LMFDB - Embedded newform 225.4.h.d.46.10

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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.10
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.426412 - 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(-10.9704 + 2.15653i) q^{5} -13.9864 q^{7} +(15.7361 - 11.4329i) q^{8} +O(q^{10})$	\(q+(0.426412 - 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(-10.9704 + 2.15653i) q^{5} -13.9864 q^{7} +(15.7361 - 11.4329i) q^{8} +(-1.84776 + 15.3167i) q^{10} +(8.55501 - 26.3296i) q^{11} +(19.3615 + 59.5885i) q^{13} +(-5.96399 + 18.3553i) q^{14} +(6.77575 + 20.8536i) q^{16} +(-76.5125 + 55.5896i) q^{17} +(-93.8251 + 68.1679i) q^{19} +(-61.8293 - 28.6723i) q^{20} +(-30.9060 - 22.4545i) q^{22} +(-35.1368 + 108.140i) q^{23} +(115.699 - 47.3159i) q^{25} +86.4576 q^{26} +(-68.9765 - 50.1144i) q^{28} +(-161.223 - 117.135i) q^{29} +(-214.777 + 156.045i) q^{31} +185.864 q^{32} +(40.3278 + 124.116i) q^{34} +(153.437 - 30.1622i) q^{35} +(88.0113 + 270.871i) q^{37} +(49.4528 + 152.200i) q^{38} +(-147.976 + 159.359i) q^{40} +(-100.917 - 310.590i) q^{41} +113.898 q^{43} +(136.531 - 99.1958i) q^{44} +(126.936 + 92.2244i) q^{46} +(-45.5242 - 33.0753i) q^{47} -147.379 q^{49} +(-12.7603 - 172.015i) q^{50} +(-118.025 + 363.244i) q^{52} +(386.969 + 281.150i) q^{53} +(-37.0712 + 307.295i) q^{55} +(-220.092 + 159.906i) q^{56} +(-222.471 + 161.635i) q^{58} +(173.406 + 533.690i) q^{59} +(160.923 - 495.270i) q^{61} +(113.204 + 348.405i) q^{62} +(25.0486 - 77.0916i) q^{64} +(-340.907 - 611.955i) q^{65} +(565.942 - 411.181i) q^{67} -576.516 q^{68} +(25.8436 - 214.226i) q^{70} +(47.8348 + 34.7540i) q^{71} +(226.377 - 696.716i) q^{73} +393.010 q^{74} -706.964 q^{76} +(-119.654 + 368.258i) q^{77} +(192.738 + 140.032i) q^{79} +(-119.304 - 214.160i) q^{80} -450.638 q^{82} +(282.783 - 205.454i) q^{83} +(719.492 - 774.841i) q^{85} +(48.5673 - 149.475i) q^{86} +(-166.403 - 512.135i) q^{88} +(240.108 - 738.975i) q^{89} +(-270.798 - 833.431i) q^{91} +(-560.756 + 407.413i) q^{92} +(-62.8188 + 45.6405i) q^{94} +(882.291 - 950.165i) q^{95} +(478.367 + 347.554i) q^{97} +(-62.8443 + 193.415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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 $

$2$	0.426412	−	1.31236i	0.150759	−	0.463990i	−0.846947	−	0.531677i	$-0.821562\pi$
$2$	0.426412	−	1.31236i	0.150759	−	0.463990i	0.997707	+	0.0676872i	$0.0215620\pi$
$3$		0			0
$3$		0			0
$4$	4.93167	+	3.58307i	0.616459	+	0.447884i
$5$	−10.9704	+	2.15653i	−0.981221	+	0.192886i
$5$	−10.9704	+	2.15653i	−0.981221	+	0.192886i
$6$		0			0
$7$	−13.9864			−0.755197			−0.377599	−	0.925969i	$-0.623250\pi$
$7$	−13.9864			−0.755197			−0.377599	+	0.925969i	$0.623250\pi$
$8$	15.7361	−	11.4329i	0.695444	−	0.505269i
$9$		0			0
$10$	−1.84776	+	15.3167i	−0.0584312	+	0.484356i
$11$	8.55501	−	26.3296i	0.234494	−	0.721698i	−0.762694	−	0.646759i	$-0.776124\pi$
$11$	8.55501	−	26.3296i	0.234494	−	0.721698i	0.997188	−	0.0749390i	$-0.0238762\pi$
$12$		0			0
$13$	19.3615	+	59.5885i	0.413070	+	1.27130i	0.913966	+	0.405790i	$0.133004\pi$
$13$	19.3615	+	59.5885i	0.413070	+	1.27130i	−0.500897	+	0.865507i	$0.666996\pi$
$14$	−5.96399	+	18.3553i	−0.113853	+	0.350404i
$15$		0			0
$16$	6.77575	+	20.8536i	0.105871	+	0.325838i
$17$	−76.5125	+	55.5896i	−1.09159	+	0.793086i	−0.979667	−	0.200631i	$-0.935701\pi$
$17$	−76.5125	+	55.5896i	−1.09159	+	0.793086i	−0.111922	+	0.993717i	$0.535701\pi$
$18$		0			0
$19$	−93.8251	+	68.1679i	−1.13289	+	0.823094i	−0.986113	−	0.166075i	$-0.946891\pi$
$19$	−93.8251	+	68.1679i	−1.13289	+	0.823094i	−0.146779	+	0.989169i	$0.546891\pi$
$20$	−61.8293	−	28.6723i	−0.691273	−	0.320567i
$21$		0			0
$22$	−30.9060	−	22.4545i	−0.299509	−	0.217606i
$23$	−35.1368	+	108.140i	−0.318545	+	0.980380i	0.655726	+	0.754999i	$0.272363\pi$
$23$	−35.1368	+	108.140i	−0.318545	+	0.980380i	−0.974271	+	0.225381i	$0.927637\pi$
$24$		0			0
$25$	115.699	−	47.3159i	0.925590	−	0.378528i
$26$	86.4576			0.652143
$27$		0			0
$28$	−68.9765	−	50.1144i	−0.465548	−	0.338240i
$29$	−161.223	−	117.135i	−1.03236	−	0.750051i	−0.0635781	−	0.997977i	$-0.520251\pi$
$29$	−161.223	−	117.135i	−1.03236	−	0.750051i	−0.968779	+	0.247925i	$0.920251\pi$
$30$		0			0
$31$	−214.777	+	156.045i	−1.24436	+	0.904080i	−0.997881	−	0.0650678i	$-0.979274\pi$
$31$	−214.777	+	156.045i	−1.24436	+	0.904080i	−0.246479	+	0.969148i	$0.579274\pi$
$32$	185.864			1.02676
$33$		0			0
$34$	40.3278	+	124.116i	0.203417	+	0.626052i
$35$	153.437	−	30.1622i	0.741015	−	0.145667i
$36$		0			0
$37$	88.0113	+	270.871i	0.391053	+	1.20354i	0.931993	+	0.362477i	$0.118069\pi$
$37$	88.0113	+	270.871i	0.391053	+	1.20354i	−0.540939	+	0.841062i	$0.681931\pi$
$38$	49.4528	+	152.200i	0.211113	+	0.649740i
$39$		0			0
$40$	−147.976	+	159.359i	−0.584925	+	0.629922i
$41$	−100.917	−	310.590i	−0.384404	−	1.18307i	−0.936912	−	0.349565i	$-0.886329\pi$
$41$	−100.917	−	310.590i	−0.384404	−	1.18307i	0.552508	−	0.833507i	$-0.313671\pi$
$42$		0			0
$43$	113.898			0.403935			0.201968	−	0.979392i	$-0.435266\pi$
$43$	113.898			0.403935			0.201968	+	0.979392i	$0.435266\pi$
$44$	136.531	−	99.1958i	0.467793	−	0.339871i
$45$		0			0
$46$	126.936	+	92.2244i	0.406863	+	0.295603i
$47$	−45.5242	−	33.0753i	−0.141285	−	0.102649i	0.514898	−	0.857252i	$-0.327830\pi$
$47$	−45.5242	−	33.0753i	−0.141285	−	0.102649i	−0.656183	+	0.754602i	$0.727830\pi$
$48$		0			0
$49$	−147.379			−0.429677
$50$	−12.7603	−	172.015i	−0.0360915	−	0.486531i
$51$		0			0
$52$	−118.025	+	363.244i	−0.314753	+	0.968709i
$53$	386.969	+	281.150i	1.00291	+	0.728658i	0.962711	−	0.270534i	$-0.0872001\pi$
$53$	386.969	+	281.150i	1.00291	+	0.728658i	0.0402011	+	0.999192i	$0.487200\pi$
$54$		0			0
$55$	−37.0712	+	307.295i	−0.0908850	+	0.753376i
$56$	−220.092	+	159.906i	−0.525197	+	0.381578i
$57$		0			0
$58$	−222.471	+	161.635i	−0.503654	+	0.365926i
$59$	173.406	+	533.690i	0.382637	+	1.17764i	0.938180	+	0.346148i	$0.112511\pi$
$59$	173.406	+	533.690i	0.382637	+	1.17764i	−0.555543	+	0.831488i	$0.687489\pi$
$60$		0			0
$61$	160.923	−	495.270i	0.337772	−	1.03955i	−0.627569	−	0.778561i	$-0.715950\pi$
$61$	160.923	−	495.270i	0.337772	−	1.03955i	0.965341	−	0.260993i	$-0.0840500\pi$
$62$	113.204	+	348.405i	0.231885	+	0.713669i
$63$		0			0
$64$	25.0486	−	77.0916i	0.0489230	−	0.150570i
$65$	−340.907	−	611.955i	−0.650528	−	1.16775i
$66$		0			0
$67$	565.942	−	411.181i	1.03195	−	0.749758i	0.0632546	−	0.997997i	$-0.479852\pi$
$67$	565.942	−	411.181i	1.03195	−	0.749758i	0.968699	+	0.248239i	$0.0798520\pi$
$68$	−576.516			−1.02813
$69$		0			0
$70$	25.8436	−	214.226i	0.0441271	−	0.365784i
$71$	47.8348	+	34.7540i	0.0799570	+	0.0580921i	0.627046	−	0.778983i	$-0.284264\pi$
$71$	47.8348	+	34.7540i	0.0799570	+	0.0580921i	−0.547089	+	0.837075i	$0.684264\pi$
$72$		0			0
$73$	226.377	−	696.716i	0.362951	−	1.11705i	−0.588304	−	0.808640i	$-0.700204\pi$
$73$	226.377	−	696.716i	0.362951	−	1.11705i	0.951254	−	0.308407i	$-0.0997959\pi$
$74$	393.010			0.617385
$75$		0			0
$76$	−706.964			−1.06703
$77$	−119.654	+	368.258i	−0.177089	+	0.545024i
$78$		0			0
$79$	192.738	+	140.032i	0.274489	+	0.199428i	0.716510	−	0.697577i	$-0.245738\pi$
$79$	192.738	+	140.032i	0.274489	+	0.199428i	−0.442021	+	0.897005i	$0.645738\pi$
