LMFDB - Embedded newform 538.3.c.a.187.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, 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:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.13
Character	$\chi$	$=$	538.187
Dual form			538.3.c.a.351.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(0.991340 + 0.991340i) q^{3} +2.00000i q^{4} -6.41200 q^{5} +1.98268i q^{6} +(-6.33449 + 6.33449i) q^{7} +(-2.00000 + 2.00000i) q^{8} -7.03449i q^{9} +(-6.41200 - 6.41200i) q^{10} +6.36762i q^{11} +(-1.98268 + 1.98268i) q^{12} -22.5179i q^{13} -12.6690 q^{14} +(-6.35647 - 6.35647i) q^{15} -4.00000 q^{16} +(-1.76724 - 1.76724i) q^{17} +(7.03449 - 7.03449i) q^{18} +(21.8646 - 21.8646i) q^{19} -12.8240i q^{20} -12.5593 q^{21} +(-6.36762 + 6.36762i) q^{22} +10.5715 q^{23} -3.96536 q^{24} +16.1137 q^{25} +(22.5179 - 22.5179i) q^{26} +(15.8956 - 15.8956i) q^{27} +(-12.6690 - 12.6690i) q^{28} +(-15.1258 + 15.1258i) q^{29} -12.7129i q^{30} +(1.42750 - 1.42750i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-6.31248 + 6.31248i) q^{33} -3.53448i q^{34} +(40.6167 - 40.6167i) q^{35} +14.0690 q^{36} -51.9512 q^{37} +43.7292 q^{38} +(22.3229 - 22.3229i) q^{39} +(12.8240 - 12.8240i) q^{40} -28.6890 q^{41} +(-12.5593 - 12.5593i) q^{42} -49.5541i q^{43} -12.7352 q^{44} +45.1051i q^{45} +(10.5715 + 10.5715i) q^{46} -57.7822 q^{47} +(-3.96536 - 3.96536i) q^{48} -31.2514i q^{49} +(16.1137 + 16.1137i) q^{50} -3.50387i q^{51} +45.0358 q^{52} +20.7061 q^{53} +31.7913 q^{54} -40.8292i q^{55} -25.3379i q^{56} +43.3506 q^{57} -30.2516 q^{58} +(-38.8717 + 38.8717i) q^{59} +(12.7129 - 12.7129i) q^{60} -110.933 q^{61} +2.85501 q^{62} +(44.5599 + 44.5599i) q^{63} -8.00000i q^{64} +144.385i q^{65} -12.6250 q^{66} -80.9397 q^{67} +(3.53448 - 3.53448i) q^{68} +(10.4800 + 10.4800i) q^{69} +81.2334 q^{70} +(34.1676 - 34.1676i) q^{71} +(14.0690 + 14.0690i) q^{72} +3.81788i q^{73} +(-51.9512 - 51.9512i) q^{74} +(15.9742 + 15.9742i) q^{75} +(43.7292 + 43.7292i) q^{76} +(-40.3356 - 40.3356i) q^{77} +44.6458 q^{78} +62.5004i q^{79} +25.6480 q^{80} -31.7945 q^{81} +(-28.6890 - 28.6890i) q^{82} +(55.4429 - 55.4429i) q^{83} -25.1185i q^{84} +(11.3315 + 11.3315i) q^{85} +(49.5541 - 49.5541i) q^{86} -29.9896 q^{87} +(-12.7352 - 12.7352i) q^{88} -78.4368i q^{89} +(-45.1051 + 45.1051i) q^{90} +(142.639 + 142.639i) q^{91} +21.1431i q^{92} +2.83028 q^{93} +(-57.7822 - 57.7822i) q^{94} +(-140.196 + 140.196i) q^{95} -7.93072i q^{96} -42.6280i q^{97} +(31.2514 - 31.2514i) q^{98} +44.7930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 44 q^{2} + 2 q^{3} + 4 q^{7} - 88 q^{8} - 4 q^{12} + 8 q^{14} + 38 q^{15} - 176 q^{16} - 120 q^{18} + 18 q^{19} - 16 q^{21} + 68 q^{23} - 8 q^{24} + 196 q^{25} + 16 q^{26} - 22 q^{27} + 8 q^{28}+ \cdots - 188 q^{99}+O(q^{100}) $ 44 * q + 44 * q^2 + 2 * q^3 + 4 * q^7 - 88 * q^8 - 4 * q^12 + 8 * q^14 + 38 * q^15 - 176 * q^16 - 120 * q^18 + 18 * q^19 - 16 * q^21 + 68 * q^23 - 8 * q^24 + 196 * q^25 + 16 * q^26 - 22 * q^27 + 8 * q^28 + 18 * q^29 + 88 * q^31 - 176 * q^32 + 96 * q^33 + 10 * q^35 - 240 * q^36 + 180 * q^37 + 36 * q^38 - 54 * q^39 + 144 * q^41 - 16 * q^42 + 68 * q^46 - 156 * q^47 - 8 * q^48 + 196 * q^50 + 32 * q^52 - 188 * q^53 - 44 * q^54 - 88 * q^57 + 36 * q^58 - 98 * q^59 - 76 * q^60 - 244 * q^61 + 176 * q^62 - 10 * q^63 + 192 * q^66 + 220 * q^67 - 70 * q^69 + 20 * q^70 + 156 * q^71 - 240 * q^72 + 180 * q^74 - 102 * q^75 + 36 * q^76 - 28 * q^77 - 108 * q^78 + 392 * q^81 + 144 * q^82 - 250 * q^83 - 342 * q^85 - 44 * q^86 - 60 * q^87 - 192 * q^90 + 66 * q^91 - 536 * q^93 - 156 * q^94 - 472 * q^95 + 404 * q^98 - 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	0.991340	+	0.991340i	0.330447	+	0.330447i	0.852756	−	0.522309i	$-0.174929\pi$
$3$	0.991340	+	0.991340i	0.330447	+	0.330447i	−0.522309	+	0.852756i	$0.674929\pi$
$4$			2.00000i			0.500000i
$5$	−6.41200			−1.28240			−0.641200	−	0.767374i	$-0.721563\pi$
$5$	−6.41200			−1.28240			−0.641200	+	0.767374i	$0.721563\pi$
$6$			1.98268i			0.330447i
$7$	−6.33449	+	6.33449i	−0.904927	+	0.904927i	−0.995857	−	0.0909306i	$-0.971016\pi$
$7$	−6.33449	+	6.33449i	−0.904927	+	0.904927i	0.0909306	+	0.995857i	$0.471016\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	7.03449i		−	0.781610i
$10$	−6.41200	−	6.41200i	−0.641200	−	0.641200i
$11$			6.36762i			0.578875i	0.957197	+	0.289437i	$0.0934682\pi$
$11$			6.36762i			0.578875i	−0.957197	+	0.289437i	$0.906532\pi$
$12$	−1.98268	+	1.98268i	−0.165223	+	0.165223i
$13$		−	22.5179i		−	1.73215i	−0.499917	−	0.866073i	$-0.666636\pi$
$13$		−	22.5179i		−	1.73215i	0.499917	−	0.866073i	$-0.333364\pi$
$14$	−12.6690			−0.904927
$15$	−6.35647	−	6.35647i	−0.423765	−	0.423765i
$16$	−4.00000			−0.250000
$17$	−1.76724	−	1.76724i	−0.103955	−	0.103955i	0.653216	−	0.757171i	$-0.273419\pi$
$17$	−1.76724	−	1.76724i	−0.103955	−	0.103955i	−0.757171	+	0.653216i	$0.773419\pi$
$18$	7.03449	−	7.03449i	0.390805	−	0.390805i
$19$	21.8646	−	21.8646i	1.15077	−	1.15077i	0.164371	−	0.986399i	$-0.447441\pi$
$19$	21.8646	−	21.8646i	1.15077	−	1.15077i	0.986399	−	0.164371i	$-0.0525595\pi$
$20$		−	12.8240i		−	0.641200i
$21$	−12.5593			−0.598060
$22$	−6.36762	+	6.36762i	−0.289437	+	0.289437i
$23$	10.5715			0.459632			0.229816	−	0.973234i	$-0.426188\pi$
$23$	10.5715			0.459632			0.229816	+	0.973234i	$0.426188\pi$
$24$	−3.96536			−0.165223
$25$	16.1137			0.644548
$26$	22.5179	−	22.5179i	0.866073	−	0.866073i
$27$	15.8956	−	15.8956i	0.588727	−	0.588727i
$28$	−12.6690	−	12.6690i	−0.452463	−	0.452463i
$29$	−15.1258	+	15.1258i	−0.521579	+	0.521579i	−0.918048	−	0.396469i	$-0.870235\pi$
$29$	−15.1258	+	15.1258i	−0.521579	+	0.521579i	0.396469	+	0.918048i	$0.370235\pi$
$30$		−	12.7129i		−	0.423765i
$31$	1.42750	−	1.42750i	0.0460485	−	0.0460485i	−0.683708	−	0.729756i	$-0.739634\pi$
$31$	1.42750	−	1.42750i	0.0460485	−	0.0460485i	0.729756	+	0.683708i	$0.239634\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−6.31248	+	6.31248i	−0.191287	+	0.191287i
$34$		−	3.53448i		−	0.103955i
$35$	40.6167	−	40.6167i	1.16048	−	1.16048i
$36$	14.0690			0.390805
$37$	−51.9512			−1.40409			−0.702043	−	0.712135i	$-0.747728\pi$
$37$	−51.9512			−1.40409			−0.702043	+	0.712135i	$0.747728\pi$
$38$	43.7292			1.15077
$39$	22.3229	−	22.3229i	0.572382	−	0.572382i
$40$	12.8240	−	12.8240i	0.320600	−	0.320600i
$41$	−28.6890			−0.699731			−0.349865	−	0.936800i	$-0.613773\pi$
$41$	−28.6890			−0.699731			−0.349865	+	0.936800i	$0.613773\pi$
$42$	−12.5593	−	12.5593i	−0.299030	−	0.299030i
$43$		−	49.5541i		−	1.15242i	−0.817302	−	0.576210i	$-0.804531\pi$
$43$		−	49.5541i		−	1.15242i	0.817302	−	0.576210i	$-0.195469\pi$
$44$	−12.7352			−0.289437
$45$			45.1051i			1.00234i
$46$	10.5715	+	10.5715i	0.229816	+	0.229816i
$47$	−57.7822			−1.22941			−0.614704	−	0.788758i	$-0.710724\pi$
$47$	−57.7822			−1.22941			−0.614704	+	0.788758i	$0.710724\pi$
$48$	−3.96536	−	3.96536i	−0.0826117	−	0.0826117i
$49$		−	31.2514i		−	0.637785i
$50$	16.1137	+	16.1137i	0.322274	+	0.322274i
$51$		−	3.50387i		−	0.0687033i
$52$	45.0358			0.866073
$53$	20.7061			0.390680			0.195340	−	0.980736i	$-0.437419\pi$
$53$	20.7061			0.390680			0.195340	+	0.980736i	$0.437419\pi$
$54$	31.7913			0.588727
$55$		−	40.8292i		−	0.742349i
$56$		−	25.3379i		−	0.452463i
$57$	43.3506			0.760536
$58$	−30.2516			−0.521579
$59$	−38.8717	+	38.8717i	−0.658843	+	0.658843i	−0.955106	−	0.296263i	$-0.904259\pi$
$59$	−38.8717	+	38.8717i	−0.658843	+	0.658843i	0.296263	+	0.955106i	$0.404259\pi$
$60$	12.7129	−	12.7129i	0.211882	−	0.211882i
$61$	−110.933			−1.81857			−0.909284	−	0.416177i	$-0.863370\pi$
$61$	−110.933			−1.81857			−0.909284	+	0.416177i	$0.863370\pi$
$62$	2.85501			0.0460485
$63$	44.5599	+	44.5599i	0.707300	+	0.707300i
$64$		−	8.00000i		−	0.125000i
$65$			144.385i			2.22130i
$66$	−12.6250			−0.191287
$67$	−80.9397			−1.20806			−0.604028	−	0.796963i	$-0.706438\pi$
$67$	−80.9397			−1.20806			−0.604028	+	0.796963i	$0.706438\pi$
$68$	3.53448	−	3.53448i	0.0519776	−	0.0519776i
$69$	10.4800	+	10.4800i	0.151884	+	0.151884i
