LMFDB - Embedded newform 2513.1.l.a.181.1

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			181.1
Root			$0.569175 - 0.822216i$ of defining polynomial
Character	$\chi$	$=$	2513.181
Dual form			2513.1.l.a.958.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0583943 + 0.0654670i) q^{2} +(0.112957 + 0.985854i) q^{4} +(0.432754 - 0.901512i) q^{7} +(-0.142826 - 0.100736i) q^{8} +(-0.999846 + 0.0175499i) q^{9} +O(q^{10})$	\(q+(-0.0583943 + 0.0654670i) q^{2} +(0.112957 + 0.985854i) q^{4} +(0.432754 - 0.901512i) q^{7} +(-0.142826 - 0.100736i) q^{8} +(-0.999846 + 0.0175499i) q^{9} +(1.67151 - 0.0880903i) q^{11} +(0.0337489 + 0.0809743i) q^{14} +(-0.951653 + 0.220977i) q^{16} +(0.0572363 - 0.0664817i) q^{18} +(-0.0918395 + 0.114573i) q^{22} +(1.94497 + 0.415796i) q^{23} +(0.368451 - 0.929647i) q^{25} +(0.937642 + 0.324800i) q^{28} +(-1.13555 - 0.0798502i) q^{29} +(0.124927 - 0.228570i) q^{32} +(-0.130241 - 0.983720i) q^{36} +(0.197890 + 1.06165i) q^{37} +(1.51549 + 0.554942i) q^{43} +(0.275652 + 1.63791i) q^{44} +(-0.140796 + 0.103051i) q^{46} +(-0.625448 - 0.780266i) q^{49} +(0.0393458 + 0.0784075i) q^{50} +(-0.397905 - 0.620239i) q^{53} +(-0.152623 + 0.0851652i) q^{56} +(0.0715370 - 0.0696780i) q^{58} +(-0.416866 + 0.908968i) q^{63} +(-0.320202 - 0.898787i) q^{64} +(1.11508 - 0.430663i) q^{67} +(-0.296126 + 0.565147i) q^{71} +(0.144572 + 0.0982136i) q^{72} +(-0.0810589 - 0.0490392i) q^{74} +(0.643937 - 1.54501i) q^{77} +(-0.870075 + 1.73387i) q^{79} +(0.999384 - 0.0350944i) q^{81} +(-0.124826 + 0.0668091i) q^{86} +(-0.247608 - 0.155799i) q^{88} +(-0.190216 + 1.96443i) q^{92} +(0.0876043 + 0.00461684i) q^{98} +(-1.66970 + 0.117412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{115}{179}\right)$

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 $

$2$	−0.0583943	+	0.0654670i	−0.0583943	+	0.0654670i	−0.774747	−	0.632271i	$-0.782123\pi$
$2$	−0.0583943	+	0.0654670i	−0.0583943	+	0.0654670i	0.716353	+	0.697738i	$0.245810\pi$
$3$		0			0		−0.00877529	−	0.999961i	$-0.502793\pi$
$3$		0			0		0.00877529	+	0.999961i	$0.497207\pi$
$4$	0.112957	+	0.985854i	0.112957	+	0.985854i
$5$		0			0		0.827179	−	0.561938i	$-0.189944\pi$
$5$		0			0		−0.827179	+	0.561938i	$0.810056\pi$
$6$		0			0
$7$	0.432754	−	0.901512i	0.432754	−	0.901512i
$7$	0.432754	−	0.901512i	0.432754	−	0.901512i
$8$	−0.142826	−	0.100736i	−0.142826	−	0.100736i
$9$	−0.999846	+	0.0175499i	−0.999846	+	0.0175499i
$10$		0			0
$11$	1.67151	−	0.0880903i	1.67151	−	0.0880903i	0.806949	−	0.590621i	$-0.201117\pi$
$11$	1.67151	−	0.0880903i	1.67151	−	0.0880903i	0.864559	+	0.502531i	$0.167598\pi$
$12$		0			0
$13$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$13$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$14$	0.0337489	+	0.0809743i	0.0337489	+	0.0809743i
$15$		0			0
$16$	−0.951653	+	0.220977i	−0.951653	+	0.220977i
$17$		0			0		0.285558	−	0.958362i	$-0.407821\pi$
$17$		0			0		−0.285558	+	0.958362i	$0.592179\pi$
$18$	0.0572363	−	0.0664817i	0.0572363	−	0.0664817i
$19$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$19$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$20$		0			0
$21$		0			0
$22$	−0.0918395	+	0.114573i	−0.0918395	+	0.114573i
$23$	1.94497	+	0.415796i	1.94497	+	0.415796i	0.994461	+	0.105110i	$0.0335196\pi$
$23$	1.94497	+	0.415796i	1.94497	+	0.415796i	0.950513	+	0.310686i	$0.100559\pi$
$24$		0			0
$25$	0.368451	−	0.929647i	0.368451	−	0.929647i
$26$		0			0
$27$		0			0
$28$	0.937642	+	0.324800i	0.937642	+	0.324800i
$29$	−1.13555	−	0.0798502i	−1.13555	−	0.0798502i	−0.510099	−	0.860116i	$-0.670391\pi$
$29$	−1.13555	−	0.0798502i	−1.13555	−	0.0798502i	−0.625448	+	0.780266i	$0.715084\pi$
$30$		0			0
$31$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$31$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$32$	0.124927	−	0.228570i	0.124927	−	0.228570i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.130241	−	0.983720i	−0.130241	−	0.983720i
$37$	0.197890	+	1.06165i	0.197890	+	1.06165i	0.926378	+	0.376595i	$0.122905\pi$
$37$	0.197890	+	1.06165i	0.197890	+	1.06165i	−0.728488	+	0.685059i	$0.759777\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.148629	−	0.988893i	$-0.452514\pi$
$41$		0			0		−0.148629	+	0.988893i	$0.547486\pi$
$42$		0			0
$43$	1.51549	+	0.554942i	1.51549	+	0.554942i	0.960831	−	0.277137i	$-0.0893855\pi$
$43$	1.51549	+	0.554942i	1.51549	+	0.554942i	0.554658	+	0.832079i	$0.312849\pi$
$44$	0.275652	+	1.63791i	0.275652	+	1.63791i
$45$		0			0
$46$	−0.140796	+	0.103051i	−0.140796	+	0.103051i
$47$		0			0		−0.319015	−	0.947750i	$-0.603352\pi$
$47$		0			0		0.319015	+	0.947750i	$0.396648\pi$
$48$		0			0
$49$	−0.625448	−	0.780266i	−0.625448	−	0.780266i
$50$	0.0393458	+	0.0784075i	0.0393458	+	0.0784075i
$51$		0			0
$52$		0			0
$53$	−0.397905	−	0.620239i	−0.397905	−	0.620239i	0.583517	−	0.812101i	$-0.301676\pi$
$53$	−0.397905	−	0.620239i	−0.397905	−	0.620239i	−0.981422	+	0.191862i	$0.938547\pi$
$54$		0			0
$55$		0			0
$56$	−0.152623	+	0.0851652i	−0.152623	+	0.0851652i
$57$		0			0
$58$	0.0715370	−	0.0696780i	0.0715370	−	0.0696780i
$59$		0			0		0.251749	−	0.967793i	$-0.418994\pi$
$59$		0			0		−0.251749	+	0.967793i	$0.581006\pi$
$60$		0			0
$61$		0			0		−0.268694	−	0.963225i	$-0.586592\pi$
$61$		0			0		0.268694	+	0.963225i	$0.413408\pi$
$62$		0			0
$63$	−0.416866	+	0.908968i	−0.416866	+	0.908968i
$64$	−0.320202	−	0.898787i	−0.320202	−	0.898787i
$65$		0			0
$66$		0			0
$67$	1.11508	−	0.430663i	1.11508	−	0.430663i	0.268694	−	0.963225i	$-0.413408\pi$
