LMFDB - Embedded newform 1300.2.y.b.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(101,1300)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1300.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.y (of order $6$, degree $2$, 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}\cdot 3 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	1300.901
Dual form			1300.2.y.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16612 + 2.01978i) q^{3} +(-0.346241 + 0.199902i) q^{7} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(q+(-1.16612 + 2.01978i) q^{3} +(-0.346241 + 0.199902i) q^{7} +(-1.21969 - 2.11256i) q^{9} +(1.50000 + 0.866025i) q^{11} +(0.619491 + 3.55193i) q^{13} +(-0.346241 - 0.599706i) q^{17} +(-4.65213 + 2.68591i) q^{19} -0.932442i q^{21} +(0.0535636 - 0.0927749i) q^{23} -1.30752 q^{27} +(2.45174 - 4.24653i) q^{29} +7.86488i q^{31} +(-3.49837 + 2.01978i) q^{33} +(-1.96128 - 1.13234i) q^{37} +(-7.89654 - 2.89075i) q^{39} +(6.69615 + 3.86603i) q^{41} +(-3.00530 - 5.20533i) q^{43} +3.46410i q^{47} +(-3.42008 + 5.92375i) q^{49} +1.61504 q^{51} -11.7189 q^{53} -12.5284i q^{57} +(-6.30059 + 3.63765i) q^{59} +(-4.34461 - 7.52509i) q^{61} +(0.844610 + 0.487636i) q^{63} +(1.15009 + 0.664004i) q^{67} +(0.124924 + 0.216374i) q^{69} +(-3.35847 + 1.93902i) q^{71} -10.2251i q^{73} -0.692481 q^{77} -13.1533 q^{79} +(5.18379 - 8.97859i) q^{81} -14.0791i q^{83} +(5.71806 + 9.90396i) q^{87} +(0.300587 + 0.173544i) q^{89} +(-0.924532 - 1.10599i) q^{91} +(-15.8854 - 9.17142i) q^{93} +(7.66436 - 4.42502i) q^{97} -4.22512i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 6 * q^7 - 4 * q^9	$ 8 q + 2 q^{3} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{13} - 6 q^{17} + 6 q^{23} - 4 q^{27} + 6 q^{33} - 6 q^{37} - 4 q^{39} + 12 q^{41} - 10 q^{43} - 4 q^{49} - 24 q^{53} - 24 q^{59} - 4 q^{61} - 24 q^{63} + 54 q^{67} - 24 q^{69} - 36 q^{71} - 12 q^{77} - 16 q^{79} + 8 q^{81} + 6 q^{87} - 24 q^{89} - 24 q^{93} + 30 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^13 - 6 * q^17 + 6 * q^23 - 4 * q^27 + 6 * q^33 - 6 * q^37 - 4 * q^39 + 12 * q^41 - 10 * q^43 - 4 * q^49 - 24 * q^53 - 24 * q^59 - 4 * q^61 - 24 * q^63 + 54 * q^67 - 24 * q^69 - 36 * q^71 - 12 * q^77 - 16 * q^79 + 8 * q^81 + 6 * q^87 - 24 * q^89 - 24 * q^93 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	0.303712	+	0.952764i	$0.401774\pi$
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	−0.976974	+	0.213359i	$0.931559\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.346241	+	0.199902i	−0.130867	+	0.0755559i	−0.564004	−	0.825772i	$-0.690740\pi$
$7$	−0.346241	+	0.199902i	−0.130867	+	0.0755559i	0.433137	+	0.901328i	$0.357406\pi$
$8$		0			0
$9$	−1.21969	−	2.11256i	−0.406562	−	0.704187i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.346241	−	0.599706i	−0.0839757	−	0.145450i	0.820979	−	0.570959i	$-0.193428\pi$
$17$	−0.346241	−	0.599706i	−0.0839757	−	0.145450i	−0.904954	+	0.425509i	$0.860095\pi$
$18$		0			0
$19$	−4.65213	+	2.68591i	−1.06727	+	0.616190i	−0.927435	−	0.373985i	$-0.877991\pi$
$19$	−4.65213	+	2.68591i	−1.06727	+	0.616190i	−0.139837	+	0.990175i	$0.544658\pi$
$20$		0			0
$21$		−	0.932442i		−	0.203476i
$22$		0			0
$23$	0.0535636	−	0.0927749i	0.0111688	−	0.0193449i	−0.860387	−	0.509641i	$-0.829778\pi$
$23$	0.0535636	−	0.0927749i	0.0111688	−	0.0193449i	0.871556	+	0.490296i	$0.163111\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.30752			−0.251632
$28$		0			0
$29$	2.45174	−	4.24653i	0.455276	−	0.788562i	−0.543428	−	0.839456i	$-0.682874\pi$
$29$	2.45174	−	4.24653i	0.455276	−	0.788562i	0.998704	+	0.0508943i	$0.0162072\pi$
$30$		0			0
$31$			7.86488i			1.41257i	0.707925	+	0.706287i	$0.249631\pi$
$31$			7.86488i			1.41257i	−0.707925	+	0.706287i	$0.750369\pi$
$32$		0			0
$33$	−3.49837	+	2.01978i	−0.608988	+	0.351599i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.96128	−	1.13234i	−0.322432	−	0.186156i	0.330044	−	0.943966i	$-0.392936\pi$
$37$	−1.96128	−	1.13234i	−0.322432	−	0.186156i	−0.652476	+	0.757809i	$0.726270\pi$
$38$		0			0
$39$	−7.89654	−	2.89075i	−1.26446	−	0.462891i
$40$		0			0
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.921460	−	0.388473i	$-0.126997\pi$
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.124303	+	0.992244i	$0.460331\pi$
$42$		0			0
$43$	−3.00530	−	5.20533i	−0.458304	−	0.793806i	0.540567	−	0.841301i	$-0.318210\pi$
$43$	−3.00530	−	5.20533i	−0.458304	−	0.793806i	−0.998871	+	0.0474947i	$0.984876\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.46410i			0.505291i	0.967559	+	0.252646i	$0.0813007\pi$
$47$			3.46410i			0.505291i	−0.967559	+	0.252646i	$0.918699\pi$
$48$		0			0
$49$	−3.42008	+	5.92375i	−0.488583	+	0.846250i
$50$		0			0
$51$	1.61504			0.226150
$52$		0			0
$53$	−11.7189			−1.60972			−0.804858	−	0.593468i	$-0.797758\pi$
$53$	−11.7189			−1.60972			−0.804858	+	0.593468i	$0.797758\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	12.5284i		−	1.65943i
$58$		0			0
$59$	−6.30059	+	3.63765i	−0.820267	+	0.473581i	−0.850508	−	0.525961i	$-0.823706\pi$
$59$	−6.30059	+	3.63765i	−0.820267	+	0.473581i	0.0302418	+	0.999543i	$0.490372\pi$
$60$		0			0
$61$	−4.34461	−	7.52509i	−0.556270	−	0.963489i	−0.997803	−	0.0662436i	$-0.978899\pi$
$61$	−4.34461	−	7.52509i	−0.556270	−	0.963489i	0.441533	−	0.897245i	$-0.354435\pi$
$62$		0			0
$63$	0.844610	+	0.487636i	0.106411	+	0.0614364i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.15009	+	0.664004i	0.140506	+	0.0811210i	0.568605	−	0.822611i	$-0.307483\pi$
$67$	1.15009	+	0.664004i	0.140506	+	0.0811210i	−0.428099	+	0.903732i	$0.640817\pi$
$68$		0			0
$69$	0.124924	+	0.216374i	0.0150390	+	0.0260484i
$70$		0			0
$71$	−3.35847	+	1.93902i	−0.398577	+	0.230119i	−0.685870	−	0.727724i	$-0.740578\pi$
