LMFDB - Embedded newform 76.4.e.a.45.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(45,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("76.45");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 90 x^{8} - 212 x^{7} + 7012 x^{6} - 14448 x^{5} + 100896 x^{4} - 25920 x^{3} + \cdots + 1016064 $ x^10 - 2x^9 + 90x^8 - 212x^7 + 7012x^6 - 14448x^5 + 100896x^4 - 25920x^3 + 783360x^2 - 774144*x + 1016064
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.2
Root			$-1.41615 + 2.45284i$ of defining polynomial
Character	$\chi$	$=$	76.45
Dual form			76.4.e.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.916150 - 1.58682i) q^{3} +(2.48769 + 4.30880i) q^{5} +19.2102 q^{7} +(11.8213 - 20.4752i) q^{9} +O(q^{10})$	\(q+(-0.916150 - 1.58682i) q^{3} +(2.48769 + 4.30880i) q^{5} +19.2102 q^{7} +(11.8213 - 20.4752i) q^{9} +27.9535 q^{11} +(18.9388 - 32.8029i) q^{13} +(4.55819 - 7.89502i) q^{15} +(-1.97434 - 3.41966i) q^{17} +(32.9626 + 75.9768i) q^{19} +(-17.5994 - 30.4831i) q^{21} +(-41.8650 + 72.5122i) q^{23} +(50.1228 - 86.8152i) q^{25} -92.7926 q^{27} +(-60.6390 + 105.030i) q^{29} -211.230 q^{31} +(-25.6096 - 44.3571i) q^{33} +(47.7891 + 82.7731i) q^{35} -82.7900 q^{37} -69.4030 q^{39} +(-119.752 - 207.416i) q^{41} +(74.2051 + 128.527i) q^{43} +117.631 q^{45} +(-119.041 + 206.185i) q^{47} +26.0326 q^{49} +(-3.61759 + 6.26584i) q^{51} +(0.969975 - 1.68005i) q^{53} +(69.5395 + 120.446i) q^{55} +(90.3627 - 121.912i) q^{57} +(129.859 + 224.922i) q^{59} +(365.410 - 632.909i) q^{61} +(227.091 - 393.332i) q^{63} +188.455 q^{65} +(116.463 - 201.720i) q^{67} +153.418 q^{69} +(483.781 + 837.933i) q^{71} +(-80.2051 - 138.919i) q^{73} -183.680 q^{75} +536.992 q^{77} +(-198.595 - 343.977i) q^{79} +(-234.164 - 405.584i) q^{81} -461.162 q^{83} +(9.82310 - 17.0141i) q^{85} +222.218 q^{87} +(-552.519 + 956.991i) q^{89} +(363.818 - 630.151i) q^{91} +(193.518 + 335.183i) q^{93} +(-245.368 + 331.036i) q^{95} +(-391.827 - 678.664i) q^{97} +(330.447 - 572.352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9}+O(q^{10}) $ 10 * q + 7 * q^3 - 4 * q^5 - 20 * q^7 - 50 * q^9	$ 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9} - 50 q^{11} - 56 q^{13} + 10 q^{15} + 32 q^{17} + 77 q^{19} + 126 q^{21} + 184 q^{23} - 121 q^{25} - 218 q^{27} + 352 q^{29} + 264 q^{31} + 83 q^{33} - 132 q^{35} - 640 q^{37} - 324 q^{39} - 57 q^{41} - 528 q^{43} - 232 q^{45} - 434 q^{47} + 2138 q^{49} - 242 q^{51} + 780 q^{53} + 598 q^{55} + 1482 q^{57} - 343 q^{59} + 536 q^{61} - 1568 q^{63} - 1988 q^{65} + 779 q^{67} - 1156 q^{69} + 474 q^{71} + 1453 q^{73} - 2994 q^{75} - 2956 q^{77} - 1968 q^{79} - 1097 q^{81} - 698 q^{83} - 2334 q^{85} + 8372 q^{87} + 380 q^{89} + 1348 q^{91} + 1684 q^{93} + 4312 q^{95} + 883 q^{97} + 5230 q^{99}+O(q^{100}) $ 10 * q + 7 * q^3 - 4 * q^5 - 20 * q^7 - 50 * q^9 - 50 * q^11 - 56 * q^13 + 10 * q^15 + 32 * q^17 + 77 * q^19 + 126 * q^21 + 184 * q^23 - 121 * q^25 - 218 * q^27 + 352 * q^29 + 264 * q^31 + 83 * q^33 - 132 * q^35 - 640 * q^37 - 324 * q^39 - 57 * q^41 - 528 * q^43 - 232 * q^45 - 434 * q^47 + 2138 * q^49 - 242 * q^51 + 780 * q^53 + 598 * q^55 + 1482 * q^57 - 343 * q^59 + 536 * q^61 - 1568 * q^63 - 1988 * q^65 + 779 * q^67 - 1156 * q^69 + 474 * q^71 + 1453 * q^73 - 2994 * q^75 - 2956 * q^77 - 1968 * q^79 - 1097 * q^81 - 698 * q^83 - 2334 * q^85 + 8372 * q^87 + 380 * q^89 + 1348 * q^91 + 1684 * q^93 + 4312 * q^95 + 883 * q^97 + 5230 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.916150	−	1.58682i	−0.176313	−	0.305383i	0.764302	−	0.644859i	$-0.223084\pi$
$3$	−0.916150	−	1.58682i	−0.176313	−	0.305383i	−0.940615	+	0.339475i	$0.889750\pi$
$4$		0			0
$5$	2.48769	+	4.30880i	0.222506	+	0.385391i	0.955568	−	0.294770i	$-0.0952431\pi$
$5$	2.48769	+	4.30880i	0.222506	+	0.385391i	−0.733062	+	0.680161i	$0.761910\pi$
$6$		0			0
$7$	19.2102			1.03725			0.518627	−	0.855000i	$-0.326443\pi$
$7$	19.2102			1.03725			0.518627	+	0.855000i	$0.326443\pi$
$8$		0			0
$9$	11.8213	−	20.4752i	0.437827	−	0.758339i
$10$		0			0
$11$	27.9535			0.766208			0.383104	−	0.923705i	$-0.374855\pi$
$11$	27.9535			0.766208			0.383104	+	0.923705i	$0.374855\pi$
$12$		0			0
$13$	18.9388	−	32.8029i	0.404051	−	0.699837i	−0.590159	−	0.807287i	$-0.700935\pi$
$13$	18.9388	−	32.8029i	0.404051	−	0.699837i	0.994211	+	0.107449i	$0.0342684\pi$
$14$		0			0
$15$	4.55819	−	7.89502i	0.0784613	−	0.135899i
$16$		0			0
$17$	−1.97434	−	3.41966i	−0.0281675	−	0.0487876i	0.851598	−	0.524195i	$-0.175634\pi$
$17$	−1.97434	−	3.41966i	−0.0281675	−	0.0487876i	−0.879766	+	0.475408i	$0.842301\pi$
$18$		0			0
$19$	32.9626	+	75.9768i	0.398007	+	0.917382i
$19$	32.9626	+	75.9768i	0.398007	+	0.917382i
$20$		0			0
$21$	−17.5994	−	30.4831i	−0.182882	−	0.316760i
$22$		0			0
$23$	−41.8650	+	72.5122i	−0.379541	+	0.657385i	−0.990996	−	0.133895i	$-0.957251\pi$
$23$	−41.8650	+	72.5122i	−0.379541	+	0.657385i	0.611454	+	0.791280i	$0.290585\pi$
$24$		0			0
$25$	50.1228	−	86.8152i	0.400982	−	0.694522i
$26$		0			0
$27$	−92.7926			−0.661405
$28$		0			0
$29$	−60.6390	+	105.030i	−0.388289	+	0.672536i	−0.992219	−	0.124501i	$-0.960267\pi$
$29$	−60.6390	+	105.030i	−0.388289	+	0.672536i	0.603931	+	0.797037i	$0.293600\pi$
$30$		0			0
$31$	−211.230			−1.22381			−0.611903	−	0.790933i	$-0.709596\pi$
$31$	−211.230			−1.22381			−0.611903	+	0.790933i	$0.709596\pi$
$32$		0			0
$33$	−25.6096	−	44.3571i	−0.135092	−	0.233987i
$34$		0			0
$35$	47.7891	+	82.7731i	0.230795	+	0.399749i
$36$		0			0
$37$	−82.7900			−0.367854			−0.183927	−	0.982940i	$-0.558881\pi$
$37$	−82.7900			−0.367854			−0.183927	+	0.982940i	$0.558881\pi$
$38$		0			0
$39$	−69.4030			−0.284958
$40$		0			0
$41$	−119.752	−	207.416i	−0.456149	−	0.790073i	0.542604	−	0.839988i	$-0.317438\pi$
$41$	−119.752	−	207.416i	−0.456149	−	0.790073i	−0.998753	+	0.0499150i	$0.984105\pi$
$42$		0			0
$43$	74.2051	+	128.527i	0.263167	+	0.455818i	0.967082	−	0.254466i	$-0.0818997\pi$
$43$	74.2051	+	128.527i	0.263167	+	0.455818i	−0.703915	+	0.710284i	$0.748566\pi$
$44$		0			0
$45$	117.631			0.389676
$46$		0			0
$47$	−119.041	+	206.185i	−0.369445	+	0.639898i	−0.989479	−	0.144677i	$-0.953786\pi$
$47$	−119.041	+	206.185i	−0.369445	+	0.639898i	0.620034	+	0.784575i	$0.287119\pi$
$48$		0			0
$49$	26.0326			0.0758969
$50$		0			0
$51$	−3.61759	+	6.26584i	−0.00993262	+	0.0172038i
$52$		0			0
$53$	0.969975	−	1.68005i	0.00251389	−	0.00435419i	−0.864766	−	0.502176i	$-0.832533\pi$
$53$	0.969975	−	1.68005i	0.00251389	−	0.00435419i	0.867280	+	0.497821i	$0.165866\pi$
$54$		0			0
$55$	69.5395	+	120.446i	0.170486	+	0.295290i
$56$		0			0
$57$	90.3627	−	121.912i	0.209979	−	0.283291i
$58$		0			0
