LMFDB - Embedded newform 276.3.f.b.139.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,3,Mod(139,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	276.f (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:	$7.52045529634$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.34
Character	$\chi$	$=$	276.139
Dual form			276.3.f.b.139.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66998 + 1.10052i) q^{2} -1.73205i q^{3} +(1.57770 + 3.67571i) q^{4} -4.68367 q^{5} +(1.90616 - 2.89250i) q^{6} +5.31567i q^{7} +(-1.41048 + 7.87468i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.66998 + 1.10052i) q^{2} -1.73205i q^{3} +(1.57770 + 3.67571i) q^{4} -4.68367 q^{5} +(1.90616 - 2.89250i) q^{6} +5.31567i q^{7} +(-1.41048 + 7.87468i) q^{8} -3.00000 q^{9} +(-7.82165 - 5.15448i) q^{10} +18.3860i q^{11} +(6.36652 - 2.73265i) q^{12} -5.17088 q^{13} +(-5.85002 + 8.87709i) q^{14} +8.11235i q^{15} +(-11.0217 + 11.5983i) q^{16} +26.4710 q^{17} +(-5.00995 - 3.30157i) q^{18} +3.79310i q^{19} +(-7.38941 - 17.2158i) q^{20} +9.20701 q^{21} +(-20.2343 + 30.7044i) q^{22} +4.79583i q^{23} +(13.6393 + 2.44302i) q^{24} -3.06327 q^{25} +(-8.63530 - 5.69068i) q^{26} +5.19615i q^{27} +(-19.5389 + 8.38652i) q^{28} +10.6479 q^{29} +(-8.92783 + 13.5475i) q^{30} -17.0983i q^{31} +(-31.1704 + 7.23936i) q^{32} +31.8456 q^{33} +(44.2061 + 29.1319i) q^{34} -24.8968i q^{35} +(-4.73309 - 11.0271i) q^{36} -33.2036 q^{37} +(-4.17440 + 6.33442i) q^{38} +8.95623i q^{39} +(6.60620 - 36.8824i) q^{40} +17.0709 q^{41} +(15.3756 + 10.1325i) q^{42} -67.4953i q^{43} +(-67.5818 + 29.0076i) q^{44} +14.0510 q^{45} +(-5.27792 + 8.00897i) q^{46} +19.2878i q^{47} +(20.0889 + 19.0902i) q^{48} +20.7436 q^{49} +(-5.11561 - 3.37119i) q^{50} -45.8491i q^{51} +(-8.15809 - 19.0067i) q^{52} +8.27647 q^{53} +(-5.71849 + 8.67750i) q^{54} -86.1141i q^{55} +(-41.8592 - 7.49762i) q^{56} +6.56985 q^{57} +(17.7819 + 11.7183i) q^{58} +71.6785i q^{59} +(-29.8187 + 12.7988i) q^{60} +66.2939 q^{61} +(18.8171 - 28.5539i) q^{62} -15.9470i q^{63} +(-60.0211 - 22.2141i) q^{64} +24.2187 q^{65} +(53.1816 + 35.0468i) q^{66} +25.1268i q^{67} +(41.7632 + 97.2998i) q^{68} +8.30662 q^{69} +(27.3995 - 41.5773i) q^{70} -113.322i q^{71} +(4.23143 - 23.6240i) q^{72} -67.2871 q^{73} +(-55.4495 - 36.5414i) q^{74} +5.30573i q^{75} +(-13.9424 + 5.98437i) q^{76} -97.7341 q^{77} +(-9.85654 + 14.9568i) q^{78} +11.2664i q^{79} +(51.6221 - 54.3227i) q^{80} +9.00000 q^{81} +(28.5082 + 18.7869i) q^{82} +72.0466i q^{83} +(14.5259 + 33.8423i) q^{84} -123.981 q^{85} +(74.2802 - 112.716i) q^{86} -18.4428i q^{87} +(-144.784 - 25.9331i) q^{88} +143.041 q^{89} +(23.4650 + 15.4634i) q^{90} -27.4867i q^{91} +(-17.6281 + 7.56637i) q^{92} -29.6152 q^{93} +(-21.2267 + 32.2103i) q^{94} -17.7656i q^{95} +(12.5389 + 53.9887i) q^{96} +121.656 q^{97} +(34.6416 + 22.8289i) q^{98} -55.1581i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.66998	+	1.10052i	0.834992	+	0.550262i
$2$	1.66998	+	1.10052i	0.834992	+	0.550262i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.57770	+	3.67571i	0.394425	+	0.918928i
$5$	−4.68367			−0.936733			−0.468367	−	0.883534i	$-0.655157\pi$
$5$	−4.68367			−0.936733			−0.468367	+	0.883534i	$0.655157\pi$
$6$	1.90616	−	2.89250i	0.317694	−	0.482083i
$7$			5.31567i			0.759382i	0.925113	+	0.379691i	$0.123970\pi$
$7$			5.31567i			0.759382i	−0.925113	+	0.379691i	$0.876030\pi$
$8$	−1.41048	+	7.87468i	−0.176309	+	0.984335i
$9$	−3.00000			−0.333333
$10$	−7.82165	−	5.15448i	−0.782165	−	0.515448i
$11$			18.3860i			1.67146i	0.549142	+	0.835729i	$0.314955\pi$
$11$			18.3860i			1.67146i	−0.549142	+	0.835729i	$0.685045\pi$
$12$	6.36652	−	2.73265i	0.530544	−	0.227721i
$13$	−5.17088			−0.397760			−0.198880	−	0.980024i	$-0.563730\pi$
$13$	−5.17088			−0.397760			−0.198880	+	0.980024i	$0.563730\pi$
$14$	−5.85002	+	8.87709i	−0.417858	+	0.634078i
$15$			8.11235i			0.540823i
$16$	−11.0217	+	11.5983i	−0.688859	+	0.724896i
$17$	26.4710			1.55712			0.778558	−	0.627572i	$-0.215951\pi$
$17$	26.4710			1.55712			0.778558	+	0.627572i	$0.215951\pi$
$18$	−5.00995	−	3.30157i	−0.278331	−	0.183421i
$19$			3.79310i			0.199637i	0.995006	+	0.0998185i	$0.0318262\pi$
$19$			3.79310i			0.199637i	−0.995006	+	0.0998185i	$0.968174\pi$
$20$	−7.38941	−	17.2158i	−0.369471	−	0.860791i
$21$	9.20701			0.438429
$22$	−20.2343	+	30.7044i	−0.919739	+	1.39566i
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	13.6393	+	2.44302i	0.568306	+	0.101792i
$25$	−3.06327			−0.122531
$26$	−8.63530	−	5.69068i	−0.332127	−	0.218872i
$27$			5.19615i			0.192450i
$28$	−19.5389	+	8.38652i	−0.697817	+	0.299519i
$29$	10.6479			0.367170			0.183585	−	0.983004i	$-0.441230\pi$
$29$	10.6479			0.367170			0.183585	+	0.983004i	$0.441230\pi$
$30$	−8.92783	+	13.5475i	−0.297594	+	0.451583i
$31$		−	17.0983i		−	0.551559i	−0.961221	−	0.275779i	$-0.911064\pi$
$31$		−	17.0983i		−	0.551559i	0.961221	−	0.275779i	$-0.0889359\pi$
$32$	−31.1704	+	7.23936i	−0.974074	+	0.226230i
$33$	31.8456			0.965017
$34$	44.2061	+	29.1319i	1.30018	+	0.856821i
$35$		−	24.8968i		−	0.711338i
$36$	−4.73309	−	11.0271i	−0.131475	−	0.306309i
$37$	−33.2036			−0.897395			−0.448698	−	0.893684i	$-0.648112\pi$
$37$	−33.2036			−0.897395			−0.448698	+	0.893684i	$0.648112\pi$
$38$	−4.17440	+	6.33442i	−0.109853	+	0.166695i
$39$			8.95623i			0.229647i
$40$	6.60620	−	36.8824i	0.165155	−	0.922059i
$41$	17.0709			0.416364			0.208182	−	0.978090i	$-0.433245\pi$
$41$	17.0709			0.416364			0.208182	+	0.978090i	$0.433245\pi$
$42$	15.3756	+	10.1325i	0.366085	+	0.241251i
$43$		−	67.4953i		−	1.56966i	−0.619712	−	0.784829i	$-0.712751\pi$
$43$		−	67.4953i		−	1.56966i	0.619712	−	0.784829i	$-0.287249\pi$
$44$	−67.5818	+	29.0076i	−1.53595	+	0.659264i
$45$	14.0510			0.312244
$46$	−5.27792	+	8.00897i	−0.114737	+	0.174108i
$47$			19.2878i			0.410378i	0.978722	+	0.205189i	$0.0657810\pi$
$47$			19.2878i			0.410378i	−0.978722	+	0.205189i	$0.934219\pi$
$48$	20.0889	+	19.0902i	0.418519	+	0.397713i
$49$	20.7436			0.423340
$50$	−5.11561	−	3.37119i	−0.102312	−	0.0674239i
$51$		−	45.8491i		−	0.899002i
$52$	−8.15809	−	19.0067i	−0.156886	−	0.365513i
$53$	8.27647			0.156160			0.0780799	−	0.996947i	$-0.475121\pi$
$53$	8.27647			0.156160			0.0780799	+	0.996947i	$0.475121\pi$
$54$	−5.71849	+	8.67750i	−0.105898	+	0.160694i
$55$		−	86.1141i		−	1.56571i
$56$	−41.8592	−	7.49762i	−0.747486	−	0.133886i
$57$	6.56985			0.115260
$58$	17.7819	+	11.7183i	0.306584	+	0.202040i
$59$			71.6785i			1.21489i	0.794362	+	0.607445i	$0.207806\pi$
$59$			71.6785i			1.21489i	−0.794362	+	0.607445i	$0.792194\pi$
$60$	−29.8187	+	12.7988i	−0.496978	+	0.213314i
$61$	66.2939			1.08679			0.543393	−	0.839479i	$-0.317139\pi$
$61$	66.2939			1.08679			0.543393	+	0.839479i	$0.317139\pi$
$62$	18.8171	−	28.5539i	0.303502	−	0.460547i
$63$		−	15.9470i		−	0.253127i
$64$	−60.0211	−	22.2141i	−0.937830	−	0.347095i
$65$	24.2187			0.372595
$66$	53.1816	+	35.0468i	0.805782	+	0.531012i
$67$			25.1268i			0.375027i	0.982262	+	0.187514i	$0.0600429\pi$
$67$			25.1268i			0.375027i	−0.982262	+	0.187514i	$0.939957\pi$
$68$	41.7632	+	97.2998i	0.614165	+	1.43088i
$69$	8.30662			0.120386
$70$	27.3995	−	41.5773i	0.391422	−	0.593962i
$71$		−	113.322i		−	1.59608i	−0.602605	−	0.798039i	$-0.705871\pi$
$71$		−	113.322i		−	1.59608i	0.602605	−	0.798039i	$-0.294129\pi$
$72$	4.23143	−	23.6240i	0.0587698	−	0.328112i
$73$	−67.2871			−0.921741			−0.460871	−	0.887467i	$-0.652463\pi$
$73$	−67.2871			−0.921741			−0.460871	+	0.887467i	$0.652463\pi$
$74$	−55.4495	−	36.5414i	−0.749318	−	0.493802i
$75$			5.30573i			0.0707431i
$76$	−13.9424	+	5.98437i	−0.183452	+	0.0787417i
