LMFDB - Embedded newform 308.2.w.a.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(13,308)]

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, 5, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("308.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.w (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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	308.41
Dual form			308.2.w.a.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51783 - 0.493173i) q^{3} +(0.260986 - 0.359216i) q^{5} +(1.55179 + 2.14288i) q^{7} +(-0.366459 + 0.266248i) q^{9} +(2.44672 + 2.23910i) q^{11} +(2.91934 - 2.12103i) q^{13} +(0.218977 - 0.673941i) q^{15} +(-1.73549 - 1.26091i) q^{17} +(-2.60996 - 8.03264i) q^{19} +(3.41217 + 2.48723i) q^{21} +1.73292 q^{23} +(1.48416 + 4.56778i) q^{25} +(-3.23913 + 4.45828i) q^{27} +(-6.19038 - 2.01138i) q^{29} +(-2.85173 - 3.92507i) q^{31} +(4.81797 + 2.19192i) q^{33} +(1.17475 + 0.00183136i) q^{35} +(0.305486 - 0.940189i) q^{37} +(3.38504 - 4.65910i) q^{39} +(2.71242 + 8.34796i) q^{41} -4.32100i q^{43} +0.201125i q^{45} +(-6.63136 + 2.15466i) q^{47} +(-2.18387 + 6.65062i) q^{49} +(-3.25602 - 1.05795i) q^{51} +(-7.09454 + 5.15449i) q^{53} +(1.44288 - 0.294528i) q^{55} +(-7.92297 - 10.9050i) q^{57} +(10.2903 + 3.34352i) q^{59} +(-5.62339 - 4.08563i) q^{61} +(-1.13921 - 0.372115i) q^{63} -1.60223i q^{65} +11.4870 q^{67} +(2.63028 - 0.854629i) q^{69} +(-10.6035 - 7.70387i) q^{71} +(-2.23211 + 6.86973i) q^{73} +(4.50542 + 6.20117i) q^{75} +(-1.00131 + 8.71765i) q^{77} +(-5.15765 - 7.09890i) q^{79} +(-2.29782 + 7.07198i) q^{81} +(-12.6408 - 9.18404i) q^{83} +(-0.905876 + 0.294337i) q^{85} -10.3879 q^{87} -3.04406i q^{89} +(9.07533 + 2.96440i) q^{91} +(-6.26418 - 4.55119i) q^{93} +(-3.56662 - 1.15887i) q^{95} +(0.726346 + 0.999730i) q^{97} +(-1.49278 - 0.169103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{7} + 14 q^{9} - 4 q^{11} - 6 q^{15} + 4 q^{23} + 32 q^{25} - 20 q^{29} + 15 q^{35} - 28 q^{37} - 20 q^{39} - 15 q^{49} + 60 q^{51} - 56 q^{53} + 80 q^{57} - 80 q^{63} - 88 q^{67} + 32 q^{71}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q - 5 * q^7 + 14 * q^9 - 4 * q^11 - 6 * q^15 + 4 * q^23 + 32 * q^25 - 20 * q^29 + 15 * q^35 - 28 * q^37 - 20 * q^39 - 15 * q^49 + 60 * q^51 - 56 * q^53 + 80 * q^57 - 80 * q^63 - 88 * q^67 + 32 * q^71 - 37 * q^77 - 30 * q^79 - 66 * q^81 + 10 * q^85 - 49 * q^91 - 22 * q^93 - 50 * q^95 + 64 * q^99

Character values

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

$n$	$45$	$57$	$155$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	1.51783	−	0.493173i	0.876320	−	0.284734i	0.163892	−	0.986478i	$-0.447595\pi$
$3$	1.51783	−	0.493173i	0.876320	−	0.284734i	0.712429	+	0.701745i	$0.247595\pi$
$4$		0			0
$5$	0.260986	−	0.359216i	0.116716	−	0.160646i	−0.746661	−	0.665204i	$-0.768344\pi$
$5$	0.260986	−	0.359216i	0.116716	−	0.160646i	0.863378	+	0.504558i	$0.168344\pi$
$6$		0			0
$7$	1.55179	+	2.14288i	0.586523	+	0.809932i
$7$	1.55179	+	2.14288i	0.586523	+	0.809932i
$8$		0			0
$9$	−0.366459	+	0.266248i	−0.122153	+	0.0887493i
$10$		0			0
$11$	2.44672	+	2.23910i	0.737714	+	0.675114i
$11$	2.44672	+	2.23910i	0.737714	+	0.675114i
$12$		0			0
$13$	2.91934	−	2.12103i	0.809680	−	0.588267i	−0.104058	−	0.994571i	$-0.533183\pi$
$13$	2.91934	−	2.12103i	0.809680	−	0.588267i	0.913738	+	0.406304i	$0.133183\pi$
$14$		0			0
$15$	0.218977	−	0.673941i	0.0565396	−	0.174011i
$16$		0			0
$17$	−1.73549	−	1.26091i	−0.420917	−	0.305814i	0.357089	−	0.934070i	$-0.383769\pi$
$17$	−1.73549	−	1.26091i	−0.420917	−	0.305814i	−0.778007	+	0.628256i	$0.783769\pi$
$18$		0			0
$19$	−2.60996	−	8.03264i	−0.598767	−	1.84282i	−0.535003	−	0.844850i	$-0.679690\pi$
$19$	−2.60996	−	8.03264i	−0.598767	−	1.84282i	−0.0637637	−	0.997965i	$-0.520310\pi$
$20$		0			0
$21$	3.41217	+	2.48723i	0.744597	+	0.542757i
$22$		0			0
$23$	1.73292			0.361338			0.180669	−	0.983544i	$-0.442174\pi$
$23$	1.73292			0.361338			0.180669	+	0.983544i	$0.442174\pi$
$24$		0			0
$25$	1.48416	+	4.56778i	0.296832	+	0.913556i
$26$		0			0
$27$	−3.23913	+	4.45828i	−0.623371	+	0.857996i
$28$		0			0
$29$	−6.19038	−	2.01138i	−1.14952	−	0.373503i	−0.328560	−	0.944483i	$-0.606563\pi$
$29$	−6.19038	−	2.01138i	−1.14952	−	0.373503i	−0.820964	+	0.570980i	$0.806563\pi$
$30$		0			0
$31$	−2.85173	−	3.92507i	−0.512186	−	0.704963i	0.472100	−	0.881545i	$-0.343496\pi$
$31$	−2.85173	−	3.92507i	−0.512186	−	0.704963i	−0.984286	+	0.176582i	$0.943496\pi$
$32$		0			0
$33$	4.81797	+	2.19192i	0.838701	+	0.381564i
$34$		0			0
$35$	1.17475	+	0.00183136i	0.198570	+	0.000309556i
$36$		0			0
$37$	0.305486	−	0.940189i	0.0502216	−	0.154566i	−0.922801	−	0.385278i	$-0.874106\pi$
$37$	0.305486	−	0.940189i	0.0502216	−	0.154566i	0.973022	+	0.230712i	$0.0741055\pi$
$38$		0			0
$39$	3.38504	−	4.65910i	0.542040	−	0.746054i
$40$		0			0
$41$	2.71242	+	8.34796i	0.423608	+	1.30373i	0.904321	+	0.426854i	$0.140378\pi$
$41$	2.71242	+	8.34796i	0.423608	+	1.30373i	−0.480712	+	0.876878i	$0.659622\pi$
$42$		0			0
$43$		−	4.32100i		−	0.658946i	−0.944165	−	0.329473i	$-0.893129\pi$
$43$		−	4.32100i		−	0.658946i	0.944165	−	0.329473i	$-0.106871\pi$
$44$		0			0
$45$			0.201125i			0.0299819i
$46$		0			0
$47$	−6.63136	+	2.15466i	−0.967284	+	0.314289i	−0.749719	−	0.661756i	$-0.769811\pi$
$47$	−6.63136	+	2.15466i	−0.967284	+	0.314289i	−0.217565	+	0.976046i	$0.569811\pi$
$48$		0			0
$49$	−2.18387	+	6.65062i	−0.311981	+	0.950088i
$50$		0			0
$51$	−3.25602	−	1.05795i	−0.455934	−	0.148142i
$52$		0			0
$53$	−7.09454	+	5.15449i	−0.974510	+	0.708023i	−0.956475	−	0.291814i	$-0.905741\pi$
$53$	−7.09454	+	5.15449i	−0.974510	+	0.708023i	−0.0180352	+	0.999837i	$0.505741\pi$
$54$		0			0
$55$	1.44288	−	0.294528i	0.194558	−	0.0397142i
$56$		0			0
$57$	−7.92297	−	10.9050i	−1.04942	−	1.44441i
$58$		0			0
$59$	10.2903	+	3.34352i	1.33968	+	0.435289i	0.889209	−	0.457500i	$-0.151255\pi$
$59$	10.2903	+	3.34352i	1.33968	+	0.435289i	0.450474	+	0.892790i	$0.351255\pi$
$60$		0			0
$61$	−5.62339	−	4.08563i	−0.720001	−	0.523112i	0.166383	−	0.986061i	$-0.446791\pi$
$61$	−5.62339	−	4.08563i	−0.720001	−	0.523112i	−0.886385	+	0.462949i	$0.846791\pi$
$62$		0			0
$63$	−1.13921	−	0.372115i	−0.143526	−	0.0468821i
$64$		0			0
$65$		−	1.60223i		−	0.198733i
$66$		0			0
$67$	11.4870			1.40336			0.701682	−	0.712491i	$-0.252433\pi$
$67$	11.4870			1.40336			0.701682	+	0.712491i	$0.252433\pi$
$68$		0			0
$69$	2.63028	−	0.854629i	0.316648	−	0.102885i
$70$		0			0
$71$	−10.6035	−	7.70387i	−1.25840	−	0.914282i	−0.259723	−	0.965683i	$-0.583631\pi$
$71$	−10.6035	−	7.70387i	−1.25840	−	0.914282i	−0.998678	+	0.0514017i	$0.983631\pi$
$72$		0			0
$73$	−2.23211	+	6.86973i	−0.261249	+	0.804041i	0.731285	+	0.682072i	$0.238921\pi$
