LMFDB - Embedded newform 156.3.e.c.103.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(103,156)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("156.103");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	156.103
Dual form			156.3.e.c.103.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.570481 + 1.91691i) q^{2} -1.73205i q^{3} +(-3.34910 + 2.18712i) q^{4} -7.79890i q^{5} +(3.32019 - 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 - 5.17222i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.570481 + 1.91691i) q^{2} -1.73205i q^{3} +(-3.34910 + 2.18712i) q^{4} -7.79890i q^{5} +(3.32019 - 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 - 5.17222i) q^{8} -3.00000 q^{9} +(14.9498 - 4.44912i) q^{10} -13.1778 q^{11} +(3.78821 + 5.80082i) q^{12} +(-10.3889 - 7.81476i) q^{13} +(-4.47702 - 15.0435i) q^{14} -13.5081 q^{15} +(6.43298 - 14.6498i) q^{16} +22.5790 q^{17} +(-1.71144 - 5.75074i) q^{18} +26.2312 q^{19} +(17.0572 + 26.1193i) q^{20} +13.5928i q^{21} +(-7.51768 - 25.2607i) q^{22} +10.4194i q^{23} +(-8.95855 + 10.5709i) q^{24} -35.8228 q^{25} +(9.05354 - 24.3728i) q^{26} +5.19615i q^{27} +(26.2831 - 17.1641i) q^{28} +37.2030 q^{29} +(-7.70611 - 25.8938i) q^{30} -49.6331 q^{31} +(31.7523 + 3.97401i) q^{32} +22.8246i q^{33} +(12.8809 + 43.2820i) q^{34} +61.2042i q^{35} +(10.0473 - 6.56137i) q^{36} -38.6578i q^{37} +(14.9644 + 50.2829i) q^{38} +(-13.5356 + 17.9941i) q^{39} +(-40.3376 + 47.5976i) q^{40} -11.4818i q^{41} +(-26.0562 + 7.75442i) q^{42} -67.3590i q^{43} +(44.1337 - 28.8214i) q^{44} +23.3967i q^{45} +(-19.9730 + 5.94405i) q^{46} -10.7509 q^{47} +(-25.3742 - 11.1422i) q^{48} +12.5879 q^{49} +(-20.4362 - 68.6692i) q^{50} -39.1080i q^{51} +(51.8854 + 3.45061i) q^{52} -57.9959 q^{53} +(-9.96057 + 2.96431i) q^{54} +102.772i q^{55} +(47.8961 + 40.5905i) q^{56} -45.4338i q^{57} +(21.2236 + 71.3150i) q^{58} +16.0034 q^{59} +(45.2400 - 29.5439i) q^{60} -55.0061 q^{61} +(-28.3148 - 95.1423i) q^{62} +23.5434 q^{63} +(10.4962 + 63.1334i) q^{64} +(-60.9466 + 81.0221i) q^{65} +(-43.7527 + 13.0210i) q^{66} +36.6889 q^{67} +(-75.6194 + 49.3831i) q^{68} +18.0469 q^{69} +(-117.323 + 34.9158i) q^{70} +56.5184 q^{71} +(18.3094 + 15.5167i) q^{72} +37.3642i q^{73} +(74.1036 - 22.0535i) q^{74} +62.0470i q^{75} +(-87.8510 + 57.3709i) q^{76} +103.417 q^{77} +(-42.2149 - 15.6812i) q^{78} -57.2222i q^{79} +(-114.252 - 50.1701i) q^{80} +9.00000 q^{81} +(22.0097 - 6.55017i) q^{82} +14.2141 q^{83} +(-29.7291 - 45.5236i) q^{84} -176.091i q^{85} +(129.121 - 38.4270i) q^{86} -64.4376i q^{87} +(80.4256 + 68.1584i) q^{88} -10.3684i q^{89} +(-44.8494 + 13.3474i) q^{90} +(81.5300 + 61.3287i) q^{91} +(-22.7884 - 34.8955i) q^{92} +85.9671i q^{93} +(-6.13316 - 20.6085i) q^{94} -204.575i q^{95} +(6.88320 - 54.9966i) q^{96} +30.8813i q^{97} +(7.18114 + 24.1298i) q^{98} +39.5334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 - 72 * q^9	$ 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) $ 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.570481	+	1.91691i	0.285241	+	0.958456i
$2$	0.570481	+	1.91691i	0.285241	+	0.958456i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.34910	+	2.18712i	−0.837276	+	0.546781i
$5$		−	7.79890i		−	1.55978i	−0.625917	−	0.779890i	$-0.715275\pi$
$5$		−	7.79890i		−	1.55978i	0.625917	−	0.779890i	$-0.284725\pi$
$6$	3.32019	−	0.988102i	0.553365	−	0.164684i
$7$	−7.84779			−1.12111			−0.560557	−	0.828116i	$-0.689413\pi$
$7$	−7.84779			−1.12111			−0.560557	+	0.828116i	$0.689413\pi$
$8$	−6.10312	−	5.17222i	−0.762890	−	0.646528i
$9$	−3.00000			−0.333333
$10$	14.9498	−	4.44912i	1.49498	−	0.444912i
$11$	−13.1778			−1.19798			−0.598990	−	0.800756i	$-0.704431\pi$
$11$	−13.1778			−1.19798			−0.598990	+	0.800756i	$0.704431\pi$
$12$	3.78821	+	5.80082i	0.315684	+	0.483401i
$13$	−10.3889	−	7.81476i	−0.799147	−	0.601136i
$13$	−10.3889	−	7.81476i	−0.799147	−	0.601136i
$14$	−4.47702	−	15.0435i	−0.319787	−	1.07454i
$15$	−13.5081			−0.900539
$16$	6.43298	−	14.6498i	0.402061	−	0.915613i
$17$	22.5790			1.32818			0.664089	−	0.747654i	$-0.268820\pi$
$17$	22.5790			1.32818			0.664089	+	0.747654i	$0.268820\pi$
$18$	−1.71144	−	5.75074i	−0.0950802	−	0.319485i
$19$	26.2312			1.38059			0.690295	−	0.723528i	$-0.257481\pi$
$19$	26.2312			1.38059			0.690295	+	0.723528i	$0.257481\pi$
$20$	17.0572	+	26.1193i	0.852858	+	1.30597i
$21$			13.5928i			0.647275i
$22$	−7.51768	−	25.2607i	−0.341713	−	1.14821i
$23$			10.4194i			0.453016i	0.974009	+	0.226508i	$0.0727309\pi$
$23$			10.4194i			0.453016i	−0.974009	+	0.226508i	$0.927269\pi$
$24$	−8.95855	+	10.5709i	−0.373273	+	0.440455i
$25$	−35.8228			−1.43291
$26$	9.05354	−	24.3728i	0.348213	−	0.937415i
$27$			5.19615i			0.192450i
$28$	26.2831	−	17.1641i	0.938681	−	0.613004i
$29$	37.2030			1.28286			0.641432	−	0.767180i	$-0.278341\pi$
$29$	37.2030			1.28286			0.641432	+	0.767180i	$0.278341\pi$
$30$	−7.70611	−	25.8938i	−0.256870	−	0.863127i
$31$	−49.6331			−1.60107			−0.800534	−	0.599287i	$-0.795451\pi$
$31$	−49.6331			−1.60107			−0.800534	+	0.599287i	$0.795451\pi$
$32$	31.7523	+	3.97401i	0.992259	+	0.124188i
$33$			22.8246i			0.691654i
$34$	12.8809	+	43.2820i	0.378850	+	1.27300i
$35$			61.2042i			1.74869i
$36$	10.0473	−	6.56137i	0.279092	−	0.182260i
$37$		−	38.6578i		−	1.04481i	−0.852699	−	0.522403i	$-0.825036\pi$
$37$		−	38.6578i		−	1.04481i	0.852699	−	0.522403i	$-0.174964\pi$
$38$	14.9644	+	50.2829i	0.393800	+	1.32323i
$39$	−13.5356	+	17.9941i	−0.347066	+	0.461388i
$40$	−40.3376	+	47.5976i	−1.00844	+	1.18994i
$41$		−	11.4818i		−	0.280045i	−0.990148	−	0.140022i	$-0.955283\pi$
$41$		−	11.4818i		−	0.280045i	0.990148	−	0.140022i	$-0.0447175\pi$
$42$	−26.0562	+	7.75442i	−0.620385	+	0.184629i
$43$		−	67.3590i		−	1.56649i	−0.621714	−	0.783244i	$-0.713564\pi$
$43$		−	67.3590i		−	1.56649i	0.621714	−	0.783244i	$-0.286436\pi$
$44$	44.1337	−	28.8214i	1.00304	−	0.655033i
$45$			23.3967i			0.519927i
$46$	−19.9730	+	5.94405i	−0.434196	+	0.129218i
$47$	−10.7509			−0.228742			−0.114371	−	0.993438i	$-0.536485\pi$
$47$	−10.7509			−0.228742			−0.114371	+	0.993438i	$0.536485\pi$
$48$	−25.3742	−	11.1422i	−0.528629	−	0.232130i
$49$	12.5879			0.256895
$50$	−20.4362	−	68.6692i	−0.408725	−	1.37338i
$51$		−	39.1080i		−	0.766824i
$52$	51.8854	+	3.45061i	0.997796	+	0.0663579i
$53$	−57.9959			−1.09426			−0.547131	−	0.837047i	$-0.684280\pi$
$53$	−57.9959			−1.09426			−0.547131	+	0.837047i	$0.684280\pi$
$54$	−9.96057	+	2.96431i	−0.184455	+	0.0548946i
$55$			102.772i			1.86859i
$56$	47.8961	+	40.5905i	0.855287	+	0.724831i
$57$		−	45.4338i		−	0.797084i
$58$	21.2236	+	71.3150i	0.365925	+	1.22957i
$59$	16.0034			0.271244			0.135622	−	0.990761i	$-0.456697\pi$
$59$	16.0034			0.271244			0.135622	+	0.990761i	$0.456697\pi$
$60$	45.2400	−	29.5439i	0.754000	−	0.492398i
$61$	−55.0061			−0.901739			−0.450870	−	0.892590i	$-0.648886\pi$
$61$	−55.0061			−0.901739			−0.450870	+	0.892590i	$0.648886\pi$
$62$	−28.3148	−	95.1423i	−0.456690	−	1.53455i
$63$	23.5434			0.373704
$64$	10.4962	+	63.1334i	0.164004	+	0.986460i
$65$	−60.9466	+	81.0221i	−0.937639	+	1.24649i
$66$	−43.7527	+	13.0210i	−0.662920	+	0.197288i
$67$	36.6889			0.547596			0.273798	−	0.961787i	$-0.411720\pi$
$67$	36.6889			0.547596			0.273798	+	0.961787i	$0.411720\pi$
$68$	−75.6194	+	49.3831i	−1.11205	+	0.726222i
$69$	18.0469			0.261549
$70$	−117.323	+	34.9158i	−1.67604	+	0.498797i
$71$	56.5184			0.796033			0.398017	−	0.917378i	$-0.369699\pi$
$71$	56.5184			0.796033			0.398017	+	0.917378i	$0.369699\pi$
$72$	18.3094	+	15.5167i	0.254297	+	0.215509i
$73$			37.3642i			0.511839i	0.966698	+	0.255919i	$0.0823782\pi$
$73$			37.3642i			0.511839i	−0.966698	+	0.255919i	$0.917622\pi$
$74$	74.1036	−	22.0535i	1.00140	−	0.298021i
$75$			62.0470i			0.827293i
$76$	−87.8510	+	57.3709i	−1.15593	+	0.754880i
$77$	103.417			1.34307
$78$	−42.2149	−	15.6812i	−0.541217	−	0.201041i
