LMFDB - Embedded newform 177.4.e.a.4.6

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	177.4
Dual form			177.4.e.a.133.6

$q$-expansion

$f(q)$	$=$	$q+(-2.03313 - 0.221116i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-3.72826 - 0.820651i) q^{4} +(16.1269 + 12.2594i) q^{5} +(4.45423 - 4.21927i) q^{6} +(-2.36180 + 5.92767i) q^{7} +(22.9030 + 7.71693i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(-2.03313 - 0.221116i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-3.72826 - 0.820651i) q^{4} +(16.1269 + 12.2594i) q^{5} +(4.45423 - 4.21927i) q^{6} +(-2.36180 + 5.92767i) q^{7} +(22.9030 + 7.71693i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-30.0773 - 28.4907i) q^{10} +(9.15701 - 4.23648i) q^{11} +(9.11727 - 6.93077i) q^{12} +(4.88429 - 29.7928i) q^{13} +(6.11253 - 11.5295i) q^{14} +(-59.3519 + 13.0643i) q^{15} +(-17.1410 - 7.93027i) q^{16} +(13.2050 + 33.1420i) q^{17} +(0.996482 + 18.3790i) q^{18} +(24.5922 + 36.2708i) q^{19} +(-50.0646 - 58.9406i) q^{20} +(-8.96654 - 16.9127i) q^{21} +(-19.5541 + 6.58855i) q^{22} +(-4.67865 + 86.2927i) q^{23} +(-62.1260 + 37.3800i) q^{24} +(76.3443 + 274.967i) q^{25} +(-16.5180 + 59.4926i) q^{26} +(23.1351 + 13.9200i) q^{27} +(13.6699 - 20.1616i) q^{28} +(-80.0540 + 8.70639i) q^{29} +(123.559 - 13.4378i) q^{30} +(-183.374 + 270.457i) q^{31} +(-132.573 - 79.7665i) q^{32} +(-8.09771 + 29.1653i) q^{33} +(-19.5191 - 70.3016i) q^{34} +(-110.758 + 66.6408i) q^{35} +(-1.86008 + 34.3072i) q^{36} +(-11.7771 + 3.96816i) q^{37} +(-41.9790 - 79.1808i) q^{38} +(58.6349 + 69.0303i) q^{39} +(274.750 + 405.227i) q^{40} +(-10.8283 - 199.716i) q^{41} +(14.4904 + 36.3683i) q^{42} +(-17.4299 - 8.06392i) q^{43} +(-37.6164 + 8.27999i) q^{44} +(85.3993 - 161.080i) q^{45} +(28.5930 - 174.409i) q^{46} +(-49.3229 + 37.4943i) q^{47} +(51.4230 - 23.7908i) q^{48} +(219.457 + 207.881i) q^{49} +(-94.4180 - 575.924i) q^{50} +(-101.425 - 34.1740i) q^{51} +(-42.6594 + 107.067i) q^{52} +(-161.287 + 152.779i) q^{53} +(-43.9587 - 33.4166i) q^{54} +(199.611 + 43.9377i) q^{55} +(-99.8357 + 117.536i) q^{56} +(-130.695 - 14.2139i) q^{57} +164.685 q^{58} +(-448.795 - 62.9462i) q^{59} +232.000 q^{60} +(-28.2997 - 3.07777i) q^{61} +(432.625 - 509.326i) q^{62} +(56.0851 + 12.3453i) q^{63} +(372.184 + 282.927i) q^{64} +(444.010 - 420.588i) q^{65} +(22.9126 - 57.5062i) q^{66} +(-157.146 - 52.9486i) q^{67} +(-22.0335 - 134.398i) q^{68} +(-188.220 - 178.292i) q^{69} +(239.920 - 110.999i) q^{70} +(-365.568 + 277.898i) q^{71} +(35.1897 - 214.648i) q^{72} +(263.714 - 497.417i) q^{73} +(24.8217 - 5.46367i) q^{74} +(-776.982 - 359.470i) q^{75} +(-61.9204 - 155.409i) q^{76} +(3.48545 + 64.2854i) q^{77} +(-103.948 - 153.312i) q^{78} +(520.229 + 612.461i) q^{79} +(-179.211 - 338.028i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-22.1451 + 408.442i) q^{82} +(451.620 - 271.731i) q^{83} +(19.5501 + 70.4132i) q^{84} +(-193.344 + 696.362i) q^{85} +(33.6541 + 20.2490i) q^{86} +(135.570 - 199.951i) q^{87} +(242.416 - 26.3643i) q^{88} +(1223.98 - 133.116i) q^{89} +(-209.245 + 308.613i) q^{90} +(165.066 + 99.3171i) q^{91} +(88.2595 - 317.882i) q^{92} +(-262.254 - 944.553i) q^{93} +(108.570 - 65.3246i) q^{94} +(-48.0603 + 886.421i) q^{95} +(439.863 - 148.207i) q^{96} +(-745.126 - 1405.46i) q^{97} +(-400.219 - 471.174i) q^{98} +(-50.9590 - 75.1589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) $	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{29}\right)$	$1$

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 $

$2$	−2.03313	−	0.221116i	−0.718818	−	0.0781762i	−0.258603	−	0.965984i	$-0.583262\pi$
$2$	−2.03313	−	0.221116i	−0.718818	−	0.0781762i	−0.460215	+	0.887807i	$0.652228\pi$
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$3$	−1.94216	+	2.28649i	−0.373769	+	0.440034i
$4$	−3.72826	−	0.820651i	−0.466032	−	0.102581i
$5$	16.1269	+	12.2594i	1.44243	+	1.09651i	0.977444	+	0.211195i	$0.0677354\pi$
$5$	16.1269	+	12.2594i	1.44243	+	1.09651i	0.464991	+	0.885316i	$0.346058\pi$
$6$	4.45423	−	4.21927i	0.303072	−	0.287085i
$7$	−2.36180	+	5.92767i	−0.127525	+	0.320064i	−0.978851	−	0.204573i	$-0.934419\pi$
$7$	−2.36180	+	5.92767i	−0.127525	+	0.320064i	0.851326	+	0.524637i	$0.175799\pi$
$8$	22.9030	+	7.71693i	1.01218	+	0.341043i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	−30.0773	−	28.4907i	−0.951128	−	0.900956i
$11$	9.15701	−	4.23648i	0.250995	−	0.116123i	−0.290358	−	0.956918i	$-0.593774\pi$
$11$	9.15701	−	4.23648i	0.250995	−	0.116123i	0.541353	+	0.840796i	$0.317912\pi$
$12$	9.11727	−	6.93077i	0.219328	−	0.166728i
$13$	4.88429	−	29.7928i	0.104204	−	0.635619i	−0.882148	−	0.470972i	$-0.843903\pi$
$13$	4.88429	−	29.7928i	0.104204	−	0.635619i	0.986353	−	0.164647i	$-0.0526485\pi$
$14$	6.11253	−	11.5295i	0.116689	−	0.220098i
$15$	−59.3519	+	13.0643i	−1.02164	+	0.224880i
$16$	−17.1410	−	7.93027i	−0.267828	−	0.123910i
$17$	13.2050	+	33.1420i	0.188393	+	0.472830i	0.992587	−	0.121537i	$-0.0387822\pi$
$17$	13.2050	+	33.1420i	0.188393	+	0.472830i	−0.804194	+	0.594366i	$0.797403\pi$
$18$	0.996482	+	18.3790i	0.0130485	+	0.240666i
$19$	24.5922	+	36.2708i	0.296939	+	0.437952i	0.946667	−	0.322215i	$-0.104427\pi$
$19$	24.5922	+	36.2708i	0.296939	+	0.437952i	−0.649727	+	0.760167i	$0.725117\pi$
$20$	−50.0646	−	58.9406i	−0.559739	−	0.658976i
$21$	−8.96654	−	16.9127i	−0.0931743	−	0.175745i
$22$	−19.5541	+	6.58855i	−0.189498	+	0.0638492i
$23$	−4.67865	+	86.2927i	−0.0424160	+	0.782316i	0.897522	+	0.440970i	$0.145366\pi$
$23$	−4.67865	+	86.2927i	−0.0424160	+	0.782316i	−0.939938	+	0.341346i	$0.889117\pi$
$24$	−62.1260	+	37.3800i	−0.528392	+	0.317923i
$25$	76.3443	+	274.967i	0.610754	+	2.19974i
$26$	−16.5180	+	59.4926i	−0.124594	+	0.448748i
$27$	23.1351	+	13.9200i	0.164902	+	0.0992184i
$28$	13.6699	−	20.1616i	0.0922634	−	0.136078i
$29$	−80.0540	+	8.70639i	−0.512609	+	0.0557495i	−0.360768	−	0.932655i	$-0.617485\pi$
$29$	−80.0540	+	8.70639i	−0.512609	+	0.0557495i	−0.151840	+	0.988405i	$0.548520\pi$
$30$	123.559	−	13.4378i	0.751953	−	0.0817799i
$31$	−183.374	+	270.457i	−1.06242	+	1.56695i	−0.264310	+	0.964438i	$0.585144\pi$
$31$	−183.374	+	270.457i	−1.06242	+	1.56695i	−0.798109	+	0.602513i	$0.794166\pi$
$32$	−132.573	−	79.7665i	−0.732369	−	0.440652i
$33$	−8.09771	+	29.1653i	−0.0427161	+	0.153849i
$34$	−19.5191	−	70.3016i	−0.0984560	−	0.354607i
$35$	−110.758	+	66.6408i	−0.534900	+	0.321839i
$36$	−1.86008	+	34.3072i	−0.00861149	+	0.158830i
$37$	−11.7771	+	3.96816i	−0.0523281	+	0.0176314i	−0.345344	−	0.938476i	$-0.612238\pi$
$37$	−11.7771	+	3.96816i	−0.0523281	+	0.0176314i	0.293016	+	0.956108i	$0.405341\pi$
$38$	−41.9790	−	79.1808i	−0.179208	−	0.338022i
$39$	58.6349	+	69.0303i	0.240746	+	0.283428i
$40$	274.750	+	405.227i	1.08605	+	1.60180i
$41$	−10.8283	−	199.716i	−0.0412462	−	0.760742i	−0.943871	−	0.330314i	$-0.892845\pi$
$41$	−10.8283	−	199.716i	−0.0412462	−	0.760742i	0.902625	−	0.430428i	$-0.141637\pi$
$42$	14.4904	+	36.3683i	0.0532363	+	0.133613i
$43$	−17.4299	−	8.06392i	−0.0618147	−	0.0285985i	0.388738	−	0.921348i	$-0.372911\pi$
$43$	−17.4299	−	8.06392i	−0.0618147	−	0.0285985i	−0.450553	+	0.892750i	$0.648773\pi$
$44$	−37.6164	+	8.27999i	−0.128884	+	0.0283694i
$45$	85.3993	−	161.080i	0.282902	−	0.533609i
$46$	28.5930	−	174.409i	0.0916479	−	0.559027i
$47$	−49.3229	+	37.4943i	−0.153074	+	0.116364i	−0.678908	−	0.734223i	$-0.737546\pi$
$47$	−49.3229	+	37.4943i	−0.153074	+	0.116364i	0.525834	+	0.850587i	$0.323753\pi$
$48$	51.4230	−	23.7908i	0.154631	−	0.0715397i
$49$	219.457	+	207.881i	0.639817	+	0.606067i
$50$	−94.4180	−	575.924i	−0.267054	−	1.62896i
