LMFDB - Embedded newform 78.2.k.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(11,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 7]))

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

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

chi := DirichletCharacter("78.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.k (of order $12$, 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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.4
Root			$0.500000 + 2.74530i$ of defining polynomial
Character	$\chi$	$=$	78.11
Dual form			78.2.k.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.76293 + 2.76293i) q^{5} +(1.27970 - 1.16721i) q^{6} +(-0.657464 - 2.45369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.76293 + 2.76293i) q^{5} +(1.27970 - 1.16721i) q^{6} +(-0.657464 - 2.45369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(-3.38389 + 1.95369i) q^{10} +(-0.150860 + 0.563016i) q^{11} +(1.53819 - 0.796225i) q^{12} +(-1.20856 + 3.39697i) q^{13} -2.54025i q^{14} +(1.44957 + 6.61072i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.547000 - 0.947432i) q^{17} +(-0.507306 - 2.95680i) q^{18} +(1.32717 - 0.355613i) q^{19} +(-3.77424 + 1.01130i) q^{20} +(-4.19313 - 1.33273i) q^{21} +(-0.291439 + 0.504787i) q^{22} +(-0.876460 - 1.51807i) q^{23} +(1.69185 - 0.370982i) q^{24} -10.2676i q^{25} +(-2.04658 + 2.96842i) q^{26} +(-5.14688 - 0.713876i) q^{27} +(0.657464 - 2.45369i) q^{28} +(5.12973 - 2.96165i) q^{29} +(-0.310806 + 6.76064i) q^{30} +(6.49983 + 6.49983i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.680339 + 0.745907i) q^{33} +(0.773575 - 0.773575i) q^{34} +(8.59591 + 4.96285i) q^{35} +(0.275255 - 2.98735i) q^{36} +(-2.98942 - 0.801012i) q^{37} +1.37398 q^{38} +(3.82618 + 4.93562i) q^{39} -3.90738 q^{40} +(-5.11781 - 1.37131i) q^{41} +(-3.70532 - 2.37259i) q^{42} +(3.26299 + 1.88389i) q^{43} +(-0.412157 + 0.412157i) q^{44} +(10.9966 + 4.05999i) q^{45} +(-0.453689 - 1.69319i) q^{46} +(-5.51114 - 5.51114i) q^{47} +(1.73022 + 0.0795432i) q^{48} +(0.473846 - 0.273575i) q^{49} +(2.65745 - 9.91775i) q^{50} +(-0.871071 - 1.68278i) q^{51} +(-2.74513 + 2.33758i) q^{52} +3.04435i q^{53} +(-4.78674 - 2.02166i) q^{54} +(-1.13876 - 1.97239i) q^{55} +(1.27012 - 2.19992i) q^{56} +(0.720857 - 2.26801i) q^{57} +(5.72147 - 1.53306i) q^{58} +(8.19009 - 2.19453i) q^{59} +(-2.05000 + 6.44983i) q^{60} +(-4.67266 + 8.09329i) q^{61} +(4.59607 + 7.96063i) q^{62} +(-5.86037 + 4.87153i) q^{63} +1.00000i q^{64} +(-6.04642 - 12.7248i) q^{65} +(0.464102 + 0.896575i) q^{66} +(1.70856 - 6.37644i) q^{67} +(0.947432 - 0.547000i) q^{68} +(-3.03294 - 0.139433i) q^{69} +(7.01853 + 7.01853i) q^{70} +(0.220122 + 0.821505i) q^{71} +(1.03906 - 2.81431i) q^{72} +(-5.18078 + 5.18078i) q^{73} +(-2.68024 - 1.54744i) q^{74} +(-14.9768 - 9.58993i) q^{75} +(1.32717 + 0.355613i) q^{76} +1.48065 q^{77} +(2.41837 + 5.75773i) q^{78} -13.1089 q^{79} +(-3.77424 - 1.01130i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(-4.58850 - 2.64917i) q^{82} +(-5.15394 + 5.15394i) q^{83} +(-2.96499 - 3.25075i) q^{84} +(1.10637 + 4.12902i) q^{85} +(2.66422 + 2.66422i) q^{86} +(0.471158 - 10.2486i) q^{87} +(-0.504787 + 0.291439i) q^{88} +(-2.50797 + 9.35988i) q^{89} +(9.57108 + 6.76778i) q^{90} +(9.12969 + 0.732051i) q^{91} -1.75292i q^{92} +(15.5518 - 3.41012i) q^{93} +(-3.89697 - 6.74974i) q^{94} +(-2.68434 + 4.64941i) q^{95} +(1.65068 + 0.524648i) q^{96} +(-0.592450 + 0.158747i) q^{97} +(0.528506 - 0.141613i) q^{98} +(1.72345 - 0.295697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.933998	−	1.45865i	0.539244	−	0.842150i
$3$	0.933998	−	1.45865i	0.539244	−	0.842150i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.76293	+	2.76293i	−1.23562	+	1.23562i	−0.273849	+	0.961773i	$0.588297\pi$
$5$	−2.76293	+	2.76293i	−1.23562	+	1.23562i	−0.961773	+	0.273849i	$0.911703\pi$
$6$	1.27970	−	1.16721i	0.522435	−	0.476510i
$7$	−0.657464	−	2.45369i	−0.248498	−	0.927407i	−0.971593	−	0.236659i	$-0.923948\pi$
$7$	−0.657464	−	2.45369i	−0.248498	−	0.927407i	0.723095	−	0.690749i	$-0.242719\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.25529	−	2.72474i	−0.418432	−	0.908248i
$10$	−3.38389	+	1.95369i	−1.07008	+	0.617811i
$11$	−0.150860	+	0.563016i	−0.0454859	+	0.169756i	−0.984932	−	0.172940i	$-0.944673\pi$
$11$	−0.150860	+	0.563016i	−0.0454859	+	0.169756i	0.939446	+	0.342696i	$0.111340\pi$
$12$	1.53819	−	0.796225i	0.444037	−	0.229850i
$13$	−1.20856	+	3.39697i	−0.335195	+	0.942149i
$13$	−1.20856	+	3.39697i	−0.335195	+	0.942149i
$14$		−	2.54025i		−	0.678909i
$15$	1.44957	+	6.61072i	0.374277	+	1.70688i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.547000	−	0.947432i	0.132667	−	0.229786i	−0.792037	−	0.610473i	$-0.790979\pi$
$17$	0.547000	−	0.947432i	0.132667	−	0.229786i	0.924704	+	0.380687i	$0.124313\pi$
$18$	−0.507306	−	2.95680i	−0.119573	−	0.696923i
$19$	1.32717	−	0.355613i	0.304473	−	0.0815832i	−0.103348	−	0.994645i	$-0.532956\pi$
$19$	1.32717	−	0.355613i	0.304473	−	0.0815832i	0.407821	+	0.913062i	$0.366289\pi$
$20$	−3.77424	+	1.01130i	−0.843945	+	0.226134i
$21$	−4.19313	−	1.33273i	−0.915017	−	0.290826i
$22$	−0.291439	+	0.504787i	−0.0621349	+	0.107621i
$23$	−0.876460	−	1.51807i	−0.182755	−	0.316540i	0.760063	−	0.649849i	$-0.225168\pi$
$23$	−0.876460	−	1.51807i	−0.182755	−	0.316540i	−0.942818	+	0.333309i	$0.891835\pi$
$24$	1.69185	−	0.370982i	0.345348	−	0.0757264i
$25$		−	10.2676i		−	2.05352i
$26$	−2.04658	+	2.96842i	−0.401367	+	0.582155i
$27$	−5.14688	−	0.713876i	−0.990518	−	0.137386i
$28$	0.657464	−	2.45369i	0.124249	−	0.463704i
$29$	5.12973	−	2.96165i	0.952566	−	0.549965i	0.0586892	−	0.998276i	$-0.481308\pi$
$29$	5.12973	−	2.96165i	0.952566	−	0.549965i	0.893877	+	0.448312i	$0.147975\pi$
$30$	−0.310806	+	6.76064i	−0.0567451	+	1.23432i
$31$	6.49983	+	6.49983i	1.16740	+	1.16740i	0.982816	+	0.184588i	$0.0590950\pi$
$31$	6.49983	+	6.49983i	1.16740	+	1.16740i	0.184588	+	0.982816i	$0.440905\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.680339	+	0.745907i	0.118432	+	0.129846i
$34$	0.773575	−	0.773575i	0.132667	−	0.132667i
$35$	8.59591	+	4.96285i	1.45297	+	0.838875i
$36$	0.275255	−	2.98735i	0.0458759	−	0.497891i
$37$	−2.98942	−	0.801012i	−0.491457	−	0.131686i	0.00457534	−	0.999990i	$-0.498544\pi$
$37$	−2.98942	−	0.801012i	−0.491457	−	0.131686i	−0.496032	+	0.868304i	$0.665210\pi$
$38$	1.37398			0.222890
$39$	3.82618	+	4.93562i	0.612679	+	0.790332i
$40$	−3.90738			−0.617811
$41$	−5.11781	−	1.37131i	−0.799268	−	0.214163i	−0.164005	−	0.986459i	$-0.552441\pi$
$41$	−5.11781	−	1.37131i	−0.799268	−	0.214163i	−0.635262	+	0.772296i	$0.719108\pi$
$42$	−3.70532	−	2.37259i	−0.571743	−	0.366098i
$43$	3.26299	+	1.88389i	0.497602	+	0.287290i	0.727723	−	0.685872i	$-0.240579\pi$
$43$	3.26299	+	1.88389i	0.497602	+	0.287290i	−0.230121	+	0.973162i	$0.573912\pi$
$44$	−0.412157	+	0.412157i	−0.0621349	+	0.0621349i
$45$	10.9966	+	4.05999i	1.63927	+	0.605228i
$46$	−0.453689	−	1.69319i	−0.0668928	−	0.249647i
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	0.179817	−	0.983700i	$-0.442449\pi$
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	−0.983700	+	0.179817i	$0.942449\pi$
$48$	1.73022	+	0.0795432i	0.249736	+	0.0114811i
$49$	0.473846	−	0.273575i	0.0676922	−	0.0390821i
$50$	2.65745	−	9.91775i	0.375821	−	1.40258i
$51$	−0.871071	−	1.68278i	−0.121974	−	0.235636i
$52$	−2.74513	+	2.33758i	−0.380681	+	0.324164i
$53$			3.04435i			0.418173i	0.977897	+	0.209087i	$0.0670490\pi$
$53$			3.04435i			0.418173i	−0.977897	+	0.209087i	$0.932951\pi$
$54$	−4.78674	−	2.02166i	−0.651393	−	0.275113i
$55$	−1.13876	−	1.97239i	−0.153551	−	0.265957i
$56$	1.27012	−	2.19992i	0.169727	−	0.293976i
$57$	0.720857	−	2.26801i	0.0954799	−	0.300405i
$58$	5.72147	−	1.53306i	0.751265	−	0.201301i
$59$	8.19009	−	2.19453i	1.06626	−	0.285703i	0.317304	−	0.948324i	$-0.397223\pi$
$59$	8.19009	−	2.19453i	1.06626	−	0.285703i	0.748955	+	0.662621i	$0.230556\pi$
$60$	−2.05000	+	6.44983i	−0.264653	+	0.832670i
$61$	−4.67266	+	8.09329i	−0.598273	+	1.03624i	0.394803	+	0.918766i	$0.370813\pi$
$61$	−4.67266	+	8.09329i	−0.598273	+	1.03624i	−0.993076	+	0.117474i	$0.962520\pi$
$62$	4.59607	+	7.96063i	0.583702	+	1.01100i
$63$	−5.86037	+	4.87153i	−0.738337	+	0.613755i
$64$			1.00000i			0.125000i
$65$	−6.04642	−	12.7248i	−0.749966	−	1.57831i
$66$	0.464102	+	0.896575i	0.0571270	+	0.110361i
$67$	1.70856	−	6.37644i	0.208734	−	0.779006i	−0.779545	−	0.626346i	$-0.784550\pi$
$67$	1.70856	−	6.37644i	0.208734	−	0.779006i	0.988279	−	0.152659i	$-0.0487838\pi$
$68$	0.947432	−	0.547000i	0.114893	−	0.0663335i
$69$	−3.03294	−	0.139433i	−0.365124	−	0.0167858i
$70$	7.01853	+	7.01853i	0.838875	+	0.838875i
$71$	0.220122	+	0.821505i	0.0261236	+	0.0974947i	0.977757	−	0.209742i	$-0.0672624\pi$
$71$	0.220122	+	0.821505i	0.0261236	+	0.0974947i	−0.951633	+	0.307237i	$0.900596\pi$
$72$	1.03906	−	2.81431i	0.122454	−	0.331670i
$73$	−5.18078	+	5.18078i	−0.606365	+	0.606365i	−0.941994	−	0.335629i	$-0.891051\pi$
$73$	−5.18078	+	5.18078i	−0.606365	+	0.606365i	0.335629	+	0.941994i	$0.391051\pi$
$74$	−2.68024	−	1.54744i	−0.311571	−	0.179886i
$75$	−14.9768	−	9.58993i	−1.72937	−	1.10735i
$76$	1.32717	+	0.355613i	0.152236	+	0.0407916i
