LMFDB - Embedded newform 156.3.e.c.103.10

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			103.10
Character	$\chi$	$=$	156.103
Dual form			156.3.e.c.103.9

$q$-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} +(20.9069 - 15.4565i) 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} +(17.7017 + 48.8943i) 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} +(26.7714 + 36.2118i) 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	$-0.310587\pi$
$7$	7.84779			1.12111			0.560557	+	0.828116i	$0.310587\pi$
$8$	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	$-0.295569\pi$
$11$	13.1778			1.19798			0.598990	+	0.800756i	$0.295569\pi$
$12$	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	$-0.742519\pi$
$19$	−26.2312			−1.38059			−0.690295	+	0.723528i	$0.742519\pi$
$20$	−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	$-0.927269\pi$
$23$		−	10.4194i		−	0.453016i	0.974009	−	0.226508i	$-0.0727309\pi$
$24$	8.95855	+	10.5709i	0.373273	+	0.440455i
$25$	−35.8228			−1.43291
$26$	20.9069	−	15.4565i	0.804111	−	0.594479i
$27$		−	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	$-0.204549\pi$
$31$	49.6331			1.60107			0.800534	+	0.599287i	$0.204549\pi$
$32$	−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	$0.286436\pi$
$43$			67.3590i			1.56649i	−0.621714	+	0.783244i	$0.713564\pi$
$44$	−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	$-0.463515\pi$
$47$	10.7509			0.228742			0.114371	+	0.993438i	$0.463515\pi$
$48$	−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
$52$	17.7017	+	48.8943i	0.340417	+	0.940275i
$53$	−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	$-0.543303\pi$
$59$	−16.0034			−0.271244			−0.135622	+	0.990761i	$0.543303\pi$
$60$	−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	$-0.588280\pi$
$67$	−36.6889			−0.547596			−0.273798	+	0.961787i	$0.588280\pi$
$68$	−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	$-0.630301\pi$
$71$	−56.5184			−0.796033			−0.398017	+	0.917378i	$0.630301\pi$
$72$	−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
$78$	26.7714	+	36.2118i	0.343223	+	0.464254i
$79$			57.2222i			0.724332i	0.932114	+	0.362166i	$0.117963\pi$
$79$			57.2222i			0.724332i	−0.932114	+	0.362166i	$0.882037\pi$
$80$	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	$-0.527289\pi$
$83$	−14.2141			−0.171255			−0.0856273	+	0.996327i	$0.527289\pi$
$84$	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	$0.207037\pi$
$103$			124.738i			1.21105i	−0.795825	+	0.605526i	$0.792963\pi$
$104$	−103.825	+	6.03928i	−0.998313	+	0.0580700i
$105$	106.009			1.00961
$106$	33.0856	−	111.173i	0.312128	−	1.04880i
$107$			53.3555i			0.498650i	0.968420	+	0.249325i	$0.0802087\pi$
$107$			53.3555i			0.498650i	−0.968420	+	0.249325i	$0.919791\pi$
$108$	−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	$0.258606\pi$
$127$			184.395i			1.45193i	−0.687733	+	0.725963i	$0.741394\pi$
$128$	115.033	+	56.1368i	0.898698	+	0.438569i
$129$	−116.669			−0.904412
$130$	−120.543	−	163.051i	−0.927256	−	1.25424i
$131$			9.22179i			0.0703953i	0.999380	+	0.0351977i	$0.0112061\pi$
$131$			9.22179i			0.0703953i	−0.999380	+	0.0351977i	$0.988794\pi$
$132$	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	$-0.854521\pi$
$139$		−	122.678i		−	0.882578i	0.897365	−	0.441289i	$-0.145479\pi$
$140$	−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	$-0.317402\pi$
$151$	163.895			1.08540			0.542700	+	0.839927i	$0.317402\pi$
$152$	−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
$156$	−84.6874	+	30.6602i	−0.542868	+	0.196540i
