LMFDB - Embedded newform 912.3.be.i.145.7

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 51 x^{18} + 314 x^{17} + 631 x^{16} - 7264 x^{15} + 8030 x^{14} + 12664 x^{13} + \cdots + 26753228352 $ x^20 - 2x^19 - 51x^18 + 314x^17 + 631x^16 - 7264x^15 + 8030x^14 + 12664x^13 + 393231x^12 - 447686x^11 - 9929427x^10 + 44358366x^9 - 34218119x^8 - 65904712x^7 + 1769085384x^6 - 7530122944x^5 + 6630672896x^4 + 46763900480x^3 - 4377536384x^2 - 53791886208*x + 26753228352
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.7
Root			$-1.45625 + 0.503882i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.i.673.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(1.07526 + 1.86241i) q^{5} +5.32572 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(1.07526 + 1.86241i) q^{5} +5.32572 q^{7} +(1.50000 - 2.59808i) q^{9} +18.2063 q^{11} +(-9.90684 - 5.71972i) q^{13} +(-3.22578 - 1.86241i) q^{15} +(-8.69628 - 15.0624i) q^{17} +(12.2511 - 14.5228i) q^{19} +(-7.98858 + 4.61221i) q^{21} +(-4.73979 + 8.20955i) q^{23} +(10.1876 - 17.6455i) q^{25} +5.19615i q^{27} +(-8.05732 - 4.65189i) q^{29} +10.1162i q^{31} +(-27.3094 + 15.7671i) q^{33} +(5.72654 + 9.91866i) q^{35} +5.66509i q^{37} +19.8137 q^{39} +(-1.13056 + 0.652727i) q^{41} +(-8.23253 - 14.2592i) q^{43} +6.45156 q^{45} +(11.7234 - 20.3055i) q^{47} -20.6367 q^{49} +(26.0888 + 15.0624i) q^{51} +(9.79486 + 5.65506i) q^{53} +(19.5765 + 33.9074i) q^{55} +(-5.79957 + 32.3939i) q^{57} +(65.2854 - 37.6925i) q^{59} +(45.9426 - 79.5749i) q^{61} +(7.98858 - 13.8366i) q^{63} -24.6007i q^{65} +(-9.19896 - 5.31102i) q^{67} -16.4191i q^{69} +(102.889 - 59.4032i) q^{71} +(70.7697 + 122.577i) q^{73} +35.2910i q^{75} +96.9614 q^{77} +(-58.0107 + 33.4925i) q^{79} +(-4.50000 - 7.79423i) q^{81} +135.251 q^{83} +(18.7015 - 32.3920i) q^{85} +16.1146 q^{87} +(-68.1236 - 39.3312i) q^{89} +(-52.7611 - 30.4616i) q^{91} +(-8.76091 - 15.1743i) q^{93} +(40.2204 + 7.20077i) q^{95} +(41.2162 - 23.7962i) q^{97} +(27.3094 - 47.3012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	$ 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$5$	1.07526	+	1.86241i	0.215052	+	0.372481i	0.953289	−	0.302061i	$-0.0976745\pi$
$5$	1.07526	+	1.86241i	0.215052	+	0.372481i	−0.738237	+	0.674542i	$0.764341\pi$
$6$		0			0
$7$	5.32572			0.760817			0.380409	−	0.924818i	$-0.375783\pi$
$7$	5.32572			0.760817			0.380409	+	0.924818i	$0.375783\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	18.2063			1.65511			0.827557	−	0.561382i	$-0.189730\pi$
$11$	18.2063			1.65511			0.827557	+	0.561382i	$0.189730\pi$
$12$		0			0
$13$	−9.90684	−	5.71972i	−0.762065	−	0.439978i	0.0679720	−	0.997687i	$-0.478347\pi$
$13$	−9.90684	−	5.71972i	−0.762065	−	0.439978i	−0.830036	+	0.557709i	$0.811680\pi$
$14$		0			0
$15$	−3.22578	−	1.86241i	−0.215052	−	0.124160i
$16$		0			0
$17$	−8.69628	−	15.0624i	−0.511546	−	0.886023i	−0.999910	−	0.0133837i	$-0.995740\pi$
$17$	−8.69628	−	15.0624i	−0.511546	−	0.886023i	0.488365	−	0.872640i	$-0.337594\pi$
$18$		0			0
$19$	12.2511	−	14.5228i	0.644795	−	0.764356i
$19$	12.2511	−	14.5228i	0.644795	−	0.764356i
$20$		0			0
$21$	−7.98858	+	4.61221i	−0.380409	+	0.219629i
$22$		0			0
$23$	−4.73979	+	8.20955i	−0.206078	+	0.356937i	−0.950476	−	0.310799i	$-0.899403\pi$
$23$	−4.73979	+	8.20955i	−0.206078	+	0.356937i	0.744398	+	0.667736i	$0.232737\pi$
$24$		0			0
$25$	10.1876	−	17.6455i	0.407505	−	0.705820i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−8.05732	−	4.65189i	−0.277839	−	0.160410i	0.354606	−	0.935016i	$-0.384615\pi$
$29$	−8.05732	−	4.65189i	−0.277839	−	0.160410i	−0.632445	+	0.774606i	$0.717948\pi$
$30$		0			0
$31$			10.1162i			0.326330i	0.986599	+	0.163165i	$0.0521703\pi$
$31$			10.1162i			0.326330i	−0.986599	+	0.163165i	$0.947830\pi$
$32$		0			0
$33$	−27.3094	+	15.7671i	−0.827557	+	0.477790i
$34$		0			0
$35$	5.72654	+	9.91866i	0.163615	+	0.283390i
$36$		0			0
$37$			5.66509i			0.153111i	0.997065	+	0.0765553i	$0.0243922\pi$
$37$			5.66509i			0.153111i	−0.997065	+	0.0765553i	$0.975608\pi$
$38$		0			0
$39$	19.8137			0.508043
$40$		0			0
$41$	−1.13056	+	0.652727i	−0.0275745	+	0.0159202i	−0.513724	−	0.857956i	$-0.671734\pi$
$41$	−1.13056	+	0.652727i	−0.0275745	+	0.0159202i	0.486149	+	0.873876i	$0.338401\pi$
$42$		0			0
$43$	−8.23253	−	14.2592i	−0.191454	−	0.331608i	0.754278	−	0.656555i	$-0.227987\pi$
$43$	−8.23253	−	14.2592i	−0.191454	−	0.331608i	−0.945732	+	0.324947i	$0.894654\pi$
$44$		0			0
$45$	6.45156			0.143368
$46$		0			0
$47$	11.7234	−	20.3055i	0.249433	−	0.432031i	−0.713935	−	0.700212i	$-0.753089\pi$
$47$	11.7234	−	20.3055i	0.249433	−	0.432031i	0.963369	+	0.268180i	$0.0864223\pi$
$48$		0			0
$49$	−20.6367			−0.421157
$50$		0			0
$51$	26.0888	+	15.0624i	0.511546	+	0.295341i
$52$		0			0
$53$	9.79486	+	5.65506i	0.184809	+	0.106699i	0.589550	−	0.807732i	$-0.299305\pi$
$53$	9.79486	+	5.65506i	0.184809	+	0.106699i	−0.404741	+	0.914431i	$0.632638\pi$
$54$		0			0
$55$	19.5765	+	33.9074i	0.355936	+	0.616499i
$56$		0			0
$57$	−5.79957	+	32.3939i	−0.101747	+	0.568314i
$58$		0			0
$59$	65.2854	−	37.6925i	1.10653	−	0.638857i	0.168603	−	0.985684i	$-0.446074\pi$
$59$	65.2854	−	37.6925i	1.10653	−	0.638857i	0.937929	+	0.346827i	$0.112741\pi$
$60$		0			0
$61$	45.9426	−	79.5749i	0.753158	−	1.30451i	−0.193127	−	0.981174i	$-0.561863\pi$
$61$	45.9426	−	79.5749i	0.753158	−	1.30451i	0.946285	−	0.323334i	$-0.104804\pi$
$62$		0			0
$63$	7.98858	−	13.8366i	0.126803	−	0.219629i
$64$		0			0
$65$		−	24.6007i		−	0.378473i
$66$		0			0
$67$	−9.19896	−	5.31102i	−0.137298	−	0.0792689i	0.429778	−	0.902935i	$-0.358592\pi$
$67$	−9.19896	−	5.31102i	−0.137298	−	0.0792689i	−0.567076	+	0.823666i	$0.691925\pi$
$68$		0			0
$69$		−	16.4191i		−	0.237958i
$70$		0			0
$71$	102.889	−	59.4032i	1.44914	−	0.836664i	0.450714	−	0.892668i	$-0.351169\pi$
$71$	102.889	−	59.4032i	1.44914	−	0.836664i	0.998431	+	0.0560041i	$0.0178360\pi$
$72$		0			0
$73$	70.7697	+	122.577i	0.969447	+	1.67913i	0.697159	+	0.716916i	$0.254447\pi$
$73$	70.7697	+	122.577i	0.969447	+	1.67913i	0.272288	+	0.962216i	$0.412220\pi$
$74$		0			0
$75$			35.2910i			0.470546i
$76$		0			0
$77$	96.9614			1.25924
$78$		0			0
$79$	−58.0107	+	33.4925i	−0.734312	+	0.423955i	−0.819998	−	0.572367i	$-0.806025\pi$
$79$	−58.0107	+	33.4925i	−0.734312	+	0.423955i	0.0856854	+	0.996322i	$0.472692\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	135.251			1.62953			0.814766	−	0.579790i	$-0.196865\pi$