$71$	−3.35847	+	1.93902i	−0.398577	+	0.230119i	0.287293	+	0.957843i	$0.407245\pi$
$72$		0			0
$73$		−	10.2251i		−	1.19676i	−0.801213	−	0.598380i	$-0.795811\pi$
$73$		−	10.2251i		−	1.19676i	0.801213	−	0.598380i	$-0.204189\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.692481			−0.0789156
$78$		0			0
$79$	−13.1533			−1.47986			−0.739932	−	0.672681i	$-0.765142\pi$
$79$	−13.1533			−1.47986			−0.739932	+	0.672681i	$0.765142\pi$
$80$		0			0
$81$	5.18379	−	8.97859i	0.575976	−	0.997621i
$82$		0			0
$83$		−	14.0791i		−	1.54539i	−0.634780	−	0.772693i	$-0.718909\pi$
$83$		−	14.0791i		−	1.54539i	0.634780	−	0.772693i	$-0.281091\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.71806	+	9.90396i	0.613040	+	1.06182i
$88$		0			0
$89$	0.300587	+	0.173544i	0.0318622	+	0.0183956i	0.515846	−	0.856681i	$-0.327477\pi$
$89$	0.300587	+	0.173544i	0.0318622	+	0.0183956i	−0.483984	+	0.875077i	$0.660811\pi$
$90$		0			0
$91$	−0.924532	−	1.10599i	−0.0969173	−	0.115939i
$92$		0			0
$93$	−15.8854	−	9.17142i	−1.64724	−	0.951032i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.66436	−	4.42502i	0.778198	−	0.449293i	−0.0575932	−	0.998340i	$-0.518343\pi$
$97$	7.66436	−	4.42502i	0.778198	−	0.449293i	0.835791	+	0.549047i	$0.185009\pi$
$98$		0			0
$99$		−	4.22512i		−	0.424640i
$100$		0			0
$101$	2.05193	−	3.55405i	0.204175	−	0.353641i	−0.745695	−	0.666288i	$-0.767882\pi$
$101$	2.05193	−	3.55405i	0.204175	−	0.353641i	0.949870	+	0.312646i	$0.101216\pi$
$102$		0			0
$103$	11.2325			1.10677			0.553384	−	0.832926i	$-0.313336\pi$
$103$	11.2325			1.10677			0.553384	+	0.832926i	$0.313336\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.80165	+	15.2449i	−0.850888	+	1.47378i	0.0295208	+	0.999564i	$0.490602\pi$
$107$	−8.80165	+	15.2449i	−0.850888	+	1.47378i	−0.880408	+	0.474216i	$0.842731\pi$
$108$		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
$113$	4.45011	+	7.70781i	0.418631	+	0.725090i	0.995802	−	0.0915332i	$-0.0291768\pi$
$113$	4.45011	+	7.70781i	0.418631	+	0.725090i	−0.577171	+	0.816623i	$0.695843\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.74809	−	5.64096i	0.623861	−	0.521507i
$118$		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
$123$	−15.6171	+	9.01652i	−1.40814	+	0.812993i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.07829	+	10.5279i	−0.539361	+	0.934201i	0.459577	+	0.888138i	$0.348001\pi$
$127$	−6.07829	+	10.5279i	−0.539361	+	0.934201i	−0.998939	+	0.0460632i	$0.985332\pi$
$128$		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
$133$	1.07384	−	1.85994i	0.0931135	−	0.161277i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.6171	+	9.01652i	−1.33426	+	0.770334i	−0.985949	−	0.167046i	$-0.946577\pi$
$137$	−15.6171	+	9.01652i	−1.33426	+	0.770334i	−0.348308	+	0.937380i	$0.613244\pi$
$138$		0			0
$139$	4.92008	+	8.52183i	0.417316	+	0.722812i	0.995668	−	0.0929749i	$-0.0296376\pi$
$139$	4.92008	+	8.52183i	0.417316	+	0.722812i	−0.578353	+	0.815787i	$0.696304\pi$
$140$		0			0
$141$	−6.99674	−	4.03957i	−0.589232	−	0.340193i
$142$		0			0
$143$	−2.14683	+	5.86440i	−0.179527	+	0.490405i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.97647	−	13.8156i	−0.657888	−	1.13950i
$148$		0			0
$149$	−7.69289	+	4.44149i	−0.630226	+	0.363861i	−0.780840	−	0.624731i	$-0.785208\pi$
$149$	−7.69289	+	4.44149i	−0.630226	+	0.363861i	0.150613	+	0.988593i	$0.451875\pi$
$150$		0			0
$151$			4.43937i			0.361271i	0.983550	+	0.180636i	$0.0578155\pi$
$151$			4.43937i			0.361271i	−0.983550	+	0.180636i	$0.942185\pi$
$152$		0			0
$153$	−0.844610	+	1.46291i	−0.0682827	+	0.118269i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.16719			0.332578			0.166289	−	0.986077i	$-0.446822\pi$
$157$	4.16719			0.332578			0.166289	+	0.986077i	$0.446822\pi$
$158$		0			0
$159$	13.6657	−	23.6697i	1.08376	−	1.87713i
$160$		0			0
$161$			0.0428299i			0.00337547i
$162$		0			0
$163$	−3.20145	+	1.84836i	−0.250757	+	0.144775i	−0.620111	−	0.784514i	$-0.712912\pi$
$163$	−3.20145	+	1.84836i	−0.250757	+	0.144775i	0.369354	+	0.929289i	$0.379579\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.6171	+	10.7486i	1.44063	+	0.831750i	0.997892	−	0.0648999i	$-0.0206728\pi$
$167$	18.6171	+	10.7486i	1.44063	+	0.831750i	0.442741	+	0.896650i	$0.354006\pi$
$168$		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
$173$	5.80589	+	10.0561i	0.441414	+	0.764551i	0.997795	−	0.0663766i	$-0.0211439\pi$
$173$	5.80589	+	10.0561i	0.441414	+	0.764551i	−0.556381	+	0.830927i	$0.687811\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	16.9678i		−	1.27538i
$178$		0			0
$179$	−2.48516	+	4.30442i	−0.185749	+	0.321728i	−0.943829	−	0.330435i	$-0.892805\pi$
$179$	−2.48516	+	4.30442i	−0.185749	+	0.321728i	0.758079	+	0.652162i	$0.226138\pi$
$180$		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
$183$	20.2654			1.49806
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	1.19941i		−	0.0877098i
$188$		0			0
$189$	0.452716	−	0.261376i	0.0329303	−	0.0190123i
$190$		0			0
$191$	10.2523	+	17.7575i	0.741832	+	1.28489i	0.951660	+	0.307153i	$0.0993762\pi$
$191$	10.2523	+	17.7575i	0.741832	+	1.28489i	−0.209828	+	0.977738i	$0.567290\pi$
$192$		0			0
$193$	23.0428	+	13.3038i	1.65866	+	0.957626i	0.973336	+	0.229386i	$0.0736717\pi$
$193$	23.0428	+	13.3038i	1.65866	+	0.957626i	0.685322	+	0.728240i	$0.259662\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.353583	−	0.204141i	−0.0251917	−	0.0145445i	0.487351	−	0.873206i	$-0.337963\pi$
$197$	−0.353583	−	0.204141i	−0.0251917	−	0.0145445i	−0.512543	+	0.858662i	$0.671296\pi$
$198$		0			0
$199$	12.1998	+	21.1307i	0.864823	+	1.49792i	0.867223	+	0.497919i	$0.165902\pi$
$199$	12.1998	+	21.1307i	0.864823	+	1.49792i	−0.00240070	+	0.999997i	$0.500764\pi$
$200$		0			0
$201$	−2.68229	+	1.54862i	−0.189194	+	0.109231i
$202$		0			0
