LMFDB - Embedded newform 308.2.w.a.293.3

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			293.3
Character	$\chi$	$=$	308.293
Dual form			308.2.w.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.51783 - 0.493173i) q^{3} +(-0.260986 - 0.359216i) q^{5} +(2.51498 + 0.821504i) q^{7} +(-0.366459 - 0.266248i) q^{9} +(2.44672 - 2.23910i) q^{11} +(-2.91934 - 2.12103i) q^{13} +(0.218977 + 0.673941i) q^{15} +(1.73549 - 1.26091i) q^{17} +(2.60996 - 8.03264i) q^{19} +(-3.41217 - 2.48723i) q^{21} +1.73292 q^{23} +(1.48416 - 4.56778i) q^{25} +(3.23913 + 4.45828i) q^{27} +(-6.19038 + 2.01138i) q^{29} +(2.85173 - 3.92507i) q^{31} +(-4.81797 + 2.19192i) q^{33} +(-0.361277 - 1.11782i) q^{35} +(0.305486 + 0.940189i) q^{37} +(3.38504 + 4.65910i) q^{39} +(-2.71242 + 8.34796i) q^{41} +4.32100i q^{43} +0.201125i q^{45} +(6.63136 + 2.15466i) q^{47} +(5.65026 + 4.13213i) q^{49} +(-3.25602 + 1.05795i) q^{51} +(-7.09454 - 5.15449i) q^{53} +(-1.44288 - 0.294528i) q^{55} +(-7.92297 + 10.9050i) q^{57} +(-10.2903 + 3.34352i) q^{59} +(5.62339 - 4.08563i) q^{61} +(-0.702913 - 0.970656i) q^{63} +1.60223i q^{65} +11.4870 q^{67} +(-2.63028 - 0.854629i) q^{69} +(-10.6035 + 7.70387i) q^{71} +(2.23211 + 6.86973i) q^{73} +(-4.50542 + 6.20117i) q^{75} +(7.99288 - 3.62130i) q^{77} +(-5.15765 + 7.09890i) q^{79} +(-2.29782 - 7.07198i) q^{81} +(12.6408 - 9.18404i) q^{83} +(-0.905876 - 0.294337i) q^{85} +10.3879 q^{87} -3.04406i q^{89} +(-5.59966 - 7.73260i) q^{91} +(-6.26418 + 4.55119i) q^{93} +(-3.56662 + 1.15887i) q^{95} +(-0.726346 + 0.999730i) q^{97} +(-1.49278 + 0.169103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$	$1$

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	$-0.552405\pi$
$3$	−1.51783	−	0.493173i	−0.876320	−	0.284734i	−0.712429	+	0.701745i	$0.752405\pi$
$4$		0			0
$5$	−0.260986	−	0.359216i	−0.116716	−	0.160646i	0.746661	−	0.665204i	$-0.231656\pi$
$5$	−0.260986	−	0.359216i	−0.116716	−	0.160646i	−0.863378	+	0.504558i	$0.831656\pi$
$6$		0			0
$7$	2.51498	+	0.821504i	0.950574	+	0.310499i
$7$	2.51498	+	0.821504i	0.950574	+	0.310499i
$8$		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	$-0.466817\pi$
$13$	−2.91934	−	2.12103i	−0.809680	−	0.588267i	−0.913738	+	0.406304i	$0.866817\pi$
$14$		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	$-0.616231\pi$
$17$	1.73549	−	1.26091i	0.420917	−	0.305814i	0.778007	+	0.628256i	$0.216231\pi$
$18$		0			0
$19$	2.60996	−	8.03264i	0.598767	−	1.84282i	0.0637637	−	0.997965i	$-0.479690\pi$
$19$	2.60996	−	8.03264i	0.598767	−	1.84282i	0.535003	−	0.844850i	$-0.320310\pi$
$20$		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	−0.820964	−	0.570980i	$-0.806563\pi$
$29$	−6.19038	+	2.01138i	−1.14952	+	0.373503i	−0.328560	+	0.944483i	$0.606563\pi$
$30$		0			0
$31$	2.85173	−	3.92507i	0.512186	−	0.704963i	−0.472100	−	0.881545i	$-0.656504\pi$
$31$	2.85173	−	3.92507i	0.512186	−	0.704963i	0.984286	+	0.176582i	$0.0565040\pi$
$32$		0			0
$33$	−4.81797	+	2.19192i	−0.838701	+	0.381564i
$34$		0			0
$35$	−0.361277	−	1.11782i	−0.0610670	−	0.188947i
$36$		0			0
$37$	0.305486	+	0.940189i	0.0502216	+	0.154566i	0.973022	−	0.230712i	$-0.0741055\pi$
$37$	0.305486	+	0.940189i	0.0502216	+	0.154566i	−0.922801	+	0.385278i	$0.874106\pi$
$38$		0			0
$39$	3.38504	+	4.65910i	0.542040	+	0.746054i
$40$		0			0
$41$	−2.71242	+	8.34796i	−0.423608	+	1.30373i	0.480712	+	0.876878i	$0.340378\pi$
$41$	−2.71242	+	8.34796i	−0.423608	+	1.30373i	−0.904321	+	0.426854i	$0.859622\pi$
$42$		0			0
$43$			4.32100i			0.658946i	0.944165	+	0.329473i	$0.106871\pi$
$43$			4.32100i			0.658946i	−0.944165	+	0.329473i	$0.893129\pi$
$44$		0			0
$45$			0.201125i			0.0299819i
$46$		0			0
$47$	6.63136	+	2.15466i	0.967284	+	0.314289i	0.749719	−	0.661756i	$-0.230189\pi$
$47$	6.63136	+	2.15466i	0.967284	+	0.314289i	0.217565	+	0.976046i	$0.430189\pi$
$48$		0			0
$49$	5.65026	+	4.13213i	0.807180	+	0.590305i
$50$		0			0
$51$	−3.25602	+	1.05795i	−0.455934	+	0.148142i
$52$		0			0
$53$	−7.09454	−	5.15449i	−0.974510	−	0.708023i	−0.0180352	−	0.999837i	$-0.505741\pi$
$53$	−7.09454	−	5.15449i	−0.974510	−	0.708023i	−0.956475	+	0.291814i	$0.905741\pi$
$54$		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	$-0.848745\pi$
$59$	−10.2903	+	3.34352i	−1.33968	+	0.435289i	−0.450474	+	0.892790i	$0.648745\pi$
$60$		0			0
$61$	5.62339	−	4.08563i	0.720001	−	0.523112i	−0.166383	−	0.986061i	$-0.553209\pi$
$61$	5.62339	−	4.08563i	0.720001	−	0.523112i	0.886385	+	0.462949i	$0.153209\pi$
$62$		0			0
$63$	−0.702913	−	0.970656i	−0.0885587	−	0.122291i
$64$		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	−0.998678	−	0.0514017i	$-0.983631\pi$
$71$	−10.6035	+	7.70387i	−1.25840	+	0.914282i	−0.259723	+	0.965683i	$0.583631\pi$
