LMFDB - Embedded newform 315.3.ca.b.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +O(q^{10})$	\(q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +(8.31195 + 7.26192i) q^{10} +(4.69282 + 8.12820i) q^{11} +(-0.405222 + 0.405222i) q^{13} +(-2.15427 + 15.3014i) q^{14} +(-9.36489 + 16.2205i) q^{16} +(-2.82961 + 10.5602i) q^{17} +(-23.8500 - 13.7698i) q^{19} +(-3.91828 - 1.92317i) q^{20} +(-14.6503 - 14.6503i) q^{22} +(-1.02354 - 3.81990i) q^{23} +(-9.48058 + 23.1326i) q^{25} +(0.632520 - 1.09556i) q^{26} +(-0.743235 - 6.06535i) q^{28} -34.6601i q^{29} +(-11.8284 - 20.4874i) q^{31} +(3.55465 - 13.2661i) q^{32} -24.1338i q^{34} +(-34.3751 + 6.58431i) q^{35} +(25.6130 - 6.86297i) q^{37} +(58.7215 + 15.7344i) q^{38} +(-33.8637 - 6.67007i) q^{40} -54.6731 q^{41} +(-47.3942 + 47.3942i) q^{43} +(7.09560 + 4.09664i) q^{44} +(4.36491 + 7.56024i) q^{46} +(16.9830 - 4.55058i) q^{47} +(-34.0211 - 35.2642i) q^{49} +(6.99854 - 54.7414i) q^{50} +(-0.129479 + 0.483221i) q^{52} +(-14.7503 - 3.95234i) q^{53} +(20.6770 - 42.1274i) q^{55} +(-18.0901 - 44.8060i) q^{56} +(19.8026 + 73.9044i) q^{58} +(-90.3630 + 52.1711i) q^{59} +(-12.5803 + 21.7897i) q^{61} +(36.9264 + 36.9264i) q^{62} -44.6014i q^{64} +(2.81133 + 0.553743i) q^{65} +(0.364564 - 1.36057i) q^{67} +(2.47014 + 9.21867i) q^{68} +(69.5348 - 33.6792i) q^{70} -86.5935 q^{71} +(-84.9471 - 22.7615i) q^{73} +(-50.6924 + 29.2673i) q^{74} -24.0409 q^{76} +(65.2117 - 7.99089i) q^{77} +(128.353 + 74.1049i) q^{79} +(93.4368 - 6.29977i) q^{80} +(116.577 - 31.2368i) q^{82} +(-35.5711 + 35.5711i) q^{83} +(51.7299 - 17.6679i) q^{85} +(73.9787 - 128.135i) q^{86} +(62.5803 + 16.7683i) q^{88} +(-130.143 - 75.1382i) q^{89} +(1.50183 + 3.71975i) q^{91} +(-2.44111 - 2.44111i) q^{92} +(-33.6122 + 19.4060i) q^{94} +(9.26295 + 137.386i) q^{95} +(74.8462 + 74.8462i) q^{97} +(92.6896 + 55.7549i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−2.13226	+	0.571337i	−1.06613	+	0.285669i	−0.748902	−	0.662681i	$-0.769419\pi$
$2$	−2.13226	+	0.571337i	−1.06613	+	0.285669i	−0.317228	+	0.948349i	$0.602752\pi$
$3$		0			0
$3$		0			0
$4$	0.756006	−	0.436480i	0.189001	−	0.109120i
$5$	−2.78563	−	4.15214i	−0.557125	−	0.830429i
$5$	−2.78563	−	4.15214i	−0.557125	−	0.830429i
$6$		0			0
$7$	2.73668	−	6.44287i	0.390955	−	0.920410i
$7$	2.73668	−	6.44287i	0.390955	−	0.920410i
$8$	4.88107	−	4.88107i	0.610133	−	0.610133i
$9$		0			0
$10$	8.31195	+	7.26192i	0.831195	+	0.726192i
$11$	4.69282	+	8.12820i	0.426620	+	0.738927i	0.996570	−	0.0827519i	$-0.0263709\pi$
$11$	4.69282	+	8.12820i	0.426620	+	0.738927i	−0.569950	+	0.821679i	$0.693038\pi$
$12$		0			0
$13$	−0.405222	+	0.405222i	−0.0311709	+	0.0311709i	−0.722520	−	0.691350i	$-0.757016\pi$
$13$	−0.405222	+	0.405222i	−0.0311709	+	0.0311709i	0.691350	+	0.722520i	$0.257016\pi$
$14$	−2.15427	+	15.3014i	−0.153877	+	1.09296i
$15$		0			0
$16$	−9.36489	+	16.2205i	−0.585306	+	1.01378i
$17$	−2.82961	+	10.5602i	−0.166448	+	0.621191i	0.831404	+	0.555669i	$0.187538\pi$
$17$	−2.82961	+	10.5602i	−0.166448	+	0.621191i	−0.997851	+	0.0655217i	$0.979129\pi$
$18$		0			0
$19$	−23.8500	−	13.7698i	−1.25526	−	0.724725i	−0.283111	−	0.959087i	$-0.591367\pi$
$19$	−23.8500	−	13.7698i	−1.25526	−	0.724725i	−0.972149	+	0.234362i	$0.924700\pi$
$20$	−3.91828	−	1.92317i	−0.195914	−	0.0961587i
$21$		0			0
$22$	−14.6503	−	14.6503i	−0.665921	−	0.665921i
$23$	−1.02354	−	3.81990i	−0.0445017	−	0.166083i	0.940099	−	0.340902i	$-0.110732\pi$
$23$	−1.02354	−	3.81990i	−0.0445017	−	0.166083i	−0.984601	+	0.174819i	$0.944066\pi$
$24$		0			0
$25$	−9.48058	+	23.1326i	−0.379223	+	0.925305i
$26$	0.632520	−	1.09556i	0.0243277	−	0.0421368i
$27$		0			0
$28$	−0.743235	−	6.06535i	−0.0265441	−	0.216620i
$29$		−	34.6601i		−	1.19518i	−0.801803	−	0.597588i	$-0.796126\pi$
$29$		−	34.6601i		−	1.19518i	0.801803	−	0.597588i	$-0.203874\pi$
$30$		0			0
$31$	−11.8284	−	20.4874i	−0.381561	−	0.660883i	0.609724	−	0.792613i	$-0.291280\pi$
$31$	−11.8284	−	20.4874i	−0.381561	−	0.660883i	−0.991286	+	0.131730i	$0.957947\pi$
$32$	3.55465	−	13.2661i	0.111083	−	0.414566i
$33$		0			0
$34$		−	24.1338i		−	0.709819i
$35$	−34.3751	+	6.58431i	−0.982145	+	0.188123i
$36$		0			0
$37$	25.6130	−	6.86297i	0.692242	−	0.185486i	0.104489	−	0.994526i	$-0.466679\pi$
$37$	25.6130	−	6.86297i	0.692242	−	0.185486i	0.587753	+	0.809040i	$0.300013\pi$
$38$	58.7215	+	15.7344i	1.54530	+	0.414063i
$39$		0			0
$40$	−33.8637	−	6.67007i	−0.846593	−	0.166752i
$41$	−54.6731			−1.33349			−0.666745	−	0.745286i	$-0.732313\pi$
$41$	−54.6731			−1.33349			−0.666745	+	0.745286i	$0.732313\pi$
$42$		0			0
$43$	−47.3942	+	47.3942i	−1.10219	+	1.10219i	−0.108044	+	0.994146i	$0.534459\pi$
$43$	−47.3942	+	47.3942i	−1.10219	+	1.10219i	−0.994146	+	0.108044i	$0.965541\pi$
$44$	7.09560	+	4.09664i	0.161264	+	0.0931055i
$45$		0			0
$46$	4.36491	+	7.56024i	0.0948893	+	0.164353i
$47$	16.9830	−	4.55058i	0.361340	−	0.0968208i	−0.0735811	−	0.997289i	$-0.523443\pi$
$47$	16.9830	−	4.55058i	0.361340	−	0.0968208i	0.434921	+	0.900468i	$0.356776\pi$
$48$		0			0
$49$	−34.0211	−	35.2642i	−0.694308	−	0.719678i
$50$	6.99854	−	54.7414i	0.139971	−	1.09483i
$51$		0			0
$52$	−0.129479	+	0.483221i	−0.00248997	+	0.00929271i
$53$	−14.7503	−	3.95234i	−0.278308	−	0.0745725i	0.116965	−	0.993136i	$-0.462683\pi$
$53$	−14.7503	−	3.95234i	−0.278308	−	0.0745725i	−0.395273	+	0.918564i	$0.629350\pi$
$54$		0			0
$55$	20.6770	−	42.1274i	0.375946	−	0.765952i
$56$	−18.0901	−	44.8060i	−0.323038	−	0.800108i
$57$		0			0
$58$	19.8026	+	73.9044i	0.341424	+	1.27421i
$59$	−90.3630	+	52.1711i	−1.53158	+	0.884256i	−0.532288	+	0.846564i	$0.678667\pi$
$59$	−90.3630	+	52.1711i	−1.53158	+	0.884256i	−0.999289	+	0.0376927i	$0.987999\pi$
$60$		0			0
$61$	−12.5803	+	21.7897i	−0.206235	+	0.357209i	−0.950525	−	0.310647i	$-0.899454\pi$
$61$	−12.5803	+	21.7897i	−0.206235	+	0.357209i	0.744291	+	0.667856i	$0.232788\pi$
$62$	36.9264	+	36.9264i	0.595587	+	0.595587i
$63$		0			0
$64$		−	44.6014i		−	0.696897i
$65$	2.81133	+	0.553743i	0.0432513	+	0.00851912i
$66$		0			0
$67$	0.364564	−	1.36057i	0.00544126	−	0.0203071i	−0.963152	−	0.268958i	$-0.913321\pi$
$67$	0.364564	−	1.36057i	0.00544126	−	0.0203071i	0.968593	+	0.248651i	$0.0799873\pi$
$68$	2.47014	+	9.21867i	0.0363255	+	0.135569i
$69$		0			0
$70$	69.5348	−	33.6792i	0.993354	−	0.481132i
$71$	−86.5935			−1.21963			−0.609813	−	0.792545i	$-0.708756\pi$
$71$	−86.5935			−1.21963			−0.609813	+	0.792545i	$0.708756\pi$
$72$		0			0
$73$	−84.9471	−	22.7615i	−1.16366	−	0.311802i	−0.375233	−	0.926931i	$-0.622437\pi$
$73$	−84.9471	−	22.7615i	−1.16366	−	0.311802i	−0.788427	+	0.615129i	$0.789104\pi$
$74$	−50.6924	+	29.2673i	−0.685033	+	0.395504i
$75$		0			0
$76$	−24.0409			−0.316328
$77$	65.2117	−	7.99089i	0.846905	−	0.103778i
$78$		0			0
$79$	128.353	+	74.1049i	1.62473	+	0.938036i	0.985632	+	0.168909i	$0.0540243\pi$
$79$	128.353	+	74.1049i	1.62473	+	0.938036i	0.639095	+	0.769128i	$0.279309\pi$
$80$	93.4368	−	6.29977i	1.16796	−	0.0787472i
$81$		0			0
$82$	116.577	−	31.2368i	1.42167	−	0.380936i
$83$	−35.5711	+	35.5711i	−0.428567	+	0.428567i	−0.888140	−	0.459573i	$-0.848002\pi$
$83$	−35.5711	+	35.5711i	−0.428567	+	0.428567i	0.459573	+	0.888140i	$0.348002\pi$
$84$		0			0
$85$	51.7299	−	17.6679i	0.608587	−	0.207858i
$86$	73.9787	−	128.135i	0.860217	−	1.48994i
$87$		0			0
$88$	62.5803	+	16.7683i	0.711139	+	0.190549i