$70$	81.2334			1.16048
$71$	34.1676	−	34.1676i	0.481234	−	0.481234i	−0.424292	−	0.905526i	$-0.639477\pi$
$71$	34.1676	−	34.1676i	0.481234	−	0.481234i	0.905526	+	0.424292i	$0.139477\pi$
$72$	14.0690	+	14.0690i	0.195402	+	0.195402i
$73$			3.81788i			0.0522998i	0.999658	+	0.0261499i	$0.00832472\pi$
$73$			3.81788i			0.0522998i	−0.999658	+	0.0261499i	$0.991675\pi$
$74$	−51.9512	−	51.9512i	−0.702043	−	0.702043i
$75$	15.9742	+	15.9742i	0.212989	+	0.212989i
$76$	43.7292	+	43.7292i	0.575385	+	0.575385i
$77$	−40.3356	−	40.3356i	−0.523839	−	0.523839i
$78$	44.6458			0.572382
$79$			62.5004i			0.791145i	0.918435	+	0.395572i	$0.129454\pi$
$79$			62.5004i			0.791145i	−0.918435	+	0.395572i	$0.870546\pi$
$80$	25.6480			0.320600
$81$	−31.7945			−0.392524
$82$	−28.6890	−	28.6890i	−0.349865	−	0.349865i
$83$	55.4429	−	55.4429i	0.667987	−	0.667987i	−0.289263	−	0.957250i	$-0.593410\pi$
$83$	55.4429	−	55.4429i	0.667987	−	0.667987i	0.957250	+	0.289263i	$0.0934101\pi$
$84$		−	25.1185i		−	0.299030i
$85$	11.3315	+	11.3315i	0.133312	+	0.133312i
$86$	49.5541	−	49.5541i	0.576210	−	0.576210i
$87$	−29.9896			−0.344708
$88$	−12.7352	−	12.7352i	−0.144719	−	0.144719i
$89$		−	78.4368i		−	0.881312i	−0.897676	−	0.440656i	$-0.854746\pi$
$89$		−	78.4368i		−	0.881312i	0.897676	−	0.440656i	$-0.145254\pi$
$90$	−45.1051	+	45.1051i	−0.501168	+	0.501168i
$91$	142.639	+	142.639i	1.56747	+	1.56747i
$92$			21.1431i			0.229816i
$93$	2.83028			0.0304331
$94$	−57.7822	−	57.7822i	−0.614704	−	0.614704i
$95$	−140.196	+	140.196i	−1.47575	+	1.47575i
$96$		−	7.93072i		−	0.0826117i
$97$		−	42.6280i		−	0.439464i	−0.975560	−	0.219732i	$-0.929482\pi$
$97$		−	42.6280i		−	0.439464i	0.975560	−	0.219732i	$-0.0705183\pi$
$98$	31.2514	−	31.2514i	0.318892	−	0.318892i
$99$	44.7930			0.452454
$100$			32.2274i			0.322274i
$101$	−27.5749	−	27.5749i	−0.273019	−	0.273019i	0.557295	−	0.830314i	$-0.311839\pi$
$101$	−27.5749	−	27.5749i	−0.273019	−	0.273019i	−0.830314	+	0.557295i	$0.811839\pi$
$102$	3.50387	−	3.50387i	0.0343517	−	0.0343517i
$103$		−	3.93602i		−	0.0382138i	−0.999817	−	0.0191069i	$-0.993918\pi$
$103$		−	3.93602i		−	0.0382138i	0.999817	−	0.0191069i	$-0.00608229\pi$
$104$	45.0358	+	45.0358i	0.433037	+	0.433037i
$105$	80.5299			0.766952
$106$	20.7061	+	20.7061i	0.195340	+	0.195340i
$107$	57.6823	−	57.6823i	0.539087	−	0.539087i	−0.384174	−	0.923261i	$-0.625514\pi$
$107$	57.6823	−	57.6823i	0.539087	−	0.539087i	0.923261	+	0.384174i	$0.125514\pi$
$108$	31.7913	+	31.7913i	0.294364	+	0.294364i
$109$	−2.94540	+	2.94540i	−0.0270220	+	0.0270220i	−0.720489	−	0.693467i	$-0.756082\pi$
$109$	−2.94540	+	2.94540i	−0.0270220	+	0.0270220i	0.693467	+	0.720489i	$0.256082\pi$
$110$	40.8292	−	40.8292i	0.371174	−	0.371174i
$111$	−51.5013	−	51.5013i	−0.463975	−	0.463975i
$112$	25.3379	−	25.3379i	0.226232	−	0.226232i
$113$	111.910	−	111.910i	0.990353	−	0.990353i	−0.00960126	−	0.999954i	$-0.503056\pi$
$113$	111.910	−	111.910i	0.990353	−	0.990353i	0.999954	+	0.00960126i	$0.00305622\pi$
$114$	43.3506	+	43.3506i	0.380268	+	0.380268i
$115$	−67.7847			−0.589432
$116$	−30.2516	−	30.2516i	−0.260789	−	0.260789i
$117$	−158.402			−1.35386
$118$	−77.7435			−0.658843
$119$	22.3891			0.188144
$120$	25.4259			0.211882
$121$	80.4534			0.664904
$122$	−110.933	−	110.933i	−0.909284	−	0.909284i
$123$	−28.4405	−	28.4405i	−0.231224	−	0.231224i
$124$	2.85501	+	2.85501i	0.0230242	+	0.0230242i
$125$	56.9789			0.455831
$126$			89.1198i			0.707300i
$127$			154.068i			1.21313i	0.795034	+	0.606565i	$0.207453\pi$
$127$			154.068i			1.21313i	−0.795034	+	0.606565i	$0.792547\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	49.1249	−	49.1249i	0.380813	−	0.380813i
$130$	−144.385	+	144.385i	−1.11065	+	1.11065i
$131$	−150.928			−1.15212			−0.576060	−	0.817407i	$-0.695411\pi$
$131$	−150.928			−1.15212			−0.576060	+	0.817407i	$0.695411\pi$
$132$	−12.6250	−	12.6250i	−0.0956436	−	0.0956436i
$133$			277.002i			2.08272i
$134$	−80.9397	−	80.9397i	−0.604028	−	0.604028i
$135$	−101.923	+	101.923i	−0.754983	+	0.754983i
$136$	7.06896			0.0519776
$137$	−25.2624	+	25.2624i	−0.184397	+	0.184397i	−0.793269	−	0.608872i	$-0.791622\pi$
$137$	−25.2624	+	25.2624i	−0.184397	+	0.184397i	0.608872	+	0.793269i	$0.291622\pi$
$138$			20.9600i			0.151884i
$139$	−90.9388	−	90.9388i	−0.654236	−	0.654236i	0.299774	−	0.954010i	$-0.403089\pi$
$139$	−90.9388	−	90.9388i	−0.654236	−	0.654236i	−0.954010	+	0.299774i	$0.903089\pi$
$140$	81.2334	+	81.2334i	0.580239	+	0.580239i
$141$	−57.2818	−	57.2818i	−0.406254	−	0.406254i
$142$	68.3352			0.481234
$143$	143.386			1.00270
$144$			28.1380i			0.195402i
$145$	96.9865	−	96.9865i	0.668872	−	0.668872i
$146$	−3.81788	+	3.81788i	−0.0261499	+	0.0261499i
$147$	30.9808	−	30.9808i	0.210754	−	0.210754i
$148$		−	103.902i		−	0.702043i
$149$			46.1538i			0.309757i	0.987934	+	0.154878i	$0.0494986\pi$
$149$			46.1538i			0.309757i	−0.987934	+	0.154878i	$0.950501\pi$
$150$			31.9483i			0.212989i
$151$		−	142.489i		−	0.943634i	−0.881696	−	0.471817i	$-0.843598\pi$
$151$		−	142.489i		−	0.943634i	0.881696	−	0.471817i	$-0.156402\pi$
$152$			87.4585i			0.575385i
$153$	−12.4316	+	12.4316i	−0.0812524	+	0.0812524i
$154$		−	80.6712i		−	0.523839i
$155$	−9.15314	+	9.15314i	−0.0590525	+	0.0590525i
$156$	44.6458	+	44.6458i	0.286191	+	0.286191i
$157$	−73.3568	−	73.3568i	−0.467241	−	0.467241i	0.433779	−	0.901019i	$-0.357180\pi$
$157$	−73.3568	−	73.3568i	−0.467241	−	0.467241i	−0.901019	+	0.433779i	$0.857180\pi$
$158$	−62.5004	+	62.5004i	−0.395572	+	0.395572i
$159$	20.5267	+	20.5267i	0.129099	+	0.129099i
$160$	25.6480	+	25.6480i	0.160300	+	0.160300i
$161$	−66.9653	+	66.9653i	−0.415933	+	0.415933i
$162$	−31.7945	−	31.7945i	−0.196262	−	0.196262i
$163$	−65.1109	+	65.1109i	−0.399453	+	0.399453i	−0.878040	−	0.478587i	$-0.841149\pi$
$163$	−65.1109	+	65.1109i	−0.399453	+	0.399453i	0.478587	+	0.878040i	$0.341149\pi$
$164$		−	57.3779i		−	0.349865i
$165$	40.4756	−	40.4756i	0.245307	−	0.245307i
$166$	110.886			0.667987
$167$	62.5088	+	62.5088i	0.374304	+	0.374304i	0.869042	−	0.494738i	$-0.164736\pi$
$167$	62.5088	+	62.5088i	0.374304	+	0.374304i	−0.494738	+	0.869042i	$0.664736\pi$
$168$	25.1185	−	25.1185i	0.149515	−	0.149515i
$169$	−338.056			−2.00033
$170$			22.6631i			0.133312i
$171$	−153.806	−	153.806i	−0.899453	−	0.899453i
$172$	99.1081			0.576210
$173$	325.926			1.88396			0.941982	−	0.335662i	$-0.108960\pi$
$173$	325.926			1.88396			0.941982	+	0.335662i	$0.108960\pi$
$174$	−29.9896	−	29.9896i	−0.172354	−	0.172354i
$175$	−102.072	+	102.072i	−0.583269	+	0.583269i
$176$		−	25.4705i		−	0.144719i
$177$	−77.0702			−0.435425
$178$	78.4368	−	78.4368i	0.440656	−	0.440656i
$179$	120.070	+	120.070i	0.670784	+	0.670784i	0.957897	−	0.287113i	$-0.0926955\pi$
$179$	120.070	+	120.070i	0.670784	+	0.670784i	−0.287113	+	0.957897i	$0.592696\pi$
$180$	−90.2103			−0.501168
$181$	24.9854	−	24.9854i	0.138041	−	0.138041i	−0.634710	−	0.772751i	$-0.718880\pi$
$181$	24.9854	−	24.9854i	0.138041	−	0.138041i	0.772751	+	0.634710i	$0.218880\pi$
$182$			285.279i			1.56747i
$183$	−109.972	−	109.972i	−0.600940	−	0.600940i
$184$	−21.1431	+	21.1431i	−0.114908	+	0.114908i
$185$	333.111			1.80060
$186$	2.83028	+	2.83028i	0.0152166	+	0.0152166i
$187$	11.2531	−	11.2531i	0.0601771	−	0.0601771i
$188$		−	115.564i		−	0.614704i
$189$			201.381i			1.06551i
$190$	−280.392			−1.47575
$191$			280.960i			1.47099i	0.677528	+	0.735497i	$0.263051\pi$
$191$			280.960i			1.47099i	−0.677528	+	0.735497i	$0.736949\pi$
$192$	7.93072	−	7.93072i	0.0413058	−	0.0413058i
$193$	−252.488	+	252.488i	−1.30823	+	1.30823i	−0.385531	+	0.922695i	$0.625982\pi$
$193$	−252.488	+	252.488i	−1.30823	+	1.30823i	−0.922695	+	0.385531i	$0.874018\pi$
$194$	42.6280	−	42.6280i	0.219732	−	0.219732i
$195$	−143.134	+	143.134i	−0.734022	+	0.734022i
$196$	62.5029			0.318892
$197$	−19.9644	+	19.9644i	−0.101342	+	0.101342i	−0.755960	−	0.654618i	$-0.772830\pi$
$197$	−19.9644	+	19.9644i	−0.101342	+	0.101342i	0.654618	+	0.755960i	$0.272830\pi$
$198$	44.7930	+	44.7930i	0.226227	+	0.226227i