$203$			1.96043i			0.137595i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.261323			−0.0181632
$208$		0			0
$209$	−9.30426			−0.643589
$210$		0			0
$211$	−0.880509	+	1.52509i	−0.0606167	+	0.104991i	−0.894741	−	0.446585i	$-0.852640\pi$
$211$	−0.880509	+	1.52509i	−0.0606167	+	0.104991i	0.834125	+	0.551576i	$0.185973\pi$
$212$		0			0
$213$		−	9.04452i		−	0.619721i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.57221	−	2.72314i	−0.106728	−	0.184859i
$218$		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
$223$	−9.80263	−	5.65955i	−0.656433	−	0.378991i	0.134484	−	0.990916i	$-0.457062\pi$
$223$	−9.80263	−	5.65955i	−0.656433	−	0.378991i	−0.790916	+	0.611924i	$0.790396\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.98084	−	4.03039i	0.463334	−	0.267506i	−0.250111	−	0.968217i	$-0.580467\pi$
$227$	6.98084	−	4.03039i	0.463334	−	0.267506i	0.713445	+	0.700711i	$0.247134\pi$
$228$		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
$233$	24.0900			1.57819			0.789094	−	0.614272i	$-0.210550\pi$
$233$	24.0900			1.57819			0.789094	+	0.614272i	$0.210550\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	15.3384	−	26.5669i	0.996336	−	1.72570i
$238$		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	−0.262308	−	0.964984i	$-0.584483\pi$
$241$	6.86541	−	3.96374i	0.442240	−	0.255327i	0.704547	+	0.709657i	$0.251150\pi$
$242$		0			0
$243$	10.1286	+	17.5432i	0.649750	+	1.12540i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.4221	−	14.8602i	−0.790401	−	0.945529i
$248$		0			0
$249$	28.4368	+	16.4180i	1.80211	+	1.04045i
$250$		0			0
$251$	11.3112	+	19.5916i	0.713956	+	1.23661i	0.963361	+	0.268209i	$0.0864317\pi$
$251$	11.3112	+	19.5916i	0.713956	+	1.23661i	−0.249405	+	0.968399i	$0.580235\pi$
$252$		0			0
$253$	0.160691	−	0.0927749i	0.0101025	−	0.00583271i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.8982	+	22.3403i	−0.804566	+	1.39355i	0.112018	+	0.993706i	$0.464269\pi$
$257$	−12.8982	+	22.3403i	−0.804566	+	1.39355i	−0.916584	+	0.399843i	$0.869065\pi$
$258$		0			0
$259$	0.905432			0.0562608
$260$		0			0
$261$	−11.9614			−0.740393
$262$		0			0
$263$	0.795286	−	1.37748i	0.0490394	−	0.0849388i	−0.840464	−	0.541868i	$-0.817717\pi$
$263$	0.795286	−	1.37748i	0.0490394	−	0.0849388i	0.889503	+	0.456929i	$0.151051\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.701043	+	0.404747i	−0.0429031	+	0.0247701i
$268$		0			0
$269$	13.9114	+	24.0952i	0.848192	+	1.46911i	0.882820	+	0.469712i	$0.155642\pi$
$269$	13.9114	+	24.0952i	0.848192	+	1.46911i	−0.0346278	+	0.999400i	$0.511025\pi$
$270$		0			0
$271$	−20.3520	−	11.7502i	−1.23629	−	0.713774i	−0.267959	−	0.963430i	$-0.586349\pi$
$271$	−20.3520	−	11.7502i	−1.23629	−	0.713774i	−0.968335	+	0.249656i	$0.919682\pi$
$272$		0			0
$273$	3.31197	−	0.577640i	0.200450	−	0.0349603i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.49837	+	2.59525i	0.0900283	+	0.155934i	0.907523	−	0.420003i	$-0.137971\pi$
$277$	1.49837	+	2.59525i	0.0900283	+	0.155934i	−0.817494	+	0.575936i	$0.804638\pi$
$278$		0			0
$279$	16.6150	−	9.59270i	0.994716	−	0.574300i
$280$		0			0
$281$			24.6085i			1.46802i	0.679138	+	0.734011i	$0.262354\pi$
$281$			24.6085i			1.46802i	−0.679138	+	0.734011i	$0.737646\pi$
$282$		0			0
$283$	−4.08444	+	7.07446i	−0.242795	+	0.420533i	−0.961509	−	0.274772i	$-0.911397\pi$
$283$	−4.08444	+	7.07446i	−0.242795	+	0.420533i	0.718715	+	0.695305i	$0.244731\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.09131			−0.182474
$288$		0			0
$289$	8.26023	−	14.3071i	0.485896	−	0.841597i
$290$		0			0
$291$			20.6405i			1.20997i
$292$		0			0
$293$	6.49837	−	3.75184i	0.379639	−	0.219185i	−0.298022	−	0.954559i	$-0.596327\pi$
$293$	6.49837	−	3.75184i	0.379639	−	0.219185i	0.677661	+	0.735374i	$0.262994\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.96128	−	1.13234i	−0.113805	−	0.0657053i
$298$		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
$303$	4.78561	+	8.28893i	0.274926	+	0.476186i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	5.95293i		−	0.339752i	−0.985465	−	0.169876i	$-0.945663\pi$
$307$		−	5.95293i		−	0.339752i	0.985465	−	0.169876i	$-0.0543367\pi$
$308$		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
$313$	17.0073			0.961312			0.480656	−	0.876909i	$-0.340399\pi$
$313$	17.0073			0.961312			0.480656	+	0.876909i	$0.340399\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.09300i		−	0.173720i	−0.996221	−	0.0868601i	$-0.972317\pi$
$317$		−	3.09300i		−	0.173720i	0.996221	−	0.0868601i	$-0.0276833\pi$
$318$		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
$323$	3.22151	+	1.85994i	0.179250	+	0.103490i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	30.6664	+	17.7053i	1.69586	+	0.979103i
$328$		0			0
$329$	−0.692481	−	1.19941i	−0.0381777	−	0.0661258i
$330$		0			0
$331$	19.5481	−	11.2861i	1.07446	−	0.620340i	0.145064	−	0.989422i	$-0.453661\pi$
$331$	19.5481	−	11.2861i	1.07446	−	0.620340i	0.929397	+	0.369082i	$0.120328\pi$
$332$		0			0
$333$			5.52442i			0.302736i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−18.0603			−0.983808			−0.491904	−	0.870649i	$-0.663699\pi$
$337$	−18.0603			−0.983808			−0.491904	+	0.870649i	$0.663699\pi$
$338$		0			0
$339$	−20.7575			−1.12739
$340$		0			0
$341$	−6.81119	+	11.7973i	−0.368847	+	0.638861i
$342$		0			0
$343$		−	5.53335i		−	0.298773i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.2359	+	22.9252i	0.710538	+	1.23069i	0.964655	+	0.263514i	$0.0848816\pi$
$347$	13.2359	+	22.9252i	0.710538	+	1.23069i	−0.254118	+	0.967173i	$0.581785\pi$
$348$		0			0
$349$	10.7190	+	6.18860i	0.573773	+	0.331268i	0.758655	−	0.651493i	$-0.225857\pi$
$349$	10.7190	+	6.18860i	0.573773	+	0.331268i	−0.184882	+	0.982761i	$0.559190\pi$
$350$		0			0
$351$	−0.809996	−	4.64422i	−0.0432344	−	0.247890i
$352$		0			0
