LMFDB - Embedded newform 912.3.be.e.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.1
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	912.673
Dual form			912.3.be.e.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(-1.41016 + 2.44247i) q^{5} -2.35194 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(-1.41016 + 2.44247i) q^{5} -2.35194 q^{7} +(1.50000 + 2.59808i) q^{9} +6.75970 q^{11} +(-5.81421 + 3.35683i) q^{13} +(-4.23048 + 2.44247i) q^{15} +(-14.4865 + 25.0913i) q^{17} +(-3.49389 - 18.6760i) q^{19} +(-3.52791 - 2.03684i) q^{21} +(-10.0508 - 17.4085i) q^{23} +(8.52289 + 14.7621i) q^{25} +5.19615i q^{27} +(-21.4036 + 12.3574i) q^{29} +2.95953i q^{31} +(10.1395 + 5.85407i) q^{33} +(3.31661 - 5.74454i) q^{35} -18.6235i q^{37} -11.6284 q^{39} +(-2.27909 - 1.31583i) q^{41} +(-22.7715 + 39.4413i) q^{43} -8.46096 q^{45} +(-6.93937 - 12.0193i) q^{47} -43.4684 q^{49} +(-43.4594 + 25.0913i) q^{51} +(-53.8718 + 31.1029i) q^{53} +(-9.53226 + 16.5104i) q^{55} +(10.9331 - 31.0398i) q^{57} +(38.4538 + 22.2013i) q^{59} +(-23.4474 - 40.6121i) q^{61} +(-3.52791 - 6.11052i) q^{63} -18.9347i q^{65} +(-100.692 + 58.1347i) q^{67} -34.8170i q^{69} +(-16.3365 - 9.43186i) q^{71} +(16.0800 - 27.8514i) q^{73} +29.5242i q^{75} -15.8984 q^{77} +(-95.8390 - 55.3327i) q^{79} +(-4.50000 + 7.79423i) q^{81} +43.1910 q^{83} +(-40.8565 - 70.7655i) q^{85} -42.8072 q^{87} +(26.7488 - 15.4434i) q^{89} +(13.6747 - 7.89507i) q^{91} +(-2.56303 + 4.43930i) q^{93} +(50.5425 + 17.8024i) q^{95} +(33.9282 + 19.5885i) q^{97} +(10.1395 + 17.5622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	−1.41016	+	2.44247i	−0.282032	+	0.488494i	−0.971885	−	0.235456i	$-0.924342\pi$
$5$	−1.41016	+	2.44247i	−0.282032	+	0.488494i	0.689853	+	0.723949i	$0.257675\pi$
$6$		0			0
$7$	−2.35194			−0.335991			−0.167996	−	0.985788i	$-0.553729\pi$
$7$	−2.35194			−0.335991			−0.167996	+	0.985788i	$0.553729\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	6.75970			0.614518			0.307259	−	0.951626i	$-0.400588\pi$
$11$	6.75970			0.614518			0.307259	+	0.951626i	$0.400588\pi$
$12$		0			0
$13$	−5.81421	+	3.35683i	−0.447247	+	0.258218i	−0.706667	−	0.707547i	$-0.749802\pi$
$13$	−5.81421	+	3.35683i	−0.447247	+	0.258218i	0.259420	+	0.965765i	$0.416469\pi$
$14$		0			0
$15$	−4.23048	+	2.44247i	−0.282032	+	0.162831i
$16$		0			0
$17$	−14.4865	+	25.0913i	−0.852145	+	1.47596i	0.0271232	+	0.999632i	$0.491365\pi$
$17$	−14.4865	+	25.0913i	−0.852145	+	1.47596i	−0.879268	+	0.476327i	$0.841968\pi$
$18$		0			0
$19$	−3.49389	−	18.6760i	−0.183889	−	0.982947i
$19$	−3.49389	−	18.6760i	−0.183889	−	0.982947i
$20$		0			0
$21$	−3.52791	−	2.03684i	−0.167996	−	0.0969923i
$22$		0			0
$23$	−10.0508	−	17.4085i	−0.436991	−	0.756891i	0.560464	−	0.828179i	$-0.310623\pi$
$23$	−10.0508	−	17.4085i	−0.436991	−	0.756891i	−0.997456	+	0.0712872i	$0.977289\pi$
$24$		0			0
$25$	8.52289	+	14.7621i	0.340916	+	0.590483i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−21.4036	+	12.3574i	−0.738055	+	0.426116i	−0.821362	−	0.570408i	$-0.806785\pi$
$29$	−21.4036	+	12.3574i	−0.738055	+	0.426116i	0.0833069	+	0.996524i	$0.473452\pi$
$30$		0			0
$31$			2.95953i			0.0954687i	0.998860	+	0.0477344i	$0.0152001\pi$
$31$			2.95953i			0.0954687i	−0.998860	+	0.0477344i	$0.984800\pi$
$32$		0			0
$33$	10.1395	+	5.85407i	0.307259	+	0.177396i
$34$		0			0
$35$	3.31661	−	5.74454i	0.0947603	−	0.164130i
$36$		0			0
$37$		−	18.6235i		−	0.503338i	−0.967813	−	0.251669i	$-0.919021\pi$
$37$		−	18.6235i		−	0.503338i	0.967813	−	0.251669i	$-0.0809794\pi$
$38$		0			0
$39$	−11.6284			−0.298165
$40$		0			0
$41$	−2.27909	−	1.31583i	−0.0555875	−	0.0320935i	0.471949	−	0.881626i	$-0.343551\pi$
$41$	−2.27909	−	1.31583i	−0.0555875	−	0.0320935i	−0.527536	+	0.849533i	$0.676884\pi$
$42$		0			0
$43$	−22.7715	+	39.4413i	−0.529569	+	0.917240i	0.469836	+	0.882754i	$0.344313\pi$
$43$	−22.7715	+	39.4413i	−0.529569	+	0.917240i	−0.999405	+	0.0344867i	$0.989020\pi$
$44$		0			0
$45$	−8.46096			−0.188021
$46$		0			0
$47$	−6.93937	−	12.0193i	−0.147646	−	0.255731i	0.782711	−	0.622386i	$-0.213836\pi$
$47$	−6.93937	−	12.0193i	−0.147646	−	0.255731i	−0.930357	+	0.366655i	$0.880503\pi$
$48$		0			0
$49$	−43.4684			−0.887110
$50$		0			0
$51$	−43.4594	+	25.0913i	−0.852145	+	0.491986i
$52$		0			0
$53$	−53.8718	+	31.1029i	−1.01645	+	0.586847i	−0.913073	−	0.407796i	$-0.866298\pi$
$53$	−53.8718	+	31.1029i	−1.01645	+	0.586847i	−0.103375	+	0.994642i	$0.532964\pi$
$54$		0			0
$55$	−9.53226	+	16.5104i	−0.173314	+	0.300188i
$56$		0			0
$57$	10.9331	−	31.0398i	0.191808	−	0.544558i
$58$		0			0
$59$	38.4538	+	22.2013i	0.651759	+	0.376293i	0.789130	−	0.614227i	$-0.210532\pi$
$59$	38.4538	+	22.2013i	0.651759	+	0.376293i	−0.137371	+	0.990520i	$0.543865\pi$
$60$		0			0
$61$	−23.4474	−	40.6121i	−0.384384	−	0.665773i	0.607299	−	0.794473i	$-0.292253\pi$
$61$	−23.4474	−	40.6121i	−0.384384	−	0.665773i	−0.991684	+	0.128700i	$0.958920\pi$
$62$		0			0
$63$	−3.52791	−	6.11052i	−0.0559986	−	0.0969923i
$64$		0			0
$65$		−	18.9347i		−	0.291303i
$66$		0			0
$67$	−100.692	+	58.1347i	−1.50287	+	0.867682i	−0.502875	+	0.864359i	$0.667724\pi$
$67$	−100.692	+	58.1347i	−1.50287	+	0.867682i	−0.999994	+	0.00332279i	$0.998942\pi$
$68$		0			0
$69$		−	34.8170i		−	0.504594i
$70$		0			0
$71$	−16.3365	−	9.43186i	−0.230091	−	0.132843i	0.380523	−	0.924771i	$-0.375744\pi$
$71$	−16.3365	−	9.43186i	−0.230091	−	0.132843i	−0.610614	+	0.791928i	$0.709077\pi$
$72$		0			0
$73$	16.0800	−	27.8514i	0.220274	−	0.381526i	−0.734617	−	0.678482i	$-0.762638\pi$
$73$	16.0800	−	27.8514i	0.220274	−	0.381526i	0.954891	+	0.296956i	$0.0959714\pi$
$74$		0			0
$75$			29.5242i			0.393656i
$76$		0			0
$77$	−15.8984			−0.206473
$78$		0			0
$79$	−95.8390	−	55.3327i	−1.21315	−	0.700414i	−0.249707	−	0.968321i	$-0.580334\pi$
$79$	−95.8390	−	55.3327i	−1.21315	−	0.700414i	−0.963445	+	0.267908i	$0.913668\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	43.1910			0.520373			0.260187	−	0.965558i	$-0.416216\pi$
$83$	43.1910			0.520373			0.260187	+	0.965558i	$0.416216\pi$
$84$		0			0
$85$	−40.8565	−	70.7655i	−0.480665	−	0.832536i
$86$		0			0
$87$	−42.8072			−0.492037
$88$		0			0
$89$	26.7488	−	15.4434i	0.300549	−	0.173522i	−0.342141	−	0.939649i	$-0.611152\pi$
