LMFDB - Embedded newform 177.4.e.a.7.2

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			7.2
Character	$\chi$	$=$	177.7
Dual form			177.4.e.a.76.2

$q$-expansion

$f(q)$	$=$	$q+(-2.77836 - 4.09778i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-6.11139 + 15.3384i) q^{4} +(11.4034 - 5.27577i) q^{5} +(12.7266 - 7.65732i) q^{6} +(-0.571992 + 2.06013i) q^{7} +(41.1522 - 9.05829i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})$	\(q+(-2.77836 - 4.09778i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-6.11139 + 15.3384i) q^{4} +(11.4034 - 5.27577i) q^{5} +(12.7266 - 7.65732i) q^{6} +(-0.571992 + 2.06013i) q^{7} +(41.1522 - 9.05829i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(-53.3017 - 32.0706i) q^{10} +(-14.9759 + 14.1859i) q^{11} +(-44.9552 - 20.7985i) q^{12} +(-56.4345 + 6.13762i) q^{13} +(10.0312 - 3.37989i) q^{14} +(13.9520 + 35.0169i) q^{15} +(-55.5589 - 52.6281i) q^{16} +(19.2438 + 69.3100i) q^{17} +(20.8713 + 39.3674i) q^{18} +(-23.2702 + 17.6896i) q^{19} +(11.2315 + 207.152i) q^{20} +(-6.07842 - 2.04806i) q^{21} +(99.7391 + 21.9542i) q^{22} +(-14.4763 + 27.3051i) q^{23} +(20.4512 + 124.747i) q^{24} +(21.2803 - 25.0531i) q^{25} +(181.946 + 214.204i) q^{26} +(4.36811 - 26.6443i) q^{27} +(-28.1035 - 21.3637i) q^{28} +(-66.6093 + 98.2414i) q^{29} +(104.728 - 154.462i) q^{30} +(24.1423 + 18.3525i) q^{31} +(-6.75928 + 41.2298i) q^{32} +(-40.0630 - 47.1658i) q^{33} +(230.551 - 271.425i) q^{34} +(4.34612 + 26.5101i) q^{35} +(69.6055 - 131.290i) q^{36} +(-126.670 - 27.8822i) q^{37} +(137.141 + 46.2083i) q^{38} +(-9.21995 - 170.052i) q^{39} +(421.486 - 320.405i) q^{40} +(113.382 + 213.860i) q^{41} +(8.49557 + 30.5983i) q^{42} +(153.916 + 145.797i) q^{43} +(-126.066 - 316.402i) q^{44} +(-107.163 + 36.1073i) q^{45} +(152.111 - 16.5430i) q^{46} +(457.088 + 211.472i) q^{47} +(166.677 - 157.884i) q^{48} +(289.985 + 174.478i) q^{49} +(-161.787 - 17.5953i) q^{50} +(-210.751 + 46.3897i) q^{51} +(250.752 - 903.126i) q^{52} +(-384.406 + 231.289i) q^{53} +(-121.319 + 56.1280i) q^{54} +(-95.9342 + 240.777i) q^{55} +(-4.87750 + 89.9601i) q^{56} +(-49.2114 - 72.5814i) q^{57} +587.636 q^{58} +(-417.646 - 175.928i) q^{59} -622.370 q^{60} +(150.073 + 221.341i) q^{61} +(8.12840 - 149.919i) q^{62} +(7.12240 - 17.8759i) q^{63} +(-367.908 + 170.212i) q^{64} +(-611.164 + 367.725i) q^{65} +(-81.9655 + 295.213i) q^{66} +(-589.841 + 129.834i) q^{67} +(-1180.71 - 128.410i) q^{68} +(-79.4441 - 47.7999i) q^{69} +(96.5576 - 91.4642i) q^{70} +(821.844 + 380.226i) q^{71} +(-377.013 + 41.0027i) q^{72} +(-614.150 + 206.931i) q^{73} +(237.681 + 596.533i) q^{74} +(71.5928 + 67.8163i) q^{75} +(-129.117 - 465.037i) q^{76} +(-20.6587 - 38.9664i) q^{77} +(-671.220 + 510.248i) q^{78} +(-19.7878 - 364.965i) q^{79} +(-911.213 - 307.024i) q^{80} +(79.1063 + 17.4126i) q^{81} +(561.338 - 1058.80i) q^{82} +(-16.4105 - 100.099i) q^{83} +(68.5616 - 80.7169i) q^{84} +(585.109 + 688.843i) q^{85} +(169.809 - 1035.79i) q^{86} +(-283.473 - 215.491i) q^{87} +(-487.791 + 719.438i) q^{88} +(-346.139 + 510.516i) q^{89} +(445.696 + 338.810i) q^{90} +(19.6358 - 119.773i) q^{91} +(-330.348 - 388.916i) q^{92} +(-58.8978 + 69.3398i) q^{93} +(-403.394 - 2460.59i) q^{94} +(-172.034 + 324.490i) q^{95} +(-122.410 - 26.9445i) q^{96} +(-696.898 - 234.812i) q^{97} +(-90.7106 - 1673.06i) q^{98} +(147.797 - 112.352i) 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 $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	−2.77836	−	4.09778i	−0.982300	−	1.44878i	−0.891556	−	0.452910i	$-0.850386\pi$
$2$	−2.77836	−	4.09778i	−0.982300	−	1.44878i	−0.0907436	−	0.995874i	$-0.528924\pi$
$3$	−0.162417	+	2.99560i	−0.0312571	+	0.576504i
$3$	−0.162417	+	2.99560i	−0.0312571	+	0.576504i
$4$	−6.11139	+	15.3384i	−0.763924	+	1.91730i
$5$	11.4034	−	5.27577i	1.01995	−	0.471879i	0.162643	−	0.986685i	$-0.447998\pi$
$5$	11.4034	−	5.27577i	1.01995	−	0.471879i	0.857307	+	0.514806i	$0.172136\pi$
$6$	12.7266	−	7.65732i	0.865933	−	0.521015i
$7$	−0.571992	+	2.06013i	−0.0308846	+	0.111236i	−0.977386	−	0.211464i	$-0.932177\pi$
$7$	−0.571992	+	2.06013i	−0.0308846	+	0.111236i	0.946501	+	0.322701i	$0.104591\pi$
$8$	41.1522	−	9.05829i	1.81869	−	0.400324i
$9$	−8.94724	−	0.973071i	−0.331379	−	0.0360397i
$10$	−53.3017	−	32.0706i	−1.68555	−	1.01416i
$11$	−14.9759	+	14.1859i	−0.410491	+	0.388837i	−0.864891	−	0.501960i	$-0.832612\pi$
$11$	−14.9759	+	14.1859i	−0.410491	+	0.388837i	0.454400	+	0.890798i	$0.349854\pi$
$12$	−44.9552	−	20.7985i	−1.08145	−	0.500334i
$13$	−56.4345	+	6.13762i	−1.20401	+	0.130944i	−0.688046	−	0.725667i	$-0.741531\pi$
$13$	−56.4345	+	6.13762i	−1.20401	+	0.130944i	−0.515963	+	0.856611i	$0.672566\pi$
$14$	10.0312	−	3.37989i	0.191496	−	0.0645224i
$15$	13.9520	+	35.0169i	0.240159	+	0.602755i
$16$	−55.5589	−	52.6281i	−0.868107	−	0.822315i
$17$	19.2438	+	69.3100i	0.274548	+	0.988832i	0.964306	+	0.264792i	$0.0853032\pi$
$17$	19.2438	+	69.3100i	0.274548	+	0.988832i	−0.689758	+	0.724040i	$0.742283\pi$
$18$	20.8713	+	39.3674i	0.273300	+	0.515499i
$19$	−23.2702	+	17.6896i	−0.280977	+	0.213593i	−0.736165	−	0.676802i	$-0.763365\pi$
$19$	−23.2702	+	17.6896i	−0.280977	+	0.213593i	0.455188	+	0.890395i	$0.349572\pi$
$20$	11.2315	+	207.152i	0.125572	+	2.31604i
$21$	−6.07842	−	2.04806i	−0.0631628	−	0.0212820i
$22$	99.7391	+	21.9542i	0.966566	+	0.212757i
$23$	−14.4763	+	27.3051i	−0.131240	+	0.247544i	−0.940419	−	0.340017i	$-0.889567\pi$
$23$	−14.4763	+	27.3051i	−0.131240	+	0.247544i	0.809180	+	0.587561i	$0.199912\pi$
$24$	20.4512	+	124.747i	0.173941	+	1.06099i
$25$	21.2803	−	25.0531i	0.170242	−	0.200425i
$26$	181.946	+	214.204i	1.37241	+	1.61572i
$27$	4.36811	−	26.6443i	0.0311350	−	0.189915i
$28$	−28.1035	−	21.3637i	−0.189681	−	0.144191i
$29$	−66.6093	+	98.2414i	−0.426518	+	0.629068i	−0.978855	−	0.204553i	$-0.934426\pi$
$29$	−66.6093	+	98.2414i	−0.426518	+	0.629068i	0.552337	+	0.833621i	$0.313736\pi$
$30$	104.728	−	154.462i	0.637353	−	0.940025i
$31$	24.1423	+	18.3525i	0.139873	+	0.106329i	0.672771	−	0.739851i	$-0.265104\pi$
$31$	24.1423	+	18.3525i	0.139873	+	0.106329i	−0.532898	+	0.846180i	$0.678897\pi$
$32$	−6.75928	+	41.2298i	−0.0373401	+	0.227765i
$33$	−40.0630	−	47.1658i	−0.211335	−	0.248803i
$34$	230.551	−	271.425i	1.16292	−	1.36909i
$35$	4.34612	+	26.5101i	0.0209894	+	0.128029i
$36$	69.6055	−	131.290i	0.322248	−	0.607823i
$37$	−126.670	−	27.8822i	−0.562823	−	0.123887i	−0.0755587	−	0.997141i	$-0.524074\pi$
$37$	−126.670	−	27.8822i	−0.562823	−	0.123887i	−0.487264	+	0.873255i	$0.662005\pi$
$38$	137.141	+	46.2083i	0.585454	+	0.197262i
$39$	−9.21995	−	170.052i	−0.0378558	−	0.698208i
$40$	421.486	−	320.405i	1.66607	−	1.26651i
$41$	113.382	+	213.860i	0.431884	+	0.814619i	0.999965	−	0.00835312i	$-0.00265891\pi$
$41$	113.382	+	213.860i	0.431884	+	0.814619i	−0.568081	+	0.822972i	$0.692314\pi$
$42$	8.49557	+	30.5983i	0.0312118	+	0.112415i
$43$	153.916	+	145.797i	0.545859	+	0.517065i	0.910182	−	0.414208i	$-0.135941\pi$
$43$	153.916	+	145.797i	0.545859	+	0.517065i	−0.364324	+	0.931272i	$0.618700\pi$
$44$	−126.066	−	316.402i	−0.431936	−	1.08408i
$45$	−107.163	+	36.1073i	−0.354997	+	0.119612i
$46$	152.111	−	16.5430i	0.487555	−	0.0530248i
$47$	457.088	+	211.472i	1.41858	+	0.656304i	0.971249	−	0.238065i	$-0.0765133\pi$
$47$	457.088	+	211.472i	1.41858	+	0.656304i	0.447329	+	0.894370i	$0.352375\pi$
$48$	166.677	−	157.884i	0.501202	−	0.474764i