$89$	−130.143	−	75.1382i	−1.46228	−	0.844250i	−0.463166	−	0.886271i	$-0.653287\pi$
$89$	−130.143	−	75.1382i	−1.46228	−	0.844250i	−0.999117	+	0.0420218i	$0.986620\pi$
$90$		0			0
$91$	1.50183	+	3.71975i	0.0165036	+	0.0408764i
$92$	−2.44111	−	2.44111i	−0.0265338	−	0.0265338i
$93$		0			0
$94$	−33.6122	+	19.4060i	−0.357577	+	0.206447i
$95$	9.26295	+	137.386i	0.0975047	+	1.44617i
$96$		0			0
$97$	74.8462	+	74.8462i	0.771610	+	0.771610i	0.978388	−	0.206778i	$-0.0662977\pi$
$97$	74.8462	+	74.8462i	0.771610	+	0.771610i	−0.206778	+	0.978388i	$0.566298\pi$
$98$	92.6896	+	55.7549i	0.945812	+	0.568928i
$99$		0			0
$100$	2.92956	+	21.6265i	0.0292956	+	0.216265i
$101$	65.3840	+	113.248i	0.647366	+	1.12127i	0.983750	+	0.179546i	$0.0574628\pi$
$101$	65.3840	+	113.248i	0.647366	+	1.12127i	−0.336384	+	0.941725i	$0.609204\pi$
$102$		0			0
$103$	9.95292	+	37.1448i	0.0966303	+	0.360629i	0.997262	−	0.0739549i	$-0.0235621\pi$
$103$	9.95292	+	37.1448i	0.0966303	+	0.360629i	−0.900631	+	0.434584i	$0.856895\pi$
$104$			3.95583i			0.0380368i
$105$		0			0
$106$	33.7097			0.318016
$107$	193.691	−	51.8993i	1.81019	−	0.485040i	0.814701	−	0.579881i	$-0.196901\pi$
$107$	193.691	−	51.8993i	1.81019	−	0.485040i	0.995492	+	0.0948408i	$0.0302342\pi$
$108$		0			0
$109$	−126.264	+	72.8985i	−1.15838	+	0.668793i	−0.950916	−	0.309449i	$-0.899856\pi$
$109$	−126.264	+	72.8985i	−1.15838	+	0.668793i	−0.207468	+	0.978242i	$0.566522\pi$
$110$	−20.0198	+	101.640i	−0.181998	+	0.924001i
$111$		0			0
$112$	78.8776	+	104.727i	0.704264	+	0.935063i
$113$	50.0612	−	50.0612i	0.443020	−	0.443020i	−0.450006	−	0.893026i	$-0.648578\pi$
$113$	50.0612	−	50.0612i	0.443020	−	0.443020i	0.893026	+	0.450006i	$0.148578\pi$
$114$		0			0
$115$	−13.0096	+	14.8907i	−0.113127	+	0.129484i
$116$	−15.1284	−	26.2032i	−0.130418	−	0.225890i
$117$		0			0
$118$	162.870	−	162.870i	1.38026	−	1.38026i
$119$	60.2945	+	47.1308i	0.506677	+	0.396058i
$120$		0			0
$121$	16.4549	−	28.5007i	0.135991	−	0.235543i
$122$	14.3752	−	53.6490i	0.117830	−	0.439746i
$123$		0			0
$124$	−17.8847	−	10.3257i	−0.144231	−	0.0832719i
$125$	122.459	−	25.0741i	0.979675	−	0.200593i
$126$		0			0
$127$	−120.362	−	120.362i	−0.947736	−	0.947736i	0.0509644	−	0.998700i	$-0.483771\pi$
$127$	−120.362	−	120.362i	−0.947736	−	0.947736i	−0.998700	+	0.0509644i	$0.983771\pi$
$128$	39.7010	+	148.166i	0.310164	+	1.15755i
$129$		0			0
$130$	−6.31087	+	0.425497i	−0.0485451	+	0.00327305i
$131$	61.7290	−	106.918i	0.471214	−	0.816166i	−0.528244	−	0.849093i	$-0.677149\pi$
$131$	61.7290	−	106.918i	0.471214	−	0.816166i	0.999458	+	0.0329263i	$0.0104827\pi$
$132$		0			0
$133$	−153.987	+	115.979i	−1.15779	+	0.872019i
$134$			3.10939i			0.0232044i
$135$		0			0
$136$	37.7337	+	65.3568i	0.277454	+	0.480564i
$137$	38.7216	−	144.511i	0.282639	−	1.05482i	−0.667908	−	0.744244i	$-0.732810\pi$
$137$	38.7216	−	144.511i	0.282639	−	1.05482i	0.950547	−	0.310581i	$-0.100523\pi$
$138$		0			0
$139$		−	86.7413i		−	0.624038i	−0.950076	−	0.312019i	$-0.898995\pi$
$139$		−	86.7413i		−	0.624038i	0.950076	−	0.312019i	$-0.101005\pi$
$140$	−23.1138	+	19.9818i	−0.165099	+	0.142727i
$141$		0			0
$142$	184.640	−	49.4741i	1.30028	−	0.348409i
$143$	−5.19535	−	1.39209i	−0.0363311	−	0.00973490i
$144$		0			0
$145$	−143.914	+	96.5501i	−0.992508	+	0.665863i
$146$	194.134			1.32968
$147$		0			0
$148$	16.3680	−	16.3680i	0.110595	−	0.110595i
$149$	21.7762	+	12.5725i	0.146149	+	0.0843791i	0.571291	−	0.820747i	$-0.306443\pi$
$149$	21.7762	+	12.5725i	0.146149	+	0.0843791i	−0.425142	+	0.905126i	$0.639776\pi$
$150$		0			0
$151$	−100.832	−	174.647i	−0.667765	−	1.15660i	−0.978528	−	0.206115i	$-0.933918\pi$
$151$	−100.832	−	174.647i	−0.667765	−	1.15660i	0.310763	−	0.950487i	$-0.399415\pi$
$152$	−183.624	+	49.2020i	−1.20806	+	0.323697i
$153$		0			0
$154$	−134.483	+	54.2965i	−0.873265	+	0.352575i
$155$	−52.1171	+	106.183i	−0.336239	+	0.685054i
$156$		0			0
$157$	7.52733	−	28.0924i	0.0479448	−	0.178932i	−0.937801	−	0.347173i	$-0.887142\pi$
$157$	7.52733	−	28.0924i	0.0479448	−	0.178932i	0.985746	+	0.168240i	$0.0538084\pi$
$158$	−316.022	−	84.6778i	−2.00014	−	0.535935i
$159$		0			0
$160$	−64.9847	+	22.1950i	−0.406155	+	0.138719i
$161$	−27.4122	−	3.85934i	−0.170262	−	0.0239710i
$162$		0			0
$163$	−21.9253	−	81.8264i	−0.134511	−	0.502003i	−0.999999	−	0.00107335i	$-0.999658\pi$
$163$	−21.9253	−	81.8264i	−0.134511	−	0.502003i	0.865488	−	0.500929i	$-0.167008\pi$
$164$	−41.3332	+	23.8637i	−0.252032	+	0.145510i
$165$		0			0
$166$	55.5237	−	96.1699i	0.334480	−	0.579336i
$167$	−147.643	−	147.643i	−0.884091	−	0.884091i	0.109856	−	0.993947i	$-0.464961\pi$
$167$	−147.643	−	147.643i	−0.884091	−	0.884091i	−0.993947	+	0.109856i	$0.964961\pi$
$168$		0			0
$169$			168.672i			0.998057i
$170$	−100.207	+	67.2279i	−0.589454	+	0.395458i
$171$		0			0
$172$	−15.1437	+	56.5169i	−0.0880445	+	0.328587i
$173$	18.0662	+	67.4239i	0.104429	+	0.389733i	0.998280	−	0.0586307i	$-0.0186734\pi$
$173$	18.0662	+	67.4239i	0.104429	+	0.389733i	−0.893851	+	0.448364i	$0.852007\pi$
$174$		0			0
$175$	123.095	+	124.389i	0.703401	+	0.710794i
$176$	−175.791			−0.998812
$177$		0			0
$178$	320.428	+	85.8585i	1.80016	+	0.482351i
$179$	10.7449	−	6.20357i	0.0600273	−	0.0346568i	−0.469686	−	0.882834i	$-0.655633\pi$
$179$	10.7449	−	6.20357i	0.0600273	−	0.0346568i	0.529713	+	0.848177i	$0.322300\pi$
$180$		0			0
$181$	−163.979			−0.905964			−0.452982	−	0.891520i	$-0.649640\pi$
$181$	−163.979			−0.905964			−0.452982	+	0.891520i	$0.649640\pi$
$182$	−5.32752	−	7.07343i	−0.0292721	−	0.0388650i
$183$		0			0
$184$	−23.6412	−	13.6492i	−0.128485	−	0.0741806i
$185$	−99.8441	−	87.2310i	−0.539698	−	0.471519i
$186$		0			0
$187$	−99.1146	+	26.5577i	−0.530025	+	0.142020i
$188$	10.8530	−	10.8530i	0.0577287	−	0.0577287i
$189$		0			0
$190$	−98.2447	−	287.650i	−0.517077	−	1.51395i
$191$	−63.0093	+	109.135i	−0.329892	+	0.571389i	−0.982490	−	0.186315i	$-0.940346\pi$
$191$	−63.0093	+	109.135i	−0.329892	+	0.571389i	0.652598	+	0.757704i	$0.273679\pi$
$192$		0			0
$193$	53.1737	+	14.2479i	0.275512	+	0.0738231i	0.393929	−	0.919141i	$-0.371115\pi$
$193$	53.1737	+	14.2479i	0.275512	+	0.0738231i	−0.118418	+	0.992964i	$0.537782\pi$
$194$	−202.354	−	116.829i	−1.04306	−	0.602212i
$195$		0			0
$196$	−41.1123	−	11.8104i	−0.209757	−	0.0602571i
$197$	−62.0394	−	62.0394i	−0.314921	−	0.314921i	0.531892	−	0.846812i	$-0.321481\pi$
$197$	−62.0394	−	62.0394i	−0.314921	−	0.314921i	−0.846812	+	0.531892i	$0.821481\pi$
$198$		0			0
$199$	242.793	−	140.177i	1.22007	−	0.704405i	0.255134	−	0.966906i	$-0.417880\pi$
$199$	242.793	−	140.177i	1.22007	−	0.704405i	0.964932	+	0.262501i	$0.0845472\pi$
$200$	66.6366	+	159.187i	0.333183	+	0.795937i
$201$		0			0
$202$	−204.119	−	204.119i	−1.01049	−	1.01049i
$203$	−223.311	−	94.8538i	−1.10005	−	0.467260i
$204$		0			0
$205$	152.299	+	227.011i	0.742921	+	1.10737i
$206$	−42.4444	−	73.5159i	−0.206041	−	0.356873i
$207$		0			0
$208$	−2.77803	−	10.3677i	−0.0133559	−	0.0498449i
$209$		−	258.476i		−	1.23673i
$210$		0			0
$211$	215.254			1.02016			0.510081	−	0.860126i	$-0.329615\pi$
$211$	215.254			1.02016			0.510081	+	0.860126i	$0.329615\pi$
$212$	−12.8765	+	3.45024i	−0.0607380	+	0.0162747i
$213$		0			0
$214$	−383.347	+	221.326i	−1.79134	+	1.03423i
$215$	328.810	+	64.7650i	1.52935	+	0.301233i
$216$		0			0
$217$	−164.368	+	20.1413i	−0.757457	+	0.0928170i
$218$	227.578	−	227.578i	1.04393	−	1.04393i
