LMFDB - Embedded newform 2513.1.l.a.20.1

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			20.1
Root			$0.0788965 - 0.996883i$ of defining polynomial
Character	$\chi$	$=$	2513.20
Dual form			2513.1.l.a.377.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08480 + 1.62739i) q^{2} +(-1.08687 + 2.60775i) q^{4} +(-0.965546 - 0.260231i) q^{7} +(-3.50339 + 0.684890i) q^{8} +(-0.855607 - 0.517627i) q^{9} +O(q^{10})$	\(q+(1.08480 + 1.62739i) q^{2} +(-1.08687 + 2.60775i) q^{4} +(-0.965546 - 0.260231i) q^{7} +(-3.50339 + 0.684890i) q^{8} +(-0.855607 - 0.517627i) q^{9} +(-0.0767915 + 1.24854i) q^{11} +(-0.623931 - 1.85362i) q^{14} +(-2.92615 - 2.95194i) q^{16} +(-0.0857874 - 1.95392i) q^{18} +(-2.11515 + 1.22945i) q^{22} +(-1.92531 + 0.482826i) q^{23} +(0.763532 - 0.645770i) q^{25} +(1.72805 - 2.23506i) q^{28} +(0.0898119 + 0.129740i) q^{29} +(0.914038 - 4.46700i) q^{32} +(2.27978 - 1.66861i) q^{36} +(0.993140 + 1.54807i) q^{37} +(-0.168563 + 1.47117i) q^{43} +(-3.17241 - 1.55726i) q^{44} +(-2.87432 - 2.60945i) q^{46} +(0.864559 + 0.502531i) q^{49} +(1.87920 + 0.542026i) q^{50} +(-1.40433 - 0.599822i) q^{53} +(3.56091 + 0.250399i) q^{56} +(-0.113709 + 0.286901i) q^{58} +(0.691425 + 0.722448i) q^{63} +(4.41061 - 1.79302i) q^{64} +(-0.705663 + 1.53868i) q^{67} +(0.811218 - 0.877958i) q^{71} +(3.35204 + 1.22745i) q^{72} +(-1.44194 + 3.29557i) q^{74} +(0.399054 - 1.18554i) q^{77} +(0.451062 - 0.130102i) q^{79} +(0.464125 + 0.885770i) q^{81} +(-2.57702 + 1.32161i) q^{86} +(-0.586080 - 4.42670i) q^{88} +(0.833478 - 5.54549i) q^{92} +(0.120065 + 1.95212i) q^{98} +(0.711979 - 1.02851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{15}{179}\right)$

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 $

$2$	1.08480	+	1.62739i	1.08480	+	1.62739i	0.716353	+	0.697738i	$0.245810\pi$
$2$	1.08480	+	1.62739i	1.08480	+	1.62739i	0.368451	+	0.929647i	$0.379888\pi$
$3$		0			0		0.268694	−	0.963225i	$-0.413408\pi$
$3$		0			0		−0.268694	+	0.963225i	$0.586592\pi$
$4$	−1.08687	+	2.60775i	−1.08687	+	2.60775i
$5$		0			0		0.939024	−	0.343852i	$-0.111732\pi$
$5$		0			0		−0.939024	+	0.343852i	$0.888268\pi$
$6$		0			0
$7$	−0.965546	−	0.260231i	−0.965546	−	0.260231i
$7$	−0.965546	−	0.260231i	−0.965546	−	0.260231i
$8$	−3.50339	+	0.684890i	−3.50339	+	0.684890i
$9$	−0.855607	−	0.517627i	−0.855607	−	0.517627i
$10$		0			0
$11$	−0.0767915	+	1.24854i	−0.0767915	+	1.24854i	0.740398	+	0.672168i	$0.234637\pi$
$11$	−0.0767915	+	1.24854i	−0.0767915	+	1.24854i	−0.817190	+	0.576369i	$0.804469\pi$
$12$		0			0
$13$		0			0		−0.846391	−	0.532563i	$-0.821229\pi$
$13$		0			0		0.846391	+	0.532563i	$0.178771\pi$
$14$	−0.623931	−	1.85362i	−0.623931	−	1.85362i
$15$		0			0
$16$	−2.92615	−	2.95194i	−2.92615	−	2.95194i
$17$		0			0		0.432754	−	0.901512i	$-0.357542\pi$
$17$		0			0		−0.432754	+	0.901512i	$0.642458\pi$
$18$	−0.0857874	−	1.95392i	−0.0857874	−	1.95392i
$19$		0			0		−0.881663	−	0.471880i	$-0.843575\pi$
$19$		0			0		0.881663	+	0.471880i	$0.156425\pi$
$20$		0			0
$21$		0			0
$22$	−2.11515	+	1.22945i	−2.11515	+	1.22945i
$23$	−1.92531	+	0.482826i	−1.92531	+	0.482826i	−0.932845	+	0.360279i	$0.882682\pi$
$23$	−1.92531	+	0.482826i	−1.92531	+	0.482826i	−0.992463	+	0.122547i	$0.960894\pi$
$24$		0			0
$25$	0.763532	−	0.645770i	0.763532	−	0.645770i
$26$		0			0
$27$		0			0
$28$	1.72805	−	2.23506i	1.72805	−	2.23506i
$29$	0.0898119	+	0.129740i	0.0898119	+	0.129740i	0.864559	−	0.502531i	$-0.167598\pi$
$29$	0.0898119	+	0.129740i	0.0898119	+	0.129740i	−0.774747	+	0.632271i	$0.782123\pi$
$30$		0			0
$31$		0			0		0.994461	−	0.105110i	$-0.0335196\pi$
$31$		0			0		−0.994461	+	0.105110i	$0.966480\pi$
$32$	0.914038	−	4.46700i	0.914038	−	4.46700i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.27978	−	1.66861i	2.27978	−	1.66861i
$37$	0.993140	+	1.54807i	0.993140	+	1.54807i	0.827179	+	0.561938i	$0.189944\pi$
$37$	0.993140	+	1.54807i	0.993140	+	1.54807i	0.165961	+	0.986132i	$0.446927\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.996152	−	0.0876414i	$-0.972067\pi$
$41$		0			0		0.996152	+	0.0876414i	$0.0279330\pi$
$42$		0			0
$43$	−0.168563	+	1.47117i	−0.168563	+	1.47117i	0.583517	+	0.812101i	$0.301676\pi$
$43$	−0.168563	+	1.47117i	−0.168563	+	1.47117i	−0.752081	+	0.659071i	$0.770950\pi$
$44$	−3.17241	−	1.55726i	−3.17241	−	1.55726i
$45$		0			0
$46$	−2.87432	−	2.60945i	−2.87432	−	2.60945i
$47$		0			0		0.597680	−	0.801735i	$-0.296089\pi$
$47$		0			0		−0.597680	+	0.801735i	$0.703911\pi$
$48$		0			0
$49$	0.864559	+	0.502531i	0.864559	+	0.502531i
$50$	1.87920	+	0.542026i	1.87920	+	0.542026i
$51$		0			0
$52$		0			0
$53$	−1.40433	−	0.599822i	−1.40433	−	0.599822i	−0.448509	−	0.893778i	$-0.648045\pi$
$53$	−1.40433	−	0.599822i	−1.40433	−	0.599822i	−0.955819	+	0.293956i	$0.905028\pi$
$54$		0			0
$55$		0			0
$56$	3.56091	+	0.250399i	3.56091	+	0.250399i
$57$		0			0
$58$	−0.113709	+	0.286901i	−0.113709	+	0.286901i
$59$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$59$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$60$		0			0
$61$		0			0		−0.836914	−	0.547335i	$-0.815642\pi$
$61$		0			0		0.836914	+	0.547335i	$0.184358\pi$
$62$		0			0
$63$	0.691425	+	0.722448i	0.691425	+	0.722448i
$64$	4.41061	−	1.79302i	4.41061	−	1.79302i
$65$		0			0
$66$		0			0
$67$	−0.705663	+	1.53868i	−0.705663	+	1.53868i	0.131251	+	0.991349i	$0.458101\pi$
$67$	−0.705663	+	1.53868i	−0.705663	+	1.53868i	−0.836914	+	0.547335i	$0.815642\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.811218	−	0.877958i	0.811218	−	0.877958i	−0.183242	−	0.983068i	$-0.558659\pi$