$49$	289.985	+	174.478i	0.845437	+	0.508683i
$50$	−161.787	−	17.5953i	−0.457601	−	0.0497672i
$51$	−210.751	+	46.3897i	−0.578647	+	0.127370i
$52$	250.752	−	903.126i	0.668712	−	2.40848i
$53$	−384.406	+	231.289i	−0.996269	+	0.599435i	−0.917616	−	0.397467i	$-0.869889\pi$
$53$	−384.406	+	231.289i	−0.996269	+	0.599435i	−0.0786522	+	0.996902i	$0.525062\pi$
$54$	−121.319	+	56.1280i	−0.305729	+	0.141446i
$55$	−95.9342	+	240.777i	−0.235196	+	0.590297i
$56$	−4.87750	+	89.9601i	−0.0116390	+	0.214668i
$57$	−49.2114	−	72.5814i	−0.114355	−	0.168660i
$58$	587.636			1.33035
$59$	−417.646	−	175.928i	−0.921575	−	0.388201i
$59$	−417.646	−	175.928i	−0.921575	−	0.388201i
$60$	−622.370			−1.33913
$61$	150.073	+	221.341i	0.314998	+	0.464587i	0.951922	−	0.306339i	$-0.0991041\pi$
$61$	150.073	+	221.341i	0.314998	+	0.464587i	−0.636925	+	0.770926i	$0.719794\pi$
$62$	8.12840	−	149.919i	0.0166501	−	0.307093i
$63$	7.12240	−	17.8759i	0.0142435	−	0.0357484i
$64$	−367.908	+	170.212i	−0.718570	+	0.332446i
$65$	−611.164	+	367.725i	−1.16624	+	0.701703i
$66$	−81.9655	+	295.213i	−0.152867	+	0.550579i
$67$	−589.841	+	129.834i	−1.07553	+	0.236742i	−0.717211	−	0.696856i	$-0.754582\pi$
$67$	−589.841	+	129.834i	−1.07553	+	0.236742i	−0.358320	+	0.933599i	$0.616650\pi$
$68$	−1180.71	−	128.410i	−2.10563	−	0.229001i
$69$	−79.4441	−	47.7999i	−0.138608	−	0.0833976i
$70$	96.5576	−	91.4642i	0.164869	−	0.156172i
$71$	821.844	+	380.226i	1.37373	+	0.635556i	0.961318	−	0.275441i	$-0.0888237\pi$
$71$	821.844	+	380.226i	1.37373	+	0.635556i	0.412414	+	0.910997i	$0.364686\pi$
$72$	−377.013	+	41.0027i	−0.617103	+	0.0671140i
$73$	−614.150	+	206.931i	−0.984668	+	0.331773i	−0.765162	−	0.643838i	$-0.777341\pi$
$73$	−614.150	+	206.931i	−0.984668	+	0.331773i	−0.219506	+	0.975611i	$0.570445\pi$
$74$	237.681	+	596.533i	0.373376	+	0.937102i
$75$	71.5928	+	67.8163i	0.110224	+	0.104410i
$76$	−129.117	−	465.037i	−0.194878	−	0.701887i
$77$	−20.6587	−	38.9664i	−0.0305750	−	0.0576706i
$78$	−671.220	+	510.248i	−0.974367	+	0.740695i
$79$	−19.7878	−	364.965i	−0.0281810	−	0.519769i	−0.978211	−	0.207611i	$-0.933431\pi$
$79$	−19.7878	−	364.965i	−0.0281810	−	0.519769i	0.950030	−	0.312157i	$-0.101052\pi$
$80$	−911.213	−	307.024i	−1.27346	−	0.429078i
$81$	79.1063	+	17.4126i	0.108513	+	0.0238856i
$82$	561.338	−	1058.80i	0.755968	−	1.42591i
$83$	−16.4105	−	100.099i	−0.0217022	−	0.132378i	0.973753	−	0.227606i	$-0.0730900\pi$
$83$	−16.4105	−	100.099i	−0.0217022	−	0.132378i	−0.995455	+	0.0952289i	$0.969642\pi$
$84$	68.5616	−	80.7169i	0.0890557	−	0.104845i
$85$	585.109	+	688.843i	0.746634	+	0.879006i
$86$	169.809	−	1035.79i	0.212918	−	1.29874i
$87$	−283.473	−	215.491i	−0.349328	−	0.265552i
$88$	−487.791	+	719.438i	−0.590894	+	0.871503i
$89$	−346.139	+	510.516i	−0.412254	+	0.608029i	−0.975961	−	0.217946i	$-0.930064\pi$
$89$	−346.139	+	510.516i	−0.412254	+	0.608029i	0.563707	+	0.825975i	$0.309375\pi$
$90$	445.696	+	338.810i	0.522006	+	0.396819i
$91$	19.6358	−	119.773i	0.0226197	−	0.137974i
$92$	−330.348	−	388.916i	−0.374360	−	0.440731i
$93$	−58.8978	+	69.3398i	−0.0656711	+	0.0773140i
$94$	−403.394	−	2460.59i	−0.442626	−	2.69990i
$95$	−172.034	+	324.490i	−0.185792	+	0.350441i
$96$	−122.410	−	26.9445i	−0.130140	−	0.0286460i
$97$	−696.898	−	234.812i	−0.729477	−	0.245789i	−0.0700344	−	0.997545i	$-0.522311\pi$
$97$	−696.898	−	234.812i	−0.729477	−	0.245789i	−0.659442	+	0.751755i	$0.729207\pi$
$98$	−90.7106	−	1673.06i	−0.0935016	−	1.72454i
$99$	147.797	−	112.352i	0.150042	−	0.114059i
$100$	254.223	+	479.516i	0.254223	+	0.479516i
$101$	54.5325	+	196.408i	0.0537246	+	0.193499i	0.985543	−	0.169427i	$-0.0541917\pi$
$101$	54.5325	+	196.408i	0.0537246	+	0.193499i	−0.931818	+	0.362926i	$0.881778\pi$
$102$	775.637	+	734.722i	0.752936	+	0.713219i
$103$	−736.816	−	1849.27i	−0.704860	−	1.76907i	−0.636330	−	0.771417i	$-0.719548\pi$
$103$	−736.816	−	1849.27i	−0.704860	−	1.76907i	−0.0685301	−	0.997649i	$-0.521831\pi$
$104$	−2266.81	+	763.777i	−2.13730	+	0.720139i
$105$	−80.1197	+	8.71354i	−0.0744655	+	0.00809861i
$106$	2015.79	+	932.605i	1.84709	+	0.854553i
$107$	1481.04	−	1402.92i	1.33811	−	1.26752i	0.402079	−	0.915605i	$-0.368288\pi$
$107$	1481.04	−	1402.92i	1.33811	−	1.26752i	0.936030	−	0.351920i	$-0.114471\pi$
$108$	381.987	+	229.834i	0.340340	+	0.204776i
$109$	−1294.36	−	140.770i	−1.13740	−	0.123700i	−0.480021	−	0.877257i	$-0.659371\pi$
$109$	−1294.36	−	140.770i	−1.13740	−	0.123700i	−0.657383	+	0.753557i	$0.728337\pi$
$110$	1253.19	−	275.848i	1.08625	−	0.239101i
$111$	104.097	−	374.924i	0.0890133	−	0.320597i
$112$	140.200	−	84.3555i	0.118283	−	0.0711682i
$113$	1041.29	−	481.753i	0.866872	−	0.401058i	0.0645255	−	0.997916i	$-0.479447\pi$
$113$	1041.29	−	481.753i	0.866872	−	0.401058i	0.802347	+	0.596858i	$0.203585\pi$
$114$	−160.695	+	403.315i	−0.132022	+	0.331350i
$115$	−21.0229	+	387.745i	−0.0170469	+	0.314412i
$116$	−1099.79	−	1622.07i	−0.880286	−	1.29833i
$117$	510.905			0.403703
$118$	439.459	+	2200.21i	0.342843	+	1.71649i
$119$	−153.795			−0.118473
$120$	891.349	+	1314.64i	0.678072	+	1.00008i
$121$	−49.0219	+	904.155i	−0.0368309	+	0.679305i
$122$	490.049	−	1229.93i	0.363664	−	0.912728i
$123$	−659.056	+	304.912i	−0.483130	+	0.223520i
$124$	−429.041	+	258.145i	−0.310718	+	0.186953i
$125$	−309.683	+	1115.38i	−0.221591	+	0.798098i
$126$	−93.0400	+	20.4797i	−0.0657830	+	0.0144799i
$127$	−725.253	−	78.8760i	−0.506739	−	0.0551111i	−0.148821	−	0.988864i	$-0.547548\pi$
$127$	−725.253	−	78.8760i	−0.506739	−	0.0551111i	−0.357918	+	0.933753i	$0.616513\pi$
$128$	2006.07	+	1207.01i	1.38526	+	0.833484i
$129$	−461.747	+	437.390i	−0.315152	+	0.298528i
$130$	3204.89	+	1482.74i	2.16221	+	1.00035i
$131$	968.326	−	105.312i	0.645825	−	0.0702377i	0.220656	−	0.975352i	$-0.429180\pi$
$131$	968.326	−	105.312i	0.645825	−	0.0702377i	0.425169	+	0.905114i	$0.360215\pi$
$132$	968.289	−	326.255i	0.638476	−	0.215127i
$133$	−23.1324	−	58.0580i	−0.0150815	−	0.0378516i
$134$	2170.82	+	2056.31i	1.39948	+	1.32566i
$135$	−90.7580	−	326.881i	−0.0578608	−	0.208396i
$136$	1419.76	+	2677.95i	0.895170	+	1.68847i
$137$	1133.89	−	861.964i	0.707118	−	0.537537i	−0.188658	−	0.982043i	$-0.560414\pi$
$137$	1133.89	−	861.964i	0.707118	−	0.537537i	0.895776	+	0.444506i	$0.146621\pi$
$138$	24.8510	+	458.350i	0.0153294	+	0.282734i
$139$	−870.800	−	293.407i	−0.531369	−	0.179039i	0.0408114	−	0.999167i	$-0.487006\pi$
$139$	−870.800	−	293.407i	−0.531369	−	0.179039i	−0.572180	+	0.820128i	$0.693902\pi$
$140$	−433.185	−	95.3512i	−0.261506	−	0.0575618i
$141$	−707.723	+	1334.91i	−0.422702	+	0.797301i
$142$	−725.301	−	4424.14i	−0.428633	−	2.61455i
$143$	758.088	−	892.491i	0.443318	−	0.521915i
$144$	445.888	+	524.939i	0.258037	+	0.303784i
$145$	−241.273	+	1471.70i	−0.138184	+	0.842883i
$146$	2554.29	+	1941.72i	1.44791	+	1.10067i
$147$	−569.765	+	840.341i	−0.319683	+	0.471498i
$148$	1201.80	−	1772.52i	0.667482	−	0.984462i
$149$	−2558.02	−	1944.56i	−1.40645	−	1.06916i	−0.986884	−	0.161432i	$-0.948389\pi$
$149$	−2558.02	−	1944.56i	−1.40645	−	1.06916i	−0.419567	−	0.907724i	$-0.637818\pi$
$150$	78.9855	−	481.790i	0.0429942	−	0.262253i
$151$	628.140	+	739.504i	0.338525	+	0.398543i	0.904913	−	0.425596i	$-0.139936\pi$
$151$	628.140	+	739.504i	0.338525	+	0.398543i	−0.566388	+	0.824139i	$0.691660\pi$
$152$	−797.385	+	938.754i	−0.425503	+	0.500941i
$153$	−104.736	−	638.859i	−0.0553423	−	0.337573i
$154$	−102.279	+	192.918i	−0.0535184	+	0.100946i
$155$	372.127	+	81.9114i	0.192838	+	0.0424470i
