LMFDB - Embedded newform 76.3.h.a.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 56x^{6} - 154x^{5} + 917x^{4} - 1582x^{3} + 4294x^{2} - 3528x + 4971 $ x^8 - 4x^7 + 56x^6 - 154x^5 + 917x^4 - 1582x^3 + 4294x^2 - 3528*x + 4971
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Root			$0.500000 + 4.59025i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.3.h.a.69.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.72527 + 2.72814i) q^{3} +(3.36497 - 5.82829i) q^{5} -10.3204 q^{7} +(10.3855 + 17.9882i) q^{9} +O(q^{10})$	\(q+(4.72527 + 2.72814i) q^{3} +(3.36497 - 5.82829i) q^{5} -10.3204 q^{7} +(10.3855 + 17.9882i) q^{9} -11.0410 q^{11} +(2.58092 - 1.49010i) q^{13} +(31.8008 - 18.3602i) q^{15} +(3.79523 - 6.57354i) q^{17} +(-13.7250 + 13.1386i) q^{19} +(-48.7667 - 28.1555i) q^{21} +(6.15997 + 10.6694i) q^{23} +(-10.1460 - 17.5734i) q^{25} +64.2255i q^{27} +(0.256743 - 0.148230i) q^{29} -43.6849i q^{31} +(-52.1718 - 30.1214i) q^{33} +(-34.7278 + 60.1503i) q^{35} -36.3892i q^{37} +16.2607 q^{39} +(21.8850 + 12.6353i) q^{41} +(25.2213 - 43.6845i) q^{43} +139.787 q^{45} +(31.4613 + 54.4925i) q^{47} +57.5107 q^{49} +(35.8670 - 20.7078i) q^{51} +(-49.5033 + 28.5808i) q^{53} +(-37.1526 + 64.3503i) q^{55} +(-100.699 + 24.6397i) q^{57} +(53.8188 + 31.0723i) q^{59} +(17.4470 + 30.2191i) q^{61} +(-107.182 - 185.645i) q^{63} -20.0565i q^{65} +(27.8737 - 16.0929i) q^{67} +67.2210i q^{69} +(12.9605 + 7.48276i) q^{71} +(-30.6243 + 53.0428i) q^{73} -110.719i q^{75} +113.948 q^{77} +(0.933929 + 0.539204i) q^{79} +(-81.7469 + 141.590i) q^{81} -128.336 q^{83} +(-25.5417 - 44.2395i) q^{85} +1.61757 q^{87} +(73.8495 - 42.6371i) q^{89} +(-26.6361 + 15.3784i) q^{91} +(119.178 - 206.423i) q^{93} +(30.3914 + 124.205i) q^{95} +(24.9851 + 14.4252i) q^{97} +(-114.666 - 198.608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9	$ 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9 - 10 * q^11 + 9 * q^13 + 33 * q^15 + 23 * q^17 - 33 * q^19 - 31 * q^23 - 73 * q^25 - 105 * q^29 - 111 * q^33 - 68 * q^35 + 234 * q^39 + 18 * q^41 - 41 * q^43 + 200 * q^45 + 107 * q^47 + 312 * q^49 - 9 * q^51 + 39 * q^53 + 70 * q^55 - 381 * q^57 + 348 * q^59 - 45 * q^61 - 358 * q^63 - 432 * q^67 - 243 * q^71 + 16 * q^73 + 544 * q^77 + 75 * q^79 - 68 * q^81 - 82 * q^83 + 109 * q^85 + 414 * q^87 - 213 * q^89 + 222 * q^91 + 288 * q^93 - 385 * q^95 + 144 * q^97 - 388 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	4.72527	+	2.72814i	1.57509	+	0.909379i	0.995530	+	0.0944509i	$0.0301095\pi$
$3$	4.72527	+	2.72814i	1.57509	+	0.909379i	0.579562	+	0.814928i	$0.303224\pi$
$4$		0			0
$5$	3.36497	−	5.82829i	0.672993	−	1.16566i	−0.304058	−	0.952654i	$-0.598342\pi$
$5$	3.36497	−	5.82829i	0.672993	−	1.16566i	0.977051	−	0.213005i	$-0.0683250\pi$