$59$	129.859	+	224.922i	0.286545	+	0.496310i	0.972983	−	0.230878i	$-0.0741600\pi$
$59$	129.859	+	224.922i	0.286545	+	0.496310i	−0.686438	+	0.727188i	$0.740827\pi$
$60$		0			0
$61$	365.410	−	632.909i	0.766983	−	1.32845i	−0.172208	−	0.985061i	$-0.555090\pi$
$61$	365.410	−	632.909i	0.766983	−	1.32845i	0.939192	−	0.343393i	$-0.111576\pi$
$62$		0			0
$63$	227.091	−	393.332i	0.454138	−	0.786591i
$64$		0			0
$65$	188.455			0.359615
$66$		0			0
$67$	116.463	−	201.720i	0.212362	−	0.367822i	−0.740091	−	0.672507i	$-0.765218\pi$
$67$	116.463	−	201.720i	0.212362	−	0.367822i	0.952453	+	0.304685i	$0.0985510\pi$
$68$		0			0
$69$	153.418			0.267672
$70$		0			0
$71$	483.781	+	837.933i	0.808651	+	1.40063i	0.913798	+	0.406169i	$0.133135\pi$
$71$	483.781	+	837.933i	0.808651	+	1.40063i	−0.105147	+	0.994457i	$0.533531\pi$
$72$		0			0
$73$	−80.2051	−	138.919i	−0.128593	−	0.222730i	0.794539	−	0.607214i	$-0.207713\pi$
$73$	−80.2051	−	138.919i	−0.128593	−	0.222730i	−0.923132	+	0.384484i	$0.874379\pi$
$74$		0			0
$75$	−183.680			−0.282794
$76$		0			0
$77$	536.992			0.794752
$78$		0			0
$79$	−198.595	−	343.977i	−0.282832	−	0.489879i	0.689249	−	0.724524i	$-0.257941\pi$
$79$	−198.595	−	343.977i	−0.282832	−	0.489879i	−0.972081	+	0.234645i	$0.924607\pi$
$80$		0			0
$81$	−234.164	−	405.584i	−0.321213	−	0.556357i
$82$		0			0
$83$	−461.162			−0.609868			−0.304934	−	0.952373i	$-0.598634\pi$
$83$	−461.162			−0.609868			−0.304934	+	0.952373i	$0.598634\pi$
$84$		0			0
$85$	9.82310	−	17.0141i	0.0125349	−	0.0217111i
$86$		0			0
$87$	222.218			0.273842
$88$		0			0
$89$	−552.519	+	956.991i	−0.658055	+	1.13978i	0.323063	+	0.946377i	$0.395287\pi$
$89$	−552.519	+	956.991i	−0.658055	+	1.13978i	−0.981119	+	0.193408i	$0.938046\pi$
$90$		0			0
$91$	363.818	−	630.151i	0.419104	−	0.725910i
$92$		0			0
$93$	193.518	+	335.183i	0.215773	+	0.373730i
$94$		0			0
$95$	−245.368	+	331.036i	−0.264992	+	0.357511i
$96$		0			0
$97$	−391.827	−	678.664i	−0.410144	−	0.710391i	0.584761	−	0.811206i	$-0.301188\pi$
$97$	−391.827	−	678.664i	−0.410144	−	0.710391i	−0.994905	+	0.100815i	$0.967855\pi$
$98$		0			0
$99$	330.447	−	572.352i	0.335467	−	0.581045i
$100$		0			0
$101$	−944.164	+	1635.34i	−0.930176	+	1.61111i	−0.147159	+	0.989113i	$0.547013\pi$
$101$	−944.164	+	1635.34i	−0.930176	+	1.61111i	−0.783018	+	0.621999i	$0.786321\pi$
$102$		0			0
$103$	−724.057			−0.692655			−0.346327	−	0.938114i	$-0.612571\pi$
$103$	−724.057			−0.692655			−0.346327	+	0.938114i	$0.612571\pi$
$104$		0			0
$105$	87.5639	−	151.665i	0.0813844	−	0.140962i
$106$		0			0
$107$	−510.377			−0.461121			−0.230561	−	0.973058i	$-0.574056\pi$
$107$	−510.377			−0.461121			−0.230561	+	0.973058i	$0.574056\pi$
$108$		0			0
$109$	634.347	+	1098.72i	0.557426	+	0.965490i	0.997710	+	0.0676315i	$0.0215442\pi$
$109$	634.347	+	1098.72i	0.557426	+	0.965490i	−0.440285	+	0.897858i	$0.645122\pi$
$110$		0			0
$111$	75.8480	+	131.373i	0.0648574	+	0.112336i
$112$		0			0
$113$	−2043.56			−1.70125			−0.850626	−	0.525771i	$-0.823777\pi$
$113$	−2043.56			−1.70125			−0.850626	+	0.525771i	$0.823777\pi$
$114$		0			0
$115$	−416.588			−0.337800
$116$		0			0
$117$	−447.763	−	775.548i	−0.353809	−	0.612816i
$118$		0			0
$119$	−37.9276	−	65.6925i	−0.0292169	−	0.0506052i
$120$		0			0
$121$	−549.604			−0.412926
$122$		0			0
$123$	−219.421	+	380.049i	−0.160850	+	0.278601i
$124$		0			0
$125$	1120.68			0.801895
$126$		0			0
$127$	676.054	−	1170.96i	0.472363	−	0.818156i	−0.527137	−	0.849780i	$-0.676735\pi$
$127$	676.054	−	1170.96i	0.472363	−	0.818156i	0.999500	+	0.0316240i	$0.0100679\pi$
$128$		0			0
$129$	135.966	−	235.500i	0.0927995	−	0.160734i
$130$		0			0
$131$	222.347	+	385.116i	0.148294	+	0.256853i	0.930597	−	0.366045i	$-0.119288\pi$
$131$	222.347	+	385.116i	0.148294	+	0.256853i	−0.782303	+	0.622898i	$0.785955\pi$
$132$		0			0
$133$	633.218	+	1459.53i	0.412834	+	0.951559i
$134$		0			0
$135$	−230.839	−	399.825i	−0.147166	−	0.254900i
$136$		0			0
$137$	900.889	−	1560.39i	0.561812	−	0.973086i	−0.435527	−	0.900176i	$-0.643438\pi$
$137$	900.889	−	1560.39i	0.561812	−	0.973086i	0.997338	−	0.0729105i	$-0.0232287\pi$
$138$		0			0
$139$	171.047	−	296.262i	0.104374	−	0.180782i	−0.809108	−	0.587660i	$-0.800049\pi$
$139$	171.047	−	296.262i	0.104374	−	0.180782i	0.913482	+	0.406878i	$0.133383\pi$
$140$		0			0
$141$	436.238			0.260552
$142$		0			0
$143$	529.404	−	916.954i	0.309587	−	0.536221i
$144$		0			0
$145$	−603.404			−0.345586
$146$		0			0
$147$	−23.8498	−	41.3091i	−0.0133816	−	0.0231777i
$148$		0			0
$149$	1792.13	+	3104.06i	0.985348	+	1.70667i	0.640380	+	0.768058i	$0.278777\pi$
$149$	1792.13	+	3104.06i	0.985348	+	1.70667i	0.344968	+	0.938615i	$0.387890\pi$
$150$		0			0
$151$	−938.930			−0.506020			−0.253010	−	0.967464i	$-0.581421\pi$
$151$	−938.930			−0.506020			−0.253010	+	0.967464i	$0.581421\pi$
$152$		0			0
$153$	−93.3575			−0.0493301
$154$		0			0
$155$	−525.474	−	910.148i	−0.272304	−	0.471644i
$156$		0			0
$157$	−581.416	−	1007.04i	−0.295554	−	0.511915i	0.679559	−	0.733621i	$-0.262171\pi$
$157$	−581.416	−	1007.04i	−0.295554	−	0.511915i	−0.975114	+	0.221705i	$0.928838\pi$
$158$		0			0
$159$	−3.55457			−0.00177293
$160$		0			0
$161$	−804.235	+	1392.98i	−0.393681	+	0.681875i
$162$		0			0
$163$	4108.02			1.97402			0.987010	−	0.160660i	$-0.0513623\pi$
$163$	4108.02			1.97402			0.987010	+	0.160660i	$0.0513623\pi$
$164$		0			0
$165$	127.417	−	220.693i	0.0601177	−	0.104127i
$166$		0			0
$167$	1959.10	−	3393.27i	0.907785	−	1.57233i	0.0906493	−	0.995883i	$-0.471106\pi$
$167$	1959.10	−	3393.27i	0.907785	−	1.57233i	0.817135	−	0.576446i	$-0.195561\pi$
$168$		0			0
$169$	381.147	+	660.165i	0.173485	+	0.300485i
$170$		0			0
$171$	1945.30	+	223.234i	0.869945	+	0.0998310i
$172$		0			0
$173$	1508.99	+	2613.65i	0.663158	+	1.14862i	0.979781	+	0.200072i	$0.0641175\pi$
$173$	1508.99	+	2613.65i	0.663158	+	1.14862i	−0.316623	+	0.948551i	$0.602549\pi$
$174$		0			0
$175$	962.870	−	1667.74i	0.415921	−	0.720396i
$176$		0			0
$177$	237.940	−	412.124i	0.101043	−	0.175012i
$178$		0			0
$179$	−2855.70			−1.19243			−0.596216	−	0.802824i	$-0.703330\pi$
$179$	−2855.70			−1.19243			−0.596216	+	0.802824i	$0.703330\pi$
$180$		0			0
$181$	591.836	−	1025.09i	0.243043	−	0.420964i	−0.718536	−	0.695489i	$-0.755188\pi$
$181$	591.836	−	1025.09i	0.243043	−	0.420964i	0.961580	+	0.274526i	$0.0885209\pi$
$182$		0			0
$183$	−1339.08			−0.540917
$184$		0			0
$185$	−205.956	−	356.726i	−0.0818495	−	0.141768i
$186$		0			0
$187$	−55.1897	−	95.5914i	−0.0215822	−	0.0373815i
$188$		0			0
$189$	−1782.57			−0.686045
$190$		0			0
$191$	−1262.46			−0.478265			−0.239133	−	0.970987i	$-0.576863\pi$
$191$	−1262.46			−0.478265			−0.239133	+	0.970987i	$0.576863\pi$
