LMFDB - Embedded newform 2513.1.l.a.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2513,1,Mod(6,2513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2513, base_ring=CyclotomicField(358))

chi = DirichletCharacter(H, H._module([179, 142]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2513.6");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2513 = 7 \cdot 359 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2513.l (of order $358$, degree $178$, 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:	$1.25415037675$
Analytic rank:	$0$
Dimension:	$178$
Coefficient field:	$\Q(\zeta_{358})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{178} - x^{177} + x^{176} - x^{175} + x^{174} - x^{173} + x^{172} - x^{171} + x^{170} - x^{169} + \cdots + 1 $ x^178 - x^177 + x^176 - x^175 + x^174 - x^173 + x^172 - x^171 + x^170 - x^169 + x^168 - x^167 + x^166 - x^165 + x^164 - x^163 + x^162 - x^161 + x^160 - x^159 + x^158 - x^157 + x^156 - x^155 + x^154 - x^153 + x^152 - x^151 + x^150 - x^149 + x^148 - x^147 + x^146 - x^145 + x^144 - x^143 + x^142 - x^141 + x^140 - x^139 + x^138 - x^137 + x^136 - x^135 + x^134 - x^133 + x^132 - x^131 + x^130 - x^129 + x^128 - x^127 + x^126 - x^125 + x^124 - x^123 + x^122 - x^121 + x^120 - x^119 + x^118 - x^117 + x^116 - x^115 + x^114 - x^113 + x^112 - x^111 + x^110 - x^109 + x^108 - x^107 + x^106 - x^105 + x^104 - x^103 + x^102 - x^101 + x^100 - x^99 + x^98 - x^97 + x^96 - x^95 + x^94 - x^93 + x^92 - x^91 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^82 - x^81 + x^80 - x^79 + x^78 - x^77 + x^76 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^68 - x^67 + x^66 - x^65 + x^64 - x^63 + x^62 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^53 + x^52 - x^51 + x^50 - x^49 + x^48 - x^47 + x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{179}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{179} - \cdots)$

Embedding invariants

Embedding label			391.1
Root			$0.836914 - 0.547335i$ of defining polynomial
Character	$\chi$	$=$	2513.391
Dual form			2513.1.l.a.1896.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0522495 - 0.00645163i) q^{2} +(-0.967276 - 0.242572i) q^{4} +(-0.352079 - 0.935970i) q^{7} +(0.0980855 + 0.0378821i) q^{8} +(-0.319015 - 0.947750i) q^{9} +O(q^{10})$	\(q+(-0.0522495 - 0.00645163i) q^{2} +(-0.967276 - 0.242572i) q^{4} +(-0.352079 - 0.935970i) q^{7} +(0.0980855 + 0.0378821i) q^{8} +(-0.319015 - 0.947750i) q^{9} +(1.58956 + 1.07985i) q^{11} +(0.0123574 + 0.0511755i) q^{14} +(0.874338 + 0.467960i) q^{16} +(0.0105538 + 0.0515776i) q^{18} +(-0.0760868 - 0.0666771i) q^{22} +(-0.536824 - 0.504821i) q^{23} +(-0.996152 + 0.0876414i) q^{25} +(0.113517 + 0.990746i) q^{28} +(-0.449748 - 1.61227i) q^{29} +(-0.128589 - 0.0906949i) q^{32} +(0.0786778 + 0.994120i) q^{36} +(0.332192 - 0.583227i) q^{37} +(1.24985 + 0.267193i) q^{43} +(-1.27560 - 1.43010i) q^{44} +(0.0247919 + 0.0298400i) q^{46} +(-0.752081 + 0.659071i) q^{49} +(0.0526139 + 0.00184759i) q^{50} +(-0.668614 - 1.87676i) q^{53} +(0.000922692 - 0.105143i) q^{56} +(0.0130973 + 0.0871421i) q^{58} +(-0.774747 + 0.632271i) q^{63} +(-0.728114 - 0.661016i) q^{64} +(-1.01768 - 1.71599i) q^{67} +(0.498724 - 1.67377i) q^{71} +(0.00461204 - 0.105046i) q^{72} +(-0.0211196 + 0.0283301i) q^{74} +(0.451062 - 1.86797i) q^{77} +(0.331718 - 0.0116486i) q^{79} +(-0.796459 + 0.604692i) q^{81} +(-0.0635802 - 0.0220243i) q^{86} +(0.115005 + 0.166134i) q^{88} +(0.396802 + 0.618520i) q^{92} +(0.0435479 - 0.0295840i) q^{98} +(0.516340 - 1.85099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 178 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	$ 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} - 6 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} - 7 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} - 4 q^{74} - 2 q^{77} - 2 q^{79} - q^{81} - 4 q^{86} - 8 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 178 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 - 6 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 - 7 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 - 4 * q^74 - 2 * q^77 - 2 * q^79 - q^81 - 4 * q^86 - 8 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{69}{179}\right)$

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 $

$2$	−0.0522495	−	0.00645163i	−0.0522495	−	0.00645163i	0.0963795	−	0.995345i	$-0.469274\pi$
$2$	−0.0522495	−	0.00645163i	−0.0522495	−	0.00645163i	−0.148629	+	0.988893i	$0.547486\pi$
$3$		0			0		0.583517	−	0.812101i	$-0.301676\pi$
$3$		0			0		−0.583517	+	0.812101i	$0.698324\pi$
$4$	−0.967276	−	0.242572i	−0.967276	−	0.242572i
$5$		0			0		−0.0438629	−	0.999038i	$-0.513966\pi$
$5$		0			0		0.0438629	+	0.999038i	$0.486034\pi$
$6$		0			0
$7$	−0.352079	−	0.935970i	−0.352079	−	0.935970i
$7$	−0.352079	−	0.935970i	−0.352079	−	0.935970i
$8$	0.0980855	+	0.0378821i	0.0980855	+	0.0378821i
$9$	−0.319015	−	0.947750i	−0.319015	−	0.947750i
$10$		0			0
$11$	1.58956	+	1.07985i	1.58956	+	1.07985i	0.950513	+	0.310686i	$0.100559\pi$
$11$	1.58956	+	1.07985i	1.58956	+	1.07985i	0.639045	+	0.769169i	$0.279330\pi$
$12$		0			0
$13$		0			0		−0.997537	−	0.0701455i	$-0.977654\pi$
$13$		0			0		0.997537	+	0.0701455i	$0.0223464\pi$
$14$	0.0123574	+	0.0511755i	0.0123574	+	0.0511755i
$15$		0			0
$16$	0.874338	+	0.467960i	0.874338	+	0.467960i
$17$		0			0		0.990159	−	0.139946i	$-0.0446927\pi$
$17$		0			0		−0.990159	+	0.139946i	$0.955307\pi$
$18$	0.0105538	+	0.0515776i	0.0105538	+	0.0515776i
$19$		0			0		0.0613892	−	0.998114i	$-0.480447\pi$
$19$		0			0		−0.0613892	+	0.998114i	$0.519553\pi$
$20$		0			0
$21$		0			0
$22$	−0.0760868	−	0.0666771i	−0.0760868	−	0.0666771i
$23$	−0.536824	−	0.504821i	−0.536824	−	0.504821i	0.368451	−	0.929647i	$-0.379888\pi$
$23$	−0.536824	−	0.504821i	−0.536824	−	0.504821i	−0.905275	+	0.424826i	$0.860335\pi$
$24$		0			0
$25$	−0.996152	+	0.0876414i	−0.996152	+	0.0876414i
$26$		0			0
$27$		0			0
$28$	0.113517	+	0.990746i	0.113517	+	0.990746i