$6$		0			0
$7$	−10.3204			−1.47434			−0.737171	−	0.675706i	$-0.763839\pi$
$7$	−10.3204			−1.47434			−0.737171	+	0.675706i	$0.763839\pi$
$8$		0			0
$9$	10.3855	+	17.9882i	1.15394	+	1.99869i
$10$		0			0
$11$	−11.0410			−1.00373			−0.501864	−	0.864946i	$-0.667352\pi$
$11$	−11.0410			−1.00373			−0.501864	+	0.864946i	$0.667352\pi$
$12$		0			0
$13$	2.58092	−	1.49010i	0.198532	−	0.114623i	−0.397438	−	0.917629i	$-0.630101\pi$
$13$	2.58092	−	1.49010i	0.198532	−	0.114623i	0.595971	+	0.803006i	$0.296767\pi$
$14$		0			0
$15$	31.8008	−	18.3602i	2.12005	−	1.22401i
$16$		0			0
$17$	3.79523	−	6.57354i	0.223249	−	0.386679i	−0.732544	−	0.680720i	$-0.761667\pi$
$17$	3.79523	−	6.57354i	0.223249	−	0.386679i	0.955793	+	0.294041i	$0.0950004\pi$
$18$		0			0
$19$	−13.7250	+	13.1386i	−0.722371	+	0.691506i
$19$	−13.7250	+	13.1386i	−0.722371	+	0.691506i
$20$		0			0
$21$	−48.7667	−	28.1555i	−2.32222	−	1.34074i
$22$		0			0
$23$	6.15997	+	10.6694i	0.267825	+	0.463886i	0.968300	−	0.249791i	$-0.0803618\pi$
$23$	6.15997	+	10.6694i	0.267825	+	0.463886i	−0.700475	+	0.713677i	$0.747028\pi$
$24$		0			0
$25$	−10.1460	−	17.5734i	−0.405840	−	0.702935i
$26$		0			0
$27$			64.2255i			2.37872i
$28$		0			0
$29$	0.256743	−	0.148230i	0.00885319	−	0.00511139i	−0.495567	−	0.868570i	$-0.665040\pi$
$29$	0.256743	−	0.148230i	0.00885319	−	0.00511139i	0.504420	+	0.863458i	$0.331706\pi$
$30$		0			0
$31$		−	43.6849i		−	1.40919i	−0.709609	−	0.704595i	$-0.751129\pi$
$31$		−	43.6849i		−	1.40919i	0.709609	−	0.704595i	$-0.248871\pi$
$32$		0			0
$33$	−52.1718	−	30.1214i	−1.58096	−	0.912770i
$34$		0			0
$35$	−34.7278	+	60.1503i	−0.992223	+	1.71858i
$36$		0			0
$37$		−	36.3892i		−	0.983492i	−0.870739	−	0.491746i	$-0.836359\pi$
$37$		−	36.3892i		−	0.983492i	0.870739	−	0.491746i	$-0.163641\pi$
$38$		0			0
$39$	16.2607			0.416942
$40$		0			0
$41$	21.8850	+	12.6353i	0.533781	+	0.308179i	0.742555	−	0.669785i	$-0.233614\pi$
$41$	21.8850	+	12.6353i	0.533781	+	0.308179i	−0.208774	+	0.977964i	$0.566947\pi$
$42$		0			0
$43$	25.2213	−	43.6845i	0.586541	−	1.01592i	−0.408140	−	0.912919i	$-0.633823\pi$
$43$	25.2213	−	43.6845i	0.586541	−	1.01592i	0.994681	−	0.103000i	$-0.0328441\pi$
$44$		0			0
$45$	139.787			3.10638
$46$		0			0
$47$	31.4613	+	54.4925i	0.669389	+	1.15942i	0.978075	+	0.208252i	$0.0667773\pi$
$47$	31.4613	+	54.4925i	0.669389	+	1.15942i	−0.308686	+	0.951164i	$0.599889\pi$
$48$		0			0
$49$	57.5107			1.17369
$50$		0			0
$51$	35.8670	−	20.7078i	0.703275	−	0.406036i
$52$		0			0
$53$	−49.5033	+	28.5808i	−0.934025	+	0.539260i	−0.888082	−	0.459685i	$-0.847962\pi$
$53$	−49.5033	+	28.5808i	−0.934025	+	0.539260i	−0.0459426	+	0.998944i	$0.514629\pi$
$54$		0			0
$55$	−37.1526	+	64.3503i	−0.675503	+	1.17000i
