LMFDB - Embedded newform 2513.1.l.a.188.1

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			188.1
Root			$0.796459 - 0.604692i$ of defining polynomial
Character	$\chi$	$=$	2513.188
Dual form			2513.1.l.a.1056.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54735 - 0.0815469i) q^{2} +(1.39317 - 0.147252i) q^{4} +(0.997537 - 0.0701455i) q^{7} +(0.613510 - 0.0977224i) q^{8} +(0.554658 - 0.832079i) q^{9} +O(q^{10})$	\(q+(1.54735 - 0.0815469i) q^{2} +(1.39317 - 0.147252i) q^{4} +(0.997537 - 0.0701455i) q^{7} +(0.613510 - 0.0977224i) q^{8} +(0.554658 - 0.832079i) q^{9} +(-1.03072 - 0.201499i) q^{11} +(1.53782 - 0.189886i) q^{14} +(-0.428634 + 0.0916333i) q^{16} +(0.790395 - 1.33274i) q^{18} +(-1.61131 - 0.227737i) q^{22} +(1.32723 - 1.29274i) q^{23} +(-0.652446 + 0.757835i) q^{25} +(1.37941 - 0.244615i) q^{28} +(1.12141 + 1.13129i) q^{29} +(-1.25561 + 0.338410i) q^{32} +(0.650209 - 1.24090i) q^{36} +(-1.08147 + 1.34917i) q^{37} +(-0.938457 - 0.980564i) q^{43} +(-1.46564 - 0.128947i) q^{44} +(1.94826 - 2.10855i) q^{46} +(0.990159 - 0.139946i) q^{49} +(-0.947761 + 1.22584i) q^{50} +(-1.12816 + 0.655749i) q^{53} +(0.605144 - 0.140517i) q^{56} +(1.82746 + 1.65906i) q^{58} +(0.494925 - 0.868936i) q^{63} +(-1.49864 + 0.489849i) q^{64} +(0.109576 + 0.491429i) q^{67} +(-0.501315 + 1.48934i) q^{71} +(0.258975 - 0.564691i) q^{72} +(-1.56339 + 2.17583i) q^{74} +(-1.04231 - 0.128702i) q^{77} +(0.450732 + 0.582979i) q^{79} +(-0.384709 - 0.923038i) q^{81} +(-1.53208 - 1.44074i) q^{86} +(-0.652047 - 0.0228973i) q^{88} +(1.65870 - 1.99645i) q^{92} +(1.52071 - 0.297289i) q^{98} +(-0.739359 + 0.745876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2513\mathbb{Z}\right)^\times$.

$n$	$360$	$1443$
$\chi(n)$	$-1$	$e\left(\frac{175}{179}\right)$

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 $

$2$	1.54735	−	0.0815469i	1.54735	−	0.0815469i	0.740398	−	0.672168i	$-0.234637\pi$
$2$	1.54735	−	0.0815469i	1.54735	−	0.0815469i	0.806949	+	0.590621i	$0.201117\pi$
$3$		0			0		0.881663	−	0.471880i	$-0.156425\pi$
$3$		0			0		−0.881663	+	0.471880i	$0.843575\pi$
$4$	1.39317	−	0.147252i	1.39317	−	0.147252i
$5$		0			0		−0.416866	−	0.908968i	$-0.636872\pi$
$5$		0			0		0.416866	+	0.908968i	$0.363128\pi$
$6$		0			0
$7$	0.997537	−	0.0701455i	0.997537	−	0.0701455i
$7$	0.997537	−	0.0701455i	0.997537	−	0.0701455i
$8$	0.613510	−	0.0977224i	0.613510	−	0.0977224i
$9$	0.554658	−	0.832079i	0.554658	−	0.832079i
$10$		0			0
$11$	−1.03072	−	0.201499i	−1.03072	−	0.201499i	−0.352079	−	0.935970i	$-0.614525\pi$
$11$	−1.03072	−	0.201499i	−1.03072	−	0.201499i	−0.678640	+	0.734471i	$0.737430\pi$
$12$		0			0
$13$		0			0		−0.251749	−	0.967793i	$-0.581006\pi$
$13$		0			0		0.251749	+	0.967793i	$0.418994\pi$
$14$	1.53782	−	0.189886i	1.53782	−	0.189886i
$15$		0			0
$16$	−0.428634	+	0.0916333i	−0.428634	+	0.0916333i
$17$		0			0		−0.873245	−	0.487281i	$-0.837989\pi$
$17$		0			0		0.873245	+	0.487281i	$0.162011\pi$
$18$	0.790395	−	1.33274i	0.790395	−	1.33274i
$19$		0			0		−0.0263232	−	0.999653i	$-0.508380\pi$
$19$		0			0		0.0263232	+	0.999653i	$0.491620\pi$
$20$		0			0
$21$		0			0
$22$	−1.61131	−	0.227737i	−1.61131	−	0.227737i
$23$	1.32723	−	1.29274i	1.32723	−	1.29274i	0.400849	−	0.916144i	$-0.368715\pi$
$23$	1.32723	−	1.29274i	1.32723	−	1.29274i	0.926378	−	0.376595i	$-0.122905\pi$
$24$		0			0
$25$	−0.652446	+	0.757835i	−0.652446	+	0.757835i
$26$		0			0
$27$		0			0
$28$	1.37941	−	0.244615i	1.37941	−	0.244615i
$29$	1.12141	+	1.13129i	1.12141	+	1.13129i	0.990159	+	0.139946i	$0.0446927\pi$
$29$	1.12141	+	1.13129i	1.12141	+	1.13129i	0.131251	+	0.991349i	$0.458101\pi$
$30$		0			0
$31$		0			0		0.335599	−	0.942005i	$-0.391061\pi$
$31$		0			0		−0.335599	+	0.942005i	$0.608939\pi$
$32$	−1.25561	+	0.338410i	−1.25561	+	0.338410i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.650209	−	1.24090i	0.650209	−	1.24090i
$37$	−1.08147	+	1.34917i	−1.08147	+	1.34917i	−0.148629	+	0.988893i	$0.547486\pi$
$37$	−1.08147	+	1.34917i	−1.08147	+	1.34917i	−0.932845	+	0.360279i	$0.882682\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$41$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$42$		0			0
$43$	−0.938457	−	0.980564i	−0.938457	−	0.980564i	0.0613892	−	0.998114i	$-0.480447\pi$
$43$	−0.938457	−	0.980564i	−0.938457	−	0.980564i	−0.999846	+	0.0175499i	$0.994413\pi$
$44$	−1.46564	−	0.128947i	−1.46564	−	0.128947i
$45$		0			0
$46$	1.94826	−	2.10855i	1.94826	−	2.10855i
$47$		0			0		−0.785724	−	0.618577i	$-0.787709\pi$
$47$		0			0		0.785724	+	0.618577i	$0.212291\pi$
$48$		0			0
$49$	0.990159	−	0.139946i	0.990159	−	0.139946i
$50$	−0.947761	+	1.22584i	−0.947761	+	1.22584i
$51$		0			0
$52$		0			0
$53$	−1.12816	+	0.655749i	−1.12816	+	0.655749i	−0.944914	−	0.327319i	$-0.893855\pi$
$53$	−1.12816	+	0.655749i	−1.12816	+	0.655749i	−0.183242	+	0.983068i	$0.558659\pi$
$54$		0			0
$55$		0			0
$56$	0.605144	−	0.140517i	0.605144	−	0.140517i
$57$		0			0
$58$	1.82746	+	1.65906i	1.82746	+	1.65906i
$59$		0			0		0.113833	−	0.993500i	$-0.463687\pi$
$59$		0			0		−0.113833	+	0.993500i	$0.536313\pi$
$60$		0			0
$61$		0			0		−0.889808	−	0.456335i	$-0.849162\pi$
$61$		0			0		0.889808	+	0.456335i	$0.150838\pi$
$62$		0			0
$63$	0.494925	−	0.868936i	0.494925	−	0.868936i
$64$	−1.49864	+	0.489849i	−1.49864	+	0.489849i
$65$		0			0
$66$		0			0
$67$	0.109576	+	0.491429i	0.109576	+	0.491429i	0.999384	+	0.0350944i	$0.0111732\pi$
$67$	0.109576	+	0.491429i	0.109576	+	0.491429i	−0.889808	+	0.456335i	$0.849162\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.501315	+	1.48934i	−0.501315	+	1.48934i	0.335599	+	0.942005i	$0.391061\pi$
