LMFDB - Embedded newform 324.3.f.m.55.2

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			55.2
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.m.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65139 - 1.12824i) q^{2} +(1.45416 - 3.72631i) q^{4} +(1.80278 + 3.12250i) q^{5} +(5.40833 + 3.12250i) q^{7} +(-1.80278 - 7.79423i) q^{8} +O(q^{10})$	\(q+(1.65139 - 1.12824i) q^{2} +(1.45416 - 3.72631i) q^{4} +(1.80278 + 3.12250i) q^{5} +(5.40833 + 3.12250i) q^{7} +(-1.80278 - 7.79423i) q^{8} +(6.50000 + 3.12250i) q^{10} +(10.5000 + 6.06218i) q^{11} +(8.00000 + 13.8564i) q^{13} +(12.4542 - 0.945417i) q^{14} +(-11.7708 - 10.8373i) q^{16} -14.4222 q^{17} -37.4700i q^{19} +(14.2569 - 2.17708i) q^{20} +(24.1791 - 1.83548i) q^{22} +(15.0000 - 8.66025i) q^{23} +(6.00000 - 10.3923i) q^{25} +(28.8444 + 13.8564i) q^{26} +(19.5000 - 15.6125i) q^{28} +(-25.2389 + 43.7150i) q^{29} +(5.40833 - 3.12250i) q^{31} +(-31.6653 - 4.61638i) q^{32} +(-23.8167 + 16.2717i) q^{34} +22.5167i q^{35} +26.0000 q^{37} +(-42.2750 - 61.8775i) q^{38} +(21.0875 - 19.6804i) q^{40} +(-3.60555 - 6.24500i) q^{41} +(-10.8167 - 6.24500i) q^{43} +(37.8583 - 30.3109i) q^{44} +(15.0000 - 31.2250i) q^{46} +(-3.00000 - 1.73205i) q^{47} +(-5.00000 - 8.66025i) q^{49} +(-1.81665 - 23.9311i) q^{50} +(63.2666 - 9.66102i) q^{52} -68.5055 q^{53} +43.7150i q^{55} +(14.5875 - 47.7829i) q^{56} +(7.64171 + 100.666i) q^{58} +(-66.0000 + 38.1051i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(5.40833 - 11.2583i) q^{62} +(-57.5000 + 28.1025i) q^{64} +(-28.8444 + 49.9600i) q^{65} +(54.0833 - 31.2250i) q^{67} +(-20.9722 + 53.7417i) q^{68} +(25.4041 + 37.1837i) q^{70} +62.3538i q^{71} -19.0000 q^{73} +(42.9361 - 29.3342i) q^{74} +(-139.625 - 54.4875i) q^{76} +(37.8583 + 65.5725i) q^{77} +(-43.2666 - 24.9800i) q^{79} +(12.6194 - 56.2917i) q^{80} +(-13.0000 - 6.24500i) q^{82} +(100.500 + 58.0237i) q^{83} +(-26.0000 - 45.0333i) q^{85} +(-24.9083 + 1.89083i) q^{86} +(28.3209 - 92.7681i) q^{88} -79.3221 q^{89} +99.9200i q^{91} +(-10.4584 - 68.4881i) q^{92} +(-6.90833 + 0.524423i) q^{94} +(117.000 - 67.5500i) q^{95} +(-59.5000 + 103.057i) q^{97} +(-18.0278 - 8.66025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.65139	−	1.12824i	0.825694	−	0.564118i
$2$	1.65139	−	1.12824i	0.825694	−	0.564118i
$3$		0			0
$3$		0			0
$4$	1.45416	−	3.72631i	0.363541	−	0.931578i
$5$	1.80278	+	3.12250i	0.360555	+	0.624500i	0.988052	−	0.154119i	$-0.0492539\pi$
$5$	1.80278	+	3.12250i	0.360555	+	0.624500i	−0.627497	+	0.778619i	$0.715921\pi$
$6$		0			0
$7$	5.40833	+	3.12250i	0.772618	+	0.446071i	0.833808	−	0.552055i	$-0.186156\pi$
$7$	5.40833	+	3.12250i	0.772618	+	0.446071i	−0.0611897	+	0.998126i	$0.519489\pi$
$8$	−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	$0.622334\pi$
$14$	12.4542	−	0.945417i	0.889583	−	0.0675298i
$15$		0			0
$16$	−11.7708	−	10.8373i	−0.735676	−	0.677334i
$17$	−14.4222			−0.848365			−0.424183	−	0.905577i	$-0.639438\pi$
$17$	−14.4222			−0.848365			−0.424183	+	0.905577i	$0.639438\pi$
$18$		0			0
$19$		−	37.4700i		−	1.97210i	−0.166436	−	0.986052i	$-0.553226\pi$
$19$		−	37.4700i		−	1.97210i	0.166436	−	0.986052i	$-0.446774\pi$
$20$	14.2569	−	2.17708i	0.712847	−	0.108854i
$21$		0			0
$22$	24.1791	−	1.83548i	1.09905	−	0.0834309i
$23$	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	$0.502745\pi$
$29$	−25.2389	+	43.7150i	−0.870305	+	1.50741i	−0.861681	+	0.507451i	$0.830588\pi$
$30$		0			0
$31$	5.40833	−	3.12250i	0.174462	−	0.100726i	−0.410226	−	0.911984i	$-0.634550\pi$
$31$	5.40833	−	3.12250i	0.174462	−	0.100726i	0.584688	+	0.811258i	$0.301217\pi$
$32$	−31.6653	−	4.61638i	−0.989540	−	0.144262i
$33$		0			0
$34$	−23.8167	+	16.2717i	−0.700490	+	0.478578i
$35$			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	$0.385722\pi$
$38$	−42.2750	−	61.8775i	−1.11250	−	1.62835i
$39$		0			0
$40$	21.0875	−	19.6804i	0.527187	−	0.492010i
$41$	−3.60555	−	6.24500i	−0.0879403	−	0.152317i	0.818700	−	0.574221i	$-0.194695\pi$
$41$	−3.60555	−	6.24500i	−0.0879403	−	0.152317i	−0.906640	+	0.421904i	$0.861362\pi$
$42$		0			0
$43$	−10.8167	−	6.24500i	−0.251550	−	0.145233i	0.368924	−	0.929460i	$-0.379726\pi$
$43$	−10.8167	−	6.24500i	−0.251550	−	0.145233i	−0.620474	+	0.784227i	$0.713060\pi$
$44$	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
$50$	−1.81665	−	23.9311i	−0.0363331	−	0.478623i
$51$		0			0
$52$	63.2666	−	9.66102i	1.21667	−	0.185789i
$53$	−68.5055			−1.29256			−0.646278	−	0.763102i	$-0.723675\pi$
$53$	−68.5055			−1.29256			−0.646278	+	0.763102i	$0.723675\pi$
$54$		0			0
$55$			43.7150i			0.794818i
$56$	14.5875	−	47.7829i	0.260491	−	0.853266i
$57$		0			0