$219$		0			0
$220$	−2.75582	−	40.8736i	−0.0125264	−	0.185789i
$221$	−3.13262	−	5.42586i	−0.0141747	−	0.0245514i
$222$		0			0
$223$	129.293	−	129.293i	0.579788	−	0.579788i	−0.355057	−	0.934845i	$-0.615538\pi$
$223$	129.293	−	129.293i	0.579788	−	0.579788i	0.934845	+	0.355057i	$0.115538\pi$
$224$	−75.7439	−	59.2073i	−0.338142	−	0.264318i
$225$		0			0
$226$	−78.1417	+	135.345i	−0.345760	+	0.598874i
$227$	12.3978	−	46.2690i	0.0546156	−	0.203828i	−0.933227	−	0.359289i	$-0.883019\pi$
$227$	12.3978	−	46.2690i	0.0546156	−	0.203828i	0.987842	+	0.155460i	$0.0496860\pi$
$228$		0			0
$229$	−275.307	−	158.949i	−1.20221	−	0.694099i	−0.241168	−	0.970483i	$-0.577530\pi$
$229$	−275.307	−	158.949i	−1.20221	−	0.694099i	−0.961047	+	0.276384i	$0.910864\pi$
$230$	19.2322	−	39.1837i	0.0836183	−	0.170364i
$231$		0			0
$232$	−169.178	−	169.178i	−0.729217	−	0.729217i
$233$	70.2155	+	262.048i	0.301354	+	1.12467i	0.936039	+	0.351897i	$0.114463\pi$
$233$	70.2155	+	262.048i	0.301354	+	1.12467i	−0.634685	+	0.772771i	$0.718870\pi$
$234$		0			0
$235$	−66.2029	−	57.8396i	−0.281715	−	0.246126i
$236$	−45.5433	+	78.8833i	−0.192980	+	0.334251i
$237$		0			0
$238$	−155.491	−	66.0467i	−0.653324	−	0.277507i
$239$			18.7596i			0.0784918i	0.999230	+	0.0392459i	$0.0124956\pi$
$239$			18.7596i			0.0784918i	−0.999230	+	0.0392459i	$0.987504\pi$
$240$		0			0
$241$	−39.4000	−	68.2427i	−0.163485	−	0.283165i	0.772631	−	0.634855i	$-0.218940\pi$
$241$	−39.4000	−	68.2427i	−0.163485	−	0.283165i	−0.936116	+	0.351690i	$0.885607\pi$
$242$	−18.8026	+	70.1723i	−0.0776968	+	0.289968i
$243$		0			0
$244$			21.9642i			0.0900173i
$245$	−51.6519	+	239.493i	−0.210824	+	0.977524i
$246$		0			0
$247$	15.2443	−	4.08470i	0.0617179	−	0.0165373i
$248$	−157.735	−	42.2651i	−0.636030	−	0.170424i
$249$		0			0
$250$	−246.789	+	123.430i	−0.987158	+	0.493720i
$251$	86.2825			0.343755			0.171877	−	0.985118i	$-0.445017\pi$
$251$	86.2825			0.343755			0.171877	+	0.985118i	$0.445017\pi$
$252$		0			0
$253$	26.2456	−	26.2456i	0.103738	−	0.103738i
$254$	325.412	+	187.877i	1.28115	+	0.739671i
$255$		0			0
$256$	−80.1031	−	138.743i	−0.312903	−	0.541963i
$257$	241.586	−	64.7328i	0.940024	−	0.251879i	0.243900	−	0.969800i	$-0.421573\pi$
$257$	241.586	−	64.7328i	0.940024	−	0.251879i	0.696124	+	0.717922i	$0.254906\pi$
$258$		0			0
$259$	25.8774	−	183.803i	0.0999126	−	0.709663i
$260$	2.36708	−	0.808459i	0.00910416	−	0.00310946i
$261$		0			0
$262$	−70.5362	+	263.245i	−0.269222	+	1.00475i
$263$	350.527	+	93.9235i	1.33280	+	0.357123i	0.853759	−	0.520668i	$-0.174317\pi$
$263$	350.527	+	93.9235i	1.33280	+	0.357123i	0.479043	+	0.877791i	$0.340984\pi$
$264$		0			0
$265$	24.6782	+	72.2553i	0.0931254	+	0.272661i
$266$	262.077	−	335.275i	0.985251	−	1.26043i
$267$		0			0
$268$	−0.318250	−	1.18773i	−0.00118750	−	0.00443181i
$269$	−255.637	+	147.592i	−0.950323	+	0.548669i	−0.893181	−	0.449697i	$-0.851532\pi$
$269$	−255.637	+	147.592i	−0.950323	+	0.548669i	−0.0571419	+	0.998366i	$0.518199\pi$
$270$		0			0
$271$	208.489	−	361.113i	0.769332	−	1.33252i	−0.168594	−	0.985686i	$-0.553923\pi$
$271$	208.489	−	361.113i	0.769332	−	1.33252i	0.937926	−	0.346836i	$-0.112744\pi$
$272$	−144.793	−	144.793i	−0.532328	−	0.532328i
$273$		0			0
$274$			330.258i			1.20532i
$275$	−232.517	+	31.4971i	−0.845517	+	0.114535i
$276$		0			0
$277$	−65.5326	+	244.571i	−0.236580	+	0.882927i	0.740851	+	0.671670i	$0.234423\pi$
$277$	−65.5326	+	244.571i	−0.236580	+	0.882927i	−0.977430	+	0.211258i	$0.932244\pi$
$278$	49.5586	+	184.955i	0.178268	+	0.665306i
$279$		0			0
$280$	−135.649	+	199.926i	−0.484460	+	0.714020i
$281$	−235.018			−0.836363			−0.418181	−	0.908363i	$-0.637332\pi$
$281$	−235.018			−0.836363			−0.418181	+	0.908363i	$0.637332\pi$
$282$		0			0
$283$	45.4761	+	12.1853i	0.160693	+	0.0430576i	0.338269	−	0.941050i	$-0.390159\pi$
$283$	45.4761	+	12.1853i	0.160693	+	0.0430576i	−0.177576	+	0.984107i	$0.556825\pi$
$284$	−65.4652	+	37.7963i	−0.230511	+	0.133086i
$285$		0			0
$286$	11.8732			0.0415147
$287$	−149.623	+	352.252i	−0.521335	+	1.22736i
$288$		0			0
$289$	146.769	+	84.7373i	0.507852	+	0.293209i
$290$	251.699	−	288.093i	0.867927	−	0.993425i
$291$		0			0
$292$	−74.1555	+	19.8699i	−0.253957	+	0.0680476i
$293$	12.1766	−	12.1766i	0.0415584	−	0.0415584i	−0.686022	−	0.727581i	$-0.740645\pi$
$293$	12.1766	−	12.1766i	0.0415584	−	0.0415584i	0.727581	+	0.686022i	$0.240645\pi$
$294$		0			0
$295$	468.340	+	229.871i	1.58759	+	0.779224i
$296$	91.5200	−	158.517i	0.309189	−	0.535531i
$297$		0			0
$298$	−53.6156	−	14.3663i	−0.179918	−	0.0482089i
$299$	1.96267	+	1.13315i	0.00656410	+	0.00378979i
$300$		0			0
$301$	175.652	+	435.058i	0.583560	+	1.44537i
$302$	314.783	+	314.783i	1.04233	+	1.04233i
$303$		0			0
$304$	446.704	−	257.905i	1.46942	−	0.848371i
$305$	125.518	−	8.46279i	0.411535	−	0.0277468i
$306$		0			0
$307$	−104.260	−	104.260i	−0.339609	−	0.339609i	0.516611	−	0.856220i	$-0.327193\pi$
$307$	−104.260	−	104.260i	−0.339609	−	0.339609i	−0.856220	+	0.516611i	$0.827193\pi$
$308$	45.8125	−	34.5048i	0.148742	−	0.112028i
$309$		0			0
$310$	50.4606	−	256.187i	0.162776	−	0.826410i
$311$	16.5632	+	28.6884i	0.0532580	+	0.0922455i	0.891425	−	0.453168i	$-0.149706\pi$
$311$	16.5632	+	28.6884i	0.0532580	+	0.0922455i	−0.838167	+	0.545413i	$0.816373\pi$
$312$		0			0
$313$	−112.285	−	419.052i	−0.358737	−	1.33882i	−0.875716	−	0.482826i	$-0.839610\pi$
$313$	−112.285	−	419.052i	−0.358737	−	1.33882i	0.516980	−	0.855998i	$-0.327056\pi$
$314$			64.2009i			0.204462i
$315$		0			0
$316$	129.381			0.409434
$317$	−270.012	+	72.3496i	−0.851774	+	0.228232i	−0.658190	−	0.752852i	$-0.728678\pi$
$317$	−270.012	+	72.3496i	−0.851774	+	0.228232i	−0.193584	+	0.981084i	$0.562011\pi$
$318$		0			0
$319$	281.724	−	162.654i	0.883148	−	0.509886i
$320$	−185.191	+	124.243i	−0.578723	+	0.388259i
$321$		0			0
$322$	60.6550	−	7.43252i	0.188370	−	0.0230824i
$323$	212.898	−	212.898i	0.659128	−	0.659128i
$324$		0			0
$325$	−5.53210	−	13.2156i	−0.0170219	−	0.0406633i
$326$	93.5010	+	161.948i	0.286813	+	0.496774i
$327$		0			0
$328$	−266.863	+	266.863i	−0.813607	+	0.813607i
$329$	17.1583	−	121.873i	0.0521529	−	0.370434i
$330$		0			0
$331$	−125.181	+	216.820i	−0.378191	+	0.655047i	−0.990799	−	0.135340i	$-0.956787\pi$
$331$	−125.181	+	216.820i	−0.378191	+	0.655047i	0.612608	+	0.790387i	$0.290121\pi$
$332$	−11.3659	+	42.4180i	−0.0342345	+	0.127765i
$333$		0			0
$334$	399.168	+	230.460i	1.19511	+	0.689999i
$335$	−6.66483	+	2.27632i	−0.0198950	+	0.00679499i
$336$		0			0
$337$	−7.57759	−	7.57759i	−0.0224854	−	0.0224854i	0.695775	−	0.718260i	$-0.255061\pi$
$337$	−7.57759	−	7.57759i	−0.0224854	−	0.0224854i	−0.718260	+	0.695775i	$0.755061\pi$
$338$	−96.3684	−	359.652i	−0.285114	−	1.06406i
$339$		0			0
$340$	31.3964	−	35.9361i	0.0923423	−	0.105694i
$341$	111.017	−	192.287i	0.325563	−	0.563892i
$342$		0			0
$343$	−320.308	+	122.687i	−0.933842	+	0.357687i
$344$			462.669i			1.34497i
$345$		0			0
$346$	−77.0436	−	133.443i	−0.222669	−	0.385675i
$347$	80.6472	−	300.979i	0.232413	−	0.867376i	−0.746885	−	0.664953i	$-0.768452\pi$
$347$	80.6472	−	300.979i	0.232413	−	0.867376i	0.979298	−	0.202423i	$-0.0648817\pi$
$348$		0			0
$349$		−	396.973i		−	1.13746i	−0.822525	−	0.568729i	$-0.807435\pi$
$349$		−	396.973i		−	1.13746i	0.822525	−	0.568729i	$-0.192565\pi$
$350$	−333.539	−	194.901i	−0.952968	−	0.556859i
$351$		0			0
