LMFDB - Embedded newform 912.3.be.f.673.2

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:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Root			$0.500000 + 2.69511i$ of defining polynomial
Character	$\chi$	$=$	912.673
Dual form			912.3.be.f.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(6.98167 - 4.03087i) q^{15} +(-5.84976 + 10.1321i) q^{17} +(3.88643 + 18.5983i) q^{19} +(16.0225 + 9.25062i) q^{21} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} +5.19615i q^{27} +(-33.2498 + 19.1968i) q^{29} -42.9440i q^{31} +(9.55920 + 5.51901i) q^{33} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +30.7540 q^{39} +(16.3728 + 9.45284i) q^{41} +(-26.5089 + 45.9148i) q^{43} +13.9633 q^{45} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} +(-17.5493 + 10.1321i) q^{51} +(-13.3224 + 7.69168i) q^{53} +(14.8309 - 25.6879i) q^{55} +(-10.2769 + 31.2632i) q^{57} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(16.0225 + 27.7519i) q^{63} -82.6436i q^{65} +(15.1585 - 8.75178i) q^{67} -48.4339i q^{69} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +5.77836i q^{75} +68.0723 q^{77} +(26.3908 + 15.2367i) q^{79} +(-4.50000 + 7.79423i) q^{81} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} -66.4996 q^{87} +(-76.8129 + 44.3479i) q^{89} +(164.253 - 94.8312i) q^{91} +(37.1906 - 64.4160i) q^{93} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(9.55920 + 16.5570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * 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
$5$	2.32722	−	4.03087i	0.465445	−	0.806174i	−0.533777	−	0.845625i	$-0.679228\pi$
$5$	2.32722	−	4.03087i	0.465445	−	0.806174i	0.999221	+	0.0394517i	$0.0125611\pi$
$6$		0			0
$7$	10.6817			1.52596			0.762978	−	0.646424i	$-0.223736\pi$
$7$	10.6817			1.52596			0.762978	+	0.646424i	$0.223736\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	6.37280			0.579346			0.289673	−	0.957126i	$-0.406453\pi$
$11$	6.37280			0.579346			0.289673	+	0.957126i	$0.406453\pi$
$12$		0			0
$13$	15.3770	−	8.87792i	1.18285	−	0.682917i	0.226176	−	0.974087i	$-0.427378\pi$
$13$	15.3770	−	8.87792i	1.18285	−	0.682917i	0.956671	+	0.291170i	$0.0940444\pi$
$14$		0			0
$15$	6.98167	−	4.03087i	0.465445	−	0.268725i
$16$		0			0
$17$	−5.84976	+	10.1321i	−0.344104	+	0.596005i	−0.985191	−	0.171463i	$-0.945151\pi$
$17$	−5.84976	+	10.1321i	−0.344104	+	0.596005i	0.641087	+	0.767468i	$0.278484\pi$
$18$		0			0
$19$	3.88643	+	18.5983i	0.204549	+	0.978856i
$19$	3.88643	+	18.5983i	0.204549	+	0.978856i
$20$		0			0
$21$	16.0225	+	9.25062i	0.762978	+	0.440506i
$22$		0			0
$23$	−13.9817	−	24.2170i	−0.607899	−	1.05291i	−0.991586	−	0.129448i	$-0.958679\pi$
$23$	−13.9817	−	24.2170i	−0.607899	−	1.05291i	0.383688	−	0.923463i	$-0.374654\pi$
$24$		0			0
$25$	1.66807	+	2.88918i	0.0667228	+	0.115567i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−33.2498	+	19.1968i	−1.14655	+	0.661958i	−0.948043	−	0.318142i	$-0.896941\pi$
$29$	−33.2498	+	19.1968i	−1.14655	+	0.661958i	−0.198502	+	0.980100i	$0.563608\pi$
$30$		0			0
$31$		−	42.9440i		−	1.38529i	−0.721278	−	0.692645i	$-0.756445\pi$
$31$		−	42.9440i		−	1.38529i	0.721278	−	0.692645i	$-0.243555\pi$
$32$		0			0
$33$	9.55920	+	5.51901i	0.289673	+	0.167243i
$34$		0			0
$35$	24.8587	−	43.0565i	0.710248	−	1.23019i
$36$		0			0
$37$		−	33.9790i		−	0.918351i	−0.888346	−	0.459176i	$-0.848145\pi$
$37$		−	33.9790i		−	0.918351i	0.888346	−	0.459176i	$-0.151855\pi$
$38$		0			0
$39$	30.7540			0.788565
$40$		0			0
$41$	16.3728	+	9.45284i	0.399337	+	0.230557i	0.686198	−	0.727415i	$-0.259278\pi$
$41$	16.3728	+	9.45284i	0.399337	+	0.230557i	−0.286861	+	0.957972i	$0.592612\pi$
$42$		0			0
$43$	−26.5089	+	45.9148i	−0.616486	+	1.06779i	0.373635	+	0.927576i	$0.378111\pi$
$43$	−26.5089	+	45.9148i	−0.616486	+	1.06779i	−0.990122	+	0.140210i	$0.955222\pi$
$44$		0			0
$45$	13.9633			0.310296
$46$		0			0
$47$	12.0272	+	20.8318i	0.255899	+	0.443230i	0.965139	−	0.261737i	$-0.0842952\pi$
$47$	12.0272	+	20.8318i	0.255899	+	0.443230i	−0.709240	+	0.704967i	$0.750962\pi$
$48$		0			0
$49$	65.0986			1.32854
$50$		0			0
$51$	−17.5493	+	10.1321i	−0.344104	+	0.198668i
$52$		0			0
$53$	−13.3224	+	7.69168i	−0.251366	+	0.145126i	−0.620389	−	0.784294i	$-0.713025\pi$
$53$	−13.3224	+	7.69168i	−0.251366	+	0.145126i	0.369024	+	0.929420i	$0.379692\pi$
$54$		0			0
$55$	14.8309	−	25.6879i	0.269653	−	0.467053i
$56$		0			0
$57$	−10.2769	+	31.2632i	−0.180297	+	0.548476i
$58$		0			0
$59$	−25.6539	−	14.8113i	−0.434813	−	0.251039i	0.266582	−	0.963812i	$-0.414106\pi$
$59$	−25.6539	−	14.8113i	−0.434813	−	0.251039i	−0.701395	+	0.712773i	$0.747439\pi$
$60$		0			0
$61$	−21.3403	−	36.9626i	−0.349842	−	0.605944i	0.636379	−	0.771376i	$-0.280431\pi$
$61$	−21.3403	−	36.9626i	−0.349842	−	0.605944i	−0.986221	+	0.165433i	$0.947098\pi$
$62$		0			0
$63$	16.0225	+	27.7519i	0.254326	+	0.440506i
$64$		0			0
$65$		−	82.6436i		−	1.27144i
$66$		0			0
$67$	15.1585	−	8.75178i	0.226247	−	0.130624i	−0.382593	−	0.923917i	$-0.624969\pi$
$67$	15.1585	−	8.75178i	0.226247	−	0.130624i	0.608839	+	0.793294i	$0.291635\pi$
$68$		0			0
$69$		−	48.4339i		−	0.701941i
$70$		0			0
$71$	74.6028	+	43.0719i	1.05074	+	0.606647i	0.922857	−	0.385142i	$-0.125847\pi$
$71$	74.6028	+	43.0719i	1.05074	+	0.606647i	0.127886	+	0.991789i	$0.459181\pi$
$72$		0			0
$73$	46.2352	−	80.0817i	0.633359	−	1.09701i	−0.353502	−	0.935434i	$-0.615009\pi$
$73$	46.2352	−	80.0817i	0.633359	−	1.09701i	0.986860	−	0.161576i	$-0.0516576\pi$
$74$		0			0
$75$			5.77836i			0.0770448i
$76$		0			0
$77$	68.0723			0.884056
$78$		0			0
$79$	26.3908	+	15.2367i	0.334060	+	0.192870i	0.657642	−	0.753330i	$-0.271554\pi$
$79$	26.3908	+	15.2367i	0.334060	+	0.192870i	−0.323582	+	0.946200i	$0.604887\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−77.1154			−0.929101			−0.464551	−	0.885547i	$-0.653784\pi$
$83$	−77.1154			−0.929101			−0.464551	+	0.885547i	$0.653784\pi$
$84$		0			0
$85$	27.2274	+	47.1592i	0.320322	+	0.554815i
$86$		0			0
$87$	−66.4996			−0.764364
$88$		0			0
$89$	−76.8129	+	44.3479i	−0.863066	+	0.498291i	−0.865038	−	0.501707i	$-0.832706\pi$
$89$	−76.8129	+	44.3479i	−0.863066	+	0.498291i	0.00197195	+	0.999998i	$0.499372\pi$
$90$		0			0
$91$	164.253	−	94.8312i	1.80497	−	1.04210i
$92$		0			0
