LMFDB - Embedded newform 225.4.h.b.91.4

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			91.4
Character	$\chi$	$=$	225.91
Dual form			225.4.h.b.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269925 - 0.196112i) q^{2} +(-2.43774 - 7.50258i) q^{4} +(0.131697 - 11.1796i) q^{5} +30.0089 q^{7} +(-1.63816 + 5.04172i) q^{8} +O(q^{10})$	\(q+(-0.269925 - 0.196112i) q^{2} +(-2.43774 - 7.50258i) q^{4} +(0.131697 - 11.1796i) q^{5} +30.0089 q^{7} +(-1.63816 + 5.04172i) q^{8} +(-2.22799 + 2.99181i) q^{10} +(3.55842 + 2.58534i) q^{11} +(34.4108 - 25.0009i) q^{13} +(-8.10015 - 5.88510i) q^{14} +(-49.6257 + 36.0552i) q^{16} +(13.2605 - 40.8115i) q^{17} +(0.802076 - 2.46853i) q^{19} +(-84.1966 + 26.2648i) q^{20} +(-0.453489 - 1.39570i) q^{22} +(-91.3902 - 66.3989i) q^{23} +(-124.965 - 2.94462i) q^{25} -14.1913 q^{26} +(-73.1539 - 225.144i) q^{28} +(-31.2811 - 96.2735i) q^{29} +(-28.6337 + 88.1256i) q^{31} +62.8755 q^{32} +(-11.5829 + 8.41549i) q^{34} +(3.95207 - 335.487i) q^{35} +(111.842 - 81.2576i) q^{37} +(-0.700608 + 0.509022i) q^{38} +(56.1485 + 18.9778i) q^{40} +(160.841 - 116.858i) q^{41} -254.402 q^{43} +(10.7223 - 32.9997i) q^{44} +(11.6469 + 35.8454i) q^{46} +(73.2388 + 225.406i) q^{47} +557.536 q^{49} +(33.1537 + 25.3020i) q^{50} +(-271.456 - 197.224i) q^{52} +(-0.435948 - 1.34171i) q^{53} +(29.3716 - 39.4411i) q^{55} +(-49.1593 + 151.297i) q^{56} +(-10.4368 + 32.1212i) q^{58} +(-248.893 + 180.831i) q^{59} +(-401.584 - 291.768i) q^{61} +(25.0114 - 18.1719i) q^{62} +(380.034 + 276.111i) q^{64} +(-274.968 - 387.991i) q^{65} +(-37.4053 + 115.122i) q^{67} -338.517 q^{68} +(-66.8597 + 89.7811i) q^{70} +(-275.086 - 846.629i) q^{71} +(90.3458 + 65.6400i) q^{73} -46.1244 q^{74} -20.4756 q^{76} +(106.784 + 77.5834i) q^{77} +(165.407 + 509.070i) q^{79} +(396.546 + 559.542i) q^{80} -66.3320 q^{82} +(-387.980 + 1194.08i) q^{83} +(-454.508 - 153.621i) q^{85} +(68.6694 + 49.8912i) q^{86} +(-18.8638 + 13.7054i) q^{88} +(952.696 + 692.174i) q^{89} +(1032.63 - 750.251i) q^{91} +(-275.378 + 847.526i) q^{92} +(24.4358 - 75.2056i) q^{94} +(-27.4915 - 9.29195i) q^{95} +(360.388 + 1109.16i) q^{97} +(-150.493 - 109.339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.269925	−	0.196112i	−0.0954328	−	0.0693360i	0.539046	−	0.842277i	$-0.318785\pi$
$2$	−0.269925	−	0.196112i	−0.0954328	−	0.0693360i	−0.634478	+	0.772941i	$0.718785\pi$
$3$		0			0
$3$		0			0
$4$	−2.43774	−	7.50258i	−0.304717	−	0.937823i
$5$	0.131697	−	11.1796i	0.0117793	−	0.999931i
$5$	0.131697	−	11.1796i	0.0117793	−	0.999931i
$6$		0			0
$7$	30.0089			1.62033			0.810165	−	0.586202i	$-0.199377\pi$
$7$	30.0089			1.62033			0.810165	+	0.586202i	$0.199377\pi$
$8$	−1.63816	+	5.04172i	−0.0723969	+	0.222815i
$9$		0			0
$10$	−2.22799	+	2.99181i	−0.0704553	+	0.0946094i
$11$	3.55842	+	2.58534i	0.0975367	+	0.0708646i	0.635485	−	0.772113i	$-0.280800\pi$
$11$	3.55842	+	2.58534i	0.0975367	+	0.0708646i	−0.537948	+	0.842978i	$0.680800\pi$
$12$		0			0
$13$	34.4108	−	25.0009i	0.734142	−	0.533386i	−0.156729	−	0.987642i	$-0.550095\pi$
$13$	34.4108	−	25.0009i	0.734142	−	0.533386i	0.890871	+	0.454256i	$0.150095\pi$
$14$	−8.10015	−	5.88510i	−0.154633	−	0.112347i
$15$		0			0
$16$	−49.6257	+	36.0552i	−0.775401	+	0.563362i
$17$	13.2605	−	40.8115i	0.189184	−	0.582249i	−0.810811	−	0.585308i	$-0.800974\pi$
$17$	13.2605	−	40.8115i	0.189184	−	0.582249i	0.999995	+	0.00305870i	$0.000973617\pi$
$18$		0			0
$19$	0.802076	−	2.46853i	0.00968467	−	0.0298064i	−0.946097	−	0.323882i	$-0.895012\pi$
$19$	0.802076	−	2.46853i	0.00968467	−	0.0298064i	0.955782	+	0.294076i	$0.0950118\pi$
$20$	−84.1966	+	26.2648i	−0.941347	+	0.293649i
$21$		0			0
$22$	−0.453489	−	1.39570i	−0.00439473	−	0.0135256i
$23$	−91.3902	−	66.3989i	−0.828530	−	0.601962i	0.0906132	−	0.995886i	$-0.471117\pi$
$23$	−91.3902	−	66.3989i	−0.828530	−	0.601962i	−0.919143	+	0.393924i	$0.871117\pi$
$24$		0			0
$25$	−124.965	−	2.94462i	−0.999722	−	0.0235570i
$26$	−14.1913			−0.107044
$27$		0			0
$28$	−73.1539	−	225.144i	−0.493742	−	1.51958i
$29$	−31.2811	−	96.2735i	−0.200302	−	0.616467i	−0.999874	−	0.0158958i	$-0.994940\pi$
$29$	−31.2811	−	96.2735i	−0.200302	−	0.616467i	0.799571	−	0.600571i	$-0.205060\pi$
$30$		0			0
$31$	−28.6337	+	88.1256i	−0.165896	+	0.510575i	−0.999101	−	0.0423888i	$-0.986503\pi$
$31$	−28.6337	+	88.1256i	−0.165896	+	0.510575i	0.833205	+	0.552964i	$0.186503\pi$
$32$	62.8755			0.347341
$33$		0			0
$34$	−11.5829	+	8.41549i	−0.0584252	+	0.0424484i
$35$	3.95207	−	335.487i	0.0190863	−	1.62022i
$36$		0			0
$37$	111.842	−	81.2576i	0.496936	−	0.361045i	−0.310909	−	0.950440i	$-0.600634\pi$
$37$	111.842	−	81.2576i	0.496936	−	0.361045i	0.807845	+	0.589394i	$0.200634\pi$
$38$	−0.700608	+	0.509022i	−0.00299089	+	0.00217301i
$39$		0			0
$40$	56.1485	+	18.9778i	0.221947	+	0.0750165i
$41$	160.841	−	116.858i	0.612661	−	0.445124i	−0.237690	−	0.971341i	$-0.576390\pi$
$41$	160.841	−	116.858i	0.612661	−	0.445124i	0.850350	+	0.526217i	$0.176390\pi$
$42$		0			0
$43$	−254.402			−0.902231			−0.451116	−	0.892466i	$-0.648974\pi$
$43$	−254.402			−0.902231			−0.451116	+	0.892466i	$0.648974\pi$
$44$	10.7223	−	32.9997i	0.0367373	−	0.113066i
$45$		0			0
$46$	11.6469	+	35.8454i	0.0373313	+	0.114894i
$47$	73.2388	+	225.406i	0.227297	+	0.699549i	0.998050	+	0.0624151i	$0.0198803\pi$
$47$	73.2388	+	225.406i	0.227297	+	0.699549i	−0.770753	+	0.637134i	$0.780120\pi$
$48$		0			0
$49$	557.536			1.62547
$50$	33.1537	+	25.3020i	0.0937729	+	0.0715648i
$51$		0			0
$52$	−271.456	−	197.224i	−0.723927	−	0.525964i
$53$	−0.435948	−	1.34171i	−0.00112985	−	0.00347732i	0.950490	−	0.310755i	$-0.100582\pi$
$53$	−0.435948	−	1.34171i	−0.00112985	−	0.00347732i	−0.951620	+	0.307278i	$0.900582\pi$
$54$		0			0
$55$	29.3716	−	39.4411i	0.0720085	−	0.0966952i
$56$	−49.1593	+	151.297i	−0.117307	+	0.361034i
$57$		0			0
$58$	−10.4368	+	32.1212i	−0.0236279	+	0.0727193i
$59$	−248.893	+	180.831i	−0.549205	+	0.399021i	−0.827492	−	0.561477i	$-0.810233\pi$
$59$	−248.893	+	180.831i	−0.549205	+	0.399021i	0.278287	+	0.960498i	$0.410233\pi$
$60$		0			0
$61$	−401.584	−	291.768i	−0.842910	−	0.612410i	0.0802721	−	0.996773i	$-0.474421\pi$
$61$	−401.584	−	291.768i	−0.842910	−	0.612410i	−0.923182	+	0.384363i	$0.874421\pi$
$62$	25.0114	−	18.1719i	0.0512331	−	0.0372230i
$63$		0			0
$64$	380.034	+	276.111i	0.742254	+	0.539279i
$65$	−274.968	−	387.991i	−0.524701	−	0.740374i
$66$		0			0
$67$	−37.4053	+	115.122i	−0.0682057	+	0.209916i	−0.979350	−	0.202172i	$-0.935200\pi$
$67$	−37.4053	+	115.122i	−0.0682057	+	0.209916i	0.911144	+	0.412087i	$0.135200\pi$
$68$	−338.517			−0.603694
$69$		0			0
$70$	−66.8597	+	89.7811i	−0.114161	+	0.153298i
$71$	−275.086	−	846.629i	−0.459813	−	1.41516i	−0.865390	−	0.501099i	$-0.832929\pi$
$71$	−275.086	−	846.629i	−0.459813	−	1.41516i	0.405577	−	0.914061i	$-0.367071\pi$
$72$		0			0
$73$	90.3458	+	65.6400i	0.144852	+	0.105241i	0.657851	−	0.753148i	$-0.271466\pi$
$73$	90.3458	+	65.6400i	0.144852	+	0.105241i	−0.512999	+	0.858389i	$0.671466\pi$
$74$	−46.1244			−0.0724574
$75$		0			0
$76$	−20.4756			−0.0309042
$77$	106.784	+	77.5834i	0.158042	+	0.114824i
$78$		0			0
$79$	165.407	+	509.070i	0.235566	+	0.724998i	0.997046	+	0.0768091i	$0.0244732\pi$
$79$	165.407	+	509.070i	0.235566	+	0.724998i	−0.761480	+	0.648189i	$0.775527\pi$
$80$	396.546	+	559.542i	0.554189	+	0.781984i
$81$		0			0
$82$	−66.3320			−0.0893310