$79$		−	57.2222i		−	0.724332i	−0.932114	−	0.362166i	$-0.882037\pi$
$79$		−	57.2222i		−	0.724332i	0.932114	−	0.362166i	$-0.117963\pi$
$80$	−114.252	−	50.1701i	−1.42815	−	0.627127i
$81$	9.00000			0.111111
$82$	22.0097	−	6.55017i	0.268411	−	0.0798801i
$83$	14.2141			0.171255			0.0856273	−	0.996327i	$-0.472711\pi$
$83$	14.2141			0.171255			0.0856273	+	0.996327i	$0.472711\pi$
$84$	−29.7291	−	45.5236i	−0.353918	−	0.541948i
$85$		−	176.091i		−	2.07166i
$86$	129.121	−	38.4270i	1.50141	−	0.446826i
$87$		−	64.4376i		−	0.740662i
$88$	80.4256	+	68.1584i	0.913928	+	0.774528i
$89$		−	10.3684i		−	0.116498i	−0.998302	−	0.0582492i	$-0.981448\pi$
$89$		−	10.3684i		−	0.116498i	0.998302	−	0.0582492i	$-0.0185518\pi$
$90$	−44.8494	+	13.3474i	−0.498327	+	0.148304i
$91$	81.5300	+	61.3287i	0.895934	+	0.673941i
$92$	−22.7884	−	34.8955i	−0.247700	−	0.379299i
$93$			85.9671i			0.924377i
$94$	−6.13316	−	20.6085i	−0.0652464	−	0.219239i
$95$		−	204.575i		−	2.15342i
$96$	6.88320	−	54.9966i	0.0717000	−	0.572881i
$97$			30.8813i			0.318364i	0.987249	+	0.159182i	$0.0508856\pi$
$97$			30.8813i			0.318364i	−0.987249	+	0.159182i	$0.949114\pi$
$98$	7.18114	+	24.1298i	0.0732770	+	0.246223i
$99$	39.5334			0.399327
$100$	119.974	−	78.3490i	1.19974	−	0.783490i
$101$	136.133			1.34785			0.673925	−	0.738799i	$-0.264607\pi$
$101$	136.133			1.34785			0.673925	+	0.738799i	$0.264607\pi$
$102$	74.9666	−	22.3104i	0.734967	−	0.218729i
$103$		−	124.738i		−	1.21105i	−0.795825	−	0.605526i	$-0.792963\pi$
$103$		−	124.738i		−	1.21105i	0.795825	−	0.605526i	$-0.207037\pi$
$104$	22.9851	+	101.428i	0.221011	+	0.975271i
$105$	106.009			1.00961
$106$	−33.0856	−	111.173i	−0.312128	−	1.04880i
$107$		−	53.3555i		−	0.498650i	−0.968420	−	0.249325i	$-0.919791\pi$
$107$		−	53.3555i		−	0.498650i	0.968420	−	0.249325i	$-0.0802087\pi$
$108$	−11.3646	−	17.4024i	−0.105228	−	0.161134i
$109$			50.9829i			0.467733i	0.972269	+	0.233867i	$0.0751379\pi$
$109$			50.9829i			0.467733i	−0.972269	+	0.233867i	$0.924862\pi$
$110$	−197.005	+	58.6296i	−1.79096	+	0.532996i
$111$	−66.9573			−0.603219
$112$	−50.4847	+	114.969i	−0.450756	+	1.02651i
$113$	−33.1089			−0.293000			−0.146500	−	0.989211i	$-0.546801\pi$
$113$	−33.1089			−0.293000			−0.146500	+	0.989211i	$0.546801\pi$
$114$	87.0926	−	25.9191i	0.763970	−	0.227361i
$115$	81.2595			0.706605
$116$	−124.597	+	81.3677i	−1.07411	+	0.701446i
$117$	31.1667	+	23.4443i	0.266382	+	0.200379i
$118$	9.12964	+	30.6771i	0.0773698	+	0.259976i
$119$	−177.195			−1.48904
$120$	82.4415	+	69.8668i	0.687013	+	0.582224i
$121$	52.6540			0.435157
$122$	−31.3799	−	105.442i	−0.257213	−	0.864277i
$123$	−19.8871			−0.161684
$124$	166.226	−	108.554i	1.34054	−	0.875434i
$125$			84.4062i			0.675250i
$126$	13.4311	+	45.1306i	0.106596	+	0.358179i
$127$		−	184.395i		−	1.45193i	−0.687733	−	0.725963i	$-0.741394\pi$
$127$		−	184.395i		−	1.45193i	0.687733	−	0.725963i	$-0.258606\pi$
$128$	−115.033	+	56.1368i	−0.898698	+	0.438569i
$129$	−116.669			−0.904412
$130$	−190.081	−	70.6076i	−1.46216	−	0.543136i
$131$		−	9.22179i		−	0.0703953i	−0.999380	−	0.0351977i	$-0.988794\pi$
$131$		−	9.22179i		−	0.0703953i	0.999380	−	0.0351977i	$-0.0112061\pi$
$132$	−49.9202	−	76.4419i	−0.378183	−	0.579105i
$133$	−205.857			−1.54780
$134$	20.9303	+	70.3295i	0.156197	+	0.524847i
$135$	40.5243			0.300180
$136$	−137.803	−	116.784i	−1.01325	−	0.858704i
$137$			25.1044i			0.183244i	0.995794	+	0.0916218i	$0.0292051\pi$
$137$			25.1044i			0.183244i	−0.995794	+	0.0916218i	$0.970795\pi$
$138$	10.2954	+	34.5942i	0.0746043	+	0.250683i
$139$			122.678i			0.882578i	0.897365	+	0.441289i	$0.145479\pi$
$139$			122.678i			0.882578i	−0.897365	+	0.441289i	$0.854521\pi$
$140$	−133.861	−	204.979i	−0.956151	−	1.46414i
$141$			18.6210i			0.132064i
$142$	32.2427	+	108.341i	0.227061	+	0.762963i
$143$	136.903	+	102.981i	0.957362	+	0.720149i
$144$	−19.2989	+	43.9494i	−0.134020	+	0.305204i
$145$		−	290.143i		−	2.00099i
$146$	−71.6239	+	21.3156i	−0.490575	+	0.145997i
$147$		−	21.8028i		−	0.148319i
$148$	84.5494	+	129.469i	0.571280	+	0.874790i
$149$			24.4303i			0.163962i	0.996634	+	0.0819809i	$0.0261246\pi$
$149$			24.4303i			0.163962i	−0.996634	+	0.0819809i	$0.973875\pi$
$150$	−118.939	+	35.3966i	−0.792924	+	0.235977i
$151$	−163.895			−1.08540			−0.542700	−	0.839927i	$-0.682598\pi$
$151$	−163.895			−1.08540			−0.542700	+	0.839927i	$0.682598\pi$
$152$	−160.092	−	135.674i	−1.05324	−	0.892590i
$153$	−67.7371			−0.442726
$154$	58.9972	+	198.240i	0.383099	+	1.28728i
$155$			387.084i			2.49731i
$156$	5.97663	−	89.8681i	0.0383118	−	0.576078i
$157$	148.220			0.944077			0.472039	−	0.881578i	$-0.343518\pi$
$157$	148.220			0.944077			0.472039	+	0.881578i	$0.343518\pi$
$158$	109.690	−	32.6442i	0.694240	−	0.206609i
$159$			100.452i			0.631773i
$160$	30.9929	−	247.633i	0.193706	−	1.54771i
$161$		−	81.7690i		−	0.507882i
$162$	5.13433	+	17.2522i	0.0316934	+	0.106495i
$163$	67.4230			0.413638			0.206819	−	0.978379i	$-0.433689\pi$
$163$	67.4230			0.413638			0.206819	+	0.978379i	$0.433689\pi$
$164$	25.1122	+	38.4539i	0.153123	+	0.234475i
$165$	178.007			1.07883
$166$	8.10889	+	27.2472i	0.0488487	+	0.164140i
$167$	148.240			0.887668			0.443834	−	0.896109i	$-0.353618\pi$
$167$	148.240			0.887668			0.443834	+	0.896109i	$0.353618\pi$
$168$	70.3049	−	82.9584i	0.418481	−	0.493800i
$169$	46.8589	+	162.374i	0.277272	+	0.960792i
$170$	337.552	−	100.457i	1.98560	−	0.590923i
$171$	−78.6936			−0.460197
$172$	147.322	+	225.592i	0.856526	+	1.31158i
$173$	23.5907			0.136362			0.0681811	−	0.997673i	$-0.478280\pi$
$173$	23.5907			0.136362			0.0681811	+	0.997673i	$0.478280\pi$
$174$	123.521	−	36.7604i	0.709892	−	0.211267i
$175$	281.130			1.60646
$176$	−84.7724	+	193.052i	−0.481661	+	1.09689i
$177$		−	27.7187i		−	0.156603i
$178$	19.8752	−	5.91496i	0.111659	−	0.0332301i
$179$		−	87.8770i		−	0.490933i	−0.969405	−	0.245466i	$-0.921059\pi$
$179$		−	87.8770i		−	0.490933i	0.969405	−	0.245466i	$-0.0789411\pi$
$180$	−51.1715	−	78.3579i	−0.284286	−	0.435322i
$181$	−156.626			−0.865338			−0.432669	−	0.901553i	$-0.642428\pi$
$181$	−156.626			−0.865338			−0.432669	+	0.901553i	$0.642428\pi$
$182$	−71.0503	+	191.273i	−0.390386	+	1.05095i
$183$			95.2734i			0.520619i
$184$	53.8912	−	63.5906i	0.292887	−	0.345601i
$185$	−301.488			−1.62967
$186$	−164.791	+	49.0426i	−0.885975	+	0.263670i
$187$	−297.541			−1.59113
$188$	36.0057	−	23.5135i	0.191520	−	0.125072i
$189$		−	40.7783i		−	0.215758i
$190$	392.151	−	116.706i	2.06395	−	0.614242i
$191$		−	365.952i		−	1.91598i	−0.286800	−	0.957990i	$-0.592591\pi$
$191$		−	365.952i		−	1.91598i	0.286800	−	0.957990i	$-0.407409\pi$
$192$	109.350	−	18.1800i	0.569533	−	0.0946876i
$193$			28.6209i			0.148295i	0.997247	+	0.0741473i	$0.0236235\pi$
$193$			28.6209i			0.148295i	−0.997247	+	0.0741473i	$0.976377\pi$
$194$	−59.1967	+	17.6172i	−0.305138	+	0.0908103i
$195$	140.334	+	105.563i	0.719663	+	0.541346i
$196$	−42.1581	+	27.5312i	−0.215092	+	0.140465i
$197$			312.113i			1.58433i	0.610307	+	0.792165i	$0.291046\pi$
$197$			312.113i			1.58433i	−0.610307	+	0.792165i	$0.708954\pi$
$198$	22.5530	+	75.7820i	0.113904	+	0.382737i
$199$			155.166i			0.779729i	0.920872	+	0.389865i	$0.127478\pi$
$199$			155.166i			0.779729i	−0.920872	+	0.389865i	$0.872522\pi$
$200$	218.631	+	185.284i	1.09316	+	0.926418i
$201$		−	63.5471i		−	0.316155i
$202$	77.6613	+	260.955i	0.384462	+	1.29186i
$203$	−291.962			−1.43824
$204$	85.5341	+	130.977i	0.419285	+	0.642043i
$205$	−89.5457			−0.436808
$206$	239.113	−	71.1609i	1.16074	−	0.345441i
$207$		−	31.2581i		−	0.151005i
$208$	−181.316	+	101.923i	−0.871713	+	0.490016i
$209$	−345.669			−1.65392
$210$	60.4760	+	203.209i	0.287981	+	0.967664i
$211$			294.581i			1.39612i	0.716040	+	0.698059i	$0.245953\pi$
$211$			294.581i			1.39612i	−0.716040	+	0.698059i	$0.754047\pi$
$212$	194.234	−	126.844i	0.916200	−	0.598322i
$213$		−	97.8927i		−	0.459590i
$214$	102.278	−	30.4383i	0.477934	−	0.142235i