$353$	−16.6978	−	9.64047i	−0.888733	−	0.513110i	−0.0152053	−	0.999884i	$-0.504840\pi$
$353$	−16.6978	−	9.64047i	−0.888733	−	0.513110i	−0.873528	+	0.486774i	$0.838174\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.559192	+	0.322849i	−0.0295956	+	0.0170870i
$358$		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
$363$	18.6580			0.979290
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.68718	−	6.38638i	0.192469	−	0.333366i	−0.753599	−	0.657335i	$-0.771684\pi$
$367$	3.68718	−	6.38638i	0.192469	−	0.333366i	0.946068	+	0.323968i	$0.105017\pi$
$368$		0			0
$369$		−	18.8614i		−	0.981883i
$370$		0			0
$371$	4.05756	−	2.34263i	0.210658	−	0.121624i
$372$		0			0
$373$	−14.1574	−	24.5214i	−0.733044	−	1.26967i	−0.955576	−	0.294744i	$-0.904766\pi$
$373$	−14.1574	−	24.5214i	−0.733044	−	1.26967i	0.222532	−	0.974925i	$-0.428568\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.6022	+	6.07772i	0.855059	+	0.313018i
$378$		0			0
$379$	9.02975	+	5.21333i	0.463827	+	0.267791i	0.713652	−	0.700500i	$-0.247040\pi$
$379$	9.02975	+	5.21333i	0.463827	+	0.267791i	−0.249825	+	0.968291i	$0.580373\pi$
$380$		0			0
$381$	−14.1761	−	24.5537i	−0.726262	−	1.25792i
$382$		0			0
$383$	9.39811	−	5.42600i	0.480221	−	0.277256i	−0.240288	−	0.970702i	$-0.577242\pi$
$383$	9.39811	−	5.42600i	0.480221	−	0.277256i	0.720509	+	0.693446i	$0.243908\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.33105	+	12.6978i	−0.372658	+	0.645463i
$388$		0			0
$389$	20.2893			1.02871			0.514353	−	0.857578i	$-0.328032\pi$
$389$	20.2893			1.02871			0.514353	+	0.857578i	$0.328032\pi$
$390$		0			0
$391$	−0.0741836			−0.00375163
$392$		0			0
$393$	2.46953	−	4.27736i	0.124572	−	0.215764i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.8695	+	12.6263i	−1.09760	+	0.633698i	−0.935589	−	0.353091i	$-0.885130\pi$
$397$	−21.8695	+	12.6263i	−1.09760	+	0.633698i	−0.162008	+	0.986789i	$0.551797\pi$
$398$		0			0
$399$	2.50445	+	4.33784i	0.125380	+	0.217164i
$400$		0			0
$401$	10.8377	+	6.25714i	0.541208	+	0.312467i	0.745568	−	0.666429i	$-0.232178\pi$
$401$	10.8377	+	6.25714i	0.541208	+	0.312467i	−0.204360	+	0.978896i	$0.565511\pi$
$402$		0			0
$403$	−27.9355	+	4.87223i	−1.39157	+	0.242703i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.96128	−	3.39703i	−0.0972169	−	0.168385i
$408$		0			0
$409$	5.19248	−	2.99788i	0.256752	−	0.148236i	−0.366100	−	0.930575i	$-0.619307\pi$
$409$	5.19248	−	2.99788i	0.256752	−	0.148236i	0.622852	+	0.782340i	$0.285974\pi$
$410$		0			0
$411$		−	42.0575i		−	2.07454i
$412$		0			0
$413$	1.45435	−	2.51900i	0.0715637	−	0.123952i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−22.9497			−1.12385
$418$		0			0
$419$	5.48516	−	9.50057i	0.267968	−	0.464133i	−0.700369	−	0.713781i	$-0.746981\pi$
$419$	5.48516	−	9.50057i	0.267968	−	0.464133i	0.968337	+	0.249647i	$0.0803147\pi$
$420$		0			0
$421$		−	36.6085i		−	1.78419i	−0.451848	−	0.892095i	$-0.649235\pi$
$421$		−	36.6085i		−	1.78419i	0.451848	−	0.892095i	$-0.350765\pi$
$422$		0			0
$423$	7.31812	−	4.22512i	0.355819	−	0.205432i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.00856	+	1.73699i	0.145595	+	0.0840590i
$428$		0			0
$429$	−9.34135	−	11.1747i	−0.451005	−	0.539521i
$430$		0			0
$431$	−10.4873	−	6.05484i	−0.505155	−	0.291651i	0.225685	−	0.974200i	$-0.427538\pi$
$431$	−10.4873	−	6.05484i	−0.505155	−	0.291651i	−0.730840	+	0.682549i	$0.760871\pi$
$432$		0			0
$433$	4.50897	+	7.80977i	0.216687	+	0.375314i	0.953793	−	0.300464i	$-0.0971414\pi$
$433$	4.50897	+	7.80977i	0.216687	+	0.375314i	−0.737106	+	0.675777i	$0.763808\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			0.575468i			0.0275284i
$438$		0			0
$439$	−6.07547	+	10.5230i	−0.289966	+	0.502236i	−0.973801	−	0.227400i	$-0.926977\pi$
$439$	−6.07547	+	10.5230i	−0.289966	+	0.502236i	0.683835	+	0.729637i	$0.260311\pi$
$440$		0			0
$441$	16.6857			0.794557
$442$		0			0
$443$	−15.3116			−0.727476			−0.363738	−	0.931501i	$-0.618500\pi$
$443$	−15.3116			−0.727476			−0.363738	+	0.931501i	$0.618500\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	20.7173i		−	0.979895i
$448$		0			0
$449$	−19.6929	+	11.3697i	−0.929365	+	0.536569i	−0.886611	−	0.462516i	$-0.846947\pi$
$449$	−19.6929	+	11.3697i	−0.929365	+	0.536569i	−0.0427543	+	0.999086i	$0.513613\pi$
$450$		0			0
$451$	6.69615	+	11.5981i	0.315310	+	0.546132i
$452$		0			0
$453$	−8.96658	−	5.17686i	−0.421287	−	0.243230i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.30548	+	5.37252i	0.435292	+	0.251316i	0.701599	−	0.712572i	$-0.252470\pi$
$457$	9.30548	+	5.37252i	0.435292	+	0.251316i	−0.266307	+	0.963888i	$0.585803\pi$
$458$		0			0
$459$	0.452716	+	0.784127i	0.0211310	+	0.0365999i
$460$		0			0
$461$	10.2973	−	5.94516i	0.479594	−	0.276894i	−0.240653	−	0.970611i	$-0.577362\pi$
$461$	10.2973	−	5.94516i	0.479594	−	0.276894i	0.720247	+	0.693717i	$0.244028\pi$
$462$		0			0
$463$		−	3.39726i		−	0.157884i	−0.996879	−	0.0789420i	$-0.974846\pi$
$463$		−	3.39726i		−	0.157884i	0.996879	−	0.0789420i	$-0.0251542\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.39426			0.295891			0.147946	−	0.988996i	$-0.452734\pi$
$467$	6.39426			0.295891			0.147946	+	0.988996i	$0.452734\pi$
$468$		0			0
$469$	−0.530943			−0.0245167
$470$		0			0
$471$	−4.85945	+	8.41682i	−0.223912	+	0.387826i
$472$		0			0
$473$		−	10.4107i		−	0.478683i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	14.2934	+	24.7569i	0.654450	+	1.13354i
$478$		0			0
$479$	14.1330	+	8.15968i	0.645752	+	0.372825i	0.786827	−	0.617174i	$-0.211722\pi$
$479$	14.1330	+	8.15968i	0.645752	+	0.372825i	−0.141075	+	0.989999i	$0.545056\pi$
$480$		0			0
$481$	2.80702	−	7.66781i	0.127989	−	0.349622i
$482$		0			0
$483$	−0.0865072	−	0.0499450i	−0.00393622	−	0.00227258i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.3356	−	5.96728i	0.468352	−	0.270403i	−0.247197	−	0.968965i	$-0.579510\pi$