$71$	−0.501315	+	1.48934i	−0.501315	+	1.48934i	−0.836914	+	0.547335i	$0.815642\pi$
$72$	0.258975	−	0.564691i	0.258975	−	0.564691i
$73$		0			0		−0.113833	−	0.993500i	$-0.536313\pi$
$73$		0			0		0.113833	+	0.993500i	$0.463687\pi$
$74$	−1.56339	+	2.17583i	−1.56339	+	2.17583i
$75$		0			0
$76$		0			0
$77$	−1.04231	−	0.128702i	−1.04231	−	0.128702i
$78$		0			0
$79$	0.450732	+	0.582979i	0.450732	+	0.582979i	0.960831	−	0.277137i	$-0.0893855\pi$
$79$	0.450732	+	0.582979i	0.450732	+	0.582979i	−0.510099	+	0.860116i	$0.670391\pi$
$80$		0			0
$81$	−0.384709	−	0.923038i	−0.384709	−	0.923038i
$82$		0			0
$83$		0			0		0.200467	−	0.979701i	$-0.435754\pi$
$83$		0			0		−0.200467	+	0.979701i	$0.564246\pi$
$84$		0			0
$85$		0			0
$86$	−1.53208	−	1.44074i	−1.53208	−	1.44074i
$87$		0			0
$88$	−0.652047	−	0.0228973i	−0.652047	−	0.0228973i
$89$		0			0		0.926378	−	0.376595i	$-0.122905\pi$
$89$		0			0		−0.926378	+	0.376595i	$0.877095\pi$
$90$		0			0
$91$		0			0
$92$	1.65870	−	1.99645i	1.65870	−	1.99645i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.625448	−	0.780266i	$-0.715084\pi$
$97$		0			0		0.625448	+	0.780266i	$0.284916\pi$
$98$	1.52071	−	0.297289i	1.52071	−	0.297289i
$99$	−0.739359	+	0.745876i	−0.739359	+	0.745876i
$100$	−0.797377	+	1.15187i	−0.797377	+	1.15187i
$101$		0			0		−0.965546	−	0.260231i	$-0.916201\pi$
$101$		0			0		0.965546	+	0.260231i	$0.0837989\pi$
$102$		0			0
$103$		0			0		0.912591	−	0.408873i	$-0.134078\pi$
$103$		0			0		−0.912591	+	0.408873i	$0.865922\pi$
$104$		0			0
$105$		0			0
$106$	−1.69217	+	1.10667i	−1.69217	+	1.10667i
$107$	0.663148	−	1.51563i	0.663148	−	1.51563i	−0.183242	−	0.983068i	$-0.558659\pi$
$107$	0.663148	−	1.51563i	0.663148	−	1.51563i	0.846391	−	0.532563i	$-0.178771\pi$
$108$		0			0
$109$	−1.64891	−	0.382883i	−1.64891	−	0.382883i	−0.703997	−	0.710203i	$-0.748603\pi$
$109$	−1.64891	−	0.382883i	−1.64891	−	0.382883i	−0.944914	+	0.327319i	$0.893855\pi$
$110$		0			0
$111$		0			0
$112$	−0.421151	+	0.121474i	−0.421151	+	0.121474i
$113$	−0.0857874	−	1.95392i	−0.0857874	−	1.95392i	−0.251749	−	0.967793i	$-0.581006\pi$
$113$	−0.0857874	−	1.95392i	−0.0857874	−	1.95392i	0.165961	−	0.986132i	$-0.446927\pi$
$114$		0			0
$115$		0			0
$116$	1.72890	+	1.41096i	1.72890	+	1.41096i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.0954008	+	0.0387827i	0.0954008	+	0.0387827i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.694962	−	1.38490i	0.694962	−	1.38490i
$127$	1.53403	+	1.12279i	1.53403	+	1.12279i	0.950513	+	0.310686i	$0.100559\pi$
$127$	1.53403	+	1.12279i	1.53403	+	1.12279i	0.583517	+	0.812101i	$0.301676\pi$
$128$	−1.06589	+	0.411663i	−1.06589	+	0.411663i
$129$		0			0
$130$		0			0
$131$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$131$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$132$		0			0
$133$		0			0
$134$	0.209626	+	0.751476i	0.209626	+	0.751476i
$135$		0			0
$136$		0			0
$137$	−0.0115141	+	0.0869669i	−0.0115141	+	0.0869669i	−0.996152	−	0.0876414i	$-0.972067\pi$
$137$	−0.0115141	+	0.0869669i	−0.0115141	+	0.0869669i	0.984638	+	0.174608i	$0.0558659\pi$
$138$		0			0
$139$		0			0		−0.335599	−	0.942005i	$-0.608939\pi$
$139$		0			0		0.335599	+	0.942005i	$0.391061\pi$
$140$		0			0
$141$		0			0
$142$	−0.654258	+	2.34541i	−0.654258	+	2.34541i
$143$		0			0
$144$	−0.161499	+	0.407482i	−0.161499	+	0.407482i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.30801	+	2.03888i	−1.30801	+	2.03888i
$149$	−1.68431	−	0.979015i	−1.68431	−	0.979015i	−0.955819	−	0.293956i	$-0.905028\pi$
$149$	−1.68431	−	0.979015i	−1.68431	−	0.979015i	−0.728488	−	0.685059i	$-0.759777\pi$
$150$		0			0
$151$	0.561038	+	1.11802i	0.561038	+	1.11802i	0.977904	+	0.209056i	$0.0670391\pi$
$151$	0.561038	+	1.11802i	0.561038	+	1.11802i	−0.416866	+	0.908968i	$0.636872\pi$
$152$		0			0
$153$		0			0
$154$	−1.62332	−	0.114150i	−1.62332	−	0.114150i
$155$		0			0
$156$		0			0
$157$		0			0		−0.977904	−	0.209056i	$-0.932961\pi$
$157$		0			0		0.977904	+	0.209056i	$0.0670391\pi$
$158$	0.744979	+	0.865316i	0.744979	+	0.865316i
$159$		0			0
$160$		0			0
$161$	1.23328	−	1.38265i	1.23328	−	1.38265i
$162$	−0.670550	−	1.39689i	−0.670550	−	1.39689i
$163$	−0.553961	+	0.138922i	−0.553961	+	0.138922i	−0.510099	−	0.860116i	$-0.670391\pi$
$163$	−0.553961	+	0.138922i	−0.553961	+	0.138922i	−0.0438629	+	0.999038i	$0.513966\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.691425	−	0.722448i	$-0.256983\pi$
$167$		0			0		−0.691425	+	0.722448i	$0.743017\pi$
$168$		0			0
$169$	−0.873245	+	0.487281i	−0.873245	+	0.487281i
$170$		0			0
$171$		0			0
$172$	−1.45182	−	1.22791i	−1.45182	−	1.22791i
$173$		0			0		−0.200467	−	0.979701i	$-0.564246\pi$
$173$		0			0		0.200467	+	0.979701i	$0.435754\pi$
$174$		0			0
$175$	−0.597680	+	0.801735i	−0.597680	+	0.801735i
$176$	0.460265	−	0.00807885i	0.460265	−	0.00807885i
$177$		0			0
$178$		0			0
$179$	1.07844	+	0.0568351i	1.07844	+	0.0568351i	0.583517	−	0.812101i	$-0.301676\pi$
$179$	1.07844	+	0.0568351i	1.07844	+	0.0568351i	0.494925	+	0.868936i	$0.335196\pi$
$180$		0			0
$181$		0			0		0.905275	−	0.424826i	$-0.139665\pi$
$181$		0			0		−0.905275	+	0.424826i	$0.860335\pi$
$182$		0			0
$183$		0			0
$184$	0.687938	−	0.922808i	0.687938	−	0.922808i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.28697	−	1.12781i	1.28697	−	1.12781i	0.302333	−	0.953202i	$-0.402235\pi$
$191$	1.28697	−	1.12781i	1.28697	−	1.12781i	0.984638	−	0.174608i	$-0.0558659\pi$
$192$		0			0
$193$	−0.288330	+	1.91838i	−0.288330	+	1.91838i	0.0963795	+	0.995345i	$0.469274\pi$