$67$	1.11508	−	0.430663i	1.11508	−	0.430663i	0.846391	+	0.532563i	$0.178771\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.296126	+	0.565147i	−0.296126	+	0.565147i	−0.987551	−	0.157301i	$-0.949721\pi$
$71$	−0.296126	+	0.565147i	−0.296126	+	0.565147i	0.691425	+	0.722448i	$0.256983\pi$
$72$	0.144572	+	0.0982136i	0.144572	+	0.0982136i
$73$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$73$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$74$	−0.0810589	−	0.0490392i	−0.0810589	−	0.0490392i
$75$		0			0
$76$		0			0
$77$	0.643937	−	1.54501i	0.643937	−	1.54501i
$78$		0			0
$79$	−0.870075	+	1.73387i	−0.870075	+	1.73387i	−0.217629	+	0.976031i	$0.569832\pi$
$79$	−0.870075	+	1.73387i	−0.870075	+	1.73387i	−0.652446	+	0.757835i	$0.726257\pi$
$80$		0			0
$81$	0.999384	−	0.0350944i	0.999384	−	0.0350944i
$82$		0			0
$83$		0			0		−0.996152	−	0.0876414i	$-0.972067\pi$
$83$		0			0		0.996152	+	0.0876414i	$0.0279330\pi$
$84$		0			0
$85$		0			0
$86$	−0.124826	+	0.0668091i	−0.124826	+	0.0668091i
$87$		0			0
$88$	−0.247608	−	0.155799i	−0.247608	−	0.155799i
$89$		0			0		−0.994461	−	0.105110i	$-0.966480\pi$
$89$		0			0		0.994461	+	0.105110i	$0.0335196\pi$
$90$		0			0
$91$		0			0
$92$	−0.190216	+	1.96443i	−0.190216	+	1.96443i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$97$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$98$	0.0876043	+	0.00461684i	0.0876043	+	0.00461684i
$99$	−1.66970	+	0.117412i	−1.66970	+	0.117412i
$100$	0.958116	+	0.258229i	0.958116	+	0.258229i
$101$		0			0		−0.479599	−	0.877488i	$-0.659218\pi$
$101$		0			0		0.479599	+	0.877488i	$0.340782\pi$
$102$		0			0
$103$		0			0		0.897680	−	0.440648i	$-0.145251\pi$
$103$		0			0		−0.897680	+	0.440648i	$0.854749\pi$
$104$		0			0
$105$		0			0
$106$	0.0638405	+	0.0101688i	0.0638405	+	0.0101688i
$107$	−1.88670	−	0.616688i	−1.88670	−	0.616688i	−0.981422	−	0.191862i	$-0.938547\pi$
$107$	−1.88670	−	0.616688i	−1.88670	−	0.616688i	−0.905275	−	0.424826i	$-0.860335\pi$
$108$		0			0
$109$	1.58105	+	0.882246i	1.58105	+	0.882246i	0.997537	+	0.0701455i	$0.0223464\pi$
$109$	1.58105	+	0.882246i	1.58105	+	0.882246i	0.583517	+	0.812101i	$0.301676\pi$
$110$		0			0
$111$		0			0
$112$	−0.212618	+	0.953555i	−0.212618	+	0.953555i
$113$	−1.48749	+	1.25807i	−1.48749	+	1.25807i	−0.597680	+	0.801735i	$0.703911\pi$
$113$	−1.48749	+	1.25807i	−1.48749	+	1.25807i	−0.889808	+	0.456335i	$0.849162\pi$
$114$		0			0
$115$		0			0
$116$	−0.0495471	−	1.12850i	−0.0495471	−	1.12850i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.79172	−	0.189377i	1.79172	−	0.189377i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.0351648	−	0.0803695i	−0.0351648	−	0.0803695i
$127$	−0.520008	−	0.424378i	−0.520008	−	0.424378i	0.335599	−	0.942005i	$-0.391061\pi$
$127$	−0.520008	−	0.424378i	−0.520008	−	0.424378i	−0.855607	+	0.517627i	$0.826816\pi$
$128$	0.318844	+	0.129618i	0.318844	+	0.129618i
$129$		0			0
$130$		0			0
$131$		0			0		0.855607	−	0.517627i	$-0.173184\pi$
$131$		0			0		−0.855607	+	0.517627i	$0.826816\pi$
$132$		0			0
$133$		0			0
$134$	−0.0369204	+	0.0981495i	−0.0369204	+	0.0981495i
$135$		0			0
$136$		0			0
$137$	−0.778953	+	1.31345i	−0.778953	+	1.31345i	0.165961	+	0.986132i	$0.446927\pi$
$137$	−0.778953	+	1.31345i	−0.778953	+	1.31345i	−0.944914	+	0.327319i	$0.893855\pi$
$138$		0			0
$139$		0			0		−0.691425	−	0.722448i	$-0.743017\pi$
$139$		0			0		0.691425	+	0.722448i	$0.256983\pi$
$140$		0			0
$141$		0			0
$142$	−0.0197064	−	0.0523878i	−0.0197064	−	0.0523878i
$143$		0			0
$144$	0.947628	−	0.237645i	0.947628	−	0.237645i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.02428	+	0.315012i	−1.02428	+	0.315012i
$149$	0.943052	−	1.46999i	0.943052	−	1.46999i	0.0613892	−	0.998114i	$-0.480447\pi$
$149$	0.943052	−	1.46999i	0.943052	−	1.46999i	0.881663	−	0.471880i	$-0.156425\pi$
$150$		0			0
$151$	−0.146905	+	0.335752i	−0.146905	+	0.335752i	−0.974084	−	0.226186i	$-0.927374\pi$
$151$	−0.146905	+	0.335752i	−0.146905	+	0.335752i	0.827179	+	0.561938i	$0.189944\pi$
$152$		0			0
$153$		0			0
$154$	0.0635447	+	0.132376i	0.0635447	+	0.132376i
$155$		0			0
$156$		0			0
$157$		0			0		−0.974084	−	0.226186i	$-0.927374\pi$
$157$		0			0		0.974084	+	0.226186i	$0.0726257\pi$
$158$	−0.0627037	−	0.158209i	−0.0627037	−	0.158209i
$159$		0			0
$160$		0			0
$161$	1.21654	−	1.57348i	1.21654	−	1.57348i
$162$	−0.0560608	+	0.0674760i	−0.0560608	+	0.0674760i
$163$	0.111086	−	0.112065i	0.111086	−	0.112065i	−0.652446	−	0.757835i	$-0.726257\pi$
$163$	0.111086	−	0.112065i	0.111086	−	0.112065i	0.763532	+	0.645770i	$0.223464\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.939024	−	0.343852i	$-0.111732\pi$
$167$		0			0		−0.939024	+	0.343852i	$0.888268\pi$
$168$		0			0
$169$	−0.285558	−	0.958362i	−0.285558	−	0.958362i
$170$		0			0
$171$		0			0
$172$	−0.375907	+	1.55673i	−0.375907	+	1.55673i
$173$		0			0		0.996152	−	0.0876414i	$-0.0279330\pi$
$173$		0			0		−0.996152	+	0.0876414i	$0.972067\pi$
$174$		0			0
$175$	−0.678640	−	0.734471i	−0.678640	−	0.734471i
$176$	−1.57123	+	0.453197i	−1.57123	+	0.453197i
$177$		0			0
$178$		0			0
$179$	−1.27247	−	1.42659i	−1.27247	−	1.42659i	−0.855607	−	0.517627i	$-0.826816\pi$
$179$	−1.27247	−	1.42659i	−1.27247	−	1.42659i	−0.416866	−	0.908968i	$-0.636872\pi$
$180$		0			0
$181$		0			0		0.740398	−	0.672168i	$-0.234637\pi$
$181$		0			0		−0.740398	+	0.672168i	$0.765363\pi$
$182$		0			0
$183$		0			0
$184$	−0.235907	−	0.255315i	−0.235907	−	0.255315i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.744447	−	1.30702i	−0.744447	−	1.30702i	−0.944914	−	0.327319i	$-0.893855\pi$
$191$	−0.744447	−	1.30702i	−0.744447	−	1.30702i	0.200467	−	0.979701i	$-0.435754\pi$
$192$		0			0
