LMFDB - Embedded newform 324.3.f.m.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.m.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.151388 + 1.99426i) q^{2} +(-3.95416 - 0.603814i) q^{4} +(-1.80278 - 3.12250i) q^{5} +(-5.40833 - 3.12250i) q^{7} +(1.80278 - 7.79423i) q^{8} +O(q^{10})$	\(q+(-0.151388 + 1.99426i) q^{2} +(-3.95416 - 0.603814i) q^{4} +(-1.80278 - 3.12250i) q^{5} +(-5.40833 - 3.12250i) q^{7} +(1.80278 - 7.79423i) q^{8} +(6.50000 - 3.12250i) q^{10} +(10.5000 + 6.06218i) q^{11} +(8.00000 + 13.8564i) q^{13} +(7.04584 - 10.3129i) q^{14} +(15.2708 + 4.77516i) q^{16} +14.4222 q^{17} +37.4700i q^{19} +(5.24306 + 13.4354i) q^{20} +(-13.6791 + 20.0220i) q^{22} +(15.0000 - 8.66025i) q^{23} +(6.00000 - 10.3923i) q^{25} +(-28.8444 + 13.8564i) q^{26} +(19.5000 + 15.6125i) q^{28} +(25.2389 - 43.7150i) q^{29} +(-5.40833 + 3.12250i) q^{31} +(-11.8347 + 29.7311i) q^{32} +(-2.18335 + 28.7617i) q^{34} +22.5167i q^{35} +26.0000 q^{37} +(-74.7250 - 5.67250i) q^{38} +(-27.5875 + 8.42208i) q^{40} +(3.60555 + 6.24500i) q^{41} +(10.8167 + 6.24500i) q^{43} +(-37.8583 - 30.3109i) q^{44} +(15.0000 + 31.2250i) q^{46} +(-3.00000 - 1.73205i) q^{47} +(-5.00000 - 8.66025i) q^{49} +(19.8167 + 13.5388i) q^{50} +(-23.2666 - 59.6210i) q^{52} +68.5055 q^{53} -43.7150i q^{55} +(-34.0875 + 36.5246i) q^{56} +(83.3583 + 56.9508i) q^{58} +(-66.0000 + 38.1051i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-5.40833 - 11.2583i) q^{62} +(-57.5000 - 28.1025i) q^{64} +(28.8444 - 49.9600i) q^{65} +(-54.0833 + 31.2250i) q^{67} +(-57.0278 - 8.70833i) q^{68} +(-44.9041 - 3.40875i) q^{70} +62.3538i q^{71} -19.0000 q^{73} +(-3.93608 + 51.8508i) q^{74} +(22.6249 - 148.162i) q^{76} +(-37.8583 - 65.5725i) q^{77} +(43.2666 + 24.9800i) q^{79} +(-12.6194 - 56.2917i) q^{80} +(-13.0000 + 6.24500i) q^{82} +(100.500 + 58.0237i) q^{83} +(-26.0000 - 45.0333i) q^{85} +(-14.0917 + 20.6258i) q^{86} +(66.1791 - 70.9107i) q^{88} +79.3221 q^{89} -99.9200i q^{91} +(-64.5416 + 25.1868i) q^{92} +(3.90833 - 5.72058i) q^{94} +(117.000 - 67.5500i) q^{95} +(-59.5000 + 103.057i) q^{97} +(18.0278 - 8.66025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 4 * q + 3 * q^2 - 5 * q^4	$ 4 q + 3 q^{2} - 5 q^{4} + 26 q^{10} + 42 q^{11} + 32 q^{13} + 39 q^{14} + 7 q^{16} + 39 q^{20} + 21 q^{22} + 60 q^{23} + 24 q^{25} + 78 q^{28} - 87 q^{32} - 52 q^{34} + 104 q^{37} - 234 q^{38} - 13 q^{40} + 60 q^{46} - 12 q^{47} - 20 q^{49} + 36 q^{50} + 80 q^{52} - 39 q^{56} + 182 q^{58} - 264 q^{59} - 16 q^{61} - 230 q^{64} - 156 q^{68} - 39 q^{70} - 76 q^{73} + 78 q^{74} - 234 q^{76} - 52 q^{82} + 402 q^{83} - 104 q^{85} - 78 q^{86} + 189 q^{88} - 150 q^{92} - 6 q^{94} + 468 q^{95} - 238 q^{97}+O(q^{100}) $ 4 * q + 3 * q^2 - 5 * q^4 + 26 * q^10 + 42 * q^11 + 32 * q^13 + 39 * q^14 + 7 * q^16 + 39 * q^20 + 21 * q^22 + 60 * q^23 + 24 * q^25 + 78 * q^28 - 87 * q^32 - 52 * q^34 + 104 * q^37 - 234 * q^38 - 13 * q^40 + 60 * q^46 - 12 * q^47 - 20 * q^49 + 36 * q^50 + 80 * q^52 - 39 * q^56 + 182 * q^58 - 264 * q^59 - 16 * q^61 - 230 * q^64 - 156 * q^68 - 39 * q^70 - 76 * q^73 + 78 * q^74 - 234 * q^76 - 52 * q^82 + 402 * q^83 - 104 * q^85 - 78 * q^86 + 189 * q^88 - 150 * q^92 - 6 * q^94 + 468 * q^95 - 238 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.151388	+	1.99426i	−0.0756939	+	0.997131i
$2$	−0.151388	+	1.99426i	−0.0756939	+	0.997131i
$3$		0			0
$3$		0			0
$4$	−3.95416	−	0.603814i	−0.988541	−	0.150954i
$5$	−1.80278	−	3.12250i	−0.360555	−	0.624500i	0.627497	−	0.778619i	$-0.284079\pi$
$5$	−1.80278	−	3.12250i	−0.360555	−	0.624500i	−0.988052	+	0.154119i	$0.950746\pi$
$6$		0			0
$7$	−5.40833	−	3.12250i	−0.772618	−	0.446071i	0.0611897	−	0.998126i	$-0.480511\pi$
$7$	−5.40833	−	3.12250i	−0.772618	−	0.446071i	−0.833808	+	0.552055i	$0.813844\pi$
$8$	1.80278	−	7.79423i	0.225347	−	0.974279i
$9$		0			0
$10$	6.50000	−	3.12250i	0.650000	−	0.312250i
$11$	10.5000	+	6.06218i	0.954545	+	0.551107i	0.894490	−	0.447088i	$-0.147539\pi$
$11$	10.5000	+	6.06218i	0.954545	+	0.551107i	0.0600555	+	0.998195i	$0.480872\pi$
$12$		0			0
$13$	8.00000	+	13.8564i	0.615385	+	1.06588i	0.990317	+	0.138825i	$0.0443326\pi$
$13$	8.00000	+	13.8564i	0.615385	+	1.06588i	−0.374932	+	0.927052i	$0.622334\pi$
$14$	7.04584	−	10.3129i	0.503274	−	0.736637i
$15$		0			0
$16$	15.2708	+	4.77516i	0.954426	+	0.298447i
$17$	14.4222			0.848365			0.424183	−	0.905577i	$-0.360562\pi$
$17$	14.4222			0.848365			0.424183	+	0.905577i	$0.360562\pi$
$18$		0			0
$19$			37.4700i			1.97210i	0.166436	+	0.986052i	$0.446774\pi$
$19$			37.4700i			1.97210i	−0.166436	+	0.986052i	$0.553226\pi$
$20$	5.24306	+	13.4354i	0.262153	+	0.671771i
$21$		0			0
$22$	−13.6791	+	20.0220i	−0.621779	+	0.910092i
$23$	15.0000	−	8.66025i	0.652174	−	0.376533i	−0.137115	−	0.990555i	$-0.543783\pi$
$23$	15.0000	−	8.66025i	0.652174	−	0.376533i	0.789289	+	0.614022i	$0.210450\pi$
$24$		0			0
$25$	6.00000	−	10.3923i	0.240000	−	0.415692i
$26$	−28.8444	+	13.8564i	−1.10940	+	0.532939i
$27$		0			0
$28$	19.5000	+	15.6125i	0.696429	+	0.557589i
$29$	25.2389	−	43.7150i	0.870305	−	1.50741i	0.00862457	−	0.999963i	$-0.497255\pi$
$29$	25.2389	−	43.7150i	0.870305	−	1.50741i	0.861681	−	0.507451i	$-0.169412\pi$
$30$		0			0
$31$	−5.40833	+	3.12250i	−0.174462	+	0.100726i	−0.584688	−	0.811258i	$-0.698783\pi$
$31$	−5.40833	+	3.12250i	−0.174462	+	0.100726i	0.410226	+	0.911984i	$0.365450\pi$
$32$	−11.8347	+	29.7311i	−0.369835	+	0.929097i
$33$		0			0
$34$	−2.18335	+	28.7617i	−0.0642161	+	0.845931i
$35$			22.5167i			0.643333i
$36$		0			0
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$	−74.7250	−	5.67250i	−1.96645	−	0.149276i
$39$		0			0
$40$	−27.5875	+	8.42208i	−0.689687	+	0.210552i
$41$	3.60555	+	6.24500i	0.0879403	+	0.152317i	0.906640	−	0.421904i	$-0.138638\pi$
$41$	3.60555	+	6.24500i	0.0879403	+	0.152317i	−0.818700	+	0.574221i	$0.805305\pi$
$42$		0			0
$43$	10.8167	+	6.24500i	0.251550	+	0.145233i	0.620474	−	0.784227i	$-0.286940\pi$
$43$	10.8167	+	6.24500i	0.251550	+	0.145233i	−0.368924	+	0.929460i	$0.620274\pi$
$44$	−37.8583	−	30.3109i	−0.860416	−	0.688884i
$45$		0			0
$46$	15.0000	+	31.2250i	0.326087	+	0.678804i
$47$	−3.00000	−	1.73205i	−0.0638298	−	0.0368521i	0.467745	−	0.883863i	$-0.345066\pi$
$47$	−3.00000	−	1.73205i	−0.0638298	−	0.0368521i	−0.531575	+	0.847011i	$0.678400\pi$
$48$		0			0
$49$	−5.00000	−	8.66025i	−0.102041	−	0.176740i
$50$	19.8167	+	13.5388i	0.396333	+	0.270777i
$51$		0			0
$52$	−23.2666	−	59.6210i	−0.447435	−	1.14656i
$53$	68.5055			1.29256			0.646278	−	0.763102i	$-0.276325\pi$
$53$	68.5055			1.29256			0.646278	+	0.763102i	$0.276325\pi$
$54$		0			0
$55$		−	43.7150i		−	0.794818i
$56$	−34.0875	+	36.5246i	−0.608705	+	0.652224i
$57$		0			0
$58$	83.3583	+	56.9508i	1.43721	+	0.981911i
$59$	−66.0000	+	38.1051i	−1.11864	+	0.645849i	−0.941054	−	0.338255i	$-0.890163\pi$
$59$	−66.0000	+	38.1051i	−1.11864	+	0.645849i	−0.177590	+	0.984105i	$0.556830\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.0655738	+	0.113577i	−0.896948	−	0.442135i	$-0.854221\pi$
$61$	−4.00000	+	6.92820i	−0.0655738	+	0.113577i	0.831375	+	0.555712i	$0.187554\pi$
$62$	−5.40833	−	11.2583i	−0.0872311	−	0.181586i
$63$		0			0
$64$	−57.5000	−	28.1025i	−0.898438	−	0.439101i
$65$	28.8444	−	49.9600i	0.443760	−	0.768615i
$66$		0			0
$67$	−54.0833	+	31.2250i	−0.807213	+	0.466045i	−0.845987	−	0.533203i	$-0.820988\pi$
$67$	−54.0833	+	31.2250i	−0.807213	+	0.466045i	0.0387741	+	0.999248i	$0.487655\pi$
$68$	−57.0278	−	8.70833i	−0.838643	−	0.128064i
$69$		0			0
$70$	−44.9041	−	3.40875i	−0.641487	−	0.0486964i
