LMFDB - Embedded newform 567.2.i.c.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(215,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("567.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.i (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	567.269
Dual form			567.2.i.c.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} +2.23607i q^{8} +O(q^{10})$	\(q-2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} +2.23607i q^{8} +(3.87298 - 2.23607i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(-1.93649 - 5.59017i) q^{14} -1.00000 q^{16} +(3.87298 - 6.70820i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} +(-3.87298 - 2.23607i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.93649 + 3.35410i) q^{26} +(-7.50000 + 2.59808i) q^{28} +(-3.87298 - 2.23607i) q^{29} +1.73205i q^{31} +6.70820i q^{32} +(-15.0000 - 8.66025i) q^{34} +(-2.50000 - 4.33013i) q^{37} +(3.87298 + 6.70820i) q^{38} +(3.87298 + 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-11.6190 + 6.70820i) q^{44} +(-5.00000 + 8.66025i) q^{46} -7.74597 q^{47} +(5.50000 - 4.33013i) q^{49} +(9.68246 - 5.59017i) q^{50} +(4.50000 - 2.59808i) q^{52} +(-3.87298 - 2.23607i) q^{53} +(1.93649 + 5.59017i) q^{56} +(-5.00000 + 8.66025i) q^{58} +7.74597 q^{59} +8.66025i q^{61} +3.87298 q^{62} +13.0000 q^{64} -1.00000 q^{67} +(-11.6190 + 20.1246i) q^{68} -8.94427i q^{71} +(6.00000 + 3.46410i) q^{73} +(-9.68246 + 5.59017i) q^{74} +(9.00000 - 5.19615i) q^{76} +(7.74597 - 8.94427i) q^{77} +11.0000 q^{79} +(15.0000 - 8.66025i) q^{82} +(-3.87298 + 6.70820i) q^{83} +(-13.5554 - 7.82624i) q^{86} +(5.00000 + 8.66025i) q^{88} +(7.74597 + 13.4164i) q^{89} +(-3.00000 + 3.46410i) q^{91} +(11.6190 + 6.70820i) q^{92} +17.3205i q^{94} +(-1.50000 - 0.866025i) q^{97} +(-9.68246 - 12.2984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{4} + 10 q^{7}+O(q^{10}) $ 4 * q - 12 * q^4 + 10 * q^7	$ 4 q - 12 q^{4} + 10 q^{7} - 6 q^{13} - 4 q^{16} - 12 q^{19} - 20 q^{22} + 10 q^{25} - 30 q^{28} - 60 q^{34} - 10 q^{37} + 14 q^{43} - 20 q^{46} + 22 q^{49} + 18 q^{52} - 20 q^{58} + 52 q^{64} - 4 q^{67} + 24 q^{73} + 36 q^{76} + 44 q^{79} + 60 q^{82} + 20 q^{88} - 12 q^{91} - 6 q^{97}+O(q^{100}) $ 4 * q - 12 * q^4 + 10 * q^7 - 6 * q^13 - 4 * q^16 - 12 * q^19 - 20 * q^22 + 10 * q^25 - 30 * q^28 - 60 * q^34 - 10 * q^37 + 14 * q^43 - 20 * q^46 + 22 * q^49 + 18 * q^52 - 20 * q^58 + 52 * q^64 - 4 * q^67 + 24 * q^73 + 36 * q^76 + 44 * q^79 + 60 * q^82 + 20 * q^88 - 12 * q^91 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	2.23607i		−	1.58114i	−0.612372	−	0.790569i	$-0.709785\pi$
$2$		−	2.23607i		−	1.58114i	0.612372	−	0.790569i	$-0.290215\pi$
$3$		0			0
$3$		0			0
$4$	−3.00000			−1.50000
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$			2.23607i			0.790569i
$9$		0			0
$10$		0			0
$11$	3.87298	−	2.23607i	1.16775	−	0.674200i	0.214600	−	0.976702i	$-0.431155\pi$
$11$	3.87298	−	2.23607i	1.16775	−	0.674200i	0.953149	+	0.302502i	$0.0978220\pi$
$12$		0			0
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.50000	+	0.866025i	−0.416025	+	0.240192i	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.93649	−	5.59017i	−0.517549	−	1.49404i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.87298	−	6.70820i	0.939336	−	1.62698i	0.172624	−	0.984988i	$-0.444775\pi$
$17$	3.87298	−	6.70820i	0.939336	−	1.62698i	0.766712	−	0.641991i	$-0.221891\pi$
$18$		0			0
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$	−5.00000	−	8.66025i	−1.06600	−	1.84637i
$23$	−3.87298	−	2.23607i	−0.807573	−	0.466252i	0.0385394	−	0.999257i	$-0.487729\pi$
$23$	−3.87298	−	2.23607i	−0.807573	−	0.466252i	−0.846112	+	0.533005i	$0.821063\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	1.93649	+	3.35410i	0.379777	+	0.657794i
$27$		0			0
$28$	−7.50000	+	2.59808i	−1.41737	+	0.490990i
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	0.0952614	−	0.995452i	$-0.469631\pi$
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	−0.814456	+	0.580225i	$0.802965\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$			6.70820i			1.18585i
$33$		0			0
$34$	−15.0000	−	8.66025i	−2.57248	−	1.48522i
$35$		0			0
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$	3.87298	+	6.70820i	0.628281	+	1.08821i
$39$		0			0
$40$		0			0
$41$	3.87298	+	6.70820i	0.604858	+	1.04765i	0.992074	+	0.125656i	$0.0401036\pi$
$41$	3.87298	+	6.70820i	0.604858	+	1.04765i	−0.387215	+	0.921989i	$0.626563\pi$
$42$		0			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$	−11.6190	+	6.70820i	−1.75162	+	1.01130i
$45$		0			0
$46$	−5.00000	+	8.66025i	−0.737210	+	1.27688i
$47$	−7.74597			−1.12987			−0.564933	−	0.825137i	$-0.691098\pi$
$47$	−7.74597			−1.12987			−0.564933	+	0.825137i	$0.691098\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	9.68246	−	5.59017i	1.36931	−	0.790569i
$51$		0			0
$52$	4.50000	−	2.59808i	0.624038	−	0.360288i
$53$	−3.87298	−	2.23607i	−0.531995	−	0.307148i	0.209833	−	0.977737i	$-0.432708\pi$
$53$	−3.87298	−	2.23607i	−0.531995	−	0.307148i	−0.741829	+	0.670590i	$0.766041\pi$
$54$		0			0
$55$		0			0
$56$	1.93649	+	5.59017i	0.258775	+	0.747018i
$57$		0			0
$58$	−5.00000	+	8.66025i	−0.656532	+	1.13715i
$59$	7.74597			1.00844			0.504219	−	0.863576i	$-0.331780\pi$
$59$	7.74597			1.00844			0.504219	+	0.863576i	$0.331780\pi$
$60$		0			0
$61$			8.66025i			1.10883i	0.832240	+	0.554416i	$0.187058\pi$
$61$			8.66025i			1.10883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	3.87298			0.491869
$63$		0			0
$64$	13.0000			1.62500
$65$		0			0
$66$		0			0
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$	−11.6190	+	20.1246i	−1.40900	+	2.44047i
$69$		0			0
$70$		0			0
$71$		−	8.94427i		−	1.06149i	−0.847532	−	0.530745i	$-0.821912\pi$
$71$		−	8.94427i		−	1.06149i	0.847532	−	0.530745i	$-0.178088\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$	−9.68246	+	5.59017i	−1.12556	+	0.649844i
$75$		0			0
$76$	9.00000	−	5.19615i	1.03237	−	0.596040i
$77$	7.74597	−	8.94427i	0.882735	−	1.01929i
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$		0			0
$82$	15.0000	−	8.66025i	1.65647	−	0.956365i
$83$	−3.87298	+	6.70820i	−0.425115	+	0.736321i	−0.996431	−	0.0844091i	$-0.973100\pi$