$83$	135.251			1.62953			0.814766	+	0.579790i	$0.196865\pi$
$84$		0			0
$85$	18.7015	−	32.3920i	0.220018	−	0.381083i
$86$		0			0
$87$	16.1146			0.185226
$88$		0			0
$89$	−68.1236	−	39.3312i	−0.765434	−	0.441923i	0.0658096	−	0.997832i	$-0.479037\pi$
$89$	−68.1236	−	39.3312i	−0.765434	−	0.441923i	−0.831243	+	0.555909i	$0.812370\pi$
$90$		0			0
$91$	−52.7611	−	30.4616i	−0.579792	−	0.334743i
$92$		0			0
$93$	−8.76091	−	15.1743i	−0.0942033	−	0.163165i
$94$		0			0
$95$	40.2204	+	7.20077i	0.423373	+	0.0757975i
$96$		0			0
$97$	41.2162	−	23.7962i	0.424910	−	0.245322i	−0.272266	−	0.962222i	$-0.587773\pi$
$97$	41.2162	−	23.7962i	0.424910	−	0.245322i	0.697176	+	0.716900i	$0.254440\pi$
$98$		0			0
$99$	27.3094	−	47.3012i	0.275852	−	0.477790i
$100$		0			0
$101$	50.3741	−	87.2505i	0.498753	−	0.863866i	−0.501246	−	0.865305i	$-0.667125\pi$
$101$	50.3741	−	87.2505i	0.498753	−	0.863866i	0.999999	+	0.00143892i	$0.000458022\pi$
$102$		0			0
$103$			157.065i			1.52490i	0.647046	+	0.762451i	$0.276004\pi$
$103$			157.065i			1.52490i	−0.647046	+	0.762451i	$0.723996\pi$
$104$		0			0
$105$	−17.1796	−	9.91866i	−0.163615	−	0.0944634i
$106$		0			0
$107$			29.1037i			0.271997i	0.990709	+	0.135999i	$0.0434243\pi$
$107$			29.1037i			0.271997i	−0.990709	+	0.135999i	$0.956576\pi$
$108$		0			0
$109$	−14.0563	+	8.11539i	−0.128957	+	0.0744531i	−0.563091	−	0.826395i	$-0.690388\pi$
$109$	−14.0563	+	8.11539i	−0.128957	+	0.0744531i	0.434134	+	0.900848i	$0.357054\pi$
$110$		0			0
$111$	−4.90611	−	8.49764i	−0.0441992	−	0.0765553i
$112$		0			0
$113$			150.287i			1.32997i	0.746857	+	0.664985i	$0.231562\pi$
$113$			150.287i			1.32997i	−0.746857	+	0.664985i	$0.768438\pi$
$114$		0			0
$115$	−20.3860			−0.177270
$116$		0			0
$117$	−29.7205	+	17.1591i	−0.254022	+	0.146659i
$118$		0			0
$119$	−46.3140	−	80.2181i	−0.389193	−	0.674102i
$120$		0			0
$121$	210.468			1.73940
$122$		0			0
$123$	1.13056	−	1.95818i	0.00919151	−	0.0159202i
$124$		0			0
$125$	97.5805			0.780644
$126$		0			0
$127$	−88.4466	−	51.0647i	−0.696430	−	0.402084i	0.109587	−	0.993977i	$-0.465047\pi$
$127$	−88.4466	−	51.0647i	−0.696430	−	0.402084i	−0.806016	+	0.591893i	$0.798381\pi$
$128$		0			0
$129$	24.6976	+	14.2592i	0.191454	+	0.110536i
$130$		0			0
$131$	−32.8459	−	56.8908i	−0.250732	−	0.434281i	0.712995	−	0.701169i	$-0.247338\pi$
$131$	−32.8459	−	56.8908i	−0.250732	−	0.434281i	−0.963728	+	0.266888i	$0.914005\pi$
$132$		0			0
$133$	65.2459	−	77.3442i	0.490571	−	0.581535i
$134$		0			0
$135$	−9.67735	+	5.58722i	−0.0716841	+	0.0413868i
$136$		0			0
$137$	81.0444	−	140.373i	0.591565	−	1.02462i	−0.402457	−	0.915439i	$-0.631844\pi$
$137$	81.0444	−	140.373i	0.591565	−	1.02462i	0.994022	−	0.109181i	$-0.0348229\pi$
$138$		0			0
$139$	74.4092	−	128.881i	0.535318	−	0.927198i	−0.463830	−	0.885924i	$-0.653525\pi$
$139$	74.4092	−	128.881i	0.535318	−	0.927198i	0.999148	−	0.0412740i	$-0.0131417\pi$
$140$		0			0
$141$			40.6109i			0.288021i
$142$		0			0
$143$	−180.366	−	104.135i	−1.26130	−	0.728214i
$144$		0			0
$145$		−	20.0080i		−	0.137986i
$146$		0			0
$147$	30.9550	−	17.8719i	0.210578	−	0.121578i
$148$		0			0
$149$	33.5596	+	58.1270i	0.225232	+	0.390114i	0.956389	−	0.292096i	$-0.0943525\pi$
$149$	33.5596	+	58.1270i	0.225232	+	0.390114i	−0.731157	+	0.682210i	$0.761019\pi$
$150$		0			0
$151$			139.749i			0.925491i	0.886491	+	0.462745i	$0.153136\pi$
$151$			139.749i			0.925491i	−0.886491	+	0.462745i	$0.846864\pi$
$152$		0			0
$153$	−52.1777			−0.341031
$154$		0			0
$155$	−18.8405	+	10.8776i	−0.121552	+	0.0701780i
$156$		0			0
$157$	51.0203	+	88.3697i	0.324970	+	0.562864i	0.981506	−	0.191430i	$-0.0613125\pi$
$157$	51.0203	+	88.3697i	0.324970	+	0.562864i	−0.656536	+	0.754294i	$0.727979\pi$
$158$		0			0
$159$	−19.5897			−0.123206
$160$		0			0
$161$	−25.2428	+	43.7218i	−0.156787	+	0.271564i
$162$		0			0
$163$	−100.064			−0.613890			−0.306945	−	0.951727i	$-0.599307\pi$
$163$	−100.064			−0.613890			−0.306945	+	0.951727i	$0.599307\pi$
$164$		0			0
$165$	−58.7294	−	33.9074i	−0.355936	−	0.205500i
$166$		0			0
$167$	232.549	+	134.262i	1.39251	+	0.803966i	0.993593	−	0.113021i	$-0.0360526\pi$
$167$	232.549	+	134.262i	1.39251	+	0.803966i	0.398918	+	0.916987i	$0.369386\pi$
$168$		0			0
$169$	−19.0697	−	33.0297i	−0.112838	−	0.195442i
$170$		0			0
$171$	−19.3546	−	53.6134i	−0.113185	−	0.313529i
$172$		0			0
$173$	33.4499	−	19.3123i	0.193352	−	0.111632i	−0.400199	−	0.916428i	$-0.631059\pi$
$173$	33.4499	−	19.3123i	0.193352	−	0.111632i	0.593551	+	0.804796i	$0.297726\pi$
$174$		0			0
$175$	54.2565	−	93.9750i	0.310037	−	0.537000i
$176$		0			0
$177$	−65.2854	+	113.078i	−0.368844	+	0.638857i
$178$		0			0
$179$		−	31.8753i		−	0.178074i	−0.996028	−	0.0890372i	$-0.971621\pi$
$179$		−	31.8753i		−	0.178074i	0.996028	−	0.0890372i	$-0.0283790\pi$
$180$		0			0
$181$	189.426	+	109.365i	1.04655	+	0.604228i	0.921682	−	0.387945i	$-0.126815\pi$
$181$	189.426	+	109.365i	1.04655	+	0.604228i	0.124871	+	0.992173i	$0.460148\pi$
$182$		0			0
$183$			159.150i			0.869672i
$184$		0			0
$185$	−10.5507	+	6.09145i	−0.0570308	+	0.0329268i
$186$		0			0
$187$	−158.327	−	274.230i	−0.846667	−	1.46647i
$188$		0			0
$189$			27.6733i			0.146419i
$190$		0			0
$191$	−188.366			−0.986207			−0.493103	−	0.869971i	$-0.664138\pi$
$191$	−188.366			−0.986207			−0.493103	+	0.869971i	$0.664138\pi$
$192$		0			0
$193$	−85.5465	+	49.3903i	−0.443246	+	0.255908i	−0.704974	−	0.709234i	$-0.749041\pi$
$193$	−85.5465	+	49.3903i	−0.443246	+	0.255908i	0.261728	+	0.965142i	$0.415708\pi$
$194$		0			0
$195$	21.3049	+	36.9011i	0.109256	+	0.189237i
$196$		0			0
$197$	−247.935			−1.25855			−0.629276	−	0.777182i	$-0.716649\pi$
$197$	−247.935			−1.25855			−0.629276	+	0.777182i	$0.716649\pi$
$198$		0			0
$199$	−106.619	+	184.669i	−0.535772	+	0.927985i	0.463353	+	0.886174i	$0.346646\pi$
$199$	−106.619	+	184.669i	−0.535772	+	0.927985i	−0.999126	+	0.0418111i	$0.986687\pi$
$200$		0			0
$201$	18.3979			0.0915319
$202$		0			0
$203$	−42.9110	−	24.7747i	−0.211384	−	0.122043i
$204$		0			0
$205$	−2.43128	−	1.40370i	−0.0118599	−	0.00684733i
$206$		0			0
$207$	14.2194	+	24.6287i	0.0686925	+	0.118979i
$208$		0			0
$209$	223.047	−	264.405i	1.06721	−	1.26510i
$210$		0			0
$211$	−247.414	+	142.845i	−1.17258	+	0.676989i	−0.954286	−	0.298894i	$-0.903382\pi$
$211$	−247.414	+	142.845i	−1.17258	+	0.676989i	−0.218293	+	0.975883i	$0.570049\pi$
$212$		0			0
$213$	−102.889	+	178.209i	−0.483048	+	0.836664i