$71$			62.3538i			0.878223i	0.898433	+	0.439111i	$0.144707\pi$
$71$			62.3538i			0.878223i	−0.898433	+	0.439111i	$0.855293\pi$
$72$		0			0
$73$	−19.0000			−0.260274			−0.130137	−	0.991496i	$-0.541542\pi$
$73$	−19.0000			−0.260274			−0.130137	+	0.991496i	$0.541542\pi$
$74$	−3.93608	+	51.8508i	−0.0531903	+	0.700687i
$75$		0			0
$76$	22.6249	−	148.162i	0.297696	−	1.94951i
$77$	−37.8583	−	65.5725i	−0.491666	−	0.851591i
$78$		0			0
$79$	43.2666	+	24.9800i	0.547679	+	0.316202i	0.748185	−	0.663490i	$-0.230925\pi$
$79$	43.2666	+	24.9800i	0.547679	+	0.316202i	−0.200507	+	0.979692i	$0.564259\pi$
$80$	−12.6194	−	56.2917i	−0.157743	−	0.703646i
$81$		0			0
$82$	−13.0000	+	6.24500i	−0.158537	+	0.0761585i
$83$	100.500	+	58.0237i	1.21084	+	0.699081i	0.962943	−	0.269705i	$-0.0869261\pi$
$83$	100.500	+	58.0237i	1.21084	+	0.699081i	0.247900	+	0.968786i	$0.420259\pi$
$84$		0			0
$85$	−26.0000	−	45.0333i	−0.305882	−	0.529804i
$86$	−14.0917	+	20.6258i	−0.163857	+	0.239835i
$87$		0			0
$88$	66.1791	−	70.9107i	0.752036	−	0.805803i
$89$	79.3221			0.891260			0.445630	−	0.895217i	$-0.352980\pi$
$89$	79.3221			0.891260			0.445630	+	0.895217i	$0.352980\pi$
$90$		0			0
$91$		−	99.9200i		−	1.09802i
$92$	−64.5416	+	25.1868i	−0.701540	+	0.273770i
$93$		0			0
$94$	3.90833	−	5.72058i	0.0415779	−	0.0608572i
$95$	117.000	−	67.5500i	1.23158	−	0.711052i
$96$		0			0
$97$	−59.5000	+	103.057i	−0.613402	+	1.06244i	0.377261	+	0.926107i	$0.376866\pi$
$97$	−59.5000	+	103.057i	−0.613402	+	1.06244i	−0.990663	+	0.136336i	$0.956467\pi$
$98$	18.0278	−	8.66025i	0.183957	−	0.0883699i
$99$		0			0
$100$	−30.0000	+	37.4700i	−0.300000	+	0.374700i
$101$	30.6472	−	53.0825i	0.303437	−	0.525569i	−0.673475	−	0.739210i	$-0.735199\pi$
$101$	30.6472	−	53.0825i	0.303437	−	0.525569i	0.976912	+	0.213641i	$0.0685323\pi$
$102$		0			0
$103$	108.167	−	62.4500i	1.05016	−	0.606310i	0.127466	−	0.991843i	$-0.459316\pi$
$103$	108.167	−	62.4500i	1.05016	−	0.606310i	0.922694	+	0.385532i	$0.125982\pi$
$104$	122.422	−	37.3738i	1.17714	−	0.359364i
$105$		0			0
$106$	−10.3709	+	136.618i	−0.0978386	+	1.28885i
$107$		−	129.904i		−	1.21405i	−0.794681	−	0.607027i	$-0.792362\pi$
$107$		−	129.904i		−	1.21405i	0.794681	−	0.607027i	$-0.207638\pi$
$108$		0			0
$109$	−46.0000			−0.422018			−0.211009	−	0.977484i	$-0.567675\pi$
$109$	−46.0000			−0.422018			−0.211009	+	0.977484i	$0.567675\pi$
$110$	87.1791	+	6.61792i	0.792538	+	0.0601629i
$111$		0			0
$112$	−67.6791	−	73.5087i	−0.604278	−	0.656328i
$113$	46.8722	+	81.1850i	0.414798	+	0.718451i	0.995407	−	0.0957312i	$-0.0305189\pi$
$113$	46.8722	+	81.1850i	0.414798	+	0.718451i	−0.580609	+	0.814182i	$0.697186\pi$
$114$		0			0
$115$	−54.0833	−	31.2250i	−0.470289	−	0.271522i
$116$	−126.194	+	157.617i	−1.08788	+	1.35876i
$117$		0			0
$118$	−66.0000	−	137.390i	−0.559322	−	1.16432i
$119$	−78.0000	−	45.0333i	−0.655462	−	0.378431i
$120$		0			0
$121$	13.0000	+	22.5167i	0.107438	+	0.186088i
$122$	−13.2111	−	9.02589i	−0.108288	−	0.0739827i
$123$		0			0
$124$	23.2708	−	9.08125i	0.187668	−	0.0732359i
$125$	−133.405			−1.06724
$126$		0			0
$127$			18.7350i			0.147520i	0.997276	+	0.0737598i	$0.0234998\pi$
$127$			18.7350i			0.147520i	−0.997276	+	0.0737598i	$0.976500\pi$
$128$	64.7485	−	110.416i	0.505848	−	0.862623i
$129$		0			0
$130$	95.2666	+	65.0866i	0.732820	+	0.500667i
$131$	37.5000	−	21.6506i	0.286260	−	0.165272i	−0.349994	−	0.936752i	$-0.613816\pi$
$131$	37.5000	−	21.6506i	0.286260	−	0.165272i	0.636254	+	0.771480i	$0.280483\pi$
$132$		0			0
$133$	117.000	−	202.650i	0.879699	−	1.52368i
$134$	−54.0833	−	112.583i	−0.403606	−	0.840174i
$135$		0			0
$136$	26.0000	−	112.410i	0.191176	−	0.826544i
$137$	−39.6611	+	68.6950i	−0.289497	+	0.501423i	−0.973690	−	0.227878i	$-0.926821\pi$
$137$	−39.6611	+	68.6950i	−0.289497	+	0.501423i	0.684193	+	0.729301i	$0.260155\pi$
$138$		0			0
$139$	108.167	−	62.4500i	0.778177	−	0.449280i	−0.0576071	−	0.998339i	$-0.518347\pi$
$139$	108.167	−	62.4500i	0.778177	−	0.449280i	0.835784	+	0.549059i	$0.185014\pi$
$140$	13.5959	−	89.0346i	0.0971134	−	0.635961i
$141$		0			0
$142$	−124.350	−	9.43961i	−0.875703	−	0.0664761i
$143$			193.990i			1.35657i
$144$		0			0
$145$	−182.000			−1.25517
$146$	2.87637	−	37.8910i	0.0197012	−	0.259527i
$147$		0			0
$148$	−102.808	−	15.6992i	−0.694650	−	0.106075i
$149$	−1.80278	−	3.12250i	−0.0120992	−	0.0209564i	0.859912	−	0.510442i	$-0.170518\pi$
$149$	−1.80278	−	3.12250i	−0.0120992	−	0.0209564i	−0.872012	+	0.489485i	$0.837185\pi$
$150$		0			0
$151$	−167.658	−	96.7975i	−1.11032	−	0.641043i	−0.171407	−	0.985200i	$-0.554831\pi$
$151$	−167.658	−	96.7975i	−1.11032	−	0.641043i	−0.938912	+	0.344157i	$0.888165\pi$
$152$	292.050	+	67.5500i	1.92138	+	0.444408i
$153$		0			0
$154$	136.500	−	65.5725i	0.886364	−	0.425795i
$155$	19.5000	+	11.2583i	0.125806	+	0.0726344i
$156$		0			0
$157$	−46.0000	−	79.6743i	−0.292994	−	0.507480i	0.681523	−	0.731797i	$-0.261318\pi$
$157$	−46.0000	−	79.6743i	−0.292994	−	0.507480i	−0.974516	+	0.224317i	$0.927985\pi$
$158$	−56.3667	+	82.5033i	−0.356751	+	0.522173i
$159$		0			0
$160$	114.171	−	16.6446i	0.713567	−	0.104029i
$161$	−108.167			−0.671842
$162$		0			0
$163$			149.880i			0.919509i	0.888046	+	0.459754i	$0.152063\pi$
$163$			149.880i			0.919509i	−0.888046	+	0.459754i	$0.847937\pi$
$164$	−10.4861	−	26.8708i	−0.0639398	−	0.163846i
$165$		0			0
$166$	−130.929	+	191.639i	−0.788729	+	1.15445i
$167$	−147.000	+	84.8705i	−0.880240	+	0.508207i	−0.870737	−	0.491748i	$-0.836358\pi$
$167$	−147.000	+	84.8705i	−0.880240	+	0.508207i	−0.00950214	+	0.999955i	$0.503025\pi$
$168$		0			0
$169$	−43.5000	+	75.3442i	−0.257396	+	0.445824i
$170$	93.7443	−	45.0333i	0.551437	−	0.264902i
$171$		0			0
$172$	−39.0000	−	31.2250i	−0.226744	−	0.181541i
$173$	−88.3360	+	153.002i	−0.510613	+	0.884407i	0.489312	+	0.872109i	$0.337248\pi$
$173$	−88.3360	+	153.002i	−0.510613	+	0.884407i	−0.999924	+	0.0122982i	$0.996085\pi$
$174$		0			0
$175$	−64.8999	+	37.4700i	−0.370857	+	0.214114i
$176$	131.396	+	142.714i	0.746567	+	0.810873i
$177$		0			0
$178$	−12.0084	+	158.189i	−0.0674629	+	0.888703i
$179$		−	265.004i		−	1.48047i	−0.672349	−	0.740234i	$-0.734715\pi$
$179$		−	265.004i		−	1.48047i	0.672349	−	0.740234i	$-0.265285\pi$
$180$		0			0
$181$	272.000			1.50276			0.751381	−	0.659868i	$-0.229388\pi$
$181$	272.000			1.50276			0.751381	+	0.659868i	$0.229388\pi$
$182$	199.267	+	15.1267i	1.09487	+	0.0831135i
$183$		0			0
$184$	−40.4584	−	132.526i	−0.219882	−	0.720250i
$185$	−46.8722	−	81.1850i	−0.253363	−	0.438838i
$186$		0			0
$187$	151.433	+	87.4300i	0.809803	+	0.467540i
$188$	10.8167	+	8.66025i	0.0575354	+	0.0460652i
$189$		0			0
$190$	117.000	+	243.555i	0.615789	+	1.28187i
$191$	−228.000	−	131.636i	−1.19372	−	0.689193i	−0.234570	−	0.972099i	$-0.575368\pi$
$191$	−228.000	−	131.636i	−1.19372	−	0.689193i	−0.959148	+	0.282906i	$0.908701\pi$
$192$		0			0
$193$	93.5000	+	161.947i	0.484456	+	0.839102i	0.999841	−	0.0178567i	$-0.00568425\pi$
$193$	93.5000	+	161.947i	0.484456	+	0.839102i	−0.515385	+	0.856959i	$0.672351\pi$
$194$	−196.515	−	134.260i	−1.01296	−	0.692063i
$195$		0			0
$196$	14.5416	+	37.2631i	0.0741920	+	0.190118i
$197$	−18.0278			−0.0915115			−0.0457557	−	0.998953i	$-0.514570\pi$
$197$	−18.0278			−0.0915115			−0.0457557	+	0.998953i	$0.514570\pi$
$198$		0			0
$199$			93.6750i			0.470728i	0.971907	+	0.235364i	$0.0756283\pi$
$199$			93.6750i			0.470728i	−0.971907	+	0.235364i	$0.924372\pi$
$200$	−70.1833	−	65.5004i	−0.350917	−	0.327502i
$201$		0			0
$202$	101.221	+	69.1546i	0.501093	+	0.342349i
$203$	−273.000	+	157.617i	−1.34483	+	0.776437i
$204$		0			0
$205$	13.0000	−	22.5167i	0.0634146	−	0.109837i