$77$	−97.7341			−1.26927
$78$	−9.85654	+	14.9568i	−0.126366	+	0.191754i
$79$			11.2664i			0.142613i	0.997454	+	0.0713065i	$0.0227169\pi$
$79$			11.2664i			0.142613i	−0.997454	+	0.0713065i	$0.977283\pi$
$80$	51.6221	−	54.3227i	0.645277	−	0.679034i
$81$	9.00000			0.111111
$82$	28.5082	+	18.7869i	0.347661	+	0.229109i
$83$			72.0466i			0.868032i	0.900905	+	0.434016i	$0.142904\pi$
$83$			72.0466i			0.868032i	−0.900905	+	0.434016i	$0.857096\pi$
$84$	14.5259	+	33.8423i	0.172927	+	0.402885i
$85$	−123.981			−1.45860
$86$	74.2802	−	112.716i	0.863723	−	1.31065i
$87$		−	18.4428i		−	0.211986i
$88$	−144.784	−	25.9331i	−1.64527	−	0.294694i
$89$	143.041			1.60720			0.803601	−	0.595169i	$-0.202915\pi$
$89$	143.041			1.60720			0.803601	+	0.595169i	$0.202915\pi$
$90$	23.4650	+	15.4634i	0.260722	+	0.171816i
$91$		−	27.4867i		−	0.302052i
$92$	−17.6281	+	7.56637i	−0.191610	+	0.0822432i
$93$	−29.6152			−0.318443
$94$	−21.2267	+	32.2103i	−0.225815	+	0.342663i
$95$		−	17.7656i		−	0.187007i
$96$	12.5389	+	53.9887i	0.130614	+	0.562382i
$97$	121.656			1.25419			0.627095	−	0.778943i	$-0.284244\pi$
$97$	121.656			1.25419			0.627095	+	0.778943i	$0.284244\pi$
$98$	34.6416	+	22.8289i	0.353485	+	0.232948i
$99$		−	55.1581i		−	0.557153i
$100$	−4.83291	−	11.2597i	−0.0483291	−	0.112597i
$101$	48.7393			0.482567			0.241284	−	0.970455i	$-0.422432\pi$
$101$	48.7393			0.482567			0.241284	+	0.970455i	$0.422432\pi$
$102$	50.4580	−	76.5673i	0.494686	−	0.750660i
$103$		−	120.309i		−	1.16805i	−0.811736	−	0.584025i	$-0.801477\pi$
$103$		−	120.309i		−	1.16805i	0.811736	−	0.584025i	$-0.198523\pi$
$104$	7.29341	−	40.7190i	0.0701289	−	0.391529i
$105$	−43.1226			−0.410691
$106$	13.8216	+	9.10845i	0.130392	+	0.0859288i
$107$			77.4458i			0.723792i	0.932218	+	0.361896i	$0.117870\pi$
$107$			77.4458i			0.723792i	−0.932218	+	0.361896i	$0.882130\pi$
$108$	−19.0996	+	8.19796i	−0.176848	+	0.0759070i
$109$	129.339			1.18659			0.593296	−	0.804984i	$-0.297826\pi$
$109$	129.339			1.18659			0.593296	+	0.804984i	$0.297826\pi$
$110$	94.7706	−	143.809i	0.861550	−	1.30736i
$111$			57.5104i			0.518111i
$112$	−61.6529	−	58.5879i	−0.550472	−	0.523106i
$113$	140.800			1.24601			0.623007	−	0.782216i	$-0.285911\pi$
$113$	140.800			1.24601			0.623007	+	0.782216i	$0.285911\pi$
$114$	10.9715	+	7.23027i	0.0962416	+	0.0634234i
$115$		−	22.4621i		−	0.195322i
$116$	16.7992	+	39.1388i	0.144821	+	0.337403i
$117$	15.5127			0.132587
$118$	−78.8839	+	119.702i	−0.668507	+	1.01442i
$119$			140.711i			1.18245i
$120$	−63.8821	−	11.4423i	−0.532351	−	0.0953523i
$121$	−217.047			−1.79377
$122$	110.710	+	72.9580i	0.907457	+	0.598016i
$123$		−	29.5677i		−	0.240388i
$124$	62.8485	−	26.9760i	0.506843	−	0.217548i
$125$	131.439			1.05151
$126$	17.5501	−	26.6313i	0.139286	−	0.211359i
$127$			121.890i			0.959762i	0.877333	+	0.479881i	$0.159320\pi$
$127$			121.890i			0.959762i	−0.877333	+	0.479881i	$0.840680\pi$
$128$	−75.7872	−	103.152i	−0.592088	−	0.805873i
$129$	−116.905			−0.906243
$130$	40.4449	+	26.6532i	0.311114	+	0.205025i
$131$			162.068i			1.23716i	0.785721	+	0.618582i	$0.212292\pi$
$131$			162.068i			1.23716i	−0.785721	+	0.618582i	$0.787708\pi$
$132$	50.2427	+	117.055i	0.380626	+	0.886781i
$133$	−20.1629			−0.151601
$134$	−27.6527	+	41.9614i	−0.206363	+	0.313145i
$135$		−	24.3370i		−	0.180274i
$136$	−37.3367	+	208.450i	−0.274534	+	1.53272i
$137$	250.097			1.82553			0.912764	−	0.408488i	$-0.133944\pi$
$137$	250.097			1.82553			0.912764	+	0.408488i	$0.133944\pi$
$138$	13.8719	+	9.14163i	0.100521	+	0.0662437i
$139$			95.5782i			0.687613i	0.939041	+	0.343806i	$0.111716\pi$
$139$			95.5782i			0.687613i	−0.939041	+	0.343806i	$0.888284\pi$
$140$	91.5136	−	39.2797i	0.653669	−	0.280569i
$141$	33.4074			0.236932
$142$	124.713	−	189.245i	0.878261	−	1.33271i
$143$		−	95.0721i		−	0.664840i
$144$	33.0652	−	34.7950i	0.229620	−	0.241632i
$145$	−49.8714			−0.343941
$146$	−112.368	−	74.0510i	−0.769647	−	0.507199i
$147$		−	35.9290i		−	0.244415i
$148$	−52.3853	−	122.047i	−0.353955	−	0.824642i
$149$	−265.833			−1.78412			−0.892058	−	0.451922i	$-0.850739\pi$
$149$	−265.833			−1.78412			−0.892058	+	0.451922i	$0.850739\pi$
$150$	−5.83908	+	8.86049i	−0.0389272	+	0.0590699i
$151$		−	19.5605i		−	0.129539i	−0.997900	−	0.0647697i	$-0.979369\pi$
$151$		−	19.5605i		−	0.129539i	0.997900	−	0.0647697i	$-0.0206313\pi$
$152$	−29.8695	−	5.35008i	−0.196510	−	0.0351979i
$153$	−79.4130			−0.519039
$154$	−163.215	−	107.559i	−1.05983	−	0.698433i
$155$			80.0829i			0.516664i
$156$	−32.9205	+	14.1302i	−0.211029	+	0.0905784i
$157$	−245.842			−1.56587			−0.782936	−	0.622102i	$-0.786279\pi$
$157$	−245.842			−1.56587			−0.782936	+	0.622102i	$0.786279\pi$
$158$	−12.3990	+	18.8148i	−0.0784745	+	0.119081i
$159$		−	14.3353i		−	0.0901590i
$160$	145.992	−	33.9068i	0.912448	−	0.211917i
$161$	−25.4931			−0.158342
$162$	15.0299	+	9.90471i	0.0927769	+	0.0611402i
$163$		−	160.454i		−	0.984383i	−0.870487	−	0.492192i	$-0.836196\pi$
$163$		−	160.454i		−	0.984383i	0.870487	−	0.492192i	$-0.163804\pi$
$164$	26.9327	+	62.7478i	0.164224	+	0.382608i
$165$	−149.154			−0.903964
$166$	−79.2890	+	120.317i	−0.477644	+	0.724800i
$167$		−	231.318i		−	1.38514i	−0.721352	−	0.692568i	$-0.756479\pi$
$167$		−	231.318i		−	1.38514i	0.721352	−	0.692568i	$-0.243521\pi$
$168$	−12.9863	+	72.5023i	−0.0772992	+	0.431561i
$169$	−142.262			−0.841787
$170$	−207.047	−	136.444i	−1.21792	−	0.802613i
$171$		−	11.3793i		−	0.0665457i
$172$	248.093	−	106.487i	1.44240	−	0.619112i
$173$	−301.566			−1.74315			−0.871577	−	0.490258i	$-0.836902\pi$
$173$	−301.566			−1.74315			−0.871577	+	0.490258i	$0.836902\pi$
$174$	20.2967	−	30.7992i	0.116648	−	0.177007i
$175$		−	16.2833i		−	0.0930475i
$176$	−213.247	−	202.646i	−1.21163	−	1.15140i
$177$	124.151			0.701417
$178$	238.876	+	157.420i	1.34200	+	0.884381i
$179$			39.0134i			0.217952i	0.994044	+	0.108976i	$0.0347571\pi$
$179$			39.0134i			0.217952i	−0.994044	+	0.108976i	$0.965243\pi$
$180$	22.1682	+	51.6475i	0.123157	+	0.286930i
$181$	−148.128			−0.818389			−0.409194	−	0.912447i	$-0.634190\pi$
$181$	−148.128			−0.818389			−0.409194	+	0.912447i	$0.634190\pi$
$182$	30.2498	−	45.9024i	0.166207	−	0.252211i
$183$		−	114.824i		−	0.627456i
$184$	−37.7656	−	6.76440i	−0.205248	−	0.0367631i
$185$	155.515			0.840620
$186$	−49.4569	−	32.5922i	−0.265897	−	0.175227i
$187$			486.697i			2.60266i
$188$	−70.8964	+	30.4303i	−0.377108	+	0.161863i
$189$	−27.6210			−0.146143
$190$	19.5515	−	29.6683i	0.102903	−	0.156149i
$191$			217.500i			1.13874i	0.822081	+	0.569370i	$0.192813\pi$
$191$			217.500i			1.13874i	−0.822081	+	0.569370i	$0.807187\pi$
$192$	−38.4759	+	103.960i	−0.200395	+	0.541456i
$193$	−11.9204			−0.0617638			−0.0308819	−	0.999523i	$-0.509832\pi$
$193$	−11.9204			−0.0617638			−0.0308819	+	0.999523i	$0.509832\pi$
$194$	203.164	+	133.886i	1.04724	+	0.690132i
$195$		−	41.9480i		−	0.215118i
$196$	32.7272	+	76.2477i	0.166976	+	0.389019i
$197$	172.705			0.876677			0.438339	−	0.898810i	$-0.355567\pi$
$197$	172.705			0.876677			0.438339	+	0.898810i	$0.355567\pi$
$198$	60.7028	−	92.1132i	0.306580	−	0.465218i
$199$			45.3172i			0.227725i	0.993497	+	0.113862i	$0.0363223\pi$
$199$			45.3172i			0.227725i	−0.993497	+	0.113862i	$0.963678\pi$
$200$	4.32066	−	24.1222i	0.0216033	−	0.120611i
$201$	43.5210			0.216522
$202$	81.3939	+	53.6387i	0.402940	+	0.265538i
$203$			56.6009i			0.278822i
$204$	168.528	−	72.3360i	0.826118	−	0.354588i
$205$	−79.9545			−0.390022
$206$	132.403	−	200.914i	0.642733	−	0.975312i
$207$		−	14.3875i		−	0.0695048i
$208$	56.9921	−	59.9736i	0.274001	−	0.288335i
$209$	−69.7401			−0.333685