$71$	0.811218	−	0.877958i	0.811218	−	0.877958i	0.994461	+	0.105110i	$0.0335196\pi$
$72$	3.35204	+	1.22745i	3.35204	+	1.22745i
$73$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$73$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$74$	−1.44194	+	3.29557i	−1.44194	+	3.29557i
$75$		0			0
$76$		0			0
$77$	0.399054	−	1.18554i	0.399054	−	1.18554i
$78$		0			0
$79$	0.451062	−	0.130102i	0.451062	−	0.130102i	−0.0438629	−	0.999038i	$-0.513966\pi$
$79$	0.451062	−	0.130102i	0.451062	−	0.130102i	0.494925	+	0.868936i	$0.335196\pi$
$80$		0			0
$81$	0.464125	+	0.885770i	0.464125	+	0.885770i
$82$		0			0
$83$		0			0		−0.912591	−	0.408873i	$-0.865922\pi$
$83$		0			0		0.912591	+	0.408873i	$0.134078\pi$
$84$		0			0
$85$		0			0
$86$	−2.57702	+	1.32161i	−2.57702	+	1.32161i
$87$		0			0
$88$	−0.586080	−	4.42670i	−0.586080	−	4.42670i
$89$		0			0		0.992463	−	0.122547i	$-0.0391061\pi$
$89$		0			0		−0.992463	+	0.122547i	$0.960894\pi$
$90$		0			0
$91$		0			0
$92$	0.833478	−	5.54549i	0.833478	−	5.54549i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.539970	−	0.841685i	$-0.318436\pi$
$97$		0			0		−0.539970	+	0.841685i	$0.681564\pi$
$98$	0.120065	+	1.95212i	0.120065	+	1.95212i
$99$	0.711979	−	1.02851i	0.711979	−	1.02851i
$100$	0.854145	+	2.69297i	0.854145	+	2.69297i
$101$		0			0		−0.200467	−	0.979701i	$-0.564246\pi$
$101$		0			0		0.200467	+	0.979701i	$0.435754\pi$
$102$		0			0
$103$		0			0		0.00877529	−	0.999961i	$-0.497207\pi$
$103$		0			0		−0.00877529	+	0.999961i	$0.502793\pi$
$104$		0			0
$105$		0			0
$106$	−0.547278	−	2.93607i	−0.547278	−	2.93607i
$107$	−1.46592	+	0.566160i	−1.46592	+	0.566160i	−0.955819	−	0.293956i	$-0.905028\pi$
$107$	−1.46592	+	0.566160i	−1.46592	+	0.566160i	−0.510099	+	0.860116i	$0.670391\pi$
$108$		0			0
$109$	−1.01768	+	0.0715623i	−1.01768	+	0.0715623i	−0.569175	−	0.822216i	$-0.692737\pi$
$109$	−1.01768	+	0.0715623i	−1.01768	+	0.0715623i	−0.448509	+	0.893778i	$0.648045\pi$
$110$		0			0
$111$		0			0
$112$	2.05714	+	3.61171i	2.05714	+	3.61171i
$113$	1.37151	−	0.318469i	1.37151	−	0.318469i	0.525115	−	0.851031i	$-0.324022\pi$
$113$	1.37151	−	0.318469i	1.37151	−	0.318469i	0.846391	+	0.532563i	$0.178771\pi$
$114$		0			0
$115$		0			0
$116$	−0.435944	+	0.0931959i	−0.435944	+	0.0931959i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.560485	−	0.0692072i	−0.560485	−	0.0692072i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.425641	+	1.90893i	−0.425641	+	1.90893i
$127$	1.32723	+	1.29274i	1.32723	+	1.29274i	0.926378	+	0.376595i	$0.122905\pi$
$127$	1.32723	+	1.29274i	1.32723	+	1.29274i	0.400849	+	0.916144i	$0.368715\pi$
$128$	3.93102	+	2.67051i	3.93102	+	2.67051i
$129$		0			0
$130$		0			0
$131$		0			0		−0.400849	−	0.916144i	$-0.631285\pi$
$131$		0			0		0.400849	+	0.916144i	$0.368715\pi$
$132$		0			0
$133$		0			0
$134$	−3.26954	+	0.520785i	−3.26954	+	0.520785i
$135$		0			0
$136$		0			0
$137$	1.50934	+	1.23177i	1.50934	+	1.23177i	0.897680	+	0.440648i	$0.145251\pi$
$137$	1.50934	+	1.23177i	1.50934	+	1.23177i	0.611658	+	0.791122i	$0.290503\pi$
$138$		0			0
$139$		0			0		−0.994461	−	0.105110i	$-0.966480\pi$
$139$		0			0		0.994461	+	0.105110i	$0.0335196\pi$
$140$		0			0
$141$		0			0
$142$	2.30879	+	0.367753i	2.30879	+	0.367753i
$143$		0			0
$144$	0.975628	+	4.04035i	0.975628	+	4.04035i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−5.11640	+	0.907304i	−5.11640	+	0.907304i
$149$	−1.83472	+	0.783654i	−1.83472	+	0.783654i	−0.889808	+	0.456335i	$0.849162\pi$
$149$	−1.83472	+	0.783654i	−1.83472	+	0.783654i	−0.944914	+	0.327319i	$0.893855\pi$
$150$		0			0
$151$	0.235026	+	1.05405i	0.235026	+	1.05405i	0.939024	+	0.343852i	$0.111732\pi$
$151$	0.235026	+	1.05405i	0.235026	+	1.05405i	−0.703997	+	0.710203i	$0.748603\pi$
$152$		0			0
$153$		0			0
$154$	2.36222	−	0.636659i	2.36222	−	0.636659i
$155$		0			0
$156$		0			0
$157$		0			0		0.703997	−	0.710203i	$-0.251397\pi$
$157$		0			0		−0.703997	+	0.710203i	$0.748603\pi$
$158$	0.701040	+	0.592917i	0.701040	+	0.592917i
$159$		0			0
$160$		0			0
$161$	1.98462	+	0.0348352i	1.98462	+	0.0348352i
$162$	−0.938003	+	1.71620i	−0.938003	+	1.71620i
$163$	−1.01795	+	0.772852i	−1.01795	+	0.772852i	−0.974084	−	0.226186i	$-0.927374\pi$
$163$	−1.01795	+	0.772852i	−1.01795	+	0.772852i	−0.0438629	+	0.999038i	$0.513966\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.113833	−	0.993500i	$-0.536313\pi$
$167$		0			0		0.113833	+	0.993500i	$0.463687\pi$
$168$		0			0
$169$	0.432754	+	0.901512i	0.432754	+	0.901512i
$170$		0			0
$171$		0			0
$172$	−3.65324	−	2.03855i	−3.65324	−	2.03855i
$173$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$173$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$174$		0			0
$175$	−0.905275	+	0.424826i	−0.905275	+	0.424826i
$176$	3.91031	−	3.42672i	3.91031	−	3.42672i
$177$		0			0
$178$		0			0
$179$	1.09227	−	1.63859i	1.09227	−	1.63859i	0.400849	−	0.916144i	$-0.368715\pi$
$179$	1.09227	−	1.63859i	1.09227	−	1.63859i	0.691425	−	0.722448i	$-0.256983\pi$
$180$		0			0
$181$		0			0		−0.652446	−	0.757835i	$-0.726257\pi$
$181$		0			0		0.652446	+	0.757835i	$0.273743\pi$
$182$		0			0
$183$		0			0
$184$	6.41441	−	3.01015i	6.41441	−	3.01015i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.637981	−	1.79078i	0.637981	−	1.79078i	0.0263232	−	0.999653i	$-0.491620\pi$
$191$	0.637981	−	1.79078i	0.637981	−	1.79078i	0.611658	−	0.791122i	$-0.290503\pi$
$192$		0			0
$193$	−0.264363	−	1.57083i	−0.264363	−	1.57083i	−0.728488	−	0.685059i	$-0.759777\pi$
