LMFDB - Embedded newform 2513.1.l.a.216.1

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			216.1
Root			$-0.691425 - 0.722448i$ of defining polynomial
Character	$\chi$	$=$	2513.216
Dual form			2513.1.l.a.2036.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388188 + 0.808672i) q^{2} +(0.122187 + 0.152433i) q^{4} +(0.827179 + 0.561938i) q^{7} +(-1.04447 + 0.242530i) q^{8} +(-0.479599 + 0.877488i) q^{9} +O(q^{10})$	\(q+(-0.388188 + 0.808672i) q^{2} +(0.122187 + 0.152433i) q^{4} +(0.827179 + 0.561938i) q^{7} +(-1.04447 + 0.242530i) q^{8} +(-0.479599 + 0.877488i) q^{9} +(1.42918 - 0.100498i) q^{11} +(-0.775525 + 0.450779i) q^{14} +(0.166807 - 0.748104i) q^{16} +(-0.523425 - 0.728468i) q^{18} +(-0.473519 + 1.19475i) q^{22} +(1.90275 + 0.548819i) q^{23} +(-0.855607 + 0.517627i) q^{25} +(0.0154132 + 0.194751i) q^{28} +(-0.576463 - 1.25697i) q^{29} +(-0.302282 - 0.237977i) q^{32} +(-0.192359 + 0.0341114i) q^{36} +(0.455350 - 0.114192i) q^{37} +(-1.11418 + 0.728662i) q^{43} +(0.189947 + 0.205573i) q^{44} +(-1.18244 + 1.32566i) q^{46} +(0.368451 + 0.929647i) q^{49} +(-0.0864541 - 0.892842i) q^{50} +(-0.401665 - 1.66340i) q^{53} +(-1.00025 - 0.386312i) q^{56} +(1.24025 + 0.0217696i) q^{58} +(-0.889808 + 0.456335i) q^{63} +(0.997837 - 0.489813i) q^{64} +(-1.73057 + 0.926228i) q^{67} +(1.50302 - 0.641975i) q^{71} +(0.288110 - 1.03283i) q^{72} +(-0.0844175 + 0.412557i) q^{74} +(1.23866 + 0.719979i) q^{77} +(-0.144970 + 1.49716i) q^{79} +(-0.539970 - 0.841685i) q^{81} +(-0.156739 - 1.18386i) q^{86} +(-1.46836 + 0.451585i) q^{88} +(0.148834 + 0.357100i) q^{92} +(-0.894808 - 0.0629218i) q^{98} +(-0.597246 + 1.30228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{34}{179}\right)$

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 $

$2$	−0.388188	+	0.808672i	−0.388188	+	0.808672i	0.611658	+	0.791122i	$0.290503\pi$
$2$	−0.388188	+	0.808672i	−0.388188	+	0.808672i	−0.999846	+	0.0175499i	$0.994413\pi$
$3$		0			0		−0.510099	−	0.860116i	$-0.670391\pi$
$3$		0			0		0.510099	+	0.860116i	$0.329609\pi$
$4$	0.122187	+	0.152433i	0.122187	+	0.152433i
$5$		0			0		−0.268694	−	0.963225i	$-0.586592\pi$
$5$		0			0		0.268694	+	0.963225i	$0.413408\pi$
$6$		0			0
$7$	0.827179	+	0.561938i	0.827179	+	0.561938i
$7$	0.827179	+	0.561938i	0.827179	+	0.561938i
$8$	−1.04447	+	0.242530i	−1.04447	+	0.242530i
$9$	−0.479599	+	0.877488i	−0.479599	+	0.877488i
$10$		0			0
$11$	1.42918	−	0.100498i	1.42918	−	0.100498i	0.665645	−	0.746268i	$-0.268156\pi$
$11$	1.42918	−	0.100498i	1.42918	−	0.100498i	0.763532	+	0.645770i	$0.223464\pi$
$12$		0			0
$13$		0			0		0.981422	−	0.191862i	$-0.0614525\pi$
$13$		0			0		−0.981422	+	0.191862i	$0.938547\pi$
$14$	−0.775525	+	0.450779i	−0.775525	+	0.450779i
$15$		0			0
$16$	0.166807	−	0.748104i	0.166807	−	0.748104i
$17$		0			0		−0.926378	−	0.376595i	$-0.877095\pi$
$17$		0			0		0.926378	+	0.376595i	$0.122905\pi$
$18$	−0.523425	−	0.728468i	−0.523425	−	0.728468i
$19$		0			0		0.846391	−	0.532563i	$-0.178771\pi$
$19$		0			0		−0.846391	+	0.532563i	$0.821229\pi$
$20$		0			0
$21$		0			0
$22$	−0.473519	+	1.19475i	−0.473519	+	1.19475i
$23$	1.90275	+	0.548819i	1.90275	+	0.548819i	0.990159	+	0.139946i	$0.0446927\pi$
$23$	1.90275	+	0.548819i	1.90275	+	0.548819i	0.912591	+	0.408873i	$0.134078\pi$
$24$		0			0
$25$	−0.855607	+	0.517627i	−0.855607	+	0.517627i
$26$		0			0
$27$		0			0
$28$	0.0154132	+	0.194751i	0.0154132	+	0.194751i
$29$	−0.576463	−	1.25697i	−0.576463	−	1.25697i	−0.944914	−	0.327319i	$-0.893855\pi$
$29$	−0.576463	−	1.25697i	−0.576463	−	1.25697i	0.368451	−	0.929647i	$-0.379888\pi$
$30$		0			0
$31$		0			0		−0.525115	−	0.851031i	$-0.675978\pi$
$31$		0			0		0.525115	+	0.851031i	$0.324022\pi$
$32$	−0.302282	−	0.237977i	−0.302282	−	0.237977i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.192359	+	0.0341114i	−0.192359	+	0.0341114i
$37$	0.455350	−	0.114192i	0.455350	−	0.114192i	−0.00877529	−	0.999961i	$-0.502793\pi$
$37$	0.455350	−	0.114192i	0.455350	−	0.114192i	0.464125	+	0.885770i	$0.346369\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.319015	−	0.947750i	$-0.603352\pi$
$41$		0			0		0.319015	+	0.947750i	$0.396648\pi$
$42$		0			0
$43$	−1.11418	+	0.728662i	−1.11418	+	0.728662i	−0.965546	−	0.260231i	$-0.916201\pi$
$43$	−1.11418	+	0.728662i	−1.11418	+	0.728662i	−0.148629	+	0.988893i	$0.547486\pi$
$44$	0.189947	+	0.205573i	0.189947	+	0.205573i
$45$		0			0
$46$	−1.18244	+	1.32566i	−1.18244	+	1.32566i
$47$		0			0		−0.817190	−	0.576369i	$-0.804469\pi$
$47$		0			0		0.817190	+	0.576369i	$0.195531\pi$
$48$		0			0
$49$	0.368451	+	0.929647i	0.368451	+	0.929647i
$50$	−0.0864541	−	0.892842i	−0.0864541	−	0.892842i
$51$		0			0
$52$		0			0
$53$	−0.401665	−	1.66340i	−0.401665	−	1.66340i	−0.703997	−	0.710203i	$-0.748603\pi$
$53$	−0.401665	−	1.66340i	−0.401665	−	1.66340i	0.302333	−	0.953202i	$-0.402235\pi$
$54$		0			0
$55$		0			0
$56$	−1.00025	−	0.386312i	−1.00025	−	0.386312i
$57$		0			0
$58$	1.24025	+	0.0217696i	1.24025	+	0.0217696i
$59$		0			0		−0.183242	−	0.983068i	$-0.558659\pi$
$59$		0			0		0.183242	+	0.983068i	$0.441341\pi$
$60$		0			0
$61$		0			0		−0.774747	−	0.632271i	$-0.782123\pi$
$61$		0			0		0.774747	+	0.632271i	$0.217877\pi$
$62$		0			0
$63$	−0.889808	+	0.456335i	−0.889808	+	0.456335i
$64$	0.997837	−	0.489813i	0.997837	−	0.489813i
$65$		0			0
$66$		0			0
$67$	−1.73057	+	0.926228i	−1.73057	+	0.926228i	−0.774747	+	0.632271i	$0.782123\pi$
$67$	−1.73057	+	0.926228i	−1.73057	+	0.926228i	−0.955819	+	0.293956i	$0.905028\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.50302	−	0.641975i	1.50302	−	0.641975i	0.525115	−	0.851031i	$-0.324022\pi$
