LMFDB - Embedded newform 78.2.k.a.71.1

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} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \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			71.1
Root			$0.500000 + 1.74530i$ of defining polynomial
Character	$\chi$	$=$	78.71
Dual form			78.2.k.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.76293 + 2.76293i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-0.657464 + 2.45369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.76293 + 2.76293i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-0.657464 + 2.45369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) 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} +(-4.56072 - 5.00027i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.547000 - 0.947432i) q^{17} +(-2.95680 + 0.507306i) q^{18} +(1.32717 + 0.355613i) q^{19} +(3.77424 + 1.01130i) q^{20} +(1.33273 - 4.19313i) q^{21} +(-0.291439 - 0.504787i) q^{22} +(0.876460 - 1.51807i) q^{23} +(1.27970 - 1.16721i) 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} +(5.69948 + 3.64948i) q^{30} +(6.49983 - 6.49983i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.216237 - 0.986144i) q^{33} +(0.773575 + 0.773575i) q^{34} +(-8.59591 + 4.96285i) q^{35} +(2.72474 - 1.25529i) q^{36} +(-2.98942 + 0.801012i) q^{37} -1.37398 q^{38} +(1.82088 + 5.97364i) q^{39} -3.90738 q^{40} +(5.11781 - 1.37131i) q^{41} +(-0.202059 + 4.39519i) q^{42} +(3.26299 - 1.88389i) q^{43} +(0.412157 + 0.412157i) q^{44} +(7.49333 + 9.01435i) q^{45} +(-0.453689 + 1.69319i) q^{46} +(5.51114 - 5.51114i) q^{47} +(-0.933998 + 1.45865i) 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} +(5.15627 - 0.642559i) q^{54} +(-1.13876 + 1.97239i) q^{55} +(-1.27012 - 2.19992i) q^{56} +(-2.26801 - 0.720857i) q^{57} +(5.72147 + 1.53306i) q^{58} +(-8.19009 - 2.19453i) q^{59} +(-6.44983 - 2.05000i) q^{60} +(-4.67266 - 8.09329i) q^{61} +(-4.59607 + 7.96063i) q^{62} +(-2.63946 + 7.14905i) 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} +(-1.63722 + 2.55689i) q^{69} +(7.01853 - 7.01853i) q^{70} +(-0.220122 + 0.821505i) q^{71} +(-2.30701 + 1.91774i) q^{72} +(-5.18078 - 5.18078i) q^{73} +(2.68024 - 1.54744i) q^{74} +(0.816719 - 17.7653i) q^{75} +(1.32717 - 0.355613i) q^{76} -1.48065 q^{77} +(-3.30492 - 5.29882i) q^{78} -13.1089 q^{79} +(3.77424 - 1.01130i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-4.58850 + 2.64917i) q^{82} +(5.15394 + 5.15394i) q^{83} +(-0.942385 - 4.29773i) q^{84} +(1.10637 - 4.12902i) q^{85} +(-2.66422 + 2.66422i) q^{86} +(8.63999 + 5.53235i) 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} +(-11.7632 + 10.7291i) q^{93} +(-3.89697 + 6.74974i) q^{94} +(2.68434 + 4.64941i) q^{95} +(0.524648 - 1.65068i) q^{96} +(-0.592450 - 0.158747i) q^{97} +(-0.528506 - 0.141613i) q^{98} +(0.295697 + 1.72345i) 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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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
$3$	−1.73022	−	0.0795432i	−0.998945	−	0.0459243i
$3$	−1.73022	−	0.0795432i	−0.998945	−	0.0459243i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.76293	+	2.76293i	1.23562	+	1.23562i	0.961773	+	0.273849i	$0.0882968\pi$
$5$	2.76293	+	2.76293i	1.23562	+	1.23562i	0.273849	+	0.961773i	$0.411703\pi$
$6$	1.69185	−	0.370982i	0.690697	−	0.151453i
$7$	−0.657464	+	2.45369i	−0.248498	+	0.927407i	0.723095	+	0.690749i	$0.242719\pi$
$7$	−0.657464	+	2.45369i	−0.248498	+	0.927407i	−0.971593	+	0.236659i	$0.923948\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.98735	+	0.275255i	0.995782	+	0.0917517i
$10$	−3.38389	−	1.95369i	−1.07008	−	0.617811i
$11$	0.150860	+	0.563016i	0.0454859	+	0.169756i	0.984932	−	0.172940i	$-0.0553267\pi$
$11$	0.150860	+	0.563016i	0.0454859	+	0.169756i	−0.939446	+	0.342696i	$0.888660\pi$
$12$	−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
$15$	−4.56072	−	5.00027i	−1.17757	−	1.29106i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.547000	−	0.947432i	−0.132667	−	0.229786i	0.792037	−	0.610473i	$-0.209021\pi$
$17$	−0.547000	−	0.947432i	−0.132667	−	0.229786i	−0.924704	+	0.380687i	$0.875687\pi$
$18$	−2.95680	+	0.507306i	−0.696923	+	0.119573i
$19$	1.32717	+	0.355613i	0.304473	+	0.0815832i	0.407821	−	0.913062i	$-0.366289\pi$
$19$	1.32717	+	0.355613i	0.304473	+	0.0815832i	−0.103348	+	0.994645i	$0.532956\pi$
$20$	3.77424	+	1.01130i	0.843945	+	0.226134i
$21$	1.33273	−	4.19313i	0.290826	−	0.915017i
$22$	−0.291439	−	0.504787i	−0.0621349	−	0.107621i
$23$	0.876460	−	1.51807i	0.182755	−	0.316540i	−0.760063	−	0.649849i	$-0.774832\pi$
$23$	0.876460	−	1.51807i	0.182755	−	0.316540i	0.942818	+	0.333309i	$0.108165\pi$
$24$	1.27970	−	1.16721i	0.261217	−	0.238255i
$25$			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	$-0.518692\pi$
$29$	−5.12973	−	2.96165i	−0.952566	−	0.549965i	−0.893877	+	0.448312i	$0.852025\pi$
$30$	5.69948	+	3.64948i	1.04058	+	0.666302i
$31$	6.49983	−	6.49983i	1.16740	−	1.16740i	0.184588	−	0.982816i	$-0.440905\pi$
$31$	6.49983	−	6.49983i	1.16740	−	1.16740i	0.982816	−	0.184588i	$-0.0590950\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.216237	−	0.986144i	−0.0376420	−	0.171666i
$34$	0.773575	+	0.773575i	0.132667	+	0.132667i
$35$	−8.59591	+	4.96285i	−1.45297	+	0.838875i
$36$	2.72474	−	1.25529i	0.454124	−	0.209216i
$37$	−2.98942	+	0.801012i	−0.491457	+	0.131686i	−0.496032	−	0.868304i	$-0.665210\pi$
$37$	−2.98942	+	0.801012i	−0.491457	+	0.131686i	0.00457534	+	0.999990i	$0.498544\pi$
$38$	−1.37398			−0.222890
$39$	1.82088	+	5.97364i	0.291573	+	0.956548i
$40$	−3.90738			−0.617811
$41$	5.11781	−	1.37131i	0.799268	−	0.214163i	0.164005	−	0.986459i	$-0.447559\pi$
$41$	5.11781	−	1.37131i	0.799268	−	0.214163i	0.635262	+	0.772296i	$0.280892\pi$
$42$	−0.202059	+	4.39519i	−0.0311784	+	0.678193i
$43$	3.26299	−	1.88389i	0.497602	−	0.287290i	−0.230121	−	0.973162i	$-0.573912\pi$
$43$	3.26299	−	1.88389i	0.497602	−	0.287290i	0.727723	+	0.685872i	$0.240579\pi$
$44$	0.412157	+	0.412157i	0.0621349	+	0.0621349i
$45$	7.49333	+	9.01435i	1.11704	+	1.34378i
$46$	−0.453689	+	1.69319i	−0.0668928	+	0.249647i
$47$	5.51114	−	5.51114i	0.803883	−	0.803883i	−0.179817	−	0.983700i	$-0.557551\pi$
$47$	5.51114	−	5.51114i	0.803883	−	0.803883i	0.983700	+	0.179817i	$0.0575506\pi$
$48$	−0.933998	+	1.45865i	−0.134811	+	0.210537i