$199$			117.670i			0.591305i	0.955296	+	0.295652i	$0.0955370\pi$
$199$			117.670i			0.591305i	−0.955296	+	0.295652i	$0.904463\pi$
$200$	−32.2274	+	32.2274i	−0.161137	+	0.161137i
$201$	−80.2388	−	80.2388i	−0.399198	−	0.399198i
$202$		−	55.1498i		−	0.273019i
$203$		−	191.628i		−	0.943981i
$204$	7.00774			0.0343517
$205$	183.954			0.897334
$206$	3.93602	−	3.93602i	0.0191069	−	0.0191069i
$207$		−	74.3654i		−	0.359253i
$208$			90.0716i			0.433037i
$209$	139.226	+	139.226i	0.666152	+	0.666152i
$210$	80.5299	+	80.5299i	0.383476	+	0.383476i
$211$			224.155i			1.06235i	0.847263	+	0.531173i	$0.178249\pi$
$211$			224.155i			1.06235i	−0.847263	+	0.531173i	$0.821751\pi$
$212$			41.4121i			0.195340i
$213$	67.7434			0.318044
$214$	115.365			0.539087
$215$			317.741i			1.47786i
$216$			63.5825i			0.294364i
$217$			18.0850i			0.0833410i
$218$	−5.89081			−0.0270220
$219$	−3.78482	+	3.78482i	−0.0172823	+	0.0172823i
$220$	81.6584			0.371174
$221$	−39.7945	+	39.7945i	−0.180066	+	0.180066i
$222$		−	103.003i		−	0.463975i
$223$	158.366	−	158.366i	0.710163	−	0.710163i	−0.256406	−	0.966569i	$-0.582538\pi$
$223$	158.366	−	158.366i	0.710163	−	0.710163i	0.966569	+	0.256406i	$0.0825384\pi$
$224$	50.6759			0.226232
$225$		−	113.352i		−	0.503785i
$226$	223.820			0.990353
$227$	101.337	−	101.337i	0.446417	−	0.446417i	−0.447745	−	0.894162i	$-0.647773\pi$
$227$	101.337	−	101.337i	0.446417	−	0.446417i	0.894162	+	0.447745i	$0.147773\pi$
$228$			86.7011i			0.380268i
$229$	−98.9733	−	98.9733i	−0.432198	−	0.432198i	0.457178	−	0.889375i	$-0.348860\pi$
$229$	−98.9733	−	98.9733i	−0.432198	−	0.432198i	−0.889375	+	0.457178i	$0.848860\pi$
$230$	−67.7847	−	67.7847i	−0.294716	−	0.294716i
$231$		−	79.9726i		−	0.346202i
$232$		−	60.5031i		−	0.260789i
$233$		−	226.083i		−	0.970315i	−0.874427	−	0.485157i	$-0.838762\pi$
$233$		−	226.083i		−	0.970315i	0.874427	−	0.485157i	$-0.161238\pi$
$234$	−158.402	−	158.402i	−0.676932	−	0.676932i
$235$	370.499			1.57659
$236$	−77.7435	−	77.7435i	−0.329421	−	0.329421i
$237$	−61.9592	+	61.9592i	−0.261431	+	0.261431i
$238$	22.3891	+	22.3891i	0.0940719	+	0.0940719i
$239$	−83.1841			−0.348051			−0.174025	−	0.984741i	$-0.555677\pi$
$239$	−83.1841			−0.348051			−0.174025	+	0.984741i	$0.555677\pi$
$240$	25.4259	+	25.4259i	0.105941	+	0.105941i
$241$	−179.153	+	179.153i	−0.743373	+	0.743373i	−0.973225	−	0.229853i	$-0.926175\pi$
$241$	−179.153	+	179.153i	−0.743373	+	0.743373i	0.229853	+	0.973225i	$0.426175\pi$
$242$	80.4534	+	80.4534i	0.332452	+	0.332452i
$243$	−174.580	−	174.580i	−0.718435	−	0.718435i
$244$		−	221.865i		−	0.909284i
$245$			200.384i			0.817895i
$246$		−	56.8810i		−	0.231224i
$247$	−492.346	−	492.346i	−1.99330	−	1.99330i
$248$			5.71001i			0.0230242i
$249$	109.926			0.441468
$250$	56.9789	+	56.9789i	0.227916	+	0.227916i
$251$	−4.04762	−	4.04762i	−0.0161260	−	0.0161260i	0.698998	−	0.715124i	$-0.253630\pi$
$251$	−4.04762	−	4.04762i	−0.0161260	−	0.0161260i	−0.715124	+	0.698998i	$0.753630\pi$
$252$	−89.1198	+	89.1198i	−0.353650	+	0.353650i
$253$			67.3156i			0.266069i
$254$	−154.068	+	154.068i	−0.606565	+	0.606565i
$255$			22.4668i			0.0881051i
$256$	16.0000			0.0625000
$257$	252.824	+	252.824i	0.983752	+	0.983752i	0.999870	−	0.0161178i	$-0.00513067\pi$
$257$	252.824	+	252.824i	0.983752	+	0.983752i	−0.0161178	+	0.999870i	$0.505131\pi$
$258$	98.2499			0.380813
$259$	329.084	−	329.084i	1.27059	−	1.27059i
$260$	−288.769			−1.11065
$261$	106.402	+	106.402i	0.407671	+	0.407671i
$262$	−150.928	−	150.928i	−0.576060	−	0.576060i
$263$	−467.712			−1.77837			−0.889187	−	0.457543i	$-0.848729\pi$
$263$	−467.712			−1.77837			−0.889187	+	0.457543i	$0.848729\pi$
$264$		−	25.2499i		−	0.0956436i
$265$	−132.767			−0.501008
$266$	−277.002	+	277.002i	−1.04136	+	1.04136i
$267$	77.7575	−	77.7575i	0.291227	−	0.291227i
$268$		−	161.879i		−	0.604028i
$269$	−219.678	+	155.251i	−0.816645	+	0.577140i
$269$	−219.678	+	155.251i	−0.816645	+	0.577140i
$270$	−203.845			−0.754983
$271$	−262.448	−	262.448i	−0.968443	−	0.968443i	0.0310742	−	0.999517i	$-0.490107\pi$
$271$	−262.448	−	262.448i	−0.968443	−	0.968443i	−0.999517	+	0.0310742i	$0.990107\pi$
$272$	7.06896	+	7.06896i	0.0259888	+	0.0259888i
$273$			282.808i			1.03593i
$274$	−50.5249			−0.184397
$275$			102.606i			0.373113i
$276$	−20.9600	+	20.9600i	−0.0759420	+	0.0759420i
$277$	59.3242	−	59.3242i	0.214167	−	0.214167i	−0.591868	−	0.806035i	$-0.701609\pi$
$277$	59.3242	−	59.3242i	0.214167	−	0.214167i	0.806035	+	0.591868i	$0.201609\pi$
$278$		−	181.878i		−	0.654236i
$279$	−10.0418	−	10.0418i	−0.0359920	−	0.0359920i
$280$			162.467i			0.580239i
$281$	−277.019	+	277.019i	−0.985832	+	0.985832i	−0.999901	−	0.0140687i	$-0.995522\pi$
$281$	−277.019	+	277.019i	−0.985832	+	0.985832i	0.0140687	+	0.999901i	$0.495522\pi$
$282$		−	114.564i		−	0.406254i
$283$	128.710			0.454806			0.227403	−	0.973801i	$-0.426976\pi$
$283$	128.710			0.454806			0.227403	+	0.973801i	$0.426976\pi$
$284$	68.3352	+	68.3352i	0.240617	+	0.240617i
$285$	−277.964			−0.975311
$286$	143.386	+	143.386i	0.501348	+	0.501348i
$287$	181.730	−	181.730i	0.633205	−	0.633205i
$288$	−28.1380	+	28.1380i	−0.0977012	+	0.0977012i
$289$		−	282.754i		−	0.978387i
$290$	193.973			0.668872
$291$	42.2588	−	42.2588i	0.145219	−	0.145219i
$292$	−7.63577			−0.0261499
$293$	−133.570			−0.455872			−0.227936	−	0.973676i	$-0.573198\pi$
$293$	−133.570			−0.455872			−0.227936	+	0.973676i	$0.573198\pi$
$294$	61.9616			0.210754
$295$	249.245	−	249.245i	0.844900	−	0.844900i
$296$	103.902	−	103.902i	0.351021	−	0.351021i
$297$	101.217	+	101.217i	0.340799	+	0.340799i
$298$	−46.1538	+	46.1538i	−0.154878	+	0.154878i
$299$		−	238.049i		−	0.796150i
$300$	−31.9483	+	31.9483i	−0.106494	+	0.106494i
$301$	313.900	+	313.900i	1.04286	+	1.04286i
$302$	142.489	−	142.489i	0.471817	−	0.471817i
$303$		−	54.6722i		−	0.180436i
$304$	−87.4585	+	87.4585i	−0.287692	+	0.287692i
$305$	711.300			2.33213
$306$	−24.8632			−0.0812524
$307$	442.521			1.44144			0.720718	−	0.693229i	$-0.243812\pi$
$307$	442.521			1.44144			0.720718	+	0.693229i	$0.243812\pi$
$308$	80.6712	−	80.6712i	0.261920	−	0.261920i
$309$	3.90194	−	3.90194i	0.0126276	−	0.0126276i
$310$	−18.3063			−0.0590525
$311$	−89.4245	−	89.4245i	−0.287539	−	0.287539i	0.548568	−	0.836106i	$-0.315173\pi$
$311$	−89.4245	−	89.4245i	−0.287539	−	0.287539i	−0.836106	+	0.548568i	$0.815173\pi$
$312$			89.2916i			0.286191i
$313$	572.254			1.82829			0.914143	−	0.405392i	$-0.132865\pi$
$313$	572.254			1.82829			0.914143	+	0.405392i	$0.132865\pi$
$314$		−	146.714i		−	0.467241i
$315$	−285.718	−	285.718i	−0.907041	−	0.907041i
$316$	−125.001			−0.395572
$317$	272.380	+	272.380i	0.859242	+	0.859242i	0.991249	−	0.132007i	$-0.0421421\pi$
$317$	272.380	+	272.380i	0.859242	+	0.859242i	−0.132007	+	0.991249i	$0.542142\pi$
$318$			41.0535i			0.129099i
$319$	−96.3153	−	96.3153i	−0.301929	−	0.301929i
$320$			51.2960i			0.160300i
$321$	114.365			0.356279
$322$	−133.931			−0.415933
$323$	−77.2800			−0.239257
$324$		−	63.5889i		−	0.196262i
$325$		−	362.847i		−	1.11645i
$326$	−130.222			−0.399453
$327$	−5.83979			−0.0178587
$328$	57.3779	−	57.3779i	0.174933	−	0.174933i
$329$	366.020	−	366.020i	1.11252	−	1.11252i
$330$	80.9512			0.245307
$331$	−288.089			−0.870360			−0.435180	−	0.900343i	$-0.643315\pi$
$331$	−288.089			−0.870360			−0.435180	+	0.900343i	$0.643315\pi$
$332$	110.886	+	110.886i	0.333994	+	0.333994i
$333$			365.450i			1.09745i
$334$			125.018i			0.374304i
$335$	518.985			1.54921
$336$	50.2370			0.149515
$337$	182.866	−	182.866i	0.542629	−	0.542629i	−0.381670	−	0.924299i	$-0.624651\pi$
$337$	182.866	−	182.866i	0.542629	−	0.542629i	0.924299	+	0.381670i	$0.124651\pi$
$338$	−338.056	−	338.056i	−1.00017	−	1.00017i
$339$	221.881			0.654517
$340$	−22.6631	+	22.6631i	−0.0666561	+	0.0666561i
$341$	9.08980	+	9.08980i	0.0266563	+	0.0266563i
$342$		−	307.613i		−	0.899453i
$343$	−112.428	−	112.428i	−0.327778	−	0.327778i
$344$	99.1081	+	99.1081i	0.288105	+	0.288105i
$345$	−67.1977	−	67.1977i	−0.194776	−	0.194776i
$346$	325.926	+	325.926i	0.941982	+	0.941982i
