LMFDB - Embedded newform 380.3.b.a.191.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, 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("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.11
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70466 - 1.04601i) q^{2} -1.85712i q^{3} +(1.81172 + 3.56618i) q^{4} -2.23607 q^{5} +(-1.94256 + 3.16575i) q^{6} -8.17539i q^{7} +(0.641893 - 7.97421i) q^{8} +5.55112 q^{9} +O(q^{10})$	\(q+(-1.70466 - 1.04601i) q^{2} -1.85712i q^{3} +(1.81172 + 3.56618i) q^{4} -2.23607 q^{5} +(-1.94256 + 3.16575i) q^{6} -8.17539i q^{7} +(0.641893 - 7.97421i) q^{8} +5.55112 q^{9} +(3.81173 + 2.33895i) q^{10} +1.28015i q^{11} +(6.62281 - 3.36458i) q^{12} +13.9097 q^{13} +(-8.55155 + 13.9363i) q^{14} +4.15264i q^{15} +(-9.43531 + 12.9219i) q^{16} -1.52283 q^{17} +(-9.46277 - 5.80653i) q^{18} -4.35890i q^{19} +(-4.05114 - 7.97423i) q^{20} -15.1826 q^{21} +(1.33905 - 2.18221i) q^{22} -16.2368i q^{23} +(-14.8090 - 1.19207i) q^{24} +5.00000 q^{25} +(-23.7113 - 14.5497i) q^{26} -27.0231i q^{27} +(29.1549 - 14.8116i) q^{28} -10.9442 q^{29} +(4.34370 - 7.07883i) q^{30} -21.3804i q^{31} +(29.6004 - 12.1580i) q^{32} +2.37738 q^{33} +(2.59590 + 1.59289i) q^{34} +18.2807i q^{35} +(10.0571 + 19.7963i) q^{36} -21.4981 q^{37} +(-4.55945 + 7.43044i) q^{38} -25.8319i q^{39} +(-1.43532 + 17.8309i) q^{40} -63.5609 q^{41} +(25.8812 + 15.8812i) q^{42} -37.8772i q^{43} +(-4.56523 + 2.31927i) q^{44} -12.4127 q^{45} +(-16.9839 + 27.6782i) q^{46} +3.23165i q^{47} +(23.9974 + 17.5225i) q^{48} -17.8371 q^{49} +(-8.52329 - 5.23005i) q^{50} +2.82807i q^{51} +(25.2006 + 49.6046i) q^{52} -66.1970 q^{53} +(-28.2665 + 46.0652i) q^{54} -2.86249i q^{55} +(-65.1923 - 5.24773i) q^{56} -8.09498 q^{57} +(18.6561 + 11.4478i) q^{58} +0.130585i q^{59} +(-14.8091 + 7.52343i) q^{60} -20.5145 q^{61} +(-22.3642 + 36.4464i) q^{62} -45.3826i q^{63} +(-63.1759 - 10.2372i) q^{64} -31.1031 q^{65} +(-4.05262 - 2.48676i) q^{66} +17.8398i q^{67} +(-2.75894 - 5.43068i) q^{68} -30.1536 q^{69} +(19.1218 - 31.1624i) q^{70} -32.6229i q^{71} +(3.56323 - 44.2658i) q^{72} -4.61935 q^{73} +(36.6468 + 22.4872i) q^{74} -9.28558i q^{75} +(15.5446 - 7.89712i) q^{76} +10.4657 q^{77} +(-27.0205 + 44.0346i) q^{78} -10.5643i q^{79} +(21.0980 - 28.8942i) q^{80} -0.224921 q^{81} +(108.350 + 66.4853i) q^{82} -4.80581i q^{83} +(-27.5068 - 54.1441i) q^{84} +3.40515 q^{85} +(-39.6200 + 64.5678i) q^{86} +20.3246i q^{87} +(10.2081 + 0.821716i) q^{88} +3.34629 q^{89} +(21.1594 + 12.9838i) q^{90} -113.717i q^{91} +(57.9034 - 29.4166i) q^{92} -39.7059 q^{93} +(3.38034 - 5.50886i) q^{94} +9.74679i q^{95} +(-22.5787 - 54.9714i) q^{96} +153.549 q^{97} +(30.4061 + 18.6578i) q^{98} +7.10625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−1.70466	−	1.04601i	−0.852329	−	0.523005i
$2$	−1.70466	−	1.04601i	−0.852329	−	0.523005i
$3$		−	1.85712i		−	0.619038i	−0.950893	−	0.309519i	$-0.899832\pi$
$3$		−	1.85712i		−	0.619038i	0.950893	−	0.309519i	$-0.100168\pi$
$4$	1.81172	+	3.56618i	0.452931	+	0.891546i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	−1.94256	+	3.16575i	−0.323760	+	0.527625i
$7$		−	8.17539i		−	1.16791i	−0.811785	−	0.583957i	$-0.801504\pi$
$7$		−	8.17539i		−	1.16791i	0.811785	−	0.583957i	$-0.198496\pi$
$8$	0.641893	−	7.97421i	0.0802366	−	0.996776i
$9$	5.55112			0.616791
$10$	3.81173	+	2.33895i	0.381173	+	0.233895i
$11$			1.28015i			0.116377i	0.998306	+	0.0581884i	$0.0185324\pi$
$11$			1.28015i			0.116377i	−0.998306	+	0.0581884i	$0.981468\pi$
$12$	6.62281	−	3.36458i	0.551901	−	0.280382i
$13$	13.9097			1.06998			0.534989	−	0.844859i	$-0.320316\pi$
$13$	13.9097			1.06998			0.534989	+	0.844859i	$0.320316\pi$
$14$	−8.55155	+	13.9363i	−0.610825	+	0.995447i
$15$			4.15264i			0.276842i
$16$	−9.43531	+	12.9219i	−0.589707	+	0.807617i
$17$	−1.52283			−0.0895781			−0.0447890	−	0.998996i	$-0.514262\pi$
$17$	−1.52283			−0.0895781			−0.0447890	+	0.998996i	$0.514262\pi$
$18$	−9.46277	−	5.80653i	−0.525710	−	0.322585i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	−4.05114	−	7.97423i	−0.202557	−	0.398711i
$21$	−15.1826			−0.722983
$22$	1.33905	−	2.18221i	0.0608657	−	0.0991915i
$23$		−	16.2368i		−	0.705948i	−0.935633	−	0.352974i	$-0.885170\pi$
$23$		−	16.2368i		−	0.705948i	0.935633	−	0.352974i	$-0.114830\pi$
$24$	−14.8090	−	1.19207i	−0.617043	−	0.0496695i
$25$	5.00000			0.200000
$26$	−23.7113	−	14.5497i	−0.911973	−	0.559604i
$27$		−	27.0231i		−	1.00086i
$28$	29.1549	−	14.8116i	1.04125	−	0.528984i
$29$	−10.9442			−0.377386			−0.188693	−	0.982036i	$-0.560425\pi$
$29$	−10.9442			−0.377386			−0.188693	+	0.982036i	$0.560425\pi$
$30$	4.34370	−	7.07883i	0.144790	−	0.235961i
$31$		−	21.3804i		−	0.689692i	−0.938659	−	0.344846i	$-0.887931\pi$
$31$		−	21.3804i		−	0.689692i	0.938659	−	0.344846i	$-0.112069\pi$
$32$	29.6004	−	12.1580i	0.925013	−	0.379936i
$33$	2.37738			0.0720418
$34$	2.59590	+	1.59289i	0.0763500	+	0.0468498i
$35$			18.2807i			0.522307i
$36$	10.0571	+	19.7963i	0.279364	+	0.549898i
$37$	−21.4981			−0.581028			−0.290514	−	0.956871i	$-0.593826\pi$
$37$	−21.4981			−0.581028			−0.290514	+	0.956871i	$0.593826\pi$
$38$	−4.55945	+	7.43044i	−0.119986	+	0.195538i
$39$		−	25.8319i		−	0.662357i
$40$	−1.43532	+	17.8309i	−0.0358829	+	0.445772i
$41$	−63.5609			−1.55026			−0.775132	−	0.631799i	$-0.782317\pi$
$41$	−63.5609			−1.55026			−0.775132	+	0.631799i	$0.782317\pi$
$42$	25.8812	+	15.8812i	0.616220	+	0.378124i
$43$		−	37.8772i		−	0.880866i	−0.897786	−	0.440433i	$-0.854825\pi$
$43$		−	37.8772i		−	0.880866i	0.897786	−	0.440433i	$-0.145175\pi$
$44$	−4.56523	+	2.31927i	−0.103755	+	0.0527107i
$45$	−12.4127			−0.275838
$46$	−16.9839	+	27.6782i	−0.369214	+	0.601700i
$47$			3.23165i			0.0687585i	0.999409	+	0.0343792i	$0.0109454\pi$
$47$			3.23165i			0.0687585i	−0.999409	+	0.0343792i	$0.989055\pi$
$48$	23.9974	+	17.5225i	0.499946	+	0.365051i
$49$	−17.8371			−0.364022
$50$	−8.52329	−	5.23005i	−0.170466	−	0.104601i
$51$			2.82807i			0.0554523i
$52$	25.2006	+	49.6046i	0.484626	+	0.953934i
$53$	−66.1970			−1.24900			−0.624500	−	0.781025i	$-0.714697\pi$
$53$	−66.1970			−1.24900			−0.624500	+	0.781025i	$0.714697\pi$
$54$	−28.2665	+	46.0652i	−0.523453	+	0.853059i
$55$		−	2.86249i		−	0.0520453i
$56$	−65.1923	−	5.24773i	−1.16415	−	0.0937094i
$57$	−8.09498			−0.142017
$58$	18.6561	+	11.4478i	0.321657	+	0.197375i
$59$			0.130585i			0.00221331i	0.999999	+	0.00110665i	$0.000352259\pi$
$59$			0.130585i			0.00221331i	−0.999999	+	0.00110665i	$0.999648\pi$
$60$	−14.8091	+	7.52343i	−0.246818	+	0.125390i
$61$	−20.5145			−0.336302			−0.168151	−	0.985761i	$-0.553780\pi$
$61$	−20.5145			−0.336302			−0.168151	+	0.985761i	$0.553780\pi$
$62$	−22.3642	+	36.4464i	−0.360712	+	0.587845i
$63$		−	45.3826i		−	0.720359i
$64$	−63.1759	−	10.2372i	−0.987124	−	0.159956i
$65$	−31.1031			−0.478508
$66$	−4.05262	−	2.48676i	−0.0614033	−	0.0376782i
$67$			17.8398i			0.266265i	0.991098	+	0.133133i	$0.0425036\pi$
$67$			17.8398i			0.266265i	−0.991098	+	0.133133i	$0.957496\pi$
$68$	−2.75894	−	5.43068i	−0.0405727	−	0.0798629i
$69$	−30.1536			−0.437009
$70$	19.1218	−	31.1624i	0.273169	−	0.445177i
$71$		−	32.6229i		−	0.459478i	−0.973252	−	0.229739i	$-0.926213\pi$
$71$		−	32.6229i		−	0.459478i	0.973252	−	0.229739i	$-0.0737873\pi$
$72$	3.56323	−	44.2658i	0.0494892	−	0.614803i
$73$	−4.61935			−0.0632788			−0.0316394	−	0.999499i	$-0.510073\pi$
$73$	−4.61935			−0.0632788			−0.0316394	+	0.999499i	$0.510073\pi$
$74$	36.6468	+	22.4872i	0.495228	+	0.303881i
$75$		−	9.28558i		−	0.123808i
$76$	15.5446	−	7.89712i	0.204535	−	0.103909i
$77$	10.4657			0.135918
$78$	−27.0205	+	44.0346i	−0.346416	+	0.564547i
