LMFDB - Embedded newform 333.3.bb.c.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(82,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("333.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.1
Character	$\chi$	$=$	333.82
Dual form			333.3.bb.c.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24096 - 0.868412i) q^{2} +(6.28557 + 3.62898i) q^{4} +(-4.12843 + 1.10621i) q^{5} +(-1.96785 + 3.40842i) q^{7} +(-7.72965 - 7.72965i) q^{8} +O(q^{10})$	\(q+(-3.24096 - 0.868412i) q^{2} +(6.28557 + 3.62898i) q^{4} +(-4.12843 + 1.10621i) q^{5} +(-1.96785 + 3.40842i) q^{7} +(-7.72965 - 7.72965i) q^{8} +14.3407 q^{10} +8.41369i q^{11} +(-9.09577 + 2.43721i) q^{13} +(9.33764 - 9.33764i) q^{14} +(3.82304 + 6.62170i) q^{16} +(2.75215 - 10.2712i) q^{17} +(0.967236 - 0.259170i) q^{19} +(-29.9640 - 8.02882i) q^{20} +(7.30655 - 27.2684i) q^{22} +(20.6761 + 20.6761i) q^{23} +(-5.83039 + 3.36618i) q^{25} +31.5955 q^{26} +(-24.7382 + 14.2826i) q^{28} +(24.6508 - 24.6508i) q^{29} +(20.3729 - 20.3729i) q^{31} +(4.67704 + 17.4549i) q^{32} +(-17.8392 + 30.8984i) q^{34} +(4.35371 - 16.2483i) q^{35} +(-6.94326 - 36.3427i) q^{37} -3.35984 q^{38} +(40.4619 + 23.3607i) q^{40} +(-64.7228 - 37.3677i) q^{41} +(-14.4283 - 14.4283i) q^{43} +(-30.5331 + 52.8849i) q^{44} +(-49.0551 - 84.9659i) q^{46} -85.5062 q^{47} +(16.7551 + 29.0207i) q^{49} +(21.8193 - 5.84646i) q^{50} +(-66.0167 - 17.6891i) q^{52} +(-41.2911 - 71.5183i) q^{53} +(-9.30731 - 34.7353i) q^{55} +(41.5567 - 11.1351i) q^{56} +(-101.299 + 58.4852i) q^{58} +(12.3462 - 46.0768i) q^{59} +(8.49873 + 31.7177i) q^{61} +(-83.7199 + 48.3357i) q^{62} -91.2167i q^{64} +(34.8552 - 20.1237i) q^{65} +(-61.5349 - 35.5272i) q^{67} +(54.5727 - 54.5727i) q^{68} +(-28.2204 + 48.8792i) q^{70} +(38.0622 - 65.9256i) q^{71} -66.9877i q^{73} +(-9.05763 + 123.815i) q^{74} +(7.02015 + 1.88104i) q^{76} +(-28.6774 - 16.5569i) q^{77} +(76.1401 - 20.4017i) q^{79} +(-23.1081 - 23.1081i) q^{80} +(177.313 + 177.313i) q^{82} +(27.9038 + 48.3307i) q^{83} +45.4483i q^{85} +(34.2317 + 59.2911i) q^{86} +(65.0349 - 65.0349i) q^{88} +(-24.3178 - 6.51594i) q^{89} +(9.59212 - 35.7983i) q^{91} +(54.9281 + 204.994i) q^{92} +(277.122 + 74.2546i) q^{94} +(-3.70647 + 2.13993i) q^{95} +(23.4437 + 23.4437i) q^{97} +(-29.1007 - 108.605i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−3.24096	−	0.868412i	−1.62048	−	0.434206i	−0.669337	−	0.742959i	$-0.733422\pi$
$2$	−3.24096	−	0.868412i	−1.62048	−	0.434206i	−0.951142	+	0.308753i	$0.900088\pi$
$3$		0			0
$3$		0			0
$4$	6.28557	+	3.62898i	1.57139	+	0.907244i
$5$	−4.12843	+	1.10621i	−0.825686	+	0.221242i	−0.646831	−	0.762633i	$-0.723906\pi$
$5$	−4.12843	+	1.10621i	−0.825686	+	0.221242i	−0.178855	+	0.983875i	$0.557239\pi$
$6$		0			0
$7$	−1.96785	+	3.40842i	−0.281122	+	0.486917i	−0.971661	−	0.236377i	$-0.924040\pi$
$7$	−1.96785	+	3.40842i	−0.281122	+	0.486917i	0.690540	+	0.723295i	$0.257373\pi$
$8$	−7.72965	−	7.72965i	−0.966206	−	0.966206i
$9$		0			0
$10$	14.3407			1.43407
$11$			8.41369i			0.764881i	0.923980	+	0.382440i	$0.124916\pi$
$11$			8.41369i			0.764881i	−0.923980	+	0.382440i	$0.875084\pi$
$12$		0			0
$13$	−9.09577	+	2.43721i	−0.699675	+	0.187477i	−0.591085	−	0.806609i	$-0.701300\pi$
$13$	−9.09577	+	2.43721i	−0.699675	+	0.187477i	−0.108590	+	0.994087i	$0.534634\pi$
$14$	9.33764	−	9.33764i	0.666974	−	0.666974i
$15$		0			0
$16$	3.82304	+	6.62170i	0.238940	+	0.413856i
$17$	2.75215	−	10.2712i	0.161891	−	0.604187i	−0.836525	−	0.547929i	$-0.815416\pi$
$17$	2.75215	−	10.2712i	0.161891	−	0.604187i	0.998416	−	0.0562578i	$-0.0179169\pi$
$18$		0			0
$19$	0.967236	−	0.259170i	0.0509071	−	0.0136405i	−0.233276	−	0.972411i	$-0.574944\pi$
$19$	0.967236	−	0.259170i	0.0509071	−	0.0136405i	0.284183	+	0.958770i	$0.408278\pi$
$20$	−29.9640	−	8.02882i	−1.49820	−	0.401441i
$21$		0			0
$22$	7.30655	−	27.2684i	0.332116	−	1.23947i
$23$	20.6761	+	20.6761i	0.898962	+	0.898962i	0.995344	−	0.0963825i	$-0.0307272\pi$
$23$	20.6761	+	20.6761i	0.898962	+	0.898962i	−0.0963825	+	0.995344i	$0.530727\pi$
$24$		0			0
$25$	−5.83039	+	3.36618i	−0.233216	+	0.134647i
$26$	31.5955			1.21521
$27$		0			0
$28$	−24.7382	+	14.2826i	−0.883506	+	0.510092i
$29$	24.6508	−	24.6508i	0.850028	−	0.850028i	−0.140109	−	0.990136i	$-0.544745\pi$
$29$	24.6508	−	24.6508i	0.850028	−	0.850028i	0.990136	+	0.140109i	$0.0447451\pi$
$30$		0			0
$31$	20.3729	−	20.3729i	0.657191	−	0.657191i	−0.297523	−	0.954715i	$-0.596161\pi$
$31$	20.3729	−	20.3729i	0.657191	−	0.657191i	0.954715	+	0.297523i	$0.0961606\pi$
$32$	4.67704	+	17.4549i	0.146157	+	0.545467i
$33$		0			0
$34$	−17.8392	+	30.8984i	−0.524683	+	0.908778i
$35$	4.35371	−	16.2483i	0.124392	−	0.464237i
$36$		0			0
$37$	−6.94326	−	36.3427i	−0.187656	−	0.982235i
$37$	−6.94326	−	36.3427i	−0.187656	−	0.982235i
$38$	−3.35984			−0.0884168
$39$		0			0
$40$	40.4619	+	23.3607i	1.01155	+	0.584018i
$41$	−64.7228	−	37.3677i	−1.57860	−	0.911408i	−0.995054	−	0.0993307i	$-0.968330\pi$
$41$	−64.7228	−	37.3677i	−1.57860	−	0.911408i	−0.583550	−	0.812077i	$-0.698337\pi$
$42$		0			0
$43$	−14.4283	−	14.4283i	−0.335541	−	0.335541i	0.519145	−	0.854686i	$-0.326250\pi$
$43$	−14.4283	−	14.4283i	−0.335541	−	0.335541i	−0.854686	+	0.519145i	$0.826250\pi$
$44$	−30.5331	+	52.8849i	−0.693934	+	1.20193i
$45$		0			0
$46$	−49.0551	−	84.9659i	−1.06641	−	1.84708i
$47$	−85.5062			−1.81928			−0.909640	−	0.415397i	$-0.863643\pi$
$47$	−85.5062			−1.81928			−0.909640	+	0.415397i	$0.863643\pi$
$48$		0			0
$49$	16.7551	+	29.0207i	0.341941	+	0.592259i
$50$	21.8193	−	5.84646i	0.436386	−	0.116929i
$51$		0			0
$52$	−66.0167	−	17.6891i	−1.26955	−	0.340175i
$53$	−41.2911	−	71.5183i	−0.779077	−	1.34940i	−0.932474	−	0.361237i	$-0.882355\pi$
$53$	−41.2911	−	71.5183i	−0.779077	−	1.34940i	0.153397	−	0.988165i	$-0.450979\pi$
$54$		0			0
$55$	−9.30731	−	34.7353i	−0.169224	−	0.631552i
$56$	41.5567	−	11.1351i	0.742084	−	0.198841i
$57$		0			0
$58$	−101.299	+	58.4852i	−1.74654	+	1.00837i
$59$	12.3462	−	46.0768i	0.209258	−	0.780963i	−0.778851	−	0.627209i	$-0.784197\pi$
$59$	12.3462	−	46.0768i	0.209258	−	0.780963i	0.988109	−	0.153754i	$-0.0491362\pi$
$60$		0			0
$61$	8.49873	+	31.7177i	0.139323	+	0.519962i	0.999943	+	0.0107131i	$0.00341014\pi$
$61$	8.49873	+	31.7177i	0.139323	+	0.519962i	−0.860619	+	0.509249i	$0.829923\pi$
$62$	−83.7199	+	48.3357i	−1.35032	+	0.779608i
$63$		0			0
$64$		−	91.2167i		−	1.42526i
$65$	34.8552	−	20.1237i	0.536234	−	0.309595i
$66$		0			0
$67$	−61.5349	−	35.5272i	−0.918431	−	0.530257i	−0.0352970	−	0.999377i	$-0.511238\pi$
$67$	−61.5349	−	35.5272i	−0.918431	−	0.530257i	−0.883134	+	0.469120i	$0.844571\pi$
$68$	54.5727	−	54.5727i	0.802540	−	0.802540i
$69$		0			0
$70$	−28.2204	+	48.8792i	−0.403149	+	0.698274i
$71$	38.0622	−	65.9256i	0.536087	−	0.928529i	−0.463023	−	0.886346i	$-0.653235\pi$
$71$	38.0622	−	65.9256i	0.536087	−	0.928529i	0.999110	−	0.0421833i	$-0.0134313\pi$
$72$		0			0
$73$		−	66.9877i		−	0.917639i	−0.888529	−	0.458820i	$-0.848272\pi$
$73$		−	66.9877i		−	0.917639i	0.888529	−	0.458820i	$-0.151728\pi$
$74$	−9.05763	+	123.815i	−0.122400	+	1.67317i
$75$		0			0
$76$	7.02015	+	1.88104i	0.0923704	+	0.0247506i
$77$	−28.6774	−	16.5569i	−0.372434	−	0.215025i
$78$		0			0
$79$	76.1401	−	20.4017i	0.963798	−	0.258249i	0.257591	−	0.966254i	$-0.417071\pi$