$89$	26.7488	−	15.4434i	0.300549	−	0.173522i	0.642689	+	0.766127i	$0.277819\pi$
$90$		0			0
$91$	13.6747	−	7.89507i	0.150271	−	0.0867590i
$92$		0			0
$93$	−2.56303	+	4.43930i	−0.0275595	+	0.0477344i
$94$		0			0
$95$	50.5425	+	17.8024i	0.532026	+	0.187394i
$96$		0			0
$97$	33.9282	+	19.5885i	0.349775	+	0.201943i	0.664586	−	0.747212i	$-0.268608\pi$
$97$	33.9282	+	19.5885i	0.349775	+	0.201943i	−0.314811	+	0.949154i	$0.601941\pi$
$98$		0			0
$99$	10.1395	+	17.5622i	0.102420	+	0.177396i
$100$		0			0
$101$	74.5397	+	129.107i	0.738017	+	1.27828i	0.953387	+	0.301750i	$0.0975707\pi$
$101$	74.5397	+	129.107i	0.738017	+	1.27828i	−0.215371	+	0.976532i	$0.569096\pi$
$102$		0			0
$103$			2.46781i			0.0239593i	0.999928	+	0.0119797i	$0.00381333\pi$
$103$			2.46781i			0.0239593i	−0.999928	+	0.0119797i	$0.996187\pi$
$104$		0			0
$105$	9.94984	−	5.74454i	0.0947603	−	0.0547099i
$106$		0			0
$107$			100.899i			0.942984i	0.881870	+	0.471492i	$0.156284\pi$
$107$			100.899i			0.942984i	−0.881870	+	0.471492i	$0.843716\pi$
$108$		0			0
$109$	4.39540	+	2.53768i	0.0403247	+	0.0232815i	0.520027	−	0.854150i	$-0.325922\pi$
$109$	4.39540	+	2.53768i	0.0403247	+	0.0232815i	−0.479702	+	0.877431i	$0.659255\pi$
$110$		0			0
$111$	16.1284	−	27.9352i	0.145301	−	0.251669i
$112$		0			0
$113$		−	18.2239i		−	0.161274i	−0.996744	−	0.0806368i	$-0.974305\pi$
$113$		−	18.2239i		−	0.161274i	0.996744	−	0.0806368i	$-0.0256954\pi$
$114$		0			0
$115$	56.6930			0.492982
$116$		0			0
$117$	−17.4426	−	10.0705i	−0.149082	−	0.0860727i
$118$		0			0
$119$	34.0713	−	59.0132i	0.286313	−	0.495909i
$120$		0			0
$121$	−75.3065			−0.622368
$122$		0			0
$123$	−2.27909	−	3.94750i	−0.0185292	−	0.0320935i
$124$		0			0
$125$	−118.583			−0.948661
$126$		0			0
$127$	−57.6764	+	33.2995i	−0.454145	+	0.262201i	−0.709579	−	0.704626i	$-0.751115\pi$
$127$	−57.6764	+	33.2995i	−0.454145	+	0.262201i	0.255434	+	0.966826i	$0.417782\pi$
$128$		0			0
$129$	−68.3144	+	39.4413i	−0.529569	+	0.305747i
$130$		0			0
$131$	27.5567	−	47.7296i	0.210357	−	0.364348i	−0.741470	−	0.670986i	$-0.765871\pi$
$131$	27.5567	−	47.7296i	0.210357	−	0.364348i	0.951826	+	0.306638i	$0.0992042\pi$
$132$		0			0
$133$	8.21741	+	43.9248i	0.0617850	+	0.330262i
$134$		0			0
$135$	−12.6914	−	7.32741i	−0.0940107	−	0.0542771i
$136$		0			0
$137$	56.7337	+	98.2656i	0.414114	+	0.717267i	0.995335	−	0.0964787i	$-0.0307580\pi$
$137$	56.7337	+	98.2656i	0.414114	+	0.717267i	−0.581221	+	0.813746i	$0.697425\pi$
$138$		0			0
$139$	−68.8443	−	119.242i	−0.495283	−	0.857855i	0.504702	−	0.863293i	$-0.331602\pi$
$139$	−68.8443	−	119.242i	−0.495283	−	0.857855i	−0.999985	+	0.00543838i	$0.998269\pi$
$140$		0			0
$141$		−	24.0387i		−	0.170487i
$142$		0			0
$143$	−39.3023	+	22.6912i	−0.274841	+	0.158680i
$144$		0			0
$145$		−	69.7035i		−	0.480714i
$146$		0			0
$147$	−65.2026	−	37.6447i	−0.443555	−	0.256087i
$148$		0			0
$149$	82.1773	−	142.335i	0.551525	−	0.955270i	−0.446639	−	0.894714i	$-0.647379\pi$
$149$	82.1773	−	142.335i	0.551525	−	0.955270i	0.998165	−	0.0605559i	$-0.0192873\pi$
$150$		0			0
$151$		−	47.7299i		−	0.316092i	−0.987432	−	0.158046i	$-0.949481\pi$
$151$		−	47.7299i		−	0.316092i	0.987432	−	0.158046i	$-0.0505194\pi$
$152$		0			0
$153$	−86.9188			−0.568097
$154$		0			0
$155$	−7.22856	−	4.17341i	−0.0466359	−	0.0269253i
$156$		0			0
$157$	−93.6430	+	162.194i	−0.596452	+	1.03309i	0.396888	+	0.917867i	$0.370090\pi$
$157$	−93.6430	+	162.194i	−0.596452	+	1.03309i	−0.993340	+	0.115219i	$0.963243\pi$
$158$		0			0
$159$	−107.744			−0.677632
$160$		0			0
$161$	23.6389	+	40.9437i	0.146825	+	0.254309i
$162$		0			0
$163$	230.607			1.41477			0.707385	−	0.706829i	$-0.249875\pi$
$163$	230.607			1.41477			0.707385	+	0.706829i	$0.249875\pi$
$164$		0			0
$165$	−28.5968	+	16.5104i	−0.173314	+	0.100063i
$166$		0			0
$167$	−34.8702	+	20.1323i	−0.208804	+	0.120553i	−0.600755	−	0.799433i	$-0.705133\pi$
$167$	−34.8702	+	20.1323i	−0.208804	+	0.120553i	0.391952	+	0.919986i	$0.371800\pi$
$168$		0			0
$169$	−61.9633	+	107.324i	−0.366647	+	0.635051i
$170$		0			0
$171$	43.2808	−	37.0914i	0.253104	−	0.216909i
$172$		0			0
$173$	83.4851	+	48.2002i	0.482573	+	0.278614i	0.721488	−	0.692427i	$-0.243458\pi$
$173$	83.4851	+	48.2002i	0.482573	+	0.278614i	−0.238915	+	0.971040i	$0.576792\pi$
$174$		0			0
$175$	−20.0453	−	34.7195i	−0.114545	−	0.198397i
$176$		0			0
$177$	38.4538	+	66.6039i	0.217253	+	0.376293i
$178$		0			0
$179$		−	54.2148i		−	0.302876i	−0.988467	−	0.151438i	$-0.951610\pi$
$179$		−	54.2148i		−	0.302876i	0.988467	−	0.151438i	$-0.0483904\pi$
$180$		0			0
$181$	−256.951	+	148.351i	−1.41962	+	0.819618i	−0.996265	−	0.0863462i	$-0.972481\pi$
$181$	−256.951	+	148.351i	−1.41962	+	0.819618i	−0.423355	+	0.905964i	$0.639148\pi$
$182$		0			0
$183$		−	81.2243i		−	0.443849i
$184$		0			0
$185$	45.4873	+	26.2621i	0.245877	+	0.141957i
$186$		0			0
$187$	−97.9241	+	169.610i	−0.523658	+	0.907003i
$188$		0			0
$189$		−	12.2210i		−	0.0646616i
$190$		0			0
$191$	114.715			0.600603			0.300302	−	0.953844i	$-0.402913\pi$
$191$	114.715			0.600603			0.300302	+	0.953844i	$0.402913\pi$
$192$		0			0
$193$	173.609	+	100.233i	0.899528	+	0.519343i	0.877047	−	0.480405i	$-0.159510\pi$
$193$	173.609	+	100.233i	0.899528	+	0.519343i	0.0224807	+	0.999747i	$0.492844\pi$
$194$		0			0
$195$	16.3979	−	28.4021i	0.0840920	−	0.145652i
$196$		0			0
$197$	321.376			1.63135			0.815675	−	0.578510i	$-0.196366\pi$
$197$	321.376			1.63135			0.815675	+	0.578510i	$0.196366\pi$
$198$		0			0
$199$	−20.4701	−	35.4553i	−0.102865	−	0.178167i	0.809999	−	0.586431i	$-0.199468\pi$
$199$	−20.4701	−	35.4553i	−0.102865	−	0.178167i	−0.912864	+	0.408264i	$0.866134\pi$
$200$		0			0
$201$	−201.384			−1.00191
$202$		0			0
$203$	50.3399	−	29.0638i	0.247980	−	0.143171i
$204$		0			0
$205$	6.42776	−	3.71107i	0.0313549	−	0.0181028i
$206$		0			0
$207$	30.1524	−	52.2255i	0.145664	−	0.252297i
$208$		0			0
$209$	−23.6176	−	126.244i	−0.113003	−	0.604038i
$210$		0			0
$211$	264.717	+	152.834i	1.25458	+	0.724333i	0.972016	−	0.234915i	$-0.0754811\pi$
$211$	264.717	+	152.834i	1.25458	+	0.724333i	0.282566	+	0.959248i	$0.408814\pi$
$212$		0			0
$213$	−16.3365	−	28.2956i	−0.0766970	−	0.132843i
$214$		0			0
$215$	−64.2228	−	111.237i	−0.298711	−	0.517382i