$206$	108.167	+	225.167i	0.525080	+	1.09304i
$207$		0			0
$208$	56.0000	+	249.800i	0.269231	+	1.20096i
$209$	−227.150	+	393.435i	−1.08684	+	1.88246i
$210$		0			0
$211$	−54.0833	+	31.2250i	−0.256319	+	0.147986i	−0.622654	−	0.782497i	$-0.713946\pi$
$211$	−54.0833	+	31.2250i	−0.256319	+	0.147986i	0.366335	+	0.930483i	$0.380612\pi$
$212$	−270.882	−	41.3646i	−1.27774	−	0.195116i
$213$		0			0
$214$	259.062	+	19.6659i	1.21057	+	0.0918965i
$215$		−	45.0333i		−	0.209457i
$216$		0			0
$217$	39.0000			0.179724
$218$	6.96384	−	91.7361i	0.0319442	−	0.420808i
$219$		0			0
$220$	−26.3957	+	172.856i	−0.119981	+	0.785710i
$221$	115.378	+	199.840i	0.522071	+	0.904253i
$222$		0			0
$223$	173.066	+	99.9200i	0.776083	+	0.448072i	0.835040	−	0.550189i	$-0.185444\pi$
$223$	173.066	+	99.9200i	0.776083	+	0.448072i	−0.0589574	+	0.998260i	$0.518778\pi$
$224$	156.841	−	123.842i	0.700185	−	0.552864i
$225$		0			0
$226$	−169.000	+	81.1850i	−0.747788	+	0.359226i
$227$	−66.0000	−	38.1051i	−0.290749	−	0.167864i	0.347531	−	0.937669i	$-0.387020\pi$
$227$	−66.0000	−	38.1051i	−0.290749	−	0.167864i	−0.638280	+	0.769805i	$0.720354\pi$
$228$		0			0
$229$	107.000	+	185.329i	0.467249	+	0.809299i	0.999300	−	0.0374135i	$-0.0119119\pi$
$229$	107.000	+	185.329i	0.467249	+	0.809299i	−0.532051	+	0.846712i	$0.678579\pi$
$230$	70.4584	−	103.129i	0.306341	−	0.448388i
$231$		0			0
$232$	−295.225	−	275.526i	−1.27252	−	1.18761i
$233$	−310.077			−1.33080			−0.665402	−	0.746485i	$-0.731740\pi$
$233$	−310.077			−1.33080			−0.665402	+	0.746485i	$0.731740\pi$
$234$		0			0
$235$			12.4900i			0.0531489i
$236$	283.983	−	110.822i	1.20332	−	0.469585i
$237$		0			0
$238$	101.616	−	148.735i	0.426960	−	0.624937i
$239$	357.000	−	206.114i	1.49372	−	0.862402i	0.493750	−	0.869604i	$-0.335626\pi$
$239$	357.000	−	206.114i	1.49372	−	0.862402i	0.999974	+	0.00720215i	$0.00229254\pi$
$240$		0			0
$241$	−103.000	+	178.401i	−0.427386	+	0.740254i	−0.996640	−	0.0819076i	$-0.973899\pi$
$241$	−103.000	+	178.401i	−0.427386	+	0.740254i	0.569254	+	0.822162i	$0.307232\pi$
$242$	−46.8722	+	22.5167i	−0.193687	+	0.0930441i
$243$		0			0
$244$	20.0000	−	24.9800i	0.0819672	−	0.102377i
$245$	−18.0278	+	31.2250i	−0.0735827	+	0.127449i
$246$		0			0
$247$	−519.199	+	299.760i	−2.10202	+	1.21360i
$248$	14.5875	+	47.7829i	0.0588204	+	0.192673i
$249$		0			0
$250$	20.1960	−	266.045i	0.0807838	−	1.06418i
$251$		−	83.1384i		−	0.331229i	−0.986191	−	0.165614i	$-0.947039\pi$
$251$		−	83.1384i		−	0.331229i	0.986191	−	0.165614i	$-0.0529607\pi$
$252$		0			0
$253$	210.000			0.830040
$254$	−37.3625	−	2.83625i	−0.147096	−	0.0111663i
$255$		0			0
$256$	210.396	+	145.841i	0.821858	+	0.569692i
$257$	14.4222	+	24.9800i	0.0561175	+	0.0971984i	0.892719	−	0.450613i	$-0.148795\pi$
$257$	14.4222	+	24.9800i	0.0561175	+	0.0971984i	−0.836602	+	0.547811i	$0.815461\pi$
$258$		0			0
$259$	−140.616	−	81.1850i	−0.542921	−	0.313455i
$260$	−144.222	+	180.133i	−0.554700	+	0.692820i
$261$		0			0
$262$	37.5000	+	78.0625i	0.143130	+	0.297948i
$263$	−39.0000	−	22.5167i	−0.148289	−	0.0856147i	0.424020	−	0.905653i	$-0.360619\pi$
$263$	−39.0000	−	22.5167i	−0.148289	−	0.0856147i	−0.572309	+	0.820038i	$0.693952\pi$
$264$		0			0
$265$	−123.500	−	213.908i	−0.466038	−	0.807201i
$266$	386.425	+	264.007i	1.45272	+	0.992509i
$267$		0			0
$268$	232.708	−	90.8125i	0.868314	−	0.338853i
$269$	−50.4777			−0.187650			−0.0938248	−	0.995589i	$-0.529909\pi$
$269$	−50.4777			−0.187650			−0.0938248	+	0.995589i	$0.529909\pi$
$270$		0			0
$271$		−	18.7350i		−	0.0691328i	−0.999402	−	0.0345664i	$-0.988995\pi$
$271$		−	18.7350i		−	0.0691328i	0.999402	−	0.0345664i	$-0.0110050\pi$
$272$	220.239	+	68.8683i	0.809702	+	0.253192i
$273$		0			0
$274$	−130.992	−	89.4941i	−0.478072	−	0.326621i
$275$	126.000	−	72.7461i	0.458182	−	0.264531i
$276$		0			0
$277$	80.0000	−	138.564i	0.288809	−	0.500231i	−0.684717	−	0.728809i	$-0.740074\pi$
$277$	80.0000	−	138.564i	0.288809	−	0.500231i	0.973526	+	0.228578i	$0.0734075\pi$
$278$	108.167	+	225.167i	0.389088	+	0.809952i
$279$		0			0
$280$	175.500	+	40.5925i	0.626786	+	0.144973i
$281$	252.389	−	437.150i	0.898180	−	1.55569i	0.0683611	−	0.997661i	$-0.478223\pi$
$281$	252.389	−	437.150i	0.898180	−	1.55569i	0.829819	−	0.558033i	$-0.188444\pi$
$282$		0			0
$283$	10.8167	−	6.24500i	0.0382214	−	0.0220671i	−0.480768	−	0.876848i	$-0.659642\pi$
$283$	10.8167	−	6.24500i	0.0382214	−	0.0220671i	0.518989	+	0.854781i	$0.326309\pi$
$284$	37.6501	−	246.557i	0.132571	−	0.868159i
$285$		0			0
$286$	−386.866	−	29.3677i	−1.35268	−	0.102684i
$287$		−	45.0333i		−	0.156911i
$288$		0			0
$289$	−81.0000			−0.280277
$290$	27.5526	−	362.956i	0.0950089	−	1.25157i
$291$		0			0
$292$	75.1291	+	11.4725i	0.257291	+	0.0392893i
$293$	−82.9277	−	143.635i	−0.283030	−	0.490222i	0.689100	−	0.724666i	$-0.258006\pi$
$293$	−82.9277	−	143.635i	−0.283030	−	0.490222i	−0.972129	+	0.234445i	$0.924673\pi$
$294$		0			0
$295$	237.966	+	137.390i	0.806666	+	0.465729i
$296$	46.8722	−	202.650i	0.158352	−	0.684628i
$297$		0			0
$298$	6.50000	−	3.12250i	0.0218121	−	0.0104782i
$299$	240.000	+	138.564i	0.802676	+	0.463425i
$300$		0			0
$301$	−39.0000	−	67.5500i	−0.129568	−	0.224419i
$302$	218.421	−	319.700i	0.723248	−	1.05861i
$303$		0			0
$304$	−178.925	+	572.197i	−0.588570	+	1.88223i
$305$	28.8444			0.0945718
$306$		0			0
$307$		−	524.580i		−	1.70873i	−0.519674	−	0.854365i	$-0.673947\pi$
$307$		−	524.580i		−	1.70873i	0.519674	−	0.854365i	$-0.326053\pi$
$308$	110.104	+	282.144i	0.357481	+	0.916051i
$309$		0			0
$310$	−25.4041	+	37.1837i	−0.0819488	+	0.119948i
$311$	−21.0000	+	12.1244i	−0.0675241	+	0.0389851i	−0.533382	−	0.845875i	$-0.679079\pi$
$311$	−21.0000	+	12.1244i	−0.0675241	+	0.0389851i	0.465858	+	0.884860i	$0.345746\pi$
$312$		0			0
$313$	−116.500	+	201.784i	−0.372204	+	0.644677i	−0.989904	−	0.141737i	$-0.954731\pi$
$313$	−116.500	+	201.784i	−0.372204	+	0.644677i	0.617700	+	0.786414i	$0.288065\pi$
$314$	165.855	−	79.6743i	0.528202	−	0.253740i
$315$		0			0
$316$	−156.000	−	124.900i	−0.493671	−	0.395253i
$317$	−250.586	+	434.027i	−0.790492	+	1.36917i	0.135171	+	0.990822i	$0.456841\pi$
$317$	−250.586	+	434.027i	−0.790492	+	1.36917i	−0.925663	+	0.378349i	$0.876492\pi$
$318$		0			0
$319$	530.016	−	306.005i	1.66149	−	0.959263i
$320$	15.9096	+	230.206i	0.0497175	+	0.719394i
$321$		0			0
$322$	16.3751	−	215.712i	0.0508543	−	0.669914i
$323$			540.400i			1.67306i
$324$		0			0
$325$	192.000			0.590769
$326$	−298.900	−	22.6900i	−0.916871	−	0.0696012i
$327$		0			0
$328$	55.1749	−	16.8442i	0.168216	−	0.0513541i
$329$	10.8167	+	18.7350i	0.0328774	+	0.0569453i
$330$		0			0
$331$	−118.983	−	68.6950i	−0.359466	−	0.207538i	0.309381	−	0.950938i	$-0.399878\pi$
$331$	−118.983	−	68.6950i	−0.359466	−	0.207538i	−0.668846	+	0.743401i	$0.733212\pi$
$332$	−362.358	−	290.119i	−1.09144	−	0.873851i
$333$		0			0
$334$	−147.000	−	306.005i	−0.440120	−	0.916182i
$335$	195.000	+	112.583i	0.582090	+	0.336070i
$336$		0			0
$337$	−25.0000	−	43.3013i	−0.0741840	−	0.128490i	0.826547	−	0.562867i	$-0.190302\pi$
$337$	−25.0000	−	43.3013i	−0.0741840	−	0.128490i	−0.900731	+	0.434377i	$0.856969\pi$
$338$	−143.671	−	98.1566i	−0.425061	−	0.290404i
$339$		0			0
$340$	75.6165	+	193.768i	0.222401	+	0.569907i
$341$	−75.7166			−0.222043
$342$		0			0
$343$			368.455i			1.07421i
$344$	68.1749	−	73.0491i	0.198183	−	0.212352i
$345$		0			0
$346$	−291.754	−	199.328i	−0.843220	−	0.576092i
$347$	−169.500	+	97.8609i	−0.488473	+	0.282020i	−0.723941	−	0.689862i	$-0.757671\pi$
$347$	−169.500	+	97.8609i	−0.488473	+	0.282020i	0.235468	+	0.971882i	$0.424338\pi$
