LMFDB - Embedded newform 308.3.r.a.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70156 + 1.23625i) q^{3} +(2.48745 + 7.65558i) q^{5} +(1.55513 - 2.14046i) q^{7} +(-1.41418 + 4.35239i) q^{9} +O(q^{10})$	\(q+(-1.70156 + 1.23625i) q^{3} +(2.48745 + 7.65558i) q^{5} +(1.55513 - 2.14046i) q^{7} +(-1.41418 + 4.35239i) q^{9} +(9.10127 + 6.17793i) q^{11} +(-21.4174 - 6.95895i) q^{13} +(-13.6968 - 9.95129i) q^{15} +(16.8506 - 5.47509i) q^{17} +(4.10030 + 5.64357i) q^{19} +5.56465i q^{21} -18.8311 q^{23} +(-32.1950 + 23.3911i) q^{25} +(-8.82379 - 27.1568i) q^{27} +(-31.6812 + 43.6055i) q^{29} +(-3.81434 + 11.7393i) q^{31} +(-23.1238 + 0.739380i) q^{33} +(20.2547 + 6.58117i) q^{35} +(-53.6087 - 38.9490i) q^{37} +(45.0461 - 14.6364i) q^{39} +(17.0663 + 23.4897i) q^{41} +73.8614i q^{43} -36.8378 q^{45} +(60.6882 - 44.0926i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-21.9036 + 30.1478i) q^{51} +(-11.1662 + 34.3661i) q^{53} +(-24.6567 + 85.0428i) q^{55} +(-13.9538 - 4.53386i) q^{57} +(37.0223 + 26.8983i) q^{59} +(33.8442 - 10.9966i) q^{61} +(7.11688 + 9.79554i) q^{63} -181.273i q^{65} +1.65692 q^{67} +(32.0422 - 23.2800i) q^{69} +(-27.5812 - 84.8861i) q^{71} +(43.4307 - 59.7772i) q^{73} +(25.8644 - 79.6025i) q^{75} +(27.3773 - 9.87338i) q^{77} +(59.1306 + 19.2127i) q^{79} +(15.2657 + 11.0912i) q^{81} +(42.5071 - 13.8114i) q^{83} +(83.8299 + 115.382i) q^{85} -113.363i q^{87} -104.276 q^{89} +(-48.2023 + 35.0210i) q^{91} +(-8.02248 - 24.6906i) q^{93} +(-33.0055 + 45.4282i) q^{95} +(20.1581 - 62.0404i) q^{97} +(-39.7596 + 30.8756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	−1.70156	+	1.23625i	−0.567186	+	0.412085i	−0.834082	−	0.551641i	$-0.814002\pi$
$3$	−1.70156	+	1.23625i	−0.567186	+	0.412085i	0.266896	+	0.963725i	$0.414002\pi$
$4$		0			0
$5$	2.48745	+	7.65558i	0.497489	+	1.53112i	0.813041	+	0.582207i	$0.197811\pi$
$5$	2.48745	+	7.65558i	0.497489	+	1.53112i	−0.315551	+	0.948908i	$0.602189\pi$
$6$		0			0
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$8$		0			0
$9$	−1.41418	+	4.35239i	−0.157131	+	0.483599i
$10$		0			0
$11$	9.10127	+	6.17793i	0.827388	+	0.561630i
$11$	9.10127	+	6.17793i	0.827388	+	0.561630i
$12$		0			0
$13$	−21.4174	−	6.95895i	−1.64750	−	0.535304i	−0.669301	−	0.742992i	$-0.733406\pi$
$13$	−21.4174	−	6.95895i	−1.64750	−	0.535304i	−0.978195	+	0.207688i	$0.933406\pi$
$14$		0			0
$15$	−13.6968	−	9.95129i	−0.913118	−	0.663419i
$16$		0			0
$17$	16.8506	−	5.47509i	0.991211	−	0.322064i	0.231863	−	0.972749i	$-0.425518\pi$
$17$	16.8506	−	5.47509i	0.991211	−	0.322064i	0.759348	+	0.650685i	$0.225518\pi$
$18$		0			0
$19$	4.10030	+	5.64357i	0.215805	+	0.297030i	0.903171	−	0.429281i	$-0.141233\pi$
$19$	4.10030	+	5.64357i	0.215805	+	0.297030i	−0.687366	+	0.726311i	$0.741233\pi$
$20$		0			0
$21$			5.56465i			0.264983i
$22$		0			0
$23$	−18.8311			−0.818744			−0.409372	−	0.912368i	$-0.634252\pi$
$23$	−18.8311			−0.818744			−0.409372	+	0.912368i	$0.634252\pi$
$24$		0			0
$25$	−32.1950	+	23.3911i	−1.28780	+	0.935642i
$26$		0			0
$27$	−8.82379	−	27.1568i	−0.326807	−	1.00581i
$28$		0			0
$29$	−31.6812	+	43.6055i	−1.09246	+	1.50364i	−0.247434	+	0.968905i	$0.579587\pi$
$29$	−31.6812	+	43.6055i	−1.09246	+	1.50364i	−0.845022	+	0.534732i	$0.820413\pi$
$30$		0			0
$31$	−3.81434	+	11.7393i	−0.123043	+	0.378688i	−0.993539	−	0.113487i	$-0.963798\pi$
$31$	−3.81434	+	11.7393i	−0.123043	+	0.378688i	0.870496	+	0.492175i	$0.163798\pi$
$32$		0			0
$33$	−23.1238	+	0.739380i	−0.700722	+	0.0224054i
$34$		0			0
$35$	20.2547	+	6.58117i	0.578707	+	0.188033i
$36$		0			0
$37$	−53.6087	−	38.9490i	−1.44888	−	1.05268i	−0.986090	−	0.166211i	$-0.946847\pi$
$37$	−53.6087	−	38.9490i	−1.44888	−	1.05268i	−0.462795	−	0.886465i	$-0.653153\pi$
$38$		0			0
$39$	45.0461	−	14.6364i	1.15503	−	0.375291i
$40$		0			0
$41$	17.0663	+	23.4897i	0.416250	+	0.572919i	0.964729	−	0.263245i	$-0.0847928\pi$
$41$	17.0663	+	23.4897i	0.416250	+	0.572919i	−0.548479	+	0.836165i	$0.684793\pi$
$42$		0			0
$43$			73.8614i			1.71771i	0.512222	+	0.858853i	$0.328822\pi$
$43$			73.8614i			1.71771i	−0.512222	+	0.858853i	$0.671178\pi$
$44$		0			0
$45$	−36.8378			−0.818617
$46$		0			0
$47$	60.6882	−	44.0926i	1.29124	−	0.938139i	0.291409	−	0.956599i	$-0.405876\pi$
$47$	60.6882	−	44.0926i	1.29124	−	0.938139i	0.999830	+	0.0184592i	$0.00587608\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−21.9036	+	30.1478i	−0.429483	+	0.591133i
$52$		0			0
$53$	−11.1662	+	34.3661i	−0.210684	+	0.648418i	0.788748	+	0.614716i	$0.210730\pi$
$53$	−11.1662	+	34.3661i	−0.210684	+	0.648418i	−0.999432	+	0.0337014i	$0.989270\pi$
$54$		0			0
$55$	−24.6567	+	85.0428i	−0.448303	+	1.54623i
$56$		0			0
$57$	−13.9538	−	4.53386i	−0.244803	−	0.0795414i
$58$		0			0
$59$	37.0223	+	26.8983i	0.627497	+	0.455903i	0.855532	−	0.517750i	$-0.173230\pi$
$59$	37.0223	+	26.8983i	0.627497	+	0.455903i	−0.228035	+	0.973653i	$0.573230\pi$
$60$		0			0
$61$	33.8442	−	10.9966i	0.554822	−	0.180273i	−0.0181679	−	0.999835i	$-0.505783\pi$
$61$	33.8442	−	10.9966i	0.554822	−	0.180273i	0.572990	+	0.819562i	$0.305783\pi$
$62$		0			0
$63$	7.11688	+	9.79554i	0.112966	+	0.155485i
$64$		0			0
$65$		−	181.273i		−	2.78881i
$66$		0			0
$67$	1.65692			0.0247302			0.0123651	−	0.999924i	$-0.496064\pi$
$67$	1.65692			0.0247302			0.0123651	+	0.999924i	$0.496064\pi$
$68$		0			0
$69$	32.0422	−	23.2800i	0.464380	−	0.337392i
$70$		0			0
$71$	−27.5812	−	84.8861i	−0.388467	−	1.19558i	−0.933934	−	0.357446i	$-0.883648\pi$
$71$	−27.5812	−	84.8861i	−0.388467	−	1.19558i	0.545467	−	0.838132i	$-0.316352\pi$
$72$		0			0
$73$	43.4307	−	59.7772i	0.594941	−	0.818866i	−0.400293	−	0.916387i	$-0.631092\pi$
$73$	43.4307	−	59.7772i	0.594941	−	0.818866i	0.995233	+	0.0975218i	$0.0310916\pi$
$74$		0			0
$75$	25.8644	−	79.6025i	0.344859	−	1.06137i
$76$		0			0
$77$	27.3773	−	9.87338i	0.355549	−	0.128226i
$78$		0			0
$79$	59.1306	+	19.2127i	0.748488	+	0.243198i	0.658330	−	0.752729i	$-0.271263\pi$
$79$	59.1306	+	19.2127i	0.748488	+	0.243198i	0.0901575	+	0.995928i	$0.471263\pi$
$80$		0			0
$81$	15.2657	+	11.0912i	0.188465	+	0.136928i
$82$		0			0
$83$	42.5071	−	13.8114i	0.512134	−	0.166402i	−0.0415388	−	0.999137i	$-0.513226\pi$
$83$	42.5071	−	13.8114i	0.512134	−	0.166402i	0.553672	+	0.832735i	$0.313226\pi$
$84$		0			0
$85$	83.8299	+	115.382i	0.986234	+	1.35743i
$86$		0			0
$87$		−	113.363i		−	1.30303i
$88$		0			0
$89$	−104.276			−1.17164			−0.585822	−	0.810440i	$-0.699228\pi$