$73$	−2.23211	+	6.86973i	−0.261249	+	0.804041i	−0.992534	+	0.121969i	$0.961079\pi$
$74$		0			0
$75$	4.50542	+	6.20117i	0.520241	+	0.716050i
$76$		0			0
$77$	−1.00131	+	8.71765i	−0.114110	+	0.993468i
$78$		0			0
$79$	−5.15765	−	7.09890i	−0.580281	−	0.798688i	0.413445	−	0.910529i	$-0.364325\pi$
$79$	−5.15765	−	7.09890i	−0.580281	−	0.798688i	−0.993726	+	0.111841i	$0.964325\pi$
$80$		0			0
$81$	−2.29782	+	7.07198i	−0.255314	+	0.785775i
$82$		0			0
$83$	−12.6408	−	9.18404i	−1.38750	−	1.00808i	−0.996134	−	0.0878459i	$-0.972002\pi$
$83$	−12.6408	−	9.18404i	−1.38750	−	1.00808i	−0.391369	−	0.920234i	$-0.627998\pi$
$84$		0			0
$85$	−0.905876	+	0.294337i	−0.0982560	+	0.0319253i
$86$		0			0
$87$	−10.3879			−1.11370
$88$		0			0
$89$		−	3.04406i		−	0.322670i	−0.986900	−	0.161335i	$-0.948420\pi$
$89$		−	3.04406i		−	0.322670i	0.986900	−	0.161335i	$-0.0515799\pi$
$90$		0			0
$91$	9.07533	+	2.96440i	0.951353	+	0.310754i
$92$		0			0
$93$	−6.26418	−	4.55119i	−0.649565	−	0.471937i
$94$		0			0
$95$	−3.56662	−	1.15887i	−0.365928	−	0.118897i
$96$		0			0
$97$	0.726346	+	0.999730i	0.0737493	+	0.101507i	0.844298	−	0.535874i	$-0.180018\pi$
$97$	0.726346	+	0.999730i	0.0737493	+	0.101507i	−0.770549	+	0.637381i	$0.780018\pi$
$98$		0			0
$99$	−1.49278	−	0.169103i	−0.150030	−	0.0169955i
$100$		0			0
$101$	−5.28642	+	3.84081i	−0.526018	+	0.382175i	−0.818866	−	0.573984i	$-0.805397\pi$
$101$	−5.28642	+	3.84081i	−0.526018	+	0.382175i	0.292848	+	0.956159i	$0.405397\pi$
$102$		0			0
$103$	6.52767	+	2.12097i	0.643190	+	0.208985i	0.612409	−	0.790541i	$-0.290201\pi$
$103$	6.52767	+	2.12097i	0.643190	+	0.208985i	0.0307811	+	0.999526i	$0.490201\pi$
$104$		0			0
$105$	1.78398	−	0.576578i	0.174099	−	0.0562682i
$106$		0			0
$107$	−4.19341	+	1.36252i	−0.405392	+	0.131720i	−0.504613	−	0.863346i	$-0.668365\pi$
$107$	−4.19341	+	1.36252i	−0.405392	+	0.131720i	0.0992212	+	0.995065i	$0.468365\pi$
$108$		0			0
$109$			2.33520i			0.223671i	0.993727	+	0.111836i	$0.0356730\pi$
$109$			2.33520i			0.223671i	−0.993727	+	0.111836i	$0.964327\pi$
$110$		0			0
$111$		−	1.57771i		−	0.149749i
$112$		0			0
$113$	−0.309026	−	0.951085i	−0.0290707	−	0.0894705i	0.935468	−	0.353410i	$-0.114978\pi$
$113$	−0.309026	−	0.951085i	−0.0290707	−	0.0894705i	−0.964539	+	0.263940i	$0.914978\pi$
$114$		0			0
$115$	0.452267	−	0.622492i	0.0421741	−	0.0580477i
$116$		0			0
$117$	−0.505100	+	1.55454i	−0.0466965	+	0.143717i
$118$		0			0
$119$	0.00884787	−	5.67561i	0.000811083	−	0.520282i
$120$		0			0
$121$	0.972876	+	10.9569i	0.0884433	+	0.996081i
$122$		0			0
$123$	8.23398	+	11.3331i	0.742433	+	1.02187i
$124$		0			0
$125$	4.13959	+	1.34503i	0.370256	+	0.120303i
$126$		0			0
$127$	11.3191	−	15.5794i	1.00440	−	1.38244i	0.0818207	−	0.996647i	$-0.473927\pi$
$127$	11.3191	−	15.5794i	1.00440	−	1.38244i	0.922584	−	0.385797i	$-0.126073\pi$
$128$		0			0
$129$	−2.13100	−	6.55855i	−0.187624	−	0.577448i
$130$		0			0
$131$	8.11514			0.709023			0.354512	−	0.935052i	$-0.384647\pi$
$131$	8.11514			0.709023			0.354512	+	0.935052i	$0.384647\pi$
$132$		0			0
$133$	13.1629	−	18.0579i	1.14136	−	1.56581i
$134$		0			0
$135$	0.756120	+	2.32710i	0.0650764	+	0.200285i
$136$		0			0
$137$	4.69203	+	3.40896i	0.400867	+	0.291247i	0.769894	−	0.638172i	$-0.220309\pi$
$137$	4.69203	+	3.40896i	0.400867	+	0.291247i	−0.369027	+	0.929419i	$0.620309\pi$
$138$		0			0
$139$	2.50684	−	7.71526i	0.212627	−	0.654399i	−0.786686	−	0.617353i	$-0.788205\pi$
$139$	2.50684	−	7.71526i	0.212627	−	0.654399i	0.999314	−	0.0370465i	$-0.0117950\pi$
$140$		0			0
$141$	−9.00267	+	6.54082i	−0.758161	+	0.550837i
$142$		0			0
$143$	11.8920	+	1.34714i	0.994460	+	0.112653i
$144$		0			0
$145$	−2.33812	+	1.69874i	−0.194170	+	0.141073i
$146$		0			0
$147$	−0.0348314	+	11.1715i	−0.00287284	+	0.921413i
$148$		0			0
$149$	7.95668	−	10.9514i	0.651836	−	0.897176i	−0.347340	−	0.937739i	$-0.612915\pi$
$149$	7.95668	−	10.9514i	0.651836	−	0.897176i	0.999177	+	0.0405631i	$0.0129152\pi$
$150$		0			0
$151$	10.2668	−	3.33588i	0.835498	−	0.271470i	0.140138	−	0.990132i	$-0.455245\pi$
$151$	10.2668	−	3.33588i	0.835498	−	0.271470i	0.695359	+	0.718662i	$0.255245\pi$
$152$		0			0
$153$	0.971698			0.0785571
$154$		0			0
$155$	−2.15421			−0.173030
$156$		0			0
$157$	15.4769	−	5.02875i	1.23519	−	0.401338i	0.382599	−	0.923914i	$-0.375029\pi$
$157$	15.4769	−	5.02875i	1.23519	−	0.401338i	0.852593	+	0.522576i	$0.175029\pi$
$158$		0			0
$159$	−8.22626	+	11.3225i	−0.652385	+	0.897931i
$160$		0			0
$161$	2.68913	+	3.71343i	0.211933	+	0.292660i
$162$		0			0
$163$	3.86774	−	2.81008i	0.302945	−	0.220102i	−0.425919	−	0.904761i	$-0.640049\pi$
$163$	3.86774	−	2.81008i	0.302945	−	0.220102i	0.728863	+	0.684659i	$0.240049\pi$
$164$		0			0
$165$	2.04480	−	1.15863i	0.159187	−	0.0901996i
$166$		0			0
$167$	−1.74020	+	1.26433i	−0.134661	+	0.0978367i	−0.653076	−	0.757292i	$-0.726522\pi$
$167$	−1.74020	+	1.26433i	−0.134661	+	0.0978367i	0.518416	+	0.855129i	$0.326522\pi$
$168$		0			0
$169$	0.00659036	−	0.0202831i	0.000506951	−	0.00156024i
$170$		0			0
$171$	3.09512	+	2.24874i	0.236690	+	0.171965i
$172$		0			0
$173$	5.67980	+	17.4806i	0.431827	+	1.32903i	0.896303	+	0.443442i	$0.146243\pi$
$173$	5.67980	+	17.4806i	0.431827	+	1.32903i	−0.464476	+	0.885586i	$0.653757\pi$
$174$		0			0
$175$	−7.48509	+	10.2686i	−0.565820	+	0.776236i
$176$		0			0
$177$	17.2679			1.29793
$178$		0			0
$179$	4.86637	+	14.9771i	0.363730	+	1.11944i	0.950773	+	0.309889i	$0.100292\pi$
$179$	4.86637	+	14.9771i	0.363730	+	1.11944i	−0.587043	+	0.809556i	$0.699708\pi$
$180$		0			0
$181$	2.36514	−	3.25534i	0.175800	−	0.241968i	−0.712020	−	0.702159i	$-0.752219\pi$
$181$	2.36514	−	3.25534i	0.175800	−	0.241968i	0.887820	+	0.460192i	$0.152219\pi$
$182$		0			0
$183$	−10.5503	−	3.42800i	−0.779900	−	0.253405i
$184$		0			0
$185$	−0.258004	−	0.355112i	−0.0189688	−	0.0261083i
$186$		0			0
$187$	−1.42296	−	6.97101i	−0.104057	−	0.509771i
$188$		0			0
$189$	−14.5800	−	0.0227292i	−1.06054	−	0.00165331i
$190$		0			0
$191$	−3.46219	+	10.6555i	−0.250516	+	0.771008i	0.744165	+	0.667996i	$0.232848\pi$
$191$	−3.46219	+	10.6555i	−0.250516	+	0.771008i	−0.994680	+	0.103011i	$0.967152\pi$
$192$		0			0
$193$	4.05772	−	5.58497i	0.292081	−	0.402015i	−0.637608	−	0.770361i	$-0.720076\pi$
$193$	4.05772	−	5.58497i	0.292081	−	0.402015i	0.929689	+	0.368346i	$0.120076\pi$
$194$		0			0
$195$	−0.790179	−	2.43192i	−0.0565859	−	0.174154i
$196$		0			0
$197$		−	7.21142i		−	0.513792i	−0.966439	−	0.256896i	$-0.917300\pi$
$197$		−	7.21142i		−	0.513792i	0.966439	−	0.256896i	$-0.0826998\pi$
$198$		0			0
$199$		−	11.2445i		−	0.797102i	−0.917146	−	0.398551i	$-0.869513\pi$
$199$		−	11.2445i		−	0.797102i	0.917146	−	0.398551i	$-0.130487\pi$
$200$		0			0
$201$	17.4354	−	5.66509i	1.22980	−	0.399585i
$202$		0			0