$83$	−3.87298	+	6.70820i	−0.425115	+	0.736321i	0.571316	+	0.820730i	$0.306433\pi$
$84$		0			0
$85$		0			0
$86$	−13.5554	−	7.82624i	−1.46172	−	0.843925i
$87$		0			0
$88$	5.00000	+	8.66025i	0.533002	+	0.923186i
$89$	7.74597	+	13.4164i	0.821071	+	1.42214i	0.904886	+	0.425655i	$0.139956\pi$
$89$	7.74597	+	13.4164i	0.821071	+	1.42214i	−0.0838147	+	0.996481i	$0.526710\pi$
$90$		0			0
$91$	−3.00000	+	3.46410i	−0.314485	+	0.363137i
$92$	11.6190	+	6.70820i	1.21136	+	0.699379i
$93$		0			0
$94$			17.3205i			1.78647i
$95$		0			0
$96$		0			0
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	0.421912	−	0.906637i	$-0.361359\pi$
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	−0.574214	+	0.818705i	$0.694692\pi$
$98$	−9.68246	−	12.2984i	−0.978076	−	1.24232i
$99$		0			0
$100$	−7.50000	−	12.9904i	−0.750000	−	1.29904i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	0.705038	−	0.709170i	$-0.250930\pi$
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	−0.261640	+	0.965166i	$0.584263\pi$
$104$	−1.93649	−	3.35410i	−0.189889	−	0.328897i
$105$		0			0
$106$	−5.00000	+	8.66025i	−0.485643	+	0.841158i
$107$	3.87298	−	2.23607i	0.374415	−	0.216169i	−0.300970	−	0.953634i	$-0.597310\pi$
$107$	3.87298	−	2.23607i	0.374415	−	0.216169i	0.675386	+	0.737465i	$0.263977\pi$
$108$		0			0
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$		0			0
$111$		0			0
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	−7.74597	+	4.47214i	−0.728679	+	0.420703i	−0.817939	−	0.575305i	$-0.804883\pi$
$113$	−7.74597	+	4.47214i	−0.728679	+	0.420703i	0.0892596	+	0.996008i	$0.471550\pi$
$114$		0			0
$115$		0			0
$116$	11.6190	+	6.70820i	1.07879	+	0.622841i
$117$		0			0
$118$		−	17.3205i		−	1.59448i
$119$	3.87298	−	20.1246i	0.355036	−	1.84482i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$	19.3649			1.75322
$123$		0			0
$124$		−	5.19615i		−	0.466628i
$125$		0			0
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$		−	15.6525i		−	1.38350i
$129$		0			0
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	−6.00000	+	6.92820i	−0.520266	+	0.600751i
$134$			2.23607i			0.193167i
$135$		0			0
$136$	15.0000	+	8.66025i	1.28624	+	0.742611i
$137$	3.87298	−	2.23607i	0.330891	−	0.191040i	−0.325345	−	0.945595i	$-0.605481\pi$
$137$	3.87298	−	2.23607i	0.330891	−	0.191040i	0.656237	+	0.754555i	$0.272147\pi$
$138$		0			0
$139$	7.50000	−	4.33013i	0.636142	−	0.367277i	−0.146985	−	0.989139i	$-0.546957\pi$
$139$	7.50000	−	4.33013i	0.636142	−	0.367277i	0.783127	+	0.621862i	$0.213624\pi$
$140$		0			0
$141$		0			0
$142$	−20.0000			−1.67836
$143$	−3.87298	+	6.70820i	−0.323875	+	0.560968i
$144$		0			0
$145$		0			0
$146$	7.74597	−	13.4164i	0.641061	−	1.11035i
$147$		0			0
$148$	7.50000	+	12.9904i	0.616496	+	1.06780i
$149$	−15.4919	−	8.94427i	−1.26915	−	0.732743i	−0.294322	−	0.955706i	$-0.595094\pi$
$149$	−15.4919	−	8.94427i	−1.26915	−	0.732743i	−0.974827	+	0.222963i	$0.928427\pi$
$150$		0			0
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	0.999430	+	0.0337724i	$0.0107521\pi$
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	−0.470467	+	0.882418i	$0.655915\pi$
$152$	−3.87298	−	6.70820i	−0.314140	−	0.544107i
$153$		0			0
$154$	−20.0000	−	17.3205i	−1.61165	−	1.39573i
$155$		0			0
$156$		0			0
$157$		−	13.8564i		−	1.10586i	−0.833227	−	0.552931i	$-0.813509\pi$
$157$		−	13.8564i		−	1.10586i	0.833227	−	0.552931i	$-0.186491\pi$
$158$		−	24.5967i		−	1.95681i
$159$		0			0
$160$		0			0
$161$	−11.6190	−	2.23607i	−0.915702	−	0.176227i
$162$		0			0
$163$	6.50000	+	11.2583i	0.509119	+	0.881820i	0.999944	+	0.0105623i	$0.00336213\pi$
$163$	6.50000	+	11.2583i	0.509119	+	0.881820i	−0.490825	+	0.871258i	$0.663305\pi$
$164$	−11.6190	−	20.1246i	−0.907288	−	1.57147i
$165$		0			0
$166$	15.0000	+	8.66025i	1.16423	+	0.672166i
$167$	3.87298	+	6.70820i	0.299700	+	0.519096i	0.976067	−	0.217468i	$-0.0697799\pi$
$167$	3.87298	+	6.70820i	0.299700	+	0.519096i	−0.676367	+	0.736565i	$0.736447\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$		0			0
$172$	−10.5000	+	18.1865i	−0.800617	+	1.38671i
$173$	15.4919			1.17783			0.588915	−	0.808195i	$-0.299555\pi$
$173$	15.4919			1.17783			0.588915	+	0.808195i	$0.299555\pi$
$174$		0			0
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	−3.87298	+	2.23607i	−0.291937	+	0.168550i
$177$		0			0
$178$	30.0000	−	17.3205i	2.24860	−	1.29823i
$179$	7.74597	+	4.47214i	0.578961	+	0.334263i	0.760720	−	0.649080i	$-0.224846\pi$
$179$	7.74597	+	4.47214i	0.578961	+	0.334263i	−0.181760	+	0.983343i	$0.558179\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	7.74597	+	6.70820i	0.574169	+	0.497245i
$183$		0			0
$184$	5.00000	−	8.66025i	0.368605	−	0.638442i
$185$		0			0
$186$		0			0
$187$		−	34.6410i		−	2.53320i
$188$	23.2379			1.69480
$189$		0			0
$190$		0			0
$191$			17.8885i			1.29437i	0.762333	+	0.647185i	$0.224054\pi$
$191$			17.8885i			1.29437i	−0.762333	+	0.647185i	$0.775946\pi$
$192$		0			0
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	−1.93649	+	3.35410i	−0.139032	+	0.240810i
$195$		0			0
$196$	−16.5000	+	12.9904i	−1.17857	+	0.927884i
$197$		−	8.94427i		−	0.637253i	−0.947880	−	0.318626i	$-0.896778\pi$
$197$		−	8.94427i		−	0.637253i	0.947880	−	0.318626i	$-0.103222\pi$
$198$		0			0
$199$	19.5000	+	11.2583i	1.38232	+	0.798082i	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	19.5000	+	11.2583i	1.38232	+	0.798082i	0.389885	+	0.920864i	$0.372515\pi$
$200$	−9.68246	+	5.59017i	−0.684653	+	0.395285i
$201$		0			0
$202$		0			0
$203$	−11.6190	−	2.23607i	−0.815490	−	0.156941i
$204$		0			0
$205$		0			0
$206$	5.80948	−	10.0623i	0.404765	−	0.701074i
$207$		0			0
$208$	1.50000	−	0.866025i	0.104006	−	0.0600481i
$209$	−7.74597	+	13.4164i	−0.535800	+	0.928032i
$210$		0			0
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	0.982142	+	0.188142i	$0.0602466\pi$
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	−0.328135	+	0.944631i	$0.606420\pi$
$212$	11.6190	+	6.70820i	0.797993	+	0.460721i
$213$		0			0
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$		0			0
$216$		0			0
$217$	1.50000	+	4.33013i	0.101827	+	0.293948i
$218$	−1.93649	−	1.11803i	−0.131156	−	0.0757228i
$219$		0			0
$220$		0			0
$221$			13.4164i			0.902485i
$222$		0			0
$223$	21.0000	+	12.1244i	1.40626	+	0.811907i	0.995025	−	0.0996209i	$-0.0317630\pi$