$79$	76.1401	−	20.4017i	0.963798	−	0.258249i	0.706207	+	0.708005i	$0.250405\pi$
$80$	−23.1081	−	23.1081i	−0.288852	−	0.288852i
$81$		0			0
$82$	177.313	+	177.313i	2.16236	+	2.16236i
$83$	27.9038	+	48.3307i	0.336190	+	0.582298i	0.983713	−	0.179748i	$-0.0575282\pi$
$83$	27.9038	+	48.3307i	0.336190	+	0.582298i	−0.647523	+	0.762046i	$0.724195\pi$
$84$		0			0
$85$			45.4483i			0.534686i
$86$	34.2317	+	59.2911i	0.398043	+	0.689431i
$87$		0			0
$88$	65.0349	−	65.0349i	0.739032	−	0.739032i
$89$	−24.3178	−	6.51594i	−0.273234	−	0.0732128i	0.119600	−	0.992822i	$-0.461839\pi$
$89$	−24.3178	−	6.51594i	−0.273234	−	0.0732128i	−0.392834	+	0.919609i	$0.628505\pi$
$90$		0			0
$91$	9.59212	−	35.7983i	0.105408	−	0.393388i
$92$	54.9281	+	204.994i	0.597044	+	2.22820i
$93$		0			0
$94$	277.122	+	74.2546i	2.94811	+	0.789943i
$95$	−3.70647	+	2.13993i	−0.0390155	+	0.0225256i
$96$		0			0
$97$	23.4437	+	23.4437i	0.241688	+	0.241688i	0.817548	−	0.575860i	$-0.195333\pi$
$97$	23.4437	+	23.4437i	0.241688	+	0.241688i	−0.575860	+	0.817548i	$0.695333\pi$
$98$	−29.1007	−	108.605i	−0.296946	−	1.10822i
$99$		0			0
$100$	−48.8631			−0.488631
$101$			106.697i			1.05640i	0.849119	+	0.528202i	$0.177134\pi$
$101$			106.697i			1.05640i	−0.849119	+	0.528202i	$0.822866\pi$
$102$		0			0
$103$	−89.2495	+	89.2495i	−0.866500	+	0.866500i	−0.992083	−	0.125583i	$-0.959920\pi$
$103$	−89.2495	+	89.2495i	−0.866500	+	0.866500i	0.125583	+	0.992083i	$0.459920\pi$
$104$	89.1459	+	51.4684i	0.857172	+	0.494888i
$105$		0			0
$106$	71.7154	+	267.646i	0.676560	+	2.52496i
$107$	14.5155	−	25.1416i	0.135659	−	0.234968i	−0.790190	−	0.612862i	$-0.790018\pi$
$107$	14.5155	−	25.1416i	0.135659	−	0.234968i	0.925849	+	0.377894i	$0.123352\pi$
$108$		0			0
$109$	44.8498	−	167.382i	0.411466	−	1.53561i	−0.380343	−	0.924845i	$-0.624194\pi$
$109$	44.8498	−	167.382i	0.411466	−	1.53561i	0.791810	−	0.610768i	$-0.209139\pi$
$110$			120.658i			1.09689i
$111$		0			0
$112$	−30.0927			−0.268685
$113$	−94.5685	−	25.3395i	−0.836889	−	0.224244i	−0.185172	−	0.982706i	$-0.559284\pi$
$113$	−94.5685	−	25.3395i	−0.836889	−	0.224244i	−0.651717	+	0.758462i	$0.725951\pi$
$114$		0			0
$115$	−108.232	−	62.4878i	−0.941148	−	0.543372i
$116$	244.402	−	65.4872i	2.10691	−	0.564545i
$117$		0			0
$118$	−80.0273	+	138.611i	−0.678198	+	1.17467i
$119$	29.5926	+	29.5926i	0.248678	+	0.248678i
$120$		0			0
$121$	50.2098			0.414957
$122$		−	110.176i		−	0.903083i
$123$		0			0
$124$	201.988	−	54.1226i	1.62894	−	0.436473i
$125$	95.9022	−	95.9022i	0.767218	−	0.767218i
$126$		0			0
$127$	−13.7228	−	23.7685i	−0.108053	−	0.187154i	0.806928	−	0.590649i	$-0.201128\pi$
$127$	−13.7228	−	23.7685i	−0.108053	−	0.187154i	−0.914982	+	0.403496i	$0.867795\pi$
$128$	−60.5055	+	225.810i	−0.472699	+	1.76414i
$129$		0			0
$130$	−130.440	+	34.9513i	−1.00338	+	0.268856i
$131$	140.668	+	37.6919i	1.07380	+	0.287724i	0.752055	−	0.659101i	$-0.229063\pi$
$131$	140.668	+	37.6919i	1.07380	+	0.287724i	0.321748	+	0.946825i	$0.395730\pi$
$132$		0			0
$133$	−1.02002	+	3.80675i	−0.00766930	+	0.0286222i
$134$	168.580	+	168.580i	1.25806	+	1.25806i
$135$		0			0
$136$	−100.666	+	58.1194i	−0.740189	+	0.427348i
$137$	213.296			1.55690			0.778452	−	0.627704i	$-0.216005\pi$
$137$	213.296			1.55690			0.778452	+	0.627704i	$0.216005\pi$
$138$		0			0
$139$	197.210	−	113.859i	1.41877	−	0.819130i	0.422583	−	0.906324i	$-0.361124\pi$
$139$	197.210	−	113.859i	1.41877	−	0.819130i	0.996191	+	0.0871949i	$0.0277903\pi$
$140$	86.3302	−	86.3302i	0.616645	−	0.616645i
$141$		0			0
$142$	−180.608	+	180.608i	−1.27189	+	1.27189i
$143$	−20.5059	−	76.5290i	−0.143398	−	0.535168i
$144$		0			0
$145$	−74.5002	+	129.038i	−0.513794	+	0.889918i
$146$	−58.1729	+	217.104i	−0.398445	+	1.48702i
$147$		0			0
$148$	88.2444	−	253.632i	0.596246	−	1.71373i
$149$	−110.758			−0.743344			−0.371672	−	0.928364i	$-0.621215\pi$
$149$	−110.758			−0.743344			−0.371672	+	0.928364i	$0.621215\pi$
$150$		0			0
$151$	−187.686	−	108.360i	−1.24295	−	0.717618i	−0.273257	−	0.961941i	$-0.588101\pi$
$151$	−187.686	−	108.360i	−1.24295	−	0.717618i	−0.969694	+	0.244323i	$0.921434\pi$
$152$	−9.47968	−	5.47310i	−0.0623663	−	0.0360072i
$153$		0			0
$154$	78.5640	+	78.5640i	0.510156	+	0.510156i
$155$	−61.5715	+	106.645i	−0.397235	+	0.688032i
$156$		0			0
$157$	12.0349	+	20.8450i	0.0766553	+	0.132771i	0.901805	−	0.432143i	$-0.142243\pi$
$157$	12.0349	+	20.8450i	0.0766553	+	0.132771i	−0.825150	+	0.564914i	$0.808909\pi$
$158$	−264.484			−1.67395
$159$		0			0
$160$	−38.6177	−	66.8878i	−0.241360	−	0.418049i
$161$	−111.160	+	29.7854i	−0.690438	+	0.185002i
$162$		0			0
$163$	8.91223	+	2.38803i	0.0546763	+	0.0146505i	0.286054	−	0.958214i	$-0.407656\pi$
$163$	8.91223	+	2.38803i	0.0546763	+	0.0146505i	−0.231377	+	0.972864i	$0.574323\pi$
$164$	−271.213	−	469.755i	−1.65374	−	2.86436i
$165$		0			0
$166$	−48.4640	−	180.870i	−0.291952	−	1.08958i
$167$	−128.885	+	34.5348i	−0.771769	+	0.206795i	−0.623153	−	0.782100i	$-0.714149\pi$
$167$	−128.885	+	34.5348i	−0.771769	+	0.206795i	−0.148616	+	0.988895i	$0.547482\pi$
$168$		0			0
$169$	−69.5652	+	40.1635i	−0.411628	+	0.237654i
$170$	39.4679	−	147.296i	0.232164	−	0.866447i
$171$		0			0
$172$	−38.3300	−	143.050i	−0.222849	−	0.831684i
$173$	75.7743	−	43.7483i	0.438002	−	0.252881i	−0.264748	−	0.964318i	$-0.585289\pi$
$173$	75.7743	−	43.7483i	0.438002	−	0.252881i	0.702750	+	0.711437i	$0.251955\pi$
$174$		0			0
$175$		−	26.4966i		−	0.151409i
$176$	−55.7129	+	32.1659i	−0.316551	+	0.182761i
$177$		0			0
$178$	73.1545	+	42.2358i	0.410981	+	0.237280i
$179$	97.8120	−	97.8120i	0.546435	−	0.546435i	−0.378972	−	0.925408i	$-0.623722\pi$
$179$	97.8120	−	97.8120i	0.546435	−	0.546435i	0.925408	+	0.378972i	$0.123722\pi$
$180$		0			0
$181$	−145.475	+	251.971i	−0.803732	+	1.39210i	0.113412	+	0.993548i	$0.463822\pi$
$181$	−145.475	+	251.971i	−0.803732	+	1.39210i	−0.917144	+	0.398556i	$0.869511\pi$
$182$	−62.1753	+	107.691i	−0.341623	+	0.591708i
$183$		0			0
$184$		−	319.638i		−	1.73716i
$185$	68.8674	+	142.358i	0.372256	+	0.769501i
$186$		0			0
$187$	86.4185	+	23.1558i	0.462131	+	0.123828i
$188$	−537.455	−	310.300i	−2.85880	−	1.65053i
$189$		0			0
$190$	13.8709	−	3.71668i	0.0730045	−	0.0195615i
$191$	−122.047	−	122.047i	−0.638989	−	0.638989i	0.311317	−	0.950306i	$-0.399230\pi$
$191$	−122.047	−	122.047i	−0.638989	−	0.638989i	−0.950306	+	0.311317i	$0.899230\pi$
$192$		0			0
$193$	−198.661	−	198.661i	−1.02933	−	1.02933i	−0.999557	−	0.0297770i	$-0.990520\pi$
$193$	−198.661	−	198.661i	−1.02933	−	1.02933i	−0.0297770	−	0.999557i	$-0.509480\pi$
$194$	−55.6214	−	96.3390i	−0.286708	−	0.496593i
$195$		0			0
$196$			243.216i			1.24090i
$197$	21.5217	+	37.2766i	0.109247	+	0.189222i	0.915465	−	0.402397i	$-0.131823\pi$
$197$	21.5217	+	37.2766i	0.109247	+	0.189222i	−0.806218	+	0.591618i	$0.798489\pi$
$198$		0			0
$199$	−81.6502	+	81.6502i	−0.410303	+	0.410303i	−0.881844	−	0.471541i	$-0.843698\pi$
$199$	−81.6502	+	81.6502i	−0.410303	+	0.410303i	0.471541	+	0.881844i	$0.343698\pi$
$200$	71.0862	+	19.0475i	0.355431	+	0.0952375i
$201$		0			0
$202$	92.6568	−	345.800i	0.458697	−	1.71188i
$203$	35.5112	+	132.529i	0.174932	+	0.652854i
$204$		0			0
$205$	308.540	+	82.6731i	1.50507	+	0.403283i
$206$	366.759	−	211.748i	1.78038	−	1.02791i
$207$		0			0
$208$	−50.9119	−	50.9119i	−0.244769	−	0.244769i