$193$	−0.264363	−	1.57083i	−0.264363	−	1.57083i	0.464125	−	0.885770i	$-0.346369\pi$
$194$		0			0
$195$		0			0
$196$	−2.25014	+	1.70837i	−2.25014	+	1.70837i
$197$	0.175765	−	0.321585i	0.175765	−	0.321585i	−0.774747	−	0.632271i	$-0.782123\pi$
$197$	0.175765	−	0.321585i	0.175765	−	0.321585i	0.950513	+	0.310686i	$0.100559\pi$
$198$	2.44614	+	0.0429360i	2.44614	+	0.0429360i
$199$		0			0		−0.148629	−	0.988893i	$-0.547486\pi$
$199$		0			0		0.148629	+	0.988893i	$0.452514\pi$
$200$	−2.23267	+	2.78532i	−2.23267	+	2.78532i
$201$		0			0
$202$		0			0
$203$	−0.0529551	−	0.148642i	−0.0529551	−	0.148642i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.89723	+	0.583482i	1.89723	+	0.583482i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.326823	−	0.0579564i	0.326823	−	0.0579564i	−0.00877529	−	0.999961i	$-0.502793\pi$
$211$	0.326823	−	0.0579564i	0.326823	−	0.0579564i	0.335599	+	0.942005i	$0.391061\pi$
$212$	3.09051	−	3.01020i	3.09051	−	3.01020i
$213$		0			0
$214$	−2.51159	−	1.77144i	−2.51159	−	1.77144i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.22045	−	1.57853i	−1.22045	−	1.57853i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.251749	−	0.967793i	$-0.418994\pi$
$223$		0			0		−0.251749	+	0.967793i	$0.581006\pi$
$224$	−2.04500	+	4.07523i	−2.04500	+	4.07523i
$225$	−0.987551	+	0.157301i	−0.987551	+	0.157301i
$226$	2.00609	+	1.88649i	2.00609	+	1.88649i
$227$		0			0		0.665645	−	0.746268i	$-0.268156\pi$
$227$		0			0		−0.665645	+	0.746268i	$0.731844\pi$
$228$		0			0
$229$		0			0		−0.368451	−	0.929647i	$-0.620112\pi$
$229$		0			0		0.368451	+	0.929647i	$0.379888\pi$
$230$		0			0
$231$		0			0
$232$	−0.403503	−	0.393018i	−0.403503	−	0.393018i
$233$	−0.174473	+	0.782483i	−0.174473	+	0.782483i	0.806949	+	0.590621i	$0.201117\pi$
$233$	−0.174473	+	0.782483i	−0.174473	+	0.782483i	−0.981422	+	0.191862i	$0.938547\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.536644	−	1.92378i	−0.536644	−	1.92378i	−0.319015	−	0.947750i	$-0.603352\pi$
$239$	−0.536644	−	1.92378i	−0.536644	−	1.92378i	−0.217629	−	0.976031i	$-0.569832\pi$
$240$		0			0
$241$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$241$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$242$	−0.495389	−	0.987201i	−0.495389	−	0.987201i
$243$		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		−0.352079	−	0.935970i	$-0.614525\pi$
$251$		0			0		0.352079	+	0.935970i	$0.385475\pi$
$252$	−2.63546	+	1.01785i	−2.63546	+	1.01785i
$253$	−0.454978	−	2.44089i	−0.454978	−	2.44089i
$254$	−0.664002	+	3.56228i	−0.664002	+	3.56228i
$255$		0			0
$256$	−0.0397825	+	4.53330i	−0.0397825	+	4.53330i
$257$		0			0		0.131251	−	0.991349i	$-0.458101\pi$
$257$		0			0		−0.131251	+	0.991349i	$0.541899\pi$
$258$		0			0
$259$	−0.556066	−	1.75318i	−0.556066	−	1.75318i
$260$		0			0
$261$	−0.00968678	−	0.157495i	−0.00968678	−	0.157495i
$262$		0			0
$263$	0.264503	+	0.135649i	0.264503	+	0.135649i	0.583517	−	0.812101i	$-0.301676\pi$
$263$	0.264503	+	0.135649i	0.264503	+	0.135649i	−0.319015	+	0.947750i	$0.603352\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−3.24554	−	3.51255i	−3.24554	−	3.51255i
$269$		0			0		−0.384709	−	0.923038i	$-0.625698\pi$
$269$		0			0		0.384709	+	0.923038i	$0.374302\pi$
$270$		0			0
$271$		0			0		−0.131251	−	0.991349i	$-0.541899\pi$
$271$		0			0		0.131251	+	0.991349i	$0.458101\pi$
$272$		0			0
$273$		0			0
$274$	−0.367229	+	3.79250i	−0.367229	+	3.79250i
$275$	0.747635	+	1.00289i	0.747635	+	1.00289i
$276$		0			0
$277$	−0.0924471	−	0.169144i	−0.0924471	−	0.169144i	0.827179	−	0.561938i	$-0.189944\pi$
$277$	−0.0924471	−	0.169144i	−0.0924471	−	0.169144i	−0.919626	+	0.392794i	$0.871508\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.119091	+	0.0298654i	0.119091	+	0.0298654i	0.302333	−	0.953202i	$-0.402235\pi$
$281$	0.119091	+	0.0298654i	0.119091	+	0.0298654i	−0.183242	+	0.983068i	$0.558659\pi$
$282$		0			0
$283$		0			0		0.774747	−	0.632271i	$-0.217877\pi$
$283$		0			0		−0.774747	+	0.632271i	$0.782123\pi$
$284$	1.40780	+	3.06968i	1.40780	+	3.06968i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−3.09429	+	3.34886i	−3.09429	+	3.34886i
$289$	−0.625448	−	0.780266i	−0.625448	−	0.780266i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$293$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$294$		0			0
$295$		0			0
$296$	−4.53961	−	4.74330i	−4.53961	−	4.74330i
$297$		0			0
$298$	−3.26562	−	2.13569i	−3.26562	−	2.13569i
$299$		0			0
$300$		0			0
$301$	0.545601	−	1.37662i	0.545601	−	1.37662i
$302$	−1.46040	+	1.52592i	−1.46040	+	1.52592i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.817190	−	0.576369i	$-0.195531\pi$
$307$		0			0		−0.817190	+	0.576369i	$0.804469\pi$
$308$	2.65786	+	2.32916i	2.65786	+	2.32916i
$309$		0			0
$310$		0			0
$311$		0			0		0.873245	−	0.487281i	$-0.162011\pi$
$311$		0			0		−0.873245	+	0.487281i	$0.837989\pi$
$312$		0			0
$313$		0			0		−0.740398	−	0.672168i	$-0.765363\pi$
$313$		0			0		0.740398	+	0.672168i	$0.234637\pi$
$314$		0			0
$315$		0			0
$316$	−0.150975	+	1.31766i	−0.150975	+	1.31766i
$317$	0.957869	−	0.0504807i	0.957869	−	0.0504807i	0.432754	−	0.901512i	$-0.357542\pi$
$317$	0.957869	−	0.0504807i	0.957869	−	0.0504807i	0.525115	+	0.851031i	$0.324022\pi$
$318$		0			0
$319$	−0.168882	+	0.102171i	−0.168882	+	0.102171i
$320$		0			0
$321$		0			0
$322$	2.09623	+	3.26753i	2.09623	+	3.26753i
$323$		0			0
$324$	−2.81431	+	0.247603i	−2.81431	+	0.247603i
$325$		0			0
$326$	−2.36200	−	0.818200i	−2.36200	−	0.818200i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.14116	+	1.47599i	−1.14116	+	1.47599i	−0.285558	+	0.958362i	$0.592179\pi$
