LMFDB - Embedded newform 380.3.b.a.191.14

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			191.14
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68205 + 1.08200i) q^{2} -2.49923i q^{3} +(1.65856 - 3.63994i) q^{4} +2.23607 q^{5} +(2.70416 + 4.20382i) q^{6} -6.10491i q^{7} +(1.14864 + 7.91711i) q^{8} +2.75385 q^{9} +O(q^{10})$	\(q+(-1.68205 + 1.08200i) q^{2} -2.49923i q^{3} +(1.65856 - 3.63994i) q^{4} +2.23607 q^{5} +(2.70416 + 4.20382i) q^{6} -6.10491i q^{7} +(1.14864 + 7.91711i) q^{8} +2.75385 q^{9} +(-3.76117 + 2.41942i) q^{10} +18.7802i q^{11} +(-9.09705 - 4.14512i) q^{12} +14.2115 q^{13} +(6.60550 + 10.2687i) q^{14} -5.58845i q^{15} +(-10.4984 - 12.0741i) q^{16} +21.0934 q^{17} +(-4.63210 + 2.97966i) q^{18} +4.35890i q^{19} +(3.70865 - 8.13916i) q^{20} -15.2576 q^{21} +(-20.3201 - 31.5892i) q^{22} +12.6756i q^{23} +(19.7867 - 2.87072i) q^{24} +5.00000 q^{25} +(-23.9045 + 15.3769i) q^{26} -29.3756i q^{27} +(-22.2215 - 10.1253i) q^{28} -34.4845 q^{29} +(6.04669 + 9.40003i) q^{30} -52.6923i q^{31} +(30.7229 + 8.94999i) q^{32} +46.9360 q^{33} +(-35.4801 + 22.8230i) q^{34} -13.6510i q^{35} +(4.56742 - 10.0239i) q^{36} +39.8041 q^{37} +(-4.71632 - 7.33187i) q^{38} -35.5179i q^{39} +(2.56844 + 17.7032i) q^{40} +18.8629 q^{41} +(25.6639 - 16.5087i) q^{42} +3.95899i q^{43} +(68.3589 + 31.1481i) q^{44} +6.15779 q^{45} +(-13.7150 - 21.3210i) q^{46} -9.60341i q^{47} +(-30.1760 + 26.2378i) q^{48} +11.7301 q^{49} +(-8.41023 + 5.40999i) q^{50} -52.7173i q^{51} +(23.5707 - 51.7292i) q^{52} +26.1562 q^{53} +(31.7843 + 49.4111i) q^{54} +41.9938i q^{55} +(48.3332 - 7.01235i) q^{56} +10.8939 q^{57} +(58.0045 - 37.3122i) q^{58} -43.1203i q^{59} +(-20.3416 - 9.26877i) q^{60} -65.8043 q^{61} +(57.0130 + 88.6309i) q^{62} -16.8120i q^{63} +(-61.3612 + 18.1879i) q^{64} +31.7780 q^{65} +(-78.9486 + 50.7847i) q^{66} +15.7939i q^{67} +(34.9847 - 76.7788i) q^{68} +31.6793 q^{69} +(14.7703 + 22.9616i) q^{70} +1.28925i q^{71} +(3.16319 + 21.8025i) q^{72} +30.7485 q^{73} +(-66.9523 + 43.0680i) q^{74} -12.4961i q^{75} +(15.8661 + 7.22949i) q^{76} +114.651 q^{77} +(38.4303 + 59.7427i) q^{78} +30.6032i q^{79} +(-23.4751 - 26.9985i) q^{80} -48.6317 q^{81} +(-31.7282 + 20.4096i) q^{82} -7.26306i q^{83} +(-25.3056 + 55.5367i) q^{84} +47.1663 q^{85} +(-4.28362 - 6.65920i) q^{86} +86.1846i q^{87} +(-148.685 + 21.5717i) q^{88} +153.630 q^{89} +(-10.3577 + 6.66273i) q^{90} -86.7601i q^{91} +(46.1385 + 21.0233i) q^{92} -131.690 q^{93} +(10.3909 + 16.1534i) q^{94} +9.74679i q^{95} +(22.3681 - 76.7836i) q^{96} +37.0899 q^{97} +(-19.7306 + 12.6920i) q^{98} +51.7178i 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 $

$2$	−1.68205	+	1.08200i	−0.841023	+	0.540999i
$2$	−1.68205	+	1.08200i	−0.841023	+	0.540999i
$3$		−	2.49923i		−	0.833077i	−0.909118	−	0.416538i	$-0.863243\pi$
$3$		−	2.49923i		−	0.833077i	0.909118	−	0.416538i	$-0.136757\pi$
$4$	1.65856	−	3.63994i	0.414640	−	0.909986i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	2.70416	+	4.20382i	0.450694	+	0.700637i
$7$		−	6.10491i		−	0.872130i	−0.899915	−	0.436065i	$-0.856372\pi$
$7$		−	6.10491i		−	0.872130i	0.899915	−	0.436065i	$-0.143628\pi$
$8$	1.14864	+	7.91711i	0.143580	+	0.989639i
$9$	2.75385			0.305983
$10$	−3.76117	+	2.41942i	−0.376117	+	0.241942i
$11$			18.7802i			1.70729i	0.520855	+	0.853645i	$0.325613\pi$
$11$			18.7802i			1.70729i	−0.520855	+	0.853645i	$0.674387\pi$
$12$	−9.09705	−	4.14512i	−0.758088	−	0.345427i
$13$	14.2115			1.09319			0.546597	−	0.837396i	$-0.315923\pi$
$13$	14.2115			1.09319			0.546597	+	0.837396i	$0.315923\pi$
$14$	6.60550	+	10.2687i	0.471821	+	0.733481i
$15$		−	5.58845i		−	0.372563i
$16$	−10.4984	−	12.0741i	−0.656148	−	0.754632i
$17$	21.0934			1.24079			0.620395	−	0.784290i	$-0.286972\pi$
$17$	21.0934			1.24079			0.620395	+	0.784290i	$0.286972\pi$
$18$	−4.63210	+	2.97966i	−0.257339	+	0.165537i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	3.70865	−	8.13916i	0.185432	−	0.406958i
$21$	−15.2576			−0.726551
$22$	−20.3201	−	31.5892i	−0.923643	−	1.43587i
$23$			12.6756i			0.551114i	0.961285	+	0.275557i	$0.0888623\pi$
$23$			12.6756i			0.551114i	−0.961285	+	0.275557i	$0.911138\pi$
$24$	19.7867	−	2.87072i	0.824445	−	0.119613i
$25$	5.00000			0.200000
$26$	−23.9045	+	15.3769i	−0.919402	+	0.591418i
$27$		−	29.3756i		−	1.08798i
$28$	−22.2215	−	10.1253i	−0.793625	−	0.361619i
$29$	−34.4845			−1.18912			−0.594560	−	0.804051i	$-0.702674\pi$
$29$	−34.4845			−1.18912			−0.594560	+	0.804051i	$0.702674\pi$
$30$	6.04669	+	9.40003i	0.201556	+	0.313334i
$31$		−	52.6923i		−	1.69975i	−0.526982	−	0.849876i	$-0.676677\pi$
$31$		−	52.6923i		−	1.69975i	0.526982	−	0.849876i	$-0.323323\pi$
$32$	30.7229	+	8.94999i	0.960091	+	0.279687i
$33$	46.9360			1.42230
$34$	−35.4801	+	22.8230i	−1.04353	+	0.671266i
$35$		−	13.6510i		−	0.390028i
$36$	4.56742	−	10.0239i	0.126873	−	0.278440i
$37$	39.8041			1.07579			0.537893	−	0.843013i	$-0.319220\pi$
$37$	39.8041			1.07579			0.537893	+	0.843013i	$0.319220\pi$
$38$	−4.71632	−	7.33187i	−0.124114	−	0.192944i
$39$		−	35.5179i		−	0.910715i
$40$	2.56844	+	17.7032i	0.0642110	+	0.442580i
$41$	18.8629			0.460070			0.230035	−	0.973182i	$-0.426116\pi$
$41$	18.8629			0.460070			0.230035	+	0.973182i	$0.426116\pi$
$42$	25.6639	−	16.5087i	0.611046	−	0.393063i
$43$			3.95899i			0.0920695i	0.998940	+	0.0460347i	$0.0146585\pi$
$43$			3.95899i			0.0920695i	−0.998940	+	0.0460347i	$0.985342\pi$
$44$	68.3589	+	31.1481i	1.55361	+	0.707910i
$45$	6.15779			0.136840
$46$	−13.7150	−	21.3210i	−0.298152	−	0.463500i
$47$		−	9.60341i		−	0.204328i	−0.994768	−	0.102164i	$-0.967423\pi$
$47$		−	9.60341i		−	0.204328i	0.994768	−	0.102164i	$-0.0325766\pi$
$48$	−30.1760	+	26.2378i	−0.628666	+	0.546622i
$49$	11.7301			0.239390
$50$	−8.41023	+	5.40999i	−0.168205	+	0.108200i
$51$		−	52.7173i		−	1.03367i
$52$	23.5707	−	51.7292i	0.453282	−	0.994792i
$53$	26.1562			0.493513			0.246757	−	0.969078i	$-0.420635\pi$
$53$	26.1562			0.493513			0.246757	+	0.969078i	$0.420635\pi$
$54$	31.7843	+	49.4111i	0.588599	+	0.915020i
$55$			41.9938i			0.763524i
$56$	48.3332	−	7.01235i	0.863093	−	0.125221i
$57$	10.8939			0.191121
$58$	58.0045	−	37.3122i	1.00008	−	0.643313i
$59$		−	43.1203i		−	0.730853i	−0.930840	−	0.365426i	$-0.880923\pi$
$59$		−	43.1203i		−	0.730853i	0.930840	−	0.365426i	$-0.119077\pi$
$60$	−20.3416	−	9.26877i	−0.339027	−	0.154479i
$61$	−65.8043			−1.07876			−0.539380	−	0.842063i	$-0.681341\pi$
$61$	−65.8043			−1.07876			−0.539380	+	0.842063i	$0.681341\pi$
$62$	57.0130	+	88.6309i	0.919565	+	1.42953i
$63$		−	16.8120i		−	0.266857i
$64$	−61.3612	+	18.1879i	−0.958769	+	0.284185i
$65$	31.7780			0.488892
$66$	−78.9486	+	50.7847i	−1.19619	+	0.769466i
$67$			15.7939i			0.235729i	0.993030	+	0.117865i	$0.0376049\pi$
$67$			15.7939i			0.235729i	−0.993030	+	0.117865i	$0.962395\pi$
$68$	34.9847	−	76.7788i	0.514480	−	1.12910i
$69$	31.6793			0.459120
$70$	14.7703	+	22.9616i	0.211005	+	0.328023i
$71$			1.28925i			0.0181585i	0.999959	+	0.00907924i	$0.00289005\pi$
$71$			1.28925i			0.0181585i	−0.999959	+	0.00907924i	$0.997110\pi$
$72$	3.16319	+	21.8025i	0.0439332	+	0.302813i
$73$	30.7485			0.421212			0.210606	−	0.977571i	$-0.432456\pi$
$73$	30.7485			0.421212			0.210606	+	0.977571i	$0.432456\pi$
$74$	−66.9523	+	43.0680i	−0.904761	+	0.582000i
$75$		−	12.4961i		−	0.166615i
$76$	15.8661	+	7.22949i	0.208765	+	0.0951248i
$77$	114.651			1.48898
$78$	38.4303	+	59.7427i	0.492696	+	0.765932i
$79$			30.6032i			0.387382i	0.981063	+	0.193691i	$0.0620459\pi$
$79$			30.6032i			0.387382i	−0.981063	+	0.193691i	$0.937954\pi$