$203$	−5.29606	−	16.3865i	−0.371711	−	1.15011i
$204$		0			0
$205$	3.70663	+	1.20436i	0.258882	+	0.0841159i
$206$		0			0
$207$	−0.635043	+	0.461385i	−0.0441385	+	0.0320685i
$208$		0			0
$209$	11.6000	−	25.4976i	0.802391	−	1.76371i
$210$		0			0
$211$	9.47316	+	13.0387i	0.652159	+	0.897620i	0.999190	−	0.0402337i	$-0.0128103\pi$
$211$	9.47316	+	13.0387i	0.652159	+	0.897620i	−0.347031	+	0.937854i	$0.612810\pi$
$212$		0			0
$213$	−19.8936	−	6.46383i	−1.36309	−	0.442894i
$214$		0			0
$215$	−1.55217	−	1.12772i	−0.105857	−	0.0769099i
$216$		0			0
$217$	3.98565	−	12.2018i	0.270564	−	0.828313i
$218$		0			0
$219$			11.5279i			0.778984i
$220$		0			0
$221$	−7.74090			−0.520709
$222$		0			0
$223$	−27.4072	+	8.90514i	−1.83532	+	0.596333i	−0.836493	+	0.547978i	$0.815398\pi$
$223$	−27.4072	+	8.90514i	−1.83532	+	0.596333i	−0.998830	+	0.0483543i	$0.984602\pi$
$224$		0			0
$225$	−1.76005	−	1.27875i	−0.117336	−	0.0852499i
$226$		0			0
$227$	−6.19616	+	19.0698i	−0.411253	+	1.26571i	0.504306	+	0.863525i	$0.331748\pi$
$227$	−6.19616	+	19.0698i	−0.411253	+	1.26571i	−0.915559	+	0.402183i	$0.868252\pi$
$228$		0			0
$229$	1.89669	+	2.61056i	0.125337	+	0.172511i	0.867074	−	0.498179i	$-0.165998\pi$
$229$	1.89669	+	2.61056i	0.125337	+	0.172511i	−0.741737	+	0.670690i	$0.765998\pi$
$230$		0			0
$231$	2.77949	+	13.7257i	0.182877	+	0.903087i
$232$		0			0
$233$	−4.51877	−	6.21955i	−0.296034	−	0.407456i	0.634928	−	0.772571i	$-0.281030\pi$
$233$	−4.51877	−	6.21955i	−0.296034	−	0.407456i	−0.930962	+	0.365115i	$0.881030\pi$
$234$		0			0
$235$	−0.956703	+	2.94443i	−0.0624084	+	0.192073i
$236$		0			0
$237$	−11.3294	−	8.23131i	−0.735925	−	0.534681i
$238$		0			0
$239$	−1.84016	+	0.597905i	−0.119030	+	0.0386752i	−0.367926	−	0.929855i	$-0.619932\pi$
$239$	−1.84016	+	0.597905i	−0.119030	+	0.0386752i	0.248896	+	0.968530i	$0.419932\pi$
$240$		0			0
$241$	13.4236			0.864692			0.432346	−	0.901708i	$-0.357686\pi$
$241$	13.4236			0.864692			0.432346	+	0.901708i	$0.357686\pi$
$242$		0			0
$243$		−	4.66492i		−	0.299255i
$244$		0			0
$245$	1.81905	+	2.52020i	0.116215	+	0.161010i
$246$		0			0
$247$	−24.6568	−	17.9142i	−1.56888	−	1.13986i
$248$		0			0
$249$	−23.7159	−	7.70575i	−1.50293	−	0.488332i
$250$		0			0
$251$	17.4436	+	24.0090i	1.10103	+	1.51544i	0.834014	+	0.551744i	$0.186037\pi$
$251$	17.4436	+	24.0090i	1.10103	+	1.51544i	0.267015	+	0.963692i	$0.413963\pi$
$252$		0			0
$253$	4.23996	+	3.88017i	0.266564	+	0.243944i
$254$		0			0
$255$	−1.22981	+	0.893507i	−0.0770135	+	0.0559536i
$256$		0			0
$257$	−20.4663	−	6.64992i	−1.27666	−	0.414810i	−0.409254	−	0.912420i	$-0.634211\pi$
$257$	−20.4663	−	6.64992i	−1.27666	−	0.414810i	−0.867401	+	0.497610i	$0.834211\pi$
$258$		0			0
$259$	2.48876	−	0.804361i	0.154644	−	0.0499806i
$260$		0			0
$261$	2.80404	−	0.911089i	0.173566	−	0.0563950i
$262$		0			0
$263$		−	18.6389i		−	1.14932i	−0.818392	−	0.574660i	$-0.805134\pi$
$263$		−	18.6389i		−	1.14932i	0.818392	−	0.574660i	$-0.194866\pi$
$264$		0			0
$265$			3.89372i			0.239190i
$266$		0			0
$267$	−1.50125	−	4.62037i	−0.0918750	−	0.282762i
$268$		0			0
$269$	−11.3715	+	15.6516i	−0.693335	+	0.954293i	0.306662	+	0.951818i	$0.400788\pi$
$269$	−11.3715	+	15.6516i	−0.693335	+	0.954293i	−0.999997	+	0.00247482i	$0.999212\pi$
$270$		0			0
$271$	−3.14727	+	9.68630i	−0.191183	+	0.588401i	0.808817	+	0.588061i	$0.200108\pi$
$271$	−3.14727	+	9.68630i	−0.191183	+	0.588401i	−1.00000		0.000340354i	$0.999892\pi$
$272$		0			0
$273$	15.2368	+	0.0237531i	0.922172	+	0.00143760i
$274$		0			0
$275$	−6.59638	+	14.4993i	−0.397777	+	0.874339i
$276$		0			0
$277$	−0.827606	−	1.13910i	−0.0497260	−	0.0684420i	0.783430	−	0.621480i	$-0.213468\pi$
$277$	−0.827606	−	1.13910i	−0.0497260	−	0.0684420i	−0.833156	+	0.553038i	$0.813468\pi$
$278$		0			0
$279$	2.09008	+	0.679109i	0.125130	+	0.0406572i
$280$		0			0
$281$	0.401849	−	0.553097i	0.0239723	−	0.0329950i	−0.796863	−	0.604161i	$-0.793509\pi$
$281$	0.401849	−	0.553097i	0.0239723	−	0.0329950i	0.820835	+	0.571166i	$0.193509\pi$
$282$		0			0
$283$	−2.07722	−	6.39302i	−0.123478	−	0.380026i	0.870143	−	0.492800i	$-0.164026\pi$
$283$	−2.07722	−	6.39302i	−0.123478	−	0.380026i	−0.993621	+	0.112774i	$0.964026\pi$
$284$		0			0
$285$	−5.98505			−0.354524
$286$		0			0
$287$	−13.6796	+	18.7667i	−0.807479	+	1.10776i
$288$		0			0
$289$	−3.83126	−	11.7914i	−0.225368	−	0.693611i
$290$		0			0
$291$	1.59551	+	1.15921i	0.0935305	+	0.0679539i
$292$		0			0
$293$	−1.60874	+	4.95120i	−0.0939837	+	0.289252i	−0.986987	−	0.160797i	$-0.948594\pi$
$293$	−1.60874	+	4.95120i	−0.0939837	+	0.289252i	0.893004	+	0.450049i	$0.148594\pi$
$294$		0			0
$295$	3.88667	−	2.82383i	0.226291	−	0.164410i
$296$		0			0
$297$	−17.9078	+	3.65543i	−1.03911	+	0.212110i
$298$		0			0
$299$	5.05898	−	3.67557i	0.292568	−	0.212563i
$300$		0			0
$301$	9.25938	−	6.70530i	0.533702	−	0.386487i
$302$		0			0
$303$	−6.12971	+	8.43682i	−0.352142	+	0.484683i
$304$		0			0
$305$	−2.93525	+	0.953721i	−0.168072	+	0.0546099i
$306$		0			0
$307$	12.5775			0.717835			0.358917	−	0.933369i	$-0.383146\pi$
$307$	12.5775			0.717835			0.358917	+	0.933369i	$0.383146\pi$
$308$		0			0
$309$	10.9539			0.623146
$310$		0			0
$311$	18.5680	−	6.03310i	1.05289	−	0.342105i	0.269090	−	0.963115i	$-0.413277\pi$
$311$	18.5680	−	6.03310i	1.05289	−	0.342105i	0.783803	+	0.621010i	$0.213277\pi$
$312$		0			0
$313$	−1.42488	+	1.96118i	−0.0805389	+	0.110852i	−0.847386	−	0.530978i	$-0.821825\pi$
$313$	−1.42488	+	1.96118i	−0.0805389	+	0.110852i	0.766847	+	0.641830i	$0.221825\pi$
$314$		0			0
$315$	−0.430986	+	0.312105i	−0.0242833	+	0.0175851i
$316$		0			0
$317$	17.9456	−	13.0383i	1.00793	−	0.732303i	0.0441545	−	0.999025i	$-0.485941\pi$
$317$	17.9456	−	13.0383i	1.00793	−	0.732303i	0.963773	+	0.266722i	$0.0859406\pi$
$318$		0			0
$319$	−10.6425	−	18.7821i	−0.595863	−	1.05160i
$320$		0			0
$321$	−5.69293	+	4.13615i	−0.317748	+	0.230858i
$322$		0			0
$323$	−5.59884	+	17.2315i	−0.311528	+	0.958785i
$324$		0			0
$325$	14.0212	+	10.1870i	0.777755	+	0.565072i
$326$		0			0
$327$	1.15166	+	3.54444i	0.0636868	+	0.196008i
$328$		0			0
$329$	−14.9077	−	10.8666i	−0.821888	−	0.599096i
$330$		0			0
$331$	−17.0689			−0.938192			−0.469096	−	0.883147i	$-0.655420\pi$
$331$	−17.0689			−0.938192			−0.469096	+	0.883147i	$0.655420\pi$
$332$		0			0
$333$	0.138375	+	0.425875i	0.00758292	+	0.0233378i
$334$		0			0
$335$	2.99795	−	4.12633i	0.163796	−	0.225445i
$336$		0			0
$337$	3.56954	+	1.15981i	0.194445	+	0.0631791i	0.404621	−	0.914485i	$-0.367404\pi$
$337$	3.56954	+	1.15981i	0.194445	+	0.0631791i	−0.210176	+	0.977664i	$0.567404\pi$
$338$		0			0
$339$	−0.938099	−	1.29118i	−0.0509506	−	0.0701274i
$340$		0			0
$341$	1.81123	−	15.9888i	0.0980837	−	0.865844i
$342$		0			0
$343$	−17.6404	+	5.64064i	−0.952491	+	0.304566i