$215$	−525.326			−2.44338
$216$	26.8757	−	31.7128i	0.124424	−	0.146818i
$217$	389.511			1.79498
$218$	−97.7297	+	29.0848i	−0.448301	+	0.133416i
$219$	64.7167			0.295510
$220$	−224.776	−	344.195i	−1.02171	−	1.56452i
$221$	−234.571	−	176.450i	−1.06141	−	0.798415i
$222$	−38.1979	−	128.351i	−0.172062	−	0.578159i
$223$	130.127			0.583529			0.291765	−	0.956490i	$-0.405758\pi$
$223$	130.127			0.583529			0.291765	+	0.956490i	$0.405758\pi$
$224$	−249.185	−	31.1873i	−1.11243	−	0.139229i
$225$	107.469			0.477638
$226$	−18.8880	−	63.4669i	−0.0835753	−	0.280827i
$227$	129.292			0.569567			0.284783	−	0.958592i	$-0.408078\pi$
$227$	129.292			0.569567			0.284783	+	0.958592i	$0.408078\pi$
$228$	99.3693	+	152.162i	0.435830	+	0.667379i
$229$		−	163.279i		−	0.713007i	−0.934294	−	0.356504i	$-0.883969\pi$
$229$		−	163.279i		−	0.713007i	0.934294	−	0.356504i	$-0.116031\pi$
$230$	46.3570	+	155.767i	0.201552	+	0.677250i
$231$		−	179.123i		−	0.775423i
$232$	−227.055	−	192.422i	−0.978685	−	0.829407i
$233$	419.074			1.79860			0.899301	−	0.437330i	$-0.144076\pi$
$233$	419.074			1.79860			0.899301	+	0.437330i	$0.144076\pi$
$234$	−27.1606	+	73.1184i	−0.116071	+	0.312472i
$235$			83.8449i			0.356787i
$236$	−53.5971	+	35.0014i	−0.227106	+	0.148311i
$237$	−99.1118			−0.418193
$238$	−101.087	−	339.668i	−0.424734	−	1.42718i
$239$	−11.5936			−0.0485089			−0.0242545	−	0.999706i	$-0.507721\pi$
$239$	−11.5936			−0.0485089			−0.0242545	+	0.999706i	$0.507721\pi$
$240$	−86.8972	+	197.891i	−0.362072	+	0.824545i
$241$			183.134i			0.759892i	0.925009	+	0.379946i	$0.124057\pi$
$241$			183.134i			0.759892i	−0.925009	+	0.379946i	$0.875943\pi$
$242$	30.0381	+	100.933i	0.124124	+	0.417079i
$243$		−	15.5885i		−	0.0641500i
$244$	184.221	−	120.305i	0.755004	−	0.493054i
$245$		−	98.1715i		−	0.400700i
$246$	−11.3452	−	38.1219i	−0.0461188	−	0.154967i
$247$	−272.514	−	204.991i	−1.10329	−	0.829922i
$248$	302.917	+	256.714i	1.22144	+	1.03514i
$249$		−	24.6196i		−	0.0988738i
$250$	−161.799	+	48.1521i	−0.647197	+	0.192609i
$251$			192.907i			0.768555i	0.923218	+	0.384278i	$0.125549\pi$
$251$			192.907i			0.768555i	−0.923218	+	0.384278i	$0.874451\pi$
$252$	−78.8492	+	51.4923i	−0.312894	+	0.204335i
$253$		−	137.304i		−	0.542704i
$254$	353.468	−	105.194i	1.39161	−	0.414148i
$255$	−304.999			−1.19608
$256$	−173.234	−	188.484i	−0.676694	−	0.736265i
$257$	192.474			0.748925			0.374462	−	0.927242i	$-0.377827\pi$
$257$	192.474			0.748925			0.374462	+	0.927242i	$0.377827\pi$
$258$	−66.5576	−	223.645i	−0.257975	−	0.866839i
$259$			303.378i			1.17135i
$260$	26.9110	−	404.649i	0.103504	−	1.55634i
$261$	−111.609			−0.427621
$262$	17.6774	−	5.26086i	0.0674708	−	0.0200796i
$263$			38.1415i			0.145025i	0.997368	+	0.0725124i	$0.0231017\pi$
$263$			38.1415i			0.145025i	−0.997368	+	0.0725124i	$0.976898\pi$
$264$	118.054	−	139.301i	0.447174	−	0.527656i
$265$			452.304i			1.70681i
$266$	−117.438	−	394.610i	−0.441495	−	1.48350i
$267$	−17.9585			−0.0672604
$268$	−122.875	+	80.2433i	−0.458489	+	0.299415i
$269$	−80.2898			−0.298475			−0.149238	−	0.988801i	$-0.547682\pi$
$269$	−80.2898			−0.298475			−0.149238	+	0.988801i	$0.547682\pi$
$270$	23.1183	+	77.6815i	0.0856234	+	0.287709i
$271$	−241.183			−0.889975			−0.444987	−	0.895537i	$-0.646792\pi$
$271$	−241.183			−0.889975			−0.444987	+	0.895537i	$0.646792\pi$
$272$	145.250	−	330.778i	0.534009	−	1.21610i
$273$	106.224	−	141.214i	0.389100	−	0.517268i
$274$	−48.1229	+	14.3216i	−0.175631	+	0.0522685i
$275$	472.066			1.71660
$276$	−60.4408	+	39.4707i	−0.218988	+	0.143010i
$277$	115.454			0.416800			0.208400	−	0.978044i	$-0.433174\pi$
$277$	115.454			0.416800			0.208400	+	0.978044i	$0.433174\pi$
$278$	−235.164	+	69.9857i	−0.845912	+	0.251747i
$279$	148.899			0.533690
$280$	316.561	−	373.537i	1.13058	−	1.33406i
$281$		−	362.576i		−	1.29031i	−0.764053	−	0.645153i	$-0.776794\pi$
$281$		−	362.576i		−	1.29031i	0.764053	−	0.645153i	$-0.223206\pi$
$282$	−35.6949	+	10.6229i	−0.126578	+	0.0376700i
$283$		−	239.084i		−	0.844820i	−0.906405	−	0.422410i	$-0.861184\pi$
$283$		−	239.084i		−	0.844820i	0.906405	−	0.422410i	$-0.138816\pi$
$284$	−189.286	+	123.613i	−0.666499	+	0.435256i
$285$	−354.333			−1.24328
$286$	−119.306	+	321.180i	−0.417152	+	1.12301i
$287$			90.1071i			0.313962i
$288$	−95.2568	−	11.9220i	−0.330753	−	0.0413960i
$289$	220.812			0.764056
$290$	556.178	−	165.521i	1.91786	−	0.570762i
$291$	53.4880			0.183807
$292$	−81.7202	−	125.137i	−0.279864	−	0.428550i
$293$		−	439.949i		−	1.50153i	−0.660569	−	0.750766i	$-0.729685\pi$
$293$		−	439.949i		−	1.50153i	0.660569	−	0.750766i	$-0.270315\pi$
$294$	41.7941	−	12.4381i	0.142157	−	0.0423065i
$295$		−	124.809i		−	0.423081i
$296$	−199.947	+	235.933i	−0.675496	+	0.797072i
$297$		−	68.4738i		−	0.230551i
$298$	−46.8307	+	13.9370i	−0.157150	+	0.0467685i
$299$	81.4248	−	108.246i	0.272324	−	0.362026i
$300$	−135.704	−	207.802i	−0.452348	−	0.692672i
$301$			528.619i			1.75621i
$302$	−93.4992	−	314.173i	−0.309600	−	1.04031i
$303$		−	235.789i		−	0.778182i
$304$	168.745	−	384.282i	0.555081	−	1.26409i
$305$			428.987i			1.40651i
$306$	−38.6427	−	129.846i	−0.126283	−	0.424333i
$307$	−409.415			−1.33360			−0.666800	−	0.745237i	$-0.732336\pi$
$307$	−409.415			−1.33360			−0.666800	+	0.745237i	$0.732336\pi$
$308$	−346.353	+	226.185i	−1.12452	+	0.734366i
$309$	−216.053			−0.699202
$310$	−742.006	+	220.824i	−2.39357	+	0.712335i
$311$			298.658i			0.960315i	0.877182	+	0.480157i	$0.159420\pi$
$311$			298.658i			0.960315i	−0.877182	+	0.480157i	$0.840580\pi$
$312$	175.679	−	39.8114i	0.563073	−	0.127601i
$313$	20.3892			0.0651412			0.0325706	−	0.999469i	$-0.489631\pi$
$313$	20.3892			0.0651412			0.0325706	+	0.999469i	$0.489631\pi$
$314$	84.5568	+	284.125i	0.269289	+	0.904856i
$315$		−	183.612i		−	0.582897i
$316$	125.152	+	191.643i	0.396051	+	0.606465i
$317$		−	514.348i		−	1.62255i	−0.584665	−	0.811275i	$-0.698774\pi$
$317$		−	514.348i		−	1.62255i	0.584665	−	0.811275i	$-0.301226\pi$
$318$	−192.557	+	57.3059i	−0.605526	+	0.180207i
$319$	−490.254			−1.53685
$320$	492.371	−	81.8591i	1.53866	−	0.255810i
$321$	−92.4145			−0.287896
$322$	156.744	−	46.6477i	0.486782	−	0.144869i
$323$	592.275			1.83367
$324$	−30.1419	+	19.6841i	−0.0930306	+	0.0607534i
$325$	372.160	+	279.947i	1.14511	+	0.861375i
$326$	38.4635	+	129.244i	0.117986	+	0.396454i
$327$	88.3050			0.270046
$328$	−59.3866	+	70.0751i	−0.181057	+	0.213644i
$329$	84.3705			0.256445
$330$	101.549	+	341.223i	0.307726	+	1.03401i
$331$	456.718			1.37981			0.689906	−	0.723899i	$-0.257652\pi$
$331$	456.718			1.37981			0.689906	+	0.723899i	$0.257652\pi$
$332$	−47.6046	+	31.0881i	−0.143387	+	0.0936387i
$333$			115.973i			0.348269i
$334$	84.5684	+	284.164i	0.253199	+	0.850790i
$335$		−	286.133i		−	0.854130i
$336$	199.132	+	87.4420i	0.592653	+	0.260244i
$337$	−597.668			−1.77349			−0.886747	−	0.462254i	$-0.847041\pi$
$337$	−597.668			−1.77349			−0.886747	+	0.462254i	$0.847041\pi$
$338$	−284.524	+	182.456i	−0.841787	+	0.539809i
$339$			57.3464i			0.169163i
$340$	385.134	+	589.748i	1.13275	+	1.73455i
$341$	654.055			1.91805
$342$	−44.8932	−	150.849i	−0.131267	−	0.441078i
$343$	285.755			0.833105
$344$	−348.396	+	411.100i	−1.01278	+	1.19506i
$345$		−	140.746i		−	0.407958i
$346$	13.4580	+	45.2212i	0.0388960	+	0.130697i
$347$		−	354.809i		−	1.02251i	−0.859430	−	0.511253i	$-0.829182\pi$
$347$		−	354.809i		−	1.02251i	0.859430	−	0.511253i	$-0.170818\pi$
$348$	140.933	+	215.808i	0.404980	+	0.620138i
$349$			443.875i			1.27185i	0.771752	+	0.635923i	$0.219381\pi$
$349$			443.875i			1.27185i	−0.771752	+	0.635923i	$0.780619\pi$
$350$	160.379	+	538.902i	0.458227	+	1.53972i
$351$	40.6067	−	53.9824i	0.115689	−	0.153796i
$352$	−418.425	−	52.3687i	−1.18871	−	0.148775i
$353$		−	138.241i		−	0.391617i	−0.980642	−	0.195808i	$-0.937267\pi$
$353$		−	138.241i		−	0.391617i	0.980642	−	0.195808i	$-0.0627331\pi$