$80$	−23.4751	−	26.9985i	−0.293438	−	0.337482i
$81$	−48.6317			−0.600391
$82$	−31.7282	+	20.4096i	−0.386929	+	0.248897i
$83$		−	7.26306i		−	0.0875067i	−0.999042	−	0.0437534i	$-0.986068\pi$
$83$		−	7.26306i		−	0.0875067i	0.999042	−	0.0437534i	$-0.0139316\pi$
$84$	−25.3056	+	55.5367i	−0.301257	+	0.661151i
$85$	47.1663			0.554898
$86$	−4.28362	−	6.65920i	−0.0498095	−	0.0774326i
$87$			86.1846i			0.990628i
$88$	−148.685	+	21.5717i	−1.68960	+	0.245133i
$89$	153.630			1.72618			0.863090	−	0.505051i	$-0.168526\pi$
$89$	153.630			1.72618			0.863090	+	0.505051i	$0.168526\pi$
$90$	−10.3577	+	6.66273i	−0.115085	+	0.0740303i
$91$		−	86.7601i		−	0.953408i
$92$	46.1385	+	21.0233i	0.501506	+	0.228514i
$93$	−131.690			−1.41602
$94$	10.3909	+	16.1534i	0.110541	+	0.171844i
$95$			9.74679i			0.102598i
$96$	22.3681	−	76.7836i	0.233001	−	0.799830i
$97$	37.0899			0.382370			0.191185	−	0.981554i	$-0.438767\pi$
$97$	37.0899			0.382370			0.191185	+	0.981554i	$0.438767\pi$
$98$	−19.7306	+	12.6920i	−0.201333	+	0.129510i
$99$			51.7178i			0.522402i
$100$	8.29279	−	18.1997i	0.0829279	−	0.181997i
$101$	−105.274			−1.04232			−0.521159	−	0.853460i	$-0.674500\pi$
$101$	−105.274			−1.04232			−0.521159	+	0.853460i	$0.674500\pi$
$102$	57.0400	+	88.6729i	0.559216	+	0.869342i
$103$		−	15.4482i		−	0.149982i	−0.997184	−	0.0749912i	$-0.976107\pi$
$103$		−	15.4482i		−	0.149982i	0.997184	−	0.0749912i	$-0.0238929\pi$
$104$	16.3240	+	112.514i	0.156961	+	1.08187i
$105$	−34.1170			−0.324923
$106$	−43.9959	+	28.3010i	−0.415056	+	0.266990i
$107$		−	101.370i		−	0.947384i	−0.880691	−	0.473692i	$-0.842921\pi$
$107$		−	101.370i		−	0.947384i	0.880691	−	0.473692i	$-0.157079\pi$
$108$	−106.925	−	48.7211i	−0.990050	−	0.451121i
$109$	−102.637			−0.941626			−0.470813	−	0.882233i	$-0.656039\pi$
$109$	−102.637			−0.941626			−0.470813	+	0.882233i	$0.656039\pi$
$110$	−45.4372	−	70.6355i	−0.413066	−	0.642141i
$111$		−	99.4796i		−	0.896213i
$112$	−73.7113	+	64.0916i	−0.658137	+	0.572246i
$113$	−219.581			−1.94319			−0.971596	−	0.236644i	$-0.923952\pi$
$113$	−219.581			−1.94319			−0.971596	+	0.236644i	$0.923952\pi$
$114$	−18.3240	+	11.7872i	−0.160737	+	0.103396i
$115$			28.3436i			0.246466i
$116$	−57.1945	+	125.522i	−0.493056	+	1.08208i
$117$	39.1364			0.334499
$118$	46.6561	+	72.5304i	0.395391	+	0.614664i
$119$		−	128.773i		−	1.08213i
$120$	44.2444	−	6.41913i	0.368703	−	0.0534927i
$121$	−231.696			−1.91484
$122$	110.686	−	71.2002i	0.907262	−	0.583608i
$123$		−	47.1426i		−	0.383273i
$124$	−191.797	−	87.3933i	−1.54675	−	0.704785i
$125$	11.1803			0.0894427
$126$	18.1906	+	28.2786i	0.144369	+	0.224433i
$127$		−	187.766i		−	1.47848i	−0.673444	−	0.739238i	$-0.735186\pi$
$127$		−	187.766i		−	1.47848i	0.673444	−	0.739238i	$-0.264814\pi$
$128$	83.5332	−	96.9856i	0.652603	−	0.757700i
$129$	9.89442			0.0767009
$130$	−53.4520	+	34.3837i	−0.411169	+	0.264490i
$131$			114.066i			0.870730i	0.900254	+	0.435365i	$0.143381\pi$
$131$			114.066i			0.870730i	−0.900254	+	0.435365i	$0.856619\pi$
$132$	77.8461	−	170.844i	0.589744	−	1.29428i
$133$	26.6107			0.200080
$134$	−17.0889	−	26.5660i	−0.127529	−	0.198254i
$135$		−	65.6858i		−	0.486561i
$136$	24.2288	+	166.999i	0.178153	+	1.22793i
$137$	−130.861			−0.955186			−0.477593	−	0.878581i	$-0.658491\pi$
$137$	−130.861			−0.955186			−0.477593	+	0.878581i	$0.658491\pi$
$138$	−53.2860	+	34.2770i	−0.386131	+	0.248384i
$139$			111.014i			0.798662i	0.916807	+	0.399331i	$0.130758\pi$
$139$			111.014i			0.798662i	−0.916807	+	0.399331i	$0.869242\pi$
$140$	−49.6888	−	22.6410i	−0.354920	−	0.161721i
$141$	−24.0011			−0.170221
$142$	−1.39497	−	2.16858i	−0.00982372	−	0.0152717i
$143$			266.895i			1.86640i
$144$	−28.9109	−	33.2503i	−0.200770	−	0.230905i
$145$	−77.1096			−0.531791
$146$	−51.7204	+	33.2698i	−0.354249	+	0.227875i
$147$		−	29.3162i		−	0.199430i
$148$	66.0174	−	144.885i	0.446064	−	0.978950i
$149$	−86.1409			−0.578127			−0.289063	−	0.957310i	$-0.593344\pi$
$149$	−86.1409			−0.578127			−0.289063	+	0.957310i	$0.593344\pi$
$150$	13.5208	+	21.0191i	0.0901388	+	0.140127i
$151$			161.598i			1.07018i	0.844794	+	0.535091i	$0.179723\pi$
$151$			161.598i			1.07018i	−0.844794	+	0.535091i	$0.820277\pi$
$152$	−34.5099	+	5.00681i	−0.227039	+	0.0329396i
$153$	58.0881			0.379661
$154$	−192.849	+	124.053i	−1.25227	+	0.805536i
$155$		−	117.824i		−	0.760153i
$156$	−129.283	−	58.9085i	−0.828738	−	0.377618i
$157$	136.590			0.870002			0.435001	−	0.900430i	$-0.356748\pi$
$157$	136.590			0.870002			0.435001	+	0.900430i	$0.356748\pi$
$158$	−33.1126	−	51.4759i	−0.209573	−	0.325797i
$159$		−	65.3703i		−	0.411134i
$160$	68.6985	+	20.0128i	0.429366	+	0.125080i
$161$	77.3835			0.480643
$162$	81.8007	−	52.6194i	0.504943	−	0.324811i
$163$			220.735i			1.35420i	0.735890	+	0.677102i	$0.236764\pi$
$163$			220.735i			1.35420i	−0.735890	+	0.677102i	$0.763236\pi$
$164$	31.2851	−	68.6597i	0.190763	−	0.418657i
$165$	104.952			0.636074
$166$	7.85862	+	12.2168i	0.0473411	+	0.0735952i
$167$		−	192.109i		−	1.15035i	−0.818029	−	0.575177i	$-0.804933\pi$
$167$		−	192.109i		−	1.15035i	0.818029	−	0.575177i	$-0.195067\pi$
$168$	−17.5255	−	120.796i	−0.104318	−	0.719023i
$169$	32.9677			0.195075
$170$	−79.3359	+	51.0339i	−0.466682	+	0.300199i
$171$			12.0038i			0.0701974i
$172$	14.4105	+	6.56621i	0.0837819	+	0.0381756i
$173$	276.229			1.59670			0.798350	−	0.602194i	$-0.205706\pi$
$173$	276.229			1.59670			0.798350	+	0.602194i	$0.205706\pi$
$174$	−93.2516	−	144.967i	−0.535929	−	0.833141i
$175$		−	30.5245i		−	0.174426i
$176$	226.754	−	197.161i	1.28838	−	1.12024i
$177$	−107.768			−0.608857
$178$	−258.413	+	166.227i	−1.45176	+	0.933862i
$179$			131.168i			0.732780i	0.930461	+	0.366390i	$0.119406\pi$
$179$			131.168i			0.732780i	−0.930461	+	0.366390i	$0.880594\pi$
$180$	10.2131	−	22.4140i	0.0567392	−	0.124522i
$181$	145.014			0.801184			0.400592	−	0.916256i	$-0.368804\pi$
$181$	145.014			0.801184			0.400592	+	0.916256i	$0.368804\pi$
$182$	93.8743	+	145.934i	0.515793	+	0.801838i
$183$			164.460i			0.898690i
$184$	−100.354	+	14.5598i	−0.545404	+	0.0791291i
$185$	89.0047			0.481106
$186$	221.509	−	142.489i	1.19091	−	0.766068i
$187$			396.139i			2.11839i
$188$	−34.9559	−	15.9278i	−0.185935	−	0.0847224i
$189$	−179.335			−0.948863
$190$	−10.5460	−	16.3946i	−0.0555054	−	0.0862871i
$191$			363.413i			1.90268i	0.308136	+	0.951342i	$0.400295\pi$
$191$			363.413i			1.90268i	−0.308136	+	0.951342i	$0.599705\pi$
$192$	45.4556	+	153.356i	0.236748	+	0.798728i
$193$	−361.447			−1.87278			−0.936392	−	0.350955i	$-0.885857\pi$
$193$	−361.447			−1.87278			−0.936392	+	0.350955i	$0.885857\pi$
$194$	−62.3870	+	40.1313i	−0.321582	+	0.206862i
$195$		−	79.4204i		−	0.407284i
$196$	19.4551	−	42.6969i	0.0992606	−	0.217842i
$197$	365.250			1.85406			0.927031	−	0.374986i	$-0.122352\pi$
$197$	365.250			1.85406			0.927031	+	0.374986i	$0.122352\pi$
$198$	−55.9586	−	86.9918i	−0.282619	−	0.439353i
$199$		−	299.605i		−	1.50555i	−0.658278	−	0.752775i	$-0.728715\pi$
$199$		−	299.605i		−	1.50555i	0.658278	−	0.752775i	$-0.271285\pi$
$200$	5.74321	+	39.5855i	0.0287161	+	0.197928i
$201$	39.4725			0.196381
$202$	177.076	−	113.906i	0.876613	−	0.563893i
$203$			210.525i			1.03707i
$204$	−191.888	−	87.4347i	−0.940627	−	0.428601i
$205$	42.1786			0.205749
$206$	16.7149	+	25.9846i	0.0811404	+	0.126139i
$207$			34.9068i			0.168632i
$208$	−149.198	−	171.592i	−0.717298	−	0.824960i
$209$	−81.8610			−0.391679
$210$	57.3863	−	36.9145i	0.273268	−	0.175783i
$211$			293.518i			1.39108i	0.718486	+	0.695541i	$0.244835\pi$
$211$			293.518i			1.39108i	−0.718486	+	0.695541i	$0.755165\pi$