$80$	−119.304	−	214.160i	−0.166733	−	0.299298i
$81$		0			0
$82$	−450.638			−0.606886
$83$	282.783	−	205.454i	0.373969	−	0.271705i	−0.384886	−	0.922964i	$-0.625759\pi$
$83$	282.783	−	205.454i	0.373969	−	0.271705i	0.758855	+	0.651260i	$0.225759\pi$
$84$		0			0
$85$	719.492	−	774.841i	0.918115	−	0.988745i
$86$	48.5673	−	149.475i	0.0608971	−	0.187422i
$87$		0			0
$88$	−166.403	−	512.135i	−0.201575	−	0.620383i
$89$	240.108	−	738.975i	0.285970	−	0.880126i	−0.700136	−	0.714010i	$-0.746877\pi$
$89$	240.108	−	738.975i	0.285970	−	0.880126i	0.986106	−	0.166116i	$-0.0531227\pi$
$90$		0			0
$91$	−270.798	−	833.431i	−0.311949	−	0.960080i
$92$	−560.756	+	407.413i	−0.635466	+	0.461693i
$93$		0			0
$94$	−62.8188	+	45.6405i	−0.0689283	+	0.0500794i
$95$	882.291	−	950.165i	0.952854	−	1.02616i
$96$		0			0
$97$	478.367	+	347.554i	0.500730	+	0.363802i	0.809296	−	0.587401i	$-0.199849\pi$
$97$	478.367	+	347.554i	0.500730	+	0.363802i	−0.308565	+	0.951203i	$0.599849\pi$
$98$	−62.8443	+	193.415i	−0.0647779	+	0.199366i
$99$		0			0
$100$	740.124	+	181.210i	0.740124	+	0.181210i
$101$	−1781.73			−1.75534			−0.877668	−	0.479270i	$-0.840902\pi$
$101$	−1781.73			−1.75534			−0.877668	+	0.479270i	$0.840902\pi$
$102$		0			0
$103$	−300.280	−	218.166i	−0.287257	−	0.208704i	0.434820	−	0.900518i	$-0.356812\pi$
$103$	−300.280	−	218.166i	−0.287257	−	0.208704i	−0.722076	+	0.691813i	$0.756812\pi$
$104$	985.945	+	716.331i	0.929614	+	0.675404i
$105$		0			0
$106$	533.978	−	387.958i	0.489288	−	0.355489i
$107$	−1427.47			−1.28971			−0.644854	−	0.764306i	$-0.723082\pi$
$107$	−1427.47			−1.28971			−0.644854	+	0.764306i	$0.723082\pi$
$108$		0			0
$109$	85.3484	+	262.675i	0.0749991	+	0.230823i	0.981527	−	0.191322i	$-0.0612773\pi$
$109$	85.3484	+	262.675i	0.0749991	+	0.230823i	−0.906528	+	0.422145i	$0.861277\pi$
$110$	387.475	+	179.685i	0.335857	+	0.155748i
$111$		0			0
$112$	−94.7687	−	291.668i	−0.0799536	−	0.246072i
$113$	430.521	+	1325.01i	0.358407	+	1.10306i	0.954007	+	0.299783i	$0.0969143\pi$
$113$	430.521	+	1325.01i	0.358407	+	1.10306i	−0.595600	+	0.803281i	$0.703086\pi$
$114$		0			0
$115$	152.257	−	1262.11i	0.123461	−	1.02341i
$116$	−375.395	−	1155.35i	−0.300470	−	0.924752i
$117$		0			0
$118$	774.337			0.604097
$119$	1070.14	−	777.501i	0.824365	−	0.598936i
$120$		0			0
$121$	456.741	+	331.841i	0.343156	+	0.249317i
$122$	−581.354	−	422.378i	−0.431420	−	0.313445i
$123$		0			0
$124$	−1618.33			−1.17202
$125$	−1167.22	+	768.582i	−0.835196	+	0.549953i
$126$		0			0
$127$	269.996	−	830.961i	0.188648	−	0.580598i	−0.811345	−	0.584568i	$-0.801264\pi$
$127$	269.996	−	830.961i	0.188648	−	0.580598i	0.999992	+	0.00397069i	$0.00126391\pi$
$128$	1112.44	+	808.239i	0.768181	+	0.558116i
$129$		0			0
$130$	−948.473	+	186.448i	−0.639897	+	0.125789i
$131$	−1869.82	+	1358.50i	−1.24707	+	0.906052i	−0.998048	−	0.0624445i	$-0.980110\pi$
$131$	−1869.82	+	1358.50i	−1.24707	+	0.906052i	−0.249026	+	0.968497i	$0.580110\pi$
$132$		0			0
$133$	1312.28	−	953.426i	0.855556	−	0.621598i
$134$	−298.294	−	918.054i	−0.192303	−	0.591849i
$135$		0			0
$136$	−568.456	+	1749.53i	−0.358417	+	1.10309i
$137$	2.56402	+	7.89125i	0.00159897	+	0.00492113i	0.951853	−	0.306555i	$-0.0991765\pi$
$137$	2.56402	+	7.89125i	0.00159897	+	0.00492113i	−0.950254	+	0.311477i	$0.899176\pi$
$138$		0			0
$139$	655.033	−	2015.98i	0.399706	−	1.23017i	−0.525529	−	0.850776i	$-0.676133\pi$
$139$	655.033	−	2015.98i	0.399706	−	1.23017i	0.925235	−	0.379394i	$-0.123867\pi$
$140$	864.772	+	401.024i	0.522047	+	0.242091i
$141$		0			0
$142$	66.0071	−	47.9570i	0.0390084	−	0.0283413i
$143$	1734.58			1.01436
$144$		0			0
$145$	2021.28	+	937.338i	1.15765	+	0.536839i
$146$	−817.813	−	594.176i	−0.463580	−	0.336811i
$147$		0			0
$148$	−536.506	+	1651.20i	−0.297977	+	0.917078i
$149$	2602.21			1.43075			0.715373	−	0.698743i	$-0.246257\pi$
$149$	2602.21			1.43075			0.715373	+	0.698743i	$0.246257\pi$
$150$		0			0
$151$	−635.859			−0.342685			−0.171343	−	0.985211i	$-0.554811\pi$
$151$	−635.859			−0.342685			−0.171343	+	0.985211i	$0.554811\pi$
$152$	−697.080	+	2145.39i	−0.371978	+	1.14483i
$153$		0			0
$154$	432.265	+	314.059i	0.226188	+	0.164335i
$155$	2019.68	−	2175.05i	1.04661	−	1.12712i
$156$		0			0
$157$	−1282.78			−0.652081			−0.326040	−	0.945356i	$-0.605715\pi$
$157$	−1282.78			−0.652081			−0.326040	+	0.945356i	$0.605715\pi$
$158$	265.958	−	193.230i	0.133915	−	0.0972946i
$159$		0			0
$160$	−2039.00	+	400.821i	−1.00748	+	0.198048i
$161$	491.439	−	1512.49i	0.240564	−	0.740380i
$162$		0			0
$163$	127.898	+	393.629i	0.0614584	+	0.189150i	0.977072	−	0.212911i	$-0.0682943\pi$
$163$	127.898	+	393.629i	0.0614584	+	0.189150i	−0.915613	+	0.402060i	$0.868294\pi$
$164$	615.176	−	1893.32i	0.292910	−	0.901483i
$165$		0			0
$166$	−149.048	−	458.721i	−0.0696888	−	0.214480i
$167$	−2674.52	+	1943.15i	−1.23929	+	0.900394i	−0.997551	−	0.0699486i	$-0.977716\pi$
$167$	−2674.52	+	1943.15i	−1.23929	+	0.900394i	−0.241735	+	0.970342i	$0.577716\pi$
$168$		0			0
$169$	−1398.51	+	1016.08i	−0.636553	+	0.462483i
$170$	−710.072	−	1274.63i	−0.320353	−	0.575059i
$171$		0			0
$172$	561.706	+	408.103i	0.249010	+	0.180916i
$173$	−757.000	+	2329.81i	−0.332680	+	1.02388i	0.635173	+	0.772370i	$0.280929\pi$
$173$	−757.000	+	2329.81i	−0.332680	+	1.02388i	−0.967853	+	0.251515i	$0.919071\pi$
$174$		0			0
$175$	−1618.21	+	661.782i	−0.699003	+	0.285863i
$176$	607.035			0.259983
$177$		0			0
$178$	−867.418	−	630.216i	−0.365257	−	0.265375i
$179$	2319.38	+	1685.13i	0.968486	+	0.703646i	0.955106	−	0.296265i	$-0.0957410\pi$
$179$	2319.38	+	1685.13i	0.968486	+	0.703646i	0.0133796	+	0.999910i	$0.495741\pi$
$180$		0			0
$181$	1470.27	−	1068.21i	0.603779	−	0.438671i	−0.243439	−	0.969916i	$-0.578276\pi$
$181$	1470.27	−	1068.21i	0.603779	−	0.438671i	0.847218	+	0.531245i	$0.178276\pi$
$182$	−1209.23			−0.492497
$183$		0			0
$184$	683.442	+	2103.42i	0.273826	+	0.842751i
$185$	−1549.66	−	2781.76i	−0.615855	−	1.10551i
$186$		0			0
$187$	809.088	+	2490.12i	0.316398	+	0.973772i
$188$	−105.999	−	326.233i	−0.0411213	−	0.126558i
$189$		0			0
$190$	−870.740	−	1563.05i	−0.332474	−	0.596817i
$191$	−298.679	−	919.239i	−0.113150	−	0.348240i	0.878407	−	0.477914i	$-0.158607\pi$
$191$	−298.679	−	919.239i	−0.113150	−	0.348240i	−0.991557	+	0.129674i	$0.958607\pi$
$192$		0			0
$193$	−1504.57			−0.561148			−0.280574	−	0.959832i	$-0.590525\pi$
$193$	−1504.57			−0.561148			−0.280574	+	0.959832i	$0.590525\pi$
$194$	660.099	−	479.590i	0.244290	−	0.177487i
$195$		0			0
$196$	−726.826	−	528.070i	−0.264878	−	0.192445i
$197$	640.764	+	465.542i	0.231739	+	0.168368i	0.697595	−	0.716492i	$-0.254254\pi$
$197$	640.764	+	465.542i	0.231739	+	0.168368i	−0.465856	+	0.884860i	$0.654254\pi$
$198$		0			0
$199$	3270.72			1.16510			0.582551	−	0.812794i	$-0.302055\pi$
$199$	3270.72			1.16510			0.582551	+	0.812794i	$0.302055\pi$
$200$	1279.69	−	2067.35i	0.452437	−	0.730917i
$201$		0			0
$202$	−759.752	+	2338.28i	−0.264633	+	0.814458i
$203$	2254.94	+	1638.31i	0.779633	+	0.566437i
$204$		0			0
$205$	1776.89	+	3189.66i	0.605383	+	1.08671i
$206$	−414.356	+	301.047i	−0.140143	+	0.101820i
$207$		0			0
$208$	−1111.45	+	807.513i	−0.370505	+	0.269187i
$209$	992.161	+	3053.56i	0.328369	+	1.01062i
$210$		0			0
$211$	−1098.34	+	3380.33i	−0.358354	+	1.10290i	0.595686	+	0.803218i	$0.296880\pi$
