LMFDB - Embedded newform 128.3.h.a.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			79.4
Character	$\chi$	$=$	128.79
Dual form			128.3.h.a.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.299792 - 0.723762i) q^{3} +(1.34740 - 3.25291i) q^{5} +(-0.583225 + 0.583225i) q^{7} +(5.93000 - 5.93000i) q^{9} +O(q^{10})$	\(q+(-0.299792 - 0.723762i) q^{3} +(1.34740 - 3.25291i) q^{5} +(-0.583225 + 0.583225i) q^{7} +(5.93000 - 5.93000i) q^{9} +(3.03620 - 7.33003i) q^{11} +(-6.38385 - 15.4120i) q^{13} -2.75827 q^{15} +19.0889i q^{17} +(29.6679 - 12.2888i) q^{19} +(0.596962 + 0.247270i) q^{21} +(-15.2998 - 15.2998i) q^{23} +(8.91173 + 8.91173i) q^{25} +(-12.5835 - 5.21227i) q^{27} +(-20.5148 + 8.49749i) q^{29} +53.6582i q^{31} -6.21542 q^{33} +(1.11134 + 2.68301i) q^{35} +(-3.80237 + 9.17973i) q^{37} +(-9.24078 + 9.24078i) q^{39} +(14.5108 - 14.5108i) q^{41} +(-20.3685 + 49.1739i) q^{43} +(-11.2997 - 27.2799i) q^{45} -4.73351 q^{47} +48.3197i q^{49} +(13.8158 - 5.72269i) q^{51} +(61.4006 + 25.4330i) q^{53} +(-19.7530 - 19.7530i) q^{55} +(-17.7884 - 17.7884i) q^{57} +(-42.4656 - 17.5898i) q^{59} +(-27.7452 + 11.4924i) q^{61} +6.91705i q^{63} -58.7354 q^{65} +(9.42323 + 22.7497i) q^{67} +(-6.48665 + 15.6602i) q^{69} +(95.1299 - 95.1299i) q^{71} +(37.1241 - 37.1241i) q^{73} +(3.77831 - 9.12164i) q^{75} +(2.50427 + 6.04584i) q^{77} +70.3394 q^{79} -64.8066i q^{81} +(-14.5221 + 6.01526i) q^{83} +(62.0944 + 25.7203i) q^{85} +(12.3003 + 12.3003i) q^{87} +(-60.8411 - 60.8411i) q^{89} +(12.7119 + 5.26543i) q^{91} +(38.8357 - 16.0863i) q^{93} -113.065i q^{95} +31.8287 q^{97} +(-25.4624 - 61.4718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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
$3$	−0.299792	−	0.723762i	−0.0999307	−	0.241254i	0.866005	−	0.500035i	$-0.166679\pi$
$3$	−0.299792	−	0.723762i	−0.0999307	−	0.241254i	−0.965936	+	0.258781i	$0.916679\pi$
$4$		0			0
$5$	1.34740	−	3.25291i	0.269480	−	0.650582i	−0.729979	−	0.683469i	$-0.760470\pi$
$5$	1.34740	−	3.25291i	0.269480	−	0.650582i	0.999459	+	0.0328874i	$0.0104703\pi$
$6$		0			0
$7$	−0.583225	+	0.583225i	−0.0833178	+	0.0833178i	−0.747537	−	0.664220i	$-0.768764\pi$
$7$	−0.583225	+	0.583225i	−0.0833178	+	0.0833178i	0.664220	+	0.747537i	$0.268764\pi$
$8$		0			0
$9$	5.93000	−	5.93000i	0.658889	−	0.658889i
$10$		0			0
$11$	3.03620	−	7.33003i	0.276018	−	0.666366i	−0.723700	−	0.690115i	$-0.757560\pi$
$11$	3.03620	−	7.33003i	0.276018	−	0.666366i	0.999718	+	0.0237484i	$0.00756007\pi$
$12$		0			0
$13$	−6.38385	−	15.4120i	−0.491065	−	1.18554i	−0.954179	−	0.299238i	$-0.903268\pi$
$13$	−6.38385	−	15.4120i	−0.491065	−	1.18554i	0.463113	−	0.886299i	$-0.346732\pi$
$14$		0			0
$15$	−2.75827			−0.183885
$16$		0			0
$17$			19.0889i			1.12287i	0.827519	+	0.561437i	$0.189751\pi$
$17$			19.0889i			1.12287i	−0.827519	+	0.561437i	$0.810249\pi$
$18$		0			0
$19$	29.6679	−	12.2888i	1.56147	−	0.646781i	0.576123	−	0.817363i	$-0.304565\pi$
$19$	29.6679	−	12.2888i	1.56147	−	0.646781i	0.985343	+	0.170582i	$0.0545648\pi$
$20$		0			0
$21$	0.596962	+	0.247270i	0.0284268	+	0.0117748i
$22$		0			0
$23$	−15.2998	−	15.2998i	−0.665208	−	0.665208i	0.291395	−	0.956603i	$-0.405881\pi$
$23$	−15.2998	−	15.2998i	−0.665208	−	0.665208i	−0.956603	+	0.291395i	$0.905881\pi$
$24$		0			0
$25$	8.91173	+	8.91173i	0.356469	+	0.356469i
$26$		0			0
$27$	−12.5835	−	5.21227i	−0.466057	−	0.193047i
$28$		0			0
$29$	−20.5148	+	8.49749i	−0.707405	+	0.293017i	−0.707231	−	0.706983i	$-0.750056\pi$
$29$	−20.5148	+	8.49749i	−0.707405	+	0.293017i	−0.000174983		1.00000i	$0.500056\pi$
$30$		0			0
$31$			53.6582i			1.73091i	0.500988	+	0.865454i	$0.332970\pi$
$31$			53.6582i			1.73091i	−0.500988	+	0.865454i	$0.667030\pi$
$32$		0			0
$33$	−6.21542			−0.188346
$34$		0			0
$35$	1.11134	+	2.68301i	0.0317526	+	0.0766575i
$36$		0			0
$37$	−3.80237	+	9.17973i	−0.102767	+	0.248101i	−0.966897	−	0.255168i	$-0.917869\pi$
$37$	−3.80237	+	9.17973i	−0.102767	+	0.248101i	0.864130	+	0.503268i	$0.167869\pi$
$38$		0			0
$39$	−9.24078	+	9.24078i	−0.236943	+	0.236943i
$40$		0			0
$41$	14.5108	−	14.5108i	0.353922	−	0.353922i	−0.507644	−	0.861567i	$-0.669484\pi$
$41$	14.5108	−	14.5108i	0.353922	−	0.353922i	0.861567	+	0.507644i	$0.169484\pi$
$42$		0			0
$43$	−20.3685	+	49.1739i	−0.473686	+	1.14358i	0.488837	+	0.872375i	$0.337421\pi$
$43$	−20.3685	+	49.1739i	−0.473686	+	1.14358i	−0.962522	+	0.271203i	$0.912579\pi$
$44$		0			0
$45$	−11.2997	−	27.2799i	−0.251104	−	0.606219i
$46$		0			0
$47$	−4.73351			−0.100713			−0.0503565	−	0.998731i	$-0.516036\pi$
$47$	−4.73351			−0.100713			−0.0503565	+	0.998731i	$0.516036\pi$
$48$		0			0
$49$			48.3197i			0.986116i
$50$		0			0
$51$	13.8158	−	5.72269i	0.270898	−	0.112210i
$52$		0			0
$53$	61.4006	+	25.4330i	1.15850	+	0.479867i	0.877376	−	0.479803i	$-0.159292\pi$
$53$	61.4006	+	25.4330i	1.15850	+	0.479867i	0.281126	+	0.959671i	$0.409292\pi$
$54$		0			0
$55$	−19.7530	−	19.7530i	−0.359145	−	0.359145i
$56$		0			0
$57$	−17.7884	−	17.7884i	−0.312077	−	0.312077i
$58$		0			0
$59$	−42.4656	−	17.5898i	−0.719757	−	0.298133i	−0.00742152	−	0.999972i	$-0.502362\pi$
$59$	−42.4656	−	17.5898i	−0.719757	−	0.298133i	−0.712335	+	0.701840i	$0.752362\pi$
$60$		0			0
$61$	−27.7452	+	11.4924i	−0.454839	+	0.188400i	−0.598328	−	0.801251i	$-0.704168\pi$
$61$	−27.7452	+	11.4924i	−0.454839	+	0.188400i	0.143489	+	0.989652i	$0.454168\pi$
$62$		0			0
$63$			6.91705i			0.109794i
$64$		0			0
$65$	−58.7354			−0.903621
$66$		0			0
$67$	9.42323	+	22.7497i	0.140645	+	0.339548i	0.978469	−	0.206393i	$-0.0661725\pi$
$67$	9.42323	+	22.7497i	0.140645	+	0.339548i	−0.837824	+	0.545940i	$0.816172\pi$
$68$		0			0
$69$	−6.48665	+	15.6602i	−0.0940094	+	0.226959i
$70$		0			0
$71$	95.1299	−	95.1299i	1.33986	−	1.33986i	0.443664	−	0.896193i	$-0.353678\pi$
$71$	95.1299	−	95.1299i	1.33986	−	1.33986i	0.896193	−	0.443664i	$-0.146322\pi$
$72$		0			0
$73$	37.1241	−	37.1241i	0.508550	−	0.508550i	−0.405531	−	0.914081i	$-0.632913\pi$
$73$	37.1241	−	37.1241i	0.508550	−	0.508550i	0.914081	+	0.405531i	$0.132913\pi$
$74$		0			0
$75$	3.77831	−	9.12164i	0.0503774	−	0.121622i
$76$		0			0
$77$	2.50427	+	6.04584i	0.0325230	+	0.0785174i
$78$		0			0
$79$	70.3394			0.890372			0.445186	−	0.895438i	$-0.353138\pi$
$79$	70.3394			0.890372			0.445186	+	0.895438i	$0.353138\pi$
$80$		0			0
$81$		−	64.8066i		−	0.800081i
$82$		0			0
$83$	−14.5221	+	6.01526i	−0.174965	+	0.0724730i	−0.468447	−	0.883492i	$-0.655186\pi$
