LMFDB - Embedded newform 2513.1.l.a.34.1

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			34.1
Root			$-0.0613892 + 0.998114i$ of defining polynomial
Character	$\chi$	$=$	2513.34
Dual form			2513.1.l.a.1700.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.568219 + 0.415891i) q^{2} +(-0.152425 + 0.480568i) q^{4} +(0.665645 - 0.746268i) q^{7} +(-0.337890 - 1.00383i) q^{8} +(0.716353 + 0.697738i) q^{9} +O(q^{10})$	\(q+(-0.568219 + 0.415891i) q^{2} +(-0.152425 + 0.480568i) q^{4} +(0.665645 - 0.746268i) q^{7} +(-0.337890 - 1.00383i) q^{8} +(0.716353 + 0.697738i) q^{9} +(-1.27452 + 1.37937i) q^{11} +(-0.0678664 + 0.700880i) q^{14} +(0.197482 + 0.139285i) q^{16} +(-0.697228 - 0.0985437i) q^{18} +(0.150537 - 1.31385i) q^{22} +(0.155829 + 0.0248210i) q^{23} +(-0.625448 + 0.780266i) q^{25} +(0.257172 + 0.433638i) q^{28} +(-0.122608 - 0.00646159i) q^{29} +(0.888864 - 0.0156019i) q^{32} +(-0.444500 + 0.237904i) q^{36} +(-0.503187 + 1.93439i) q^{37} +(1.71830 + 0.463112i) q^{43} +(-0.468615 - 0.822743i) q^{44} +(-0.0988677 + 0.0507039i) q^{46} +(-0.113833 - 0.993500i) q^{49} +(0.0308864 - 0.703480i) q^{50} +(-1.25013 + 0.0438994i) q^{53} +(-0.974038 - 0.416035i) q^{56} +(0.0723557 - 0.0473200i) q^{58} +(0.997537 - 0.0701455i) q^{63} +(-0.691053 + 0.524665i) q^{64} +(1.73977 + 0.970812i) q^{67} +(0.216549 + 0.203639i) q^{71} +(0.458359 - 0.954852i) q^{72} +(-0.518576 - 1.30843i) q^{74} +(0.181005 + 1.86930i) q^{77} +(0.0160751 + 0.366131i) q^{79} +(0.0263232 + 0.999653i) q^{81} +(-1.16898 + 0.451477i) q^{86} +(1.81530 + 0.813317i) q^{88} +(-0.0356803 + 0.0711029i) q^{92} +(0.477869 + 0.517184i) q^{98} +(-1.87545 + 0.0988380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{131}{179}\right)$

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 $

$2$	−0.568219	+	0.415891i	−0.568219	+	0.415891i	−0.836914	−	0.547335i	$-0.815642\pi$
$2$	−0.568219	+	0.415891i	−0.568219	+	0.415891i	0.268694	+	0.963225i	$0.413408\pi$
$3$		0			0		−0.926378	−	0.376595i	$-0.877095\pi$
$3$		0			0		0.926378	+	0.376595i	$0.122905\pi$
$4$	−0.152425	+	0.480568i	−0.152425	+	0.480568i
$5$		0			0		−0.432754	−	0.901512i	$-0.642458\pi$
$5$		0			0		0.432754	+	0.901512i	$0.357542\pi$
$6$		0			0
$7$	0.665645	−	0.746268i	0.665645	−	0.746268i
$7$	0.665645	−	0.746268i	0.665645	−	0.746268i
$8$	−0.337890	−	1.00383i	−0.337890	−	1.00383i
$9$	0.716353	+	0.697738i	0.716353	+	0.697738i
$10$		0			0
$11$	−1.27452	+	1.37937i	−1.27452	+	1.37937i	−0.384709	+	0.923038i	$0.625698\pi$
$11$	−1.27452	+	1.37937i	−1.27452	+	1.37937i	−0.889808	+	0.456335i	$0.849162\pi$
$12$		0			0
$13$		0			0		−0.996152	−	0.0876414i	$-0.972067\pi$
$13$		0			0		0.996152	+	0.0876414i	$0.0279330\pi$
$14$	−0.0678664	+	0.700880i	−0.0678664	+	0.700880i
$15$		0			0
$16$	0.197482	+	0.139285i	0.197482	+	0.139285i
$17$		0			0		0.984638	−	0.174608i	$-0.0558659\pi$
$17$		0			0		−0.984638	+	0.174608i	$0.944134\pi$
$18$	−0.697228	−	0.0985437i	−0.697228	−	0.0985437i
$19$		0			0		0.950513	−	0.310686i	$-0.100559\pi$
$19$		0			0		−0.950513	+	0.310686i	$0.899441\pi$
$20$		0			0
$21$		0			0
$22$	0.150537	−	1.31385i	0.150537	−	1.31385i
$23$	0.155829	+	0.0248210i	0.155829	+	0.0248210i	0.234725	−	0.972062i	$-0.424581\pi$
$23$	0.155829	+	0.0248210i	0.155829	+	0.0248210i	−0.0788965	+	0.996883i	$0.525140\pi$
$24$		0			0
$25$	−0.625448	+	0.780266i	−0.625448	+	0.780266i
$26$		0			0
$27$		0			0
$28$	0.257172	+	0.433638i	0.257172	+	0.433638i
$29$	−0.122608	−	0.00646159i	−0.122608	−	0.00646159i	−0.00877529	−	0.999961i	$-0.502793\pi$
$29$	−0.122608	−	0.00646159i	−0.122608	−	0.00646159i	−0.113833	+	0.993500i	$0.536313\pi$
$30$		0			0
$31$		0			0		−0.569175	−	0.822216i	$-0.692737\pi$
$31$		0			0		0.569175	+	0.822216i	$0.307263\pi$
$32$	0.888864	−	0.0156019i	0.888864	−	0.0156019i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.444500	+	0.237904i	−0.444500	+	0.237904i
$37$	−0.503187	+	1.93439i	−0.503187	+	1.93439i	−0.217629	+	0.976031i	$0.569832\pi$
$37$	−0.503187	+	1.93439i	−0.503187	+	1.93439i	−0.285558	+	0.958362i	$0.592179\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.960831	−	0.277137i	$-0.0893855\pi$
$41$		0			0		−0.960831	+	0.277137i	$0.910615\pi$
$42$		0			0
$43$	1.71830	+	0.463112i	1.71830	+	0.463112i	0.977904	−	0.209056i	$-0.0670391\pi$
$43$	1.71830	+	0.463112i	1.71830	+	0.463112i	0.740398	+	0.672168i	$0.234637\pi$
$44$	−0.468615	−	0.822743i	−0.468615	−	0.822743i
$45$		0			0
$46$	−0.0988677	+	0.0507039i	−0.0988677	+	0.0507039i
$47$		0			0		0.148629	−	0.988893i	$-0.452514\pi$
$47$		0			0		−0.148629	+	0.988893i	$0.547486\pi$
$48$		0			0
$49$	−0.113833	−	0.993500i	−0.113833	−	0.993500i
$50$	0.0308864	−	0.703480i	0.0308864	−	0.703480i
$51$		0			0
$52$		0			0
$53$	−1.25013	+	0.0438994i	−1.25013	+	0.0438994i	−0.652446	−	0.757835i	$-0.726257\pi$
$53$	−1.25013	+	0.0438994i	−1.25013	+	0.0438994i	−0.597680	+	0.801735i	$0.703911\pi$
$54$		0			0
$55$		0			0
$56$	−0.974038	−	0.416035i	−0.974038	−	0.416035i
$57$		0			0
$58$	0.0723557	−	0.0473200i	0.0723557	−	0.0473200i
$59$		0			0		−0.200467	−	0.979701i	$-0.564246\pi$
$59$		0			0		0.200467	+	0.979701i	$0.435754\pi$
$60$		0			0
$61$		0			0		0.827179	−	0.561938i	$-0.189944\pi$
$61$		0			0		−0.827179	+	0.561938i	$0.810056\pi$
$62$		0			0
$63$	0.997537	−	0.0701455i	0.997537	−	0.0701455i
$64$	−0.691053	+	0.524665i	−0.691053	+	0.524665i
$65$		0			0
$66$		0			0
$67$	1.73977	+	0.970812i	1.73977	+	0.970812i	0.912591	+	0.408873i	$0.134078\pi$
$67$	1.73977	+	0.970812i	1.73977	+	0.970812i	0.827179	+	0.561938i	$0.189944\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.216549	+	0.203639i	0.216549	+	0.203639i	0.785724	−	0.618577i	$-0.212291\pi$
