LMFDB - Embedded newform 225.4.h.b.46.4

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			46.4
Character	$\chi$	$=$	225.46
Dual form			225.4.h.b.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.132779 - 0.408651i) q^{2} +(6.32277 + 4.59376i) q^{4} +(-11.1601 + 0.672002i) q^{5} -16.1597 q^{7} +(5.49773 - 3.99433i) q^{8} +O(q^{10})$	\(q+(0.132779 - 0.408651i) q^{2} +(6.32277 + 4.59376i) q^{4} +(-11.1601 + 0.672002i) q^{5} -16.1597 q^{7} +(5.49773 - 3.99433i) q^{8} +(-1.20721 + 4.64982i) q^{10} +(10.1515 - 31.2432i) q^{11} +(-24.0686 - 74.0757i) q^{13} +(-2.14566 + 6.60366i) q^{14} +(18.4184 + 56.6859i) q^{16} +(57.3840 - 41.6919i) q^{17} +(80.7756 - 58.6869i) q^{19} +(-73.6499 - 47.0180i) q^{20} +(-11.4197 - 8.29687i) q^{22} +(14.5415 - 44.7540i) q^{23} +(124.097 - 14.9993i) q^{25} -33.4669 q^{26} +(-102.174 - 74.2337i) q^{28} +(-16.9169 - 12.2908i) q^{29} +(-120.948 + 87.8738i) q^{31} +79.9748 q^{32} +(-9.41807 - 28.9858i) q^{34} +(180.344 - 10.8593i) q^{35} +(-17.1502 - 52.7828i) q^{37} +(-13.2572 - 40.8014i) q^{38} +(-58.6711 + 48.2718i) q^{40} +(-10.6827 - 32.8778i) q^{41} +149.171 q^{43} +(207.710 - 150.910i) q^{44} +(-16.3580 - 11.8848i) q^{46} +(-483.450 - 351.247i) q^{47} -81.8652 q^{49} +(10.3480 - 52.7039i) q^{50} +(188.105 - 578.929i) q^{52} +(-392.226 - 284.969i) q^{53} +(-92.2969 + 355.500i) q^{55} +(-88.8415 + 64.5471i) q^{56} +(-7.26886 + 5.28114i) q^{58} +(-91.3523 - 281.153i) q^{59} +(153.931 - 473.752i) q^{61} +(19.8504 + 61.0932i) q^{62} +(-136.728 + 420.805i) q^{64} +(318.388 + 810.519i) q^{65} +(-419.059 + 304.464i) q^{67} +554.349 q^{68} +(19.5082 - 75.1396i) q^{70} +(701.761 + 509.860i) q^{71} +(50.3894 - 155.083i) q^{73} -23.8469 q^{74} +780.320 q^{76} +(-164.045 + 504.880i) q^{77} +(-342.139 - 248.578i) q^{79} +(-243.644 - 620.244i) q^{80} -14.8540 q^{82} +(-331.422 + 240.792i) q^{83} +(-612.396 + 503.849i) q^{85} +(19.8067 - 60.9588i) q^{86} +(-68.9854 - 212.315i) q^{88} +(-353.657 + 1088.44i) q^{89} +(388.941 + 1197.04i) q^{91} +(297.532 - 216.169i) q^{92} +(-207.729 + 150.924i) q^{94} +(-862.029 + 709.235i) q^{95} +(1127.96 + 819.508i) q^{97} +(-10.8700 + 33.4543i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.132779	−	0.408651i	0.0469444	−	0.144480i	−0.924837	−	0.380364i	$-0.875799\pi$
$2$	0.132779	−	0.408651i	0.0469444	−	0.144480i	0.971781	+	0.235884i	$0.0757986\pi$
$3$		0			0
$3$		0			0
$4$	6.32277	+	4.59376i	0.790346	+	0.574220i
$5$	−11.1601	+	0.672002i	−0.998192	+	0.0601057i
$5$	−11.1601	+	0.672002i	−0.998192	+	0.0601057i
$6$		0			0
$7$	−16.1597			−0.872540			−0.436270	−	0.899816i	$-0.643701\pi$
$7$	−16.1597			−0.872540			−0.436270	+	0.899816i	$0.643701\pi$
$8$	5.49773	−	3.99433i	0.242968	−	0.176526i
$9$		0			0
$10$	−1.20721	+	4.64982i	−0.0381754	+	0.147040i
$11$	10.1515	−	31.2432i	0.278255	−	0.856380i	−0.710085	−	0.704116i	$-0.751344\pi$
$11$	10.1515	−	31.2432i	0.278255	−	0.856380i	0.988340	−	0.152264i	$-0.0486564\pi$
$12$		0			0
$13$	−24.0686	−	74.0757i	−0.513495	−	1.58038i	−0.786003	−	0.618223i	$-0.787853\pi$
$13$	−24.0686	−	74.0757i	−0.513495	−	1.58038i	0.272508	−	0.962154i	$-0.412147\pi$
$14$	−2.14566	+	6.60366i	−0.0409608	+	0.126065i
$15$		0			0
$16$	18.4184	+	56.6859i	0.287787	+	0.885717i
$17$	57.3840	−	41.6919i	0.818686	−	0.594811i	−0.0976495	−	0.995221i	$-0.531132\pi$
$17$	57.3840	−	41.6919i	0.818686	−	0.594811i	0.916336	+	0.400410i	$0.131132\pi$
$18$		0			0
$19$	80.7756	−	58.6869i	0.975326	−	0.708616i	0.0186672	−	0.999826i	$-0.494058\pi$
$19$	80.7756	−	58.6869i	0.975326	−	0.708616i	0.956659	+	0.291210i	$0.0940577\pi$
$20$	−73.6499	−	47.0180i	−0.823431	−	0.525678i
$21$		0			0
$22$	−11.4197	−	8.29687i	−0.110667	−	0.0804044i
$23$	14.5415	−	44.7540i	0.131831	−	0.405733i	−0.863253	−	0.504772i	$-0.831577\pi$
$23$	14.5415	−	44.7540i	0.131831	−	0.405733i	0.995084	+	0.0990386i	$0.0315767\pi$
$24$		0			0
$25$	124.097	−	14.9993i	0.992775	−	0.119994i
$26$	−33.4669			−0.252438
$27$		0			0
$28$	−102.174	−	74.2337i	−0.689609	−	0.501030i
$29$	−16.9169	−	12.2908i	−0.108324	−	0.0787017i	0.532305	−	0.846553i	$-0.321326\pi$
$29$	−16.9169	−	12.2908i	−0.108324	−	0.0787017i	−0.640628	+	0.767851i	$0.721326\pi$
$30$		0			0
$31$	−120.948	+	87.8738i	−0.700738	+	0.509116i	−0.880173	−	0.474654i	$-0.842573\pi$
$31$	−120.948	+	87.8738i	−0.700738	+	0.509116i	0.179434	+	0.983770i	$0.442573\pi$
$32$	79.9748			0.441803
$33$		0			0
$34$	−9.41807	−	28.9858i	−0.0475055	−	0.146207i
$35$	180.344	−	10.8593i	0.870962	−	0.0524446i
$36$		0			0
$37$	−17.1502	−	52.7828i	−0.0762019	−	0.234525i	0.905699	−	0.423922i	$-0.139347\pi$
$37$	−17.1502	−	52.7828i	−0.0762019	−	0.234525i	−0.981901	+	0.189396i	$0.939347\pi$
$38$	−13.2572	−	40.8014i	−0.0565947	−	0.174181i
$39$		0			0
$40$	−58.6711	+	48.2718i	−0.231918	+	0.190811i
$41$	−10.6827	−	32.8778i	−0.0406915	−	0.125235i	0.928647	−	0.370964i	$-0.120973\pi$
$41$	−10.6827	−	32.8778i	−0.0406915	−	0.125235i	−0.969339	+	0.245729i	$0.920973\pi$
$42$		0			0
$43$	149.171			0.529031			0.264515	−	0.964381i	$-0.414788\pi$
$43$	149.171			0.529031			0.264515	+	0.964381i	$0.414788\pi$
$44$	207.710	−	150.910i	0.711668	−	0.517057i
$45$		0			0
$46$	−16.3580	−	11.8848i	−0.0524316	−	0.0380938i
$47$	−483.450	−	351.247i	−1.50039	−	1.09010i	−0.970225	−	0.242207i	$-0.922129\pi$
$47$	−483.450	−	351.247i	−1.50039	−	1.09010i	−0.530168	−	0.847892i	$-0.677871\pi$
$48$		0			0
$49$	−81.8652			−0.238674
$50$	10.3480	−	52.7039i	0.0292685	−	0.149069i
$51$		0			0
$52$	188.105	−	578.929i	0.501645	−	1.54390i
$53$	−392.226	−	284.969i	−1.01654	−	0.738557i	−0.0509666	−	0.998700i	$-0.516230\pi$
$53$	−392.226	−	284.969i	−1.01654	−	0.738557i	−0.965570	+	0.260143i	$0.916230\pi$
$54$		0			0
$55$	−92.2969	+	355.500i	−0.226278	+	0.871556i
$56$	−88.8415	+	64.5471i	−0.211999	+	0.154026i
$57$		0			0
$58$	−7.26886	+	5.28114i	−0.0164560	+	0.0119560i
$59$	−91.3523	−	281.153i	−0.201577	−	0.620391i	−0.999837	−	0.0180770i	$-0.994246\pi$
$59$	−91.3523	−	281.153i	−0.201577	−	0.620391i	0.798259	−	0.602314i	$-0.205754\pi$
$60$		0			0
$61$	153.931	−	473.752i	0.323097	−	0.994389i	−0.649196	−	0.760621i	$-0.724894\pi$
$61$	153.931	−	473.752i	0.323097	−	0.994389i	0.972292	−	0.233768i	$-0.0751055\pi$
$62$	19.8504	+	61.0932i	0.0406613	+	0.125143i
$63$		0			0
$64$	−136.728	+	420.805i	−0.267047	+	0.821885i
$65$	318.388	+	810.519i	0.607557	+	1.54665i
$66$		0			0
$67$	−419.059	+	304.464i	−0.764122	+	0.555167i	−0.900172	−	0.435535i	$-0.856559\pi$
$67$	−419.059	+	304.464i	−0.764122	+	0.555167i	0.136050	+	0.990702i	$0.456559\pi$
$68$	554.349			0.988598
$69$		0			0
$70$	19.5082	−	75.1396i	0.0333096	−	0.128299i
$71$	701.761	+	509.860i	1.17301	+	0.852242i	0.991366	−	0.131122i	$-0.0418580\pi$
$71$	701.761	+	509.860i	1.17301	+	0.852242i	0.181644	+	0.983364i	$0.441858\pi$
$72$		0			0
$73$	50.3894	−	155.083i	0.0807895	−	0.248644i	−0.902501	−	0.430688i	$-0.858271\pi$
$73$	50.3894	−	155.083i	0.0807895	−	0.248644i	0.983291	+	0.182043i	$0.0582711\pi$
$74$	−23.8469			−0.0374615
$75$		0			0
$76$	780.320			1.17775
$77$	−164.045	+	504.880i	−0.242788	+	0.747226i
$78$		0			0
$79$	−342.139	−	248.578i	−0.487261	−	0.354016i	0.316869	−	0.948469i	$-0.397368\pi$
$79$	−342.139	−	248.578i	−0.487261	−	0.354016i	−0.804130	+	0.594453i	$0.797368\pi$
$80$	−243.644	−	620.244i	−0.340503	−	0.866818i
$81$		0			0
$82$	−14.8540			−0.0200042