$352$	124.511	−	33.3626i	0.353724	−	0.0947802i
$353$	127.946	+	34.2831i	0.362454	+	0.0971193i	0.435450	−	0.900213i	$-0.356589\pi$
$353$	127.946	+	34.2831i	0.362454	+	0.0971193i	−0.0729959	+	0.997332i	$0.523256\pi$
$354$		0			0
$355$	241.217	+	359.548i	0.679484	+	1.01281i
$356$	−131.185			−0.368498
$357$		0			0
$358$	−19.3666	+	19.3666i	−0.0540966	+	0.0540966i
$359$	66.6339	+	38.4711i	0.185610	+	0.107162i	0.589926	−	0.807458i	$-0.299157\pi$
$359$	66.6339	+	38.4711i	0.185610	+	0.107162i	−0.404316	+	0.914619i	$0.632490\pi$
$360$		0			0
$361$	198.713	+	344.182i	0.550453	+	0.953412i
$362$	349.647	−	93.6876i	0.965875	−	0.258805i
$363$		0			0
$364$	2.75899	+	2.15664i	0.00757963	+	0.00592483i
$365$	142.122	+	416.118i	0.389375	+	1.14005i
$366$		0			0
$367$	60.6221	−	226.245i	0.165183	−	0.616471i	−0.832834	−	0.553523i	$-0.813283\pi$
$367$	60.6221	−	226.245i	0.165183	−	0.616471i	0.998017	−	0.0629479i	$-0.0200502\pi$
$368$	71.5459	+	19.1707i	0.194418	+	0.0520942i
$369$		0			0
$370$	262.732	+	128.955i	0.710087	+	0.348526i
$371$	−65.8315	+	84.2182i	−0.177443	+	0.227003i
$372$		0			0
$373$	−98.3605	−	367.087i	−0.263701	−	0.984146i	−0.963041	−	0.269356i	$-0.913189\pi$
$373$	−98.3605	−	367.087i	−0.263701	−	0.984146i	0.699339	−	0.714790i	$-0.253478\pi$
$374$	196.165	−	113.256i	0.524505	−	0.302823i
$375$		0			0
$376$	60.6835	−	105.107i	0.161392	−	0.279539i
$377$	14.0450	+	14.0450i	0.0372547	+	0.0372547i
$378$		0			0
$379$			369.290i			0.974379i	0.873296	+	0.487190i	$0.161978\pi$
$379$			369.290i			0.974379i	−0.873296	+	0.487190i	$0.838022\pi$
$380$	66.9690	+	99.8214i	0.176234	+	0.262688i
$381$		0			0
$382$	71.9991	−	268.704i	0.188479	−	0.703415i
$383$	−187.821	−	700.956i	−0.490393	−	1.83017i	−0.554439	−	0.832224i	$-0.687067\pi$
$383$	−187.821	−	700.956i	−0.490393	−	1.83017i	0.0640459	−	0.997947i	$-0.479600\pi$
$384$		0			0
$385$	−214.835	−	248.509i	−0.558012	−	0.645477i
$386$	−121.521			−0.314820
$387$		0			0
$388$	89.2530	+	23.9153i	0.230034	+	0.0616373i
$389$	−135.464	+	78.2101i	−0.348236	+	0.201054i	−0.663908	−	0.747814i	$-0.731103\pi$
$389$	−135.464	+	78.2101i	−0.348236	+	0.201054i	0.315672	+	0.948868i	$0.397770\pi$
$390$		0			0
$391$	43.2353			0.110576
$392$	−338.186	−	6.06760i	−0.862720	−	0.0154786i
$393$		0			0
$394$	167.730	+	96.8387i	0.425710	+	0.245784i
$395$	−49.8504	−	739.370i	−0.126204	−	1.87182i
$396$		0			0
$397$	608.327	−	163.001i	1.53231	−	0.410581i	0.608538	−	0.793525i	$-0.291756\pi$
$397$	608.327	−	163.001i	1.53231	−	0.410581i	0.923772	+	0.382944i	$0.125090\pi$
$398$	−437.610	+	437.610i	−1.09952	+	1.09952i
$399$		0			0
$400$	−286.437	−	370.414i	−0.716093	−	0.926035i
$401$	−175.823	+	304.535i	−0.438463	+	0.759439i	−0.997571	−	0.0696551i	$-0.977810\pi$
$401$	−175.823	+	304.535i	−0.438463	+	0.759439i	0.559109	+	0.829094i	$0.311143\pi$
$402$		0			0
$403$	13.0950	+	3.50881i	0.0324939	+	0.00870672i
$404$	98.8613	+	57.0776i	0.244706	+	0.141281i
$405$		0			0
$406$	530.350	+	74.6673i	1.30628	+	0.183910i
$407$	175.981	+	175.981i	0.432385	+	0.432385i
$408$		0			0
$409$	63.4064	−	36.6077i	0.155028	−	0.0895055i	−0.420479	−	0.907302i	$-0.638138\pi$
$409$	63.4064	−	36.6077i	0.155028	−	0.0895055i	0.575507	+	0.817797i	$0.304805\pi$
$410$	−454.440	−	397.032i	−1.10839	−	0.968370i
$411$		0			0
$412$	23.7374	+	23.7374i	0.0576151	+	0.0576151i
$413$	88.8365	+	724.973i	0.215101	+	1.75538i
$414$		0			0
$415$	246.784	+	48.6085i	0.594660	+	0.117129i
$416$	3.93530	+	6.81614i	0.00945985	+	0.0163849i
$417$		0			0
$418$	147.677	+	551.139i	0.353295	+	1.31851i
$419$		−	19.8543i		−	0.0473849i	−0.999719	−	0.0236925i	$-0.992458\pi$
$419$		−	19.8543i		−	0.0473849i	0.999719	−	0.0236925i	$-0.00754225\pi$
$420$		0			0
$421$	−19.3162			−0.0458817			−0.0229408	−	0.999737i	$-0.507303\pi$
$421$	−19.3162			−0.0458817			−0.0229408	+	0.999737i	$0.507303\pi$
$422$	−458.978	+	122.983i	−1.08763	+	0.291429i
$423$		0			0
$424$	−91.2891	+	52.7058i	−0.215304	+	0.124306i
$425$	−217.460	−	165.574i	−0.511670	−	0.389585i
$426$		0			0
$427$	105.960	+	140.685i	0.248150	+	0.329473i
$428$	123.778	−	123.778i	0.289202	−	0.289202i
$429$		0			0
$430$	−738.111	+	49.7655i	−1.71654	+	0.115734i
$431$	129.158	+	223.709i	0.299671	+	0.519046i	0.976061	−	0.217498i	$-0.0697897\pi$
$431$	129.158	+	223.709i	0.299671	+	0.519046i	−0.676389	+	0.736544i	$0.736456\pi$
$432$		0			0
$433$	−307.927	+	307.927i	−0.711147	+	0.711147i	−0.966775	−	0.255628i	$-0.917718\pi$
$433$	−307.927	+	307.927i	−0.711147	+	0.711147i	0.255628	+	0.966775i	$0.417718\pi$
$434$	338.968	−	136.856i	0.781032	−	0.315337i
$435$		0			0
$436$	−63.6375	+	110.223i	−0.145957	+	0.252806i
$437$	−28.1878	+	105.198i	−0.0645030	+	0.240729i
$438$		0			0
$439$	−544.482	−	314.357i	−1.24028	−	0.716074i	−0.271127	−	0.962544i	$-0.587396\pi$
$439$	−544.482	−	314.357i	−1.24028	−	0.716074i	−0.969151	+	0.246469i	$0.920730\pi$
$440$	−104.701	−	306.552i	−0.237956	−	0.696710i
$441$		0			0
$442$	9.77955	+	9.77955i	0.0221257	+	0.0221257i
$443$	−173.821	−	648.708i	−0.392372	−	1.46435i	−0.826211	−	0.563361i	$-0.809508\pi$
$443$	−173.821	−	648.708i	−0.392372	−	1.46435i	0.433839	−	0.900990i	$-0.357159\pi$
$444$		0			0
$445$	50.5456	+	749.680i	0.113586	+	1.68467i
$446$	−201.816	+	349.556i	−0.452502	+	0.783757i
$447$		0			0
$448$	−287.361	−	122.060i	−0.641431	−	0.272455i
$449$			36.1975i			0.0806181i	0.999187	+	0.0403091i	$0.0128342\pi$
$449$			36.1975i			0.0806181i	−0.999187	+	0.0403091i	$0.987166\pi$
$450$		0			0
$451$	−256.571	−	444.394i	−0.568893	−	0.985352i
$452$	15.9958	−	59.6973i	0.0353890	−	0.132074i
$453$		0			0
$454$			105.741i			0.232910i
$455$	11.2614	−	16.5976i	0.0247504	−	0.0364783i
$456$		0			0
$457$	−628.547	+	168.419i	−1.37538	+	0.368531i	−0.869440	−	0.494039i	$-0.835520\pi$
$457$	−628.547	+	168.419i	−1.37538	+	0.368531i	−0.505937	+	0.862570i	$0.668853\pi$
$458$	677.840	+	181.627i	1.48000	+	0.396565i
$459$		0			0
$460$	−3.33582	+	16.9359i	−0.00725179	+	0.0368171i
$461$	224.604			0.487210			0.243605	−	0.969875i	$-0.421670\pi$
$461$	224.604			0.487210			0.243605	+	0.969875i	$0.421670\pi$
$462$		0			0
$463$	36.7738	−	36.7738i	0.0794250	−	0.0794250i	−0.666278	−	0.745703i	$-0.732114\pi$
$463$	36.7738	−	36.7738i	0.0794250	−	0.0794250i	0.745703	+	0.666278i	$0.232114\pi$
$464$	562.203	+	324.588i	1.21164	+	0.699543i
$465$		0			0
$466$	−299.435	−	518.637i	−0.642565	−	1.11296i
$467$	249.401	−	66.8267i	0.534049	−	0.143098i	0.0182915	−	0.999833i	$-0.494177\pi$
$467$	249.401	−	66.8267i	0.534049	−	0.143098i	0.515757	+	0.856735i	$0.327511\pi$
$468$		0			0
$469$	−7.76830	−	6.07230i	−0.0165635	−	0.0129473i
$470$	174.208	+	85.5049i	0.370655	+	0.181925i
$471$		0			0
$472$	−186.417	+	695.719i	−0.394952	+	1.47398i
$473$	−607.642	−	162.817i	−1.28465	−	0.344222i
$474$		0			0
$475$	544.643	−	421.167i	1.14662	−	0.886666i
$476$	66.1547	+	9.31384i	0.138980	+	0.0195669i
$477$		0			0
$478$	−10.7180	−	40.0002i	−0.0224227	−	0.0836825i
$479$	633.380	−	365.682i	1.32230	−	0.763429i	0.338202	−	0.941073i	$-0.390181\pi$
$479$	633.380	−	365.682i	1.32230	−	0.763429i	0.984095	+	0.177645i	$0.0568478\pi$
$480$		0			0
$481$	−7.59790	+	13.1599i	−0.0157960	+	0.0273596i
$482$	123.001	+	123.001i	0.255188	+	0.255188i
$483$		0			0
$484$		−	28.7290i		−	0.0593574i
$485$	102.279	−	519.266i	0.210884	−	1.07065i
$486$		0			0
$487$	194.148	−	724.570i	0.398661	−	1.48782i	−0.416792	−	0.909002i	$-0.636846\pi$