$89$	−104.276			−1.17164			−0.585822	+	0.810440i	$0.699228\pi$
$90$		0			0
$91$	−48.2023	+	35.0210i	−0.529696	+	0.384847i
$92$		0			0
$93$	−8.02248	−	24.6906i	−0.0862632	−	0.265491i
$94$		0			0
$95$	−33.0055	+	45.4282i	−0.347427	+	0.478192i
$96$		0			0
$97$	20.1581	−	62.0404i	0.207816	−	0.639591i	−0.791770	−	0.610819i	$-0.790840\pi$
$97$	20.1581	−	62.0404i	0.207816	−	0.639591i	0.999586	−	0.0287722i	$-0.00915973\pi$
$98$		0			0
$99$	−39.7596	+	30.8756i	−0.401612	+	0.311875i
$100$		0			0
$101$	30.7115	+	9.97877i	0.304074	+	0.0987997i	0.457080	−	0.889426i	$-0.348895\pi$
$101$	30.7115	+	9.97877i	0.304074	+	0.0987997i	−0.153006	+	0.988225i	$0.548895\pi$
$102$		0			0
$103$	133.786	+	97.2014i	1.29890	+	0.943703i	0.999944	−	0.0105657i	$-0.00336322\pi$
$103$	133.786	+	97.2014i	1.29890	+	0.943703i	0.298951	+	0.954268i	$0.403363\pi$
$104$		0			0
$105$	−42.6006	+	13.8418i	−0.405720	+	0.131826i
$106$		0			0
$107$	93.0394	+	128.058i	0.869527	+	1.19680i	0.979213	+	0.202836i	$0.0650157\pi$
$107$	93.0394	+	128.058i	0.869527	+	1.19680i	−0.109685	+	0.993966i	$0.534984\pi$
$108$		0			0
$109$			17.2872i			0.158598i	0.996851	+	0.0792992i	$0.0252683\pi$
$109$			17.2872i			0.158598i	−0.996851	+	0.0792992i	$0.974732\pi$
$110$		0			0
$111$	139.369			1.25558
$112$		0			0
$113$	−46.3150	+	33.6498i	−0.409867	+	0.297786i	−0.773548	−	0.633738i	$-0.781520\pi$
$113$	−46.3150	+	33.6498i	−0.409867	+	0.297786i	0.363681	+	0.931524i	$0.381520\pi$
$114$		0			0
$115$	−46.8414	−	144.163i	−0.407316	−	1.25359i
$116$		0			0
$117$	60.5762	−	83.3759i	0.517745	−	0.712615i
$118$		0			0
$119$	14.4857	−	44.5824i	0.121729	−	0.374642i
$120$		0			0
$121$	44.6663	+	112.454i	0.369143	+	0.929372i
$122$		0			0
$123$	−58.0785	−	18.8708i	−0.472183	−	0.153421i
$124$		0			0
$125$	−96.3499	−	70.0023i	−0.770799	−	0.560018i
$126$		0			0
$127$	156.833	−	50.9583i	1.23491	−	0.401246i	0.382419	−	0.923989i	$-0.375091\pi$
$127$	156.833	−	50.9583i	1.23491	−	0.401246i	0.852490	+	0.522743i	$0.175091\pi$
$128$		0			0
$129$	−91.3114	−	125.679i	−0.707840	−	0.974259i
$130$		0			0
$131$		−	5.10983i		−	0.0390063i	−0.999810	−	0.0195031i	$-0.993792\pi$
$131$		−	5.10983i		−	0.0390063i	0.999810	−	0.0195031i	$-0.00620844\pi$
$132$		0			0
$133$	18.4563			0.138769
$134$		0			0
$135$	185.953	−	135.102i	1.37743	−	1.00076i
$136$		0			0
$137$	78.2212	+	240.740i	0.570957	+	1.75723i	0.649549	+	0.760320i	$0.274958\pi$
$137$	78.2212	+	240.740i	0.570957	+	1.75723i	−0.0785917	+	0.996907i	$0.525042\pi$
$138$		0			0
$139$	−50.2529	+	69.1672i	−0.361532	+	0.497606i	−0.950575	−	0.310496i	$-0.899505\pi$
$139$	−50.2529	+	69.1672i	−0.361532	+	0.497606i	0.589043	+	0.808102i	$0.299505\pi$
$140$		0			0
$141$	−48.7549	+	150.052i	−0.345779	+	1.06420i
$142$		0			0
$143$	−151.934	−	195.651i	−1.06248	−	1.36819i
$144$		0			0
$145$	−412.630	−	134.072i	−2.84573	−	0.924633i
$146$		0			0
$147$	11.9109	+	8.65378i	0.0810266	+	0.0588692i
$148$		0			0
$149$	141.248	−	45.8942i	0.947972	−	0.308015i	0.206081	−	0.978535i	$-0.433929\pi$
$149$	141.248	−	45.8942i	0.947972	−	0.308015i	0.741891	+	0.670520i	$0.233929\pi$
$150$		0			0
$151$	26.7539	+	36.8235i	0.177178	+	0.243864i	0.888365	−	0.459139i	$-0.151842\pi$
$151$	26.7539	+	36.8235i	0.177178	+	0.243864i	−0.711187	+	0.703003i	$0.751842\pi$
$152$		0			0
$153$			81.0831i			0.529955i
$154$		0			0
$155$	−99.3593			−0.641028
$156$		0			0
$157$	−91.6742	+	66.6052i	−0.583912	+	0.424237i	−0.840132	−	0.542381i	$-0.817523\pi$
$157$	−91.6742	+	66.6052i	−0.583912	+	0.424237i	0.256220	+	0.966618i	$0.417523\pi$
$158$		0			0
$159$	−23.4853	−	72.2803i	−0.147706	−	0.454593i
$160$		0			0
$161$	−29.2849	+	40.3072i	−0.181894	+	0.250355i
$162$		0			0
$163$	69.5852	−	214.161i	0.426903	−	1.31387i	−0.474257	−	0.880386i	$-0.657283\pi$
$163$	69.5852	−	214.161i	0.426903	−	1.31387i	0.901160	−	0.433486i	$-0.142717\pi$
$164$		0			0
$165$	−63.1797	−	175.187i	−0.382907	−	1.06174i
$166$		0			0
$167$	−66.7107	−	21.6756i	−0.399465	−	0.129794i	0.102393	−	0.994744i	$-0.467350\pi$
$167$	−66.7107	−	21.6756i	−0.399465	−	0.129794i	−0.501858	+	0.864950i	$0.667350\pi$
$168$		0			0
$169$	273.556	+	198.750i	1.61868	+	1.17604i
$170$		0			0
$171$	−30.3616	+	9.86508i	−0.177553	+	0.0576905i
$172$		0			0
$173$	45.1473	+	62.1400i	0.260967	+	0.359190i	0.919314	−	0.393524i	$-0.128744\pi$
$173$	45.1473	+	62.1400i	0.260967	+	0.359190i	−0.658347	+	0.752714i	$0.728744\pi$
$174$		0			0
$175$			105.288i			0.601647i
$176$		0			0
$177$	−96.2487			−0.543778
$178$		0			0
$179$	−91.4533	+	66.4447i	−0.510912	+	0.371199i	−0.813169	−	0.582027i	$-0.802260\pi$
$179$	−91.4533	+	66.4447i	−0.510912	+	0.371199i	0.302257	+	0.953226i	$0.402260\pi$
$180$		0			0
$181$	71.9952	+	221.578i	0.397763	+	1.22419i	0.926789	+	0.375584i	$0.122558\pi$
$181$	71.9952	+	221.578i	0.397763	+	1.22419i	−0.529025	+	0.848606i	$0.677442\pi$
$182$		0			0
$183$	−43.9932	+	60.5514i	−0.240400	+	0.330882i
$184$		0			0
$185$	164.828	−	507.289i	0.890964	−	2.74211i
$186$		0			0
$187$	187.186	+	54.2715i	1.00100	+	0.290222i
$188$		0			0
$189$	−71.8503	−	23.3456i	−0.380160	−	0.123521i
$190$		0			0
$191$	−146.448	−	106.400i	−0.766741	−	0.557070i	0.134229	−	0.990950i	$-0.457144\pi$
$191$	−146.448	−	106.400i	−0.766741	−	0.557070i	−0.900971	+	0.433880i	$0.857144\pi$
$192$		0			0
$193$	−9.80626	+	3.18625i	−0.0508097	+	0.0165091i	−0.334312	−	0.942463i	$-0.608504\pi$
$193$	−9.80626	+	3.18625i	−0.0508097	+	0.0165091i	0.283502	+	0.958972i	$0.408504\pi$
$194$		0			0
$195$	224.099	+	308.446i	1.14923	+	1.58178i
$196$		0			0
$197$			250.253i			1.27032i	0.772381	+	0.635159i	$0.219066\pi$
$197$			250.253i			1.27032i	−0.772381	+	0.635159i	$0.780934\pi$
$198$		0			0
$199$	50.3246			0.252887			0.126444	−	0.991974i	$-0.459644\pi$
$199$	50.3246			0.252887			0.126444	+	0.991974i	$0.459644\pi$
$200$		0			0
$201$	−2.81935	+	2.04838i	−0.0140266	+	0.0101909i
$202$		0			0
$203$	44.0671	+	135.625i	0.217079	+	0.668102i
$204$		0			0
$205$	−137.376	+	189.081i	−0.670125	+	0.922349i
$206$		0			0
$207$	26.6305	−	81.9604i	0.128650	−	0.395944i
$208$		0			0
$209$	2.45231	+	76.6951i	0.0117335	+	0.366962i
$210$		0			0
$211$	−24.5469	−	7.97576i	−0.116336	−	0.0377998i	0.250271	−	0.968176i	$-0.419480\pi$
$211$	−24.5469	−	7.97576i	−0.116336	−	0.0377998i	−0.366606	+	0.930376i	$0.619480\pi$
$212$		0			0
$213$	151.872	+	110.341i	0.713013	+	0.518034i
$214$		0			0
$215$	−565.451	+	183.726i	−2.63001	+	0.854541i
$216$		0			0
