi$
$888$		0			0
$889$	8667.67	+	6297.43i	0.327002	+	0.237581i
$890$	37877.4	+	45229.2i	1.42658	+	1.70347i
$891$		0			0
$892$	−27038.3	+	83215.5i	−1.01492	+	3.12361i
$893$	944.405			0.0353900
$894$		0			0
$895$	−12259.8	−	14639.4i	−0.457879	−	0.546750i
$896$	−5683.36	−	17491.6i	−0.211906	−	0.652179i
$897$		0			0
$898$	42880.7	+	31154.7i	1.59348	+	1.15773i
$899$	−44416.8			−1.64781
$900$		0			0
$901$	8909.28			0.329424
$902$	66523.1	+	48331.9i	2.45563	+	1.78412i
$903$		0			0
$904$	−36252.2	−	111573.i	−1.33377	−	4.10493i
$905$	−1978.21	−	28687.8i	−0.0726607	−	1.05372i
$906$		0			0
$907$	−31727.2			−1.16150			−0.580752	−	0.814080i	$-0.697242\pi$
$907$	−31727.2			−1.16150			−0.580752	+	0.814080i	$0.697242\pi$
$908$	−28694.7	+	88313.1i	−1.04875	+	3.22772i
$909$		0			0
$910$	19517.4	−	7863.61i	0.710982	−	0.286457i
$911$	20546.4	+	14927.9i	0.747238	+	0.542900i	0.894969	−	0.446128i	$-0.147197\pi$
$911$	20546.4	+	14927.9i	0.747238	+	0.542900i	−0.147732	+	0.989027i	$0.547197\pi$
$912$		0			0
$913$	23592.3	−	17140.8i	0.855192	−	0.621333i
$914$	30624.4	+	22249.9i	1.10828	+	0.805211i
$915$		0			0
$916$	−41097.5	+	29859.1i	−1.48242	+	1.07704i
$917$	3556.78	−	10946.6i	0.128086	−	0.394209i
$918$		0			0
$919$	−3080.16	+	9479.76i	−0.110561	+	0.340270i	−0.990995	−	0.133897i	$-0.957251\pi$
$919$	−3080.16	+	9479.76i	−0.110561	+	0.340270i	0.880435	+	0.474167i	$0.157251\pi$
$920$	17800.3	−	28425.3i	0.637890	−	1.01865i
$921$		0			0
$922$	18200.2	+	56014.6i	0.650101	+	2.00081i
$923$	6275.22	+	4559.22i	0.223783	+	0.162588i
$924$		0			0
$925$	−1379.50	+	7736.15i	−0.0490355	+	0.274987i
$926$	−83945.4			−2.97907
$927$		0			0
$928$	8388.03	+	25815.7i	0.296714	+	0.913192i
$929$	11956.9	+	36799.5i	0.422274	+	1.29963i	0.905580	+	0.424175i	$0.139436\pi$
$929$	11956.9	+	36799.5i	0.422274	+	1.29963i	−0.483306	+	0.875452i	$0.660564\pi$
$930$		0			0
$931$	−394.159	+	1213.10i	−0.0138755	+	0.0427043i
$932$	64951.7			2.28279
$933$		0			0
$934$	23599.5	−	17146.0i	0.826766	−	0.600680i
$935$	−19502.1	+	31143.0i	−0.682126	+	1.08929i
$936$		0			0
$937$	15212.9	−	11052.8i	0.530399	−	0.385357i	−0.290108	−	0.956994i	$-0.593691\pi$
$937$	15212.9	−	11052.8i	0.530399	−	0.385357i	0.820507	+	0.571636i	$0.193691\pi$
$938$	−21343.7	+	15507.1i	−0.742960	+	0.539792i
$939$		0			0
$940$	−15292.8	+	24421.1i	−0.530634	+	0.847370i
$941$	−20218.8	+	14689.9i	−0.700442	+	0.508901i	−0.880076	−	0.474833i	$-0.842509\pi$
$941$	−20218.8	+	14689.9i	−0.700442	+	0.508901i	0.179634	+	0.983733i	$0.442509\pi$
$942$		0			0
$943$	−14657.7			−0.506172
$944$	5390.93	−	16591.6i	0.185869	−	0.572044i
$945$		0			0
$946$	−3996.41	−	12299.7i	−0.137352	−	0.422725i
$947$	−12009.3	−	36960.9i	−0.412092	−	1.26829i	−0.914827	−	0.403847i	$-0.867673\pi$
$947$	−12009.3	−	36960.9i	−0.412092	−	1.26829i	0.502735	−	0.864441i	$-0.332327\pi$