$49$	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	$0.932951\pi$
$54$	5.15627	−	0.642559i	0.701679	−	0.0874413i
$55$	−1.13876	+	1.97239i	−0.153551	+	0.265957i
$56$	−1.27012	−	2.19992i	−0.169727	−	0.293976i
$57$	−2.26801	−	0.720857i	−0.300405	−	0.0954799i
$58$	5.72147	+	1.53306i	0.751265	+	0.201301i
$59$	−8.19009	−	2.19453i	−1.06626	−	0.285703i	−0.317304	−	0.948324i	$-0.602777\pi$
$59$	−8.19009	−	2.19453i	−1.06626	−	0.285703i	−0.748955	+	0.662621i	$0.769444\pi$
$60$	−6.44983	−	2.05000i	−0.832670	−	0.264653i
$61$	−4.67266	−	8.09329i	−0.598273	−	1.03624i	−0.993076	−	0.117474i	$-0.962520\pi$
$61$	−4.67266	−	8.09329i	−0.598273	−	1.03624i	0.394803	−	0.918766i	$-0.370813\pi$
$62$	−4.59607	+	7.96063i	−0.583702	+	1.01100i
$63$	−2.63946	+	7.14905i	−0.332541	+	0.900695i
$64$		−	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	0.988279	+	0.152659i	$0.0487838\pi$
$67$	1.70856	+	6.37644i	0.208734	+	0.779006i	−0.779545	+	0.626346i	$0.784550\pi$
$68$	−0.947432	−	0.547000i	−0.114893	−	0.0663335i
$69$	−1.63722	+	2.55689i	−0.197099	+	0.307813i
$70$	7.01853	−	7.01853i	0.838875	−	0.838875i
$71$	−0.220122	+	0.821505i	−0.0261236	+	0.0974947i	−0.977757	−	0.209742i	$-0.932738\pi$
$71$	−0.220122	+	0.821505i	−0.0261236	+	0.0974947i	0.951633	+	0.307237i	$0.0994043\pi$
$72$	−2.30701	+	1.91774i	−0.271883	+	0.226008i
$73$	−5.18078	−	5.18078i	−0.606365	−	0.606365i	0.335629	−	0.941994i	$-0.391051\pi$
$73$	−5.18078	−	5.18078i	−0.606365	−	0.606365i	−0.941994	+	0.335629i	$0.891051\pi$
$74$	2.68024	−	1.54744i	0.311571	−	0.179886i
$75$	0.816719	−	17.7653i	0.0943066	−	2.05135i
$76$	1.32717	−	0.355613i	0.152236	−	0.0407916i
$77$	−1.48065			−0.168736
$78$	−3.30492	−	5.29882i	−0.374209	−	0.599973i
$79$	−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
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$	−4.58850	+	2.64917i	−0.506715	+	0.292552i
$83$	5.15394	+	5.15394i	0.565719	+	0.565719i	0.930926	−	0.365208i	$-0.119002\pi$
$83$	5.15394	+	5.15394i	0.565719	+	0.565719i	−0.365208	+	0.930926i	$0.619002\pi$
$84$	−0.942385	−	4.29773i	−0.102823	−	0.468920i
$85$	1.10637	−	4.12902i	0.120002	−	0.447855i
$86$	−2.66422	+	2.66422i	−0.287290	+	0.287290i
$87$	8.63999	+	5.53235i	0.926305	+	0.593130i
$88$	−0.504787	−	0.291439i	−0.0538104	−	0.0310675i
$89$	2.50797	+	9.35988i	0.265844	+	0.992145i	0.961731	+	0.273994i	$0.0883448\pi$
$89$	2.50797	+	9.35988i	0.265844	+	0.992145i	−0.695887	+	0.718151i	$0.744989\pi$
$90$	−9.57108	−	6.76778i	−1.00888	−	0.713386i
$91$	9.12969	−	0.732051i	0.957051	−	0.0767398i
$92$		−	1.75292i		−	0.182755i
$93$	−11.7632	+	10.7291i	−1.21978	+	1.11256i
$94$	−3.89697	+	6.74974i	−0.401941	+	0.696183i
$95$	2.68434	+	4.64941i	0.275407	+	0.477019i
$96$	0.524648	−	1.65068i	0.0535466	−	0.168472i
$97$	−0.592450	−	0.158747i	−0.0601542	−	0.0161183i	0.228616	−	0.973517i	$-0.426580\pi$
$97$	−0.592450	−	0.158747i	−0.0601542	−	0.0161183i	−0.288771	+	0.957398i	$0.593247\pi$
$98$	−0.528506	−	0.141613i	−0.0533872	−	0.0143051i
$99$	0.295697	+	1.72345i	0.0297187	+	0.173213i
$100$	5.13380	+	8.89201i	0.513380	+	0.889201i
$101$	−2.91789	+	5.05394i	−0.290341	+	0.502886i	−0.973890	−	0.227019i	$-0.927102\pi$
$101$	−2.91789	+	5.05394i	−0.290341	+	0.502886i	0.683549	+	0.729904i	$0.260435\pi$
$102$	−1.27692	−	1.39999i	−0.126434	−	0.138620i
$103$			2.07313i			0.204272i	0.994770	+	0.102136i	$0.0325677\pi$
$103$			2.07313i			0.204272i	−0.994770	+	0.102136i	$0.967432\pi$
$104$	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	$-0.386798\pi$
$107$	−2.99520	−	1.72928i	−0.289557	−	0.167176i	−0.637742	+	0.770250i	$0.720131\pi$
$108$	−4.81427	+	1.95521i	−0.463253	+	0.188140i
$109$	−10.9901	+	10.9901i	−1.05266	+	1.05266i	−0.0541251	+	0.998534i	$0.517237\pi$
$109$	−10.9901	+	10.9901i	−1.05266	+	1.05266i	−0.998534	+	0.0541251i	$0.982763\pi$
$110$	0.589466	−	2.19992i	0.0562034	−	0.209754i
$111$	5.23607	−	1.14814i	0.496986	−	0.108977i
$112$	1.79623	+	1.79623i	0.169727	+	0.169727i
$113$	9.43719	−	5.44856i	0.887776	−	0.512558i	0.0145614	−	0.999894i	$-0.495365\pi$
$113$	9.43719	−	5.44856i	0.887776	−	0.512558i	0.873214	+	0.487336i	$0.162031\pi$
$114$	2.37730	+	0.109291i	0.222654	+	0.0102360i
$115$	6.61594	−	1.77274i	0.616940	−	0.165308i
$116$	−5.92330			−0.549965
$117$	−2.67536	−	10.4806i	−0.247337	−	0.968930i
$118$	8.47900			0.780556
$119$	2.68434	−	0.719266i	0.246073	−	0.0659350i
$120$	6.76064	+	0.310806i	0.617159	+	0.0283725i
$121$	9.23205	−	5.33013i	0.839277	−	0.484557i
$122$	6.60814	+	6.60814i	0.598273	+	0.598273i
$123$	−8.96403	+	1.96559i	−0.808260	+	0.177231i
$124$	2.37910	−	8.87893i	0.213650	−	0.797352i
$125$	−14.5541	+	14.5541i	−1.30175	+	1.30175i
$126$	0.699216	−	7.58859i	0.0622911	−	0.676046i
$127$	8.06551	+	4.65662i	0.715698	+	0.413209i	0.813167	−	0.582030i	$-0.197741\pi$
$127$	8.06551	+	4.65662i	0.715698	+	0.413209i	−0.0974690	+	0.995239i	$0.531075\pi$
$128$	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	$0.987234\pi$
$132$	−0.680339	−	0.745907i	−0.0592159	−	0.0649229i
$133$	−1.74513	+	3.02265i	−0.151322	+	0.262097i
$134$	−3.30069	−	5.71696i	−0.285136	−	0.493870i
$135$	−12.2481	−	16.1929i	−1.05415	−	1.39366i
$136$	1.05672	+	0.283148i	0.0906133	+	0.0242797i
$137$	−8.32493	−	2.23066i	−0.711247	−	0.190578i	−0.114984	−	0.993367i	$-0.536682\pi$
$137$	−8.32493	−	2.23066i	−0.711247	−	0.190578i	−0.596263	+	0.802789i	$0.703348\pi$
$138$	0.919666	−	2.89351i	0.0782871	−	0.246312i
$139$	−1.65662	−	2.86936i	−0.140513	−	0.243376i	0.787177	−	0.616727i	$-0.211542\pi$
$139$	−1.65662	−	2.86936i	−0.140513	−	0.243376i	−0.927690	+	0.373352i	$0.878209\pi$
$140$	−4.96285	+	8.59591i	−0.419438	+	0.726487i
$141$	−9.97388	+	9.09713i	−0.839952	+	0.766117i
$142$		−	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
$147$	−0.798098	−	0.511037i	−0.0658260	−	0.0421496i
$148$	−2.18840	+	2.18840i	−0.179886	+	0.179886i
$149$	−2.03304	+	7.58742i	−0.166553	+	0.621585i	0.831284	+	0.555848i	$0.187606\pi$
$149$	−2.03304	+	7.58742i	−0.166553	+	0.621585i	−0.997837	+	0.0657369i	$0.979060\pi$
$150$	3.80910	+	17.3713i	0.311011	+	1.41836i
$151$	10.2600	+	10.2600i	0.834946	+	0.834946i	0.988189	−	0.153243i	$-0.0489717\pi$
$151$	10.2600	+	10.2600i	0.834946	+	0.834946i	−0.153243	+	0.988189i	$0.548972\pi$
$152$	−1.18990	+	0.686992i	−0.0965140	+	0.0557224i
$153$	−1.37329	−	2.98087i	−0.111024	−	0.240989i
$154$	1.43020	−	0.383221i	0.115249	−	0.0308808i
