LMFDB - Embedded newform 324.3.j.a.19.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			19.17
Character	$\chi$	$=$	324.19
Dual form			324.3.j.a.307.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.210380 + 1.98890i) q^{2} +(-3.91148 - 0.836851i) q^{4} +(0.133306 + 0.756014i) q^{5} +(3.08121 - 3.67204i) q^{7} +(2.48731 - 7.60350i) q^{8} +O(q^{10})$	\(q+(-0.210380 + 1.98890i) q^{2} +(-3.91148 - 0.836851i) q^{4} +(0.133306 + 0.756014i) q^{5} +(3.08121 - 3.67204i) q^{7} +(2.48731 - 7.60350i) q^{8} +(-1.53168 + 0.106082i) q^{10} +(7.79262 + 1.37405i) q^{11} +(7.52188 + 2.73774i) q^{13} +(6.65511 + 6.90075i) q^{14} +(14.5994 + 6.54666i) q^{16} +(-6.81117 - 11.7973i) q^{17} +(11.9343 + 6.89025i) q^{19} +(0.111249 - 3.06869i) q^{20} +(-4.37226 + 15.2097i) q^{22} +(22.4825 + 26.7936i) q^{23} +(22.9385 - 8.34894i) q^{25} +(-7.02756 + 14.3843i) q^{26} +(-15.1250 + 11.7846i) q^{28} +(-38.1507 + 13.8857i) q^{29} +(14.9912 + 17.8658i) q^{31} +(-16.0921 + 27.6594i) q^{32} +(24.8966 - 11.0648i) q^{34} +(3.18685 + 1.83993i) q^{35} +(-1.05245 - 1.82290i) q^{37} +(-16.2148 + 22.2865i) q^{38} +(6.07993 + 0.866854i) q^{40} +(-14.0090 - 5.09885i) q^{41} +(57.3675 + 10.1154i) q^{43} +(-29.3308 - 11.8958i) q^{44} +(-58.0198 + 39.0787i) q^{46} +(49.8023 - 59.3520i) q^{47} +(4.51872 + 25.6270i) q^{49} +(11.7794 + 47.3790i) q^{50} +(-27.1306 - 17.0033i) q^{52} +43.6318 q^{53} +6.07450i q^{55} +(-20.2564 - 32.5615i) q^{56} +(-19.5912 - 78.7993i) q^{58} +(-43.0425 + 7.58956i) q^{59} +(-66.2578 - 55.5969i) q^{61} +(-38.6873 + 26.0575i) q^{62} +(-51.6265 - 37.8246i) q^{64} +(-1.06706 + 6.05160i) q^{65} +(-14.0519 + 38.6072i) q^{67} +(16.7692 + 51.8448i) q^{68} +(-4.32990 + 5.95126i) q^{70} +(74.9269 - 43.2591i) q^{71} +(-42.9421 + 74.3779i) q^{73} +(3.84699 - 1.70973i) q^{74} +(-40.9145 - 36.9383i) q^{76} +(29.0562 - 24.3811i) q^{77} +(7.58889 + 20.8503i) q^{79} +(-3.00319 + 11.9100i) q^{80} +(13.0883 - 26.7898i) q^{82} +(7.46796 + 20.5180i) q^{83} +(8.01094 - 6.72198i) q^{85} +(-32.1876 + 111.970i) q^{86} +(29.8303 - 55.8335i) q^{88} +(66.5965 - 115.349i) q^{89} +(33.2296 - 19.1851i) q^{91} +(-65.5176 - 123.617i) q^{92} +(107.568 + 111.538i) q^{94} +(-3.61822 + 9.94098i) q^{95} +(28.3954 - 161.038i) q^{97} +(-51.9202 + 3.59591i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.210380	+	1.98890i	−0.105190	+	0.994452i
$2$	−0.210380	+	1.98890i	−0.105190	+	0.994452i
$3$		0			0
$3$		0			0
$4$	−3.91148	−	0.836851i	−0.977870	−	0.209213i
$5$	0.133306	+	0.756014i	0.0266611	+	0.151203i	0.995232	−	0.0975344i	$-0.0310956\pi$
$5$	0.133306	+	0.756014i	0.0266611	+	0.151203i	−0.968571	+	0.248737i	$0.919984\pi$
$6$		0			0
$7$	3.08121	−	3.67204i	0.440172	−	0.524577i	−0.499656	−	0.866224i	$-0.666540\pi$
$7$	3.08121	−	3.67204i	0.440172	−	0.524577i	0.939828	+	0.341647i	$0.110985\pi$
$8$	2.48731	−	7.60350i	0.310914	−	0.950438i
$9$		0			0
$10$	−1.53168	+	0.106082i	−0.153168	+	0.0106082i
$11$	7.79262	+	1.37405i	0.708420	+	0.124914i	0.516237	−	0.856446i	$-0.327332\pi$
$11$	7.79262	+	1.37405i	0.708420	+	0.124914i	0.192183	+	0.981359i	$0.438443\pi$
$12$		0			0
$13$	7.52188	+	2.73774i	0.578606	+	0.210595i	0.614711	−	0.788753i	$-0.289273\pi$
$13$	7.52188	+	2.73774i	0.578606	+	0.210595i	−0.0361046	+	0.999348i	$0.511495\pi$
$14$	6.65511	+	6.90075i	0.475365	+	0.492911i
$15$		0			0
$16$	14.5994	+	6.54666i	0.912460	+	0.409166i
$17$	−6.81117	−	11.7973i	−0.400657	−	0.693958i	0.593149	−	0.805093i	$-0.297885\pi$
$17$	−6.81117	−	11.7973i	−0.400657	−	0.693958i	−0.993805	+	0.111135i	$0.964551\pi$
$18$		0			0
$19$	11.9343	+	6.89025i	0.628119	+	0.362645i	0.780023	−	0.625750i	$-0.215207\pi$
$19$	11.9343	+	6.89025i	0.628119	+	0.362645i	−0.151904	+	0.988395i	$0.548541\pi$
$20$	0.111249	−	3.06869i	0.00556244	−	0.153435i
$21$		0			0
$22$	−4.37226	+	15.2097i	−0.198739	+	0.691350i
$23$	22.4825	+	26.7936i	0.977500	+	1.16494i	0.986297	+	0.164978i	$0.0527554\pi$
$23$	22.4825	+	26.7936i	0.977500	+	1.16494i	−0.00879696	+	0.999961i	$0.502800\pi$
$24$		0			0
$25$	22.9385	−	8.34894i	0.917541	−	0.333958i
$26$	−7.02756	+	14.3843i	−0.270291	+	0.553244i
$27$		0			0
$28$	−15.1250	+	11.7846i	−0.540180	+	0.420878i
$29$	−38.1507	+	13.8857i	−1.31554	+	0.478817i	−0.902026	−	0.431681i	$-0.857921\pi$
$29$	−38.1507	+	13.8857i	−1.31554	+	0.478817i	−0.413513	+	0.910498i	$0.635698\pi$
$30$		0			0
$31$	14.9912	+	17.8658i	0.483588	+	0.576317i	0.951575	−	0.307418i	$-0.0994650\pi$
$31$	14.9912	+	17.8658i	0.483588	+	0.576317i	−0.467987	+	0.883735i	$0.655021\pi$
$32$	−16.0921	+	27.6594i	−0.502878	+	0.864358i
$33$		0			0
$34$	24.8966	−	11.0648i	0.732253	−	0.325437i
$35$	3.18685	+	1.83993i	0.0910530	+	0.0525695i
$36$		0			0
$37$	−1.05245	−	1.82290i	−0.0284447	−	0.0492676i	0.851453	−	0.524431i	$-0.175722\pi$
$37$	−1.05245	−	1.82290i	−0.0284447	−	0.0492676i	−0.879897	+	0.475164i	$0.842389\pi$
$38$	−16.2148	+	22.2865i	−0.426705	+	0.586488i
$39$		0			0
$40$	6.07993	+	0.866854i	0.151998	+	0.0216714i
$41$	−14.0090	−	5.09885i	−0.341683	−	0.124362i	0.165479	−	0.986213i	$-0.447083\pi$
$41$	−14.0090	−	5.09885i	−0.341683	−	0.124362i	−0.507161	+	0.861851i	$0.669305\pi$
$42$		0			0
$43$	57.3675	+	10.1154i	1.33413	+	0.235243i	0.794809	−	0.606860i	$-0.207571\pi$
$43$	57.3675	+	10.1154i	1.33413	+	0.235243i	0.539318	+	0.842102i	$0.318682\pi$
$44$	−29.3308	−	11.8958i	−0.666609	−	0.270360i
$45$		0			0
$46$	−58.0198	+	39.0787i	−1.26130	+	0.849537i
$47$	49.8023	−	59.3520i	1.05962	−	1.26281i	0.0960456	−	0.995377i	$-0.469381\pi$
$47$	49.8023	−	59.3520i	1.05962	−	1.26281i	0.963577	−	0.267432i	$-0.0861750\pi$
$48$		0			0
$49$	4.51872	+	25.6270i	0.0922189	+	0.522999i
$50$	11.7794	+	47.3790i	0.235589	+	0.947580i
$51$		0			0
$52$	−27.1306	−	17.0033i	−0.521742	−	0.326987i
$53$	43.6318			0.823241			0.411620	−	0.911355i	$-0.364963\pi$
$53$	43.6318			0.823241			0.411620	+	0.911355i	$0.364963\pi$
$54$		0			0
$55$			6.07450i			0.110445i
$56$	−20.2564	−	32.5615i	−0.361722	−	0.581455i
$57$		0			0
$58$	−19.5912	−	78.7993i	−0.337779	−	1.35861i
$59$	−43.0425	+	7.58956i	−0.729534	+	0.128637i	−0.526065	−	0.850445i	$-0.676333\pi$
$59$	−43.0425	+	7.58956i	−0.729534	+	0.128637i	−0.203470	+	0.979081i	$0.565222\pi$
$60$		0			0
$61$	−66.2578	−	55.5969i	−1.08619	−	0.911425i	−0.0897734	−	0.995962i	$-0.528614\pi$
$61$	−66.2578	−	55.5969i	−1.08619	−	0.911425i	−0.996420	+	0.0845375i	$0.973059\pi$
$62$	−38.6873	+	26.0575i	−0.623989	+	0.420282i
$63$		0			0
$64$	−51.6265	−	37.8246i	−0.806665	−	0.591010i
$65$	−1.06706	+	6.05160i	−0.0164163	+	0.0931016i
$66$		0			0
$67$	−14.0519	+	38.6072i	−0.209730	+	0.576227i	−0.999299	−	0.0374339i	$-0.988082\pi$
$67$	−14.0519	+	38.6072i	−0.209730	+	0.576227i	0.789570	+	0.613661i	$0.210304\pi$
$68$	16.7692	+	51.8448i	0.246605	+	0.762423i
$69$		0			0
$70$	−4.32990	+	5.95126i	−0.0618557	+	0.0850181i
$71$	74.9269	−	43.2591i	1.05531	−	0.609283i	0.131178	−	0.991359i	$-0.458124\pi$
$71$	74.9269	−	43.2591i	1.05531	−	0.609283i	0.924131	+	0.382076i	$0.124791\pi$
$72$		0			0
$73$	−42.9421	+	74.3779i	−0.588248	+	1.01888i	0.406214	+	0.913778i	$0.366849\pi$
$73$	−42.9421	+	74.3779i	−0.588248	+	1.01888i	−0.994462	+	0.105097i	$0.966485\pi$
$74$	3.84699	−	1.70973i	0.0519864	−	0.0231044i
$75$		0			0
$76$	−40.9145	−	36.9383i	−0.538349	−	0.486030i
$77$	29.0562	−	24.3811i	0.377354	−	0.316637i
$78$		0			0
$79$	7.58889	+	20.8503i	0.0960619	+	0.263928i	0.978411	−	0.206667i	$-0.0662616\pi$
$79$	7.58889	+	20.8503i	0.0960619	+	0.263928i	−0.882349	+	0.470595i	$0.844039\pi$
$80$	−3.00319	+	11.9100i	−0.0375398	+	0.148875i
$81$		0			0