$79$		−	10.5643i		−	0.133726i	−0.997762	−	0.0668629i	$-0.978701\pi$
$79$		−	10.5643i		−	0.133726i	0.997762	−	0.0668629i	$-0.0212990\pi$
$80$	21.0980	−	28.8942i	0.263725	−	0.361177i
$81$	−0.224921			−0.00277680
$82$	108.350	+	66.4853i	1.32134	+	0.810797i
$83$		−	4.80581i		−	0.0579014i	−0.999581	−	0.0289507i	$-0.990783\pi$
$83$		−	4.80581i		−	0.0579014i	0.999581	−	0.0289507i	$-0.00921658\pi$
$84$	−27.5068	−	54.1441i	−0.327462	−	0.644573i
$85$	3.40515			0.0400605
$86$	−39.6200	+	64.5678i	−0.460697	+	0.750788i
$87$			20.3246i			0.233617i
$88$	10.2081	+	0.821716i	0.116002	+	0.00933768i
$89$	3.34629			0.0375988			0.0187994	−	0.999823i	$-0.494016\pi$
$89$	3.34629			0.0375988			0.0187994	+	0.999823i	$0.494016\pi$
$90$	21.1594	+	12.9838i	0.235104	+	0.144264i
$91$		−	113.717i		−	1.24964i
$92$	57.9034	−	29.4166i	0.629385	−	0.319746i
$93$	−39.7059			−0.426946
$94$	3.38034	−	5.50886i	0.0359611	−	0.0586049i
$95$			9.74679i			0.102598i
$96$	−22.5787	−	54.9714i	−0.235195	−	0.572618i
$97$	153.549			1.58298			0.791492	−	0.611180i	$-0.209305\pi$
$97$	153.549			1.58298			0.791492	+	0.611180i	$0.209305\pi$
$98$	30.4061	+	18.6578i	0.310266	+	0.190385i
$99$			7.10625i			0.0717803i
$100$	9.05862	+	17.8309i	0.0905862	+	0.178309i
$101$	−17.1906			−0.170204			−0.0851021	−	0.996372i	$-0.527122\pi$
$101$	−17.1906			−0.170204			−0.0851021	+	0.996372i	$0.527122\pi$
$102$	2.95819	−	4.82089i	0.0290018	−	0.0472636i
$103$		−	174.847i		−	1.69754i	−0.528761	−	0.848771i	$-0.677343\pi$
$103$		−	174.847i		−	1.69754i	0.528761	−	0.848771i	$-0.322657\pi$
$104$	8.92854	−	110.919i	0.0858513	−	1.06653i
$105$	33.9494			0.323328
$106$	112.843	+	69.2427i	1.06456	+	0.653233i
$107$			92.0588i			0.860362i	0.902743	+	0.430181i	$0.141550\pi$
$107$			92.0588i			0.860362i	−0.902743	+	0.430181i	$0.858450\pi$
$108$	96.3693	−	48.9584i	0.892309	−	0.453319i
$109$	151.218			1.38733			0.693663	−	0.720300i	$-0.255996\pi$
$109$	151.218			1.38733			0.693663	+	0.720300i	$0.255996\pi$
$110$	−2.99420	+	4.87957i	−0.0272200	+	0.0443598i
$111$			39.9244i			0.359679i
$112$	105.641	+	77.1374i	0.943227	+	0.688727i
$113$	−173.604			−1.53632			−0.768160	−	0.640258i	$-0.778828\pi$
$113$	−173.604			−1.53632			−0.768160	+	0.640258i	$0.778828\pi$
$114$	13.7992	+	8.46743i	0.121045	+	0.0742757i
$115$			36.3066i			0.315709i
$116$	−19.8279	−	39.0290i	−0.170930	−	0.336457i
$117$	77.2145			0.659953
$118$	0.136593	−	0.222603i	0.00115757	−	0.00188647i
$119$			12.4497i			0.104619i
$120$	33.1140	+	2.66555i	0.275950	+	0.0222129i
$121$	119.361			0.986456
$122$	34.9701	+	21.4583i	0.286641	+	0.175888i
$123$			118.040i			0.959673i
$124$	76.2466	−	38.7355i	0.614892	−	0.312383i
$125$	−11.1803			−0.0894427
$126$	−47.4707	+	77.3619i	−0.376752	+	0.613983i
$127$			60.9999i			0.480314i	0.970734	+	0.240157i	$0.0771989\pi$
$127$			60.9999i			0.480314i	−0.970734	+	0.240157i	$0.922801\pi$
$128$	96.9853	+	83.5336i	0.757697	+	0.652606i
$129$	−70.3424			−0.545290
$130$	53.0201	+	32.5341i	0.407847	+	0.250262i
$131$			77.1999i			0.589312i	0.955603	+	0.294656i	$0.0952051\pi$
$131$			77.1999i			0.589312i	−0.955603	+	0.294656i	$0.904795\pi$
$132$	4.30715	+	8.47816i	0.0326299	+	0.0642285i
$133$	−35.6357			−0.267938
$134$	18.6606	−	30.4107i	0.139258	−	0.226946i
$135$			60.4255i			0.447596i
$136$	−0.977492	+	12.1433i	−0.00718744	+	0.0892893i
$137$	219.603			1.60294			0.801469	−	0.598036i	$-0.204052\pi$
$137$	219.603			1.60294			0.801469	+	0.598036i	$0.204052\pi$
$138$	51.4016	+	31.5410i	0.372475	+	0.228558i
$139$			68.1306i			0.490148i	0.969504	+	0.245074i	$0.0788123\pi$
$139$			68.1306i			0.490148i	−0.969504	+	0.245074i	$0.921188\pi$
$140$	−65.1924	+	33.1196i	−0.465660	+	0.236569i
$141$	6.00154			0.0425641
$142$	−34.1239	+	55.6110i	−0.240309	+	0.391627i
$143$			17.8065i			0.124521i
$144$	−52.3766	+	71.7309i	−0.363726	+	0.498131i
$145$	24.4720			0.168772
$146$	7.87442	+	4.83189i	0.0539344	+	0.0330951i
$147$			33.1255i			0.225343i
$148$	−38.9485	−	76.6660i	−0.263166	−	0.518013i
$149$	−43.1782			−0.289787			−0.144893	−	0.989447i	$-0.546284\pi$
$149$	−43.1782			−0.289787			−0.144893	+	0.989447i	$0.546284\pi$
$150$	−9.71281	+	15.8287i	−0.0647521	+	0.105525i
$151$		−	237.860i		−	1.57523i	−0.616166	−	0.787616i	$-0.711315\pi$
$151$		−	237.860i		−	1.57523i	0.616166	−	0.787616i	$-0.288685\pi$
$152$	−34.7588	−	2.79795i	−0.228676	−	0.0184075i
$153$	−8.45340			−0.0552510
$154$	−17.8404	−	10.9472i	−0.115847	−	0.0710859i
$155$			47.8081i			0.308440i
$156$	92.1214	−	46.8003i	0.590522	−	0.300002i
$157$	224.175			1.42787			0.713935	−	0.700212i	$-0.246911\pi$
$157$	224.175			1.42787			0.713935	+	0.700212i	$0.246911\pi$
$158$	−11.0504	+	18.0086i	−0.0699393	+	0.113978i
$159$			122.935i			0.773179i
$160$	−66.1885	+	27.1860i	−0.413678	+	0.169913i
$161$	−132.742			−0.824486
$162$	0.383413	+	0.235270i	0.00236675	+	0.00145228i
$163$			149.085i			0.914634i	0.889304	+	0.457317i	$0.151189\pi$
$163$			149.085i			0.914634i	−0.889304	+	0.457317i	$0.848811\pi$
$164$	−115.155	−	226.670i	−0.702163	−	1.38213i
$165$	−5.31598			−0.0322181
$166$	−5.02693	+	8.19227i	−0.0302827	+	0.0493510i
$167$		−	319.003i		−	1.91020i	−0.296287	−	0.955099i	$-0.595749\pi$
$167$		−	319.003i		−	1.91020i	0.296287	−	0.955099i	$-0.404251\pi$
$168$	−9.74563	+	121.070i	−0.0580097	+	0.720652i
$169$	24.4800			0.144852
$170$	−5.80461	−	3.56182i	−0.0341448	−	0.0209519i
$171$		−	24.1968i		−	0.141502i
$172$	135.077	−	68.6231i	0.785332	−	0.398971i
$173$	25.2102			0.145724			0.0728620	−	0.997342i	$-0.476787\pi$
$173$	25.2102			0.145724			0.0728620	+	0.997342i	$0.476787\pi$
$174$	21.2598	−	34.6466i	0.122183	−	0.199118i
$175$		−	40.8770i		−	0.233583i
$176$	−16.5419	−	12.0786i	−0.0939880	−	0.0686283i
$177$	0.242512			0.00137012
$178$	−5.70429	−	3.50026i	−0.0320465	−	0.0196644i
$179$		−	156.325i		−	0.873326i	−0.899625	−	0.436663i	$-0.856160\pi$
$179$		−	156.325i		−	0.873326i	0.899625	−	0.436663i	$-0.143840\pi$
$180$	−22.4884	−	44.2659i	−0.124935	−	0.245922i
$181$	15.0392			0.0830894			0.0415447	−	0.999137i	$-0.486772\pi$
$181$	15.0392			0.0830894			0.0415447	+	0.999137i	$0.486772\pi$
$182$	−118.950	+	193.849i	−0.653569	+	1.06511i
$183$			38.0977i			0.208184i
$184$	−129.476	−	10.4223i	−0.703672	−	0.0566428i
$185$	48.0711			0.259844
$186$	67.6851	+	41.5328i	0.363898	+	0.223295i
$187$		−	1.94944i		−	0.0104248i
$188$	−11.5246	+	5.85486i	−0.0613013	+	0.0311429i
$189$	−220.925			−1.16891
$190$	10.1952	−	16.6150i	0.0536592	−	0.0874472i
$191$		−	100.439i		−	0.525860i	−0.964815	−	0.262930i	$-0.915311\pi$
$191$		−	100.439i		−	0.525860i	0.964815	−	0.262930i	$-0.0846889\pi$
$192$	−19.0116	+	117.325i	−0.0990188	+	0.611068i
$193$	−60.2380			−0.312114			−0.156057	−	0.987748i	$-0.549878\pi$
$193$	−60.2380			−0.312114			−0.156057	+	0.987748i	$0.549878\pi$
$194$	−261.749	−	160.614i	−1.34922	−	0.827909i
$195$			57.7619i			0.296215i
$196$	−32.3158	−	63.6102i	−0.164877	−	0.324542i
$197$	315.357			1.60080			0.800399	−	0.599468i	$-0.204621\pi$
$197$	315.357			1.60080			0.800399	+	0.599468i	$0.204621\pi$
$198$	7.43321	−	12.1137i	0.0375415	−	0.0611804i
$199$			271.266i			1.36315i	0.731750	+	0.681573i	$0.238704\pi$
$199$			271.266i			1.36315i	−0.731750	+	0.681573i	$0.761296\pi$
$200$	3.20946	−	39.8710i	0.0160473	−	0.199355i
$201$	33.1305			0.164828
$202$	29.3042	+	17.9816i	0.145070	+	0.0890177i
$203$			89.4732i			0.440755i
$204$	−10.0854	+	5.12367i	−0.0494382	+	0.0251161i
$205$	142.126			0.693300
$206$	−182.892	+	298.054i	−0.887823	+	1.44686i
$207$		−	90.1325i		−	0.435423i
$208$	−131.242	+	179.740i	−0.630973	+	0.864132i
$209$	5.58003			0.0266987
$210$	−57.8722	−	35.5115i	−0.275582	−	0.169102i