$348$		0			0
$349$	269.000	−	465.922i	0.770774	−	1.33502i	−0.166366	−	0.986064i	$-0.553203\pi$
$349$	269.000	−	465.922i	0.770774	−	1.33502i	0.937139	−	0.348955i	$-0.113463\pi$
$350$	−64.8999	−	135.100i	−0.185428	−	0.386000i
$351$		0			0
$352$	−304.500	+	240.432i	−0.865057	+	0.683047i
$353$	111.772	−	193.595i	0.316635	−	0.548428i	−0.663149	−	0.748488i	$-0.730780\pi$
$353$	111.772	−	193.595i	0.316635	−	0.548428i	0.979784	+	0.200060i	$0.0641137\pi$
$354$		0			0
$355$	194.700	−	112.410i	0.548450	−	0.316648i
$356$	−313.653	−	47.8958i	−0.881047	−	0.134539i
$357$		0			0
$358$	528.487	+	40.1183i	1.47622	+	0.112062i
$359$		−	446.869i		−	1.24476i	−0.782715	−	0.622380i	$-0.786166\pi$
$359$		−	446.869i		−	1.24476i	0.782715	−	0.622380i	$-0.213834\pi$
$360$		0			0
$361$	−1043.00			−2.88920
$362$	−41.1775	+	542.439i	−0.113750	+	1.49845i
$363$		0			0
$364$	−60.3331	+	395.100i	−0.165750	+	1.08544i
$365$	34.2527	+	59.3275i	0.0938431	+	0.162541i
$366$		0			0
$367$	−232.558	−	134.267i	−0.633673	−	0.365851i	0.148500	−	0.988912i	$-0.452555\pi$
$367$	−232.558	−	134.267i	−0.633673	−	0.365851i	−0.782173	+	0.623061i	$0.785889\pi$
$368$	270.416	−	60.6218i	0.734827	−	0.164733i
$369$		0			0
$370$	169.000	−	81.1850i	0.456757	−	0.219419i
$371$	−370.500	−	213.908i	−0.998652	−	0.576572i
$372$		0			0
$373$	−106.000	−	183.597i	−0.284182	−	0.492218i	0.688228	−	0.725494i	$-0.258389\pi$
$373$	−106.000	−	183.597i	−0.284182	−	0.492218i	−0.972411	+	0.233276i	$0.925055\pi$
$374$	−197.283	+	288.762i	−0.527496	+	0.772090i
$375$		0			0
$376$	−18.9083	+	20.2602i	−0.0502881	+	0.0538835i
$377$	807.643			2.14229
$378$		0			0
$379$			224.820i			0.593192i	0.955003	+	0.296596i	$0.0958515\pi$
$379$			224.820i			0.593192i	−0.955003	+	0.296596i	$0.904148\pi$
$380$	−503.425	+	196.457i	−1.32480	+	0.516993i
$381$		0			0
$382$	297.033	−	434.764i	0.777573	−	1.13812i
$383$	−210.000	+	121.244i	−0.548303	+	0.316563i	−0.748437	−	0.663206i	$-0.769195\pi$
$383$	−210.000	+	121.244i	−0.548303	+	0.316563i	0.200134	+	0.979768i	$0.435862\pi$
$384$		0			0
$385$	−136.500	+	236.425i	−0.354545	+	0.614091i
$386$	−337.119	+	161.947i	−0.873365	+	0.419551i
$387$		0			0
$388$	297.500	−	371.577i	0.766753	−	0.957674i
$389$	257.797	−	446.517i	0.662717	−	1.14786i	−0.317182	−	0.948365i	$-0.602737\pi$
$389$	257.797	−	446.517i	0.662717	−	1.14786i	0.979899	−	0.199495i	$-0.0639301\pi$
$390$		0			0
$391$	216.333	−	124.900i	0.553282	−	0.319437i
$392$	−76.5139	+	23.3586i	−0.195188	+	0.0595884i
$393$		0			0
$394$	2.72918	−	35.9521i	0.00692686	−	0.0912489i
$395$		−	180.133i		−	0.456034i
$396$		0			0
$397$	80.0000			0.201511			0.100756	−	0.994911i	$-0.467874\pi$
$397$	80.0000			0.201511			0.100756	+	0.994911i	$0.467874\pi$
$398$	−186.812	−	14.1812i	−0.469378	−	0.0356313i
$399$		0			0
$400$	141.250	−	130.048i	0.353125	−	0.325120i
$401$	−310.077	−	537.070i	−0.773260	−	1.33933i	−0.935767	−	0.352619i	$-0.885291\pi$
$401$	−310.077	−	537.070i	−0.773260	−	1.33933i	0.162507	−	0.986707i	$-0.448042\pi$
$402$		0			0
$403$	−86.5332	−	49.9600i	−0.214723	−	0.123970i
$404$	−153.236	+	191.392i	−0.379297	+	0.473742i
$405$		0			0
$406$	−273.000	−	568.295i	−0.672414	−	1.39974i
$407$	273.000	+	157.617i	0.670762	+	0.387264i
$408$		0			0
$409$	174.500	+	302.243i	0.426650	+	0.738980i	0.996573	−	0.0827183i	$-0.0263602\pi$
$409$	174.500	+	302.243i	0.426650	+	0.738980i	−0.569923	+	0.821698i	$0.693027\pi$
$410$	42.9361	+	29.3342i	0.104722	+	0.0715467i
$411$		0			0
$412$	−465.416	+	181.625i	−1.12965	+	0.440837i
$413$	475.933			1.15238
$414$		0			0
$415$		−	418.415i		−	1.00823i
$416$	−506.644	+	73.8620i	−1.21789	+	0.177553i
$417$		0			0
$418$	−750.225	−	512.557i	−1.79480	−	1.22621i
$419$	258.000	−	148.956i	0.615752	−	0.355504i	−0.159461	−	0.987204i	$-0.550976\pi$
$419$	258.000	−	148.956i	0.615752	−	0.355504i	0.775213	+	0.631700i	$0.217642\pi$
$420$		0			0
$421$	104.000	−	180.133i	0.247031	−	0.427870i	−0.715670	−	0.698439i	$-0.753878\pi$
$421$	104.000	−	180.133i	0.247031	−	0.427870i	0.962701	+	0.270569i	$0.0872118\pi$
$422$	−54.0833	−	112.583i	−0.128159	−	0.266785i
$423$		0			0
$424$	123.500	−	533.947i	0.291274	−	1.25931i
$425$	86.5332	−	149.880i	0.203608	−	0.352659i
$426$		0			0
$427$	43.2666	−	24.9800i	0.101327	−	0.0585012i
$428$	−78.4377	+	513.661i	−0.183266	+	1.20014i
$429$		0			0
$430$	89.8082	+	6.81750i	0.208856	+	0.0158546i
$431$			550.792i			1.27794i	0.769232	+	0.638970i	$0.220639\pi$
$431$			550.792i			1.27794i	−0.769232	+	0.638970i	$0.779361\pi$
$432$		0			0
$433$	125.000			0.288684			0.144342	−	0.989528i	$-0.453894\pi$
$433$	125.000			0.288684			0.144342	+	0.989528i	$0.453894\pi$
$434$	−5.90412	+	77.7762i	−0.0136040	+	0.179208i
$435$		0			0
$436$	181.892	+	27.7754i	0.417182	+	0.0637051i
$437$	324.500	+	562.050i	0.742562	+	1.28616i
$438$		0			0
$439$	−492.158	−	284.147i	−1.12109	−	0.647261i	−0.179410	−	0.983774i	$-0.557419\pi$
$439$	−492.158	−	284.147i	−1.12109	−	0.647261i	−0.941679	+	0.336514i	$0.890752\pi$
$440$	−340.725	−	78.8083i	−0.774374	−	0.179110i
$441$		0			0
$442$	−416.000	+	199.840i	−0.941176	+	0.452127i
$443$	330.000	+	190.526i	0.744921	+	0.430080i	0.823856	−	0.566799i	$-0.191819\pi$
$443$	330.000	+	190.526i	0.744921	+	0.430080i	−0.0789348	+	0.996880i	$0.525152\pi$
$444$		0			0
$445$	−143.000	−	247.683i	−0.321348	−	0.556592i
$446$	−225.467	+	330.013i	−0.505531	+	0.739940i
$447$		0			0
$448$	223.229	+	331.531i	0.498279	+	0.740025i
$449$	−483.144			−1.07604			−0.538022	−	0.842931i	$-0.680828\pi$
$449$	−483.144			−1.07604			−0.538022	+	0.842931i	$0.680828\pi$
$450$		0			0
$451$			87.4300i			0.193858i
$452$	−136.320	−	349.321i	−0.301592	−	0.772833i
$453$		0			0
$454$	85.9832	−	125.853i	0.189390	−	0.277208i
$455$	−312.000	+	180.133i	−0.685714	+	0.395897i
$456$		0			0
$457$	−413.500	+	716.203i	−0.904814	+	1.56718i	−0.0836473	+	0.996495i	$0.526657\pi$
$457$	−413.500	+	716.203i	−0.904814	+	1.56718i	−0.821167	+	0.570688i	$0.806676\pi$
$458$	−385.794	+	185.329i	−0.842345	+	0.404649i
$459$		0			0
$460$	195.000	+	156.125i	0.423913	+	0.339402i
$461$	322.697	−	558.927i	0.699993	−	1.21242i	−0.268475	−	0.963287i	$-0.586520\pi$
$461$	322.697	−	558.927i	0.699993	−	1.21242i	0.968468	−	0.249137i	$-0.0801470\pi$
$462$		0			0
$463$	91.9416	−	53.0825i	0.198578	−	0.114649i	−0.397414	−	0.917639i	$-0.630092\pi$
$463$	91.9416	−	53.0825i	0.198578	−	0.114649i	0.595992	+	0.802990i	$0.296759\pi$
$464$	594.164	−	547.044i	1.28053	−	1.17897i
$465$		0			0
$466$	46.9419	−	618.376i	0.100734	−	1.32699i
$467$			743.050i			1.59111i	0.605879	+	0.795557i	$0.292821\pi$
$467$			743.050i			1.59111i	−0.605879	+	0.795557i	$0.707179\pi$
$468$		0			0
$469$	390.000			0.831557
$470$	−24.9083	−	1.89083i	−0.0529964	−	0.00402305i
$471$		0			0
$472$	178.017	+	583.114i	0.377154	+	1.23541i
$473$	75.7166	+	131.145i	0.160077	+	0.277262i
$474$		0			0
$475$	389.400	+	224.820i	0.819789	+	0.473305i
$476$	281.233	+	225.167i	0.590826	+	0.473039i
$477$		0			0
$478$	357.000	+	743.155i	0.746862	+	1.55472i
$479$	−291.000	−	168.009i	−0.607516	−	0.350749i	0.164477	−	0.986381i	$-0.447406\pi$
$479$	−291.000	−	168.009i	−0.607516	−	0.350749i	−0.771993	+	0.635632i	$0.780740\pi$
$480$		0			0
$481$	208.000	+	360.267i	0.432432	+	0.748995i
$482$	−340.186	−	232.417i	−0.705780	−	0.482192i
$483$		0			0
$484$	−37.8082	−	96.8841i	−0.0781162	−	0.200174i
$485$	429.061			0.884661
$486$		0			0
$487$		−	599.520i		−	1.23105i	−0.788119	−	0.615523i	$-0.788945\pi$
$487$		−	599.520i		−	1.23105i	0.788119	−	0.615523i	$-0.211055\pi$
$488$	46.7889	+	43.6669i	0.0958789	+	0.0894814i
$489$		0			0