$29$	−0.449748	−	1.61227i	−0.449748	−	1.61227i	−0.752081	−	0.659071i	$-0.770950\pi$
$29$	−0.449748	−	1.61227i	−0.449748	−	1.61227i	0.302333	−	0.953202i	$-0.402235\pi$
$30$		0			0
$31$		0			0		−0.716353	−	0.697738i	$-0.754190\pi$
$31$		0			0		0.716353	+	0.697738i	$0.245810\pi$
$32$	−0.128589	−	0.0906949i	−0.128589	−	0.0906949i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.0786778	+	0.994120i	0.0786778	+	0.994120i
$37$	0.332192	−	0.583227i	0.332192	−	0.583227i	−0.652446	−	0.757835i	$-0.726257\pi$
$37$	0.332192	−	0.583227i	0.332192	−	0.583227i	0.984638	+	0.174608i	$0.0558659\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.919626	−	0.392794i	$-0.871508\pi$
$41$		0			0		0.919626	+	0.392794i	$0.128492\pi$
$42$		0			0
$43$	1.24985	+	0.267193i	1.24985	+	0.267193i	0.785724	−	0.618577i	$-0.212291\pi$
$43$	1.24985	+	0.267193i	1.24985	+	0.267193i	0.464125	+	0.885770i	$0.346369\pi$
$44$	−1.27560	−	1.43010i	−1.27560	−	1.43010i
$45$		0			0
$46$	0.0247919	+	0.0298400i	0.0247919	+	0.0298400i
$47$		0			0		0.873245	−	0.487281i	$-0.162011\pi$
$47$		0			0		−0.873245	+	0.487281i	$0.837989\pi$
$48$		0			0
$49$	−0.752081	+	0.659071i	−0.752081	+	0.659071i
$50$	0.0526139	+	0.00184759i	0.0526139	+	0.00184759i
$51$		0			0
$52$		0			0
$53$	−0.668614	−	1.87676i	−0.668614	−	1.87676i	−0.416866	−	0.908968i	$-0.636872\pi$
$53$	−0.668614	−	1.87676i	−0.668614	−	1.87676i	−0.251749	−	0.967793i	$-0.581006\pi$
$54$		0			0
$55$		0			0
$56$	0.000922692	−	0.105143i	0.000922692	−	0.105143i
$57$		0			0
$58$	0.0130973	+	0.0871421i	0.0130973	+	0.0871421i
$59$		0			0		0.703997	−	0.710203i	$-0.251397\pi$
$59$		0			0		−0.703997	+	0.710203i	$0.748603\pi$
$60$		0			0
$61$		0			0		0.448509	−	0.893778i	$-0.351955\pi$
$61$		0			0		−0.448509	+	0.893778i	$0.648045\pi$
$62$		0			0
$63$	−0.774747	+	0.632271i	−0.774747	+	0.632271i
$64$	−0.728114	−	0.661016i	−0.728114	−	0.661016i
$65$		0			0
$66$		0			0
$67$	−1.01768	−	1.71599i	−1.01768	−	1.71599i	−0.569175	−	0.822216i	$-0.692737\pi$
$67$	−1.01768	−	1.71599i	−1.01768	−	1.71599i	−0.448509	−	0.893778i	$-0.648045\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.498724	−	1.67377i	0.498724	−	1.67377i	−0.217629	−	0.976031i	$-0.569832\pi$
$71$	0.498724	−	1.67377i	0.498724	−	1.67377i	0.716353	−	0.697738i	$-0.245810\pi$
$72$	0.00461204	−	0.105046i	0.00461204	−	0.105046i
$73$		0			0		−0.703997	−	0.710203i	$-0.748603\pi$
$73$		0			0		0.703997	+	0.710203i	$0.251397\pi$
$74$	−0.0211196	+	0.0283301i	−0.0211196	+	0.0283301i
$75$		0			0
$76$		0			0
$77$	0.451062	−	1.86797i	0.451062	−	1.86797i
$78$		0			0
$79$	0.331718	−	0.0116486i	0.331718	−	0.0116486i	0.131251	−	0.991349i	$-0.458101\pi$
$79$	0.331718	−	0.0116486i	0.331718	−	0.0116486i	0.200467	+	0.979701i	$0.435754\pi$
$80$		0			0
$81$	−0.796459	+	0.604692i	−0.796459	+	0.604692i
$82$		0			0
$83$		0			0		−0.998614	−	0.0526281i	$-0.983240\pi$
$83$		0			0		0.998614	+	0.0526281i	$0.0167598\pi$
$84$		0			0
$85$		0			0
$86$	−0.0635802	−	0.0220243i	−0.0635802	−	0.0220243i
$87$		0			0
$88$	0.115005	+	0.166134i	0.115005	+	0.166134i
$89$		0			0		0.368451	−	0.929647i	$-0.379888\pi$
$89$		0			0		−0.368451	+	0.929647i	$0.620112\pi$
$90$		0			0
$91$		0			0
$92$	0.396802	+	0.618520i	0.396802	+	0.618520i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.494925	−	0.868936i	$-0.664804\pi$
$97$		0			0		0.494925	+	0.868936i	$0.335196\pi$
$98$	0.0435479	−	0.0295840i	0.0435479	−	0.0295840i
$99$	0.516340	−	1.85099i	0.516340	−	1.85099i
$100$	0.984814	+	0.156865i	0.984814	+	0.156865i
$101$		0			0		0.817190	−	0.576369i	$-0.195531\pi$
$101$		0			0		−0.817190	+	0.576369i	$0.804469\pi$
$102$		0			0
$103$		0			0		−0.554658	−	0.832079i	$-0.687151\pi$
$103$		0			0		0.554658	+	0.832079i	$0.312849\pi$
$104$		0			0
$105$		0			0
$106$	0.0228266	+	0.102373i	0.0228266	+	0.102373i
$107$	−1.38241	+	0.648737i	−1.38241	+	0.648737i	−0.965546	−	0.260231i	$-0.916201\pi$
$107$	−1.38241	+	0.648737i	−1.38241	+	0.648737i	−0.416866	+	0.908968i	$0.636872\pi$
$108$		0			0
$109$	0.0169459	+	1.93102i	0.0169459	+	1.93102i	0.268694	+	0.963225i	$0.413408\pi$
$109$	0.0169459	+	1.93102i	0.0169459	+	1.93102i	−0.251749	+	0.967793i	$0.581006\pi$
$110$		0			0
$111$		0			0
$112$	0.130161	−	0.983114i	0.130161	−	0.983114i
$113$	1.60919	−	0.720977i	1.60919	−	0.720977i	0.611658	−	0.791122i	$-0.290503\pi$
$113$	1.60919	−	0.720977i	1.60919	−	0.720977i	0.997537	+	0.0701455i	$0.0223464\pi$
$114$		0			0
$115$		0			0
$116$	0.0439383	+	1.66861i	0.0439383	+	1.66861i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.992158	+	2.50334i	0.992158	+	2.50334i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.0445593	−	0.0280375i	0.0445593	−	0.0280375i
$127$	0.142719	−	1.47390i	0.142719	−	1.47390i	−0.597680	−	0.801735i	$-0.703911\pi$
$127$	0.142719	−	1.47390i	0.142719	−	1.47390i	0.740398	−	0.672168i	$-0.234637\pi$
$128$	0.136445	+	0.158485i	0.136445	+	0.158485i
$129$		0			0
$130$		0			0
$131$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$131$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$132$		0			0
$133$		0			0
$134$	0.0421025	+	0.0962256i	0.0421025	+	0.0962256i
$135$		0			0
$136$		0			0
$137$	0.551812	+	1.73977i	0.551812	+	1.73977i	0.665645	+	0.746268i	$0.268156\pi$
$137$	0.551812	+	1.73977i	0.551812	+	1.73977i	−0.113833	+	0.993500i	$0.536313\pi$
$138$		0			0
$139$		0			0		0.716353	−	0.697738i	$-0.245810\pi$
$139$		0			0		−0.716353	+	0.697738i	$0.754190\pi$
$140$		0			0
$141$		0			0
$142$	−0.0368566	+	0.0842360i	−0.0368566	+	0.0842360i
$143$		0			0
$144$	0.164582	−	0.977940i	0.164582	−	0.977940i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.462796	+	0.483561i	−0.462796	+	0.483561i
$149$	−0.00588995	+	0.0165327i	−0.00588995	+	0.0165327i	−0.944914	−	0.327319i	$-0.893855\pi$
$149$	−0.00588995	+	0.0165327i	−0.00588995	+	0.0165327i	0.939024	+	0.343852i	$0.111732\pi$
$150$		0			0
$151$	0.837800	+	0.527157i	0.837800	+	0.527157i	0.881663	−	0.471880i	$-0.156425\pi$
$151$	0.837800	+	0.527157i	0.837800	+	0.527157i	−0.0438629	+	0.999038i	$0.513966\pi$