$354$	53.1343	−	15.8130i	0.150097	−	0.0446695i
$355$		−	440.781i		−	1.24164i
$356$	22.6769	+	34.7247i	0.0636992	+	0.0975414i
$357$			306.912i			0.859696i
$358$	168.452	−	50.1322i	0.470538	−	0.140034i
$359$	−245.747			−0.684533			−0.342266	−	0.939603i	$-0.611194\pi$
$359$	−245.747			−0.684533			−0.342266	+	0.939603i	$0.611194\pi$
$360$	121.013	−	142.793i	0.336147	−	0.396647i
$361$	327.076			0.906028
$362$	−89.3523	−	300.239i	−0.246829	−	0.829388i
$363$		−	91.1994i		−	0.251238i
$364$	−407.186	−	27.0797i	−1.11864	−	0.0743948i
$365$	291.400			0.798356
$366$	−182.631	+	54.3516i	−0.498991	+	0.148502i
$367$		−	458.704i		−	1.24988i	−0.780674	−	0.624938i	$-0.785124\pi$
$367$		−	458.704i		−	1.24988i	0.780674	−	0.624938i	$-0.214876\pi$
$368$	152.642	+	67.0275i	0.414787	+	0.182140i
$369$			34.4455i			0.0933483i
$370$	−171.993	−	577.927i	−0.464847	−	1.56196i
$371$	455.140			1.22679
$372$	−188.021	−	287.913i	−0.505432	−	0.773959i
$373$	−269.970			−0.723780			−0.361890	−	0.932221i	$-0.617868\pi$
$373$	−269.970			−0.723780			−0.361890	+	0.932221i	$0.617868\pi$
$374$	−169.742	−	570.361i	−0.453855	−	1.52503i
$375$	146.196			0.389856
$376$	65.6138	+	55.6058i	0.174505	+	0.147888i
$377$	−386.499	−	290.733i	−1.02520	−	0.771175i
$378$	78.1685	−	23.2633i	0.206795	−	0.0615430i
$379$	474.173			1.25112			0.625559	−	0.780177i	$-0.284871\pi$
$379$	474.173			1.25112			0.625559	+	0.780177i	$0.284871\pi$
$380$	447.430	+	685.141i	1.17745	+	1.80300i
$381$	−319.381			−0.838270
$382$	701.498	−	208.769i	1.83638	−	0.546515i
$383$	237.625			0.620431			0.310215	−	0.950666i	$-0.399599\pi$
$383$	237.625			0.620431			0.310215	+	0.950666i	$0.399599\pi$
$384$	97.2318	+	199.244i	0.253208	+	0.518863i
$385$		−	806.535i		−	2.09490i
$386$	−54.8637	+	16.3277i	−0.142134	+	0.0422996i
$387$			202.077i			0.522163i
$388$	−67.5412	−	103.425i	−0.174075	−	0.266558i
$389$	94.1823			0.242114			0.121057	−	0.992646i	$-0.461372\pi$
$389$	94.1823			0.242114			0.121057	+	0.992646i	$0.461372\pi$
$390$	−122.296	+	329.230i	−0.313579	+	0.844179i
$391$			235.259i			0.601685i
$392$	−76.8253	−	65.1073i	−0.195983	−	0.166090i
$393$	−15.9726			−0.0406428
$394$	−598.293	+	178.054i	−1.51851	+	0.451915i
$395$	−446.270			−1.12980
$396$	−132.401	+	86.4643i	−0.334347	+	0.218344i
$397$			418.475i			1.05409i	0.849836	+	0.527047i	$0.176701\pi$
$397$			418.475i			1.05409i	−0.849836	+	0.527047i	$0.823299\pi$
$398$	−297.440	+	88.5193i	−0.747336	+	0.222410i
$399$			356.555i			0.893621i
$400$	−230.447	+	524.798i	−0.576119	+	1.31199i
$401$			673.251i			1.67893i	0.543413	+	0.839465i	$0.317132\pi$
$401$			673.251i			1.67893i	−0.543413	+	0.839465i	$0.682868\pi$
$402$	121.814	−	36.2524i	0.303020	−	0.0901802i
$403$	515.634	+	387.871i	1.27949	+	0.962460i
$404$	−455.923	+	297.740i	−1.12852	+	0.736979i
$405$		−	70.1901i		−	0.173309i
$406$	−166.559	−	559.665i	−0.410243	−	1.37849i
$407$			509.424i			1.25166i
$408$	−202.275	+	238.681i	−0.495773	+	0.585002i
$409$		−	159.073i		−	0.388932i	−0.980909	−	0.194466i	$-0.937703\pi$
$409$		−	159.073i		−	0.388932i	0.980909	−	0.194466i	$-0.0622973\pi$
$410$	−51.0841	−	171.651i	−0.124595	−	0.418662i
$411$	43.4821			0.105796
$412$	272.818	+	417.762i	0.662181	+	1.01398i
$413$	−125.591			−0.304095
$414$	59.9190	−	17.8321i	0.144732	−	0.0430728i
$415$		−	110.855i		−	0.267119i
$416$	−298.816	−	289.422i	−0.718307	−	0.695727i
$417$	212.485			0.509557
$418$	−197.198	−	662.617i	−0.471765	−	1.58521i
$419$			706.798i			1.68687i	0.537232	+	0.843435i	$0.319470\pi$
$419$			706.798i			1.68687i	−0.537232	+	0.843435i	$0.680530\pi$
$420$	−355.034	+	231.854i	−0.845319	+	0.552034i
$421$			181.323i			0.430696i	0.976537	+	0.215348i	$0.0690885\pi$
$421$			181.323i			0.430696i	−0.976537	+	0.215348i	$0.930911\pi$
$422$	−564.686	+	168.053i	−1.33812	+	0.398229i
$423$	32.2526			0.0762472
$424$	353.956	+	299.968i	0.834803	+	0.707471i
$425$	−808.844			−1.90316
$426$	187.652	−	55.8459i	0.440497	−	0.131094i
$427$	431.676			1.01095
$428$	116.695	+	178.693i	0.272652	+	0.417507i
$429$	178.369	−	237.123i	0.415778	−	0.552733i
$430$	−299.689	−	1007.00i	−0.696950	−	2.34187i
$431$	−430.786			−0.999505			−0.499752	−	0.866168i	$-0.666576\pi$
$431$	−430.786			−0.999505			−0.499752	+	0.866168i	$0.666576\pi$
$432$	76.1226	+	33.4267i	0.176210	+	0.0773767i
$433$	12.3174			0.0284467			0.0142233	−	0.999899i	$-0.495472\pi$
$433$	12.3174			0.0284467			0.0142233	+	0.999899i	$0.495472\pi$
$434$	222.208	+	746.658i	0.512001	+	1.72041i
$435$	−502.542			−1.15527
$436$	−111.506	−	170.747i	−0.255748	−	0.391621i
$437$			273.312i			0.625429i
$438$	36.9197	+	124.056i	0.0842915	+	0.283234i
$439$			499.229i			1.13719i	0.822616	+	0.568597i	$0.192514\pi$
$439$			499.229i			1.13719i	−0.822616	+	0.568597i	$0.807486\pi$
$440$	531.561	−	627.231i	1.20809	−	1.42553i
$441$	−37.7636			−0.0856318
$442$	204.420	−	550.314i	0.462489	−	1.24505i
$443$		−	417.285i		−	0.941953i	−0.882146	−	0.470976i	$-0.843902\pi$
$443$		−	417.285i		−	0.941953i	0.882146	−	0.470976i	$-0.156098\pi$
$444$	224.247	−	146.444i	0.505060	−	0.329829i
$445$	−80.8618			−0.181712
$446$	74.2350	+	249.442i	0.166446	+	0.559287i
$447$	42.3145			0.0946634
$448$	−82.3723	−	495.458i	−0.183867	−	1.10593i
$449$			290.199i			0.646323i	0.946344	+	0.323161i	$0.104746\pi$
$449$			290.199i			0.646323i	−0.946344	+	0.323161i	$0.895254\pi$
$450$	61.3087	+	206.008i	0.136242	+	0.457795i
$451$			151.305i			0.335488i
$452$	110.885	−	72.4134i	0.245321	−	0.160207i
$453$			283.875i			0.626656i
$454$	73.7584	+	247.841i	0.162464	+	0.545905i
$455$	478.296	−	635.845i	1.05120	−	1.39746i
$456$	−234.994	+	277.288i	−0.515337	+	0.608088i
$457$		−	561.395i		−	1.22844i	−0.789137	−	0.614218i	$-0.789472\pi$
$457$		−	561.395i		−	1.22844i	0.789137	−	0.614218i	$-0.210528\pi$
$458$	312.991	−	93.1474i	0.683386	−	0.203379i
$459$			117.324i			0.255608i
$460$	−272.147	+	177.725i	−0.591623	+	0.386358i
$461$		−	381.251i		−	0.827009i	−0.910502	−	0.413505i	$-0.864305\pi$
$461$		−	381.251i		−	0.827009i	0.910502	−	0.413505i	$-0.135695\pi$
$462$	343.362	−	102.186i	0.743209	−	0.221182i
$463$	24.2335			0.0523401			0.0261700	−	0.999658i	$-0.491669\pi$
$463$	24.2335			0.0523401			0.0261700	+	0.999658i	$0.491669\pi$
$464$	239.326	−	545.017i	0.515790	−	1.17461i
$465$	670.449			1.44183
$466$	239.074	+	803.329i	0.513034	+	1.72388i
$467$		−	813.014i		−	1.74093i	−0.492230	−	0.870465i	$-0.663818\pi$
$467$		−	813.014i		−	1.74093i	0.492230	−	0.870465i	$-0.336182\pi$
$468$	−155.656	−	10.3518i	−0.332599	−	0.0221193i
$469$	−287.927			−0.613917
$470$	−160.723	+	47.8319i	−0.341964	+	0.101770i
$471$		−	256.725i		−	0.545063i
$472$	−97.6708	−	82.7732i	−0.206930	−	0.175367i
$473$			887.642i			1.87662i
$474$	−56.5414	−	189.989i	−0.119286	−	0.400820i
$475$	−939.676			−1.97827
$476$	593.446	−	387.548i	1.24673	−	0.814177i
$477$	173.988			0.364754
$478$	−6.61395	−	22.2240i	−0.0138367	−	0.0464936i
$479$	−10.7399			−0.0224214			−0.0112107	−	0.999937i	$-0.503569\pi$
$479$	−10.7399			−0.0224214			−0.0112107	+	0.999937i	$0.503569\pi$
$480$	−428.913	−	53.6814i	−0.893568	−	0.111836i
$481$	−302.102	+	401.612i	−0.628070	+	0.834953i
$482$	−351.052	+	104.474i	−0.728323	+	0.216752i
$483$	−141.628			−0.293226
$484$	−176.344	+	115.161i	−0.364346	+	0.237935i
$485$	240.840			0.496577
$486$	29.8817	−	8.89292i	0.0614850	−	0.0182982i
$487$	561.520			1.15302			0.576509	−	0.817091i	$-0.304414\pi$
$487$	561.520			1.15302			0.576509	+	0.817091i	$0.304414\pi$
$488$	335.709	+	284.504i	0.687928	+	0.582999i
$489$		−	116.780i		−	0.238814i
$490$	188.186	−	56.0050i	0.384053	−	0.114296i
$491$			573.500i			1.16803i	0.811745	+	0.584013i	$0.198518\pi$
$491$			573.500i			1.16803i	−0.811745	+	0.584013i	$0.801482\pi$
$492$	66.6040	−	43.4956i	0.135374	−	0.0884057i
$493$	840.008			1.70387
$494$	237.485	−	639.328i	0.480739	−	1.29419i
$495$		−	308.317i		−	0.622862i
$496$	−319.289	+	727.116i	−0.643727	+	1.46596i
$497$	−443.545			−0.892444