$193$	−0.288330	+	1.91838i	−0.288330	+	1.91838i	−0.384709	+	0.923038i	$0.625698\pi$
$194$		0			0
$195$		0			0
$196$	1.35886	−	0.340772i	1.35886	−	0.340772i
$197$	−0.724355	−	1.50898i	−0.724355	−	1.50898i	−0.855607	−	0.517627i	$-0.826816\pi$
$197$	−0.724355	−	1.50898i	−0.724355	−	1.50898i	0.131251	−	0.991349i	$-0.458101\pi$
$198$	−1.08322	+	1.21442i	−1.08322	+	1.21442i
$199$		0			0		−0.639045	−	0.769169i	$-0.720670\pi$
$199$		0			0		0.639045	+	0.769169i	$0.279330\pi$
$200$	−0.326224	+	0.528698i	−0.326224	+	0.528698i
$201$		0			0
$202$		0			0
$203$	1.19800	+	1.04985i	1.19800	+	1.04985i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.339503	−	1.82139i	−0.339503	−	1.82139i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.160510	−	0.250198i	0.160510	−	0.250198i	−0.752081	−	0.659071i	$-0.770950\pi$
$211$	0.160510	−	0.250198i	0.160510	−	0.250198i	0.912591	+	0.408873i	$0.134078\pi$
$212$	−1.47516	+	1.07969i	−1.47516	+	1.07969i
$213$		0			0
$214$	0.902526	−	2.39928i	0.902526	−	2.39928i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−2.58266	−	0.457990i	−2.58266	−	0.457990i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.939024	−	0.343852i	$-0.888268\pi$
$223$		0			0		0.939024	+	0.343852i	$0.111732\pi$
$224$	−1.22878	+	0.425652i	−1.22878	+	0.425652i
$225$	0.268694	+	0.963225i	0.268694	+	0.963225i
$226$	−0.292079	−	3.01640i	−0.292079	−	3.01640i
$227$		0			0		0.919626	−	0.392794i	$-0.128492\pi$
$227$		0			0		−0.919626	+	0.392794i	$0.871508\pi$
$228$		0			0
$229$		0			0		0.740398	−	0.672168i	$-0.234637\pi$
$229$		0			0		−0.740398	+	0.672168i	$0.765363\pi$
$230$		0			0
$231$		0			0
$232$	0.798549	+	0.584473i	0.798549	+	0.584473i
$233$	−0.523425	+	1.04307i	−0.523425	+	1.04307i	0.464125	+	0.885770i	$0.346369\pi$
$233$	−0.523425	+	1.04307i	−0.523425	+	1.04307i	−0.987551	+	0.157301i	$0.949721\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.44097	−	0.771232i	−1.44097	−	0.771232i	−0.448509	−	0.893778i	$-0.648045\pi$
$239$	−1.44097	−	0.771232i	−1.44097	−	0.771232i	−0.992463	+	0.122547i	$0.960894\pi$
$240$		0			0
$241$		0			0		0.0613892	−	0.998114i	$-0.480447\pi$
$241$		0			0		−0.0613892	+	0.998114i	$0.519553\pi$
$242$	0.150781	+	0.0522306i	0.150781	+	0.0522306i
$243$		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		−0.00877529	−	0.999961i	$-0.502793\pi$
$251$		0			0		0.00877529	+	0.999961i	$0.497207\pi$
$252$	0.561563	−	1.28346i	0.561563	−	1.28346i
$253$	−1.62848	+	1.06501i	−1.62848	+	1.06501i
$254$	2.46524	+	1.61224i	2.46524	+	1.61224i
$255$		0			0
$256$	−0.176878	+	0.0792478i	−0.176878	+	0.0792478i
$257$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$257$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$258$		0			0
$259$	−0.984171	+	1.42171i	−0.984171	+	1.42171i
$260$		0			0
$261$	1.56333	−	0.305620i	1.56333	−	0.305620i
$262$		0			0
$263$	−0.931074	+	0.875567i	−0.931074	+	0.875567i	−0.992463	−	0.122547i	$-0.960894\pi$
$263$	−0.931074	+	0.875567i	−0.931074	+	0.875567i	0.0613892	+	0.998114i	$0.480447\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.225022	+	0.668510i	0.225022	+	0.668510i
$269$		0			0		−0.994461	−	0.105110i	$-0.966480\pi$
$269$		0			0		0.994461	+	0.105110i	$0.0335196\pi$
$270$		0			0
$271$		0			0		−0.999384	−	0.0350944i	$-0.988827\pi$
$271$		0			0		0.999384	+	0.0350944i	$0.0111732\pi$
$272$		0			0
$273$		0			0
$274$	−0.0107245	+	0.135507i	−0.0107245	+	0.135507i
$275$	0.825191	−	0.649648i	0.825191	−	0.649648i
$276$		0			0
$277$	−0.0682855	+	0.142252i	−0.0682855	+	0.142252i	−0.932845	−	0.360279i	$-0.882682\pi$
$277$	−0.0682855	+	0.142252i	−0.0682855	+	0.142252i	0.864559	+	0.502531i	$0.167598\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.40609	−	1.36955i	−1.40609	−	1.36955i	−0.836914	−	0.547335i	$-0.815642\pi$
$281$	−1.40609	−	1.36955i	−1.40609	−	1.36955i	−0.569175	−	0.822216i	$-0.692737\pi$
$282$		0			0
$283$		0			0		−0.131251	−	0.991349i	$-0.541899\pi$
$283$		0			0		0.131251	+	0.991349i	$0.458101\pi$
$284$	−0.479110	+	2.14873i	−0.479110	+	2.14873i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.414852	+	1.23247i	−0.414852	+	1.23247i
$289$	0.525115	+	0.851031i	0.525115	+	0.851031i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.939024	−	0.343852i	$-0.111732\pi$
$293$		0			0		−0.939024	+	0.343852i	$0.888268\pi$
$294$		0			0
$295$		0			0
$296$	−0.531650	+	0.933414i	−0.531650	+	0.933414i
$297$		0			0
$298$	−2.68604	−	1.37753i	−2.68604	−	1.37753i
$299$		0			0
$300$		0			0
$301$	−1.00493	−	0.912320i	−1.00493	−	0.912320i
$302$	0.959292	+	1.68422i	0.959292	+	1.68422i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.352079	−	0.935970i	$-0.614525\pi$
$307$		0			0		0.352079	+	0.935970i	$0.385475\pi$
$308$	−1.47108	−	0.0258212i	−1.47108	−	0.0258212i
$309$		0			0
$310$		0			0
$311$		0			0		0.763532	−	0.645770i	$-0.223464\pi$
$311$		0			0		−0.763532	+	0.645770i	$0.776536\pi$
$312$		0			0
$313$		0			0		0.678640	−	0.734471i	$-0.262570\pi$
$313$		0			0		−0.678640	+	0.734471i	$0.737430\pi$
$314$		0			0
$315$		0			0
$316$	0.713793	+	0.745820i	0.713793	+	0.745820i
$317$	−0.707284	+	0.498852i	−0.707284	+	0.498852i	−0.873245	−	0.487281i	$-0.837989\pi$
$317$	−0.707284	+	0.498852i	−0.707284	+	0.498852i	0.165961	+	0.986132i	$0.446927\pi$
$318$		0			0
$319$	−0.927904	−	1.39201i	−0.927904	−	1.39201i
$320$		0			0
$321$		0			0
$322$	1.79556	−	2.24001i	1.79556	−	2.24001i
$323$		0			0
$324$	−0.671886	−	1.22930i	−0.671886	−	1.22930i
$325$		0			0