$487$	10.3356	−	5.96728i	0.468352	−	0.270403i	0.715550	+	0.698562i	$0.246176\pi$
$488$		0			0
$489$		−	8.62166i		−	0.389885i
$490$		0			0
$491$	−17.0259	+	29.4896i	−0.768366	+	1.33085i	0.170082	+	0.985430i	$0.445597\pi$
$491$	−17.0259	+	29.4896i	−0.768366	+	1.33085i	−0.938448	+	0.345419i	$0.887737\pi$
$492$		0			0
$493$	−3.39557			−0.152929
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.775227	−	1.34273i	0.0347737	−	0.0602298i
$498$		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
$503$	−9.09433	−	15.7518i	−0.405496	−	0.702340i	0.588883	−	0.808218i	$-0.299568\pi$
$503$	−9.09433	−	15.7518i	−0.405496	−	0.702340i	−0.994379	+	0.105879i	$0.966235\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.37592	−	29.8388i	0.238753	−	1.32519i
$508$		0			0
$509$	−25.1265	−	14.5068i	−1.11371	−	0.643001i	−0.173923	−	0.984759i	$-0.555644\pi$
$509$	−25.1265	−	14.5068i	−1.11371	−	0.643001i	−0.939788	+	0.341758i	$0.888978\pi$
$510$		0			0
$511$	2.04402	+	3.54035i	0.0904223	+	0.156616i
$512$		0			0
$513$	6.08275	−	3.51187i	0.268560	−	0.155053i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.00000	+	5.19615i	−0.131940	+	0.228527i
$518$		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
$523$	−4.63870	+	8.03447i	−0.202836	+	0.351323i	−0.949441	−	0.313945i	$-0.898349\pi$
$523$	−4.63870	+	8.03447i	−0.202836	+	0.351323i	0.746605	+	0.665268i	$0.231683\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.71662	−	2.72314i	0.205459	−	0.118622i
$528$		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
$533$	−9.58366	+	26.1793i	−0.415114	+	1.13395i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.79600	−	10.0390i	−0.250116	−	0.433214i
$538$		0			0
$539$	−10.2602	+	5.92375i	−0.441940	+	0.255154i
$540$		0			0
$541$			24.3814i			1.04824i	0.851644	+	0.524120i	$0.175606\pi$
$541$			24.3814i			1.04824i	−0.851644	+	0.524120i	$0.824394\pi$
$542$		0			0
$543$	20.2550	−	35.0827i	0.869226	−	1.50554i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−26.5270			−1.13421			−0.567106	−	0.823645i	$-0.691937\pi$
$547$	−26.5270			−1.13421			−0.567106	+	0.823645i	$0.691937\pi$
$548$		0			0
$549$	−10.5981	+	18.3565i	−0.452317	+	0.783436i
$550$		0			0
$551$			26.3406i			1.12215i
$552$		0			0
$553$	4.55422	−	2.62938i	0.193665	−	0.111813i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.78142	+	1.60586i	0.117853	+	0.0680423i	0.557768	−	0.829997i	$-0.311658\pi$
$557$	2.78142	+	1.60586i	0.117853	+	0.0680423i	−0.439915	+	0.898039i	$0.644991\pi$
$558$		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
$563$	17.1426	+	29.6918i	0.722474	+	1.25136i	0.960005	+	0.279982i	$0.0903284\pi$
$563$	17.1426	+	29.6918i	0.722474	+	1.25136i	−0.237531	+	0.971380i	$0.576338\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			4.14500i			0.174074i
$568$		0			0
$569$	−17.8228	+	30.8701i	−0.747172	+	1.29414i	0.202001	+	0.979385i	$0.435256\pi$
$569$	−17.8228	+	30.8701i	−0.747172	+	1.29414i	−0.949173	+	0.314755i	$0.898078\pi$
$570$		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
$573$	−47.8219			−1.99779
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	18.4475i		−	0.767981i	−0.923337	−	0.383991i	$-0.874550\pi$
$577$		−	18.4475i		−	0.767981i	0.923337	−	0.383991i	$-0.125450\pi$
$578$		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
$583$	−17.5784	−	10.1489i	−0.728021	−	0.420323i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.2316	+	21.4957i	1.53671	+	0.887222i	0.999028	+	0.0440760i	$0.0140344\pi$
$587$	37.2316	+	21.4957i	1.53671	+	0.887222i	0.537685	+	0.843146i	$0.319299\pi$
$588$		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
$593$			12.8614i			0.528153i	0.964502	+	0.264076i	$0.0850671\pi$
$593$			12.8614i			0.528153i	−0.964502	+	0.264076i	$0.914933\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−56.9060			−2.32901
$598$		0			0
$599$	28.3170			1.15700			0.578500	−	0.815682i	$-0.303638\pi$
$599$	28.3170			1.15700			0.578500	+	0.815682i	$0.303638\pi$
$600$		0			0
$601$	3.56734	−	6.17882i	0.145515	−	0.252039i	−0.784050	−	0.620698i	$-0.786849\pi$
$601$	3.56734	−	6.17882i	0.145515	−	0.252039i	0.929565	+	0.368658i	$0.120183\pi$
$602$		0			0
$603$		−	3.23951i		−	0.131923i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.0901	−	19.2086i	−0.450133	−	0.779653i	0.548261	−	0.836307i	$-0.315290\pi$
$607$	−11.0901	−	19.2086i	−0.450133	−	0.779653i	−0.998394	+	0.0566544i	$0.981957\pi$
$608$		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
$613$	0.279399	+	0.161311i	0.0112848	+	0.00651530i	0.505632	−	0.862749i	$-0.331259\pi$
$613$	0.279399	+	0.161311i	0.0112848	+	0.00651530i	−0.494347	+	0.869265i	$0.664593\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.2150	−	18.5993i	1.29693	−	0.748781i	0.317055	−	0.948407i	$-0.397306\pi$
$617$	32.2150	−	18.5993i	1.29693	−	0.748781i	0.979872	+	0.199626i	$0.0639728\pi$
$618$		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
$623$	−0.138767			−0.00555959
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.8499	−	18.7926i	0.433304	−	0.750504i
$628$		0			0
$629$			1.56825i			0.0625304i
$630$		0			0
$631$	29.0824	−	16.7908i	1.15775	−	0.668429i	0.206989	−	0.978343i	$-0.433634\pi$
$631$	29.0824	−	16.7908i	1.15775	−	0.668429i	0.950765	+	0.309914i	$0.100300\pi$
$632$		0			0
$633$	−2.05356	−	3.55688i	−0.0816218	−	0.141373i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−23.1595	−	8.47818i	−0.917612	−	0.335918i
$638$		0			0
$639$	8.19257	+	4.72998i	0.324093	+	0.187115i
$640$		0			0
$641$	16.5900	+	28.7347i	0.655266	+	1.13495i	0.981827	+	0.189778i	$0.0607767\pi$
$641$	16.5900	+	28.7347i	0.655266	+	1.13495i	−0.326561	+	0.945176i	$0.605890\pi$
$642$		0			0
$643$	−27.1643	+	15.6833i	−1.07125	+	0.618489i	−0.928524	−	0.371273i	$-0.878922\pi$