$157$	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	$-0.566311\pi$
$163$	−67.4230			−0.413638			−0.206819	+	0.978379i	$0.566311\pi$
$164$	−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	$-0.646382\pi$
$167$	−148.240			−0.887668			−0.443834	+	0.896109i	$0.646382\pi$
$168$	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	$0.0789411\pi$
$179$			87.8770i			0.490933i	−0.969405	+	0.245466i	$0.921059\pi$
$180$	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	$0.642428\pi$
$182$	164.073	−	121.299i	0.901500	−	0.666478i
$183$		−	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	$0.407409\pi$
$191$			365.952i			1.91598i	−0.286800	+	0.957990i	$0.592591\pi$
$192$	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	$-0.872522\pi$
$199$		−	155.166i		−	0.779729i	0.920872	−	0.389865i	$-0.127478\pi$
$200$	−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
$208$	47.6531	−	202.468i	0.229102	−	0.973403i
$209$	−345.669			−1.65392
$210$	−60.4760	+	203.209i	−0.287981	+	0.967664i
$211$		−	294.581i		−	1.39612i	−0.716040	−	0.698059i	$-0.754047\pi$
$211$		−	294.581i		−	1.39612i	0.716040	−	0.698059i	$-0.245953\pi$
$212$	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	$-0.594242\pi$
$223$	−130.127			−0.583529			−0.291765	+	0.956490i	$0.594242\pi$
$224$	−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	$-0.591922\pi$
$227$	−129.292			−0.569567			−0.284783	+	0.958592i	$0.591922\pi$
$228$	−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	$0.144076\pi$
$234$	−62.7207	+	46.3694i	−0.268037	+	0.198160i
$235$		−	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	$-0.492279\pi$
$239$	11.5936			0.0485089			0.0242545	+	0.999706i	$0.492279\pi$
$240$	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	$-0.874451\pi$
$251$		−	192.907i		−	0.768555i	0.923218	−	0.384278i	$-0.125549\pi$
$252$	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
$260$	381.322	−	138.054i	1.46662	−	0.530975i
$261$	−111.609			−0.427621
$262$	−17.6774	−	5.26086i	−0.0674708	−	0.0200796i
$263$		−	38.1415i		−	0.145025i	−0.997368	−	0.0725124i	$-0.976898\pi$
$263$		−	38.1415i		−	0.145025i	0.997368	−	0.0725124i	$-0.0231017\pi$
$264$	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	$-0.353208\pi$
$271$	241.183			0.889975			0.444987	+	0.895537i	$0.353208\pi$
$272$	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	$0.138816\pi$
$283$			239.084i			0.844820i	−0.906405	+	0.422410i	$0.861184\pi$
$284$	189.286	+	123.613i	0.666499	+	0.435256i
$285$	−354.333			−1.24328
$286$	275.506	−	203.682i	0.963309	−	0.712174i
$287$		−	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	$-0.267664\pi$
$307$	409.415			1.33360			0.666800	+	0.745237i	$0.267664\pi$
$308$	−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	$-0.840580\pi$
$311$		−	298.658i		−	0.960315i	0.877182	−	0.480157i	$-0.159420\pi$
$312$	−10.4603	−	179.829i	−0.0335267	−	0.576376i
$313$	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	$-0.742348\pi$
$331$	−456.718			−1.37981			−0.689906	+	0.723899i	$0.742348\pi$
$332$	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	$0.847041\pi$
$338$	−337.988	−	2.80672i	−0.999966	−	0.00830391i
$339$		−	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	$0.170818\pi$
$347$			354.809i			1.02251i	−0.859430	+	0.511253i	$0.829182\pi$
$348$	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	$-0.388806\pi$
$359$	245.747			0.684533			0.342266	+	0.939603i	$0.388806\pi$
$360$	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
$364$	138.919	+	383.712i	0.381646	+	1.05415i
$365$	291.400			0.798356
$366$	182.631	+	54.3516i	0.498991	+	0.148502i