$193$	1.02571	−	0.964559i	1.02571	−	0.964559i	0.0263232	−	0.999653i	$-0.491620\pi$
$193$	1.02571	−	0.964559i	1.02571	−	0.964559i	0.999384	+	0.0350944i	$0.0111732\pi$
$194$		0			0
$195$		0			0
$196$	0.698580	−	0.704737i	0.698580	−	0.704737i
$197$	−1.26218	+	1.51919i	−1.26218	+	1.51919i	−0.510099	+	0.860116i	$0.670391\pi$
$197$	−1.26218	+	1.51919i	−1.26218	+	1.51919i	−0.752081	+	0.659071i	$0.770950\pi$
$198$	0.0898146	−	0.116167i	0.0898146	−	0.116167i
$199$		0			0		−0.0963795	−	0.995345i	$-0.530726\pi$
$199$		0			0		0.0963795	+	0.995345i	$0.469274\pi$
$200$	−0.146273	+	0.0956613i	−0.146273	+	0.0956613i
$201$		0			0
$202$		0			0
$203$	−0.563398	+	0.989153i	−0.563398	+	0.989153i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.95197	−	0.381598i	−1.95197	−	0.381598i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.39260	−	0.428287i	1.39260	−	0.428287i	0.494925	−	0.868936i	$-0.335196\pi$
$211$	1.39260	−	0.428287i	1.39260	−	0.428287i	0.897680	+	0.440648i	$0.145251\pi$
$212$	0.566519	−	0.462336i	0.566519	−	0.462336i
$213$		0			0
$214$	0.150545	−	0.0875054i	0.150545	−	0.0875054i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.150083	+	0.0519888i	−0.150083	+	0.0519888i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$223$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$224$	−0.151996	−	0.211538i	−0.151996	−	0.211538i
$225$	−0.352079	+	0.935970i	−0.352079	+	0.935970i
$226$	0.00449875	−	0.170845i	0.00449875	−	0.170845i
$227$		0			0		0.984638	−	0.174608i	$-0.0558659\pi$
$227$		0			0		−0.984638	+	0.174608i	$0.944134\pi$
$228$		0			0
$229$		0			0		−0.716353	−	0.697738i	$-0.754190\pi$
$229$		0			0		0.716353	+	0.697738i	$0.245810\pi$
$230$		0			0
$231$		0			0
$232$	0.154141	+	0.125795i	0.154141	+	0.125795i
$233$	−0.685939	−	1.56772i	−0.685939	−	1.56772i	−0.817190	−	0.576369i	$-0.804469\pi$
$233$	−0.685939	−	1.56772i	−0.685939	−	1.56772i	0.131251	−	0.991349i	$-0.458101\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.0161400	−	1.83918i	0.0161400	−	1.83918i	−0.384709	−	0.923038i	$-0.625698\pi$
$239$	0.0161400	−	1.83918i	0.0161400	−	1.83918i	0.400849	−	0.916144i	$-0.368715\pi$
$240$		0			0
$241$		0			0		−0.554658	−	0.832079i	$-0.687151\pi$
$241$		0			0		0.554658	+	0.832079i	$0.312849\pi$
$242$	−0.0922281	+	0.128357i	−0.0922281	+	0.128357i
$243$		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		0.990159	−	0.139946i	$-0.0446927\pi$
$251$		0			0		−0.990159	+	0.139946i	$0.955307\pi$
$252$	−0.943198	−	0.308295i	−0.943198	−	0.308295i
$253$	3.28767	+	0.523673i	3.28767	+	0.523673i
$254$	0.0581483	−	0.00926210i	0.0581483	−	0.00926210i
$255$		0			0
$256$	0.829391	−	0.407127i	0.829391	−	0.407127i
$257$		0			0		0.846391	−	0.532563i	$-0.178771\pi$
$257$		0			0		−0.846391	+	0.532563i	$0.821229\pi$
$258$		0			0
$259$	1.04273	+	0.281034i	1.04273	+	0.281034i
$260$		0			0
$261$	1.13677	+	0.0599092i	1.13677	+	0.0599092i
$262$		0			0
$263$	0.169948	+	0.0909592i	0.169948	+	0.0909592i	0.554658	−	0.832079i	$-0.312849\pi$
$263$	0.169948	+	0.0909592i	0.169948	+	0.0909592i	−0.384709	+	0.923038i	$0.625698\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.550527	+	1.05066i	0.550527	+	1.05066i
$269$		0			0		0.113833	−	0.993500i	$-0.463687\pi$
$269$		0			0		−0.113833	+	0.993500i	$0.536313\pi$
$270$		0			0
$271$		0			0		−0.846391	−	0.532563i	$-0.821229\pi$
$271$		0			0		0.846391	+	0.532563i	$0.178771\pi$
$272$		0			0
$273$		0			0
$274$	−0.0405014	−	0.127694i	−0.0405014	−	0.127694i
$275$	0.533976	−	1.58637i	0.533976	−	1.58637i
$276$		0			0
$277$	0.386409	+	0.465090i	0.386409	+	0.465090i	0.926378	−	0.376595i	$-0.122905\pi$
$277$	0.386409	+	0.465090i	0.386409	+	0.465090i	−0.539970	+	0.841685i	$0.681564\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.95310	+	0.417533i	−1.95310	+	0.417533i	−0.965546	+	0.260231i	$0.916201\pi$
$281$	−1.95310	+	0.417533i	−1.95310	+	0.417533i	−0.987551	+	0.157301i	$0.949721\pi$
$282$		0			0
$283$		0			0		−0.510099	−	0.860116i	$-0.670391\pi$
$283$		0			0		0.510099	+	0.860116i	$0.329609\pi$
$284$	−0.590602	−	0.228099i	−0.590602	−	0.228099i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.120896	+	0.230727i	−0.120896	+	0.230727i
$289$	−0.836914	−	0.547335i	−0.836914	−	0.547335i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.785724	−	0.618577i	$-0.787709\pi$
$293$		0			0		0.785724	+	0.618577i	$0.212291\pi$
$294$		0			0
$295$		0			0
$296$	0.0786826	−	0.171566i	0.0786826	−	0.171566i
$297$		0			0
$298$	0.0411673	+	0.147578i	0.0411673	+	0.147578i
$299$		0			0
$300$		0			0
$301$	1.15612	−	1.12608i	1.15612	−	1.12608i
$302$	−0.0134023	−	0.0292234i	−0.0134023	−	0.0292234i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.864559	−	0.502531i	$-0.832402\pi$
$307$		0			0		0.864559	+	0.502531i	$0.167598\pi$
$308$	1.59589	+	0.460309i	1.59589	+	0.460309i
$309$		0			0
$310$		0			0
$311$		0			0		−0.234725	−	0.972062i	$-0.575419\pi$
$311$		0			0		0.234725	+	0.972062i	$0.424581\pi$
$312$		0			0
$313$		0			0		0.806949	−	0.590621i	$-0.201117\pi$
$313$		0			0		−0.806949	+	0.590621i	$0.798883\pi$
$314$		0			0
$315$		0			0
$316$	−1.80762	−	0.661915i	−1.80762	−	0.661915i
$317$	−1.17537	+	0.502027i	−1.17537	+	0.502027i	−0.889808	−	0.456335i	$-0.849162\pi$
$317$	−1.17537	+	0.502027i	−1.17537	+	0.502027i	−0.285558	+	0.958362i	$0.592179\pi$
$318$		0			0
$319$	−1.90511	−	0.0334396i	−1.90511	−	0.0334396i
$320$		0			0
$321$		0			0
$322$	0.0319720	+	0.171525i	0.0319720	+	0.171525i
$323$		0			0
$324$	0.147485	+	0.981283i	0.147485	+	0.981283i
$325$		0			0
$326$	0.000849781		0.0138164i	0.000849781		0.0138164i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.79631	−	0.622242i	−1.79631	−	0.622242i	−0.999846	−	0.0175499i	$-0.994413\pi$