$331$	−1.14116	+	1.47599i	−1.14116	+	1.47599i	−0.855607	+	0.517627i	$0.826816\pi$
$332$		0			0
$333$	−0.0484149	−	1.83862i	−0.0484149	−	1.83862i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.67718	−	0.974875i	1.67718	−	0.974875i	0.716353	−	0.697738i	$-0.245810\pi$
$337$	1.67718	−	0.974875i	1.67718	−	0.974875i	0.960831	−	0.277137i	$-0.0893855\pi$
$338$	−0.997654	+	1.68222i	−0.997654	+	1.68222i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.703997	−	0.710203i	−0.703997	−	0.710203i
$344$	−0.417048	−	5.26953i	−0.417048	−	5.26953i
$345$		0			0
$346$		0			0
$347$	0.422239	+	0.332416i	0.422239	+	0.332416i	0.806949	−	0.590621i	$-0.201117\pi$
$347$	0.422239	+	0.332416i	0.422239	+	0.332416i	−0.384709	+	0.923038i	$0.625698\pi$
$348$		0			0
$349$		0			0		−0.806949	−	0.590621i	$-0.798883\pi$
$349$		0			0		0.806949	+	0.590621i	$0.201117\pi$
$350$	−1.67340	−	1.01238i	−1.67340	−	1.01238i
$351$		0			0
$352$	5.50702	+	1.48424i	5.50702	+	1.48424i
$353$		0			0		0.950513	−	0.310686i	$-0.100559\pi$
$353$		0			0		−0.950513	+	0.310686i	$0.899441\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	3.85152			3.85152
$359$	0.926378	−	0.376595i	0.926378	−	0.376595i
$359$	0.926378	−	0.376595i	0.926378	−	0.376595i
$360$		0			0
$361$	0.554658	+	0.832079i	0.554658	+	0.832079i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.981422	−	0.191862i	$-0.0614525\pi$
$367$		0			0		−0.981422	+	0.191862i	$0.938547\pi$
$368$	7.05900	+	4.27057i	7.05900	+	4.27057i
$369$		0			0
$370$		0			0
$371$	1.19985	+	0.944606i	1.19985	+	0.944606i
$372$		0			0
$373$	0.363151	+	1.07887i	0.363151	+	1.07887i	0.960831	+	0.277137i	$0.0893855\pi$
$373$	0.363151	+	1.07887i	0.363151	+	1.07887i	−0.597680	+	0.801735i	$0.703911\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.0823766	+	1.87624i	−0.0823766	+	1.87624i	0.302333	+	0.953202i	$0.402235\pi$
$379$	−0.0823766	+	1.87624i	−0.0823766	+	1.87624i	−0.384709	+	0.923038i	$0.625698\pi$
$380$		0			0
$381$		0			0
$382$	3.60637	−	0.904399i	3.60637	−	0.904399i
$383$		0			0		0.0788965	−	0.996883i	$-0.474860\pi$
$383$		0			0		−0.0788965	+	0.996883i	$0.525140\pi$
$384$		0			0
$385$		0			0
$386$	2.26956	−	2.13426i	2.26956	−	2.13426i
$387$	0.905741	−	1.17149i	0.905741	−	1.17149i
$388$		0			0
$389$	−0.604551	+	0.475945i	−0.604551	+	0.475945i	−0.873245	−	0.487281i	$-0.837989\pi$
$389$	−0.604551	+	0.475945i	−0.604551	+	0.475945i	0.268694	+	0.963225i	$0.413408\pi$
$390$		0			0
$391$		0			0
$392$	−3.37306	−	1.16843i	−3.37306	−	1.16843i
$393$		0			0
$394$	0.714014	−	0.0628189i	0.714014	−	0.0628189i
$395$		0			0
$396$	1.90826	+	2.97452i	1.90826	+	2.97452i
$397$		0			0		−0.0963795	−	0.995345i	$-0.530726\pi$
$397$		0			0		0.0963795	+	0.995345i	$0.469274\pi$
$398$		0			0
$399$		0			0
$400$	−4.14048	−	0.364279i	−4.14048	−	0.364279i
$401$	−1.79287	+	0.0944863i	−1.79287	+	0.0944863i	−0.919626	−	0.392794i	$-0.871508\pi$
$401$	−1.79287	+	0.0944863i	−1.79287	+	0.0944863i	−0.873245	+	0.487281i	$0.837989\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.184452	−	0.247426i	0.184452	−	0.247426i
$407$	−2.00909	+	1.12109i	−2.00909	+	1.12109i
$408$		0			0
$409$		0			0		−0.960831	−	0.277137i	$-0.910615\pi$
$409$		0			0		0.960831	+	0.277137i	$0.0893855\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	1.10857	+	3.72049i	1.10857	+	3.72049i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.950513	−	0.310686i	$-0.899441\pi$
$419$		0			0		0.950513	+	0.310686i	$0.100559\pi$
$420$		0			0
$421$	−1.09354	−	1.31621i	−1.09354	−	1.31621i	−0.944914	−	0.327319i	$-0.893855\pi$
$421$	−1.09354	−	1.31621i	−1.09354	−	1.31621i	−0.148629	−	0.988893i	$-0.547486\pi$
$422$	0.448856	+	0.468996i	0.448856	+	0.468996i
$423$		0			0
$424$	5.33071	+	1.13960i	5.33071	+	1.13960i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.116865	−	4.43809i	0.116865	−	4.43809i
$429$		0			0
$430$		0			0
$431$	−1.57176	−	0.575549i	−1.57176	−	0.575549i	−0.597680	−	0.801735i	$-0.703911\pi$
$431$	−1.57176	−	0.575549i	−1.57176	−	0.575549i	−0.974084	+	0.226186i	$0.927374\pi$
$432$		0			0
$433$		0			0		0.400849	−	0.916144i	$-0.368715\pi$
$433$		0			0		−0.400849	+	0.916144i	$0.631285\pi$
$434$		0			0
$435$		0			0
$436$	0.919478	−	2.73164i	0.919478	−	2.73164i
$437$		0			0
$438$		0			0
$439$		0			0		−0.905275	−	0.424826i	$-0.860335\pi$
$439$		0			0		0.905275	+	0.424826i	$0.139665\pi$
$440$		0			0
$441$	−0.479599	−	0.877488i	−0.479599	−	0.877488i
$442$		0			0
$443$	0.0104896	+	0.0140709i	0.0104896	+	0.0140709i	0.806949	−	0.590621i	$-0.201117\pi$
$443$	0.0104896	+	0.0140709i	0.0104896	+	0.0140709i	−0.796459	+	0.604692i	$0.793296\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−4.72525	+	0.583462i	−4.72525	+	0.583462i
$449$	−0.768945	−	1.84494i	−0.768945	−	1.84494i	−0.416866	−	0.908968i	$-0.636872\pi$
$449$	−0.768945	−	1.84494i	−0.768945	−	1.84494i	−0.352079	−	0.935970i	$-0.614525\pi$
$450$	−1.32729	−	1.43648i	−1.32729	−	1.43648i
$451$		0			0
$452$	−0.660167	+	3.92268i	−0.660167	+	3.92268i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0412042	+	0.669931i	0.0412042	+	0.669931i	0.960831	+	0.277137i	$0.0893855\pi$
$457$	0.0412042	+	0.669931i	0.0412042	+	0.669931i	−0.919626	+	0.392794i	$0.871508\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.131251	−	0.991349i	$-0.458101\pi$
$461$		0			0		−0.131251	+	0.991349i	$0.541899\pi$
$462$		0			0
$463$	1.78326	+	0.688722i	1.78326	+	0.688722i	0.997537	+	0.0701455i	$0.0223464\pi$