$152$		0			0
$153$		0			0
$154$	−0.0356192	+	0.0946906i	−0.0356192	+	0.0946906i
$155$		0			0
$156$		0			0
$157$		0			0		0.881663	−	0.471880i	$-0.156425\pi$
$157$		0			0		−0.881663	+	0.471880i	$0.843575\pi$
$158$	−0.0174072	−	0.00153149i	−0.0174072	−	0.00153149i
$159$		0			0
$160$		0			0
$161$	−0.283493	+	0.680188i	−0.283493	+	0.680188i
$162$	0.0455158	−	0.0264564i	0.0455158	−	0.0264564i
$163$	1.11306	−	0.570827i	1.11306	−	0.570827i	0.200467	−	0.979701i	$-0.435754\pi$
$163$	1.11306	−	0.570827i	1.11306	−	0.570827i	0.912591	+	0.408873i	$0.134078\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.977904	−	0.209056i	$-0.0670391\pi$
$167$		0			0		−0.977904	+	0.209056i	$0.932961\pi$
$168$		0			0
$169$	0.990159	+	0.139946i	0.990159	+	0.139946i
$170$		0			0
$171$		0			0
$172$	−1.14414	−	0.561628i	−1.14414	−	0.561628i
$173$		0			0		0.998614	−	0.0526281i	$-0.0167598\pi$
$173$		0			0		−0.998614	+	0.0526281i	$0.983240\pi$
$174$		0			0
$175$	0.432754	+	0.901512i	0.432754	+	0.901512i
$176$	0.884482	+	1.68801i	0.884482	+	1.68801i
$177$		0			0
$178$		0			0
$179$	−1.37243	+	0.169464i	−1.37243	+	0.169464i	−0.774747	−	0.632271i	$-0.782123\pi$
$179$	−1.37243	+	0.169464i	−1.37243	+	0.169464i	−0.597680	+	0.801735i	$0.703911\pi$
$180$		0			0
$181$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$181$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$182$		0			0
$183$		0			0
$184$	−0.0335310	−	0.0698517i	−0.0335310	−	0.0698517i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.09525	−	0.801638i	−1.09525	−	0.801638i	−0.113833	−	0.993500i	$-0.536313\pi$
$191$	−1.09525	−	0.801638i	−1.09525	−	0.801638i	−0.981422	+	0.191862i	$0.938547\pi$
$192$		0			0
$193$	−1.75228	−	0.310736i	−1.75228	−	0.310736i	−0.796459	−	0.604692i	$-0.793296\pi$
$193$	−1.75228	−	0.310736i	−1.75228	−	0.310736i	−0.955819	+	0.293956i	$0.905028\pi$
$194$		0			0
$195$		0			0
$196$	0.887342	−	0.455070i	0.887342	−	0.455070i
$197$	−0.376307	+	0.218731i	−0.376307	+	0.218731i	−0.678640	−	0.734471i	$-0.737430\pi$
$197$	−0.376307	+	0.218731i	−0.376307	+	0.218731i	0.302333	+	0.953202i	$0.402235\pi$
$198$	−0.0389204	+	0.0933822i	−0.0389204	+	0.0933822i
$199$		0			0		0.539970	−	0.841685i	$-0.318436\pi$
$199$		0			0		−0.539970	+	0.841685i	$0.681564\pi$
$200$	−0.101028	−	0.0291400i	−0.101028	−	0.0291400i
$201$		0			0
$202$		0			0
$203$	−1.35069	+	0.988598i	−1.35069	+	0.988598i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.307189	+	0.669820i	−0.307189	+	0.669820i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.36161	−	1.42270i	1.36161	−	1.42270i	0.554658	−	0.832079i	$-0.312849\pi$
$211$	1.36161	−	1.42270i	1.36161	−	1.42270i	0.806949	−	0.590621i	$-0.201117\pi$
$212$	0.191485	+	1.97753i	0.191485	+	1.97753i
$213$		0			0
$214$	0.0764158	−	0.0249773i	0.0764158	−	0.0249773i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.0115728	−	0.101004i	0.0115728	−	0.101004i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.974084	−	0.226186i	$-0.927374\pi$
$223$		0			0		0.974084	+	0.226186i	$0.0726257\pi$
$224$	−0.0396141	+	0.152288i	−0.0396141	+	0.152288i
$225$	0.400849	+	0.916144i	0.400849	+	0.916144i
$226$	−0.0887311	+	0.0272887i	−0.0887311	+	0.0272887i
$227$		0			0		0.994461	−	0.105110i	$-0.0335196\pi$
$227$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$228$		0			0
$229$		0			0		0.148629	−	0.988893i	$-0.452514\pi$
$229$		0			0		−0.148629	+	0.988893i	$0.547486\pi$
$230$		0			0
$231$		0			0
$232$	0.0169626	−	0.175178i	0.0169626	−	0.175178i
$233$	−1.01174	+	0.636604i	−1.01174	+	0.636604i	−0.932845	−	0.360279i	$-0.882682\pi$
$233$	−1.01174	+	0.636604i	−1.01174	+	0.636604i	−0.0788965	+	0.996883i	$0.525140\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.08112	+	1.50462i	1.08112	+	1.50462i	0.846391	+	0.532563i	$0.178771\pi$
$239$	1.08112	+	1.50462i	1.08112	+	1.50462i	0.234725	+	0.972062i	$0.424581\pi$
$240$		0			0
$241$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$241$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$242$	−0.0356891	−	0.137199i	−0.0356891	−	0.137199i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$251$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$252$	0.902766	−	0.423649i	0.902766	−	0.423649i
$253$	−0.308180	−	1.38213i	−0.308180	−	1.38213i
$254$	−0.0169661	+	0.0760899i	−0.0169661	+	0.0760899i
$255$		0			0
$256$	0.539349	+	0.809112i	0.539349	+	0.809112i
$257$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$257$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$258$		0			0
$259$	−0.662841	−	0.105580i	−0.662841	−	0.105580i
$260$		0			0
$261$	−1.38456	+	0.940588i	−1.38456	+	0.940588i
$262$		0			0
$263$	1.02045	−	0.353485i	1.02045	−	0.353485i	0.234725	−	0.972062i	$-0.424581\pi$
$263$	1.02045	−	0.353485i	1.02045	−	0.353485i	0.785724	+	0.618577i	$0.212291\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.568129	+	1.90670i	0.568129	+	1.90670i
$269$		0			0		0.969965	−	0.243246i	$-0.0782123\pi$
$269$		0			0		−0.969965	+	0.243246i	$0.921788\pi$
$270$		0			0
$271$		0			0		−0.569175	−	0.822216i	$-0.692737\pi$
$271$		0			0		0.569175	+	0.822216i	$0.307263\pi$
$272$		0			0
$273$		0			0
$274$	−0.0176076	−	0.0944621i	−0.0176076	−	0.0944621i
$275$	−1.67808	−	0.936388i	−1.67808	−	0.936388i
$276$		0			0
$277$	−0.316847	−	0.184170i	−0.316847	−	0.184170i	0.335599	−	0.942005i	$-0.391061\pi$
$277$	−0.316847	−	0.184170i	−0.316847	−	0.184170i	−0.652446	+	0.757835i	$0.726257\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.20518	+	1.13333i	−1.20518	+	1.13333i	−0.217629	+	0.976031i	$0.569832\pi$
$281$	−1.20518	+	1.13333i	−1.20518	+	1.13333i	−0.987551	+	0.157301i	$0.949721\pi$
$282$		0			0
$283$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$283$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$284$	−0.888413	+	1.49802i	−0.888413	+	1.49802i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0449341	+	0.150804i	−0.0449341	+	0.150804i
$289$	0.960831	−	0.277137i	0.960831	−	0.277137i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.974084	−	0.226186i	$-0.0726257\pi$