$347$	373.550			1.07651			0.538257	−	0.842781i	$-0.319083\pi$
$347$	373.550			1.07651			0.538257	+	0.842781i	$0.319083\pi$
$348$		−	59.9792i		−	0.172354i
$349$	−160.856			−0.460906			−0.230453	−	0.973083i	$-0.574021\pi$
$349$	−160.856			−0.460906			−0.230453	+	0.973083i	$0.574021\pi$
$350$	−204.144			−0.583269
$351$	−357.936	−	357.936i	−1.01976	−	1.01976i
$352$	25.4705	−	25.4705i	0.0723593	−	0.0723593i
$353$			378.801i			1.07309i	0.843871	+	0.536546i	$0.180271\pi$
$353$			378.801i			1.07309i	−0.843871	+	0.536546i	$0.819729\pi$
$354$	−77.0702	−	77.0702i	−0.217712	−	0.217712i
$355$	−219.083	+	219.083i	−0.617134	+	0.617134i
$356$	156.874			0.440656
$357$	22.1952	+	22.1952i	0.0621715	+	0.0621715i
$358$			240.141i			0.670784i
$359$	−355.250	+	355.250i	−0.989554	+	0.989554i	−0.999946	−	0.0103919i	$-0.996692\pi$
$359$	−355.250	+	355.250i	−0.989554	+	0.989554i	0.0103919	+	0.999946i	$0.496692\pi$
$360$	−90.2103	−	90.2103i	−0.250584	−	0.250584i
$361$		−	595.124i		−	1.64854i
$362$	49.9708			0.138041
$363$	79.7567	+	79.7567i	0.219715	+	0.219715i
$364$	−285.279	+	285.279i	−0.783733	+	0.783733i
$365$		−	24.4803i		−	0.0670692i
$366$		−	219.944i		−	0.600940i
$367$	335.691	−	335.691i	0.914690	−	0.914690i	−0.0819464	−	0.996637i	$-0.526114\pi$
$367$	335.691	−	335.691i	0.914690	−	0.914690i	0.996637	+	0.0819464i	$0.0261136\pi$
$368$	−42.2862			−0.114908
$369$			201.812i			0.546917i
$370$	333.111	+	333.111i	0.900299	+	0.900299i
$371$	−131.162	+	131.162i	−0.353537	+	0.353537i
$372$			5.66056i			0.0152166i
$373$	−493.944	−	493.944i	−1.32425	−	1.32425i	−0.910303	−	0.413944i	$-0.864151\pi$
$373$	−493.944	−	493.944i	−1.32425	−	1.32425i	−0.413944	−	0.910303i	$-0.635849\pi$
$374$	22.5062			0.0601771
$375$	56.4854	+	56.4854i	0.150628	+	0.150628i
$376$	115.564	−	115.564i	0.307352	−	0.307352i
$377$	340.601	+	340.601i	0.903451	+	0.903451i
$378$	−201.381	+	201.381i	−0.532755	+	0.532755i
$379$	438.979	−	438.979i	1.15825	−	1.15825i	0.173404	−	0.984851i	$-0.444523\pi$
$379$	438.979	−	438.979i	1.15825	−	1.15825i	0.984851	−	0.173404i	$-0.0554767\pi$
$380$	−280.392	−	280.392i	−0.737873	−	0.737873i
$381$	−152.733	+	152.733i	−0.400875	+	0.400875i
$382$	−280.960	+	280.960i	−0.735497	+	0.735497i
$383$	11.3128	+	11.3128i	0.0295373	+	0.0295373i	0.721721	−	0.692184i	$-0.243351\pi$
$383$	11.3128	+	11.3128i	0.0295373	+	0.0295373i	−0.692184	+	0.721721i	$0.743351\pi$
$384$	15.8614			0.0413058
$385$	258.632	+	258.632i	0.671771	+	0.671771i
$386$	−504.975			−1.30823
$387$	−348.588			−0.900743
$388$	85.2560			0.219732
$389$	645.474			1.65932			0.829659	−	0.558271i	$-0.188535\pi$
$389$	645.474			1.65932			0.829659	+	0.558271i	$0.188535\pi$
$390$	−286.269			−0.734022
$391$	−18.6824	−	18.6824i	−0.0477812	−	0.0477812i
$392$	62.5029	+	62.5029i	0.159446	+	0.159446i
$393$	−149.621	−	149.621i	−0.380714	−	0.380714i
$394$	−39.9288			−0.101342
$395$		−	400.753i		−	1.01456i
$396$			89.5859i			0.226227i
$397$	−121.715	+	121.715i	−0.306588	+	0.306588i	−0.843585	−	0.536996i	$-0.819559\pi$
$397$	−121.715	+	121.715i	−0.306588	+	0.306588i	0.536996	+	0.843585i	$0.319559\pi$
$398$	−117.670	+	117.670i	−0.295652	+	0.295652i
$399$	−274.604	+	274.604i	−0.688229	+	0.688229i
$400$	−64.4548			−0.161137
$401$	−442.617	−	442.617i	−1.10378	−	1.10378i	−0.993950	−	0.109832i	$-0.964969\pi$
$401$	−442.617	−	442.617i	−1.10378	−	1.10378i	−0.109832	−	0.993950i	$-0.535031\pi$
$402$		−	160.478i		−	0.399198i
$403$	−32.1444	−	32.1444i	−0.0797627	−	0.0797627i
$404$	55.1498	−	55.1498i	0.136509	−	0.136509i
$405$	203.866			0.503373
$406$	191.628	−	191.628i	0.471991	−	0.471991i
$407$		−	330.805i		−	0.812790i
$408$	7.00774	+	7.00774i	0.0171758	+	0.0171758i
$409$	−140.975	−	140.975i	−0.344681	−	0.344681i	0.513443	−	0.858124i	$-0.328370\pi$
$409$	−140.975	−	140.975i	−0.344681	−	0.344681i	−0.858124	+	0.513443i	$0.828370\pi$
$410$	183.954	+	183.954i	0.448667	+	0.448667i
$411$	−50.0873			−0.121867
$412$	7.87205			0.0191069
$413$		−	492.465i		−	1.19241i
$414$	74.3654	−	74.3654i	0.179627	−	0.179627i
$415$	−355.500	+	355.500i	−0.856627	+	0.856627i
$416$	−90.0716	+	90.0716i	−0.216518	+	0.216518i
$417$		−	180.302i		−	0.432380i
$418$			278.451i			0.666152i
$419$		−	13.3616i		−	0.0318893i	−0.999873	−	0.0159447i	$-0.994924\pi$
$419$		−	13.3616i		−	0.0318893i	0.999873	−	0.0159447i	$-0.00507556\pi$
$420$			161.060i			0.383476i
$421$		−	737.559i		−	1.75192i	−0.482382	−	0.875961i	$-0.660228\pi$
$421$		−	737.559i		−	1.75192i	0.482382	−	0.875961i	$-0.339772\pi$
$422$	−224.155	+	224.155i	−0.531173	+	0.531173i
$423$			406.468i			0.960917i
$424$	−41.4121	+	41.4121i	−0.0976701	+	0.0976701i
$425$	−28.4768	−	28.4768i	−0.0670042	−	0.0670042i
$426$	67.7434	+	67.7434i	0.159022	+	0.159022i
$427$	702.701	−	702.701i	1.64567	−	1.64567i
$428$	115.365	+	115.365i	0.269543	+	0.269543i
$429$	142.144	+	142.144i	0.331338	+	0.331338i
$430$	−317.741	+	317.741i	−0.738931	+	0.738931i
$431$	−203.971	−	203.971i	−0.473250	−	0.473250i	0.429715	−	0.902965i	$-0.358614\pi$
$431$	−203.971	−	203.971i	−0.473250	−	0.473250i	−0.902965	+	0.429715i	$0.858614\pi$
$432$	−63.5825	+	63.5825i	−0.147182	+	0.147182i
$433$			274.696i			0.634401i	0.948359	+	0.317200i	$0.102743\pi$
$433$			274.696i			0.634401i	−0.948359	+	0.317200i	$0.897257\pi$
$434$	−18.0850	+	18.0850i	−0.0416705	+	0.0416705i
$435$	192.293			0.442053
$436$	−5.89081	−	5.89081i	−0.0135110	−	0.0135110i
$437$	231.143	−	231.143i	0.528931	−	0.528931i
$438$	−7.56964			−0.0172823
$439$			117.275i			0.267141i	0.991039	+	0.133571i	$0.0426443\pi$
$439$			117.275i			0.267141i	−0.991039	+	0.133571i	$0.957356\pi$
$440$	81.6584	+	81.6584i	0.185587	+	0.185587i
$441$	−219.838			−0.498499
$442$	−79.5890			−0.180066
$443$	123.642	+	123.642i	0.279102	+	0.279102i	0.832751	−	0.553648i	$-0.186765\pi$
$443$	123.642	+	123.642i	0.279102	+	0.279102i	−0.553648	+	0.832751i	$0.686765\pi$
$444$	103.003	−	103.003i	0.231988	−	0.231988i
$445$			502.936i			1.13019i
$446$	316.733			0.710163
$447$	−45.7541	+	45.7541i	−0.102358	+	0.102358i
$448$	50.6759	+	50.6759i	0.113116	+	0.113116i
$449$	−156.476			−0.348499			−0.174250	−	0.984701i	$-0.555750\pi$
$449$	−156.476			−0.348499			−0.174250	+	0.984701i	$0.555750\pi$
$450$	113.352	−	113.352i	0.251893	−	0.251893i
$451$		−	182.680i		−	0.405056i
$452$	223.820	+	223.820i	0.495176	+	0.495176i
$453$	141.255	−	141.255i	0.311821	−	0.311821i
$454$	202.673			0.446417
$455$	−914.603	−	914.603i	−2.01012	−	2.01012i
$456$	−86.7011	+	86.7011i	−0.190134	+	0.190134i
$457$			285.962i			0.625738i	0.949796	+	0.312869i	$0.101290\pi$
$457$			285.962i			0.625738i	−0.949796	+	0.312869i	$0.898710\pi$
$458$		−	197.947i		−	0.432198i
$459$	−56.1828			−0.122403
$460$		−	135.569i		−	0.294716i
$461$	285.686	−	285.686i	0.619709	−	0.619709i	−0.325748	−	0.945457i	$-0.605616\pi$
$461$	285.686	−	285.686i	0.619709	−	0.619709i	0.945457	+	0.325748i	$0.105616\pi$
$462$	79.9726	−	79.9726i	0.173101	−	0.173101i
$463$	−496.650	+	496.650i	−1.07268	+	1.07268i	−0.0755346	+	0.997143i	$0.524066\pi$
$463$	−496.650	+	496.650i	−1.07268	+	1.07268i	−0.997143	+	0.0755346i	$0.975934\pi$
$464$	60.5031	−	60.5031i	0.130395	−	0.130395i
$465$	−18.1478			−0.0390274
$466$	226.083	−	226.083i	0.485157	−	0.485157i
$467$	−156.516	−	156.516i	−0.335152	−	0.335152i	0.519387	−	0.854539i	$-0.326160\pi$
$467$	−156.516	−	156.516i	−0.335152	−	0.335152i	−0.854539	+	0.519387i	$0.826160\pi$
$468$		−	316.804i		−	0.676932i
$469$	512.712	−	512.712i	1.09320	−	1.09320i
$470$	370.499	+	370.499i	0.788296	+	0.788296i
$471$		−	145.443i		−	0.308796i
$472$		−	155.487i		−	0.329421i
$473$	315.542			0.667107
$474$	−123.918			−0.261431
$475$	352.320	−	352.320i	0.741727	−	0.741727i
$476$			44.7782i			0.0940719i
$477$		−	145.657i		−	0.305360i
$478$	−83.1841	−	83.1841i	−0.174025	−	0.174025i
$479$	−320.044	−	320.044i	−0.668150	−	0.668150i	0.289137	−	0.957288i	$-0.406632\pi$
$479$	−320.044	−	320.044i	−0.668150	−	0.668150i	−0.957288	+	0.289137i	$0.906632\pi$
$480$			50.8518i			0.105941i
$481$			1169.83i			2.43208i
$482$	−358.306			−0.743373