$82$	13.0883	−	26.7898i	0.159614	−	0.326705i
$83$	7.46796	+	20.5180i	0.0899754	+	0.247205i	0.976516	−	0.215446i	$-0.0691205\pi$
$83$	7.46796	+	20.5180i	0.0899754	+	0.247205i	−0.886540	+	0.462651i	$0.846898\pi$
$84$		0			0
$85$	8.01094	−	6.72198i	0.0942464	−	0.0790821i
$86$	−32.1876	+	111.970i	−0.374274	+	1.30198i
$87$		0			0
$88$	29.8303	−	55.8335i	0.338981	−	0.634472i
$89$	66.5965	−	115.349i	0.748275	−	1.29605i	−0.200373	−	0.979720i	$-0.564216\pi$
$89$	66.5965	−	115.349i	0.748275	−	1.29605i	0.948649	−	0.316331i	$-0.102451\pi$
$90$		0			0
$91$	33.2296	−	19.1851i	0.365160	−	0.210825i
$92$	−65.5176	−	123.617i	−0.712148	−	1.34367i
$93$		0			0
$94$	107.568	+	111.538i	1.14434	+	1.18658i
$95$	−3.61822	+	9.94098i	−0.0380865	+	0.104642i
$96$		0			0
$97$	28.3954	−	161.038i	0.292736	−	1.66019i	−0.383529	−	0.923529i	$-0.625291\pi$
$97$	28.3954	−	161.038i	0.292736	−	1.66019i	0.676265	−	0.736659i	$-0.263598\pi$
$98$	−51.9202	+	3.59591i	−0.529798	+	0.0366930i
$99$		0			0
$100$	−96.7104	+	13.4606i	−0.967104	+	0.134606i
$101$	20.6121	+	17.2956i	0.204081	+	0.171244i	0.739100	−	0.673596i	$-0.235251\pi$
$101$	20.6121	+	17.2956i	0.204081	+	0.171244i	−0.535019	+	0.844840i	$0.679696\pi$
$102$		0			0
$103$	−47.0573	+	8.29747i	−0.456867	+	0.0805580i	−0.397346	−	0.917669i	$-0.630069\pi$
$103$	−47.0573	+	8.29747i	−0.456867	+	0.0805580i	−0.0595214	+	0.998227i	$0.518957\pi$
$104$	39.5257	−	50.3830i	0.380055	−	0.484452i
$105$		0			0
$106$	−9.17925	+	86.7794i	−0.0865967	+	0.818673i
$107$		−	61.2748i		−	0.572661i	−0.958131	−	0.286331i	$-0.907564\pi$
$107$		−	61.2748i		−	0.572661i	0.958131	−	0.286331i	$-0.0924356\pi$
$108$		0			0
$109$	193.438			1.77466			0.887331	−	0.461133i	$-0.152557\pi$
$109$	193.438			1.77466			0.887331	+	0.461133i	$0.152557\pi$
$110$	−12.0816	−	1.27795i	−0.109833	−	0.0116178i
$111$		0			0
$112$	69.0232	−	33.4378i	0.616279	−	0.298552i
$113$	−13.4483	−	76.2690i	−0.119011	−	0.674947i	−0.984686	−	0.174339i	$-0.944221\pi$
$113$	−13.4483	−	76.2690i	−0.119011	−	0.674947i	0.865674	−	0.500608i	$-0.166890\pi$
$114$		0			0
$115$	−17.2593	+	20.5688i	−0.150081	+	0.178859i
$116$	160.846	−	22.3872i	1.38660	−	0.192993i
$117$		0			0
$118$	−6.03962	−	87.2042i	−0.0511832	−	0.739018i
$119$	−64.3067	−	11.3390i	−0.540392	−	0.0952858i
$120$		0			0
$121$	−54.8659	−	19.9695i	−0.453437	−	0.165038i
$122$	124.516	−	120.084i	1.02063	−	0.984295i
$123$		0			0
$124$	−43.6868	−	82.4273i	−0.352313	−	0.664736i
$125$	18.9657	+	32.8496i	0.151726	+	0.262797i
$126$		0			0
$127$	−134.077	−	77.4091i	−1.05572	−	0.609521i	−0.131475	−	0.991319i	$-0.541971\pi$
$127$	−134.077	−	77.4091i	−1.05572	−	0.609521i	−0.924246	+	0.381799i	$0.875305\pi$
$128$	86.0907	−	94.7227i	0.672584	−	0.740021i
$129$		0			0
$130$	−11.8116	−	3.39542i	−0.0908582	−	0.0261186i
$131$	−56.4836	−	67.3145i	−0.431173	−	0.513851i	0.506088	−	0.862482i	$-0.331091\pi$
$131$	−56.4836	−	67.3145i	−0.431173	−	0.513851i	−0.937260	+	0.348631i	$0.886647\pi$
$132$		0			0
$133$	62.0732	−	22.5928i	0.466716	−	0.169871i
$134$	−73.8298	−	36.0700i	−0.550969	−	0.269179i
$135$		0			0
$136$	−106.642	+	22.4452i	−0.784134	+	0.165038i
$137$	−247.706	+	90.1577i	−1.80807	+	0.658085i	−0.810717	+	0.585438i	$0.800923\pi$
$137$	−247.706	+	90.1577i	−1.80807	+	0.658085i	−0.997358	+	0.0726476i	$0.976855\pi$
$138$		0			0
$139$	142.549	+	169.883i	1.02553	+	1.22218i	0.974710	+	0.223475i	$0.0717401\pi$
$139$	142.549	+	169.883i	1.02553	+	1.22218i	0.0508232	+	0.998708i	$0.483816\pi$
$140$	−10.9256	−	9.86378i	−0.0780398	−	0.0704556i
$141$		0			0
$142$	70.2750	+	158.123i	0.494895	+	1.11354i
$143$	54.8534	+	31.6696i	0.383590	+	0.221466i
$144$		0			0
$145$	−15.5835	−	26.9914i	−0.107472	−	0.186147i
$146$	−138.896	−	101.055i	−0.951345	−	0.692160i
$147$		0			0
$148$	2.59115	+	8.01099i	0.0175078	+	0.0541283i
$149$	−0.892365	−	0.324794i	−0.00598903	−	0.00217983i	0.339024	−	0.940778i	$-0.389903\pi$
$149$	−0.892365	−	0.324794i	−0.00598903	−	0.00217983i	−0.345013	+	0.938598i	$0.612125\pi$
$150$		0			0
$151$	−219.805	−	38.7576i	−1.45566	−	0.256673i	−0.610855	−	0.791743i	$-0.709174\pi$
$151$	−219.805	−	38.7576i	−1.45566	−	0.256673i	−0.844808	+	0.535070i	$0.820285\pi$
$152$	82.0743	−	73.6040i	0.539963	−	0.484237i
$153$		0			0
$154$	42.3788	+	62.9194i	0.275187	+	0.408567i
$155$	−11.5084	+	13.7152i	−0.0742478	+	0.0884851i
$156$		0			0
$157$	32.0271	+	181.635i	0.203994	+	1.15691i	0.899014	+	0.437919i	$0.144284\pi$
$157$	32.0271	+	181.635i	0.203994	+	1.15691i	−0.695020	+	0.718990i	$0.744604\pi$
$158$	−43.0658	+	10.7071i	−0.272569	+	0.0677664i
$159$		0			0
$160$	−23.0561	−	8.47868i	−0.144101	−	0.0529917i
$161$	167.660			1.04137
$162$		0			0
$163$		−	210.034i		−	1.28855i	−0.764793	−	0.644276i	$-0.777159\pi$
$163$		−	210.034i		−	1.28855i	0.764793	−	0.644276i	$-0.222841\pi$
$164$	50.5289	+	31.6675i	0.308103	+	0.193095i
$165$		0			0
$166$	−42.3795	+	10.5365i	−0.255298	+	0.0634727i
$167$	−129.841	+	22.8945i	−0.777493	+	0.137093i	−0.548293	−	0.836286i	$-0.684722\pi$
$167$	−129.841	+	22.8945i	−0.777493	+	0.137093i	−0.229200	+	0.973379i	$0.573611\pi$
$168$		0			0
$169$	−80.3780	−	67.4452i	−0.475610	−	0.399084i
$170$	11.6840	+	17.3472i	0.0687296	+	0.102042i
$171$		0			0
$172$	−215.927	−	87.5743i	−1.25539	−	0.509153i
$173$	−35.2162	+	199.721i	−0.203562	+	1.15446i	0.696125	+	0.717921i	$0.254906\pi$
$173$	−35.2162	+	199.721i	−0.203562	+	1.15446i	−0.899687	+	0.436536i	$0.856205\pi$
$174$		0			0
$175$	40.0207	−	109.956i	0.228690	−	0.628320i
$176$	104.772	+	71.0758i	0.595295	+	0.403840i
$177$		0			0
$178$	215.407	+	156.721i	1.21015	+	0.880456i
$179$	−59.8299	+	34.5428i	−0.334245	+	0.192976i	−0.657724	−	0.753259i	$-0.728481\pi$
$179$	−59.8299	+	34.5428i	−0.334245	+	0.192976i	0.323479	+	0.946235i	$0.395147\pi$
$180$		0			0
$181$	−44.8622	+	77.7036i	−0.247858	+	0.429302i	−0.962931	−	0.269747i	$-0.913060\pi$
$181$	−44.8622	+	77.7036i	−0.247858	+	0.429302i	0.715074	+	0.699049i	$0.246393\pi$
$182$	31.1665	+	70.1266i	0.171244	+	0.385311i
$183$		0			0
$184$	259.646	−	104.302i	1.41112	−	0.566857i
$185$	1.23784	−	1.03867i	0.00669103	−	0.00561444i
$186$		0			0
$187$	−36.8668	−	101.291i	−0.197149	−	0.541661i
$188$	−244.469	+	190.477i	−1.30037	+	1.01318i
$189$		0			0
$190$	−19.0104	−	9.28767i	−0.100055	−	0.0488825i
$191$	101.142	+	277.887i	0.529542	+	1.45490i	0.859612	+	0.510947i	$0.170705\pi$
$191$	101.142	+	277.887i	0.529542	+	1.45490i	−0.330071	+	0.943956i	$0.607073\pi$
$192$		0			0
$193$	−238.508	+	200.132i	−1.23579	+	1.03695i	−0.237949	+	0.971278i	$0.576475\pi$
$193$	−238.508	+	200.132i	−1.23579	+	1.03695i	−0.997841	+	0.0656734i	$0.979080\pi$
$194$	314.316	+	90.3549i	1.62018	+	0.465747i
$195$		0			0
$196$	3.77105	−	104.021i	0.0192401	−	0.530719i
$197$	−72.0482	+	124.791i	−0.365727	+	0.633457i	−0.988892	−	0.148633i	$-0.952513\pi$
$197$	−72.0482	+	124.791i	−0.365727	+	0.633457i	0.623166	+	0.782090i	$0.285846\pi$
$198$		0			0
$199$	168.765	−	97.4366i	0.848066	−	0.489631i	−0.0119320	−	0.999929i	$-0.503798\pi$
$199$	168.765	−	97.4366i	0.848066	−	0.489631i	0.859998	+	0.510298i	$0.170465\pi$
$200$	−6.42587	−	195.180i	−0.0321294	−	0.975898i
$201$		0			0
$202$	−38.7358	+	37.3569i	−0.191761	+	0.184935i
$203$	−66.5612	+	182.875i	−0.327888	+	0.900864i
$204$		0			0
$205$	1.98733	−	11.2707i	0.00969428	−	0.0549790i
$206$	−6.60296	−	95.3381i	−0.0320532	−	0.462806i
$207$		0			0
$208$	91.8916	+	89.2124i	0.441787	+	0.428906i
$209$	83.5316	+	70.0914i	0.399673	+	0.335365i
$210$		0			0
$211$	−114.338	+	20.1608i	−0.541884	+	0.0955488i	−0.437889	−	0.899029i	$-0.644274\pi$
$211$	−114.338	+	20.1608i	−0.541884	+	0.0955488i	−0.103995	+	0.994578i	$0.533163\pi$