$293$		0			0		−0.974084	+	0.226186i	$0.927374\pi$
$294$		0			0
$295$		0			0
$296$	0.0546771	−	0.0446220i	0.0546771	−	0.0446220i
$297$		0			0
$298$	0.000414410	0	0.000825827i	0.000414410	0	0.000825827i
$299$		0			0
$300$		0			0
$301$	−0.189961	−	1.26389i	−0.189961	−	1.26389i
$302$	−0.0403736	−	0.0329489i	−0.0403736	−	0.0329489i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.950513	−	0.310686i	$-0.899441\pi$
$307$		0			0		0.950513	+	0.310686i	$0.100559\pi$
$308$	−0.889420	+	1.69743i	−0.889420	+	1.69743i
$309$		0			0
$310$		0			0
$311$		0			0		0.897680	−	0.440648i	$-0.145251\pi$
$311$		0			0		−0.897680	+	0.440648i	$0.854749\pi$
$312$		0			0
$313$		0			0		−0.639045	−	0.769169i	$-0.720670\pi$
$313$		0			0		0.639045	+	0.769169i	$0.279330\pi$
$314$		0			0
$315$		0			0
$316$	−0.323688	−	0.0691980i	−0.323688	−	0.0691980i
$317$	1.60182	+	0.651177i	1.60182	+	0.651177i	0.990159	−	0.139946i	$-0.0446927\pi$
$317$	1.60182	+	0.651177i	1.60182	+	0.651177i	0.611658	+	0.791122i	$0.290503\pi$
$318$		0			0
$319$	1.02612	−	3.04846i	1.02612	−	3.04846i
$320$		0			0
$321$		0			0
$322$	0.0192007	−	0.0337105i	0.0192007	−	0.0337105i
$323$		0			0
$324$	0.917077	−	0.391706i	0.917077	−	0.391706i
$325$		0			0
$326$	−0.0618395	+	0.0226444i	−0.0618395	+	0.0226444i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.206100	+	1.79878i	0.206100	+	1.79878i	0.525115	+	0.851031i	$0.324022\pi$
$331$	0.206100	+	1.79878i	0.206100	+	1.79878i	−0.319015	+	0.947750i	$0.603352\pi$
$332$		0			0
$333$	−0.658728	−	0.128777i	−0.658728	−	0.128777i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.09576	+	0.960250i	1.09576	+	0.960250i	0.999384	−	0.0350944i	$-0.0111732\pi$
$337$	1.09576	+	0.960250i	1.09576	+	0.960250i	0.0963795	+	0.995345i	$0.469274\pi$
$338$	−0.0508324	−	0.0137002i	−0.0508324	−	0.0137002i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.881663	+	0.471880i	0.881663	+	0.471880i
$344$	0.112470	+	0.0735547i	0.112470	+	0.0735547i
$345$		0			0
$346$		0			0
$347$	0.891068	−	0.753637i	0.891068	−	0.753637i	−0.0788965	−	0.996883i	$-0.525140\pi$
$347$	0.891068	−	0.753637i	0.891068	−	0.753637i	0.969965	+	0.243246i	$0.0782123\pi$
$348$		0			0
$349$		0			0		0.0788965	−	0.996883i	$-0.474860\pi$
$349$		0			0		−0.0788965	+	0.996883i	$0.525140\pi$
$350$	−0.0167949	−	0.0498955i	−0.0167949	−	0.0498955i
$351$		0			0
$352$	−0.106463	−	0.283023i	−0.106463	−	0.283023i
$353$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$353$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0728019			0.0728019
$359$	0.740398	+	0.672168i	0.740398	+	0.672168i
$359$	0.740398	+	0.672168i	0.740398	+	0.672168i
$360$		0			0
$361$	−0.992463	−	0.122547i	−0.992463	−	0.122547i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.932845	−	0.360279i	$-0.882682\pi$
$367$		0			0		0.932845	+	0.360279i	$0.117318\pi$
$368$	−0.233130	−	0.692597i	−0.233130	−	0.692597i
$369$		0			0
$370$		0			0
$371$	−1.52119	+	1.28657i	−1.52119	+	1.28657i
$372$		0			0
$373$	0.126139	+	0.522375i	0.126139	+	0.522375i	0.999384	+	0.0350944i	$0.0111732\pi$
$373$	0.126139	+	0.522375i	0.126139	+	0.522375i	−0.873245	+	0.487281i	$0.837989\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.0175861	+	0.0859450i	−0.0175861	+	0.0859450i	−0.987551	−	0.157301i	$-0.949721\pi$
$379$	−0.0175861	+	0.0859450i	−0.0175861	+	0.0859450i	0.969965	+	0.243246i	$0.0782123\pi$
$380$		0			0
$381$		0			0
$382$	0.0520546	+	0.0489514i	0.0520546	+	0.0489514i
$383$		0			0		0.836914	−	0.547335i	$-0.184358\pi$
$383$		0			0		−0.836914	+	0.547335i	$0.815642\pi$
$384$		0			0
$385$		0			0
$386$	0.0895509	+	0.0275409i	0.0895509	+	0.0275409i
$387$	−0.145489	−	1.26978i	−0.145489	−	1.26978i
$388$		0			0
$389$	1.48120	+	1.25275i	1.48120	+	1.25275i	0.897680	+	0.440648i	$0.145251\pi$
$389$	1.48120	+	1.25275i	1.48120	+	1.25275i	0.583517	+	0.812101i	$0.301676\pi$
$390$		0			0
$391$		0			0
$392$	−0.0987353	+	0.0361549i	−0.0987353	+	0.0361549i
$393$		0			0
$394$	0.0210730	−	0.00900079i	0.0210730	−	0.00900079i
$395$		0			0
$396$	−0.948442	+	1.66517i	−0.948442	+	1.66517i
$397$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$397$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$398$		0			0
$399$		0			0
$400$	−0.911987	−	0.389531i	−0.911987	−	0.389531i
$401$	1.23328	+	0.501357i	1.23328	+	0.501357i	0.897680	−	0.440648i	$-0.145251\pi$
$401$	1.23328	+	0.501357i	1.23328	+	0.501357i	0.335599	+	0.942005i	$0.391061\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.0769511	−	0.0429396i	0.0769511	−	0.0429396i
$407$	1.15784	−	0.568354i	1.15784	−	0.568354i
$408$		0			0
$409$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$409$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0203719	−	0.0330159i	0.0203719	−	0.0330159i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.678640	−	0.734471i	$-0.737430\pi$
$419$		0			0		0.678640	+	0.734471i	$0.262570\pi$
$420$		0			0
$421$	0.399054	+	0.497833i	0.399054	+	0.497833i	0.939024	−	0.343852i	$-0.111732\pi$
$421$	0.399054	+	0.497833i	0.399054	+	0.497833i	−0.539970	+	0.841685i	$0.681564\pi$
$422$	−0.0803220	+	0.0655508i	−0.0803220	+	0.0655508i
$423$		0			0
$424$	0.00551429	−	0.209412i	0.00551429	−	0.209412i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.49454	−	0.292173i	1.49454	−	0.292173i
$429$		0			0
$430$		0			0
$431$	0.0393458	−	0.896154i	0.0393458	−	0.896154i	−0.873245	−	0.487281i	$-0.837989\pi$
$431$	0.0393458	−	0.896154i	0.0393458	−	0.896154i	0.912591	−	0.408873i	$-0.134078\pi$
$432$		0			0
$433$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$433$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$434$		0			0
$435$		0			0
$436$	0.452020	−	1.87194i	0.452020	−	1.87194i
$437$		0			0
$438$		0			0
$439$		0			0		0.432754	−	0.901512i	$-0.357542\pi$
$439$		0			0		−0.432754	+	0.901512i	$0.642458\pi$
$440$		0			0
$441$	0.864559	+	0.502531i	0.864559	+	0.502531i
$442$		0			0
$443$	−0.968705	−	0.540548i	−0.968705	−	0.540548i	−0.0788965	−	0.996883i	$-0.525140\pi$
