LMFDB - Embedded newform 1300.2.ba.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(49,1300)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1300.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.ba (of order $6$, degree $2$, not 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	1300.49
Dual form			1300.2.ba.b.849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01978 + 1.16612i) q^{3} +(0.199902 - 0.346241i) q^{7} +(1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(q+(-2.01978 + 1.16612i) q^{3} +(0.199902 - 0.346241i) q^{7} +(1.21969 - 2.11256i) q^{9} +(1.50000 - 0.866025i) q^{11} +(-3.55193 - 0.619491i) q^{13} +(-0.599706 - 0.346241i) q^{17} +(4.65213 + 2.68591i) q^{19} +0.932442i q^{21} +(0.0927749 - 0.0535636i) q^{23} -1.30752i q^{27} +(-2.45174 - 4.24653i) q^{29} -7.86488i q^{31} +(-2.01978 + 3.49837i) q^{33} +(-1.13234 - 1.96128i) q^{37} +(7.89654 - 2.89075i) q^{39} +(6.69615 - 3.86603i) q^{41} +(5.20533 + 3.00530i) q^{43} +3.46410 q^{47} +(3.42008 + 5.92375i) q^{49} +1.61504 q^{51} +11.7189i q^{53} -12.5284 q^{57} +(6.30059 + 3.63765i) q^{59} +(-4.34461 + 7.52509i) q^{61} +(-0.487636 - 0.844610i) q^{63} +(0.664004 + 1.15009i) q^{67} +(-0.124924 + 0.216374i) q^{69} +(-3.35847 - 1.93902i) q^{71} +10.2251 q^{73} -0.692481i q^{77} +13.1533 q^{79} +(5.18379 + 8.97859i) q^{81} +14.0791 q^{83} +(9.90396 + 5.71806i) q^{87} +(-0.300587 + 0.173544i) q^{89} +(-0.924532 + 1.10599i) q^{91} +(9.17142 + 15.8854i) q^{93} +(-4.42502 + 7.66436i) q^{97} -4.22512i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9	$ 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 18 q^{17} - 6 q^{23} - 6 q^{33} + 18 q^{37} + 4 q^{39} + 12 q^{41} + 18 q^{43} + 4 q^{49} - 36 q^{57} + 24 q^{59} - 4 q^{61} - 12 q^{63} - 18 q^{67} + 24 q^{69} - 36 q^{71} + 48 q^{73} + 16 q^{79} + 8 q^{81} + 72 q^{83} + 18 q^{87} + 24 q^{89} + 48 q^{93} - 6 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 18 * q^17 - 6 * q^23 - 6 * q^33 + 18 * q^37 + 4 * q^39 + 12 * q^41 + 18 * q^43 + 4 * q^49 - 36 * q^57 + 24 * q^59 - 4 * q^61 - 12 * q^63 - 18 * q^67 + 24 * q^69 - 36 * q^71 + 48 * q^73 + 16 * q^79 + 8 * q^81 + 72 * q^83 + 18 * q^87 + 24 * q^89 + 48 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.01978	+	1.16612i	−1.16612	+	0.673262i	−0.952764	−	0.303712i	$-0.901774\pi$
$3$	−2.01978	+	1.16612i	−1.16612	+	0.673262i	−0.213359	+	0.976974i	$0.568441\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.199902	−	0.346241i	0.0755559	−	0.130867i	−0.825772	−	0.564004i	$-0.809260\pi$
$7$	0.199902	−	0.346241i	0.0755559	−	0.130867i	0.901328	+	0.433137i	$0.142594\pi$
$8$		0			0
$9$	1.21969	−	2.11256i	0.406562	−	0.704187i
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		0			0
$13$	−3.55193	−	0.619491i	−0.985129	−	0.171816i
$13$	−3.55193	−	0.619491i	−0.985129	−	0.171816i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.599706	−	0.346241i	−0.145450	−	0.0839757i	0.425509	−	0.904954i	$-0.360095\pi$
$17$	−0.599706	−	0.346241i	−0.145450	−	0.0839757i	−0.570959	+	0.820979i	$0.693428\pi$
$18$		0			0
$19$	4.65213	+	2.68591i	1.06727	+	0.616190i	0.927435	−	0.373985i	$-0.122009\pi$
$19$	4.65213	+	2.68591i	1.06727	+	0.616190i	0.139837	+	0.990175i	$0.455342\pi$
$20$		0			0
$21$			0.932442i			0.203476i
$22$		0			0
$23$	0.0927749	−	0.0535636i	0.0193449	−	0.0111688i	−0.490296	−	0.871556i	$-0.663111\pi$
$23$	0.0927749	−	0.0535636i	0.0193449	−	0.0111688i	0.509641	+	0.860387i	$0.329778\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.30752i		−	0.251632i
$28$		0			0
$29$	−2.45174	−	4.24653i	−0.455276	−	0.788562i	0.543428	−	0.839456i	$-0.317126\pi$
$29$	−2.45174	−	4.24653i	−0.455276	−	0.788562i	−0.998704	+	0.0508943i	$0.983793\pi$
$30$		0			0
$31$		−	7.86488i		−	1.41257i	−0.707925	−	0.706287i	$-0.750369\pi$
$31$		−	7.86488i		−	1.41257i	0.707925	−	0.706287i	$-0.249631\pi$
$32$		0			0
$33$	−2.01978	+	3.49837i	−0.351599	+	0.608988i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.13234	−	1.96128i	−0.186156	−	0.322432i	0.757809	−	0.652476i	$-0.226270\pi$
$37$	−1.13234	−	1.96128i	−0.186156	−	0.322432i	−0.943966	+	0.330044i	$0.892936\pi$
$38$		0			0
$39$	7.89654	−	2.89075i	1.26446	−	0.462891i
$40$		0			0
$41$	6.69615	−	3.86603i	1.04576	−	0.603772i	0.124303	−	0.992244i	$-0.460331\pi$
$41$	6.69615	−	3.86603i	1.04576	−	0.603772i	0.921460	+	0.388473i	$0.126997\pi$
$42$		0			0
$43$	5.20533	+	3.00530i	0.793806	+	0.458304i	0.841301	−	0.540567i	$-0.181790\pi$
$43$	5.20533	+	3.00530i	0.793806	+	0.458304i	−0.0474947	+	0.998871i	$0.515124\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$		0			0
$49$	3.42008	+	5.92375i	0.488583	+	0.846250i
$50$		0			0
$51$	1.61504			0.226150
$52$		0			0
$53$			11.7189i			1.60972i	0.593468	+	0.804858i	$0.297758\pi$
$53$			11.7189i			1.60972i	−0.593468	+	0.804858i	$0.702242\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−12.5284			−1.65943
$58$		0			0
$59$	6.30059	+	3.63765i	0.820267	+	0.473581i	0.850508	−	0.525961i	$-0.176294\pi$
$59$	6.30059	+	3.63765i	0.820267	+	0.473581i	−0.0302418	+	0.999543i	$0.509628\pi$
$60$		0			0
$61$	−4.34461	+	7.52509i	−0.556270	+	0.963489i	0.441533	+	0.897245i	$0.354435\pi$
$61$	−4.34461	+	7.52509i	−0.556270	+	0.963489i	−0.997803	+	0.0662436i	$0.978899\pi$
$62$		0			0
$63$	−0.487636	−	0.844610i	−0.0614364	−	0.106411i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.664004	+	1.15009i	0.0811210	+	0.140506i	0.903732	−	0.428099i	$-0.140817\pi$
$67$	0.664004	+	1.15009i	0.0811210	+	0.140506i	−0.822611	+	0.568605i	$0.807483\pi$
$68$		0			0
$69$	−0.124924	+	0.216374i	−0.0150390	+	0.0260484i
$70$		0			0
$71$	−3.35847	−	1.93902i	−0.398577	−	0.230119i	0.287293	−	0.957843i	$-0.407245\pi$
$71$	−3.35847	−	1.93902i	−0.398577	−	0.230119i	−0.685870	+	0.727724i	$0.740578\pi$
$72$		0			0
$73$	10.2251			1.19676			0.598380	−	0.801213i	$-0.295811\pi$
$73$	10.2251			1.19676			0.598380	+	0.801213i	$0.295811\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	0.692481i		−	0.0789156i
$78$		0			0
$79$	13.1533			1.47986			0.739932	−	0.672681i	$-0.234858\pi$
$79$	13.1533			1.47986			0.739932	+	0.672681i	$0.234858\pi$
$80$		0			0