$72$		0			0
$73$	2.23211	+	6.86973i	0.261249	+	0.804041i	0.992534	+	0.121969i	$0.0389209\pi$
$73$	2.23211	+	6.86973i	0.261249	+	0.804041i	−0.731285	+	0.682072i	$0.761079\pi$
$74$		0			0
$75$	−4.50542	+	6.20117i	−0.520241	+	0.716050i
$76$		0			0
$77$	7.99288	−	3.62130i	0.910874	−	0.412686i
$78$		0			0
$79$	−5.15765	+	7.09890i	−0.580281	+	0.798688i	−0.993726	−	0.111841i	$-0.964325\pi$
$79$	−5.15765	+	7.09890i	−0.580281	+	0.798688i	0.413445	+	0.910529i	$0.364325\pi$
$80$		0			0
$81$	−2.29782	−	7.07198i	−0.255314	−	0.785775i
$82$		0			0
$83$	12.6408	−	9.18404i	1.38750	−	1.00808i	0.391369	−	0.920234i	$-0.372002\pi$
$83$	12.6408	−	9.18404i	1.38750	−	1.00808i	0.996134	−	0.0878459i	$-0.0279983\pi$
$84$		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
$91$	−5.59966	−	7.73260i	−0.587004	−	0.810596i
$92$		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	$-0.819982\pi$
$97$	−0.726346	+	0.999730i	−0.0737493	+	0.101507i	0.770549	+	0.637381i	$0.219982\pi$
$98$		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	$-0.194603\pi$
$101$	5.28642	+	3.84081i	0.526018	+	0.382175i	−0.292848	+	0.956159i	$0.594603\pi$
$102$		0			0
$103$	−6.52767	+	2.12097i	−0.643190	+	0.208985i	−0.612409	−	0.790541i	$-0.709799\pi$
$103$	−6.52767	+	2.12097i	−0.643190	+	0.208985i	−0.0307811	+	0.999526i	$0.509799\pi$
$104$		0			0
$105$	−0.00292274	+	1.87484i	−0.000285231	+	0.182966i
$106$		0			0
$107$	−4.19341	−	1.36252i	−0.405392	−	0.131720i	0.0992212	−	0.995065i	$-0.468365\pi$
$107$	−4.19341	−	1.36252i	−0.405392	−	0.131720i	−0.504613	+	0.863346i	$0.668365\pi$
$108$		0			0
$109$		−	2.33520i		−	0.223671i	−0.993727	−	0.111836i	$-0.964327\pi$
$109$		−	2.33520i		−	0.223671i	0.993727	−	0.111836i	$-0.0356730\pi$
$110$		0			0
$111$		−	1.57771i		−	0.149749i
$112$		0			0
$113$	−0.309026	+	0.951085i	−0.0290707	+	0.0894705i	−0.964539	−	0.263940i	$-0.914978\pi$
$113$	−0.309026	+	0.951085i	−0.0290707	+	0.0894705i	0.935468	+	0.353410i	$0.114978\pi$
$114$		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
$119$	5.40056	−	1.74544i	0.495068	−	0.160005i
$120$		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	0.922584	+	0.385797i	$0.126073\pi$
$127$	11.3191	+	15.5794i	1.00440	+	1.38244i	0.0818207	+	0.996647i	$0.473927\pi$
$128$		0			0
$129$	2.13100	−	6.55855i	0.187624	−	0.577448i
$130$		0			0
$131$	−8.11514			−0.709023			−0.354512	−	0.935052i	$-0.615353\pi$
$131$	−8.11514			−0.709023			−0.354512	+	0.935052i	$0.615353\pi$
$132$		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	−0.369027	−	0.929419i	$-0.620309\pi$
$137$	4.69203	−	3.40896i	0.400867	−	0.291247i	0.769894	+	0.638172i	$0.220309\pi$
$138$		0			0
$139$	−2.50684	−	7.71526i	−0.212627	−	0.654399i	−0.999314	−	0.0370465i	$-0.988205\pi$
$139$	−2.50684	−	7.71526i	−0.212627	−	0.654399i	0.786686	−	0.617353i	$-0.211795\pi$
$140$		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
$147$	−6.53829	−	9.05844i	−0.539269	−	0.747128i
$148$		0			0
$149$	7.95668	+	10.9514i	0.651836	+	0.897176i	0.999177	−	0.0405631i	$-0.0129152\pi$
$149$	7.95668	+	10.9514i	0.651836	+	0.897176i	−0.347340	+	0.937739i	$0.612915\pi$
$150$		0			0
$151$	10.2668	+	3.33588i	0.835498	+	0.271470i	0.695359	−	0.718662i	$-0.255245\pi$
$151$	10.2668	+	3.33588i	0.835498	+	0.271470i	0.140138	+	0.990132i	$0.455245\pi$
$152$		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	$-0.624971\pi$
$157$	−15.4769	−	5.02875i	−1.23519	−	0.401338i	−0.852593	+	0.522576i	$0.824971\pi$
$158$		0			0
$159$	8.22626	+	11.3225i	0.652385	+	0.897931i
$160$		0			0
$161$	4.35825	+	1.42360i	0.343479	+	0.112195i
$162$		0			0
$163$	3.86774	+	2.81008i	0.302945	+	0.220102i	0.728863	−	0.684659i	$-0.240049\pi$
$163$	3.86774	+	2.81008i	0.302945	+	0.220102i	−0.425919	+	0.904761i	$0.640049\pi$
$164$		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	$-0.273478\pi$
$167$	1.74020	+	1.26433i	0.134661	+	0.0978367i	−0.518416	+	0.855129i	$0.673478\pi$
$168$		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	0.464476	+	0.885586i	$0.346243\pi$
$173$	−5.67980	+	17.4806i	−0.431827	+	1.32903i	−0.896303	+	0.443442i	$0.853757\pi$
$174$		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	−0.587043	−	0.809556i	$-0.699708\pi$
$179$	4.86637	−	14.9771i	0.363730	−	1.11944i	0.950773	−	0.309889i	$-0.100292\pi$
$180$		0			0
$181$	−2.36514	−	3.25534i	−0.175800	−	0.241968i	0.712020	−	0.702159i	$-0.247781\pi$
$181$	−2.36514	−	3.25534i	−0.175800	−	0.241968i	−0.887820	+	0.460192i	$0.847781\pi$
$182$		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
$189$	4.48386	+	13.8735i	0.326153	+	1.00915i
$190$		0			0
$191$	−3.46219	−	10.6555i	−0.250516	−	0.771008i	−0.994680	−	0.103011i	$-0.967152\pi$
