LMFDB - Embedded newform 260.2.m.c.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(57,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("260.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.m (of order $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.31678304256.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 8x^{5} + 32x^{4} - 20x^{3} + 8x^{2} + 8x + 4 $ x^8 - 2x^7 + 2x^6 + 8x^5 + 32x^4 - 20x^3 + 8x^2 + 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.4
Root			$2.13456 + 2.13456i$ of defining polynomial
Character	$\chi$	$=$	260.57
Dual form			260.2.m.c.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13456 - 2.13456i) q^{3} +(-0.666078 + 2.13456i) q^{5} -2.84356i q^{7} -6.11268i q^{9} +O(q^{10})$	\(q+(2.13456 - 2.13456i) q^{3} +(-0.666078 + 2.13456i) q^{5} -2.84356i q^{7} -6.11268i q^{9} +(2.66608 + 2.66608i) q^{11} +(-0.134559 - 3.60304i) q^{13} +(3.13456 + 5.97812i) q^{15} +(-2.80064 + 2.80064i) q^{17} +(3.97812 + 3.97812i) q^{19} +(-6.06975 - 6.06975i) q^{21} +(-3.66608 - 3.66608i) q^{23} +(-4.11268 - 2.84356i) q^{25} +(-6.64420 - 6.64420i) q^{27} +8.17572i q^{29} +(-3.60304 + 3.60304i) q^{31} +11.3818 q^{33} +(6.06975 + 1.89403i) q^{35} +3.11268i q^{37} +(-7.97812 - 7.40368i) q^{39} +(3.64420 - 3.64420i) q^{41} +(0.998233 + 0.998233i) q^{43} +(13.0479 + 4.07152i) q^{45} +9.46765i q^{47} -1.08585 q^{49} +11.9562i q^{51} +(2.78053 - 2.78053i) q^{53} +(-7.46671 + 3.91508i) q^{55} +16.9831 q^{57} +(3.97812 - 3.97812i) q^{59} -10.9866 q^{61} -17.3818 q^{63} +(7.78053 + 2.11268i) q^{65} +0.574447 q^{67} -15.6509 q^{69} +(-4.73937 + 4.73937i) q^{71} -8.92588 q^{73} +(-14.8485 + 2.70901i) q^{75} +(7.58116 - 7.58116i) q^{77} -5.51895i q^{79} -10.0268 q^{81} -2.75771i q^{83} +(-4.11268 - 7.84356i) q^{85} +(17.4516 + 17.4516i) q^{87} +(-3.36252 + 3.36252i) q^{89} +(-10.2455 + 0.382626i) q^{91} +15.3818i q^{93} +(-11.1413 + 5.84180i) q^{95} +9.12022 q^{97} +(16.2969 - 16.2969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^5	$ 8 q + 2 q^{3} + 2 q^{5} + 14 q^{11} + 14 q^{13} + 10 q^{15} + 2 q^{19} + 4 q^{21} - 22 q^{23} + 12 q^{25} - 16 q^{27} - 6 q^{31} + 16 q^{33} - 4 q^{35} - 34 q^{39} - 8 q^{41} - 14 q^{43} + 22 q^{45} - 24 q^{49} - 8 q^{53} - 30 q^{55} + 16 q^{57} + 2 q^{59} - 12 q^{61} - 64 q^{63} + 32 q^{65} + 20 q^{67} - 20 q^{69} - 22 q^{71} - 28 q^{73} - 14 q^{75} + 8 q^{77} - 20 q^{81} + 12 q^{85} + 12 q^{87} + 4 q^{89} - 6 q^{95} + 12 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^5 + 14 * q^11 + 14 * q^13 + 10 * q^15 + 2 * q^19 + 4 * q^21 - 22 * q^23 + 12 * q^25 - 16 * q^27 - 6 * q^31 + 16 * q^33 - 4 * q^35 - 34 * q^39 - 8 * q^41 - 14 * q^43 + 22 * q^45 - 24 * q^49 - 8 * q^53 - 30 * q^55 + 16 * q^57 + 2 * q^59 - 12 * q^61 - 64 * q^63 + 32 * q^65 + 20 * q^67 - 20 * q^69 - 22 * q^71 - 28 * q^73 - 14 * q^75 + 8 * q^77 - 20 * q^81 + 12 * q^85 + 12 * q^87 + 4 * q^89 - 6 * q^95 + 12 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.13456	−	2.13456i	1.23239	−	1.23239i	0.269344	−	0.963044i	$-0.413193\pi$
$3$	2.13456	−	2.13456i	1.23239	−	1.23239i	0.963044	−	0.269344i	$-0.0868068\pi$
$4$		0			0
$5$	−0.666078	+	2.13456i	−0.297879	+	0.954604i
$5$	−0.666078	+	2.13456i	−0.297879	+	0.954604i
$6$		0			0
$7$		−	2.84356i		−	1.07477i	−0.843338	−	0.537383i	$-0.819413\pi$
$7$		−	2.84356i		−	1.07477i	0.843338	−	0.537383i	$-0.180587\pi$
$8$		0			0
$9$		−	6.11268i		−	2.03756i
$10$		0			0
$11$	2.66608	+	2.66608i	0.803853	+	0.803853i	0.983695	−	0.179843i	$-0.0575589\pi$
$11$	2.66608	+	2.66608i	0.803853	+	0.803853i	−0.179843	+	0.983695i	$0.557559\pi$
$12$		0			0
$13$	−0.134559	−	3.60304i	−0.0373198	−	0.999303i
$13$	−0.134559	−	3.60304i	−0.0373198	−	0.999303i
$14$		0			0
$15$	3.13456	+	5.97812i	0.809340	+	1.54354i
$16$		0			0
$17$	−2.80064	+	2.80064i	−0.679254	+	0.679254i	−0.959831	−	0.280577i	$-0.909474\pi$
$17$	−2.80064	+	2.80064i	−0.679254	+	0.679254i	0.280577	+	0.959831i	$0.409474\pi$
$18$		0			0
$19$	3.97812	+	3.97812i	0.912644	+	0.912644i	0.996480	−	0.0838357i	$-0.0267171\pi$
$19$	3.97812	+	3.97812i	0.912644	+	0.912644i	−0.0838357	+	0.996480i	$0.526717\pi$
$20$		0			0
$21$	−6.06975	−	6.06975i	−1.32453	−	1.32453i
$22$		0			0
$23$	−3.66608	−	3.66608i	−0.764430	−	0.764430i	0.212690	−	0.977120i	$-0.431778\pi$
$23$	−3.66608	−	3.66608i	−0.764430	−	0.764430i	−0.977120	+	0.212690i	$0.931778\pi$
$24$		0			0
$25$	−4.11268	−	2.84356i	−0.822536	−	0.568713i
$26$		0			0
$27$	−6.64420	−	6.64420i	−1.27868	−	1.27868i
$28$		0			0
$29$			8.17572i			1.51819i	0.650978	+	0.759096i	$0.274359\pi$
$29$			8.17572i			1.51819i	−0.650978	+	0.759096i	$0.725641\pi$
$30$		0			0
$31$	−3.60304	+	3.60304i	−0.647125	+	0.647125i	−0.952297	−	0.305172i	$-0.901286\pi$
$31$	−3.60304	+	3.60304i	−0.647125	+	0.647125i	0.305172	+	0.952297i	$0.401286\pi$
$32$		0			0
$33$	11.3818			1.98132
$34$		0			0
$35$	6.06975	+	1.89403i	1.02598	+	0.320150i
$36$		0			0
$37$			3.11268i			0.511722i	0.966714	+	0.255861i	$0.0823589\pi$
$37$			3.11268i			0.511722i	−0.966714	+	0.255861i	$0.917641\pi$
$38$		0			0
$39$	−7.97812	−	7.40368i	−1.27752	−	1.18554i
$40$		0			0
$41$	3.64420	−	3.64420i	0.569128	−	0.569128i	−0.362756	−	0.931884i	$-0.618164\pi$
$41$	3.64420	−	3.64420i	0.569128	−	0.569128i	0.931884	+	0.362756i	$0.118164\pi$
$42$		0			0
$43$	0.998233	+	0.998233i	0.152229	+	0.152229i	0.779113	−	0.626884i	$-0.215670\pi$
$43$	0.998233	+	0.998233i	0.152229	+	0.152229i	−0.626884	+	0.779113i	$0.715670\pi$
$44$		0			0
$45$	13.0479	+	4.07152i	1.94506	+	0.606946i
$46$		0			0
$47$			9.46765i			1.38100i	0.723333	+	0.690500i	$0.242609\pi$
$47$			9.46765i			1.38100i	−0.723333	+	0.690500i	$0.757391\pi$
$48$		0			0
$49$	−1.08585			−0.155122
$50$		0			0
$51$			11.9562i			1.67421i
$52$		0			0
$53$	2.78053	−	2.78053i	0.381935	−	0.381935i	−0.489864	−	0.871799i	$-0.662954\pi$
$53$	2.78053	−	2.78053i	0.381935	−	0.381935i	0.871799	+	0.489864i	$0.162954\pi$
$54$		0			0
$55$	−7.46671	+	3.91508i	−1.00681	+	0.527910i
$56$		0			0
$57$	16.9831			2.24946
$58$		0			0
$59$	3.97812	−	3.97812i	0.517907	−	0.517907i	−0.399030	−	0.916938i	$-0.630653\pi$
$59$	3.97812	−	3.97812i	0.517907	−	0.517907i	0.916938	+	0.399030i	$0.130653\pi$
$60$		0			0
$61$	−10.9866			−1.40669			−0.703345	−	0.710848i	$-0.748311\pi$
$61$	−10.9866			−1.40669			−0.703345	+	0.710848i	$0.748311\pi$
$62$		0			0
$63$	−17.3818			−2.18990
$64$		0			0
$65$	7.78053	+	2.11268i	0.965055	+	0.262046i
$66$		0			0
$67$	0.574447			0.0701798			0.0350899	−	0.999384i	$-0.488828\pi$