$58$	7.64171	+	100.666i	0.131754	+	1.73562i
$59$	−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	−0.0387741	−	0.999248i	$-0.512345\pi$
$67$	54.0833	−	31.2250i	0.807213	−	0.466045i	0.845987	+	0.533203i	$0.179012\pi$
$68$	−20.9722	+	53.7417i	−0.308415	+	0.790318i
$69$		0			0
$70$	25.4041	+	37.1837i	0.362916	+	0.531196i
$71$			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	$0.541542\pi$
$74$	42.9361	−	29.3342i	0.580217	−	0.396408i
$75$		0			0
$76$	−139.625	−	54.4875i	−1.83717	−	0.716941i
$77$	37.8583	+	65.5725i	0.491666	+	0.851591i
$78$		0			0
$79$	−43.2666	−	24.9800i	−0.547679	−	0.316202i	0.200507	−	0.979692i	$-0.435741\pi$
$79$	−43.2666	−	24.9800i	−0.547679	−	0.316202i	−0.748185	+	0.663490i	$0.769075\pi$
$80$	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
$86$	−24.9083	+	1.89083i	−0.289632	+	0.0219864i
$87$		0			0
$88$	28.3209	−	92.7681i	0.321828	−	1.05418i
$89$	−79.3221			−0.891260			−0.445630	−	0.895217i	$-0.647020\pi$
$89$	−79.3221			−0.891260			−0.445630	+	0.895217i	$0.647020\pi$
$90$		0			0
$91$			99.9200i			1.09802i
$92$	−10.4584	−	68.4881i	−0.113678	−	0.744436i
$93$		0			0
$94$	−6.90833	+	0.524423i	−0.0734928	+	0.00557897i
$95$	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	−0.976912	−	0.213641i	$-0.931468\pi$
$101$	−30.6472	+	53.0825i	−0.303437	+	0.525569i	0.673475	+	0.739210i	$0.264801\pi$
$102$		0			0
$103$	−108.167	+	62.4500i	−1.05016	+	0.606310i	−0.922694	−	0.385532i	$-0.874018\pi$
$103$	−108.167	+	62.4500i	−1.05016	+	0.606310i	−0.127466	+	0.991843i	$0.540684\pi$
$104$	93.5778	−	87.3338i	0.899786	−	0.839748i
$105$		0			0
$106$	−113.129	+	77.2904i	−1.06726	+	0.729155i
$107$		−	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	$0.567675\pi$
$110$	49.3209	+	72.1904i	0.448371	+	0.656276i
$111$		0			0
$112$	−29.8209	−	95.3662i	−0.266258	−	0.851484i
$113$	−46.8722	−	81.1850i	−0.414798	−	0.718451i	0.580609	−	0.814182i	$-0.302814\pi$
$113$	−46.8722	−	81.1850i	−0.414798	−	0.718451i	−0.995407	+	0.0957312i	$0.969481\pi$
$114$		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
$122$	1.21110	+	15.9541i	0.00992707	+	0.130771i
$123$		0			0
$124$	−3.77082	−	24.6937i	−0.0304098	−	0.199143i
$125$	133.405			1.06724
$126$		0			0
$127$		−	18.7350i		−	0.147520i	−0.997276	−	0.0737598i	$-0.976500\pi$
$127$		−	18.7350i		−	0.147520i	0.997276	−	0.0737598i	$-0.0234998\pi$
$128$	−63.2485	+	111.282i	−0.494129	+	0.869388i
$129$		0			0
$130$	8.73338	+	115.047i	0.0671799	+	0.884974i
$131$	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	−0.684193	−	0.729301i	$-0.739845\pi$
$137$	39.6611	−	68.6950i	0.289497	−	0.501423i	0.973690	+	0.227878i	$0.0731787\pi$
$138$		0			0
$139$	−108.167	+	62.4500i	−0.778177	+	0.449280i	−0.835784	−	0.549059i	$-0.814986\pi$
$139$	−108.167	+	62.4500i	−0.778177	+	0.449280i	0.0576071	+	0.998339i	$0.481653\pi$
$140$	83.9041	+	32.7429i	0.599315	+	0.233878i
$141$		0			0
$142$	70.3499	+	102.970i	0.495422	+	0.725143i
$143$			193.990i			1.35657i
$144$		0			0
$145$	−182.000			−1.25517
$146$	−31.3764	+	21.4365i	−0.214907	+	0.146825i
$147$		0			0
$148$	37.8082	−	96.8841i	0.255461	−	0.654623i
$149$	1.80278	+	3.12250i	0.0120992	+	0.0209564i	0.872012	−	0.489485i	$-0.162815\pi$
$149$	1.80278	+	3.12250i	0.0120992	+	0.0209564i	−0.859912	+	0.510442i	$0.829482\pi$
$150$		0			0
$151$	167.658	+	96.7975i	1.11032	+	0.641043i	0.938912	−	0.344157i	$-0.111835\pi$
$151$	167.658	+	96.7975i	1.11032	+	0.641043i	0.171407	+	0.985200i	$0.445169\pi$
$152$	−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	$0.927985\pi$
$158$	−99.6333	+	7.56333i	−0.630591	+	0.0478692i
$159$		0			0
$160$	−42.6707	−	107.197i	−0.266692	−	0.669982i
$161$	108.167			0.671842
$162$		0			0
$163$		−	149.880i		−	0.919509i	−0.888046	−	0.459754i	$-0.847937\pi$
$163$		−	149.880i		−	0.919509i	0.888046	−	0.459754i	$-0.152063\pi$
$164$	−28.5139	+	4.35416i	−0.173865	+	0.0265498i
$165$		0			0
$166$	231.429	−	17.5682i	1.39415	−	0.105832i
$167$	−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	$-0.662752\pi$
$173$	88.3360	−	153.002i	0.510613	−	0.884407i	0.999924	−	0.0122982i	$-0.00391474\pi$
$174$		0			0
$175$	64.8999	−	37.4700i	0.370857	−	0.214114i
$176$	−57.8957	−	185.149i	−0.328953	−	1.05198i
$177$		0			0
$178$	−130.992	+	89.4941i	−0.735908	+	0.502776i
$179$		−	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	$0.229388\pi$
$182$	112.733	+	165.007i	0.619414	+	0.906630i
$183$		0			0
$184$	−94.5416	−	101.301i	−0.513813	−	0.550549i
$185$	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	$0.672351\pi$
$194$	18.0152	+	237.317i	0.0928616	+	1.22328i
$195$		0			0
$196$	−39.5416	+	6.03814i	−0.201743	+	0.0308068i