$71$	0.216549	+	0.203639i	0.216549	+	0.203639i	−0.569175	+	0.822216i	$0.692737\pi$
$72$	0.458359	−	0.954852i	0.458359	−	0.954852i
$73$		0			0		0.200467	−	0.979701i	$-0.435754\pi$
$73$		0			0		−0.200467	+	0.979701i	$0.564246\pi$
$74$	−0.518576	−	1.30843i	−0.518576	−	1.30843i
$75$		0			0
$76$		0			0
$77$	0.181005	+	1.86930i	0.181005	+	1.86930i
$78$		0			0
$79$	0.0160751	+	0.366131i	0.0160751	+	0.366131i	0.990159	+	0.139946i	$0.0446927\pi$
$79$	0.0160751	+	0.366131i	0.0160751	+	0.366131i	−0.974084	+	0.226186i	$0.927374\pi$
$80$		0			0
$81$	0.0263232	+	0.999653i	0.0263232	+	0.999653i
$82$		0			0
$83$		0			0		0.752081	−	0.659071i	$-0.229050\pi$
$83$		0			0		−0.752081	+	0.659071i	$0.770950\pi$
$84$		0			0
$85$		0			0
$86$	−1.16898	+	0.451477i	−1.16898	+	0.451477i
$87$		0			0
$88$	1.81530	+	0.813317i	1.81530	+	0.813317i
$89$		0			0		0.0788965	−	0.996883i	$-0.474860\pi$
$89$		0			0		−0.0788965	+	0.996883i	$0.525140\pi$
$90$		0			0
$91$		0			0
$92$	−0.0356803	+	0.0711029i	−0.0356803	+	0.0711029i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$97$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$98$	0.477869	+	0.517184i	0.477869	+	0.517184i
$99$	−1.87545	+	0.0988380i	−1.87545	+	0.0988380i
$100$	−0.279637	−	0.419502i	−0.279637	−	0.419502i
$101$		0			0		−0.999846	−	0.0175499i	$-0.994413\pi$
$101$		0			0		0.999846	+	0.0175499i	$0.00558659\pi$
$102$		0			0
$103$		0			0		−0.335599	−	0.942005i	$-0.608939\pi$
$103$		0			0		0.335599	+	0.942005i	$0.391061\pi$
$104$		0			0
$105$		0			0
$106$	0.692088	−	0.544860i	0.692088	−	0.544860i
$107$	0.300000	−	1.24238i	0.300000	−	1.24238i	−0.597680	−	0.801735i	$-0.703911\pi$
$107$	0.300000	−	1.24238i	0.300000	−	1.24238i	0.897680	−	0.440648i	$-0.145251\pi$
$108$		0			0
$109$	−1.65106	+	0.705207i	−1.65106	+	0.705207i	−0.998614	−	0.0526281i	$-0.983240\pi$
$109$	−1.65106	+	0.705207i	−1.65106	+	0.705207i	−0.652446	+	0.757835i	$0.726257\pi$
$110$		0			0
$111$		0			0
$112$	0.235397	−	0.0546599i	0.235397	−	0.0546599i
$113$	−1.41302	+	0.821327i	−1.41302	+	0.821327i	−0.996152	−	0.0876414i	$-0.972067\pi$
$113$	−1.41302	+	0.821327i	−1.41302	+	0.821327i	−0.416866	+	0.908968i	$0.636872\pi$
$114$		0			0
$115$		0			0
$116$	0.0217937	−	0.0579367i	0.0217937	−	0.0579367i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.199376	−	2.51919i	−0.199376	−	2.51919i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.537647	+	0.454724i	−0.537647	+	0.454724i
$127$	−0.428008	−	1.53434i	−0.428008	−	1.53434i	−0.796459	−	0.604692i	$-0.793296\pi$
$127$	−0.428008	−	1.53434i	−0.428008	−	1.53434i	0.368451	−	0.929647i	$-0.379888\pi$
$128$	−0.0793947	+	0.266457i	−0.0793947	+	0.266457i
$129$		0			0
$130$		0			0
$131$		0			0		0.368451	−	0.929647i	$-0.379888\pi$
$131$		0			0		−0.368451	+	0.929647i	$0.620112\pi$
$132$		0			0
$133$		0			0
$134$	−1.39232	+	0.171920i	−1.39232	+	0.171920i
$135$		0			0
$136$		0			0
$137$	−0.0151735	+	1.72905i	−0.0151735	+	1.72905i	0.494925	+	0.868936i	$0.335196\pi$
$137$	−0.0151735	+	1.72905i	−0.0151735	+	1.72905i	−0.510099	+	0.860116i	$0.670391\pi$
$138$		0			0
$139$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$139$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$140$		0			0
$141$		0			0
$142$	−0.207739	−	0.0256511i	−0.207739	−	0.0256511i
$143$		0			0
$144$	0.0442822	+	0.237567i	0.0442822	+	0.237567i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.852910	−	0.536665i	−0.852910	−	0.536665i
$149$	−1.83812	−	0.0645474i	−1.83812	−	0.0645474i	−0.905275	−	0.424826i	$-0.860335\pi$
$149$	−1.83812	−	0.0645474i	−1.83812	−	0.0645474i	−0.932845	+	0.360279i	$0.882682\pi$
$150$		0			0
$151$	−0.384436	−	0.325144i	−0.384436	−	0.325144i	0.432754	−	0.901512i	$-0.357542\pi$
$151$	−0.384436	−	0.325144i	−0.384436	−	0.325144i	−0.817190	+	0.576369i	$0.804469\pi$
$152$		0			0
$153$		0			0
$154$	−0.880277	−	0.986897i	−0.880277	−	0.986897i
$155$		0			0
$156$		0			0
$157$		0			0		0.817190	−	0.576369i	$-0.195531\pi$
$157$		0			0		−0.817190	+	0.576369i	$0.804469\pi$
$158$	−0.161405	−	0.201358i	−0.161405	−	0.201358i
$159$		0			0
$160$		0			0
$161$	0.122250	−	0.0997680i	0.122250	−	0.0997680i
$162$	−0.430704	−	0.557075i	−0.430704	−	0.557075i
$163$	1.85472	+	0.362586i	1.85472	+	0.362586i	0.990159	−	0.139946i	$-0.0446927\pi$
$163$	1.85472	+	0.362586i	1.85472	+	0.362586i	0.864559	+	0.502531i	$0.167598\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.965546	−	0.260231i	$-0.0837989\pi$
$167$		0			0		−0.965546	+	0.260231i	$0.916201\pi$
$168$		0			0
$169$	0.984638	+	0.174608i	0.984638	+	0.174608i
$170$		0			0
$171$		0			0
$172$	−0.484468	+	0.755172i	−0.484468	+	0.755172i
$173$		0			0		−0.752081	−	0.659071i	$-0.770950\pi$
$173$		0			0		0.752081	+	0.659071i	$0.229050\pi$
$174$		0			0
$175$	0.165961	+	0.986132i	0.165961	+	0.986132i
$176$	−0.443819	+	0.0948796i	−0.443819	+	0.0948796i
$177$		0			0
$178$		0			0
$179$	1.36599	+	0.999793i	1.36599	+	0.999793i	0.997537	+	0.0701455i	$0.0223464\pi$
$179$	1.36599	+	0.999793i	1.36599	+	0.999793i	0.368451	+	0.929647i	$0.379888\pi$
$180$		0			0
$181$		0			0		−0.525115	−	0.851031i	$-0.675978\pi$
$181$		0			0		0.525115	+	0.851031i	$0.324022\pi$
$182$		0			0
$183$		0			0
$184$	−0.0277369	−	0.164811i	−0.0277369	−	0.164811i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.36571	−	1.37774i	−1.36571	−	1.37774i	−0.855607	−	0.517627i	$-0.826816\pi$
$191$	−1.36571	−	1.37774i	−1.36571	−	1.37774i	−0.510099	−	0.860116i	$-0.670391\pi$
$192$		0			0
$193$	0.427172	−	1.91580i	0.427172	−	1.91580i	0.0263232	−	0.999653i	$-0.491620\pi$