$93$	37.1906	−	64.4160i	0.399899	−	0.692645i
$94$		0			0
$95$	84.0118	+	27.6166i	0.884334	+	0.290702i
$96$		0			0
$97$	−1.82351	−	1.05281i	−0.0187991	−	0.0108537i	0.490571	−	0.871401i	$-0.336788\pi$
$97$	−1.82351	−	1.05281i	−0.0187991	−	0.0108537i	−0.509370	+	0.860548i	$0.670122\pi$
$98$		0			0
$99$	9.55920	+	16.5570i	0.0965576	+	0.167243i
$100$		0			0
$101$	−13.7690	−	23.8486i	−0.136327	−	0.236125i	0.789777	−	0.613395i	$-0.210196\pi$
$101$	−13.7690	−	23.8486i	−0.136327	−	0.236125i	−0.926104	+	0.377269i	$0.876863\pi$
$102$		0			0
$103$			102.351i			0.993696i	0.867837	+	0.496848i	$0.165509\pi$
$103$			102.351i			0.993696i	−0.867837	+	0.496848i	$0.834491\pi$
$104$		0			0
$105$	74.5760	−	43.0565i	0.710248	−	0.410062i
$106$		0			0
$107$			0.549592i			0.00513638i	0.999997	+	0.00256819i	$0.000817481\pi$
$107$			0.549592i			0.00513638i	−0.999997	+	0.00256819i	$0.999183\pi$
$108$		0			0
$109$	80.7219	+	46.6048i	0.740568	+	0.427567i	0.822276	−	0.569089i	$-0.192704\pi$
$109$	80.7219	+	46.6048i	0.740568	+	0.427567i	−0.0817076	+	0.996656i	$0.526037\pi$
$110$		0			0
$111$	29.4267	−	50.9685i	0.265105	−	0.459176i
$112$		0			0
$113$			55.4186i			0.490430i	0.969469	+	0.245215i	$0.0788586\pi$
$113$			55.4186i			0.490430i	−0.969469	+	0.245215i	$0.921141\pi$
$114$		0			0
$115$	−130.154			−1.13177
$116$		0			0
$117$	46.1310	+	26.6338i	0.394282	+	0.227639i
$118$		0			0
$119$	−62.4854	+	108.228i	−0.525087	+	0.909478i
$120$		0			0
$121$	−80.3874			−0.664359
$122$		0			0
$123$	16.3728	+	28.3585i	0.133112	+	0.230557i
$124$		0			0
$125$	131.889			1.05511
$126$		0			0
$127$	82.7181	−	47.7573i	0.651324	−	0.376042i	−0.137640	−	0.990482i	$-0.543952\pi$
$127$	82.7181	−	47.7573i	0.651324	−	0.376042i	0.788963	+	0.614441i	$0.210618\pi$
$128$		0			0
$129$	−79.5267	+	45.9148i	−0.616486	+	0.355929i
$130$		0			0
$131$	84.0762	−	145.624i	0.641803	−	1.11164i	−0.343227	−	0.939252i	$-0.611520\pi$
$131$	84.0762	−	145.624i	0.641803	−	1.11164i	0.985030	−	0.172383i	$-0.0551466\pi$
$132$		0			0
$133$	41.5136	+	198.661i	0.312133	+	1.49369i
$134$		0			0
$135$	20.9450	+	12.0926i	0.155148	+	0.0895748i
$136$		0			0
$137$	59.3774	+	102.845i	0.433412	+	0.750691i	0.997165	−	0.0752526i	$-0.0239763\pi$
$137$	59.3774	+	102.845i	0.433412	+	0.750691i	−0.563753	+	0.825943i	$0.690643\pi$
$138$		0			0
$139$	55.1822	+	95.5784i	0.396994	+	0.687614i	0.993354	−	0.115104i	$-0.0367200\pi$
$139$	55.1822	+	95.5784i	0.396994	+	0.687614i	−0.596359	+	0.802718i	$0.703387\pi$
$140$		0			0
$141$			41.6636i			0.295487i
$142$		0			0
$143$	97.9947	−	56.5772i	0.685277	−	0.395645i
$144$		0			0
$145$			178.701i			1.23242i
$146$		0			0
$147$	97.6479	+	56.3770i	0.664271	+	0.383517i
$148$		0			0
$149$	28.8719	−	50.0077i	0.193771	−	0.335622i	−0.752726	−	0.658334i	$-0.771261\pi$
$149$	28.8719	−	50.0077i	0.193771	−	0.335622i	0.946497	+	0.322712i	$0.104595\pi$
$150$		0			0
$151$		−	205.459i		−	1.36066i	−0.732908	−	0.680328i	$-0.761837\pi$
$151$		−	205.459i		−	1.36066i	0.732908	−	0.680328i	$-0.238163\pi$
$152$		0			0
$153$	−35.0986			−0.229402
$154$		0			0
$155$	−173.102	−	99.9403i	−1.11678	−	0.644776i
$156$		0			0
$157$	−55.6080	+	96.3159i	−0.354191	+	0.613477i	−0.986979	−	0.160848i	$-0.948577\pi$
$157$	−55.6080	+	96.3159i	−0.354191	+	0.613477i	0.632788	+	0.774325i	$0.281910\pi$
$158$		0			0
$159$	−26.6448			−0.167577
$160$		0			0
$161$	−149.348	−	258.678i	−0.927627	−	1.60670i
$162$		0			0
$163$	−69.1905			−0.424481			−0.212241	−	0.977217i	$-0.568076\pi$
$163$	−69.1905			−0.424481			−0.212241	+	0.977217i	$0.568076\pi$
$164$		0			0
$165$	44.4928	−	25.6879i	0.269653	−	0.155684i
$166$		0			0
$167$	−181.817	+	104.972i	−1.08873	+	0.628577i	−0.933237	−	0.359261i	$-0.883029\pi$
$167$	−181.817	+	104.972i	−1.08873	+	0.628577i	−0.155490	+	0.987837i	$0.549696\pi$
$168$		0			0
$169$	73.1350	−	126.674i	0.432751	−	0.749547i
$170$		0			0
$171$	−42.4901	+	37.9946i	−0.248480	+	0.222191i
$172$		0			0
$173$	−264.781	−	152.871i	−1.53053	−	0.883649i	−0.999337	−	0.0363949i	$-0.988413\pi$
$173$	−264.781	−	152.871i	−1.53053	−	0.883649i	−0.531188	−	0.847254i	$-0.678254\pi$
$174$		0			0
$175$	17.8178	+	30.8613i	0.101816	+	0.176351i
$176$		0			0
$177$	−25.6539	−	44.4339i	−0.144938	−	0.251039i
$178$		0			0
$179$		−	303.001i		−	1.69274i	−0.532593	−	0.846371i	$-0.678782\pi$
$179$		−	303.001i		−	1.69274i	0.532593	−	0.846371i	$-0.321218\pi$
$180$		0			0
$181$	−62.8763	+	36.3016i	−0.347383	+	0.200561i	−0.663532	−	0.748148i	$-0.730943\pi$
$181$	−62.8763	+	36.3016i	−0.347383	+	0.200561i	0.316149	+	0.948709i	$0.397610\pi$
$182$		0			0
$183$		−	73.9251i		−	0.403962i
$184$		0			0
$185$	−136.965	−	79.0767i	−0.740350	−	0.427442i
$186$		0			0
$187$	−37.2794	+	64.5698i	−0.199355	+	0.345293i
$188$		0			0
$189$			55.5037i			0.293670i
$190$		0			0
$191$	48.5734			0.254311			0.127156	−	0.991883i	$-0.459415\pi$
$191$	48.5734			0.254311			0.127156	+	0.991883i	$0.459415\pi$
$192$		0			0
$193$	9.48401	+	5.47559i	0.0491399	+	0.0283710i	0.524369	−	0.851491i	$-0.324301\pi$
$193$	9.48401	+	5.47559i	0.0491399	+	0.0283710i	−0.475229	+	0.879862i	$0.657635\pi$
$194$		0			0
$195$	71.5715	−	123.965i	0.367033	−	0.635720i
$196$		0			0
$197$	104.442			0.530163			0.265082	−	0.964226i	$-0.414601\pi$
$197$	104.442			0.530163			0.265082	+	0.964226i	$0.414601\pi$
$198$		0			0
$199$	140.643	+	243.602i	0.706751	+	1.22413i	0.966056	+	0.258333i	$0.0831731\pi$
$199$	140.643	+	243.602i	0.706751	+	1.22413i	−0.259305	+	0.965795i	$0.583494\pi$
$200$		0			0
$201$	30.3171			0.150831
$202$		0			0
$203$	−355.164	+	205.054i	−1.74958	+	1.01012i
$204$		0			0
$205$	76.2063	−	43.9977i	0.371738	−	0.214623i
$206$		0			0
$207$	41.9450	−	72.6509i	0.202633	−	0.350970i
$208$		0			0
$209$	24.7674	+	118.523i	0.118504	+	0.567096i
$210$		0			0
$211$	−89.2808	−	51.5463i	−0.423132	−	0.244295i	0.273285	−	0.961933i	$-0.411890\pi$
$211$	−89.2808	−	51.5463i	−0.423132	−	0.244295i	−0.696416	+	0.717638i	$0.745223\pi$
$212$		0			0
$213$	74.6028	+	129.216i	0.350248	+	0.606647i
$214$		0			0
$215$	123.384	+	213.708i	0.573880	+	0.993990i
$216$		0			0
$217$		−	458.715i		−	2.11389i
$218$		0			0
$219$	138.706	−	80.0817i	0.633359	−	0.365670i
$220$		0			0
$221$			207.735i			0.939977i
$222$		0			0
$223$	68.9560	+	39.8118i	0.309220	+	0.178528i	0.646577	−	0.762848i	$-0.276200\pi$