$51$	−101.425	−	34.1740i	−0.278477	−	0.0938297i
$52$	−42.6594	+	107.067i	−0.113765	+	0.285529i
$53$	−161.287	+	152.779i	−0.418009	+	0.395959i	−0.867590	−	0.497281i	$-0.834332\pi$
$53$	−161.287	+	152.779i	−0.418009	+	0.395959i	0.449581	+	0.893240i	$0.351573\pi$
$54$	−43.9587	−	33.4166i	−0.110778	−	0.0842114i
$55$	199.611	+	43.9377i	0.489373	+	0.107719i
$56$	−99.8357	+	117.536i	−0.238234	+	0.280471i
$57$	−130.695	−	14.2139i	−0.303701	−	0.0330294i
$58$	164.685			0.372831
$59$	−448.795	−	62.9462i	−0.990307	−	0.138897i
$59$	−448.795	−	62.9462i	−0.990307	−	0.138897i
$60$	232.000			0.499185
$61$	−28.2997	−	3.07777i	−0.0594000	−	0.00646014i	0.0783708	−	0.996924i	$-0.475028\pi$
$61$	−28.2997	−	3.07777i	−0.0594000	−	0.00646014i	−0.137771	+	0.990464i	$0.543994\pi$
$62$	432.625	−	509.326i	0.886185	−	1.04330i
$63$	56.0851	+	12.3453i	0.112160	+	0.0246882i
$64$	372.184	+	282.927i	0.726921	+	0.552591i
$65$	444.010	−	420.588i	0.847271	−	0.802578i
$66$	22.9126	−	57.5062i	0.0427324	−	0.107250i
$67$	−157.146	−	52.9486i	−0.286544	−	0.0965478i	0.172359	−	0.985034i	$-0.444861\pi$
$67$	−157.146	−	52.9486i	−0.286544	−	0.0965478i	−0.458903	+	0.888486i	$0.651758\pi$
$68$	−22.0335	−	134.398i	−0.0392934	−	0.239679i
$69$	−188.220	−	178.292i	−0.328392	−	0.311070i
$70$	239.920	−	110.999i	0.409656	−	0.189527i
$71$	−365.568	+	277.898i	−0.611056	+	0.464512i	−0.864360	−	0.502874i	$-0.832276\pi$
$71$	−365.568	+	277.898i	−0.611056	+	0.464512i	0.253304	+	0.967387i	$0.418483\pi$
$72$	35.1897	−	214.648i	0.0575993	−	0.351340i
$73$	263.714	−	497.417i	0.422813	−	0.797510i	−0.577002	−	0.816743i	$-0.695778\pi$
$73$	263.714	−	497.417i	0.422813	−	0.797510i	0.999815	+	0.0192328i	$0.00612235\pi$
$74$	24.8217	−	5.46367i	0.0389928	−	0.00858296i
$75$	−776.982	−	359.470i	−1.19624	−	0.553440i
$76$	−61.9204	−	155.409i	−0.0934574	−	0.234560i
$77$	3.48545	+	64.2854i	0.00515850	+	0.0951429i
$78$	−103.948	−	153.312i	−0.150895	−	0.222554i
$79$	520.229	+	612.461i	0.740890	+	0.872244i	0.995496	−	0.0948013i	$-0.0302216\pi$
$79$	520.229	+	612.461i	0.740890	+	0.872244i	−0.254606	+	0.967045i	$0.581946\pi$
$80$	−179.211	−	338.028i	−0.250455	−	0.472409i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	−22.1451	+	408.442i	−0.0298234	+	0.550060i
$83$	451.620	−	271.731i	0.597250	−	0.359353i	−0.184606	−	0.982813i	$-0.559101\pi$
$83$	451.620	−	271.731i	0.597250	−	0.359353i	0.781856	+	0.623459i	$0.214273\pi$
$84$	19.5501	+	70.4132i	0.0253940	+	0.0914609i
$85$	−193.344	+	696.362i	−0.246719	+	0.888600i
$86$	33.6541	+	20.2490i	0.0421978	+	0.0253896i
$87$	135.570	−	199.951i	0.167065	−	0.246403i
$88$	242.416	−	26.3643i	0.293655	−	0.0319369i
$89$	1223.98	−	133.116i	1.45778	−	0.158543i	0.655363	−	0.755314i	$-0.272515\pi$
$89$	1223.98	−	133.116i	1.45778	−	0.158543i	0.802412	+	0.596771i	$0.203550\pi$
$90$	−209.245	+	308.613i	−0.245071	+	0.361452i
$91$	165.066	+	99.3171i	0.190150	+	0.114409i
$92$	88.2595	−	317.882i	0.100018	−	0.360233i
$93$	−262.254	−	944.553i	−0.292413	−	1.05318i
$94$	108.570	−	65.3246i	0.119129	−	0.0716778i
$95$	−48.0603	+	886.421i	−0.0519041	+	0.957314i
$96$	439.863	−	148.207i	0.467639	−	0.157566i
$97$	−745.126	−	1405.46i	−0.779960	−	1.47116i	−0.879383	−	0.476115i	$-0.842045\pi$
$97$	−745.126	−	1405.46i	−0.779960	−	1.47116i	0.0994232	−	0.995045i	$-0.468300\pi$
$98$	−400.219	−	471.174i	−0.412532	−	0.485671i
$99$	−50.9590	−	75.1589i	−0.0517331	−	0.0763006i
$100$	−58.9788	−	1087.80i	−0.0589788	−	1.08780i
$101$	−394.654	−	990.507i	−0.388807	−	0.975833i	−0.984932	−	0.172941i	$-0.944673\pi$
$101$	−394.654	−	990.507i	−0.388807	−	0.975833i	0.596125	−	0.802892i	$-0.296706\pi$
$102$	198.653	+	91.9066i	0.192839	+	0.0892168i
$103$	−926.836	+	204.012i	−0.886640	+	0.195164i	−0.634866	−	0.772622i	$-0.718945\pi$
$103$	−926.836	+	204.012i	−0.886640	+	0.195164i	−0.251774	+	0.967786i	$0.581014\pi$
$104$	341.774	−	644.655i	0.322247	−	0.607823i
$105$	62.7361	−	382.673i	0.0583087	−	0.355668i
$106$	361.698	−	274.956i	0.331427	−	0.251944i
$107$	142.618	−	65.9821i	0.128854	−	0.0596143i	−0.354403	−	0.935093i	$-0.615316\pi$
$107$	142.618	−	65.9821i	0.128854	−	0.0596143i	0.483257	+	0.875479i	$0.339454\pi$
$108$	−74.8303	−	70.8830i	−0.0666718	−	0.0631549i
$109$	−81.0291	−	494.256i	−0.0712035	−	0.434322i	−0.998238	−	0.0593450i	$-0.981099\pi$
$109$	−81.0291	−	494.256i	−0.0712035	−	0.434322i	0.927034	−	0.374977i	$-0.122349\pi$
$110$	−396.119	−	133.468i	−0.343349	−	0.115688i
$111$	13.7998	−	34.6349i	0.0118002	−	0.0296162i
$112$	87.4915	−	82.8764i	0.0738140	−	0.0699204i
$113$	1502.13	+	1141.89i	1.25052	+	0.950620i	0.999848	−	0.0174517i	$-0.00555534\pi$
$113$	1502.13	+	1141.89i	1.25052	+	0.950620i	0.250672	+	0.968072i	$0.419348\pi$
$114$	262.576	+	57.7973i	0.215724	+	0.0474843i
$115$	−1133.35	+	1334.28i	−0.919000	+	1.08193i
$116$	305.607	+	33.2367i	0.244611	+	0.0266030i
$117$	−271.715			−0.214701
$118$	898.538	+	227.213i	0.700992	+	0.177260i
$119$	−227.642			−0.175361
$120$	−1460.15	−	158.801i	−1.11078	−	0.120804i
$121$	−795.768	+	936.851i	−0.597872	+	0.703870i
$122$	56.8562	+	12.5150i	0.0421928	+	0.00928733i
$123$	477.678	+	363.122i	0.350169	+	0.266192i
$124$	905.617	−	857.846i	0.655861	−	0.621265i
$125$	−1202.46	+	3017.95i	−0.860412	+	2.15947i
$126$	−111.298	−	37.5008i	−0.0786924	−	0.0265145i
$127$	200.706	+	1224.25i	0.140234	+	0.855392i	0.959444	+	0.281898i	$0.0909641\pi$
$127$	200.706	+	1224.25i	0.140234	+	0.855392i	−0.819210	+	0.573494i	$0.805588\pi$
$128$	204.472	+	193.686i	0.141195	+	0.133747i
$129$	52.2897	−	24.1918i	0.0356887	−	0.0165114i
$130$	−995.726	+	756.931i	−0.671776	+	0.510671i
$131$	−274.580	+	1674.86i	−0.183131	+	1.11705i	0.721993	+	0.691900i	$0.243226\pi$
$131$	−274.580	+	1674.86i	−0.183131	+	1.11705i	−0.905124	+	0.425148i	$0.860222\pi$
$132$	54.1249	−	102.090i	0.0356891	−	0.0673168i
$133$	−273.083	+	60.1101i	−0.178040	+	0.0391896i
$134$	307.790	+	142.399i	0.198425	+	0.0918013i
$135$	202.449	+	508.108i	0.129067	+	0.323933i
$136$	46.6795	+	860.953i	0.0294319	+	0.542839i
$137$	897.826	+	1324.19i	0.559901	+	0.825792i	0.997297	−	0.0734767i	$-0.0234095\pi$
$137$	897.826	+	1324.19i	0.559901	+	0.825792i	−0.437396	+	0.899269i	$0.644099\pi$
$138$	343.253	+	404.108i	0.211736	+	0.249275i
$139$	1317.17	+	2484.45i	0.803750	+	1.51603i	0.855752	+	0.517386i	$0.173095\pi$
$139$	1317.17	+	2484.45i	0.803750	+	1.51603i	−0.0520026	+	0.998647i	$0.516560\pi$
$140$	467.623	−	157.560i	0.282295	−	0.0951163i
$141$	10.0627	−	185.596i	0.00601018	−	0.110851i
$142$	804.693	−	484.168i	0.475552	−	0.286130i
$143$	−81.4914	−	293.506i	−0.0476549	−	0.171638i
$144$	−45.4742	+	163.783i	−0.0263161	+	0.0947821i
$145$	−1397.76	−	841.003i	−0.800534	−	0.481666i
$146$	−646.150	+	953.000i	−0.366272	+	0.540211i
$147$	−901.538	+	98.0482i	−0.505834	+	0.0550128i
$148$	47.1644	−	5.12944i	0.0261952	−	0.00284890i
$149$	1983.71	−	2925.75i	1.09068	−	1.60864i	0.350043	−	0.936734i	$-0.386167\pi$
$149$	1983.71	−	2925.75i	1.09068	−	1.60864i	0.740639	−	0.671903i	$-0.234523\pi$
$150$	1500.22	+	902.651i	0.816615	+	0.491341i
$151$	−28.0497	+	101.026i	−0.0151169	+	0.0544462i	−0.970724	−	0.240198i	$-0.922787\pi$
$151$	−28.0497	+	101.026i	−0.0151169	+	0.0544462i	0.955607	+	0.294645i	$0.0952013\pi$
$152$	283.337	+	1020.49i	0.151195	+	0.544556i
$153$	275.121	−	165.535i	0.145374	−	0.0874687i
$154$	7.12815	−	131.471i	0.00372989	−	0.0687938i
$155$	−6272.89	+	2113.58i	−3.25065	+	1.09527i
$156$	−161.956	−	305.481i	−0.0831209	−	0.156783i
$157$	2196.32	+	2585.70i	1.11647	+	1.31441i	0.944207	+	0.329353i	$0.106831\pi$
$157$	2196.32	+	2585.70i	1.11647	+	1.31441i	0.172259	+	0.985052i	$0.444893\pi$
$158$	−922.266	−	1360.24i	−0.464377	−	0.684905i