$77$	1.48065			0.168736
$78$	2.41837	+	5.75773i	0.273826	+	0.651935i
$79$	−13.1089			−1.47486			−0.737431	−	0.675422i	$-0.763961\pi$
$79$	−13.1089			−1.47486			−0.737431	+	0.675422i	$0.763961\pi$
$80$	−3.77424	−	1.01130i	−0.421973	−	0.113067i
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	−4.58850	−	2.64917i	−0.506715	−	0.292552i
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	−0.930926	−	0.365208i	$-0.880998\pi$
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	0.365208	+	0.930926i	$0.380998\pi$
$84$	−2.96499	−	3.25075i	−0.323507	−	0.354686i
$85$	1.10637	+	4.12902i	0.120002	+	0.447855i
$86$	2.66422	+	2.66422i	0.287290	+	0.287290i
$87$	0.471158	−	10.2486i	0.0505135	−	1.09877i
$88$	−0.504787	+	0.291439i	−0.0538104	+	0.0310675i
$89$	−2.50797	+	9.35988i	−0.265844	+	0.992145i	0.695887	+	0.718151i	$0.255011\pi$
$89$	−2.50797	+	9.35988i	−0.265844	+	0.992145i	−0.961731	+	0.273994i	$0.911655\pi$
$90$	9.57108	+	6.76778i	1.00888	+	0.713386i
$91$	9.12969	+	0.732051i	0.957051	+	0.0767398i
$92$		−	1.75292i		−	0.182755i
$93$	15.5518	−	3.41012i	1.61264	−	0.353613i
$94$	−3.89697	−	6.74974i	−0.401941	−	0.696183i
$95$	−2.68434	+	4.64941i	−0.275407	+	0.477019i
$96$	1.65068	+	0.524648i	0.168472	+	0.0535466i
$97$	−0.592450	+	0.158747i	−0.0601542	+	0.0161183i	−0.288771	−	0.957398i	$-0.593247\pi$
$97$	−0.592450	+	0.158747i	−0.0601542	+	0.0161183i	0.228616	+	0.973517i	$0.426580\pi$
$98$	0.528506	−	0.141613i	0.0533872	−	0.0143051i
$99$	1.72345	−	0.295697i	0.173213	−	0.0297187i
$100$	5.13380	−	8.89201i	0.513380	−	0.889201i
$101$	2.91789	+	5.05394i	0.290341	+	0.502886i	0.973890	−	0.227019i	$-0.0728979\pi$
$101$	2.91789	+	5.05394i	0.290341	+	0.502886i	−0.683549	+	0.729904i	$0.739565\pi$
$102$	−0.405854	−	1.85089i	−0.0401856	−	0.183265i
$103$		−	2.07313i		−	0.204272i	−0.994770	−	0.102136i	$-0.967432\pi$
$103$		−	2.07313i		−	0.204272i	0.994770	−	0.102136i	$-0.0325677\pi$
$104$	−3.25660	+	1.54744i	−0.319336	+	0.151739i
$105$	15.2676	−	7.90310i	1.48997	−	0.771263i
$106$	−0.787935	+	2.94061i	−0.0765310	+	0.285618i
$107$	2.99520	−	1.72928i	0.289557	−	0.167176i	−0.348185	−	0.937426i	$-0.613202\pi$
$107$	2.99520	−	1.72928i	0.289557	−	0.167176i	0.637742	+	0.770250i	$0.279869\pi$
$108$	−4.10039	−	3.19168i	−0.394560	−	0.307119i
$109$	−10.9901	−	10.9901i	−1.05266	−	1.05266i	−0.998534	−	0.0541251i	$-0.982763\pi$
$109$	−10.9901	−	10.9901i	−1.05266	−	1.05266i	−0.0541251	−	0.998534i	$-0.517237\pi$
$110$	−0.589466	−	2.19992i	−0.0562034	−	0.209754i
$111$	−3.96050	+	3.61236i	−0.375914	+	0.342870i
$112$	1.79623	−	1.79623i	0.169727	−	0.169727i
$113$	−9.43719	−	5.44856i	−0.887776	−	0.512558i	−0.0145614	−	0.999894i	$-0.504635\pi$
$113$	−9.43719	−	5.44856i	−0.887776	−	0.512558i	−0.873214	+	0.487336i	$0.837969\pi$
$114$	1.28330	−	2.00416i	0.120192	−	0.187706i
$115$	6.61594	+	1.77274i	0.616940	+	0.165308i
$116$	5.92330			0.549965
$117$	10.7730	−	0.971173i	0.995961	−	0.0897850i
$118$	8.47900			0.780556
$119$	−2.68434	−	0.719266i	−0.246073	−	0.0659350i
$120$	−3.64948	+	5.69948i	−0.333151	+	0.520289i
$121$	9.23205	+	5.33013i	0.839277	+	0.484557i
$122$	−6.60814	+	6.60814i	−0.598273	+	0.598273i
$123$	−6.78029	+	6.18427i	−0.611358	+	0.557617i
$124$	2.37910	+	8.87893i	0.213650	+	0.797352i
$125$	14.5541	+	14.5541i	1.30175	+	1.30175i
$126$	−6.92152	+	3.18876i	−0.616618	+	0.284077i
$127$	8.06551	−	4.65662i	0.715698	−	0.413209i	−0.0974690	−	0.995239i	$-0.531075\pi$
$127$	8.06551	−	4.65662i	0.715698	−	0.413209i	0.813167	+	0.582030i	$0.197741\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.79555	−	3.00000i	0.510270	−	0.264135i
$130$	−2.54698	−	13.8561i	−0.223385	−	1.21526i
$131$			0.917828i			0.0801910i	0.999196	+	0.0400955i	$0.0127662\pi$
$131$			0.917828i			0.0801910i	−0.999196	+	0.0400955i	$0.987234\pi$
$132$	0.216237	+	0.986144i	0.0188210	+	0.0858328i
$133$	−1.74513	−	3.02265i	−0.151322	−	0.262097i
$134$	3.30069	−	5.71696i	0.285136	−	0.493870i
$135$	16.1929	−	12.2481i	1.39366	−	1.05415i
$136$	1.05672	−	0.283148i	0.0906133	−	0.0242797i
$137$	8.32493	−	2.23066i	0.711247	−	0.190578i	0.114984	−	0.993367i	$-0.463318\pi$
$137$	8.32493	−	2.23066i	0.711247	−	0.190578i	0.596263	+	0.802789i	$0.296652\pi$
$138$	−2.89351	−	0.919666i	−0.246312	−	0.0782871i
$139$	−1.65662	+	2.86936i	−0.140513	+	0.243376i	−0.927690	−	0.373352i	$-0.878209\pi$
$139$	−1.65662	+	2.86936i	−0.140513	+	0.243376i	0.787177	+	0.616727i	$0.211542\pi$
$140$	4.96285	+	8.59591i	0.419438	+	0.726487i
$141$	−13.1862	+	2.89141i	−1.11048	+	0.243500i
$142$			0.850484i			0.0713711i
$143$	−1.73022	−	1.19291i	−0.144689	−	0.0997557i
$144$	1.73205	−	2.44949i	0.144338	−	0.204124i
$145$	−5.99026	+	22.3559i	−0.497464	+	1.85656i
$146$	−6.34514	+	3.66337i	−0.525127	+	0.303182i
$147$	0.0435221	−	0.946692i	0.00358964	−	0.0780818i
$148$	−2.18840	−	2.18840i	−0.179886	−	0.179886i
$149$	2.03304	+	7.58742i	0.166553	+	0.621585i	0.997837	+	0.0657369i	$0.0209398\pi$
$149$	2.03304	+	7.58742i	0.166553	+	0.621585i	−0.831284	+	0.555848i	$0.812394\pi$
$150$	−11.9844	−	13.1394i	−0.978524	−	1.07283i
$151$	10.2600	−	10.2600i	0.834946	−	0.834946i	−0.153243	−	0.988189i	$-0.548972\pi$
$151$	10.2600	−	10.2600i	0.834946	−	0.834946i	0.988189	+	0.153243i	$0.0489717\pi$
$152$	1.18990	+	0.686992i	0.0965140	+	0.0557224i
$153$	−3.26816	−	0.301129i	−0.264215	−	0.0243449i
$154$	1.43020	+	0.383221i	0.115249	+	0.0308808i
$155$	−35.9172			−2.88494
$156$	0.845754	+	6.18746i	0.0677145	+	0.495394i
$157$	−6.71547			−0.535953			−0.267976	−	0.963425i	$-0.586355\pi$
$157$	−6.71547			−0.535953			−0.267976	+	0.963425i	$0.586355\pi$
$158$	−12.6622	−	3.39282i	−1.00735	−	0.269918i
$159$	4.44062	+	2.84341i	0.352164	+	0.225497i
$160$	−3.38389	−	1.95369i	−0.267520	−	0.154453i
$161$	−3.14864	+	3.14864i	−0.248148	+	0.248148i
$162$	−7.41970	+	5.09393i	−0.582946	+	0.400217i
$163$	−0.407550	−	1.52100i	−0.0319217	−	0.119134i	0.948127	−	0.317893i	$-0.102975\pi$
$163$	−0.407550	−	1.52100i	−0.0319217	−	0.119134i	−0.980048	+	0.198760i	$0.936309\pi$
$164$	−3.74650	−	3.74650i	−0.292552	−	0.292552i
$165$	−3.94062	−	0.181161i	−0.306777	−	0.0141034i
$166$	−6.31226	+	3.64439i	−0.489927	+	0.282859i
$167$	6.32673	−	23.6117i	0.489577	−	1.82713i	−0.0689223	−	0.997622i	$-0.521956\pi$
$167$	6.32673	−	23.6117i	0.489577	−	1.82713i	0.558499	−	0.829505i	$-0.311377\pi$
$168$	−2.02261	−	3.90738i	−0.156048	−	0.301461i
$169$	−10.0788	−	8.21088i	−0.775289	−	0.631606i
$170$			4.27467i			0.327852i
$171$	−2.63494	−	3.16979i	−0.201499	−	0.242400i
$172$	1.88389	+	3.26299i	0.143645	+	0.248801i
$173$	10.3837	−	17.9850i	0.789456	−	1.36738i	−0.136845	−	0.990593i	$-0.543696\pi$
$173$	10.3837	−	17.9850i	0.789456	−	1.36738i	0.926301	−	0.376785i	$-0.122971\pi$
$174$	3.10764	−	9.77747i	0.235590	−	0.741228i
$175$	−25.1935	+	6.75058i	−1.90445	+	0.510296i
$176$	−0.563016	+	0.150860i	−0.0424389	+	0.0113715i
$177$	4.44849	−	13.9961i	0.334369	−	1.05201i
$178$	−4.84503	+	8.39184i	−0.363150	+	0.628995i
$179$	7.00018	+	12.1247i	0.523218	+	0.906241i	0.999635	+	0.0270211i	$0.00860212\pi$
$179$	7.00018	+	12.1247i	0.523218	+	0.906241i	−0.476416	+	0.879220i	$0.658065\pi$
$180$	7.49333	+	9.01435i	0.558520	+	0.671890i
$181$			25.5405i			1.89841i	0.314653	+	0.949207i	$0.398112\pi$
$181$			25.5405i			1.89841i	−0.314653	+	0.949207i	$0.601888\pi$
$182$	8.62913	+	3.07004i	0.639634	+	0.227567i
$183$	7.44098	+	14.3749i	0.550053	+	1.06262i
$184$	0.453689	−	1.69319i	0.0334464	−	0.124824i
$185$	10.4727	−	6.04642i	0.769968	−	0.444541i
$186$	15.9045	+	0.731173i	1.16617	+	0.0536122i
$187$	0.450899	+	0.450899i	0.0329730	+	0.0329730i
$188$	−2.01722	−	7.52836i	−0.147121	−	0.549062i
$189$	1.63226	+	13.0982i	0.118729	+	0.952753i
$190$	−3.79623	+	3.79623i	−0.275407	+	0.275407i
$191$	20.4783	+	11.8231i	1.48176	+	0.855493i	0.999786	−	0.0206939i	$-0.00658754\pi$
$191$	20.4783	+	11.8231i	1.48176	+	0.855493i	0.481972	+	0.876187i	$0.339921\pi$
$192$	1.45865	+	0.933998i	0.105269	+	0.0674055i
$193$	10.2375	+	2.74313i	0.736912	+	0.197455i	0.607705	−	0.794163i	$-0.292090\pi$
$193$	10.2375	+	2.74313i	0.736912	+	0.197455i	0.129207	+	0.991618i	$0.458757\pi$
$194$	−0.613350			−0.0440360
$195$	−24.2083	−	3.06533i	−1.73359	−	0.219513i
$196$	0.547150			0.0390821
$197$	3.34959	+	0.897520i	0.238649	+	0.0639457i	0.376161	−	0.926554i	$-0.377244\pi$
$197$	3.34959	+	0.897520i	0.238649	+	0.0639457i	−0.137512	+	0.990500i	$0.543911\pi$
$198$	1.74126	+	0.160440i	0.123746	+	0.0114020i
$199$	−2.67432	−	1.54402i	−0.189577	−	0.109453i	0.402207	−	0.915549i	$-0.368243\pi$
$199$	−2.67432	−	1.54402i	−0.189577	−	0.109453i	−0.591785	+	0.806096i	$0.701576\pi$
$200$	7.26029	−	7.26029i	0.513380	−	0.513380i
$201$	−7.70517	−	8.44777i	−0.543481	−	0.595860i
$202$	1.51041	+	5.63694i	0.106272	+	0.396613i
$203$	−10.6396	−	10.6396i	−0.746752	−	0.746752i
$204$	0.0870203	−	1.89286i	0.00609264	−	0.132527i
$205$	17.9290	−	10.3513i	1.25222	−	0.722968i
$206$	0.536566	−	2.00249i	0.0373843	−	0.139520i
$207$	−3.03615	+	4.29376i	−0.211027	+	0.298437i
$208$	−3.54614	+	0.651838i	−0.245881	+	0.0451969i
$209$			0.800864i			0.0553969i
$210$	16.7928	−	3.68226i	1.15882	−	0.254100i
$211$	2.47900	+	4.29376i	0.170662	+	0.295595i	0.938651	−	0.344867i	$-0.112076\pi$