$193$	0.427172	−	1.91580i	0.427172	−	1.91580i	0.400849	−	0.916144i	$-0.368715\pi$
$194$		0			0
$195$		0			0
$196$	0.494795	+	0.0967293i	0.494795	+	0.0967293i
$197$	0.961189	+	1.24321i	0.961189	+	1.24321i	0.969965	+	0.243246i	$0.0782123\pi$
$197$	0.961189	+	1.24321i	0.961189	+	1.24321i	−0.00877529	+	0.999961i	$0.502793\pi$
$198$	1.02456	−	0.836142i	1.02456	−	0.836142i
$199$		0			0		−0.448509	−	0.893778i	$-0.648045\pi$
$199$		0			0		0.448509	+	0.893778i	$0.351955\pi$
$200$	0.994583	+	0.364197i	0.994583	+	0.364197i
$201$		0			0
$202$		0			0
$203$	−0.0864356	+	0.0871975i	−0.0864356	+	0.0871975i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0943097	+	0.126508i	0.0943097	+	0.126508i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.368399	−	0.231803i	−0.368399	−	0.231803i	0.335599	−	0.942005i	$-0.391061\pi$
$211$	−0.368399	−	0.231803i	−0.368399	−	0.231803i	−0.703997	+	0.710203i	$0.748603\pi$
$212$	0.169453	−	0.607462i	0.169453	−	0.607462i
$213$		0			0
$214$	0.346230	+	0.830713i	0.346230	+	0.830713i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.644875	−	1.08737i	0.644875	−	1.08737i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.479599	−	0.877488i	$-0.659218\pi$
$223$		0			0		0.479599	+	0.877488i	$0.340782\pi$
$224$	0.580025	−	0.673716i	0.580025	−	0.673716i
$225$	−0.992463	+	0.122547i	−0.992463	+	0.122547i
$226$	0.461322	−	1.05435i	0.461322	−	1.05435i
$227$		0			0		−0.131251	−	0.991349i	$-0.541899\pi$
$227$		0			0		0.131251	+	0.991349i	$0.458101\pi$
$228$		0			0
$229$		0			0		−0.836914	−	0.547335i	$-0.815642\pi$
$229$		0			0		0.836914	+	0.547335i	$0.184358\pi$
$230$		0			0
$231$		0			0
$232$	0.0349418	+	0.125261i	0.0349418	+	0.125261i
$233$	0.562648	−	0.475869i	0.562648	−	0.475869i	−0.319015	−	0.947750i	$-0.603352\pi$
$233$	0.562648	−	0.475869i	0.562648	−	0.475869i	0.881663	+	0.471880i	$0.156425\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.859911	−	0.349574i	0.859911	−	0.349574i	0.0963795	−	0.995345i	$-0.469274\pi$
$239$	0.859911	−	0.349574i	0.859911	−	0.349574i	0.763532	+	0.645770i	$0.223464\pi$
$240$		0			0
$241$		0			0		−0.740398	−	0.672168i	$-0.765363\pi$
$241$		0			0		0.740398	+	0.672168i	$0.234637\pi$
$242$	1.16100	+	1.34853i	1.16100	+	1.34853i
$243$		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		0.994461	−	0.105110i	$-0.0335196\pi$
$251$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$252$	−0.118339	+	0.490076i	−0.118339	+	0.490076i
$253$	−0.232844	+	0.183311i	−0.232844	+	0.183311i
$254$	0.881320	+	0.693837i	0.881320	+	0.693837i
$255$		0			0
$256$	−0.356888	−	1.00176i	−0.356888	−	1.00176i
$257$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$257$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$258$		0			0
$259$	1.10863	+	1.66313i	1.10863	+	1.66313i
$260$		0			0
$261$	−0.0833222	−	0.0901772i	−0.0833222	−	0.0901772i
$262$		0			0
$263$	0.836778	+	0.323176i	0.836778	+	0.323176i	0.740398	−	0.672168i	$-0.234637\pi$
$263$	0.836778	+	0.323176i	0.836778	+	0.323176i	0.0963795	+	0.995345i	$0.469274\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.731725	+	0.688103i	−0.731725	+	0.688103i
$269$		0			0		−0.302333	−	0.953202i	$-0.597765\pi$
$269$		0			0		0.302333	+	0.953202i	$0.402235\pi$
$270$		0			0
$271$		0			0		−0.912591	−	0.408873i	$-0.865922\pi$
$271$		0			0		0.912591	+	0.408873i	$0.134078\pi$
$272$		0			0
$273$		0			0
$274$	−0.710475	−	0.988791i	−0.710475	−	0.988791i
$275$	−0.279132	−	1.85719i	−0.279132	−	1.85719i
$276$		0			0
$277$	0.713826	−	0.923267i	0.713826	−	0.923267i	−0.285558	−	0.958362i	$-0.592179\pi$
$277$	0.713826	−	0.923267i	0.713826	−	0.923267i	0.999384	+	0.0350944i	$0.0111732\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.34038	−	0.213502i	1.34038	−	0.213502i	0.554658	−	0.832079i	$-0.312849\pi$
$281$	1.34038	−	0.213502i	1.34038	−	0.213502i	0.785724	+	0.618577i	$0.212291\pi$
$282$		0			0
$283$		0			0		−0.00877529	−	0.999961i	$-0.502793\pi$
$283$		0			0		0.00877529	+	0.999961i	$0.497207\pi$
$284$	−0.130870	+	0.0730269i	−0.130870	+	0.0730269i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.647626	+	0.609018i	0.647626	+	0.609018i
$289$	0.939024	−	0.343852i	0.939024	−	0.343852i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$293$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$294$		0			0
$295$		0			0
$296$	2.11181	−	0.148500i	2.11181	−	0.148500i
$297$		0			0
$298$	1.07130	−	0.727780i	1.07130	−	0.727780i
$299$		0			0
$300$		0			0
$301$	1.48939	−	0.974046i	1.48939	−	0.974046i
$302$	0.353668	+	0.0248695i	0.353668	+	0.0248695i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.384709	−	0.923038i	$-0.374302\pi$
$307$		0			0		−0.384709	+	0.923038i	$0.625698\pi$
$308$	−0.925918	−	0.197943i	−0.925918	−	0.197943i
$309$		0			0
$310$		0			0
$311$		0			0		−0.539970	−	0.841685i	$-0.681564\pi$
$311$		0			0		0.539970	+	0.841685i	$0.318436\pi$
$312$		0			0
$313$		0			0		0.889808	−	0.456335i	$-0.150838\pi$
$313$		0			0		−0.889808	+	0.456335i	$0.849162\pi$
$314$		0			0
$315$		0			0
$316$	−0.178401	−	0.0480823i	−0.178401	−	0.0480823i
$317$	0.567772	−	1.08358i	0.567772	−	1.08358i	−0.416866	−	0.908968i	$-0.636872\pi$
$317$	0.567772	−	1.08358i	0.567772	−	1.08358i	0.984638	−	0.174608i	$-0.0558659\pi$
$318$		0			0
$319$	0.165179	−	0.160887i	0.165179	−	0.160887i
$320$		0			0
$321$		0			0
$322$	−0.0279721	+	0.107533i	−0.0279721	+	0.107533i
$323$		0			0
$324$	−0.484414	−	0.139722i	−0.484414	−	0.139722i
$325$		0			0
$326$	−1.20468	+	0.565332i	−1.20468	+	0.565332i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.239466	−	0.403782i	−0.239466	−	0.403782i	0.716353	−	0.697738i	$-0.245810\pi$