$643$	−27.1643	+	15.6833i	−1.07125	+	0.618489i	−0.142730	+	0.989762i	$0.545588\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.79529	+	16.9659i	−0.385092	+	0.667000i	−0.991782	−	0.127939i	$-0.959164\pi$
$647$	−9.79529	+	16.9659i	−0.385092	+	0.667000i	0.606690	+	0.794939i	$0.292497\pi$
$648$		0			0
$649$	−12.6012			−0.494639
$650$		0			0
$651$	7.33355			0.287424
$652$		0			0
$653$	3.55626	−	6.15962i	0.139167	−	0.241044i	−0.788015	−	0.615657i	$-0.788891\pi$
$653$	3.55626	−	6.15962i	0.139167	−	0.241044i	0.927182	+	0.374612i	$0.122224\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−21.6012	+	12.4714i	−0.842742	+	0.486557i
$658$		0			0
$659$	−9.29211	−	16.0944i	−0.361969	−	0.626949i	0.626316	−	0.779570i	$-0.284562\pi$
$659$	−9.29211	−	16.0944i	−0.361969	−	0.626949i	−0.988285	+	0.152621i	$0.951229\pi$
$660$		0			0
$661$	14.5413	+	8.39540i	0.565590	+	0.326543i	0.755386	−	0.655280i	$-0.227449\pi$
$661$	14.5413	+	8.39540i	0.565590	+	0.326543i	−0.189796	+	0.981823i	$0.560783\pi$
$662$		0			0
$663$	1.00050	+	5.73650i	0.0388563	+	0.222787i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.262648	−	0.454919i	−0.0101698	−	0.0176146i
$668$		0			0
$669$	22.8621	−	13.1995i	0.883902	−	0.510321i
$670$		0			0
$671$		−	15.0502i		−	0.581005i
$672$		0			0
$673$	−11.2957	+	19.5647i	−0.435417	+	0.754165i	−0.997330	−	0.0730322i	$-0.976732\pi$
$673$	−11.2957	+	19.5647i	−0.435417	+	0.754165i	0.561912	+	0.827197i	$0.310066\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.31616			−0.204317			−0.102158	−	0.994768i	$-0.532575\pi$
$677$	−5.31616			−0.204317			−0.102158	+	0.994768i	$0.532575\pi$
$678$		0			0
$679$	−1.76914	+	3.06424i	−0.0678935	+	0.117595i
$680$		0			0
$681$			18.7997i			0.720407i
$682$		0			0
$683$	−3.42419	+	1.97695i	−0.131023	+	0.0756461i	−0.564079	−	0.825721i	$-0.690769\pi$
$683$	−3.42419	+	1.97695i	−0.131023	+	0.0756461i	0.433056	+	0.901367i	$0.357435\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−23.3719	−	13.4938i	−0.891694	−	0.514820i
$688$		0			0
$689$	−7.25976	−	41.6248i	−0.276575	−	1.58578i
$690$		0			0
$691$	−11.1493	−	6.43704i	−0.424139	−	0.244877i	0.272708	−	0.962097i	$-0.412081\pi$
$691$	−11.1493	−	6.43704i	−0.424139	−	0.244877i	−0.696846	+	0.717220i	$0.745414\pi$
$692$		0			0
$693$	0.844610	+	1.46291i	0.0320841	+	0.0555713i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	5.35430i		−	0.202809i
$698$		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
$703$	12.1655			0.458830
$704$		0			0
$705$		0			0
$706$		0			0
$707$			1.64074i			0.0617065i
$708$		0			0
$709$	−17.1183	+	9.88325i	−0.642891	+	0.371173i	−0.785727	−	0.618573i	$-0.787711\pi$
$709$	−17.1183	+	9.88325i	−0.642891	+	0.371173i	0.142836	+	0.989746i	$0.454378\pi$
$710$		0			0
$711$	16.0429	+	27.7872i	0.601657	+	1.04210i
$712$		0			0
$713$	0.729664	+	0.421272i	0.0273261	+	0.0157767i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	62.0253	+	35.8103i	2.31638	+	1.33736i
$718$		0			0
$719$	−22.1234	−	38.3188i	−0.825062	−	1.42905i	−0.901872	−	0.432004i	$-0.857807\pi$
$719$	−22.1234	−	38.3188i	−0.825062	−	1.42905i	0.0768099	−	0.997046i	$-0.475527\pi$
$720$		0			0
$721$	−3.88914	+	2.24539i	−0.144839	+	0.0836228i
$722$		0			0
$723$			18.4889i			0.687608i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	31.4877			1.16781			0.583907	−	0.811821i	$-0.301523\pi$
$727$	31.4877			1.16781			0.583907	+	0.811821i	$0.301523\pi$
$728$		0			0
$729$	−16.1420			−0.597853
$730$		0			0
$731$	−2.08112	+	3.60460i	−0.0769728	+	0.133321i
$732$		0			0
$733$			42.4714i			1.56872i	0.620307	+	0.784359i	$0.287008\pi$
$733$			42.4714i			1.56872i	−0.620307	+	0.784359i	$0.712992\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.15009	+	1.99201i	0.0423640	+	0.0733767i
$738$		0			0
$739$	−11.9368	−	6.89173i	−0.439103	−	0.253516i	0.264114	−	0.964492i	$-0.414921\pi$
$739$	−11.9368	−	6.89173i	−0.439103	−	0.253516i	−0.703217	+	0.710975i	$0.748254\pi$
$740$		0			0
$741$	44.5000	−	7.76123i	1.63475	−	0.285116i
$742$		0			0
$743$	13.8038	+	7.96961i	0.506411	+	0.292377i	0.731357	−	0.681995i	$-0.238887\pi$
$743$	13.8038	+	7.96961i	0.506411	+	0.292377i	−0.224946	+	0.974371i	$0.572221\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−29.7430	+	17.1721i	−1.08824	+	0.628296i
$748$		0			0
$749$		−	7.03787i		−	0.257158i
$750$		0			0
$751$	−0.758540	+	1.31383i	−0.0276795	+	0.0479423i	−0.879533	−	0.475837i	$-0.842145\pi$
$751$	−0.758540	+	1.31383i	−0.0276795	+	0.0479423i	0.851854	+	0.523780i	$0.175478\pi$
$752$		0			0
$753$	−52.7610			−1.92272
$754$		0			0
$755$		0			0
$756$		0			0
$757$	23.7414	−	41.1214i	0.862897	−	1.49458i	−0.00622310	−	0.999981i	$-0.501981\pi$
$757$	23.7414	−	41.1214i	0.862897	−	1.49458i	0.869120	−	0.494601i	$-0.164686\pi$
$758$		0			0
$759$			0.432748i			0.0157078i
$760$		0			0
$761$	−33.3805	+	19.2722i	−1.21004	+	0.698618i	−0.962768	−	0.270327i	$-0.912868\pi$
$761$	−33.3805	+	19.2722i	−1.21004	+	0.698618i	−0.247274	+	0.968946i	$0.579535\pi$
$762$		0			0
$763$	3.03512	+	5.25697i	0.109879	+	0.190315i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.8238	−	20.1258i	−0.607473	−	0.726700i
$768$		0			0
$769$	34.5236	+	19.9322i	1.24495	+	0.718775i	0.970099	−	0.242711i	$-0.0780366\pi$
$769$	34.5236	+	19.9322i	1.24495	+	0.718775i	0.274856	+	0.961486i	$0.411370\pi$
$770$		0			0
$771$	−30.0817	−	52.1031i	−1.08337	−	1.87645i
$772$		0			0
$773$	−28.5396	+	16.4774i	−1.02650	+	0.592650i	−0.915980	−	0.401224i	$-0.868585\pi$
$773$	−28.5396	+	16.4774i	−1.02650	+	0.592650i	−0.110519	+	0.993874i	$0.535251\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.05585	+	1.82878i	−0.0378783	+	0.0656071i
$778$		0			0
$779$	−41.5352			−1.48815
$780$		0			0
$781$	−6.71695			−0.240351
$782$		0			0