$197$	18.0278			0.0915115			0.0457557	−	0.998953i	$-0.485430\pi$
$197$	18.0278			0.0915115			0.0457557	+	0.998953i	$0.485430\pi$
$198$		0			0
$199$		−	93.6750i		−	0.470728i	−0.971907	−	0.235364i	$-0.924372\pi$
$199$		−	93.6750i		−	0.470728i	0.971907	−	0.235364i	$-0.0756283\pi$
$200$	−91.8167	−	28.0304i	−0.459083	−	0.140152i
$201$		0			0
$202$	9.27922	+	122.237i	0.0459367	+	0.605134i
$203$	−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	−0.366335	−	0.930483i	$-0.619388\pi$
$211$	54.0833	−	31.2250i	0.256319	−	0.147986i	0.622654	+	0.782497i	$0.286054\pi$
$212$	−99.6182	+	255.273i	−0.469897	+	1.20412i
$213$		0			0
$214$	−146.562	−	214.522i	−0.684870	−	1.00244i
$215$		−	45.0333i		−	0.209457i
$216$		0			0
$217$	39.0000			0.179724
$218$	−75.9638	+	51.8989i	−0.348458	+	0.238068i
$219$		0			0
$220$	162.896	+	63.5687i	0.740435	+	0.288949i
$221$	−115.378	−	199.840i	−0.522071	−	0.904253i
$222$		0			0
$223$	−173.066	−	99.9200i	−0.776083	−	0.448072i	0.0589574	−	0.998260i	$-0.481222\pi$
$223$	−173.066	−	99.9200i	−0.776083	−	0.448072i	−0.835040	+	0.550189i	$0.814556\pi$
$224$	−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	$0.678579\pi$
$230$	124.542	−	9.45417i	0.541485	−	0.0411051i
$231$		0			0
$232$	386.225	+	117.909i	1.66476	+	0.508229i
$233$	310.077			1.33080			0.665402	−	0.746485i	$-0.268260\pi$
$233$	310.077			1.33080			0.665402	+	0.746485i	$0.268260\pi$
$234$		0			0
$235$		−	12.4900i		−	0.0531489i
$236$	46.0168	+	301.348i	0.194986	+	1.27690i
$237$		0			0
$238$	−179.616	+	13.6350i	−0.754691	+	0.0572899i
$239$	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
$248$	−34.0875	−	36.5246i	−0.137449	−	0.147276i
$249$		0			0
$250$	220.304	−	150.513i	0.881216	−	0.602052i
$251$		−	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
$254$	−21.1375	−	30.9387i	−0.0832185	−	0.121806i
$255$		0			0
$256$	21.1043	+	255.129i	0.0824386	+	0.996596i
$257$	−14.4222	−	24.9800i	−0.0561175	−	0.0971984i	0.836602	−	0.547811i	$-0.184539\pi$
$257$	−14.4222	−	24.9800i	−0.0561175	−	0.0971984i	−0.892719	+	0.450613i	$0.851205\pi$
$258$		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
$266$	−35.4247	−	466.657i	−0.133176	−	1.75435i
$267$		0			0
$268$	−37.7082	−	246.937i	−0.140702	−	0.921408i
$269$	50.4777			0.187650			0.0938248	−	0.995589i	$-0.470091\pi$
$269$	50.4777			0.187650			0.0938248	+	0.995589i	$0.470091\pi$
$270$		0			0
$271$			18.7350i			0.0691328i	0.999402	+	0.0345664i	$0.0110050\pi$
$271$			18.7350i			0.0691328i	−0.999402	+	0.0345664i	$0.988995\pi$
$272$	169.761	+	156.298i	0.624122	+	0.574626i
$273$		0			0
$274$	−12.0084	−	158.189i	−0.0438263	−	0.577333i
$275$	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	$0.521777\pi$
$281$	−252.389	+	437.150i	−0.898180	+	1.55569i	−0.829819	+	0.558033i	$0.811556\pi$
$282$		0			0
$283$	−10.8167	+	6.24500i	−0.0382214	+	0.0220671i	−0.518989	−	0.854781i	$-0.673691\pi$
$283$	−10.8167	+	6.24500i	−0.0382214	+	0.0220671i	0.480768	+	0.876848i	$0.340358\pi$
$284$	232.350	+	90.6727i	0.818133	+	0.319270i
$285$		0			0
$286$	218.866	+	320.352i	0.765267	+	1.12011i
$287$		−	45.0333i		−	0.156911i
$288$		0			0
$289$	−81.0000			−0.280277
$290$	−300.553	+	205.339i	−1.03639	+	0.708066i
$291$		0			0
$292$	−27.6291	+	70.7999i	−0.0946202	+	0.242466i
$293$	82.9277	+	143.635i	0.283030	+	0.490222i	0.972129	−	0.234445i	$-0.0753272\pi$
$293$	82.9277	+	143.635i	0.283030	+	0.490222i	−0.689100	+	0.724666i	$0.741994\pi$
$294$		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
$302$	386.079	−	29.3079i	1.27841	−	0.0970461i
$303$		0			0
$304$	−406.075	+	441.052i	−1.33577	+	1.45083i
$305$	−28.8444			−0.0945718
$306$		0			0
$307$			524.580i			1.70873i	0.519674	+	0.854365i	$0.326053\pi$
$307$			524.580i			1.70873i	−0.519674	+	0.854365i	$0.673947\pi$
$308$	299.396	−	45.7187i	0.972064	−	0.148437i
$309$		0			0
$310$	44.9041	−	3.40875i	0.144852	−	0.0109960i
$311$	−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	$-0.543159\pi$
$317$	250.586	−	434.027i	0.790492	−	1.36917i	0.925663	−	0.378349i	$-0.123508\pi$
$318$		0			0
$319$	−530.016	+	306.005i	−1.66149	+	0.959263i
$320$	−191.410	−	128.881i	−0.598155	−	0.402754i
$321$		0			0
$322$	178.625	−	122.037i	0.554736	−	0.378998i
$323$			540.400i			1.67306i
$324$		0			0
$325$	192.000			0.590769
$326$	−169.100	−	247.510i	−0.518712	−	0.759233i
$327$		0			0
$328$	−42.1749	+	39.3608i	−0.128582	+	0.120003i
$329$	−10.8167	−	18.7350i	−0.0328774	−	0.0569453i
$330$		0			0
$331$	118.983	+	68.6950i	0.359466	+	0.207538i	0.668846	−	0.743401i	$-0.266788\pi$
$331$	118.983	+	68.6950i	0.359466	+	0.207538i	−0.309381	+	0.950938i	$0.600122\pi$
$332$	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	$0.856969\pi$