$344$		0			0
$345$	0.379469	−	1.16788i	0.0204299	−	0.0628768i
$346$		0			0
$347$	19.8432	−	27.3118i	1.06524	−	1.46617i	0.190430	−	0.981701i	$-0.439012\pi$
$347$	19.8432	−	27.3118i	1.06524	−	1.46617i	0.874807	−	0.484472i	$-0.160988\pi$
$348$		0			0
$349$	7.15449	+	22.0193i	0.382971	+	1.17866i	0.937941	+	0.346794i	$0.112730\pi$
$349$	7.15449	+	22.0193i	0.382971	+	1.17866i	−0.554970	+	0.831870i	$0.687270\pi$
$350$		0			0
$351$			19.8855i			1.06141i
$352$		0			0
$353$		−	16.2534i		−	0.865082i	−0.901614	−	0.432541i	$-0.857617\pi$
$353$		−	16.2534i		−	0.865082i	0.901614	−	0.432541i	$-0.142383\pi$
$354$		0			0
$355$	−5.53471	+	1.79834i	−0.293752	+	0.0954459i
$356$		0			0
$357$	−2.78563	−	8.61898i	−0.147431	−	0.456165i
$358$		0			0
$359$	14.3580	+	4.66519i	0.757785	+	0.246219i	0.662328	−	0.749214i	$-0.269569\pi$
$359$	14.3580	+	4.66519i	0.757785	+	0.246219i	0.0954573	+	0.995434i	$0.469569\pi$
$360$		0			0
$361$	−42.3401	+	30.7619i	−2.22843	+	1.61905i
$362$		0			0
$363$	6.88031	+	16.1509i	0.361123	+	0.847703i
$364$		0			0
$365$	1.88517	+	2.59471i	0.0986743	+	0.135813i
$366$		0			0
$367$	2.21153	+	0.718570i	0.115441	+	0.0375090i	0.366168	−	0.930549i	$-0.380670\pi$
$367$	2.21153	+	0.718570i	0.115441	+	0.0375090i	−0.250727	+	0.968058i	$0.580670\pi$
$368$		0			0
$369$	−3.21661	−	2.33701i	−0.167450	−	0.121660i
$370$		0			0
$371$	−22.0547	−	7.20404i	−1.14502	−	0.374015i
$372$		0			0
$373$			3.48084i			0.180231i	0.995931	+	0.0901156i	$0.0287236\pi$
$373$			3.48084i			0.180231i	−0.995931	+	0.0901156i	$0.971276\pi$
$374$		0			0
$375$	6.94653			0.358717
$376$		0			0
$377$	−22.3380	+	7.25807i	−1.15047	+	0.373809i
$378$		0			0
$379$	19.2469	+	13.9837i	0.988647	+	0.718294i	0.959624	−	0.281285i	$-0.0907606\pi$
$379$	19.2469	+	13.9837i	0.988647	+	0.718294i	0.0290224	+	0.999579i	$0.490761\pi$
$380$		0			0
$381$	9.49711	−	29.2291i	0.486552	−	1.49745i
$382$		0			0
$383$	−18.8512	−	25.9464i	−0.963249	−	1.32580i	−0.945384	−	0.325958i	$-0.894313\pi$
$383$	−18.8512	−	25.9464i	−0.963249	−	1.32580i	−0.0178650	−	0.999840i	$-0.505687\pi$
$384$		0			0
$385$	2.87019	+	2.63487i	0.146279	+	0.134285i
$386$		0			0
$387$	1.15046	+	1.58347i	0.0584810	+	0.0804922i
$388$		0			0
$389$	3.64253	−	11.2106i	0.184684	−	0.568398i	−0.815259	−	0.579096i	$-0.803406\pi$
$389$	3.64253	−	11.2106i	0.184684	−	0.568398i	0.999943	+	0.0106986i	$0.00340555\pi$
$390$		0			0
$391$	−3.00746	−	2.18504i	−0.152094	−	0.110502i
$392$		0			0
$393$	12.3174	−	4.00217i	0.621332	−	0.201883i
$394$		0			0
$395$	−3.89611			−0.196035
$396$		0			0
$397$		−	6.42269i		−	0.322346i	−0.986926	−	0.161173i	$-0.948472\pi$
$397$		−	6.42269i		−	0.322346i	0.986926	−	0.161173i	$-0.0515276\pi$
$398$		0			0
$399$	11.0733	−	33.9004i	0.554361	−	1.69714i
$400$		0			0
$401$	23.7999	+	17.2916i	1.18851	+	0.863503i	0.993106	−	0.117220i	$-0.0373984\pi$
$401$	23.7999	+	17.2916i	1.18851	+	0.863503i	0.195403	+	0.980723i	$0.437398\pi$
$402$		0			0
$403$	−16.6504	−	5.41003i	−0.829413	−	0.269493i
$404$		0			0
$405$	1.94067	+	2.67110i	0.0964327	+	0.132728i
$406$		0			0
$407$	2.85261	−	1.61637i	0.141399	−	0.0801203i
$408$		0			0
$409$	−17.6354	+	12.8129i	−0.872015	+	0.633556i	−0.931127	−	0.364695i	$-0.881173\pi$
$409$	−17.6354	+	12.8129i	−0.872015	+	0.633556i	0.0591118	+	0.998251i	$0.481173\pi$
$410$		0			0
$411$	8.80292	+	2.86024i	0.434216	+	0.141085i
$412$		0			0
$413$	8.80367	+	27.2393i	0.433200	+	1.34036i
$414$		0			0
$415$	−6.59812	+	2.14386i	−0.323889	+	0.105238i
$416$		0			0
$417$		−	12.9468i		−	0.634006i
$418$		0			0
$419$		−	3.55781i		−	0.173810i	−0.996217	−	0.0869052i	$-0.972302\pi$
$419$		−	3.55781i		−	0.173810i	0.996217	−	0.0869052i	$-0.0276977\pi$
$420$		0			0
$421$	12.4365	+	38.2757i	0.606120	+	1.86545i	0.488901	+	0.872339i	$0.337398\pi$
$421$	12.4365	+	38.2757i	0.606120	+	1.86545i	0.117219	+	0.993106i	$0.462602\pi$
$422$		0			0
$423$	1.85645	−	2.55518i	0.0902635	−	0.124237i
$424$		0			0
$425$	3.18380	−	9.79872i	0.154437	−	0.475308i
$426$		0			0
$427$	0.0286692	−	18.3903i	0.00138740	−	0.889970i
$428$		0			0
$429$	18.7144	−	3.82009i	0.903541	−	0.184436i
$430$		0			0
$431$	14.5687	+	20.0520i	0.701748	+	0.965873i	0.999935	+	0.0113655i	$0.00361782\pi$
$431$	14.5687	+	20.0520i	0.701748	+	0.965873i	−0.298188	+	0.954507i	$0.596382\pi$
$432$		0			0
$433$	4.75912	+	1.54633i	0.228709	+	0.0743120i	0.421129	−	0.907001i	$-0.361634\pi$
$433$	4.75912	+	1.54633i	0.228709	+	0.0743120i	−0.192421	+	0.981313i	$0.561634\pi$
$434$		0			0
$435$	−2.71110	+	3.73151i	−0.129987	+	0.178912i
$436$		0			0
$437$	−4.52285	−	13.9199i	−0.216357	−	0.665880i
$438$		0			0
$439$	5.36847			0.256223			0.128112	−	0.991760i	$-0.459108\pi$
$439$	5.36847			0.256223			0.128112	+	0.991760i	$0.459108\pi$
$440$		0			0
$441$	−0.970416	−	3.01863i	−0.0462103	−	0.143744i
$442$		0			0
$443$	3.07670	+	9.46910i	0.146178	+	0.449891i	0.997161	−	0.0753037i	$-0.0239926\pi$
$443$	3.07670	+	9.46910i	0.146178	+	0.449891i	−0.850982	+	0.525194i	$0.823993\pi$
$444$		0			0
$445$	−1.09348	−	0.794457i	−0.0518358	−	0.0376609i
$446$		0			0
$447$	6.67594	−	20.5464i	0.315761	−	0.971813i
$448$		0			0
$449$	−5.95718	+	4.32815i	−0.281137	+	0.204258i	−0.719413	−	0.694582i	$-0.755589\pi$
$449$	−5.95718	+	4.32815i	−0.281137	+	0.204258i	0.438276	+	0.898840i	$0.355589\pi$
$450$		0			0
$451$	−12.0554	+	26.4985i	−0.567666	+	1.24776i
$452$		0			0
$453$	13.9381	−	10.1266i	0.654867	−	0.475789i
$454$		0			0
$455$	3.43340	−	2.48634i	0.160960	−	0.116561i
$456$		0			0
$457$	−18.4581	+	25.4054i	−0.863434	+	1.18842i	0.117305	+	0.993096i	$0.462574\pi$
$457$	−18.4581	+	25.4054i	−0.863434	+	1.18842i	−0.980740	+	0.195319i	$0.937426\pi$
$458$		0			0
$459$	11.2429	−	3.65305i	0.524775	−	0.170510i
$460$		0			0
$461$	−5.60541			−0.261070			−0.130535	−	0.991444i	$-0.541670\pi$
$461$	−5.60541			−0.261070			−0.130535	+	0.991444i	$0.541670\pi$
$462$		0			0
$463$	9.20728			0.427899			0.213949	−	0.976845i	$-0.431367\pi$
$463$	9.20728			0.427899			0.213949	+	0.976845i	$0.431367\pi$
$464$		0			0
$465$	−3.26973	+	1.06240i	−0.151630	+	0.0492676i
$466$		0			0
$467$	15.4473	−	21.2614i	0.714816	−	0.983860i	−0.284864	−	0.958568i	$-0.591948\pi$
$467$	15.4473	−	21.2614i	0.714816	−	0.983860i	0.999680	−	0.0252920i	$-0.00805156\pi$
$468$		0			0
$469$	17.8255	+	24.6153i	0.823105	+	1.13663i
$470$		0			0
$471$	21.0113	−	15.2656i	0.968149	−	0.703402i
$472$		0			0
$473$	9.67514	−	10.5723i	0.444863	−	0.486114i
$474$		0			0
$475$	32.8178	−	23.8435i	1.50578	−	1.09401i
$476$		0			0
$477$	1.22749	−	3.77781i	0.0562027	−	0.172974i
$478$		0			0
$479$	−8.65578	−	6.28879i	−0.395493	−	0.287342i	0.372210	−	0.928149i	$-0.378600\pi$
$479$	−8.65578	−	6.28879i	−0.395493	−	0.287342i	−0.767703	+	0.640806i	$0.778600\pi$
$480$		0			0