$71$	1.50302	−	0.641975i	1.50302	−	0.641975i	0.977904	+	0.209056i	$0.0670391\pi$
$72$	0.288110	−	1.03283i	0.288110	−	1.03283i
$73$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$73$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$74$	−0.0844175	+	0.412557i	−0.0844175	+	0.412557i
$75$		0			0
$76$		0			0
$77$	1.23866	+	0.719979i	1.23866	+	0.719979i
$78$		0			0
$79$	−0.144970	+	1.49716i	−0.144970	+	1.49716i	0.583517	+	0.812101i	$0.301676\pi$
$79$	−0.144970	+	1.49716i	−0.144970	+	1.49716i	−0.728488	+	0.685059i	$0.759777\pi$
$80$		0			0
$81$	−0.539970	−	0.841685i	−0.539970	−	0.841685i
$82$		0			0
$83$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$83$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$84$		0			0
$85$		0			0
$86$	−0.156739	−	1.18386i	−0.156739	−	1.18386i
$87$		0			0
$88$	−1.46836	+	0.451585i	−1.46836	+	0.451585i
$89$		0			0		−0.990159	−	0.139946i	$-0.955307\pi$
$89$		0			0		0.990159	+	0.139946i	$0.0446927\pi$
$90$		0			0
$91$		0			0
$92$	0.148834	+	0.357100i	0.148834	+	0.357100i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.969965	−	0.243246i	$-0.921788\pi$
$97$		0			0		0.969965	+	0.243246i	$0.0782123\pi$
$98$	−0.894808	−	0.0629218i	−0.894808	−	0.0629218i
$99$	−0.597246	+	1.30228i	−0.597246	+	1.30228i
$100$	−0.183447	−	0.0671748i	−0.183447	−	0.0671748i
$101$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$101$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$102$		0			0
$103$		0			0		−0.905275	−	0.424826i	$-0.860335\pi$
$103$		0			0		0.905275	+	0.424826i	$0.139665\pi$
$104$		0			0
$105$		0			0
$106$	1.50107	+	0.320899i	1.50107	+	0.320899i
$107$	−0.642608	−	0.287911i	−0.642608	−	0.287911i	0.0613892	−	0.998114i	$-0.480447\pi$
$107$	−0.642608	−	0.287911i	−0.642608	−	0.287911i	−0.703997	+	0.710203i	$0.748603\pi$
$108$		0			0
$109$	−0.114533	+	0.0442344i	−0.114533	+	0.0442344i	−0.416866	−	0.908968i	$-0.636872\pi$
$109$	−0.114533	+	0.0442344i	−0.114533	+	0.0442344i	0.302333	+	0.953202i	$0.402235\pi$
$110$		0			0
$111$		0			0
$112$	0.558368	−	0.525080i	0.558368	−	0.525080i
$113$	−0.174473	−	0.398760i	−0.174473	−	0.398760i	0.806949	−	0.590621i	$-0.201117\pi$
$113$	−0.174473	−	0.398760i	−0.174473	−	0.398760i	−0.981422	+	0.191862i	$0.938547\pi$
$114$		0			0
$115$		0			0
$116$	0.121166	−	0.241457i	0.121166	−	0.241457i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.04229	−	0.147313i	1.04229	−	0.147313i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.0236123	−	0.896707i	−0.0236123	−	0.896707i
$127$	1.09815	+	1.42035i	1.09815	+	1.42035i	0.897680	+	0.440648i	$0.145251\pi$
$127$	1.09815	+	1.42035i	1.09815	+	1.42035i	0.200467	+	0.979701i	$0.435754\pi$
$128$	0.00537384	+	0.612359i	0.00537384	+	0.612359i
$129$		0			0
$130$		0			0
$131$		0			0		−0.200467	−	0.979701i	$-0.564246\pi$
$131$		0			0		0.200467	+	0.979701i	$0.435754\pi$
$132$		0			0
$133$		0			0
$134$	−0.0772297	−	1.75901i	−0.0772297	−	1.75901i
$135$		0			0
$136$		0			0
$137$	−0.757536	+	0.262411i	−0.757536	+	0.262411i	−0.678640	−	0.734471i	$-0.737430\pi$
$137$	−0.757536	+	0.262411i	−0.757536	+	0.262411i	−0.0788965	+	0.996883i	$0.525140\pi$
$138$		0			0
$139$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$139$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$140$		0			0
$141$		0			0
$142$	−0.0643060	+	1.46466i	−0.0643060	+	1.46466i
$143$		0			0
$144$	0.576451	+	0.505161i	0.576451	+	0.505161i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.0730446	+	0.0554573i	0.0730446	+	0.0554573i
$149$	−0.437924	+	1.81357i	−0.437924	+	1.81357i	0.131251	+	0.991349i	$0.458101\pi$
$149$	−0.437924	+	1.81357i	−0.437924	+	1.81357i	−0.569175	+	0.822216i	$0.692737\pi$
$150$		0			0
$151$	0.0510651	−	1.93926i	0.0510651	−	1.93926i	−0.217629	−	0.976031i	$-0.569832\pi$
$151$	0.0510651	−	1.93926i	0.0510651	−	1.93926i	0.268694	−	0.963225i	$-0.413408\pi$
$152$		0			0
$153$		0			0
$154$	−1.06306	+	0.722182i	−1.06306	+	0.722182i
$155$		0			0
$156$		0			0
$157$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$157$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$158$	−1.15444	−	0.698413i	−1.15444	−	0.698413i
$159$		0			0
$160$		0			0
$161$	1.26551	+	1.52320i	1.26551	+	1.52320i
$162$	0.890256	−	0.109927i	0.890256	−	0.109927i
$163$	0.984367	−	1.72824i	0.984367	−	1.72824i	0.400849	−	0.916144i	$-0.368715\pi$
$163$	0.984367	−	1.72824i	0.984367	−	1.72824i	0.583517	−	0.812101i	$-0.301676\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.836914	−	0.547335i	$-0.815642\pi$
$167$		0			0		0.836914	+	0.547335i	$0.184358\pi$
$168$		0			0
$169$	0.926378	−	0.376595i	0.926378	−	0.376595i
$170$		0			0
$171$		0			0
$172$	−0.247210	−	0.0808033i	−0.247210	−	0.0808033i
$173$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$173$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$174$		0			0
$175$	−0.998614	−	0.0526281i	−0.998614	−	0.0526281i
$176$	0.163214	−	1.08594i	0.163214	−	1.08594i
$177$		0			0
$178$		0			0
$179$	−0.689342	−	1.43604i	−0.689342	−	1.43604i	−0.889808	−	0.456335i	$-0.849162\pi$
$179$	−0.689342	−	1.43604i	−0.689342	−	1.43604i	0.200467	−	0.979701i	$-0.435754\pi$
$180$		0			0
$181$		0			0		0.554658	−	0.832079i	$-0.312849\pi$
$181$		0			0		−0.554658	+	0.832079i	$0.687151\pi$
$182$		0			0
$183$		0			0
$184$	−2.12047	−	0.111751i	−2.12047	−	0.111751i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.330645	−	1.96468i	−0.330645	−	1.96468i	−0.251749	−	0.967793i	$-0.581006\pi$
$191$	−0.330645	−	1.96468i	−0.330645	−	1.96468i	−0.0788965	−	0.996883i	$-0.525140\pi$
$192$		0			0