$192$		0			0
$193$	−1794.07	−	3107.43i	−0.669121	−	1.15895i	−0.978150	−	0.207899i	$-0.933338\pi$
$193$	−1794.07	−	3107.43i	−0.669121	−	1.15895i	0.309030	−	0.951052i	$-0.399996\pi$
$194$		0			0
$195$	−172.653	−	299.044i	−0.0634048	−	0.109820i
$196$		0			0
$197$	1966.06			0.711047			0.355524	−	0.934667i	$-0.384303\pi$
$197$	1966.06			0.711047			0.355524	+	0.934667i	$0.384303\pi$
$198$		0			0
$199$	−2504.97	+	4338.73i	−0.892324	+	1.54555i	−0.0552409	+	0.998473i	$0.517593\pi$
$199$	−2504.97	+	4338.73i	−0.892324	+	1.54555i	−0.837083	+	0.547077i	$0.815741\pi$
$200$		0			0
$201$	−426.791			−0.149769
$202$		0			0
$203$	−1164.89	+	2017.65i	−0.402754	+	0.697591i
$204$		0			0
$205$	595.811	−	1031.98i	0.202992	−	0.351592i
$206$		0			0
$207$	989.800	+	1714.38i	0.332347	+	0.575642i
$208$		0			0
$209$	921.417	+	2123.81i	0.304956	+	0.702906i
$210$		0			0
$211$	−210.398	−	364.421i	−0.0686465	−	0.118899i	0.829659	−	0.558270i	$-0.188535\pi$
$211$	−210.398	−	364.421i	−0.0686465	−	0.118899i	−0.898306	+	0.439371i	$0.855201\pi$
$212$		0			0
$213$	886.432	−	1535.35i	0.285152	−	0.493897i
$214$		0			0
$215$	−369.199	+	639.471i	−0.117112	+	0.202844i
$216$		0			0
$217$	−4057.77			−1.26940
$218$		0			0
$219$	−146.960	+	254.542i	−0.0453453	+	0.0785404i
$220$		0			0
$221$	−149.566			−0.0455245
$222$		0			0
$223$	2406.50	+	4168.17i	0.722650	+	1.25167i	0.959934	+	0.280226i	$0.0904095\pi$
$223$	2406.50	+	4168.17i	0.722650	+	1.25167i	−0.237284	+	0.971440i	$0.576257\pi$
$224$		0			0
$225$	−1185.04	−	2052.54i	−0.351122	−	0.608161i
$226$		0			0
$227$	−5727.35			−1.67462			−0.837308	−	0.546732i	$-0.815872\pi$
$227$	−5727.35			−1.67462			−0.837308	+	0.546732i	$0.815872\pi$
$228$		0			0
$229$	−2274.28			−0.656282			−0.328141	−	0.944629i	$-0.606422\pi$
$229$	−2274.28			−0.656282			−0.328141	+	0.944629i	$0.606422\pi$
$230$		0			0
$231$	−491.965	−	852.109i	−0.140125	−	0.242704i
$232$		0			0
$233$	−1627.97	−	2819.73i	−0.457734	−	0.792819i	0.541106	−	0.840954i	$-0.318006\pi$
$233$	−1627.97	−	2819.73i	−0.457734	−	0.792819i	−0.998841	+	0.0481349i	$0.984672\pi$
$234$		0			0
$235$	−1184.55			−0.328815
$236$		0			0
$237$	−363.886	+	630.269i	−0.0997339	+	0.172744i
$238$		0			0
$239$	3370.88			0.912317			0.456159	−	0.889899i	$-0.349225\pi$
$239$	3370.88			0.912317			0.456159	+	0.889899i	$0.349225\pi$
$240$		0			0
$241$	−765.510	+	1325.90i	−0.204609	+	0.354394i	−0.950008	−	0.312225i	$-0.898926\pi$
$241$	−765.510	+	1325.90i	−0.204609	+	0.354394i	0.745399	+	0.666619i	$0.232259\pi$
$242$		0			0
$243$	−1681.76	+	2912.89i	−0.443971	+	0.768980i
$244$		0			0
$245$	64.7611	+	112.170i	0.0168875	+	0.0292500i
$246$		0			0
$247$	3116.53	+	357.639i	0.802834	+	0.0921296i
$248$		0			0
$249$	422.493	+	731.779i	0.107528	+	0.186244i
$250$		0			0
$251$	1956.36	−	3388.51i	0.491969	−	0.852116i	−0.507988	−	0.861364i	$-0.669611\pi$
$251$	1956.36	−	3388.51i	0.491969	−	0.852116i	0.999957	+	0.00924841i	$0.00294390\pi$
$252$		0			0
$253$	−1170.27	+	2026.97i	−0.290807	+	0.503693i
$254$		0			0
$255$	−35.9977			−0.00884026
$256$		0			0
$257$	3529.55	−	6113.36i	0.856683	−	1.48382i	−0.0183927	−	0.999831i	$-0.505855\pi$
$257$	3529.55	−	6113.36i	0.856683	−	1.48382i	0.875075	−	0.483987i	$-0.160812\pi$
$258$		0			0
$259$	−1590.41			−0.381558
$260$		0			0
$261$	1433.67	+	2483.19i	0.340007	+	0.588909i
$262$		0			0
$263$	−750.312	−	1299.58i	−0.175917	−	0.304697i	0.764561	−	0.644551i	$-0.222956\pi$
$263$	−750.312	−	1299.58i	−0.175917	−	0.304697i	−0.940478	+	0.339854i	$0.889622\pi$
$264$		0			0
$265$	9.65199			0.00223742
$266$		0			0
$267$	2024.76			0.464095
$268$		0			0
$269$	−336.084	−	582.115i	−0.0761762	−	0.131941i	0.825421	−	0.564518i	$-0.190938\pi$
$269$	−336.084	−	582.115i	−0.0761762	−	0.131941i	−0.901597	+	0.432577i	$0.857604\pi$
$270$		0			0
$271$	136.363	+	236.187i	0.0305662	+	0.0529422i	0.880904	−	0.473295i	$-0.156936\pi$
$271$	136.363	+	236.187i	0.0305662	+	0.0529422i	−0.850338	+	0.526237i	$0.823602\pi$
$272$		0			0
$273$	−1333.25			−0.295574
$274$		0			0
$275$	1401.11	−	2426.79i	0.307236	−	0.532148i
$276$		0			0
$277$	6410.16			1.39043			0.695215	−	0.718802i	$-0.255309\pi$
$277$	6410.16			1.39043			0.695215	+	0.718802i	$0.255309\pi$
$278$		0			0
$279$	−2497.02	+	4324.96i	−0.535816	+	0.928060i
$280$		0			0
$281$	3803.42	−	6587.72i	0.807449	−	1.39854i	−0.107176	−	0.994240i	$-0.534181\pi$
$281$	3803.42	−	6587.72i	0.807449	−	1.39854i	0.914625	−	0.404303i	$-0.132486\pi$
$282$		0			0
$283$	3406.99	+	5901.08i	0.715634	+	1.23951i	0.962714	+	0.270520i	$0.0871955\pi$
$283$	3406.99	+	5901.08i	0.715634	+	1.23951i	−0.247080	+	0.968995i	$0.579471\pi$
$284$		0			0
$285$	750.088	+	86.0767i	0.155900	+	0.0178903i
$286$		0			0
$287$	−2300.46	−	3984.52i	−0.473143	−	0.819507i
$288$		0			0
$289$	2448.70	−	4241.28i	0.498413	−	0.863277i
$290$		0			0
$291$	−717.944	+	1243.52i	−0.144628	+	0.250502i
$292$		0			0
$293$	1477.00			0.294495			0.147248	−	0.989100i	$-0.452959\pi$
$293$	1477.00			0.294495			0.147248	+	0.989100i	$0.452959\pi$
$294$		0			0
$295$	−646.095	+	1119.07i	−0.127516	+	0.220864i
$296$		0			0
$297$	−2593.87			−0.506774
$298$		0			0
$299$	1585.74	+	2746.58i	0.306708	+	0.531234i
$300$		0			0
$301$	1425.50	+	2469.03i	0.272971	+	0.472800i
$302$		0			0
$303$	3459.98			0.656009
$304$		0			0
$305$	3636.11			0.682633
$306$		0			0
$307$	−2761.51	−	4783.08i	−0.513380	−	0.889201i	−0.999880	−	0.0155197i	$-0.995060\pi$
$307$	−2761.51	−	4783.08i	−0.513380	−	0.889201i	0.486499	−	0.873681i	$-0.338274\pi$
$308$		0			0
$309$	663.345	+	1148.95i	0.122124	+	0.211525i
$310$		0			0
$311$	−3594.21			−0.655335			−0.327667	−	0.944793i	$-0.606263\pi$
$311$	−3594.21			−0.655335			−0.327667	+	0.944793i	$0.606263\pi$
$312$		0			0
$313$	−1661.82	+	2878.36i	−0.300102	+	0.519791i	−0.976159	−	0.217058i	$-0.930354\pi$
$313$	−1661.82	+	2878.36i	−0.300102	+	0.519791i	0.676057	+	0.736849i	$0.263687\pi$
$314$		0			0
$315$	2259.72			0.404194
$316$		0			0
$317$	4246.88	−	7355.82i	0.752457	−	1.30329i	−0.194172	−	0.980967i	$-0.562202\pi$
$317$	4246.88	−	7355.82i	0.752457	−	1.30329i	0.946629	−	0.322326i	$-0.104465\pi$
$318$		0			0
$319$	−1695.07	+	2935.95i	−0.297510	+	0.515302i
$320$		0			0
$321$	467.582	+	809.875i	0.0813017	+	0.140819i
$322$		0			0
$323$	194.735	−	262.725i	0.0335460	−	0.0452582i
$324$		0			0
$325$	−1898.53	−	3288.35i	−0.324035	−	0.561245i
$326$		0			0
$327$	1162.31	−	2013.19i	0.196563	−	0.340457i
$328$		0			0
$329$	−2286.80	+	3960.86i	−0.383209	+	0.663737i
$330$		0			0
$331$	6493.50			1.07829			0.539147	−	0.842212i	$-0.318747\pi$
$331$	6493.50			1.07829			0.539147	+	0.842212i	$0.318747\pi$
$332$		0			0
$333$	−978.688	+	1695.14i	−0.161056	+	0.278958i