$487$	194.148	−	724.570i	0.398661	−	1.48782i	0.815454	−	0.578823i	$-0.196488\pi$
$488$	44.9518	+	167.762i	0.0921144	+	0.343776i
$489$		0			0
$490$	−26.6961	−	540.173i	−0.0544819	−	1.10239i
$491$	114.225			0.232638			0.116319	−	0.993212i	$-0.462891\pi$
$491$	114.225			0.232638			0.116319	+	0.993212i	$0.462891\pi$
$492$		0			0
$493$	366.019	+	98.0745i	0.742432	+	0.198934i
$494$	−30.1711	+	17.4193i	−0.0610751	+	0.0352618i
$495$		0			0
$496$	443.087			0.893320
$497$	−236.979	+	557.910i	−0.476819	+	1.12256i
$498$		0			0
$499$	−326.723	−	188.633i	−0.654755	−	0.378023i	0.135521	−	0.990775i	$-0.456729\pi$
$499$	−326.723	−	188.633i	−0.654755	−	0.378023i	−0.790275	+	0.612752i	$0.790063\pi$
$500$	81.6356	−	72.4072i	0.163271	−	0.144814i
$501$		0			0
$502$	−183.977	+	49.2964i	−0.366487	+	0.0982000i
$503$	29.7057	−	29.7057i	0.0590572	−	0.0590572i	−0.676961	−	0.736019i	$-0.736704\pi$
$503$	29.7057	−	29.7057i	0.0590572	−	0.0590572i	0.736019	+	0.676961i	$0.236704\pi$
$504$		0			0
$505$	288.088	−	586.951i	0.570472	−	1.16228i
$506$	−40.9674	+	70.9576i	−0.0809633	+	0.140233i
$507$		0			0
$508$	−143.531	−	38.4589i	−0.282540	−	0.0757065i
$509$	147.952	+	85.4202i	0.290672	+	0.167820i	0.638245	−	0.769833i	$-0.279661\pi$
$509$	147.952	+	85.4202i	0.290672	+	0.167820i	−0.347573	+	0.937653i	$0.612994\pi$
$510$		0			0
$511$	−379.123	+	485.012i	−0.741924	+	0.949143i
$512$	−183.792	−	183.792i	−0.358968	−	0.358968i
$513$		0			0
$514$	−478.141	+	276.055i	−0.930234	+	0.537071i
$515$	126.505	−	144.797i	0.245642	−	0.281160i
$516$		0			0
$517$	116.686	+	116.686i	0.225699	+	0.225699i
$518$	49.8361	+	406.700i	0.0962087	+	0.785135i
$519$		0			0
$520$	16.4252	−	11.0195i	0.0315869	−	0.0211913i
$521$	75.4299	+	130.648i	0.144779	+	0.250765i	0.929291	−	0.369350i	$-0.120420\pi$
$521$	75.4299	+	130.648i	0.144779	+	0.250765i	−0.784511	+	0.620114i	$0.787086\pi$
$522$		0			0
$523$	210.608	+	786.001i	0.402693	+	1.50287i	0.808271	+	0.588810i	$0.200403\pi$
$523$	210.608	+	786.001i	0.402693	+	1.50287i	−0.405579	+	0.914060i	$0.632930\pi$
$524$		−	107.774i		−	0.205676i
$525$		0			0
$526$	−801.077			−1.52296
$527$	249.821	−	66.9395i	0.474044	−	0.127020i
$528$		0			0
$529$	444.583	−	256.680i	0.840422	−	0.485218i
$530$	−93.9026	−	139.967i	−0.177175	−	0.264090i
$531$		0			0
$532$	−65.7925	+	154.893i	−0.123670	+	0.291151i
$533$	22.1547	−	22.1547i	0.0415661	−	0.0415661i
$534$		0			0
$535$	−755.043	−	659.660i	−1.41130	−	1.23301i
$536$	−4.86159	−	8.42051i	−0.00907012	−	0.0157099i
$537$		0			0
$538$	460.760	−	460.760i	0.856431	−	0.856431i
$539$	126.980	−	442.019i	0.235584	−	0.820072i
$540$		0			0
$541$	−525.462	+	910.127i	−0.971280	+	1.68231i	−0.279577	+	0.960123i	$0.590194\pi$
$541$	−525.462	+	910.127i	−0.971280	+	1.68231i	−0.691702	+	0.722183i	$0.743139\pi$
$542$	−238.235	+	889.105i	−0.439548	+	1.64042i
$543$		0			0
$544$	130.035	+	75.0758i	0.239035	+	0.138007i
$545$	654.409	+	321.198i	1.20075	+	0.589354i
$546$		0			0
$547$	332.845	+	332.845i	0.608492	+	0.608492i	0.942552	−	0.334060i	$-0.108419\pi$
$547$	332.845	+	332.845i	0.608492	+	0.608492i	−0.334060	+	0.942552i	$0.608419\pi$
$548$	−33.8024	−	126.152i	−0.0616833	−	0.230205i
$549$		0			0
$550$	477.792	−	200.006i	0.868712	−	0.363647i
$551$	−477.262	+	826.642i	−0.866174	+	1.50026i
$552$		0			0
$553$	828.711	−	624.163i	1.49857	−	1.12868i
$554$		−	558.930i		−	1.00890i
$555$		0			0
$556$	−37.8609	−	65.5769i	−0.0680951	−	0.117944i
$557$	−177.542	+	662.596i	−0.318747	+	1.18958i	0.601703	+	0.798720i	$0.294489\pi$
$557$	−177.542	+	662.596i	−0.318747	+	1.18958i	−0.920450	+	0.390860i	$0.872177\pi$
$558$		0			0
$559$		−	38.4103i		−	0.0687125i
$560$	215.118	−	619.241i	0.384140	−	1.10579i
$561$		0			0
$562$	501.120	−	134.275i	0.891672	−	0.238923i
$563$	−451.611	−	121.009i	−0.802152	−	0.214936i	−0.165623	−	0.986189i	$-0.552964\pi$
$563$	−451.611	−	121.009i	−0.802152	−	0.214936i	−0.636528	+	0.771253i	$0.719630\pi$
$564$		0			0
$565$	−347.313	−	68.4096i	−0.614714	−	0.121079i
$566$	−103.929			−0.183620
$567$		0			0
$568$	−422.669	+	422.669i	−0.744135	+	0.744135i
$569$	−492.294	−	284.226i	−0.865192	−	0.499519i	0.000555696	−	1.00000i	$-0.499823\pi$
$569$	−492.294	−	284.226i	−0.865192	−	0.499519i	−0.865747	+	0.500481i	$0.833156\pi$
$570$		0			0
$571$	377.172	+	653.280i	0.660546	+	1.14410i	0.980472	+	0.196657i	$0.0630084\pi$
$571$	377.172	+	653.280i	0.660546	+	1.14410i	−0.319927	+	0.947442i	$0.603658\pi$
$572$	−4.53534	+	1.21524i	−0.00792891	+	0.00212455i
$573$		0			0
$574$	117.781	−	836.577i	0.205193	−	1.45745i
$575$	98.0681	+	12.5377i	0.170553	+	0.0218048i
$576$		0			0
$577$	−146.947	+	548.414i	−0.254675	+	0.950458i	0.713597	+	0.700557i	$0.247065\pi$
$577$	−146.947	+	548.414i	−0.254675	+	0.950458i	−0.968271	+	0.249902i	$0.919602\pi$
$578$	−361.364	−	96.8272i	−0.625197	−	0.167521i
$579$		0			0
$580$	−66.6574	+	135.808i	−0.114927	+	0.234152i
$581$	131.833	+	326.527i	0.226907	+	0.562008i
$582$		0			0
$583$	−37.0953	−	138.441i	−0.0636282	−	0.237464i
$584$	−525.733	+	303.532i	−0.900228	+	0.519747i
$585$		0			0
$586$	−19.0067	+	32.9206i	−0.0324347	+	0.0561786i
$587$	−191.752	−	191.752i	−0.326665	−	0.326665i	0.524652	−	0.851317i	$-0.324195\pi$
$587$	−191.752	−	191.752i	−0.326665	−	0.326665i	−0.851317	+	0.524652i	$0.824195\pi$
$588$		0			0
$589$			651.497i			1.10611i
$590$	−1129.96	−	222.565i	−1.91518	−	0.377229i
$591$		0			0
$592$	−128.542	+	479.725i	−0.217132	+	0.810346i
$593$	−158.838	−	592.793i	−0.267856	−	0.999651i	−0.960479	−	0.278352i	$-0.910212\pi$
$593$	−158.838	−	592.793i	−0.267856	−	0.999651i	0.692623	−	0.721299i	$-0.256455\pi$
$594$		0			0
$595$	27.7361	−	381.640i	0.0466154	−	0.641412i
$596$	21.9506			0.0368298
$597$		0			0
$598$	−4.83233	−	1.29482i	−0.00808081	−	0.00216525i
$599$	649.805	−	375.165i	1.08482	−	0.626319i	0.152625	−	0.988284i	$-0.451227\pi$
$599$	649.805	−	375.165i	1.08482	−	0.626319i	0.932192	+	0.361965i	$0.117894\pi$
$600$		0			0
$601$	−592.685			−0.986165			−0.493083	−	0.869982i	$-0.664130\pi$
$601$	−592.685			−0.986165			−0.493083	+	0.869982i	$0.664130\pi$
$602$	−623.100	−	827.300i	−1.03505	−	1.37425i
$603$		0			0
$604$	−152.460	−	88.0227i	−0.252417	−	0.145733i
$605$	−164.176	+	11.0692i	−0.271366	+	0.0182963i
$606$		0			0
$607$	387.642	−	103.868i	0.638619	−	0.171117i	0.0750410	−	0.997180i	$-0.476091\pi$
$607$	387.642	−	103.868i	0.638619	−	0.171117i	0.563578	+	0.826063i	$0.309425\pi$
$608$	−267.450	+	267.450i	−0.439884	+	0.439884i
$609$		0			0
$610$	−262.802	+	89.7581i	−0.430823	+	0.147144i
$611$	−5.03788	+	8.72587i	−0.00824531	+	0.0142813i
$612$		0			0
$613$	−212.730	−	57.0009i	−0.347031	−	0.0929868i	0.0810932	−	0.996707i	$-0.474159\pi$
$613$	−212.730	−	57.0009i	−0.347031	−	0.0929868i	−0.428125	+	0.903720i	$0.640826\pi$
$614$	281.877	+	162.742i	0.459084	+	0.265052i
$615$		0			0
$616$	279.299	−	357.307i	0.453407	−	0.580043i
$617$	−338.020	−	338.020i	−0.547844	−	0.547844i	0.377973	−	0.925817i	$-0.376621\pi$
$617$	−338.020	−	338.020i	−0.547844	−	0.547844i	−0.925817	+	0.377973i	$0.876621\pi$
$618$		0			0
$619$	266.400	−	153.806i	0.430371	−	0.248475i	−0.269134	−	0.963103i	$-0.586737\pi$
$619$	266.400	−	153.806i	0.430371	−	0.248475i	0.699505	+	0.714628i	$0.253404\pi$
$620$	6.94612	+	103.023i	0.0112034	+	0.166167i
$621$		0			0
$622$	−51.7078	−	51.7078i	−0.0831316	−	0.0831316i
$623$	−840.266	+	632.866i	−1.34874	+	1.01584i
$624$		0			0