$67$	0.574447			0.0701798			0.0350899	+	0.999384i	$0.488828\pi$
$68$		0			0
$69$	−15.6509			−1.88415
$70$		0			0
$71$	−4.73937	+	4.73937i	−0.562459	+	0.562459i	−0.930005	−	0.367546i	$-0.880198\pi$
$71$	−4.73937	+	4.73937i	−0.562459	+	0.562459i	0.367546	+	0.930005i	$0.380198\pi$
$72$		0			0
$73$	−8.92588			−1.04470			−0.522348	−	0.852732i	$-0.674944\pi$
$73$	−8.92588			−1.04470			−0.522348	+	0.852732i	$0.674944\pi$
$74$		0			0
$75$	−14.8485	+	2.70901i	−1.71456	+	0.312809i
$76$		0			0
$77$	7.58116	−	7.58116i	0.863954	−	0.863954i
$78$		0			0
$79$		−	5.51895i		−	0.620931i	−0.950585	−	0.310465i	$-0.899515\pi$
$79$		−	5.51895i		−	0.620931i	0.950585	−	0.310465i	$-0.100485\pi$
$80$		0			0
$81$	−10.0268			−1.11409
$82$		0			0
$83$		−	2.75771i		−	0.302698i	−0.988480	−	0.151349i	$-0.951638\pi$
$83$		−	2.75771i		−	0.302698i	0.988480	−	0.151349i	$-0.0483617\pi$
$84$		0			0
$85$	−4.11268	−	7.84356i	−0.446083	−	0.850754i
$86$		0			0
$87$	17.4516	+	17.4516i	1.87100	+	1.87100i
$88$		0			0
$89$	−3.36252	+	3.36252i	−0.356426	+	0.356426i	−0.862494	−	0.506068i	$-0.831099\pi$
$89$	−3.36252	+	3.36252i	−0.356426	+	0.356426i	0.506068	+	0.862494i	$0.331099\pi$
$90$		0			0
$91$	−10.2455	+	0.382626i	−1.07402	+	0.0401101i
$92$		0			0
$93$			15.3818i			1.59502i
$94$		0			0
$95$	−11.1413	+	5.84180i	−1.14307	+	0.599356i
$96$		0			0
$97$	9.12022			0.926018			0.463009	−	0.886353i	$-0.346770\pi$
$97$	9.12022			0.926018			0.463009	+	0.886353i	$0.346770\pi$
$98$		0			0
$99$	16.2969	−	16.2969i	1.63790	−	1.63790i
$100$		0			0
$101$		−	10.1395i		−	1.00892i	−0.863435	−	0.504459i	$-0.831692\pi$
$101$		−	10.1395i		−	1.00892i	0.863435	−	0.504459i	$-0.168308\pi$
$102$		0			0
$103$	8.57940	+	8.57940i	0.845353	+	0.845353i	0.989549	−	0.144196i	$-0.0460596\pi$
$103$	8.57940	+	8.57940i	0.845353	+	0.845353i	−0.144196	+	0.989549i	$0.546060\pi$
$104$		0			0
$105$	16.9992	−	8.91332i	1.65895	−	0.869851i
$106$		0			0
$107$	−5.04788	−	5.04788i	−0.487997	−	0.487997i	0.419677	−	0.907674i	$-0.362143\pi$
$107$	−5.04788	−	5.04788i	−0.487997	−	0.487997i	−0.907674	+	0.419677i	$0.862143\pi$
$108$		0			0
$109$	−5.73760	−	5.73760i	−0.549562	−	0.549562i	0.376752	−	0.926314i	$-0.377041\pi$
$109$	−5.73760	−	5.73760i	−0.549562	−	0.549562i	−0.926314	+	0.376752i	$0.877041\pi$
$110$		0			0
$111$	6.64420	+	6.64420i	0.630640	+	0.630640i
$112$		0			0
$113$	7.55835	−	7.55835i	0.711029	−	0.711029i	−0.255721	−	0.966751i	$-0.582313\pi$
$113$	7.55835	−	7.55835i	0.711029	−	0.711029i	0.966751	+	0.255721i	$0.0823129\pi$
$114$		0			0
$115$	10.2674	−	5.38357i	0.957435	−	0.502020i
$116$		0			0
$117$	−22.0242	+	0.822514i	−2.03614	+	0.0760414i
$118$		0			0
$119$	7.96379	+	7.96379i	0.730039	+	0.730039i
$120$		0			0
$121$			3.21594i			0.292358i
$122$		0			0
$123$		−	15.5575i		−	1.40277i
$124$		0			0
$125$	8.80912	−	6.88472i	0.787912	−	0.615788i
$126$		0			0
$127$	10.3103	−	10.3103i	0.914889	−	0.914889i	−0.0817626	−	0.996652i	$-0.526055\pi$
$127$	10.3103	−	10.3103i	0.914889	−	0.914889i	0.996652	+	0.0817626i	$0.0260549\pi$
$128$		0			0
$129$	4.26157			0.375211
$130$		0			0
$131$	−10.0386			−0.877074			−0.438537	−	0.898713i	$-0.644503\pi$
$131$	−10.0386			−0.877074			−0.438537	+	0.898713i	$0.644503\pi$
$132$		0			0
$133$	11.3120	−	11.3120i	0.980879	−	0.980879i
$134$		0			0
$135$	18.6080	−	9.75688i	1.60152	−	0.839739i
$136$		0			0
$137$			7.41801i			0.633763i	0.948465	+	0.316882i	$0.102636\pi$
$137$			7.41801i			0.633763i	−0.948465	+	0.316882i	$0.897364\pi$
$138$		0			0
$139$			2.26912i			0.192464i	0.995359	+	0.0962320i	$0.0306791\pi$
$139$			2.26912i			0.192464i	−0.995359	+	0.0962320i	$0.969321\pi$
$140$		0			0
$141$	20.2093	+	20.2093i	1.70193	+	1.70193i
$142$		0			0
$143$	9.24724	−	9.96473i	0.773293	−	0.833292i
$144$		0			0
$145$	−17.4516	−	5.44566i	−1.44927	−	0.452238i
$146$		0			0
$147$	−2.31782	+	2.31782i	−0.191171	+	0.191171i
$148$		0			0
$149$	−0.976355	−	0.976355i	−0.0799862	−	0.0799862i	0.665982	−	0.745968i	$-0.268013\pi$
$149$	−0.976355	−	0.976355i	−0.0799862	−	0.0799862i	−0.745968	+	0.665982i	$0.768013\pi$
$150$		0			0
$151$	−3.79887	−	3.79887i	−0.309148	−	0.309148i	0.535431	−	0.844579i	$-0.320149\pi$
$151$	−3.79887	−	3.79887i	−0.309148	−	0.309148i	−0.844579	+	0.535431i	$0.820149\pi$
$152$		0			0
$153$	17.1194	+	17.1194i	1.38402	+	1.38402i
$154$		0			0
$155$	−5.29099	−	10.0908i	−0.424983	−	0.810513i
$156$		0			0
$157$	−11.0698	−	11.0698i	−0.883463	−	0.883463i	0.110422	−	0.993885i	$-0.464780\pi$
$157$	−11.0698	−	11.0698i	−0.883463	−	0.883463i	−0.993885	+	0.110422i	$0.964780\pi$
$158$		0			0
$159$		−	11.8704i		−	0.941383i
$160$		0			0
$161$	−10.4247	+	10.4247i	−0.821583	+	0.821583i
$162$		0			0
$163$	−21.4776			−1.68225			−0.841126	−	0.540840i	$-0.818107\pi$
$163$	−21.4776			−1.68225			−0.841126	+	0.540840i	$0.818107\pi$
$164$		0			0
$165$	−7.58116	+	24.2951i	−0.590193	+	1.89137i
$166$		0			0
$167$		−	2.71749i		−	0.210285i	−0.994457	−	0.105143i	$-0.966470\pi$
$167$		−	2.71749i		−	0.210285i	0.994457	−	0.105143i	$-0.0335299\pi$
$168$		0			0
$169$	−12.9638	+	0.969640i	−0.997214	+	0.0745877i
$170$		0			0
$171$	24.3170	−	24.3170i	1.85957	−	1.85957i
$172$		0			0
$173$	−4.24983	−	4.24983i	−0.323109	−	0.323109i	0.526850	−	0.849959i	$-0.323373\pi$
$173$	−4.24983	−	4.24983i	−0.323109	−	0.323109i	−0.849959	+	0.526850i	$0.823373\pi$
$174$		0			0
$175$	−8.08585	+	11.6947i	−0.611233	+	0.884034i
$176$		0			0
$177$		−	16.9831i		−	1.27653i
$178$		0			0
$179$	16.8109			1.25650			0.628252	−	0.778010i	$-0.283771\pi$
$179$	16.8109			1.25650			0.628252	+	0.778010i	$0.283771\pi$
$180$		0			0
$181$		−	21.6509i		−	1.60930i	−0.593750	−	0.804650i	$-0.702353\pi$
$181$		−	21.6509i		−	1.60930i	0.593750	−	0.804650i	$-0.297647\pi$
$182$		0			0
$183$	−23.4516	+	23.4516i	−1.73359	+	1.73359i
$184$		0			0
$185$	−6.64420	−	2.07329i	−0.488491	−	0.152431i
$186$		0			0
$187$	−14.9334			−1.09204
$188$		0			0
$189$	−18.8932	+	18.8932i	−1.37428	+	1.37428i
$190$		0			0
$191$	−2.10094			−0.152019			−0.0760094	−	0.997107i	$-0.524218\pi$
$191$	−2.10094			−0.152019			−0.0760094	+	0.997107i	$0.524218\pi$
$192$		0			0
$193$	−5.39288			−0.388188			−0.194094	−	0.980983i	$-0.562177\pi$
$193$	−5.39288			−0.388188			−0.194094	+	0.980983i	$0.562177\pi$
$194$		0			0
$195$	21.1176	−	12.0983i	1.51226	−	0.866381i
$196$		0			0
$197$	−8.66784			−0.617558			−0.308779	−	0.951134i	$-0.599920\pi$
$197$	−8.66784			−0.617558			−0.308779	+	0.951134i	$0.599920\pi$
$198$		0			0