$326$	−0.845842	+	0.260134i	−0.845842	+	0.260134i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.789383	−	0.139983i	0.789383	−	0.139983i	0.234725	−	0.972062i	$-0.424581\pi$
$331$	0.789383	−	0.139983i	0.789383	−	0.139983i	0.554658	+	0.832079i	$0.312849\pi$
$332$		0			0
$333$	0.522769	+	1.64820i	0.522769	+	1.64820i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.41861	+	0.200501i	1.41861	+	0.200501i	0.806949	−	0.590621i	$-0.201117\pi$
$337$	1.41861	+	0.200501i	1.41861	+	0.200501i	0.611658	+	0.791122i	$0.290503\pi$
$338$	−1.31148	+	0.825203i	−1.31148	+	0.825203i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.977904	−	0.209056i	0.977904	−	0.209056i
$344$	−0.671575	−	0.509877i	−0.671575	−	0.509877i
$345$		0			0
$346$		0			0
$347$	1.45859	−	0.990880i	1.45859	−	0.990880i	0.464125	−	0.885770i	$-0.346369\pi$
$347$	1.45859	−	0.990880i	1.45859	−	0.990880i	0.994461	−	0.105110i	$-0.0335196\pi$
$348$		0			0
$349$		0			0		−0.464125	−	0.885770i	$-0.653631\pi$
$349$		0			0		0.464125	+	0.885770i	$0.346369\pi$
$350$	−0.859439	+	1.28930i	−0.859439	+	1.28930i
$351$		0			0
$352$	1.36237	−	0.0958003i	1.36237	−	0.0958003i
$353$		0			0		0.855607	−	0.517627i	$-0.173184\pi$
$353$		0			0		−0.855607	+	0.517627i	$0.826816\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.67336			1.67336
$359$	0.950513	−	0.310686i	0.950513	−	0.310686i
$359$	0.950513	−	0.310686i	0.950513	−	0.310686i
$360$		0			0
$361$	−0.998614	+	0.0526281i	−0.998614	+	0.0526281i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.987551	−	0.157301i	$-0.0502793\pi$
$367$		0			0		−0.987551	+	0.157301i	$0.949721\pi$
$368$	−0.450437	+	0.675730i	−0.450437	+	0.675730i
$369$		0			0
$370$		0			0
$371$	−1.07938	+	0.733268i	−1.07938	+	0.733268i
$372$		0			0
$373$	1.39738	−	0.172545i	1.39738	−	0.172545i	0.611658	−	0.791122i	$-0.290503\pi$
$373$	1.39738	−	0.172545i	1.39738	−	0.172545i	0.785724	+	0.618577i	$0.212291\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.425285	+	0.717106i	0.425285	+	0.717106i	0.994461	−	0.105110i	$-0.0335196\pi$
$379$	0.425285	+	0.717106i	0.425285	+	0.717106i	−0.569175	+	0.822216i	$0.692737\pi$
$380$		0			0
$381$		0			0
$382$	1.89942	−	1.85006i	1.89942	−	1.85006i
$383$		0			0		0.796459	−	0.604692i	$-0.206704\pi$
$383$		0			0		−0.796459	+	0.604692i	$0.793296\pi$
$384$		0			0
$385$		0			0
$386$	−0.289708	+	2.99192i	−0.289708	+	2.99192i
$387$	−1.33643	+	0.236992i	−1.33643	+	0.236992i
$388$		0			0
$389$	1.64519	+	1.11765i	1.64519	+	1.11765i	0.881663	+	0.471880i	$0.156425\pi$
$389$	1.64519	+	1.11765i	1.64519	+	1.11765i	0.763532	+	0.645770i	$0.223464\pi$
$390$		0			0
$391$		0			0
$392$	0.593796	−	0.182619i	0.593796	−	0.182619i
$393$		0			0
$394$	−1.24388	−	2.27584i	−1.24388	−	2.27584i
$395$		0			0
$396$	−0.920223	+	1.14801i	−0.920223	+	1.14801i
$397$		0			0		−0.0788965	−	0.996883i	$-0.525140\pi$
$397$		0			0		0.0788965	+	0.996883i	$0.474860\pi$
$398$		0			0
$399$		0			0
$400$	0.210218	−	0.384620i	0.210218	−	0.384620i
$401$	1.62809	−	1.14830i	1.62809	−	1.14830i	0.763532	−	0.645770i	$-0.223464\pi$
$401$	1.62809	−	1.14830i	1.62809	−	1.14830i	0.864559	−	0.502531i	$-0.167598\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.93934	+	1.52678i	1.93934	+	1.52678i
$407$	1.38655	−	1.17270i	1.38655	−	1.17270i
$408$		0			0
$409$		0			0		0.611658	−	0.791122i	$-0.290503\pi$
$409$		0			0		−0.611658	+	0.791122i	$0.709497\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.673857	−	2.79063i	−0.673857	−	2.79063i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.855607	−	0.517627i	$-0.826816\pi$
$419$		0			0		0.855607	+	0.517627i	$0.173184\pi$
$420$		0			0
$421$	−0.316773	+	1.06313i	−0.316773	+	1.06313i	0.639045	+	0.769169i	$0.279330\pi$
$421$	−0.316773	+	1.06313i	−0.316773	+	1.06313i	−0.955819	+	0.293956i	$0.905028\pi$
$422$	0.227962	−	0.400232i	0.227962	−	0.400232i
$423$		0			0
$424$	−0.628053	+	0.512554i	−0.628053	+	0.512554i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.700700	−	2.20919i	0.700700	−	2.20919i
$429$		0			0
$430$		0			0
$431$	0.741861	−	1.61761i	0.741861	−	1.61761i	−0.0438629	−	0.999038i	$-0.513966\pi$
$431$	0.741861	−	1.61761i	0.741861	−	1.61761i	0.785724	−	0.618577i	$-0.212291\pi$
$432$		0			0
$433$		0			0		0.583517	−	0.812101i	$-0.301676\pi$
$433$		0			0		−0.583517	+	0.812101i	$0.698324\pi$
$434$		0			0
$435$		0			0
$436$	−2.35360	−	0.290616i	−2.35360	−	0.290616i
$437$		0			0
$438$		0			0
$439$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$439$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$440$		0			0
$441$	0.432754	−	0.901512i	0.432754	−	0.901512i
$442$		0			0
$443$	1.43409	−	1.12902i	1.43409	−	1.12902i	0.464125	−	0.885770i	$-0.346369\pi$
$443$	1.43409	−	1.12902i	1.43409	−	1.12902i	0.969965	−	0.243246i	$-0.0782123\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−1.46059	+	0.593765i	−1.46059	+	0.593765i
$449$	−0.226405	−	0.0239300i	−0.226405	−	0.0239300i	−0.00877529	−	0.999961i	$-0.502793\pi$
$449$	−0.226405	−	0.0239300i	−0.226405	−	0.0239300i	−0.217629	+	0.976031i	$0.569832\pi$
$450$	0.494312	+	1.46853i	0.494312	+	1.46853i
$451$		0			0
$452$	−0.407237	−	2.70952i	−0.407237	−	2.70952i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.47622	−	0.288591i	1.47622	−	0.288591i	0.611658	−	0.791122i	$-0.290503\pi$
$457$	1.47622	−	0.288591i	1.47622	−	0.288591i	0.864559	+	0.502531i	$0.167598\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.999384	−	0.0350944i	$-0.0111732\pi$
$461$		0			0		−0.999384	+	0.0350944i	$0.988827\pi$
$462$		0			0
$463$	−0.146905	−	0.335752i	−0.146905	−	0.335752i	0.827179	−	0.561938i	$-0.189944\pi$