$948$		0			0
$949$	−10024.8			−0.342905
$950$	732.662	−	4108.71i	0.0250218	−	0.140320i
$951$		0			0
$952$	24896.3	+	18088.2i	0.847577	+	0.615801i
$953$	3614.26	+	11123.5i	0.122851	+	0.378098i	0.993503	−	0.113802i	$-0.0363028\pi$
$953$	3614.26	+	11123.5i	0.122851	+	0.378098i	−0.870652	+	0.491899i	$0.836303\pi$
$954$		0			0
$955$	−22347.6	+	35686.9i	−0.757227	+	1.20922i
$956$	21822.3	−	67162.2i	0.738268	−	2.27216i
$957$		0			0
$958$	7177.50	−	22090.1i	0.242061	−	0.744987i
$959$	29828.8	−	21671.9i	1.00440	−	0.729740i
$960$		0			0
$961$	−40993.5	−	29783.5i	−1.37604	−	0.999749i
$962$	7853.05	−	5705.57i	0.263194	−	0.191222i
$963$		0			0
$964$	40300.0	+	29279.6i	1.34645	+	0.978251i
$965$	−41340.9	+	16656.4i	−1.37908	+	0.555636i
$966$		0			0
$967$	16302.5	−	50173.9i	0.542143	−	1.66855i	−0.185543	−	0.982636i	$-0.559404\pi$
$967$	16302.5	−	50173.9i	0.542143	−	1.66855i	0.727687	−	0.685910i	$-0.240596\pi$
$968$	−149850.			−4.97558
$969$		0			0
$970$	425.245	+	6166.86i	0.0140761	+	0.204130i
$971$	−10231.0	−	31487.7i	−0.338134	−	1.04067i	−0.965158	−	0.261668i	$-0.915727\pi$
$971$	−10231.0	−	31487.7i	−0.338134	−	1.04067i	0.627024	−	0.779000i	$-0.284273\pi$
$972$		0			0
$973$	14285.1	+	10378.7i	0.470668	+	0.341960i
$974$	−25163.6			−0.827817
$975$		0			0
$976$	13907.3			0.456107
$977$	8689.24	+	6313.10i	0.284538	+	0.206729i	0.720894	−	0.693045i	$-0.243731\pi$
$977$	8689.24	+	6313.10i	0.284538	+	0.206729i	−0.436357	+	0.899774i	$0.643731\pi$
$978$		0			0
$979$	21019.4	+	64691.0i	0.686192	+	2.11188i
$980$	−24986.5	−	29836.2i	−0.814453	−	0.972533i
$981$		0			0
$982$	9332.91			0.303284
$983$	13324.0	−	41007.0i	0.432319	−	1.33054i	−0.463491	−	0.886102i	$-0.653403\pi$
$983$	13324.0	−	41007.0i	0.432319	−	1.33054i	0.895809	−	0.444438i	$-0.146597\pi$
$984$		0			0
$985$	32183.7	+	38430.3i	1.04107	+	1.24314i
$986$	32298.1	+	23466.0i	1.04319	+	0.757919i
$987$		0			0
$988$	−2882.65	+	2094.37i	−0.0928231	+	0.0674399i
$989$	1865.08	+	1355.06i	0.0599656	+	0.0435676i
$990$		0			0
$991$	−13965.8	+	10146.7i	−0.447666	+	0.325248i	−0.788674	−	0.614812i	$-0.789232\pi$
$991$	−13965.8	+	10146.7i	−0.447666	+	0.325248i	0.341008	+	0.940061i	$0.389232\pi$
$992$	−15195.1	+	46765.6i	−0.486334	+	1.49678i
$993$		0			0
$994$	−4901.07	+	15083.9i	−0.156391	+	0.481321i
$995$	−21828.5	+	8794.79i	−0.695489	+	0.280215i
$996$		0			0
$997$	−15988.8	−	49208.5i	−0.507894	−	1.56314i	−0.795850	−	0.605493i	$-0.792976\pi$
$997$	−15988.8	−	49208.5i	−0.507894	−	1.56314i	0.287956	−	0.957644i	$-0.407024\pi$
$998$	88907.2	+	64594.9i	2.81995	+	2.04881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.91.7		28
3.2	odd	2		25.4.d.a.16.1	yes	28
15.2	even	4		125.4.e.b.49.13		56
15.8	even	4		125.4.e.b.49.2		56
15.14	odd	2		125.4.d.a.76.7		28
25.11	even	5	inner	225.4.h.b.136.7		28