$223$	21.0000	+	12.1244i	1.40626	+	0.811907i	0.411239	+	0.911528i	$0.365096\pi$
$224$	5.80948	+	16.7705i	0.388162	+	1.12053i
$225$		0			0
$226$	10.0000	+	17.3205i	0.665190	+	1.15214i
$227$	11.6190	+	20.1246i	0.771177	+	1.33572i	0.936918	+	0.349548i	$0.113665\pi$
$227$	11.6190	+	20.1246i	0.771177	+	1.33572i	−0.165742	+	0.986169i	$0.553002\pi$
$228$		0			0
$229$	−22.5000	−	12.9904i	−1.48684	−	0.858429i	−0.486954	−	0.873427i	$-0.661892\pi$
$229$	−22.5000	−	12.9904i	−1.48684	−	0.858429i	−0.999888	+	0.0149989i	$0.995226\pi$
$230$		0			0
$231$		0			0
$232$	5.00000	−	8.66025i	0.328266	−	0.568574i
$233$	−7.74597	+	4.47214i	−0.507455	+	0.292979i	−0.731787	−	0.681533i	$-0.761313\pi$
$233$	−7.74597	+	4.47214i	−0.507455	+	0.292979i	0.224332	+	0.974513i	$0.427980\pi$
$234$		0			0
$235$		0			0
$236$	−23.2379			−1.51266
$237$		0			0
$238$	−45.0000	−	8.66025i	−2.91692	−	0.561361i
$239$	−7.74597	+	4.47214i	−0.501045	+	0.289278i	−0.729145	−	0.684359i	$-0.760082\pi$
$239$	−7.74597	+	4.47214i	−0.501045	+	0.289278i	0.228100	+	0.973638i	$0.426749\pi$
$240$		0			0
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.867219	−	0.497927i	$-0.834095\pi$
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.00239235	+	0.999997i	$0.500762\pi$
$242$	−17.4284	−	10.0623i	−1.12034	−	0.646830i
$243$		0			0
$244$		−	25.9808i		−	1.66325i
$245$		0			0
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$	−3.87298			−0.245935
$249$		0			0
$250$		0			0
$251$	−23.2379			−1.46676			−0.733382	−	0.679817i	$-0.762059\pi$
$251$	−23.2379			−1.46676			−0.733382	+	0.679817i	$0.762059\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$			2.23607i			0.140303i
$255$		0			0
$256$	−9.00000			−0.562500
$257$	11.6190	−	20.1246i	0.724770	−	1.25534i	−0.234298	−	0.972165i	$-0.575279\pi$
$257$	11.6190	−	20.1246i	0.724770	−	1.25534i	0.959069	−	0.283174i	$-0.0913874\pi$
$258$		0			0
$259$	−10.0000	−	8.66025i	−0.621370	−	0.538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.87298	−	2.23607i	0.238818	−	0.137882i	−0.375815	−	0.926695i	$-0.622637\pi$
$263$	3.87298	−	2.23607i	0.238818	−	0.137882i	0.614634	+	0.788813i	$0.289304\pi$
$264$		0			0
$265$		0			0
$266$	15.4919	+	13.4164i	0.949871	+	0.822613i
$267$		0			0
$268$	3.00000			0.183254
$269$	−7.74597	+	13.4164i	−0.472280	+	0.818013i	−0.999497	−	0.0317179i	$-0.989902\pi$
$269$	−7.74597	+	13.4164i	−0.472280	+	0.818013i	0.527217	+	0.849731i	$0.323236\pi$
$270$		0			0
$271$	1.50000	−	0.866025i	0.0911185	−	0.0526073i	−0.453748	−	0.891130i	$-0.649914\pi$
$271$	1.50000	−	0.866025i	0.0911185	−	0.0526073i	0.544867	+	0.838523i	$0.316580\pi$
$272$	−3.87298	+	6.70820i	−0.234834	+	0.406745i
$273$		0			0
$274$	−5.00000	−	8.66025i	−0.302061	−	0.523185i
$275$	19.3649	+	11.1803i	1.16775	+	0.674200i
$276$		0			0
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−9.68246	−	16.7705i	−0.580715	−	1.00583i
$279$		0			0
$280$		0			0
$281$	−15.4919	−	8.94427i	−0.924171	−	0.533571i	−0.0392078	−	0.999231i	$-0.512483\pi$
$281$	−15.4919	−	8.94427i	−0.924171	−	0.533571i	−0.884963	+	0.465661i	$0.845817\pi$
$282$		0			0
$283$			12.1244i			0.720718i	0.932814	+	0.360359i	$0.117346\pi$
$283$			12.1244i			0.720718i	−0.932814	+	0.360359i	$0.882654\pi$
$284$			26.8328i			1.59223i
$285$		0			0
$286$	15.0000	+	8.66025i	0.886969	+	0.512092i
$287$	15.4919	+	13.4164i	0.914460	+	0.791946i
$288$		0			0
$289$	−21.5000	−	37.2391i	−1.26471	−	2.19053i
$290$		0			0
$291$		0			0
$292$	−18.0000	−	10.3923i	−1.05337	−	0.608164i
$293$	3.87298	+	6.70820i	0.226262	+	0.391897i	0.956697	−	0.291084i	$-0.0940161\pi$
$293$	3.87298	+	6.70820i	0.226262	+	0.391897i	−0.730435	+	0.682982i	$0.760683\pi$
$294$		0			0
$295$		0			0
$296$	9.68246	−	5.59017i	0.562781	−	0.324922i
$297$		0			0
$298$	−20.0000	+	34.6410i	−1.15857	+	2.00670i
$299$	7.74597			0.447961
$300$		0			0
$301$	3.50000	−	18.1865i	0.201737	−	1.04825i
$302$	25.1744	−	14.5344i	1.44862	−	0.836363i
$303$		0			0
$304$	3.00000	−	1.73205i	0.172062	−	0.0993399i
$305$		0			0
$306$		0			0
$307$			5.19615i			0.296560i	0.988945	+	0.148280i	$0.0473737\pi$
$307$			5.19615i			0.296560i	−0.988945	+	0.148280i	$0.952626\pi$
$308$	−23.2379	+	26.8328i	−1.32410	+	1.52894i
$309$		0			0
$310$		0			0
$311$	−15.4919			−0.878467			−0.439233	−	0.898373i	$-0.644750\pi$
$311$	−15.4919			−0.878467			−0.439233	+	0.898373i	$0.644750\pi$
$312$		0			0
$313$			13.8564i			0.783210i	0.920133	+	0.391605i	$0.128080\pi$
$313$			13.8564i			0.783210i	−0.920133	+	0.391605i	$0.871920\pi$
$314$	−30.9839			−1.74852
$315$		0			0
$316$	−33.0000			−1.85640
$317$			4.47214i			0.251180i	0.992082	+	0.125590i	$0.0400824\pi$
$317$			4.47214i			0.251180i	−0.992082	+	0.125590i	$0.959918\pi$
$318$		0			0
$319$	−20.0000			−1.11979
$320$		0			0
$321$		0			0
$322$	−5.00000	+	25.9808i	−0.278639	+	1.44785i
$323$			26.8328i			1.49302i
$324$		0			0
$325$	−7.50000	−	4.33013i	−0.416025	−	0.240192i
$326$	25.1744	−	14.5344i	1.39428	−	0.804988i
$327$		0			0
$328$	−15.0000	+	8.66025i	−0.828236	+	0.478183i
$329$	−19.3649	+	6.70820i	−1.06762	+	0.369835i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	11.6190	−	20.1246i	0.637673	−	1.10448i
$333$		0			0
$334$	15.0000	−	8.66025i	0.820763	−	0.473868i
$335$		0			0
$336$		0			0
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	0.969468	−	0.245220i	$-0.0788601\pi$
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	−0.697100	+	0.716974i	$0.745527\pi$
$338$	19.3649	+	11.1803i	1.05331	+	0.608130i
$339$		0			0
$340$		0			0
$341$	3.87298	+	6.70820i	0.209734	+	0.363270i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	13.5554	+	7.82624i	0.730860	+	0.421962i
$345$		0			0
$346$		−	34.6410i		−	1.86231i
$347$		−	8.94427i		−	0.480154i	−0.970754	−	0.240077i	$-0.922827\pi$
$347$		−	8.94427i		−	0.480154i	0.970754	−	0.240077i	$-0.0771726\pi$
$348$		0			0
$349$	−19.5000	−	11.2583i	−1.04381	−	0.602645i	−0.122901	−	0.992419i	$-0.539220\pi$
$349$	−19.5000	−	11.2583i	−1.04381	−	0.602645i	−0.920910	+	0.389774i	$0.872553\pi$
$350$	19.3649	−	22.3607i	1.03510	−	1.19523i
$351$		0			0
$352$	15.0000	+	25.9808i	0.799503	+	1.38478i
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$	−23.2379	−	40.2492i	−1.23161	−	2.13320i
