LMFDB - Embedded newform 324.3.j.a.307.22

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			307.22
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00307 - 1.73027i) q^{2} +(-1.98770 - 3.47117i) q^{4} +(-0.608002 + 3.44815i) q^{5} +(5.71739 + 6.81372i) q^{7} +(-7.99989 - 0.0425704i) q^{8} +O(q^{10})$	\(q+(1.00307 - 1.73027i) q^{2} +(-1.98770 - 3.47117i) q^{4} +(-0.608002 + 3.44815i) q^{5} +(5.71739 + 6.81372i) q^{7} +(-7.99989 - 0.0425704i) q^{8} +(5.35638 + 4.51075i) q^{10} +(5.38256 - 0.949091i) q^{11} +(21.3373 - 7.76615i) q^{13} +(17.5245 - 3.05801i) q^{14} +(-8.09811 + 13.7993i) q^{16} +(8.12631 - 14.0752i) q^{17} +(19.5372 - 11.2798i) q^{19} +(13.1777 - 4.74341i) q^{20} +(3.75690 - 10.2653i) q^{22} +(-22.1707 + 26.4221i) q^{23} +(11.9722 + 4.35753i) q^{25} +(7.96527 - 44.7094i) q^{26} +(12.2872 - 33.3897i) q^{28} +(-24.1480 - 8.78914i) q^{29} +(-14.3967 + 17.1573i) q^{31} +(15.7536 + 27.8536i) q^{32} +(-16.2027 - 28.1791i) q^{34} +(-26.9709 + 15.5717i) q^{35} +(7.88574 - 13.6585i) q^{37} +(0.0800315 - 45.1192i) q^{38} +(5.01074 - 27.5590i) q^{40} +(49.6190 - 18.0598i) q^{41} +(-9.61800 + 1.69591i) q^{43} +(-13.9934 - 16.7973i) q^{44} +(23.4786 + 64.8646i) q^{46} +(14.9904 + 17.8648i) q^{47} +(-5.22945 + 29.6577i) q^{49} +(19.5487 - 16.3443i) q^{50} +(-69.3698 - 58.6288i) q^{52} -4.09859 q^{53} +19.1370i q^{55} +(-45.4484 - 54.7523i) q^{56} +(-39.4297 + 32.9665i) q^{58} +(28.0094 + 4.93882i) q^{59} +(-31.1357 + 26.1260i) q^{61} +(15.2459 + 42.1201i) q^{62} +(63.9964 + 0.681117i) q^{64} +(13.8057 + 78.2962i) q^{65} +(30.9299 + 84.9793i) q^{67} +(-65.0100 - 0.230627i) q^{68} +(-0.110483 + 62.2866i) q^{70} +(-87.8991 - 50.7486i) q^{71} +(-16.0025 - 27.7171i) q^{73} +(-15.7230 - 27.3449i) q^{74} +(-77.9884 - 45.3963i) q^{76} +(37.2410 + 31.2489i) q^{77} +(8.65102 - 23.7685i) q^{79} +(-42.6584 - 36.3135i) q^{80} +(18.5229 - 103.970i) q^{82} +(-16.3859 + 45.0198i) q^{83} +(43.5925 + 36.5785i) q^{85} +(-6.71314 + 18.3429i) q^{86} +(-43.1003 + 7.36348i) q^{88} +(-45.0663 - 78.0571i) q^{89} +(174.910 + 100.984i) q^{91} +(135.784 + 24.4394i) q^{92} +(45.9475 - 8.01777i) q^{94} +(27.0159 + 74.2255i) q^{95} +(-25.7741 - 146.172i) q^{97} +(46.0705 + 38.7972i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00307	−	1.73027i	0.501535	−	0.865137i
$2$	1.00307	−	1.73027i	0.501535	−	0.865137i
$3$		0			0
$3$		0			0
$4$	−1.98770	−	3.47117i	−0.496925	−	0.867794i
$5$	−0.608002	+	3.44815i	−0.121600	+	0.689631i	0.861669	+	0.507471i	$0.169420\pi$
$5$	−0.608002	+	3.44815i	−0.121600	+	0.689631i	−0.983269	+	0.182159i	$0.941691\pi$
$6$		0			0
$7$	5.71739	+	6.81372i	0.816769	+	0.973388i	0.999953	−	0.00969079i	$-0.00308472\pi$
$7$	5.71739	+	6.81372i	0.816769	+	0.973388i	−0.183184	+	0.983079i	$0.558640\pi$
$8$	−7.99989	−	0.0425704i	−0.999986	−	0.00532130i
$9$		0			0
$10$	5.35638	+	4.51075i	0.535638	+	0.451075i
$11$	5.38256	−	0.949091i	0.489324	−	0.0862810i	0.0764579	−	0.997073i	$-0.475639\pi$
$11$	5.38256	−	0.949091i	0.489324	−	0.0862810i	0.412866	+	0.910792i	$0.364528\pi$
$12$		0			0
$13$	21.3373	−	7.76615i	1.64133	−	0.597396i	0.654061	−	0.756442i	$-0.273064\pi$
$13$	21.3373	−	7.76615i	1.64133	−	0.597396i	0.987271	+	0.159046i	$0.0508418\pi$
$14$	17.5245	−	3.05801i	1.25175	−	0.218429i
$15$		0			0
$16$	−8.09811	+	13.7993i	−0.506132	+	0.862456i
$17$	8.12631	−	14.0752i	0.478018	−	0.827951i	−0.521664	−	0.853151i	$-0.674689\pi$
$17$	8.12631	−	14.0752i	0.478018	−	0.827951i	0.999682	+	0.0251993i	$0.00802204\pi$
$18$		0			0
$19$	19.5372	−	11.2798i	1.02828	−	0.593675i	0.111785	−	0.993732i	$-0.464343\pi$
$19$	19.5372	−	11.2798i	1.02828	−	0.593675i	0.916490	+	0.400057i	$0.131010\pi$
$20$	13.1777	−	4.74341i	0.658883	−	0.237170i
$21$		0			0
$22$	3.75690	−	10.2653i	0.170768	−	0.466605i
$23$	−22.1707	+	26.4221i	−0.963945	+	1.14879i	0.0248778	+	0.999690i	$0.492080\pi$
$23$	−22.1707	+	26.4221i	−0.963945	+	1.14879i	−0.988823	+	0.149095i	$0.952364\pi$
$24$		0			0
$25$	11.9722	+	4.35753i	0.478889	+	0.174301i
$26$	7.96527	−	44.7094i	0.306357	−	1.71959i
$27$		0			0
$28$	12.2872	−	33.3897i	0.438827	−	1.19249i
$29$	−24.1480	−	8.78914i	−0.832688	−	0.303074i	−0.109727	−	0.993962i	$-0.534998\pi$
$29$	−24.1480	−	8.78914i	−0.832688	−	0.303074i	−0.722962	+	0.690888i	$0.757220\pi$
$30$		0			0
$31$	−14.3967	+	17.1573i	−0.464408	+	0.553460i	−0.946518	−	0.322651i	$-0.895426\pi$
$31$	−14.3967	+	17.1573i	−0.464408	+	0.553460i	0.482110	+	0.876111i	$0.339871\pi$
$32$	15.7536	+	27.8536i	0.492300	+	0.870426i
$33$		0			0
$34$	−16.2027	−	28.1791i	−0.476549	−	0.828798i
$35$	−26.9709	+	15.5717i	−0.770598	+	0.444905i
$36$		0			0
$37$	7.88574	−	13.6585i	0.213128	−	0.369149i	−0.739564	−	0.673086i	$-0.764968\pi$
$37$	7.88574	−	13.6585i	0.213128	−	0.369149i	0.952692	+	0.303938i	$0.0983015\pi$
$38$	0.0800315	−	45.1192i	0.00210609	−	1.18735i
$39$		0			0
$40$	5.01074	−	27.5590i	0.125268	−	0.688974i
$41$	49.6190	−	18.0598i	1.21022	−	0.440484i	0.343439	−	0.939175i	$-0.388408\pi$
$41$	49.6190	−	18.0598i	1.21022	−	0.440484i	0.866780	+	0.498691i	$0.166186\pi$
$42$		0			0
$43$	−9.61800	+	1.69591i	−0.223674	+	0.0394398i	−0.284362	−	0.958717i	$-0.591782\pi$
$43$	−9.61800	+	1.69591i	−0.223674	+	0.0394398i	0.0606877	+	0.998157i	$0.480671\pi$
$44$	−13.9934	−	16.7973i	−0.318031	−	0.381757i
$45$		0			0
$46$	23.4786	+	64.8646i	0.510404	+	1.41010i
$47$	14.9904	+	17.8648i	0.318944	+	0.380103i	0.901567	−	0.432640i	$-0.142418\pi$
$47$	14.9904	+	17.8648i	0.318944	+	0.380103i	−0.582623	+	0.812743i	$0.697973\pi$
$48$		0			0
$49$	−5.22945	+	29.6577i	−0.106724	+	0.605259i
$50$	19.5487	−	16.3443i	0.390974	−	0.326886i
$51$		0			0
$52$	−69.3698	−	58.6288i	−1.33403	−	1.12748i
$53$	−4.09859			−0.0773318			−0.0386659	−	0.999252i	$-0.512311\pi$
$53$	−4.09859			−0.0773318			−0.0386659	+	0.999252i	$0.512311\pi$
$54$		0			0
$55$			19.1370i			0.347945i
$56$	−45.4484	−	54.7523i	−0.811578	−	0.977720i
$57$		0			0
$58$	−39.4297	+	32.9665i	−0.679823	+	0.568387i
$59$	28.0094	+	4.93882i	0.474736	+	0.0837088i	0.405897	−	0.913919i	$-0.366959\pi$
$59$	28.0094	+	4.93882i	0.474736	+	0.0837088i	0.0688395	+	0.997628i	$0.478070\pi$
$60$		0			0
$61$	−31.1357	+	26.1260i	−0.510422	+	0.428295i	−0.861278	−	0.508135i	$-0.830335\pi$
$61$	−31.1357	+	26.1260i	−0.510422	+	0.428295i	0.350856	+	0.936430i	$0.385891\pi$
$62$	15.2459	+	42.1201i	0.245902	+	0.679357i
$63$		0			0
$64$	63.9964	+	0.681117i	0.999943	+	0.0106425i
$65$	13.8057	+	78.2962i	0.212396	+	1.20456i
$66$		0			0
$67$	30.9299	+	84.9793i	0.461641	+	1.26835i	0.924251	+	0.381785i	$0.124691\pi$
$67$	30.9299	+	84.9793i	0.461641	+	1.26835i	−0.462610	+	0.886562i	$0.653087\pi$
$68$	−65.0100	−	0.230627i	−0.956030	−	0.00339158i
$69$		0			0
$70$	−0.110483	+	62.2866i	−0.00157832	+	0.889808i
$71$	−87.8991	−	50.7486i	−1.23802	−	0.714769i	−0.269328	−	0.963049i	$-0.586801\pi$
$71$	−87.8991	−	50.7486i	−1.23802	−	0.714769i	−0.968688	+	0.248280i	$0.920135\pi$
$72$		0			0
$73$	−16.0025	−	27.7171i	−0.219212	−	0.379687i	0.735355	−	0.677682i	$-0.237015\pi$
$73$	−16.0025	−	27.7171i	−0.219212	−	0.379687i	−0.954567	+	0.297995i	$0.903682\pi$
$74$	−15.7230	−	27.3449i	−0.212473	−	0.369526i
$75$		0			0
$76$	−77.9884	−	45.3963i	−1.02616	−	0.597319i
$77$	37.2410	+	31.2489i	0.483650	+	0.405830i
$78$		0			0
$79$	8.65102	−	23.7685i	0.109507	−	0.300867i	−0.872820	−	0.488042i	$-0.837711\pi$
$79$	8.65102	−	23.7685i	0.109507	−	0.300867i	0.982326	+	0.187176i	$0.0599334\pi$
$80$	−42.6584	−	36.3135i	−0.533230	−	0.453919i
$81$		0			0
$82$	18.5229	−	103.970i	0.225889	−	1.26792i