$211$			197.215i			0.934668i	0.884081	+	0.467334i	$0.154785\pi$
$211$			197.215i			0.934668i	−0.884081	+	0.467334i	$0.845215\pi$
$212$	−119.931	−	236.070i	−0.565711	−	1.11354i
$213$	−60.5846			−0.284435
$214$	96.2944	−	156.929i	0.449974	−	0.733312i
$215$			84.6961i			0.393935i
$216$	−215.488	−	17.3459i	−0.997629	−	0.0803053i
$217$	−174.794			−0.805500
$218$	−257.776	−	158.176i	−1.18246	−	0.725579i
$219$			8.57867i			0.0391720i
$220$	10.2082	−	5.18605i	0.0464008	−	0.0235729i
$221$	−21.1821			−0.0958465
$222$	41.7613	−	68.0574i	0.188114	−	0.306565i
$223$		−	303.797i		−	1.36232i	−0.732134	−	0.681160i	$-0.761476\pi$
$223$		−	303.797i		−	1.36232i	0.732134	−	0.681160i	$-0.238524\pi$
$224$	−99.3961	−	241.995i	−0.443732	−	1.08033i
$225$	27.7556			0.123358
$226$	295.936	+	181.592i	1.30945	+	0.803504i
$227$			269.086i			1.18540i	0.805423	+	0.592701i	$0.201938\pi$
$227$			269.086i			1.18540i	−0.805423	+	0.592701i	$0.798062\pi$
$228$	−14.6659	−	28.8682i	−0.0643240	−	0.126615i
$229$	220.055			0.960938			0.480469	−	0.877012i	$-0.340466\pi$
$229$	220.055			0.960938			0.480469	+	0.877012i	$0.340466\pi$
$230$	37.9771	−	61.8903i	0.165118	−	0.269088i
$231$		−	19.4360i		−	0.0841385i
$232$	−7.02500	+	87.2713i	−0.0302802	+	0.376170i
$233$	−353.511			−1.51721			−0.758606	−	0.651549i	$-0.774119\pi$
$233$	−353.511			−1.51721			−0.758606	+	0.651549i	$0.774119\pi$
$234$	−131.624	−	80.7672i	−0.562497	−	0.345159i
$235$		−	7.22619i		−	0.0307497i
$236$	−0.465690	+	0.236584i	−0.00197326	+	0.00100247i
$237$	−19.6192			−0.0827814
$238$	13.0225	−	21.2225i	0.0547165	−	0.0891702i
$239$			301.934i			1.26332i	0.775244	+	0.631661i	$0.217627\pi$
$239$			301.934i			1.26332i	−0.775244	+	0.631661i	$0.782373\pi$
$240$	−53.6598	−	39.1814i	−0.223583	−	0.163256i
$241$	−94.8112			−0.393408			−0.196704	−	0.980463i	$-0.563024\pi$
$241$	−94.8112			−0.393408			−0.196704	+	0.980463i	$0.563024\pi$
$242$	−203.470	−	124.853i	−0.840786	−	0.515922i
$243$		−	242.790i		−	0.999137i
$244$	−37.1665	−	73.1583i	−0.152322	−	0.299829i
$245$	39.8849			0.162795
$246$	123.471	−	201.218i	0.501914	−	0.817958i
$247$		−	60.6310i		−	0.245470i
$248$	−170.492	−	13.7239i	−0.687468	−	0.0553385i
$249$	−8.92495			−0.0358432
$250$	19.0587	+	11.6948i	0.0762347	+	0.0467790i
$251$		−	49.3291i		−	0.196530i	−0.995160	−	0.0982652i	$-0.968671\pi$
$251$		−	49.3291i		−	0.196530i	0.995160	−	0.0982652i	$-0.0313293\pi$
$252$	161.843	−	82.2208i	0.642233	−	0.326273i
$253$	20.7855			0.0821560
$254$	63.8065	−	103.984i	0.251207	−	0.409386i
$255$		−	6.32375i		−	0.0247990i
$256$	−77.9498	−	243.844i	−0.304491	−	0.952515i
$257$	−444.392			−1.72915			−0.864577	−	0.502501i	$-0.832413\pi$
$257$	−444.392			−1.72915			−0.864577	+	0.502501i	$0.832413\pi$
$258$	119.910	+	73.5789i	0.464766	+	0.285189i
$259$			175.755i			0.678591i
$260$	−56.3501	−	110.919i	−0.216731	−	0.426612i
$261$	−60.7526			−0.232769
$262$	80.7519	−	131.600i	0.308213	−	0.502288i
$263$		−	122.135i		−	0.464393i	−0.972669	−	0.232196i	$-0.925409\pi$
$263$		−	122.135i		−	0.464393i	0.972669	−	0.232196i	$-0.0745912\pi$
$264$	1.52602	−	18.9577i	0.00578039	−	0.0718095i
$265$	148.021			0.558570
$266$	60.7467	+	37.2753i	0.228371	+	0.140133i
$267$		−	6.21445i		−	0.0232751i
$268$	−63.6199	+	32.3208i	−0.237388	+	0.120600i
$269$	348.304			1.29481			0.647406	−	0.762146i	$-0.275854\pi$
$269$	348.304			1.29481			0.647406	+	0.762146i	$0.275854\pi$
$270$	63.2057	−	103.005i	0.234095	−	0.381500i
$271$			414.498i			1.52951i	0.644320	+	0.764756i	$0.277140\pi$
$271$			414.498i			1.52951i	−0.644320	+	0.764756i	$0.722860\pi$
$272$	14.3684	−	19.6778i	0.0528248	−	0.0723448i
$273$	−211.186			−0.773576
$274$	−374.348	−	229.707i	−1.36623	−	0.838345i
$275$			6.40073i			0.0232754i
$276$	−54.6300	−	107.533i	−0.197935	−	0.389613i
$277$	−41.5582			−0.150030			−0.0750148	−	0.997182i	$-0.523900\pi$
$277$	−41.5582			−0.150030			−0.0750148	+	0.997182i	$0.523900\pi$
$278$	71.2654	−	116.139i	0.256350	−	0.417768i
$279$		−	118.685i		−	0.425396i
$280$	145.774	+	11.7343i	0.520623	+	0.0419081i
$281$	481.771			1.71449			0.857243	−	0.514912i	$-0.172175\pi$
$281$	481.771			1.71449			0.857243	+	0.514912i	$0.172175\pi$
$282$	−10.2306	−	6.27768i	−0.0362787	−	0.0222613i
$283$			191.254i			0.675811i	0.941180	+	0.337905i	$0.109718\pi$
$283$			191.254i			0.675811i	−0.941180	+	0.337905i	$0.890282\pi$
$284$	116.339	−	59.1038i	0.409646	−	0.208112i
$285$	18.1009			0.0635120
$286$	18.6257	−	30.3539i	0.0651250	−	0.106133i
$287$			519.635i			1.81058i
$288$	164.316	−	67.4903i	0.570540	−	0.234341i
$289$	−286.681			−0.991976
$290$	−41.7164	−	25.5980i	−0.143850	−	0.0882688i
$291$		−	285.159i		−	0.979928i
$292$	−8.36899	−	16.4734i	−0.0286609	−	0.0564159i
$293$	−35.2863			−0.120431			−0.0602154	−	0.998185i	$-0.519179\pi$
$293$	−35.2863			−0.120431			−0.0602154	+	0.998185i	$0.519179\pi$
$294$	34.6496	−	56.4677i	0.117856	−	0.192067i
$295$		−	0.291997i		−	0.000989821i
$296$	−13.7994	+	171.430i	−0.0466197	+	0.579155i
$297$	34.5935			0.116477
$298$	73.6042	+	45.1649i	0.246994	+	0.151560i
$299$		−	225.849i		−	0.755348i
$300$	33.1141	−	16.8229i	0.110380	−	0.0560763i
$301$	−309.661			−1.02877
$302$	−248.804	+	405.470i	−0.823855	+	1.34262i
$303$			31.9250i			0.105363i
$304$	56.3252	+	41.1276i	0.185280	+	0.135288i
$305$	45.8717			0.150399
$306$	14.4102	+	8.84235i	0.0470921	+	0.0288966i
$307$			111.567i			0.363411i	0.983353	+	0.181706i	$0.0581618\pi$
$307$			111.567i			0.363411i	−0.983353	+	0.181706i	$0.941838\pi$
$308$	18.9610	+	37.3226i	0.0615615	+	0.121177i
$309$	−324.711			−1.05084
$310$	50.0078	−	81.4965i	0.161315	−	0.262892i
$311$			317.697i			1.02154i	0.859719	+	0.510768i	$0.170639\pi$
$311$			317.697i			1.02154i	−0.859719	+	0.510768i	$0.829361\pi$
$312$	−205.989	−	16.5813i	−0.660222	−	0.0531453i
$313$	−68.8351			−0.219920			−0.109960	−	0.993936i	$-0.535072\pi$
$313$	−68.8351			−0.219920			−0.109960	+	0.993936i	$0.535072\pi$
$314$	−382.143	−	234.490i	−1.21702	−	0.746783i
$315$			101.479i			0.322154i
$316$	37.6743	−	19.1397i	0.119223	−	0.0605685i
$317$	−156.039			−0.492235			−0.246118	−	0.969240i	$-0.579155\pi$
$317$	−156.039			−0.492235			−0.246118	+	0.969240i	$0.579155\pi$
$318$	128.592	−	209.563i	0.404377	−	0.659003i
$319$		−	14.0102i		−	0.0439190i
$320$	141.266	+	22.8910i	0.441455	+	0.0715344i
$321$	170.964			0.532597
$322$	226.280	+	138.850i	0.702734	+	0.431210i
$323$			6.63785i			0.0205506i
$324$	−0.407495	−	0.802109i	−0.00125770	−	0.00247564i
$325$	69.5485			0.213996
$326$	155.945	−	254.140i	0.478358	−	0.779569i
$327$		−	280.830i		−	0.858808i
$328$	−40.7993	+	506.847i	−0.124388	+	1.54527i
$329$	26.4200			0.0803040
$330$	9.06193	+	5.56057i	0.0274604	+	0.0168502i
$331$		−	127.828i		−	0.386186i	−0.981180	−	0.193093i	$-0.938148\pi$
$331$		−	127.828i		−	0.386186i	0.981180	−	0.193093i	$-0.0618520\pi$
$332$	17.1384	−	8.70681i	0.0516217	−	0.0262253i
$333$	−119.338			−0.358373
$334$	−333.681	+	543.791i	−0.999044	+	1.62812i
$335$		−	39.8910i		−	0.119078i
$336$	143.253	−	196.188i	0.426348	−	0.583894i
$337$	−486.406			−1.44334			−0.721670	−	0.692237i	$-0.756625\pi$
$337$	−486.406			−1.44334			−0.721670	+	0.692237i	$0.756625\pi$
$338$	−41.7300	−	25.6063i	−0.123462	−	0.0757583i
$339$			322.403i			0.951041i
$340$	6.16918	+	12.1434i	0.0181447	+	0.0357158i
$341$	27.3701			0.0802642
$342$	−25.3101	+	41.2473i	−0.0740061	+	0.120606i
$343$		−	254.769i		−	0.742768i
$344$	−302.041	−	24.3131i	−0.878026	−	0.0706777i
$345$	67.4255			0.195436
$346$	−42.9749	−	26.3702i	−0.124205	−	0.0762144i
$347$			361.957i			1.04310i	0.853220	+	0.521551i	$0.174646\pi$
$347$			361.957i			1.04310i	−0.853220	+	0.521551i	$0.825354\pi$