$210$	−72.0140	−	47.4574i	−0.342924	−	0.225988i
$211$		−	62.5520i		−	0.296455i	−0.988953	−	0.148228i	$-0.952643\pi$
$211$		−	62.5520i		−	0.296455i	0.988953	−	0.148228i	$-0.0473568\pi$
$212$	13.0578	+	30.4219i	0.0615933	+	0.143500i
$213$	−196.279			−0.921496
$214$	−85.2308	+	129.333i	−0.398275	+	0.604361i
$215$			316.126i			1.47035i
$216$	−40.9180	−	7.32905i	−0.189435	−	0.0339308i
$217$	90.8891			0.418844
$218$	215.994	+	142.340i	0.990796	+	0.652936i
$219$			116.545i			0.532167i
$220$	316.531	−	135.862i	1.43878	−	0.617555i
$221$	−136.878			−0.619359
$222$	−63.2915	+	96.0414i	−0.285097	+	0.432619i
$223$			12.0199i			0.0539011i	0.999637	+	0.0269505i	$0.00857966\pi$
$223$			12.0199i			0.0539011i	−0.999637	+	0.0269505i	$0.991420\pi$
$224$	−38.4821	−	165.691i	−0.171795	−	0.739694i
$225$	9.18980			0.0408435
$226$	235.133	+	154.953i	1.04041	+	0.685633i
$227$			207.877i			0.915760i	0.889014	+	0.457880i	$0.151391\pi$
$227$			207.877i			0.915760i	−0.889014	+	0.457880i	$0.848609\pi$
$228$	10.3652	+	24.1489i	0.0454615	+	0.105916i
$229$	139.717			0.610118			0.305059	−	0.952333i	$-0.401324\pi$
$229$	139.717			0.610118			0.305059	+	0.952333i	$0.401324\pi$
$230$	24.7200	−	37.5113i	0.107478	−	0.163093i
$231$			169.281i			0.732816i
$232$	−15.0187	+	83.8491i	−0.0647356	+	0.361419i
$233$	−397.573			−1.70632			−0.853162	−	0.521646i	$-0.825318\pi$
$233$	−397.573			−1.70632			−0.853162	+	0.521646i	$0.825318\pi$
$234$	25.9059	+	17.0720i	0.110709	+	0.0729574i
$235$		−	90.3376i		−	0.384415i
$236$	−263.470	+	113.087i	−1.11640	+	0.479182i
$237$	19.5140			0.0823377
$238$	−154.856	+	234.985i	−0.650654	+	0.987333i
$239$			444.885i			1.86144i	0.365727	+	0.930722i	$0.380820\pi$
$239$			444.885i			1.86144i	−0.365727	+	0.930722i	$0.619180\pi$
$240$	−94.0897	−	89.4122i	−0.392040	−	0.372551i
$241$	277.798			1.15269			0.576344	−	0.817207i	$-0.304479\pi$
$241$	277.798			1.15269			0.576344	+	0.817207i	$0.304479\pi$
$242$	−362.464	−	238.865i	−1.49779	−	0.987044i
$243$		−	15.5885i		−	0.0641500i
$244$	104.592	+	243.677i	0.428655	+	0.998678i
$245$	−97.1563			−0.396556
$246$	32.5399	−	49.3776i	0.132276	−	0.200722i
$247$		−	19.6137i		−	0.0794077i
$248$	134.644	+	24.1168i	0.542919	+	0.0972450i
$249$	124.788			0.501158
$250$	219.501	+	144.652i	0.878004	+	0.578607i
$251$		−	420.503i		−	1.67531i	−0.546200	−	0.837655i	$-0.683926\pi$
$251$		−	420.503i		−	1.67531i	0.546200	−	0.837655i	$-0.316074\pi$
$252$	58.6166	−	25.1596i	0.232606	−	0.0998396i
$253$	−88.1764			−0.348523
$254$	−134.143	+	203.554i	−0.528120	+	0.801394i
$255$			214.742i			0.842125i
$256$	−13.0426	−	255.668i	−0.0509476	−	0.998701i
$257$	216.304			0.841651			0.420826	−	0.907142i	$-0.361740\pi$
$257$	216.304			0.841651			0.420826	+	0.907142i	$0.361740\pi$
$258$	−195.230	−	128.657i	−0.756706	−	0.498671i
$259$		−	176.500i		−	0.681465i
$260$	38.2098	+	89.0210i	0.146961	+	0.342388i
$261$	−31.9438			−0.122390
$262$	−178.360	+	270.652i	−0.680763	+	1.03302i
$263$		−	93.9948i		−	0.357395i	−0.983904	−	0.178697i	$-0.942812\pi$
$263$		−	93.9948i		−	0.357395i	0.983904	−	0.178697i	$-0.0571883\pi$
$264$	−44.9174	+	250.774i	−0.170142	+	0.949900i
$265$	−38.7642			−0.146280
$266$	−33.6717	−	22.1897i	−0.126585	−	0.0834200i
$267$		−	247.754i		−	0.927918i
$268$	−92.3591	+	39.6426i	−0.344623	+	0.147920i
$269$	−237.509			−0.882935			−0.441467	−	0.897277i	$-0.645542\pi$
$269$	−237.509			−0.882935			−0.441467	+	0.897277i	$0.645542\pi$
$270$	26.7835	−	40.6425i	0.0991981	−	0.150528i
$271$		−	247.697i		−	0.914011i	−0.889464	−	0.457006i	$-0.848922\pi$
$271$		−	247.697i		−	0.914011i	0.889464	−	0.457006i	$-0.151078\pi$
$272$	−291.756	+	307.019i	−1.07263	+	1.12875i
$273$	−47.6084			−0.174390
$274$	417.659	+	275.238i	1.52430	+	1.00452i
$275$		−	56.3213i		−	0.204805i
$276$	13.1053	+	30.5328i	0.0474831	+	0.110626i
$277$	523.033			1.88820			0.944102	−	0.329653i	$-0.106932\pi$
$277$	523.033			1.88820			0.944102	+	0.329653i	$0.106932\pi$
$278$	−105.186	+	159.614i	−0.378367	+	0.574152i
$279$			51.2950i			0.183853i
$280$	196.055	+	35.1164i	0.700195	+	0.125416i
$281$	−65.3687			−0.232629			−0.116314	−	0.993212i	$-0.537108\pi$
$281$	−65.3687			−0.232629			−0.116314	+	0.993212i	$0.537108\pi$
$282$	55.7899	+	36.7656i	0.197836	+	0.130375i
$283$		−	147.876i		−	0.522530i	−0.965267	−	0.261265i	$-0.915860\pi$
$283$		−	147.876i		−	0.522530i	0.965267	−	0.261265i	$-0.0841397\pi$
$284$	416.538	−	178.787i	1.46668	−	0.629532i
$285$	−30.7710			−0.107968
$286$	104.629	−	158.769i	0.365836	−	0.555136i
$287$			90.7434i			0.316179i
$288$	93.5111	−	21.7181i	0.324691	−	0.0754100i
$289$	411.713			1.42461
$290$	−83.2845	−	54.8846i	−0.287188	−	0.189257i
$291$		−	210.715i		−	0.724107i
$292$	−106.159	−	247.328i	−0.363557	−	0.847014i
$293$	329.864			1.12582			0.562908	−	0.826519i	$-0.309682\pi$
$293$	329.864			1.12582			0.562908	+	0.826519i	$0.309682\pi$
$294$	39.5407	−	60.0010i	0.134492	−	0.204085i
$295$		−	335.718i		−	1.13803i
$296$	46.8329	−	261.468i	0.158219	−	0.883337i
$297$	−95.5367			−0.321672
$298$	−443.937	−	292.555i	−1.48972	−	0.981730i
$299$		−	24.7987i		−	0.0829388i
$300$	−19.5023	+	8.37084i	−0.0650078	+	0.0279028i
$301$	358.783			1.19197
$302$	21.5267	−	32.6657i	0.0712806	−	0.108164i
$303$		−	84.4189i		−	0.278610i
$304$	−43.9937	−	41.8066i	−0.144716	−	0.137522i
$305$	−310.499			−1.01803
$306$	−132.618	−	87.3958i	−0.433394	−	0.285607i
$307$		−	295.644i		−	0.963010i	−0.876443	−	0.481505i	$-0.840090\pi$
$307$		−	295.644i		−	0.963010i	0.876443	−	0.481505i	$-0.159910\pi$
$308$	−154.195	−	359.243i	−0.500633	−	1.16637i
$309$	−208.381			−0.674374
$310$	−88.1330	+	133.737i	−0.284300	+	0.431410i
$311$		−	442.204i		−	1.42188i	−0.703253	−	0.710940i	$-0.748270\pi$
$311$		−	442.204i		−	1.42188i	0.703253	−	0.710940i	$-0.251730\pi$
$312$	−70.5275	−	12.6325i	−0.226050	−	0.0404889i
$313$	40.9312			0.130771			0.0653853	−	0.997860i	$-0.479172\pi$
$313$	40.9312			0.130771			0.0653853	+	0.997860i	$0.479172\pi$
$314$	−410.552	−	270.555i	−1.30749	−	0.861639i
$315$			74.6905i			0.237113i
$316$	−41.4122	+	17.7750i	−0.131051	+	0.0562501i
$317$	−103.967			−0.327970			−0.163985	−	0.986463i	$-0.552435\pi$
$317$	−103.967			−0.327970			−0.163985	+	0.986463i	$0.552435\pi$
$318$	15.7763	−	23.9397i	0.0496110	−	0.0752820i
$319$			195.774i			0.613710i
$320$	281.119	+	104.043i	0.878497	+	0.325136i
$321$	134.140			0.417882
$322$	−42.5730	−	28.0557i	−0.132214	−	0.0871295i
$323$			100.407i			0.310858i
$324$	14.1993	+	33.0814i	0.0438249	+	0.102103i
$325$	15.8398			0.0487378
$326$	176.584	−	267.956i	0.541668	−	0.821952i
$327$		−	224.021i		−	0.685080i
$328$	−24.0781	+	134.428i	−0.0734089	+	0.409841i
$329$	−102.528			−0.311634
$330$	−249.085	−	164.147i	−0.754803	−	0.497416i
$331$			220.550i			0.666316i	0.942871	+	0.333158i	$0.108114\pi$
$331$			220.550i			0.666316i	−0.942871	+	0.333158i	$0.891886\pi$
$332$	−264.823	+	113.668i	−0.797659	+	0.342373i
$333$	99.6109			0.299132
$334$	254.571	−	386.297i	0.762188	−	1.15658i
$335$		−	117.686i		−	0.351301i
$336$	−101.477	+	106.786i	−0.302016	+	0.317815i
$337$	−200.674			−0.595472			−0.297736	−	0.954648i	$-0.596231\pi$
$337$	−200.674			−0.595472			−0.297736	+	0.954648i	$0.596231\pi$
$338$	−237.575	−	156.563i	−0.702886	−	0.463203i
$339$		−	243.872i		−	0.719386i
$340$	−195.605	−	455.720i	−0.575309	−	1.34035i
$341$	314.371			0.921908
$342$	12.5232	−	19.0033i	0.0366175	−	0.0555651i
$343$			370.734i			1.08086i
$344$	531.504	+	95.2005i	1.54507	+	0.276746i
$345$	−38.9055			−0.112769
$346$	−503.610	−	331.880i	−1.45552	−	0.959191i
$347$		−	582.738i		−	1.67936i	−0.543082	−	0.839680i	$-0.682743\pi$