$83$	−16.3859	+	45.0198i	−0.197420	+	0.542408i	−0.998416	−	0.0562623i	$-0.982082\pi$
$83$	−16.3859	+	45.0198i	−0.197420	+	0.542408i	0.800996	+	0.598670i	$0.204304\pi$
$84$		0			0
$85$	43.5925	+	36.5785i	0.512853	+	0.430335i
$86$	−6.71314	+	18.3429i	−0.0780597	+	0.213289i
$87$		0			0
$88$	−43.1003	+	7.36348i	−0.489776	+	0.0836759i
$89$	−45.0663	−	78.0571i	−0.506363	−	0.877047i	−0.999973	−	0.00736306i	$-0.997656\pi$
$89$	−45.0663	−	78.0571i	−0.506363	−	0.877047i	0.493610	−	0.869683i	$-0.335677\pi$
$90$		0			0
$91$	174.910	+	100.984i	1.92209	+	1.10972i
$92$	135.784	+	24.4394i	1.47592	+	0.265646i
$93$		0			0
$94$	45.9475	−	8.01777i	0.488803	−	0.0852954i
$95$	27.0159	+	74.2255i	0.284378	+	0.781321i
$96$		0			0
$97$	−25.7741	−	146.172i	−0.265713	−	1.50693i	−0.766998	−	0.641650i	$-0.778250\pi$
$97$	−25.7741	−	146.172i	−0.265713	−	1.50693i	0.501285	−	0.865282i	$-0.332861\pi$
$98$	46.0705	+	38.7972i	0.470107	+	0.395889i
$99$		0			0
$100$	−8.67141	−	50.2191i	−0.0867141	−	0.502191i
$101$	−7.81270	+	6.55563i	−0.0773534	+	0.0649072i	−0.680645	−	0.732614i	$-0.738300\pi$
$101$	−7.81270	+	6.55563i	−0.0773534	+	0.0649072i	0.603291	+	0.797521i	$0.293856\pi$
$102$		0			0
$103$	−14.2078	−	2.50522i	−0.137940	−	0.0243226i	0.104252	−	0.994551i	$-0.466755\pi$
$103$	−14.2078	−	2.50522i	−0.137940	−	0.0243226i	−0.242192	+	0.970228i	$0.577866\pi$
$104$	−171.027	+	61.2200i	−1.64449	+	0.588653i
$105$		0			0
$106$	−4.11117	+	7.09168i	−0.0387846	+	0.0669026i
$107$			81.7160i			0.763701i	0.924224	+	0.381851i	$0.124713\pi$
$107$			81.7160i			0.763701i	−0.924224	+	0.381851i	$0.875287\pi$
$108$		0			0
$109$	−193.369			−1.77402			−0.887012	−	0.461747i	$-0.847223\pi$
$109$	−193.369			−1.77402			−0.887012	+	0.461747i	$0.847223\pi$
$110$	33.1122	+	19.1957i	0.301020	+	0.174506i
$111$		0			0
$112$	−140.325	+	23.7177i	−1.25290	+	0.211765i
$113$	−0.255201	+	1.44731i	−0.00225841	+	0.0128081i	−0.985916	−	0.167240i	$-0.946514\pi$
$113$	−0.255201	+	1.44731i	−0.00225841	+	0.0128081i	0.983658	+	0.180049i	$0.0576255\pi$
$114$		0			0
$115$	−77.6274	−	92.5128i	−0.675021	−	0.804459i
$116$	17.4902	+	101.292i	0.150778	+	0.873206i
$117$		0			0
$118$	36.6410	−	43.5100i	0.310517	−	0.368729i
$119$	142.365	−	25.1029i	1.19635	−	0.210949i
$120$		0			0
$121$	−85.6316	+	31.1674i	−0.707699	+	0.257581i
$122$	13.9738	+	80.0796i	0.114539	+	0.656390i
$123$		0			0
$124$	88.1721	+	15.8698i	0.711065	+	0.127983i
$125$	−66.0714	+	114.439i	−0.528571	+	0.915512i
$126$		0			0
$127$	−136.000	+	78.5197i	−1.07087	+	0.618266i	−0.928418	−	0.371537i	$-0.878831\pi$
$127$	−136.000	+	78.5197i	−1.07087	+	0.618266i	−0.142449	+	0.989802i	$0.545498\pi$
$128$	65.3714	−	110.048i	0.510714	−	0.859751i
$129$		0			0
$130$	149.322	+	54.6489i	1.14863	+	0.420376i
$131$	−32.6480	+	38.9084i	−0.249222	+	0.297011i	−0.876123	−	0.482088i	$-0.839879\pi$
$131$	−32.6480	+	38.9084i	−0.249222	+	0.297011i	0.626901	+	0.779099i	$0.284323\pi$
$132$		0			0
$133$	188.559	+	68.6300i	1.41774	+	0.516015i
$134$	178.062	+	31.7230i	1.32882	+	0.236738i
$135$		0			0
$136$	−65.6087	+	112.254i	−0.482417	+	0.825396i
$137$	−83.6505	−	30.4463i	−0.610588	−	0.222236i	0.0181727	−	0.999835i	$-0.494215\pi$
$137$	−83.6505	−	30.4463i	−0.610588	−	0.222236i	−0.628760	+	0.777599i	$0.716437\pi$
$138$		0			0
$139$	44.4026	−	52.9170i	0.319443	−	0.380698i	−0.582297	−	0.812976i	$-0.697846\pi$
$139$	44.4026	−	52.9170i	0.319443	−	0.380698i	0.901740	+	0.432279i	$0.142290\pi$
$140$	107.662	+	62.6690i	0.769015	+	0.447636i
$141$		0			0
$142$	−175.978	+	101.185i	−1.23928	+	0.712572i
$143$	107.479	−	62.0528i	0.751599	−	0.433936i
$144$		0			0
$145$	44.9883	−	77.9220i	0.310264	−	0.537393i
$146$	−64.0099	−	0.113539i	−0.438424	−	0.000777666i
$147$		0			0
$148$	−63.0855	−	0.223800i	−0.426253	−	0.00151216i
$149$	200.510	−	72.9797i	1.34571	−	0.489797i	0.434101	−	0.900864i	$-0.357066\pi$
$149$	200.510	−	72.9797i	1.34571	−	0.489797i	0.911605	+	0.411067i	$0.134844\pi$
$150$		0			0
$151$	−70.6394	+	12.4556i	−0.467811	+	0.0824877i	−0.402585	−	0.915383i	$-0.631888\pi$
$151$	−70.6394	+	12.4556i	−0.467811	+	0.0824877i	−0.0652263	+	0.997870i	$0.520777\pi$
$152$	−156.776	+	89.4056i	−1.03142	+	0.588195i
$153$		0			0
$154$	91.4246	−	33.0923i	0.593666	−	0.214885i
$155$	−50.4077	−	60.0735i	−0.325211	−	0.387571i
$156$		0			0
$157$	−45.4824	+	257.943i	−0.289697	+	1.64295i	0.398312	+	0.917250i	$0.369596\pi$
$157$	−45.4824	+	257.943i	−0.289697	+	1.64295i	−0.688009	+	0.725702i	$0.741515\pi$
$158$	−32.4484	−	38.8101i	−0.205370	−	0.245634i
$159$		0			0
$160$	−105.622	+	37.3857i	−0.660136	+	0.233661i
$161$	−306.791			−1.90553
$162$		0			0
$163$		−	302.114i		−	1.85346i	−0.375725	−	0.926731i	$-0.622606\pi$
$163$		−	302.114i		−	1.85346i	0.375725	−	0.926731i	$-0.377394\pi$
$164$	−161.316	−	136.339i	−0.983637	−	0.831333i
$165$		0			0
$166$	61.4605	+	73.5102i	0.370244	+	0.442832i
$167$	−111.528	−	19.6654i	−0.667833	−	0.117757i	−0.170555	−	0.985348i	$-0.554556\pi$
$167$	−111.528	−	19.6654i	−0.667833	−	0.117757i	−0.497278	+	0.867591i	$0.665667\pi$
$168$		0			0
$169$	265.506	−	222.786i	1.57104	−	1.31826i
$170$	107.017	−	38.7362i	0.629513	−	0.227860i
$171$		0			0
$172$	25.0045	+	30.0148i	0.145375	+	0.174505i
$173$	47.6724	+	270.364i	0.275563	+	1.56280i	0.737168	+	0.675710i	$0.236163\pi$
$173$	47.6724	+	270.364i	0.275563	+	1.56280i	−0.461605	+	0.887086i	$0.652726\pi$
$174$		0			0
$175$	38.7588	+	106.489i	0.221479	+	0.608509i
$176$	−30.4918	+	81.9614i	−0.173249	+	0.465690i
$177$		0			0
$178$	−180.265	−	0.319750i	−1.01272	−	0.00179635i
$179$	−42.5533	−	24.5682i	−0.237728	−	0.137252i	0.376404	−	0.926456i	$-0.377160\pi$
$179$	−42.5533	−	24.5682i	−0.237728	−	0.137252i	−0.614132	+	0.789203i	$0.710494\pi$
$180$		0			0
$181$	−71.8830	−	124.505i	−0.397144	−	0.687873i	0.596229	−	0.802815i	$-0.296665\pi$
$181$	−71.8830	−	124.505i	−0.397144	−	0.687873i	−0.993372	+	0.114942i	$0.963332\pi$
$182$	350.178	−	201.348i	1.92405	−	1.10631i
$183$		0			0
$184$	178.488	−	210.430i	0.970044	−	1.14364i
$185$	42.3020	+	35.4956i	0.228660	+	0.191868i
$186$		0			0
$187$	30.3817	−	83.4731i	0.162469	−	0.446380i
$188$	32.2156	−	87.5441i	0.171360	−	0.465660i
$189$		0			0
$190$	155.529	+	27.7086i	0.818576	+	0.145835i
$191$	96.1293	−	264.113i	0.503295	−	1.38279i	−0.384744	−	0.923023i	$-0.625710\pi$
$191$	96.1293	−	264.113i	0.503295	−	1.38279i	0.888039	−	0.459768i	$-0.152067\pi$
$192$		0			0
$193$	133.817	+	112.286i	0.693352	+	0.581791i	0.919874	−	0.392215i	$-0.128291\pi$
$193$	133.817	+	112.286i	0.693352	+	0.581791i	−0.226522	+	0.974006i	$0.572735\pi$
$194$	−278.772	−	102.025i	−1.43697	−	0.525902i
$195$		0			0
$196$	113.342	−	40.7982i	0.578274	−	0.208154i
$197$	−75.0398	−	129.973i	−0.380913	−	0.659761i	0.610280	−	0.792186i	$-0.291057\pi$
$197$	−75.0398	−	129.973i	−0.380913	−	0.659761i	−0.991193	+	0.132425i	$0.957724\pi$
$198$		0			0
$199$	−144.287	−	83.3043i	−0.725062	−	0.418615i	0.0915512	−	0.995800i	$-0.470817\pi$
$199$	−144.287	−	83.3043i	−0.725062	−	0.418615i	−0.816613	+	0.577186i	$0.804151\pi$
$200$	−95.5909	−	35.3694i	−0.477955	−	0.176847i
$201$		0			0
$202$	3.50635	+	20.0939i	0.0173582	+	0.0994746i
$203$	−78.1765	−	214.788i	−0.385106	−	1.05807i
$204$		0			0
$205$	32.1046	+	182.074i	0.156608	+	0.888167i
$206$	−18.5862	+	22.0705i	−0.0902242	+	0.107138i
$207$		0			0
$208$	−65.6246	+	357.331i	−0.315503	+	1.71794i
$209$	94.4548	−	79.2570i	0.451937	−	0.379220i
$210$		0			0
$211$	−305.846	−	53.9289i	−1.44951	−	0.255587i	−0.607184	−	0.794561i	$-0.707701\pi$
$211$	−305.846	−	53.9289i	−1.44951	−	0.255587i	−0.842323	+	0.538974i	$0.818812\pi$