$212$	−170.665	−	36.5133i	−0.805022	−	0.172233i
$213$		0			0
$214$	121.870	+	12.8910i	0.569484	+	0.0602382i
$215$			44.7190i			0.207996i
$216$		0			0
$217$	111.795			0.515185
$218$	−40.6955	+	384.730i	−0.186677	+	1.76482i
$219$		0			0
$220$	5.08345	−	23.7603i	0.0231066	−	0.108001i
$221$	−18.9349	−	107.385i	−0.0856781	−	0.485905i
$222$		0			0
$223$	−95.4717	+	113.779i	−0.428124	+	0.510219i	−0.936380	−	0.350987i	$-0.885846\pi$
$223$	−95.4717	+	113.779i	−0.428124	+	0.510219i	0.508256	+	0.861206i	$0.330290\pi$
$224$	51.9835	+	144.315i	0.232069	+	0.644264i
$225$		0			0
$226$	154.521	−	10.7019i	0.683721	−	0.0473534i
$227$	−163.627	−	28.8519i	−0.720826	−	0.127101i	−0.198812	−	0.980038i	$-0.563708\pi$
$227$	−163.627	−	28.8519i	−0.720826	−	0.127101i	−0.522014	+	0.852937i	$0.674819\pi$
$228$		0			0
$229$	−218.671	−	79.5896i	−0.954894	−	0.347553i	−0.182863	−	0.983138i	$-0.558537\pi$
$229$	−218.671	−	79.5896i	−0.954894	−	0.347553i	−0.772031	+	0.635585i	$0.780759\pi$
$230$	−37.2784	−	38.6543i	−0.162080	−	0.168062i
$231$		0			0
$232$	10.6873	+	324.617i	0.0460660	+	1.39921i
$233$	102.146	+	176.922i	0.438394	+	0.759320i	0.997566	−	0.0697314i	$-0.0222142\pi$
$233$	102.146	+	176.922i	0.438394	+	0.759320i	−0.559172	+	0.829052i	$0.688881\pi$
$234$		0			0
$235$	51.5099	+	29.7392i	0.219191	+	0.126550i
$236$	174.711	+	6.33379i	0.740302	+	0.0268381i
$237$		0			0
$238$	36.0810	−	125.514i	0.151601	−	0.527371i
$239$	−59.1551	−	70.4983i	−0.247511	−	0.294972i	0.627957	−	0.778248i	$-0.283891\pi$
$239$	−59.1551	−	70.4983i	−0.247511	−	0.294972i	−0.875468	+	0.483276i	$0.839447\pi$
$240$		0			0
$241$	−194.954	+	70.9574i	−0.808938	+	0.294429i	−0.713185	−	0.700976i	$-0.752748\pi$
$241$	−194.954	+	70.9574i	−0.808938	+	0.294429i	−0.0957527	+	0.995405i	$0.530526\pi$
$242$	51.2602	−	104.922i	0.211819	−	0.433561i
$243$		0			0
$244$	212.640	+	272.914i	0.871475	+	1.11850i
$245$	−18.7720	+	6.83244i	−0.0766203	+	0.0278875i
$246$		0			0
$247$	70.9044	+	84.5006i	0.287062	+	0.342108i
$248$	173.131	−	69.5478i	0.698108	−	0.280435i
$249$		0			0
$250$	−69.3247	+	30.8101i	−0.277299	+	0.123240i
$251$	−269.842	−	155.793i	−1.07507	−	0.620690i	−0.145505	−	0.989357i	$-0.546481\pi$
$251$	−269.842	−	155.793i	−1.07507	−	0.620690i	−0.929561	+	0.368667i	$0.879814\pi$
$252$		0			0
$253$	138.382	+	239.684i	0.546964	+	0.947370i
$254$	182.166	−	250.380i	0.717191	−	0.985749i
$255$		0			0
$256$	170.283	+	191.154i	0.665166	+	0.746695i
$257$	−281.815	−	102.572i	−1.09656	−	0.399114i	−0.270511	−	0.962717i	$-0.587192\pi$
$257$	−281.815	−	102.572i	−1.09656	−	0.399114i	−0.826046	+	0.563603i	$0.809415\pi$
$258$		0			0
$259$	−9.93659	−	1.75209i	−0.0383652	−	0.00676482i
$260$	9.23808	−	22.7778i	0.0355311	−	0.0876067i
$261$		0			0
$262$	145.765	−	98.1788i	0.556356	−	0.374728i
$263$	126.004	−	150.166i	0.479102	−	0.570972i	−0.471309	−	0.881968i	$-0.656218\pi$
$263$	126.004	−	150.166i	0.479102	−	0.570972i	0.950411	+	0.310996i	$0.100663\pi$
$264$		0			0
$265$	5.81636	+	32.9862i	0.0219485	+	0.124476i
$266$	31.8759	+	128.211i	0.119834	+	0.481995i
$267$		0			0
$268$	87.2722	−	139.252i	0.325642	−	0.519597i
$269$	110.390			0.410372			0.205186	−	0.978723i	$-0.434220\pi$
$269$	110.390			0.410372			0.205186	+	0.978723i	$0.434220\pi$
$270$		0			0
$271$			157.984i			0.582967i	0.956576	+	0.291484i	$0.0941489\pi$
$271$			157.984i			0.582967i	−0.956576	+	0.291484i	$0.905851\pi$
$272$	−22.2059	−	216.823i	−0.0816393	−	0.797144i
$273$		0			0
$274$	−127.203	−	511.631i	−0.464243	−	1.86727i
$275$	190.223	−	33.5415i	0.691720	−	0.121969i
$276$		0			0
$277$	133.295	+	111.848i	0.481210	+	0.403783i	0.850864	−	0.525386i	$-0.176079\pi$
$277$	133.295	+	111.848i	0.481210	+	0.403783i	−0.369654	+	0.929170i	$0.620524\pi$
$278$	−367.871	+	247.776i	−1.32328	+	0.891282i
$279$		0			0
$280$	21.9166	−	19.6548i	0.0782737	−	0.0701956i
$281$	64.5172	−	365.895i	0.229599	−	1.30212i	−0.624098	−	0.781346i	$-0.714533\pi$
$281$	64.5172	−	365.895i	0.229599	−	1.30212i	0.853696	−	0.520772i	$-0.174356\pi$
$282$		0			0
$283$	142.624	−	391.857i	0.503973	−	1.38465i	−0.383392	−	0.923586i	$-0.625244\pi$
$283$	142.624	−	391.857i	0.503973	−	1.38465i	0.887365	−	0.461068i	$-0.152534\pi$
$284$	−329.277	+	106.504i	−1.15942	+	0.375015i
$285$		0			0
$286$	−74.5279	+	102.435i	−0.260587	+	0.358166i
$287$	−61.8878	+	35.7309i	−0.215637	+	0.124498i
$288$		0			0
$289$	51.7160	−	89.5748i	0.178948	−	0.309947i
$290$	56.9617	−	25.3156i	0.196420	−	0.0872952i
$291$		0			0
$292$	230.210	−	254.992i	0.788392	−	0.873259i
$293$	−33.9075	+	28.4518i	−0.115725	+	0.0971050i	−0.698814	−	0.715304i	$-0.746288\pi$
$293$	−33.9075	+	28.4518i	−0.115725	+	0.0971050i	0.583089	+	0.812408i	$0.301844\pi$
$294$		0			0
$295$	−11.4756	−	31.5290i	−0.0389004	−	0.106878i
$296$	−16.4782	+	3.46820i	−0.0556697	+	0.0117169i
$297$		0			0
$298$	0.833720	−	1.70650i	0.00279772	−	0.00572650i
$299$	95.7568	+	263.090i	0.320257	+	0.879898i
$300$		0			0
$301$	213.905	−	179.488i	0.710649	−	0.596305i
$302$	123.328	−	429.017i	0.408370	−	1.42059i
$303$		0			0
$304$	129.125	+	178.723i	0.424752	+	0.587904i
$305$	33.1995	−	57.5032i	0.108851	−	0.188535i
$306$		0			0
$307$	−279.865	+	161.580i	−0.911612	+	0.526320i	−0.880950	−	0.473210i	$-0.843095\pi$
$307$	−279.865	+	161.580i	−0.911612	+	0.526320i	−0.0306628	+	0.999530i	$0.509762\pi$
$308$	−134.056	+	71.0504i	−0.435248	+	0.230683i
$309$		0			0
$310$	−24.8571	−	25.7745i	−0.0801841	−	0.0831436i
$311$	−1.32044	+	3.62789i	−0.00424580	+	0.0116652i	−0.941797	−	0.336181i	$-0.890865\pi$
$311$	−1.32044	+	3.62789i	−0.00424580	+	0.0116652i	0.937552	+	0.347846i	$0.113087\pi$
$312$		0			0
$313$	−5.20268	+	29.5059i	−0.0166220	+	0.0942679i	−0.991990	−	0.126315i	$-0.959685\pi$
$313$	−5.20268	+	29.5059i	−0.0166220	+	0.0942679i	0.975368	+	0.220583i	$0.0707960\pi$
$314$	−367.992	+	25.4865i	−1.17195	+	0.0811673i
$315$		0			0
$316$	−12.2352	−	87.9064i	−0.0387190	−	0.278185i
$317$	429.901	+	360.730i	1.35615	+	1.13795i	0.977150	+	0.212553i	$0.0681778\pi$
$317$	429.901	+	360.730i	1.35615	+	1.13795i	0.379004	+	0.925395i	$0.376267\pi$
$318$		0			0
$319$	−316.373	+	55.7851i	−0.991766	+	0.174875i
$320$	21.7138	−	44.0726i	0.0678557	−	0.137727i
$321$		0			0
$322$	−35.2724	+	333.461i	−0.109542	+	1.03559i
$323$		−	187.723i		−	0.581184i
$324$		0			0
$325$	195.398			0.601225
$326$	417.737	+	44.1869i	1.28140	+	0.135543i
$327$		0			0
$328$	−73.6139	+	93.8349i	−0.224433	+	0.286082i
$329$	−64.4919	−	365.752i	−0.196024	−	1.11171i
$330$		0			0
$331$	90.3131	−	107.631i	0.272849	−	0.325169i	−0.612168	−	0.790728i	$-0.709702\pi$
$331$	90.3131	−	107.631i	0.272849	−	0.325169i	0.885017	+	0.465559i	$0.154147\pi$
$332$	−12.0402	−	86.5055i	−0.0362657	−	0.260559i
$333$		0			0
$334$	−18.2190	−	263.059i	−0.0545479	−	0.787601i
$335$	−31.0608	−	5.47685i	−0.0927188	−	0.0163488i
$336$		0			0
$337$	−398.458	−	145.027i	−1.18237	−	0.430346i	−0.325330	−	0.945601i	$-0.605475\pi$
$337$	−398.458	−	145.027i	−1.18237	−	0.430346i	−0.857037	+	0.515254i	$0.827697\pi$
$338$	151.052	−	145.675i	0.446899	−	0.430991i
$339$		0			0
$340$	−36.9599	+	19.5889i	−0.108706	+	0.0576145i
$341$	92.2724	+	159.820i	0.270593	+	0.468682i
$342$		0			0
$343$	311.440	+	179.810i	0.907988	+	0.524227i
$344$	219.604	−	411.033i	0.638383	−	1.19486i
$345$		0			0
$346$	−389.817	−	112.059i	−1.12664	−	0.323870i
$347$	73.0006	+	86.9988i	0.210376	+	0.250717i	0.860906	−	0.508764i	$-0.169897\pi$
$347$	73.0006	+	86.9988i	0.210376	+	0.250717i	−0.650530	+	0.759481i	$0.725453\pi$
$348$		0			0