$331$	−1.79631	−	0.622242i	−1.79631	−	0.622242i	−0.796459	−	0.604692i	$-0.793296\pi$
$332$		0			0
$333$	−0.216492	−	1.05802i	−0.216492	−	1.05802i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.22326	+	1.52605i	−1.22326	+	1.52605i	−0.448509	+	0.893778i	$0.648045\pi$
$337$	−1.22326	+	1.52605i	−1.22326	+	1.52605i	−0.774747	+	0.632271i	$0.782123\pi$
$338$	0.0794160	+	0.0372682i	0.0794160	+	0.0372682i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.974084	+	0.226186i	−0.974084	+	0.226186i
$344$	−0.160548	−	0.231924i	−0.160548	−	0.231924i
$345$		0			0
$346$		0			0
$347$	0.0174183	−	0.00215077i	0.0174183	−	0.00215077i	−0.113833	−	0.993500i	$-0.536313\pi$
$347$	0.0174183	−	0.00215077i	0.0174183	−	0.00215077i	0.131251	+	0.991349i	$0.458101\pi$
$348$		0			0
$349$		0			0		0.131251	−	0.991349i	$-0.458101\pi$
$349$		0			0		−0.131251	+	0.991349i	$0.541899\pi$
$350$	0.0877123	−	0.00153958i	0.0877123	−	0.00153958i
$351$		0			0
$352$	0.188682	−	0.393061i	0.188682	−	0.393061i
$353$		0			0		−0.752081	−	0.659071i	$-0.770950\pi$
$353$		0			0		0.752081	+	0.659071i	$0.229050\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.167700			0.167700
$359$	0.335599	+	0.942005i	0.335599	+	0.942005i
$359$	0.335599	+	0.942005i	0.335599	+	0.942005i
$360$		0			0
$361$	0.665645	−	0.746268i	0.665645	−	0.746268i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.817190	−	0.576369i	$-0.804469\pi$
$367$		0			0		0.817190	+	0.576369i	$0.195531\pi$
$368$	−1.94282	+	0.0341016i	−1.94282	+	0.0341016i
$369$		0			0
$370$		0			0
$371$	−0.731348	+	0.0903049i	−0.731348	+	0.0903049i
$372$		0			0
$373$	−0.767523	−	1.84153i	−0.767523	−	1.84153i	−0.448509	−	0.893778i	$-0.648045\pi$
$373$	−0.767523	−	1.84153i	−0.767523	−	1.84153i	−0.319015	−	0.947750i	$-0.603352\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.07938	−	1.25373i	−1.07938	−	1.25373i	−0.965546	−	0.260231i	$-0.916201\pi$
$379$	−1.07938	−	1.25373i	−1.07938	−	1.25373i	−0.113833	−	0.993500i	$-0.536313\pi$
$380$		0			0
$381$		0			0
$382$	0.129038	+	0.0275857i	0.129038	+	0.0275857i
$383$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$383$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$384$		0			0
$385$		0			0
$386$	0.00325137	+	0.123475i	0.00325137	+	0.123475i
$387$	−1.52499	−	0.528260i	−1.52499	−	0.528260i
$388$		0			0
$389$	0.225950	+	0.0278997i	0.225950	+	0.0278997i	0.234725	−	0.972062i	$-0.424581\pi$
$389$	0.225950	+	0.0278997i	0.225950	+	0.0278997i	−0.00877529	+	0.999961i	$0.502793\pi$
$390$		0			0
$391$		0			0
$392$	0.0107294	+	0.174447i	0.0107294	+	0.174447i
$393$		0			0
$394$	−0.0257526	−	0.171343i	−0.0257526	−	0.171343i
$395$		0			0
$396$	−0.304355	−	1.63282i	−0.304355	−	1.63282i
$397$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$397$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$398$		0			0
$399$		0			0
$400$	−0.145206	+	0.966121i	−0.145206	+	0.966121i
$401$	−0.305244	+	0.130377i	−0.305244	+	0.130377i	−0.539970	−	0.841685i	$-0.681564\pi$
$401$	−0.305244	+	0.130377i	−0.305244	+	0.130377i	0.234725	+	0.972062i	$0.424581\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.0318577	−	0.0946449i	−0.0318577	−	0.0946449i
$407$	0.424297	+	1.75713i	0.424297	+	1.75713i
$408$		0			0
$409$		0			0		−0.448509	−	0.893778i	$-0.648045\pi$
$409$		0			0		0.448509	+	0.893778i	$0.351955\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.138966	−	0.105507i	0.138966	−	0.105507i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.752081	−	0.659071i	$-0.229050\pi$
$419$		0			0		−0.752081	+	0.659071i	$0.770950\pi$
$420$		0			0
$421$	0.157769	+	1.99346i	0.157769	+	1.99346i	0.0963795	+	0.995345i	$0.469274\pi$
$421$	0.157769	+	1.99346i	0.157769	+	1.99346i	0.0613892	+	0.998114i	$0.480447\pi$
$422$	−0.0532815	+	0.116179i	−0.0532815	+	0.116179i
$423$		0			0
$424$	−0.00564924	+	0.128669i	−0.00564924	+	0.128669i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.394849	−	1.92967i	0.394849	−	1.92967i
$429$		0			0
$430$		0			0
$431$	0.444517	+	0.301979i	0.444517	+	0.301979i	0.763532	−	0.645770i	$-0.223464\pi$
$431$	0.444517	+	0.301979i	0.444517	+	0.301979i	−0.319015	+	0.947750i	$0.603352\pi$
$432$		0			0
$433$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$433$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$434$		0			0
$435$		0			0
$436$	−0.691175	+	1.65834i	−0.691175	+	1.65834i
$437$		0			0
$438$		0			0
$439$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$439$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$440$		0			0
$441$	0.639045	+	0.769169i	0.639045	+	0.769169i
$442$		0			0
$443$	−0.572746	+	1.70155i	−0.572746	+	1.70155i	0.131251	+	0.991349i	$0.458101\pi$
$443$	−0.572746	+	1.70155i	−0.572746	+	1.70155i	−0.703997	+	0.710203i	$0.748603\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.948835	−	0.100288i	−0.948835	−	0.100288i
$449$	0.0573145	−	0.500224i	0.0573145	−	0.500224i	−0.932845	−	0.360279i	$-0.882682\pi$
$449$	0.0573145	−	0.500224i	0.0573145	−	0.500224i	0.990159	−	0.139946i	$-0.0446927\pi$
$450$	−0.0407158	−	0.0777049i	−0.0407158	−	0.0777049i
$451$		0			0
$452$	−1.40829	−	1.32434i	−1.40829	−	1.32434i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.988478	−	0.0520939i	−0.988478	−	0.0520939i	−0.448509	−	0.893778i	$-0.648045\pi$
$457$	−0.988478	−	0.0520939i	−0.988478	−	0.0520939i	−0.539970	+	0.841685i	$0.681564\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.846391	−	0.532563i	$-0.178771\pi$
$461$		0			0		−0.846391	+	0.532563i	$0.821229\pi$
$462$		0			0
