LMFDB - Embedded newform 2513.1.l.a.48.1

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			48.1
Root			$-0.0263232 + 0.999653i$ of defining polynomial
Character	$\chi$	$=$	2513.48
Dual form			2513.1.l.a.1623.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50046 + 1.31489i) q^{2} +(0.391170 - 2.95454i) q^{4} +(-0.996152 - 0.0876414i) q^{7} +(2.19139 + 3.28744i) q^{8} +(0.335599 + 0.942005i) q^{9} +O(q^{10})$	\(q+(-1.50046 + 1.31489i) q^{2} +(0.391170 - 2.95454i) q^{4} +(-0.996152 - 0.0876414i) q^{7} +(2.19139 + 3.28744i) q^{8} +(0.335599 + 0.942005i) q^{9} +(1.63561 + 0.989515i) q^{11} +(1.60992 - 1.17833i) q^{14} +(-4.73309 - 1.27565i) q^{16} +(-1.74219 - 0.972161i) q^{18} +(-3.75527 + 0.665931i) q^{22} +(-0.528337 - 0.763223i) q^{23} +(-0.285558 + 0.958362i) q^{25} +(-0.648605 + 2.90888i) q^{28} +(0.0105538 + 0.0515776i) q^{29} +(5.23251 - 2.56851i) q^{32} +(2.91446 - 0.623054i) q^{36} +(-1.15593 - 0.400415i) q^{37} +(1.64194 + 1.03313i) q^{43} +(3.56336 - 4.44540i) q^{44} +(1.79630 + 0.450475i) q^{46} +(0.984638 + 0.174608i) q^{49} +(-0.831678 - 1.81346i) q^{50} +(-0.349327 + 0.451822i) q^{53} +(-1.89484 - 3.46685i) q^{56} +(-0.0836547 - 0.0635128i) q^{58} +(-0.251749 - 0.967793i) q^{63} +(-2.58800 + 6.20942i) q^{64} +(-1.02528 - 0.807176i) q^{67} +(1.06077 + 1.03321i) q^{71} +(-2.36136 + 3.16756i) q^{72} +(2.26092 - 0.919119i) q^{74} +(-1.54259 - 1.12905i) q^{77} +(0.0657785 - 0.143429i) q^{79} +(-0.774747 + 0.632271i) q^{81} +(-3.82212 + 0.608803i) q^{86} +(0.331281 + 7.54538i) q^{88} +(-2.46164 + 1.26244i) q^{92} +(-1.70700 + 1.03270i) q^{98} +(-0.383219 + 1.87283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{5}{179}\right)$

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 $

$2$	−1.50046	+	1.31489i	−1.50046	+	1.31489i	−0.703997	+	0.710203i	$0.748603\pi$
$2$	−1.50046	+	1.31489i	−1.50046	+	1.31489i	−0.796459	+	0.604692i	$0.793296\pi$
$3$		0			0		−0.817190	−	0.576369i	$-0.804469\pi$
$3$		0			0		0.817190	+	0.576369i	$0.195531\pi$
$4$	0.391170	−	2.95454i	0.391170	−	2.95454i
$5$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$5$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$6$		0			0
$7$	−0.996152	−	0.0876414i	−0.996152	−	0.0876414i
$7$	−0.996152	−	0.0876414i	−0.996152	−	0.0876414i
$8$	2.19139	+	3.28744i	2.19139	+	3.28744i
$9$	0.335599	+	0.942005i	0.335599	+	0.942005i
$10$		0			0
$11$	1.63561	+	0.989515i	1.63561	+	0.989515i	0.969965	+	0.243246i	$0.0782123\pi$
$11$	1.63561	+	0.989515i	1.63561	+	0.989515i	0.665645	+	0.746268i	$0.268156\pi$
$12$		0			0
$13$		0			0		0.652446	−	0.757835i	$-0.273743\pi$
$13$		0			0		−0.652446	+	0.757835i	$0.726257\pi$
$14$	1.60992	−	1.17833i	1.60992	−	1.17833i
$15$		0			0
$16$	−4.73309	−	1.27565i	−4.73309	−	1.27565i
$17$		0			0		0.148629	−	0.988893i	$-0.452514\pi$
$17$		0			0		−0.148629	+	0.988893i	$0.547486\pi$
$18$	−1.74219	−	0.972161i	−1.74219	−	0.972161i
$19$		0			0		−0.352079	−	0.935970i	$-0.614525\pi$
$19$		0			0		0.352079	+	0.935970i	$0.385475\pi$
$20$		0			0
$21$		0			0
$22$	−3.75527	+	0.665931i	−3.75527	+	0.665931i
$23$	−0.528337	−	0.763223i	−0.528337	−	0.763223i	0.464125	−	0.885770i	$-0.346369\pi$
$23$	−0.528337	−	0.763223i	−0.528337	−	0.763223i	−0.992463	+	0.122547i	$0.960894\pi$
$24$		0			0
$25$	−0.285558	+	0.958362i	−0.285558	+	0.958362i
$26$		0			0
$27$		0			0
$28$	−0.648605	+	2.90888i	−0.648605	+	2.90888i
$29$	0.0105538	+	0.0515776i	0.0105538	+	0.0515776i	0.984638	−	0.174608i	$-0.0558659\pi$
$29$	0.0105538	+	0.0515776i	0.0105538	+	0.0515776i	−0.974084	+	0.226186i	$0.927374\pi$
$30$		0			0
$31$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$31$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$32$	5.23251	−	2.56851i	5.23251	−	2.56851i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.91446	−	0.623054i	2.91446	−	0.623054i
$37$	−1.15593	−	0.400415i	−1.15593	−	0.400415i	−0.319015	−	0.947750i	$-0.603352\pi$
$37$	−1.15593	−	0.400415i	−1.15593	−	0.400415i	−0.836914	+	0.547335i	$0.815642\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$41$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$42$		0			0
$43$	1.64194	+	1.03313i	1.64194	+	1.03313i	0.950513	+	0.310686i	$0.100559\pi$
$43$	1.64194	+	1.03313i	1.64194	+	1.03313i	0.691425	+	0.722448i	$0.256983\pi$
$44$	3.56336	−	4.44540i	3.56336	−	4.44540i
$45$		0			0
$46$	1.79630	+	0.450475i	1.79630	+	0.450475i
$47$		0			0		−0.740398	−	0.672168i	$-0.765363\pi$
$47$		0			0		0.740398	+	0.672168i	$0.234637\pi$
$48$		0			0
$49$	0.984638	+	0.174608i	0.984638	+	0.174608i
$50$	−0.831678	−	1.81346i	−0.831678	−	1.81346i
$51$		0			0
$52$		0			0
$53$	−0.349327	+	0.451822i	−0.349327	+	0.451822i	−0.932845	−	0.360279i	$-0.882682\pi$
$53$	−0.349327	+	0.451822i	−0.349327	+	0.451822i	0.583517	+	0.812101i	$0.301676\pi$
$54$		0			0
$55$		0			0
$56$	−1.89484	−	3.46685i	−1.89484	−	3.46685i
$57$		0			0
$58$	−0.0836547	−	0.0635128i	−0.0836547	−	0.0635128i
$59$		0			0		−0.510099	−	0.860116i	$-0.670391\pi$
$59$		0			0		0.510099	+	0.860116i	$0.329609\pi$
$60$		0			0
$61$		0			0		−0.981422	−	0.191862i	$-0.938547\pi$
$61$		0			0		0.981422	+	0.191862i	$0.0614525\pi$
$62$		0			0
$63$	−0.251749	−	0.967793i	−0.251749	−	0.967793i
$64$	−2.58800	+	6.20942i	−2.58800	+	6.20942i
$65$		0			0
$66$		0			0
$67$	−1.02528	−	0.807176i	−1.02528	−	0.807176i	−0.0438629	−	0.999038i	$-0.513966\pi$
$67$	−1.02528	−	0.807176i	−1.02528	−	0.807176i	−0.981422	+	0.191862i	$0.938547\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.06077	+	1.03321i	1.06077	+	1.03321i	0.999384	+	0.0350944i	$0.0111732\pi$