$159$	−36.0824	−	665.501i	−0.0179970	−	0.331935i
$160$	−1160.11	−	2911.65i	−0.573215	−	1.43866i
$161$	−500.464	−	231.539i	−0.244982	−	0.113341i
$162$	161.781	−	35.6108i	0.0784614	−	0.0172707i
$163$	1392.02	−	2625.62i	0.668903	−	1.26168i	−0.284121	−	0.958788i	$-0.591702\pi$
$163$	1392.02	−	2625.62i	0.668903	−	1.26168i	0.953024	−	0.302896i	$-0.0979534\pi$
$164$	−123.527	+	753.479i	−0.0588159	+	0.358761i
$165$	−488.139	+	371.074i	−0.230312	+	0.175079i
$166$	−978.284	+	452.603i	−0.457407	+	0.211619i
$167$	−2702.20	−	2559.66i	−1.25211	−	1.18606i	−0.974257	−	0.225439i	$-0.927618\pi$
$167$	−2702.20	−	2559.66i	−1.25211	−	1.18606i	−0.277853	−	0.960624i	$-0.589623\pi$
$168$	−74.8469	−	456.546i	−0.0343724	−	0.209662i
$169$	1218.24	+	410.472i	0.554500	+	0.186833i
$170$	547.069	−	1373.04i	0.246813	−	0.619455i
$171$	286.330	−	271.226i	0.128048	−	0.121293i
$172$	58.3654	+	44.3682i	0.0258740	+	0.0196689i
$173$	311.213	+	68.5032i	0.136769	+	0.0301052i	0.282827	−	0.959171i	$-0.408728\pi$
$173$	311.213	+	68.5032i	0.136769	+	0.0301052i	−0.146058	+	0.989276i	$0.546659\pi$
$174$	−319.844	+	376.550i	−0.139352	+	0.164058i
$175$	−1810.22	−	196.874i	−0.781943	−	0.0850415i
$176$	−190.557			−0.0816122
$177$	1015.56	−	903.912i	0.431265	−	0.383854i
$178$	−2517.95			−1.06027
$179$	1190.40	+	129.463i	0.497064	+	0.0540590i	0.353218	−	0.935541i	$-0.385087\pi$
$179$	1190.40	+	129.463i	0.497064	+	0.0540590i	0.143846	+	0.989600i	$0.454053\pi$
$180$	−450.581	+	530.465i	−0.186580	+	0.219659i
$181$	2207.57	+	485.924i	0.906562	+	0.199549i	0.643694	−	0.765283i	$-0.277401\pi$
$181$	2207.57	+	485.924i	0.906562	+	0.199549i	0.262867	+	0.964832i	$0.415332\pi$
$182$	−313.640	−	238.423i	−0.127739	−	0.0971048i
$183$	61.9997	−	58.7292i	0.0250445	−	0.0237234i
$184$	−773.070	+	1940.26i	−0.309736	+	0.777379i
$185$	−238.575	−	80.3853i	−0.0948129	−	0.0319462i
$186$	324.339	+	1978.38i	0.127859	+	0.779904i
$187$	261.323	+	247.539i	0.102192	+	0.0968012i
$188$	214.658	−	99.3115i	0.0832743	−	0.0385268i
$189$	−137.153	+	104.261i	−0.0527854	+	0.0401264i
$190$	293.714	−	1791.58i	0.112149	−	0.684078i
$191$	2289.65	−	4318.73i	0.867398	−	1.63609i	0.0999342	−	0.994994i	$-0.468137\pi$
$191$	2289.65	−	4318.73i	0.867398	−	1.63609i	0.767464	−	0.641092i	$-0.221518\pi$
$192$	−1369.75	+	301.504i	−0.514859	+	0.113329i
$193$	−3631.54	−	1680.13i	−1.35442	−	0.626623i	−0.397671	−	0.917528i	$-0.630181\pi$
$193$	−3631.54	−	1680.13i	−1.35442	−	0.626623i	−0.956752	+	0.290905i	$0.906044\pi$
$194$	1204.17	+	3022.23i	0.445640	+	1.11847i
$195$	99.3320	+	1832.07i	0.0364785	+	0.672807i
$196$	−647.595	−	955.132i	−0.236004	−	0.348080i
$197$	−672.066	−	791.217i	−0.243059	−	0.286152i	0.627083	−	0.778953i	$-0.284249\pi$
$197$	−672.066	−	791.217i	−0.243059	−	0.286152i	−0.870142	+	0.492801i	$0.835973\pi$
$198$	86.9873	+	164.075i	0.0312218	+	0.0588906i
$199$	1409.87	−	475.040i	0.502225	−	0.169219i	−0.0567748	−	0.998387i	$-0.518082\pi$
$199$	1409.87	−	475.040i	0.502225	−	0.169219i	0.559000	+	0.829168i	$0.311185\pi$
$200$	−373.388	+	6886.73i	−0.132012	+	2.43483i
$201$	426.269	−	256.477i	0.149585	−	0.0900026i
$202$	583.364	+	2101.09i	0.203195	+	0.731842i
$203$	137.463	−	495.096i	0.0475270	−	0.171177i
$204$	350.093	+	210.644i	0.120154	+	0.0722942i
$205$	2273.76	−	3353.55i	0.774666	−	1.14255i
$206$	1929.49	−	209.844i	0.652590	−	0.0709735i
$207$	773.216	−	84.0923i	0.259624	−	0.0282358i
$208$	−319.987	+	471.945i	−0.106669	+	0.157325i
$209$	378.852	+	227.948i	0.125386	+	0.0754424i
$210$	−212.166	+	764.151i	−0.0697182	+	0.251102i
$211$	163.149	+	587.608i	0.0532304	+	0.191719i	0.985385	−	0.170342i	$-0.0544872\pi$
$211$	163.149	+	587.608i	0.0532304	+	0.191719i	−0.932155	+	0.362060i	$0.882073\pi$
$212$	726.697	−	437.239i	0.235423	−	0.141650i
$213$	74.5822	−	1375.59i	0.0239920	−	0.442506i
$214$	−304.550	+	102.615i	−0.0972832	+	0.0327785i
$215$	−182.232	−	343.725i	−0.0578051	−	0.109032i
$216$	422.446	+	497.341i	0.133073	+	0.156666i
$217$	−1170.08	−	1725.75i	−0.366039	−	0.539867i
$218$	55.4547	+	1022.80i	0.0172287	+	0.317765i
$219$	625.163	+	1569.04i	0.192898	+	0.484137i
$220$	−708.143	−	327.622i	−0.217014	−	0.100401i
$221$	1051.89	−	231.538i	0.320171	−	0.0704749i
$222$	−35.7151	+	67.3658i	−0.0107975	+	0.0203662i
$223$	274.777	−	1676.06i	0.0825130	−	0.503307i	−0.912943	−	0.408087i	$-0.866196\pi$
$223$	274.777	−	1676.06i	0.0825130	−	0.503307i	0.995456	−	0.0952204i	$-0.0303556\pi$
$224$	785.940	−	597.456i	0.234432	−	0.178211i
$225$	2330.95	−	1078.41i	0.690650	−	0.319529i
$226$	−2801.53	−	2653.75i	−0.824581	−	0.781084i
$227$	−15.2640	−	93.1064i	−0.00446303	−	0.0272233i	0.984501	−	0.175378i	$-0.0561148\pi$
$227$	−15.2640	−	93.1064i	−0.00446303	−	0.0272233i	−0.988964	+	0.148155i	$0.952667\pi$
$228$	475.599	+	160.248i	0.138146	+	0.0465468i
$229$	−745.711	+	1871.59i	−0.215188	+	0.540080i	−0.996456	−	0.0841150i	$-0.973194\pi$
$229$	−745.711	+	1871.59i	−0.215188	+	0.540080i	0.781268	+	0.624195i	$0.214573\pi$
$230$	2599.26	−	2462.15i	0.745175	−	0.705868i
$231$	−153.757	−	116.883i	−0.0437942	−	0.0332915i
$232$	−1900.66	−	418.368i	−0.537865	−	0.118393i
$233$	2716.30	−	3197.88i	0.763738	−	0.899141i	−0.233580	−	0.972338i	$-0.575044\pi$
$233$	2716.30	−	3197.88i	0.763738	−	0.899141i	0.997318	+	0.0731961i	$0.0233199\pi$
$234$	552.431	+	60.0805i	0.154331	+	0.0167845i
$235$	−1255.08			−0.348394
$236$	1621.57	+	602.984i	0.447267	+	0.166317i
$237$	−2410.75			−0.660739
$238$	462.825	+	50.3352i	0.126052	+	0.0137090i
$239$	2504.15	−	2948.12i	0.677742	−	0.797899i	−0.310537	−	0.950561i	$-0.600509\pi$
$239$	2504.15	−	2948.12i	0.677742	−	0.797899i	0.988278	+	0.152662i	$0.0487846\pi$
$240$	1120.95	+	246.740i	0.301488	+	0.0663626i
$241$	3260.89	+	2478.86i	0.871586	+	0.662563i	0.942240	−	0.334938i	$-0.108715\pi$
$241$	3260.89	+	2478.86i	0.871586	+	0.662563i	−0.0706537	+	0.997501i	$0.522509\pi$
$242$	1825.05	−	1728.78i	0.484788	−	0.459215i
$243$	89.9436	−	225.741i	0.0237444	−	0.0595939i
$244$	102.983	+	34.6989i	0.0270196	+	0.00910397i
$245$	990.681	+	6042.88i	0.258336	+	1.57578i
$246$	−890.888	−	843.894i	−0.230898	−	0.218718i
$247$	1200.73	−	555.515i	0.309313	−	0.143104i
$248$	−6286.92	+	4779.19i	−1.60976	+	1.22371i
$249$	−255.809	+	1560.37i	−0.0651054	+	0.397126i
$250$	3112.08	−	5870.00i	0.787300	−	1.48500i
$251$	−1592.10	+	350.447i	−0.400368	+	0.0881277i	−0.410590	−	0.911820i	$-0.634677\pi$
$251$	−1592.10	+	350.447i	−0.400368	+	0.0881277i	0.0102220	+	0.999948i	$0.496746\pi$
$252$	−198.968	−	92.0526i	−0.0497374	−	0.0230110i
$253$	322.735	+	810.004i	0.0801984	+	0.201283i
$254$	−137.359	−	2533.44i	−0.0339318	−	0.625835i
$255$	−1216.72	−	1794.52i	−0.298799	−	0.440696i
$256$	−2794.18	−	3289.56i	−0.682173	−	0.803116i
$257$	1203.76	+	2270.54i	0.292174	+	0.551098i	0.985531	−	0.169496i	$-0.0542140\pi$
$257$	1203.76	+	2270.54i	0.292174	+	0.551098i	−0.693357	+	0.720594i	$0.743869\pi$
$258$	−111.661	+	37.6228i	−0.0269445	+	0.00907867i
$259$	4.29315	−	79.1826i	0.00102998	−	0.0189968i
$260$	−2000.54	+	1203.68i	−0.477185	+	0.287113i
$261$	193.887	+	698.318i	0.0459820	+	0.165612i
$262$	928.593	−	3344.49i	0.218964	−	0.788638i
$263$	−5609.45	−	3375.09i	−1.31518	−	0.791320i	−0.327063	−	0.945002i	$-0.606059\pi$
$263$	−5609.45	−	3375.09i	−1.31518	−	0.791320i	−0.988120	+	0.153683i	$0.950887\pi$
$264$	−410.529	+	605.484i	−0.0957056	+	0.141155i
$265$	−4474.03	+	486.580i	−1.03712	+	0.112794i
$266$	568.504	−	61.8285i	0.131042	−	0.0142517i
$267$	−2072.80	+	3057.15i	−0.475106	+	0.700730i
$268$	542.428	+	326.368i	0.123635	+	0.0743884i
$269$	1779.37	−	6408.71i	0.403309	−	1.45259i	−0.431533	−	0.902097i	$-0.642027\pi$