$212$	8.14675	+	14.2269i	0.0384281	+	0.0671081i
$213$		0			0
$214$	141.391	+	81.9670i	0.660706	+	0.383023i
$215$		−	34.1954i		−	0.159049i
$216$		0			0
$217$	−199.216			−0.918046
$218$	−193.962	+	334.581i	−0.889736	+	1.53477i
$219$		0			0
$220$	66.4277	−	38.0385i	0.301944	−	0.172902i
$221$	64.0837	−	363.437i	0.289971	−	1.64451i
$222$		0			0
$223$	−12.9953	−	15.4873i	−0.0582751	−	0.0694496i	0.736119	−	0.676852i	$-0.236656\pi$
$223$	−12.9953	−	15.4873i	−0.0582751	−	0.0694496i	−0.794395	+	0.607402i	$0.792212\pi$
$224$	−99.7173	+	266.590i	−0.445166	+	1.19014i
$225$		0			0
$226$	2.24827	+	1.89333i	0.00994808	+	0.00837754i
$227$	46.8151	−	8.25477i	0.206234	−	0.0363646i	−0.0695767	−	0.997577i	$-0.522165\pi$
$227$	46.8151	−	8.25477i	0.206234	−	0.0363646i	0.275811	+	0.961212i	$0.411054\pi$
$228$		0			0
$229$	66.3275	−	24.1412i	0.289640	−	0.105420i	−0.193114	−	0.981176i	$-0.561859\pi$
$229$	66.3275	−	24.1412i	0.289640	−	0.105420i	0.482754	+	0.875756i	$0.339637\pi$
$230$	−237.938	+	41.5199i	−1.03451	+	0.180521i
$231$		0			0
$232$	192.807	+	71.3401i	0.831064	+	0.307500i
$233$	191.622	−	331.898i	0.822411	−	1.42446i	−0.0814716	−	0.996676i	$-0.525962\pi$
$233$	191.622	−	331.898i	0.822411	−	1.42446i	0.903882	−	0.427781i	$-0.140705\pi$
$234$		0			0
$235$	−70.7149	+	40.8272i	−0.300914	+	0.173733i
$236$	−38.5308	−	107.043i	−0.163266	−	0.453570i
$237$		0			0
$238$	99.3678	−	271.511i	0.417512	−	1.14080i
$239$	220.713	−	263.036i	0.923486	−	1.10057i	−0.0711850	−	0.997463i	$-0.522678\pi$
$239$	220.713	−	263.036i	0.923486	−	1.10057i	0.994671	−	0.103104i	$-0.0328775\pi$
$240$		0			0
$241$	−226.848	−	82.5658i	−0.941276	−	0.342597i	−0.174607	−	0.984638i	$-0.555865\pi$
$241$	−226.848	−	82.5658i	−0.941276	−	0.342597i	−0.766670	+	0.642042i	$0.778088\pi$
$242$	−31.9665	+	179.429i	−0.132093	+	0.741443i
$243$		0			0
$244$	152.576	+	56.1470i	0.625313	+	0.230111i
$245$	−99.0848	−	36.0639i	−0.404428	−	0.147200i
$246$		0			0
$247$	329.271	−	392.410i	1.33308	−	1.58871i
$248$	115.902	−	136.643i	0.467347	−	0.550981i
$249$		0			0
$250$	131.737	+	229.112i	0.526947	+	0.916448i
$251$	−36.5452	+	21.0994i	−0.145598	+	0.0840612i	−0.571029	−	0.820930i	$-0.693456\pi$
$251$	−36.5452	+	21.0994i	−0.145598	+	0.0840612i	0.425431	+	0.904991i	$0.360122\pi$
$252$		0			0
$253$	−94.2584	+	163.260i	−0.372563	+	0.645298i
$254$	−0.557105	+	314.078i	−0.00219333	+	1.23653i
$255$		0			0
$256$	−124.841	−	223.496i	−0.487661	−	0.873033i
$257$	−201.446	+	73.3205i	−0.783838	+	0.285294i	−0.702772	−	0.711415i	$-0.748055\pi$
$257$	−201.446	+	73.3205i	−0.783838	+	0.285294i	−0.0810661	+	0.996709i	$0.525832\pi$
$258$		0			0
$259$	138.151	−	24.3597i	0.533401	−	0.0940530i
$260$	244.338	−	203.551i	0.939762	−	0.782889i
$261$		0			0
$262$	34.5739	+	95.5179i	0.131962	+	0.364572i
$263$	−68.4293	−	81.5508i	−0.260187	−	0.310079i	0.620098	−	0.784525i	$-0.287093\pi$
$263$	−68.4293	−	81.5508i	−0.260187	−	0.310079i	−0.880285	+	0.474446i	$0.842649\pi$
$264$		0			0
$265$	2.49195	−	14.1326i	0.00940359	−	0.0533304i
$266$	307.887	−	257.419i	1.15747	−	0.967740i
$267$		0			0
$268$	233.498	−	276.276i	0.871263	−	1.03088i
$269$	443.421			1.64841			0.824203	−	0.566294i	$-0.191623\pi$
$269$	443.421			1.64841			0.824203	+	0.566294i	$0.191623\pi$
$270$		0			0
$271$			315.051i			1.16255i	0.813707	+	0.581275i	$0.197446\pi$
$271$			315.051i			1.16255i	−0.813707	+	0.581275i	$0.802554\pi$
$272$	128.420	+	226.120i	0.472132	+	0.831322i
$273$		0			0
$274$	−136.588	+	114.199i	−0.498496	+	0.416783i
$275$	68.5769	+	12.0920i	0.249371	+	0.0439708i
$276$		0			0
$277$	123.961	−	104.016i	0.447514	−	0.375509i	−0.390999	−	0.920391i	$-0.627870\pi$
$277$	123.961	−	104.016i	0.447514	−	0.375509i	0.838512	+	0.544883i	$0.183426\pi$
$278$	−47.0219	−	129.908i	−0.169144	−	0.467296i
$279$		0			0
$280$	216.427	−	123.423i	0.772954	−	0.440798i
$281$	72.5198	+	411.280i	0.258078	+	1.46363i	0.788048	+	0.615614i	$0.211092\pi$
$281$	72.5198	+	411.280i	0.258078	+	1.46363i	−0.529970	+	0.848016i	$0.677797\pi$
$282$		0			0
$283$	−18.4189	−	50.6056i	−0.0650845	−	0.178818i	0.902887	−	0.429878i	$-0.141443\pi$
$283$	−18.4189	−	50.6056i	−0.0650845	−	0.178818i	−0.967972	+	0.251059i	$0.919221\pi$
$284$	−1.44026	+	405.986i	−0.00507135	+	1.42953i
$285$		0			0
$286$	0.440271	−	248.211i	0.00153941	−	0.867870i
$287$	406.745	+	234.835i	1.41723	+	0.818239i
$288$		0			0
$289$	12.4263	+	21.5230i	0.0429976	+	0.0744741i
$290$	−89.7001	−	156.003i	−0.309311	−	0.537943i
$291$		0			0
$292$	−64.4029	+	110.641i	−0.220558	+	0.378907i
$293$	188.522	+	158.189i	0.643419	+	0.539893i	0.905066	−	0.425271i	$-0.139821\pi$
$293$	188.522	+	158.189i	0.643419	+	0.539893i	−0.261647	+	0.965164i	$0.584266\pi$
$294$		0			0
$295$	−34.0596	+	93.5780i	−0.115456	+	0.317214i
$296$	−63.6664	+	108.931i	−0.215089	+	0.368009i
$297$		0			0
$298$	74.8509	−	420.142i	0.251178	−	1.40987i
$299$	−267.866	+	735.957i	−0.895874	+	2.46139i
$300$		0			0
$301$	−66.5453	−	55.8381i	−0.221081	−	0.185509i
$302$	−49.3047	+	134.719i	−0.163261	+	0.446091i
$303$		0			0
$304$	−2.56099	+	360.945i	−0.00842430	+	1.18732i
$305$	−71.1558	−	123.245i	−0.233298	−	0.404084i
$306$		0			0
$307$	−237.614	−	137.186i	−0.773987	−	0.446861i	0.0603082	−	0.998180i	$-0.480792\pi$
$307$	−237.614	−	137.186i	−0.773987	−	0.446861i	−0.834295	+	0.551318i	$0.814125\pi$
$308$	34.4466	−	191.384i	0.111840	−	0.621375i
$309$		0			0
$310$	−154.506	+	26.9611i	−0.498407	+	0.0869713i
$311$	−4.91549	−	13.5052i	−0.0158054	−	0.0434251i	0.931539	−	0.363641i	$-0.118467\pi$
$311$	−4.91549	−	13.5052i	−0.0158054	−	0.0434251i	−0.947344	+	0.320216i	$0.896244\pi$
$312$		0			0
$313$	3.07623	+	17.4462i	0.00982822	+	0.0557386i	0.989327	−	0.145709i	$-0.0465464\pi$
$313$	3.07623	+	17.4462i	0.00982822	+	0.0557386i	−0.979499	+	0.201448i	$0.935435\pi$
$314$	400.691	+	337.433i	1.27609	+	1.07463i
$315$		0			0
$316$	−99.7001	+	17.2154i	−0.315507	+	0.0544790i
$317$	−20.5145	+	17.2137i	−0.0647144	+	0.0543018i	−0.674571	−	0.738210i	$-0.735671\pi$
$317$	−20.5145	+	17.2137i	−0.0647144	+	0.0543018i	0.609857	+	0.792512i	$0.291227\pi$
$318$		0			0
$319$	−138.320	−	24.3895i	−0.433604	−	0.0764560i
$320$	−41.2585	+	220.255i	−0.128933	+	0.688297i
$321$		0			0
$322$	−307.733	+	530.833i	−0.955693	+	1.64855i
$323$		−	366.653i		−	1.13515i
$324$		0			0
$325$	289.296			0.890143
$326$	−522.741	−	303.042i	−1.60350	−	0.929577i
$327$		0			0
$328$	−397.715	+	142.364i	−1.21255	+	0.434038i
$329$	−36.0201	+	204.280i	−0.109484	+	0.620913i
$330$		0			0
$331$	171.799	+	204.742i	0.519031	+	0.618557i	0.960351	−	0.278793i	$-0.0899342\pi$
$331$	171.799	+	204.742i	0.519031	+	0.618557i	−0.441320	+	0.897350i	$0.645490\pi$
$332$	188.842	−	32.6076i	0.568801	−	0.0982157i
$333$		0			0
$334$	−145.897	+	173.248i	−0.436818	+	0.518708i
$335$	−311.827	+	54.9835i	−0.930827	+	0.164130i
$336$		0			0
$337$	−45.3861	+	16.5192i	−0.134677	+	0.0490184i	−0.408479	−	0.912768i	$-0.633941\pi$
$337$	−45.3861	+	16.5192i	−0.134677	+	0.0490184i	0.273802	+	0.961786i	$0.411719\pi$
$338$	−119.160	−	682.869i	−0.352544	−	2.02032i
$339$		0			0
$340$	40.3215	−	224.024i	0.118593	−	0.658895i
$341$	−61.2071	+	106.014i	−0.179493	+	0.310891i
$342$		0			0
$343$	145.470	−	83.9870i	0.424110	−	0.244860i
$344$	77.0151	−	13.1577i	0.223881	−	0.0382490i
$345$		0			0
$346$	515.622	+	188.707i	1.49024	+	0.545397i
$347$	132.441	−	157.837i	0.381673	−	0.454860i	−0.540668	−	0.841236i	$-0.681829\pi$
$347$	132.441	−	157.837i	0.381673	−	0.454860i	0.922342	+	0.386375i	$0.126273\pi$
$348$		0			0
$349$	−154.612	−	56.2741i	−0.443013	−	0.161244i	0.110875	−	0.993834i	$-0.464635\pi$