$211$	−1098.34	+	3380.33i	−0.358354	+	1.10290i	−0.954039	+	0.299681i	$0.903120\pi$
$212$	901.027	+	2773.07i	0.291900	+	0.898375i
$213$		0			0
$214$	−608.691	+	1873.36i	−0.194436	+	0.598411i
$215$	−1249.50	+	245.624i	−0.396350	+	0.0779135i
$216$		0			0
$217$	3003.97	−	2182.51i	0.939737	−	0.682759i
$218$	381.119			0.118407
$219$		0			0
$220$	−1283.88	+	1382.65i	−0.393452	+	0.423720i
$221$	−4793.89	−	3482.97i	−1.45915	−	1.06013i
$222$		0			0
$223$	−1769.03	+	5444.53i	−0.531225	+	1.63494i	0.220441	+	0.975400i	$0.429250\pi$
$223$	−1769.03	+	5444.53i	−0.531225	+	1.63494i	−0.751667	+	0.659543i	$0.770750\pi$
$224$	−2599.57			−0.775408
$225$		0			0
$226$	1922.47			0.565844
$227$	397.881	−	1224.55i	0.116336	−	0.358045i	−0.875887	−	0.482516i	$-0.839723\pi$
$227$	397.881	−	1224.55i	0.116336	−	0.358045i	0.992223	+	0.124470i	$0.0397231\pi$
$228$		0			0
$229$	−1106.51	−	803.928i	−0.319303	−	0.231987i	0.416575	−	0.909101i	$-0.363230\pi$
$229$	−1106.51	−	803.928i	−0.319303	−	0.231987i	−0.735878	+	0.677114i	$0.763230\pi$
$230$	−1591.42	−	737.996i	−0.456240	−	0.211574i
$231$		0			0
$232$	−3876.22			−1.09692
$233$	−2138.13	+	1553.45i	−0.601175	+	0.436779i	−0.846296	−	0.532713i	$-0.821172\pi$
$233$	−2138.13	+	1553.45i	−0.601175	+	0.436779i	0.245121	+	0.969493i	$0.421172\pi$
$234$		0			0
$235$	570.746	+	264.674i	0.158431	+	0.0734700i
$236$	−1057.06	+	3253.31i	−0.291564	+	0.897341i
$237$		0			0
$238$	−564.043	−	1735.94i	−0.153620	−	0.472792i
$239$	128.836	−	396.516i	0.0348690	−	0.107316i	−0.932107	−	0.362183i	$-0.882032\pi$
$239$	128.836	−	396.516i	0.0348690	−	0.107316i	0.966976	+	0.254867i	$0.0820316\pi$
$240$		0			0
$241$	331.859	+	1021.36i	0.0887010	+	0.272994i	0.985561	−	0.169321i	$-0.0541575\pi$
$241$	331.859	+	1021.36i	0.0887010	+	0.272994i	−0.896860	+	0.442315i	$0.854157\pi$
$242$	630.256	−	457.908i	0.167415	−	0.121634i
$243$		0			0
$244$	2568.20	−	1865.91i	0.673822	−	0.489560i
$245$	1616.81	−	317.828i	0.421609	−	0.0828787i
$246$		0			0
$247$	−5878.61	−	4271.06i	−1.51436	−	1.10025i
$248$	−1595.70	+	4911.07i	−0.408578	+	1.25747i
$249$		0			0
$250$	510.940	+	1859.55i	0.129259	+	0.470433i
$251$	−3269.53			−0.822194			−0.411097	−	0.911592i	$-0.634854\pi$
$251$	−3269.53			−0.822194			−0.411097	+	0.911592i	$0.634854\pi$
$252$		0			0
$253$	2546.69	+	1850.28i	0.632842	+	0.459787i
$254$	−975.392	−	708.664i	−0.240951	−	0.175061i
$255$		0			0
$256$	2059.69	−	1496.45i	0.502853	−	0.365344i
$257$	2452.88			0.595357			0.297678	−	0.954666i	$-0.403788\pi$
$257$	2452.88			0.595357			0.297678	+	0.954666i	$0.403788\pi$
$258$		0			0
$259$	−1230.97	−	3788.52i	−0.295322	−	0.908909i
$260$	511.435	−	4239.45i	0.121992	−	1.01123i
$261$		0			0
$262$	985.533	+	3033.16i	0.232391	+	0.715226i
$263$	991.490	+	3051.49i	0.232463	+	0.715449i	0.997448	+	0.0714001i	$0.0227467\pi$
$263$	991.490	+	3051.49i	0.232463	+	0.715449i	−0.764984	+	0.644049i	$0.777253\pi$
$264$		0			0
$265$	−4851.51	−	2249.81i	−1.12463	−	0.521527i
$266$	−691.669	−	2128.74i	−0.159432	−	0.490681i
$267$		0			0
$268$	4264.33			0.971961
$269$	5153.23	−	3744.04i	1.16802	−	0.848619i	0.177252	−	0.984165i	$-0.443279\pi$
$269$	5153.23	−	3744.04i	1.16802	−	0.848619i	0.990771	+	0.135547i	$0.0432791\pi$
$270$		0			0
$271$	1631.25	+	1185.17i	0.365651	+	0.265661i	0.755405	−	0.655258i	$-0.227440\pi$
$271$	1631.25	+	1185.17i	0.365651	+	0.265661i	−0.389754	+	0.920919i	$0.627440\pi$
$272$	−1677.67	−	1218.90i	−0.373985	−	0.271716i
$273$		0			0
$274$	11.4495			0.00252441
$275$	−256.007	−	3451.09i	−0.0561374	−	0.756759i
$276$		0			0
$277$	1503.94	−	4628.66i	0.326221	−	1.00400i	−0.644666	−	0.764464i	$-0.723004\pi$
$277$	1503.94	−	4628.66i	0.326221	−	1.00400i	0.970887	−	0.239539i	$-0.0769964\pi$
$278$	−2366.39	−	1719.28i	−0.510527	−	0.370919i
$279$		0			0
$280$	2069.65	−	2228.87i	0.441733	−	0.475716i
$281$	4288.67	−	3115.90i	0.910464	−	0.661491i	−0.0306683	−	0.999530i	$-0.509764\pi$
$281$	4288.67	−	3115.90i	0.910464	−	0.661491i	0.941132	+	0.338039i	$0.109764\pi$
$282$		0			0
$283$	−477.121	+	346.649i	−0.100219	+	0.0728132i	−0.636766	−	0.771057i	$-0.719728\pi$
$283$	−477.121	+	346.649i	−0.100219	+	0.0728132i	0.536547	+	0.843870i	$0.319728\pi$
$284$	111.379	+	342.791i	0.0232717	+	0.0716228i
$285$		0			0
$286$	739.646	−	2276.40i	0.152924	−	0.470651i
$287$	1411.47	+	4344.05i	0.290300	+	0.893453i
$288$		0			0
$289$	1245.76	−	3834.07i	0.253565	−	0.780392i
$290$	2092.03	−	2252.96i	0.423614	−	0.456202i
$291$		0			0
$292$	3612.80	−	2624.85i	0.724051	−	0.526054i
$293$	5328.13			1.06236			0.531182	−	0.847258i	$-0.321748\pi$
$293$	5328.13			1.06236			0.531182	+	0.847258i	$0.321748\pi$
$294$		0			0
$295$	−3053.25	−	5480.83i	−0.602601	−	1.08172i
$296$	4481.81	+	3256.22i	0.880067	+	0.639406i
$297$		0			0
$298$	1109.61	−	3415.04i	0.215698	−	0.663852i
$299$	−7124.20			−1.37794
$300$		0			0
$301$	−1593.02			−0.305051
$302$	−271.138	+	834.477i	−0.0516631	+	0.159003i
$303$		0			0
$304$	−2057.28	−	1494.70i	−0.388136	−	0.281997i
$305$	−697.322	+	5780.34i	−0.130913	+	1.08518i
$306$		0			0
$307$	3716.68			0.690952			0.345476	−	0.938428i	$-0.387717\pi$
$307$	3716.68			0.690952			0.345476	+	0.938428i	$0.387717\pi$
$308$	−1909.59	+	1387.40i	−0.353276	+	0.256670i
$309$		0			0
$310$	−1993.23	−	3578.01i	−0.365187	−	0.655540i
$311$	1016.45	−	3128.32i	0.185330	−	0.570388i	−0.814624	−	0.579990i	$-0.803056\pi$
$311$	1016.45	−	3128.32i	0.185330	−	0.570388i	0.999954	+	0.00960189i	$0.00305642\pi$
$312$		0			0
$313$	−565.534	−	1740.54i	−0.102127	−	0.314316i	0.886918	−	0.461927i	$-0.152842\pi$
$313$	−565.534	−	1740.54i	−0.102127	−	0.314316i	−0.989046	+	0.147611i	$0.952842\pi$
$314$	−546.991	+	1683.47i	−0.0983074	+	0.302559i
$315$		0			0
$316$	448.774	+	1381.18i	0.0798908	+	0.245879i
$317$	−3830.09	+	2782.73i	−0.678610	+	0.493039i	−0.872896	−	0.487906i	$-0.837761\pi$
$317$	−3830.09	+	2782.73i	−0.678610	+	0.493039i	0.194286	+	0.980945i	$0.437761\pi$
$318$		0			0
$319$	−4463.40	+	3242.85i	−0.783392	+	0.569168i
$320$	−108.542	+	899.742i	−0.0189615	+	0.157179i
$321$		0			0
$322$	−1775.38	−	1289.89i	−0.307262	−	0.223239i
$323$	3389.37	−	10431.4i	0.583868	−	1.79696i
$324$		0			0
$325$	5059.58	+	5978.20i	0.863554	+	1.02034i
$326$	571.120			0.0970289
$327$		0			0
$328$	−5138.99	−	3733.70i	−0.865101	−	0.628533i
$329$	636.722	+	462.606i	0.106698	+	0.0775206i
$330$		0			0
$331$	−3430.48	+	2492.39i	−0.569656	+	0.413879i	−0.834980	−	0.550280i	$-0.814521\pi$
$331$	−3430.48	+	2492.39i	−0.569656	+	0.413879i	0.265324	+	0.964159i	$0.414521\pi$
$332$	2130.75			0.352229
$333$		0			0
$334$	1409.67	+	4338.52i	0.230940	+	0.710759i
$335$	−5321.88	+	5731.29i	−0.867957	+	0.934728i
$336$		0			0
$337$	−152.626	−	469.735i	−0.0246709	−	0.0759291i	0.937963	−	0.346735i	$-0.112710\pi$
$337$	−152.626	−	469.735i	−0.0246709	−	0.0759291i	−0.962634	+	0.270806i	$0.912710\pi$
$338$	737.118	+	2268.61i	0.118621	+	0.365078i
$339$		0			0
$340$	6324.60	−	1243.27i	1.00882	−	0.198312i
$341$	2271.18	+	6989.97i	0.360678	+	1.11005i
$342$		0			0
$343$	6858.66			1.07969
$344$	1792.30	−	1302.19i	0.280914	−	0.204096i
$345$		0			0
$346$	2734.76	+	1986.92i	0.424917	+	0.308721i
$347$	−5680.75	−	4127.31i	−0.878844	−	0.638517i	0.0541015	−	0.998535i	$-0.482771\pi$