$216$		0			0
$217$		−	6.96064i		−	0.0320767i
$218$		0			0
$219$	48.2401	−	27.8514i	0.220274	−	0.127175i
$220$		0			0
$221$		−	194.515i		−	0.880157i
$222$		0			0
$223$	−368.516	−	212.763i	−1.65254	−	0.954093i	−0.976024	−	0.217662i	$-0.930157\pi$
$223$	−368.516	−	212.763i	−1.65254	−	0.954093i	−0.676513	−	0.736431i	$-0.736510\pi$
$224$		0			0
$225$	−25.5687	+	44.2863i	−0.113639	+	0.196828i
$226$		0			0
$227$			345.452i			1.52182i	0.648860	+	0.760908i	$0.275246\pi$
$227$			345.452i			1.52182i	−0.648860	+	0.760908i	$0.724754\pi$
$228$		0			0
$229$	−15.6468			−0.0683267			−0.0341634	−	0.999416i	$-0.510877\pi$
$229$	−15.6468			−0.0683267			−0.0341634	+	0.999416i	$0.510877\pi$
$230$		0			0
$231$	−23.8476	−	13.7684i	−0.103236	−	0.0596035i
$232$		0			0
$233$	48.2247	−	83.5276i	0.206973	−	0.358488i	−0.743787	−	0.668417i	$-0.766972\pi$
$233$	48.2247	−	83.5276i	0.206973	−	0.358488i	0.950760	+	0.309930i	$0.100305\pi$
$234$		0			0
$235$	39.1425			0.166564
$236$		0			0
$237$	−95.8390	−	165.998i	−0.404384	−	0.700414i
$238$		0			0
$239$	141.353			0.591435			0.295717	−	0.955275i	$-0.404441\pi$
$239$	141.353			0.591435			0.295717	+	0.955275i	$0.404441\pi$
$240$		0			0
$241$	237.947	−	137.378i	0.987330	−	0.570035i	0.0828549	−	0.996562i	$-0.473596\pi$
$241$	237.947	−	137.378i	0.987330	−	0.570035i	0.904475	+	0.426526i	$0.140263\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	61.2974	−	106.170i	0.250193	−	0.433348i
$246$		0			0
$247$	83.0064	+	96.8577i	0.336058	+	0.392137i
$248$		0			0
$249$	64.7865	+	37.4045i	0.260187	+	0.150219i
$250$		0			0
$251$	125.319	+	217.058i	0.499277	+	0.864774i	1.00000		0.000834104i	$-0.000265504\pi$
$251$	125.319	+	217.058i	0.499277	+	0.864774i	−0.500722	+	0.865608i	$0.666932\pi$
$252$		0			0
$253$	−67.9404	−	117.676i	−0.268539	−	0.465123i
$254$		0			0
$255$		−	141.531i		−	0.555024i
$256$		0			0
$257$	429.209	−	247.804i	1.67007	−	0.964218i	0.702481	−	0.711703i	$-0.252076\pi$
$257$	429.209	−	247.804i	1.67007	−	0.964218i	0.967593	−	0.252515i	$-0.0812577\pi$
$258$		0			0
$259$			43.8013i			0.169117i
$260$		0			0
$261$	−64.2108	−	37.0721i	−0.246018	−	0.142039i
$262$		0			0
$263$	−233.154	+	403.834i	−0.886516	+	1.53549i	−0.0425495	+	0.999094i	$0.513548\pi$
$263$	−233.154	+	403.834i	−0.886516	+	1.53549i	−0.843966	+	0.536396i	$0.819785\pi$
$264$		0			0
$265$		−	175.440i		−	0.662039i
$266$		0			0
$267$	53.4976			0.200366
$268$		0			0
$269$	281.703	+	162.641i	1.04722	+	0.604614i	0.921870	−	0.387498i	$-0.126661\pi$
$269$	281.703	+	162.641i	1.04722	+	0.604614i	0.125352	+	0.992112i	$0.459994\pi$
$270$		0			0
$271$	199.048	−	344.762i	0.734496	−	1.27218i	−0.220448	−	0.975399i	$-0.570752\pi$
$271$	199.048	−	344.762i	0.734496	−	1.27218i	0.954944	−	0.296785i	$-0.0959146\pi$
$272$		0			0
$273$	27.3493			0.100181
$274$		0			0
$275$	57.6122	+	99.7872i	0.209499	+	0.362863i
$276$		0			0
$277$	−33.7242			−0.121748			−0.0608740	−	0.998145i	$-0.519389\pi$
$277$	−33.7242			−0.121748			−0.0608740	+	0.998145i	$0.519389\pi$
$278$		0			0
$279$	−7.68909	+	4.43930i	−0.0275595	+	0.0159115i
$280$		0			0
$281$	−163.706	+	94.5154i	−0.582582	+	0.336354i	−0.762159	−	0.647390i	$-0.775860\pi$
$281$	−163.706	+	94.5154i	−0.582582	+	0.336354i	0.179577	+	0.983744i	$0.442527\pi$
$282$		0			0
$283$	46.4571	−	80.4660i	0.164159	−	0.284332i	−0.772197	−	0.635383i	$-0.780842\pi$
$283$	46.4571	−	80.4660i	0.164159	−	0.284332i	0.936356	+	0.351051i	$0.114176\pi$
$284$		0			0
$285$	60.3964	+	70.4747i	0.211917	+	0.247280i
$286$		0			0
$287$	5.36028	+	3.09476i	0.0186769	+	0.0107831i
$288$		0			0
$289$	−275.216	−	476.687i	−0.952303	−	1.64944i
$290$		0			0
$291$	33.9282	+	58.7654i	0.116592	+	0.201943i
$292$		0			0
$293$			306.874i			1.04735i	0.851918	+	0.523676i	$0.175440\pi$
$293$			306.874i			1.04735i	−0.851918	+	0.523676i	$0.824560\pi$
$294$		0			0
$295$	−108.452	+	62.6148i	−0.367634	+	0.212253i
$296$		0			0
$297$			35.1244i			0.118264i
$298$		0			0
$299$	116.875	+	67.4778i	0.390886	+	0.225678i
$300$		0			0
$301$	53.5571	−	92.7636i	0.177931	−	0.308185i
$302$		0			0
$303$			258.213i			0.852188i
$304$		0			0
$305$	132.259			0.433635
$306$		0			0
$307$	31.6241	+	18.2582i	0.103010	+	0.0594729i	0.550620	−	0.834756i	$-0.314391\pi$
$307$	31.6241	+	18.2582i	0.103010	+	0.0594729i	−0.447610	+	0.894229i	$0.647725\pi$
$308$		0			0
$309$	−2.13719	+	3.70171i	−0.00691646	+	0.0119797i
$310$		0			0
$311$	21.3679			0.0687070			0.0343535	−	0.999410i	$-0.489063\pi$
$311$	21.3679			0.0687070			0.0343535	+	0.999410i	$0.489063\pi$
$312$		0			0
$313$	145.251	+	251.583i	0.464061	+	0.803778i	0.999159	−	0.0410125i	$-0.0130583\pi$
$313$	145.251	+	251.583i	0.464061	+	0.803778i	−0.535097	+	0.844791i	$0.679725\pi$
$314$		0			0
$315$	19.8997			0.0631736
$316$		0			0
$317$	467.864	−	270.122i	1.47591	−	0.852119i	0.476282	−	0.879293i	$-0.341984\pi$
$317$	467.864	−	270.122i	1.47591	−	0.852119i	0.999631	+	0.0271740i	$0.00865081\pi$
$318$		0			0
$319$	−144.682	+	83.5320i	−0.453548	+	0.261856i
$320$		0			0
$321$	−87.3813	+	151.349i	−0.272216	+	0.471492i
$322$		0			0
$323$	519.219	+	182.883i	1.60749	+	0.566201i
$324$		0			0
$325$	−99.1078	−	57.2199i	−0.304947	−	0.176061i
$326$		0			0
$327$	4.39540	+	7.61305i	0.0134416	+	0.0232815i
$328$		0			0
$329$	16.3210	+	28.2688i	0.0496079	+	0.0859233i
$330$		0			0
$331$		−	140.221i		−	0.423630i	−0.977310	−	0.211815i	$-0.932063\pi$
$331$		−	140.221i		−	0.423630i	0.977310	−	0.211815i	$-0.0679374\pi$
$332$		0			0
$333$	48.3852	−	27.9352i	0.145301	−	0.0838896i
$334$		0			0
$335$		−	327.917i		−	0.978857i
$336$		0			0
$337$	341.470	+	197.148i	1.01326	+	0.585008i	0.912146	−	0.409866i	$-0.134425\pi$
$337$	341.470	+	197.148i	1.01326	+	0.585008i	0.101118	+	0.994874i	$0.467758\pi$
$338$		0			0
$339$	15.7824	−	27.3359i	0.0465557	−	0.0806368i
$340$		0			0
$341$			20.0055i			0.0586672i
$342$		0			0
$343$	217.480			0.634053
$344$		0			0
$345$	85.0395	+	49.0976i	0.246491	+	0.142312i
$346$		0			0
$347$	313.848	−	543.600i	0.904460	−	1.56657i	0.0828199	−	0.996565i	$-0.473607\pi$
$347$	313.848	−	543.600i	0.904460	−	1.56657i	0.821640	−	0.570006i	$-0.193059\pi$
$348$		0			0
$349$	298.804			0.856172			0.428086	−	0.903738i	$-0.359188\pi$
$349$	298.804			0.856172			0.428086	+	0.903738i	$0.359188\pi$