$83$	−14.5221	+	6.01526i	−0.174965	+	0.0724730i	0.293481	+	0.955965i	$0.405186\pi$
$84$		0			0
$85$	62.0944	+	25.7203i	0.730522	+	0.302592i
$86$		0			0
$87$	12.3003	+	12.3003i	0.141383	+	0.141383i
$88$		0			0
$89$	−60.8411	−	60.8411i	−0.683608	−	0.683608i	0.277204	−	0.960811i	$-0.410592\pi$
$89$	−60.8411	−	60.8411i	−0.683608	−	0.683608i	−0.960811	+	0.277204i	$0.910592\pi$
$90$		0			0
$91$	12.7119	+	5.26543i	0.139691	+	0.0578618i
$92$		0			0
$93$	38.8357	−	16.0863i	0.417589	−	0.172971i
$94$		0			0
$95$		−	113.065i		−	1.19016i
$96$		0			0
$97$	31.8287			0.328131			0.164066	−	0.986449i	$-0.447539\pi$
$97$	31.8287			0.328131			0.164066	+	0.986449i	$0.447539\pi$
$98$		0			0
$99$	−25.4624	−	61.4718i	−0.257196	−	0.620927i
$100$		0			0
$101$	11.0397	−	26.6521i	0.109304	−	0.263883i	−0.859758	−	0.510702i	$-0.829385\pi$
$101$	11.0397	−	26.6521i	0.109304	−	0.263883i	0.969061	+	0.246820i	$0.0793855\pi$
$102$		0			0
$103$	−56.0862	+	56.0862i	−0.544526	+	0.544526i	−0.924852	−	0.380326i	$-0.875812\pi$
$103$	−56.0862	+	56.0862i	−0.544526	+	0.544526i	0.380326	+	0.924852i	$0.375812\pi$
$104$		0			0
$105$	1.60869	−	1.60869i	0.0153209	−	0.0153209i
$106$		0			0
$107$	−5.85623	+	14.1382i	−0.0547311	+	0.132133i	−0.948880	−	0.315637i	$-0.897782\pi$
$107$	−5.85623	+	14.1382i	−0.0547311	+	0.132133i	0.894149	+	0.447770i	$0.147782\pi$
$108$		0			0
$109$	37.6258	+	90.8367i	0.345191	+	0.833364i	0.997174	+	0.0751304i	$0.0239373\pi$
$109$	37.6258	+	90.8367i	0.345191	+	0.833364i	−0.651983	+	0.758233i	$0.726063\pi$
$110$		0			0
$111$	7.78386			0.0701248
$112$		0			0
$113$		−	82.4104i		−	0.729295i	−0.931146	−	0.364648i	$-0.881189\pi$
$113$		−	82.4104i		−	0.729295i	0.931146	−	0.364648i	$-0.118811\pi$
$114$		0			0
$115$	−70.3837	+	29.1539i	−0.612032	+	0.253512i
$116$		0			0
$117$	−129.249	−	53.5368i	−1.10470	−	0.457580i
$118$		0			0
$119$	−11.1331	−	11.1331i	−0.0935555	−	0.0935555i
$120$		0			0
$121$	41.0491	+	41.0491i	0.339249	+	0.339249i
$122$		0			0
$123$	−14.8526	−	6.15215i	−0.120753	−	0.0500175i
$124$		0			0
$125$	122.319	−	50.6664i	0.978556	−	0.405331i
$126$		0			0
$127$			60.4972i			0.476356i	0.971221	+	0.238178i	$0.0765502\pi$
$127$			60.4972i			0.476356i	−0.971221	+	0.238178i	$0.923450\pi$
$128$		0			0
$129$	41.6965			0.323229
$130$		0			0
$131$	56.4124	+	136.192i	0.430629	+	1.03963i	0.979085	+	0.203451i	$0.0652157\pi$
$131$	56.4124	+	136.192i	0.430629	+	1.03963i	−0.548456	+	0.836179i	$0.684784\pi$
$132$		0			0
$133$	−10.1359	+	24.4702i	−0.0762096	+	0.183986i
$134$		0			0
$135$	−33.9101	+	33.9101i	−0.251186	+	0.251186i
$136$		0			0
$137$	−139.949	+	139.949i	−1.02152	+	1.02152i	−0.0217604	+	0.999763i	$0.506927\pi$
$137$	−139.949	+	139.949i	−1.02152	+	1.02152i	−0.999763	+	0.0217604i	$0.993073\pi$
$138$		0			0
$139$	2.63118	−	6.35223i	0.0189293	−	0.0456995i	−0.914132	−	0.405416i	$-0.867127\pi$
$139$	2.63118	−	6.35223i	0.0189293	−	0.0456995i	0.933062	+	0.359717i	$0.117127\pi$
$140$		0			0
$141$	1.41907	+	3.42593i	0.0100643	+	0.0242974i
$142$		0			0
$143$	−132.353			−0.925545
$144$		0			0
$145$			78.1822i			0.539187i
$146$		0			0
$147$	34.9720	−	14.4859i	0.237905	−	0.0985433i
$148$		0			0
$149$	−134.849	−	55.8563i	−0.905027	−	0.374874i	−0.118876	−	0.992909i	$-0.537929\pi$
$149$	−134.849	−	55.8563i	−0.905027	−	0.374874i	−0.786151	+	0.618035i	$0.787929\pi$
$150$		0			0
$151$	131.423	+	131.423i	0.870353	+	0.870353i	0.992511	−	0.122158i	$-0.0389814\pi$
$151$	131.423	+	131.423i	0.870353	+	0.870353i	−0.122158	+	0.992511i	$0.538981\pi$
$152$		0			0
$153$	113.197	+	113.197i	0.739850	+	0.739850i
$154$		0			0
$155$	174.545	+	72.2990i	1.12610	+	0.466445i
$156$		0			0
$157$	−151.775	+	62.8673i	−0.966720	+	0.400429i	−0.809490	−	0.587133i	$-0.800256\pi$
$157$	−151.775	+	62.8673i	−0.966720	+	0.400429i	−0.157230	+	0.987562i	$0.550256\pi$
$158$		0			0
$159$		−	52.0640i		−	0.327447i
$160$		0			0
$161$	17.8464			0.110847
$162$		0			0
$163$	−75.6492	−	182.633i	−0.464106	−	1.12045i	−0.966696	−	0.255926i	$-0.917620\pi$
$163$	−75.6492	−	182.633i	−0.464106	−	1.12045i	0.502591	−	0.864524i	$-0.332380\pi$
$164$		0			0
$165$	−8.37466	+	20.2182i	−0.0507555	+	0.122535i
$166$		0			0
$167$	−148.515	+	148.515i	−0.889310	+	0.889310i	−0.994457	−	0.105147i	$-0.966469\pi$
$167$	−148.515	+	148.515i	−0.889310	+	0.889310i	0.105147	+	0.994457i	$0.466469\pi$
$168$		0			0
$169$	−77.2745	+	77.2745i	−0.457246	+	0.457246i
$170$		0			0
$171$	103.058	−	248.803i	0.602677	−	1.45499i
$172$		0			0
$173$	14.9093	+	35.9942i	0.0861808	+	0.208059i	0.961094	−	0.276220i	$-0.0890819\pi$
$173$	14.9093	+	35.9942i	0.0861808	+	0.208059i	−0.874914	+	0.484279i	$0.839082\pi$
$174$		0			0
$175$	−10.3951			−0.0594005
$176$		0			0
$177$			36.0083i			0.203437i
$178$		0			0
$179$	−276.876	+	114.686i	−1.54679	+	0.640703i	−0.982733	−	0.185029i	$-0.940762\pi$
$179$	−276.876	+	114.686i	−1.54679	+	0.640703i	−0.564062	+	0.825733i	$0.690762\pi$
$180$		0			0
$181$	−82.1686	−	34.0354i	−0.453970	−	0.188041i	0.143969	−	0.989582i	$-0.454014\pi$
$181$	−82.1686	−	34.0354i	−0.453970	−	0.188041i	−0.597939	+	0.801542i	$0.704014\pi$
$182$		0			0
$183$	16.6356	+	16.6356i	0.0909047	+	0.0909047i
$184$		0			0
$185$	24.7375	+	24.7375i	0.133716	+	0.133716i
$186$		0			0
$187$	139.922	+	57.9576i	0.748246	+	0.309933i
$188$		0			0
$189$	10.3790	−	4.29911i	0.0549151	−	0.0227466i
$190$		0			0
$191$		−	178.857i		−	0.936426i	−0.883616	−	0.468213i	$-0.844898\pi$
$191$		−	178.857i		−	0.936426i	0.883616	−	0.468213i	$-0.155102\pi$
$192$		0			0
$193$	197.034			1.02090			0.510450	−	0.859908i	$-0.329479\pi$
$193$	197.034			1.02090			0.510450	+	0.859908i	$0.329479\pi$
$194$		0			0
$195$	17.6084	+	42.5104i	0.0902995	+	0.218002i
$196$		0			0
$197$	62.3398	−	150.502i	0.316446	−	0.763968i	−0.682992	−	0.730426i	$-0.739321\pi$
$197$	62.3398	−	150.502i	0.316446	−	0.763968i	0.999437	−	0.0335413i	$-0.0106785\pi$
$198$		0			0
$199$	−22.3835	+	22.3835i	−0.112480	+	0.112480i	−0.761107	−	0.648627i	$-0.775344\pi$
$199$	−22.3835	+	22.3835i	−0.112480	+	0.112480i	0.648627	+	0.761107i	$0.275344\pi$
$200$		0			0
$201$	13.6404	−	13.6404i	0.0678625	−	0.0678625i
$202$		0			0
$203$	7.00877	−	16.9207i	0.0345260	−	0.0833530i
$204$		0			0
$205$	−27.6505	−	66.7542i	−0.134881	−	0.325630i
$206$		0			0
$207$	−181.456			−0.876597
$208$		0			0
$209$		−	254.778i		−	1.21903i
$210$		0			0
$211$	315.926	−	130.861i	1.49728	−	0.620194i	0.524394	−	0.851476i	$-0.324292\pi$
$211$	315.926	−	130.861i	1.49728	−	0.620194i	0.972887	+	0.231282i	$0.0742919\pi$