$463$	−0.146905	−	0.335752i	−0.146905	−	0.335752i	−0.974084	+	0.226186i	$0.927374\pi$
$464$	−0.584339	−	0.382153i	−0.584339	−	0.382153i
$465$		0			0
$466$	−0.724862	+	1.65668i	−0.724862	+	1.65668i
$467$		0			0		−0.00877529	−	0.999961i	$-0.502793\pi$
$467$		0			0		0.00877529	+	0.999961i	$0.497207\pi$
$468$		0			0
$469$	0.143777	+	0.482532i	0.143777	+	0.482532i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.769702	+	1.19978i	0.769702	+	1.19978i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.0801062	+	1.30243i	−0.0801062	+	1.30243i
$478$	−2.29257	−	1.07586i	−2.29257	−	1.07586i
$479$		0			0		−0.881663	−	0.471880i	$-0.843575\pi$
$479$		0			0		0.881663	+	0.471880i	$0.156425\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.138621	+	0.0399830i	0.138621	+	0.0399830i
$485$		0			0
$486$		0			0
$487$	1.86310	−	0.719559i	1.86310	−	0.719559i	0.912591	−	0.408873i	$-0.134078\pi$
$487$	1.86310	−	0.719559i	1.86310	−	0.719559i	0.950513	−	0.310686i	$-0.100559\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.17537	+	0.502027i	−1.17537	+	0.502027i	−0.889808	−	0.456335i	$-0.849162\pi$
$491$	−1.17537	+	0.502027i	−1.17537	+	0.502027i	−0.285558	+	0.958362i	$0.592179\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.395610	+	1.52084i	−0.395610	+	1.52084i
$498$		0			0
$499$	−0.456307	−	0.659170i	−0.456307	−	0.659170i	0.525115	−	0.851031i	$-0.324022\pi$
$499$	−0.456307	−	0.659170i	−0.456307	−	0.659170i	−0.981422	+	0.191862i	$0.938547\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.368451	−	0.929647i	$-0.379888\pi$
$503$		0			0		−0.368451	+	0.929647i	$0.620112\pi$
$504$	0.218727	−	0.581466i	0.218727	−	0.581466i
$505$		0			0
$506$	−2.43298	+	1.78075i	−2.43298	+	1.78075i
$507$		0			0
$508$	2.30250	+	1.33835i	2.30250	+	1.33835i
$509$		0			0		0.165961	−	0.986132i	$-0.446927\pi$
$509$		0			0		−0.165961	+	0.986132i	$0.553073\pi$
$510$		0			0
$511$		0			0
$512$	0.749487	−	0.384371i	0.749487	−	0.384371i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.40692	+	2.28013i	−1.40692	+	2.28013i
$519$		0			0
$520$		0			0
$521$		0			0		−0.432754	−	0.901512i	$-0.642458\pi$
$521$		0			0		0.432754	+	0.901512i	$0.357542\pi$
$522$	2.39408	−	0.600385i	2.39408	−	0.600385i
$523$		0			0		0.384709	−	0.923038i	$-0.374302\pi$
$523$		0			0		−0.384709	+	0.923038i	$0.625698\pi$
$524$		0			0
$525$		0			0
$526$	−1.36929	+	1.43073i	−1.36929	+	1.43073i
$527$		0			0
$528$		0			0
$529$	0.0640365	−	2.43186i	0.0640365	−	2.43186i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.115249	+	0.290788i	0.115249	+	0.290788i
$537$		0			0
$538$		0			0
$539$	−1.04877	−	0.0552716i	−1.04877	−	0.0552716i
$540$		0			0
$541$	−0.283493	−	0.715288i	−0.283493	−	0.715288i	−0.999846	−	0.0175499i	$-0.994413\pi$
$541$	−0.283493	−	0.715288i	−0.283493	−	0.715288i	0.716353	−	0.697738i	$-0.245810\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.68002	−	1.05710i	−1.68002	−	1.05710i	−0.905275	−	0.424826i	$-0.860335\pi$
$547$	−1.68002	−	1.05710i	−1.68002	−	1.05710i	−0.774747	−	0.632271i	$-0.782123\pi$
$548$	−0.00323506	+	0.122855i	−0.00323506	+	0.122855i
$549$		0			0
$550$	1.22388	−	1.07252i	1.22388	−	1.07252i
$551$		0			0
$552$		0			0
$553$	0.490515	+	0.549926i	0.490515	+	0.549926i
$554$	−0.0940612	+	0.225682i	−0.0940612	+	0.225682i
$555$		0			0
$556$		0			0
$557$	1.33047	−	1.49162i	1.33047	−	1.49162i	0.639045	−	0.769169i	$-0.279330\pi$
$557$	1.33047	−	1.49162i	1.33047	−	1.49162i	0.691425	−	0.722448i	$-0.256983\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−2.28739	−	2.00451i	−2.28739	−	2.00451i
$563$		0			0		0.996152	−	0.0876414i	$-0.0279330\pi$
$563$		0			0		−0.996152	+	0.0876414i	$0.972067\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.448509	−	0.893778i	−0.448509	−	0.893778i
$568$	−0.162020	+	0.962714i	−0.162020	+	0.962714i
$569$	1.72486	+	1.00259i	1.72486	+	1.00259i	0.897680	+	0.440648i	$0.145251\pi$
$569$	1.72486	+	1.00259i	1.72486	+	1.00259i	0.827179	+	0.561938i	$0.189944\pi$
$570$		0			0
$571$	0.798758	−	0.584627i	0.798758	−	0.584627i	−0.113833	−	0.993500i	$-0.536313\pi$
$571$	0.798758	−	0.584627i	0.798758	−	0.584627i	0.912591	+	0.408873i	$0.134078\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.113739	+	1.84926i	0.113739	+	1.84926i
$576$	−0.423642	+	1.51869i	−0.423642	+	1.51869i
$577$		0			0		−0.984638	−	0.174608i	$-0.944134\pi$
$577$		0			0		0.984638	+	0.174608i	$0.0558659\pi$
$578$	0.881934	+	1.27402i	0.881934	+	1.27402i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.29494	−	0.448570i	1.29494	−	0.448570i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.583517	−	0.812101i	$-0.698324\pi$
$587$		0			0		0.583517	+	0.812101i	$0.301676\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.339927	−	0.677400i	0.339927	−	0.677400i
$593$		0			0		−0.960831	−	0.277137i	$-0.910615\pi$
$593$		0			0		0.960831	+	0.277137i	$0.0893855\pi$
$594$		0			0
$595$		0			0
$596$	−2.49069	−	1.11592i	−2.49069	−	1.11592i
$597$		0			0
$598$		0			0
$599$	−0.111148	−	0.0521595i	−0.111148	−	0.0521595i	0.368451	−	0.929647i	$-0.379888\pi$
$599$	−0.111148	−	0.0521595i	−0.111148	−	0.0521595i	−0.479599	+	0.877488i	$0.659218\pi$
$600$		0			0
$601$		0			0		−0.944914	−	0.327319i	$-0.893855\pi$
$601$		0			0		0.944914	+	0.327319i	$0.106145\pi$
$602$	−1.62937	−	1.32973i	−1.62937	−	1.32973i
$603$	0.469685	+	0.181399i	0.469685	+	0.181399i
$604$	0.946254	+	1.47499i	0.946254	+	1.47499i
$605$		0			0
$606$		0			0
$607$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$607$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.67357	+	1.09450i	1.67357	+	1.09450i	0.846391	+	0.532563i	$0.178771\pi$