$83$	−331.422	+	240.792i	−0.438292	+	0.318438i	−0.784956	−	0.619551i	$-0.787315\pi$
$83$	−331.422	+	240.792i	−0.438292	+	0.318438i	0.346664	+	0.937990i	$0.387315\pi$
$84$		0			0
$85$	−612.396	+	503.849i	−0.781455	+	0.642943i
$86$	19.8067	−	60.9588i	0.0248350	−	0.0764344i
$87$		0			0
$88$	−68.9854	−	212.315i	−0.0835667	−	0.257192i
$89$	−353.657	+	1088.44i	−0.421208	+	1.29635i	0.485370	+	0.874309i	$0.338685\pi$
$89$	−353.657	+	1088.44i	−0.421208	+	1.29635i	−0.906578	+	0.422037i	$0.861315\pi$
$90$		0			0
$91$	388.941	+	1197.04i	0.448045	+	1.37894i
$92$	297.532	−	216.169i	0.337172	−	0.244970i
$93$		0			0
$94$	−207.729	+	150.924i	−0.227932	+	0.165603i
$95$	−862.029	+	709.235i	−0.930971	+	0.765958i
$96$		0			0
$97$	1127.96	+	819.508i	1.18069	+	0.857819i	0.992249	−	0.124266i	$-0.0396577\pi$
$97$	1127.96	+	819.508i	1.18069	+	0.857819i	0.188438	+	0.982085i	$0.439658\pi$
$98$	−10.8700	+	33.4543i	−0.0112044	+	0.0344836i
$99$		0			0
$100$	853.539	+	475.234i	0.853539	+	0.475234i
$101$	−174.865			−0.172274			−0.0861372	−	0.996283i	$-0.527452\pi$
$101$	−174.865			−0.172274			−0.0861372	+	0.996283i	$0.527452\pi$
$102$		0			0
$103$	−746.468	−	542.341i	−0.714094	−	0.518820i	0.170398	−	0.985375i	$-0.445495\pi$
$103$	−746.468	−	542.341i	−0.714094	−	0.518820i	−0.884492	+	0.466556i	$0.845495\pi$
$104$	−428.206	−	311.110i	−0.403741	−	0.293335i
$105$		0			0
$106$	−168.532	+	122.446i	−0.154427	+	0.112198i
$107$	1957.78			1.76884			0.884420	−	0.466692i	$-0.154554\pi$
$107$	1957.78			1.76884			0.884420	+	0.466692i	$0.154554\pi$
$108$		0			0
$109$	−161.965	−	498.476i	−0.142325	−	0.438031i	0.854332	−	0.519727i	$-0.173966\pi$
$109$	−161.965	−	498.476i	−0.142325	−	0.438031i	−0.996657	+	0.0816960i	$0.973966\pi$
$110$	133.020	+	84.9200i	0.115300	+	0.0736073i
$111$		0			0
$112$	−297.635	−	916.025i	−0.251106	−	0.772823i
$113$	212.446	+	653.842i	0.176861	+	0.544321i	0.999714	−	0.0239334i	$-0.00761897\pi$
$113$	212.446	+	653.842i	0.176861	+	0.544321i	−0.822853	+	0.568254i	$0.807619\pi$
$114$		0			0
$115$	−132.210	+	509.232i	−0.107205	+	0.412923i
$116$	−50.5004	−	155.424i	−0.0404211	−	0.124403i
$117$		0			0
$118$	−127.023			−0.0990969
$119$	−927.307	+	673.728i	−0.714337	+	0.518996i
$120$		0			0
$121$	203.718	+	148.010i	0.153056	+	0.111202i
$122$	−173.160	−	125.808i	−0.128502	−	0.0933619i
$123$		0			0
$124$	−1168.40			−0.846170
$125$	−1374.86	+	250.787i	−0.983767	+	0.179448i
$126$		0			0
$127$	571.272	−	1758.20i	0.399151	−	1.22846i	−0.526530	−	0.850157i	$-0.676507\pi$
$127$	571.272	−	1758.20i	0.399151	−	1.22846i	0.925681	−	0.378305i	$-0.123493\pi$
$128$	671.416	+	487.812i	0.463636	+	0.336851i
$129$		0			0
$130$	373.495	−	22.4898i	0.251982	−	0.0151730i
$131$	1080.44	−	784.987i	0.720600	−	0.523547i	−0.165976	−	0.986130i	$-0.553077\pi$
$131$	1080.44	−	784.987i	0.720600	−	0.523547i	0.886576	+	0.462583i	$0.153077\pi$
$132$		0			0
$133$	−1305.31	+	948.361i	−0.851011	+	0.618296i
$134$	68.7774	+	211.675i	0.0443393	+	0.136462i
$135$		0			0
$136$	148.950	−	458.422i	0.0939146	−	0.289039i
$137$	−389.732	−	1199.47i	−0.243044	−	0.748013i	−0.995952	−	0.0898872i	$-0.971349\pi$
$137$	−389.732	−	1199.47i	−0.243044	−	0.748013i	0.752908	−	0.658126i	$-0.228651\pi$
$138$		0			0
$139$	−454.784	+	1399.68i	−0.277513	+	0.854097i	0.711031	+	0.703161i	$0.248229\pi$
$139$	−454.784	+	1399.68i	−0.277513	+	0.854097i	−0.988544	+	0.150936i	$0.951771\pi$
$140$	1190.16	+	759.796i	0.718477	+	0.458675i
$141$		0			0
$142$	301.534	−	219.077i	0.178198	−	0.129469i
$143$	−2558.69			−1.49628
$144$		0			0
$145$	197.054	+	125.799i	0.112858	+	0.0720486i
$146$	−56.6840	−	41.1833i	−0.0321315	−	0.0233449i
$147$		0			0
$148$	134.035	−	412.517i	0.0744433	−	0.229113i
$149$	391.740			0.215386			0.107693	−	0.994184i	$-0.465654\pi$
$149$	391.740			0.215386			0.107693	+	0.994184i	$0.465654\pi$
$150$		0			0
$151$	2110.18			1.13724			0.568622	−	0.822599i	$-0.307477\pi$
$151$	2110.18			1.13724			0.568622	+	0.822599i	$0.307477\pi$
$152$	209.667	−	645.290i	0.111883	−	0.344342i
$153$		0			0
$154$	184.538	+	134.075i	0.0965616	+	0.0701561i
$155$	1290.74	−	1061.96i	0.668870	−	0.550314i
$156$		0			0
$157$	2186.27			1.11136			0.555678	−	0.831397i	$-0.312459\pi$
$157$	2186.27			1.11136			0.555678	+	0.831397i	$0.312459\pi$
$158$	−147.011	+	106.809i	−0.0740224	+	0.0537804i
$159$		0			0
$160$	−892.529	+	53.7433i	−0.441004	+	0.0265549i
$161$	−234.985	+	723.210i	−0.115028	+	0.354018i
$162$		0			0
$163$	−512.057	−	1575.95i	−0.246058	−	0.757288i	−0.995461	−	0.0951736i	$-0.969659\pi$
$163$	−512.057	−	1575.95i	−0.246058	−	0.757288i	0.749403	−	0.662114i	$-0.230341\pi$
$164$	83.4889	−	256.952i	0.0397524	−	0.122345i
$165$		0			0
$166$	54.3941	+	167.408i	0.0254325	+	0.0782733i
$167$	−1599.49	+	1162.09i	−0.741149	+	0.538476i	−0.893071	−	0.449916i	$-0.851454\pi$
$167$	−1599.49	+	1162.09i	−0.741149	+	0.538476i	0.151922	+	0.988393i	$0.451454\pi$
$168$		0			0
$169$	−3130.49	+	2274.44i	−1.42489	+	1.03525i
$170$	124.585	+	317.157i	0.0562074	+	0.143087i
$171$		0			0
$172$	943.173	+	685.255i	0.418118	+	0.303780i
$173$	724.056	−	2228.41i	0.318202	−	0.979325i	−0.656214	−	0.754575i	$-0.727843\pi$
$173$	724.056	−	2228.41i	0.318202	−	0.979325i	0.974416	−	0.224751i	$-0.0721567\pi$
$174$		0			0
$175$	−2005.36	+	242.383i	−0.866235	+	0.104700i
$176$	1958.02			0.838588
$177$		0			0
$178$	397.836	+	289.044i	0.167523	+	0.121712i
$179$	−449.675	−	326.708i	−0.187767	−	0.136421i	0.489930	−	0.871762i	$-0.337022\pi$
$179$	−449.675	−	326.708i	−0.187767	−	0.136421i	−0.677698	+	0.735341i	$0.737022\pi$
$180$		0			0
$181$	2539.21	−	1844.84i	1.04275	−	0.757603i	0.0719307	−	0.997410i	$-0.477084\pi$
$181$	2539.21	−	1844.84i	1.04275	−	0.757603i	0.970821	+	0.239806i	$0.0770840\pi$
$182$	540.814			0.220263
$183$		0			0
$184$	−98.8175	−	304.129i	−0.0395920	−	0.121852i
$185$	226.868	+	577.538i	0.0901604	+	0.229521i
$186$		0			0
$187$	−720.054	−	2216.10i	−0.281580	−	0.866615i
$188$	−1443.20	−	4441.71i	−0.559873	−	1.72311i
$189$		0			0
$190$	175.370	+	446.440i	0.0669616	+	0.170464i
$191$	971.580	+	2990.22i	0.368069	+	1.13280i	0.948037	+	0.318160i	$0.103065\pi$
$191$	971.580	+	2990.22i	0.368069	+	1.13280i	−0.579969	+	0.814639i	$0.696935\pi$
$192$		0			0
$193$	−3116.00			−1.16215			−0.581074	−	0.813851i	$-0.697367\pi$
$193$	−3116.00			−1.16215			−0.581074	+	0.813851i	$0.697367\pi$
$194$	484.661	−	352.127i	0.179364	−	0.130316i
$195$		0			0
$196$	−517.615	−	376.069i	−0.188635	−	0.137051i
$197$	1192.33	+	866.278i	0.431218	+	0.313298i	0.782136	−	0.623108i	$-0.214130\pi$
$197$	1192.33	+	866.278i	0.431218	+	0.313298i	−0.350918	+	0.936406i	$0.614130\pi$
$198$		0			0
$199$	475.734			0.169467			0.0847334	−	0.996404i	$-0.472996\pi$
$199$	475.734			0.169467			0.0847334	+	0.996404i	$0.472996\pi$
$200$	622.339	−	578.146i	0.220030	−	0.204405i
$201$		0			0
$202$	−23.2184	+	71.4587i	−0.00808732	+	0.0248902i
$203$	273.371	+	198.616i	0.0945167	+	0.0686704i
$204$		0			0
$205$	141.314	+	359.742i	0.0481453	+	0.122563i
$206$	−320.743	+	233.034i	−0.108482	+	0.0788166i
$207$		0			0
$208$	3755.74	−	2728.70i	1.25199	−	0.909623i
$209$	−1013.57	−	3119.45i	−0.335455	−	1.03243i
$210$		0			0
$211$	−576.264	+	1773.56i	−0.188017	+	0.578657i	−0.999987	−	0.00504161i	$-0.998395\pi$
$211$	−576.264	+	1773.56i	−0.188017	+	0.578657i	0.811970	+	0.583699i	$0.198395\pi$
$212$	−1170.88	−	3603.59i	−0.379322	−	1.16743i
$213$		0			0