$348$	−72.4814	+	36.8226i	−0.208280	+	0.105812i
$349$	483.043			1.38408			0.692038	−	0.721861i	$-0.256713\pi$
$349$	483.043			1.38408			0.692038	+	0.721861i	$0.256713\pi$
$350$	−42.7577	+	69.6813i	−0.122165	+	0.199089i
$351$		−	375.884i		−	1.07089i
$352$	15.5640	+	37.8928i	0.0442158	+	0.107650i
$353$	690.031			1.95476			0.977381	−	0.211486i	$-0.0678304\pi$
$353$	690.031			1.95476			0.977381	+	0.211486i	$0.0678304\pi$
$354$	−0.413399	−	0.253670i	−0.00116779	−	0.000716581i
$355$			72.9471i			0.205485i
$356$	6.06256	+	11.9335i	0.0170297	+	0.0335210i
$357$	23.1206			0.0647635
$358$	−163.518	+	266.481i	−0.456754	+	0.744361i
$359$			92.2998i			0.257102i	0.991703	+	0.128551i	$0.0410327\pi$
$359$			92.2998i			0.257102i	−0.991703	+	0.128551i	$0.958967\pi$
$360$	−7.96761	+	98.9813i	−0.0221323	+	0.274948i
$361$	−19.0000			−0.0526316
$362$	−25.6367	−	15.7311i	−0.0708195	−	0.0434562i
$363$		−	221.668i		−	0.610654i
$364$	405.537	−	206.024i	1.11411	−	0.566001i
$365$	10.3292			0.0282991
$366$	39.8506	−	64.9436i	0.108881	−	0.177441i
$367$		−	19.5821i		−	0.0533571i	−0.999644	−	0.0266786i	$-0.991507\pi$
$367$		−	19.5821i		−	0.0533571i	0.999644	−	0.0266786i	$-0.00849306\pi$
$368$	209.810	+	153.199i	0.570136	+	0.416302i
$369$	−352.834			−0.956190
$370$	−81.9448	−	50.2829i	−0.221473	−	0.135900i
$371$			541.186i			1.45872i
$372$	−71.9362	−	141.599i	−0.193377	−	0.380641i
$373$	484.796			1.29972			0.649860	−	0.760054i	$-0.274827\pi$
$373$	484.796			1.29972			0.649860	+	0.760054i	$0.274827\pi$
$374$	−2.03914	+	3.32313i	−0.00545224	+	0.00888538i
$375$			20.7632i			0.0553685i
$376$	25.7698	+	2.07437i	0.0685368	+	0.00551695i
$377$	−152.231			−0.403795
$378$	376.601	+	231.089i	0.996299	+	0.611348i
$379$			470.481i			1.24138i	0.784058	+	0.620688i	$0.213146\pi$
$379$			470.481i			1.24138i	−0.784058	+	0.620688i	$0.786854\pi$
$380$	−34.7588	+	17.6585i	−0.0914706	+	0.0464697i
$381$	113.284			0.297333
$382$	−105.061	+	171.215i	−0.275028	+	0.448206i
$383$		−	699.541i		−	1.82648i	−0.407425	−	0.913239i	$-0.633573\pi$
$383$		−	699.541i		−	1.82648i	0.407425	−	0.913239i	$-0.366427\pi$
$384$	155.131	−	180.113i	0.403988	−	0.469044i
$385$	−23.4020			−0.0607844
$386$	102.685	+	63.0095i	0.266024	+	0.163237i
$387$		−	210.261i		−	0.543310i
$388$	278.189	+	547.585i	0.716982	+	1.41130i
$389$	674.975			1.73515			0.867577	−	0.497303i	$-0.165676\pi$
$389$	674.975			1.73515			0.867577	+	0.497303i	$0.165676\pi$
$390$	60.4196	−	98.4644i	0.154922	−	0.252473i
$391$			24.7258i			0.0632374i
$392$	−11.4495	+	142.236i	−0.0292079	+	0.362848i
$393$	143.369			0.364807
$394$	−537.576	−	329.867i	−1.36441	−	0.837226i
$395$			23.6226i			0.0598040i
$396$	−25.3422	+	12.8746i	−0.0639954	+	0.0325115i
$397$	96.0622			0.241970			0.120985	−	0.992654i	$-0.461395\pi$
$397$	96.0622			0.241970			0.120985	+	0.992654i	$0.461395\pi$
$398$	283.747	−	462.416i	0.712932	−	1.16185i
$399$			66.1796i			0.165864i
$400$	−47.1766	+	64.6094i	−0.117941	+	0.161523i
$401$	234.848			0.585656			0.292828	−	0.956165i	$-0.405404\pi$
$401$	234.848			0.585656			0.292828	+	0.956165i	$0.405404\pi$
$402$	−56.4762	−	34.6549i	−0.140488	−	0.0862062i
$403$		−	297.396i		−	0.737955i
$404$	−31.1447	−	61.3049i	−0.0770908	−	0.151745i
$405$	0.502938			0.00124182
$406$	93.5899	−	152.521i	0.230517	−	0.375668i
$407$		−	27.5206i		−	0.0676183i
$408$	22.5516	+	1.81531i	0.0552735	+	0.00444930i
$409$	408.817			0.999552			0.499776	−	0.866155i	$-0.333416\pi$
$409$	408.817			0.999552			0.499776	+	0.866155i	$0.333416\pi$
$410$	−242.277	−	148.666i	−0.590920	−	0.362599i
$411$		−	407.827i		−	0.992281i
$412$	623.536	−	316.774i	1.51344	−	0.768869i
$413$	1.06758			0.00258495
$414$	−94.2795	+	153.645i	−0.227728	+	0.371123i
$415$			10.7461i			0.0258943i
$416$	411.733	−	169.114i	0.989743	−	0.406523i
$417$	126.526			0.303421
$418$	−9.51204	−	5.83677i	−0.0227561	−	0.0139636i
$419$			276.957i			0.660996i	0.943807	+	0.330498i	$0.107217\pi$
$419$			276.957i			0.660996i	−0.943807	+	0.330498i	$0.892783\pi$
$420$	61.5070	+	121.070i	0.146445	+	0.288262i
$421$	−465.271			−1.10516			−0.552579	−	0.833461i	$-0.686356\pi$
$421$	−465.271			−1.10516			−0.552579	+	0.833461i	$0.686356\pi$
$422$	206.289	−	336.184i	0.488836	−	0.796645i
$423$			17.9393i			0.0424097i
$424$	−42.4914	+	527.868i	−0.100215	+	1.24497i
$425$	−7.61414			−0.0179156
$426$	103.276	+	63.3721i	0.242432	+	0.148761i
$427$			167.714i			0.392772i
$428$	−328.298	+	166.785i	−0.767052	+	0.389685i
$429$	33.0686			0.0770831
$430$	88.5930	−	144.378i	0.206030	−	0.335763i
$431$		−	635.325i		−	1.47407i	−0.675854	−	0.737036i	$-0.736225\pi$
$431$		−	635.325i		−	1.47407i	0.675854	−	0.737036i	$-0.263775\pi$
$432$	349.189	+	254.971i	0.808309	+	0.590212i
$433$	344.189			0.794894			0.397447	−	0.917625i	$-0.369896\pi$
$433$	344.189			0.794894			0.397447	+	0.917625i	$0.369896\pi$
$434$	297.963	+	182.836i	0.686552	+	0.421281i
$435$		−	45.4473i		−	0.104477i
$436$	273.966	+	539.273i	0.628363	+	1.23686i
$437$	−70.7746			−0.161956
$438$	8.97337	−	14.6237i	0.0204872	−	0.0333874i
$439$			303.262i			0.690802i	0.938455	+	0.345401i	$0.112257\pi$
$439$			303.262i			0.690802i	−0.938455	+	0.345401i	$0.887743\pi$
$440$	−22.8261	−	1.83741i	−0.0518775	−	0.00417594i
$441$	−99.0157			−0.224526
$442$	36.1082	+	22.1567i	0.0816928	+	0.0501282i
$443$		−	833.153i		−	1.88071i	−0.340198	−	0.940354i	$-0.610494\pi$
$443$		−	833.153i		−	1.88071i	0.340198	−	0.940354i	$-0.389506\pi$
$444$	−142.378	+	72.3319i	−0.320670	+	0.162910i
$445$	−7.48254			−0.0168147
$446$	−317.775	+	517.871i	−0.712501	+	1.16115i
$447$			80.1870i			0.179389i
$448$	−83.6929	+	516.488i	−0.186815	+	1.15288i
$449$	−310.068			−0.690575			−0.345287	−	0.938497i	$-0.612219\pi$
$449$	−310.068			−0.690575			−0.345287	+	0.938497i	$0.612219\pi$
$450$	−47.3139	−	29.0327i	−0.105142	−	0.0645170i
$451$		−	81.3672i		−	0.180415i
$452$	−314.523	−	619.104i	−0.695847	−	1.36970i
$453$	−441.734			−0.975130
$454$	281.467	−	458.700i	0.619971	−	1.01035i
$455$			254.280i			0.558856i
$456$	−5.19611	+	64.5510i	−0.0113950	+	0.141559i
$457$	−279.919			−0.612515			−0.306257	−	0.951949i	$-0.599077\pi$
$457$	−279.919			−0.612515			−0.306257	+	0.951949i	$0.599077\pi$
$458$	−375.118	−	230.180i	−0.819036	−	0.502576i
$459$			41.1515i			0.0896548i
$460$	−129.476	+	65.7775i	−0.281469	+	0.142995i
$461$	−42.2298			−0.0916048			−0.0458024	−	0.998951i	$-0.514584\pi$
$461$	−42.2298			−0.0916048			−0.0458024	+	0.998951i	$0.514584\pi$
$462$	−20.3303	+	33.1318i	−0.0440049	+	0.0717138i
$463$		−	714.026i		−	1.54217i	−0.636730	−	0.771087i	$-0.719714\pi$
$463$		−	714.026i		−	1.54217i	0.636730	−	0.771087i	$-0.280286\pi$
$464$	103.262	−	141.420i	0.222547	−	0.304784i
$465$	88.7852			0.190936
$466$	602.615	+	369.776i	1.29316	+	0.793510i
$467$		−	132.381i		−	0.283472i	−0.989905	−	0.141736i	$-0.954732\pi$
$467$		−	132.381i		−	0.283472i	0.989905	−	0.141736i	$-0.0452683\pi$
$468$	139.891	+	275.361i	0.298913	+	0.588378i
$469$	145.847			0.310975
$470$	−7.55867	+	12.3182i	−0.0160823	+	0.0262089i
$471$		−	416.320i		−	0.883906i
$472$	1.04131	+	0.0838216i	0.00220617	+	0.000177588i
$473$	48.4884			0.102512
$474$	33.4440	+	20.5219i	0.0705570	+	0.0432951i
$475$		−	21.7945i		−	0.0458831i
$476$	−44.3979	+	22.5554i	−0.0932730	+	0.0473854i
$477$	−367.468			−0.770372
$478$	315.826	−	514.695i	0.660724	−	1.07677i
$479$		−	331.142i		−	0.691319i	−0.938360	−	0.345659i	$-0.887655\pi$
$479$		−	331.142i		−	0.691319i	0.938360	−	0.345659i	$-0.112345\pi$
$480$	50.4876	+	122.920i	0.105182	+	0.256083i
$481$	−299.032			−0.621687
$482$	161.621	+	99.1736i	0.335313	+	0.205754i
$483$			246.518i			0.510388i