$338$	13.1707	+	173.501i	0.0389667	+	0.513316i
$339$		0			0
$340$	−205.616	+	31.3983i	−0.604754	+	0.0923480i
$341$	75.7166			0.222043
$342$		0			0
$343$		−	368.455i		−	1.07421i
$344$	−29.1749	+	95.5658i	−0.0848109	+	0.277808i
$345$		0			0
$346$	−26.7460	−	352.330i	−0.0773006	−	1.01830i
$347$	−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	−0.979784	−	0.200060i	$-0.935886\pi$
$353$	−111.772	+	193.595i	−0.316635	+	0.548428i	0.663149	+	0.748488i	$0.269220\pi$
$354$		0			0
$355$	−194.700	+	112.410i	−0.548450	+	0.316648i
$356$	−115.347	+	295.579i	−0.324009	+	0.830278i
$357$		0			0
$358$	−298.987	−	437.624i	−0.835159	−	1.22241i
$359$		−	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
$362$	449.177	−	306.880i	1.24082	−	0.847736i
$363$		0			0
$364$	372.333	+	145.300i	1.02289	+	0.399176i
$365$	−34.2527	−	59.3275i	−0.0938431	−	0.162541i
$366$		0			0
$367$	232.558	+	134.267i	0.633673	+	0.365851i	0.782173	−	0.623061i	$-0.214111\pi$
$367$	232.558	+	134.267i	0.633673	+	0.365851i	−0.148500	+	0.988912i	$0.547445\pi$
$368$	−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	$0.925055\pi$
$374$	−348.717	+	26.4717i	−0.932397	+	0.0707799i
$375$		0			0
$376$	−8.09167	+	26.5052i	−0.0215204	+	0.0704925i
$377$	−807.643			−2.14229
$378$		0			0
$379$		−	224.820i		−	0.593192i	−0.955003	−	0.296596i	$-0.904148\pi$
$379$		−	224.820i		−	0.593192i	0.955003	−	0.296596i	$-0.0958515\pi$
$380$	−81.5753	−	534.207i	−0.214672	−	1.40581i
$381$		0			0
$382$	−525.033	+	39.8561i	−1.37443	+	0.104335i
$383$	−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	$0.397263\pi$
$389$	−257.797	+	446.517i	−0.662717	+	1.14786i	−0.979899	+	0.199495i	$0.936070\pi$
$390$		0			0
$391$	−216.333	+	124.900i	−0.553282	+	0.319437i
$392$	−58.4861	+	54.5836i	−0.149199	+	0.139244i
$393$		0			0
$394$	29.7708	−	20.3396i	0.0755604	−	0.0516233i
$395$		−	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	$0.467874\pi$
$398$	−105.688	−	154.694i	−0.265547	−	0.388678i
$399$		0			0
$400$	−183.250	+	57.3019i	−0.458125	+	0.143255i
$401$	310.077	+	537.070i	0.773260	+	1.33933i	0.935767	+	0.352619i	$0.114709\pi$
$401$	310.077	+	537.070i	0.773260	+	1.33933i	−0.162507	+	0.986707i	$0.551958\pi$
$402$		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	$0.693027\pi$
$410$	−3.93608	−	51.8508i	−0.00960020	−	0.126465i
$411$		0			0
$412$	75.4163	+	493.875i	0.183049	+	1.19873i
$413$	−475.933			−1.15238
$414$		0			0
$415$			418.415i			1.00823i
$416$	−189.356	−	475.698i	−0.455182	−	1.14350i
$417$		0			0
$418$	−68.7754	−	905.992i	−0.164534	−	2.16745i
$419$	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
$428$	−484.062	−	188.901i	−1.13099	−	0.441358i
$429$		0			0
$430$	−50.8082	−	74.3675i	−0.118159	−	0.172948i
$431$			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	$0.453894\pi$
$434$	64.4041	−	44.0012i	0.148397	−	0.101385i
$435$		0			0
$436$	−66.8915	+	171.410i	−0.153421	+	0.393143i
$437$	−324.500	−	562.050i	−0.742562	−	1.28616i
$438$		0			0
$439$	492.158	+	284.147i	1.12109	+	0.647261i	0.941679	−	0.336514i	$-0.109248\pi$
$439$	492.158	+	284.147i	1.12109	+	0.647261i	0.179410	+	0.983774i	$0.442581\pi$
$440$	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
$446$	−398.533	+	30.2533i	−0.893572	+	0.0678326i
$447$		0			0
$448$	−398.729	−	27.5562i	−0.890020	−	0.0615095i
$449$	483.144			1.07604			0.538022	−	0.842931i	$-0.319172\pi$
$449$	483.144			1.07604			0.538022	+	0.842931i	$0.319172\pi$
$450$		0			0
$451$		−	87.4300i		−	0.193858i
$452$	−370.680	+	56.6041i	−0.820089	+	0.125230i
$453$		0			0
$454$	−151.983	+	11.5373i	−0.334765	+	0.0254126i
$455$	−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	$0.413480\pi$
$461$	−322.697	+	558.927i	−0.699993	+	1.21242i	−0.968468	+	0.249137i	$0.919853\pi$
$462$		0			0
$463$	−91.9416	+	53.0825i	−0.198578	+	0.114649i	−0.595992	−	0.802990i	$-0.703241\pi$
$463$	−91.9416	+	53.0825i	−0.198578	+	0.114649i	0.397414	+	0.917639i	$0.369908\pi$
$464$	770.836	−	241.039i	1.66128	−	0.519481i
$465$		0			0
$466$	512.058	−	349.841i	1.09884	−	0.750731i
$467$			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
$470$	−14.0917	−	20.6258i	−0.0299823	−	0.0438847i
$471$		0			0
$472$	415.983	+	445.724i	0.881320	+	0.944331i
$473$	−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
$482$	31.1859	+	410.818i	0.0647010	+	0.852320i
$483$		0			0
$484$	102.808	−	15.6992i	0.212414	−	0.0324363i
$485$	−429.061			−0.884661
$486$		0			0
$487$			599.520i			1.23105i	0.788119	+	0.615523i	$0.211055\pi$
$487$			599.520i			1.23105i	−0.788119	+	0.615523i	$0.788945\pi$
$488$	61.2111	+	18.6869i	0.125433	+	0.0382929i
$489$		0			0