$367$			458.704i			1.24988i	0.780674	+	0.624938i	$0.214876\pi$
$367$			458.704i			1.24988i	−0.780674	+	0.624938i	$0.785124\pi$
$368$	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	$-0.715129\pi$
$379$	−474.173			−1.25112			−0.625559	+	0.780177i	$0.715129\pi$
$380$	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	$-0.600401\pi$
$383$	−237.625			−0.620431			−0.310215	+	0.950666i	$0.600401\pi$
$384$	−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	$0.461372\pi$
$390$	282.412	−	208.787i	0.724134	−	0.535352i
$391$		−	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
$416$	360.928	+	206.851i	0.867614	+	0.497238i
$417$	212.485			0.509557
$418$	197.198	−	662.617i	0.471765	−	1.58521i
$419$		−	706.798i		−	1.68687i	−0.537232	−	0.843435i	$-0.680530\pi$
$419$		−	706.798i		−	1.68687i	0.537232	−	0.843435i	$-0.319470\pi$
$420$	−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	$-0.333424\pi$
$431$	430.786			0.999505			0.499752	+	0.866168i	$0.333424\pi$
$432$	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	$-0.807486\pi$
$439$		−	499.229i		−	1.13719i	0.822616	−	0.568597i	$-0.192514\pi$
$440$	−531.561	−	627.231i	−1.20809	−	1.42553i
$441$	−37.7636			−0.0856318
$442$	472.057	−	348.992i	1.06800	−	0.789574i
$443$			417.285i			0.941953i	0.882146	+	0.470976i	$0.156098\pi$
$443$			417.285i			0.941953i	−0.882146	+	0.470976i	$0.843902\pi$
$444$	−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	$-0.508331\pi$
$463$	−24.2335			−0.0523401			−0.0261700	+	0.999658i	$0.508331\pi$
$464$	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	$0.336182\pi$
$467$			813.014i			1.74093i	−0.492230	+	0.870465i	$0.663818\pi$
$468$	−53.1050	−	146.683i	−0.113472	−	0.313425i
$469$	−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	$-0.496431\pi$
$479$	10.7399			0.0224214			0.0112107	+	0.999937i	$0.496431\pi$
$480$	−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	$-0.695586\pi$
$487$	−561.520			−1.15302			−0.576509	+	0.817091i	$0.695586\pi$
$488$	−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	$-0.801482\pi$
$491$		−	573.500i		−	1.16803i	0.811745	−	0.584013i	$-0.198518\pi$
$492$	−66.6040	−	43.4956i	−0.135374	−	0.0884057i
$493$	840.008			1.70387
$494$	−548.413	+	405.441i	−1.11015	+	0.820731i
$495$			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	$-0.252179\pi$
$499$	700.846			1.40450			0.702250	+	0.711930i	$0.252179\pi$
$500$	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	$-0.929504\pi$
$503$		−	220.983i		−	0.439330i	0.975575	−	0.219665i	$-0.0704964\pi$
$504$	−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
$520$	47.0998	+	809.717i	0.0905765	+	1.55715i
$521$	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	$0.114398\pi$
$523$			367.884i			0.703411i	−0.936111	+	0.351706i	$0.885602\pi$
$524$	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
$546$	210.096	+	284.183i	0.384791	+	0.520481i
$547$			230.496i			0.421382i	0.977553	+	0.210691i	$0.0675714\pi$
$547$			230.496i			0.421382i	−0.977553	+	0.210691i	$0.932429\pi$
$548$	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	$0.00310011\pi$
$563$			10.9662i			0.0194782i	−0.999953	+	0.00973912i	$0.996900\pi$
$564$	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	$0.380144\pi$
$571$			1062.00i			1.85989i	−0.367703	+	0.929943i	$0.619856\pi$
$572$	233.269	+	644.318i	0.407813	+	1.12643i
$573$	−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	$-0.517523\pi$
$587$	−64.5958			−0.110044			−0.0550220	+	0.998485i	$0.517523\pi$
$588$	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