$56$		0			0
$57$	−100.699	+	24.6397i	−1.76664	+	0.432276i
$58$		0			0
$59$	53.8188	+	31.0723i	0.912182	+	0.526649i	0.881133	−	0.472869i	$-0.156782\pi$
$59$	53.8188	+	31.0723i	0.912182	+	0.526649i	0.0310496	+	0.999518i	$0.490115\pi$
$60$		0			0
$61$	17.4470	+	30.2191i	0.286016	+	0.495395i	0.972855	−	0.231415i	$-0.0743355\pi$
$61$	17.4470	+	30.2191i	0.286016	+	0.495395i	−0.686839	+	0.726810i	$0.741002\pi$
$62$		0			0
$63$	−107.182	−	185.645i	−1.70131	−	2.94675i
$64$		0			0
$65$		−	20.0565i		−	0.308561i
$66$		0			0
$67$	27.8737	−	16.0929i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$67$	27.8737	−	16.0929i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$68$		0			0
$69$			67.2210i			0.974218i
$70$		0			0
$71$	12.9605	+	7.48276i	0.182542	+	0.105391i	0.588487	−	0.808507i	$-0.299724\pi$
$71$	12.9605	+	7.48276i	0.182542	+	0.105391i	−0.405944	+	0.913898i	$0.633057\pi$
$72$		0			0
$73$	−30.6243	+	53.0428i	−0.419511	+	0.726614i	−0.995890	−	0.0905685i	$-0.971132\pi$
$73$	−30.6243	+	53.0428i	−0.419511	+	0.726614i	0.576380	+	0.817182i	$0.304465\pi$
$74$		0			0
$75$		−	110.719i		−	1.47625i
$76$		0			0
$77$	113.948			1.47984
$78$		0			0
$79$	0.933929	+	0.539204i	0.0118219	+	0.00682537i	0.505899	−	0.862593i	$-0.331161\pi$
$79$	0.933929	+	0.539204i	0.0118219	+	0.00682537i	−0.494077	+	0.869418i	$0.664494\pi$
$80$		0			0
$81$	−81.7469	+	141.590i	−1.00922	+	1.74802i
$82$		0			0
$83$	−128.336			−1.54622			−0.773109	−	0.634273i	$-0.781299\pi$
$83$	−128.336			−1.54622			−0.773109	+	0.634273i	$0.781299\pi$
$84$		0			0
$85$	−25.5417	−	44.2395i	−0.300490	−	0.520464i
$86$		0			0
$87$	1.61757			0.0185928
$88$		0			0
$89$	73.8495	−	42.6371i	0.829770	−	0.479068i	−0.0240038	−	0.999712i	$-0.507641\pi$
$89$	73.8495	−	42.6371i	0.829770	−	0.479068i	0.853774	+	0.520644i	$0.174308\pi$
$90$		0			0
$91$	−26.6361	+	15.3784i	−0.292705	+	0.168993i
$92$		0			0
$93$	119.178	−	206.423i	1.28149	−	2.21960i
$94$		0			0
$95$	30.3914	+	124.205i	0.319909	+	1.30742i
$96$		0			0
$97$	24.9851	+	14.4252i	0.257579	+	0.148713i	0.623230	−	0.782039i	$-0.285820\pi$
$97$	24.9851	+	14.4252i	0.257579	+	0.148713i	−0.365651	+	0.930752i	$0.619154\pi$
$98$		0			0
$99$	−114.666	−	198.608i	−1.15824	−	2.00614i
$100$		0			0
$101$	0.478237	+	0.828330i	0.00473502	+	0.00820129i	0.868383	−	0.495894i	$-0.165159\pi$
$101$	0.478237	+	0.828330i	0.00473502	+	0.00820129i	−0.863648	+	0.504095i	$0.831826\pi$
$102$		0			0
$103$			0.859595i			0.00834559i	0.999991	+	0.00417279i	$0.00132825\pi$
$103$			0.859595i			0.00834559i	−0.999991	+	0.00417279i	$0.998672\pi$
$104$		0			0
$105$	−328.197	+	189.484i	−3.12568	+	1.80461i
$106$		0			0
$107$			76.2862i			0.712955i	0.934304	+	0.356477i	$0.116022\pi$
$107$			76.2862i			0.712955i	−0.934304	+	0.356477i	$0.883978\pi$