$490$	−5.45837	−	71.9041i	−0.0111395	−	0.146743i
$491$	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	0.200253	−	0.979744i	$-0.435824\pi$
$499$	573.283	−	330.985i	1.14886	−	0.663296i	0.948610	+	0.316448i	$0.102490\pi$
$500$	193.993	−	497.110i	0.387987	−	0.994221i
$501$		0			0
$502$	−93.7998	−	137.294i	−0.186852	−	0.273494i
$503$		−	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
$506$	346.791	−	236.930i	0.685359	−	0.468241i
$507$		0			0
$508$	−69.8125	−	27.2437i	−0.137426	−	0.0536294i
$509$	272.219	+	471.497i	0.534812	+	0.926321i	0.999172	+	0.0406748i	$0.0129508\pi$
$509$	272.219	+	471.497i	0.534812	+	0.926321i	−0.464361	+	0.885646i	$0.653716\pi$
$510$		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
$518$	323.808	−	24.5808i	0.625112	−	0.0474533i
$519$		0			0
$520$	441.400	+	134.753i	0.848845	+	0.259141i
$521$	−230.755			−0.442908			−0.221454	−	0.975171i	$-0.571080\pi$
$521$	−230.755			−0.442908			−0.221454	+	0.975171i	$0.571080\pi$
$522$		0			0
$523$		−	674.460i		−	1.28960i	−0.764352	−	0.644799i	$-0.776941\pi$
$523$		−	674.460i		−	1.28960i	0.764352	−	0.644799i	$-0.223059\pi$
$524$	−26.1459	−	171.220i	−0.0498968	−	0.326756i
$525$		0			0
$526$	−89.8082	+	6.81750i	−0.170738	+	0.0129610i
$527$	−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
$536$	−340.875	−	365.246i	−0.635960	−	0.681429i
$537$		0			0
$538$	83.3583	−	56.9508i	0.154941	−	0.105857i
$539$		−	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	$0.422756\pi$
$542$	21.1375	+	30.9387i	0.0389991	+	0.0570825i
$543$		0			0
$544$	456.683	+	66.5783i	0.839491	+	0.122387i
$545$	−82.9277	−	143.635i	−0.152161	−	0.263550i
$546$		0			0
$547$	−757.166	−	437.150i	−1.38422	−	0.799177i	−0.391560	−	0.920153i	$-0.628064\pi$
$547$	−757.166	−	437.150i	−1.38422	−	0.799177i	−0.992655	+	0.120976i	$0.961398\pi$
$548$	−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
$554$	−24.2221	−	319.082i	−0.0437221	−	0.575960i
$555$		0			0
$556$	75.4163	+	493.875i	0.135641	+	0.888264i
$557$	472.327			0.847984			0.423992	−	0.905666i	$-0.360628\pi$
$557$	472.327			0.847984			0.423992	+	0.905666i	$0.360628\pi$
$558$		0			0
$559$		−	199.840i		−	0.357495i
$560$	244.021	−	265.039i	0.435751	−	0.473285i
$561$		0			0
$562$	76.4171	+	1006.66i	0.135974	+	1.79121i
$563$	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	−0.720148	−	0.693821i	$-0.755926\pi$
$569$	137.011	−	237.310i	0.240793	−	0.417065i	0.960940	+	0.276756i	$0.0892593\pi$
$570$		0			0
$571$	216.333	−	124.900i	0.378867	−	0.218739i	−0.298458	−	0.954423i	$-0.596472\pi$
$571$	216.333	−	124.900i	0.378867	−	0.218739i	0.677325	+	0.735684i	$0.263139\pi$
$572$	722.866	+	282.093i	1.26375	+	0.493169i
$573$		0			0
$574$	−50.8082	−	74.3675i	−0.0885161	−	0.129560i
$575$		−	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	$0.359191\pi$
$578$	−133.762	+	91.3872i	−0.231423	+	0.158109i
$579$		0			0
$580$	−264.658	+	678.189i	−0.456306	+	1.16929i
$581$	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
$590$	−547.983	+	41.5983i	−0.928785	+	0.0705056i
$591$		0			0
$592$	−306.041	−	281.771i	−0.516962	−	0.475964i
$593$	−468.722			−0.790424			−0.395212	−	0.918590i	$-0.629329\pi$
$593$	−468.722			−0.790424			−0.395212	+	0.918590i	$0.629329\pi$
$594$		0			0
$595$		−	324.740i		−	0.545781i
$596$	14.2569	−	2.17708i	0.0239210	−	0.00365282i
$597$		0			0
$598$	552.666	−	41.9538i	0.924191	−	0.0701569i
$599$	−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	−0.187008	−	0.982358i	$-0.559879\pi$
$607$	346.133	−	199.840i	0.570235	−	0.329226i	0.757243	+	0.653133i	$0.226546\pi$
$608$	−172.976	+	1186.50i	−0.284499	+	1.95148i
$609$		0			0
$610$	−47.6333	+	32.5433i	−0.0780874	+	0.0533497i
$611$		−	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	$0.250335\pi$
$614$	591.850	+	866.285i	0.963926	+	1.41089i
$615$		0			0
$616$	442.837	−	413.289i	0.718891	−	0.670923i
$617$	−111.772	−	193.595i	−0.181154	−	0.313768i	0.761120	−	0.648611i	$-0.224650\pi$
$617$	−111.772	−	193.595i	−0.181154	−	0.313768i	−0.942274	+	0.334843i	$0.891317\pi$
$618$		0			0
$619$	865.332	+	499.600i	1.39795	+	0.807108i	0.994178	−	0.107751i	$-0.0343648\pi$
$619$	865.332	+	499.600i	1.39795	+	0.807108i	0.403774	+	0.914859i	$0.367698\pi$
$620$	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
$626$	35.2734	+	464.663i	0.0563472	+	0.742273i
$627$		0			0
$628$	−363.783	+	55.5509i	−0.579272	+	0.0884568i
$629$	−374.977			−0.596148
$630$		0			0
$631$			93.6750i			0.148455i	0.997241	+	0.0742274i	$0.0236491\pi$
$631$			93.6750i			0.148455i	−0.997241	+	0.0742274i	$0.976351\pi$
$632$	−116.700	+	382.263i	−0.184652	+	0.604847i
$633$		0			0