$193$	0.459414	+	0.876779i	0.459414	+	0.876779i	0.999384	+	0.0350944i	$0.0111732\pi$
$193$	0.459414	+	0.876779i	0.459414	+	0.876779i	−0.539970	+	0.841685i	$0.681564\pi$
$194$		0			0
$195$		0			0
$196$	−0.0966884	+	0.169755i	−0.0966884	+	0.169755i
$197$	−1.94107	+	0.239678i	−1.94107	+	0.239678i	−0.996152	−	0.0876414i	$-0.972067\pi$
$197$	−1.94107	+	0.239678i	−1.94107	+	0.239678i	−0.944914	+	0.327319i	$0.893855\pi$
$198$	−0.821277	−	0.988507i	−0.821277	−	0.988507i
$199$		0			0		0.384709	−	0.923038i	$-0.374302\pi$
$199$		0			0		−0.384709	+	0.923038i	$0.625698\pi$
$200$	0.768116	−	0.748156i	0.768116	−	0.748156i
$201$		0			0
$202$		0			0
$203$	0.229499	−	1.36367i	0.229499	−	1.36367i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.39414	+	1.40643i	−1.39414	+	1.40643i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.739314	−	0.561306i	−0.739314	−	0.561306i	0.165961	−	0.986132i	$-0.446927\pi$
$211$	−0.739314	−	0.561306i	−0.739314	−	0.561306i	−0.905275	+	0.424826i	$0.860335\pi$
$212$	0.204479	−	0.264474i	0.204479	−	0.264474i
$213$		0			0
$214$	0.482279	−	0.407896i	0.482279	−	0.407896i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.00868921	−	0.109791i	0.00868921	−	0.109791i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.987551	−	0.157301i	$-0.949721\pi$
$223$		0			0		0.987551	+	0.157301i	$0.0502793\pi$
$224$	−0.116313	−	0.366713i	−0.116313	−	0.366713i
$225$	−0.0438629	−	0.999038i	−0.0438629	−	0.999038i
$226$	0.390194	+	0.0137021i	0.390194	+	0.0137021i
$227$		0			0		0.285558	−	0.958362i	$-0.407821\pi$
$227$		0			0		−0.285558	+	0.958362i	$0.592179\pi$
$228$		0			0
$229$		0			0		0.999846	−	0.0175499i	$-0.00558659\pi$
$229$		0			0		−0.999846	+	0.0175499i	$0.994413\pi$
$230$		0			0
$231$		0			0
$232$	0.906950	+	1.17305i	0.906950	+	1.17305i
$233$	0.0105538	+	0.400794i	0.0105538	+	0.400794i	0.984638	+	0.174608i	$0.0558659\pi$
$233$	0.0105538	+	0.400794i	0.0105538	+	0.400794i	−0.974084	+	0.226186i	$0.927374\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.890882	−	1.50218i	0.890882	−	1.50218i	0.0263232	−	0.999653i	$-0.491620\pi$
$239$	0.890882	−	1.50218i	0.890882	−	1.50218i	0.864559	−	0.502531i	$-0.167598\pi$
$240$		0			0
$241$		0			0		−0.965546	−	0.260231i	$-0.916201\pi$
$241$		0			0		0.965546	+	0.260231i	$0.0837989\pi$
$242$	−0.285475	+	0.900054i	−0.285475	+	0.900054i
$243$		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		−0.652446	−	0.757835i	$-0.726257\pi$
$251$		0			0		0.652446	+	0.757835i	$0.273743\pi$
$252$	−0.178284	−	0.0798774i	−0.178284	−	0.0798774i
$253$	2.77452	+	0.593137i	2.77452	+	0.593137i
$254$	−1.57488	+	0.336678i	−1.57488	+	0.336678i
$255$		0			0
$256$	0.508995	+	0.238861i	0.508995	+	0.238861i
$257$		0			0		−0.955819	−	0.293956i	$-0.905028\pi$
$257$		0			0		0.955819	+	0.293956i	$0.0949721\pi$
$258$		0			0
$259$	0.440825	+	0.161421i	0.440825	+	0.161421i
$260$		0			0
$261$	1.37944	+	0.0970008i	1.37944	+	0.0970008i
$262$		0			0
$263$	−0.100987	+	0.762763i	−0.100987	+	0.762763i	0.864559	+	0.502531i	$0.167598\pi$
$263$	−0.100987	+	0.762763i	−0.100987	+	0.762763i	−0.965546	+	0.260231i	$0.916201\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.352641	−	0.150621i	−0.352641	−	0.150621i
$269$		0			0		0.625448	−	0.780266i	$-0.284916\pi$
$269$		0			0		−0.625448	+	0.780266i	$0.715084\pi$
$270$		0			0
$271$		0			0		0.955819	−	0.293956i	$-0.0949721\pi$
$271$		0			0		−0.955819	+	0.293956i	$0.905028\pi$
$272$		0			0
$273$		0			0
$274$	0.0818615	−	0.714463i	0.0818615	−	0.714463i
$275$	−1.17079	+	0.825767i	−1.17079	+	0.825767i
$276$		0			0
$277$	0.225950	+	0.0278997i	0.225950	+	0.0278997i	0.234725	−	0.972062i	$-0.424581\pi$
$277$	0.225950	+	0.0278997i	0.225950	+	0.0278997i	−0.00877529	+	0.999961i	$0.502793\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.91693	−	0.552908i	1.91693	−	0.552908i	0.939024	−	0.343852i	$-0.111732\pi$
$281$	1.91693	−	0.552908i	1.91693	−	0.552908i	0.977904	−	0.209056i	$-0.0670391\pi$
$282$		0			0
$283$		0			0		−0.944914	−	0.327319i	$-0.893855\pi$
$283$		0			0		0.944914	+	0.327319i	$0.106145\pi$
$284$	0.281508	+	0.150668i	0.281508	+	0.150668i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.353796	−	0.151115i	0.353796	−	0.151115i
$289$	0.716353	+	0.697738i	0.716353	+	0.697738i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.987551	−	0.157301i	$-0.0502793\pi$
$293$		0			0		−0.987551	+	0.157301i	$0.949721\pi$
$294$		0			0
$295$		0			0
$296$	−0.447905	+	0.229706i	−0.447905	+	0.229706i
$297$		0			0
$298$	−1.29658	−	1.05814i	−1.29658	−	1.05814i
$299$		0			0
$300$		0			0
$301$	−1.33109	−	0.0233640i	−1.33109	−	0.0233640i
$302$	1.54840	+	0.794091i	1.54840	+	0.794091i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.763532	−	0.645770i	$-0.776536\pi$
$307$		0			0		0.763532	+	0.645770i	$0.223464\pi$
$308$	0.0416002	+	0.276784i	0.0416002	+	0.276784i
$309$		0			0
$310$		0			0
$311$		0			0		0.950513	−	0.310686i	$-0.100559\pi$
$311$		0			0		−0.950513	+	0.310686i	$0.899441\pi$
$312$		0			0
$313$		0			0		0.665645	−	0.746268i	$-0.268156\pi$
$313$		0			0		−0.665645	+	0.746268i	$0.731844\pi$
$314$		0			0
$315$		0			0
$316$	−0.245929	+	0.160836i	−0.245929	+	0.160836i
$317$	1.73333	+	0.967216i	1.73333	+	0.967216i	0.926378	+	0.376595i	$0.122905\pi$
$317$	1.73333	+	0.967216i	1.73333	+	0.967216i	0.806949	+	0.590621i	$0.201117\pi$
$318$		0			0
$319$	−0.950190	−	1.73849i	−0.950190	−	1.73849i
$320$		0			0
$321$		0			0
$322$	−1.72303	+	0.432098i	−1.72303	+	0.432098i
$323$		0			0
$324$	0.0623226	−	0.185152i	0.0623226	−	0.185152i
$325$		0			0