$783$	−3.20569	+	5.55242i	−0.114562	+	0.198427i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.934698	−	0.539648i	0.0333184	−	0.0192364i	−0.483248	−	0.875483i	$-0.660543\pi$
$787$	0.934698	−	0.539648i	0.0333184	−	0.0192364i	0.516567	+	0.856247i	$0.327210\pi$
$788$		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
$793$	24.0372	−	20.0935i	0.853584	−	0.713541i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.55071	+	16.5423i	0.338304	+	0.585959i	0.984114	−	0.177539i	$-0.0568136\pi$
$797$	9.55071	+	16.5423i	0.338304	+	0.585959i	−0.645810	+	0.763498i	$0.723480\pi$
$798$		0			0
$799$	2.07744	−	1.19941i	0.0734947	−	0.0424322i
$800$		0			0
$801$		−	0.846678i		−	0.0299159i
$802$		0			0
$803$	8.85521	−	15.3377i	0.312494	−	0.541255i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−64.8896			−2.28422
$808$		0			0
$809$	−0.881702	+	1.52715i	−0.0309990	+	0.0536918i	−0.881109	−	0.472914i	$-0.843202\pi$
$809$	−0.881702	+	1.52715i	−0.0309990	+	0.0536918i	0.850110	+	0.526606i	$0.176536\pi$
$810$		0			0
$811$		−	52.3298i		−	1.83755i	−0.394784	−	0.918774i	$-0.629181\pi$
$811$		−	52.3298i		−	1.83755i	0.394784	−	0.918774i	$-0.370819\pi$
$812$		0			0
$813$	47.4658	−	27.4044i	1.66470	−	0.961113i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	27.9621	+	16.1439i	0.978270	+	0.564804i
$818$		0			0
$819$	−1.20882	+	3.30209i	−0.0422397	+	0.115384i
$820$		0			0
$821$	−12.3585	−	7.13517i	−0.431314	−	0.249019i	0.268592	−	0.963254i	$-0.413442\pi$
$821$	−12.3585	−	7.13517i	−0.431314	−	0.249019i	−0.699906	+	0.714235i	$0.746775\pi$
$822$		0			0
$823$	−21.8573	−	37.8579i	−0.761896	−	1.31964i	−0.941872	−	0.335972i	$-0.890935\pi$
$823$	−21.8573	−	37.8579i	−0.761896	−	1.31964i	0.179976	−	0.983671i	$-0.442398\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			22.5962i			0.785748i	0.919592	+	0.392874i	$0.128519\pi$
$827$			22.5962i			0.785748i	−0.919592	+	0.392874i	$0.871481\pi$
$828$		0			0
$829$	27.0473	−	46.8473i	0.939392	−	1.62708i	0.172784	−	0.984960i	$-0.444724\pi$
$829$	27.0473	−	46.8473i	0.939392	−	1.62708i	0.766608	−	0.642116i	$-0.221943\pi$
$830$		0			0
$831$	−6.98914			−0.242450
$832$		0			0
$833$	4.73668			0.164116
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	10.2835i		−	0.355449i
$838$		0			0
$839$	19.2550	−	11.1169i	0.664755	−	0.383796i	−0.129332	−	0.991601i	$-0.541283\pi$
$839$	19.2550	−	11.1169i	0.664755	−	0.383796i	0.794086	+	0.607805i	$0.207950\pi$
$840$		0			0
$841$	2.47796	+	4.29196i	0.0854471	+	0.147999i
$842$		0			0
$843$	−49.7039	−	28.6966i	−1.71189	−	0.988362i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.76993	+	1.59922i	0.0951758	+	0.0549498i
$848$		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
$853$			16.5312i			0.566019i	0.959117	+	0.283009i	$0.0913328\pi$
$853$			16.5312i			0.566019i	−0.959117	+	0.283009i	$0.908667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5842			−0.942259			−0.471129	−	0.882064i	$-0.656154\pi$
$857$	−27.5842			−0.942259			−0.471129	+	0.882064i	$0.656154\pi$
$858$		0			0
$859$	−32.5016			−1.10894			−0.554469	−	0.832204i	$-0.687079\pi$
$859$	−32.5016			−1.10894			−0.554469	+	0.832204i	$0.687079\pi$
$860$		0			0
$861$	3.60485	−	6.24378i	0.122853	−	0.212787i
$862$		0			0
$863$			29.7986i			1.01436i	0.861842	+	0.507178i	$0.169311\pi$
$863$			29.7986i			1.01436i	−0.861842	+	0.507178i	$0.830689\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.2649	+	33.3678i	0.654270	+	1.13323i
$868$		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
$873$	−18.6962	−	10.7943i	−0.632772	−	0.365331i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.4739	−	7.20181i	0.421214	−	0.243188i	−0.274383	−	0.961621i	$-0.588474\pi$
$877$	12.4739	−	7.20181i	0.421214	−	0.243188i	0.695597	+	0.718433i	$0.255140\pi$
$878$		0			0
$879$			17.5004i			0.590274i
$880$		0			0
$881$	−3.68457	+	6.38186i	−0.124136	+	0.215010i	−0.921395	−	0.388627i	$-0.872949\pi$
$881$	−3.68457	+	6.38186i	−0.124136	+	0.215010i	0.797259	+	0.603638i	$0.206283\pi$
$882$		0			0
$883$	−24.3646			−0.819933			−0.409967	−	0.912101i	$-0.634460\pi$
$883$	−24.3646			−0.819933			−0.409967	+	0.912101i	$0.634460\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.0322	+	20.8404i	−0.404002	+	0.699752i	−0.994205	−	0.107503i	$-0.965714\pi$
$887$	−12.0322	+	20.8404i	−0.404002	+	0.699752i	0.590203	+	0.807255i	$0.299048\pi$
$888$		0			0
$889$		−	4.86025i		−	0.163008i
$890$		0			0
$891$	15.5514	−	8.97859i	0.520990	−	0.300794i
$892$		0			0
$893$	−9.30426	−	16.1154i	−0.311355	−	0.539283i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.691157	+	0.577762i	−0.0230771	+	0.0192909i
$898$		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
$903$	−4.85367	+	2.80227i	−0.161520	+	0.0932537i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−18.7536	+	32.4823i	−0.622705	+	1.07856i	0.366275	+	0.930507i	$0.380633\pi$
$907$	−18.7536	+	32.4823i	−0.622705	+	1.07856i	−0.988980	+	0.148050i	$0.952700\pi$
$908$		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
$913$	12.1929	−	21.1187i	0.403526	−	0.698927i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.733244	−	0.423339i	0.0242139	−	0.0139799i
$918$		0			0
$919$	15.8332	+	27.4239i	0.522288	+	0.904630i	0.999664	+	0.0259305i	$0.00825486\pi$
$919$	15.8332	+	27.4239i	0.522288	+	0.904630i	−0.477375	+	0.878699i	$0.658412\pi$
$920$		0			0
$921$	12.0236	+	6.94185i	0.396192	+	0.228742i
$922$		0			0
$923$	−8.96780	−	10.7279i	−0.295179	−	0.353112i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.7001	−	23.7292i	−0.449970	−	0.779371i
$928$		0			0
$929$	25.7537	−	14.8689i	0.844952	−	0.487833i	−0.0139925	−	0.999902i	$-0.504454\pi$
$929$	25.7537	−	14.8689i	0.844952	−	0.487833i	0.858944	+	0.512069i	$0.171121\pi$
$930$		0			0
$931$		−	36.7441i		−	1.20424i
$932$		0			0