$191$	−3.46219	−	10.6555i	−0.250516	−	0.771008i	0.744165	−	0.667996i	$-0.232848\pi$
$192$		0			0
$193$	4.05772	+	5.58497i	0.292081	+	0.402015i	0.929689	−	0.368346i	$-0.120076\pi$
$193$	4.05772	+	5.58497i	0.292081	+	0.402015i	−0.637608	+	0.770361i	$0.720076\pi$
$194$		0			0
$195$	0.790179	−	2.43192i	0.0565859	−	0.174154i
$196$		0			0
$197$			7.21142i			0.513792i	0.966439	+	0.256896i	$0.0826998\pi$
$197$			7.21142i			0.513792i	−0.966439	+	0.256896i	$0.917300\pi$
$198$		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
$203$	−17.2210	−	0.0268464i	−1.20868	−	0.00188425i
$204$		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	−0.347031	−	0.937854i	$-0.612810\pi$
$211$	9.47316	−	13.0387i	0.652159	−	0.897620i	0.999190	+	0.0402337i	$0.0128103\pi$
$212$		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
$217$	10.3965	−	7.52877i	0.705761	−	0.511086i
$218$		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	0.998830	+	0.0483543i	$0.0153977\pi$
$223$	27.4072	+	8.90514i	1.83532	+	0.596333i	0.836493	+	0.547978i	$0.184602\pi$
$224$		0			0
$225$	−1.76005	+	1.27875i	−0.117336	+	0.0852499i
$226$		0			0
$227$	6.19616	+	19.0698i	0.411253	+	1.26571i	0.915559	+	0.402183i	$0.131748\pi$
$227$	6.19616	+	19.0698i	0.411253	+	1.26571i	−0.504306	+	0.863525i	$0.668252\pi$
$228$		0			0
$229$	−1.89669	+	2.61056i	−0.125337	+	0.172511i	−0.867074	−	0.498179i	$-0.834002\pi$
$229$	−1.89669	+	2.61056i	−0.125337	+	0.172511i	0.741737	+	0.670690i	$0.234002\pi$
$230$		0			0
$231$	−13.9178	+	1.55465i	−0.915723	+	0.102288i
$232$		0			0
$233$	−4.51877	+	6.21955i	−0.296034	+	0.407456i	−0.930962	−	0.365115i	$-0.881030\pi$
$233$	−4.51877	+	6.21955i	−0.296034	+	0.407456i	0.634928	+	0.772571i	$0.281030\pi$
$234$		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	0.248896	−	0.968530i	$-0.419932\pi$
$239$	−1.84016	−	0.597905i	−0.119030	−	0.0386752i	−0.367926	+	0.929855i	$0.619932\pi$
$240$		0			0
$241$	−13.4236			−0.864692			−0.432346	−	0.901708i	$-0.642314\pi$
$241$	−13.4236			−0.864692			−0.432346	+	0.901708i	$0.642314\pi$
$242$		0			0
$243$		−	4.66492i		−	0.299255i
$244$		0			0
$245$	0.00969063	−	3.10810i	0.000619112	−	0.198569i
$246$		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	−0.267015	+	0.963692i	$0.586037\pi$
$251$	−17.4436	+	24.0090i	−1.10103	+	1.51544i	−0.834014	+	0.551744i	$0.813963\pi$
$252$		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	$-0.365789\pi$
$257$	20.4663	−	6.64992i	1.27666	−	0.414810i	0.867401	+	0.497610i	$0.165789\pi$
$258$		0			0
$259$	−0.00407741	+	2.61552i	−0.000253358	+	0.162520i
$260$		0			0
$261$	2.80404	+	0.911089i	0.173566	+	0.0563950i
$262$		0			0
$263$			18.6389i			1.14932i	0.818392	+	0.574660i	$0.194866\pi$
$263$			18.6389i			1.14932i	−0.818392	+	0.574660i	$0.805134\pi$
$264$		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	0.999997	+	0.00247482i	$0.000787760\pi$
$269$	11.3715	+	15.6516i	0.693335	+	0.954293i	−0.306662	+	0.951818i	$0.599212\pi$
$270$		0			0
$271$	3.14727	+	9.68630i	0.191183	+	0.588401i	1.00000		0.000340354i	$0.000108338\pi$
$271$	3.14727	+	9.68630i	0.191183	+	0.588401i	−0.808817	+	0.588061i	$0.799892\pi$
$272$		0			0
$273$	4.68583	+	14.4984i	0.283600	+	0.877482i
$274$		0			0
$275$	−6.59638	−	14.4993i	−0.397777	−	0.874339i
$276$		0			0
$277$	−0.827606	+	1.13910i	−0.0497260	+	0.0684420i	−0.833156	−	0.553038i	$-0.813468\pi$
$277$	−0.827606	+	1.13910i	−0.0497260	+	0.0684420i	0.783430	+	0.621480i	$0.213468\pi$
$278$		0			0
$279$	−2.09008	+	0.679109i	−0.125130	+	0.0406572i
$280$		0			0
$281$	0.401849	+	0.553097i	0.0239723	+	0.0329950i	0.820835	−	0.571166i	$-0.193509\pi$
$281$	0.401849	+	0.553097i	0.0239723	+	0.0329950i	−0.796863	+	0.604161i	$0.793509\pi$
$282$		0			0
$283$	2.07722	−	6.39302i	0.123478	−	0.380026i	−0.870143	−	0.492800i	$-0.835974\pi$
$283$	2.07722	−	6.39302i	0.123478	−	0.380026i	0.993621	+	0.112774i	$0.0359736\pi$
$284$		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	$-0.0514065\pi$
$293$	1.60874	+	4.95120i	0.0939837	+	0.289252i	−0.893004	+	0.450049i	$0.851406\pi$
$294$		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
$301$	−3.54972	+	10.8672i	−0.204602	+	0.626377i
$302$		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	$-0.616854\pi$
$307$	−12.5775			−0.717835			−0.358917	+	0.933369i	$0.616854\pi$
$308$		0			0
$309$	10.9539			0.623146
$310$		0			0
$311$	−18.5680	−	6.03310i	−1.05289	−	0.342105i	−0.269090	−	0.963115i	$-0.586723\pi$
$311$	−18.5680	−	6.03310i	−1.05289	−	0.342105i	−0.783803	+	0.621010i	$0.786723\pi$
$312$		0			0
$313$	1.42488	+	1.96118i	0.0805389	+	0.110852i	0.847386	−	0.530978i	$-0.178175\pi$