$211$	2.47900	+	4.29376i	0.170662	+	0.295595i	−0.767990	+	0.640462i	$0.778743\pi$
$212$	−1.52217	+	2.63648i	−0.104543	+	0.181074i
$213$	1.40388	+	0.446205i	0.0961921	+	0.0305734i
$214$	3.34071	−	0.895141i	0.228366	−	0.0611906i
$215$	−14.2205	+	3.81037i	−0.969829	+	0.259865i
$216$	−3.13461	−	4.14418i	−0.213283	−	0.281976i
$217$	11.6752	−	20.2220i	0.792561	−	1.37276i
$218$	−7.77116	−	13.4601i	−0.526330	−	0.911630i
$219$	2.71809	+	12.3958i	0.183671	+	0.837628i
$220$		−	2.27752i		−	0.153551i
$221$	2.55731	+	3.00317i	0.172023	+	0.202015i
$222$	−4.76050	+	2.46422i	−0.319504	+	0.165387i
$223$	4.93415	−	18.4145i	0.330415	−	1.23313i	−0.578340	−	0.815796i	$-0.696299\pi$
$223$	4.93415	−	18.4145i	0.330415	−	1.23313i	0.908755	−	0.417330i	$-0.137034\pi$
$224$	2.19992	−	1.27012i	0.146988	−	0.0848637i
$225$	−27.9766	+	12.8889i	−1.86511	+	0.859258i
$226$	−7.70543	−	7.70543i	−0.512558	−	0.512558i
$227$	−1.38733	−	5.17758i	−0.0920803	−	0.343648i	0.904480	−	0.426515i	$-0.140259\pi$
$227$	−1.38733	−	5.17758i	−0.0920803	−	0.343648i	−0.996561	+	0.0828671i	$0.973592\pi$
$228$	1.75828	−	1.60372i	0.116445	−	0.106209i
$229$	2.78436	−	2.78436i	0.183996	−	0.183996i	−0.609099	−	0.793094i	$-0.708469\pi$
$229$	2.78436	−	2.78436i	0.183996	−	0.183996i	0.793094	+	0.609099i	$0.208469\pi$
$230$	5.93169	+	3.42466i	0.391124	+	0.225816i
$231$	1.38293	−	2.15975i	0.0909899	−	0.142101i
$232$	5.72147	+	1.53306i	0.375633	+	0.100650i
$233$	−3.83663			−0.251346			−0.125673	−	0.992072i	$-0.540109\pi$
$233$	−3.83663			−0.251346			−0.125673	+	0.992072i	$0.540109\pi$
$234$	10.6572	+	1.85017i	0.696686	+	0.120949i
$235$	30.4538			1.98659
$236$	8.19009	+	2.19453i	0.533129	+	0.142852i
$237$	−12.2437	+	19.1212i	−0.795311	+	1.24205i
$238$	−2.40671	−	1.38951i	−0.156004	−	0.0900689i
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	−0.730995	−	0.682383i	$-0.760944\pi$
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	0.682383	+	0.730995i	$0.260944\pi$
$240$	−5.00027	+	4.56072i	−0.322766	+	0.294393i
$241$	−7.23751	−	27.0107i	−0.466209	−	1.73991i	−0.652851	−	0.757487i	$-0.726427\pi$
$241$	−7.23751	−	27.0107i	−0.466209	−	1.73991i	0.186642	−	0.982428i	$-0.440240\pi$
$242$	7.53794	+	7.53794i	0.484557	+	0.484557i
$243$	4.51572	+	14.9201i	0.289684	+	0.957122i
$244$	−8.09329	+	4.67266i	−0.518120	+	0.299137i
$245$	−0.553335	+	2.06507i	−0.0353513	+	0.131933i
$246$	−8.14986	+	4.21868i	−0.519616	+	0.268973i
$247$	−0.395956	+	4.93812i	−0.0251941	+	0.314205i
$248$			9.19215i			0.583702i
$249$	2.70400	+	12.3315i	0.171359	+	0.781480i
$250$	10.2913	+	17.8250i	0.650877	+	1.12735i
$251$	7.56320	−	13.0998i	0.477385	−	0.826855i	−0.522279	−	0.852775i	$-0.674918\pi$
$251$	7.56320	−	13.0998i	0.477385	−	0.826855i	0.999664	+	0.0259196i	$0.00825138\pi$
$252$	−7.51099	+	1.28868i	−0.473148	+	0.0811793i
$253$	0.986923	−	0.264445i	0.0620473	−	0.0166255i
$254$	8.99591	−	2.41045i	0.564453	−	0.151245i
$255$	7.05612	+	2.24270i	0.441871	+	0.140443i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.178601	+	0.309345i	0.0111408	+	0.0192964i	0.871542	−	0.490321i	$-0.163120\pi$
$257$	0.178601	+	0.309345i	0.0111408	+	0.0192964i	−0.860401	+	0.509617i	$0.829787\pi$
$258$	6.37453	−	1.39778i	0.396861	−	0.0870218i
$259$			7.86174i			0.488505i
$260$	1.12603	−	14.0432i	0.0698336	−	0.870921i
$261$	−14.5091	−	10.2595i	−0.898088	−	0.635044i
$262$	−0.237551	+	0.886554i	−0.0146760	+	0.0547715i
$263$	−1.86002	+	1.07389i	−0.114694	+	0.0662186i	−0.556250	−	0.831015i	$-0.687760\pi$
$263$	−1.86002	+	1.07389i	−0.114694	+	0.0662186i	0.441556	+	0.897234i	$0.354427\pi$
$264$	−0.0463639	+	1.00851i	−0.00285350	+	0.0620694i
$265$	−8.41133	−	8.41133i	−0.516704	−	0.516704i
$266$	−0.903345	−	3.37133i	−0.0553876	−	0.206709i
$267$	11.3103	+	12.4004i	0.692180	+	0.758889i
$268$	4.66788	−	4.66788i	0.285136	−	0.285136i
$269$	−21.2380	−	12.2618i	−1.29490	−	0.747612i	−0.315384	−	0.948964i	$-0.602133\pi$
$269$	−21.2380	−	12.2618i	−1.29490	−	0.747612i	−0.979519	+	0.201352i	$0.935467\pi$
$270$	18.8112	−	7.63973i	1.14481	−	0.464939i
$271$	−21.1790	−	5.67488i	−1.28653	−	0.344725i	−0.450189	−	0.892934i	$-0.648643\pi$
$271$	−21.1790	−	5.67488i	−1.28653	−	0.344725i	−0.836341	+	0.548209i	$0.815310\pi$
$272$	1.09400			0.0663335
$273$	9.59491	−	12.6332i	0.580710	−	0.764599i
$274$	8.61860			0.520669
$275$	5.78083	+	1.54897i	0.348597	+	0.0934063i
$276$	−2.55689	−	1.63722i	−0.153907	−	0.0985493i
$277$	−16.1517	−	9.32517i	−0.970460	−	0.560295i	−0.0710833	−	0.997470i	$-0.522646\pi$
$277$	−16.1517	−	9.32517i	−0.970460	−	0.560295i	−0.899376	+	0.437175i	$0.855979\pi$
$278$	−2.34282	+	2.34282i	−0.140513	+	0.140513i
$279$	9.55117	−	25.8696i	0.571814	−	1.54877i
$280$	2.56896	+	9.58749i	0.153525	+	0.572962i
$281$	11.2782	+	11.2782i	0.672801	+	0.672801i	0.958361	−	0.285560i	$-0.0921797\pi$
$281$	11.2782	+	11.2782i	0.672801	+	0.672801i	−0.285560	+	0.958361i	$0.592180\pi$
$282$	−13.4852	−	0.619955i	−0.803035	−	0.0369178i
$283$	4.08342	−	2.35756i	0.242734	−	0.140143i	−0.373699	−	0.927550i	$-0.621911\pi$
$283$	4.08342	−	2.35756i	0.242734	−	0.140143i	0.616433	+	0.787408i	$0.288577\pi$
$284$	−0.220122	+	0.821505i	−0.0130618	+	0.0487473i
$285$	4.27467	+	8.25803i	0.253210	+	0.489164i
$286$	−1.36252	−	1.60007i	−0.0805676	−	0.0946143i
$287$			13.4591i			0.794466i
$288$	2.30701	−	1.91774i	0.135942	−	0.113004i
$289$	7.90158	+	13.6859i	0.464799	+	0.805055i
$290$	−11.5723	+	20.0438i	−0.679548	+	1.17701i
$291$	−0.321793	+	1.01244i	−0.0188638	+	0.0593505i
$292$	−7.07708	+	1.89630i	−0.414155	+	0.110972i
$293$	−20.6276	+	5.52716i	−1.20508	+	0.322900i	−0.804830	−	0.593506i	$-0.797743\pi$
$293$	−20.6276	+	5.52716i	−1.20508	+	0.322900i	−0.400250	+	0.916406i	$0.631077\pi$
$294$	0.287061	−	0.903170i	0.0167417	−	0.0526739i
$295$	−16.5653	+	28.6920i	−0.964471	+	1.67051i
$296$	−1.54744	−	2.68024i	−0.0899429	−	0.155786i
$297$	1.17838	−	2.79008i	0.0683766	−	0.161897i
$298$			7.85507i			0.455032i
$299$	6.21610	−	1.14262i	0.359486	−	0.0660795i
$300$	−8.17533	−	15.7935i	−0.472003	−	0.911839i
$301$	2.47718	−	9.24496i	0.142782	−	0.532870i
$302$	12.5659	−	7.25490i	0.723084	−	0.417473i
$303$	10.0972	+	0.464197i	0.580070	+	0.0266674i
$304$	0.971553	+	0.971553i	0.0557224	+	0.0557224i
$305$	−9.45097	−	35.2715i	−0.541161	−	2.01964i
$306$	−3.07886	−	1.13673i	−0.176007	−	0.0649825i
$307$	−16.2259	+	16.2259i	−0.926063	+	0.926063i	−0.997449	−	0.0713857i	$-0.977258\pi$
$307$	−16.2259	+	16.2259i	−0.926063	+	0.926063i	0.0713857	+	0.997449i	$0.477258\pi$
$308$	1.28228	+	0.740326i	0.0730648	+	0.0421840i
$309$	−3.02397	−	1.93630i	−0.172027	−	0.110152i
$310$	−34.6933	−	9.29605i	−1.97045	−	0.527980i
$311$	32.8464			1.86255			0.931275	−	0.364317i	$-0.118697\pi$
$311$	32.8464			1.86255			0.931275	+	0.364317i	$0.118697\pi$
$312$	−0.784497	+	6.19553i	−0.0444134	+	0.350753i
$313$	11.0629			0.625311			0.312655	−	0.949867i	$-0.398782\pi$
$313$	11.0629			0.625311			0.312655	+	0.949867i	$0.398782\pi$
$314$	−6.48665	−	1.73809i	−0.366063	−	0.0980862i
$315$	2.73210	−	29.6515i	0.153936	−	1.67067i
$316$	−11.3526	−	6.55443i	−0.638634	−	0.368716i
$317$	−17.5500	+	17.5500i	−0.985704	+	0.985704i	−0.999899	−	0.0141948i	$-0.995481\pi$
$317$	−17.5500	+	17.5500i	−0.985704	+	0.985704i	0.0141948	+	0.999899i	$0.495481\pi$
$318$	3.55338	+	3.89584i	0.199264	+	0.218468i
$319$	0.893587	+	3.33491i	0.0500313	+	0.186719i
$320$	−2.76293	−	2.76293i	−0.154453	−	0.154453i
$321$	0.275105	−	5.98408i	0.0153549	−	0.333999i
$322$	−3.85628	+	2.22643i	−0.214902	+	0.124074i
$323$	0.389041	−	1.45192i	0.0216468	−	0.0807870i
$324$	−8.48528	+	3.00000i	−0.471405	+	0.166667i
$325$	34.8787	+	12.4090i	1.93472	+	0.688329i
$326$		−	1.57465i		−	0.0872118i
$327$	−26.2954	+	5.76592i	−1.45414	+	0.318856i
$328$	−2.64917	−	4.58850i	−0.146276	−	0.253358i
$329$	−9.89925	+	17.1460i	−0.545763	+	0.945290i
$330$	−3.75946	−	1.19490i	−0.206952	−	0.0657769i
$331$	4.46639	−	1.19677i	0.245495	−	0.0657803i	−0.133973	−	0.990985i	$-0.542774\pi$
$331$	4.46639	−	1.19677i	0.245495	−	0.0657803i	0.379468	+	0.925205i	$0.376107\pi$
$332$	−7.04041	+	1.88647i	−0.386393	+	0.103534i
$333$	1.57005	+	9.15090i	0.0860380	+	0.501466i
$334$	12.2223	−	21.1697i	0.668775	−	1.15835i
$335$	12.8970	+	22.3383i	0.704640	+	1.22047i
$336$	−0.942385	−	4.29773i	−0.0514113	−	0.234460i
$337$			7.78436i			0.424041i	0.977265	+	0.212021i	$0.0680044\pi$
$337$			7.78436i			0.424041i	−0.977265	+	0.212021i	$0.931996\pi$
$338$	−7.61020	−	10.5397i	−0.413940	−	0.573283i
$339$	−16.7618	+	8.67656i	−0.910378	+	0.471246i
$340$	−1.10637	+	4.12902i	−0.0600012	+	0.223927i
$341$	−4.64007	+	2.67895i	−0.251274	+	0.145073i
$342$	−1.72475	−	3.74375i	−0.0932640	−	0.202439i
$343$	−13.5564	−	13.5564i	−0.731976	−	0.731976i
$344$	0.975173	+	3.63939i	0.0525778	+	0.196223i
$345$	8.76507	−	7.99458i	0.471895	−	0.430414i
$346$	14.6847	−	14.6847i	0.789456	−	0.789456i
$347$	9.39077	+	5.42177i	0.504123	+	0.291056i	0.730415	−	0.683004i	$-0.239327\pi$
$347$	9.39077	+	5.42177i	0.504123	+	0.291056i	−0.226292	+	0.974060i	$0.572660\pi$
$348$	5.53235	−	8.63999i	0.296565	−	0.463152i
$349$	14.8487	+	3.97869i	0.794830	+	0.212974i	0.633313	−	0.773896i	$-0.281695\pi$
$349$	14.8487	+	3.97869i	0.794830	+	0.212974i	0.161517	+	0.986870i	$0.448361\pi$