$199$	11.5154			0.816306			0.408153	−	0.912913i	$-0.366173\pi$
$199$	11.5154			0.816306			0.408153	+	0.912913i	$0.366173\pi$
$200$		0			0
$201$	1.22619	−	1.22619i	0.0864888	−	0.0864888i
$202$		0			0
$203$	23.2482			1.63170
$204$		0			0
$205$	5.35144	+	10.2061i	0.373761	+	0.712823i
$206$		0			0
$207$	−22.4096	+	22.4096i	−1.55757	+	1.55757i
$208$		0			0
$209$			21.2120i			1.46726i
$210$		0			0
$211$	25.4886			1.75471			0.877355	−	0.479842i	$-0.159306\pi$
$211$	25.4886			1.75471			0.877355	+	0.479842i	$0.159306\pi$
$212$		0			0
$213$			20.2329i			1.38634i
$214$		0			0
$215$	−2.79569	+	1.46589i	−0.190664	+	0.0999726i
$216$		0			0
$217$	10.2455	+	10.2455i	0.695508	+	0.695508i
$218$		0			0
$219$	−19.0528	+	19.0528i	−1.28747	+	1.28747i
$220$		0			0
$221$	10.4677	+	9.71395i	0.704131	+	0.653431i
$222$		0			0
$223$		−	1.50787i		−	0.100975i	−0.998725	−	0.0504874i	$-0.983923\pi$
$223$		−	1.50787i		−	0.100975i	0.998725	−	0.0504874i	$-0.0160775\pi$
$224$		0			0
$225$	−17.3818	+	25.1395i	−1.15879	+	1.67597i
$226$		0			0
$227$	12.7542			0.846524			0.423262	−	0.906007i	$-0.360885\pi$
$227$	12.7542			0.846524			0.423262	+	0.906007i	$0.360885\pi$
$228$		0			0
$229$	17.0461	−	17.0461i	1.12644	−	1.12644i	0.135687	−	0.990752i	$-0.456676\pi$
$229$	17.0461	−	17.0461i	1.12644	−	1.12644i	0.990752	−	0.135687i	$-0.0433241\pi$
$230$		0			0
$231$		−	32.3649i		−	2.12945i
$232$		0			0
$233$	−19.9755	−	19.9755i	−1.30864	−	1.30864i	−0.922397	−	0.386243i	$-0.873772\pi$
$233$	−19.9755	−	19.9755i	−1.30864	−	1.30864i	−0.386243	−	0.922397i	$-0.626228\pi$
$234$		0			0
$235$	−20.2093	−	6.30619i	−1.31831	−	0.411371i
$236$		0			0
$237$	−11.7805	−	11.7805i	−0.765227	−	0.765227i
$238$		0			0
$239$	1.96555	+	1.96555i	0.127141	+	0.127141i	0.767814	−	0.640673i	$-0.221344\pi$
$239$	1.96555	+	1.96555i	0.127141	+	0.127141i	−0.640673	+	0.767814i	$0.721344\pi$
$240$		0			0
$241$	−13.3751	−	13.3751i	−0.861565	−	0.861565i	0.129955	−	0.991520i	$-0.458517\pi$
$241$	−13.3751	−	13.3751i	−0.861565	−	0.861565i	−0.991520	+	0.129955i	$0.958517\pi$
$242$		0			0
$243$	−1.47025	+	1.47025i	−0.0943164	+	0.0943164i
$244$		0			0
$245$	0.723264	−	2.31782i	0.0462076	−	0.148080i
$246$		0			0
$247$	13.7980	−	14.8686i	0.877948	−	0.946068i
$248$		0			0
$249$	−5.88649	−	5.88649i	−0.373041	−	0.373041i
$250$		0			0
$251$			21.1588i			1.33553i	0.744372	+	0.667765i	$0.232749\pi$
$251$			21.1588i			1.33553i	−0.744372	+	0.667765i	$0.767251\pi$
$252$		0			0
$253$		−	19.5481i		−	1.22898i
$254$		0			0
$255$	−25.5213	−	7.96379i	−1.59821	−	0.498712i
$256$		0			0
$257$	−14.9638	+	14.9638i	−0.933415	+	0.933415i	−0.997918	−	0.0645021i	$-0.979454\pi$
$257$	−14.9638	+	14.9638i	−0.933415	+	0.933415i	0.0645021	+	0.997918i	$0.479454\pi$
$258$		0			0
$259$	8.85111			0.549981
$260$		0			0
$261$	49.9756			3.09341
$262$		0			0
$263$	2.80240	−	2.80240i	0.172804	−	0.172804i	−0.615406	−	0.788210i	$-0.711008\pi$
$263$	2.80240	−	2.80240i	0.172804	−	0.172804i	0.788210	+	0.615406i	$0.211008\pi$
$264$		0			0
$265$	4.08315	+	7.78724i	0.250826	+	0.478366i
$266$		0			0
$267$			14.3550i			0.878510i
$268$		0			0
$269$			22.0993i			1.34742i	0.738997	+	0.673709i	$0.235300\pi$
$269$			22.0993i			1.34742i	−0.738997	+	0.673709i	$0.764700\pi$
$270$		0			0
$271$	14.2969	+	14.2969i	0.868474	+	0.868474i	0.992303	−	0.123830i	$-0.0395177\pi$
$271$	14.2969	+	14.2969i	0.868474	+	0.868474i	−0.123830	+	0.992303i	$0.539518\pi$
$272$		0			0
$273$	−21.0528	+	22.6863i	−1.27417	+	1.37304i
$274$		0			0
$275$	−3.38357	−	18.5459i	−0.204037	−	1.11836i
$276$		0			0
$277$	−4.01928	+	4.01928i	−0.241495	+	0.241495i	−0.817469	−	0.575973i	$-0.804623\pi$
$277$	−4.01928	+	4.01928i	−0.241495	+	0.241495i	0.575973	+	0.817469i	$0.304623\pi$
$278$		0			0
$279$	22.0242	+	22.0242i	1.31856	+	1.31856i
$280$		0			0
$281$	−10.2262	−	10.2262i	−0.610043	−	0.610043i	0.332914	−	0.942957i	$-0.391968\pi$
$281$	−10.2262	−	10.2262i	−0.610043	−	0.610043i	−0.942957	+	0.332914i	$0.891968\pi$
$282$		0			0
$283$	20.4734	+	20.4734i	1.21702	+	1.21702i	0.968671	+	0.248348i	$0.0798877\pi$
$283$	20.4734	+	20.4734i	1.21702	+	1.21702i	0.248348	+	0.968671i	$0.420112\pi$
$284$		0			0
$285$	−11.3120	+	36.2514i	−0.670068	+	2.14735i
$286$		0			0
$287$	−10.3625	−	10.3625i	−0.611680	−	0.611680i
$288$		0			0
$289$			1.31287i			0.0772278i
$290$		0			0
$291$	19.4677	−	19.4677i	1.14121	−	1.14121i
$292$		0			0
$293$	23.7770			1.38907			0.694533	−	0.719461i	$-0.255611\pi$
$293$	23.7770			1.38907			0.694533	+	0.719461i	$0.255611\pi$
$294$		0			0
$295$	5.84180	+	11.1413i	0.340123	+	0.648670i
$296$		0			0
$297$		−	35.4279i		−	2.05574i
$298$		0			0
$299$	−12.7157	+	13.7023i	−0.735369	+	0.792426i
$300$		0			0
$301$	2.83854	−	2.83854i	0.163611	−	0.163611i
$302$		0			0
$303$	−21.6434	−	21.6434i	−1.24338	−	1.24338i
$304$		0			0
$305$	7.31793	−	23.4516i	0.419024	−	1.34283i
$306$		0			0
$307$			1.46931i			0.0838579i	0.999121	+	0.0419289i	$0.0133503\pi$
$307$			1.46931i			0.0838579i	−0.999121	+	0.0419289i	$0.986650\pi$
$308$		0			0
$309$	36.6264			2.08361
$310$		0			0
$311$			0.708066i			0.0401507i	0.999798	+	0.0200754i	$0.00639062\pi$
$311$			0.708066i			0.0401507i	−0.999798	+	0.0200754i	$0.993609\pi$
$312$		0			0
$313$	−13.7376	+	13.7376i	−0.776495	+	0.776495i	−0.979233	−	0.202738i	$-0.935016\pi$
$313$	−13.7376	+	13.7376i	−0.776495	+	0.776495i	0.202738	+	0.979233i	$0.435016\pi$
$314$		0			0
$315$	11.5776	−	37.1025i	0.652325	−	2.09049i
$316$		0			0
$317$	−11.3853			−0.639464			−0.319732	−	0.947508i	$-0.603593\pi$
$317$	−11.3853			−0.639464			−0.319732	+	0.947508i	$0.603593\pi$
$318$		0			0
$319$	−21.7971	+	21.7971i	−1.22040	+	1.22040i
$320$		0			0
$321$	−21.5500			−1.20280
$322$		0			0
$323$	−22.2825			−1.23983
$324$		0			0
$325$	−9.69208	+	15.2008i	−0.537620	+	0.843187i
$326$		0			0
$327$	−24.4945			−1.35455
$328$		0			0
$329$	26.9219			1.48425
$330$		0			0
$331$	−14.8056	+	14.8056i	−0.813789	+	0.813789i	−0.985200	−	0.171411i	$-0.945167\pi$
$331$	−14.8056	+	14.8056i	−0.813789	+	0.813789i	0.171411	+	0.985200i	$0.445167\pi$
$332$		0			0
$333$	19.0268			1.04266
$334$		0			0
$335$	−0.382626	+	1.22619i	−0.0209051	+	0.0669939i
$336$		0			0
$337$	2.22972	−	2.22972i	0.121461	−	0.121461i	−0.643764	−	0.765224i	$-0.722628\pi$
$337$	2.22972	−	2.22972i	0.121461	−	0.121461i	0.765224	+	0.643764i	$0.222628\pi$
$338$		0			0
$339$		−	32.2675i		−	1.75253i
$340$		0			0
$341$	−19.2120			−1.04039
$342$		0			0
$343$		−	16.8172i		−	0.908046i
$344$		0			0