$212$		0			0
$213$	−97.3706	−	40.3322i	−0.457139	−	0.189353i
$214$		0			0
$215$	132.514	+	132.514i	0.616343	+	0.616343i
$216$		0			0
$217$	−31.2948	−	31.2948i	−0.144216	−	0.144216i
$218$		0			0
$219$	−37.9986	−	15.7395i	−0.173509	−	0.0718699i
$220$		0			0
$221$	294.197	−	121.860i	1.33121	−	0.551405i
$222$		0			0
$223$			103.995i			0.466346i	0.972435	+	0.233173i	$0.0749109\pi$
$223$			103.995i			0.466346i	−0.972435	+	0.233173i	$0.925089\pi$
$224$		0			0
$225$	105.693			0.469748
$226$		0			0
$227$	−19.9655	−	48.2010i	−0.0879538	−	0.212339i	0.873782	−	0.486318i	$-0.161660\pi$
$227$	−19.9655	−	48.2010i	−0.0879538	−	0.212339i	−0.961736	+	0.273979i	$0.911660\pi$
$228$		0			0
$229$	52.0405	−	125.637i	0.227251	−	0.548633i	−0.768590	−	0.639742i	$-0.779041\pi$
$229$	52.0405	−	125.637i	0.227251	−	0.548633i	0.995841	+	0.0911090i	$0.0290412\pi$
$230$		0			0
$231$	3.62499	−	3.62499i	0.0156926	−	0.0156926i
$232$		0			0
$233$	−0.497550	+	0.497550i	−0.00213541	+	0.00213541i	−0.708174	−	0.706038i	$-0.750481\pi$
$233$	−0.497550	+	0.497550i	−0.00213541	+	0.00213541i	0.706038	+	0.708174i	$0.250481\pi$
$234$		0			0
$235$	−6.37793	+	15.3977i	−0.0271401	+	0.0655220i
$236$		0			0
$237$	−21.0872	−	50.9090i	−0.0889755	−	0.214806i
$238$		0			0
$239$	80.2602			0.335817			0.167908	−	0.985803i	$-0.446299\pi$
$239$	80.2602			0.335817			0.167908	+	0.985803i	$0.446299\pi$
$240$		0			0
$241$			9.94799i			0.0412780i	0.999787	+	0.0206390i	$0.00657006\pi$
$241$			9.94799i			0.0412780i	−0.999787	+	0.0206390i	$0.993430\pi$
$242$		0			0
$243$	−160.156	+	66.3389i	−0.659080	+	0.273000i
$244$		0			0
$245$	157.180	+	65.1059i	0.641549	+	0.265738i
$246$		0			0
$247$	−378.790	−	378.790i	−1.53356	−	1.53356i
$248$		0			0
$249$	8.70723	+	8.70723i	0.0349688	+	0.0349688i
$250$		0			0
$251$	37.4569	+	15.5152i	0.149231	+	0.0618134i	0.456049	−	0.889955i	$-0.349264\pi$
$251$	37.4569	+	15.5152i	0.149231	+	0.0618134i	−0.306818	+	0.951768i	$0.599264\pi$
$252$		0			0
$253$	−158.601	+	65.6947i	−0.626881	+	0.259663i
$254$		0			0
$255$		−	52.6523i		−	0.206480i
$256$		0			0
$257$	−351.412			−1.36736			−0.683680	−	0.729782i	$-0.739622\pi$
$257$	−351.412			−1.36736			−0.683680	+	0.729782i	$0.739622\pi$
$258$		0			0
$259$	−3.13621	−	7.57148i	−0.0121089	−	0.0292335i
$260$		0			0
$261$	−71.2625	+	172.043i	−0.273036	+	0.659168i
$262$		0			0
$263$	347.609	−	347.609i	1.32171	−	1.32171i	0.409316	−	0.912393i	$-0.365767\pi$
$263$	347.609	−	347.609i	1.32171	−	1.32171i	0.912393	−	0.409316i	$-0.134233\pi$
$264$		0			0
$265$	165.462	−	165.462i	0.624386	−	0.624386i
$266$		0			0
$267$	−25.7948	+	62.2741i	−0.0966097	+	0.233236i
$268$		0			0
$269$	77.8419	+	187.927i	0.289375	+	0.698613i	0.999988	−	0.00497024i	$-0.00158208\pi$
$269$	77.8419	+	187.927i	0.289375	+	0.698613i	−0.710613	+	0.703584i	$0.751582\pi$
$270$		0			0
$271$	380.417			1.40375			0.701876	−	0.712299i	$-0.252346\pi$
$271$	380.417			1.40375			0.701876	+	0.712299i	$0.252346\pi$
$272$		0			0
$273$		−	10.7789i		−	0.0394832i
$274$		0			0
$275$	92.3810	−	38.2655i	0.335931	−	0.139147i
$276$		0			0
$277$	130.082	+	53.8819i	0.469612	+	0.194519i	0.604924	−	0.796284i	$-0.293204\pi$
$277$	130.082	+	53.8819i	0.469612	+	0.194519i	−0.135312	+	0.990803i	$0.543204\pi$
$278$		0			0
$279$	318.193	+	318.193i	1.14048	+	1.14048i
$280$		0			0
$281$	−40.5881	−	40.5881i	−0.144442	−	0.144442i	0.631188	−	0.775630i	$-0.282568\pi$
$281$	−40.5881	−	40.5881i	−0.144442	−	0.144442i	−0.775630	+	0.631188i	$0.782568\pi$
$282$		0			0
$283$	−442.450	−	183.269i	−1.56343	−	0.647593i	−0.577748	−	0.816215i	$-0.696068\pi$
$283$	−442.450	−	183.269i	−1.56343	−	0.647593i	−0.985681	+	0.168622i	$0.946068\pi$
$284$		0			0
$285$	−81.8320	+	33.8959i	−0.287130	+	0.118933i
$286$		0			0
$287$			16.9261i			0.0589761i
$288$		0			0
$289$	−75.3848			−0.260847
$290$		0			0
$291$	−9.54200	−	23.0364i	−0.0327904	−	0.0791629i
$292$		0			0
$293$	−141.261	+	341.035i	−0.482120	+	1.16394i	0.476479	+	0.879186i	$0.341913\pi$
$293$	−141.261	+	341.035i	−0.482120	+	1.16394i	−0.958600	+	0.284756i	$0.908087\pi$
$294$		0			0
$295$	−114.436	+	114.436i	−0.387920	+	0.387920i
$296$		0			0
$297$	−76.4122	+	76.4122i	−0.257280	+	0.257280i
$298$		0			0
$299$	−138.128	+	333.471i	−0.461968	+	1.11529i
$300$		0			0
$301$	−16.8000	−	40.5588i	−0.0558140	−	0.134747i
$302$		0			0
$303$	−22.5994			−0.0745856
$304$		0			0
$305$			105.737i			0.346680i
$306$		0			0
$307$	−27.5569	+	11.4145i	−0.0897620	+	0.0371807i	−0.427113	−	0.904198i	$-0.640469\pi$
$307$	−27.5569	+	11.4145i	−0.0897620	+	0.0371807i	0.337351	+	0.941379i	$0.390469\pi$
$308$		0			0
$309$	57.4073	+	23.7789i	0.185784	+	0.0769543i
$310$		0			0
$311$	−262.516	−	262.516i	−0.844102	−	0.844102i	0.145288	−	0.989389i	$-0.453589\pi$
$311$	−262.516	−	262.516i	−0.844102	−	0.844102i	−0.989389	+	0.145288i	$0.953589\pi$
$312$		0			0
$313$	−346.338	−	346.338i	−1.10651	−	1.10651i	−0.993606	−	0.112907i	$-0.963984\pi$
$313$	−346.338	−	346.338i	−1.10651	−	1.10651i	−0.112907	−	0.993606i	$-0.536016\pi$
$314$		0			0
$315$	22.5005	+	9.32003i	0.0714303	+	0.0295874i
$316$		0			0
$317$	37.8371	−	15.6726i	0.119360	−	0.0494405i	−0.322204	−	0.946670i	$-0.604424\pi$
$317$	37.8371	−	15.6726i	0.119360	−	0.0494405i	0.441564	+	0.897230i	$0.354424\pi$
$318$		0			0
$319$			176.174i			0.552269i
$320$		0			0
$321$	11.9883			0.0373469
$322$		0			0
$323$	234.580	+	566.326i	0.726253	+	1.75333i
$324$		0			0
$325$	80.4563	−	194.239i	0.247558	−	0.597657i
$326$		0			0
$327$	54.4642	−	54.4642i	0.166557	−	0.166557i
$328$		0			0
$329$	2.76070	−	2.76070i	0.00839118	−	0.00839118i
$330$		0			0
$331$	−123.850	+	298.999i	−0.374168	+	0.903321i	0.618867	+	0.785496i	$0.287592\pi$
$331$	−123.850	+	298.999i	−0.374168	+	0.903321i	−0.993034	+	0.117825i	$0.962408\pi$
$332$		0			0
$333$	31.8878	+	76.9839i	0.0957591	+	0.231183i
$334$		0			0
$335$	86.6995			0.258805
$336$		0			0
$337$			553.901i			1.64362i	0.569759	+	0.821812i	$0.307037\pi$
$337$			553.901i			1.64362i	−0.569759	+	0.821812i	$0.692963\pi$
$338$		0			0
$339$	−59.6455	+	24.7060i	−0.175945	+	0.0728790i
$340$		0			0
$341$	393.316	+	162.917i	1.15342	+	0.477762i
$342$		0			0
$343$	−56.7593	−	56.7593i	−0.165479	−	0.165479i
$344$		0			0
$345$	42.2010	+	42.2010i	0.122322	+	0.122322i
$346$		0			0
$347$	−149.596	−	61.9645i	−0.431111	−	0.178572i	0.156566	−	0.987667i	$-0.449958\pi$
$347$	−149.596	−	61.9645i	−0.431111	−	0.178572i	−0.587677	+	0.809095i	$0.699958\pi$
$348$		0			0