$933$	20.9024	−	36.2040i	0.684313	−	1.18527i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	52.3124			1.70897			0.854486	−	0.519474i	$-0.173872\pi$
$937$	52.3124			1.70897			0.854486	+	0.519474i	$0.173872\pi$
$938$		0			0
$939$	−19.8327	+	34.3512i	−0.647214	+	1.12101i
$940$		0			0
$941$		−	29.5767i		−	0.964174i	−0.876123	−	0.482087i	$-0.839879\pi$
$941$		−	29.5767i		−	0.964174i	0.876123	−	0.482087i	$-0.160121\pi$
$942$		0			0
$943$	0.717340	−	0.414157i	0.0233598	−	0.0134868i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−41.5978	−	24.0165i	−1.35175	−	0.780432i	−0.363254	−	0.931690i	$-0.618334\pi$
$947$	−41.5978	−	24.0165i	−1.35175	−	0.780432i	−0.988494	+	0.151258i	$0.951668\pi$
$948$		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
$953$	−14.8912	−	25.7923i	−0.482373	−	0.835494i	0.517423	−	0.855730i	$-0.326891\pi$
$953$	−14.8912	−	25.7923i	−0.482373	−	0.835494i	−0.999795	+	0.0202363i	$0.993558\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			19.8079i			0.640299i
$958$		0			0
$959$	3.60485	−	6.24378i	0.116407	−	0.201622i
$960$		0			0
$961$	−30.8564			−0.995368
$962$		0			0
$963$	42.9410			1.38376
$964$		0			0
$965$		0			0
$966$		0			0
$967$			20.6730i			0.664798i	0.943139	+	0.332399i	$0.107858\pi$
$967$			20.6730i			0.664798i	−0.943139	+	0.332399i	$0.892142\pi$
$968$		0			0
$969$	−7.51336	+	4.33784i	−0.241364	+	0.139352i
$970$		0			0
$971$	9.99307	+	17.3085i	0.320693	+	0.555456i	0.980631	−	0.195863i	$-0.0627509\pi$
$971$	9.99307	+	17.3085i	0.320693	+	0.555456i	−0.659938	+	0.751320i	$0.729418\pi$
$972$		0			0
$973$	−3.40706	−	1.96707i	−0.109225	−	0.0630613i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.5147	+	22.8138i	1.26419	+	0.729878i	0.973882	−	0.227056i	$-0.0729101\pi$
$977$	39.5147	+	22.8138i	1.26419	+	0.729878i	0.290305	+	0.956934i	$0.406243\pi$
$978$		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
$983$		−	54.1966i		−	1.72860i	−0.502975	−	0.864301i	$-0.667761\pi$
$983$		−	54.1966i		−	1.72860i	0.502975	−	0.864301i	$-0.332239\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.23007			0.102814
$988$		0			0
$989$	−0.643899			−0.0204748
$990$		0			0
$991$	−23.2639	+	40.2943i	−0.739002	+	1.27999i	0.213943	+	0.976846i	$0.431369\pi$
$991$	−23.2639	+	40.2943i	−0.739002	+	1.27999i	−0.952945	+	0.303143i	$0.901964\pi$
$992$		0			0
$993$			52.6440i			1.67061i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−19.5514	−	33.8641i	−0.619200	−	1.07249i	−0.989632	−	0.143626i	$-0.954124\pi$
$997$	−19.5514	−	33.8641i	−0.619200	−	1.07249i	0.370432	−	0.928860i	$-0.379210\pi$
$998$		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.y.b.901.1		8
5.2	odd	4		1300.2.ba.c.849.3		8
5.3	odd	4		1300.2.ba.b.849.2		8
5.4	even	2		260.2.x.a.121.4	yes	8
13.10	even	6	inner	1300.2.y.b.101.1		8
15.14	odd	2		2340.2.dj.d.901.3		8
20.19	odd	2		1040.2.da.c.641.1		8
65.4	even	6		3380.2.f.i.3041.2		8
65.9	even	6		3380.2.f.i.3041.1		8
65.19	odd	12		3380.2.a.p.1.1		4
65.23	odd	12		1300.2.ba.c.49.3		8
65.49	even	6		260.2.x.a.101.4	✓	8
65.59	odd	12		3380.2.a.q.1.1		4
65.62	odd	12		1300.2.ba.b.49.2		8
195.179	odd	6		2340.2.dj.d.361.1		8
260.179	odd	6		1040.2.da.c.881.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.4	✓	8	65.49	even	6
260.2.x.a.121.4	yes	8	5.4	even	2
1040.2.da.c.641.1		8	20.19	odd	2
1040.2.da.c.881.1		8	260.179	odd	6
1300.2.y.b.101.1		8	13.10	even	6	inner
1300.2.y.b.901.1		8	1.1	even	1	trivial
1300.2.ba.b.49.2		8	65.62	odd	12
1300.2.ba.b.849.2		8	5.3	odd	4
1300.2.ba.c.49.3		8	65.23	odd	12
1300.2.ba.c.849.3		8	5.2	odd	4
2340.2.dj.d.361.1		8	195.179	odd	6
2340.2.dj.d.901.3		8	15.14	odd	2
3380.2.a.p.1.1		4	65.19	odd	12
3380.2.a.q.1.1		4	65.59	odd	12
3380.2.f.i.3041.1		8	65.9	even	6
3380.2.f.i.3041.2		8	65.4	even	6

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.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16612 + 2.01978i) q^{3} +(-0.346241 + 0.199902i) q^{7} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})\)	\(q+(-1.16612 + 2.01978i) q^{3} +(-0.346241 + 0.199902i) q^{7} +(-1.21969 - 2.11256i) q^{9} +(1.50000 + 0.866025i) q^{11} +(0.619491 + 3.55193i) q^{13} +(-0.346241 - 0.599706i) q^{17} +(-4.65213 + 2.68591i) q^{19} -0.932442i q^{21} +(0.0535636 - 0.0927749i) q^{23} -1.30752 q^{27} +(2.45174 - 4.24653i) q^{29} +7.86488i q^{31} +(-3.49837 + 2.01978i) q^{33} +(-1.96128 - 1.13234i) q^{37} +(-7.89654 - 2.89075i) q^{39} +(6.69615 + 3.86603i) q^{41} +(-3.00530 - 5.20533i) q^{43} +3.46410i q^{47} +(-3.42008 + 5.92375i) q^{49} +1.61504 q^{51} -11.7189 q^{53} -12.5284i q^{57} +(-6.30059 + 3.63765i) q^{59} +(-4.34461 - 7.52509i) q^{61} +(0.844610 + 0.487636i) q^{63} +(1.15009 + 0.664004i) q^{67} +(0.124924 + 0.216374i) q^{69} +(-3.35847 + 1.93902i) q^{71} -10.2251i q^{73} -0.692481 q^{77} -13.1533 q^{79} +(5.18379 - 8.97859i) q^{81} -14.0791i q^{83} +(5.71806 + 9.90396i) q^{87} +(0.300587 + 0.173544i) q^{89} +(-0.924532 - 1.10599i) q^{91} +(-15.8854 - 9.17142i) q^{93} +(7.66436 - 4.42502i) q^{97} -4.22512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 6 * q^7 - 4 * q^9	\( 8 q + 2 q^{3} - 6 q^{7} - 4 q^{9} + 12 q^{11} + 8 q^{13} - 6 q^{17} + 6 q^{23} - 4 q^{27} + 6 q^{33} - 6 q^{37} - 4 q^{39} + 12 q^{41} - 10 q^{43} - 4 q^{49} - 24 q^{53} - 24 q^{59} - 4 q^{61} - 24 q^{63} + 54 q^{67} - 24 q^{69} - 36 q^{71} - 12 q^{77} - 16 q^{79} + 8 q^{81} + 6 q^{87} - 24 q^{89} - 24 q^{93} + 30 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 6 * q^7 - 4 * q^9 + 12 * q^11 + 8 * q^13 - 6 * q^17 + 6 * q^23 - 4 * q^27 + 6 * q^33 - 6 * q^37 - 4 * q^39 + 12 * q^41 - 10 * q^43 - 4 * q^49 - 24 * q^53 - 24 * q^59 - 4 * q^61 - 24 * q^63 + 54 * q^67 - 24 * q^69 - 36 * q^71 - 12 * q^77 - 16 * q^79 + 8 * q^81 + 6 * q^87 - 24 * q^89 - 24 * q^93 + 30 * q^97

Introduction

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