$214$		0			0
$215$	17.7042	−	30.6646i	0.0823453	−	0.142626i
$216$		0			0
$217$			53.8762i			0.248278i
$218$		0			0
$219$	−212.309	−	122.577i	−0.969447	−	0.559711i
$220$		0			0
$221$			198.961i			0.900276i
$222$		0			0
$223$	−227.339	+	131.254i	−1.01946	+	0.588584i	−0.913947	−	0.405834i	$-0.866981\pi$
$223$	−227.339	+	131.254i	−1.01946	+	0.588584i	−0.105511	+	0.994418i	$0.533648\pi$
$224$		0			0
$225$	−30.5629	−	52.9365i	−0.135835	−	0.235273i
$226$		0			0
$227$		−	125.918i		−	0.554707i	−0.960768	−	0.277353i	$-0.910543\pi$
$227$		−	125.918i		−	0.554707i	0.960768	−	0.277353i	$-0.0894572\pi$
$228$		0			0
$229$	−152.277			−0.664963			−0.332482	−	0.943110i	$-0.607886\pi$
$229$	−152.277			−0.664963			−0.332482	+	0.943110i	$0.607886\pi$
$230$		0			0
$231$	−145.442	+	83.9711i	−0.629620	+	0.363511i
$232$		0			0
$233$	−107.867	−	186.832i	−0.462951	−	0.801854i	0.536156	−	0.844119i	$-0.319876\pi$
$233$	−107.867	−	186.832i	−0.462951	−	0.801854i	−0.999106	+	0.0422652i	$0.986543\pi$
$234$		0			0
$235$	50.4227			0.214565
$236$		0			0
$237$	58.0107	−	100.477i	0.244771	−	0.423955i
$238$		0			0
$239$	254.240			1.06377			0.531884	−	0.846817i	$-0.321484\pi$
$239$	254.240			1.06377			0.531884	+	0.846817i	$0.321484\pi$
$240$		0			0
$241$	−207.811	−	119.980i	−0.862288	−	0.497842i	0.00248988	−	0.999997i	$-0.499207\pi$
$241$	−207.811	−	119.980i	−0.862288	−	0.497842i	−0.864778	+	0.502155i	$0.832541\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−22.1898	−	38.4339i	−0.0905707	−	0.156873i
$246$		0			0
$247$	−204.436	+	73.8019i	−0.827675	+	0.298793i
$248$		0			0
$249$	−202.877	+	117.131i	−0.814766	+	0.470406i
$250$		0			0
$251$	206.901	−	358.363i	0.824308	−	1.42774i	−0.0781396	−	0.996942i	$-0.524898\pi$
$251$	206.901	−	358.363i	0.824308	−	1.42774i	0.902447	−	0.430800i	$-0.141769\pi$
$252$		0			0
$253$	−86.2937	+	149.465i	−0.341082	+	0.590771i
$254$		0			0
$255$			64.7840i			0.254055i
$256$		0			0
$257$	21.3939	+	12.3518i	0.0832448	+	0.0480614i	0.541045	−	0.840994i	$-0.318029\pi$
$257$	21.3939	+	12.3518i	0.0832448	+	0.0480614i	−0.457800	+	0.889055i	$0.651362\pi$
$258$		0			0
$259$			30.1707i			0.116489i
$260$		0			0
$261$	−24.1720	+	13.9557i	−0.0926129	+	0.0534701i
$262$		0			0
$263$	173.909	+	301.219i	0.661250	+	1.14532i	0.980288	+	0.197576i	$0.0633069\pi$
$263$	173.909	+	301.219i	0.661250	+	1.14532i	−0.319038	+	0.947742i	$0.603360\pi$
$264$		0			0
$265$			24.3227i			0.0917837i
$266$		0			0
$267$	136.247			0.510289
$268$		0			0
$269$	161.992	−	93.5262i	0.602201	−	0.347681i	−0.167706	−	0.985837i	$-0.553636\pi$
$269$	161.992	−	93.5262i	0.602201	−	0.347681i	0.769907	+	0.638156i	$0.220303\pi$
$270$		0			0
$271$	161.253	+	279.298i	0.595029	+	1.03062i	0.993543	+	0.113458i	$0.0361929\pi$
$271$	161.253	+	279.298i	0.595029	+	1.03062i	−0.398513	+	0.917162i	$0.630474\pi$
$272$		0			0
$273$	105.522			0.386528
$274$		0			0
$275$	185.479	−	321.258i	0.674467	−	1.16821i
$276$		0			0
$277$	−430.362			−1.55365			−0.776827	−	0.629714i	$-0.783172\pi$
$277$	−430.362			−1.55365			−0.776827	+	0.629714i	$0.783172\pi$
$278$		0			0
$279$	26.2827	+	15.1743i	0.0942033	+	0.0543883i
$280$		0			0
$281$	−343.289	−	198.198i	−1.22167	−	0.705332i	−0.256396	−	0.966572i	$-0.582535\pi$
$281$	−343.289	−	198.198i	−1.22167	−	0.705332i	−0.965274	+	0.261240i	$0.915869\pi$
$282$		0			0
$283$	197.271	+	341.684i	0.697072	+	1.20736i	0.969477	+	0.245181i	$0.0788474\pi$
$283$	197.271	+	341.684i	0.697072	+	1.20736i	−0.272406	+	0.962182i	$0.587819\pi$
$284$		0			0
$285$	−66.5667	+	24.0307i	−0.233567	+	0.0843184i
$286$		0			0
$287$	−6.02103	+	3.47624i	−0.0209792	+	0.0121123i
$288$		0			0
$289$	−6.75057	+	11.6923i	−0.0233584	+	0.0404579i
$290$		0			0
$291$	−41.2162	+	71.3886i	−0.141637	+	0.245322i
$292$		0			0
$293$		−	206.585i		−	0.705067i	−0.935799	−	0.352533i	$-0.885320\pi$
$293$		−	206.585i		−	0.705067i	0.935799	−	0.352533i	$-0.114680\pi$
$294$		0			0
$295$	140.398	+	81.0586i	0.475924	+	0.274775i
$296$		0			0
$297$			94.6025i			0.318527i
$298$		0			0
$299$	93.9126	−	54.2205i	0.314089	−	0.181339i
$300$		0			0
$301$	−43.8442	−	75.9403i	−0.145662	−	0.252293i
$302$		0			0
$303$			174.501i			0.575911i
$304$		0			0
$305$	197.601			0.647873
$306$		0			0
$307$	260.211	−	150.233i	0.847593	−	0.489358i	−0.0122451	−	0.999925i	$-0.503898\pi$
$307$	260.211	−	150.233i	0.847593	−	0.489358i	0.859838	+	0.510567i	$0.170565\pi$
$308$		0			0
$309$	−136.022	−	235.597i	−0.440201	−	0.762451i
$310$		0			0
$311$	−257.552			−0.828140			−0.414070	−	0.910245i	$-0.635893\pi$
$311$	−257.552			−0.828140			−0.414070	+	0.910245i	$0.635893\pi$
$312$		0			0
$313$	−225.508	+	390.591i	−0.720473	+	1.24790i	0.240338	+	0.970689i	$0.422742\pi$
$313$	−225.508	+	390.591i	−0.720473	+	1.24790i	−0.960811	+	0.277206i	$0.910592\pi$
$314$		0			0
$315$	34.3592			0.109077
$316$		0			0
$317$	−171.188	−	98.8353i	−0.540025	−	0.311783i	0.205064	−	0.978749i	$-0.434260\pi$
$317$	−171.188	−	98.8353i	−0.540025	−	0.311783i	−0.745089	+	0.666965i	$0.767593\pi$
$318$		0			0
$319$	−146.694	−	84.6936i	−0.459854	−	0.265497i
$320$		0			0
$321$	−25.2046	−	43.6556i	−0.0785189	−	0.135999i
$322$		0			0
$323$	−325.287	−	58.2369i	−1.00708	−	0.180300i
$324$		0			0
$325$	−201.854	+	116.541i	−0.621090	+	0.358587i
$326$		0			0
$327$	14.0563	−	24.3462i	0.0429855	−	0.0744531i
$328$		0			0
$329$	62.4354	−	108.141i	0.189773	−	0.328697i
$330$		0			0
$331$		−	117.443i		−	0.354814i	−0.984138	−	0.177407i	$-0.943229\pi$
$331$		−	117.443i		−	0.354814i	0.984138	−	0.177407i	$-0.0567708\pi$
$332$		0			0
$333$	14.7183	+	8.49764i	0.0441992	+	0.0255184i
$334$		0			0
$335$		−	22.8429i		−	0.0681878i
$336$		0			0
$337$	−476.437	+	275.071i	−1.41376	+	0.816235i	−0.995740	−	0.0922030i	$-0.970609\pi$
$337$	−476.437	+	275.071i	−1.41376	+	0.816235i	−0.418020	+	0.908438i	$0.637276\pi$
$338$		0			0
$339$	−130.152	−	225.430i	−0.383929	−	0.664985i
$340$		0			0
$341$			184.179i			0.540113i
$342$		0			0
$343$	−370.866			−1.08124
$344$		0			0
$345$	30.5790	−	17.6548i	0.0886349	−	0.0511734i
$346$		0			0
$347$	42.4626	+	73.5474i	0.122371	+	0.211952i	0.920702	−	0.390266i	$-0.127617\pi$
$347$	42.4626	+	73.5474i	0.122371	+	0.211952i	−0.798331	+	0.602218i	$0.794284\pi$
$348$		0			0
$349$	−354.536			−1.01586			−0.507931	−	0.861398i	$-0.669589\pi$
$349$	−354.536			−1.01586			−0.507931	+	0.861398i	$0.669589\pi$
$350$		0			0
$351$	29.7205	−	51.4774i	0.0846738	−	0.146659i