$634$	−75.8713	−	999.468i	−0.119671	−	1.57645i
$635$	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	$-0.599901\pi$
$641$	429.061	−	743.155i	0.669361	−	1.15937i	0.978083	−	0.208215i	$-0.0667655\pi$
$642$		0			0
$643$	21.6333	−	12.4900i	0.0336443	−	0.0194246i	−0.483083	−	0.875574i	$-0.660483\pi$
$643$	21.6333	−	12.4900i	0.0336443	−	0.0194246i	0.516728	+	0.856150i	$0.327150\pi$
$644$	157.292	−	403.062i	0.244242	−	0.625873i
$645$		0			0
$646$	609.699	+	892.410i	0.943806	+	1.38144i
$647$		−	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
$650$	317.066	−	216.621i	0.487795	−	0.333264i
$651$		0			0
$652$	−558.500	−	217.950i	−0.856595	−	0.334279i
$653$	−214.530	−	371.577i	−0.328530	−	0.569031i	0.653690	−	0.756762i	$-0.273220\pi$
$653$	−214.530	−	371.577i	−0.328530	−	0.569031i	−0.982220	+	0.187731i	$0.939887\pi$
$654$		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	$0.571108\pi$
$662$	273.992	−	20.7992i	0.413885	−	0.0314187i
$663$		0			0
$664$	271.071	−	887.924i	0.408240	−	1.33723i
$665$	843.699			1.26872
$666$		0			0
$667$			874.300i			1.31079i
$668$	102.492	+	671.184i	0.153431	+	1.00477i
$669$		0			0
$670$	449.041	−	34.0875i	0.670211	−	0.0508768i
$671$	−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	−0.665051	−	0.746798i	$-0.731590\pi$
$677$	212.728	−	368.455i	0.314221	−	0.544247i	0.979272	+	0.202552i	$0.0649234\pi$
$678$		0			0
$679$	−643.591	+	371.577i	−0.947851	+	0.547242i
$680$	−304.128	+	283.835i	−0.447247	+	0.417404i
$681$		0			0
$682$	125.037	−	85.4262i	0.183339	−	0.125258i
$683$		−	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
$686$	−415.704	−	608.462i	−0.605983	−	0.886971i
$687$		0			0
$688$	59.6417	+	190.732i	0.0866885	+	0.277227i
$689$	−548.044	−	949.240i	−0.795419	−	1.37771i
$690$		0			0
$691$	930.232	+	537.070i	1.34621	+	0.777236i	0.987711	−	0.156294i	$-0.0499546\pi$
$691$	930.232	+	537.070i	1.34621	+	0.777236i	0.358501	+	0.933529i	$0.383288\pi$
$692$	−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
$698$	−81.4466	−	1072.91i	−0.116686	−	1.53712i
$699$		0			0
$700$	−45.2498	−	296.325i	−0.0646426	−	0.423321i
$701$	926.627			1.32186			0.660932	−	0.750446i	$-0.270161\pi$
$701$	926.627			1.32186			0.660932	+	0.750446i	$0.270161\pi$
$702$		0			0
$703$		−	974.220i		−	1.38580i
$704$	−774.112	−	53.4991i	−1.09959	−	0.0759930i
$705$		0			0
$706$	33.8419	+	445.806i	0.0479347	+	0.631453i
$707$	−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
$716$	−987.487	−	385.359i	−1.37917	−	0.538211i
$717$		0			0
$718$	−504.174	−	737.954i	−0.702192	−	1.02779i
$719$			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
$722$	−1722.40	+	1176.75i	−2.38559	+	1.62985i
$723$		0			0
$724$	395.532	−	1013.56i	0.546316	−	1.39994i
$725$	302.866	+	524.580i	0.417747	+	0.723558i
$726$		0			0
$727$	5.40833	+	3.12250i	0.00743924	+	0.00429505i	0.503715	−	0.863870i	$-0.331966\pi$
$727$	5.40833	+	3.12250i	0.00743924	+	0.00429505i	−0.496276	+	0.868165i	$0.665300\pi$
$728$	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	$0.907389\pi$
$734$	535.529	−	40.6529i	0.729604	−	0.0553854i
$735$		0			0
$736$	−514.958	+	204.984i	−0.699671	+	0.278510i
$737$	757.166			1.02736
$738$		0			0
$739$		−	824.340i		−	1.11548i	−0.830016	−	0.557740i	$-0.811669\pi$
$739$		−	824.340i		−	1.11548i	0.830016	−	0.557740i	$-0.188331\pi$
$740$	370.680	−	56.6041i	0.500919	−	0.0764921i
$741$		0			0
$742$	−853.178	+	64.7662i	−1.14984	+	0.0872860i
$743$	−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	−0.161670	−	0.986845i	$-0.551688\pi$
$751$	459.708	−	265.412i	0.612128	−	0.353412i	0.773798	+	0.633433i	$0.218355\pi$
$752$	16.5416	+	52.8997i	0.0219969	+	0.0703453i
$753$		0			0
$754$	−1333.73	+	911.213i	−1.76888	+	1.20851i
$755$			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	$0.552803\pi$
$758$	−253.650	−	371.265i	−0.334631	−	0.489795i
$759$		0			0
$760$	−737.425	−	790.147i	−0.970296	−	1.03967i
$761$	245.177	+	424.660i	0.322178	+	0.558029i	0.980937	−	0.194325i	$-0.0622517\pi$
$761$	245.177	+	424.660i	0.322178	+	0.558029i	−0.658759	+	0.752354i	$0.728918\pi$
$762$		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	$0.846790\pi$
$770$	41.3289	+	544.434i	0.0536739	+	0.707057i
$771$		0			0
$772$	739.429	−	112.913i	0.957809	−	0.146261i
$773$	829.277			1.07280			0.536402	−	0.843963i	$-0.319783\pi$
$773$	829.277			1.07280			0.536402	+	0.843963i	$0.319783\pi$
$774$		0			0
$775$		−	74.9400i		−	0.0966967i
$776$	910.515	+	277.968i	1.17334	+	0.358206i
$777$		0			0
$778$	78.0546	+	1028.23i	0.100327	+	1.32163i
$779$	−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	−0.870535	−	0.492106i	$-0.836227\pi$