$483$	−132.771			−0.274888
$484$			160.907i			0.332452i
$485$			273.331i			0.563568i
$486$		−	349.160i		−	0.718435i
$487$	95.3811			0.195855			0.0979273	−	0.995194i	$-0.468779\pi$
$487$	95.3811			0.195855			0.0979273	+	0.995194i	$0.468779\pi$
$488$	221.865	−	221.865i	0.454642	−	0.454642i
$489$	−129.094			−0.263996
$490$	−200.384	+	200.384i	−0.408947	+	0.408947i
$491$		−	493.132i		−	1.00434i	−0.864768	−	0.502171i	$-0.832535\pi$
$491$		−	493.132i		−	1.00434i	0.864768	−	0.502171i	$-0.167465\pi$
$492$	56.8810	−	56.8810i	0.115612	−	0.115612i
$493$	53.4618			0.108442
$494$		−	984.691i		−	1.99330i
$495$	−287.212			−0.580227
$496$	−5.71001	+	5.71001i	−0.0115121	+	0.0115121i
$497$			432.869i			0.870963i
$498$	109.926	+	109.926i	0.220734	+	0.220734i
$499$	−357.308	−	357.308i	−0.716048	−	0.716048i	0.251746	−	0.967793i	$-0.418995\pi$
$499$	−357.308	−	357.308i	−0.716048	−	0.716048i	−0.967793	+	0.251746i	$0.918995\pi$
$500$			113.958i			0.227916i
$501$			123.935i			0.247375i
$502$		−	8.09523i		−	0.0161260i
$503$	541.782	+	541.782i	1.07710	+	1.07710i	0.996768	+	0.0803332i	$0.0255984\pi$
$503$	541.782	+	541.782i	1.07710	+	1.07710i	0.0803332	+	0.996768i	$0.474402\pi$
$504$	−178.240			−0.353650
$505$	176.810	+	176.810i	0.350119	+	0.350119i
$506$	−67.3156	+	67.3156i	−0.133035	+	0.133035i
$507$	−335.129	−	335.129i	−0.661003	−	0.661003i
$508$	−308.135			−0.606565
$509$	163.757	+	163.757i	0.321723	+	0.321723i	0.849428	−	0.527705i	$-0.176947\pi$
$509$	163.757	+	163.757i	0.321723	+	0.321723i	−0.527705	+	0.849428i	$0.676947\pi$
$510$	−22.4668	+	22.4668i	−0.0440525	+	0.0440525i
$511$	−24.1843	−	24.1843i	−0.0473275	−	0.0473275i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	695.104i		−	1.35498i
$514$			505.649i			0.983752i
$515$			25.2378i			0.0490054i
$516$	98.2499	+	98.2499i	0.190407	+	0.190407i
$517$		−	367.935i		−	0.711673i
$518$	658.168			1.27059
$519$	323.103	+	323.103i	0.622550	+	0.622550i
$520$	−288.769	−	288.769i	−0.555326	−	0.555326i
$521$	486.022	−	486.022i	0.932863	−	0.932863i	−0.0650210	−	0.997884i	$-0.520711\pi$
$521$	486.022	−	486.022i	0.932863	−	0.932863i	0.997884	+	0.0650210i	$0.0207114\pi$
$522$			212.804i			0.407671i
$523$	223.919	−	223.919i	0.428144	−	0.428144i	−0.459852	−	0.887996i	$-0.652097\pi$
$523$	223.919	−	223.919i	0.428144	−	0.428144i	0.887996	+	0.459852i	$0.152097\pi$
$524$		−	301.856i		−	0.576060i
$525$	−202.376			−0.385479
$526$	−467.712	−	467.712i	−0.889187	−	0.889187i
$527$	−5.04548			−0.00957396
$528$	25.2499	−	25.2499i	0.0478218	−	0.0478218i
$529$	−417.243			−0.788738
$530$	−132.767	−	132.767i	−0.250504	−	0.250504i
$531$	273.443	+	273.443i	0.514958	+	0.514958i
$532$	−554.005			−1.04136
$533$			646.015i			1.21204i
$534$	155.515			0.291227
$535$	−369.858	+	369.858i	−0.691324	+	0.691324i
$536$	161.879	−	161.879i	0.302014	−	0.302014i
$537$			238.061i			0.443317i
$538$	−374.928	−	64.4269i	−0.696893	−	0.119753i
$539$	198.997			0.369197
$540$	−203.845	−	203.845i	−0.377492	−	0.377492i
$541$	487.266	+	487.266i	0.900677	+	0.900677i	0.995495	−	0.0948180i	$-0.0302269\pi$
$541$	487.266	+	487.266i	0.900677	+	0.900677i	−0.0948180	+	0.995495i	$0.530227\pi$
$542$		−	524.896i		−	0.968443i
$543$	49.5380			0.0912303
$544$			14.1379i			0.0259888i
$545$	18.8859	−	18.8859i	0.0346531	−	0.0346531i
$546$	−282.808	+	282.808i	−0.517964	+	0.517964i
$547$		−	395.005i		−	0.722129i	−0.932541	−	0.361064i	$-0.882413\pi$
$547$		−	395.005i		−	0.722129i	0.932541	−	0.361064i	$-0.117587\pi$
$548$	−50.5249	−	50.5249i	−0.0921986	−	0.0921986i
$549$			780.354i			1.42141i
$550$	−102.606	+	102.606i	−0.186556	+	0.186556i
$551$			661.439i			1.20043i
$552$	−41.9200			−0.0759420
$553$	−395.908	−	395.908i	−0.715928	−	0.715928i
$554$	118.648			0.214167
$555$	330.226	+	330.226i	0.595002	+	0.595002i
$556$	181.878	−	181.878i	0.327118	−	0.327118i
$557$	267.835	−	267.835i	0.480854	−	0.480854i	−0.424551	−	0.905404i	$-0.639568\pi$
$557$	267.835	−	267.835i	0.480854	−	0.480854i	0.905404	+	0.424551i	$0.139568\pi$
$558$		−	20.0835i		−	0.0359920i
$559$	−1115.85			−1.99616
$560$	−162.467	+	162.467i	−0.290119	+	0.290119i
$561$	22.3113			0.0397706
$562$	−554.038			−0.985832
$563$	259.253			0.460485			0.230242	−	0.973133i	$-0.426048\pi$
$563$	259.253			0.460485			0.230242	+	0.973133i	$0.426048\pi$
$564$	114.564	−	114.564i	0.203127	−	0.203127i
$565$	−717.566	+	717.566i	−1.27003	+	1.27003i
$566$	128.710	+	128.710i	0.227403	+	0.227403i
$567$	201.402	−	201.402i	0.355206	−	0.355206i
$568$			136.670i			0.240617i
$569$	379.163	−	379.163i	0.666367	−	0.666367i	−0.290506	−	0.956873i	$-0.593824\pi$
$569$	379.163	−	379.163i	0.666367	−	0.666367i	0.956873	+	0.290506i	$0.0938237\pi$
$570$	−277.964	−	277.964i	−0.487656	−	0.487656i
$571$	−335.093	+	335.093i	−0.586853	+	0.586853i	−0.936778	−	0.349925i	$-0.886207\pi$
$571$	−335.093	+	335.093i	−0.586853	+	0.586853i	0.349925	+	0.936778i	$0.386207\pi$
$572$			286.771i			0.501348i
$573$	−278.527	+	278.527i	−0.486085	+	0.486085i
$574$	363.460			0.633205
$575$	170.347			0.296255
$576$	−56.2759			−0.0977012
$577$	−532.363	+	532.363i	−0.922639	+	0.922639i	−0.997215	−	0.0745759i	$-0.976240\pi$
$577$	−532.363	+	532.363i	−0.922639	+	0.922639i	0.0745759	+	0.997215i	$0.476240\pi$
$578$	282.754	−	282.754i	0.489193	−	0.489193i
$579$	−500.602			−0.864598
$580$	193.973	+	193.973i	0.334436	+	0.334436i
$581$			702.405i			1.20896i
$582$	84.5177			0.145219
$583$			131.848i			0.226155i
$584$	−7.63577	−	7.63577i	−0.0130749	−	0.0130749i
$585$	1015.67			1.73619
$586$	−133.570	−	133.570i	−0.227936	−	0.227936i
$587$			827.681i			1.41002i	0.709198	+	0.705010i	$0.249057\pi$
$587$			827.681i			1.41002i	−0.709198	+	0.705010i	$0.750943\pi$
$588$	61.9616	+	61.9616i	0.105377	+	0.105377i
$589$		−	62.4236i		−	0.105982i
$590$	498.491			0.844900
$591$	−39.5830			−0.0669763
$592$	207.805			0.351021
$593$		−	94.0788i		−	0.158649i	−0.996849	−	0.0793244i	$-0.974724\pi$
$593$		−	94.0788i		−	0.158649i	0.996849	−	0.0793244i	$-0.0252763\pi$
$594$			202.435i			0.340799i
$595$	−143.559			−0.241275
$596$	−92.3075			−0.154878
$597$	−116.651	+	116.651i	−0.195395	+	0.195395i
$598$	238.049	−	238.049i	0.398075	−	0.398075i
$599$	208.432			0.347966			0.173983	−	0.984749i	$-0.444336\pi$
$599$	208.432			0.347966			0.173983	+	0.984749i	$0.444336\pi$
$600$	−63.8967			−0.106494
$601$	−202.970	−	202.970i	−0.337720	−	0.337720i	0.517789	−	0.855509i	$-0.326755\pi$
$601$	−202.970	−	202.970i	−0.337720	−	0.337720i	−0.855509	+	0.517789i	$0.826755\pi$
$602$			627.799i			1.04286i
$603$			569.370i			0.944228i
$604$	284.977			0.471817
$605$	−515.867			−0.852673
$606$	54.6722	−	54.6722i	0.0902182	−	0.0902182i
$607$	−93.8072	−	93.8072i	−0.154542	−	0.154542i	0.625601	−	0.780143i	$-0.284854\pi$
$607$	−93.8072	−	93.8072i	−0.154542	−	0.154542i	−0.780143	+	0.625601i	$0.784854\pi$
$608$	−174.917			−0.287692
$609$	189.969	−	189.969i	0.311935	−	0.311935i
$610$	711.300	+	711.300i	1.16607	+	1.16607i
$611$			1301.13i			2.12951i
$612$	−24.8632	−	24.8632i	−0.0406262	−	0.0406262i
$613$	−414.113	−	414.113i	−0.675552	−	0.675552i	0.283439	−	0.958990i	$-0.408525\pi$
$613$	−414.113	−	414.113i	−0.675552	−	0.675552i	−0.958990	+	0.283439i	$0.908525\pi$
$614$	442.521	+	442.521i	0.720718	+	0.720718i
$615$	182.361	+	182.361i	0.296521	+	0.296521i
$616$	161.342			0.261920
$617$			730.500i			1.18395i	0.805955	+	0.591977i	$0.201653\pi$
$617$			730.500i			1.18395i	−0.805955	+	0.591977i	$0.798347\pi$
$618$	7.80388			0.0126276
$619$	764.675			1.23534			0.617670	−	0.786437i	$-0.288077\pi$
$619$	764.675			1.23534			0.617670	+	0.786437i	$0.288077\pi$
$620$	−18.3063	−	18.3063i	−0.0295263	−	0.0295263i
$621$	168.041	−	168.041i	0.270598	−	0.270598i
$622$		−	178.849i		−	0.287539i
$623$	496.857	+	496.857i	0.797523	+	0.797523i
$624$	−89.2916	+	89.2916i	−0.143096	+	0.143096i
$625$	−768.191			−1.22911
$626$	572.254	+	572.254i	0.914143	+	0.914143i
$627$			276.040i			0.440255i
$628$	146.714	−	146.714i	0.233620	−	0.233620i
$629$	91.8101	+	91.8101i	0.145962	+	0.145962i
$630$		−	571.436i		−	0.907041i