$352$		0			0
$353$	450.927			1.27741			0.638706	−	0.769451i	$-0.279470\pi$
$353$	450.927			1.27741			0.638706	+	0.769451i	$0.279470\pi$
$354$		0			0
$355$	221.266	+	127.748i	0.623283	+	0.359853i
$356$		0			0
$357$	138.942	+	80.2181i	0.389193	+	0.224701i
$358$		0			0
$359$	157.812	+	273.338i	0.439588	+	0.761389i	0.997658	−	0.0684055i	$-0.0217912\pi$
$359$	157.812	+	273.338i	0.439588	+	0.761389i	−0.558070	+	0.829794i	$0.688458\pi$
$360$		0			0
$361$	−60.8212	−	355.840i	−0.168480	−	0.985705i
$362$		0			0
$363$	−315.702	+	182.270i	−0.869701	+	0.502122i
$364$		0			0
$365$	−152.192	+	263.604i	−0.416964	+	0.722202i
$366$		0			0
$367$	342.205	−	592.716i	0.932439	−	1.61503i	0.153300	−	0.988180i	$-0.451010\pi$
$367$	342.205	−	592.716i	0.932439	−	1.61503i	0.779139	−	0.626851i	$-0.215657\pi$
$368$		0			0
$369$			3.91636i			0.0106134i
$370$		0			0
$371$	52.1647	+	30.1173i	0.140606	+	0.0811787i
$372$		0			0
$373$			26.3414i			0.0706203i	0.999376	+	0.0353101i	$0.0112419\pi$
$373$			26.3414i			0.0706203i	−0.999376	+	0.0353101i	$0.988758\pi$
$374$		0			0
$375$	−146.371	+	84.5072i	−0.390322	+	0.225352i
$376$		0			0
$377$	53.2150	+	92.1711i	0.141154	+	0.244486i
$378$		0			0
$379$			148.044i			0.390617i	0.980742	+	0.195309i	$0.0625708\pi$
$379$			148.044i			0.390617i	−0.980742	+	0.195309i	$0.937429\pi$
$380$		0			0
$381$	176.893			0.464286
$382$		0			0
$383$	−514.266	+	296.912i	−1.34273	+	0.775226i	−0.987207	−	0.159441i	$-0.949031\pi$
$383$	−514.266	+	296.912i	−1.34273	+	0.775226i	−0.355524	+	0.934667i	$0.615697\pi$
$384$		0			0
$385$	104.259	+	180.582i	0.270802	+	0.469043i
$386$		0			0
$387$	−49.3952			−0.127636
$388$		0			0
$389$	19.7594	−	34.2242i	0.0507952	−	0.0879800i	−0.839510	−	0.543345i	$-0.817158\pi$
$389$	19.7594	−	34.2242i	0.0507952	−	0.0879800i	0.890305	+	0.455365i	$0.150491\pi$
$390$		0			0
$391$	164.874			0.421673
$392$		0			0
$393$	98.5378	+	56.8908i	0.250732	+	0.144760i
$394$		0			0
$395$	−124.753	−	72.0263i	−0.315831	−	0.182345i
$396$		0			0
$397$	−291.238	−	504.439i	−0.733597	−	1.27063i	−0.955336	−	0.295522i	$-0.904507\pi$
$397$	−291.238	−	504.439i	−0.733597	−	1.27063i	0.221739	−	0.975106i	$-0.428827\pi$
$398$		0			0
$399$	−30.8869	+	172.521i	−0.0774107	+	0.432383i
$400$		0			0
$401$	−326.654	+	188.594i	−0.814599	+	0.470309i	−0.848551	−	0.529114i	$-0.822524\pi$
$401$	−326.654	+	188.594i	−0.814599	+	0.470309i	0.0339512	+	0.999423i	$0.489191\pi$
$402$		0			0
$403$	57.8620	−	100.220i	0.143578	−	0.248684i
$404$		0			0
$405$	9.67735	−	16.7617i	0.0238947	−	0.0413868i
$406$		0			0
$407$			103.140i			0.253416i
$408$		0			0
$409$	12.0685	+	6.96776i	0.0295074	+	0.0170361i	0.514681	−	0.857382i	$-0.327910\pi$
$409$	12.0685	+	6.96776i	0.0295074	+	0.0170361i	−0.485174	+	0.874418i	$0.661244\pi$
$410$		0			0
$411$			280.746i			0.683080i
$412$		0			0
$413$	347.692	−	200.740i	0.841869	−	0.486053i
$414$		0			0
$415$	145.430	+	251.893i	0.350435	+	0.606970i
$416$		0			0
$417$			257.761i			0.618132i
$418$		0			0
$419$	166.159			0.396561			0.198281	−	0.980145i	$-0.436464\pi$
$419$	166.159			0.396561			0.198281	+	0.980145i	$0.436464\pi$
$420$		0			0
$421$	269.187	−	155.415i	0.639399	−	0.369157i	−0.144984	−	0.989434i	$-0.546313\pi$
$421$	269.187	−	155.415i	0.639399	−	0.369157i	0.784383	+	0.620277i	$0.212980\pi$
$422$		0			0
$423$	−35.1701	−	60.9164i	−0.0831445	−	0.144010i
$424$		0			0
$425$	−354.378			−0.833830
$426$		0			0
$427$	244.678	−	423.794i	0.573015	−	0.992492i
$428$		0			0
$429$	360.733			0.840869
$430$		0			0
$431$	294.668	+	170.127i	0.683685	+	0.394725i	0.801242	−	0.598341i	$-0.204173\pi$
$431$	294.668	+	170.127i	0.683685	+	0.394725i	−0.117557	+	0.993066i	$0.537506\pi$
$432$		0			0
$433$	287.149	+	165.786i	0.663162	+	0.382877i	0.793481	−	0.608595i	$-0.208267\pi$
$433$	287.149	+	165.786i	0.663162	+	0.382877i	−0.130318	+	0.991472i	$0.541600\pi$
$434$		0			0
$435$	17.3274	+	30.0120i	0.0398332	+	0.0689931i
$436$		0			0
$437$	61.1578	+	169.411i	0.139949	+	0.387668i
$438$		0			0
$439$	4.45526	−	2.57224i	0.0101486	−	0.00585932i	−0.494917	−	0.868940i	$-0.664802\pi$
$439$	4.45526	−	2.57224i	0.0101486	−	0.00585932i	0.505066	+	0.863081i	$0.331468\pi$
$440$		0			0
$441$	−30.9550	+	53.6157i	−0.0701928	+	0.121578i
$442$		0			0
$443$	240.180	−	416.004i	0.542167	−	0.939061i	−0.456612	−	0.889666i	$-0.650937\pi$
$443$	240.180	−	416.004i	0.542167	−	0.939061i	0.998779	−	0.0493948i	$-0.0157293\pi$
$444$		0			0
$445$		−	169.165i		−	0.380146i
$446$		0			0
$447$	−100.679	−	58.1270i	−0.225232	−	0.130038i
$448$		0			0
$449$		−	14.1547i		−	0.0315250i	−0.999876	−	0.0157625i	$-0.994982\pi$
$449$		−	14.1547i		−	0.0315250i	0.999876	−	0.0157625i	$-0.00501756\pi$
$450$		0			0
$451$	−20.5832	+	11.8837i	−0.0456390	+	0.0263497i
$452$		0			0
$453$	−121.026	−	209.624i	−0.267166	−	0.462745i
$454$		0			0
$455$		−	131.017i		−	0.287949i
$456$		0			0
$457$	338.053			0.739723			0.369861	−	0.929087i	$-0.379405\pi$
$457$	338.053			0.739723			0.369861	+	0.929087i	$0.379405\pi$
$458$		0			0
$459$	78.2665	−	45.1872i	0.170515	−	0.0984471i
$460$		0			0
$461$	286.865	+	496.865i	0.622267	+	1.07780i	0.989062	+	0.147497i	$0.0471217\pi$
$461$	286.865	+	496.865i	0.622267	+	1.07780i	−0.366795	+	0.930302i	$0.619545\pi$
$462$		0			0
$463$	−158.357			−0.342024			−0.171012	−	0.985269i	$-0.554704\pi$
$463$	−158.357			−0.342024			−0.171012	+	0.985269i	$0.554704\pi$
$464$		0			0
$465$	18.8405	−	32.6328i	0.0405173	−	0.0701780i
$466$		0			0
$467$	−60.0616			−0.128611			−0.0643057	−	0.997930i	$-0.520483\pi$
$467$	−60.0616			−0.128611			−0.0643057	+	0.997930i	$0.520483\pi$
$468$		0			0
$469$	−48.9911	−	28.2850i	−0.104459	−	0.0603092i
$470$		0			0
$471$	−153.061	−	88.3697i	−0.324970	−	0.187621i
$472$		0			0
$473$	−149.883	−	259.606i	−0.316878	−	0.548850i
$474$		0			0
$475$	−131.452	−	364.129i	−0.276740	−	0.766588i
$476$		0			0
$477$	29.3846	−	16.9652i	0.0616029	−	0.0355664i
$478$		0			0
$479$	−323.067	+	559.569i	−0.674462	+	1.16820i	0.302164	+	0.953256i	$0.402291\pi$
$479$	−323.067	+	559.569i	−0.674462	+	1.16820i	−0.976626	+	0.214947i	$0.931042\pi$
$480$		0			0
$481$	32.4027	−	56.1232i	0.0673653	−	0.116680i
$482$		0			0
$483$		−	87.4436i		−	0.181043i
$484$		0			0
$485$	88.6364	+	51.1742i	0.182755	+	0.105514i
$486$		0			0
$487$		−	841.255i		−	1.72742i	−0.503986	−	0.863712i	$-0.668134\pi$
$487$		−	841.255i		−	1.72742i	0.503986	−	0.863712i	$-0.331866\pi$
$488$		0			0