$223$	68.9560	+	39.8118i	0.309220	+	0.178528i	−0.337357	+	0.941377i	$0.609533\pi$
$224$		0			0
$225$	−5.00421	+	8.66754i	−0.0222409	+	0.0385224i
$226$		0			0
$227$		−	131.031i		−	0.577228i	−0.957446	−	0.288614i	$-0.906806\pi$
$227$		−	131.031i		−	0.577228i	0.957446	−	0.288614i	$-0.0931944\pi$
$228$		0			0
$229$	30.3537			0.132549			0.0662745	−	0.997801i	$-0.478889\pi$
$229$	30.3537			0.132549			0.0662745	+	0.997801i	$0.478889\pi$
$230$		0			0
$231$	102.108	+	58.9524i	0.442028	+	0.255205i
$232$		0			0
$233$	−47.0484	+	81.4902i	−0.201924	+	0.349743i	−0.949148	−	0.314829i	$-0.898053\pi$
$233$	−47.0484	+	81.4902i	−0.201924	+	0.349743i	0.747224	+	0.664572i	$0.231386\pi$
$234$		0			0
$235$	111.960			0.476427
$236$		0			0
$237$	26.3908	+	45.7101i	0.111353	+	0.192870i
$238$		0			0
$239$	−375.297			−1.57028			−0.785141	−	0.619317i	$-0.787409\pi$
$239$	−375.297			−1.57028			−0.785141	+	0.619317i	$0.787409\pi$
$240$		0			0
$241$	0.482424	−	0.278528i	0.00200176	−	0.00115572i	−0.498999	−	0.866603i	$-0.666299\pi$
$241$	0.482424	−	0.278528i	0.00200176	−	0.00115572i	0.501001	+	0.865447i	$0.332965\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	151.499	−	262.404i	0.618363	−	1.07104i
$246$		0			0
$247$	224.876	+	251.482i	0.910428	+	1.01815i
$248$		0			0
$249$	−115.673	−	66.7839i	−0.464551	−	0.268208i
$250$		0			0
$251$	−117.309	−	203.185i	−0.467367	−	0.809504i	0.531938	−	0.846783i	$-0.321464\pi$
$251$	−117.309	−	203.185i	−0.467367	−	0.809504i	−0.999305	+	0.0372799i	$0.988131\pi$
$252$		0			0
$253$	−89.1024	−	154.330i	−0.352183	−	0.610000i
$254$		0			0
$255$			94.3185i			0.369876i
$256$		0			0
$257$	−11.0702	+	6.39141i	−0.0430749	+	0.0248693i	−0.521383	−	0.853323i	$-0.674584\pi$
$257$	−11.0702	+	6.39141i	−0.0430749	+	0.0248693i	0.478308	+	0.878192i	$0.341250\pi$
$258$		0			0
$259$		−	362.953i		−	1.40136i
$260$		0			0
$261$	−99.7494	−	57.5904i	−0.382182	−	0.220653i
$262$		0			0
$263$	−106.457	+	184.389i	−0.404780	+	0.701099i	−0.994296	−	0.106657i	$-0.965985\pi$
$263$	−106.457	+	184.389i	−0.404780	+	0.701099i	0.589516	+	0.807757i	$0.299319\pi$
$264$		0			0
$265$			71.6010i			0.270193i
$266$		0			0
$267$	−153.626			−0.575377
$268$		0			0
$269$	−438.717	−	253.293i	−1.63092	−	0.941610i	−0.983811	−	0.179211i	$-0.942646\pi$
$269$	−438.717	−	253.293i	−1.63092	−	0.941610i	−0.647106	−	0.762400i	$-0.724021\pi$
$270$		0			0
$271$	−110.063	+	190.635i	−0.406136	+	0.703449i	−0.994453	−	0.105182i	$-0.966457\pi$
$271$	−110.063	+	190.635i	−0.406136	+	0.703449i	0.588317	+	0.808631i	$0.299791\pi$
$272$		0			0
$273$	328.505			1.20332
$274$		0			0
$275$	10.6303	+	18.4122i	0.0386556	+	0.0669534i
$276$		0			0
$277$	262.083			0.946148			0.473074	−	0.881023i	$-0.343144\pi$
$277$	262.083			0.946148			0.473074	+	0.881023i	$0.343144\pi$
$278$		0			0
$279$	111.572	−	64.4160i	0.399899	−	0.230882i
$280$		0			0
$281$	−346.203	+	199.880i	−1.23204	+	0.711317i	−0.967454	−	0.253046i	$-0.918568\pi$
$281$	−346.203	+	199.880i	−1.23204	+	0.711317i	−0.264583	+	0.964363i	$0.585234\pi$
$282$		0			0
$283$	−41.2358	+	71.4225i	−0.145710	+	0.252376i	−0.929637	−	0.368475i	$-0.879880\pi$
$283$	−41.2358	+	71.4225i	−0.145710	+	0.252376i	0.783928	+	0.620852i	$0.213213\pi$
$284$		0			0
$285$	102.101	+	114.181i	0.358249	+	0.400636i
$286$		0			0
$287$	174.889	+	100.972i	0.609370	+	0.351820i
$288$		0			0
$289$	76.0605	+	131.741i	0.263185	+	0.455850i
$290$		0			0
$291$	−1.82351	−	3.15842i	−0.00626637	−	0.0108537i
$292$		0			0
$293$		−	223.552i		−	0.762977i	−0.924374	−	0.381489i	$-0.875412\pi$
$293$		−	223.552i		−	0.762977i	0.924374	−	0.381489i	$-0.124588\pi$
$294$		0			0
$295$	−119.405	+	68.9384i	−0.404762	+	0.233690i
$296$		0			0
$297$			33.1141i			0.111495i
$298$		0			0
$299$	−429.993	−	248.256i	−1.43810	−	0.830289i
$300$		0			0
$301$	−283.160	+	490.448i	−0.940731	+	1.62939i
$302$		0			0
$303$		−	47.6973i		−	0.157417i
$304$		0			0
$305$	−198.655			−0.651328
$306$		0			0
$307$	−339.034	−	195.741i	−1.10434	−	0.637594i	−0.166986	−	0.985959i	$-0.553403\pi$
$307$	−339.034	−	195.741i	−1.10434	−	0.637594i	−0.937359	+	0.348366i	$0.886737\pi$
$308$		0			0
$309$	−88.6383	+	153.526i	−0.286855	+	0.496848i
$310$		0			0
$311$	−375.828			−1.20845			−0.604224	−	0.796814i	$-0.706517\pi$
$311$	−375.828			−1.20845			−0.604224	+	0.796814i	$0.706517\pi$
$312$		0			0
$313$	75.3935	+	130.585i	0.240874	+	0.417206i	0.960963	−	0.276675i	$-0.0892327\pi$
$313$	75.3935	+	130.585i	0.240874	+	0.417206i	−0.720090	+	0.693881i	$0.755899\pi$
$314$		0			0
$315$	149.152			0.473499
$316$		0			0
$317$	−438.163	+	252.973i	−1.38222	+	0.798024i	−0.992422	−	0.122878i	$-0.960788\pi$
$317$	−438.163	+	252.973i	−1.38222	+	0.798024i	−0.389796	+	0.920901i	$0.627454\pi$
$318$		0			0
$319$	−211.895	+	122.337i	−0.664246	+	0.383503i
$320$		0			0
$321$	−0.475961	+	0.824389i	−0.00148274	+	0.00256819i
$322$		0			0
$323$	−211.174	−	69.4179i	−0.653789	−	0.214916i
$324$		0			0
$325$	51.2998	+	29.6180i	0.157846	+	0.0911322i
$326$		0			0
$327$	80.7219	+	139.814i	0.246856	+	0.427567i
$328$		0			0
$329$	128.471	+	222.519i	0.390491	+	0.676349i
$330$		0			0
$331$			443.028i			1.33845i	0.743058	+	0.669227i	$0.233374\pi$
$331$			443.028i			1.33845i	−0.743058	+	0.669227i	$0.766626\pi$
$332$		0			0
$333$	88.2800	−	50.9685i	0.265105	−	0.153059i
$334$		0			0
$335$		−	81.4694i		−	0.243192i
$336$		0			0
$337$	168.764	+	97.4357i	0.500782	+	0.289127i	0.729037	−	0.684475i	$-0.239968\pi$
$337$	168.764	+	97.4357i	0.500782	+	0.289127i	−0.228254	+	0.973602i	$0.573302\pi$
$338$		0			0
$339$	−47.9939	+	83.1279i	−0.141575	+	0.245215i
$340$		0			0
$341$		−	273.674i		−	0.802562i
$342$		0			0
$343$	171.960			0.501341
$344$		0			0
$345$	−195.231	−	112.717i	−0.565886	−	0.326715i
$346$		0			0
$347$	−262.446	+	454.570i	−0.756329	+	1.31000i	0.188382	+	0.982096i	$0.439676\pi$
$347$	−262.446	+	454.570i	−0.756329	+	1.31000i	−0.944711	+	0.327905i	$0.893658\pi$
$348$		0			0
$349$	−369.064			−1.05749			−0.528745	−	0.848781i	$-0.677337\pi$
$349$	−369.064			−1.05749			−0.528745	+	0.848781i	$0.677337\pi$
$350$		0			0
$351$	46.1310	+	79.9013i	0.131427	+	0.227639i
$352$		0			0
$353$	323.725			0.917067			0.458533	−	0.888677i	$-0.348375\pi$
$353$	323.725			0.917067			0.458533	+	0.888677i	$0.348375\pi$