$357$		0			0
$358$	10.0000	−	17.3205i	0.528516	−	0.915417i
$359$	3.87298	−	2.23607i	0.204408	−	0.118015i	−0.394302	−	0.918981i	$-0.629014\pi$
$359$	3.87298	−	2.23607i	0.204408	−	0.118015i	0.598710	+	0.800966i	$0.295680\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$		0			0
$363$		0			0
$364$	9.00000	−	10.3923i	0.471728	−	0.544705i
$365$		0			0
$366$		0			0
$367$	9.00000	−	5.19615i	0.469796	−	0.271237i	−0.246358	−	0.969179i	$-0.579234\pi$
$367$	9.00000	−	5.19615i	0.469796	−	0.271237i	0.716154	+	0.697942i	$0.245901\pi$
$368$	3.87298	+	2.23607i	0.201893	+	0.116563i
$369$		0			0
$370$		0			0
$371$	−11.6190	−	2.23607i	−0.603226	−	0.116091i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	−77.4597			−4.00534
$375$		0			0
$376$		−	17.3205i		−	0.893237i
$377$	7.74597			0.398938
$378$		0			0
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$		0			0
$381$		0			0
$382$	40.0000			2.04658
$383$	11.6190	−	20.1246i	0.593701	−	1.02832i	−0.400028	−	0.916503i	$-0.631000\pi$
$383$	11.6190	−	20.1246i	0.593701	−	1.02832i	0.993729	−	0.111817i	$-0.0356670\pi$
$384$		0			0
$385$		0			0
$386$			15.6525i			0.796690i
$387$		0			0
$388$	4.50000	+	2.59808i	0.228453	+	0.131897i
$389$	−7.74597	+	4.47214i	−0.392736	+	0.226746i	−0.683345	−	0.730096i	$-0.739475\pi$
$389$	−7.74597	+	4.47214i	−0.392736	+	0.226746i	0.290609	+	0.956842i	$0.406142\pi$
$390$		0			0
$391$	−30.0000	+	17.3205i	−1.51717	+	0.875936i
$392$	9.68246	+	12.2984i	0.489038	+	0.621162i
$393$		0			0
$394$	−20.0000			−1.00759
$395$		0			0
$396$		0			0
$397$	−25.5000	+	14.7224i	−1.27981	+	0.738898i	−0.976813	−	0.214094i	$-0.931320\pi$
$397$	−25.5000	+	14.7224i	−1.27981	+	0.738898i	−0.302995	+	0.952992i	$0.597987\pi$
$398$	25.1744	−	43.6033i	1.26188	−	2.18564i
$399$		0			0
$400$	−2.50000	−	4.33013i	−0.125000	−	0.216506i
$401$	19.3649	+	11.1803i	0.967038	+	0.558320i	0.898332	−	0.439317i	$-0.144780\pi$
$401$	19.3649	+	11.1803i	0.967038	+	0.558320i	0.0687059	+	0.997637i	$0.478113\pi$
$402$		0			0
$403$	−1.50000	−	2.59808i	−0.0747203	−	0.129419i
$404$		0			0
$405$		0			0
$406$	−5.00000	+	25.9808i	−0.248146	+	1.28940i
$407$	−19.3649	−	11.1803i	−0.959883	−	0.554189i
$408$		0			0
$409$			22.5167i			1.11338i	0.830721	+	0.556689i	$0.187928\pi$
$409$			22.5167i			1.11338i	−0.830721	+	0.556689i	$0.812072\pi$
$410$		0			0
$411$		0			0
$412$	−13.5000	−	7.79423i	−0.665097	−	0.383994i
$413$	19.3649	−	6.70820i	0.952885	−	0.330089i
$414$		0			0
$415$		0			0
$416$	−5.80948	−	10.0623i	−0.284833	−	0.493345i
$417$		0			0
$418$	30.0000	+	17.3205i	1.46735	+	0.847174i
$419$	−7.74597	−	13.4164i	−0.378415	−	0.655434i	0.612417	−	0.790535i	$-0.290198\pi$
$419$	−7.74597	−	13.4164i	−0.378415	−	0.655434i	−0.990832	+	0.135101i	$0.956864\pi$
$420$		0			0
$421$	17.0000	−	29.4449i	0.828529	−	1.43505i	−0.0706626	−	0.997500i	$-0.522511\pi$
$421$	17.0000	−	29.4449i	0.828529	−	1.43505i	0.899192	−	0.437555i	$-0.144155\pi$
$422$	36.7933	−	21.2426i	1.79107	−	1.03408i
$423$		0			0
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$	38.7298			1.87867
$426$		0			0
$427$	7.50000	+	21.6506i	0.362950	+	1.04775i
$428$	−11.6190	+	6.70820i	−0.561623	+	0.324253i
$429$		0			0
$430$		0			0
$431$	−27.1109	−	15.6525i	−1.30589	−	0.753953i	−0.324479	−	0.945893i	$-0.605189\pi$
$431$	−27.1109	−	15.6525i	−1.30589	−	0.753953i	−0.981407	+	0.191940i	$0.938522\pi$
$432$		0			0
$433$		−	15.5885i		−	0.749133i	−0.927200	−	0.374567i	$-0.877791\pi$
$433$		−	15.5885i		−	0.749133i	0.927200	−	0.374567i	$-0.122209\pi$
$434$	9.68246	−	3.35410i	0.464773	−	0.161002i
$435$		0			0
$436$	−1.50000	+	2.59808i	−0.0718370	+	0.124425i
$437$	15.4919			0.741080
$438$		0			0
$439$			3.46410i			0.165333i	0.996577	+	0.0826663i	$0.0263436\pi$
$439$			3.46410i			0.165333i	−0.996577	+	0.0826663i	$0.973656\pi$
$440$		0			0
$441$		0			0
$442$	30.0000			1.42695
$443$		−	35.7771i		−	1.69982i	−0.526927	−	0.849910i	$-0.676656\pi$
$443$		−	35.7771i		−	1.69982i	0.526927	−	0.849910i	$-0.323344\pi$
$444$		0			0
$445$		0			0
$446$	27.1109	−	46.9574i	1.28374	−	2.22350i
$447$		0			0
$448$	32.5000	−	11.2583i	1.53548	−	0.531906i
$449$		−	8.94427i		−	0.422106i	−0.977475	−	0.211053i	$-0.932311\pi$
$449$		−	8.94427i		−	0.422106i	0.977475	−	0.211053i	$-0.0676893\pi$
$450$		0			0
$451$	30.0000	+	17.3205i	1.41264	+	0.815591i
$452$	23.2379	−	13.4164i	1.09302	−	0.631055i
$453$		0			0
$454$	45.0000	−	25.9808i	2.11195	−	1.21934i
$455$		0			0
$456$		0			0
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	−29.0474	+	50.3115i	−1.35729	+	2.35090i
$459$		0			0
$460$		0			0
$461$	−3.87298	+	6.70820i	−0.180383	+	0.312432i	−0.942011	−	0.335582i	$-0.891067\pi$
$461$	−3.87298	+	6.70820i	−0.180383	+	0.312432i	0.761628	+	0.648014i	$0.224400\pi$
$462$		0			0
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	0.757982	−	0.652275i	$-0.226185\pi$
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	−0.943878	+	0.330294i	$0.892852\pi$
$464$	3.87298	+	2.23607i	0.179799	+	0.103807i
$465$		0			0
$466$	10.0000	+	17.3205i	0.463241	+	0.802357i
$467$	−15.4919	−	26.8328i	−0.716881	−	1.24167i	−0.962229	−	0.272240i	$-0.912236\pi$
$467$	−15.4919	−	26.8328i	−0.716881	−	1.24167i	0.245348	−	0.969435i	$-0.421098\pi$
$468$		0			0
$469$	−2.50000	+	0.866025i	−0.115439	+	0.0399893i
$470$		0			0
$471$		0			0
$472$			17.3205i			0.797241i
$473$		−	31.3050i		−	1.43940i
$474$		0			0
$475$	−15.0000	−	8.66025i	−0.688247	−	0.397360i
$476$	−11.6190	+	60.3738i	−0.532554	+	2.76723i
$477$		0			0
$478$	10.0000	+	17.3205i	0.457389	+	0.792222i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	7.50000	+	4.33013i	0.341971	+	0.197437i
$482$	17.4284	+	30.1869i	0.793843	+	1.37498i
$483$		0			0
$484$	−13.5000	+	23.3827i	−0.613636	+	1.06285i
$485$		0			0
$486$		0			0
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.0871056	−	0.996199i	$-0.472238\pi$
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.819181	−	0.573535i	$-0.194428\pi$
$488$	−19.3649			−0.876609
$489$		0			0
$490$		0			0
$491$	−19.3649	+	11.1803i	−0.873926	+	0.504562i	−0.868651	−	0.495424i	$-0.835013\pi$
$491$	−19.3649	+	11.1803i	−0.873926	+	0.504562i	−0.00527540	+	0.999986i	$0.501679\pi$
$492$		0			0
$493$	−30.0000	+	17.3205i	−1.35113	+	0.780076i