$71$	1.06077	+	1.03321i	1.06077	+	1.03321i	0.0613892	+	0.998114i	$0.480447\pi$
$72$	−2.36136	+	3.16756i	−2.36136	+	3.16756i
$73$		0			0		0.510099	−	0.860116i	$-0.329609\pi$
$73$		0			0		−0.510099	+	0.860116i	$0.670391\pi$
$74$	2.26092	−	0.919119i	2.26092	−	0.919119i
$75$		0			0
$76$		0			0
$77$	−1.54259	−	1.12905i	−1.54259	−	1.12905i
$78$		0			0
$79$	0.0657785	−	0.143429i	0.0657785	−	0.143429i	−0.873245	−	0.487281i	$-0.837989\pi$
$79$	0.0657785	−	0.143429i	0.0657785	−	0.143429i	0.939024	+	0.343852i	$0.111732\pi$
$80$		0			0
$81$	−0.774747	+	0.632271i	−0.774747	+	0.632271i
$82$		0			0
$83$		0			0		−0.990159	−	0.139946i	$-0.955307\pi$
$83$		0			0		0.990159	+	0.139946i	$0.0446927\pi$
$84$		0			0
$85$		0			0
$86$	−3.82212	+	0.608803i	−3.82212	+	0.608803i
$87$		0			0
$88$	0.331281	+	7.54538i	0.331281	+	7.54538i
$89$		0			0		0.464125	−	0.885770i	$-0.346369\pi$
$89$		0			0		−0.464125	+	0.885770i	$0.653631\pi$
$90$		0			0
$91$		0			0
$92$	−2.46164	+	1.26244i	−2.46164	+	1.26244i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.944914	−	0.327319i	$-0.106145\pi$
$97$		0			0		−0.944914	+	0.327319i	$0.893855\pi$
$98$	−1.70700	+	1.03270i	−1.70700	+	1.03270i
$99$	−0.383219	+	1.87283i	−0.383219	+	1.87283i
$100$	2.71981	+	1.21857i	2.71981	+	1.21857i
$101$		0			0		−0.897680	−	0.440648i	$-0.854749\pi$
$101$		0			0		0.897680	+	0.440648i	$0.145251\pi$
$102$		0			0
$103$		0			0		−0.864559	−	0.502531i	$-0.832402\pi$
$103$		0			0		0.864559	+	0.502531i	$0.167598\pi$
$104$		0			0
$105$		0			0
$106$	−0.0699478	−	1.13727i	−0.0699478	−	1.13727i
$107$	1.34705	−	0.166330i	1.34705	−	0.166330i	0.583517	−	0.812101i	$-0.301676\pi$
$107$	1.34705	−	0.166330i	1.34705	−	0.166330i	0.763532	+	0.645770i	$0.223464\pi$
$108$		0			0
$109$	−0.732378	+	1.33998i	−0.732378	+	1.33998i	0.200467	+	0.979701i	$0.435754\pi$
$109$	−0.732378	+	1.33998i	−0.732378	+	1.33998i	−0.932845	+	0.360279i	$0.882682\pi$
$110$		0			0
$111$		0			0
$112$	4.60308	+	1.68556i	4.60308	+	1.68556i
$113$	−0.835688	+	1.74090i	−0.835688	+	1.74090i	−0.183242	+	0.983068i	$0.558659\pi$
$113$	−0.835688	+	1.74090i	−0.835688	+	1.74090i	−0.652446	+	0.757835i	$0.726257\pi$
$114$		0			0
$115$		0			0
$116$	0.156516	−	0.0110060i	0.156516	−	0.0110060i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.23196	+	2.35115i	1.23196	+	2.35115i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.65028	+	1.12111i	1.65028	+	1.12111i
$127$	0.541669	−	0.546443i	0.541669	−	0.546443i	−0.384709	−	0.923038i	$-0.625698\pi$
$127$	0.541669	−	0.546443i	0.541669	−	0.546443i	0.926378	+	0.376595i	$0.122905\pi$
$128$	−2.42204	−	7.19556i	−2.42204	−	7.19556i
$129$		0			0
$130$		0			0
$131$		0			0		−0.926378	−	0.376595i	$-0.877095\pi$
$131$		0			0		0.926378	+	0.376595i	$0.122905\pi$
$132$		0			0
$133$		0			0
$134$	2.59975	−	0.137010i	2.59975	−	0.137010i
$135$		0			0
$136$		0			0
$137$	−0.843077	−	0.195766i	−0.843077	−	0.195766i	−0.217629	−	0.976031i	$-0.569832\pi$
$137$	−0.843077	−	0.195766i	−0.843077	−	0.195766i	−0.625448	+	0.780266i	$0.715084\pi$
$138$		0			0
$139$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$139$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$140$		0			0
$141$		0			0
$142$	−2.95020	−	0.155479i	−2.95020	−	0.155479i
$143$		0			0
$144$	−0.386749	−	4.88670i	−0.386749	−	4.88670i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.63521	+	3.25860i	−1.63521	+	3.25860i
$149$	−0.586701	−	0.758843i	−0.586701	−	0.758843i	0.400849	−	0.916144i	$-0.368715\pi$
$149$	−0.586701	−	0.758843i	−0.586701	−	0.758843i	−0.987551	+	0.157301i	$0.949721\pi$
$150$		0			0
$151$	−1.56323	+	1.06197i	−1.56323	+	1.06197i	−0.597680	+	0.801735i	$0.703911\pi$
$151$	−1.56323	+	1.06197i	−1.56323	+	1.06197i	−0.965546	+	0.260231i	$0.916201\pi$
$152$		0			0
$153$		0			0
$154$	3.79918	−	0.334252i	3.79918	−	0.334252i
$155$		0			0
$156$		0			0
$157$		0			0		0.965546	−	0.260231i	$-0.0837989\pi$
$157$		0			0		−0.965546	+	0.260231i	$0.916201\pi$
$158$	0.0898960	+	0.301701i	0.0898960	+	0.301701i
$159$		0			0
$160$		0			0
$161$	0.459414	+	0.806590i	0.459414	+	0.806590i
$162$	0.331105	−	1.96741i	0.331105	−	1.96741i
$163$	−0.440491	+	1.38879i	−0.440491	+	1.38879i	0.432754	+	0.901512i	$0.357542\pi$
$163$	−0.440491	+	1.38879i	−0.440491	+	1.38879i	−0.873245	+	0.487281i	$0.837989\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.846391	−	0.532563i	$-0.178771\pi$
$167$		0			0		−0.846391	+	0.532563i	$0.821229\pi$
$168$		0			0
$169$	−0.148629	−	0.988893i	−0.148629	−	0.988893i
$170$		0			0
$171$		0			0
$172$	3.69471	−	4.44703i	3.69471	−	4.44703i
$173$		0			0		0.990159	−	0.139946i	$-0.0446927\pi$
$173$		0			0		−0.990159	+	0.139946i	$0.955307\pi$
$174$		0			0
$175$	0.368451	−	0.929647i	0.368451	−	0.929647i
$176$	−6.47921	−	6.76992i	−6.47921	−	6.76992i
$177$		0			0
$178$		0			0
$179$	0.674630	+	0.591198i	0.674630	+	0.591198i	0.926378	−	0.376595i	$-0.122905\pi$
$179$	0.674630	+	0.591198i	0.674630	+	0.591198i	−0.251749	+	0.967793i	$0.581006\pi$
$180$		0			0
$181$		0			0		−0.234725	−	0.972062i	$-0.575419\pi$
$181$		0			0		0.234725	+	0.972062i	$0.424581\pi$
$182$		0			0
$183$		0			0
$184$	1.35126	−	3.40940i	1.35126	−	3.40940i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.226405	+	1.97599i	−0.226405	+	1.97599i	−0.00877529	+	0.999961i	$0.502793\pi$
$191$	−0.226405	+	1.97599i	−0.226405	+	1.97599i	−0.217629	+	0.976031i	$0.569832\pi$
$192$		0			0