$350$		0			0
$351$	−17.4426	−	30.2115i	−0.0496941	−	0.0860727i
$352$		0			0
$353$	−318.660			−0.902719			−0.451359	−	0.892342i	$-0.649061\pi$
$353$	−318.660			−0.902719			−0.451359	+	0.892342i	$0.649061\pi$
$354$		0			0
$355$	46.0741	−	26.6009i	0.129786	−	0.0749321i
$356$		0			0
$357$	102.214	−	59.0132i	0.286313	−	0.165303i
$358$		0			0
$359$	45.4701	−	78.7565i	0.126658	−	0.219377i	−0.795722	−	0.605662i	$-0.792908\pi$
$359$	45.4701	−	78.7565i	0.126658	−	0.219377i	0.922380	+	0.386285i	$0.126242\pi$
$360$		0			0
$361$	−336.586	+	130.504i	−0.932370	+	0.361506i
$362$		0			0
$363$	−112.960	−	65.2174i	−0.311184	−	0.179662i
$364$		0			0
$365$	45.3508	+	78.5499i	0.124249	+	0.215205i
$366$		0			0
$367$	−227.216	−	393.549i	−0.619116	−	1.07234i	−0.989647	−	0.143521i	$-0.954158\pi$
$367$	−227.216	−	393.549i	−0.619116	−	1.07234i	0.370531	−	0.928820i	$-0.379176\pi$
$368$		0			0
$369$		−	7.89499i		−	0.0213956i
$370$		0			0
$371$	126.703	−	73.1521i	0.341518	−	0.197175i
$372$		0			0
$373$		−	210.767i		−	0.565059i	−0.959259	−	0.282530i	$-0.908826\pi$
$373$		−	210.767i		−	0.565059i	0.959259	−	0.282530i	$-0.0911735\pi$
$374$		0			0
$375$	−177.874	−	102.696i	−0.474331	−	0.273855i
$376$		0			0
$377$	82.9633	−	143.697i	0.220062	−	0.381158i
$378$		0			0
$379$			347.379i			0.916566i	0.888806	+	0.458283i	$0.151535\pi$
$379$			347.379i			0.916566i	−0.888806	+	0.458283i	$0.848465\pi$
$380$		0			0
$381$	−115.353			−0.302763
$382$		0			0
$383$	−181.476	−	104.775i	−0.473828	−	0.273564i	0.244013	−	0.969772i	$-0.421536\pi$
$383$	−181.476	−	104.775i	−0.473828	−	0.273564i	−0.717841	+	0.696207i	$0.754869\pi$
$384$		0			0
$385$	22.4193	−	38.8313i	0.0582319	−	0.100861i
$386$		0			0
$387$	−136.629			−0.353046
$388$		0			0
$389$	280.670	+	486.135i	0.721517	+	1.24970i	0.960392	+	0.278654i	$0.0898883\pi$
$389$	280.670	+	486.135i	0.721517	+	1.24970i	−0.238874	+	0.971050i	$0.576778\pi$
$390$		0			0
$391$	582.403			1.48952
$392$		0			0
$393$	82.6701	−	47.7296i	0.210357	−	0.121449i
$394$		0			0
$395$	270.297	−	156.056i	0.684296	−	0.395078i
$396$		0			0
$397$	102.291	−	177.174i	0.257660	−	0.446281i	−0.707954	−	0.706258i	$-0.750382\pi$
$397$	102.291	−	177.174i	0.257660	−	0.446281i	0.965615	+	0.259977i	$0.0837151\pi$
$398$		0			0
$399$	−25.7139	+	73.0037i	−0.0644458	+	0.182967i
$400$		0			0
$401$	302.139	+	174.440i	0.753464	+	0.435013i	0.826944	−	0.562284i	$-0.190077\pi$
$401$	302.139	+	174.440i	0.753464	+	0.435013i	−0.0734800	+	0.997297i	$0.523411\pi$
$402$		0			0
$403$	−9.93466	−	17.2073i	−0.0246518	−	0.0426981i
$404$		0			0
$405$	−12.6914	−	21.9822i	−0.0313369	−	0.0542771i
$406$		0			0
$407$		−	125.889i		−	0.309310i
$408$		0			0
$409$	−516.744	+	298.342i	−1.26343	+	0.729443i	−0.973737	−	0.227676i	$-0.926887\pi$
$409$	−516.744	+	298.342i	−1.26343	+	0.729443i	−0.289695	+	0.957119i	$0.593554\pi$
$410$		0			0
$411$			196.531i			0.478178i
$412$		0			0
$413$	−90.4409	−	52.2161i	−0.218985	−	0.126431i
$414$		0			0
$415$	−60.9062	+	105.493i	−0.146762	+	0.254199i
$416$		0			0
$417$		−	238.484i		−	0.571903i
$418$		0			0
$419$	−44.7118			−0.106711			−0.0533554	−	0.998576i	$-0.516992\pi$
$419$	−44.7118			−0.106711			−0.0533554	+	0.998576i	$0.516992\pi$
$420$		0			0
$421$	428.701	+	247.511i	1.01829	+	0.587911i	0.913609	−	0.406594i	$-0.133284\pi$
$421$	428.701	+	247.511i	1.01829	+	0.587911i	0.104683	+	0.994506i	$0.466617\pi$
$422$		0			0
$423$	20.8181	−	36.0580i	0.0492154	−	0.0852436i
$424$		0			0
$425$	−493.867			−1.16204
$426$		0			0
$427$	55.1469	+	95.5173i	0.129150	+	0.223694i
$428$		0			0
$429$	−78.6046			−0.183227
$430$		0			0
$431$	570.905	−	329.612i	1.32461	−	0.764761i	0.340146	−	0.940373i	$-0.389524\pi$
$431$	570.905	−	329.612i	1.32461	−	0.764761i	0.984460	+	0.175612i	$0.0561903\pi$
$432$		0			0
$433$	−256.448	+	148.061i	−0.592259	+	0.341941i	−0.765990	−	0.642852i	$-0.777751\pi$
$433$	−256.448	+	148.061i	−0.592259	+	0.341941i	0.173731	+	0.984793i	$0.444418\pi$
$434$		0			0
$435$	60.3650	−	104.555i	0.138770	−	0.240357i
$436$		0			0
$437$	−290.005	+	248.532i	−0.663626	+	0.568723i
$438$		0			0
$439$	−472.076	−	272.553i	−1.07534	−	0.620850i	−0.145707	−	0.989328i	$-0.546546\pi$
$439$	−472.076	−	272.553i	−1.07534	−	0.620850i	−0.929636	+	0.368478i	$0.879879\pi$
$440$		0			0
$441$	−65.2026	−	112.934i	−0.147852	−	0.256087i
$442$		0			0
$443$	108.889	+	188.602i	0.245800	+	0.425738i	0.962356	−	0.271791i	$-0.0876161\pi$
$443$	108.889	+	188.602i	0.245800	+	0.425738i	−0.716556	+	0.697529i	$0.754283\pi$
$444$		0			0
$445$			87.1109i			0.195755i
$446$		0			0
$447$	246.532	−	142.335i	0.551525	−	0.318423i
$448$		0			0
$449$		−	698.865i		−	1.55649i	−0.627959	−	0.778246i	$-0.716110\pi$
$449$		−	698.865i		−	1.55649i	0.627959	−	0.778246i	$-0.283890\pi$
$450$		0			0
$451$	−15.4059	−	8.89462i	−0.0341595	−	0.0197220i
$452$		0			0
$453$	41.3353	−	71.5948i	0.0912478	−	0.158046i
$454$		0			0
$455$			44.5333i			0.0978753i
$456$		0			0
$457$	489.719			1.07159			0.535797	−	0.844347i	$-0.320011\pi$
$457$	489.719			1.07159			0.535797	+	0.844347i	$0.320011\pi$
$458$		0			0
$459$	−130.378	−	75.2739i	−0.284048	−	0.163995i
$460$		0			0
$461$	−401.484	+	695.391i	−0.870899	+	1.50844i	−0.00983043	+	0.999952i	$0.503129\pi$
$461$	−401.484	+	695.391i	−0.870899	+	1.50844i	−0.861068	+	0.508489i	$0.830204\pi$
$462$		0			0
$463$	−480.895			−1.03865			−0.519325	−	0.854577i	$-0.673817\pi$
$463$	−480.895			−1.03865			−0.519325	+	0.854577i	$0.673817\pi$
$464$		0			0
$465$	−7.22856	−	12.5202i	−0.0155453	−	0.0269253i
$466$		0			0
$467$	154.794			0.331464			0.165732	−	0.986171i	$-0.447001\pi$
$467$	154.794			0.331464			0.165732	+	0.986171i	$0.447001\pi$
$468$		0			0
$469$	236.822	−	136.729i	0.504951	−	0.291534i
$470$		0			0
$471$	−280.929	+	162.194i	−0.596452	+	0.344362i
$472$		0			0
$473$	−153.928	+	266.611i	−0.325430	+	0.563660i
$474$		0			0
$475$	245.919	−	210.751i	0.517723	−	0.443685i
$476$		0			0
$477$	−161.615	−	93.3086i	−0.338816	−	0.195616i
$478$		0			0
$479$	−250.612	−	434.073i	−0.523198	−	0.906206i	−0.999636	−	0.0269973i	$-0.991405\pi$
$479$	−250.612	−	434.073i	−0.523198	−	0.906206i	0.476437	−	0.879208i	$-0.341928\pi$
$480$		0			0
$481$	62.5160	+	108.281i	0.129971	+	0.225116i
$482$		0			0
$483$			81.8875i			0.169539i