$81$	5.18379	+	8.97859i	0.575976	+	0.997621i
$82$		0			0
$83$	14.0791			1.54539			0.772693	−	0.634780i	$-0.218909\pi$
$83$	14.0791			1.54539			0.772693	+	0.634780i	$0.218909\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.90396	+	5.71806i	1.06182	+	0.613040i
$88$		0			0
$89$	−0.300587	+	0.173544i	−0.0318622	+	0.0183956i	−0.515846	−	0.856681i	$-0.672523\pi$
$89$	−0.300587	+	0.173544i	−0.0318622	+	0.0183956i	0.483984	+	0.875077i	$0.339189\pi$
$90$		0			0
$91$	−0.924532	+	1.10599i	−0.0969173	+	0.115939i
$92$		0			0
$93$	9.17142	+	15.8854i	0.951032	+	1.64724i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.42502	+	7.66436i	−0.449293	+	0.778198i	−0.998340	−	0.0575932i	$-0.981657\pi$
$97$	−4.42502	+	7.66436i	−0.449293	+	0.778198i	0.549047	+	0.835791i	$0.314991\pi$
$98$		0			0
$99$		−	4.22512i		−	0.424640i
$100$		0			0
$101$	2.05193	+	3.55405i	0.204175	+	0.353641i	0.949870	−	0.312646i	$-0.101216\pi$
$101$	2.05193	+	3.55405i	0.204175	+	0.353641i	−0.745695	+	0.666288i	$0.767882\pi$
$102$		0			0
$103$		−	11.2325i		−	1.10677i	−0.832926	−	0.553384i	$-0.813336\pi$
$103$		−	11.2325i		−	1.10677i	0.832926	−	0.553384i	$-0.186664\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.2449	−	8.80165i	1.47378	−	0.850888i	0.474216	−	0.880408i	$-0.342731\pi$
$107$	15.2449	−	8.80165i	1.47378	−	0.850888i	0.999564	+	0.0295208i	$0.00939813\pi$
$108$		0			0
$109$		−	15.1830i		−	1.45427i	−0.686495	−	0.727134i	$-0.740852\pi$
$109$		−	15.1830i		−	1.45427i	0.686495	−	0.727134i	$-0.259148\pi$
$110$		0			0
$111$	4.57418	+	2.64091i	0.434162	+	0.250664i
$112$		0			0
$113$	−7.70781	−	4.45011i	−0.725090	−	0.418631i	0.0915332	−	0.995802i	$-0.470823\pi$
$113$	−7.70781	−	4.45011i	−0.725090	−	0.418631i	−0.816623	+	0.577171i	$0.804157\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.64096	+	6.74809i	−0.521507	+	0.623861i
$118$		0			0
$119$	−0.239765	+	0.138429i	−0.0219792	+	0.0126897i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		0			0
$123$	−9.01652	+	15.6171i	−0.812993	+	1.40814i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.5279	−	6.07829i	0.934201	−	0.539361i	0.0460632	−	0.998939i	$-0.485332\pi$
$127$	10.5279	−	6.07829i	0.934201	−	0.539361i	0.888138	+	0.459577i	$0.151999\pi$
$128$		0			0
$129$	−14.0182			−1.23423
$130$		0			0
$131$	−2.11773			−0.185027			−0.0925135	−	0.995711i	$-0.529490\pi$
$131$	−2.11773			−0.185027			−0.0925135	+	0.995711i	$0.529490\pi$
$132$		0			0
$133$	1.85994	−	1.07384i	0.161277	−	0.0931135i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.01652	−	15.6171i	0.770334	−	1.33426i	−0.167046	−	0.985949i	$-0.553423\pi$
$137$	9.01652	−	15.6171i	0.770334	−	1.33426i	0.937380	−	0.348308i	$-0.113244\pi$
$138$		0			0
$139$	−4.92008	+	8.52183i	−0.417316	+	0.722812i	−0.995668	−	0.0929749i	$-0.970362\pi$
$139$	−4.92008	+	8.52183i	−0.417316	+	0.722812i	0.578353	+	0.815787i	$0.303696\pi$
$140$		0			0
$141$	−6.99674	+	4.03957i	−0.589232	+	0.340193i
$142$		0			0
$143$	−5.86440	+	2.14683i	−0.490405	+	0.179527i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−13.8156	−	7.97647i	−1.13950	−	0.657888i
$148$		0			0
$149$	7.69289	+	4.44149i	0.630226	+	0.363861i	0.780840	−	0.624731i	$-0.214792\pi$
$149$	7.69289	+	4.44149i	0.630226	+	0.363861i	−0.150613	+	0.988593i	$0.548125\pi$
$150$		0			0
$151$		−	4.43937i		−	0.361271i	−0.983550	−	0.180636i	$-0.942185\pi$
$151$		−	4.43937i		−	0.361271i	0.983550	−	0.180636i	$-0.0578155\pi$
$152$		0			0
$153$	−1.46291	+	0.844610i	−0.118269	+	0.0682827i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			4.16719i			0.332578i	0.986077	+	0.166289i	$0.0531784\pi$
$157$			4.16719i			0.332578i	−0.986077	+	0.166289i	$0.946822\pi$
$158$		0			0
$159$	−13.6657	−	23.6697i	−1.08376	−	1.87713i
$160$		0			0
$161$		−	0.0428299i		−	0.00337547i
$162$		0			0
$163$	−1.84836	+	3.20145i	−0.144775	+	0.250757i	−0.929289	−	0.369354i	$-0.879579\pi$
$163$	−1.84836	+	3.20145i	−0.144775	+	0.250757i	0.784514	+	0.620111i	$0.212912\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.7486	+	18.6171i	0.831750	+	1.44063i	0.896650	+	0.442741i	$0.145994\pi$
$167$	10.7486	+	18.6171i	0.831750	+	1.44063i	−0.0648999	+	0.997892i	$0.520673\pi$
$168$		0			0
$169$	12.2325	+	4.40078i	0.940959	+	0.338522i
$170$		0			0
$171$	11.3483	−	6.55193i	0.867825	−	0.501039i
$172$		0			0
$173$	−10.0561	−	5.80589i	−0.764551	−	0.441414i	0.0663766	−	0.997795i	$-0.478856\pi$
$173$	−10.0561	−	5.80589i	−0.764551	−	0.441414i	−0.830927	+	0.556381i	$0.812189\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−16.9678			−1.27538
$178$		0			0
$179$	2.48516	+	4.30442i	0.185749	+	0.321728i	0.943829	−	0.330435i	$-0.107195\pi$
$179$	2.48516	+	4.30442i	0.185749	+	0.321728i	−0.758079	+	0.652162i	$0.773862\pi$
$180$		0			0
$181$	−17.3695			−1.29107			−0.645534	−	0.763732i	$-0.723365\pi$
$181$	−17.3695			−1.29107			−0.645534	+	0.763732i	$0.723365\pi$
$182$		0			0
$183$		−	20.2654i		−	1.49806i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.19941			−0.0877098
$188$		0			0
$189$	−0.452716	−	0.261376i	−0.0329303	−	0.0190123i
$190$		0			0
$191$	10.2523	−	17.7575i	0.741832	−	1.28489i	−0.209828	−	0.977738i	$-0.567290\pi$
$191$	10.2523	−	17.7575i	0.741832	−	1.28489i	0.951660	−	0.307153i	$-0.0993762\pi$
$192$		0			0
$193$	−13.3038	−	23.0428i	−0.957626	−	1.65866i	−0.728240	−	0.685322i	$-0.759662\pi$
$193$	−13.3038	−	23.0428i	−0.957626	−	1.65866i	−0.229386	−	0.973336i	$-0.573672\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.204141	−	0.353583i	−0.0145445	−	0.0251917i	0.858662	−	0.512543i	$-0.171296\pi$
$197$	−0.204141	−	0.353583i	−0.0145445	−	0.0251917i	−0.873206	+	0.487351i	$0.837963\pi$
$198$		0			0
$199$	−12.1998	+	21.1307i	−0.864823	+	1.49792i	0.00240070	+	0.999997i	$0.499236\pi$
$199$	−12.1998	+	21.1307i	−0.864823	+	1.49792i	−0.867223	+	0.497919i	$0.834098\pi$
$200$		0			0
$201$	−2.68229	−	1.54862i	−0.189194	−	0.109231i
$202$		0			0
$203$	−1.96043			−0.137595
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	0.261323i		−	0.0181632i
$208$		0			0
$209$	9.30426			0.643589
$210$		0			0
$211$	−0.880509	−	1.52509i	−0.0606167	−	0.104991i	0.834125	−	0.551576i	$-0.185973\pi$