$193$	−0.506053	+	0.330954i	−0.506053	+	0.330954i	−0.774747	−	0.632271i	$-0.782123\pi$
$193$	−0.506053	+	0.330954i	−0.506053	+	0.330954i	0.268694	+	0.963225i	$0.413408\pi$
$194$		0			0
$195$		0			0
$196$	0.901048	−	2.84085i	0.901048	−	2.84085i
$197$	0.0203764	−	0.121076i	0.0203764	−	0.121076i	−0.974084	−	0.226186i	$-0.927374\pi$
$197$	0.0203764	−	0.121076i	0.0203764	−	0.121076i	0.994461	+	0.105110i	$0.0335196\pi$
$198$	−1.88757	−	3.31400i	−1.88757	−	3.31400i
$199$		0			0		−0.889808	−	0.456335i	$-0.849162\pi$
$199$		0			0		0.889808	+	0.456335i	$0.150838\pi$
$200$	−3.77633	+	1.16139i	−3.77633	+	1.16139i
$201$		0			0
$202$		0			0
$203$	−0.00599288	−	0.0523041i	−0.00599288	−	0.0523041i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.541650	−	0.753833i	0.541650	−	0.753833i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.750726	−	1.49603i	0.750726	−	1.49603i	−0.113833	−	0.993500i	$-0.536313\pi$
$211$	0.750726	−	1.49603i	0.750726	−	1.49603i	0.864559	−	0.502531i	$-0.167598\pi$
$212$	1.19828	+	1.20884i	1.19828	+	1.20884i
$213$		0			0
$214$	−1.80248	+	2.02080i	−1.80248	+	2.02080i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.663030	−	2.97358i	−0.663030	−	2.97358i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.905275	−	0.424826i	$-0.139665\pi$
$223$		0			0		−0.905275	+	0.424826i	$0.860335\pi$
$224$	−5.43749	+	2.10004i	−5.43749	+	2.10004i
$225$	−0.998614	+	0.0526281i	−0.998614	+	0.0526281i
$226$	−1.03519	−	3.71099i	−1.03519	−	3.71099i
$227$		0			0		0.960831	−	0.277137i	$-0.0893855\pi$
$227$		0			0		−0.960831	+	0.277137i	$0.910615\pi$
$228$		0			0
$229$		0			0		0.796459	−	0.604692i	$-0.206704\pi$
$229$		0			0		−0.796459	+	0.604692i	$0.793296\pi$
$230$		0			0
$231$		0			0
$232$	−0.146431	+	0.147722i	−0.146431	+	0.147722i
$233$	1.53256	+	1.04113i	1.53256	+	1.04113i	0.977904	+	0.209056i	$0.0670391\pi$
$233$	1.53256	+	1.04113i	1.53256	+	1.04113i	0.554658	+	0.832079i	$0.312849\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.63413	−	1.15256i	1.63413	−	1.15256i	0.806949	−	0.590621i	$-0.201117\pi$
$239$	1.63413	−	1.15256i	1.63413	−	1.15256i	0.827179	−	0.561938i	$-0.189944\pi$
$240$		0			0
$241$		0			0		−0.950513	−	0.310686i	$-0.899441\pi$
$241$		0			0		0.950513	+	0.310686i	$0.100559\pi$
$242$	−4.94001	−	1.90791i	−4.94001	−	1.90791i
$243$		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		−0.919626	−	0.392794i	$-0.871508\pi$
$251$		0			0		0.919626	+	0.392794i	$0.128492\pi$
$252$	−2.95785	+	0.365228i	−2.95785	+	0.365228i
$253$	−0.108934	−	1.77113i	−0.108934	−	1.77113i
$254$	−0.0942352	+	1.53215i	−0.0942352	+	1.53215i
$255$		0			0
$256$	7.27954	+	4.23128i	7.27954	+	4.23128i
$257$		0			0		0.0438629	−	0.999038i	$-0.486034\pi$
$257$		0			0		−0.0438629	+	0.999038i	$0.513966\pi$
$258$		0			0
$259$	1.11639	+	0.500181i	1.11639	+	0.500181i
$260$		0			0
$261$	−0.0450445	+	0.0272511i	−0.0450445	+	0.0272511i
$262$		0			0
$263$	1.75746	+	0.279936i	1.75746	+	0.279936i	0.950513	−	0.310686i	$-0.100559\pi$
$263$	1.75746	+	0.279936i	1.75746	+	0.279936i	0.806949	+	0.590621i	$0.201117\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−2.78589	+	2.71350i	−2.78589	+	2.71350i
$269$		0			0		−0.131251	−	0.991349i	$-0.541899\pi$
$269$		0			0		0.131251	+	0.991349i	$0.458101\pi$
$270$		0			0
$271$		0			0		−0.0438629	−	0.999038i	$-0.513966\pi$
$271$		0			0		0.0438629	+	0.999038i	$0.486034\pi$
$272$		0			0
$273$		0			0
$274$	1.52241	−	0.814820i	1.52241	−	0.814820i
$275$	−1.41537	+	1.28494i	−1.41537	+	1.28494i
$276$		0			0
$277$	0.292643	+	1.73887i	0.292643	+	1.73887i	0.611658	+	0.791122i	$0.290503\pi$
$277$	0.292643	+	1.73887i	0.292643	+	1.73887i	−0.319015	+	0.947750i	$0.603352\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.973980	−	1.40699i	0.973980	−	1.40699i	0.0613892	−	0.998114i	$-0.480447\pi$
$281$	0.973980	−	1.40699i	0.973980	−	1.40699i	0.912591	−	0.408873i	$-0.134078\pi$
$282$		0			0
$283$		0			0		0.974084	−	0.226186i	$-0.0726257\pi$
$283$		0			0		−0.974084	+	0.226186i	$0.927374\pi$
$284$	3.46759	−	2.72993i	3.46759	−	2.72993i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	4.17557	+	4.06707i	4.17557	+	4.06707i
$289$	−0.955819	−	0.293956i	−0.955819	−	0.293956i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.905275	−	0.424826i	$-0.860335\pi$
$293$		0			0		0.905275	+	0.424826i	$0.139665\pi$
$294$		0			0
$295$		0			0
$296$	−1.21675	−	4.67751i	−1.21675	−	4.67751i
$297$		0			0
$298$	1.87812	+	0.367160i	1.87812	+	0.367160i
$299$		0			0
$300$		0			0
$301$	−1.54507	−	1.17306i	−1.54507	−	1.17306i
$302$	0.949179	−	3.64891i	0.949179	−	3.64891i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.665645	−	0.746268i	$-0.731844\pi$
$307$		0			0		0.665645	+	0.746268i	$0.268156\pi$
$308$	−3.93925	+	4.11600i	−3.93925	+	4.11600i
$309$		0			0
$310$		0			0
$311$		0			0		−0.639045	−	0.769169i	$-0.720670\pi$
$311$		0			0		0.639045	+	0.769169i	$0.279330\pi$
$312$		0			0
$313$		0			0		−0.969965	−	0.243246i	$-0.921788\pi$
$313$		0			0		0.969965	+	0.243246i	$0.0782123\pi$
$314$		0			0
$315$		0			0
$316$	−0.398035	−	0.250450i	−0.398035	−	0.250450i
$317$	−0.331871	+	0.00582520i	−0.331871	+	0.00582520i	−0.183242	−	0.983068i	$-0.558659\pi$
$317$	−0.331871	+	0.00582520i	−0.331871	+	0.00582520i	−0.148629	+	0.988893i	$0.547486\pi$
$318$		0			0
$319$	−0.0337749	+	0.0948040i	−0.0337749	+	0.0948040i
$320$		0			0
$321$		0			0
$322$	−1.74991	−	0.606172i	−1.74991	−	0.606172i
$323$		0			0
$324$	1.56501	+	2.53634i	1.56501	+	2.53634i
$325$		0			0