$484$		0			0
$485$	−95.6884	+	55.2457i	−0.197296	+	0.113909i
$486$		0			0
$487$		−	168.961i		−	0.346943i	−0.984839	−	0.173472i	$-0.944502\pi$
$487$		−	168.961i		−	0.346943i	0.984839	−	0.173472i	$-0.0554985\pi$
$488$		0			0
$489$	345.911	+	199.712i	0.707385	+	0.408409i
$490$		0			0
$491$	−315.495	+	546.453i	−0.642556	+	1.11294i	0.342305	+	0.939589i	$0.388793\pi$
$491$	−315.495	+	546.453i	−0.642556	+	1.11294i	−0.984860	+	0.173350i	$0.944541\pi$
$492$		0			0
$493$		−	716.058i		−	1.45245i
$494$		0			0
$495$	−57.1935			−0.115543
$496$		0			0
$497$	38.4224	+	22.1832i	0.0773086	+	0.0446341i
$498$		0			0
$499$	−328.545	+	569.056i	−0.658406	+	1.14039i	0.322622	+	0.946528i	$0.395436\pi$
$499$	−328.545	+	569.056i	−0.658406	+	1.14039i	−0.981028	+	0.193865i	$0.937898\pi$
$500$		0			0
$501$	−69.7404			−0.139202
$502$		0			0
$503$	−184.339	−	319.284i	−0.366478	−	0.634759i	0.622534	−	0.782593i	$-0.286103\pi$
$503$	−184.339	−	319.284i	−0.366478	−	0.634759i	−0.989012	+	0.147834i	$0.952770\pi$
$504$		0			0
$505$	−420.452			−0.832578
$506$		0			0
$507$	−185.890	+	107.324i	−0.366647	+	0.211684i
$508$		0			0
$509$	−731.132	+	422.119i	−1.43641	+	0.829311i	−0.997598	−	0.0692679i	$-0.977934\pi$
$509$	−731.132	+	422.119i	−1.43641	+	0.829311i	−0.438811	+	0.898579i	$0.644600\pi$
$510$		0			0
$511$	−37.8192	+	65.5048i	−0.0740102	+	0.128189i
$512$		0			0
$513$	97.0433	−	18.1548i	0.189168	−	0.0353894i
$514$		0			0
$515$	−6.02755	−	3.48001i	−0.0117040	−	0.00675730i
$516$		0			0
$517$	−46.9081	−	81.2472i	−0.0907313	−	0.157151i
$518$		0			0
$519$	83.4851	+	144.600i	0.160858	+	0.278614i
$520$		0			0
$521$			112.707i			0.216329i	0.994133	+	0.108164i	$0.0344973\pi$
$521$			112.707i			0.216329i	−0.994133	+	0.108164i	$0.965503\pi$
$522$		0			0
$523$	50.3441	−	29.0662i	0.0962602	−	0.0555758i	−0.451097	−	0.892475i	$-0.648967\pi$
$523$	50.3441	−	29.0662i	0.0962602	−	0.0555758i	0.547357	+	0.836899i	$0.315634\pi$
$524$		0			0
$525$		−	69.4391i		−	0.132265i
$526$		0			0
$527$	−74.2585	−	42.8732i	−0.140908	−	0.0813532i
$528$		0			0
$529$	62.4627	−	108.189i	0.118077	−	0.204515i
$530$		0			0
$531$			133.208i			0.250862i
$532$		0			0
$533$	17.6681			0.0331484
$534$		0			0
$535$	−246.443	−	142.284i	−0.460642	−	0.265952i
$536$		0			0
$537$	46.9514	−	81.3222i	0.0874328	−	0.151438i
$538$		0			0
$539$	−293.833			−0.545145
$540$		0			0
$541$	−424.000	−	734.390i	−0.783734	−	1.35747i	−0.929752	−	0.368186i	$-0.879979\pi$
$541$	−424.000	−	734.390i	−0.783734	−	1.35747i	0.146018	−	0.989282i	$-0.453354\pi$
$542$		0			0
$543$	−513.902			−0.946413
$544$		0			0
$545$	−12.3964	+	7.15708i	−0.0227457	+	0.0131323i
$546$		0			0
$547$	−887.787	+	512.564i	−1.62301	+	0.937046i	−0.636903	+	0.770944i	$0.719785\pi$
$547$	−887.787	+	512.564i	−1.62301	+	0.937046i	−0.986108	+	0.166103i	$0.946882\pi$
$548$		0			0
$549$	70.3423	−	121.836i	0.128128	−	0.221924i
$550$		0			0
$551$	305.568	+	356.558i	0.554570	+	0.647111i
$552$		0			0
$553$	225.408	+	130.139i	0.407609	+	0.235333i
$554$		0			0
$555$	45.4873	+	78.7863i	0.0819591	+	0.141957i
$556$		0			0
$557$	305.692	+	529.474i	0.548819	+	0.950583i	0.998356	+	0.0573207i	$0.0182558\pi$
$557$	305.692	+	529.474i	0.548819	+	0.950583i	−0.449537	+	0.893262i	$0.648411\pi$
$558$		0			0
$559$		−	305.760i		−	0.546977i
$560$		0			0
$561$	−293.772	+	169.610i	−0.523658	+	0.302334i
$562$		0			0
$563$			655.098i			1.16358i	0.813338	+	0.581792i	$0.197648\pi$
$563$			655.098i			1.16358i	−0.813338	+	0.581792i	$0.802352\pi$
$564$		0			0
$565$	44.5114	+	25.6987i	0.0787812	+	0.0454844i
$566$		0			0
$567$	10.5837	−	18.3316i	0.0186662	−	0.0323308i
$568$		0			0
$569$		−	641.059i		−	1.12664i	−0.826238	−	0.563321i	$-0.809523\pi$
$569$		−	641.059i		−	1.12664i	0.826238	−	0.563321i	$-0.190477\pi$
$570$		0			0
$571$	688.224			1.20530			0.602648	−	0.798007i	$-0.294112\pi$
$571$	688.224			1.20530			0.602648	+	0.798007i	$0.294112\pi$
$572$		0			0
$573$	172.073	+	99.3463i	0.300302	+	0.173379i
$574$		0			0
$575$	171.324	−	296.742i	0.297955	−	0.516072i
$576$		0			0
$577$	−541.358			−0.938229			−0.469114	−	0.883137i	$-0.655427\pi$
$577$	−541.358			−0.938229			−0.469114	+	0.883137i	$0.655427\pi$
$578$		0			0
$579$	173.609	+	300.699i	0.299843	+	0.519343i
$580$		0			0
$581$	−101.583			−0.174841
$582$		0			0
$583$	−364.157	+	210.246i	−0.624626	+	0.360628i
$584$		0			0
$585$	49.1938	−	28.4021i	0.0840920	−	0.0485505i
$586$		0			0
$587$	−238.485	+	413.068i	−0.406278	+	0.703694i	−0.994469	−	0.105028i	$-0.966507\pi$
$587$	−238.485	+	413.068i	−0.406278	+	0.703694i	0.588191	+	0.808722i	$0.299840\pi$
$588$		0			0
$589$	55.2722	−	10.3403i	0.0938407	−	0.0175556i
$590$		0			0
$591$	482.064	+	278.320i	0.815675	+	0.470930i
$592$		0			0
$593$	−398.478	−	690.184i	−0.671970	−	1.16389i	−0.977345	−	0.211654i	$-0.932115\pi$
$593$	−398.478	−	690.184i	−0.671970	−	1.16389i	0.305375	−	0.952232i	$-0.401218\pi$
$594$		0			0
$595$	96.0920	+	166.436i	0.161499	+	0.279725i
$596$		0			0
$597$		−	70.9106i		−	0.118778i
$598$		0			0
$599$	−279.241	+	161.220i	−0.466178	+	0.269148i	−0.714639	−	0.699494i	$-0.753409\pi$
$599$	−279.241	+	161.220i	−0.466178	+	0.269148i	0.248460	+	0.968642i	$0.420075\pi$
$600$		0			0
$601$			540.159i			0.898767i	0.893339	+	0.449384i	$0.148356\pi$
$601$			540.159i			0.898767i	−0.893339	+	0.449384i	$0.851644\pi$
$602$		0			0
$603$	−302.077	−	174.404i	−0.500956	−	0.289227i
$604$		0			0
$605$	106.194	−	183.934i	0.175528	−	0.304023i
$606$		0			0
$607$			947.387i			1.56077i	0.625300	+	0.780385i	$0.284977\pi$
$607$			947.387i			1.56077i	−0.625300	+	0.780385i	$0.715023\pi$
$608$		0			0
$609$	100.680			0.165320
$610$		0			0
$611$	80.6939	+	46.5887i	0.132069	+	0.0762499i
$612$		0			0
$613$	−117.817	+	204.064i	−0.192197	+	0.332895i	−0.945978	−	0.324231i	$-0.894895\pi$
$613$	−117.817	+	204.064i	−0.192197	+	0.332895i	0.753781	+	0.657126i	$0.228228\pi$
$614$		0			0
$615$	12.8555			0.0209033
$616$		0			0
$617$	42.0430	+	72.8207i	0.0681410	+	0.118024i	0.898083	−	0.439826i	$-0.144960\pi$
$617$	42.0430	+	72.8207i	0.0681410	+	0.118024i	−0.829942	+	0.557850i	$0.811627\pi$
$618$		0			0
$619$	−272.377			−0.440027			−0.220014	−	0.975497i	$-0.570610\pi$
$619$	−272.377			−0.440027			−0.220014	+	0.975497i	$0.570610\pi$