$354$		0			0
$355$	347.235	−	200.476i	0.978126	−	0.564721i
$356$		0			0
$357$	−187.456	+	108.228i	−0.525087	+	0.303159i
$358$		0			0
$359$	6.25614	−	10.8359i	0.0174266	−	0.0301837i	−0.857181	−	0.515016i	$-0.827786\pi$
$359$	6.25614	−	10.8359i	0.0174266	−	0.0301837i	0.874607	+	0.484832i	$0.161119\pi$
$360$		0			0
$361$	−330.791	+	144.562i	−0.916320	+	0.400448i
$362$		0			0
$363$	−120.581	−	69.6175i	−0.332179	−	0.191784i
$364$		0			0
$365$	−215.199	−	372.736i	−0.589587	−	1.02119i
$366$		0			0
$367$	44.3159	+	76.7574i	0.120752	+	0.209148i	0.920064	−	0.391767i	$-0.128136\pi$
$367$	44.3159	+	76.7574i	0.120752	+	0.209148i	−0.799313	+	0.600916i	$0.794803\pi$
$368$		0			0
$369$			56.7171i			0.153705i
$370$		0			0
$371$	−142.306	+	82.1602i	−0.383573	+	0.221456i
$372$		0			0
$373$		−	406.489i		−	1.08978i	−0.838507	−	0.544892i	$-0.816571\pi$
$373$		−	406.489i		−	1.08978i	0.838507	−	0.544892i	$-0.183429\pi$
$374$		0			0
$375$	197.834	+	114.219i	0.527556	+	0.304585i
$376$		0			0
$377$	−340.855	+	590.378i	−0.904125	+	1.56599i
$378$		0			0
$379$		−	433.800i		−	1.14459i	−0.820047	−	0.572296i	$-0.806053\pi$
$379$		−	433.800i		−	1.14459i	0.820047	−	0.572296i	$-0.193947\pi$
$380$		0			0
$381$	165.436			0.434216
$382$		0			0
$383$	355.819	+	205.432i	0.929031	+	0.536377i	0.886505	−	0.462719i	$-0.153126\pi$
$383$	355.819	+	205.432i	0.929031	+	0.536377i	0.0425263	+	0.999095i	$0.486459\pi$
$384$		0			0
$385$	158.419	−	274.391i	0.411479	−	0.712703i
$386$		0			0
$387$	−159.053			−0.410991
$388$		0			0
$389$	−94.6013	−	163.854i	−0.243191	−	0.421219i	0.718430	−	0.695599i	$-0.244861\pi$
$389$	−94.6013	−	163.854i	−0.243191	−	0.421219i	−0.961621	+	0.274380i	$0.911528\pi$
$390$		0			0
$391$	327.158			0.836721
$392$		0			0
$393$	252.228	−	145.624i	0.641803	−	0.370545i
$394$		0			0
$395$	122.834	−	70.9185i	0.310973	−	0.179540i
$396$		0			0
$397$	−220.839	+	382.504i	−0.556269	+	0.963487i	0.441534	+	0.897244i	$0.354434\pi$
$397$	−220.839	+	382.504i	−0.556269	+	0.963487i	−0.997804	+	0.0662425i	$0.978899\pi$
$398$		0			0
$399$	−109.775	+	333.943i	−0.275125	+	0.836951i
$400$		0			0
$401$	320.526	+	185.056i	0.799316	+	0.461485i	0.843232	−	0.537550i	$-0.180650\pi$
$401$	320.526	+	185.056i	0.799316	+	0.461485i	−0.0439159	+	0.999035i	$0.513983\pi$
$402$		0			0
$403$	−381.254	−	660.351i	−0.946039	−	1.63859i
$404$		0			0
$405$	20.9450	+	36.2778i	0.0517161	+	0.0895748i
$406$		0			0
$407$		−	216.541i		−	0.532043i
$408$		0			0
$409$	418.387	−	241.556i	1.02295	−	0.590602i	0.107995	−	0.994151i	$-0.465557\pi$
$409$	418.387	−	241.556i	1.02295	−	0.590602i	0.914958	+	0.403550i	$0.132224\pi$
$410$		0			0
$411$			205.689i			0.500461i
$412$		0			0
$413$	−274.028	−	158.210i	−0.663505	−	0.383075i
$414$		0			0
$415$	−179.465	+	310.842i	−0.432445	+	0.749017i
$416$		0			0
$417$			191.157i			0.458409i
$418$		0			0
$419$	295.264			0.704687			0.352344	−	0.935871i	$-0.385385\pi$
$419$	295.264			0.704687			0.352344	+	0.935871i	$0.385385\pi$
$420$		0			0
$421$	−449.581	−	259.566i	−1.06789	−	0.616545i	−0.140284	−	0.990111i	$-0.544802\pi$
$421$	−449.581	−	259.566i	−1.06789	−	0.616545i	−0.927604	+	0.373566i	$0.878135\pi$
$422$		0			0
$423$	−36.0817	+	62.4954i	−0.0852996	+	0.147743i
$424$		0			0
$425$	−39.0312			−0.0918382
$426$		0			0
$427$	−227.951	−	394.823i	−0.533843	−	0.924644i
$428$		0			0
$429$	195.989			0.456852
$430$		0			0
$431$	195.895	−	113.100i	0.454514	−	0.262414i	−0.255221	−	0.966883i	$-0.582148\pi$
$431$	195.895	−	113.100i	0.454514	−	0.262414i	0.709735	+	0.704469i	$0.248815\pi$
$432$		0			0
$433$	−251.769	+	145.359i	−0.581452	+	0.335702i	−0.761710	−	0.647918i	$-0.775640\pi$
$433$	−251.769	+	145.359i	−0.581452	+	0.335702i	0.180258	+	0.983619i	$0.442307\pi$
$434$		0			0
$435$	−154.759	+	268.051i	−0.355769	+	0.616210i
$436$		0			0
$437$	396.055	−	354.152i	0.906304	−	0.810417i
$438$		0			0
$439$	−251.921	−	145.447i	−0.573852	−	0.331314i	0.184834	−	0.982770i	$-0.440825\pi$
$439$	−251.921	−	145.447i	−0.573852	−	0.331314i	−0.758686	+	0.651456i	$0.774158\pi$
$440$		0			0
$441$	97.6479	+	169.131i	0.221424	+	0.383517i
$442$		0			0
$443$	217.722	+	377.106i	0.491473	+	0.851256i	0.999952	−	0.00981853i	$-0.00312539\pi$
$443$	217.722	+	377.106i	0.491473	+	0.851256i	−0.508479	+	0.861074i	$0.669792\pi$
$444$		0			0
$445$			412.830i			0.927708i
$446$		0			0
$447$	86.6158	−	50.0077i	0.193771	−	0.111874i
$448$		0			0
$449$			263.736i			0.587385i	0.955900	+	0.293692i	$0.0948842\pi$
$449$			263.736i			0.587385i	−0.955900	+	0.293692i	$0.905116\pi$
$450$		0			0
$451$	104.341	+	60.2411i	0.231354	+	0.133572i
$452$		0			0
$453$	177.933	−	308.189i	0.392788	−	0.680328i
$454$		0			0
$455$		−	882.774i		−	1.94016i
$456$		0			0
$457$	641.042			1.40272			0.701359	−	0.712809i	$-0.252577\pi$
$457$	641.042			1.40272			0.701359	+	0.712809i	$0.252577\pi$
$458$		0			0
$459$	−52.6479	−	30.3963i	−0.114701	−	0.0662228i
$460$		0			0
$461$	−323.490	+	560.302i	−0.701714	+	1.21540i	0.266150	+	0.963932i	$0.414248\pi$
$461$	−323.490	+	560.302i	−0.701714	+	1.21540i	−0.967864	+	0.251473i	$0.919085\pi$
$462$		0			0
$463$	407.362			0.879831			0.439916	−	0.898039i	$-0.355008\pi$
$463$	407.362			0.879831			0.439916	+	0.898039i	$0.355008\pi$
$464$		0			0
$465$	−173.102	−	299.821i	−0.372262	−	0.644776i
$466$		0			0
$467$	−146.962			−0.314694			−0.157347	−	0.987543i	$-0.550294\pi$
$467$	−146.962			−0.314694			−0.157347	+	0.987543i	$0.550294\pi$
$468$		0			0
$469$	161.919	−	93.4838i	0.345242	−	0.199326i
$470$		0			0
$471$	−166.824	+	96.3159i	−0.354191	+	0.204492i
$472$		0			0
$473$	−168.936	+	292.606i	−0.357159	+	0.618617i
$474$		0			0
$475$	−47.2509	+	42.2518i	−0.0994757	+	0.0889512i
$476$		0			0
$477$	−39.9672	−	23.0751i	−0.0837886	−	0.0483754i
$478$		0			0
$479$	309.698	+	536.413i	0.646552	+	1.11986i	0.983941	+	0.178495i	$0.0571230\pi$
$479$	309.698	+	536.413i	0.646552	+	1.11986i	−0.337389	+	0.941365i	$0.609544\pi$
$480$		0			0
$481$	−301.663	−	522.495i	−0.627158	−	1.08627i
$482$		0			0
$483$		−	517.356i		−	1.07113i
$484$		0			0
$485$	−8.48745	+	4.90023i	−0.0174999	+	0.0101036i
$486$		0			0
$487$		−	343.861i		−	0.706080i	−0.935608	−	0.353040i	$-0.885148\pi$
$487$		−	343.861i		−	0.706080i	0.935608	−	0.353040i	$-0.114852\pi$
$488$		0			0