$498$	47.1936	−	14.0450i	0.0947662	−	0.0282028i
$499$	−700.846			−1.40450			−0.702250	−	0.711930i	$-0.747821\pi$
$499$	−700.846			−1.40450			−0.702250	+	0.711930i	$0.747821\pi$
$500$	−184.607	−	282.685i	−0.369214	−	0.565370i
$501$		−	256.760i		−	0.512495i
$502$	−369.786	+	110.050i	−0.736626	+	0.219223i
$503$			220.983i			0.439330i	0.975575	+	0.219665i	$0.0704964\pi$
$503$			220.983i			0.439330i	−0.975575	+	0.219665i	$0.929504\pi$
$504$	−143.688	−	121.772i	−0.285096	−	0.241610i
$505$		−	1061.69i		−	2.10235i
$506$	263.200	−	78.3294i	0.520158	−	0.154801i
$507$	281.240	−	81.1620i	0.554713	−	0.160083i
$508$	403.294	+	617.557i	0.793886	+	1.21566i
$509$		−	686.143i		−	1.34802i	−0.738721	−	0.674011i	$-0.764570\pi$
$509$		−	686.143i		−	1.34802i	0.738721	−	0.674011i	$-0.235430\pi$
$510$	−173.996	−	584.657i	−0.341169	−	1.14639i
$511$		−	293.227i		−	0.573829i
$512$	262.480	−	439.600i	0.512657	−	0.858594i
$513$			136.301i			0.265695i
$514$	109.803	+	368.955i	0.213624	+	0.717811i
$515$	−972.823			−1.88898
$516$	390.737	−	255.170i	0.757242	−	0.494515i
$517$	141.673			0.274028
$518$	−581.550	+	173.072i	−1.12268	+	0.334115i
$519$		−	40.8602i		−	0.0787288i
$520$	791.029	−	179.259i	1.52121	−	0.344728i
$521$	384.581			0.738160			0.369080	−	0.929398i	$-0.379673\pi$
$521$	384.581			0.738160			0.369080	+	0.929398i	$0.379673\pi$
$522$	−63.6709	−	213.945i	−0.121975	−	0.409856i
$523$		−	367.884i		−	0.703411i	−0.936111	−	0.351706i	$-0.885602\pi$
$523$		−	367.884i		−	0.703411i	0.936111	−	0.351706i	$-0.114398\pi$
$524$	20.1692	+	30.8847i	0.0384908	+	0.0589403i
$525$		−	486.932i		−	0.927489i
$526$	−73.1139	+	21.7590i	−0.139000	+	0.0413670i
$527$	−1120.67			−2.12650
$528$	334.376	+	146.830i	0.633288	+	0.278087i
$529$	420.437			0.794777
$530$	−867.028	+	258.031i	−1.63590	+	0.486851i
$531$	−48.0102			−0.0904147
$532$	689.437	−	450.235i	1.29593	−	0.846306i
$533$	−89.7279	+	119.284i	−0.168345	+	0.223797i
$534$	−10.2450	−	34.4249i	−0.0191854	−	0.0644662i
$535$	−416.114			−0.777784
$536$	−223.917	−	189.763i	−0.417756	−	0.354036i
$537$	−152.207			−0.283440
$538$	−45.8038	−	153.909i	−0.0851372	−	0.286075i
$539$	−165.880			−0.307756
$540$	−135.720	+	88.6316i	−0.251333	+	0.164133i
$541$		−	235.088i		−	0.434544i	−0.976111	−	0.217272i	$-0.930284\pi$
$541$		−	235.088i		−	0.434544i	0.976111	−	0.217272i	$-0.0697158\pi$
$542$	−137.590	−	462.327i	−0.253857	−	0.853001i
$543$			271.285i			0.499603i
$544$	716.935	+	89.7294i	1.31790	+	0.164944i
$545$	397.610			0.729561
$546$	331.294	+	123.063i	0.606766	+	0.225390i
$547$		−	230.496i		−	0.421382i	−0.977553	−	0.210691i	$-0.932429\pi$
$547$		−	230.496i		−	0.421382i	0.977553	−	0.210691i	$-0.0675714\pi$
$548$	−54.9064	−	84.0771i	−0.100194	−	0.153425i
$549$	165.018			0.300580
$550$	269.304	+	904.908i	0.489644	+	1.64529i
$551$	975.881			1.77111
$552$	−110.142	−	93.3424i	−0.199533	−	0.169099i
$553$			449.068i			0.812058i
$554$	65.8641	+	221.315i	0.118888	+	0.399485i
$555$			522.193i			0.940888i
$556$	−268.313	−	410.862i	−0.482577	−	0.738961i
$557$			497.920i			0.893933i	0.894551	+	0.446966i	$0.147496\pi$
$557$			497.920i			0.893933i	−0.894551	+	0.446966i	$0.852504\pi$
$558$	84.9443	+	285.427i	0.152230	+	0.511518i
$559$	−526.395	+	699.787i	−0.941672	+	1.25185i
$560$	896.629	+	393.725i	1.60112	+	0.703080i
$561$			515.357i			0.918640i
$562$	695.026	−	206.843i	1.23670	−	0.368048i
$563$		−	10.9662i		−	0.0194782i	−0.999953	−	0.00973912i	$-0.996900\pi$
$563$		−	10.9662i		−	0.0194782i	0.999953	−	0.00973912i	$-0.00310011\pi$
$564$	−40.7265	−	62.3638i	−0.0722101	−	0.110574i
$565$			258.213i			0.457015i
$566$	458.303	−	136.393i	0.809723	−	0.240977i
$567$	−70.6301			−0.124568
$568$	−344.939	−	292.326i	−0.607286	−	0.514658i
$569$	−1049.19			−1.84393			−0.921964	−	0.387276i	$-0.873416\pi$
$569$	−1049.19			−1.84393			−0.921964	+	0.387276i	$0.873416\pi$
$570$	−202.141	−	679.226i	−0.354633	−	1.19162i
$571$		−	1062.00i		−	1.85989i	−0.367703	−	0.929943i	$-0.619856\pi$
$571$		−	1062.00i		−	1.85989i	0.367703	−	0.929943i	$-0.380144\pi$
$572$	−683.734	−	45.4714i	−1.19534	−	0.0794955i
$573$	−633.848			−1.10619
$574$	−172.727	+	51.4044i	−0.300919	+	0.0895547i
$575$		−	373.251i		−	0.649132i
$576$	−31.4887	−	189.400i	−0.0546679	−	0.328820i
$577$		−	634.074i		−	1.09892i	−0.835521	−	0.549458i	$-0.814834\pi$
$577$		−	634.074i		−	1.09892i	0.835521	−	0.549458i	$-0.185166\pi$
$578$	125.969	+	423.277i	0.217940	+	0.732314i
$579$	49.5728			0.0856179
$580$	634.578	+	971.718i	1.09410	+	1.67538i
$581$	−111.550			−0.191996
$582$	30.5139	+	102.532i	0.0524293	+	0.176171i
$583$	764.258			1.31091
$584$	193.256	−	228.038i	0.330918	−	0.390477i
$585$	182.840	−	243.066i	0.312546	−	0.415498i
$586$	843.343	−	250.982i	1.43915	−	0.428298i
$587$	64.5958			0.110044			0.0550220	−	0.998485i	$-0.482477\pi$
$587$	64.5958			0.110044			0.0550220	+	0.998485i	$0.482477\pi$
$588$	47.6855	+	73.0199i	0.0810978	+	0.124184i
$589$	−1301.94			−2.21042
$590$	239.248	−	71.2011i	0.405505	−	0.120680i
$591$	540.595			0.914713
$592$	−566.329	−	248.685i	−0.956637	−	0.420076i
$593$			146.523i			0.247087i	0.992339	+	0.123544i	$0.0394259\pi$
$593$			146.523i			0.247087i	−0.992339	+	0.123544i	$0.960574\pi$
$594$	131.258	−	39.0630i	0.220973	−	0.0657626i
$595$			1381.93i			2.32257i
$596$	−53.4321	−	81.8196i	−0.0896512	−	0.137281i
$597$	268.756			0.450177
$598$	253.949	+	94.3321i	0.424664	+	0.157746i
$599$			469.062i			0.783074i	0.920162	+	0.391537i	$0.128057\pi$
$599$			469.062i			0.783074i	−0.920162	+	0.391537i	$0.871943\pi$
$600$	320.921	−	378.680i	0.534868	−	0.631134i
$601$	287.117			0.477732			0.238866	−	0.971052i	$-0.423224\pi$
$601$	287.117			0.477732			0.238866	+	0.971052i	$0.423224\pi$
$602$	−1013.32	+	301.567i	−1.68325	+	0.500943i
$603$	−110.067			−0.182532
$604$	548.902	−	358.459i	0.908778	−	0.593476i
$605$		−	410.643i		−	0.678749i
$606$	451.987	−	134.513i	0.745853	−	0.221969i
$607$			534.181i			0.880035i	0.897989	+	0.440017i	$0.145028\pi$
$607$			534.181i			0.880035i	−0.897989	+	0.440017i	$0.854972\pi$
$608$	832.901	+	104.243i	1.36990	+	0.171453i
$609$			505.693i			0.830366i
$610$	−822.330	+	244.729i	−1.34808	+	0.401195i
$611$	111.690	+	84.0154i	0.182798	+	0.137505i
$612$	226.858	−	148.149i	0.370684	−	0.242074i
$613$		−	845.316i		−	1.37898i	−0.724294	−	0.689491i	$-0.757834\pi$
$613$		−	845.316i		−	1.37898i	0.724294	−	0.689491i	$-0.242166\pi$
$614$	−233.564	−	784.813i	−0.380397	−	1.27820i
$615$			155.098i			0.252191i
$616$	−631.164	−	534.893i	−1.02462	−	0.868333i
$617$		−	30.9449i		−	0.0501538i	−0.999686	−	0.0250769i	$-0.992017\pi$
$617$		−	30.9449i		−	0.0501538i	0.999686	−	0.0250769i	$-0.00798305\pi$
$618$	−123.254	−	414.155i	−0.199441	−	0.670154i
$619$	−637.250			−1.02948			−0.514741	−	0.857346i	$-0.672112\pi$
$619$	−637.250			−1.02948			−0.514741	+	0.857346i	$0.672112\pi$
$620$	−846.600	−	1296.38i	−1.36548	−	2.09094i
$621$	−54.1406			−0.0871829
$622$	−572.501	+	170.379i	−0.920419	+	0.273921i
$623$			81.3688i			0.130608i
$624$	176.536	+	314.049i	0.282911	+	0.503284i
$625$	−237.295			−0.379673
$626$	11.6316	+	39.0843i	0.0185809	+	0.0624349i
$627$			598.716i			0.954891i
$628$	−496.404	+	324.176i	−0.790453	+	0.516203i
$629$		−	872.855i		−	1.38769i
$630$	351.969	−	104.747i	0.558681	−	0.166266i
$631$	440.047			0.697380			0.348690	−	0.937238i	$-0.386627\pi$
$631$	440.047			0.697380			0.348690	+	0.937238i	$0.386627\pi$
$632$	−295.966	+	349.234i	−0.468301	+	0.552586i
$633$	510.229			0.806049
$634$	985.960	−	293.426i	1.55514	−	0.462817i
$635$	−1438.08			−2.26469
$636$	−219.701	−	336.424i	−0.345441	−	0.528968i
$637$	−130.774	−	98.3712i	−0.205297	−	0.154429i
$638$	−279.680	−	939.773i	−0.438371	−	1.47300i
$639$	−169.555			−0.265344
$640$	437.805	+	897.133i	0.684071	+	1.40177i
$641$	203.080			0.316817			0.158408	−	0.987374i	$-0.449364\pi$
$641$	203.080			0.316817			0.158408	+	0.987374i	$0.449364\pi$