$209$	2.18058	+	8.13802i	0.0104334	+	0.0389379i
$210$		0			0
$211$	121.913			0.577785			0.288892	−	0.957362i	$-0.406713\pi$
$211$	121.913			0.577785			0.288892	+	0.957362i	$0.406713\pi$
$212$		−	599.378i		−	2.82725i
$213$		0			0
$214$	−68.8773	+	68.8773i	−0.321857	+	0.321857i
$215$	75.5268	+	43.6054i	0.351287	+	0.202816i
$216$		0			0
$217$	29.3486	+	109.530i	0.135247	+	0.504748i
$218$	−290.713	+	503.530i	−1.33355	+	2.30977i
$219$		0			0
$220$	67.5520	−	252.108i	0.307055	−	1.14594i
$221$			100.132i			0.453085i
$222$		0			0
$223$	−180.370			−0.808834			−0.404417	−	0.914575i	$-0.632526\pi$
$223$	−180.370			−0.808834			−0.404417	+	0.914575i	$0.632526\pi$
$224$	−68.6975	−	18.4074i	−0.306685	−	0.0821761i
$225$		0			0
$226$	284.487	+	164.249i	1.25879	+	0.726765i
$227$	27.1831	−	7.28370i	0.119749	−	0.0320868i	−0.198447	−	0.980112i	$-0.563590\pi$
$227$	27.1831	−	7.28370i	0.119749	−	0.0320868i	0.318196	+	0.948025i	$0.396923\pi$
$228$		0			0
$229$	−40.1400	+	69.5245i	−0.175284	+	0.303601i	−0.940259	−	0.340459i	$-0.889418\pi$
$229$	−40.1400	+	69.5245i	−0.175284	+	0.303601i	0.764976	+	0.644059i	$0.222751\pi$
$230$	296.511	+	296.511i	1.28918	+	1.28918i
$231$		0			0
$232$	−381.084			−1.64260
$233$		−	110.359i		−	0.473643i	−0.971553	−	0.236821i	$-0.923894\pi$
$233$		−	110.359i		−	0.473643i	0.971553	−	0.236821i	$-0.0761056\pi$
$234$		0			0
$235$	353.006	−	94.5878i	1.50215	−	0.402501i
$236$	244.815	−	244.815i	1.03735	−	1.03735i
$237$		0			0
$238$	−70.2099	−	121.607i	−0.295000	−	0.510954i
$239$	−75.7294	+	282.626i	−0.316859	+	1.18253i	0.605387	+	0.795931i	$0.293018\pi$
$239$	−75.7294	+	282.626i	−0.316859	+	1.18253i	−0.922246	+	0.386603i	$0.873648\pi$
$240$		0			0
$241$	81.1004	−	21.7308i	0.336516	−	0.0901692i	−0.0866041	−	0.996243i	$-0.527602\pi$
$241$	81.1004	−	21.7308i	0.336516	−	0.0901692i	0.423120	+	0.906074i	$0.360935\pi$
$242$	−162.728	−	43.6028i	−0.672430	−	0.180177i
$243$		0			0
$244$	−61.6834	+	230.206i	−0.252801	+	0.943465i
$245$	−101.275	−	101.275i	−0.413369	−	0.413369i
$246$		0			0
$247$	−8.16611	+	4.71470i	−0.0330612	+	0.0190879i
$248$	−314.951			−1.26996
$249$		0			0
$250$	−394.098	+	227.532i	−1.57639	+	0.910130i
$251$	206.628	−	206.628i	0.823219	−	0.823219i	−0.163349	−	0.986568i	$-0.552230\pi$
$251$	206.628	−	206.628i	0.823219	−	0.823219i	0.986568	+	0.163349i	$0.0522297\pi$
$252$		0			0
$253$	−173.962	+	173.962i	−0.687599	+	0.687599i
$254$	23.8340	+	88.9498i	0.0938348	+	0.350196i
$255$		0			0
$256$	209.759	−	363.312i	0.819369	−	1.41919i
$257$	45.2029	−	168.699i	0.175887	−	0.656418i	−0.820512	−	0.571629i	$-0.806312\pi$
$257$	45.2029	−	168.699i	0.175887	−	0.656418i	0.996399	−	0.0847890i	$-0.0270216\pi$
$258$		0			0
$259$	137.534	+	47.8515i	0.531021	+	0.184755i
$260$	292.113			1.12351
$261$		0			0
$262$	−423.167	−	244.316i	−1.61514	−	0.932503i
$263$	−135.644	−	78.3144i	−0.515758	−	0.297773i	0.219439	−	0.975626i	$-0.429577\pi$
$263$	−135.644	−	78.3144i	−0.515758	−	0.297773i	−0.735197	+	0.677853i	$0.762911\pi$
$264$		0			0
$265$	249.582	+	249.582i	0.941818	+	0.941818i
$266$	6.61166	−	11.4517i	0.0248559	−	0.0430516i
$267$		0			0
$268$	−257.855	−	446.617i	−0.962144	−	1.66648i
$269$	−30.5892			−0.113714			−0.0568572	−	0.998382i	$-0.518108\pi$
$269$	−30.5892			−0.113714			−0.0568572	+	0.998382i	$0.518108\pi$
$270$		0			0
$271$	72.0039	+	124.714i	0.265697	+	0.460201i	0.967746	−	0.251928i	$-0.0810645\pi$
$271$	72.0039	+	124.714i	0.265697	+	0.460201i	−0.702049	+	0.712129i	$0.747731\pi$
$272$	78.5342	−	21.0432i	0.288729	−	0.0773646i
$273$		0			0
$274$	−691.283	−	185.229i	−2.52293	−	0.676017i
$275$	−28.3220	−	49.0551i	−0.102989	−	0.178382i
$276$		0			0
$277$	50.1998	+	187.348i	0.181227	+	0.676347i	0.995407	+	0.0957350i	$0.0305201\pi$
$277$	50.1998	+	187.348i	0.181227	+	0.676347i	−0.814180	+	0.580612i	$0.802813\pi$
$278$	−738.025	+	197.753i	−2.65476	+	0.711342i
$279$		0			0
$280$	−159.246	+	91.9408i	−0.568736	+	0.328360i
$281$	−15.6165	+	58.2818i	−0.0555749	+	0.207408i	−0.988130	−	0.153619i	$-0.950907\pi$
$281$	−15.6165	+	58.2818i	−0.0555749	+	0.207408i	0.932555	+	0.361027i	$0.117574\pi$
$282$		0			0
$283$	−113.528	−	423.693i	−0.401160	−	1.49715i	−0.811029	−	0.585005i	$-0.801092\pi$
$283$	−113.528	−	423.693i	−0.401160	−	1.49715i	0.409869	−	0.912144i	$-0.365574\pi$
$284$	478.485	−	276.253i	1.68481	−	0.972723i
$285$		0			0
$286$			265.835i			0.929493i
$287$	254.730	−	147.068i	0.887560	−	0.512433i
$288$		0			0
$289$	152.359	+	87.9643i	0.527193	+	0.304375i
$290$	353.510	−	353.510i	1.21900	−	1.21900i
$291$		0			0
$292$	243.097	−	421.056i	0.832523	−	1.44197i
$293$	−235.954	+	408.684i	−0.805302	+	1.39482i	0.110785	+	0.993844i	$0.464664\pi$
$293$	−235.954	+	408.684i	−0.805302	+	1.39482i	−0.916087	+	0.400980i	$0.868670\pi$
$294$		0			0
$295$			203.882i			0.691127i
$296$	−227.247	+	334.585i	−0.767727	+	1.13036i
$297$		0			0
$298$	358.963	+	96.1838i	1.20457	+	0.322765i
$299$	−238.457	−	137.673i	−0.797516	−	0.460446i
$300$		0			0
$301$	77.5702	−	20.7849i	0.257708	−	0.0690528i
$302$	514.180	+	514.180i	1.70258	+	1.70258i
$303$		0			0
$304$	5.41393	+	5.41393i	0.0178090	+	0.0178090i
$305$	−70.1728	−	121.543i	−0.230075	−	0.398501i
$306$		0			0
$307$			194.720i			0.634266i	0.948381	+	0.317133i	$0.102720\pi$
$307$			194.720i			0.634266i	−0.948381	+	0.317133i	$0.897280\pi$
$308$	−120.169	−	208.139i	−0.390160	−	0.675777i
$309$		0			0
$310$	292.162	−	292.162i	0.942460	−	0.942460i
$311$	−474.229	−	127.069i	−1.52485	−	0.408583i	−0.603516	−	0.797351i	$-0.706234\pi$
$311$	−474.229	−	127.069i	−1.52485	−	0.408583i	−0.921336	+	0.388768i	$0.872901\pi$
$312$		0			0
$313$	−64.1502	+	239.412i	−0.204953	+	0.764894i	0.784511	+	0.620115i	$0.212914\pi$
$313$	−64.1502	+	239.412i	−0.204953	+	0.764894i	−0.989464	+	0.144780i	$0.953753\pi$
$314$	−20.9025	−	78.0092i	−0.0665684	−	0.248437i
$315$		0			0
$316$	552.621	+	148.074i	1.74880	+	0.468590i
$317$	−331.516	+	191.401i	−1.04579	+	0.603788i	−0.921468	−	0.388454i	$-0.873009\pi$
$317$	−331.516	+	191.401i	−1.04579	+	0.603788i	−0.124323	+	0.992242i	$0.539676\pi$
$318$		0			0
$319$	207.404	+	207.404i	0.650170	+	0.650170i
$320$	100.905	+	376.582i	0.315327	+	1.17682i
$321$		0			0
$322$	386.132			1.19917
$323$		−	10.6479i		−	0.0329657i
$324$		0			0
$325$	44.8279	−	44.8279i	0.137932	−	0.137932i
$326$	−26.8104	−	15.4790i	−0.0822405	−	0.0474816i
$327$		0			0
$328$	211.445	+	789.124i	0.644650	+	2.40586i
$329$	168.264	−	291.441i	0.511439	−	0.885839i
$330$		0			0
$331$	132.575	−	494.777i	0.400529	−	1.49479i	−0.411627	−	0.911352i	$-0.635039\pi$
$331$	132.575	−	494.777i	0.400529	−	1.49479i	0.812156	−	0.583441i	$-0.198294\pi$
$332$			405.049i			1.22003i
$333$		0			0
$334$	447.703			1.34043
$335$	293.343	+	78.6010i	0.875651	+	0.234630i
$336$		0			0
$337$	190.838	+	110.180i	0.566285	+	0.326945i	0.755664	−	0.654959i	$-0.227314\pi$
$337$	190.838	+	110.180i	0.566285	+	0.326945i	−0.189379	+	0.981904i	$0.560648\pi$
$338$	260.336	−	69.7569i	0.770226	−	0.206381i
$339$		0			0
$340$	−164.931	+	285.669i	−0.485091	+	0.840202i
$341$	171.412	+	171.412i	0.502673	+	0.502673i
$342$		0			0
$343$	−324.736			−0.946752
$344$			223.051i			0.648403i
$345$		0			0
$346$	−283.573	+	75.9832i	−0.819575	+	0.219605i
$347$	164.365	−	164.365i	0.473676	−	0.473676i	−0.429426	−	0.903102i	$-0.641284\pi$