$494$	−11.6190	−	6.70820i	−0.522761	−	0.301816i
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	−7.74597	−	22.3607i	−0.347454	−	1.00301i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$		0			0
$501$		0			0
$502$			51.9615i			2.31916i
$503$	23.2379			1.03613			0.518063	−	0.855342i	$-0.326653\pi$
$503$	23.2379			1.03613			0.518063	+	0.855342i	$0.326653\pi$
$504$		0			0
$505$		0			0
$506$			44.7214i			1.98811i
$507$		0			0
$508$	3.00000			0.133103
$509$	−11.6190	+	20.1246i	−0.515001	+	0.892008i	0.484848	+	0.874599i	$0.338875\pi$
$509$	−11.6190	+	20.1246i	−0.515001	+	0.892008i	−0.999848	+	0.0174091i	$0.994458\pi$
$510$		0			0
$511$	18.0000	+	3.46410i	0.796273	+	0.153243i
$512$		−	11.1803i		−	0.494106i
$513$		0			0
$514$	−45.0000	−	25.9808i	−1.98486	−	1.14596i
$515$		0			0
$516$		0			0
$517$	−30.0000	+	17.3205i	−1.31940	+	0.761755i
$518$	−19.3649	+	22.3607i	−0.850846	+	0.982472i
$519$		0			0
$520$		0			0
$521$	3.87298	−	6.70820i	0.169678	−	0.293892i	−0.768628	−	0.639696i	$-0.779060\pi$
$521$	3.87298	−	6.70820i	0.169678	−	0.293892i	0.938307	+	0.345804i	$0.112394\pi$
$522$		0			0
$523$	−16.5000	+	9.52628i	−0.721495	+	0.416555i	−0.815303	−	0.579035i	$-0.803429\pi$
$523$	−16.5000	+	9.52628i	−0.721495	+	0.416555i	0.0938079	+	0.995590i	$0.470096\pi$
$524$		0			0
$525$		0			0
$526$	−5.00000	−	8.66025i	−0.218010	−	0.377605i
$527$	11.6190	+	6.70820i	0.506129	+	0.292214i
$528$		0			0
$529$	−1.50000	−	2.59808i	−0.0652174	−	0.112960i
$530$		0			0
$531$		0			0
$532$	18.0000	−	20.7846i	0.780399	−	0.901127i
$533$	−11.6190	−	6.70820i	−0.503273	−	0.290565i
$534$		0			0
$535$		0			0
$536$		−	2.23607i		−	0.0965834i
$537$		0			0
$538$	30.0000	+	17.3205i	1.29339	+	0.746740i
$539$	11.6190	−	29.0689i	0.500464	−	1.25209i
$540$		0			0
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	0.675399	−	0.737453i	$-0.263972\pi$
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	−0.976352	+	0.216186i	$0.930638\pi$
$542$	−1.93649	−	3.35410i	−0.0831794	−	0.144071i
$543$		0			0
$544$	45.0000	+	25.9808i	1.92936	+	1.11392i
$545$		0			0
$546$		0			0
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	−11.6190	+	6.70820i	−0.496337	+	0.286560i
$549$		0			0
$550$	25.0000	−	43.3013i	1.06600	−	1.84637i
$551$	15.4919			0.659979
$552$		0			0
$553$	27.5000	−	9.52628i	1.16942	−	0.405099i
$554$	−9.68246	+	5.59017i	−0.411368	+	0.237504i
$555$		0			0
$556$	−22.5000	+	12.9904i	−0.954213	+	0.550915i
$557$	30.9839	+	17.8885i	1.31283	+	0.757962i	0.982564	−	0.185926i	$-0.0595286\pi$
$557$	30.9839	+	17.8885i	1.31283	+	0.757962i	0.330265	+	0.943888i	$0.392862\pi$
$558$		0			0
$559$			12.1244i			0.512806i
$560$		0			0
$561$		0			0
$562$	−20.0000	+	34.6410i	−0.843649	+	1.46124i
$563$	7.74597			0.326454			0.163227	−	0.986589i	$-0.447810\pi$
$563$	7.74597			0.326454			0.163227	+	0.986589i	$0.447810\pi$
$564$		0			0
$565$		0			0
$566$	27.1109			1.13956
$567$		0			0
$568$	20.0000			0.839181
$569$			17.8885i			0.749927i	0.927040	+	0.374963i	$0.122345\pi$
$569$			17.8885i			0.749927i	−0.927040	+	0.374963i	$0.877655\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	11.6190	−	20.1246i	0.485813	−	0.841452i
$573$		0			0
$574$	30.0000	−	34.6410i	1.25218	−	1.44589i
$575$		−	22.3607i		−	0.932505i
$576$		0			0
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.438667	−	0.898650i	$-0.644549\pi$
$577$	−34.5000	−	19.9186i	−1.43625	−	0.829222i	−0.997587	+	0.0694283i	$0.977883\pi$
$578$	−83.2691	+	48.0755i	−3.46354	+	1.99968i
$579$		0			0
$580$		0			0
$581$	−3.87298	+	20.1246i	−0.160678	+	0.834910i
$582$		0			0
$583$	−20.0000			−0.828315
$584$	−7.74597	+	13.4164i	−0.320530	+	0.555175i
$585$		0			0
$586$	15.0000	−	8.66025i	0.619644	−	0.357752i
$587$	−15.4919	+	26.8328i	−0.639421	+	1.10751i	0.346140	+	0.938183i	$0.387492\pi$
$587$	−15.4919	+	26.8328i	−0.639421	+	1.10751i	−0.985560	+	0.169326i	$0.945841\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$		0			0
$591$		0			0
$592$	2.50000	+	4.33013i	0.102749	+	0.177967i
$593$	−15.4919	−	26.8328i	−0.636177	−	1.10189i	−0.986264	−	0.165174i	$-0.947181\pi$
$593$	−15.4919	−	26.8328i	−0.636177	−	1.10189i	0.350087	−	0.936717i	$-0.386152\pi$
$594$		0			0
$595$		0			0
$596$	46.4758	+	26.8328i	1.90372	+	1.09911i
$597$		0			0
$598$		−	17.3205i		−	0.708288i
$599$		−	8.94427i		−	0.365453i	−0.983164	−	0.182727i	$-0.941508\pi$
$599$		−	8.94427i		−	0.365453i	0.983164	−	0.182727i	$-0.0584923\pi$
$600$		0			0
$601$	−37.5000	−	21.6506i	−1.52966	−	0.883148i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−37.5000	−	21.6506i	−1.52966	−	0.883148i	−0.530281	−	0.847822i	$-0.677914\pi$
$602$	−40.6663	−	7.82624i	−1.65744	−	0.318974i
$603$		0			0
$604$	−19.5000	−	33.7750i	−0.793444	−	1.37428i
$605$		0			0
$606$		0			0
$607$	−27.0000	−	15.5885i	−1.09590	−	0.632716i	−0.160756	−	0.986994i	$-0.551393\pi$
$607$	−27.0000	−	15.5885i	−1.09590	−	0.632716i	−0.935140	+	0.354278i	$0.884727\pi$
$608$	−11.6190	−	20.1246i	−0.471211	−	0.816161i
$609$		0			0
$610$		0			0
$611$	11.6190	−	6.70820i	0.470052	−	0.271385i
$612$		0			0
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$	11.6190			0.468903
$615$		0			0
$616$	20.0000	+	17.3205i	0.805823	+	0.697863i
$617$	−19.3649	+	11.1803i	−0.779602	+	0.450104i	−0.836289	−	0.548288i	$-0.815280\pi$
$617$	−19.3649	+	11.1803i	−0.779602	+	0.450104i	0.0566871	+	0.998392i	$0.481946\pi$
$618$		0			0
$619$	−4.50000	+	2.59808i	−0.180870	+	0.104425i	−0.587701	−	0.809078i	$-0.699967\pi$
$619$	−4.50000	+	2.59808i	−0.180870	+	0.104425i	0.406831	+	0.913503i	$0.366634\pi$
$620$		0			0
$621$		0			0
$622$			34.6410i			1.38898i
$623$	30.9839	+	26.8328i	1.24134	+	1.07503i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	30.9839			1.23836
$627$		0			0
$628$			41.5692i			1.65879i
$629$	−38.7298			−1.54426
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$			24.5967i			0.978406i
$633$		0			0
$634$	10.0000			0.397151
$635$		0			0
$636$		0			0
$637$	−4.50000	+	11.2583i	−0.178296	+	0.446071i
$638$			44.7214i			1.77054i
$639$		0			0
$640$		0			0
$641$	3.87298	−	2.23607i	0.152974	−	0.0883194i	−0.421559	−	0.906801i	$-0.638517\pi$
$641$	3.87298	−	2.23607i	0.152974	−	0.0883194i	0.574533	+	0.818481i	$0.305184\pi$
$642$		0			0