$269$	1779.37	−	6408.71i	0.403309	−	1.45259i	0.834842	−	0.550490i	$-0.185559\pi$
$270$	−299.253	−	1077.81i	−0.0674517	−	0.242939i
$271$	6049.51	−	3639.87i	1.35602	−	0.815891i	0.362770	−	0.931879i	$-0.381831\pi$
$271$	6049.51	−	3639.87i	1.35602	−	0.815891i	0.993251	+	0.115988i	$0.0370034\pi$
$272$	36.4784	−	672.805i	0.00813172	−	0.149981i
$273$	−547.672	+	184.532i	−0.121416	+	0.0409099i
$274$	−1532.59	−	2890.78i	−0.337910	−	0.637366i
$275$	1863.98	+	2194.45i	0.408735	+	0.481201i
$276$	555.419	+	819.181i	0.121131	+	0.178655i
$277$	−45.5218	−	839.599i	−0.00987414	−	0.182118i	−0.999310	−	0.0371456i	$-0.988173\pi$
$277$	−45.5218	−	839.599i	−0.00987414	−	0.182118i	0.989436	−	0.144972i	$-0.0463093\pi$
$278$	−2128.63	−	5342.45i	−0.459232	−	1.15259i
$279$	2669.05	+	1234.83i	0.572730	+	0.264973i
$280$	−3050.95	+	671.566i	−0.651176	+	0.143335i
$281$	−2780.56	+	5244.69i	−0.590299	+	1.11342i	0.390901	+	0.920433i	$0.372163\pi$
$281$	−2780.56	+	5244.69i	−0.590299	+	1.11342i	−0.981201	+	0.192990i	$0.938181\pi$
$282$	−61.4970	+	375.115i	−0.0129862	+	0.0792120i
$283$	−774.844	+	589.021i	−0.162755	+	0.123723i	−0.683382	−	0.730061i	$-0.739491\pi$
$283$	−774.844	+	589.021i	−0.162755	+	0.123723i	0.520627	+	0.853785i	$0.325698\pi$
$284$	1590.99	−	736.070i	0.332422	−	0.153795i
$285$	−1933.45	−	1831.46i	−0.401851	−	0.380654i
$286$	100.784	+	614.753i	0.0208373	+	0.127102i
$287$	1209.42	+	407.502i	0.248746	+	0.0838122i
$288$	−515.410	+	1293.58i	−0.105454	+	0.264670i
$289$	2642.80	−	2503.39i	0.537919	−	0.509544i
$290$	2655.86	+	2018.93i	0.537784	+	0.408813i
$291$	4660.71	+	1025.90i	0.938886	+	0.206664i
$292$	−1391.40	+	1638.08i	−0.278854	+	0.328292i
$293$	3259.88	+	354.534i	0.649981	+	0.0706897i	0.427169	−	0.904172i	$-0.359511\pi$
$293$	3259.88	+	354.534i	0.649981	+	0.0706897i	0.222812	+	0.974861i	$0.428476\pi$
$294$	1854.62			0.367904
$295$	−6465.99	−	6517.06i	−1.27615	−	1.28623i
$296$	−300.353			−0.0589785
$297$	270.820	+	29.4535i	0.0529111	+	0.00575443i
$298$	−4680.06	+	5509.79i	−0.909760	+	1.07105i
$299$	2548.05	+	560.869i	0.492835	+	0.108481i
$300$	2601.79	+	1977.83i	0.500714	+	0.380633i
$301$	88.9661	−	84.2732i	0.0170363	−	0.0161376i
$302$	79.3670	−	199.196i	0.0151227	−	0.0379551i
$303$	3031.26	+	1021.35i	0.574724	+	0.193647i
$304$	−133.898	−	816.740i	−0.0252617	−	0.154090i
$305$	−418.654	−	396.571i	−0.0785970	−	0.0744510i
$306$	−595.959	+	275.720i	−0.111336	+	0.0515093i
$307$	−3436.40	+	2612.28i	−0.638846	+	0.485638i	−0.873747	−	0.486381i	$-0.838317\pi$
$307$	−3436.40	+	2612.28i	−0.638846	+	0.485638i	0.234901	+	0.972019i	$0.424524\pi$
$308$	39.7612	−	242.533i	0.00735587	−	0.0448688i
$309$	1333.59	−	2515.42i	0.245519	−	0.463098i
$310$	13220.9	−	2910.14i	2.42225	−	0.533177i
$311$	−6185.44	−	2861.69i	−1.12779	−	0.521773i	−0.234891	−	0.972022i	$-0.575473\pi$
$311$	−6185.44	−	2861.69i	−1.12779	−	0.521773i	−0.892903	+	0.450249i	$0.851335\pi$
$312$	810.214	+	2033.48i	0.147017	+	0.368985i
$313$	556.956	+	10272.4i	0.100578	+	1.85506i	0.420100	+	0.907478i	$0.361995\pi$
$313$	556.956	+	10272.4i	0.100578	+	1.85506i	−0.319522	+	0.947579i	$0.603522\pi$
$314$	−3893.65	−	5742.70i	−0.699781	−	1.03210i
$315$	753.134	+	886.658i	0.134712	+	0.158595i
$316$	−1436.93	−	2710.34i	−0.255803	−	0.482495i
$317$	−7904.04	+	2663.18i	−1.40043	+	0.471859i	−0.915366	−	0.402622i	$-0.868099\pi$
$317$	−7904.04	+	2663.18i	−1.40043	+	0.471859i	−0.485060	+	0.874481i	$0.661202\pi$
$318$	−73.7927	+	1361.03i	−0.0130129	+	0.240008i
$319$	−696.171	+	418.872i	−0.122188	+	0.0735183i
$320$	2533.67	+	9125.46i	0.442614	+	1.59415i
$321$	−126.120	+	454.242i	−0.0219293	+	0.0789823i
$322$	966.310	+	581.409i	0.167237	+	0.100623i
$323$	−877.346	+	1293.99i	−0.151136	+	0.222909i
$324$	307.405	−	33.4324i	0.0527101	−	0.00573257i
$325$	8564.95	−	931.494i	1.46184	−	0.158985i
$326$	−3410.71	+	5030.42i	−0.579453	+	0.854630i
$327$	1287.48	+	774.651i	0.217730	+	0.131004i
$328$	1293.19	−	4657.66i	0.217697	−	0.784074i
$329$	−105.763	−	380.924i	−0.0177231	−	0.0638329i
$330$	1074.50	−	646.504i	0.179240	−	0.107845i
$331$	−350.504	+	6464.67i	−0.0582038	+	1.07351i	0.812899	+	0.582405i	$0.197888\pi$
$331$	−350.504	+	6464.67i	−0.0582038	+	1.07351i	−0.871102	+	0.491101i	$0.836594\pi$
$332$	−1906.75	+	642.459i	−0.315201	+	0.106203i
$333$	52.3908	+	98.8196i	0.00862162	+	0.0162621i
$334$	4927.93	+	5801.61i	0.807318	+	0.950449i
$335$	−1885.16	−	2780.41i	−0.307455	−	0.453462i
$336$	19.5732	+	361.007i	0.00317800	+	0.0586148i
$337$	−2100.85	−	5272.74i	−0.339587	−	0.852298i	−0.995260	−	0.0972530i	$-0.968994\pi$
$337$	−2100.85	−	5272.74i	−0.339587	−	0.852298i	0.655673	−	0.755045i	$-0.272385\pi$
$338$	−2386.07	−	1103.91i	−0.383979	−	0.177648i
$339$	−5528.30	+	1216.87i	−0.885711	+	0.194960i
$340$	1292.31	−	2437.55i	0.206133	−	0.388808i
$341$	−533.374	+	3253.44i	−0.0847033	+	0.516667i
$342$	−642.117	+	488.124i	−0.101525	+	0.0771776i
$343$	−3736.91	+	1728.88i	−0.588263	+	0.272160i
$344$	−336.968	−	319.193i	−0.0528143	−	0.0500284i
$345$	−849.670	−	5182.76i	−0.132593	−	0.808783i
$346$	−617.588	−	208.090i	−0.0959588	−	0.0323323i
$347$	3792.30	−	9517.95i	0.586689	−	1.47248i	−0.273179	−	0.961963i	$-0.588075\pi$
$347$	3792.30	−	9517.95i	0.586689	−	1.47248i	0.859868	−	0.510516i	$-0.170546\pi$
$348$	−669.532	+	634.214i	−0.103134	+	0.0976938i
$349$	1777.07	+	1350.89i	0.272563	+	0.207197i	0.732522	−	0.680743i	$-0.238343\pi$
$349$	1777.07	+	1350.89i	0.272563	+	0.207197i	−0.459960	+	0.887940i	$0.652136\pi$
$350$	3636.88	+	800.538i	0.555427	+	0.122259i
$351$	527.714	−	621.273i	0.0802486	−	0.0944760i
$352$	−1551.90	−	168.779i	−0.234990	−	0.0255568i
$353$	3331.16			0.502265			0.251133	−	0.967953i	$-0.419197\pi$
$353$	3331.16			0.502265			0.251133	+	0.967953i	$0.419197\pi$
$354$	−2264.62	+	1613.21i	−0.340009	+	0.242207i
$355$	−9302.33			−1.39075
$356$	−4672.57	−	508.172i	−0.695633	−	0.0756547i
$357$	442.117	−	520.500i	0.0655443	−	0.0771647i
$358$	−2391.60	−	526.431i	−0.353073	−	0.0777172i
$359$	10242.2	+	7785.92i	1.50575	+	1.14464i	0.949562	+	0.313580i	$0.101528\pi$
$359$	10242.2	+	7785.92i	1.50575	+	1.14464i	0.556184	+	0.831059i	$0.312265\pi$
$360$	3198.95	−	3030.20i	0.468332	−	0.443627i
$361$	1827.98	−	4587.89i	0.266509	−	0.668886i
$362$	−4380.83	−	1476.07i	−0.636053	−	0.214311i
$363$	−596.588	−	3639.03i	−0.0862610	−	0.526169i
$364$	−533.905	−	505.742i	−0.0768797	−	0.0728243i
$365$	10350.9	−	4788.83i	1.48436	−	0.686737i
$366$	−139.039	+	105.695i	−0.0198571	+	0.0150950i
$367$	−1047.60	+	6390.06i	−0.149003	+	0.908878i	0.801462	+	0.598046i	$0.204056\pi$
$367$	−1047.60	+	6390.06i	−0.149003	+	0.908878i	−0.950465	+	0.310832i	$0.899392\pi$
$368$	764.521	−	1442.04i	0.108297	−	0.204270i
$369$	−1758.00	+	386.965i	−0.248016	+	0.0545924i
$370$	467.278	+	216.186i	0.0656558	+	0.0303756i
$371$	−524.696	−	1316.89i	−0.0734255	−	0.184284i
$372$	202.601	+	3736.75i	0.0282375	+	0.520811i
$373$	−3140.82	−	4632.36i	−0.435993	−	0.643041i	0.544692	−	0.838636i	$-0.316647\pi$
$373$	−3140.82	−	4632.36i	−0.435993	−	0.643041i	−0.980685	+	0.195595i	$0.937336\pi$
$374$	−476.569	−	561.060i	−0.0658898	−	0.0775714i
$375$	−4565.14	−	8610.76i	−0.628647	−	1.18575i
$376$	−1418.99	+	478.112i	−0.194624	+	0.0655764i
$377$	−131.618	+	2427.56i	−0.0179806	+	0.331633i
$378$	301.904	−	181.650i	0.0410801	−	0.0247170i
$379$	970.843	+	3496.66i	0.131580	+	0.473909i	0.999750	−	0.0223584i	$-0.00711750\pi$
$379$	970.843	+	3496.66i	0.131580	+	0.473909i	−0.868170	+	0.496267i	$0.834704\pi$
$380$	906.624	−	3265.36i	0.122392	−	0.440815i
$381$	−3189.04	−	1918.78i	−0.428817	−	0.258011i
$382$	−5610.08	+	8274.25i	−0.751405	+	1.10824i