$83$	−387.980	+	1194.08i	−0.513088	+	1.57912i	0.273646	+	0.961831i	$0.411770\pi$
$83$	−387.980	+	1194.08i	−0.513088	+	1.57912i	−0.786734	+	0.617292i	$0.788230\pi$
$84$		0			0
$85$	−454.508	−	153.621i	−0.579980	−	0.196030i
$86$	68.6694	+	49.8912i	0.0861024	+	0.0625571i
$87$		0			0
$88$	−18.8638	+	13.7054i	−0.0228510	+	0.0166022i
$89$	952.696	+	692.174i	1.13467	+	0.824386i	0.986368	−	0.164556i	$-0.0526192\pi$
$89$	952.696	+	692.174i	1.13467	+	0.824386i	0.148302	+	0.988942i	$0.452619\pi$
$90$		0			0
$91$	1032.63	−	750.251i	1.18955	−	0.864261i
$92$	−275.378	+	847.526i	−0.312067	+	0.960442i
$93$		0			0
$94$	24.4358	−	75.2056i	0.0268123	−	0.0825198i
$95$	−27.4915	−	9.29195i	−0.0296902	−	0.0100351i
$96$		0			0
$97$	360.388	+	1109.16i	0.377236	+	1.16101i	0.941958	+	0.335731i	$0.108983\pi$
$97$	360.388	+	1109.16i	0.377236	+	1.16101i	−0.564722	+	0.825281i	$0.691017\pi$
$98$	−150.493	−	109.339i	−0.155123	−	0.112704i
$99$		0			0
$100$	282.540	+	944.741i	0.282540	+	0.944741i
$101$	1945.75			1.91693			0.958463	−	0.285216i	$-0.0920652\pi$
$101$	1945.75			1.91693			0.958463	+	0.285216i	$0.0920652\pi$
$102$		0			0
$103$	−329.844	−	1015.16i	−0.315539	−	0.971129i	−0.975532	−	0.219858i	$-0.929441\pi$
$103$	−329.844	−	1015.16i	−0.315539	−	0.971129i	0.659993	−	0.751272i	$-0.270559\pi$
$104$	69.6775	+	214.445i	0.0656966	+	0.202193i
$105$		0			0
$106$	−0.145452	+	0.447655i	−0.000133279	+	0.000410189i
$107$	178.742			0.161492			0.0807461	−	0.996735i	$-0.474270\pi$
$107$	178.742			0.161492			0.0807461	+	0.996735i	$0.474270\pi$
$108$		0			0
$109$	505.217	−	367.061i	0.443954	−	0.322551i	−0.343250	−	0.939244i	$-0.611528\pi$
$109$	505.217	−	367.061i	0.443954	−	0.322551i	0.787204	+	0.616693i	$0.211528\pi$
$110$	−15.6630	+	4.88600i	−0.0135764	+	0.00423511i
$111$		0			0
$112$	−1489.21	+	1081.98i	−1.25641	+	0.912833i
$113$	1474.30	−	1071.14i	1.22735	−	0.891719i	0.230657	−	0.973035i	$-0.425912\pi$
$113$	1474.30	−	1071.14i	1.22735	−	0.891719i	0.996688	+	0.0813163i	$0.0259124\pi$
$114$		0			0
$115$	−754.347	+	1012.96i	−0.611680	+	0.821382i
$116$	−646.044	+	469.379i	−0.517101	+	0.375696i
$117$		0			0
$118$	102.645			0.0800787
$119$	397.932	−	1224.71i	0.306541	−	0.943436i
$120$		0			0
$121$	−405.323	−	1247.46i	−0.304525	−	0.937233i
$122$	51.1783	+	157.510i	0.0379792	+	0.116888i
$123$		0			0
$124$	730.971			0.529380
$125$	−49.3771	+	1396.67i	−0.0353313	+	0.999376i
$126$		0			0
$127$	1216.55	+	883.877i	0.850012	+	0.617570i	0.925149	−	0.379603i	$-0.123939\pi$
$127$	1216.55	+	883.877i	0.850012	+	0.617570i	−0.0751371	+	0.997173i	$0.523939\pi$
$128$	−203.869	−	627.443i	−0.140778	−	0.433271i
$129$		0			0
$130$	−1.86895	+	158.653i	−0.00126090	+	0.107037i
$131$	−263.610	+	811.309i	−0.175815	+	0.541103i	−0.999670	−	0.0256982i	$-0.991819\pi$
$131$	−263.610	+	811.309i	−0.175815	+	0.541103i	0.823855	+	0.566801i	$0.191819\pi$
$132$		0			0
$133$	24.0694	−	74.0781i	0.0156924	−	0.0482961i
$134$	32.6733	−	23.7386i	0.0210638	−	0.0153037i
$135$		0			0
$136$	184.038	+	133.711i	0.116037	+	0.0843061i
$137$	−238.980	+	173.629i	−0.149032	+	0.108278i	−0.659803	−	0.751439i	$-0.729360\pi$
$137$	−238.980	+	173.629i	−0.149032	+	0.108278i	0.510771	+	0.859717i	$0.329360\pi$
$138$		0			0
$139$	−1712.87	−	1244.47i	−1.04521	−	0.759388i	−0.0739122	−	0.997265i	$-0.523548\pi$
$139$	−1712.87	−	1244.47i	−1.04521	−	0.759388i	−0.971295	+	0.237877i	$0.923548\pi$
$140$	−2526.65	+	788.178i	−1.52529	+	0.475808i
$141$		0			0
$142$	−91.7812	+	282.474i	−0.0542402	+	0.166934i
$143$	187.084			0.109404
$144$		0			0
$145$	−1080.42	+	337.031i	−0.618783	+	0.193027i
$146$	−11.5138	−	35.4357i	−0.00652662	−	0.0200869i
$147$		0			0
$148$	−882.282	−	641.015i	−0.490021	−	0.356021i
$149$	1332.34			0.732548			0.366274	−	0.930507i	$-0.380633\pi$
$149$	1332.34			0.732548			0.366274	+	0.930507i	$0.380633\pi$
$150$		0			0
$151$	3222.29			1.73660			0.868300	−	0.496040i	$-0.165213\pi$
$151$	3222.29			1.73660			0.868300	+	0.496040i	$0.165213\pi$
$152$	11.1317	+	8.08769i	0.00594016	+	0.00431578i
$153$		0			0
$154$	−13.6087	−	41.8833i	−0.00712092	−	0.0219159i
$155$	981.435	+	331.719i	0.508585	+	0.171899i
$156$		0			0
$157$	1670.77			0.849312			0.424656	−	0.905355i	$-0.360395\pi$
$157$	1670.77			0.849312			0.424656	+	0.905355i	$0.360395\pi$
$158$	55.1872	−	169.849i	0.0277877	−	0.0855218i
$159$		0			0
$160$	8.28048	−	702.921i	0.00409144	−	0.347317i
$161$	−2742.52	−	1992.56i	−1.34249	−	0.975377i
$162$		0			0
$163$	598.105	−	434.548i	0.287406	−	0.208813i	−0.434735	−	0.900558i	$-0.643158\pi$
$163$	598.105	−	434.548i	0.287406	−	0.208813i	0.722141	+	0.691746i	$0.243158\pi$
$164$	−1268.82	−	921.852i	−0.604136	−	0.438930i
$165$		0			0
$166$	338.898	−	246.224i	0.158455	−	0.115125i
$167$	−471.942	+	1452.49i	−0.218682	+	0.673035i	0.780189	+	0.625544i	$0.215123\pi$
$167$	−471.942	+	1452.49i	−0.218682	+	0.673035i	−0.998872	+	0.0474917i	$0.984877\pi$
$168$		0			0
$169$	−119.852	+	368.865i	−0.0545524	+	0.167895i
$170$	92.5561	+	130.600i	0.0417572	+	0.0589211i
$171$		0			0
$172$	620.165	+	1908.67i	0.274925	+	0.846133i
$173$	−2425.32	−	1762.10i	−1.06586	−	0.774391i	−0.0906951	−	0.995879i	$-0.528909\pi$
$173$	−2425.32	−	1762.10i	−1.06586	−	0.774391i	−0.975163	+	0.221487i	$0.928909\pi$
$174$		0			0
$175$	−3750.08	−	88.3649i	−1.61988	−	0.0381700i
$176$	−269.804			−0.115553
$177$		0			0
$178$	−121.413	−	373.670i	−0.0511251	−	0.157347i
$179$	686.013	+	2111.33i	0.286453	+	0.881610i	0.985960	+	0.166984i	$0.0534030\pi$
$179$	686.013	+	2111.33i	0.286453	+	0.881610i	−0.699507	+	0.714626i	$0.746597\pi$
$180$		0			0
$181$	455.526	−	1401.97i	0.187066	−	0.575731i	−0.812912	−	0.582387i	$-0.802119\pi$
$181$	455.526	−	1401.97i	0.187066	−	0.575731i	0.999978	+	0.00665624i	$0.00211876\pi$
$182$	−425.866			−0.173447
$183$		0			0
$184$	484.476	−	351.993i	0.194109	−	0.141028i
$185$	−893.696	−	1261.04i	−0.355167	−	0.501154i
$186$		0			0
$187$	152.698	−	110.942i	0.0597132	−	0.0433842i
$188$	1512.59	−	1098.96i	0.586792	−	0.426329i
$189$		0			0
$190$	5.59837	+	7.89953i	0.00213763	+	0.00301628i
$191$	3033.42	−	2203.91i	1.14917	−	0.834918i	0.160796	−	0.986988i	$-0.448594\pi$
$191$	3033.42	−	2203.91i	1.14917	−	0.834918i	0.988370	+	0.152070i	$0.0485938\pi$
$192$		0			0
$193$	−2602.05			−0.970464			−0.485232	−	0.874385i	$-0.661265\pi$
$193$	−2602.05			−0.970464			−0.485232	+	0.874385i	$0.661265\pi$
$194$	120.242	−	370.066i	0.0444993	−	0.136955i
$195$		0			0
$196$	−1359.13	−	4182.96i	−0.495308	−	1.52440i
$197$	−1339.92	−	4123.85i	−0.484596	−	1.49143i	−0.832565	−	0.553927i	$-0.813129\pi$
$197$	−1339.92	−	4123.85i	−0.484596	−	1.49143i	0.347969	−	0.937506i	$-0.386871\pi$
$198$		0			0
$199$	4248.11			1.51327			0.756635	−	0.653837i	$-0.226842\pi$
$199$	4248.11			1.51327			0.756635	+	0.653837i	$0.226842\pi$
$200$	219.559	−	625.217i	0.0776257	−	0.221048i
$201$		0			0
$202$	−525.206	−	381.585i	−0.182938	−	0.132912i
$203$	−938.714	−	2889.06i	−0.324556	−	0.998880i
$204$		0			0
$205$	−1285.23	−	1813.52i	−0.437876	−	0.617861i
$206$	−110.051	+	338.702i	−0.0372214	+	0.114556i
$207$		0			0
$208$	−806.248	+	2481.38i	−0.268766	+	0.827176i
$209$	9.23613	−	6.71044i	0.00305682	−	0.00222091i
$210$		0			0
$211$	798.900	+	580.435i	0.260657	+	0.189378i	0.710436	−	0.703761i	$-0.248498\pi$
$211$	798.900	+	580.435i	0.260657	+	0.189378i	−0.449780	+	0.893139i	$0.648498\pi$
$212$	−9.00356	+	6.54147i	−0.00291682	+	0.00211920i