$156$	2664.68	+	897.835i	1.36760	+	0.460797i
$157$	−98.4075	−	1815.02i	−0.0500240	−	0.922639i	−0.910593	−	0.413305i	$-0.864374\pi$
$157$	−98.4075	−	1815.02i	−0.0500240	−	0.922639i	0.860569	−	0.509334i	$-0.170108\pi$
$158$	−1440.57	+	1095.09i	−0.725350	+	0.551397i
$159$	−630.417	−	1189.09i	−0.314436	−	0.593089i
$160$	140.440	+	505.820i	0.0693923	+	0.249929i
$161$	−47.9718	−	45.4413i	−0.0234826	−	0.0222439i
$162$	−148.433	−	372.539i	−0.0719876	−	0.180675i
$163$	−115.002	+	38.7488i	−0.0552618	+	0.0186199i	−0.346797	−	0.937940i	$-0.612731\pi$
$163$	−115.002	+	38.7488i	−0.0552618	+	0.0186199i	0.291535	+	0.956560i	$0.405834\pi$
$164$	−3973.20	+	432.112i	−1.89180	+	0.205746i
$165$	−705.689	−	326.487i	−0.332957	−	0.154042i
$166$	−364.591	+	345.359i	−0.170468	+	0.161476i
$167$	−3118.48	−	1876.33i	−1.44500	−	0.869429i	−0.445338	−	0.895363i	$-0.646916\pi$
$167$	−3118.48	−	1876.33i	−1.44500	−	0.869429i	−0.999664	+	0.0259339i	$0.991744\pi$
$168$	−268.692	−	29.2221i	−0.123393	−	0.0134198i
$169$	1001.55	−	220.457i	0.455870	−	0.100345i
$170$	1197.08	−	4311.50i	0.540071	−	1.94516i
$171$	225.418	−	135.629i	0.100808	−	0.0606540i
$172$	−3176.93	+	1469.81i	−1.40837	+	0.651579i
$173$	528.850	−	1327.31i	0.232414	−	0.583316i	−0.765798	−	0.643081i	$-0.777656\pi$
$173$	528.850	−	1327.31i	0.232414	−	0.583316i	0.998212	+	0.0597649i	$0.0190351\pi$
$174$	−95.4420	+	1760.32i	−0.0415830	+	0.766953i
$175$	39.4404	+	58.1703i	0.0170367	+	0.0251272i
$176$	1578.62			0.676096
$177$	594.842	−	1222.53i	0.252605	−	0.519157i
$178$	3053.68			1.28586
$179$	1203.57	+	1775.13i	0.502563	+	0.741225i	0.991360	−	0.131173i	$-0.0418742\pi$
$179$	1203.57	+	1775.13i	0.502563	+	0.741225i	−0.488796	+	0.872398i	$0.662564\pi$
$180$	101.083	−	1864.37i	0.0418573	−	0.772012i
$181$	−576.960	+	1448.06i	−0.236934	+	0.594660i	−0.998577	−	0.0533375i	$-0.983014\pi$
$181$	−576.960	+	1448.06i	−0.236934	+	0.594660i	0.761642	+	0.647998i	$0.224393\pi$
$182$	−545.359	+	252.310i	−0.222114	+	0.102761i
$183$	−687.423	+	413.609i	−0.277682	+	0.167076i
$184$	−348.393	+	1254.80i	−0.139586	+	0.502744i
$185$	−1591.57	+	350.331i	−0.632511	+	0.139226i
$186$	447.779	+	48.6989i	0.176520	+	0.0191977i
$187$	−1271.42	−	764.987i	−0.497194	−	0.299152i
$188$	−6037.09	+	5718.63i	−2.34202	+	2.21848i
$189$	52.3922	+	24.2392i	0.0201639	+	0.00932880i
$190$	1807.66	−	196.595i	0.690218	−	0.0750657i
$191$	3396.03	−	1144.26i	1.28654	−	0.433484i	0.408797	−	0.912625i	$-0.365948\pi$
$191$	3396.03	−	1144.26i	1.28654	−	0.433484i	0.877738	+	0.479141i	$0.159052\pi$
$192$	−450.134	−	1129.75i	−0.169196	−	0.424649i
$193$	2738.87	+	2594.40i	1.02149	+	0.967611i	0.999483	−	0.0321467i	$-0.0102344\pi$
$193$	2738.87	+	2594.40i	1.02149	+	0.967611i	0.0220114	+	0.999758i	$0.492993\pi$
$194$	974.027	+	3508.13i	0.360469	+	1.29829i
$195$	−1002.29	−	1890.53i	−0.368081	−	0.694274i
$196$	−4448.43	+	3381.61i	−1.62115	+	1.23237i
$197$	31.3519	+	578.251i	0.0113387	+	0.209131i	0.998713	+	0.0507240i	$0.0161529\pi$
$197$	31.3519	+	578.251i	0.0113387	+	0.209131i	−0.987374	+	0.158406i	$0.949364\pi$
$198$	−871.027	−	293.483i	−0.312632	−	0.105338i
$199$	3849.59	+	847.360i	1.37131	+	0.301848i	0.838737	−	0.544537i	$-0.183294\pi$
$199$	3849.59	+	847.360i	1.37131	+	0.301848i	0.532572	+	0.846385i	$0.321226\pi$
$200$	648.794	−	1223.75i	0.229383	−	0.432663i
$201$	−293.130	−	1788.02i	−0.102865	−	0.627447i
$202$	653.327	−	769.156i	0.227564	−	0.267909i
$203$	−164.290	−	193.417i	−0.0568024	−	0.0668729i
$204$	576.434	−	3516.09i	0.197835	−	1.20674i
$205$	2421.21	+	1840.56i	0.824902	+	0.627074i
$206$	−5530.75	+	8157.25i	−1.87061	+	2.75894i
$207$	156.092	−	230.219i	0.0524115	−	0.0773012i
$208$	3458.45	+	2629.04i	1.15289	+	0.876401i
$209$	97.5496	−	595.026i	0.0322854	−	0.196932i
$210$	258.308	+	304.103i	0.0848806	+	0.0999292i
$211$	−1046.31	+	1231.81i	−0.341377	+	0.401900i	−0.905883	−	0.423529i	$-0.860791\pi$
$211$	−1046.31	+	1231.81i	−0.341377	+	0.401900i	0.564505	+	0.825430i	$0.309067\pi$
$212$	−1198.36	−	7309.69i	−0.388226	−	2.36807i
$213$	−1272.49	+	2400.16i	−0.409339	+	0.772096i
$214$	−9863.72	−	2171.17i	−3.15079	−	0.693542i
$215$	2524.35	+	850.553i	0.800741	+	0.269801i
$216$	−61.5943	−	1136.04i	−0.0194026	−	0.357860i
$217$	−51.6176	+	39.2387i	−0.0161476	+	0.0122751i
$218$	3019.35	+	5695.11i	0.938057	+	1.76936i
$219$	−520.135	−	1873.36i	−0.160491	−	0.578035i
$220$	−3106.85	−	2942.96i	−0.952107	−	0.901884i
$221$	−1511.41	−	3793.36i	−0.460039	−	1.15461i
$222$	−1825.58	+	615.109i	−0.551913	+	0.185961i
$223$	−3882.78	+	422.277i	−1.16596	+	0.126806i	−0.670559	−	0.741856i	$-0.733946\pi$
$223$	−3882.78	+	422.277i	−1.16596	+	0.126806i	−0.495405	+	0.868662i	$0.664980\pi$
$224$	−81.0724	−	37.5081i	−0.0241825	−	0.0111880i
$225$	−214.778	+	203.449i	−0.0636381	+	0.0602812i
$226$	−4867.21	−	2928.50i	−1.43257	−	0.861952i
$227$	313.277	+	34.0710i	0.0915989	+	0.00996198i	0.153804	−	0.988101i	$-0.450848\pi$
$227$	313.277	+	34.0710i	0.0915989	+	0.00996198i	−0.0622048	+	0.998063i	$0.519813\pi$
$228$	1414.04	−	311.253i	0.410732	−	0.0904089i
$229$	1491.39	−	5371.51i	0.430367	−	1.55004i	−0.357330	−	0.933978i	$-0.616313\pi$
$229$	1491.39	−	5371.51i	0.430367	−	1.55004i	0.787697	−	0.616063i	$-0.211273\pi$
$230$	1647.30	−	991.148i	0.472260	−	0.284150i
$231$	120.083	−	55.5564i	0.0342030	−	0.0158240i
$232$	−1851.22	+	4646.22i	−0.523874	+	1.31482i
$233$	34.9097	−	643.872i	0.00981550	−	0.181036i	−0.989514	−	0.144434i	$-0.953864\pi$
$233$	34.9097	−	643.872i	0.00981550	−	0.181036i	0.999330	−	0.0366021i	$-0.0116534\pi$
$234$	−1419.48	−	2093.58i	−0.396557	−	0.584878i
$235$	6328.03			1.75658
$236$	5250.86	−	5330.88i	1.44831	−	1.47038i
$237$	1096.50			0.300529
$238$	427.298	+	630.217i	0.116376	+	0.171642i
$239$	−160.940	+	2968.36i	−0.0435579	+	0.803379i	0.892395	+	0.451254i	$0.149023\pi$
$239$	−160.940	+	2968.36i	−0.0435579	+	0.803379i	−0.935953	+	0.352124i	$0.885459\pi$
$240$	1067.72	−	2679.77i	0.287170	−	0.720742i
$241$	−4393.84	+	2032.81i	−1.17441	+	0.543338i	−0.907364	−	0.420346i	$-0.861909\pi$
$241$	−4393.84	+	2032.81i	−1.17441	+	0.543338i	−0.267043	+	0.963685i	$0.586047\pi$
$242$	3841.23	−	2311.19i	1.02035	−	0.613922i
$243$	−65.0094	+	234.143i	−0.0171620	+	0.0618118i
$244$	−4312.18	+	949.182i	−1.13139	+	0.249038i
$245$	4227.32	+	459.749i	1.10234	+	0.119887i
$246$	3080.56	+	1853.51i	0.798411	+	0.480388i
$247$	1204.67	−	1141.13i	0.310330	−	0.293960i
$248$	1159.75	+	536.557i	0.296952	+	0.137385i
$249$	302.523	−	32.9014i	0.0769945	−	0.00837366i
$250$	5430.98	−	1829.91i	1.37394	−	0.462935i
$251$	2063.48	+	5178.93i	0.518906	+	1.30236i	0.921997	+	0.387196i	$0.126556\pi$
$251$	2063.48	+	5178.93i	0.518906	+	1.30236i	−0.403091	+	0.915160i	$0.632064\pi$
$252$	230.660	+	218.493i	0.0576596	+	0.0546181i
$253$	−170.553	−	614.277i	−0.0423818	−	0.152645i
$254$	1691.80	+	3191.07i	0.417925	+	0.788290i
$255$	−2158.53	+	1640.87i	−0.530088	+	0.402962i
$256$	−451.950	−	8335.72i	−0.110339	−	2.03509i
$257$	4859.27	+	1637.28i	1.17943	+	0.397396i	0.839660	−	0.543113i	$-0.182754\pi$
$257$	4859.27	+	1637.28i	1.17943	+	0.397396i	0.339769	+	0.940509i	$0.389651\pi$
$258$	3075.23	+	676.909i	0.742075	+	0.163343i
$259$	129.895	−	245.008i	0.0311633	−	0.0587802i
$260$	−1905.27	−	11621.6i	−0.454460	−	2.77208i
$261$	691.565	−	814.174i	0.164011	−	0.193088i
$262$	−3121.91	−	3675.39i	−0.736153	−	0.866666i
$263$	1091.73	−	6659.27i	0.255966	−	1.56132i	−0.475667	−	0.879626i	$-0.657793\pi$