$383$	−11388.0	+	1238.52i	−1.51932	+	0.165236i	−0.829400	−	0.558655i	$-0.811318\pi$
$383$	−11388.0	+	1238.52i	−1.51932	+	0.165236i	−0.689915	+	0.723890i	$0.742352\pi$
$384$	−839.977	+	91.3530i	−0.111627	+	0.0121402i
$385$	−731.888	+	1079.45i	−0.0968844	+	0.142894i
$386$	7011.86	+	4218.90i	0.924597	+	0.556312i
$387$	−46.2407	+	166.544i	−0.00607376	+	0.0218757i
$388$	1624.63	+	5851.39i	0.212573	+	0.765617i
$389$	9677.75	−	5822.91i	1.26139	−	0.758954i	0.281708	−	0.959500i	$-0.409099\pi$
$389$	9677.75	−	5822.91i	1.26139	−	0.758954i	0.979684	+	0.200546i	$0.0642716\pi$
$390$	203.145	−	3746.79i	0.0263761	−	0.486478i
$391$	−2921.69	+	984.432i	−0.377893	+	0.127327i
$392$	3422.03	+	6454.64i	0.440915	+	0.831655i
$393$	−3296.27	−	3880.67i	−0.423091	−	0.498101i
$394$	1191.44	+	1757.25i	0.152345	+	0.224693i
$395$	881.308	+	16254.8i	0.112262	+	2.07055i
$396$	128.309	+	322.031i	0.0162823	+	0.0408654i
$397$	−3527.35	−	1631.92i	−0.445926	−	0.206307i	0.184058	−	0.982915i	$-0.441076\pi$
$397$	−3527.35	−	1631.92i	−0.445926	−	0.206307i	−0.629984	+	0.776608i	$0.716939\pi$
$398$	−2971.48	+	654.071i	−0.374238	+	0.0823760i
$399$	392.930	−	741.144i	0.0493010	−	0.0929915i
$400$	871.947	−	5318.64i	0.108993	−	0.664830i
$401$	6793.44	−	5164.24i	0.846005	−	0.643116i	−0.0896731	−	0.995971i	$-0.528582\pi$
$401$	6793.44	−	5164.24i	0.846005	−	0.643116i	0.935678	+	0.352855i	$0.114789\pi$
$402$	−923.369	+	427.196i	−0.114561	+	0.0530015i
$403$	7162.02	+	6784.23i	0.885275	+	0.838577i
$404$	658.510	+	4016.74i	0.0810944	+	0.494654i
$405$	−1554.97	−	523.930i	−0.190783	−	0.0642822i
$406$	−388.952	+	976.197i	−0.0475453	+	0.119330i
$407$	−91.0318	+	86.2299i	−0.0110867	+	0.0105019i
$408$	−2059.22	−	1565.38i	−0.249869	−	0.189945i
$409$	11560.1	+	2544.57i	1.39758	+	0.307631i	0.848967	−	0.528446i	$-0.177225\pi$
$409$	11560.1	+	2544.57i	1.39758	+	0.307631i	0.548613	+	0.836076i	$0.315156\pi$
$410$	−5364.37	+	6315.42i	−0.646164	+	0.760723i
$411$	−4771.47	−	518.929i	−0.572651	−	0.0622795i
$412$	3622.91			0.433223
$413$	1433.09	−	2511.64i	0.170745	−	0.299249i
$414$	−1590.64			−0.188830
$415$	10614.5	+	1154.39i	1.25553	+	0.136547i
$416$	−3024.00	+	3560.12i	−0.356403	+	0.419590i
$417$	−8238.83	−	1813.50i	−0.967523	−	0.212968i
$418$	−719.851	−	547.216i	−0.0842322	−	0.0640316i
$419$	−78.1337	+	74.0122i	−0.00910998	+	0.00862943i	−0.692241	−	0.721666i	$-0.743376\pi$
$419$	−78.1337	+	74.0122i	−0.00910998	+	0.00862943i	0.683131	+	0.730296i	$0.260618\pi$
$420$	−547.938	+	1375.22i	−0.0636586	+	0.159771i
$421$	−9997.16	−	3368.44i	−1.15732	−	0.389947i	−0.325799	−	0.945439i	$-0.605633\pi$
$421$	−9997.16	−	3368.44i	−1.15732	−	0.389947i	−0.831522	+	0.555493i	$0.812530\pi$
$422$	−201.772	−	1230.76i	−0.0232752	−	0.141972i
$423$	404.820	+	383.465i	0.0465319	+	0.0440774i
$424$	−4872.94	+	2254.46i	−0.558139	+	0.258223i
$425$	−8104.83	+	6161.13i	−0.925040	+	0.703197i
$426$	−455.799	+	2780.25i	−0.0518393	+	0.316206i
$427$	85.0821	−	160.482i	0.00964265	−	0.0181880i
$428$	−585.865	+	128.959i	−0.0661655	+	0.0145641i
$429$	829.366	+	383.705i	0.0933384	+	0.0431829i
$430$	294.497	+	739.131i	0.0330277	+	0.0828932i
$431$	430.956	+	7948.52i	0.0481634	+	0.888322i	0.918391	+	0.395673i	$0.129489\pi$
$431$	430.956	+	7948.52i	0.0481634	+	0.888322i	−0.870228	+	0.492649i	$0.836029\pi$
$432$	−286.170	−	422.070i	−0.0318712	−	0.0470066i
$433$	−3129.23	−	3684.01i	−0.347300	−	0.408874i	0.560582	−	0.828099i	$-0.310578\pi$
$433$	−3129.23	−	3684.01i	−0.347300	−	0.408874i	−0.907882	+	0.419225i	$0.862302\pi$
$434$	1997.34	+	3767.38i	0.220911	+	0.416682i
$435$	4637.61	−	1562.59i	0.511164	−	0.172231i
$436$	−103.514	+	1909.21i	−0.0113703	+	0.209712i
$437$	−3244.97	+	1952.43i	−0.355212	+	0.213724i
$438$	−924.095	−	3328.29i	−0.100810	−	0.363086i
$439$	−3349.60	+	12064.2i	−0.364163	+	1.31160i	0.523863	+	0.851803i	$0.324490\pi$
$439$	−3349.60	+	12064.2i	−0.364163	+	1.31160i	−0.888026	+	0.459794i	$0.847923\pi$
$440$	4232.63	+	2546.69i	0.458597	+	0.275929i
$441$	1526.74	−	2251.78i	0.164857	−	0.243146i
$442$	−2189.82	+	238.157i	−0.235654	+	0.0256289i
$443$	1032.80	−	112.324i	0.110767	−	0.0120467i	−0.0525675	−	0.998617i	$-0.516740\pi$
$443$	1032.80	−	112.324i	0.110767	−	0.0120467i	0.163335	+	0.986571i	$0.447775\pi$
$444$	−79.8725	+	117.803i	−0.00853734	+	0.0125916i
$445$	21371.0	+	12858.5i	2.27659	+	1.36978i
$446$	−929.259	+	3346.89i	−0.0986585	+	0.355336i
$447$	2837.01	+	10218.0i	0.300193	+	1.08120i
$448$	−2556.12	+	1537.96i	−0.269565	+	0.162192i
$449$	386.983	−	7137.48i	0.0406745	−	0.750197i	−0.905065	−	0.425272i	$-0.860178\pi$
$449$	386.983	−	7137.48i	0.0406745	−	0.750197i	0.945740	−	0.324924i	$-0.105339\pi$
$450$	−4977.56	+	1677.13i	−0.521432	+	0.175691i
$451$	−945.249	−	1782.93i	−0.0986918	−	0.186153i
$452$	−4663.24	−	5489.99i	−0.485266	−	0.571300i
$453$	−176.517	−	260.344i	−0.0183080	−	0.0270022i
$454$	10.4464	+	192.672i	0.00107990	+	0.0199175i
$455$	1444.45	+	3625.28i	0.148828	+	0.373530i
$456$	−2883.62	−	1334.10i	−0.296135	−	0.137007i
$457$	−10618.4	+	2337.29i	−1.08689	+	0.239242i	−0.722059	−	0.691832i	$-0.756804\pi$
$457$	−10618.4	+	2337.29i	−1.08689	+	0.239242i	−0.364830	+	0.931074i	$0.618873\pi$
$458$	1929.96	−	3640.30i	0.196902	−	0.371397i
$459$	−155.836	+	950.556i	−0.0158470	+	0.0966627i
$460$	5320.38	−	4044.45i	0.539269	−	0.409942i
$461$	−279.804	+	129.451i	−0.0282685	+	0.0130784i	−0.433972	−	0.900926i	$-0.642888\pi$
$461$	−279.804	+	129.451i	−0.0282685	+	0.0130784i	0.405704	+	0.914005i	$0.367026\pi$
$462$	286.763	+	271.636i	0.0288775	+	0.0273542i
$463$	−376.657	−	2297.50i	−0.0378072	−	0.230614i	0.961163	−	0.275981i	$-0.0890025\pi$
$463$	−376.657	−	2297.50i	−0.0378072	−	0.230614i	−0.998970	+	0.0453670i	$0.985554\pi$
$464$	1441.25	+	485.613i	0.144199	+	0.0485862i
$465$	7350.27	−	18447.8i	0.733033	−	1.83977i
$466$	−6229.69	+	5901.07i	−0.619280	+	0.586613i
$467$	−9451.26	−	7184.66i	−0.936514	−	0.711919i	0.0211596	−	0.999776i	$-0.493264\pi$
$467$	−9451.26	−	7184.66i	−0.936514	−	0.711919i	−0.957673	+	0.287857i	$0.907057\pi$
$468$	1013.02	+	222.983i	0.100058	+	0.0220244i
$469$	685.009	−	806.455i	0.0674430	−	0.0794000i
$470$	2551.74	+	277.519i	0.250432	+	0.0272361i
$471$	−10177.8			−0.995683
$472$	−9793.01	−	4904.98i	−0.954999	−	0.478326i
$473$	−193.768			−0.0188361
$474$	4901.36	+	533.055i	0.474951	+	0.0516541i
$475$	−8095.81	+	9531.13i	−0.782024	+	0.920670i
$476$	848.707	+	186.815i	0.0817236	+	0.0179887i
$477$	1591.74	+	1210.01i	0.152790	+	0.116148i
$478$	−5743.14	+	5440.19i	−0.549550	+	0.520562i
$479$	3257.93	−	8176.79i	0.310770	−	0.779973i	−0.687769	−	0.725930i	$-0.741410\pi$
$479$	3257.93	−	8176.79i	0.310770	−	0.779973i	0.998539	−	0.0540432i	$-0.0172109\pi$
$480$	8910.55	+	3002.31i	0.847311	+	0.285492i
$481$	60.7001	+	370.254i	0.00575403	+	0.0350980i
$482$	−6081.68	−	5760.87i	−0.574716	−	0.544400i
$483$	1501.39	−	694.618i	0.141440	−	0.0654373i
$484$	3735.66	−	2839.77i	0.350832	−	0.266695i
$485$	5213.42	−	31800.4i	0.488101	−	2.97729i
$486$	−232.782	+	439.073i	−0.0217267	+	0.0409809i
$487$	13172.0	−	2899.37i	1.22563	−	0.269781i	0.445430	−	0.895317i	$-0.353051\pi$
$487$	13172.0	−	2899.37i	1.22563	−	0.269781i	0.780195	+	0.625536i	$0.215120\pi$
$488$	−624.397	−	288.877i	−0.0579203	−	0.0267968i
$489$	3299.93	+	8282.20i	0.305170	+	0.765918i
$490$	−678.001	−	12505.0i	−0.0625081	−	1.15289i
$491$	−4217.67	−	6220.60i	−0.387660	−	0.571755i	0.582922	−	0.812528i	$-0.301909\pi$
$491$	−4217.67	−	6220.60i	−0.387660	−	0.571755i	−0.970581	+	0.240773i	$0.922599\pi$
$492$	−1482.91	−	1745.82i	−0.135884	−	0.159975i
$493$	−1345.66	−	2538.18i	−0.122932	−	0.231874i