$620$		0			0
$621$	90.4572	−	52.2255i	0.145664	−	0.0840990i
$622$		0			0
$623$	−62.9116	+	36.3220i	−0.100982	+	0.0583018i
$624$		0			0
$625$	−45.8518	+	79.4177i	−0.0733629	+	0.127068i
$626$		0			0
$627$	73.9041	−	209.820i	0.117869	−	0.334640i
$628$		0			0
$629$	467.288	+	269.789i	0.742906	+	0.428917i
$630$		0			0
$631$	312.587	+	541.417i	0.495384	+	0.858030i	0.999986	−	0.00532179i	$-0.00169398\pi$
$631$	312.587	+	541.417i	0.495384	+	0.858030i	−0.504602	+	0.863352i	$0.668361\pi$
$632$		0			0
$633$	264.717	+	458.503i	0.418194	+	0.724333i
$634$		0			0
$635$		−	187.830i		−	0.295796i
$636$		0			0
$637$	252.734	−	145.916i	0.396757	−	0.229068i
$638$		0			0
$639$		−	56.5912i		−	0.0885621i
$640$		0			0
$641$	−807.314	−	466.103i	−1.25946	−	0.727149i	−0.286490	−	0.958083i	$-0.592489\pi$
$641$	−807.314	−	466.103i	−1.25946	−	0.727149i	−0.972969	+	0.230934i	$0.925822\pi$
$642$		0			0
$643$	81.1863	−	140.619i	0.126262	−	0.218692i	−0.795964	−	0.605344i	$-0.793035\pi$
$643$	81.1863	−	140.619i	0.126262	−	0.218692i	0.922225	+	0.386653i	$0.126369\pi$
$644$		0			0
$645$		−	222.474i		−	0.344922i
$646$		0			0
$647$	−1201.46			−1.85697			−0.928483	−	0.371375i	$-0.878886\pi$
$647$	−1201.46			−1.85697			−0.928483	+	0.371375i	$0.878886\pi$
$648$		0			0
$649$	259.936	+	150.074i	0.400517	+	0.231239i
$650$		0			0
$651$	6.02809	−	10.4410i	0.00925974	−	0.0160383i
$652$		0			0
$653$	−603.359			−0.923981			−0.461990	−	0.886885i	$-0.652865\pi$
$653$	−603.359			−0.923981			−0.461990	+	0.886885i	$0.652865\pi$
$654$		0			0
$655$	77.7188	+	134.613i	0.118655	+	0.205516i
$656$		0			0
$657$	96.4801			0.146849
$658$		0			0
$659$	−830.205	+	479.319i	−1.25980	+	0.727343i	−0.973035	−	0.230659i	$-0.925912\pi$
$659$	−830.205	+	479.319i	−1.25980	+	0.727343i	−0.286761	+	0.958002i	$0.592578\pi$
$660$		0			0
$661$	−902.774	+	521.217i	−1.36577	+	0.788528i	−0.990385	−	0.138341i	$-0.955823\pi$
$661$	−902.774	+	521.217i	−1.36577	+	0.788528i	−0.375386	+	0.926869i	$0.622490\pi$
$662$		0			0
$663$	168.455	−	291.772i	0.254079	−	0.440079i
$664$		0			0
$665$	−118.873	−	41.8703i	−0.178756	−	0.0629628i
$666$		0			0
$667$	430.246	+	248.403i	0.645047	+	0.372418i
$668$		0			0
$669$	−368.516	−	638.288i	−0.550846	−	0.954093i
$670$		0			0
$671$	−158.498	−	274.526i	−0.236211	−	0.409129i
$672$		0			0
$673$			67.4023i			0.100152i	0.998745	+	0.0500760i	$0.0159464\pi$
$673$			67.4023i			0.100152i	−0.998745	+	0.0500760i	$0.984054\pi$
$674$		0			0
$675$	−76.7060	+	44.2863i	−0.113639	+	0.0656093i
$676$		0			0
$677$		−	44.1092i		−	0.0651539i	−0.999469	−	0.0325770i	$-0.989629\pi$
$677$		−	44.1092i		−	0.0651539i	0.999469	−	0.0325770i	$-0.0103714\pi$
$678$		0			0
$679$	−79.7971	−	46.0709i	−0.117521	−	0.0678510i
$680$		0			0
$681$	−299.170	+	518.178i	−0.439310	+	0.760908i
$682$		0			0
$683$		−	1184.23i		−	1.73387i	−0.498424	−	0.866934i	$-0.666088\pi$
$683$		−	1184.23i		−	1.73387i	0.498424	−	0.866934i	$-0.333912\pi$
$684$		0			0
$685$	−320.014			−0.467174
$686$		0			0
$687$	−23.4702	−	13.5505i	−0.0341634	−	0.0197242i
$688$		0			0
$689$	208.814	−	361.677i	0.303069	−	0.524931i
$690$		0			0
$691$	−611.480			−0.884921			−0.442460	−	0.896788i	$-0.645894\pi$
$691$	−611.480			−0.884921			−0.442460	+	0.896788i	$0.645894\pi$
$692$		0			0
$693$	−23.8476	−	41.3052i	−0.0344121	−	0.0596035i
$694$		0			0
$695$	388.326			0.558743
$696$		0			0
$697$	66.0319	−	38.1235i	0.0947373	−	0.0546966i
$698$		0			0
$699$	144.674	−	83.5276i	0.206973	−	0.119496i
$700$		0			0
$701$	338.177	−	585.740i	0.482421	−	0.835578i	−0.517375	−	0.855759i	$-0.673091\pi$
$701$	338.177	−	585.740i	0.482421	−	0.835578i	0.999796	+	0.0201807i	$0.00642416\pi$
$702$		0			0
$703$	−347.812	+	65.0684i	−0.494754	+	0.0925581i
$704$		0			0
$705$	58.7138	+	33.8984i	0.0832820	+	0.0480829i
$706$		0			0
$707$	−175.313	−	303.651i	−0.247967	−	0.429492i
$708$		0			0
$709$	453.456	+	785.409i	0.639571	+	1.10777i	0.985527	+	0.169519i	$0.0542214\pi$
$709$	453.456	+	785.409i	0.639571	+	1.10777i	−0.345956	+	0.938251i	$0.612445\pi$
$710$		0			0
$711$		−	331.996i		−	0.466942i
$712$		0			0
$713$	51.5210	−	29.7457i	0.0722595	−	0.0417190i
$714$		0			0
$715$		−	127.993i		−	0.179011i
$716$		0			0
$717$	212.029	+	122.415i	0.295717	+	0.170733i
$718$		0			0
$719$	−448.812	+	777.366i	−0.624217	+	1.08118i	0.364474	+	0.931213i	$0.381249\pi$
$719$	−448.812	+	777.366i	−0.624217	+	1.08118i	−0.988692	+	0.149963i	$0.952085\pi$
$720$		0			0
$721$		−	5.80414i		−	0.00805012i
$722$		0			0
$723$	475.893			0.658220
$724$		0			0
$725$	−364.841	−	210.641i	−0.503229	−	0.290539i
$726$		0			0
$727$	302.095	−	523.243i	0.415536	−	0.719729i	−0.579949	−	0.814653i	$-0.696927\pi$
$727$	302.095	−	523.243i	0.415536	−	0.719729i	0.995485	+	0.0949236i	$0.0302607\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−659.756	−	1142.73i	−0.902539	−	1.56324i
$732$		0			0
$733$	530.145			0.723254			0.361627	−	0.932323i	$-0.382221\pi$
$733$	530.145			0.723254			0.361627	+	0.932323i	$0.382221\pi$
$734$		0			0
$735$	183.892	−	106.170i	0.250193	−	0.144449i
$736$		0			0
$737$	−680.649	+	392.973i	−0.923540	+	0.533206i
$738$		0			0
$739$	618.713	−	1071.64i	0.837231	−	1.45013i	−0.0549708	−	0.998488i	$-0.517507\pi$
$739$	618.713	−	1071.64i	0.837231	−	1.45013i	0.892201	−	0.451638i	$-0.149160\pi$
$740$		0			0
$741$	40.6284	+	217.172i	0.0548291	+	0.293080i
$742$		0			0
$743$	239.092	+	138.040i	0.321793	+	0.185787i	0.652191	−	0.758054i	$-0.273850\pi$
$743$	239.092	+	138.040i	0.321793	+	0.185787i	−0.330399	+	0.943842i	$0.607183\pi$
$744$		0			0
$745$	231.766	+	401.431i	0.311096	+	0.538834i
$746$		0			0
$747$	64.7865	+	112.213i	0.0867289	+	0.150219i
$748$		0			0
$749$		−	237.309i		−	0.316834i
$750$		0			0
$751$	444.309	−	256.522i	0.591623	−	0.341574i	−0.174116	−	0.984725i	$-0.555707\pi$
$751$	444.309	−	256.522i	0.591623	−	0.341574i	0.765739	+	0.643151i	$0.222373\pi$
$752$		0			0
$753$			434.117i			0.576516i
$754$		0			0
$755$	116.579	+	67.3068i	0.154409	+	0.0891480i
$756$		0			0
$757$	−328.379	+	568.769i	−0.433790	+	0.751346i	−0.997196	−	0.0748339i	$-0.976157\pi$
$757$	−328.379	+	568.769i	−0.433790	+	0.751346i	0.563406	+	0.826180i	$0.309491\pi$
$758$		0			0
$759$		−	235.352i		−	0.310082i
$760$		0			0