$349$	−154.612	−	56.2741i	−0.443013	−	0.161244i	−0.553889	+	0.832591i	$0.686857\pi$
$350$	223.133	+	39.7526i	0.637523	+	0.113579i
$351$		0			0
$352$	111.230	+	134.972i	0.315995	+	0.383444i
$353$	−448.666	−	163.301i	−1.27101	−	0.462609i	−0.383560	−	0.923516i	$-0.625302\pi$
$353$	−448.666	−	163.301i	−1.27101	−	0.462609i	−0.887449	+	0.460907i	$0.847524\pi$
$354$		0			0
$355$	228.432	−	272.234i	0.643470	−	0.766857i
$356$	−181.372	+	311.587i	−0.509471	+	0.875245i
$357$		0			0
$358$	−85.1937	+	48.9853i	−0.237971	+	0.136831i
$359$	−361.309	+	208.602i	−1.00643	+	0.581064i	−0.910145	−	0.414290i	$-0.864030\pi$
$359$	−361.309	+	208.602i	−1.00643	+	0.581064i	−0.0962869	+	0.995354i	$0.530697\pi$
$360$		0			0
$361$	73.9690	−	128.118i	0.204900	−	0.354898i
$362$	−287.532	−	0.510017i	−0.794286	−	0.00140889i
$363$		0			0
$364$	2.86597	−	807.870i	0.00787355	−	2.21942i
$365$	105.302	−	38.3270i	0.288500	−	0.105005i
$366$		0			0
$367$	−46.8441	+	8.25989i	−0.127641	+	0.0225065i	−0.237104	−	0.971484i	$-0.576198\pi$
$367$	−46.8441	+	8.25989i	−0.127641	+	0.0225065i	0.109463	+	0.993991i	$0.465087\pi$
$368$	−185.065	−	519.909i	−0.502893	−	1.41280i
$369$		0			0
$370$	103.849	−	37.5895i	0.280673	−	0.101593i
$371$	−23.4332	−	27.9266i	−0.0631623	−	0.0752739i
$372$		0			0
$373$	−3.14422	+	17.8318i	−0.00842956	+	0.0478064i	−0.988732	−	0.149694i	$-0.952171\pi$
$373$	−3.14422	+	17.8318i	−0.00842956	+	0.0478064i	0.980303	+	0.197500i	$0.0632823\pi$
$374$	−113.956	−	136.298i	−0.304696	−	0.364434i
$375$		0			0
$376$	−119.161	−	143.555i	−0.316917	−	0.381795i
$377$	−583.510			−1.54777
$378$		0			0
$379$			492.502i			1.29948i	0.760157	+	0.649739i	$0.225122\pi$
$379$			492.502i			1.29948i	−0.760157	+	0.649739i	$0.774878\pi$
$380$	203.950	−	241.315i	0.536712	−	0.635039i
$381$		0			0
$382$	−360.564	−	431.254i	−0.943884	−	1.12894i
$383$	43.2067	+	7.61850i	0.112811	+	0.0198916i	0.229769	−	0.973245i	$-0.426203\pi$
$383$	43.2067	+	7.61850i	0.112811	+	0.0198916i	−0.116958	+	0.993137i	$0.537314\pi$
$384$		0			0
$385$	−130.394	+	109.413i	−0.338685	+	0.284190i
$386$	328.513	−	118.909i	0.851070	−	0.308056i
$387$		0			0
$388$	−456.159	+	380.013i	−1.17567	+	0.979415i
$389$	43.7808	+	248.293i	0.112547	+	0.638286i	0.987936	+	0.154866i	$0.0494945\pi$
$389$	43.7808	+	248.293i	0.112547	+	0.638286i	−0.875388	+	0.483420i	$0.839394\pi$
$390$		0			0
$391$	191.729	+	526.771i	0.490355	+	1.34724i
$392$	43.0976	−	237.036i	0.109943	−	0.604683i
$393$		0			0
$394$	−300.159	−	0.532415i	−0.761825	−	0.00135131i
$395$	76.6975	+	44.2813i	0.194171	+	0.112105i
$396$		0			0
$397$	62.6518	+	108.516i	0.157813	+	0.273340i	0.934080	−	0.357064i	$-0.116222\pi$
$397$	62.6518	+	108.516i	0.157813	+	0.273340i	−0.776267	+	0.630405i	$0.782889\pi$
$398$	−288.870	+	166.096i	−0.725803	+	0.417328i
$399$		0			0
$400$	−157.083	+	129.920i	−0.392708	+	0.324801i
$401$	−390.899	−	328.004i	−0.974812	−	0.817964i	0.00848695	−	0.999964i	$-0.497298\pi$
$401$	−390.899	−	328.004i	−0.974812	−	0.817964i	−0.983299	+	0.182000i	$0.941743\pi$
$402$		0			0
$403$	−173.940	+	477.896i	−0.431613	+	1.18585i
$404$	38.2850	+	14.0886i	0.0947649	+	0.0348728i
$405$		0			0
$406$	−450.059	−	80.1810i	−1.10852	−	0.197490i
$407$	29.4823	−	81.0020i	0.0724381	−	0.199022i
$408$		0			0
$409$	−518.054	−	434.699i	−1.26664	−	1.06283i	−0.994942	−	0.100451i	$-0.967972\pi$
$409$	−518.054	−	434.699i	−1.26664	−	1.06283i	−0.271694	−	0.962384i	$-0.587584\pi$
$410$	347.242	+	127.084i	0.846931	+	0.309960i
$411$		0			0
$412$	19.5448	+	54.2975i	0.0474389	+	0.131790i
$413$	126.489	+	219.085i	0.306269	+	0.530473i
$414$		0			0
$415$	−145.273	−	83.8732i	−0.350055	−	0.202104i
$416$	552.455	+	471.977i	1.32802	+	1.13456i
$417$		0			0
$418$	−42.3915	−	242.933i	−0.101415	−	0.581180i
$419$	13.5624	+	37.2623i	0.0323684	+	0.0889315i	0.954824	−	0.297171i	$-0.0960432\pi$
$419$	13.5624	+	37.2623i	0.0323684	+	0.0889315i	−0.922456	+	0.386103i	$0.873821\pi$
$420$		0			0
$421$	4.01215	+	22.7540i	0.00953005	+	0.0540476i	0.989202	−	0.146559i	$-0.0468198\pi$
$421$	4.01215	+	22.7540i	0.00953005	+	0.0540476i	−0.979672	+	0.200607i	$0.935709\pi$
$422$	−400.097	+	475.103i	−0.948097	+	1.12584i
$423$		0			0
$424$	32.7882	+	0.174479i	0.0773307	+	0.000411506i
$425$	158.623	−	133.100i	0.373231	−	0.313178i
$426$		0			0
$427$	−356.030	−	62.7777i	−0.833794	−	0.147020i
$428$	283.651	−	162.427i	0.662735	−	0.379502i
$429$		0			0
$430$	−59.1675	−	34.3004i	−0.137599	−	0.0797685i
$431$			617.967i			1.43380i	0.697177	+	0.716899i	$0.254439\pi$
$431$			617.967i			1.43380i	−0.697177	+	0.716899i	$0.745561\pi$
$432$		0			0
$433$	135.919			0.313902			0.156951	−	0.987606i	$-0.449834\pi$
$433$	135.919			0.313902			0.156951	+	0.987606i	$0.449834\pi$
$434$	−199.828	+	344.698i	−0.460432	+	0.794235i
$435$		0			0
$436$	384.358	+	671.216i	0.881556	+	1.53949i
$437$	−135.119	+	766.296i	−0.309196	+	1.75354i
$438$		0			0
$439$	217.856	+	259.631i	0.496255	+	0.591414i	0.954797	−	0.297259i	$-0.0960725\pi$
$439$	217.856	+	259.631i	0.496255	+	0.591414i	−0.458542	+	0.888673i	$0.651628\pi$
$440$	0.814668	−	153.093i	0.00185152	−	0.347940i
$441$		0			0
$442$	−564.564	−	475.435i	−1.27730	−	1.07564i
$443$	329.343	−	58.0721i	0.743439	−	0.131088i	0.210916	−	0.977504i	$-0.432355\pi$
$443$	329.343	−	58.0721i	0.743439	−	0.131088i	0.532523	+	0.846416i	$0.321244\pi$
$444$		0			0
$445$	296.553	−	107.937i	0.666412	−	0.242554i
$446$	−39.8324	+	6.95071i	−0.0893104	+	0.0155845i
$447$		0			0
$448$	361.251	+	439.947i	0.806364	+	0.982025i
$449$	−33.3868	+	57.8276i	−0.0743581	+	0.128792i	−0.900807	−	0.434220i	$-0.857024\pi$
$449$	−33.3868	+	57.8276i	−0.0743581	+	0.128792i	0.826449	+	0.563012i	$0.190357\pi$
$450$		0			0
$451$	249.937	−	144.301i	0.554184	−	0.319958i
$452$	5.53114	−	1.99098i	0.0122370	−	0.00440482i
$453$		0			0
$454$	32.6759	−	89.2831i	0.0719732	−	0.196659i
$455$	−454.555	+	541.718i	−0.999022	+	1.19059i
$456$		0			0
$457$	400.777	+	145.871i	0.876974	+	0.319192i	0.740988	−	0.671518i	$-0.234358\pi$
$457$	400.777	+	145.871i	0.876974	+	0.319192i	0.135986	+	0.990711i	$0.456580\pi$
$458$	24.7602	−	138.980i	0.0540616	−	0.303450i
$459$		0			0
$460$	−166.828	+	453.346i	−0.362670	+	0.985535i
$461$	107.797	+	39.2350i	0.233834	+	0.0851084i	0.456279	−	0.889837i	$-0.349182\pi$
$461$	107.797	+	39.2350i	0.233834	+	0.0851084i	−0.222446	+	0.974945i	$0.571404\pi$
$462$		0			0
$463$	203.177	−	242.137i	0.438827	−	0.522973i	−0.500621	−	0.865667i	$-0.666895\pi$
$463$	203.177	−	242.137i	0.438827	−	0.522973i	0.939447	+	0.342694i	$0.111339\pi$
$464$	316.837	−	262.049i	0.682838	−	0.564762i
$465$		0			0
$466$	−382.065	−	664.476i	−0.819883	−	1.42591i
$467$	368.289	−	212.632i	0.788627	−	0.455314i	−0.0508517	−	0.998706i	$-0.516194\pi$
$467$	368.289	−	212.632i	0.788627	−	0.455314i	0.839479	+	0.543392i	$0.182860\pi$
$468$		0			0
$469$	−402.186	+	696.607i	−0.857540	+	1.48530i
$470$	−0.289673	+	163.309i	−0.000616326	+	0.347465i
$471$		0			0
$472$	−223.862	−	40.7024i	−0.474284	−	0.0862338i
$473$	−50.1599	+	18.2567i	−0.106046	+	0.0385977i
$474$		0			0
$475$	283.056	−	49.9105i	0.595908	−	0.105075i
$476$	−370.116	−	444.278i	−0.777555	−	0.933358i
$477$		0			0
$478$	−233.733	−	645.737i	−0.488981	−	1.35092i
$479$	100.261	+	119.487i	0.209314	+	0.249450i	0.860479	−	0.509485i	$-0.170164\pi$
$479$	100.261	+	119.487i	0.209314	+	0.249450i	−0.651166	+	0.758936i	$0.725720\pi$
$480$		0			0
$481$	62.1865	−	352.677i	0.129286	−	0.733217i
$482$	−370.406	+	309.689i	−0.768476	+	0.642509i
$483$		0			0
$484$	278.397	+	235.291i	0.575201	+	0.486138i