$642$	−52.7207	−	177.150i	−0.0821195	−	0.275935i
$643$	−130.355			−0.202729			−0.101365	−	0.994849i	$-0.532321\pi$
$643$	−130.355			−0.202729			−0.101365	+	0.994849i	$0.532321\pi$
$644$	178.839	+	273.853i	0.277700	+	0.425237i
$645$			909.891i			1.41068i
$646$	337.882	+	1135.34i	0.523036	+	1.75749i
$647$		−	423.596i		−	0.654709i	−0.944902	−	0.327354i	$-0.893843\pi$
$647$		−	423.596i		−	0.654709i	0.944902	−	0.327354i	$-0.106157\pi$
$648$	−54.9281	−	46.5500i	−0.0847656	−	0.0718364i
$649$	−210.889			−0.324945
$650$	−324.323	+	873.103i	−0.498959	+	1.34324i
$651$		−	674.652i		−	1.03633i
$652$	−225.807	+	147.462i	−0.346329	+	0.226169i
$653$	149.879			0.229524			0.114762	−	0.993393i	$-0.463389\pi$
$653$	149.879			0.229524			0.114762	+	0.993393i	$0.463389\pi$
$654$	50.3763	+	169.273i	0.0770280	+	0.258827i
$655$	−71.9198			−0.109801
$656$	−168.207	−	73.8624i	−0.256413	−	0.112595i
$657$		−	112.093i		−	0.170613i
$658$	48.1318	+	161.731i	0.0731486	+	0.245792i
$659$			590.762i			0.896452i	0.893920	+	0.448226i	$0.147944\pi$
$659$			590.762i			0.896452i	−0.893920	+	0.448226i	$0.852056\pi$
$660$	−596.163	+	389.323i	−0.903277	+	0.589883i
$661$		−	668.639i		−	1.01156i	−0.862664	−	0.505778i	$-0.831205\pi$
$661$		−	668.639i		−	1.01156i	0.862664	−	0.505778i	$-0.168795\pi$
$662$	260.549	+	875.487i	0.393578	+	1.32249i
$663$	−305.620	+	406.290i	−0.460965	+	0.612805i
$664$	−86.7506	−	73.5186i	−0.130648	−	0.110721i
$665$			1605.46i			2.41422i
$666$	−222.311	+	66.1606i	−0.333800	+	0.0993403i
$667$			387.632i			0.581157i
$668$	−496.473	+	324.220i	−0.743223	+	0.485360i
$669$		−	225.387i		−	0.336901i
$670$	548.493	−	163.234i	0.818646	−	0.243632i
$671$	724.858			1.08027
$672$	−54.0179	+	431.602i	−0.0803838	+	0.642264i
$673$	−1223.15			−1.81746			−0.908729	−	0.417388i	$-0.862946\pi$
$673$	−1223.15			−1.81746			−0.908729	+	0.417388i	$0.862946\pi$
$674$	−340.958	−	1145.68i	−0.505873	−	1.69982i
$675$		−	186.141i		−	0.275764i
$676$	−512.067	−	441.320i	−0.757495	−	0.652840i
$677$	1157.62			1.70992			0.854961	−	0.518692i	$-0.173581\pi$
$677$	1157.62			1.70992			0.854961	+	0.518692i	$0.173581\pi$
$678$	−109.928	+	32.7150i	−0.162136	+	0.0482522i
$679$		−	242.350i		−	0.356922i
$680$	−910.784	+	1074.71i	−1.33939	+	1.58045i
$681$		−	223.940i		−	0.328839i
$682$	373.126	+	1253.77i	0.547105	+	1.83837i
$683$	1000.21			1.46443			0.732217	−	0.681072i	$-0.238486\pi$
$683$	1000.21			1.46443			0.732217	+	0.681072i	$0.238486\pi$
$684$	263.553	−	172.113i	0.385311	−	0.251627i
$685$	195.787			0.285820
$686$	163.018	+	547.767i	0.237635	+	0.798494i
$687$	−282.807			−0.411655
$688$	−986.796	−	433.319i	−1.43430	−	0.629824i
$689$	602.514	+	453.224i	0.874477	+	0.657800i
$690$	269.797	−	80.2927i	0.391010	−	0.116366i
$691$	120.026			0.173699			0.0868496	−	0.996221i	$-0.472320\pi$
$691$	120.026			0.173699			0.0868496	+	0.996221i	$0.472320\pi$
$692$	−79.0076	+	51.5957i	−0.114173	+	0.0745603i
$693$	−310.250			−0.447691
$694$	680.138	−	202.412i	0.980027	−	0.291660i
$695$	956.756			1.37663
$696$	−333.285	+	393.270i	−0.478858	+	0.565044i
$697$		−	259.249i		−	0.371949i
$698$	−850.868	+	253.222i	−1.21901	+	0.362782i
$699$		−	725.858i		−	1.03842i
$700$	−941.534	+	614.867i	−1.34505	+	0.878381i
$701$	882.073			1.25831			0.629153	−	0.777281i	$-0.283402\pi$
$701$	882.073			1.25831			0.629153	+	0.777281i	$0.283402\pi$
$702$	126.645	+	47.0436i	0.180406	+	0.0670136i
$703$		−	1014.04i		−	1.44245i
$704$	−138.317	−	831.959i	−0.196473	−	1.18176i
$705$	145.224			0.205991
$706$	264.995	−	78.8637i	0.375348	−	0.111705i
$707$	−1068.34			−1.51109
$708$	60.6243	+	92.8328i	0.0856275	+	0.131120i
$709$		−	285.806i		−	0.403112i	−0.979477	−	0.201556i	$-0.935400\pi$
$709$		−	285.806i		−	0.403112i	0.979477	−	0.201556i	$-0.0645998\pi$
$710$	844.939	−	251.457i	1.19005	−	0.354165i
$711$			171.667i			0.241444i
$712$	−53.6275	+	63.2794i	−0.0753195	+	0.0888756i
$713$		−	517.146i		−	0.725309i
$714$	−588.322	+	175.087i	−0.823981	+	0.245220i
$715$	803.141	−	1067.69i	1.12327	−	1.49327i
$716$	192.198	+	294.309i	0.268433	+	0.411046i
$717$			20.0808i			0.0280066i
$718$	−140.194	−	471.076i	−0.195256	−	0.656094i
$719$			984.643i			1.36946i	0.728796	+	0.684731i	$0.240080\pi$
$719$			984.643i			1.36946i	−0.728796	+	0.684731i	$0.759920\pi$
$720$	342.757	+	150.510i	0.476052	+	0.209042i
$721$			978.922i			1.35773i
$722$	186.591	+	626.976i	0.258436	+	0.868388i
$723$	317.197			0.438724
$724$	524.557	−	342.561i	0.724526	−	0.473150i
$725$	−1332.72			−1.83823
$726$	174.821	−	52.0275i	0.240800	−	0.0716632i
$727$			566.297i			0.778950i	0.921037	+	0.389475i	$0.127344\pi$
$727$			566.297i			0.778950i	−0.921037	+	0.389475i	$0.872656\pi$
$728$	−180.382	−	795.988i	−0.247778	−	1.09339i
$729$	−27.0000			−0.0370370
$730$	166.238	+	558.588i	0.227723	+	0.765189i
$731$		−	1520.90i		−	2.08057i
$732$	−208.375	−	319.080i	−0.284665	−	0.435902i
$733$			1398.80i			1.90832i	0.299303	+	0.954158i	$0.403246\pi$
$733$			1398.80i			1.90832i	−0.299303	+	0.954158i	$0.596754\pi$
$734$	879.296	−	261.682i	1.19795	−	0.356515i
$735$	−170.038			−0.231344
$736$	−41.4067	+	330.838i	−0.0562591	+	0.449509i
$737$	−483.479			−0.656009
$738$	−66.0290	+	19.6505i	−0.0894702	+	0.0266267i
$739$	500.468			0.677223			0.338611	−	0.940926i	$-0.390043\pi$
$739$	500.468			0.677223			0.338611	+	0.940926i	$0.390043\pi$
$740$	1009.72	−	659.392i	1.36448	−	0.891071i
$741$	−355.054	+	472.007i	−0.479156	+	0.636987i
$742$	259.649	+	872.463i	0.349931	+	1.17583i
$743$	349.050			0.469784			0.234892	−	0.972021i	$-0.424526\pi$
$743$	349.050			0.469784			0.234892	+	0.972021i	$0.424526\pi$
$744$	444.641	−	524.668i	0.597636	−	0.705199i
$745$	190.529			0.255744
$746$	−154.013	−	517.509i	−0.206451	−	0.693711i
$747$	−42.6424			−0.0570848
$748$	996.497	−	650.760i	1.33221	−	0.870000i
$749$			418.723i			0.559043i
$750$	83.4019	+	280.245i	0.111203	+	0.373659i
$751$		−	25.5035i		−	0.0339594i	−0.999856	−	0.0169797i	$-0.994595\pi$
$751$		−	25.5035i		−	0.0339594i	0.999856	−	0.0169797i	$-0.00540507\pi$
$752$	−69.1601	+	157.498i	−0.0919682	+	0.209439i
$753$	334.125			0.443725
$754$	336.819	−	906.743i	0.446710	−	1.20258i
$755$			1278.20i			1.69298i
$756$	89.1873	+	136.571i	0.117973	+	0.180649i
$757$	371.325			0.490522			0.245261	−	0.969457i	$-0.421126\pi$
$757$	371.325			0.490522			0.245261	+	0.969457i	$0.421126\pi$
$758$	270.507	+	908.949i	0.356869	+	1.19914i
$759$	−237.818			−0.313330
$760$	−1058.10	+	1248.54i	−1.39224	+	1.64282i
$761$		−	30.6207i		−	0.0402374i	−0.999798	−	0.0201187i	$-0.993596\pi$
$761$		−	30.6207i		−	0.0402374i	0.999798	−	0.0201187i	$-0.00640441\pi$
$762$	−182.201	−	612.225i	−0.239109	−	0.803445i
$763$		−	400.103i		−	0.524382i
$764$	800.383	+	1225.61i	1.04762	+	1.60420i
$765$			528.274i			0.690555i
$766$	135.561	+	455.506i	0.176972	+	0.594655i
$767$	−166.258	−	125.063i	−0.216764	−	0.163055i
$768$	−326.463	+	300.049i	−0.425083	+	0.390689i
$769$		−	563.426i		−	0.732674i	−0.930482	−	0.366337i	$-0.880612\pi$
$769$		−	563.426i		−	0.732674i	0.930482	−	0.366337i	$-0.119388\pi$
$770$	1546.06	−	460.113i	2.00787	−	0.597549i
$771$		−	333.374i		−	0.432392i
$772$	−62.5974	−	95.8542i	−0.0810847	−	0.124163i
$773$			1408.83i			1.82255i	0.411800	+	0.911274i	$0.364900\pi$
$773$			1408.83i			1.82255i	−0.411800	+	0.911274i	$0.635100\pi$
$774$	−387.364	+	115.281i	−0.500470	+	0.148942i
$775$	1778.00			2.29419
$776$	159.725	−	188.472i	0.205831	−	0.242877i
$777$	525.467			0.676277
$778$	53.7292	+	180.539i	0.0690607	+	0.232055i
$779$		−	301.182i		−	0.386627i
$780$	−700.872	−	46.6112i	−0.898554	−	0.0597579i
$781$	−744.787			−0.953632
$782$	−450.971	+	134.211i	−0.576689	+	0.171625i
$783$			193.313i			0.246887i
$784$	80.9775	−	184.410i	0.103288	−	0.235217i
$785$		−	1155.95i		−	1.47255i
$786$	−9.11207	−	30.6181i	−0.0115930	−	0.0389543i
$787$	740.379			0.940761			0.470381	−	0.882464i	$-0.344117\pi$
$787$	740.379			0.940761			0.470381	+	0.882464i	$0.344117\pi$