$313$	1.42488	+	1.96118i	0.0805389	+	0.110852i	−0.766847	+	0.641830i	$0.778175\pi$
$314$		0			0
$315$	−0.165225	+	0.505825i	−0.00930937	+	0.0285000i
$316$		0			0
$317$	17.9456	+	13.0383i	1.00793	+	0.732303i	0.963773	−	0.266722i	$-0.0859406\pi$
$317$	17.9456	+	13.0383i	1.00793	+	0.732303i	0.0441545	+	0.999025i	$0.485941\pi$
$318$		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	−0.210176	−	0.977664i	$-0.567404\pi$
$337$	3.56954	−	1.15981i	0.194445	−	0.0631791i	0.404621	+	0.914485i	$0.367404\pi$
$338$		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
$343$	10.8157	+	15.0340i	0.583995	+	0.811757i
$344$		0			0
$345$	0.379469	+	1.16788i	0.0204299	+	0.0628768i
$346$		0			0
$347$	19.8432	+	27.3118i	1.06524	+	1.46617i	0.874807	+	0.484472i	$0.160988\pi$
$347$	19.8432	+	27.3118i	1.06524	+	1.46617i	0.190430	+	0.981701i	$0.439012\pi$
$348$		0			0
$349$	−7.15449	+	22.0193i	−0.382971	+	1.17866i	0.554970	+	0.831870i	$0.312730\pi$
$349$	−7.15449	+	22.0193i	−0.382971	+	1.17866i	−0.937941	+	0.346794i	$0.887270\pi$
$350$		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
$357$	−9.05794	−	0.0141207i	−0.479397	−	0.000747346i
$358$		0			0
$359$	14.3580	−	4.66519i	0.757785	−	0.246219i	0.0954573	−	0.995434i	$-0.469569\pi$
$359$	14.3580	−	4.66519i	0.757785	−	0.246219i	0.662328	+	0.749214i	$0.269569\pi$
$360$		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	$-0.619330\pi$
$367$	−2.21153	+	0.718570i	−0.115441	+	0.0375090i	0.250727	+	0.968058i	$0.419330\pi$
$368$		0			0
$369$	3.21661	−	2.33701i	0.167450	−	0.121660i
$370$		0			0
$371$	−13.6082	−	18.7916i	−0.706503	−	0.975613i
$372$		0			0
$373$		−	3.48084i		−	0.180231i	−0.995931	−	0.0901156i	$-0.971276\pi$
$373$		−	3.48084i		−	0.180231i	0.995931	−	0.0901156i	$-0.0287236\pi$
$374$		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	0.0290224	−	0.999579i	$-0.490761\pi$
$379$	19.2469	−	13.9837i	0.988647	−	0.718294i	0.959624	+	0.281285i	$0.0907606\pi$
$380$		0			0
$381$	−9.49711	−	29.2291i	−0.486552	−	1.49745i
$382$		0			0
$383$	18.8512	−	25.9464i	0.963249	−	1.32580i	0.0178650	−	0.999840i	$-0.494313\pi$
$383$	18.8512	−	25.9464i	0.963249	−	1.32580i	0.945384	−	0.325958i	$-0.105687\pi$
$384$		0			0
$385$	−3.38686	−	1.92607i	−0.172610	−	0.0981614i
$386$		0			0
$387$	1.15046	−	1.58347i	0.0584810	−	0.0804922i
$388$		0			0
$389$	3.64253	+	11.2106i	0.184684	+	0.568398i	0.999943	−	0.0106986i	$-0.00340555\pi$
$389$	3.64253	+	11.2106i	0.184684	+	0.568398i	−0.815259	+	0.579096i	$0.803406\pi$
$390$		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
$399$	−28.8847	+	20.9172i	−1.44604	+	1.04717i
$400$		0			0
$401$	23.7999	−	17.2916i	1.18851	−	0.863503i	0.195403	−	0.980723i	$-0.437398\pi$
$401$	23.7999	−	17.2916i	1.18851	−	0.863503i	0.993106	+	0.117220i	$0.0373984\pi$
$402$		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	$-0.118827\pi$
$409$	17.6354	+	12.8129i	0.872015	+	0.633556i	−0.0591118	+	0.998251i	$0.518827\pi$
$410$		0			0
$411$	−8.80292	+	2.86024i	−0.434216	+	0.141085i
$412$		0			0
$413$	−28.6266	−	0.0446269i	−1.40862	−	0.00219595i
$414$		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	0.117219	−	0.993106i	$-0.462602\pi$
$421$	12.4365	−	38.2757i	0.606120	−	1.86545i	0.488901	−	0.872339i	$-0.337398\pi$
$422$		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
$427$	17.4991	−	5.65565i	0.846840	−	0.273696i
$428$		0			0
$429$	18.7144	+	3.82009i	0.903541	+	0.184436i
$430$		0			0
$431$	14.5687	−	20.0520i	0.701748	−	0.965873i	−0.298188	−	0.954507i	$-0.596382\pi$
$431$	14.5687	−	20.0520i	0.701748	−	0.965873i	0.999935	−	0.0113655i	$-0.00361782\pi$
$432$		0			0
$433$	−4.75912	+	1.54633i	−0.228709	+	0.0743120i	−0.421129	−	0.907001i	$-0.638366\pi$
$433$	−4.75912	+	1.54633i	−0.228709	+	0.0743120i	0.192421	+	0.981313i	$0.438366\pi$
$434$		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	$-0.540892\pi$
$439$	−5.36847			−0.256223			−0.128112	+	0.991760i	$0.540892\pi$
$440$		0			0
$441$	−0.970416	−	3.01863i	−0.0462103	−	0.143744i
$442$		0			0
$443$	3.07670	−	9.46910i	0.146178	−	0.449891i	−0.850982	−	0.525194i	$-0.823993\pi$
$443$	3.07670	−	9.46910i	0.146178	−	0.449891i	0.997161	+	0.0753037i	$0.0239926\pi$
$444$		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	0.438276	−	0.898840i	$-0.355589\pi$
$449$	−5.95718	−	4.32815i	−0.281137	−	0.204258i	−0.719413	+	0.694582i	$0.755589\pi$
$450$		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
$455$	−1.31624	+	4.02959i	−0.0617064	+	0.188910i
$456$		0			0
$457$	−18.4581	−	25.4054i	−0.863434	−	1.18842i	−0.980740	−	0.195319i	$-0.937426\pi$
$457$	−18.4581	−	25.4054i	−0.863434	−	1.18842i	0.117305	−	0.993096i	$-0.462574\pi$
$458$		0			0
$459$	11.2429	+	3.65305i	0.524775	+	0.170510i