$334$		0			0
$335$	1158.90			0.189007
$336$		0			0
$337$	−207.747	−	359.829i	−0.0335808	−	0.0581636i	0.848747	−	0.528800i	$-0.177358\pi$
$337$	−207.747	−	359.829i	−0.0335808	−	0.0581636i	−0.882327	+	0.470636i	$0.844024\pi$
$338$		0			0
$339$	1872.20	+	3242.75i	0.299953	+	0.519534i
$340$		0			0
$341$	−5904.60			−0.937689
$342$		0			0
$343$	−6089.01			−0.958530
$344$		0			0
$345$	381.657	+	661.049i	0.0595586	+	0.103159i
$346$		0			0
$347$	−2900.67	−	5024.11i	−0.448750	−	0.777257i	0.549555	−	0.835457i	$-0.314797\pi$
$347$	−2900.67	−	5024.11i	−0.448750	−	0.777257i	−0.998305	+	0.0582001i	$0.981464\pi$
$348$		0			0
$349$	−1128.87			−0.173144			−0.0865719	−	0.996246i	$-0.527591\pi$
$349$	−1128.87			−0.173144			−0.0865719	+	0.996246i	$0.527591\pi$
$350$		0			0
$351$	−1757.38	+	3043.86i	−0.267242	+	0.462876i
$352$		0			0
$353$	−4164.68			−0.627942			−0.313971	−	0.949433i	$-0.601659\pi$
$353$	−4164.68			−0.627942			−0.313971	+	0.949433i	$0.601659\pi$
$354$		0			0
$355$	−2406.99	+	4169.04i	−0.359859	+	0.623294i
$356$		0			0
$357$	−69.4946	+	120.368i	−0.0103027	+	0.0178447i
$358$		0			0
$359$	−1238.37	−	2144.92i	−0.182057	−	0.315332i	0.760524	−	0.649310i	$-0.224942\pi$
$359$	−1238.37	−	2144.92i	−0.182057	−	0.315332i	−0.942581	+	0.333978i	$0.891609\pi$
$360$		0			0
$361$	−4685.94	+	5008.78i	−0.683181	+	0.730249i
$362$		0			0
$363$	503.520	+	872.122i	0.0728042	+	0.126101i
$364$		0			0
$365$	399.051	−	691.176i	0.0572254	−	0.0991173i
$366$		0			0
$367$	1600.37	−	2771.92i	0.227626	−	0.394259i	−0.729478	−	0.684004i	$-0.760237\pi$
$367$	1600.37	−	2771.92i	0.227626	−	0.394259i	0.957104	+	0.289745i	$0.0935704\pi$
$368$		0			0
$369$	−5662.51			−0.798858
$370$		0			0
$371$	18.6334	−	32.2741i	0.00260755	−	0.00451640i
$372$		0			0
$373$	−821.035			−0.113972			−0.0569860	−	0.998375i	$-0.518149\pi$
$373$	−821.035			−0.113972			−0.0569860	+	0.998375i	$0.518149\pi$
$374$		0			0
$375$	−1026.71	−	1778.32i	−0.141385	−	0.244885i
$376$		0			0
$377$	2296.85	+	3978.27i	0.313777	+	0.543478i
$378$		0			0
$379$	−2271.88			−0.307911			−0.153956	−	0.988078i	$-0.549201\pi$
$379$	−2271.88			−0.307911			−0.153956	+	0.988078i	$0.549201\pi$
$380$		0			0
$381$	−2477.47			−0.333135
$382$		0			0
$383$	−2756.39	−	4774.22i	−0.367742	−	0.636948i	0.621470	−	0.783438i	$-0.286536\pi$
$383$	−2756.39	−	4774.22i	−0.367742	−	0.636948i	−0.989212	+	0.146490i	$0.953202\pi$
$384$		0			0
$385$	1335.87	+	2313.79i	0.176837	+	0.306291i
$386$		0			0
$387$	3508.82			0.460887
$388$		0			0
$389$	−1297.35	+	2247.07i	−0.169095	+	0.292882i	−0.938102	−	0.346359i	$-0.887418\pi$
$389$	−1297.35	+	2247.07i	−0.169095	+	0.292882i	0.769007	+	0.639241i	$0.220751\pi$
$390$		0			0
$391$	330.623			0.0427630
$392$		0			0
$393$	407.406	−	705.649i	0.0522925	−	0.0905732i
$394$		0			0
$395$	988.087	−	1711.42i	0.125863	−	0.218002i
$396$		0			0
$397$	−5143.14	−	8908.18i	−0.650193	−	1.12617i	−0.983076	−	0.183200i	$-0.941355\pi$
$397$	−5143.14	−	8908.18i	−0.650193	−	1.12617i	0.332882	−	0.942968i	$-0.391979\pi$
$398$		0			0
$399$	1735.89	−	2341.95i	0.217802	−	0.293845i
$400$		0			0
$401$	5500.42	+	9527.01i	0.684982	+	1.18642i	0.973442	+	0.228932i	$0.0735235\pi$
$401$	5500.42	+	9527.01i	0.684982	+	1.18642i	−0.288460	+	0.957492i	$0.593143\pi$
$402$		0			0
$403$	−4000.43	+	6928.95i	−0.494480	+	0.856465i
$404$		0			0
$405$	1165.06	−	2017.94i	0.142943	−	0.247585i
$406$		0			0
$407$	−2314.27			−0.281852
$408$		0			0
$409$	−5137.33	+	8898.12i	−0.621088	+	1.07576i	0.368196	+	0.929748i	$0.379976\pi$
$409$	−5137.33	+	8898.12i	−0.621088	+	1.07576i	−0.989284	+	0.146007i	$0.953358\pi$
$410$		0			0
$411$	−3301.40			−0.396219
$412$		0			0
$413$	2494.61	+	4320.79i	0.297220	+	0.514800i
$414$		0			0
$415$	−1147.23	−	1987.05i	−0.135699	−	0.235038i
$416$		0			0
$417$	−626.820			−0.0736103
$418$		0			0
$419$	2101.98			0.245080			0.122540	−	0.992464i	$-0.460896\pi$
$419$	2101.98			0.245080			0.122540	+	0.992464i	$0.460896\pi$
$420$		0			0
$421$	3725.44	+	6452.66i	0.431275	+	0.746991i	0.996983	−	0.0776146i	$-0.0247304\pi$
$421$	3725.44	+	6452.66i	0.431275	+	0.746991i	−0.565708	+	0.824606i	$0.691397\pi$
$422$		0			0
$423$	2814.45	+	4874.77i	0.323506	+	0.560329i
$424$		0			0
$425$	−395.838			−0.0451788
$426$		0			0
$427$	7019.61	−	12158.3i	0.795557	−	1.37794i
$428$		0			0
$429$	−1940.05			−0.218337
$430$		0			0
$431$	1575.97	−	2729.67i	0.176130	−	0.305066i	−0.764422	−	0.644716i	$-0.776975\pi$
$431$	1575.97	−	2729.67i	0.176130	−	0.305066i	0.940552	+	0.339651i	$0.110309\pi$
$432$		0			0
$433$	4573.02	−	7920.70i	0.507541	−	0.879087i	−0.492421	−	0.870357i	$-0.663888\pi$
$433$	4573.02	−	7920.70i	0.507541	−	0.879087i	0.999962	−	0.00872954i	$-0.00277873\pi$
$434$		0			0
$435$	552.808	+	957.492i	0.0609313	+	0.105536i
$436$		0			0
$437$	−6889.22	−	790.576i	−0.754133	−	0.0865409i
$438$		0			0
$439$	495.563	+	858.340i	0.0538768	+	0.0933174i	0.891706	−	0.452615i	$-0.149509\pi$
$439$	495.563	+	858.340i	0.0538768	+	0.0933174i	−0.837829	+	0.545932i	$0.816176\pi$
$440$		0			0
$441$	307.741	−	533.023i	0.0332298	−	0.0575556i
$442$		0			0
$443$	6885.50	−	11926.0i	0.738465	−	1.27906i	−0.214722	−	0.976675i	$-0.568884\pi$
$443$	6885.50	−	11926.0i	0.738465	−	1.27906i	0.953186	−	0.302383i	$-0.0977822\pi$
$444$		0			0
$445$	−5497.98			−0.585684
$446$		0			0
$447$	3283.72	−	5687.56i	0.347460	−	0.601818i
$448$		0			0
$449$	15734.2			1.65377			0.826887	−	0.562368i	$-0.190110\pi$
$449$	15734.2			1.65377			0.826887	+	0.562368i	$0.190110\pi$
$450$		0			0
$451$	−3347.48	−	5798.01i	−0.349505	−	0.605360i
$452$		0			0
$453$	860.201	+	1489.91i	0.0892180	+	0.154530i
$454$		0			0
$455$	3620.26			0.373012
$456$		0			0
$457$	15096.8			1.54529			0.772647	−	0.634836i	$-0.218933\pi$
$457$	15096.8			1.54529			0.772647	+	0.634836i	$0.218933\pi$
$458$		0			0
$459$	183.204	+	317.319i	0.0186302	+	0.0322684i
$460$		0			0
$461$	218.281	+	378.074i	0.0220528	+	0.0381966i	0.876841	−	0.480780i	$-0.159646\pi$
$461$	218.281	+	378.074i	0.0220528	+	0.0381966i	−0.854788	+	0.518977i	$0.826313\pi$
$462$		0			0
$463$	14930.3			1.49864			0.749318	−	0.662210i	$-0.230381\pi$
$463$	14930.3			1.49864			0.749318	+	0.662210i	$0.230381\pi$
$464$		0			0
$465$	−962.826	+	1667.66i	−0.0960215	+	0.166314i
$466$		0			0
$467$	−13543.2			−1.34198			−0.670989	−	0.741467i	$-0.734130\pi$
$467$	−13543.2			−1.34198			−0.670989	+	0.741467i	$0.734130\pi$
$468$		0			0
$469$	2237.29	−	3875.09i	0.220274	−	0.381525i
$470$		0			0
$471$	−1065.33	+	1845.20i	−0.104220	+	0.180515i
$472$		0			0
$473$	2074.29	+	3592.78i	0.201640	+	0.349252i
$474$		0			0
$475$	8248.12	+	946.517i	0.796736	+	0.0914299i
$476$		0			0