$326$	−1.16518	−	2.66302i	−1.16518	−	2.66302i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.431978	−	1.93735i	0.431978	−	1.93735i	0.0963795	−	0.995345i	$-0.469274\pi$
$331$	0.431978	−	1.93735i	0.431978	−	1.93735i	0.335599	−	0.942005i	$-0.391061\pi$
$332$		0			0
$333$	−0.0107350	−	1.22327i	−0.0107350	−	1.22327i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.12086	+	0.198765i	−1.12086	+	0.198765i	−0.703997	−	0.710203i	$-0.748603\pi$
$337$	−1.12086	+	0.198765i	−1.12086	+	0.198765i	−0.416866	+	0.908968i	$0.636872\pi$
$338$	1.52330	+	1.28836i	1.52330	+	1.28836i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.965546	−	0.260231i	−0.965546	−	0.260231i
$344$	0.201752	+	7.66177i	0.201752	+	7.66177i
$345$		0			0
$346$		0			0
$347$	1.10915	−	1.20041i	1.10915	−	1.20041i	0.131251	−	0.991349i	$-0.458101\pi$
$347$	1.10915	−	1.20041i	1.10915	−	1.20041i	0.977904	−	0.209056i	$-0.0670391\pi$
$348$		0			0
$349$		0			0		−0.977904	−	0.209056i	$-0.932961\pi$
$349$		0			0		0.977904	+	0.209056i	$0.0670391\pi$
$350$	0.669544	+	1.87937i	0.669544	+	1.87937i
$351$		0			0
$352$	11.0999	+	0.976571i	11.0999	+	0.976571i
$353$		0			0		0.994461	−	0.105110i	$-0.0335196\pi$
$353$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.78962			−1.78962
$359$	−0.384709	+	0.923038i	−0.384709	+	0.923038i
$359$	−0.384709	+	0.923038i	−0.384709	+	0.923038i
$360$		0			0
$361$	−0.752081	+	0.659071i	−0.752081	+	0.659071i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.554658	−	0.832079i	$-0.687151\pi$
$367$		0			0		0.554658	+	0.832079i	$0.312849\pi$
$368$	1.52706	+	4.28637i	1.52706	+	4.28637i
$369$		0			0
$370$		0			0
$371$	0.387581	−	0.419468i	0.387581	−	0.419468i
$372$		0			0
$373$	0.323533	−	0.236800i	0.323533	−	0.236800i	−0.416866	−	0.908968i	$-0.636872\pi$
$373$	0.323533	−	0.236800i	0.323533	−	0.236800i	0.740398	+	0.672168i	$0.234637\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.04384	−	0.582476i	1.04384	−	0.582476i	0.131251	−	0.991349i	$-0.458101\pi$
$379$	1.04384	−	0.582476i	1.04384	−	0.582476i	0.912591	+	0.408873i	$0.134078\pi$
$380$		0			0
$381$		0			0
$382$	−2.25851	−	3.26259i	−2.25851	−	3.26259i
$383$		0			0		0.0263232	−	0.999653i	$-0.491620\pi$
$383$		0			0		−0.0263232	+	0.999653i	$0.508380\pi$
$384$		0			0
$385$		0			0
$386$	0.324140	−	1.16199i	0.324140	−	1.16199i
$387$	−0.422186	+	1.89343i	−0.422186	+	1.89343i
$388$		0			0
$389$	−0.178145	−	0.192800i	−0.178145	−	0.192800i	0.639045	−	0.769169i	$-0.279330\pi$
$389$	−0.178145	−	0.192800i	−0.178145	−	0.192800i	−0.817190	+	0.576369i	$0.804469\pi$
$390$		0			0
$391$		0			0
$392$	1.58371	+	3.61958i	1.58371	+	3.61958i
$393$		0			0
$394$	0.128628	+	0.208462i	0.128628	+	0.208462i
$395$		0			0
$396$	5.38345	+	1.86483i	5.38345	+	1.86483i
$397$		0			0		−0.881663	−	0.471880i	$-0.843575\pi$
$397$		0			0		0.881663	+	0.471880i	$0.156425\pi$
$398$		0			0
$399$		0			0
$400$	2.57410	−	4.17174i	2.57410	−	4.17174i
$401$	1.25070	−	0.0219531i	1.25070	−	0.0219531i	0.611658	−	0.791122i	$-0.290503\pi$
$401$	1.25070	−	0.0219531i	1.25070	−	0.0219531i	0.639045	+	0.769169i	$0.279330\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.0777665	+	0.0706000i	0.0777665	+	0.0706000i
$407$	−1.49443	−	1.79873i	−1.49443	−	1.79873i
$408$		0			0
$409$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$409$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.178488	+	1.84331i	0.178488	+	1.84331i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.994461	−	0.105110i	$-0.966480\pi$
$419$		0			0		0.994461	+	0.105110i	$0.0335196\pi$
$420$		0			0
$421$	−0.488959	+	0.459809i	−0.488959	+	0.459809i	−0.889808	−	0.456335i	$-0.849162\pi$
$421$	−0.488959	+	0.459809i	−0.488959	+	0.459809i	0.400849	+	0.916144i	$0.368715\pi$
$422$	0.840691	+	3.23186i	0.840691	+	3.23186i
$423$		0			0
$424$	−2.25085	−	0.158277i	−2.25085	−	0.158277i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.0354971	−	4.04497i	0.0354971	−	4.04497i
$429$		0			0
$430$		0			0
$431$	1.17315	−	1.57368i	1.17315	−	1.57368i	0.432754	−	0.901512i	$-0.357542\pi$
$431$	1.17315	−	1.57368i	1.17315	−	1.57368i	0.740398	−	0.672168i	$-0.234637\pi$
$432$		0			0
$433$		0			0		0.926378	−	0.376595i	$-0.122905\pi$
$433$		0			0		−0.926378	+	0.376595i	$0.877095\pi$
$434$		0			0
$435$		0			0
$436$	3.67253	+	2.68800i	3.67253	+	2.68800i
$437$		0			0
$438$		0			0
$439$		0			0		−0.368451	−	0.929647i	$-0.620112\pi$
$439$		0			0		0.368451	+	0.929647i	$0.379888\pi$
$440$		0			0
$441$	0.165961	+	0.986132i	0.165961	+	0.986132i
$442$		0			0
$443$	1.28024	−	1.16226i	1.28024	−	1.16226i	0.302333	−	0.953202i	$-0.402235\pi$
$443$	1.28024	−	1.16226i	1.28024	−	1.16226i	0.977904	−	0.209056i	$-0.0670391\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	3.12225	−	5.95871i	3.12225	−	5.95871i
$449$	−0.133902	−	1.01137i	−0.133902	−	1.01137i	−0.919626	−	0.392794i	$-0.871508\pi$
$449$	−0.133902	−	1.01137i	−0.133902	−	1.01137i	0.785724	−	0.618577i	$-0.212291\pi$
$450$	1.42918	−	1.39204i	1.42918	−	1.39204i
$451$		0			0
$452$	4.81667	+	3.15006i	4.81667	+	3.15006i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.194792	−	0.117846i	0.194792	−	0.117846i	−0.416866	−	0.908968i	$-0.636872\pi$
$457$	0.194792	−	0.117846i	0.194792	−	0.117846i	0.611658	+	0.791122i	$0.290503\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.0438629	−	0.999038i	$-0.486034\pi$
$461$		0			0		−0.0438629	+	0.999038i	$0.513966\pi$
$462$		0			0
$463$	−1.15824	−	0.143016i	−1.15824	−	0.143016i	−0.479599	−	0.877488i	$-0.659218\pi$