$481$	−1.10235	−	3.39268i	−0.0502628	−	0.154693i
$482$		0			0
$483$	5.91302	+	4.31016i	0.269052	+	0.196119i
$484$		0			0
$485$	0.548685			0.0249145
$486$		0			0
$487$	−5.62084	−	17.2992i	−0.254705	−	0.783900i	−0.993888	−	0.110396i	$-0.964788\pi$
$487$	−5.62084	−	17.2992i	−0.254705	−	0.783900i	0.739183	−	0.673505i	$-0.235212\pi$
$488$		0			0
$489$	4.48472	−	6.17268i	0.202806	−	0.279138i
$490$		0			0
$491$	19.5042	+	6.33731i	0.880214	+	0.285999i	0.714046	−	0.700099i	$-0.246861\pi$
$491$	19.5042	+	6.33731i	0.880214	+	0.285999i	0.166168	+	0.986098i	$0.446861\pi$
$492$		0			0
$493$	8.20717	+	11.2962i	0.369632	+	0.508755i
$494$		0			0
$495$	−0.450338	+	0.492096i	−0.0202412	+	0.0221181i
$496$		0			0
$497$	0.0540587	−	34.6768i	0.00242486	−	1.55547i
$498$		0			0
$499$	0.232751	−	0.716334i	0.0104194	−	0.0320675i	−0.945712	−	0.325007i	$-0.894633\pi$
$499$	0.232751	−	0.716334i	0.0104194	−	0.0320675i	0.956131	+	0.292939i	$0.0946334\pi$
$500$		0			0
$501$	−2.01780	+	2.77726i	−0.0901484	+	0.124079i
$502$		0			0
$503$	4.80094	+	14.7758i	0.214063	+	0.658819i	0.999219	+	0.0395202i	$0.0125829\pi$
$503$	4.80094	+	14.7758i	0.214063	+	0.658819i	−0.785156	+	0.619299i	$0.787417\pi$
$504$		0			0
$505$			2.90136i			0.129109i
$506$		0			0
$507$		−	0.0340365i		−	0.00151161i
$508$		0			0
$509$	−17.8539	+	5.80107i	−0.791359	+	0.257128i	−0.676683	−	0.736275i	$-0.736583\pi$
$509$	−17.8539	+	5.80107i	−0.791359	+	0.257128i	−0.114676	+	0.993403i	$0.536583\pi$
$510$		0			0
$511$	−18.1848	+	5.87727i	−0.804447	+	0.259995i
$512$		0			0
$513$	44.2658	+	14.3828i	1.95438	+	0.635017i
$514$		0			0
$515$	2.46552	−	1.79130i	0.108644	−	0.0789342i
$516$		0			0
$517$	−21.0496	−	9.57642i	−0.925759	−	0.421171i
$518$		0			0
$519$	17.2420	+	23.7315i	0.756838	+	1.04170i
$520$		0			0
$521$	33.6176	+	10.9230i	1.47281	+	0.478546i	0.931957	−	0.362570i	$-0.118100\pi$
$521$	33.6176	+	10.9230i	1.47281	+	0.478546i	0.540856	+	0.841115i	$0.318100\pi$
$522$		0			0
$523$	−9.67925	−	7.03239i	−0.423244	−	0.307505i	0.355698	−	0.934601i	$-0.384243\pi$
$523$	−9.67925	−	7.03239i	−0.423244	−	0.307505i	−0.778942	+	0.627096i	$0.784243\pi$
$524$		0			0
$525$	−6.29689	+	19.2775i	−0.274819	+	0.841340i
$526$		0			0
$527$			10.4077i			0.453365i
$528$		0			0
$529$	−19.9970			−0.869435
$530$		0			0
$531$	−4.66118	+	1.51451i	−0.202278	+	0.0657240i
$532$		0			0
$533$	25.6247	+	18.6175i	1.10993	+	0.806411i
$534$		0			0
$535$	−0.604981	+	1.86194i	−0.0261556	+	0.0804986i
$536$		0			0
$537$	14.7727	+	20.3328i	0.637487	+	0.877426i
$538$		0			0
$539$	−20.2347	+	11.3823i	−0.871570	+	0.490271i
$540$		0			0
$541$	−18.6807	−	25.7117i	−0.803145	−	1.10543i	−0.992345	−	0.123496i	$-0.960589\pi$
$541$	−18.6807	−	25.7117i	−0.803145	−	1.10543i	0.189200	−	0.981939i	$-0.439411\pi$
$542$		0			0
$543$	1.98444	−	6.10749i	0.0851606	−	0.262097i
$544$		0			0
$545$	0.838842	+	0.609454i	0.0359320	+	0.0261061i
$546$		0			0
$547$	17.9119	−	5.81992i	0.765856	−	0.248842i	0.100066	−	0.994981i	$-0.468095\pi$
$547$	17.9119	−	5.81992i	0.765856	−	0.248842i	0.665790	+	0.746139i	$0.268095\pi$
$548$		0			0
$549$	3.14853			0.134376
$550$		0			0
$551$			54.9747i			2.34200i
$552$		0			0
$553$	7.20846	−	22.0682i	0.306535	−	0.938437i
$554$		0			0
$555$	−0.566738	−	0.411759i	−0.0240567	−	0.0174782i
$556$		0			0
$557$	−39.4101	−	12.8051i	−1.66986	−	0.542571i	−0.686958	−	0.726697i	$-0.741054\pi$
$557$	−39.4101	−	12.8051i	−1.66986	−	0.542571i	−0.982903	+	0.184127i	$0.941054\pi$
$558$		0			0
$559$	−9.16496	−	12.6145i	−0.387636	−	0.533536i
$560$		0			0
$561$	−5.59773	−	9.87905i	−0.236336	−	0.417094i
$562$		0			0
$563$	15.5284	−	11.2821i	0.654445	−	0.475482i	−0.210338	−	0.977629i	$-0.567456\pi$
$563$	15.5284	−	11.2821i	0.654445	−	0.475482i	0.864782	+	0.502147i	$0.167456\pi$
$564$		0			0
$565$	−0.422297	−	0.137213i	−0.0177662	−	0.00577257i
$566$		0			0
$567$	−18.7201	+	6.05030i	−0.786172	+	0.254089i
$568$		0			0
$569$	−12.8183	+	4.16491i	−0.537370	+	0.174602i	−0.565114	−	0.825013i	$-0.691168\pi$
$569$	−12.8183	+	4.16491i	−0.537370	+	0.174602i	0.0277437	+	0.999615i	$0.491168\pi$
$570$		0			0
$571$		−	20.4722i		−	0.856736i	−0.903604	−	0.428368i	$-0.859089\pi$
$571$		−	20.4722i		−	0.856736i	0.903604	−	0.428368i	$-0.140911\pi$
$572$		0			0
$573$			17.8808i			0.746980i
$574$		0			0
$575$	2.57193	+	7.91559i	0.107257	+	0.330103i
$576$		0			0
$577$	18.7638	−	25.8262i	0.781148	−	1.07516i	−0.214006	−	0.976832i	$-0.568651\pi$
$577$	18.7638	−	25.8262i	0.781148	−	1.07516i	0.995154	−	0.0983260i	$-0.0313488\pi$
$578$		0			0
$579$	3.40458	−	10.4782i	0.141489	−	0.435459i
$580$		0			0
$581$	0.0644452	−	41.3394i	0.00267364	−	1.71505i
$582$		0			0
$583$	−28.8998	−	3.27379i	−1.19691	−	0.135587i
$584$		0			0
$585$	0.426591	+	0.587153i	0.0176374	+	0.0242758i
$586$		0			0
$587$	−4.79284	−	1.55729i	−0.197822	−	0.0642762i	0.208430	−	0.978037i	$-0.433165\pi$
$587$	−4.79284	−	1.55729i	−0.197822	−	0.0642762i	−0.406252	+	0.913761i	$0.633165\pi$
$588$		0			0
$589$	−24.0858	+	33.1512i	−0.992437	+	1.36597i
$590$		0			0
$591$	−3.55648	−	10.9457i	−0.146294	−	0.450247i
$592$		0			0
$593$	−22.5830			−0.927373			−0.463686	−	0.885999i	$-0.653474\pi$
$593$	−22.5830			−0.927373			−0.463686	+	0.885999i	$0.653474\pi$
$594$		0			0
$595$	−2.03646	−	1.48443i	−0.0834868	−	0.0608558i
$596$		0			0
$597$	−5.54549	−	17.0673i	−0.226962	−	0.698516i
$598$		0			0
$599$	31.9037	+	23.1794i	1.30355	+	0.947084i	0.999984	−	0.00572612i	$-0.00182269\pi$
$599$	31.9037	+	23.1794i	1.30355	+	0.947084i	0.303566	+	0.952810i	$0.401823\pi$
$600$		0			0
$601$	4.65003	−	14.3113i	0.189679	−	0.583771i	−0.810319	−	0.585989i	$-0.800706\pi$
$601$	4.65003	−	14.3113i	0.189679	−	0.583771i	0.999998	+	0.00221837i	$0.000706130\pi$
$602$		0			0
$603$	−4.20952	+	3.05839i	−0.171425	+	0.124547i
$604$		0			0
$605$	4.18980	+	2.51012i	0.170340	+	0.102051i
$606$		0			0
$607$	−3.06776	+	2.22886i	−0.124517	+	0.0904666i	−0.648300	−	0.761385i	$-0.724520\pi$
$607$	−3.06776	+	2.22886i	−0.124517	+	0.0904666i	0.523784	+	0.851851i	$0.324520\pi$
$608$		0			0
$609$	−16.1199	−	22.2600i	−0.653211	−	0.902022i
$610$		0			0
$611$	−14.7891	+	20.3555i	−0.598304	+	0.823495i
$612$		0			0
$613$	−20.4135	+	6.63276i	−0.824495	+	0.267895i	−0.690725	−	0.723118i	$-0.742708\pi$
$613$	−20.4135	+	6.63276i	−0.824495	+	0.267895i	−0.133770	+	0.991012i	$0.542708\pi$
$614$		0			0
$615$	6.21999			0.250814
$616$		0			0
$617$	−5.69432			−0.229245			−0.114622	−	0.993409i	$-0.536566\pi$
$617$	−5.69432			−0.229245			−0.114622	+	0.993409i	$0.536566\pi$
$618$		0			0
$619$	−41.2403	+	13.3998i	−1.65759	+	0.538582i	−0.980364	−	0.197196i	$-0.936816\pi$
$619$	−41.2403	+	13.3998i	−1.65759	+	0.538582i	−0.677222	+	0.735778i	$0.736816\pi$
$620$		0			0
$621$	−5.61315	+	7.72583i	−0.225248	+	0.310027i