$477$	−22.9328	−	39.7208i	−0.00220130	−	0.00381277i
$478$		0			0
$479$	−3228.29	+	5591.57i	−0.307943	+	0.533372i	−0.977912	−	0.209016i	$-0.932974\pi$
$479$	−3228.29	+	5591.57i	−0.307943	+	0.533372i	0.669970	+	0.742389i	$0.266307\pi$
$480$		0			0
$481$	−1567.94	+	2715.75i	−0.148632	+	0.257438i
$482$		0			0
$483$	2947.20			0.277644
$484$		0			0
$485$	1949.49	−	3376.61i	0.182519	−	0.316132i
$486$		0			0
$487$	−4872.85			−0.453408			−0.226704	−	0.973964i	$-0.572795\pi$
$487$	−4872.85			−0.453408			−0.226704	+	0.973964i	$0.572795\pi$
$488$		0			0
$489$	−3763.56	−	6518.68i	−0.348046	−	0.602833i
$490$		0			0
$491$	−5902.29	−	10223.1i	−0.542498	−	0.939634i	−0.998760	−	0.0497886i	$-0.984145\pi$
$491$	−5902.29	−	10223.1i	−0.542498	−	0.939634i	0.456262	−	0.889846i	$-0.349188\pi$
$492$		0			0
$493$	478.888			0.0437486
$494$		0			0
$495$	3288.20			0.298573
$496$		0			0
$497$	9293.54	+	16096.9i	0.838777	+	1.45281i
$498$		0			0
$499$	2358.23	+	4084.58i	0.211561	+	0.366435i	0.952203	−	0.305465i	$-0.0988119\pi$
$499$	2358.23	+	4084.58i	0.211561	+	0.366435i	−0.740642	+	0.671900i	$0.765479\pi$
$500$		0			0
$501$	−7179.33			−0.640217
$502$		0			0
$503$	−1074.12	+	1860.43i	−0.0952142	+	0.164916i	−0.909698	−	0.415271i	$-0.863687\pi$
$503$	−1074.12	+	1860.43i	−0.0952142	+	0.164916i	0.814484	+	0.580186i	$0.197020\pi$
$504$		0			0
$505$	−9395.14			−0.827878
$506$		0			0
$507$	698.375	−	1209.62i	0.0611754	−	0.105959i
$508$		0			0
$509$	−5312.70	+	9201.87i	−0.462636	+	0.801308i	−0.999091	−	0.0426202i	$-0.986429\pi$
$509$	−5312.70	+	9201.87i	−0.462636	+	0.801308i	0.536456	+	0.843928i	$0.319763\pi$
$510$		0			0
$511$	−1540.76	−	2668.67i	−0.133384	−	0.231028i
$512$		0			0
$513$	−3058.68	−	7050.08i	−0.263244	−	0.606761i
$514$		0			0
$515$	−1801.23	−	3119.82i	−0.154120	−	0.266943i
$516$		0			0
$517$	−3327.61	+	5763.59i	−0.283072	+	0.490295i
$518$		0			0
$519$	2764.92	−	4788.98i	0.233847	−	0.405035i
$520$		0			0
$521$	10629.1			0.893800			0.446900	−	0.894584i	$-0.352528\pi$
$521$	10629.1			0.893800			0.446900	+	0.894584i	$0.352528\pi$
$522$		0			0
$523$	−3063.70	+	5306.48i	−0.256149	+	0.443663i	−0.965207	−	0.261487i	$-0.915787\pi$
$523$	−3063.70	+	5306.48i	−0.256149	+	0.443663i	0.709058	+	0.705150i	$0.249121\pi$
$524$		0			0
$525$	−3528.53			−0.293329
$526$		0			0
$527$	417.040	+	722.334i	0.0344716	+	0.0597066i
$528$		0			0
$529$	2578.15	+	4465.49i	0.211897	+	0.367016i
$530$		0			0
$531$	6140.41			0.501828
$532$		0			0
$533$	−9071.81			−0.737231
$534$		0			0
$535$	−1269.66	−	2199.11i	−0.102602	−	0.177712i
$536$		0			0
$537$	2616.25	+	4531.48i	0.210241	+	0.364149i
$538$		0			0
$539$	727.703			0.0581528
$540$		0			0
$541$	8555.21	−	14818.0i	0.679884	−	1.17759i	−0.295132	−	0.955456i	$-0.595364\pi$
$541$	8555.21	−	14818.0i	0.679884	−	1.17759i	0.975016	−	0.222136i	$-0.0713030\pi$
$542$		0			0
$543$	−2168.84			−0.171407
$544$		0			0
$545$	−3156.12	+	5466.55i	−0.248061	+	0.429654i
$546$		0			0
$547$	−11301.4	+	19574.6i	−0.883386	+	1.53007i	−0.0358340	+	0.999358i	$0.511409\pi$
$547$	−11301.4	+	19574.6i	−0.883386	+	1.53007i	−0.847552	+	0.530712i	$0.821925\pi$
$548$		0			0
$549$	−8639.28	−	14963.7i	−0.671613	−	1.16327i
$550$		0			0
$551$	−9978.64	−	1145.10i	−0.771514	−	0.0885355i
$552$		0			0
$553$	−3815.06	−	6607.88i	−0.293369	−	0.508129i
$554$		0			0
$555$	−377.373	+	653.629i	−0.0288623	+	0.0499910i
$556$		0			0
$557$	−7822.66	+	13549.2i	−0.595075	+	1.03070i	0.398462	+	0.917185i	$0.369544\pi$
$557$	−7822.66	+	13549.2i	−0.595075	+	1.03070i	−0.993536	+	0.113515i	$0.963789\pi$
$558$		0			0
$559$	5621.41			0.425332
$560$		0			0
$561$	−101.124	+	175.152i	−0.00761045	+	0.0131817i
$562$		0			0
$563$	−17105.4			−1.28047			−0.640235	−	0.768179i	$-0.721163\pi$
$563$	−17105.4			−1.28047			−0.640235	+	0.768179i	$0.721163\pi$
$564$		0			0
$565$	−5083.73	−	8805.28i	−0.378538	−	0.655648i
$566$		0			0
$567$	−4498.35	−	7791.37i	−0.333180	−	0.577084i
$568$		0			0
$569$	18550.1			1.36672			0.683359	−	0.730083i	$-0.260518\pi$
$569$	18550.1			1.36672			0.683359	+	0.730083i	$0.260518\pi$
$570$		0			0
$571$	−6288.10			−0.460856			−0.230428	−	0.973089i	$-0.574013\pi$
$571$	−6288.10			−0.460856			−0.230428	+	0.973089i	$0.574013\pi$
$572$		0			0
$573$	1156.61	+	2003.30i	0.0843244	+	0.146054i
$574$		0			0
$575$	4196.78	+	7269.03i	0.304379	+	0.527199i
$576$		0			0
$577$	−17519.3			−1.26402			−0.632009	−	0.774961i	$-0.717770\pi$
$577$	−17519.3			−1.26402			−0.632009	+	0.774961i	$0.717770\pi$
$578$		0			0
$579$	−3287.28	+	5693.74i	−0.235950	+	0.408677i
$580$		0			0
$581$	−8859.02			−0.632588
$582$		0			0
$583$	27.1142	−	46.9631i	0.00192616	−	0.00333621i
$584$		0			0
$585$	2227.79	−	3858.65i	0.157449	−	0.272710i
$586$		0			0
$587$	7779.02	+	13473.7i	0.546975	+	0.947389i	0.998480	+	0.0551202i	$0.0175542\pi$
$587$	7779.02	+	13473.7i	0.546975	+	0.947389i	−0.451504	+	0.892269i	$0.649112\pi$
$588$		0			0
$589$	−6962.67	−	16048.6i	−0.487083	−	1.12270i
$590$		0			0
$591$	−1801.21	−	3119.79i	−0.125367	−	0.217142i
$592$		0			0
$593$	−10895.4	+	18871.3i	−0.754501	+	1.30683i	0.191121	+	0.981567i	$0.438788\pi$
$593$	−10895.4	+	18871.3i	−0.754501	+	1.30683i	−0.945622	+	0.325268i	$0.894546\pi$
$594$		0			0
$595$	188.704	−	326.845i	0.0130019	−	0.0225199i
$596$		0			0
$597$	9179.70			0.629313
$598$		0			0
$599$	−10420.5	+	18048.9i	−0.710804	+	1.23115i	0.253752	+	0.967269i	$0.418335\pi$
$599$	−10420.5	+	18048.9i	−0.710804	+	1.23115i	−0.964556	+	0.263879i	$0.914998\pi$
$600$		0			0
$601$	23707.7			1.60908			0.804541	−	0.593897i	$-0.202411\pi$
$601$	23707.7			1.60908			0.804541	+	0.593897i	$0.202411\pi$
$602$		0			0
$603$	−2753.51	−	4769.21i	−0.185956	−	0.322085i
$604$		0			0
$605$	−1367.24	−	2368.14i	−0.0918783	−	0.159138i
$606$		0			0
$607$	25378.0			1.69697			0.848484	−	0.529221i	$-0.177516\pi$
$607$	25378.0			1.69697			0.848484	+	0.529221i	$0.177516\pi$
$608$		0			0
$609$	4268.85			0.284043
$610$		0			0
$611$	4508.98	+	7809.78i	0.298550	+	0.517103i
$612$		0			0
$613$	−11222.2	−	19437.4i	−0.739413	−	1.28070i	−0.952760	−	0.303724i	$-0.901770\pi$
$613$	−11222.2	−	19437.4i	−0.739413	−	1.28070i	0.213347	−	0.976976i	$-0.431563\pi$
$614$		0			0
$615$	−2183.41			−0.143160
$616$		0			0
$617$	8597.76	−	14891.8i	0.560993	−	0.971669i	−0.436417	−	0.899745i	$-0.643753\pi$
$617$	8597.76	−	14891.8i	0.560993	−	0.971669i	0.997410	−	0.0719245i	$-0.0229141\pi$
$618$		0			0
$619$	9839.91			0.638933			0.319466	−	0.947598i	$-0.396496\pi$
$619$	9839.91			0.638933			0.319466	+	0.947598i	$0.396496\pi$
$620$		0			0
$621$	3884.76	−	6728.59i	0.251030	−	0.434797i
$622$		0			0
$623$	−10614.0	+	18384.0i	−0.682571	+	1.18225i
$624$		0			0
$625$	−3477.44	−	6023.10i	−0.222556	−	0.385479i