$463$	−1.15824	−	0.143016i	−1.15824	−	0.143016i	−0.678640	+	0.734471i	$0.737430\pi$
$464$	0.0158428	−	0.257584i	0.0158428	−	0.257584i
$465$		0			0
$466$	−3.66852	+	0.452980i	−3.66852	+	0.452980i
$467$		0			0		−0.919626	−	0.392794i	$-0.871508\pi$
$467$		0			0		0.919626	+	0.392794i	$0.128492\pi$
$468$		0			0
$469$	0.950598	+	0.893927i	0.950598	+	0.893927i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.66327	+	3.31453i	1.66327	+	3.31453i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.542852	−	0.177437i	−0.542852	−	0.177437i
$478$	−0.936443	+	3.87807i	−0.936443	+	3.87807i
$479$		0			0		0.817190	−	0.576369i	$-0.195531\pi$
$479$		0			0		−0.817190	+	0.576369i	$0.804469\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	7.42846	−	2.72016i	7.42846	−	2.72016i
$485$		0			0
$486$		0			0
$487$	0.479850	+	1.42557i	0.479850	+	1.42557i	0.864559	+	0.502531i	$0.167598\pi$
$487$	0.479850	+	1.42557i	0.479850	+	1.42557i	−0.384709	+	0.923038i	$0.625698\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.70991	+	0.493197i	−1.70991	+	0.493197i	−0.981422	−	0.191862i	$-0.938547\pi$
$491$	−1.70991	+	0.493197i	−1.70991	+	0.493197i	−0.728488	+	0.685059i	$0.759777\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.966140	−	1.12220i	−0.966140	−	1.12220i
$498$		0			0
$499$	−1.81143	+	0.811583i	−1.81143	+	0.811583i	−0.855607	+	0.517627i	$0.826816\pi$
$499$	−1.81143	+	0.811583i	−1.81143	+	0.811583i	−0.955819	+	0.293956i	$0.905028\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.0788965	−	0.996883i	$-0.525140\pi$
$503$		0			0		0.0788965	+	0.996883i	$0.474860\pi$
$504$	2.62988	−	2.94842i	2.62988	−	2.94842i
$505$		0			0
$506$	2.49230	+	2.51427i	2.49230	+	2.51427i
$507$		0			0
$508$	−1.40260	−	1.81413i	−1.40260	−	1.81413i
$509$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$509$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$510$		0			0
$511$		0			0
$512$	−9.03512	+	1.76631i	−9.03512	+	1.76631i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−2.33278	+	0.717432i	−2.33278	+	0.717432i
$519$		0			0
$520$		0			0
$521$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$521$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$522$	0.0317550	−	0.100118i	0.0317550	−	0.100118i
$523$		0			0		−0.774747	−	0.632271i	$-0.782123\pi$
$523$		0			0		0.774747	+	0.632271i	$0.217877\pi$
$524$		0			0
$525$		0			0
$526$	−3.00508	+	1.89085i	−3.00508	+	1.89085i
$527$		0			0
$528$		0			0
$529$	0.0487103	−	0.129492i	0.0487103	−	0.129492i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.406749	−	5.13940i	0.406749	−	5.13940i
$537$		0			0
$538$		0			0
$539$	1.43771	+	1.25990i	1.43771	+	1.25990i
$540$		0			0
$541$	0.122250	−	1.54466i	0.122250	−	1.54466i	−0.569175	−	0.822216i	$-0.692737\pi$
$541$	0.122250	−	1.54466i	0.122250	−	1.54466i	0.691425	−	0.722448i	$-0.256983\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.23226	−	1.04221i	1.23226	−	1.04221i	0.234725	−	0.972062i	$-0.424581\pi$
$547$	1.23226	−	1.04221i	1.23226	−	1.04221i	0.997537	−	0.0701455i	$-0.0223464\pi$
$548$	−0.908184	+	2.41433i	−0.908184	+	2.41433i
$549$		0			0
$550$	0.434142	−	3.78907i	0.434142	−	3.78907i
$551$		0			0
$552$		0			0
$553$	−0.0780957	+	0.137112i	−0.0780957	+	0.137112i
$554$	−2.72553	−	2.22431i	−2.72553	−	2.22431i
$555$		0			0
$556$		0			0
$557$	−0.0434177	−	0.0762281i	−0.0434177	−	0.0762281i	0.846391	−	0.532563i	$-0.178771\pi$
$557$	−0.0434177	−	0.0762281i	−0.0434177	−	0.0762281i	−0.889808	+	0.456335i	$0.849162\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.388625	+	3.39180i	0.388625	+	3.39180i
$563$		0			0		−0.625448	−	0.780266i	$-0.715084\pi$
$563$		0			0		0.625448	+	0.780266i	$0.284916\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.827179	−	0.561938i	0.827179	−	0.561938i
$568$	−1.07205	+	5.75139i	−1.07205	+	5.75139i
$569$	−1.21861	−	1.57616i	−1.21861	−	1.57616i	−0.678640	−	0.734471i	$-0.737430\pi$
$569$	−1.21861	−	1.57616i	−1.21861	−	1.57616i	−0.539970	−	0.841685i	$-0.681564\pi$
$570$		0			0
$571$	0.354461	+	0.357585i	0.354461	+	0.357585i	0.864559	−	0.502531i	$-0.167598\pi$
$571$	0.354461	+	0.357585i	0.354461	+	0.357585i	−0.510099	+	0.860116i	$0.670391\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.882314	−	0.288394i	0.882314	−	0.288394i
$576$	−6.71784	−	0.354038i	−6.71784	−	0.354038i
$577$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$577$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$578$	1.82069	−	0.815732i	1.82069	−	0.815732i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.01845	+	0.393340i	−1.01845	+	0.393340i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.926378	−	0.376595i	$-0.877095\pi$
$587$		0			0		0.926378	+	0.376595i	$0.122905\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	4.96032	+	3.36976i	4.96032	+	3.36976i
$593$		0			0		0.939024	−	0.343852i	$-0.111732\pi$
$593$		0			0		−0.939024	+	0.343852i	$0.888268\pi$
$594$		0			0
$595$		0			0
$596$	−2.47153	+	1.43659i	−2.47153	+	1.43659i
$597$		0			0
$598$		0			0
$599$	0.446218	−	1.84791i	0.446218	−	1.84791i	−0.0788965	−	0.996883i	$-0.525140\pi$
$599$	0.446218	−	1.84791i	0.446218	−	1.84791i	0.525115	−	0.851031i	$-0.324022\pi$
$600$		0			0
$601$		0			0		−0.932845	−	0.360279i	$-0.882682\pi$
$601$		0			0		0.932845	+	0.360279i	$0.117318\pi$
$602$	3.86077	−	0.271484i	3.86077	−	0.271484i
$603$	0.416280	−	1.23671i	0.416280	−	1.23671i
$604$	2.52613	+	5.03402i	2.52613	+	5.03402i
$605$		0			0
$606$		0			0