$463$	−1.86571	+	0.609828i	−1.86571	+	0.609828i	−0.873245	+	0.487281i	$0.837989\pi$
$463$	−1.86571	+	0.609828i	−1.86571	+	0.609828i	−0.992463	+	0.122547i	$0.960894\pi$
$464$	1.09829	−	0.174940i	1.09829	−	0.174940i
$465$		0			0
$466$	0.142689	+	0.0466394i	0.142689	+	0.0466394i
$467$		0			0		0.990159	−	0.139946i	$-0.0446927\pi$
$467$		0			0		−0.990159	+	0.139946i	$0.955307\pi$
$468$		0			0
$469$	0.0943097	−	1.19163i	0.0943097	−	1.19163i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.58204	+	0.794090i	2.58204	+	0.794090i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.408728	+	0.613160i	0.408728	+	0.613160i
$478$	0.119463	+	0.108454i	0.119463	+	0.108454i
$479$		0			0		0.00877529	−	0.999961i	$-0.497207\pi$
$479$		0			0		−0.00877529	+	0.999961i	$0.502793\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.389085	+	1.74498i	0.389085	+	1.74498i
$485$		0			0
$486$		0			0
$487$	1.23328	+	0.501357i	1.23328	+	0.501357i	0.897680	−	0.440648i	$-0.145251\pi$
$487$	1.23328	+	0.501357i	1.23328	+	0.501357i	0.335599	+	0.942005i	$0.391061\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.189798	−	0.0336573i	0.189798	−	0.0336573i	−0.0788965	−	0.996883i	$-0.525140\pi$
$491$	0.189798	−	0.0336573i	0.189798	−	0.0336573i	0.268694	+	0.963225i	$0.413408\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.381337	+	0.511530i	0.381337	+	0.511530i
$498$		0			0
$499$	−1.83553	+	0.494707i	−1.83553	+	0.494707i	−0.998614	−	0.0526281i	$-0.983240\pi$
$499$	−1.83553	+	0.494707i	−1.83553	+	0.494707i	−0.836914	+	0.547335i	$0.815642\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.969965	−	0.243246i	$-0.0782123\pi$
$503$		0			0		−0.969965	+	0.243246i	$0.921788\pi$
$504$	0.151105	−	0.0878306i	0.151105	−	0.0878306i
$505$		0			0
$506$	−0.226264	+	0.184654i	−0.226264	+	0.184654i
$507$		0			0
$508$	0.359637	−	0.560589i	0.359637	−	0.560589i
$509$		0			0		0.889808	−	0.456335i	$-0.150838\pi$
$509$		0			0		−0.889808	+	0.456335i	$0.849162\pi$
$510$		0			0
$511$		0			0
$512$	−0.114258	+	0.409598i	−0.114258	+	0.409598i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.0792880	+	0.0518537i	−0.0792880	+	0.0518537i
$519$		0			0
$520$		0			0
$521$		0			0		0.639045	−	0.769169i	$-0.279330\pi$
$521$		0			0		−0.639045	+	0.769169i	$0.720670\pi$
$522$	−0.0703031	+	0.0709228i	−0.0703031	+	0.0709228i
$523$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$523$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$524$		0			0
$525$		0			0
$526$	−0.0158788	+	0.00581452i	−0.0158788	+	0.00581452i
$527$		0			0
$528$		0			0
$529$	2.69744	+	1.20855i	2.69744	+	1.20855i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.202646	−	0.0508192i	−0.202646	−	0.0508192i
$537$		0			0
$538$		0			0
$539$	−1.11418	−	1.24912i	−1.11418	−	1.24912i
$540$		0			0
$541$	1.93873	+	0.486193i	1.93873	+	0.486193i	0.977904	+	0.209056i	$0.0670391\pi$
$541$	1.93873	+	0.486193i	1.93873	+	0.486193i	0.960831	+	0.277137i	$0.0893855\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.696535	−	0.326869i	0.696535	−	0.326869i	−0.0438629	−	0.999038i	$-0.513966\pi$
$547$	0.696535	−	0.326869i	0.696535	−	0.326869i	0.740398	+	0.672168i	$0.234637\pi$
$548$	−1.38286	−	0.619570i	−1.38286	−	0.619570i
$549$		0			0
$550$	0.0726738	+	0.127593i	0.0726738	+	0.127593i
$551$		0			0
$552$		0			0
$553$	1.18657	+	1.53472i	1.18657	+	1.53472i
$554$	−0.0530121	−	0.00186157i	−0.0530121	−	0.00186157i
$555$		0			0
$556$		0			0
$557$	1.03540	−	1.33920i	1.03540	−	1.33920i	0.0963795	−	0.995345i	$-0.469274\pi$
$557$	1.03540	−	1.33920i	1.03540	−	1.33920i	0.939024	−	0.343852i	$-0.111732\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0867151	−	0.152245i	0.0867151	−	0.152245i
$563$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$563$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.400849	−	0.916144i	0.400849	−	0.916144i
$568$	0.0992248	−	0.0508871i	0.0992248	−	0.0508871i
$569$	−0.467348	+	0.728485i	−0.467348	+	0.728485i	−0.992463	−	0.122547i	$-0.960894\pi$
$569$	−0.467348	+	0.728485i	−0.467348	+	0.728485i	0.525115	+	0.851031i	$0.324022\pi$
$570$		0			0
$571$	0.645931	−	0.527144i	0.645931	−	0.527144i	−0.251749	−	0.967793i	$-0.581006\pi$
$571$	0.645931	−	0.527144i	0.645931	−	0.527144i	0.897680	+	0.440648i	$0.145251\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.10317	−	1.65494i	1.10317	−	1.65494i
$576$	0.335926	+	0.893029i	0.335926	+	0.893029i
$577$		0			0		0.944914	−	0.327319i	$-0.106145\pi$
$577$		0			0		−0.944914	+	0.327319i	$0.893855\pi$
$578$	0.0847033	−	0.0228290i	0.0847033	−	0.0228290i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.719738	−	1.00168i	−0.719738	−	1.00168i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.855607	−	0.517627i	$-0.173184\pi$
$587$		0			0		−0.855607	+	0.517627i	$0.826816\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.422924	−	0.966596i	−0.422924	−	0.966596i
$593$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$593$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$594$		0			0
$595$		0			0
$596$	1.55572	+	0.763666i	1.55572	+	0.763666i
$597$		0			0
$598$		0			0
$599$	0.821336	+	0.745647i	0.821336	+	0.745647i	0.969965	−	0.243246i	$-0.0782123\pi$
$599$	0.821336	+	0.745647i	0.821336	+	0.745647i	−0.148629	+	0.988893i	$0.547486\pi$
$600$		0			0
$601$		0			0		0.583517	−	0.812101i	$-0.301676\pi$
$601$		0			0		−0.583517	+	0.812101i	$0.698324\pi$
$602$	0.00621013	+	0.141444i	0.00621013	+	0.141444i
$603$	−1.10736	+	0.450166i	−1.10736	+	0.450166i
$604$	−0.347597	−	0.106901i	−0.347597	−	0.106901i
$605$		0			0
$606$		0			0
$607$		0			0		0.981422	−	0.191862i	$-0.0614525\pi$