$489$	150.096	−	86.6580i	0.306945	−	0.177215i
$490$		0			0
$491$	−338.146	−	585.687i	−0.688689	−	1.19284i	−0.972262	−	0.233894i	$-0.924853\pi$
$491$	−338.146	−	585.687i	−0.688689	−	1.19284i	0.283573	−	0.958951i	$-0.408480\pi$
$492$		0			0
$493$			161.817i			0.328229i
$494$		0			0
$495$	117.459			0.237291
$496$		0			0
$497$	547.960	−	316.365i	1.10253	−	0.636549i
$498$		0			0
$499$	138.841	+	240.480i	0.278239	+	0.481924i	0.970947	−	0.239294i	$-0.0769160\pi$
$499$	138.841	+	240.480i	0.278239	+	0.481924i	−0.692708	+	0.721218i	$0.743583\pi$
$500$		0			0
$501$	−465.098			−0.928340
$502$		0			0
$503$	−184.762	+	320.017i	−0.367320	+	0.636217i	−0.989146	−	0.146939i	$-0.953058\pi$
$503$	−184.762	+	320.017i	−0.367320	+	0.636217i	0.621826	+	0.783156i	$0.286391\pi$
$504$		0			0
$505$	216.661			0.429032
$506$		0			0
$507$	57.2091	+	33.0297i	0.112838	+	0.0651473i
$508$		0			0
$509$	466.003	+	269.047i	0.915526	+	0.528579i	0.882205	−	0.470865i	$-0.156058\pi$
$509$	466.003	+	269.047i	0.915526	+	0.528579i	0.0333213	+	0.999445i	$0.489392\pi$
$510$		0			0
$511$	376.900	+	652.809i	0.737572	+	1.27751i
$512$		0			0
$513$	75.4625	+	63.6586i	0.147100	+	0.124091i
$514$		0			0
$515$	−292.519	+	168.886i	−0.567997	+	0.327933i
$516$		0			0
$517$	213.439	−	369.687i	0.412841	−	0.715061i
$518$		0			0
$519$	−33.4499	+	57.9370i	−0.0644507	+	0.111632i
$520$		0			0
$521$		−	911.479i		−	1.74948i	−0.484592	−	0.874740i	$-0.661032\pi$
$521$		−	911.479i		−	1.74948i	0.484592	−	0.874740i	$-0.338968\pi$
$522$		0			0
$523$	427.205	+	246.647i	0.816835	+	0.471600i	0.849324	−	0.527872i	$-0.177010\pi$
$523$	427.205	+	246.647i	0.816835	+	0.471600i	−0.0324886	+	0.999472i	$0.510343\pi$
$524$		0			0
$525$			187.950i			0.358000i
$526$		0			0
$527$	152.375	−	87.9736i	0.289136	−	0.166933i
$528$		0			0
$529$	219.569	+	380.304i	0.415064	+	0.718912i
$530$		0			0
$531$		−	226.155i		−	0.425904i
$532$		0			0
$533$	14.9336			0.0280181
$534$		0			0
$535$	−54.2029	+	31.2941i	−0.101314	+	0.0584936i
$536$		0			0
$537$	27.6048	+	47.8130i	0.0514056	+	0.0890372i
$538$		0			0
$539$	−375.717			−0.697063
$540$		0			0
$541$	−386.653	+	669.702i	−0.714700	+	1.23790i	0.248375	+	0.968664i	$0.420104\pi$
$541$	−386.653	+	669.702i	−0.714700	+	1.23790i	−0.963075	+	0.269233i	$0.913230\pi$
$542$		0			0
$543$	−378.852			−0.697702
$544$		0			0
$545$	−30.2283	−	17.4523i	−0.0554648	−	0.0320226i
$546$		0			0
$547$	−563.689	−	325.446i	−1.03051	−	0.594965i	−0.113379	−	0.993552i	$-0.536167\pi$
$547$	−563.689	−	325.446i	−1.03051	−	0.594965i	−0.917131	+	0.398587i	$0.869501\pi$
$548$		0			0
$549$	−137.828	−	238.725i	−0.251053	−	0.434836i
$550$		0			0
$551$	−166.269	+	60.0237i	−0.301759	+	0.108936i
$552$		0			0
$553$	−308.949	+	178.372i	−0.558678	+	0.322553i
$554$		0			0
$555$	10.5507	−	18.2744i	0.0190103	−	0.0329268i
$556$		0			0
$557$	−199.474	+	345.499i	−0.358122	+	0.620285i	−0.987647	−	0.156695i	$-0.949916\pi$
$557$	−199.474	+	345.499i	−0.358122	+	0.620285i	0.629525	+	0.776980i	$0.283249\pi$
$558$		0			0
$559$			188.351i			0.336943i
$560$		0			0
$561$	474.980	+	274.230i	0.846667	+	0.488823i
$562$		0			0
$563$		−	339.093i		−	0.602296i	−0.953577	−	0.301148i	$-0.902630\pi$
$563$		−	339.093i		−	0.602296i	0.953577	−	0.301148i	$-0.0973699\pi$
$564$		0			0
$565$	−279.895	+	161.597i	−0.495389	+	0.286013i
$566$		0			0
$567$	−23.9657	−	41.5099i	−0.0422676	−	0.0732097i
$568$		0			0
$569$		−	495.876i		−	0.871486i	−0.900071	−	0.435743i	$-0.856486\pi$
$569$		−	495.876i		−	0.871486i	0.900071	−	0.435743i	$-0.143514\pi$
$570$		0			0
$571$	215.684			0.377730			0.188865	−	0.982003i	$-0.439519\pi$
$571$	215.684			0.377730			0.188865	+	0.982003i	$0.439519\pi$
$572$		0			0
$573$	282.548	−	163.129i	0.493103	−	0.284693i
$574$		0			0
$575$	96.5744	+	167.272i	0.167955	+	0.290907i
$576$		0			0
$577$	−344.857			−0.597672			−0.298836	−	0.954305i	$-0.596598\pi$
$577$	−344.857			−0.597672			−0.298836	+	0.954305i	$0.596598\pi$
$578$		0			0
$579$	85.5465	−	148.171i	0.147749	−	0.255908i
$580$		0			0
$581$	720.310			1.23978
$582$		0			0
$583$	178.328	+	102.958i	0.305879	+	0.176600i
$584$		0			0
$585$	−63.9146	−	36.9011i	−0.109256	−	0.0630788i
$586$		0			0
$587$	198.805	+	344.341i	0.338680	+	0.586611i	0.984185	−	0.177145i	$-0.0566862\pi$
$587$	198.805	+	344.341i	0.338680	+	0.586611i	−0.645505	+	0.763756i	$0.723353\pi$
$588$		0			0
$589$	146.916	+	123.935i	0.249432	+	0.210416i
$590$		0			0
$591$	371.902	−	214.718i	0.629276	−	0.363313i
$592$		0			0
$593$	83.4215	−	144.490i	0.140677	−	0.243660i	−0.787075	−	0.616858i	$-0.788405\pi$
$593$	83.4215	−	144.490i	0.140677	−	0.243660i	0.927752	+	0.373198i	$0.121739\pi$
$594$		0			0
$595$	99.5992	−	172.511i	0.167394	−	0.289934i
$596$		0			0
$597$		−	369.338i		−	0.618657i
$598$		0			0
$599$	−876.361	−	505.967i	−1.46304	−	0.844686i	−0.463889	−	0.885893i	$-0.653546\pi$
$599$	−876.361	−	505.967i	−1.46304	−	0.844686i	−0.999151	+	0.0412073i	$0.986880\pi$
$600$		0			0
$601$		−	194.111i		−	0.322979i	−0.986874	−	0.161490i	$-0.948370\pi$
$601$		−	194.111i		−	0.322979i	0.986874	−	0.161490i	$-0.0516299\pi$
$602$		0			0
$603$	−27.5969	+	15.9331i	−0.0457659	+	0.0264230i
$604$		0			0
$605$	226.308	+	391.976i	0.374062	+	0.647895i
$606$		0			0
$607$			282.027i			0.464625i	0.972641	+	0.232312i	$0.0746292\pi$
$607$			282.027i			0.464625i	−0.972641	+	0.232312i	$0.925371\pi$
$608$		0			0
$609$	85.8221			0.140923
$610$		0			0
$611$	−232.283	+	134.109i	−0.380169	+	0.219491i
$612$		0			0
$613$	151.450	+	262.318i	0.247063	+	0.427926i	0.962710	−	0.270537i	$-0.0872012\pi$
$613$	151.450	+	262.318i	0.247063	+	0.427926i	−0.715647	+	0.698463i	$0.753868\pi$
$614$		0			0
$615$	4.86257			0.00790662
$616$		0			0
$617$	−129.735	+	224.707i	−0.210267	+	0.364192i	−0.951798	−	0.306726i	$-0.900767\pi$
$617$	−129.735	+	224.707i	−0.210267	+	0.364192i	0.741531	+	0.670918i	$0.234100\pi$
$618$		0			0
$619$	−174.325			−0.281624			−0.140812	−	0.990036i	$-0.544971\pi$
$619$	−174.325			−0.281624			−0.140812	+	0.990036i	$0.544971\pi$
$620$		0			0
$621$	−42.6581	−	24.6287i	−0.0686925	−	0.0396597i
$622$		0			0
$623$	−362.807	−	209.467i	−0.582355	−	0.336223i
$624$		0			0
$625$	−149.766	−	259.403i	−0.239626	−	0.415044i
$626$		0			0
$627$	−105.588	+	589.772i	−0.168403	+	0.940625i
$628$		0			0
$629$	85.3299	−	49.2652i	0.135660	−	0.0783231i
$630$		0			0
$631$	−108.403	+	187.760i	−0.171796	+	0.297559i	−0.939048	−	0.343787i	$-0.888290\pi$