$213$		0			0
$214$	−48.2469	−	35.0534i	−0.0154116	−	0.0111972i
$215$	−33.5039	+	2844.10i	−0.0106276	+	0.902169i
$216$		0			0
$217$	−859.268	+	2644.55i	−0.268806	+	0.827300i
$218$	−208.356			−0.0647322
$219$		0			0
$220$	−367.510	−	124.216i	−0.112625	−	0.0380666i
$221$	−564.022	−	1735.88i	−0.171675	−	0.528362i
$222$		0			0
$223$	−4367.71	−	3173.33i	−1.31158	−	0.952922i	−0.999996	−	0.00270496i	$-0.999139\pi$
$223$	−4367.71	−	3173.33i	−1.31158	−	0.952922i	−0.311588	−	0.950217i	$-0.600861\pi$
$224$	1886.83			0.562808
$225$		0			0
$226$	−608.011			−0.178957
$227$	2530.38	+	1838.43i	0.739856	+	0.537537i	0.892666	−	0.450719i	$-0.148832\pi$
$227$	2530.38	+	1838.43i	0.739856	+	0.537537i	−0.152810	+	0.988256i	$0.548832\pi$
$228$		0			0
$229$	890.313	+	2740.10i	0.256915	+	0.790703i	0.993446	+	0.114299i	$0.0364623\pi$
$229$	890.313	+	2740.10i	0.256915	+	0.790703i	−0.736531	+	0.676403i	$0.763538\pi$
$230$	402.270	−	125.486i	0.115326	−	0.0359753i
$231$		0			0
$232$	536.628			0.151859
$233$	−1021.35	+	3143.40i	−0.287172	+	0.883824i	0.698567	+	0.715544i	$0.253821\pi$
$233$	−1021.35	+	3143.40i	−0.287172	+	0.883824i	−0.985739	+	0.168280i	$0.946179\pi$
$234$		0			0
$235$	2529.58	−	789.093i	0.702178	−	0.219041i
$236$	1963.44	+	1426.52i	0.541563	+	0.393469i
$237$		0			0
$238$	−347.591	+	252.540i	−0.0946681	+	0.0687804i
$239$	3601.97	+	2616.98i	0.974862	+	0.708279i	0.956555	−	0.291553i	$-0.0941721\pi$
$239$	3601.97	+	2616.98i	0.974862	+	0.708279i	0.0183078	+	0.999832i	$0.494172\pi$
$240$		0			0
$241$	−1086.58	+	789.444i	−0.290426	+	0.211007i	−0.723452	−	0.690375i	$-0.757446\pi$
$241$	−1086.58	+	789.444i	−0.290426	+	0.211007i	0.433026	+	0.901381i	$0.357446\pi$
$242$	−135.234	+	416.208i	−0.0359222	+	0.110557i
$243$		0			0
$244$	−1210.05	+	3724.17i	−0.317483	+	0.977112i
$245$	73.4256	−	6233.01i	0.0191469	−	1.62536i
$246$		0			0
$247$	−34.1156	−	104.997i	−0.00878835	−	0.0270478i
$248$	−397.398	−	288.727i	−0.101753	−	0.0739281i
$249$		0			0
$250$	287.231	−	367.312i	0.0726644	−	0.0929234i
$251$	−3819.99			−0.960620			−0.480310	−	0.877099i	$-0.659476\pi$
$251$	−3819.99			−0.960620			−0.480310	+	0.877099i	$0.659476\pi$
$252$		0			0
$253$	−153.541	−	472.550i	−0.0381543	−	0.117427i
$254$	−155.039	−	477.160i	−0.0382992	−	0.117873i
$255$		0			0
$256$	1093.26	−	3364.71i	0.266909	−	0.821462i
$257$	−2155.09			−0.523076			−0.261538	−	0.965193i	$-0.584230\pi$
$257$	−2155.09			−0.523076			−0.261538	+	0.965193i	$0.584230\pi$
$258$		0			0
$259$	3356.24	−	2438.45i	0.805200	−	0.585012i
$260$	−2240.63	+	3008.79i	−0.534454	+	0.717681i
$261$		0			0
$262$	230.262	−	167.295i	0.0542964	−	0.0394486i
$263$	−2395.54	+	1740.46i	−0.561656	+	0.408067i	−0.832065	−	0.554679i	$-0.812841\pi$
$263$	−2395.54	+	1740.46i	−0.561656	+	0.408067i	0.270409	+	0.962746i	$0.412841\pi$
$264$		0			0
$265$	−15.0571	+	4.69701i	−0.00349039	+	0.00108881i
$266$	−21.0245	+	15.2752i	−0.00484622	+	0.00352099i
$267$		0			0
$268$	954.894			0.217647
$269$	2409.51	−	7415.70i	0.546135	−	1.68083i	−0.172141	−	0.985072i	$-0.555068\pi$
$269$	2409.51	−	7415.70i	0.546135	−	1.68083i	0.718276	−	0.695758i	$-0.244932\pi$
$270$		0			0
$271$	1781.44	+	5482.71i	0.399316	+	1.22897i	0.925549	+	0.378628i	$0.123604\pi$
$271$	1781.44	+	5482.71i	0.399316	+	1.22897i	−0.526232	+	0.850341i	$0.676396\pi$
$272$	813.406	+	2503.41i	0.181323	+	0.558056i
$273$		0			0
$274$	98.5572			0.0217301
$275$	−437.066	−	333.556i	−0.0958403	−	0.0731426i
$276$		0			0
$277$	−2645.65	−	1922.18i	−0.573870	−	0.416941i	0.262639	−	0.964894i	$-0.415407\pi$
$277$	−2645.65	−	1922.18i	−0.573870	−	0.416941i	−0.836509	+	0.547953i	$0.815407\pi$
$278$	218.290	+	671.828i	0.0470942	+	0.144941i
$279$		0			0
$280$	1684.96	+	569.505i	0.359627	+	0.121551i
$281$	−437.055	+	1345.12i	−0.0927848	+	0.285562i	−0.986670	−	0.162734i	$-0.947969\pi$
$281$	−437.055	+	1345.12i	−0.0927848	+	0.285562i	0.893885	+	0.448296i	$0.147969\pi$
$282$		0			0
$283$	1084.43	−	3337.53i	0.227783	−	0.701045i	−0.770214	−	0.637786i	$-0.779850\pi$
$283$	1084.43	−	3337.53i	0.227783	−	0.701045i	0.997997	−	0.0632593i	$-0.0201495\pi$
$284$	−5681.31	+	4127.72i	−1.18706	+	0.862447i
$285$		0			0
$286$	−50.4986	−	36.6894i	−0.0104407	−	0.00758563i
$287$	4826.66	−	3506.77i	0.992713	−	0.721248i
$288$		0			0
$289$	2484.96	+	1805.43i	0.505793	+	0.367480i
$290$	357.726	+	120.909i	0.0724359	+	0.0244829i
$291$		0			0
$292$	272.231	−	837.839i	0.0545585	−	0.167914i
$293$	5.06248			0.00100940			0.000504698	−	1.00000i	$-0.499839\pi$
$293$	5.06248			0.00100940			0.000504698		1.00000i	$0.499839\pi$
$294$		0			0
$295$	1988.84	+	2806.33i	0.392524	+	0.553867i
$296$	226.465	+	696.987i	0.0444696	+	0.136863i
$297$		0			0
$298$	−359.631	−	261.288i	−0.0699090	−	0.0507919i
$299$	−4804.85			−0.929337
$300$		0			0
$301$	−7634.33			−1.46191
$302$	−869.776	−	631.929i	−0.165728	−	0.120409i
$303$		0			0
$304$	49.1999	+	151.422i	0.00928226	+	0.0285679i
$305$	−3314.72	+	4451.10i	−0.622296	+	0.835638i
$306$		0			0
$307$	5233.44			0.972926			0.486463	−	0.873701i	$-0.338287\pi$
$307$	5233.44			0.972926			0.486463	+	0.873701i	$0.338287\pi$
$308$	321.763	−	990.286i	0.0595265	−	0.183204i
$309$		0			0
$310$	−199.859	−	282.010i	−0.0366170	−	0.0516680i
$311$	8694.60	+	6316.99i	1.58529	+	1.15178i	0.910296	+	0.413958i	$0.135854\pi$
$311$	8694.60	+	6316.99i	1.58529	+	1.15178i	0.674994	+	0.737823i	$0.264146\pi$
$312$		0			0
$313$	964.420	−	700.692i	0.174160	−	0.126535i	−0.497290	−	0.867584i	$-0.665672\pi$
$313$	964.420	−	700.692i	0.174160	−	0.126535i	0.671451	+	0.741049i	$0.265672\pi$
$314$	−450.982	−	327.657i	−0.0810521	−	0.0588878i
$315$		0			0
$316$	3416.12	−	2481.96i	0.608138	−	0.441838i
$317$	−3167.99	+	9750.06i	−0.561299	+	1.72750i	0.117400	+	0.993085i	$0.462544\pi$
$317$	−3167.99	+	9750.06i	−0.561299	+	1.72750i	−0.678699	+	0.734416i	$0.737456\pi$
$318$		0			0
$319$	137.588	−	423.454i	0.0241488	−	0.0743224i
$320$	3136.85	−	4212.25i	0.547985	−	0.735850i
$321$		0			0
$322$	349.510	+	1075.68i	0.0604890	+	0.186166i
$323$	−90.1087	−	65.4678i	−0.0155225	−	0.0112778i
$324$		0			0
$325$	−4373.78	+	3022.92i	−0.746503	+	0.515943i
$326$	−246.663			−0.0419062
$327$		0			0
$328$	325.682	+	1002.34i	0.0548255	+	0.168735i
$329$	2197.82	+	6764.19i	0.368297	+	1.13350i
$330$		0			0
$331$	−2338.04	+	7195.76i	−0.388249	+	1.19491i	0.545846	+	0.837885i	$0.316208\pi$
$331$	−2338.04	+	7195.76i	−0.388249	+	1.19491i	−0.934095	+	0.357023i	$0.883792\pi$
$332$	9904.47			1.63728
$333$		0			0
$334$	412.239	−	299.509i	0.0675350	−	0.0490671i
$335$	1282.08	+	433.336i	0.209098	+	0.0706737i
$336$		0			0
$337$	−1133.05	+	823.208i	−0.183149	+	0.133065i	−0.675582	−	0.737285i	$-0.736108\pi$
$337$	−1133.05	+	823.208i	−0.183149	+	0.133065i	0.492433	+	0.870350i	$0.336108\pi$
$338$	104.690	−	76.0615i	0.0168472	−	0.0122402i
$339$		0			0
$340$	−44.5815	+	3784.47i	−0.00711109	+	0.603652i
$341$	−329.726	+	239.560i	−0.0523626	+	0.0380437i
$342$		0			0
$343$	6438.00			1.01347
$344$	416.750	−	1282.62i	0.0653188	−	0.201030i
$345$		0			0
$346$	309.085	+	951.266i	0.0480246	+	0.147805i
$347$	−593.182	−	1825.63i	−0.0917686	−	0.282435i	0.894629	−	0.446809i	$-0.147440\pi$
$347$	−593.182	−	1825.63i	−0.0917686	−	0.282435i	−0.986398	+	0.164374i	$0.947440\pi$
$348$		0			0
$349$	−1831.69			−0.280940			−0.140470	−	0.990085i	$-0.544861\pi$
$349$	−1831.69			−0.280940			−0.140470	+	0.990085i	$0.544861\pi$