$347$		−	582.738i		−	1.67936i	0.543082	−	0.839680i	$-0.317257\pi$
$348$	67.7904	−	29.0971i	0.194800	−	0.0836124i
$349$	−12.6342			−0.0362012			−0.0181006	−	0.999836i	$-0.505762\pi$
$349$	−12.6342			−0.0362012			−0.0181006	+	0.999836i	$0.505762\pi$
$350$	17.9202	−	27.1929i	0.0512004	−	0.0776939i
$351$		−	26.8687i		−	0.0765490i
$352$	−133.103	−	573.100i	−0.378134	−	1.62812i
$353$	403.033			1.14174			0.570869	−	0.821041i	$-0.306606\pi$
$353$	403.033			1.14174			0.570869	+	0.821041i	$0.306606\pi$
$354$	207.330	+	136.631i	0.585678	+	0.385963i
$355$			530.760i			1.49510i
$356$	225.675	+	525.778i	0.633920	+	1.47690i
$357$	243.719			0.682685
$358$	−42.9351	+	65.1518i	−0.119931	+	0.181988i
$359$			206.559i			0.575373i	0.957725	+	0.287686i	$0.0928861\pi$
$359$			206.559i			0.575373i	−0.957725	+	0.287686i	$0.907114\pi$
$360$	−19.8186	+	110.647i	−0.0550516	+	0.307353i
$361$	346.612			0.960145
$362$	−247.372	−	163.019i	−0.683348	−	0.450328i
$363$			375.936i			1.03564i
$364$	101.033	−	43.3657i	0.277564	−	0.119137i
$365$	315.150			0.863426
$366$	126.367	−	191.755i	0.345265	−	0.523921i
$367$			334.669i			0.911906i	0.890004	+	0.455953i	$0.150701\pi$
$367$			334.669i			0.911906i	−0.890004	+	0.455953i	$0.849299\pi$
$368$	−55.6236	−	52.8584i	−0.151151	−	0.143637i
$369$	−51.2127			−0.138788
$370$	259.707	+	171.148i	0.701911	+	0.462561i
$371$			43.9950i			0.118585i
$372$	−46.7238	−	108.857i	−0.125602	−	0.292626i
$373$	−319.470			−0.856487			−0.428243	−	0.903663i	$-0.640867\pi$
$373$	−319.470			−0.856487			−0.428243	+	0.903663i	$0.640867\pi$
$374$	−535.621	+	812.776i	−1.43214	+	2.17320i
$375$		−	227.659i		−	0.607091i
$376$	−151.885	−	27.2049i	−0.403950	−	0.0723536i
$377$	−55.0593			−0.146046
$378$	−46.1267	−	30.3976i	−0.122028	−	0.0804169i
$379$		−	520.350i		−	1.37295i	−0.727151	−	0.686477i	$-0.759156\pi$
$379$		−	520.350i		−	1.37295i	0.727151	−	0.686477i	$-0.240844\pi$
$380$	65.3014	−	28.0288i	0.171846	−	0.0737600i
$381$	211.119			0.554119
$382$	−239.363	+	363.221i	−0.626605	+	0.950840i
$383$		−	539.699i		−	1.40913i	−0.709637	−	0.704567i	$-0.751141\pi$
$383$		−	539.699i		−	1.40913i	0.709637	−	0.704567i	$-0.248859\pi$
$384$	−178.664	+	131.267i	−0.465271	+	0.341842i
$385$	457.754			1.18897
$386$	−19.9069	−	13.1187i	−0.0515723	−	0.0339862i
$387$			202.486i			0.523220i
$388$	191.937	+	447.174i	0.494683	+	1.15251i
$389$	107.111			0.275349			0.137675	−	0.990478i	$-0.456037\pi$
$389$	107.111			0.275349			0.137675	+	0.990478i	$0.456037\pi$
$390$	46.1648	−	70.0525i	0.118371	−	0.179622i
$391$			126.950i			0.324681i
$392$	−29.2584	+	163.350i	−0.0746388	+	0.416708i
$393$	280.711			0.714277
$394$	288.415	+	190.066i	0.732019	+	0.482402i
$395$		−	52.7682i		−	0.133590i
$396$	202.745	−	87.0229i	0.511984	−	0.219755i
$397$	−680.877			−1.71506			−0.857528	−	0.514437i	$-0.828001\pi$
$397$	−680.877			−1.71506			−0.857528	+	0.514437i	$0.828001\pi$
$398$	−49.8726	+	75.6790i	−0.125308	+	0.190148i
$399$			34.9231i			0.0875267i
$400$	33.7625	−	35.5288i	0.0844063	−	0.0888219i
$401$	−147.574			−0.368016			−0.184008	−	0.982925i	$-0.558907\pi$
$401$	−147.574			−0.368016			−0.184008	+	0.982925i	$0.558907\pi$
$402$	72.6793	+	47.8958i	0.180794	+	0.119144i
$403$			88.4134i			0.219388i
$404$	76.8959	+	179.152i	0.190336	+	0.443445i
$405$	−42.1530			−0.104081
$406$	−62.2906	+	94.5227i	−0.153425	+	0.232815i
$407$		−	610.483i		−	1.49996i
$408$	361.047	+	64.6690i	0.884919	+	0.158503i
$409$	−39.8236			−0.0973682			−0.0486841	−	0.998814i	$-0.515503\pi$
$409$	−39.8236			−0.0973682			−0.0486841	+	0.998814i	$0.515503\pi$
$410$	−133.523	−	87.9917i	−0.325665	−	0.214614i
$411$		−	433.181i		−	1.05397i
$412$	442.222	−	189.811i	1.07335	−	0.460707i
$413$	−381.019			−0.922565
$414$	15.8338	−	24.0269i	0.0382458	−	0.0580360i
$415$		−	337.442i		−	0.813114i
$416$	161.178	−	37.4339i	0.387448	−	0.0899853i
$417$	165.546			0.396993
$418$	−116.465	−	76.7506i	−0.278624	−	0.183614i
$419$			124.800i			0.297851i	0.988848	+	0.148926i	$0.0475815\pi$
$419$			124.800i			0.297851i	−0.988848	+	0.148926i	$0.952418\pi$
$420$	−68.0344	−	158.506i	−0.161987	−	0.377396i
$421$	93.7694			0.222730			0.111365	−	0.993780i	$-0.464478\pi$
$421$	93.7694			0.222730			0.111365	+	0.993780i	$0.464478\pi$
$422$	68.8399	−	104.461i	0.163128	−	0.247538i
$423$		−	57.8634i		−	0.136793i
$424$	−11.6738	+	65.1746i	−0.0275325	+	0.153714i
$425$	−81.0876			−0.190794
$426$	−327.782	−	216.009i	−0.769442	−	0.507064i
$427$			352.397i			0.825285i
$428$	−284.668	+	122.186i	−0.665113	+	0.285481i
$429$	−164.670			−0.383845
$430$	−347.903	+	527.925i	−0.809078	+	1.22773i
$431$		−	63.8451i		−	0.148132i	−0.997253	−	0.0740662i	$-0.976402\pi$
$431$		−	63.8451i		−	0.148132i	0.997253	−	0.0740662i	$-0.0235976\pi$
$432$	−60.2667	−	57.2706i	−0.139506	−	0.132571i
$433$	850.413			1.96400			0.982001	−	0.188877i	$-0.0604849\pi$
$433$	850.413			1.96400			0.982001	+	0.188877i	$0.0604849\pi$
$434$	151.783	+	100.025i	0.349731	+	0.230474i
$435$			86.3798i			0.198574i
$436$	204.057	+	475.412i	0.468021	+	1.09039i
$437$	−18.1911			−0.0416272
$438$	−128.260	+	194.628i	−0.292831	+	0.444356i
$439$			38.7032i			0.0881621i	0.999028	+	0.0440811i	$0.0140360\pi$
$439$			38.7032i			0.0881621i	−0.999028	+	0.0440811i	$0.985964\pi$
$440$	678.121	+	121.462i	1.54118	+	0.276050i
$441$	−62.2309			−0.141113
$442$	−228.585	−	150.638i	−0.517160	−	0.340810i
$443$		−	417.689i		−	0.942866i	−0.881902	−	0.471433i	$-0.843737\pi$
$443$		−	417.689i		−	0.942866i	0.881902	−	0.471433i	$-0.156263\pi$
$444$	−211.392	+	90.7340i	−0.476107	+	0.204356i
$445$	−669.956			−1.50552
$446$	−13.2282	+	20.0731i	−0.0296597	+	0.0450070i
$447$			460.437i			1.03006i
$448$	118.083	−	319.052i	0.263578	−	0.712171i
$449$	−228.319			−0.508506			−0.254253	−	0.967138i	$-0.581830\pi$
$449$	−228.319			−0.508506			−0.254253	+	0.967138i	$0.581830\pi$
$450$	15.3468	+	10.1136i	0.0341040	+	0.0224746i
$451$			313.867i			0.695935i
$452$	222.139	+	517.539i	0.491458	+	1.14500i
$453$	−33.8797			−0.0747896
$454$	−228.774	+	347.152i	−0.503907	+	0.764652i
$455$			128.739i			0.282942i
$456$	−9.26661	+	51.7354i	−0.0203215	+	0.113455i
$457$	−9.59348			−0.0209923			−0.0104962	−	0.999945i	$-0.503341\pi$
$457$	−9.59348			−0.0209923			−0.0104962	+	0.999945i	$0.503341\pi$
$458$	233.325	+	153.762i	0.509444	+	0.335725i
$459$			137.547i			0.299667i
$460$	82.5642	−	35.4384i	0.179487	−	0.0770399i
$461$	252.500			0.547723			0.273861	−	0.961769i	$-0.411699\pi$
$461$	252.500			0.547723			0.273861	+	0.961769i	$0.411699\pi$
$462$	−186.297	+	282.696i	−0.403240	+	0.611896i
$463$			122.737i			0.265091i	0.991177	+	0.132546i	$0.0423151\pi$
$463$			122.737i			0.265091i	−0.991177	+	0.132546i	$0.957685\pi$
$464$	−117.359	+	123.498i	−0.252928	+	0.266160i
$465$	138.708			0.298296
$466$	−663.942	−	437.539i	−1.42477	−	0.938924i
$467$		−	504.406i		−	1.08010i	−0.841633	−	0.540049i	$-0.818406\pi$
$467$		−	504.406i		−	1.08010i	0.841633	−	0.540049i	$-0.181594\pi$
$468$	24.4743	+	57.0201i	0.0522955	+	0.121838i
$469$	−133.566			−0.284789
$470$	99.4186	−	150.862i	0.211529	−	0.320984i
$471$			425.811i			0.904057i
$472$	−564.445	−	101.101i	−1.19586	−	0.214197i
$473$	1240.97			2.62362
$474$	32.5881	+	21.4756i	0.0687514	+	0.0453073i
$475$		−	11.6193i		−	0.0244616i
$476$	−517.213	+	222.000i	−1.08658	+	0.466386i
$477$	−24.8294			−0.0520533
$478$	−489.606	+	742.951i	−1.02428	+	1.55429i
$479$			91.9020i			0.191862i	0.995388	+	0.0959312i	$0.0305829\pi$
$479$			91.9020i			0.191862i	−0.995388	+	0.0959312i	$0.969417\pi$
$480$	−58.7282	−	252.865i	−0.122350	−	0.526802i
$481$	171.692			0.356948
$482$	463.918	+	305.723i	0.962486	+	0.634280i