$631$	−789.308			−1.25088			−0.625442	−	0.780270i	$-0.715081\pi$
$631$	−789.308			−1.25088			−0.625442	+	0.780270i	$0.715081\pi$
$632$	−125.001	−	125.001i	−0.197786	−	0.197786i
$633$	−222.214	+	222.214i	−0.351049	+	0.351049i
$634$			544.759i			0.859242i
$635$		−	987.881i		−	1.55572i
$636$	−41.0535	+	41.0535i	−0.0645495	+	0.0645495i
$637$	−703.717			−1.10474
$638$		−	192.631i		−	0.301929i
$639$	−240.352	−	240.352i	−0.376137	−	0.376137i
$640$	−51.2960	+	51.2960i	−0.0801500	+	0.0801500i
$641$			890.796i			1.38970i	0.719156	+	0.694849i	$0.244529\pi$
$641$			890.796i			1.38970i	−0.719156	+	0.694849i	$0.755471\pi$
$642$	114.365	+	114.365i	0.178139	+	0.178139i
$643$	881.166			1.37040			0.685199	−	0.728356i	$-0.259715\pi$
$643$	881.166			1.37040			0.685199	+	0.728356i	$0.259715\pi$
$644$	−133.931	−	133.931i	−0.207967	−	0.207967i
$645$	−314.989	+	314.989i	−0.488355	+	0.488355i
$646$	−77.2800	−	77.2800i	−0.119629	−	0.119629i
$647$	−376.475	+	376.475i	−0.581878	+	0.581878i	−0.935419	−	0.353541i	$-0.884978\pi$
$647$	−376.475	+	376.475i	−0.581878	+	0.581878i	0.353541	+	0.935419i	$0.384978\pi$
$648$	63.5889	−	63.5889i	0.0981310	−	0.0981310i
$649$	−247.521	−	247.521i	−0.381388	−	0.381388i
$650$	362.847	−	362.847i	0.558226	−	0.558226i
$651$	−17.9284	+	17.9284i	−0.0275398	+	0.0275398i
$652$	−130.222	−	130.222i	−0.199727	−	0.199727i
$653$	−293.323			−0.449193			−0.224597	−	0.974452i	$-0.572106\pi$
$653$	−293.323			−0.449193			−0.224597	+	0.974452i	$0.572106\pi$
$654$	−5.83979	−	5.83979i	−0.00892934	−	0.00892934i
$655$	967.748			1.47748
$656$	114.756			0.174933
$657$	26.8569			0.0408780
$658$	732.041			1.11252
$659$	−859.697			−1.30455			−0.652274	−	0.757983i	$-0.726185\pi$
$659$	−859.697			−1.30455			−0.652274	+	0.757983i	$0.726185\pi$
$660$	80.9512	+	80.9512i	0.122653	+	0.122653i
$661$	311.082	+	311.082i	0.470624	+	0.470624i	0.902116	−	0.431493i	$-0.142013\pi$
$661$	311.082	+	311.082i	0.470624	+	0.470624i	−0.431493	+	0.902116i	$0.642013\pi$
$662$	−288.089	−	288.089i	−0.435180	−	0.435180i
$663$	−78.8998			−0.119004
$664$			221.772i			0.333994i
$665$		−	1776.14i		−	2.67088i
$666$	−365.450	+	365.450i	−0.548724	+	0.548724i
$667$	−159.903	+	159.903i	−0.239734	+	0.239734i
$668$	−125.018	+	125.018i	−0.187152	+	0.187152i
$669$	313.990			0.469342
$670$	518.985	+	518.985i	0.774605	+	0.774605i
$671$		−	706.377i		−	1.05272i
$672$	50.2370	+	50.2370i	0.0747575	+	0.0747575i
$673$	−634.052	+	634.052i	−0.942127	+	0.942127i	−0.998415	−	0.0562875i	$-0.982074\pi$
$673$	−634.052	+	634.052i	−0.942127	+	0.942127i	0.0562875	+	0.998415i	$0.482074\pi$
$674$	365.732			0.542629
$675$	256.138	−	256.138i	0.379463	−	0.379463i
$676$		−	676.112i		−	1.00017i
$677$	154.111	+	154.111i	0.227638	+	0.227638i	0.811705	−	0.584067i	$-0.198540\pi$
$677$	154.111	+	154.111i	0.227638	+	0.227638i	−0.584067	+	0.811705i	$0.698540\pi$
$678$	221.881	+	221.881i	0.327259	+	0.327259i
$679$	270.026	+	270.026i	0.397682	+	0.397682i
$680$	−45.3261			−0.0666561
$681$	200.918			0.295034
$682$			18.1796i			0.0266563i
$683$	−87.9359	+	87.9359i	−0.128750	+	0.128750i	−0.768545	−	0.639796i	$-0.779019\pi$
$683$	−87.9359	+	87.9359i	−0.128750	+	0.128750i	0.639796	+	0.768545i	$0.279019\pi$
$684$	307.613	−	307.613i	0.449727	−	0.449727i
$685$	161.983	−	161.983i	0.236471	−	0.236471i
$686$		−	224.856i		−	0.327778i
$687$		−	196.232i		−	0.285637i
$688$			198.216i			0.288105i
$689$		−	466.257i		−	0.676716i
$690$		−	134.395i		−	0.194776i
$691$	−362.360	+	362.360i	−0.524399	+	0.524399i	−0.918897	−	0.394498i	$-0.870919\pi$
$691$	−362.360	+	362.360i	−0.524399	+	0.524399i	0.394498	+	0.918897i	$0.370919\pi$
$692$			651.852i			0.941982i
$693$	−283.740	+	283.740i	−0.409438	+	0.409438i
$694$	373.550	+	373.550i	0.538257	+	0.538257i
$695$	583.099	+	583.099i	0.838992	+	0.838992i
$696$	59.9792	−	59.9792i	0.0861770	−	0.0861770i
$697$	50.7002	+	50.7002i	0.0727407	+	0.0727407i
$698$	−160.856	−	160.856i	−0.230453	−	0.230453i
$699$	224.126	−	224.126i	0.320637	−	0.320637i
$700$	−204.144	−	204.144i	−0.291634	−	0.291634i
$701$	−219.488	+	219.488i	−0.313107	+	0.313107i	−0.846112	−	0.533005i	$-0.821063\pi$
$701$	−219.488	+	219.488i	−0.313107	+	0.313107i	0.533005	+	0.846112i	$0.321063\pi$
$702$		−	715.873i		−	1.01976i
$703$	−1135.89	+	1135.89i	−1.61578	+	1.61578i
$704$	50.9410			0.0723593
$705$	367.291	+	367.291i	0.520979	+	0.520979i
$706$	−378.801	+	378.801i	−0.536546	+	0.536546i
$707$	349.346			0.494124
$708$		−	154.140i		−	0.217712i
$709$	−816.923	−	816.923i	−1.15222	−	1.15222i	−0.986107	−	0.166111i	$-0.946879\pi$
$709$	−816.923	−	816.923i	−1.15222	−	1.15222i	−0.166111	−	0.986107i	$-0.553121\pi$
$710$	−438.165			−0.617134
$711$	439.659			0.618367
$712$	156.874	+	156.874i	0.220328	+	0.220328i
$713$	15.0909	−	15.0909i	0.0211654	−	0.0211654i
$714$			44.3904i			0.0621715i
$715$	−919.388			−1.28586
$716$	−240.141	+	240.141i	−0.335392	+	0.335392i
$717$	−82.4637	−	82.4637i	−0.115012	−	0.115012i
$718$	−710.500			−0.989554
$719$	656.173	−	656.173i	0.912619	−	0.912619i	−0.0838582	−	0.996478i	$-0.526724\pi$
$719$	656.173	−	656.173i	0.912619	−	0.912619i	0.996478	+	0.0838582i	$0.0267243\pi$
$720$		−	180.421i		−	0.250584i
$721$	24.9327	+	24.9327i	0.0345807	+	0.0345807i
$722$	595.124	−	595.124i	0.824271	−	0.824271i
$723$	−355.203			−0.491290
$724$	49.9708	+	49.9708i	0.0690204	+	0.0690204i
$725$	−243.733	+	243.733i	−0.336183	+	0.336183i
$726$			159.513i			0.219715i
$727$		−	1148.36i		−	1.57959i	−0.613373	−	0.789793i	$-0.710188\pi$
$727$		−	1148.36i		−	1.57959i	0.613373	−	0.789793i	$-0.289812\pi$
$728$	−570.557			−0.783733
$729$		−	59.9858i		−	0.0822850i
$730$	24.4803	−	24.4803i	0.0335346	−	0.0335346i
$731$	−87.5739	+	87.5739i	−0.119800	+	0.119800i
$732$	219.944	−	219.944i	0.300470	−	0.300470i
$733$	169.128	−	169.128i	0.230733	−	0.230733i	−0.582265	−	0.812999i	$-0.697834\pi$
$733$	169.128	−	169.128i	0.230733	−	0.230733i	0.812999	+	0.582265i	$0.197834\pi$
$734$	671.383			0.914690
$735$	−198.649	+	198.649i	−0.270271	+	0.270271i
$736$	−42.2862	−	42.2862i	−0.0574540	−	0.0574540i
$737$		−	515.393i		−	0.699313i
$738$	−201.812	+	201.812i	−0.273458	+	0.273458i
$739$	581.492	+	581.492i	0.786863	+	0.786863i	0.980979	−	0.194115i	$-0.0621836\pi$
$739$	581.492	+	581.492i	0.786863	+	0.786863i	−0.194115	+	0.980979i	$0.562184\pi$
$740$			666.221i			0.900299i
$741$		−	976.164i		−	1.31736i
$742$	−262.324			−0.353537
$743$	−990.308			−1.33285			−0.666425	−	0.745572i	$-0.732177\pi$
$743$	−990.308			−1.33285			−0.666425	+	0.745572i	$0.732177\pi$
$744$	−5.66056	+	5.66056i	−0.00760828	+	0.00760828i
$745$		−	295.938i		−	0.397232i
$746$		−	987.888i		−	1.32425i
$747$	−390.013	−	390.013i	−0.522106	−	0.522106i
$748$	22.5062	+	22.5062i	0.0300885	+	0.0300885i
$749$			730.775i			0.975668i
$750$			112.971i			0.150628i
$751$	359.197			0.478292			0.239146	−	0.970984i	$-0.423133\pi$
$751$	359.197			0.478292			0.239146	+	0.970984i	$0.423133\pi$
$752$	231.129			0.307352
$753$		−	8.02513i		−	0.0106575i
$754$			681.202i			0.903451i
$755$			913.637i			1.21012i
$756$	−402.763			−0.532755
$757$	−356.772	+	356.772i	−0.471298	+	0.471298i	−0.902334	−	0.431037i	$-0.858148\pi$
$757$	−356.772	+	356.772i	−0.471298	+	0.471298i	0.431037	+	0.902334i	$0.358148\pi$
$758$	877.957			1.15825
$759$	−66.7326	+	66.7326i	−0.0879218	+	0.0879218i
$760$		−	560.784i		−	0.737873i
$761$	662.285	−	662.285i	0.870282	−	0.870282i	−0.122220	−	0.992503i	$-0.539002\pi$
$761$	662.285	−	662.285i	0.870282	−	0.870282i	0.992503	+	0.122220i	$0.0390015\pi$
$762$	−305.467			−0.400875
$763$		−	37.3152i		−	0.0489059i
$764$	−561.919			−0.735497
$765$	79.7115	−	79.7115i	0.104198	−	0.104198i
$766$			22.6256i			0.0295373i
$767$	875.310	+	875.310i	1.14121	+	1.14121i
$768$	15.8614	+	15.8614i	0.0206529	+	0.0206529i
$769$		−	767.929i		−	0.998607i	−0.866427	−	0.499303i	$-0.833589\pi$
$769$		−	767.929i		−	0.998607i	0.866427	−	0.499303i	$-0.166411\pi$
$770$			517.264i			0.671771i
$771$			501.270i			0.650155i
$772$	−504.975	−	504.975i	−0.654113	−	0.654113i