$155$	35.9172			2.88494
$156$	4.56375	+	4.26289i	0.365392	+	0.341304i
$157$	−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
$159$	0.242157	−	5.26740i	0.0192043	−	0.417732i
$160$	−3.38389	+	1.95369i	−0.267520	+	0.154453i
$161$	3.14864	+	3.14864i	0.248148	+	0.248148i
$162$	−8.97261	+	0.701625i	−0.704955	+	0.0551249i
$163$	−0.407550	+	1.52100i	−0.0319217	+	0.119134i	−0.980048	−	0.198760i	$-0.936309\pi$
$163$	−0.407550	+	1.52100i	−0.0319217	+	0.119134i	0.948127	+	0.317893i	$0.102975\pi$
$164$	3.74650	−	3.74650i	0.292552	−	0.292552i
$165$	2.12720	−	3.32210i	0.165602	−	0.258625i
$166$	−6.31226	−	3.64439i	−0.489927	−	0.282859i
$167$	−6.32673	−	23.6117i	−0.489577	−	1.82713i	−0.558499	−	0.829505i	$-0.688623\pi$
$167$	−6.32673	−	23.6117i	−0.489577	−	1.82713i	0.0689223	−	0.997622i	$-0.478044\pi$
$168$	2.02261	+	3.90738i	0.156048	+	0.301461i
$169$	−10.0788	+	8.21088i	−0.775289	+	0.631606i
$170$			4.27467i			0.327852i
$171$	3.86682	+	1.42765i	0.295703	+	0.109175i
$172$	1.88389	−	3.26299i	0.143645	−	0.248801i
$173$	−10.3837	−	17.9850i	−0.789456	−	1.36738i	−0.926301	−	0.376785i	$-0.877029\pi$
$173$	−10.3837	−	17.9850i	−0.789456	−	1.36738i	0.136845	−	0.990593i	$-0.456304\pi$
$174$	−9.77747	−	3.10764i	−0.741228	−	0.235590i
$175$	−25.1935	−	6.75058i	−1.90445	−	0.510296i
$176$	0.563016	+	0.150860i	0.0424389	+	0.0113715i
$177$	13.9961	+	4.44849i	1.05201	+	0.334369i
$178$	−4.84503	−	8.39184i	−0.363150	−	0.628995i
$179$	−7.00018	+	12.1247i	−0.523218	+	0.906241i	0.476416	+	0.879220i	$0.341935\pi$
$179$	−7.00018	+	12.1247i	−0.523218	+	0.906241i	−0.999635	+	0.0270211i	$0.991398\pi$
$180$	10.9966	+	4.05999i	0.819637	+	0.302614i
$181$		−	25.5405i		−	1.89841i	−0.314653	−	0.949207i	$-0.601888\pi$
$181$		−	25.5405i		−	1.89841i	0.314653	−	0.949207i	$-0.398112\pi$
$182$	−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
$186$	8.58545	−	13.4081i	0.629516	−	0.983129i
$187$	0.450899	−	0.450899i	0.0329730	−	0.0329730i
$188$	2.01722	−	7.52836i	0.147121	−	0.549062i
$189$	5.13552	−	12.1595i	0.373554	−	0.884473i
$190$	−3.79623	−	3.79623i	−0.275407	−	0.275407i
$191$	−20.4783	+	11.8231i	−1.48176	+	0.855493i	−0.999786	−	0.0206939i	$-0.993412\pi$
$191$	−20.4783	+	11.8231i	−1.48176	+	0.855493i	−0.481972	+	0.876187i	$0.660079\pi$
$192$	−0.0795432	+	1.73022i	−0.00574054	+	0.124868i
$193$	10.2375	−	2.74313i	0.736912	−	0.197455i	0.129207	−	0.991618i	$-0.458757\pi$
$193$	10.2375	−	2.74313i	0.736912	−	0.197455i	0.607705	+	0.794163i	$0.292090\pi$
$194$	0.613350			0.0440360
$195$	−11.4738	+	21.5357i	−0.821658	+	1.54221i
$196$	0.547150			0.0390821
$197$	−3.34959	+	0.897520i	−0.238649	+	0.0639457i	−0.376161	−	0.926554i	$-0.622756\pi$
$197$	−3.34959	+	0.897520i	−0.238649	+	0.0639457i	0.137512	+	0.990500i	$0.456089\pi$
$198$	−0.731683	−	1.58819i	−0.0519984	−	0.112868i
$199$	−2.67432	+	1.54402i	−0.189577	+	0.109453i	−0.591785	−	0.806096i	$-0.701576\pi$
$199$	−2.67432	+	1.54402i	−0.189577	+	0.109453i	0.402207	+	0.915549i	$0.368243\pi$
$200$	−7.26029	−	7.26029i	−0.513380	−	0.513380i
$201$	−2.44899	−	11.1686i	−0.172738	−	0.787770i
$202$	1.51041	−	5.63694i	0.106272	−	0.396613i
$203$	10.6396	−	10.6396i	0.746752	−	0.746752i
$204$	1.59576	+	1.02179i	0.111725	+	0.0715399i
$205$	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
$210$	−12.7019	+	11.5854i	−0.876515	+	0.799465i
$211$	2.47900	−	4.29376i	0.170662	−	0.295595i	−0.767990	−	0.640462i	$-0.778743\pi$
$211$	2.47900	−	4.29376i	0.170662	−	0.295595i	0.938651	+	0.344867i	$0.112076\pi$
$212$	1.52217	+	2.63648i	0.104543	+	0.181074i
$213$	0.446205	−	1.40388i	0.0305734	−	0.0961921i
$214$	3.34071	+	0.895141i	0.228366	+	0.0611906i
$215$	14.2205	+	3.81037i	0.969829	+	0.259865i
$216$	4.14418	−	3.13461i	0.281976	−	0.213283i
$217$	11.6752	+	20.2220i	0.792561	+	1.37276i
$218$	7.77116	−	13.4601i	0.526330	−	0.911630i
$219$	8.55181	+	9.37601i	0.577878	+	0.633572i
$220$			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	0.908755	+	0.417330i	$0.137034\pi$
$223$	4.93415	+	18.4145i	0.330415	+	1.23313i	−0.578340	+	0.815796i	$0.696299\pi$
$224$	−2.19992	−	1.27012i	−0.146988	−	0.0848637i
$225$	−2.82621	+	30.6729i	−0.188414	+	2.04486i
$226$	−7.70543	+	7.70543i	−0.512558	+	0.512558i
$227$	1.38733	−	5.17758i	0.0920803	−	0.343648i	−0.904480	−	0.426515i	$-0.859741\pi$
$227$	1.38733	−	5.17758i	0.0920803	−	0.343648i	0.996561	+	0.0828671i	$0.0264077\pi$
$228$	−2.32458	+	0.509723i	−0.153949	+	0.0337572i
$229$	2.78436	+	2.78436i	0.183996	+	0.183996i	0.793094	−	0.609099i	$-0.208469\pi$
$229$	2.78436	+	2.78436i	0.183996	+	0.183996i	−0.609099	+	0.793094i	$0.708469\pi$
$230$	−5.93169	+	3.42466i	−0.391124	+	0.225816i
$231$	2.56186	+	0.117776i	0.168558	+	0.00774908i
$232$	5.72147	−	1.53306i	0.375633	−	0.100650i
$233$	3.83663			0.251346			0.125673	−	0.992072i	$-0.459891\pi$
$233$	3.83663			0.251346			0.125673	+	0.992072i	$0.459891\pi$
$234$	5.29677	+	9.43102i	0.346261	+	0.616525i
$235$	30.4538			1.98659
$236$	−8.19009	+	2.19453i	−0.533129	+	0.142852i
$237$	22.6813	+	1.04272i	1.47331	+	0.0677320i
$238$	−2.40671	+	1.38951i	−0.156004	+	0.0900689i
$239$	0.751524	+	0.751524i	0.0486121	+	0.0486121i	0.730995	−	0.682383i	$-0.239056\pi$
$239$	0.751524	+	0.751524i	0.0486121	+	0.0486121i	−0.682383	+	0.730995i	$0.739056\pi$
$240$	−6.61072	+	1.44957i	−0.426720	+	0.0935691i
$241$	−7.23751	+	27.0107i	−0.466209	+	1.73991i	0.186642	+	0.982428i	$0.440240\pi$
$241$	−7.23751	+	27.0107i	−0.466209	+	1.73991i	−0.652851	+	0.757487i	$0.726427\pi$
$242$	−7.53794	+	7.53794i	−0.484557	+	0.484557i
$243$	−15.1790	−	3.54930i	−0.973734	−	0.227688i
$244$	−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
$249$	−8.50751	−	9.32743i	−0.539141	−	0.591102i
$250$	10.2913	−	17.8250i	0.650877	−	1.12735i
$251$	−7.56320	−	13.0998i	−0.477385	−	0.826855i	0.522279	−	0.852775i	$-0.325082\pi$
$251$	−7.56320	−	13.0998i	−0.477385	−	0.826855i	−0.999664	+	0.0259196i	$0.991749\pi$
$252$	1.28868	+	7.51099i	0.0811793	+	0.473148i
$253$	0.986923	+	0.264445i	0.0620473	+	0.0166255i
$254$	−8.99591	−	2.41045i	−0.564453	−	0.151245i
$255$	−2.24270	+	7.05612i	−0.140443	+	0.441871i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.178601	+	0.309345i	−0.0111408	+	0.0192964i	−0.871542	−	0.490321i	$-0.836880\pi$
$257$	−0.178601	+	0.309345i	−0.0111408	+	0.0192964i	0.860401	+	0.509617i	$0.170213\pi$
$258$	4.82162	−	4.39778i	0.300181	−	0.273794i