$607$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$607$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.0848920	−	1.38024i	0.0848920	−	1.38024i	−0.678640	−	0.734471i	$-0.737430\pi$
$613$	0.0848920	−	1.38024i	0.0848920	−	1.38024i	0.763532	−	0.645770i	$-0.223464\pi$
$614$		0			0
$615$		0			0
$616$	0.331281	−	7.54538i	0.331281	−	7.54538i
$617$	0.235643	+	0.115671i	0.235643	+	0.115671i	0.554658	−	0.832079i	$-0.312849\pi$
$617$	0.235643	+	0.115671i	0.235643	+	0.115671i	−0.319015	+	0.947750i	$0.603352\pi$
$618$		0			0
$619$		0			0		0.200467	−	0.979701i	$-0.435754\pi$
$619$		0			0		−0.200467	+	0.979701i	$0.564246\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.836914	−	0.547335i	−0.836914	−	0.547335i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.801205	−	1.83116i	0.801205	−	1.83116i	0.368451	−	0.929647i	$-0.379888\pi$
$631$	0.801205	−	1.83116i	0.801205	−	1.83116i	0.432754	−	0.901512i	$-0.357542\pi$
$632$	0.615660	−	0.0980649i	0.615660	−	0.0980649i
$633$		0			0
$634$	0.490299	−	0.445116i	0.490299	−	0.445116i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0739796	−	0.186660i	−0.0739796	−	0.186660i
$639$	−0.617294	+	1.34600i	−0.617294	+	1.34600i
$640$		0			0
$641$	−1.28540	−	0.940812i	−1.28540	−	0.940812i	−0.285558	−	0.958362i	$-0.592179\pi$
$641$	−1.28540	−	0.940812i	−1.28540	−	0.940812i	−0.999846	+	0.0175499i	$0.994413\pi$
$642$		0			0
$643$		0			0		0.785724	−	0.618577i	$-0.212291\pi$
$643$		0			0		−0.785724	+	0.618577i	$0.787709\pi$
$644$	2.56281	−	1.04184i	2.56281	−	1.04184i
$645$		0			0
$646$		0			0
$647$		0			0		−0.716353	−	0.697738i	$-0.754190\pi$
$647$		0			0		0.716353	+	0.697738i	$0.245810\pi$
$648$	−3.77633	−	1.16139i	−3.77633	−	1.16139i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	3.93093	+	1.84470i	3.93093	+	1.84470i
$653$	0.399946	+	0.0281237i	0.399946	+	0.0281237i	0.268694	−	0.963225i	$-0.413408\pi$
$653$	0.399946	+	0.0281237i	0.399946	+	0.0281237i	0.131251	+	0.991349i	$0.458101\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.256833	+	0.433066i	0.256833	+	0.433066i	0.960831	−	0.277137i	$-0.0893855\pi$
$659$	0.256833	+	0.433066i	0.256833	+	0.433066i	−0.703997	+	0.710203i	$0.748603\pi$
$660$		0			0
$661$		0			0		0.251749	−	0.967793i	$-0.418994\pi$
$661$		0			0		−0.251749	+	0.967793i	$0.581006\pi$
$662$	1.89925	+	3.47491i	1.89925	+	3.47491i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.62458	+	1.82135i	1.62458	+	1.82135i
$667$	0.0337892	−	0.0353053i	0.0337892	−	0.0353053i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.335382	−	0.503129i	0.335382	−	0.503129i	−0.625448	−	0.780266i	$-0.715084\pi$
$673$	0.335382	−	0.503129i	0.335382	−	0.503129i	0.960831	+	0.277137i	$0.0893855\pi$
$674$	1.42045	−	1.77206i	1.42045	−	1.77206i
$675$		0			0
$676$	−2.97986	+	0.0523043i	−2.97986	+	0.0523043i
$677$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$677$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.101221	+	0.164044i	0.101221	+	0.164044i	0.897680	−	0.440648i	$-0.145251\pi$
$683$	0.101221	+	0.164044i	0.101221	+	0.164044i	−0.796459	+	0.604692i	$0.793296\pi$
$684$		0			0
$685$		0			0
$686$	1.79094	−	0.879126i	1.79094	−	0.879126i
$687$		0			0
$688$	−6.45352	−	6.98445i	−6.45352	−	6.98445i
$689$		0			0
$690$		0			0
$691$		0			0		0.268694	−	0.963225i	$-0.413408\pi$
$691$		0			0		−0.268694	+	0.963225i	$0.586592\pi$
$692$		0			0
$693$	0.545883	−	1.83204i	0.545883	−	1.83204i
$694$	−0.0858321	+	3.25958i	−0.0858321	+	3.25958i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.60255	−	1.45225i	−2.60255	−	1.45225i
$701$	−0.271275	+	1.80491i	−0.271275	+	1.80491i	0.268694	+	0.963225i	$0.413408\pi$
$701$	−0.271275	+	1.80491i	−0.271275	+	1.80491i	−0.539970	+	0.841685i	$0.681564\pi$
$702$		0			0
$703$		0			0
$704$	−10.3773	+	7.59533i	−10.3773	+	7.59533i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.352456	+	0.989322i	0.352456	+	0.989322i	0.977904	+	0.209056i	$0.0670391\pi$
$709$	0.352456	+	0.989322i	0.352456	+	0.989322i	−0.625448	+	0.780266i	$0.715084\pi$
$710$		0			0
$711$	0.157186	+	0.0138292i	0.157186	+	0.0138292i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.01061	−	1.76196i	2.01061	−	1.76196i
$717$		0			0
$718$	−0.636458	−	1.89083i	−0.636458	−	1.89083i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.261856	−	1.97781i	0.261856	−	1.97781i
$723$		0			0
$724$		0			0
$725$	−0.0524437	−	0.00461400i	−0.0524437	−	0.00461400i
$726$		0			0
$727$		0			0		−0.335599	−	0.942005i	$-0.608939\pi$
$727$		0			0		0.335599	+	0.942005i	$0.391061\pi$
$728$		0			0
$729$	−0.855607	−	0.517627i	−0.855607	−	0.517627i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.0263232	−	0.999653i	$-0.508380\pi$
$733$		0			0		0.0263232	+	0.999653i	$0.491620\pi$
$734$		0			0
$735$		0			0
$736$	−4.72487	−	2.63653i	−4.72487	−	2.63653i
$737$	−0.878254	−	2.33476i	−0.878254	−	2.33476i
$738$		0			0
$739$	−1.50805	−	1.27546i	−1.50805	−	1.27546i	−0.855607	−	0.517627i	$-0.826816\pi$
$739$	−1.50805	−	1.27546i	−1.50805	−	1.27546i	−0.652446	−	0.757835i	$-0.726257\pi$
$740$		0			0
$741$		0			0
$742$	−0.0299930	+	1.13902i	−0.0299930	+	1.13902i
$743$	−0.134055	+	0.449903i	−0.134055	+	0.449903i	−0.998614	−	0.0526281i	$-0.983240\pi$
$743$	−0.134055	+	0.449903i	−0.134055	+	0.449903i	0.864559	+	0.502531i	$0.167598\pi$
$744$		0			0
$745$		0			0
$746$	−0.174080	+	0.780719i	−0.174080	+	0.780719i
$747$		0			0
$748$		0			0
$749$	−1.35644	+	0.0476329i	−1.35644	+	0.0476329i
$750$		0			0
$751$	−0.737263	−	1.68502i	−0.737263	−	1.68502i	−0.728488	−	0.685059i	$-0.759777\pi$