$350$	−26.0822			−1.39415
$351$	8.64533	−	16.6210i	0.461454	−	0.887164i
$352$	−0.582877			−0.0310675
$353$	−1.80378	−	0.483321i	−0.0960054	−	0.0257246i	0.210497	−	0.977595i	$-0.432492\pi$
$353$	−1.80378	−	0.483321i	−0.0960054	−	0.0257246i	−0.306502	+	0.951870i	$0.599159\pi$
$354$	7.91937	−	12.3679i	0.420910	−	0.657345i
$355$	−2.87795	−	1.66158i	−0.152745	−	0.0881876i
$356$	−6.85191	+	6.85191i	−0.363150	+	0.363150i
$357$	−3.55632	+	3.24370i	−0.188220	+	0.171675i
$358$	3.62356	+	13.5233i	0.191511	+	0.714730i
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	0.310264	−	0.950650i	$-0.399583\pi$
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	−0.950650	+	0.310264i	$0.899583\pi$
$360$	4.90491	+	10.6466i	0.258512	+	0.561126i
$361$	−14.8196	+	8.55608i	−0.779978	+	0.450320i
$362$	−6.61038	+	24.6703i	−0.347434	+	1.29664i
$363$	16.3975	−	8.48796i	0.860645	−	0.445503i
$364$	7.54051	+	5.19882i	0.395230	+	0.272492i
$365$		−	28.6283i		−	1.49847i
$366$	3.46695	+	15.8109i	0.181220	+	0.826451i
$367$	4.53141	+	7.84863i	0.236538	+	0.409695i	0.959718	−	0.280964i	$-0.0906540\pi$
$367$	4.53141	+	7.84863i	0.236538	+	0.409695i	−0.723181	+	0.690659i	$0.757321\pi$
$368$	0.876460	−	1.51807i	0.0456887	−	0.0791351i
$369$	2.68788	+	15.6661i	0.139926	+	0.815546i
$370$	11.6808	−	3.12986i	0.607255	−	0.162713i
$371$	7.46988	−	2.00155i	0.387817	−	0.103915i
$372$	15.1733	+	4.82264i	0.786699	+	0.250042i
$373$	3.78793	−	6.56090i	0.196132	−	0.339710i	−0.751139	−	0.660144i	$-0.770495\pi$
$373$	3.78793	−	6.56090i	0.196132	−	0.339710i	0.947271	+	0.320434i	$0.103829\pi$
$374$	0.318834	+	0.552237i	0.0164865	+	0.0285555i
$375$	34.8227	−	7.63575i	1.79823	−	0.394308i
$376$		−	7.79393i		−	0.401941i
$377$	3.86103	+	21.0048i	0.198853	+	1.08180i
$378$	−1.81342	+	13.0743i	−0.0932723	+	0.672472i
$379$	3.12578	−	11.6656i	0.160561	−	0.599221i	−0.838004	−	0.545664i	$-0.816278\pi$
$379$	3.12578	−	11.6656i	0.160561	−	0.599221i	0.998565	−	0.0535568i	$-0.0170558\pi$
$380$	−4.64941	+	2.68434i	−0.238510	+	0.137704i
$381$	0.740806	−	16.1140i	0.0379526	−	0.825545i
$382$	16.7205	+	16.7205i	0.855493	+	0.855493i
$383$	9.53291	+	35.5773i	0.487109	+	1.81792i	0.570371	+	0.821387i	$0.306800\pi$
$383$	9.53291	+	35.5773i	0.487109	+	1.81792i	−0.0832617	+	0.996528i	$0.526534\pi$
$384$	1.16721	+	1.27970i	0.0595638	+	0.0653043i
$385$	−4.09094	+	4.09094i	−0.208494	+	0.208494i
$386$	9.17870	+	5.29932i	0.467183	+	0.269728i
$387$	1.03710	−	11.2557i	0.0527188	−	0.572157i
$388$	−0.592450	−	0.158747i	−0.0300771	−	0.00805914i
$389$	14.1012			0.714961			0.357481	−	0.933921i	$-0.383636\pi$
$389$	14.1012			0.714961			0.357481	+	0.933921i	$0.383636\pi$
$390$	−22.5900	−	9.22644i	−1.14389	−	0.467199i
$391$	−1.91770			−0.0969820
$392$	0.528506	+	0.141613i	0.0266936	+	0.00715253i
$393$	1.33879	+	0.857250i	0.0675328	+	0.0432425i
$394$	3.00316	+	1.73388i	0.151297	+	0.0873514i
$395$	36.2189	−	36.2189i	1.82237	−	1.82237i
$396$	1.64040	+	0.605643i	0.0824332	+	0.0304347i
$397$	−2.03222	−	7.58436i	−0.101994	−	0.380648i	0.895992	−	0.444069i	$-0.146466\pi$
$397$	−2.03222	−	7.58436i	−0.101994	−	0.380648i	−0.997987	+	0.0634210i	$0.979799\pi$
$398$	−2.18357	−	2.18357i	−0.109453	−	0.109453i
$399$	−6.03892	−	0.277626i	−0.302324	−	0.0138987i
$400$	8.89201	−	5.13380i	0.444600	−	0.256690i
$401$	−5.65677	+	21.1113i	−0.282485	+	1.05425i	0.668172	+	0.744007i	$0.267077\pi$
$401$	−5.65677	+	21.1113i	−0.282485	+	1.05425i	−0.950657	+	0.310243i	$0.899590\pi$
$402$	−5.25618	−	10.1542i	−0.262154	−	0.506444i
$403$	−29.9351	+	14.2243i	−1.49118	+	0.708561i
$404$			5.83579i			0.290341i
$405$	−2.74151	−	35.0594i	−0.136227	−	1.74211i
$406$	−7.52332	−	13.0308i	−0.373376	−	0.646706i
$407$	0.901965	−	1.56225i	0.0447088	−	0.0774378i
$408$	0.573965	−	1.80584i	0.0284155	−	0.0894026i
$409$	2.16512	−	0.580141i	0.107058	−	0.0286861i	−0.204892	−	0.978785i	$-0.565684\pi$
$409$	2.16512	−	0.580141i	0.107058	−	0.0286861i	0.311950	+	0.950098i	$0.399018\pi$
$410$	19.9972	−	5.35824i	0.987592	−	0.264625i
$411$	4.52173	−	14.2266i	0.223041	−	0.701744i
$412$	1.03657	−	1.79539i	0.0510680	−	0.0884523i
$413$	−10.7694	−	18.6531i	−0.529926	−	0.917860i
$414$	−4.04400	+	3.36164i	−0.198752	+	0.165216i
$415$		−	28.4800i		−	1.39803i
$416$	−3.59402	−	0.288181i	−0.176211	−	0.0141292i
$417$	2.63809	+	5.09640i	0.129188	+	0.249572i
$418$	−0.207279	+	0.773575i	−0.0101383	+	0.0378368i
$419$	−28.9126	+	16.6927i	−1.41247	+	0.815491i	−0.995621	−	0.0934844i	$-0.970199\pi$
$419$	−28.9126	+	16.6927i	−1.41247	+	0.815491i	−0.416851	+	0.908975i	$0.636866\pi$
$420$	17.1737	+	0.789523i	0.837990	+	0.0385248i
$421$	2.25285	+	2.25285i	0.109797	+	0.109797i	0.759871	−	0.650074i	$-0.225262\pi$
$421$	2.25285	+	2.25285i	0.109797	+	0.109797i	−0.650074	+	0.759871i	$0.725262\pi$
$422$	1.28323	+	4.78907i	0.0624665	+	0.233128i
$423$	−8.09835	+	21.9346i	−0.393755	+	1.06650i
$424$	−2.15268	+	2.15268i	−0.104543	+	0.104543i
$425$	−9.72786	−	5.61638i	−0.471870	−	0.272435i
$426$	1.24056	+	0.794351i	0.0601051	+	0.0384864i
$427$	22.9305	+	6.14422i	1.10969	+	0.297339i
$428$	3.45856			0.167176
$429$	−3.35605	+	1.40961i	−0.162032	+	0.0680567i
$430$	−14.7221			−0.709964
$431$	−20.9452	−	5.61224i	−1.00889	−	0.270332i	−0.283727	−	0.958905i	$-0.591571\pi$
$431$	−20.9452	−	5.61224i	−1.00889	−	0.270332i	−0.725167	+	0.688573i	$0.758238\pi$
$432$	−1.95521	−	4.81427i	−0.0940699	−	0.231627i
$433$	26.0258	+	15.0260i	1.25072	+	0.722103i	0.971252	−	0.238053i	$-0.0765091\pi$
$433$	26.0258	+	15.0260i	1.25072	+	0.722103i	0.279466	+	0.960155i	$0.409842\pi$
$434$	16.5112	−	16.5112i	0.792561	−	0.792561i
$435$	27.0145	+	29.6181i	1.29525	+	1.42008i
$436$	−4.02265	−	15.0127i	−0.192650	−	0.718980i
$437$	−1.70306	−	1.70306i	−0.0814682	−	0.0814682i
$438$	−0.582792	+	12.6769i	−0.0278469	+	0.605725i
$439$	−18.0531	+	10.4229i	−0.861626	+	0.497460i	−0.864557	−	0.502535i	$-0.832401\pi$
$439$	−18.0531	+	10.4229i	−0.861626	+	0.497460i	0.00293019	+	0.999996i	$0.499067\pi$
$440$	0.589466	−	2.19992i	0.0281017	−	0.104877i
$441$	−1.34024	−	0.947691i	−0.0638209	−	0.0451282i
$442$	1.69290	+	3.56272i	0.0805228	+	0.169461i
$443$			13.0363i			0.619374i	0.950839	+	0.309687i	$0.100224\pi$
$443$			13.0363i			0.619374i	−0.950839	+	0.309687i	$0.899776\pi$
$444$	−5.23607	+	1.14814i	−0.248493	+	0.0544884i
$445$	−18.9314	−	32.7901i	−0.897433	−	1.55440i
$446$	9.53204	−	16.5100i	0.451355	−	0.781770i
$447$	12.9662	+	4.12114i	0.613281	+	0.194923i
$448$	2.45369	−	0.657464i	0.115926	−	0.0310623i
$449$	18.3916	−	4.92801i	0.867953	−	0.232567i	0.202750	−	0.979230i	$-0.435012\pi$
$449$	18.3916	−	4.92801i	0.867953	−	0.232567i	0.665202	+	0.746663i	$0.268345\pi$
$450$	−30.3592	+	5.20882i	−1.43115	+	0.245546i
$451$	1.54414	−	2.67453i	0.0727109	−	0.125939i
$452$	−5.44856	−	9.43719i	−0.256279	−	0.443888i
$453$	−5.38288	−	24.5485i	−0.252910	−	1.15339i
$454$		−	5.36023i		−	0.251568i
$455$	−27.2473	+	23.2021i	−1.27737	+	1.08773i
$456$	2.11345	−	1.09400i	0.0989712	−	0.0512313i
$457$	−5.50257	+	20.5359i	−0.257399	+	0.960627i	0.709341	+	0.704866i	$0.248993\pi$
$457$	−5.50257	+	20.5359i	−0.257399	+	0.960627i	−0.966740	+	0.255761i	$0.917674\pi$
$458$	3.41013	−	1.96884i	0.159345	−	0.0919978i
$459$	−3.49169	+	4.48583i	−0.162978	+	0.209381i
$460$	4.84320	+	4.84320i	0.225816	+	0.225816i
$461$	−0.395195	−	1.47489i	−0.0184061	−	0.0686924i	0.956112	−	0.293002i	$-0.0946541\pi$
$461$	−0.395195	−	1.47489i	−0.0184061	−	0.0686924i	−0.974518	+	0.224309i	$0.927987\pi$
$462$	1.89479	−	1.72823i	0.0881535	−	0.0804044i
$463$	−21.3272	+	21.3272i	−0.991159	+	0.991159i	−0.999961	−	0.00880240i	$-0.997198\pi$
$463$	−21.3272	+	21.3272i	−0.991159	+	0.991159i	0.00880240	+	0.999961i	$0.497198\pi$
$464$	5.12973	+	2.96165i	0.238142	+	0.137491i
$465$	−33.5466	+	52.3905i	−1.55569	+	2.42955i
$466$	−3.70590	−	0.992992i	−0.171672	−	0.0459995i
$467$	−11.2935			−0.522601			−0.261300	−	0.965258i	$-0.584151\pi$
$467$	−11.2935			−0.522601			−0.261300	+	0.965258i	$0.584151\pi$
$468$	9.81525	+	4.54542i	0.453710	+	0.210112i
$469$	−16.7691			−0.774326
$470$	29.4162	+	7.88203i	1.35687	+	0.363571i
$471$	−6.27224	+	9.79549i	−0.289009	+	0.451352i
$472$	7.34303	+	4.23950i	0.337990	+	0.195139i
$473$	−1.55291	+	1.55291i	−0.0714031	+	0.0714031i
$474$	−16.7754	+	15.3008i	−0.770519	+	0.702787i
$475$	−3.65130	−	13.6268i	−0.167533	−	0.625241i
$476$	−1.96507	−	1.96507i	−0.0900689	−	0.0900689i
$477$	8.29507	−	3.82155i	0.379805	−	0.174977i
$478$	−0.920426	+	0.531408i	−0.0420993	+	0.0243060i
$479$	7.52517	−	28.0843i	0.343834	−	1.28320i	−0.550135	−	0.835076i	$-0.685424\pi$
$479$	7.52517	−	28.0843i	0.343834	−	1.28320i	0.893969	−	0.448129i	$-0.147910\pi$
$480$	−6.01029	+	3.11115i	−0.274331	+	0.142004i
$481$	6.33390	−	9.18688i	0.288801	−	0.418885i
$482$		−	27.9636i		−	1.27371i
$483$	1.65193	+	7.53358i	0.0751653	+	0.342790i
$484$	5.33013	+	9.23205i	0.242279	+	0.419639i
$485$	1.19829	−	2.07551i	0.0544118	−	0.0942440i
$486$	0.500258	+	15.5804i	0.0226921	+	0.706743i
$487$	2.44743	−	0.655786i	0.110903	−	0.0297165i	−0.202940	−	0.979191i	$-0.565050\pi$
$487$	2.44743	−	0.655786i	0.110903	−	0.0297165i	0.313844	+	0.949475i	$0.398383\pi$
$488$	−9.02689	+	2.41875i	−0.408628	+	0.109492i
$489$	−2.59924	−	0.826137i	−0.117542	−	0.0373592i