$443$	−0.968705	−	0.540548i	−0.968705	−	0.540548i	−0.889808	+	0.456335i	$0.849162\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.362338	+	0.914223i	−0.362338	+	0.914223i
$449$	−1.36571	+	0.342489i	−1.36571	+	0.342489i	−0.855607	−	0.517627i	$-0.826816\pi$
$449$	−1.36571	+	0.342489i	−1.36571	+	0.342489i	−0.510099	+	0.860116i	$0.670391\pi$
$450$	−0.0150336	−	0.0504542i	−0.0150336	−	0.0504542i
$451$		0			0
$452$	−1.73142	+	0.307038i	−1.73142	+	0.307038i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.33498	−	0.906911i	1.33498	−	0.906911i	0.335599	−	0.942005i	$-0.391061\pi$
$457$	1.33498	−	0.906911i	1.33498	−	0.906911i	0.999384	+	0.0350944i	$0.0111732\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$461$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$462$		0			0
$463$	0.754756	+	0.354191i	0.754756	+	0.354191i	0.763532	−	0.645770i	$-0.223464\pi$
$463$	0.754756	+	0.354191i	0.754756	+	0.354191i	−0.00877529	+	0.999961i	$0.502793\pi$
$464$	0.361248	−	1.62014i	0.361248	−	1.62014i
$465$		0			0
$466$	0.0569701	−	0.0267349i	0.0569701	−	0.0267349i
$467$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$467$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$468$		0			0
$469$	−1.24781	+	1.55669i	−1.24781	+	1.55669i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.69818	+	1.77437i	1.69818	+	1.77437i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.56540	+	1.23239i	−1.56540	+	1.23239i
$478$	−0.0467805	−	0.0855908i	−0.0467805	−	0.0855908i
$479$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$479$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.352451	−	2.66209i	−0.352451	−	2.66209i
$485$		0			0
$486$		0			0
$487$	1.29506	+	1.50425i	1.29506	+	1.50425i	0.740398	+	0.672168i	$0.234637\pi$
$487$	1.29506	+	1.50425i	1.29506	+	1.50425i	0.554658	+	0.832079i	$0.312849\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.07396	+	0.113513i	−1.07396	+	0.113513i	−0.625448	−	0.780266i	$-0.715084\pi$
$491$	−1.07396	+	0.113513i	−1.07396	+	0.113513i	−0.448509	+	0.893778i	$0.648045\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.74219	+	0.122509i	−1.74219	+	0.122509i
$498$		0			0
$499$	1.78801	−	0.284802i	1.78801	−	0.284802i	0.827179	−	0.561938i	$-0.189944\pi$
$499$	1.78801	−	0.284802i	1.78801	−	0.284802i	0.960831	+	0.277137i	$0.0893855\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$503$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$504$	−0.0999433	+	0.0326676i	−0.0999433	+	0.0326676i
$505$		0			0
$506$	0.00718521	+	0.0742041i	0.00718521	+	0.0742041i
$507$		0			0
$508$	−0.495576	+	1.39105i	−0.495576	+	1.39105i
$509$		0			0		0.611658	−	0.791122i	$-0.290503\pi$
$509$		0			0		−0.611658	+	0.791122i	$0.709497\pi$
$510$		0			0
$511$		0			0
$512$	−0.116757	−	0.232670i	−0.116757	−	0.232670i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.0339520	+	0.00979291i	0.0339520	+	0.00979291i
$519$		0			0
$520$		0			0
$521$		0			0		0.864559	−	0.502531i	$-0.167598\pi$
$521$		0			0		−0.864559	+	0.502531i	$0.832402\pi$
$522$	0.0784107	−	0.0402126i	0.0784107	−	0.0402126i
$523$		0			0		−0.796459	−	0.604692i	$-0.793296\pi$
$523$		0			0		0.796459	+	0.604692i	$0.206704\pi$
$524$		0			0
$525$		0			0
$526$	−0.0555985	+	0.0118858i	−0.0555985	+	0.0118858i
$527$		0			0
$528$		0			0
$529$	−0.0280534	−	0.456114i	−0.0280534	−	0.456114i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.0348146	−	0.206866i	−0.0348146	−	0.206866i
$537$		0			0
$538$		0			0
$539$	−1.90718	+	0.235493i	−1.90718	+	0.235493i
$540$		0			0
$541$	−0.264363	−	1.57083i	−0.264363	−	1.57083i	−0.728488	−	0.685059i	$-0.759777\pi$
$541$	−0.264363	−	1.57083i	−0.264363	−	1.57083i	0.464125	−	0.885770i	$-0.346369\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.453276	+	0.122166i	−0.453276	+	0.122166i	−0.479599	−	0.877488i	$-0.659218\pi$
$547$	−0.453276	+	0.122166i	−0.453276	+	0.122166i	0.0263232	+	0.999653i	$0.491620\pi$
$548$	−0.111736	−	1.81669i	−0.111736	−	1.81669i
$549$		0			0
$550$	0.0816377	+	0.0597522i	0.0816377	+	0.0597522i
$551$		0			0
$552$		0			0
$553$	−0.127694	−	0.306377i	−0.127694	−	0.306377i
$554$	0.0153669	+	0.0116670i	0.0153669	+	0.0116670i
$555$		0			0
$556$		0			0
$557$	0.437934	−	1.05074i	0.437934	−	1.05074i	−0.539970	−	0.841685i	$-0.681564\pi$
$557$	0.437934	−	1.05074i	0.437934	−	1.05074i	0.977904	−	0.209056i	$-0.0670391\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0702819	−	0.0514407i	0.0702819	−	0.0514407i
$563$		0			0		0.665645	−	0.746268i	$-0.268156\pi$
$563$		0			0		−0.665645	+	0.746268i	$0.731844\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.846391	+	0.532563i	0.846391	+	0.532563i
$568$	0.112324	−	0.145280i	0.112324	−	0.145280i
$569$	−0.236314	+	0.663320i	−0.236314	+	0.663320i	0.763532	+	0.645770i	$0.223464\pi$
$569$	−0.236314	+	0.663320i	−0.236314	+	0.663320i	−0.999846	+	0.0175499i	$0.994413\pi$
$570$		0			0
$571$	−0.149340	−	1.54228i	−0.149340	−	1.54228i	−0.703997	−	0.710203i	$-0.748603\pi$
$571$	−0.149340	−	1.54228i	−0.149340	−	1.54228i	0.554658	−	0.832079i	$-0.312849\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.579002	+	0.455830i	0.579002	+	0.455830i
$576$	−0.394199	+	0.900944i	−0.394199	+	0.900944i
$577$		0			0		0.113833	−	0.993500i	$-0.463687\pi$
$577$		0			0		−0.113833	+	0.993500i	$0.536313\pi$
$578$	−0.0519909	+	0.00828132i	−0.0519909	+	0.00828132i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.963828	−	3.70523i	0.963828	−	3.70523i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$587$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.563376	−	0.354485i	0.563376	−	0.354485i
$593$		0			0		−0.131251	−	0.991349i	$-0.541899\pi$
$593$		0			0		0.131251	+	0.991349i	$0.458101\pi$
$594$		0			0
$595$		0			0
$596$	0.00970758	−	0.0145630i	0.00970758	−	0.0145630i
$597$		0			0
$598$		0			0
$599$	−0.753665	−	1.37893i	−0.753665	−	1.37893i	−0.919626	−	0.392794i	$-0.871508\pi$
$599$	−0.753665	−	1.37893i	−0.753665	−	1.37893i	0.165961	−	0.986132i	$-0.446927\pi$
$600$		0			0