$607$		0			0		−0.981422	+	0.191862i	$0.938547\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.89774	+	0.302279i	−1.89774	+	0.302279i	−0.992463	−	0.122547i	$-0.960894\pi$
$613$	−1.89774	+	0.302279i	−1.89774	+	0.302279i	−0.905275	+	0.424826i	$0.860335\pi$
$614$		0			0
$615$		0			0
$616$	−0.247608	+	0.155799i	−0.247608	+	0.155799i
$617$	0.109188	+	0.199774i	0.109188	+	0.199774i	0.926378	−	0.376595i	$-0.122905\pi$
$617$	0.109188	+	0.199774i	0.109188	+	0.199774i	−0.817190	+	0.576369i	$0.804469\pi$
$618$		0			0
$619$		0			0		0.997537	−	0.0701455i	$-0.0223464\pi$
$619$		0			0		−0.997537	+	0.0701455i	$0.977654\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.728488	−	0.685059i	−0.728488	−	0.685059i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.0848920	−	1.38024i	0.0848920	−	1.38024i	−0.678640	−	0.734471i	$-0.737430\pi$
$631$	0.0848920	−	1.38024i	0.0848920	−	1.38024i	0.763532	−	0.645770i	$-0.223464\pi$
$632$	0.298931	−	0.159993i	0.298931	−	0.159993i
$633$		0			0
$634$	0.0357684	−	0.106263i	0.0357684	−	0.106263i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.113437	−	0.122769i	0.113437	−	0.122769i
$639$	0.286162	−	0.570257i	0.286162	−	0.570257i
$640$		0			0
$641$	−0.551175	+	1.32244i	−0.551175	+	1.32244i	0.368451	+	0.929647i	$0.379888\pi$
$641$	−0.551175	+	1.32244i	−0.551175	+	1.32244i	−0.919626	+	0.392794i	$0.871508\pi$
$642$		0			0
$643$		0			0		−0.932845	−	0.360279i	$-0.882682\pi$
$643$		0			0		0.932845	+	0.360279i	$0.117318\pi$
$644$	1.68864	+	1.02160i	1.68864	+	1.02160i
$645$		0			0
$646$		0			0
$647$		0			0		0.464125	−	0.885770i	$-0.346369\pi$
$647$		0			0		−0.464125	+	0.885770i	$0.653631\pi$
$648$	−0.146273	−	0.0956613i	−0.146273	−	0.0956613i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.123028	+	0.0968560i	0.123028	+	0.0968560i
$653$	−0.0875097	+	1.99315i	−0.0875097	+	1.99315i	0.0263232	+	0.999653i	$0.491620\pi$
$653$	−0.0875097	+	1.99315i	−0.0875097	+	1.99315i	−0.113833	+	0.993500i	$0.536313\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.209891	−	0.806879i	0.209891	−	0.806879i	−0.774747	−	0.632271i	$-0.782123\pi$
$659$	0.209891	−	0.806879i	0.209891	−	0.806879i	0.984638	−	0.174608i	$-0.0558659\pi$
$660$		0			0
$661$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$661$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$662$	0.145630	−	0.0812633i	0.145630	−	0.0812633i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0819071	+	0.0476091i	0.0819071	+	0.0476091i
$667$	−2.17541	−	0.627462i	−2.17541	−	0.627462i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.15060	−	0.811524i	1.15060	−	0.811524i	0.165961	−	0.986132i	$-0.446927\pi$
$673$	1.15060	−	0.811524i	1.15060	−	0.811524i	0.984638	+	0.174608i	$0.0558659\pi$
$674$	−0.0284748	−	0.169195i	−0.0284748	−	0.169195i
$675$		0			0
$676$	0.912549	−	0.389772i	0.912549	−	0.389772i
$677$		0			0		0.148629	−	0.988893i	$-0.452514\pi$
$677$		0			0		−0.148629	+	0.988893i	$0.547486\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.236754	+	1.57523i	0.236754	+	1.57523i	0.716353	+	0.697738i	$0.245810\pi$
$683$	0.236754	+	1.57523i	0.236754	+	1.57523i	−0.479599	+	0.877488i	$0.659218\pi$
$684$		0			0
$685$		0			0
$686$	0.0420732	−	0.0769783i	0.0420732	−	0.0769783i
$687$		0			0
$688$	−1.56485	−	0.193223i	−1.56485	−	0.193223i
$689$		0			0
$690$		0			0
$691$		0			0		−0.0263232	−	0.999653i	$-0.508380\pi$
$691$		0			0		0.0263232	+	0.999653i	$0.491620\pi$
$692$		0			0
$693$	−0.616723	+	1.55607i	−0.616723	+	1.55607i
$694$	−0.000876324		0.00126592i	−0.000876324		0.00126592i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.647425	−	0.752003i	0.647425	−	0.752003i
$701$	0.551438	−	1.85068i	0.551438	−	1.85068i	0.0263232	−	0.999653i	$-0.491620\pi$
$701$	0.551438	−	1.85068i	0.551438	−	1.85068i	0.525115	−	0.851031i	$-0.324022\pi$
$702$		0			0
$703$		0			0
$704$	−0.614394	−	1.47412i	−0.614394	−	1.47412i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.297212	−	0.00521685i	0.297212	−	0.00521685i	0.131251	−	0.991349i	$-0.458101\pi$
$709$	0.297212	−	0.00521685i	0.297212	−	0.00521685i	0.165961	+	0.986132i	$0.446927\pi$
$710$		0			0
$711$	0.839512	−	1.74887i	0.839512	−	1.74887i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.26268	−	1.41562i	1.26268	−	1.41562i
$717$		0			0
$718$	−0.0812673	−	0.0330371i	−0.0812673	−	0.0330371i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.00998609	+	0.0871556i	0.00998609	+	0.0871556i
$723$		0			0
$724$		0			0
$725$	−0.492626	+	1.02624i	−0.492626	+	1.02624i
$726$		0			0
$727$		0			0		0.999846	−	0.0175499i	$-0.00558659\pi$
$727$		0			0		−0.999846	+	0.0175499i	$0.994413\pi$
$728$		0			0
$729$	−0.998614	+	0.0526281i	−0.998614	+	0.0526281i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.569175	−	0.822216i	$-0.692737\pi$
$733$		0			0		0.569175	+	0.822216i	$0.307263\pi$
$734$		0			0
$735$		0			0
$736$	0.338018	−	0.392618i	0.338018	−	0.392618i
$737$	1.82594	−	0.818084i	1.82594	−	0.818084i
$738$		0			0
$739$	−1.59629	−	0.749107i	−1.59629	−	0.749107i	−0.597680	−	0.801735i	$-0.703911\pi$
$739$	−1.59629	−	0.749107i	−1.59629	−	0.749107i	−0.998614	+	0.0526281i	$0.983240\pi$
$740$		0			0
$741$		0			0
$742$	0.0367945	−	0.0531524i	0.0367945	−	0.0531524i
$743$	0.545601	−	1.37662i	0.545601	−	1.37662i	−0.352079	−	0.935970i	$-0.614525\pi$
$743$	0.545601	−	1.37662i	0.545601	−	1.37662i	0.897680	−	0.440648i	$-0.145251\pi$
$744$		0			0
$745$		0			0
$746$	0.165378	+	0.0572872i	0.165378	+	0.0572872i
$747$		0			0
$748$		0			0
$749$	−1.37243	+	1.43401i	−1.37243	+	1.43401i
$750$		0			0