$490$	−59.5416	−	40.6792i	−0.121514	−	0.0830187i
$491$	424.500	−	245.085i	0.864562	−	0.499155i	−0.000975249	−	1.00000i	$-0.500310\pi$
$491$	424.500	−	245.085i	0.864562	−	0.499155i	0.865537	+	0.500844i	$0.166977\pi$
$492$		0			0
$493$	364.000	−	630.466i	0.738337	−	1.27884i
$494$	−519.199	−	1080.80i	−1.05101	−	2.18785i
$495$		0			0
$496$	−97.5000	+	21.8575i	−0.196573	+	0.0440675i
$497$	194.700	−	337.230i	0.391750	−	0.678531i
$498$		0			0
$499$	−573.283	+	330.985i	−1.14886	+	0.663296i	−0.948610	−	0.316448i	$-0.897510\pi$
$499$	−573.283	+	330.985i	−1.14886	+	0.663296i	−0.200253	+	0.979744i	$0.564176\pi$
$500$	527.507	+	80.5520i	1.05501	+	0.161104i
$501$		0			0
$502$	165.800	+	12.5861i	0.330279	+	0.0250720i
$503$		−	322.161i		−	0.640480i	−0.947336	−	0.320240i	$-0.896236\pi$
$503$		−	322.161i		−	0.640480i	0.947336	−	0.320240i	$-0.103764\pi$
$504$		0			0
$505$	−221.000			−0.437624
$506$	−31.7914	+	418.795i	−0.0628289	+	0.827658i
$507$		0			0
$508$	11.3125	−	74.0812i	0.0222686	−	0.145829i
$509$	−272.219	−	471.497i	−0.534812	−	0.926321i	−0.999172	−	0.0406748i	$-0.987049\pi$
$509$	−272.219	−	471.497i	−0.534812	−	0.926321i	0.464361	−	0.885646i	$-0.346284\pi$
$510$		0			0
$511$	102.758	+	59.3275i	0.201092	+	0.116101i
$512$	−322.697	+	397.506i	−0.630267	+	0.776378i
$513$		0			0
$514$	−52.0000	+	24.9800i	−0.101167	+	0.0485992i
$515$	−390.000	−	225.167i	−0.757282	−	0.437217i
$516$		0			0
$517$	−21.0000	−	36.3731i	−0.0406190	−	0.0703541i
$518$	183.192	−	268.136i	0.353652	−	0.517637i
$519$		0			0
$520$	−337.400	−	314.887i	−0.648845	−	0.605551i
$521$	230.755			0.442908			0.221454	−	0.975171i	$-0.428920\pi$
$521$	230.755			0.442908			0.221454	+	0.975171i	$0.428920\pi$
$522$		0			0
$523$			674.460i			1.28960i	0.764352	+	0.644799i	$0.223059\pi$
$523$			674.460i			1.28960i	−0.764352	+	0.644799i	$0.776941\pi$
$524$	−161.354	+	62.9671i	−0.307928	+	0.120166i
$525$		0			0
$526$	50.8082	−	74.3675i	0.0965936	−	0.141383i
$527$	−78.0000	+	45.0333i	−0.148008	+	0.0854522i
$528$		0			0
$529$	−114.500	+	198.320i	−0.216446	+	0.374896i
$530$	445.286	−	213.908i	0.840161	−	0.403601i
$531$		0			0
$532$	−585.000	+	730.665i	−1.09962	+	1.37343i
$533$	−57.6888	+	99.9200i	−0.108234	+	0.187467i
$534$		0			0
$535$	−405.625	+	234.187i	−0.758177	+	0.437734i
$536$	145.875	+	477.829i	0.272154	+	0.891472i
$537$		0			0
$538$	7.64171	−	100.666i	0.0142039	−	0.187111i
$539$		−	121.244i		−	0.224942i
$540$		0			0
$541$	260.000			0.480591			0.240296	−	0.970700i	$-0.422756\pi$
$541$	260.000			0.480591			0.240296	+	0.970700i	$0.422756\pi$
$542$	37.3625	+	2.83625i	0.0689345	+	0.00523293i
$543$		0			0
$544$	−170.683	+	428.788i	−0.313755	+	0.788214i
$545$	82.9277	+	143.635i	0.152161	+	0.263550i
$546$		0			0
$547$	757.166	+	437.150i	1.38422	+	0.799177i	0.992655	−	0.120976i	$-0.0386023\pi$
$547$	757.166	+	437.150i	1.38422	+	0.799177i	0.391560	+	0.920153i	$0.371936\pi$
$548$	198.305	−	247.683i	0.361871	−	0.451977i
$549$		0			0
$550$	126.000	+	262.290i	0.229091	+	0.476891i
$551$	1638.00	+	945.700i	2.97278	+	1.71633i
$552$		0			0
$553$	−156.000	−	270.200i	−0.282098	−	0.488607i
$554$	264.222	+	180.518i	0.476935	+	0.325845i
$555$		0			0
$556$	−465.416	+	181.625i	−0.837080	+	0.326664i
$557$	−472.327			−0.847984			−0.423992	−	0.905666i	$-0.639372\pi$
$557$	−472.327			−0.847984			−0.423992	+	0.905666i	$0.639372\pi$
$558$		0			0
$559$			199.840i			0.357495i
$560$	−107.521	+	343.848i	−0.192001	+	0.614014i
$561$		0			0
$562$	833.583	+	569.508i	1.48324	+	1.01336i
$563$	604.500	−	349.008i	1.07371	−	0.619908i	0.144519	−	0.989502i	$-0.453837\pi$
$563$	604.500	−	349.008i	1.07371	−	0.619908i	0.929193	+	0.369594i	$0.120503\pi$
$564$		0			0
$565$	169.000	−	292.717i	0.299115	−	0.518082i
$566$	10.8167	+	22.5167i	0.0191107	+	0.0397821i
$567$		0			0
$568$	486.000	+	112.410i	0.855634	+	0.197905i
$569$	−137.011	+	237.310i	−0.240793	+	0.417065i	−0.960940	−	0.276756i	$-0.910741\pi$
$569$	−137.011	+	237.310i	−0.240793	+	0.417065i	0.720148	+	0.693821i	$0.244074\pi$
$570$		0			0
$571$	−216.333	+	124.900i	−0.378867	+	0.218739i	−0.677325	−	0.735684i	$-0.736861\pi$
$571$	−216.333	+	124.900i	−0.378867	+	0.218739i	0.298458	+	0.954423i	$0.403528\pi$
$572$	117.134	−	767.067i	0.204779	−	1.34103i
$573$		0			0
$574$	89.8082	+	6.81750i	0.156460	+	0.0118772i
$575$		−	207.846i		−	0.361471i
$576$		0			0
$577$	494.000			0.856153			0.428076	−	0.903743i	$-0.359191\pi$
$577$	494.000			0.856153			0.428076	+	0.903743i	$0.359191\pi$
$578$	12.2624	−	161.535i	0.0212152	−	0.279473i
$579$		0			0
$580$	719.658	+	109.894i	1.24079	+	0.189473i
$581$	−362.358	−	627.622i	−0.623680	−	1.08024i
$582$		0			0
$583$	719.307	+	415.292i	1.23380	+	0.712337i
$584$	−34.2527	+	148.090i	−0.0586519	+	0.253579i
$585$		0			0
$586$	299.000	−	143.635i	0.510239	−	0.245111i
$587$	−205.500	−	118.645i	−0.350085	−	0.202122i	0.314638	−	0.949212i	$-0.398117\pi$
$587$	−205.500	−	118.645i	−0.350085	−	0.202122i	−0.664723	+	0.747090i	$0.731450\pi$
$588$		0			0
$589$	−117.000	−	202.650i	−0.198642	−	0.344058i
$590$	−310.017	+	453.768i	−0.525452	+	0.769099i
$591$		0			0
$592$	397.041	+	124.154i	0.670678	+	0.209720i
$593$	468.722			0.790424			0.395212	−	0.918590i	$-0.370671\pi$
$593$	468.722			0.790424			0.395212	+	0.918590i	$0.370671\pi$
$594$		0			0
$595$			324.740i			0.545781i
$596$	5.24306	+	13.4354i	0.00879708	+	0.0225426i
$597$		0			0
$598$	−312.666	+	457.646i	−0.522853	+	0.765294i
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	−0.849160	−	0.528136i	$-0.822891\pi$
$599$	−489.000	+	282.324i	−0.816361	+	0.471326i	0.0327992	+	0.999462i	$0.489558\pi$
$600$		0			0
$601$	−323.500	+	560.318i	−0.538270	+	0.932310i	0.460728	+	0.887541i	$0.347588\pi$
$601$	−323.500	+	560.318i	−0.538270	+	0.932310i	−0.998997	+	0.0447687i	$0.985745\pi$
$602$	140.616	−	67.5500i	0.233582	−	0.112209i
$603$		0			0
$604$	604.500	+	483.987i	1.00083	+	0.801304i
$605$	46.8722	−	81.1850i	0.0774747	−	0.134190i
$606$		0			0
$607$	−346.133	+	199.840i	−0.570235	+	0.329226i	−0.757243	−	0.653133i	$-0.773454\pi$
$607$	−346.133	+	199.840i	−0.570235	+	0.329226i	0.187008	+	0.982358i	$0.440121\pi$
$608$	−1114.02	−	443.447i	−1.83228	−	0.729354i
$609$		0			0
$610$	−4.36669	+	57.5233i	−0.00715851	+	0.0943005i
$611$		−	55.4256i		−	0.0907130i
$612$		0			0
$613$	866.000			1.41272			0.706362	−	0.707851i	$-0.250335\pi$
$613$	866.000			1.41272			0.706362	+	0.707851i	$0.250335\pi$
$614$	1046.15	+	79.4150i	1.70383	+	0.129340i
$615$		0			0
$616$	−579.337	+	176.864i	−0.940482	+	0.287116i
$617$	111.772	+	193.595i	0.181154	+	0.313768i	0.942274	−	0.334843i	$-0.108683\pi$
$617$	111.772	+	193.595i	0.181154	+	0.313768i	−0.761120	+	0.648611i	$0.775350\pi$
$618$		0			0
$619$	−865.332	−	499.600i	−1.39795	−	0.807108i	−0.403774	−	0.914859i	$-0.632302\pi$
$619$	−865.332	−	499.600i	−1.39795	−	0.807108i	−0.994178	+	0.107751i	$0.965635\pi$
$620$	−70.3082	−	56.2917i	−0.113400	−	0.0907930i
$621$		0			0
$622$	−21.0000	−	43.7150i	−0.0337621	−	0.0702813i
$623$	−429.000	−	247.683i	−0.688604	−	0.397565i
$624$		0			0
$625$	90.5000	+	156.751i	0.144800	+	0.250801i
$626$	−384.773	−	262.879i	−0.614654	−	0.419935i
$627$		0			0
$628$	133.783	+	342.821i	0.213030	+	0.545893i
$629$	374.977			0.596148
$630$		0			0
$631$		−	93.6750i		−	0.148455i	−0.997241	−	0.0742274i	$-0.976351\pi$
$631$		−	93.6750i		−	0.148455i	0.997241	−	0.0742274i	$-0.0236491\pi$
$632$	272.700	−	292.197i	0.431487	−	0.462336i
$633$		0			0
$634$	−827.629	−	565.440i	−1.30541	−	0.891862i
$635$	58.5000	−	33.7750i	0.0921260	−	0.0531890i
$636$		0			0
$637$	80.0000	−	138.564i	0.125589	−	0.217526i