$347$	−5680.75	−	4127.31i	−0.878844	−	0.638517i	−0.932945	+	0.360018i	$0.882771\pi$
$348$		0			0
$349$	9562.87			1.46673			0.733365	−	0.679835i	$-0.237949\pi$
$349$	9562.87			1.46673			0.733365	+	0.679835i	$0.237949\pi$
$350$	178.471	+	2405.87i	0.0272562	+	0.367427i
$351$		0			0
$352$	1590.07	−	4893.73i	0.240770	−	0.741013i
$353$	−1305.15	−	948.244i	−0.196787	−	0.142974i	0.485028	−	0.874498i	$-0.338809\pi$
$353$	−1305.15	−	948.244i	−0.196787	−	0.142974i	−0.681816	+	0.731524i	$0.738809\pi$
$354$		0			0
$355$	−599.714	−	278.108i	−0.0896606	−	0.0415787i
$356$	3831.93	−	2784.06i	0.570483	−	0.414480i
$357$		0			0
$358$	3200.51	−	2325.31i	0.472493	−	0.343286i
$359$	2375.00	+	7309.50i	0.349158	+	1.07460i	0.959320	+	0.282321i	$0.0911044\pi$
$359$	2375.00	+	7309.50i	0.349158	+	1.07460i	−0.610162	+	0.792277i	$0.708896\pi$
$360$		0			0
$361$	2036.73	−	6268.42i	0.296943	−	0.913896i
$362$	−774.940	−	2385.02i	−0.112514	−	0.346281i
$363$		0			0
$364$	1650.75	−	5080.49i	0.237700	−	0.731566i
$365$	−980.951	+	8131.43i	−0.140672	+	1.16608i
$366$		0			0
$367$	−6425.12	+	4668.12i	−0.913865	+	0.663961i	−0.941989	−	0.335643i	$-0.891046\pi$
$367$	−6425.12	+	4668.12i	−0.913865	+	0.663961i	0.0281247	+	0.999604i	$0.491046\pi$
$368$	−2493.19			−0.353170
$369$		0			0
$370$	−4311.47	+	847.537i	−0.605791	+	0.119085i
$371$	−5412.32	−	3932.28i	−0.757396	−	0.550280i
$372$		0			0
$373$	−3174.37	+	9769.71i	−0.440651	+	1.35618i	0.446533	+	0.894767i	$0.352659\pi$
$373$	−3174.37	+	9769.71i	−0.440651	+	1.35618i	−0.887184	+	0.461417i	$0.847341\pi$
$374$	3612.94			0.499520
$375$		0			0
$376$	−1094.52			−0.150121
$377$	3858.40	−	11874.9i	0.527103	−	1.62226i
$378$		0			0
$379$	−9272.49	−	6736.86i	−1.25672	−	0.913059i	−0.258126	−	0.966111i	$-0.583105\pi$
$379$	−9272.49	−	6736.86i	−1.25672	−	0.913059i	−0.998592	+	0.0530524i	$0.983105\pi$
$380$	7755.67	−	1524.59i	1.04699	−	0.205815i
$381$		0			0
$382$	−1333.73			−0.178638
$383$	3116.57	−	2264.32i	0.415795	−	0.302092i	−0.360149	−	0.932895i	$-0.617274\pi$
$383$	3116.57	−	2264.32i	0.415795	−	0.302092i	0.775944	+	0.630802i	$0.217274\pi$
$384$		0			0
$385$	518.494	−	4297.97i	0.0686361	−	0.568948i
$386$	−641.568	+	1974.54i	−0.0845984	+	0.260367i
$387$		0			0
$388$	1113.84	+	3428.05i	0.145739	+	0.448538i
$389$	2243.60	−	6905.09i	0.292429	−	0.900005i	−0.691644	−	0.722239i	$-0.743113\pi$
$389$	2243.60	−	6905.09i	0.292429	−	0.900005i	0.984073	−	0.177766i	$-0.0568869\pi$
$390$		0			0
$391$	−3323.05	−	10227.3i	−0.429806	−	1.32281i
$392$	−2319.18	+	1684.98i	−0.298817	+	0.217103i
$393$		0			0
$394$	884.189	−	642.401i	0.113058	−	0.0821414i
$395$	−2416.39	−	1120.56i	−0.307802	−	0.142738i
$396$		0			0
$397$	5893.38	+	4281.79i	0.745039	+	0.541302i	0.894285	−	0.447498i	$-0.147685\pi$
$397$	5893.38	+	4281.79i	0.745039	+	0.541302i	−0.149246	+	0.988800i	$0.547685\pi$
$398$	1394.67	−	4292.37i	0.175650	−	0.540595i
$399$		0			0
$400$	1770.65	+	2092.14i	0.221332	+	0.261517i
$401$	793.134			0.0987711			0.0493856	−	0.998780i	$-0.484274\pi$
$401$	793.134			0.0987711			0.0493856	+	0.998780i	$0.484274\pi$
$402$		0			0
$403$	−13456.9	−	9776.99i	−1.66336	−	1.20850i
$404$	−8786.91	−	6384.06i	−1.08209	−	0.786186i
$405$		0			0
$406$	3111.58	−	2260.70i	0.380358	−	0.276346i
$407$	7884.87			0.960291
$408$		0			0
$409$	1761.04	+	5419.93i	0.212905	+	0.655253i	0.999296	+	0.0375240i	$0.0119471\pi$
$409$	1761.04	+	5419.93i	0.212905	+	0.655253i	−0.786391	+	0.617729i	$0.788053\pi$
$410$	4943.67	−	971.815i	0.595490	−	0.117060i
$411$		0			0
$412$	−699.177	−	2151.85i	−0.0836068	−	0.257315i
$413$	−2425.34	−	7464.43i	−0.288966	−	0.889347i
$414$		0			0
$415$	−2659.17	+	2863.74i	−0.314539	+	0.338736i
$416$	3598.60	+	11075.3i	0.424124	+	1.30532i
$417$		0			0
$418$	4430.44			0.518421
$419$	−11029.1	+	8013.13i	−1.28594	+	0.934289i	−0.999715	−	0.0238738i	$-0.992400\pi$
$419$	−11029.1	+	8013.13i	−1.28594	+	0.934289i	−0.286224	+	0.958163i	$0.592400\pi$
$420$		0			0
$421$	5536.49	+	4022.50i	0.640931	+	0.465664i	0.860170	−	0.510007i	$-0.170357\pi$
$421$	5536.49	+	4022.50i	0.640931	+	0.465664i	−0.219239	+	0.975671i	$0.570357\pi$
$422$	3967.87	+	2882.83i	0.457709	+	0.332545i
$423$		0			0
$424$	9303.75			1.06564
$425$	−6222.13	+	10051.9i	−0.710159	+	1.14727i
$426$		0			0
$427$	−2250.74	+	6927.06i	−0.255084	+	0.785068i
$428$	−7039.81	−	5114.72i	−0.795052	−	0.577639i
$429$		0			0
$430$	−210.455	+	1744.53i	−0.0236025	+	0.195649i
$431$	−4408.94	+	3203.28i	−0.492741	+	0.357997i	−0.806237	−	0.591592i	$-0.798500\pi$
$431$	−4408.94	+	3203.28i	−0.492741	+	0.357997i	0.313497	+	0.949589i	$0.398500\pi$
$432$		0			0
$433$	−3891.33	+	2827.21i	−0.431883	+	0.313781i	−0.782401	−	0.622775i	$-0.786005\pi$
$433$	−3891.33	+	2827.21i	−0.431883	+	0.313781i	0.350519	+	0.936556i	$0.386005\pi$
$434$	−1583.32	−	4872.95i	−0.175119	−	0.538961i
$435$		0			0
$436$	−520.274	+	1601.24i	−0.0571482	+	0.175884i
$437$	−4074.96	−	12541.4i	−0.446068	−	1.37286i
$438$		0			0
$439$	−4451.87	+	13701.4i	−0.484000	+	1.48960i	0.349424	+	0.936965i	$0.386377\pi$
$439$	−4451.87	+	13701.4i	−0.484000	+	1.48960i	−0.833424	+	0.552634i	$0.813623\pi$
$440$	2929.93	+	5259.46i	0.317453	+	0.569852i
$441$		0			0
$442$	−6615.09	+	4806.14i	−0.711873	+	0.517206i
$443$	−12023.5			−1.28951			−0.644756	−	0.764389i	$-0.723041\pi$
$443$	−12023.5			−1.28951			−0.644756	+	0.764389i	$0.723041\pi$
$444$		0			0
$445$	−1040.45	+	8624.64i	−0.110836	+	0.918758i
$446$	6390.85	+	4643.22i	0.678510	+	0.492966i
$447$		0			0
$448$	−350.340	+	1078.24i	−0.0369465	+	0.113710i
$449$	−10740.5			−1.12889			−0.564447	−	0.825469i	$-0.690910\pi$
$449$	−10740.5			−1.12889			−0.564447	+	0.825469i	$0.690910\pi$
$450$		0			0
$451$	−9041.06			−0.943962
$452$	−2624.40	+	8077.09i	−0.273101	+	0.840518i
$453$		0			0
$454$	−1437.39	−	1044.33i	−0.148591	−	0.107957i
$455$	4768.08	+	8559.07i	0.491277	+	0.881880i
$456$		0			0
$457$	5957.31			0.609783			0.304892	−	0.952387i	$-0.401380\pi$
$457$	5957.31			0.609783			0.304892	+	0.952387i	$0.401380\pi$
$458$	−1526.87	+	1109.34i	−0.155778	+	0.113179i
$459$		0			0
$460$	5273.11	−	5678.77i	0.534479	−	0.575596i
$461$	−3710.77	+	11420.6i	−0.374898	+	1.15382i	0.568650	+	0.822580i	$0.307466\pi$
$461$	−3710.77	+	11420.6i	−0.374898	+	1.15382i	−0.943548	+	0.331237i	$0.892534\pi$
$462$		0			0
$463$	−2488.82	−	7659.79i	−0.249817	−	0.768856i	−0.994807	−	0.101781i	$-0.967546\pi$
$463$	−2488.82	−	7659.79i	−0.249817	−	0.768856i	0.744990	−	0.667075i	$-0.232454\pi$
$464$	1350.29	−	4155.76i	0.135098	−	0.415790i
$465$		0			0
$466$	1126.96	+	3468.41i	0.112028	+	0.344788i
$467$	15143.7	−	11002.5i	1.50057	−	1.09023i	0.530415	−	0.847738i	$-0.322036\pi$
$467$	15143.7	−	11002.5i	1.50057	−	1.09023i	0.970154	−	0.242490i	$-0.0779640\pi$
$468$		0			0
$469$	−7915.52	+	5750.96i	−0.779328	+	0.566215i
$470$	590.721	−	636.165i	0.0579743	−	0.0624343i
$471$		0			0
$472$	8830.39	+	6415.65i	0.861126	+	0.625645i
$473$	974.396	−	2998.88i	0.0947204	−	0.291520i
$474$		0			0
$475$	−7630.01	+	12326.4i	−0.737030	+	1.19068i
$476$	8063.41			0.776441
$477$		0			0
$478$	−465.435	−	338.159i	−0.0445366	−	0.0323578i
$479$	11883.0	+	8633.47i	1.13350	+	0.823535i	0.986200	−	0.165557i	$-0.0529422\pi$
$479$	11883.0	+	8633.47i	1.13350	+	0.823535i	0.147299	+	0.989092i	$0.452942\pi$
$480$		0			0
$481$	−14436.8	+	10488.9i	−1.36852	+	0.994290i