$751$	0.121570	+	1.97658i	0.121570	+	1.97658i	0.200467	+	0.979701i	$0.435754\pi$
$751$	0.121570	+	1.97658i	0.121570	+	1.97658i	−0.0788965	+	0.996883i	$0.525140\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.59802	+	1.16962i	1.59802	+	1.16962i	0.881663	+	0.471880i	$0.156425\pi$
$757$	1.59802	+	1.16962i	1.59802	+	1.16962i	0.716353	+	0.697738i	$0.245810\pi$
$758$	0.145108	+	0.00254702i	0.145108	+	0.00254702i
$759$		0			0
$760$		0			0
$761$		0			0		−0.939024	−	0.343852i	$-0.888268\pi$
$761$		0			0		0.939024	+	0.343852i	$0.111732\pi$
$762$		0			0
$763$	1.47956	−	1.04354i	1.47956	−	1.04354i
$764$	1.20444	−	0.881553i	1.20444	−	0.881553i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.960831	−	0.277137i	$-0.910615\pi$
$769$		0			0		0.960831	+	0.277137i	$0.0893855\pi$
$770$		0			0
$771$		0			0
$772$	1.06678	+	0.902244i	1.06678	+	0.902244i
$773$		0			0		0.796459	−	0.604692i	$-0.206704\pi$
$773$		0			0		−0.796459	+	0.604692i	$0.793296\pi$
$774$	0.123635	−	0.0689895i	0.123635	−	0.0689895i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0150207	+	0.0131631i	−0.0150207	+	0.0131631i
$779$		0			0
$780$		0			0
$781$	−0.445192	+	0.970734i	−0.445192	+	0.970734i
$782$		0			0
$783$		0			0
$784$	0.767630	+	0.604332i	0.767630	+	0.604332i
$785$		0			0
$786$		0			0
$787$		0			0		0.200467	−	0.979701i	$-0.435754\pi$
$787$		0			0		−0.200467	+	0.979701i	$0.564246\pi$
$788$	−1.64027	−	1.07272i	−1.64027	−	1.07272i
$789$		0			0
$790$		0			0
$791$	0.490449	+	1.88542i	0.490449	+	1.88542i
$792$	0.250304	+	0.151429i	0.250304	+	0.151429i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.448509	−	0.893778i	$-0.351955\pi$
$797$		0			0		−0.448509	+	0.893778i	$0.648045\pi$
$798$		0			0
$799$		0			0
$800$	−0.166460	−	0.200355i	−0.166460	−	0.200355i
$801$		0			0
$802$	0.00928912	−	0.0275967i	0.00928912	−	0.0275967i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.916695	−	1.74948i	−0.916695	−	1.74948i	−0.597680	−	0.801735i	$-0.703911\pi$
$809$	−0.916695	−	1.74948i	−0.916695	−	1.74948i	−0.319015	−	0.947750i	$-0.603352\pi$
$810$		0			0
$811$		0			0		−0.728488	−	0.685059i	$-0.759777\pi$
$811$		0			0		0.728488	+	0.685059i	$0.240223\pi$
$812$	−1.03880	−	0.443697i	−1.03880	−	0.443697i
$813$		0			0
$814$	−0.139811	−	0.0748289i	−0.139811	−	0.0748289i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.24136	−	0.609350i	1.24136	−	0.609350i	0.302333	−	0.953202i	$-0.402235\pi$
$821$	1.24136	−	0.609350i	1.24136	−	0.609350i	0.939024	+	0.343852i	$0.111732\pi$
$822$		0			0
$823$	−0.463606	+	0.0738451i	−0.463606	+	0.0738451i	−0.384709	−	0.923038i	$-0.625698\pi$
$823$	−0.463606	+	0.0738451i	−0.463606	+	0.0738451i	−0.0788965	+	0.996883i	$0.525140\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.06826	−	0.596099i	−1.06826	−	0.596099i	−0.148629	−	0.988893i	$-0.547486\pi$
$827$	−1.06826	−	0.596099i	−1.06826	−	0.596099i	−0.919626	+	0.392794i	$0.871508\pi$
$828$	0.155711	−	1.96746i	0.155711	−	1.96746i
$829$		0			0		0.981422	−	0.191862i	$-0.0614525\pi$
$829$		0			0		−0.981422	+	0.191862i	$0.938547\pi$
$830$		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		0.994461	−	0.105110i	$-0.0335196\pi$
$839$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$840$		0			0
$841$	0.292931	+	0.0414018i	0.292931	+	0.0414018i
$842$	−0.139719	−	0.106078i	−0.139719	−	0.106078i
$843$		0			0
$844$	0.579533	+	1.32453i	0.579533	+	1.32453i
$845$		0			0
$846$		0			0
$847$	0.604647	−	1.69721i	0.604647	−	1.69721i
$848$	0.515726	+	0.502324i	0.515726	+	0.502324i
$849$		0			0
$850$		0			0
$851$	−0.0565399	+	2.14717i	−0.0565399	+	2.14717i
$852$		0			0
$853$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$853$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$854$		0			0
$855$		0			0
$856$	0.207346	+	0.278137i	0.207346	+	0.278137i
$857$		0			0		−0.691425	−	0.722448i	$-0.743017\pi$
$857$		0			0		0.691425	+	0.722448i	$0.256983\pi$
$858$		0			0
$859$		0			0		0.944914	−	0.327319i	$-0.106145\pi$
$859$		0			0		−0.944914	+	0.327319i	$0.893855\pi$
$860$		0			0
$861$		0			0
$862$	−0.0457269	+	0.0114673i	−0.0457269	+	0.0114673i
$863$	−1.17345	+	0.682075i	−1.17345	+	0.682075i	−0.955819	−	0.293956i	$-0.905028\pi$
$863$	−1.17345	+	0.682075i	−1.17345	+	0.682075i	−0.217629	+	0.976031i	$0.569832\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.30160	+	2.97482i	−1.30160	+	2.97482i
$870$		0			0
$871$		0			0
$872$	−0.136941	−	0.285276i	−0.136941	−	0.285276i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.46166	−	0.955915i	1.46166	−	0.955915i	0.464125	−	0.885770i	$-0.346369\pi$
$877$	1.46166	−	0.955915i	1.46166	−	0.955915i	0.997537	−	0.0701455i	$-0.0223464\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.703997	−	0.710203i	$-0.251397\pi$
$881$		0			0		−0.703997	+	0.710203i	$0.748603\pi$
$882$	−0.0876718	−	0.00307868i	−0.0876718	−	0.00307868i
$883$	1.14872	+	1.48577i	1.14872	+	1.48577i	0.846391	+	0.532563i	$0.178771\pi$
$883$	1.14872	+	1.48577i	1.14872	+	1.48577i	0.302333	+	0.953202i	$0.402235\pi$
$884$		0			0
$885$		0			0
$886$	−0.0779504	−	0.136857i	−0.0779504	−	0.136857i
$887$		0			0		−0.285558	−	0.958362i	$-0.592179\pi$
$887$		0			0		0.285558	+	0.958362i	$0.407821\pi$
$888$		0			0
$889$	−0.607618	+	0.285142i	−0.607618	+	0.285142i
$890$		0			0
$891$	1.66739	−	0.146697i	1.66739	−	0.146697i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.254833	−	0.231349i	0.254833	−	0.231349i
$897$		0			0
$898$	0.0294013	+	0.0329624i	0.0294013	+	0.0329624i
$899$		0			0
$900$	−0.962500	−	0.241374i	−0.962500	−	0.241374i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.339184	−	0.0298414i	0.339184	−	0.0298414i
$905$		0			0