$349$	94.6615	−	34.4540i	0.271236	−	0.0987220i	−0.202821	−	0.979216i	$-0.565011\pi$
$349$	94.6615	−	34.4540i	0.271236	−	0.0987220i	0.474058	+	0.880494i	$0.342789\pi$
$350$	210.272	+	102.730i	0.600778	+	0.293514i
$351$		0			0
$352$	−163.405	+	193.428i	−0.464219	+	0.549512i
$353$	24.4299	−	8.89174i	0.0692064	−	0.0251891i	−0.307185	−	0.951650i	$-0.599387\pi$
$353$	24.4299	−	8.89174i	0.0692064	−	0.0251891i	0.376391	+	0.926461i	$0.377165\pi$
$354$		0			0
$355$	42.6926	+	50.8791i	0.120261	+	0.143321i
$356$	−357.021	+	395.452i	−1.00287	+	1.11082i
$357$		0			0
$358$	−56.1153	−	126.263i	−0.156747	−	0.352690i
$359$	−50.8289	−	29.3461i	−0.141585	−	0.0817439i	0.427534	−	0.903999i	$-0.359382\pi$
$359$	−50.8289	−	29.3461i	−0.141585	−	0.0817439i	−0.569119	+	0.822255i	$0.692716\pi$
$360$		0			0
$361$	−85.5489	−	148.175i	−0.236978	−	0.410457i
$362$	−145.107	−	105.574i	−0.400848	−	0.291641i
$363$		0			0
$364$	−146.032	+	47.2339i	−0.401186	+	0.129764i
$365$	−61.9551	−	22.5498i	−0.169740	−	0.0617803i
$366$		0			0
$367$	−107.710	−	18.9921i	−0.293487	−	0.0517497i	0.0249660	−	0.999688i	$-0.492052\pi$
$367$	−107.710	−	18.9921i	−0.293487	−	0.0517497i	−0.318453	+	0.947939i	$0.603163\pi$
$368$	152.822	+	538.355i	0.415276	+	1.46292i
$369$		0			0
$370$	1.80540	+	2.68046i	0.00487946	+	0.00724449i
$371$	134.438	−	160.218i	0.362368	−	0.431853i
$372$		0			0
$373$	11.6320	+	65.9686i	0.0311851	+	0.176859i	0.996422	−	0.0845170i	$-0.0269347\pi$
$373$	11.6320	+	65.9686i	0.0311851	+	0.176859i	−0.965237	+	0.261376i	$0.915824\pi$
$374$	209.213	−	52.0150i	0.559394	−	0.139077i
$375$		0			0
$376$	−327.409	−	526.299i	−0.870770	−	1.39973i
$377$	−324.980			−0.862016
$378$		0			0
$379$			276.576i			0.729753i	0.931056	+	0.364876i	$0.118889\pi$
$379$			276.576i			0.729753i	−0.931056	+	0.364876i	$0.881111\pi$
$380$	22.4717	−	35.8560i	0.0591361	−	0.0943580i
$381$		0			0
$382$	−573.968	+	142.701i	−1.50253	+	0.373562i
$383$	39.6849	−	6.99751i	0.103616	−	0.0182703i	−0.121600	−	0.992579i	$-0.538802\pi$
$383$	39.6849	−	6.99751i	0.103616	−	0.0182703i	0.225216	+	0.974309i	$0.427691\pi$
$384$		0			0
$385$	22.3058	+	18.7168i	0.0579371	+	0.0486150i
$386$	−347.865	−	516.472i	−0.901205	−	1.33801i
$387$		0			0
$388$	−245.833	+	606.135i	−0.633590	+	1.56220i
$389$	25.8684	−	146.707i	0.0664998	−	0.377139i	−0.933336	−	0.359005i	$-0.883116\pi$
$389$	25.8684	−	146.707i	0.0664998	−	0.377139i	0.999836	−	0.0181346i	$-0.00577273\pi$
$390$		0			0
$391$	162.960	−	447.728i	0.416777	−	1.14508i
$392$	206.094	+	29.3842i	0.525750	+	0.0749596i
$393$		0			0
$394$	−233.040	−	169.550i	−0.591472	−	0.430331i
$395$	−14.7515	+	8.51677i	−0.0373455	+	0.0215614i
$396$		0			0
$397$	373.378	−	646.710i	0.940499	−	1.62899i	0.175978	−	0.984394i	$-0.443691\pi$
$397$	373.378	−	646.710i	0.940499	−	1.62899i	0.764521	−	0.644598i	$-0.222975\pi$
$398$	158.287	+	356.156i	0.397707	+	0.894865i
$399$		0			0
$400$	389.545	+	28.2814i	0.973864	+	0.0707036i
$401$	−44.3852	+	37.2436i	−0.110686	+	0.0928768i	−0.696451	−	0.717604i	$-0.745239\pi$
$401$	−44.3852	+	37.2436i	−0.110686	+	0.0928768i	0.585765	+	0.810481i	$0.300794\pi$
$402$		0			0
$403$	63.8501	+	175.427i	0.158437	+	0.435302i
$404$	−66.1501	−	84.9009i	−0.163738	−	0.210151i
$405$		0			0
$406$	−349.719	−	170.857i	−0.861376	−	0.420830i
$407$	−5.69661	−	15.6513i	−0.0139966	−	0.0384553i
$408$		0			0
$409$	226.059	−	189.686i	0.552712	−	0.463780i	−0.323146	−	0.946349i	$-0.604741\pi$
$409$	226.059	−	189.686i	0.552712	−	0.463780i	0.875858	+	0.482569i	$0.160296\pi$
$410$	21.9982	+	6.32373i	0.0536542	+	0.0154237i
$411$		0			0
$412$	191.007	+	6.92457i	0.463610	+	0.0168072i
$413$	−104.754	+	181.439i	−0.253641	+	0.439319i
$414$		0			0
$415$	−14.5164	+	8.38105i	−0.0349793	+	0.0201953i
$416$	−196.767	+	163.995i	−0.472998	+	0.394219i
$417$		0			0
$418$	−156.978	+	151.391i	−0.375546	+	0.362179i
$419$	150.722	−	414.106i	0.359719	−	0.988320i	−0.619408	−	0.785069i	$-0.712627\pi$
$419$	150.722	−	414.106i	0.359719	−	0.988320i	0.979127	−	0.203250i	$-0.0651506\pi$
$420$		0			0
$421$	11.8192	−	67.0301i	0.0280742	−	0.159216i	−0.967548	−	0.252688i	$-0.918685\pi$
$421$	11.8192	−	67.0301i	0.0280742	−	0.159216i	0.995622	+	0.0934717i	$0.0297965\pi$
$422$	−16.0436	−	231.648i	−0.0380179	−	0.548929i
$423$		0			0
$424$	108.526	−	331.754i	0.255957	−	0.782439i
$425$	−254.733	−	213.746i	−0.599372	−	0.502933i
$426$		0			0
$427$	−408.308	+	71.9957i	−0.956225	+	0.168608i
$428$	−51.2779	+	239.675i	−0.119808	+	0.559988i
$429$		0			0
$430$	−88.9419	−	9.40799i	−0.206842	−	0.0218790i
$431$		−	53.6108i		−	0.124387i	−0.998064	−	0.0621935i	$-0.980190\pi$
$431$		−	53.6108i		−	0.124387i	0.998064	−	0.0621935i	$-0.0198096\pi$
$432$		0			0
$433$	−686.735			−1.58599			−0.792997	−	0.609226i	$-0.791480\pi$
$433$	−686.735			−1.58599			−0.792997	+	0.609226i	$0.791480\pi$
$434$	−23.5195	+	222.350i	−0.0541923	+	0.512327i
$435$		0			0
$436$	−756.629	−	161.879i	−1.73539	−	0.371282i
$437$	83.6975	+	474.672i	0.191527	+	1.08621i
$438$		0			0
$439$	74.5743	−	88.8742i	0.169873	−	0.202447i	−0.674391	−	0.738375i	$-0.735594\pi$
$439$	74.5743	−	88.8742i	0.169873	−	0.202447i	0.844264	+	0.535928i	$0.180038\pi$
$440$	46.1875	+	15.1092i	0.104972	+	0.0343391i
$441$		0			0
$442$	217.562	−	15.0680i	0.492222	−	0.0340905i
$443$	126.688	+	22.3386i	0.285978	+	0.0504257i	0.314797	−	0.949159i	$-0.398063\pi$
$443$	126.688	+	22.3386i	0.285978	+	0.0504257i	−0.0288188	+	0.999585i	$0.509175\pi$
$444$		0			0
$445$	96.0828	+	34.9713i	0.215916	+	0.0785871i
$446$	−206.210	−	213.821i	−0.462354	−	0.479419i
$447$		0			0
$448$	−297.965	+	73.0292i	−0.665101	+	0.163012i
$449$	−361.840	−	626.725i	−0.805880	−	1.39583i	−0.915695	−	0.401873i	$-0.868359\pi$
$449$	−361.840	−	626.725i	−0.805880	−	1.39583i	0.109815	−	0.993952i	$-0.464974\pi$
$450$		0			0
$451$	−102.161	−	58.9825i	−0.226520	−	0.130782i
$452$	−11.2231	+	309.579i	−0.0248299	+	0.684909i
$453$		0			0
$454$	91.8077	−	319.370i	0.202220	−	0.703457i
$455$	18.9339	+	22.5645i	0.0416129	+	0.0495924i
$456$		0			0
$457$	49.8588	−	18.1471i	0.109100	−	0.0397092i	−0.286893	−	0.957963i	$-0.592623\pi$
$457$	49.8588	−	18.1471i	0.109100	−	0.0397092i	0.395993	+	0.918253i	$0.370400\pi$
$458$	204.300	−	418.171i	0.446070	−	0.913037i
$459$		0			0
$460$	84.7224	−	66.0111i	0.184179	−	0.143502i
$461$	−198.117	+	72.1085i	−0.429754	+	0.156418i	−0.547835	−	0.836586i	$-0.684548\pi$
$461$	−198.117	+	72.1085i	−0.429754	+	0.156418i	0.118081	+	0.993004i	$0.462326\pi$
$462$		0			0
$463$	407.123	+	485.190i	0.879315	+	1.04793i	0.998483	+	0.0550524i	$0.0175326\pi$
$463$	407.123	+	485.190i	0.879315	+	1.04793i	−0.119169	+	0.992874i	$0.538023\pi$
$464$	−647.880	−	47.0368i	−1.39629	−	0.101372i
$465$		0			0
$466$	−373.370	+	165.937i	−0.801222	+	0.356089i
$467$	254.886	+	147.159i	0.545795	+	0.315115i	0.747424	−	0.664347i	$-0.231290\pi$
$467$	254.886	+	147.159i	0.545795	+	0.315115i	−0.201629	+	0.979462i	$0.564624\pi$
$468$		0			0
$469$	98.4705	+	170.556i	0.209958	+	0.363659i
$470$	−69.9851	+	96.1916i	−0.148905	+	0.204663i
$471$		0			0
$472$	−49.3531	+	346.152i	−0.104562	+	0.733372i
$473$	433.144	+	157.651i	0.915737	+	0.333301i
$474$		0			0
$475$	331.281	+	58.4137i	0.697433	+	0.122976i
$476$	242.045	+	98.1674i	0.508499	+	0.206234i
$477$		0			0
$478$	152.659	−	102.822i	0.319371	−	0.215110i
$479$	349.313	−	416.295i	0.729255	−	0.869092i	−0.266240	−	0.963907i	$-0.585781\pi$
$479$	349.313	−	416.295i	0.729255	−	0.869092i	0.995495	+	0.0948146i	$0.0302258\pi$
$480$		0			0
$481$	−2.92579	−	16.5930i	−0.00608273	−	0.0344969i
$482$	−100.113	−	402.673i	−0.207704	−	0.835421i
$483$		0			0