$601$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$601$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$602$	0.00177120	+	0.0672634i	0.00177120	+	0.0672634i
$603$	−1.30168	+	1.51194i	−1.30168	+	1.51194i
$604$	−0.682510	−	0.713133i	−0.682510	−	0.713133i
$605$		0			0
$606$		0			0
$607$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$607$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.202015	+	0.906002i	−0.202015	+	0.906002i	0.763532	+	0.645770i	$0.223464\pi$
$613$	−0.202015	+	0.906002i	−0.202015	+	0.906002i	−0.965546	+	0.260231i	$0.916201\pi$
$614$		0			0
$615$		0			0
$616$	0.115005	−	0.166134i	0.115005	−	0.166134i
$617$	−1.58529	+	1.11811i	−1.58529	+	1.11811i	−0.652446	+	0.757835i	$0.726257\pi$
$617$	−1.58529	+	1.11811i	−1.58529	+	1.11811i	−0.932845	+	0.360279i	$0.882682\pi$
$618$		0			0
$619$		0			0		0.268694	−	0.963225i	$-0.413408\pi$
$619$		0			0		−0.268694	+	0.963225i	$0.586592\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.984638	−	0.174608i	0.984638	−	0.174608i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.34535	+	0.492639i	1.34535	+	0.492639i	0.912591	−	0.408873i	$-0.134078\pi$
$631$	1.34535	+	0.492639i	1.34535	+	0.492639i	0.432754	+	0.901512i	$0.357542\pi$
$632$	0.0329780	+	0.0114236i	0.0329780	+	0.0114236i
$633$		0			0
$634$	−0.0794930	−	0.0443580i	−0.0794930	−	0.0443580i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0732819	+	0.152661i	−0.0732819	+	0.152661i
$639$	−1.74541	+	0.0612920i	−1.74541	+	0.0612920i
$640$		0			0
$641$	−0.0697739	+	0.288953i	−0.0697739	+	0.288953i	−0.996152	−	0.0876414i	$-0.972067\pi$
$641$	−0.0697739	+	0.288953i	−0.0697739	+	0.288953i	0.926378	+	0.376595i	$0.122905\pi$
$642$		0			0
$643$		0			0		0.510099	−	0.860116i	$-0.329609\pi$
$643$		0			0		−0.510099	+	0.860116i	$0.670391\pi$
$644$	0.439211	−	0.589162i	0.439211	−	0.589162i
$645$		0			0
$646$		0			0
$647$		0			0		0.285558	−	0.958362i	$-0.407821\pi$
$647$		0			0		−0.285558	+	0.958362i	$0.592179\pi$
$648$	−0.101028	+	0.0291400i	−0.101028	+	0.0291400i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.21510	+	0.282151i	−1.21510	+	0.282151i
$653$	0.0141458	−	0.537203i	0.0141458	−	0.537203i	−0.955819	−	0.293956i	$-0.905028\pi$
$653$	0.0141458	−	0.537203i	0.0141458	−	0.537203i	0.969965	−	0.243246i	$-0.0782123\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.09084	−	1.10045i	1.09084	−	1.10045i	0.0963795	−	0.995345i	$-0.469274\pi$
$659$	1.09084	−	1.10045i	1.09084	−	1.10045i	0.994461	−	0.105110i	$-0.0335196\pi$
$660$		0			0
$661$		0			0		−0.774747	−	0.632271i	$-0.782123\pi$
$661$		0			0		0.774747	+	0.632271i	$0.217877\pi$
$662$	0.000836449	−	0.0953151i	0.000836449	−	0.0953151i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0335874	+	0.0109784i	0.0335874	+	0.0109784i
$667$	−0.572474	+	1.09255i	−0.572474	+	1.09255i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.66011	−	0.641158i	1.66011	−	0.641158i	0.665645	−	0.746268i	$-0.268156\pi$
$673$	1.66011	−	0.641158i	1.66011	−	0.641158i	0.994461	+	0.105110i	$0.0335196\pi$
$674$	−0.0510579	−	0.0572421i	−0.0510579	−	0.0572421i
$675$		0			0
$676$	−0.923811	−	0.375551i	−0.923811	−	0.375551i
$677$		0			0		−0.919626	−	0.392794i	$-0.871508\pi$
$677$		0			0		0.919626	+	0.392794i	$0.128492\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.965819	+	0.412524i	−0.965819	+	0.412524i	−0.817190	−	0.576369i	$-0.804469\pi$
$683$	−0.965819	+	0.412524i	−0.965819	+	0.412524i	−0.148629	+	0.988893i	$0.547486\pi$
$684$		0			0
$685$		0			0
$686$	−0.0430220	−	0.0303437i	−0.0430220	−	0.0303437i
$687$		0			0
$688$	0.967756	+	0.818497i	0.967756	+	0.818497i
$689$		0			0
$690$		0			0
$691$		0			0		−0.955819	−	0.293956i	$-0.905028\pi$
$691$		0			0		0.955819	+	0.293956i	$0.0949721\pi$
$692$		0			0
$693$	−1.91427	+	0.168417i	−1.91427	+	0.168417i
$694$	−0.0514200	+	0.0336283i	−0.0514200	+	0.0336283i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.199911	−	0.976985i	−0.199911	−	0.976985i
$701$	−1.95566	+	0.276407i	−1.95566	+	0.276407i	−0.999846	−	0.0175499i	$-0.994413\pi$
$701$	−1.95566	+	0.276407i	−1.95566	+	0.276407i	−0.955819	+	0.293956i	$0.905028\pi$
$702$		0			0
$703$		0			0
$704$	−0.443578	−	1.83698i	−0.443578	−	1.83698i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.586749	+	1.74315i	0.586749	+	1.74315i	0.665645	+	0.746268i	$0.268156\pi$
$709$	0.586749	+	1.74315i	0.586749	+	1.74315i	−0.0788965	+	0.996883i	$0.525140\pi$
$710$		0			0
$711$	−0.116863	−	0.310669i	−0.116863	−	0.310669i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.36862	+	0.168994i	1.36862	+	0.168994i
$717$		0			0
$718$	−0.0343489	−	0.0398972i	−0.0343489	−	0.0398972i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.0510651	+	0.0128060i	0.0510651	+	0.0128060i
$723$		0			0
$724$		0			0
$725$	0.589319	+	1.56665i	0.589319	+	1.56665i
$726$		0			0
$727$		0			0		−0.319015	−	0.947750i	$-0.603352\pi$
$727$		0			0		0.319015	+	0.947750i	$0.396648\pi$
$728$		0			0
$729$	0.827179	+	0.561938i	0.827179	+	0.561938i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.836914	−	0.547335i	$-0.815642\pi$
$733$		0			0		0.836914	+	0.547335i	$0.184358\pi$
$734$		0			0
$735$		0			0
$736$	0.0232452	+	0.113602i	0.0232452	+	0.113602i
$737$	0.235357	−	3.82662i	0.235357	−	3.82662i
$738$		0			0
$739$	1.82472	+	0.491793i	1.82472	+	0.491793i	0.997537	−	0.0701455i	$-0.0223464\pi$
$739$	1.82472	+	0.491793i	1.82472	+	0.491793i	0.827179	+	0.561938i	$0.189944\pi$
$740$		0			0
$741$		0			0
$742$	0.0877818	−	0.0574086i	0.0877818	−	0.0574086i
$743$	0.955507	−	0.0840655i	0.955507	−	0.0840655i	0.400849	−	0.916144i	$-0.368715\pi$
$743$	0.955507	−	0.0840655i	0.955507	−	0.0840655i	0.554658	+	0.832079i	$0.312849\pi$
$744$		0			0
$745$		0			0
$746$	−0.00322051	−	0.0281076i	−0.00322051	−	0.0281076i
$747$		0			0
$748$		0			0
$749$	1.09392	+	1.06549i	1.09392	+	1.06549i
$750$		0			0
$751$	−1.60687	+	0.588404i	−1.60687	+	0.588404i	−0.981422	−	0.191862i	$-0.938547\pi$