$345$	10.4247	−	33.4078i	0.561248	−	1.79862i
$346$		0			0
$347$	−14.3162	−	14.3162i	−0.768532	−	0.768532i	0.209316	−	0.977848i	$-0.432876\pi$
$347$	−14.3162	−	14.3162i	−0.768532	−	0.768532i	−0.977848	+	0.209316i	$0.932876\pi$
$348$		0			0
$349$	−5.93696	+	5.93696i	−0.317798	+	0.317798i	−0.847921	−	0.530123i	$-0.822146\pi$
$349$	−5.93696	+	5.93696i	−0.317798	+	0.317798i	0.530123	+	0.847921i	$0.322146\pi$
$350$		0			0
$351$	−23.0453	+	24.8334i	−1.23007	+	1.32551i
$352$		0			0
$353$			22.5020i			1.19766i	0.800875	+	0.598831i	$0.204368\pi$
$353$			22.5020i			1.19766i	−0.800875	+	0.598831i	$0.795632\pi$
$354$		0			0
$355$	−6.95967	−	13.2732i	−0.369381	−	0.704470i
$356$		0			0
$357$	33.9983			1.79938
$358$		0			0
$359$	−21.1369	+	21.1369i	−1.11556	+	1.11556i	−0.123179	+	0.992384i	$0.539309\pi$
$359$	−21.1369	+	21.1369i	−1.11556	+	1.11556i	−0.992384	+	0.123179i	$0.960691\pi$
$360$		0			0
$361$			12.6509i			0.665838i
$362$		0			0
$363$	6.86461	+	6.86461i	0.360299	+	0.360299i
$364$		0			0
$365$	5.94533	−	19.0528i	0.311193	−	0.997270i
$366$		0			0
$367$	25.5695	+	25.5695i	1.33472	+	1.33472i	0.901093	+	0.433626i	$0.142766\pi$
$367$	25.5695	+	25.5695i	1.33472	+	1.33472i	0.433626	+	0.901093i	$0.357234\pi$
$368$		0			0
$369$	−22.2758	−	22.2758i	−1.15963	−	1.15963i
$370$		0			0
$371$	−7.90660	−	7.90660i	−0.410490	−	0.410490i
$372$		0			0
$373$	6.17843	−	6.17843i	0.319907	−	0.319907i	−0.528824	−	0.848731i	$-0.677367\pi$
$373$	6.17843	−	6.17843i	0.319907	−	0.319907i	0.848731	+	0.528824i	$0.177367\pi$
$374$		0			0
$375$	4.10773	−	33.4994i	0.212122	−	1.72990i
$376$		0			0
$377$	29.4574	−	1.10011i	1.51714	−	0.0566587i
$378$		0			0
$379$	−8.75594	−	8.75594i	−0.449763	−	0.449763i	0.445513	−	0.895275i	$-0.353021\pi$
$379$	−8.75594	−	8.75594i	−0.449763	−	0.449763i	−0.895275	+	0.445513i	$0.853021\pi$
$380$		0			0
$381$		−	44.0158i		−	2.25500i
$382$		0			0
$383$			11.9586i			0.611056i	0.952183	+	0.305528i	$0.0988329\pi$
$383$			11.9586i			0.611056i	−0.952183	+	0.305528i	$0.901167\pi$
$384$		0			0
$385$	11.1328	+	21.2321i	0.567380	+	1.08209i
$386$		0			0
$387$	6.10188	−	6.10188i	0.310176	−	0.310176i
$388$		0			0
$389$	11.1640			0.566036			0.283018	−	0.959115i	$-0.408664\pi$
$389$	11.1640			0.566036			0.283018	+	0.959115i	$0.408664\pi$
$390$		0			0
$391$	20.5347			1.03848
$392$		0			0
$393$	−21.4279	+	21.4279i	−1.08089	+	1.08089i
$394$		0			0
$395$	11.7805	+	3.67605i	0.592743	+	0.184962i
$396$		0			0
$397$			22.0040i			1.10435i	0.833728	+	0.552175i	$0.186202\pi$
$397$			22.0040i			1.10435i	−0.833728	+	0.552175i	$0.813798\pi$
$398$		0			0
$399$		−	48.2924i		−	2.41765i
$400$		0			0
$401$	17.2767	+	17.2767i	0.862755	+	0.862755i	0.991657	−	0.128902i	$-0.0411453\pi$
$401$	17.2767	+	17.2767i	0.862755	+	0.862755i	−0.128902	+	0.991657i	$0.541145\pi$
$402$		0			0
$403$	13.4667	+	12.4971i	0.670825	+	0.622524i
$404$		0			0
$405$	6.67865	−	21.4028i	0.331865	−	1.06352i
$406$		0			0
$407$	−8.29865	+	8.29865i	−0.411349	+	0.411349i
$408$		0			0
$409$	−17.7400	−	17.7400i	−0.877184	−	0.877184i	0.116058	−	0.993242i	$-0.462974\pi$
$409$	−17.7400	−	17.7400i	−0.877184	−	0.877184i	−0.993242	+	0.116058i	$0.962974\pi$
$410$		0			0
$411$	15.8342	+	15.8342i	0.781042	+	0.781042i
$412$		0			0
$413$	−11.3120	−	11.3120i	−0.556629	−	0.556629i
$414$		0			0
$415$	5.88649	+	1.83685i	0.288956	+	0.0901673i
$416$		0			0
$417$	4.84356	+	4.84356i	0.237190	+	0.237190i
$418$		0			0
$419$		−	12.4338i		−	0.607429i	−0.952763	−	0.303714i	$-0.901773\pi$
$419$		−	12.4338i		−	0.607429i	0.952763	−	0.303714i	$-0.0982269\pi$
$420$		0			0
$421$	15.6938	−	15.6938i	0.764871	−	0.764871i	−0.212327	−	0.977199i	$-0.568104\pi$
$421$	15.6938	−	15.6938i	0.764871	−	0.764871i	0.977199	+	0.212327i	$0.0681043\pi$
$422$		0			0
$423$	57.8727			2.81387
$424$		0			0
$425$	19.4819	−	3.55434i	0.945012	−	0.172411i
$426$		0			0
$427$			31.2411i			1.51186i
$428$		0			0
$429$	−1.53152	−	41.0091i	−0.0739424	−	1.97994i
$430$		0			0
$431$	6.08409	−	6.08409i	0.293060	−	0.293060i	−0.545228	−	0.838288i	$-0.683557\pi$
$431$	6.08409	−	6.08409i	0.293060	−	0.293060i	0.838288	+	0.545228i	$0.183557\pi$
$432$		0			0
$433$	11.3684	+	11.3684i	0.546331	+	0.546331i	0.925377	−	0.379047i	$-0.123748\pi$
$433$	11.3684	+	11.3684i	0.546331	+	0.546331i	−0.379047	+	0.925377i	$0.623748\pi$
$434$		0			0
$435$	−48.8754	+	25.6273i	−2.34340	+	1.22873i
$436$		0			0
$437$		−	29.1682i		−	1.39530i
$438$		0			0
$439$	1.91249			0.0912781			0.0456391	−	0.998958i	$-0.485468\pi$
$439$	1.91249			0.0912781			0.0456391	+	0.998958i	$0.485468\pi$
$440$		0			0
$441$			6.63748i			0.316071i
$442$		0			0
$443$	−10.5333	+	10.5333i	−0.500452	+	0.500452i	−0.911578	−	0.411127i	$-0.865135\pi$
$443$	−10.5333	+	10.5333i	−0.500452	+	0.500452i	0.411127	+	0.911578i	$0.365135\pi$
$444$		0			0
$445$	−4.93779	−	9.41718i	−0.234074	−	0.446417i
$446$		0			0
$447$	−4.16818			−0.197148
$448$		0			0
$449$	12.4842	−	12.4842i	0.589167	−	0.589167i	−0.348239	−	0.937406i	$-0.613220\pi$
$449$	12.4842	−	12.4842i	0.589167	−	0.589167i	0.937406	+	0.348239i	$0.113220\pi$
$450$		0			0
$451$	19.4314			0.914991
$452$		0			0
$453$	−16.2178			−0.761980
$454$		0			0
$455$	6.00754	−	22.1244i	0.281638	−	1.03721i
$456$		0			0
$457$	23.2061			1.08553			0.542767	−	0.839883i	$-0.317377\pi$
$457$	23.2061			1.08553			0.542767	+	0.839883i	$0.317377\pi$
$458$		0			0
$459$	37.2160			1.73709
$460$		0			0
$461$	−18.5154	+	18.5154i	−0.862349	+	0.862349i	−0.991611	−	0.129262i	$-0.958739\pi$
$461$	−18.5154	+	18.5154i	−0.862349	+	0.862349i	0.129262	+	0.991611i	$0.458739\pi$
$462$		0			0
$463$	15.0654			0.700148			0.350074	−	0.936722i	$-0.386156\pi$
$463$	15.0654			0.700148			0.350074	+	0.936722i	$0.386156\pi$
$464$		0			0
$465$	−32.8334	−	10.2455i	−1.52261	−	0.475122i
$466$		0			0
$467$	17.0569	−	17.0569i	0.789300	−	0.789300i	−0.192080	−	0.981379i	$-0.561523\pi$
$467$	17.0569	−	17.0569i	0.789300	−	0.789300i	0.981379	+	0.192080i	$0.0615232\pi$
$468$		0			0
$469$		−	1.63348i		−	0.0754269i
$470$		0			0
$471$	−47.2581			−2.17754
$472$		0			0
$473$			5.32273i			0.244740i
$474$		0			0
$475$	−5.04870	−	27.6728i	−0.231650	−	1.26971i
$476$		0			0
$477$	−16.9965	−	16.9965i	−0.778215	−	0.778215i
$478$		0			0
$479$	−6.91155	+	6.91155i	−0.315797	+	0.315797i	−0.847150	−	0.531353i	$-0.821684\pi$
$479$	−6.91155	+	6.91155i	−0.315797	+	0.315797i	0.531353	+	0.847150i	$0.321684\pi$
$480$		0			0
$481$	11.2151	−	0.418838i	0.511365	−	0.0190974i
$482$		0			0
$483$			44.5044i			2.02502i