$773$	1510.48			1.95405			0.977023	−	0.213132i	$-0.0683665\pi$
$773$	1510.48			1.95405			0.977023	+	0.213132i	$0.0683665\pi$
$774$	−348.588	−	348.588i	−0.450372	−	0.450372i
$775$	23.0024	−	23.0024i	0.0296805	−	0.0296805i
$776$	85.2560	+	85.2560i	0.109866	+	0.109866i
$777$	652.468			0.839727
$778$	645.474	+	645.474i	0.829659	+	0.829659i
$779$	−627.273	+	627.273i	−0.805229	+	0.805229i
$780$	−286.269	−	286.269i	−0.367011	−	0.367011i
$781$	217.566	+	217.566i	0.278574	+	0.278574i
$782$		−	37.3649i		−	0.0477812i
$783$			480.868i			0.614135i
$784$			125.006i			0.159446i
$785$	470.363	+	470.363i	0.599189	+	0.599189i
$786$		−	299.241i		−	0.380714i
$787$	699.447			0.888751			0.444376	−	0.895841i	$-0.353426\pi$
$787$	699.447			0.888751			0.444376	+	0.895841i	$0.353426\pi$
$788$	−39.9288	−	39.9288i	−0.0506711	−	0.0506711i
$789$	−463.662	−	463.662i	−0.587658	−	0.587658i
$790$	400.753	−	400.753i	0.507282	−	0.507282i
$791$			1417.78i			1.79239i
$792$	−89.5859	+	89.5859i	−0.113114	+	0.113114i
$793$			2497.97i			3.15003i
$794$	−243.431			−0.306588
$795$	−131.617	−	131.617i	−0.165557	−	0.165557i
$796$	−235.339			−0.295652
$797$	218.570	−	218.570i	0.274241	−	0.274241i	−0.556564	−	0.830805i	$-0.687881\pi$
$797$	218.570	−	218.570i	0.274241	−	0.274241i	0.830805	+	0.556564i	$0.187881\pi$
$798$	−549.207			−0.688229
$799$	102.115	+	102.115i	0.127803	+	0.127803i
$800$	−64.4548	−	64.4548i	−0.0805685	−	0.0805685i
$801$	−551.763			−0.688842
$802$		−	885.233i		−	1.10378i
$803$	−24.3108			−0.0302750
$804$	160.478	−	160.478i	0.199599	−	0.199599i
$805$	429.381	−	429.381i	0.533393	−	0.533393i
$806$		−	64.2887i		−	0.0797627i
$807$	−371.681	−	63.8689i	−0.460572	−	0.0791437i
$808$	110.300			0.136509
$809$	−244.778	−	244.778i	−0.302568	−	0.302568i	0.539450	−	0.842018i	$-0.318632\pi$
$809$	−244.778	−	244.778i	−0.302568	−	0.302568i	−0.842018	+	0.539450i	$0.818632\pi$
$810$	203.866	+	203.866i	0.251686	+	0.251686i
$811$		−	167.379i		−	0.206386i	−0.994661	−	0.103193i	$-0.967094\pi$
$811$		−	167.379i		−	0.206386i	0.994661	−	0.103193i	$-0.0329060\pi$
$812$	383.256			0.471991
$813$		−	520.350i		−	0.640037i
$814$	330.805	−	330.805i	0.406395	−	0.406395i
$815$	417.491	−	417.491i	0.512259	−	0.512259i
$816$			14.0155i			0.0171758i
$817$	−1083.48	−	1083.48i	−1.32617	−	1.32617i
$818$		−	281.949i		−	0.344681i
$819$	1003.40	−	1003.40i	1.22515	−	1.22515i
$820$			367.907i			0.448667i
$821$	−127.525			−0.155329			−0.0776644	−	0.996980i	$-0.524746\pi$
$821$	−127.525			−0.155329			−0.0776644	+	0.996980i	$0.524746\pi$
$822$	−50.0873	−	50.0873i	−0.0609335	−	0.0609335i
$823$	1216.65			1.47831			0.739154	−	0.673536i	$-0.235225\pi$
$823$	1216.65			1.47831			0.739154	+	0.673536i	$0.235225\pi$
$824$	7.87205	+	7.87205i	0.00955346	+	0.00955346i
$825$	−101.717	+	101.717i	−0.123294	+	0.123294i
$826$	492.465	−	492.465i	0.596205	−	0.596205i
$827$		−	1139.01i		−	1.37728i	−0.725101	−	0.688642i	$-0.758207\pi$
$827$		−	1139.01i		−	1.37728i	0.725101	−	0.688642i	$-0.241793\pi$
$828$	148.731			0.179627
$829$	28.8369	−	28.8369i	0.0347851	−	0.0347851i	−0.689500	−	0.724285i	$-0.742170\pi$
$829$	28.8369	−	28.8369i	0.0347851	−	0.0347851i	0.724285	+	0.689500i	$0.242170\pi$
$830$	−711.000			−0.856627
$831$	117.621			0.141541
$832$	−180.143			−0.216518
$833$	−55.2288	+	55.2288i	−0.0663010	+	0.0663010i
$834$	180.302	−	180.302i	0.216190	−	0.216190i
$835$	−400.806	−	400.806i	−0.480007	−	0.480007i
$836$	−278.451	+	278.451i	−0.333076	+	0.333076i
$837$		−	45.3821i		−	0.0542200i
$838$	13.3616	−	13.3616i	0.0159447	−	0.0159447i
$839$	−757.495	−	757.495i	−0.902855	−	0.902855i	0.0928276	−	0.995682i	$-0.470409\pi$
$839$	−757.495	−	757.495i	−0.902855	−	0.902855i	−0.995682	+	0.0928276i	$0.970409\pi$
$840$	−161.060	+	161.060i	−0.191738	+	0.191738i
$841$			383.421i			0.455911i
$842$	737.559	−	737.559i	0.875961	−	0.875961i
$843$	−549.240			−0.651530
$844$	−448.310			−0.531173
$845$	2167.61			2.56522
$846$	−406.468	+	406.468i	−0.480459	+	0.480459i
$847$	−509.631	+	509.631i	−0.601689	+	0.601689i
$848$	−82.8242			−0.0976701
$849$	127.596	+	127.596i	0.150289	+	0.150289i
$850$		−	56.9535i		−	0.0670042i
$851$	−549.204			−0.645363
$852$			135.487i			0.159022i
$853$	622.712	+	622.712i	0.730026	+	0.730026i	0.970625	−	0.240599i	$-0.0773438\pi$
$853$	622.712	+	622.712i	0.730026	+	0.730026i	−0.240599	+	0.970625i	$0.577344\pi$
$854$	1405.40			1.64567
$855$	986.207	+	986.207i	1.15346	+	1.15346i
$856$			230.729i			0.269543i
$857$	−239.663	−	239.663i	−0.279653	−	0.279653i	0.553317	−	0.832971i	$-0.313362\pi$
$857$	−239.663	−	239.663i	−0.279653	−	0.279653i	−0.832971	+	0.553317i	$0.813362\pi$
$858$			284.288i			0.331338i
$859$	7.61446			0.00886433			0.00443217	−	0.999990i	$-0.498589\pi$
$859$	7.61446			0.00886433			0.00443217	+	0.999990i	$0.498589\pi$
$860$	−635.481			−0.738931
$861$	360.312			0.418481
$862$		−	407.941i		−	0.473250i
$863$			759.625i			0.880215i	0.897945	+	0.440107i	$0.145060\pi$
$863$			759.625i			0.880215i	−0.897945	+	0.440107i	$0.854940\pi$
$864$	−127.165			−0.147182
$865$	−2089.84			−2.41600
$866$	−274.696	+	274.696i	−0.317200	+	0.317200i
$867$	280.305	−	280.305i	0.323305	−	0.323305i
$868$	−36.1700			−0.0416705
$869$	−397.979			−0.457974
$870$	192.293	+	192.293i	0.221027	+	0.221027i
$871$			1822.59i			2.09253i
$872$		−	11.7816i		−	0.0135110i
$873$	−299.866			−0.343489
$874$	462.286			0.528931
$875$	−360.932	+	360.932i	−0.412494	+	0.412494i
$876$	−7.56964	−	7.56964i	−0.00864114	−	0.00864114i
$877$	−875.408			−0.998185			−0.499093	−	0.866549i	$-0.666333\pi$
$877$	−875.408			−0.998185			−0.499093	+	0.866549i	$0.666333\pi$
$878$	−117.275	+	117.275i	−0.133571	+	0.133571i
$879$	−132.414	−	132.414i	−0.150641	−	0.150641i
$880$			163.317i			0.185587i
$881$	−344.009	−	344.009i	−0.390476	−	0.390476i	0.484381	−	0.874857i	$-0.339045\pi$
$881$	−344.009	−	344.009i	−0.390476	−	0.390476i	−0.874857	+	0.484381i	$0.839045\pi$
$882$	−219.838	−	219.838i	−0.249249	−	0.249249i
$883$	−958.578	−	958.578i	−1.08559	−	1.08559i	−0.995976	−	0.0896154i	$-0.971436\pi$
$883$	−958.578	−	958.578i	−1.08559	−	1.08559i	−0.0896154	−	0.995976i	$-0.528564\pi$
$884$	−79.5890	−	79.5890i	−0.0900328	−	0.0900328i
$885$	494.174			0.558389
$886$			247.284i			0.279102i
$887$	−209.839			−0.236571			−0.118286	−	0.992980i	$-0.537740\pi$
$887$	−209.839			−0.236571			−0.118286	+	0.992980i	$0.537740\pi$
$888$	206.005			0.231988
$889$	−975.939	−	975.939i	−1.09779	−	1.09779i
$890$	−502.936	+	502.936i	−0.565097	+	0.565097i
$891$		−	202.455i		−	0.227222i
$892$	316.733	+	316.733i	0.355082	+	0.355082i
$893$	−1263.39	+	1263.39i	−1.41477	+	1.41477i
$894$	−91.5081			−0.102358
$895$	−769.890	−	769.890i	−0.860213	−	0.860213i
$896$			101.352i			0.113116i
$897$	235.987	−	235.987i	0.263085	−	0.263085i
$898$	−156.476	−	156.476i	−0.174250	−	0.174250i
$899$			43.1842i			0.0480358i
$900$	226.703			0.251893
$901$	−36.5925	−	36.5925i	−0.0406133	−	0.0406133i
$902$	182.680	−	182.680i	0.202528	−	0.202528i
$903$			622.362i			0.689216i
$904$			447.639i			0.495176i
$905$	−160.206	+	160.206i	−0.177023	+	0.177023i
$906$	282.510			0.311821
$907$		−	1101.62i		−	1.21457i	−0.794482	−	0.607287i	$-0.792258\pi$
$907$		−	1101.62i		−	1.21457i	0.794482	−	0.607287i	$-0.207742\pi$
$908$	202.673	+	202.673i	0.223208	+	0.223208i
$909$	−193.975	+	193.975i	−0.213394	+	0.213394i
$910$		−	1829.21i		−	2.01012i
$911$	−575.563	−	575.563i	−0.631792	−	0.631792i	0.316725	−	0.948517i	$-0.397417\pi$
$911$	−575.563	−	575.563i	−0.631792	−	0.631792i	−0.948517	+	0.316725i	$0.897417\pi$
$912$	−173.402			−0.190134
$913$	353.040	+	353.040i	0.386681	+	0.386681i
$914$	−285.962	+	285.962i	−0.312869	+	0.312869i
$915$	705.140	+	705.140i	0.770645	+	0.770645i
$916$	197.947	−	197.947i	0.216099	−	0.216099i
$917$	956.050	−	956.050i	1.04258	−	1.04258i
$918$	−56.1828	−	56.1828i	−0.0612013	−	0.0612013i
$919$	918.539	−	918.539i	0.999498	−	0.999498i	−0.000501941	−	1.00000i	$-0.500160\pi$
$919$	918.539	−	918.539i	0.999498	−	0.999498i	1.00000		0.000501941i	$0.000159773\pi$
$920$	135.569	−	135.569i	0.147358	−	0.147358i