$326$	1.01546	+	1.46691i	1.01546	+	1.46691i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.144001	−	1.81949i	−0.144001	−	1.81949i	−0.479599	−	0.877488i	$-0.659218\pi$
$331$	−0.144001	−	1.81949i	−0.144001	−	1.81949i	0.335599	−	0.942005i	$-0.391061\pi$
$332$		0			0
$333$	−0.118183	+	0.454330i	−0.118183	+	0.454330i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.708038	−	1.78647i	0.708038	−	1.78647i	0.0963795	−	0.995345i	$-0.469274\pi$
$337$	0.708038	−	1.78647i	0.708038	−	1.78647i	0.611658	−	0.791122i	$-0.290503\pi$
$338$	−0.0550672	+	0.895326i	−0.0550672	+	0.895326i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.217629	+	0.976031i	−0.217629	+	0.976031i
$344$	0.987001	−	1.03129i	0.987001	−	1.03129i
$345$		0			0
$346$		0			0
$347$	0.359190	−	0.954874i	0.359190	−	0.954874i	−0.625448	−	0.780266i	$-0.715084\pi$
$347$	0.359190	−	0.954874i	0.359190	−	0.954874i	0.984638	−	0.174608i	$-0.0558659\pi$
$348$		0			0
$349$		0			0		−0.984638	−	0.174608i	$-0.944134\pi$
$349$		0			0		0.984638	+	0.174608i	$0.0558659\pi$
$350$	0.430209	−	0.787122i	0.430209	−	0.787122i
$351$		0			0
$352$	−0.455930	−	0.309733i	−0.455930	−	0.309733i
$353$		0			0		0.996152	−	0.0876414i	$-0.0279330\pi$
$353$		0			0		−0.996152	+	0.0876414i	$0.972067\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.42888			1.42888
$359$	0.897680	−	0.440648i	0.897680	−	0.440648i
$359$	0.897680	−	0.440648i	0.897680	−	0.440648i
$360$		0			0
$361$	0.432754	−	0.901512i	0.432754	−	0.901512i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.974084	−	0.226186i	$-0.0726257\pi$
$367$		0			0		−0.974084	+	0.226186i	$0.927374\pi$
$368$	0.727966	−	1.33191i	0.727966	−	1.33191i
$369$		0			0
$370$		0			0
$371$	0.602482	−	1.60164i	0.602482	−	1.60164i
$372$		0			0
$373$	−0.720810	+	0.418976i	−0.720810	+	0.418976i	−0.817190	−	0.576369i	$-0.804469\pi$
$373$	−0.720810	+	0.418976i	−0.720810	+	0.418976i	0.0963795	+	0.995345i	$0.469274\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.313576	−	0.436414i	0.313576	−	0.436414i	−0.625448	−	0.780266i	$-0.715084\pi$
$379$	0.313576	−	0.436414i	0.313576	−	0.436414i	0.939024	+	0.343852i	$0.111732\pi$
$380$		0			0
$381$		0			0
$382$	1.71713	+	0.495280i	1.71713	+	0.495280i
$383$		0			0		−0.691425	−	0.722448i	$-0.743017\pi$
$383$		0			0		0.691425	+	0.722448i	$0.256983\pi$
$384$		0			0
$385$		0			0
$386$	−0.887366	+	0.0311608i	−0.887366	+	0.0311608i
$387$	−0.105034	−	1.32714i	−0.105034	−	1.32714i
$388$		0			0
$389$	0.440414	+	1.17080i	0.440414	+	1.17080i	0.950513	+	0.310686i	$0.100559\pi$
$389$	0.440414	+	1.17080i	0.440414	+	1.17080i	−0.510099	+	0.860116i	$0.670391\pi$
$390$		0			0
$391$		0			0
$392$	−0.610303	−	0.881628i	−0.610303	−	0.881628i
$393$		0			0
$394$	0.559677	−	1.66273i	0.559677	−	1.66273i
$395$		0			0
$396$	−0.271486	+	0.0680829i	−0.271486	+	0.0680829i
$397$		0			0		−0.113833	−	0.993500i	$-0.536313\pi$
$397$		0			0		0.113833	+	0.993500i	$0.463687\pi$
$398$		0			0
$399$		0			0
$400$	0.244517	+	0.726426i	0.244517	+	0.726426i
$401$	1.18524	+	0.661376i	1.18524	+	0.661376i	0.950513	−	0.310686i	$-0.100559\pi$
$401$	1.18524	+	0.661376i	1.18524	+	0.661376i	0.234725	+	0.972062i	$0.424581\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.01368	+	0.714951i	1.01368	+	0.714951i
$407$	0.639300	−	0.208962i	0.639300	−	0.208962i
$408$		0			0
$409$		0			0		−0.0963795	−	0.995345i	$-0.530726\pi$
$409$		0			0		0.0963795	+	0.995345i	$0.469274\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.596151	−	1.67336i	−0.596151	−	1.67336i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.996152	−	0.0876414i	$-0.972067\pi$
$419$		0			0		0.996152	+	0.0876414i	$0.0279330\pi$
$420$		0			0
$421$	−0.953885	+	0.100822i	−0.953885	+	0.100822i	−0.569175	−	0.822216i	$-0.692737\pi$
$421$	−0.953885	+	0.100822i	−0.953885	+	0.100822i	−0.384709	+	0.923038i	$0.625698\pi$
$422$	0.740905	−	0.379970i	0.740905	−	0.379970i
$423$		0			0
$424$	0.822952	+	1.63996i	0.822952	+	1.63996i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.0346316	−	0.133134i	−0.0346316	−	0.133134i
$429$		0			0
$430$		0			0
$431$	−0.416341	+	1.49251i	−0.416341	+	1.49251i	0.400849	+	0.916144i	$0.368715\pi$
$431$	−0.416341	+	1.49251i	−0.416341	+	1.49251i	−0.817190	+	0.576369i	$0.804469\pi$
$432$		0			0
$433$		0			0		0.200467	−	0.979701i	$-0.435754\pi$
$433$		0			0		−0.200467	+	0.979701i	$0.564246\pi$
$434$		0			0
$435$		0			0
$436$	−0.0207373	−	0.0120537i	−0.0207373	−	0.0120537i
$437$		0			0
$438$		0			0
$439$		0			0		0.998614	−	0.0526281i	$-0.0167598\pi$
$439$		0			0		−0.998614	+	0.0526281i	$0.983240\pi$
$440$		0			0
$441$	−0.992463	−	0.122547i	−0.992463	−	0.122547i
$442$		0			0
$443$	1.47956	−	1.04354i	1.47956	−	1.04354i	0.494925	−	0.868936i	$-0.335196\pi$
$443$	1.47956	−	1.04354i	1.47956	−	1.04354i	0.984638	−	0.174608i	$-0.0558659\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	1.10063	+	0.155560i	1.10063	+	0.155560i
$449$	0.229217	−	0.285955i	0.229217	−	0.285955i	−0.652446	−	0.757835i	$-0.726257\pi$
$449$	0.229217	−	0.285955i	0.229217	−	0.285955i	0.881663	+	0.471880i	$0.156425\pi$
$450$	0.824921	+	0.352343i	0.824921	+	0.352343i
$451$		0			0
$452$	0.0394655	−	0.0753188i	0.0394655	−	0.0753188i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.331105	+	0.0232829i	0.331105	+	0.0232829i	0.234725	−	0.972062i	$-0.424581\pi$
$457$	0.331105	+	0.0232829i	0.331105	+	0.0232829i	0.0963795	+	0.995345i	$0.469274\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.955819	−	0.293956i	$-0.905028\pi$
$461$		0			0		0.955819	+	0.293956i	$0.0949721\pi$
$462$		0			0
$463$	−1.28492	+	0.575692i	−1.28492	+	0.575692i	−0.932845	−	0.360279i	$-0.882682\pi$