$263$	1091.73	−	6659.27i	0.255966	−	1.56132i	0.731633	−	0.681699i	$-0.238759\pi$
$264$	−2075.92	−	1578.07i	−0.483955	−	0.367893i
$265$	−3163.30	+	4665.52i	−0.733284	+	1.08151i
$266$	−173.639	+	256.098i	−0.0400243	+	0.0590314i
$267$	−1473.08	−	1119.81i	−0.337645	−	0.256671i
$268$	1613.30	−	9840.71i	0.367717	−	2.24297i
$269$	5018.53	+	5908.27i	1.13749	+	1.33916i	0.932827	+	0.360325i	$0.117334\pi$
$269$	5018.53	+	5908.27i	1.13749	+	1.33916i	0.204664	+	0.978832i	$0.434390\pi$
$270$	−1087.33	+	1280.10i	−0.245084	+	0.288535i
$271$	−54.6510	−	333.357i	−0.0122502	−	0.0747231i	0.979994	−	0.199028i	$-0.0637783\pi$
$271$	−54.6510	−	333.357i	−0.0122502	−	0.0747231i	−0.992244	+	0.124304i	$0.960330\pi$
$272$	2578.49	−	4863.55i	0.574794	−	1.08418i
$273$	355.603	+	78.2741i	0.0788354	+	0.0173530i
$274$	−6682.51	−	2251.60i	−1.47338	−	0.496439i
$275$	36.7098	+	677.073i	0.00804976	+	0.148469i
$276$	1218.69	−	926.424i	0.265784	−	0.202044i
$277$	1980.08	+	3734.82i	0.429499	+	0.810122i	0.999937	−	0.0112190i	$-0.00357120\pi$
$277$	1980.08	+	3734.82i	0.429499	+	0.810122i	−0.570438	+	0.821341i	$0.693226\pi$
$278$	1217.08	+	4383.54i	0.262575	+	0.945709i
$279$	−198.148	−	187.696i	−0.0425191	−	0.0402762i
$280$	418.989	+	1051.58i	0.0894264	+	0.224443i
$281$	−6387.17	+	2152.09i	−1.35597	+	0.456879i	−0.901073	−	0.433667i	$-0.857219\pi$
$281$	−6387.17	+	2152.09i	−1.35597	+	0.456879i	−0.454894	+	0.890546i	$0.650323\pi$
$282$	7436.47	−	808.765i	1.57034	−	0.170784i
$283$	−1918.78	−	887.720i	−0.403037	−	0.186465i	0.207889	−	0.978152i	$-0.433341\pi$
$283$	−1918.78	−	887.720i	−0.403037	−	0.186465i	−0.610926	+	0.791688i	$0.709203\pi$
$284$	−10854.7	+	10282.1i	−2.26798	+	2.14835i
$285$	−944.100	−	568.046i	−0.196223	−	0.118064i
$286$	−5763.48	−	626.816i	−1.19161	−	0.129596i
$287$	−505.433	+	111.254i	−0.103954	+	0.0228820i
$288$	100.596	−	362.316i	0.0205823	−	0.0741307i
$289$	−223.811	+	134.663i	−0.0455549	+	0.0274095i
$290$	6701.05	−	3100.23i	1.35689	−	0.627766i
$291$	816.591	−	2049.49i	0.164500	−	0.412863i
$292$	579.309	−	10684.7i	0.116101	−	2.14136i
$293$	−987.018	−	1455.74i	−0.196799	−	0.290257i	0.716466	−	0.697622i	$-0.245758\pi$
$293$	−987.018	−	1455.74i	−0.196799	−	0.290257i	−0.913266	+	0.407364i	$0.866448\pi$
$294$	5026.55			0.997123
$295$	−5690.74	+	197.231i	−1.12314	+	0.0389262i
$296$	−5465.32			−1.07319
$297$	312.557	+	460.988i	0.0610654	+	0.0900647i
$298$	−861.254	+	15884.9i	−0.167420	+	3.08788i
$299$	649.372	−	1629.80i	0.125599	−	0.315230i
$300$	−1477.73	+	683.670i	−0.284389	+	0.131572i
$301$	−388.398	+	233.692i	−0.0743751	+	0.0447500i
$302$	1285.12	−	4628.59i	0.244869	−	0.881938i
$303$	−597.218	+	131.458i	−0.113232	+	0.0249242i
$304$	2223.84	+	241.857i	0.419559	+	0.0456298i
$305$	2879.08	+	1732.29i	0.540511	+	0.325215i
$306$	−2326.91	+	2204.17i	−0.434708	+	0.411777i
$307$	5100.00	+	2359.51i	0.948119	+	0.438647i	0.832116	−	0.554602i	$-0.187130\pi$
$307$	5100.00	+	2359.51i	0.948119	+	0.438647i	0.116004	+	0.993249i	$0.462992\pi$
$308$	723.938	−	78.7329i	0.133929	−	0.0145657i
$309$	5659.34	−	1906.85i	1.04190	−	0.351059i
$310$	−698.250	−	1752.47i	−0.127929	−	0.321077i
$311$	−4875.84	−	4618.64i	−0.889015	−	0.842120i	0.0992198	−	0.995066i	$-0.468365\pi$
$311$	−4875.84	−	4618.64i	−0.889015	−	0.842120i	−0.988235	+	0.152946i	$0.951124\pi$
$312$	−1919.80	−	6914.51i	−0.348357	−	1.25467i
$313$	700.086	+	1320.50i	0.126426	+	0.238464i	0.938643	−	0.344891i	$-0.112084\pi$
$313$	700.086	+	1320.50i	0.126426	+	0.238464i	−0.812217	+	0.583355i	$0.801739\pi$
$314$	−7164.14	+	5446.04i	−1.28757	+	0.978783i
$315$	−13.0895	−	241.422i	−0.00234130	−	0.0431828i
$316$	5718.92	+	1926.93i	1.01808	+	0.343032i
$317$	−6296.02	−	1385.86i	−1.11552	−	0.245544i	−0.381296	−	0.924453i	$-0.624522\pi$
$317$	−6296.02	−	1385.86i	−1.11552	−	0.245544i	−0.734223	+	0.678908i	$0.762453\pi$
$318$	−3121.11	+	5887.04i	−0.550388	+	1.03814i
$319$	−396.110	−	2416.16i	−0.0695232	−	0.424073i
$320$	−3297.40	+	3881.99i	−0.576031	+	0.678157i
$321$	3962.03	+	4664.47i	0.688907	+	0.811044i
$322$	−52.9253	+	322.830i	−0.00915966	+	0.0558715i
$323$	−1673.87	−	1272.45i	−0.288349	−	0.219197i
$324$	−750.531	+	1106.95i	−0.128692	+	0.189806i
$325$	−1047.18	+	1544.47i	−0.178729	+	0.263606i
$326$	478.302	+	363.596i	0.0812599	+	0.0617722i
$327$	631.916	−	3854.52i	0.106866	−	0.651851i
$328$	6603.12	+	7773.79i	1.11157	+	1.30865i
$329$	−697.109	+	820.700i	−0.116817	+	0.137528i
$330$	622.791	+	3798.86i	0.103889	+	0.633698i
$331$	−191.278	+	360.789i	−0.0317632	+	0.0599117i	−0.898886	−	0.438183i	$-0.855622\pi$
$331$	−191.278	+	360.789i	−0.0317632	+	0.0599117i	0.867122	+	0.498095i	$0.165967\pi$
$332$	1635.66	+	360.036i	0.270387	+	0.0595167i
$333$	1106.22	+	372.728i	0.182043	+	0.0613374i
$334$	975.496	+	17992.0i	0.159811	+	2.94754i
$335$	−6041.22	+	4592.41i	−0.985275	+	0.748986i
$336$	229.924	+	433.684i	0.0373316	+	0.0704148i
$337$	−1316.09	−	4740.14i	−0.212737	−	0.766208i	−0.990484	−	0.137631i	$-0.956051\pi$
$337$	−1316.09	−	4740.14i	−0.212737	−	0.766208i	0.777747	−	0.628577i	$-0.216362\pi$
$338$	−3686.05	−	3491.61i	−0.593179	−	0.561889i
$339$	1274.02	+	3197.54i	0.204115	+	0.512291i
$340$	−14141.6	+	4764.86i	−2.25569	+	0.760032i
$341$	−621.898	+	67.6355i	−0.0987614	+	0.0107410i
$342$	−1182.07	−	546.885i	−0.186898	−	0.0864682i
$343$	−1057.73	+	1001.93i	−0.166507	+	0.157724i
$344$	7654.64	+	4605.65i	1.19974	+	0.721860i
$345$	−1158.11	−	125.952i	−0.180727	−	0.0196552i
$346$	−6908.37	+	1520.65i	−1.07340	+	0.236273i
$347$	899.023	−	3237.99i	0.139084	−	0.500935i	−0.860885	−	0.508799i	$-0.830090\pi$
$347$	899.023	−	3237.99i	0.139084	−	0.500935i	0.999969	+	0.00786449i	$0.00250337\pi$
$348$	5037.71	−	3031.09i	0.776004	−	0.466906i
$349$	−5004.80	+	2315.47i	−0.767625	+	0.355141i	−0.764306	−	0.644853i	$-0.776918\pi$
$349$	−5004.80	+	2315.47i	−0.767625	+	0.355141i	−0.00331855	+	0.999994i	$0.501056\pi$
$350$	128.789	−	323.237i	0.0196688	−	0.0493649i
$351$	−82.9796	+	1530.47i	−0.0126186	+	0.232736i
$352$	−483.656	−	713.339i	−0.0732356	−	0.108014i
$353$	9101.03			1.37224			0.686118	−	0.727490i	$-0.259313\pi$
$353$	9101.03			1.37224			0.686118	+	0.727490i	$0.259313\pi$
$354$	−6662.34	+	959.093i	−1.00028	+	0.143998i
$355$	11377.8			1.70104
$356$	−5715.13	−	8429.19i	−0.850847	−	1.25490i
$357$	24.9788	−	460.708i	0.00370314	−	0.0683004i
$358$	3930.14	−	9863.91i	0.580208	−	1.45621i
$359$	−7093.19	+	3281.66i	−1.04280	+	0.482449i	−0.865081	−	0.501632i	$-0.832733\pi$
$359$	−7093.19	+	3281.66i	−1.04280	+	0.482449i	−0.177716	+	0.984082i	$0.556871\pi$
$360$	−4082.91	+	2456.61i	−0.597745	+	0.359651i
$361$	−1606.39	+	5785.71i	−0.234202	+	0.843521i
$362$	7536.84	−	1658.98i	1.09427	−	0.240868i
$363$	−2700.53	−	293.700i	−0.390471	−	0.0424662i
$364$	1717.13	+	1033.16i	0.247258	+	0.148770i
$365$	−5911.67	+	5599.83i	−0.847756	+	0.803037i
$366$	3604.79	+	1667.75i	0.514824	+	0.238183i
$367$	2333.90	−	253.827i	0.331958	−	0.0361026i	0.0593774	−	0.998236i	$-0.481088\pi$
$367$	2333.90	−	253.827i	0.331958	−	0.0361026i	0.272580	+	0.962133i	$0.412123\pi$
$368$	2241.30	−	755.183i	0.317489	−	0.106975i
$369$	−806.351	−	2023.79i	−0.113759	−	0.285513i
$370$	5857.54	+	5548.55i	0.823024	+	0.779610i
$371$	−256.609	−	924.221i	−0.0359096	−	0.129335i
$372$	−703.617	−	1327.16i	−0.0980668	−	0.184974i
$373$	8678.31	−	6597.08i	1.20468	−	0.915774i	0.206644	−	0.978416i	$-0.433746\pi$