$349$	−354.488	+	146.834i	−1.01572	+	0.420727i	−0.827540	−	0.561407i	$-0.810260\pi$
$349$	−354.488	+	146.834i	−1.01572	+	0.420727i	−0.188184	+	0.982134i	$0.560260\pi$
$350$		0			0
$351$			227.212i			0.647327i
$352$		0			0
$353$	−360.254			−1.02055			−0.510275	−	0.860011i	$-0.670456\pi$
$353$	−360.254			−1.02055			−0.510275	+	0.860011i	$0.670456\pi$
$354$		0			0
$355$	−181.271	−	437.627i	−0.510622	−	1.23275i
$356$		0			0
$357$	−4.72010	+	11.3953i	−0.0132216	+	0.0319197i
$358$		0			0
$359$	−92.0047	+	92.0047i	−0.256280	+	0.256280i	−0.823539	−	0.567259i	$-0.808004\pi$
$359$	−92.0047	+	92.0047i	−0.256280	+	0.256280i	0.567259	+	0.823539i	$0.308004\pi$
$360$		0			0
$361$	473.901	−	473.901i	1.31275	−	1.31275i
$362$		0			0
$363$	17.4036	−	42.0160i	0.0479438	−	0.115746i
$364$		0			0
$365$	−70.7404	−	170.782i	−0.193809	−	0.467897i
$366$		0			0
$367$	−254.513			−0.693496			−0.346748	−	0.937958i	$-0.612714\pi$
$367$	−254.513			−0.693496			−0.346748	+	0.937958i	$0.612714\pi$
$368$		0			0
$369$		−	172.098i		−	0.466391i
$370$		0			0
$371$	−50.6435	+	20.9772i	−0.136505	+	0.0565424i
$372$		0			0
$373$	440.477	+	182.452i	1.18090	+	0.489147i	0.884783	−	0.466004i	$-0.154307\pi$
$373$	440.477	+	182.452i	1.18090	+	0.489147i	0.296122	+	0.955150i	$0.404307\pi$
$374$		0			0
$375$	−73.3408	−	73.3408i	−0.195575	−	0.195575i
$376$		0			0
$377$	261.926	+	261.926i	0.694765	+	0.694765i
$378$		0			0
$379$	−124.964	−	51.7618i	−0.329720	−	0.136575i	0.211681	−	0.977339i	$-0.432106\pi$
$379$	−124.964	−	51.7618i	−0.329720	−	0.136575i	−0.541402	+	0.840764i	$0.682106\pi$
$380$		0			0
$381$	43.7856	−	18.1366i	0.114923	−	0.0476026i
$382$		0			0
$383$			182.483i			0.476458i	0.971209	+	0.238229i	$0.0765669\pi$
$383$			182.483i			0.476458i	−0.971209	+	0.238229i	$0.923433\pi$
$384$		0			0
$385$	23.0408			0.0598463
$386$		0			0
$387$	170.816	+	412.386i	0.441385	+	1.06560i
$388$		0			0
$389$	−134.979	+	325.868i	−0.346990	+	0.837708i	0.649982	+	0.759949i	$0.274776\pi$
$389$	−134.979	+	325.868i	−0.346990	+	0.837708i	−0.996972	+	0.0777583i	$0.975224\pi$
$390$		0			0
$391$	292.055	−	292.055i	0.746945	−	0.746945i
$392$		0			0
$393$	81.6583	−	81.6583i	0.207782	−	0.207782i
$394$		0			0
$395$	94.7752	−	228.808i	0.239937	−	0.579260i
$396$		0			0
$397$	−272.283	−	657.350i	−0.685852	−	1.65579i	−0.752976	−	0.658048i	$-0.771382\pi$
$397$	−272.283	−	657.350i	−0.685852	−	1.65579i	0.0671236	−	0.997745i	$-0.478618\pi$
$398$		0			0
$399$	20.7492			0.0520031
$400$		0			0
$401$			74.4996i			0.185785i	0.995676	+	0.0928923i	$0.0296112\pi$
$401$			74.4996i			0.185785i	−0.995676	+	0.0928923i	$0.970389\pi$
$402$		0			0
$403$	826.978	−	342.546i	2.05206	−	0.849989i
$404$		0			0
$405$	−210.810	−	87.3203i	−0.520518	−	0.215606i
$406$		0			0
$407$	55.7429	+	55.7429i	0.136961	+	0.136961i
$408$		0			0
$409$	−289.633	−	289.633i	−0.708149	−	0.708149i	0.257997	−	0.966146i	$-0.416938\pi$
$409$	−289.633	−	289.633i	−0.708149	−	0.708149i	−0.966146	+	0.257997i	$0.916938\pi$
$410$		0			0
$411$	143.245	+	59.3341i	0.348528	+	0.144365i
$412$		0			0
$413$	35.0258	−	14.5082i	0.0848083	−	0.0351288i
$414$		0			0
$415$			55.3441i			0.133359i
$416$		0			0
$417$	−5.38631			−0.0129168
$418$		0			0
$419$	−234.290	−	565.626i	−0.559165	−	1.34994i	−0.910428	−	0.413667i	$-0.864248\pi$
$419$	−234.290	−	565.626i	−0.559165	−	1.34994i	0.351264	−	0.936277i	$-0.385752\pi$
$420$		0			0
$421$	205.463	−	496.031i	0.488035	−	1.17822i	−0.467672	−	0.883902i	$-0.654907\pi$
$421$	205.463	−	496.031i	0.488035	−	1.17822i	0.955707	−	0.294319i	$-0.0950929\pi$
$422$		0			0
$423$	−28.0697	+	28.0697i	−0.0663587	+	0.0663587i
$424$		0			0
$425$	−170.115	+	170.115i	−0.400270	+	0.400270i
$426$		0			0
$427$	9.47901	−	22.8843i	0.0221991	−	0.0535933i
$428$		0			0
$429$	39.6783	+	95.7920i	0.0924903	+	0.223291i
$430$		0			0
$431$	94.1706			0.218493			0.109247	−	0.994015i	$-0.465156\pi$
$431$	94.1706			0.218493			0.109247	+	0.994015i	$0.465156\pi$
$432$		0			0
$433$			66.2703i			0.153049i	0.997068	+	0.0765246i	$0.0243824\pi$
$433$			66.2703i			0.153049i	−0.997068	+	0.0765246i	$0.975618\pi$
$434$		0			0
$435$	56.5853	−	23.4384i	0.130081	−	0.0538814i
$436$		0			0
$437$	−641.928	−	265.895i	−1.46894	−	0.608456i
$438$		0			0
$439$	−393.404	−	393.404i	−0.896137	−	0.896137i	0.0989551	−	0.995092i	$-0.468450\pi$
$439$	−393.404	−	393.404i	−0.896137	−	0.896137i	−0.995092	+	0.0989551i	$0.968450\pi$
$440$		0			0
$441$	286.536	+	286.536i	0.649742	+	0.649742i
$442$		0			0
$443$	−124.298	−	51.4859i	−0.280583	−	0.116221i	0.237954	−	0.971276i	$-0.423523\pi$
$443$	−124.298	−	51.4859i	−0.280583	−	0.116221i	−0.518537	+	0.855055i	$0.673523\pi$
$444$		0			0
$445$	−279.888	+	115.933i	−0.628961	+	0.260524i
$446$		0			0
$447$			114.344i			0.255803i
$448$		0			0
$449$	621.505			1.38420			0.692099	−	0.721802i	$-0.256686\pi$
$449$	621.505			1.38420			0.692099	+	0.721802i	$0.256686\pi$
$450$		0			0
$451$	−62.3070	−	150.422i	−0.138153	−	0.333531i
$452$		0			0
$453$	55.7195	−	134.519i	0.123001	−	0.296951i
$454$		0			0
$455$	34.2559	−	34.2559i	0.0752877	−	0.0752877i
$456$		0			0
$457$	−121.890	+	121.890i	−0.266718	+	0.266718i	−0.827776	−	0.561058i	$-0.810394\pi$
$457$	−121.890	+	121.890i	−0.266718	+	0.266718i	0.561058	+	0.827776i	$0.310394\pi$
$458$		0			0
$459$	99.4964	−	240.205i	0.216768	−	0.523323i
$460$		0			0
$461$	92.0148	+	222.143i	0.199598	+	0.481873i	0.991709	−	0.128505i	$-0.0410177\pi$
$461$	92.0148	+	222.143i	0.199598	+	0.481873i	−0.792111	+	0.610378i	$0.791018\pi$
$462$		0			0
$463$	133.158			0.287598			0.143799	−	0.989607i	$-0.454068\pi$
$463$	133.158			0.287598			0.143799	+	0.989607i	$0.454068\pi$
$464$		0			0
$465$		−	148.004i		−	0.318288i
$466$		0			0
$467$	414.267	−	171.595i	0.887082	−	0.367441i	0.107843	−	0.994168i	$-0.465606\pi$
$467$	414.267	−	171.595i	0.887082	−	0.367441i	0.779239	+	0.626727i	$0.215606\pi$
$468$		0			0
$469$	−18.7640	−	7.77232i	−0.0400086	−	0.0165721i
$470$		0			0
$471$	91.0019	+	91.0019i	0.193210	+	0.193210i
$472$		0			0
$473$	298.603	+	298.603i	0.631296	+	0.631296i
$474$		0			0
$475$	373.907	+	154.877i	0.787172	+	0.326058i
$476$		0			0
$477$	514.924	−	213.288i	1.07950	−	0.447145i
$478$		0			0
$479$		−	293.655i		−	0.613059i	−0.951861	−	0.306530i	$-0.900832\pi$
$479$		−	293.655i		−	0.613059i	0.951861	−	0.306530i	$-0.0991679\pi$
$480$		0			0
$481$	165.752			0.344598
$482$		0			0
$483$	−5.35022	−	12.9166i	−0.0110771	−	0.0267424i
$484$		0			0
$485$	42.8860	−	103.536i	0.0884247	−	0.213476i