$350$	994.908	+	759.286i	0.151943	+	0.115959i
$351$		0			0
$352$	223.737	+	162.555i	0.0338785	+	0.0246142i
$353$	2642.85	+	8133.87i	0.398484	+	1.22641i	0.926215	+	0.376996i	$0.123043\pi$
$353$	2642.85	+	8133.87i	0.398484	+	1.22641i	−0.527731	+	0.849412i	$0.676957\pi$
$354$		0			0
$355$	−9501.17	+	2963.85i	−1.42048	+	0.443112i
$356$	2870.67	−	8835.02i	0.427374	−	1.31532i
$357$		0			0
$358$	228.885	−	704.435i	0.0337903	−	0.103996i
$359$	−2843.61	+	2066.01i	−0.418051	+	0.303732i	−0.776853	−	0.629682i	$-0.783185\pi$
$359$	−2843.61	+	2066.01i	−0.418051	+	0.303732i	0.358802	+	0.933414i	$0.383185\pi$
$360$		0			0
$361$	5543.60	+	4027.66i	0.808222	+	0.587208i
$362$	−397.900	+	289.091i	−0.0577711	+	0.0419732i
$363$		0			0
$364$	−8146.11	−	5918.49i	−1.17300	−	0.852235i
$365$	745.725	−	1001.38i	0.106940	−	0.143602i
$366$		0			0
$367$	1463.96	−	4505.62i	0.208224	−	0.640848i	−0.791341	−	0.611375i	$-0.790617\pi$
$367$	1463.96	−	4505.62i	0.208224	−	0.640848i	0.999566	−	0.0294738i	$-0.00938315\pi$
$368$	6929.33			0.981566
$369$		0			0
$370$	−6.07442	+	515.650i	−0.000853497	+	0.0724524i
$371$	−13.0823	−	40.2633i	−0.00183073	−	0.00563441i
$372$		0			0
$373$	944.433	+	686.171i	0.131102	+	0.0952509i	0.651403	−	0.758732i	$-0.274181\pi$
$373$	944.433	+	686.171i	0.131102	+	0.0952509i	−0.520302	+	0.853982i	$0.674181\pi$
$374$	−62.9738			−0.00870669
$375$		0			0
$376$	−1256.41			−0.172326
$377$	−3483.34	−	2530.79i	−0.475865	−	0.345736i
$378$		0			0
$379$	−1174.39	−	3614.41i	−0.159167	−	0.489867i	0.839392	−	0.543527i	$-0.182911\pi$
$379$	−1174.39	−	3614.41i	−0.159167	−	0.489867i	−0.998559	+	0.0536597i	$0.982911\pi$
$380$	−2.69657	+	228.909i	−0.000364029	+	0.0309020i
$381$		0			0
$382$	−1251.01			−0.167558
$383$	1136.52	−	3497.85i	0.151628	−	0.466663i	−0.846176	−	0.532904i	$-0.821101\pi$
$383$	1136.52	−	3497.85i	0.151628	−	0.466663i	0.997804	+	0.0662411i	$0.0211006\pi$
$384$		0			0
$385$	881.411	−	1183.59i	0.116678	−	0.156678i
$386$	702.357	+	510.292i	0.0926141	+	0.0672881i
$387$		0			0
$388$	7443.04	−	5407.68i	0.973873	−	0.707560i
$389$	−1525.71	−	1108.50i	−0.198861	−	0.144481i	0.483899	−	0.875124i	$-0.339220\pi$
$389$	−1525.71	−	1108.50i	−0.198861	−	0.144481i	−0.682759	+	0.730643i	$0.739220\pi$
$390$		0			0
$391$	−3921.71	+	2849.29i	−0.507237	+	0.368529i
$392$	−913.331	+	2810.94i	−0.117679	+	0.362179i
$393$		0			0
$394$	−447.058	+	1375.90i	−0.0571636	+	0.175931i
$395$	5712.96	−	1782.13i	0.727722	−	0.227010i
$396$		0			0
$397$	−1787.58	−	5501.61i	−0.225985	−	0.695511i	−0.998190	−	0.0601375i	$-0.980846\pi$
$397$	−1787.58	−	5501.61i	−0.225985	−	0.695511i	0.772205	−	0.635374i	$-0.219154\pi$
$398$	−1146.67	−	833.105i	−0.144416	−	0.104924i
$399$		0			0
$400$	6307.66	−	4359.52i	0.788457	−	0.544940i
$401$	−8673.48			−1.08013			−0.540066	−	0.841622i	$-0.681601\pi$
$401$	−8673.48			−1.08013			−0.540066	+	0.841622i	$0.681601\pi$
$402$		0			0
$403$	1217.91	+	3748.35i	0.150542	+	0.463321i
$404$	−4743.23	−	14598.2i	−0.584120	−	1.79774i
$405$		0			0
$406$	−313.197	+	963.922i	−0.0382850	+	0.117829i
$407$	608.058			0.0740548
$408$		0			0
$409$	1254.94	−	911.764i	0.151718	−	0.110229i	−0.509337	−	0.860567i	$-0.670109\pi$
$409$	1254.94	−	911.764i	0.151718	−	0.110229i	0.661054	+	0.750338i	$0.270109\pi$
$410$	−8.73569	+	741.563i	−0.00105226	+	0.0893248i
$411$		0			0
$412$	−6812.22	+	4949.37i	−0.814597	+	0.591839i
$413$	−7469.01	+	5426.56i	−0.889894	+	0.646546i
$414$		0			0
$415$	13298.2	+	4494.70i	1.57297	+	0.531654i
$416$	2163.60	−	1571.95i	0.254998	−	0.185267i
$417$		0			0
$418$	−3.80905			−0.000445710
$419$	−879.484	+	2706.77i	−0.102543	+	0.315596i	−0.989146	−	0.146936i	$-0.953059\pi$
$419$	−879.484	+	2706.77i	−0.102543	+	0.315596i	0.886603	+	0.462532i	$0.153059\pi$
$420$		0			0
$421$	−1772.98	−	5456.69i	−0.205249	−	0.631693i	−0.999703	−	0.0243678i	$-0.992243\pi$
$421$	−1772.98	−	5456.69i	−0.205249	−	0.631693i	0.794454	−	0.607325i	$-0.207757\pi$
$422$	−101.813	−	313.347i	−0.0117445	−	0.0361458i
$423$		0			0
$424$	7.47868			0.000856596
$425$	−1777.27	+	5060.97i	−0.202848	+	0.577631i
$426$		0			0
$427$	−12051.1	−	8755.63i	−1.36579	−	0.992306i
$428$	−435.726	−	1341.03i	−0.0492094	−	0.151451i
$429$		0			0
$430$	566.806	−	761.123i	0.0635670	−	0.0853596i
$431$	−1080.69	+	3326.03i	−0.120778	+	0.371715i	−0.993108	−	0.117201i	$-0.962608\pi$
$431$	−1080.69	+	3326.03i	−0.120778	+	0.371715i	0.872331	+	0.488916i	$0.162608\pi$
$432$		0			0
$433$	−4003.90	+	12322.7i	−0.444377	+	1.36765i	0.438789	+	0.898590i	$0.355408\pi$
$433$	−4003.90	+	12322.7i	−0.444377	+	1.36765i	−0.883166	+	0.469061i	$0.844592\pi$
$434$	750.566	−	545.318i	0.0830145	−	0.0603136i
$435$		0			0
$436$	−3985.49	−	2895.63i	−0.437776	−	0.318063i
$437$	−237.210	+	172.343i	−0.0259663	+	0.0188656i
$438$		0			0
$439$	−4780.87	−	3473.51i	−0.519769	−	0.377634i	0.296748	−	0.954956i	$-0.404098\pi$
$439$	−4780.87	−	3473.51i	−0.519769	−	0.377634i	−0.816517	+	0.577322i	$0.804098\pi$
$440$	150.736	+	212.694i	0.0163319	+	0.0230450i
$441$		0			0
$442$	−188.183	+	579.168i	−0.0202510	+	0.0623263i
$443$	5526.18			0.592679			0.296339	−	0.955083i	$-0.404234\pi$
$443$	5526.18			0.592679			0.296339	+	0.955083i	$0.404234\pi$
$444$		0			0
$445$	7863.67	−	10559.6i	0.837694	−	1.12488i
$446$	556.626	+	1713.12i	0.0590964	+	0.181880i
$447$		0			0
$448$	11404.4	+	8285.79i	1.20270	+	0.873810i
$449$	−7613.56			−0.800236			−0.400118	−	0.916464i	$-0.631031\pi$
$449$	−7613.56			−0.800236			−0.400118	+	0.916464i	$0.631031\pi$
$450$		0			0
$451$	874.455			0.0913004
$452$	−11630.2	−	8449.87i	−1.21027	−	0.879311i
$453$		0			0
$454$	−322.475	−	992.475i	−0.0333359	−	0.102597i
$455$	−8251.49	−	11643.2i	−0.850189	−	1.19965i
$456$		0			0
$457$	2162.92			0.221394			0.110697	−	0.993854i	$-0.464692\pi$
$457$	2162.92			0.221394			0.110697	+	0.993854i	$0.464692\pi$
$458$	297.049	−	914.221i	0.0303060	−	0.0932724i
$459$		0			0
$460$	9438.70	+	3190.22i	0.956700	+	0.323358i
$461$	2070.84	+	1504.56i	0.209216	+	0.152005i	0.687459	−	0.726223i	$-0.258726\pi$
$461$	2070.84	+	1504.56i	0.209216	+	0.152005i	−0.478243	+	0.878228i	$0.658726\pi$
$462$		0			0
$463$	−10286.6	+	7473.64i	−1.03252	+	0.750172i	−0.968812	−	0.247796i	$-0.920294\pi$
$463$	−10286.6	+	7473.64i	−1.03252	+	0.750172i	−0.0637111	+	0.997968i	$0.520294\pi$
$464$	5023.51	+	3649.79i	0.502609	+	0.365167i
$465$		0			0
$466$	892.146	−	648.182i	0.0886864	−	0.0644344i
$467$	378.522	−	1164.97i	0.0375073	−	0.115436i	−0.930550	−	0.366165i	$-0.880671\pi$
$467$	378.522	−	1164.97i	0.0375073	−	0.115436i	0.968057	+	0.250730i	$0.0806705\pi$
$468$		0			0
$469$	−1122.49	+	3454.68i	−0.110516	+	0.340133i
$470$	−837.547	−	283.086i	−0.0821982	−	0.0277825i
$471$		0			0
$472$	−503.976	−	1551.08i	−0.0491470	−	0.151259i
$473$	−905.269	−	657.716i	−0.0880006	−	0.0639362i
$474$		0			0
$475$	−107.501	+	306.119i	−0.0103841	+	0.0295699i
$476$	−10158.5			−0.978184
$477$		0			0
$478$	−459.039	−	1412.78i	−0.0439246	−	0.135186i
$479$	486.157	+	1496.24i	0.0463739	+	0.142724i	0.971562	−	0.236784i	$-0.0760933\pi$
$479$	486.157	+	1496.24i	0.0463739	+	0.142724i	−0.925188	+	0.379508i	$0.876093\pi$
$480$		0			0
$481$	1817.04	−	5592.29i	0.172245	−	0.530117i
$482$	448.113			0.0423465
$483$		0			0
$484$	−8371.07	+	6081.94i	−0.786164	+	0.571182i
$485$	12447.4	−	3882.91i	1.16538	−	0.363534i
$486$		0			0
$487$	9327.35	−	6776.71i	0.867890	−	0.630559i	−0.0621299	−	0.998068i	$-0.519789\pi$