$751$	−1.60687	+	0.588404i	−1.60687	+	0.588404i	−0.625448	+	0.780266i	$0.715084\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.09354	+	1.31621i	−1.09354	+	1.31621i	−0.148629	+	0.988893i	$0.547486\pi$
$757$	−1.09354	+	1.31621i	−1.09354	+	1.31621i	−0.944914	+	0.327319i	$0.893855\pi$
$758$	0.00147335	−	0.00437713i	0.00147335	−	0.00437713i
$759$		0			0
$760$		0			0
$761$		0			0		−0.977904	−	0.209056i	$-0.932961\pi$
$761$		0			0		0.977904	+	0.209056i	$0.0670391\pi$
$762$		0			0
$763$	1.80141	−	0.695732i	1.80141	−	0.695732i
$764$	0.864959	+	1.04108i	0.864959	+	1.04108i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.464125	−	0.885770i	$-0.346369\pi$
$769$		0			0		−0.464125	+	0.885770i	$0.653631\pi$
$770$		0			0
$771$		0			0
$772$	1.61956	+	0.725621i	1.61956	+	0.725621i
$773$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$773$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$774$	−0.000590461		0.0672842i	−0.000590461		0.0672842i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0693095	−	0.0750116i	−0.0693095	−	0.0750116i
$779$		0			0
$780$		0			0
$781$	2.60018	−	2.12200i	2.60018	−	2.12200i
$782$		0			0
$783$		0			0
$784$	−0.965992	+	0.224307i	−0.965992	+	0.224307i
$785$		0			0
$786$		0			0
$787$		0			0		0.981422	−	0.191862i	$-0.0614525\pi$
$787$		0			0		−0.981422	+	0.191862i	$0.938547\pi$
$788$	0.417051	−	0.120292i	0.417051	−	0.120292i
$789$		0			0
$790$		0			0
$791$	−1.24138	−	1.25232i	−1.24138	−	1.25232i
$792$	0.120765	−	0.161996i	0.120765	−	0.161996i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$797$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$798$		0			0
$799$		0			0
$800$	0.136043	+	0.0790761i	0.136043	+	0.0790761i
$801$		0			0
$802$	−0.0612036	−	0.0341523i	−0.0612036	−	0.0341523i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.124291	+	0.417135i	0.124291	+	0.417135i	0.997537	−	0.0701455i	$-0.0223464\pi$
$809$	0.124291	+	0.417135i	0.124291	+	0.417135i	−0.873245	+	0.487281i	$0.837989\pi$
$810$		0			0
$811$		0			0		0.984638	−	0.174608i	$-0.0558659\pi$
$811$		0			0		−0.984638	+	0.174608i	$0.944134\pi$
$812$	1.54630	−	0.628607i	1.54630	−	0.628607i
$813$		0			0
$814$	−0.0641633	+	0.0222263i	−0.0641633	+	0.0222263i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.794662	+	1.19212i	0.794662	+	1.19212i	0.977904	+	0.209056i	$0.0670391\pi$
$821$	0.794662	+	1.19212i	0.794662	+	1.19212i	−0.183242	+	0.983068i	$0.558659\pi$
$822$		0			0
$823$	−0.390723	+	1.75233i	−0.390723	+	1.75233i	0.234725	+	0.972062i	$0.424581\pi$
$823$	−0.390723	+	1.75233i	−0.390723	+	1.75233i	−0.625448	+	0.780266i	$0.715084\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.00675187	+	0.769389i	0.00675187	+	0.769389i	0.926378	+	0.376595i	$0.122905\pi$
$827$	0.00675187	+	0.769389i	0.00675187	+	0.769389i	−0.919626	+	0.392794i	$0.871508\pi$
$828$	0.459616	−	0.573386i	0.459616	−	0.573386i
$829$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$829$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.368451	−	0.929647i	$-0.620112\pi$
$839$		0			0		0.368451	+	0.929647i	$0.379888\pi$
$840$		0			0
$841$	−1.54155	+	0.932607i	−1.54155	+	0.932607i
$842$	−0.0176386	−	0.0285861i	−0.0176386	−	0.0285861i
$843$		0			0
$844$	−1.66216	+	1.04586i	−1.66216	+	1.04586i
$845$		0			0
$846$		0			0
$847$	1.99373	−	1.81000i	1.99373	−	1.81000i
$848$	0.293654	−	1.95381i	0.293654	−	1.95381i
$849$		0			0
$850$		0			0
$851$	−0.472754	+	0.145393i	−0.472754	+	0.145393i
$852$		0			0
$853$		0			0		0.251749	−	0.967793i	$-0.418994\pi$
$853$		0			0		−0.251749	+	0.967793i	$0.581006\pi$
$854$		0			0
$855$		0			0
$856$	−0.160170	+	0.0112630i	−0.160170	+	0.0112630i
$857$		0			0		0.716353	−	0.697738i	$-0.245810\pi$
$857$		0			0		−0.716353	+	0.697738i	$0.754190\pi$
$858$		0			0
$859$		0			0		0.113833	−	0.993500i	$-0.463687\pi$
$859$		0			0		−0.113833	+	0.993500i	$0.536313\pi$
$860$		0			0
$861$		0			0
$862$	−0.00783746	+	0.0465698i	−0.00783746	+	0.0465698i
$863$	0.822676	−	0.268901i	0.822676	−	0.268901i	0.131251	−	0.991349i	$-0.458101\pi$
$863$	0.822676	−	0.268901i	0.822676	−	0.268901i	0.691425	+	0.722448i	$0.256983\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.539863	+	0.339691i	0.539863	+	0.339691i
$870$		0			0
$871$		0			0
$872$	−0.0714889	+	0.190047i	−0.0714889	+	0.190047i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.0168631	−	0.00486391i	−0.0168631	−	0.00486391i	0.268694	−	0.963225i	$-0.413408\pi$
$877$	−0.0168631	−	0.00486391i	−0.0168631	−	0.00486391i	−0.285558	+	0.958362i	$0.592179\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.889808	−	0.456335i	$-0.150838\pi$
$881$		0			0		−0.889808	+	0.456335i	$0.849162\pi$
$882$	−0.0419306	−	0.0318348i	−0.0419306	−	0.0318348i
$883$	−0.752417	−	1.80528i	−0.752417	−	1.80528i	−0.569175	−	0.822216i	$-0.692737\pi$
$883$	−0.752417	−	1.80528i	−0.752417	−	1.80528i	−0.183242	−	0.983068i	$-0.558659\pi$
$884$		0			0
$885$		0			0
$886$	0.0471269	+	0.0344931i	0.0471269	+	0.0344931i
$887$		0			0		−0.990159	−	0.139946i	$-0.955307\pi$
$887$		0			0		0.990159	+	0.139946i	$0.0446927\pi$
$888$		0			0
$889$	−1.42978	+	0.385350i	−1.42978	+	0.385350i
$890$		0			0
$891$	−1.91900	+	0.101133i	−1.91900	+	0.101133i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.100298	−	0.183508i	0.100298	−	0.183508i
$897$		0			0
$898$	0.0735670	−	0.00908387i	0.0735670	−	0.00908387i
$899$		0			0
$900$	−0.165501	−	0.983399i	−0.165501	−	0.983399i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.185151	−	0.00975766i	0.185151	−	0.00975766i
$905$		0			0
$906$		0			0
$907$	−0.0182484	−	0.296697i	−0.0182484	−	0.296697i	−0.996152	−	0.0876414i	$-0.972067\pi$
$907$	−0.0182484	−	0.296697i	−0.0182484	−	0.296697i	0.977904	−	0.209056i	$-0.0670391\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.28485	−	0.227845i	−1.28485	−	0.227845i	−0.510099	−	0.860116i	$-0.670391\pi$
$911$	−1.28485	−	0.227845i	−1.28485	−	0.227845i	−0.774747	+	0.632271i	$0.782123\pi$
$912$		0			0
$913$		0			0
$914$	−0.0756032	+	0.0387728i	−0.0756032	+	0.0387728i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.89371	−	0.166609i	−1.89371	−	0.166609i	−0.919626	−	0.392794i	$-0.871508\pi$