$626$		0			0
$627$	2525.95	−	3407.85i	0.160888	−	0.217060i
$628$		0			0
$629$	163.456	+	283.114i	0.0103615	+	0.0179467i
$630$		0			0
$631$	−5415.42	+	9379.79i	−0.341656	+	0.591765i	−0.984740	−	0.174030i	$-0.944321\pi$
$631$	−5415.42	+	9379.79i	−0.341656	+	0.591765i	0.643085	+	0.765795i	$0.277654\pi$
$632$		0			0
$633$	−385.513	+	667.728i	−0.0242066	+	0.0419270i
$634$		0			0
$635$	6727.25			0.420414
$636$		0			0
$637$	493.026	−	853.946i	0.0306663	−	0.0531155i
$638$		0			0
$639$	22875.8			1.41620
$640$		0			0
$641$	−3630.29	−	6287.85i	−0.223694	−	0.387450i	0.732233	−	0.681055i	$-0.238478\pi$
$641$	−3630.29	−	6287.85i	−0.223694	−	0.387450i	−0.955927	+	0.293605i	$0.905145\pi$
$642$		0			0
$643$	−9174.16	−	15890.1i	−0.562665	−	0.974564i	−0.997263	−	0.0739397i	$-0.976443\pi$
$643$	−9174.16	−	15890.1i	−0.562665	−	0.974564i	0.434598	−	0.900625i	$-0.356891\pi$
$644$		0			0
$645$	1352.96			0.0825937
$646$		0			0
$647$	−14872.0			−0.903678			−0.451839	−	0.892099i	$-0.649232\pi$
$647$	−14872.0			−0.903678			−0.451839	+	0.892099i	$0.649232\pi$
$648$		0			0
$649$	3629.99	+	6287.33i	0.219553	+	0.380277i
$650$		0			0
$651$	3717.53	+	6438.94i	0.223812	+	0.387653i
$652$		0			0
$653$	16813.1			1.00758			0.503788	−	0.863827i	$-0.331939\pi$
$653$	16813.1			1.00758			0.503788	+	0.863827i	$0.331939\pi$
$654$		0			0
$655$	−1106.26	+	1916.10i	−0.0659927	+	0.114303i
$656$		0			0
$657$	−3792.53			−0.225206
$658$		0			0
$659$	−891.846	+	1544.72i	−0.0527183	+	0.0913108i	−0.891180	−	0.453649i	$-0.850122\pi$
$659$	−891.846	+	1544.72i	−0.0527183	+	0.0913108i	0.838462	+	0.544960i	$0.183455\pi$
$660$		0			0
$661$	1388.39	−	2404.77i	0.0816978	−	0.141505i	−0.822281	−	0.569081i	$-0.807299\pi$
$661$	1388.39	−	2404.77i	0.0816978	−	0.141505i	0.903979	+	0.427576i	$0.140632\pi$
$662$		0			0
$663$	137.025	+	237.335i	0.00802657	+	0.0139024i
$664$		0			0
$665$	−4713.58	+	6359.27i	−0.274865	+	0.370830i
$666$		0			0
$667$	−5077.29	−	8794.13i	−0.294743	−	0.510510i
$668$		0			0
$669$	4409.42	−	7637.34i	0.254825	−	0.441370i
$670$		0			0
$671$	10214.5	−	17692.0i	0.587669	−	1.01787i
$672$		0			0
$673$	23019.5			1.31848			0.659241	−	0.751932i	$-0.270878\pi$
$673$	23019.5			1.31848			0.659241	+	0.751932i	$0.270878\pi$
$674$		0			0
$675$	−4651.02	+	8055.81i	−0.265212	+	0.459360i
$676$		0			0
$677$	6623.28			0.376002			0.188001	−	0.982169i	$-0.439799\pi$
$677$	6623.28			0.376002			0.188001	+	0.982169i	$0.439799\pi$
$678$		0			0
$679$	−7527.08	−	13037.3i	−0.425424	−	0.736856i
$680$		0			0
$681$	5247.11	+	9088.27i	0.295257	+	0.511400i
$682$		0			0
$683$	33703.6			1.88819			0.944093	−	0.329680i	$-0.106941\pi$
$683$	33703.6			1.88819			0.944093	+	0.329680i	$0.106941\pi$
$684$		0			0
$685$	8964.53			0.500025
$686$		0			0
$687$	2083.58	+	3608.87i	0.115711	+	0.200418i
$688$		0			0
$689$	−36.7402	−	63.6360i	−0.00203148	−	0.00351863i
$690$		0			0
$691$	14467.5			0.796481			0.398241	−	0.917281i	$-0.369621\pi$
$691$	14467.5			0.796481			0.398241	+	0.917281i	$0.369621\pi$
$692$		0			0
$693$	6347.97	−	10995.0i	0.347964	−	0.602692i
$694$		0			0
$695$	1702.05			0.0928956
$696$		0			0
$697$	−472.863	+	819.022i	−0.0256972	+	0.0445089i
$698$		0			0
$699$	−2982.94	+	5166.60i	−0.161409	+	0.279569i
$700$		0			0
$701$	−3879.78	−	6719.97i	−0.209040	−	0.362068i	0.742372	−	0.669988i	$-0.233701\pi$
$701$	−3879.78	−	6719.97i	−0.209040	−	0.362068i	−0.951412	+	0.307920i	$0.900367\pi$
$702$		0			0
$703$	−2728.97	−	6290.11i	−0.146408	−	0.337463i
$704$		0			0
$705$	1085.22	+	1879.66i	0.0579743	+	0.100414i
$706$		0			0
$707$	−18137.6	+	31415.2i	−0.964829	+	1.67113i
$708$		0			0
$709$	−717.418	+	1242.60i	−0.0380017	+	0.0658208i	−0.884401	−	0.466728i	$-0.845433\pi$
$709$	−717.418	+	1242.60i	−0.0380017	+	0.0658208i	0.846399	+	0.532549i	$0.178766\pi$
$710$		0			0
$711$	−9390.65			−0.495326
$712$		0			0
$713$	8843.12	−	15316.7i	0.464485	−	0.804511i
$714$		0			0
$715$	5267.97			0.275540
$716$		0			0
$717$	−3088.23	−	5348.97i	−0.160853	−	0.278606i
$718$		0			0
$719$	−14953.5	−	25900.2i	−0.775619	−	1.34341i	−0.934446	−	0.356106i	$-0.884104\pi$
$719$	−14953.5	−	25900.2i	−0.775619	−	1.34341i	0.158826	−	0.987307i	$-0.449229\pi$
$720$		0			0
$721$	−13909.3			−0.718459
$722$		0			0
$723$	2805.29			0.144301
$724$		0			0
$725$	6078.79	+	10528.8i	0.311394	+	0.539350i
$726$		0			0
$727$	10583.8	+	18331.7i	0.539934	+	0.935193i	0.998907	+	0.0467425i	$0.0148840\pi$
$727$	10583.8	+	18331.7i	0.539934	+	0.935193i	−0.458973	+	0.888450i	$0.651783\pi$
$728$		0			0
$729$	−6481.90			−0.329315
$730$		0			0
$731$	293.013	−	507.513i	0.0148255	−	0.0256786i
$732$		0			0
$733$	−31326.1			−1.57852			−0.789260	−	0.614059i	$-0.789536\pi$
$733$	−31326.1			−1.57852			−0.789260	+	0.614059i	$0.789536\pi$
$734$		0			0
$735$	118.662	−	205.528i	0.00595498	−	0.0103143i
$736$		0			0
$737$	3255.55	−	5638.78i	0.162713	−	0.281828i
$738$		0			0
$739$	−14725.7	−	25505.6i	−0.733007	−	1.26961i	−0.955592	−	0.294692i	$-0.904783\pi$
$739$	−14725.7	−	25505.6i	−0.733007	−	1.26961i	0.222585	−	0.974913i	$-0.428550\pi$
$740$		0			0
$741$	−2287.70	−	5273.01i	−0.113415	−	0.261416i
$742$		0			0
$743$	9052.76	+	15679.8i	0.446990	+	0.774209i	0.998188	−	0.0601649i	$-0.0191627\pi$
$743$	9052.76	+	15679.8i	0.446990	+	0.774209i	−0.551199	+	0.834374i	$0.685829\pi$
$744$		0			0
$745$	−8916.52	+	15443.9i	−0.438491	+	0.759489i
$746$		0			0
$747$	−5451.55	+	9442.36i	−0.267017	+	0.462487i
$748$		0			0
$749$	−9804.45			−0.478300
$750$		0			0
$751$	−761.636	+	1319.19i	−0.0370073	+	0.0640985i	−0.883936	−	0.467608i	$-0.845116\pi$
$751$	−761.636	+	1319.19i	−0.0370073	+	0.0640985i	0.846929	+	0.531707i	$0.178449\pi$
$752$		0			0
$753$	−7169.27			−0.346963
$754$		0			0
$755$	−2335.77	−	4045.67i	−0.112592	−	0.195016i
$756$		0			0
$757$	10665.7	+	18473.5i	0.512089	+	0.886965i	0.999902	+	0.0140164i	$0.00446169\pi$
$757$	10665.7	+	18473.5i	0.512089	+	0.886965i	−0.487812	+	0.872949i	$0.662205\pi$
$758$		0			0
$759$	4288.57			0.205093
$760$		0			0
$761$	−7889.35			−0.375806			−0.187903	−	0.982188i	$-0.560169\pi$
$761$	−7889.35			−0.375806			−0.187903	+	0.982188i	$0.560169\pi$
$762$		0			0
$763$	12185.9	+	21106.7i	0.578192	+	1.00146i
$764$		0			0
$765$	−232.244	−	402.259i	−0.0109762	−	0.0190114i
$766$		0			0
$767$	9837.44			0.463115
$768$		0			0
$769$	1702.39	−	2948.62i	0.0798306	−	0.138271i	−0.823346	−	0.567540i	$-0.807895\pi$
$769$	1702.39	−	2948.62i	0.0798306	−	0.138271i	0.903177	+	0.429269i	$0.141229\pi$
$770$		0			0
$771$	−12934.4			−0.604177
$772$		0			0
$773$	3845.43	−	6660.48i	0.178927	−	0.309911i	−0.762586	−	0.646886i	$-0.776071\pi$
$773$	3845.43	−	6660.48i	0.178927	−	0.309911i	0.941513	+	0.336976i	$0.109404\pi$