$622$		0			0
$623$	6.52306	−	4.72376i	0.261341	−	0.189253i
$624$		0			0
$625$	−17.8644	+	12.9792i	−0.714576	+	0.519170i
$626$		0			0
$627$	5.03216	−	44.4219i	0.200965	−	1.77404i
$628$		0			0
$629$	−1.71566	+	1.24650i	−0.0684077	+	0.0497011i
$630$		0			0
$631$	7.23686	−	22.2728i	0.288095	−	0.886665i	−0.697359	−	0.716722i	$-0.745642\pi$
$631$	7.23686	−	22.2728i	0.288095	−	0.886665i	0.985454	−	0.169943i	$-0.0543583\pi$
$632$		0			0
$633$	20.8090	+	15.1186i	0.827083	+	0.600911i
$634$		0			0
$635$	−2.64224	−	8.13198i	−0.104854	−	0.322708i
$636$		0			0
$637$	7.73069	+	24.0475i	0.306301	+	0.952796i
$638$		0			0
$639$	5.93687			0.234859
$640$		0			0
$641$	3.56318	+	10.9663i	0.140737	+	0.433145i	0.996438	−	0.0843259i	$-0.0268737\pi$
$641$	3.56318	+	10.9663i	0.140737	+	0.433145i	−0.855701	+	0.517471i	$0.826874\pi$
$642$		0			0
$643$	−22.4020	+	30.8337i	−0.883449	+	1.21596i	0.0920053	+	0.995759i	$0.470672\pi$
$643$	−22.4020	+	30.8337i	−0.883449	+	1.21596i	−0.975454	+	0.220204i	$0.929328\pi$
$644$		0			0
$645$	−2.91210	−	0.946198i	−0.114664	−	0.0372565i
$646$		0			0
$647$	−25.2211	−	34.7139i	−0.991545	−	1.36475i	−0.930372	−	0.366618i	$-0.880516\pi$
$647$	−25.2211	−	34.7139i	−0.991545	−	1.36475i	−0.0611738	−	0.998127i	$-0.519484\pi$
$648$		0			0
$649$	17.6910	+	31.2217i	0.694433	+	1.22556i
$650$		0			0
$651$	0.0319361	−	20.4859i	0.00125167	−	0.802906i
$652$		0			0
$653$	12.1563	−	37.4131i	0.475711	−	1.46409i	−0.369285	−	0.929316i	$-0.620397\pi$
$653$	12.1563	−	37.4131i	0.475711	−	1.46409i	0.844996	−	0.534772i	$-0.179603\pi$
$654$		0			0
$655$	2.11794	−	2.91509i	0.0827547	−	0.113902i
$656$		0			0
$657$	−1.01107	−	3.11177i	−0.0394458	−	0.121402i
$658$		0			0
$659$		−	32.6010i		−	1.26995i	−0.772531	−	0.634977i	$-0.781009\pi$
$659$		−	32.6010i		−	1.26995i	0.772531	−	0.634977i	$-0.218991\pi$
$660$		0			0
$661$			35.0666i			1.36393i	0.731383	+	0.681967i	$0.238875\pi$
$661$			35.0666i			1.36393i	−0.731383	+	0.681967i	$0.761125\pi$
$662$		0			0
$663$	−11.7494	+	3.81760i	−0.456308	+	0.148263i
$664$		0			0
$665$	−3.05136	−	9.44116i	−0.118326	−	0.366113i
$666$		0			0
$667$	−10.7274	−	3.48555i	−0.415367	−	0.134961i
$668$		0			0
$669$	−37.2078	+	27.0330i	−1.43853	+	1.04516i
$670$		0			0
$671$	−4.61073	−	22.5877i	−0.177995	−	0.871990i
$672$		0			0
$673$	4.29258	+	5.90822i	0.165467	+	0.227745i	0.883696	−	0.468061i	$-0.155047\pi$
$673$	4.29258	+	5.90822i	0.165467	+	0.227745i	−0.718230	+	0.695806i	$0.755047\pi$
$674$		0			0
$675$	−25.1718	−	8.17883i	−0.968865	−	0.314803i
$676$		0			0
$677$	36.0174	+	26.1682i	1.38426	+	1.00572i	0.996468	+	0.0839776i	$0.0267624\pi$
$677$	36.0174	+	26.1682i	1.38426	+	1.00572i	0.387793	+	0.921747i	$0.373238\pi$
$678$		0			0
$679$	−1.01516	+	3.10785i	−0.0389583	+	0.119268i
$680$		0			0
$681$			32.0005i			1.22626i
$682$		0			0
$683$	−48.6281			−1.86070			−0.930351	−	0.366671i	$-0.880498\pi$
$683$	−48.6281			−1.86070			−0.930351	+	0.366671i	$0.880498\pi$
$684$		0			0
$685$	2.44911	−	0.795764i	0.0935756	−	0.0304046i
$686$		0			0
$687$	4.16631	+	3.02700i	0.158955	+	0.115487i
$688$		0			0
$689$	−9.77860	+	30.0954i	−0.372535	+	1.14654i
$690$		0			0
$691$	6.10596	+	8.40414i	0.232282	+	0.319709i	0.909208	−	0.416343i	$-0.136688\pi$
$691$	6.10596	+	8.40414i	0.232282	+	0.319709i	−0.676926	+	0.736051i	$0.736688\pi$
$692$		0			0
$693$	−1.95412	−	3.46125i	−0.0742307	−	0.131482i
$694$		0			0
$695$	−2.11720	−	2.91407i	−0.0803098	−	0.110537i
$696$		0			0
$697$	5.81862	−	17.9079i	0.220396	−	0.678309i
$698$		0			0
$699$	−9.92605	−	7.21169i	−0.375438	−	0.272771i
$700$		0			0
$701$	−32.1350	+	10.4413i	−1.21372	+	0.394362i	−0.844791	−	0.535096i	$-0.820275\pi$
$701$	−32.1350	+	10.4413i	−1.21372	+	0.394362i	−0.368929	+	0.929458i	$0.620275\pi$
$702$		0			0
$703$	−8.34951			−0.314908
$704$		0			0
$705$			4.94097i			0.186088i
$706$		0			0
$707$	−16.4338	−	5.36801i	−0.618058	−	0.201885i
$708$		0			0
$709$	−20.5659	−	14.9420i	−0.772369	−	0.561159i	0.130310	−	0.991473i	$-0.458403\pi$
$709$	−20.5659	−	14.9420i	−0.772369	−	0.561159i	−0.902679	+	0.430314i	$0.858403\pi$
$710$		0			0
$711$	3.78013	+	1.22824i	0.141766	+	0.0460626i
$712$		0			0
$713$	−4.94181	−	6.80182i	−0.185072	−	0.254730i
$714$		0			0
$715$	3.58756	−	3.92022i	0.134167	−	0.146608i
$716$		0			0
$717$	−2.49818	+	1.81504i	−0.0932964	+	0.0677838i
$718$		0			0
$719$	25.7655	+	8.37173i	0.960893	+	0.312213i	0.747134	−	0.664674i	$-0.231429\pi$
$719$	25.7655	+	8.37173i	0.960893	+	0.312213i	0.213759	+	0.976886i	$0.431429\pi$
$720$		0			0
$721$	5.58462	+	17.2793i	0.207982	+	0.643515i
$722$		0			0
$723$	20.3748	−	6.62018i	0.757747	−	0.246207i
$724$		0			0
$725$		−	31.2615i		−	1.16102i
$726$		0			0
$727$			33.1937i			1.23109i	0.788103	+	0.615543i	$0.211063\pi$
$727$			33.1937i			1.23109i	−0.788103	+	0.615543i	$0.788937\pi$
$728$		0			0
$729$	−9.19409	−	28.2965i	−0.340522	−	1.04802i
$730$		0			0
$731$	−5.44837	+	7.49904i	−0.201515	+	0.277362i
$732$		0			0
$733$	−2.28281	+	7.02575i	−0.0843174	+	0.259502i	−0.984323	−	0.176377i	$-0.943562\pi$
$733$	−2.28281	+	7.02575i	−0.0843174	+	0.259502i	0.900005	+	0.435879i	$0.143562\pi$
$734$		0			0
$735$	4.00391	+	2.92813i	0.147686	+	0.108006i
$736$		0			0
$737$	28.1055	+	25.7206i	1.03528	+	0.947430i
$738$		0			0
$739$	21.5322	+	29.6365i	0.792074	+	1.09020i	0.993847	+	0.110763i	$0.0353296\pi$
$739$	21.5322	+	29.6365i	0.792074	+	1.09020i	−0.201773	+	0.979432i	$0.564670\pi$
$740$		0			0
$741$	−46.2598	−	15.0307i	−1.69939	−	0.552167i
$742$		0			0
$743$	−1.33518	+	1.83771i	−0.0489828	+	0.0674191i	−0.832806	−	0.553565i	$-0.813267\pi$
$743$	−1.33518	+	1.83771i	−0.0489828	+	0.0674191i	0.783823	+	0.620984i	$0.213267\pi$
$744$		0			0
$745$	−1.85735	−	5.71634i	−0.0680481	−	0.209430i
$746$		0			0
$747$	7.07755			0.258954
$748$		0			0
$749$	−9.42703	−	6.87161i	−0.344456	−	0.251083i
$750$		0			0
$751$	−7.28375	−	22.4171i	−0.265788	−	0.818010i	−0.991511	−	0.130024i	$-0.958495\pi$
$751$	−7.28375	−	22.4171i	−0.265788	−	0.818010i	0.725723	−	0.687987i	$-0.241505\pi$
$752$		0			0
$753$	38.3170	+	27.8389i	1.39635	+	1.01451i
$754$		0			0
$755$	1.48118	−	4.55861i	0.0539057	−	0.165905i
$756$		0			0
$757$	−2.26770	+	1.64758i	−0.0824211	+	0.0598824i	−0.628233	−	0.778025i	$-0.716221\pi$
$757$	−2.26770	+	1.64758i	−0.0824211	+	0.0598824i	0.545812	+	0.837908i	$0.316221\pi$
$758$		0			0
$759$	8.34915	+	3.79841i	0.303055	+	0.137874i
$760$		0			0
$761$	−18.9065	+	13.7363i	−0.685358	+	0.497942i	−0.875131	−	0.483886i	$-0.839225\pi$
$761$	−18.9065	+	13.7363i	−0.685358	+	0.497942i	0.189773	+	0.981828i	$0.439225\pi$
$762$		0			0
$763$	−5.00405	+	3.62375i	−0.181159	+	0.131189i
$764$		0			0
$765$	0.253599	−	0.349050i	0.00916891	−	0.0126199i
$766$		0			0
$767$	37.1326	−	12.0651i	1.34078	−	0.435646i