$347$	164.365	−	164.365i	0.473676	−	0.473676i	0.903102	+	0.429426i	$0.141284\pi$
$348$		0			0
$349$	−141.700	−	245.431i	−0.406016	−	0.703241i	0.588423	−	0.808553i	$-0.299749\pi$
$349$	−141.700	−	245.431i	−0.406016	−	0.703241i	−0.994439	+	0.105312i	$0.966416\pi$
$350$	−23.0099	+	85.8743i	−0.0657427	+	0.245355i
$351$		0			0
$352$	−146.861	+	39.3512i	−0.417217	+	0.111793i
$353$	352.276	+	94.3922i	0.997950	+	0.267400i	0.720586	−	0.693365i	$-0.243873\pi$
$353$	352.276	+	94.3922i	0.997950	+	0.267400i	0.277364	+	0.960765i	$0.410539\pi$
$354$		0			0
$355$	−84.2095	+	314.274i	−0.237210	+	0.885279i
$356$	−129.205	−	129.205i	−0.362936	−	0.362936i
$357$		0			0
$358$	−401.946	+	232.063i	−1.12275	+	0.648222i
$359$	495.171			1.37931			0.689653	−	0.724140i	$-0.257763\pi$
$359$	495.171			1.37931			0.689653	+	0.724140i	$0.257763\pi$
$360$		0			0
$361$	−311.767	+	179.999i	−0.863620	+	0.498611i
$362$	690.295	−	690.295i	1.90689	−	1.90689i
$363$		0			0
$364$	190.203	−	190.203i	0.522536	−	0.522536i
$365$	74.1024	+	276.554i	0.203020	+	0.757682i
$366$		0			0
$367$	324.136	−	561.420i	0.883204	−	1.52975i	0.0354452	−	0.999372i	$-0.488715\pi$
$367$	324.136	−	561.420i	0.883204	−	1.52975i	0.847759	−	0.530382i	$-0.177952\pi$
$368$	−57.8654	+	215.957i	−0.157243	+	0.586839i
$369$		0			0
$370$	−99.5713	−	521.180i	−0.269112	−	1.40860i
$371$	325.019			0.876062
$372$		0			0
$373$	−581.692	−	335.840i	−1.55950	−	0.900376i	−0.997305	−	0.0733685i	$-0.976625\pi$
$373$	−581.692	−	335.840i	−1.55950	−	0.900376i	−0.562191	−	0.827007i	$-0.690042\pi$
$374$	−259.970	−	150.094i	−0.695107	−	0.401320i
$375$		0			0
$376$	660.933	+	660.933i	1.75780	+	1.75780i
$377$	−164.139	+	284.297i	−0.435382	+	0.754104i
$378$		0			0
$379$	−58.7083	−	101.686i	−0.154903	−	0.268300i	0.778121	−	0.628115i	$-0.216173\pi$
$379$	−58.7083	−	101.686i	−0.154903	−	0.268300i	−0.933024	+	0.359815i	$0.882840\pi$
$380$	−31.0630			−0.0817448
$381$		0			0
$382$	289.562	+	501.536i	0.758015	+	1.31292i
$383$	−232.031	+	62.1726i	−0.605826	+	0.162330i	−0.548676	−	0.836035i	$-0.684868\pi$
$383$	−232.031	+	62.1726i	−0.605826	+	0.162330i	−0.0571497	+	0.998366i	$0.518201\pi$
$384$		0			0
$385$	136.708	+	36.6308i	0.355086	+	0.0951450i
$386$	471.333	+	816.373i	1.22107	+	2.11496i
$387$		0			0
$388$	62.2805	+	232.434i	0.160517	+	0.599057i
$389$	−653.520	+	175.110i	−1.68000	+	0.450155i	−0.967779	−	0.251800i	$-0.918978\pi$
$389$	−653.520	+	175.110i	−1.68000	+	0.450155i	−0.712222	+	0.701955i	$0.752311\pi$
$390$		0			0
$391$	269.272	−	155.464i	0.688675	−	0.397607i
$392$	94.8087	−	353.831i	0.241859	−	0.902630i
$393$		0			0
$394$	−37.3794	−	139.502i	−0.0948715	−	0.354065i
$395$	−291.771	+	168.454i	−0.738660	+	0.426465i
$396$		0			0
$397$			266.162i			0.670434i	0.942141	+	0.335217i	$0.108810\pi$
$397$			266.162i			0.670434i	−0.942141	+	0.335217i	$0.891190\pi$
$398$	335.531	−	193.719i	0.843043	−	0.486731i
$399$		0			0
$400$	−44.5796	−	25.7381i	−0.111449	−	0.0643452i
$401$	−116.563	+	116.563i	−0.290681	+	0.290681i	−0.837349	−	0.546668i	$-0.815896\pi$
$401$	−116.563	+	116.563i	−0.290681	+	0.290681i	0.546668	+	0.837349i	$0.315896\pi$
$402$		0			0
$403$	−135.655	+	234.961i	−0.336612	+	0.583029i
$404$	−387.200	+	670.651i	−0.958417	+	1.66003i
$405$		0			0
$406$		−	460.361i		−	1.13389i
$407$	305.776	−	58.4184i	0.751293	−	0.143534i
$408$		0			0
$409$	−260.057	−	69.6820i	−0.635836	−	0.170372i	−0.0735194	−	0.997294i	$-0.523423\pi$
$409$	−260.057	−	69.6820i	−0.635836	−	0.170372i	−0.562317	+	0.826922i	$0.690090\pi$
$410$	−928.171	−	535.880i	−2.26383	−	1.30702i
$411$		0			0
$412$	−884.868	+	237.100i	−2.14774	+	0.575485i
$413$	132.754	+	132.754i	0.321437	+	0.321437i
$414$		0			0
$415$	−168.663	−	168.663i	−0.406416	−	0.406416i
$416$	−85.0826	−	147.367i	−0.204525	−	0.354248i
$417$		0			0
$418$		−	28.2686i		−	0.0676283i
$419$	−12.0562	−	20.8819i	−0.0287737	−	0.0498376i	0.851280	−	0.524712i	$-0.175827\pi$
$419$	−12.0562	−	20.8819i	−0.0287737	−	0.0498376i	−0.880054	+	0.474874i	$0.842494\pi$
$420$		0			0
$421$	564.307	−	564.307i	1.34040	−	1.34040i	0.444732	−	0.895664i	$-0.353299\pi$
$421$	564.307	−	564.307i	1.34040	−	1.34040i	0.895664	−	0.444732i	$-0.146701\pi$
$422$	−395.114	−	105.870i	−0.936288	−	0.250878i
$423$		0			0
$424$	−233.645	+	871.977i	−0.551051	+	2.05655i
$425$	18.5285	+	69.1492i	0.0435964	+	0.162704i
$426$		0			0
$427$	−124.831	−	33.4485i	−0.292345	−	0.0783337i
$428$	182.476	−	105.353i	0.426346	−	0.246151i
$429$		0			0
$430$	−206.912	−	206.912i	−0.481190	−	0.481190i
$431$	−115.882	−	432.476i	−0.268867	−	1.00342i	−0.959841	−	0.280545i	$-0.909485\pi$
$431$	−115.882	−	432.476i	−0.268867	−	1.00342i	0.690974	−	0.722880i	$-0.257182\pi$
$432$		0			0
$433$	−780.939			−1.80356			−0.901778	−	0.432200i	$-0.857737\pi$
$433$	−780.939			−1.80356			−0.901778	+	0.432200i	$0.857737\pi$
$434$		−	380.470i		−	0.876659i
$435$		0			0
$436$	889.332	−	889.332i	2.03975	−	2.03975i
$437$	25.3573	+	14.6401i	0.0580259	+	0.0335013i
$438$		0			0
$439$	62.2068	+	232.159i	0.141701	+	0.528836i	0.999880	+	0.0154851i	$0.00492925\pi$
$439$	62.2068	+	232.159i	0.141701	+	0.528836i	−0.858179	+	0.513351i	$0.828404\pi$
$440$	−196.550	+	340.434i	−0.446704	+	0.773714i
$441$		0			0
$442$	86.9557	−	324.523i	0.196732	−	0.734215i
$443$		−	756.980i		−	1.70876i	−0.519649	−	0.854380i	$-0.673937\pi$
$443$		−	756.980i		−	1.70876i	0.519649	−	0.854380i	$-0.326063\pi$
$444$		0			0
$445$	107.602			0.241803
$446$	584.572	+	156.636i	1.31070	+	0.351201i
$447$		0			0
$448$	310.905	+	179.501i	0.693984	+	0.400672i
$449$	124.127	−	33.2598i	0.276453	−	0.0740752i	−0.117929	−	0.993022i	$-0.537626\pi$
$449$	124.127	−	33.2598i	0.276453	−	0.0740752i	0.394382	+	0.918947i	$0.370959\pi$
$450$		0			0
$451$	314.400	−	544.558i	0.697118	−	1.20744i
$452$	−502.460	−	502.460i	−1.11164	−	1.11164i
$453$		0			0
$454$	−94.4246			−0.207984
$455$			158.402i			0.348135i
$456$		0			0
$457$	−460.623	+	123.424i	−1.00793	+	0.270073i	−0.724763	−	0.688998i	$-0.758051\pi$
$457$	−460.623	+	123.424i	−1.00793	+	0.270073i	−0.283164	+	0.959071i	$0.591384\pi$
$458$	190.468	−	190.468i	0.415869	−	0.415869i
$459$		0			0
$460$	−453.534	−	785.543i	−0.985943	−	1.70770i
$461$	−224.657	+	838.433i	−0.487326	+	1.81873i	0.0820239	+	0.996630i	$0.473862\pi$
$461$	−224.657	+	838.433i	−0.487326	+	1.81873i	−0.569350	+	0.822095i	$0.692805\pi$
$462$		0			0
$463$	−748.867	+	200.658i	−1.61742	+	0.433387i	−0.950243	−	0.311509i	$-0.899165\pi$
$463$	−748.867	+	200.658i	−1.61742	+	0.433387i	−0.667180	+	0.744897i	$0.732499\pi$
$464$	257.471	+	68.9892i	0.554895	+	0.148684i
$465$		0			0
$466$	−95.8369	+	357.668i	−0.205659	+	0.767528i
$467$	302.619	+	302.619i	0.648005	+	0.648005i	0.952511	−	0.304505i	$-0.0984911\pi$
$467$	302.619	+	302.619i	0.648005	+	0.648005i	−0.304505	+	0.952511i	$0.598491\pi$
$468$		0			0
$469$	242.183	−	139.825i	0.516382	−	0.298133i
$470$	−1226.22			−2.60898
$471$		0			0
$472$	−451.590	+	260.725i	−0.956758	+	0.552384i
$473$	121.395	−	121.395i	0.256649	−	0.256649i
$474$		0			0
$475$	−4.76695	+	4.76695i	−0.0100357	+	0.0100357i
$476$	78.6157	+	293.398i	0.165159	+	0.616382i
$477$		0			0
$478$	490.872	−	850.214i	1.02693	−	1.77869i
$479$	−13.4813	+	50.3131i	−0.0281448	+	0.105038i	−0.978569	−	0.205917i	$-0.933982\pi$
$479$	−13.4813	+	50.3131i	−0.0281448	+	0.105038i	0.950425	+	0.310955i	$0.100649\pi$