$217$	19.1957	+	26.4207i	0.0884596	+	0.121754i
$218$		0			0
$219$			155.406i			0.709615i
$220$		0			0
$221$	−398.997			−1.80542
$222$		0			0
$223$	−272.767	+	198.177i	−1.22317	+	0.888686i	−0.996359	−	0.0852525i	$-0.972830\pi$
$223$	−272.767	+	198.177i	−1.22317	+	0.888686i	−0.226812	+	0.973939i	$0.572830\pi$
$224$		0			0
$225$	−56.2775	−	173.204i	−0.250122	−	0.769798i
$226$		0			0
$227$	135.640	−	186.693i	0.597533	−	0.822434i	−0.397946	−	0.917409i	$-0.630277\pi$
$227$	135.640	−	186.693i	0.597533	−	0.822434i	0.995480	+	0.0949745i	$0.0302770\pi$
$228$		0			0
$229$	35.4735	−	109.176i	0.154906	−	0.476752i	−0.843245	−	0.537529i	$-0.819358\pi$
$229$	35.4735	−	109.176i	0.154906	−	0.476752i	0.998151	+	0.0607769i	$0.0193578\pi$
$230$		0			0
$231$	−34.3780	+	50.6454i	−0.148823	+	0.219244i
$232$		0			0
$233$	−163.436	−	53.1035i	−0.701441	−	0.227912i	−0.0634825	−	0.997983i	$-0.520221\pi$
$233$	−163.436	−	53.1035i	−0.701441	−	0.227912i	−0.637958	+	0.770071i	$0.720221\pi$
$234$		0			0
$235$	488.513	+	354.925i	2.07878	+	1.51032i
$236$		0			0
$237$	−124.366	+	40.4089i	−0.524750	+	0.170502i
$238$		0			0
$239$	−171.904	−	236.606i	−0.719264	−	0.989981i	−0.999548	−	0.0300644i	$-0.990429\pi$
$239$	−171.904	−	236.606i	−0.719264	−	0.989981i	0.280284	−	0.959917i	$-0.409571\pi$
$240$		0			0
$241$			308.809i			1.28136i	0.767807	+	0.640682i	$0.221348\pi$
$241$			308.809i			1.28136i	−0.767807	+	0.640682i	$0.778652\pi$
$242$		0			0
$243$	217.303			0.894250
$244$		0			0
$245$	45.5856	−	33.1198i	0.186063	−	0.135183i
$246$		0			0
$247$	−48.5445	−	149.405i	−0.196537	−	0.604877i
$248$		0			0
$249$	−55.2539	+	76.0504i	−0.221903	+	0.305423i
$250$		0			0
$251$	65.0889	−	200.323i	0.259318	−	0.798099i	−0.733630	−	0.679549i	$-0.762175\pi$
$251$	65.0889	−	200.323i	0.259318	−	0.798099i	0.992948	−	0.118550i	$-0.0378246\pi$
$252$		0			0
$253$	−171.387	−	116.337i	−0.677419	−	0.459831i
$254$		0			0
$255$	−285.283	−	92.6940i	−1.11876	−	0.363506i
$256$		0			0
$257$	39.6107	+	28.7789i	0.154127	+	0.111980i	0.662176	−	0.749348i	$-0.269633\pi$
$257$	39.6107	+	28.7789i	0.154127	+	0.111980i	−0.508049	+	0.861328i	$0.669633\pi$
$258$		0			0
$259$	−166.738	+	54.1763i	−0.643774	+	0.209175i
$260$		0			0
$261$	−144.985	−	199.555i	−0.555499	−	0.764579i
$262$		0			0
$263$		−	5.52582i		−	0.0210107i	−0.999945	−	0.0105054i	$-0.996656\pi$
$263$		−	5.52582i		−	0.0210107i	0.999945	−	0.0105054i	$-0.00334402\pi$
$264$		0			0
$265$	−290.868			−1.09762
$266$		0			0
$267$	177.432	−	128.912i	0.664540	−	0.482817i
$268$		0			0
$269$	−83.7386	−	257.721i	−0.311296	−	0.958070i	−0.977252	−	0.212080i	$-0.931976\pi$
$269$	−83.7386	−	257.721i	−0.311296	−	0.958070i	0.665956	−	0.745991i	$-0.268024\pi$
$270$		0			0
$271$	105.479	−	145.180i	0.389222	−	0.535718i	−0.568776	−	0.822492i	$-0.692583\pi$
$271$	105.479	−	145.180i	0.389222	−	0.535718i	0.957998	+	0.286774i	$0.0925830\pi$
$272$		0			0
$273$	38.7241	−	119.181i	0.141847	−	0.436559i
$274$		0			0
$275$	−437.524	+	13.9897i	−1.59100	+	0.0508718i
$276$		0			0
$277$	220.540	+	71.6579i	0.796174	+	0.258693i	0.678731	−	0.734387i	$-0.262530\pi$
$277$	220.540	+	71.6579i	0.796174	+	0.258693i	0.117443	+	0.993080i	$0.462530\pi$
$278$		0			0
$279$	−45.7000	−	33.2030i	−0.163799	−	0.119007i
$280$		0			0
$281$	420.623	−	136.669i	1.49688	−	0.486365i	0.557772	−	0.829994i	$-0.311656\pi$
$281$	420.623	−	136.669i	1.49688	−	0.486365i	0.939105	+	0.343629i	$0.111656\pi$
$282$		0			0
$283$	52.2022	+	71.8502i	0.184460	+	0.253888i	0.891226	−	0.453560i	$-0.149846\pi$
$283$	52.2022	+	71.8502i	0.184460	+	0.253888i	−0.706765	+	0.707448i	$0.749846\pi$
$284$		0			0
$285$		−	118.102i		−	0.414393i
$286$		0			0
$287$	76.8190			0.267662
$288$		0			0
$289$	20.1596	−	14.6468i	0.0697564	−	0.0506810i
$290$		0			0
$291$	42.3974	+	130.486i	0.145696	+	0.448405i
$292$		0			0
$293$	51.9398	−	71.4890i	0.177269	−	0.243990i	−0.711132	−	0.703059i	$-0.751817\pi$
$293$	51.9398	−	71.4890i	0.177269	−	0.243990i	0.888401	+	0.459069i	$0.151817\pi$
$294$		0			0
$295$	−113.831	+	350.335i	−0.385867	+	1.18758i
$296$		0			0
$297$	87.4653	−	301.675i	0.294496	−	1.01574i
$298$		0			0
$299$	403.314	+	131.045i	1.34888	+	0.438277i
$300$		0			0
$301$	158.097	+	114.864i	0.525240	+	0.381609i
$302$		0			0
$303$	−64.5937	+	20.9878i	−0.213181	+	0.0692665i
$304$		0			0
$305$	168.371	+	231.743i	0.552036	+	0.759813i
$306$		0			0
$307$		−	89.1291i		−	0.290323i	−0.989408	−	0.145161i	$-0.953630\pi$
$307$		−	89.1291i		−	0.290323i	0.989408	−	0.145161i	$-0.0463702\pi$
$308$		0			0
$309$	−347.811			−1.12560
$310$		0			0
$311$	93.5883	−	67.9959i	0.300927	−	0.218636i	−0.427067	−	0.904220i	$-0.640453\pi$
$311$	93.5883	−	67.9959i	0.300927	−	0.218636i	0.727994	+	0.685584i	$0.240453\pi$
$312$		0			0
$313$	182.704	+	562.305i	0.583718	+	1.79650i	0.604358	+	0.796713i	$0.293430\pi$
$313$	182.704	+	562.305i	0.583718	+	1.79650i	−0.0206393	+	0.999787i	$0.506570\pi$
$314$		0			0
$315$	−57.2876	+	78.8497i	−0.181866	+	0.250316i
$316$		0			0
$317$	118.194	−	363.765i	0.372853	−	1.14752i	−0.572063	−	0.820210i	$-0.693857\pi$
$317$	118.194	−	363.765i	0.372853	−	1.14752i	0.944916	−	0.327313i	$-0.106143\pi$
$318$		0			0
$319$	−557.731	+	201.141i	−1.74837	+	0.630536i
$320$		0			0
$321$	−316.624	−	102.877i	−0.986368	−	0.320490i
$322$		0			0
$323$	99.9914	+	72.6480i	0.309571	+	0.224916i
$324$		0			0
$325$	852.312	−	276.933i	2.62250	−	0.852102i
$326$		0			0
$327$	−21.3714	−	29.4152i	−0.0653560	−	0.0899548i
$328$		0			0
$329$		−	198.470i		−	0.603253i
$330$		0			0
$331$	60.8609			0.183870			0.0919349	−	0.995765i	$-0.470695\pi$
$331$	60.8609			0.183870			0.0919349	+	0.995765i	$0.470695\pi$
$332$		0			0
$333$	245.334	−	178.245i	0.736738	−	0.535272i
$334$		0			0
$335$	4.12150	+	12.6847i	0.0123030	+	0.0378647i
$336$		0			0
$337$	27.3144	−	37.5951i	0.0810518	−	0.111558i	−0.766566	−	0.642166i	$-0.778036\pi$
$337$	27.3144	−	37.5951i	0.0810518	−	0.111558i	0.847618	+	0.530607i	$0.178036\pi$
$338$		0			0
$339$	37.2079	−	114.514i	0.109758	−	0.337800i
$340$		0			0
$341$	−107.240	+	83.2781i	−0.314487	+	0.244217i
$342$		0			0
$343$	−17.6138	−	5.72307i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	257.925	+	187.394i	0.747610	+	0.543170i
$346$		0			0
$347$	95.3290	−	30.9743i	0.274723	−	0.0892630i	−0.168415	−	0.985716i	$-0.553865\pi$
$347$	95.3290	−	30.9743i	0.274723	−	0.0892630i	0.443139	+	0.896453i	$0.353865\pi$
$348$		0			0
$349$	183.883	+	253.093i	0.526885	+	0.725195i	0.986652	−	0.162845i	$-0.0520669\pi$