$494$	−2564.06	+	863.932i	−0.233527	+	0.0786845i
$495$	99.5888	−	1836.81i	0.00904279	−	0.166784i
$496$	5288.01	−	3181.69i	0.478707	−	0.288028i
$497$	−783.886	−	2823.30i	−0.0707487	−	0.254814i
$498$	865.114	−	3115.86i	0.0778448	−	0.280372i
$499$	7284.08	+	4382.68i	0.653467	+	0.393178i	0.803335	−	0.595528i	$-0.203057\pi$
$499$	7284.08	+	4382.68i	0.653467	+	0.393178i	−0.149867	+	0.988706i	$0.547885\pi$
$500$	6959.78	−	10264.9i	0.622501	−	0.918121i
$501$	11100.7	−	1207.28i	0.989908	−	0.107659i
$502$	3314.43	−	360.466i	0.294681	−	0.0320485i
$503$	4917.00	−	7252.03i	0.435861	−	0.642847i	−0.544799	−	0.838567i	$-0.683394\pi$
$503$	4917.00	−	7252.03i	0.435861	−	0.642847i	0.980660	+	0.195720i	$0.0627043\pi$
$504$	1189.25	+	715.548i	0.105106	+	0.0632402i
$505$	5778.43	−	20812.0i	0.509181	−	1.83391i
$506$	−477.057	−	1718.20i	−0.0419126	−	0.150955i
$507$	−3304.55	+	1988.28i	−0.289468	+	0.174167i
$508$	256.401	−	4729.04i	0.0223936	−	0.413026i
$509$	−3639.73	+	1226.37i	−0.316951	+	0.106793i	−0.473281	−	0.880912i	$-0.656930\pi$
$509$	−3639.73	+	1226.37i	−0.316951	+	0.106793i	0.156330	+	0.987705i	$0.450034\pi$
$510$	2076.94	+	3917.53i	0.180330	+	0.340139i
$511$	2325.68	+	2738.00i	0.201335	+	0.237030i
$512$	3689.11	+	5441.03i	0.318432	+	0.469652i
$513$	64.0565	+	1181.45i	0.00551299	+	0.101681i
$514$	−1945.35	−	4882.46i	−0.166937	−	0.418980i
$515$	−17448.1	−	8072.33i	−1.49292	−	0.690698i
$516$	−214.802	+	47.2816i	−0.0183259	+	0.00403383i
$517$	−292.807	+	552.292i	−0.0249084	+	0.0469821i
$518$	−26.2370	+	160.039i	−0.00222546	+	0.0135747i
$519$	−761.057	+	578.541i	−0.0643674	+	0.0489309i
$520$	13414.8	−	6206.35i	1.13130	−	0.523397i
$521$	−9983.65	−	9457.02i	−0.839523	−	0.795239i	0.141335	−	0.989962i	$-0.454861\pi$
$521$	−9983.65	−	9457.02i	−0.839523	−	0.795239i	−0.980858	+	0.194723i	$0.937619\pi$
$522$	−239.787	−	1462.64i	−0.0201058	−	0.122640i
$523$	16325.4	+	5500.66i	1.36493	+	0.459899i	0.903998	−	0.427536i	$-0.140618\pi$
$523$	16325.4	+	5500.66i	1.36493	+	0.459899i	0.460933	+	0.887435i	$0.347515\pi$
$524$	2398.18	−	6018.98i	0.199933	−	0.501794i
$525$	3965.89	−	3756.69i	0.329687	−	0.312296i
$526$	10658.4	+	8102.32i	0.883516	+	0.671631i
$527$	−11384.9	−	2506.01i	−0.941053	−	0.207141i
$528$	370.091	−	435.705i	0.0305041	−	0.0359122i
$529$	4671.13	+	508.016i	0.383918	+	0.0417536i
$530$	9203.86			0.754321
$531$	94.4095	+	4077.60i	0.00771568	+	0.333244i
$532$	1067.45			0.0869924
$533$	−6003.00	−	652.865i	−0.487840	−	0.0530558i
$534$	4890.25	−	5757.25i	0.396296	−	0.466555i
$535$	3108.89	+	684.318i	0.251232	+	0.0553002i
$536$	−3190.52	−	2425.37i	−0.257107	−	0.195448i
$537$	−2607.96	+	2470.39i	−0.209575	+	0.198520i
$538$	−5034.75	+	12636.3i	−0.403464	+	1.01262i
$539$	2890.26	+	973.841i	0.230969	+	0.0778225i
$540$	−337.801	−	2060.50i	−0.0269197	−	0.164203i
$541$	10234.1	+	9694.27i	0.813307	+	0.770405i	0.976346	−	0.216215i	$-0.0693711\pi$
$541$	10234.1	+	9694.27i	0.813307	+	0.770405i	−0.163039	+	0.986620i	$0.552130\pi$
$542$	−13104.3	+	6062.67i	−1.03852	+	0.480469i
$543$	−5398.52	+	4103.85i	−0.426653	+	0.324333i
$544$	892.997	−	5447.04i	0.0703804	−	0.429301i
$545$	4752.51	−	8964.18i	0.373532	−	0.704557i
$546$	1154.29	−	254.078i	0.0904744	−	0.0199149i
$547$	3318.46	+	1535.28i	0.259391	+	0.120007i	0.545275	−	0.838257i	$-0.316425\pi$
$547$	3318.46	+	1535.28i	0.259391	+	0.120007i	−0.285884	+	0.958264i	$0.592287\pi$
$548$	−2260.62	−	5673.74i	−0.176221	−	0.442281i
$549$	13.8703	+	255.823i	0.00107827	+	0.0198875i
$550$	−3304.48	−	4873.74i	−0.256188	−	0.377849i
$551$	−2284.49	−	2689.51i	−0.176629	−	0.207944i
$552$	−2934.95	−	5535.91i	−0.226304	−	0.426855i
$553$	−4859.14	+	1637.23i	−0.373656	+	0.125899i
$554$	−93.0972	+	1717.08i	−0.00713957	+	0.131682i
$555$	647.150	−	389.377i	0.0494955	−	0.0297805i
$556$	−2871.89	−	10343.6i	−0.219056	−	0.788970i
$557$	5582.92	−	20107.8i	0.424696	−	1.52962i	−0.373738	−	0.927534i	$-0.621924\pi$
$557$	5582.92	−	20107.8i	0.424696	−	1.52962i	0.798434	−	0.602083i	$-0.205662\pi$
$558$	−5153.46	−	3100.74i	−0.390974	−	0.235241i
$559$	−325.380	+	479.899i	−0.0246191	+	0.0363105i
$560$	2426.98	−	263.950i	0.183140	−	0.0199177i
$561$	−1073.53	+	116.753i	−0.0807919	+	0.00878665i
$562$	6812.91	−	10048.3i	0.511361	−	0.754202i
$563$	20516.6	+	12344.4i	1.53583	+	0.924077i	0.996641	+	0.0818911i	$0.0260960\pi$
$563$	20516.6	+	12344.4i	1.53583	+	0.924077i	0.539187	+	0.842186i	$0.318732\pi$
$564$	−189.826	+	683.692i	−0.0141722	+	0.0510437i
$565$	10225.9	+	36830.4i	0.761428	+	2.74242i
$566$	1705.60	−	1026.22i	0.126664	−	0.0762110i
$567$	27.9817	−	516.091i	0.00207252	−	0.0382254i
$568$	−10517.1	+	3543.63i	−0.776917	+	0.261774i
$569$	7427.89	+	14010.5i	0.547264	+	1.03225i	0.990716	+	0.135951i	$0.0434091\pi$
$569$	7427.89	+	14010.5i	0.547264	+	1.03225i	−0.443451	+	0.896298i	$0.646246\pi$
$570$	3525.98	+	4151.10i	0.259100	+	0.305036i
$571$	−3814.12	−	5625.40i	−0.279537	−	0.412287i	0.661838	−	0.749647i	$-0.269777\pi$
$571$	−3814.12	−	5625.40i	−0.279537	−	0.412287i	−0.941376	+	0.337360i	$0.890466\pi$
$572$	62.9552	+	1161.14i	0.00460190	+	0.0848771i
$573$	5427.86	+	13622.9i	0.395728	+	0.993203i
$574$	−2368.81	−	1095.93i	−0.172251	−	0.0796918i
$575$	−24084.9	+	5301.48i	−1.74680	+	0.384499i
$576$	1970.88	−	3717.48i	0.142570	−	0.268915i
$577$	−1154.73	+	7043.52i	−0.0833135	+	0.508190i	0.911896	+	0.410422i	$0.134619\pi$
$577$	−1154.73	+	7043.52i	−0.0833135	+	0.508190i	−0.995209	+	0.0977681i	$0.968830\pi$
$578$	−5926.68	+	4505.34i	−0.426501	+	0.324217i
$579$	10894.6	−	5040.38i	0.781976	−	0.361781i
$580$	4521.03	+	4282.55i	0.323665	+	0.306592i
$581$	544.094	+	3318.83i	0.0388517	+	0.236985i
$582$	−9248.97	−	3116.34i	−0.658732	−	0.221953i
$583$	−829.660	+	2082.29i	−0.0589382	+	0.147924i
$584$	9878.37	−	9357.29i	0.699948	−	0.663026i
$585$	−4381.92	−	3331.05i	−0.309693	−	0.235422i
$586$	−6549.36	−	1441.62i	−0.461692	−	0.101626i
$587$	−3708.48	+	4365.96i	−0.260759	+	0.306989i	−0.876925	−	0.480627i	$-0.840409\pi$
$587$	−3708.48	+	4365.96i	−0.260759	+	0.306989i	0.616166	+	0.787616i	$0.288685\pi$
$588$	3441.63	+	374.300i	0.241378	+	0.0262515i
$589$	−14319.3			−1.00172
$590$	11705.2	+	14679.7i	0.816769	+	1.02433i
$591$	3114.37			0.216765
$592$	233.339	+	25.3772i	0.0161996	+	0.00176182i
$593$	11546.3	−	13593.3i	0.799577	−	0.941335i	−0.199681	−	0.979861i	$-0.563990\pi$
$593$	11546.3	−	13593.3i	0.799577	−	0.941335i	0.999258	+	0.0385263i	$0.0122663\pi$
$594$	−544.099	−	119.765i	−0.0375836	−	0.00827278i
$595$	−3671.16	−	2790.74i	−0.252946	−	0.192285i
$596$	−9796.79	+	9280.02i	−0.673309	+	0.637792i
$597$	−1652.01	+	4146.24i	−0.113254	+	0.284245i
$598$	−5056.50	−	1703.73i	−0.345778	−	0.116506i
$599$	1865.23	+	11377.4i	0.127231	+	0.776073i	0.970949	+	0.239287i	$0.0769135\pi$
$599$	1865.23	+	11377.4i	0.127231	+	0.776073i	−0.843718	+	0.536786i	$0.819638\pi$
$600$	−15021.2	−	14228.9i	−1.02207	−	0.968152i
$601$	−1704.40	+	788.541i	−0.115681	+	0.0535196i	−0.476876	−	0.878971i	$-0.658231\pi$
$601$	−1704.40	+	788.541i	−0.115681	+	0.0535196i	0.361195	+	0.932490i	$0.382369\pi$
$602$	−199.513	+	151.666i	−0.0135076	+	0.0102682i
$603$	−241.450	+	1472.78i	−0.0163061	+	0.0994629i
$604$	187.484	−	353.632i	0.0126301	−	0.0238230i
$605$	−24318.5	+	5352.90i	−1.63419	+	0.359713i
$606$	−5937.10	−	2746.79i	−0.397984	−	0.184127i
$607$	−7364.37	−	18483.2i	−0.492439	−	1.23593i	−0.939846	−	0.341599i	$-0.889032\pi$
$607$	−7364.37	−	18483.2i	−0.492439	−	1.23593i	0.447407	−	0.894331i	$-0.352348\pi$
$608$	−367.068	−	6770.16i	−0.0244845	−	0.451590i
$609$	865.056	+	1275.86i	0.0575596	+	0.0848941i
$610$	763.489	+	898.849i	0.0506767	+	0.0596612i