$906$		0			0
$907$	1.30747	+	0.585795i	1.30747	+	0.585795i	0.939024	−	0.343852i	$-0.111732\pi$
$907$	1.30747	+	0.585795i	1.30747	+	0.585795i	0.368451	+	0.929647i	$0.379888\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.34971	+	1.26925i	−1.34971	+	1.26925i	−0.416866	+	0.908968i	$0.636872\pi$
$911$	−1.34971	+	1.26925i	−1.34971	+	1.26925i	−0.932845	+	0.360279i	$0.882682\pi$
$912$		0			0
$913$		0			0
$914$	0.0611319	−	0.0616707i	0.0611319	−	0.0616707i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.637095	+	1.60747i	0.637095	+	1.60747i	0.785724	+	0.618577i	$0.212291\pi$
$919$	0.637095	+	1.60747i	0.637095	+	1.60747i	−0.148629	+	0.988893i	$0.547486\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.05988	+	0.207199i	1.05988	+	0.207199i
$926$	0.0690231	−	0.157753i	0.0690231	−	0.157753i
$927$		0			0
$928$	−0.160112	+	0.249576i	−0.160112	+	0.249576i
$929$		0			0		0.955819	−	0.293956i	$-0.0949721\pi$
$929$		0			0		−0.955819	+	0.293956i	$0.905028\pi$
$930$		0			0
$931$		0			0
$932$	1.46806	−	0.853320i	1.46806	−	0.853320i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.965546	−	0.260231i	$-0.0837989\pi$
$937$		0			0		−0.965546	+	0.260231i	$0.916201\pi$
$938$	0.0725055	+	0.0757588i	0.0725055	+	0.0757588i
$939$		0			0
$940$		0			0
$941$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$941$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.202763	+	0.122668i	−0.202763	+	0.122668i
$947$	−0.687124	−	0.669269i	−0.687124	−	0.669269i	0.268694	−	0.963225i	$-0.413408\pi$
$947$	−0.687124	−	0.669269i	−0.687124	−	0.669269i	−0.955819	+	0.293956i	$0.905028\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.763962	+	0.580020i	0.763962	+	0.580020i	0.912591	−	0.408873i	$-0.134078\pi$
$953$	0.763962	+	0.580020i	0.763962	+	0.580020i	−0.148629	+	0.988893i	$0.547486\pi$
$954$	−0.0640092	−	0.00904682i	−0.0640092	−	0.00904682i
$955$		0			0
$956$	1.81499	−	0.191837i	1.81499	−	0.191837i
$957$		0			0
$958$		0			0
$959$	0.846998	+	1.27064i	0.846998	+	1.27064i
$960$		0			0
$961$	−0.0438629	−	0.999038i	−0.0438629	−	0.999038i
$962$		0			0
$963$	1.89723	+	0.583482i	1.89723	+	0.583482i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.157696	+	1.99254i	−0.157696	+	1.99254i	−0.0438629	+	0.999038i	$0.513966\pi$
$967$	−0.157696	+	1.99254i	−0.157696	+	1.99254i	−0.113833	+	0.993500i	$0.536313\pi$
$968$	−0.274980	−	0.153442i	−0.274980	−	0.153442i
$969$		0			0
$970$		0			0
$971$		0			0		−0.987551	−	0.157301i	$-0.949721\pi$
$971$		0			0		0.987551	+	0.157301i	$0.0502793\pi$
$972$		0			0
$973$		0			0
$974$	−0.104839	+	0.0514627i	−0.104839	+	0.0514627i
$975$		0			0
$976$		0			0
$977$	1.71830	+	0.463112i	1.71830	+	0.463112i	0.977904	−	0.209056i	$-0.0670391\pi$
$977$	1.71830	+	0.463112i	1.71830	+	0.463112i	0.740398	+	0.672168i	$0.234637\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.59629	−	0.854363i	−1.59629	−	0.854363i
$982$	−0.00887967	+	0.0143909i	−0.00887967	+	0.0143909i
$983$		0			0		−0.919626	−	0.392794i	$-0.871508\pi$
$983$		0			0		0.919626	+	0.392794i	$0.128492\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.71684	+	1.70948i	2.71684	+	1.70948i
$990$		0			0
$991$	−1.64491	+	0.880382i	−1.64491	+	0.880382i	−0.652446	+	0.757835i	$0.726257\pi$
$991$	−1.64491	+	0.880382i	−1.64491	+	0.880382i	−0.992463	+	0.122547i	$0.960894\pi$
$992$		0			0
$993$		0			0
$994$	−0.0557563	−	0.00490544i	−0.0557563	−	0.00490544i
$995$		0			0
$996$		0			0
$997$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$997$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$998$	0.0747974	−	0.149055i	0.0747974	−	0.149055i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.181.1	✓	178
7.6	odd	2	CM	2513.1.l.a.181.1	✓	178
359.240	even	179	inner	2513.1.l.a.958.1	yes	178
2513.958	odd	358	inner	2513.1.l.a.958.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.181.1	✓	178	1.1	even	1	trivial
2513.1.l.a.181.1	✓	178	7.6	odd	2	CM
2513.1.l.a.958.1	yes	178	359.240	even	179	inner
2513.1.l.a.958.1	yes	178	2513.958	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)

\(f(q)\)	\(=\)	\(q+(-0.0583943 + 0.0654670i) q^{2} +(0.112957 + 0.985854i) q^{4} +(0.432754 - 0.901512i) q^{7} +(-0.142826 - 0.100736i) q^{8} +(-0.999846 + 0.0175499i) q^{9} +O(q^{10})\)	\(q+(-0.0583943 + 0.0654670i) q^{2} +(0.112957 + 0.985854i) q^{4} +(0.432754 - 0.901512i) q^{7} +(-0.142826 - 0.100736i) q^{8} +(-0.999846 + 0.0175499i) q^{9} +(1.67151 - 0.0880903i) q^{11} +(0.0337489 + 0.0809743i) q^{14} +(-0.951653 + 0.220977i) q^{16} +(0.0572363 - 0.0664817i) q^{18} +(-0.0918395 + 0.114573i) q^{22} +(1.94497 + 0.415796i) q^{23} +(0.368451 - 0.929647i) q^{25} +(0.937642 + 0.324800i) q^{28} +(-1.13555 - 0.0798502i) q^{29} +(0.124927 - 0.228570i) q^{32} +(-0.130241 - 0.983720i) q^{36} +(0.197890 + 1.06165i) q^{37} +(1.51549 + 0.554942i) q^{43} +(0.275652 + 1.63791i) q^{44} +(-0.140796 + 0.103051i) q^{46} +(-0.625448 - 0.780266i) q^{49} +(0.0393458 + 0.0784075i) q^{50} +(-0.397905 - 0.620239i) q^{53} +(-0.152623 + 0.0851652i) q^{56} +(0.0715370 - 0.0696780i) q^{58} +(-0.416866 + 0.908968i) q^{63} +(-0.320202 - 0.898787i) q^{64} +(1.11508 - 0.430663i) q^{67} +(-0.296126 + 0.565147i) q^{71} +(0.144572 + 0.0982136i) q^{72} +(-0.0810589 - 0.0490392i) q^{74} +(0.643937 - 1.54501i) q^{77} +(-0.870075 + 1.73387i) q^{79} +(0.999384 - 0.0350944i) q^{81} +(-0.124826 + 0.0668091i) q^{86} +(-0.247608 - 0.155799i) q^{88} +(-0.190216 + 1.96443i) q^{92} +(0.0876043 + 0.00461684i) q^{98} +(-1.66970 + 0.117412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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