$214$	259.952	−	800.049i	0.0830371	−	0.255562i
$215$	−1664.76	+	100.243i	−0.528074	+	0.0317978i
$216$		0			0
$217$	1954.48	−	1420.01i	0.611422	−	0.444224i
$218$	−225.208			−0.0699681
$219$		0			0
$220$	−2216.65	+	1823.75i	−0.679303	+	0.558898i
$221$	−4469.51	−	3247.29i	−1.36042	−	0.988400i
$222$		0			0
$223$	1254.25	−	3860.20i	0.376642	−	1.15918i	−0.565723	−	0.824595i	$-0.691403\pi$
$223$	1254.25	−	3860.20i	0.376642	−	1.15918i	0.942364	−	0.334588i	$-0.108597\pi$
$224$	−1292.37			−0.385491
$225$		0			0
$226$	295.401			0.0869461
$227$	676.107	−	2080.84i	0.197686	−	0.608416i	−0.802249	−	0.596990i	$-0.796363\pi$
$227$	676.107	−	2080.84i	0.197686	−	0.608416i	0.999935	−	0.0114254i	$-0.00363689\pi$
$228$		0			0
$229$	−3695.57	−	2684.99i	−1.06642	−	0.774798i	−0.0911533	−	0.995837i	$-0.529055\pi$
$229$	−3695.57	−	2684.99i	−1.06642	−	0.774798i	−0.975265	+	0.221039i	$0.929055\pi$
$230$	190.544	+	121.643i	0.0546264	+	0.0348735i
$231$		0			0
$232$	−142.098			−0.0402121
$233$	2841.92	−	2064.77i	0.799057	−	0.580549i	−0.111580	−	0.993755i	$-0.535591\pi$
$233$	2841.92	−	2064.77i	0.799057	−	0.580549i	0.910637	+	0.413207i	$0.135591\pi$
$234$		0			0
$235$	5631.40	+	3595.08i	1.56320	+	0.997946i
$236$	713.952	−	2197.32i	0.196925	−	0.606073i
$237$		0			0
$238$	152.193	+	468.401i	0.0414504	+	0.127571i
$239$	−699.816	+	2153.81i	−0.189403	+	0.582923i	−0.999996	−	0.00268657i	$-0.999145\pi$
$239$	−699.816	+	2153.81i	−0.189403	+	0.582923i	0.810593	+	0.585610i	$0.199145\pi$
$240$		0			0
$241$	367.193	+	1130.10i	0.0981450	+	0.302059i	0.988061	−	0.154066i	$-0.0492369\pi$
$241$	367.193	+	1130.10i	0.0981450	+	0.302059i	−0.889916	+	0.456125i	$0.849237\pi$
$242$	87.5336	−	63.5969i	0.0232516	−	0.0168932i
$243$		0			0
$244$	3149.58	−	2288.30i	0.826356	−	0.600383i
$245$	913.626	−	55.0136i	0.238243	−	0.0143457i
$246$		0			0
$247$	−6291.43	−	4570.99i	−1.62071	−	1.17751i
$248$	−313.941	+	966.212i	−0.0803843	+	0.247397i
$249$		0			0
$250$	−80.0675	+	595.136i	−0.0202556	+	0.150559i
$251$	5391.95			1.35592			0.677962	−	0.735097i	$-0.262863\pi$
$251$	5391.95			1.35592			0.677962	+	0.735097i	$0.262863\pi$
$252$		0			0
$253$	−1250.64	−	908.644i	−0.310779	−	0.225794i
$254$	−642.635	−	466.902i	−0.158750	−	0.115339i
$255$		0			0
$256$	−2575.17	+	1870.97i	−0.628704	+	0.456780i
$257$	352.549			0.0855695			0.0427848	−	0.999084i	$-0.486377\pi$
$257$	352.549			0.0855695			0.0427848	+	0.999084i	$0.486377\pi$
$258$		0			0
$259$	277.141	+	852.952i	0.0664892	+	0.204633i
$260$	−1710.24	+	6587.33i	−0.407940	+	1.57126i
$261$		0			0
$262$	−177.326	−	545.753i	−0.0418139	−	0.128690i
$263$	1823.75	+	5612.93i	0.427594	+	1.31600i	0.900488	+	0.434881i	$0.143209\pi$
$263$	1823.75	+	5612.93i	0.427594	+	1.31600i	−0.472894	+	0.881119i	$0.656791\pi$
$264$		0			0
$265$	4568.80	+	2916.71i	1.05909	+	0.676122i
$266$	214.232	+	659.337i	0.0493812	+	0.151980i
$267$		0			0
$268$	−4048.24			−0.922709
$269$	205.635	−	149.403i	0.0466089	−	0.0338633i	−0.564237	−	0.825613i	$-0.690830\pi$
$269$	205.635	−	149.403i	0.0466089	−	0.0338633i	0.610846	+	0.791750i	$0.290830\pi$
$270$		0			0
$271$	4481.04	+	3255.67i	1.00444	+	0.729770i	0.963036	−	0.269373i	$-0.0868164\pi$
$271$	4481.04	+	3255.67i	1.00444	+	0.729770i	0.0414058	+	0.999142i	$0.486816\pi$
$272$	3420.26	+	2484.97i	0.762441	+	0.553946i
$273$		0			0
$274$	−541.914			−0.119482
$275$	791.148	−	4029.45i	0.173484	−	0.883581i
$276$		0			0
$277$	−2150.27	+	6617.86i	−0.466417	+	1.43548i	0.390775	+	0.920486i	$0.372207\pi$
$277$	−2150.27	+	6617.86i	−0.466417	+	1.43548i	−0.857192	+	0.514997i	$0.827793\pi$
$278$	511.596	+	371.696i	0.110372	+	0.0801901i
$279$		0			0
$280$	948.106	−	780.055i	0.202358	−	0.166490i
$281$	−4487.15	+	3260.10i	−0.952600	+	0.692105i	−0.951420	−	0.307895i	$-0.900376\pi$
$281$	−4487.15	+	3260.10i	−0.952600	+	0.692105i	−0.00117988	+	0.999999i	$0.500376\pi$
$282$		0			0
$283$	−2292.25	+	1665.42i	−0.481485	+	0.349820i	−0.801900	−	0.597458i	$-0.796178\pi$
$283$	−2292.25	+	1665.42i	−0.481485	+	0.349820i	0.320415	+	0.947277i	$0.396178\pi$
$284$	2094.90	+	6447.45i	0.437710	+	1.34713i
$285$		0			0
$286$	−339.740	+	1045.61i	−0.0702422	+	0.216183i
$287$	172.628	+	531.295i	0.0355049	+	0.109273i
$288$		0			0
$289$	36.5082	−	112.361i	0.00743093	−	0.0228701i
$290$	77.5725	−	63.8229i	0.0157076	−	0.0129235i
$291$		0			0
$292$	1031.01	−	749.075i	0.206628	−	0.150124i
$293$	−4593.67			−0.915921			−0.457961	−	0.888973i	$-0.651420\pi$
$293$	−4593.67			−0.915921			−0.457961	+	0.888973i	$0.651420\pi$
$294$		0			0
$295$	1208.44	+	3076.32i	0.238502	+	0.607153i
$296$	−305.119	−	221.682i	−0.0599145	−	0.0435304i
$297$		0			0
$298$	52.0147	−	160.085i	0.0101112	−	0.0311190i
$299$	−3665.18			−0.708905
$300$		0			0
$301$	−2410.55			−0.461601
$302$	280.187	−	862.327i	0.0533873	−	0.164309i
$303$		0			0
$304$	4814.48	+	3497.92i	0.908320	+	0.659933i
$305$	−1399.53	+	5390.57i	−0.262744	+	1.01201i
$306$		0			0
$307$	3322.26			0.617628			0.308814	−	0.951123i	$-0.400068\pi$
$307$	3322.26			0.617628			0.308814	+	0.951123i	$0.400068\pi$
$308$	−3356.52	+	2438.65i	−0.620959	+	0.451153i
$309$		0			0
$310$	−262.588	−	668.469i	−0.0481096	−	0.122472i
$311$	1541.54	−	4744.38i	0.281070	−	0.865046i	−0.706479	−	0.707734i	$-0.749717\pi$
$311$	1541.54	−	4744.38i	0.281070	−	0.865046i	0.987549	−	0.157311i	$-0.0502826\pi$
$312$		0			0
$313$	−600.953	−	1849.54i	−0.108523	−	0.334001i	0.882018	−	0.471216i	$-0.156185\pi$
$313$	−600.953	−	1849.54i	−0.108523	−	0.334001i	−0.990541	+	0.137215i	$0.956185\pi$
$314$	290.290	−	893.419i	0.0521719	−	0.160569i
$315$		0			0
$316$	−1021.36	−	3143.41i	−0.181822	−	0.559590i
$317$	−5447.24	+	3957.65i	−0.965134	+	0.701211i	−0.954337	−	0.298731i	$-0.903437\pi$
$317$	−5447.24	+	3957.65i	−0.965134	+	0.701211i	−0.0107969	+	0.999942i	$0.503437\pi$
$318$		0			0
$319$	−555.737	+	403.767i	−0.0975402	+	0.0708671i
$320$	1243.12	−	4788.12i	0.217164	−	0.836450i
$321$		0			0
$322$	264.339	+	192.054i	0.0457486	+	0.0332383i
$323$	2188.46	−	6735.38i	0.376994	−	1.16027i
$324$		0			0
$325$	−4097.92	−	8831.54i	−0.699421	−	1.50734i
$326$	−712.004			−0.120964
$327$		0			0
$328$	−190.055	−	138.083i	−0.0319941	−	0.0232450i
$329$	7812.39	+	5676.04i	1.30915	+	0.951155i
$330$		0			0
$331$	779.872	−	566.610i	0.129503	−	0.0940898i	−0.521148	−	0.853466i	$-0.674496\pi$
$331$	779.872	−	566.610i	0.129503	−	0.0940898i	0.650651	+	0.759377i	$0.274496\pi$
$332$	−3201.65			−0.529256
$333$		0			0
$334$	262.513	+	807.933i	0.0430062	+	0.132360i
$335$	4472.15	−	3679.46i	0.729371	−	0.600091i
$336$		0			0
$337$	1551.16	+	4773.97i	0.250733	+	0.771676i	0.994640	+	0.103394i	$0.0329702\pi$
$337$	1551.16	+	4773.97i	0.250733	+	0.771676i	−0.743908	+	0.668282i	$0.767030\pi$
$338$	513.788	+	1581.28i	0.0826816	+	0.254468i
$339$		0			0
$340$	−6186.60	+	372.523i	−0.986811	+	0.0594204i
$341$	1517.65	+	4670.85i	0.241013	+	0.741762i
$342$		0			0
$343$	6865.68			1.08079
$344$	820.100	−	595.838i	0.128537	−	0.0933879i
$345$		0			0
$346$	−814.505	−	591.772i	−0.126555	−	0.0919476i
$347$	4929.09	+	3581.19i	0.762557	+	0.554030i	0.899693	−	0.436522i	$-0.143790\pi$
$347$	4929.09	+	3581.19i	0.762557	+	0.554030i	−0.137137	+	0.990552i	$0.543790\pi$
$348$		0			0
$349$	−2624.86			−0.402594			−0.201297	−	0.979530i	$-0.564516\pi$
$349$	−2624.86			−0.402594			−0.201297	+	0.979530i	$0.564516\pi$
$350$	−167.220	+	851.677i	−0.0255379	+	0.130069i