$489$	−103.786	−	59.9207i	−0.212241	−	0.122537i
$490$		0			0
$491$	250.993	−	434.733i	0.511187	−	0.885402i	−0.488729	−	0.872436i	$-0.662539\pi$
$491$	250.993	−	434.733i	0.511187	−	0.885402i	0.999916	−	0.0129665i	$-0.00412747\pi$
$492$		0			0
$493$		−	449.187i		−	0.911129i
$494$		0			0
$495$	88.9856			0.179769
$496$		0			0
$497$	796.884	+	460.081i	1.60339	+	0.925717i
$498$		0			0
$499$	−453.717	+	785.861i	−0.909253	+	1.57487i	−0.0941479	+	0.995558i	$0.530013\pi$
$499$	−453.717	+	785.861i	−0.909253	+	1.57487i	−0.815105	+	0.579314i	$0.803321\pi$
$500$		0			0
$501$	−363.635			−0.725818
$502$		0			0
$503$	−183.800	−	318.352i	−0.365408	−	0.632906i	0.623433	−	0.781877i	$-0.285737\pi$
$503$	−183.800	−	318.352i	−0.365408	−	0.632906i	−0.988842	+	0.148971i	$0.952404\pi$
$504$		0			0
$505$	−128.174			−0.253810
$506$		0			0
$507$	219.405	−	126.674i	0.432751	−	0.249849i
$508$		0			0
$509$	406.585	−	234.742i	0.798791	−	0.461182i	−0.0442573	−	0.999020i	$-0.514092\pi$
$509$	406.585	−	234.742i	0.798791	−	0.461182i	0.843048	+	0.537838i	$0.180759\pi$
$510$		0			0
$511$	493.870	−	855.408i	0.966478	−	1.67399i
$512$		0			0
$513$	−96.6395	+	20.1945i	−0.188381	+	0.0393654i
$514$		0			0
$515$	412.562	+	238.193i	0.801092	+	0.462511i
$516$		0			0
$517$	76.6473	+	132.757i	0.148254	+	0.256783i
$518$		0			0
$519$	−264.781	−	458.614i	−0.510175	−	0.883649i
$520$		0			0
$521$		−	691.695i		−	1.32763i	−0.747897	−	0.663815i	$-0.768936\pi$
$521$		−	691.695i		−	1.32763i	0.747897	−	0.663815i	$-0.231064\pi$
$522$		0			0
$523$	70.7545	−	40.8501i	0.135286	−	0.0781073i	−0.430830	−	0.902433i	$-0.641779\pi$
$523$	70.7545	−	40.8501i	0.135286	−	0.0781073i	0.566115	+	0.824326i	$0.308446\pi$
$524$		0			0
$525$			61.7227i			0.117567i
$526$		0			0
$527$	435.113	+	251.212i	0.825640	+	0.476684i
$528$		0			0
$529$	−126.474	+	219.060i	−0.239081	+	0.414101i
$530$		0			0
$531$		−	88.8679i		−	0.167359i
$532$		0			0
$533$	335.686			0.629806
$534$		0			0
$535$	2.21533	+	1.27902i	0.00414081	+	0.00239070i
$536$		0			0
$537$	262.406	−	454.501i	0.488653	−	0.846371i
$538$		0			0
$539$	414.860			0.769685
$540$		0			0
$541$	373.182	+	646.370i	0.689800	+	1.19477i	0.971902	+	0.235384i	$0.0756349\pi$
$541$	373.182	+	646.370i	0.689800	+	1.19477i	−0.282102	+	0.959384i	$0.591032\pi$
$542$		0			0
$543$	−125.753			−0.231588
$544$		0			0
$545$	375.716	−	216.920i	0.689387	−	0.398018i
$546$		0			0
$547$	−404.687	+	233.646i	−0.739830	+	0.427141i	−0.822008	−	0.569476i	$-0.807146\pi$
$547$	−404.687	+	233.646i	−0.739830	+	0.427141i	0.0821772	+	0.996618i	$0.473813\pi$
$548$		0			0
$549$	64.0210	−	110.888i	0.116614	−	0.201981i
$550$		0			0
$551$	−486.250	−	543.782i	−0.882487	−	0.986900i
$552$		0			0
$553$	281.898	+	162.754i	0.509761	+	0.294311i
$554$		0			0
$555$	−136.965	−	237.230i	−0.246783	−	0.427442i
$556$		0			0
$557$	386.099	+	668.743i	0.693175	+	1.20061i	0.970792	+	0.239923i	$0.0771222\pi$
$557$	386.099	+	668.743i	0.693175	+	1.20061i	−0.277617	+	0.960692i	$0.589544\pi$
$558$		0			0
$559$			941.376i			1.68404i
$560$		0			0
$561$	−111.838	+	64.5698i	−0.199355	+	0.115098i
$562$		0			0
$563$			195.273i			0.346844i	0.984848	+	0.173422i	$0.0554825\pi$
$563$			195.273i			0.346844i	−0.984848	+	0.173422i	$0.944518\pi$
$564$		0			0
$565$	223.385	+	128.971i	0.395372	+	0.228268i
$566$		0			0
$567$	−48.0676	+	83.2556i	−0.0847753	+	0.146835i
$568$		0			0
$569$		−	579.517i		−	1.01848i	−0.860624	−	0.509242i	$-0.829926\pi$
$569$		−	579.517i		−	1.01848i	0.860624	−	0.509242i	$-0.170074\pi$
$570$		0			0
$571$	145.886			0.255492			0.127746	−	0.991807i	$-0.459226\pi$
$571$	145.886			0.255492			0.127746	+	0.991807i	$0.459226\pi$
$572$		0			0
$573$	72.8602	+	42.0658i	0.127156	+	0.0734133i
$574$		0			0
$575$	46.6448	−	80.7911i	0.0811214	−	0.140506i
$576$		0			0
$577$	−1037.54			−1.79817			−0.899084	−	0.437777i	$-0.855766\pi$
$577$	−1037.54			−1.79817			−0.899084	+	0.437777i	$0.855766\pi$
$578$		0			0
$579$	9.48401	+	16.4268i	0.0163800	+	0.0283710i
$580$		0			0
$581$	−823.723			−1.41777
$582$		0			0
$583$	−84.9009	+	49.0176i	−0.145628	+	0.0840782i
$584$		0			0
$585$	214.714	−	123.965i	0.367033	−	0.211907i
$586$		0			0
$587$	−441.521	+	764.737i	−0.752165	+	1.30279i	0.194606	+	0.980882i	$0.437657\pi$
$587$	−441.521	+	764.737i	−0.752165	+	1.30279i	−0.946771	+	0.321907i	$0.895676\pi$
$588$		0			0
$589$	798.684	−	166.899i	1.35600	−	0.283360i
$590$		0			0
$591$	156.663	+	90.4495i	0.265082	+	0.153045i
$592$		0			0
$593$	119.583	+	207.125i	0.201658	+	0.349283i	0.949063	−	0.315087i	$-0.102034\pi$
$593$	119.583	+	207.125i	0.201658	+	0.349283i	−0.747404	+	0.664369i	$0.768700\pi$
$594$		0			0
$595$	290.835	+	503.741i	0.488798	+	0.846623i
$596$		0			0
$597$			487.203i			0.816086i
$598$		0			0
$599$	793.604	−	458.187i	1.32488	−	0.764920i	0.340378	−	0.940289i	$-0.389445\pi$
$599$	793.604	−	458.187i	1.32488	−	0.764920i	0.984503	+	0.175368i	$0.0561116\pi$
$600$		0			0
$601$		−	789.891i		−	1.31429i	−0.753762	−	0.657147i	$-0.771763\pi$
$601$		−	789.891i		−	1.31429i	0.753762	−	0.657147i	$-0.228237\pi$
$602$		0			0
$603$	45.4756	+	26.2553i	0.0754155	+	0.0435412i
$604$		0			0
$605$	−187.079	+	324.031i	−0.309222	+	0.535588i
$606$		0			0
$607$			653.712i			1.07696i	0.842640	+	0.538478i	$0.181000\pi$
$607$			653.712i			1.07696i	−0.842640	+	0.538478i	$0.819000\pi$
$608$		0			0
$609$	−710.329			−1.16639
$610$		0			0
$611$	369.886	+	213.554i	0.605379	+	0.349515i
$612$		0			0
$613$	528.343	−	915.118i	0.861898	−	1.49285i	−0.00819687	−	0.999966i	$-0.502609\pi$
$613$	528.343	−	915.118i	0.861898	−	1.49285i	0.870095	−	0.492885i	$-0.164057\pi$
$614$		0			0
$615$	152.413			0.247825
$616$		0			0
$617$	−501.032	−	867.813i	−0.812045	−	1.40650i	−0.911430	−	0.411455i	$-0.865021\pi$
$617$	−501.032	−	867.813i	−0.812045	−	1.40650i	0.0993850	−	0.995049i	$-0.468312\pi$
$618$		0			0
$619$	−252.948			−0.408640			−0.204320	−	0.978904i	$-0.565498\pi$
$619$	−252.948			−0.408640			−0.204320	+	0.978904i	$0.565498\pi$
$620$		0			0
$621$	125.835	−	72.6509i	0.202633	−	0.116990i
$622$		0			0
$623$	−820.491	+	473.711i	−1.31700	+	0.760371i
$624$		0			0
$625$	265.233	−	459.398i	0.424373	−	0.735036i
$626$		0			0
$627$	−65.4929	+	199.234i	−0.104454	+	0.317757i
$628$		0			0
$629$	344.278	+	198.769i	0.547342	+	0.316008i