$460$		0			0
$461$	5.60541			0.261070			0.130535	−	0.991444i	$-0.458330\pi$
$461$	5.60541			0.261070			0.130535	+	0.991444i	$0.458330\pi$
$462$		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	−0.999680	−	0.0252920i	$-0.991948\pi$
$467$	−15.4473	−	21.2614i	−0.714816	−	0.983860i	0.284864	−	0.958568i	$-0.408052\pi$
$468$		0			0
$469$	28.8896	+	9.43663i	1.33400	+	0.435743i
$470$		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	$-0.621400\pi$
$479$	8.65578	−	6.28879i	0.395493	−	0.287342i	0.767703	+	0.640806i	$0.221400\pi$
$480$		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	0.739183	+	0.673505i	$0.235212\pi$
$487$	−5.62084	+	17.2992i	−0.254705	+	0.783900i	−0.993888	+	0.110396i	$0.964788\pi$
$488$		0			0
$489$	−4.48472	−	6.17268i	−0.202806	−	0.279138i
$490$		0			0
$491$	19.5042	−	6.33731i	0.880214	−	0.285999i	0.166168	−	0.986098i	$-0.446861\pi$
$491$	19.5042	−	6.33731i	0.880214	−	0.285999i	0.714046	+	0.700099i	$0.246861\pi$
$492$		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
$497$	−32.9963	+	10.6643i	−1.48009	+	0.478360i
$498$		0			0
$499$	0.232751	+	0.716334i	0.0104194	+	0.0320675i	0.956131	−	0.292939i	$-0.0946334\pi$
$499$	0.232751	+	0.716334i	0.0104194	+	0.0320675i	−0.945712	+	0.325007i	$0.894633\pi$
$500$		0			0
$501$	−2.01780	−	2.77726i	−0.0901484	−	0.124079i
$502$		0			0
$503$	−4.80094	+	14.7758i	−0.214063	+	0.658819i	0.785156	+	0.619299i	$0.212583\pi$
$503$	−4.80094	+	14.7758i	−0.214063	+	0.658819i	−0.999219	+	0.0395202i	$0.987417\pi$
$504$		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	$-0.263417\pi$
$509$	17.8539	+	5.80107i	0.791359	+	0.257128i	0.114676	+	0.993403i	$0.463417\pi$
$510$		0			0
$511$	−0.0297926	+	19.1109i	−0.00131795	+	0.845418i
$512$		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	$-0.881900\pi$
$521$	−33.6176	+	10.9230i	−1.47281	+	0.478546i	−0.540856	+	0.841115i	$0.681900\pi$
$522$		0			0
$523$	9.67925	−	7.03239i	0.423244	−	0.307505i	−0.355698	−	0.934601i	$-0.615757\pi$
$523$	9.67925	−	7.03239i	0.423244	−	0.307505i	0.778942	+	0.627096i	$0.215757\pi$
$524$		0			0
$525$	−16.4253	+	11.8946i	−0.716860	+	0.519124i
$526$		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
$539$	23.0769	−	2.54132i	0.993991	−	0.109463i
$540$		0			0
$541$	−18.6807	+	25.7117i	−0.803145	+	1.10543i	0.189200	+	0.981939i	$0.439411\pi$
$541$	−18.6807	+	25.7117i	−0.803145	+	1.10543i	−0.992345	+	0.123496i	$0.960589\pi$
$542$		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	0.665790	−	0.746139i	$-0.268095\pi$
$547$	17.9119	+	5.81992i	0.765856	+	0.248842i	0.100066	+	0.994981i	$0.468095\pi$
$548$		0			0
$549$	−3.14853			−0.134376
$550$		0			0
$551$			54.9747i			2.34200i
$552$		0			0
$553$	−18.8032	+	13.6166i	−0.799592	+	0.579035i
$554$		0			0
$555$	−0.566738	+	0.411759i	−0.0240567	+	0.0174782i
$556$		0			0
$557$	−39.4101	+	12.8051i	−1.66986	+	0.542571i	−0.982903	−	0.184127i	$-0.941054\pi$
$557$	−39.4101	+	12.8051i	−1.66986	+	0.542571i	−0.686958	+	0.726697i	$0.741054\pi$
$558$		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	$-0.432544\pi$
$563$	−15.5284	−	11.2821i	−0.654445	−	0.475482i	−0.864782	+	0.502147i	$0.832544\pi$
$564$		0			0
$565$	0.422297	−	0.137213i	0.0177662	−	0.00577257i
$566$		0			0
$567$	0.0306697	−	19.6736i	0.00128801	−	0.826212i
$568$		0			0
$569$	−12.8183	−	4.16491i	−0.537370	−	0.174602i	0.0277437	−	0.999615i	$-0.491168\pi$
$569$	−12.8183	−	4.16491i	−0.537370	−	0.174602i	−0.565114	+	0.825013i	$0.691168\pi$
$570$		0			0
$571$			20.4722i			0.856736i	0.903604	+	0.428368i	$0.140911\pi$
$571$			20.4722i			0.856736i	−0.903604	+	0.428368i	$0.859089\pi$
$572$		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	−0.995154	−	0.0983260i	$-0.968651\pi$
$577$	−18.7638	−	25.8262i	−0.781148	−	1.07516i	0.214006	−	0.976832i	$-0.431349\pi$
$578$		0			0
$579$	−3.40458	−	10.4782i	−0.141489	−	0.435459i
$580$		0			0
$581$	39.3360	−	12.7133i	1.63193	−	0.527436i
$582$		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	$-0.566835\pi$
$587$	4.79284	−	1.55729i	0.197822	−	0.0642762i	0.406252	+	0.913761i	$0.366835\pi$
$588$		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	$-0.346526\pi$
$593$	22.5830			0.927373			0.463686	+	0.885999i	$0.346526\pi$
$594$		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	0.303566	−	0.952810i	$-0.401823\pi$
$599$	31.9037	−	23.1794i	1.30355	−	0.947084i	0.999984	+	0.00572612i	$0.00182269\pi$
$600$		0			0
$601$	−4.65003	−	14.3113i	−0.189679	−	0.583771i	0.810319	−	0.585989i	$-0.199294\pi$
$601$	−4.65003	−	14.3113i	−0.189679	−	0.583771i	−0.999998	+	0.00221837i	$0.999294\pi$
$602$		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	$-0.275480\pi$