75.2	even	20		125.4.e.b.74.2		56
75.11	odd	10		25.4.d.a.11.1	✓	28
75.14	odd	10		125.4.d.a.51.7		28
75.23	even	20		125.4.e.b.74.13		56
75.44	odd	10		625.4.a.d.1.1		14
75.56	odd	10		625.4.a.c.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.1	✓	28	75.11	odd	10
25.4.d.a.16.1	yes	28	3.2	odd	2
125.4.d.a.51.7		28	75.14	odd	10
125.4.d.a.76.7		28	15.14	odd	2
125.4.e.b.49.2		56	15.8	even	4
125.4.e.b.49.13		56	15.2	even	4
125.4.e.b.74.2		56	75.2	even	20
125.4.e.b.74.13		56	75.23	even	20
225.4.h.b.91.7		28	1.1	even	1	trivial
225.4.h.b.136.7		28	25.11	even	5	inner
625.4.a.c.1.14		14	75.56	odd	10
625.4.a.d.1.1		14	75.44	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.11746 + 2.99151i) q^{2} +(5.53220 + 17.0263i) q^{4} +(10.3703 - 4.17822i) q^{5} -12.1888 q^{7} +(-15.5740 + 47.9320i) q^{8} +O(q^{10})\)	\(q+(4.11746 + 2.99151i) q^{2} +(5.53220 + 17.0263i) q^{4} +(10.3703 - 4.17822i) q^{5} -12.1888 q^{7} +(-15.5740 + 47.9320i) q^{8} +(55.1983 + 13.8191i) q^{10} +(53.0773 + 38.5629i) q^{11} +(-24.5445 + 17.8326i) q^{13} +(-50.1870 - 36.4630i) q^{14} +(-91.6464 + 66.5850i) q^{16} +(-15.4803 + 47.6433i) q^{17} +(2.02724 - 6.23919i) q^{19} +(128.510 + 153.453i) q^{20} +(103.182 + 317.562i) q^{22} +(-48.1539 - 34.9858i) q^{23} +(90.0850 - 86.6585i) q^{25} -154.407 q^{26} +(-67.4311 - 207.532i) q^{28} +(-48.3877 - 148.922i) q^{29} +(87.6551 - 269.775i) q^{31} -173.351 q^{32} +(-206.265 + 149.860i) q^{34} +(-126.402 + 50.9276i) q^{35} +(-50.8593 + 36.9514i) q^{37} +(27.0116 - 19.6251i) q^{38} +(38.7631 + 562.139i) q^{40} +(199.228 - 144.748i) q^{41} -38.7316 q^{43} +(-362.951 + 1117.05i) q^{44} +(-93.6111 - 288.105i) q^{46} +(44.4855 + 136.912i) q^{47} -194.432 q^{49} +(630.161 - 87.3224i) q^{50} +(-439.410 - 319.250i) q^{52} +(-54.9578 - 169.143i) q^{53} +(711.550 + 178.139i) q^{55} +(189.830 - 584.235i) q^{56} +(246.267 - 757.932i) q^{58} +(-124.589 + 90.5195i) q^{59} +(-99.3211 - 72.1610i) q^{61} +(1167.95 - 848.564i) q^{62} +(19.4081 + 14.1008i) q^{64} +(-180.025 + 287.482i) q^{65} +(131.420 - 404.468i) q^{67} -896.831 q^{68} +(-672.804 - 168.439i) q^{70} +(-79.0054 - 243.154i) q^{71} +(267.322 + 194.221i) q^{73} -319.951 q^{74} +117.446 q^{76} +(-646.951 - 470.037i) q^{77} +(-225.825 - 695.018i) q^{79} +(-672.192 + 1073.42i) q^{80} +1253.33 q^{82} +(137.355 - 422.734i) q^{83} +(38.5297 + 558.754i) q^{85} +(-159.476 - 115.866i) q^{86} +(-2675.02 + 1943.52i) q^{88} +(838.773 + 609.404i) q^{89} +(299.169 - 217.359i) q^{91} +(329.284 - 1013.43i) q^{92} +(-226.407 + 696.810i) q^{94} +(-5.04570 - 73.1723i) q^{95} +(33.5699 + 103.318i) q^{97} +(-800.565 - 581.645i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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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