$211$	−0.880509	−	1.52509i	−0.0606167	−	0.104991i	−0.894741	+	0.446585i	$0.852640\pi$
$212$		0			0
$213$	9.04452			0.619721
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.72314	−	1.57221i	−0.184859	−	0.106728i
$218$		0			0
$219$	−20.6525	+	11.9237i	−1.39557	+	0.805732i
$220$		0			0
$221$	1.91562	+	1.60134i	0.128859	+	0.107718i
$222$		0			0
$223$	5.65955	+	9.80263i	0.378991	+	0.656433i	0.990916	−	0.134484i	$-0.0429376\pi$
$223$	5.65955	+	9.80263i	0.378991	+	0.656433i	−0.611924	+	0.790916i	$0.709604\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.03039	+	6.98084i	−0.267506	+	0.463334i	−0.968217	−	0.250111i	$-0.919533\pi$
$227$	−4.03039	+	6.98084i	−0.267506	+	0.463334i	0.700711	+	0.713445i	$0.252866\pi$
$228$		0			0
$229$			11.5715i			0.764666i	0.924025	+	0.382333i	$0.124879\pi$
$229$			11.5715i			0.764666i	−0.924025	+	0.382333i	$0.875121\pi$
$230$		0			0
$231$	0.807519	+	1.39866i	0.0531308	+	0.0920253i
$232$		0			0
$233$		−	24.0900i		−	1.57819i	−0.614272	−	0.789094i	$-0.710550\pi$
$233$		−	24.0900i		−	1.57819i	0.614272	−	0.789094i	$-0.289450\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−26.5669	+	15.3384i	−1.72570	+	0.996336i
$238$		0			0
$239$		−	30.7089i		−	1.98639i	−0.116459	−	0.993196i	$-0.537154\pi$
$239$		−	30.7089i		−	1.98639i	0.116459	−	0.993196i	$-0.462846\pi$
$240$		0			0
$241$	6.86541	+	3.96374i	0.442240	+	0.255327i	0.704547	−	0.709657i	$-0.251150\pi$
$241$	6.86541	+	3.96374i	0.442240	+	0.255327i	−0.262308	+	0.964984i	$0.584483\pi$
$242$		0			0
$243$	−17.5432	−	10.1286i	−1.12540	−	0.649750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.8602	−	12.4221i	−0.945529	−	0.790401i
$248$		0			0
$249$	−28.4368	+	16.4180i	−1.80211	+	1.04045i
$250$		0			0
$251$	11.3112	−	19.5916i	0.713956	−	1.23661i	−0.249405	−	0.968399i	$-0.580235\pi$
$251$	11.3112	−	19.5916i	0.713956	−	1.23661i	0.963361	−	0.268209i	$-0.0864317\pi$
$252$		0			0
$253$	0.0927749	−	0.160691i	0.00583271	−	0.0101025i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	22.3403	−	12.8982i	1.39355	−	0.804566i	0.399843	−	0.916584i	$-0.369065\pi$
$257$	22.3403	−	12.8982i	1.39355	−	0.804566i	0.993706	+	0.112018i	$0.0357313\pi$
$258$		0			0
$259$	−0.905432			−0.0562608
$260$		0			0
$261$	−11.9614			−0.740393
$262$		0			0
$263$	1.37748	−	0.795286i	0.0849388	−	0.0490394i	−0.456929	−	0.889503i	$-0.651051\pi$
$263$	1.37748	−	0.795286i	0.0849388	−	0.0490394i	0.541868	+	0.840464i	$0.317717\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.404747	−	0.701043i	0.0247701	−	0.0429031i
$268$		0			0
$269$	−13.9114	+	24.0952i	−0.848192	+	1.46911i	0.0346278	+	0.999400i	$0.488975\pi$
$269$	−13.9114	+	24.0952i	−0.848192	+	1.46911i	−0.882820	+	0.469712i	$0.844358\pi$
$270$		0			0
$271$	−20.3520	+	11.7502i	−1.23629	+	0.713774i	−0.968335	−	0.249656i	$-0.919682\pi$
$271$	−20.3520	+	11.7502i	−1.23629	+	0.713774i	−0.267959	+	0.963430i	$0.586349\pi$
$272$		0			0
$273$	0.577640	−	3.31197i	0.0349603	−	0.200450i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.59525	+	1.49837i	0.155934	+	0.0900283i	0.575936	−	0.817494i	$-0.304638\pi$
$277$	2.59525	+	1.49837i	0.155934	+	0.0900283i	−0.420003	+	0.907523i	$0.637971\pi$
$278$		0			0
$279$	−16.6150	−	9.59270i	−0.994716	−	0.574300i
$280$		0			0
$281$		−	24.6085i		−	1.46802i	−0.679138	−	0.734011i	$-0.737646\pi$
$281$		−	24.6085i		−	1.46802i	0.679138	−	0.734011i	$-0.262354\pi$
$282$		0			0
$283$	−7.07446	+	4.08444i	−0.420533	+	0.242795i	−0.695305	−	0.718715i	$-0.744731\pi$
$283$	−7.07446	+	4.08444i	−0.420533	+	0.242795i	0.274772	+	0.961509i	$0.411397\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	3.09131i		−	0.182474i
$288$		0			0
$289$	−8.26023	−	14.3071i	−0.485896	−	0.841597i
$290$		0			0
$291$		−	20.6405i		−	1.20997i
$292$		0			0
$293$	3.75184	−	6.49837i	0.219185	−	0.379639i	−0.735374	−	0.677661i	$-0.762994\pi$
$293$	3.75184	−	6.49837i	0.219185	−	0.379639i	0.954559	+	0.298022i	$0.0963270\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.13234	−	1.96128i	−0.0657053	−	0.113805i
$298$		0			0
$299$	−0.362712	+	0.132781i	−0.0209762	+	0.00767893i
$300$		0			0
$301$	2.08112	−	1.20153i	0.119953	−	0.0692552i
$302$		0			0
$303$	−8.28893	−	4.78561i	−0.476186	−	0.274926i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−5.95293			−0.339752			−0.169876	−	0.985465i	$-0.554337\pi$
$307$	−5.95293			−0.339752			−0.169876	+	0.985465i	$0.554337\pi$
$308$		0			0
$309$	13.0984	+	22.6872i	0.745144	+	1.29063i
$310$		0			0
$311$	−17.9247			−1.01642			−0.508208	−	0.861235i	$-0.669692\pi$
$311$	−17.9247			−1.01642			−0.508208	+	0.861235i	$0.669692\pi$
$312$		0			0
$313$		−	17.0073i		−	0.961312i	−0.876909	−	0.480656i	$-0.840399\pi$
$313$		−	17.0073i		−	0.961312i	0.876909	−	0.480656i	$-0.159601\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.09300			−0.173720			−0.0868601	−	0.996221i	$-0.527683\pi$
$317$	−3.09300			−0.173720			−0.0868601	+	0.996221i	$0.527683\pi$
$318$		0			0
$319$	−7.35521	−	4.24653i	−0.411813	−	0.237760i
$320$		0			0
$321$	−20.5276	+	35.5549i	−1.14574	+	1.98448i
$322$		0			0
$323$	−1.85994	−	3.22151i	−0.103490	−	0.179250i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	17.7053	+	30.6664i	0.979103	+	1.69586i
$328$		0			0
$329$	0.692481	−	1.19941i	0.0381777	−	0.0661258i
$330$		0			0
$331$	19.5481	+	11.2861i	1.07446	+	0.620340i	0.929397	−	0.369082i	$-0.120328\pi$
$331$	19.5481	+	11.2861i	1.07446	+	0.620340i	0.145064	+	0.989422i	$0.453661\pi$
$332$		0			0
$333$	−5.52442			−0.302736
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	18.0603i		−	0.983808i	−0.870649	−	0.491904i	$-0.836301\pi$
$337$		−	18.0603i		−	0.983808i	0.870649	−	0.491904i	$-0.163699\pi$
$338$		0			0
$339$	20.7575			1.12739
$340$		0			0
$341$	−6.81119	−	11.7973i	−0.368847	−	0.638861i
$342$		0			0
$343$	5.53335			0.298773
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.9252	+	13.2359i	1.23069	+	0.710538i	0.967173	−	0.254118i	$-0.0817851\pi$
$347$	22.9252	+	13.2359i	1.23069	+	0.710538i	0.263514	+	0.964655i	$0.415118\pi$
$348$		0			0
$349$	−10.7190	+	6.18860i	−0.573773	+	0.331268i	−0.758655	−	0.651493i	$-0.774143\pi$
$349$	−10.7190	+	6.18860i	−0.573773	+	0.331268i	0.184882	+	0.982761i	$0.440810\pi$