$484$	197.895	+	124.025i	0.408875	+	0.256250i
$485$	125.532			0.258830
$486$		0			0
$487$		−	168.509i		−	0.346015i	−0.984921	−	0.173007i	$-0.944652\pi$
$487$		−	168.509i		−	0.346015i	0.984921	−	0.173007i	$-0.0553484\pi$
$488$	−587.535	+	365.505i	−1.20397	+	0.748985i
$489$		0			0
$490$	−9.63981	−	38.7730i	−0.0196731	−	0.0791287i
$491$	394.774	−	69.6093i	0.804021	−	0.141771i	0.243489	−	0.969904i	$-0.421708\pi$
$491$	394.774	−	69.6093i	0.804021	−	0.141771i	0.560532	+	0.828133i	$0.310597\pi$
$492$		0			0
$493$	423.664	+	355.496i	0.859359	+	0.721088i
$494$	−182.980	+	123.245i	−0.370406	+	0.249483i
$495$		0			0
$496$	101.901	+	358.972i	0.205445	+	0.723734i
$497$	72.0163	−	408.425i	0.144902	−	0.821780i
$498$		0			0
$499$	−54.0863	+	148.601i	−0.108389	+	0.297797i	−0.982015	−	0.188800i	$-0.939540\pi$
$499$	−54.0863	+	148.601i	−0.108389	+	0.297797i	0.873626	+	0.486598i	$0.161762\pi$
$500$	−46.6938	−	144.362i	−0.0933876	−	0.288724i
$501$		0			0
$502$	366.627	−	503.914i	0.730333	−	1.00381i
$503$	−94.5144	+	54.5679i	−0.187901	+	0.108485i	−0.591000	−	0.806672i	$-0.701267\pi$
$503$	−94.5144	+	54.5679i	−0.187901	+	0.108485i	0.403098	+	0.915157i	$0.367933\pi$
$504$		0			0
$505$	−10.3280	+	17.8887i	−0.0204515	+	0.0354231i
$506$	−505.822	+	224.804i	−0.999649	+	0.444276i
$507$		0			0
$508$	459.658	+	414.987i	0.904838	+	0.816903i
$509$	177.370	−	148.831i	0.348467	−	0.292399i	−0.451707	−	0.892166i	$-0.649185\pi$
$509$	177.370	−	148.831i	0.348467	−	0.292399i	0.800174	+	0.599768i	$0.204740\pi$
$510$		0			0
$511$	140.805	+	386.859i	0.275548	+	0.757062i
$512$	−416.011	+	298.461i	−0.812521	+	0.582931i
$513$		0			0
$514$	263.295	−	538.924i	0.512246	−	1.04849i
$515$	−12.5460	−	34.4699i	−0.0243612	−	0.0669318i
$516$		0			0
$517$	469.643	−	394.077i	0.908400	−	0.762238i
$518$	5.57520	−	19.3943i	0.0107629	−	0.0374408i
$519$		0			0
$520$	43.3593	+	23.1656i	0.0833832	+	0.0445493i
$521$	96.0523	−	166.367i	0.184361	−	0.319323i	−0.759000	−	0.651091i	$-0.774312\pi$
$521$	96.0523	−	166.367i	0.184361	−	0.319323i	0.943361	+	0.331768i	$0.107645\pi$
$522$		0			0
$523$	295.086	−	170.368i	0.564217	−	0.325751i	−0.190619	−	0.981664i	$-0.561050\pi$
$523$	295.086	−	170.368i	0.564217	−	0.325751i	0.754836	+	0.655913i	$0.227716\pi$
$524$	164.602	+	310.568i	0.314126	+	0.592687i
$525$		0			0
$526$	272.156	+	282.202i	0.517408	+	0.536505i
$527$	108.661	−	298.543i	0.206187	−	0.566495i
$528$		0			0
$529$	−120.574	+	683.812i	−0.227929	+	1.29265i
$530$	−66.8301	+	4.62854i	−0.126094	+	0.00873310i
$531$		0			0
$532$	−261.705	+	36.4252i	−0.491927	+	0.0684685i
$533$	−91.4146	−	76.7059i	−0.171509	−	0.143914i
$534$		0			0
$535$	46.3246	−	8.16827i	0.0865880	−	0.0152678i
$536$	258.599	+	202.872i	0.482460	+	0.378492i
$537$		0			0
$538$	−23.2239	+	219.555i	−0.0431671	+	0.408096i
$539$			205.910i			0.382022i
$540$		0			0
$541$	−543.807			−1.00519			−0.502595	−	0.864522i	$-0.667621\pi$
$541$	−543.807			−1.00519			−0.502595	+	0.864522i	$0.667621\pi$
$542$	−314.215	−	33.2367i	−0.579733	−	0.0613223i
$543$		0			0
$544$	435.912	+	1.44986i	0.801309	+	0.00266518i
$545$	25.7864	+	146.242i	0.0473145	+	0.268334i
$546$		0			0
$547$	−163.630	+	195.007i	−0.299141	+	0.356502i	−0.894588	−	0.446893i	$-0.852531\pi$
$547$	−163.630	+	195.007i	−0.299141	+	0.356502i	0.595447	+	0.803395i	$0.296975\pi$
$548$	1044.35	−	145.357i	1.90574	−	0.265250i
$549$		0			0
$550$	26.6916	+	385.392i	0.0485302	+	0.700713i
$551$	−550.976	−	97.1519i	−0.999956	−	0.176319i
$552$		0			0
$553$	99.9461	+	36.3774i	0.180734	+	0.0657819i
$554$	−250.497	+	241.581i	−0.452161	+	0.436066i
$555$		0			0
$556$	−415.411	−	783.788i	−0.747142	−	1.40969i
$557$	104.885	+	181.666i	0.188303	+	0.326150i	0.944685	−	0.327980i	$-0.106368\pi$
$557$	104.885	+	181.666i	0.188303	+	0.326150i	−0.756382	+	0.654131i	$0.773035\pi$
$558$		0			0
$559$	403.818	+	233.144i	0.722393	+	0.417074i
$560$	34.4806	+	47.7251i	0.0615726	+	0.0852233i
$561$		0			0
$562$	714.157	+	205.296i	1.27074	+	0.365295i
$563$	436.787	+	520.543i	0.775821	+	0.924588i	0.998737	−	0.0502501i	$-0.0160018\pi$
$563$	436.787	+	520.543i	0.775821	+	0.924588i	−0.222916	+	0.974838i	$0.571557\pi$
$564$		0			0
$565$	55.8677	−	20.3342i	0.0988809	−	0.0359897i
$566$	749.361	+	366.105i	1.32396	+	0.646829i
$567$		0			0
$568$	−142.554	−	677.306i	−0.250975	−	1.19244i
$569$	727.101	−	264.643i	1.27786	−	0.465102i	0.388135	−	0.921603i	$-0.373120\pi$
$569$	727.101	−	264.643i	1.27786	−	0.465102i	0.889723	+	0.456501i	$0.150897\pi$
$570$		0			0
$571$	706.930	+	842.487i	1.23806	+	1.47546i	0.825377	+	0.564582i	$0.190962\pi$
$571$	706.930	+	842.487i	1.23806	+	1.47546i	0.412679	+	0.910876i	$0.364593\pi$
$572$	−188.055	−	169.779i	−0.328768	−	0.296817i
$573$		0			0
$574$	−58.0454	−	130.606i	−0.101124	−	0.227536i
$575$	739.414	+	426.901i	1.28594	+	0.742436i
$576$		0			0
$577$	−26.4305	−	45.7790i	−0.0458068	−	0.0793398i	0.842213	−	0.539145i	$-0.181253\pi$
$577$	−26.4305	−	45.7790i	−0.0458068	−	0.0793398i	−0.888020	+	0.459805i	$0.847919\pi$
$578$	167.276	+	121.703i	0.289404	+	0.210559i
$579$		0			0
$580$	38.3667	+	118.617i	0.0661495	+	0.204513i
$581$	98.3534	+	35.7977i	0.169283	+	0.0616139i
$582$		0			0
$583$	340.006	+	59.9522i	0.583200	+	0.102834i
$584$	458.722	+	511.512i	0.785483	+	0.875876i
$585$		0			0
$586$	−49.4544	−	73.4244i	−0.0843931	−	0.125298i
$587$	−714.090	+	851.019i	−1.21651	+	1.44978i	−0.360543	+	0.932743i	$0.617409\pi$
$587$	−714.090	+	851.019i	−1.21651	+	1.44978i	−0.855965	+	0.517034i	$0.827036\pi$
$588$		0			0
$589$	55.8091	+	316.509i	0.0947522	+	0.537367i
$590$	65.1224	−	16.1908i	0.110377	−	0.0274421i
$591$		0			0
$592$	−3.43123	−	33.5032i	−0.00579599	−	0.0565933i
$593$	−1059.78			−1.78715			−0.893575	−	0.448914i	$-0.851811\pi$
$593$	−1059.78			−1.78715			−0.893575	+	0.448914i	$0.851811\pi$
$594$		0			0
$595$		−	50.1283i		−	0.0842492i
$596$	3.21866	+	2.01720i	0.00540044	+	0.00338457i
$597$		0			0
$598$	−543.405	+	135.102i	−0.908705	+	0.225924i
$599$	−771.927	+	136.112i	−1.28869	+	0.227231i	−0.775668	−	0.631142i	$-0.782587\pi$
$599$	−771.927	+	136.112i	−1.28869	+	0.227231i	−0.513026	+	0.858373i	$0.671476\pi$
$600$		0			0
$601$	−733.365	−	615.367i	−1.22024	−	1.02390i	−0.998812	−	0.0487281i	$-0.984483\pi$
$601$	−733.365	−	615.367i	−1.22024	−	1.02390i	−0.221430	−	0.975176i	$-0.571072\pi$
$602$	311.983	+	463.198i	0.518244	+	0.769431i
$603$		0			0
$604$	827.329	+	335.544i	1.36975	+	0.555536i
$605$	7.78332	−	44.1414i	0.0128650	−	0.0729610i
$606$		0			0
$607$	354.168	−	973.069i	0.583473	−	1.60308i	−0.198729	−	0.980055i	$-0.563681\pi$
$607$	354.168	−	973.069i	0.583473	−	1.60308i	0.782202	−	0.623025i	$-0.214096\pi$
$608$	−382.628	+	219.217i	−0.629322	+	0.360554i
$609$		0			0
$610$	107.384	+	78.1281i	0.176039	+	0.128079i
$611$	537.097	−	310.093i	0.879046	−	0.507517i
$612$		0			0
$613$	−366.538	+	634.862i	−0.597941	+	1.03566i	0.395184	+	0.918602i	$0.370681\pi$
$613$	−366.538	+	634.862i	−0.597941	+	1.03566i	−0.993125	+	0.117062i	$0.962652\pi$
$614$	−262.489	−	590.618i	−0.427507	−	0.961919i
$615$		0			0
$616$	−113.110	−	281.573i	−0.183620	−	0.457098i
$617$	46.7240	−	39.2061i	0.0757278	−	0.0635431i	−0.604138	−	0.796880i	$-0.706482\pi$
$617$	46.7240	−	39.2061i	0.0757278	−	0.0635431i	0.679866	+	0.733337i	$0.262038\pi$
$618$		0			0
$619$	−283.250	−	778.223i	−0.457593	−	1.25723i	−0.927272	−	0.374389i	$-0.877852\pi$
$619$	−283.250	−	778.223i	−0.457593	−	1.25723i	0.469678	−	0.882838i	$-0.344370\pi$
$620$	56.4925	−	44.0159i	0.0911169	−	0.0709933i
$621$		0			0
$622$	−6.93773	−	3.38947i	−0.0111539	−	0.00544931i