$487$	9327.35	−	6776.71i	0.867890	−	0.630559i	0.930020	+	0.367509i	$0.119789\pi$
$488$	2128.87	−	1546.71i	0.197478	−	0.143476i
$489$		0			0
$490$	−1242.19	+	1668.04i	−0.114523	+	0.153785i
$491$	−2525.68	+	1835.01i	−0.232143	+	0.168662i	−0.697776	−	0.716316i	$-0.745827\pi$
$491$	−2525.68	+	1835.01i	−0.232143	+	0.168662i	0.465633	+	0.884978i	$0.345827\pi$
$492$		0			0
$493$	−4343.86			−0.396831
$494$	−11.3825	+	35.0317i	−0.00103669	+	0.00319059i
$495$		0			0
$496$	−1756.41	−	5405.69i	−0.159003	−	0.489360i
$497$	−8255.05	−	25406.4i	−0.745049	−	2.29303i
$498$		0			0
$499$	−10363.6			−0.929733			−0.464866	−	0.885381i	$-0.653898\pi$
$499$	−10363.6			−0.929733			−0.464866	+	0.885381i	$0.653898\pi$
$500$	10599.0	−	3034.26i	0.948003	−	0.271392i
$501$		0			0
$502$	1031.11	+	749.145i	0.0916747	+	0.0666055i
$503$	2333.02	+	7180.28i	0.206807	+	0.636487i	0.999634	+	0.0270405i	$0.00860830\pi$
$503$	2333.02	+	7180.28i	0.206807	+	0.636487i	−0.792827	+	0.609447i	$0.791392\pi$
$504$		0			0
$505$	256.249	−	21752.7i	0.0225800	−	1.91679i
$506$	−51.2282	+	157.664i	−0.00450073	+	0.0138518i
$507$		0			0
$508$	3665.73	−	11281.9i	0.320158	−	0.985345i
$509$	6190.43	−	4497.61i	0.539069	−	0.391657i	−0.284670	−	0.958626i	$-0.591884\pi$
$509$	6190.43	−	4497.61i	0.539069	−	0.391657i	0.823739	+	0.566969i	$0.191884\pi$
$510$		0			0
$511$	2711.18	+	1969.79i	0.234708	+	0.170525i
$512$	−5224.84	+	3796.07i	−0.450991	+	0.327664i
$513$		0			0
$514$	581.711	+	422.638i	0.0499186	+	0.0362680i
$515$	−11392.4	+	3553.82i	−0.974779	+	0.304078i
$516$		0			0
$517$	−322.137	+	991.436i	−0.0274034	+	0.0843390i
$518$	−1384.14			−0.117405
$519$		0			0
$520$	2406.58	−	750.723i	0.202953	−	0.0633103i
$521$	−2994.08	−	9214.83i	−0.251772	−	0.774874i	−0.994449	−	0.105224i	$-0.966444\pi$
$521$	−2994.08	−	9214.83i	−0.251772	−	0.774874i	0.742677	−	0.669650i	$-0.233556\pi$
$522$		0			0
$523$	5443.80	+	3955.15i	0.455145	+	0.330682i	0.791624	−	0.611009i	$-0.209236\pi$
$523$	5443.80	+	3955.15i	0.455145	+	0.330682i	−0.336479	+	0.941691i	$0.609236\pi$
$524$	6729.53			0.561032
$525$		0			0
$526$	987.942			0.0818941
$527$	3216.84	+	2337.17i	0.265897	+	0.193185i
$528$		0			0
$529$	183.553	+	564.919i	0.0150862	+	0.0464305i
$530$	4.98543	+	1.68504i	0.000408591	+	0.000138101i
$531$		0			0
$532$	−614.452			−0.0500749
$533$	2613.11	−	8042.33i	0.212357	−	0.653569i
$534$		0			0
$535$	23.5397	−	1998.26i	0.00190226	−	0.161481i
$536$	−519.136	−	377.174i	−0.0418344	−	0.0303945i
$537$		0			0
$538$	−2104.69	+	1529.15i	−0.168661	+	0.122540i
$539$	1983.95	+	1441.42i	0.158543	+	0.115188i
$540$		0			0
$541$	−7081.43	+	5144.96i	−0.562762	+	0.408871i	−0.832469	−	0.554072i	$-0.813073\pi$
$541$	−7081.43	+	5144.96i	−0.562762	+	0.408871i	0.269707	+	0.962943i	$0.413073\pi$
$542$	594.369	−	1829.28i	0.0471039	−	0.144971i
$543$		0			0
$544$	833.758	−	2566.04i	0.0657115	−	0.202239i
$545$	−4037.05	−	5696.44i	−0.317300	−	0.447723i
$546$		0			0
$547$	−4600.63	−	14159.3i	−0.359613	−	1.10678i	−0.953286	−	0.302070i	$-0.902322\pi$
$547$	−4600.63	−	14159.3i	−0.359613	−	1.10678i	0.593672	−	0.804707i	$-0.297678\pi$
$548$	1885.23	+	1369.70i	0.146958	+	0.106772i
$549$		0			0
$550$	52.5606	+	175.749i	0.00407489	+	0.0136254i
$551$	−262.744			−0.0203145
$552$		0			0
$553$	4963.68	+	15276.6i	0.381695	+	1.17474i
$554$	337.165	+	1037.69i	0.0258570	+	0.0795796i
$555$		0			0
$556$	−5161.24	+	15884.7i	−0.393678	+	1.21162i
$557$	8700.83			0.661878			0.330939	−	0.943652i	$-0.392635\pi$
$557$	8700.83			0.661878			0.330939	+	0.943652i	$0.392635\pi$
$558$		0			0
$559$	−8754.19	+	6360.29i	−0.662366	+	0.481237i
$560$	11899.9	+	16791.3i	0.897970	+	1.26707i
$561$		0			0
$562$	381.765	−	277.369i	0.0286544	−	0.0208187i
$563$	9548.09	−	6937.09i	0.714749	−	0.519296i	−0.169953	−	0.985452i	$-0.554362\pi$
$563$	9548.09	−	6937.09i	0.714749	−	0.519296i	0.884702	+	0.466156i	$0.154362\pi$
$564$		0			0
$565$	−11780.7	−	16623.0i	−0.877200	−	1.23776i
$566$	−947.244	+	688.213i	−0.0703456	+	0.0511091i
$567$		0			0
$568$	4719.10			0.348608
$569$	−651.071	+	2003.79i	−0.0479689	+	0.147633i	−0.972172	−	0.234268i	$-0.924731\pi$
$569$	−651.071	+	2003.79i	−0.0479689	+	0.147633i	0.924203	+	0.381901i	$0.124731\pi$
$570$		0			0
$571$	6827.98	+	21014.3i	0.500424	+	1.54015i	0.808330	+	0.588729i	$0.200372\pi$
$571$	6827.98	+	21014.3i	0.500424	+	1.54015i	−0.307907	+	0.951417i	$0.599628\pi$
$572$	−456.062	−	1403.61i	−0.0333372	−	0.102601i
$573$		0			0
$574$	−1990.55			−0.144746
$575$	11225.1	+	8566.67i	0.814119	+	0.621313i
$576$		0			0
$577$	4506.84	+	3274.41i	0.325169	+	0.236249i	0.738378	−	0.674387i	$-0.235592\pi$
$577$	4506.84	+	3274.41i	0.325169	+	0.236249i	−0.413209	+	0.910636i	$0.635592\pi$
$578$	−316.687	−	974.661i	−0.0227897	−	0.0701394i
$579$		0			0
$580$	5162.37	+	7284.31i	0.369579	+	0.521491i
$581$	−11642.9	+	35833.0i	−0.831372	+	2.55870i
$582$		0			0
$583$	1.91749	−	5.90144i	0.000136217	−	0.000419233i
$584$	−478.939	+	347.970i	−0.0339360	+	0.0246560i
$585$		0			0
$586$	−1.36649	−	0.992812i	−9.63295e−5	−	6.99875e-5i
$587$	8528.93	−	6196.63i	0.599705	−	0.435711i	−0.246069	−	0.969252i	$-0.579139\pi$
$587$	8528.93	−	6196.63i	0.599705	−	0.435711i	0.845774	+	0.533541i	$0.179139\pi$
$588$		0			0
$589$	194.575	+	141.367i	0.0136117	+	0.00988950i
$590$	13.5181	−	1147.53i	0.000943270	−	0.0800731i
$591$		0			0
$592$	−2620.46	+	8064.93i	−0.181926	+	0.559910i
$593$	−27399.0			−1.89737			−0.948687	−	0.316215i	$-0.897588\pi$
$593$	−27399.0			−1.89737			−0.948687	+	0.316215i	$0.897588\pi$
$594$		0			0
$595$	−13639.3	−	4610.00i	−0.939760	−	0.317633i
$596$	−3247.89	−	9995.99i	−0.223220	−	0.687000i
$597$		0			0
$598$	1296.95	+	942.287i	0.0886892	+	0.0644364i
$599$	−13271.6			−0.905282			−0.452641	−	0.891693i	$-0.649518\pi$
$599$	−13271.6			−0.905282			−0.452641	+	0.891693i	$0.649518\pi$
$600$		0			0
$601$	−6877.92			−0.466816			−0.233408	−	0.972379i	$-0.574988\pi$
$601$	−6877.92			−0.466816			−0.233408	+	0.972379i	$0.574988\pi$
$602$	2060.69	+	1497.18i	0.139514	+	0.101363i
$603$		0			0
$604$	−7855.10	−	24175.5i	−0.529171	−	1.62862i
$605$	−13999.4	+	4367.05i	−0.940755	+	0.293464i
$606$		0			0
$607$	26271.0			1.75668			0.878340	−	0.478036i	$-0.158651\pi$
$607$	26271.0			1.75668			0.878340	+	0.478036i	$0.158651\pi$
$608$	50.4309	−	155.210i	0.00336389	−	0.0103530i
$609$		0			0
$610$	1767.64	−	551.407i	0.117327	−	0.0365997i
$611$	8155.56	+	5925.36i	0.539998	+	0.392332i
$612$		0			0
$613$	−13072.7	+	9497.88i	−0.861340	+	0.625800i	−0.928249	−	0.371959i	$-0.878686\pi$
$613$	−13072.7	+	9497.88i	−0.861340	+	0.625800i	0.0669090	+	0.997759i	$0.478686\pi$
$614$	−1412.64	−	1026.34i	−0.0928490	−	0.0674588i
$615$		0			0
$616$	−566.083	+	411.284i	−0.0370262	+	0.0269011i
$617$	−4487.16	+	13810.1i	−0.292782	+	0.901090i	0.691176	+	0.722687i	$0.257093\pi$
$617$	−4487.16	+	13810.1i	−0.292782	+	0.901090i	−0.983958	+	0.178403i	$0.942907\pi$
$618$		0			0
$619$	−74.2046	+	228.378i	−0.00481831	+	0.0148292i	−0.953437	−	0.301593i	$-0.902482\pi$
$619$	−74.2046	+	228.378i	−0.00481831	+	0.0148292i	0.948618	+	0.316422i	$0.102482\pi$
$620$	96.2663	−	8171.94i	0.00623572	−	0.529343i
$621$		0			0
$622$	−1108.05	−	3410.22i	−0.0714288	−	0.219835i
$623$	28589.4	+	20771.4i	1.83854	+	1.33578i
$624$		0			0
$625$	15607.7	+	735.951i	0.998890	+	0.0471008i
$626$	−397.735			−0.0253940
$627$		0			0
$628$	−4072.90	−	12535.1i	−0.258800	−	0.796504i