$350$		0			0
$351$	−0.809996	+	4.64422i	−0.0432344	+	0.247890i
$352$		0			0
$353$	9.64047	+	16.6978i	0.513110	+	0.888733i	0.999884	+	0.0152053i	$0.00484020\pi$
$353$	9.64047	+	16.6978i	0.513110	+	0.888733i	−0.486774	+	0.873528i	$0.661826\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.322849	−	0.559192i	0.0170870	−	0.0295956i
$358$		0			0
$359$		−	26.5506i		−	1.40129i	−0.713512	−	0.700643i	$-0.752897\pi$
$359$		−	26.5506i		−	1.40129i	0.713512	−	0.700643i	$-0.247103\pi$
$360$		0			0
$361$	4.92820	+	8.53590i	0.259379	+	0.449258i
$362$		0			0
$363$		−	18.6580i		−	0.979290i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.38638	+	3.68718i	−0.333366	+	0.192469i	−0.657335	−	0.753599i	$-0.728316\pi$
$367$	−6.38638	+	3.68718i	−0.333366	+	0.192469i	0.323968	+	0.946068i	$0.394983\pi$
$368$		0			0
$369$		−	18.8614i		−	0.981883i
$370$		0			0
$371$	4.05756	+	2.34263i	0.210658	+	0.121624i
$372$		0			0
$373$	24.5214	+	14.1574i	1.26967	+	0.733044i	0.974925	−	0.222532i	$-0.0714323\pi$
$373$	24.5214	+	14.1574i	1.26967	+	0.733044i	0.294744	+	0.955576i	$0.404766\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.07772	+	16.6022i	0.313018	+	0.855059i
$378$		0			0
$379$	−9.02975	+	5.21333i	−0.463827	+	0.267791i	−0.713652	−	0.700500i	$-0.752960\pi$
$379$	−9.02975	+	5.21333i	−0.463827	+	0.267791i	0.249825	+	0.968291i	$0.419627\pi$
$380$		0			0
$381$	−14.1761	+	24.5537i	−0.726262	+	1.25792i
$382$		0			0
$383$	5.42600	−	9.39811i	0.277256	−	0.480221i	−0.693446	−	0.720509i	$-0.743908\pi$
$383$	5.42600	−	9.39811i	0.277256	−	0.480221i	0.970702	+	0.240288i	$0.0772418\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.6978	−	7.33105i	0.645463	−	0.372658i
$388$		0			0
$389$	−20.2893			−1.02871			−0.514353	−	0.857578i	$-0.671968\pi$
$389$	−20.2893			−1.02871			−0.514353	+	0.857578i	$0.671968\pi$
$390$		0			0
$391$	−0.0741836			−0.00375163
$392$		0			0
$393$	4.27736	−	2.46953i	0.215764	−	0.124572i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	12.6263	−	21.8695i	0.633698	−	1.09760i	−0.353091	−	0.935589i	$-0.614870\pi$
$397$	12.6263	−	21.8695i	0.633698	−	1.09760i	0.986789	−	0.162008i	$-0.0517972\pi$
$398$		0			0
$399$	−2.50445	+	4.33784i	−0.125380	+	0.217164i
$400$		0			0
$401$	10.8377	−	6.25714i	0.541208	−	0.312467i	−0.204360	−	0.978896i	$-0.565511\pi$
$401$	10.8377	−	6.25714i	0.541208	−	0.312467i	0.745568	+	0.666429i	$0.232178\pi$
$402$		0			0
$403$	−4.87223	+	27.9355i	−0.242703	+	1.39157i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.39703	−	1.96128i	−0.168385	−	0.0972169i
$408$		0			0
$409$	−5.19248	−	2.99788i	−0.256752	−	0.148236i	0.366100	−	0.930575i	$-0.380693\pi$
$409$	−5.19248	−	2.99788i	−0.256752	−	0.148236i	−0.622852	+	0.782340i	$0.714026\pi$
$410$		0			0
$411$			42.0575i			2.07454i
$412$		0			0
$413$	2.51900	−	1.45435i	0.123952	−	0.0715637i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	22.9497i		−	1.12385i
$418$		0			0
$419$	−5.48516	−	9.50057i	−0.267968	−	0.464133i	0.700369	−	0.713781i	$-0.253019\pi$
$419$	−5.48516	−	9.50057i	−0.267968	−	0.464133i	−0.968337	+	0.249647i	$0.919685\pi$
$420$		0			0
$421$			36.6085i			1.78419i	0.451848	+	0.892095i	$0.350765\pi$
$421$			36.6085i			1.78419i	−0.451848	+	0.892095i	$0.649235\pi$
$422$		0			0
$423$	4.22512	−	7.31812i	0.205432	−	0.355819i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.73699	+	3.00856i	0.0840590	+	0.145595i
$428$		0			0
$429$	9.34135	−	11.1747i	0.451005	−	0.539521i
$430$		0			0
$431$	−10.4873	+	6.05484i	−0.505155	+	0.291651i	−0.730840	−	0.682549i	$-0.760871\pi$
$431$	−10.4873	+	6.05484i	−0.505155	+	0.291651i	0.225685	+	0.974200i	$0.427538\pi$
$432$		0			0
$433$	−7.80977	−	4.50897i	−0.375314	−	0.216687i	0.300464	−	0.953793i	$-0.402859\pi$
$433$	−7.80977	−	4.50897i	−0.375314	−	0.216687i	−0.675777	+	0.737106i	$0.736192\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.575468			0.0275284
$438$		0			0
$439$	6.07547	+	10.5230i	0.289966	+	0.502236i	0.973801	−	0.227400i	$-0.0730226\pi$
$439$	6.07547	+	10.5230i	0.289966	+	0.502236i	−0.683835	+	0.729637i	$0.739689\pi$
$440$		0			0
$441$	16.6857			0.794557
$442$		0			0
$443$			15.3116i			0.727476i	0.931501	+	0.363738i	$0.118500\pi$
$443$			15.3116i			0.727476i	−0.931501	+	0.363738i	$0.881500\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−20.7173			−0.979895
$448$		0			0
$449$	19.6929	+	11.3697i	0.929365	+	0.536569i	0.886611	−	0.462516i	$-0.153053\pi$
$449$	19.6929	+	11.3697i	0.929365	+	0.536569i	0.0427543	+	0.999086i	$0.486387\pi$
$450$		0			0
$451$	6.69615	−	11.5981i	0.315310	−	0.546132i
$452$		0			0
$453$	5.17686	+	8.96658i	0.243230	+	0.421287i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.37252	+	9.30548i	0.251316	+	0.435292i	0.963888	−	0.266307i	$-0.0858034\pi$
$457$	5.37252	+	9.30548i	0.251316	+	0.435292i	−0.712572	+	0.701599i	$0.752470\pi$
$458$		0			0
$459$	−0.452716	+	0.784127i	−0.0211310	+	0.0365999i
$460$		0			0
$461$	10.2973	+	5.94516i	0.479594	+	0.276894i	0.720247	−	0.693717i	$-0.244028\pi$
$461$	10.2973	+	5.94516i	0.479594	+	0.276894i	−0.240653	+	0.970611i	$0.577362\pi$
$462$		0			0
$463$	3.39726			0.157884			0.0789420	−	0.996879i	$-0.474846\pi$
$463$	3.39726			0.157884			0.0789420	+	0.996879i	$0.474846\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			6.39426i			0.295891i	0.988996	+	0.147946i	$0.0472660\pi$
$467$			6.39426i			0.295891i	−0.988996	+	0.147946i	$0.952734\pi$
$468$		0			0
$469$	0.530943			0.0245167
$470$		0			0
$471$	−4.85945	−	8.41682i	−0.223912	−	0.387826i
$472$		0			0
$473$	10.4107			0.478683
$474$		0			0
$475$		0			0
$476$		0			0
$477$	24.7569	+	14.2934i	1.13354	+	0.654450i
$478$		0			0
$479$	−14.1330	+	8.15968i	−0.645752	+	0.372825i	−0.786827	−	0.617174i	$-0.788278\pi$
$479$	−14.1330	+	8.15968i	−0.645752	+	0.372825i	0.141075	+	0.989999i	$0.454944\pi$
$480$		0			0
$481$	2.80702	+	7.66781i	0.127989	+	0.349622i
$482$		0			0
$483$	0.0499450	+	0.0865072i	0.00227258	+	0.00393622i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.96728	+	10.3356i	−0.270403	+	0.468352i	−0.968965	−	0.247197i	$-0.920490\pi$
$487$	−5.96728	+	10.3356i	−0.270403	+	0.468352i	0.698562	+	0.715550i	$0.253824\pi$