$480$		0			0
$481$	151.729	+	313.643i	0.315445	+	0.652064i
$482$	−281.714			−0.584469
$483$		0			0
$484$	315.597	+	182.210i	0.652061	+	0.376467i
$485$	−122.720	−	70.8522i	−0.253030	−	0.146087i
$486$		0			0
$487$	145.961	+	145.961i	0.299714	+	0.299714i	0.840902	−	0.541188i	$-0.182025\pi$
$487$	145.961	+	145.961i	0.299714	+	0.299714i	−0.541188	+	0.840902i	$0.682025\pi$
$488$	179.474	−	310.859i	0.367775	−	0.637006i
$489$		0			0
$490$	240.280	+	416.178i	0.490368	+	0.849343i
$491$	212.014			0.431801			0.215901	−	0.976415i	$-0.430731\pi$
$491$	212.014			0.431801			0.215901	+	0.976415i	$0.430731\pi$
$492$		0			0
$493$	−185.350	−	321.035i	−0.375963	−	0.651187i
$494$	30.5603	−	8.18861i	0.0618630	−	0.0165761i
$495$		0			0
$496$	212.790	+	57.0169i	0.429012	+	0.114953i
$497$	149.801	+	259.464i	0.301411	+	0.522060i
$498$		0			0
$499$	16.0550	+	59.9182i	0.0321744	+	0.120076i	0.980145	−	0.198280i	$-0.0635356\pi$
$499$	16.0550	+	59.9182i	0.0321744	+	0.120076i	−0.947971	+	0.318357i	$0.896869\pi$
$500$	950.827	−	254.773i	1.90165	−	0.509547i
$501$		0			0
$502$	−849.111	+	490.235i	−1.69146	+	0.976563i
$503$	39.8609	−	148.763i	0.0792463	−	0.295751i	−0.914916	−	0.403644i	$-0.867744\pi$
$503$	39.8609	−	148.763i	0.0792463	−	0.295751i	0.994163	+	0.107892i	$0.0344102\pi$
$504$		0			0
$505$	−118.029	−	440.491i	−0.233721	−	0.872259i
$506$	714.876	−	412.734i	1.41280	−	0.815680i
$507$		0			0
$508$		−	199.198i		−	0.392123i
$509$	−818.376	+	472.490i	−1.60781	+	0.928271i	−0.617953	+	0.786215i	$0.712038\pi$
$509$	−818.376	+	472.490i	−1.60781	+	0.928271i	−0.989859	+	0.142056i	$0.954629\pi$
$510$		0			0
$511$	228.322	+	131.822i	0.446814	+	0.257968i
$512$	−334.107	+	334.107i	−0.652553	+	0.652553i
$513$		0			0
$514$	−293.001	+	507.493i	−0.570041	+	0.987341i
$515$	269.732	−	467.189i	0.523751	−	0.907163i
$516$		0			0
$517$		−	719.422i		−	1.39153i
$518$	−404.189	−	274.521i	−0.780287	−	0.529964i
$519$		0			0
$520$	−424.967	−	113.870i	−0.817245	−	0.218980i
$521$	−212.478	−	122.674i	−0.407828	−	0.235460i	0.282028	−	0.959406i	$-0.408993\pi$
$521$	−212.478	−	122.674i	−0.407828	−	0.235460i	−0.689856	+	0.723947i	$0.742326\pi$
$522$		0			0
$523$	−350.894	+	94.0218i	−0.670926	+	0.179774i	−0.578172	−	0.815915i	$-0.696234\pi$
$523$	−350.894	+	94.0218i	−0.670926	+	0.179774i	−0.0927540	+	0.995689i	$0.529567\pi$
$524$	747.397	+	747.397i	1.42633	+	1.42633i
$525$		0			0
$526$	371.609	+	371.609i	0.706481	+	0.706481i
$527$	−153.184	−	265.323i	−0.290673	−	0.503460i
$528$		0			0
$529$			326.004i			0.616265i
$530$	−592.144	−	1025.62i	−1.11725	−	1.93514i
$531$		0			0
$532$	−20.2260	+	20.2260i	−0.0380188	+	0.0380188i
$533$	679.777	+	182.146i	1.27538	+	0.341737i
$534$		0			0
$535$	−32.1143	+	119.852i	−0.0600268	+	0.224023i
$536$	201.030	+	750.256i	0.375057	+	1.39973i
$537$		0			0
$538$	99.1383	+	26.5640i	0.184272	+	0.0493755i
$539$	−244.171	+	140.972i	−0.453008	+	0.261544i
$540$		0			0
$541$	31.1705	+	31.1705i	0.0576165	+	0.0576165i	0.735328	−	0.677711i	$-0.237028\pi$
$541$	31.1705	+	31.1705i	0.0576165	+	0.0576165i	−0.677711	+	0.735328i	$0.737028\pi$
$542$	−125.058	−	466.724i	−0.230735	−	0.861114i
$543$		0			0
$544$	192.155			0.353226
$545$			740.638i			1.35897i
$546$		0			0
$547$	121.114	−	121.114i	0.221415	−	0.221415i	−0.587679	−	0.809094i	$-0.699958\pi$
$547$	121.114	−	121.114i	0.221415	−	0.221415i	0.809094	+	0.587679i	$0.199958\pi$
$548$	1340.69	+	774.046i	2.44651	+	1.41249i
$549$		0			0
$550$	49.1903	+	183.581i	0.0894369	+	0.333783i
$551$	17.4544	−	30.2319i	0.0316776	−	0.0548673i
$552$		0			0
$553$	−80.2949	+	299.665i	−0.145199	+	0.541889i
$554$		−	650.782i		−	1.17470i
$555$		0			0
$556$	1652.77			2.97260
$557$	975.200	+	261.304i	1.75081	+	0.469128i	0.984798	−	0.173702i	$-0.0555729\pi$
$557$	975.200	+	261.304i	1.75081	+	0.469128i	0.766010	+	0.642829i	$0.222240\pi$
$558$		0			0
$559$	166.401	+	96.0715i	0.297676	+	0.171863i
$560$	124.236	−	33.2889i	0.221849	−	0.0594444i
$561$		0			0
$562$	101.225	−	175.327i	0.180116	−	0.311970i
$563$	379.754	+	379.754i	0.674519	+	0.674519i	0.958754	−	0.284236i	$-0.0917398\pi$
$563$	379.754	+	379.754i	0.674519	+	0.674519i	−0.284236	+	0.958754i	$0.591740\pi$
$564$		0			0
$565$	418.450			0.740620
$566$			1471.76i			2.60029i
$567$		0			0
$568$	−803.789	+	215.375i	−1.41512	+	0.379180i
$569$	343.477	−	343.477i	0.603650	−	0.603650i	−0.337629	−	0.941279i	$-0.609625\pi$
$569$	343.477	−	343.477i	0.603650	−	0.603650i	0.941279	+	0.337629i	$0.109625\pi$
$570$		0			0
$571$	354.344	+	613.742i	0.620567	+	1.07485i	0.989380	+	0.145350i	$0.0464309\pi$
$571$	354.344	+	613.742i	0.620567	+	1.07485i	−0.368813	+	0.929504i	$0.620236\pi$
$572$	148.831	−	555.444i	0.260194	−	0.971056i
$573$		0			0
$574$	−953.285	+	255.432i	−1.66077	+	0.445003i
$575$	−190.149	−	50.9504i	−0.330695	−	0.0886093i
$576$		0			0
$577$	−118.754	+	443.198i	−0.205814	+	0.768107i	0.783386	+	0.621535i	$0.213491\pi$
$577$	−118.754	+	443.198i	−0.205814	+	0.768107i	−0.989200	+	0.146572i	$0.953176\pi$
$578$	−417.399	−	417.399i	−0.722143	−	0.722143i
$579$		0			0
$580$	−936.553	+	540.719i	−1.61475	+	0.932274i
$581$	−219.642			−0.378041
$582$		0			0
$583$	601.733	−	347.411i	1.03213	−	0.595901i
$584$	−517.791	+	517.791i	−0.886628	+	0.886628i
$585$		0			0
$586$	1119.62	−	1119.62i	1.91062	−	1.91062i
$587$	−247.039	−	921.964i	−0.420851	−	1.57064i	−0.772820	−	0.634625i	$-0.781154\pi$
$587$	−247.039	−	921.964i	−0.420851	−	1.57064i	0.351969	−	0.936012i	$-0.385512\pi$
$588$		0			0
$589$	14.4254	−	24.9855i	0.0244913	−	0.0424202i
$590$	177.054	−	660.775i	0.300092	−	1.11996i
$591$		0			0
$592$	214.106	−	184.916i	0.361666	−	0.312358i
$593$	−734.484			−1.23859			−0.619295	−	0.785159i	$-0.712581\pi$
$593$	−734.484			−1.23859			−0.619295	+	0.785159i	$0.712581\pi$
$594$		0			0
$595$	−154.907	−	89.4355i	−0.260348	−	0.150312i
$596$	−696.179	−	401.939i	−1.16809	−	0.674395i
$597$		0			0
$598$	653.273	+	653.273i	1.09243	+	1.09243i
$599$	27.7241	−	48.0196i	0.0462840	−	0.0801663i	−0.841955	−	0.539547i	$-0.818595\pi$
$599$	27.7241	−	48.0196i	0.0462840	−	0.0801663i	0.888239	+	0.459381i	$0.151929\pi$
$600$		0			0
$601$	575.592	+	996.955i	0.957724	+	1.65883i	0.728007	+	0.685570i	$0.240447\pi$
$601$	575.592	+	996.955i	0.957724	+	1.65883i	0.229717	+	0.973257i	$0.426220\pi$
$602$	−269.452			−0.447594
$603$		0			0
$604$	−786.474	−	1362.21i	−1.30211	−	2.25532i
$605$	−207.288	+	55.5426i	−0.342624	+	0.0918059i
$606$		0			0
$607$	183.576	+	49.1889i	0.302431	+	0.0810361i	0.406843	−	0.913498i	$-0.366630\pi$
$607$	183.576	+	49.1889i	0.302431	+	0.0810361i	−0.104412	+	0.994534i	$0.533296\pi$
$608$	9.04760	+	15.6709i	0.0148809	+	0.0257745i
$609$		0			0
$610$	121.878	+	454.855i	0.199800	+	0.745663i
$611$	777.745	−	208.396i	1.27290	−	0.341074i
$612$		0			0
$613$	557.061	−	321.620i	0.908746	−	0.524665i	0.0287187	−	0.999588i	$-0.490857\pi$
$613$	557.061	−	321.620i	0.908746	−	0.524665i	0.880028	+	0.474923i	$0.157524\pi$
$614$	169.097	−	631.078i	0.275402	−	1.02782i
$615$		0			0
$616$	93.6871	+	349.645i	0.152089	+	0.567606i
$617$	−537.059	+	310.071i	−0.870435	+	0.502546i	−0.867493	−	0.497450i	$-0.834270\pi$
$617$	−537.059	+	310.071i	−0.870435	+	0.502546i	−0.00294247	+	0.999996i	$0.500937\pi$
$618$		0			0
$619$		−	994.739i		−	1.60701i	−0.595298	−	0.803505i	$-0.702966\pi$