$485$	519.696			1.07154
$486$		0			0
$487$		−	545.789i		−	1.12072i	−0.828250	−	0.560359i	$-0.810663\pi$
$487$		−	545.789i		−	1.12072i	0.828250	−	0.560359i	$-0.189337\pi$
$488$	250.195	−	207.680i	0.512694	−	0.425573i
$489$		0			0
$490$	−161.790	+	135.269i	−0.330183	+	0.276060i
$491$	−193.358	−	34.0942i	−0.393804	−	0.0694383i	−0.0267601	−	0.999642i	$-0.508519\pi$
$491$	−193.358	−	34.0942i	−0.393804	−	0.0694383i	−0.367044	+	0.930204i	$0.619630\pi$
$492$		0			0
$493$	−319.942	+	268.464i	−0.648970	+	0.544551i
$494$	−348.695	−	963.345i	−0.705860	−	1.95009i
$495$		0			0
$496$	−120.172	−	337.605i	−0.242283	−	0.680655i
$497$	−156.767	−	889.069i	−0.315426	−	1.78887i
$498$		0			0
$499$	329.193	+	904.449i	0.659705	+	1.81252i	0.578270	+	0.815845i	$0.303728\pi$
$499$	329.193	+	904.449i	0.659705	+	1.81252i	0.0814345	+	0.996679i	$0.474050\pi$
$500$	528.568	+	1.87513i	1.05714	+	0.00375026i
$501$		0			0
$502$	−0.149702	+	84.3973i	−0.000298211	+	0.168122i
$503$	−379.909	−	219.340i	−0.755285	−	0.436064i	0.0723150	−	0.997382i	$-0.476961\pi$
$503$	−379.909	−	219.340i	−0.755285	−	0.436064i	−0.827600	+	0.561318i	$0.810295\pi$
$504$		0			0
$505$	−17.8547	−	30.9252i	−0.0353558	−	0.0612380i
$506$	187.937	+	326.855i	0.371418	+	0.645958i
$507$		0			0
$508$	542.883	+	316.007i	1.06867	+	0.622061i
$509$	193.632	+	162.477i	0.380417	+	0.319208i	0.812866	−	0.582450i	$-0.197906\pi$
$509$	193.632	+	162.477i	0.380417	+	0.319208i	−0.432449	+	0.901658i	$0.642350\pi$
$510$		0			0
$511$	97.3642	−	267.506i	0.190537	−	0.523495i
$512$	−511.935	−	8.17321i	−0.999873	−	0.0159633i
$513$		0			0
$514$	−75.2004	+	422.103i	−0.146304	+	0.821213i
$515$	17.2768	−	47.4676i	0.0335472	−	0.0921701i
$516$		0			0
$517$	97.6420	+	81.9313i	0.188863	+	0.158475i
$518$	96.4261	−	263.473i	0.186151	−	0.508636i
$519$		0			0
$520$	−107.111	−	626.948i	−0.205983	−	1.20567i
$521$	364.963	+	632.134i	0.700504	+	1.21331i	0.968290	+	0.249830i	$0.0803749\pi$
$521$	364.963	+	632.134i	0.700504	+	1.21331i	−0.267785	+	0.963479i	$0.586292\pi$
$522$		0			0
$523$	405.945	+	234.373i	0.776186	+	0.448131i	0.835077	−	0.550133i	$-0.185423\pi$
$523$	405.945	+	234.373i	0.776186	+	0.448131i	−0.0588911	+	0.998264i	$0.518756\pi$
$524$	199.952	+	35.9888i	0.381588	+	0.0686810i
$525$		0			0
$526$	−209.745	+	36.6002i	−0.398754	+	0.0695821i
$527$	124.500	+	342.061i	0.236243	+	0.649071i
$528$		0			0
$529$	−114.724	−	650.630i	−0.216869	−	1.22992i
$530$	−21.9536	−	18.4877i	−0.0414219	−	0.0348825i
$531$		0			0
$532$	−136.572	−	790.939i	−0.256715	−	1.48673i
$533$	918.481	−	770.697i	1.72323	−	1.44596i
$534$		0			0
$535$	−281.769	−	49.6836i	−0.526672	−	0.0928665i
$536$	−243.818	−	681.141i	−0.454885	−	1.27079i
$537$		0			0
$538$	444.783	−	767.241i	0.826734	−	1.42610i
$539$			164.598i			0.305376i
$540$		0			0
$541$	578.608			1.06952			0.534758	−	0.845005i	$-0.320403\pi$
$541$	578.608			1.06952			0.534758	+	0.845005i	$0.320403\pi$
$542$	545.125	+	316.019i	1.00577	+	0.583060i
$543$		0			0
$544$	520.063	+	4.61250i	0.955998	+	0.00847886i
$545$	117.569	−	666.765i	0.215722	−	1.22342i
$546$		0			0
$547$	−163.148	−	194.432i	−0.298259	−	0.355451i	0.596013	−	0.802975i	$-0.296751\pi$
$547$	−163.148	−	194.432i	−0.298259	−	0.355451i	−0.894272	+	0.447524i	$0.852306\pi$
$548$	60.5876	+	350.884i	0.110561	+	0.640299i
$549$		0			0
$550$	89.7099	−	106.528i	0.163109	−	0.193687i
$551$	−570.924	+	100.669i	−1.03616	+	0.182703i
$552$		0			0
$553$	211.413	−	76.9480i	0.382302	−	0.139146i
$554$	−55.6341	−	318.822i	−0.100422	−	0.575492i
$555$		0			0
$556$	−271.943	−	48.9463i	−0.489106	−	0.0880328i
$557$	−65.6464	+	113.703i	−0.117857	+	0.204135i	−0.918918	−	0.394448i	$-0.870936\pi$
$557$	−65.6464	+	113.703i	−0.117857	+	0.204135i	0.801061	+	0.598583i	$0.204269\pi$
$558$		0			0
$559$	−192.052	+	110.881i	−0.343563	+	0.198356i
$560$	3.53541	−	498.281i	0.00631324	−	0.889787i
$561$		0			0
$562$	784.370	+	287.064i	1.39568	+	0.510790i
$563$	−233.686	+	278.496i	−0.415072	+	0.494664i	−0.932554	−	0.361030i	$-0.882425\pi$
$563$	−233.686	+	278.496i	−0.415072	+	0.494664i	0.517482	+	0.855694i	$0.326870\pi$
$564$		0			0
$565$	−4.83540	−	1.75994i	−0.00855823	−	0.00311494i
$566$	−106.037	−	18.8912i	−0.187344	−	0.0333766i
$567$		0			0
$568$	701.023	+	409.725i	1.23419	+	0.721347i
$569$	285.161	+	103.790i	0.501161	+	0.182408i	0.580216	−	0.814463i	$-0.302968\pi$
$569$	285.161	+	103.790i	0.501161	+	0.182408i	−0.0790551	+	0.996870i	$0.525190\pi$
$570$		0			0
$571$	−186.268	+	221.985i	−0.326213	+	0.388765i	−0.904078	−	0.427367i	$-0.859441\pi$
$571$	−186.268	+	221.985i	−0.326213	+	0.388765i	0.577866	+	0.816132i	$0.303886\pi$
$572$	−429.031	−	249.735i	−0.750055	−	0.436599i
$573$		0			0
$574$	814.323	−	468.226i	1.41868	−	0.815724i
$575$	−380.568	+	219.721i	−0.661857	+	0.382124i
$576$		0			0
$577$	493.417	−	854.624i	0.855143	−	1.48115i	−0.0213695	−	0.999772i	$-0.506803\pi$
$577$	493.417	−	854.624i	0.855143	−	1.48115i	0.876512	−	0.481379i	$-0.159864\pi$
$578$	49.7052	+	0.0881659i	0.0859951	+	0.000152536i
$579$		0			0
$580$	−359.904	−	1.27678i	−0.620525	−	0.00220135i
$581$	−400.437	+	145.747i	−0.689220	+	0.250856i
$582$		0			0
$583$	−22.0609	+	3.88993i	−0.0378403	+	0.00667227i
$584$	126.838	+	222.415i	0.217189	+	0.380848i
$585$		0			0
$586$	462.810	−	167.520i	0.789779	−	0.285870i
$587$	−183.011	−	218.104i	−0.311773	−	0.371557i	0.587289	−	0.809377i	$-0.300195\pi$
$587$	−183.011	−	218.104i	−0.311773	−	0.371557i	−0.899062	+	0.437820i	$0.855751\pi$
$588$		0			0
$589$	−87.7398	+	497.597i	−0.148964	+	0.844817i
$590$	127.751	+	152.798i	0.216528	+	0.258979i
$591$		0			0
$592$	124.618	+	219.426i	0.210504	+	0.370651i
$593$	669.113			1.12835			0.564176	−	0.825654i	$-0.309194\pi$
$593$	669.113			1.12835			0.564176	+	0.825654i	$0.309194\pi$
$594$		0			0
$595$			506.161i			0.850690i
$596$	−651.879	−	550.944i	−1.09376	−	0.924403i
$597$		0			0
$598$	1004.72	+	1201.70i	1.68013	+	2.00953i
$599$	363.236	+	64.0483i	0.606404	+	0.106925i	0.468415	−	0.883508i	$-0.344825\pi$
$599$	363.236	+	64.0483i	0.606404	+	0.106925i	0.137989	+	0.990434i	$0.455936\pi$
$600$		0			0
$601$	−489.063	+	410.373i	−0.813750	+	0.682817i	−0.951500	−	0.307650i	$-0.900457\pi$
$601$	−489.063	+	410.373i	−0.813750	+	0.682817i	0.137750	+	0.990467i	$0.456013\pi$
$602$	−163.365	+	59.1320i	−0.271370	+	0.0982259i
$603$		0			0
$604$	183.646	+	220.444i	0.304049	+	0.364973i
$605$	−55.4056	−	314.221i	−0.0915795	−	0.519373i
$606$		0			0
$607$	38.7649	+	106.506i	0.0638631	+	0.175463i	0.967520	−	0.252795i	$-0.0813498\pi$
$607$	38.7649	+	106.506i	0.0638631	+	0.175463i	−0.903657	+	0.428258i	$0.859128\pi$
$608$	621.966	+	366.485i	1.02297	+	0.602771i
$609$		0			0
$610$	−284.623	−	0.504858i	−0.466595	−	0.000827635i
$611$	458.595	+	264.770i	0.750565	+	0.433339i
$612$		0			0
$613$	132.437	+	229.387i	0.216047	+	0.374204i	0.953596	−	0.301089i	$-0.0973502\pi$
$613$	132.437	+	229.387i	0.216047	+	0.374204i	−0.737549	+	0.675294i	$0.764017\pi$
$614$	−475.714	+	273.530i	−0.774778	+	0.445488i
$615$		0			0
$616$	−296.594	−	251.573i	−0.481483	−	0.408398i
$617$	−616.167	−	517.025i	−0.998649	−	0.837966i	−0.0118524	−	0.999930i	$-0.503773\pi$
$617$	−616.167	−	517.025i	−0.998649	−	0.837966i	−0.986797	+	0.161964i	$0.948217\pi$
$618$		0			0
$619$	266.035	−	730.924i	0.429781	−	1.18081i	−0.516164	−	0.856490i	$-0.672641\pi$
$619$	266.035	−	730.924i	0.429781	−	1.18081i	0.945946	−	0.324325i	$-0.105137\pi$
$620$	−108.330	+	294.382i	−0.174727	+	0.474809i
$621$		0			0
$622$	−28.2983	−	5.04152i	−0.0454956	−	0.00810534i
$623$	274.198	−	753.352i	0.440125	−	1.20923i