$212$	43.3816	−	95.2070i	0.204630	−	0.449090i
$213$	3.22214			0.0151274
$214$	109.682	+	170.509i	0.512534	+	0.796771i
$215$			8.85257i			0.0411747i
$216$	232.570	−	33.7420i	1.07671	−	0.156213i
$217$	−321.682			−1.48240
$218$	172.641	−	111.053i	0.791929	−	0.509419i
$219$		−	76.8475i		−	0.350902i
$220$	152.855	+	69.6492i	0.694796	+	0.316587i
$221$	299.770			1.35642
$222$	107.637	+	167.329i	0.484850	+	0.753736i
$223$		−	186.137i		−	0.834694i	−0.908747	−	0.417347i	$-0.862960\pi$
$223$		−	186.137i		−	0.834694i	0.908747	−	0.417347i	$-0.137040\pi$
$224$	54.6389	−	187.561i	0.243924	−	0.837324i
$225$	13.7692			0.0611967
$226$	369.345	−	237.586i	1.63427	−	1.05127i
$227$			61.3196i			0.270130i	0.990837	+	0.135065i	$0.0431244\pi$
$227$			61.3196i			0.270130i	−0.990837	+	0.135065i	$0.956876\pi$
$228$	18.0682	−	39.6531i	0.0792463	−	0.173917i
$229$	180.903			0.789970			0.394985	−	0.918688i	$-0.370750\pi$
$229$	180.903			0.789970			0.394985	+	0.918688i	$0.370750\pi$
$230$	−30.6677	−	47.6752i	−0.133338	−	0.207283i
$231$		−	286.540i		−	1.24043i
$232$	−39.6103	−	273.017i	−0.170734	−	1.17680i
$233$	398.190			1.70897			0.854484	−	0.519477i	$-0.173873\pi$
$233$	398.190			1.70897			0.854484	+	0.519477i	$0.173873\pi$
$234$	−65.8293	+	42.3456i	−0.281322	+	0.180964i
$235$		−	21.4739i		−	0.0913782i
$236$	−156.956	−	71.5176i	−0.665066	−	0.303041i
$237$	76.4844			0.322719
$238$	139.333	+	216.603i	0.585431	+	0.910095i
$239$		−	72.7480i		−	0.304385i	−0.988351	−	0.152192i	$-0.951367\pi$
$239$		−	72.7480i		−	0.304385i	0.988351	−	0.152192i	$-0.0486334\pi$
$240$	−67.4756	+	58.6696i	−0.281148	+	0.244457i
$241$	−375.793			−1.55931			−0.779654	−	0.626211i	$-0.784605\pi$
$241$	−375.793			−1.55931			−0.779654	+	0.626211i	$0.784605\pi$
$242$	389.723	−	250.695i	1.61043	−	1.03593i
$243$		−	142.838i		−	0.587813i
$244$	−109.140	+	239.524i	−0.447296	+	0.981656i
$245$	26.2293			0.107058
$246$	51.0082	+	79.2960i	0.207351	+	0.322342i
$247$			61.9466i			0.250796i
$248$	417.171	−	60.5246i	1.68214	−	0.244051i
$249$	−18.1520			−0.0728998
$250$	−18.8058	+	12.0971i	−0.0752234	+	0.0483884i
$251$		−	11.0126i		−	0.0438751i	−0.999759	−	0.0219375i	$-0.993017\pi$
$251$		−	11.0126i		−	0.0438751i	0.999759	−	0.0219375i	$-0.00698349\pi$
$252$	−61.1947	−	27.8837i	−0.242836	−	0.110649i
$253$	−238.051			−0.940912
$254$	203.163	+	315.832i	0.799854	+	1.24343i
$255$		−	117.879i		−	0.462272i
$256$	−35.5684	+	253.517i	−0.138939	+	0.990301i
$257$	−22.3742			−0.0870591			−0.0435295	−	0.999052i	$-0.513860\pi$
$257$	−22.3742			−0.0870591			−0.0435295	+	0.999052i	$0.513860\pi$
$258$	−16.6429	+	10.7057i	−0.0645073	+	0.0414952i
$259$		−	243.000i		−	0.938225i
$260$	52.7056	−	115.670i	0.202714	−	0.444884i
$261$	−94.9651			−0.363851
$262$	−123.419	−	191.864i	−0.471064	−	0.732304i
$263$			392.306i			1.49166i	0.666137	+	0.745829i	$0.267947\pi$
$263$			392.306i			1.49166i	−0.666137	+	0.745829i	$0.732053\pi$
$264$	53.9127	+	371.598i	0.204215	+	1.40757i
$265$	58.4870			0.220706
$266$	−44.7604	+	28.7927i	−0.168272	+	0.108243i
$267$		−	383.957i		−	1.43804i
$268$	57.4887	+	26.1950i	0.214510	+	0.0977427i
$269$	−134.878			−0.501406			−0.250703	−	0.968064i	$-0.580662\pi$
$269$	−134.878			−0.501406			−0.250703	+	0.968064i	$0.580662\pi$
$270$	71.0719	+	110.487i	0.263229	+	0.409209i
$271$			494.327i			1.82408i	0.410097	+	0.912042i	$0.365495\pi$
$271$			494.327i			1.82408i	−0.410097	+	0.912042i	$0.634505\pi$
$272$	−221.446	−	254.684i	−0.814141	−	0.936339i
$273$	−216.833			−0.794262
$274$	220.113	−	141.591i	0.803334	−	0.516755i
$275$			93.9010i			0.341458i
$276$	52.5419	−	115.311i	0.190369	−	0.417793i
$277$	−171.040			−0.617473			−0.308736	−	0.951148i	$-0.599906\pi$
$277$	−171.040			−0.617473			−0.308736	+	0.951148i	$0.599906\pi$
$278$	−120.117	−	186.731i	−0.432076	−	0.671693i
$279$		−	145.107i		−	0.520096i
$280$	108.076	−	15.6801i	0.385987	−	0.0560004i
$281$	223.298			0.794654			0.397327	−	0.917677i	$-0.369938\pi$
$281$	223.298			0.794654			0.397327	+	0.917677i	$0.369938\pi$
$282$	40.3710	−	25.9692i	0.143160	−	0.0920893i
$283$			271.376i			0.958926i	0.877562	+	0.479463i	$0.159169\pi$
$283$			271.376i			0.958926i	−0.877562	+	0.479463i	$0.840831\pi$
$284$	4.69280	+	2.13830i	0.0165240	+	0.00752922i
$285$	24.3595			0.0854719
$286$	−288.780	−	448.930i	−1.00972	−	1.56969i
$287$		−	115.156i		−	0.401240i
$288$	84.6063	+	24.6469i	0.293772	+	0.0855796i
$289$	155.932			0.539558
$290$	129.702	−	83.4325i	0.447248	−	0.287698i
$291$		−	92.6963i		−	0.318544i
$292$	50.9982	−	111.923i	0.174651	−	0.383297i
$293$	−336.927			−1.14992			−0.574962	−	0.818180i	$-0.694983\pi$
$293$	−336.927			−1.14992			−0.574962	+	0.818180i	$0.694983\pi$
$294$	31.7201	+	49.3113i	0.107892	+	0.167725i
$295$		−	96.4200i		−	0.326847i
$296$	45.7207	+	315.133i	0.154462	+	1.06464i
$297$	551.679			1.85751
$298$	144.893	−	93.2043i	0.486218	−	0.312766i
$299$			180.140i			0.602475i
$300$	−45.4853	−	20.7256i	−0.151618	−	0.0690853i
$301$	24.1692			0.0802965
$302$	−174.848	−	271.815i	−0.578968	−	0.900048i
$303$			263.104i			0.868331i
$304$	52.6298	−	45.7613i	0.173124	−	0.150531i
$305$	−147.143			−0.482436
$306$	−97.7068	+	62.8512i	−0.319303	+	0.205396i
$307$			299.731i			0.976322i	0.872753	+	0.488161i	$0.162332\pi$
$307$			299.731i			0.976322i	−0.872753	+	0.488161i	$0.837668\pi$
$308$	190.156	−	417.324i	0.617389	−	1.35495i
$309$	−38.6086			−0.124947
$310$	127.485	+	198.185i	0.411242	+	0.639306i
$311$		−	224.717i		−	0.722562i	−0.932457	−	0.361281i	$-0.882339\pi$
$311$		−	224.717i		−	0.722562i	0.932457	−	0.361281i	$-0.117661\pi$
$312$	281.199	−	40.7973i	0.901279	−	0.130761i
$313$	115.619			0.369390			0.184695	−	0.982796i	$-0.440870\pi$
$313$	115.619			0.369390			0.184695	+	0.982796i	$0.440870\pi$
$314$	−229.751	+	147.791i	−0.731692	+	0.470671i
$315$		−	37.5928i		−	0.119342i
$316$	111.394	+	50.7571i	0.352512	+	0.160624i
$317$	−575.911			−1.81675			−0.908377	−	0.418153i	$-0.862678\pi$
$317$	−575.911			−1.81675			−0.908377	+	0.418153i	$0.862678\pi$
$318$	70.7306	+	109.956i	0.222423	+	0.345773i
$319$		−	647.625i		−	2.03017i
$320$	−137.208	+	40.6693i	−0.428775	+	0.127091i
$321$	−253.347			−0.789243
$322$	−130.163	+	83.7288i	−0.404232	+	0.260027i
$323$			91.9441i			0.284657i
$324$	−80.6584	+	177.016i	−0.248946	+	0.546347i
$325$	71.0577			0.218639
$326$	−238.835	−	371.287i	−0.732623	−	1.13892i
$327$			256.514i			0.784447i
$328$	21.6667	+	149.339i	0.0660569	+	0.455303i
$329$	−58.6279			−0.178200
$330$	−176.534	+	113.558i	−0.534953	+	0.344115i
$331$		−	209.021i		−	0.631484i	−0.948845	−	0.315742i	$-0.897747\pi$
$331$		−	209.021i		−	0.631484i	0.948845	−	0.315742i	$-0.102253\pi$
$332$	−26.4371	−	12.0462i	−0.0796299	−	0.0362837i
$333$	109.615			0.329173
$334$	207.862	+	323.136i	0.622341	+	0.967474i
$335$			35.3161i			0.105421i
$336$	160.180	+	184.222i	0.476725	+	0.548279i
$337$	137.536			0.408119			0.204060	−	0.978958i	$-0.434586\pi$
$337$	137.536			0.408119			0.204060	+	0.978958i	$0.434586\pi$
$338$	−55.4532	+	35.6710i	−0.164063	+	0.105535i
$339$			548.783i			1.61883i
$340$	78.2281	−	171.683i	0.230083	−	0.504949i
$341$	989.573			2.90197
$342$	−12.9880	−	20.1909i	−0.0379767	−	0.0590376i
$343$		−	370.752i		−	1.08091i
$344$	−31.3437	+	4.54746i	−0.0911155	+	0.0132194i
$345$	70.8371			0.205325
$346$	−464.630	+	298.880i	−1.34286	+	0.863814i
$347$		−	28.2816i		−	0.0815031i	−0.999169	−	0.0407516i	$-0.987025\pi$
$347$		−	28.2816i		−	0.0815031i	0.999169	−	0.0407516i	$-0.0129752\pi$
$348$	313.707	+	142.942i	0.901457	+	0.410753i
$349$	−115.566			−0.331135			−0.165568	−	0.986198i	$-0.552946\pi$