$631$	−108.403	+	187.760i	−0.171796	+	0.297559i	0.767252	+	0.641346i	$0.221624\pi$
$632$		0			0
$633$	247.414	−	428.534i	0.390860	−	0.676989i
$634$		0			0
$635$		−	219.631i		−	0.345876i
$636$		0			0
$637$	204.444	+	118.036i	0.320949	+	0.185300i
$638$		0			0
$639$		−	356.419i		−	0.557776i
$640$		0			0
$641$	589.260	−	340.209i	0.919282	−	0.530748i	0.0358764	−	0.999356i	$-0.488578\pi$
$641$	589.260	−	340.209i	0.919282	−	0.530748i	0.883406	+	0.468608i	$0.155244\pi$
$642$		0			0
$643$	−428.884	−	742.849i	−0.667005	−	1.15529i	−0.978738	−	0.205116i	$-0.934243\pi$
$643$	−428.884	−	742.849i	−0.667005	−	1.15529i	0.311733	−	0.950170i	$-0.399091\pi$
$644$		0			0
$645$			61.3293i			0.0950841i
$646$		0			0
$647$	810.087			1.25207			0.626033	−	0.779796i	$-0.284677\pi$
$647$	810.087			1.25207			0.626033	+	0.779796i	$0.284677\pi$
$648$		0			0
$649$	1188.60	−	686.240i	1.83144	−	1.05738i
$650$		0			0
$651$	−46.6582	−	80.8143i	−0.0716715	−	0.124139i
$652$		0			0
$653$	−838.225			−1.28365			−0.641827	−	0.766850i	$-0.721823\pi$
$653$	−838.225			−1.28365			−0.641827	+	0.766850i	$0.721823\pi$
$654$		0			0
$655$	70.6359	−	122.345i	0.107841	−	0.186786i
$656$		0			0
$657$	424.618			0.646298
$658$		0			0
$659$	887.282	+	512.273i	1.34641	+	0.777349i	0.987739	−	0.156116i	$-0.0498975\pi$
$659$	887.282	+	512.273i	1.34641	+	0.777349i	0.358669	+	0.933465i	$0.383231\pi$
$660$		0			0
$661$	−13.3515	−	7.70848i	−0.0201989	−	0.0116619i	0.489867	−	0.871797i	$-0.337046\pi$
$661$	−13.3515	−	7.70848i	−0.0201989	−	0.0116619i	−0.510065	+	0.860136i	$0.670379\pi$
$662$		0			0
$663$	−172.305	−	298.442i	−0.259887	−	0.450138i
$664$		0			0
$665$	214.203	+	38.3493i	0.322109	+	0.0576681i
$666$		0			0
$667$	76.3799	−	44.0980i	0.114513	−	0.0661139i
$668$		0			0
$669$	227.339	−	393.763i	0.339819	−	0.588584i
$670$		0			0
$671$	836.443	−	1448.76i	1.24656	−	2.15911i
$672$		0			0
$673$		−	93.2725i		−	0.138592i	−0.997596	−	0.0692960i	$-0.977925\pi$
$673$		−	93.2725i		−	0.138592i	0.997596	−	0.0692960i	$-0.0220753\pi$
$674$		0			0
$675$	91.6887	+	52.9365i	0.135835	+	0.0784244i
$676$		0			0
$677$			795.742i			1.17539i	0.809081	+	0.587697i	$0.199965\pi$
$677$			795.742i			1.17539i	−0.809081	+	0.587697i	$0.800035\pi$
$678$		0			0
$679$	219.506	−	126.732i	0.323279	−	0.186645i
$680$		0			0
$681$	109.049	+	188.878i	0.160130	+	0.277353i
$682$		0			0
$683$			538.636i			0.788633i	0.918975	+	0.394316i	$0.129019\pi$
$683$			538.636i			0.788633i	−0.918975	+	0.394316i	$0.870981\pi$
$684$		0			0
$685$	348.575			0.508869
$686$		0			0
$687$	228.415	−	131.875i	0.332482	−	0.191958i
$688$		0			0
$689$	−64.6907	−	112.048i	−0.0938908	−	0.162624i
$690$		0			0
$691$	1161.26			1.68056			0.840278	−	0.542156i	$-0.182392\pi$
$691$	1161.26			1.68056			0.840278	+	0.542156i	$0.182392\pi$
$692$		0			0
$693$	145.442	−	251.913i	0.209873	−	0.363511i
$694$		0			0
$695$	320.037			0.460485
$696$		0			0
$697$	19.6633	+	11.3526i	0.0282113	+	0.0162878i
$698$		0			0
$699$	323.602	+	186.832i	0.462951	+	0.267285i
$700$		0			0
$701$	249.064	+	431.392i	0.355298	+	0.615395i	0.987169	−	0.159679i	$-0.0510460\pi$
$701$	249.064	+	431.392i	0.355298	+	0.615395i	−0.631871	+	0.775074i	$0.717713\pi$
$702$		0			0
$703$	82.2728	+	69.4036i	0.117031	+	0.0987249i
$704$		0			0
$705$	−75.6341	+	43.6674i	−0.107282	+	0.0619395i
$706$		0			0
$707$	268.278	−	464.672i	0.379460	−	0.657244i
$708$		0			0
$709$	603.632	−	1045.52i	0.851385	−	1.47464i	−0.0285740	−	0.999592i	$-0.509097\pi$
$709$	603.632	−	1045.52i	0.851385	−	1.47464i	0.879959	−	0.475050i	$-0.157570\pi$
$710$		0			0
$711$			200.955i			0.282637i
$712$		0			0
$713$	−83.0497	−	47.9488i	−0.116479	−	0.0672493i
$714$		0			0
$715$		−	447.887i		−	0.626416i
$716$		0			0
$717$	−381.361	+	220.179i	−0.531884	+	0.307083i
$718$		0			0
$719$	256.761	+	444.724i	0.357109	+	0.618531i	0.987477	−	0.157766i	$-0.0504292\pi$
$719$	256.761	+	444.724i	0.357109	+	0.618531i	−0.630368	+	0.776297i	$0.717096\pi$
$720$		0			0
$721$			836.484i			1.16017i
$722$		0			0
$723$	415.623			0.574859
$724$		0			0
$725$	−164.170	+	94.7836i	−0.226441	+	0.130736i
$726$		0			0
$727$	514.018	+	890.306i	0.707040	+	1.22463i	0.965950	+	0.258728i	$0.0833033\pi$
$727$	514.018	+	890.306i	0.707040	+	1.22463i	−0.258910	+	0.965901i	$0.583363\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−143.185	+	248.003i	−0.195875	+	0.339266i
$732$		0			0
$733$	196.779			0.268457			0.134228	−	0.990950i	$-0.457144\pi$
$733$	196.779			0.268457			0.134228	+	0.990950i	$0.457144\pi$
$734$		0			0
$735$	66.5695	+	38.4339i	0.0905707	+	0.0522910i
$736$		0			0
$737$	−167.479	−	96.6938i	−0.227244	−	0.131199i
$738$		0			0
$739$	193.725	+	335.542i	0.262145	+	0.454048i	0.966812	−	0.255490i	$-0.0822368\pi$
$739$	193.725	+	335.542i	0.262145	+	0.454048i	−0.704667	+	0.709538i	$0.748903\pi$
$740$		0			0
$741$	242.739	−	287.749i	0.327583	−	0.388326i
$742$		0			0
$743$	403.643	−	233.043i	0.543261	−	0.313652i	−0.203139	−	0.979150i	$-0.565114\pi$
$743$	403.643	−	233.043i	0.543261	−	0.313652i	0.746399	+	0.665498i	$0.231781\pi$
$744$		0			0
$745$	−72.1707	+	125.003i	−0.0968735	+	0.167790i
$746$		0			0
$747$	202.877	−	351.393i	0.271589	−	0.470406i
$748$		0			0
$749$			154.998i			0.206940i
$750$		0			0
$751$	−767.840	−	443.313i	−1.02242	−	0.590297i	−0.107619	−	0.994192i	$-0.534323\pi$
$751$	−767.840	−	443.313i	−1.02242	−	0.590297i	−0.914805	+	0.403896i	$0.867656\pi$
$752$		0			0
$753$			716.727i			0.951829i
$754$		0			0
$755$	−260.270	+	150.267i	−0.344728	+	0.199029i
$756$		0			0
$757$	−474.903	−	822.556i	−0.627348	−	1.08660i	−0.988082	−	0.153930i	$-0.950807\pi$
$757$	−474.903	−	822.556i	−0.627348	−	1.08660i	0.360733	−	0.932669i	$-0.382526\pi$
$758$		0			0
$759$		−	298.930i		−	0.393848i
$760$		0			0
$761$	−1122.09			−1.47449			−0.737247	−	0.675623i	$-0.763875\pi$
$761$	−1122.09			−1.47449			−0.737247	+	0.675623i	$0.763875\pi$
$762$		0			0
$763$	−74.8597	+	43.2203i	−0.0981124	+	0.0566452i
$764$		0			0
$765$	−56.1046	−	97.1760i	−0.0733394	−	0.127028i
$766$		0			0
$767$	−862.362			−1.12433
$768$		0			0
$769$	−297.797	+	515.799i	−0.387252	+	0.670740i	−0.992079	−	0.125617i	$-0.959909\pi$
$769$	−297.797	+	515.799i	−0.387252	+	0.670740i	0.604827	+	0.796357i	$0.293242\pi$
$770$		0			0
$771$	−42.7878			−0.0554965
$772$		0			0
$773$	−457.003	−	263.851i	−0.591207	−	0.341333i	0.174368	−	0.984681i	$-0.444212\pi$
$773$	−457.003	−	263.851i	−0.591207	−	0.341333i	−0.765574	+	0.643347i	$0.777545\pi$