$108$		0			0
$109$	−113.312	−	65.4208i	−1.03956	−	0.600191i	−0.119852	−	0.992792i	$-0.538242\pi$
$109$	−113.312	−	65.4208i	−1.03956	−	0.600191i	−0.919709	+	0.392601i	$0.871575\pi$
$110$		0			0
$111$	99.2748	−	171.949i	0.894367	−	1.54909i
$112$		0			0
$113$			146.404i			1.29561i	0.761806	+	0.647805i	$0.224313\pi$
$113$			146.404i			1.29561i	−0.761806	+	0.647805i	$0.775687\pi$
$114$		0			0
$115$	82.9124			0.720977
$116$		0			0
$117$	53.6082	+	30.9507i	0.458190	+	0.264536i
$118$		0			0
$119$	−39.1683	+	67.8415i	−0.329146	+	0.570097i
$120$		0			0
$121$	0.904000			0.00747107
$122$		0			0
$123$	68.9418	+	119.411i	0.560502	+	0.970819i
$124$		0			0
$125$	31.6846			0.253477
$126$		0			0
$127$	−201.167	+	116.144i	−1.58399	+	0.914517i	−0.589722	+	0.807606i	$0.700763\pi$
$127$	−201.167	+	116.144i	−1.58399	+	0.914517i	−0.994269	+	0.106911i	$0.965904\pi$
$128$		0			0
$129$	238.355	−	137.614i	1.84771	−	1.06678i
$130$		0			0
$131$	100.146	−	173.459i	0.764476	−	1.32411i	−0.176047	−	0.984382i	$-0.556331\pi$
$131$	100.146	−	173.459i	0.764476	−	1.32411i	0.940523	−	0.339729i	$-0.110335\pi$
$132$		0			0
$133$	141.648	−	135.596i	1.06502	−	1.01952i
$134$		0			0
$135$	374.325	+	216.117i	2.77278	+	1.60086i
$136$		0			0
$137$	−104.955	−	181.787i	−0.766091	−	1.32691i	−0.939668	−	0.342089i	$-0.888866\pi$
$137$	−104.955	−	181.787i	−0.766091	−	1.32691i	0.173576	−	0.984820i	$-0.444468\pi$
$138$		0			0
$139$	−2.57641	−	4.46248i	−0.0185353	−	0.0321041i	0.856609	−	0.515966i	$-0.172567\pi$
$139$	−2.57641	−	4.46248i	−0.0185353	−	0.0321041i	−0.875144	+	0.483862i	$0.839234\pi$
$140$		0			0
$141$			343.323i			2.43491i
$142$		0			0
$143$	−28.4960	+	16.4522i	−0.199273	+	0.115050i
$144$		0			0
$145$		−	1.99516i		−	0.0137597i
$146$		0			0
$147$	271.754	+	156.897i	1.84866	+	1.06733i
$148$		0			0
$149$	52.1864	−	90.3895i	0.350244	−	0.606641i	−0.636048	−	0.771650i	$-0.719432\pi$
$149$	52.1864	−	90.3895i	0.350244	−	0.606641i	0.986292	+	0.165009i	$0.0527652\pi$
$150$		0			0
$151$		−	248.789i		−	1.64761i	−0.566874	−	0.823804i	$-0.691847\pi$
$151$		−	248.789i		−	1.64761i	0.566874	−	0.823804i	$-0.308153\pi$
$152$		0			0
$153$	157.661			1.03047
$154$		0			0
$155$	−254.608	−	146.998i	−1.64264	−	0.948376i
$156$		0			0
$157$	16.7683	−	29.0436i	0.106805	−	0.184991i	−0.807669	−	0.589636i	$-0.799271\pi$
$157$	16.7683	−	29.0436i	0.106805	−	0.184991i	0.914474	+	0.404644i	$0.132605\pi$
$158$		0			0
$159$	−311.889			−1.96157
$160$		0			0
$161$	−63.5734	−	110.112i	−0.394866	−	0.683927i
$162$		0			0
$163$	289.865			1.77831			0.889157	−	0.457602i	$-0.151291\pi$
$163$	289.865			1.77831			0.889157	+	0.457602i	$0.151291\pi$
$164$		0			0
$165$	−351.113	+	202.715i	−2.12796	+	1.22858i
$166$		0			0