$349$	183.883	+	253.093i	0.526885	+	0.725195i	−0.459767	+	0.888040i	$0.652067\pi$
$350$		0			0
$351$			643.035i			1.83201i
$352$		0			0
$353$	123.827			0.350784			0.175392	−	0.984499i	$-0.443881\pi$
$353$	123.827			0.350784			0.175392	+	0.984499i	$0.443881\pi$
$354$		0			0
$355$	581.245	−	422.299i	1.63731	−	1.18958i
$356$		0			0
$357$	30.4670	+	93.7676i	0.0853416	+	0.262654i
$358$		0			0
$359$	−93.3654	+	128.506i	−0.260071	+	0.357957i	−0.919006	−	0.394243i	$-0.871007\pi$
$359$	−93.3654	+	128.506i	−0.260071	+	0.357957i	0.658936	+	0.752199i	$0.271007\pi$
$360$		0			0
$361$	96.5176	−	297.051i	0.267362	−	0.822855i
$362$		0			0
$363$	−215.024	−	136.128i	−0.592353	−	0.375009i
$364$		0			0
$365$	565.660	+	183.794i	1.54975	+	0.503546i
$366$		0			0
$367$	−367.281	−	266.845i	−1.00077	−	0.727099i	−0.0385136	−	0.999258i	$-0.512262\pi$
$367$	−367.281	−	266.845i	−1.00077	−	0.727099i	−0.962252	+	0.272159i	$0.912262\pi$
$368$		0			0
$369$	−126.371	+	41.0605i	−0.342469	+	0.111275i
$370$		0			0
$371$	56.1943	+	77.3448i	0.151467	+	0.208477i
$372$		0			0
$373$		−	524.955i		−	1.40739i	−0.710505	−	0.703693i	$-0.751533\pi$
$373$		−	524.955i		−	1.40739i	0.710505	−	0.703693i	$-0.248467\pi$
$374$		0			0
$375$	250.485			0.667961
$376$		0			0
$377$	981.979	−	713.450i	2.60472	−	1.89244i
$378$		0			0
$379$	−77.9422	−	239.881i	−0.205652	−	0.632933i	−0.999686	−	0.0250589i	$-0.992023\pi$
$379$	−77.9422	−	239.881i	−0.205652	−	0.632933i	0.794034	−	0.607874i	$-0.207977\pi$
$380$		0			0
$381$	−203.864	+	280.595i	−0.535076	+	0.736469i
$382$		0			0
$383$	174.577	−	537.292i	0.455814	−	1.40285i	−0.414362	−	0.910112i	$-0.635995\pi$
$383$	174.577	−	537.292i	0.455814	−	1.40285i	0.870177	−	0.492740i	$-0.164005\pi$
$384$		0			0
$385$	143.686	+	185.029i	0.373210	+	0.480596i
$386$		0			0
$387$	−321.474	−	104.453i	−0.830681	−	0.269905i
$388$		0			0
$389$	106.466	+	77.3522i	0.273692	+	0.198849i	0.716161	−	0.697935i	$-0.245897\pi$
$389$	106.466	+	77.3522i	0.273692	+	0.198849i	−0.442469	+	0.896784i	$0.645897\pi$
$390$		0			0
$391$	−317.315	+	103.102i	−0.811547	+	0.263688i
$392$		0			0
$393$	6.31704	+	8.69466i	0.0160739	+	0.0221238i
$394$		0			0
$395$			500.469i			1.26701i
$396$		0			0
$397$	−276.364			−0.696130			−0.348065	−	0.937470i	$-0.613161\pi$
$397$	−276.364			−0.696130			−0.348065	+	0.937470i	$0.613161\pi$
$398$		0			0
$399$	−31.4045	+	22.8167i	−0.0787081	+	0.0571848i
$400$		0			0
$401$	49.6512	+	152.811i	0.123818	+	0.381074i	0.993684	−	0.112215i	$-0.0357945\pi$
$401$	49.6512	+	152.811i	0.123818	+	0.381074i	−0.869866	+	0.493289i	$0.835795\pi$
$402$		0			0
$403$	163.387	−	224.883i	0.405426	−	0.558022i
$404$		0			0
$405$	−46.9366	+	144.456i	−0.115893	+	0.356682i
$406$		0			0
$407$	−247.283	−	685.677i	−0.607576	−	1.68471i
$408$		0			0
$409$	−459.977	−	149.456i	−1.12464	−	0.365417i	−0.313102	−	0.949719i	$-0.601368\pi$
$409$	−459.977	−	149.456i	−1.12464	−	0.365417i	−0.811536	+	0.584302i	$0.801368\pi$
$410$		0			0
$411$	−430.714	−	312.932i	−1.04797	−	0.761391i
$412$		0			0
$413$	115.149	−	37.4143i	0.278812	−	0.0905915i
$414$		0			0
$415$	211.468	+	291.061i	0.509562	+	0.701352i
$416$		0			0
$417$		−	179.817i		−	0.431217i
$418$		0			0
$419$	522.769			1.24766			0.623830	−	0.781560i	$-0.285576\pi$
$419$	522.769			1.24766			0.623830	+	0.781560i	$0.285576\pi$
$420$		0			0
$421$	−620.823	+	451.055i	−1.47464	+	1.07139i	−0.495404	+	0.868663i	$0.664980\pi$
$421$	−620.823	+	451.055i	−1.47464	+	1.07139i	−0.979236	+	0.202726i	$0.935020\pi$
$422$		0			0
$423$	106.084	+	326.494i	0.250790	+	0.771852i
$424$		0			0
$425$	−414.437	+	570.423i	−0.975145	+	1.34217i
$426$		0			0
$427$	29.0944	−	89.5432i	0.0681367	−	0.209703i
$428$		0			0
$429$	500.399	+	145.082i	1.16643	+	0.338187i
$430$		0			0
$431$	−176.320	−	57.2898i	−0.409095	−	0.132923i	0.0972380	−	0.995261i	$-0.468999\pi$
$431$	−176.320	−	57.2898i	−0.409095	−	0.132923i	−0.506333	+	0.862338i	$0.668999\pi$
$432$		0			0
$433$	−195.696	−	142.181i	−0.451953	−	0.328363i	0.338413	−	0.940998i	$-0.390110\pi$
$433$	−195.696	−	142.181i	−0.451953	−	0.328363i	−0.790366	+	0.612634i	$0.790110\pi$
$434$		0			0
$435$	867.861	−	281.985i	1.99508	−	0.648242i
$436$		0			0
$437$	−77.2131	−	106.275i	−0.176689	−	0.243192i
$438$		0			0
$439$		−	354.078i		−	0.806555i	−0.915078	−	0.403277i	$-0.867871\pi$
$439$		−	354.078i		−	0.806555i	0.915078	−	0.403277i	$-0.132129\pi$
$440$		0			0
$441$	32.0346			0.0726409
$442$		0			0
$443$	−52.9049	+	38.4377i	−0.119424	+	0.0867668i	−0.645894	−	0.763427i	$-0.723515\pi$
$443$	−52.9049	+	38.4377i	−0.119424	+	0.0867668i	0.526470	+	0.850194i	$0.323515\pi$
$444$		0			0
$445$	−259.382	−	798.295i	−0.582881	−	1.79392i
$446$		0			0
$447$	−183.605	+	252.710i	−0.410748	+	0.565347i
$448$		0			0
$449$	60.6803	−	186.755i	0.135145	−	0.415935i	−0.860467	−	0.509506i	$-0.829828\pi$
$449$	60.6803	−	186.755i	0.135145	−	0.415935i	0.995613	+	0.0935711i	$0.0298283\pi$
$450$		0			0
$451$	10.2070	+	319.220i	0.0226319	+	0.707806i
$452$		0			0
$453$	−91.0465	−	29.5828i	−0.200986	−	0.0653042i
$454$		0			0
$455$	−388.007	−	281.904i	−0.852763	−	0.619568i
$456$		0			0
$457$	8.31870	−	2.70291i	0.0182029	−	0.00591447i	−0.299901	−	0.953970i	$-0.596954\pi$
$457$	8.31870	−	2.70291i	0.0182029	−	0.00591447i	0.318104	+	0.948056i	$0.396954\pi$
$458$		0			0
$459$	−297.372	−	409.298i	−0.647869	−	0.891716i
$460$		0			0
$461$			466.045i			1.01094i	0.862843	+	0.505471i	$0.168681\pi$
$461$			466.045i			1.01094i	−0.862843	+	0.505471i	$0.831319\pi$
$462$		0			0
$463$	−390.176			−0.842713			−0.421357	−	0.906895i	$-0.638446\pi$
$463$	−390.176			−0.842713			−0.421357	+	0.906895i	$0.638446\pi$
$464$		0			0
$465$	169.066	−	122.833i	0.363582	−	0.264158i
$466$		0			0
$467$	−185.784	−	571.786i	−0.397825	−	1.22438i	−0.926739	−	0.375705i	$-0.877401\pi$
$467$	−185.784	−	571.786i	−0.397825	−	1.22438i	0.528914	−	0.848675i	$-0.322599\pi$
$468$		0			0
$469$	2.57673	−	3.54657i	0.00549410	−	0.00756198i
$470$		0			0
$471$	73.6480	−	226.665i	0.156365	−	0.481243i
$472$		0			0
$473$	−456.310	+	672.232i	−0.964715	+	1.42121i
$474$		0			0
$475$	−264.018	−	85.7847i	−0.555828	−	0.180599i
$476$		0			0
$477$	−133.784	−	97.1997i	−0.280469	−	0.203773i
$478$		0			0
$479$	370.588	−	120.411i	0.773670	−	0.251381i	0.104535	−	0.994521i	$-0.466665\pi$
$479$	370.588	−	120.411i	0.773670	−	0.251381i	0.669135	+	0.743140i	$0.266665\pi$
$480$		0			0
$481$	877.118	+	1207.25i	1.82353	+	2.50987i