$788$	−682.630	−	1045.30i	−0.866281	−	1.32652i
$789$	66.0631			0.0837301
$790$	−254.589	−	855.461i	−0.322264	−	1.08286i
$791$	259.832			0.328486
$792$	−241.277	−	204.475i	−0.304643	−	0.258176i
$793$	571.453	+	429.860i	0.720622	+	0.542068i
$794$	−802.180	+	238.732i	−1.01030	+	0.300670i
$795$	783.414			0.985427
$796$	−339.367	−	519.667i	−0.426341	−	0.652848i
$797$	1439.36			1.80597			0.902985	−	0.429673i	$-0.141371\pi$
$797$	1439.36			1.80597			0.902985	+	0.429673i	$0.141371\pi$
$798$	−683.484	+	203.408i	−0.856497	+	0.254897i
$799$	−242.744			−0.303810
$800$	−1137.46	−	142.360i	−1.42182	−	0.177951i
$801$			31.1051i			0.0388328i
$802$	−1290.56	+	384.077i	−1.60918	+	0.478899i
$803$		−	492.378i		−	0.613173i
$804$	138.985	+	212.826i	0.172867	+	0.264709i
$805$	−637.708			−0.792184
$806$	−449.355	+	1209.70i	−0.557513	+	1.50087i
$807$			139.066i			0.172325i
$808$	−830.836	−	704.110i	−1.02826	−	0.871423i
$809$	−676.465			−0.836174			−0.418087	−	0.908407i	$-0.637299\pi$
$809$	−676.465			−0.836174			−0.418087	+	0.908407i	$0.637299\pi$
$810$	134.548	−	40.0421i	0.166109	−	0.0494347i
$811$	−839.069			−1.03461			−0.517305	−	0.855801i	$-0.673065\pi$
$811$	−839.069			−1.03461			−0.517305	+	0.855801i	$0.673065\pi$
$812$	977.810	−	638.557i	1.20420	−	0.786400i
$813$			417.741i			0.513827i
$814$	−976.521	+	290.617i	−1.19966	+	0.357023i
$815$		−	525.825i		−	0.645184i
$816$	−572.925	−	251.581i	−0.702114	−	0.308310i
$817$		−	1766.91i		−	2.16268i
$818$	304.929	−	90.7481i	0.372774	−	0.110939i
$819$	−244.590	−	183.986i	−0.298645	−	0.224647i
$820$	299.898	−	195.848i	0.365729	−	0.238838i
$821$		−	1228.30i		−	1.49611i	−0.663638	−	0.748054i	$-0.730988\pi$
$821$		−	1228.30i		−	1.49611i	0.663638	−	0.748054i	$-0.269012\pi$
$822$	24.8057	+	83.3513i	0.0301772	+	0.101401i
$823$			1171.99i			1.42405i	0.702154	+	0.712025i	$0.252222\pi$
$823$			1171.99i			1.42405i	−0.702154	+	0.712025i	$0.747778\pi$
$824$	−645.175	+	761.294i	−0.782979	+	0.923901i
$825$		−	817.642i		−	0.991081i
$826$	−71.6475	−	240.748i	−0.0867404	−	0.291462i
$827$	750.467			0.907457			0.453729	−	0.891140i	$-0.350094\pi$
$827$	750.467			0.907457			0.453729	+	0.891140i	$0.350094\pi$
$828$	68.3653	+	104.687i	0.0825668	+	0.126433i
$829$	766.089			0.924113			0.462056	−	0.886851i	$-0.347112\pi$
$829$	766.089			0.924113			0.462056	+	0.886851i	$0.347112\pi$
$830$	212.498	−	63.2404i	0.256022	−	0.0761933i
$831$		−	199.972i		−	0.240640i
$832$	384.328	−	737.913i	0.461933	−	0.886915i
$833$	284.222			0.341203
$834$	121.219	+	407.315i	0.145346	+	0.488388i
$835$		−	1156.11i		−	1.38457i
$836$	1157.68	−	756.021i	1.38479	−	0.904332i
$837$		−	257.901i		−	0.308126i
$838$	−1354.87	+	403.215i	−1.61679	+	0.481163i
$839$	−180.988			−0.215719			−0.107859	−	0.994166i	$-0.534400\pi$
$839$	−180.988			−0.215719			−0.107859	+	0.994166i	$0.534400\pi$
$840$	−646.984	−	548.301i	−0.770219	−	0.652739i
$841$	543.067			0.645739
$842$	−347.580	+	103.441i	−0.412803	+	0.122852i
$843$	−628.000			−0.744959
$844$	−644.285	−	986.581i	−0.763371	−	1.16894i
$845$	1266.34	−	365.448i	1.49862	−	0.432483i
$846$	18.3995	+	61.8254i	0.0217488	+	0.0730796i
$847$	−413.218			−0.487860
$848$	−373.086	+	849.629i	−0.439960	+	1.00192i
$849$	−414.106			−0.487757
$850$	−461.430	−	1550.48i	−0.542859	−	1.82410i
$851$	402.790			0.473313
$852$	214.103	+	327.853i	0.251295	+	0.384804i
$853$		−	984.643i		−	1.15433i	−0.816628	−	0.577165i	$-0.804159\pi$
$853$		−	984.643i		−	1.15433i	0.816628	−	0.577165i	$-0.195841\pi$
$854$	246.263	+	827.486i	0.288364	+	0.968953i
$855$			613.724i			0.717805i
$856$	−275.967	+	325.635i	−0.322391	+	0.380415i
$857$	−1513.36			−1.76588			−0.882939	−	0.469488i	$-0.844439\pi$
$857$	−1513.36			−1.76588			−0.882939	+	0.469488i	$0.844439\pi$
$858$	556.299	+	206.643i	0.648367	+	0.240843i
$859$			107.816i			0.125513i	0.998029	+	0.0627564i	$0.0199891\pi$
$859$			107.816i			0.125513i	−0.998029	+	0.0627564i	$0.980011\pi$
$860$	1759.37	−	1148.95i	2.04578	−	1.33599i
$861$	156.070			0.181266
$862$	−245.756	−	825.780i	−0.285099	−	0.957981i
$863$	642.697			0.744725			0.372362	−	0.928087i	$-0.378548\pi$
$863$	642.697			0.744725			0.372362	+	0.928087i	$0.378548\pi$
$864$	−20.6496	+	164.990i	−0.0239000	+	0.190960i
$865$		−	183.981i		−	0.212695i
$866$	7.02685	+	23.6114i	0.00811414	+	0.0272649i
$867$		−	382.458i		−	0.441128i
$868$	−1304.51	+	851.908i	−1.50289	+	0.981461i
$869$			754.062i			0.867735i
$870$	−286.691	−	963.329i	−0.329530	−	1.10727i
$871$	−381.158	−	286.715i	−0.437610	−	0.329180i
$872$	263.695	−	311.155i	0.302402	−	0.356829i
$873$		−	92.6439i		−	0.106121i
$874$	−523.916	+	155.920i	−0.599446	+	0.178398i
$875$		−	662.402i		−	0.757031i
$876$	−216.743	+	141.544i	−0.247424	+	0.161579i
$877$		−	235.180i		−	0.268164i	−0.990970	−	0.134082i	$-0.957191\pi$
$877$		−	235.180i		−	0.268164i	0.990970	−	0.134082i	$-0.0428085\pi$
$878$	−956.977	+	284.800i	−1.08995	+	0.324374i
$879$	−762.013			−0.866909
$880$	1505.59	+	661.131i	1.71090	+	0.751286i
$881$	370.037			0.420019			0.210010	−	0.977699i	$-0.432650\pi$
$881$	370.037			0.420019			0.210010	+	0.977699i	$0.432650\pi$
$882$	−21.5434	−	72.3895i	−0.0244257	−	0.0820743i
$883$		−	1004.78i		−	1.13792i	−0.822367	−	0.568958i	$-0.807347\pi$
$883$		−	1004.78i		−	1.13792i	0.822367	−	0.568958i	$-0.192653\pi$
$884$	1171.52	+	77.9114i	1.32525	+	0.0881351i
$885$	−216.175			−0.244266
$886$	799.899	−	238.053i	0.902820	−	0.268683i
$887$			301.209i			0.339582i	0.985480	+	0.169791i	$0.0543093\pi$
$887$			301.209i			0.339582i	−0.985480	+	0.169791i	$0.945691\pi$
$888$	408.649	+	346.318i	0.460190	+	0.389998i
$889$			1447.09i			1.62777i
$890$	−46.1302	−	155.005i	−0.0518316	−	0.174163i
$891$	−118.600			−0.133109
$892$	−435.809	+	284.604i	−0.488575	+	0.319063i
$893$	−282.008			−0.315798
$894$	24.1396	+	81.1132i	0.0270018	+	0.0907307i
$895$	−685.344			−0.765747
$896$	902.758	−	440.550i	1.00754	−	0.491685i
$897$	−187.487	−	141.032i	−0.209016	−	0.157226i
$898$	−556.286	+	165.553i	−0.619472	+	0.184357i
$899$	−1846.50			−2.05395
$900$	−359.923	+	235.047i	−0.399914	+	0.261163i
$901$	−1309.49			−1.45338
$902$	−290.039	+	86.3167i	−0.321551	+	0.0956948i
$903$	915.596			1.01395
$904$	202.068	+	171.247i	0.223527	+	0.189432i
$905$			1221.51i			1.34974i
$906$	−544.163	+	161.945i	−0.600622	+	0.178748i
$907$		−	446.087i		−	0.491827i	−0.969292	−	0.245914i	$-0.920912\pi$
$907$		−	446.087i		−	0.491827i	0.969292	−	0.245914i	$-0.0790879\pi$
$908$	−433.011	+	282.777i	−0.476884	+	0.311428i
$909$	−408.399			−0.449284
$910$	1491.72	+	554.114i	1.63925	+	0.608917i
$911$		−	12.3523i		−	0.0135591i	−0.999977	−	0.00677954i	$-0.997842\pi$
$911$		−	12.3523i		−	0.0135591i	0.999977	−	0.00677954i	$-0.00215801\pi$
$912$	−665.596	−	292.274i	−0.729820	−	0.320476i
$913$	−187.311			−0.205160
$914$	1076.14	−	320.265i	1.17740	−	0.350399i
$915$	743.027			0.812052
$916$	357.111	+	546.837i	0.389859	+	0.596984i
$917$			72.3707i			0.0789212i
$918$	−224.900	+	66.9311i	−0.244989	+	0.0729097i
$919$		−	1314.71i		−	1.43059i	−0.698822	−	0.715295i	$-0.746292\pi$
$919$		−	1314.71i		−	1.43059i	0.698822	−	0.715295i	$-0.253708\pi$
$920$	−495.937	−	420.292i	−0.539062	−	0.456840i
$921$			709.128i			0.769954i
$922$	730.825	−	217.497i	0.792652	−	0.235897i
$923$	−587.164	−	441.678i	−0.636148	−	0.478524i
$924$	391.764	+	599.900i	0.423986	+	0.649243i
$925$			1384.83i			1.49712i
$926$	13.8247	+	46.4534i	0.0149295	+	0.0501657i
$927$			374.215i			0.403684i
$928$	1181.28	+	147.845i	1.27293	+	0.159316i
$929$		−	1683.34i		−	1.81199i	−0.423292	−	0.905993i	$-0.639126\pi$
$929$		−	1683.34i		−	1.81199i	0.423292	−	0.905993i	$-0.360874\pi$
$930$	382.478	+	1285.19i	0.411267	+	1.38193i
$931$	330.195			0.354667
$932$	−1403.52	+	916.568i	−1.50593	+	0.983442i
$933$	517.291			0.554438
$934$	1558.48	−	463.809i	1.66860	−	0.496584i
$935$			2320.50i			2.48181i
$936$	−68.9553	−	304.285i	−0.0736702	−	0.325090i