$483$			44.1553i			0.0914188i
$484$	−342.434	−	797.801i	−0.707508	−	1.64835i
$485$	−569.798			−1.17484
$486$	17.1555	−	26.0325i	0.0352993	−	0.0535648i
$487$		−	682.414i		−	1.40126i	−0.713524	−	0.700631i	$-0.752902\pi$
$487$		−	682.414i		−	1.40126i	0.713524	−	0.700631i	$-0.247098\pi$
$488$	−93.5059	+	522.043i	−0.191611	+	1.06976i
$489$	−277.915			−0.568334
$490$	−162.250	−	106.923i	−0.331122	−	0.218210i
$491$			407.357i			0.829647i	0.909902	+	0.414823i	$0.136157\pi$
$491$			407.357i			0.829647i	−0.909902	+	0.414823i	$0.863843\pi$
$492$	108.682	−	46.6489i	0.220899	−	0.0948148i
$493$	281.861			0.571727
$494$	21.5853	−	32.7546i	0.0436950	−	0.0663048i
$495$			258.342i			0.521904i
$496$	198.312	+	188.453i	0.399823	+	0.379946i
$497$	602.380			1.21203
$498$	208.395	+	137.333i	0.418463	+	0.275768i
$499$			65.0952i			0.130451i	0.997871	+	0.0652257i	$0.0207767\pi$
$499$			65.0952i			0.130451i	−0.997871	+	0.0652257i	$0.979223\pi$
$500$	207.371	+	483.132i	0.414742	+	0.966264i
$501$	−400.654			−0.799709
$502$	462.773	−	702.233i	0.921858	−	1.39887i
$503$			145.113i			0.288495i	0.989542	+	0.144247i	$0.0460761\pi$
$503$			145.113i			0.288495i	−0.989542	+	0.144247i	$0.953924\pi$
$504$	125.578	+	22.4929i	0.249162	+	0.0446287i
$505$	−228.279			−0.452037
$506$	−147.253	−	97.0401i	−0.291014	−	0.191779i
$507$			246.405i			0.486006i
$508$	−448.032	+	192.305i	−0.881953	+	0.378554i
$509$	138.923			0.272933			0.136466	−	0.990645i	$-0.456425\pi$
$509$	138.923			0.272933			0.136466	+	0.990645i	$0.456425\pi$
$510$	−236.328	+	358.616i	−0.463389	+	0.703168i
$511$		−	357.676i		−	0.699953i
$512$	259.587	−	441.315i	0.507006	−	0.861943i
$513$	−19.7095			−0.0384202
$514$	361.225	+	238.048i	0.702772	+	0.463128i
$515$			563.488i			1.09415i
$516$	−184.441	−	429.710i	−0.357444	−	0.832772i
$517$	−354.626			−0.685930
$518$	194.242	−	294.752i	0.374984	−	0.569018i
$519$			522.327i			1.00641i
$520$	−34.1599	+	190.714i	−0.0656921	+	0.366759i
$521$	−976.261			−1.87382			−0.936911	−	0.349568i	$-0.886328\pi$
$521$	−976.261			−1.87382			−0.936911	+	0.349568i	$0.886328\pi$
$522$	−53.3457	−	35.1549i	−0.102195	−	0.0673466i
$523$			990.510i			1.89390i	0.321381	+	0.946950i	$0.395853\pi$
$523$			990.510i			1.89390i	−0.321381	+	0.946950i	$0.604147\pi$
$524$	−595.717	+	255.695i	−1.13686	+	0.487968i
$525$	−28.2035			−0.0537210
$526$	103.443	−	156.970i	0.196661	−	0.298422i
$527$		−	452.609i		−	0.858842i
$528$	−350.993	+	369.355i	−0.664760	+	0.699537i
$529$	−23.0000			−0.0434783
$530$	−64.7357	−	42.6609i	−0.122143	−	0.0804924i
$531$		−	215.036i		−	0.404963i
$532$	−31.8109	−	74.1130i	−0.0597950	−	0.139310i
$533$	−88.2717			−0.165613
$534$	272.659	−	413.746i	0.510598	−	0.774805i
$535$		−	362.730i		−	0.678000i
$536$	−197.866	−	35.4408i	−0.369153	−	0.0661209i
$537$	67.5732			0.125835
$538$	−396.637	−	261.385i	−0.737244	−	0.485845i
$539$			381.394i			0.707595i
$540$	89.4560	−	38.3965i	0.165659	−	0.0711047i
$541$	−182.791			−0.337877			−0.168938	−	0.985627i	$-0.554034\pi$
$541$	−182.791			−0.337877			−0.168938	+	0.985627i	$0.554034\pi$
$542$	272.596	−	413.650i	0.502945	−	0.763192i
$543$			256.566i			0.472497i
$544$	−825.110	+	191.633i	−1.51675	+	0.352267i
$545$	−605.779			−1.11152
$546$	−79.5053	−	52.3941i	−0.145614	−	0.0959599i
$547$			248.364i			0.454047i	0.973889	+	0.227023i	$0.0728994\pi$
$547$			248.364i			0.454047i	−0.973889	+	0.227023i	$0.927101\pi$
$548$	394.578	+	919.286i	0.720033	+	1.67753i
$549$	−198.882			−0.362262
$550$	61.9829	−	94.0558i	0.112696	−	0.171010i
$551$			40.3887i			0.0733008i
$552$	−11.7163	+	65.4120i	−0.0212252	+	0.118500i
$553$	−59.8887			−0.108298
$554$	873.457	+	575.610i	1.57664	+	1.03901i
$555$		−	269.359i		−	0.485332i
$556$	−351.318	+	150.794i	−0.631867	+	0.271211i
$557$	−816.385			−1.46568			−0.732841	−	0.680399i	$-0.761806\pi$
$557$	−816.385			−1.46568			−0.732841	+	0.680399i	$0.761806\pi$
$558$	−56.4513	+	85.6618i	−0.101167	+	0.153516i
$559$			349.010i			0.624348i
$560$	288.762	+	274.406i	0.515646	+	0.490011i
$561$	842.983			1.50264
$562$	−109.165	−	71.9398i	−0.194243	−	0.128007i
$563$		−	376.727i		−	0.669142i	−0.942371	−	0.334571i	$-0.891409\pi$
$563$		−	376.727i		−	0.669142i	0.942371	−	0.334571i	$-0.108591\pi$
$564$	52.7068	+	122.796i	0.0934518	+	0.217724i
$565$	−659.458			−1.16718
$566$	162.741	−	246.951i	0.287528	−	0.436309i
$567$			47.8410i			0.0843757i
$568$	892.371	+	159.837i	1.57108	+	0.281404i
$569$	79.7840			0.140218			0.0701089	−	0.997539i	$-0.477665\pi$
$569$	79.7840			0.140218			0.0701089	+	0.997539i	$0.477665\pi$
$570$	−51.3870	−	33.8642i	−0.0901527	−	0.0594108i
$571$		−	393.986i		−	0.689993i	−0.938604	−	0.344997i	$-0.887880\pi$
$571$		−	393.986i		−	0.689993i	0.938604	−	0.344997i	$-0.112120\pi$
$572$	349.458	−	149.995i	0.610940	−	0.262229i
$573$	376.720			0.657452
$574$	−99.8652	+	151.540i	−0.173981	+	0.264007i
$575$		−	14.6909i		−	0.0255494i
$576$	180.063	+	66.6423i	0.312610	+	0.115698i
$577$	349.796			0.606232			0.303116	−	0.952954i	$-0.401973\pi$
$577$	349.796			0.606232			0.303116	+	0.952954i	$0.401973\pi$
$578$	687.555	+	453.100i	1.18954	+	0.783910i
$579$			20.6467i			0.0356593i
$580$	−78.6820	−	183.313i	−0.135659	−	0.316057i
$581$	−382.976			−0.659167
$582$	231.897	−	351.891i	0.398448	−	0.604623i
$583$			152.172i			0.261015i
$584$	94.9068	−	529.864i	0.162512	−	0.907302i
$585$	−72.6561			−0.124198
$586$	550.868	+	363.023i	0.940048	+	0.619494i
$587$			565.552i			0.963461i	0.876319	+	0.481731i	$0.159992\pi$
$587$			565.552i			0.963461i	−0.876319	+	0.481731i	$0.840008\pi$
$588$	132.065	−	56.6852i	0.224600	−	0.0964034i
$589$	64.8557			0.110112
$590$	369.466	−	560.644i	0.626213	−	0.950245i
$591$		−	299.135i		−	0.506150i
$592$	365.962	−	385.107i	0.618178	−	0.650518i
$593$	789.930			1.33209			0.666046	−	0.745911i	$-0.267986\pi$
$593$	789.930			1.33209			0.666046	+	0.745911i	$0.267986\pi$
$594$	−159.545	−	105.140i	−0.268594	−	0.177004i
$595$		−	659.044i		−	1.10764i
$596$	−419.404	−	977.126i	−0.703699	−	1.63947i
$597$	78.4917			0.131477
$598$	27.2915	−	41.4134i	0.0456380	−	0.0692532i
$599$			580.745i			0.969524i	0.874646	+	0.484762i	$0.161094\pi$
$599$			580.745i			0.969524i	−0.874646	+	0.484762i	$0.838906\pi$
$600$	−41.7809	−	7.48360i	−0.0696349	−	0.0124727i
$601$	−55.2357			−0.0919063			−0.0459532	−	0.998944i	$-0.514632\pi$
$601$	−55.2357			−0.0919063			−0.0459532	+	0.998944i	$0.514632\pi$
$602$	599.162	+	394.849i	0.995286	+	0.655895i
$603$		−	75.3805i		−	0.125009i
$604$	71.8986	−	30.8605i	0.119037	−	0.0510935i
$605$	1016.57			1.68029
$606$	92.9050	−	140.978i	0.153309	−	0.232637i
$607$		−	888.273i		−	1.46338i	−0.681636	−	0.731691i	$-0.738731\pi$
$607$		−	888.273i		−	1.46338i	0.681636	−	0.731691i	$-0.261269\pi$
$608$	−27.4596	−	118.232i	−0.0451639	−	0.194461i
$609$	98.0357			0.160978
$610$	−518.528	−	341.711i	−0.850046	−	0.560182i
$611$		−	99.7349i		−	0.163232i
$612$	−125.290	−	291.899i	−0.204722	−	0.476960i
$613$	−581.515			−0.948638			−0.474319	−	0.880353i	$-0.657306\pi$
$613$	−581.515			−0.948638			−0.474319	+	0.880353i	$0.657306\pi$
$614$	325.363	−	493.721i	0.529907	−	0.804106i
$615$			138.485i			0.225179i
$616$	137.852	−	769.625i	0.223785	−	1.24939i
$617$	875.149			1.41839			0.709197	−	0.705011i	$-0.249058\pi$
$617$	875.149			1.41839			0.709197	+	0.705011i	$0.249058\pi$
$618$	−347.994	−	229.329i	−0.563097	−	0.371082i
$619$			171.748i			0.277460i	0.990330	+	0.138730i	$0.0443020\pi$
$619$			171.748i			0.277460i	−0.990330	+	0.138730i	$0.955698\pi$
$620$	−294.362	+	126.347i	−0.474777	+	0.203785i
$621$	−24.9199			−0.0401286
$622$	486.656	−	738.475i	0.782405	−	1.18726i
$623$			760.359i			1.22048i