$774$		0			0
$775$	178.506	+	103.060i	0.230330	+	0.132981i
$776$		0			0
$777$	−26.1286	−	45.2561i	−0.0336275	−	0.0582446i
$778$		0			0
$779$	−4.37116	+	24.4154i	−0.00561124	+	0.0313420i
$780$		0			0
$781$	1873.23	−	1081.51i	2.39850	−	1.38477i
$782$		0			0
$783$	24.1720	−	41.8671i	0.0308710	−	0.0534701i
$784$		0			0
$785$	−109.720	+	190.041i	−0.139771	+	0.242090i
$786$		0			0
$787$			324.625i			0.412484i	0.978501	+	0.206242i	$0.0661235\pi$
$787$			324.625i			0.412484i	−0.978501	+	0.206242i	$0.933877\pi$
$788$		0			0
$789$	−521.726	−	301.219i	−0.661250	−	0.381773i
$790$		0			0
$791$			800.385i			1.01186i
$792$		0			0
$793$	−910.292	+	525.557i	−1.14791	+	0.662746i
$794$		0			0
$795$	−21.0641	−	36.4840i	−0.0264957	−	0.0458918i
$796$		0			0
$797$			531.704i			0.667131i	0.942727	+	0.333566i	$0.108252\pi$
$797$			531.704i			0.667131i	−0.942727	+	0.333566i	$0.891748\pi$
$798$		0			0
$799$	−407.799			−0.510387
$800$		0			0
$801$	−204.371	+	117.994i	−0.255145	+	0.147308i
$802$		0			0
$803$	1288.45	+	2231.66i	1.60455	+	2.77916i
$804$		0			0
$805$	−108.570			−0.134870
$806$		0			0
$807$	−161.992	+	280.578i	−0.200734	+	0.347681i
$808$		0			0
$809$	−337.852			−0.417617			−0.208809	−	0.977957i	$-0.566959\pi$
$809$	−337.852			−0.417617			−0.208809	+	0.977957i	$0.566959\pi$
$810$		0			0
$811$	−232.154	−	134.034i	−0.286257	−	0.165271i	0.349996	−	0.936751i	$-0.386183\pi$
$811$	−232.154	−	134.034i	−0.286257	−	0.165271i	−0.636253	+	0.771481i	$0.719516\pi$
$812$		0			0
$813$	−483.759	−	279.298i	−0.595029	−	0.343540i
$814$		0			0
$815$	−107.595	−	186.360i	−0.132018	−	0.228662i
$816$		0			0
$817$	−307.940	−	55.1313i	−0.376915	−	0.0674802i
$818$		0			0
$819$	−158.283	+	91.3848i	−0.193264	+	0.111581i
$820$		0			0
$821$	40.6080	−	70.3352i	0.0494617	−	0.0856701i	−0.840235	−	0.542223i	$-0.817583\pi$
$821$	40.6080	−	70.3352i	0.0494617	−	0.0856701i	0.889696	+	0.456553i	$0.150916\pi$
$822$		0			0
$823$	526.691	−	912.255i	0.639964	−	1.10845i	−0.345476	−	0.938428i	$-0.612282\pi$
$823$	526.691	−	912.255i	0.639964	−	1.10845i	0.985440	−	0.170023i	$-0.0543842\pi$
$824$		0			0
$825$			642.517i			0.778808i
$826$		0			0
$827$	−840.838	−	485.458i	−1.01673	−	0.587011i	−0.103577	−	0.994621i	$-0.533029\pi$
$827$	−840.838	−	485.458i	−1.01673	−	0.587011i	−0.913156	+	0.407610i	$0.866362\pi$
$828$		0			0
$829$			1264.48i			1.52530i	0.646809	+	0.762652i	$0.276103\pi$
$829$			1264.48i			1.52530i	−0.646809	+	0.762652i	$0.723897\pi$
$830$		0			0
$831$	645.543	−	372.705i	0.776827	−	0.448501i
$832$		0			0
$833$	179.462	+	310.838i	0.215441	+	0.373155i
$834$		0			0
$835$			577.468i			0.691579i
$836$		0			0
$837$	−52.5655			−0.0628022
$838$		0			0
$839$	−797.042	+	460.172i	−0.949990	+	0.548477i	−0.893078	−	0.449902i	$-0.851459\pi$
$839$	−797.042	+	460.172i	−0.949990	+	0.548477i	−0.0569121	+	0.998379i	$0.518125\pi$
$840$		0			0
$841$	−377.220	−	653.364i	−0.448537	−	0.776889i
$842$		0			0
$843$	686.579			0.814447
$844$		0			0
$845$	41.0098	−	71.0311i	0.0485323	−	0.0840604i
$846$		0			0
$847$	1120.89			1.32337
$848$		0			0
$849$	−591.814	−	341.684i	−0.697072	−	0.402454i
$850$		0			0
$851$	−46.5079	−	26.8513i	−0.0546508	−	0.0315527i
$852$		0			0
$853$	−628.515	−	1088.62i	−0.736829	−	1.27622i	−0.953916	−	0.300073i	$-0.902989\pi$
$853$	−628.515	−	1088.62i	−0.736829	−	1.27622i	0.217088	−	0.976152i	$-0.430344\pi$
$854$		0			0
$855$	79.0388	−	93.6945i	0.0924430	−	0.109584i
$856$		0			0
$857$	−11.9886	+	6.92161i	−0.0139890	+	0.00807655i	−0.506978	−	0.861959i	$-0.669238\pi$
$857$	−11.9886	+	6.92161i	−0.0139890	+	0.00807655i	0.492989	+	0.870035i	$0.335904\pi$
$858$		0			0
$859$	128.617	−	222.771i	0.149729	−	0.259338i	−0.781398	−	0.624032i	$-0.785493\pi$
$859$	128.617	−	222.771i	0.149729	−	0.259338i	0.931127	+	0.364695i	$0.118827\pi$
$860$		0			0
$861$	6.02103	−	10.4287i	0.00699306	−	0.0121123i
$862$		0			0
$863$		−	191.233i		−	0.221591i	−0.993843	−	0.110795i	$-0.964660\pi$
$863$		−	191.233i		−	0.221591i	0.993843	−	0.110795i	$-0.0353398\pi$
$864$		0			0
$865$	71.9348	+	41.5316i	0.0831616	+	0.0480134i
$866$		0			0
$867$		−	23.3847i		−	0.0269719i
$868$		0			0
$869$	−1056.16	+	609.773i	−1.21537	+	0.701695i
$870$		0			0
$871$	60.7550	+	105.231i	0.0697532	+	0.120816i
$872$		0			0
$873$		−	142.777i		−	0.163548i
$874$		0			0
$875$	519.686			0.593927
$876$		0			0
$877$	1171.82	−	676.549i	1.33617	−	0.771435i	0.349929	−	0.936776i	$-0.386206\pi$
$877$	1171.82	−	676.549i	1.33617	−	0.771435i	0.986236	+	0.165341i	$0.0528725\pi$
$878$		0			0
$879$	178.907	+	309.877i	0.203535	+	0.352533i
$880$		0			0
$881$	−1352.82			−1.53555			−0.767775	−	0.640720i	$-0.778636\pi$
$881$	−1352.82			−1.53555			−0.767775	+	0.640720i	$0.778636\pi$
$882$		0			0
$883$	−297.338	+	515.005i	−0.336737	+	0.583245i	−0.983817	−	0.179177i	$-0.942657\pi$
$883$	−297.338	+	515.005i	−0.336737	+	0.583245i	0.647080	+	0.762422i	$0.275990\pi$
$884$		0			0
$885$	−280.795			−0.317283
$886$		0			0
$887$	1431.47	+	826.459i	1.61383	+	0.931747i	0.988471	+	0.151412i	$0.0483819\pi$
$887$	1431.47	+	826.459i	1.61383	+	0.931747i	0.625362	+	0.780335i	$0.284951\pi$
$888$		0			0
$889$	−471.042	−	271.956i	−0.529856	−	0.305912i
$890$		0			0
$891$	−81.9281	−	141.904i	−0.0919508	−	0.159263i
$892$		0			0
$893$	−151.267	−	419.020i	−0.169392	−	0.469227i
$894$		0			0
$895$	59.3648	−	34.2743i	0.0663294	−	0.0382953i
$896$		0			0
$897$	−93.9126	+	162.661i	−0.104696	+	0.181339i
$898$		0			0
$899$	47.0596	−	81.5097i	0.0523466	−	0.0906670i
$900$		0			0
$901$		−	196.712i		−	0.218326i
$902$		0			0
$903$	131.532	+	75.9403i	0.145662	+	0.0840978i
$904$		0			0
$905$			470.385i			0.519762i
$906$		0			0
$907$	−206.183	+	119.040i	−0.227325	+	0.131246i	−0.609337	−	0.792911i	$-0.708564\pi$
$907$	−206.183	+	119.040i	−0.227325	+	0.131246i	0.382013	+	0.924157i	$0.375231\pi$
$908$		0			0
$909$	−151.122	−	261.751i	−0.166251	−	0.287955i
$910$		0			0
$911$		−	177.732i		−	0.195096i	−0.995231	−	0.0975480i	$-0.968900\pi$
$911$		−	177.732i		−	0.195096i	0.995231	−	0.0975480i	$-0.0310999\pi$
$912$		0			0
$913$	2462.42			2.69706
$914$		0			0
$915$	−296.402	+	171.128i	−0.323936	+	0.187025i
$916$		0			0
$917$	−174.928	−	302.985i	−0.190762	−	0.330409i
$918$		0			0
$919$	−132.015			−0.143651			−0.0718254	−	0.997417i	$-0.522882\pi$
$919$	−132.015			−0.143651			−0.0718254	+	0.997417i	$0.522882\pi$
$920$		0			0
$921$	−260.211	+	450.699i	−0.282531	+	0.489358i
$922$		0			0