$463$	1.78326	+	0.688722i	1.78326	+	0.688722i	0.785724	+	0.618577i	$0.212291\pi$
$464$	0.120182	−	0.644757i	0.120182	−	0.644757i
$465$		0			0
$466$	−1.46267	+	0.564906i	−1.46267	+	0.564906i
$467$		0			0		−0.352079	−	0.935970i	$-0.614525\pi$
$467$		0			0		0.352079	+	0.935970i	$0.385475\pi$
$468$		0			0
$469$	1.08176	−	1.30203i	1.08176	−	1.30203i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.82387	−	0.323431i	−1.82387	−	0.323431i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.891068	+	1.24013i	0.891068	+	1.24013i
$478$	2.54858	−	2.96025i	2.54858	−	2.96025i
$479$		0			0		−0.268694	−	0.963225i	$-0.586592\pi$
$479$		0			0		0.268694	+	0.963225i	$0.413408\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.789651	−	1.38638i	0.789651	−	1.38638i
$485$		0			0
$486$		0			0
$487$	0.917603	+	0.623367i	0.917603	+	0.623367i	0.926378	−	0.376595i	$-0.122905\pi$
$487$	0.917603	+	0.623367i	0.917603	+	0.623367i	−0.00877529	+	0.999961i	$0.502793\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.197868	+	0.221834i	−0.197868	+	0.221834i	−0.836914	−	0.547335i	$-0.815642\pi$
$491$	−0.197868	+	0.221834i	−0.197868	+	0.221834i	0.639045	+	0.769169i	$0.279330\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.01174	+	0.636604i	−1.01174	+	0.636604i
$498$		0			0
$499$	−0.564059	+	1.77838i	−0.564059	+	1.77838i	0.0613892	+	0.998114i	$0.480447\pi$
$499$	−0.564059	+	1.77838i	−0.564059	+	1.77838i	−0.625448	+	0.780266i	$0.715084\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.234725	−	0.972062i	$-0.575419\pi$
$503$		0			0		0.234725	+	0.972062i	$0.424581\pi$
$504$	−2.91713	−	2.05747i	−2.91713	−	2.05747i
$505$		0			0
$506$	3.47871	−	3.38832i	3.47871	−	3.38832i
$507$		0			0
$508$	−4.81367	+	2.05603i	−4.81367	+	2.05603i
$509$		0			0		0.525115	−	0.851031i	$-0.324022\pi$
$509$		0			0		−0.525115	+	0.851031i	$0.675978\pi$
$510$		0			0
$511$		0			0
$512$	−3.44330	+	2.25189i	−3.44330	+	2.25189i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	2.24988	−	2.80679i	2.24988	−	2.80679i
$519$		0			0
$520$		0			0
$521$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$521$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$522$	0.245797	−	0.186616i	0.245797	−	0.186616i
$523$		0			0		0.464125	−	0.885770i	$-0.346369\pi$
$523$		0			0		−0.464125	+	0.885770i	$0.653631\pi$
$524$		0			0
$525$		0			0
$526$	0.0661801	+	0.577601i	0.0661801	+	0.577601i
$527$		0			0
$528$		0			0
$529$	2.59203	−	1.38729i	2.59203	−	1.38729i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.41838	−	5.87391i	1.41838	−	5.87391i
$537$		0			0
$538$		0			0
$539$	−0.693819	+	1.04084i	−0.693819	+	1.04084i
$540$		0			0
$541$	0.217884	−	0.902317i	0.217884	−	0.902317i	−0.752081	−	0.659071i	$-0.770950\pi$
$541$	0.217884	−	0.902317i	0.217884	−	0.902317i	0.969965	−	0.243246i	$-0.0782123\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.325458	+	0.548779i	0.325458	+	0.548779i	0.977904	−	0.209056i	$-0.0670391\pi$
$547$	0.325458	+	0.548779i	0.325458	+	0.548779i	−0.652446	+	0.757835i	$0.726257\pi$
$548$	−4.85261	+	2.59720i	−4.85261	+	2.59720i
$549$		0			0
$550$	−0.821046	+	2.30463i	−0.821046	+	2.30463i
$551$		0			0
$552$		0			0
$553$	−0.469378	+	0.00823880i	−0.469378	+	0.00823880i
$554$	0.174975	−	0.333935i	0.174975	−	0.333935i
$555$		0			0
$556$		0			0
$557$	−0.262462	−	0.00460689i	−0.262462	−	0.00460689i	−0.113833	−	0.993500i	$-0.536313\pi$
$557$	−0.262462	−	0.00460689i	−0.262462	−	0.00460689i	−0.148629	+	0.988893i	$0.547486\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0805875	+	0.226204i	0.0805875	+	0.226204i
$563$		0			0		0.897680	−	0.440648i	$-0.145251\pi$
$563$		0			0		−0.897680	+	0.440648i	$0.854749\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.217629	−	0.976031i	−0.217629	−	0.976031i
$568$	−2.24071	+	3.63142i	−2.24071	+	3.63142i
$569$	1.77588	−	0.758522i	1.77588	−	0.758522i	0.785724	−	0.618577i	$-0.212291\pi$
$569$	1.77588	−	0.758522i	1.77588	−	0.758522i	0.990159	−	0.139946i	$-0.0446927\pi$
$570$		0			0
$571$	0.990609	−	0.964867i	0.990609	−	0.964867i	−0.00877529	−	0.999961i	$-0.502793\pi$
$571$	0.990609	−	0.964867i	0.990609	−	0.964867i	0.999384	+	0.0350944i	$0.0111732\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.15824	+	1.61196i	−1.15824	+	1.61196i
$576$	−4.70187	−	0.748932i	−4.70187	−	0.748932i
$577$		0			0		−0.611658	−	0.791122i	$-0.709497\pi$
$577$		0			0		0.611658	+	0.791122i	$0.290503\pi$
$578$	0.591305	−	1.86428i	0.591305	−	1.86428i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.856740	−	1.70729i	0.856740	−	1.70729i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.400849	−	0.916144i	$-0.631285\pi$
$587$		0			0		0.400849	+	0.916144i	$0.368715\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.66373	−	7.46157i	1.66373	−	7.46157i
$593$		0			0		0.494925	−	0.868936i	$-0.335196\pi$
$593$		0			0		−0.494925	+	0.868936i	$0.664804\pi$
$594$		0			0
$595$		0			0
$596$	−0.0494614	−	5.63623i	−0.0494614	−	5.63623i
$597$		0			0
$598$		0			0
$599$	−0.761427	+	0.884420i	−0.761427	+	0.884420i	−0.996152	−	0.0876414i	$-0.972067\pi$
$599$	−0.761427	+	0.884420i	−0.761427	+	0.884420i	0.234725	+	0.972062i	$0.424581\pi$
$600$		0			0
$601$		0			0		−0.448509	−	0.893778i	$-0.648045\pi$
$601$		0			0		0.448509	+	0.893778i	$0.351955\pi$
$602$	2.83216	−	0.605458i	2.83216	−	0.605458i
$603$	1.40023	−	0.951238i	1.40023	−	0.951238i
$604$	−3.00415	−	0.532734i	−3.00415	−	0.532734i
$605$		0			0
$606$		0			0
$607$		0			0		0.955819	−	0.293956i	$-0.0949721\pi$