$259$		−	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	$-0.312240\pi$
$263$	1.86002	+	1.07389i	0.114694	+	0.0662186i	−0.441556	+	0.897234i	$0.645573\pi$
$264$	0.850212	+	0.544406i	0.0523269	+	0.0335059i
$265$	−8.41133	+	8.41133i	−0.516704	+	0.516704i
$266$	0.903345	−	3.37133i	0.0553876	−	0.206709i
$267$	−3.59484	−	16.3942i	−0.220000	−	1.00331i
$268$	4.66788	+	4.66788i	0.285136	+	0.285136i
$269$	21.2380	−	12.2618i	1.29490	−	0.747612i	0.315384	−	0.948964i	$-0.397867\pi$
$269$	21.2380	−	12.2618i	1.29490	−	0.747612i	0.979519	+	0.201352i	$0.0645335\pi$
$270$	16.0218	+	12.4711i	0.975055	+	0.758966i
$271$	−21.1790	+	5.67488i	−1.28653	+	0.344725i	−0.836341	−	0.548209i	$-0.815310\pi$
$271$	−21.1790	+	5.67488i	−1.28653	+	0.344725i	−0.450189	+	0.892934i	$0.648643\pi$
$272$	−1.09400			−0.0663335
$273$	−15.8546	+	0.540407i	−0.959566	+	0.0327069i
$274$	8.61860			0.520669
$275$	−5.78083	+	1.54897i	−0.348597	+	0.0934063i
$276$	−0.139433	+	3.03294i	−0.00839288	+	0.182562i
$277$	−16.1517	+	9.32517i	−0.970460	+	0.560295i	−0.899376	−	0.437175i	$-0.855979\pi$
$277$	−16.1517	+	9.32517i	−0.970460	+	0.560295i	−0.0710833	+	0.997470i	$0.522646\pi$
$278$	2.34282	+	2.34282i	0.140513	+	0.140513i
$279$	21.2063	−	17.6281i	1.26959	−	1.05537i
$280$	2.56896	−	9.58749i	0.153525	−	0.572962i
$281$	−11.2782	+	11.2782i	−0.672801	+	0.672801i	−0.958361	−	0.285560i	$-0.907820\pi$
$281$	−11.2782	+	11.2782i	−0.672801	+	0.672801i	0.285560	+	0.958361i	$0.407820\pi$
$282$	7.27952	−	11.3686i	0.433489	−	0.676989i
$283$	4.08342	+	2.35756i	0.242734	+	0.140143i	0.616433	−	0.787408i	$-0.288577\pi$
$283$	4.08342	+	2.35756i	0.242734	+	0.140143i	−0.373699	+	0.927550i	$0.621911\pi$
$284$	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
$288$	−1.03906	+	2.81431i	−0.0612271	+	0.165835i
$289$	7.90158	−	13.6859i	0.464799	−	0.805055i
$290$	11.5723	+	20.0438i	0.679548	+	1.17701i
$291$	1.01244	+	0.321793i	0.0593505	+	0.0188638i
$292$	−7.07708	−	1.89630i	−0.414155	−	0.110972i
$293$	20.6276	+	5.52716i	1.20508	+	0.322900i	0.804830	−	0.593506i	$-0.202257\pi$
$293$	20.6276	+	5.52716i	1.20508	+	0.322900i	0.400250	+	0.916406i	$0.368923\pi$
$294$	0.903170	+	0.287061i	0.0526739	+	0.0167417i
$295$	−16.5653	−	28.6920i	−0.964471	−	1.67051i
$296$	1.54744	−	2.68024i	0.0899429	−	0.155786i
$297$	−0.374533	−	3.00547i	−0.0217326	−	0.174395i
$298$		−	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
$303$	5.45061	−	8.51234i	0.313130	−	0.489021i
$304$	0.971553	−	0.971553i	0.0557224	−	0.0557224i
$305$	9.45097	−	35.2715i	0.541161	−	2.01964i
$306$	2.09801	+	2.52387i	0.119935	+	0.144280i
$307$	−16.2259	−	16.2259i	−0.926063	−	0.926063i	0.0713857	−	0.997449i	$-0.477258\pi$
$307$	−16.2259	−	16.2259i	−0.926063	−	0.926063i	−0.997449	+	0.0713857i	$0.977258\pi$
$308$	−1.28228	+	0.740326i	−0.0730648	+	0.0421840i
$309$	0.164904	−	3.58698i	0.00938104	−	0.204056i
$310$	−34.6933	+	9.29605i	−1.97045	+	0.527980i
$311$	−32.8464			−1.86255			−0.931275	−	0.364317i	$-0.881303\pi$
$311$	−32.8464			−1.86255			−0.931275	+	0.364317i	$0.881303\pi$
$312$	−5.51156	−	2.93645i	−0.312030	−	0.166244i
$313$	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
$315$	−27.0450	+	12.4597i	−1.52381	+	0.702024i
$316$	−11.3526	+	6.55443i	−0.638634	+	0.368716i
$317$	17.5500	+	17.5500i	0.985704	+	0.985704i	0.999899	−	0.0141948i	$-0.00451851\pi$
$317$	17.5500	+	17.5500i	0.985704	+	0.985704i	−0.0141948	+	0.999899i	$0.504519\pi$
$318$	1.12940	+	5.15059i	0.0633334	+	0.288831i
$319$	0.893587	−	3.33491i	0.0500313	−	0.186719i
$320$	2.76293	−	2.76293i	0.154453	−	0.154453i
$321$	5.04481	+	3.23029i	0.281574	+	0.180297i
$322$	−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
$327$	19.8895	−	18.1411i	1.09989	−	1.00321i
$328$	−2.64917	+	4.58850i	−0.146276	+	0.253358i
$329$	9.89925	+	17.1460i	0.545763	+	0.945290i
$330$	−1.19490	+	3.75946i	−0.0657769	+	0.206952i
$331$	4.46639	+	1.19677i	0.245495	+	0.0657803i	0.379468	−	0.925205i	$-0.376107\pi$
$331$	4.46639	+	1.19677i	0.245495	+	0.0657803i	−0.133973	+	0.990985i	$0.542774\pi$
$332$	7.04041	+	1.88647i	0.386393	+	0.103534i
$333$	−9.15090	+	1.57005i	−0.501466	+	0.0860380i
$334$	12.2223	+	21.1697i	0.668775	+	1.15835i
$335$	−12.8970	+	22.3383i	−0.704640	+	1.22047i
$336$	−2.96499	−	3.25075i	−0.161754	−	0.177343i
$337$		−	7.78436i		−	0.424041i	−0.977265	−	0.212021i	$-0.931996\pi$
$337$		−	7.78436i		−	0.424041i	0.977265	−	0.212021i	$-0.0680044\pi$
$338$	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
$342$	−4.10456	−	0.378196i	−0.221949	−	0.0204505i
$343$	−13.5564	+	13.5564i	−0.731976	+	0.731976i
$344$	−0.975173	+	3.63939i	−0.0525778	+	0.196223i
$345$	−11.5881	+	2.54098i	−0.623880	+	0.136802i
$346$	14.6847	+	14.6847i	0.789456	+	0.789456i
$347$	−9.39077	+	5.42177i	−0.504123	+	0.291056i	−0.730415	−	0.683004i	$-0.760673\pi$
$347$	−9.39077	+	5.42177i	−0.504123	+	0.291056i	0.226292	+	0.974060i	$0.427340\pi$
$348$	10.2486	+	0.471158i	0.549384	+	0.0252567i
$349$	14.8487	−	3.97869i	0.794830	−	0.212974i	0.161517	−	0.986870i	$-0.448361\pi$
$349$	14.8487	−	3.97869i	0.794830	−	0.212974i	0.633313	+	0.773896i	$0.281695\pi$
$350$	26.0822			1.39415
$351$	3.79531	+	18.3465i	0.202579	+	0.979266i
$352$	−0.582877			−0.0310675
$353$	1.80378	−	0.483321i	0.0960054	−	0.0257246i	−0.210497	−	0.977595i	$-0.567508\pi$
$353$	1.80378	−	0.483321i	0.0960054	−	0.0257246i	0.306502	+	0.951870i	$0.400841\pi$
$354$	−14.6706	−	0.674447i	−0.779732	−	0.0358465i
$355$	−2.87795	+	1.66158i	−0.152745	+	0.0881876i
$356$	6.85191	+	6.85191i	0.363150	+	0.363150i
$357$	−4.70171	+	1.03097i	−0.248841	+	0.0545647i
$358$	3.62356	−	13.5233i	0.191511	−	0.714730i
$359$	12.1336	−	12.1336i	0.640387	−	0.640387i	−0.310264	−	0.950650i	$-0.600417\pi$
$359$	12.1336	−	12.1336i	0.640387	−	0.640387i	0.950650	+	0.310264i	$0.100417\pi$
$360$	−11.6727	−	1.07553i	−0.615205	−	0.0566852i
$361$	−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
$366$	−10.9079	−	11.9592i	−0.570167	−	0.625117i
$367$	4.53141	−	7.84863i	0.236538	−	0.409695i	−0.723181	−	0.690659i	$-0.757321\pi$
$367$	4.53141	−	7.84863i	0.236538	−	0.409695i	0.959718	+	0.280964i	$0.0906540\pi$
$368$	−0.876460	−	1.51807i	−0.0456887	−	0.0791351i
$369$	15.6661	−	2.68788i	0.815546	−	0.139926i
$370$	11.6808	+	3.12986i	0.607255	+	0.162713i
$371$	−7.46988	−	2.00155i	−0.387817	−	0.103915i
$372$	−4.82264	+	15.1733i	−0.250042	+	0.786699i