$463$	−1.28492	+	0.575692i	−1.28492	+	0.575692i	−0.352079	+	0.935970i	$0.614525\pi$
$464$	−1.03650	+	0.221583i	−1.03650	+	0.221583i
$465$		0			0
$466$	−0.328208	−	0.147049i	−0.328208	−	0.147049i
$467$		0			0		−0.652446	−	0.757835i	$-0.726257\pi$
$467$		0			0		0.652446	+	0.757835i	$0.273743\pi$
$468$		0			0
$469$	−1.95197	−	0.206315i	−1.95197	−	0.206315i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.51912	+	1.15336i	−1.51912	+	1.15336i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.65226	+	0.445312i	1.65226	+	0.445312i
$478$	0.868945	+	1.30356i	0.868945	+	1.30356i
$479$		0			0		0.510099	−	0.860116i	$-0.329609\pi$
$479$		0			0		−0.510099	+	0.860116i	$0.670391\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.149810	+	0.140879i	0.149810	+	0.140879i
$485$		0			0
$486$		0			0
$487$	−0.00759508	−	0.865475i	−0.00759508	−	0.865475i	−0.905275	−	0.424826i	$-0.860335\pi$
$487$	−0.00759508	−	0.865475i	−0.00759508	−	0.865475i	0.897680	−	0.440648i	$-0.145251\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.219713	−	0.737381i	0.219713	−	0.737381i	−0.774747	−	0.632271i	$-0.782123\pi$
$491$	0.219713	−	0.737381i	0.219713	−	0.737381i	0.994461	−	0.105110i	$-0.0335196\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.60402	+	0.313575i	1.60402	+	0.313575i
$498$		0			0
$499$	1.71389	−	0.627593i	1.71389	−	0.627593i	0.716353	−	0.697738i	$-0.245810\pi$
$499$	1.71389	−	0.627593i	1.71389	−	0.627593i	0.997537	+	0.0701455i	$0.0223464\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.752081	−	0.659071i	$-0.770950\pi$
$503$		0			0		0.752081	+	0.659071i	$0.229050\pi$
$504$	0.818703	−	0.692433i	0.818703	−	0.692433i
$505$		0			0
$506$	−1.55669	+	2.01343i	−1.55669	+	2.01343i
$507$		0			0
$508$	−0.0823277	+	0.340942i	−0.0823277	+	0.340942i
$509$		0			0		0.806949	−	0.590621i	$-0.201117\pi$
$509$		0			0		−0.806949	+	0.590621i	$0.798883\pi$
$510$		0			0
$511$		0			0
$512$	−0.865188	+	0.706079i	−0.865188	+	0.706079i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.301660	+	0.293821i	−0.301660	+	0.293821i
$519$		0			0
$520$		0			0
$521$		0			0		0.992463	−	0.122547i	$-0.0391061\pi$
$521$		0			0		−0.992463	+	0.122547i	$0.960894\pi$
$522$	−0.613925	+	1.07786i	−0.613925	+	1.07786i
$523$		0			0		0.539970	−	0.841685i	$-0.318436\pi$
$523$		0			0		−0.539970	+	0.841685i	$0.681564\pi$
$524$		0			0
$525$		0			0
$526$	−0.577623	−	0.377761i	−0.577623	−	0.377761i
$527$		0			0
$528$		0			0
$529$	2.47287	+	1.55597i	2.47287	+	1.55597i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.58289	−	1.38713i	1.58289	−	1.38713i
$537$		0			0
$538$		0			0
$539$	0.620009	+	1.29160i	0.620009	+	1.29160i
$540$		0			0
$541$	0.812201	−	0.711756i	0.812201	−	0.711756i	−0.148629	−	0.988893i	$-0.547486\pi$
$541$	0.812201	−	0.711756i	0.812201	−	0.711756i	0.960831	+	0.277137i	$0.0893855\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.106149	+	1.72586i	0.106149	+	1.72586i	0.554658	+	0.832079i	$0.312849\pi$
$547$	0.106149	+	1.72586i	0.106149	+	1.72586i	−0.448509	+	0.893778i	$0.648045\pi$
$548$	−0.132561	−	0.0834098i	−0.132561	−	0.0834098i
$549$		0			0
$550$	−0.213287	−	1.26734i	−0.213287	−	1.26734i
$551$		0			0
$552$		0			0
$553$	−0.961228	+	1.15695i	−0.961228	+	1.15695i
$554$	−0.110273	+	0.171889i	−0.110273	+	0.171889i
$555$		0			0
$556$		0			0
$557$	−1.22162	−	1.47037i	−1.22162	−	1.47037i	−0.836914	−	0.547335i	$-0.815642\pi$
$557$	−1.22162	−	1.47037i	−1.22162	−	1.47037i	−0.384709	−	0.923038i	$-0.625698\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.297007	+	1.76480i	−0.297007	+	1.76480i
$563$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$563$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0263232	−	0.999653i	0.0263232	−	0.999653i
$568$	−1.41416	+	1.03505i	−1.41416	+	1.03505i
$569$	0.388319	−	1.60814i	0.388319	−	1.60814i	−0.352079	−	0.935970i	$-0.614525\pi$
$569$	0.388319	−	1.60814i	0.388319	−	1.60814i	0.740398	−	0.672168i	$-0.234637\pi$
$570$		0			0
$571$	−1.08852	+	1.40789i	−1.08852	+	1.40789i	−0.183242	+	0.983068i	$0.558659\pi$
$571$	−1.08852	+	1.40789i	−1.08852	+	1.40789i	−0.905275	+	0.424826i	$0.860335\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.91209	+	0.515341i	−1.91209	+	0.515341i
$576$	−0.0487568	+	1.11050i	−0.0487568	+	1.11050i
$577$		0			0		0.0788965	−	0.996883i	$-0.474860\pi$
$577$		0			0		−0.0788965	+	0.996883i	$0.525140\pi$
$578$	−0.842321	+	0.308441i	−0.842321	+	0.308441i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.741219	−	2.33693i	−0.741219	−	2.33693i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.200467	−	0.979701i	$-0.564246\pi$
$587$		0			0		0.200467	+	0.979701i	$0.435754\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.00947164	−	0.359697i	−0.00947164	−	0.359697i
$593$		0			0		−0.728488	−	0.685059i	$-0.759777\pi$
$593$		0			0		0.728488	+	0.685059i	$0.240223\pi$
$594$		0			0
$595$		0			0
$596$	−0.329955	+	0.154841i	−0.329955	+	0.154841i
$597$		0			0
$598$		0			0
$599$	−1.07110	−	1.60682i	−1.07110	−	1.60682i	−0.752081	−	0.659071i	$-0.770950\pi$
$599$	−1.07110	−	1.60682i	−1.07110	−	1.60682i	−0.319015	−	0.947750i	$-0.603352\pi$
$600$		0			0
$601$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$601$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$602$	0.535605	−	1.06734i	0.535605	−	1.06734i
$603$	0.0172245	−	1.96277i	0.0172245	−	1.96277i
$604$	0.301845	−	0.229169i	0.301845	−	0.229169i
$605$		0			0
$606$		0			0
$607$		0			0		−0.703997	−	0.710203i	$-0.748603\pi$