$167$	−111.219	+	64.2122i	−0.665981	+	0.384504i	−0.794552	−	0.607196i	$-0.792294\pi$
$167$	−111.219	+	64.2122i	−0.665981	+	0.384504i	0.128571	+	0.991700i	$0.458961\pi$
$168$		0			0
$169$	−80.0592	+	138.667i	−0.473723	+	0.820513i
$170$		0			0
$171$	−378.881	−	110.438i	−2.21568	−	0.645835i
$172$		0			0
$173$	89.5330	+	51.6919i	0.517532	+	0.298797i	0.735924	−	0.677064i	$-0.236748\pi$
$173$	89.5330	+	51.6919i	0.517532	+	0.298797i	−0.218392	+	0.975861i	$0.570081\pi$
$174$		0			0
$175$	104.711	+	181.364i	0.598347	+	1.03637i
$176$		0			0
$177$	169.539	+	293.650i	0.957847	+	1.65904i
$178$		0			0
$179$		−	259.049i		−	1.44720i	−0.690220	−	0.723599i	$-0.742486\pi$
$179$		−	259.049i		−	1.44720i	0.690220	−	0.723599i	$-0.257514\pi$
$180$		0			0
$181$	−136.428	+	78.7668i	−0.753746	+	0.435176i	−0.827046	−	0.562134i	$-0.809980\pi$
$181$	−136.428	+	78.7668i	−0.753746	+	0.435176i	0.0732997	+	0.997310i	$0.476647\pi$
$182$		0			0
$183$			190.391i			1.04039i
$184$		0			0
$185$	−212.087	−	122.448i	−1.14642	−	0.661884i
$186$		0			0
$187$	−41.9032	+	72.5785i	−0.224081	+	0.388120i
$188$		0			0
$189$		−	662.833i		−	3.50705i
$190$		0			0
$191$	27.7996			0.145548			0.0727738	−	0.997348i	$-0.476815\pi$
$191$	27.7996			0.145548			0.0727738	+	0.997348i	$0.476815\pi$
$192$		0			0
$193$	−184.942	−	106.776i	−0.958248	−	0.553245i	−0.0626147	−	0.998038i	$-0.519944\pi$
$193$	−184.942	−	106.776i	−0.958248	−	0.553245i	−0.895633	+	0.444793i	$0.853277\pi$
$194$		0			0
$195$	54.7169	−	94.7724i	0.280599	−	0.486012i
$196$		0			0
$197$	166.104			0.843168			0.421584	−	0.906789i	$-0.361474\pi$
$197$	166.104			0.843168			0.421584	+	0.906789i	$0.361474\pi$
$198$		0			0
$199$	−85.2426	−	147.644i	−0.428355	−	0.741932i	0.568373	−	0.822771i	$-0.307573\pi$
$199$	−85.2426	−	147.644i	−0.428355	−	0.741932i	−0.996727	+	0.0808394i	$0.974240\pi$
$200$		0			0
$201$	175.614			0.873703
$202$		0			0
$203$	−2.64969	+	1.52980i	−0.0130526	+	0.00753595i
$204$		0			0
$205$	147.285	−	85.0349i	0.718462	−	0.414804i
$206$		0			0
$207$	−127.948	+	221.613i	−0.618108	+	1.07060i
$208$		0			0
$209$	151.538	−	145.064i	0.725064	−	0.694084i
$210$		0			0
$211$	140.299	+	81.0017i	0.664925	+	0.383894i	0.794151	−	0.607721i	$-0.207916\pi$
$211$	140.299	+	81.0017i	0.664925	+	0.383894i	−0.129226	+	0.991615i	$0.541249\pi$
$212$		0			0
$213$	40.8280	+	70.7162i	0.191681	+	0.332001i
$214$		0			0
$215$	−169.737	−	293.994i	−0.789476	−	1.36741i
$216$		0			0
$217$			450.846i			2.07763i
$218$		0			0
$219$	−289.416	+	167.094i	−1.32153	+	0.762988i
$220$		0			0
$221$		−	22.6210i		−	0.102358i
$222$		0			0
$223$	−105.933	−	61.1604i	−0.475035	−	0.274262i	0.243310	−	0.969949i	$-0.421767\pi$
$223$	−105.933	−	61.1604i	−0.475035	−	0.274262i	−0.718345	+	0.695687i	$0.755100\pi$