$629$	−1833.17	−	5641.93i	−0.116206	−	0.357645i
$630$		0			0
$631$	−6189.79	+	19050.2i	−0.390510	+	1.20187i	0.541894	+	0.840447i	$0.317707\pi$
$631$	−6189.79	+	19050.2i	−0.390510	+	1.20187i	−0.932404	+	0.361419i	$0.882293\pi$
$632$	−2837.55			−0.178595
$633$		0			0
$634$	2767.22	−	2010.50i	0.173344	−	0.125942i
$635$	10041.6	−	13484.1i	0.627540	−	0.842679i
$636$		0			0
$637$	19185.3	−	13938.9i	1.19333	−	0.867002i
$638$	−120.183	+	87.3179i	−0.00745781	+	0.00541841i
$639$		0			0
$640$	−7041.39	+	2196.53i	−0.434899	+	0.135665i
$641$	960.288	−	697.690i	0.0591718	−	0.0429908i	−0.557806	−	0.829971i	$-0.688357\pi$
$641$	960.288	−	697.690i	0.0591718	−	0.0429908i	0.616978	+	0.786980i	$0.288357\pi$
$642$		0			0
$643$	−3888.22			−0.238470			−0.119235	−	0.992866i	$-0.538044\pi$
$643$	−3888.22			−0.238470			−0.119235	+	0.992866i	$0.538044\pi$
$644$	−8263.80	+	25433.3i	−0.505651	+	1.55623i
$645$		0			0
$646$	11.4835	+	35.3427i	0.000699403	+	0.00215254i
$647$	1580.02	+	4862.81i	0.0960080	+	0.295482i	0.987515	−	0.157525i	$-0.0503513\pi$
$647$	1580.02	+	4862.81i	0.0960080	+	0.295482i	−0.891507	+	0.453007i	$0.850351\pi$
$648$		0			0
$649$	−1353.18			−0.0818441
$650$	1773.42	+	41.7880i	0.107014	+	0.00252163i
$651$		0			0
$652$	−4718.26	−	3428.01i	−0.283407	−	0.205907i
$653$	−7156.24	−	22024.6i	−0.428859	−	1.31989i	−0.899250	−	0.437435i	$-0.855887\pi$
$653$	−7156.24	−	22024.6i	−0.428859	−	1.31989i	0.470390	−	0.882458i	$-0.344113\pi$
$654$		0			0
$655$	9035.37	+	3053.90i	0.538994	+	0.182176i
$656$	−3768.51	+	11598.3i	−0.224292	+	0.690300i
$657$		0			0
$658$	733.291	−	2256.84i	0.0434448	−	0.133709i
$659$	16616.7	−	12072.7i	0.982239	−	0.713638i	0.0240308	−	0.999711i	$-0.492350\pi$
$659$	16616.7	−	12072.7i	0.982239	−	0.713638i	0.958208	+	0.286073i	$0.0923500\pi$
$660$		0			0
$661$	15840.0	+	11508.4i	0.932077	+	0.677194i	0.946501	−	0.322702i	$-0.104591\pi$
$661$	15840.0	+	11508.4i	0.932077	+	0.677194i	−0.0144232	+	0.999896i	$0.504591\pi$
$662$	2042.27	−	1483.80i	0.119902	−	0.0871138i
$663$		0			0
$664$	−5384.65	−	3912.17i	−0.314706	−	0.228647i
$665$	−824.991	−	278.842i	−0.0481079	−	0.0162602i
$666$		0			0
$667$	−3533.66	+	10875.5i	−0.205133	+	0.631335i
$668$	12047.9			0.697824
$669$		0			0
$670$	−261.084	−	368.400i	−0.0150545	−	0.0212426i
$671$	−674.683	−	2076.46i	−0.0388165	−	0.119465i
$672$		0			0
$673$	9345.74	+	6790.08i	0.535293	+	0.388913i	0.822334	−	0.569005i	$-0.192672\pi$
$673$	9345.74	+	6790.08i	0.535293	+	0.388913i	−0.287041	+	0.957918i	$0.592672\pi$
$674$	467.279			0.0267046
$675$		0			0
$676$	3059.61			0.174079
$677$	−18724.9	−	13604.5i	−1.06301	−	0.772322i	−0.0883672	−	0.996088i	$-0.528165\pi$
$677$	−18724.9	−	13604.5i	−1.06301	−	0.772322i	−0.974643	+	0.223766i	$0.928165\pi$
$678$		0			0
$679$	10814.9	+	33284.7i	0.611246	+	1.88122i
$680$	1519.07	−	2039.85i	0.0856671	−	0.115036i
$681$		0			0
$682$	135.982			0.00763490
$683$	−6453.37	+	19861.4i	−0.361539	+	1.11270i	0.590580	+	0.806979i	$0.298899\pi$
$683$	−6453.37	+	19861.4i	−0.361539	+	1.11270i	−0.952120	+	0.305725i	$0.901101\pi$
$684$		0			0
$685$	1909.62	+	2694.56i	0.106515	+	0.150297i
$686$	−1737.77	−	1262.57i	−0.0967180	−	0.0702698i
$687$		0			0
$688$	12624.9	−	9172.51i	0.699591	−	0.508283i
$689$	−48.5453	−	35.2702i	−0.00268422	−	0.00195020i
$690$		0			0
$691$	6731.34	−	4890.61i	0.370582	−	0.269244i	−0.386870	−	0.922134i	$-0.626444\pi$
$691$	6731.34	−	4890.61i	0.370582	−	0.269244i	0.757452	+	0.652891i	$0.226444\pi$
$692$	−7307.99	+	22491.7i	−0.401457	+	1.23556i
$693$		0			0
$694$	−197.912	+	609.112i	−0.0108251	+	0.0333164i
$695$	−14138.3	+	18985.3i	−0.771647	+	1.03619i
$696$		0			0
$697$	−2636.31	−	8113.73i	−0.143267	−	0.440932i
$698$	494.418	+	359.216i	0.0268109	+	0.0194792i
$699$		0			0
$700$	8478.73	+	28350.7i	0.457808	+	1.53079i
$701$	17726.6			0.955096			0.477548	−	0.878606i	$-0.341526\pi$
$701$	17726.6			0.955096			0.477548	+	0.878606i	$0.341526\pi$
$702$		0			0
$703$	−110.882	−	341.259i	−0.00594878	−	0.0183085i
$704$	638.479	+	1965.04i	0.0341812	+	0.105199i
$705$		0			0
$706$	881.775	−	2713.83i	0.0470057	−	0.144669i
$707$	58390.0			3.10605
$708$		0			0
$709$	17039.8	−	12380.1i	0.902599	−	0.655776i	−0.0365336	−	0.999332i	$-0.511632\pi$
$709$	17039.8	−	12380.1i	0.902599	−	0.655776i	0.939132	+	0.343556i	$0.111632\pi$
$710$	3145.84	+	1063.27i	0.166284	+	0.0562028i
$711$		0			0
$712$	−5050.42	+	3669.34i	−0.265832	+	0.193138i
$713$	8468.29	−	6152.57i	0.444796	−	0.323163i
$714$		0			0
$715$	24.6383	−	2091.52i	0.00128870	−	0.109396i
$716$	14168.1	−	10293.7i	0.739507	−	0.537283i
$717$		0			0
$718$	1172.73			0.0609553
$719$	−2215.42	+	6818.37i	−0.114911	+	0.353661i	−0.991929	−	0.126798i	$-0.959530\pi$
$719$	−2215.42	+	6818.37i	−0.114911	+	0.353661i	0.877017	+	0.480459i	$0.159530\pi$
$720$		0			0
$721$	−9898.27	−	30463.8i	−0.511277	−	1.57355i
$722$	−706.482	−	2174.33i	−0.0364163	−	0.112078i
$723$		0			0
$724$	−11628.8			−0.596936
$725$	3625.57	+	12123.0i	0.185725	+	0.621014i
$726$		0			0
$727$	−12118.9	−	8804.90i	−0.618246	−	0.449182i	0.234062	−	0.972222i	$-0.424798\pi$
$727$	−12118.9	−	8804.90i	−0.618246	−	0.449182i	−0.852309	+	0.523039i	$0.824798\pi$
$728$	2090.95	+	6435.28i	0.106450	+	0.327620i
$729$		0			0
$730$	−397.672	+	124.052i	−0.0201623	+	0.00628955i
$731$	−3373.49	+	10382.5i	−0.170688	+	0.525323i
$732$		0			0
$733$	−1543.21	+	4749.52i	−0.0777625	+	0.239328i	−0.982380	−	0.186897i	$-0.940157\pi$
$733$	−1543.21	+	4749.52i	−0.0777625	+	0.239328i	0.904617	+	0.426225i	$0.140157\pi$
$734$	−1278.76	+	929.077i	−0.0643053	+	0.0467205i
$735$		0			0
$736$	−5746.21	−	4174.86i	−0.287783	−	0.209086i
$737$	−430.733	+	312.946i	−0.0215281	+	0.0156411i
$738$		0			0
$739$	24582.0	+	17859.9i	1.22363	+	0.889021i	0.996396	−	0.0848193i	$-0.0270313\pi$
$739$	24582.0	+	17859.9i	1.22363	+	0.889021i	0.227235	+	0.973840i	$0.427031\pi$
$740$	−7282.47	+	9779.11i	−0.361769	+	0.485794i
$741$		0			0
$742$	−4.36486	+	13.4336i	−0.000215955	+	0.000664642i
$743$	−22967.9			−1.13406			−0.567032	−	0.823696i	$-0.691908\pi$
$743$	−22967.9			−1.13406			−0.567032	+	0.823696i	$0.691908\pi$
$744$		0			0
$745$	175.465	−	14895.0i	0.00862889	−	0.732497i
$746$	−120.360	−	370.429i	−0.00590707	−	0.0181801i
$747$		0			0
$748$	−1204.58	−	875.182i	−0.0588823	−	0.0427805i
$749$	5363.86			0.261671
$750$		0			0
$751$	−10710.0			−0.520391			−0.260196	−	0.965556i	$-0.583787\pi$
$751$	−10710.0			−0.520391			−0.260196	+	0.965556i	$0.583787\pi$
$752$	−11761.6	−	8545.28i	−0.570346	−	0.414381i
$753$		0			0
$754$	443.920	+	1366.25i	0.0214412	+	0.0659891i
$755$	424.365	−	36023.8i	0.0204559	−	1.73648i
$756$		0			0
$757$	−32701.0			−1.57006			−0.785031	−	0.619457i	$-0.787353\pi$
$757$	−32701.0			−1.57006			−0.785031	+	0.619457i	$0.787353\pi$
$758$	−391.830	+	1205.93i	−0.0187756	+	0.0577854i
$759$		0			0
$760$	91.8828	−	123.383i	0.00438545	−	0.00588891i
$761$	−9026.96	−	6558.47i	−0.429996	−	0.312411i	0.351651	−	0.936131i	$-0.385620\pi$
$761$	−9026.96	−	6558.47i	−0.429996	−	0.312411i	−0.781647	+	0.623721i	$0.785620\pi$
$762$		0			0
$763$	15161.0	−	11015.1i	0.719352	−	0.522640i
$764$	−23929.7	−	17385.9i	−1.13318	−	0.823300i
$765$		0			0
$766$	−992.745	+	721.272i	−0.0468268	+	0.0340217i
$767$	−4043.66	+	12445.1i	−0.190363	+	0.585876i
$768$		0			0
$769$	2661.27	−	8190.54i	0.124796	−	0.384081i	−0.869068	−	0.494692i	$-0.835281\pi$