$484$		0			0
$485$	−6.07478	+	19.4677i	−0.275841	+	0.883981i
$486$		0			0
$487$	18.6737			0.846188			0.423094	−	0.906086i	$-0.360944\pi$
$487$	18.6737			0.846188			0.423094	+	0.906086i	$0.360944\pi$
$488$		0			0
$489$	−45.8451	+	45.8451i	−2.07319	+	2.07319i
$490$		0			0
$491$		−	28.0706i		−	1.26681i	−0.773821	−	0.633405i	$-0.781657\pi$
$491$		−	28.0706i		−	1.26681i	0.773821	−	0.633405i	$-0.218343\pi$
$492$		0			0
$493$	−22.8972	−	22.8972i	−1.03124	−	1.03124i
$494$		0			0
$495$	23.9317	+	45.6416i	1.07565	+	2.05144i
$496$		0			0
$497$	13.4767	+	13.4767i	0.604512	+	0.604512i
$498$		0			0
$499$	20.8276	+	20.8276i	0.932370	+	0.932370i	0.997854	−	0.0654834i	$-0.0208589\pi$
$499$	20.8276	+	20.8276i	0.932370	+	0.932370i	−0.0654834	+	0.997854i	$0.520859\pi$
$500$		0			0
$501$	−5.80064	−	5.80064i	−0.259153	−	0.259153i
$502$		0			0
$503$	0.528262	−	0.528262i	0.0235540	−	0.0235540i	−0.695232	−	0.718786i	$-0.744698\pi$
$503$	0.528262	−	0.528262i	0.0235540	−	0.0235540i	0.718786	+	0.695232i	$0.244698\pi$
$504$		0			0
$505$	21.6434	+	6.75370i	0.963117	+	0.300536i
$506$		0			0
$507$	−25.6022	+	29.7417i	−1.13703	+	1.32088i
$508$		0			0
$509$	16.3305	+	16.3305i	0.723837	+	0.723837i	0.969384	−	0.245548i	$-0.0789678\pi$
$509$	16.3305	+	16.3305i	0.723837	+	0.723837i	−0.245548	+	0.969384i	$0.578968\pi$
$510$		0			0
$511$			25.3813i			1.12280i
$512$		0			0
$513$		−	52.8629i		−	2.33395i
$514$		0			0
$515$	−24.0278	+	12.5987i	−1.05879	+	0.555164i
$516$		0			0
$517$	−25.2415	+	25.2415i	−1.11012	+	1.11012i
$518$		0			0
$519$	−18.1430			−0.796391
$520$		0			0
$521$	−27.5785			−1.20824			−0.604118	−	0.796895i	$-0.706474\pi$
$521$	−27.5785			−1.20824			−0.604118	+	0.796895i	$0.706474\pi$
$522$		0			0
$523$	2.83909	−	2.83909i	0.124145	−	0.124145i	−0.642305	−	0.766449i	$-0.722022\pi$
$523$	2.83909	−	2.83909i	0.124145	−	0.124145i	0.766449	+	0.642305i	$0.222022\pi$
$524$		0			0
$525$	7.70323	+	42.2227i	0.336196	+	1.84275i
$526$		0			0
$527$		−	20.1816i		−	0.879125i
$528$		0			0
$529$			3.88025i			0.168707i
$530$		0			0
$531$	−24.3170	−	24.3170i	−1.05527	−	1.05527i
$532$		0			0
$533$	−13.6206	−	12.6398i	−0.589972	−	0.547492i
$534$		0			0
$535$	14.1373	−	7.41271i	0.611207	−	0.320479i
$536$		0			0
$537$	35.8838	−	35.8838i	1.54850	−	1.54850i
$538$		0			0
$539$	−2.89497	−	2.89497i	−0.124695	−	0.124695i
$540$		0			0
$541$	9.13196	+	9.13196i	0.392614	+	0.392614i	0.875618	−	0.483004i	$-0.160454\pi$
$541$	9.13196	+	9.13196i	0.392614	+	0.392614i	−0.483004	+	0.875618i	$0.660454\pi$
$542$		0			0
$543$	−46.2151	−	46.2151i	−1.98328	−	1.98328i
$544$		0			0
$545$	16.0689	−	8.42555i	0.688317	−	0.360911i
$546$		0			0
$547$	−4.28428	−	4.28428i	−0.183183	−	0.183183i	0.609559	−	0.792741i	$-0.291347\pi$
$547$	−4.28428	−	4.28428i	−0.183183	−	0.183183i	−0.792741	+	0.609559i	$0.791347\pi$
$548$		0			0
$549$			67.1576i			2.86622i
$550$		0			0
$551$	−32.5240	+	32.5240i	−1.38557	+	1.38557i
$552$		0			0
$553$	−15.6935			−0.667355
$554$		0			0
$555$	−18.6080	+	9.75688i	−0.789865	+	0.414157i
$556$		0			0
$557$		−	10.2159i		−	0.432863i	−0.976298	−	0.216432i	$-0.930558\pi$
$557$		−	10.2159i		−	0.432863i	0.976298	−	0.216432i	$-0.0694418\pi$
$558$		0			0
$559$	3.46235	−	3.73099i	0.146442	−	0.157804i
$560$		0			0
$561$	−31.8763	+	31.8763i	−1.34582	+	1.34582i
$562$		0			0
$563$	−2.19088	−	2.19088i	−0.0923346	−	0.0923346i	0.659431	−	0.751765i	$-0.270797\pi$
$563$	−2.19088	−	2.19088i	−0.0923346	−	0.0923346i	−0.751765	+	0.659431i	$0.770797\pi$
$564$		0			0
$565$	11.0993	+	21.1682i	0.466950	+	0.890552i
$566$		0			0
$567$			28.5119i			1.19739i
$568$		0			0
$569$	−14.1338			−0.592521			−0.296261	−	0.955107i	$-0.595740\pi$
$569$	−14.1338			−0.592521			−0.296261	+	0.955107i	$0.595740\pi$
$570$		0			0
$571$		−	31.7222i		−	1.32753i	−0.747941	−	0.663766i	$-0.768957\pi$
$571$		−	31.7222i		−	1.32753i	0.747941	−	0.663766i	$-0.231043\pi$
$572$		0			0
$573$	−4.48458	+	4.48458i	−0.187346	+	0.187346i
$574$		0			0
$575$	4.65268	+	25.5021i	0.194030	+	1.06351i
$576$		0			0
$577$	−24.9259			−1.03768			−0.518839	−	0.854872i	$-0.673636\pi$
$577$	−24.9259			−1.03768			−0.518839	+	0.854872i	$0.673636\pi$
$578$		0			0
$579$	−11.5114	+	11.5114i	−0.478398	+	0.478398i
$580$		0			0
$581$	−7.84172			−0.325329
$582$		0			0
$583$	14.8262			0.614038
$584$		0			0
$585$	12.9141	−	47.5599i	0.533934	−	1.96636i
$586$		0			0
$587$	−28.8873			−1.19231			−0.596154	−	0.802870i	$-0.703305\pi$
$587$	−28.8873			−1.19231			−0.596154	+	0.802870i	$0.703305\pi$
$588$		0			0
$589$	−28.6667			−1.18119
$590$		0			0
$591$	−18.5020	+	18.5020i	−0.761072	+	0.761072i
$592$		0			0
$593$	−3.65210			−0.149974			−0.0749868	−	0.997185i	$-0.523891\pi$
$593$	−3.65210			−0.149974			−0.0749868	+	0.997185i	$0.523891\pi$
$594$		0			0
$595$	−22.3037	+	11.6947i	−0.914361	+	0.479435i
$596$		0			0
$597$	24.5803	−	24.5803i	1.00601	−	1.00601i
$598$		0			0
$599$		−	20.4810i		−	0.836833i	−0.908255	−	0.418416i	$-0.862585\pi$
$599$		−	20.4810i		−	0.836833i	0.908255	−	0.418416i	$-0.137415\pi$
$600$		0			0
$601$	34.6154			1.41199			0.705995	−	0.708217i	$-0.250500\pi$
$601$	34.6154			1.41199			0.705995	+	0.708217i	$0.250500\pi$
$602$		0			0
$603$		−	3.51141i		−	0.142996i
$604$		0			0
$605$	−6.86461	−	2.14207i	−0.279086	−	0.0870874i
$606$		0			0
$607$	−12.3800	−	12.3800i	−0.502490	−	0.502490i	0.409721	−	0.912211i	$-0.365626\pi$
$607$	−12.3800	−	12.3800i	−0.502490	−	0.502490i	−0.912211	+	0.409721i	$0.865626\pi$
$608$		0			0
$609$	49.6246	−	49.6246i	2.01089	−	2.01089i
$610$		0			0
$611$	34.1123	−	1.27395i	1.38004	−	0.0515387i
$612$		0			0
$613$		−	0.906637i		−	0.0366187i	−0.999832	−	0.0183094i	$-0.994172\pi$
$613$		−	0.906637i		−	0.0366187i	0.999832	−	0.0183094i	$-0.00582838\pi$
$614$		0			0
$615$	33.2084	+	10.3625i	1.33909	+	0.417857i
$616$		0			0
$617$	−38.1880			−1.53739			−0.768695	−	0.639616i	$-0.779094\pi$
$617$	−38.1880			−1.53739			−0.768695	+	0.639616i	$0.779094\pi$
$618$		0			0
$619$	−2.38038	+	2.38038i	−0.0956757	+	0.0956757i	−0.753325	−	0.657649i	$-0.771551\pi$
$619$	−2.38038	+	2.38038i	−0.0956757	+	0.0956757i	0.657649	+	0.753325i	$0.271551\pi$
$620$		0			0
$621$			48.7163i			1.95492i
$622$		0			0
$623$	9.56153	+	9.56153i	0.383074	+	0.383074i
$624$		0			0
$625$	8.82829	+	23.3893i	0.353132	+	0.935574i
$626$		0			0
$627$	45.2782	+	45.2782i	1.80824	+	1.80824i
$628$		0			0
$629$	−8.71749	−	8.71749i	−0.347589	−	0.347589i
$630$		0			0
$631$	−0.726798	−	0.726798i	−0.0289334	−	0.0289334i	0.692492	−	0.721425i	$-0.256513\pi$