$482$	1481.90			0.140039
$483$		0			0
$484$	1063.48	+	3273.07i	0.0998763	+	0.307388i
$485$	−5997.39	−	2781.19i	−0.561500	−	0.260386i
$486$		0			0
$487$	1129.41	+	3475.96i	0.105089	+	0.323430i	0.989751	−	0.142802i	$-0.0456112\pi$
$487$	1129.41	+	3475.96i	0.105089	+	0.323430i	−0.884662	+	0.466232i	$0.845611\pi$
$488$	−3130.09	−	9633.44i	−0.290354	−	0.893617i
$489$		0			0
$490$	272.321	−	2257.36i	0.0251066	−	0.208117i
$491$	−3658.40	−	11259.4i	−0.336255	−	1.03489i	−0.966101	−	0.258166i	$-0.916882\pi$
$491$	−3658.40	−	11259.4i	−0.336255	−	1.03489i	0.629846	−	0.776720i	$-0.283118\pi$
$492$		0			0
$493$	18847.1			1.72177
$494$	−8111.89	+	5893.63i	−0.738808	+	0.536775i
$495$		0			0
$496$	−4709.38	−	3421.56i	−0.426325	−	0.309743i
$497$	−669.039	−	486.085i	−0.0603833	−	0.0438710i
$498$		0			0
$499$	−11497.8			−1.03149			−0.515744	−	0.856743i	$-0.672484\pi$
$499$	−11497.8			−1.03149			−0.515744	+	0.856743i	$0.672484\pi$
$500$	−8510.24	−	391.842i	−0.761179	−	0.0350474i
$501$		0			0
$502$	−1394.17	+	4290.80i	−0.123953	+	0.381490i
$503$	−2539.40	−	1844.98i	−0.225102	−	0.163546i	0.469518	−	0.882923i	$-0.344428\pi$
$503$	−2539.40	−	1844.98i	−0.225102	−	0.163546i	−0.694620	+	0.719377i	$0.744428\pi$
$504$		0			0
$505$	19546.3	−	3842.36i	1.72237	−	0.338579i
$506$	3514.17	−	2553.20i	0.308743	−	0.224315i
$507$		0			0
$508$	4308.92	−	3130.61i	0.376334	−	0.273422i
$509$	4595.77	+	14144.3i	0.400204	+	1.23170i	0.924834	+	0.380372i	$0.124204\pi$
$509$	4595.77	+	14144.3i	0.400204	+	1.23170i	−0.524629	+	0.851331i	$0.675796\pi$
$510$		0			0
$511$	−3166.21	+	9744.58i	−0.274099	+	0.843591i
$512$	2313.72	+	7120.90i	0.199713	+	0.614653i
$513$		0			0
$514$	1045.94	−	3219.07i	0.0897557	−	0.276240i
$515$	3764.67	+	1745.80i	0.322119	+	0.149377i
$516$		0			0
$517$	−1260.32	+	915.676i	−0.107212	+	0.0778944i
$518$	−5496.81			−0.466247
$519$		0			0
$520$	−12361.0	−	5732.21i	−1.04243	−	0.483412i
$521$	14314.4	+	10400.0i	1.20370	+	0.874538i	0.994643	−	0.103366i	$-0.0329611\pi$
$521$	14314.4	+	10400.0i	1.20370	+	0.874538i	0.209055	+	0.977904i	$0.432961\pi$
$522$		0			0
$523$	−6931.04	+	21331.5i	−0.579490	+	1.78349i	0.0408650	+	0.999165i	$0.486989\pi$
$523$	−6931.04	+	21331.5i	−0.579490	+	1.78349i	−0.620355	+	0.784321i	$0.713011\pi$
$524$	−14088.9			−1.17458
$525$		0			0
$526$	4427.44			0.367007
$527$	7758.69	−	23878.8i	0.641316	−	1.97377i
$528$		0			0
$529$	−616.356	−	447.809i	−0.0506580	−	0.0368052i
$530$	−5021.31	+	5407.59i	−0.411531	+	0.443190i
$531$		0			0
$532$	9887.92			0.805819
$533$	16553.7	−	12026.9i	1.34525	−	0.977382i
$534$		0			0
$535$	15659.9	−	3078.38i	1.26549	−	0.248767i
$536$	4204.71	−	12940.8i	0.338836	−	1.04283i
$537$		0			0
$538$	−2716.14	−	8359.41i	−0.217660	−	0.669888i
$539$	−1260.83	+	3880.44i	−0.100757	+	0.310098i
$540$		0			0
$541$	3503.70	+	10783.3i	0.278440	+	0.856950i	0.988289	+	0.152596i	$0.0487633\pi$
$541$	3503.70	+	10783.3i	0.278440	+	0.856950i	−0.709849	+	0.704354i	$0.751237\pi$
$542$	2250.96	−	1635.42i	0.178389	−	0.129607i
$543$		0			0
$544$	−14220.9	+	10332.1i	−1.12080	+	0.814311i
$545$	−1502.77	−	2697.60i	−0.118113	−	0.212023i
$546$		0			0
$547$	−9244.76	−	6716.71i	−0.722627	−	0.525020i	0.164595	−	0.986361i	$-0.447368\pi$
$547$	−9244.76	−	6716.71i	−0.722627	−	0.525020i	−0.887223	+	0.461342i	$0.847368\pi$
$548$	−15.6300	+	48.1041i	−0.00121839	+	0.00374983i
$549$		0			0
$550$	−4638.25	−	1135.62i	−0.359592	−	0.0880414i
$551$	23111.6			1.78691
$552$		0			0
$553$	−2695.71	−	1958.55i	−0.207294	−	0.150608i
$554$	−5433.17	−	3947.43i	−0.416667	−	0.302726i
$555$		0			0
$556$	10453.8	−	7595.14i	0.797375	−	0.579327i
$557$	1742.79			0.132575			0.0662875	−	0.997801i	$-0.478885\pi$
$557$	1742.79			0.132575			0.0662875	+	0.997801i	$0.478885\pi$
$558$		0			0
$559$	2205.22	+	6786.98i	0.166853	+	0.513522i
$560$	1668.64	+	2995.34i	0.125916	+	0.226029i
$561$		0			0
$562$	−2260.45	−	6956.94i	−0.169664	−	0.522172i
$563$	−1390.29	−	4278.88i	−0.104074	−	0.320308i	0.885438	−	0.464758i	$-0.153859\pi$
$563$	−1390.29	−	4278.88i	−0.104074	−	0.320308i	−0.989512	+	0.144450i	$0.953859\pi$
$564$		0			0
$565$	−7580.40	−	13607.4i	−0.564442	−	1.01322i
$566$	251.478	+	773.971i	0.0186757	+	0.0574778i
$567$		0			0
$568$	1150.07			0.0849578
$569$	−4717.52	+	3427.48i	−0.347573	+	0.252526i	−0.747850	−	0.663868i	$-0.768914\pi$
$569$	−4717.52	+	3427.48i	−0.347573	+	0.252526i	0.400277	+	0.916394i	$0.368914\pi$
$570$		0			0
$571$	−21104.6	−	15333.4i	−1.54676	−	1.12379i	−0.945910	−	0.324430i	$-0.894827\pi$
$571$	−21104.6	−	15333.4i	−1.54676	−	1.12379i	−0.600854	−	0.799359i	$-0.705173\pi$
$572$	8554.37	+	6215.12i	0.625308	+	0.454313i
$573$		0			0
$574$	6302.83			0.458319
$575$	1051.46	+	14174.2i	0.0762590	+	1.02801i
$576$		0			0
$577$	691.064	−	2126.88i	0.0498603	−	0.153454i	−0.923026	−	0.384737i	$-0.874292\pi$
$577$	691.064	−	2126.88i	0.0498603	−	0.153454i	0.972887	+	0.231283i	$0.0742922\pi$
$578$	−4500.47	−	3269.78i	−0.323867	−	0.235303i
$579$		0			0
$580$	6609.76	+	11865.0i	0.473199	+	0.849429i
$581$	−3955.13	+	2873.57i	−0.282420	+	0.205190i
$582$		0			0
$583$	10713.1	−	7783.52i	0.761048	−	0.552934i
$584$	−4403.23	−	13551.7i	−0.311998	−	0.960231i
$585$		0			0
$586$	2271.98	−	6992.43i	0.160161	−	0.492926i
$587$	3302.89	+	10165.2i	0.232240	+	0.714761i	0.997476	+	0.0710105i	$0.0226224\pi$
$587$	3302.89	+	10165.2i	0.232240	+	0.714761i	−0.765236	+	0.643750i	$0.777378\pi$
$588$		0			0
$589$	9514.25	−	29281.8i	0.665582	−	2.04845i
$590$	−8494.77	+	1669.88i	−0.592753	+	0.116522i
$591$		0			0
$592$	−5052.30	+	3670.71i	−0.350757	+	0.254840i
$593$	3071.33			0.212689			0.106344	−	0.994329i	$-0.466085\pi$
$593$	3071.33			0.212689			0.106344	+	0.994329i	$0.466085\pi$
$594$		0			0
$595$	−10063.1	+	10837.3i	−0.693358	+	0.746697i
$596$	12833.2	+	9323.89i	0.881996	+	0.640808i
$597$		0			0
$598$	−3037.84	+	9349.52i	−0.207737	+	0.639348i
$599$	−19658.8			−1.34097			−0.670483	−	0.741925i	$-0.733913\pi$
$599$	−19658.8			−1.34097			−0.670483	+	0.741925i	$0.733913\pi$
$600$		0			0
$601$	24937.5			1.69255			0.846276	−	0.532745i	$-0.178840\pi$
$601$	24937.5			1.69255			0.846276	+	0.532745i	$0.178840\pi$
$602$	−679.284	+	2090.62i	−0.0459893	+	0.141541i
$603$		0			0
$604$	−3135.85	−	2278.33i	−0.211251	−	0.153483i
$605$	−5726.25	−	2655.45i	−0.384802	−	0.178446i
$606$		0			0
$607$	−6767.35			−0.452518			−0.226259	−	0.974067i	$-0.572650\pi$
$607$	−6767.35			−0.452518			−0.226259	+	0.974067i	$0.572650\pi$
$608$	−17438.7	+	12669.9i	−1.16321	+	0.845122i
$609$		0			0
$610$	7288.55	+	3379.94i	0.483778	+	0.224344i
$611$	1089.49	−	3353.10i	0.0721375	−	0.222016i
$612$		0			0
$613$	−7732.44	−	23798.0i	−0.509478	−	1.56801i	−0.793109	−	0.609080i	$-0.791539\pi$
$613$	−7732.44	−	23798.0i	−0.509478	−	1.56801i	0.283631	−	0.958934i	$-0.408461\pi$
$614$	1584.84	−	4877.63i	0.104168	−	0.320595i
$615$		0			0
$616$	2327.38	+	7162.94i	0.152229	+	0.468512i
$617$	8292.13	−	6024.59i	0.541051	−	0.393097i	−0.283424	−	0.958995i	$-0.591470\pi$
$617$	8292.13	−	6024.59i	0.541051	−	0.393097i	0.824475	+	0.565898i	$0.191470\pi$
$618$		0			0
$619$	1384.10	−	1005.60i	0.0898732	−	0.0652967i	−0.541941	−	0.840416i	$-0.682310\pi$
$619$	1384.10	−	1005.60i	0.0898732	−	0.0652967i	0.631814	+	0.775120i	$0.282310\pi$