$373$	3.78793	+	6.56090i	0.196132	+	0.339710i	0.947271	−	0.320434i	$-0.103829\pi$
$373$	3.78793	+	6.56090i	0.196132	+	0.339710i	−0.751139	+	0.660144i	$0.770495\pi$
$374$	−0.318834	+	0.552237i	−0.0164865	+	0.0285555i
$375$	26.3394	−	24.0241i	1.36016	−	1.24060i
$376$			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	0.998565	+	0.0535568i	$0.0170558\pi$
$379$	3.12578	+	11.6656i	0.160561	+	0.599221i	−0.838004	+	0.545664i	$0.816278\pi$
$380$	4.64941	+	2.68434i	0.238510	+	0.137704i
$381$	−13.5847	−	8.69856i	−0.695967	−	0.445641i
$382$	16.7205	−	16.7205i	0.855493	−	0.855493i
$383$	−9.53291	+	35.5773i	−0.487109	+	1.81792i	0.0832617	+	0.996528i	$0.473466\pi$
$383$	−9.53291	+	35.5773i	−0.487109	+	1.81792i	−0.570371	+	0.821387i	$0.693200\pi$
$384$	−0.370982	−	1.69185i	−0.0189316	−	0.0863371i
$385$	−4.09094	−	4.09094i	−0.208494	−	0.208494i
$386$	−9.17870	+	5.29932i	−0.467183	+	0.269728i
$387$	10.2662	−	4.72967i	0.521862	−	0.240423i
$388$	−0.592450	+	0.158747i	−0.0300771	+	0.00805914i
$389$	−14.1012			−0.714961			−0.357481	−	0.933921i	$-0.616364\pi$
$389$	−14.1012			−0.714961			−0.357481	+	0.933921i	$0.616364\pi$
$390$	5.50900	−	23.7716i	0.278959	−	1.20372i
$391$	−1.91770			−0.0969820
$392$	−0.528506	+	0.141613i	−0.0266936	+	0.00715253i
$393$	0.0730070	−	1.58805i	0.00368272	−	0.0801064i
$394$	3.00316	−	1.73388i	0.151297	−	0.0873514i
$395$	−36.2189	−	36.2189i	−1.82237	−	1.82237i
$396$	1.11781	+	1.34470i	0.0561719	+	0.0675738i
$397$	−2.03222	+	7.58436i	−0.101994	+	0.380648i	−0.997987	−	0.0634210i	$-0.979799\pi$
$397$	−2.03222	+	7.58436i	−0.101994	+	0.380648i	0.895992	+	0.444069i	$0.146466\pi$
$398$	2.18357	−	2.18357i	0.109453	−	0.109453i
$399$	3.25989	−	5.09105i	0.163199	−	0.254871i
$400$	8.89201	+	5.13380i	0.444600	+	0.256690i
$401$	5.65677	+	21.1113i	0.282485	+	1.05425i	0.950657	+	0.310243i	$0.100410\pi$
$401$	5.65677	+	21.1113i	0.282485	+	1.05425i	−0.668172	+	0.744007i	$0.732923\pi$
$402$	5.25618	+	10.1542i	0.262154	+	0.506444i
$403$	−29.9351	−	14.2243i	−1.49118	−	0.708561i
$404$			5.83579i			0.290341i
$405$	19.9039	+	28.9916i	0.989033	+	1.44060i
$406$	−7.52332	+	13.0308i	−0.373376	+	0.646706i
$407$	−0.901965	−	1.56225i	−0.0447088	−	0.0774378i
$408$	−1.80584	−	0.573965i	−0.0894026	−	0.0284155i
$409$	2.16512	+	0.580141i	0.107058	+	0.0286861i	0.311950	−	0.950098i	$-0.399018\pi$
$409$	2.16512	+	0.580141i	0.107058	+	0.0286861i	−0.204892	+	0.978785i	$0.565684\pi$
$410$	−19.9972	−	5.35824i	−0.987592	−	0.264625i
$411$	14.2266	+	4.52173i	0.701744	+	0.223041i
$412$	1.03657	+	1.79539i	0.0510680	+	0.0884523i
$413$	10.7694	−	18.6531i	0.529926	−	0.917860i
$414$	−1.82139	+	4.93327i	−0.0895163	+	0.242457i
$415$			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	$-0.0298005\pi$
$419$	28.9126	+	16.6927i	1.41247	+	0.815491i	0.416851	+	0.908975i	$0.363134\pi$
$420$	9.27059	−	14.4781i	0.452358	−	0.706458i
$421$	2.25285	−	2.25285i	0.109797	−	0.109797i	−0.650074	−	0.759871i	$-0.725262\pi$
$421$	2.25285	−	2.25285i	0.109797	−	0.109797i	0.759871	+	0.650074i	$0.225262\pi$
$422$	−1.28323	+	4.78907i	−0.0624665	+	0.233128i
$423$	17.9807	−	14.9467i	0.874250	−	0.726734i
$424$	−2.15268	−	2.15268i	−0.104543	−	0.104543i
$425$	9.72786	−	5.61638i	0.471870	−	0.272435i
$426$	−0.0676503	+	1.47153i	−0.00327767	+	0.0712958i
$427$	22.9305	−	6.14422i	1.10969	−	0.297339i
$428$	−3.45856			−0.167176
$429$	−3.08856	+	1.92636i	−0.149117	+	0.0930058i
$430$	−14.7221			−0.709964
$431$	20.9452	−	5.61224i	1.00889	−	0.270332i	0.283727	−	0.958905i	$-0.408429\pi$
$431$	20.9452	−	5.61224i	1.00889	−	0.270332i	0.725167	+	0.688573i	$0.241762\pi$
$432$	−3.19168	+	4.10039i	−0.153560	+	0.197280i
$433$	26.0258	−	15.0260i	1.25072	−	0.722103i	0.279466	−	0.960155i	$-0.409842\pi$
$433$	26.0258	−	15.0260i	1.25072	−	0.722103i	0.971252	+	0.238053i	$0.0765091\pi$
$434$	−16.5112	−	16.5112i	−0.792561	−	0.792561i
$435$	8.58622	+	39.1573i	0.411678	+	1.87745i
$436$	−4.02265	+	15.0127i	−0.192650	+	0.718980i
$437$	1.70306	−	1.70306i	0.0814682	−	0.0814682i
$438$	−10.6871	−	6.84315i	−0.510650	−	0.326979i
$439$	−18.0531	−	10.4229i	−0.861626	−	0.497460i	0.00293019	−	0.999996i	$-0.499067\pi$
$439$	−18.0531	−	10.4229i	−0.861626	−	0.497460i	−0.864557	+	0.502535i	$0.832401\pi$
$440$	−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	$0.899776\pi$
$444$	3.96050	−	3.61236i	0.187957	−	0.171435i
$445$	−18.9314	+	32.7901i	−0.897433	+	1.55440i
$446$	−9.53204	−	16.5100i	−0.451355	−	0.781770i
$447$	4.12114	−	12.9662i	0.194923	−	0.613281i
$448$	2.45369	+	0.657464i	0.115926	+	0.0310623i
$449$	−18.3916	−	4.92801i	−0.867953	−	0.232567i	−0.202750	−	0.979230i	$-0.564988\pi$
$449$	−18.3916	−	4.92801i	−0.867953	−	0.232567i	−0.665202	+	0.746663i	$0.731655\pi$
$450$	−5.20882	−	30.3592i	−0.245546	−	1.43115i
$451$	1.54414	+	2.67453i	0.0727109	+	0.125939i
$452$	5.44856	−	9.43719i	0.256279	−	0.443888i
$453$	−16.9360	−	18.5682i	−0.795720	−	0.872409i
$454$			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	−0.966740	−	0.255761i	$-0.917674\pi$
$457$	−5.50257	−	20.5359i	−0.257399	−	0.960627i	0.709341	−	0.704866i	$-0.248993\pi$
$458$	−3.41013	−	1.96884i	−0.159345	−	0.0919978i
$459$	2.13900	+	5.26681i	0.0998398	+	0.245834i
$460$	4.84320	−	4.84320i	0.225816	−	0.225816i
$461$	0.395195	−	1.47489i	0.0184061	−	0.0686924i	−0.956112	−	0.293002i	$-0.905346\pi$
$461$	0.395195	−	1.47489i	0.0184061	−	0.0686924i	0.974518	+	0.224309i	$0.0720125\pi$
$462$	−2.50505	+	0.549295i	−0.116545	+	0.0255555i
$463$	−21.3272	−	21.3272i	−0.991159	−	0.991159i	0.00880240	−	0.999961i	$-0.497198\pi$
$463$	−21.3272	−	21.3272i	−0.991159	−	0.991159i	−0.999961	+	0.00880240i	$0.997198\pi$
$464$	−5.12973	+	2.96165i	−0.238142	+	0.137491i
$465$	−62.1448	−	2.85697i	−2.88189	−	0.132489i
$466$	−3.70590	+	0.992992i	−0.171672	+	0.0459995i
$467$	11.2935			0.522601			0.261300	−	0.965258i	$-0.415849\pi$
$467$	11.2935			0.522601			0.261300	+	0.965258i	$0.415849\pi$
$468$	−7.55722	−	7.73877i	−0.349332	−	0.357725i
$469$	−16.7691			−0.774326
$470$	−29.4162	+	7.88203i	−1.35687	+	0.363571i
$471$	11.6193	+	0.534170i	0.535387	+	0.0246133i
$472$	7.34303	−	4.23950i	0.337990	−	0.195139i
$473$	1.55291	+	1.55291i	0.0714031	+	0.0714031i
$474$	−22.1783	+	4.86315i	−1.01868	+	0.223372i
$475$	−3.65130	+	13.6268i	−0.167533	+	0.625241i
$476$	1.96507	−	1.96507i	0.0900689	−	0.0900689i
$477$	−0.837972	+	9.09451i	−0.0383681	+	0.416409i