$631$	−0.726798	−	0.726798i	−0.0289334	−	0.0289334i	−0.721425	+	0.692492i	$0.756513\pi$
$632$		0			0
$633$	54.4070	−	54.4070i	2.16248	−	2.16248i
$634$		0			0
$635$	15.1404	+	28.8753i	0.600830	+	1.14588i
$636$		0			0
$637$	0.146111	+	3.91238i	0.00578913	+	0.155014i
$638$		0			0
$639$	28.9702	+	28.9702i	1.14604	+	1.14604i
$640$		0			0
$641$		−	27.5067i		−	1.08645i	−0.839587	−	0.543225i	$-0.817203\pi$
$641$		−	27.5067i		−	1.08645i	0.839587	−	0.543225i	$-0.182797\pi$
$642$		0			0
$643$		−	6.23997i		−	0.246081i	−0.992402	−	0.123040i	$-0.960736\pi$
$643$		−	6.23997i		−	0.246081i	0.992402	−	0.123040i	$-0.0392644\pi$
$644$		0			0
$645$	−2.83854	+	9.09658i	−0.111767	+	0.358177i
$646$		0			0
$647$	−17.0569	+	17.0569i	−0.670576	+	0.670576i	−0.957849	−	0.287273i	$-0.907251\pi$
$647$	−17.0569	+	17.0569i	−0.670576	+	0.670576i	0.287273	+	0.957849i	$0.407251\pi$
$648$		0			0
$649$	21.2120			0.832643
$650$		0			0
$651$	43.7391			1.71427
$652$		0			0
$653$	12.3558	−	12.3558i	0.483520	−	0.483520i	−0.422734	−	0.906254i	$-0.638930\pi$
$653$	12.3558	−	12.3558i	0.483520	−	0.483520i	0.906254	+	0.422734i	$0.138930\pi$
$654$		0			0
$655$	6.68646	−	21.4279i	0.261262	−	0.837258i
$656$		0			0
$657$			54.5611i			2.12863i
$658$		0			0
$659$			4.97906i			0.193957i	0.995286	+	0.0969784i	$0.0309178\pi$
$659$			4.97906i			0.193957i	−0.995286	+	0.0969784i	$0.969082\pi$
$660$		0			0
$661$	−5.06622	−	5.06622i	−0.197053	−	0.197053i	0.601682	−	0.798735i	$-0.294497\pi$
$661$	−5.06622	−	5.06622i	−0.197053	−	0.197053i	−0.798735	+	0.601682i	$0.794497\pi$
$662$		0			0
$663$	43.0788	−	1.60882i	1.67304	−	0.0624812i
$664$		0			0
$665$	16.6115	+	31.6809i	0.644167	+	1.22853i
$666$		0			0
$667$	29.9728	−	29.9728i	1.16055	−	1.16055i
$668$		0			0
$669$	−3.21865	−	3.21865i	−0.124440	−	0.124440i
$670$		0			0
$671$	−29.2911	−	29.2911i	−1.13077	−	1.13077i
$672$		0			0
$673$	2.39838	+	2.39838i	0.0924506	+	0.0924506i	0.751820	−	0.659369i	$-0.229176\pi$
$673$	2.39838	+	2.39838i	0.0924506	+	0.0924506i	−0.659369	+	0.751820i	$0.729176\pi$
$674$		0			0
$675$	8.43227	+	46.2187i	0.324558	+	1.77896i
$676$		0			0
$677$	−16.5114	−	16.5114i	−0.634585	−	0.634585i	0.314630	−	0.949215i	$-0.398120\pi$
$677$	−16.5114	−	16.5114i	−0.634585	−	0.634585i	−0.949215	+	0.314630i	$0.898120\pi$
$678$		0			0
$679$		−	25.9339i		−	0.995253i
$680$		0			0
$681$	27.2245	−	27.2245i	1.04325	−	1.04325i
$682$		0			0
$683$	25.6982			0.983314			0.491657	−	0.870789i	$-0.336391\pi$
$683$	25.6982			0.983314			0.491657	+	0.870789i	$0.336391\pi$
$684$		0			0
$685$	−15.8342	−	4.94097i	−0.604993	−	0.188785i
$686$		0			0
$687$		−	72.7718i		−	2.77642i
$688$		0			0
$689$	−10.3925	−	9.64420i	−0.395922	−	0.367415i
$690$		0			0
$691$	−3.68536	+	3.68536i	−0.140198	+	0.140198i	−0.773722	−	0.633525i	$-0.781607\pi$
$691$	−3.68536	+	3.68536i	−0.140198	+	0.140198i	0.633525	+	0.773722i	$0.281607\pi$
$692$		0			0
$693$	−46.3412	−	46.3412i	−1.76036	−	1.76036i
$694$		0			0
$695$	−4.84356	−	1.51141i	−0.183727	−	0.0573310i
$696$		0			0
$697$			20.4122i			0.773166i
$698$		0			0
$699$	−85.2779			−3.22551
$700$		0			0
$701$			24.4122i			0.922034i	0.887391	+	0.461017i	$0.152515\pi$
$701$			24.4122i			0.922034i	−0.887391	+	0.461017i	$0.847485\pi$
$702$		0			0
$703$	−12.3826	+	12.3826i	−0.467020	+	0.467020i
$704$		0			0
$705$	−56.5988	+	29.6769i	−2.13163	+	1.11770i
$706$		0			0
$707$	−28.8323			−1.08435
$708$		0			0
$709$	22.9370	−	22.9370i	0.861417	−	0.861417i	−0.130086	−	0.991503i	$-0.541525\pi$
$709$	22.9370	−	22.9370i	0.861417	−	0.861417i	0.991503	+	0.130086i	$0.0415253\pi$
$710$		0			0
$711$	−33.7356			−1.26518
$712$		0			0
$713$	26.4180			0.989364
$714$		0			0
$715$	15.1109	+	26.3761i	0.565116	+	0.986409i
$716$		0			0
$717$	8.39118			0.313375
$718$		0			0
$719$	31.4886			1.17433			0.587164	−	0.809468i	$-0.300244\pi$
$719$	31.4886			1.17433			0.587164	+	0.809468i	$0.300244\pi$
$720$		0			0
$721$	24.3961	−	24.3961i	0.908557	−	0.908557i
$722$		0			0
$723$	−57.0998			−2.12356
$724$		0			0
$725$	23.2482	−	33.6241i	0.863416	−	1.24877i
$726$		0			0
$727$	−13.1780	+	13.1780i	−0.488744	+	0.488744i	−0.907910	−	0.419166i	$-0.862323\pi$
$727$	−13.1780	+	13.1780i	−0.488744	+	0.488744i	0.419166	+	0.907910i	$0.362323\pi$
$728$		0			0
$729$		−	23.8038i		−	0.881623i
$730$		0			0
$731$	−5.59138			−0.206804
$732$		0			0
$733$			37.8822i			1.39921i	0.714530	+	0.699605i	$0.246641\pi$
$733$			37.8822i			1.39921i	−0.714530	+	0.699605i	$0.753359\pi$
$734$		0			0
$735$	−3.40368	−	6.49137i	−0.125546	−	0.239438i
$736$		0			0
$737$	1.53152	+	1.53152i	0.0564142	+	0.0564142i
$738$		0			0
$739$	8.49036	−	8.49036i	0.312323	−	0.312323i	−0.533486	−	0.845809i	$-0.679118\pi$
$739$	8.49036	−	8.49036i	0.312323	−	0.312323i	0.845809	+	0.533486i	$0.179118\pi$
$740$		0			0
$741$	−2.28522	−	61.1907i	−0.0839496	−	2.24790i
$742$		0			0
$743$		−	38.4331i		−	1.40997i	−0.709220	−	0.704987i	$-0.750953\pi$
$743$		−	38.4331i		−	1.40997i	0.709220	−	0.704987i	$-0.249047\pi$
$744$		0			0
$745$	2.73442	−	1.43376i	0.100181	−	0.0525289i
$746$		0			0
$747$	−16.8570			−0.616765
$748$		0			0
$749$	−14.3540	+	14.3540i	−0.524482	+	0.524482i
$750$		0			0
$751$			20.4961i			0.747915i	0.927446	+	0.373957i	$0.121999\pi$
$751$			20.4961i			0.747915i	−0.927446	+	0.373957i	$0.878001\pi$
$752$		0			0
$753$	45.1647	+	45.1647i	1.64589	+	1.64589i
$754$		0			0
$755$	10.6393	−	5.57857i	0.387202	−	0.203025i
$756$		0			0
$757$	−10.3305	−	10.3305i	−0.375468	−	0.375468i	0.493996	−	0.869464i	$-0.335536\pi$
$757$	−10.3305	−	10.3305i	−0.375468	−	0.375468i	−0.869464	+	0.493996i	$0.835536\pi$
$758$		0			0
$759$	−41.7266	−	41.7266i	−1.51458	−	1.51458i
$760$		0			0
$761$	12.0344	+	12.0344i	0.436246	+	0.436246i	0.890746	−	0.454501i	$-0.150182\pi$
$761$	12.0344	+	12.0344i	0.436246	+	0.436246i	−0.454501	+	0.890746i	$0.650182\pi$
$762$		0			0
$763$	−16.3152	+	16.3152i	−0.590651	+	0.590651i
$764$		0			0
$765$	−47.9452	+	25.1395i	−1.73346	+	0.908921i
$766$		0			0
$767$	−14.8686	−	13.7980i	−0.536875	−	0.498218i
$768$		0			0
$769$	−36.7408	−	36.7408i	−1.32491	−	1.32491i	−0.909750	−	0.415156i	$-0.863727\pi$
$769$	−36.7408	−	36.7408i	−1.32491	−	1.32491i	−0.415156	−	0.909750i	$-0.636273\pi$
$770$		0			0
$771$			63.8822i			2.30066i
$772$		0			0
$773$			21.0047i			0.755486i	0.925911	+	0.377743i	$0.123300\pi$
$773$			21.0047i			0.755486i	−0.925911	+	0.377743i	$0.876700\pi$
$774$		0			0
$775$	25.0636	−	4.57268i	0.900312	−	0.164256i
$776$		0			0