$488$		0			0
$489$		−	8.62166i		−	0.389885i
$490$		0			0
$491$	−17.0259	−	29.4896i	−0.768366	−	1.33085i	−0.938448	−	0.345419i	$-0.887737\pi$
$491$	−17.0259	−	29.4896i	−0.768366	−	1.33085i	0.170082	−	0.985430i	$-0.445597\pi$
$492$		0			0
$493$			3.39557i			0.152929i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.34273	+	0.775227i	−0.0602298	+	0.0347737i
$498$		0			0
$499$		−	12.5854i		−	0.563398i	−0.959503	−	0.281699i	$-0.909102\pi$
$499$		−	12.5854i		−	0.563398i	0.959503	−	0.281699i	$-0.0908979\pi$
$500$		0			0
$501$	−43.4196	−	25.0683i	−1.93985	−	1.11997i
$502$		0			0
$503$	15.7518	+	9.09433i	0.702340	+	0.405496i	0.808218	−	0.588883i	$-0.200432\pi$
$503$	15.7518	+	9.09433i	0.702340	+	0.405496i	−0.105879	+	0.994379i	$0.533765\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−29.8388	+	5.37592i	−1.32519	+	0.238753i
$508$		0			0
$509$	25.1265	−	14.5068i	1.11371	−	0.643001i	0.173923	−	0.984759i	$-0.444356\pi$
$509$	25.1265	−	14.5068i	1.11371	−	0.643001i	0.939788	+	0.341758i	$0.111022\pi$
$510$		0			0
$511$	2.04402	−	3.54035i	0.0904223	−	0.156616i
$512$		0			0
$513$	3.51187	−	6.08275i	0.155053	−	0.268560i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.19615	−	3.00000i	0.228527	−	0.131940i
$518$		0			0
$519$	27.0815			1.18875
$520$		0			0
$521$	35.0240			1.53443			0.767214	−	0.641391i	$-0.221642\pi$
$521$	35.0240			1.53443			0.767214	+	0.641391i	$0.221642\pi$
$522$		0			0
$523$	−8.03447	+	4.63870i	−0.351323	+	0.202836i	−0.665268	−	0.746605i	$-0.731683\pi$
$523$	−8.03447	+	4.63870i	−0.351323	+	0.202836i	0.313945	+	0.949441i	$0.398349\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.72314	+	4.71662i	−0.118622	+	0.205459i
$528$		0			0
$529$	−11.4943	+	19.9086i	−0.499751	+	0.865593i
$530$		0			0
$531$	15.3695	−	8.87358i	0.666979	−	0.385080i
$532$		0			0
$533$	−26.1793	+	9.58366i	−1.13395	+	0.415114i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.0390	−	5.79600i	−0.433214	−	0.250116i
$538$		0			0
$539$	10.2602	+	5.92375i	0.441940	+	0.255154i
$540$		0			0
$541$		−	24.3814i		−	1.04824i	−0.851644	−	0.524120i	$-0.824394\pi$
$541$		−	24.3814i		−	1.04824i	0.851644	−	0.524120i	$-0.175606\pi$
$542$		0			0
$543$	35.0827	−	20.2550i	1.50554	−	0.869226i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	26.5270i		−	1.13421i	−0.823645	−	0.567106i	$-0.808063\pi$
$547$		−	26.5270i		−	1.13421i	0.823645	−	0.567106i	$-0.191937\pi$
$548$		0			0
$549$	10.5981	+	18.3565i	0.452317	+	0.783436i
$550$		0			0
$551$		−	26.3406i		−	1.12215i
$552$		0			0
$553$	2.62938	−	4.55422i	0.111813	−	0.193665i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.60586	+	2.78142i	0.0680423	+	0.117853i	0.898039	−	0.439915i	$-0.144991\pi$
$557$	1.60586	+	2.78142i	0.0680423	+	0.117853i	−0.829997	+	0.557768i	$0.811658\pi$
$558$		0			0
$559$	−16.6272	−	13.8993i	−0.703257	−	0.587877i
$560$		0			0
$561$	2.42256	−	1.39866i	0.102280	−	0.0590516i
$562$		0			0
$563$	−29.6918	−	17.1426i	−1.25136	−	0.722474i	−0.279982	−	0.960005i	$-0.590328\pi$
$563$	−29.6918	−	17.1426i	−1.25136	−	0.722474i	−0.971380	+	0.237531i	$0.923662\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.14500			0.174074
$568$		0			0
$569$	17.8228	+	30.8701i	0.747172	+	1.29414i	0.949173	+	0.314755i	$0.101922\pi$
$569$	17.8228	+	30.8701i	0.747172	+	1.29414i	−0.202001	+	0.979385i	$0.564744\pi$
$570$		0			0
$571$	−4.53590			−0.189821			−0.0949107	−	0.995486i	$-0.530257\pi$
$571$	−4.53590			−0.189821			−0.0949107	+	0.995486i	$0.530257\pi$
$572$		0			0
$573$			47.8219i			1.99779i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−18.4475			−0.767981			−0.383991	−	0.923337i	$-0.625450\pi$
$577$	−18.4475			−0.767981			−0.383991	+	0.923337i	$0.625450\pi$
$578$		0			0
$579$	53.7415	+	31.0277i	2.23342	+	1.28947i
$580$		0			0
$581$	2.81445	−	4.87477i	0.116763	−	0.202240i
$582$		0			0
$583$	10.1489	+	17.5784i	0.420323	+	0.728021i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.4957	+	37.2316i	0.887222	+	1.53671i	0.843146	+	0.537685i	$0.180701\pi$
$587$	21.4957	+	37.2316i	0.887222	+	1.53671i	0.0440760	+	0.999028i	$0.485966\pi$
$588$		0			0
$589$	21.1244	−	36.5885i	0.870414	−	1.50760i
$590$		0			0
$591$	0.824642	+	0.476107i	0.0339212	+	0.0195844i
$592$		0			0
$593$	−12.8614			−0.528153			−0.264076	−	0.964502i	$-0.585067\pi$
$593$	−12.8614			−0.528153			−0.264076	+	0.964502i	$0.585067\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	56.9060i		−	2.32901i
$598$		0			0
$599$	−28.3170			−1.15700			−0.578500	−	0.815682i	$-0.696362\pi$
$599$	−28.3170			−1.15700			−0.578500	+	0.815682i	$0.696362\pi$
$600$		0			0
$601$	3.56734	+	6.17882i	0.145515	+	0.252039i	0.929565	−	0.368658i	$-0.120183\pi$
$601$	3.56734	+	6.17882i	0.145515	+	0.252039i	−0.784050	+	0.620698i	$0.786849\pi$
$602$		0			0
$603$	3.23951			0.131923
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−19.2086	−	11.0901i	−0.779653	−	0.450133i	0.0566544	−	0.998394i	$-0.481957\pi$
$607$	−19.2086	−	11.0901i	−0.779653	−	0.450133i	−0.836307	+	0.548261i	$0.815290\pi$
$608$		0			0
$609$	3.95965	−	2.28610i	0.160453	−	0.0926376i
$610$		0			0
$611$	−12.3043	−	2.14598i	−0.497777	−	0.0868171i
$612$		0			0
$613$	−0.161311	−	0.279399i	−0.00651530	−	0.0112848i	0.862749	−	0.505632i	$-0.168741\pi$
$613$	−0.161311	−	0.279399i	−0.00651530	−	0.0112848i	−0.869265	+	0.494347i	$0.835407\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.5993	+	32.2150i	−0.748781	+	1.29693i	0.199626	+	0.979872i	$0.436027\pi$
$617$	−18.5993	+	32.2150i	−0.748781	+	1.29693i	−0.948407	+	0.317055i	$0.897306\pi$
$618$		0			0
$619$		−	3.94911i		−	0.158728i	−0.996846	−	0.0793641i	$-0.974711\pi$
$619$		−	3.94911i		−	0.158728i	0.996846	−	0.0793641i	$-0.0252890\pi$
$620$		0			0
$621$	−0.0700354	−	0.121305i	−0.00281043	−	0.00486780i
$622$		0			0
$623$			0.138767i			0.00555959i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−18.7926	+	10.8499i	−0.750504	+	0.433304i
$628$		0			0
$629$			1.56825i			0.0625304i
$630$		0			0
$631$	29.0824	+	16.7908i	1.15775	+	0.668429i	0.950765	−	0.309914i	$-0.100300\pi$
$631$	29.0824	+	16.7908i	1.15775	+	0.668429i	0.206989	+	0.978343i	$0.433634\pi$
$632$		0			0