$769$	2661.27	−	8190.54i	0.124796	−	0.384081i	0.993864	+	0.110611i	$0.0352807\pi$
$770$	−470.030	+	146.624i	−0.0219983	+	0.00686227i
$771$		0			0
$772$	6343.11	+	19522.1i	0.295717	+	0.910123i
$773$	10084.7	+	7326.96i	0.469239	+	0.340922i	0.797144	−	0.603789i	$-0.206343\pi$
$773$	10084.7	+	7326.96i	0.469239	+	0.340922i	−0.327906	+	0.944710i	$0.606343\pi$
$774$		0			0
$775$	3837.72	−	10928.3i	0.177877	−	0.506525i
$776$	−6182.45			−0.286001
$777$		0			0
$778$	194.439	+	598.421i	0.00896011	+	0.0275764i
$779$	−159.461	−	490.769i	−0.00733411	−	0.0225721i
$780$		0			0
$781$	1209.95	−	3723.85i	0.0554360	−	0.170614i
$782$	1617.35			0.0739593
$783$		0			0
$784$	−27668.1	+	20102.1i	−1.26039	+	0.915728i
$785$	220.035	−	18678.5i	0.0100043	−	0.849253i
$786$		0			0
$787$	−25626.9	+	18619.0i	−1.16074	+	0.843325i	−0.989871	−	0.141969i	$-0.954657\pi$
$787$	−25626.9	+	18619.0i	−1.16074	+	0.843325i	−0.170867	+	0.985294i	$0.554657\pi$
$788$	−27673.2	+	20105.7i	−1.25103	+	0.908930i
$789$		0			0
$790$	−1891.57	−	639.337i	−0.0851885	−	0.0287932i
$791$	44242.0	−	32143.7i	1.98871	−	1.44488i
$792$		0			0
$793$	−21113.3			−0.945466
$794$	−596.418	+	1835.59i	−0.0266575	+	0.0820435i
$795$		0			0
$796$	−10355.8	−	31871.8i	−0.461119	−	1.41918i
$797$	1013.26	+	3118.51i	0.0450334	+	0.138599i	0.971045	−	0.238896i	$-0.0767856\pi$
$797$	1013.26	+	3118.51i	0.0450334	+	0.138599i	−0.926012	+	0.377495i	$0.876786\pi$
$798$		0			0
$799$	10170.3			0.450313
$800$	−7857.26	−	185.144i	−0.347245	−	0.00818230i
$801$		0			0
$802$	2341.19	+	1700.97i	0.103080	+	0.0748920i
$803$	151.786	+	467.149i	0.00667050	+	0.0205297i
$804$		0			0
$805$	−22637.1	+	30397.8i	−0.991123	+	1.33091i
$806$	406.350	−	1250.62i	0.0177582	−	0.0546540i
$807$		0			0
$808$	−3187.44	+	9809.95i	−0.138780	+	0.427120i
$809$	9511.59	−	6910.57i	0.413362	−	0.300325i	−0.361600	−	0.932333i	$-0.617769\pi$
$809$	9511.59	−	6910.57i	0.413362	−	0.300325i	0.774961	+	0.632009i	$0.217769\pi$
$810$		0			0
$811$	−2885.64	−	2096.54i	−0.124943	−	0.0907762i	0.523559	−	0.851989i	$-0.324604\pi$
$811$	−2885.64	−	2096.54i	−0.124943	−	0.0907762i	−0.648502	+	0.761213i	$0.724604\pi$
$812$	−19387.1	+	14085.6i	−0.837874	+	0.608751i
$813$		0			0
$814$	−164.130	−	119.247i	−0.00706725	−	0.00513466i
$815$	−4779.29	−	6743.78i	−0.205413	−	0.289846i
$816$		0			0
$817$	−204.050	+	628.000i	−0.00873781	+	0.0268922i
$818$	−517.546			−0.0221217
$819$		0			0
$820$	−10473.0	+	14063.5i	−0.446016	+	0.598923i
$821$	−7770.73	−	23915.9i	−0.330329	−	1.01665i	−0.968977	−	0.247150i	$-0.920506\pi$
$821$	−7770.73	−	23915.9i	−0.330329	−	1.01665i	0.638648	−	0.769499i	$-0.279494\pi$
$822$		0			0
$823$	−4823.85	−	3504.74i	−0.204312	−	0.148442i	0.480924	−	0.876762i	$-0.340301\pi$
$823$	−4823.85	−	3504.74i	−0.204312	−	0.148442i	−0.685237	+	0.728321i	$0.740301\pi$
$824$	5658.47			0.239226
$825$		0			0
$826$	3080.28			0.129754
$827$	−33192.9	−	24116.0i	−1.39568	−	1.01402i	−0.995215	−	0.0977126i	$-0.968847\pi$
$827$	−33192.9	−	24116.0i	−1.39568	−	1.01402i	−0.400468	−	0.916311i	$-0.631153\pi$
$828$		0			0
$829$	−11451.4	−	35243.7i	−0.479761	−	1.47655i	−0.839427	−	0.543473i	$-0.817109\pi$
$829$	−11451.4	−	35243.7i	−0.479761	−	1.47655i	0.359665	−	0.933081i	$-0.382891\pi$
$830$	−2708.04	−	3821.16i	−0.113250	−	0.159801i
$831$		0			0
$832$	19980.3			0.832563
$833$	7393.18	−	22753.9i	0.307513	−	0.946429i
$834$		0			0
$835$	16176.0	+	5467.39i	0.670413	+	0.226595i
$836$	−72.8609	−	52.9365i	−0.00301429	−	0.00219001i
$837$		0			0
$838$	768.224	−	558.148i	0.0316681	−	0.0230082i
$839$	−7086.37	−	5148.55i	−0.291596	−	0.211857i	0.432364	−	0.901699i	$-0.357680\pi$
$839$	−7086.37	−	5148.55i	−0.291596	−	0.211857i	−0.723959	+	0.689843i	$0.757680\pi$
$840$		0			0
$841$	11441.0	−	8312.41i	0.469107	−	0.340826i
$842$	−591.548	+	1820.60i	−0.0242115	+	0.0745153i
$843$		0			0
$844$	2407.25	−	7408.76i	0.0981766	−	0.302156i
$845$	4107.97	+	1388.47i	0.167241	+	0.0565263i
$846$		0			0
$847$	−12163.3	−	37434.8i	−0.493432	−	1.51863i
$848$	70.0098	+	50.8651i	0.00283508	+	0.00205980i
$849$		0			0
$850$	1472.25	−	1017.54i	0.0594089	−	0.0410603i
$851$	−15616.6			−0.629062
$852$		0			0
$853$	−7767.18	−	23904.9i	−0.311774	−	0.959541i	−0.977062	−	0.212955i	$-0.931691\pi$
$853$	−7767.18	−	23904.9i	−0.311774	−	0.959541i	0.665288	−	0.746587i	$-0.268309\pi$
$854$	1535.80	+	4726.72i	0.0615388	+	0.189397i
$855$		0			0
$856$	−292.807	+	901.169i	−0.0116915	+	0.0359828i
$857$	20757.6			0.827381			0.413691	−	0.910418i	$-0.364240\pi$
$857$	20757.6			0.827381			0.413691	+	0.910418i	$0.364240\pi$
$858$		0			0
$859$	29433.2	−	21384.5i	1.16909	−	0.849393i	0.178190	−	0.983996i	$-0.442976\pi$
$859$	29433.2	−	21384.5i	1.16909	−	0.849393i	0.990900	+	0.134603i	$0.0429759\pi$
$860$	21419.8	−	6681.81i	0.849313	−	0.264939i
$861$		0			0
$862$	943.979	−	685.841i	0.0372994	−	0.0270996i
$863$	2057.61	−	1494.94i	0.0811610	−	0.0589669i	−0.546465	−	0.837482i	$-0.684027\pi$
$863$	2057.61	−	1494.94i	0.0811610	−	0.0589669i	0.627626	+	0.778515i	$0.284027\pi$
$864$		0			0
$865$	−20018.9	+	26881.9i	−0.786893	+	1.05666i
$866$	3497.39	−	2541.00i	0.137236	−	0.0997075i
$867$		0			0
$868$	21935.7			0.857770
$869$	−727.533	+	2239.12i	−0.0284003	+	0.0874072i
$870$		0			0
$871$	1591.00	+	4896.60i	0.0618933	+	0.190488i
$872$	1023.00	+	3148.47i	0.0397283	+	0.122271i
$873$		0			0
$874$	97.8273			0.00378611
$875$	−1481.75	+	41912.6i	−0.0572484	+	1.61932i
$876$		0			0
$877$	9569.69	+	6952.79i	0.368467	+	0.267707i	0.756575	−	0.653907i	$-0.226871\pi$
$877$	9569.69	+	6952.79i	0.368467	+	0.267707i	−0.388108	+	0.921614i	$0.626871\pi$
$878$	609.280	+	1875.17i	0.0234193	+	0.0720773i
$879$		0			0
$880$	−35.5322	+	3016.29i	−0.00136113	+	0.115544i
$881$	−345.956	+	1064.74i	−0.0132299	+	0.0407175i	−0.957454	−	0.288587i	$-0.906814\pi$
$881$	−345.956	+	1064.74i	−0.0132299	+	0.0407175i	0.944224	+	0.329305i	$0.106814\pi$
$882$		0			0
$883$	10588.6	−	32588.2i	0.403549	−	1.24199i	−0.518553	−	0.855046i	$-0.673529\pi$
$883$	10588.6	−	32588.2i	0.403549	−	1.24199i	0.922101	−	0.386949i	$-0.126471\pi$
$884$	−11648.7	+	8463.24i	−0.443197	+	0.322002i
$885$		0			0
$886$	−1491.65	−	1083.75i	−0.0565610	−	0.0410940i
$887$	5900.13	−	4286.69i	0.223345	−	0.162270i	−0.470486	−	0.882407i	$-0.655921\pi$
$887$	5900.13	−	4286.69i	0.223345	−	0.162270i	0.693831	+	0.720138i	$0.255921\pi$
$888$		0			0
$889$	36507.4	+	26524.2i	1.37730	+	1.00067i
$890$	−4193.45	+	1308.13i	−0.157938	+	0.0492681i
$891$		0			0
$892$	−13160.8	+	40504.8i	−0.494010	+	1.52041i
$893$	615.165			0.0230523
$894$		0			0
$895$	23694.1	−	7391.27i	0.884923	−	0.276048i
$896$	−6117.88	−	18828.9i	−0.228107	−	0.702042i
$897$		0			0
$898$	2055.09	+	1493.11i	0.0763687	+	0.0554851i
$899$	9379.85			0.347982
$900$		0			0
$901$	−60.5380			−0.00223842
$902$	−236.037	−	171.491i	−0.00871305	−	0.00633040i
$903$		0			0
$904$	2985.26	+	9187.68i	0.109832	+	0.338028i
$905$	−15613.4	−	5277.22i	−0.573488	−	0.193835i
$906$		0			0
$907$	−12701.0			−0.464973			−0.232486	−	0.972600i	$-0.574686\pi$
$907$	−12701.0			−0.464973			−0.232486	+	0.972600i	$0.574686\pi$
$908$	7624.56	−	23466.0i	0.278667	−	0.857650i
$909$		0			0
$910$	−56.0851	+	4761.00i	−0.00204308	+	0.173435i
$911$	26666.2	+	19374.2i	0.969805	+	0.704604i	0.955407	−	0.295292i	$-0.0954170\pi$
$911$	26666.2	+	19374.2i	0.969805	+	0.704604i	0.0143976	+	0.999896i	$0.495417\pi$
$912$		0			0
$913$	−4467.70	+	3245.97i	−0.161949	+	0.117663i