$624$	−103.877	−	98.7133i	−0.166470	−	0.158194i
$625$	−539.035			−0.862456
$626$	68.3545	+	45.0457i	0.109192	+	0.0719580i
$627$			120.793i			0.192653i
$628$	−387.864	−	903.645i	−0.617618	−	1.43892i
$629$	−878.933			−1.39735
$630$	−82.1986	+	124.732i	−0.130474	+	0.197987i
$631$			1056.83i			1.67485i	0.546553	+	0.837425i	$0.315940\pi$
$631$			1056.83i			1.67485i	−0.546553	+	0.837425i	$0.684060\pi$
$632$	−88.7195	−	15.8910i	−0.140379	−	0.0251440i
$633$	−108.343			−0.171158
$634$	−173.622	−	114.418i	−0.273852	−	0.180469i
$635$		−	570.891i		−	0.899042i
$636$	52.6924	−	22.6167i	0.0828496	−	0.0355609i
$637$	−107.263			−0.168388
$638$	−215.453	+	326.939i	−0.337701	+	0.512443i
$639$			339.965i			0.532026i
$640$	354.962	+	483.129i	0.554628	+	0.754889i
$641$	−1049.04			−1.63657			−0.818283	−	0.574816i	$-0.805074\pi$
$641$	−1049.04			−1.63657			−0.818283	+	0.574816i	$0.805074\pi$
$642$	224.012	+	147.624i	0.348928	+	0.229944i
$643$		−	466.518i		−	0.725533i	−0.931880	−	0.362767i	$-0.881832\pi$
$643$		−	466.518i		−	0.725533i	0.931880	−	0.362767i	$-0.118168\pi$
$644$	−40.2204	−	93.7052i	−0.0624540	−	0.145505i
$645$	547.546			0.848908
$646$	−110.500	+	167.678i	−0.171053	+	0.259564i
$647$		−	933.672i		−	1.44308i	−0.692373	−	0.721540i	$-0.743435\pi$
$647$		−	933.672i		−	1.44308i	0.692373	−	0.721540i	$-0.256565\pi$
$648$	−12.6943	+	70.8721i	−0.0195899	+	0.109371i
$649$	−1317.88			−2.03064
$650$	26.4522	+	17.4321i	0.0406957	+	0.0268185i
$651$		−	157.424i		−	0.241819i
$652$	589.785	−	253.149i	0.904577	−	0.388265i
$653$	−601.748			−0.921513			−0.460756	−	0.887527i	$-0.652422\pi$
$653$	−601.748			−0.921513			−0.460756	+	0.887527i	$0.652422\pi$
$654$	246.540	−	374.112i	0.376973	−	0.572036i
$655$		−	759.074i		−	1.15889i
$656$	−188.151	+	197.994i	−0.286816	+	0.301820i
$657$	201.861			0.307247
$658$	−171.219	−	112.834i	−0.260212	−	0.171480i
$659$		−	524.014i		−	0.795166i	−0.917566	−	0.397583i	$-0.869849\pi$
$659$		−	524.014i		−	0.795166i	0.917566	−	0.397583i	$-0.130151\pi$
$660$	−235.320	−	548.247i	−0.356545	−	0.830678i
$661$	684.387			1.03538			0.517690	−	0.855568i	$-0.326792\pi$
$661$	684.387			1.03538			0.517690	+	0.855568i	$0.326792\pi$
$662$	−242.721	+	368.316i	−0.366648	+	0.556368i
$663$			237.080i			0.357587i
$664$	−567.344	−	101.620i	−0.854434	−	0.153042i
$665$	94.4362			0.142009
$666$	166.349	+	109.624i	0.249773	+	0.164601i
$667$			51.0657i			0.0765603i
$668$	850.258	−	364.950i	1.27284	−	0.546332i
$669$	20.8192			0.0311198
$670$	129.516	−	196.533i	0.193307	−	0.293333i
$671$			1218.88i			1.81652i
$672$	−286.986	+	66.6529i	−0.427062	+	0.0991858i
$673$	7.21396			0.0107191			0.00535955	−	0.999986i	$-0.498294\pi$
$673$	7.21396			0.0107191			0.00535955	+	0.999986i	$0.498294\pi$
$674$	−335.122	−	220.846i	−0.497214	−	0.327665i
$675$		−	15.9172i		−	0.0235810i
$676$	−224.446	−	522.914i	−0.332021	−	0.773542i
$677$	100.662			0.148689			0.0743444	−	0.997233i	$-0.476314\pi$
$677$	100.662			0.148689			0.0743444	+	0.997233i	$0.476314\pi$
$678$	268.387	−	407.262i	0.395851	−	0.600682i
$679$			646.685i			0.952408i
$680$	174.873	−	976.313i	0.257166	−	1.43575i
$681$	360.054			0.528714
$682$	524.994	+	345.972i	0.769786	+	0.507290i
$683$		−	1255.33i		−	1.83796i	−0.394307	−	0.918979i	$-0.629015\pi$
$683$		−	1255.33i		−	1.83796i	0.394307	−	0.918979i	$-0.370985\pi$
$684$	41.8271	−	17.9531i	0.0611507	−	0.0262472i
$685$	−1171.37			−1.71003
$686$	−408.002	+	619.121i	−0.594754	+	0.902508i
$687$		−	241.997i		−	0.352252i
$688$	782.833	+	743.916i	1.13784	+	1.08127i
$689$	−42.7967			−0.0621142
$690$	−64.9715	−	42.8164i	−0.0941616	−	0.0620527i
$691$			1058.46i			1.53179i	0.642968	+	0.765893i	$0.277703\pi$
$691$			1058.46i			1.53179i	−0.642968	+	0.765893i	$0.722297\pi$
$692$	−475.780	−	1108.47i	−0.687543	−	1.60183i
$693$	293.202			0.423092
$694$	641.316	−	973.163i	0.924087	−	1.40225i
$695$		−	447.656i		−	0.644110i
$696$	145.231	+	26.0131i	0.208665	+	0.0373751i
$697$	451.884			0.648327
$698$	−21.0990	−	13.9042i	−0.0302277	−	0.0199201i
$699$			688.617i			0.985147i
$700$	59.8528	−	25.6901i	0.0855040	−	0.0367002i
$701$	−825.089			−1.17702			−0.588509	−	0.808491i	$-0.700285\pi$
$701$	−825.089			−1.17702			−0.588509	+	0.808491i	$0.700285\pi$
$702$	29.5696	−	44.8703i	0.0421220	−	0.0639178i
$703$		−	125.945i		−	0.179153i
$704$	408.429	−	1103.55i	0.580155	−	1.56754i
$705$	−156.469			−0.221942
$706$	673.060	+	443.548i	0.953342	+	0.628254i
$707$			259.082i			0.366453i
$708$	195.873	+	456.343i	0.276656	+	0.644552i
$709$	−997.019			−1.40623			−0.703117	−	0.711075i	$-0.748209\pi$
$709$	−997.019			−1.40623			−0.703117	+	0.711075i	$0.748209\pi$
$710$	−584.114	+	886.362i	−0.822696	+	1.24840i
$711$		−	33.7993i		−	0.0475377i
$712$	−201.756	+	1126.40i	−0.283365	+	1.58202i
$713$	82.0007			0.115008
$714$	407.006	+	268.218i	0.570037	+	0.375655i
$715$			445.286i			0.622778i
$716$	−143.402	+	61.5513i	−0.200282	+	0.0859656i
$717$	770.564			1.07471
$718$	−227.323	+	344.950i	−0.316605	+	0.480432i
$719$		−	419.611i		−	0.583604i	−0.956479	−	0.291802i	$-0.905745\pi$
$719$		−	419.611i		−	0.583604i	0.956479	−	0.291802i	$-0.0942548\pi$
$720$	−154.866	+	162.968i	−0.215092	+	0.226345i
$721$	639.523			0.886995
$722$	578.837	+	381.455i	0.801714	+	0.528331i
$723$		−	481.160i		−	0.665505i
$724$	−233.702	−	544.477i	−0.322793	−	0.752040i
$725$	−32.6175			−0.0449896
$726$	−413.726	+	627.807i	−0.569870	+	0.864748i
$727$			568.833i			0.782439i	0.920297	+	0.391219i	$0.127947\pi$
$727$			568.833i			0.782439i	−0.920297	+	0.391219i	$0.872053\pi$
$728$	216.449	+	38.7693i	0.297320	+	0.0532546i
$729$	−27.0000			−0.0370370
$730$	526.296	+	346.830i	0.720954	+	0.475110i
$731$		−	1786.67i		−	2.44414i
$732$	422.062	−	181.158i	0.576587	−	0.247484i
$733$	862.917			1.17724			0.588620	−	0.808410i	$-0.299671\pi$
$733$	862.917			1.17724			0.588620	+	0.808410i	$0.299671\pi$
$734$	−368.311	+	558.893i	−0.501787	+	0.761434i
$735$			168.280i			0.228952i
$736$	−34.7188	−	149.488i	−0.0471722	−	0.203108i
$737$	−461.983			−0.626843
$738$	−85.5245	−	56.3608i	−0.115887	−	0.0763697i
$739$			93.9090i			0.127076i	0.997979	+	0.0635379i	$0.0202384\pi$
$739$			93.9090i			0.127076i	−0.997979	+	0.0635379i	$0.979762\pi$
$740$	245.355	+	571.628i	0.331561	+	0.772470i
$741$	−33.9719			−0.0458460
$742$	−48.4175	+	73.4710i	−0.0652527	+	0.0990175i
$743$			1137.80i			1.53136i	0.643222	+	0.765679i	$0.277597\pi$
$743$			1137.80i			1.53136i	−0.643222	+	0.765679i	$0.722403\pi$
$744$	41.7715	−	233.210i	0.0561444	−	0.313454i
$745$	1245.07			1.67124
$746$	−533.509	−	351.584i	−0.715160	−	0.471292i
$747$		−	216.140i		−	0.289344i
$748$	−1788.96	+	767.860i	−2.39165	+	1.02655i
$749$	−411.676			−0.549634
$750$	250.544	−	380.187i	0.334059	−	0.506916i
$751$		−	797.539i		−	1.06197i	−0.847381	−	0.530985i	$-0.821822\pi$
$751$		−	797.539i		−	1.06197i	0.847381	−	0.530985i	$-0.178178\pi$
$752$	−223.706	−	212.585i	−0.297482	−	0.282693i
$753$	−728.332			−0.967240
$754$	−91.9481	−	60.5940i	−0.121947	−	0.0803634i
$755$			91.6147i			0.121344i
$756$	−43.5777	−	101.527i	−0.0576424	−	0.134295i
$757$	−1015.36			−1.34130			−0.670650	−	0.741774i	$-0.733985\pi$
$757$	−1015.36			−1.34130			−0.670650	+	0.741774i	$0.733985\pi$
$758$	572.657	−	868.976i	0.755484	−	1.14641i
$759$			152.726i			0.201220i
$760$	139.899	+	25.0580i	0.184077	+	0.0329710i
$761$	−167.261			−0.219791			−0.109896	−	0.993943i	$-0.535052\pi$
$761$	−167.261			−0.219791			−0.109896	+	0.993943i	$0.535052\pi$
$762$	352.566	+	232.342i	0.462685	+	0.304910i
$763$			687.521i			0.901077i
$764$	−799.466	+	343.149i	−1.04642	+	0.449147i
$765$	371.944			0.486201