$607$		0			0		0.703997	+	0.710203i	$0.251397\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.290690	+	0.0621436i	−0.290690	+	0.0621436i	−0.352079	−	0.935970i	$-0.614525\pi$
$613$	−0.290690	+	0.0621436i	−0.290690	+	0.0621436i	0.0613892	+	0.998114i	$0.480447\pi$
$614$		0			0
$615$		0			0
$616$	−1.46836	−	0.451585i	−1.46836	−	0.451585i
$617$	−0.982859	+	0.773776i	−0.982859	+	0.773776i	−0.974084	−	0.226186i	$-0.927374\pi$
$617$	−0.982859	+	0.773776i	−0.982859	+	0.773776i	−0.00877529	+	0.999961i	$0.502793\pi$
$618$		0			0
$619$		0			0		0.416866	−	0.908968i	$-0.363128\pi$
$619$		0			0		−0.416866	+	0.908968i	$0.636872\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.464125	−	0.885770i	0.464125	−	0.885770i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.597765	+	0.863516i	−0.597765	+	0.863516i	−0.998614	−	0.0526281i	$-0.983240\pi$
$631$	−0.597765	+	0.863516i	−0.597765	+	0.863516i	0.400849	+	0.916144i	$0.368715\pi$
$632$	−0.211688	−	1.59890i	−0.211688	−	1.59890i
$633$		0			0
$634$	−1.45502	+	1.02623i	−1.45502	+	1.02623i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.77472	−	0.0935299i	1.77472	−	0.0935299i
$639$	−0.157521	+	1.62677i	−0.157521	+	1.62677i
$640$		0			0
$641$	−1.72885	−	1.00491i	−1.72885	−	1.00491i	−0.873245	−	0.487281i	$-0.837989\pi$
$641$	−1.72885	−	1.00491i	−1.72885	−	1.00491i	−0.855607	−	0.517627i	$-0.826816\pi$
$642$		0			0
$643$		0			0		−0.881663	−	0.471880i	$-0.843575\pi$
$643$		0			0		0.881663	+	0.471880i	$0.156425\pi$
$644$	−0.0775554	+	0.379021i	−0.0775554	+	0.379021i
$645$		0			0
$646$		0			0
$647$		0			0		0.919626	−	0.392794i	$-0.128492\pi$
$647$		0			0		−0.919626	+	0.392794i	$0.871508\pi$
$648$	0.768116	+	0.748156i	0.768116	+	0.748156i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.383718	−	0.0611202i	0.383718	−	0.0611202i
$653$	0.373936	+	0.745171i	0.373936	+	0.745171i	0.999384	−	0.0350944i	$-0.0111732\pi$
$653$	0.373936	+	0.745171i	0.373936	+	0.745171i	−0.625448	+	0.780266i	$0.715084\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.326101	+	1.74948i	0.326101	+	1.74948i	0.611658	+	0.791122i	$0.290503\pi$
$659$	0.326101	+	1.74948i	0.326101	+	1.74948i	−0.285558	+	0.958362i	$0.592179\pi$
$660$		0			0
$661$		0			0		−0.889808	−	0.456335i	$-0.849162\pi$
$661$		0			0		0.889808	+	0.456335i	$0.150838\pi$
$662$	1.52727	+	0.589856i	1.52727	+	0.589856i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.321527	−	0.271937i	−0.321527	−	0.271937i
$667$	−0.407018	−	2.70807i	−0.407018	−	2.70807i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.964197	−	0.223890i	−0.964197	−	0.223890i	−0.285558	−	0.958362i	$-0.592179\pi$
$673$	−0.964197	−	0.223890i	−0.964197	−	0.223890i	−0.678640	+	0.734471i	$0.737430\pi$
$674$	1.16981	+	1.26605i	1.16981	+	1.26605i
$675$		0			0
$676$	0.170597	+	0.0951950i	0.170597	+	0.0951950i
$677$		0			0		−0.319015	−	0.947750i	$-0.603352\pi$
$677$		0			0		0.319015	+	0.947750i	$0.396648\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.214122	+	0.636127i	−0.214122	+	0.636127i	0.785724	+	0.618577i	$0.212291\pi$
$683$	−0.214122	+	0.636127i	−0.214122	+	0.636127i	−0.999846	+	0.0175499i	$0.994413\pi$
$684$		0			0
$685$		0			0
$686$	−0.704808	−	0.554874i	−0.704808	−	0.554874i
$687$		0			0
$688$	0.359262	+	0.955065i	0.359262	+	0.955065i
$689$		0			0
$690$		0			0
$691$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$691$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$692$		0			0
$693$	−1.22583	+	0.741607i	−1.22583	+	0.741607i
$694$	0.632747	+	0.661137i	0.632747	+	0.661137i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.113996	−	0.158652i	−0.113996	−	0.158652i
$701$	1.73978	+	0.707263i	1.73978	+	0.707263i	0.999384	+	0.0350944i	$0.0111732\pi$
$701$	1.73978	+	0.707263i	1.73978	+	0.707263i	0.740398	+	0.672168i	$0.234637\pi$
$702$		0			0
$703$		0			0
$704$	1.37686	−	0.800309i	1.37686	−	0.800309i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.305998	−	0.559863i	0.305998	−	0.559863i	−0.678640	−	0.734471i	$-0.737430\pi$
$709$	0.305998	−	0.559863i	0.305998	−	0.559863i	0.984638	+	0.174608i	$0.0558659\pi$
$710$		0			0
$711$	−1.24421	−	0.845246i	−1.24421	−	0.845246i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.134670	−	0.280543i	0.134670	−	0.280543i
$717$		0			0
$718$	0.00787158	+	0.896983i	0.00787158	+	0.896983i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.561038	+	0.699912i	0.561038	+	0.699912i
$723$		0			0
$724$		0			0
$725$	1.14386	+	0.777076i	1.14386	+	0.777076i
$726$		0			0
$727$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$727$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$728$		0			0
$729$	0.997537	−	0.0701455i	0.997537	−	0.0701455i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$733$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$734$		0			0
$735$		0			0
$736$	−0.444560	−	0.618709i	−0.444560	−	0.618709i
$737$	−2.38020	+	1.49766i	−2.38020	+	1.49766i
$738$		0			0
$739$	0.0161148	−	0.262007i	0.0161148	−	0.262007i	−0.981422	−	0.191862i	$-0.938547\pi$
$739$	0.0161148	−	0.262007i	0.0161148	−	0.262007i	0.997537	−	0.0701455i	$-0.0223464\pi$
$740$		0			0
$741$		0			0
$742$	1.06133	+	1.10895i	1.06133	+	1.10895i
$743$	−0.949138	+	0.574211i	−0.949138	+	0.574211i	−0.905275	−	0.424826i	$-0.860335\pi$
$743$	−0.949138	+	0.574211i	−0.949138	+	0.574211i	−0.0438629	+	0.999038i	$0.513966\pi$
$744$		0			0
$745$		0			0
$746$	−0.0590045	−	0.745541i	−0.0590045	−	0.745541i
$747$		0			0
$748$		0			0
$749$	−0.369764	−	0.599260i	−0.369764	−	0.599260i
$750$		0			0
$751$	0.742712	+	1.07290i	0.742712	+	1.07290i	0.994461	+	0.105110i	$0.0335196\pi$