$349$	−115.566			−0.331135			−0.165568	+	0.986198i	$0.552946\pi$
$350$	33.0275	+	51.3437i	0.0943643	+	0.146696i
$351$		−	417.472i		−	1.18938i
$352$	−168.083	+	576.982i	−0.477508	+	1.63915i
$353$	−665.356			−1.88486			−0.942430	−	0.334403i	$-0.891465\pi$
$353$	−665.356			−1.88486			−0.942430	+	0.334403i	$0.891465\pi$
$354$	181.270	−	116.604i	0.512062	−	0.329391i
$355$			2.88285i			0.00812072i
$356$	254.804	−	559.204i	0.715742	−	1.57080i
$357$	−321.834			−0.901496
$358$	−141.923	−	220.630i	−0.396433	−	0.616285i
$359$			26.1461i			0.0728304i	0.999337	+	0.0364152i	$0.0115939\pi$
$359$			26.1461i			0.0728304i	−0.999337	+	0.0364152i	$0.988406\pi$
$360$	7.07310	+	48.7519i	0.0196475	+	0.135422i
$361$	−19.0000			−0.0526316
$362$	−243.921	+	156.905i	−0.673814	+	0.433440i
$363$			579.061i			1.59521i
$364$	−315.802	−	143.897i	−0.867587	−	0.395320i
$365$	68.7557			0.188372
$366$	−177.946	−	276.630i	−0.486190	−	0.755819i
$367$		−	435.125i		−	1.18563i	−0.805340	−	0.592813i	$-0.798017\pi$
$367$		−	435.125i		−	1.18563i	0.805340	−	0.592813i	$-0.201983\pi$
$368$	153.047	−	133.073i	0.415888	−	0.361612i
$369$	51.9455			0.140774
$370$	−149.710	+	96.3029i	−0.404622	+	0.260278i
$371$		−	159.681i		−	0.430407i
$372$	−218.416	+	479.345i	−0.587140	+	1.28856i
$373$	−471.615			−1.26438			−0.632192	−	0.774812i	$-0.717845\pi$
$373$	−471.615			−1.26438			−0.632192	+	0.774812i	$0.717845\pi$
$374$	−428.621	−	666.323i	−1.14605	−	1.78161i
$375$		−	27.9422i		−	0.0745126i
$376$	76.0312	−	11.0309i	0.202211	−	0.0293374i
$377$	−490.077			−1.29994
$378$	301.650	−	194.040i	0.798016	−	0.513334i
$379$			152.981i			0.403643i	0.979422	+	0.201822i	$0.0646862\pi$
$379$			152.981i			0.403643i	−0.979422	+	0.201822i	$0.935314\pi$
$380$	35.4778	+	16.1656i	0.0933626	+	0.0425411i
$381$	−469.271			−1.23168
$382$	−393.212	−	611.277i	−1.02935	−	1.60020i
$383$		−	211.036i		−	0.551008i	−0.961300	−	0.275504i	$-0.911155\pi$
$383$		−	211.036i		−	0.551008i	0.961300	−	0.275504i	$-0.0888447\pi$
$384$	−242.389	−	208.769i	−0.631222	−	0.543668i
$385$	256.368			0.665892
$386$	607.971	−	391.086i	1.57506	−	1.01318i
$387$			10.9025i			0.0281717i
$388$	61.5158	−	135.005i	0.158546	−	0.347952i
$389$	−396.644			−1.01965			−0.509825	−	0.860278i	$-0.670290\pi$
$389$	−396.644			−1.01965			−0.509825	+	0.860278i	$0.670290\pi$
$390$	85.9328	+	133.589i	0.220340	+	0.342535i
$391$			267.372i			0.683816i
$392$	13.4737	+	92.8686i	0.0343717	+	0.236910i
$393$	285.076			0.725385
$394$	−614.367	+	395.200i	−1.55931	+	1.00305i
$395$			68.4308i			0.173242i
$396$	188.250	+	85.7770i	0.475379	+	0.216609i
$397$	250.129			0.630049			0.315024	−	0.949084i	$-0.397987\pi$
$397$	250.129			0.630049			0.315024	+	0.949084i	$0.397987\pi$
$398$	324.172	+	503.949i	0.814502	+	1.26620i
$399$		−	66.5062i		−	0.166682i
$400$	−52.4919	−	60.3706i	−0.131230	−	0.150926i
$401$	−651.162			−1.62385			−0.811923	−	0.583764i	$-0.801579\pi$
$401$	−651.162			−1.62385			−0.811923	+	0.583764i	$0.801579\pi$
$402$	−66.3945	+	42.7092i	−0.165161	+	0.106242i
$403$		−	748.839i		−	1.85816i
$404$	−174.603	+	383.192i	−0.432186	+	0.948494i
$405$	−108.744			−0.268503
$406$	−227.787	−	354.112i	−0.561052	−	0.872197i
$407$			747.529i			1.83668i
$408$	417.369	−	60.5533i	1.02296	−	0.148415i
$409$	582.632			1.42453			0.712264	−	0.701912i	$-0.247670\pi$
$409$	582.632			1.42453			0.712264	+	0.701912i	$0.247670\pi$
$410$	−70.9464	+	45.6372i	−0.173040	+	0.111310i
$411$			327.051i			0.795743i
$412$	−56.2305	−	25.6217i	−0.136482	−	0.0621886i
$413$	−263.246			−0.637398
$414$	−37.7691	−	58.7148i	−0.0912296	−	0.141823i
$415$		−	16.2407i		−	0.0391342i
$416$	436.620	+	127.193i	1.04957	+	0.305753i
$417$	277.450			0.665347
$418$	137.694	−	88.5735i	0.329411	−	0.211898i
$419$		−	355.932i		−	0.849481i	−0.905315	−	0.424740i	$-0.860365\pi$
$419$		−	355.932i		−	0.849481i	0.905315	−	0.424740i	$-0.139635\pi$
$420$	−56.5850	+	124.184i	−0.134726	+	0.295676i
$421$	295.765			0.702530			0.351265	−	0.936276i	$-0.385752\pi$
$421$	295.765			0.702530			0.351265	+	0.936276i	$0.385752\pi$
$422$	−317.586	−	493.711i	−0.752574	−	1.16993i
$423$		−	26.4463i		−	0.0625209i
$424$	30.0441	+	207.081i	0.0708587	+	0.488400i
$425$	105.467			0.248158
$426$	−5.41978	+	3.48635i	−0.0127225	+	0.00818391i
$427$			401.729i			0.940818i
$428$	−368.981	−	168.128i	−0.862106	−	0.392823i
$429$	667.033			1.55486
$430$	−9.57846	−	14.8904i	−0.0222755	−	0.0346289i
$431$			370.946i			0.860665i	0.902671	+	0.430332i	$0.141604\pi$
$431$			370.946i			0.860665i	−0.902671	+	0.430332i	$0.858396\pi$
$432$	−354.684	+	308.396i	−0.821028	+	0.713879i
$433$	−540.423			−1.24809			−0.624045	−	0.781388i	$-0.714512\pi$
$433$	−540.423			−1.24809			−0.624045	+	0.781388i	$0.714512\pi$
$434$	541.084	−	348.059i	1.24674	−	0.801980i
$435$			192.715i			0.443022i
$436$	−170.230	+	373.594i	−0.390436	+	0.856867i
$437$	−55.2518			−0.126434
$438$	83.1489	+	129.261i	0.189838	+	0.295117i
$439$			104.731i			0.238566i	0.992860	+	0.119283i	$0.0380596\pi$
$439$			104.731i			0.238566i	−0.992860	+	0.119283i	$0.961940\pi$
$440$	−332.470	+	48.2358i	−0.755613	+	0.109627i
$441$	32.3030			0.0732493
$442$	−504.227	+	324.350i	−1.14078	+	0.733825i
$443$			538.230i			1.21497i	0.794332	+	0.607483i	$0.207821\pi$
$443$			538.230i			1.21497i	−0.794332	+	0.607483i	$0.792179\pi$
$444$	−362.100	−	164.993i	−0.815541	−	0.371605i
$445$	343.527			0.771971
$446$	201.400	+	313.091i	0.451569	+	0.701997i
$447$			215.286i			0.481624i
$448$	111.035	+	374.605i	0.247846	+	0.836171i
$449$	686.295			1.52850			0.764249	−	0.644922i	$-0.223110\pi$
$449$	686.295			1.52850			0.764249	+	0.644922i	$0.223110\pi$
$450$	−23.1605	+	14.8983i	−0.0514678	+	0.0331073i
$451$			354.248i			0.785473i
$452$	−364.187	+	799.262i	−0.805725	+	1.76828i
$453$	403.870			0.891544
$454$	−66.3477	−	103.142i	−0.146140	−	0.227186i
$455$		−	194.001i		−	0.426377i
$456$	12.5132	+	86.2481i	0.0274412	+	0.189141i
$457$	314.409			0.687985			0.343992	−	0.938972i	$-0.388221\pi$
$457$	314.409			0.687985			0.343992	+	0.938972i	$0.388221\pi$
$458$	−304.287	+	195.737i	−0.664383	+	0.427373i
$459$		−	619.631i		−	1.34996i
$460$	103.169	+	47.0094i	0.224280	+	0.102194i
$461$	56.6285			0.122838			0.0614192	−	0.998112i	$-0.480437\pi$
$461$	56.6285			0.122838			0.0614192	+	0.998112i	$0.480437\pi$
$462$	310.036	+	481.974i	0.671074	+	1.04323i
$463$		−	153.774i		−	0.332125i	−0.986115	−	0.166062i	$-0.946895\pi$
$463$		−	153.774i		−	0.332125i	0.986115	−	0.166062i	$-0.0531053\pi$
$464$	362.031	+	416.369i	0.780239	+	0.897348i
$465$	−294.468			−0.633265
$466$	−669.773	+	430.841i	−1.43728	+	0.924551i
$467$			113.941i			0.243985i	0.992531	+	0.121992i	$0.0389283\pi$
$467$			113.941i			0.243985i	−0.992531	+	0.121992i	$0.961072\pi$
$468$	64.9100	−	142.454i	0.138697	−	0.304390i
$469$	96.4200			0.205586
$470$	23.2347	+	36.1200i	0.0494355	+	0.0768512i
$471$		−	341.371i		−	0.724779i
$472$	341.388	−	49.5298i	0.723280	−	0.104936i
$473$	−74.3506			−0.157189
$474$	−128.650	+	82.7560i	−0.271414	+	0.174591i
$475$			21.7945i			0.0458831i
$476$	−468.728	−	213.578i	−0.984722	−	0.448693i
$477$	72.0302			0.151007
$478$	78.7132	+	122.365i	0.164672	+	0.255995i
$479$		−	724.949i		−	1.51346i	−0.653725	−	0.756732i	$-0.726795\pi$
$479$		−	724.949i		−	1.51346i	0.653725	−	0.756732i	$-0.273205\pi$
$480$	50.0166	−	171.693i	0.104201	−	0.357695i
$481$	565.677			1.17604
$482$	632.101	−	406.608i	1.31141	−	0.843584i
$483$		−	193.399i		−	0.400412i
$484$	−384.281	+	843.360i	−0.793969	+	1.74248i
$485$	82.9356			0.171001
$486$	154.551	+	240.261i	0.318006	+	0.494364i