$624$		0			0
$625$	−110.436	−	92.6665i	−0.176697	−	0.148266i
$626$	33.2724	+	12.1770i	0.0531507	+	0.0194521i
$627$		0			0
$628$	985.772	−	354.836i	1.56970	−	0.565026i
$629$	−128.164	−	221.986i	−0.203758	−	0.352919i
$630$		0			0
$631$	56.8376	+	32.8152i	0.0900754	+	0.0520051i	0.544361	−	0.838851i	$-0.316772\pi$
$631$	56.8376	+	32.8152i	0.0900754	+	0.0520051i	−0.454286	+	0.890856i	$0.650105\pi$
$632$	−70.2190	+	189.777i	−0.111106	+	0.300280i
$633$		0			0
$634$	9.20692	+	52.7622i	0.0145220	+	0.0832211i
$635$	−188.060	−	516.690i	−0.296157	−	0.813684i
$636$		0			0
$637$	118.744	+	673.429i	0.186411	+	1.05719i
$638$	−180.945	+	214.866i	−0.283613	+	0.336781i
$639$		0			0
$640$	339.717	+	292.320i	0.530807	+	0.456750i
$641$	−593.381	+	497.905i	−0.925711	+	0.776764i	−0.975042	−	0.222019i	$-0.928735\pi$
$641$	−593.381	+	497.905i	−0.925711	+	0.776764i	0.0493316	+	0.998782i	$0.484291\pi$
$642$		0			0
$643$	−1077.13	−	189.927i	−1.67516	−	0.295376i	−0.746247	−	0.665670i	$-0.768146\pi$
$643$	−1077.13	−	189.927i	−1.67516	−	0.295376i	−0.928915	+	0.370293i	$0.879257\pi$
$644$	609.808	+	1064.93i	0.946907	+	1.65361i
$645$		0			0
$646$	−634.411	−	367.779i	−0.982060	−	0.569318i
$647$		−	1076.11i		−	1.66323i	−0.555356	−	0.831613i	$-0.687418\pi$
$647$		−	1076.11i		−	1.66323i	0.555356	−	0.831613i	$-0.312582\pi$
$648$		0			0
$649$	155.450			0.239522
$650$	290.185	−	500.562i	0.446438	−	0.770095i
$651$		0			0
$652$	−1048.69	+	600.512i	−1.60842	+	0.921031i
$653$	44.4135	−	251.881i	0.0680145	−	0.385729i	−0.931731	−	0.363150i	$-0.881701\pi$
$653$	44.4135	−	251.881i	0.0680145	−	0.385729i	0.999745	−	0.0225791i	$-0.00718776\pi$
$654$		0			0
$655$	−114.312	−	136.232i	−0.174522	−	0.207987i
$656$	−152.607	+	830.958i	−0.232633	+	1.26670i
$657$		0			0
$658$	317.330	+	267.232i	0.482265	+	0.406128i
$659$	672.381	−	118.559i	1.02030	−	0.179907i	0.361620	−	0.932326i	$-0.382224\pi$
$659$	672.381	−	118.559i	1.02030	−	0.179907i	0.658685	+	0.752418i	$0.271113\pi$
$660$		0			0
$661$	−296.947	+	108.080i	−0.449239	+	0.163510i	−0.556725	−	0.830697i	$-0.687942\pi$
$661$	−296.947	+	108.080i	−0.449239	+	0.163510i	0.107486	+	0.994207i	$0.465720\pi$
$662$	526.587	−	91.8888i	0.795449	−	0.138805i
$663$		0			0
$664$	133.002	−	359.456i	0.200304	−	0.541350i
$665$	−351.291	+	608.455i	−0.528258	+	0.914969i
$666$		0			0
$667$	767.605	−	443.177i	1.15083	−	0.664433i
$668$	153.422	+	426.223i	0.229674	+	0.638058i
$669$		0			0
$670$	−217.648	+	594.698i	−0.324848	+	0.887610i
$671$	−142.794	+	170.175i	−0.212808	+	0.253615i
$672$		0			0
$673$	−161.836	−	58.9034i	−0.240469	−	0.0875236i	0.218974	−	0.975731i	$-0.429729\pi$
$673$	−161.836	−	58.9034i	−0.240469	−	0.0875236i	−0.459444	+	0.888207i	$0.651951\pi$
$674$	−16.9427	+	95.1003i	−0.0251376	+	0.141098i
$675$		0			0
$676$	−1301.08	−	478.787i	−1.92467	−	0.708265i
$677$	723.236	+	263.236i	1.06829	+	0.388828i	0.815539	−	0.578702i	$-0.196441\pi$
$677$	723.236	+	263.236i	1.06829	+	0.388828i	0.252756	+	0.967530i	$0.418663\pi$
$678$		0			0
$679$	848.616	−	1011.34i	1.24980	−	1.48946i
$680$	−347.178	−	294.480i	−0.510556	−	0.433058i
$681$		0			0
$682$	122.038	+	212.244i	0.178941	+	0.311209i
$683$	534.500	−	308.594i	0.782577	−	0.451821i	−0.0547656	−	0.998499i	$-0.517441\pi$
$683$	534.500	−	308.594i	0.782577	−	0.451821i	0.837343	+	0.546678i	$0.184108\pi$
$684$		0			0
$685$	155.843	−	269.928i	0.227508	−	0.394056i
$686$	0.595896	−	335.947i	0.000868653	−	0.489719i
$687$		0			0
$688$	54.4852	−	146.455i	0.0791936	−	0.212871i
$689$	−87.4528	+	31.8302i	−0.126927	+	0.0461977i
$690$		0			0
$691$	−1107.65	+	195.308i	−1.60296	+	0.282645i	−0.902384	−	0.430933i	$-0.858185\pi$
$691$	−1107.65	+	195.308i	−1.60296	+	0.282645i	−0.700576	+	0.713578i	$0.747074\pi$
$692$	843.721	−	702.881i	1.21925	−	1.01572i
$693$		0			0
$694$	−140.253	−	387.480i	−0.202094	−	0.558328i
$695$	155.469	+	185.281i	0.223696	+	0.266591i
$696$		0			0
$697$	149.024	−	845.156i	0.213807	−	1.21256i
$698$	−252.456	+	211.074i	−0.361685	+	0.302398i
$699$		0			0
$700$	292.601	−	346.207i	0.418002	−	0.494581i
$701$	−368.048			−0.525032			−0.262516	−	0.964928i	$-0.584552\pi$
$701$	−368.048			−0.525032			−0.262516	+	0.964928i	$0.584552\pi$
$702$		0			0
$703$		−	355.799i		−	0.506115i
$704$	345.111	−	57.0722i	0.490214	−	0.0810685i
$705$		0			0
$706$	−732.599	+	612.513i	−1.03768	+	0.867582i
$707$	−89.3364	−	15.7524i	−0.126360	−	0.0222806i
$708$		0			0
$709$	−565.166	+	474.230i	−0.797131	+	0.668872i	−0.947499	−	0.319758i	$-0.896398\pi$
$709$	−565.166	+	474.230i	−0.797131	+	0.668872i	0.150369	+	0.988630i	$0.451954\pi$
$710$	−241.907	−	668.320i	−0.340714	−	0.941296i
$711$		0			0
$712$	357.202	+	626.367i	0.501689	+	0.879729i
$713$	−134.146	−	760.778i	−0.188143	−	1.06701i
$714$		0			0
$715$	148.620	+	408.331i	0.207861	+	0.571092i
$716$	−0.697254	+	196.544i	−0.000973818	+	0.274503i
$717$		0			0
$718$	−1.48005	+	834.406i	−0.00206135	+	1.16213i
$719$	−1138.67	−	657.410i	−1.58368	−	0.914340i	−0.994315	−	0.106475i	$-0.966044\pi$
$719$	−1138.67	−	657.410i	−1.58368	−	0.914340i	−0.589367	−	0.807865i	$-0.700623\pi$
$720$		0			0
$721$	−64.1618	−	111.131i	−0.0889900	−	0.154135i
$722$	−147.483	−	256.498i	−0.204270	−	0.355260i
$723$		0			0
$724$	−289.297	+	496.997i	−0.399581	+	0.686460i
$725$	−250.806	−	210.451i	−0.345939	−	0.290277i
$726$		0			0
$727$	−64.9919	+	178.564i	−0.0893974	+	0.245617i	−0.976332	−	0.216278i	$-0.930608\pi$
$727$	−64.9919	+	178.564i	−0.0893974	+	0.245617i	0.886934	+	0.461895i	$0.152830\pi$
$728$	−1394.96	−	815.309i	−1.91616	−	1.11993i
$729$		0			0
$730$	39.3097	−	220.647i	0.0538489	−	0.302256i
$731$	−54.2885	+	149.156i	−0.0742661	+	0.204044i
$732$		0			0
$733$	42.1532	+	35.3708i	0.0575078	+	0.0482548i	0.671089	−	0.741377i	$-0.265827\pi$
$733$	42.1532	+	35.3708i	0.0575078	+	0.0482548i	−0.613581	+	0.789632i	$0.710271\pi$
$734$	−32.6961	+	89.3385i	−0.0445451	+	0.121715i
$735$		0			0
$736$	−1085.22	−	201.293i	−1.47448	−	0.273496i
$737$	247.135	+	428.051i	0.335326	+	0.580802i
$738$		0			0
$739$	−190.459	−	109.961i	−0.257725	−	0.148798i	0.365571	−	0.930783i	$-0.380874\pi$
$739$	−190.459	−	109.961i	−0.257725	−	0.148798i	−0.623296	+	0.781986i	$0.714207\pi$
$740$	39.1278	−	217.392i	0.0528754	−	0.293773i
$741$		0			0
$742$	−71.8258	+	12.5335i	−0.0968003	+	0.0168915i
$743$	324.288	+	890.974i	0.436458	+	1.19916i	0.941781	+	0.336228i	$0.109151\pi$
$743$	324.288	+	890.974i	0.436458	+	1.19916i	−0.505323	+	0.862930i	$0.668627\pi$
$744$		0			0
$745$	129.735	+	735.762i	0.174140	+	0.987600i
$746$	27.7000	+	23.3269i	0.0371314	+	0.0312693i
$747$		0			0
$748$	−350.139	+	60.4591i	−0.468101	+	0.0808276i
$749$	−556.790	+	467.202i	−0.743378	+	0.623768i
$750$		0			0
$751$	−462.740	−	81.5936i	−0.616166	−	0.108647i	−0.143150	−	0.989701i	$-0.545723\pi$
$751$	−462.740	−	81.5936i	−0.616166	−	0.108647i	−0.473015	+	0.881054i	$0.656834\pi$
$752$	−367.916	+	62.1852i	−0.489250	+	0.0826931i
$753$		0			0
$754$	−585.302	+	1009.63i	−0.776263	+	1.33904i
$755$		−	251.149i		−	0.332647i
$756$		0			0
$757$	503.693			0.665380			0.332690	−	0.943036i	$-0.392044\pi$
$757$	503.693			0.665380			0.332690	+	0.943036i	$0.392044\pi$
$758$	852.164	+	494.015i	1.12423	+	0.651734i
$759$		0			0
$760$	−212.964	−	594.946i	−0.280216	−	0.782824i
$761$	−223.541	+	1267.76i	−0.293746	+	1.66592i	0.378509	+	0.925598i	$0.376437\pi$
$761$	−223.541	+	1267.76i	−0.293746	+	1.66592i	−0.672255	+	0.740320i	$0.734674\pi$
$762$		0			0
$763$	−1105.56	−	1317.56i	−1.44897	−	1.72681i
$764$	−1107.86	+	191.296i	−1.45008	+	0.250387i
$765$		0			0