$638$	530.016	+	1103.32i	0.830746	+	1.72934i
$639$		0			0
$640$	−461.500	−	3.12250i	−0.721094	−	0.00487890i
$641$	−429.061	+	743.155i	−0.669361	+	1.15937i	0.308722	+	0.951152i	$0.400099\pi$
$641$	−429.061	+	743.155i	−0.669361	+	1.15937i	−0.978083	+	0.208215i	$0.933235\pi$
$642$		0			0
$643$	−21.6333	+	12.4900i	−0.0336443	+	0.0194246i	−0.516728	−	0.856150i	$-0.672850\pi$
$643$	−21.6333	+	12.4900i	−0.0336443	+	0.0194246i	0.483083	+	0.875574i	$0.339517\pi$
$644$	427.708	+	65.3125i	0.664143	+	0.101417i
$645$		0			0
$646$	−1077.70	−	81.8100i	−1.66826	−	0.126641i
$647$		−	540.400i		−	0.835239i	−0.908622	−	0.417620i	$-0.862864\pi$
$647$		−	540.400i		−	0.835239i	0.908622	−	0.417620i	$-0.137136\pi$
$648$		0			0
$649$	−924.000			−1.42373
$650$	−29.0665	+	382.898i	−0.0447176	+	0.589074i
$651$		0			0
$652$	90.4996	−	592.650i	0.138803	−	0.908972i
$653$	214.530	+	371.577i	0.328530	+	0.569031i	0.982220	−	0.187731i	$-0.0601134\pi$
$653$	214.530	+	371.577i	0.328530	+	0.569031i	−0.653690	+	0.756762i	$0.726780\pi$
$654$		0			0
$655$	−135.208	−	78.0625i	−0.206425	−	0.119179i
$656$	25.2389	+	112.583i	0.0384739	+	0.171621i
$657$		0			0
$658$	−39.0000	+	18.7350i	−0.0592705	+	0.0284726i
$659$	−844.500	−	487.572i	−1.28149	−	0.739867i	−0.304367	−	0.952555i	$-0.598445\pi$
$659$	−844.500	−	487.572i	−1.28149	−	0.739867i	−0.977120	+	0.212688i	$0.931778\pi$
$660$		0			0
$661$	485.000	+	840.045i	0.733737	+	1.27087i	0.955275	+	0.295718i	$0.0955588\pi$
$661$	485.000	+	840.045i	0.733737	+	1.27087i	−0.221539	+	0.975152i	$0.571108\pi$
$662$	155.008	−	226.884i	0.234152	−	0.342725i
$663$		0			0
$664$	633.429	−	678.716i	0.953959	−	1.02216i
$665$	−843.699			−1.26872
$666$		0			0
$667$		−	874.300i		−	1.31079i
$668$	632.508	−	246.831i	0.946868	−	0.369508i
$669$		0			0
$670$	−254.041	+	371.837i	−0.379166	+	0.554981i
$671$	−84.0000	+	48.4974i	−0.125186	+	0.0722763i
$672$		0			0
$673$	297.500	−	515.285i	0.442051	−	0.765654i	−0.555791	−	0.831322i	$-0.687585\pi$
$673$	297.500	−	515.285i	0.442051	−	0.765654i	0.997842	+	0.0656681i	$0.0209179\pi$
$674$	90.1388	−	43.3013i	0.133737	−	0.0642452i
$675$		0			0
$676$	217.500	−	271.657i	0.321746	−	0.401860i
$677$	−212.728	+	368.455i	−0.314221	+	0.544247i	−0.979272	−	0.202552i	$-0.935077\pi$
$677$	−212.728	+	368.455i	−0.314221	+	0.544247i	0.665051	+	0.746798i	$0.268410\pi$
$678$		0			0
$679$	643.591	−	371.577i	0.947851	−	0.547242i
$680$	−397.872	+	121.465i	−0.585106	+	0.178625i
$681$		0			0
$682$	11.4626	−	150.999i	0.0168073	−	0.221406i
$683$		−	62.3538i		−	0.0912940i	−0.998958	−	0.0456470i	$-0.985465\pi$
$683$		−	62.3538i		−	0.0912940i	0.998958	−	0.0456470i	$-0.0145349\pi$
$684$		0			0
$685$	286.000			0.417518
$686$	−734.796	−	55.7796i	−1.07113	−	0.0813113i
$687$		0			0
$688$	135.358	+	147.017i	0.196742	+	0.213688i
$689$	548.044	+	949.240i	0.795419	+	1.37771i
$690$		0			0
$691$	−930.232	−	537.070i	−1.34621	−	0.777236i	−0.358501	−	0.933529i	$-0.616712\pi$
$691$	−930.232	−	537.070i	−1.34621	−	0.777236i	−0.987711	+	0.156294i	$0.950045\pi$
$692$	441.680	−	551.658i	0.638266	−	0.797194i
$693$		0			0
$694$	−169.500	−	352.842i	−0.244236	−	0.508418i
$695$	−390.000	−	225.167i	−0.561151	−	0.323981i
$696$		0			0
$697$	52.0000	+	90.0666i	0.0746055	+	0.129220i
$698$	888.447	+	606.991i	1.27285	+	0.869615i
$699$		0			0
$700$	279.250	−	108.975i	0.398928	−	0.155679i
$701$	−926.627			−1.32186			−0.660932	−	0.750446i	$-0.729839\pi$
$701$	−926.627			−1.32186			−0.660932	+	0.750446i	$0.729839\pi$
$702$		0			0
$703$			974.220i			1.38580i
$704$	−433.388	−	643.651i	−0.615608	−	0.914278i
$705$		0			0
$706$	369.158	+	252.211i	0.522887	+	0.357239i
$707$	−331.500	+	191.392i	−0.468883	+	0.270709i
$708$		0			0
$709$	14.0000	−	24.2487i	0.0197461	−	0.0342013i	−0.855983	−	0.517003i	$-0.827048\pi$
$709$	14.0000	−	24.2487i	0.0197461	−	0.0342013i	0.875730	+	0.482802i	$0.160381\pi$
$710$	194.700	+	405.300i	0.274225	+	0.570845i
$711$		0			0
$712$	143.000	−	618.255i	0.200843	−	0.868335i
$713$	−54.0833	+	93.6750i	−0.0758531	+	0.131381i
$714$		0			0
$715$	605.733	−	349.720i	0.847178	−	0.489119i
$716$	−160.013	+	1047.87i	−0.223482	+	1.46350i
$717$		0			0
$718$	891.174	+	67.6505i	1.24119	+	0.0942208i
$719$			270.200i			0.375800i	0.982188	+	0.187900i	$0.0601680\pi$
$719$			270.200i			0.375800i	−0.982188	+	0.187900i	$0.939832\pi$
$720$		0			0
$721$	−780.000			−1.08183
$722$	157.897	−	2080.02i	0.218695	−	2.88091i
$723$		0			0
$724$	−1075.53	−	164.237i	−1.48554	−	0.226847i
$725$	−302.866	−	524.580i	−0.417747	−	0.723558i
$726$		0			0
$727$	−5.40833	−	3.12250i	−0.00743924	−	0.00429505i	0.496276	−	0.868165i	$-0.334700\pi$
$727$	−5.40833	−	3.12250i	−0.00743924	−	0.00429505i	−0.503715	+	0.863870i	$0.668034\pi$
$728$	−778.799	−	180.133i	−1.06978	−	0.247436i
$729$		0			0
$730$	−123.500	+	59.3275i	−0.169178	+	0.0812705i
$731$	156.000	+	90.0666i	0.213406	+	0.123210i
$732$		0			0
$733$	−169.000	−	292.717i	−0.230559	−	0.399340i	0.727414	−	0.686199i	$-0.240722\pi$
$733$	−169.000	−	292.717i	−0.230559	−	0.399340i	−0.957973	+	0.286859i	$0.907389\pi$
$734$	302.971	−	443.455i	0.412767	−	0.604163i
$735$		0			0
$736$	79.9580	+	548.458i	0.108639	+	0.745188i
$737$	−757.166			−1.02736
$738$		0			0
$739$			824.340i			1.11548i	0.830016	+	0.557740i	$0.188331\pi$
$739$			824.340i			1.11548i	−0.830016	+	0.557740i	$0.811669\pi$
$740$	136.320	+	349.321i	0.184216	+	0.472055i
$741$		0			0
$742$	482.678	−	706.491i	0.650510	−	0.952144i
$743$	−516.000	+	297.913i	−0.694482	+	0.400959i	−0.805289	−	0.592883i	$-0.797990\pi$
$743$	−516.000	+	297.913i	−0.694482	+	0.400959i	0.110807	+	0.993842i	$0.464656\pi$
$744$		0			0
$745$	−6.50000	+	11.2583i	−0.00872483	+	0.0151119i
$746$	382.188	−	183.597i	0.512317	−	0.246109i
$747$		0			0
$748$	−546.000	−	437.150i	−0.729947	−	0.584425i
$749$	−405.625	+	702.562i	−0.541555	+	0.938000i
$750$		0			0
$751$	−459.708	+	265.412i	−0.612128	+	0.353412i	−0.773798	−	0.633433i	$-0.781645\pi$
$751$	−459.708	+	265.412i	−0.612128	+	0.353412i	0.161670	+	0.986845i	$0.448312\pi$
$752$	−37.5416	−	40.7753i	−0.0499224	−	0.0542225i
$753$		0			0
$754$	−122.267	+	1610.65i	−0.162158	+	2.13614i
$755$			698.016i			0.924525i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$	−448.350	−	34.0350i	−0.591491	−	0.0449011i
$759$		0			0
$760$	−315.575	−	1033.70i	−0.415231	−	1.36013i
$761$	−245.177	−	424.660i	−0.322178	−	0.558029i	0.658759	−	0.752354i	$-0.271082\pi$
$761$	−245.177	−	424.660i	−0.322178	−	0.558029i	−0.980937	+	0.194325i	$0.937748\pi$
$762$		0			0
$763$	248.783	+	143.635i	0.326059	+	0.188250i
$764$	822.066	+	658.179i	1.07600	+	0.861491i
$765$		0			0
$766$	−210.000	−	437.150i	−0.274151	−	0.570692i
$767$	−1056.00	−	609.682i	−1.37679	−	0.794892i
$768$		0			0
$769$	−32.5000	−	56.2917i	−0.0422627	−	0.0732011i	0.844120	−	0.536154i	$-0.180123\pi$
$769$	−32.5000	−	56.2917i	−0.0422627	−	0.0732011i	−0.886383	+	0.462953i	$0.846790\pi$
$770$	−450.829	−	308.009i	−0.585492	−	0.400011i
$771$		0			0
$772$	−271.929	−	696.821i	−0.352239	−	0.902617i
$773$	−829.277			−1.07280			−0.536402	−	0.843963i	$-0.680217\pi$
$773$	−829.277			−1.07280			−0.536402	+	0.843963i	$0.680217\pi$
$774$		0			0
$775$			74.9400i			0.0966967i
$776$	695.985	+	649.545i	0.896888	+	0.837043i
$777$		0			0
$778$	851.445	+	581.712i	1.09440	+	0.747702i
$779$	−234.000	+	135.100i	−0.300385	+	0.173427i
$780$		0			0
$781$	−378.000	+	654.715i	−0.483995	+	0.838304i
$782$	216.333	+	450.333i	0.276641	+	0.575874i
$783$		0			0
$784$	−35.0000	−	156.125i	−0.0446429	−	0.199139i
$785$	−165.855	+	287.270i	−0.211281	+	0.365949i
$786$		0			0