$937$	−652.570			−0.696447			−0.348223	−	0.937412i	$-0.613215\pi$
$937$	−652.570			−0.696447			−0.348223	+	0.937412i	$0.613215\pi$
$938$	−164.257	−	551.931i	−0.175114	−	0.588413i
$939$		−	35.3151i		−	0.0376093i
$940$	−183.379	−	280.805i	−0.195084	−	0.298729i
$941$		−	857.642i		−	0.911416i	−0.890129	−	0.455708i	$-0.849386\pi$
$941$		−	857.642i		−	0.911416i	0.890129	−	0.455708i	$-0.150614\pi$
$942$	492.119	−	146.457i	0.522419	−	0.155474i
$943$	119.633			0.126865
$944$	102.950	−	234.447i	0.109057	−	0.248355i
$945$	−318.026			−0.336536
$946$	−1701.53	+	506.383i	−1.79866	+	0.535289i
$947$	1477.66			1.56036			0.780181	−	0.625554i	$-0.215127\pi$
$947$	1477.66			1.56036			0.780181	+	0.625554i	$0.215127\pi$
$948$	331.936	−	216.770i	0.350143	−	0.228660i
$949$	291.993	−	388.174i	0.307685	−	0.409034i
$950$	−536.067	−	1801.28i	−0.564281	−	1.89608i
$951$	−890.877			−0.936780
$952$	1081.45	+	916.494i	1.13597	+	0.962704i
$953$	589.275			0.618337			0.309169	−	0.951007i	$-0.399949\pi$
$953$	589.275			0.618337			0.309169	+	0.951007i	$0.399949\pi$
$954$	99.2567	+	333.519i	0.104043	+	0.349601i
$955$	−2854.03			−2.98851
$956$	38.8282	−	25.3567i	0.0406153	−	0.0265237i
$957$			849.144i			0.887298i
$958$	−6.12688	−	20.5874i	−0.00639549	−	0.0214899i
$959$		−	197.014i		−	0.205437i
$960$	−141.784	−	852.812i	−0.147692	−	0.888346i
$961$	1502.45			1.56342
$962$	−942.199	−	349.990i	−0.979417	−	0.363815i
$963$			160.067i			0.166217i
$964$	−400.537	−	613.334i	−0.415494	−	0.636239i
$965$	223.211			0.231307
$966$	−80.7961	−	271.489i	−0.0836399	−	0.281044i
$967$	834.227			0.862696			0.431348	−	0.902186i	$-0.358038\pi$
$967$	834.227			0.862696			0.431348	+	0.902186i	$0.358038\pi$
$968$	−321.354	−	272.338i	−0.331977	−	0.281341i
$969$		−	1025.85i		−	1.05867i
$970$	137.395	+	461.669i	0.141644	+	0.475948i
$971$		−	489.291i		−	0.503905i	−0.967740	−	0.251952i	$-0.918927\pi$
$971$		−	489.291i		−	0.503905i	0.967740	−	0.251952i	$-0.0810726\pi$
$972$	34.0939	+	52.2073i	0.0350760	+	0.0537113i
$973$		−	962.754i		−	0.989470i
$974$	320.337	+	1076.38i	0.328888	+	1.10512i
$975$	484.882	−	644.600i	0.497315	−	0.661129i
$976$	−353.853	+	805.829i	−0.362554	+	0.825644i
$977$			665.403i			0.681068i	0.940232	+	0.340534i	$0.110608\pi$
$977$			665.403i			0.681068i	−0.940232	+	0.340534i	$0.889392\pi$
$978$	223.857	−	66.6208i	0.228893	−	0.0681194i
$979$			136.632i			0.139563i
$980$	214.713	+	328.787i	0.219095	+	0.335496i
$981$		−	152.949i		−	0.155911i
$982$	−1099.35	+	327.171i	−1.11950	+	0.333168i
$983$	−1117.01			−1.13633			−0.568164	−	0.822915i	$-0.692346\pi$
$983$	−1117.01			−1.13633			−0.568164	+	0.822915i	$0.692346\pi$
$984$	121.374	+	102.861i	0.123347	+	0.104533i
$985$	2434.14			2.47121
$986$	479.209	+	1610.22i	0.486013	+	1.63309i
$987$		−	146.134i		−	0.148059i
$988$	1361.02	+	90.5137i	1.37755	+	0.0916131i
$989$	701.838			0.709644
$990$	591.016	−	175.889i	0.596986	−	0.177665i
$991$			1643.98i			1.65891i	0.558575	+	0.829454i	$0.311348\pi$
$991$			1643.98i			1.65891i	−0.558575	+	0.829454i	$0.688652\pi$
$992$	−1575.97	−	197.243i	−1.58867	−	0.198833i
$993$		−	791.058i		−	0.796635i
$994$	−253.034	−	850.236i	−0.254561	−	0.855368i
$995$	1210.12			1.21621
$996$	53.8461	+	82.4535i	0.0540623	+	0.0827847i
$997$	−1794.73			−1.80013			−0.900066	−	0.435754i	$-0.856482\pi$
$997$	−1794.73			−1.80013			−0.900066	+	0.435754i	$0.856482\pi$
$998$	−399.819	−	1343.46i	−0.400621	−	1.34615i
$999$	200.872			0.201073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.e.c.103.16	yes	24
3.2	odd	2		468.3.e.m.415.9		24
4.3	odd	2	inner	156.3.e.c.103.10	yes	24
12.11	even	2		468.3.e.m.415.15		24
13.12	even	2	inner	156.3.e.c.103.9	✓	24
39.38	odd	2		468.3.e.m.415.16		24
52.51	odd	2	inner	156.3.e.c.103.15	yes	24
156.155	even	2		468.3.e.m.415.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.e.c.103.9	✓	24	13.12	even	2	inner
156.3.e.c.103.10	yes	24	4.3	odd	2	inner
156.3.e.c.103.15	yes	24	52.51	odd	2	inner
156.3.e.c.103.16	yes	24	1.1	even	1	trivial
468.3.e.m.415.9		24	3.2	odd	2
468.3.e.m.415.10		24	156.155	even	2
468.3.e.m.415.15		24	12.11	even	2
468.3.e.m.415.16		24	39.38	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.570481 + 1.91691i) q^{2} -1.73205i q^{3} +(-3.34910 + 2.18712i) q^{4} -7.79890i q^{5} +(3.32019 - 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 - 5.17222i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.570481 + 1.91691i) q^{2} -1.73205i q^{3} +(-3.34910 + 2.18712i) q^{4} -7.79890i q^{5} +(3.32019 - 0.988102i) q^{6} -7.84779 q^{7} +(-6.10312 - 5.17222i) q^{8} -3.00000 q^{9} +(14.9498 - 4.44912i) q^{10} -13.1778 q^{11} +(3.78821 + 5.80082i) q^{12} +(-10.3889 - 7.81476i) q^{13} +(-4.47702 - 15.0435i) q^{14} -13.5081 q^{15} +(6.43298 - 14.6498i) q^{16} +22.5790 q^{17} +(-1.71144 - 5.75074i) q^{18} +26.2312 q^{19} +(17.0572 + 26.1193i) q^{20} +13.5928i q^{21} +(-7.51768 - 25.2607i) q^{22} +10.4194i q^{23} +(-8.95855 + 10.5709i) q^{24} -35.8228 q^{25} +(9.05354 - 24.3728i) q^{26} +5.19615i q^{27} +(26.2831 - 17.1641i) q^{28} +37.2030 q^{29} +(-7.70611 - 25.8938i) q^{30} -49.6331 q^{31} +(31.7523 + 3.97401i) q^{32} +22.8246i q^{33} +(12.8809 + 43.2820i) q^{34} +61.2042i q^{35} +(10.0473 - 6.56137i) q^{36} -38.6578i q^{37} +(14.9644 + 50.2829i) q^{38} +(-13.5356 + 17.9941i) q^{39} +(-40.3376 + 47.5976i) q^{40} -11.4818i q^{41} +(-26.0562 + 7.75442i) q^{42} -67.3590i q^{43} +(44.1337 - 28.8214i) q^{44} +23.3967i q^{45} +(-19.9730 + 5.94405i) q^{46} -10.7509 q^{47} +(-25.3742 - 11.1422i) q^{48} +12.5879 q^{49} +(-20.4362 - 68.6692i) q^{50} -39.1080i q^{51} +(51.8854 + 3.45061i) q^{52} -57.9959 q^{53} +(-9.96057 + 2.96431i) q^{54} +102.772i q^{55} +(47.8961 + 40.5905i) q^{56} -45.4338i q^{57} +(21.2236 + 71.3150i) q^{58} +16.0034 q^{59} +(45.2400 - 29.5439i) q^{60} -55.0061 q^{61} +(-28.3148 - 95.1423i) q^{62} +23.5434 q^{63} +(10.4962 + 63.1334i) q^{64} +(-60.9466 + 81.0221i) q^{65} +(-43.7527 + 13.0210i) q^{66} +36.6889 q^{67} +(-75.6194 + 49.3831i) q^{68} +18.0469 q^{69} +(-117.323 + 34.9158i) q^{70} +56.5184 q^{71} +(18.3094 + 15.5167i) q^{72} +37.3642i q^{73} +(74.1036 - 22.0535i) q^{74} +62.0470i q^{75} +(-87.8510 + 57.3709i) q^{76} +103.417 q^{77} +(-42.2149 - 15.6812i) q^{78} -57.2222i q^{79} +(-114.252 - 50.1701i) q^{80} +9.00000 q^{81} +(22.0097 - 6.55017i) q^{82} +14.2141 q^{83} +(-29.7291 - 45.5236i) q^{84} -176.091i q^{85} +(129.121 - 38.4270i) q^{86} -64.4376i q^{87} +(80.4256 + 68.1584i) q^{88} -10.3684i q^{89} +(-44.8494 + 13.3474i) q^{90} +(81.5300 + 61.3287i) q^{91} +(-22.7884 - 34.8955i) q^{92} +85.9671i q^{93} +(-6.13316 - 20.6085i) q^{94} -204.575i q^{95} +(6.88320 - 54.9966i) q^{96} +30.8813i q^{97} +(7.18114 + 24.1298i) q^{98} +39.5334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 72 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 - 72 * q^9	\( 24 q + 8 q^{4} - 72 q^{9} + 28 q^{10} + 36 q^{12} + 48 q^{13} - 40 q^{14} + 100 q^{16} + 32 q^{17} + 84 q^{22} - 312 q^{25} - 16 q^{26} - 80 q^{29} + 60 q^{30} - 24 q^{36} + 120 q^{38} - 204 q^{40} - 96 q^{42} - 144 q^{48} + 392 q^{49} + 28 q^{52} - 224 q^{53} + 800 q^{56} - 96 q^{61} - 352 q^{62} - 184 q^{64} - 112 q^{65} + 252 q^{66} - 344 q^{68} + 144 q^{69} + 232 q^{74} - 16 q^{77} - 168 q^{78} + 216 q^{81} + 20 q^{82} - 92 q^{88} - 84 q^{90} - 616 q^{92} - 684 q^{94}+O(q^{100}) \) 24 * q + 8 * q^4 - 72 * q^9 + 28 * q^10 + 36 * q^12 + 48 * q^13 - 40 * q^14 + 100 * q^16 + 32 * q^17 + 84 * q^22 - 312 * q^25 - 16 * q^26 - 80 * q^29 + 60 * q^30 - 24 * q^36 + 120 * q^38 - 204 * q^40 - 96 * q^42 - 144 * q^48 + 392 * q^49 + 28 * q^52 - 224 * q^53 + 800 * q^56 - 96 * q^61 - 352 * q^62 - 184 * q^64 - 112 * q^65 + 252 * q^66 - 344 * q^68 + 144 * q^69 + 232 * q^74 - 16 * q^77 - 168 * q^78 + 216 * q^81 + 20 * q^82 - 92 * q^88 - 84 * q^90 - 616 * q^92 - 684 * q^94

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