$607$		0			0		−0.955819	+	0.293956i	$0.905028\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.275626	−	1.47869i	0.275626	−	1.47869i	−0.510099	−	0.860116i	$-0.670391\pi$
$613$	0.275626	−	1.47869i	0.275626	−	1.47869i	0.785724	−	0.618577i	$-0.212291\pi$
$614$		0			0
$615$		0			0
$616$	−0.586080	+	4.42670i	−0.586080	+	4.42670i
$617$	−0.154243	−	0.753800i	−0.154243	−	0.753800i	−0.981422	−	0.191862i	$-0.938547\pi$
$617$	−0.154243	−	0.753800i	−0.154243	−	0.753800i	0.827179	−	0.561938i	$-0.189944\pi$
$618$		0			0
$619$		0			0		0.569175	−	0.822216i	$-0.307263\pi$
$619$		0			0		−0.569175	+	0.822216i	$0.692737\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.165961	−	0.986132i	0.165961	−	0.986132i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.87936	+	0.651012i	−1.87936	+	0.651012i	−0.905275	+	0.424826i	$0.860335\pi$
$631$	−1.87936	+	0.651012i	−1.87936	+	0.651012i	−0.974084	+	0.226186i	$0.927374\pi$
$632$	−1.49114	+	0.764725i	−1.49114	+	0.764725i
$633$		0			0
$634$	1.12125	+	1.50406i	1.12125	+	1.50406i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.349475	−	0.164001i	−0.349475	−	0.164001i
$639$	−1.14854	+	0.331278i	−1.14854	+	0.331278i
$640$		0			0
$641$	−0.235083	+	0.698398i	−0.235083	+	0.698398i	0.763532	+	0.645770i	$0.223464\pi$
$641$	−0.235083	+	0.698398i	−0.235083	+	0.698398i	−0.998614	+	0.0526281i	$0.983240\pi$
$642$		0			0
$643$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$643$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$644$	−2.24787	+	5.13753i	−2.24787	+	5.13753i
$645$		0			0
$646$		0			0
$647$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$647$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$648$	−2.23267	−	2.78532i	−2.23267	−	2.78532i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.909023	−	3.49454i	−0.909023	−	3.49454i
$653$	−1.11320	−	0.237979i	−1.11320	−	0.237979i	−0.384709	−	0.923038i	$-0.625698\pi$
$653$	−1.11320	−	0.237979i	−1.11320	−	0.237979i	−0.728488	+	0.685059i	$0.759777\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.38200	−	0.0485303i	1.38200	−	0.0485303i	0.665645	−	0.746268i	$-0.268156\pi$
$659$	1.38200	−	0.0485303i	1.38200	−	0.0485303i	0.716353	+	0.697738i	$0.245810\pi$
$660$		0			0
$661$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$661$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$662$	−3.63994	−	0.255956i	−3.63994	−	0.255956i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.93961	−	2.07333i	2.93961	−	2.07333i
$667$	−0.235557	−	0.206426i	−0.235557	−	0.206426i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.56333	+	0.305620i	1.56333	+	0.305620i	0.897680	−	0.440648i	$-0.145251\pi$
$673$	1.56333	+	0.305620i	1.56333	+	0.305620i	0.665645	+	0.746268i	$0.268156\pi$
$674$	3.40591	+	1.67188i	3.40591	+	1.67188i
$675$		0			0
$676$	−2.82127	+	0.148684i	−2.82127	+	0.148684i
$677$		0			0		−0.996152	−	0.0876414i	$-0.972067\pi$
$677$		0			0		0.996152	+	0.0876414i	$0.0279330\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.568917	−	0.0500533i	0.568917	−	0.0500533i	0.200467	−	0.979701i	$-0.435754\pi$
$683$	0.568917	−	0.0500533i	0.568917	−	0.0500533i	0.368451	+	0.929647i	$0.379888\pi$
$684$		0			0
$685$		0			0
$686$	0.392074	−	1.91611i	0.392074	−	1.91611i
$687$		0			0
$688$	4.83605	−	3.80727i	4.83605	−	3.80727i
$689$		0			0
$690$		0			0
$691$		0			0		0.728488	−	0.685059i	$-0.240223\pi$
$691$		0			0		−0.728488	+	0.685059i	$0.759777\pi$
$692$		0			0
$693$	−0.955099	+	0.807792i	−0.955099	+	0.807792i
$694$	−0.0829225	+	1.04775i	−0.0829225	+	1.04775i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.123921	−	2.82246i	−0.123921	−	2.82246i
$701$	0.261671	−	0.545113i	0.261671	−	0.545113i	−0.728488	−	0.685059i	$-0.759777\pi$
$701$	0.261671	−	0.545113i	0.261671	−	0.545113i	0.990159	+	0.139946i	$0.0446927\pi$
$702$		0			0
$703$		0			0
$704$	1.89995	+	5.64450i	1.89995	+	5.64450i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.70463	+	1.03127i	1.70463	+	1.03127i	0.897680	+	0.440648i	$0.145251\pi$
$709$	1.70463	+	1.03127i	1.70463	+	1.03127i	0.806949	+	0.590621i	$0.201117\pi$
$710$		0			0
$711$	−0.453276	−	0.122166i	−0.453276	−	0.122166i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	3.08587	+	4.62932i	3.08587	+	4.62932i
$717$		0			0
$718$	1.61780	+	1.09904i	1.61780	+	1.09904i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−0.752417	+	1.80528i	−0.752417	+	1.80528i
$723$		0			0
$724$		0			0
$725$	0.152356	+	0.0410627i	0.152356	+	0.0410627i
$726$		0			0
$727$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$727$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$728$		0			0
$729$	0.0613892	−	0.998114i	0.0613892	−	0.998114i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.0788965	−	0.996883i	$-0.525140\pi$
$733$		0			0		0.0788965	+	0.996883i	$0.474860\pi$
$734$		0			0
$735$		0			0
$736$	0.396976	+	9.04167i	0.396976	+	9.04167i
$737$	−1.86691	−	0.999204i	−1.86691	−	0.999204i
$738$		0			0
$739$	0.907780	−	1.53068i	0.907780	−	1.53068i	0.0613892	−	0.998114i	$-0.480447\pi$
$739$	0.907780	−	1.53068i	0.907780	−	1.53068i	0.846391	−	0.532563i	$-0.178771\pi$
$740$		0			0
$741$		0			0
$742$	−0.235636	+	2.97733i	−0.235636	+	2.97733i
$743$	−0.996326	+	0.842660i	−0.996326	+	0.842660i	−0.987551	−	0.157301i	$-0.949721\pi$
$743$	−0.996326	+	0.842660i	−0.996326	+	0.842660i	−0.00877529	+	0.999961i	$0.502793\pi$
$744$		0			0
$745$		0			0
$746$	−1.36179	+	1.76135i	−1.36179	+	1.76135i
$747$		0			0
$748$		0			0
$749$	1.56274	−	0.165175i	1.56274	−	0.165175i
$750$		0			0
$751$	0.665369	+	0.230484i	0.665369	+	0.230484i	0.639045	−	0.769169i	$-0.279330\pi$