$630$		0			0
$631$	605.640	+	1049.00i	0.959809	+	1.66244i	0.722957	+	0.690893i	$0.242783\pi$
$631$	605.640	+	1049.00i	0.959809	+	1.66244i	0.236853	+	0.971546i	$0.423884\pi$
$632$		0			0
$633$	−89.2808	−	154.639i	−0.141044	−	0.244295i
$634$		0			0
$635$		−	444.568i		−	0.700107i
$636$		0			0
$637$	1001.02	−	577.940i	1.57146	−	0.907284i
$638$		0			0
$639$			258.432i			0.404431i
$640$		0			0
$641$	89.1040	+	51.4442i	0.139008	+	0.0802562i	0.567891	−	0.823104i	$-0.307759\pi$
$641$	89.1040	+	51.4442i	0.139008	+	0.0802562i	−0.428883	+	0.903360i	$0.641093\pi$
$642$		0			0
$643$	384.990	−	666.822i	0.598740	−	1.03705i	−0.394267	−	0.918996i	$-0.629002\pi$
$643$	384.990	−	666.822i	0.598740	−	1.03705i	0.993007	−	0.118052i	$-0.0376650\pi$
$644$		0			0
$645$			427.416i			0.662660i
$646$		0			0
$647$	790.984			1.22254			0.611270	−	0.791422i	$-0.290659\pi$
$647$	790.984			1.22254			0.611270	+	0.791422i	$0.290659\pi$
$648$		0			0
$649$	−163.488	−	94.3896i	−0.251907	−	0.145438i
$650$		0			0
$651$	397.259	−	688.072i	0.610228	−	1.05695i
$652$		0			0
$653$	320.503			0.490816			0.245408	−	0.969420i	$-0.421078\pi$
$653$	320.503			0.490816			0.245408	+	0.969420i	$0.421078\pi$
$654$		0			0
$655$	−391.328	−	677.800i	−0.597447	−	1.03481i
$656$		0			0
$657$	277.411			0.422239
$658$		0			0
$659$	616.112	−	355.713i	0.934920	−	0.539776i	0.0465558	−	0.998916i	$-0.485175\pi$
$659$	616.112	−	355.713i	0.934920	−	0.539776i	0.888364	+	0.459139i	$0.151842\pi$
$660$		0			0
$661$	−410.779	+	237.163i	−0.621451	+	0.358795i	−0.777434	−	0.628965i	$-0.783479\pi$
$661$	−410.779	+	237.163i	−0.621451	+	0.358795i	0.155983	+	0.987760i	$0.450146\pi$
$662$		0			0
$663$	−179.904	+	311.602i	−0.271348	+	0.469989i
$664$		0			0
$665$	897.388	+	294.993i	1.34946	+	0.443598i
$666$		0			0
$667$	929.776	+	536.806i	1.39397	+	0.804807i
$668$		0			0
$669$	68.9560	+	119.435i	0.103073	+	0.178528i
$670$		0			0
$671$	−135.998	−	235.555i	−0.202679	−	0.351051i
$672$		0			0
$673$			648.662i			0.963836i	0.876216	+	0.481918i	$0.160060\pi$
$673$			648.662i			0.963836i	−0.876216	+	0.481918i	$0.839940\pi$
$674$		0			0
$675$	−15.0126	+	8.66754i	−0.0222409	+	0.0128408i
$676$		0			0
$677$		−	860.699i		−	1.27134i	−0.771960	−	0.635671i	$-0.780723\pi$
$677$		−	860.699i		−	1.27134i	0.771960	−	0.635671i	$-0.219277\pi$
$678$		0			0
$679$	−19.4782	−	11.2458i	−0.0286866	−	0.0165622i
$680$		0			0
$681$	113.476	−	196.546i	0.166631	−	0.288614i
$682$		0			0
$683$			194.789i			0.285196i	0.989781	+	0.142598i	$0.0455456\pi$
$683$			194.789i			0.285196i	−0.989781	+	0.142598i	$0.954454\pi$
$684$		0			0
$685$	552.738			0.806916
$686$		0			0
$687$	45.5306	+	26.2871i	0.0662745	+	0.0382636i
$688$		0			0
$689$	−136.572	+	236.550i	−0.198218	+	0.343324i
$690$		0			0
$691$	−719.067			−1.04062			−0.520309	−	0.853978i	$-0.674183\pi$
$691$	−719.067			−1.04062			−0.520309	+	0.853978i	$0.674183\pi$
$692$		0			0
$693$	102.108	+	176.857i	0.147343	+	0.255205i
$694$		0			0
$695$	513.685			0.739115
$696$		0			0
$697$	−191.554	+	110.594i	−0.274826	+	0.158671i
$698$		0			0
$699$	−141.145	+	81.4902i	−0.201924	+	0.116581i
$700$		0			0
$701$	242.353	−	419.767i	0.345724	−	0.598812i	−0.639761	−	0.768574i	$-0.720967\pi$
$701$	242.353	−	419.767i	0.345724	−	0.598812i	0.985485	+	0.169762i	$0.0542999\pi$
$702$		0			0
$703$	631.951	−	132.057i	0.898934	−	0.187848i
$704$		0			0
$705$	167.941	+	96.9605i	0.238213	+	0.137533i
$706$		0			0
$707$	−147.076	−	254.744i	−0.208029	−	0.360317i
$708$		0			0
$709$	620.485	+	1074.71i	0.875156	+	1.51581i	0.856597	+	0.515987i	$0.172575\pi$
$709$	620.485	+	1074.71i	0.875156	+	1.51581i	0.0185591	+	0.999828i	$0.494092\pi$
$710$		0			0
$711$			91.4203i			0.128580i
$712$		0			0
$713$	−1039.97	+	600.429i	−1.45859	+	0.842116i
$714$		0			0
$715$		−	526.671i		−	0.736603i
$716$		0			0
$717$	−562.946	−	325.017i	−0.785141	−	0.453301i
$718$		0			0
$719$	−65.3191	+	113.136i	−0.0908471	+	0.157352i	−0.907868	−	0.419256i	$-0.862291\pi$
$719$	−65.3191	+	113.136i	−0.0908471	+	0.157352i	0.817021	+	0.576608i	$0.195624\pi$
$720$		0			0
$721$			1093.28i			1.51634i
$722$		0			0
$723$	0.964848			0.00133451
$724$		0			0
$725$	−110.926	−	64.0432i	−0.153001	−	0.0883354i
$726$		0			0
$727$	566.505	−	981.216i	0.779237	−	1.34968i	−0.153145	−	0.988204i	$-0.548940\pi$
$727$	566.505	−	981.216i	0.779237	−	1.34968i	0.932382	−	0.361475i	$-0.117727\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−310.142	−	537.181i	−0.424271	−	0.734858i
$732$		0			0
$733$	−837.144			−1.14208			−0.571040	−	0.820922i	$-0.693460\pi$
$733$	−837.144			−1.14208			−0.571040	+	0.820922i	$0.693460\pi$
$734$		0			0
$735$	454.497	−	262.404i	0.618363	−	0.357012i
$736$		0			0
$737$	96.6023	−	55.7734i	0.131075	−	0.0756762i
$738$		0			0
$739$	−144.463	+	250.216i	−0.195484	+	0.338588i	−0.947059	−	0.321060i	$-0.895961\pi$
$739$	−144.463	+	250.216i	−0.195484	+	0.338588i	0.751575	+	0.659647i	$0.229294\pi$
$740$		0			0
$741$	119.523	+	571.972i	0.161300	+	0.771892i
$742$		0			0
$743$	66.4928	+	38.3896i	0.0894923	+	0.0516684i	0.544078	−	0.839034i	$-0.316879\pi$
$743$	66.4928	+	38.3896i	0.0894923	+	0.0516684i	−0.454586	+	0.890703i	$0.650213\pi$
$744$		0			0
$745$	−134.383	−	232.758i	−0.180380	−	0.312427i
$746$		0			0
$747$	−115.673	−	200.352i	−0.154850	−	0.268208i
$748$		0			0
$749$			5.87058i			0.00783789i
$750$		0			0
$751$	−923.318	+	533.078i	−1.22945	+	0.709824i	−0.966915	−	0.255098i	$-0.917892\pi$
$751$	−923.318	+	533.078i	−1.22945	+	0.709824i	−0.262536	+	0.964922i	$0.584559\pi$
$752$		0			0
$753$		−	406.371i		−	0.539669i
$754$		0			0
$755$	−828.179	−	478.149i	−1.09693	−	0.633310i
$756$		0			0
$757$	4.94030	−	8.55684i	0.00652615	−	0.0113036i	−0.862744	−	0.505641i	$-0.831256\pi$
$757$	4.94030	−	8.55684i	0.00652615	−	0.0113036i	0.869270	+	0.494338i	$0.164589\pi$
$758$		0			0
$759$		−	308.660i		−	0.406666i
$760$		0			0
$761$	1147.50			1.50788			0.753940	−	0.656944i	$-0.228151\pi$
$761$	1147.50			1.50788			0.753940	+	0.656944i	$0.228151\pi$
$762$		0			0
$763$	862.247	+	497.819i	1.13007	+	0.652449i
$764$		0			0
$765$	−81.6822	+	141.478i	−0.106774	+	0.184938i
$766$		0			0
$767$	−525.975			−0.685756
$768$		0			0
$769$	299.227	+	518.276i	0.389112	+	0.673961i	0.992330	−	0.123615i	$-0.0394486\pi$