$766$	56.5214	−	67.1175i	0.0737878	−	0.0876207i
$767$	636.002	−	112.144i	0.829207	−	0.146212i
$768$		0			0
$769$	1172.81	−	426.869i	1.52511	−	0.555096i	0.562695	−	0.826665i	$-0.309765\pi$
$769$	1172.81	−	426.869i	1.52511	−	0.555096i	0.962419	+	0.271569i	$0.0875425\pi$
$770$	58.5209	+	335.366i	0.0760012	+	0.435541i
$771$		0			0
$772$	123.776	−	687.692i	0.160331	−	0.890793i
$773$	192.043	−	332.627i	0.248438	−	0.430307i	−0.714655	−	0.699477i	$-0.753416\pi$
$773$	192.043	−	332.627i	0.248438	−	0.430307i	0.963093	+	0.269170i	$0.0867495\pi$
$774$		0			0
$775$	−247.123	+	142.677i	−0.318869	+	0.184099i
$776$	199.968	+	1170.46i	0.257690	+	1.50832i
$777$		0			0
$778$	473.531	+	173.303i	0.608651	+	0.222754i
$779$	765.706	−	912.533i	0.982934	−	1.17142i
$780$		0			0
$781$	−521.288	−	189.733i	−0.667462	−	0.242936i
$782$	1103.78	+	196.645i	1.41148	+	0.251464i
$783$		0			0
$784$	−366.907	−	312.334i	−0.467993	−	0.398385i
$785$	−861.775	−	313.661i	−1.09780	−	0.399568i
$786$		0			0
$787$	−446.143	+	531.692i	−0.566890	+	0.675594i	−0.970990	−	0.239121i	$-0.923141\pi$
$787$	−446.143	+	531.692i	−0.566890	+	0.675594i	0.404099	+	0.914715i	$0.367585\pi$
$788$	−302.002	+	518.823i	−0.383251	+	0.658405i
$789$		0			0
$790$	153.552	−	88.2904i	0.194369	−	0.111760i
$791$	−11.3207	+	6.53599i	−0.0143118	+	0.00826294i
$792$		0			0
$793$	−461.455	+	799.263i	−0.581910	+	1.00790i
$794$	250.607	+	0.444521i	0.315626	+	0.000559850i
$795$		0			0
$796$	−2.36421	+	666.430i	−0.00297011	+	0.837224i
$797$	−1135.48	+	413.283i	−1.42470	+	0.518548i	−0.935407	−	0.353573i	$-0.884967\pi$
$797$	−1135.48	+	413.283i	−1.42470	+	0.518548i	−0.489291	+	0.872120i	$0.662744\pi$
$798$		0			0
$799$	373.267	−	65.8170i	0.467168	−	0.0823743i
$800$	67.2324	+	402.117i	0.0840405	+	0.502646i
$801$		0			0
$802$	−959.636	+	347.352i	−1.19655	+	0.433108i
$803$	−112.441	−	134.001i	−0.140026	−	0.166876i
$804$		0			0
$805$	186.530	−	1057.86i	0.231714	−	1.31411i
$806$	652.418	+	780.328i	0.809451	+	0.968149i
$807$		0			0
$808$	62.7798	−	52.1117i	0.0776977	−	0.0644947i
$809$	270.237			0.334038			0.167019	−	0.985954i	$-0.446586\pi$
$809$	270.237			0.334038			0.167019	+	0.985954i	$0.446586\pi$
$810$		0			0
$811$		−	207.241i		−	0.255538i	−0.991804	−	0.127769i	$-0.959218\pi$
$811$		−	207.241i		−	0.255538i	0.991804	−	0.127769i	$-0.0407816\pi$
$812$	−590.176	+	698.299i	−0.726818	+	0.859974i
$813$		0			0
$814$	−110.583	−	132.263i	−0.135851	−	0.162486i
$815$	1041.74	+	183.686i	1.27820	+	0.225382i
$816$		0			0
$817$	−168.779	+	141.623i	−0.206584	+	0.173345i
$818$	−1271.79	+	460.342i	−1.55476	+	0.562765i
$819$		0			0
$820$	568.197	−	473.349i	0.692924	−	0.577255i
$821$	−176.322	−	999.970i	−0.214765	−	1.21799i	−0.881315	−	0.472530i	$-0.843341\pi$
$821$	−176.322	−	999.970i	−0.214765	−	1.21799i	0.666550	−	0.745460i	$-0.267770\pi$
$822$		0			0
$823$	−5.31063	−	14.5908i	−0.00645277	−	0.0177288i	0.936424	−	0.350869i	$-0.114114\pi$
$823$	−5.31063	−	14.5908i	−0.00645277	−	0.0177288i	−0.942877	+	0.333141i	$0.891892\pi$
$824$	113.554	+	20.6463i	0.137809	+	0.0250562i
$825$		0			0
$826$	505.955	+	0.897452i	0.612537	+	0.00108650i
$827$	−327.468	−	189.064i	−0.395971	−	0.228614i	0.288773	−	0.957398i	$-0.406753\pi$
$827$	−327.468	−	189.064i	−0.395971	−	0.228614i	−0.684744	+	0.728784i	$0.740086\pi$
$828$		0			0
$829$	258.295	+	447.381i	0.311575	+	0.539663i	0.978703	−	0.205279i	$-0.0658102\pi$
$829$	258.295	+	447.381i	0.311575	+	0.539663i	−0.667129	+	0.744942i	$0.732477\pi$
$830$	−290.842	+	167.231i	−0.350413	+	0.201483i
$831$		0			0
$832$	1370.80	−	482.472i	1.64760	−	0.579894i
$833$	374.941	+	314.613i	0.450110	+	0.377687i
$834$		0			0
$835$	135.619	−	372.610i	0.162418	−	0.446239i
$836$	−462.863	−	170.330i	−0.553663	−	0.203744i
$837$		0			0
$838$	78.0780	+	13.9101i	0.0931719	+	0.0165992i
$839$	328.333	−	902.088i	0.391339	−	1.07519i	−0.575052	−	0.818117i	$-0.695018\pi$
$839$	328.333	−	902.088i	0.391339	−	1.07519i	0.966391	−	0.257077i	$-0.0827595\pi$
$840$		0			0
$841$	−138.368	−	116.105i	−0.164528	−	0.138056i
$842$	43.3952	+	15.8818i	0.0515382	+	0.0188620i
$843$		0			0
$844$	420.733	+	1168.84i	0.498499	+	1.38488i
$845$	606.773	+	1050.96i	0.718075	+	1.24374i
$846$		0			0
$847$	−701.954	−	405.274i	−0.828754	−	0.478481i
$848$	33.1908	−	56.5576i	0.0391401	−	0.0666953i
$849$		0			0
$850$	−71.1903	−	407.970i	−0.0837533	−	0.479965i
$851$	186.053	+	511.176i	0.218629	+	0.600677i
$852$		0			0
$853$	−112.090	−	635.694i	−0.131407	−	0.745245i	−0.977295	−	0.211884i	$-0.932040\pi$
$853$	−112.090	−	635.694i	−0.131407	−	0.745245i	0.845888	−	0.533361i	$-0.179071\pi$
$854$	−465.746	+	553.059i	−0.545370	+	0.647611i
$855$		0			0
$856$	3.47869	−	653.719i	0.00406389	−	0.763691i
$857$	61.7208	−	51.7899i	0.0720196	−	0.0604316i	−0.606067	−	0.795413i	$-0.707254\pi$
$857$	61.7208	−	51.7899i	0.0720196	−	0.0604316i	0.678087	+	0.734982i	$0.262809\pi$
$858$		0			0
$859$	−152.417	−	26.8752i	−0.177435	−	0.0312866i	0.0842245	−	0.996447i	$-0.473159\pi$
$859$	−152.417	−	26.8752i	−0.177435	−	0.0312866i	−0.261660	+	0.965160i	$0.584270\pi$
$860$	−118.698	+	67.9702i	−0.138021	+	0.0790351i
$861$		0			0
$862$	1069.25	+	619.865i	1.24043	+	0.719100i
$863$			29.9557i			0.0347111i	0.999849	+	0.0173556i	$0.00552472\pi$
$863$			29.9557i			0.0347111i	−0.999849	+	0.0173556i	$0.994475\pi$
$864$		0			0
$865$	−961.240			−1.11126
$866$	136.337	−	235.178i	0.157433	−	0.271568i
$867$		0			0
$868$	395.981	+	691.513i	0.456200	+	0.796674i
$869$	24.0062	−	136.146i	0.0276251	−	0.156670i
$870$		0			0
$871$	1319.92	+	1573.02i	1.51541	+	1.80600i
$872$	1546.93	+	8.23178i	1.77400	+	0.00944012i
$873$		0			0
$874$	1190.37	+	1002.44i	1.36198	+	1.14696i
$875$	−1157.51	+	204.100i	−1.32287	+	0.233258i
$876$		0			0
$877$	−1523.86	+	554.639i	−1.73758	+	0.632428i	−0.999123	−	0.0418712i	$-0.986668\pi$
$877$	−1523.86	+	554.639i	−1.73758	+	0.632428i	−0.738458	+	0.674299i	$0.764446\pi$
$878$	667.757	−	116.523i	0.760543	−	0.132714i
$879$		0			0
$880$	−264.076	−	154.973i	−0.300087	−	0.176106i
$881$	123.078	−	213.177i	0.139703	−	0.241972i	−0.787681	−	0.616083i	$-0.788719\pi$
$881$	123.078	−	213.177i	0.139703	−	0.241972i	0.927384	+	0.374111i	$0.122052\pi$
$882$		0			0
$883$	649.429	−	374.948i	0.735481	−	0.424630i	−0.0849433	−	0.996386i	$-0.527071\pi$
$883$	649.429	−	374.948i	0.735481	−	0.424630i	0.820424	+	0.571756i	$0.193738\pi$
$884$	−1388.93	+	499.957i	−1.57119	+	0.565562i
$885$		0			0
$886$	229.874	−	628.105i	0.259451	−	0.708922i
$887$	−102.658	+	122.344i	−0.115737	+	0.137930i	−0.820802	−	0.571213i	$-0.806473\pi$
$887$	−102.658	+	122.344i	−0.115737	+	0.137930i	0.705065	+	0.709142i	$0.250918\pi$
$888$		0			0
$889$	−1312.58	−	477.739i	−1.47646	−	0.537389i
$890$	110.704	−	621.387i	0.124387	−	0.698187i
$891$		0			0
$892$	−27.9281	+	75.8931i	−0.0313096	+	0.0850820i
$893$	494.383	+	179.941i	0.553620	+	0.201501i
$894$		0			0
$895$	110.587	−	131.793i	0.123561	−	0.147255i
$896$	1123.59	−	183.765i	1.25401	−	0.205095i
$897$		0			0
$898$	66.5683	+	115.773i	0.0741295	+	0.128924i
$899$	498.447	−	287.779i	0.554446	−	0.320110i
$900$		0			0
$901$	−33.3064	+	57.6883i	−0.0369660	+	0.0640270i
$902$	1.02383	−	577.204i	0.00113507	−	0.639915i
$903$		0			0
$904$	2.10319	−	11.5675i	0.00232654	−	0.0127959i
$905$	473.017	−	172.164i	0.522671	−	0.190237i
$906$		0			0
$907$	372.598	−	65.6990i	0.410802	−	0.0724355i	0.0355719	−	0.999367i	$-0.488675\pi$
$907$	372.598	−	65.6990i	0.410802	−	0.0724355i	0.375230	+	0.926932i	$0.377564\pi$
$908$	−121.708	−	146.095i	−0.134040	−	0.160898i
$909$		0			0
$910$	481.369	+	1329.89i	0.528977	+	1.46141i