$351$		0			0
$352$	811.867	−	2498.67i	0.122934	−	0.378351i
$353$	−2357.93	−	1713.13i	−0.355523	−	0.258303i	0.395659	−	0.918397i	$-0.370516\pi$
$353$	−2357.93	−	1713.13i	−0.355523	−	0.258303i	−0.751183	+	0.660095i	$0.770516\pi$
$354$		0			0
$355$	−8174.37	−	5218.51i	−1.22211	−	0.780197i
$356$	−7236.14	+	5257.37i	−1.07729	+	0.782696i
$357$		0			0
$358$	−193.217	+	140.380i	−0.0285247	+	0.0207244i
$359$	−2999.85	−	9232.60i	−0.441020	−	1.35732i	−0.886790	−	0.462172i	$-0.847070\pi$
$359$	−2999.85	−	9232.60i	−0.441020	−	1.35732i	0.445770	−	0.895148i	$-0.352930\pi$
$360$		0			0
$361$	961.000	−	2957.65i	0.140108	−	0.431208i
$362$	−416.744	−	1282.61i	−0.0605072	−	0.186222i
$363$		0			0
$364$	−3039.72	+	9355.30i	−0.437705	+	1.34712i
$365$	−458.136	+	1764.60i	−0.0656985	+	0.253051i
$366$		0			0
$367$	1084.14	−	787.677i	0.154201	−	0.112034i	−0.508009	−	0.861352i	$-0.669618\pi$
$367$	1084.14	−	787.677i	0.154201	−	0.112034i	0.662211	+	0.749318i	$0.269618\pi$
$368$	2804.75			0.397304
$369$		0			0
$370$	266.135	−	16.0252i	0.0373937	−	0.00225165i
$371$	6338.25	+	4605.01i	0.886969	+	0.644421i
$372$		0			0
$373$	−1836.73	+	5652.88i	−0.254966	+	0.784705i	0.738870	+	0.673848i	$0.235360\pi$
$373$	−1836.73	+	5652.88i	−0.254966	+	0.784705i	−0.993836	+	0.110857i	$0.964640\pi$
$374$	−1001.22			−0.138427
$375$		0			0
$376$	−4060.88			−0.556978
$377$	−503.285	+	1548.95i	−0.0687547	+	0.211605i
$378$		0			0
$379$	3296.44	+	2395.00i	0.446772	+	0.324599i	0.788320	−	0.615265i	$-0.210951\pi$
$379$	3296.44	+	2395.00i	0.446772	+	0.324599i	−0.341548	+	0.939864i	$0.610951\pi$
$380$	−8708.47	+	524.376i	−1.17562	+	0.0707893i
$381$		0			0
$382$	1350.96			0.180945
$383$	−2087.46	+	1516.63i	−0.278497	+	0.202340i	−0.718261	−	0.695773i	$-0.755062\pi$
$383$	−2087.46	+	1516.63i	−0.278497	+	0.202340i	0.439765	+	0.898113i	$0.355062\pi$
$384$		0			0
$385$	1491.49	−	5744.76i	0.197437	−	0.760468i
$386$	−413.738	+	1273.36i	−0.0545563	+	0.167907i
$387$		0			0
$388$	3367.18	+	10363.1i	0.440574	+	1.35595i
$389$	−388.355	+	1195.23i	−0.0506180	+	0.155786i	−0.973170	−	0.230086i	$-0.926099\pi$
$389$	−388.355	+	1195.23i	−0.0506180	+	0.155786i	0.922552	+	0.385872i	$0.126099\pi$
$390$		0			0
$391$	−1031.43	−	3174.43i	−0.133406	−	0.410582i
$392$	−450.073	+	326.997i	−0.0579901	+	0.0421322i
$393$		0			0
$394$	512.321	−	372.223i	0.0655086	−	0.0475948i
$395$	3985.36	+	2544.25i	0.507658	+	0.324089i
$396$		0			0
$397$	8359.25	+	6073.35i	1.05677	+	0.767791i	0.973489	−	0.228735i	$-0.0734590\pi$
$397$	8359.25	+	6073.35i	1.05677	+	0.767791i	0.0832844	+	0.996526i	$0.473459\pi$
$398$	63.1673	−	194.409i	0.00795551	−	0.0244845i
$399$		0			0
$400$	3135.91	+	6758.28i	0.391988	+	0.844785i
$401$	−6749.76			−0.840566			−0.420283	−	0.907393i	$-0.638069\pi$
$401$	−6749.76			−0.840566			−0.420283	+	0.907393i	$0.638069\pi$
$402$		0			0
$403$	9420.36	+	6844.29i	1.16442	+	0.846001i
$404$	−1105.63	−	803.288i	−0.136156	−	0.0989235i
$405$		0			0
$406$	117.462	−	85.3414i	0.0143585	−	0.0104321i
$407$	−1823.20			−0.222046
$408$		0			0
$409$	−2869.94	−	8832.78i	−0.346967	−	1.06786i	−0.960522	−	0.278203i	$-0.910261\pi$
$409$	−2869.94	−	8832.78i	−0.346967	−	1.06786i	0.613555	−	0.789652i	$-0.289739\pi$
$410$	165.772	−	9.98191i	0.0199681	−	0.00120237i
$411$		0			0
$412$	−2228.36	−	6858.19i	−0.266465	−	0.820094i
$413$	1476.22	+	4543.35i	0.175884	+	0.541316i
$414$		0			0
$415$	3536.90	−	2909.99i	0.418360	−	0.344206i
$416$	−1924.89	−	5924.19i	−0.226864	−	0.698215i
$417$		0			0
$418$	−1409.35			−0.164913
$419$	6524.78	−	4740.53i	0.760755	−	0.552721i	−0.138387	−	0.990378i	$-0.544192\pi$
$419$	6524.78	−	4740.53i	0.760755	−	0.552721i	0.899142	+	0.437657i	$0.144192\pi$
$420$		0			0
$421$	−1254.19	−	911.219i	−0.145191	−	0.105487i	0.512819	−	0.858497i	$-0.328601\pi$
$421$	−1254.19	−	911.219i	−0.145191	−	0.105487i	−0.658009	+	0.753010i	$0.728601\pi$
$422$	648.250	+	470.981i	0.0747780	+	0.0543294i
$423$		0			0
$424$	−3294.62			−0.377360
$425$	6495.83	−	6034.55i	0.741397	−	0.688750i
$426$		0			0
$427$	−2487.48	+	7655.67i	−0.281915	+	0.867644i
$428$	12378.6	+	8993.58i	1.39800	+	1.01570i
$429$		0			0
$430$	−180.081	+	693.618i	−0.0201960	+	0.0777889i
$431$	13247.9	−	9625.18i	1.48058	−	1.07570i	0.503211	−	0.864164i	$-0.332152\pi$
$431$	13247.9	−	9625.18i	1.48058	−	1.07570i	0.977369	−	0.211541i	$-0.0678482\pi$
$432$		0			0
$433$	−7532.91	+	5472.98i	−0.836047	+	0.607424i	−0.921264	−	0.388938i	$-0.872842\pi$
$433$	−7532.91	+	5472.98i	−0.836047	+	0.607424i	0.0852163	+	0.996362i	$0.472842\pi$
$434$	−320.776	−	987.246i	−0.0354786	−	0.109192i
$435$		0			0
$436$	1265.82	−	3895.78i	0.139040	−	0.427922i
$437$	−1451.88	−	4468.43i	−0.158931	−	0.489139i
$438$		0			0
$439$	4823.55	−	14845.4i	0.524409	−	1.61397i	−0.241071	−	0.970507i	$-0.577499\pi$
$439$	4823.55	−	14845.4i	0.524409	−	1.61397i	0.765481	−	0.643459i	$-0.222501\pi$
$440$	912.562	+	2323.11i	0.0988743	+	0.251704i
$441$		0			0
$442$	−1920.46	+	1395.30i	−0.206668	+	0.150153i
$443$	−4452.27			−0.477503			−0.238751	−	0.971081i	$-0.576738\pi$
$443$	−4452.27			−0.477503			−0.238751	+	0.971081i	$0.576738\pi$
$444$		0			0
$445$	3215.42	−	12384.8i	0.342529	−	1.31932i
$446$	−1410.94	−	1025.10i	−0.149798	−	0.108834i
$447$		0			0
$448$	2209.48	−	6800.07i	0.233009	−	0.717128i
$449$	−9647.98			−1.01407			−0.507034	−	0.861926i	$-0.669258\pi$
$449$	−9647.98			−1.01407			−0.507034	+	0.861926i	$0.669258\pi$
$450$		0			0
$451$	−1135.65			−0.118572
$452$	−1660.35	+	5110.02i	−0.172779	+	0.531759i
$453$		0			0
$454$	−760.566	−	552.583i	−0.0786236	−	0.0571234i
$455$	−5145.04	−	13097.7i	−0.530117	−	1.34952i
$456$		0			0
$457$	−15792.6			−1.61652			−0.808258	−	0.588829i	$-0.799589\pi$
$457$	−15792.6			−1.61652			−0.808258	+	0.588829i	$0.799589\pi$
$458$	−1587.91	+	1153.69i	−0.162005	+	0.117704i
$459$		0			0
$460$	−3175.22	+	2612.42i	−0.321838	+	0.264793i
$461$	894.642	−	2753.42i	0.0903853	−	0.278177i	−0.895638	−	0.444783i	$-0.853281\pi$
$461$	894.642	−	2753.42i	0.0903853	−	0.278177i	0.986024	+	0.166606i	$0.0532808\pi$
$462$		0			0
$463$	95.6053	+	294.243i	0.00959644	+	0.0295348i	0.955740	−	0.294212i	$-0.0950573\pi$
$463$	95.6053	+	294.243i	0.00959644	+	0.0295348i	−0.946144	+	0.323747i	$0.895057\pi$
$464$	385.136	−	1185.33i	0.0385333	−	0.118593i
$465$		0			0
$466$	−466.426	−	1435.51i	−0.0463664	−	0.142701i
$467$	12422.9	−	9025.80i	1.23098	−	0.894356i	0.234012	−	0.972234i	$-0.424814\pi$
$467$	12422.9	−	9025.80i	1.23098	−	0.894356i	0.996963	+	0.0778780i	$0.0248145\pi$
$468$		0			0
$469$	6771.85	−	4920.03i	0.666727	−	0.484405i
$470$	2216.87	−	1823.93i	0.217567	−	0.179003i
$471$		0			0
$472$	−1625.25	−	1180.81i	−0.158492	−	0.115151i
$473$	1514.31	−	4660.57i	0.147205	−	0.453051i
$474$		0			0
$475$	9143.74	−	8494.44i	0.883250	−	0.820529i
$476$	−8958.09			−0.862591
$477$		0			0
$478$	787.237	+	571.961i	0.0753293	+	0.0547299i
$479$	7809.42	+	5673.88i	0.744930	+	0.541224i	0.894251	−	0.447565i	$-0.147709\pi$
$479$	7809.42	+	5673.88i	0.744930	+	0.541224i	−0.149321	+	0.988789i	$0.547709\pi$
$480$		0			0
$481$	−3497.14	+	2540.82i	−0.331509	+	0.240855i
$482$	510.573			0.0482489
$483$		0			0
$484$	608.140	+	1871.66i	0.0571130	+	0.175776i
$485$	−13138.8	−	8387.82i	−1.23011	−	0.785302i
$486$		0			0
$487$	1972.58	+	6070.98i	0.183545	+	0.564892i	0.999920	−	0.0126290i	$-0.00402005\pi$
$487$	1972.58	+	6070.98i	0.183545	+	0.564892i	−0.816376	+	0.577521i	$0.804020\pi$