$625$	−445.237	−	438.622i	−0.712379	−	0.701795i
$626$	478.840	+	829.375i	0.764920	+	1.32488i
$627$		0			0
$628$	−6.57106	−	24.5235i	−0.0104635	−	0.0390502i
$629$			289.899i			0.460888i
$630$		0			0
$631$	−219.545			−0.347931			−0.173966	−	0.984752i	$-0.555658\pi$
$631$	−219.545			−0.347931			−0.173966	+	0.984752i	$0.555658\pi$
$632$	988.213	−	264.791i	1.56363	−	0.418973i
$633$		0			0
$634$	534.401	−	308.536i	0.842903	−	0.486650i
$635$	−164.477	+	835.047i	−0.259020	+	1.31503i
$636$		0			0
$637$	28.0759	+	0.503726i	0.0440752	+	0.000790779i
$638$	−507.779	+	507.779i	−0.795892	+	0.795892i
$639$		0			0
$640$	504.615	−	577.580i	0.788462	−	0.902469i
$641$	−417.537	−	723.194i	−0.651383	−	1.12823i	−0.982787	−	0.184740i	$-0.940856\pi$
$641$	−417.537	−	723.194i	−0.651383	−	1.12823i	0.331404	−	0.943489i	$-0.392478\pi$
$642$		0			0
$643$	−649.916	+	649.916i	−1.01076	+	1.01076i	−0.0108149	+	0.999942i	$0.503443\pi$
$643$	−649.916	+	649.916i	−1.01076	+	1.01076i	−0.999942	+	0.0108149i	$0.996557\pi$
$644$	−22.4083	+	9.04721i	−0.0347955	+	0.0140485i
$645$		0			0
$646$	−332.318	+	575.591i	−0.514424	+	0.891008i
$647$	−95.3328	+	355.787i	−0.147346	+	0.549902i	0.852294	+	0.523063i	$0.175211\pi$
$647$	−95.3328	+	355.787i	−0.147346	+	0.549902i	−0.999640	+	0.0268391i	$0.991456\pi$
$648$		0			0
$649$	−848.115	−	489.659i	−1.30680	−	0.754483i
$650$	19.3464	+	25.0184i	0.0297637	+	0.0384898i
$651$		0			0
$652$	−52.2913	−	52.2913i	−0.0802014	−	0.0802014i
$653$	−117.038	−	436.792i	−0.179232	−	0.668901i	−0.995792	−	0.0916414i	$-0.970789\pi$
$653$	−117.038	−	436.792i	−0.179232	−	0.668901i	0.816561	−	0.577260i	$-0.195878\pi$
$654$		0			0
$655$	−615.892	+	41.5252i	−0.940293	+	0.0633972i
$656$	512.008	−	886.823i	0.780499	−	1.35186i
$657$		0			0
$658$	33.0444	+	269.668i	0.0502195	+	0.409829i
$659$		−	395.881i		−	0.600730i	−0.953824	−	0.300365i	$-0.902892\pi$
$659$		−	395.881i		−	0.600730i	0.953824	−	0.300365i	$-0.0971085\pi$
$660$		0			0
$661$	−41.2693	−	71.4804i	−0.0624346	−	0.108140i	0.833119	−	0.553094i	$-0.186553\pi$
$661$	−41.2693	−	71.4804i	−0.0624346	−	0.108140i	−0.895553	+	0.444955i	$0.853220\pi$
$662$	143.042	−	533.838i	0.216075	−	0.806403i
$663$		0			0
$664$			347.250i			0.522966i
$665$	910.509	+	316.302i	1.36919	+	0.475642i
$666$		0			0
$667$	−132.398	+	35.4760i	−0.198498	+	0.0531874i
$668$	−176.062	−	47.1758i	−0.263567	−	0.0706225i
$669$		0			0
$670$	12.9106	−	8.66158i	0.0192696	−	0.0129277i
$671$	−236.148			−0.351935
$672$		0			0
$673$	923.540	−	923.540i	1.37227	−	1.37227i	0.515207	−	0.857066i	$-0.327715\pi$
$673$	923.540	−	923.540i	1.37227	−	1.37227i	0.857066	−	0.515207i	$-0.172285\pi$
$674$	20.4868	+	11.8280i	0.0303958	+	0.0175490i
$675$		0			0
$676$	73.6218	+	127.517i	0.108908	+	0.188634i
$677$	242.099	−	64.8703i	0.357606	−	0.0958203i	−0.0755429	−	0.997143i	$-0.524069\pi$
$677$	242.099	−	64.8703i	0.357606	−	0.0958203i	0.433149	+	0.901322i	$0.357402\pi$
$678$		0			0
$679$	687.055	−	277.394i	1.01186	−	0.408533i
$680$	166.259	−	338.735i	0.244498	−	0.498140i
$681$		0			0
$682$	−126.856	+	473.434i	−0.186006	+	0.694185i
$683$	1283.82	+	344.000i	1.87968	+	0.503660i	0.999583	+	0.0288723i	$0.00919162\pi$
$683$	1283.82	+	344.000i	1.87968	+	0.503660i	0.880101	+	0.474787i	$0.157475\pi$
$684$		0			0
$685$	−707.894	+	241.776i	−1.03342	+	0.352957i
$686$	612.884	−	444.603i	0.893417	−	0.648110i
$687$		0			0
$688$	−324.914	−	1212.60i	−0.472259	−	1.76250i
$689$	7.57873	−	4.37558i	0.0109996	−	0.00635063i
$690$		0			0
$691$	161.274	−	279.335i	0.233392	−	0.404247i	−0.725412	−	0.688315i	$-0.758351\pi$
$691$	161.274	−	279.335i	0.233392	−	0.404247i	0.958804	+	0.284068i	$0.0916840\pi$
$692$	43.0873	+	43.0873i	0.0622649	+	0.0622649i
$693$		0			0
$694$			687.843i			0.991129i
$695$	−360.162	+	241.629i	−0.518219	+	0.347667i
$696$		0			0
$697$	154.703	−	577.361i	0.221956	−	0.828352i
$698$	226.805	+	846.449i	0.324936	+	1.21268i
$699$		0			0
$700$	147.354	+	40.3101i	0.210506	+	0.0575859i
$701$	−993.695			−1.41754			−0.708769	−	0.705440i	$-0.750749\pi$
$701$	−993.695			−1.41754			−0.708769	+	0.705440i	$0.750749\pi$
$702$		0			0
$703$	−705.369	−	189.003i	−1.00337	−	0.268852i
$704$	362.529	−	209.306i	0.514956	−	0.297310i
$705$		0			0
$706$	−292.402			−0.414167
$707$	908.580	−	111.335i	1.28512	−	0.157476i
$708$		0			0
$709$	594.099	+	343.003i	0.837940	+	0.483785i	0.856563	−	0.516042i	$-0.172595\pi$
$709$	594.099	+	343.003i	0.837940	+	0.483785i	−0.0186238	+	0.999827i	$0.505928\pi$
$710$	−719.761	−	628.835i	−1.01375	−	0.885683i
$711$		0			0
$712$	−1001.99	+	268.483i	−1.40729	+	0.377083i
$713$	−66.1530	+	66.1530i	−0.0927811	+	0.0927811i
$714$		0			0
$715$	8.69215	+	25.4497i	0.0121568	+	0.0355940i
$716$	5.41547	−	9.37986i	0.00756350	−	0.0131004i
$717$		0			0
$718$	−164.061	−	43.9599i	−0.228497	−	0.0612255i
$719$	−258.622	−	149.315i	−0.359696	−	0.207671i	0.309251	−	0.950980i	$-0.399922\pi$
$719$	−258.622	−	149.315i	−0.359696	−	0.207671i	−0.668948	+	0.743310i	$0.733255\pi$
$720$		0			0
$721$	266.557	+	37.5282i	0.369705	+	0.0520503i
$722$	−620.353	−	620.353i	−0.859214	−	0.859214i
$723$		0			0
$724$	−123.969	+	71.5738i	−0.171228	+	0.0988588i
$725$	801.779	+	328.598i	1.10590	+	0.453239i
$726$		0			0
$727$	427.959	+	427.959i	0.588665	+	0.588665i	0.937270	−	0.348605i	$-0.113344\pi$
$727$	427.959	+	427.959i	0.588665	+	0.588665i	−0.348605	+	0.937270i	$0.613344\pi$
$728$	25.4869	+	10.8259i	0.0350094	+	0.0148707i
$729$		0			0
$730$	−540.784	−	806.072i	−0.740800	−	1.10421i
$731$	−366.387	−	634.601i	−0.501214	−	0.868127i
$732$		0			0
$733$	112.025	+	418.082i	0.152830	+	0.570370i	0.999281	+	0.0379039i	$0.0120681\pi$
$733$	112.025	+	418.082i	0.152830	+	0.570370i	−0.846451	+	0.532466i	$0.821265\pi$
$734$			517.048i			0.704426i
$735$		0			0
$736$	−54.3136			−0.0737956
$737$	12.7698	−	3.42167i	0.0173268	−	0.00464270i
$738$		0			0
$739$	−160.126	+	92.4489i	−0.216680	+	0.125100i	−0.604412	−	0.796672i	$-0.706592\pi$
$739$	−160.126	+	92.4489i	−0.216680	+	0.125100i	0.387732	+	0.921772i	$0.373259\pi$
$740$	−113.557	−	22.3672i	−0.153456	−	0.0302259i
$741$		0			0
$742$	92.2528	−	217.187i	0.124330	−	0.292705i
$743$	576.263	−	576.263i	0.775589	−	0.775589i	−0.203488	−	0.979077i	$-0.565228\pi$
$743$	576.263	−	576.263i	0.775589	−	0.775589i	0.979077	+	0.203488i	$0.0652278\pi$
$744$		0			0
$745$	−8.45753	−	125.440i	−0.0113524	−	0.168376i
$746$	419.461	+	726.527i	0.562280	+	0.973897i
$747$		0			0
$748$	−63.3393	+	63.3393i	−0.0846782	+	0.0846782i
$749$	195.690	−	1389.96i	0.261269	−	1.85575i
$750$		0			0
$751$	710.061	−	1229.86i	0.945487	−	1.63763i	0.190715	−	0.981645i	$-0.438919\pi$
$751$	710.061	−	1229.86i	0.945487	−	1.63763i	0.754772	−	0.655987i	$-0.227747\pi$
$752$	−85.2314	+	318.088i	−0.113340	+	0.422989i
$753$		0			0
$754$	−37.9721	−	21.9232i	−0.0503609	−	0.0290759i
$755$	−444.278	+	905.172i	−0.588447	+	1.19890i
$756$		0			0
$757$	−316.057	−	316.057i	−0.417512	−	0.417512i	0.466833	−	0.884345i	$-0.345395\pi$
$757$	−316.057	−	316.057i	−0.417512	−	0.417512i	−0.884345	+	0.466833i	$0.845395\pi$
$758$	−210.989	−	787.422i	−0.278350	−	1.03882i
$759$		0			0
$760$	715.803	+	625.377i	0.941846	+	0.822864i
$761$	−393.410	+	681.407i	−0.516965	+	0.895409i	0.482841	+	0.875708i	$0.339605\pi$
$761$	−393.410	+	681.407i	−0.516965	+	0.895409i	−0.999806	+	0.0197013i	$0.993728\pi$
$762$		0			0
$763$	124.131	+	1013.00i	0.162688	+	1.32766i