$643$	16.5000	−	9.52628i	0.650696	−	0.375680i	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	16.5000	−	9.52628i	0.650696	−	0.375680i	0.788723	+	0.614749i	$0.210743\pi$
$644$	34.8569	+	6.70820i	1.37355	+	0.264340i
$645$		0			0
$646$	60.0000			2.36067
$647$	−7.74597	+	13.4164i	−0.304525	+	0.527453i	−0.977156	−	0.212525i	$-0.931831\pi$
$647$	−7.74597	+	13.4164i	−0.304525	+	0.527453i	0.672630	+	0.739979i	$0.265165\pi$
$648$		0			0
$649$	30.0000	−	17.3205i	1.17760	−	0.679889i
$650$	−9.68246	+	16.7705i	−0.379777	+	0.657794i
$651$		0			0
$652$	−19.5000	−	33.7750i	−0.763679	−	1.32273i
$653$	19.3649	+	11.1803i	0.757808	+	0.437521i	0.828508	−	0.559977i	$-0.189190\pi$
$653$	19.3649	+	11.1803i	0.757808	+	0.437521i	−0.0707003	+	0.997498i	$0.522523\pi$
$654$		0			0
$655$		0			0
$656$	−3.87298	−	6.70820i	−0.151215	−	0.261911i
$657$		0			0
$658$	15.0000	+	43.3013i	0.584761	+	1.68806i
$659$	−15.4919	−	8.94427i	−0.603480	−	0.348419i	0.166929	−	0.985969i	$-0.446615\pi$
$659$	−15.4919	−	8.94427i	−0.603480	−	0.348419i	−0.770409	+	0.637549i	$0.779948\pi$
$660$		0			0
$661$			27.7128i			1.07790i	0.842337	+	0.538952i	$0.181179\pi$
$661$			27.7128i			1.07790i	−0.842337	+	0.538952i	$0.818821\pi$
$662$			8.94427i			0.347629i
$663$		0			0
$664$	−15.0000	−	8.66025i	−0.582113	−	0.336083i
$665$		0			0
$666$		0			0
$667$	10.0000	+	17.3205i	0.387202	+	0.670653i
$668$	−11.6190	−	20.1246i	−0.449551	−	0.778645i
$669$		0			0
$670$		0			0
$671$	19.3649	+	33.5410i	0.747574	+	1.29484i
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	19.3649	−	11.1803i	0.745909	−	0.430651i
$675$		0			0
$676$	15.0000	−	25.9808i	0.576923	−	0.999260i
$677$	−30.9839			−1.19081			−0.595403	−	0.803427i	$-0.703008\pi$
$677$	−30.9839			−1.19081			−0.595403	+	0.803427i	$0.703008\pi$
$678$		0			0
$679$	−4.50000	−	0.866025i	−0.172694	−	0.0332350i
$680$		0			0
$681$		0			0
$682$	15.0000	−	8.66025i	0.574380	−	0.331618i
$683$	30.9839	+	17.8885i	1.18556	+	0.684486i	0.957295	−	0.289112i	$-0.0933600\pi$
$683$	30.9839	+	17.8885i	1.18556	+	0.684486i	0.228269	+	0.973598i	$0.426693\pi$
$684$		0			0
$685$		0			0
$686$	−34.8569	−	22.3607i	−1.33084	−	0.853735i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	7.74597			0.295098
$690$		0			0
$691$		−	32.9090i		−	1.25192i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$		−	32.9090i		−	1.25192i	0.779857	−	0.625958i	$-0.215292\pi$
$692$	−46.4758			−1.76674
$693$		0			0
$694$	−20.0000			−0.759190
$695$		0			0
$696$		0			0
$697$	60.0000			2.27266
$698$	−25.1744	+	43.6033i	−0.952865	+	1.65041i
$699$		0			0
$700$	−30.0000	−	25.9808i	−1.13389	−	0.981981i
$701$		−	8.94427i		−	0.337820i	−0.985631	−	0.168910i	$-0.945975\pi$
$701$		−	8.94427i		−	0.337820i	0.985631	−	0.168910i	$-0.0540248\pi$
$702$		0			0
$703$	15.0000	+	8.66025i	0.565736	+	0.326628i
$704$	50.3488	−	29.0689i	1.89759	−	1.09557i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	11.0000			0.413114			0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000			0.413114			0.206557	+	0.978435i	$0.433774\pi$
$710$		0			0
$711$		0			0
$712$	−30.0000	+	17.3205i	−1.12430	+	0.649113i
$713$	3.87298	−	6.70820i	0.145044	−	0.251224i
$714$		0			0
$715$		0			0
$716$	−23.2379	−	13.4164i	−0.868441	−	0.501395i
$717$		0			0
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	7.74597	+	13.4164i	0.288876	+	0.500348i	0.973542	−	0.228509i	$-0.0733852\pi$
$719$	7.74597	+	13.4164i	0.288876	+	0.500348i	−0.684666	+	0.728857i	$0.740052\pi$
$720$		0			0
$721$	13.5000	+	2.59808i	0.502766	+	0.0967574i
$722$	13.5554	+	7.82624i	0.504481	+	0.291262i
$723$		0			0
$724$		0			0
$725$		−	22.3607i		−	0.830455i
$726$		0			0
$727$	16.5000	+	9.52628i	0.611951	+	0.353310i	0.773729	−	0.633517i	$-0.218389\pi$
$727$	16.5000	+	9.52628i	0.611951	+	0.353310i	−0.161778	+	0.986827i	$0.551723\pi$
$728$	−7.74597	−	6.70820i	−0.287085	−	0.248623i
$729$		0			0
$730$		0			0
$731$	−27.1109	−	46.9574i	−1.00273	−	1.73678i
$732$		0			0
$733$	−31.5000	−	18.1865i	−1.16348	−	0.671735i	−0.211344	−	0.977412i	$-0.567784\pi$
$733$	−31.5000	−	18.1865i	−1.16348	−	0.671735i	−0.952135	+	0.305677i	$0.901117\pi$
$734$	−11.6190	−	20.1246i	−0.428863	−	0.742813i
$735$		0			0
$736$	15.0000	−	25.9808i	0.552907	−	0.957664i
$737$	−3.87298	+	2.23607i	−0.142663	+	0.0823666i
$738$		0			0
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	−0.996235	−	0.0866983i	$-0.972368\pi$
$739$	−11.5000	+	19.9186i	−0.423034	+	0.732717i	0.573200	+	0.819415i	$0.305702\pi$
$740$		0			0
$741$		0			0
$742$	−5.00000	+	25.9808i	−0.183556	+	0.953784i
$743$	27.1109	−	15.6525i	0.994602	−	0.574234i	0.0879552	−	0.996124i	$-0.471967\pi$
$743$	27.1109	−	15.6525i	0.994602	−	0.574234i	0.906647	+	0.421891i	$0.138633\pi$
$744$		0			0
$745$		0			0
$746$	3.87298	+	2.23607i	0.141800	+	0.0818683i
$747$		0			0
$748$			103.923i			3.79980i
$749$	7.74597	−	8.94427i	0.283031	−	0.326817i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	7.74597			0.282466
$753$		0			0
$754$		−	17.3205i		−	0.630776i
$755$		0			0
$756$		0			0
$757$	−25.0000			−0.908640			−0.454320	−	0.890838i	$-0.650118\pi$
$757$	−25.0000			−0.908640			−0.454320	+	0.890838i	$0.650118\pi$
$758$		−	38.0132i		−	1.38070i
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		0			0
$763$	0.500000	−	2.59808i	0.0181012	−	0.0940567i
$764$		−	53.6656i		−	1.94155i
$765$		0			0
$766$	−45.0000	−	25.9808i	−1.62592	−	0.938723i
$767$	−11.6190	+	6.70820i	−0.419536	+	0.242219i
$768$		0			0
$769$	30.0000	−	17.3205i	1.08183	−	0.624593i	0.150439	−	0.988619i	$-0.451931\pi$
$769$	30.0000	−	17.3205i	1.08183	−	0.624593i	0.931389	+	0.364026i	$0.118598\pi$
$770$		0			0
$771$		0			0
$772$	21.0000			0.755807
$773$	15.4919	−	26.8328i	0.557206	−	0.965109i	−0.440522	−	0.897742i	$-0.645207\pi$
$773$	15.4919	−	26.8328i	0.557206	−	0.965109i	0.997728	−	0.0673675i	$-0.0214600\pi$
$774$		0			0
$775$	−7.50000	+	4.33013i	−0.269408	+	0.155543i
$776$	1.93649	−	3.35410i	0.0695160	−	0.120405i
$777$		0			0
$778$	10.0000	+	17.3205i	0.358517	+	0.620970i
$779$	−23.2379	−	13.4164i	−0.832584	−	0.480693i
$780$		0			0
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$	38.7298	+	67.0820i	1.38498	+	2.39885i
$783$		0			0
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$		0			0