$768$		0			0
$769$	28.5824			1.03071			0.515354	−	0.856978i	$-0.327661\pi$
$769$	28.5824			1.03071			0.515354	+	0.856978i	$0.327661\pi$
$770$		0			0
$771$	−34.3440			−1.23687
$772$		0			0
$773$	39.0657	−	12.6932i	1.40510	−	0.456543i	0.494261	−	0.869314i	$-0.335439\pi$
$773$	39.0657	−	12.6932i	1.40510	−	0.456543i	0.910835	+	0.412770i	$0.135439\pi$
$774$		0			0
$775$	13.6964	−	18.8515i	0.491990	−	0.677166i
$776$		0			0
$777$	3.38083	−	2.44828i	0.121287	−	0.0878314i
$778$		0			0
$779$	59.9769	−	43.5758i	2.14889	−	1.56126i
$780$		0			0
$781$	−8.69399	−	42.5914i	−0.311096	−	1.52404i
$782$		0			0
$783$	29.0187	−	21.0833i	1.03704	−	0.753457i
$784$		0			0
$785$	2.23285	−	6.87199i	0.0796937	−	0.245272i
$786$		0			0
$787$	36.8738	+	26.7904i	1.31441	+	0.954974i	0.999984	+	0.00569143i	$0.00181165\pi$
$787$	36.8738	+	26.7904i	1.31441	+	0.954974i	0.314425	+	0.949282i	$0.398188\pi$
$788$		0			0
$789$	−9.19218	−	28.2906i	−0.327250	−	1.00717i
$790$		0			0
$791$	1.55851	−	2.13809i	0.0554144	−	0.0760219i
$792$		0			0
$793$	−25.0824			−0.890700
$794$		0			0
$795$	1.92028	+	5.91002i	0.0681053	+	0.209607i
$796$		0			0
$797$	14.1160	−	19.4290i	0.500014	−	0.688210i	−0.482182	−	0.876071i	$-0.660155\pi$
$797$	14.1160	−	19.4290i	0.500014	−	0.688210i	0.982196	+	0.187861i	$0.0601554\pi$
$798$		0			0
$799$	14.2255	+	4.62213i	0.503261	+	0.163519i
$800$		0			0
$801$	0.810475	+	1.11552i	0.0286367	+	0.0394151i
$802$		0			0
$803$	−20.8433	+	11.8104i	−0.735546	+	0.416779i
$804$		0			0
$805$	2.03575	+	0.00317359i	0.0717508	+	0.000111854i
$806$		0			0
$807$	−9.54113	+	29.3646i	−0.335864	+	1.03368i
$808$		0			0
$809$	−20.7362	+	28.5409i	−0.729045	+	1.00344i	0.270129	+	0.962824i	$0.412934\pi$
$809$	−20.7362	+	28.5409i	−0.729045	+	1.00344i	−0.999175	+	0.0406209i	$0.987066\pi$
$810$		0			0
$811$	0.102098	+	0.314226i	0.00358516	+	0.0110340i	0.952833	−	0.303495i	$-0.0981535\pi$
$811$	0.102098	+	0.314226i	0.00358516	+	0.0110340i	−0.949248	+	0.314529i	$0.898154\pi$
$812$		0			0
$813$			16.2543i			0.570064i
$814$		0			0
$815$		−	2.12274i		−	0.0743565i
$816$		0			0
$817$	−34.7090	+	11.2777i	−1.21432	+	0.394555i
$818$		0			0
$819$	−4.11500	+	1.32996i	−0.143790	+	0.0464724i
$820$		0			0
$821$	38.2380	+	12.4243i	1.33451	+	0.433610i	0.887455	−	0.460894i	$-0.152471\pi$
$821$	38.2380	+	12.4243i	1.33451	+	0.433610i	0.447059	+	0.894504i	$0.352471\pi$
$822$		0			0
$823$	−27.9511	+	20.3076i	−0.974313	+	0.707880i	−0.956430	−	0.291960i	$-0.905693\pi$
$823$	−27.9511	+	20.3076i	−0.974313	+	0.707880i	−0.0178826	+	0.999840i	$0.505693\pi$
$824$		0			0
$825$	−2.86155	+	25.2606i	−0.0996263	+	0.879461i
$826$		0			0
$827$	0.991748	+	1.36502i	0.0344865	+	0.0474665i	0.825912	−	0.563799i	$-0.190661\pi$
$827$	0.991748	+	1.36502i	0.0344865	+	0.0474665i	−0.791426	+	0.611266i	$0.790661\pi$
$828$		0			0
$829$	−18.0317	−	5.85886i	−0.626267	−	0.203486i	−0.0213463	−	0.999772i	$-0.506795\pi$
$829$	−18.0317	−	5.85886i	−0.626267	−	0.203486i	−0.604921	+	0.796286i	$0.706795\pi$
$830$		0			0
$831$	−1.81794	−	1.32081i	−0.0630637	−	0.0458185i
$832$		0			0
$833$	12.1759	−	8.78842i	0.421869	−	0.304501i
$834$		0			0
$835$			0.955080i			0.0330519i
$836$		0			0
$837$	26.7362			0.924137
$838$		0			0
$839$	32.6897	−	10.6215i	1.12857	−	0.366696i	0.315540	−	0.948912i	$-0.397814\pi$
$839$	32.6897	−	10.6215i	1.12857	−	0.366696i	0.813034	+	0.582216i	$0.197814\pi$
$840$		0			0
$841$	10.8137	+	7.85659i	0.372885	+	0.270917i
$842$		0			0
$843$	0.337166	−	1.03769i	0.0116126	−	0.0357399i
$844$		0			0
$845$	−0.00556601	−	0.00766096i	−0.000191477	−	0.000263545i
$846$		0			0
$847$	−21.9696	+	19.0876i	−0.754884	+	0.655858i
$848$		0			0
$849$	−6.30574	−	8.67910i	−0.216412	−	0.297866i
$850$		0			0
$851$	0.529382	−	1.62927i	0.0181470	−	0.0558507i
$852$		0			0
$853$	−2.77371	−	2.01522i	−0.0949699	−	0.0689997i	0.539287	−	0.842122i	$-0.318694\pi$
$853$	−2.77371	−	2.01522i	−0.0949699	−	0.0689997i	−0.634257	+	0.773122i	$0.718694\pi$
$854$		0			0
$855$	1.61556	−	0.524929i	0.0552511	−	0.0179522i
$856$		0			0
$857$	−17.2507			−0.589271			−0.294636	−	0.955610i	$-0.595198\pi$
$857$	−17.2507			−0.589271			−0.294636	+	0.955610i	$0.595198\pi$
$858$		0			0
$859$		−	19.9333i		−	0.680115i	−0.940405	−	0.340057i	$-0.889554\pi$
$859$		−	19.9333i		−	0.680115i	0.940405	−	0.340057i	$-0.110446\pi$
$860$		0			0
$861$	−11.5080	+	35.2311i	−0.392192	+	1.20067i
$862$		0			0
$863$	3.10629	+	2.25685i	0.105739	+	0.0768240i	0.639398	−	0.768876i	$-0.279183\pi$
$863$	3.10629	+	2.25685i	0.105739	+	0.0768240i	−0.533659	+	0.845700i	$0.679183\pi$
$864$		0			0
$865$	7.76168	+	2.52192i	0.263905	+	0.0857479i
$866$		0			0
$867$	−11.6304	−	16.0079i	−0.394989	−	0.543656i
$868$		0			0
$869$	3.27580	−	28.9175i	0.111124	−	0.980959i
$870$		0			0
$871$	33.5346	−	24.3643i	1.13628	−	0.825552i
$872$		0			0
$873$	−0.532352	−	0.172972i	−0.0180174	−	0.00585420i
$874$		0			0
$875$	3.54155	+	10.9579i	0.119726	+	0.370443i
$876$		0			0
$877$	−47.3831	+	15.3957i	−1.60001	+	0.519876i	−0.967111	−	0.254355i	$-0.918137\pi$
$877$	−47.3831	+	15.3957i	−1.60001	+	0.519876i	−0.632903	+	0.774231i	$0.718137\pi$
$878$		0			0
$879$			8.30847i			0.280238i
$880$		0			0
$881$		−	2.18519i		−	0.0736210i	−0.999322	−	0.0368105i	$-0.988280\pi$
$881$		−	2.18519i		−	0.0736210i	0.999322	−	0.0368105i	$-0.0117198\pi$
$882$		0			0
$883$	−15.1574	−	46.6496i	−0.510086	−	1.56988i	−0.792049	−	0.610458i	$-0.790985\pi$
$883$	−15.1574	−	46.6496i	−0.510086	−	1.56988i	0.281963	−	0.959425i	$-0.409015\pi$
$884$		0			0
$885$	4.50667	−	6.20290i	0.151490	−	0.208508i
$886$		0			0
$887$	4.76899	−	14.6774i	0.160127	−	0.492820i	−0.838517	−	0.544875i	$-0.816577\pi$
$887$	4.76899	−	14.6774i	0.160127	−	0.492820i	0.998644	+	0.0520548i	$0.0165771\pi$
$888$		0			0
$889$	50.9495	+	0.0794268i	1.70879	+	0.00266389i
$890$		0			0
$891$	−21.4570	+	12.1581i	−0.718836	+	0.407311i
$892$		0			0
$893$	34.6152	+	47.6438i	1.15835	+	1.59434i
$894$		0			0
$895$	6.65009	+	2.16074i	0.222288	+	0.0722257i
$896$		0			0
$897$	5.86599	−	8.07384i	0.195860	−	0.269578i
$898$		0			0
$899$	9.75849	+	30.0336i	0.325464	+	1.00168i
$900$		0			0
$901$	18.8118			0.626712
$902$		0			0
$903$	10.7473	−	14.7440i	0.357648	−	0.490650i
$904$		0			0
$905$	−0.552103	−	1.69920i	−0.0183525	−	0.0564832i
$906$		0			0
$907$	16.2886	+	11.8344i	0.540855	+	0.392954i	0.824403	−	0.566004i	$-0.191511\pi$
$907$	16.2886	+	11.8344i	0.540855	+	0.392954i	−0.283547	+	0.958958i	$0.591511\pi$
$908$		0			0
$909$	0.914647	−	2.81499i	0.0303369	−	0.0933675i
$910$		0			0
$911$	−8.24104	+	5.98747i	−0.273038	+	0.198374i	−0.715875	−	0.698228i	$-0.753972\pi$
$911$	−8.24104	+	5.98747i	−0.273038	+	0.198374i	0.442837	+	0.896602i	$0.353972\pi$
$912$		0			0
$913$	−10.3644	−	50.7747i	−0.343012	−	1.68040i