$484$	216.250	+	425.664i	0.446797	+	0.879471i
$485$	−343.347			−0.707932
$486$	−253.961	+	413.875i	−0.522554	+	0.851594i
$487$		−	770.905i		−	1.58297i	−0.611191	−	0.791483i	$-0.709309\pi$
$487$		−	770.905i		−	1.58297i	0.611191	−	0.791483i	$-0.290691\pi$
$488$	−13.1681	+	163.586i	−0.0269838	+	0.335218i
$489$	276.869			0.566193
$490$	−67.9901	−	41.7200i	−0.138755	−	0.0851429i
$491$			631.698i			1.28655i	0.765634	+	0.643277i	$0.222426\pi$
$491$			631.698i			1.28655i	−0.765634	+	0.643277i	$0.777574\pi$
$492$	−420.952	+	213.856i	−0.855593	+	0.434666i
$493$	16.6661			0.0338055
$494$	−63.4207	+	103.355i	−0.128382	+	0.209221i
$495$		−	15.8901i		−	0.0321011i
$496$	276.275	+	201.731i	0.557007	+	0.406716i
$497$	−266.705			−0.536631
$498$	15.2140	+	9.33559i	0.0305502	+	0.0187462i
$499$			731.949i			1.46683i	0.679780	+	0.733416i	$0.262075\pi$
$499$			731.949i			1.46683i	−0.679780	+	0.733416i	$0.737925\pi$
$500$	−20.2557	−	39.8711i	−0.0405114	−	0.0797423i
$501$	−592.425			−1.18249
$502$	−51.5988	+	84.0893i	−0.102786	+	0.167509i
$503$			488.482i			0.971137i	0.874199	+	0.485568i	$0.161387\pi$
$503$			488.482i			0.971137i	−0.874199	+	0.485568i	$0.838613\pi$
$504$	−361.890	−	29.1308i	−0.718036	−	0.0577991i
$505$	38.4394			0.0761177
$506$	−35.4321	−	21.7418i	−0.0700240	−	0.0429680i
$507$		−	45.4621i		−	0.0896689i
$508$	−217.537	+	110.515i	−0.428222	+	0.217549i
$509$	411.107			0.807677			0.403838	−	0.914830i	$-0.367676\pi$
$509$	411.107			0.807677			0.403838	+	0.914830i	$0.367676\pi$
$510$	−6.61471	+	10.7798i	−0.0129700	+	0.0211369i
$511$			37.7650i			0.0739041i
$512$	−122.185	+	497.207i	−0.238644	+	0.971107i
$513$	−117.791			−0.229612
$514$	757.538	+	464.839i	1.47381	+	0.904356i
$515$			390.969i			0.759164i
$516$	−127.441	−	250.854i	−0.246979	−	0.486151i
$517$	−4.13698			−0.00800190
$518$	183.842	−	299.602i	0.354907	−	0.578383i
$519$		−	46.8183i		−	0.0902087i
$520$	−19.9648	+	248.022i	−0.0383939	+	0.476966i
$521$	883.975			1.69669			0.848345	−	0.529444i	$-0.177599\pi$
$521$	883.975			1.69669			0.848345	+	0.529444i	$0.177599\pi$
$522$	103.562	+	63.5479i	0.198396	+	0.121739i
$523$			800.103i			1.52983i	0.644129	+	0.764917i	$0.277220\pi$
$523$			800.103i			1.52983i	−0.644129	+	0.764917i	$0.722780\pi$
$524$	−275.309	+	139.865i	−0.525399	+	0.266918i
$525$	−75.9132			−0.144597
$526$	−127.755	+	208.199i	−0.242880	+	0.395816i
$527$			32.5587i			0.0617813i
$528$	−22.4313	+	30.7202i	−0.0424835	+	0.0581822i
$529$	265.366			0.501638
$530$	−252.325	−	154.831i	−0.476085	−	0.292135i
$531$			0.724894i			0.00136515i
$532$	−64.5621	−	127.083i	−0.121357	−	0.238879i
$533$	−884.113			−1.65875
$534$	−6.50038	+	10.5935i	−0.0121730	+	0.0198380i
$535$		−	205.850i		−	0.384766i
$536$	142.258	+	11.4512i	0.265407	+	0.0213642i
$537$	−290.314			−0.540622
$538$	−593.740	−	364.330i	−1.10361	−	0.677193i
$539$		−	22.8340i		−	0.0423637i
$540$	−215.488	+	109.474i	−0.399053	+	0.202730i
$541$	−620.328			−1.14663			−0.573316	−	0.819334i	$-0.694343\pi$
$541$	−620.328			−1.14663			−0.573316	+	0.819334i	$0.694343\pi$
$542$	433.569	−	706.577i	0.799943	−	1.30365i
$543$		−	27.9295i		−	0.0514355i
$544$	−45.0763	+	18.5145i	−0.0828609	+	0.0340339i
$545$	−338.135			−0.620431
$546$	360.000	+	220.903i	0.659341	+	0.404584i
$547$		−	347.136i		−	0.634619i	−0.948322	−	0.317309i	$-0.897221\pi$
$547$		−	347.136i		−	0.634619i	0.948322	−	0.317309i	$-0.102779\pi$
$548$	397.859	+	783.143i	0.726021	+	1.42909i
$549$	−113.878			−0.207429
$550$	6.69523	−	10.9111i	0.0121731	−	0.0198383i
$551$			47.7047i			0.0865784i
$552$	−19.3554	+	240.451i	−0.0350641	+	0.435600i
$553$	−86.3676			−0.156180
$554$	70.8425	+	43.4703i	0.127875	+	0.0784663i
$555$		−	89.2736i		−	0.160853i
$556$	−242.966	+	123.434i	−0.436990	+	0.222003i
$557$	95.2075			0.170929			0.0854645	−	0.996341i	$-0.472763\pi$
$557$	95.2075			0.170929			0.0854645	+	0.996341i	$0.472763\pi$
$558$	−124.146	+	202.318i	−0.222484	+	0.362578i
$559$		−	526.861i		−	0.942507i
$560$	−236.221	−	172.484i	−0.421824	−	0.308008i
$561$	−3.62034			−0.00645336
$562$	−821.255	−	503.937i	−1.46131	−	0.896685i
$563$			448.547i			0.796709i	0.917232	+	0.398354i	$0.130419\pi$
$563$			448.547i			0.796709i	−0.917232	+	0.398354i	$0.869581\pi$
$564$	10.8731	+	21.4026i	0.0192786	+	0.0379479i
$565$	388.191			0.687063
$566$	200.054	−	326.024i	0.353453	−	0.576013i
$567$			1.83882i			0.00324306i
$568$	−260.142	−	20.9404i	−0.457997	−	0.0368669i
$569$	137.458			0.241578			0.120789	−	0.992678i	$-0.461457\pi$
$569$	137.458			0.241578			0.120789	+	0.992678i	$0.461457\pi$
$570$	−30.8559	−	18.9338i	−0.0541331	−	0.0332171i
$571$		−	234.952i		−	0.411475i	−0.978607	−	0.205737i	$-0.934041\pi$
$571$		−	234.952i		−	0.411475i	0.978607	−	0.205737i	$-0.0659592\pi$
$572$	−63.5011	+	32.2604i	−0.111016	+	0.0563993i
$573$	−186.527			−0.325528
$574$	543.544	−	885.801i	0.946940	−	1.54321i
$575$		−	81.1840i		−	0.141190i
$576$	−350.697	−	56.8278i	−0.608850	−	0.0986594i
$577$	786.011			1.36224			0.681118	−	0.732173i	$-0.261494\pi$
$577$	786.011			1.36224			0.681118	+	0.732173i	$0.261494\pi$
$578$	488.693	+	299.871i	0.845490	+	0.518809i
$579$			111.869i			0.193210i
$580$	44.3365	+	87.2715i	0.0764422	+	0.150468i
$581$	−39.2894			−0.0676238
$582$	−298.279	+	486.099i	−0.512507	+	0.835221i
$583$		−	84.7418i		−	0.145355i
$584$	−2.96513	+	36.8357i	−0.00507727	+	0.0630748i
$585$	−172.657			−0.295140
$586$	60.1510	+	36.9098i	0.102647	+	0.0629860i
$587$		−	652.719i		−	1.11196i	−0.831197	−	0.555978i	$-0.812344\pi$
$587$		−	652.719i		−	1.11196i	0.831197	−	0.555978i	$-0.187656\pi$
$588$	−118.132	+	60.0142i	−0.200904	+	0.102065i
$589$	−93.1952			−0.158226
$590$	−0.305432	+	0.497755i	−0.000517681	+	0.000843653i
$591$		−	585.654i		−	0.990955i
$592$	202.841	−	277.795i	0.342637	−	0.469249i
$593$	672.379			1.13386			0.566930	−	0.823766i	$-0.308131\pi$
$593$	672.379			1.13386			0.566930	+	0.823766i	$0.308131\pi$
$594$	−58.9702	−	36.1852i	−0.0992764	−	0.0609178i
$595$		−	27.8384i		−	0.0467872i
$596$	−78.2271	−	153.981i	−0.131253	−	0.258358i
$597$	503.772			0.843839
$598$	−236.241	+	384.996i	−0.395051	+	0.643805i
$599$			503.861i			0.841170i	0.907253	+	0.420585i	$0.138175\pi$
$599$			503.861i			0.841170i	−0.907253	+	0.420585i	$0.861825\pi$
$600$	−74.0451	−	5.96034i	−0.123409	−	0.00993391i
$601$	−841.167			−1.39961			−0.699806	−	0.714333i	$-0.746730\pi$
$601$	−841.167			−1.39961			−0.699806	+	0.714333i	$0.746730\pi$
$602$	527.867	+	323.909i	0.876855	+	0.538055i
$603$			99.0308i			0.164230i
$604$	848.253	−	430.937i	1.40439	−	0.713472i
$605$	−266.900			−0.441157
$606$	33.3939	−	54.4212i	0.0551054	−	0.0898040i
$607$		−	835.852i		−	1.37702i	−0.725226	−	0.688511i	$-0.758265\pi$
$607$		−	835.852i		−	1.37702i	0.725226	−	0.688511i	$-0.241735\pi$
$608$	−52.9953	−	129.025i	−0.0871633	−	0.212212i
$609$	166.162			0.272844
$610$	−78.1956	−	47.9823i	−0.128190	−	0.0786595i
$611$			44.9513i			0.0735700i
$612$	−15.3152	−	30.1464i	−0.0250249	−	0.0492588i
$613$	−418.953			−0.683447			−0.341723	−	0.939801i	$-0.611011\pi$
$613$	−418.953			−0.683447			−0.341723	+	0.939801i	$0.611011\pi$
$614$	116.701	−	190.184i	0.190066	−	0.309746i
$615$		−	263.945i		−	0.429179i
$616$	6.71785	−	83.4556i	0.0109056	−	0.135480i
$617$	103.772			0.168188			0.0840940	−	0.996458i	$-0.473200\pi$
$617$	103.772			0.168188			0.0840940	+	0.996458i	$0.473200\pi$
$618$	553.521	+	339.651i	0.895665	+	0.549597i
$619$			233.917i			0.377896i	0.981987	+	0.188948i	$0.0605077\pi$
$619$			233.917i			0.377896i	−0.981987	+	0.188948i	$0.939492\pi$
$620$	−170.492	+	86.6151i	−0.274988	+	0.139702i
$621$	−438.769			−0.706552
$622$	332.315	−	541.566i	0.534268	−	0.870685i