$619$		−	994.739i		−	1.60701i	0.595298	−	0.803505i	$-0.297034\pi$
$620$	−774.024	+	446.883i	−1.24843	+	0.720779i
$621$		0			0
$622$	1426.61	+	823.653i	2.29358	+	1.32420i
$623$	70.0630	−	70.0630i	0.112461	−	0.112461i
$624$		0			0
$625$	−205.683	+	356.254i	−0.329093	+	0.570006i
$626$	415.817	−	720.215i	0.664244	−	1.15050i
$627$		0			0
$628$			174.697i			0.278180i
$629$	−392.391	−	28.7052i	−0.623833	−	0.0456363i
$630$		0			0
$631$	−613.082	−	164.275i	−0.971603	−	0.260340i	−0.262099	−	0.965041i	$-0.584415\pi$
$631$	−613.082	−	164.275i	−0.971603	−	0.260340i	−0.709505	+	0.704701i	$0.751081\pi$
$632$	−746.234	−	430.838i	−1.18075	−	0.681706i
$633$		0			0
$634$	1240.64	−	332.430i	1.95685	−	0.524337i
$635$	82.9465	+	82.9465i	0.130624	+	0.130624i
$636$		0			0
$637$	−223.130	−	223.130i	−0.350283	−	0.350283i
$638$	−492.076	−	852.301i	−0.771279	−	1.33589i
$639$		0			0
$640$		−	999.172i		−	1.56121i
$641$	−183.802	−	318.355i	−0.286743	−	0.496653i	0.686287	−	0.727330i	$-0.259239\pi$
$641$	−183.802	−	318.355i	−0.286743	−	0.496653i	−0.973030	+	0.230677i	$0.925906\pi$
$642$		0			0
$643$	143.990	−	143.990i	0.223935	−	0.223935i	−0.586218	−	0.810153i	$-0.699384\pi$
$643$	143.990	−	143.990i	0.223935	−	0.223935i	0.810153	+	0.586218i	$0.199384\pi$
$644$	−806.798	−	216.181i	−1.25279	−	0.335684i
$645$		0			0
$646$	−9.24679	+	34.5095i	−0.0143139	+	0.0534202i
$647$	−35.3274	−	131.844i	−0.0546019	−	0.203777i	0.933236	−	0.359264i	$-0.116972\pi$
$647$	−35.3274	−	131.844i	−0.0546019	−	0.203777i	−0.987838	+	0.155487i	$0.950305\pi$
$648$		0			0
$649$	387.676	+	103.877i	0.597344	+	0.160058i
$650$	−184.214	+	106.356i	−0.283407	+	0.163625i
$651$		0			0
$652$	47.3524	+	47.3524i	0.0726264	+	0.0726264i
$653$	93.8618	+	350.297i	0.143739	+	0.536442i	0.999808	+	0.0195808i	$0.00623317\pi$
$653$	93.8618	+	350.297i	0.143739	+	0.536442i	−0.856069	+	0.516862i	$0.827100\pi$
$654$		0			0
$655$	−622.434			−0.950281
$656$		−	571.433i		−	0.871087i
$657$		0			0
$658$	−798.426	+	798.426i	−1.21341	+	1.21341i
$659$	−1077.59	−	622.146i	−1.63519	−	0.944076i	−0.982458	−	0.186487i	$-0.940290\pi$
$659$	−1077.59	−	622.146i	−1.63519	−	0.944076i	−0.652731	−	0.757590i	$-0.726377\pi$
$660$		0			0
$661$	−161.129	−	601.340i	−0.243765	−	0.909743i	−0.974000	−	0.226547i	$-0.927256\pi$
$661$	−161.129	−	601.340i	−0.243765	−	0.909743i	0.730235	−	0.683196i	$-0.239410\pi$
$662$	−859.340	+	1488.42i	−1.29810	+	2.24837i
$663$		0			0
$664$	157.893	−	589.266i	0.237791	−	0.887449i
$665$		−	16.8443i		−	0.0253297i
$666$		0			0
$667$	1019.37			1.52828
$668$	−935.445	−	250.652i	−1.40037	−	0.375227i
$669$		0			0
$670$	−882.455	−	509.486i	−1.31710	−	0.760426i
$671$	−266.863	+	71.5057i	−0.397709	+	0.106566i
$672$		0			0
$673$	437.532	−	757.827i	0.650121	−	1.12604i	−0.332972	−	0.942937i	$-0.608051\pi$
$673$	437.532	−	757.827i	0.650121	−	1.12604i	0.983093	−	0.183106i	$-0.0586153\pi$
$674$	−522.816	−	522.816i	−0.775692	−	0.775692i
$675$		0			0
$676$	−583.009			−0.862440
$677$			338.204i			0.499562i	0.968302	+	0.249781i	$0.0803587\pi$
$677$			338.204i			0.499562i	−0.968302	+	0.249781i	$0.919641\pi$
$678$		0			0
$679$	−126.040	+	33.7723i	−0.185626	+	0.0497383i
$680$	351.299	−	351.299i	0.516617	−	0.516617i
$681$		0			0
$682$	−406.682	−	704.393i	−0.596308	−	1.03284i
$683$	188.719	−	704.308i	0.276309	−	1.03120i	−0.678651	−	0.734461i	$-0.737435\pi$
$683$	188.719	−	704.308i	0.276309	−	1.03120i	0.954959	−	0.296737i	$-0.0958984\pi$
$684$		0			0
$685$	−880.577	+	235.950i	−1.28551	+	0.344453i
$686$	1052.46	+	282.005i	1.53419	+	0.411085i
$687$		0			0
$688$	40.3798	−	150.699i	0.0586915	−	0.219040i
$689$	549.879	+	549.879i	0.798083	+	0.798083i
$690$		0			0
$691$	−1082.11	+	624.757i	−1.56601	+	0.904135i	−0.569380	+	0.822074i	$0.692817\pi$
$691$	−1082.11	+	624.757i	−1.56601	+	0.904135i	−0.996627	+	0.0820609i	$0.973850\pi$
$692$	635.047			0.917698
$693$		0			0
$694$	−675.438	+	389.965i	−0.973254	+	0.561909i
$695$	−688.214	+	688.214i	−0.990236	+	0.990236i
$696$		0			0
$697$	−561.937	+	561.937i	−0.806223	+	0.806223i
$698$	246.108	+	918.486i	0.352590	+	1.31588i
$699$		0			0
$700$	96.1554	−	166.546i	0.137365	−	0.237923i
$701$	131.877	−	492.170i	0.188126	−	0.702097i	−0.805813	−	0.592170i	$-0.798272\pi$
$701$	131.877	−	492.170i	0.188126	−	0.702097i	0.993940	−	0.109927i	$-0.0350618\pi$
$702$		0			0
$703$	−16.1347	−	33.3525i	−0.0229512	−	0.0474430i
$704$	767.469			1.09015
$705$		0			0
$706$	−1059.74	−	611.842i	−1.50105	−	0.866632i
$707$	−363.668	−	209.964i	−0.514381	−	0.296978i
$708$		0			0
$709$	−987.565	−	987.565i	−1.39290	−	1.39290i	−0.818754	−	0.574144i	$-0.805335\pi$
$709$	−987.565	−	987.565i	−1.39290	−	1.39290i	−0.574144	−	0.818754i	$-0.694665\pi$
$710$	545.839	−	945.421i	0.768787	−	1.33158i
$711$		0			0
$712$	137.602	+	238.334i	0.193262	+	0.334739i
$713$	842.466			1.18158
$714$		0			0
$715$	169.314	+	293.261i	0.236803	+	0.410155i
$716$	969.761	−	259.847i	1.35442	−	0.362915i
$717$		0			0
$718$	−1604.83	−	430.013i	−2.23514	−	0.598903i
$719$	−80.2150	−	138.936i	−0.111565	−	0.193236i	0.804837	−	0.593496i	$-0.202253\pi$
$719$	−80.2150	−	138.936i	−0.111565	−	0.193236i	−0.916401	+	0.400261i	$0.868920\pi$
$720$		0			0
$721$	−128.570	−	479.829i	−0.178322	−	0.665505i
$722$	1166.74	−	312.626i	1.61598	−	0.433000i
$723$		0			0
$724$	−1828.79	+	1055.85i	−2.52596	+	1.45836i
$725$	−60.7448	+	226.703i	−0.0837860	+	0.312694i
$726$		0			0
$727$	64.9798	+	242.508i	0.0893808	+	0.333574i	0.996108	−	0.0881447i	$-0.0280938\pi$
$727$	64.9798	+	242.508i	0.0893808	+	0.333574i	−0.906727	+	0.421718i	$0.861427\pi$
$728$	−350.852	+	202.564i	−0.481939	+	0.278248i
$729$		0			0
$730$		−	960.651i		−	1.31596i
$731$	−187.904	+	108.486i	−0.257051	+	0.148408i
$732$		0			0
$733$	115.919	+	66.9257i	0.158143	+	0.0913039i	0.576983	−	0.816756i	$-0.304230\pi$
$733$	115.919	+	66.9257i	0.158143	+	0.0913039i	−0.418840	+	0.908060i	$0.637563\pi$
$734$	−1538.05	+	1538.05i	−2.09544	+	2.09544i
$735$		0			0
$736$	−264.198	+	457.604i	−0.358964	+	0.621744i
$737$	298.915	−	517.736i	0.405583	−	0.702491i
$738$		0			0
$739$			985.094i			1.33301i	0.745501	+	0.666505i	$0.232210\pi$
$739$			985.094i			1.33301i	−0.745501	+	0.666505i	$0.767790\pi$
$740$	−83.7414	+	1144.72i	−0.113164	+	1.54692i
$741$		0			0
$742$	−1053.37	−	282.251i	−1.41964	−	0.380392i
$743$	562.799	+	324.932i	0.757469	+	0.437325i	0.828386	−	0.560157i	$-0.189259\pi$
$743$	562.799	+	324.932i	0.757469	+	0.437325i	−0.0709174	+	0.997482i	$0.522593\pi$
$744$		0			0
$745$	457.258	−	122.522i	0.613769	−	0.164459i
$746$	1593.59	+	1593.59i	2.13618	+	2.13618i
$747$		0			0
$748$	459.158	+	459.158i	0.613847	+	0.613847i
$749$	57.1287	+	98.9498i	0.0762733	+	0.132109i
$750$		0			0
$751$			983.310i			1.30933i	0.755917	+	0.654667i	$0.227191\pi$
$751$			983.310i			1.30933i	−0.755917	+	0.654667i	$0.772809\pi$
$752$	−326.894	−	566.196i	−0.434699	−	0.752920i
$753$		0			0
$754$	778.855	−	778.855i	1.03296	−	1.03296i
$755$	894.716	+	239.738i	1.18505	+	0.317534i
$756$		0			0
$757$	−48.5631	+	181.240i	−0.0641521	+	0.239419i	−0.990555	−	0.137114i	$-0.956217\pi$
$757$	−48.5631	+	181.240i	−0.0641521	+	0.239419i	0.926403	+	0.376533i	$0.122884\pi$
$758$	101.966	+	380.542i	0.134520	+	0.502035i
$759$		0			0
$760$	45.1906	+	12.1088i	0.0594613	+	0.0159326i
$761$	283.606	−	163.740i	0.372675	−	0.215164i	−0.301951	−	0.953323i	$-0.597638\pi$