$787$		−	19.0526i		−	0.679150i	−0.940579	−	0.339575i	$-0.889717\pi$
$787$		−	19.0526i		−	0.679150i	0.940579	−	0.339575i	$-0.110283\pi$
$788$			26.8328i			0.955879i
$789$		0			0
$790$		0			0
$791$	−15.4919	+	17.8885i	−0.550830	+	0.636043i
$792$		0			0
$793$	−7.50000	−	12.9904i	−0.266333	−	0.461302i
$794$	32.9204	+	57.0197i	1.16830	+	2.02355i
$795$		0			0
$796$	−58.5000	−	33.7750i	−2.07348	−	1.19712i
$797$	−19.3649	−	33.5410i	−0.685941	−	1.18808i	−0.973140	−	0.230213i	$-0.926058\pi$
$797$	−19.3649	−	33.5410i	−0.685941	−	1.18808i	0.287200	−	0.957871i	$-0.407276\pi$
$798$		0			0
$799$	−30.0000	+	51.9615i	−1.06132	+	1.83827i
$800$	−29.0474	+	16.7705i	−1.02698	+	0.592927i
$801$		0			0
$802$	25.0000	−	43.3013i	0.882781	−	1.52902i
$803$	30.9839			1.09340
$804$		0			0
$805$		0			0
$806$	−5.80948	+	3.35410i	−0.204630	+	0.118143i
$807$		0			0
$808$		0			0
$809$	−3.87298	−	2.23607i	−0.136167	−	0.0786160i	0.430369	−	0.902653i	$-0.358383\pi$
$809$	−3.87298	−	2.23607i	−0.136167	−	0.0786160i	−0.566536	+	0.824037i	$0.691717\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	34.8569	+	6.70820i	1.22324	+	0.235412i
$813$		0			0
$814$	−25.0000	+	43.3013i	−0.876250	+	1.51771i
$815$		0			0
$816$		0			0
$817$			24.2487i			0.848355i
$818$	50.3488			1.76040
$819$		0			0
$820$		0			0
$821$		−	22.3607i		−	0.780393i	−0.920732	−	0.390197i	$-0.872407\pi$
$821$		−	22.3607i		−	0.780393i	0.920732	−	0.390197i	$-0.127593\pi$
$822$		0			0
$823$	−43.0000			−1.49889			−0.749443	−	0.662069i	$-0.769679\pi$
$823$	−43.0000			−1.49889			−0.749443	+	0.662069i	$0.769679\pi$
$824$	−5.80948	+	10.0623i	−0.202383	+	0.350537i
$825$		0			0
$826$	−15.0000	−	43.3013i	−0.521917	−	1.50664i
$827$		−	8.94427i		−	0.311023i	−0.987834	−	0.155511i	$-0.950297\pi$
$827$		−	8.94427i		−	0.311023i	0.987834	−	0.155511i	$-0.0497025\pi$
$828$		0			0
$829$	−12.0000	−	6.92820i	−0.416777	−	0.240626i	0.276920	−	0.960893i	$-0.410686\pi$
$829$	−12.0000	−	6.92820i	−0.416777	−	0.240626i	−0.693698	+	0.720266i	$0.744020\pi$
$830$		0			0
$831$		0			0
$832$	−19.5000	+	11.2583i	−0.676041	+	0.390312i
$833$	−7.74597	−	53.6656i	−0.268382	−	1.85940i
$834$		0			0
$835$		0			0
$836$	23.2379	−	40.2492i	0.803700	−	1.39205i
$837$		0			0
$838$	−30.0000	+	17.3205i	−1.03633	+	0.598327i
$839$	−3.87298	+	6.70820i	−0.133710	+	0.231593i	−0.925104	−	0.379714i	$-0.876022\pi$
$839$	−3.87298	+	6.70820i	−0.133710	+	0.231593i	0.791394	+	0.611307i	$0.209356\pi$
$840$		0			0
$841$	−4.50000	−	7.79423i	−0.155172	−	0.268767i
$842$	−65.8407	−	38.0132i	−2.26902	−	1.31002i
$843$		0			0
$844$	−28.5000	−	49.3634i	−0.981010	−	1.69916i
$845$		0			0
$846$		0			0
$847$	4.50000	−	23.3827i	0.154622	−	0.803439i
$848$	3.87298	+	2.23607i	0.132999	+	0.0767869i
$849$		0			0
$850$		−	86.6025i		−	2.97044i
$851$			22.3607i			0.766514i
$852$		0			0
$853$	12.0000	+	6.92820i	0.410872	+	0.237217i	0.691164	−	0.722698i	$-0.257098\pi$
$853$	12.0000	+	6.92820i	0.410872	+	0.237217i	−0.280292	+	0.959915i	$0.590431\pi$
$854$	48.4123	−	16.7705i	1.65663	−	0.573875i
$855$		0			0
$856$	5.00000	+	8.66025i	0.170896	+	0.296001i
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	−4.50000	−	2.59808i	−0.153538	−	0.0886452i	0.421263	−	0.906939i	$-0.361587\pi$
$859$	−4.50000	−	2.59808i	−0.153538	−	0.0886452i	−0.574801	+	0.818293i	$0.694920\pi$
$860$		0			0
$861$		0			0
$862$	−35.0000	+	60.6218i	−1.19210	+	2.06479i
$863$	−30.9839	+	17.8885i	−1.05470	+	0.608933i	−0.923962	−	0.382483i	$-0.875069\pi$
$863$	−30.9839	+	17.8885i	−1.05470	+	0.608933i	−0.130741	+	0.991417i	$0.541736\pi$
$864$		0			0
$865$		0			0
$866$	−34.8569			−1.18448
$867$		0			0
$868$	−4.50000	−	12.9904i	−0.152740	−	0.440922i
$869$	42.6028	−	24.5967i	1.44520	−	0.834388i
$870$		0			0
$871$	1.50000	−	0.866025i	0.0508256	−	0.0293442i
$872$	1.93649	+	1.11803i	0.0655779	+	0.0378614i
$873$		0			0
$874$		−	34.6410i		−	1.17175i
$875$		0			0
$876$		0			0
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	7.74597			0.261414
$879$		0			0
$880$		0			0
$881$	23.2379			0.782905			0.391452	−	0.920198i	$-0.371973\pi$
$881$	23.2379			0.782905			0.391452	+	0.920198i	$0.371973\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		−	40.2492i		−	1.35373i
$885$		0			0
$886$	−80.0000			−2.68765
$887$	−11.6190	+	20.1246i	−0.390126	+	0.675718i	−0.992466	−	0.122522i	$-0.960902\pi$
$887$	−11.6190	+	20.1246i	−0.390126	+	0.675718i	0.602340	+	0.798240i	$0.294235\pi$
$888$		0			0
$889$	−2.50000	+	0.866025i	−0.0838473	+	0.0290456i
$890$		0			0
$891$		0			0
$892$	−63.0000	−	36.3731i	−2.10940	−	1.21786i
$893$	23.2379	−	13.4164i	0.777627	−	0.448963i
$894$		0			0
$895$		0			0
$896$	−13.5554	−	39.1312i	−0.452856	−	1.30728i
$897$		0			0
$898$	−20.0000			−0.667409
$899$	3.87298	−	6.70820i	0.129171	−	0.223731i
$900$		0			0
$901$	−30.0000	+	17.3205i	−0.999445	+	0.577030i
$902$	38.7298	−	67.0820i	1.28956	−	2.23359i
$903$		0			0
$904$	−10.0000	−	17.3205i	−0.332595	−	0.576072i
$905$		0			0
$906$		0			0
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	−34.8569	−	60.3738i	−1.15677	−	2.00358i
$909$		0			0
$910$		0			0
$911$	−3.87298	−	2.23607i	−0.128318	−	0.0740842i	0.434467	−	0.900688i	$-0.356937\pi$
$911$	−3.87298	−	2.23607i	−0.128318	−	0.0740842i	−0.562785	+	0.826603i	$0.690270\pi$
$912$		0			0
$913$			34.6410i			1.14645i
$914$		−	24.5967i		−	0.813588i
$915$		0			0
$916$	67.5000	+	38.9711i	2.23026	+	1.28764i
$917$		0			0
$918$		0			0
$919$	6.50000	+	11.2583i	0.214415	+	0.371378i	0.953092	−	0.302682i	$-0.0978821\pi$
$919$	6.50000	+	11.2583i	0.214415	+	0.371378i	−0.738676	+	0.674060i	$0.764549\pi$
$920$		0			0
$921$		0			0
$922$	15.0000	+	8.66025i	0.493999	+	0.285210i
$923$	7.74597	+	13.4164i	0.254962	+	0.441606i
$924$		0			0
$925$	12.5000	−	21.6506i	0.410997	−	0.711868i
$926$	−15.4919	+	8.94427i	−0.509097	+	0.293927i
$927$		0			0
$928$	15.0000	−	25.9808i	0.492399	−	0.852860i
$929$	−30.9839			−1.01655			−0.508274	−	0.861196i	$-0.669716\pi$
$929$	−30.9839			−1.01655			−0.508274	+	0.861196i	$0.669716\pi$
$930$		0			0
$931$	−9.00000	+	22.5167i	−0.294963	+	0.737954i
$932$	23.2379	−	13.4164i	0.761183	−	0.439469i
$933$		0			0
$934$	−60.0000	+	34.6410i	−1.96326	+	1.13349i
$935$		0			0
$936$		0			0
$937$			46.7654i			1.52776i	0.645359	+	0.763879i	$0.276708\pi$