$787$	692.266	−	399.680i	0.879626	−	0.507852i	0.00909108	−	0.999959i	$-0.497106\pi$
$787$	692.266	−	399.680i	0.879626	−	0.507852i	0.870535	+	0.492106i	$0.163773\pi$
$788$	71.2847	+	10.8854i	0.0904628	+	0.0138140i
$789$		0			0
$790$	359.233	+	27.2700i	0.454725	+	0.0345190i
$791$		−	585.433i		−	0.740118i
$792$		0			0
$793$	−128.000			−0.161412
$794$	−12.1110	+	159.541i	−0.0152532	+	0.200933i
$795$		0			0
$796$	56.5623	−	370.406i	0.0710581	−	0.465334i
$797$	387.597	+	671.337i	0.486320	+	0.842330i	0.999876	−	0.0157253i	$-0.00500573\pi$
$797$	387.597	+	671.337i	0.486320	+	0.842330i	−0.513557	+	0.858056i	$0.671672\pi$
$798$		0			0
$799$	−43.2666	−	24.9800i	−0.0541510	−	0.0312641i
$800$	237.966	+	301.377i	0.297458	+	0.376721i
$801$		0			0
$802$	1118.00	−	537.070i	1.39401	−	0.669663i
$803$	−199.500	−	115.181i	−0.248443	−	0.143439i
$804$		0			0
$805$	195.000	+	337.750i	0.242236	+	0.419565i
$806$	112.733	−	165.007i	0.139868	−	0.204723i
$807$		0			0
$808$	−358.487	−	334.567i	−0.443672	−	0.414068i
$809$	209.122			0.258494			0.129247	−	0.991612i	$-0.458744\pi$
$809$	209.122			0.258494			0.129247	+	0.991612i	$0.458744\pi$
$810$		0			0
$811$		−	1461.33i		−	1.80189i	−0.433937	−	0.900943i	$-0.642876\pi$
$811$		−	1461.33i		−	1.80189i	0.433937	−	0.900943i	$-0.357124\pi$
$812$	1174.66	−	458.401i	1.44662	−	0.564533i
$813$		0			0
$814$	−355.658	+	520.572i	−0.436926	+	0.639524i
$815$	468.000	−	270.200i	0.574233	−	0.331534i
$816$		0			0
$817$	−234.000	+	405.300i	−0.286414	+	0.496083i
$818$	−629.169	+	302.243i	−0.769155	+	0.369490i
$819$		0			0
$820$	−65.0000	+	81.1850i	−0.0792683	+	0.0990061i
$821$	25.2389	−	43.7150i	0.0307416	−	0.0532460i	−0.850245	−	0.526387i	$-0.823546\pi$
$821$	25.2389	−	43.7150i	0.0307416	−	0.0532460i	0.880987	+	0.473141i	$0.156880\pi$
$822$		0			0
$823$	1162.79	−	671.337i	1.41287	−	0.815720i	0.417210	−	0.908810i	$-0.363008\pi$
$823$	1162.79	−	671.337i	1.41287	−	0.815720i	0.995658	+	0.0930903i	$0.0296745\pi$
$824$	−291.749	−	955.658i	−0.354065	−	1.15978i
$825$		0			0
$826$	−72.0504	+	949.135i	−0.0872281	+	1.14907i
$827$		−	581.969i		−	0.703711i	−0.936054	−	0.351856i	$-0.885551\pi$
$827$		−	581.969i		−	0.703711i	0.936054	−	0.351856i	$-0.114449\pi$
$828$		0			0
$829$	−1186.00			−1.43064			−0.715320	−	0.698797i	$-0.753719\pi$
$829$	−1186.00			−1.43064			−0.715320	+	0.698797i	$0.753719\pi$
$830$	834.429	+	63.3429i	1.00534	+	0.0763168i
$831$		0			0
$832$	−70.6005	−	1021.56i	−0.0848563	−	1.22784i
$833$	−72.1110	−	124.900i	−0.0865679	−	0.149940i
$834$		0			0
$835$	530.016	+	306.005i	0.634750	+	0.366473i
$836$	1135.75	−	1418.55i	1.35855	−	1.69683i
$837$		0			0
$838$	258.000	+	537.070i	0.307876	+	0.640895i
$839$	726.000	+	419.156i	0.865316	+	0.499590i	0.865789	−	0.500410i	$-0.166817\pi$
$839$	726.000	+	419.156i	0.865316	+	0.499590i	−0.000472970		1.00000i	$0.500151\pi$
$840$		0			0
$841$	−853.500	−	1478.31i	−1.01486	−	1.75779i
$842$	343.489	+	234.673i	0.407944	+	0.278709i
$843$		0			0
$844$	232.708	−	90.8125i	0.275721	−	0.107598i
$845$	313.683			0.371222
$846$		0			0
$847$		−	162.370i		−	0.191700i
$848$	1046.13	+	327.125i	1.23365	+	0.385760i
$849$		0			0
$850$	285.800	+	195.260i	0.336235	+	0.229718i
$851$	390.000	−	225.167i	0.458284	−	0.264591i
$852$		0			0
$853$	647.000	−	1120.64i	0.758499	−	1.31376i	−0.185116	−	0.982717i	$-0.559266\pi$
$853$	647.000	−	1120.64i	0.758499	−	1.31376i	0.943616	−	0.331043i	$-0.107400\pi$
$854$	43.2666	+	90.0666i	0.0506635	+	0.105464i
$855$		0			0
$856$	−1012.50	−	234.187i	−1.18283	−	0.273583i
$857$	−656.210	+	1136.59i	−0.765706	+	1.32624i	0.174166	+	0.984716i	$0.444277\pi$
$857$	−656.210	+	1136.59i	−0.765706	+	1.32624i	−0.939872	+	0.341526i	$0.889056\pi$
$858$		0			0
$859$	−346.133	+	199.840i	−0.402949	+	0.232643i	−0.687755	−	0.725942i	$-0.741404\pi$
$859$	−346.133	+	199.840i	−0.402949	+	0.232643i	0.284807	+	0.958585i	$0.408071\pi$
$860$	−27.1918	+	178.069i	−0.0316183	+	0.207057i
$861$		0			0
$862$	−1098.42	−	83.3832i	−1.27427	−	0.0967323i
$863$		−	852.169i		−	0.987450i	−0.869618	−	0.493725i	$-0.835635\pi$
$863$		−	852.169i		−	0.987450i	0.869618	−	0.493725i	$-0.164365\pi$
$864$		0			0
$865$	637.000			0.736416
$866$	−18.9235	+	249.283i	−0.0218516	+	0.287855i
$867$		0			0
$868$	−154.212	−	23.5487i	−0.177664	−	0.0271299i
$869$	302.866	+	524.580i	0.348523	+	0.603659i
$870$		0			0
$871$	−865.332	−	499.600i	−0.993493	−	0.573593i
$872$	−82.9277	+	358.535i	−0.0951005	+	0.411163i
$873$		0			0
$874$	−1170.00	+	562.050i	−1.33867	+	0.643078i
$875$	721.500	+	416.558i	0.824571	+	0.476067i
$876$		0			0
$877$	−559.000	−	968.216i	−0.637400	−	1.10401i	−0.986001	−	0.166738i	$-0.946676\pi$
$877$	−559.000	−	968.216i	−0.637400	−	1.10401i	0.348601	−	0.937271i	$-0.386657\pi$
$878$	641.171	−	938.475i	0.730263	−	1.06888i
$879$		0			0
$880$	208.746	−	667.564i	0.237211	−	0.758595i
$881$	749.955			0.851254			0.425627	−	0.904899i	$-0.360054\pi$
$881$	749.955			0.851254			0.425627	+	0.904899i	$0.360054\pi$
$882$		0			0
$883$		−	1311.45i		−	1.48522i	−0.669724	−	0.742610i	$-0.733588\pi$
$883$		−	1311.45i		−	1.48522i	0.669724	−	0.742610i	$-0.266412\pi$
$884$	−335.556	−	859.866i	−0.379588	−	0.972700i
$885$		0			0
$886$	−429.916	+	629.263i	−0.485232	+	0.710229i
$887$	960.000	−	554.256i	1.08230	−	0.624866i	0.150784	−	0.988567i	$-0.451820\pi$
$887$	960.000	−	554.256i	1.08230	−	0.624866i	0.931516	+	0.363701i	$0.118487\pi$
$888$		0			0
$889$	58.5000	−	101.325i	0.0658043	−	0.113976i
$890$	515.594	−	247.683i	0.579319	−	0.278296i
$891$		0			0
$892$	−624.000	−	499.600i	−0.699552	−	0.560090i
$893$	64.8999	−	112.410i	0.0726763	−	0.125879i
$894$		0			0
$895$	−827.474	+	477.742i	−0.924552	+	0.533790i
$896$	−694.954	+	394.987i	−0.775618	+	0.440834i
$897$		0			0
$898$	73.1421	−	963.516i	0.0814500	−	1.07296i
$899$			315.233i			0.350649i
$900$		0			0
$901$	988.000			1.09656
$902$	−174.358	−	13.2358i	−0.193302	−	0.0146739i
$903$		0			0
$904$	717.274	−	218.974i	0.793445	−	0.242228i
$905$	−490.355	−	849.320i	−0.541829	−	0.938475i
$906$		0			0
$907$	530.016	+	306.005i	0.584362	+	0.337381i	0.762865	−	0.646558i	$-0.223792\pi$
$907$	530.016	+	306.005i	0.584362	+	0.337381i	−0.178503	+	0.983939i	$0.557125\pi$
$908$	237.966	+	190.526i	0.262078	+	0.209830i
$909$		0			0
$910$	−312.000	−	649.480i	−0.342857	−	0.713714i
$911$	681.000	+	393.176i	0.747530	+	0.431587i	0.824801	−	0.565423i	$-0.191287\pi$
$911$	681.000	+	393.176i	0.747530	+	0.431587i	−0.0772706	+	0.997010i	$0.524621\pi$
$912$		0			0
$913$	703.500	+	1218.50i	0.770537	+	1.33461i
$914$	−1365.70	−	933.052i	−1.49420	−	1.02084i
$915$		0			0
$916$	−311.191	−	797.431i	−0.339728	−	0.870558i
$917$	−270.416			−0.294892
$918$		0			0
$919$		−	880.545i		−	0.958155i	−0.877773	−	0.479078i	$-0.840971\pi$
$919$		−	880.545i		−	0.958155i	0.877773	−	0.479078i	$-0.159029\pi$
$920$	−340.875	+	365.246i	−0.370516	+	0.397006i
$921$		0			0
$922$	1065.80	+	728.157i	1.15596	+	0.789758i
$923$	−864.000	+	498.831i	−0.936078	+	0.540445i
$924$		0			0
$925$	156.000	−	270.200i	0.168649	−	0.292108i
$926$	91.9416	+	191.392i	0.0992889	+	0.206686i
$927$		0			0
$928$	1001.00	+	1267.73i	1.07866	+	1.36609i
$929$	122.589	−	212.330i	0.131958	−	0.228558i	−0.792473	−	0.609906i	$-0.791207\pi$
$929$	122.589	−	212.330i	0.131958	−	0.228558i	0.924431	+	0.381349i	$0.124540\pi$
$930$		0			0
$931$	324.500	−	187.350i	0.348550	−	0.201235i
$932$	1226.10	+	187.229i	1.31555	+	0.200890i
$933$		0			0
$934$	−1481.84	−	112.489i	−1.58655	−	0.120438i
$935$		−	630.466i		−	0.674296i
$936$		0			0
$937$	−649.000			−0.692636			−0.346318	−	0.938117i	$-0.612568\pi$
$937$	−649.000			−0.692636			−0.346318	+	0.938117i	$0.612568\pi$