$769$	299.227	+	518.276i	0.389112	+	0.673961i	−0.603218	+	0.797576i	$0.706115\pi$
$770$		0			0
$771$	−22.1405			−0.0287166
$772$		0			0
$773$	858.414	−	495.605i	1.11050	−	0.641145i	0.171538	−	0.985177i	$-0.445126\pi$
$773$	858.414	−	495.605i	1.11050	−	0.641145i	0.938958	+	0.344032i	$0.111793\pi$
$774$		0			0
$775$	124.073	−	71.6336i	0.160094	−	0.0924305i
$776$		0			0
$777$	314.327	−	544.430i	0.404539	−	0.700682i
$778$		0			0
$779$	−112.175	+	341.244i	−0.143998	+	0.438053i
$780$		0			0
$781$	475.429	+	274.489i	0.608744	+	0.351458i
$782$		0			0
$783$	−99.7494	−	172.771i	−0.127394	−	0.220653i
$784$		0			0
$785$	258.824	+	448.297i	0.329713	+	0.571079i
$786$		0			0
$787$		−	1226.83i		−	1.55887i	−0.626480	−	0.779437i	$-0.715505\pi$
$787$		−	1226.83i		−	1.55887i	0.626480	−	0.779437i	$-0.284495\pi$
$788$		0			0
$789$	−319.371	+	184.389i	−0.404780	+	0.233700i
$790$		0			0
$791$			591.965i			0.748375i
$792$		0			0
$793$	−656.302	−	378.916i	−0.827619	−	0.477826i
$794$		0			0
$795$	−62.0083	+	107.402i	−0.0779979	+	0.135096i
$796$		0			0
$797$			788.636i			0.989506i	0.869034	+	0.494753i	$0.164741\pi$
$797$			788.636i			0.989506i	−0.869034	+	0.494753i	$0.835259\pi$
$798$		0			0
$799$	−281.426			−0.352223
$800$		0			0
$801$	−230.439	−	133.044i	−0.287689	−	0.166097i
$802$		0			0
$803$	294.648	−	510.345i	0.366934	−	0.635548i
$804$		0			0
$805$	−1390.26			−1.72704
$806$		0			0
$807$	−438.717	−	759.880i	−0.543639	−	0.941610i
$808$		0			0
$809$	640.524			0.791748			0.395874	−	0.918305i	$-0.370442\pi$
$809$	640.524			0.791748			0.395874	+	0.918305i	$0.370442\pi$
$810$		0			0
$811$	811.945	−	468.777i	1.00117	−	0.578023i	0.0925727	−	0.995706i	$-0.470491\pi$
$811$	811.945	−	468.777i	1.00117	−	0.578023i	0.908593	+	0.417683i	$0.137158\pi$
$812$		0			0
$813$	−330.189	+	190.635i	−0.406136	+	0.234483i
$814$		0			0
$815$	−161.022	+	278.898i	−0.197573	+	0.342206i
$816$		0			0
$817$	−956.961	−	314.576i	−1.17131	−	0.385037i
$818$		0			0
$819$	492.758	+	284.494i	0.601658	+	0.347367i
$820$		0			0
$821$	−671.718	−	1163.45i	−0.818170	−	1.41711i	−0.907029	−	0.421068i	$-0.861655\pi$
$821$	−671.718	−	1163.45i	−0.818170	−	1.41711i	0.0888591	−	0.996044i	$-0.471678\pi$
$822$		0			0
$823$	−435.019	−	753.475i	−0.528577	−	0.915522i	−0.999445	−	0.0333184i	$-0.989392\pi$
$823$	−435.019	−	753.475i	−0.528577	−	0.915522i	0.470868	−	0.882204i	$-0.343941\pi$
$824$		0			0
$825$			36.8244i			0.0446356i
$826$		0			0
$827$	−583.285	+	336.760i	−0.705303	+	0.407207i	−0.809319	−	0.587369i	$-0.800164\pi$
$827$	−583.285	+	336.760i	−0.705303	+	0.407207i	0.104017	+	0.994576i	$0.466830\pi$
$828$		0			0
$829$			516.908i			0.623532i	0.950159	+	0.311766i	$0.100920\pi$
$829$			516.908i			0.623532i	−0.950159	+	0.311766i	$0.899080\pi$
$830$		0			0
$831$	393.125	+	226.971i	0.473074	+	0.273129i
$832$		0			0
$833$	−380.811	+	659.584i	−0.457156	+	0.791818i
$834$		0			0
$835$			977.176i			1.17027i
$836$		0			0
$837$	223.144			0.266599
$838$		0			0
$839$	1050.53	+	606.526i	1.25213	+	0.722915i	0.971531	−	0.236911i	$-0.0761350\pi$
$839$	1050.53	+	606.526i	1.25213	+	0.722915i	0.280595	+	0.959826i	$0.409468\pi$
$840$		0			0
$841$	316.533	−	548.252i	0.376377	−	0.651905i
$842$		0			0
$843$	−692.405			−0.821358
$844$		0			0
$845$	−340.403	−	589.595i	−0.402844	−	0.697745i
$846$		0			0
$847$	−858.673			−1.01378
$848$		0			0
$849$	−123.707	+	71.4225i	−0.145710	+	0.0841255i
$850$		0			0
$851$	−822.868	+	475.083i	−0.966942	+	0.558264i
$852$		0			0
$853$	−267.766	+	463.785i	−0.313911	+	0.543710i	−0.979205	−	0.202871i	$-0.934973\pi$
$853$	−267.766	+	463.785i	−0.313911	+	0.543710i	0.665294	+	0.746581i	$0.268306\pi$
$854$		0			0
$855$	54.2675	+	259.694i	0.0634707	+	0.303736i
$856$		0			0
$857$	655.156	+	378.254i	0.764476	+	0.441370i	0.830901	−	0.556421i	$-0.187826\pi$
$857$	655.156	+	378.254i	0.764476	+	0.441370i	−0.0664245	+	0.997791i	$0.521159\pi$
$858$		0			0
$859$	−538.135	−	932.077i	−0.626466	−	1.08507i	−0.988255	−	0.152812i	$-0.951167\pi$
$859$	−538.135	−	932.077i	−0.626466	−	1.08507i	0.361789	−	0.932260i	$-0.382166\pi$
$860$		0			0
$861$	174.889	+	302.917i	0.203123	+	0.351820i
$862$		0			0
$863$		−	939.206i		−	1.08830i	−0.838987	−	0.544152i	$-0.816852\pi$
$863$		−	939.206i		−	1.08830i	0.838987	−	0.544152i	$-0.183148\pi$
$864$		0			0
$865$	−1232.41	+	711.531i	−1.42475	+	0.822579i
$866$		0			0
$867$			263.481i			0.303900i
$868$		0			0
$869$	168.183	+	97.1006i	0.193536	+	0.111738i
$870$		0			0
$871$	155.395	−	269.152i	0.178410	−	0.309015i
$872$		0			0
$873$		−	6.31684i		−	0.00723578i
$874$		0			0
$875$	1408.80			1.61005
$876$		0			0
$877$	−1011.30	−	583.873i	−1.15313	−	0.665761i	−0.203484	−	0.979078i	$-0.565226\pi$
$877$	−1011.30	−	583.873i	−1.15313	−	0.665761i	−0.949649	+	0.313317i	$0.898560\pi$
$878$		0			0
$879$	193.602	−	335.328i	0.220252	−	0.381489i
$880$		0			0
$881$	68.2541			0.0774734			0.0387367	−	0.999249i	$-0.487667\pi$
$881$	68.2541			0.0774734			0.0387367	+	0.999249i	$0.487667\pi$
$882$		0			0
$883$	134.599	+	233.133i	0.152434	+	0.264023i	0.932122	−	0.362145i	$-0.117956\pi$
$883$	134.599	+	233.133i	0.152434	+	0.264023i	−0.779688	+	0.626169i	$0.784622\pi$
$884$		0			0
$885$	−238.810			−0.269842
$886$		0			0
$887$	−795.589	+	459.333i	−0.896943	+	0.517850i	−0.876207	−	0.481935i	$-0.839934\pi$
$887$	−795.589	+	459.333i	−0.896943	+	0.517850i	−0.0207361	+	0.999785i	$0.506601\pi$
$888$		0			0
$889$	883.569	−	510.129i	0.993891	−	0.573823i
$890$		0			0
$891$	−28.6776	+	49.6711i	−0.0321859	+	0.0557476i
$892$		0			0
$893$	−340.693	+	304.647i	−0.381515	+	0.341150i
$894$		0			0
$895$	−1221.36	−	705.151i	−1.36464	−	0.787878i
$896$		0			0
$897$	−429.993	−	744.769i	−0.479367	−	0.830289i
$898$		0			0
$899$	824.387	+	1427.88i	0.917005	+	1.58830i
$900$		0			0
$901$		−	179.978i		−	0.199754i
$902$		0			0
$903$	−849.480	+	490.448i	−0.940731	+	0.543131i
$904$		0			0
$905$			337.928i			0.373401i
$906$		0			0
$907$	−654.944	−	378.132i	−0.722099	−	0.416904i	0.0934255	−	0.995626i	$-0.470218\pi$
$907$	−654.944	−	378.132i	−0.722099	−	0.416904i	−0.815525	+	0.578722i	$0.803552\pi$
$908$		0			0
$909$	41.3071	−	71.5459i	0.0454423	−	0.0787084i
$910$		0			0
$911$			945.788i			1.03819i	0.854718	+	0.519093i	$0.173730\pi$
$911$			945.788i			1.03819i	−0.854718	+	0.519093i	$0.826270\pi$