$487$		−	333.743i		−	0.685303i	−0.939463	−	0.342651i	$-0.888675\pi$
$487$		−	333.743i		−	0.685303i	0.939463	−	0.342651i	$-0.111325\pi$
$488$	−75.5856	−	520.980i	−0.154889	−	1.06758i
$489$	551.668			1.12815
$490$	−44.1189	+	28.3801i	−0.0900386	+	0.0579186i
$491$			967.949i			1.97138i	0.168559	+	0.985692i	$0.446089\pi$
$491$			967.949i			1.97138i	−0.168559	+	0.985692i	$0.553911\pi$
$492$	−171.596	−	78.1888i	−0.348773	−	0.158920i
$493$	−727.395			−1.47545
$494$	−67.0262	−	104.197i	−0.135681	−	0.210925i
$495$			115.645i			0.233625i
$496$	−636.213	+	553.184i	−1.28269	+	1.11529i
$497$	7.87076			0.0158365
$498$	30.5326	−	19.6405i	0.0613104	−	0.0394387i
$499$		−	57.3937i		−	0.115017i	−0.998345	−	0.0575087i	$-0.981684\pi$
$499$		−	57.3937i		−	0.115017i	0.998345	−	0.0575087i	$-0.0183157\pi$
$500$	18.5432	−	40.6958i	0.0370865	−	0.0813916i
$501$	−480.125			−0.958333
$502$	11.9157	+	18.5238i	0.0237364	+	0.0368999i
$503$		−	357.590i		−	0.710914i	−0.934693	−	0.355457i	$-0.884325\pi$
$503$		−	357.590i		−	0.710914i	0.934693	−	0.355457i	$-0.115675\pi$
$504$	133.102	−	19.3110i	0.264092	−	0.0383154i
$505$	−235.400			−0.466139
$506$	400.412	−	257.571i	0.791329	−	0.509033i
$507$		−	82.3938i		−	0.162512i
$508$	−683.459	−	311.422i	−1.34539	−	0.613034i
$509$	−69.7317			−0.136998			−0.0684988	−	0.997651i	$-0.521821\pi$
$509$	−69.7317			−0.136998			−0.0684988	+	0.997651i	$0.521821\pi$
$510$	127.545	+	198.279i	0.250089	+	0.388782i
$511$		−	187.717i		−	0.367352i
$512$	−214.477	−	464.912i	−0.418901	−	0.908032i
$513$	128.045			0.249601
$514$	37.6344	−	24.2088i	0.0732187	−	0.0470989i
$515$		−	34.5432i		−	0.0670742i
$516$	16.4105	−	36.0151i	0.0318032	−	0.0697968i
$517$	180.354			0.348847
$518$	262.926	+	408.738i	0.507579	+	0.789069i
$519$		−	690.360i		−	1.33017i
$520$	36.5015	+	251.590i	0.0701952	+	0.483826i
$521$	−44.8598			−0.0861032			−0.0430516	−	0.999073i	$-0.513708\pi$
$521$	−44.8598			−0.0861032			−0.0430516	+	0.999073i	$0.513708\pi$
$522$	159.736	−	102.752i	0.306007	−	0.196843i
$523$		−	567.289i		−	1.08468i	−0.840159	−	0.542341i	$-0.817538\pi$
$523$		−	567.289i		−	1.08468i	0.840159	−	0.542341i	$-0.182462\pi$
$524$	415.192	+	189.184i	0.792352	+	0.361039i
$525$	−76.2878			−0.145310
$526$	−424.475	−	659.877i	−0.806986	−	1.25452i
$527$		−	1111.46i		−	2.10903i
$528$	−492.752	−	566.711i	−0.933242	−	1.07332i
$529$	368.329			0.696273
$530$	−98.3779	+	63.2829i	−0.185619	+	0.119402i
$531$		−	118.747i		−	0.223629i
$532$	44.1353	−	96.8613i	0.0829612	−	0.182070i
$533$	268.070			0.502946
$534$	415.440	+	645.833i	0.777978	+	1.20942i
$535$		−	226.670i		−	0.423683i
$536$	−125.042	+	18.1415i	−0.233287	+	0.0338461i
$537$	327.818			0.610462
$538$	226.871	−	145.938i	0.421694	−	0.271260i
$539$			220.294i			0.408708i
$540$	−239.092	−	108.944i	−0.442764	−	0.201748i
$541$	346.722			0.640891			0.320445	−	0.947267i	$-0.396167\pi$
$541$	346.722			0.640891			0.320445	+	0.947267i	$0.396167\pi$
$542$	−534.861	−	831.480i	−0.986828	−	1.53410i
$543$		−	362.424i		−	0.667448i
$544$	648.051	+	188.786i	1.19127	+	0.347033i
$545$	−229.504			−0.421108
$546$	364.724	−	234.613i	0.667992	−	0.429695i
$547$		−	309.354i		−	0.565547i	−0.959187	−	0.282773i	$-0.908746\pi$
$547$		−	309.354i		−	0.565547i	0.959187	−	0.282773i	$-0.0912544\pi$
$548$	−217.040	+	476.325i	−0.396058	+	0.869206i
$549$	−181.215			−0.330082
$550$	−101.601	−	157.946i	−0.184729	−	0.287174i
$551$		−	150.314i		−	0.272803i
$552$	36.3882	+	250.808i	0.0659206	+	0.454363i
$553$	186.830			0.337847
$554$	287.697	−	185.065i	0.519309	−	0.334052i
$555$		−	222.443i		−	0.400799i
$556$	404.085	+	184.123i	0.726771	+	0.331157i
$557$	−779.151			−1.39883			−0.699417	−	0.714714i	$-0.746557\pi$
$557$	−779.151			−1.39883			−0.699417	+	0.714714i	$0.746557\pi$
$558$	157.005	+	244.076i	0.281372	+	0.437413i
$559$			56.2633i			0.100650i
$560$	−164.824	+	143.313i	−0.294328	+	0.255916i
$561$	990.041			1.76478
$562$	−375.597	+	241.608i	−0.668322	+	0.429907i
$563$			633.179i			1.12465i	0.826916	+	0.562326i	$0.190093\pi$
$563$			633.179i			1.12465i	−0.826916	+	0.562326i	$0.809907\pi$
$564$	−39.8073	+	87.3627i	−0.0705803	+	0.154898i
$565$	−490.998			−0.869022
$566$	−293.629	−	456.467i	−0.518778	−	0.806479i
$567$			296.892i			0.523619i
$568$	−10.2071	+	1.48089i	−0.0179703	+	0.00260720i
$569$	−585.267			−1.02859			−0.514294	−	0.857614i	$-0.671946\pi$
$569$	−585.267			−1.02859			−0.514294	+	0.857614i	$0.671946\pi$
$570$	−40.9738	+	26.3569i	−0.0718838	+	0.0462402i
$571$			827.530i			1.44927i	0.689135	+	0.724633i	$0.257990\pi$
$571$			827.530i			1.44927i	−0.689135	+	0.724633i	$0.742010\pi$
$572$	971.484	+	442.662i	1.69840	+	0.773884i
$573$	908.252			1.58508
$574$	124.599	+	193.698i	0.217071	+	0.337452i
$575$			63.3781i			0.110223i
$576$	−168.980	+	50.0866i	−0.293367	+	0.0869559i
$577$	−53.5448			−0.0927986			−0.0463993	−	0.998923i	$-0.514775\pi$
$577$	−53.5448			−0.0927986			−0.0463993	+	0.998923i	$0.514775\pi$
$578$	−262.285	+	168.718i	−0.453780	+	0.291900i
$579$			903.340i			1.56017i
$580$	−127.891	+	280.675i	−0.220501	+	0.483922i
$581$	−44.3403			−0.0763172
$582$	100.297	+	155.919i	0.172332	+	0.267903i
$583$			491.218i			0.842570i
$584$	35.3190	+	243.439i	0.0604778	+	0.416848i
$585$	87.5117			0.149593
$586$	566.728	−	364.555i	0.967112	−	0.622108i
$587$		−	13.8513i		−	0.0235968i	−0.999930	−	0.0117984i	$-0.996244\pi$
$587$		−	13.8513i		−	0.0235968i	0.999930	−	0.0117984i	$-0.00375563\pi$
$588$	−106.709	−	48.6227i	−0.181479	−	0.0826917i
$589$	229.681			0.389950
$590$	104.326	+	162.183i	0.176824	+	0.274886i
$591$		−	912.844i		−	1.54458i
$592$	−417.878	−	480.599i	−0.705875	−	0.811823i
$593$	−481.491			−0.811958			−0.405979	−	0.913882i	$-0.633069\pi$
$593$	−481.491			−0.811958			−0.405979	+	0.913882i	$0.633069\pi$
$594$	−927.950	+	596.916i	−1.56220	+	1.00491i
$595$		−	287.946i		−	0.483943i
$596$	−142.870	+	313.548i	−0.239714	+	0.526087i
$597$	−748.781			−1.25424
$598$	−194.911	−	303.004i	−0.325939	−	0.506695i
$599$			827.375i			1.38126i	0.723208	+	0.690630i	$0.242667\pi$
$599$			827.375i			1.38126i	−0.723208	+	0.690630i	$0.757333\pi$
$600$	98.9334	−	14.3536i	0.164889	−	0.0239227i
$601$	−974.226			−1.62101			−0.810504	−	0.585733i	$-0.800807\pi$
$601$	−974.226			−1.62101			−0.810504	+	0.585733i	$0.800807\pi$
$602$	−40.6538	+	26.1511i	−0.0675312	+	0.0434404i
$603$			43.4939i			0.0721292i
$604$	588.206	+	268.019i	0.973851	+	0.443740i
$605$	−518.088			−0.856343
$606$	−284.678	−	442.553i	−0.469766	−	0.730286i
$607$			159.112i			0.262128i	0.991374	+	0.131064i	$0.0418393\pi$
$607$			159.112i			0.262128i	−0.991374	+	0.131064i	$0.958161\pi$
$608$	−39.0121	+	133.918i	−0.0641647	+	0.220260i
$609$	526.149			0.863956
$610$	247.501	−	159.209i	0.405740	−	0.260998i
$611$		−	136.479i		−	0.223370i
$612$	96.3425	−	211.437i	0.157422	−	0.345486i
$613$	180.155			0.293890			0.146945	−	0.989145i	$-0.453056\pi$
$613$	180.155			0.293890			0.146945	+	0.989145i	$0.453056\pi$
$614$	−324.309	−	504.161i	−0.528190	−	0.821110i
$615$		−	105.414i		−	0.171405i
$616$	131.693	+	907.707i	0.213788	+	1.47355i
$617$	−866.103			−1.40373			−0.701866	−	0.712309i	$-0.747650\pi$
$617$	−866.103			−1.40373			−0.701866	+	0.712309i	$0.747650\pi$
$618$	64.9414	−	41.7744i	0.105083	−	0.0675961i
$619$		−	844.856i		−	1.36487i	−0.730945	−	0.682436i	$-0.760920\pi$
$619$		−	844.856i		−	1.36487i	0.730945	−	0.682436i	$-0.239080\pi$
$620$	−428.871	−	195.417i	−0.691728	−	0.315189i
$621$	372.354			0.599603
$622$	243.143	+	377.984i	0.390906	+	0.607692i
$623$		−	937.896i		−	1.50545i
$624$	−428.847	+	372.880i	−0.687255	+	0.597564i