$623$		−	27.3573i		−	0.0439121i
$624$	333.797	+	243.732i	0.534931	+	0.390597i
$625$	25.0000			0.0400000
$626$	117.340	+	72.0022i	0.187445	+	0.115020i
$627$		−	10.3628i		−	0.0165275i
$628$	406.144	+	799.451i	0.646726	+	1.27301i
$629$	32.7378			0.0520474
$630$	106.148	−	172.986i	0.168488	−	0.274582i
$631$		−	406.859i		−	0.644784i	−0.946606	−	0.322392i	$-0.895513\pi$
$631$		−	406.859i		−	0.644784i	0.946606	−	0.322392i	$-0.104487\pi$
$632$	−84.2422	−	6.78117i	−0.133295	−	0.0107297i
$633$	366.251			0.578595
$634$	265.993	+	163.218i	0.419547	+	0.257442i
$635$		−	136.400i		−	0.214803i
$636$	−438.410	+	222.725i	−0.689324	+	0.350197i
$637$	−248.108			−0.389495
$638$	−14.6548	+	23.8826i	−0.0229699	+	0.0374335i
$639$		−	181.094i		−	0.283402i
$640$	−216.866	−	186.787i	−0.338853	−	0.291854i
$641$	699.752			1.09166			0.545829	−	0.837897i	$-0.316215\pi$
$641$	699.752			1.09166			0.545829	+	0.837897i	$0.316215\pi$
$642$	−291.435	−	178.830i	−0.453948	−	0.278551i
$643$		−	403.352i		−	0.627298i	−0.949539	−	0.313649i	$-0.898449\pi$
$643$		−	403.352i		−	0.627298i	0.949539	−	0.313649i	$-0.101551\pi$
$644$	−240.492	−	473.383i	−0.373435	−	0.735067i
$645$	157.290			0.243861
$646$	6.94326	−	11.3153i	0.0107481	−	0.0175159i
$647$		−	407.762i		−	0.630234i	−0.949053	−	0.315117i	$-0.897956\pi$
$647$		−	407.762i		−	0.630234i	0.949053	−	0.315117i	$-0.102044\pi$
$648$	−0.144375	+	1.79357i	−0.000222801	+	0.00276785i
$649$	−0.167168			−0.000257578
$650$	−118.557	−	72.7485i	−0.182395	−	0.111921i
$651$			324.612i			0.498636i
$652$	−531.665	+	270.101i	−0.815437	+	0.414266i
$653$	−282.048			−0.431927			−0.215963	−	0.976401i	$-0.569289\pi$
$653$	−282.048			−0.431927			−0.215963	+	0.976401i	$0.569289\pi$
$654$	−293.751	+	478.720i	−0.449161	+	0.731987i
$655$		−	172.624i		−	0.263549i
$656$	599.717	−	821.326i	0.914202	−	1.25202i
$657$	−25.6426			−0.0390298
$658$	−45.0371	−	27.6356i	−0.0684454	−	0.0419994i
$659$		−	60.7464i		−	0.0921796i	−0.998937	−	0.0460898i	$-0.985324\pi$
$659$		−	60.7464i		−	0.0921796i	0.998937	−	0.0460898i	$-0.0146760\pi$
$660$	−9.63109	−	18.9578i	−0.0145926	−	0.0287239i
$661$	895.639			1.35498			0.677488	−	0.735534i	$-0.263069\pi$
$661$	895.639			1.35498			0.677488	+	0.735534i	$0.263069\pi$
$662$	−133.709	+	217.903i	−0.201978	+	0.329158i
$663$			39.3376i			0.0593327i
$664$	−38.3225	−	3.08482i	−0.0577147	−	0.00464581i
$665$	79.6839			0.119825
$666$	203.431	+	124.829i	0.305452	+	0.187431i
$667$			177.699i			0.266415i
$668$	1137.62	−	577.945i	1.70303	−	0.865188i
$669$	−564.187			−0.843329
$670$	−41.7264	+	68.0005i	−0.0622782	+	0.101493i
$671$		−	26.2615i		−	0.0391378i
$672$	−449.413	+	184.590i	−0.668769	+	0.274687i
$673$	−127.602			−0.189601			−0.0948007	−	0.995496i	$-0.530221\pi$
$673$	−127.602			−0.189601			−0.0948007	+	0.995496i	$0.530221\pi$
$674$	829.156	+	508.786i	1.23020	+	0.754875i
$675$		−	135.116i		−	0.200171i
$676$	44.3509	+	87.3000i	0.0656079	+	0.129142i
$677$	−920.239			−1.35929			−0.679644	−	0.733542i	$-0.737866\pi$
$677$	−920.239			−1.35929			−0.679644	+	0.733542i	$0.737866\pi$
$678$	337.237	−	549.587i	0.497400	−	0.810601i
$679$		−	1255.33i		−	1.84879i
$680$	2.18574	−	27.1533i	0.00321432	−	0.0399314i
$681$	499.724			0.733809
$682$	−46.6567	−	28.6294i	−0.0684115	−	0.0419786i
$683$			796.164i			1.16569i	0.812585	+	0.582843i	$0.198060\pi$
$683$			796.164i			1.16569i	−0.812585	+	0.582843i	$0.801940\pi$
$684$	86.2901	−	43.8379i	0.126155	−	0.0640905i
$685$	−491.046			−0.716856
$686$	−266.491	+	434.295i	−0.388471	+	0.633083i
$687$		−	408.667i		−	0.594858i
$688$	489.445	+	357.383i	0.711402	+	0.519453i
$689$	−920.781			−1.33640
$690$	−114.937	−	70.5278i	−0.166576	−	0.102214i
$691$		−	518.339i		−	0.750129i	−0.926999	−	0.375065i	$-0.877620\pi$
$691$		−	518.339i		−	0.750129i	0.926999	−	0.375065i	$-0.122380\pi$
$692$	45.6740	+	89.9043i	0.0660029	+	0.129920i
$693$	58.0964			0.0838331
$694$	378.610	−	617.012i	0.545548	−	0.889067i
$695$		−	152.345i		−	0.219201i
$696$	162.073	+	13.0462i	0.232863	+	0.0187446i
$697$	96.7922			0.138870
$698$	−823.423	−	505.268i	−1.17969	−	0.723879i
$699$			656.510i			0.939213i
$700$	145.775	−	74.0578i	0.208250	−	0.105797i
$701$	−938.374			−1.33862			−0.669311	−	0.742982i	$-0.733411\pi$
$701$	−938.374			−1.33862			−0.669311	+	0.742982i	$0.733411\pi$
$702$	−393.178	+	640.753i	−0.560083	+	0.912754i
$703$			93.7078i			0.133297i
$704$	13.1051	−	80.8744i	0.0186152	−	0.114878i
$705$	−13.4199			−0.0190353
$706$	−1176.27	−	721.780i	−1.66610	−	1.02235i
$707$			140.540i			0.198784i
$708$	0.439364	+	0.864840i	0.000620571	+	0.00122153i
$709$	1222.24			1.72389			0.861945	−	0.507002i	$-0.169246\pi$
$709$	1222.24			1.72389			0.861945	+	0.507002i	$0.169246\pi$
$710$	76.3034	−	124.350i	0.107470	−	0.175141i
$711$		−	58.6439i		−	0.0824809i
$712$	2.14796	−	26.6840i	0.00301680	−	0.0374776i
$713$	−347.150			−0.486886
$714$	−39.4127	−	24.1843i	−0.0551998	−	0.0338716i
$715$		−	39.8164i		−	0.0556873i
$716$	557.485	−	283.218i	0.778610	−	0.395556i
$717$	560.726			0.782045
$718$	96.5465	−	157.340i	0.134466	−	0.219136i
$719$			968.957i			1.34764i	0.738893	+	0.673822i	$0.235349\pi$
$719$			968.957i			1.34764i	−0.738893	+	0.673822i	$0.764651\pi$
$720$	117.118	−	160.395i	0.162663	−	0.222771i
$721$	−1429.44			−1.98258
$722$	32.3885	+	19.8742i	0.0448594	+	0.0275266i
$723$			176.075i			0.243534i
$724$	27.2468	+	53.6324i	0.0376338	+	0.0740780i
$725$	−54.7210			−0.0754773
$726$	−231.867	+	377.868i	−0.319375	+	0.520479i
$727$			1141.20i			1.56974i	0.619658	+	0.784872i	$0.287271\pi$
$727$			1141.20i			1.56974i	−0.619658	+	0.784872i	$0.712729\pi$
$728$	−906.806	−	72.9943i	−1.24561	−	0.100267i
$729$	−452.914			−0.621281
$730$	−17.6077	−	10.8044i	−0.0241202	−	0.0148006i
$731$			57.6805i			0.0789063i
$732$	−135.863	+	69.0225i	−0.185606	+	0.0942931i
$733$	−346.877			−0.473230			−0.236615	−	0.971604i	$-0.576038\pi$
$733$	−346.877			−0.473230			−0.236615	+	0.971604i	$0.576038\pi$
$734$	−20.4830	+	33.3807i	−0.0279061	+	0.0454779i
$735$		−	74.0708i		−	0.100777i
$736$	−197.406	−	480.616i	−0.268215	−	0.653011i
$737$	−22.8375			−0.0309871
$738$	601.462	+	369.068i	0.814989	+	0.500092i
$739$		−	802.229i		−	1.08556i	−0.839875	−	0.542780i	$-0.817372\pi$
$739$		−	802.229i		−	1.08556i	0.839875	−	0.542780i	$-0.182628\pi$
$740$	87.0916	+	171.430i	0.117691	+	0.231663i
$741$	−112.599			−0.151955
$742$	566.087	−	922.538i	0.762920	−	1.24331i
$743$		−	64.1284i		−	0.0863101i	−0.999068	−	0.0431550i	$-0.986259\pi$
$743$		−	64.1284i		−	0.0863101i	0.999068	−	0.0431550i	$-0.0137409\pi$
$744$	−25.4870	+	316.623i	−0.0342567	+	0.425569i
$745$	96.5495			0.129597
$746$	−826.411	−	507.101i	−1.10779	−	0.679761i
$747$		−	26.6777i		−	0.0357131i
$748$	6.95206	−	3.53185i	0.00929420	−	0.00472172i
$749$	752.617			1.00483
$750$	21.7185	−	35.3941i	0.0289580	−	0.0471922i
$751$			850.108i			1.13197i	0.824416	+	0.565984i	$0.191504\pi$
$751$			850.108i			1.13197i	−0.824416	+	0.565984i	$0.808496\pi$
$752$	−41.7590	−	30.4916i	−0.0555305	−	0.0405474i
$753$	−91.6099			−0.121660
$754$	259.501	+	159.235i	0.344166	+	0.211187i
$755$			531.871i			0.704466i
$756$	−400.254	−	787.857i	−0.529437	−	1.04214i
$757$	−1205.86			−1.59294			−0.796472	−	0.604675i	$-0.793303\pi$
$757$	−1205.86			−1.59294			−0.796472	+	0.604675i	$0.793303\pi$
$758$	492.128	−	802.010i	0.649246	−	1.05806i
$759$		−	38.6010i		−	0.0508577i
$760$	77.7230	+	6.25640i	0.102267	+	0.00823210i
$761$	88.4463			0.116224			0.0581119	−	0.998310i	$-0.481492\pi$
$761$	88.4463			0.116224			0.0581119	+	0.998310i	$0.481492\pi$
$762$	−193.110	−	118.496i	−0.253425	−	0.155507i
$763$		−	1236.27i		−	1.62028i