$774$		0			0
$775$	−10587.4	+	18338.0i	−0.490725	+	0.849960i
$776$		0			0
$777$	1457.06	+	2523.70i	0.0672737	+	0.116521i
$778$		0			0
$779$	11811.5	−	15935.3i	0.543249	−	0.732918i
$780$		0			0
$781$	13523.4	+	23423.1i	0.619595	+	1.07317i
$782$		0			0
$783$	5626.84	−	9745.98i	0.256816	−	0.444819i
$784$		0			0
$785$	2892.76	−	5010.41i	0.131525	−	0.227808i
$786$		0			0
$787$	−35522.4			−1.60894			−0.804472	−	0.593991i	$-0.797551\pi$
$787$	−35522.4			−1.60894			−0.804472	+	0.593991i	$0.797551\pi$
$788$		0			0
$789$	−1374.80	+	2381.22i	−0.0620330	+	0.107444i
$790$		0			0
$791$	−39257.2			−1.76463
$792$		0			0
$793$	−13840.8	−	23973.0i	−0.619801	−	1.07353i
$794$		0			0
$795$	−8.84266	−	15.3159i	−0.000394487	−	0.000683271i
$796$		0			0
$797$	−26754.4			−1.18907			−0.594536	−	0.804069i	$-0.702664\pi$
$797$	−26754.4			−1.18907			−0.594536	+	0.804069i	$0.702664\pi$
$798$		0			0
$799$	940.111			0.0416255
$800$		0			0
$801$	13063.0	+	22625.8i	0.576229	+	0.998058i
$802$		0			0
$803$	−2242.01	−	3883.28i	−0.0985291	−	0.170657i
$804$		0			0
$805$	−8002.75			−0.350385
$806$		0			0
$807$	−615.807	+	1066.61i	−0.0268617	+	0.0465259i
$808$		0			0
$809$	−16837.1			−0.731721			−0.365861	−	0.930670i	$-0.619225\pi$
$809$	−16837.1			−0.731721			−0.365861	+	0.930670i	$0.619225\pi$
$810$		0			0
$811$	5557.32	−	9625.57i	0.240621	−	0.416769i	−0.720270	−	0.693694i	$-0.755982\pi$
$811$	5557.32	−	9625.57i	0.240621	−	0.416769i	0.960891	+	0.276925i	$0.0893154\pi$
$812$		0			0
$813$	249.857	−	432.765i	0.0107784	−	0.0186688i
$814$		0			0
$815$	10219.5	+	17700.7i	0.439231	+	0.760770i
$816$		0			0
$817$	−7319.08	+	9874.44i	−0.313418	+	0.422843i
$818$		0			0
$819$	−8601.63	−	14898.5i	−0.366990	−	0.635646i
$820$		0			0
$821$	−15815.2	+	27392.7i	−0.672294	+	1.16445i	0.304958	+	0.952366i	$0.401358\pi$
$821$	−15815.2	+	27392.7i	−0.672294	+	1.16445i	−0.977252	+	0.212082i	$0.931976\pi$
$822$		0			0
$823$	6549.70	−	11344.4i	0.277410	−	0.480487i	−0.693331	−	0.720620i	$-0.743857\pi$
$823$	6549.70	−	11344.4i	0.277410	−	0.480487i	0.970740	+	0.240132i	$0.0771908\pi$
$824$		0			0
$825$	−5134.49			−0.216679
$826$		0			0
$827$	2048.08	−	3547.37i	0.0861168	−	0.149159i	−0.819750	−	0.572722i	$-0.805888\pi$
$827$	2048.08	−	3547.37i	0.0861168	−	0.149159i	0.905867	+	0.423563i	$0.139221\pi$
$828$		0			0
$829$	36021.5			1.50914			0.754571	−	0.656218i	$-0.227845\pi$
$829$	36021.5			1.50914			0.754571	+	0.656218i	$0.227845\pi$
$830$		0			0
$831$	−5872.67	−	10171.8i	−0.245151	−	0.424614i
$832$		0			0
$833$	−51.3974	−	89.0228i	−0.00213783	−	0.00370283i
$834$		0			0
$835$	19494.6			0.807949
$836$		0			0
$837$	19600.5			0.809431
$838$		0			0
$839$	−14895.4	−	25799.5i	−0.612926	−	1.06162i	−0.990745	−	0.135740i	$-0.956659\pi$
$839$	−14895.4	−	25799.5i	−0.612926	−	1.06162i	0.377818	−	0.925880i	$-0.376674\pi$
$840$		0			0
$841$	4840.33	+	8383.70i	0.198464	+	0.343749i
$842$		0			0
$843$	−13938.0			−0.569455
$844$		0			0
$845$	−1896.35	+	3284.57i	−0.0772028	+	0.133719i
$846$		0			0
$847$	−10558.0			−0.428309
$848$		0			0
$849$	6242.62	−	10812.5i	0.252351	−	0.437085i
$850$		0			0
$851$	3466.00	−	6003.28i	0.139616	−	0.241821i
$852$		0			0
$853$	−1449.22	−	2510.13i	−0.0581717	−	0.100756i	0.835473	−	0.549531i	$-0.185194\pi$
$853$	−1449.22	−	2510.13i	−0.0581717	−	0.100756i	−0.893645	+	0.448775i	$0.851860\pi$
$854$		0			0
$855$	3877.43	+	8937.25i	0.155094	+	0.357482i
$856$		0			0
$857$	5287.30	+	9157.87i	0.210748	+	0.365026i	0.951949	−	0.306257i	$-0.0990769\pi$
$857$	5287.30	+	9157.87i	0.210748	+	0.365026i	−0.741201	+	0.671283i	$0.765744\pi$
$858$		0			0
$859$	15167.7	−	26271.3i	0.602464	−	1.04350i	−0.389983	−	0.920822i	$-0.627519\pi$
$859$	15167.7	−	26271.3i	0.602464	−	1.04350i	0.992447	−	0.122676i	$-0.0391476\pi$
$860$		0			0
$861$	−4215.13	+	7300.83i	−0.166843	+	0.288980i
$862$		0			0
$863$	41423.4			1.63391			0.816957	−	0.576699i	$-0.195659\pi$
$863$	41423.4			1.63391			0.816957	+	0.576699i	$0.195659\pi$
$864$		0			0
$865$	−7507.79	+	13003.9i	−0.295113	+	0.511150i
$866$		0			0
$867$	−8973.52			−0.351507
$868$		0			0
$869$	−5551.43	−	9615.35i	−0.216708	−	0.375349i
$870$		0			0
$871$	−4411.34	−	7640.67i	−0.171610	−	0.297238i
$872$		0			0
$873$	−18527.7			−0.718289
$874$		0			0
$875$	21528.6			0.831769
$876$		0			0
$877$	13974.4	+	24204.4i	0.538064	+	0.931955i	0.999008	+	0.0445255i	$0.0141776\pi$
$877$	13974.4	+	24204.4i	0.538064	+	0.931955i	−0.460944	+	0.887429i	$0.652489\pi$
$878$		0			0
$879$	−1353.15	−	2343.73i	−0.0519234	−	0.0899339i
$880$		0			0
$881$	23632.4			0.903739			0.451870	−	0.892084i	$-0.350757\pi$
$881$	23632.4			0.903739			0.451870	+	0.892084i	$0.350757\pi$
$882$		0			0
$883$	3447.82	−	5971.80i	0.131402	−	0.227596i	−0.792815	−	0.609462i	$-0.791385\pi$
$883$	3447.82	−	5971.80i	0.131402	−	0.227596i	0.924217	+	0.381867i	$0.124719\pi$
$884$		0			0
$885$	2367.68			0.0899307
$886$		0			0
$887$	−2749.51	+	4762.29i	−0.104081	+	0.180273i	−0.913362	−	0.407148i	$-0.866523\pi$
$887$	−2749.51	+	4762.29i	−0.104081	+	0.180273i	0.809282	+	0.587421i	$0.199857\pi$
$888$		0			0
$889$	12987.1	−	22494.4i	0.489960	−	0.848636i
$890$		0			0
$891$	−6545.70	−	11337.5i	−0.246116	−	0.426285i
$892$		0			0
$893$	−19589.2	−	2247.97i	−0.734073	−	0.0842389i
$894$		0			0
$895$	−7104.10	−	12304.7i	−0.265323	−	0.459553i
$896$		0			0
$897$	2905.55	−	5032.56i	0.108153	−	0.187327i
$898$		0			0
$899$	12808.8	−	22185.4i	0.475190	−	0.823053i
$900$		0			0
$901$	−7.66025			−0.000283241
$902$		0			0
$903$	2611.94	−	4524.01i	0.0962567	−	0.166722i
$904$		0			0
$905$	5889.22			0.216314
$906$		0			0
$907$	21390.8	+	37050.0i	0.783098	+	1.35637i	0.930129	+	0.367234i	$0.119695\pi$
$907$	21390.8	+	37050.0i	0.783098	+	1.35637i	−0.147031	+	0.989132i	$0.546972\pi$
$908$		0			0
$909$	22322.6	+	38663.8i	0.814513	+	1.41078i
$910$		0			0
$911$	29902.9			1.08752			0.543758	−	0.839242i	$-0.317001\pi$
$911$	29902.9			1.08752			0.543758	+	0.839242i	$0.317001\pi$
$912$		0			0
$913$	−12891.1			−0.467286
$914$		0			0
$915$	−3331.22	−	5769.84i	−0.120357	−	0.208465i
$916$		0			0
$917$	4271.34	+	7398.17i	0.153819	+	0.266422i
$918$		0			0
$919$	−1181.94			−0.0424250			−0.0212125	−	0.999775i	$-0.506753\pi$
$919$	−1181.94			−0.0424250			−0.0212125	+	0.999775i	$0.506753\pi$
$920$		0			0
$921$	−5059.91	+	8764.03i	−0.181031	+	0.313555i
$922$		0			0
$923$	36648.9			1.30695
$924$		0			0
$925$	−4149.67	+	7187.43i	−0.147503	+	0.255482i
$926$		0			0
$927$	−8559.32	+	14825.2i	−0.303263	+	0.525267i
$928$		0			0
$929$	−9443.84	−	16357.2i	−0.333522	−	0.577678i	0.649678	−	0.760210i	$-0.274904\pi$
$929$	−9443.84	−	16357.2i	−0.333522	−	0.577678i	−0.983200	+	0.182532i	$0.941571\pi$