$331$	−0.239466	−	0.403782i	−0.239466	−	0.403782i	−0.955819	+	0.293956i	$0.905028\pi$
$332$		0			0
$333$	−1.71016	+	1.03462i	−1.71016	+	1.03462i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.224832	−	1.96226i	0.224832	−	1.96226i	−0.0438629	−	0.999038i	$-0.513966\pi$
$337$	0.224832	−	1.96226i	0.224832	−	1.96226i	0.268694	−	0.963225i	$-0.413408\pi$
$338$	−0.632108	+	0.310286i	−0.632108	+	0.310286i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.817190	−	0.576369i	−0.817190	−	0.576369i
$344$	−0.115713	−	1.88136i	−0.115713	−	1.88136i
$345$		0			0
$346$		0			0
$347$	1.18400	−	1.42508i	1.18400	−	1.42508i	0.302333	−	0.953202i	$-0.402235\pi$
$347$	1.18400	−	1.42508i	1.18400	−	1.42508i	0.881663	−	0.471880i	$-0.156425\pi$
$348$		0			0
$349$		0			0		−0.881663	−	0.471880i	$-0.843575\pi$
$349$		0			0		0.881663	+	0.471880i	$0.156425\pi$
$350$	−0.504426	−	0.491318i	−0.504426	−	0.491318i
$351$		0			0
$352$	−1.11135	+	1.24596i	−1.11135	+	1.24596i
$353$		0			0		0.969965	−	0.243246i	$-0.0782123\pi$
$353$		0			0		−0.969965	+	0.243246i	$0.921788\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.19199			−1.19199
$359$	−0.796459	+	0.604692i	−0.796459	+	0.604692i
$359$	−0.796459	+	0.604692i	−0.796459	+	0.604692i
$360$		0			0
$361$	0.806949	−	0.590621i	0.806949	−	0.590621i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.319015	−	0.947750i	$-0.603352\pi$
$367$		0			0		0.319015	+	0.947750i	$0.396648\pi$
$368$	0.0273161	+	0.0266063i	0.0273161	+	0.0266063i
$369$		0			0
$370$		0			0
$371$	−0.799379	+	0.962151i	−0.799379	+	0.962151i
$372$		0			0
$373$	−0.192492	+	1.98793i	−0.192492	+	1.98793i	−0.0438629	+	0.999038i	$0.513966\pi$
$373$	−0.192492	+	1.98793i	−0.192492	+	1.98793i	−0.148629	+	0.988893i	$0.547486\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.856991	−	0.121124i	0.856991	−	0.121124i	0.302333	−	0.953202i	$-0.402235\pi$
$379$	0.856991	−	0.121124i	0.856991	−	0.121124i	0.554658	+	0.832079i	$0.312849\pi$
$380$		0			0
$381$		0			0
$382$	1.34901	+	0.214876i	1.34901	+	0.214876i
$383$		0			0		0.0613892	−	0.998114i	$-0.480447\pi$
$383$		0			0		−0.0613892	+	0.998114i	$0.519553\pi$
$384$		0			0
$385$		0			0
$386$	0.554035	+	1.26625i	0.554035	+	1.26625i
$387$	0.907780	+	1.53068i	0.907780	+	1.53068i
$388$		0			0
$389$	0.386409	+	0.465090i	0.386409	+	0.465090i	0.926378	−	0.376595i	$-0.122905\pi$
$389$	0.386409	+	0.465090i	0.386409	+	0.465090i	−0.539970	+	0.841685i	$0.681564\pi$
$390$		0			0
$391$		0			0
$392$	−0.958838	+	0.449962i	−0.958838	+	0.449962i
$393$		0			0
$394$	−1.06320	−	0.306665i	−1.06320	−	0.306665i
$395$		0			0
$396$	0.238366	−	0.916345i	0.238366	−	0.916345i
$397$		0			0		0.583517	−	0.812101i	$-0.301676\pi$
$397$		0			0		−0.583517	+	0.812101i	$0.698324\pi$
$398$		0			0
$399$		0			0
$400$	−0.232194	+	0.0669727i	−0.232194	+	0.0669727i
$401$	0.459414	−	0.876779i	0.459414	−	0.876779i	−0.539970	−	0.841685i	$-0.681564\pi$
$401$	0.459414	−	0.876779i	0.459414	−	0.876779i	0.999384	−	0.0350944i	$-0.0111732\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.0128498	−	0.0854951i	0.0128498	−	0.0854951i
$407$	−2.02693	−	3.15950i	−2.02693	−	3.15950i
$408$		0			0
$409$		0			0		0.0438629	−	0.999038i	$-0.486034\pi$
$409$		0			0		−0.0438629	+	0.999038i	$0.513966\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.106202	−	0.0326619i	−0.106202	−	0.0326619i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.969965	−	0.243246i	$-0.921788\pi$
$419$		0			0		0.969965	+	0.243246i	$0.0782123\pi$
$420$		0			0
$421$	−1.35378	−	0.468952i	−1.35378	−	0.468952i	−0.448509	−	0.893778i	$-0.648045\pi$
$421$	−1.35378	−	0.468952i	−1.35378	−	0.468952i	−0.905275	+	0.424826i	$0.860335\pi$
$422$	0.305736	−	0.0214990i	0.305736	−	0.0214990i
$423$		0			0
$424$	0.466472	+	1.24007i	0.466472	+	1.24007i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.551322	+	0.333540i	0.551322	+	0.333540i
$429$		0			0
$430$		0			0
$431$	0.715930	−	1.49142i	0.715930	−	1.49142i	−0.148629	−	0.988893i	$-0.547486\pi$
$431$	0.715930	−	1.49142i	0.715930	−	1.49142i	0.864559	−	0.502531i	$-0.167598\pi$
$432$		0			0
$433$		0			0		−0.368451	−	0.929647i	$-0.620112\pi$
$433$		0			0		0.368451	+	0.929647i	$0.379888\pi$
$434$		0			0
$435$		0			0
$436$	−0.0872381	−	0.900938i	−0.0872381	−	0.900938i
$437$		0			0
$438$		0			0
$439$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$439$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$440$		0			0
$441$	0.611658	−	0.791122i	0.611658	−	0.791122i
$442$		0			0
$443$	−0.0997594	−	0.663742i	−0.0997594	−	0.663742i	−0.981422	−	0.191862i	$-0.938547\pi$
$443$	−0.0997594	−	0.663742i	−0.0997594	−	0.663742i	0.881663	−	0.471880i	$-0.156425\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.0684551	+	0.864952i	−0.0684551	+	0.864952i
$449$	0.121215	+	0.382171i	0.121215	+	0.382171i	0.994461	−	0.105110i	$-0.0335196\pi$
$449$	0.121215	+	0.382171i	0.121215	+	0.382171i	−0.873245	+	0.487281i	$0.837989\pi$
$450$	0.512970	−	0.482389i	0.512970	−	0.482389i
$451$		0			0
$452$	−0.179325	−	0.804242i	−0.179325	−	0.804242i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.955521	+	1.03413i	0.955521	+	1.03413i	0.999384	+	0.0350944i	$0.0111732\pi$
$457$	0.955521	+	1.03413i	0.955521	+	1.03413i	−0.0438629	+	0.999038i	$0.513966\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$461$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$462$		0			0
$463$	−0.280581	−	1.16196i	−0.280581	−	1.16196i	−0.919626	−	0.392794i	$-0.871508\pi$