$482$		0			0
$483$		−	104.789i		−	0.216954i
$484$		0			0
$485$	525.097			1.08267
$486$		0			0
$487$	102.119	−	74.1935i	0.209689	−	0.152348i	−0.477984	−	0.878369i	$-0.658632\pi$
$487$	102.119	−	74.1935i	0.209689	−	0.152348i	0.687673	+	0.726021i	$0.258632\pi$
$488$		0			0
$489$	146.354	+	450.433i	0.299293	+	0.921130i
$490$		0			0
$491$	−497.549	+	684.818i	−1.01334	+	1.39474i	−0.0965678	+	0.995326i	$0.530786\pi$
$491$	−497.549	+	684.818i	−1.01334	+	1.39474i	−0.916771	+	0.399414i	$0.869214\pi$
$492$		0			0
$493$	−295.103	+	908.235i	−0.598587	+	1.84226i
$494$		0			0
$495$	−335.271	−	227.581i	−0.677314	−	0.459760i
$496$		0			0
$497$	−224.587	−	72.9729i	−0.451886	−	0.146827i
$498$		0			0
$499$	442.583	+	321.555i	0.886939	+	0.644399i	0.935078	−	0.354442i	$-0.115329\pi$
$499$	442.583	+	321.555i	0.886939	+	0.644399i	−0.0481392	+	0.998841i	$0.515329\pi$
$500$		0			0
$501$	140.309	−	45.5891i	0.280057	−	0.0909961i
$502$		0			0
$503$	−56.3330	−	77.5358i	−0.111994	−	0.154147i	0.749340	−	0.662185i	$-0.230371\pi$
$503$	−56.3330	−	77.5358i	−0.111994	−	0.154147i	−0.861334	+	0.508038i	$0.830371\pi$
$504$		0			0
$505$			259.936i			0.514725i
$506$		0			0
$507$	−711.178			−1.40272
$508$		0			0
$509$	−100.645	+	73.1225i	−0.197730	+	0.143659i	−0.682245	−	0.731124i	$-0.738996\pi$
$509$	−100.645	+	73.1225i	−0.197730	+	0.143659i	0.484515	+	0.874783i	$0.338996\pi$
$510$		0			0
$511$	−60.4100	−	185.923i	−0.118219	−	0.363842i
$512$		0			0
$513$	117.081	−	161.149i	0.228229	−	0.314130i
$514$		0			0
$515$	−411.346	+	1265.99i	−0.798731	+	2.45824i
$516$		0			0
$517$	824.741	−	26.3709i	1.59524	−	0.0510075i
$518$		0			0
$519$	−153.642	−	49.9212i	−0.296034	−	0.0961872i
$520$		0			0
$521$	−19.7673	−	14.3618i	−0.0379411	−	0.0275658i	0.568653	−	0.822577i	$-0.307465\pi$
$521$	−19.7673	−	14.3618i	−0.0379411	−	0.0275658i	−0.606594	+	0.795012i	$0.707465\pi$
$522$		0			0
$523$	−303.422	+	98.5877i	−0.580156	+	0.188504i	−0.584371	−	0.811487i	$-0.698659\pi$
$523$	−303.422	+	98.5877i	−0.580156	+	0.188504i	0.00421436	+	0.999991i	$0.498659\pi$
$524$		0			0
$525$	−130.163	−	179.154i	−0.247930	−	0.341246i
$526$		0			0
$527$			218.698i			0.414987i
$528$		0			0
$529$	−174.389			−0.329659
$530$		0			0
$531$	−169.428	+	123.097i	−0.319074	+	0.231820i
$532$		0			0
$533$	−202.052	−	621.853i	−0.379085	−	1.16670i
$534$		0			0
$535$	−748.926	+	1030.81i	−1.39986	+	1.92674i
$536$		0			0
$537$	73.4705	−	226.119i	0.136817	−	0.421078i
$538$		0			0
$539$	21.4418	−	73.9544i	0.0397807	−	0.137207i
$540$		0			0
$541$	356.109	+	115.707i	0.658242	+	0.213876i	0.619045	−	0.785356i	$-0.287520\pi$
$541$	356.109	+	115.707i	0.658242	+	0.213876i	0.0391971	+	0.999231i	$0.487520\pi$
$542$		0			0
$543$	−396.431	−	288.024i	−0.730076	−	0.530431i
$544$		0			0
$545$	−132.344	+	43.0011i	−0.242832	+	0.0789011i
$546$		0			0
$547$	205.385	+	282.688i	0.375475	+	0.516797i	0.954379	−	0.298599i	$-0.0965194\pi$
$547$	205.385	+	282.688i	0.375475	+	0.516797i	−0.578904	+	0.815396i	$0.696519\pi$
$548$		0			0
$549$			162.854i			0.296638i
$550$		0			0
$551$	−375.993			−0.682383
$552$		0			0
$553$	133.080	−	96.6882i	0.240651	−	0.174843i
$554$		0			0
$555$	346.674	+	1066.95i	0.624637	+	1.92244i
$556$		0			0
$557$	221.732	−	305.188i	0.398083	−	0.547914i	−0.562179	−	0.827016i	$-0.690037\pi$
$557$	221.732	−	305.188i	0.398083	−	0.547914i	0.960261	+	0.279102i	$0.0900367\pi$
$558$		0			0
$559$	513.998	−	1581.92i	0.919495	−	2.82991i
$560$		0			0
$561$	−385.602	+	139.064i	−0.687347	+	0.247886i
$562$		0			0
$563$	786.086	+	255.415i	1.39624	+	0.453667i	0.907975	−	0.419025i	$-0.137628\pi$
$563$	786.086	+	255.415i	1.39624	+	0.453667i	0.488270	+	0.872693i	$0.337628\pi$
$564$		0			0
$565$	−372.815	−	270.866i	−0.659849	−	0.479408i
$566$		0			0
$567$	47.4803	−	15.4273i	0.0837395	−	0.0272086i
$568$		0			0
$569$	−212.190	−	292.055i	−0.372918	−	0.513277i	0.580773	−	0.814065i	$-0.302750\pi$
$569$	−212.190	−	292.055i	−0.372918	−	0.513277i	−0.953691	+	0.300788i	$0.902750\pi$
$570$		0			0
$571$		−	40.0874i		−	0.0702055i	−0.999384	−	0.0351028i	$-0.988824\pi$
$571$		−	40.0874i		−	0.0702055i	0.999384	−	0.0351028i	$-0.0111759\pi$
$572$		0			0
$573$	380.727			0.664445
$574$		0			0
$575$	606.268	−	440.479i	1.05438	−	0.766051i
$576$		0			0
$577$	−232.268	−	714.847i	−0.402544	−	1.23890i	−0.922929	−	0.384971i	$-0.874211\pi$
$577$	−232.268	−	714.847i	−0.402544	−	1.23890i	0.520385	−	0.853932i	$-0.325789\pi$
$578$		0			0
$579$	12.7469	−	17.5446i	0.0220154	−	0.0303016i
$580$		0			0
$581$	36.5415	−	112.463i	0.0628941	−	0.193568i
$582$		0			0
$583$	−313.939	+	243.791i	−0.538488	+	0.418167i
$584$		0			0
$585$	788.971	+	256.352i	1.34867	+	0.438209i
$586$		0			0
$587$	−141.010	−	102.450i	−0.240222	−	0.174531i	0.461160	−	0.887317i	$-0.347433\pi$
$587$	−141.010	−	102.450i	−0.240222	−	0.174531i	−0.701382	+	0.712786i	$0.747433\pi$
$588$		0			0
$589$	−81.8917	+	26.6082i	−0.139035	+	0.0451753i
$590$		0			0
$591$	−309.376	−	425.820i	−0.523479	−	0.720507i
$592$		0			0
$593$		−	468.822i		−	0.790594i	−0.918553	−	0.395297i	$-0.870642\pi$
$593$		−	468.822i		−	0.790594i	0.918553	−	0.395297i	$-0.129358\pi$
$594$		0			0
$595$	377.337			0.634179
$596$		0			0
$597$	−85.6302	+	62.2140i	−0.143434	+	0.104211i
$598$		0			0
$599$	−16.5097	−	50.8115i	−0.0275620	−	0.0848272i	0.936329	−	0.351123i	$-0.114200\pi$
$599$	−16.5097	−	50.8115i	−0.0275620	−	0.0848272i	−0.963891	+	0.266296i	$0.914200\pi$
$600$		0			0
$601$	167.119	−	230.020i	0.278069	−	0.382729i	−0.647024	−	0.762469i	$-0.723987\pi$
$601$	167.119	−	230.020i	0.278069	−	0.382729i	0.925093	+	0.379741i	$0.123987\pi$
$602$		0			0
$603$	−2.34318	+	7.21157i	−0.00388587	+	0.0119595i
$604$		0			0
$605$	−749.795	+	621.670i	−1.23933	+	1.02755i
$606$		0			0
$607$	178.409	+	57.9684i	0.293918	+	0.0954999i	0.452265	−	0.891884i	$-0.350616\pi$
$607$	178.409	+	57.9684i	0.293918	+	0.0954999i	−0.158346	+	0.987384i	$0.550616\pi$
$608$		0			0
$609$	−242.649	−	176.295i	−0.398439	−	0.289483i
$610$		0			0
$611$	−1606.62	+	522.024i	−2.62950	+	0.854376i
$612$		0			0
$613$	−350.372	−	482.246i	−0.571570	−	0.786698i	0.421170	−	0.906982i	$-0.361620\pi$
$613$	−350.372	−	482.246i	−0.571570	−	0.786698i	−0.992740	+	0.120284i	$0.961620\pi$
$614$		0			0
$615$		−	491.564i		−	0.799292i
$616$		0			0
$617$	−552.882			−0.896080			−0.448040	−	0.894013i	$-0.647878\pi$
$617$	−552.882			−0.896080			−0.448040	+	0.894013i	$0.647878\pi$
$618$		0			0