$623$	−218.367	−	599.958i	−0.350508	−	0.963014i
$624$		0			0
$625$	445.185	−	373.555i	0.712296	−	0.597687i
$626$	−57.5898	−	16.5551i	−0.0919965	−	0.0264458i
$627$		0			0
$628$	26.7279	−	737.263i	0.0425603	−	1.17399i
$629$	−14.3369	+	24.8322i	−0.0227931	+	0.0394788i
$630$		0			0
$631$	−273.648	+	157.991i	−0.433673	+	0.250381i	−0.700910	−	0.713250i	$-0.747223\pi$
$631$	−273.648	+	157.991i	−0.433673	+	0.250381i	0.267237	+	0.963631i	$0.413889\pi$
$632$	177.411	−	5.84089i	0.280714	−	0.00924192i
$633$		0			0
$634$	−807.899	+	779.141i	−1.27429	+	1.22893i
$635$	40.6492	−	111.683i	0.0640145	−	0.175878i
$636$		0			0
$637$	−36.1707	+	205.134i	−0.0567828	+	0.322031i
$638$	−44.3927	−	640.972i	−0.0695810	−	1.00466i
$639$		0			0
$640$	83.0880	+	52.4587i	0.129825	+	0.0819667i
$641$	−445.886	−	374.143i	−0.695610	−	0.583686i	0.224911	−	0.974379i	$-0.427791\pi$
$641$	−445.886	−	374.143i	−0.695610	−	0.583686i	−0.920521	+	0.390693i	$0.872235\pi$
$642$		0			0
$643$	−884.213	+	155.911i	−1.37514	+	0.242474i	−0.811888	−	0.583814i	$-0.801560\pi$
$643$	−884.213	+	155.911i	−1.37514	+	0.242474i	−0.563249	+	0.826287i	$0.690449\pi$
$644$	−655.800	−	140.307i	−1.01832	−	0.217868i
$645$		0			0
$646$	373.362	+	39.4931i	0.577960	+	0.0611348i
$647$			822.404i			1.27110i	0.772058	+	0.635552i	$0.219227\pi$
$647$			822.404i			1.27110i	−0.772058	+	0.635552i	$0.780773\pi$
$648$		0			0
$649$	−345.843			−0.532885
$650$	−41.1079	+	388.628i	−0.0632429	+	0.597889i
$651$		0			0
$652$	−175.767	+	821.544i	−0.269582	+	1.26004i
$653$	199.644	+	1132.24i	0.305734	+	1.73390i	0.620030	+	0.784578i	$0.287120\pi$
$653$	199.644	+	1132.24i	0.305734	+	1.73390i	−0.314296	+	0.949325i	$0.601768\pi$
$654$		0			0
$655$	43.3611	−	51.6758i	0.0662002	−	0.0788943i
$656$	−171.142	−	166.152i	−0.260887	−	0.253280i
$657$		0			0
$658$	741.013	−	51.3214i	1.12616	−	0.0779960i
$659$	354.825	+	62.5652i	0.538430	+	0.0949397i	0.436249	−	0.899826i	$-0.356307\pi$
$659$	354.825	+	62.5652i	0.538430	+	0.0949397i	0.102181	+	0.994766i	$0.467418\pi$
$660$		0			0
$661$	766.959	+	279.150i	1.16030	+	0.422315i	0.849205	−	0.528063i	$-0.177082\pi$
$661$	766.959	+	279.150i	1.16030	+	0.422315i	0.311097	+	0.950378i	$0.399304\pi$
$662$	195.068	+	202.267i	0.294664	+	0.305540i
$663$		0			0
$664$	174.584	−	5.74781i	0.262928	−	0.00865634i
$665$	25.3552	+	43.9164i	0.0381281	+	0.0660398i
$666$		0			0
$667$	−1229.77	−	710.008i	−1.84373	−	1.06448i
$668$	527.031	+	19.1064i	0.788969	+	0.0286024i
$669$		0			0
$670$	17.4275	−	60.6247i	0.0260112	−	0.0904846i
$671$	−439.929	−	524.287i	−0.655632	−	0.781352i
$672$		0			0
$673$	−218.010	+	79.3492i	−0.323938	+	0.117904i	−0.498870	−	0.866677i	$-0.666252\pi$
$673$	−218.010	+	79.3492i	−0.323938	+	0.117904i	0.174932	+	0.984580i	$0.444029\pi$
$674$	372.272	−	761.983i	0.552332	−	1.13054i
$675$		0			0
$676$	257.956	+	331.075i	0.381591	+	0.489756i
$677$	115.647	−	42.0921i	0.170823	−	0.0621744i	−0.255193	−	0.966890i	$-0.582139\pi$
$677$	115.647	−	42.0921i	0.170823	−	0.0621744i	0.426016	+	0.904716i	$0.359917\pi$
$678$		0			0
$679$	−503.847	−	600.461i	−0.742042	−	0.884331i
$680$	−31.1849	−	77.6309i	−0.0458601	−	0.114163i
$681$		0			0
$682$	−337.280	+	149.898i	−0.494545	+	0.219792i
$683$	−293.573	−	169.494i	−0.429829	−	0.248162i	0.269445	−	0.963016i	$-0.413160\pi$
$683$	−293.573	−	169.494i	−0.429829	−	0.248162i	−0.699274	+	0.714854i	$0.746493\pi$
$684$		0			0
$685$	−101.181	−	175.251i	−0.147710	−	0.255841i
$686$	−423.145	+	581.596i	−0.616830	+	0.847807i
$687$		0			0
$688$	771.306	+	523.244i	1.12108	+	0.760529i
$689$	328.193	+	119.452i	0.476332	+	0.173371i
$690$		0			0
$691$	757.805	+	133.621i	1.09668	+	0.193374i	0.692580	−	0.721342i	$-0.256474\pi$
$691$	757.805	+	133.621i	1.09668	+	0.193374i	0.404099	+	0.914715i	$0.367585\pi$
$692$	304.884	−	751.734i	0.440584	−	1.08632i
$693$		0			0
$694$	−188.390	+	126.888i	−0.271455	+	0.182836i
$695$	−109.432	+	130.415i	−0.157456	+	0.187648i
$696$		0			0
$697$	35.2649	+	199.997i	0.0505952	+	0.286940i
$698$	48.6108	+	195.521i	0.0696429	+	0.280116i
$699$		0			0
$700$	−248.557	+	396.599i	−0.355081	+	0.566570i
$701$	−118.777			−0.169440			−0.0847199	−	0.996405i	$-0.527000\pi$
$701$	−118.777			−0.169440			−0.0847199	+	0.996405i	$0.527000\pi$
$702$		0			0
$703$		−	29.0066i		−	0.0412612i
$704$	−350.333	−	365.690i	−0.497632	−	0.519446i
$705$		0			0
$706$	12.5453	+	50.4593i	0.0177695	+	0.0714721i
$707$	127.021	−	22.3971i	0.179661	−	0.0316791i
$708$		0			0
$709$	176.615	+	148.198i	0.249104	+	0.209023i	0.758787	−	0.651339i	$-0.225793\pi$
$709$	176.615	+	148.198i	0.249104	+	0.209023i	−0.509682	+	0.860363i	$0.670237\pi$
$710$	−110.175	+	74.2076i	−0.155177	+	0.104518i
$711$		0			0
$712$	−711.407	−	793.275i	−0.999167	−	1.11415i
$713$	−141.650	+	803.338i	−0.198668	+	1.12670i
$714$		0			0
$715$	−16.6304	+	45.6916i	−0.0232593	+	0.0639044i
$716$	262.930	−	85.0447i	0.367221	−	0.118778i
$717$		0			0
$718$	69.0599	−	94.9199i	0.0961837	−	0.132200i
$719$	−157.002	+	90.6454i	−0.218362	+	0.126072i	−0.605192	−	0.796080i	$-0.706904\pi$
$719$	−157.002	+	90.6454i	−0.218362	+	0.126072i	0.386829	+	0.922151i	$0.373570\pi$
$720$		0			0
$721$	−114.525	+	198.362i	−0.158841	+	0.275121i
$722$	312.704	−	138.976i	0.433108	−	0.192487i
$723$		0			0
$724$	240.504	−	266.393i	0.332188	−	0.367946i
$725$	−759.189	+	637.035i	−1.04716	+	0.878669i
$726$		0			0
$727$	129.850	+	356.761i	0.178611	+	0.490730i	0.996399	−	0.0847899i	$-0.0270219\pi$
$727$	129.850	+	356.761i	0.178611	+	0.490730i	−0.817788	+	0.575520i	$0.804800\pi$
$728$	−63.2216	−	300.380i	−0.0868428	−	0.412610i
$729$		0			0
$730$	57.8836	−	118.479i	0.0792926	−	0.162300i
$731$	−271.405	−	745.678i	−0.371279	−	1.02008i
$732$		0			0
$733$	201.798	−	169.329i	0.275305	−	0.231008i	−0.494672	−	0.869079i	$-0.664712\pi$
$733$	201.798	−	169.329i	0.275305	−	0.231008i	0.769977	+	0.638071i	$0.220268\pi$
$734$	60.4335	−	210.229i	0.0823345	−	0.286415i
$735$		0			0
$736$	−1102.89	+	190.689i	−1.49849	+	0.259088i
$737$	−162.549	+	281.543i	−0.220555	+	0.382013i
$738$		0			0
$739$	−515.106	+	297.397i	−0.697032	+	0.402431i	−0.806241	−	0.591587i	$-0.798501\pi$
$739$	−515.106	+	297.397i	−0.697032	+	0.402431i	0.109209	+	0.994019i	$0.465168\pi$
$740$	−5.71100	+	3.02686i	−0.00771757	+	0.00409035i
$741$		0			0
$742$	290.374	+	301.092i	0.391340	+	0.405784i
$743$	−364.905	+	1002.57i	−0.491124	+	1.34935i	0.408528	+	0.912746i	$0.366042\pi$
$743$	−364.905	+	1002.57i	−0.491124	+	1.34935i	−0.899652	+	0.436607i	$0.856180\pi$
$744$		0			0
$745$	0.126592	−	0.717937i	0.000169922	−	0.000963674i
$746$	−133.652	+	9.25655i	−0.179159	+	0.0124082i
$747$		0			0
$748$	59.4385	+	427.048i	0.0794632	+	0.570920i
$749$	−225.003	−	188.800i	−0.300405	−	0.252070i
$750$		0			0
$751$	−923.903	+	162.909i	−1.23023	+	0.216923i	−0.750724	−	0.660616i	$-0.770295\pi$
$751$	−923.903	+	162.909i	−1.23023	+	0.216923i	−0.479506	+	0.877539i	$0.659184\pi$
$752$	1115.64	−	540.463i	1.48356	−	0.718701i
$753$		0			0
$754$	68.3693	−	646.354i	0.0906755	−	0.857234i
$755$		−	171.342i		−	0.226943i
$756$		0			0
$757$	−496.473			−0.655843			−0.327922	−	0.944705i	$-0.606348\pi$
$757$	−496.473			−0.655843			−0.327922	+	0.944705i	$0.606348\pi$
$758$	−550.084	−	58.1861i	−0.725704	−	0.0767627i
$759$		0			0
$760$	66.5866	+	52.2375i	0.0876139	+	0.0687335i
$761$	34.9002	+	197.929i	0.0458610	+	0.260091i	0.999114	−	0.0420821i	$-0.0133991\pi$
$761$	34.9002	+	197.929i	0.0458610	+	0.260091i	−0.953253	+	0.302173i	$0.902288\pi$
$762$		0			0
$763$	596.023	−	710.312i	0.781157	−	0.930947i
$764$	−163.067	−	1171.59i	−0.213438	−	1.53349i
$765$		0			0