$761$	354.668			0.466055			0.233028	−	0.972470i	$-0.425137\pi$
$761$	354.668			0.466055			0.233028	+	0.972470i	$0.425137\pi$
$762$		0			0
$763$	−10.3377	−	5.96848i	−0.0135488	−	0.00782238i
$764$		0			0
$765$	122.569	−	212.297i	0.160222	−	0.277512i
$766$		0			0
$767$	−298.104			−0.388663
$768$		0			0
$769$	−21.0025	−	36.3774i	−0.0273114	−	0.0473048i	0.852047	−	0.523466i	$-0.175361\pi$
$769$	−21.0025	−	36.3774i	−0.0273114	−	0.0473048i	−0.879358	+	0.476161i	$0.842028\pi$
$770$		0			0
$771$	858.418			1.11338
$772$		0			0
$773$	−691.558	+	399.271i	−0.894641	+	0.516521i	−0.875458	−	0.483295i	$-0.839440\pi$
$773$	−691.558	+	399.271i	−0.894641	+	0.516521i	−0.0191835	+	0.999816i	$0.506107\pi$
$774$		0			0
$775$	−43.6888	+	25.2238i	−0.0563727	+	0.0325468i
$776$		0			0
$777$	−37.9331	+	65.7020i	−0.0488199	+	0.0845585i
$778$		0			0
$779$	−16.6116	+	47.1616i	−0.0213243	+	0.0605412i
$780$		0			0
$781$	−110.430	−	63.7565i	−0.141395	−	0.0816345i
$782$		0			0
$783$	−64.2108	−	111.216i	−0.0820061	−	0.142039i
$784$		0			0
$785$	−264.103	−	457.440i	−0.336437	−	0.582727i
$786$		0			0
$787$		−	1056.59i		−	1.34255i	−0.741209	−	0.671274i	$-0.765747\pi$
$787$		−	1056.59i		−	1.34255i	0.741209	−	0.671274i	$-0.234253\pi$
$788$		0			0
$789$	−699.461	+	403.834i	−0.886516	+	0.511830i
$790$		0			0
$791$			42.8616i			0.0541866i
$792$		0			0
$793$	272.657	+	157.418i	0.343829	+	0.198510i
$794$		0			0
$795$	151.936	−	263.160i	0.191114	−	0.331019i
$796$		0			0
$797$			502.567i			0.630574i	0.948996	+	0.315287i	$0.102101\pi$
$797$			502.567i			0.630574i	−0.948996	+	0.315287i	$0.897899\pi$
$798$		0			0
$799$	402.108			0.503264
$800$		0			0
$801$	80.2465	+	46.3303i	0.100183	+	0.0578406i
$802$		0			0
$803$	108.696	−	188.267i	0.135362	−	0.234455i
$804$		0			0
$805$	−133.338			−0.165638
$806$		0			0
$807$	281.703	+	487.924i	0.349074	+	0.604614i
$808$		0			0
$809$	−359.621			−0.444525			−0.222262	−	0.974987i	$-0.571344\pi$
$809$	−359.621			−0.444525			−0.222262	+	0.974987i	$0.571344\pi$
$810$		0			0
$811$	636.875	−	367.700i	0.785295	−	0.453391i	−0.0530083	−	0.998594i	$-0.516881\pi$
$811$	636.875	−	367.700i	0.785295	−	0.453391i	0.838304	+	0.545204i	$0.183548\pi$
$812$		0			0
$813$	597.145	−	344.762i	0.734496	−	0.424061i
$814$		0			0
$815$	−325.194	+	563.252i	−0.399010	+	0.691106i
$816$		0			0
$817$	816.167	+	287.476i	0.998980	+	0.351868i
$818$		0			0
$819$	41.0240	+	23.6852i	0.0500903	+	0.0289197i
$820$		0			0
$821$	725.721	+	1256.99i	0.883947	+	1.53104i	0.846915	+	0.531728i	$0.178457\pi$
$821$	725.721	+	1256.99i	0.883947	+	1.53104i	0.0370320	+	0.999314i	$0.488210\pi$
$822$		0			0
$823$	649.344	+	1124.70i	0.788997	+	1.36658i	0.926582	+	0.376093i	$0.122733\pi$
$823$	649.344	+	1124.70i	0.788997	+	1.36658i	−0.137585	+	0.990490i	$0.543934\pi$
$824$		0			0
$825$			199.574i			0.241908i
$826$		0			0
$827$	−1293.14	+	746.597i	−1.56366	+	0.902778i	−0.566775	+	0.823873i	$0.691809\pi$
$827$	−1293.14	+	746.597i	−1.56366	+	0.902778i	−0.996882	+	0.0789047i	$0.974858\pi$
$828$		0			0
$829$		−	1308.23i		−	1.57808i	−0.614341	−	0.789041i	$-0.710578\pi$
$829$		−	1308.23i		−	1.57808i	0.614341	−	0.789041i	$-0.289422\pi$
$830$		0			0
$831$	−50.5863	−	29.2060i	−0.0608740	−	0.0351456i
$832$		0			0
$833$	629.703	−	1090.68i	0.755946	−	1.30934i
$834$		0			0
$835$		−	113.559i		−	0.135999i
$836$		0			0
$837$	−15.3782			−0.0183730
$838$		0			0
$839$	−443.149	−	255.852i	−0.528187	−	0.304949i	0.212091	−	0.977250i	$-0.431973\pi$
$839$	−443.149	−	255.852i	−0.528187	−	0.304949i	−0.740278	+	0.672301i	$0.765306\pi$
$840$		0			0
$841$	−115.091	+	199.343i	−0.136850	+	0.237031i
$842$		0			0
$843$	−327.411			−0.388388
$844$		0			0
$845$	−174.756	−	302.687i	−0.206812	−	0.358210i
$846$		0			0
$847$	177.116			0.209110
$848$		0			0
$849$	139.371	−	80.4660i	0.164159	−	0.0947774i
$850$		0			0
$851$	−324.207	+	187.181i	−0.380972	+	0.219954i
$852$		0			0
$853$	−445.497	+	771.624i	−0.522271	+	0.904600i	0.477393	+	0.878690i	$0.341582\pi$
$853$	−445.497	+	771.624i	−0.522271	+	0.904600i	−0.999664	+	0.0259104i	$0.991752\pi$
$854$		0			0
$855$	29.5617	+	158.017i	0.0345750	+	0.184815i
$856$		0			0
$857$	191.419	+	110.516i	0.223359	+	0.128957i	0.607505	−	0.794316i	$-0.292171\pi$
$857$	191.419	+	110.516i	0.223359	+	0.128957i	−0.384145	+	0.923273i	$0.625504\pi$
$858$		0			0
$859$	−83.6137	−	144.823i	−0.0973384	−	0.168595i	0.813244	−	0.581923i	$-0.197700\pi$
$859$	−83.6137	−	144.823i	−0.0973384	−	0.168595i	−0.910582	+	0.413328i	$0.864366\pi$
$860$		0			0
$861$	5.36028	+	9.28427i	0.00622564	+	0.0107831i
$862$		0			0
$863$			944.803i			1.09479i	0.836875	+	0.547395i	$0.184380\pi$
$863$			944.803i			1.09479i	−0.836875	+	0.547395i	$0.815620\pi$
$864$		0			0
$865$	−235.455	+	135.940i	−0.272202	+	0.157156i
$866$		0			0
$867$		−	953.375i		−	1.09962i
$868$		0			0
$869$	−647.843	−	374.032i	−0.745503	−	0.430417i
$870$		0			0
$871$	390.297	−	676.014i	0.448102	−	0.776136i
$872$		0			0
$873$			117.531i			0.134629i
$874$		0			0
$875$	278.899			0.318742
$876$		0			0
$877$	−516.211	−	298.035i	−0.588610	−	0.339834i	0.175937	−	0.984401i	$-0.443704\pi$
$877$	−516.211	−	298.035i	−0.588610	−	0.339834i	−0.764548	+	0.644567i	$0.777038\pi$
$878$		0			0
$879$	−265.761	+	460.311i	−0.302344	+	0.523676i
$880$		0			0
$881$	433.667			0.492245			0.246122	−	0.969239i	$-0.420844\pi$
$881$	433.667			0.492245			0.246122	+	0.969239i	$0.420844\pi$
$882$		0			0
$883$	−157.080	−	272.071i	−0.177894	−	0.308121i	0.763265	−	0.646085i	$-0.223595\pi$
$883$	−157.080	−	272.071i	−0.177894	−	0.308121i	−0.941159	+	0.337965i	$0.890262\pi$
$884$		0			0
$885$	−216.904			−0.245089
$886$		0			0
$887$	166.737	−	96.2657i	0.187979	−	0.108530i	−0.403057	−	0.915175i	$-0.632052\pi$
$887$	166.737	−	96.2657i	0.187979	−	0.108530i	0.591036	+	0.806645i	$0.298719\pi$
$888$		0			0
$889$	135.651	−	78.3184i	0.152589	−	0.0880972i
$890$		0			0
$891$	−30.4186	+	52.6866i	−0.0341399	+	0.0591320i
$892$		0			0
$893$	−200.228	+	171.594i	−0.224219	+	0.192155i
$894$		0			0
$895$	132.418	+	76.4516i	0.147953	+	0.0854208i
$896$		0			0
$897$	116.875	+	202.433i	0.130295	+	0.225678i
$898$		0			0
$899$	−36.5720	−	63.3446i	−0.0406808	−	0.0704612i
$900$		0			0
$901$		−	1802.28i		−	2.00031i
$902$		0			0
$903$	160.671	−	92.7636i	0.177931	−	0.102728i