$777$	18.8932	−	18.8932i	0.677790	−	0.677790i
$778$		0			0
$779$	28.9941			1.03882
$780$		0			0
$781$	−25.2710			−0.904269
$782$		0			0
$783$	54.3211	−	54.3211i	1.94128	−	1.94128i
$784$		0			0
$785$	31.0024	−	16.2557i	1.10652	−	0.580192i
$786$		0			0
$787$		−	45.9942i		−	1.63952i	−0.572710	−	0.819758i	$-0.694108\pi$
$787$		−	45.9942i		−	1.63952i	0.572710	−	0.819758i	$-0.305892\pi$
$788$		0			0
$789$		−	11.9638i		−	0.425922i
$790$		0			0
$791$	−21.4926	−	21.4926i	−0.764190	−	0.764190i
$792$		0			0
$793$	1.47834	+	39.5852i	0.0524975	+	1.40571i
$794$		0			0
$795$	25.3380	+	7.90660i	0.898648	+	0.280418i
$796$		0			0
$797$	1.79478	−	1.79478i	0.0635745	−	0.0635745i	−0.674605	−	0.738179i	$-0.735686\pi$
$797$	1.79478	−	1.79478i	0.0635745	−	0.0635745i	0.738179	+	0.674605i	$0.235686\pi$
$798$		0			0
$799$	−26.5155	−	26.5155i	−0.938049	−	0.938049i
$800$		0			0
$801$	20.5540	+	20.5540i	0.726239	+	0.726239i
$802$		0			0
$803$	−23.7971	−	23.7971i	−0.839782	−	0.839782i
$804$		0			0
$805$	−15.3085	−	29.1959i	−0.539554	−	1.02902i
$806$		0			0
$807$	47.1722	+	47.1722i	1.66054	+	1.66054i
$808$		0			0
$809$			41.9702i			1.47559i	0.675024	+	0.737796i	$0.264133\pi$
$809$			41.9702i			1.47559i	−0.675024	+	0.737796i	$0.735867\pi$
$810$		0			0
$811$	−21.5522	+	21.5522i	−0.756801	+	0.756801i	−0.975739	−	0.218938i	$-0.929741\pi$
$811$	−21.5522	+	21.5522i	−0.756801	+	0.756801i	0.218938	+	0.975739i	$0.429741\pi$
$812$		0			0
$813$	61.0351			2.14059
$814$		0			0
$815$	14.3057	−	45.8451i	0.501107	−	1.60588i
$816$		0			0
$817$			7.94219i			0.277862i
$818$		0			0
$819$	2.33887	+	62.6273i	0.0817268	+	2.18838i
$820$		0			0
$821$	7.98221	−	7.98221i	0.278581	−	0.278581i	−0.553961	−	0.832542i	$-0.686884\pi$
$821$	7.98221	−	7.98221i	0.278581	−	0.278581i	0.832542	+	0.553961i	$0.186884\pi$
$822$		0			0
$823$	−5.95531	−	5.95531i	−0.207589	−	0.207589i	0.595653	−	0.803242i	$-0.296893\pi$
$823$	−5.95531	−	5.95531i	−0.207589	−	0.207589i	−0.803242	+	0.595653i	$0.796893\pi$
$824$		0			0
$825$	−46.8097	−	32.3649i	−1.62970	−	1.12680i
$826$		0			0
$827$			9.00821i			0.313246i	0.987658	+	0.156623i	$0.0500608\pi$
$827$			9.00821i			0.313246i	−0.987658	+	0.156623i	$0.949939\pi$
$828$		0			0
$829$	47.2837			1.64223			0.821115	−	0.570763i	$-0.193352\pi$
$829$	47.2837			1.64223			0.821115	+	0.570763i	$0.193352\pi$
$830$		0			0
$831$			17.1588i			0.595232i
$832$		0			0
$833$	3.04108	−	3.04108i	0.105367	−	0.105367i
$834$		0			0
$835$	5.80064	+	1.81006i	0.200739	+	0.0626396i
$836$		0			0
$837$	47.8786			1.65493
$838$		0			0
$839$	−20.6334	+	20.6334i	−0.712344	+	0.712344i	−0.967025	−	0.254681i	$-0.918030\pi$
$839$	−20.6334	+	20.6334i	−0.712344	+	0.712344i	0.254681	+	0.967025i	$0.418030\pi$
$840$		0			0
$841$	−37.8424			−1.30491
$842$		0			0
$843$	−43.6568			−1.50362
$844$		0			0
$845$	6.56514	−	28.3178i	0.225848	−	0.974163i
$846$		0			0
$847$	9.14473			0.314217
$848$		0			0
$849$	87.4035			2.99968
$850$		0			0
$851$	11.4113	−	11.4113i	0.391175	−	0.391175i
$852$		0			0
$853$	24.5422			0.840310			0.420155	−	0.907452i	$-0.361976\pi$
$853$	24.5422			0.840310			0.420155	+	0.907452i	$0.361976\pi$
$854$		0			0
$855$	35.7090	+	68.1031i	1.22122	+	2.32908i
$856$		0			0
$857$	−27.2312	+	27.2312i	−0.930202	+	0.930202i	−0.997718	−	0.0675164i	$-0.978493\pi$
$857$	−27.2312	+	27.2312i	−0.930202	+	0.930202i	0.0675164	+	0.997718i	$0.478493\pi$
$858$		0			0
$859$		−	9.87746i		−	0.337015i	−0.985700	−	0.168507i	$-0.946105\pi$
$859$		−	9.87746i		−	0.337015i	0.985700	−	0.168507i	$-0.0538947\pi$
$860$		0			0
$861$	−44.2388			−1.50765
$862$		0			0
$863$			7.46931i			0.254258i	0.991886	+	0.127129i	$0.0405763\pi$
$863$			7.46931i			0.254258i	−0.991886	+	0.127129i	$0.959424\pi$
$864$		0			0
$865$	11.9022	−	6.24080i	0.404688	−	0.212194i
$866$		0			0
$867$	2.80240	+	2.80240i	0.0951746	+	0.0951746i
$868$		0			0
$869$	14.7140	−	14.7140i	0.499137	−	0.499137i
$870$		0			0
$871$	−0.0772967	−	2.06975i	−0.00261910	−	0.0701309i
$872$		0			0
$873$		−	55.7490i		−	1.88682i
$874$		0			0
$875$	−19.5772	−	25.0493i	−0.661829	−	0.846821i
$876$		0			0
$877$	−16.1762			−0.546231			−0.273116	−	0.961981i	$-0.588054\pi$
$877$	−16.1762			−0.546231			−0.273116	+	0.961981i	$0.588054\pi$
$878$		0			0
$879$	50.7534	−	50.7534i	1.71187	−	1.71187i
$880$		0			0
$881$			32.0765i			1.08068i	0.841445	+	0.540342i	$0.181705\pi$
$881$			32.0765i			1.08068i	−0.841445	+	0.540342i	$0.818295\pi$
$882$		0			0
$883$	−29.7870	−	29.7870i	−1.00241	−	1.00241i	−0.999997	−	0.00241408i	$-0.999232\pi$
$883$	−29.7870	−	29.7870i	−1.00241	−	1.00241i	−0.00241408	−	0.999997i	$-0.500768\pi$
$884$		0			0
$885$	36.2514	+	11.3120i	1.21858	+	0.380250i
$886$		0			0
$887$	−6.13290	−	6.13290i	−0.205923	−	0.205923i	0.596609	−	0.802532i	$-0.296514\pi$
$887$	−6.13290	−	6.13290i	−0.205923	−	0.205923i	−0.802532	+	0.596609i	$0.796514\pi$
$888$		0			0
$889$	−29.3179	−	29.3179i	−0.983292	−	0.983292i
$890$		0			0
$891$	−26.7323	−	26.7323i	−0.895566	−	0.895566i
$892$		0			0
$893$	−37.6635	+	37.6635i	−1.26036	+	1.26036i
$894$		0			0
$895$	−11.1974	+	35.8838i	−0.374286	+	1.19946i
$896$		0			0
$897$	2.10597	+	56.3909i	0.0703161	+	1.88284i
$898$		0			0
$899$	−29.4574	−	29.4574i	−0.982461	−	0.982461i
$900$		0			0
$901$			15.5745i			0.518861i
$902$		0			0
$903$		−	12.1181i		−	0.403264i
$904$		0			0
$905$	46.2151	+	14.4212i	1.53624	+	0.479377i
$906$		0			0
$907$	35.2823	−	35.2823i	1.17153	−	1.17153i	0.189683	−	0.981845i	$-0.439254\pi$
$907$	35.2823	−	35.2823i	1.17153	−	1.17153i	0.981845	−	0.189683i	$-0.0607461\pi$
$908$		0			0
$909$	−61.9796			−2.05573
$910$		0			0
$911$	40.1710			1.33092			0.665462	−	0.746431i	$-0.268234\pi$
$911$	40.1710			1.33092			0.665462	+	0.746431i	$0.268234\pi$
$912$		0			0
$913$	7.35227	−	7.35227i	0.243324	−	0.243324i
$914$		0			0
$915$	−34.4382	−	65.6793i	−1.13849	−	2.17129i
$916$		0			0
$917$			28.5453i			0.942649i
$918$		0			0
$919$		−	1.33757i		−	0.0441223i	−0.999757	−	0.0220611i	$-0.992977\pi$
$919$		−	1.33757i		−	0.0441223i	0.999757	−	0.0220611i	$-0.00702285\pi$
$920$		0			0
$921$	3.13633	+	3.13633i	0.103345	+	0.103345i
$922$		0			0
$923$	17.7138	+	16.4384i	0.583058	+	0.541076i
$924$		0			0
$925$	8.85111	−	12.8015i	0.291023	−	0.420910i
$926$		0			0
$927$	52.4431	−	52.4431i	1.72246	−	1.72246i
$928$		0			0
$929$	23.1253	+	23.1253i	0.758716	+	0.758716i	0.976089	−	0.217373i	$-0.0697487\pi$
$929$	23.1253	+	23.1253i	0.758716	+	0.758716i	−0.217373	+	0.976089i	$0.569749\pi$
$930$		0			0