$911$	819.489	+	976.629i	0.899549	+	1.07204i	0.997046	+	0.0768047i	$0.0244718\pi$
$911$	819.489	+	976.629i	0.899549	+	1.07204i	−0.0974974	+	0.995236i	$0.531084\pi$
$912$		0			0
$913$	−45.4701	+	257.874i	−0.0498030	+	0.282447i
$914$	654.404	−	547.135i	0.715979	−	0.598616i
$915$		0			0
$916$	−215.637	−	182.249i	−0.235412	−	0.198962i
$917$	−451.772			−0.492663
$918$		0			0
$919$		−	552.951i		−	0.601687i	−0.953673	−	0.300844i	$-0.902732\pi$
$919$		−	552.951i		−	0.601687i	0.953673	−	0.300844i	$-0.0972682\pi$
$920$	617.072	+	743.396i	0.670731	+	0.808040i
$921$		0			0
$922$	176.016	−	147.163i	0.190906	−	0.159613i
$923$	−2269.65	−	400.201i	−2.45900	−	0.433587i
$924$		0			0
$925$	153.927	−	129.160i	0.166408	−	0.139633i
$926$	−215.162	−	594.432i	−0.232356	−	0.641935i
$927$		0			0
$928$	−135.608	−	811.069i	−0.146129	−	0.873996i
$929$	−37.1959	−	210.948i	−0.0400386	−	0.227070i	0.958222	−	0.286026i	$-0.0923342\pi$
$929$	−37.1959	−	210.948i	−0.0400386	−	0.227070i	−0.998261	+	0.0589551i	$0.981223\pi$
$930$		0			0
$931$	232.365	+	638.417i	0.249586	+	0.685732i
$932$	−1532.96	−	5.43829i	−1.64481	−	0.00583508i
$933$		0			0
$934$	1.50864	−	850.526i	0.00161525	−	0.910627i
$935$	269.356	+	155.513i	0.288081	+	0.166324i
$936$		0			0
$937$	245.511	+	425.237i	0.262018	+	0.453829i	0.966778	−	0.255617i	$-0.0822787\pi$
$937$	245.511	+	425.237i	0.262018	+	0.453829i	−0.704760	+	0.709446i	$0.748945\pi$
$938$	801.900	+	1394.64i	0.854904	+	1.48682i
$939$		0			0
$940$	282.278	+	164.311i	0.300296	+	0.174799i
$941$	1364.30	+	1144.79i	1.44984	+	1.21656i	0.932694	+	0.360668i	$0.117451\pi$
$941$	1364.30	+	1144.79i	1.44984	+	1.21656i	0.517150	+	0.855895i	$0.326993\pi$
$942$		0			0
$943$	−622.912	+	1711.44i	−0.660564	+	1.81488i
$944$	−294.976	+	346.515i	−0.312474	+	0.367071i
$945$		0			0
$946$	−18.7248	+	105.103i	−0.0197937	+	0.111103i
$947$	−282.162	+	775.235i	−0.297954	+	0.818622i	0.696887	+	0.717180i	$0.254568\pi$
$947$	−282.162	+	775.235i	−0.297954	+	0.818622i	−0.994842	+	0.101441i	$0.967655\pi$
$948$		0			0
$949$	−556.706	−	467.131i	−0.586623	−	0.492236i
$950$	197.567	−	539.829i	0.207965	−	0.568241i
$951$		0			0
$952$	−1139.98	+	194.760i	−1.19745	+	0.204579i
$953$	−857.960	−	1486.03i	−0.900273	−	1.55932i	−0.827140	−	0.561996i	$-0.810034\pi$
$953$	−857.960	−	1486.03i	−0.900273	−	1.55932i	−0.0731332	−	0.997322i	$-0.523300\pi$
$954$		0			0
$955$	852.256	+	492.050i	0.892414	+	0.515236i
$956$	−1351.75	−	243.298i	−1.41397	−	0.254496i
$957$		0			0
$958$	307.314	−	53.6259i	0.320787	−	0.0559769i
$959$	−270.810	−	744.044i	−0.282388	−	0.775854i
$960$		0			0
$961$	79.7679	+	452.386i	0.0830050	+	0.470745i
$962$	−547.851	−	461.360i	−0.569492	−	0.479584i
$963$		0			0
$964$	164.304	+	951.543i	0.170440	+	0.987078i
$965$	−468.540	+	393.151i	−0.485533	+	0.407411i
$966$		0			0
$967$	−254.880	−	44.9423i	−0.263578	−	0.0464760i	0.0402972	−	0.999188i	$-0.487170\pi$
$967$	−254.880	−	44.9423i	−0.263578	−	0.0464760i	−0.303875	+	0.952712i	$0.598281\pi$
$968$	686.370	−	245.690i	0.709060	−	0.253812i
$969$		0			0
$970$	521.291	−	899.216i	0.537414	−	0.927027i
$971$			1362.29i			1.40298i	0.712681	+	0.701488i	$0.247481\pi$
$971$			1362.29i			1.40298i	−0.712681	+	0.701488i	$0.752519\pi$
$972$		0			0
$973$	614.428			0.631478
$974$	−944.365	−	547.465i	−0.969574	−	0.562079i
$975$		0			0
$976$	−108.380	−	641.223i	−0.111045	−	0.656990i
$977$	185.676	−	1053.02i	0.190047	−	1.07781i	−0.729251	−	0.684246i	$-0.760131\pi$
$977$	185.676	−	1053.02i	0.190047	−	1.07781i	0.919298	−	0.393562i	$-0.128757\pi$
$978$		0			0
$979$	−316.656	−	377.375i	−0.323448	−	0.385470i
$980$	71.7665	+	415.625i	0.0732311	+	0.424107i
$981$		0			0
$982$	−252.944	+	300.363i	−0.257580	+	0.305869i
$983$	427.195	−	75.3260i	0.434583	−	0.0766287i	0.0479229	−	0.998851i	$-0.484740\pi$
$983$	427.195	−	75.3260i	0.434583	−	0.0766287i	0.386660	+	0.922222i	$0.373629\pi$
$984$		0			0
$985$	493.791	−	179.725i	0.501310	−	0.182462i
$986$	143.591	+	822.876i	0.145630	+	0.834560i
$987$		0			0
$988$	−2016.62	−	362.965i	−2.04111	−	0.367374i
$989$	168.429	−	291.727i	0.170302	−	0.294972i
$990$		0			0
$991$	−866.750	+	500.419i	−0.874622	+	0.504963i	−0.868881	−	0.495020i	$-0.835161\pi$
$991$	−866.750	+	500.419i	−0.874622	+	0.504963i	−0.00574052	+	0.999984i	$0.501827\pi$
$992$	−704.691	−	130.710i	−0.710374	−	0.131765i
$993$		0			0
$994$	−1695.58	−	620.549i	−1.70582	−	0.624295i
$995$	374.973	−	446.875i	0.376857	−	0.449121i
$996$		0			0
$997$	834.713	+	303.811i	0.837225	+	0.304725i	0.724820	−	0.688938i	$-0.241923\pi$
$997$	834.713	+	303.811i	0.837225	+	0.304725i	0.112404	+	0.993663i	$0.464145\pi$
$998$	1895.15	+	337.633i	1.89895	+	0.338310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.22		204
3.2	odd	2		108.3.j.a.31.13	yes	204
4.3	odd	2	inner	324.3.j.a.307.15		204
12.11	even	2		108.3.j.a.31.20	yes	204
27.7	even	9	inner	324.3.j.a.19.15		204
27.20	odd	18		108.3.j.a.7.20	yes	204
108.7	odd	18	inner	324.3.j.a.19.22		204
108.47	even	18		108.3.j.a.7.13	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.13	✓	204	108.47	even	18
108.3.j.a.7.20	yes	204	27.20	odd	18
108.3.j.a.31.13	yes	204	3.2	odd	2
108.3.j.a.31.20	yes	204	12.11	even	2
324.3.j.a.19.15		204	27.7	even	9	inner
324.3.j.a.19.22		204	108.7	odd	18	inner
324.3.j.a.307.15		204	4.3	odd	2	inner
324.3.j.a.307.22		204	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00307 - 1.73027i) q^{2} +(-1.98770 - 3.47117i) q^{4} +(-0.608002 + 3.44815i) q^{5} +(5.71739 + 6.81372i) q^{7} +(-7.99989 - 0.0425704i) q^{8} +O(q^{10})\)	\(q+(1.00307 - 1.73027i) q^{2} +(-1.98770 - 3.47117i) q^{4} +(-0.608002 + 3.44815i) q^{5} +(5.71739 + 6.81372i) q^{7} +(-7.99989 - 0.0425704i) q^{8} +(5.35638 + 4.51075i) q^{10} +(5.38256 - 0.949091i) q^{11} +(21.3373 - 7.76615i) q^{13} +(17.5245 - 3.05801i) q^{14} +(-8.09811 + 13.7993i) q^{16} +(8.12631 - 14.0752i) q^{17} +(19.5372 - 11.2798i) q^{19} +(13.1777 - 4.74341i) q^{20} +(3.75690 - 10.2653i) q^{22} +(-22.1707 + 26.4221i) q^{23} +(11.9722 + 4.35753i) q^{25} +(7.96527 - 44.7094i) q^{26} +(12.2872 - 33.3897i) q^{28} +(-24.1480 - 8.78914i) q^{29} +(-14.3967 + 17.1573i) q^{31} +(15.7536 + 27.8536i) q^{32} +(-16.2027 - 28.1791i) q^{34} +(-26.9709 + 15.5717i) q^{35} +(7.88574 - 13.6585i) q^{37} +(0.0800315 - 45.1192i) q^{38} +(5.01074 - 27.5590i) q^{40} +(49.6190 - 18.0598i) q^{41} +(-9.61800 + 1.69591i) q^{43} +(-13.9934 - 16.7973i) q^{44} +(23.4786 + 64.8646i) q^{46} +(14.9904 + 17.8648i) q^{47} +(-5.22945 + 29.6577i) q^{49} +(19.5487 - 16.3443i) q^{50} +(-69.3698 - 58.6288i) q^{52} -4.09859 q^{53} +19.1370i q^{55} +(-45.4484 - 54.7523i) q^{56} +(-39.4297 + 32.9665i) q^{58} +(28.0094 + 4.93882i) q^{59} +(-31.1357 + 26.1260i) q^{61} +(15.2459 + 42.1201i) q^{62} +(63.9964 + 0.681117i) q^{64} +(13.8057 + 78.2962i) q^{65} +(30.9299 + 84.9793i) q^{67} +(-65.0100 - 0.230627i) q^{68} +(-0.110483 + 62.2866i) q^{70} +(-87.8991 - 50.7486i) q^{71} +(-16.0025 - 27.7171i) q^{73} +(-15.7230 - 27.3449i) q^{74} +(-77.9884 - 45.3963i) q^{76} +(37.2410 + 31.2489i) q^{77} +(8.65102 - 23.7685i) q^{79} +(-42.6584 - 36.3135i) q^{80} +(18.5229 - 103.970i) q^{82} +(-16.3859 + 45.0198i) q^{83} +(43.5925 + 36.5785i) q^{85} +(-6.71314 + 18.3429i) q^{86} +(-43.1003 + 7.36348i) q^{88} +(-45.0663 - 78.0571i) q^{89} +(174.910 + 100.984i) q^{91} +(135.784 + 24.4394i) q^{92} +(45.9475 - 8.01777i) q^{94} +(27.0159 + 74.2255i) q^{95} +(-25.7741 - 146.172i) q^{97} +(46.0705 + 38.7972i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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