$787$	−692.266	+	399.680i	−0.879626	+	0.507852i	−0.00909108	+	0.999959i	$0.502894\pi$
$788$	26.2153	−	67.1771i	0.0332682	−	0.0852501i
$789$		0			0
$790$	−203.233	−	297.470i	−0.257257	−	0.376544i
$791$		−	585.433i		−	0.740118i
$792$		0			0
$793$	−128.000			−0.161412
$794$	132.111	−	90.2589i	0.166387	−	0.113676i
$795$		0			0
$796$	−349.062	−	136.219i	−0.438520	−	0.171129i
$797$	−387.597	−	671.337i	−0.486320	−	0.842330i	0.513557	−	0.858056i	$-0.328328\pi$
$797$	−387.597	−	671.337i	−0.486320	−	0.842330i	−0.999876	+	0.0157253i	$0.994994\pi$
$798$		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
$806$	199.267	−	15.1267i	0.247229	−	0.0187676i
$807$		0			0
$808$	468.987	+	143.175i	0.580429	+	0.177197i
$809$	−209.122			−0.258494			−0.129247	−	0.991612i	$-0.541256\pi$
$809$	−209.122			−0.258494			−0.129247	+	0.991612i	$0.541256\pi$
$810$		0			0
$811$			1461.33i			1.80189i	0.433937	+	0.900943i	$0.357124\pi$
$811$			1461.33i			1.80189i	−0.433937	+	0.900943i	$0.642876\pi$
$812$	190.342	+	1246.48i	0.234412	+	1.53508i
$813$		0			0
$814$	628.658	−	47.7225i	0.772307	−	0.0586271i
$815$	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	−0.880987	−	0.473141i	$-0.843120\pi$
$821$	−25.2389	+	43.7150i	−0.0307416	+	0.0532460i	0.850245	+	0.526387i	$0.176454\pi$
$822$		0			0
$823$	−1162.79	+	671.337i	−1.41287	+	0.815720i	−0.995658	−	0.0930903i	$-0.970325\pi$
$823$	−1162.79	+	671.337i	−1.41287	+	0.815720i	−0.417210	+	0.908810i	$0.636992\pi$
$824$	681.749	+	730.491i	0.827366	+	0.886519i
$825$		0			0
$826$	−785.950	+	536.965i	−0.951513	+	0.650079i
$827$		−	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	$0.753719\pi$
$830$	472.071	+	690.965i	0.568760	+	0.832488i
$831$		0			0
$832$	−849.400	−	571.923i	−1.02091	−	0.687408i
$833$	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
$842$	−31.4887	−	414.807i	−0.0373975	−	0.492644i
$843$		0			0
$844$	−37.7082	−	246.937i	−0.0446779	−	0.292580i
$845$	−313.683			−0.371222
$846$		0			0
$847$			162.370i			0.191700i
$848$	806.365	+	742.417i	0.950903	+	0.875492i
$849$		0			0
$850$	26.2002	+	345.140i	0.0308237	+	0.406047i
$851$	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	$-0.555723\pi$
$857$	656.210	−	1136.59i	0.765706	−	1.32624i	0.939872	−	0.341526i	$-0.110944\pi$
$858$		0			0
$859$	346.133	−	199.840i	0.402949	−	0.232643i	−0.284807	−	0.958585i	$-0.591929\pi$
$859$	346.133	−	199.840i	0.402949	−	0.232643i	0.687755	+	0.725942i	$0.258596\pi$
$860$	−167.808	−	65.4858i	−0.195126	−	0.0761463i
$861$		0			0
$862$	621.424	+	909.571i	0.720909	+	1.05519i
$863$		−	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
$866$	206.423	−	141.030i	0.238364	−	0.162852i
$867$		0			0
$868$	56.7124	−	145.326i	0.0653368	−	0.167427i
$869$	−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	$-0.386657\pi$
$878$	1133.33	−	86.0329i	1.29081	−	0.0979874i
$879$		0			0
$880$	473.754	−	514.561i	0.538357	−	0.584729i
$881$	−749.955			−0.851254			−0.425627	−	0.904899i	$-0.639946\pi$
$881$	−749.955			−0.851254			−0.425627	+	0.904899i	$0.639946\pi$
$882$		0			0
$883$			1311.45i			1.48522i	0.669724	+	0.742610i	$0.266412\pi$
$883$			1311.45i			1.48522i	−0.669724	+	0.742610i	$0.733588\pi$
$884$	−912.444	+	139.333i	−1.03218	+	0.157617i
$885$		0			0
$886$	759.916	−	57.6865i	0.857693	−	0.0651089i
$887$	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
$896$	−689.546	+	404.354i	−0.769582	+	0.451288i
$897$		0			0
$898$	797.858	−	545.101i	0.888483	−	0.607016i
$899$			315.233i			0.350649i
$900$		0			0
$901$	988.000			1.09656
$902$	−98.6417	−	144.381i	−0.109359	−	0.160067i
$903$		0			0
$904$	−548.274	+	511.691i	−0.606498	+	0.566030i
$905$	490.355	+	849.320i	0.541829	+	0.938475i
$906$		0			0
$907$	−530.016	−	306.005i	−0.584362	−	0.337381i	0.178503	−	0.983939i	$-0.442875\pi$
$907$	−530.016	−	306.005i	−0.584362	−	0.337381i	−0.762865	+	0.646558i	$0.776208\pi$
$908$	−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
$914$	125.198	+	1649.25i	0.136978	+	1.80444i
$915$		0			0
$916$	846.191	−	129.216i	0.923789	−	0.141066i
$917$	270.416			0.294892
$918$		0			0
$919$			880.545i			0.958155i	0.877773	+	0.479078i	$0.159029\pi$
$919$			880.545i			0.958155i	−0.877773	+	0.479078i	$0.840971\pi$
$920$	145.875	−	477.829i	0.158559	−	0.519379i
$921$		0			0
$922$	97.7047	+	1287.08i	0.105970	+	1.39597i
$923$	−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	−0.924431	−	0.381349i	$-0.875460\pi$
$929$	−122.589	+	212.330i	−0.131958	+	0.228558i	0.792473	+	0.609906i	$0.208793\pi$
$930$		0			0
$931$	−324.500	+	187.350i	−0.348550	+	0.201235i
$932$	450.903	−	1155.45i	0.483802	−	1.23975i
$933$		0			0
$934$	838.336	+	1227.06i	0.897576	+	1.31377i