$764$	358.185	−	181.968i	0.468828	−	0.238178i
$765$	18.9024			0.0247090
$766$	−731.727	+	1192.48i	−0.955257	+	1.55676i
$767$			1.81640i			0.00236819i
$768$	−452.846	+	144.762i	−0.589643	+	0.188492i
$769$	282.910			0.367894			0.183947	−	0.982936i	$-0.441113\pi$
$769$	282.910			0.367894			0.183947	+	0.982936i	$0.441113\pi$
$770$	39.8924	+	24.4787i	0.0518084	+	0.0317906i
$771$			825.288i			1.07041i
$772$	−109.135	−	214.820i	−0.141366	−	0.278264i
$773$	471.596			0.610085			0.305042	−	0.952339i	$-0.401329\pi$
$773$	471.596			0.610085			0.305042	+	0.952339i	$0.401329\pi$
$774$	−219.935	+	358.424i	−0.284154	+	0.463080i
$775$		−	106.902i		−	0.137938i
$776$	98.5622	−	1224.43i	0.127013	−	1.57788i
$777$	326.397			0.420074
$778$	−1150.60	−	706.031i	−1.47892	−	0.907495i
$779$			277.055i			0.355655i
$780$	−205.990	+	104.649i	−0.264089	+	0.134165i
$781$	41.7621			0.0534726
$782$	25.8635	−	42.1491i	0.0330735	−	0.0538991i
$783$			295.746i			0.377709i
$784$	168.298	−	230.488i	0.214666	−	0.293990i
$785$	−501.272			−0.638563
$786$	−244.395	−	149.966i	−0.310936	−	0.190796i
$787$			1199.05i			1.52357i	0.647829	+	0.761786i	$0.275677\pi$
$787$			1199.05i			1.52357i	−0.647829	+	0.761786i	$0.724323\pi$
$788$	571.340	+	1124.62i	0.725051	+	1.42718i
$789$	−226.819			−0.287477
$790$	24.7095	−	40.2684i	0.0312778	−	0.0509727i
$791$			1419.28i			1.79429i
$792$	56.6667	+	4.56145i	0.0715488	+	0.00575940i
$793$	−285.350			−0.359836
$794$	−163.753	−	100.482i	−0.206238	−	0.126552i
$795$		−	274.892i		−	0.345776i
$796$	−967.384	+	491.459i	−1.21531	+	0.617411i
$797$	282.679			0.354679			0.177340	−	0.984150i	$-0.443251\pi$
$797$	282.679			0.354679			0.177340	+	0.984150i	$0.443251\pi$
$798$	69.2246	−	112.814i	0.0867476	−	0.141371i
$799$		−	4.92124i		−	0.00615925i
$800$	148.002	−	60.7898i	0.185003	−	0.0759872i
$801$	18.5757			0.0231906
$802$	−400.336	−	245.654i	−0.499172	−	0.306301i
$803$		−	5.91344i		−	0.00736419i
$804$	60.0234	+	118.150i	0.0746559	+	0.146952i
$805$	296.821			0.368721
$806$	−311.079	+	506.958i	−0.385954	+	0.628980i
$807$		−	646.841i		−	0.801538i
$808$	−11.0345	+	137.082i	−0.0136566	+	0.169655i
$809$	1089.57			1.34681			0.673407	−	0.739272i	$-0.264830\pi$
$809$	1089.57			1.34681			0.673407	+	0.739272i	$0.264830\pi$
$810$	−0.857338	−	0.526079i	−0.00105844	−	0.000649480i
$811$		−	503.159i		−	0.620418i	−0.950668	−	0.310209i	$-0.899601\pi$
$811$		−	503.159i		−	0.620418i	0.950668	−	0.310209i	$-0.100399\pi$
$812$	−319.078	+	162.101i	−0.392953	+	0.199631i
$813$	769.770			0.946827
$814$	−28.7869	+	46.9133i	−0.0353647	+	0.0576331i
$815$		−	333.365i		−	0.409037i
$816$	−36.5439	−	26.6837i	−0.0447842	−	0.0327006i
$817$	−165.103			−0.202084
$818$	−696.893	−	427.627i	−0.851948	−	0.522771i
$819$		−	631.259i		−	0.770768i
$820$	257.494	+	506.849i	0.314017	+	0.618108i
$821$	972.057			1.18399			0.591996	−	0.805941i	$-0.298340\pi$
$821$	972.057			1.18399			0.591996	+	0.805941i	$0.298340\pi$
$822$	−426.592	+	695.207i	−0.518968	+	0.845750i
$823$			428.909i			0.521153i	0.965453	+	0.260577i	$0.0839127\pi$
$823$			428.909i			0.521153i	−0.965453	+	0.260577i	$0.916087\pi$
$824$	−1394.26	−	112.233i	−1.69207	−	0.136205i
$825$	11.8869			0.0144084
$826$	−1.81987	−	1.11670i	−0.00220323	−	0.00135194i
$827$			638.697i			0.772306i	0.922435	+	0.386153i	$0.126196\pi$
$827$			638.697i			0.772306i	−0.922435	+	0.386153i	$0.873804\pi$
$828$	321.429	−	163.295i	0.388199	−	0.197216i
$829$	−651.021			−0.785309			−0.392654	−	0.919686i	$-0.628443\pi$
$829$	−651.021			−0.785309			−0.392654	+	0.919686i	$0.628443\pi$
$830$	11.2406	−	18.3185i	0.0135428	−	0.0220705i
$831$			77.1784i			0.0928741i
$832$	−878.759	−	142.396i	−1.05620	−	0.171149i
$833$	27.1628			0.0326084
$834$	−215.684	−	132.348i	−0.258614	−	0.158691i
$835$			713.312i			0.854266i
$836$	10.1095	+	19.8994i	0.0120927	+	0.0238031i
$837$	−577.766			−0.690282
$838$	289.700	−	472.118i	0.345704	−	0.563386i
$839$			1498.62i			1.78620i	0.449857	+	0.893100i	$0.351475\pi$
$839$			1498.62i			1.78620i	−0.449857	+	0.893100i	$0.648525\pi$
$840$	21.7919	−	270.720i	0.0259427	−	0.322285i
$841$	−721.224			−0.857580
$842$	793.129	+	486.679i	0.941958	+	0.578003i
$843$		−	894.704i		−	1.06133i
$844$	−703.304	+	357.299i	−0.833299	+	0.423340i
$845$	−54.7389			−0.0647797
$846$	18.7647	−	30.5804i	0.0221805	−	0.0361470i
$847$		−	975.825i		−	1.15210i
$848$	624.589	−	855.389i	0.736544	−	1.00871i
$849$	355.182			0.418353
$850$	12.9795	+	7.96447i	0.0152700	+	0.00936996i
$851$			349.059i			0.410176i
$852$	−109.762	−	216.056i	−0.128829	−	0.253586i
$853$	32.2748			0.0378368			0.0189184	−	0.999821i	$-0.493978\pi$
$853$	32.2748			0.0378368			0.0189184	+	0.999821i	$0.493978\pi$
$854$	175.430	−	285.895i	0.205422	−	0.334771i
$855$			54.1057i			0.0632815i
$856$	734.096	+	59.0918i	0.857588	+	0.0690325i
$857$	823.345			0.960729			0.480364	−	0.877069i	$-0.340504\pi$
$857$	823.345			0.960729			0.480364	+	0.877069i	$0.340504\pi$
$858$	−56.3707	−	34.5901i	−0.0657002	−	0.0403148i
$859$		−	1404.35i		−	1.63487i	−0.576022	−	0.817434i	$-0.695396\pi$
$859$		−	1404.35i		−	1.63487i	0.576022	−	0.817434i	$-0.304604\pi$
$860$	−302.042	+	153.446i	−0.351211	+	0.178425i
$861$	965.022			1.12082
$862$	−664.556	+	1083.01i	−0.770947	+	1.25639i
$863$			437.443i			0.506886i	0.967350	+	0.253443i	$0.0815630\pi$
$863$			437.443i			0.506886i	−0.967350	+	0.253443i	$0.918437\pi$
$864$	−328.546	−	799.895i	−0.380261	−	0.925805i
$865$	−56.3718			−0.0651697
$866$	−586.725	−	360.026i	−0.677512	−	0.415734i
$867$			532.400i			0.614071i
$868$	−316.678	−	623.346i	−0.364836	−	0.718140i
$869$	13.5239			0.0155626
$870$	−47.5383	+	77.4721i	−0.0546418	+	0.0890484i
$871$			248.146i			0.284898i
$872$	97.0660	−	1205.85i	0.111314	−	1.38285i
$873$	852.372			0.976371
$874$	120.646	+	74.0309i	0.138039	+	0.0847036i
$875$			91.4037i			0.104461i
$876$	−30.5931	+	15.5422i	−0.0349236	+	0.0177422i
$877$	11.6381			0.0132704			0.00663520	−	0.999978i	$-0.497888\pi$
$877$	11.6381			0.0132704			0.00663520	+	0.999978i	$0.497888\pi$
$878$	317.215	−	516.958i	0.361293	−	0.588791i
$879$			65.5306i			0.0745513i
$880$	36.9888	+	27.0085i	0.0420327	+	0.0306915i
$881$	1598.37			1.81427			0.907135	−	0.420840i	$-0.138265\pi$
$881$	1598.37			1.81427			0.907135	+	0.420840i	$0.138265\pi$
$882$	168.788	+	103.572i	0.191370	+	0.117428i
$883$			1649.44i			1.86800i	0.357279	+	0.933998i	$0.383705\pi$
$883$			1649.44i			1.86800i	−0.357279	+	0.933998i	$0.616295\pi$
$884$	−38.3761	−	75.5392i	−0.0434119	−	0.0854516i
$885$	−0.542272			−0.000612737
$886$	−871.487	+	1420.24i	−0.983620	+	1.60298i
$887$		−	478.051i		−	0.538953i	−0.963007	−	0.269476i	$-0.913149\pi$
$887$		−	478.051i		−	0.538953i	0.963007	−	0.269476i	$-0.0868506\pi$
$888$	318.365	+	25.6272i	0.358519	+	0.0288594i
$889$	498.698			0.560965
$890$	12.7552	+	7.82681i	0.0143317	+	0.00879417i
$891$		−	0.287932i		−	0.000323155i
$892$	1083.40	−	550.397i	1.21457	−	0.617037i
$893$	14.0864			0.0157743
$894$	83.8764	−	136.691i	0.0938215	−	0.152899i
$895$			349.554i			0.390563i
$896$	682.920	−	792.893i	0.762187	−	0.884925i
$897$	−419.428			−0.467590
$898$	528.560	+	324.335i	0.588597	+	0.361174i
$899$			233.992i			0.260280i
$900$	50.2855	+	98.9816i	0.0558728	+	0.109980i
$901$	100.807			0.111883
$902$	−85.1109	+	138.703i	−0.0943580	+	0.153773i
$903$			575.077i			0.636851i
$904$	−111.435	+	1384.36i	−0.123269	+	1.53137i
$905$	−33.6286			−0.0371587
$906$	753.005	+	462.058i	0.831132	+	0.509998i
$907$			965.553i			1.06456i	0.846569	+	0.532278i	$0.178664\pi$
$907$			965.553i			1.06456i	−0.846569	+	0.532278i	$0.821336\pi$
$908$	−959.610	+	487.510i	−1.05684	+	0.536905i