$598$	−161.046	−	217.836i	−0.269308	−	0.364275i
$599$		−	469.062i		−	0.783074i	−0.920162	−	0.391537i	$-0.871943\pi$
$599$		−	469.062i		−	0.783074i	0.920162	−	0.391537i	$-0.128057\pi$
$600$	−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	$-0.854972\pi$
$607$		−	534.181i		−	0.880035i	0.897989	−	0.440017i	$-0.145028\pi$
$608$	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	$-0.327888\pi$
$619$	637.250			1.02948			0.514741	+	0.857346i	$0.327888\pi$
$620$	−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
$624$	350.684	+	82.5377i	0.561994	+	0.132272i
$625$	−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	$-0.613373\pi$
$631$	−440.047			−0.697380			−0.348690	+	0.937238i	$0.613373\pi$
$632$	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	$-0.467679\pi$
$643$	130.355			0.202729			0.101365	+	0.994849i	$0.467679\pi$
$644$	−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	$0.106157\pi$
$647$			423.596i			0.654709i	−0.944902	+	0.327354i	$0.893843\pi$
$648$	54.9281	−	46.5500i	0.0847656	−	0.0718364i
$649$	−210.889			−0.324945
$650$	−748.944	+	553.694i	−1.15222	+	0.851837i
$651$			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	$-0.852056\pi$
$659$		−	590.762i		−	0.896452i	0.893920	−	0.448226i	$-0.147944\pi$
$660$	−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
$676$	198.196	−	646.293i	0.293190	−	0.956054i
$677$	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	$-0.761514\pi$
$683$	−1000.21			−1.46443			−0.732217	+	0.681072i	$0.761514\pi$
$684$	−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	$-0.527680\pi$
$691$	−120.026			−0.173699			−0.0868496	+	0.996221i	$0.527680\pi$
$692$	−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	$0.283402\pi$
$702$	−80.3141	−	108.635i	−0.114408	−	0.154751i
$703$			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	$-0.759920\pi$
$719$		−	984.643i		−	1.36946i	0.728796	−	0.684731i	$-0.240080\pi$
$720$	−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	$-0.872656\pi$
$727$		−	566.297i		−	0.778950i	0.921037	−	0.389475i	$-0.127344\pi$
$728$	−814.793	+	47.3950i	−1.11922	+	0.0651031i
$729$	−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	$-0.609957\pi$
$739$	−500.468			−0.677223			−0.338611	+	0.940926i	$0.609957\pi$
$740$	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	$-0.575474\pi$
$743$	−349.050			−0.469784			−0.234892	+	0.972021i	$0.575474\pi$
$744$	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	$0.00540507\pi$
$751$			25.5035i			0.0339594i	−0.999856	+	0.0169797i	$0.994595\pi$
$752$	69.1601	+	157.498i	0.0919682	+	0.209439i
$753$	334.125			0.443725
$754$	777.800	−	575.027i	1.03157	−	0.762635i
$755$		−	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
$780$	239.116	+	660.468i	0.306559	+	0.846754i
$781$	−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	$-0.655883\pi$
$787$	−740.379			−0.940761			−0.470381	+	0.882464i	$0.655883\pi$
$788$	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
$806$	1037.67	−	767.152i	1.28744	−	0.951802i
$807$		−	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	$-0.326935\pi$
$811$	839.069			1.03461			0.517305	+	0.855801i	$0.326935\pi$
$812$	−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	$-0.747778\pi$
$823$		−	1171.99i		−	1.42405i	0.702154	−	0.712025i	$-0.252222\pi$
$824$	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	$-0.649906\pi$
$827$	−750.467			−0.907457			−0.453729	+	0.891140i	$0.649906\pi$
$828$	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
$832$	−602.417	+	573.862i	−0.724059	+	0.689738i