$490$	−1.06896	+	1.85149i	−0.0482907	+	0.0836420i
$491$	−18.4575	−	31.9694i	−0.832978	−	1.44276i	−0.895667	−	0.444726i	$-0.853301\pi$
$491$	−18.4575	−	31.9694i	−0.832978	−	1.44276i	0.0626890	−	0.998033i	$-0.480032\pi$
$492$	−8.96403	+	1.96559i	−0.404130	+	0.0886157i
$493$		−	6.48009i		−	0.291849i
$494$	−1.66054	+	4.66738i	−0.0747114	+	0.209995i
$495$	−3.94478	+	5.57877i	−0.177305	+	0.250747i
$496$	−2.37910	+	8.87893i	−0.106825	+	0.398676i
$497$	1.87100	−	1.08022i	0.0839256	−	0.0484545i
$498$	−0.579773	+	12.6112i	−0.0259802	+	0.565122i
$499$	22.3461	+	22.3461i	1.00035	+	1.00035i	1.00000		0.000347536i	$0.000110624\pi$
$499$	22.3461	+	22.3461i	1.00035	+	1.00035i	0.000347536		1.00000i	$0.499889\pi$
$500$	5.32715	+	19.8812i	0.238237	+	0.889114i
$501$	−28.5319	−	31.2817i	−1.27471	−	1.39756i
$502$	10.6960	−	10.6960i	0.477385	−	0.477385i
$503$	−20.2177	−	11.6727i	−0.901464	−	0.520460i	−0.0237889	−	0.999717i	$-0.507573\pi$
$503$	−20.2177	−	11.6727i	−0.901464	−	0.520460i	−0.877675	+	0.479257i	$0.840906\pi$
$504$	−7.58859	−	0.699216i	−0.338023	−	0.0311455i
$505$	−22.0256	−	5.90175i	−0.980128	−	0.262625i
$506$	1.02174			0.0454218
$507$	−21.3903	+	7.03239i	−0.949977	+	0.312319i
$508$	9.31325			0.413209
$509$	18.0113	+	4.82612i	0.798338	+	0.213914i	0.634854	−	0.772632i	$-0.281060\pi$
$509$	18.0113	+	4.82612i	0.798338	+	0.213914i	0.163484	+	0.986546i	$0.447727\pi$
$510$	6.23523	+	3.99254i	0.276101	+	0.176792i
$511$	16.1182	+	9.30585i	0.713028	+	0.411667i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.08463	+	0.882866i	−0.312794	+	0.0389795i
$514$	0.0924504	+	0.345030i	0.00407781	+	0.0152186i
$515$	5.72793	+	5.72793i	0.252403	+	0.252403i
$516$	6.51910	+	0.299701i	0.286987	+	0.0131936i
$517$	3.93427	−	2.27145i	0.173029	−	0.0998984i
$518$	−2.03477	+	7.59385i	−0.0894025	+	0.333655i
$519$	−16.5355	−	31.9441i	−0.725827	−	1.40219i
$520$	4.72231	−	13.2732i	0.207087	−	0.582070i
$521$		−	20.1922i		−	0.884637i	−0.896858	−	0.442318i	$-0.854156\pi$
$521$		−	20.1922i		−	0.884637i	0.896858	−	0.442318i	$-0.145844\pi$
$522$	−11.3593	−	13.6651i	−0.497185	−	0.598105i
$523$	−14.1118	−	24.4424i	−0.617066	−	1.06879i	−0.990018	−	0.140939i	$-0.954988\pi$
$523$	−14.1118	−	24.4424i	−0.617066	−	1.06879i	0.372952	−	0.927850i	$-0.378345\pi$
$524$	−0.458914	+	0.794862i	−0.0200478	+	0.0347237i
$525$	−13.6840	+	43.0534i	−0.597218	+	1.87901i
$526$	−2.07459	+	0.555884i	−0.0904563	+	0.0242377i
$527$	9.71355	−	2.60274i	0.423129	−	0.113377i
$528$	−0.305805	+	0.962144i	−0.0133085	+	0.0418719i
$529$	9.96363	−	17.2575i	0.433201	−	0.750327i
$530$	−5.94771	−	10.3017i	−0.258352	−	0.447478i
$531$	−16.2605	−	19.5611i	−0.705646	−	0.848880i
$532$		−	3.49026i		−	0.151322i
$533$	10.8435	−	15.7277i	0.469684	−	0.681243i
$534$	7.71547	+	14.9051i	0.333881	+	0.645009i
$535$	−3.49765	+	13.0534i	−0.151217	+	0.564349i
$536$	5.71696	−	3.30069i	0.246935	−	0.142568i
$537$	24.2238	+	1.11363i	1.04533	+	0.0480569i
$538$	−17.3407	−	17.3407i	−0.747612	−	0.747612i
$539$	0.0825429	+	0.308054i	0.00355537	+	0.0132688i
$540$	20.1475	−	2.51072i	0.867010	−	0.108044i
$541$	−13.2334	+	13.2334i	−0.568947	+	0.568947i	−0.931833	−	0.362887i	$-0.881791\pi$
$541$	−13.2334	+	13.2334i	−0.568947	+	0.568947i	0.362887	+	0.931833i	$0.381791\pi$
$542$	−18.9885	−	10.9630i	−0.815627	−	0.470903i
$543$	37.2546	+	23.8548i	1.59875	+	1.02371i
$544$	1.05672	+	0.283148i	0.0453066	+	0.0121399i
$545$	60.7298			2.60138
$546$	12.5377	−	9.71943i	0.536564	−	0.415953i
$547$	−14.7212			−0.629433			−0.314717	−	0.949186i	$-0.601909\pi$
$547$	−14.7212			−0.629433			−0.314717	+	0.949186i	$0.601909\pi$
$548$	8.32493	+	2.23066i	0.355624	+	0.0952890i
$549$	27.9177	+	2.57235i	1.19150	+	0.109785i
$550$	5.18295	+	2.99238i	0.221002	+	0.127595i
$551$	5.75480	−	5.75480i	0.245163	−	0.245163i
$552$	−2.04602	−	2.24321i	−0.0870845	−	0.0954773i
$553$	8.61860	+	32.1651i	0.366500	+	1.36780i
$554$	−13.1878	−	13.1878i	−0.560295	−	0.560295i
$555$	0.961903	−	20.9233i	0.0408305	−	0.888145i
$556$	−2.86936	+	1.65662i	−0.121688	+	0.0702565i
$557$	3.19111	−	11.9094i	0.135212	−	0.504616i	−0.864785	−	0.502142i	$-0.832546\pi$
$557$	3.19111	−	11.9094i	0.135212	−	0.504616i	0.999997	−	0.00247467i	$-0.000787714\pi$
$558$	15.9213	−	22.5161i	0.674001	−	0.953181i
$559$	−10.3430	+	8.80748i	−0.437464	+	0.372517i
$560$			9.92570i			0.419438i
$561$	1.07884	−	0.236563i	0.0455487	−	0.00998771i
$562$	7.97489	+	13.8129i	0.336400	+	0.582662i
$563$	−9.86628	+	17.0889i	−0.415814	+	0.720211i	−0.995514	−	0.0946194i	$-0.969837\pi$
$563$	−9.86628	+	17.0889i	−0.415814	+	0.720211i	0.579700	+	0.814830i	$0.303170\pi$
$564$	−12.8653	−	4.08907i	−0.541726	−	0.172181i
$565$	41.1283	−	11.0203i	1.73028	−	0.463628i
$566$	4.55446	−	1.22036i	0.191438	−	0.0512958i
$567$	20.6302	+	9.85280i	0.866385	+	0.413779i
$568$	−0.425242	+	0.736541i	−0.0178428	+	0.0309046i
$569$	17.4503	+	30.2248i	0.731555	+	1.26709i	0.956218	+	0.292654i	$0.0945384\pi$
$569$	17.4503	+	30.2248i	0.731555	+	1.26709i	−0.224663	+	0.974436i	$0.572128\pi$
$570$	1.99168	+	9.08302i	0.0834223	+	0.380446i
$571$			2.37582i			0.0994248i	0.998764	+	0.0497124i	$0.0158305\pi$
$571$			2.37582i			0.0994248i	−0.998764	+	0.0497124i	$0.984170\pi$
$572$	−0.901965	−	1.89820i	−0.0377131	−	0.0793677i
$573$	36.3725	−	18.8278i	1.51948	−	0.786542i
$574$	−3.48347	+	13.0005i	−0.145397	+	0.542630i
$575$	−15.5870	+	8.99915i	−0.650022	+	0.375291i
$576$	2.72474	−	1.25529i	0.113531	−	0.0523040i
$577$	3.78848	+	3.78848i	0.157716	+	0.157716i	0.781554	−	0.623838i	$-0.214427\pi$
$577$	3.78848	+	3.78848i	0.157716	+	0.157716i	−0.623838	+	0.781554i	$0.714427\pi$
$578$	4.09016	+	15.2647i	0.170128	+	0.634927i
$579$	13.5631	−	12.3708i	0.563662	−	0.514114i
$580$	−16.3657	+	16.3657i	−0.679548	+	0.679548i
$581$	16.0347	+	9.25764i	0.665232	+	0.384072i
$582$	−0.572868	+	0.894660i	−0.0237461	+	0.0370849i
$583$	−1.71402	−	0.459269i	−0.0709873	−	0.0190210i
$584$	−7.32673			−0.303182
$585$	−27.0817	+	32.4483i	−1.11969	+	1.34157i
$586$	−21.3553			−0.882179
$587$	−9.81579	−	2.63013i	−0.405141	−	0.108557i	0.0504929	−	0.998724i	$-0.483921\pi$
$587$	−9.81579	−	2.63013i	−0.405141	−	0.108557i	−0.455634	+	0.890167i	$0.650587\pi$
$588$	0.511037	−	0.798098i	0.0210748	−	0.0329130i
$589$	10.9378	+	6.31493i	0.450683	+	0.260202i
$590$	−23.4269	+	23.4269i	−0.964471	+	0.964471i
$591$	4.43768	−	4.04759i	0.182542	−	0.166495i
$592$	−0.801012	−	2.98942i	−0.0329214	−	0.122864i
$593$	9.76893	+	9.76893i	0.401162	+	0.401162i	0.878642	−	0.477481i	$-0.158450\pi$
$593$	9.76893	+	9.76893i	0.401162	+	0.401162i	−0.477481	+	0.878642i	$0.658450\pi$
$594$	1.86036	−	2.39003i	0.0763313	−	0.0980639i
$595$	9.40393	−	5.42936i	0.385523	−	0.222582i
$596$	−2.03304	+	7.58742i	−0.0832766	+	0.310793i
$597$	−4.74998	+	2.45877i	−0.194404	+	0.100631i
$598$	6.30003	+	0.505159i	0.257627	+	0.0206575i
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$	−3.80910	−	17.3713i	−0.155506	−	0.709180i
$601$	−4.57192	−	7.91880i	−0.186493	−	0.323015i	0.757586	−	0.652736i	$-0.226379\pi$
$601$	−4.57192	−	7.91880i	−0.186493	−	0.323015i	−0.944078	+	0.329721i	$0.893045\pi$
$602$	4.78554	−	8.28880i	0.195044	−	0.337826i
$603$	−19.5189	+	3.34892i	−0.794872	+	0.136378i
$604$	14.0154	−	3.75542i	0.570279	−	0.152806i
$605$	−40.2343	+	10.7808i	−1.63576	+	0.438300i
$606$	9.63301	+	3.06173i	0.391314	+	0.124374i
$607$	9.96393	−	17.2580i	0.404423	−	0.700482i	−0.589831	−	0.807527i	$-0.700806\pi$
$607$	9.96393	−	17.2580i	0.404423	−	0.700482i	0.994254	+	0.107045i	$0.0341389\pi$
$608$	0.686992	+	1.18990i	0.0278612	+	0.0482570i
$609$	−25.4567	+	5.58203i	−1.03156	+	0.226195i
$610$		−	36.5157i		−	1.47848i
$611$	25.3817	−	12.0606i	1.02683	−	0.487920i
$612$	−2.67974	−	1.89486i	−0.108322	−	0.0765953i
$613$	−3.88890	+	14.5136i	−0.157071	+	0.586198i	0.841848	+	0.539715i	$0.181468\pi$
$613$	−3.88890	+	14.5136i	−0.157071	+	0.586198i	−0.998919	+	0.0464829i	$0.985199\pi$
$614$	−19.8726	+	11.4735i	−0.801994	+	0.463032i
$615$	1.64676	−	35.8202i	0.0664036	−	1.44441i
$616$	1.04698	+	1.04698i	0.0421840	+	0.0421840i
$617$	2.63629	+	9.83876i	0.106133	+	0.396094i	0.998471	−	0.0552736i	$-0.0176031\pi$
$617$	2.63629	+	9.83876i	0.106133	+	0.396094i	−0.892338	+	0.451367i	$0.850936\pi$
$618$	−2.41978	−	2.65298i	−0.0973377	−	0.106719i
$619$	18.1131	−	18.1131i	0.728027	−	0.728027i	−0.242199	−	0.970226i	$-0.577869\pi$
$619$	18.1131	−	18.1131i	0.728027	−	0.728027i	0.970226	+	0.242199i	$0.0778688\pi$
$620$	−31.1052	−	17.9586i	−1.24922	−	0.721235i
$621$	3.42732	+	8.43903i	0.137534	+	0.338647i
$622$	31.7272	+	8.50128i	1.27215	+	0.340870i
$623$	24.6151			0.986185
$624$	−2.36129	+	5.78138i	−0.0945271	+	0.231440i
$625$	−29.0857			−1.16343
$626$	10.6859	+	2.86328i	0.427095	+	0.114440i
$627$	1.16818	+	0.748005i	0.0466525	+	0.0298725i
$628$	−5.81577	−	3.35773i	−0.232074	−	0.133988i
$629$	−2.39412	+	2.39412i	−0.0954596	+	0.0954596i
$630$	10.3134	−	27.9340i	0.410895	−	1.11292i
$631$	−5.19785	−	19.3987i	−0.206923	−	0.772248i	−0.988855	−	0.148884i	$-0.952432\pi$
$631$	−5.19785	−	19.3987i	−0.206923	−	0.772248i	0.781931	−	0.623364i	$-0.214235\pi$
$632$	−9.26936	−	9.26936i	−0.368716	−	0.368716i
$633$	8.57846	+	0.394376i	0.340963	+	0.0156750i