$761$	283.606	−	163.740i	0.372675	−	0.215164i	0.674626	+	0.738159i	$0.264305\pi$
$762$		0			0
$763$	482.250	+	482.250i	0.632044	+	0.632044i
$764$	−324.229	−	1210.04i	−0.424384	−	1.58382i
$765$		0			0
$766$	805.995			1.05221
$767$			449.195i			0.585651i
$768$		0			0
$769$	397.074	−	397.074i	0.516351	−	0.516351i	−0.400114	−	0.916465i	$-0.631030\pi$
$769$	397.074	−	397.074i	0.516351	−	0.516351i	0.916465	+	0.400114i	$0.131030\pi$
$770$	−411.254	−	237.438i	−0.534097	−	0.308361i
$771$		0			0
$772$	−527.763	−	1969.64i	−0.683631	−	2.55134i
$773$	18.4436	−	31.9453i	0.0238598	−	0.0413263i	−0.853849	−	0.520521i	$-0.825738\pi$
$773$	18.4436	−	31.9453i	0.0238598	−	0.0413263i	0.877709	+	0.479194i	$0.159071\pi$
$774$		0			0
$775$	−50.2032	+	187.361i	−0.0647784	+	0.241756i
$776$		−	362.424i		−	0.467041i
$777$		0			0
$778$	2270.10			2.91787
$779$	−72.2868	−	19.3692i	−0.0927943	−	0.0248642i
$780$		0			0
$781$	554.678	+	320.243i	0.710215	+	0.410043i
$782$	−1007.71	+	270.014i	−1.28863	+	0.345286i
$783$		0			0
$784$	−128.111	+	221.895i	−0.163407	+	0.283029i
$785$	−72.7442	−	72.7442i	−0.0926678	−	0.0926678i
$786$		0			0
$787$	697.915			0.886805			0.443402	−	0.896323i	$-0.353771\pi$
$787$	697.915			0.886805			0.443402	+	0.896323i	$0.353771\pi$
$788$			312.407i			0.396455i
$789$		0			0
$790$	1091.90	−	292.575i	1.38216	−	0.370348i
$791$	272.465	−	272.465i	0.344456	−	0.344456i
$792$		0			0
$793$	−154.605	−	267.784i	−0.194962	−	0.337684i
$794$	231.139	−	862.621i	0.291106	−	1.08642i
$795$		0			0
$796$	−809.525	+	216.912i	−1.01699	+	0.272502i
$797$	−384.659	−	103.069i	−0.482634	−	0.129321i	0.00929475	−	0.999957i	$-0.497041\pi$
$797$	−384.659	−	103.069i	−0.482634	−	0.129321i	−0.491929	+	0.870635i	$0.663708\pi$
$798$		0			0
$799$	−235.326	+	878.249i	−0.294526	+	1.09918i
$800$	−86.0254	−	86.0254i	−0.107532	−	0.107532i
$801$		0			0
$802$	479.002	−	276.552i	0.597259	−	0.344828i
$803$	563.613			0.701885
$804$		0			0
$805$	425.969	−	245.934i	0.529155	−	0.305508i
$806$	643.693	−	643.693i	0.798627	−	0.798627i
$807$		0			0
$808$	824.729	−	824.729i	1.02070	−	1.02070i
$809$	−106.753	−	398.406i	−0.131956	−	0.492467i	0.868036	−	0.496502i	$-0.165382\pi$
$809$	−106.753	−	398.406i	−0.131956	−	0.492467i	−0.999992	+	0.00403453i	$0.998716\pi$
$810$		0			0
$811$	−180.784	+	313.128i	−0.222916	+	0.386101i	−0.955692	−	0.294368i	$-0.904891\pi$
$811$	−180.784	+	313.128i	−0.222916	+	0.386101i	0.732777	+	0.680469i	$0.238224\pi$
$812$	−257.738	+	961.892i	−0.317412	+	1.18460i
$813$		0			0
$814$	−1041.74	−	76.2081i	−1.27978	−	0.0936217i
$815$	−39.4352			−0.0483868
$816$		0			0
$817$	−17.6949	−	10.2162i	−0.0216584	−	0.0125045i
$818$	782.321	+	451.673i	0.956383	+	0.552168i
$819$		0			0
$820$	1639.33	+	1639.33i	1.99919	+	1.99919i
$821$	−361.941	+	626.901i	−0.440854	+	0.763582i	−0.997753	−	0.0669982i	$-0.978658\pi$
$821$	−361.941	+	626.901i	−0.440854	+	0.763582i	0.556899	+	0.830580i	$0.311991\pi$
$822$		0			0
$823$	−552.028	−	956.141i	−0.670751	−	1.16177i	−0.977691	−	0.210046i	$-0.932639\pi$
$823$	−552.028	−	956.141i	−0.670751	−	1.16177i	0.306940	−	0.951729i	$-0.400695\pi$
$824$	1379.73			1.67443
$825$		0			0
$826$	−314.964	−	545.534i	−0.381312	−	0.660452i
$827$	−75.9664	+	20.3551i	−0.0918578	+	0.0246132i	−0.304455	−	0.952527i	$-0.598474\pi$
$827$	−75.9664	+	20.3551i	−0.0918578	+	0.0246132i	0.212597	+	0.977140i	$0.431808\pi$
$828$		0			0
$829$	605.059	+	162.125i	0.729866	+	0.195567i	0.604570	−	0.796552i	$-0.293345\pi$
$829$	605.059	+	162.125i	0.729866	+	0.195567i	0.125296	+	0.992119i	$0.460012\pi$
$830$	400.160	+	693.098i	0.482121	+	0.835058i
$831$		0			0
$832$	222.314	+	829.686i	0.267204	+	0.997219i
$833$	344.189	−	92.2253i	0.413193	−	0.110715i
$834$		0			0
$835$	493.892	−	285.149i	0.591488	−	0.341495i
$836$	−15.8265	+	59.0654i	−0.0189312	+	0.0706524i
$837$		0			0
$838$	20.9395	+	78.1472i	0.0249875	+	0.0932545i
$839$	−1314.59	+	758.978i	−1.56685	+	0.904623i	−0.570319	+	0.821423i	$0.693181\pi$
$839$	−1314.59	+	758.978i	−1.56685	+	0.904623i	−0.996533	+	0.0831996i	$0.973486\pi$
$840$		0			0
$841$		−	374.324i		−	0.445094i
$842$	−2318.95	+	1338.84i	−2.75409	+	1.59008i
$843$		0			0
$844$	766.290	+	442.418i	0.907927	+	0.524192i
$845$	242.766	−	242.766i	0.287297	−	0.287297i
$846$		0			0
$847$	−98.8055	+	171.136i	−0.116653	+	0.202050i
$848$	315.715	−	546.835i	0.372305	−	0.644852i
$849$		0			0
$850$		−	240.200i		−	0.282588i
$851$	607.866	−	894.986i	0.714296	−	1.05169i
$852$		0			0
$853$	577.595	+	154.766i	0.677133	+	0.181437i	0.580966	−	0.813928i	$-0.302675\pi$
$853$	577.595	+	154.766i	0.677133	+	0.181437i	0.0961673	+	0.995365i	$0.469342\pi$
$854$	375.527	+	216.810i	0.439727	+	0.253876i
$855$		0			0
$856$	−306.535	+	82.1358i	−0.358102	+	0.0959530i
$857$	50.5087	+	50.5087i	0.0589366	+	0.0589366i	0.735961	−	0.677024i	$-0.236731\pi$
$857$	50.5087	+	50.5087i	0.0589366	+	0.0589366i	−0.677024	+	0.735961i	$0.736731\pi$
$858$		0			0
$859$	−928.313	−	928.313i	−1.08069	−	1.08069i	−0.996445	−	0.0842454i	$-0.973152\pi$
$859$	−928.313	−	928.313i	−1.08069	−	1.08069i	−0.0842454	−	0.996445i	$-0.526848\pi$
$860$	316.486	+	548.170i	0.368007	+	0.637407i
$861$		0			0
$862$			1502.27i			1.74277i
$863$	−112.236	−	194.398i	−0.130053	−	0.225258i	0.793644	−	0.608383i	$-0.208181\pi$
$863$	−112.236	−	194.398i	−0.130053	−	0.225258i	−0.923697	+	0.383124i	$0.874848\pi$
$864$		0			0
$865$	−264.434	+	264.434i	−0.305704	+	0.305704i
$866$	2530.99	+	678.177i	2.92262	+	0.783115i
$867$		0			0
$868$	−213.011	+	794.967i	−0.245404	+	0.915860i
$869$	171.653	+	640.619i	0.197530	+	0.737191i
$870$		0			0
$871$	646.294	+	173.174i	0.742014	+	0.198822i
$872$	−1640.48	+	947.129i	−1.88128	+	1.08616i
$873$		0			0
$874$	−69.4684	−	69.4684i	−0.0794833	−	0.0794833i
$875$	138.154	+	515.596i	0.157890	+	0.589253i
$876$		0			0
$877$	243.840			0.278039			0.139019	−	0.990290i	$-0.455605\pi$
$877$	243.840			0.278039			0.139019	+	0.990290i	$0.455605\pi$
$878$		−	806.438i		−	0.918495i
$879$		0			0
$880$	194.425	−	194.425i	0.220937	−	0.220937i
$881$	536.585	+	309.798i	0.609064	+	0.351643i	0.772599	−	0.634894i	$-0.218956\pi$
$881$	536.585	+	309.798i	0.609064	+	0.351643i	−0.163535	+	0.986538i	$0.552290\pi$
$882$		0			0
$883$	242.200	+	903.904i	0.274293	+	1.02367i	0.956314	+	0.292342i	$0.0944344\pi$
$883$	242.200	+	903.904i	0.274293	+	1.02367i	−0.682021	+	0.731332i	$0.738899\pi$
$884$	−363.376	+	629.386i	−0.411059	+	0.711975i
$885$		0			0
$886$	−657.371	+	2453.34i	−0.741954	+	2.76901i
$887$		−	1560.96i		−	1.75982i	−0.475145	−	0.879908i	$-0.657604\pi$
$887$		−	1560.96i		−	1.75982i	0.475145	−	0.879908i	$-0.342396\pi$
$888$		0			0
$889$	108.017			0.121504
$890$	−348.735	−	93.4433i	−0.391837	−	0.104992i
$891$		0			0
$892$	−1133.73	−	654.558i	−1.27100	−	0.733810i
$893$	−82.7046	+	22.1606i	−0.0926144	+	0.0248159i
$894$		0			0
$895$	−295.609	+	512.010i	−0.330290	+	0.572079i
$896$	−650.588	−	650.588i	−0.726103	−	0.726103i
$897$		0			0
$898$	−431.174			−0.480150
$899$		−	1004.42i		−	1.11726i
$900$		0			0
$901$	−848.216	+	227.279i	−0.941416	+	0.252252i
$902$	−1491.86	+	1491.86i	−1.65395	+	1.65395i
$903$		0			0
$904$	535.115	+	926.847i	0.591942	+	1.02527i
$905$	321.853	−	1201.17i	0.355638	−	1.32726i
$906$		0			0
$907$	601.823	−	161.258i	0.663531	−	0.177793i	0.0886920	−	0.996059i	$-0.471731\pi$