$613$	1.67357	+	1.09450i	1.67357	+	1.09450i	0.827179	+	0.561938i	$0.189944\pi$
$614$		0			0
$615$		0			0
$616$	−0.652047	+	0.0228973i	−0.652047	+	0.0228973i
$617$	−1.92040	−	0.517580i	−1.92040	−	0.517580i	−0.987551	−	0.157301i	$-0.949721\pi$
$617$	−1.92040	−	0.517580i	−1.92040	−	0.517580i	−0.932845	−	0.360279i	$-0.882682\pi$
$618$		0			0
$619$		0			0		0.703997	−	0.710203i	$-0.251397\pi$
$619$		0			0		−0.703997	+	0.710203i	$0.748603\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.148629	−	0.988893i	−0.148629	−	0.988893i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.641543	−	0.197303i	−0.641543	−	0.197303i	−0.0438629	−	0.999038i	$-0.513966\pi$
$631$	−0.641543	−	0.197303i	−0.641543	−	0.197303i	−0.597680	+	0.801735i	$0.703911\pi$
$632$	0.333499	+	0.313617i	0.333499	+	0.313617i
$633$		0			0
$634$	−1.05373	+	0.829573i	−1.05373	+	0.829573i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.54930	−	2.07825i	−1.54930	−	2.07825i
$639$	0.961189	+	1.24321i	0.961189	+	1.24321i
$640$		0			0
$641$	−1.46964	−	0.181467i	−1.46964	−	0.181467i	−0.652446	−	0.757835i	$-0.726257\pi$
$641$	−1.46964	−	0.181467i	−1.46964	−	0.181467i	−0.817190	+	0.576369i	$0.804469\pi$
$642$		0			0
$643$		0			0		0.217629	−	0.976031i	$-0.430168\pi$
$643$		0			0		−0.217629	+	0.976031i	$0.569832\pi$
$644$	1.51457	−	2.10788i	1.51457	−	2.10788i
$645$		0			0
$646$		0			0
$647$		0			0		0.319015	−	0.947750i	$-0.396648\pi$
$647$		0			0		−0.319015	+	0.947750i	$0.603352\pi$
$648$	−0.326224	−	0.528698i	−0.326224	−	0.528698i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.751307	+	0.275114i	−0.751307	+	0.275114i
$653$	1.09084	−	0.890234i	1.09084	−	0.890234i	0.0963795	−	0.995345i	$-0.469274\pi$
$653$	1.09084	−	0.890234i	1.09084	−	0.890234i	0.994461	+	0.105110i	$0.0335196\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.112677	+	0.983416i	−0.112677	+	0.983416i	0.806949	+	0.590621i	$0.201117\pi$
$659$	−0.112677	+	0.983416i	−0.112677	+	0.983416i	−0.919626	+	0.392794i	$0.871508\pi$
$660$		0			0
$661$		0			0		−0.494925	−	0.868936i	$-0.664804\pi$
$661$		0			0		0.494925	+	0.868936i	$0.335196\pi$
$662$	1.21003	−	0.280974i	1.21003	−	0.280974i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.943311	+	2.50771i	0.943311	+	2.50771i
$667$	2.95083	+	0.0517948i	2.95083	+	0.0517948i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.91578	−	0.305153i	−1.91578	−	0.305153i	−0.919626	−	0.392794i	$-0.871508\pi$
$673$	−1.91578	−	0.305153i	−1.91578	−	0.305153i	−0.996152	+	0.0876414i	$0.972067\pi$
$674$	2.21143	+	0.194561i	2.21143	+	0.194561i
$675$		0			0
$676$	−1.14483	+	0.807454i	−1.14483	+	0.807454i
$677$		0			0		0.479599	−	0.877488i	$-0.340782\pi$
$677$		0			0		−0.479599	+	0.877488i	$0.659218\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.225148	−	0.411937i	−0.225148	−	0.411937i	0.740398	−	0.672168i	$-0.234637\pi$
$683$	−0.225148	−	0.411937i	−0.225148	−	0.411937i	−0.965546	+	0.260231i	$0.916201\pi$
$684$		0			0
$685$		0			0
$686$	1.49611	−	0.403227i	1.49611	−	0.403227i
$687$		0			0
$688$	0.492107	+	0.334309i	0.492107	+	0.334309i
$689$		0			0
$690$		0			0
$691$		0			0		0.0963795	−	0.995345i	$-0.469274\pi$
$691$		0			0		−0.0963795	+	0.995345i	$0.530726\pi$
$692$		0			0
$693$	−0.685218	+	0.795901i	−0.685218	+	0.795901i
$694$	2.17614	−	1.65218i	2.17614	−	1.65218i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.714614	+	1.20497i	−0.714614	+	1.20497i
$701$	0.994059	+	0.554696i	0.994059	+	0.554696i	0.897680	−	0.440648i	$-0.145251\pi$
$701$	0.994059	+	0.554696i	0.994059	+	0.554696i	0.0963795	+	0.995345i	$0.469274\pi$
$702$		0			0
$703$		0			0
$704$	1.64339	−	0.202921i	1.64339	−	0.202921i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.532027	+	0.798128i	−0.532027	+	0.798128i	−0.996152	−	0.0876414i	$-0.972067\pi$
$709$	−0.532027	+	0.798128i	−0.532027	+	0.798128i	0.464125	+	0.885770i	$0.346369\pi$
$710$		0			0
$711$	0.735087	−	0.0516904i	0.735087	−	0.0516904i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.51083	−	0.0796222i	1.51083	−	0.0796222i
$717$		0			0
$718$	1.44544	−	0.558250i	1.44544	−	0.558250i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−1.54091	+	0.162868i	−1.54091	+	0.162868i
$723$		0			0
$724$		0			0
$725$	−1.58899	+	0.111736i	−1.58899	+	0.111736i
$726$		0			0
$727$		0			0		0.554658	−	0.832079i	$-0.312849\pi$
$727$		0			0		−0.554658	+	0.832079i	$0.687151\pi$
$728$		0			0
$729$	−0.981422	−	0.191862i	−0.981422	−	0.191862i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.796459	−	0.604692i	$-0.793296\pi$
$733$		0			0		0.796459	+	0.604692i	$0.206704\pi$
$734$		0			0
$735$		0			0
$736$	−1.22901	+	2.07233i	−1.22901	+	2.07233i
$737$	−0.0139194	−	0.528604i	−0.0139194	−	0.528604i
$738$		0			0
$739$	−1.23317	+	0.775931i	−1.23317	+	0.775931i	−0.981422	−	0.191862i	$-0.938547\pi$
$739$	−1.23317	+	0.775931i	−1.23317	+	0.775931i	−0.251749	+	0.967793i	$0.581006\pi$
$740$		0			0
$741$		0			0
$742$	−1.61038	+	1.22264i	−1.61038	+	1.22264i
$743$	1.18129	−	1.37210i	1.18129	−	1.37210i	0.268694	−	0.963225i	$-0.413408\pi$
$743$	1.18129	−	1.37210i	1.18129	−	1.37210i	0.912591	−	0.408873i	$-0.134078\pi$
$744$		0			0
$745$		0			0
$746$	2.14817	−	0.380940i	2.14817	−	0.380940i
$747$		0			0
$748$		0			0
$749$	0.555200	−	1.55841i	0.555200	−	1.55841i
$750$		0			0
$751$	0.0167752	−	0.00515910i	0.0167752	−	0.00515910i	−0.285558	−	0.958362i	$-0.592179\pi$