$611$	876.155	+	1652.60i	0.0580122	+	0.109423i
$612$	−1161.57	+	391.378i	−0.0767217	+	0.0258505i
$613$	1120.31	−	20663.0i	0.0738157	−	1.36145i	−0.693628	−	0.720334i	$-0.743989\pi$
$613$	1120.31	−	20663.0i	0.0738157	−	1.36145i	0.767443	−	0.641117i	$-0.221529\pi$
$614$	7564.25	−	4551.26i	0.497180	−	0.299143i
$615$	3251.84	+	11712.1i	0.213214	+	0.767928i
$616$	−416.259	+	1499.23i	−0.0272265	+	0.0980611i
$617$	2924.80	+	1759.79i	0.190840	+	0.114824i	0.607767	−	0.794115i	$-0.292065\pi$
$617$	2924.80	+	1759.79i	0.190840	+	0.114824i	−0.416927	+	0.908940i	$0.636893\pi$
$618$	−3267.56	+	4819.29i	−0.212687	+	0.313690i
$619$	−10181.5	+	1107.30i	−0.661111	+	0.0719002i	−0.432523	−	0.901623i	$-0.642376\pi$
$619$	−10181.5	+	1107.30i	−0.661111	+	0.0719002i	−0.228588	+	0.973523i	$0.573411\pi$
$620$	25121.4	−	2732.12i	1.62726	−	0.176975i
$621$	−1309.43	+	1931.27i	−0.0846146	+	0.124797i
$622$	11943.0	+	7185.87i	0.769889	+	0.463227i
$623$	−2101.73	+	7569.76i	−0.135159	+	0.486799i
$624$	−457.631	−	1648.24i	−0.0293588	−	0.105741i
$625$	−25825.1	+	15538.5i	−1.65281	+	0.994461i
$626$	1139.04	−	21008.3i	0.0727238	−	1.34131i
$627$	−1256.99	+	423.529i	−0.0800627	+	0.0269763i
$628$	−6066.47	−	11442.6i	−0.385475	−	0.727084i
$629$	−287.028	−	337.916i	−0.0181949	−	0.0214207i
$630$	−1335.16	−	1969.22i	−0.0844351	−	0.124532i
$631$	−735.661	−	13568.5i	−0.0464124	−	0.856026i	−0.925356	−	0.379100i	$-0.876234\pi$
$631$	−735.661	−	13568.5i	−0.0464124	−	0.856026i	0.878943	−	0.476926i	$-0.158249\pi$
$632$	7188.50	+	18041.8i	0.452442	+	1.13554i
$633$	−1660.42	−	768.192i	−0.104259	−	0.0482352i
$634$	16658.8	−	3666.87i	1.04354	−	0.229701i
$635$	−11771.8	+	22203.9i	−0.735667	+	1.38762i
$636$	−411.620	+	2510.77i	−0.0256632	+	0.156539i
$637$	7265.26	−	5522.91i	0.451900	−	0.343525i
$638$	1508.02	−	697.685i	0.0935786	−	0.0432941i
$639$	3000.41	+	2842.14i	0.185750	+	0.175952i
$640$	923.033	+	5630.25i	0.0570095	+	0.347742i
$641$	−10913.6	−	3677.22i	−0.672483	−	0.226586i	−0.0377146	−	0.999289i	$-0.512008\pi$
$641$	−10913.6	−	3677.22i	−0.672483	−	0.226586i	−0.634768	+	0.772703i	$0.718904\pi$
$642$	356.857	−	895.644i	0.0219377	−	0.0550596i
$643$	−14909.4	+	14122.9i	−0.914414	+	0.866179i	−0.991402	−	0.130853i	$-0.958228\pi$
$643$	−14909.4	+	14122.9i	−0.914414	+	0.866179i	0.0769876	+	0.997032i	$0.475470\pi$
$644$	1675.85	+	1273.95i	0.102543	+	0.0779510i
$645$	1139.85	+	250.899i	0.0695836	+	0.0153165i
$646$	2069.88	−	2436.85i	0.126065	−	0.148416i
$647$	23269.8	+	2530.74i	1.41395	+	0.153777i	0.782990	−	0.622034i	$-0.213694\pi$
$647$	23269.8	+	2530.74i	1.41395	+	0.153777i	0.630965	+	0.775811i	$0.282659\pi$
$648$	−1957.62			−0.118677
$649$	−4376.29	+	1324.91i	−0.264691	+	0.0801347i
$650$	−17619.6			−1.06323
$651$	6218.38	+	676.290i	0.374374	+	0.0407157i
$652$	−7344.51	+	8646.63i	−0.441155	+	0.519368i
$653$	−7974.10	−	1755.23i	−0.477872	−	0.105188i	−0.0304986	−	0.999535i	$-0.509710\pi$
$653$	−7974.10	−	1755.23i	−0.477872	−	0.105188i	−0.447374	+	0.894347i	$0.647641\pi$
$654$	−2446.32	−	1859.65i	−0.146267	−	0.111189i
$655$	−24960.8	+	23644.2i	−1.48901	+	1.41046i
$656$	−1398.19	+	3509.20i	−0.0832169	+	0.208859i
$657$	−4801.75	−	1617.90i	−0.285136	−	0.0960735i
$658$	130.801	+	797.852i	0.00774949	+	0.0472698i
$659$	9915.07	+	9392.05i	0.586095	+	0.555178i	0.922233	−	0.386634i	$-0.126362\pi$
$659$	9915.07	+	9392.05i	0.586095	+	0.555178i	−0.336139	+	0.941813i	$0.609121\pi$
$660$	2124.43	−	982.865i	0.125293	−	0.0579666i
$661$	5247.43	−	3989.00i	0.308777	−	0.234726i	−0.439296	−	0.898342i	$-0.644772\pi$
$661$	5247.43	−	3989.00i	0.308777	−	0.234726i	0.748073	+	0.663616i	$0.230979\pi$
$662$	2142.06	−	13066.0i	0.125761	−	0.767106i
$663$	−1513.53	+	2854.82i	−0.0886584	+	0.167228i
$664$	12440.4	−	2738.34i	0.727080	−	0.160042i
$665$	−5140.90	−	2378.43i	−0.299783	−	0.138694i
$666$	−84.6666	−	212.497i	−0.00492607	−	0.0123635i
$667$	−376.753	−	6948.81i	−0.0218710	−	0.403387i
$668$	7973.91	+	11760.6i	0.461856	+	0.681186i
$669$	3298.63	+	3883.45i	0.190632	+	0.224429i
$670$	3217.98	+	6069.75i	0.185554	+	0.349993i
$671$	−272.179	+	91.7079i	−0.0156593	+	0.00527622i
$672$	−160.345	+	2957.39i	−0.00920454	+	0.169768i
$673$	−10702.3	+	6439.34i	−0.612989	+	0.368823i	−0.787938	−	0.615754i	$-0.788851\pi$
$673$	−10702.3	+	6439.34i	−0.612989	+	0.368823i	0.174949	+	0.984577i	$0.444024\pi$
$674$	3105.41	+	11184.7i	0.177472	+	0.639195i
$675$	−2061.30	+	7424.12i	−0.117540	+	0.423340i
$676$	−4205.05	−	2530.09i	−0.239249	−	0.143952i
$677$	8860.95	−	13068.9i	0.503034	−	0.741919i	−0.488387	−	0.872627i	$-0.662415\pi$
$677$	8860.95	−	13068.9i	0.503034	−	0.741919i	0.991421	+	0.130708i	$0.0417250\pi$
$678$	11508.8	−	1251.66i	0.651906	−	0.0708991i
$679$	10090.9	−	1097.45i	0.570330	−	0.0620271i
$680$	−9801.93	+	14456.8i	−0.552775	+	0.815282i
$681$	242.532	+	145.926i	0.0136473	+	0.00821132i
$682$	1803.80	−	6496.71i	0.101277	−	0.364768i
$683$	277.506	+	999.485i	0.0155468	+	0.0559945i	0.970917	−	0.239418i	$-0.0769567\pi$
$683$	277.506	+	999.485i	0.0155468	+	0.0559945i	−0.955370	+	0.295413i	$0.904543\pi$
$684$	−1290.09	+	776.223i	−0.0721169	+	0.0433913i
$685$	−1754.61	+	32361.9i	−0.0978691	+	1.80509i
$686$	7979.90	−	2688.74i	0.444131	−	0.149645i
$687$	−2831.08	−	5339.99i	−0.157224	−	0.296555i
$688$	234.816	+	276.447i	0.0130121	+	0.0153190i
$689$	3763.95	+	5551.41i	0.208121	+	0.306955i
$690$	581.497	+	10725.1i	0.0320829	+	0.591734i
$691$	−9254.62	−	23227.3i	−0.509497	−	1.27874i	−0.928694	−	0.370846i	$-0.879068\pi$
$691$	−9254.62	−	23227.3i	−0.509497	−	1.27874i	0.419198	−	0.907895i	$-0.362311\pi$
$692$	−1104.07	−	510.795i	−0.0606507	−	0.0280600i
$693$	565.872	−	124.558i	0.0310183	−	0.00682765i
$694$	−9814.79	+	18512.7i	−0.536836	+	1.01258i
$695$	−9215.86	+	56214.2i	−0.502989	+	3.06810i
$696$	4647.99	−	3533.31i	0.253134	−	0.192428i
$697$	6475.99	−	2996.11i	0.351931	−	0.162820i
$698$	−3314.30	−	3139.48i	−0.179725	−	0.170245i
$699$	2036.41	+	12421.6i	0.110192	+	0.672142i
$700$	6587.42	+	2219.56i	0.355687	+	0.119845i
$701$	−7475.71	+	18762.6i	−0.402787	+	1.01092i	0.578034	+	0.816012i	$0.303820\pi$
$701$	−7475.71	+	18762.6i	−0.402787	+	1.01092i	−0.980822	+	0.194907i	$0.937559\pi$
$702$	−1210.28	+	1146.44i	−0.0650700	+	0.0616376i
$703$	−433.553	−	329.578i	−0.0232600	−	0.0176818i
$704$	4606.70	+	1014.01i	0.246622	+	0.0542855i
$705$	2437.57	−	2869.73i	0.130219	−	0.153305i
$706$	−6772.66	−	736.572i	−0.361038	−	0.0392652i
$707$	6803.48			0.361911
$708$	−4528.05	+	2536.60i	−0.240360	+	0.134649i
$709$	3848.80			0.203871			0.101936	−	0.994791i	$-0.467496\pi$
$709$	3848.80			0.203871			0.101936	+	0.994791i	$0.467496\pi$
$710$	18912.8	+	2056.89i	0.999697	+	0.108724i
$711$	4682.06	−	5512.15i	0.246963	−	0.290748i
$712$	29060.2	+	6396.63i	1.52960	+	0.336691i
$713$	−22480.5	−	17089.2i	−1.18079	−	0.897611i
$714$	−1013.97	+	960.483i	−0.0531469	+	0.0503434i
$715$	2283.99	−	5732.37i	0.119463	−	0.299830i
$716$	−4331.86	−	1459.57i	−0.226102	−	0.0761827i
$717$	1877.37	+	11451.4i	0.0977846	+	0.596460i
$718$	−19102.1	−	18094.5i	−0.992875	−	0.940501i
$719$	21073.7	−	9749.74i	1.09307	−	0.505708i	0.211316	−	0.977418i	$-0.432225\pi$
$719$	21073.7	−	9749.74i	1.09307	−	0.505708i	0.881754	+	0.471710i	$0.156363\pi$
$720$	−2741.24	+	2083.84i	−0.141889	+	0.107861i
$721$	979.685	−	5975.81i	0.0506038	−	0.308670i
$722$	−4730.97	+	8923.56i	−0.243862	+	0.459973i
$723$	−12001.1	+	2641.63i	−0.617322	+	0.135883i
$724$	−7831.63	−	3623.30i	−0.402017	−	0.185993i
$725$	−8505.64	−	21347.5i	−0.435712	−	1.09356i
$726$	408.292	+	7530.51i	0.0208721	+	0.384963i
$727$	−17829.4	−	26296.4i	−0.909567	−	1.34151i	−0.939712	−	0.341966i	$-0.888907\pi$