$486$		0			0
$487$	−468.368	+	468.368i	−0.961741	+	0.961741i	−0.999295	−	0.0375532i	$-0.988044\pi$
$487$	−468.368	+	468.368i	−0.961741	+	0.961741i	0.0375532	+	0.999295i	$0.488044\pi$
$488$		0			0
$489$	−109.504	+	109.504i	−0.223935	+	0.223935i
$490$		0			0
$491$	120.443	−	290.775i	0.245301	−	0.592210i	−0.752492	−	0.658601i	$-0.771149\pi$
$491$	120.443	−	290.775i	0.245301	−	0.592210i	0.997794	+	0.0663911i	$0.0211485\pi$
$492$		0			0
$493$	−162.207	−	391.603i	−0.329021	−	0.794328i
$494$		0			0
$495$	−234.270			−0.473273
$496$		0			0
$497$			110.964i			0.223268i
$498$		0			0
$499$	−572.626	+	237.190i	−1.14755	+	0.475330i	−0.873711	−	0.486446i	$-0.838293\pi$
$499$	−572.626	+	237.190i	−1.14755	+	0.475330i	−0.273837	+	0.961776i	$0.588293\pi$
$500$		0			0
$501$	152.013	+	62.9658i	0.303419	+	0.125680i
$502$		0			0
$503$	397.129	+	397.129i	0.789520	+	0.789520i	0.981415	−	0.191895i	$-0.0614634\pi$
$503$	397.129	+	397.129i	0.789520	+	0.789520i	−0.191895	+	0.981415i	$0.561463\pi$
$504$		0			0
$505$	−71.8222	−	71.8222i	−0.142222	−	0.142222i
$506$		0			0
$507$	79.0946	+	32.7621i	0.156005	+	0.0646195i
$508$		0			0
$509$	−16.5014	+	6.83509i	−0.0324192	+	0.0134285i	−0.398834	−	0.917023i	$-0.630585\pi$
$509$	−16.5014	+	6.83509i	−0.0324192	+	0.0134285i	0.366415	+	0.930452i	$0.380585\pi$
$510$		0			0
$511$			43.3034i			0.0847425i
$512$		0			0
$513$	−437.380			−0.852592
$514$		0			0
$515$	106.873	+	258.014i	0.207520	+	0.500998i
$516$		0			0
$517$	−14.3719	+	34.6968i	−0.0277986	+	0.0671117i
$518$		0			0
$519$	21.5815	−	21.5815i	0.0415829	−	0.0415829i
$520$		0			0
$521$	−11.8175	+	11.8175i	−0.0226824	+	0.0226824i	−0.718357	−	0.695675i	$-0.755106\pi$
$521$	−11.8175	+	11.8175i	−0.0226824	+	0.0226824i	0.695675	+	0.718357i	$0.255106\pi$
$522$		0			0
$523$	−141.420	+	341.417i	−0.270401	+	0.652806i	−0.999501	−	0.0316019i	$-0.989939\pi$
$523$	−141.420	+	341.417i	−0.270401	+	0.652806i	0.729100	+	0.684408i	$0.239939\pi$
$524$		0			0
$525$	3.11636	+	7.52357i	0.00593593	+	0.0143306i
$526$		0			0
$527$	−1024.27			−1.94359
$528$		0			0
$529$		−	60.8334i		−	0.114997i
$530$		0			0
$531$	−356.129	+	147.514i	−0.670677	+	0.277803i
$532$		0			0
$533$	−316.275	−	131.006i	−0.593387	−	0.245789i
$534$		0			0
$535$	38.0996	+	38.0996i	0.0712142	+	0.0712142i
$536$		0			0
$537$	166.011	+	166.011i	0.309145	+	0.309145i
$538$		0			0
$539$	354.185	+	146.708i	0.657115	+	0.272186i
$540$		0			0
$541$	−117.048	+	48.4829i	−0.216355	+	0.0896172i	−0.488229	−	0.872716i	$-0.662357\pi$
$541$	−117.048	+	48.4829i	−0.216355	+	0.0896172i	0.271874	+	0.962333i	$0.412357\pi$
$542$		0			0
$543$			69.6741i			0.128313i
$544$		0			0
$545$	346.180			0.635193
$546$		0			0
$547$	113.911	+	275.005i	0.208247	+	0.502752i	0.993147	−	0.116870i	$-0.0372860\pi$
$547$	113.911	+	275.005i	0.208247	+	0.502752i	−0.784901	+	0.619622i	$0.787286\pi$
$548$		0			0
$549$	−96.3789	+	232.679i	−0.175553	+	0.423824i
$550$		0			0
$551$	−504.205	+	504.205i	−0.915072	+	0.915072i
$552$		0			0
$553$	−41.0237	+	41.0237i	−0.0741838	+	0.0741838i
$554$		0			0
$555$	10.4880	−	25.3202i	0.0188972	−	0.0456220i
$556$		0			0
$557$	87.2197	+	210.567i	0.156588	+	0.378037i	0.982631	−	0.185570i	$-0.0594131\pi$
$557$	87.2197	+	210.567i	0.156588	+	0.378037i	−0.826043	+	0.563607i	$0.809413\pi$
$558$		0			0
$559$	887.896			1.58836
$560$		0			0
$561$		−	118.645i		−	0.211489i
$562$		0			0
$563$	−697.221	+	288.798i	−1.23840	+	0.512963i	−0.903215	−	0.429188i	$-0.858800\pi$
$563$	−697.221	+	288.798i	−1.23840	+	0.512963i	−0.335188	+	0.942151i	$0.608800\pi$
$564$		0			0
$565$	−268.074	−	111.040i	−0.474466	−	0.196530i
$566$		0			0
$567$	37.7968	+	37.7968i	0.0666610	+	0.0666610i
$568$		0			0
$569$	−252.850	−	252.850i	−0.444376	−	0.444376i	0.449104	−	0.893480i	$-0.351743\pi$
$569$	−252.850	−	252.850i	−0.444376	−	0.444376i	−0.893480	+	0.449104i	$0.851743\pi$
$570$		0			0
$571$	−352.993	−	146.215i	−0.618202	−	0.256068i	0.0515290	−	0.998672i	$-0.483591\pi$
$571$	−352.993	−	146.215i	−0.618202	−	0.256068i	−0.669731	+	0.742604i	$0.733591\pi$
$572$		0			0
$573$	−129.450	+	53.6200i	−0.225917	+	0.0935777i
$574$		0			0
$575$		−	272.695i		−	0.474252i
$576$		0			0
$577$	−197.099			−0.341593			−0.170797	−	0.985306i	$-0.554634\pi$
$577$	−197.099			−0.341593			−0.170797	+	0.985306i	$0.554634\pi$
$578$		0			0
$579$	−59.0691	−	142.605i	−0.102019	−	0.246296i
$580$		0			0
$581$	4.96141	−	11.9779i	0.00853944	−	0.0206160i
$582$		0			0
$583$	372.849	−	372.849i	0.639535	−	0.639535i
$584$		0			0
$585$	−348.301	+	348.301i	−0.595386	+	0.595386i
$586$		0			0
$587$	238.745	−	576.382i	0.406721	−	0.981912i	−0.579273	−	0.815134i	$-0.696664\pi$
$587$	238.745	−	576.382i	0.406721	−	0.981912i	0.985994	−	0.166778i	$-0.0533365\pi$
$588$		0			0
$589$	659.396	+	1591.92i	1.11952	+	2.70276i
$590$		0			0
$591$	−127.616			−0.215933
$592$		0			0
$593$		−	276.598i		−	0.466438i	−0.972424	−	0.233219i	$-0.925074\pi$
$593$		−	276.598i		−	0.466438i	0.972424	−	0.233219i	$-0.0749260\pi$
$594$		0			0
$595$	−51.2157	+	21.2142i	−0.0860768	+	0.0356542i
$596$		0			0
$597$	22.9108	+	9.48995i	0.0383765	+	0.0158961i
$598$		0			0
$599$	710.727	+	710.727i	1.18652	+	1.18652i	0.978022	+	0.208501i	$0.0668585\pi$
$599$	710.727	+	710.727i	1.18652	+	1.18652i	0.208501	+	0.978022i	$0.433141\pi$
$600$		0			0
$601$	−215.219	−	215.219i	−0.358102	−	0.358102i	0.505011	−	0.863113i	$-0.331488\pi$
$601$	−215.219	−	215.219i	−0.358102	−	0.358102i	−0.863113	+	0.505011i	$0.831488\pi$
$602$		0			0
$603$	190.786	+	79.0260i	0.316394	+	0.131055i
$604$		0			0
$605$	188.839	−	78.2195i	0.312130	−	0.129288i
$606$		0			0
$607$		−	683.779i		−	1.12649i	−0.826290	−	0.563245i	$-0.809553\pi$
$607$		−	683.779i		−	1.12649i	0.826290	−	0.563245i	$-0.190447\pi$
$608$		0			0
$609$	−14.3477			−0.0235595
$610$		0			0
$611$	30.2180	+	72.9527i	0.0494566	+	0.119399i
$612$		0			0
$613$	−296.111	+	714.875i	−0.483052	+	1.16619i	0.475100	+	0.879932i	$0.342412\pi$
$613$	−296.111	+	714.875i	−0.483052	+	1.16619i	−0.958152	+	0.286259i	$0.907588\pi$
$614$		0			0
$615$	−40.0248	+	40.0248i	−0.0650809	+	0.0650809i
$616$		0			0
$617$	−275.822	+	275.822i	−0.447037	+	0.447037i	−0.894368	−	0.447331i	$-0.852374\pi$
$617$	−275.822	+	275.822i	−0.447037	+	0.447037i	0.447331	+	0.894368i	$0.352374\pi$
$618$		0			0
$619$	−201.130	+	485.570i	−0.324927	+	0.784443i	0.674027	+	0.738707i	$0.264563\pi$
$619$	−201.130	+	485.570i	−0.324927	+	0.784443i	−0.998954	+	0.0457357i	$0.985437\pi$
$620$		0			0