$751$	0.0167752	−	0.00515910i	0.0167752	−	0.00515910i	0.302333	+	0.953202i	$0.402235\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.0119105	+	0.0128904i	0.0119105	+	0.0128904i	0.740398	−	0.672168i	$-0.234637\pi$
$757$	0.0119105	+	0.0128904i	0.0119105	+	0.0128904i	−0.728488	+	0.685059i	$0.759777\pi$
$758$	0.716542	+	1.07493i	0.716542	+	1.07493i
$759$		0			0
$760$		0			0
$761$		0			0		−0.691425	−	0.722448i	$-0.743017\pi$
$761$		0			0		0.691425	+	0.722448i	$0.256983\pi$
$762$		0			0
$763$	−1.67171	−	0.266276i	−1.67171	−	0.266276i
$764$	1.62690	−	1.76074i	1.62690	−	1.76074i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.999846	−	0.0175499i	$-0.994413\pi$
$769$		0			0		0.999846	+	0.0175499i	$0.00558659\pi$
$770$		0			0
$771$		0			0
$772$	−0.119207	+	2.71510i	−0.119207	+	2.71510i
$773$		0			0		−0.234725	−	0.972062i	$-0.575419\pi$
$773$		0			0		0.234725	+	0.972062i	$0.424581\pi$
$774$	−2.04859	+	0.475691i	−2.04859	+	0.475691i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	2.63683	+	1.59523i	2.63683	+	1.59523i
$779$		0			0
$780$		0			0
$781$	0.816815	−	1.43408i	0.816815	−	1.43408i
$782$		0			0
$783$		0			0
$784$	−0.411592	+	0.150717i	−0.411592	+	0.150717i
$785$		0			0
$786$		0			0
$787$		0			0		0.302333	−	0.953202i	$-0.402235\pi$
$787$		0			0		−0.302333	+	0.953202i	$0.597765\pi$
$788$	−1.23135	−	1.99560i	−1.23135	−	1.99560i
$789$		0			0
$790$		0			0
$791$	−0.222635	−	1.94309i	−0.222635	−	1.94309i
$792$	−0.380715	+	0.529854i	−0.380715	+	0.529854i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.611658	−	0.791122i	$-0.709497\pi$
$797$		0			0		0.611658	+	0.791122i	$0.290503\pi$
$798$		0			0
$799$		0			0
$800$	0.562761	−	1.17234i	0.562761	−	1.17234i
$801$		0			0
$802$	2.42558	−	1.90959i	2.42558	−	1.90959i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.533976	+	1.58637i	0.533976	+	1.58637i	0.785724	+	0.618577i	$0.212291\pi$
$809$	0.533976	+	1.58637i	0.533976	+	1.58637i	−0.251749	+	0.967793i	$0.581006\pi$
$810$		0			0
$811$		0			0		−0.148629	−	0.988893i	$-0.547486\pi$
$811$		0			0		0.148629	+	0.988893i	$0.452514\pi$
$812$	1.82362	+	1.28621i	1.82362	+	1.28621i
$813$		0			0
$814$	2.04985	−	1.92764i	2.04985	−	1.92764i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.612529	−	0.274435i	0.612529	−	0.274435i	−0.0788965	−	0.996883i	$-0.525140\pi$
$821$	0.612529	−	0.274435i	0.612529	−	0.274435i	0.691425	+	0.722448i	$0.256983\pi$
$822$		0			0
$823$	−1.27802	−	0.835815i	−1.27802	−	0.835815i	−0.285558	−	0.958362i	$-0.592179\pi$
$823$	−1.27802	−	0.835815i	−1.27802	−	0.835815i	−0.992463	+	0.122547i	$0.960894\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.29679	−	0.301119i	−1.29679	−	0.301119i	−0.479599	−	0.877488i	$-0.659218\pi$
$827$	−1.29679	−	0.301119i	−1.29679	−	0.301119i	−0.817190	+	0.576369i	$0.804469\pi$
$828$	−0.741190	−	2.48751i	−0.741190	−	2.48751i
$829$		0			0		0.183242	−	0.983068i	$-0.441341\pi$
$829$		0			0		−0.183242	+	0.983068i	$0.558659\pi$
$830$		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		−0.926378	−	0.376595i	$-0.877095\pi$
$839$		0			0		0.926378	+	0.376595i	$0.122905\pi$
$840$		0			0
$841$	−0.0134910	+	1.53733i	−0.0134910	+	1.53733i
$842$	−0.403464	+	1.67086i	−0.403464	+	1.67086i
$843$		0			0
$844$	0.186776	−	0.372204i	0.186776	−	0.372204i
$845$		0			0
$846$		0			0
$847$	0.0978862	+	0.0319952i	0.0978862	+	0.0319952i
$848$	0.423478	−	0.384453i	0.423478	−	0.384453i
$849$		0			0
$850$		0			0
$851$	0.308765	+	3.18872i	0.308765	+	3.18872i
$852$		0			0
$853$		0			0		0.944914	−	0.327319i	$-0.106145\pi$
$853$		0			0		−0.944914	+	0.327319i	$0.893855\pi$
$854$		0			0
$855$		0			0
$856$	0.258737	−	0.994658i	0.258737	−	0.994658i
$857$		0			0		−0.335599	−	0.942005i	$-0.608939\pi$
$857$		0			0		0.335599	+	0.942005i	$0.391061\pi$
$858$		0			0
$859$		0			0		−0.984638	−	0.174608i	$-0.944134\pi$
$859$		0			0		0.984638	+	0.174608i	$0.0558659\pi$
$860$		0			0
$861$		0			0
$862$	1.01601	−	2.56351i	1.01601	−	2.56351i
$863$	0.420861	−	1.11882i	0.420861	−	1.11882i	−0.539970	−	0.841685i	$-0.681564\pi$
$863$	0.420861	−	1.11882i	0.420861	−	1.11882i	0.960831	−	0.277137i	$-0.0893855\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.347108	−	0.691710i	−0.347108	−	0.691710i
$870$		0			0
$871$		0			0
$872$	−1.04904	−	0.0737671i	−1.04904	−	0.0737671i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.02301	+	1.65795i	−1.02301	+	1.65795i	−0.319015	+	0.947750i	$0.603352\pi$
$877$	−1.02301	+	1.65795i	−1.02301	+	1.65795i	−0.703997	+	0.710203i	$0.748603\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.969965	−	0.243246i	$-0.0782123\pi$
$881$		0			0		−0.969965	+	0.243246i	$0.921788\pi$
$882$	0.596105	−	1.43024i	0.596105	−	1.43024i
$883$	0.920487	+	1.03198i	0.920487	+	1.03198i	0.999384	+	0.0350944i	$0.0111732\pi$
$883$	0.920487	+	1.03198i	0.920487	+	1.03198i	−0.0788965	+	0.996883i	$0.525140\pi$
$884$		0			0
$885$		0			0
$886$	2.12697	−	1.86392i	2.12697	−	1.86392i
$887$		0			0		0.873245	−	0.487281i	$-0.162011\pi$
$887$		0			0		−0.873245	+	0.487281i	$0.837989\pi$
$888$		0			0
$889$	1.60901	+	1.01242i	1.60901	+	1.01242i
$890$		0			0
$891$	0.210536	+	1.02891i	0.210536	+	1.02891i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−1.03439	+	0.485417i	−1.03439	+	0.485417i
$897$		0			0
$898$	−0.352278	−	0.0185654i	−0.352278	−	0.0185654i
$899$		0			0
$900$	0.516175	+	1.30237i	0.516175	+	1.30237i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.243574	−	1.19037i	−0.243574	−	1.19037i
$905$		0			0
$906$		0			0
$907$	0.0389792	−	1.48028i	0.0389792	−	1.48028i	−0.652446	−	0.757835i	$-0.726257\pi$