$935$		−	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	$0.612568\pi$
$938$	644.041	−	440.012i	0.686611	−	0.469096i
$939$		0			0
$940$	−46.5416	−	18.1625i	−0.0495124	−	0.0193218i
$941$	780.602	+	1352.04i	0.829545	+	1.43681i	0.898396	+	0.439187i	$0.144733\pi$
$941$	780.602	+	1352.04i	0.829545	+	1.43681i	−0.0688506	+	0.997627i	$0.521933\pi$
$942$		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
$950$	−896.700	+	68.0700i	−0.943894	+	0.0716526i
$951$		0			0
$952$	−210.384	+	689.135i	−0.220991	+	0.723881i
$953$	504.777			0.529672			0.264836	−	0.964294i	$-0.414682\pi$
$953$	504.777			0.529672			0.264836	+	0.964294i	$0.414682\pi$
$954$		0			0
$955$		−	949.240i		−	0.993968i
$956$	−248.909	−	1630.02i	−0.260365	−	1.70504i
$957$		0			0
$958$	−670.108	+	50.8690i	−0.699486	+	0.0530992i
$959$	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	−0.0142736	−	0.999898i	$-0.504544\pi$
$967$	816.657	−	471.497i	0.844527	−	0.487588i	0.858800	+	0.512310i	$0.171210\pi$
$968$	152.064	−	141.917i	0.157091	−	0.146609i
$969$		0			0
$970$	−708.545	+	484.082i	−0.730459	+	0.499054i
$971$		−	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
$974$	676.400	+	990.040i	0.694456	+	1.01647i
$975$		0			0
$976$	122.167	−	38.2013i	0.125171	−	0.0391406i
$977$	−652.605	−	1130.34i	−0.667968	−	1.15695i	−0.978471	−	0.206382i	$-0.933831\pi$
$977$	−652.605	−	1130.34i	−0.667968	−	1.15695i	0.310503	−	0.950572i	$-0.399502\pi$
$978$		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
$986$	−110.210	−	1451.82i	−0.111775	−	1.47244i
$987$		0			0
$988$	−361.998	−	2370.60i	−0.366395	−	2.39939i
$989$	−216.333			−0.218739
$990$		0			0
$991$			318.495i			0.321387i	0.987004	+	0.160694i	$0.0513731\pi$
$991$			318.495i			0.321387i	−0.987004	+	0.160694i	$0.948627\pi$
$992$	−185.671	+	73.9079i	−0.187168	+	0.0745039i
$993$		0			0
$994$	58.9503	+	776.565i	0.0593062	+	0.781252i
$995$	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.55.2		4
3.2	odd	2		324.3.f.l.55.1		4
4.3	odd	2		324.3.f.l.55.2		4
9.2	odd	6		108.3.d.c.55.4	yes	4
9.4	even	3		324.3.f.l.271.2		4
9.5	odd	6	inner	324.3.f.m.271.1		4
9.7	even	3		108.3.d.c.55.1	✓	4
12.11	even	2	inner	324.3.f.m.55.1		4
36.7	odd	6		108.3.d.c.55.2	yes	4
36.11	even	6		108.3.d.c.55.3	yes	4
36.23	even	6		324.3.f.l.271.1		4
36.31	odd	6	inner	324.3.f.m.271.2		4
72.11	even	6		1728.3.g.i.703.2		4
72.29	odd	6		1728.3.g.i.703.1		4
72.43	odd	6		1728.3.g.i.703.4		4
72.61	even	6		1728.3.g.i.703.3		4

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

\(f(q)\)	\(=\)	\(q+(1.65139 - 1.12824i) q^{2} +(1.45416 - 3.72631i) q^{4} +(1.80278 + 3.12250i) q^{5} +(5.40833 + 3.12250i) q^{7} +(-1.80278 - 7.79423i) q^{8} +O(q^{10})\)	\(q+(1.65139 - 1.12824i) q^{2} +(1.45416 - 3.72631i) q^{4} +(1.80278 + 3.12250i) q^{5} +(5.40833 + 3.12250i) q^{7} +(-1.80278 - 7.79423i) q^{8} +(6.50000 + 3.12250i) q^{10} +(10.5000 + 6.06218i) q^{11} +(8.00000 + 13.8564i) q^{13} +(12.4542 - 0.945417i) q^{14} +(-11.7708 - 10.8373i) q^{16} -14.4222 q^{17} -37.4700i q^{19} +(14.2569 - 2.17708i) q^{20} +(24.1791 - 1.83548i) q^{22} +(15.0000 - 8.66025i) q^{23} +(6.00000 - 10.3923i) q^{25} +(28.8444 + 13.8564i) q^{26} +(19.5000 - 15.6125i) q^{28} +(-25.2389 + 43.7150i) q^{29} +(5.40833 - 3.12250i) q^{31} +(-31.6653 - 4.61638i) q^{32} +(-23.8167 + 16.2717i) q^{34} +22.5167i q^{35} +26.0000 q^{37} +(-42.2750 - 61.8775i) q^{38} +(21.0875 - 19.6804i) q^{40} +(-3.60555 - 6.24500i) q^{41} +(-10.8167 - 6.24500i) q^{43} +(37.8583 - 30.3109i) q^{44} +(15.0000 - 31.2250i) q^{46} +(-3.00000 - 1.73205i) q^{47} +(-5.00000 - 8.66025i) q^{49} +(-1.81665 - 23.9311i) q^{50} +(63.2666 - 9.66102i) q^{52} -68.5055 q^{53} +43.7150i q^{55} +(14.5875 - 47.7829i) q^{56} +(7.64171 + 100.666i) q^{58} +(-66.0000 + 38.1051i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(5.40833 - 11.2583i) q^{62} +(-57.5000 + 28.1025i) q^{64} +(-28.8444 + 49.9600i) q^{65} +(54.0833 - 31.2250i) q^{67} +(-20.9722 + 53.7417i) q^{68} +(25.4041 + 37.1837i) q^{70} +62.3538i q^{71} -19.0000 q^{73} +(42.9361 - 29.3342i) q^{74} +(-139.625 - 54.4875i) q^{76} +(37.8583 + 65.5725i) q^{77} +(-43.2666 - 24.9800i) q^{79} +(12.6194 - 56.2917i) q^{80} +(-13.0000 - 6.24500i) q^{82} +(100.500 + 58.0237i) q^{83} +(-26.0000 - 45.0333i) q^{85} +(-24.9083 + 1.89083i) q^{86} +(28.3209 - 92.7681i) q^{88} -79.3221 q^{89} +99.9200i q^{91} +(-10.4584 - 68.4881i) q^{92} +(-6.90833 + 0.524423i) q^{94} +(117.000 - 67.5500i) q^{95} +(-59.5000 + 103.057i) q^{97} +(-18.0278 - 8.66025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 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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