$766$	5.56848	+	80.4015i	0.00726956	+	0.104963i
$767$	−344.539	−	60.7515i	−0.449203	−	0.0792067i
$768$		0			0
$769$	−608.961	−	221.644i	−0.791886	−	0.288223i	−0.0857663	−	0.996315i	$-0.527334\pi$
$769$	−608.961	−	221.644i	−0.791886	−	0.288223i	−0.706120	+	0.708092i	$0.749556\pi$
$770$	−41.9186	+	40.4264i	−0.0544397	+	0.0525019i
$771$		0			0
$772$	1100.40	−	583.215i	1.42539	−	0.755460i
$773$	−581.802	−	1007.71i	−0.752654	−	1.30364i	−0.946532	−	0.322610i	$-0.895440\pi$
$773$	−581.802	−	1007.71i	−0.752654	−	1.30364i	0.193878	−	0.981026i	$-0.437893\pi$
$774$		0			0
$775$	493.037	+	284.655i	0.636177	+	0.367297i
$776$	−1153.83	−	616.457i	−1.48689	−	0.794404i
$777$		0			0
$778$	286.344	+	82.3141i	0.368052	+	0.105802i
$779$	−132.055	−	157.376i	−0.169518	−	0.202024i
$780$		0			0
$781$	643.317	−	234.148i	0.823710	−	0.299806i
$782$	856.205	+	418.304i	1.09489	+	0.534916i
$783$		0			0
$784$	−101.800	+	403.720i	−0.129847	+	0.514949i
$785$	−133.049	+	48.4259i	−0.169489	+	0.0616890i
$786$		0			0
$787$	−179.534	−	213.961i	−0.228125	−	0.271869i	0.639825	−	0.768521i	$-0.279007\pi$
$787$	−179.534	−	213.961i	−0.228125	−	0.271869i	−0.867950	+	0.496652i	$0.834563\pi$
$788$	386.247	−	427.824i	0.490161	−	0.542924i
$789$		0			0
$790$	−13.8356	−	31.1310i	−0.0175135	−	0.0394064i
$791$	−321.500	−	185.618i	−0.406447	−	0.234662i
$792$		0			0
$793$	−346.173	−	599.590i	−0.436537	−	0.756103i
$794$	1207.69	+	878.668i	1.52102	+	1.10664i
$795$		0			0
$796$	−741.661	+	239.890i	−0.931735	+	0.301369i
$797$	1142.08	+	415.682i	1.43297	+	0.521558i	0.937781	−	0.347228i	$-0.112877\pi$
$797$	1142.08	+	415.682i	1.43297	+	0.521558i	0.495188	+	0.868786i	$0.335099\pi$
$798$		0			0
$799$	−1039.40	−	183.275i	−1.30088	−	0.229380i
$800$	−138.202	+	768.819i	−0.172752	+	0.961024i
$801$		0			0
$802$	−64.7362	−	96.1132i	−0.0807185	−	0.119842i
$803$	−436.830	+	520.594i	−0.543998	+	0.648312i
$804$		0			0
$805$	22.3501	+	126.754i	0.0277641	+	0.157458i
$806$	−362.340	+	90.0855i	−0.449553	+	0.111769i
$807$		0			0
$808$	182.776	−	113.705i	0.226208	−	0.140724i
$809$	1111.49			1.37390			0.686952	−	0.726703i	$-0.258948\pi$
$809$	1111.49			1.37390			0.686952	+	0.726703i	$0.258948\pi$
$810$		0			0
$811$		−	553.768i		−	0.682821i	−0.939914	−	0.341411i	$-0.889095\pi$
$811$		−	553.768i		−	0.682821i	0.939914	−	0.341411i	$-0.110905\pi$
$812$	413.392	−	659.612i	0.509104	−	0.812330i
$813$		0			0
$814$	32.3274	−	8.03729i	0.0397142	−	0.00987382i
$815$	158.789	−	27.9987i	0.194833	−	0.0343542i
$816$		0			0
$817$	614.940	+	515.996i	0.752681	+	0.631574i
$818$	329.709	+	489.516i	0.403067	+	0.598430i
$819$		0			0
$820$	−17.2053	+	42.4220i	−0.0209821	+	0.0517341i
$821$	41.0204	−	232.638i	0.0499639	−	0.283360i	−0.949581	−	0.313522i	$-0.898491\pi$
$821$	41.0204	−	232.638i	0.0499639	−	0.283360i	0.999545	+	0.0301620i	$0.00960231\pi$
$822$		0			0
$823$	204.440	−	561.693i	0.248408	−	0.682495i	−0.751337	−	0.659918i	$-0.770591\pi$
$823$	204.440	−	561.693i	0.248408	−	0.682495i	0.999745	−	0.0225763i	$-0.00718688\pi$
$824$	−53.9564	+	378.439i	−0.0654811	+	0.459270i
$825$		0			0
$826$	−338.826	−	246.516i	−0.410201	−	0.298446i
$827$	−888.113	+	512.752i	−1.07390	+	0.620015i	−0.929244	−	0.369467i	$-0.879540\pi$
$827$	−888.113	+	512.752i	−1.07390	+	0.620015i	−0.144654	+	0.989482i	$0.546207\pi$
$828$		0			0
$829$	11.4162	−	19.7735i	0.0137711	−	0.0238522i	−0.859058	−	0.511879i	$-0.828950\pi$
$829$	11.4162	−	19.7735i	0.0137711	−	0.0238522i	0.872829	+	0.488026i	$0.162283\pi$
$830$	−13.6151	−	30.6349i	−0.0164038	−	0.0369096i
$831$		0			0
$832$	−284.775	−	425.852i	−0.342277	−	0.511842i
$833$	271.551	−	227.858i	0.325991	−	0.273539i
$834$		0			0
$835$	−34.6172	−	95.1099i	−0.0414577	−	0.113904i
$836$	−268.076	−	344.065i	−0.320665	−	0.411561i
$837$		0			0
$838$	791.908	+	386.892i	0.944998	+	0.461685i
$839$	−217.276	−	596.961i	−0.258970	−	0.711515i	−0.999232	−	0.0391958i	$-0.987520\pi$
$839$	−217.276	−	596.961i	−0.258970	−	0.711515i	0.740261	−	0.672319i	$-0.234702\pi$
$840$		0			0
$841$	618.416	−	518.913i	0.735334	−	0.617019i
$842$	130.830	+	37.6091i	0.155380	+	0.0446664i
$843$		0			0
$844$	464.101	+	16.8250i	0.549882	+	0.0199348i
$845$	40.2746	−	69.7577i	0.0476623	−	0.0825535i
$846$		0			0
$847$	−242.382	+	139.939i	−0.286165	+	0.165218i
$848$	636.996	+	285.642i	0.751174	+	0.336842i
$849$		0			0
$850$	478.712	−	461.672i	0.563190	−	0.543143i
$851$	25.1803	−	69.1824i	0.0295891	−	0.0812954i
$852$		0			0
$853$	13.1002	−	74.2950i	0.0153578	−	0.0870984i	−0.976165	−	0.217028i	$-0.930364\pi$
$853$	13.1002	−	74.2950i	0.0153578	−	0.0870984i	0.991523	+	0.129929i	$0.0414750\pi$
$854$	−57.2928	−	827.232i	−0.0670875	−	0.968656i
$855$		0			0
$856$	−465.903	−	152.410i	−0.544279	−	0.178049i
$857$	186.048	+	156.113i	0.217093	+	0.182162i	0.744848	−	0.667234i	$-0.232522\pi$
$857$	186.048	+	156.113i	0.217093	+	0.182162i	−0.527756	+	0.849396i	$0.676966\pi$
$858$		0			0
$859$	−832.750	+	146.836i	−0.969442	+	0.170939i	−0.635879	−	0.771789i	$-0.719362\pi$
$859$	−832.750	+	146.836i	−0.969442	+	0.170939i	−0.333563	+	0.942728i	$0.608251\pi$
$860$	37.4232	−	174.918i	0.0435153	−	0.203393i
$861$		0			0
$862$	106.627	+	11.2786i	0.123697	+	0.0130843i
$863$			411.636i			0.476983i	0.971145	+	0.238491i	$0.0766529\pi$
$863$			411.636i			0.476983i	−0.971145	+	0.238491i	$0.923347\pi$
$864$		0			0
$865$	−155.686			−0.179984
$866$	144.475	−	1365.85i	0.166831	−	1.57719i
$867$		0			0
$868$	−437.284	−	93.5559i	−0.503784	−	0.107783i
$869$	30.4880	+	172.906i	0.0350840	+	0.198971i
$870$		0			0
$871$	−211.393	+	251.928i	−0.242702	+	0.289241i
$872$	481.141	−	1470.81i	0.551768	−	1.68671i
$873$		0			0
$874$	−961.686	+	66.6048i	−1.10033	+	0.0762069i
$875$	179.062	+	31.5735i	0.204642	+	0.0360840i
$876$		0			0
$877$	−107.037	−	38.9581i	−0.122049	−	0.0444221i	0.280274	−	0.959920i	$-0.409575\pi$
$877$	−107.037	−	38.9581i	−0.122049	−	0.0444221i	−0.402322	+	0.915498i	$0.631797\pi$
$878$	161.073	+	167.018i	0.183455	+	0.190226i
$879$		0			0
$880$	−39.7676	+	88.6838i	−0.0451905	+	0.100777i
$881$	−238.369	−	412.868i	−0.270567	−	0.468635i	0.698440	−	0.715668i	$-0.253878\pi$
$881$	−238.369	−	412.868i	−0.270567	−	0.468635i	−0.969007	+	0.247033i	$0.920544\pi$
$882$		0			0
$883$	−554.004	−	319.854i	−0.627411	−	0.362236i	0.152338	−	0.988328i	$-0.451320\pi$
$883$	−554.004	−	319.854i	−0.627411	−	0.362236i	−0.779749	+	0.626093i	$0.784653\pi$
$884$	−15.8019	+	435.880i	−0.0178754	+	0.493077i
$885$		0			0
$886$	−71.0820	+	247.272i	−0.0802280	+	0.279088i
$887$	−106.718	−	127.182i	−0.120314	−	0.143384i	0.702525	−	0.711659i	$-0.252056\pi$
$887$	−106.718	−	127.182i	−0.120314	−	0.143384i	−0.822839	+	0.568274i	$0.807611\pi$
$888$		0			0
$889$	−697.367	+	253.821i	−0.784440	+	0.285513i
$890$	−89.7684	+	183.742i	−0.100863	+	0.206452i
$891$		0			0
$892$	468.652	−	365.148i	0.525394	−	0.409359i
$893$	1003.30	−	365.173i	1.12352	−	0.408928i
$894$		0			0
$895$	−34.0905	−	40.6274i	−0.0380899	−	0.0453938i
$896$	−82.5621	−	607.989i	−0.0921452	−	0.678559i
$897$		0			0
$898$	1322.62	−	587.815i	1.47285	−	0.654582i
$899$	−820.005	−	473.430i	−0.912130	−	0.526618i
$900$		0			0
$901$	−297.183	−	514.736i	−0.329837	−	0.571294i
$902$	138.803	−	190.779i	0.153884	−	0.211507i
$903$		0			0
$904$	−613.362	−	87.4510i	−0.678498	−	0.0967378i
$905$	−64.7254	−	23.5581i	−0.0715198	−	0.0260311i
$906$		0			0
$907$	75.7474	+	13.3563i	0.0835142	+	0.0147258i	0.215249	−	0.976559i	$-0.430944\pi$
$907$	75.7474	+	13.3563i	0.0835142	+	0.0147258i	−0.131735	+	0.991285i	$0.542055\pi$
$908$	615.881	+	249.786i	0.678283	+	0.275094i
$909$		0			0