$373$	8678.31	−	6597.08i	1.20468	−	0.915774i	0.998036	+	0.0626419i	$0.0199526\pi$
$374$	397.714	+	7335.40i	0.0549874	+	1.01418i
$375$	−3290.92	−	1108.84i	−0.453180	−	0.152694i
$376$	20725.8	+	4562.09i	2.84269	+	0.625723i
$377$	3156.09	−	5953.02i	0.431159	−	0.813253i
$378$	−46.2376	−	282.037i	−0.00629155	−	0.0383768i
$379$	3944.95	−	4644.35i	0.534666	−	0.629457i	−0.426812	−	0.904340i	$-0.640363\pi$
$379$	3944.95	−	4644.35i	0.534666	−	0.629457i	0.961478	+	0.274883i	$0.0886392\pi$
$380$	−3925.80	−	4621.81i	−0.529972	−	0.623931i
$381$	354.074	−	2159.76i	0.0476110	−	0.290414i
$382$	−14124.3	−	10737.0i	−1.89179	−	1.43810i
$383$	3277.20	−	4833.51i	0.437225	−	0.644858i	−0.543692	−	0.839285i	$-0.682974\pi$
$383$	3277.20	−	4833.51i	0.437225	−	0.644858i	0.980917	+	0.194426i	$0.0622845\pi$
$384$	−3941.55	+	5813.35i	−0.523805	+	0.772555i
$385$	−441.157	−	335.359i	−0.0583986	−	0.0443934i
$386$	3021.69	−	18431.5i	0.398445	−	2.43041i
$387$	−1235.25	−	1454.25i	−0.162251	−	0.191017i
$388$	7860.66	−	9254.29i	1.02852	−	1.21086i
$389$	131.077	+	799.534i	0.0170845	+	0.104211i	0.993992	−	0.109451i	$-0.0349093\pi$
$389$	131.077	+	799.534i	0.0170845	+	0.104211i	−0.976908	+	0.213662i	$0.931461\pi$
$390$	−4962.23	+	9359.76i	−0.644288	+	1.21526i
$391$	−2171.10	−	477.895i	−0.280811	−	0.0618112i
$392$	13514.0	+	4553.40i	1.74123	+	0.586687i
$393$	158.200	+	2917.82i	0.0203056	+	0.374516i
$394$	2282.44	−	1735.07i	0.291847	−	0.221856i
$395$	−2151.12	−	4057.44i	−0.274011	−	0.516840i
$396$	820.062	+	2953.60i	0.104065	+	0.374808i
$397$	9894.77	+	9372.83i	1.25089	+	1.18491i	0.974629	+	0.223827i	$0.0718549\pi$
$397$	9894.77	+	9372.83i	1.25089	+	1.18491i	0.276264	+	0.961082i	$0.410904\pi$
$398$	−7223.28	−	18129.1i	−0.909724	−	2.28324i
$399$	177.676	−	59.8659i	0.0222930	−	0.00751138i
$400$	−2500.81	+	271.979i	−0.312601	+	0.0339974i
$401$	−782.066	−	361.822i	−0.0973928	−	0.0450587i	0.370588	−	0.928797i	$-0.379156\pi$
$401$	−782.066	−	361.822i	−0.0973928	−	0.0450587i	−0.467981	+	0.883739i	$0.655018\pi$
$402$	−6512.47	+	6168.94i	−0.807992	+	0.765370i
$403$	−1475.10	−	887.536i	−0.182332	−	0.109706i
$404$	−3345.87	−	363.885i	−0.412037	−	0.0448117i
$405$	993.945	−	218.784i	0.121949	−	0.0268431i
$406$	−336.123	+	1210.61i	−0.0410875	+	0.147984i
$407$	2292.53	−	1379.37i	0.279205	−	0.167992i
$408$	−8252.65	+	3818.08i	−1.00139	+	0.463292i
$409$	−4543.65	+	11403.7i	−0.549313	+	1.37867i	0.348090	+	0.937461i	$0.386830\pi$
$409$	−4543.65	+	11403.7i	−0.549313	+	1.37867i	−0.897403	+	0.441211i	$0.854549\pi$
$410$	815.193	−	15035.3i	0.0981939	−	1.81108i
$411$	2397.94	+	3536.69i	0.287790	+	0.424458i
$412$	32867.8			3.93030
$413$	601.324	−	759.775i	0.0716446	−	0.0905232i
$414$	−1377.07			−0.163476
$415$	−715.237	−	1054.90i	−0.0846014	−	0.124778i
$416$	128.404	−	2368.27i	0.0151334	−	0.279120i
$417$	1020.36	−	2560.91i	0.119826	−	0.300740i
$418$	−2709.32	+	1253.46i	−0.317026	+	0.146672i
$419$	4333.50	−	2607.38i	0.505263	−	0.304007i	−0.240005	−	0.970772i	$-0.577149\pi$
$419$	4333.50	−	2607.38i	0.505263	−	0.304007i	0.745268	+	0.666765i	$0.232322\pi$
$420$	355.991	−	1282.16i	0.0413585	−	0.148960i
$421$	14639.2	−	3222.33i	1.69470	−	0.373033i	0.740469	−	0.672090i	$-0.234603\pi$
$421$	14639.2	−	3222.33i	1.69470	−	0.373033i	0.954235	+	0.299058i	$0.0966723\pi$
$422$	7954.68	+	865.124i	0.917602	+	0.0997952i
$423$	−3883.90	−	2336.87i	−0.446434	−	0.268611i
$424$	−13724.1	+	13000.1i	−1.57193	+	1.48902i
$425$	2145.95	+	992.820i	0.244926	+	0.113315i
$426$	13370.8	−	1454.16i	1.52069	−	0.165385i
$427$	−541.831	+	182.564i	−0.0614076	+	0.0206906i
$428$	12467.3	+	31290.6i	1.40802	+	3.53386i
$429$	2550.42	+	2415.89i	0.287029	+	0.271888i
$430$	−3528.19	−	12707.4i	−0.395684	−	1.42513i
$431$	−7944.87	−	14985.6i	−0.887914	−	1.67478i	−0.725682	−	0.688030i	$-0.758476\pi$
$431$	−7944.87	−	14985.6i	−0.887914	−	1.67478i	−0.162232	−	0.986753i	$-0.551869\pi$
$432$	−1644.93	+	1250.44i	−0.183198	+	0.139264i
$433$	−48.8749	−	901.444i	−0.00542442	−	0.100048i	0.994567	−	0.104095i	$-0.0331945\pi$
$433$	−48.8749	−	901.444i	−0.00542442	−	0.100048i	−0.999992	+	0.00404711i	$0.998712\pi$
$434$	304.204	+	102.498i	0.0336458	+	0.0113366i
$435$	−4369.44	−	961.786i	−0.481606	−	0.106009i
$436$	10069.5	−	18993.1i	1.10606	−	2.08625i
$437$	−146.150	−	891.476i	−0.0159984	−	0.0975860i
$438$	−6231.48	+	7336.26i	−0.679798	+	0.800320i
$439$	7762.52	+	9138.75i	0.843929	+	0.993550i	0.999983	+	0.00580191i	$0.00184682\pi$
$439$	7762.52	+	9138.75i	0.843929	+	0.993550i	−0.156054	+	0.987749i	$0.549877\pi$
$440$	−1766.88	+	10777.5i	−0.191438	+	1.16772i
$441$	−2424.79	−	1843.27i	−0.261828	−	0.199036i
$442$	−11345.1	+	16732.8i	−1.22089	+	1.80067i
$443$	−5261.06	+	7759.48i	−0.564245	+	0.832199i	−0.997615	−	0.0690170i	$-0.978014\pi$
$443$	−5261.06	+	7759.48i	−0.564245	+	0.832199i	0.433371	+	0.901216i	$0.357324\pi$
$444$	5114.58	+	3888.00i	0.546682	+	0.415577i
$445$	−1253.79	+	7647.77i	−0.133562	+	0.814694i
$446$	12518.2	+	14737.5i	1.32904	+	1.56467i
$447$	6240.58	−	7346.98i	0.660334	−	0.777405i
$448$	−140.219	−	855.297i	−0.0147873	−	0.0901986i
$449$	1214.44	−	2290.67i	0.127646	−	0.240765i	−0.811449	−	0.584423i	$-0.801321\pi$
$449$	1214.44	−	2290.67i	0.127646	−	0.240765i	0.939095	+	0.343657i	$0.111666\pi$
$450$	1430.42	+	314.860i	0.149846	+	0.0329836i
$451$	−4731.79	−	1594.33i	−0.494039	−	0.166461i
$452$	1025.59	+	18916.0i	0.106725	+	1.96844i
$453$	−2317.28	+	1761.55i	−0.240343	+	0.182704i
$454$	−730.783	−	1378.40i	−0.0755448	−	0.142493i
$455$	−407.980	−	1469.41i	−0.0420361	−	0.151400i
$456$	−2682.62	−	2541.12i	−0.275494	−	0.260962i
$457$	135.668	+	340.501i	0.0138868	+	0.0348533i	0.935757	−	0.352646i	$-0.114718\pi$
$457$	135.668	+	340.501i	0.0138868	+	0.0348533i	−0.921870	+	0.387500i	$0.873339\pi$
$458$	−26154.9	+	8812.61i	−2.66842	+	0.899097i
$459$	1930.78	−	209.985i	0.196342	−	0.0213535i
$460$	−5818.92	−	2692.12i	−0.589801	−	0.272871i
$461$	−10139.6	+	9604.69i	−1.02439	+	0.970358i	−0.999570	−	0.0293335i	$-0.990662\pi$
$461$	−10139.6	+	9604.69i	−1.02439	+	0.970358i	−0.0248252	+	0.999692i	$0.507903\pi$
$462$	−561.293	−	337.719i	−0.0565232	−	0.0340089i
$463$	13781.1	+	1498.78i	1.38328	+	0.150441i	0.769305	−	0.638882i	$-0.220603\pi$
$463$	13781.1	+	1498.78i	1.38328	+	0.150441i	0.613978	+	0.789323i	$0.289568\pi$
$464$	8871.00	−	1952.65i	0.887555	−	0.195366i
$465$	−305.813	+	1101.44i	−0.0304984	+	0.109845i
$466$	−2735.44	+	1645.86i	−0.271924	+	0.163611i
$467$	8862.12	−	4100.06i	0.878138	−	0.406270i	0.0715867	−	0.997434i	$-0.477194\pi$
$467$	8862.12	−	4100.06i	0.878138	−	0.406270i	0.806551	+	0.591165i	$0.201332\pi$
$468$	−3122.34	+	7836.49i	−0.308398	+	0.774021i
$469$	69.9099	−	1289.41i	0.00688303	−	0.126950i
$470$	−17581.6	−	25930.9i	−1.72548	−	2.54490i
$471$	5453.06			0.533468
$472$	−18780.7	−	3456.66i	−1.83146	−	0.337089i
$473$	−4373.28			−0.425124
$474$	−3046.48	−	4493.22i	−0.295210	−	0.435402i
$475$	−52.0189	+	959.432i	−0.00502482	+	0.0926774i
$476$	939.900	−	2358.97i	0.0905047	−	0.227150i
$477$	3664.44	−	1695.35i	0.351746	−	0.162735i
$478$	12610.9	−	7587.70i	1.20671	−	0.726053i
$479$	−1408.08	+	5071.45i	−0.134315	+	0.483759i	−0.999854	−	0.0170826i	$-0.994562\pi$
$479$	−1408.08	+	5071.45i	−0.134315	+	0.483759i	0.865539	+	0.500841i	$0.166976\pi$
$480$	−1538.04	+	338.549i	−0.146254	+	0.0321929i
$481$	7319.69	+	796.065i	0.693866	+	0.0754624i
$482$	20537.7	+	12357.1i	1.94080	+	1.16774i
$483$	143.915	−	136.324i	0.0135577	−	0.0128425i