$224$		0			0
$225$	210.742	−	365.016i	0.936631	−	1.62229i
$226$		0			0
$227$			419.076i			1.84615i	0.384622	+	0.923074i	$0.374332\pi$
$227$			419.076i			1.84615i	−0.384622	+	0.923074i	$0.625668\pi$
$228$		0			0
$229$	−451.995			−1.97378			−0.986890	−	0.161397i	$-0.948400\pi$
$229$	−451.995			−1.97378			−0.986890	+	0.161397i	$0.948400\pi$
$230$		0			0
$231$	538.434	+	310.865i	2.33088	+	1.34574i
$232$		0			0
$233$	−50.8110	+	88.0072i	−0.218073	+	0.377713i	−0.954219	−	0.299110i	$-0.903310\pi$
$233$	−50.8110	+	88.0072i	−0.218073	+	0.377713i	0.736146	+	0.676823i	$0.236644\pi$
$234$		0			0
$235$	423.465			1.80198
$236$		0			0
$237$	2.94205	+	5.09577i	0.0124137	+	0.0215011i
$238$		0			0
$239$	69.5081			0.290829			0.145415	−	0.989371i	$-0.453548\pi$
$239$	69.5081			0.290829			0.145415	+	0.989371i	$0.453548\pi$
$240$		0			0
$241$	38.4255	−	22.1850i	0.159442	−	0.0920538i	−0.418156	−	0.908375i	$-0.637324\pi$
$241$	38.4255	−	22.1850i	0.159442	−	0.0920538i	0.577598	+	0.816321i	$0.303990\pi$
$242$		0			0
$243$	−271.964	+	157.019i	−1.11919	+	0.646167i
$244$		0			0
$245$	193.521	−	335.189i	0.789883	−	1.36812i
$246$		0			0
$247$	−15.8455	+	54.3614i	−0.0641517	+	0.220087i
$248$		0			0
$249$	−606.423	−	350.118i	−2.43543	−	1.40610i
$250$		0			0
$251$	9.26488	+	16.0472i	0.0369119	+	0.0639332i	0.883891	−	0.467693i	$-0.154915\pi$
$251$	9.26488	+	16.0472i	0.0369119	+	0.0639332i	−0.846979	+	0.531626i	$0.821581\pi$
$252$		0			0
$253$	−68.0123	−	117.801i	−0.268823	−	0.465616i
$254$		0			0
$255$		−	278.725i		−	1.09304i
$256$		0			0
$257$	96.4666	−	55.6950i	0.375357	−	0.216712i	−0.300440	−	0.953801i	$-0.597133\pi$
$257$	96.4666	−	55.6950i	0.375357	−	0.216712i	0.675796	+	0.737089i	$0.263800\pi$
$258$		0			0
$259$			375.551i			1.45000i
$260$		0			0
$261$	5.33279	+	3.07889i	0.0204321	+	0.0117965i
$262$		0			0
$263$	−48.4277	+	83.8792i	−0.184136	+	0.318932i	−0.943285	−	0.331984i	$-0.892282\pi$
$263$	−48.4277	+	83.8792i	−0.184136	+	0.318932i	0.759149	+	0.650917i	$0.225615\pi$
$264$		0			0
$265$			384.693i			1.45167i
$266$		0			0
$267$	465.279			1.74262
$268$		0			0
$269$	201.634	+	116.413i	0.749569	+	0.432764i	0.825538	−	0.564346i	$-0.190872\pi$
$269$	201.634	+	116.413i	0.749569	+	0.432764i	−0.0759693	+	0.997110i	$0.524205\pi$
$270$		0			0
$271$	28.8040	−	49.8900i	0.106288	−	0.184096i	−0.807976	−	0.589216i	$-0.799437\pi$
$271$	28.8040	−	49.8900i	0.106288	−	0.184096i	0.914264	+	0.405120i	$0.132770\pi$
$272$		0			0
$273$	−167.817			−0.614716
$274$		0			0
$275$	112.022	+	194.028i	0.407353	+	0.705556i
$276$		0			0
$277$	218.559			0.789023			0.394512	−	0.918891i	$-0.370914\pi$
$277$	218.559			0.789023			0.394512	+	0.918891i	$0.370914\pi$
$278$		0			0
$279$	785.811	−	453.688i	2.81653	−	1.62612i