$937$			46.7654i			1.52776i	−0.645359	+	0.763879i	$0.723292\pi$
$938$	1.93649	+	5.59017i	0.0632287	+	0.182526i
$939$		0			0
$940$		0			0
$941$	−38.7298			−1.26256			−0.631278	−	0.775556i	$-0.717469\pi$
$941$	−38.7298			−1.26256			−0.631278	+	0.775556i	$0.717469\pi$
$942$		0			0
$943$		−	34.6410i		−	1.12807i
$944$	−7.74597			−0.252110
$945$		0			0
$946$	−70.0000			−2.27590
$947$			4.47214i			0.145325i	0.997357	+	0.0726624i	$0.0231496\pi$
$947$			4.47214i			0.145325i	−0.997357	+	0.0726624i	$0.976850\pi$
$948$		0			0
$949$	−12.0000			−0.389536
$950$	−19.3649	+	33.5410i	−0.628281	+	1.08821i
$951$		0			0
$952$	45.0000	+	8.66025i	1.45846	+	0.280680i
$953$			58.1378i			1.88327i	0.336640	+	0.941634i	$0.390710\pi$
$953$			58.1378i			1.88327i	−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$		0			0
$956$	23.2379	−	13.4164i	0.751567	−	0.433918i
$957$		0			0
$958$		0			0
$959$	7.74597	−	8.94427i	0.250130	−	0.288826i
$960$		0			0
$961$	28.0000			0.903226
$962$	9.68246	−	16.7705i	0.312175	−	0.540703i
$963$		0			0
$964$	40.5000	−	23.3827i	1.30442	−	0.753106i
$965$		0			0
$966$		0			0
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	0.993964	−	0.109707i	$-0.0349913\pi$
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	−0.591991	+	0.805945i	$0.701658\pi$
$968$	17.4284	+	10.0623i	0.560171	+	0.323415i
$969$		0			0
$970$		0			0
$971$	30.9839	+	53.6656i	0.994320	+	1.72221i	0.589336	+	0.807888i	$0.299390\pi$
$971$	30.9839	+	53.6656i	0.994320	+	1.72221i	0.404984	+	0.914324i	$0.367277\pi$
$972$		0			0
$973$	15.0000	−	17.3205i	0.480878	−	0.555270i
$974$	−77.4597	−	44.7214i	−2.48197	−	1.43296i
$975$		0			0
$976$		−	8.66025i		−	0.277208i
$977$			58.1378i			1.85999i	0.367570	+	0.929996i	$0.380190\pi$
$977$			58.1378i			1.85999i	−0.367570	+	0.929996i	$0.619810\pi$
$978$		0			0
$979$	60.0000	+	34.6410i	1.91761	+	1.10713i
$980$		0			0
$981$		0			0
$982$	25.0000	+	43.3013i	0.797782	+	1.38180i
$983$	23.2379	+	40.2492i	0.741174	+	1.28375i	0.951961	+	0.306219i	$0.0990639\pi$
$983$	23.2379	+	40.2492i	0.741174	+	1.28375i	−0.210787	+	0.977532i	$0.567603\pi$
$984$		0			0
$985$		0			0
$986$	38.7298	+	67.0820i	1.23341	+	2.13633i
$987$		0			0
$988$	−9.00000	+	15.5885i	−0.286328	+	0.495935i
$989$	−27.1109	+	15.6525i	−0.862076	+	0.497720i
$990$		0			0
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	−0.154671	−	0.987966i	$-0.549432\pi$
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	0.932939	−	0.360034i	$-0.117235\pi$
$992$	−11.6190			−0.368902
$993$		0			0
$994$	−50.0000	+	17.3205i	−1.58590	+	0.549373i
$995$		0			0
$996$		0			0
$997$	40.5000	−	23.3827i	1.28265	−	0.740537i	0.305316	−	0.952251i	$-0.401238\pi$
$997$	40.5000	−	23.3827i	1.28265	−	0.740537i	0.977332	+	0.211714i	$0.0679045\pi$
$998$	−60.0312	−	34.6591i	−1.90026	−	1.09711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.i.c.269.1		4
3.2	odd	2	inner	567.2.i.c.269.2		4
7.5	odd	6		567.2.s.e.26.1		4
9.2	odd	6		189.2.p.c.80.2	yes	4
9.4	even	3		567.2.s.e.458.2		4
9.5	odd	6		567.2.s.e.458.1		4
9.7	even	3		189.2.p.c.80.1	yes	4
21.5	even	6		567.2.s.e.26.2		4
63.5	even	6	inner	567.2.i.c.215.2		4
63.11	odd	6		1323.2.c.b.1322.3		4
63.25	even	3		1323.2.c.b.1322.1		4
63.38	even	6		1323.2.c.b.1322.4		4
63.40	odd	6	inner	567.2.i.c.215.1		4
63.47	even	6		189.2.p.c.26.1	✓	4
63.52	odd	6		1323.2.c.b.1322.2		4
63.61	odd	6		189.2.p.c.26.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.c.26.1	✓	4	63.47	even	6
189.2.p.c.26.2	yes	4	63.61	odd	6
189.2.p.c.80.1	yes	4	9.7	even	3
189.2.p.c.80.2	yes	4	9.2	odd	6
567.2.i.c.215.1		4	63.40	odd	6	inner
567.2.i.c.215.2		4	63.5	even	6	inner
567.2.i.c.269.1		4	1.1	even	1	trivial
567.2.i.c.269.2		4	3.2	odd	2	inner
567.2.s.e.26.1		4	7.5	odd	6
567.2.s.e.26.2		4	21.5	even	6
567.2.s.e.458.1		4	9.5	odd	6
567.2.s.e.458.2		4	9.4	even	3
1323.2.c.b.1322.1		4	63.25	even	3
1323.2.c.b.1322.2		4	63.52	odd	6
1323.2.c.b.1322.3		4	63.11	odd	6
1323.2.c.b.1322.4		4	63.38	even	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} +2.23607i q^{8} +O(q^{10})\)	\(q-2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} +2.23607i q^{8} +(3.87298 - 2.23607i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(-1.93649 - 5.59017i) q^{14} -1.00000 q^{16} +(3.87298 - 6.70820i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} +(-3.87298 - 2.23607i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.93649 + 3.35410i) q^{26} +(-7.50000 + 2.59808i) q^{28} +(-3.87298 - 2.23607i) q^{29} +1.73205i q^{31} +6.70820i q^{32} +(-15.0000 - 8.66025i) q^{34} +(-2.50000 - 4.33013i) q^{37} +(3.87298 + 6.70820i) q^{38} +(3.87298 + 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-11.6190 + 6.70820i) q^{44} +(-5.00000 + 8.66025i) q^{46} -7.74597 q^{47} +(5.50000 - 4.33013i) q^{49} +(9.68246 - 5.59017i) q^{50} +(4.50000 - 2.59808i) q^{52} +(-3.87298 - 2.23607i) q^{53} +(1.93649 + 5.59017i) q^{56} +(-5.00000 + 8.66025i) q^{58} +7.74597 q^{59} +8.66025i q^{61} +3.87298 q^{62} +13.0000 q^{64} -1.00000 q^{67} +(-11.6190 + 20.1246i) q^{68} -8.94427i q^{71} +(6.00000 + 3.46410i) q^{73} +(-9.68246 + 5.59017i) q^{74} +(9.00000 - 5.19615i) q^{76} +(7.74597 - 8.94427i) q^{77} +11.0000 q^{79} +(15.0000 - 8.66025i) q^{82} +(-3.87298 + 6.70820i) q^{83} +(-13.5554 - 7.82624i) q^{86} +(5.00000 + 8.66025i) q^{88} +(7.74597 + 13.4164i) q^{89} +(-3.00000 + 3.46410i) q^{91} +(11.6190 + 6.70820i) q^{92} +17.3205i q^{94} +(-1.50000 - 0.866025i) q^{97} +(-9.68246 - 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{4} + 10 q^{7}+O(q^{10}) \) 4 * q - 12 * q^4 + 10 * q^7	\( 4 q - 12 q^{4} + 10 q^{7} - 6 q^{13} - 4 q^{16} - 12 q^{19} - 20 q^{22} + 10 q^{25} - 30 q^{28} - 60 q^{34} - 10 q^{37} + 14 q^{43} - 20 q^{46} + 22 q^{49} + 18 q^{52} - 20 q^{58} + 52 q^{64} - 4 q^{67} + 24 q^{73} + 36 q^{76} + 44 q^{79} + 60 q^{82} + 20 q^{88} - 12 q^{91} - 6 q^{97}+O(q^{100}) \) 4 * q - 12 * q^4 + 10 * q^7 - 6 * q^13 - 4 * q^16 - 12 * q^19 - 20 * q^22 + 10 * q^25 - 30 * q^28 - 60 * q^34 - 10 * q^37 + 14 * q^43 - 20 * q^46 + 22 * q^49 + 18 * q^52 - 20 * q^58 + 52 * q^64 - 4 * q^67 + 24 * q^73 + 36 * q^76 + 44 * q^79 + 60 * q^82 + 20 * q^88 - 12 * q^91 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more