$910$	−48.8620	+	32.9106i	−0.0536945	+	0.0361654i
$911$	913.726	−	1088.94i	1.00299	−	1.19532i	0.0223018	−	0.999751i	$-0.492901\pi$
$911$	913.726	−	1088.94i	1.00299	−	1.19532i	0.980690	−	0.195568i	$-0.0626550\pi$
$912$		0			0
$913$	30.0022	+	170.151i	0.0328611	+	0.186364i
$914$	25.6036	+	102.982i	0.0280127	+	0.112672i
$915$		0			0
$916$	788.722	+	494.308i	0.861050	+	0.539638i
$917$	−421.219			−0.459345
$918$		0			0
$919$			1228.21i			1.33646i	0.743955	+	0.668229i	$0.232948\pi$
$919$			1228.21i			1.33646i	−0.743955	+	0.668229i	$0.767052\pi$
$920$	113.466	+	182.392i	0.123332	+	0.198252i
$921$		0			0
$922$	−101.737	−	409.205i	−0.110344	−	0.443823i
$923$	682.023	−	120.259i	0.738920	−	0.130292i
$924$		0			0
$925$	−39.3610	−	33.0278i	−0.0425524	−	0.0357057i
$926$	−1050.65	+	707.654i	−1.13461	+	0.764205i
$927$		0			0
$928$	229.853	−	1278.68i	0.247686	−	1.37788i
$929$	36.4353	−	206.635i	0.0392200	−	0.222427i	−0.958898	−	0.283751i	$-0.908421\pi$
$929$	36.4353	−	206.635i	0.0392200	−	0.222427i	0.998118	+	0.0613236i	$0.0195322\pi$
$930$		0			0
$931$	−122.649	+	336.974i	−0.131738	+	0.361948i
$932$	−251.484	−	777.506i	−0.269833	−	0.834234i
$933$		0			0
$934$	−346.307	+	475.985i	−0.370779	+	0.509620i
$935$	71.6626	−	41.3744i	0.0766445	−	0.0442507i
$936$		0			0
$937$	−227.457	+	393.966i	−0.242750	+	0.420455i	−0.961497	−	0.274817i	$-0.911383\pi$
$937$	−227.457	+	393.966i	−0.242750	+	0.420455i	0.718747	+	0.695272i	$0.244716\pi$
$938$	−359.936	+	159.967i	−0.383727	+	0.170540i
$939$		0			0
$940$	−176.593	−	159.431i	−0.187864	−	0.169607i
$941$	869.171	−	729.321i	0.923667	−	0.775049i	−0.0510024	−	0.998699i	$-0.516242\pi$
$941$	869.171	−	729.321i	0.923667	−	0.775049i	0.974670	+	0.223650i	$0.0717972\pi$
$942$		0			0
$943$	−178.340	−	489.986i	−0.189120	−	0.519604i
$944$	−678.080	−	170.982i	−0.718305	−	0.181125i
$945$		0			0
$946$	−404.678	+	828.315i	−0.427778	+	0.875597i
$947$	−4.02952	−	11.0710i	−0.00425503	−	0.0116906i	0.937547	−	0.347859i	$-0.113091\pi$
$947$	−4.02952	−	11.0710i	−0.00425503	−	0.0116906i	−0.941802	+	0.336168i	$0.890869\pi$
$948$		0			0
$949$	−526.633	+	441.897i	−0.554934	+	0.465645i
$950$	−185.874	+	646.597i	−0.195657	+	0.680628i
$951$		0			0
$952$	−246.167	+	460.753i	−0.258579	+	0.483984i
$953$	67.1825	−	116.364i	0.0704958	−	0.122102i	−0.828623	−	0.559807i	$-0.810875\pi$
$953$	67.1825	−	116.364i	0.0704958	−	0.122102i	0.899119	+	0.437705i	$0.144209\pi$
$954$		0			0
$955$	−196.603	+	113.509i	−0.205867	+	0.118858i
$956$	172.387	+	325.257i	0.180322	+	0.340227i
$957$		0			0
$958$	754.483	+	782.330i	0.787560	+	0.816629i
$959$	−432.172	+	1187.38i	−0.450648	+	1.23815i
$960$		0			0
$961$	72.4243	−	410.739i	0.0753635	−	0.427408i
$962$	33.6174	−	2.32829i	0.0349453	−	0.00242026i
$963$		0			0
$964$	821.940	−	114.401i	0.852634	−	0.118673i
$965$	−183.097	−	153.636i	−0.189737	−	0.159209i
$966$		0			0
$967$	946.293	−	166.857i	0.978586	−	0.172551i	0.338594	−	0.940933i	$-0.390049\pi$
$967$	946.293	−	166.857i	0.978586	−	0.172551i	0.639992	+	0.768381i	$0.278938\pi$
$968$	−288.307	+	367.502i	−0.297838	+	0.379651i
$969$		0			0
$970$	−26.4095	+	249.672i	−0.0272263	+	0.257394i
$971$		−	1270.91i		−	1.30887i	−0.756118	−	0.654435i	$-0.772906\pi$
$971$		−	1270.91i		−	1.30887i	0.756118	−	0.654435i	$-0.227094\pi$
$972$		0			0
$973$	1063.04			1.09254
$974$	335.149	+	35.4510i	0.344095	+	0.0363973i
$975$		0			0
$976$	−603.348	−	1245.45i	−0.618184	−	1.27607i
$977$	−298.940	−	1695.37i	−0.305977	−	1.73528i	−0.618869	−	0.785494i	$-0.712409\pi$
$977$	−298.940	−	1695.37i	−0.305977	−	1.73528i	0.312892	−	0.949789i	$-0.398702\pi$
$978$		0			0
$979$	677.456	−	807.361i	0.691988	−	0.824679i
$980$	79.1439	−	11.0156i	0.0807591	−	0.0112404i
$981$		0			0
$982$	55.3937	+	799.812i	0.0564091	+	0.814473i
$983$	1386.92	+	244.552i	1.41091	+	0.248781i	0.826619	−	0.562763i	$-0.190261\pi$
$983$	1386.92	+	244.552i	1.41091	+	0.248781i	0.584291	+	0.811544i	$0.301373\pi$
$984$		0			0
$985$	−103.948	−	37.8340i	−0.105531	−	0.0384102i
$986$	−796.179	+	767.838i	−0.807483	+	0.778740i
$987$		0			0
$988$	−206.627	−	389.859i	−0.209136	−	0.394594i
$989$	1018.74	+	1764.50i	1.03007	+	1.78413i
$990$		0			0
$991$	918.471	+	530.279i	0.926812	+	0.535095i	0.885802	−	0.464064i	$-0.153609\pi$
$991$	918.471	+	530.279i	0.926812	+	0.535095i	0.0410102	+	0.999159i	$0.486942\pi$
$992$	−735.399	+	127.150i	−0.741330	+	0.128176i
$993$		0			0
$994$	797.167	+	229.158i	0.801979	+	0.230541i
$995$	96.1607	+	114.600i	0.0966440	+	0.115176i
$996$		0			0
$997$	−1156.49	+	420.929i	−1.15997	+	0.422195i	−0.849087	−	0.528252i	$-0.822847\pi$
$997$	−1156.49	+	420.929i	−1.15997	+	0.422195i	−0.310885	+	0.950448i	$0.600625\pi$
$998$	−284.174	−	138.835i	−0.284744	−	0.139113i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.19.17		204
3.2	odd	2		108.3.j.a.7.18	✓	204
4.3	odd	2	inner	324.3.j.a.19.9		204
12.11	even	2		108.3.j.a.7.26	yes	204
27.4	even	9	inner	324.3.j.a.307.9		204
27.23	odd	18		108.3.j.a.31.26	yes	204
108.23	even	18		108.3.j.a.31.18	yes	204
108.31	odd	18	inner	324.3.j.a.307.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.18	✓	204	3.2	odd	2
108.3.j.a.7.26	yes	204	12.11	even	2
108.3.j.a.31.18	yes	204	108.23	even	18
108.3.j.a.31.26	yes	204	27.23	odd	18
324.3.j.a.19.9		204	4.3	odd	2	inner
324.3.j.a.19.17		204	1.1	even	1	trivial
324.3.j.a.307.9		204	27.4	even	9	inner
324.3.j.a.307.17		204	108.31	odd	18	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.210380 + 1.98890i) q^{2} +(-3.91148 - 0.836851i) q^{4} +(0.133306 + 0.756014i) q^{5} +(3.08121 - 3.67204i) q^{7} +(2.48731 - 7.60350i) q^{8} +O(q^{10})\)	\(q+(-0.210380 + 1.98890i) q^{2} +(-3.91148 - 0.836851i) q^{4} +(0.133306 + 0.756014i) q^{5} +(3.08121 - 3.67204i) q^{7} +(2.48731 - 7.60350i) q^{8} +(-1.53168 + 0.106082i) q^{10} +(7.79262 + 1.37405i) q^{11} +(7.52188 + 2.73774i) q^{13} +(6.65511 + 6.90075i) q^{14} +(14.5994 + 6.54666i) q^{16} +(-6.81117 - 11.7973i) q^{17} +(11.9343 + 6.89025i) q^{19} +(0.111249 - 3.06869i) q^{20} +(-4.37226 + 15.2097i) q^{22} +(22.4825 + 26.7936i) q^{23} +(22.9385 - 8.34894i) q^{25} +(-7.02756 + 14.3843i) q^{26} +(-15.1250 + 11.7846i) q^{28} +(-38.1507 + 13.8857i) q^{29} +(14.9912 + 17.8658i) q^{31} +(-16.0921 + 27.6594i) q^{32} +(24.8966 - 11.0648i) q^{34} +(3.18685 + 1.83993i) q^{35} +(-1.05245 - 1.82290i) q^{37} +(-16.2148 + 22.2865i) q^{38} +(6.07993 + 0.866854i) q^{40} +(-14.0090 - 5.09885i) q^{41} +(57.3675 + 10.1154i) q^{43} +(-29.3308 - 11.8958i) q^{44} +(-58.0198 + 39.0787i) q^{46} +(49.8023 - 59.3520i) q^{47} +(4.51872 + 25.6270i) q^{49} +(11.7794 + 47.3790i) q^{50} +(-27.1306 - 17.0033i) q^{52} +43.6318 q^{53} +6.07450i q^{55} +(-20.2564 - 32.5615i) q^{56} +(-19.5912 - 78.7993i) q^{58} +(-43.0425 + 7.58956i) q^{59} +(-66.2578 - 55.5969i) q^{61} +(-38.6873 + 26.0575i) q^{62} +(-51.6265 - 37.8246i) q^{64} +(-1.06706 + 6.05160i) q^{65} +(-14.0519 + 38.6072i) q^{67} +(16.7692 + 51.8448i) q^{68} +(-4.32990 + 5.95126i) q^{70} +(74.9269 - 43.2591i) q^{71} +(-42.9421 + 74.3779i) q^{73} +(3.84699 - 1.70973i) q^{74} +(-40.9145 - 36.9383i) q^{76} +(29.0562 - 24.3811i) q^{77} +(7.58889 + 20.8503i) q^{79} +(-3.00319 + 11.9100i) q^{80} +(13.0883 - 26.7898i) q^{82} +(7.46796 + 20.5180i) q^{83} +(8.01094 - 6.72198i) q^{85} +(-32.1876 + 111.970i) q^{86} +(29.8303 - 55.8335i) q^{88} +(66.5965 - 115.349i) q^{89} +(33.2296 - 19.1851i) q^{91} +(-65.5176 - 123.617i) q^{92} +(107.568 + 111.538i) q^{94} +(-3.61822 + 9.94098i) q^{95} +(28.3954 - 161.038i) q^{97} +(-51.9202 + 3.59591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more