$478$	−0.920426	−	0.531408i	−0.0420993	−	0.0243060i
$479$	−7.52517	−	28.0843i	−0.343834	−	1.28320i	−0.893969	−	0.448129i	$-0.852090\pi$
$479$	−7.52517	−	28.0843i	−0.343834	−	1.28320i	0.550135	−	0.835076i	$-0.314576\pi$
$480$	6.01029	−	3.11115i	0.274331	−	0.142004i
$481$	6.33390	+	9.18688i	0.288801	+	0.418885i
$482$		−	27.9636i		−	1.27371i
$483$	−5.19740	−	5.69830i	−0.236490	−	0.259282i
$484$	5.33013	−	9.23205i	0.242279	−	0.419639i
$485$	−1.19829	−	2.07551i	−0.0544118	−	0.0942440i
$486$	15.5804	−	0.500258i	0.706743	−	0.0226921i
$487$	2.44743	+	0.655786i	0.110903	+	0.0297165i	0.313844	−	0.949475i	$-0.398383\pi$
$487$	2.44743	+	0.655786i	0.110903	+	0.0297165i	−0.202940	+	0.979191i	$0.565050\pi$
$488$	9.02689	+	2.41875i	0.408628	+	0.109492i
$489$	0.826137	−	2.59924i	0.0373592	−	0.117542i
$490$	−1.06896	−	1.85149i	−0.0482907	−	0.0836420i
$491$	18.4575	−	31.9694i	0.832978	−	1.44276i	−0.0626890	−	0.998033i	$-0.519968\pi$
$491$	18.4575	−	31.9694i	0.832978	−	1.44276i	0.895667	−	0.444726i	$-0.146699\pi$
$492$	−6.78029	+	6.18427i	−0.305679	+	0.278808i
$493$			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
$498$	10.6317	+	6.80770i	0.476420	+	0.305060i
$499$	22.3461	−	22.3461i	1.00035	−	1.00035i	0.000347536	−	1.00000i	$-0.499889\pi$
$499$	22.3461	−	22.3461i	1.00035	−	1.00035i	1.00000		0.000347536i	$-0.000110624\pi$
$500$	−5.32715	+	19.8812i	−0.238237	+	0.889114i
$501$	9.06851	+	41.3567i	0.405151	+	1.84768i
$502$	10.6960	+	10.6960i	0.477385	+	0.477385i
$503$	20.2177	−	11.6727i	0.901464	−	0.520460i	0.0237889	−	0.999717i	$-0.492427\pi$
$503$	20.2177	−	11.6727i	0.901464	−	0.520460i	0.877675	+	0.479257i	$0.159094\pi$
$504$	−3.18876	−	6.92152i	−0.142039	−	0.308309i
$505$	−22.0256	+	5.90175i	−0.980128	+	0.262625i
$506$	−1.02174			−0.0454218
$507$	18.0916	−	13.4050i	0.803477	−	0.595335i
$508$	9.31325			0.413209
$509$	−18.0113	+	4.82612i	−0.798338	+	0.213914i	−0.634854	−	0.772632i	$-0.718940\pi$
$509$	−18.0113	+	4.82612i	−0.798338	+	0.213914i	−0.163484	+	0.986546i	$0.552273\pi$
$510$	0.340021	−	7.39614i	0.0150564	−	0.327507i
$511$	16.1182	−	9.30585i	0.713028	−	0.411667i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−6.57690	−	2.77773i	−0.290377	−	0.122640i
$514$	0.0924504	−	0.345030i	0.00407781	−	0.0152186i
$515$	−5.72793	+	5.72793i	−0.252403	+	0.252403i
$516$	−3.51910	+	5.49585i	−0.154920	+	0.241941i
$517$	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	$-0.145844\pi$
$522$	16.6700	+	6.15465i	0.729627	+	0.269382i
$523$	−14.1118	+	24.4424i	−0.617066	+	1.06879i	0.372952	+	0.927850i	$0.378345\pi$
$523$	−14.1118	+	24.4424i	−0.617066	+	1.06879i	−0.990018	+	0.140939i	$0.954988\pi$
$524$	0.458914	+	0.794862i	0.0200478	+	0.0347237i
$525$	43.0534	+	13.6840i	1.87901	+	0.597218i
$526$	−2.07459	−	0.555884i	−0.0904563	−	0.0242377i
$527$	−9.71355	−	2.60274i	−0.423129	−	0.113377i
$528$	−0.962144	−	0.305805i	−0.0418719	−	0.0133085i
$529$	9.96363	+	17.2575i	0.433201	+	0.750327i
$530$	5.94771	−	10.3017i	0.258352	−	0.447478i
$531$	−23.8626	−	8.81018i	−1.03555	−	0.382329i
$532$			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
$537$	13.0763	−	20.4216i	0.564285	−	0.881256i
$538$	−17.3407	+	17.3407i	−0.747612	+	0.747612i
$539$	−0.0825429	+	0.308054i	−0.00355537	+	0.0132688i
$540$	−18.7036	−	7.89940i	−0.804875	−	0.339936i
$541$	−13.2334	−	13.2334i	−0.568947	−	0.568947i	0.362887	−	0.931833i	$-0.381791\pi$
$541$	−13.2334	−	13.2334i	−0.568947	−	0.568947i	−0.931833	+	0.362887i	$0.881791\pi$
$542$	18.9885	−	10.9630i	0.815627	−	0.470903i
$543$	−2.03158	+	44.1908i	−0.0871833	+	1.89641i
$544$	1.05672	−	0.283148i	0.0453066	−	0.0121399i
$545$	−60.7298			−2.60138
$546$	15.1745	−	4.62547i	0.649410	−	0.197952i
$547$	−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
$549$	−11.7311	−	25.4636i	−0.500673	−	1.08676i
$550$	5.18295	−	2.99238i	0.221002	−	0.127595i
$551$	−5.75480	−	5.75480i	−0.245163	−	0.245163i
$552$	−0.650302	−	2.96569i	−0.0276787	−	0.126228i
$553$	8.61860	−	32.1651i	0.366500	−	1.36780i
$554$	13.1878	−	13.1878i	0.560295	−	0.560295i
$555$	17.6392	+	11.2947i	0.748741	+	0.479433i
$556$	−2.86936	−	1.65662i	−0.121688	−	0.0702565i
$557$	−3.19111	−	11.9094i	−0.135212	−	0.504616i	−0.999997	−	0.00247467i	$-0.999212\pi$
$557$	−3.19111	−	11.9094i	−0.135212	−	0.504616i	0.864785	−	0.502142i	$-0.167454\pi$
$558$	−15.9213	+	22.5161i	−0.674001	+	0.953181i
$559$	−10.3430	−	8.80748i	−0.437464	−	0.372517i
$560$			9.92570i			0.419438i
$561$	−0.816022	+	0.744291i	−0.0344525	+	0.0314240i
$562$	7.97489	−	13.8129i	0.336400	−	0.582662i
$563$	9.86628	+	17.0889i	0.415814	+	0.720211i	0.995514	−	0.0946194i	$-0.0301634\pi$
$563$	9.86628	+	17.0889i	0.415814	+	0.720211i	−0.579700	+	0.814830i	$0.696830\pi$
$564$	−4.08907	+	12.8653i	−0.172181	+	0.541726i
$565$	41.1283	+	11.0203i	1.73028	+	0.463628i
$566$	−4.55446	−	1.22036i	−0.191438	−	0.0512958i
$567$	−9.85280	+	20.6302i	−0.413779	+	0.866385i
$568$	−0.425242	−	0.736541i	−0.0178428	−	0.0309046i
$569$	−17.4503	+	30.2248i	−0.731555	+	1.26709i	0.224663	+	0.974436i	$0.427872\pi$
$569$	−17.4503	+	30.2248i	−0.731555	+	1.26709i	−0.956218	+	0.292654i	$0.905462\pi$
$570$	6.26635	+	6.87028i	0.262469	+	0.287764i
$571$		−	2.37582i		−	0.0994248i	−0.998764	−	0.0497124i	$-0.984170\pi$
$571$		−	2.37582i		−	0.0994248i	0.998764	−	0.0497124i	$-0.0158305\pi$
$572$	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
$576$	0.275255	−	2.98735i	0.0114690	−	0.124473i
$577$	3.78848	−	3.78848i	0.157716	−	0.157716i	−0.623838	−	0.781554i	$-0.714427\pi$
$577$	3.78848	−	3.78848i	0.157716	−	0.157716i	0.781554	+	0.623838i	$0.214427\pi$
$578$	−4.09016	+	15.2647i	−0.170128	+	0.634927i
$579$	−17.9314	+	3.93191i	−0.745202	+	0.163404i
$580$	−16.3657	−	16.3657i	−0.679548	−	0.679548i
$581$	−16.0347	+	9.25764i	−0.665232	+	0.384072i
$582$	−1.06123	−	0.0487878i	−0.0439895	−	0.00202232i
$583$	−1.71402	+	0.459269i	−0.0709873	+	0.0190210i
$584$	7.32673			0.303182
$585$	21.5653	−	36.3490i	0.891615	−	1.50285i
$586$	−21.3553			−0.882179
$587$	9.81579	−	2.63013i	0.405141	−	0.108557i	−0.0504929	−	0.998724i	$-0.516079\pi$
$587$	9.81579	−	2.63013i	0.405141	−	0.108557i	0.455634	+	0.890167i	$0.349413\pi$
$588$	−0.946692	−	0.0435221i	−0.0390409	−	0.00179482i
$589$	10.9378	−	6.31493i	0.450683	−	0.260202i
$590$	23.4269	+	23.4269i	0.964471	+	0.964471i
$591$	5.86693	−	1.28647i	0.241333	−	0.0529184i