$904$		0			0
$905$		−	836.794i		−	0.924634i
$906$		0			0
$907$	−475.032	−	274.260i	−0.523740	−	0.302382i	0.214723	−	0.976675i	$-0.431115\pi$
$907$	−475.032	−	274.260i	−0.523740	−	0.302382i	−0.738464	+	0.674293i	$0.764448\pi$
$908$		0			0
$909$	−223.619	+	387.320i	−0.246006	+	0.426094i
$910$		0			0
$911$		−	1112.17i		−	1.22083i	−0.792083	−	0.610413i	$-0.791003\pi$
$911$		−	1112.17i		−	1.22083i	0.792083	−	0.610413i	$-0.208997\pi$
$912$		0			0
$913$	291.958			0.319779
$914$		0			0
$915$	198.388	+	114.539i	0.216817	+	0.125180i
$916$		0			0
$917$	−64.8117	+	112.257i	−0.0706780	+	0.122418i
$918$		0			0
$919$	24.3541			0.0265006			0.0132503	−	0.999912i	$-0.495782\pi$
$919$	24.3541			0.0265006			0.0132503	+	0.999912i	$0.495782\pi$
$920$		0			0
$921$	31.6241	+	54.7746i	0.0343367	+	0.0594729i
$922$		0			0
$923$	126.645			0.137210
$924$		0			0
$925$	274.922	−	158.726i	0.297213	−	0.171596i
$926$		0			0
$927$	−6.41156	+	3.70171i	−0.00691646	+	0.00399322i
$928$		0			0
$929$	306.683	−	531.190i	0.330121	−	0.571787i	−0.652414	−	0.757863i	$-0.726244\pi$
$929$	306.683	−	531.190i	0.330121	−	0.571787i	0.982535	+	0.186076i	$0.0595770\pi$
$930$		0			0
$931$	151.874	+	811.815i	0.163130	+	0.871982i
$932$		0			0
$933$	32.0518	+	18.5051i	0.0343535	+	0.0198340i
$934$		0			0
$935$	−276.177	−	478.353i	−0.295377	−	0.511608i
$936$		0			0
$937$	159.561	+	276.367i	0.170289	+	0.294949i	0.938521	−	0.345222i	$-0.112197\pi$
$937$	159.561	+	276.367i	0.170289	+	0.294949i	−0.768232	+	0.640172i	$0.778863\pi$
$938$		0			0
$939$			503.165i			0.535852i
$940$		0			0
$941$	1128.61	−	651.606i	1.19938	−	0.692461i	0.238962	−	0.971029i	$-0.423193\pi$
$941$	1128.61	−	651.606i	1.19938	−	0.692461i	0.960417	+	0.278568i	$0.0898597\pi$
$942$		0			0
$943$			52.9007i			0.0560983i
$944$		0			0
$945$	29.8495	+	17.2336i	0.0315868	+	0.0182366i
$946$		0			0
$947$	−546.794	+	947.076i	−0.577396	+	1.00008i	0.418380	+	0.908272i	$0.362598\pi$
$947$	−546.794	+	947.076i	−0.577396	+	1.00008i	−0.995777	+	0.0918080i	$0.970735\pi$
$948$		0			0
$949$			215.912i			0.227515i
$950$		0			0
$951$	935.729			0.983942
$952$		0			0
$953$	−831.313	−	479.959i	−0.872312	−	0.503629i	−0.00419587	−	0.999991i	$-0.501336\pi$
$953$	−831.313	−	479.959i	−0.872312	−	0.503629i	−0.868116	+	0.496362i	$0.834669\pi$
$954$		0			0
$955$	−161.767	+	280.188i	−0.169389	+	0.293391i
$956$		0			0
$957$	−289.363			−0.302365
$958$		0			0
$959$	−133.434	−	231.115i	−0.139139	−	0.240996i
$960$		0			0
$961$	952.241			0.990886
$962$		0			0
$963$	−262.144	+	151.349i	−0.272216	+	0.157164i
$964$		0			0
$965$	−489.633	+	282.690i	−0.507391	+	0.292943i
$966$		0			0
$967$	−0.0676711	+	0.117210i	−6.99805e−5	+	0.000121210i	−0.866060	−	0.499939i	$-0.833356\pi$
$967$	−0.0676711	+	0.117210i	−6.99805e−5	+	0.000121210i	0.865990	+	0.500061i	$0.166689\pi$
$968$		0			0
$969$	620.447	+	723.981i	0.640296	+	0.747143i
$970$		0			0
$971$	−35.5538	−	20.5270i	−0.0366157	−	0.0211401i	0.481580	−	0.876402i	$-0.340063\pi$
$971$	−35.5538	−	20.5270i	−0.0366157	−	0.0211401i	−0.518196	+	0.855262i	$0.673396\pi$
$972$		0			0
$973$	161.918	+	280.450i	0.166411	+	0.288232i
$974$		0			0
$975$	−99.1078	−	171.660i	−0.101649	−	0.176061i
$976$		0			0
$977$		−	275.013i		−	0.281487i	−0.990046	−	0.140744i	$-0.955051\pi$
$977$		−	275.013i		−	0.281487i	0.990046	−	0.140744i	$-0.0449494\pi$
$978$		0			0
$979$	180.814	−	104.393i	0.184692	−	0.106632i
$980$		0			0
$981$			15.2261i			0.0155210i
$982$		0			0
$983$	1164.70	+	672.440i	1.18484	+	0.684069i	0.957130	−	0.289660i	$-0.0935421\pi$
$983$	1164.70	+	672.440i	1.18484	+	0.684069i	0.227712	+	0.973728i	$0.426875\pi$
$984$		0			0
$985$	−453.192	+	784.951i	−0.460093	+	0.796905i
$986$		0			0
$987$			56.5376i			0.0572822i
$988$		0			0
$989$	915.486			0.925668
$990$		0			0
$991$	903.854	+	521.840i	0.912063	+	0.526580i	0.881094	−	0.472941i	$-0.156808\pi$
$991$	903.854	+	521.840i	0.912063	+	0.526580i	0.0309683	+	0.999520i	$0.490141\pi$
$992$		0			0
$993$	121.435	−	210.332i	0.122291	−	0.211815i
$994$		0			0
$995$	115.465			0.116045
$996$		0			0
$997$	−398.017	−	689.385i	−0.399214	−	0.691460i	0.594415	−	0.804159i	$-0.297384\pi$
$997$	−398.017	−	689.385i	−0.399214	−	0.691460i	−0.993629	+	0.112699i	$0.964050\pi$
$998$		0			0
$999$	96.7705			0.0968674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.e.673.1		6
4.3	odd	2		228.3.l.d.217.1	yes	6
12.11	even	2		684.3.y.f.217.3		6
19.12	odd	6	inner	912.3.be.e.145.1		6
76.31	even	6		228.3.l.d.145.1	✓	6
228.107	odd	6		684.3.y.f.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.d.145.1	✓	6	76.31	even	6
228.3.l.d.217.1	yes	6	4.3	odd	2
684.3.y.f.145.3		6	228.107	odd	6
684.3.y.f.217.3		6	12.11	even	2
912.3.be.e.145.1		6	19.12	odd	6	inner
912.3.be.e.673.1		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(-1.41016 + 2.44247i) q^{5} -2.35194 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(-1.41016 + 2.44247i) q^{5} -2.35194 q^{7} +(1.50000 + 2.59808i) q^{9} +6.75970 q^{11} +(-5.81421 + 3.35683i) q^{13} +(-4.23048 + 2.44247i) q^{15} +(-14.4865 + 25.0913i) q^{17} +(-3.49389 - 18.6760i) q^{19} +(-3.52791 - 2.03684i) q^{21} +(-10.0508 - 17.4085i) q^{23} +(8.52289 + 14.7621i) q^{25} +5.19615i q^{27} +(-21.4036 + 12.3574i) q^{29} +2.95953i q^{31} +(10.1395 + 5.85407i) q^{33} +(3.31661 - 5.74454i) q^{35} -18.6235i q^{37} -11.6284 q^{39} +(-2.27909 - 1.31583i) q^{41} +(-22.7715 + 39.4413i) q^{43} -8.46096 q^{45} +(-6.93937 - 12.0193i) q^{47} -43.4684 q^{49} +(-43.4594 + 25.0913i) q^{51} +(-53.8718 + 31.1029i) q^{53} +(-9.53226 + 16.5104i) q^{55} +(10.9331 - 31.0398i) q^{57} +(38.4538 + 22.2013i) q^{59} +(-23.4474 - 40.6121i) q^{61} +(-3.52791 - 6.11052i) q^{63} -18.9347i q^{65} +(-100.692 + 58.1347i) q^{67} -34.8170i q^{69} +(-16.3365 - 9.43186i) q^{71} +(16.0800 - 27.8514i) q^{73} +29.5242i q^{75} -15.8984 q^{77} +(-95.8390 - 55.3327i) q^{79} +(-4.50000 + 7.79423i) q^{81} +43.1910 q^{83} +(-40.8565 - 70.7655i) q^{85} -42.8072 q^{87} +(26.7488 - 15.4434i) q^{89} +(13.6747 - 7.89507i) q^{91} +(-2.56303 + 4.43930i) q^{93} +(50.5425 + 17.8024i) q^{95} +(33.9282 + 19.5885i) q^{97} +(10.1395 + 17.5622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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