$607$	3.06776	+	2.22886i	0.124517	+	0.0904666i	−0.523784	+	0.851851i	$0.675480\pi$
$608$		0			0
$609$	26.1254	+	8.53371i	1.05865	+	0.345803i
$610$		0			0
$611$	−14.7891	−	20.3555i	−0.598304	−	0.823495i
$612$		0			0
$613$	−20.4135	−	6.63276i	−0.824495	−	0.267895i	−0.133770	−	0.991012i	$-0.542708\pi$
$613$	−20.4135	−	6.63276i	−0.824495	−	0.267895i	−0.690725	+	0.723118i	$0.742708\pi$
$614$		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	$-0.0631835\pi$
$619$	41.2403	+	13.3998i	1.65759	+	0.538582i	0.677222	+	0.735778i	$0.263184\pi$
$620$		0			0
$621$	5.61315	+	7.72583i	0.225248	+	0.310027i
$622$		0			0
$623$	2.50071	−	7.65576i	0.100189	−	0.306721i
$624$		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	0.985454	+	0.169943i	$0.0543583\pi$
$631$	7.23686	+	22.2728i	0.288095	+	0.886665i	−0.697359	+	0.716722i	$0.745642\pi$
$632$		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	−0.855701	−	0.517471i	$-0.826874\pi$
$641$	3.56318	−	10.9663i	0.140737	−	0.433145i	0.996438	+	0.0843259i	$0.0268737\pi$
$642$		0			0
$643$	22.4020	+	30.8337i	0.883449	+	1.21596i	0.975454	+	0.220204i	$0.0706723\pi$
$643$	22.4020	+	30.8337i	0.883449	+	1.21596i	−0.0920053	+	0.995759i	$0.529328\pi$
$644$		0			0
$645$	−2.91210	+	0.946198i	−0.114664	+	0.0372565i
$646$		0			0
$647$	25.2211	−	34.7139i	0.991545	−	1.36475i	0.0611738	−	0.998127i	$-0.480516\pi$
$647$	25.2211	−	34.7139i	0.991545	−	1.36475i	0.930372	−	0.366618i	$-0.119484\pi$
$648$		0			0
$649$	−17.6910	+	31.2217i	−0.694433	+	1.22556i
$650$		0			0
$651$	−19.4931	+	6.30012i	−0.763996	+	0.246921i
$652$		0			0
$653$	12.1563	+	37.4131i	0.475711	+	1.46409i	0.844996	+	0.534772i	$0.179603\pi$
$653$	12.1563	+	37.4131i	0.475711	+	1.46409i	−0.369285	+	0.929316i	$0.620397\pi$
$654$		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	$0.218991\pi$
$659$			32.6010i			1.26995i	−0.772531	+	0.634977i	$0.781009\pi$
$660$		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
$665$	−9.92200	−	0.0154677i	−0.384759	−	0.000599812i
$666$		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	−0.718230	−	0.695806i	$-0.755047\pi$
$673$	4.29258	−	5.90822i	0.165467	−	0.227745i	0.883696	+	0.468061i	$0.155047\pi$
$674$		0			0
$675$	25.1718	−	8.17883i	0.968865	−	0.314803i
$676$		0			0
$677$	−36.0174	+	26.1682i	−1.38426	+	1.00572i	−0.387793	+	0.921747i	$0.626762\pi$
$677$	−36.0174	+	26.1682i	−1.38426	+	1.00572i	−0.996468	+	0.0839776i	$0.973238\pi$
$678$		0			0
$679$	−2.64803	+	1.91761i	−0.101622	+	0.0735909i
$680$		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	$-0.863312\pi$
$691$	−6.10596	+	8.40414i	−0.232282	+	0.319709i	0.676926	+	0.736051i	$0.263312\pi$
$692$		0			0
$693$	−3.89322	−	0.801030i	−0.147891	−	0.0304286i
$694$		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	−0.368929	−	0.929458i	$-0.620275\pi$
$701$	−32.1350	−	10.4413i	−1.21372	−	0.394362i	−0.844791	+	0.535096i	$0.820275\pi$
$702$		0			0
$703$	8.34951			0.314908
$704$		0			0
$705$			4.94097i			0.186088i
$706$		0			0
$707$	10.1400	+	14.0024i	0.381354	+	0.526613i
$708$		0			0
$709$	−20.5659	+	14.9420i	−0.772369	+	0.561159i	−0.902679	−	0.430314i	$-0.858403\pi$
$709$	−20.5659	+	14.9420i	−0.772369	+	0.561159i	0.130310	+	0.991473i	$0.458403\pi$
$710$		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	$-0.768571\pi$
$719$	−25.7655	+	8.37173i	−0.960893	+	0.312213i	−0.213759	+	0.976886i	$0.568571\pi$
$720$		0			0
$721$	−18.1593	−	0.0283092i	−0.676289	−	0.00105429i
$722$		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	$-0.0564376\pi$
$733$	2.28281	+	7.02575i	0.0843174	+	0.259502i	−0.900005	+	0.435879i	$0.856438\pi$
$734$		0			0
$735$	−1.54754	+	4.71279i	−0.0570818	+	0.173834i
$736$		0			0
$737$	28.1055	−	25.7206i	1.03528	−	0.947430i
$738$		0			0
$739$	21.5322	−	29.6365i	0.792074	−	1.09020i	−0.201773	−	0.979432i	$-0.564670\pi$
$739$	21.5322	−	29.6365i	0.792074	−	1.09020i	0.993847	−	0.110763i	$-0.0353296\pi$
$740$		0			0
$741$	46.2598	−	15.0307i	1.69939	−	0.552167i
$742$		0			0
$743$	−1.33518	−	1.83771i	−0.0489828	−	0.0674191i	0.783823	−	0.620984i	$-0.213267\pi$
$743$	−1.33518	−	1.83771i	−0.0489828	−	0.0674191i	−0.832806	+	0.553565i	$0.813267\pi$
$744$		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	0.725723	+	0.687987i	$0.241505\pi$
$751$	−7.28375	+	22.4171i	−0.265788	+	0.818010i	−0.991511	+	0.130024i	$0.958495\pi$
$752$		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	0.545812	−	0.837908i	$-0.316221\pi$
$757$	−2.26770	−	1.64758i	−0.0824211	−	0.0598824i	−0.628233	+	0.778025i	$0.716221\pi$
$758$		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	$-0.160775\pi$
$761$	18.9065	+	13.7363i	0.685358	+	0.497942i	−0.189773	+	0.981828i	$0.560775\pi$