$766$	593.951	−	901.288i	0.775393	−	1.17662i
$767$		−	370.641i		−	0.483235i
$768$	−442.829	+	22.5904i	−0.576600	+	0.0294146i
$769$	520.950			0.677438			0.338719	−	0.940888i	$-0.390006\pi$
$769$	520.950			0.677438			0.338719	+	0.940888i	$0.390006\pi$
$770$	764.443	+	503.769i	0.992782	+	0.654245i
$771$		−	374.650i		−	0.485927i
$772$	−18.8068	−	43.8160i	−0.0243611	−	0.0567565i
$773$	816.966			1.05688			0.528439	−	0.848972i	$-0.322778\pi$
$773$	816.966			1.05688			0.528439	+	0.848972i	$0.322778\pi$
$774$	−222.840	+	338.148i	−0.287908	+	0.436884i
$775$			52.3767i			0.0675828i
$776$	−171.593	+	958.005i	−0.221125	+	1.23454i
$777$	−305.706			−0.393444
$778$	178.873	+	117.878i	0.229914	+	0.151514i
$779$			64.7517i			0.0831216i
$780$	154.189	−	66.1813i	0.197678	−	0.0848478i
$781$	2083.54			2.66778
$782$	−139.712	+	212.005i	−0.178660	+	0.271106i
$783$			55.3283i			0.0706620i
$784$	−228.631	+	240.592i	−0.291621	+	0.306877i
$785$	1151.44			1.46681
$786$	468.783	+	308.929i	0.596415	+	0.393039i
$787$		−	256.353i		−	0.325734i	−0.986648	−	0.162867i	$-0.947926\pi$
$787$		−	256.353i		−	0.325734i	0.986648	−	0.162867i	$-0.0520741\pi$
$788$	272.477	+	634.816i	0.345783	+	0.805603i
$789$	−162.804			−0.206342
$790$	58.0726	−	88.1221i	0.0735097	−	0.111547i
$791$			748.444i			0.946200i
$792$	434.353	+	77.7992i	0.548425	+	0.0982313i
$793$	−342.798			−0.432280
$794$	−1137.05	−	749.321i	−1.43206	−	0.943729i
$795$			67.1416i			0.0844549i
$796$	−166.573	+	71.4969i	−0.209263	+	0.0898202i
$797$	388.845			0.487886			0.243943	−	0.969790i	$-0.421559\pi$
$797$	388.845			0.487886			0.243943	+	0.969790i	$0.421559\pi$
$798$	−38.4337	+	58.3211i	−0.0481626	+	0.0730841i
$799$			510.567i			0.639007i
$800$	95.4831	−	22.1761i	0.119354	−	0.0277201i
$801$	−429.123			−0.535734
$802$	−246.447	−	162.409i	−0.307290	−	0.202505i
$803$		−	1237.14i		−	1.54065i
$804$	68.6629	+	159.971i	0.0854017	+	0.198968i
$805$	119.401			0.148324
$806$	−97.3010	+	147.649i	−0.120721	+	0.183187i
$807$			411.378i			0.509763i
$808$	−68.7456	+	383.806i	−0.0850811	+	0.475008i
$809$	−1234.05			−1.52541			−0.762703	−	0.646749i	$-0.776128\pi$
$809$	−1234.05			−1.52541			−0.762703	+	0.646749i	$0.776128\pi$
$810$	−70.3949	−	46.3903i	−0.0869072	−	0.0572720i
$811$		−	285.422i		−	0.351938i	−0.984396	−	0.175969i	$-0.943694\pi$
$811$		−	285.422i		−	0.351938i	0.984396	−	0.175969i	$-0.0563059\pi$
$812$	−208.049	+	89.2992i	−0.256218	+	0.109974i
$813$	−429.024			−0.527705
$814$	671.851	−	1019.50i	0.825370	−	1.25245i
$815$			751.515i			0.922104i
$816$	531.773	+	505.337i	0.651683	+	0.619285i
$817$	256.017			0.313362
$818$	−66.5048	−	43.8268i	−0.0813017	−	0.0535780i
$819$			82.4601i			0.100684i
$820$	−126.144	−	293.890i	−0.153834	−	0.358402i
$821$	−1248.79			−1.52106			−0.760530	−	0.649302i	$-0.775061\pi$
$821$	−1248.79			−1.52106			−0.760530	+	0.649302i	$0.775061\pi$
$822$	476.726	−	723.406i	0.579958	−	0.880056i
$823$		−	1522.07i		−	1.84941i	−0.380678	−	0.924707i	$-0.624310\pi$
$823$		−	1522.07i		−	1.84941i	0.380678	−	0.924707i	$-0.375690\pi$
$824$	947.395	+	169.693i	1.14975	+	0.205938i
$825$	−97.5514			−0.118244
$826$	−636.297	−	419.321i	−0.770335	−	0.507652i
$827$			46.7111i			0.0564826i	0.999601	+	0.0282413i	$0.00899068\pi$
$827$			46.7111i			0.0564826i	−0.999601	+	0.0282413i	$0.991009\pi$
$828$	52.8843	−	22.6991i	0.0638699	−	0.0274144i
$829$	164.896			0.198910			0.0994548	−	0.995042i	$-0.468290\pi$
$829$	164.896			0.198910			0.0994548	+	0.995042i	$0.468290\pi$
$830$	371.363	−	563.524i	0.447425	−	0.678944i
$831$		−	905.919i		−	1.09016i
$832$	310.362	+	114.866i	0.373032	+	0.138061i
$833$	549.105			0.659189
$834$	276.460	+	182.188i	0.331487	+	0.218450i
$835$			1083.42i			1.29750i
$836$	−110.029	−	256.345i	−0.131614	−	0.306633i
$837$	88.8455			0.106148
$838$	−137.345	+	208.414i	−0.163896	+	0.248704i
$839$			1065.12i			1.26952i	0.772711	+	0.634759i	$0.218900\pi$
$839$			1065.12i			1.26952i	−0.772711	+	0.634759i	$0.781100\pi$
$840$	60.8233	−	339.576i	0.0724087	−	0.404258i
$841$	−727.621			−0.865186
$842$	156.593	+	103.195i	0.185978	+	0.122560i
$843$			113.222i			0.134308i
$844$	229.923	−	98.6882i	0.272421	−	0.116929i
$845$	666.308			0.788530
$846$	63.6800	−	96.6309i	0.0752718	−	0.114221i
$847$		−	1153.75i		−	1.36216i
$848$	−91.2211	+	95.9933i	−0.107572	+	0.113200i
$849$	−256.129			−0.301683
$850$	−135.415	−	89.2388i	−0.159312	−	0.104987i
$851$		−	159.239i		−	0.187120i
$852$	−309.669	−	721.464i	−0.363461	−	0.846789i
$853$	−276.744			−0.324436			−0.162218	−	0.986755i	$-0.551865\pi$
$853$	−276.744			−0.324436			−0.162218	+	0.986755i	$0.551865\pi$
$854$	−387.821	+	588.497i	−0.454122	+	0.689106i
$855$			53.2969i			0.0623355i
$856$	−609.860	−	109.235i	−0.712454	−	0.127611i
$857$	−1102.41			−1.28635			−0.643177	−	0.765717i	$-0.722384\pi$
$857$	−1102.41			−1.28635			−0.643177	+	0.765717i	$0.722384\pi$
$858$	−274.996	−	181.223i	−0.320508	−	0.211215i
$859$			911.847i			1.06152i	0.847522	+	0.530761i	$0.178094\pi$
$859$			911.847i			1.06152i	−0.847522	+	0.530761i	$0.821906\pi$
$860$	−1161.99	+	498.751i	−1.35115	+	0.579943i
$861$	157.172			0.182546
$862$	70.2630	−	106.620i	0.0815116	−	0.123689i
$863$			1549.70i			1.79571i	0.440293	+	0.897854i	$0.354875\pi$
$863$			1549.70i			1.79571i	−0.440293	+	0.897854i	$0.645125\pi$
$864$	−37.6168	−	161.966i	−0.0435380	−	0.187461i
$865$	1412.43			1.63287
$866$	1420.18	+	935.899i	1.63993	+	1.08071i
$867$		−	713.108i		−	0.822501i
$868$	143.395	+	334.082i	0.165202	+	0.384887i
$869$	−207.145			−0.238372
$870$	−95.0630	+	144.253i	−0.109268	+	0.165808i
$871$		−	129.928i		−	0.149171i
$872$	−182.429	+	1018.50i	−0.209208	+	1.16800i
$873$	−364.969			−0.418063
$874$	−30.3788	−	20.0197i	−0.0347584	−	0.0229058i
$875$			698.686i			0.798499i
$876$	−428.385	+	183.872i	−0.489024	+	0.209900i
$877$	1411.43			1.60938			0.804691	−	0.593694i	$-0.202331\pi$
$877$	1411.43			1.60938			0.804691	+	0.593694i	$0.202331\pi$
$878$	−42.5937	+	64.6337i	−0.0485122	+	0.0736147i
$879$		−	571.342i		−	0.649991i
$880$	998.780	+	949.127i	1.13498	+	1.07855i
$881$	−64.3455			−0.0730368			−0.0365184	−	0.999333i	$-0.511627\pi$
$881$	−64.3455			−0.0730368			−0.0365184	+	0.999333i	$0.511627\pi$
$882$	−103.925	−	68.4866i	−0.117828	−	0.0776492i
$883$		−	660.270i		−	0.747758i	−0.927477	−	0.373879i	$-0.878028\pi$
$883$		−	660.270i		−	0.747758i	0.927477	−	0.373879i	$-0.121972\pi$
$884$	−215.953	−	503.126i	−0.244290	−	0.569147i
$885$	−581.481			−0.657041
$886$	459.677	−	697.535i	0.518823	−	0.787286i
$887$		−	360.065i		−	0.405936i	−0.979185	−	0.202968i	$-0.934941\pi$
$887$		−	360.065i		−	0.405936i	0.979185	−	0.202968i	$-0.0650588\pi$
$888$	−452.876	−	81.1170i	−0.509995	−	0.0913479i
$889$	−647.926			−0.728826
$890$	−1118.82	−	737.302i	−1.25710	−	0.828429i
$891$			165.474i			0.185718i
$892$	−44.1819	+	18.9638i	−0.0495312	+	0.0212599i
$893$	−73.1605			−0.0819267
$894$	−506.721	+	768.922i	−0.566802	+	0.860092i
$895$		−	182.726i		−	0.204163i
$896$	548.321	−	402.860i	0.611965	−	0.449621i
$897$	−42.9526			−0.0478847
$898$	−381.289	−	251.270i	−0.424598	−	0.279811i
$899$		−	182.062i		−	0.202516i
$900$	14.4987	+	33.7791i	0.0161097	+	0.0375323i
$901$	219.086			0.243159
$902$	−345.417	+	524.152i	−0.382946	+	0.581100i
$903$		−	621.430i		−	0.688184i
$904$	−198.594	+	1108.75i	−0.219684	+	1.22649i
$905$	693.784			0.766612
$906$	−56.5786	−	37.2854i	−0.0624488	−	0.0411539i
$907$			109.275i			0.120480i	0.998184	+	0.0602398i	$0.0191865\pi$
$907$			109.275i			0.120480i	−0.998184	+	0.0602398i	$0.980813\pi$
$908$	−764.098	+	327.968i	−0.841518	+	0.361198i
$909$	−146.218			−0.160856
$910$	−141.680	+	214.992i	−0.155692	+	0.236254i