$463$	−0.280581	−	1.16196i	−0.280581	−	1.16196i	0.639045	−	0.769169i	$-0.279330\pi$
$464$	−0.0233129	−	0.0183535i	−0.0233129	−	0.0183535i
$465$		0			0
$466$	−0.121798	+	0.504398i	−0.121798	+	0.504398i
$467$		0			0		0.994461	−	0.105110i	$-0.0335196\pi$
$467$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$468$		0			0
$469$	1.88256	−	0.652120i	1.88256	−	0.652120i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.82881	+	1.77993i	−2.82881	+	1.77993i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.926162	−	0.840813i	−0.926162	−	0.840813i
$478$	−0.343233	+	0.556264i	−0.343233	+	0.556264i
$479$		0			0		0.926378	−	0.376595i	$-0.122905\pi$
$479$		0			0		−0.926378	+	0.376595i	$0.877095\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.24103	+	0.288172i	1.24103	+	0.288172i
$485$		0			0
$486$		0			0
$487$	−0.460861	+	1.54670i	−0.460861	+	1.54670i	0.335599	+	0.942005i	$0.391061\pi$
$487$	−0.460861	+	1.54670i	−0.460861	+	1.54670i	−0.796459	+	0.604692i	$0.793296\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.117735	−	0.889257i	−0.117735	−	0.889257i	−0.944914	−	0.327319i	$-0.893855\pi$
$491$	−0.117735	−	0.889257i	−0.117735	−	0.889257i	0.827179	−	0.561938i	$-0.189944\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.296114	−	0.0260521i	0.296114	−	0.0260521i
$498$		0			0
$499$	0.260384	−	0.390619i	0.260384	−	0.390619i	−0.678640	−	0.734471i	$-0.737430\pi$
$499$	0.260384	−	0.390619i	0.260384	−	0.390619i	0.939024	+	0.343852i	$0.111732\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.183242	−	0.983068i	$-0.558659\pi$
$503$		0			0		0.183242	+	0.983068i	$0.441341\pi$
$504$	−0.407472	−	0.977651i	−0.407472	−	0.977651i
$505$		0			0
$506$	0.0560690	−	0.200998i	0.0560690	−	0.200998i
$507$		0			0
$508$	0.802594	+	0.0281839i	0.802594	+	0.0281839i
$509$		0			0		0.416866	−	0.908968i	$-0.363128\pi$
$509$		0			0		−0.416866	+	0.908968i	$0.636872\pi$
$510$		0			0
$511$		0			0
$512$	0.389430	+	0.264557i	0.389430	+	0.264557i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.32163	−	0.483954i	−1.32163	−	0.483954i
$519$		0			0
$520$		0			0
$521$		0			0		−0.611658	−	0.791122i	$-0.709497\pi$
$521$		0			0		0.611658	+	0.791122i	$0.290503\pi$
$522$	0.0848492	+	0.0165875i	0.0848492	+	0.0165875i
$523$		0			0		0.0263232	−	0.999653i	$-0.491620\pi$
$523$		0			0		−0.0263232	+	0.999653i	$0.508380\pi$
$524$		0			0
$525$		0			0
$526$	−0.609879	+	0.164373i	−0.609879	+	0.164373i
$527$		0			0
$528$		0			0
$529$	−0.926846	−	0.302950i	−0.926846	−	0.302950i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.386674	−	2.07445i	0.386674	−	2.07445i
$537$		0			0
$538$		0			0
$539$	1.51549	+	1.10922i	1.51549	+	1.10922i
$540$		0			0
$541$	−0.00964702	+	0.0517549i	−0.00964702	+	0.0517549i	−0.987551	−	0.157301i	$-0.949721\pi$
$541$	−0.00964702	+	0.0517549i	−0.00964702	+	0.0517549i	0.977904	+	0.209056i	$0.0670391\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.173036	+	0.0849390i	0.173036	+	0.0849390i	0.525115	−	0.851031i	$-0.324022\pi$
$547$	0.173036	+	0.0849390i	0.173036	+	0.0849390i	−0.352079	+	0.935970i	$0.614525\pi$
$548$	−0.828614	−	0.270842i	−0.828614	−	0.270842i
$549$		0			0
$550$	0.930996	+	0.939202i	0.930996	+	0.939202i
$551$		0			0
$552$		0			0
$553$	0.283933	+	0.231717i	0.283933	+	0.231717i
$554$	−0.0216318	+	0.821492i	−0.0216318	+	0.821492i
$555$		0			0
$556$		0			0
$557$	−1.41405	+	1.15401i	−1.41405	+	1.15401i	−0.448509	+	0.893778i	$0.648045\pi$
$557$	−1.41405	+	1.15401i	−1.41405	+	1.15401i	−0.965546	+	0.260231i	$0.916201\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.672838	+	0.678768i	−0.672838	+	0.678768i
$563$		0			0		0.494925	−	0.868936i	$-0.335196\pi$
$563$		0			0		−0.494925	+	0.868936i	$0.664804\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.763532	+	0.645770i	0.763532	+	0.645770i
$568$	0.131249	−	0.286185i	0.131249	−	0.286185i
$569$	1.33047	+	0.0467208i	1.33047	+	0.0467208i	0.691425	−	0.722448i	$-0.256983\pi$
$569$	1.33047	+	0.0467208i	1.33047	+	0.0467208i	0.639045	+	0.769169i	$0.279330\pi$
$570$		0			0
$571$	0.536065	−	1.92171i	0.536065	−	1.92171i	0.200467	−	0.979701i	$-0.435754\pi$
$571$	0.536065	−	1.92171i	0.536065	−	1.92171i	0.335599	−	0.942005i	$-0.391061\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.116830	+	0.106063i	−0.116830	+	0.106063i
$576$	−0.861117	−	0.106328i	−0.861117	−	0.106328i
$577$		0			0		0.510099	−	0.860116i	$-0.329609\pi$
$577$		0			0		−0.510099	+	0.860116i	$0.670391\pi$
$578$	−0.390567	+	0.585915i	−0.390567	+	0.585915i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.53275	−	1.78034i	1.53275	−	1.78034i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.368451	−	0.929647i	$-0.379888\pi$
$587$		0			0		−0.368451	+	0.929647i	$0.620112\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.368802	+	0.311921i	−0.368802	+	0.311921i
$593$		0			0		−0.974084	−	0.226186i	$-0.927374\pi$
$593$		0			0		0.974084	+	0.226186i	$0.0726257\pi$
$594$		0			0
$595$		0			0
$596$	0.311194	−	0.873503i	0.311194	−	0.873503i
$597$		0			0
$598$		0			0
$599$	0.777588	−	1.26020i	0.777588	−	1.26020i	−0.183242	−	0.983068i	$-0.558659\pi$
$599$	0.777588	−	1.26020i	0.777588	−	1.26020i	0.960831	−	0.277137i	$-0.0893855\pi$
$600$		0			0
$601$		0			0		−0.652446	−	0.757835i	$-0.726257\pi$
$601$		0			0		0.652446	+	0.757835i	$0.273743\pi$
$602$	−0.441201	+	1.17289i	−0.441201	+	1.17289i
$603$	0.568917	+	1.90935i	0.568917	+	1.90935i
$604$	0.214851	−	0.135188i	0.214851	−	0.135188i
$605$		0			0
$606$		0			0
$607$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$607$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.53673	+	1.20982i	1.53673	+	1.20982i	0.897680	+	0.440648i	$0.145251\pi$