$727$	−17829.4	−	26296.4i	−0.909567	−	1.34151i	0.0301454	−	0.999546i	$-0.490403\pi$
$728$	3014.10	+	3548.47i	0.153448	+	0.180652i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	−22103.6	+	7447.56i	−1.12067	+	0.377598i
$731$	37.0932	−	684.144i	0.00187680	−	0.0346156i
$732$	−279.347	+	168.078i	−0.0141051	+	0.00848678i
$733$	4358.51	+	15697.9i	0.219625	+	0.791018i	0.988449	+	0.151557i	$0.0484286\pi$
$733$	4358.51	+	15697.9i	0.219625	+	0.791018i	−0.768824	+	0.639461i	$0.779158\pi$
$734$	3542.84	−	12760.1i	0.178159	−	0.641670i
$735$	−15741.0	−	9471.06i	−0.789955	−	0.475300i
$736$	7503.53	−	11066.9i	0.375793	−	0.554254i
$737$	−1663.30	+	180.895i	−0.0831324	+	0.00904119i
$738$	3659.80	−	398.027i	0.182546	−	0.0198531i
$739$	18223.6	−	26877.7i	0.907124	−	1.33791i	−0.0338496	−	0.999427i	$-0.510777\pi$
$739$	18223.6	−	26877.7i	0.907124	−	1.33791i	0.940973	−	0.338481i	$-0.109913\pi$
$740$	823.500	+	495.484i	0.0409088	+	0.0246140i
$741$	−1061.82	+	3824.34i	−0.0526411	+	0.189596i
$742$	775.588	+	2793.42i	0.0383730	+	0.138207i
$743$	−19013.6	+	11440.1i	−0.938819	+	0.564869i	−0.900718	−	0.434405i	$-0.856959\pi$
$743$	−19013.6	+	11440.1i	−0.938819	+	0.564869i	−0.0381017	+	0.999274i	$0.512131\pi$
$744$	1282.64	−	23656.9i	0.0632041	−	1.16573i
$745$	67858.9	−	22864.3i	3.33712	−	1.12441i
$746$	5361.39	+	10112.6i	0.263129	+	0.496314i
$747$	−3070.94	−	3615.39i	−0.150415	−	0.177082i
$748$	−771.138	−	1137.34i	−0.0376946	−	0.0555954i
$749$	54.2850	+	1001.23i	0.00264824	+	0.0488439i
$750$	7377.52	+	18516.2i	0.359185	+	0.901487i
$751$	491.599	+	227.438i	0.0238864	+	0.0110510i	0.431796	−	0.901971i	$-0.357880\pi$
$751$	491.599	+	227.438i	0.0238864	+	0.0110510i	−0.407910	+	0.913022i	$0.633742\pi$
$752$	1142.78	−	251.546i	0.0554163	−	0.0121980i
$753$	2290.81	−	4320.94i	0.110866	−	0.209115i
$754$	804.369	−	4906.43i	0.0388506	−	0.236978i
$755$	−1690.87	+	1285.36i	−0.0815060	+	0.0619592i
$756$	596.905	−	276.158i	0.0287159	−	0.0132854i
$757$	−6393.10	−	6055.87i	−0.306950	−	0.290759i	0.518682	−	0.854967i	$-0.326423\pi$
$757$	−6393.10	−	6055.87i	−0.306950	−	0.290759i	−0.825632	+	0.564208i	$0.809181\pi$
$758$	−1200.68	−	7323.82i	−0.0575338	−	0.350941i
$759$	−2478.87	−	835.227i	−0.118547	−	0.0399431i
$760$	−7941.17	+	19930.8i	−0.379022	+	0.951273i
$761$	−4753.50	+	4502.76i	−0.226431	+	0.214487i	−0.792502	−	0.609870i	$-0.791222\pi$
$761$	−4753.50	+	4502.76i	−0.226431	+	0.214487i	0.566070	+	0.824357i	$0.308463\pi$
$762$	6059.44	+	4606.27i	0.288071	+	0.218986i
$763$	3121.16	+	687.019i	0.148091	+	0.0325973i
$764$	−12080.6	+	14222.3i	−0.572067	+	0.673490i
$765$	6466.21	+	703.243i	0.305603	+	0.0332363i
$766$	23427.0			1.10503
$767$	−4067.39	+	13063.4i	−0.191480	+	0.614984i
$768$	12948.3			0.608374
$769$	21049.4	+	2289.26i	0.987077	+	0.107351i	0.587393	−	0.809302i	$-0.300154\pi$
$769$	21049.4	+	2289.26i	0.987077	+	0.107351i	0.399684	+	0.916653i	$0.369120\pi$
$770$	1726.71	−	2032.83i	0.0808132	−	0.0951406i
$771$	−7529.45	−	1657.36i	−0.351707	−	0.0774166i

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03313 - 0.221116i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-3.72826 - 0.820651i) q^{4} +(16.1269 + 12.2594i) q^{5} +(4.45423 - 4.21927i) q^{6} +(-2.36180 + 5.92767i) q^{7} +(22.9030 + 7.71693i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(-2.03313 - 0.221116i) q^{2} +(-1.94216 + 2.28649i) q^{3} +(-3.72826 - 0.820651i) q^{4} +(16.1269 + 12.2594i) q^{5} +(4.45423 - 4.21927i) q^{6} +(-2.36180 + 5.92767i) q^{7} +(22.9030 + 7.71693i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-30.0773 - 28.4907i) q^{10} +(9.15701 - 4.23648i) q^{11} +(9.11727 - 6.93077i) q^{12} +(4.88429 - 29.7928i) q^{13} +(6.11253 - 11.5295i) q^{14} +(-59.3519 + 13.0643i) q^{15} +(-17.1410 - 7.93027i) q^{16} +(13.2050 + 33.1420i) q^{17} +(0.996482 + 18.3790i) q^{18} +(24.5922 + 36.2708i) q^{19} +(-50.0646 - 58.9406i) q^{20} +(-8.96654 - 16.9127i) q^{21} +(-19.5541 + 6.58855i) q^{22} +(-4.67865 + 86.2927i) q^{23} +(-62.1260 + 37.3800i) q^{24} +(76.3443 + 274.967i) q^{25} +(-16.5180 + 59.4926i) q^{26} +(23.1351 + 13.9200i) q^{27} +(13.6699 - 20.1616i) q^{28} +(-80.0540 + 8.70639i) q^{29} +(123.559 - 13.4378i) q^{30} +(-183.374 + 270.457i) q^{31} +(-132.573 - 79.7665i) q^{32} +(-8.09771 + 29.1653i) q^{33} +(-19.5191 - 70.3016i) q^{34} +(-110.758 + 66.6408i) q^{35} +(-1.86008 + 34.3072i) q^{36} +(-11.7771 + 3.96816i) q^{37} +(-41.9790 - 79.1808i) q^{38} +(58.6349 + 69.0303i) q^{39} +(274.750 + 405.227i) q^{40} +(-10.8283 - 199.716i) q^{41} +(14.4904 + 36.3683i) q^{42} +(-17.4299 - 8.06392i) q^{43} +(-37.6164 + 8.27999i) q^{44} +(85.3993 - 161.080i) q^{45} +(28.5930 - 174.409i) q^{46} +(-49.3229 + 37.4943i) q^{47} +(51.4230 - 23.7908i) q^{48} +(219.457 + 207.881i) q^{49} +(-94.4180 - 575.924i) q^{50} +(-101.425 - 34.1740i) q^{51} +(-42.6594 + 107.067i) q^{52} +(-161.287 + 152.779i) q^{53} +(-43.9587 - 33.4166i) q^{54} +(199.611 + 43.9377i) q^{55} +(-99.8357 + 117.536i) q^{56} +(-130.695 - 14.2139i) q^{57} +164.685 q^{58} +(-448.795 - 62.9462i) q^{59} +232.000 q^{60} +(-28.2997 - 3.07777i) q^{61} +(432.625 - 509.326i) q^{62} +(56.0851 + 12.3453i) q^{63} +(372.184 + 282.927i) q^{64} +(444.010 - 420.588i) q^{65} +(22.9126 - 57.5062i) q^{66} +(-157.146 - 52.9486i) q^{67} +(-22.0335 - 134.398i) q^{68} +(-188.220 - 178.292i) q^{69} +(239.920 - 110.999i) q^{70} +(-365.568 + 277.898i) q^{71} +(35.1897 - 214.648i) q^{72} +(263.714 - 497.417i) q^{73} +(24.8217 - 5.46367i) q^{74} +(-776.982 - 359.470i) q^{75} +(-61.9204 - 155.409i) q^{76} +(3.48545 + 64.2854i) q^{77} +(-103.948 - 153.312i) q^{78} +(520.229 + 612.461i) q^{79} +(-179.211 - 338.028i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-22.1451 + 408.442i) q^{82} +(451.620 - 271.731i) q^{83} +(19.5501 + 70.4132i) q^{84} +(-193.344 + 696.362i) q^{85} +(33.6541 + 20.2490i) q^{86} +(135.570 - 199.951i) q^{87} +(242.416 - 26.3643i) q^{88} +(1223.98 - 133.116i) q^{89} +(-209.245 + 308.613i) q^{90} +(165.066 + 99.3171i) q^{91} +(88.2595 - 317.882i) q^{92} +(-262.254 - 944.553i) q^{93} +(108.570 - 65.3246i) q^{94} +(-48.0603 + 886.421i) q^{95} +(439.863 - 148.207i) q^{96} +(-745.126 - 1405.46i) q^{97} +(-400.219 - 471.174i) q^{98} +(-50.9590 - 75.1589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + O(q^{10}) \)	\( 420q - 2q^{2} + 45q^{3} - 64q^{4} + 14q^{5} + 6q^{6} + 6q^{7} + 18q^{8} - 135q^{9} + 854q^{10} + 32q^{11} + 192q^{12} - 22q^{13} - 884q^{14} - 42q^{15} - 268q^{16} - 56q^{17} - 18q^{18} - 112q^{19} - 250q^{20} + 243q^{21} + 108q^{22} + 16q^{23} - 54q^{24} - 197q^{25} - 328q^{26} + 405q^{27} + 236q^{28} - 54q^{29} - 126q^{30} + 66q^{31} + 857q^{32} - 96q^{33} + 112q^{34} + 532q^{35} - 576q^{36} + 110q^{37} + 56q^{38} + 66q^{39} - 6044q^{40} + 304q^{41} - 306q^{42} - 324q^{43} - 568q^{44} + 126q^{45} + 5842q^{46} + 4082q^{47} + 804q^{48} + 739q^{49} + 576q^{50} + 168q^{51} - 1372q^{52} - 1498q^{53} + 54q^{54} - 4422q^{55} - 12036q^{56} + 336q^{57} + 6298q^{58} - 3305q^{59} + 750q^{60} - 1718q^{61} - 4333q^{62} + 54q^{63} - 6250q^{64} - 5884q^{65} - 324q^{66} + 382q^{67} + 734q^{68} + 3780q^{69} + 8082q^{70} + 8638q^{71} + 162q^{72} + 8894q^{73} + 12428q^{74} + 243q^{75} - 15468q^{76} - 9916q^{77} + 984q^{78} - 578q^{79} + 24570q^{80} - 1215q^{81} - 1382q^{82} - 32q^{83} + 7557q^{84} + 708q^{85} + 2296q^{86} - 5928q^{87} - 17646q^{88} - 2284q^{89} + 378q^{90} + 11124q^{91} + 762q^{92} - 198q^{93} - 1232q^{94} + 24184q^{95} - 396q^{96} - 658q^{97} - 4356q^{98} + 288q^{99} + O(q^{100}) \)

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