$907$	0.0389792	−	1.48028i	0.0389792	−	1.48028i	0.691425	−	0.722448i	$-0.256983\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.277296	−	1.84497i	0.277296	−	1.84497i	−0.217629	−	0.976031i	$-0.569832\pi$
$911$	0.277296	−	1.84497i	0.277296	−	1.84497i	0.494925	−	0.868936i	$-0.335196\pi$
$912$		0			0
$913$		0			0
$914$	2.26069	−	0.566932i	2.26069	−	0.566932i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.459425	+	0.533636i	0.459425	+	0.533636i	0.939024	−	0.343852i	$-0.111732\pi$
$919$	0.459425	+	0.533636i	0.459425	+	0.533636i	−0.479599	+	0.877488i	$0.659218\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.316847	−	1.69984i	−0.316847	−	1.69984i
$926$	−0.254692	−	0.507546i	−0.254692	−	0.507546i
$927$		0			0
$928$	−1.79090	−	1.04097i	−1.79090	−	1.04097i
$929$		0			0		0.539970	−	0.841685i	$-0.318436\pi$
$929$		0			0		−0.539970	+	0.841685i	$0.681564\pi$
$930$		0			0
$931$		0			0
$932$	−0.575627	+	1.53025i	−0.575627	+	1.53025i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.569175	−	0.822216i	$-0.692737\pi$
$937$		0			0		0.569175	+	0.822216i	$0.307263\pi$
$938$	0.261823	+	0.734920i	0.261823	+	0.734920i
$939$		0			0
$940$		0			0
$941$		0			0		−0.939024	−	0.343852i	$-0.888268\pi$
$941$		0			0		0.939024	+	0.343852i	$0.111732\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.28884	+	1.79371i	1.28884	+	1.79371i
$947$	−1.42978	+	1.29802i	−1.42978	+	1.29802i	−0.539970	+	0.841685i	$0.681564\pi$
$947$	−1.42978	+	1.29802i	−1.42978	+	1.29802i	−0.889808	+	0.456335i	$0.849162\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.453276	+	1.87714i	−0.453276	+	1.87714i	0.0263232	+	0.999653i	$0.491620\pi$
$953$	−0.453276	+	1.87714i	−0.453276	+	1.87714i	−0.479599	+	0.877488i	$0.659218\pi$
$954$	−0.0177429	+	2.02184i	−0.0177429	+	2.02184i
$955$		0			0
$956$	−2.12109	−	0.862272i	−2.12109	−	0.862272i
$957$		0			0
$958$		0			0
$959$	−0.00538542	+	0.0875604i	−0.00538542	+	0.0875604i
$960$		0			0
$961$	−0.774747	−	0.632271i	−0.774747	−	0.632271i
$962$		0			0
$963$	−0.893303	−	1.39245i	−0.893303	−	1.39245i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.219713	+	0.737381i	0.219713	+	0.737381i	0.994461	+	0.105110i	$0.0335196\pi$
$967$	0.219713	+	0.737381i	0.219713	+	0.737381i	−0.774747	+	0.632271i	$0.782123\pi$
$968$	0.0623193	+	0.0144708i	0.0623193	+	0.0144708i
$969$		0			0
$970$		0			0
$971$		0			0		0.836914	−	0.547335i	$-0.184358\pi$
$971$		0			0		−0.836914	+	0.547335i	$0.815642\pi$
$972$		0			0
$973$		0			0
$974$	2.82419	−	1.26534i	2.82419	−	1.26534i
$975$		0			0
$976$		0			0
$977$	−0.188922	+	0.272912i	−0.188922	+	0.272912i	−0.905275	−	0.424826i	$-0.860335\pi$
$977$	−0.188922	+	0.272912i	−0.188922	+	0.272912i	0.716353	+	0.697738i	$0.245810\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.23317	+	1.15965i	−1.23317	+	1.15965i
$982$	−1.77776	+	0.872657i	−1.77776	+	0.872657i
$983$		0			0		−0.817190	−	0.576369i	$-0.804469\pi$
$983$		0			0		0.817190	+	0.576369i	$0.195531\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.51316	−	0.0882521i	−2.51316	−	0.0882521i
$990$		0			0
$991$	0.317081	+	0.298178i	0.317081	+	0.298178i	0.827179	−	0.561938i	$-0.189944\pi$
$991$	0.317081	+	0.298178i	0.317081	+	0.298178i	−0.510099	+	0.860116i	$0.670391\pi$
$992$		0			0
$993$		0			0
$994$	−0.488126	+	2.38552i	−0.488126	+	2.38552i
$995$		0			0
$996$		0			0
$997$		0			0		−0.597680	−	0.801735i	$-0.703911\pi$
$997$		0			0		0.597680	+	0.801735i	$0.296089\pi$
$998$	−0.759819	−	0.982754i	−0.759819	−	0.982754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2513.1.l.a.188.1	✓	178
7.6	odd	2	CM	2513.1.l.a.188.1	✓	178
359.338	even	179	inner	2513.1.l.a.1056.1	yes	178
2513.1056	odd	358	inner	2513.1.l.a.1056.1	yes	178

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2513.1.l.a.188.1	✓	178	1.1	even	1	trivial
2513.1.l.a.188.1	✓	178	7.6	odd	2	CM
2513.1.l.a.1056.1	yes	178	359.338	even	179	inner
2513.1.l.a.1056.1	yes	178	2513.1056	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)

\(f(q)\)	\(=\)	\(q+(1.54735 - 0.0815469i) q^{2} +(1.39317 - 0.147252i) q^{4} +(0.997537 - 0.0701455i) q^{7} +(0.613510 - 0.0977224i) q^{8} +(0.554658 - 0.832079i) q^{9} +O(q^{10})\)	\(q+(1.54735 - 0.0815469i) q^{2} +(1.39317 - 0.147252i) q^{4} +(0.997537 - 0.0701455i) q^{7} +(0.613510 - 0.0977224i) q^{8} +(0.554658 - 0.832079i) q^{9} +(-1.03072 - 0.201499i) q^{11} +(1.53782 - 0.189886i) q^{14} +(-0.428634 + 0.0916333i) q^{16} +(0.790395 - 1.33274i) q^{18} +(-1.61131 - 0.227737i) q^{22} +(1.32723 - 1.29274i) q^{23} +(-0.652446 + 0.757835i) q^{25} +(1.37941 - 0.244615i) q^{28} +(1.12141 + 1.13129i) q^{29} +(-1.25561 + 0.338410i) q^{32} +(0.650209 - 1.24090i) q^{36} +(-1.08147 + 1.34917i) q^{37} +(-0.938457 - 0.980564i) q^{43} +(-1.46564 - 0.128947i) q^{44} +(1.94826 - 2.10855i) q^{46} +(0.990159 - 0.139946i) q^{49} +(-0.947761 + 1.22584i) q^{50} +(-1.12816 + 0.655749i) q^{53} +(0.605144 - 0.140517i) q^{56} +(1.82746 + 1.65906i) q^{58} +(0.494925 - 0.868936i) q^{63} +(-1.49864 + 0.489849i) q^{64} +(0.109576 + 0.491429i) q^{67} +(-0.501315 + 1.48934i) q^{71} +(0.258975 - 0.564691i) q^{72} +(-1.56339 + 2.17583i) q^{74} +(-1.04231 - 0.128702i) q^{77} +(0.450732 + 0.582979i) q^{79} +(-0.384709 - 0.923038i) q^{81} +(-1.53208 - 1.44074i) q^{86} +(-0.652047 - 0.0228973i) q^{88} +(1.65870 - 1.99645i) q^{92} +(1.52071 - 0.297289i) q^{98} +(-0.739359 + 0.745876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 178 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 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

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