$621$	112.779	+	272.272i	0.181608	+	0.438441i
$622$		0			0
$623$	70.9681			0.113913
$624$		0			0
$625$		−	151.085i		−	0.241735i
$626$		0			0
$627$	−184.398	+	76.3803i	−0.294096	+	0.121819i
$628$		0			0
$629$	−175.231	−	72.5829i	−0.278586	−	0.115394i
$630$		0			0
$631$	−48.9545	−	48.9545i	−0.0775823	−	0.0775823i	0.667251	−	0.744833i	$-0.267471\pi$
$631$	−48.9545	−	48.9545i	−0.0775823	−	0.0775823i	−0.744833	+	0.667251i	$0.767471\pi$
$632$		0			0
$633$	−189.424	−	189.424i	−0.299249	−	0.299249i
$634$		0			0
$635$	196.792	+	81.5139i	0.309909	+	0.128368i
$636$		0			0
$637$	744.702	−	308.466i	1.16908	−	0.484248i
$638$		0			0
$639$		−	1128.24i		−	1.76564i
$640$		0			0
$641$	320.295			0.499680			0.249840	−	0.968287i	$-0.419622\pi$
$641$	320.295			0.499680			0.249840	+	0.968287i	$0.419622\pi$
$642$		0			0
$643$	−39.8184	−	96.1302i	−0.0619260	−	0.149503i	0.889887	−	0.456180i	$-0.150783\pi$
$643$	−39.8184	−	96.1302i	−0.0619260	−	0.149503i	−0.951813	+	0.306677i	$0.900783\pi$
$644$		0			0
$645$	56.1818	−	135.635i	0.0871036	−	0.210287i
$646$		0			0
$647$	134.372	−	134.372i	0.207684	−	0.207684i	−0.595598	−	0.803282i	$-0.703085\pi$
$647$	134.372	−	134.372i	0.207684	−	0.207684i	0.803282	+	0.595598i	$0.203085\pi$
$648$		0			0
$649$	−257.868	+	257.868i	−0.397331	+	0.397331i
$650$		0			0
$651$	−13.2680	+	32.0319i	−0.0203810	+	0.0492041i
$652$		0			0
$653$	−358.760	−	866.123i	−0.549403	−	1.32638i	−0.917924	−	0.396756i	$-0.870136\pi$
$653$	−358.760	−	866.123i	−0.549403	−	1.32638i	0.368521	−	0.929619i	$-0.379864\pi$
$654$		0			0
$655$	519.029			0.792410
$656$		0			0
$657$		−	440.293i		−	0.670156i
$658$		0			0
$659$	−596.224	+	246.964i	−0.904741	+	0.374756i	−0.786041	−	0.618174i	$-0.787873\pi$
$659$	−596.224	+	246.964i	−0.904741	+	0.374756i	−0.118700	+	0.992930i	$0.537873\pi$
$660$		0			0
$661$	16.3196	+	6.75978i	0.0246892	+	0.0102266i	0.394994	−	0.918684i	$-0.370747\pi$
$661$	16.3196	+	6.75978i	0.0246892	+	0.0102266i	−0.370305	+	0.928910i	$0.620747\pi$
$662$		0			0
$663$	−176.396	−	176.396i	−0.266057	−	0.266057i
$664$		0			0
$665$	65.9422	+	65.9422i	0.0991612	+	0.0991612i
$666$		0			0
$667$	443.881	+	183.862i	0.665489	+	0.275655i
$668$		0			0
$669$	75.2678	−	31.1769i	0.112508	−	0.0466023i
$670$		0			0
$671$			238.266i			0.355091i
$672$		0			0
$673$	−334.752			−0.497403			−0.248701	−	0.968580i	$-0.580004\pi$
$673$	−334.752			−0.497403			−0.248701	+	0.968580i	$0.580004\pi$
$674$		0			0
$675$	−65.6908	−	158.592i	−0.0973197	−	0.234950i
$676$		0			0
$677$	294.364	−	710.658i	0.434807	−	1.04972i	−0.542911	−	0.839790i	$-0.682678\pi$
$677$	294.364	−	710.658i	0.434807	−	1.04972i	0.977717	−	0.209926i	$-0.0673222\pi$
$678$		0			0
$679$	−18.5633	+	18.5633i	−0.0273392	+	0.0273392i
$680$		0			0
$681$	−28.9006	+	28.9006i	−0.0424384	+	0.0424384i
$682$		0			0
$683$	118.311	−	285.628i	0.173223	−	0.418196i	−0.813295	−	0.581851i	$-0.802328\pi$
$683$	118.311	−	285.628i	0.173223	−	0.418196i	0.986518	+	0.163655i	$0.0523285\pi$
$684$		0			0
$685$	266.674	+	643.807i	0.389305	+	0.939865i
$686$		0			0
$687$	−106.533			−0.155069
$688$		0			0
$689$		−	1108.67i		−	1.60909i
$690$		0			0
$691$	13.1275	−	5.43758i	0.0189978	−	0.00786914i	−0.373164	−	0.927765i	$-0.621727\pi$
$691$	13.1275	−	5.43758i	0.0189978	−	0.00786914i	0.392162	+	0.919896i	$0.371727\pi$
$692$		0			0
$693$	50.7022	+	21.0015i	0.0731633	+	0.0303052i
$694$		0			0
$695$	−17.1180	−	17.1180i	−0.0246302	−	0.0246302i
$696$		0			0
$697$	276.995	+	276.995i	0.397410	+	0.397410i
$698$		0			0
$699$	0.509270	+	0.210946i	0.000728569	+	0.000301783i
$700$		0			0
$701$	−100.100	+	41.4627i	−0.142796	+	0.0591480i	−0.452937	−	0.891543i	$-0.649624\pi$
$701$	−100.100	+	41.4627i	−0.142796	+	0.0591480i	0.310141	+	0.950691i	$0.399624\pi$
$702$		0			0
$703$			319.070i			0.453869i
$704$		0			0
$705$	13.0563			0.0185196
$706$		0			0
$707$	9.10558	+	21.9828i	0.0128792	+	0.0310931i
$708$		0			0
$709$	273.663	−	660.681i	0.385985	−	0.931849i	−0.604797	−	0.796380i	$-0.706746\pi$
$709$	273.663	−	660.681i	0.385985	−	0.931849i	0.990781	−	0.135470i	$-0.0432543\pi$
$710$		0			0
$711$	417.113	−	417.113i	0.586657	−	0.586657i
$712$		0			0
$713$	820.958	−	820.958i	1.15141	−	1.15141i
$714$		0			0
$715$	−178.332	+	430.532i	−0.249416	+	0.602143i
$716$		0			0
$717$	−24.0614	−	58.0893i	−0.0335584	−	0.0810171i
$718$		0			0
$719$	532.079			0.740026			0.370013	−	0.929026i	$-0.379353\pi$
$719$	532.079			0.740026			0.370013	+	0.929026i	$0.379353\pi$
$720$		0			0
$721$		−	65.4218i		−	0.0907375i
$722$		0			0
$723$	7.19998	−	2.98233i	0.00995848	−	0.00412494i
$724$		0			0
$725$	−258.549	−	107.095i	−0.356620	−	0.147717i
$726$		0			0
$727$	−305.054	−	305.054i	−0.419606	−	0.419606i	0.465462	−	0.885068i	$-0.345888\pi$
$727$	−305.054	−	305.054i	−0.419606	−	0.419606i	−0.885068	+	0.465462i	$0.845888\pi$
$728$		0			0
$729$	−316.399	−	316.399i	−0.434018	−	0.434018i
$730$		0			0
$731$	−938.673	−	388.811i	−1.28409	−	0.531889i
$732$		0			0
$733$	344.710	−	142.783i	0.470272	−	0.194793i	−0.134946	−	0.990853i	$-0.543086\pi$
$733$	344.710	−	142.783i	0.470272	−	0.194793i	0.605218	+	0.796060i	$0.293086\pi$
$734$		0			0
$735$		−	133.279i		−	0.181332i
$736$		0			0
$737$	195.367			0.265084
$738$		0			0
$739$	−107.676	−	259.954i	−0.145706	−	0.351765i	0.834131	−	0.551567i	$-0.185970\pi$
$739$	−107.676	−	259.954i	−0.145706	−	0.351765i	−0.979836	+	0.199803i	$0.935970\pi$
$740$		0			0
$741$	−160.596	+	387.713i	−0.216728	+	0.523229i
$742$		0			0
$743$	470.112	−	470.112i	0.632721	−	0.632721i	−0.316029	−	0.948750i	$-0.602350\pi$
$743$	470.112	−	470.112i	0.632721	−	0.632721i	0.948750	+	0.316029i	$0.102350\pi$
$744$		0			0
$745$	−363.391	+	363.391i	−0.487773	+	0.487773i
$746$		0			0
$747$	−50.4457	+	121.787i	−0.0675311	+	0.163034i
$748$		0			0
$749$	−4.83025	−	11.6612i	−0.00644893	−	0.0155691i
$750$		0			0
$751$	−844.801			−1.12490			−0.562451	−	0.826831i	$-0.690141\pi$
$751$	−844.801			−1.12490			−0.562451	+	0.826831i	$0.690141\pi$
$752$		0			0
$753$		−	31.7612i		−	0.0421796i
$754$		0			0
$755$	604.588	−	250.428i	0.800778	−	0.331693i
$756$		0			0
$757$	1050.78	+	435.247i	1.38808	+	0.574962i	0.946630	−	0.322322i	$-0.104464\pi$
$757$	1050.78	+	435.247i	1.38808	+	0.574962i	0.441452	+	0.897285i	$0.354464\pi$
$758$		0			0
$759$	95.0946	+	95.0946i	0.125289	+	0.125289i
$760$		0			0
$761$	−44.1359	−	44.1359i	−0.0579972	−	0.0579972i	0.677513	−	0.735511i	$-0.263058\pi$
$761$	−44.1359	−	44.1359i	−0.0579972	−	0.0579972i	−0.735511	+	0.677513i	$0.763058\pi$