$592$	−0.801012	+	2.98942i	−0.0329214	+	0.122864i
$593$	−9.76893	+	9.76893i	−0.401162	+	0.401162i	−0.878642	−	0.477481i	$-0.841550\pi$
$593$	−9.76893	+	9.76893i	−0.401162	+	0.401162i	0.477481	+	0.878642i	$0.341550\pi$
$594$	1.13964	+	2.80613i	0.0467602	+	0.115137i
$595$	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	$-0.255957\pi$
$600$	11.9844	+	13.1394i	0.489262	+	0.536415i
$601$	−4.57192	+	7.91880i	−0.186493	+	0.323015i	−0.944078	−	0.329721i	$-0.893045\pi$
$601$	−4.57192	+	7.91880i	−0.186493	+	0.323015i	0.757586	+	0.652736i	$0.226379\pi$
$602$	−4.78554	−	8.28880i	−0.195044	−	0.337826i
$603$	3.34892	+	19.5189i	0.136378	+	0.794872i
$604$	14.0154	+	3.75542i	0.570279	+	0.152806i
$605$	40.2343	+	10.7808i	1.63576	+	0.438300i
$606$	−3.06173	+	9.63301i	−0.124374	+	0.391314i
$607$	9.96393	+	17.2580i	0.404423	+	0.700482i	0.994254	−	0.107045i	$-0.0341389\pi$
$607$	9.96393	+	17.2580i	0.404423	+	0.700482i	−0.589831	+	0.807527i	$0.700806\pi$
$608$	−0.686992	+	1.18990i	−0.0278612	+	0.0482570i
$609$	−19.2552	+	17.5625i	−0.780258	+	0.711670i
$610$			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	−0.998919	−	0.0464829i	$-0.985199\pi$
$613$	−3.88890	−	14.5136i	−0.157071	−	0.586198i	0.841848	−	0.539715i	$-0.181468\pi$
$614$	19.8726	+	11.4735i	0.801994	+	0.463032i
$615$	−30.1978	−	19.3362i	−1.21769	−	0.779712i
$616$	1.04698	−	1.04698i	0.0421840	−	0.0421840i
$617$	−2.63629	+	9.83876i	−0.106133	+	0.396094i	−0.998471	−	0.0552736i	$-0.982397\pi$
$617$	−2.63629	+	9.83876i	−0.106133	+	0.396094i	0.892338	+	0.451367i	$0.149064\pi$
$618$	0.769095	+	3.50744i	0.0309375	+	0.141090i
$619$	18.1131	+	18.1131i	0.728027	+	0.728027i	0.970226	−	0.242199i	$-0.0778688\pi$
$619$	18.1131	+	18.1131i	0.728027	+	0.728027i	−0.242199	+	0.970226i	$0.577869\pi$
$620$	31.1052	−	17.9586i	1.24922	−	0.721235i
$621$	−5.59475	+	7.18766i	−0.224510	+	0.288431i
$622$	31.7272	−	8.50128i	1.27215	−	0.340870i
$623$	−24.6151			−0.986185
$624$	6.08376	+	1.40990i	0.243545	+	0.0564411i
$625$	−29.0857			−1.16343
$626$	−10.6859	+	2.86328i	−0.427095	+	0.114440i
$627$	0.0637033	−	1.38567i	0.00254406	−	0.0553385i
$628$	−5.81577	+	3.35773i	−0.232074	+	0.133988i
$629$	2.39412	+	2.39412i	0.0954596	+	0.0954596i
$630$	22.8987	−	19.0349i	0.912305	−	0.758368i
$631$	−5.19785	+	19.3987i	−0.206923	+	0.772248i	0.781931	+	0.623364i	$0.214235\pi$
$631$	−5.19785	+	19.3987i	−0.206923	+	0.772248i	−0.988855	+	0.148884i	$0.952432\pi$
$632$	9.26936	−	9.26936i	0.368716	−	0.368716i
$633$	−4.63077	+	7.23198i	−0.184057	+	0.287445i
$634$	−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
$639$	−0.883703	+	2.39353i	−0.0349587	+	0.0946866i
$640$	−1.95369	+	3.38389i	−0.0772263	+	0.133760i
$641$	22.3417	+	38.6969i	0.882443	+	1.52844i	0.848617	+	0.529008i	$0.177436\pi$
$641$	22.3417	+	38.6969i	0.882443	+	1.52844i	0.0338257	+	0.999428i	$0.489231\pi$
$642$	−5.70897	−	1.81452i	−0.225315	−	0.0716136i
$643$	8.68244	+	2.32645i	0.342402	+	0.0917463i	0.425922	−	0.904760i	$-0.359950\pi$
$643$	8.68244	+	2.32645i	0.342402	+	0.0917463i	−0.0835204	+	0.996506i	$0.526616\pi$
$644$	4.30112	+	1.15248i	0.169488	+	0.0454142i
$645$	−24.3015	−	7.72393i	−0.956872	−	0.304130i
$646$	0.751569	+	1.30176i	0.0295701	+	0.0512169i
$647$	18.9869	−	32.8862i	0.746451	−	1.29289i	−0.203063	−	0.979166i	$-0.565090\pi$
$647$	18.9869	−	32.8862i	0.746451	−	1.29289i	0.949514	−	0.313725i	$-0.101577\pi$
$648$	−7.41970	+	5.09393i	−0.291473	+	0.200108i
$649$		−	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	$-0.451156\pi$
$653$	−16.0116	−	9.24428i	−0.626581	−	0.361757i	−0.779427	+	0.626493i	$0.784490\pi$
$654$	−14.5165	+	22.6707i	−0.567640	+	0.886496i
$655$	−2.53590	+	2.53590i	−0.0990857	+	0.0990857i
$656$	1.37131	−	5.11781i	0.0535408	−	0.199817i
$657$	−14.0508	−	16.9028i	−0.548172	−	0.659442i
$658$	−13.9997	−	13.9997i	−0.545763	−	0.545763i
$659$	−0.644195	+	0.371926i	−0.0250943	+	0.0144882i	−0.512495	−	0.858690i	$-0.671279\pi$
$659$	−0.644195	+	0.371926i	−0.0250943	+	0.0144882i	0.487400	+	0.873179i	$0.337945\pi$
$660$	0.181161	−	3.94062i	0.00705170	−	0.153389i
$661$	27.0849	−	7.25737i	1.05348	−	0.282279i	0.309790	−	0.950805i	$-0.399741\pi$
$661$	27.0849	−	7.25737i	1.05348	−	0.282279i	0.743689	+	0.668526i	$0.233075\pi$
$662$	−4.62395			−0.179715
$663$	4.66360	−	4.99274i	0.181119	−	0.193902i
$664$	−7.28877			−0.282859
$665$	−13.1731	+	3.52971i	−0.510829	+	0.136876i
$666$	8.43274	−	3.88498i	0.326762	−	0.150540i
$667$	−8.99201	+	5.19154i	−0.348172	+	0.201017i
$668$	−17.2850	−	17.2850i	−0.668775	−	0.668775i
$669$	−7.07243	−	32.2537i	−0.273436	−	1.24700i
$670$	6.67600	−	24.9152i	0.257916	−	0.962556i
$671$	3.85174	−	3.85174i	0.148695	−	0.148695i
$672$	3.70532	+	2.37259i	0.142936	+	0.0915245i
$673$	23.9347	+	13.8187i	0.922615	+	0.532672i	0.884468	−	0.466600i	$-0.154521\pi$
$673$	23.9347	+	13.8187i	0.922615	+	0.532672i	0.0381465	+	0.999272i	$0.487855\pi$
$674$	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	$0.772608\pi$
$678$	13.9450	−	12.7192i	0.535556	−	0.488478i
$679$	0.779030	−	1.34932i	0.0298964	−	0.0517821i
$680$	2.13734	+	3.70198i	0.0819631	+	0.141964i
$681$	−2.81223	+	8.84802i	−0.107765	+	0.339057i
$682$	−5.17533	−	1.38672i	−0.198174	−	0.0531004i
$683$	22.5100	+	6.03154i	0.861322	+	0.230790i	0.662331	−	0.749211i	$-0.269567\pi$
$683$	22.5100	+	6.03154i	0.861322	+	0.230790i	0.198990	+	0.980001i	$0.436234\pi$
$684$	4.06259	−	0.697030i	0.155337	−	0.0266516i
$685$	−16.8381	−	29.1644i	−0.643350	−	1.11431i
$686$	9.58581	−	16.6031i	0.365988	−	0.633910i
$687$	−4.59609	−	5.03904i	−0.175352	−	0.192251i
$688$		−	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	0.997812	−	0.0661216i	$-0.0210625\pi$
$691$	2.64500	+	9.87128i	0.100621	+	0.375521i	−0.897191	+	0.441643i	$0.854396\pi$
$692$	−17.9850	−	10.3837i	−0.683689	−	0.394728i
$693$	−4.42322	−	0.407557i	−0.168024	−	0.0154818i
$694$	7.66753	−	7.66753i	0.291056	−	0.291056i
$695$	3.35070	−	12.5050i	0.127099	−	0.474341i
$696$	−10.0214	+	2.19744i	−0.379859	+	0.0832936i
$697$	−4.09867	−	4.09867i	−0.155248	−	0.155248i
$698$	−13.3129	+	7.68623i	−0.503902	+	0.290928i
$699$	−6.63822	−	0.305178i	−0.251081	−	0.0115429i
$700$	−25.1935	+	6.75058i	−0.952225	+	0.255148i
$701$	31.9420			1.20643			0.603217	−	0.797577i	$-0.293885\pi$
$701$	31.9420			1.20643			0.603217	+	0.797577i	$0.293885\pi$
$702$	−8.41442	−	16.7391i	−0.317582	−	0.631777i