$620$	17753.7	−	3489.98i	1.15001	−	0.226066i
$621$		0			0
$622$	−3672.06	−	2667.91i	−0.236714	−	0.171983i
$623$	−3358.25	+	10335.6i	−0.215964	+	0.664669i
$624$		0			0
$625$	11147.4	−	10948.8i	0.713434	−	0.700723i
$626$	−2525.36			−0.161236
$627$		0			0
$628$	−6326.23	−	4596.28i	−0.401981	−	0.292056i
$629$	−21791.6	−	15832.5i	−1.38138	−	1.00363i
$630$		0			0
$631$	132.282	−	96.1083i	0.00834557	−	0.00606341i	−0.583605	−	0.812038i	$-0.698358\pi$
$631$	132.282	−	96.1083i	0.00834557	−	0.00606341i	0.591950	+	0.805975i	$0.298358\pi$
$632$	4633.91			0.291657
$633$		0			0
$634$	2018.74	+	6213.05i	0.126458	+	0.389199i
$635$	−1169.96	+	9698.22i	−0.0731159	+	0.606082i
$636$		0			0
$637$	−2853.48	−	8782.11i	−0.177487	−	0.546248i
$638$	2352.54	+	7240.38i	0.145984	+	0.449294i
$639$		0			0
$640$	−13946.9	−	6467.67i	−0.861408	−	0.399464i
$641$	−902.479	−	2777.55i	−0.0556097	−	0.171149i	0.919394	−	0.393338i	$-0.128680\pi$
$641$	−902.479	−	2777.55i	−0.0556097	−	0.171149i	−0.975004	+	0.222189i	$0.928680\pi$
$642$		0			0
$643$	13783.9			0.845387			0.422693	−	0.906273i	$-0.361085\pi$
$643$	13783.9			0.845387			0.422693	+	0.906273i	$0.361085\pi$
$644$	7842.99	−	5698.26i	0.479902	−	0.348669i
$645$		0			0
$646$	−12244.5	−	8896.15i	−0.745748	−	0.541818i
$647$	−15672.0	−	11386.4i	−0.952288	−	0.691878i	−0.000941137	−	1.00000i	$-0.500300\pi$
$647$	−15672.0	−	11386.4i	−0.952288	−	0.691878i	−0.951347	+	0.308122i	$0.900300\pi$
$648$		0			0
$649$	15535.4			0.939624
$650$	10003.0	−	4090.82i	0.603617	−	0.246854i
$651$		0			0
$652$	−779.649	+	2399.51i	−0.0468304	+	0.144129i
$653$	21129.9	+	15351.8i	1.26628	+	0.920003i	0.999048	−	0.0436299i	$-0.0138922\pi$
$653$	21129.9	+	15351.8i	1.26628	+	0.920003i	0.267228	+	0.963633i	$0.413892\pi$
$654$		0			0
$655$	17583.0	−	18935.6i	1.04889	−	1.12958i
$656$	5793.13	−	4208.96i	0.344792	−	0.250506i
$657$		0			0
$658$	878.612	−	638.349i	0.0520545	−	0.0378198i
$659$	1860.77	+	5726.87i	0.109993	+	0.338524i	0.990870	−	0.134822i	$-0.0430462\pi$
$659$	1860.77	+	5726.87i	0.109993	+	0.338524i	−0.880877	+	0.473346i	$0.843046\pi$
$660$		0			0
$661$	7585.96	−	23347.2i	0.446384	−	1.37383i	−0.434575	−	0.900636i	$-0.643101\pi$
$661$	7585.96	−	23347.2i	0.446384	−	1.37383i	0.880959	−	0.473193i	$-0.156899\pi$
$662$	1808.12	+	5564.81i	0.106155	+	0.326711i
$663$		0			0
$664$	2100.96	−	6466.08i	0.122791	−	0.377910i
$665$	−12340.1	+	13289.4i	−0.719593	+	0.774950i
$666$		0			0
$667$	18331.9	−	13318.9i	1.06419	−	0.773178i
$668$	−20152.3			−1.16724
$669$		0			0
$670$	5252.21	+	9428.12i	0.302851	+	0.543642i
$671$	−11663.6	−	8474.08i	−0.671039	−	0.487538i
$672$		0			0
$673$	−8704.24	+	26788.9i	−0.498549	+	1.53438i	0.312802	+	0.949818i	$0.398732\pi$
$673$	−8704.24	+	26788.9i	−0.498549	+	1.53438i	−0.811351	+	0.584559i	$0.801268\pi$
$674$	−681.544			−0.0389497
$675$		0			0
$676$	−10537.6			−0.599547
$677$	3068.34	−	9443.37i	0.174189	−	0.536098i	−0.825407	−	0.564538i	$-0.809054\pi$
$677$	3068.34	−	9443.37i	0.174189	−	0.536098i	0.999595	+	0.0284408i	$0.00905422\pi$
$678$		0			0
$679$	−6690.66	−	4861.05i	−0.378150	−	0.274742i
$680$	2463.27	−	20418.9i	0.138915	−	1.15151i
$681$		0			0
$682$	10141.8			0.569429
$683$	9594.74	−	6970.99i	0.537529	−	0.390538i	−0.285637	−	0.958338i	$-0.592205\pi$
$683$	9594.74	−	6970.99i	0.537529	−	0.390538i	0.823167	+	0.567800i	$0.192205\pi$
$684$		0			0
$685$	−45.1460	−	81.0407i	−0.00251816	−	0.00452030i
$686$	2924.62	−	9001.05i	0.162773	−	0.500964i
$687$		0			0
$688$	771.742	+	2375.18i	0.0427651	+	0.131617i
$689$	−9260.98	+	28502.4i	−0.512069	+	1.57599i
$690$		0			0
$691$	−246.557	−	758.826i	−0.0135738	−	0.0417758i	0.944040	−	0.329830i	$-0.106992\pi$
$691$	−246.557	−	758.826i	−0.0135738	−	0.0417758i	−0.957614	+	0.288055i	$0.906992\pi$
$692$	−12081.1	+	8777.46i	−0.663665	+	0.482181i
$693$		0			0
$694$	−7838.86	+	5695.27i	−0.428760	+	0.311512i
$695$	−2838.43	+	23528.7i	−0.154918	+	1.28417i
$696$		0			0
$697$	24987.0	+	18154.1i	1.35789	+	0.986564i
$698$	4077.72	−	12549.9i	0.221123	−	0.680548i
$699$		0			0
$700$	−10351.7	−	2534.48i	−0.558940	−	0.136849i
$701$	−18597.0			−1.00199			−0.500997	−	0.865449i	$-0.667033\pi$
$701$	−18597.0			−1.00199			−0.500997	+	0.865449i	$0.667033\pi$
$702$		0			0
$703$	−26722.4	−	19414.9i	−1.43365	−	1.04161i
$704$	−1815.50	−	1319.04i	−0.0971936	−	0.0706153i
$705$		0			0
$706$	−1800.97	+	1308.48i	−0.0960062	+	0.0697526i
$707$	24920.1			1.32562
$708$		0			0
$709$	8099.16	+	24926.7i	0.429013	+	1.32037i	0.899099	+	0.437746i	$0.144223\pi$
$709$	8099.16	+	24926.7i	0.429013	+	1.32037i	−0.470086	+	0.882621i	$0.655777\pi$
$710$	−620.703	+	668.453i	−0.0328093	+	0.0353332i
$711$		0			0
$712$	−4670.31	−	14373.7i	−0.245825	−	0.756570i
$713$	−9328.10	−	28708.9i	−0.489958	−	1.50794i
$714$		0			0
$715$	−19029.0	+	3740.67i	−0.995307	+	0.195655i
$716$	5400.50	+	16621.0i	0.281880	+	0.867537i
$717$		0			0
$718$	10605.4			0.551241
$719$	16782.5	−	12193.2i	0.870491	−	0.632449i	−0.0602273	−	0.998185i	$-0.519183\pi$
$719$	16782.5	−	12193.2i	0.870491	−	0.632449i	0.930719	+	0.365736i	$0.119183\pi$
$720$		0			0
$721$	4199.85	+	3051.37i	0.216936	+	0.157613i
$722$	−7357.94	−	5345.86i	−0.379272	−	0.275557i
$723$		0			0
$724$	11078.3			0.568679
$725$	−24195.7	−	5924.00i	−1.23945	−	0.303465i
$726$		0			0
$727$	−3452.87	+	10626.8i	−0.176148	+	0.542129i	−0.999684	−	0.0251356i	$-0.991998\pi$
$727$	−3452.87	+	10626.8i	−0.176148	+	0.542129i	0.823536	+	0.567264i	$0.191998\pi$
$728$	−13789.9	−	10018.9i	−0.702042	−	0.510063i
$729$		0			0
$730$	10253.1	+	4754.70i	0.519841	+	0.241068i
$731$	−8714.60	+	6331.53i	−0.440932	+	0.320356i
$732$		0			0
$733$	22875.9	−	16620.3i	1.15272	−	0.837499i	0.163878	−	0.986481i	$-0.447600\pi$
$733$	22875.9	−	16620.3i	1.15272	−	0.837499i	0.988840	+	0.148982i	$0.0475996\pi$
$734$	3386.51	+	10422.6i	0.170298	+	0.524122i
$735$		0			0
$736$	−6530.66	+	20099.3i	−0.327070	+	1.00662i
$737$	−5984.60	−	18418.7i	−0.299112	−	0.920573i
$738$		0			0
$739$	12217.4	−	37601.2i	0.608151	−	1.87170i	0.134671	−	0.990890i	$-0.457002\pi$
$739$	12217.4	−	37601.2i	0.608151	−	1.87170i	0.473480	−	0.880805i	$-0.342998\pi$
$740$	2324.83	−	19271.3i	0.115490	−	0.957332i
$741$		0			0
$742$	−7468.46	+	5426.15i	−0.369509	+	0.268464i
$743$	35466.6			1.75120			0.875601	−	0.483036i	$-0.160466\pi$
$743$	35466.6			1.75120			0.875601	+	0.483036i	$0.160466\pi$
$744$		0			0
$745$	−28547.2	+	5611.74i	−1.40388	+	0.275971i
$746$	11467.8	+	8331.85i	0.562823	+	0.408915i
$747$		0			0
$748$	−4932.10	+	15179.5i	−0.241090	+	0.742000i
$749$	19965.2			0.973984
$750$		0			0
$751$	28967.6			1.40751			0.703756	−	0.710442i	$-0.251505\pi$
$751$	28967.6			1.40751			0.703756	+	0.710442i	$0.251505\pi$
$752$	381.278	−	1173.45i	0.0184891	−	0.0569036i
$753$		0			0
$754$	−13938.9	−	10127.2i	−0.673245	−	0.489141i
$755$	6975.62	−	1371.25i	0.336250	−	0.0660992i
$756$		0			0
$757$	−15068.4			−0.723476			−0.361738	−	0.932280i	$-0.617817\pi$
$757$	−15068.4			−0.723476			−0.361738	+	0.932280i	$0.617817\pi$
$758$	−12795.1	+	9296.18i	−0.613112	+	0.445452i
$759$		0			0
$760$	3020.64	−	25039.1i	0.144171	−	1.19508i
$761$	−998.600	+	3073.38i	−0.0475680	+	0.146399i	−0.972019	−	0.234901i	$-0.924523\pi$
$761$	−998.600	+	3073.38i	−0.0475680	+	0.146399i	0.924451	+	0.381300i	$0.124523\pi$
$762$		0			0