$634$	−21.4942	+	12.4097i	−0.853645	+	0.492852i
$635$	−9.41853	+	35.1504i	−0.373763	+	1.39490i
$636$	2.42398	+	4.68278i	0.0961173	+	0.185684i
$637$	0.356653	+	1.94027i	0.0141311	+	0.0768763i
$638$			3.45256i			0.136688i
$639$	1.96207	−	1.63101i	0.0776184	−	0.0645216i
$640$	−1.95369	−	3.38389i	−0.0772263	−	0.133760i
$641$	−22.3417	+	38.6969i	−0.882443	+	1.52844i	−0.0338257	+	0.999428i	$0.510769\pi$
$641$	−22.3417	+	38.6969i	−0.882443	+	1.52844i	−0.848617	+	0.529008i	$0.822564\pi$
$642$	1.81452	−	5.70897i	0.0716136	−	0.225315i
$643$	8.68244	−	2.32645i	0.342402	−	0.0917463i	−0.0835204	−	0.996506i	$-0.526616\pi$
$643$	8.68244	−	2.32645i	0.342402	−	0.0917463i	0.425922	+	0.904760i	$0.359950\pi$
$644$	−4.30112	+	1.15248i	−0.169488	+	0.0454142i
$645$	−7.72393	+	24.3015i	−0.304130	+	0.956872i
$646$	0.751569	−	1.30176i	0.0295701	−	0.0512169i
$647$	−18.9869	−	32.8862i	−0.746451	−	1.29289i	−0.949514	−	0.313725i	$-0.898423\pi$
$647$	−18.9869	−	32.8862i	−0.746451	−	1.29289i	0.203063	−	0.979166i	$-0.434910\pi$
$648$	−8.97261	+	0.701625i	−0.352477	+	0.0275624i
$649$			4.94222i			0.193999i
$650$	30.4786	+	21.0135i	1.19547	+	0.824217i
$651$	−18.5921	−	35.9172i	−0.728682	−	1.40771i
$652$	0.407550	−	1.52100i	0.0159609	−	0.0595668i
$653$	16.0116	−	9.24428i	0.626581	−	0.361757i	−0.152846	−	0.988250i	$-0.548844\pi$
$653$	16.0116	−	9.24428i	0.626581	−	0.361757i	0.779427	+	0.626493i	$0.215510\pi$
$654$	−26.8917	−	1.23629i	−1.05155	−	0.0483426i
$655$	−2.53590	−	2.53590i	−0.0990857	−	0.0990857i
$656$	−1.37131	−	5.11781i	−0.0535408	−	0.199817i
$657$	20.6197	+	7.61290i	0.804452	+	0.297008i
$658$	−13.9997	+	13.9997i	−0.545763	+	0.545763i
$659$	0.644195	+	0.371926i	0.0250943	+	0.0144882i	0.512495	−	0.858690i	$-0.328721\pi$
$659$	0.644195	+	0.371926i	0.0250943	+	0.0144882i	−0.487400	+	0.873179i	$0.662055\pi$
$660$	−3.32210	−	2.12720i	−0.129313	−	0.0828012i
$661$	27.0849	+	7.25737i	1.05348	+	0.282279i	0.743689	−	0.668526i	$-0.233075\pi$
$661$	27.0849	+	7.25737i	1.05348	+	0.282279i	0.309790	+	0.950805i	$0.399741\pi$
$662$	4.62395			0.179715
$663$	6.76909	−	0.925255i	0.262890	−	0.0359339i
$664$	−7.28877			−0.282859
$665$	13.1731	+	3.52971i	0.510829	+	0.136876i
$666$	−0.851879	+	9.24545i	−0.0330097	+	0.358254i
$667$	−8.99201	−	5.19154i	−0.348172	−	0.201017i
$668$	17.2850	−	17.2850i	0.668775	−	0.668775i
$669$	−22.2517	−	24.3963i	−0.860302	−	0.943214i
$670$	6.67600	+	24.9152i	0.257916	+	0.962556i
$671$	−3.85174	−	3.85174i	−0.148695	−	0.148695i
$672$	0.202059	−	4.39519i	0.00779461	−	0.169548i
$673$	23.9347	−	13.8187i	0.922615	−	0.532672i	0.0381465	−	0.999272i	$-0.487855\pi$
$673$	23.9347	−	13.8187i	0.922615	−	0.532672i	0.884468	+	0.466600i	$0.154521\pi$
$674$	−2.01474	+	7.51911i	−0.0776049	+	0.289625i
$675$	−7.32980	+	52.8461i	−0.282124	+	2.03405i
$676$	−4.62302	−	12.1502i	−0.177808	−	0.467316i
$677$			34.0927i			1.31029i	0.755504	+	0.655145i	$0.227392\pi$
$677$			34.0927i			1.31029i	−0.755504	+	0.655145i	$0.772608\pi$
$678$	−18.4363	+	4.04264i	−0.708044	+	0.155256i
$679$	0.779030	+	1.34932i	0.0298964	+	0.0517821i
$680$	−2.13734	+	3.70198i	−0.0819631	+	0.141964i
$681$	−8.84802	−	2.81223i	−0.339057	−	0.107765i
$682$	−5.17533	+	1.38672i	−0.198174	+	0.0531004i
$683$	−22.5100	+	6.03154i	−0.861322	+	0.230790i	−0.662331	−	0.749211i	$-0.730433\pi$
$683$	−22.5100	+	6.03154i	−0.861322	+	0.230790i	−0.198990	+	0.980001i	$0.563766\pi$
$684$	−0.697030	−	4.06259i	−0.0266516	−	0.155337i
$685$	−16.8381	+	29.1644i	−0.643350	+	1.11431i
$686$	−9.58581	−	16.6031i	−0.365988	−	0.633910i
$687$	−1.46081	−	6.66198i	−0.0557333	−	0.254170i
$688$			3.76778i			0.143645i
$689$	−10.3415	−	3.67928i	−0.393981	−	0.140169i
$690$	10.5356	−	5.45361i	0.401082	−	0.207615i
$691$	2.64500	−	9.87128i	0.100621	−	0.375521i	−0.897191	−	0.441643i	$-0.854396\pi$
$691$	2.64500	−	9.87128i	0.100621	−	0.375521i	0.997812	+	0.0661216i	$0.0210625\pi$
$692$	17.9850	−	10.3837i	0.683689	−	0.394728i
$693$	−1.85865	−	4.03440i	−0.0706045	−	0.153254i
$694$	7.66753	+	7.66753i	0.291056	+	0.291056i
$695$	−3.35070	−	12.5050i	−0.127099	−	0.474341i
$696$	7.58004	−	6.91372i	0.287320	−	0.262064i
$697$	−4.09867	+	4.09867i	−0.155248	+	0.155248i
$698$	13.3129	+	7.68623i	0.503902	+	0.290928i
$699$	−3.58340	+	5.59628i	−0.135537	+	0.211671i
$700$	−25.1935	−	6.75058i	−0.952225	−	0.255148i
$701$	−31.9420			−1.20643			−0.603217	−	0.797577i	$-0.706115\pi$
$701$	−31.9420			−1.20643			−0.603217	+	0.797577i	$0.706115\pi$
$702$	12.6526	−	13.8171i	0.477541	−	0.521493i
$703$	−4.25230			−0.160379
$704$	−0.563016	−	0.150860i	−0.0212195	−	0.00568574i
$705$	28.4438	−	44.4214i	1.07126	−	1.67301i
$706$	−1.61722	−	0.933704i	−0.0608650	−	0.0351404i
$707$	10.4824	−	10.4824i	0.394231	−	0.394231i
$708$	10.8506	−	9.89675i	0.407789	−	0.371943i
$709$	1.92196	+	7.17283i	0.0721805	+	0.269381i	0.992579	−	0.121600i	$-0.0388024\pi$
$709$	1.92196	+	7.17283i	0.0721805	+	0.269381i	−0.920399	+	0.390981i	$0.872136\pi$
$710$	−2.34983	−	2.34983i	−0.0881876	−	0.0881876i
$711$	16.4555	+	35.7183i	0.617129	+	1.33954i
$712$	−8.39184	+	4.84503i	−0.314497	+	0.181575i
$713$	4.17038	−	15.5641i	0.156182	−	0.582879i
$714$	−4.27467	+	2.21273i	−0.159976	+	0.0828095i
$715$	8.07641	−	1.48458i	0.302041	−	0.0555200i
$716$			14.0004i			0.523218i
$717$	0.394286	+	1.79813i	0.0147249	+	0.0671524i
$718$	−8.57975	−	14.8606i	−0.320193	−	0.554591i
$719$	−14.4593	+	25.0442i	−0.539240	+	0.933992i	0.459705	+	0.888072i	$0.347955\pi$
$719$	−14.4593	+	25.0442i	−0.539240	+	0.933992i	−0.998945	+	0.0459198i	$0.985378\pi$
$720$	1.98224	+	11.5533i	0.0738736	+	0.430567i
$721$	−5.08682	+	1.36301i	−0.189443	+	0.0507612i
$722$	−16.5291	+	4.42896i	−0.615149	+	0.164829i
$723$	−46.1589	−	14.6710i	−1.71667	−	0.545621i
$724$	−12.7703	+	22.1188i	−0.474603	+	0.822037i
$725$	−30.4091	−	52.6700i	−1.12936	−	1.95612i
$726$	18.0356	−	3.95476i	0.669364	−	0.146775i
$727$			13.5518i			0.502608i	0.967908	+	0.251304i	$0.0808594\pi$
$727$			13.5518i			0.502608i	−0.967908	+	0.251304i	$0.919141\pi$
$728$	5.93802	+	6.97330i	0.220078	+	0.258448i
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$	7.40955	−	27.6528i	0.274240	−	1.02348i
$731$	3.56971	−	2.06098i	0.132031	−	0.0762279i
$732$	−0.743357	+	16.1695i	−0.0274753	+	0.597642i
$733$	−13.9665	−	13.9665i	−0.515864	−	0.515864i	0.400453	−	0.916317i	$-0.368853\pi$
$733$	−13.9665	−	13.9665i	−0.515864	−	0.515864i	−0.916317	+	0.400453i	$0.868853\pi$
$734$	2.34563	+	8.75401i	0.0865788	+	0.323116i
$735$	2.49540	+	2.73589i	0.0920441	+	0.100915i
$736$	1.23950	−	1.23950i	0.0456887	−	0.0456887i
$737$	3.33228	+	1.92390i	0.122746	+	0.0708676i
$738$	−1.45840	+	15.8280i	−0.0536843	+	0.582637i
$739$	−1.90239	−	0.509744i	−0.0699806	−	0.0187512i	0.223659	−	0.974667i	$-0.428200\pi$
$739$	−1.90239	−	0.509744i	−0.0699806	−	0.0187512i	−0.293639	+	0.955916i	$0.594867\pi$
$740$	12.0928			0.444541
$741$	6.83314	+	5.18975i	0.251022	+	0.190650i
$742$	7.73339			0.283902
$743$	−5.78030	−	1.54883i	−0.212059	−	0.0568210i	0.151226	−	0.988499i	$-0.451678\pi$
$743$	−5.78030	−	1.54883i	−0.212059	−	0.0568210i	−0.363284	+	0.931678i	$0.618345\pi$
$744$	13.4081	+	8.58545i	0.491564	+	0.314758i
$745$	−26.5807	−	15.3464i	−0.973841	−	0.562247i
$746$	5.35695	−	5.35695i	0.196132	−	0.196132i
$747$	20.5129	+	7.57346i	0.750527	+	0.277098i
$748$	0.165041	+	0.615940i	0.00603448	+	0.0225210i
$749$	−6.21235	−	6.21235i	−0.226994	−	0.226994i
$750$	35.6124	+	1.63720i	1.30038	+	0.0597821i
$751$	−15.1590	+	8.75204i	−0.553159	+	0.319366i	−0.750395	−	0.660990i	$-0.770137\pi$
$751$	−15.1590	+	8.75204i	−0.553159	+	0.319366i	0.197236	+	0.980356i	$0.436803\pi$
$752$	2.01722	−	7.52836i	0.0735604	−	0.274531i
$753$	−12.0440	−	23.2673i	−0.438909	−	0.847906i
$754$	−1.70698	+	21.2884i	−0.0621646	+	0.775279i
$755$			56.6953i			2.06335i
$756$	−5.13552	+	12.1595i	−0.186777	+	0.442237i
$757$	−4.00168	−	6.93111i	−0.145443	−	0.251915i	0.784095	−	0.620641i	$-0.213128\pi$
$757$	−4.00168	−	6.93111i	−0.145443	−	0.251915i	−0.929538	+	0.368726i	$0.879794\pi$
$758$	6.03855	−	10.4591i	0.219330	−	0.379891i
$759$	0.536052	−	1.68656i	0.0194575	−	0.0612183i
$760$	−5.18574	+	1.38951i	−0.188107	+	0.0504030i
$761$	18.9310	−	5.07254i	0.686247	−	0.183879i	0.101185	−	0.994868i	$-0.467737\pi$
$761$	18.9310	−	5.07254i	0.686247	−	0.183879i	0.585062	+	0.810988i	$0.301070\pi$
$762$	4.88617	−	15.3732i	0.177007	−	0.556912i
$763$	−19.7407	+	34.1918i	−0.714660	+	1.23783i
$764$	11.8231	+	20.4783i	0.427747	+	0.740879i
$765$	9.86170	−	8.19770i	0.356551	−	0.296389i
$766$			36.8323i			1.33081i
$767$	−2.44349	+	30.4737i	−0.0882293	+	1.10034i
$768$	0.796225	+	1.53819i	0.0287313	+	0.0555046i
$769$	11.1131	−	41.4747i	0.400749	−	1.49561i	−0.411015	−	0.911629i	$-0.634826\pi$
$769$	11.1131	−	41.4747i	0.400749	−	1.49561i	0.811764	−	0.583986i	$-0.198508\pi$
$770$	−5.01036	+	2.89273i	−0.180561	+	0.104247i
$771$	0.618038	+	0.0284129i	0.0222581	+	0.00102327i
$772$	7.49437	+	7.49437i	0.269728	+	0.269728i
$773$	−2.39809	−	8.94981i	−0.0862535	−	0.321902i	0.909295	−	0.416152i	$-0.136622\pi$
$773$	−2.39809	−	8.94981i	−0.0862535	−	0.321902i	−0.995549	+	0.0942495i	$0.969955\pi$
$774$	3.91494	−	10.6037i	0.140720	−	0.381142i
$775$	66.7377	−	66.7377i	2.39729	−	2.39729i