$911$			83.5231i			0.0916828i	0.998949	+	0.0458414i	$0.0145969\pi$
$911$			83.5231i			0.0916828i	−0.998949	+	0.0458414i	$0.985403\pi$
$912$	−72.4111	+	76.1993i	−0.0793982	+	0.0835518i
$913$	−1324.65			−1.45088
$914$	−16.0210	−	10.5579i	−0.0175284	−	0.0115513i
$915$			537.799i			0.587759i
$916$	220.431	+	513.560i	0.240646	+	0.560655i
$917$	−861.502			−0.939479
$918$	−151.374	+	229.702i	−0.164895	+	0.250220i
$919$		−	135.696i		−	0.147656i	−0.997271	−	0.0738279i	$-0.976478\pi$
$919$		−	135.696i		−	0.147656i	0.997271	−	0.0738279i	$-0.0235215\pi$
$920$	176.882	+	31.6822i	0.192263	+	0.0344372i
$921$	−512.070			−0.555994
$922$	421.672	+	277.882i	0.457344	+	0.301391i
$923$			585.973i			0.634857i
$924$	−622.227	+	267.074i	−0.673405	+	0.289041i
$925$	101.712			0.109958
$926$	−135.075	+	204.969i	−0.145869	+	0.221349i
$927$			360.927i			0.389350i
$928$	−331.900	+	77.0843i	−0.357651	+	0.0830650i
$929$	264.685			0.284914			0.142457	−	0.989801i	$-0.454500\pi$
$929$	264.685			0.284914			0.142457	+	0.989801i	$0.454500\pi$
$930$	231.640	+	152.651i	0.249075	+	0.164141i
$931$			78.6828i			0.0845143i
$932$	−627.251	−	1461.37i	−0.673016	−	1.56799i
$933$	−765.921			−0.820922
$934$	555.111	−	842.350i	0.594337	−	0.901874i
$935$		−	2279.53i		−	2.43799i
$936$	−21.8802	+	122.157i	−0.0233763	+	0.130510i
$937$	9.28183			0.00990591			0.00495295	−	0.999988i	$-0.498423\pi$
$937$	9.28183			0.00990591			0.00495295	+	0.999988i	$0.498423\pi$
$938$	−223.053	−	146.992i	−0.237797	−	0.156708i
$939$		−	70.8949i		−	0.0755004i
$940$	332.055	−	142.525i	0.353250	−	0.151623i
$941$	870.074			0.924627			0.462313	−	0.886717i	$-0.347019\pi$
$941$	870.074			0.924627			0.462313	+	0.886717i	$0.347019\pi$
$942$	−468.615	+	711.098i	−0.497468	+	0.754881i
$943$			81.8692i			0.0868178i
$944$	−831.351	−	790.022i	−0.880669	−	0.836888i
$945$	129.368			0.136897
$946$	2072.40	+	1365.72i	2.19070	+	1.44368i
$947$		−	1737.04i		−	1.83426i	−0.398589	−	0.917130i	$-0.630500\pi$
$947$		−	1737.04i		−	1.83426i	0.398589	−	0.917130i	$-0.369500\pi$
$948$	30.7873	+	71.7280i	0.0324760	+	0.0756625i
$949$	347.934			0.366632
$950$	12.7873	−	19.4040i	0.0134603	−	0.0204253i
$951$			180.075i			0.189354i
$952$	−1108.05	−	198.469i	−1.16392	−	0.208476i
$953$	1375.75			1.44360			0.721800	−	0.692102i	$-0.243315\pi$
$953$	1375.75			1.44360			0.721800	+	0.692102i	$0.243315\pi$
$954$	−41.4648	−	27.3254i	−0.0434641	−	0.0286429i
$955$		−	1018.70i		−	1.06670i
$956$	−1635.27	+	701.894i	−1.71053	+	0.734199i
$957$	339.090			0.354326
$958$	−101.140	+	153.475i	−0.105574	+	0.160204i
$959$			1329.43i			1.38627i
$960$	180.208	−	486.912i	0.187717	−	0.507200i
$961$	668.647			0.695783
$962$	286.723	+	188.951i	0.298049	+	0.196415i
$963$		−	232.337i		−	0.241264i
$964$	438.281	+	1021.11i	0.454648	+	1.05924i
$965$	55.8312			0.0578562
$966$	−48.5939	+	73.7386i	−0.0503042	+	0.0763340i
$967$		−	1299.20i		−	1.34354i	−0.740759	−	0.671771i	$-0.765534\pi$
$967$		−	1299.20i		−	1.34354i	0.740759	−	0.671771i	$-0.234466\pi$
$968$	306.139	−	1709.17i	0.316259	−	1.76567i
$969$	173.910			0.179474
$970$	−951.554	−	627.076i	−0.980983	−	0.646470i
$971$			1428.52i			1.47118i	0.677426	+	0.735591i	$0.263095\pi$
$971$			1428.52i			1.47118i	−0.677426	+	0.735591i	$0.736905\pi$
$972$	57.2987	−	24.5939i	0.0589493	−	0.0253023i
$973$	−508.062			−0.522161
$974$	751.012	−	1139.62i	0.771060	−	1.17004i
$975$		−	27.4353i		−	0.0281388i
$976$	−730.674	+	768.899i	−0.748641	+	0.787806i
$977$	330.344			0.338121			0.169061	−	0.985606i	$-0.445927\pi$
$977$	330.344			0.338121			0.169061	+	0.985606i	$0.445927\pi$
$978$	−464.114	−	305.852i	−0.474554	−	0.312732i
$979$			2629.96i			2.68637i
$980$	−153.283	−	357.119i	−0.156412	−	0.364407i
$981$	−388.016			−0.395531
$982$	−448.305	+	680.279i	−0.456523	+	0.692749i
$983$		−	337.974i		−	0.343819i	−0.985113	−	0.171910i	$-0.945006\pi$
$983$		−	337.974i		−	0.343819i	0.985113	−	0.171910i	$-0.0549937\pi$
$984$	232.836	+	41.7045i	0.236622	+	0.0423826i
$985$	−808.895			−0.821213
$986$	470.704	+	310.195i	0.477388	+	0.314599i
$987$			177.583i			0.179922i
$988$	72.0943	−	30.9445i	0.0729699	−	0.0313203i
$989$	323.696			0.327296
$990$	−284.312	+	431.428i	−0.287183	+	0.435786i
$991$			44.4079i			0.0448112i	0.999749	+	0.0224056i	$0.00713252\pi$
$991$			44.4079i			0.0448112i	−0.999749	+	0.0224056i	$0.992867\pi$
$992$	123.781	+	532.961i	0.124779	+	0.537259i
$993$	382.005			0.384697
$994$	1005.97	+	662.933i	1.01204	+	0.666935i
$995$		−	212.251i		−	0.213317i
$996$	196.878	+	458.686i	0.197669	+	0.460529i
$997$	1513.28			1.51784			0.758919	−	0.651185i	$-0.225728\pi$
$997$	1513.28			1.51784			0.758919	+	0.651185i	$0.225728\pi$
$998$	−71.6388	+	108.708i	−0.0717823	+	0.108926i
$999$		−	172.531i		−	0.172704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.3.f.b.139.34	yes	40
4.3	odd	2	inner	276.3.f.b.139.33	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.3.f.b.139.33	✓	40	4.3	odd	2	inner
276.3.f.b.139.34	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66998 + 1.10052i) q^{2} -1.73205i q^{3} +(1.57770 + 3.67571i) q^{4} -4.68367 q^{5} +(1.90616 - 2.89250i) q^{6} +5.31567i q^{7} +(-1.41048 + 7.87468i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.66998 + 1.10052i) q^{2} -1.73205i q^{3} +(1.57770 + 3.67571i) q^{4} -4.68367 q^{5} +(1.90616 - 2.89250i) q^{6} +5.31567i q^{7} +(-1.41048 + 7.87468i) q^{8} -3.00000 q^{9} +(-7.82165 - 5.15448i) q^{10} +18.3860i q^{11} +(6.36652 - 2.73265i) q^{12} -5.17088 q^{13} +(-5.85002 + 8.87709i) q^{14} +8.11235i q^{15} +(-11.0217 + 11.5983i) q^{16} +26.4710 q^{17} +(-5.00995 - 3.30157i) q^{18} +3.79310i q^{19} +(-7.38941 - 17.2158i) q^{20} +9.20701 q^{21} +(-20.2343 + 30.7044i) q^{22} +4.79583i q^{23} +(13.6393 + 2.44302i) q^{24} -3.06327 q^{25} +(-8.63530 - 5.69068i) q^{26} +5.19615i q^{27} +(-19.5389 + 8.38652i) q^{28} +10.6479 q^{29} +(-8.92783 + 13.5475i) q^{30} -17.0983i q^{31} +(-31.1704 + 7.23936i) q^{32} +31.8456 q^{33} +(44.2061 + 29.1319i) q^{34} -24.8968i q^{35} +(-4.73309 - 11.0271i) q^{36} -33.2036 q^{37} +(-4.17440 + 6.33442i) q^{38} +8.95623i q^{39} +(6.60620 - 36.8824i) q^{40} +17.0709 q^{41} +(15.3756 + 10.1325i) q^{42} -67.4953i q^{43} +(-67.5818 + 29.0076i) q^{44} +14.0510 q^{45} +(-5.27792 + 8.00897i) q^{46} +19.2878i q^{47} +(20.0889 + 19.0902i) q^{48} +20.7436 q^{49} +(-5.11561 - 3.37119i) q^{50} -45.8491i q^{51} +(-8.15809 - 19.0067i) q^{52} +8.27647 q^{53} +(-5.71849 + 8.67750i) q^{54} -86.1141i q^{55} +(-41.8592 - 7.49762i) q^{56} +6.56985 q^{57} +(17.7819 + 11.7183i) q^{58} +71.6785i q^{59} +(-29.8187 + 12.7988i) q^{60} +66.2939 q^{61} +(18.8171 - 28.5539i) q^{62} -15.9470i q^{63} +(-60.0211 - 22.2141i) q^{64} +24.2187 q^{65} +(53.1816 + 35.0468i) q^{66} +25.1268i q^{67} +(41.7632 + 97.2998i) q^{68} +8.30662 q^{69} +(27.3995 - 41.5773i) q^{70} -113.322i q^{71} +(4.23143 - 23.6240i) q^{72} -67.2871 q^{73} +(-55.4495 - 36.5414i) q^{74} +5.30573i q^{75} +(-13.9424 + 5.98437i) q^{76} -97.7341 q^{77} +(-9.85654 + 14.9568i) q^{78} +11.2664i q^{79} +(51.6221 - 54.3227i) q^{80} +9.00000 q^{81} +(28.5082 + 18.7869i) q^{82} +72.0466i q^{83} +(14.5259 + 33.8423i) q^{84} -123.981 q^{85} +(74.2802 - 112.716i) q^{86} -18.4428i q^{87} +(-144.784 - 25.9331i) q^{88} +143.041 q^{89} +(23.4650 + 15.4634i) q^{90} -27.4867i q^{91} +(-17.6281 + 7.56637i) q^{92} -29.6152 q^{93} +(-21.2267 + 32.2103i) q^{94} -17.7656i q^{95} +(12.5389 + 53.9887i) q^{96} +121.656 q^{97} +(34.6416 + 22.8289i) q^{98} -55.1581i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

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