$763$	−1193.72	−	3673.90i	−0.0566391	−	0.174317i
$764$	1820.71	−	5603.57i	0.0862186	−	0.265353i
$765$		0			0
$766$	−1642.66	−	5055.60i	−0.0774829	−	0.238468i
$767$	−28444.4	+	20666.0i	−1.33907	+	0.972891i
$768$		0			0
$769$	873.705	−	634.784i	0.0409709	−	0.0297671i	−0.567111	−	0.823641i	$-0.691939\pi$
$769$	873.705	−	634.784i	0.0409709	−	0.0297671i	0.608082	+	0.793874i	$0.291939\pi$
$770$	−5419.40	−	2513.16i	−0.253638	−	0.117621i
$771$		0			0
$772$	−7420.06	−	5390.99i	−0.345925	−	0.251329i
$773$	−4957.48	+	15257.6i	−0.230670	+	0.709930i	0.766996	+	0.641652i	$0.221751\pi$
$773$	−4957.48	+	15257.6i	−0.230670	+	0.709930i	−0.997666	+	0.0682784i	$0.978249\pi$
$774$		0			0
$775$	−17466.1	+	28216.6i	−0.809548	+	1.30783i
$776$	11501.2			0.532048
$777$		0			0
$778$	−8105.27	−	5888.83i	−0.373507	−	0.271368i
$779$	30640.8	+	22261.8i	1.40927	+	1.02389i
$780$		0			0
$781$	1324.29	−	962.151i	0.0606744	−	0.0440825i
$782$	−14838.9			−0.678566
$783$		0			0
$784$	−998.606	−	3073.39i	−0.0454904	−	0.140005i
$785$	14072.6	−	2766.35i	0.639836	−	0.125777i
$786$		0			0
$787$	−8913.36	−	27432.5i	−0.403719	−	1.24252i	−0.921960	−	0.387285i	$-0.873413\pi$
$787$	−8913.36	−	27432.5i	−0.403719	−	1.24252i	0.518241	−	0.855235i	$-0.326587\pi$
$788$	1491.97	+	4591.80i	0.0674481	+	0.207584i
$789$		0			0
$790$	−2500.96	+	2693.35i	−0.112633	+	0.121298i
$791$	−6021.46	−	18532.1i	−0.270668	−	0.833031i
$792$		0			0
$793$	32628.1			1.46111
$794$	8132.27	−	5908.44i	0.363480	−	0.264084i
$795$		0			0
$796$	16130.1	+	11719.2i	0.718237	+	0.521830i
$797$	14885.4	+	10814.9i	0.661568	+	0.480657i	0.867192	−	0.497974i	$-0.165922\pi$
$797$	14885.4	+	10814.9i	0.661568	+	0.480657i	−0.205624	+	0.978631i	$0.565922\pi$
$798$		0			0
$799$	5321.82			0.235635
$800$	21504.2	−	8794.32i	0.950361	−	0.388658i
$801$		0			0
$802$	338.202	−	1040.88i	0.0148907	−	0.0458288i
$803$	−16407.6	−	11920.8i	−0.721061	−	0.523882i
$804$		0			0
$805$	−2129.54	+	17652.4i	−0.0932377	+	0.772878i
$806$	−18569.1	+	13491.3i	−0.811501	+	0.589590i
$807$		0			0
$808$	−28037.5	+	20370.4i	−1.22074	+	0.886917i
$809$	2964.66	+	9124.28i	0.128840	+	0.396530i	0.994581	−	0.103963i	$-0.0331523\pi$
$809$	2964.66	+	9124.28i	0.128840	+	0.396530i	−0.865741	+	0.500493i	$0.833152\pi$
$810$		0			0
$811$	325.871	−	1002.93i	0.0141096	−	0.0434249i	−0.943754	−	0.330649i	$-0.892732\pi$
$811$	325.871	−	1002.93i	0.0141096	−	0.0434249i	0.957863	+	0.287224i	$0.0927324\pi$
$812$	5250.44	+	16159.2i	0.226914	+	0.698370i
$813$		0			0
$814$	3362.20	−	10347.8i	0.144773	−	0.445565i
$815$	−2251.96	−	4042.44i	−0.0967886	−	0.173743i
$816$		0			0
$817$	−10686.5	+	7764.16i	−0.457615	+	0.332477i
$818$	7863.84			0.336128
$819$		0			0
$820$	−2665.72	+	22097.1i	−0.113526	+	0.941053i
$821$	−19195.3	−	13946.2i	−0.815979	−	0.592844i	0.0995787	−	0.995030i	$-0.468250\pi$
$821$	−19195.3	−	13946.2i	−0.815979	−	0.592844i	−0.915558	+	0.402186i	$0.868250\pi$
$822$		0			0
$823$	−9336.45	+	28734.6i	−0.395441	+	1.21704i	0.533176	+	0.846004i	$0.320998\pi$
$823$	−9336.45	+	28734.6i	−0.395441	+	1.21704i	−0.928618	+	0.371038i	$0.879002\pi$
$824$	−7219.51			−0.305223
$825$		0			0
$826$	−10830.2			−0.456213
$827$	−8943.30	+	27524.6i	−0.376045	+	1.15735i	0.566727	+	0.823906i	$0.308210\pi$
$827$	−8943.30	+	27524.6i	−0.376045	+	1.15735i	−0.942771	+	0.333440i	$0.891790\pi$
$828$		0			0
$829$	−11802.5	−	8575.04i	−0.494474	−	0.359256i	0.312428	−	0.949941i	$-0.398858\pi$
$829$	−11802.5	−	8575.04i	−0.494474	−	0.359256i	−0.806902	+	0.590685i	$0.798858\pi$
$830$	2624.36	+	4710.92i	0.109750	+	0.197010i
$831$		0			0
$832$	5078.75			0.211627
$833$	11276.4	−	8192.76i	0.469031	−	0.340771i
$834$		0			0
$835$	25150.1	−	27084.8i	1.04234	−	1.12253i
$836$	−6048.09	+	18614.1i	−0.250212	+	0.770075i
$837$		0			0
$838$	5813.17	+	17891.1i	0.239633	+	0.737515i
$839$	9658.42	−	29725.6i	0.397432	−	1.22317i	−0.529619	−	0.848236i	$-0.677665\pi$
$839$	9658.42	−	29725.6i	0.397432	−	1.22317i	0.927051	−	0.374935i	$-0.122335\pi$
$840$		0			0
$841$	4735.55	+	14574.5i	0.194167	+	0.597586i
$842$	7639.80	−	5550.64i	0.312690	−	0.227182i
$843$		0			0
$844$	−17528.6	+	12735.3i	−0.714881	+	0.519391i
$845$	13151.0	−	14162.7i	0.535393	−	0.576580i
$846$		0			0
$847$	−6388.18	−	4641.28i	−0.259150	−	0.188284i
$848$	−3240.98	+	9974.71i	−0.131245	+	0.403930i
$849$		0			0
$850$	10538.6	+	12451.9i	0.425258	+	0.502468i
$851$	−32384.4			−1.30449
$852$		0			0
$853$	11622.9	+	8444.51i	0.466541	+	0.338962i	0.796092	−	0.605176i	$-0.206897\pi$
$853$	11622.9	+	8444.51i	0.466541	+	0.338962i	−0.329551	+	0.944138i	$0.606897\pi$
$854$	8131.07	+	5907.57i	0.325807	+	0.236713i
$855$		0			0
$856$	−22462.8	+	16320.2i	−0.896919	+	0.651650i
$857$	−26095.3			−1.04014			−0.520068	−	0.854125i	$-0.674094\pi$
$857$	−26095.3			−1.04014			−0.520068	+	0.854125i	$0.674094\pi$
$858$		0			0
$859$	14240.2	+	43826.8i	0.565622	+	1.74080i	0.666097	+	0.745865i	$0.267963\pi$
$859$	14240.2	+	43826.8i	0.565622	+	1.74080i	−0.100476	+	0.994939i	$0.532037\pi$
$860$	−7042.21	−	3265.71i	−0.279230	−	0.129488i
$861$		0			0
$862$	2323.84	+	7152.05i	0.0918217	+	0.282598i
$863$	8806.51	+	27103.7i	0.347366	+	1.06908i	0.960305	+	0.278953i	$0.0899874\pi$
$863$	8806.51	+	27103.7i	0.347366	+	1.06908i	−0.612938	+	0.790131i	$0.710013\pi$
$864$		0			0
$865$	3280.29	−	27191.4i	0.128940	−	1.06883i
$866$	2051.02	+	6312.39i	0.0804809	+	0.247695i
$867$		0			0
$868$	22634.7			0.885105
$869$	5335.86	−	3876.73i	0.208293	−	0.151334i
$870$		0			0
$871$	35459.1	+	25762.6i	1.37943	+	1.00222i
$872$	4346.21	+	3157.70i	0.168786	+	0.122630i
$873$		0			0
$874$	−18196.5			−0.704241
$875$	16325.3	−	10749.7i	0.630737	−	0.415323i
$876$		0			0
$877$	772.961	−	2378.93i	0.0297617	−	0.0915972i	−0.935072	−	0.354457i	$-0.884666\pi$
$877$	772.961	−	2378.93i	0.0297617	−	0.0915972i	0.964834	+	0.262860i	$0.0846657\pi$
$878$	16082.9	+	11684.9i	0.618191	+	0.449142i
$879$		0			0
$880$	−6659.41	+	1309.09i	−0.255101	+	0.0501470i
$881$	11994.0	−	8714.13i	0.458669	−	0.333243i	−0.334340	−	0.942453i	$-0.608513\pi$
$881$	11994.0	−	8714.13i	0.458669	−	0.333243i	0.793009	+	0.609210i	$0.208513\pi$
$882$		0			0
$883$	−31760.0	+	23075.0i	−1.21043	+	0.879427i	−0.995270	−	0.0971518i	$-0.969027\pi$
$883$	−31760.0	+	23075.0i	−1.21043	+	0.879427i	−0.215158	+	0.976579i	$0.569027\pi$
$884$	−11162.2	−	34353.7i	−0.424689	−	1.30706i
$885$		0			0
$886$	−5126.97	+	15779.2i	−0.194406	+	0.598320i
$887$	−11024.7	−	33930.4i	−0.417330	−	1.28441i	−0.910150	−	0.414278i	$-0.864034\pi$
$887$	−11024.7	−	33930.4i	−0.417330	−	1.28441i	0.492820	−	0.870131i	$-0.335966\pi$
$888$		0			0
$889$	−3776.28	+	11622.2i	−0.142466	+	0.438466i
$890$	10875.0	+	5043.10i	0.409585	+	0.189938i
$891$		0			0
$892$	−28232.4	+	20512.0i	−1.05974	+	0.769948i
$893$	6525.98			0.244551
$894$		0			0
$895$	−29078.6	−	13484.7i	−1.08602	−	0.503625i
$896$	−15559.1	−	11304.4i	−0.580128	−	0.421488i
$897$		0			0
$898$	−4579.86	+	14095.4i	−0.170191	+	0.523795i
$899$	52905.4			1.96273
$900$		0			0
$901$	−45237.0			−1.67266
$902$	−3855.22	+	11865.1i	−0.142311	+	0.437989i
$903$		0			0
$904$	21923.5	+	15928.3i	0.806597	+	0.586027i
$905$	−13825.8	+	14889.4i	−0.507828	+	0.546894i
$906$		0			0
$907$	8273.76			0.302895			0.151448	−	0.988465i	$-0.451607\pi$
$907$	8273.76			0.302895			0.151448	+	0.988465i	$0.451607\pi$