$923$	−1359.08			−1.47246
$924$		0			0
$925$	99.9633	+	57.7139i	0.108068	+	0.0623934i
$926$		0			0
$927$	408.067	+	235.597i	0.440201	+	0.254150i
$928$		0			0
$929$	−446.860	−	773.984i	−0.481012	−	0.833137i	0.518751	−	0.854926i	$-0.326397\pi$
$929$	−446.860	−	773.984i	−0.481012	−	0.833137i	−0.999763	+	0.0217885i	$0.993064\pi$
$930$		0			0
$931$	−252.822	+	299.702i	−0.271560	+	0.321914i
$932$		0			0
$933$	386.327	−	223.046i	0.414070	−	0.239064i
$934$		0			0
$935$	340.485	−	589.737i	0.364155	−	0.630735i
$936$		0			0
$937$	−793.077	+	1373.65i	−0.846400	+	1.46601i	0.0380001	+	0.999278i	$0.487901\pi$
$937$	−793.077	+	1373.65i	−0.846400	+	1.46601i	−0.884400	+	0.466730i	$0.845432\pi$
$938$		0			0
$939$		−	781.182i		−	0.831930i
$940$		0			0
$941$	207.101	+	119.570i	0.220086	+	0.127067i	0.605990	−	0.795472i	$-0.292777\pi$
$941$	207.101	+	119.570i	0.220086	+	0.127067i	−0.385904	+	0.922539i	$0.626110\pi$
$942$		0			0
$943$		−	12.3751i		−	0.0131232i
$944$		0			0
$945$	−51.5389	+	29.7560i	−0.0545385	+	0.0314878i
$946$		0			0
$947$	−203.922	−	353.202i	−0.215334	−	0.372970i	0.738042	−	0.674755i	$-0.235751\pi$
$947$	−203.922	−	353.202i	−0.215334	−	0.372970i	−0.953376	+	0.301785i	$0.902417\pi$
$948$		0			0
$949$		−	1619.13i		−	1.70614i
$950$		0			0
$951$	342.376			0.360016
$952$		0			0
$953$	−498.924	+	288.054i	−0.523530	+	0.302260i	−0.738378	−	0.674388i	$-0.764408\pi$
$953$	−498.924	+	288.054i	−0.523530	+	0.302260i	0.214848	+	0.976648i	$0.431074\pi$
$954$		0			0
$955$	−202.542	−	350.813i	−0.212086	−	0.367344i
$956$		0			0
$957$	293.387			0.306570
$958$		0			0
$959$	431.620	−	747.587i	0.450073	−	0.779549i
$960$		0			0
$961$	858.662			0.893509
$962$		0			0
$963$	75.6137	+	43.6556i	0.0785189	+	0.0453329i
$964$		0			0
$965$	−183.970	−	106.215i	−0.190642	−	0.110067i
$966$		0			0
$967$	−703.258	−	1218.08i	−0.727258	−	1.25965i	−0.958038	−	0.286642i	$-0.907461\pi$
$967$	−703.258	−	1218.08i	−0.727258	−	1.25965i	0.230780	−	0.973006i	$-0.425872\pi$
$968$		0			0
$969$	538.365	−	194.351i	0.555588	−	0.200569i
$970$		0			0
$971$	−1318.80	+	761.408i	−1.35819	+	0.784149i	−0.989379	−	0.145358i	$-0.953567\pi$
$971$	−1318.80	+	761.408i	−1.35819	+	0.784149i	−0.368806	+	0.929506i	$0.620233\pi$
$972$		0			0
$973$	396.283	−	686.382i	0.407279	−	0.705429i
$974$		0			0
$975$	201.854	−	349.622i	0.207030	−	0.358587i
$976$		0			0
$977$			1659.09i			1.69815i	0.528275	+	0.849073i	$0.322839\pi$
$977$			1659.09i			1.69815i	−0.528275	+	0.849073i	$0.677161\pi$
$978$		0			0
$979$	−1240.28	−	716.073i	−1.26688	−	0.731433i
$980$		0			0
$981$			48.6923i			0.0496354i
$982$		0			0
$983$	−1228.87	+	709.487i	−1.25012	+	0.721757i	−0.971133	−	0.238538i	$-0.923332\pi$
$983$	−1228.87	+	709.487i	−1.25012	+	0.721757i	−0.278987	+	0.960295i	$0.589999\pi$
$984$		0			0
$985$	−266.595	−	461.755i	−0.270654	−	0.468787i
$986$		0			0
$987$			216.283i			0.219131i
$988$		0			0
$989$	156.082			0.157818
$990$		0			0
$991$	−1579.90	+	912.156i	−1.59425	+	0.920440i	−0.601682	+	0.798736i	$0.705503\pi$
$991$	−1579.90	+	912.156i	−1.59425	+	0.920440i	−0.992566	+	0.121704i	$0.961164\pi$
$992$		0			0
$993$	101.709	+	176.165i	0.102426	+	0.177407i
$994$		0			0
$995$	−458.572			−0.460876
$996$		0			0
$997$	−795.319	+	1377.53i	−0.797712	+	1.38168i	0.123391	+	0.992358i	$0.460623\pi$
$997$	−795.319	+	1377.53i	−0.797712	+	1.38168i	−0.921103	+	0.389320i	$0.872710\pi$
$998$		0			0
$999$	−29.4367			−0.0294662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.i.145.7		20
4.3	odd	2		456.3.w.b.145.7	✓	20
12.11	even	2		1368.3.bv.b.145.4		20
19.8	odd	6	inner	912.3.be.i.673.7		20
76.27	even	6		456.3.w.b.217.7	yes	20
228.179	odd	6		1368.3.bv.b.217.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.b.145.7	✓	20	4.3	odd	2
456.3.w.b.217.7	yes	20	76.27	even	6
912.3.be.i.145.7		20	1.1	even	1	trivial
912.3.be.i.673.7		20	19.8	odd	6	inner
1368.3.bv.b.145.4		20	12.11	even	2
1368.3.bv.b.217.4		20	228.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.07526 + 1.86241i) q^{5} +5.32572 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.07526 + 1.86241i) q^{5} +5.32572 q^{7} +(1.50000 - 2.59808i) q^{9} +18.2063 q^{11} +(-9.90684 - 5.71972i) q^{13} +(-3.22578 - 1.86241i) q^{15} +(-8.69628 - 15.0624i) q^{17} +(12.2511 - 14.5228i) q^{19} +(-7.98858 + 4.61221i) q^{21} +(-4.73979 + 8.20955i) q^{23} +(10.1876 - 17.6455i) q^{25} +5.19615i q^{27} +(-8.05732 - 4.65189i) q^{29} +10.1162i q^{31} +(-27.3094 + 15.7671i) q^{33} +(5.72654 + 9.91866i) q^{35} +5.66509i q^{37} +19.8137 q^{39} +(-1.13056 + 0.652727i) q^{41} +(-8.23253 - 14.2592i) q^{43} +6.45156 q^{45} +(11.7234 - 20.3055i) q^{47} -20.6367 q^{49} +(26.0888 + 15.0624i) q^{51} +(9.79486 + 5.65506i) q^{53} +(19.5765 + 33.9074i) q^{55} +(-5.79957 + 32.3939i) q^{57} +(65.2854 - 37.6925i) q^{59} +(45.9426 - 79.5749i) q^{61} +(7.98858 - 13.8366i) q^{63} -24.6007i q^{65} +(-9.19896 - 5.31102i) q^{67} -16.4191i q^{69} +(102.889 - 59.4032i) q^{71} +(70.7697 + 122.577i) q^{73} +35.2910i q^{75} +96.9614 q^{77} +(-58.0107 + 33.4925i) q^{79} +(-4.50000 - 7.79423i) q^{81} +135.251 q^{83} +(18.7015 - 32.3920i) q^{85} +16.1146 q^{87} +(-68.1236 - 39.3312i) q^{89} +(-52.7611 - 30.4616i) q^{91} +(-8.76091 - 15.1743i) q^{93} +(40.2204 + 7.20077i) q^{95} +(41.2162 - 23.7962i) q^{97} +(27.3094 - 47.3012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9	\( 20 q - 30 q^{3} + 4 q^{7} + 30 q^{9} + 8 q^{11} - 6 q^{13} + 8 q^{17} + 20 q^{19} - 6 q^{21} + 56 q^{23} - 58 q^{25} - 204 q^{29} - 12 q^{33} - 20 q^{35} + 12 q^{39} + 12 q^{41} - 34 q^{43} - 24 q^{47} + 392 q^{49} - 24 q^{51} + 24 q^{55} - 54 q^{57} - 168 q^{59} + 142 q^{61} + 6 q^{63} - 246 q^{67} - 276 q^{71} - 118 q^{73} - 152 q^{77} + 210 q^{79} - 90 q^{81} + 112 q^{83} - 208 q^{85} + 408 q^{87} - 42 q^{91} - 102 q^{93} - 100 q^{95} - 540 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 4 * q^7 + 30 * q^9 + 8 * q^11 - 6 * q^13 + 8 * q^17 + 20 * q^19 - 6 * q^21 + 56 * q^23 - 58 * q^25 - 204 * q^29 - 12 * q^33 - 20 * q^35 + 12 * q^39 + 12 * q^41 - 34 * q^43 - 24 * q^47 + 392 * q^49 - 24 * q^51 + 24 * q^55 - 54 * q^57 - 168 * q^59 + 142 * q^61 + 6 * q^63 - 246 * q^67 - 276 * q^71 - 118 * q^73 - 152 * q^77 + 210 * q^79 - 90 * q^81 + 112 * q^83 - 208 * q^85 + 408 * q^87 - 42 * q^91 - 102 * q^93 - 100 * q^95 - 540 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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