$625$	25.0000			0.0400000
$626$	−194.476	+	125.100i	−0.310665	+	0.199840i
$627$			204.589i			0.326299i
$628$	226.543	−	497.181i	0.360737	−	0.791690i
$629$	839.604			1.33482
$630$	40.6753	+	63.2328i	0.0645640	+	0.100369i
$631$		−	990.335i		−	1.56947i	−0.619832	−	0.784735i	$-0.712799\pi$
$631$		−	990.335i		−	1.56947i	0.619832	−	0.784735i	$-0.287201\pi$
$632$	−242.289	+	35.1521i	−0.383368	+	0.0556204i
$633$	733.570			1.15888
$634$	968.708	−	623.135i	1.52793	−	0.982862i
$635$		−	419.858i		−	0.661194i
$636$	−237.944	−	108.420i	−0.374126	−	0.170472i
$637$	166.703			0.261700
$638$	700.730	+	1089.34i	1.09832	+	1.70742i
$639$			3.55041i			0.00555619i
$640$	186.786	−	216.866i	0.291853	−	0.338854i
$641$	112.534			0.175560			0.0877800	−	0.996140i	$-0.472023\pi$
$641$	112.534			0.175560			0.0877800	+	0.996140i	$0.472023\pi$
$642$	426.141	−	274.121i	0.663772	−	0.426980i
$643$		−	102.432i		−	0.159303i	−0.996823	−	0.0796513i	$-0.974619\pi$
$643$		−	102.432i		−	0.159303i	0.996823	−	0.0796513i	$-0.0253807\pi$
$644$	128.345	−	281.671i	0.199293	−	0.437378i
$645$	22.1246			0.0343017
$646$	−99.4833	−	154.654i	−0.153999	−	0.239403i
$647$			763.293i			1.17974i	0.807498	+	0.589871i	$0.200821\pi$
$647$			763.293i			1.17974i	−0.807498	+	0.589871i	$0.799179\pi$
$648$	−55.8604	−	385.022i	−0.0862043	−	0.594170i
$649$	809.808			1.24778
$650$	−119.522	+	76.8843i	−0.183880	+	0.118284i
$651$			803.957i			1.23496i
$652$	803.463	+	366.102i	1.23231	+	0.561506i
$653$	232.072			0.355393			0.177697	−	0.984085i	$-0.443135\pi$
$653$	232.072			0.355393			0.177697	+	0.984085i	$0.443135\pi$
$654$	−277.548	−	431.469i	−0.424385	−	0.659738i
$655$			255.058i			0.389402i
$656$	−198.029	−	227.752i	−0.301874	−	0.347183i
$657$	84.6767			0.128884
$658$	98.6149	−	63.4353i	0.149871	−	0.0964063i
$659$		−	561.230i		−	0.851639i	−0.904808	−	0.425820i	$-0.859986\pi$
$659$		−	561.230i		−	0.851639i	0.904808	−	0.425820i	$-0.140014\pi$
$660$	174.069	−	382.020i	0.263741	−	0.578818i
$661$	−846.230			−1.28023			−0.640113	−	0.768281i	$-0.721113\pi$
$661$	−846.230			−1.28023			−0.640113	+	0.768281i	$0.721113\pi$
$662$	226.161	+	351.583i	0.341632	+	0.531092i
$663$		−	749.194i		−	1.13001i
$664$	57.5024	−	8.34265i	0.0866000	−	0.0125642i
$665$	59.5033			0.0894786
$666$	−184.377	+	118.603i	−0.276842	+	0.178082i
$667$		−	437.112i		−	0.655341i
$668$	−699.266	−	318.624i	−1.04681	−	0.476982i
$669$	−465.198			−0.695364
$670$	−38.2120	−	59.4034i	−0.0570329	−	0.0886618i
$671$		−	1235.82i		−	1.84176i
$672$	−468.757	−	136.555i	−0.697555	−	0.203207i
$673$	148.001			0.219912			0.109956	−	0.993936i	$-0.464929\pi$
$673$	148.001			0.219912			0.109956	+	0.993936i	$0.464929\pi$
$674$	−231.342	+	148.814i	−0.343238	+	0.220792i
$675$		−	146.878i		−	0.217597i
$676$	54.6788	−	120.000i	0.0808858	−	0.177516i
$677$	428.744			0.633300			0.316650	−	0.948542i	$-0.397442\pi$
$677$	428.744			0.633300			0.316650	+	0.948542i	$0.397442\pi$
$678$	−593.782	−	923.078i	−0.875785	−	1.36147i
$679$		−	226.431i		−	0.333477i
$680$	54.1772	+	373.421i	0.0796724	+	0.549148i
$681$	153.252			0.225039
$682$	−1664.51	+	1070.72i	−2.44063	+	1.56996i
$683$			1002.51i			1.46781i	0.679252	+	0.733905i	$0.262304\pi$
$683$			1002.51i			1.46781i	−0.679252	+	0.733905i	$0.737696\pi$
$684$	43.6930	+	19.9089i	0.0638786	+	0.0291066i
$685$	−292.613			−0.427172
$686$	401.153	+	623.621i	0.584771	+	0.909069i
$687$		−	452.119i		−	0.658106i
$688$	47.8013	−	41.5629i	0.0694786	−	0.0604112i
$689$	371.720			0.539506
$690$	−119.151	+	76.6456i	−0.172683	+	0.111081i
$691$			264.638i			0.382979i	0.981495	+	0.191489i	$0.0613318\pi$
$691$			264.638i			0.382979i	−0.981495	+	0.191489i	$0.938668\pi$
$692$	458.142	−	1005.46i	0.662055	−	1.45297i
$693$	315.733			0.455603
$694$	30.6006	+	47.5709i	0.0440931	+	0.0685460i
$695$			248.235i			0.357173i
$696$	−682.333	+	98.9953i	−0.980364	+	0.142235i
$697$	397.882			0.570849
$698$	194.388	−	125.042i	0.278492	−	0.179144i
$699$		−	995.168i		−	1.42370i
$700$	−111.108	−	50.6267i	−0.158725	−	0.0723239i
$701$	−649.626			−0.926713			−0.463356	−	0.886172i	$-0.653355\pi$
$701$	−649.626			−0.926713			−0.463356	+	0.886172i	$0.653355\pi$
$702$	451.704	+	702.207i	0.643453	+	1.00029i
$703$			173.502i			0.246802i
$704$	−341.571	−	1152.38i	−0.485187	−	1.63690i
$705$	−53.6682			−0.0761250
$706$	1119.16	−	719.914i	1.58521	−	1.01971i
$707$			642.689i			0.909036i
$708$	−178.739	+	392.268i	−0.252456	+	0.554051i
$709$	−1017.85			−1.43562			−0.717808	−	0.696242i	$-0.754854\pi$
$709$	−1017.85			−1.43562			−0.717808	+	0.696242i	$0.754854\pi$
$710$	−3.11924	−	4.84909i	−0.00439330	−	0.00682971i
$711$			84.2765i			0.118532i
$712$	176.466	+	1216.31i	0.247845	+	1.70829i
$713$	667.908			0.936757
$714$	541.340	−	348.224i	0.758179	−	0.487709i
$715$			596.796i			0.834680i
$716$	477.443	+	217.549i	0.666819	+	0.303840i
$717$	−181.814			−0.253576
$718$	−28.2901	−	43.9790i	−0.0394012	−	0.0612521i
$719$			264.510i			0.367886i	0.982937	+	0.183943i	$0.0588862\pi$
$719$			264.510i			0.367886i	−0.982937	+	0.183943i	$0.941114\pi$
$720$	−64.6468	−	74.3499i	−0.0897872	−	0.103264i
$721$	−94.3097			−0.130804
$722$	31.9589	−	20.5580i	0.0442644	−	0.0284736i
$723$			939.193i			1.29902i
$724$	240.515	−	527.844i	0.332203	−	0.729066i
$725$	−172.422			−0.237824
$726$	−626.544	−	974.008i	−0.863008	−	1.34161i
$727$			691.184i			0.950734i	0.879788	+	0.475367i	$0.157685\pi$
$727$			691.184i			0.950734i	−0.879788	+	0.475367i	$0.842315\pi$
$728$	686.889	−	99.6563i	0.943529	−	0.136891i
$729$	−794.671			−1.09008
$730$	−115.650	+	74.3936i	−0.158425	+	0.101909i
$731$			83.5086i			0.114239i
$732$	598.626	+	272.767i	0.817795	+	0.372632i
$733$	222.400			0.303411			0.151706	−	0.988426i	$-0.451523\pi$
$733$	222.400			0.303411			0.151706	+	0.988426i	$0.451523\pi$
$734$	470.805	+	731.900i	0.641423	+	0.997139i
$735$		−	65.5531i		−	0.0891879i
$736$	−113.447	+	389.432i	−0.154140	+	0.529120i
$737$	−296.612			−0.402458
$738$	−87.3747	+	56.2049i	−0.118394	+	0.0761584i
$739$		−	374.097i		−	0.506220i	−0.967437	−	0.253110i	$-0.918546\pi$
$739$		−	374.097i		−	0.506220i	0.967437	−	0.253110i	$-0.0814535\pi$
$740$	147.619	−	323.972i	0.199486	−	0.437800i
$741$	154.819			0.208932
$742$	172.775	+	268.591i	0.232850	+	0.361982i
$743$		−	218.509i		−	0.294090i	−0.989130	−	0.147045i	$-0.953024\pi$
$743$		−	218.509i		−	0.294090i	0.989130	−	0.147045i	$-0.0469761\pi$
$744$	−151.265	−	1042.61i	−0.203313	−	1.40135i
$745$	−192.617			−0.258546
$746$	793.278	−	510.287i	1.06338	−	0.684031i
$747$		−	20.0014i		−	0.0267756i
$748$	1441.92	+	657.019i	1.92770	+	0.878367i
$749$	−618.855			−0.826241
$750$	30.2335	+	47.0001i	0.0403113	+	0.0626668i
$751$		−	651.939i		−	0.868095i	−0.900890	−	0.434048i	$-0.857085\pi$
$751$		−	651.939i		−	0.868095i	0.900890	−	0.434048i	$-0.142915\pi$
$752$	−115.953	+	100.820i	−0.154192	+	0.134069i
$753$	−27.5231			−0.0365513
$754$	824.333	−	530.263i	1.09328	−	0.703266i
$755$			361.343i			0.478600i
$756$	−297.438	+	652.770i	−0.393436	+	0.863452i
$757$	867.396			1.14583			0.572917	−	0.819613i	$-0.305812\pi$
$757$	867.396			1.14583			0.572917	+	0.819613i	$0.305812\pi$
$758$	−165.525	−	257.321i	−0.218371	−	0.339473i
$759$			594.943i			0.783852i
$760$	−77.1664	+	11.1956i	−0.101535	+	0.0147310i
$761$	−1055.93			−1.38755			−0.693777	−	0.720190i	$-0.744055\pi$
$761$	−1055.93			−1.38755			−0.693777	+	0.720190i	$0.744055\pi$
$762$	789.336	−	507.751i	1.03587	−	0.666340i
$763$			626.591i			0.821220i
$764$	1322.80	+	602.741i	1.73142	+	0.788928i
$765$	129.889			0.169789
$766$	228.341	+	354.972i	0.298095	+	0.463410i