$907$	601.823	−	161.258i	0.663531	−	0.177793i	0.574839	+	0.818266i	$0.305065\pi$
$908$	197.294	+	52.8647i	0.217284	+	0.0582211i
$909$		0			0
$910$	137.558	−	513.373i	0.151163	−	0.564146i
$911$	−140.862	−	140.862i	−0.154624	−	0.154624i	0.625556	−	0.780179i	$-0.284872\pi$
$911$	−140.862	−	140.862i	−0.154624	−	0.154624i	−0.780179	+	0.625556i	$0.784872\pi$
$912$		0			0
$913$	−406.640	+	234.774i	−0.445389	+	0.257145i
$914$	1600.04			1.75059
$915$		0			0
$916$	−504.606	+	291.334i	−0.550880	+	0.318051i
$917$	−405.284	+	405.284i	−0.441967	+	0.441967i
$918$		0			0
$919$	367.721	−	367.721i	0.400131	−	0.400131i	−0.478148	−	0.878279i	$-0.658692\pi$
$919$	367.721	−	367.721i	0.400131	−	0.400131i	0.878279	+	0.478148i	$0.158692\pi$
$920$	353.587	+	1319.60i	0.384334	+	1.43435i
$921$		0			0
$922$	1456.21	−	2522.23i	1.57940	−	2.73561i
$923$	−185.531	+	692.410i	−0.201008	+	0.750173i
$924$		0			0
$925$	162.818	+	188.520i	0.176019	+	0.203805i
$926$	2601.30			2.80918
$927$		0			0
$928$	545.571	+	314.986i	0.587900	+	0.339424i
$929$	−1157.13	−	668.069i	−1.24557	−	0.719127i	−0.275343	−	0.961346i	$-0.588792\pi$
$929$	−1157.13	−	668.069i	−1.24557	−	0.719127i	−0.970222	+	0.242219i	$0.922125\pi$
$930$		0			0
$931$	23.7274	+	23.7274i	0.0254860	+	0.0254860i
$932$	400.489	−	693.668i	0.429710	−	0.744279i
$933$		0			0
$934$	−717.977	−	1243.57i	−0.768712	−	1.33145i
$935$	−382.388			−0.408971
$936$		0			0
$937$	857.615	+	1485.43i	0.915278	+	1.58531i	0.806494	+	0.591242i	$0.201362\pi$
$937$	857.615	+	1485.43i	0.915278	+	1.58531i	0.108784	+	0.994065i	$0.465304\pi$
$938$	−906.331	+	242.851i	−0.966238	+	0.258903i
$939$		0			0
$940$	2562.10	+	686.514i	2.72564	+	0.730334i
$941$	−724.509	−	1254.89i	−0.769935	−	1.33357i	−0.937598	−	0.347722i	$-0.886955\pi$
$941$	−724.509	−	1254.89i	−0.769935	−	1.33357i	0.167663	−	0.985844i	$-0.446378\pi$
$942$		0			0
$943$	−565.597	−	2110.84i	−0.599784	−	2.23843i
$944$	352.307	−	94.4004i	0.373207	−	0.100000i
$945$		0			0
$946$	−498.857	+	288.015i	−0.527333	+	0.304456i
$947$	83.4414	−	311.407i	0.0881113	−	0.328836i	−0.907774	−	0.419460i	$-0.862220\pi$
$947$	83.4414	−	311.407i	0.0881113	−	0.328836i	0.995885	+	0.0906241i	$0.0288862\pi$
$948$		0			0
$949$	163.263	+	609.305i	0.172037	+	0.642049i
$950$	19.5892	−	11.3098i	0.0206202	−	0.0119051i
$951$		0			0
$952$		−	457.481i		−	0.480548i
$953$	−779.456	+	450.019i	−0.817897	+	0.472213i	−0.849691	−	0.527282i	$-0.823211\pi$
$953$	−779.456	+	450.019i	−0.817897	+	0.472213i	0.0317939	+	0.999494i	$0.489878\pi$
$954$		0			0
$955$	638.872	+	368.853i	0.668975	+	0.386233i
$956$	−1501.65	+	1501.65i	−1.57076	+	1.57076i
$957$		0			0
$958$	87.3850	−	151.355i	0.0912161	−	0.157991i
$959$	−419.735	+	727.002i	−0.437680	+	0.758083i
$960$		0			0
$961$			130.888i			0.136199i
$962$	−219.376	−	1148.27i	−0.228041	−	1.19362i
$963$		0			0
$964$	588.623	+	157.721i	0.610604	+	0.163611i
$965$	1039.92	+	600.399i	1.07764	+	0.622175i
$966$		0			0
$967$	1026.62	−	275.082i	1.06165	−	0.284470i	0.314595	−	0.949226i	$-0.398131\pi$
$967$	1026.62	−	275.082i	1.06165	−	0.284470i	0.747060	+	0.664757i	$0.231465\pi$
$968$	−388.104	−	388.104i	−0.400934	−	0.400934i
$969$		0			0
$970$	336.200	+	336.200i	0.346598	+	0.346598i
$971$	−237.973	−	412.181i	−0.245080	−	0.424491i	0.717074	−	0.696997i	$-0.245481\pi$
$971$	−237.973	−	412.181i	−0.245080	−	0.424491i	−0.962154	+	0.272506i	$0.912148\pi$
$972$		0			0
$973$			896.231i			0.921100i
$974$	−346.298	−	599.806i	−0.355542	−	0.615818i
$975$		0			0
$976$	−177.534	+	177.534i	−0.181900	+	0.181900i
$977$	−610.344	−	163.541i	−0.624712	−	0.167391i	−0.0674431	−	0.997723i	$-0.521484\pi$
$977$	−610.344	−	163.541i	−0.624712	−	0.167391i	−0.557269	+	0.830332i	$0.688151\pi$
$978$		0			0
$979$	54.8231	−	204.603i	0.0559991	−	0.208991i
$980$	−269.048	−	1004.10i	−0.274538	−	1.02459i
$981$		0			0
$982$	−687.130	−	184.116i	−0.699725	−	0.187491i
$983$	−531.687	+	306.970i	−0.540882	+	0.312279i	−0.745436	−	0.666577i	$-0.767759\pi$
$983$	−531.687	+	306.970i	−0.540882	+	0.312279i	0.204554	+	0.978855i	$0.434426\pi$
$984$		0			0
$985$	−130.087	−	130.087i	−0.132068	−	0.132068i
$986$	321.920	+	1201.42i	0.326491	+	1.21848i
$987$		0			0
$988$	−68.4382			−0.0692694
$989$		−	596.641i		−	0.603277i
$990$		0			0
$991$	−583.758	+	583.758i	−0.589060	+	0.589060i	−0.937377	−	0.348317i	$-0.886753\pi$
$991$	−583.758	+	583.758i	−0.589060	+	0.589060i	0.348317	+	0.937377i	$0.386753\pi$
$992$	450.893	+	260.323i	0.454530	+	0.262423i
$993$		0			0
$994$	−260.179	−	971.000i	−0.261749	−	0.976862i
$995$	246.765	−	427.410i	0.248005	−	0.429557i
$996$		0			0
$997$	66.3495	−	247.620i	0.0665491	−	0.248365i	−0.924635	−	0.380854i	$-0.875630\pi$
$997$	66.3495	−	247.620i	0.0665491	−	0.248365i	0.991184	+	0.132489i	$0.0422969\pi$
$998$		−	208.135i		−	0.208552i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.c.82.1		24
3.2	odd	2		111.3.l.a.82.6	✓	24
37.14	odd	12	inner	333.3.bb.c.199.1		24
111.14	even	12		111.3.l.a.88.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.a.82.6	✓	24	3.2	odd	2
111.3.l.a.88.6	yes	24	111.14	even	12
333.3.bb.c.82.1		24	1.1	even	1	trivial
333.3.bb.c.199.1		24	37.14	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.24096 - 0.868412i) q^{2} +(6.28557 + 3.62898i) q^{4} +(-4.12843 + 1.10621i) q^{5} +(-1.96785 + 3.40842i) q^{7} +(-7.72965 - 7.72965i) q^{8} +O(q^{10})\)	\(q+(-3.24096 - 0.868412i) q^{2} +(6.28557 + 3.62898i) q^{4} +(-4.12843 + 1.10621i) q^{5} +(-1.96785 + 3.40842i) q^{7} +(-7.72965 - 7.72965i) q^{8} +14.3407 q^{10} +8.41369i q^{11} +(-9.09577 + 2.43721i) q^{13} +(9.33764 - 9.33764i) q^{14} +(3.82304 + 6.62170i) q^{16} +(2.75215 - 10.2712i) q^{17} +(0.967236 - 0.259170i) q^{19} +(-29.9640 - 8.02882i) q^{20} +(7.30655 - 27.2684i) q^{22} +(20.6761 + 20.6761i) q^{23} +(-5.83039 + 3.36618i) q^{25} +31.5955 q^{26} +(-24.7382 + 14.2826i) q^{28} +(24.6508 - 24.6508i) q^{29} +(20.3729 - 20.3729i) q^{31} +(4.67704 + 17.4549i) q^{32} +(-17.8392 + 30.8984i) q^{34} +(4.35371 - 16.2483i) q^{35} +(-6.94326 - 36.3427i) q^{37} -3.35984 q^{38} +(40.4619 + 23.3607i) q^{40} +(-64.7228 - 37.3677i) q^{41} +(-14.4283 - 14.4283i) q^{43} +(-30.5331 + 52.8849i) q^{44} +(-49.0551 - 84.9659i) q^{46} -85.5062 q^{47} +(16.7551 + 29.0207i) q^{49} +(21.8193 - 5.84646i) q^{50} +(-66.0167 - 17.6891i) q^{52} +(-41.2911 - 71.5183i) q^{53} +(-9.30731 - 34.7353i) q^{55} +(41.5567 - 11.1351i) q^{56} +(-101.299 + 58.4852i) q^{58} +(12.3462 - 46.0768i) q^{59} +(8.49873 + 31.7177i) q^{61} +(-83.7199 + 48.3357i) q^{62} -91.2167i q^{64} +(34.8552 - 20.1237i) q^{65} +(-61.5349 - 35.5272i) q^{67} +(54.5727 - 54.5727i) q^{68} +(-28.2204 + 48.8792i) q^{70} +(38.0622 - 65.9256i) q^{71} -66.9877i q^{73} +(-9.05763 + 123.815i) q^{74} +(7.02015 + 1.88104i) q^{76} +(-28.6774 - 16.5569i) q^{77} +(76.1401 - 20.4017i) q^{79} +(-23.1081 - 23.1081i) q^{80} +(177.313 + 177.313i) q^{82} +(27.9038 + 48.3307i) q^{83} +45.4483i q^{85} +(34.2317 + 59.2911i) q^{86} +(65.0349 - 65.0349i) q^{88} +(-24.3178 - 6.51594i) q^{89} +(9.59212 - 35.7983i) q^{91} +(54.9281 + 204.994i) q^{92} +(277.122 + 74.2546i) q^{94} +(-3.70647 + 2.13993i) q^{95} +(23.4437 + 23.4437i) q^{97} +(-29.1007 - 108.605i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

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