$930$		0			0
$931$	858.102	+	1977.88i	0.0302075	+	0.0696265i
$932$		0			0
$933$	3292.84	+	5703.36i	0.115544	+	0.200128i
$934$		0			0
$935$	274.590	−	475.603i	0.00960432	−	0.0166352i
$936$		0			0
$937$	−15839.3	+	27434.5i	−0.552238	+	0.956505i	0.445874	+	0.895096i	$0.352893\pi$
$937$	−15839.3	+	27434.5i	−0.552238	+	0.956505i	−0.998113	+	0.0614093i	$0.980441\pi$
$938$		0			0
$939$	6089.92			0.211647
$940$		0			0
$941$	14652.2	−	25378.3i	0.507596	−	0.879181i	−0.492366	−	0.870388i	$-0.663868\pi$
$941$	14652.2	−	25378.3i	0.507596	−	0.879181i	0.999961	−	0.00879302i	$-0.00279894\pi$
$942$		0			0
$943$	20053.6			0.692509
$944$		0			0
$945$	−4434.47	−	7680.73i	−0.152649	−	0.264396i
$946$		0			0
$947$	−13375.1	−	23166.4i	−0.458957	−	0.794937i	0.539949	−	0.841698i	$-0.318444\pi$
$947$	−13375.1	−	23166.4i	−0.458957	−	0.794937i	−0.998906	+	0.0467607i	$0.985110\pi$
$948$		0			0
$949$	−6075.94			−0.207833
$950$		0			0
$951$	−15563.1			−0.530672
$952$		0			0
$953$	−24597.2	−	42603.7i	−0.836078	−	1.44813i	−0.893150	−	0.449760i	$-0.851510\pi$
$953$	−24597.2	−	42603.7i	−0.836078	−	1.44813i	0.0570714	−	0.998370i	$-0.481824\pi$
$954$		0			0
$955$	−3140.62	−	5439.71i	−0.106417	−	0.184319i
$956$		0			0
$957$	6211.75			0.209820
$958$		0			0
$959$	17306.3	−	29975.4i	0.582742	−	1.00934i
$960$		0			0
$961$	14827.0			0.497701
$962$		0			0
$963$	−6033.34	+	10450.0i	−0.201892	+	0.349686i
$964$		0			0
$965$	8926.20	−	15460.6i	0.297766	−	0.515746i
$966$		0			0
$967$	4740.00	+	8209.92i	0.157630	+	0.273023i	0.934014	−	0.357238i	$-0.116281\pi$
$967$	4740.00	+	8209.92i	0.157630	+	0.273023i	−0.776384	+	0.630261i	$0.782948\pi$
$968$		0			0
$969$	−595.303	−	68.3144i	−0.0197357	−	0.00226478i
$970$		0			0
$971$	−9646.86	−	16708.9i	−0.318829	−	0.552227i	0.661415	−	0.750020i	$-0.269956\pi$
$971$	−9646.86	−	16708.9i	−0.318829	−	0.552227i	−0.980244	+	0.197793i	$0.936623\pi$
$972$		0			0
$973$	3285.86	−	5691.27i	0.108263	−	0.187517i
$974$		0			0
$975$	−3478.67	+	6025.24i	−0.114263	+	0.197910i
$976$		0			0
$977$	23348.2			0.764559			0.382279	−	0.924047i	$-0.375139\pi$
$977$	23348.2			0.764559			0.382279	+	0.924047i	$0.375139\pi$
$978$		0			0
$979$	−15444.8	+	26751.2i	−0.504207	+	0.873312i
$980$		0			0
$981$	29995.3			0.976225
$982$		0			0
$983$	19310.9	+	33447.4i	0.626573	+	1.08526i	0.988234	+	0.152947i	$0.0488763\pi$
$983$	19310.9	+	33447.4i	0.626573	+	1.08526i	−0.361662	+	0.932309i	$0.617790\pi$
$984$		0			0
$985$	4890.96	+	8471.39i	0.158212	+	0.274031i
$986$		0			0
$987$	8380.22			0.270259
$988$		0			0
$989$	−12426.4			−0.399531
$990$		0			0
$991$	−14381.5	−	24909.5i	−0.460993	−	0.798464i	0.538018	−	0.842934i	$-0.319173\pi$
$991$	−14381.5	−	24909.5i	−0.460993	−	0.798464i	−0.999011	+	0.0444700i	$0.985840\pi$
$992$		0			0
$993$	−5949.02	−	10304.0i	−0.190117	−	0.329293i
$994$		0			0
$995$	−24926.3			−0.794188
$996$		0			0
$997$	−12175.1	+	21087.9i	−0.386750	+	0.669870i	−0.992010	−	0.126157i	$-0.959736\pi$
$997$	−12175.1	+	21087.9i	−0.386750	+	0.669870i	0.605261	+	0.796027i	$0.293069\pi$
$998$		0			0
$999$	7682.29			0.243300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.e.a.45.2	✓	10
3.2	odd	2		684.4.k.c.577.2		10
4.3	odd	2		304.4.i.f.273.4		10
19.7	even	3		1444.4.a.f.1.4		5
19.11	even	3	inner	76.4.e.a.49.2	yes	10
19.12	odd	6		1444.4.a.g.1.2		5
57.11	odd	6		684.4.k.c.505.2		10
76.11	odd	6		304.4.i.f.49.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.e.a.45.2	✓	10	1.1	even	1	trivial
76.4.e.a.49.2	yes	10	19.11	even	3	inner
304.4.i.f.49.4		10	76.11	odd	6
304.4.i.f.273.4		10	4.3	odd	2
684.4.k.c.505.2		10	57.11	odd	6
684.4.k.c.577.2		10	3.2	odd	2
1444.4.a.f.1.4		5	19.7	even	3
1444.4.a.g.1.2		5	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.916150 - 1.58682i) q^{3} +(2.48769 + 4.30880i) q^{5} +19.2102 q^{7} +(11.8213 - 20.4752i) q^{9} +O(q^{10})\)	\(q+(-0.916150 - 1.58682i) q^{3} +(2.48769 + 4.30880i) q^{5} +19.2102 q^{7} +(11.8213 - 20.4752i) q^{9} +27.9535 q^{11} +(18.9388 - 32.8029i) q^{13} +(4.55819 - 7.89502i) q^{15} +(-1.97434 - 3.41966i) q^{17} +(32.9626 + 75.9768i) q^{19} +(-17.5994 - 30.4831i) q^{21} +(-41.8650 + 72.5122i) q^{23} +(50.1228 - 86.8152i) q^{25} -92.7926 q^{27} +(-60.6390 + 105.030i) q^{29} -211.230 q^{31} +(-25.6096 - 44.3571i) q^{33} +(47.7891 + 82.7731i) q^{35} -82.7900 q^{37} -69.4030 q^{39} +(-119.752 - 207.416i) q^{41} +(74.2051 + 128.527i) q^{43} +117.631 q^{45} +(-119.041 + 206.185i) q^{47} +26.0326 q^{49} +(-3.61759 + 6.26584i) q^{51} +(0.969975 - 1.68005i) q^{53} +(69.5395 + 120.446i) q^{55} +(90.3627 - 121.912i) q^{57} +(129.859 + 224.922i) q^{59} +(365.410 - 632.909i) q^{61} +(227.091 - 393.332i) q^{63} +188.455 q^{65} +(116.463 - 201.720i) q^{67} +153.418 q^{69} +(483.781 + 837.933i) q^{71} +(-80.2051 - 138.919i) q^{73} -183.680 q^{75} +536.992 q^{77} +(-198.595 - 343.977i) q^{79} +(-234.164 - 405.584i) q^{81} -461.162 q^{83} +(9.82310 - 17.0141i) q^{85} +222.218 q^{87} +(-552.519 + 956.991i) q^{89} +(363.818 - 630.151i) q^{91} +(193.518 + 335.183i) q^{93} +(-245.368 + 331.036i) q^{95} +(-391.827 - 678.664i) q^{97} +(330.447 - 572.352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9}+O(q^{10}) \) 10 * q + 7 * q^3 - 4 * q^5 - 20 * q^7 - 50 * q^9	\( 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9} - 50 q^{11} - 56 q^{13} + 10 q^{15} + 32 q^{17} + 77 q^{19} + 126 q^{21} + 184 q^{23} - 121 q^{25} - 218 q^{27} + 352 q^{29} + 264 q^{31} + 83 q^{33} - 132 q^{35} - 640 q^{37} - 324 q^{39} - 57 q^{41} - 528 q^{43} - 232 q^{45} - 434 q^{47} + 2138 q^{49} - 242 q^{51} + 780 q^{53} + 598 q^{55} + 1482 q^{57} - 343 q^{59} + 536 q^{61} - 1568 q^{63} - 1988 q^{65} + 779 q^{67} - 1156 q^{69} + 474 q^{71} + 1453 q^{73} - 2994 q^{75} - 2956 q^{77} - 1968 q^{79} - 1097 q^{81} - 698 q^{83} - 2334 q^{85} + 8372 q^{87} + 380 q^{89} + 1348 q^{91} + 1684 q^{93} + 4312 q^{95} + 883 q^{97} + 5230 q^{99}+O(q^{100}) \) 10 * q + 7 * q^3 - 4 * q^5 - 20 * q^7 - 50 * q^9 - 50 * q^11 - 56 * q^13 + 10 * q^15 + 32 * q^17 + 77 * q^19 + 126 * q^21 + 184 * q^23 - 121 * q^25 - 218 * q^27 + 352 * q^29 + 264 * q^31 + 83 * q^33 - 132 * q^35 - 640 * q^37 - 324 * q^39 - 57 * q^41 - 528 * q^43 - 232 * q^45 - 434 * q^47 + 2138 * q^49 - 242 * q^51 + 780 * q^53 + 598 * q^55 + 1482 * q^57 - 343 * q^59 + 536 * q^61 - 1568 * q^63 - 1988 * q^65 + 779 * q^67 - 1156 * q^69 + 474 * q^71 + 1453 * q^73 - 2994 * q^75 - 2956 * q^77 - 1968 * q^79 - 1097 * q^81 - 698 * q^83 - 2334 * q^85 + 8372 * q^87 + 380 * q^89 + 1348 * q^91 + 1684 * q^93 + 4312 * q^95 + 883 * q^97 + 5230 * q^99

Introduction

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