$762$		0			0
$763$	−74.9225	−	31.0339i	−0.0981946	−	0.0406735i
$764$		0			0
$765$	520.741	−	215.698i	0.680708	−	0.281958i
$766$		0			0
$767$			766.771i			0.999701i
$768$		0			0
$769$	794.025			1.03254			0.516271	−	0.856425i	$-0.327320\pi$
$769$	794.025			1.03254			0.516271	+	0.856425i	$0.327320\pi$
$770$		0			0
$771$	105.350	+	254.338i	0.136641	+	0.329881i
$772$		0			0
$773$	−395.664	+	955.218i	−0.511856	+	1.23573i	0.430947	+	0.902377i	$0.358180\pi$
$773$	−395.664	+	955.218i	−0.511856	+	1.23573i	−0.942803	+	0.333351i	$0.891820\pi$
$774$		0			0
$775$	−478.187	+	478.187i	−0.617016	+	0.617016i
$776$		0			0
$777$	−4.53974	+	4.53974i	−0.00584265	+	0.00584265i
$778$		0			0
$779$	252.184	−	608.826i	0.323728	−	0.781548i
$780$		0			0
$781$	−408.472	−	986.138i	−0.523011	−	1.26266i
$782$		0			0
$783$	302.440			0.386257
$784$		0			0
$785$			578.418i			0.736838i
$786$		0			0
$787$	445.085	−	184.360i	0.565547	−	0.234257i	−0.0815444	−	0.996670i	$-0.525985\pi$
$787$	445.085	−	184.360i	0.565547	−	0.234257i	0.647091	+	0.762413i	$0.275985\pi$
$788$		0			0
$789$	−355.797	−	147.376i	−0.450947	−	0.186788i
$790$		0			0
$791$	48.0638	+	48.0638i	0.0607633	+	0.0607633i
$792$		0			0
$793$	354.242	+	354.242i	0.446711	+	0.446711i
$794$		0			0
$795$	−169.360	−	70.1511i	−0.213031	−	0.0882403i
$796$		0			0
$797$	−1384.22	+	573.363i	−1.73679	+	0.719402i	−0.737773	+	0.675049i	$0.764123\pi$
$797$	−1384.22	+	573.363i	−1.73679	+	0.719402i	−0.999016	+	0.0443527i	$0.985877\pi$
$798$		0			0
$799$		−	90.3573i		−	0.113088i
$800$		0			0
$801$	−721.576			−0.900844
$802$		0			0
$803$	−159.405	−	384.837i	−0.198512	−	0.479249i
$804$		0			0
$805$	24.0463	−	58.0528i	0.0298711	−	0.0721153i
$806$		0			0
$807$	112.678	−	112.678i	0.139626	−	0.139626i
$808$		0			0
$809$	462.148	−	462.148i	0.571258	−	0.571258i	−0.361222	−	0.932480i	$-0.617640\pi$
$809$	462.148	−	462.148i	0.571258	−	0.571258i	0.932480	+	0.361222i	$0.117640\pi$
$810$		0			0
$811$	−32.9003	+	79.4282i	−0.0405675	+	0.0979386i	−0.942865	−	0.333176i	$-0.891880\pi$
$811$	−32.9003	+	79.4282i	−0.0405675	+	0.0979386i	0.902297	+	0.431115i	$0.141880\pi$
$812$		0			0
$813$	−114.046	−	275.331i	−0.140278	−	0.338661i
$814$		0			0
$815$	−696.019			−0.854012
$816$		0			0
$817$			1709.19i			2.09203i
$818$		0			0
$819$	106.605	−	44.1574i	0.130165	−	0.0539163i
$820$		0			0
$821$	−724.768	−	300.209i	−0.882787	−	0.365662i	−0.105210	−	0.994450i	$-0.533551\pi$
$821$	−724.768	−	300.209i	−0.882787	−	0.365662i	−0.777577	+	0.628788i	$0.783551\pi$
$822$		0			0
$823$	378.179	+	378.179i	0.459513	+	0.459513i	0.898496	−	0.438982i	$-0.144661\pi$
$823$	378.179	+	378.179i	0.459513	+	0.459513i	−0.438982	+	0.898496i	$0.644661\pi$
$824$		0			0
$825$	−55.3902	−	55.3902i	−0.0671396	−	0.0671396i
$826$		0			0
$827$	1071.43	+	443.801i	1.29556	+	0.536639i	0.920638	−	0.390416i	$-0.127669\pi$
$827$	1071.43	+	443.801i	1.29556	+	0.536639i	0.374924	+	0.927056i	$0.377669\pi$
$828$		0			0
$829$	−1023.61	+	423.991i	−1.23475	+	0.511449i	−0.902069	−	0.431592i	$-0.857952\pi$
$829$	−1023.61	+	423.991i	−1.23475	+	0.511449i	−0.332678	+	0.943041i	$0.607952\pi$
$830$		0			0
$831$		−	110.302i		−	0.132734i
$832$		0			0
$833$	−922.368			−1.10728
$834$		0			0
$835$	282.996	+	683.214i	0.338918	+	0.818220i
$836$		0			0
$837$	279.681	−	675.210i	0.334147	−	0.806702i
$838$		0			0
$839$	−1157.38	+	1157.38i	−1.37947	+	1.37947i	−0.533966	+	0.845506i	$0.679299\pi$
$839$	−1157.38	+	1157.38i	−1.37947	+	1.37947i	−0.845506	+	0.533966i	$0.820701\pi$
$840$		0			0
$841$	−246.029	+	246.029i	−0.292543	+	0.292543i
$842$		0			0
$843$	−17.2081	+	41.5441i	−0.0204130	+	0.0492813i
$844$		0			0
$845$	147.247	+	355.487i	0.174257	+	0.420694i
$846$		0			0
$847$	−47.8817			−0.0565309
$848$		0			0
$849$			375.171i			0.441898i
$850$		0			0
$851$	198.623	−	82.2724i	0.233400	−	0.0966773i
$852$		0			0
$853$	1189.88	+	492.862i	1.39493	+	0.577799i	0.948431	−	0.316985i	$-0.102671\pi$
$853$	1189.88	+	492.862i	1.39493	+	0.577799i	0.446499	+	0.894784i	$0.352671\pi$
$854$		0			0
$855$	−670.475	−	670.475i	−0.784181	−	0.784181i
$856$		0			0
$857$	240.773	+	240.773i	0.280948	+	0.280948i	0.833487	−	0.552539i	$-0.186341\pi$
$857$	240.773	+	240.773i	0.280948	+	0.280948i	−0.552539	+	0.833487i	$0.686341\pi$
$858$		0			0
$859$	577.833	+	239.346i	0.672682	+	0.278634i	0.692764	−	0.721164i	$-0.256393\pi$
$859$	577.833	+	239.346i	0.672682	+	0.278634i	−0.0200823	+	0.999798i	$0.506393\pi$
$860$		0			0
$861$	12.2505	−	5.07432i	0.0142282	−	0.00589352i
$862$		0			0
$863$			1084.57i			1.25675i	0.777912	+	0.628373i	$0.216279\pi$
$863$			1084.57i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$864$		0			0
$865$	137.175			0.158583
$866$		0			0
$867$	22.5998	+	54.5606i	0.0260666	+	0.0629304i
$868$		0			0
$869$	213.564	−	515.590i	0.245759	−	0.593314i
$870$		0			0
$871$	290.461	−	290.461i	0.333480	−	0.333480i
$872$		0			0
$873$	188.744	−	188.744i	0.216202	−	0.216202i
$874$		0			0
$875$	−41.7899	+	100.890i	−0.0477598	+	0.115302i
$876$		0			0
$877$	−331.246	−	799.700i	−0.377704	−	0.911858i	−0.992395	−	0.123090i	$-0.960719\pi$
$877$	−331.246	−	799.700i	−0.377704	−	0.911858i	0.614691	−	0.788768i	$-0.289281\pi$
$878$		0			0
$879$	289.177			0.328984
$880$		0			0
$881$			995.281i			1.12972i	0.825188	+	0.564859i	$0.191069\pi$
$881$			995.281i			1.12972i	−0.825188	+	0.564859i	$0.808931\pi$
$882$		0			0
$883$	587.282	−	243.260i	0.665098	−	0.275493i	−0.0244838	−	0.999700i	$-0.507794\pi$
$883$	587.282	−	243.260i	0.665098	−	0.275493i	0.689582	+	0.724207i	$0.257794\pi$
$884$		0			0
$885$	117.132	+	48.5176i	0.132352	+	0.0548221i
$886$		0			0
$887$	−679.194	−	679.194i	−0.765720	−	0.765720i	0.211630	−	0.977350i	$-0.432123\pi$
$887$	−679.194	−	679.194i	−0.765720	−	0.765720i	−0.977350	+	0.211630i	$0.932123\pi$
$888$		0			0
$889$	−35.2835	−	35.2835i	−0.0396890	−	0.0396890i
$890$		0			0
$891$	−475.034	−	196.765i	−0.533147	−	0.220837i
$892$		0			0
$893$	−140.433	+	58.1693i	−0.157260	+	0.0651392i
$894$		0			0
$895$			1055.18i			1.17897i
$896$		0			0
$897$	282.764			0.315233
$898$		0			0
$899$	−455.960	−	1100.78i	−0.507185	−	1.22445i
$900$		0			0
$901$	−485.487	+	1172.07i	−0.538831	+	1.30085i
$902$		0			0
$903$	−24.3184	+	24.3184i	−0.0269307	+	0.0269307i
$904$		0			0
$905$	−221.428	+	221.428i	−0.244672	+	0.244672i
$906$		0			0
$907$	−77.7483	+	187.701i	−0.0857203	+	0.206947i	−0.960927	−	0.276802i	$-0.910725\pi$
$907$	−77.7483	+	187.701i	−0.0857203	+	0.206947i	0.875207	+	0.483749i	$0.160725\pi$