$703$	−4.25230			−0.160379
$704$	0.563016	−	0.150860i	0.0212195	−	0.00568574i
$705$	−52.6920	−	2.42240i	−1.98449	−	0.0912328i
$706$	−1.61722	+	0.933704i	−0.0608650	+	0.0351404i
$707$	−10.4824	−	10.4824i	−0.394231	−	0.394231i
$708$	14.3452	−	3.14556i	0.539127	−	0.118217i
$709$	1.92196	−	7.17283i	0.0721805	−	0.269381i	−0.920399	−	0.390981i	$-0.872136\pi$
$709$	1.92196	−	7.17283i	0.0721805	−	0.269381i	0.992579	+	0.121600i	$0.0388024\pi$
$710$	2.34983	−	2.34983i	0.0881876	−	0.0881876i
$711$	−39.1607	−	3.60828i	−1.46864	−	0.135321i
$712$	−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
$717$	−1.24053	−	1.36008i	−0.0463283	−	0.0507933i
$718$	−8.57975	+	14.8606i	−0.320193	+	0.554591i
$719$	14.4593	+	25.0442i	0.539240	+	0.933992i	0.998945	+	0.0459198i	$0.0146219\pi$
$719$	14.4593	+	25.0442i	0.539240	+	0.933992i	−0.459705	+	0.888072i	$0.652045\pi$
$720$	11.5533	−	1.98224i	0.430567	−	0.0738736i
$721$	−5.08682	−	1.36301i	−0.189443	−	0.0507612i
$722$	16.5291	+	4.42896i	0.615149	+	0.164829i
$723$	14.6710	−	46.1589i	0.545621	−	1.71667i
$724$	−12.7703	−	22.1188i	−0.474603	−	0.822037i
$725$	30.4091	−	52.6700i	1.12936	−	1.95612i
$726$	13.6419	−	12.4427i	0.506299	−	0.461793i
$727$		−	13.5518i		−	0.502608i	−0.967908	−	0.251304i	$-0.919141\pi$
$727$		−	13.5518i		−	0.502608i	0.967908	−	0.251304i	$-0.0808594\pi$
$728$	−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
$732$	13.6315	+	8.72852i	0.503835	+	0.322615i
$733$	−13.9665	+	13.9665i	−0.515864	+	0.515864i	−0.916317	−	0.400453i	$-0.868853\pi$
$733$	−13.9665	+	13.9665i	−0.515864	+	0.515864i	0.400453	+	0.916317i	$0.368853\pi$
$734$	−2.34563	+	8.75401i	−0.0865788	+	0.323116i
$735$	−0.793130	−	3.61705i	−0.0292551	−	0.133417i
$736$	1.23950	+	1.23950i	0.0456887	+	0.0456887i
$737$	−3.33228	+	1.92390i	−0.122746	+	0.0708676i
$738$	−14.4366	+	6.65099i	−0.531420	+	0.244826i
$739$	−1.90239	+	0.509744i	−0.0699806	+	0.0187512i	−0.293639	−	0.955916i	$-0.594867\pi$
$739$	−1.90239	+	0.509744i	−0.0699806	+	0.0187512i	0.223659	+	0.974667i	$0.428200\pi$
$740$	−12.0928			−0.444541
$741$	0.292298	+	8.57554i	0.0107378	+	0.315030i
$742$	7.73339			0.283902
$743$	5.78030	−	1.54883i	0.212059	−	0.0568210i	−0.151226	−	0.988499i	$-0.548322\pi$
$743$	5.78030	−	1.54883i	0.212059	−	0.0568210i	0.363284	+	0.931678i	$0.381655\pi$
$744$	0.731173	−	15.9045i	0.0268061	−	0.583086i
$745$	−26.5807	+	15.3464i	−0.973841	+	0.562247i
$746$	−5.35695	−	5.35695i	−0.196132	−	0.196132i
$747$	13.9780	+	16.8153i	0.511427	+	0.615238i
$748$	0.165041	−	0.615940i	0.00603448	−	0.0225210i
$749$	6.21235	−	6.21235i	0.226994	−	0.226994i
$750$	−19.2240	+	30.0226i	−0.701963	+	1.09627i
$751$	−15.1590	−	8.75204i	−0.553159	−	0.319366i	0.197236	−	0.980356i	$-0.436803\pi$
$751$	−15.1590	−	8.75204i	−0.553159	−	0.319366i	−0.750395	+	0.660990i	$0.770137\pi$
$752$	−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
$756$	−1.63226	−	13.0982i	−0.0593647	−	0.476377i
$757$	−4.00168	+	6.93111i	−0.145443	+	0.251915i	−0.929538	−	0.368726i	$-0.879794\pi$
$757$	−4.00168	+	6.93111i	−0.145443	+	0.251915i	0.784095	+	0.620641i	$0.213128\pi$
$758$	−6.03855	−	10.4591i	−0.219330	−	0.379891i
$759$	−1.68656	−	0.536052i	−0.0612183	−	0.0194575i
$760$	−5.18574	−	1.38951i	−0.188107	−	0.0504030i
$761$	−18.9310	−	5.07254i	−0.686247	−	0.183879i	−0.101185	−	0.994868i	$-0.532263\pi$
$761$	−18.9310	−	5.07254i	−0.686247	−	0.183879i	−0.585062	+	0.810988i	$0.698930\pi$
$762$	15.3732	+	4.88617i	0.556912	+	0.177007i
$763$	−19.7407	−	34.1918i	−0.714660	−	1.23783i
$764$	−11.8231	+	20.4783i	−0.427747	+	0.740879i
$765$	4.44163	−	12.0303i	0.160588	−	0.434955i
$766$		−	36.8323i		−	1.33081i
$767$	2.44349

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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.76293 + 2.76293i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-0.657464 + 2.45369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.76293 + 2.76293i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-0.657464 + 2.45369i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) 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} +(-4.56072 - 5.00027i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.547000 - 0.947432i) q^{17} +(-2.95680 + 0.507306i) q^{18} +(1.32717 + 0.355613i) q^{19} +(3.77424 + 1.01130i) q^{20} +(1.33273 - 4.19313i) q^{21} +(-0.291439 - 0.504787i) q^{22} +(0.876460 - 1.51807i) q^{23} +(1.27970 - 1.16721i) 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} +(5.69948 + 3.64948i) q^{30} +(6.49983 - 6.49983i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.216237 - 0.986144i) q^{33} +(0.773575 + 0.773575i) q^{34} +(-8.59591 + 4.96285i) q^{35} +(2.72474 - 1.25529i) q^{36} +(-2.98942 + 0.801012i) q^{37} -1.37398 q^{38} +(1.82088 + 5.97364i) q^{39} -3.90738 q^{40} +(5.11781 - 1.37131i) q^{41} +(-0.202059 + 4.39519i) q^{42} +(3.26299 - 1.88389i) q^{43} +(0.412157 + 0.412157i) q^{44} +(7.49333 + 9.01435i) q^{45} +(-0.453689 + 1.69319i) q^{46} +(5.51114 - 5.51114i) q^{47} +(-0.933998 + 1.45865i) 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} +(5.15627 - 0.642559i) q^{54} +(-1.13876 + 1.97239i) q^{55} +(-1.27012 - 2.19992i) q^{56} +(-2.26801 - 0.720857i) q^{57} +(5.72147 + 1.53306i) q^{58} +(-8.19009 - 2.19453i) q^{59} +(-6.44983 - 2.05000i) q^{60} +(-4.67266 - 8.09329i) q^{61} +(-4.59607 + 7.96063i) q^{62} +(-2.63946 + 7.14905i) 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} +(-1.63722 + 2.55689i) q^{69} +(7.01853 - 7.01853i) q^{70} +(-0.220122 + 0.821505i) q^{71} +(-2.30701 + 1.91774i) q^{72} +(-5.18078 - 5.18078i) q^{73} +(2.68024 - 1.54744i) q^{74} +(0.816719 - 17.7653i) q^{75} +(1.32717 - 0.355613i) q^{76} -1.48065 q^{77} +(-3.30492 - 5.29882i) q^{78} -13.1089 q^{79} +(3.77424 - 1.01130i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-4.58850 + 2.64917i) q^{82} +(5.15394 + 5.15394i) q^{83} +(-0.942385 - 4.29773i) q^{84} +(1.10637 - 4.12902i) q^{85} +(-2.66422 + 2.66422i) q^{86} +(8.63999 + 5.53235i) 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} +(-11.7632 + 10.7291i) q^{93} +(-3.89697 + 6.74974i) q^{94} +(2.68434 + 4.64941i) q^{95} +(0.524648 - 1.65068i) q^{96} +(-0.592450 - 0.158747i) q^{97} +(-0.528506 - 0.141613i) q^{98} +(0.295697 + 1.72345i) 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

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