$912$		0			0
$913$	−491.441			−0.538271
$914$		0			0
$915$	−297.982	−	172.040i	−0.325664	−	0.188022i
$916$		0			0
$917$	898.076	−	1555.51i	0.979363	−	1.69631i
$918$		0			0
$919$	−1224.77			−1.33272			−0.666362	−	0.745628i	$-0.732150\pi$
$919$	−1224.77			−1.33272			−0.666362	+	0.745628i	$0.732150\pi$
$920$		0			0
$921$	−339.034	−	587.224i	−0.368115	−	0.637594i
$922$		0			0
$923$	1529.56			1.65716
$924$		0			0
$925$	98.1715	−	56.6793i	0.106131	−	0.0612749i
$926$		0			0
$927$	−265.915	+	153.526i	−0.286855	+	0.165616i
$928$		0			0
$929$	−529.236	+	916.663i	−0.569683	+	0.986721i	0.426914	+	0.904292i	$0.359601\pi$
$929$	−529.236	+	916.663i	−0.569683	+	0.986721i	−0.996597	+	0.0824281i	$0.973733\pi$
$930$		0			0
$931$	253.001	+	1210.72i	0.271752	+	1.30045i
$932$		0			0
$933$	−563.741	−	325.476i	−0.604224	−	0.348849i
$934$		0			0
$935$	173.515	+	300.537i	0.185577	+	0.321429i
$936$		0			0
$937$	−96.5921	−	167.302i	−0.103087	−	0.178551i	0.809868	−	0.586612i	$-0.199539\pi$
$937$	−96.5921	−	167.302i	−0.103087	−	0.178551i	−0.912955	+	0.408061i	$0.866205\pi$
$938$		0			0
$939$			261.171i			0.278137i
$940$		0			0
$941$	178.549	−	103.085i	0.189744	−	0.109549i	−0.402119	−	0.915587i	$-0.631726\pi$
$941$	178.549	−	103.085i	0.189744	−	0.109549i	0.591863	+	0.806039i	$0.298393\pi$
$942$		0			0
$943$		−	528.666i		−	0.560621i
$944$		0			0
$945$	223.728	+	129.169i	0.236749	+	0.136687i
$946$		0			0
$947$	−553.455	+	958.612i	−0.584430	+	1.01226i	0.410517	+	0.911853i	$0.365348\pi$
$947$	−553.455	+	958.612i	−0.584430	+	1.01226i	−0.994946	+	0.100409i	$0.967985\pi$
$948$		0			0
$949$		−	1641.89i		−	1.73013i
$950$		0			0
$951$	−876.326			−0.921478
$952$		0			0
$953$	729.970	+	421.448i	0.765970	+	0.442233i	0.831435	−	0.555622i	$-0.187520\pi$
$953$	729.970	+	421.448i	0.765970	+	0.442233i	−0.0654649	+	0.997855i	$0.520853\pi$
$954$		0			0
$955$	113.041	−	195.793i	0.118368	−	0.205019i
$956$		0			0
$957$	−423.789			−0.442831
$958$		0			0
$959$	634.251	+	1098.55i	0.661367	+	1.14552i
$960$		0			0
$961$	−883.189			−0.919031
$962$		0			0
$963$	−1.42788	+	0.824389i	−0.00148274	+	0.000856063i
$964$		0			0
$965$	44.1428	−	25.4859i	0.0457438	−	0.0264102i
$966$		0			0
$967$	404.649	−	700.873i	0.418458	−	0.724791i	−0.577326	−	0.816514i	$-0.695904\pi$
$967$	404.649	−	700.873i	0.418458	−	0.724791i	0.995785	+	0.0917223i	$0.0292372\pi$
$968$		0			0
$969$	−256.643	−	287.009i	−0.264854	−	0.296191i
$970$		0			0
$971$	29.7562	+	17.1798i	0.0306449	+	0.0176929i	0.515244	−	0.857043i	$-0.327701\pi$
$971$	29.7562	+	17.1798i	0.0306449	+	0.0176929i	−0.484599	+	0.874736i	$0.661035\pi$
$972$		0			0
$973$	589.439	+	1020.94i	0.605796	+	1.04927i
$974$		0			0
$975$	51.2998	+	88.8539i	0.0526152	+	0.0911322i
$976$		0			0
$977$			1293.09i			1.32353i	0.749711	+	0.661765i	$0.230192\pi$
$977$			1293.09i			1.32353i	−0.749711	+	0.661765i	$0.769808\pi$
$978$		0			0
$979$	−489.513	+	282.621i	−0.500013	+	0.288683i
$980$		0			0
$981$			279.629i			0.285045i
$982$		0			0
$983$	−405.649	−	234.202i	−0.412665	−	0.238252i	0.279269	−	0.960213i	$-0.409908\pi$
$983$	−405.649	−	234.202i	−0.412665	−	0.238252i	−0.691934	+	0.721961i	$0.743241\pi$
$984$		0			0
$985$	243.060	−	420.992i	0.246762	−	0.427403i
$986$		0			0
$987$			445.038i			0.450900i
$988$		0			0
$989$	1482.56			1.49904
$990$		0			0
$991$	−1362.49	−	786.632i	−1.37486	−	0.793776i	−0.383325	−	0.923614i	$-0.625221\pi$
$991$	−1362.49	−	786.632i	−1.37486	−	0.793776i	−0.991535	+	0.129838i	$0.958554\pi$
$992$		0			0
$993$	−383.674	+	664.542i	−0.386378	+	0.669227i
$994$		0			0
$995$	1309.23			1.31581
$996$		0			0
$997$	121.379	+	210.235i	0.121744	+	0.210867i	0.920456	−	0.390847i	$-0.127818\pi$
$997$	121.379	+	210.235i	0.121744	+	0.210867i	−0.798711	+	0.601714i	$0.794485\pi$
$998$		0			0
$999$	176.560			0.176737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.f.673.2		6
4.3	odd	2		57.3.g.b.46.3	yes	6
12.11	even	2		171.3.p.c.46.1		6
19.12	odd	6	inner	912.3.be.f.145.2		6
76.31	even	6		57.3.g.b.31.3	✓	6
228.107	odd	6		171.3.p.c.145.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.3	✓	6	76.31	even	6
57.3.g.b.46.3	yes	6	4.3	odd	2
171.3.p.c.46.1		6	12.11	even	2
171.3.p.c.145.1		6	228.107	odd	6
912.3.be.f.145.2		6	19.12	odd	6	inner
912.3.be.f.673.2		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)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(2.32722 - 4.03087i) q^{5} +10.6817 q^{7} +(1.50000 + 2.59808i) q^{9} +6.37280 q^{11} +(15.3770 - 8.87792i) q^{13} +(6.98167 - 4.03087i) q^{15} +(-5.84976 + 10.1321i) q^{17} +(3.88643 + 18.5983i) q^{19} +(16.0225 + 9.25062i) q^{21} +(-13.9817 - 24.2170i) q^{23} +(1.66807 + 2.88918i) q^{25} +5.19615i q^{27} +(-33.2498 + 19.1968i) q^{29} -42.9440i q^{31} +(9.55920 + 5.51901i) q^{33} +(24.8587 - 43.0565i) q^{35} -33.9790i q^{37} +30.7540 q^{39} +(16.3728 + 9.45284i) q^{41} +(-26.5089 + 45.9148i) q^{43} +13.9633 q^{45} +(12.0272 + 20.8318i) q^{47} +65.0986 q^{49} +(-17.5493 + 10.1321i) q^{51} +(-13.3224 + 7.69168i) q^{53} +(14.8309 - 25.6879i) q^{55} +(-10.2769 + 31.2632i) q^{57} +(-25.6539 - 14.8113i) q^{59} +(-21.3403 - 36.9626i) q^{61} +(16.0225 + 27.7519i) q^{63} -82.6436i q^{65} +(15.1585 - 8.75178i) q^{67} -48.4339i q^{69} +(74.6028 + 43.0719i) q^{71} +(46.2352 - 80.0817i) q^{73} +5.77836i q^{75} +68.0723 q^{77} +(26.3908 + 15.2367i) q^{79} +(-4.50000 + 7.79423i) q^{81} -77.1154 q^{83} +(27.2274 + 47.1592i) q^{85} -66.4996 q^{87} +(-76.8129 + 44.3479i) q^{89} +(164.253 - 94.8312i) q^{91} +(37.1906 - 64.4160i) q^{93} +(84.0118 + 27.6166i) q^{95} +(-1.82351 - 1.05281i) q^{97} +(9.55920 + 16.5570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 + 22 * q^7 + 9 * q^9 + 36 * q^11 - 3 * q^13 + 12 * q^15 + 38 * q^17 + 10 * q^19 + 33 * q^21 - 54 * q^23 - 21 * q^25 - 102 * q^29 + 54 * q^33 + 24 * q^35 - 6 * q^39 + 96 * q^41 - 107 * q^43 + 24 * q^45 + 50 * q^47 - 48 * q^49 + 114 * q^51 - 90 * q^53 - 148 * q^55 - 3 * q^57 + 27 * q^61 + 33 * q^63 + 39 * q^67 - 84 * q^71 - 77 * q^73 + 260 * q^77 - 9 * q^79 - 27 * q^81 + 348 * q^83 + 68 * q^85 - 204 * q^87 - 72 * q^89 + 393 * q^91 + 129 * q^93 - 104 * q^95 - 228 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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