$619$	−476.033	+	345.858i	−0.769036	+	0.558737i	−0.901668	−	0.432428i	$-0.857657\pi$
$619$	−476.033	+	345.858i	−0.769036	+	0.558737i	0.132633	+	0.991165i	$0.457657\pi$
$620$		0			0
$621$	166.162	+	511.393i	0.267571	+	0.823500i
$622$		0			0
$623$	−162.164	+	223.199i	−0.260295	+	0.358265i
$624$		0			0
$625$	−11.1926	+	34.4474i	−0.0179082	+	0.0551159i
$626$		0			0
$627$	−98.9873	−	127.469i	−0.157875	−	0.203300i
$628$		0			0
$629$	−1116.59	−	362.801i	−1.77518	−	0.576791i
$630$		0			0
$631$	439.122	+	319.041i	0.695915	+	0.505612i	0.878599	−	0.477560i	$-0.158479\pi$
$631$	439.122	+	319.041i	0.695915	+	0.505612i	−0.182684	+	0.983172i	$0.558479\pi$
$632$		0			0
$633$	51.6280	−	16.7749i	0.0815608	−	0.0265007i
$634$		0			0
$635$	780.230	+	1073.89i	1.22871	+	1.69117i
$636$		0			0
$637$			157.637i			0.247469i
$638$		0			0
$639$	408.462			0.639221
$640$		0			0
$641$	−182.561	+	132.638i	−0.284806	+	0.206924i	−0.721011	−	0.692923i	$-0.756322\pi$
$641$	−182.561	+	132.638i	−0.284806	+	0.206924i	0.436205	+	0.899847i	$0.356322\pi$
$642$		0			0
$643$	−78.2811	−	240.925i	−0.121744	−	0.374688i	0.871550	−	0.490306i	$-0.163115\pi$
$643$	−78.2811	−	240.925i	−0.121744	−	0.374688i	−0.993294	+	0.115618i	$0.963115\pi$
$644$		0			0
$645$	735.016	−	1011.66i	1.13956	−	1.56847i
$646$		0			0
$647$	−378.104	+	1163.68i	−0.584396	+	1.79859i	0.0172873	+	0.999851i	$0.494497\pi$
$647$	−378.104	+	1163.68i	−0.584396	+	1.79859i	−0.601683	+	0.798735i	$0.705503\pi$
$648$		0			0
$649$	170.774	+	473.530i	0.263135	+	0.729630i
$650$		0			0
$651$	−65.3253	−	21.2255i	−0.100346	−	0.0326044i
$652$		0			0
$653$	266.281	+	193.465i	0.407781	+	0.296270i	0.772703	−	0.634768i	$-0.218904\pi$
$653$	266.281	+	193.465i	0.407781	+	0.296270i	−0.364922	+	0.931038i	$0.618904\pi$
$654$		0			0
$655$	39.1187	−	12.7104i	0.0597231	−	0.0194052i
$656$		0			0
$657$	198.755	+	273.563i	0.302519	+	0.416382i
$658$		0			0
$659$			147.555i			0.223908i	0.993713	+	0.111954i	$0.0357109\pi$
$659$			147.555i			0.223908i	−0.993713	+	0.111954i	$0.964289\pi$
$660$		0			0
$661$	287.638			0.435155			0.217578	−	0.976043i	$-0.430184\pi$
$661$	287.638			0.435155			0.217578	+	0.976043i	$0.430184\pi$
$662$		0			0
$663$	678.917	−	493.262i	1.02401	−	0.743985i
$664$		0			0
$665$	45.9092	+	141.294i	0.0690364	+	0.212472i
$666$		0			0
$667$	596.592	−	821.139i	0.894442	−	1.23109i
$668$		0			0
$669$	219.132	−	674.419i	0.327552	−	1.00810i
$670$		0			0
$671$	375.961	+	109.004i	0.560300	+	0.162449i
$672$		0			0
$673$	−617.790	−	200.732i	−0.917965	−	0.298265i	−0.188333	−	0.982105i	$-0.560309\pi$
$673$	−617.790	−	200.732i	−0.917965	−	0.298265i	−0.729632	+	0.683840i	$0.760309\pi$
$674$		0			0
$675$	919.309	+	667.917i	1.36194	+	0.989507i
$676$		0			0
$677$	−293.565	+	95.3852i	−0.433627	+	0.140894i	−0.517693	−	0.855566i	$-0.673209\pi$
$677$	−293.565	+	95.3852i	−0.433627	+	0.140894i	0.0840664	+	0.996460i	$0.473209\pi$
$678$		0			0
$679$	−101.446	−	139.629i	−0.149405	−	0.205639i
$680$		0			0
$681$			485.354i			0.712708i
$682$		0			0
$683$	63.4213			0.0928569			0.0464284	−	0.998922i	$-0.485216\pi$
$683$	63.4213			0.0928569			0.0464284	+	0.998922i	$0.485216\pi$
$684$		0			0
$685$	−1648.43	+	1197.66i	−2.40647	+	1.74840i
$686$		0			0
$687$	74.6094	+	229.624i	0.108602	+	0.334242i
$688$		0			0
$689$	478.305	−	658.330i	0.694201	−	0.955486i
$690$		0			0
$691$	−16.1358	+	49.6610i	−0.0233514	+	0.0718683i	−0.962053	−	0.272862i	$-0.912030\pi$
$691$	−16.1358	+	49.6610i	−0.0233514	+	0.0718683i	0.938702	+	0.344731i	$0.112030\pi$
$692$		0			0
$693$	4.25647	+	133.119i	0.00614209	+	0.192092i
$694$		0			0
$695$	−654.516	−	212.665i	−0.941750	−	0.305993i
$696$		0			0
$697$	416.185	+	302.376i	0.597108	+	0.433825i
$698$		0			0
$699$	343.745	−	111.689i	0.491766	−	0.159785i
$700$		0			0
$701$	−271.762	−	374.048i	−0.387677	−	0.533592i	0.569921	−	0.821700i	$-0.306974\pi$
$701$	−271.762	−	374.048i	−0.387677	−	0.533592i	−0.957598	+	0.288108i	$0.906974\pi$
$702$		0			0
$703$		−	462.248i		−	0.657536i
$704$		0			0
$705$	−1270.01			−1.80143
$706$		0			0
$707$	69.1196	−	50.2183i	0.0977647	−	0.0710302i
$708$		0			0
$709$	129.657	+	399.042i	0.182872	+	0.562823i	0.999905	−	0.0137677i	$-0.00438254\pi$
$709$	129.657	+	399.042i	0.182872	+	0.562823i	−0.817033	+	0.576591i	$0.804383\pi$
$710$		0			0
$711$	−167.242	+	230.189i	−0.235221	+	0.323754i
$712$		0			0
$713$	71.8282	−	221.065i	0.100741	−	0.310048i
$714$		0			0
$715$	1119.89	−	1649.81i	1.56628	−	2.30743i
$716$		0			0
$717$	585.009	+	190.081i	0.815912	+	0.265106i
$718$		0			0
$719$	384.679	+	279.486i	0.535019	+	0.388714i	0.822232	−	0.569152i	$-0.192729\pi$
$719$	384.679	+	279.486i	0.535019	+	0.388714i	−0.287213	+	0.957867i	$0.592729\pi$
$720$		0			0
$721$	416.111	−	135.203i	0.577130	−	0.187521i
$722$		0			0
$723$	−381.766	−	525.456i	−0.528030	−	0.726771i
$724$		0			0
$725$		−	2144.94i		−	2.95853i
$726$		0			0
$727$	−649.309			−0.893135			−0.446567	−	0.894750i	$-0.647354\pi$
$727$	−649.309			−0.893135			−0.446567	+	0.894750i	$0.647354\pi$
$728$		0			0
$729$	−507.144	+	368.462i	−0.695671	+	0.505434i
$730$		0			0
$731$	404.397	+	1244.61i	0.553211	+	1.70261i
$732$		0			0
$733$	477.862	−	657.720i	0.651926	−	0.897299i	−0.347255	−	0.937771i	$-0.612886\pi$
$733$	477.862	−	657.720i	0.651926	−	0.897299i	0.999181	+	0.0404716i	$0.0128860\pi$
$734$		0			0
$735$	−36.6219	+	112.711i	−0.0498257	+	0.153348i
$736$		0			0
$737$	15.0801	+	10.2363i	0.0204615	+	0.0138892i
$738$		0			0
$739$	−291.484	−	94.7090i	−0.394431	−	0.128158i	0.105085	−	0.994463i	$-0.466489\pi$
$739$	−291.484	−	94.7090i	−0.394431	−	0.128158i	−0.499515	+	0.866305i	$0.666489\pi$
$740$		0			0
$741$	267.304	+	194.207i	0.360734	+	0.262088i
$742$		0			0
$743$	762.673	−	247.807i	1.02648	−	0.333523i	0.253081	−	0.967445i	$-0.418556\pi$
$743$	762.673	−	247.807i	1.02648	−	0.333523i	0.773397	+	0.633922i	$0.218556\pi$
$744$		0			0
$745$	702.693	+	967.175i	0.943213	+	1.29822i
$746$		0			0
$747$			204.539i			0.273814i
$748$		0			0
$749$	418.791			0.559134
$750$		0			0
$751$	−355.429	+	258.235i	−0.473275	+	0.343854i	−0.798716	−	0.601708i	$-0.794487\pi$
$751$	−355.429	+	258.235i	−0.473275	+	0.343854i	0.325441	+	0.945562i	$0.394487\pi$
$752$		0			0
$753$	136.898	+	421.328i	0.181803	+	0.559532i
$754$		0			0
$755$	−215.357	+	296.413i	−0.285240	+	0.392600i
$756$		0			0
$757$	−64.4611	+	198.391i	−0.0851533	+	0.262075i	−0.984563	−	0.175032i	$-0.943997\pi$