$613$	1.53673	+	1.20982i	1.53673	+	1.20982i	0.639045	+	0.769169i	$0.279330\pi$
$614$		0			0
$615$		0			0
$616$	1.81530	−	0.813317i	1.81530	−	0.813317i
$617$	−0.604572	−	0.0106118i	−0.604572	−	0.0106118i	−0.285558	−	0.958362i	$-0.592179\pi$
$617$	−0.604572	−	0.0106118i	−0.604572	−	0.0106118i	−0.319015	+	0.947750i	$0.603352\pi$
$618$		0			0
$619$		0			0		0.998614	−	0.0526281i	$-0.0167598\pi$
$619$		0			0		−0.998614	+	0.0526281i	$0.983240\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.217629	−	0.976031i	−0.217629	−	0.976031i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.03052	+	0.483601i	1.03052	+	0.483601i	0.864559	−	0.502531i	$-0.167598\pi$
$631$	1.03052	+	0.483601i	1.03052	+	0.483601i	0.165961	+	0.986132i	$0.446927\pi$
$632$	0.362100	−	0.139849i	0.362100	−	0.139849i
$633$		0			0
$634$	0.128030	+	0.851840i	0.128030	+	0.851840i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0269466	+	0.160116i	−0.0269466	+	0.160116i
$639$	0.0130386	+	0.296972i	0.0130386	+	0.296972i
$640$		0			0
$641$	−0.161323	−	1.66604i	−0.161323	−	1.66604i	−0.625448	−	0.780266i	$-0.715084\pi$
$641$	−0.161323	−	1.66604i	−0.161323	−	1.66604i	0.464125	−	0.885770i	$-0.346369\pi$
$642$		0			0
$643$		0			0		0.873245	−	0.487281i	$-0.162011\pi$
$643$		0			0		−0.873245	+	0.487281i	$0.837989\pi$
$644$	0.0293114	+	0.0739564i	0.0293114	+	0.0739564i
$645$		0			0
$646$		0			0
$647$		0			0		−0.728488	−	0.685059i	$-0.759777\pi$
$647$		0			0		0.728488	+	0.685059i	$0.240223\pi$
$648$	0.994583	−	0.364197i	0.994583	−	0.364197i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.456952	+	0.836052i	−0.456952	+	0.836052i
$653$	0.703182	+	1.86935i	0.703182	+	1.86935i	0.400849	+	0.916144i	$0.368715\pi$
$653$	0.703182	+	1.86935i	0.703182	+	1.86935i	0.302333	+	0.953202i	$0.402235\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.399946	+	1.95457i	0.399946	+	1.95457i	0.268694	+	0.963225i	$0.413408\pi$
$659$	0.399946	+	1.95457i	0.399946	+	1.95457i	0.131251	+	0.991349i	$0.458101\pi$
$660$		0			0
$661$		0			0		−0.997537	−	0.0701455i	$-0.977654\pi$
$661$		0			0		0.997537	+	0.0701455i	$0.0223464\pi$
$662$	0.303998	+	0.129845i	0.303998	+	0.129845i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.541459	−	1.29913i	0.541459	−	1.29913i
$667$	−0.0189455	−	0.00405016i	−0.0189455	−	0.00405016i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.626176	−	1.86028i	0.626176	−	1.86028i	0.131251	−	0.991349i	$-0.458101\pi$
$673$	0.626176	−	1.86028i	0.626176	−	1.86028i	0.494925	−	0.868936i	$-0.335196\pi$
$674$	0.688333	+	1.20850i	0.688333	+	1.20850i
$675$		0			0
$676$	−0.233994	+	0.446571i	−0.233994	+	0.446571i
$677$		0			0		0.960831	−	0.277137i	$-0.0893855\pi$
$677$		0			0		−0.960831	+	0.277137i	$0.910615\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.83676	−	0.529785i	−1.83676	−	0.529785i	−0.836914	−	0.547335i	$-0.815642\pi$
$683$	−1.83676	−	0.529785i	−1.83676	−	0.529785i	−0.999846	+	0.0175499i	$0.994413\pi$
$684$		0			0
$685$		0			0
$686$	0.704049	−	0.0123579i	0.704049	−	0.0123579i
$687$		0			0
$688$	0.274828	+	0.330790i	0.274828	+	0.330790i
$689$		0			0
$690$		0			0
$691$		0			0		−0.400849	−	0.916144i	$-0.631285\pi$
$691$		0			0		0.400849	+	0.916144i	$0.368715\pi$
$692$		0			0
$693$	−1.17462	+	1.46538i	−1.17462	+	1.46538i
$694$	−0.0800903	+	1.30217i	−0.0800903	+	1.30217i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.499200	−	0.0705552i	−0.499200	−	0.0705552i
$701$	1.09227	−	0.193696i	1.09227	−	0.193696i	0.400849	−	0.916144i	$-0.368715\pi$
$701$	1.09227	−	0.193696i	1.09227	−	0.193696i	0.691425	+	0.722448i	$0.256983\pi$
$702$		0			0
$703$		0			0
$704$	0.157050	−	1.62191i	0.157050	−	1.62191i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.37659	+	1.34082i	1.37659	+	1.34082i	0.881663	+	0.471880i	$0.156425\pi$
$709$	1.37659	+	1.34082i	1.37659	+	1.34082i	0.494925	+	0.868936i	$0.335196\pi$
$710$		0			0
$711$	−0.243948	+	0.273496i	−0.243948	+	0.273496i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.688679	+	0.504057i	−0.688679	+	0.504057i
$717$		0			0
$718$	0.201078	−	0.674838i	0.201078	−	0.674838i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−0.212890	+	0.671205i	−0.212890	+	0.671205i
$723$		0			0
$724$		0			0
$725$	0.0817268	−	0.0916256i	0.0817268	−	0.0916256i
$726$		0			0
$727$		0			0		−0.716353	−	0.697738i	$-0.754190\pi$
$727$		0			0		0.716353	+	0.697738i	$0.245810\pi$
$728$		0			0
$729$	−0.678640	+	0.734471i	−0.678640	+	0.734471i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.0613892	−	0.998114i	$-0.519553\pi$
$733$		0			0		0.0613892	+	0.998114i	$0.480447\pi$
$734$		0			0
$735$		0			0
$736$	0.138898	+	0.0196313i	0.138898	+	0.0196313i
$737$	−3.55648	+	1.16247i	−3.55648	+	1.16247i
$738$		0			0
$739$	−1.67479	+	0.822113i	−1.67479	+	0.822113i	−0.678640	+	0.734471i	$0.737430\pi$
$739$	−1.67479	+	0.822113i	−1.67479	+	0.822113i	−0.996152	+	0.0876414i	$0.972067\pi$
$740$		0			0
$741$		0			0
$742$	0.0540733	−	0.879167i	0.0540733	−	0.879167i
$743$	−0.656864	+	0.819458i	−0.656864	+	0.819458i	−0.992463	−	0.122547i	$-0.960894\pi$
$743$	−0.656864	+	0.819458i	−0.656864	+	0.819458i	0.335599	+	0.942005i	$0.391061\pi$
$744$		0			0
$745$		0			0
$746$	−0.717384	−	1.20964i	−0.717384	−	1.20964i
$747$		0			0
$748$		0			0
$749$	−0.727458	−	1.05087i	−0.727458	−	1.05087i
$750$		0			0
$751$	−1.80052	+	0.844946i	−1.80052	+	0.844946i	−0.855607	+	0.517627i	$0.826816\pi$
$751$	−1.80052	+	0.844946i	−1.80052	+	0.844946i	−0.944914	+	0.327319i	$0.893855\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.76976	−	0.907614i	−1.76976	−	0.907614i	−0.932845	−	0.360279i	$-0.882682\pi$