$908$	6349.87	−	4613.45i	0.232079	−	0.168615i
$909$		0			0
$910$	13265.8	−	2607.75i	0.483248	−	0.0949957i
$911$	−4728.49	+	14552.8i	−0.171967	+	0.529260i	−0.999482	−	0.0321838i	$-0.989754\pi$
$911$	−4728.49	+	14552.8i	−0.171967	+	0.529260i	0.827515	+	0.561444i	$0.189754\pi$
$912$		0			0
$913$	−2990.31	−	9203.23i	−0.108395	−	0.333606i
$914$	2540.27	−	7818.14i	0.0919306	−	0.282933i
$915$		0			0
$916$	−2576.42	−	7929.41i	−0.0929338	−	0.286021i
$917$	26152.1	−	19000.6i	0.941787	−	0.684248i
$918$		0			0
$919$	−18270.2	+	13274.0i	−0.655796	+	0.476464i	−0.865241	−	0.501357i	$-0.832834\pi$
$919$	−18270.2	+	13274.0i	−0.655796	+	0.476464i	0.209444	+	0.977821i	$0.432834\pi$
$920$	−12033.7	−	21601.5i	−0.431239	−	0.774107i
$921$		0			0
$922$	13405.6	+	9739.75i	0.478840	+	0.347898i
$923$	−1144.79	+	3523.29i	−0.0408246	+	0.125645i
$924$		0			0
$925$	22999.3	+	27175.1i	0.817527	+	0.965959i
$926$	−11113.7			−0.394404
$927$		0			0
$928$	−29965.5	−	21771.2i	−1.05999	−	0.770125i
$929$	14371.1	+	10441.2i	0.507537	+	0.368747i	0.811888	−	0.583813i	$-0.198440\pi$
$929$	14371.1	+	10441.2i	0.507537	+	0.368747i	−0.304352	+	0.952560i	$0.598440\pi$
$930$		0			0
$931$	13827.9	−	10046.5i	0.486778	−	0.353665i
$932$	−16110.7			−0.566226
$933$		0			0
$934$	−7981.85	−	24565.6i	−0.279629	−	0.860611i
$935$	−14246.0	−	25572.7i	−0.498283	−	0.894457i
$936$		0			0
$937$	1342.71	+	4132.42i	0.0468135	+	0.144077i	0.971731	−	0.236091i	$-0.0758662\pi$
$937$	1342.71	+	4132.42i	0.0468135	+	0.144077i	−0.924918	+	0.380168i	$0.875866\pi$
$938$	4172.07	+	12840.3i	0.145227	+	0.446963i
$939$		0			0
$940$	1866.39	+	3350.31i	0.0647604	+	0.116250i
$941$	−8950.54	−	27546.9i	−0.310074	−	0.954308i	−0.977735	−	0.209843i	$-0.932705\pi$
$941$	−8950.54	−	27546.9i	−0.310074	−	0.954308i	0.667662	−	0.744465i	$-0.267295\pi$
$942$		0			0
$943$	37133.1			1.28231
$944$	−9954.41	+	7232.30i	−0.343208	+	0.249355i
$945$		0			0
$946$	−3520.12	−	2557.52i	−0.120982	−	0.0878987i
$947$	−21023.3	−	15274.3i	−0.721399	−	0.524127i	0.165432	−	0.986221i	$-0.447098\pi$
$947$	−21023.3	−	15274.3i	−0.721399	−	0.524127i	−0.886831	+	0.462094i	$0.847098\pi$
$948$		0			0
$949$	45899.2			1.57002
$950$	12923.1	+	15269.4i	0.441349	+	0.521480i
$951$		0			0
$952$	7950.68	−	24469.7i	0.270675	−	0.833053i
$953$	32165.9	+	23369.9i	1.09334	+	0.794361i	0.979961	−	0.199190i	$-0.0638312\pi$
$953$	32165.9	+	23369.9i	1.09334	+	0.794361i	0.113383	+	0.993551i	$0.463831\pi$
$954$		0			0
$955$	5258.99	+	9440.30i	0.178196	+	0.319875i
$956$	2056.12	−	1493.86i	0.0695603	−	0.0505385i
$957$		0			0
$958$	16397.3	−	11913.3i	0.552998	−	0.401776i
$959$	−35.8616	−	110.371i	−0.00120754	−	0.00371642i
$960$		0			0
$961$	12573.4	−	38696.9i	0.422053	−	1.29895i
$962$	7609.24	+	23418.8i	0.255023	+	0.784879i
$963$		0			0
$964$	−2022.97	+	6226.08i	−0.0675888	+	0.208017i
$965$	16505.7	−	3244.66i	0.550610	−	0.108238i
$966$		0			0
$967$	13790.2	−	10019.2i	0.458597	−	0.333190i	−0.334384	−	0.942437i	$-0.608528\pi$
$967$	13790.2	−	10019.2i	0.458597	−	0.333190i	0.792981	+	0.609247i	$0.208528\pi$
$968$	10981.2			0.364618
$969$		0			0
$970$	−6207.29	+	6684.81i	−0.205468	+	0.221274i
$971$	−39383.0	−	28613.4i	−1.30161	−	0.945672i	−0.301636	−	0.953423i	$-0.597533\pi$
$971$	−39383.0	−	28613.4i	−1.30161	−	0.945672i	−0.999970	+	0.00775077i	$0.997533\pi$
$972$		0			0
$973$	−9161.58	+	28196.4i	−0.301857	+	0.929020i
$974$	5043.30			0.165912
$975$		0			0
$976$	11418.5			0.374486
$977$	−14639.3	+	45055.1i	−0.479378	+	1.47537i	0.360582	+	0.932727i	$0.382578\pi$
$977$	−14639.3	+	45055.1i	−0.479378	+	1.47537i	−0.839961	+	0.542647i	$0.817422\pi$
$978$		0			0
$979$	−17402.8	−	12643.9i	−0.568127	−	0.412769i
$980$	9112.37	+	4225.71i	0.297024	+	0.137740i
$981$		0			0
$982$	−16336.4			−0.530870
$983$	−25032.6	+	18187.2i	−0.812223	+	0.590114i	−0.914474	−	0.404644i	$-0.867395\pi$
$983$	−25032.6	+	18187.2i	−0.812223	+	0.590114i	0.102251	+	0.994759i	$0.467395\pi$
$984$		0			0
$985$	−8033.38	−	3725.35i	−0.259863	−	0.120507i
$986$	8036.63	−	24734.2i	0.259572	−	0.798882i
$987$		0			0
$988$	−13687.9	−	42126.9i	−0.440758	−	1.35651i
$989$	−4002.00	+	12316.9i	−0.128672	+	0.396010i
$990$		0			0
$991$	−26.6412	−	81.9932i	−0.000853972	−	0.00262825i	0.950629	−	0.310331i	$-0.100440\pi$
$991$	−26.6412	−	81.9932i	−0.000853972	−	0.00262825i	−0.951483	+	0.307703i	$0.900440\pi$
$992$	−39919.3	+	29003.1i	−1.27766	+	0.928276i
$993$		0			0
$994$	−923.205	+	670.748i	−0.0294590	+	0.0214033i
$995$	−35881.1	+	7053.41i	−1.14322	+	0.224732i
$996$		0			0
$997$	−14689.8	−	10672.8i	−0.466630	−	0.339027i	0.329496	−	0.944157i	$-0.393121\pi$
$997$	−14689.8	−	10672.8i	−0.466630	−	0.339027i	−0.796127	+	0.605130i	$0.793121\pi$
$998$	−4902.80	+	15089.3i	−0.155507	+	0.478600i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.10	yes	64
3.2	odd	2	inner	225.4.h.d.46.7	✓	64
25.6	even	5	inner	225.4.h.d.181.10	yes	64
75.56	odd	10	inner	225.4.h.d.181.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.7	✓	64	3.2	odd	2	inner
225.4.h.d.46.10	yes	64	1.1	even	1	trivial
225.4.h.d.181.7	yes	64	75.56	odd	10	inner
225.4.h.d.181.10	yes	64	25.6	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+(0.426412 - 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(-10.9704 + 2.15653i) q^{5} -13.9864 q^{7} +(15.7361 - 11.4329i) q^{8} +O(q^{10})\)	\(q+(0.426412 - 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(-10.9704 + 2.15653i) q^{5} -13.9864 q^{7} +(15.7361 - 11.4329i) q^{8} +(-1.84776 + 15.3167i) q^{10} +(8.55501 - 26.3296i) q^{11} +(19.3615 + 59.5885i) q^{13} +(-5.96399 + 18.3553i) q^{14} +(6.77575 + 20.8536i) q^{16} +(-76.5125 + 55.5896i) q^{17} +(-93.8251 + 68.1679i) q^{19} +(-61.8293 - 28.6723i) q^{20} +(-30.9060 - 22.4545i) q^{22} +(-35.1368 + 108.140i) q^{23} +(115.699 - 47.3159i) q^{25} +86.4576 q^{26} +(-68.9765 - 50.1144i) q^{28} +(-161.223 - 117.135i) q^{29} +(-214.777 + 156.045i) q^{31} +185.864 q^{32} +(40.3278 + 124.116i) q^{34} +(153.437 - 30.1622i) q^{35} +(88.0113 + 270.871i) q^{37} +(49.4528 + 152.200i) q^{38} +(-147.976 + 159.359i) q^{40} +(-100.917 - 310.590i) q^{41} +113.898 q^{43} +(136.531 - 99.1958i) q^{44} +(126.936 + 92.2244i) q^{46} +(-45.5242 - 33.0753i) q^{47} -147.379 q^{49} +(-12.7603 - 172.015i) q^{50} +(-118.025 + 363.244i) q^{52} +(386.969 + 281.150i) q^{53} +(-37.0712 + 307.295i) q^{55} +(-220.092 + 159.906i) q^{56} +(-222.471 + 161.635i) q^{58} +(173.406 + 533.690i) q^{59} +(160.923 - 495.270i) q^{61} +(113.204 + 348.405i) q^{62} +(25.0486 - 77.0916i) q^{64} +(-340.907 - 611.955i) q^{65} +(565.942 - 411.181i) q^{67} -576.516 q^{68} +(25.8436 - 214.226i) q^{70} +(47.8348 + 34.7540i) q^{71} +(226.377 - 696.716i) q^{73} +393.010 q^{74} -706.964 q^{76} +(-119.654 + 368.258i) q^{77} +(192.738 + 140.032i) q^{79} +(-119.304 - 214.160i) q^{80} -450.638 q^{82} +(282.783 - 205.454i) q^{83} +(719.492 - 774.841i) q^{85} +(48.5673 - 149.475i) q^{86} +(-166.403 - 512.135i) q^{88} +(240.108 - 738.975i) q^{89} +(-270.798 - 833.431i) q^{91} +(-560.756 + 407.413i) q^{92} +(-62.8188 + 45.6405i) q^{94} +(882.291 - 950.165i) q^{95} +(478.367 + 347.554i) q^{97} +(-62.8443 + 193.415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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