$484$	−13568.7	−	6277.57i	−1.27430	−	0.589553i
$485$	−9185.81	+	999.017i	−0.860013	+	0.0935320i
$486$	1140.08	−	384.139i	0.106410	−	0.0358537i
$487$	−1134.65	−	2847.75i	−0.105577	−	0.264977i	0.866692	−	0.498843i	$-0.166242\pi$
$487$	−1134.65	−	2847.75i	−0.105577	−	0.264977i	−0.972269	+	0.233866i	$0.924862\pi$
$488$	8180.81	+	7749.27i	0.758868	+	0.718838i
$489$	−97.3976	−	350.795i	−0.00900710	−	0.0324406i
$490$	−9861.08	−	18600.0i	−0.909140	−	1.71482i
$491$	14775.6	−	11232.1i	1.35808	−	1.03238i	0.363154	−	0.931729i	$-0.381700\pi$
$491$	14775.6	−	11232.1i	1.35808	−	1.03238i	0.994922	−	0.100653i	$-0.0320931\pi$
$492$	−649.120	−	11972.3i	−0.0594809	−	1.09706i
$493$	−8090.93	−	2726.15i	−0.739142	−	0.249046i
$494$	−8023.10	−	1766.02i	−0.730722	−	0.160844i
$495$	1092.64	−	2060.94i	0.0992131	−	0.187136i
$496$	−375.460	−	2290.20i	−0.0339892	−	0.207325i
$497$	−1253.40	+	1475.62i	−0.113124	+	0.133180i
$498$	−975.342	−	1148.26i	−0.0877633	−	0.103323i
$499$	1129.03	−	6886.79i	0.101287	−	0.617826i	−0.886586	−	0.462564i	$-0.846930\pi$
$499$	1129.03	−	6886.79i	0.101287	−	0.617826i	0.987873	−	0.155262i	$-0.0496222\pi$
$500$	−15215.5	−	11566.5i	−1.36092	−	1.03454i
$501$	6127.22	−	9036.97i	0.546395	−	0.805873i
$502$	15489.0	−	22844.6i	1.37711	−	2.03109i
$503$	−8962.66	−	6813.23i	−0.794483	−	0.603950i	0.127207	−	0.991876i	$-0.459399\pi$
$503$	−8962.66	−	6813.23i	−0.794483	−	0.603950i	−0.921691	+	0.387926i	$0.873192\pi$
$504$	131.178	−	800.149i	0.0115935	−	0.0707172i
$505$	1658.06	+	1952.02i	0.146104	+	0.172007i
$506$	−2043.31	+	2405.58i	−0.179519	+	0.211346i
$507$	497.734	+	3036.04i	0.0435998	+	0.265947i
$508$	5642.14	−	10642.2i	0.492775	−	0.929471i
$509$	5340.12	+	1175.45i	0.465023	+	0.102359i	0.441301	−	0.897359i	$-0.354517\pi$
$509$	5340.12	+	1175.45i	0.465023	+	0.102359i	0.0237224	+	0.999719i	$0.492448\pi$
$510$	12721.1	+	4286.24i	1.10451	+	0.372153i
$511$	−75.0161	−	1383.59i	−0.00649416	−	0.119778i
$512$	−17991.8	+	13677.0i	−1.55299	+	1.18055i
$513$	369.680	+	697.290i	0.0318163	+	0.0600119i
$514$	−6791.62	−	24461.2i	−0.582812	−	2.09910i
$515$	−18158.5	−	17200.7i	−1.55371	−	1.47175i
$516$	−3886.96	−	9755.54i	−0.331616	−	0.832294i
$517$	−9845.21	+	3317.24i	−0.837508	+	0.282189i
$518$	−1364.89	+	148.440i	−0.115771	+	0.0125909i
$519$	3890.20	+	1799.80i	0.329019	+	0.152221i
$520$	−21819.8	+	20668.8i	−1.84012	+	1.74305i
$521$	4738.33	+	2850.96i	0.398445	+	0.239737i	0.700648	−	0.713507i	$-0.252894\pi$
$521$	4738.33	+	2850.96i	0.398445	+	0.239737i	−0.302203	+	0.953244i	$0.597722\pi$
$522$	−5257.72	−	571.812i	−0.440851	−	0.0479455i
$523$	−17693.4	+	3894.61i	−1.47931	+	0.325621i	−0.880029	−	0.474919i	$-0.842477\pi$
$523$	−17693.4	+	3894.61i	−1.47931	+	0.325621i	−0.599280	+	0.800540i	$0.704546\pi$
$524$	−4302.50	+	15496.2i	−0.358694	+	1.29190i
$525$	−180.661	+	108.700i	−0.0150184	+	0.00903630i
$526$	−30321.5	+	14028.2i	−2.51346	+	1.16285i
$527$	−807.420	+	2026.47i	−0.0667396	+	0.167504i
$528$	−256.394	+	4728.92i	−0.0211328	+	0.389772i
$529$	6291.95	+	9279.94i	0.517133	+	0.762714i
$530$	27907.1			2.28718
$531$	3565.59	+	1980.47i	0.291400	+	0.161855i
$532$	1031.89			0.0840941
$533$	−7711.23	−	11373.2i	−0.626661	−	0.924256i
$534$	−495.969	+	9147.61i	−0.0401923	+	0.741303i
$535$	9487.43	−	23811.7i	0.766687	−	1.92424i
$536$	−23097.2	+	10685.9i	−1.86128	+	0.861121i
$537$	−5513.06	+	3317.10i	−0.443028	+	0.266561i
$538$	10267.5	−	36980.1i	0.822793	−	2.96343i
$539$	−6817.91	+	1500.74i	−0.544839	+	0.119928i
$540$	5568.50	+	605.611i	0.443759	+	0.0482617i
$541$	−8422.08	−	5067.40i	−0.669304	−	0.402707i	0.139956	−	0.990158i	$-0.455304\pi$
$541$	−8422.08	−	5067.40i	−0.669304	−	0.402707i	−0.809260	+	0.587451i	$0.800132\pi$
$542$	−1214.18	+	1150.13i	−0.0962243	+	0.0911485i
$543$	−4244.10	−	1963.53i	−0.335418	−	0.155181i
$544$	−2987.71	+	324.933i	−0.235473	+	0.0256092i
$545$	−15502.7	+	5223.48i	−1.21847	+	0.410549i
$546$	−667.244	−	1674.66i	−0.0522993	−	0.131261i
$547$	2218.31	+	2101.30i	0.173397	+	0.164250i	0.769477	−	0.638675i	$-0.220517\pi$
$547$	2218.31	+	2101.30i	0.173397	+	0.164250i	−0.596080	+	0.802925i	$0.703276\pi$
$548$	6291.51	+	22660.0i	0.490438	+	1.76640i
$549$	−1127.36	−	2126.42i	−0.0876402	−	0.165307i
$550$	2672.50	−	2031.58i	0.207192	−	0.157504i
$551$	−187.834	−	3464.39i	−0.0145227	−	0.267855i
$552$	−3702.29	−	1247.45i	−0.285471	−	0.0961863i
$553$	763.192	+	167.991i	0.0586876	+	0.0129181i
$554$	9803.11	−	18490.6i	0.751794	−	1.41803i
$555$	−790.954	−	4824.60i	−0.0604939	−	0.368996i
$556$	9822.20	−	11563.6i	0.749198	−	0.882024i
$557$	14380.0	+	16929.5i	1.09390	+	1.28784i	0.954700	+	0.297571i	$0.0961763\pi$
$557$	14380.0	+	16929.5i	1.09390	+	1.28784i	0.139197	+	0.990265i	$0.455548\pi$
$558$	−218.609	+	1333.46i	−0.0165851	+	0.101164i
$559$	−9581.00	−	7283.29i	−0.724925	−	0.551074i
$560$	1153.71	−	1701.60i	0.0870595	−	0.128403i
$561$	2498.09	−	3684.41i	0.188003	−	0.277284i
$562$	26564.7	+	20193.9i	1.99389	+	1.51571i
$563$	−1656.54	+	10104.5i	−0.124005	+	0.756399i	0.849475	+	0.527628i	$0.176919\pi$
$563$	−1656.54	+	10104.5i	−0.124005	+	0.756399i	−0.973480	+	0.228770i	$0.926530\pi$
$564$	−16150.2	−	19013.5i	−1.20576	−	1.41953i
$565$	9332.65	−	10987.2i	0.694916	−	0.818118i
$566$	1693.37	+	10329.1i	0.125756	+	0.767077i
$567$	−81.1203	+	153.009i	−0.00600835	+	0.0113329i
$568$	37264.9	+	8202.63i	2.75282	+	0.605941i
$569$	−6008.98	−	2024.66i	−0.442723	−	0.149171i	0.0891065	−	0.996022i	$-0.471599\pi$
$569$	−6008.98	−	2024.66i	−0.442723	−	0.149171i	−0.531830	+	0.846851i	$0.678495\pi$
$570$	295.325	+	5446.95i	0.0217014	+	0.400259i
$571$	−4965.94	+	3775.01i	−0.363954	+	0.276671i	−0.771128	−	0.636680i	$-0.780307\pi$
$571$	−4965.94	+	3775.01i	−0.363954	+	0.276671i	0.407174	+	0.913351i	$0.366514\pi$
$572$	9056.43	+	17082.2i	0.662008	+	1.24868i
$573$	2876.16	+	10359.0i	0.209692	+	0.755242i
$574$	1860.17	+	1762.05i	0.135265	+	0.128130i
$575$	376.019	+	943.737i	0.0272715	+	0.0684462i
$576$	3457.39	−	1164.93i	0.250100	−	0.0842687i
$577$	−17961.1	+	1953.39i	−1.29590	+	0.140937i	−0.729947	−	0.683504i	$-0.760455\pi$
$577$	−17961.1	+	1953.39i	−1.29590	+	0.140937i	−0.565948	+	0.824441i	$0.691490\pi$
$578$	1173.65	+	542.987i	0.0844590	+	0.0390749i
$579$	−8216.62	+	7783.20i	−0.589760	+	0.558651i
$580$	−21099.1	−	12694.9i	−1.51050	−	0.908839i
$581$	215.604	+	23.4484i	0.0153955	+	0.00167436i
$582$	−10667.1	+	2348.02i	−0.759738	+	0.167231i
$583$	2475.77	−	8916.91i	0.175876	−	0.633449i
$584$	−23399.2	+	14078.8i	−1.65799	+	0.997579i
$585$	5826.06	−	2695.42i	0.411757	−	0.190499i
$586$	−3223.02	+	8089.17i	−0.227204	+	0.570240i
$587$	8.45739	−	155.987i	0.000594674	−	0.0109681i	−0.998221	−	0.0596222i	$-0.981010\pi$
$587$	8.45739	−	155.987i	0.000594674	−	0.0109681i	0.998816	+	0.0486540i	$0.0154932\pi$
$588$	−9407.46	−	13875.0i	−0.659791	−	0.973119i
$589$	−886.444			−0.0620124
$590$	16619.2	+	22771.4i	1.15966	+	1.58896i
$591$	−1737.30			−0.120919
$592$	5570.26	+	8215.52i	0.386717	+	0.570364i
$593$	−1020.53	+	18822.6i	−0.0706716	+	1.30346i	0.721180	+	0.692747i	$0.243600\pi$
$593$	−1020.53	+	18822.6i	−0.0706716	+	1.30346i	−0.791852	+	0.610713i	$0.790883\pi$
$594$	1020.63	−	2561.58i	0.0704998	−	0.176941i
$595$	−1753.78	+	811.386i	−0.120837	+	0.0559052i
$596$	45459.5	−	27352.1i	3.12432	−	1.87984i
$597$	−3163.59	+	11394.2i	−0.216880	+	0.781130i
$598$	−8482.76	+	1867.20i	−0.580077	+	0.127685i
$599$	15685.1	+	1705.86i	1.06991	+	0.116360i	0.626087	−	0.779753i	$-0.284655\pi$