$488$	−1046.05	−	3219.41i	−0.0970338	−	0.298639i
$489$		0			0
$490$	98.8288	−	380.659i	0.00911149	−	0.0350947i
$491$	−5289.48	−	16279.4i	−0.486173	−	1.49629i	−0.830275	−	0.557355i	$-0.811816\pi$
$491$	−5289.48	−	16279.4i	−0.486173	−	1.49629i	0.344101	−	0.938932i	$-0.388184\pi$
$492$		0			0
$493$	−1483.19			−0.135496
$494$	−2703.31	+	1964.07i	−0.246210	+	0.178882i
$495$		0			0
$496$	−7208.86	−	5237.55i	−0.652596	−	0.474139i
$497$	−11340.2	−	8239.16i	−1.02350	−	0.743615i
$498$		0			0
$499$	17105.0			1.53452			0.767259	−	0.641337i	$-0.221620\pi$
$499$	17105.0			1.53452			0.767259	+	0.641337i	$0.221620\pi$
$500$	−9844.96	−	4730.10i	−0.880560	−	0.423073i
$501$		0			0
$502$	715.937	−	2203.43i	0.0636530	−	0.195904i
$503$	7434.74	+	5401.65i	0.659043	+	0.478823i	0.866340	−	0.499455i	$-0.166467\pi$
$503$	7434.74	+	5401.65i	0.659043	+	0.478823i	−0.207297	+	0.978278i	$0.566467\pi$
$504$		0			0
$505$	1951.52	−	117.510i	0.171963	−	0.0103547i
$506$	−537.377	+	390.427i	−0.0472121	+	0.0343016i
$507$		0			0
$508$	11688.8	−	8492.38i	1.02088	−	0.741709i
$509$	−1728.25	−	5319.02i	−0.150498	−	0.463185i	0.847179	−	0.531308i	$-0.178299\pi$
$509$	−1728.25	−	5319.02i	−0.150498	−	0.463185i	−0.997677	+	0.0681224i	$0.978299\pi$
$510$		0			0
$511$	−814.276	+	2506.08i	−0.0704920	+	0.216952i
$512$	2474.31	+	7615.15i	0.213574	+	0.657315i
$513$		0			0
$514$	46.8110	−	144.069i	0.00401701	−	0.0123631i
$515$	8695.13	+	5550.96i	0.743987	+	0.474961i
$516$		0			0
$517$	−15881.8	+	11538.8i	−1.35103	+	0.981581i
$518$	385.358			0.0326866
$519$		0			0
$520$	4987.90	+	3184.27i	0.420642	+	0.268537i
$521$	1556.71	+	1131.02i	0.130904	+	0.0951071i	0.651310	−	0.758812i	$-0.274220\pi$
$521$	1556.71	+	1131.02i	0.130904	+	0.0951071i	−0.520407	+	0.853919i	$0.674220\pi$
$522$		0			0
$523$	64.5232	−	198.582i	0.00539465	−	0.0166030i	−0.948323	−	0.317307i	$-0.897222\pi$
$523$	64.5232	−	198.582i	0.00539465	−	0.0166030i	0.953718	+	0.300704i	$0.0972215\pi$
$524$	10437.4			0.870155
$525$		0			0
$526$	2535.88			0.210209
$527$	−3276.85	+	10085.1i	−0.270857	+	0.833613i
$528$		0			0
$529$	8051.84	+	5850.01i	0.661777	+	0.480809i
$530$	1798.56	−	1479.77i	0.147404	−	0.121277i
$531$		0			0
$532$	−12609.7			−1.02763
$533$	−2178.33	+	1582.65i	−0.177024	+	0.128616i
$534$		0			0
$535$	−21849.1	+	1315.63i	−1.76564	+	0.106317i
$536$	−1087.74	+	3347.72i	−0.0876552	+	0.269775i
$537$		0			0
$538$	−33.7496	−	103.870i	−0.00270455	−	0.00832374i
$539$	−831.057	+	2557.73i	−0.0664122	+	0.204396i
$540$		0			0
$541$	814.582	+	2507.03i	0.0647350	+	0.199234i	0.978193	−	0.207700i	$-0.0665979\pi$
$541$	814.582	+	2507.03i	0.0647350	+	0.199234i	−0.913458	+	0.406934i	$0.866598\pi$
$542$	1925.42	−	1398.90i	0.152590	−	0.110863i
$543$		0			0
$544$	4589.28	−	3334.31i	0.361698	−	0.262789i
$545$	2142.52	+	5454.22i	0.168396	+	0.428685i
$546$		0			0
$547$	8650.84	+	6285.21i	0.676204	+	0.491291i	0.872096	−	0.489335i	$-0.162760\pi$
$547$	8650.84	+	6285.21i	0.676204	+	0.491291i	−0.195892	+	0.980625i	$0.562760\pi$
$548$	3045.90	−	9374.33i	0.237435	−	0.730751i
$549$		0			0
$550$	−1541.59	−	858.328i	−0.119516	−	0.0665441i
$551$	−2087.78			−0.161420
$552$		0			0
$553$	5528.85	+	4016.94i	0.425155	+	0.308893i
$554$	2418.89	+	1757.42i	0.185503	+	0.134776i
$555$		0			0
$556$	−9305.30	+	6760.70i	−0.709771	+	0.515679i
$557$	−6016.30			−0.457664			−0.228832	−	0.973466i	$-0.573491\pi$
$557$	−6016.30			−0.457664			−0.228832	+	0.973466i	$0.573491\pi$
$558$		0			0
$559$	−3590.34	−	11049.9i	−0.271655	−	0.836068i
$560$	3937.21	+	10022.9i	0.297103	+	0.756333i
$561$		0			0
$562$	736.446	+	2266.55i	0.0552760	+	0.170122i
$563$	4531.47	+	13946.4i	0.339216	+	1.04400i	0.964608	+	0.263689i	$0.0849394\pi$
$563$	4531.47	+	13946.4i	0.339216	+	1.04400i	−0.625391	+	0.780311i	$0.715061\pi$
$564$		0			0
$565$	−2810.31	−	7154.19i	−0.209258	−	0.532706i
$566$	376.213	+	1157.86i	0.0279389	+	0.0859870i
$567$		0			0
$568$	5894.64			0.435447
$569$	16744.7	−	12165.7i	1.23370	−	0.896335i	0.236537	−	0.971622i	$-0.423988\pi$
$569$	16744.7	−	12165.7i	1.23370	−	0.896335i	0.997162	+	0.0752877i	$0.0239875\pi$
$570$		0			0
$571$	−14156.6	−	10285.4i	−1.03754	−	0.753818i	−0.0677372	−	0.997703i	$-0.521578\pi$
$571$	−14156.6	−	10285.4i	−1.03754	−	0.753818i	−0.969804	+	0.243885i	$0.921578\pi$
$572$	−16178.0	−	11754.0i	−1.18258	−	0.859197i
$573$		0			0
$574$	240.035			0.0174545
$575$	1133.27	−	5771.94i	0.0821926	−	0.418620i
$576$		0			0
$577$	2430.61	−	7480.65i	0.175369	−	0.539729i	−0.824282	−	0.566180i	$-0.808421\pi$
$577$	2430.61	−	7480.65i	0.175369	−	0.539729i	0.999650	+	0.0264512i	$0.00842066\pi$
$578$	−41.0687	−	29.8382i	−0.00295542	−	0.00214724i
$579$		0			0
$580$	668.036	+	1700.62i	0.0478253	+	0.121749i
$581$	5355.67	−	3891.12i	0.382428	−	0.277850i
$582$		0			0
$583$	−12885.0	+	9361.53i	−0.915342	+	0.665035i
$584$	−342.424	−	1053.87i	−0.0242631	−	0.0746740i
$585$		0			0
$586$	−609.941	+	1877.21i	−0.0429973	+	0.132332i
$587$	7730.07	+	23790.7i	0.543533	+	1.67282i	0.724452	+	0.689325i	$0.242093\pi$
$587$	7730.07	+	23790.7i	0.543533	+	1.67282i	−0.180919	+	0.983498i	$0.557907\pi$
$588$		0			0
$589$	−4612.60	+	14196.1i	−0.322681	+	0.993109i
$590$	1417.60	−	85.3599i	0.0989178	−	0.00595629i
$591$		0			0
$592$	2676.16	−	1944.35i	0.185793	−	0.134987i
$593$	−28163.6			−1.95032			−0.975160	−	0.221501i	$-0.928905\pi$
$593$	−28163.6			−1.95032			−0.975160	+	0.221501i	$0.928905\pi$
$594$		0			0
$595$	9896.11	−	8142.04i	0.681850	−	0.560993i
$596$	2476.88	+	1799.56i	0.170230	+	0.123679i
$597$		0			0
$598$	−486.658	+	1497.78i	−0.0332791	+	0.102423i
$599$	3672.21			0.250488			0.125244	−	0.992126i	$-0.460029\pi$
$599$	3672.21			0.250488			0.125244	+	0.992126i	$0.460029\pi$
$600$		0			0
$601$	2325.56			0.157840			0.0789199	−	0.996881i	$-0.474853\pi$
$601$	2325.56			0.157840			0.0789199	+	0.996881i	$0.474853\pi$
$602$	−320.070	+	985.074i	−0.0216696	+	0.0666920i
$603$		0			0
$604$	13342.2	+	9693.66i	0.898817	+	0.653029i
$605$	−2372.98	−	1514.91i	−0.159463	−	0.101801i
$606$		0			0
$607$	6230.66			0.416630			0.208315	−	0.978062i	$-0.433202\pi$
$607$	6230.66			0.416630			0.208315	+	0.978062i	$0.433202\pi$
$608$	6460.02	−	4693.48i	0.430902	−	0.313069i
$609$		0			0
$610$	2017.04	+	1287.67i	0.133881	+	0.0854695i
$611$	−14382.9	+	44265.9i	−0.952322	+	2.93095i
$612$		0			0
$613$	2221.17	+	6836.04i	0.146349	+	0.450416i	0.997182	−	0.0750200i	$-0.0239021\pi$
$613$	2221.17	+	6836.04i	0.146349	+	0.450416i	−0.850833	+	0.525436i	$0.823902\pi$
$614$	441.126	−	1357.65i	0.0289941	−	0.0892348i
$615$		0			0
$616$	1114.78	+	3430.94i	0.0729153	+	0.224410i
$617$	2371.57	−	1723.05i	0.154742	−	0.112427i	−0.507720	−	0.861522i	$-0.669512\pi$
$617$	2371.57	−	1723.05i	0.154742	−	0.112427i	0.662462	+	0.749095i	$0.269512\pi$
$618$		0			0
$619$	8542.35	−	6206.38i	0.554678	−	0.402997i	−0.274829	−	0.961493i	$-0.588621\pi$
$619$	8542.35	−	6206.38i	0.554678	−	0.402997i	0.829507	+	0.558496i	$0.188621\pi$
$620$	13039.5	−	785.165i	0.844641	−	0.0508597i
$621$		0			0
$622$	−1734.11	−	1259.91i	−0.111787	−	0.0812181i
$623$	5714.98	−	17588.9i	0.367521	−	1.13111i
$624$		0			0
$625$	15175.0	−	3722.72i	0.971203	−	0.238254i
$626$	−835.611			−0.0533510
$627$		0			0
$628$	13823.3	+	10043.2i	0.878356	+	0.638163i
$629$	−3184.76	−	2313.87i	−0.201884	−	0.146677i
$630$		0			0