$764$			110.009i			0.143991i
$765$		0			0
$766$	800.964	+	1387.31i	1.04565	+	1.81111i
$767$	15.4762	−	57.7579i	0.0201776	−	0.0753037i
$768$		0			0
$769$			1512.03i			1.96622i	0.183008	+	0.983111i	$0.441417\pi$
$769$			1512.03i			1.96622i	−0.183008	+	0.983111i	$0.558583\pi$
$770$	600.066	+	407.142i	0.779306	+	0.528756i
$771$		0			0
$772$	46.4186	−	12.4378i	0.0601277	−	0.0161112i
$773$	228.469	+	61.2182i	0.295562	+	0.0791956i	0.403553	−	0.914956i	$-0.367775\pi$
$773$	228.469	+	61.2182i	0.295562	+	0.0791956i	−0.107991	+	0.994152i	$0.534442\pi$
$774$		0			0
$775$	586.067	−	79.3895i	0.756216	−	0.102438i
$776$	730.659			0.941570
$777$		0			0
$778$	244.160	−	244.160i	0.313830	−	0.313830i
$779$	1303.95	+	752.836i	1.67388	+	0.966414i
$780$		0			0
$781$	−406.367	−	703.849i	−0.520317	−	0.901215i
$782$	−92.1889	+	24.7019i	−0.117889	+	0.0315882i
$783$		0			0
$784$	890.606	−	221.593i	1.13598	−	0.282644i
$785$	−137.612	+	47.0003i	−0.175302	+	0.0598730i
$786$		0			0
$787$	−154.380	+	576.154i	−0.196163	+	0.732090i	0.795800	+	0.605560i	$0.207051\pi$
$787$	−154.380	+	576.154i	−0.196163	+	0.732090i	−0.991963	+	0.126530i	$0.959616\pi$
$788$	−73.9811	−	19.8232i	−0.0938847	−	0.0251563i
$789$		0			0
$790$	528.724	+	1548.05i	0.669271	+	1.95955i
$791$	−185.536	−	459.540i	−0.234559	−	0.580961i
$792$		0			0
$793$	−3.73186	−	13.9275i	−0.00470600	−	0.0175630i
$794$	−1203.98	+	695.120i	−1.51635	+	0.875466i
$795$		0			0
$796$	122.369	−	211.949i	0.153729	−	0.266267i
$797$	−650.745	−	650.745i	−0.816493	−	0.816493i	0.169105	−	0.985598i	$-0.445912\pi$
$797$	−650.745	−	650.745i	−0.816493	−	0.816493i	−0.985598	+	0.169105i	$0.945912\pi$
$798$		0			0
$799$			192.221i			0.240577i
$800$	273.180	+	207.999i	0.341475	+	0.259999i
$801$		0			0
$802$	200.909	−	749.803i	0.250510	−	0.934916i
$803$	−213.631	−	797.283i	−0.266041	−	0.992880i
$804$		0			0
$805$	60.3357	+	124.570i	0.0749512	+	0.154746i
$806$	−29.9268			−0.0371300
$807$		0			0
$808$	871.917	+	233.629i	1.07910	+	0.289145i
$809$	−1022.42	+	590.294i	−1.26381	+	0.729659i	−0.973809	−	0.227368i	$-0.926988\pi$
$809$	−1022.42	+	590.294i	−1.26381	+	0.729659i	−0.289998	+	0.957027i	$0.593655\pi$
$810$		0			0
$811$	919.216			1.13344			0.566718	−	0.823912i	$-0.308213\pi$
$811$	919.216			1.13344			0.566718	+	0.823912i	$0.308213\pi$
$812$	−210.226	+	25.7606i	−0.258899	+	0.0317249i
$813$		0			0
$814$	−475.781	−	274.692i	−0.584497	−	0.337460i
$815$	−278.679	+	318.975i	−0.341938	+	0.391380i
$816$		0			0
$817$	1782.96	−	477.742i	2.18232	−	0.584751i
$818$	−114.284	+	114.284i	−0.139711	+	0.139711i
$819$		0			0
$820$	214.224	+	105.146i	0.261249	+	0.128227i
$821$	−390.979	+	677.195i	−0.476222	+	0.824842i	−0.999629	−	0.0272416i	$-0.991328\pi$
$821$	−390.979	+	677.195i	−0.476222	+	0.824842i	0.523406	+	0.852083i	$0.324661\pi$
$822$		0			0
$823$	343.971	+	92.1667i	0.417947	+	0.111989i	0.461663	−	0.887055i	$-0.347253\pi$
$823$	343.971	+	92.1667i	0.417947	+	0.111989i	−0.0437157	+	0.999044i	$0.513920\pi$
$824$	229.887	+	132.725i	0.278989	+	0.161074i
$825$		0			0
$826$	−603.627	−	1495.08i	−0.730783	−	1.81002i
$827$	953.358	+	953.358i	1.15279	+	1.15279i	0.985991	+	0.166800i	$0.0533435\pi$
$827$	953.358	+	953.358i	1.15279	+	1.15279i	0.166800	+	0.985991i	$0.446656\pi$
$828$		0			0
$829$	−230.809	+	133.258i	−0.278419	+	0.160745i	−0.632708	−	0.774391i	$-0.718056\pi$
$829$	−230.809	+	133.258i	−0.278419	+	0.160745i	0.354288	+	0.935136i	$0.384723\pi$
$830$	−553.979	+	37.3509i	−0.667445	+	0.0450010i
$831$		0			0
$832$	18.0735	+	18.0735i	0.0217229	+	0.0217229i
$833$	468.665	−	259.487i	0.562623	−	0.311509i
$834$		0			0
$835$	−201.757	+	1024.31i	−0.241625	+	1.22672i
$836$	−112.820	−	195.410i	−0.134952	−	0.233743i
$837$		0			0
$838$	11.3435	+	42.3345i	0.0135364	+	0.0505185i
$839$			709.681i			0.845866i	0.906161	+	0.422933i	$0.138999\pi$
$839$			709.681i			0.845866i	−0.906161	+	0.422933i	$0.861001\pi$
$840$		0			0
$841$	−360.323			−0.428446
$842$	41.1871	−	11.0361i	0.0489158	−	0.0131070i
$843$		0			0
$844$	162.734	−	93.9543i	0.192812	−	0.111320i
$845$	700.349	−	469.856i	0.828815	−	0.556042i
$846$		0			0
$847$	−138.595	−	184.014i	−0.163630	−	0.217254i
$848$	202.244	−	202.244i	0.238496	−	0.238496i
$849$		0			0
$850$	558.279	+	228.803i	0.656799	+	0.269180i
$851$	−52.4318	−	90.8145i	−0.0616119	−	0.106715i
$852$		0			0
$853$	−2.10021	+	2.10021i	−0.00246214	+	0.00246214i	−0.708337	−	0.705875i	$-0.750554\pi$
$853$	−2.10021	+	2.10021i	−0.00246214	+	0.00246214i	0.705875	+	0.708337i	$0.250554\pi$
$854$	−306.313	−	239.438i	−0.358680	−	0.280372i
$855$		0			0
$856$	692.094	−	1198.74i	0.808521	−	1.40040i
$857$	−9.61382	+	35.8793i	−0.0112180	+	0.0418661i	−0.971308	−	0.237825i	$-0.923565\pi$
$857$	−9.61382	+	35.8793i	−0.0112180	+	0.0418661i	0.960090	+	0.279691i	$0.0902321\pi$
$858$		0			0
$859$	83.8106	+	48.3881i	0.0975677	+	0.0563307i	0.547990	−	0.836485i	$-0.315393\pi$
$859$	83.8106	+	48.3881i	0.0975677	+	0.0563307i	−0.450422	+	0.892816i	$0.648727\pi$
$860$	276.851	−	94.5563i	0.321920	−	0.109949i
$861$		0			0
$862$	−403.212	−	403.212i	−0.467764	−	0.467764i
$863$	33.9627	+	126.751i	0.0393543	+	0.146872i	0.982807	−	0.184634i	$-0.0591099\pi$
$863$	33.9627	+	126.751i	0.0393543	+	0.146872i	−0.943453	+	0.331506i	$0.892443\pi$
$864$		0			0
$865$	229.628	−	262.831i	0.265466	−	0.303851i
$866$	480.650	−	832.510i	0.555023	−	0.961328i
$867$		0			0
$868$	−115.472	+	86.9703i	−0.133032	+	0.100196i
$869$			1391.04i			1.60074i
$870$		0			0
$871$	0.403604	+	0.699063i	0.000463380	+	0.000802598i
$872$	−260.480	+	972.125i	−0.298716	+	1.11482i
$873$		0			0
$874$		−	240.415i		−	0.275074i
$875$	173.584	−	857.609i	0.198381	−	0.980125i
$876$		0			0
$877$	−636.168	+	170.461i	−0.725391	+	0.194368i	−0.602576	−	0.798062i	$-0.705859\pi$
$877$	−636.168	+	170.461i	−0.725391	+	0.194368i	−0.122815	+	0.992430i	$0.539192\pi$
$878$	1340.58	+	359.207i	1.52686	+	0.409120i
$879$		0			0
$880$	489.688	+	729.909i	0.556463	+	0.829442i
$881$	1005.81			1.14167			0.570834	−	0.821066i	$-0.306620\pi$
$881$	1005.81			1.14167			0.570834	+	0.821066i	$0.306620\pi$
$882$		0			0
$883$	571.004	−	571.004i	0.646664	−	0.646664i	−0.305522	−	0.952185i	$-0.598831\pi$
$883$	571.004	−	571.004i	0.646664	−	0.646664i	0.952185	+	0.305522i	$0.0988308\pi$
$884$	−4.73656	−	2.73465i	−0.00535810	−	0.00309350i
$885$		0			0
$886$	741.262	+	1283.90i	0.836639	+	1.44910i
$887$	−708.127	+	189.742i	−0.798339	+	0.213914i	−0.634855	−	0.772632i	$-0.718940\pi$
$887$	−708.127	+	189.742i	−0.798339	+	0.213914i	−0.163484	+	0.986546i	$0.552273\pi$
$888$		0			0
$889$	−1104.87	+	446.085i	−1.24283	+	0.501783i
$890$	−536.097	−	1569.63i	−0.602356	−	1.76363i
$891$		0			0
$892$	41.3123	−	154.180i	0.0463143	−	0.172847i
$893$	−467.704	−	125.321i	−0.523745	−	0.140337i
$894$		0			0
$895$	−55.6893	−	27.3335i	−0.0622227	−	0.0305402i
$896$	1063.27	+	149.696i	1.18668	+	0.167071i
$897$		0			0
$898$	−20.6810	−	77.1826i	−0.0230301	−	0.0859494i
$899$	−710.095	+	409.973i	−0.789872	+	0.456033i
$900$		0			0
$901$	83.4754	−	144.584i	0.0926475	−	0.160470i
$902$	800.975	+	800.975i	0.887999	+	0.887999i
$903$		0			0
$904$		−	488.705i		−	0.540602i
$905$	456.785	+	680.866i	0.504735	+	0.752338i
$906$		0			0
$907$	63.8934	−	238.454i	0.0704448	−	0.262904i	−0.921717	−	0.387863i	$-0.873213\pi$
$907$	63.8934	−	238.454i	0.0704448	−	0.262904i	0.992162	+	0.124959i	$0.0398800\pi$