$599$	15685.1	+	1705.86i	1.06991	+	0.116360i	0.443826	+	0.896113i	$0.353621\pi$
$600$	3560.50	+	2142.28i	0.242262	+	0.145764i
$601$	−15724.4	+	14894.9i	−1.06724	+	1.01094i	−0.0673262	+	0.997731i	$0.521447\pi$
$601$	−15724.4	+	14894.9i	−1.06724	+	1.01094i	−0.999913	+	0.0132114i	$0.995795\pi$
$602$	2036.73	+	942.291i	0.137892	+	0.0637955i
$603$	5403.79	−	587.698i	0.364941	−	0.0396897i
$604$	−15181.6	+	5115.29i	−1.02274	+	0.344600i
$605$	4211.10	+	10569.1i	0.282984	+	0.710237i
$606$	2197.97	+	2082.03i	0.147338	+	0.139566i
$607$	−4624.35	−	16655.4i	−0.309220	−	1.11371i	−0.940957	−	0.338526i	$-0.890072\pi$
$607$	−4624.35	−	16655.4i	−0.309220	−	1.11371i	0.631737	−	0.775183i	$-0.282342\pi$
$608$	−572.048	−	1079.00i	−0.0381572	−	0.0719722i
$609$	606.083	−	460.732i	0.0403280	−	0.0306565i
$610$	−900.610	−	16610.8i	−0.0597781	−	1.10254i
$611$	−27093.5	−	9128.86i	−1.79392	−	0.604442i
$612$	10439.2	+	2297.84i	0.689508	+	0.151772i
$613$	1980.23	−	3735.11i	0.130474	−	0.246101i	−0.809664	−	0.586894i	$-0.800351\pi$
$613$	1980.23	−	3735.11i	0.130474	−	0.246101i	0.940138	+	0.340793i	$0.110695\pi$
$614$	−4500.90	−	27454.3i	−0.295833	−	1.80450i
$615$	−5906.82	+	6954.05i	−0.387295	+	0.455958i
$616$	−1203.12	−	1416.42i	−0.0786934	−	0.0926450i
$617$	434.830	−	2652.34i	0.0283721	−	0.173062i	−0.968839	−	0.247690i	$-0.920329\pi$
$617$	434.830	−	2652.34i	0.0283721	−	0.173062i	0.997211	+	0.0746278i	$0.0237769\pi$
$618$	−23537.6	−	17892.8i	−1.53207	−	1.16465i
$619$	−11122.3	+	16404.2i	−0.722204	+	1.06517i	0.272476	+	0.962163i	$0.412157\pi$
$619$	−11122.3	+	16404.2i	−0.722204	+	1.06517i	−0.994680	+	0.103009i	$0.967153\pi$
$620$	−3530.61	+	5207.25i	−0.228698	+	0.337304i
$621$	664.293	+	504.982i	0.0429262	+	0.0326316i
$622$	−5379.32	+	32812.4i	−0.346770	+	2.11520i
$623$	−853.740	−	1005.10i	−0.0549027	−	0.0646365i
$624$	−8437.27	+	9933.13i	−0.541284	+	0.637249i
$625$	3017.78	+	18407.6i	0.193138	+	1.17809i
$626$	3466.04	−	6537.64i	0.221295	−	0.417407i
$627$	1766.62	+	388.862i	0.112523	+	0.0247682i
$628$	28441.0	+	9582.88i	1.80719	+	0.608915i
$629$	−505.102	−	9316.06i	−0.0320187	−	0.590550i
$630$	−952.926	+	724.395i	−0.0602626	+	0.0458105i
$631$	10315.7	+	19457.4i	0.650809	+	1.22756i	0.960912	+	0.276853i	$0.0892915\pi$
$631$	10315.7	+	19457.4i	0.650809	+	1.22756i	−0.310103	+	0.950703i	$0.600364\pi$
$632$	−4120.27	−	14839.9i	−0.259328	−	0.934016i
$633$	−3520.06	−	3334.38i	−0.221027	−	0.209367i
$634$	11813.7	+	29650.1i	0.740034	+	1.85734i
$635$	−8686.48	+	2926.81i	−0.542854	+	0.182909i
$636$	22091.5	−	2402.60i	1.37734	−	0.149794i
$637$	−17436.0	−	8066.77i	−1.08452	−	0.501754i
$638$	−8800.37	+	8336.15i	−0.546097	+	0.517291i
$639$	−6983.25	−	4201.68i	−0.432321	−	0.260119i
$640$	29243.9	+	3180.47i	1.80620	+	0.196436i
$641$	19827.7	−	4364.41i	1.22176	−	0.268930i	0.443156	−	0.896445i	$-0.353859\pi$
$641$	19827.7	−	4364.41i	1.22176	−	0.268930i	0.778605	+	0.627515i	$0.215928\pi$
$642$	8105.99	−	29195.1i	0.498314	−	1.79477i
$643$	10824.3	−	6512.79i	0.663873	−	0.399439i	−0.143361	−	0.989670i	$-0.545791\pi$
$643$	10824.3	−	6512.79i	0.663873	−	0.399439i	0.807234	+	0.590231i	$0.200963\pi$
$644$	990.172	−	458.102i	0.0605873	−	0.0280307i
$645$	−2957.91	+	7423.80i	−0.180570	+	0.453197i
$646$	−563.572	+	10394.5i	−0.0343242	+	0.633073i
$647$	875.579	+	1291.38i	0.0532033	+	0.0784690i	0.853360	−	0.521322i	$-0.174561\pi$
$647$	875.579	+	1291.38i	0.0532033	+	0.0784690i	−0.800157	+	0.599791i	$0.795250\pi$
$648$	3413.13			0.206914
$649$	8750.31	−	3290.01i	0.529245	−	0.198990i
$650$	9238.34			0.557473
$651$	−109.160	−	160.999i	−0.00657191	−	0.00969284i
$652$	108.478	−	2000.77i	0.00651586	−	0.120178i
$653$	1274.73	−	3199.33i	0.0763921	−	0.191730i	−0.885821	−	0.464027i	$-0.846404\pi$
$653$	1274.73	−	3199.33i	0.0763921	−	0.191730i	0.962213	+	0.272297i	$0.0877834\pi$
$654$	−17550.7	+	8119.80i	−1.04937	+	0.485488i
$655$	10486.6	−	6309.58i	0.625565	−	0.376390i
$656$	4955.72	−	17848.9i	0.294952	−	1.06232i
$657$	5696.31	−	1253.85i	0.338256	−	0.0744557i
$658$	5299.87	+	576.396i	0.313998	+	0.0341493i
$659$	−3176.99	−	1911.53i	−0.187797	−	0.112993i	0.418551	−	0.908193i	$-0.362538\pi$
$659$	−3176.99	−	1911.53i	−0.187797	−	0.112993i	−0.606347	+	0.795200i	$0.707366\pi$
$660$	9320.54	−	8828.88i	0.549699	−	0.520703i
$661$	22821.9	+	10558.5i	1.34292	+	0.621300i	0.953954	−	0.299952i	$-0.0969707\pi$
$661$	22821.9	+	10558.5i	1.34292	+	0.621300i	0.388965	+	0.921253i	$0.372833\pi$
$662$	2009.88	−	218.587i	0.118000	−	0.0128333i
$663$	11608.9	−	3911.49i	0.680017	−	0.229125i
$664$	−1582.06	−	3970.66i	−0.0924634	−	0.232066i
$665$	−570.088	−	540.016i	−0.0332437	−	0.0314901i
$666$	−1546.12	−	5568.61i	−0.0899561	−	0.323993i
$667$	−1718.24	−	3240.94i	−0.0997459	−	0.188141i
$668$	47838.2	−	36365.6i	2.77083	−	2.10633i
$669$	−634.346	−	11699.8i	−0.0366596	−	0.676146i
$670$	35603.4	+	11996.2i	2.05295	+	0.691721i
$671$	−5387.39	−	1185.86i	−0.309952	−	0.0682257i
$672$	125.527	−	236.769i	0.00720580	−	0.0135916i
$673$	1760.42	+	10738.1i	0.100831	+	0.615040i	0.988103	+	0.153794i	$0.0491492\pi$
$673$	1760.42	+	10738.1i	0.100831	+	0.615040i	−0.887272	+	0.461246i	$0.847403\pi$
$674$	−15767.5	+	18562.9i	−0.901099	+	1.06086i
$675$	−574.568	−	676.434i	−0.0327632	−	0.0385718i
$676$	−2739.38	+	16709.5i	−0.155859	+	0.950698i
$677$	−9756.86	−	7416.98i	−0.553895	−	0.421060i	0.290426	−	0.956897i	$-0.406203\pi$
$677$	−9756.86	−	7416.98i	−0.553895	−	0.421060i	−0.844321	+	0.535837i	$0.819996\pi$
$678$	9563.14	−	14104.6i	0.541696	−	0.798942i
$679$	882.363	−	1301.39i	0.0498703	−	0.0735533i
$680$	30318.3	+	23047.3i	1.70978	+	1.29974i
$681$	−152.944	+	932.920i	−0.00860623	+	0.0524957i
$682$	2005.01	+	2360.48i	0.112575	+	0.132533i
$683$	−381.029	+	448.582i	−0.0213465	+	0.0251311i	−0.772732	−	0.634733i	$-0.781110\pi$
$683$	−381.029	+	448.582i	−0.0213465	+	0.0251311i	0.751385	+	0.659864i	$0.229386\pi$
$684$	702.726	+	4286.44i	0.0392827	+	0.239614i
$685$	8382.72	−	15811.5i	0.467573	−	0.881935i
$686$	7044.46	+	1550.60i	0.392068	+	0.0863007i
$687$	15848.7	+	5340.04i	0.880152	+	0.296558i
$688$	−878.371	−	16200.6i	−0.0486738	−	0.897735i
$689$	20274.2	−	15412.0i	1.12102	−	0.852180i
$690$	2701.54	+	5095.64i	0.149052	+	0.281141i
$691$	−925.115	−	3331.96i	−0.0509306	−	0.183435i	0.933710	−	0.358031i	$-0.116552\pi$
$691$	−925.115	−	3331.96i	−0.0509306	−	0.183435i	−0.984640	+	0.174596i	$0.944138\pi$
$692$	17126.9	+	16223.5i	0.940848	+	0.891218i
$693$	146.921	+	368.744i	0.00805350	+	0.0202128i
$694$	−15766.4	+	5312.31i	−0.862368	+	0.290566i
$695$	−11478.0	+	1248.31i	−0.626455	+	0.0681311i
$696$	−13617.5	−	6300.15i	−0.741626	−	0.343113i
$697$	−12640.8	+	11974.0i	−0.686949	+	0.650713i
$698$	23393.5	+	14075.4i	1.26856	+	0.763268i
$699$	1923.11	+	209.151i	0.104061	+	0.0113173i
$700$	−1133.28	+	249.453i	−0.0611912	+	0.0134692i
$701$	−4665.51	+	16803.6i	−0.251375	+	0.905370i	0.724903	+	0.688851i	$0.241884\pi$
$701$	−4665.51	+	16803.6i	−0.251375	+	0.905370i	−0.976278	+	0.216520i	$0.930529\pi$
$702$	6502.07	−	3912.17i	0.349580	−	0.210335i
$703$	3440.87	−	1591.92i	0.184601	−	0.0854057i
$704$	3095.13	−	7768.18i	0.165699	−	0.415873i
$705$	−1027.78	+	18956.3i	−0.0549055	+	1.01267i
$706$	−25286.0	−	37294.0i	−1.34795	−	1.98807i
$707$	−435.818			−0.0231834
$708$	15116.3	+	16595.3i	0.802411	+	0.880917i
$709$	−13794.7			−0.730707			−0.365354	−	0.930869i	$-0.619052\pi$