$919$	−1.89371	−	0.166609i	−1.89371	−	0.166609i	−0.974084	+	0.226186i	$0.927374\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.279799	+	0.610097i	−0.279799	+	0.610097i
$926$	−0.0371505	−	0.0233757i	−0.0371505	−	0.0233757i
$927$		0			0
$928$	−0.0883920	+	0.248111i	−0.0883920	+	0.248111i
$929$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$929$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$930$		0			0
$931$		0			0
$932$	1.13306	−	0.370352i	1.13306	−	0.370352i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.987551	−	0.157301i	$-0.0502793\pi$
$937$		0			0		−0.987551	+	0.157301i	$0.949721\pi$
$938$	0.0752409	−	0.0732857i	0.0752409	−	0.0732857i
$939$		0			0
$940$		0			0
$941$		0			0		−0.974084	−	0.226186i	$-0.927374\pi$
$941$		0			0		0.974084	+	0.226186i	$0.0726257\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.0772814	−	0.103666i	−0.0772814	−	0.103666i
$947$	0.242916	−	1.61623i	0.242916	−	1.61623i	−0.448509	−	0.893778i	$-0.648045\pi$
$947$	0.242916	−	1.61623i	0.242916	−	1.61623i	0.691425	−	0.722448i	$-0.256983\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.858237	−	1.39091i	−0.858237	−	1.39091i	−0.919626	−	0.392794i	$-0.871508\pi$
$953$	−0.858237	−	1.39091i	−0.858237	−	1.39091i	0.0613892	−	0.998114i	$-0.480447\pi$
$954$	0.0897424	−	0.0542925i	0.0897424	−	0.0542925i
$955$		0			0
$956$	−0.680758	−	1.71764i	−0.680758	−	1.71764i
$957$		0			0
$958$		0			0
$959$	1.43409	−	1.12902i	1.43409	−	1.12902i
$960$		0			0
$961$	0.0263232	+	0.999653i	0.0263232	+	0.999653i
$962$		0			0
$963$	1.05585	+	1.10322i	1.05585	+	1.10322i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.996288	−	1.24290i	0.996288	−	1.24290i	0.0263232	−	0.999653i	$-0.491620\pi$
$967$	0.996288	−	1.24290i	0.996288	−	1.24290i	0.969965	−	0.243246i	$-0.0782123\pi$
$968$	0.00248461	+	0.283126i	0.00248461	+	0.283126i
$969$		0			0
$970$		0			0
$971$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$971$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$972$		0			0
$973$		0			0
$974$	−0.0579612	−	0.0869514i	−0.0579612	−	0.0869514i
$975$		0			0
$976$		0			0
$977$	−1.20809	−	0.192429i	−1.20809	−	0.192429i	−0.479599	−	0.877488i	$-0.659218\pi$
$977$	−1.20809	−	0.192429i	−1.20809	−	0.192429i	−0.728488	+	0.685059i	$0.759777\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.82472	−	0.632084i	1.82472	−	0.632084i
$982$	0.0568460		0.000997796i	0.0568460		0.000997796i
$983$		0			0		0.926378	−	0.376595i	$-0.122905\pi$
$983$		0			0		−0.926378	+	0.376595i	$0.877095\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.536065	−	0.774386i	−0.536065	−	0.774386i
$990$		0			0
$991$	0.963998	+	0.333930i	0.963998	+	0.333930i	0.763532	−	0.645770i	$-0.223464\pi$
$991$	0.963998	+	0.333930i	0.963998	+	0.333930i	0.200467	+	0.979701i	$0.435754\pi$
$992$		0			0
$993$		0			0
$994$	0.0918189	+	0.00483896i	0.0918189	+	0.00483896i
$995$		0			0
$996$		0			0
$997$		0			0		0.432754	−	0.901512i	$-0.357542\pi$
$997$		0			0		−0.432754	+	0.901512i	$0.642458\pi$
$998$	−0.0952601	+	0.00334515i	−0.0952601	+	0.00334515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.391.1	✓	178
7.6	odd	2	CM	2513.1.l.a.391.1	✓	178
359.101	even	179	inner	2513.1.l.a.1896.1	yes	178
2513.1896	odd	358	inner	2513.1.l.a.1896.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.391.1	✓	178	1.1	even	1	trivial
2513.1.l.a.391.1	✓	178	7.6	odd	2	CM
2513.1.l.a.1896.1	yes	178	359.101	even	179	inner
2513.1.l.a.1896.1	yes	178	2513.1896	odd	358	inner

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:	\( N \)	\(=\)	\( 2513 = 7 \cdot 359 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2513.l (of order \(358\), degree \(178\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0522495 - 0.00645163i) q^{2} +(-0.967276 - 0.242572i) q^{4} +(-0.352079 - 0.935970i) q^{7} +(0.0980855 + 0.0378821i) q^{8} +(-0.319015 - 0.947750i) q^{9} +O(q^{10})\)	\(q+(-0.0522495 - 0.00645163i) q^{2} +(-0.967276 - 0.242572i) q^{4} +(-0.352079 - 0.935970i) q^{7} +(0.0980855 + 0.0378821i) q^{8} +(-0.319015 - 0.947750i) q^{9} +(1.58956 + 1.07985i) q^{11} +(0.0123574 + 0.0511755i) q^{14} +(0.874338 + 0.467960i) q^{16} +(0.0105538 + 0.0515776i) q^{18} +(-0.0760868 - 0.0666771i) q^{22} +(-0.536824 - 0.504821i) q^{23} +(-0.996152 + 0.0876414i) q^{25} +(0.113517 + 0.990746i) q^{28} +(-0.449748 - 1.61227i) q^{29} +(-0.128589 - 0.0906949i) q^{32} +(0.0786778 + 0.994120i) q^{36} +(0.332192 - 0.583227i) q^{37} +(1.24985 + 0.267193i) q^{43} +(-1.27560 - 1.43010i) q^{44} +(0.0247919 + 0.0298400i) q^{46} +(-0.752081 + 0.659071i) q^{49} +(0.0526139 + 0.00184759i) q^{50} +(-0.668614 - 1.87676i) q^{53} +(0.000922692 - 0.105143i) q^{56} +(0.0130973 + 0.0871421i) q^{58} +(-0.774747 + 0.632271i) q^{63} +(-0.728114 - 0.661016i) q^{64} +(-1.01768 - 1.71599i) q^{67} +(0.498724 - 1.67377i) q^{71} +(0.00461204 - 0.105046i) q^{72} +(-0.0211196 + 0.0283301i) q^{74} +(0.451062 - 1.86797i) q^{77} +(0.331718 - 0.0116486i) q^{79} +(-0.796459 + 0.604692i) q^{81} +(-0.0635802 - 0.0220243i) q^{86} +(0.115005 + 0.166134i) q^{88} +(0.396802 + 0.618520i) q^{92} +(0.0435479 - 0.0295840i) q^{98} +(0.516340 - 1.85099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 178 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} - 6 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} - 7 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} - 4 q^{74} - 2 q^{77} - 2 q^{79} - q^{81} - 4 q^{86} - 8 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 178 * q - 2 * q^2 - 3 * q^4 - q^7 - 4 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 - 2 * q^43 - 6 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - 2 * q^53 - 4 * q^56 - 4 * q^58 - q^63 - 7 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 - 4 * q^74 - 2 * q^77 - 2 * q^79 - q^81 - 4 * q^86 - 8 * q^88 - 6 * q^92 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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