$751$	0.665369	+	0.230484i	0.665369	+	0.230484i	0.0263232	+	0.999653i	$0.491620\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.521357	+	0.473313i	−0.521357	+	0.473313i	−0.889808	−	0.456335i	$-0.849162\pi$
$757$	−0.521357	+	0.473313i	−0.521357	+	0.473313i	0.368451	+	0.929647i	$0.379888\pi$
$758$	−3.14273	+	1.90129i	−3.14273	+	1.90129i
$759$		0			0
$760$		0			0
$761$		0			0		0.113833	−	0.993500i	$-0.463687\pi$
$761$		0			0		−0.113833	+	0.993500i	$0.536313\pi$
$762$		0			0
$763$	1.00124	+	0.195737i	1.00124	+	0.195737i
$764$	3.97649	+	3.61004i	3.97649	+	3.61004i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.752081	−	0.659071i	$-0.770950\pi$
$769$		0			0		0.752081	+	0.659071i	$0.229050\pi$
$770$		0			0
$771$		0			0
$772$	4.38366	+	1.01790i	4.38366	+	1.01790i
$773$		0			0		−0.285558	−	0.958362i	$-0.592179\pi$
$773$		0			0		0.285558	+	0.958362i	$0.407821\pi$
$774$	2.88902	+	0.203152i	2.88902	+	0.203152i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.43036	−	0.467531i	−1.43036	−	0.467531i
$779$		0			0
$780$		0			0
$781$	1.03387	+	1.08026i	1.03387	+	1.08026i
$782$		0			0
$783$		0			0
$784$	−1.04639	−	4.02260i	−1.04639	−	4.02260i
$785$		0			0
$786$		0			0
$787$		0			0		0.0263232	−	0.999653i	$-0.491620\pi$
$787$		0			0		−0.0263232	+	0.999653i	$0.508380\pi$
$788$	0.647579	+	0.807875i	0.647579	+	0.807875i
$789$		0			0
$790$		0			0
$791$	−1.40713	−	0.0494127i	−1.40713	−	0.0494127i
$792$	−1.78992	+	4.09089i	−1.78992	+	4.09089i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.960831	−	0.277137i	$-0.0893855\pi$
$797$		0			0		−0.960831	+	0.277137i	$0.910615\pi$
$798$		0			0
$799$		0			0
$800$	−2.18676	−	4.00095i	−2.18676	−	4.00095i
$801$		0			0
$802$	−2.09868	−	2.81519i	−2.09868	−	2.81519i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.248711	+	0.269172i	0.248711	+	0.269172i	0.846391	−	0.532563i	$-0.178771\pi$
$809$	0.248711	+	0.269172i	0.248711	+	0.269172i	−0.597680	+	0.801735i	$0.703911\pi$
$810$		0			0
$811$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$811$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$812$	0.445176	+	0.0234613i	0.445176	+	0.0234613i
$813$		0			0
$814$	−4.00392	−	2.05339i	−4.00392	−	2.05339i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.0174534	+	1.98884i	−0.0174534	+	1.98884i	0.0963795	+	0.995345i	$0.469274\pi$
$821$	−0.0174534	+	1.98884i	−0.0174534	+	1.98884i	−0.113833	+	0.993500i	$0.536313\pi$
$822$		0			0
$823$	0.320031	−	1.71692i	0.320031	−	1.71692i	−0.319015	−	0.947750i	$-0.603352\pi$
$823$	0.320031	−	1.71692i	0.320031	−	1.71692i	0.639045	−	0.769169i	$-0.279330\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.99477	+	0.140269i	−1.99477	+	0.140269i	−0.996152	+	0.0876414i	$0.972067\pi$
$827$	−1.99477	+	0.140269i	−1.99477	+	0.140269i	−0.998614	+	0.0526281i	$0.983240\pi$
$828$	−3.58362	+	4.31333i	−3.58362	+	4.31333i
$829$		0			0		0.955819	−	0.293956i	$-0.0949721\pi$
$829$		0			0		−0.955819	+	0.293956i	$0.905028\pi$
$830$		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		−0.992463	−	0.122547i	$-0.960894\pi$
$839$		0			0		0.992463	+	0.122547i	$0.0391061\pi$
$840$		0			0
$841$	0.343313	−	0.912666i	0.343313	−	0.912666i
$842$	0.955705	−	3.20745i	0.955705	−	3.20745i
$843$		0			0
$844$	−0.204080	+	0.915265i	−0.204080	+	0.915265i
$845$		0			0
$846$		0			0
$847$	0.523164	+	0.212679i	0.523164	+	0.212679i
$848$	2.33863	+	5.90065i	2.33863	+	5.90065i
$849$		0			0
$850$		0			0
$851$	−2.65955	−	2.50100i	−2.65955	−	2.50100i
$852$		0			0
$853$		0			0		0.448509	−	0.893778i	$-0.351955\pi$
$853$		0			0		−0.448509	+	0.893778i	$0.648045\pi$
$854$		0			0
$855$		0			0
$856$	4.74792	−	2.98747i	4.74792	−	2.98747i
$857$		0			0		−0.994461	−	0.105110i	$-0.966480\pi$
$857$		0			0		0.994461	+	0.105110i	$0.0335196\pi$
$858$		0			0
$859$		0			0		−0.611658	−	0.791122i	$-0.709497\pi$
$859$		0			0		0.611658	+	0.791122i	$0.290503\pi$
$860$		0			0
$861$		0			0
$862$	−0.768416	−	3.18222i	−0.768416	−	3.18222i
$863$	1.47956	+	1.04354i	1.47956	+	1.04354i	0.984638	+	0.174608i	$0.0558659\pi$
$863$	1.47956	+	1.04354i	1.47956	+	1.04354i	0.494925	+	0.868936i	$0.335196\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.127799	+	0.573158i	0.127799	+	0.573158i
$870$		0			0
$871$		0			0
$872$	3.51633	−	0.947712i	3.51633	−	0.947712i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.24781	+	1.55669i	−1.24781	+	1.55669i	−0.569175	+	0.822216i	$0.692737\pi$
$877$	−1.24781	+	1.55669i	−1.24781	+	1.55669i	−0.678640	+	0.734471i	$0.737430\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.796459	−	0.604692i	$-0.206704\pi$
$881$		0			0		−0.796459	+	0.604692i	$0.793296\pi$
$882$	0.907740	−	1.73239i	0.907740	−	1.73239i
$883$	0.227631	−	0.00399551i	0.227631	−	0.00399551i	0.0963795	−	0.995345i	$-0.469274\pi$
$883$	0.227631	−	0.00399551i	0.227631	−	0.00399551i	0.131251	+	0.991349i	$0.458101\pi$
$884$		0			0
$885$		0			0
$886$	−0.0115196	+	0.0323348i	−0.0115196	+	0.0323348i
$887$		0			0		−0.432754	−	0.901512i	$-0.642458\pi$
$887$		0			0		0.432754	+	0.901512i	$0.357542\pi$
$888$		0			0
$889$	−0.945088	−	1.59359i	−0.945088	−	1.59359i
$890$		0			0
$891$	−1.14156	+	0.511458i	−1.14156	+	0.511458i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−3.10063	−	3.60147i	−3.10063	−	3.60147i
$897$		0			0
$898$	2.16827	−	3.25277i	2.16827	−	3.25277i
$899$		0			0
$900$	0.663141	−	2.74625i	0.663141	−	2.74625i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−4.58680	+	2.05505i	−4.58680	+	2.05505i
$905$		0			0
$906$		0			0