$751$	−0.737263	−	1.68502i	−0.737263	−	1.68502i	−0.00877529	−	0.999961i	$-0.502793\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.78401	+	0.447391i	−1.78401	+	0.447391i	−0.987551	−	0.157301i	$-0.949721\pi$
$757$	−1.78401	+	0.447391i	−1.78401	+	0.447391i	−0.796459	+	0.604692i	$0.793296\pi$
$758$	−0.800346	+	2.24652i	−0.800346	+	2.24652i
$759$		0			0
$760$		0			0
$761$		0			0		−0.846391	−	0.532563i	$-0.821229\pi$
$761$		0			0		0.846391	+	0.532563i	$0.178771\pi$
$762$		0			0
$763$	0.846998	−	1.27064i	0.846998	−	1.27064i
$764$	5.74958	+	1.44187i	5.74958	+	1.44187i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$769$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$770$		0			0
$771$		0			0
$772$	0.779864	+	1.62461i	0.779864	+	1.62461i
$773$		0			0		−0.0963795	−	0.995345i	$-0.530726\pi$
$773$		0			0		0.0963795	+	0.995345i	$0.469274\pi$
$774$	−1.85619	−	3.39614i	−1.85619	−	3.39614i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.520810	+	0.0550475i	0.520810	+	0.0550475i
$779$		0			0
$780$		0			0
$781$	0.712636	+	2.73958i	0.712636	+	2.73958i
$782$		0			0
$783$		0			0
$784$	−4.43764	−	2.08249i	−4.43764	−	2.08249i
$785$		0			0
$786$		0			0
$787$		0			0		0.00877529	−	0.999961i	$-0.497207\pi$
$787$		0			0		−0.00877529	+	0.999961i	$0.502793\pi$
$788$	−0.349752	−	0.107564i	−0.349752	−	0.107564i
$789$		0			0
$790$		0			0
$791$	0.985047	−	1.66096i	0.985047	−	1.66096i
$792$	−6.99661	+	2.84429i	−6.99661	+	2.84429i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.416866	−	0.908968i	$-0.363128\pi$
$797$		0			0		−0.416866	+	0.908968i	$0.636872\pi$
$798$		0			0
$799$		0			0
$800$	0.967376	+	5.74809i	0.967376	+	5.74809i
$801$		0			0
$802$	−1.84776	+	1.67748i	−1.84776	+	1.67748i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0879526	−	0.0856671i	0.0879526	−	0.0856671i	−0.652446	−	0.757835i	$-0.726257\pi$
$809$	0.0879526	−	0.0856671i	0.0879526	−	0.0856671i	0.740398	+	0.672168i	$0.234637\pi$
$810$		0			0
$811$		0			0		−0.836914	−	0.547335i	$-0.815642\pi$
$811$		0			0		0.836914	+	0.547335i	$0.184358\pi$
$812$	−0.156879	−	0.00275363i	−0.156879	−	0.00275363i
$813$		0			0
$814$	4.60747	+	0.733897i	4.60747	+	0.733897i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.72805	+	1.00444i	1.72805	+	1.00444i	0.881663	+	0.471880i	$0.156425\pi$
$821$	1.72805	+	1.00444i	1.72805	+	1.00444i	0.846391	+	0.532563i	$0.178771\pi$
$822$		0			0
$823$	0.0784609	−	1.27568i	0.0784609	−	1.27568i	−0.728488	−	0.685059i	$-0.759777\pi$
$823$	0.0784609	−	1.27568i	0.0784609	−	1.27568i	0.806949	−	0.590621i	$-0.201117\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.474731	+	0.868581i	−0.474731	+	0.868581i	0.525115	+	0.851031i	$0.324022\pi$
$827$	−0.474731	+	0.868581i	−0.474731	+	0.868581i	−0.999846	+	0.0175499i	$0.994413\pi$
$828$	−2.01535	−	1.89520i	−2.01535	−	1.89520i
$829$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$829$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$830$		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		−0.464125	−	0.885770i	$-0.653631\pi$
$839$		0			0		0.464125	+	0.885770i	$0.346369\pi$
$840$		0			0
$841$	0.917077	−	0.391706i	0.917077	−	0.391706i
$842$	0.129061	−	1.33285i	0.129061	−	1.33285i
$843$		0			0
$844$	−4.12642	−	2.80325i	−4.12642	−	2.80325i
$845$		0			0
$846$		0			0
$847$	−1.02116	−	2.45007i	−1.02116	−	2.45007i
$848$	2.22976	−	1.69289i	2.22976	−	1.69289i
$849$		0			0
$850$		0			0
$851$	0.305114	+	1.09379i	0.305114	+	1.09379i
$852$		0			0
$853$		0			0		0.932845	−	0.360279i	$-0.117318\pi$
$853$		0			0		−0.932845	+	0.360279i	$0.882682\pi$
$854$		0			0
$855$		0			0
$856$	3.49871	+	4.06385i	3.49871	+	4.06385i
$857$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$857$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$858$		0			0
$859$		0			0		−0.217629	−	0.976031i	$-0.569832\pi$
$859$		0			0		0.217629	+	0.976031i	$0.430168\pi$
$860$		0			0
$861$		0			0
$862$	0.308960	+	3.90381i	0.308960	+	3.90381i
$863$	0.490515	−	0.549926i	0.490515	−	0.549926i	−0.448509	−	0.893778i	$-0.648045\pi$
$863$	0.490515	−	0.549926i	0.490515	−	0.549926i	0.939024	+	0.343852i	$0.111732\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.249513	−	0.169505i	0.249513	−	0.169505i
$870$		0			0
$871$		0			0
$872$	−6.01003	+	0.528762i	−6.01003	+	0.528762i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.916820	−	0.281962i	0.916820	−	0.281962i	0.200467	−	0.979701i	$-0.435754\pi$
$877$	0.916820	−	0.281962i	0.916820	−	0.281962i	0.716353	+	0.697738i	$0.245810\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$881$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$882$	−1.54568	−	1.26143i	−1.54568	−	1.26143i
$883$	0.837800	−	1.47092i	0.837800	−	1.47092i	−0.0438629	−	0.999038i	$-0.513966\pi$
$883$	0.837800	−	1.47092i	0.837800	−	1.47092i	0.881663	−	0.471880i	$-0.156425\pi$
$884$		0			0
$885$		0			0
$886$	−0.392691	+	3.42729i	−0.392691	+	3.42729i
$887$		0			0		−0.148629	−	0.988893i	$-0.547486\pi$
$887$		0			0		0.148629	+	0.988893i	$0.452514\pi$
$888$		0			0
$889$	−0.587476	+	0.496868i	−0.587476	+	0.496868i
$890$		0			0
$891$	−1.89283	+	0.267525i	−1.89283	+	0.267525i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.78209	+	7.38014i	1.78209	+	7.38014i
$897$		0			0
$898$	1.53076	+	1.34145i	1.53076	+	1.34145i
$899$		0			0
$900$	−0.235137	+	2.97103i	−0.235137	+	2.97103i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−7.55444	+	1.06772i	−7.55444	+	1.06772i
$905$		0			0
$906$		0			0