$767$		−	612.806i		−	0.798965i
$768$	633.597	+	88.8937i	0.824997	+	0.115747i
$769$	1237.66			1.60944			0.804721	−	0.593654i	$-0.202315\pi$
$769$	1237.66			1.60944			0.804721	+	0.593654i	$0.202315\pi$
$770$	−431.223	+	277.390i	−0.560030	+	0.360247i
$771$			55.9182i			0.0725269i
$772$	−599.482	+	1315.65i	−0.776531	+	1.70421i
$773$	−894.544			−1.15724			−0.578619	−	0.815598i	$-0.696408\pi$
$773$	−894.544			−1.15724			−0.578619	+	0.815598i	$0.696408\pi$
$774$	−11.7964	−	18.3384i	−0.0152409	−	0.0236931i
$775$		−	263.462i		−	0.339951i
$776$	42.6031	+	293.645i	0.0549008	+	0.378409i
$777$	−607.314			−0.781614
$778$	667.173	−	429.168i	0.857549	−	0.551630i
$779$			82.2213i			0.105547i
$780$	−289.086	−	131.723i	−0.370623	−	0.168876i
$781$	−24.2124			−0.0310018
$782$	−289.296	−	449.732i	−0.369944	−	0.575105i
$783$			1013.00i			1.29374i
$784$	−123.147	−	141.631i	−0.157075	−	0.180651i
$785$	305.425			0.389077
$786$	−479.511	+	308.452i	−0.610065	+	0.392433i
$787$		−	267.027i		−	0.339297i	−0.985505	−	0.169649i	$-0.945737\pi$
$787$		−	267.027i		−	0.339297i	0.985505	−	0.169649i	$-0.0542633\pi$
$788$	605.788	−	1329.49i	0.768767	−	1.68717i
$789$	980.464			1.24267
$790$	−74.0420	−	115.104i	−0.0937241	−	0.145701i
$791$			1340.52i			1.69472i
$792$	−409.456	+	59.4053i	−0.516990	+	0.0750067i
$793$	−935.181			−1.17929
$794$	−420.729	+	270.640i	−0.529886	+	0.340856i
$795$		−	146.173i		−	0.183865i
$796$	−1090.54	−	496.912i	−1.37003	−	0.624261i
$797$	772.708			0.969521			0.484760	−	0.874647i	$-0.338907\pi$
$797$	772.708			0.969521			0.484760	+	0.874647i	$0.338907\pi$
$798$	71.9596	+	111.866i	0.0901749	+	0.140184i
$799$		−	202.569i		−	0.253528i
$800$	153.615	+	44.7500i	0.192018	+	0.0559375i
$801$	423.074			0.528182
$802$	1095.29	−	704.557i	1.36569	−	0.878500i
$803$			577.463i			0.719132i
$804$	65.4674	−	143.678i	0.0814271	−	0.178703i
$805$	173.035			0.214950
$806$	810.243	+	1259.58i	1.00526	+	1.56276i
$807$			337.091i			0.417709i
$808$	−120.922	−	833.466i	−0.149656	−	1.03152i
$809$	17.9244			0.0221563			0.0110781	−	0.999939i	$-0.496474\pi$
$809$	17.9244			0.0221563			0.0110781	+	0.999939i	$0.496474\pi$
$810$	182.912	−	117.661i	0.225817	−	0.145260i
$811$		−	1358.86i		−	1.67554i	−0.546024	−	0.837769i	$-0.683859\pi$
$811$		−	1358.86i		−	1.67554i	0.546024	−	0.837769i	$-0.316141\pi$
$812$	766.297	+	349.167i	0.943716	+	0.430009i
$813$	1235.44			1.51960
$814$	−808.825	−	1257.38i	−0.993643	−	1.54469i
$815$			493.579i			0.605618i
$816$	−636.515	+	553.446i	−0.780042	+	0.678242i
$817$	−17.2568			−0.0211222
$818$	−980.014	+	630.407i	−1.19806	+	0.770669i
$819$		−	238.924i		−	0.291727i
$820$	69.9557	−	153.528i	0.0853118	−	0.187229i
$821$	465.928			0.567512			0.283756	−	0.958896i	$-0.408419\pi$
$821$	465.928			0.567512			0.283756	+	0.958896i	$0.408419\pi$
$822$	−353.868	−	550.114i	−0.430497	−	0.669239i
$823$			444.626i			0.540251i	0.962825	+	0.270125i	$0.0870652\pi$
$823$			444.626i			0.540251i	−0.962825	+	0.270125i	$0.912935\pi$
$824$	122.305	−	17.7444i	0.148428	−	0.0215345i
$825$	234.680			0.284461
$826$	442.791	−	284.831i	0.536067	−	0.344832i
$827$			105.668i			0.127773i	0.997957	+	0.0638866i	$0.0203496\pi$
$827$			105.668i			0.127773i	−0.997957	+	0.0638866i	$0.979650\pi$
$828$	127.059	+	57.8949i	0.153452	+	0.0699214i
$829$	−189.802			−0.228953			−0.114477	−	0.993426i	$-0.536519\pi$
$829$	−189.802			−0.228953			−0.114477	+	0.993426i	$0.536519\pi$
$830$	17.5724	+	27.3176i	0.0211716	+	0.0329128i
$831$			427.468i			0.514402i
$832$	−872.037	+	258.477i	−1.04812	+	0.310670i
$833$	247.428			0.297033
$834$	−466.683	+	300.200i	−0.559572	+	0.359952i
$835$		−	429.569i		−	0.514454i
$836$	−135.771	+	297.969i	−0.162406	+	0.356423i
$837$	−1547.87			−1.84930
$838$	385.118	+	598.695i	0.459568	+	0.714433i
$839$		−	924.743i		−	1.10220i	−0.834440	−	0.551098i	$-0.814209\pi$
$839$		−	924.743i		−	1.10220i	0.834440	−	0.551098i	$-0.185791\pi$
$840$	−39.1882	−	270.108i	−0.0466526	−	0.321557i
$841$	348.179			0.414006
$842$	−497.491	+	320.018i	−0.590844	+	0.380068i
$843$		−	558.072i		−	0.662008i
$844$	1068.39	+	486.817i	1.26586	+	0.576798i
$845$	73.7180			0.0872402
$846$	28.6149	+	44.4840i	0.0338238	+	0.0525815i
$847$			1414.48i			1.66999i
$848$	−274.597	−	315.813i	−0.323818	−	0.372421i
$849$	678.231			0.798859
$850$	−177.400	+	114.115i	−0.208706	+	0.134253i
$851$			504.542i			0.592881i
$852$	5.34410	−	11.7284i	0.00627242	−	0.0137657i
$853$	1304.14			1.52889			0.764445	−	0.644689i	$-0.223013\pi$
$853$	1304.14			1.52889			0.764445	+	0.644689i	$0.223013\pi$
$854$	−434.671	−	675.727i	−0.508982	−	0.791250i
$855$			26.8412i			0.0313932i
$856$	802.558	−	116.438i	0.937567	−	0.136026i
$857$	980.696			1.14434			0.572168	−	0.820137i	$-0.306103\pi$
$857$	980.696			1.14434			0.572168	+	0.820137i	$0.306103\pi$
$858$	−1121.98	+	721.729i	−1.30767	+	0.841176i
$859$			886.346i			1.03184i	0.856638	+	0.515918i	$0.172549\pi$
$859$			886.346i			1.03184i	−0.856638	+	0.515918i	$0.827451\pi$
$860$	32.2228	+	14.6825i	0.0374684	+	0.0170727i
$861$	−287.801			−0.334264
$862$	−401.364	−	623.949i	−0.465619	−	0.723839i
$863$			326.460i			0.378285i	0.981950	+	0.189142i	$0.0605708\pi$
$863$			326.460i			0.378285i	−0.981950	+	0.189142i	$0.939429\pi$
$864$	262.911	−	902.503i	0.304295	−	1.04456i
$865$	617.667			0.714066
$866$	909.016	−	584.737i	1.04967	−	0.675216i
$867$		−	389.710i		−	0.449493i
$868$	−533.528	+	1170.90i	−0.614664	+	1.34897i
$869$	−574.734			−0.661374
$870$	−208.517	−	324.155i	−0.239675	−	0.372592i
$871$			224.455i			0.257698i
$872$	−117.893	−	812.591i	−0.135199	−	0.931870i
$873$	102.140			0.116999
$874$	92.9360	−	59.7823i	0.106334	−	0.0684008i
$875$		−	68.2549i		−	0.0780056i
$876$	−279.721	−	127.456i	−0.319316	−	0.145498i
$877$	−902.257			−1.02880			−0.514400	−	0.857551i	$-0.671985\pi$
$877$	−902.257			−1.02880			−0.514400	+	0.857551i	$0.671985\pi$
$878$	−113.318	−	176.162i	−0.129064	−	0.200640i
$879$			842.059i			0.957974i
$880$	507.038	−	440.866i	0.576179	−	0.500985i
$881$	−1547.47			−1.75649			−0.878245	−	0.478212i	$-0.841285\pi$
$881$	−1547.47			−1.75649			−0.878245	+	0.478212i	$0.841285\pi$
$882$	−54.3351	+	34.9518i	−0.0616044	+	0.0396278i
$883$		−	769.276i		−	0.871207i	−0.900139	−	0.435603i	$-0.856535\pi$
$883$		−	769.276i		−	0.871207i	0.900139	−	0.435603i	$-0.143465\pi$
$884$	497.186	−	1091.14i	0.562427	−	1.23433i
$885$	−240.976			−0.272289
$886$	−582.364	−	905.328i	−0.657296	−	1.02181i
$887$			1086.87i			1.22533i	0.790344	+	0.612664i	$0.209902\pi$
$887$			1086.87i			1.22533i	−0.790344	+	0.612664i	$0.790098\pi$
$888$	787.591	−	114.266i	0.886927	−	0.128678i
$889$	−1146.30			−1.28942
$890$	−577.828	+	371.696i	−0.649245	+	0.417636i
$891$		−	913.312i		−	1.02504i
$892$	−677.527	−	308.719i	−0.759559	−	0.346097i
$893$	41.8603			0.0468760
$894$	−232.939	−	362.121i	−0.260558	−	0.405057i
$895$			293.300i			0.327709i
$896$	−592.088	−	509.962i	−0.660812	−	0.569155i
$897$	450.211			0.501908
$898$	−1154.38	+	742.571i	−1.28550	+	0.826916i
$899$			1817.07i			2.02121i
$900$	22.8371	−	50.1193i	0.0253746	−	0.0556881i
$901$	551.723			0.612346
$902$	−383.296	−	595.862i	−0.424940	−	0.660601i
$903$		−	60.4045i		−	0.0668931i
$904$	−252.220	−	1738.45i	−0.279004	−	1.92306i
$905$	324.262			0.358300
$906$	−679.327	+	436.986i	−0.749809	+	0.482325i
$907$		−	1604.62i		−	1.76916i	−0.466392	−	0.884578i	$-0.654446\pi$
$907$		−	1604.62i		−	1.76916i	0.466392	−	0.884578i	$-0.345554\pi$
$908$	223.200	+	101.702i	0.245815	+	0.112007i
$909$	−289.909			−0.318932
$910$	209.909	+	326.319i	0.230670	+	0.358593i