$762$		0			0
$763$	1.91837	−	5.87298i	0.0694498	−	0.212616i
$764$		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	$-0.672339\pi$
$769$	−28.5824			−1.03071			−0.515354	+	0.856978i	$0.672339\pi$
$770$		0			0
$771$	−34.3440			−1.23687
$772$		0			0
$773$	−39.0657	−	12.6932i	−1.40510	−	0.456543i	−0.494261	−	0.869314i	$-0.664561\pi$
$773$	−39.0657	−	12.6932i	−1.40510	−	0.456543i	−0.910835	+	0.412770i	$0.864561\pi$
$774$		0			0
$775$	−13.6964	−	18.8515i	−0.491990	−	0.677166i
$776$		0			0
$777$	1.29609	−	3.96790i	0.0464970	−	0.142348i
$778$		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	−0.314425	+	0.949282i	$0.601812\pi$
$787$	−36.8738	+	26.7904i	−1.31441	+	0.954974i	−0.999984	+	0.00569143i	$0.998188\pi$
$788$		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	$-0.339845\pi$
$797$	−14.1160	−	19.4290i	−0.500014	−	0.688210i	−0.982196	+	0.187861i	$0.939845\pi$
$798$		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
$805$	−0.626064	−	1.93710i	−0.0220658	−	0.0682736i
$806$		0			0
$807$	−9.54113	−	29.3646i	−0.335864	−	1.03368i
$808$		0			0
$809$	−20.7362	−	28.5409i	−0.729045	−	1.00344i	−0.999175	−	0.0406209i	$-0.987066\pi$
$809$	−20.7362	−	28.5409i	−0.729045	−	1.00344i	0.270129	−	0.962824i	$-0.412934\pi$
$810$		0			0
$811$	−0.102098	+	0.314226i	−0.00358516	+	0.0110340i	−0.952833	−	0.303495i	$-0.901846\pi$
$811$	−0.102098	+	0.314226i	−0.00358516	+	0.0110340i	0.949248	+	0.314529i	$0.101846\pi$
$812$		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
$819$	−0.00674171	+	4.32458i	−0.000235574	+	0.151113i
$820$		0			0
$821$	38.2380	−	12.4243i	1.33451	−	0.433610i	0.447059	−	0.894504i	$-0.352471\pi$
$821$	38.2380	−	12.4243i	1.33451	−	0.433610i	0.887455	+	0.460894i	$0.152471\pi$
$822$		0			0
$823$	−27.9511	−	20.3076i	−0.974313	−	0.707880i	−0.0178826	−	0.999840i	$-0.505693\pi$
$823$	−27.9511	−	20.3076i	−0.974313	−	0.707880i	−0.956430	+	0.291960i	$0.905693\pi$
$824$		0			0
$825$	2.86155	+	25.2606i	0.0996263	+	0.879461i
$826$		0			0
$827$	0.991748	−	1.36502i	0.0344865	−	0.0474665i	−0.791426	−	0.611266i	$-0.790661\pi$
$827$	0.991748	−	1.36502i	0.0344865	−	0.0474665i	0.825912	+	0.563799i	$0.190661\pi$
$828$		0			0
$829$	18.0317	−	5.85886i	0.626267	−	0.203486i	0.0213463	−	0.999772i	$-0.493205\pi$
$829$	18.0317	−	5.85886i	0.626267	−	0.203486i	0.604921	+	0.796286i	$0.293205\pi$
$830$		0			0
$831$	1.81794	−	1.32081i	0.0630637	−	0.0458185i
$832$		0			0
$833$	15.0162	+	0.0468185i	0.520280	+	0.00162216i
$834$		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	$-0.602186\pi$
$839$	−32.6897	−	10.6215i	−1.12857	−	0.366696i	−0.813034	+	0.582216i	$0.802186\pi$
$840$		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
$847$	11.4479	−	26.7572i	0.393354	−	0.919387i
$848$		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	$-0.681306\pi$
$853$	2.77371	−	2.01522i	0.0949699	−	0.0689997i	0.634257	+	0.773122i	$0.281306\pi$
$854$		0			0
$855$	1.61556	+	0.524929i	0.0552511	+	0.0179522i
$856$		0			0
$857$	17.2507			0.589271			0.294636	−	0.955610i	$-0.404802\pi$
$857$	17.2507			0.589271			0.294636	+	0.955610i	$0.404802\pi$
$858$		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
$861$	30.0185	−	21.7383i	1.02303	−	0.740839i
$862$		0			0
$863$	3.10629	−	2.25685i	0.105739	−	0.0768240i	−0.533659	−	0.845700i	$-0.679183\pi$
$863$	3.10629	−	2.25685i	0.105739	−	0.0768240i	0.639398	+	0.768876i	$0.279183\pi$
$864$		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
$875$	−11.5159	−	0.0179525i	−0.389310	−	0.000606907i
$876$		0			0
$877$	−47.3831	−	15.3957i	−1.60001	−	0.519876i	−0.632903	−	0.774231i	$-0.718137\pi$
$877$	−47.3831	−	15.3957i	−1.60001	−	0.519876i	−0.967111	+	0.254355i	$0.918137\pi$
$878$		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	0.281963	+	0.959425i	$0.409015\pi$
$883$	−15.1574	+	46.6496i	−0.510086	+	1.56988i	−0.792049	+	0.610458i	$0.790985\pi$
$884$		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	$-0.183423\pi$
$887$	−4.76899	−	14.6774i	−0.160127	−	0.492820i	−0.998644	+	0.0520548i	$0.983423\pi$
$888$		0			0
$889$	15.6687	+	48.4804i	0.525513	+	1.62598i
$890$		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	−0.283547	−	0.958958i	$-0.591511\pi$
$907$	16.2886	−	11.8344i	0.540855	−	0.392954i	0.824403	+	0.566004i	$0.191511\pi$
$908$		0			0
$909$	−0.914647	−	2.81499i	−0.0303369	−	0.0933675i
$910$		0			0
$911$	−8.24104	−	5.98747i	−0.273038	−	0.198374i	0.442837	−	0.896602i	$-0.353972\pi$
$911$	−8.24104	−	5.98747i	−0.273038	−	0.198374i	−0.715875	+	0.698228i	$0.753972\pi$
$912$		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
$917$	−20.4094	−	6.66662i	−0.673979	−	0.220151i
$918$		0			0