$914$	−583.824	−	424.173i	−0.0211282	−	0.0153506i
$915$		0			0
$916$	18387.5	−	13359.3i	0.663253	−	0.481881i
$917$	−7910.67	+	24346.5i	−0.284878	+	0.876765i
$918$		0			0
$919$	9743.94	−	29988.8i	0.349753	−	1.07643i	−0.609237	−	0.792988i	$-0.708524\pi$
$919$	9743.94	−	29988.8i	0.349753	−	1.07643i	0.958990	−	0.283441i	$-0.0914760\pi$
$920$	−3871.32	−	5462.59i	−0.138732	−	0.195757i
$921$		0			0
$922$	−263.911	−	812.233i	−0.00942671	−	0.0290124i
$923$	−30632.5	−	22255.8i	−1.09239	−	0.793671i
$924$		0			0
$925$	−14215.6	+	9825.05i	−0.505303	+	0.349239i
$926$	4242.27			0.150550
$927$		0			0
$928$	−1966.82	−	6053.24i	−0.0695732	−	0.214124i
$929$	−12387.8	−	38125.6i	−0.437491	−	1.34646i	−0.890512	−	0.454959i	$-0.849654\pi$
$929$	−12387.8	−	38125.6i	−0.437491	−	1.34646i	0.453022	−	0.891500i	$-0.350346\pi$
$930$		0			0
$931$	447.186	−	1376.30i	0.0157421	−	0.0484493i
$932$	26073.4			0.916377
$933$		0			0
$934$	−330.637	+	240.222i	−0.0115833	+	0.00841573i
$935$	−1220.17	−	1721.71i	−0.0426778	−	0.0602201i
$936$		0			0
$937$	34755.5	−	25251.3i	1.21175	−	0.880390i	0.216364	−	0.976313i	$-0.430580\pi$
$937$	34755.5	−	25251.3i	1.21175	−	0.880390i	0.995389	+	0.0959227i	$0.0305802\pi$
$938$	980.491	−	712.369i	0.0341303	−	0.0247971i
$939$		0			0
$940$	−12086.7	−	17054.8i	−0.419388	−	0.591773i
$941$	−37686.0	+	27380.5i	−1.30556	+	0.948542i	−0.999993	−	0.00362993i	$-0.998845\pi$
$941$	−37686.0	+	27380.5i	−1.30556	+	0.948542i	−0.305563	+	0.952172i	$0.598845\pi$
$942$		0			0
$943$	−22458.5			−0.775555
$944$	5831.58	−	17947.8i	0.201061	−	0.618803i
$945$		0			0
$946$	115.368	+	355.068i	0.00396507	+	0.0122032i
$947$	−1476.29	−	4543.55i	−0.0506578	−	0.155909i	0.922527	−	0.385931i	$-0.126120\pi$
$947$	−1476.29	−	4543.55i	−0.0506578	−	0.155909i	−0.973185	+	0.230023i	$0.926120\pi$
$948$		0			0
$949$	4749.94			0.162476
$950$	89.0506	−	61.5470i	0.00304125	−	0.00210195i
$951$		0			0
$952$	5522.77	+	4012.53i	0.188019	+	0.136604i
$953$	−13249.1	−	40776.5i	−0.450346	−	1.38602i	−0.876513	−	0.481378i	$-0.840137\pi$
$953$	−13249.1	−	40776.5i	−0.450346	−	1.38602i	0.426167	−	0.904644i	$-0.359863\pi$
$954$		0			0
$955$	−24239.3	−	34202.6i	−0.821324	−	1.15892i
$956$	10853.5	−	33403.6i	0.367183	−	1.13007i
$957$		0			0
$958$	162.204	−	499.213i	0.00547033	−	0.0168359i
$959$	−7171.53	+	5210.42i	−0.241481	+	0.175447i
$960$		0			0
$961$	17155.2	+	12464.0i	0.575852	+	0.418381i
$962$	−1587.18	+	1153.15i	−0.0531940	+	0.0386477i
$963$		0			0
$964$	8571.66	+	6227.67i	0.286384	+	0.208070i
$965$	−342.681	+	29089.8i	−0.0114314	+	0.970397i
$966$		0			0
$967$	−11678.3	+	35942.1i	−0.388365	+	1.19526i	0.545645	+	0.838016i	$0.316285\pi$
$967$	−11678.3	+	35942.1i	−0.388365	+	1.19526i	−0.934010	+	0.357247i	$0.883715\pi$
$968$	6953.31			0.230876
$969$		0			0
$970$	−4121.34	−	1392.99i	−0.136421	−	0.0461094i
$971$	−3451.54	−	10622.7i	−0.114073	−	0.351081i	0.877679	−	0.479248i	$-0.159091\pi$
$971$	−3451.54	−	10622.7i	−0.114073	−	0.351081i	−0.991753	+	0.128167i	$0.959091\pi$
$972$		0			0
$973$	−51401.4	−	37345.3i	−1.69358	−	1.23046i
$974$	−3846.67			−0.126546
$975$		0			0
$976$	30448.6			0.998602
$977$	23378.1	+	16985.2i	0.765538	+	0.556196i	0.900604	−	0.434641i	$-0.143125\pi$
$977$	23378.1	+	16985.2i	0.765538	+	0.556196i	−0.135066	+	0.990837i	$0.543125\pi$
$978$		0			0
$979$	1600.58	+	4926.09i	0.0522522	+	0.160816i
$980$	−46942.7	+	14643.6i	−1.53013	+	0.477318i
$981$		0			0
$982$	1041.61			0.0338484
$983$	−5997.79	+	18459.3i	−0.194608	+	0.598942i	0.805373	+	0.592769i	$0.201965\pi$
$983$	−5997.79	+	18459.3i	−0.194608	+	0.598942i	−0.999981	+	0.00617373i	$0.998035\pi$
$984$		0			0
$985$	−46279.3	+	14436.6i	−1.49704	+	0.466994i
$986$	1172.52	+	851.883i	0.0378707	+	0.0275147i
$987$		0			0
$988$	−704.584	+	511.910i	−0.0226880	+	0.0164838i
$989$	23249.9	+	16892.0i	0.747525	+	0.543109i
$990$		0			0
$991$	25753.3	−	18710.9i	0.825509	−	0.599768i	−0.0927758	−	0.995687i	$-0.529574\pi$
$991$	25753.3	−	18710.9i	0.825509	−	0.599768i	0.918285	+	0.395919i	$0.129574\pi$
$992$	−1800.36	+	5540.94i	−0.0576225	+	0.177344i
$993$		0			0
$994$	−2754.26	+	8476.73i	−0.0878870	+	0.270489i
$995$	559.462	−	47492.1i	0.0178253	−	1.51317i
$996$		0			0
$997$	12065.9	+	37135.0i	0.383281	+	1.17962i	0.937720	+	0.347393i	$0.112933\pi$
$997$	12065.9	+	37135.0i	0.383281	+	1.17962i	−0.554439	+	0.832225i	$0.687067\pi$
$998$	2797.38	+	2032.42i	0.0887270	+	0.0644639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.91.4		28
3.2	odd	2		25.4.d.a.16.4	yes	28
15.2	even	4		125.4.e.b.49.7		56
15.8	even	4		125.4.e.b.49.8		56
15.14	odd	2		125.4.d.a.76.4		28
25.11	even	5	inner	225.4.h.b.136.4		28
75.2	even	20		125.4.e.b.74.8		56
75.11	odd	10		25.4.d.a.11.4	✓	28
75.14	odd	10		125.4.d.a.51.4		28
75.23	even	20		125.4.e.b.74.7		56
75.44	odd	10		625.4.a.d.1.7		14
75.56	odd	10		625.4.a.c.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.4	✓	28	75.11	odd	10
25.4.d.a.16.4	yes	28	3.2	odd	2
125.4.d.a.51.4		28	75.14	odd	10
125.4.d.a.76.4		28	15.14	odd	2
125.4.e.b.49.7		56	15.2	even	4
125.4.e.b.49.8		56	15.8	even	4
125.4.e.b.74.7		56	75.23	even	20
125.4.e.b.74.8		56	75.2	even	20
225.4.h.b.91.4		28	1.1	even	1	trivial
225.4.h.b.136.4		28	25.11	even	5	inner
625.4.a.c.1.8		14	75.56	odd	10
625.4.a.d.1.7		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)

\(f(q)\)	\(=\)	\(q+(-0.269925 - 0.196112i) q^{2} +(-2.43774 - 7.50258i) q^{4} +(0.131697 - 11.1796i) q^{5} +30.0089 q^{7} +(-1.63816 + 5.04172i) q^{8} +O(q^{10})\)	\(q+(-0.269925 - 0.196112i) q^{2} +(-2.43774 - 7.50258i) q^{4} +(0.131697 - 11.1796i) q^{5} +30.0089 q^{7} +(-1.63816 + 5.04172i) q^{8} +(-2.22799 + 2.99181i) q^{10} +(3.55842 + 2.58534i) q^{11} +(34.4108 - 25.0009i) q^{13} +(-8.10015 - 5.88510i) q^{14} +(-49.6257 + 36.0552i) q^{16} +(13.2605 - 40.8115i) q^{17} +(0.802076 - 2.46853i) q^{19} +(-84.1966 + 26.2648i) q^{20} +(-0.453489 - 1.39570i) q^{22} +(-91.3902 - 66.3989i) q^{23} +(-124.965 - 2.94462i) q^{25} -14.1913 q^{26} +(-73.1539 - 225.144i) q^{28} +(-31.2811 - 96.2735i) q^{29} +(-28.6337 + 88.1256i) q^{31} +62.8755 q^{32} +(-11.5829 + 8.41549i) q^{34} +(3.95207 - 335.487i) q^{35} +(111.842 - 81.2576i) q^{37} +(-0.700608 + 0.509022i) q^{38} +(56.1485 + 18.9778i) q^{40} +(160.841 - 116.858i) q^{41} -254.402 q^{43} +(10.7223 - 32.9997i) q^{44} +(11.6469 + 35.8454i) q^{46} +(73.2388 + 225.406i) q^{47} +557.536 q^{49} +(33.1537 + 25.3020i) q^{50} +(-271.456 - 197.224i) q^{52} +(-0.435948 - 1.34171i) q^{53} +(29.3716 - 39.4411i) q^{55} +(-49.1593 + 151.297i) q^{56} +(-10.4368 + 32.1212i) q^{58} +(-248.893 + 180.831i) q^{59} +(-401.584 - 291.768i) q^{61} +(25.0114 - 18.1719i) q^{62} +(380.034 + 276.111i) q^{64} +(-274.968 - 387.991i) q^{65} +(-37.4053 + 115.122i) q^{67} -338.517 q^{68} +(-66.8597 + 89.7811i) q^{70} +(-275.086 - 846.629i) q^{71} +(90.3458 + 65.6400i) q^{73} -46.1244 q^{74} -20.4756 q^{76} +(106.784 + 77.5834i) q^{77} +(165.407 + 509.070i) q^{79} +(396.546 + 559.542i) q^{80} -66.3320 q^{82} +(-387.980 + 1194.08i) q^{83} +(-454.508 - 153.621i) q^{85} +(68.6694 + 49.8912i) q^{86} +(-18.8638 + 13.7054i) q^{88} +(952.696 + 692.174i) q^{89} +(1032.63 - 750.251i) q^{91} +(-275.378 + 847.526i) q^{92} +(24.4358 - 75.2056i) q^{94} +(-27.4915 - 9.29195i) q^{95} +(360.388 + 1109.16i) q^{97} +(-150.493 - 109.339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more