$776$	−0.531177	−	0.306675i	−0.0190681	−	0.0110090i
$777$	11.4675	+	7.34285i	0.411394	+	0.263423i
$778$	13.6208	+	3.64967i	0.488328	+	0.130847i
$779$	−7.27984			−0.260827
$780$	−19.4323	−	14.7588i	−0.695788	−	0.528449i
$781$	−0.495728			−0.0177385
$782$	−1.85235	−	0.496336i	−0.0662400	−	0.0177489i
$783$	−28.5163	+	11.5813i	−1.01909	+	0.413881i
$784$	0.473846	+	0.273575i	0.0169231	+	0.00977053i
$785$	18.5544	−	18.5544i	0.662235	−	0.662235i
$786$	1.07130	+	1.17454i	0.0382118	+	0.0418946i
$787$	−11.0255	−	41.1479i	−0.393018	−	1.46676i	−0.825130	−	0.564943i	$-0.808898\pi$
$787$	−11.0255	−	41.1479i	−0.393018	−	1.46676i	0.432112	−	0.901820i	$-0.357769\pi$
$788$	2.45207	+	2.45207i	0.0873514	+	0.0873514i
$789$	−0.170841	+	3.71612i	−0.00608209	+	0.132297i
$790$	44.3589	−	25.6106i	1.57822	−	0.911186i
$791$	−7.16447	+	26.7382i	−0.254739	+	0.950699i
$792$	1.42775	+	1.00957i	0.0507330	+	0.0358736i
$793$	−21.8454	−	25.6541i	−0.775754	−	0.911004i
$794$		−	7.85191i		−	0.278654i
$795$	−20.1253	+	4.41298i	−0.713771	+	0.156512i
$796$	−1.54402	−	2.67432i	−0.0547263	−	0.0947887i
$797$	−10.5161	+	18.2144i	−0.372499	+	0.645187i	−0.989949	−	0.141423i	$-0.954832\pi$
$797$	−10.5161	+	18.2144i	−0.372499	+	0.645187i	0.617450	+	0.786610i	$0.288166\pi$
$798$	−5.76130	−	1.83115i	−0.203948	−	0.0648222i
$799$	−8.23603	+	2.20684i	−0.291370	+	0.0780723i
$800$	9.91775	−	2.65745i	0.350645	−	0.0939551i
$801$	28.6515	−	4.91582i	1.01235	−	0.173692i
$802$	−10.9280	+	18.9279i	−0.385882	+	0.668368i
$803$	−2.13529	−	3.69844i	−0.0753529	−	0.130515i
$804$	−2.44899	−	11.1686i	−0.0863692	−	0.393885i
$805$		−	17.3990i		−	0.613233i
$806$	−32.5966	+	5.99179i	−1.14817	+	0.211052i
$807$	−37.7218	+	19.5262i	−1.32787	+	0.687356i
$808$	−1.51041	+	5.63694i	−0.0531361	+	0.198307i
$809$	−23.4871	+	13.5603i	−0.825762	+	0.476754i	−0.852399	−	0.522891i	$-0.824853\pi$
$809$	−23.4871	+	13.5603i	−0.825762	+	0.476754i	0.0266373	+	0.999645i	$0.491520\pi$
$810$	6.42594	−	34.5743i	0.225784	−	1.21482i
$811$	39.1597	+	39.1597i	1.37508	+	1.37508i	0.852726	+	0.522359i	$0.174948\pi$
$811$	39.1597	+	39.1597i	1.37508	+	1.37508i	0.522359	+	0.852726i	$0.325052\pi$
$812$	−3.89436	−	14.5339i	−0.136665	−	0.510041i
$813$	−28.0588	+	25.5923i	−0.984063	+	0.897560i
$814$	1.27557	−	1.27557i	0.0447088	−	0.0447088i
$815$	5.32844	+	3.07638i	0.186647	+	0.107761i
$816$	1.02179	−	1.59576i	0.0357700	−	0.0558627i
$817$	5.00047	+	1.33987i	0.174944	+	0.0468762i
$818$	2.24149			0.0783720
$819$	−9.46580	−	25.7950i	−0.330762	−	0.901350i
$820$	20.7026			0.722968
$821$	−8.30053	−	2.22412i	−0.289690	−	0.0776223i	0.111047	−	0.993815i	$-0.464579\pi$
$821$	−8.30053	−	2.22412i	−0.289690	−	0.0776223i	−0.400738	+	0.916193i	$0.631246\pi$
$822$	8.04976	−	12.5715i	0.280768	−	0.438481i
$823$	−7.37175	−	4.25608i	−0.256963	−	0.148358i	0.365985	−	0.930621i	$-0.380732\pi$
$823$	−7.37175	−	4.25608i	−0.256963	−	0.148358i	−0.622948	+	0.782263i	$0.714065\pi$
$824$	1.46593	−	1.46593i	0.0510680	−	0.0510680i
$825$	7.65868	−	6.98545i	0.266641	−	0.243202i
$826$	−5.57464	−	20.8048i	−0.193967	−	0.723893i
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	0.955524	−	0.294912i	$-0.0952903\pi$
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	−0.294912	+	0.955524i	$0.595290\pi$
$828$	−4.77626	+	2.20043i	−0.165987	+	0.0764703i
$829$	14.3179	−	8.26645i	0.497282	−	0.287106i	−0.230309	−	0.973118i	$-0.573974\pi$
$829$	14.3179	−	8.26645i	0.497282	−	0.287106i	0.727590	+	0.686012i	$0.240640\pi$
$830$	7.37117	−	27.5096i	0.255857	−	0.954871i
$831$	−28.6877	+	14.8499i	−0.995167	+	0.515136i
$832$	−3.39697	−	1.20856i	−0.117769	−	0.0418993i
$833$		−	0.598582i		−	0.0207396i
$834$	1.22916	+	5.60554i	0.0425622	+	0.194104i
$835$	47.7572	+	82.7179i	1.65271	+	2.86257i
$836$	−0.400432	+	0.693568i	−0.0138492	+	0.0239876i
$837$	−28.8138	−	38.0939i	−0.995950	−	1.31672i
$838$	−32.2478	+	8.64077i	−1.11398	+	0.298490i
$839$	40.0647	−	10.7353i	1.38319	−	0.370623i	0.510908	−	0.859635i	$-0.329309\pi$
$839$	40.0647	−	10.7353i	1.38319	−	0.370623i	0.872277	+	0.489012i	$0.162643\pi$
$840$	16.3842	+	5.20750i	0.565307	+	0.179676i
$841$	3.04274	−	5.27017i	0.104922	−	0.181730i
$842$	1.59301	+	2.75917i	0.0548986	+	0.0950872i
$843$	26.9847	−	5.91708i	0.929402	−	0.203795i
$844$			4.95801i			0.170662i
$845$	50.5331	−	5.16081i	1.73839	−	0.177537i
$846$	−13.4995	+	19.0912i	−0.464122	+	0.656368i
$847$	7.00873	−	26.1570i	0.240823	−	0.898763i
$848$	−2.63648	+	1.52217i	−0.0905371	+	0.0522716i
$849$	0.375057	−	8.15822i	0.0128719	−	0.279990i
$850$	−7.94276	−	7.94276i	−0.272435	−	0.272435i
$851$	1.40411	+	5.24021i	0.0481323	+	0.179632i
$852$	0.992692	+	1.08836i	0.0340091	+	0.0372867i
$853$	−13.7858	+	13.7858i	−0.472018	+	0.472018i	−0.902567	−	0.430549i	$-0.858320\pi$
$853$	−13.7858	+	13.7858i	−0.472018	+	0.472018i	0.430549	+	0.902567i	$0.358320\pi$
$854$	20.5589	+	11.8697i	0.703513	+	0.406173i
$855$	16.0381	+	1.47775i	0.548491	+	0.0505381i
$856$	3.34071	+	0.895141i	0.114183	+	0.0305953i
$857$	−41.5499			−1.41932			−0.709659	−	0.704545i	$-0.751151\pi$
$857$	−41.5499			−1.41932			−0.709659	+	0.704545i	$0.751151\pi$
$858$	−3.60653	+	0.492971i	−0.123125	+	0.0168298i
$859$	44.2270			1.50900			0.754502	−	0.656298i	$-0.227878\pi$
$859$	44.2270			1.50900			0.754502	+	0.656298i	$0.227878\pi$
$860$	−14.2205	−	3.81037i	−0.484915	−	0.129933i
$861$	19.6321	+	12.5708i	0.669059	+	0.428411i
$862$	−18.7789	−	10.8420i	−0.639613	−	0.369281i
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	−0.410089	−	0.912045i	$-0.634502\pi$
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	0.912045	+	0.410089i	$0.134502\pi$
$864$	−0.642559	−	5.15627i	−0.0218603	−	0.175420i
$865$	21.0021	+	78.3809i	0.714093	+	2.66503i
$866$	21.2499	+	21.2499i	0.722103	+	0.722103i
$867$	27.3430	+	1.25703i	0.928617	+	0.0426911i
$868$	20.2220	−	11.6752i	0.686378	−	0.396281i
$869$	1.97760	−	7.38050i	0.0670855	−	0.250366i
$870$	18.4283	+	35.6007i	0.624778	+	1.20698i
$871$	19.5956	+	13.5102i	0.663973	+	0.457777i
$872$		−	15.5423i		−	0.526330i
$873$	1.17624	+	1.41500i	0.0398098	+	0.0478906i
$874$	−1.20424	−	2.08581i	−0.0407341	−	0.0705535i
$875$	26.1424	−	45.2799i	0.883773	−	1.53074i
$876$	−3.84395	+	12.0941i	−0.129875	+	0.408622i
$877$	−43.6140	+	11.6863i	−1.47274	+	0.394620i	−0.903870	−	0.427808i	$-0.859286\pi$
$877$	−43.6140	+	11.6863i	−1.47274	+	0.394620i	−0.568870	+	0.822427i	$0.692619\pi$
$878$	−20.1356	+	5.39532i	−0.679543	+	0.182083i
$879$	−11.2040	+	35.2508i	−0.377902	+	1.18898i
$880$	1.13876	−	1.97239i	0.0383876	−	0.0664893i
$881$	15.5665	+	26.9620i	0.524448	+	0.908371i	0.999595	+	0.0284646i	$0.00906178\pi$
$881$	15.5665	+	26.9620i	0.524448	+	0.908371i	−0.475146	+	0.879907i	$0.657605\pi$
$882$	−1.04929	−	1.26228i	−0.0353314	−	0.0425031i
$883$		−	45.7983i		−	1.54123i	−0.637298	−	0.770617i	$-0.719948\pi$
$883$		−	45.7983i		−	1.54123i	0.637298	−	0.770617i	$-0.280052\pi$
$884$	0.713111	+	3.87948i	0.0239845	+	0.130481i
$885$	26.3795	+	50.9612i	0.886737	+	1.71304i
$886$	−3.37405	+	12.5921i	−0.113353	+	0.423040i
$887$	25.6110	−	14.7865i	0.859933	−	0.496482i	−0.00405708	−	0.999992i	$-0.501291\pi$
$887$	25.6110	−	14.7865i	0.859933	−	0.496482i	0.863990	+	0.503509i	$0.167958\pi$
$888$	−5.35482	−	0.246176i	−0.179696	−	0.00826113i
$889$	−16.7287	−	16.7287i	−0.561062	−	0.561062i
$890$	−9.79960	−	36.5726i	−0.328483	−	1.22592i
$891$	−2.96914	−	4.32477i	−0.0994698	−	0.144885i
$892$	13.4803	−	13.4803i	0.451355	−	0.451355i
$893$	−9.27404	−	5.35437i	−0.310344	−	0.179177i
$894$	11.4578	+	7.33662i	0.383205	+	0.245373i
$895$	−52.8407	−	14.1586i	−1.76627	−	0.473271i
$896$	2.54025			0.0848637
$897$	4.13915	−	10.1343i	0.138202	−	0.338374i
$898$	19.0404			0.635385
$899$	52.5926	+	14.0921i	1.75406	+	0.469999i
$900$	−30.6729	−	2.82621i	−1.02243	−	0.0942071i
$901$	2.88431	+	1.66526i	0.0960903	+	0.0554778i
$902$	2.18375	−	2.18375i	0.0727109	−	0.0727109i
$903$	−11.1714	−	12.2481i	−0.371762	−	0.407591i
$904$	−2.82038	−	10.5258i	−0.0938045	−	0.350083i
$905$	−70.5668	−	70.5668i	−2.34572	−	2.34572i
$906$	1.15416	−	25.1052i	0.0383443	−	0.834065i
$907$	−50.3199	+	29.0522i	−1.67085	+	0.964663i	−0.703679	+	0.710518i	$0.748461\pi$
$907$	−50.3199	+	29.0522i	−1.67085	+	0.964663i	−0.967166	+	0.254145i	$0.918206\pi$
$908$	1.38733	−	5.17758i	0.0460401	−	0.171824i
$909$	10.1079	−	14.2947i	0.335257	−	0.474125i
$910$	−32.3240	+	15.3594i	−1.07153	+	0.509159i
$911$		−	52.8673i		−	1.75157i	−0.482701	−	0.875785i	$-0.660344\pi$
$911$		−	52.8673i		−	1.75157i	0.482701	−	0.875785i	$-0.339656\pi$
$912$	2.32458	−	0.509723i	0.0769745	−	0.0168786i
$913$	−2.12423	−	3.67928i	−0.0703018	−	0.121766i
$914$	−10.6301	+	18.4119i	−0.351614	+	0.609013i
$915$	−60.2758	−	19.1579i	−1.99266	−	0.633340i
$916$	3.80351	−	1.01915i	0.125671	−	0.0336735i
$917$	2.25207	−	0.603439i	0.0743697	−	0.0199273i
$918$	−4.53373	+	3.42926i	−0.149636	+	0.113182i
$919$	3.07508	−	5.32620i	0.101438	−	0.175695i	−0.810840	−	0.585269i	$-0.800989\pi$
$919$	3.07508	−	5.32620i	0.101438	−	0.175695i	0.912277	+	0.409573i	$0.134322\pi$
$920$	3.42466	+	5.93169i	0.112908	+	0.195562i
$921$	8.51290	+	38.8229i	0.280510	+	1.27926i
$922$		−	1.52692i		−	0.0502864i
$923$	−3.05665	−	0.245094i	−0.100611	−	0.00806735i