$919$	−16.4458	−	22.6358i	−0.542498	−	0.746685i	0.446472	−	0.894797i	$-0.352680\pi$
$919$	−16.4458	−	22.6358i	−0.542498	−	0.746685i	−0.988970	+	0.148113i	$0.952680\pi$
$920$		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	−0.942652	−	0.333776i	$-0.891677\pi$
$929$	−29.5284	−	40.6424i	−0.968797	−	1.33343i	−0.0261446	−	0.999658i	$-0.508323\pi$
$930$		0			0
$931$	47.9389	−	34.6018i	1.57114	−	1.13403i
$932$		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	$-0.135568\pi$
$937$	24.4626	+	17.7732i	0.799160	+	0.580624i	−0.111508	+	0.993764i	$0.535568\pi$
$938$		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	$-0.463661\pi$
$941$	33.5587	−	24.3818i	1.09398	−	0.794824i	0.980067	+	0.198667i	$0.0636612\pi$
$942$		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	−0.813300	−	0.581845i	$-0.802331\pi$
$953$	−34.8615	+	11.3272i	−1.12927	+	0.366923i	−0.315974	+	0.948768i	$0.602331\pi$
$954$		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
$959$	14.6008	−	4.71895i	0.471486	−	0.152383i
$960$		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	$-0.897109\pi$
$967$		−	19.7552i		−	0.635285i	0.948211	−	0.317642i	$-0.102891\pi$
$968$		0			0
$969$			28.9157i			0.928905i
$970$		0			0
$971$	−38.8681	−	12.6290i	−1.24734	−	0.405284i	−0.390371	−	0.920658i	$-0.627653\pi$
$971$	−38.8681	−	12.6290i	−1.24734	−	0.405284i	−0.856966	+	0.515373i	$0.827653\pi$
$972$		0			0
$973$	0.0334595	−	21.4631i	0.00107266	−	0.688075i
$974$		0			0
$975$	26.3057	−	8.54725i	0.842457	−	0.273731i
$976$		0			0
$977$	−1.74168	−	1.26541i	−0.0557214	−	0.0404840i	0.559576	−	0.828779i	$-0.310964\pi$
$977$	−1.74168	−	1.26541i	−0.0557214	−	0.0404840i	−0.615297	+	0.788295i	$0.710964\pi$
$978$		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	$-0.565757\pi$
$983$	6.40312	−	2.08050i	0.204228	−	0.0663576i	0.409345	+	0.912380i	$0.365757\pi$
$984$		0			0
$985$	2.59046	−	1.88208i	0.0825389	−	0.0599680i
$986$		0			0
$987$	−17.2682	−	23.8458i	−0.549654	−	0.759019i
$988$		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	−0.989277	−	0.146051i	$-0.953344\pi$
$997$	−8.67631	−	26.7029i	−0.274782	−	0.845691i	0.714495	−	0.699640i	$-0.246656\pi$
$998$		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.293.3	yes	32
7.6	odd	2	inner	308.2.w.a.293.6	yes	32
11.5	even	5		3388.2.c.c.1693.21		32
11.6	odd	10		3388.2.c.c.1693.11		32
11.8	odd	10	inner	308.2.w.a.41.6	yes	32
77.6	even	10		3388.2.c.c.1693.22		32
77.27	odd	10		3388.2.c.c.1693.12		32
77.41	even	10	inner	308.2.w.a.41.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.w.a.41.3	✓	32	77.41	even	10	inner
308.2.w.a.41.6	yes	32	11.8	odd	10	inner
308.2.w.a.293.3	yes	32	1.1	even	1	trivial
308.2.w.a.293.6	yes	32	7.6	odd	2	inner
3388.2.c.c.1693.11		32	11.6	odd	10
3388.2.c.c.1693.12		32	77.27	odd	10
3388.2.c.c.1693.21		32	11.5	even	5
3388.2.c.c.1693.22		32	77.6	even	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)

\(f(q)\)	\(=\)	\(q+(-1.51783 - 0.493173i) q^{3} +(-0.260986 - 0.359216i) q^{5} +(2.51498 + 0.821504i) q^{7} +(-0.366459 - 0.266248i) q^{9} +(2.44672 - 2.23910i) q^{11} +(-2.91934 - 2.12103i) q^{13} +(0.218977 + 0.673941i) q^{15} +(1.73549 - 1.26091i) q^{17} +(2.60996 - 8.03264i) q^{19} +(-3.41217 - 2.48723i) q^{21} +1.73292 q^{23} +(1.48416 - 4.56778i) q^{25} +(3.23913 + 4.45828i) q^{27} +(-6.19038 + 2.01138i) q^{29} +(2.85173 - 3.92507i) q^{31} +(-4.81797 + 2.19192i) q^{33} +(-0.361277 - 1.11782i) q^{35} +(0.305486 + 0.940189i) q^{37} +(3.38504 + 4.65910i) q^{39} +(-2.71242 + 8.34796i) q^{41} +4.32100i q^{43} +0.201125i q^{45} +(6.63136 + 2.15466i) q^{47} +(5.65026 + 4.13213i) q^{49} +(-3.25602 + 1.05795i) q^{51} +(-7.09454 - 5.15449i) q^{53} +(-1.44288 - 0.294528i) q^{55} +(-7.92297 + 10.9050i) q^{57} +(-10.2903 + 3.34352i) q^{59} +(5.62339 - 4.08563i) q^{61} +(-0.702913 - 0.970656i) q^{63} +1.60223i q^{65} +11.4870 q^{67} +(-2.63028 - 0.854629i) q^{69} +(-10.6035 + 7.70387i) q^{71} +(2.23211 + 6.86973i) q^{73} +(-4.50542 + 6.20117i) q^{75} +(7.99288 - 3.62130i) q^{77} +(-5.15765 + 7.09890i) q^{79} +(-2.29782 - 7.07198i) q^{81} +(12.6408 - 9.18404i) q^{83} +(-0.905876 - 0.294337i) q^{85} +10.3879 q^{87} -3.04406i q^{89} +(-5.59966 - 7.73260i) q^{91} +(-6.26418 + 4.55119i) q^{93} +(-3.56662 + 1.15887i) q^{95} +(-0.726346 + 0.999730i) q^{97} +(-1.49278 + 0.169103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{7} + 14 q^{9} - 4 q^{11} - 6 q^{15} + 4 q^{23} + 32 q^{25} - 20 q^{29} + 15 q^{35} - 28 q^{37} - 20 q^{39} - 15 q^{49} + 60 q^{51} - 56 q^{53} + 80 q^{57} - 80 q^{63} - 88 q^{67} + 32 q^{71}+ \cdots + 64 q^{99}+O(q^{100}) \) 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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