$757$	−1.76976	−	0.907614i	−1.76976	−	0.907614i	−0.836914	−	0.547335i	$-0.815642\pi$
$758$	−0.436584	+	0.425239i	−0.436584	+	0.425239i
$759$		0			0
$760$		0			0
$761$		0			0		−0.965546	−	0.260231i	$-0.916201\pi$
$761$		0			0		0.965546	+	0.260231i	$0.0837989\pi$
$762$		0			0
$763$	−0.572746	+	1.70155i	−0.572746	+	1.70155i
$764$	0.870266	−	0.446313i	0.870266	−	0.446313i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.977904	−	0.209056i	$-0.932961\pi$
$769$		0			0		0.977904	+	0.209056i	$0.0670391\pi$
$770$		0			0
$771$		0			0
$772$	0.855560	+	0.497300i	0.855560	+	0.497300i
$773$		0			0		−0.955819	−	0.293956i	$-0.905028\pi$
$773$		0			0		0.955819	+	0.293956i	$0.0949721\pi$
$774$	−1.15241	−	0.492223i	−1.15241	−	0.492223i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.412991	−	0.103569i	−0.412991	−	0.103569i
$779$		0			0
$780$		0			0
$781$	−0.556890	+	0.0391598i	−0.556890	+	0.0391598i
$782$		0			0
$783$		0			0
$784$	0.115900	−	0.212053i	0.115900	−	0.212053i
$785$		0			0
$786$		0			0
$787$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$787$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$788$	−0.743955	+	0.272422i	−0.743955	+	0.272422i
$789$		0			0
$790$		0			0
$791$	−0.327639	+	1.60120i	−0.327639	+	1.60120i
$792$	0.732910	+	1.84922i	0.732910	+	1.84922i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0438629	−	0.999038i	$-0.513966\pi$
$797$		0			0		0.0438629	+	0.999038i	$0.486034\pi$
$798$		0			0
$799$		0			0
$800$	−0.543765	+	0.703308i	−0.543765	+	0.703308i
$801$		0			0
$802$	0.103596	+	0.689269i	0.103596	+	0.689269i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.14478	+	1.07653i	−1.14478	+	1.07653i	−0.148629	+	0.988893i	$0.547486\pi$
$809$	−1.14478	+	1.07653i	−1.14478	+	1.07653i	−0.996152	+	0.0876414i	$0.972067\pi$
$810$		0			0
$811$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$811$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$812$	−0.0287294	−	0.0548292i	−0.0287294	−	0.0548292i
$813$		0			0
$814$	2.46575	+	0.952309i	2.46575	+	0.952309i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.382029	−	1.07233i	−0.382029	−	1.07233i	−0.965546	−	0.260231i	$-0.916201\pi$
$821$	−0.382029	−	1.07233i	−0.382029	−	1.07233i	0.583517	−	0.812101i	$-0.301676\pi$
$822$		0			0
$823$	−0.848534	−	0.668025i	−0.848534	−	0.668025i	0.0963795	−	0.995345i	$-0.469274\pi$
$823$	−0.848534	−	0.668025i	−0.848534	−	0.668025i	−0.944914	+	0.327319i	$0.893855\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.42496	−	0.608633i	1.42496	−	0.608633i	0.464125	−	0.885770i	$-0.346369\pi$
$827$	1.42496	−	0.608633i	1.42496	−	0.608633i	0.960831	+	0.277137i	$0.0893855\pi$
$828$	−0.0751709	+	0.0260393i	−0.0751709	+	0.0260393i
$829$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$829$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$830$		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		−0.0788965	−	0.996883i	$-0.525140\pi$
$839$		0			0		0.0788965	+	0.996883i	$0.474860\pi$
$840$		0			0
$841$	−0.979470	−	0.103526i	−0.979470	−	0.103526i
$842$	0.964279	−	0.296558i	0.964279	−	0.296558i
$843$		0			0
$844$	0.167550	−	0.141708i	0.167550	−	0.141708i
$845$		0			0
$846$		0			0
$847$	−2.01270	−	1.52810i	−2.01270	−	1.52810i
$848$	−0.252991	−	0.165454i	−0.252991	−	0.165454i
$849$		0			0
$850$		0			0
$851$	−0.126425	+	0.288944i	−0.126425	+	0.288944i
$852$		0			0
$853$		0			0		0.652446	−	0.757835i	$-0.273743\pi$
$853$		0			0		−0.652446	+	0.757835i	$0.726257\pi$
$854$		0			0
$855$		0			0
$856$	−1.34850	+	0.118641i	−1.34850	+	0.118641i
$857$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$857$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$858$		0			0
$859$		0			0		0.510099	−	0.860116i	$-0.329609\pi$
$859$		0			0		−0.510099	+	0.860116i	$0.670391\pi$
$860$		0			0
$861$		0			0
$862$	0.213464	+	1.14520i	0.213464	+	1.14520i
$863$	−0.127694	−	0.306377i	−0.127694	−	0.306377i	0.846391	−	0.532563i	$-0.178771\pi$
$863$	−0.127694	−	0.306377i	−0.127694	−	0.306377i	−0.974084	+	0.226186i	$0.927374\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.525520	−	0.444467i	−0.525520	−	0.444467i
$870$		0			0
$871$		0			0
$872$	1.26578	+	1.41909i	1.26578	+	1.41909i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.72710	−	0.632431i	−1.72710	−	0.632431i	−0.728488	−	0.685059i	$-0.759777\pi$
$877$	−1.72710	−	0.632431i	−1.72710	−	0.632431i	−0.998614	+	0.0526281i	$0.983240\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.981422	−	0.191862i	$-0.938547\pi$
$881$		0			0		0.981422	+	0.191862i	$0.0614525\pi$
$882$	−0.0185357	+	0.703914i	−0.0185357	+	0.703914i
$883$	1.49611	+	1.22097i	1.49611	+	1.22097i	0.912591	+	0.408873i	$0.134078\pi$
$883$	1.49611	+	1.22097i	1.49611	+	1.22097i	0.583517	+	0.812101i	$0.301676\pi$
$884$		0			0
$885$		0			0
$886$	0.332729	+	0.335662i	0.332729	+	0.335662i
$887$		0			0		−0.984638	−	0.174608i	$-0.944134\pi$
$887$		0			0		0.984638	+	0.174608i	$0.0558659\pi$
$888$		0			0
$889$	−1.42993	−	0.701917i	−1.42993	−	0.701917i
$890$		0			0
$891$	−1.41244	−	1.23777i	−1.41244	−	1.23777i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.146000	+	0.236616i	0.146000	+	0.236616i
$897$		0			0
$898$	−0.227818	−	0.166744i	−0.227818	−	0.166744i
$899$		0			0
$900$	0.0923836	−	0.495625i	0.0923836	−	0.495625i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.30191	+	1.14091i	1.30191	+	1.14091i
$905$		0			0
$906$		0			0
$907$	−1.59099	−	0.520034i	−1.59099	−	0.520034i	−0.625448	−	0.780266i	$-0.715084\pi$