$938$	−59.0412	+	777.762i	−0.0629438	+	0.829171i
$939$		0			0
$940$	7.54163	−	49.3875i	0.00802302	−	0.0525399i
$941$	−780.602	−	1352.04i	−0.829545	−	1.43681i	−0.898396	−	0.439187i	$-0.855267\pi$
$941$	−780.602	−	1352.04i	−0.829545	−	1.43681i	0.0688506	−	0.997627i	$-0.478067\pi$
$942$		0			0
$943$	108.167	+	62.4500i	0.114705	+	0.0662248i
$944$	−1189.83	+	266.736i	−1.26042	+	0.282559i
$945$		0			0
$946$	−273.000	+	131.145i	−0.288584	+	0.138631i
$947$	−88.5000	−	51.0955i	−0.0934530	−	0.0539551i	0.452545	−	0.891741i	$-0.350516\pi$
$947$	−88.5000	−	51.0955i	−0.0934530	−	0.0539551i	−0.545998	+	0.837786i	$0.683849\pi$
$948$		0			0
$949$	−152.000	−	263.272i	−0.160169	−	0.277420i
$950$	−507.300	+	742.530i	−0.534000	+	0.781610i
$951$		0			0
$952$	−491.616	+	526.765i	−0.516404	+	0.553324i
$953$	−504.777			−0.529672			−0.264836	−	0.964294i	$-0.585318\pi$
$953$	−504.777			−0.529672			−0.264836	+	0.964294i	$0.585318\pi$
$954$		0			0
$955$			949.240i			0.993968i
$956$	−1536.09	+	599.447i	−1.60679	+	0.627037i
$957$		0			0
$958$	379.108	−	554.896i	0.395728	−	0.579223i
$959$	429.000	−	247.683i	0.447341	−	0.258272i
$960$		0			0
$961$	−461.000	+	798.475i	−0.479709	+	0.830880i
$962$	−749.955	+	360.267i	−0.779579	+	0.374497i
$963$		0			0
$964$	515.000	−	643.235i	0.534232	−	0.667256i
$965$	337.119	−	583.907i	0.349346	−	0.605085i
$966$		0			0
$967$	−816.657	+	471.497i	−0.844527	+	0.487588i	−0.858800	−	0.512310i	$-0.828790\pi$
$967$	−816.657	+	471.497i	−0.844527	+	0.487588i	0.0142736	+	0.999898i	$0.495456\pi$
$968$	198.936	−	60.7325i	0.205512	−	0.0627402i
$969$		0			0
$970$	−64.9545	+	855.659i	−0.0669635	+	0.882123i
$971$		−	524.811i		−	0.540485i	−0.962792	−	0.270243i	$-0.912896\pi$
$971$		−	524.811i		−	0.540485i	0.962792	−	0.270243i	$-0.0871040\pi$
$972$		0			0
$973$	−780.000			−0.801644
$974$	1195.60	+	90.7600i	1.22752	+	0.0931827i
$975$		0			0
$976$	−94.1665	+	86.6987i	−0.0964821	+	0.0888306i
$977$	652.605	+	1130.34i	0.667968	+	1.15695i	0.978471	+	0.206382i	$0.0661691\pi$
$977$	652.605	+	1130.34i	0.667968	+	1.15695i	−0.310503	+	0.950572i	$0.600498\pi$
$978$		0			0
$979$	832.882	+	480.865i	0.850748	+	0.491180i
$980$	90.1388	−	112.583i	0.0919783	−	0.114881i
$981$		0			0
$982$	424.500	+	883.667i	0.432281	+	0.899865i
$983$	−1479.00	−	853.901i	−1.50458	−	0.868668i	−0.999986	−	0.00531044i	$-0.998310\pi$
$983$	−1479.00	−	853.901i	−1.50458	−	0.868668i	−0.504592	−	0.863358i	$-0.668357\pi$
$984$		0			0
$985$	32.5000	+	56.2917i	0.0329949	+	0.0571489i
$986$	1202.21	+	821.356i	1.21928	+	0.833019i
$987$		0			0
$988$	2234.00	−	871.800i	2.26113	−	0.882388i
$989$	216.333			0.218739
$990$		0			0
$991$		−	318.495i		−	0.321387i	−0.987004	−	0.160694i	$-0.948627\pi$
$991$		−	318.495i		−	0.321387i	0.987004	−	0.160694i	$-0.0513731\pi$
$992$	−28.8293	−	197.750i	−0.0290618	−	0.199344i
$993$		0			0
$994$	643.050	+	439.335i	0.646931	+	0.441987i
$995$	292.500	−	168.875i	0.293970	−	0.169724i
$996$		0			0
$997$	−652.000	+	1129.30i	−0.653962	+	1.13270i	0.328191	+	0.944611i	$0.393561\pi$
$997$	−652.000	+	1129.30i	−0.653962	+	1.13270i	−0.982153	+	0.188084i	$0.939772\pi$
$998$	−573.283	−	1193.38i	−0.574432	−	1.19577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.m.55.1		4
3.2	odd	2		324.3.f.l.55.2		4
4.3	odd	2		324.3.f.l.55.1		4
9.2	odd	6		108.3.d.c.55.2	yes	4
9.4	even	3		324.3.f.l.271.1		4
9.5	odd	6	inner	324.3.f.m.271.2		4
9.7	even	3		108.3.d.c.55.3	yes	4
12.11	even	2	inner	324.3.f.m.55.2		4
36.7	odd	6		108.3.d.c.55.4	yes	4
36.11	even	6		108.3.d.c.55.1	✓	4
36.23	even	6		324.3.f.l.271.2		4
36.31	odd	6	inner	324.3.f.m.271.1		4
72.11	even	6		1728.3.g.i.703.3		4
72.29	odd	6		1728.3.g.i.703.4		4
72.43	odd	6		1728.3.g.i.703.1		4
72.61	even	6		1728.3.g.i.703.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.c.55.1	✓	4	36.11	even	6
108.3.d.c.55.2	yes	4	9.2	odd	6
108.3.d.c.55.3	yes	4	9.7	even	3
108.3.d.c.55.4	yes	4	36.7	odd	6
324.3.f.l.55.1		4	4.3	odd	2
324.3.f.l.55.2		4	3.2	odd	2
324.3.f.l.271.1		4	9.4	even	3
324.3.f.l.271.2		4	36.23	even	6
324.3.f.m.55.1		4	1.1	even	1	trivial
324.3.f.m.55.2		4	12.11	even	2	inner
324.3.f.m.271.1		4	36.31	odd	6	inner
324.3.f.m.271.2		4	9.5	odd	6	inner
1728.3.g.i.703.1		4	72.43	odd	6
1728.3.g.i.703.2		4	72.61	even	6
1728.3.g.i.703.3		4	72.11	even	6
1728.3.g.i.703.4		4	72.29	odd	6

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.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.151388 + 1.99426i) q^{2} +(-3.95416 - 0.603814i) q^{4} +(-1.80278 - 3.12250i) q^{5} +(-5.40833 - 3.12250i) q^{7} +(1.80278 - 7.79423i) q^{8} +O(q^{10})\)	\(q+(-0.151388 + 1.99426i) q^{2} +(-3.95416 - 0.603814i) q^{4} +(-1.80278 - 3.12250i) q^{5} +(-5.40833 - 3.12250i) q^{7} +(1.80278 - 7.79423i) q^{8} +(6.50000 - 3.12250i) q^{10} +(10.5000 + 6.06218i) q^{11} +(8.00000 + 13.8564i) q^{13} +(7.04584 - 10.3129i) q^{14} +(15.2708 + 4.77516i) q^{16} +14.4222 q^{17} +37.4700i q^{19} +(5.24306 + 13.4354i) q^{20} +(-13.6791 + 20.0220i) q^{22} +(15.0000 - 8.66025i) q^{23} +(6.00000 - 10.3923i) q^{25} +(-28.8444 + 13.8564i) q^{26} +(19.5000 + 15.6125i) q^{28} +(25.2389 - 43.7150i) q^{29} +(-5.40833 + 3.12250i) q^{31} +(-11.8347 + 29.7311i) q^{32} +(-2.18335 + 28.7617i) q^{34} +22.5167i q^{35} +26.0000 q^{37} +(-74.7250 - 5.67250i) q^{38} +(-27.5875 + 8.42208i) q^{40} +(3.60555 + 6.24500i) q^{41} +(10.8167 + 6.24500i) q^{43} +(-37.8583 - 30.3109i) q^{44} +(15.0000 + 31.2250i) q^{46} +(-3.00000 - 1.73205i) q^{47} +(-5.00000 - 8.66025i) q^{49} +(19.8167 + 13.5388i) q^{50} +(-23.2666 - 59.6210i) q^{52} +68.5055 q^{53} -43.7150i q^{55} +(-34.0875 + 36.5246i) q^{56} +(83.3583 + 56.9508i) q^{58} +(-66.0000 + 38.1051i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-5.40833 - 11.2583i) q^{62} +(-57.5000 - 28.1025i) q^{64} +(28.8444 - 49.9600i) q^{65} +(-54.0833 + 31.2250i) q^{67} +(-57.0278 - 8.70833i) q^{68} +(-44.9041 - 3.40875i) q^{70} +62.3538i q^{71} -19.0000 q^{73} +(-3.93608 + 51.8508i) q^{74} +(22.6249 - 148.162i) q^{76} +(-37.8583 - 65.5725i) q^{77} +(43.2666 + 24.9800i) q^{79} +(-12.6194 - 56.2917i) q^{80} +(-13.0000 + 6.24500i) q^{82} +(100.500 + 58.0237i) q^{83} +(-26.0000 - 45.0333i) q^{85} +(-14.0917 + 20.6258i) q^{86} +(66.1791 - 70.9107i) q^{88} +79.3221 q^{89} -99.9200i q^{91} +(-64.5416 + 25.1868i) q^{92} +(3.90833 - 5.72058i) q^{94} +(117.000 - 67.5500i) q^{95} +(-59.5000 + 103.057i) q^{97} +(18.0278 - 8.66025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 4 * q + 3 * q^2 - 5 * q^4	\( 4 q + 3 q^{2} - 5 q^{4} + 26 q^{10} + 42 q^{11} + 32 q^{13} + 39 q^{14} + 7 q^{16} + 39 q^{20} + 21 q^{22} + 60 q^{23} + 24 q^{25} + 78 q^{28} - 87 q^{32} - 52 q^{34} + 104 q^{37} - 234 q^{38} - 13 q^{40} + 60 q^{46} - 12 q^{47} - 20 q^{49} + 36 q^{50} + 80 q^{52} - 39 q^{56} + 182 q^{58} - 264 q^{59} - 16 q^{61} - 230 q^{64} - 156 q^{68} - 39 q^{70} - 76 q^{73} + 78 q^{74} - 234 q^{76} - 52 q^{82} + 402 q^{83} - 104 q^{85} - 78 q^{86} + 189 q^{88} - 150 q^{92} - 6 q^{94} + 468 q^{95} - 238 q^{97}+O(q^{100}) \) 4 * q + 3 * q^2 - 5 * q^4 + 26 * q^10 + 42 * q^11 + 32 * q^13 + 39 * q^14 + 7 * q^16 + 39 * q^20 + 21 * q^22 + 60 * q^23 + 24 * q^25 + 78 * q^28 - 87 * q^32 - 52 * q^34 + 104 * q^37 - 234 * q^38 - 13 * q^40 + 60 * q^46 - 12 * q^47 - 20 * q^49 + 36 * q^50 + 80 * q^52 - 39 * q^56 + 182 * q^58 - 264 * q^59 - 16 * q^61 - 230 * q^64 - 156 * q^68 - 39 * q^70 - 76 * q^73 + 78 * q^74 - 234 * q^76 - 52 * q^82 + 402 * q^83 - 104 * q^85 - 78 * q^86 + 189 * q^88 - 150 * q^92 - 6 * q^94 + 468 * q^95 - 238 * q^97

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