$924$	2.27752	−	1.17893i	0.0749250	−	0.0387840i
$925$	−8.22447	+	30.6942i	−0.270419	+	1.00922i
$926$	−26.1204	+	15.0806i	−0.858369	+	0.495579i
$927$	−5.64876	+	2.60239i	−0.185530	+	0.0854738i
$928$	4.18840	+	4.18840i	0.137491	+	0.137491i
$929$	−9.26432	−	34.5749i	−0.303952	−	1.13437i	−0.933843	−	0.357682i	$-0.883567\pi$
$929$	−9.26432	−	34.5749i	−0.303952	−	1.13437i	0.629891	−	0.776684i	$-0.283100\pi$
$930$	−45.9632	+	41.9228i	−1.50719	+	1.37470i
$931$	0.531585	−	0.531585i	0.0174220	−	0.0174220i
$932$	−3.32262	−	1.91831i	−0.108836	−	0.0628364i
$933$	30.6785	−	47.9113i	1.00437	−	1.56855i
$934$	−10.9087	−	2.92297i	−0.356943	−	0.0956426i
$935$	−2.49161			−0.0814844
$936$	8.30436	+	6.93092i	0.271437	+	0.226544i
$937$	−13.8585			−0.452737			−0.226369	−	0.974042i	$-0.572685\pi$
$937$	−13.8585			−0.452737			−0.226369	+	0.974042i	$0.572685\pi$
$938$	−16.1977	−	4.34017i	−0.528874	−	0.141711i
$939$	10.3327	−	16.1368i	0.337195	−	0.526605i
$940$	26.3738	+	15.2269i	0.860219	+	0.496647i
$941$	−10.8257	+	10.8257i	−0.352908	+	0.352908i	−0.861190	−	0.508283i	$-0.830281\pi$
$941$	−10.8257	+	10.8257i	−0.352908	+	0.352908i	0.508283	+	0.861190i	$0.330281\pi$
$942$	−8.59377	+	7.83834i	−0.280000	+	0.255387i
$943$	2.40380	+	8.97112i	0.0782786	+	0.292140i
$944$	5.99556	+	5.99556i	0.195139	+	0.195139i
$945$	−40.6993	−	31.6796i	−1.32395	−	1.03054i
$946$	−1.90192	+	1.09808i	−0.0618369	+	0.0357015i
$947$	−5.50870	+	20.5588i	−0.179009	+	0.668070i	0.816825	+	0.576885i	$0.195732\pi$
$947$	−5.50870	+	20.5588i	−0.179009	+	0.668070i	−0.995834	+	0.0911846i	$0.970935\pi$
$948$	−20.1639	+	10.4376i	−0.654893	+	0.338998i
$949$	−11.3376	−	23.8602i	−0.368036	−	0.774536i
$950$		−	14.1075i		−	0.457708i
$951$	9.20755	+	41.9908i	0.298575	+	1.36165i
$952$	−1.38951	−	2.40671i	−0.0450344	−	0.0780019i
$953$	10.3217	−	17.8776i	0.334351	−	0.579114i	−0.649009	−	0.760781i	$-0.724816\pi$
$953$	10.3217	−	17.8776i	0.334351	−	0.579114i	0.983360	+	0.181667i	$0.0581494\pi$
$954$	9.00151	−	1.54441i	0.291435	−	0.0500023i
$955$	−89.2468	+	23.9136i	−2.88796	+	0.773826i
$956$	−1.02660	+	0.275077i	−0.0332027	+	0.00889663i
$957$	5.69907	+	1.81138i	0.184225	+	0.0585535i
$958$	14.5375	−	25.1797i	0.469686	−	0.813519i
$959$	−10.9467	−	18.9602i	−0.353487	−	0.612257i
$960$	−6.61072	+	1.44957i	−0.213360	+	0.0467846i
$961$			53.4956i			1.72566i
$962$	8.49582	−	7.23451i	0.273916	−	0.233250i
$963$	−8.47170	−	5.99040i	−0.272997	−	0.193038i
$964$	7.23751	−	27.0107i	0.233104	−	0.869957i
$965$	−35.8646	+	20.7065i	−1.15452	+	0.666565i
$966$	−0.354194	+	7.70443i	−0.0113960	+	0.247886i
$967$	−3.56933	−	3.56933i	−0.114782	−	0.114782i	0.647383	−	0.762165i	$-0.275863\pi$
$967$	−3.56933	−	3.56933i	−0.114782	−	0.114782i	−0.762165	+	0.647383i	$0.775863\pi$
$968$	2.75908	+	10.2970i	0.0886801	+	0.330959i
$969$	−1.75447	−	1.92356i	−0.0563618	−	0.0617938i
$970$	1.69465	−	1.69465i	0.0544118	−	0.0544118i
$971$	−32.0913	−	18.5279i	−1.02986	−	0.594590i	−0.112916	−	0.993605i	$-0.536019\pi$
$971$	−32.0913	−	18.5279i	−1.02986	−	0.594590i	−0.916945	+	0.399014i	$0.869352\pi$
$972$	−3.54930	+	15.1790i	−0.113844	+	0.486867i
$973$	8.12969	+	2.17834i	0.260626	+	0.0698345i
$974$	2.53376			0.0811869
$975$	50.6770	−	39.2857i	1.62296	−	1.25815i
$976$	−9.34533			−0.299137
$977$	47.1501	+	12.6338i	1.50847	+	0.404192i	0.915925	−	0.401349i	$-0.131458\pi$
$977$	47.1501	+	12.6338i	1.50847	+	0.404192i	0.592540	+	0.805541i	$0.298125\pi$
$978$	−2.29686	−	1.47072i	−0.0734454	−	0.0470285i
$979$	−4.89141	−	2.82406i	−0.156330	−	0.0902573i
$980$	−1.51174	+	1.51174i	−0.0482907	+	0.0482907i
$981$	−16.1494	+	43.7410i	−0.515610	+	1.39654i
$982$	−9.55433	−	35.6572i	−0.304891	−	1.13787i
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.996384	+	0.0849587i	$0.0270758\pi$
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.0849587	+	0.996384i	$0.472924\pi$
$984$	−9.16732	−	0.421448i	−0.292244	−	0.0134353i
$985$	−11.7345	+	6.77491i	−0.373892	+	0.215867i
$986$	1.67717	−	6.25929i	0.0534120	−	0.199336i
$987$	15.7641	+	30.4538i	0.501776	+	0.969357i
$988$	−2.81197	+	4.07856i	−0.0894606	+	0.129756i
$989$		−	6.60462i		−	0.210015i
$990$	−5.25426	+	4.36769i	−0.166991	+	0.138814i
$991$	24.3508	+	42.1768i	0.773529	+	1.33979i	0.935618	+	0.353015i	$0.114844\pi$
$991$	24.3508	+	42.1768i	0.773529	+	1.33979i	−0.162089	+	0.986776i	$0.551823\pi$
$992$	−4.59607	+	7.96063i	−0.145925	+	0.252750i
$993$	2.42595	−	7.63267i	0.0769850	−	0.242215i
$994$	2.08682	−	0.559163i	0.0661901	−	0.0177356i
$995$	11.6550	−	3.12294i	0.369488	−	0.0990039i
$996$	−3.82404	+	12.0314i	−0.121169	+	0.381231i
$997$	2.76696	−	4.79252i	0.0876306	−	0.151781i	−0.818879	−	0.573967i	$-0.805404\pi$
$997$	2.76696	−	4.79252i	0.0876306	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$998$	15.8011	+	27.3682i	0.500174	+	0.866326i
$999$	14.8143	+	6.25678i	0.468705	+	0.197956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.11.4	yes	16
3.2	odd	2	inner	78.2.k.a.11.1	✓	16
4.3	odd	2		624.2.cn.d.401.2		16
12.11	even	2		624.2.cn.d.401.4		16
13.2	odd	12		1014.2.g.c.239.7		16
13.3	even	3		1014.2.g.c.437.3		16
13.6	odd	12	inner	78.2.k.a.71.1	yes	16
13.10	even	6		1014.2.g.d.437.7		16
13.11	odd	12		1014.2.g.d.239.3		16
39.2	even	12		1014.2.g.c.239.3		16
39.11	even	12		1014.2.g.d.239.7		16
39.23	odd	6		1014.2.g.d.437.3		16
39.29	odd	6		1014.2.g.c.437.7		16
39.32	even	12	inner	78.2.k.a.71.4	yes	16
52.19	even	12		624.2.cn.d.305.4		16
156.71	odd	12		624.2.cn.d.305.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.1	✓	16	3.2	odd	2	inner
78.2.k.a.11.4	yes	16	1.1	even	1	trivial
78.2.k.a.71.1	yes	16	13.6	odd	12	inner
78.2.k.a.71.4	yes	16	39.32	even	12	inner
624.2.cn.d.305.2		16	156.71	odd	12
624.2.cn.d.305.4		16	52.19	even	12
624.2.cn.d.401.2		16	4.3	odd	2
624.2.cn.d.401.4		16	12.11	even	2
1014.2.g.c.239.3		16	39.2	even	12
1014.2.g.c.239.7		16	13.2	odd	12
1014.2.g.c.437.3		16	13.3	even	3
1014.2.g.c.437.7		16	39.29	odd	6
1014.2.g.d.239.3		16	13.11	odd	12
1014.2.g.d.239.7		16	39.11	even	12
1014.2.g.d.437.3		16	39.23	odd	6
1014.2.g.d.437.7		16	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.76293 + 2.76293i) q^{5} +(1.27970 - 1.16721i) q^{6} +(-0.657464 - 2.45369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.933998 - 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.76293 + 2.76293i) q^{5} +(1.27970 - 1.16721i) q^{6} +(-0.657464 - 2.45369i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(-3.38389 + 1.95369i) q^{10} +(-0.150860 + 0.563016i) q^{11} +(1.53819 - 0.796225i) q^{12} +(-1.20856 + 3.39697i) q^{13} -2.54025i q^{14} +(1.44957 + 6.61072i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.547000 - 0.947432i) q^{17} +(-0.507306 - 2.95680i) q^{18} +(1.32717 - 0.355613i) q^{19} +(-3.77424 + 1.01130i) q^{20} +(-4.19313 - 1.33273i) q^{21} +(-0.291439 + 0.504787i) q^{22} +(-0.876460 - 1.51807i) q^{23} +(1.69185 - 0.370982i) q^{24} -10.2676i q^{25} +(-2.04658 + 2.96842i) q^{26} +(-5.14688 - 0.713876i) q^{27} +(0.657464 - 2.45369i) q^{28} +(5.12973 - 2.96165i) q^{29} +(-0.310806 + 6.76064i) q^{30} +(6.49983 + 6.49983i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.680339 + 0.745907i) q^{33} +(0.773575 - 0.773575i) q^{34} +(8.59591 + 4.96285i) q^{35} +(0.275255 - 2.98735i) q^{36} +(-2.98942 - 0.801012i) q^{37} +1.37398 q^{38} +(3.82618 + 4.93562i) q^{39} -3.90738 q^{40} +(-5.11781 - 1.37131i) q^{41} +(-3.70532 - 2.37259i) q^{42} +(3.26299 + 1.88389i) q^{43} +(-0.412157 + 0.412157i) q^{44} +(10.9966 + 4.05999i) q^{45} +(-0.453689 - 1.69319i) q^{46} +(-5.51114 - 5.51114i) q^{47} +(1.73022 + 0.0795432i) q^{48} +(0.473846 - 0.273575i) q^{49} +(2.65745 - 9.91775i) q^{50} +(-0.871071 - 1.68278i) q^{51} +(-2.74513 + 2.33758i) q^{52} +3.04435i q^{53} +(-4.78674 - 2.02166i) q^{54} +(-1.13876 - 1.97239i) q^{55} +(1.27012 - 2.19992i) q^{56} +(0.720857 - 2.26801i) q^{57} +(5.72147 - 1.53306i) q^{58} +(8.19009 - 2.19453i) q^{59} +(-2.05000 + 6.44983i) q^{60} +(-4.67266 + 8.09329i) q^{61} +(4.59607 + 7.96063i) q^{62} +(-5.86037 + 4.87153i) q^{63} +1.00000i q^{64} +(-6.04642 - 12.7248i) q^{65} +(0.464102 + 0.896575i) q^{66} +(1.70856 - 6.37644i) q^{67} +(0.947432 - 0.547000i) q^{68} +(-3.03294 - 0.139433i) q^{69} +(7.01853 + 7.01853i) q^{70} +(0.220122 + 0.821505i) q^{71} +(1.03906 - 2.81431i) q^{72} +(-5.18078 + 5.18078i) q^{73} +(-2.68024 - 1.54744i) q^{74} +(-14.9768 - 9.58993i) q^{75} +(1.32717 + 0.355613i) q^{76} +1.48065 q^{77} +(2.41837 + 5.75773i) q^{78} -13.1089 q^{79} +(-3.77424 - 1.01130i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(-4.58850 - 2.64917i) q^{82} +(-5.15394 + 5.15394i) q^{83} +(-2.96499 - 3.25075i) q^{84} +(1.10637 + 4.12902i) q^{85} +(2.66422 + 2.66422i) q^{86} +(0.471158 - 10.2486i) q^{87} +(-0.504787 + 0.291439i) q^{88} +(-2.50797 + 9.35988i) q^{89} +(9.57108 + 6.76778i) q^{90} +(9.12969 + 0.732051i) q^{91} -1.75292i q^{92} +(15.5518 - 3.41012i) q^{93} +(-3.89697 - 6.74974i) q^{94} +(-2.68434 + 4.64941i) q^{95} +(1.65068 + 0.524648i) q^{96} +(-0.592450 + 0.158747i) q^{97} +(0.528506 - 0.141613i) q^{98} +(1.72345 - 0.295697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Introduction

L-functions

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