$907$	−1.59099	−	0.520034i	−1.59099	−	0.520034i	−0.965546	+	0.260231i	$0.916201\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.124291	−	0.557426i	0.124291	−	0.557426i	−0.873245	−	0.487281i	$-0.837989\pi$
$911$	0.124291	−	0.557426i	0.124291	−	0.557426i	0.997537	−	0.0701455i	$-0.0223464\pi$
$912$		0			0
$913$		0			0
$914$	−0.973031	−	0.190221i	−0.973031	−	0.190221i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.481231	+	0.600351i	0.481231	+	0.600351i	0.960831	−	0.277137i	$-0.0893855\pi$
$919$	0.481231	+	0.600351i	0.481231	+	0.600351i	−0.479599	+	0.877488i	$0.659218\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.19462	−	1.60248i	−1.19462	−	1.60248i
$926$	0.642681	+	0.543559i	0.642681	+	0.543559i
$927$		0			0
$928$	−0.109083	−	0.00383055i	−0.109083	−	0.00383055i
$929$		0			0		−0.846391	−	0.532563i	$-0.821229\pi$
$929$		0			0		0.846391	+	0.532563i	$0.178771\pi$
$930$		0			0
$931$		0			0
$932$	0.142926	+	0.342925i	0.142926	+	0.342925i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.554658	−	0.832079i	$-0.312849\pi$
$937$		0			0		−0.554658	+	0.832079i	$0.687151\pi$
$938$	−0.798494	+	1.15348i	−0.798494	+	1.15348i
$939$		0			0
$940$		0			0
$941$		0			0		−0.479599	−	0.877488i	$-0.659218\pi$
$941$		0			0		0.479599	+	0.877488i	$0.340782\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.867127	−	2.18787i	0.867127	−	2.18787i
$947$	1.67357	+	1.09450i	1.67357	+	1.09450i	0.846391	+	0.532563i	$0.178771\pi$
$947$	1.67357	+	1.09450i	1.67357	+	1.09450i	0.827179	+	0.561938i	$0.189944\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.91134	−	0.587822i	1.91134	−	0.587822i	0.950513	−	0.310686i	$-0.100559\pi$
$953$	1.91134	−	0.587822i	1.91134	−	0.587822i	0.960831	−	0.277137i	$-0.0893855\pi$
$954$	0.875949	+	0.0925841i	0.875949	+	0.0925841i
$955$		0			0
$956$	0.0369227	+	0.466530i	0.0369227	+	0.466530i
$957$		0			0
$958$		0			0
$959$	1.28024	+	1.16226i	1.28024	+	1.16226i
$960$		0			0
$961$	−0.352079	+	0.935970i	−0.352079	+	0.935970i
$962$		0			0
$963$	1.08176	−	0.680663i	1.08176	−	0.680663i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.0497462	+	0.0172322i	−0.0497462	+	0.0172322i	−0.352079	−	0.935970i	$-0.614525\pi$
$967$	−0.0497462	+	0.0172322i	−0.0497462	+	0.0172322i	0.302333	+	0.953202i	$0.402235\pi$
$968$	−2.46146	+	1.05135i	−2.46146	+	1.05135i
$969$		0			0
$970$		0			0
$971$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$971$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$972$		0			0
$973$		0			0
$974$	−0.381387	−	1.07053i	−0.381387	−	1.07053i
$975$		0			0
$976$		0			0
$977$	−0.462436	−	0.693730i	−0.462436	−	0.693730i	0.525115	−	0.851031i	$-0.324022\pi$
$977$	−0.462436	−	0.693730i	−0.462436	−	0.693730i	−0.987551	+	0.157301i	$0.949721\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.67479	−	0.646830i	−1.67479	−	0.646830i
$982$	0.436733	+	0.456329i	0.436733	+	0.456329i
$983$		0			0		−0.464125	−	0.885770i	$-0.653631\pi$
$983$		0			0		0.464125	+	0.885770i	$0.346369\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.256266	+	0.114816i	0.256266	+	0.114816i
$990$		0			0
$991$	1.62920	−	0.629224i	1.62920	−	0.629224i	0.639045	−	0.769169i	$-0.279330\pi$
$991$	1.62920	−	0.629224i	1.62920	−	0.629224i	0.990159	+	0.139946i	$0.0446927\pi$
$992$		0			0
$993$		0			0
$994$	−0.157423	+	0.137954i	−0.157423	+	0.137954i
$995$		0			0
$996$		0			0
$997$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$997$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$998$	0.0144996	+	0.330249i	0.0144996	+	0.330249i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.34.1	✓	178
7.6	odd	2	CM	2513.1.l.a.34.1	✓	178
359.264	even	179	inner	2513.1.l.a.1700.1	yes	178
2513.1700	odd	358	inner	2513.1.l.a.1700.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.34.1	✓	178	1.1	even	1	trivial
2513.1.l.a.34.1	✓	178	7.6	odd	2	CM
2513.1.l.a.1700.1	yes	178	359.264	even	179	inner
2513.1.l.a.1700.1	yes	178	2513.1700	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)

\(f(q)\)	\(=\)	\(q+(-0.568219 + 0.415891i) q^{2} +(-0.152425 + 0.480568i) q^{4} +(0.665645 - 0.746268i) q^{7} +(-0.337890 - 1.00383i) q^{8} +(0.716353 + 0.697738i) q^{9} +O(q^{10})\)	\(q+(-0.568219 + 0.415891i) q^{2} +(-0.152425 + 0.480568i) q^{4} +(0.665645 - 0.746268i) q^{7} +(-0.337890 - 1.00383i) q^{8} +(0.716353 + 0.697738i) q^{9} +(-1.27452 + 1.37937i) q^{11} +(-0.0678664 + 0.700880i) q^{14} +(0.197482 + 0.139285i) q^{16} +(-0.697228 - 0.0985437i) q^{18} +(0.150537 - 1.31385i) q^{22} +(0.155829 + 0.0248210i) q^{23} +(-0.625448 + 0.780266i) q^{25} +(0.257172 + 0.433638i) q^{28} +(-0.122608 - 0.00646159i) q^{29} +(0.888864 - 0.0156019i) q^{32} +(-0.444500 + 0.237904i) q^{36} +(-0.503187 + 1.93439i) q^{37} +(1.71830 + 0.463112i) q^{43} +(-0.468615 - 0.822743i) q^{44} +(-0.0988677 + 0.0507039i) q^{46} +(-0.113833 - 0.993500i) q^{49} +(0.0308864 - 0.703480i) q^{50} +(-1.25013 + 0.0438994i) q^{53} +(-0.974038 - 0.416035i) q^{56} +(0.0723557 - 0.0473200i) q^{58} +(0.997537 - 0.0701455i) q^{63} +(-0.691053 + 0.524665i) q^{64} +(1.73977 + 0.970812i) q^{67} +(0.216549 + 0.203639i) q^{71} +(0.458359 - 0.954852i) q^{72} +(-0.518576 - 1.30843i) q^{74} +(0.181005 + 1.86930i) q^{77} +(0.0160751 + 0.366131i) q^{79} +(0.0263232 + 0.999653i) q^{81} +(-1.16898 + 0.451477i) q^{86} +(1.81530 + 0.813317i) q^{88} +(-0.0356803 + 0.0711029i) q^{92} +(0.477869 + 0.517184i) q^{98} +(-1.87545 + 0.0988380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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

Properties

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