$751$	0.742712	+	1.07290i	0.742712	+	1.07290i	−0.251749	+	0.967793i	$0.581006\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.868595	−	0.973799i	−0.868595	−	0.973799i	0.131251	−	0.991349i	$-0.458101\pi$
$757$	−0.868595	−	0.973799i	−0.868595	−	0.973799i	−0.999846	+	0.0175499i	$0.994413\pi$
$758$	0.231189	+	0.422990i	0.231189	+	0.422990i
$759$		0			0
$760$		0			0
$761$		0			0		0.836914	−	0.547335i	$-0.184358\pi$
$761$		0			0		−0.836914	+	0.547335i	$0.815642\pi$
$762$		0			0
$763$	−0.119596	−	0.0277707i	−0.119596	−	0.0277707i
$764$	0.259080	−	0.290460i	0.259080	−	0.290460i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.148629	−	0.988893i	$-0.547486\pi$
$769$		0			0		0.148629	+	0.988893i	$0.452514\pi$
$770$		0			0
$771$		0			0
$772$	−0.0775150	+	0.177161i	−0.0775150	+	0.177161i
$773$		0			0		−0.335599	−	0.942005i	$-0.608939\pi$
$773$		0			0		0.335599	+	0.942005i	$0.391061\pi$
$774$	1.11399	+	0.430242i	1.11399	+	0.430242i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.11776	−	0.0983403i	−1.11776	−	0.0983403i
$779$		0			0
$780$		0			0
$781$	2.08356	−	1.06855i	2.08356	−	1.06855i
$782$		0			0
$783$		0			0
$784$	0.756933	−	0.120567i	0.756933	−	0.120567i
$785$		0			0
$786$		0			0
$787$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$787$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$788$	−0.273708	−	0.266596i	−0.273708	−	0.266596i
$789$		0			0
$790$		0			0
$791$	0.0797577	−	0.427889i	0.0797577	−	0.427889i
$792$	0.307963	−	1.50505i	0.307963	−	1.50505i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.0963795	−	0.995345i	$-0.469274\pi$
$797$		0			0		−0.0963795	+	0.995345i	$0.530726\pi$
$798$		0			0
$799$		0			0
$800$	0.381818	+	0.0471458i	0.381818	+	0.0471458i
$801$		0			0
$802$	−0.994931	+	0.701731i	−0.994931	+	0.701731i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.79861	−	0.768230i	−1.79861	−	0.768230i	−0.981422	−	0.191862i	$-0.938547\pi$
$809$	−1.79861	−	0.768230i	−1.79861	−	0.768230i	−0.817190	−	0.576369i	$-0.804469\pi$
$810$		0			0
$811$		0			0		0.464125	−	0.885770i	$-0.346369\pi$
$811$		0			0		−0.464125	+	0.885770i	$0.653631\pi$
$812$	0.235910	−	0.131640i	0.235910	−	0.131640i
$813$		0			0
$814$	−0.0791864	+	0.598100i	−0.0791864	+	0.598100i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.950747	−	0.446165i	−0.950747	−	0.446165i	−0.113833	−	0.993500i	$-0.536313\pi$
$821$	−0.950747	−	0.446165i	−0.950747	−	0.446165i	−0.836914	+	0.547335i	$0.815642\pi$
$822$		0			0
$823$	1.85902	−	0.397421i	1.85902	−	0.397421i	0.864559	−	0.502531i	$-0.167598\pi$
$823$	1.85902	−	0.397421i	1.85902	−	0.397421i	0.994461	+	0.105110i	$0.0335196\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.19226	+	0.460469i	−1.19226	+	0.460469i	−0.873245	−	0.487281i	$-0.837989\pi$
$827$	−1.19226	+	0.460469i	−1.19226	+	0.460469i	−0.319015	+	0.947750i	$0.603352\pi$
$828$	−0.384731	−	0.0406645i	−0.384731	−	0.0406645i
$829$		0			0		−0.703997	−	0.710203i	$-0.748603\pi$
$829$		0			0		0.703997	+	0.710203i	$0.251397\pi$
$830$		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		0.990159	−	0.139946i	$-0.0446927\pi$
$839$		0			0		−0.990159	+	0.139946i	$0.955307\pi$
$840$		0			0
$841$	−0.595209	+	0.691354i	−0.595209	+	0.691354i
$842$	0.288755	−	0.810518i	0.288755	−	0.810518i
$843$		0			0
$844$	−0.00477351	−	0.181280i	−0.00477351	−	0.181280i
$845$		0			0
$846$		0			0
$847$	0.944939	+	0.463847i	0.944939	+	0.463847i
$848$	−1.31140	+	0.0230185i	−1.31140	+	0.0230185i
$849$		0			0
$850$		0			0
$851$	0.929088	+	0.0326259i	0.929088	+	0.0326259i
$852$		0			0
$853$		0			0		−0.302333	−	0.953202i	$-0.597765\pi$
$853$		0			0		0.302333	+	0.953202i	$0.402235\pi$
$854$		0			0
$855$		0			0
$856$	0.741012	+	0.144863i	0.741012	+	0.144863i
$857$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$857$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$858$		0			0
$859$		0			0		0.0788965	−	0.996883i	$-0.474860\pi$
$859$		0			0		−0.0788965	+	0.996883i	$0.525140\pi$
$860$		0			0
$861$		0			0
$862$	−1.04533	−	0.916058i	−1.04533	−	0.916058i
$863$	−1.52495	+	1.28975i	−1.52495	+	1.28975i	−0.728488	+	0.685059i	$0.759777\pi$
$863$	−1.52495	+	1.28975i	−1.52495	+	1.28975i	−0.796459	+	0.604692i	$0.793296\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.0567270	+	2.15427i	−0.0567270	+	2.15427i
$870$		0			0
$871$		0			0
$872$	0.108898	−	0.0739792i	0.108898	−	0.0739792i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.33649	+	1.30176i	−1.33649	+	1.30176i	−0.416866	+	0.908968i	$0.636872\pi$
$877$	−1.33649	+	1.30176i	−1.33649	+	1.30176i	−0.919626	+	0.392794i	$0.871508\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.494925	−	0.868936i	$-0.335196\pi$
$881$		0			0		−0.494925	+	0.868936i	$0.664804\pi$
$882$	0.484362	−	0.755006i	0.484362	−	0.755006i
$883$	−1.06965	+	1.28746i	−1.06965	+	1.28746i	−0.113833	+	0.993500i	$0.536313\pi$
$883$	−1.06965	+	1.28746i	−1.06965	+	1.28746i	−0.955819	+	0.293956i	$0.905028\pi$
$884$		0			0
$885$		0			0
$886$	0.269537	+	1.60157i	0.269537	+	1.60157i
$887$		0			0		0.926378	−	0.376595i	$-0.122905\pi$
$887$		0			0		−0.926378	+	0.376595i	$0.877095\pi$
$888$		0			0
$889$	0.110216	+	1.79197i	0.110216	+	1.79197i
$890$		0			0
$891$	−0.856299	−	1.14865i	−0.856299	−	1.14865i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.339663	+	0.509551i	−0.339663	+	0.509551i
$897$		0			0
$898$	0.142265	+	0.296366i	0.142265	+	0.296366i
$899$		0			0
$900$	0.146926	−	0.128756i	0.146926	−	0.128756i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.278943	+	0.374178i	0.278943	+	0.374178i
$905$		0			0
$906$		0			0
$907$	−1.69252	−	1.06496i	−1.69252	−	1.06496i	−0.855607	−	0.517627i	$-0.826816\pi$