$911$		−	1175.00i		−	1.28979i	−0.764270	−	0.644897i	$-0.776900\pi$
$911$		−	1175.00i		−	1.28979i	0.764270	−	0.644897i	$-0.223100\pi$
$912$	−114.368	−	131.534i	−0.125404	−	0.144226i
$913$	136.402			0.149399
$914$	−528.851	+	340.190i	−0.578611	+	0.372199i
$915$			367.744i			0.401906i
$916$	300.038	−	658.477i	0.327553	−	0.718862i
$917$	696.360			0.759389
$918$	670.440	+	1042.25i	0.730327	+	1.13535i
$919$		−	668.405i		−	0.727317i	−0.931532	−	0.363659i	$-0.881527\pi$
$919$		−	668.405i		−	0.727317i	0.931532	−	0.363659i	$-0.118473\pi$
$920$	−224.399	+	32.5566i	−0.243912	+	0.0353876i
$921$	749.097			0.813351
$922$	−95.2517	+	61.2719i	−0.103310	+	0.0664554i
$923$			18.3222i			0.0198508i
$924$	−1042.99	−	475.243i	−1.12878	−	0.514333i
$925$	199.021			0.215157
$926$	166.383	+	258.654i	0.179679	+	0.279324i
$927$		−	42.5420i		−	0.0458921i
$928$	−1059.46	−	308.636i	−1.14166	−	0.332582i
$929$	−1394.30			−1.50086			−0.750428	−	0.660952i	$-0.770153\pi$
$929$	−1394.30			−1.50086			−0.750428	+	0.660952i	$0.770153\pi$
$930$	495.309	−	318.614i	0.532591	−	0.342596i
$931$			51.1304i			0.0549198i
$932$	660.421	−	1449.39i	0.708606	−	1.55514i
$933$	−561.619			−0.601950
$934$	−123.284	−	191.654i	−0.131996	−	0.205197i
$935$			885.793i			0.947372i
$936$	44.9537	+	309.847i	0.0480275	+	0.331034i
$937$	−1321.02			−1.40984			−0.704921	−	0.709286i	$-0.749018\pi$
$937$	−1321.02			−1.40984			−0.704921	+	0.709286i	$0.749018\pi$
$938$	−162.183	+	104.326i	−0.172903	+	0.111222i
$939$		−	288.958i		−	0.307730i
$940$	−78.1637	−	35.6157i	−0.0831529	−	0.0378890i
$941$	−157.818			−0.167713			−0.0838564	−	0.996478i	$-0.526724\pi$
$941$	−157.818			−0.167713			−0.0838564	+	0.996478i	$0.526724\pi$
$942$	369.363	+	574.201i	0.392105	+	0.609555i
$943$			239.098i			0.253551i
$944$	−520.640	+	452.693i	−0.551525	+	0.479548i
$945$	−401.006			−0.424345
$946$	125.061	−	80.4472i	0.132200	−	0.0850393i
$947$			611.749i			0.645986i	0.946401	+	0.322993i	$0.104689\pi$
$947$			611.749i			0.645986i	−0.946401	+	0.322993i	$0.895311\pi$
$948$	126.854	−	278.399i	0.133812	−	0.293670i
$949$	436.983			0.460467
$950$	−23.5816	−	36.6593i	−0.0248228	−	0.0385888i
$951$			1439.33i			1.51349i
$952$	1019.51	−	147.914i	1.07092	−	0.155372i
$953$	−247.374			−0.259574			−0.129787	−	0.991542i	$-0.541429\pi$
$953$	−247.374			−0.259574			−0.129787	+	0.991542i	$0.541429\pi$
$954$	−121.158	+	77.9366i	−0.127000	+	0.0816945i
$955$			812.616i			0.850906i
$956$	−264.799	−	120.657i	−0.276986	−	0.126210i
$957$	−1618.56			−1.69129
$958$	784.394	+	1219.40i	0.818783	+	1.27286i
$959$			798.891i			0.833046i
$960$	101.642	+	342.914i	0.105877	+	0.357202i
$961$	−1815.48			−1.88916
$962$	−951.495	+	612.062i	−0.989080	+	0.636239i
$963$		−	279.158i		−	0.289884i
$964$	−623.275	+	1367.87i	−0.646551	+	1.41895i
$965$	−808.221			−0.837535
$966$	209.258	+	325.306i	0.216623	+	0.336756i
$967$		−	950.188i		−	0.982615i	−0.870986	−	0.491307i	$-0.836519\pi$
$967$		−	950.188i		−	0.982615i	0.870986	−	0.491307i	$-0.163481\pi$
$968$	−266.136	−	1834.36i	−0.274934	−	1.89500i
$969$	229.789			0.237141
$970$	−139.502	+	89.7362i	−0.143816	+	0.0925116i
$971$		−	820.147i		−	0.844642i	−0.906446	−	0.422321i	$-0.861216\pi$
$971$		−	820.147i		−	0.844642i	0.906446	−	0.422321i	$-0.138784\pi$
$972$	−519.924	−	236.906i	−0.534901	−	0.243730i
$973$	677.731			0.696537
$974$	361.109	+	561.370i	0.370748	+	0.576356i
$975$		−	177.589i		−	0.182143i
$976$	690.838	+	794.529i	0.707826	+	0.814067i
$977$	−54.3382			−0.0556174			−0.0278087	−	0.999613i	$-0.508853\pi$
$977$	−54.3382			−0.0556174			−0.0278087	+	0.999613i	$0.508853\pi$
$978$	−927.931	+	596.904i	−0.948804	+	0.610331i
$979$			2885.20i			2.94709i
$980$	43.5029	−	95.4733i	0.0443907	−	0.0974217i
$981$	−282.648			−0.288122
$982$	−1047.32	−	1628.14i	−1.06652	−	1.65798i
$983$		−	324.307i		−	0.329916i	−0.986301	−	0.164958i	$-0.947251\pi$
$983$		−	324.307i		−	0.329916i	0.986301	−	0.164958i	$-0.0527489\pi$
$984$	373.233	−	54.1500i	0.379302	−	0.0550305i
$985$	816.724			0.829161
$986$	1223.51	−	787.041i	1.24088	−	0.798216i
$987$			146.525i			0.148455i
$988$	225.482	+	102.742i	0.228221	+	0.103990i
$989$	−50.1826			−0.0507408
$990$	−125.127	−	194.520i	−0.126391	−	0.196484i
$991$			1604.08i			1.61865i	0.587360	+	0.809326i	$0.300167\pi$
$991$			1604.08i			1.61865i	−0.587360	+	0.809326i	$0.699833\pi$
$992$	471.596	−	1618.86i	0.475399	−	1.63192i
$993$	−522.392			−0.526074
$994$	−13.2390	+	8.51615i	−0.0133189	+	0.00856756i
$995$		−	669.936i		−	0.673303i
$996$	−30.1062	+	66.0724i	−0.0302271	+	0.0663378i
$997$	−41.8970			−0.0420230			−0.0210115	−	0.999779i	$-0.506689\pi$
$997$	−41.8970			−0.0420230			−0.0210115	+	0.999779i	$0.506689\pi$
$998$	62.0999	+	96.5389i	0.0622244	+	0.0967323i
$999$		−	1169.27i		−	1.17044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.14	yes	72
4.3	odd	2	inner	380.3.b.a.191.13	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.13	✓	72	4.3	odd	2	inner
380.3.b.a.191.14	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68205 + 1.08200i) q^{2} -2.49923i q^{3} +(1.65856 - 3.63994i) q^{4} +2.23607 q^{5} +(2.70416 + 4.20382i) q^{6} -6.10491i q^{7} +(1.14864 + 7.91711i) q^{8} +2.75385 q^{9} +O(q^{10})\)	\(q+(-1.68205 + 1.08200i) q^{2} -2.49923i q^{3} +(1.65856 - 3.63994i) q^{4} +2.23607 q^{5} +(2.70416 + 4.20382i) q^{6} -6.10491i q^{7} +(1.14864 + 7.91711i) q^{8} +2.75385 q^{9} +(-3.76117 + 2.41942i) q^{10} +18.7802i q^{11} +(-9.09705 - 4.14512i) q^{12} +14.2115 q^{13} +(6.60550 + 10.2687i) q^{14} -5.58845i q^{15} +(-10.4984 - 12.0741i) q^{16} +21.0934 q^{17} +(-4.63210 + 2.97966i) q^{18} +4.35890i q^{19} +(3.70865 - 8.13916i) q^{20} -15.2576 q^{21} +(-20.3201 - 31.5892i) q^{22} +12.6756i q^{23} +(19.7867 - 2.87072i) q^{24} +5.00000 q^{25} +(-23.9045 + 15.3769i) q^{26} -29.3756i q^{27} +(-22.2215 - 10.1253i) q^{28} -34.4845 q^{29} +(6.04669 + 9.40003i) q^{30} -52.6923i q^{31} +(30.7229 + 8.94999i) q^{32} +46.9360 q^{33} +(-35.4801 + 22.8230i) q^{34} -13.6510i q^{35} +(4.56742 - 10.0239i) q^{36} +39.8041 q^{37} +(-4.71632 - 7.33187i) q^{38} -35.5179i q^{39} +(2.56844 + 17.7032i) q^{40} +18.8629 q^{41} +(25.6639 - 16.5087i) q^{42} +3.95899i q^{43} +(68.3589 + 31.1481i) q^{44} +6.15779 q^{45} +(-13.7150 - 21.3210i) q^{46} -9.60341i q^{47} +(-30.1760 + 26.2378i) q^{48} +11.7301 q^{49} +(-8.41023 + 5.40999i) q^{50} -52.7173i q^{51} +(23.5707 - 51.7292i) q^{52} +26.1562 q^{53} +(31.7843 + 49.4111i) q^{54} +41.9938i q^{55} +(48.3332 - 7.01235i) q^{56} +10.8939 q^{57} +(58.0045 - 37.3122i) q^{58} -43.1203i q^{59} +(-20.3416 - 9.26877i) q^{60} -65.8043 q^{61} +(57.0130 + 88.6309i) q^{62} -16.8120i q^{63} +(-61.3612 + 18.1879i) q^{64} +31.7780 q^{65} +(-78.9486 + 50.7847i) q^{66} +15.7939i q^{67} +(34.9847 - 76.7788i) q^{68} +31.6793 q^{69} +(14.7703 + 22.9616i) q^{70} +1.28925i q^{71} +(3.16319 + 21.8025i) q^{72} +30.7485 q^{73} +(-66.9523 + 43.0680i) q^{74} -12.4961i q^{75} +(15.8661 + 7.22949i) q^{76} +114.651 q^{77} +(38.4303 + 59.7427i) q^{78} +30.6032i q^{79} +(-23.4751 - 26.9985i) q^{80} -48.6317 q^{81} +(-31.7282 + 20.4096i) q^{82} -7.26306i q^{83} +(-25.3056 + 55.5367i) q^{84} +47.1663 q^{85} +(-4.28362 - 6.65920i) q^{86} +86.1846i q^{87} +(-148.685 + 21.5717i) q^{88} +153.630 q^{89} +(-10.3577 + 6.66273i) q^{90} -86.7601i q^{91} +(46.1385 + 21.0233i) q^{92} -131.690 q^{93} +(10.3909 + 16.1534i) q^{94} +9.74679i q^{95} +(22.3681 - 76.7836i) q^{96} +37.0899 q^{97} +(-19.7306 + 12.6920i) q^{98} +51.7178i 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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