$908$		0			0
$909$	−92.5820	−	223.513i	−0.101850	−	0.245889i
$910$		0			0
$911$	−300.365			−0.329710			−0.164855	−	0.986318i	$-0.552716\pi$
$911$	−300.365			−0.329710			−0.164855	+	0.986318i	$0.552716\pi$
$912$		0			0
$913$			124.711i			0.136595i
$914$		0			0
$915$	76.5287	−	31.6992i	0.0836380	−	0.0346440i
$916$		0			0
$917$	−112.331	−	46.5292i	−0.122499	−	0.0507407i
$918$		0			0
$919$	149.768	+	149.768i	0.162968	+	0.162968i	0.783880	−	0.620912i	$-0.213238\pi$
$919$	149.768	+	149.768i	0.162968	+	0.162968i	−0.620912	+	0.783880i	$0.713238\pi$
$920$		0			0
$921$	16.5227	+	16.5227i	0.0179400	+	0.0179400i
$922$		0			0
$923$	−2073.43	−	858.845i	−2.24641	−	0.930493i
$924$		0			0
$925$	−115.693	+	47.9216i	−0.125073	+	0.0518071i
$926$		0			0
$927$			665.183i			0.717565i
$928$		0			0
$929$	1235.73			1.33017			0.665086	−	0.746767i	$-0.268395\pi$
$929$	1235.73			1.33017			0.665086	+	0.746767i	$0.268395\pi$
$930$		0			0
$931$	593.793	+	1433.54i	0.637801	+	1.53979i
$932$		0			0
$933$	−111.299	+	268.699i	−0.119291	+	0.287995i
$934$		0			0
$935$	377.061	−	377.061i	0.403274	−	0.403274i
$936$		0			0
$937$	955.999	−	955.999i	1.02028	−	1.02028i	0.0204864	−	0.999790i	$-0.493479\pi$
$937$	955.999	−	955.999i	1.02028	−	1.02028i	0.999790	−	0.0204864i	$-0.00652149\pi$
$938$		0			0
$939$	−146.837	+	354.496i	−0.156376	+	0.377525i
$940$		0			0
$941$	−337.224	−	814.132i	−0.358368	−	0.865177i	−0.995530	−	0.0944471i	$-0.969892\pi$
$941$	−337.224	−	814.132i	−0.358368	−	0.865177i	0.637162	−	0.770730i	$-0.280108\pi$
$942$		0			0
$943$	−444.025			−0.470864
$944$		0			0
$945$		−	39.5544i		−	0.0418565i
$946$		0			0
$947$	1611.78	−	667.619i	1.70198	−	0.704983i	0.702007	−	0.712171i	$-0.252288\pi$
$947$	1611.78	−	667.619i	1.70198	−	0.704983i	0.999974	+	0.00718706i	$0.00228773\pi$
$948$		0			0
$949$	−809.151	−	335.161i	−0.852636	−	0.353173i
$950$		0			0
$951$	−22.6865	−	22.6865i	−0.0238554	−	0.0238554i
$952$		0			0
$953$	661.490	+	661.490i	0.694114	+	0.694114i	0.963134	−	0.269021i	$-0.0867000\pi$
$953$	661.490	+	661.490i	0.694114	+	0.694114i	−0.269021	+	0.963134i	$0.586700\pi$
$954$		0			0
$955$	−581.807	−	240.992i	−0.609222	−	0.252348i
$956$		0			0
$957$	127.508	−	52.8155i	0.133237	−	0.0551886i
$958$		0			0
$959$		−	163.243i		−	0.170222i
$960$		0			0
$961$	−1918.20			−1.99604
$962$		0			0
$963$	49.1121	+	118.567i	0.0509990	+	0.123123i
$964$		0			0
$965$	265.483	−	640.932i	0.275112	−	0.664179i
$966$		0			0
$967$	−38.7070	+	38.7070i	−0.0400279	+	0.0400279i	−0.726837	−	0.686810i	$-0.759011\pi$
$967$	−38.7070	+	38.7070i	−0.0400279	+	0.0400279i	0.686810	+	0.726837i	$0.259011\pi$
$968$		0			0
$969$	339.560	−	339.560i	0.350423	−	0.350423i
$970$		0			0
$971$	−253.057	+	610.934i	−0.260615	+	0.629180i	−0.998977	−	0.0452246i	$-0.985600\pi$
$971$	−253.057	+	610.934i	−0.260615	+	0.629180i	0.738362	+	0.674405i	$0.235600\pi$
$972$		0			0
$973$	2.17021	+	5.23934i	0.00223043	+	0.00538473i
$974$		0			0
$975$	−164.703			−0.168926
$976$		0			0
$977$		−	122.372i		−	0.125253i	−0.998037	−	0.0626263i	$-0.980052\pi$
$977$		−	122.372i		−	0.125253i	0.998037	−	0.0626263i	$-0.0199476\pi$
$978$		0			0
$979$	−630.692	+	261.241i	−0.644221	+	0.266845i
$980$		0			0
$981$	761.783	+	315.541i	0.776537	+	0.321652i
$982$		0			0
$983$	−696.783	−	696.783i	−0.708833	−	0.708833i	0.257457	−	0.966290i	$-0.417116\pi$
$983$	−696.783	−	696.783i	−0.708833	−	0.708833i	−0.966290	+	0.257457i	$0.917116\pi$
$984$		0			0
$985$	−405.572	−	405.572i	−0.411748	−	0.411748i
$986$		0			0
$987$	−2.82573	−	1.17045i	−0.00286294	−	0.00118587i
$988$		0			0
$989$	1063.98	−	440.716i	1.07582	−	0.445618i
$990$		0			0
$991$			536.777i			0.541652i	0.962628	+	0.270826i	$0.0872968\pi$
$991$			536.777i			0.541652i	−0.962628	+	0.270826i	$0.912703\pi$
$992$		0			0
$993$	253.533			0.255321
$994$		0			0
$995$	42.6521	+	102.971i	0.0428664	+	0.103489i
$996$		0			0
$997$	250.176	−	603.979i	0.250929	−	0.605796i	−0.747351	−	0.664430i	$-0.768674\pi$
$997$	250.176	−	603.979i	0.250929	−	0.605796i	0.998280	+	0.0586337i	$0.0186744\pi$
$998$		0			0
$999$	95.6945	−	95.6945i	0.0957903	−	0.0957903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.79.4		28
4.3	odd	2		32.3.h.a.11.5	yes	28
8.3	odd	2		256.3.h.b.159.4		28
8.5	even	2		256.3.h.a.159.4		28
12.11	even	2		288.3.u.a.235.3		28
32.3	odd	8	inner	128.3.h.a.47.4		28
32.13	even	8		256.3.h.b.95.4		28
32.19	odd	8		256.3.h.a.95.4		28
32.29	even	8		32.3.h.a.3.5	✓	28
96.29	odd	8		288.3.u.a.163.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.5	✓	28	32.29	even	8
32.3.h.a.11.5	yes	28	4.3	odd	2
128.3.h.a.47.4		28	32.3	odd	8	inner
128.3.h.a.79.4		28	1.1	even	1	trivial
256.3.h.a.95.4		28	32.19	odd	8
256.3.h.a.159.4		28	8.5	even	2
256.3.h.b.95.4		28	32.13	even	8
256.3.h.b.159.4		28	8.3	odd	2
288.3.u.a.163.3		28	96.29	odd	8
288.3.u.a.235.3		28	12.11	even	2

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.299792 - 0.723762i) q^{3} +(1.34740 - 3.25291i) q^{5} +(-0.583225 + 0.583225i) q^{7} +(5.93000 - 5.93000i) q^{9} +O(q^{10})\)	\(q+(-0.299792 - 0.723762i) q^{3} +(1.34740 - 3.25291i) q^{5} +(-0.583225 + 0.583225i) q^{7} +(5.93000 - 5.93000i) q^{9} +(3.03620 - 7.33003i) q^{11} +(-6.38385 - 15.4120i) q^{13} -2.75827 q^{15} +19.0889i q^{17} +(29.6679 - 12.2888i) q^{19} +(0.596962 + 0.247270i) q^{21} +(-15.2998 - 15.2998i) q^{23} +(8.91173 + 8.91173i) q^{25} +(-12.5835 - 5.21227i) q^{27} +(-20.5148 + 8.49749i) q^{29} +53.6582i q^{31} -6.21542 q^{33} +(1.11134 + 2.68301i) q^{35} +(-3.80237 + 9.17973i) q^{37} +(-9.24078 + 9.24078i) q^{39} +(14.5108 - 14.5108i) q^{41} +(-20.3685 + 49.1739i) q^{43} +(-11.2997 - 27.2799i) q^{45} -4.73351 q^{47} +48.3197i q^{49} +(13.8158 - 5.72269i) q^{51} +(61.4006 + 25.4330i) q^{53} +(-19.7530 - 19.7530i) q^{55} +(-17.7884 - 17.7884i) q^{57} +(-42.4656 - 17.5898i) q^{59} +(-27.7452 + 11.4924i) q^{61} +6.91705i q^{63} -58.7354 q^{65} +(9.42323 + 22.7497i) q^{67} +(-6.48665 + 15.6602i) q^{69} +(95.1299 - 95.1299i) q^{71} +(37.1241 - 37.1241i) q^{73} +(3.77831 - 9.12164i) q^{75} +(2.50427 + 6.04584i) q^{77} +70.3394 q^{79} -64.8066i q^{81} +(-14.5221 + 6.01526i) q^{83} +(62.0944 + 25.7203i) q^{85} +(12.3003 + 12.3003i) q^{87} +(-60.8411 - 60.8411i) q^{89} +(12.7119 + 5.26543i) q^{91} +(38.8357 - 16.0863i) q^{93} -113.065i q^{95} +31.8287 q^{97} +(-25.4624 - 61.4718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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