$921$	438.688	+	438.688i	0.476317	+	0.476317i
$922$	571.372			0.619709
$923$	−769.383	−	769.383i	−0.833568	−	0.833568i
$924$	159.945			0.173101
$925$	−837.126			−0.905001
$926$	−993.300			−1.07268
$927$	−27.6879			−0.0298683
$928$	121.006			0.130395
$929$	−318.878	−	318.878i	−0.343249	−	0.343249i	0.514338	−	0.857587i	$-0.328038\pi$
$929$	−318.878	−	318.878i	−0.343249	−	0.343249i	−0.857587	+	0.514338i	$0.828038\pi$
$930$	−18.1478	−	18.1478i	−0.0195137	−	0.0195137i
$931$	−683.301	−	683.301i	−0.733943	−	0.733943i
$932$	452.167			0.485157
$933$		−	177.300i		−	0.190032i
$934$		−	313.032i		−	0.335152i
$935$	−72.1549	+	72.1549i	−0.0771710	+	0.0771710i
$936$	316.804	−	316.804i	0.338466	−	0.338466i
$937$	−81.3745	+	81.3745i	−0.0868458	+	0.0868458i	−0.749195	−	0.662349i	$-0.769559\pi$
$937$	−81.3745	+	81.3745i	−0.0868458	+	0.0868458i	0.662349	+	0.749195i	$0.269559\pi$
$938$	1025.42			1.09320
$939$	567.298	+	567.298i	0.604151	+	0.604151i
$940$			740.998i			0.788296i
$941$	1144.64	+	1144.64i	1.21641	+	1.21641i	0.968880	+	0.247531i	$0.0796192\pi$
$941$	1144.64	+	1144.64i	1.21641	+	1.21641i	0.247531	+	0.968880i	$0.420381\pi$
$942$	145.443	−	145.443i	0.154398	−	0.154398i
$943$	−303.286			−0.321619
$944$	155.487	−	155.487i	0.164711	−	0.164711i
$945$		−	1291.26i		−	1.36641i
$946$	315.542	+	315.542i	0.333553	+	0.333553i
$947$	−482.785	−	482.785i	−0.509805	−	0.509805i	0.404662	−	0.914466i	$-0.367389\pi$
$947$	−482.785	−	482.785i	−0.509805	−	0.509805i	−0.914466	+	0.404662i	$0.867389\pi$
$948$	−123.918	−	123.918i	−0.130716	−	0.130716i
$949$	85.9707			0.0905909
$950$	704.640			0.741727
$951$			540.042i			0.567867i
$952$	−44.7782	+	44.7782i	−0.0470359	+	0.0470359i
$953$	1239.51	−	1239.51i	1.30064	−	1.30064i	0.372672	−	0.927963i	$-0.378442\pi$
$953$	1239.51	−	1239.51i	1.30064	−	1.30064i	0.927963	−	0.372672i	$-0.121558\pi$
$954$	145.657	−	145.657i	0.152680	−	0.152680i
$955$		−	1801.51i		−	1.88640i
$956$		−	166.368i		−	0.174025i
$957$		−	190.962i		−	0.199543i
$958$		−	640.088i		−	0.668150i
$959$		−	320.049i		−	0.333732i
$960$	−50.8518	+	50.8518i	−0.0529706	+	0.0529706i
$961$			956.924i			0.995759i
$962$	−1169.83	+	1169.83i	−1.21604	+	1.21604i
$963$	−405.765	−	405.765i	−0.421355	−	0.421355i
$964$	−358.306	−	358.306i	−0.371686	−	0.371686i
$965$	1618.95	−	1618.95i	1.67767	−	1.67767i
$966$	−132.771	−	132.771i	−0.137444	−	0.137444i
$967$	−372.529	−	372.529i	−0.385242	−	0.385242i	0.487745	−	0.872986i	$-0.337820\pi$
$967$	−372.529	−	372.529i	−0.385242	−	0.385242i	−0.872986	+	0.487745i	$0.837820\pi$
$968$	−160.907	+	160.907i	−0.166226	+	0.166226i
$969$	−76.6108	−	76.6108i	−0.0790617	−	0.0790617i
$970$	−273.331	+	273.331i	−0.281784	+	0.281784i
$971$		−	1446.27i		−	1.48947i	−0.667361	−	0.744734i	$-0.732576\pi$
$971$		−	1446.27i		−	1.48947i	0.667361	−	0.744734i	$-0.267424\pi$
$972$	349.160	−	349.160i	0.359218	−	0.359218i
$973$	1152.10			1.18407
$974$	95.3811	+	95.3811i	0.0979273	+	0.0979273i
$975$	359.705	−	359.705i	0.368928	−	0.368928i
$976$	443.730			0.454642
$977$		−	1718.78i		−	1.75924i	−0.475675	−	0.879621i	$-0.657796\pi$
$977$		−	1718.78i		−	1.75924i	0.475675	−	0.879621i	$-0.342204\pi$
$978$	−129.094	−	129.094i	−0.131998	−	0.131998i
$979$	499.456			0.510169
$980$	−400.768			−0.408947
$981$	20.7194	+	20.7194i	0.0211207	+	0.0211207i
$982$	493.132	−	493.132i	0.502171	−	0.502171i
$983$		−	1189.38i		−	1.20995i	−0.796243	−	0.604977i	$-0.793182\pi$
$983$		−	1189.38i		−	1.20995i	0.796243	−	0.604977i	$-0.206818\pi$
$984$	113.762			0.115612
$985$	128.012	−	128.012i	0.129961	−	0.129961i
$986$	53.4618	+	53.4618i	0.0542208	+	0.0542208i
$987$	725.701			0.735260
$988$	984.691	−	984.691i	0.996651	−	0.996651i
$989$		−	523.863i		−	0.529689i
$990$	−287.212	−	287.212i	−0.290114	−	0.290114i
$991$	838.159	−	838.159i	0.845771	−	0.845771i	−0.143832	−	0.989602i	$-0.545942\pi$
$991$	838.159	−	838.159i	0.845771	−	0.845771i	0.989602	+	0.143832i	$0.0459424\pi$
$992$	−11.4200			−0.0115121
$993$	−285.594	−	285.594i	−0.287608	−	0.287608i
$994$	−432.869	+	432.869i	−0.435481	+	0.435481i
$995$		−	754.498i		−	0.758289i
$996$			219.851i			0.220734i
$997$	−1918.11			−1.92389			−0.961943	−	0.273251i	$-0.911901\pi$
$997$	−1918.11			−1.92389			−0.961943	+	0.273251i	$0.911901\pi$
$998$		−	714.616i		−	0.716048i
$999$	−825.796	+	825.796i	−0.826623	+	0.826623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.a.187.13	✓	44
269.82	odd	4	inner	538.3.c.a.351.13	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.a.187.13	✓	44	1.1	even	1	trivial
538.3.c.a.351.13	yes	44	269.82	odd	4	inner

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(0.991340 + 0.991340i) q^{3} +2.00000i q^{4} -6.41200 q^{5} +1.98268i q^{6} +(-6.33449 + 6.33449i) q^{7} +(-2.00000 + 2.00000i) q^{8} -7.03449i q^{9} +(-6.41200 - 6.41200i) q^{10} +6.36762i q^{11} +(-1.98268 + 1.98268i) q^{12} -22.5179i q^{13} -12.6690 q^{14} +(-6.35647 - 6.35647i) q^{15} -4.00000 q^{16} +(-1.76724 - 1.76724i) q^{17} +(7.03449 - 7.03449i) q^{18} +(21.8646 - 21.8646i) q^{19} -12.8240i q^{20} -12.5593 q^{21} +(-6.36762 + 6.36762i) q^{22} +10.5715 q^{23} -3.96536 q^{24} +16.1137 q^{25} +(22.5179 - 22.5179i) q^{26} +(15.8956 - 15.8956i) q^{27} +(-12.6690 - 12.6690i) q^{28} +(-15.1258 + 15.1258i) q^{29} -12.7129i q^{30} +(1.42750 - 1.42750i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-6.31248 + 6.31248i) q^{33} -3.53448i q^{34} +(40.6167 - 40.6167i) q^{35} +14.0690 q^{36} -51.9512 q^{37} +43.7292 q^{38} +(22.3229 - 22.3229i) q^{39} +(12.8240 - 12.8240i) q^{40} -28.6890 q^{41} +(-12.5593 - 12.5593i) q^{42} -49.5541i q^{43} -12.7352 q^{44} +45.1051i q^{45} +(10.5715 + 10.5715i) q^{46} -57.7822 q^{47} +(-3.96536 - 3.96536i) q^{48} -31.2514i q^{49} +(16.1137 + 16.1137i) q^{50} -3.50387i q^{51} +45.0358 q^{52} +20.7061 q^{53} +31.7913 q^{54} -40.8292i q^{55} -25.3379i q^{56} +43.3506 q^{57} -30.2516 q^{58} +(-38.8717 + 38.8717i) q^{59} +(12.7129 - 12.7129i) q^{60} -110.933 q^{61} +2.85501 q^{62} +(44.5599 + 44.5599i) q^{63} -8.00000i q^{64} +144.385i q^{65} -12.6250 q^{66} -80.9397 q^{67} +(3.53448 - 3.53448i) q^{68} +(10.4800 + 10.4800i) q^{69} +81.2334 q^{70} +(34.1676 - 34.1676i) q^{71} +(14.0690 + 14.0690i) q^{72} +3.81788i q^{73} +(-51.9512 - 51.9512i) q^{74} +(15.9742 + 15.9742i) q^{75} +(43.7292 + 43.7292i) q^{76} +(-40.3356 - 40.3356i) q^{77} +44.6458 q^{78} +62.5004i q^{79} +25.6480 q^{80} -31.7945 q^{81} +(-28.6890 - 28.6890i) q^{82} +(55.4429 - 55.4429i) q^{83} -25.1185i q^{84} +(11.3315 + 11.3315i) q^{85} +(49.5541 - 49.5541i) q^{86} -29.9896 q^{87} +(-12.7352 - 12.7352i) q^{88} -78.4368i q^{89} +(-45.1051 + 45.1051i) q^{90} +(142.639 + 142.639i) q^{91} +21.1431i q^{92} +2.83028 q^{93} +(-57.7822 - 57.7822i) q^{94} +(-140.196 + 140.196i) q^{95} -7.93072i q^{96} -42.6280i q^{97} +(31.2514 - 31.2514i) q^{98} +44.7930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 44 q^{2} + 2 q^{3} + 4 q^{7} - 88 q^{8} - 4 q^{12} + 8 q^{14} + 38 q^{15} - 176 q^{16} - 120 q^{18} + 18 q^{19} - 16 q^{21} + 68 q^{23} - 8 q^{24} + 196 q^{25} + 16 q^{26} - 22 q^{27} + 8 q^{28}+ \cdots - 188 q^{99}+O(q^{100}) \) 44 * q + 44 * q^2 + 2 * q^3 + 4 * q^7 - 88 * q^8 - 4 * q^12 + 8 * q^14 + 38 * q^15 - 176 * q^16 - 120 * q^18 + 18 * q^19 - 16 * q^21 + 68 * q^23 - 8 * q^24 + 196 * q^25 + 16 * q^26 - 22 * q^27 + 8 * q^28 + 18 * q^29 + 88 * q^31 - 176 * q^32 + 96 * q^33 + 10 * q^35 - 240 * q^36 + 180 * q^37 + 36 * q^38 - 54 * q^39 + 144 * q^41 - 16 * q^42 + 68 * q^46 - 156 * q^47 - 8 * q^48 + 196 * q^50 + 32 * q^52 - 188 * q^53 - 44 * q^54 - 88 * q^57 + 36 * q^58 - 98 * q^59 - 76 * q^60 - 244 * q^61 + 176 * q^62 - 10 * q^63 + 192 * q^66 + 220 * q^67 - 70 * q^69 + 20 * q^70 + 156 * q^71 - 240 * q^72 + 180 * q^74 - 102 * q^75 + 36 * q^76 - 28 * q^77 - 108 * q^78 + 392 * q^81 + 144 * q^82 - 250 * q^83 - 342 * q^85 - 44 * q^86 - 60 * q^87 - 192 * q^90 + 66 * q^91 - 536 * q^93 - 156 * q^94 - 472 * q^95 + 404 * q^98 - 188 * q^99

Introduction

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