$907$	0.560833	−	1.49092i	0.560833	−	1.49092i	−0.285558	−	0.958362i	$-0.592179\pi$
$907$	0.560833	−	1.49092i	0.560833	−	1.49092i	0.846391	−	0.532563i	$-0.178771\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.533976	−	0.349216i	0.533976	−	0.349216i	−0.251749	−	0.967793i	$-0.581006\pi$
$911$	0.533976	−	0.349216i	0.533976	−	0.349216i	0.785724	+	0.618577i	$0.212291\pi$
$912$		0			0
$913$		0			0
$914$	−0.137323	+	0.432954i	−0.137323	+	0.432954i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.380160	−	1.27586i	−0.380160	−	1.27586i	−0.905275	−	0.424826i	$-0.860335\pi$
$919$	−0.380160	−	1.27586i	−0.380160	−	1.27586i	0.525115	−	0.851031i	$-0.324022\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.713826	−	0.993456i	0.713826	−	0.993456i
$926$	1.92594	−	1.30837i	1.92594	−	1.30837i
$927$		0			0
$928$	0.187701	+	0.242773i	0.187701	+	0.242773i
$929$		0			0		0.448509	−	0.893778i	$-0.351955\pi$
$929$		0			0		−0.448509	+	0.893778i	$0.648045\pi$
$930$		0			0
$931$		0			0
$932$	3.67556	−	4.12075i	3.67556	−	4.12075i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$937$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$938$	−2.60175	−	0.0913631i	−2.60175	−	0.0913631i
$939$		0			0
$940$		0			0
$941$		0			0		0.905275	−	0.424826i	$-0.139665\pi$
$941$		0			0		−0.905275	+	0.424826i	$0.860335\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−6.85391	−	2.78628i	−6.85391	−	2.78628i
$947$	−1.42993	+	1.08564i	−1.42993	+	1.08564i	−0.448509	+	0.893778i	$0.648045\pi$
$947$	−1.42993	+	1.08564i	−1.42993	+	1.08564i	−0.981422	+	0.191862i	$0.938547\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.173036	−	1.78700i	0.173036	−	1.78700i	−0.352079	−	0.935970i	$-0.614525\pi$
$953$	0.173036	−	1.78700i	0.173036	−	1.78700i	0.525115	−	0.851031i	$-0.324022\pi$
$954$	1.04784	−	0.447557i	1.04784	−	0.447557i
$955$		0			0
$956$	−2.76606	−	5.27894i	−2.76606	−	5.27894i
$957$		0			0
$958$		0			0
$959$	0.822676	+	0.268901i	0.822676	+	0.268901i
$960$		0			0
$961$	0.997537	−	0.0701455i	0.997537	−	0.0701455i
$962$		0			0
$963$	0.608752	+	1.21311i	0.608752	+	1.21311i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.12879	+	1.06149i	1.12879	+	1.06149i	0.997537	+	0.0701455i	$0.0223464\pi$
$967$	1.12879	+	1.06149i	1.12879	+	1.06149i	0.131251	+	0.991349i	$0.458101\pi$
$968$	−5.02958	+	9.20226i	−5.02958	+	9.20226i
$969$		0			0
$970$		0			0
$971$		0			0		−0.0613892	−	0.998114i	$-0.519553\pi$
$971$		0			0		0.0613892	+	0.998114i	$0.480447\pi$
$972$		0			0
$973$		0			0
$974$	−2.59447	−	1.50805i	−2.59447	−	1.50805i
$975$		0			0
$976$		0			0
$977$	−0.334450	−	0.149846i	−0.334450	−	0.149846i	0.234725	−	0.972062i	$-0.424581\pi$
$977$	−0.334450	−	0.149846i	−0.334450	−	0.149846i	−0.569175	+	0.822216i	$0.692737\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.50805	−	0.240209i	−1.50805	−	0.240209i
$982$	1.91714	−	2.98837i	1.91714	−	2.98837i
$983$		0			0		−0.999846	−	0.0175499i	$-0.994413\pi$
$983$		0			0		0.999846	+	0.0175499i	$0.00558659\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0789857	−	1.79901i	−0.0789857	−	1.79901i
$990$		0			0
$991$	−1.55188	+	0.247191i	−1.55188	+	0.247191i	−0.873245	−	0.487281i	$-0.837989\pi$
$991$	−1.55188	+	0.247191i	−1.55188	+	0.247191i	−0.678640	+	0.734471i	$0.737430\pi$
$992$		0			0
$993$		0			0
$994$	2.92523	+	0.413441i	2.92523	+	0.413441i
$995$		0			0
$996$		0			0
$997$		0			0		−0.368451	−	0.929647i	$-0.620112\pi$
$997$		0			0		0.368451	+	0.929647i	$0.379888\pi$
$998$	1.65082	−	3.59958i	1.65082	−	3.59958i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.48.1	✓	178
7.6	odd	2	CM	2513.1.l.a.48.1	✓	178
359.187	even	179	inner	2513.1.l.a.1623.1	yes	178
2513.1623	odd	358	inner	2513.1.l.a.1623.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.48.1	✓	178	1.1	even	1	trivial
2513.1.l.a.48.1	✓	178	7.6	odd	2	CM
2513.1.l.a.1623.1	yes	178	359.187	even	179	inner
2513.1.l.a.1623.1	yes	178	2513.1623	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)

\(f(q)\)	\(=\)	\(q+(-1.50046 + 1.31489i) q^{2} +(0.391170 - 2.95454i) q^{4} +(-0.996152 - 0.0876414i) q^{7} +(2.19139 + 3.28744i) q^{8} +(0.335599 + 0.942005i) q^{9} +O(q^{10})\)	\(q+(-1.50046 + 1.31489i) q^{2} +(0.391170 - 2.95454i) q^{4} +(-0.996152 - 0.0876414i) q^{7} +(2.19139 + 3.28744i) q^{8} +(0.335599 + 0.942005i) q^{9} +(1.63561 + 0.989515i) q^{11} +(1.60992 - 1.17833i) q^{14} +(-4.73309 - 1.27565i) q^{16} +(-1.74219 - 0.972161i) q^{18} +(-3.75527 + 0.665931i) q^{22} +(-0.528337 - 0.763223i) q^{23} +(-0.285558 + 0.958362i) q^{25} +(-0.648605 + 2.90888i) q^{28} +(0.0105538 + 0.0515776i) q^{29} +(5.23251 - 2.56851i) q^{32} +(2.91446 - 0.623054i) q^{36} +(-1.15593 - 0.400415i) q^{37} +(1.64194 + 1.03313i) q^{43} +(3.56336 - 4.44540i) q^{44} +(1.79630 + 0.450475i) q^{46} +(0.984638 + 0.174608i) q^{49} +(-0.831678 - 1.81346i) q^{50} +(-0.349327 + 0.451822i) q^{53} +(-1.89484 - 3.46685i) q^{56} +(-0.0836547 - 0.0635128i) q^{58} +(-0.251749 - 0.967793i) q^{63} +(-2.58800 + 6.20942i) q^{64} +(-1.02528 - 0.807176i) q^{67} +(1.06077 + 1.03321i) q^{71} +(-2.36136 + 3.16756i) q^{72} +(2.26092 - 0.919119i) q^{74} +(-1.54259 - 1.12905i) q^{77} +(0.0657785 - 0.143429i) q^{79} +(-0.774747 + 0.632271i) q^{81} +(-3.82212 + 0.608803i) q^{86} +(0.331281 + 7.54538i) q^{88} +(-2.46164 + 1.26244i) q^{92} +(-1.70700 + 1.03270i) q^{98} +(-0.383219 + 1.87283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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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