$633$	3.55688	+	2.05356i	0.141373	+	0.0816218i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.47818	−	23.1595i	−0.335918	−	0.917612i
$638$		0			0
$639$	−8.19257	+	4.72998i	−0.324093	+	0.187115i
$640$		0			0
$641$	16.5900	−	28.7347i	0.655266	−	1.13495i	−0.326561	−	0.945176i	$-0.605890\pi$
$641$	16.5900	−	28.7347i	0.655266	−	1.13495i	0.981827	−	0.189778i	$-0.0607767\pi$
$642$		0			0
$643$	−15.6833	+	27.1643i	−0.618489	+	1.07125i	0.371273	+	0.928524i	$0.378922\pi$
$643$	−15.6833	+	27.1643i	−0.618489	+	1.07125i	−0.989762	+	0.142730i	$0.954412\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.9659	−	9.79529i	0.667000	−	0.385092i	−0.127939	−	0.991782i	$-0.540836\pi$
$647$	16.9659	−	9.79529i	0.667000	−	0.385092i	0.794939	+	0.606690i	$0.207503\pi$
$648$		0			0
$649$	12.6012			0.494639
$650$		0			0
$651$	7.33355			0.287424
$652$		0			0
$653$	6.15962	−	3.55626i	0.241044	−	0.139167i	−0.374612	−	0.927182i	$-0.622224\pi$
$653$	6.15962	−	3.55626i	0.241044	−	0.139167i	0.615657	+	0.788015i	$0.288891\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	12.4714	−	21.6012i	0.486557	−	0.842742i
$658$		0			0
$659$	9.29211	−	16.0944i	0.361969	−	0.626949i	−0.626316	−	0.779570i	$-0.715438\pi$
$659$	9.29211	−	16.0944i	0.361969	−	0.626949i	0.988285	+	0.152621i	$0.0487712\pi$
$660$		0			0
$661$	14.5413	−	8.39540i	0.565590	−	0.326543i	−0.189796	−	0.981823i	$-0.560783\pi$
$661$	14.5413	−	8.39540i	0.565590	−	0.326543i	0.755386	+	0.655280i	$0.227449\pi$
$662$		0			0
$663$	−5.73650	−	1.00050i	−0.222787	−	0.0388563i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.454919	−	0.262648i	−0.0176146	−	0.0101698i
$668$		0			0
$669$	−22.8621	−	13.1995i	−0.883902	−	0.510321i
$670$		0			0
$671$			15.0502i			0.581005i
$672$		0			0
$673$	−19.5647	+	11.2957i	−0.754165	+	0.435417i	−0.827197	−	0.561912i	$-0.810066\pi$
$673$	−19.5647	+	11.2957i	−0.754165	+	0.435417i	0.0730322	+	0.997330i	$0.476732\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	5.31616i		−	0.204317i	−0.994768	−	0.102158i	$-0.967425\pi$
$677$		−	5.31616i		−	0.204317i	0.994768	−	0.102158i	$-0.0325749\pi$
$678$		0			0
$679$	1.76914	+	3.06424i	0.0678935	+	0.117595i
$680$		0			0
$681$		−	18.7997i		−	0.720407i
$682$		0			0
$683$	−1.97695	+	3.42419i	−0.0756461	+	0.131023i	−0.901367	−	0.433056i	$-0.857435\pi$
$683$	−1.97695	+	3.42419i	−0.0756461	+	0.131023i	0.825721	+	0.564079i	$0.190769\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.4938	−	23.3719i	−0.514820	−	0.891694i
$688$		0			0
$689$	7.25976	−	41.6248i	0.276575	−	1.58578i
$690$		0			0
$691$	−11.1493	+	6.43704i	−0.424139	+	0.244877i	−0.696846	−	0.717220i	$-0.745414\pi$
$691$	−11.1493	+	6.43704i	−0.424139	+	0.244877i	0.272708	+	0.962097i	$0.412081\pi$
$692$		0			0
$693$	−1.46291	−	0.844610i	−0.0555713	−	0.0320841i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.35430			−0.202809
$698$		0			0
$699$	28.0919	+	48.6566i	1.06253	+	1.84036i
$700$		0			0
$701$	34.9777			1.32109			0.660544	−	0.750787i	$-0.270326\pi$
$701$	34.9777			1.32109			0.660544	+	0.750787i	$0.270326\pi$
$702$		0			0
$703$		−	12.1655i		−	0.458830i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.64074			0.0617065
$708$		0			0
$709$	17.1183	+	9.88325i	0.642891	+	0.371173i	0.785727	−	0.618573i	$-0.212289\pi$
$709$	17.1183	+	9.88325i	0.642891	+	0.371173i	−0.142836	+	0.989746i	$0.545622\pi$
$710$		0			0
$711$	16.0429	−	27.7872i	0.601657	−	1.04210i
$712$		0			0
$713$	−0.421272	−	0.729664i	−0.0157767	−	0.0273261i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	35.8103	+	62.0253i	1.33736	+	2.31638i
$718$		0			0
$719$	22.1234	−	38.3188i	0.825062	−	1.42905i	−0.0768099	−	0.997046i	$-0.524473\pi$
$719$	22.1234	−	38.3188i	0.825062	−	1.42905i	0.901872	−	0.432004i	$-0.142193\pi$
$720$		0			0
$721$	−3.88914	−	2.24539i	−0.144839	−	0.0836228i
$722$		0			0
$723$	−18.4889			−0.687608
$724$		0			0
$725$		0			0
$726$		0			0
$727$			31.4877i			1.16781i	0.811821	+	0.583907i	$0.198477\pi$
$727$			31.4877i			1.16781i	−0.811821	+	0.583907i	$0.801523\pi$
$728$		0			0
$729$	16.1420			0.597853
$730$		0			0
$731$	−2.08112	−	3.60460i	−0.0769728	−	0.133321i
$732$		0			0
$733$	−42.4714			−1.56872			−0.784359	−	0.620307i	$-0.787008\pi$
$733$	−42.4714			−1.56872			−0.784359	+	0.620307i	$0.787008\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.99201	+	1.15009i	0.0733767	+	0.0423640i
$738$		0			0
$739$	11.9368	−	6.89173i	0.439103	−	0.253516i	−0.264114	−	0.964492i	$-0.585079\pi$
$739$	11.9368	−	6.89173i	0.439103	−	0.253516i	0.703217	+	0.710975i	$0.251746\pi$
$740$		0			0
$741$	44.5000	+	7.76123i	1.63475	+	0.285116i
$742$		0			0
$743$	−7.96961	−	13.8038i	−0.292377	−	0.506411i	0.681995	−	0.731357i	$-0.261113\pi$
$743$	−7.96961	−	13.8038i	−0.292377	−	0.506411i	−0.974371	+	0.224946i	$0.927779\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	17.1721	−	29.7430i	0.628296	−	1.08824i
$748$		0			0
$749$		−	7.03787i		−	0.257158i
$750$		0			0
$751$	−0.758540	−	1.31383i	−0.0276795	−	0.0479423i	0.851854	−	0.523780i	$-0.175478\pi$
$751$	−0.758540	−	1.31383i	−0.0276795	−	0.0479423i	−0.879533	+	0.475837i	$0.842145\pi$
$752$		0			0
$753$			52.7610i			1.92272i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−41.1214	+	23.7414i	−1.49458	+	0.862897i	−0.999981	−	0.00622310i	$-0.998019\pi$
$757$	−41.1214	+	23.7414i	−1.49458	+	0.862897i	−0.494601	+	0.869120i	$0.664686\pi$
$758$		0			0
$759$			0.432748i			0.0157078i
$760$		0			0
$761$	−33.3805	−	19.2722i	−1.21004	−	0.698618i	−0.247274	−	0.968946i	$-0.579535\pi$
$761$	−33.3805	−	19.2722i	−1.21004	−	0.698618i	−0.962768	+	0.270327i	$0.912868\pi$
$762$		0			0
$763$	−5.25697	−	3.03512i	−0.190315	−	0.109879i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.1258	−	16.8238i	−0.726700	−	0.607473i
$768$		0			0
$769$	−34.5236	+	19.9322i	−1.24495	+	0.718775i	−0.970099	−	0.242711i	$-0.921963\pi$
$769$	−34.5236	+	19.9322i	−1.24495	+	0.718775i	−0.274856	+	0.961486i	$0.588630\pi$
$770$		0			0
$771$	−30.0817	+	52.1031i	−1.08337	+	1.87645i
$772$		0			0
$773$	−16.4774	+	28.5396i	−0.592650	+	1.02650i	0.401224	+	0.915980i	$0.368585\pi$