$907$	−1.69252	−	1.06496i	−1.69252	−	1.06496i	−0.836914	−	0.547335i	$-0.815642\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.00814567	−	0.0155458i	−0.00814567	−	0.0155458i	0.881663	−	0.471880i	$-0.156425\pi$
$911$	−0.00814567	−	0.0155458i	−0.00814567	−	0.0155458i	−0.889808	+	0.456335i	$0.849162\pi$
$912$		0			0
$913$		0			0
$914$	−0.147359	+	0.258717i	−0.147359	+	0.258717i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.30657	−	0.790449i	−1.30657	−	0.790449i	−0.319015	−	0.947750i	$-0.603352\pi$
$919$	−1.30657	−	0.790449i	−1.30657	−	0.790449i	−0.987551	+	0.157301i	$0.949721\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.330492	+	0.333405i	−0.330492	+	0.333405i
$926$	0.0332460	−	1.26256i	0.0332460	−	1.26256i
$927$		0			0
$928$	−0.124875	+	0.517143i	−0.124875	+	0.517143i
$929$		0			0		−0.796459	−	0.604692i	$-0.793296\pi$
$929$		0			0		0.796459	+	0.604692i	$0.206704\pi$
$930$		0			0
$931$		0			0
$932$	−0.0598045	+	0.0505807i	−0.0598045	+	0.0505807i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.939024	−	0.343852i	$-0.111732\pi$
$937$		0			0		−0.939024	+	0.343852i	$0.888268\pi$
$938$	0.924573	−	1.49842i	0.924573	−	1.49842i
$939$		0			0
$940$		0			0
$941$		0			0		−0.987551	−	0.157301i	$-0.949721\pi$
$941$		0			0		0.987551	+	0.157301i	$0.0502793\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.342983	−	1.67619i	−0.342983	−	1.67619i
$947$	−1.57121	+	0.0275788i	−1.57121	+	0.0275788i	−0.796459	−	0.604692i	$-0.793296\pi$
$947$	−1.57121	+	0.0275788i	−1.57121	+	0.0275788i	−0.774747	+	0.632271i	$0.782123\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.527376	−	1.48031i	0.527376	−	1.48031i	−0.319015	−	0.947750i	$-0.603352\pi$
$953$	0.527376	−	1.48031i	0.527376	−	1.48031i	0.846391	−	0.532563i	$-0.178771\pi$
$954$	−1.00150	+	1.16327i	−1.00150	+	1.16327i
$955$		0			0
$956$	0.337836	−	0.0477486i	0.337836	−	0.0477486i
$957$		0			0
$958$		0			0
$959$	−0.774077	−	0.208627i	−0.774077	−	0.208627i
$960$		0			0
$961$	−0.448509	+	0.893778i	−0.448509	+	0.893778i
$962$		0			0
$963$	0.560833	−	0.425799i	0.560833	−	0.425799i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.07396	−	0.113513i	−1.07396	−	0.113513i	−0.448509	−	0.893778i	$-0.648045\pi$
$967$	−1.07396	−	0.113513i	−1.07396	−	0.113513i	−0.625448	+	0.780266i	$0.715084\pi$
$968$	−1.05291	+	0.406650i	−1.05291	+	0.406650i
$969$		0			0
$970$		0			0
$971$		0			0		−0.977904	−	0.209056i	$-0.932961\pi$
$971$		0			0		0.977904	+	0.209056i	$0.0670391\pi$
$972$		0			0
$973$		0			0
$974$	0.702833	+	0.329825i	0.702833	+	0.329825i
$975$		0			0
$976$		0			0
$977$	1.51549	+	0.554942i	1.51549	+	0.554942i	0.960831	−	0.277137i	$-0.0893855\pi$
$977$	1.51549	+	0.554942i	1.51549	+	0.554942i	0.554658	+	0.832079i	$0.312849\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.0161148	−	0.121716i	0.0161148	−	0.121716i
$982$	0.511010	+	0.463918i	0.511010	+	0.463918i
$983$		0			0		0.873245	−	0.487281i	$-0.162011\pi$
$983$		0			0		−0.873245	+	0.487281i	$0.837989\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.51990	+	0.774981i	−2.51990	+	0.774981i
$990$		0			0
$991$	0.231439	+	1.74807i	0.231439	+	1.74807i	0.583517	+	0.812101i	$0.301676\pi$
$991$	0.231439	+	1.74807i	0.231439	+	1.74807i	−0.352079	+	0.935970i	$0.614525\pi$
$992$		0			0
$993$		0			0
$994$	−0.876239	+	1.17540i	−0.876239	+	1.17540i
$995$		0			0
$996$		0			0
$997$		0			0		0.998614	−	0.0526281i	$-0.0167598\pi$
$997$		0			0		−0.998614	+	0.0526281i	$0.983240\pi$
$998$	−0.157795	+	1.62960i	−0.157795	+	1.62960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.216.1	✓	178
7.6	odd	2	CM	2513.1.l.a.216.1	✓	178
359.241	even	179	inner	2513.1.l.a.2036.1	yes	178
2513.2036	odd	358	inner	2513.1.l.a.2036.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.216.1	✓	178	1.1	even	1	trivial
2513.1.l.a.216.1	✓	178	7.6	odd	2	CM
2513.1.l.a.2036.1	yes	178	359.241	even	179	inner
2513.1.l.a.2036.1	yes	178	2513.2036	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)

\(f(q)\)	\(=\)	\(q+(-0.388188 + 0.808672i) q^{2} +(0.122187 + 0.152433i) q^{4} +(0.827179 + 0.561938i) q^{7} +(-1.04447 + 0.242530i) q^{8} +(-0.479599 + 0.877488i) q^{9} +O(q^{10})\)	\(q+(-0.388188 + 0.808672i) q^{2} +(0.122187 + 0.152433i) q^{4} +(0.827179 + 0.561938i) q^{7} +(-1.04447 + 0.242530i) q^{8} +(-0.479599 + 0.877488i) q^{9} +(1.42918 - 0.100498i) q^{11} +(-0.775525 + 0.450779i) q^{14} +(0.166807 - 0.748104i) q^{16} +(-0.523425 - 0.728468i) q^{18} +(-0.473519 + 1.19475i) q^{22} +(1.90275 + 0.548819i) q^{23} +(-0.855607 + 0.517627i) q^{25} +(0.0154132 + 0.194751i) q^{28} +(-0.576463 - 1.25697i) q^{29} +(-0.302282 - 0.237977i) q^{32} +(-0.192359 + 0.0341114i) q^{36} +(0.455350 - 0.114192i) q^{37} +(-1.11418 + 0.728662i) q^{43} +(0.189947 + 0.205573i) q^{44} +(-1.18244 + 1.32566i) q^{46} +(0.368451 + 0.929647i) q^{49} +(-0.0864541 - 0.892842i) q^{50} +(-0.401665 - 1.66340i) q^{53} +(-1.00025 - 0.386312i) q^{56} +(1.24025 + 0.0217696i) q^{58} +(-0.889808 + 0.456335i) q^{63} +(0.997837 - 0.489813i) q^{64} +(-1.73057 + 0.926228i) q^{67} +(1.50302 - 0.641975i) q^{71} +(0.288110 - 1.03283i) q^{72} +(-0.0844175 + 0.412557i) q^{74} +(1.23866 + 0.719979i) q^{77} +(-0.144970 + 1.49716i) q^{79} +(-0.539970 - 0.841685i) q^{81} +(-0.156739 - 1.18386i) q^{86} +(-1.46836 + 0.451585i) q^{88} +(0.148834 + 0.357100i) q^{92} +(-0.894808 - 0.0629218i) q^{98} +(-0.597246 + 1.30228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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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