$757$	−64.4611	+	198.391i	−0.0851533	+	0.262075i	0.899409	+	0.437107i	$0.143997\pi$
$758$		0			0
$759$	435.447	−	13.9233i	0.573712	−	0.0183443i
$760$		0			0
$761$	559.385	+	181.755i	0.735066	+	0.238837i	0.652543	−	0.757752i	$-0.273702\pi$
$761$	559.385	+	181.755i	0.735066	+	0.238837i	0.0825230	+	0.996589i	$0.473702\pi$
$762$		0			0
$763$	37.0026	+	26.8840i	0.0484962	+	0.0352345i
$764$		0			0
$765$	−620.738	+	201.690i	−0.811422	+	0.263647i
$766$		0			0
$767$	−605.740	−	833.729i	−0.789752	−	1.08700i
$768$		0			0
$769$		−	316.121i		−	0.411080i	−0.978649	−	0.205540i	$-0.934105\pi$
$769$		−	316.121i		−	0.411080i	0.978649	−	0.205540i	$-0.0658951\pi$
$770$		0			0
$771$	−102.978			−0.133564
$772$		0			0
$773$	−585.310	+	425.252i	−0.757192	+	0.550132i	−0.898048	−	0.439898i	$-0.855015\pi$
$773$	−585.310	+	425.252i	−0.757192	+	0.550132i	0.140856	+	0.990030i	$0.455015\pi$
$774$		0			0
$775$	−151.793	−	467.169i	−0.195861	−	0.602799i
$776$		0			0
$777$	216.738	−	298.314i	0.278942	−	0.383931i
$778$		0			0
$779$	−62.5891	+	192.629i	−0.0803454	+	0.247278i
$780$		0			0
$781$	273.397	−	942.966i	0.350060	−	1.20738i
$782$		0			0
$783$	1463.74	+	475.596i	1.86939	+	0.607403i
$784$		0			0
$785$	−737.936	−	536.142i	−0.940046	−	0.682983i
$786$		0			0
$787$	430.464	−	139.866i	0.546968	−	0.177721i	−0.0224810	−	0.999747i	$-0.507157\pi$
$787$	430.464	−	139.866i	0.546968	−	0.177721i	0.569449	+	0.822027i	$0.307157\pi$
$788$		0			0
$789$	6.83132	+	9.40251i	0.00865820	+	0.0119170i
$790$		0			0
$791$			151.465i			0.191486i
$792$		0			0
$793$	−801.381			−1.01057
$794$		0			0
$795$	494.929	−	359.587i	0.622552	−	0.452310i
$796$		0			0
$797$	−265.127	−	815.977i	−0.332656	−	1.02381i	−0.967865	−	0.251470i	$-0.919086\pi$
$797$	−265.127	−	815.977i	−0.332656	−	1.02381i	0.635209	−	0.772341i	$-0.280914\pi$
$798$		0			0
$799$	781.221	−	1075.26i	0.977748	−	1.34576i
$800$		0			0
$801$	147.465	−	453.852i	0.184101	−	0.566606i
$802$		0			0
$803$	764.574	−	275.737i	0.952147	−	0.343383i
$804$		0			0
$805$	−381.419	−	123.931i	−0.473813	−	0.153951i
$806$		0			0
$807$	461.095	+	335.005i	0.571369	+	0.415124i
$808$		0			0
$809$	1219.82	−	396.345i	1.50782	−	0.489919i	0.565530	−	0.824728i	$-0.308672\pi$
$809$	1219.82	−	396.345i	1.50782	−	0.489919i	0.942286	+	0.334808i	$0.108672\pi$
$810$		0			0
$811$	−743.938	−	1023.94i	−0.917309	−	1.26257i	−0.964608	−	0.263687i	$-0.915061\pi$
$811$	−743.938	−	1023.94i	−0.917309	−	1.26257i	0.0472988	−	0.998881i	$-0.484939\pi$
$812$		0			0
$813$			377.430i			0.464244i
$814$		0			0
$815$	1812.62			2.22407
$816$		0			0
$817$	−416.842	+	302.853i	−0.510211	+	0.370690i
$818$		0			0
$819$	−84.2586	−	259.321i	−0.102880	−	0.316632i
$820$		0			0
$821$	258.495	−	355.788i	0.314854	−	0.433360i	−0.622033	−	0.782991i	$-0.713693\pi$
$821$	258.495	−	355.788i	0.314854	−	0.433360i	0.936887	+	0.349631i	$0.113693\pi$
$822$		0			0
$823$	102.543	−	315.594i	0.124596	−	0.383468i	−0.869231	−	0.494406i	$-0.835386\pi$
$823$	102.543	−	315.594i	0.124596	−	0.383468i	0.993827	+	0.110938i	$0.0353855\pi$
$824$		0			0
$825$	727.178	−	564.695i	0.881427	−	0.684479i
$826$		0			0
$827$	−91.5199	−	29.7366i	−0.110665	−	0.0359572i	0.253161	−	0.967424i	$-0.418530\pi$
$827$	−91.5199	−	29.7366i	−0.110665	−	0.0359572i	−0.363826	+	0.931467i	$0.618530\pi$
$828$		0			0
$829$	−76.0652	−	55.2646i	−0.0917554	−	0.0666642i	0.540962	−	0.841047i	$-0.318060\pi$
$829$	−76.0652	−	55.2646i	−0.0917554	−	0.0666642i	−0.632717	+	0.774383i	$0.718060\pi$
$830$		0			0
$831$	−463.849	+	150.714i	−0.558182	+	0.181364i
$832$		0			0
$833$	−72.8996	−	100.338i	−0.0875146	−	0.120453i
$834$		0			0
$835$		−	564.626i		−	0.676199i
$836$		0			0
$837$	352.460			0.421099
$838$		0			0
$839$	1105.97	−	803.538i	1.31821	−	0.957733i	0.318253	−	0.948006i	$-0.396904\pi$
$839$	1105.97	−	803.538i	1.31821	−	0.957733i	0.999953	−	0.00972719i	$-0.00309631\pi$
$840$		0			0
$841$	−637.853	−	1963.11i	−0.758446	−	2.33426i
$842$		0			0
$843$	−546.757	+	752.546i	−0.648584	+	0.892700i
$844$		0			0
$845$	−841.091	+	2588.61i	−0.995374	+	3.06344i
$846$		0			0
$847$	310.165	+	79.2747i	0.366193	+	0.0935947i
$848$		0			0
$849$	−177.650	−	57.7221i	−0.209246	−	0.0679883i
$850$		0			0
$851$	1009.51	+	733.453i	1.18627	+	0.861872i
$852$		0			0
$853$	−1325.25	+	430.601i	−1.55364	+	0.504808i	−0.955099	−	0.296286i	$-0.904252\pi$
$853$	−1325.25	+	430.601i	−1.55364	+	0.504808i	−0.598539	+	0.801093i	$0.704252\pi$
$854$		0			0
$855$	−151.046	−	207.897i	−0.176662	−	0.243154i
$856$		0			0
$857$			1567.73i			1.82932i	0.404225	+	0.914660i	$0.367541\pi$
$857$			1567.73i			1.82932i	−0.404225	+	0.914660i	$0.632459\pi$
$858$		0			0
$859$	660.787			0.769252			0.384626	−	0.923073i	$-0.374330\pi$
$859$	660.787			0.769252			0.384626	+	0.923073i	$0.374330\pi$
$860$		0			0
$861$	−130.712	+	94.9678i	−0.151814	+	0.110299i
$862$		0			0
$863$	14.4916	+	44.6005i	0.0167921	+	0.0516808i	0.959101	−	0.283063i	$-0.0913504\pi$
$863$	14.4916	+	44.6005i	0.0167921	+	0.0516808i	−0.942309	+	0.334743i	$0.891350\pi$
$864$		0			0
$865$	−363.416	+	500.199i	−0.420134	+	0.578264i
$866$		0			0
$867$	−16.1956	+	49.8448i	−0.0186800	+	0.0574911i
$868$		0			0
$869$	419.469	+	540.164i	0.482703	+	0.621593i
$870$		0			0
$871$	−35.4870	−	11.5304i	−0.0407429	−	0.0132382i
$872$		0			0
$873$	241.517	+	175.472i	0.276652	+	0.200999i
$874$		0			0
$875$	−299.674	+	97.3699i	−0.342484	+	0.111280i
$876$		0			0
$877$	−259.182	−	356.734i	−0.295533	−	0.406766i	0.635269	−	0.772291i	$-0.280889\pi$
$877$	−259.182	−	356.734i	−0.295533	−	0.406766i	−0.930801	+	0.365525i	$0.880889\pi$
$878$		0			0
$879$			185.853i			0.211437i
$880$		0			0
$881$	371.292			0.421443			0.210722	−	0.977546i	$-0.432419\pi$
$881$	371.292			0.421443			0.210722	+	0.977546i	$0.432419\pi$
$882$		0			0
$883$	64.6888	−	46.9992i	0.0732602	−	0.0532267i	−0.550552	−	0.834801i	$-0.685583\pi$
$883$	64.6888	−	46.9992i	0.0732602	−	0.0532267i	0.623813	+	0.781574i	$0.285583\pi$
$884$		0			0
$885$	−239.414	−	736.840i	−0.270524	−	0.832587i
$886$		0			0
$887$	864.235	−	1189.52i	0.974335	−	1.34106i	0.0345080	−	0.999404i	$-0.489014\pi$
$887$	864.235	−	1189.52i	0.974335	−	1.34106i	0.939827	−	0.341652i	$-0.110986\pi$
$888$		0			0
$889$	134.823	−	414.942i	0.151657	−	0.466752i
$890$		0			0
$891$	70.4166	+	195.254i	0.0790310	+	0.219140i
$892$		0			0
$893$	497.679	+	161.706i	0.557312	+	0.181081i
$894$		0			0
$895$	−736.158	−	534.850i	−0.822522	−	0.597598i
$896$		0			0
$897$	−848.267	+	275.619i	−0.945671	+	0.307267i