$773$	−16.4774	+	28.5396i	−0.592650	+	1.02650i	−0.993874	+	0.110519i	$0.964749\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.82878	−	1.05585i	0.0656071	−	0.0378783i
$778$		0			0
$779$	41.5352			1.48815
$780$		0			0
$781$	−6.71695			−0.240351
$782$		0			0
$783$	−5.55242	+	3.20569i	−0.198427	+	0.114562i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.539648	+	0.934698i	−0.0192364	+	0.0333184i	−0.875483	−	0.483248i	$-0.839457\pi$
$787$	−0.539648	+	0.934698i	−0.0192364	+	0.0333184i	0.856247	+	0.516567i	$0.172790\pi$
$788$		0			0
$789$	−1.85480	+	3.21261i	−0.0660327	+	0.114372i
$790$		0			0
$791$	−3.08162	+	1.77917i	−0.109570	+	0.0632601i
$792$		0			0
$793$	20.0935	−	24.0372i	0.713541	−	0.853584i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.5423	+	9.55071i	0.585959	+	0.338304i	0.763498	−	0.645810i	$-0.223480\pi$
$797$	16.5423	+	9.55071i	0.585959	+	0.338304i	−0.177539	+	0.984114i	$0.556814\pi$
$798$		0			0
$799$	−2.07744	−	1.19941i	−0.0734947	−	0.0424322i
$800$		0			0
$801$			0.846678i			0.0299159i
$802$		0			0
$803$	15.3377	−	8.85521i	0.541255	−	0.312494i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	64.8896i		−	2.28422i
$808$		0			0
$809$	0.881702	+	1.52715i	0.0309990	+	0.0536918i	0.881109	−	0.472914i	$-0.156798\pi$
$809$	0.881702	+	1.52715i	0.0309990	+	0.0536918i	−0.850110	+	0.526606i	$0.823464\pi$
$810$		0			0
$811$			52.3298i			1.83755i	0.394784	+	0.918774i	$0.370819\pi$
$811$			52.3298i			1.83755i	−0.394784	+	0.918774i	$0.629181\pi$
$812$		0			0
$813$	27.4044	−	47.4658i	0.961113	−	1.66470i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.1439	+	27.9621i	0.564804	+	0.978270i
$818$		0			0
$819$	1.20882	+	3.30209i	0.0422397	+	0.115384i
$820$		0			0
$821$	−12.3585	+	7.13517i	−0.431314	+	0.249019i	−0.699906	−	0.714235i	$-0.746775\pi$
$821$	−12.3585	+	7.13517i	−0.431314	+	0.249019i	0.268592	+	0.963254i	$0.413442\pi$
$822$		0			0
$823$	37.8579	+	21.8573i	1.31964	+	0.761896i	0.983671	−	0.179976i	$-0.0576021\pi$
$823$	37.8579	+	21.8573i	1.31964	+	0.761896i	0.335972	+	0.941872i	$0.390935\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.5962			0.785748			0.392874	−	0.919592i	$-0.371481\pi$
$827$	22.5962			0.785748			0.392874	+	0.919592i	$0.371481\pi$
$828$		0			0
$829$	−27.0473	−	46.8473i	−0.939392	−	1.62708i	−0.766608	−	0.642116i	$-0.778057\pi$
$829$	−27.0473	−	46.8473i	−0.939392	−	1.62708i	−0.172784	−	0.984960i	$-0.555276\pi$
$830$		0			0
$831$	−6.98914			−0.242450
$832$		0			0
$833$		−	4.73668i		−	0.164116i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.2835			−0.355449
$838$		0			0
$839$	−19.2550	−	11.1169i	−0.664755	−	0.383796i	0.129332	−	0.991601i	$-0.458717\pi$
$839$	−19.2550	−	11.1169i	−0.664755	−	0.383796i	−0.794086	+	0.607805i	$0.792050\pi$
$840$		0			0
$841$	2.47796	−	4.29196i	0.0854471	−	0.147999i
$842$		0			0
$843$	28.6966	+	49.7039i	0.988362	+	1.71189i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.59922	+	2.76993i	0.0549498	+	0.0951758i
$848$		0			0
$849$	9.52592	−	16.4994i	0.326929	−	0.566257i
$850$		0			0
$851$	−0.210106	−	0.121305i	−0.00720235	−	0.00415828i
$852$		0			0
$853$	−16.5312			−0.566019			−0.283009	−	0.959117i	$-0.591333\pi$
$853$	−16.5312			−0.566019			−0.283009	+	0.959117i	$0.591333\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	27.5842i		−	0.942259i	−0.882064	−	0.471129i	$-0.843846\pi$
$857$		−	27.5842i		−	0.942259i	0.882064	−	0.471129i	$-0.156154\pi$
$858$		0			0
$859$	32.5016			1.10894			0.554469	−	0.832204i	$-0.312921\pi$
$859$	32.5016			1.10894			0.554469	+	0.832204i	$0.312921\pi$
$860$		0			0
$861$	3.60485	+	6.24378i	0.122853	+	0.212787i
$862$		0			0
$863$	−29.7986			−1.01436			−0.507178	−	0.861842i	$-0.669311\pi$
$863$	−29.7986			−1.01436			−0.507178	+	0.861842i	$0.669311\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	33.3678	+	19.2649i	1.13323	+	0.654270i
$868$		0			0
$869$	19.7300	−	11.3911i	0.669294	−	0.386417i
$870$		0			0
$871$	−1.64603	−	4.49638i	−0.0557735	−	0.152354i
$872$		0			0
$873$	10.7943	+	18.6962i	0.365331	+	0.632772i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.20181	+	12.4739i	−0.243188	+	0.421214i	−0.961621	−	0.274383i	$-0.911526\pi$
$877$	−7.20181	+	12.4739i	−0.243188	+	0.421214i	0.718433	+	0.695597i	$0.244860\pi$
$878$		0			0
$879$			17.5004i			0.590274i
$880$		0			0
$881$	−3.68457	−	6.38186i	−0.124136	−	0.215010i	0.797259	−	0.603638i	$-0.206283\pi$
$881$	−3.68457	−	6.38186i	−0.124136	−	0.215010i	−0.921395	+	0.388627i	$0.872949\pi$
$882$		0			0
$883$			24.3646i			0.819933i	0.912101	+	0.409967i	$0.134460\pi$
$883$			24.3646i			0.819933i	−0.912101	+	0.409967i	$0.865540\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.8404	−	12.0322i	0.699752	−	0.404002i	−0.107503	−	0.994205i	$-0.534286\pi$
$887$	20.8404	−	12.0322i	0.699752	−	0.404002i	0.807255	+	0.590203i	$0.200952\pi$
$888$		0			0
$889$		−	4.86025i		−	0.163008i
$890$		0			0
$891$	15.5514	+	8.97859i	0.520990	+	0.300794i
$892$		0			0
$893$	16.1154	+	9.30426i	0.539283	+	0.311355i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.577762	−	0.691157i	0.0192909	−	0.0230771i
$898$		0			0
$899$	−33.3985	+	19.2826i	−1.11390	+	0.643112i
$900$		0			0
$901$	4.05756	−	7.02790i	0.135177	−	0.234133i
$902$		0			0
$903$	−2.80227	+	4.85367i	−0.0932537	+	0.161520i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	32.4823	−	18.7536i	1.07856	−	0.622705i	0.148050	−	0.988980i	$-0.452700\pi$
$907$	32.4823	−	18.7536i	1.07856	−	0.622705i	0.930507	+	0.366275i	$0.119367\pi$
$908$		0			0
$909$	10.0109			0.332039
$910$		0			0
$911$	12.6000			0.417458			0.208729	−	0.977974i	$-0.433067\pi$
$911$	12.6000			0.417458			0.208729	+	0.977974i	$0.433067\pi$
$912$		0			0
$913$	21.1187	−	12.1929i	0.698927	−	0.403526i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.423339	+	0.733244i	−0.0139799	+	0.0242139i
$918$		0			0
$919$	−15.8332	+	27.4239i	−0.522288	+	0.904630i	0.477375	+	0.878699i	$0.341588\pi$
$919$	−15.8332	+	27.4239i	−0.522288	+	0.904630i	−0.999664	+	0.0259305i	$0.991745\pi$
$920$		0			0
$921$	12.0236	−	6.94185i	0.396192	−	0.228742i
$922$		0			0
$923$	10.7279	+	8.96780i	0.353112	+	0.295179i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−23.7292	−	13.7001i	−0.779371	−	0.449970i