$833$	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	$-0.465600\pi$
$839$	180.988			0.215719			0.107859	+	0.994166i	$0.465600\pi$
$840$	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	$0.844439\pi$
$858$	352.787	+	477.191i	0.411174	+	0.556167i
$859$		−	107.816i		−	0.125513i	−0.998029	−	0.0627564i	$-0.980011\pi$
$859$		−	107.816i		−	0.125513i	0.998029	−	0.0627564i	$-0.0199891\pi$
$860$	−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	$-0.621452\pi$
$863$	−642.697			−0.744725			−0.372362	+	0.928087i	$0.621452\pi$
$864$	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	$0.192653\pi$
$883$			1004.78i			1.13792i	−0.822367	+	0.568958i	$0.807347\pi$
$884$	399.686	+	1103.98i	0.452134	+	1.24885i
$885$	−216.175			−0.244266
$886$	−799.899	−	238.053i	−0.902820	−	0.268683i
$887$		−	301.209i		−	0.339582i	−0.985480	−	0.169791i	$-0.945691\pi$
$887$		−	301.209i		−	0.339582i	0.985480	−	0.169791i	$-0.0543093\pi$
$888$	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	$0.0790879\pi$
$907$			446.087i			0.491827i	−0.969292	+	0.245914i	$0.920912\pi$
$908$	433.011	+	282.777i	0.476884	+	0.311428i
$909$	−408.399			−0.449284
$910$	−945.999	−	1279.59i	−1.03956	−	1.40614i
$911$			12.3523i			0.0135591i	0.999977	+	0.00677954i	$0.00215801\pi$
$911$			12.3523i			0.0135591i	−0.999977	+	0.00677954i	$0.997842\pi$
$912$	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	$0.253708\pi$
$919$			1314.71i			1.43059i	−0.698822	+	0.715295i	$0.746292\pi$
$920$	−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
$936$	311.474	−	18.1178i	0.332771	−	0.0193567i
$937$	−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	$-0.784873\pi$
$947$	−1477.66			−1.56036			−0.780181	+	0.625554i	$0.784873\pi$
$948$	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
$962$	−597.512	−	808.215i	−0.621115	−	0.840140i
$963$		−	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	$-0.641962\pi$
$967$	−834.227			−0.862696			−0.431348	+	0.902186i	$0.641962\pi$
$968$	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	$0.0810726\pi$
$971$			489.291i			0.503905i	−0.967740	+	0.251952i	$0.918927\pi$
$972$	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	$-0.307654\pi$
$983$	1117.01			1.13633			0.568164	+	0.822915i	$0.307654\pi$
$984$	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
$988$	−464.336	−	1282.56i	−0.469976	−	1.29813i
$989$	701.838			0.709644
$990$	−591.016	−	175.889i	−0.596986	−	0.177665i
$991$		−	1643.98i		−	1.65891i	−0.558575	−	0.829454i	$-0.688652\pi$
$991$		−	1643.98i		−	1.65891i	0.558575	−	0.829454i	$-0.311348\pi$
$992$	−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.103.10	yes	24
3.2	odd	2		468.3.e.m.415.15		24
4.3	odd	2	inner	156.3.e.c.103.16	yes	24
12.11	even	2		468.3.e.m.415.9		24
13.12	even	2	inner	156.3.e.c.103.15	yes	24
39.38	odd	2		468.3.e.m.415.10		24
52.51	odd	2	inner	156.3.e.c.103.9	✓	24
156.155	even	2		468.3.e.m.415.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.e.c.103.9	✓	24	52.51	odd	2	inner
156.3.e.c.103.10	yes	24	1.1	even	1	trivial
156.3.e.c.103.15	yes	24	13.12	even	2	inner
156.3.e.c.103.16	yes	24	4.3	odd	2	inner
468.3.e.m.415.9		24	12.11	even	2
468.3.e.m.415.10		24	39.38	odd	2
468.3.e.m.415.15		24	3.2	odd	2
468.3.e.m.415.16		24	156.155	even	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} +(20.9069 - 15.4565i) 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} +(17.7017 + 48.8943i) 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} +(26.7714 + 36.2118i) 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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