$631$	3784.21	−	2749.39i	0.238743	−	0.173457i	−0.461980	−	0.886890i	$-0.652861\pi$
$631$	3784.21	−	2749.39i	0.238743	−	0.173457i	0.700723	+	0.713433i	$0.252861\pi$
$632$	−2873.89			−0.180882
$633$		0			0
$634$	894.021	+	2751.51i	0.0560033	+	0.172360i
$635$	−5193.96	+	20005.6i	−0.324592	+	1.25023i
$636$		0			0
$637$	1970.38	+	6064.22i	0.122558	+	0.377195i
$638$	91.2096	+	280.714i	0.00565991	+	0.0174194i
$639$		0			0
$640$	−7820.90	−	4992.85i	−0.483044	−	0.308375i
$641$	2830.10	+	8710.16i	0.174387	+	0.536709i	0.999605	−	0.0281058i	$-0.00894753\pi$
$641$	2830.10	+	8710.16i	0.174387	+	0.536709i	−0.825218	+	0.564815i	$0.808948\pi$
$642$		0			0
$643$	−16426.8			−1.00748			−0.503740	−	0.863855i	$-0.668043\pi$
$643$	−16426.8			−1.00748			−0.503740	+	0.863855i	$0.668043\pi$
$644$	−4808.01	+	3493.23i	−0.294196	+	0.213746i
$645$		0			0
$646$	−2461.84	−	1788.63i	−0.149938	−	0.108936i
$647$	−5909.82	−	4293.74i	−0.359102	−	0.260903i	0.393575	−	0.919292i	$-0.371238\pi$
$647$	−5909.82	−	4293.74i	−0.359102	−	0.260903i	−0.752677	+	0.658389i	$0.771238\pi$
$648$		0			0
$649$	−9711.50			−0.587380
$650$	−4153.14	+	501.978i	−0.250614	+	0.0302911i
$651$		0			0
$652$	4001.92	−	12316.6i	0.240379	−	0.739811i
$653$	19234.0	+	13974.3i	1.15266	+	0.837455i	0.988832	−	0.149034i	$-0.0476165\pi$
$653$	19234.0	+	13974.3i	1.15266	+	0.837455i	0.163826	+	0.986489i	$0.447617\pi$
$654$		0			0
$655$	−11530.4	+	9486.61i	−0.687829	+	0.565912i
$656$	1666.95	−	1211.11i	0.0992127	−	0.0720822i
$657$		0			0
$658$	3356.84	−	2438.89i	0.198880	−	0.144495i
$659$	−4385.31	−	13496.6i	−0.259222	−	0.797804i	−0.992968	−	0.118380i	$-0.962230\pi$
$659$	−4385.31	−	13496.6i	−0.259222	−	0.797804i	0.733746	−	0.679424i	$-0.237770\pi$
$660$		0			0
$661$	−2911.31	+	8960.08i	−0.171311	+	0.527242i	−0.999446	−	0.0332876i	$-0.989402\pi$
$661$	−2911.31	+	8960.08i	−0.171311	+	0.527242i	0.828135	+	0.560529i	$0.189402\pi$
$662$	−127.995	−	393.929i	−0.00751462	−	0.0231276i
$663$		0			0
$664$	−860.264	+	2647.62i	−0.0502782	+	0.154740i
$665$	13930.1	−	11461.0i	0.812310	−	0.668329i
$666$		0			0
$667$	−796.061	+	578.372i	−0.0462123	+	0.0335752i
$668$	−15451.6			−0.894968
$669$		0			0
$670$	−909.810	−	2316.10i	−0.0524612	−	0.133550i
$671$	−13238.9	−	9618.62i	−0.761672	−	0.553387i
$672$		0			0
$673$	3177.00	−	9777.79i	0.181968	−	0.560039i	−0.817915	−	0.575339i	$-0.804870\pi$
$673$	3177.00	−	9777.79i	0.181968	−	0.560039i	0.999883	+	0.0152997i	$0.00487024\pi$
$674$	2156.85			0.123262
$675$		0			0
$676$	−30241.6			−1.72062
$677$	−5470.01	+	16835.0i	−0.310531	+	0.955716i	0.667024	+	0.745036i	$0.267568\pi$
$677$	−5470.01	+	16835.0i	−0.310531	+	0.955716i	−0.977555	+	0.210680i	$0.932432\pi$
$678$		0			0
$679$	−18227.4	−	13243.0i	−1.03020	−	0.748481i
$680$	−1354.24	+	5216.14i	−0.0763719	+	0.294162i
$681$		0			0
$682$	2110.26			0.118484
$683$	−6739.31	+	4896.39i	−0.377558	+	0.274312i	−0.760338	−	0.649527i	$-0.774967\pi$
$683$	−6739.31	+	4896.39i	−0.377558	+	0.274312i	0.382780	+	0.923840i	$0.374967\pi$
$684$		0			0
$685$	5155.51	+	13124.4i	0.287565	+	0.732053i
$686$	911.616	−	2805.67i	0.0507371	−	0.156153i
$687$		0			0
$688$	2747.48	+	8455.88i	0.152248	+	0.468572i
$689$	−11668.9	+	35913.2i	−0.645211	+	1.98576i
$690$		0			0
$691$	1522.86	+	4686.87i	0.0838382	+	0.258028i	0.984184	−	0.177147i	$-0.0566867\pi$
$691$	1522.86	+	4686.87i	0.0838382	+	0.258028i	−0.900346	+	0.435174i	$0.856687\pi$
$692$	14814.8	−	10763.6i	0.813838	−	0.591288i
$693$		0			0
$694$	2117.93	−	1538.77i	0.115844	−	0.0841656i
$695$	4134.86	−	15926.2i	0.225675	−	0.869233i
$696$		0			0
$697$	−1983.75	−	1441.28i	−0.107805	−	0.0783249i
$698$	−348.525	+	1072.65i	−0.0188995	+	0.0581668i
$699$		0			0
$700$	−13792.9	−	7679.63i	−0.744747	−	0.414661i
$701$	−6865.41			−0.369904			−0.184952	−	0.982748i	$-0.559213\pi$
$701$	−6865.41			−0.369904			−0.184952	+	0.982748i	$0.559213\pi$
$702$		0			0
$703$	−4482.98	−	3257.07i	−0.240510	−	0.174741i
$704$	11759.3	+	8543.64i	0.629539	+	0.457387i
$705$		0			0
$706$	−1013.16	+	736.101i	−0.0540094	+	0.0392401i
$707$	2825.76			0.150316
$708$		0			0
$709$	3115.25	+	9587.75i	0.165015	+	0.507864i	0.999037	−	0.0438668i	$-0.0139677\pi$
$709$	3115.25	+	9587.75i	0.165015	+	0.507864i	−0.834022	+	0.551730i	$0.813968\pi$
$710$	−3217.93	+	2647.56i	−0.170094	+	0.139945i
$711$		0			0
$712$	2403.30	+	7396.59i	0.126499	+	0.389324i
$713$	2173.95	+	6690.72i	0.114186	+	0.351430i
$714$		0			0
$715$	28555.3	−	1719.45i	1.49358	−	0.0899352i
$716$	−1342.37	−	4131.40i	−0.0700655	−	0.215639i
$717$		0			0
$718$	−4171.23			−0.216809
$719$	16549.1	−	12023.6i	0.858382	−	0.623651i	−0.0690621	−	0.997612i	$-0.522001\pi$
$719$	16549.1	−	12023.6i	0.858382	−	0.623651i	0.927444	+	0.373961i	$0.122001\pi$
$720$		0			0
$721$	12062.7	+	8764.05i	0.623075	+	0.452691i
$722$	−1081.05	−	785.427i	−0.0557236	−	0.0404855i
$723$		0			0
$724$	24529.6			1.25917
$725$	−2283.68	−	1271.51i	−0.116985	−	0.0651349i
$726$		0			0
$727$	−7618.12	+	23446.2i	−0.388639	+	1.19611i	0.545167	+	0.838328i	$0.316466\pi$
$727$	−7618.12	+	23446.2i	−0.388639	+	1.19611i	−0.933806	+	0.357780i	$0.883534\pi$
$728$	6919.66	+	5027.43i	0.352280	+	0.255946i
$729$		0			0
$730$	660.276	+	421.520i	0.0334766	+	0.0213714i
$731$	8560.02	−	6219.22i	0.433110	−	0.314673i
$732$		0			0
$733$	11690.2	−	8493.46i	0.589071	−	0.427985i	−0.252912	−	0.967489i	$-0.581388\pi$
$733$	11690.2	−	8493.46i	0.589071	−	0.427985i	0.841983	+	0.539504i	$0.181388\pi$
$734$	−177.934	−	547.624i	−0.00894776	−	0.0275384i
$735$		0			0
$736$	1162.95	−	3579.20i	0.0582431	−	0.179254i
$737$	5258.34	+	16183.5i	0.262813	+	0.808856i
$738$		0			0
$739$	−314.004	+	966.405i	−0.0156303	+	0.0481052i	−0.958567	−	0.284866i	$-0.908051\pi$
$739$	−314.004	+	966.405i	−0.0156303	+	0.0481052i	0.942937	+	0.332971i	$0.108051\pi$
$740$	−1218.64	+	4693.82i	−0.0605377	+	0.233173i
$741$		0			0
$742$	2723.42	−	1978.68i	0.134744	−	0.0978973i
$743$	10739.7			0.530286			0.265143	−	0.964209i	$-0.414581\pi$
$743$	10739.7			0.530286			0.265143	+	0.964209i	$0.414581\pi$
$744$		0			0
$745$	−4371.86	+	263.250i	−0.214997	+	0.0129459i
$746$	2066.18	+	1501.16i	0.101405	+	0.0736750i
$747$		0			0
$748$	5627.49	−	17319.6i	0.275082	−	0.846615i
$749$	−31637.1			−1.54338
$750$		0			0
$751$	29772.1			1.44661			0.723303	−	0.690531i	$-0.242623\pi$
$751$	29772.1			1.44661			0.723303	+	0.690531i	$0.242623\pi$
$752$	11006.4	−	33874.2i	0.533726	−	1.64264i
$753$		0			0
$754$	566.156	+	411.336i	0.0273450	+	0.0198673i
$755$	−23549.9	+	1418.04i	−1.13519	+	0.0683549i
$756$		0			0
$757$	−20090.9			−0.964619			−0.482309	−	0.876001i	$-0.660202\pi$
$757$	−20090.9			−0.964619			−0.482309	+	0.876001i	$0.660202\pi$
$758$	1416.42	−	1029.09i	0.0678715	−	0.0493115i
$759$		0			0
$760$	−1906.28	+	7342.41i	−0.0909842	+	0.350444i
$761$	10116.4	−	31135.1i	0.481892	−	1.48311i	−0.354541	−	0.935041i	$-0.615363\pi$
$761$	10116.4	−	31135.1i	0.481892	−	1.48311i	0.836432	−	0.548070i	$-0.184637\pi$
$762$		0			0
$763$	2617.30	+	8055.21i	0.124184	+	0.382200i
$764$	−7593.27	+	23369.7i	−0.359574	+	1.10666i
$765$		0			0
$766$	342.601	+	1054.42i	0.0161602	+	0.0497359i
$767$	−18627.9	+	13534.0i	−0.876942	+	0.637136i
$768$		0			0
$769$	3248.44	−	2360.13i	0.152330	−	0.110674i	−0.509010	−	0.860761i	$-0.669988\pi$
$769$	3248.44	−	2360.13i	0.152330	−	0.110674i	0.661340	+	0.750087i	$0.269988\pi$
$770$	−2149.56	−	1372.28i	−0.100604	−	0.0642253i