$928$		0			0
$929$	−25.7537	−	14.8689i	−0.844952	−	0.487833i	0.0139925	−	0.999902i	$-0.495546\pi$
$929$	−25.7537	−	14.8689i	−0.844952	−	0.487833i	−0.858944	+	0.512069i	$0.828879\pi$
$930$		0			0
$931$			36.7441i			1.20424i
$932$		0			0
$933$	36.2040	−	20.9024i	1.18527	−	0.684313i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			52.3124i			1.70897i	0.519474	+	0.854486i	$0.326128\pi$
$937$			52.3124i			1.70897i	−0.519474	+	0.854486i	$0.673872\pi$
$938$		0			0
$939$	19.8327	+	34.3512i	0.647214	+	1.12101i
$940$		0			0
$941$			29.5767i			0.964174i	0.876123	+	0.482087i	$0.160121\pi$
$941$			29.5767i			0.964174i	−0.876123	+	0.482087i	$0.839879\pi$
$942$		0			0
$943$	0.414157	−	0.717340i	0.0134868	−	0.0233598i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.0165	−	41.5978i	−0.780432	−	1.35175i	−0.931690	−	0.363254i	$-0.881666\pi$
$947$	−24.0165	−	41.5978i	−0.780432	−	1.35175i	0.151258	−	0.988494i	$-0.451668\pi$
$948$		0			0
$949$	−36.3189	−	6.33437i	−1.17896	−	0.205622i
$950$		0			0
$951$	6.24720	−	3.60682i	0.202579	−	0.116959i
$952$		0			0
$953$	25.7923	+	14.8912i	0.835494	+	0.482373i	0.855730	−	0.517423i	$-0.173109\pi$
$953$	25.7923	+	14.8912i	0.835494	+	0.482373i	−0.0202363	+	0.999795i	$0.506442\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	19.8079			0.640299
$958$		0			0
$959$	−3.60485	−	6.24378i	−0.116407	−	0.201622i
$960$		0			0
$961$	−30.8564			−0.995368
$962$		0			0
$963$		−	42.9410i		−	1.38376i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	20.6730			0.664798			0.332399	−	0.943139i	$-0.392142\pi$
$967$	20.6730			0.664798			0.332399	+	0.943139i	$0.392142\pi$
$968$		0			0
$969$	7.51336	+	4.33784i	0.241364	+	0.139352i
$970$		0			0
$971$	9.99307	−	17.3085i	0.320693	−	0.555456i	−0.659938	−	0.751320i	$-0.729418\pi$
$971$	9.99307	−	17.3085i	0.320693	−	0.555456i	0.980631	+	0.195863i	$0.0627509\pi$
$972$		0			0
$973$	1.96707	+	3.40706i	0.0630613	+	0.109225i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.8138	+	39.5147i	0.729878	+	1.26419i	0.956934	+	0.290305i	$0.0937566\pi$
$977$	22.8138	+	39.5147i	0.729878	+	1.26419i	−0.227056	+	0.973882i	$0.572910\pi$
$978$		0			0
$979$	−0.300587	+	0.520632i	−0.00960680	+	0.0166395i
$980$		0			0
$981$	−32.0750	−	18.5185i	−1.02408	−	0.591251i
$982$		0			0
$983$	54.1966			1.72860			0.864301	−	0.502975i	$-0.167761\pi$
$983$	54.1966			1.72860			0.864301	+	0.502975i	$0.167761\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			3.23007i			0.102814i
$988$		0			0
$989$	0.643899			0.0204748
$990$		0			0
$991$	−23.2639	−	40.2943i	−0.739002	−	1.27999i	−0.952945	−	0.303143i	$-0.901964\pi$
$991$	−23.2639	−	40.2943i	−0.739002	−	1.27999i	0.213943	−	0.976846i	$-0.431369\pi$
$992$		0			0
$993$	−52.6440			−1.67061
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−33.8641	−	19.5514i	−1.07249	−	0.619200i	−0.143626	−	0.989632i	$-0.545876\pi$
$997$	−33.8641	−	19.5514i	−1.07249	−	0.619200i	−0.928860	+	0.370432i	$0.879210\pi$
$998$		0			0
$999$	−2.56441	+	1.48056i	−0.0811343	+	0.0468429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.ba.b.49.2		8
5.2	odd	4		260.2.x.a.101.4	✓	8
5.3	odd	4		1300.2.y.b.101.1		8
5.4	even	2		1300.2.ba.c.49.3		8
13.4	even	6		1300.2.ba.c.849.3		8
15.2	even	4		2340.2.dj.d.361.1		8
20.7	even	4		1040.2.da.c.881.1		8
65.2	even	12		3380.2.a.q.1.1		4
65.4	even	6	inner	1300.2.ba.b.849.2		8
65.17	odd	12		260.2.x.a.121.4	yes	8
65.37	even	12		3380.2.a.p.1.1		4
65.42	odd	12		3380.2.f.i.3041.2		8
65.43	odd	12		1300.2.y.b.901.1		8
65.62	odd	12		3380.2.f.i.3041.1		8
195.17	even	12		2340.2.dj.d.901.3		8
260.147	even	12		1040.2.da.c.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.4	✓	8	5.2	odd	4
260.2.x.a.121.4	yes	8	65.17	odd	12
1040.2.da.c.641.1		8	260.147	even	12
1040.2.da.c.881.1		8	20.7	even	4
1300.2.y.b.101.1		8	5.3	odd	4
1300.2.y.b.901.1		8	65.43	odd	12
1300.2.ba.b.49.2		8	1.1	even	1	trivial
1300.2.ba.b.849.2		8	65.4	even	6	inner
1300.2.ba.c.49.3		8	5.4	even	2
1300.2.ba.c.849.3		8	13.4	even	6
2340.2.dj.d.361.1		8	15.2	even	4
2340.2.dj.d.901.3		8	195.17	even	12
3380.2.a.p.1.1		4	65.37	even	12
3380.2.a.q.1.1		4	65.2	even	12
3380.2.f.i.3041.1		8	65.62	odd	12
3380.2.f.i.3041.2		8	65.42	odd	12

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.01978 + 1.16612i) q^{3} +(0.199902 - 0.346241i) q^{7} +(1.21969 - 2.11256i) q^{9} +O(q^{10})\)	\(q+(-2.01978 + 1.16612i) q^{3} +(0.199902 - 0.346241i) q^{7} +(1.21969 - 2.11256i) q^{9} +(1.50000 - 0.866025i) q^{11} +(-3.55193 - 0.619491i) q^{13} +(-0.599706 - 0.346241i) q^{17} +(4.65213 + 2.68591i) q^{19} +0.932442i q^{21} +(0.0927749 - 0.0535636i) q^{23} -1.30752i q^{27} +(-2.45174 - 4.24653i) q^{29} -7.86488i q^{31} +(-2.01978 + 3.49837i) q^{33} +(-1.13234 - 1.96128i) q^{37} +(7.89654 - 2.89075i) q^{39} +(6.69615 - 3.86603i) q^{41} +(5.20533 + 3.00530i) q^{43} +3.46410 q^{47} +(3.42008 + 5.92375i) q^{49} +1.61504 q^{51} +11.7189i q^{53} -12.5284 q^{57} +(6.30059 + 3.63765i) q^{59} +(-4.34461 + 7.52509i) q^{61} +(-0.487636 - 0.844610i) q^{63} +(0.664004 + 1.15009i) q^{67} +(-0.124924 + 0.216374i) q^{69} +(-3.35847 - 1.93902i) q^{71} +10.2251 q^{73} -0.692481i q^{77} +13.1533 q^{79} +(5.18379 + 8.97859i) q^{81} +14.0791 q^{83} +(9.90396 + 5.71806i) q^{87} +(-0.300587 + 0.173544i) q^{89} +(-0.924532 + 1.10599i) q^{91} +(9.17142 + 15.8854i) q^{93} +(-4.42502 + 7.66436i) q^{97} -4.22512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9	\( 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 18 q^{17} - 6 q^{23} - 6 q^{33} + 18 q^{37} + 4 q^{39} + 12 q^{41} + 18 q^{43} + 4 q^{49} - 36 q^{57} + 24 q^{59} - 4 q^{61} - 12 q^{63} - 18 q^{67} + 24 q^{69} - 36 q^{71} + 48 q^{73} + 16 q^{79} + 8 q^{81} + 72 q^{83} + 18 q^{87} + 24 q^{89} + 48 q^{93} - 6 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 18 * q^17 - 6 * q^23 - 6 * q^33 + 18 * q^37 + 4 * q^39 + 12 * q^41 + 18 * q^43 + 4 * q^49 - 36 * q^57 + 24 * q^59 - 4 * q^61 - 12 * q^63 - 18 * q^67 + 24 * q^69 - 36 * q^71 + 48 * q^73 + 16 * q^79 + 8 * q^81 + 72 * q^83 + 18 * q^87 + 24 * q^89 + 48 * q^93 - 6 * q^97

Introduction

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