$914$		0			0
$915$	−3.98487	+	2.89518i	−0.131736	+	0.0957116i
$916$		0			0
$917$	12.5930	+	17.3898i	0.415859	+	0.574261i
$918$		0			0
$919$	−16.4458	+	22.6358i	−0.542498	+	0.746685i	−0.988970	−	0.148113i	$-0.952680\pi$
$919$	−16.4458	+	22.6358i	−0.542498	+	0.746685i	0.446472	+	0.894797i	$0.352680\pi$
$920$		0			0
$921$	19.0905	−	6.20288i	0.629053	−	0.204392i
$922$		0			0
$923$	−47.2953			−1.55674
$924$		0			0
$925$	4.74797			0.156112
$926$		0			0
$927$	−2.95682	+	0.960730i	−0.0971148	+	0.0315545i
$928$		0			0
$929$	29.5284	−	40.6424i	0.968797	−	1.33343i	0.0261446	−	0.999658i	$-0.491677\pi$
$929$	29.5284	−	40.6424i	0.968797	−	1.33343i	0.942652	−	0.333776i	$-0.108323\pi$
$930$		0			0
$931$	59.1219	+	0.184334i	1.93764	+	0.00604131i
$932$		0			0
$933$	25.2077	−	18.3144i	0.825262	−	0.599588i
$934$		0			0
$935$	−2.87547	−	1.30818i	−0.0940380	−	0.0427822i
$936$		0			0
$937$	−24.4626	+	17.7732i	−0.799160	+	0.580624i	−0.910668	−	0.413140i	$-0.864432\pi$
$937$	−24.4626	+	17.7732i	−0.799160	+	0.580624i	0.111508	+	0.993764i	$0.464432\pi$
$938$		0			0
$939$	−1.19552	+	3.67945i	−0.0390145	+	0.120074i
$940$		0			0
$941$	−33.5587	−	24.3818i	−1.09398	−	0.794824i	−0.113914	−	0.993491i	$-0.536339\pi$
$941$	−33.5587	−	24.3818i	−1.09398	−	0.794824i	−0.980067	+	0.198667i	$0.936339\pi$
$942$		0			0
$943$	4.70039	+	14.4663i	0.153066	+	0.471088i
$944$		0			0
$945$	−3.81335	+	5.23145i	−0.124048	+	0.170179i
$946$		0			0
$947$	−14.2417			−0.462794			−0.231397	−	0.972859i	$-0.574330\pi$
$947$	−14.2417			−0.462794			−0.231397	+	0.972859i	$0.574330\pi$
$948$		0			0
$949$	8.05459	+	24.7895i	0.261463	+	0.804700i
$950$		0			0
$951$	20.8083	−	28.6402i	0.674757	−	0.928723i
$952$		0			0
$953$	−34.8615	−	11.3272i	−1.12927	−	0.366923i	−0.315974	−	0.948768i	$-0.602331\pi$
$953$	−34.8615	−	11.3272i	−1.12927	−	0.366923i	−0.813300	+	0.581845i	$0.802331\pi$
$954$		0			0
$955$	2.92406	+	4.02462i	0.0946203	+	0.130234i
$956$		0			0
$957$	−25.4163	−	23.2595i	−0.821592	−	0.751874i
$958$		0			0
$959$	−0.0239209	+	15.3445i	−0.000772448	+	0.495499i
$960$		0			0
$961$	2.30573	−	7.09629i	0.0743782	−	0.228913i
$962$		0			0
$963$	1.17394	−	1.61579i	0.0378298	−	0.0520682i
$964$		0			0
$965$	−0.947205	−	2.91520i	−0.0304916	−	0.0938436i
$966$		0			0
$967$			19.7552i			0.635285i	0.948211	+	0.317642i	$0.102891\pi$
$967$			19.7552i			0.635285i	−0.948211	+	0.317642i	$0.897109\pi$
$968$		0			0
$969$			28.9157i			0.928905i
$970$		0			0
$971$	38.8681	−	12.6290i	1.24734	−	0.405284i	0.390371	−	0.920658i	$-0.372347\pi$
$971$	38.8681	−	12.6290i	1.24734	−	0.405284i	0.856966	+	0.515373i	$0.172347\pi$
$972$		0			0
$973$	20.4230	−	6.60064i	0.654730	−	0.211607i
$974$		0			0
$975$	26.3057	+	8.54725i	0.842457	+	0.273731i
$976$		0			0
$977$	−1.74168	+	1.26541i	−0.0557214	+	0.0404840i	−0.615297	−	0.788295i	$-0.710964\pi$
$977$	−1.74168	+	1.26541i	−0.0557214	+	0.0404840i	0.559576	+	0.828779i	$0.310964\pi$
$978$		0			0
$979$	6.81595	−	7.44797i	0.217839	−	0.238038i
$980$		0			0
$981$	−0.621742	−	0.855754i	−0.0198507	−	0.0273221i
$982$		0			0
$983$	−6.40312	−	2.08050i	−0.204228	−	0.0663576i	0.205117	−	0.978738i	$-0.434243\pi$
$983$	−6.40312	−	2.08050i	−0.204228	−	0.0663576i	−0.409345	+	0.912380i	$0.634243\pi$
$984$		0			0
$985$	−2.59046	−	1.88208i	−0.0825389	−	0.0599680i
$986$		0			0
$987$	−27.9865	−	9.14162i	−0.890820	−	0.290981i
$988$		0			0
$989$		−	7.48793i		−	0.238102i
$990$		0			0
$991$	0.474384			0.0150693			0.00753465	−	0.999972i	$-0.497602\pi$
$991$	0.474384			0.0150693			0.00753465	+	0.999972i	$0.497602\pi$
$992$		0			0
$993$	−25.9077	+	8.41793i	−0.822157	+	0.267135i
$994$		0			0
$995$	−4.03921	−	2.93466i	−0.128052	−	0.0930349i
$996$		0			0
$997$	8.67631	−	26.7029i	0.274782	−	0.845691i	−0.714495	−	0.699640i	$-0.753344\pi$
$997$	8.67631	−	26.7029i	0.274782	−	0.845691i	0.989277	−	0.146051i	$-0.0466563\pi$
$998$		0			0
$999$	3.20212	+	4.40734i	0.101311	+	0.139442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.w.a.41.6	yes	32
7.6	odd	2	inner	308.2.w.a.41.3	✓	32
11.2	odd	10		3388.2.c.c.1693.21		32
11.7	odd	10	inner	308.2.w.a.293.3	yes	32
11.9	even	5		3388.2.c.c.1693.11		32
77.13	even	10		3388.2.c.c.1693.12		32
77.20	odd	10		3388.2.c.c.1693.22		32
77.62	even	10	inner	308.2.w.a.293.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.w.a.41.3	✓	32	7.6	odd	2	inner
308.2.w.a.41.6	yes	32	1.1	even	1	trivial
308.2.w.a.293.3	yes	32	11.7	odd	10	inner
308.2.w.a.293.6	yes	32	77.62	even	10	inner
3388.2.c.c.1693.11		32	11.9	even	5
3388.2.c.c.1693.12		32	77.13	even	10
3388.2.c.c.1693.21		32	11.2	odd	10
3388.2.c.c.1693.22		32	77.20	odd	10

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51783 - 0.493173i) q^{3} +(0.260986 - 0.359216i) q^{5} +(1.55179 + 2.14288i) q^{7} +(-0.366459 + 0.266248i) q^{9} +(2.44672 + 2.23910i) q^{11} +(2.91934 - 2.12103i) q^{13} +(0.218977 - 0.673941i) q^{15} +(-1.73549 - 1.26091i) q^{17} +(-2.60996 - 8.03264i) q^{19} +(3.41217 + 2.48723i) q^{21} +1.73292 q^{23} +(1.48416 + 4.56778i) q^{25} +(-3.23913 + 4.45828i) q^{27} +(-6.19038 - 2.01138i) q^{29} +(-2.85173 - 3.92507i) q^{31} +(4.81797 + 2.19192i) q^{33} +(1.17475 + 0.00183136i) q^{35} +(0.305486 - 0.940189i) q^{37} +(3.38504 - 4.65910i) q^{39} +(2.71242 + 8.34796i) q^{41} -4.32100i q^{43} +0.201125i q^{45} +(-6.63136 + 2.15466i) q^{47} +(-2.18387 + 6.65062i) q^{49} +(-3.25602 - 1.05795i) q^{51} +(-7.09454 + 5.15449i) q^{53} +(1.44288 - 0.294528i) q^{55} +(-7.92297 - 10.9050i) q^{57} +(10.2903 + 3.34352i) q^{59} +(-5.62339 - 4.08563i) q^{61} +(-1.13921 - 0.372115i) q^{63} -1.60223i q^{65} +11.4870 q^{67} +(2.63028 - 0.854629i) q^{69} +(-10.6035 - 7.70387i) q^{71} +(-2.23211 + 6.86973i) q^{73} +(4.50542 + 6.20117i) q^{75} +(-1.00131 + 8.71765i) q^{77} +(-5.15765 - 7.09890i) q^{79} +(-2.29782 + 7.07198i) q^{81} +(-12.6408 - 9.18404i) q^{83} +(-0.905876 + 0.294337i) q^{85} -10.3879 q^{87} -3.04406i q^{89} +(9.07533 + 2.96440i) q^{91} +(-6.26418 - 4.55119i) q^{93} +(-3.56662 - 1.15887i) q^{95} +(0.726346 + 0.999730i) q^{97} +(-1.49278 - 0.169103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{7} + 14 q^{9} - 4 q^{11} - 6 q^{15} + 4 q^{23} + 32 q^{25} - 20 q^{29} + 15 q^{35} - 28 q^{37} - 20 q^{39} - 15 q^{49} + 60 q^{51} - 56 q^{53} + 80 q^{57} - 80 q^{63} - 88 q^{67} + 32 q^{71}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q - 5 * q^7 + 14 * q^9 - 4 * q^11 - 6 * q^15 + 4 * q^23 + 32 * q^25 - 20 * q^29 + 15 * q^35 - 28 * q^37 - 20 * q^39 - 15 * q^49 + 60 * q^51 - 56 * q^53 + 80 * q^57 - 80 * q^63 - 88 * q^67 + 32 * q^71 - 37 * q^77 - 30 * q^79 - 66 * q^81 + 10 * q^85 - 49 * q^91 - 22 * q^93 - 50 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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