$898$		0			0
$899$	−391.056	−	538.242i	−0.434990	−	0.598712i
$900$		0			0
$901$			640.226i			0.710572i
$902$		0			0
$903$	−411.013			−0.455164
$904$		0			0
$905$	−1517.23	+	1102.33i	−1.67649	+	1.21804i
$906$		0			0
$907$	331.732	+	1020.96i	0.365746	+	1.12565i	0.949513	+	0.313729i	$0.101578\pi$
$907$	331.732	+	1020.96i	0.365746	+	1.12565i	−0.583767	+	0.811921i	$0.698422\pi$
$908$		0			0
$909$	−86.8631	+	119.557i	−0.0955589	+	0.131526i
$910$		0			0
$911$	−83.6952	+	257.587i	−0.0918718	+	0.282752i	−0.986426	−	0.164208i	$-0.947493\pi$
$911$	−83.6952	+	257.587i	−0.0918718	+	0.282752i	0.894554	+	0.446960i	$0.147493\pi$
$912$		0			0
$913$	472.194	+	136.905i	0.517190	+	0.149950i
$914$		0			0
$915$	−572.986	−	186.175i	−0.626215	−	0.203469i
$916$		0			0
$917$	−10.9374	−	7.94646i	−0.0119273	−	0.00866572i
$918$		0			0
$919$	1418.35	−	460.850i	1.54336	−	0.501469i	0.591062	−	0.806626i	$-0.298709\pi$
$919$	1418.35	−	460.850i	1.54336	−	0.501469i	0.952302	+	0.305157i	$0.0987089\pi$
$920$		0			0
$921$	110.186	+	151.658i	0.119638	+	0.164667i
$922$		0			0
$923$			2009.98i			2.17766i
$924$		0			0
$925$	2636.99			2.85080
$926$		0			0
$927$	−612.256	+	444.830i	−0.660470	+	0.479860i
$928$		0			0
$929$	−3.03418	−	9.33826i	−0.00326607	−	0.0100519i	0.949410	−	0.314039i	$-0.101682\pi$
$929$	−3.03418	−	9.33826i	−0.00326607	−	0.0100519i	−0.952676	+	0.303987i	$0.901682\pi$
$930$		0			0
$931$	28.7021	−	39.5050i	0.0308293	−	0.0424329i
$932$		0			0
$933$	−75.1858	+	231.398i	−0.0805849	+	0.248015i
$934$		0			0
$935$	50.1370	+	1568.02i	0.0536225	+	1.67702i
$936$		0			0
$937$	−160.094	−	52.0178i	−0.170858	−	0.0555152i	0.222339	−	0.974969i	$-0.428631\pi$
$937$	−160.094	−	52.0178i	−0.170858	−	0.0555152i	−0.393197	+	0.919454i	$0.628631\pi$
$938$		0			0
$939$	−1006.03	−	730.925i	−1.07139	−	0.778408i
$940$		0			0
$941$	−505.138	+	164.129i	−0.536809	+	0.174420i	−0.564860	−	0.825187i	$-0.691070\pi$
$941$	−505.138	+	164.129i	−0.536809	+	0.174420i	0.0280509	+	0.999606i	$0.491070\pi$
$942$		0			0
$943$	−321.377	−	442.337i	−0.340802	−	0.469074i
$944$		0			0
$945$		−	608.126i		−	0.643519i
$946$		0			0
$947$	247.383			0.261228			0.130614	−	0.991433i	$-0.458305\pi$
$947$	247.383			0.261228			0.130614	+	0.991433i	$0.458305\pi$
$948$		0			0
$949$	−1346.16	+	978.043i	−1.41850	+	1.03060i
$950$		0			0
$951$	248.591	+	765.085i	0.261400	+	0.804506i
$952$		0			0
$953$	−183.086	+	251.996i	−0.192115	+	0.264424i	−0.894198	−	0.447671i	$-0.852254\pi$
$953$	−183.086	+	251.996i	−0.192115	+	0.264424i	0.702083	+	0.712095i	$0.252254\pi$
$954$		0			0
$955$	450.276	−	1385.81i	0.471493	−	1.45111i
$956$		0			0
$957$	700.350	−	1031.75i	0.731819	−	1.07811i
$958$		0			0
$959$	636.938	+	206.954i	0.664169	+	0.215802i
$960$		0			0
$961$	654.203	+	475.306i	0.680752	+	0.494595i
$962$		0			0
$963$	−688.932	+	223.848i	−0.715402	+	0.232448i
$964$		0			0
$965$	−48.7851	−	67.1470i	−0.0505545	−	0.0695823i
$966$		0			0
$967$		−	833.673i		−	0.862123i	−0.902323	−	0.431061i	$-0.858139\pi$
$967$		−	833.673i		−	0.862123i	0.902323	−	0.431061i	$-0.141861\pi$
$968$		0			0
$969$	−259.953			−0.268269
$970$		0			0
$971$	946.506	−	687.677i	0.974774	−	0.708215i	0.0182395	−	0.999834i	$-0.494194\pi$
$971$	946.506	−	687.677i	0.974774	−	0.708215i	0.956535	+	0.291619i	$0.0941939\pi$
$972$		0			0
$973$	69.8995	+	215.128i	0.0718391	+	0.221098i
$974$		0			0
$975$	−1107.90	+	1524.89i	−1.13631	+	1.56399i
$976$		0			0
$977$	359.280	−	1105.75i	0.367738	−	1.13178i	−0.580511	−	0.814252i	$-0.697147\pi$
$977$	359.280	−	1105.75i	0.367738	−	1.13178i	0.948249	−	0.317528i	$-0.102853\pi$
$978$		0			0
$979$	−949.047	−	644.212i	−0.969405	−	0.658031i
$980$		0			0
$981$	−75.2408	−	24.4472i	−0.0766981	−	0.0249207i
$982$		0			0
$983$	−1322.31	−	960.712i	−1.34517	−	0.977326i	−0.999237	−	0.0390688i	$-0.987561\pi$
$983$	−1322.31	−	960.712i	−1.34517	−	0.977326i	−0.345938	−	0.938257i	$-0.612439\pi$
$984$		0			0
$985$	−1915.83	+	622.490i	−1.94500	+	0.631970i
$986$		0			0
$987$	245.360	+	337.709i	0.248591	+	0.342157i
$988$		0			0
$989$		−	1390.89i		−	1.40636i
$990$		0			0
$991$	−1210.89			−1.22188			−0.610941	−	0.791676i	$-0.709209\pi$
$991$	−1210.89			−1.22188			−0.610941	+	0.791676i	$0.709209\pi$
$992$		0			0
$993$	−103.558	+	75.2395i	−0.104288	+	0.0757699i
$994$		0			0
$995$	125.180	+	385.264i	0.125809	+	0.387200i
$996$		0			0
$997$	279.584	−	384.815i	0.280425	−	0.385973i	−0.645449	−	0.763803i	$-0.723330\pi$
$997$	279.584	−	384.815i	0.280425	−	0.385973i	0.925875	+	0.377831i	$0.123330\pi$
$998$		0			0
$999$	−584.700	+	1799.52i	−0.585286	+	1.80132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.4	✓	48
11.6	odd	10	inner	308.3.r.a.281.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.4	✓	48	1.1	even	1	trivial
308.3.r.a.281.4	yes	48	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70156 + 1.23625i) q^{3} +(2.48745 + 7.65558i) q^{5} +(1.55513 - 2.14046i) q^{7} +(-1.41418 + 4.35239i) q^{9} +O(q^{10})\)	\(q+(-1.70156 + 1.23625i) q^{3} +(2.48745 + 7.65558i) q^{5} +(1.55513 - 2.14046i) q^{7} +(-1.41418 + 4.35239i) q^{9} +(9.10127 + 6.17793i) q^{11} +(-21.4174 - 6.95895i) q^{13} +(-13.6968 - 9.95129i) q^{15} +(16.8506 - 5.47509i) q^{17} +(4.10030 + 5.64357i) q^{19} +5.56465i q^{21} -18.8311 q^{23} +(-32.1950 + 23.3911i) q^{25} +(-8.82379 - 27.1568i) q^{27} +(-31.6812 + 43.6055i) q^{29} +(-3.81434 + 11.7393i) q^{31} +(-23.1238 + 0.739380i) q^{33} +(20.2547 + 6.58117i) q^{35} +(-53.6087 - 38.9490i) q^{37} +(45.0461 - 14.6364i) q^{39} +(17.0663 + 23.4897i) q^{41} +73.8614i q^{43} -36.8378 q^{45} +(60.6882 - 44.0926i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-21.9036 + 30.1478i) q^{51} +(-11.1662 + 34.3661i) q^{53} +(-24.6567 + 85.0428i) q^{55} +(-13.9538 - 4.53386i) q^{57} +(37.0223 + 26.8983i) q^{59} +(33.8442 - 10.9966i) q^{61} +(7.11688 + 9.79554i) q^{63} -181.273i q^{65} +1.65692 q^{67} +(32.0422 - 23.2800i) q^{69} +(-27.5812 - 84.8861i) q^{71} +(43.4307 - 59.7772i) q^{73} +(25.8644 - 79.6025i) q^{75} +(27.3773 - 9.87338i) q^{77} +(59.1306 + 19.2127i) q^{79} +(15.2657 + 11.0912i) q^{81} +(42.5071 - 13.8114i) q^{83} +(83.8299 + 115.382i) q^{85} -113.363i q^{87} -104.276 q^{89} +(-48.2023 + 35.0210i) q^{91} +(-8.02248 - 24.6906i) q^{93} +(-33.0055 + 45.4282i) q^{95} +(20.1581 - 62.0404i) q^{97} +(-39.7596 + 30.8756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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