$709$	−13794.7			−0.730707			−0.365354	+	0.930869i	$0.619052\pi$
$710$	−31611.7	−	46623.7i	−1.67094	−	2.46445i
$711$	−178.090	+	3284.68i	−0.00939368	+	0.173256i
$712$	−9619.97	+	24144.3i	−0.506354	+	1.27085i
$713$	−850.606	+	393.532i	−0.0446781	+	0.0206703i
$714$	−1957.28	+	1177.66i	−0.102590	+	0.0617264i
$715$	3936.20	−	14176.9i	0.205882	−	0.741520i
$716$	−34583.2	+	7612.33i	−1.80507	+	0.397327i
$717$	−8865.89	−	964.224i	−0.461789	−	0.0502226i
$718$	33155.0	+	19948.7i	1.72330	+	1.03688i
$719$	−11668.4	+	11052.9i	−0.605225	+	0.573299i	−0.927722	−	0.373271i	$-0.878236\pi$
$719$	−11668.4	+	11052.9i	−0.605225	+	0.573299i	0.322498	+	0.946570i	$0.395478\pi$
$720$	7854.09	+	3633.69i	0.406534	+	0.188083i
$721$	4231.18	−	460.169i	0.218554	−	0.0237692i
$722$	28171.7	−	9492.15i	1.45214	−	0.489282i
$723$	−5375.84	−	13492.3i	−0.276528	−	0.694033i
$724$	−18685.0	−	17699.3i	−0.959145	−	0.908550i
$725$	1043.79	+	3759.38i	0.0534693	+	0.192579i
$726$	6299.53	+	11882.2i	0.322035	+	0.607422i
$727$	8327.80	−	6330.63i	0.424843	−	0.322957i	−0.370811	−	0.928708i	$-0.620920\pi$
$727$	8327.80	−	6330.63i	0.424843	−	0.322957i	0.795654	+	0.605751i	$0.207127\pi$
$728$	−276.882	−	5106.79i	−0.0140961	−	0.259987i
$729$	−690.839	−	232.771i	−0.0350983	−	0.0118260i
$730$	39371.6	+	8666.35i	1.99618	+	0.439392i
$731$	−7143.24	+	13473.6i	−0.361426	+	0.681722i
$732$	−2143.00	−	13071.7i	−0.108207	−	0.660034i
$733$	349.008	−	410.884i	0.0175865	−	0.0207044i	−0.753298	−	0.657679i	$-0.771538\pi$
$733$	349.008	−	410.884i	0.0175865	−	0.0207044i	0.770885	+	0.636974i	$0.219814\pi$
$734$	−7524.54	−	8858.58i	−0.378387	−	0.445472i
$735$	−2063.81	+	12588.7i	−0.103571	+	0.631756i
$736$	−1027.94	−	781.416i	−0.0514813	−	0.0391350i
$737$	6991.58	−	10311.8i	0.349441	−	0.515387i
$738$	−6052.71	+	8927.08i	−0.301901	+	0.445271i
$739$	6922.17	+	5262.10i	0.344569	+	0.261934i	0.763117	−	0.646260i	$-0.223668\pi$
$739$	6922.17	+	5262.10i	0.344569	+	0.261934i	−0.418549	+	0.908194i	$0.637461\pi$
$740$	4353.17	−	26553.2i	0.216251	−	1.31907i
$741$	3222.70	+	3794.06i	0.159769	+	0.188095i
$742$	−3074.30	+	3619.35i	−0.152104	+	0.179071i
$743$	3946.37	+	24071.8i	0.194857	+	1.18857i	0.885242	+	0.465131i	$0.153993\pi$
$743$	3946.37	+	24071.8i	0.194857	+	1.18857i	−0.690385	+	0.723442i	$0.742559\pi$
$744$	−1795.67	+	3387.00i	−0.0884847	+	0.166900i
$745$	−39429.1	−	8679.01i	−1.93902	−	0.426811i
$746$	−51144.9	−	17232.7i	−2.51012	−	0.845757i
$747$	49.4246	+	911.582i	0.00242082	+	0.0446493i
$748$	19503.8	−	14826.4i	0.953383	−	0.724743i
$749$	2043.05	+	3853.59i	0.0996679	+	0.187994i
$750$	4599.60	+	16566.2i	0.223938	+	0.806552i
$751$	26899.0	+	25480.1i	1.30700	+	1.23806i	0.953057	+	0.302792i	$0.0979188\pi$
$751$	26899.0	+	25480.1i	1.30700	+	1.23806i	0.353945	+	0.935266i	$0.384840\pi$
$752$	−14265.9	−	35804.8i	−0.691789	−	1.73626i
$753$	−15849.2	+	5340.20i	−0.767032	+	0.258443i
$754$	−33163.0	+	3606.69i	−1.60176	+	0.174201i
$755$	11064.4	+	5118.93i	0.533343	+	0.246751i
$756$	−691.980	+	655.479i	−0.0332898	+	0.0315338i
$757$	−17685.6	−	10641.1i	−0.849135	−	0.510907i	0.0232486	−	0.999730i	$-0.492599\pi$
$757$	−17685.6	−	10641.1i	−0.849135	−	0.510907i	−0.872383	+	0.488822i	$0.837427\pi$
$758$	−29992.0	−	3261.83i	−1.43715	−	0.156299i
$759$	1867.83	−	411.140i	0.0893253	−	0.0196620i
$760$	−4140.24	+	14911.8i	−0.197608	+	0.711721i
$761$	9006.44	−	5419.00i	0.429019	−	0.258132i	−0.284628	−	0.958638i	$-0.591870\pi$
$761$	9006.44	−	5419.00i	0.429019	−	0.258132i	0.713646	+	0.700506i	$0.247042\pi$
$762$	−9833.96	+	4549.67i	−0.467515	+	0.216296i
$763$	1030.37	−	2586.02i	0.0488883	−	0.122700i
$764$	−3203.38	+	59082.8i	−0.151694	+	2.79783i
$765$	−4564.81	−	6732.60i	−0.215740	−	0.318193i
$766$	−28911.9			−1.36375
$767$	24649.4	+	7365.05i	1.16042	+	0.346723i
$768$	25043.9			1.17668
$769$	−1596.58	−	2354.79i	−0.0748690	−	0.110424i	0.788411	−	0.615149i	$-0.210904\pi$
$769$	−1596.58	−	2354.79i	−0.0748690	−	0.110424i	−0.863280	+	0.504725i	$0.831594\pi$
$770$	−148.532	+	2739.51i	−0.00695159	+	0.128215i
$771$	−5693.86	+	14290.5i	−0.265966	+	0.667523i

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)

\(f(q)\)	\(=\)	\(q+(-2.77836 - 4.09778i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-6.11139 + 15.3384i) q^{4} +(11.4034 - 5.27577i) q^{5} +(12.7266 - 7.65732i) q^{6} +(-0.571992 + 2.06013i) q^{7} +(41.1522 - 9.05829i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})\)	\(q+(-2.77836 - 4.09778i) q^{2} +(-0.162417 + 2.99560i) q^{3} +(-6.11139 + 15.3384i) q^{4} +(11.4034 - 5.27577i) q^{5} +(12.7266 - 7.65732i) q^{6} +(-0.571992 + 2.06013i) q^{7} +(41.1522 - 9.05829i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(-53.3017 - 32.0706i) q^{10} +(-14.9759 + 14.1859i) q^{11} +(-44.9552 - 20.7985i) q^{12} +(-56.4345 + 6.13762i) q^{13} +(10.0312 - 3.37989i) q^{14} +(13.9520 + 35.0169i) q^{15} +(-55.5589 - 52.6281i) q^{16} +(19.2438 + 69.3100i) q^{17} +(20.8713 + 39.3674i) q^{18} +(-23.2702 + 17.6896i) q^{19} +(11.2315 + 207.152i) q^{20} +(-6.07842 - 2.04806i) q^{21} +(99.7391 + 21.9542i) q^{22} +(-14.4763 + 27.3051i) q^{23} +(20.4512 + 124.747i) q^{24} +(21.2803 - 25.0531i) q^{25} +(181.946 + 214.204i) q^{26} +(4.36811 - 26.6443i) q^{27} +(-28.1035 - 21.3637i) q^{28} +(-66.6093 + 98.2414i) q^{29} +(104.728 - 154.462i) q^{30} +(24.1423 + 18.3525i) q^{31} +(-6.75928 + 41.2298i) q^{32} +(-40.0630 - 47.1658i) q^{33} +(230.551 - 271.425i) q^{34} +(4.34612 + 26.5101i) q^{35} +(69.6055 - 131.290i) q^{36} +(-126.670 - 27.8822i) q^{37} +(137.141 + 46.2083i) q^{38} +(-9.21995 - 170.052i) q^{39} +(421.486 - 320.405i) q^{40} +(113.382 + 213.860i) q^{41} +(8.49557 + 30.5983i) q^{42} +(153.916 + 145.797i) q^{43} +(-126.066 - 316.402i) q^{44} +(-107.163 + 36.1073i) q^{45} +(152.111 - 16.5430i) q^{46} +(457.088 + 211.472i) q^{47} +(166.677 - 157.884i) q^{48} +(289.985 + 174.478i) q^{49} +(-161.787 - 17.5953i) q^{50} +(-210.751 + 46.3897i) q^{51} +(250.752 - 903.126i) q^{52} +(-384.406 + 231.289i) q^{53} +(-121.319 + 56.1280i) q^{54} +(-95.9342 + 240.777i) q^{55} +(-4.87750 + 89.9601i) q^{56} +(-49.2114 - 72.5814i) q^{57} +587.636 q^{58} +(-417.646 - 175.928i) q^{59} -622.370 q^{60} +(150.073 + 221.341i) q^{61} +(8.12840 - 149.919i) q^{62} +(7.12240 - 17.8759i) q^{63} +(-367.908 + 170.212i) q^{64} +(-611.164 + 367.725i) q^{65} +(-81.9655 + 295.213i) q^{66} +(-589.841 + 129.834i) q^{67} +(-1180.71 - 128.410i) q^{68} +(-79.4441 - 47.7999i) q^{69} +(96.5576 - 91.4642i) q^{70} +(821.844 + 380.226i) q^{71} +(-377.013 + 41.0027i) q^{72} +(-614.150 + 206.931i) q^{73} +(237.681 + 596.533i) q^{74} +(71.5928 + 67.8163i) q^{75} +(-129.117 - 465.037i) q^{76} +(-20.6587 - 38.9664i) q^{77} +(-671.220 + 510.248i) q^{78} +(-19.7878 - 364.965i) q^{79} +(-911.213 - 307.024i) q^{80} +(79.1063 + 17.4126i) q^{81} +(561.338 - 1058.80i) q^{82} +(-16.4105 - 100.099i) q^{83} +(68.5616 - 80.7169i) q^{84} +(585.109 + 688.843i) q^{85} +(169.809 - 1035.79i) q^{86} +(-283.473 - 215.491i) q^{87} +(-487.791 + 719.438i) q^{88} +(-346.139 + 510.516i) q^{89} +(445.696 + 338.810i) q^{90} +(19.6358 - 119.773i) q^{91} +(-330.348 - 388.916i) q^{92} +(-58.8978 + 69.3398i) q^{93} +(-403.394 - 2460.59i) q^{94} +(-172.034 + 324.490i) q^{95} +(-122.410 - 26.9445i) q^{96} +(-696.898 - 234.812i) q^{97} +(-90.7106 - 1673.06i) q^{98} +(147.797 - 112.352i) 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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