$909$	−95.4273			−0.104981
$910$	265.979	−	433.460i	0.292285	−	0.476330i
$911$		−	989.556i		−	1.08623i	−0.839658	−	0.543115i	$-0.817245\pi$
$911$		−	989.556i		−	1.08623i	0.839658	−	0.543115i	$-0.182755\pi$
$912$	76.3786	−	104.602i	0.0837485	−	0.114695i
$913$	6.15214			0.00673838
$914$	477.167	+	292.798i	0.522064	+	0.320348i
$915$		−	85.1890i		−	0.0931028i
$916$	398.679	+	784.756i	0.435239	+	0.856720i
$917$	631.140			0.688266
$918$	43.0449	−	70.1493i	0.0468899	−	0.0764154i
$919$		−	674.501i		−	0.733951i	−0.930231	−	0.366975i	$-0.880393\pi$
$919$		−	674.501i		−	0.733951i	0.930231	−	0.366975i	$-0.119607\pi$
$920$	289.516	+	23.3049i	0.314692	+	0.0253314i
$921$	207.193			0.224966
$922$	71.9875	+	44.1729i	0.0780775	+	0.0479098i
$923$		−	453.776i		−	0.491631i
$924$	69.3123	−	35.2127i	0.0750133	−	0.0381090i
$925$	−107.490			−0.116206
$926$	−746.879	+	1217.17i	−0.806565	+	1.31444i
$927$		−	970.596i		−	1.04703i
$928$	−323.953	+	133.059i	−0.349087	+	0.143383i
$929$	35.2397			0.0379329			0.0189665	−	0.999820i	$-0.493962\pi$
$929$	35.2397			0.0379329			0.0189665	+	0.999820i	$0.493962\pi$
$930$	−151.348	−	92.8702i	−0.162740	−	0.0998605i
$931$			77.7500i			0.0835123i
$932$	−640.463	−	1260.68i	−0.687193	−	1.35266i
$933$	590.001			0.632370
$934$	−138.472	+	225.665i	−0.148257	+	0.241611i
$935$			4.35908i			0.00466212i
$936$	49.5634	−	615.724i	0.0529524	−	0.657825i
$937$	29.5346			0.0315204			0.0157602	−	0.999876i	$-0.494983\pi$
$937$	29.5346			0.0315204			0.0157602	+	0.999876i	$0.494983\pi$
$938$	−248.620	−	152.558i	−0.265053	−	0.162642i
$939$			127.835i			0.136139i
$940$	25.7699	−	13.0919i	0.0274148	−	0.0139275i
$941$	140.568			0.149381			0.0746907	−	0.997207i	$-0.476203\pi$
$941$	140.568			0.149381			0.0746907	+	0.997207i	$0.476203\pi$
$942$	−435.475	+	709.683i	−0.462287	+	0.753379i
$943$			1032.02i			1.09441i
$944$	−1.68740	−	1.23211i	−0.00178750	−	0.00130520i
$945$	494.002			0.522754
$946$	−82.6561	−	50.7194i	−0.0873744	−	0.0536145i
$947$			1284.98i			1.35689i	0.734650	+	0.678447i	$0.237347\pi$
$947$			1284.98i			1.35689i	−0.734650	+	0.678447i	$0.762653\pi$
$948$	−35.5445	−	69.9656i	−0.0374942	−	0.0738034i
$949$	−64.2538			−0.0677069
$950$	−22.7973	+	37.1522i	−0.0239971	+	0.0391076i
$951$			289.782i			0.304713i
$952$	99.2766	+	7.99138i	0.104282	+	0.00839431i
$953$	125.098			0.131268			0.0656339	−	0.997844i	$-0.479093\pi$
$953$	125.098			0.131268			0.0656339	+	0.997844i	$0.479093\pi$
$954$	626.407	+	384.375i	0.656611	+	0.402909i
$955$			224.589i			0.235172i
$956$	−1076.75	+	547.021i	−1.12631	+	0.572198i
$957$	−26.0185			−0.0271876
$958$	−346.378	+	564.483i	−0.361563	+	0.589231i
$959$		−	1795.34i		−	1.87209i
$960$	42.5112	−	262.347i	0.0442825	−	0.273278i
$961$	503.877			0.524325
$962$	509.747	+	312.790i	0.529882	+	0.325146i
$963$			511.030i			0.530664i
$964$	−171.772	−	338.114i	−0.178187	−	0.350741i
$965$	134.696			0.139582
$966$	257.860	−	420.228i	0.266936	−	0.435019i
$967$		−	244.082i		−	0.252411i	−0.992004	−	0.126206i	$-0.959720\pi$
$967$		−	244.082i		−	0.252411i	0.992004	−	0.126206i	$-0.0402799\pi$
$968$	76.6171	−	951.811i	0.0791499	−	0.983276i
$969$	12.3273			0.0127216
$970$	585.289	+	359.144i	0.603391	+	0.370252i
$971$			504.688i			0.519761i	0.965641	+	0.259880i	$0.0836832\pi$
$971$			504.688i			0.519761i	−0.965641	+	0.259880i	$0.916317\pi$
$972$	865.834	−	439.869i	0.890776	−	0.452540i
$973$	556.995			0.572451
$974$	−806.375	+	1314.13i	−0.827900	+	1.34921i
$975$		−	129.160i		−	0.132471i
$976$	193.560	−	265.085i	0.198320	−	0.271604i
$977$	1537.91			1.57411			0.787057	−	0.616880i	$-0.211604\pi$
$977$	1537.91			1.57411			0.787057	+	0.616880i	$0.211604\pi$
$978$	−471.966	−	289.607i	−0.482583	−	0.296122i
$979$			4.28374i			0.00437563i
$980$	72.2604	+	142.237i	0.0737351	+	0.145140i
$981$	839.432			0.855691
$982$	660.762	−	1076.83i	0.672874	−	1.09657i
$983$			1179.80i			1.20021i	0.799923	+	0.600103i	$0.204874\pi$
$983$			1179.80i			1.20021i	−0.799923	+	0.600103i	$0.795126\pi$
$984$	941.274	+	75.7689i	0.956579	+	0.0770009i
$985$	−705.160			−0.715898
$986$	−28.4101	−	17.4329i	−0.0288135	−	0.0176805i
$987$		−	49.0650i		−	0.0497112i
$988$	216.221	−	109.847i	0.218847	−	0.111181i
$989$	−615.005			−0.621845
$990$	−16.6212	+	27.0871i	−0.0167891	+	0.0273607i
$991$			250.163i			0.252435i	0.992003	+	0.126218i	$0.0402838\pi$
$991$			250.163i			0.252435i	−0.992003	+	0.126218i	$0.959716\pi$
$992$	−259.942	−	632.870i	−0.262039	−	0.637974i
$993$	−237.391			−0.239064
$994$	454.642	+	278.977i	0.457386	+	0.280661i
$995$		−	606.569i		−	0.609617i
$996$	−16.1695	−	31.8280i	−0.0162345	−	0.0319558i
$997$	947.164			0.950014			0.475007	−	0.879982i	$-0.342446\pi$
$997$	947.164			0.950014			0.475007	+	0.879982i	$0.342446\pi$
$998$	765.627	−	1247.72i	0.767161	−	1.25022i
$999$			580.944i			0.581526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.11	✓	72
4.3	odd	2	inner	380.3.b.a.191.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.11	✓	72	1.1	even	1	trivial
380.3.b.a.191.12	yes	72	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70466 - 1.04601i) q^{2} -1.85712i q^{3} +(1.81172 + 3.56618i) q^{4} -2.23607 q^{5} +(-1.94256 + 3.16575i) q^{6} -8.17539i q^{7} +(0.641893 - 7.97421i) q^{8} +5.55112 q^{9} +O(q^{10})\)	\(q+(-1.70466 - 1.04601i) q^{2} -1.85712i q^{3} +(1.81172 + 3.56618i) q^{4} -2.23607 q^{5} +(-1.94256 + 3.16575i) q^{6} -8.17539i q^{7} +(0.641893 - 7.97421i) q^{8} +5.55112 q^{9} +(3.81173 + 2.33895i) q^{10} +1.28015i q^{11} +(6.62281 - 3.36458i) q^{12} +13.9097 q^{13} +(-8.55155 + 13.9363i) q^{14} +4.15264i q^{15} +(-9.43531 + 12.9219i) q^{16} -1.52283 q^{17} +(-9.46277 - 5.80653i) q^{18} -4.35890i q^{19} +(-4.05114 - 7.97423i) q^{20} -15.1826 q^{21} +(1.33905 - 2.18221i) q^{22} -16.2368i q^{23} +(-14.8090 - 1.19207i) q^{24} +5.00000 q^{25} +(-23.7113 - 14.5497i) q^{26} -27.0231i q^{27} +(29.1549 - 14.8116i) q^{28} -10.9442 q^{29} +(4.34370 - 7.07883i) q^{30} -21.3804i q^{31} +(29.6004 - 12.1580i) q^{32} +2.37738 q^{33} +(2.59590 + 1.59289i) q^{34} +18.2807i q^{35} +(10.0571 + 19.7963i) q^{36} -21.4981 q^{37} +(-4.55945 + 7.43044i) q^{38} -25.8319i q^{39} +(-1.43532 + 17.8309i) q^{40} -63.5609 q^{41} +(25.8812 + 15.8812i) q^{42} -37.8772i q^{43} +(-4.56523 + 2.31927i) q^{44} -12.4127 q^{45} +(-16.9839 + 27.6782i) q^{46} +3.23165i q^{47} +(23.9974 + 17.5225i) q^{48} -17.8371 q^{49} +(-8.52329 - 5.23005i) q^{50} +2.82807i q^{51} +(25.2006 + 49.6046i) q^{52} -66.1970 q^{53} +(-28.2665 + 46.0652i) q^{54} -2.86249i q^{55} +(-65.1923 - 5.24773i) q^{56} -8.09498 q^{57} +(18.6561 + 11.4478i) q^{58} +0.130585i q^{59} +(-14.8091 + 7.52343i) q^{60} -20.5145 q^{61} +(-22.3642 + 36.4464i) q^{62} -45.3826i q^{63} +(-63.1759 - 10.2372i) q^{64} -31.1031 q^{65} +(-4.05262 - 2.48676i) q^{66} +17.8398i q^{67} +(-2.75894 - 5.43068i) q^{68} -30.1536 q^{69} +(19.1218 - 31.1624i) q^{70} -32.6229i q^{71} +(3.56323 - 44.2658i) q^{72} -4.61935 q^{73} +(36.6468 + 22.4872i) q^{74} -9.28558i q^{75} +(15.5446 - 7.89712i) q^{76} +10.4657 q^{77} +(-27.0205 + 44.0346i) q^{78} -10.5643i q^{79} +(21.0980 - 28.8942i) q^{80} -0.224921 q^{81} +(108.350 + 66.4853i) q^{82} -4.80581i q^{83} +(-27.5068 - 54.1441i) q^{84} +3.40515 q^{85} +(-39.6200 + 64.5678i) q^{86} +20.3246i q^{87} +(10.2081 + 0.821716i) q^{88} +3.34629 q^{89} +(21.1594 + 12.9838i) q^{90} -113.717i q^{91} +(57.9034 - 29.4166i) q^{92} -39.7059 q^{93} +(3.38034 - 5.50886i) q^{94} +9.74679i q^{95} +(-22.5787 - 54.9714i) q^{96} +153.549 q^{97} +(30.4061 + 18.6578i) q^{98} +7.10625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

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