$771$		0			0
$772$	−19701.7	−	14314.2i	−0.918499	−	0.667329i
$773$	619.601	−	1906.94i	0.0288299	−	0.0887293i	−0.935606	−	0.353045i	$-0.885146\pi$
$773$	619.601	−	1906.94i	0.0288299	−	0.0887293i	0.964436	+	0.264316i	$0.0851462\pi$
$774$		0			0
$775$	−13691.2	+	12719.0i	−0.634584	+	0.589522i
$776$	9474.59			0.438296
$777$		0			0
$778$	436.868	+	317.403i	0.0201317	+	0.0146266i
$779$	−2792.40	−	2028.80i	−0.128431	−	0.0933108i
$780$		0			0
$781$	23053.6	−	16749.4i	1.05624	−	0.767402i
$782$	−1434.19			−0.0655836
$783$		0			0
$784$	−1507.82	−	4640.60i	−0.0686873	−	0.211398i
$785$	−24399.0	+	1469.17i	−1.10935	+	0.0667988i
$786$		0			0
$787$	3533.14	+	10873.9i	0.160029	+	0.492518i	0.998636	−	0.0522191i	$-0.0166294\pi$
$787$	3533.14	+	10873.9i	0.160029	+	0.492518i	−0.838607	+	0.544737i	$0.816629\pi$
$788$	3559.35	+	10954.6i	0.160909	+	0.495228i
$789$		0			0
$790$	1568.88	−	1290.80i	0.0706560	−	0.0581323i
$791$	−3433.06	−	10565.9i	−0.154318	−	0.474942i
$792$		0			0
$793$	−38798.4			−1.73742
$794$	3591.81	−	2609.60i	0.160540	−	0.116639i
$795$		0			0
$796$	3007.96	+	2185.41i	0.133937	+	0.0973112i
$797$	25301.7	+	18382.8i	1.12451	+	0.817002i	0.984886	−	0.173203i	$-0.0554117\pi$
$797$	25301.7	+	18382.8i	1.12451	+	0.817002i	0.139621	+	0.990205i	$0.455412\pi$
$798$		0			0
$799$	−42386.5			−1.87675
$800$	9924.62	−	1199.56i	0.438611	−	0.0530137i
$801$		0			0
$802$	−896.225	+	2758.30i	−0.0394598	+	0.121445i
$803$	−4333.75	−	3148.65i	−0.190454	−	0.138373i
$804$		0			0
$805$	2136.47	−	8229.03i	0.0935410	−	0.360292i
$806$	4047.75	−	2940.86i	0.176893	−	0.128520i
$807$		0			0
$808$	−961.360	+	698.469i	−0.0418571	+	0.0304110i
$809$	−1593.30	−	4903.68i	−0.0692430	−	0.213108i	0.910447	−	0.413625i	$-0.135738\pi$
$809$	−1593.30	−	4903.68i	−0.0692430	−	0.213108i	−0.979690	+	0.200517i	$0.935738\pi$
$810$		0			0
$811$	1284.92	−	3954.57i	0.0556344	−	0.171225i	−0.919378	−	0.393375i	$-0.871307\pi$
$811$	1284.92	−	3954.57i	0.0556344	−	0.171225i	0.975013	+	0.222150i	$0.0713074\pi$
$812$	816.070	+	2511.60i	0.0352690	+	0.108547i
$813$		0			0
$814$	−242.083	+	745.054i	−0.0104238	+	0.0320812i
$815$	6773.66	+	17243.7i	0.291130	+	0.741129i
$816$		0			0
$817$	12049.4	−	8754.38i	0.515978	−	0.374880i
$818$	−3990.59			−0.170572
$819$		0			0
$820$	−759.074	+	2923.73i	−0.0323269	+	0.124513i
$821$	19340.3	+	14051.5i	0.822144	+	0.597323i	0.917326	−	0.398137i	$-0.130343\pi$
$821$	19340.3	+	14051.5i	0.822144	+	0.597323i	−0.0951818	+	0.995460i	$0.530343\pi$
$822$		0			0
$823$	4199.66	−	12925.2i	0.177875	−	0.547443i	−0.821878	−	0.569663i	$-0.807074\pi$
$823$	4199.66	−	12925.2i	0.177875	−	0.547443i	0.999753	+	0.0222206i	$0.00707362\pi$
$824$	−6270.17			−0.265087
$825$		0			0
$826$	2052.65			0.0864660
$827$	10096.8	−	31074.7i	0.424546	−	1.30662i	−0.478883	−	0.877879i	$-0.658958\pi$
$827$	10096.8	−	31074.7i	0.424546	−	1.30662i	0.903429	−	0.428739i	$-0.141042\pi$
$828$		0			0
$829$	−12134.3	−	8816.11i	−0.508375	−	0.369356i	0.303832	−	0.952726i	$-0.401734\pi$
$829$	−12134.3	−	8816.11i	−0.508375	−	0.369356i	−0.812207	+	0.583370i	$0.801734\pi$
$830$	−719.544	−	1831.74i	−0.0300912	−	0.0766032i
$831$		0			0
$832$	34462.3			1.43602
$833$	−4697.75	+	3413.12i	−0.195399	+	0.141966i
$834$		0			0
$835$	17069.5	−	14044.0i	0.707444	−	0.582050i
$836$	7921.44	−	24379.7i	0.327714	−	1.00860i
$837$		0			0
$838$	−1070.87	−	3295.80i	−0.0441439	−	0.135861i
$839$	5629.88	−	17327.0i	0.231663	−	0.712984i	−0.765884	−	0.642979i	$-0.777698\pi$
$839$	5629.88	−	17327.0i	0.231663	−	0.712984i	0.997547	−	0.0700054i	$-0.0223017\pi$
$840$		0			0
$841$	−7401.50	−	22779.5i	−0.303477	−	0.934006i
$842$	−538.900	+	391.534i	−0.0220567	+	0.0160251i
$843$		0			0
$844$	−11790.9	+	8566.58i	−0.480875	+	0.349376i
$845$	33408.3	−	27486.7i	1.36009	−	1.11902i
$846$		0			0
$847$	−3292.01	−	2391.79i	−0.133548	−	0.0970280i
$848$	8929.56	−	27482.4i	0.361607	−	1.11291i
$849$		0			0
$850$	−1603.52	−	3455.79i	−0.0647062	−	0.139450i
$851$	−2611.63			−0.105200
$852$		0			0
$853$	−385.250	−	279.901i	−0.0154639	−	0.0112352i	0.580026	−	0.814598i	$-0.303042\pi$
$853$	−385.250	−	279.901i	−0.0154639	−	0.0112352i	−0.595490	+	0.803362i	$0.703042\pi$
$854$	2798.21	+	2033.02i	0.112123	+	0.0814620i
$855$		0			0
$856$	10763.4	−	7820.03i	0.429771	−	0.312247i
$857$	−8090.37			−0.322476			−0.161238	−	0.986916i	$-0.551549\pi$
$857$	−8090.37			−0.322476			−0.161238	+	0.986916i	$0.551549\pi$
$858$		0			0
$859$	−7077.24	−	21781.5i	−0.281109	−	0.865164i	−0.987538	−	0.157380i	$-0.949695\pi$
$859$	−7077.24	−	21781.5i	−0.281109	−	0.865164i	0.706429	−	0.707784i	$-0.250305\pi$
$860$	−10986.4	−	7013.72i	−0.435621	−	0.278100i
$861$		0			0
$862$	−2174.30	−	6691.80i	−0.0859128	−	0.264412i
$863$	203.542	+	626.437i	0.00802855	+	0.0247093i	0.954991	−	0.296636i	$-0.0958649\pi$
$863$	203.542	+	626.437i	0.00802855	+	0.0247093i	−0.946962	+	0.321346i	$0.895865\pi$
$864$		0			0
$865$	−6583.06	+	25356.0i	−0.258764	+	0.996680i
$866$	1236.33	+	3805.03i	0.0485129	+	0.149307i
$867$		0			0
$868$	18880.9			0.738318
$869$	−11239.6	+	8166.06i	−0.438755	+	0.318774i
$870$		0			0
$871$	32639.5	+	23714.0i	1.26975	+	0.922524i
$872$	−2881.52	−	2093.55i	−0.111904	−	0.0813033i
$873$		0			0
$874$	−2018.81			−0.0781318
$875$	22217.2	−	4052.63i	0.858376	−	0.156576i
$876$		0			0
$877$	8819.17	−	27142.6i	0.339569	−	1.04509i	−0.624858	−	0.780738i	$-0.714843\pi$
$877$	8819.17	−	27142.6i	0.339569	−	1.04509i	0.964427	−	0.264348i	$-0.0851568\pi$
$878$	−5426.11	−	3942.30i	−0.208568	−	0.151533i
$879$		0			0
$880$	−21851.8	+	1315.80i	−0.837072	+	0.0504039i
$881$	−22413.8	+	16284.6i	−0.857138	+	0.622747i	−0.927105	−	0.374802i	$-0.877711\pi$
$881$	−22413.8	+	16284.6i	−0.857138	+	0.622747i	0.0699667	+	0.997549i	$0.477711\pi$
$882$		0			0
$883$	−21693.4	+	15761.2i	−0.826772	+	0.600685i	−0.918644	−	0.395086i	$-0.870715\pi$
$883$	−21693.4	+	15761.2i	−0.826772	+	0.600685i	0.0918720	+	0.995771i	$0.470715\pi$
$884$	−13342.4	−	41063.8i	−0.507640	−	1.56236i
$885$		0			0
$886$	−591.167	+	1819.42i	−0.0224161	+	0.0689895i
$887$	−12653.7	−	38944.1i	−0.478997	−	1.47420i	−0.840491	−	0.541826i	$-0.817733\pi$
$887$	−12653.7	−	38944.1i	−0.478997	−	1.47420i	0.361494	−	0.932375i	$-0.382267\pi$
$888$		0			0
$889$	−9231.57	+	28411.8i	−0.348275	+	1.07188i
$890$	−4634.13	−	2958.43i	−0.174535	−	0.111423i
$891$		0			0
$892$	25663.2	−	18645.4i	0.963304	−	0.699881i
$893$	−59664.6			−2.23583
$894$		0			0
$895$	5237.98	+	3343.92i	0.195627	+	0.124888i
$896$	−10849.9	−	7882.88i	−0.404541	−	0.293916i
$897$		0			0
$898$	−1281.05	+	3942.66i	−0.0476048	+	0.146512i
$899$	3126.10			0.115975
$900$		0			0
$901$	−34388.4			−1.27153
$902$	−150.791	+	464.086i	−0.00556628	+	0.0171312i
$903$		0			0
$904$	3779.63	+	2746.06i	0.139058	+	0.101032i
$905$	−27098.2	+	22295.0i	−0.995330	+	0.818909i
$906$		0			0
$907$	42971.4			1.57314			0.786571	−	0.617499i	$-0.211854\pi$
$907$	42971.4			1.57314			0.786571	+	0.617499i	$0.211854\pi$
$908$	13833.8	−	10050.8i	0.505605	−	0.367344i
$909$		0			0
$910$	−6035.55	+	363.428i	−0.219864	+	0.0132390i
$911$	−4221.94	+	12993.8i	−0.153545	+	0.472561i	−0.998011	−	0.0630477i	$-0.979918\pi$
$911$	−4221.94	+	12993.8i	−0.153545	+	0.472561i	0.844466	+	0.535609i	$0.179918\pi$
$912$		0			0
$913$	4158.68	+	12799.1i	0.150747	+	0.463952i
$914$	−2096.92	+	6453.67i	−0.0758863	+	0.233554i
$915$		0			0
$916$	−11032.0	−	33953.1i	−0.397935	−	1.22472i