$907$	0.649699	−	0.347729i	0.649699	−	0.347729i	−0.113833	−	0.993500i	$-0.536313\pi$
$907$	0.649699	−	0.347729i	0.649699	−	0.347729i	0.763532	+	0.645770i	$0.223464\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.274559	+	1.63142i	0.274559	+	1.63142i	0.691425	+	0.722448i	$0.256983\pi$
$911$	0.274559	+	1.63142i	0.274559	+	1.63142i	−0.416866	+	0.908968i	$0.636872\pi$
$912$		0			0
$913$		0			0
$914$	−1.04554	+	0.793799i	−1.04554	+	0.793799i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.24790	−	1.05543i	−1.24790	−	1.05543i	−0.996152	−	0.0876414i	$-0.972067\pi$
$919$	−1.24790	−	1.05543i	−1.24790	−	1.05543i	−0.251749	−	0.967793i	$-0.581006\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.75799	+	0.540660i	1.75799	+	0.540660i
$926$	0.813672	+	3.64918i	0.813672	+	3.64918i
$927$		0			0
$928$	0.661640	−	0.282602i	0.661640	−	0.282602i
$929$		0			0		0.984638	−	0.174608i	$-0.0558659\pi$
$929$		0			0		−0.984638	+	0.174608i	$0.944134\pi$
$930$		0			0
$931$		0			0
$932$	−1.85089	−	1.30544i	−1.85089	−	1.30544i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$937$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$938$	3.29241	+	0.347994i	3.29241	+	0.347994i
$939$		0			0
$940$		0			0
$941$		0			0		0.251749	−	0.967793i	$-0.418994\pi$
$941$		0			0		−0.251749	+	0.967793i	$0.581006\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.45219	−	3.31899i	−1.45219	−	3.31899i
$947$	0.147724	+	0.372726i	0.147724	+	0.372726i	0.984638	−	0.174608i	$-0.0558659\pi$
$947$	0.147724	+	0.372726i	0.147724	+	0.372726i	−0.836914	+	0.547335i	$0.815642\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.114490	+	0.384239i	−0.114490	+	0.384239i	−0.996152	−	0.0876414i	$-0.972067\pi$
$953$	−0.114490	+	0.384239i	−0.114490	+	0.384239i	0.881663	+	0.471880i	$0.156425\pi$
$954$	−1.05153	+	2.79541i	−1.05153	+	2.79541i
$955$		0			0
$956$	5.60000	+	0.691474i	5.60000	+	0.691474i
$957$		0			0
$958$		0			0
$959$	−1.13679	−	1.58211i	−1.13679	−	1.58211i
$960$		0			0
$961$	0.977904	−	0.209056i	0.977904	−	0.209056i
$962$		0			0
$963$	1.54731	+	0.274388i	1.54731	+	0.274388i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.593194	−	0.713982i	0.593194	−	0.713982i	−0.384709	−	0.923038i	$-0.625698\pi$
$967$	0.593194	−	0.713982i	0.593194	−	0.713982i	0.977904	+	0.209056i	$0.0670391\pi$
$968$	2.01099	−	0.141411i	2.01099	−	0.141411i
$969$		0			0
$970$		0			0
$971$		0			0		−0.183242	−	0.983068i	$-0.558659\pi$
$971$		0			0		0.183242	+	0.983068i	$0.441341\pi$
$972$		0			0
$973$		0			0
$974$	−0.0190389	+	2.16952i	−0.0190389	+	2.16952i
$975$		0			0
$976$		0			0
$977$	0.317519	+	1.00108i	0.317519	+	1.00108i	0.969965	+	0.243246i	$0.0782123\pi$
$977$	0.317519	+	1.00108i	0.317519	+	1.00108i	−0.652446	+	0.757835i	$0.726257\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.907780	+	0.465551i	0.907780	+	0.465551i
$982$	−0.575658	−	0.0813615i	−0.575658	−	0.0813615i
$983$		0			0		−0.998614	−	0.0526281i	$-0.983240\pi$
$983$		0			0		0.998614	+	0.0526281i	$0.0167598\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.385783	−	2.91384i	−0.385783	−	2.91384i
$990$		0			0
$991$	0.741861	−	0.380461i	0.741861	−	0.380461i	−0.0438629	−	0.999038i	$-0.513966\pi$
$991$	0.741861	−	0.380461i	0.741861	−	0.380461i	0.785724	+	0.618577i	$0.212291\pi$
$992$		0			0
$993$		0			0
$994$	−2.13354	−	0.955902i	−2.13354	−	0.955902i
$995$		0			0
$996$		0			0
$997$		0			0		−0.905275	−	0.424826i	$-0.860335\pi$
$997$		0			0		0.905275	+	0.424826i	$0.139665\pi$
$998$	−3.50600	+	1.01125i	−3.50600	+	1.01125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.20.1	✓	178
7.6	odd	2	CM	2513.1.l.a.20.1	✓	178
359.18	even	179	inner	2513.1.l.a.377.1	yes	178
2513.377	odd	358	inner	2513.1.l.a.377.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.20.1	✓	178	1.1	even	1	trivial
2513.1.l.a.20.1	✓	178	7.6	odd	2	CM
2513.1.l.a.377.1	yes	178	359.18	even	179	inner
2513.1.l.a.377.1	yes	178	2513.377	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)

\(f(q)\)	\(=\)	\(q+(1.08480 + 1.62739i) q^{2} +(-1.08687 + 2.60775i) q^{4} +(-0.965546 - 0.260231i) q^{7} +(-3.50339 + 0.684890i) q^{8} +(-0.855607 - 0.517627i) q^{9} +O(q^{10})\)	\(q+(1.08480 + 1.62739i) q^{2} +(-1.08687 + 2.60775i) q^{4} +(-0.965546 - 0.260231i) q^{7} +(-3.50339 + 0.684890i) q^{8} +(-0.855607 - 0.517627i) q^{9} +(-0.0767915 + 1.24854i) q^{11} +(-0.623931 - 1.85362i) q^{14} +(-2.92615 - 2.95194i) q^{16} +(-0.0857874 - 1.95392i) q^{18} +(-2.11515 + 1.22945i) q^{22} +(-1.92531 + 0.482826i) q^{23} +(0.763532 - 0.645770i) q^{25} +(1.72805 - 2.23506i) q^{28} +(0.0898119 + 0.129740i) q^{29} +(0.914038 - 4.46700i) q^{32} +(2.27978 - 1.66861i) q^{36} +(0.993140 + 1.54807i) q^{37} +(-0.168563 + 1.47117i) q^{43} +(-3.17241 - 1.55726i) q^{44} +(-2.87432 - 2.60945i) q^{46} +(0.864559 + 0.502531i) q^{49} +(1.87920 + 0.542026i) q^{50} +(-1.40433 - 0.599822i) q^{53} +(3.56091 + 0.250399i) q^{56} +(-0.113709 + 0.286901i) q^{58} +(0.691425 + 0.722448i) q^{63} +(4.41061 - 1.79302i) q^{64} +(-0.705663 + 1.53868i) q^{67} +(0.811218 - 0.877958i) q^{71} +(3.35204 + 1.22745i) q^{72} +(-1.44194 + 3.29557i) q^{74} +(0.399054 - 1.18554i) q^{77} +(0.451062 - 0.130102i) q^{79} +(0.464125 + 0.885770i) q^{81} +(-2.57702 + 1.32161i) q^{86} +(-0.586080 - 4.42670i) q^{88} +(0.833478 - 5.54549i) q^{92} +(0.120065 + 1.95212i) q^{98} +(0.711979 - 1.02851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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

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