$931$	−4.31966	−	4.31966i	−0.141571	−	0.141571i
$932$		0			0
$933$	1.51141	+	1.51141i	0.0494813	+	0.0494813i
$934$		0			0
$935$	9.94682	−	31.8763i	0.325296	−	1.04247i
$936$		0			0
$937$	−6.50552	−	6.50552i	−0.212526	−	0.212526i	0.592814	−	0.805340i	$-0.298017\pi$
$937$	−6.50552	−	6.50552i	−0.212526	−	0.212526i	−0.805340	+	0.592814i	$0.798017\pi$
$938$		0			0
$939$			58.6474i			1.91389i
$940$		0			0
$941$	−28.4625	+	28.4625i	−0.927850	+	0.927850i	−0.997567	−	0.0697170i	$-0.977790\pi$
$941$	−28.4625	+	28.4625i	−0.927850	+	0.927850i	0.0697170	+	0.997567i	$0.477790\pi$
$942$		0			0
$943$	−26.7198			−0.870118
$944$		0			0
$945$	−27.7443	−	52.9130i	−0.902523	−	1.72126i
$946$		0			0
$947$		−	12.5474i		−	0.407737i	−0.978998	−	0.203868i	$-0.934649\pi$
$947$		−	12.5474i		−	0.407737i	0.978998	−	0.203868i	$-0.0653515\pi$
$948$		0			0
$949$	1.20105	+	32.1603i	0.0389879	+	1.04397i
$950$		0			0
$951$	−24.3027	+	24.3027i	−0.788068	+	0.788068i
$952$		0			0
$953$	0.341577	+	0.341577i	0.0110648	+	0.0110648i	0.712618	−	0.701553i	$-0.247510\pi$
$953$	0.341577	+	0.341577i	0.0110648	+	0.0110648i	−0.701553	+	0.712618i	$0.747510\pi$
$954$		0			0
$955$	1.39939	−	4.48458i	0.0452832	−	0.145118i
$956$		0			0
$957$			93.0544i			3.00802i
$958$		0			0
$959$	21.0936			0.681147
$960$		0			0
$961$			5.03621i			0.162458i
$962$		0			0
$963$	−30.8561	+	30.8561i	−0.994322	+	0.994322i
$964$		0			0
$965$	3.59207	−	11.5114i	0.115633	−	0.370565i
$966$		0			0
$967$	29.5634			0.950695			0.475348	−	0.879798i	$-0.342322\pi$
$967$	29.5634			0.950695			0.475348	+	0.879798i	$0.342322\pi$
$968$		0			0
$969$	−47.5634	+	47.5634i	−1.52796	+	1.52796i
$970$		0			0
$971$	47.7660			1.53288			0.766442	−	0.642314i	$-0.222025\pi$
$971$	47.7660			1.53288			0.766442	+	0.642314i	$0.222025\pi$
$972$		0			0
$973$	6.45238			0.206854
$974$		0			0
$975$	11.7586	+	53.1353i	0.376578	+	1.70169i
$976$		0			0
$977$	−34.4601			−1.10248			−0.551239	−	0.834347i	$-0.685845\pi$
$977$	−34.4601			−1.10248			−0.551239	+	0.834347i	$0.685845\pi$
$978$		0			0
$979$	−17.9295			−0.573028
$980$		0			0
$981$	−35.0721	+	35.0721i	−1.11977	+	1.11977i
$982$		0			0
$983$	−33.0637			−1.05457			−0.527285	−	0.849689i	$-0.676790\pi$
$983$	−33.0637			−1.05457			−0.527285	+	0.849689i	$0.676790\pi$
$984$		0			0
$985$	5.77346	−	18.5020i	0.183958	−	0.589523i
$986$		0			0
$987$	57.4663	−	57.4663i	1.82917	−	1.82917i
$988$		0			0
$989$		−	7.31920i		−	0.232737i
$990$		0			0
$991$	61.5406			1.95490			0.977451	−	0.211162i	$-0.0677246\pi$
$991$	61.5406			1.95490			0.977451	+	0.211162i	$0.0677246\pi$
$992$		0			0
$993$			63.2068i			2.00581i
$994$		0			0
$995$	−7.67016	+	24.5803i	−0.243161	+	0.779249i
$996$		0			0
$997$	9.82494	+	9.82494i	0.311159	+	0.311159i	0.845358	−	0.534199i	$-0.179387\pi$
$997$	9.82494	+	9.82494i	0.311159	+	0.311159i	−0.534199	+	0.845358i	$0.679387\pi$
$998$		0			0
$999$	20.6813	−	20.6813i	0.654327	−	0.654327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.m.c.57.4	✓	8
3.2	odd	2		2340.2.u.g.577.3		8
4.3	odd	2		1040.2.bg.m.577.1		8
5.2	odd	4		1300.2.r.c.993.1		8
5.3	odd	4		260.2.r.c.213.4	yes	8
5.4	even	2		1300.2.m.c.57.1		8
13.8	odd	4		260.2.r.c.177.4	yes	8
15.8	even	4		2340.2.bp.g.1513.4		8
20.3	even	4		1040.2.cd.m.993.1		8
39.8	even	4		2340.2.bp.g.1477.4		8
52.47	even	4		1040.2.cd.m.177.1		8
65.8	even	4	inner	260.2.m.c.73.4	yes	8
65.34	odd	4		1300.2.r.c.957.1		8
65.47	even	4		1300.2.m.c.593.1		8
195.8	odd	4		2340.2.u.g.73.3		8
260.203	odd	4		1040.2.bg.m.593.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.m.c.57.4	✓	8	1.1	even	1	trivial
260.2.m.c.73.4	yes	8	65.8	even	4	inner
260.2.r.c.177.4	yes	8	13.8	odd	4
260.2.r.c.213.4	yes	8	5.3	odd	4
1040.2.bg.m.577.1		8	4.3	odd	2
1040.2.bg.m.593.1		8	260.203	odd	4
1040.2.cd.m.177.1		8	52.47	even	4
1040.2.cd.m.993.1		8	20.3	even	4
1300.2.m.c.57.1		8	5.4	even	2
1300.2.m.c.593.1		8	65.47	even	4
1300.2.r.c.957.1		8	65.34	odd	4
1300.2.r.c.993.1		8	5.2	odd	4
2340.2.u.g.73.3		8	195.8	odd	4
2340.2.u.g.577.3		8	3.2	odd	2
2340.2.bp.g.1477.4		8	39.8	even	4
2340.2.bp.g.1513.4		8	15.8	even	4

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13456 - 2.13456i) q^{3} +(-0.666078 + 2.13456i) q^{5} -2.84356i q^{7} -6.11268i q^{9} +O(q^{10})\)	\(q+(2.13456 - 2.13456i) q^{3} +(-0.666078 + 2.13456i) q^{5} -2.84356i q^{7} -6.11268i q^{9} +(2.66608 + 2.66608i) q^{11} +(-0.134559 - 3.60304i) q^{13} +(3.13456 + 5.97812i) q^{15} +(-2.80064 + 2.80064i) q^{17} +(3.97812 + 3.97812i) q^{19} +(-6.06975 - 6.06975i) q^{21} +(-3.66608 - 3.66608i) q^{23} +(-4.11268 - 2.84356i) q^{25} +(-6.64420 - 6.64420i) q^{27} +8.17572i q^{29} +(-3.60304 + 3.60304i) q^{31} +11.3818 q^{33} +(6.06975 + 1.89403i) q^{35} +3.11268i q^{37} +(-7.97812 - 7.40368i) q^{39} +(3.64420 - 3.64420i) q^{41} +(0.998233 + 0.998233i) q^{43} +(13.0479 + 4.07152i) q^{45} +9.46765i q^{47} -1.08585 q^{49} +11.9562i q^{51} +(2.78053 - 2.78053i) q^{53} +(-7.46671 + 3.91508i) q^{55} +16.9831 q^{57} +(3.97812 - 3.97812i) q^{59} -10.9866 q^{61} -17.3818 q^{63} +(7.78053 + 2.11268i) q^{65} +0.574447 q^{67} -15.6509 q^{69} +(-4.73937 + 4.73937i) q^{71} -8.92588 q^{73} +(-14.8485 + 2.70901i) q^{75} +(7.58116 - 7.58116i) q^{77} -5.51895i q^{79} -10.0268 q^{81} -2.75771i q^{83} +(-4.11268 - 7.84356i) q^{85} +(17.4516 + 17.4516i) q^{87} +(-3.36252 + 3.36252i) q^{89} +(-10.2455 + 0.382626i) q^{91} +15.3818i q^{93} +(-11.1413 + 5.84180i) q^{95} +9.12022 q^{97} +(16.2969 - 16.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^5	\( 8 q + 2 q^{3} + 2 q^{5} + 14 q^{11} + 14 q^{13} + 10 q^{15} + 2 q^{19} + 4 q^{21} - 22 q^{23} + 12 q^{25} - 16 q^{27} - 6 q^{31} + 16 q^{33} - 4 q^{35} - 34 q^{39} - 8 q^{41} - 14 q^{43} + 22 q^{45} - 24 q^{49} - 8 q^{53} - 30 q^{55} + 16 q^{57} + 2 q^{59} - 12 q^{61} - 64 q^{63} + 32 q^{65} + 20 q^{67} - 20 q^{69} - 22 q^{71} - 28 q^{73} - 14 q^{75} + 8 q^{77} - 20 q^{81} + 12 q^{85} + 12 q^{87} + 4 q^{89} - 6 q^{95} + 12 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^5 + 14 * q^11 + 14 * q^13 + 10 * q^15 + 2 * q^19 + 4 * q^21 - 22 * q^23 + 12 * q^25 - 16 * q^27 - 6 * q^31 + 16 * q^33 - 4 * q^35 - 34 * q^39 - 8 * q^41 - 14 * q^43 + 22 * q^45 - 24 * q^49 - 8 * q^53 - 30 * q^55 + 16 * q^57 + 2 * q^59 - 12 * q^61 - 64 * q^63 + 32 * q^65 + 20 * q^67 - 20 * q^69 - 22 * q^71 - 28 * q^73 - 14 * q^75 + 8 * q^77 - 20 * q^81 + 12 * q^85 + 12 * q^87 + 4 * q^89 - 6 * q^95 + 12 * q^97 + 10 * q^99

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