$917$	−17459.6	+	12685.1i	−0.628753	+	0.456816i
$918$		0			0
$919$	−27824.2	+	20215.5i	−0.998733	+	0.725622i	−0.961816	−	0.273696i	$-0.911754\pi$
$919$	−27824.2	+	20215.5i	−0.998733	+	0.725622i	−0.0369170	+	0.999318i	$0.511754\pi$
$920$	1307.19	+	3327.71i	0.0468444	+	0.119252i
$921$		0			0
$922$	−1006.40	−	731.192i	−0.0359480	−	0.0261177i
$923$	20877.7	−	64255.1i	0.744528	−	2.29142i
$924$		0			0
$925$	−2919.98	−	6292.94i	−0.103793	−	0.223687i
$926$	132.937			0.00471769
$927$		0			0
$928$	−1352.93	−	982.958i	−0.0478577	−	0.0347707i
$929$	−13949.1	−	10134.6i	−0.492631	−	0.357917i	0.313564	−	0.949567i	$-0.398477\pi$
$929$	−13949.1	−	10134.6i	−0.492631	−	0.357917i	−0.806195	+	0.591650i	$0.798477\pi$
$930$		0			0
$931$	−6612.71	+	4804.42i	−0.232785	+	0.169128i
$932$	27453.9			0.964895
$933$		0			0
$934$	−2038.90	−	6275.08i	−0.0714291	−	0.219836i
$935$	9525.11	+	24248.0i	0.333160	+	0.848124i
$936$		0			0
$937$	−7362.47	−	22659.4i	−0.256693	−	0.790020i	−0.993491	−	0.113907i	$-0.963663\pi$
$937$	−7362.47	−	22659.4i	−0.256693	−	0.790020i	0.736798	−	0.676113i	$-0.236337\pi$
$938$	−1111.42	−	3420.60i	−0.0386878	−	0.119069i
$939$		0			0
$940$	19091.1	+	48600.2i	0.662430	+	1.68635i
$941$	9029.73	+	27790.6i	0.312817	+	0.962751i	0.976644	+	0.214865i	$0.0689312\pi$
$941$	9029.73	+	27790.6i	0.312817	+	0.962751i	−0.663827	+	0.747886i	$0.731069\pi$
$942$		0			0
$943$	−1626.76			−0.0561765
$944$	14254.9	−	10356.8i	0.491479	−	0.357081i
$945$		0			0
$946$	−1703.48	−	1237.65i	−0.0585464	−	0.0425364i
$947$	41107.6	+	29866.4i	1.41058	+	1.02484i	0.993238	+	0.116093i	$0.0370369\pi$
$947$	41107.6	+	29866.4i	1.41058	+	1.02484i	0.417338	+	0.908751i	$0.362963\pi$
$948$		0			0
$949$	−12700.6			−0.434437
$950$	−2257.17	−	4864.48i	−0.0770864	−	0.166131i
$951$		0			0
$952$	−2406.99	+	7407.94i	−0.0819442	+	0.252198i
$953$	9863.57	+	7166.30i	0.335270	+	0.243588i	0.742663	−	0.669665i	$-0.233562\pi$
$953$	9863.57	+	7166.30i	0.335270	+	0.243588i	−0.407393	+	0.913253i	$0.633562\pi$
$954$		0			0
$955$	−12852.4	−	32718.3i	−0.435491	−	1.10863i
$956$	−14318.9	+	10403.3i	−0.484420	+	0.351952i
$957$		0			0
$958$	3355.56	−	2437.96i	0.113166	−	0.0822201i
$959$	6297.94	+	19383.1i	0.212066	+	0.652672i
$960$		0			0
$961$	−2299.34	+	7076.63i	−0.0771823	+	0.237543i
$962$	573.963	+	1766.48i	0.0192363	+	0.0592032i
$963$		0			0
$964$	−2869.75	+	8832.17i	−0.0958800	+	0.295088i
$965$	34774.9	−	2093.96i	1.16005	−	0.0698517i
$966$		0			0
$967$	25583.1	−	18587.2i	0.850774	−	0.618123i	−0.0745856	−	0.997215i	$-0.523763\pi$
$967$	25583.1	−	18587.2i	0.850774	−	0.618123i	0.925359	+	0.379091i	$0.123763\pi$
$968$	1711.18			0.0568177
$969$		0			0
$970$	−5172.25	+	4255.48i	−0.171207	+	0.140861i
$971$	25418.7	+	18467.8i	0.840088	+	0.610360i	0.922395	−	0.386247i	$-0.126229\pi$
$971$	25418.7	+	18467.8i	0.840088	+	0.610360i	−0.0823074	+	0.996607i	$0.526229\pi$
$972$		0			0
$973$	7349.16	−	22618.4i	0.242141	−	0.745234i
$974$	2742.83			0.0902320
$975$		0			0
$976$	29690.2			0.973730
$977$	9290.17	−	28592.2i	0.304216	−	0.936280i	−0.675753	−	0.737128i	$-0.736181\pi$
$977$	9290.17	−	28592.2i	0.304216	−	0.936280i	0.979969	−	0.199151i	$-0.0638186\pi$
$978$		0			0
$979$	30416.3	+	22098.7i	0.992962	+	0.721429i
$980$	6029.37	+	3849.14i	0.196532	+	0.125466i
$981$		0			0
$982$	−7354.90			−0.239007
$983$	−36362.3	+	26418.7i	−1.17983	+	0.857199i	−0.992153	−	0.125031i	$-0.960097\pi$
$983$	−36362.3	+	26418.7i	−1.17983	+	0.857199i	−0.187681	+	0.982230i	$0.560097\pi$
$984$		0			0
$985$	−13888.7	−	8866.52i	−0.449269	−	0.286813i
$986$	−196.936	+	606.106i	−0.00636076	+	0.0195764i
$987$		0			0
$988$	−18781.2	−	57802.7i	−0.604768	−	1.86128i
$989$	2169.16	−	6675.99i	0.0697425	−	0.214645i
$990$		0			0
$991$	15604.2	+	48024.8i	0.500185	+	1.53941i	0.808717	+	0.588198i	$0.200162\pi$
$991$	15604.2	+	48024.8i	0.500185	+	1.53941i	−0.308532	+	0.951214i	$0.599838\pi$
$992$	−9672.79	+	7027.69i	−0.309588	+	0.224929i
$993$		0			0
$994$	−4872.68	+	3540.21i	−0.155485	+	0.112966i
$995$	−5309.25	+	319.694i	−0.169160	+	0.0101859i
$996$		0			0
$997$	7287.27	+	5294.51i	0.231485	+	0.168183i	0.697481	−	0.716603i	$-0.254304\pi$
$997$	7287.27	+	5294.51i	0.231485	+	0.168183i	−0.465997	+	0.884787i	$0.654304\pi$
$998$	2271.18	−	6989.97i	0.0720370	−	0.221707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.46.4		28
3.2	odd	2		25.4.d.a.21.4	yes	28
15.2	even	4		125.4.e.b.24.7		56
15.8	even	4		125.4.e.b.24.8		56
15.14	odd	2		125.4.d.a.101.4		28
25.6	even	5	inner	225.4.h.b.181.4		28
75.8	even	20		125.4.e.b.99.7		56
75.17	even	20		125.4.e.b.99.8		56
75.41	odd	10		625.4.a.c.1.7		14
75.44	odd	10		125.4.d.a.26.4		28
75.56	odd	10		25.4.d.a.6.4	✓	28
75.59	odd	10		625.4.a.d.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.6.4	✓	28	75.56	odd	10
25.4.d.a.21.4	yes	28	3.2	odd	2
125.4.d.a.26.4		28	75.44	odd	10
125.4.d.a.101.4		28	15.14	odd	2
125.4.e.b.24.7		56	15.2	even	4
125.4.e.b.24.8		56	15.8	even	4
125.4.e.b.99.7		56	75.8	even	20
125.4.e.b.99.8		56	75.17	even	20
225.4.h.b.46.4		28	1.1	even	1	trivial
225.4.h.b.181.4		28	25.6	even	5	inner
625.4.a.c.1.7		14	75.41	odd	10
625.4.a.d.1.8		14	75.59	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)

\(f(q)\)	\(=\)	\(q+(0.132779 - 0.408651i) q^{2} +(6.32277 + 4.59376i) q^{4} +(-11.1601 + 0.672002i) q^{5} -16.1597 q^{7} +(5.49773 - 3.99433i) q^{8} +O(q^{10})\)	\(q+(0.132779 - 0.408651i) q^{2} +(6.32277 + 4.59376i) q^{4} +(-11.1601 + 0.672002i) q^{5} -16.1597 q^{7} +(5.49773 - 3.99433i) q^{8} +(-1.20721 + 4.64982i) q^{10} +(10.1515 - 31.2432i) q^{11} +(-24.0686 - 74.0757i) q^{13} +(-2.14566 + 6.60366i) q^{14} +(18.4184 + 56.6859i) q^{16} +(57.3840 - 41.6919i) q^{17} +(80.7756 - 58.6869i) q^{19} +(-73.6499 - 47.0180i) q^{20} +(-11.4197 - 8.29687i) q^{22} +(14.5415 - 44.7540i) q^{23} +(124.097 - 14.9993i) q^{25} -33.4669 q^{26} +(-102.174 - 74.2337i) q^{28} +(-16.9169 - 12.2908i) q^{29} +(-120.948 + 87.8738i) q^{31} +79.9748 q^{32} +(-9.41807 - 28.9858i) q^{34} +(180.344 - 10.8593i) q^{35} +(-17.1502 - 52.7828i) q^{37} +(-13.2572 - 40.8014i) q^{38} +(-58.6711 + 48.2718i) q^{40} +(-10.6827 - 32.8778i) q^{41} +149.171 q^{43} +(207.710 - 150.910i) q^{44} +(-16.3580 - 11.8848i) q^{46} +(-483.450 - 351.247i) q^{47} -81.8652 q^{49} +(10.3480 - 52.7039i) q^{50} +(188.105 - 578.929i) q^{52} +(-392.226 - 284.969i) q^{53} +(-92.2969 + 355.500i) q^{55} +(-88.8415 + 64.5471i) q^{56} +(-7.26886 + 5.28114i) q^{58} +(-91.3523 - 281.153i) q^{59} +(153.931 - 473.752i) q^{61} +(19.8504 + 61.0932i) q^{62} +(-136.728 + 420.805i) q^{64} +(318.388 + 810.519i) q^{65} +(-419.059 + 304.464i) q^{67} +554.349 q^{68} +(19.5082 - 75.1396i) q^{70} +(701.761 + 509.860i) q^{71} +(50.3894 - 155.083i) q^{73} -23.8469 q^{74} +780.320 q^{76} +(-164.045 + 504.880i) q^{77} +(-342.139 - 248.578i) q^{79} +(-243.644 - 620.244i) q^{80} -14.8540 q^{82} +(-331.422 + 240.792i) q^{83} +(-612.396 + 503.849i) q^{85} +(19.8067 - 60.9588i) q^{86} +(-68.9854 - 212.315i) q^{88} +(-353.657 + 1088.44i) q^{89} +(388.941 + 1197.04i) q^{91} +(297.532 - 216.169i) q^{92} +(-207.729 + 150.924i) q^{94} +(-862.029 + 709.235i) q^{95} +(1127.96 + 819.508i) q^{97} +(-10.8700 + 33.4543i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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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