$908$	−10.8227	−	40.3910i	−0.0119193	−	0.0444835i
$909$		0			0
$910$	−14.5294	+	41.8245i	−0.0159664	+	0.0459610i
$911$	322.782			0.354316			0.177158	−	0.984182i	$-0.443310\pi$
$911$	322.782			0.354316			0.177158	+	0.984182i	$0.443310\pi$
$912$		0			0
$913$	−456.057	−	122.200i	−0.499515	−	0.133845i
$914$	1244.00	−	718.225i	1.36105	−	0.785804i
$915$		0			0
$916$	−277.512			−0.302960
$917$	−519.924	−	690.312i	−0.566984	−	0.752794i
$918$		0			0
$919$	−355.096	−	205.015i	−0.386394	−	0.223084i	0.294203	−	0.955743i	$-0.404946\pi$
$919$	−355.096	−	205.015i	−0.386394	−	0.223084i	−0.680596	+	0.732659i	$0.738279\pi$
$920$	9.18186	+	136.183i	0.00998028	+	0.148025i
$921$		0			0
$922$	−478.914	+	128.325i	−0.519429	+	0.139181i
$923$	35.0895	−	35.0895i	0.0380168	−	0.0380168i
$924$		0			0
$925$	−84.0672	+	657.560i	−0.0908835	+	0.710876i
$926$	−57.4010	+	99.4215i	−0.0619881	+	0.107367i
$927$		0			0
$928$	−459.805	−	123.204i	−0.495480	−	0.132763i
$929$	−392.860	−	226.818i	−0.422884	−	0.244152i	0.273426	−	0.961893i	$-0.411843\pi$
$929$	−392.860	−	226.818i	−0.422884	−	0.244152i	−0.696311	+	0.717741i	$0.745176\pi$
$930$		0			0
$931$	325.822	+	1309.51i	0.349970	+	1.40657i
$932$	167.462	+	167.462i	0.179680	+	0.179680i
$933$		0			0
$934$	−493.607	+	284.984i	−0.528487	+	0.305122i
$935$	386.367	+	337.558i	0.413227	+	0.361025i
$936$		0			0
$937$	−699.175	−	699.175i	−0.746184	−	0.746184i	0.227576	−	0.973760i	$-0.426920\pi$
$937$	−699.175	−	699.175i	−0.746184	−	0.746184i	−0.973760	+	0.227576i	$0.926920\pi$
$938$	20.0334	+	8.50941i	0.0213575	+	0.00907186i
$939$		0			0
$940$	−75.2956	−	14.8308i	−0.0801017	−	0.0157775i
$941$	−401.325	−	695.115i	−0.426488	−	0.738698i	0.570070	−	0.821596i	$-0.306916\pi$
$941$	−401.325	−	695.115i	−0.426488	−	0.738698i	−0.996558	+	0.0828975i	$0.973583\pi$
$942$		0			0
$943$	55.9601	+	208.846i	0.0593426	+	0.221470i
$944$		−	1954.31i		−	2.07024i
$945$		0			0
$946$	1388.67			1.46794
$947$	110.716	−	29.6662i	0.116912	−	0.0313265i	−0.199889	−	0.979819i	$-0.564058\pi$
$947$	110.716	−	29.6662i	0.116912	−	0.0313265i	0.316801	+	0.948492i	$0.397391\pi$
$948$		0			0
$949$	43.6459	−	25.1990i	0.0459914	−	0.0265532i
$950$	−920.692	+	1209.21i	−0.969149	+	1.27285i
$951$		0			0
$952$	524.350	−	64.2527i	0.550788	−	0.0674923i
$953$	−45.8367	+	45.8367i	−0.0480973	+	0.0480973i	−0.730746	−	0.682649i	$-0.760828\pi$
$953$	−45.8367	+	45.8367i	−0.0480973	+	0.0480973i	0.682649	+	0.730746i	$0.260828\pi$
$954$		0			0
$955$	628.666	−	42.3864i	0.658289	−	0.0443837i
$956$	8.18817	+	14.1823i	0.00856503	+	0.0148351i
$957$		0			0
$958$	−1141.60	+	1141.60i	−1.19165	+	1.19165i
$959$	−825.097	−	644.959i	−0.860372	−	0.672533i
$960$		0			0
$961$	200.678	−	347.585i	0.208822	−	0.361691i
$962$	8.68193	−	32.4014i	0.00902487	−	0.0336813i
$963$		0			0
$964$	−59.5732	−	34.3946i	−0.0617979	−	0.0356790i
$965$	−88.9629	−	260.474i	−0.0921896	−	0.269921i
$966$		0			0
$967$	−464.416	−	464.416i	−0.480265	−	0.480265i	0.424951	−	0.905216i	$-0.360291\pi$
$967$	−464.416	−	464.416i	−0.480265	−	0.480265i	−0.905216	+	0.424951i	$0.860291\pi$
$968$	−58.7965	−	219.432i	−0.0607402	−	0.226686i
$969$		0			0
$970$	78.5911	+	1165.64i	0.0810218	+	1.20170i
$971$	515.699	−	893.217i	0.531101	−	0.919894i	−0.468240	−	0.883601i	$-0.655112\pi$
$971$	515.699	−	893.217i	0.531101	−	0.919894i	0.999341	−	0.0362930i	$-0.0115550\pi$
$972$		0			0
$973$	−558.863	−	237.384i	−0.574371	−	0.243971i
$974$			1655.90i			1.70010i
$975$		0			0
$976$	−235.626	−	408.117i	−0.241421	−	0.418153i
$977$	36.2844	−	135.415i	0.0371386	−	0.138603i	−0.944867	−	0.327454i	$-0.893809\pi$
$977$	36.2844	−	135.415i	0.0371386	−	0.138603i	0.982006	+	0.188850i	$0.0604761\pi$
$978$		0			0
$979$		−	1410.44i		−	1.44069i
$980$	65.4849	+	203.603i	0.0668214	+	0.207759i
$981$		0			0
$982$	−243.558	+	65.2611i	−0.248022	+	0.0664574i
$983$	456.919	+	122.431i	0.464821	+	0.124549i	0.483626	−	0.875275i	$-0.339319\pi$
$983$	456.919	+	122.431i	0.464821	+	0.124549i	−0.0188048	+	0.999823i	$0.505986\pi$
$984$		0			0
$985$	−84.7780	+	430.415i	−0.0860690	+	0.436970i
$986$	−836.482			−0.848359
$987$		0			0
$988$	9.74190	−	9.74190i	0.00986023	−	0.00986023i
$989$	229.551	+	132.531i	0.232104	+	0.134005i
$990$		0			0
$991$	−423.672	−	733.822i	−0.427520	−	0.740486i	0.569132	−	0.822246i	$-0.307279\pi$
$991$	−423.672	−	733.822i	−0.427520	−	0.740486i	−0.996652	+	0.0817597i	$0.973946\pi$
$992$	−313.834	+	84.0915i	−0.316365	+	0.0847697i
$993$		0			0
$994$	186.546	−	1325.00i	0.187672	−	1.33300i
$995$	−1258.36	−	617.632i	−1.26469	−	0.620736i
$996$		0			0
$997$	−62.9660	+	234.992i	−0.0631554	+	0.235699i	−0.990287	−	0.139036i	$-0.955600\pi$
$997$	−62.9660	+	234.992i	−0.0631554	+	0.235699i	0.927132	+	0.374735i	$0.122266\pi$
$998$	804.431	+	215.547i	0.806043	+	0.215979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.5		64
3.2	odd	2		105.3.v.a.37.12	✓	64
5.3	odd	4	inner	315.3.ca.b.163.12		64
7.4	even	3	inner	315.3.ca.b.172.12		64
15.8	even	4		105.3.v.a.58.5	yes	64
21.11	odd	6		105.3.v.a.67.5	yes	64
35.18	odd	12	inner	315.3.ca.b.298.5		64
105.53	even	12		105.3.v.a.88.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.12	✓	64	3.2	odd	2
105.3.v.a.58.5	yes	64	15.8	even	4
105.3.v.a.67.5	yes	64	21.11	odd	6
105.3.v.a.88.12	yes	64	105.53	even	12
315.3.ca.b.37.5		64	1.1	even	1	trivial
315.3.ca.b.163.12		64	5.3	odd	4	inner
315.3.ca.b.172.12		64	7.4	even	3	inner
315.3.ca.b.298.5		64	35.18	odd	12	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +O(q^{10})\)	\(q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +(8.31195 + 7.26192i) q^{10} +(4.69282 + 8.12820i) q^{11} +(-0.405222 + 0.405222i) q^{13} +(-2.15427 + 15.3014i) q^{14} +(-9.36489 + 16.2205i) q^{16} +(-2.82961 + 10.5602i) q^{17} +(-23.8500 - 13.7698i) q^{19} +(-3.91828 - 1.92317i) q^{20} +(-14.6503 - 14.6503i) q^{22} +(-1.02354 - 3.81990i) q^{23} +(-9.48058 + 23.1326i) q^{25} +(0.632520 - 1.09556i) q^{26} +(-0.743235 - 6.06535i) q^{28} -34.6601i q^{29} +(-11.8284 - 20.4874i) q^{31} +(3.55465 - 13.2661i) q^{32} -24.1338i q^{34} +(-34.3751 + 6.58431i) q^{35} +(25.6130 - 6.86297i) q^{37} +(58.7215 + 15.7344i) q^{38} +(-33.8637 - 6.67007i) q^{40} -54.6731 q^{41} +(-47.3942 + 47.3942i) q^{43} +(7.09560 + 4.09664i) q^{44} +(4.36491 + 7.56024i) q^{46} +(16.9830 - 4.55058i) q^{47} +(-34.0211 - 35.2642i) q^{49} +(6.99854 - 54.7414i) q^{50} +(-0.129479 + 0.483221i) q^{52} +(-14.7503 - 3.95234i) q^{53} +(20.6770 - 42.1274i) q^{55} +(-18.0901 - 44.8060i) q^{56} +(19.8026 + 73.9044i) q^{58} +(-90.3630 + 52.1711i) q^{59} +(-12.5803 + 21.7897i) q^{61} +(36.9264 + 36.9264i) q^{62} -44.6014i q^{64} +(2.81133 + 0.553743i) q^{65} +(0.364564 - 1.36057i) q^{67} +(2.47014 + 9.21867i) q^{68} +(69.5348 - 33.6792i) q^{70} -86.5935 q^{71} +(-84.9471 - 22.7615i) q^{73} +(-50.6924 + 29.2673i) q^{74} -24.0409 q^{76} +(65.2117 - 7.99089i) q^{77} +(128.353 + 74.1049i) q^{79} +(93.4368 - 6.29977i) q^{80} +(116.577 - 31.2368i) q^{82} +(-35.5711 + 35.5711i) q^{83} +(51.7299 - 17.6679i) q^{85} +(73.9787 - 128.135i) q^{86} +(62.5803 + 16.7683i) q^{88} +(-130.143 - 75.1382i) q^{89} +(1.50183 + 3.71975i) q^{91} +(-2.44111 - 2.44111i) q^{92} +(-33.6122 + 19.4060i) q^{94} +(9.26295 + 137.386i) q^{95} +(74.8462 + 74.8462i) q^{97} +(92.6896 + 55.7549i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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