$280$		0			0
$281$	229.776	−	132.661i	0.817709	−	0.472104i	−0.0319170	−	0.999491i	$-0.510161\pi$
$281$	229.776	−	132.661i	0.817709	−	0.472104i	0.849626	+	0.527386i	$0.176828\pi$
$282$		0			0
$283$	60.9727	−	105.608i	0.215451	−	0.373173i	−0.737961	−	0.674844i	$-0.764211\pi$
$283$	60.9727	−	105.608i	0.215451	−	0.373173i	0.953412	+	0.301671i	$0.0975444\pi$
$284$		0			0
$285$	−195.240	+	669.812i	−0.685052	+	2.35022i
$286$		0			0
$287$	−225.862	−	130.402i	−0.786976	−	0.454361i
$288$		0			0
$289$	115.692	+	200.385i	0.400320	+	0.693374i
$290$		0			0
$291$	78.7078	+	136.326i	0.270473	+	0.468474i
$292$		0			0
$293$		−	118.392i		−	0.404067i	−0.979379	−	0.202033i	$-0.935245\pi$
$293$		−	118.392i		−	0.404067i	0.979379	−	0.202033i	$-0.0647549\pi$
$294$		0			0
$295$	362.197	−	209.114i	1.22779	−	0.708862i
$296$		0			0
$297$		−	709.115i		−	2.38759i
$298$		0			0
$299$	31.7968	+	18.3579i	0.106344	+	0.0613977i
$300$		0			0
$301$	−260.294	+	450.842i	−0.864763	+	1.49781i
$302$		0			0
$303$			5.21878i			0.0172237i
$304$		0			0
$305$	234.834			0.769948
$306$		0			0
$307$	−413.684	−	238.840i	−1.34750	−	0.777982i	−0.359608	−	0.933103i	$-0.617090\pi$
$307$	−413.684	−	238.840i	−1.34750	−	0.777982i	−0.987895	+	0.155122i	$0.950423\pi$
$308$		0			0
$309$	−2.34509	+	4.06182i	−0.00758930	+	0.0131451i
$310$		0			0
$311$	−447.701			−1.43955			−0.719777	−	0.694205i	$-0.755756\pi$
$311$	−447.701			−1.43955			−0.719777	+	0.694205i	$0.755756\pi$
$312$		0			0
$313$	112.793	+	195.364i	0.360362	+	0.624165i	0.988020	−	0.154324i	$-0.0493199\pi$
$313$	112.793	+	195.364i	0.360362	+	0.624165i	−0.627659	+	0.778489i	$0.715987\pi$
$314$		0			0
$315$	−1442.66			−4.57987
$316$		0			0
$317$	−288.656	+	166.656i	−0.910588	+	0.525728i	−0.880620	−	0.473823i	$-0.842874\pi$
$317$	−288.656	+	166.656i	−0.910588	+	0.525728i	−0.0299678	+	0.999551i	$0.509540\pi$
$318$		0			0
$319$	−2.83470	+	1.63661i	−0.00888620	+	0.00513045i
$320$		0			0
$321$	−208.119	+	360.473i	−0.648347	+	1.12297i
$322$		0			0
$323$	34.2774	+	140.086i	0.106122	+	0.433703i
$324$		0			0
$325$	−52.3720	−	30.2370i	−0.161145	−	0.0930370i
$326$		0			0
$327$	−356.954	−	618.262i	−1.09160	−	1.89071i
$328$		0			0
$329$	−324.693	−	562.385i	−0.986909	−	1.70938i
$330$		0			0
$331$		−	571.970i		−	1.72801i	−0.503487	−	0.864003i	$-0.667950\pi$
$331$		−	571.970i		−	1.72801i	0.503487	−	0.864003i	$-0.332050\pi$
$332$		0			0
$333$	654.575	−	377.919i	1.96569	−	1.13489i
$334$		0			0
$335$		−	216.608i		−	0.646591i
$336$		0			0
$337$	141.442	+	81.6615i	0.419709	+	0.242319i	0.694953	−	0.719055i	$-0.255425\pi$
$337$	141.442	+	81.6615i	0.419709	+	0.242319i	−0.275244	+	0.961374i	$0.588759\pi$
$338$		0			0
$339$	−399.410	+	691.798i	−1.17820	+	2.04070i
$340$		0			0
$341$			482.326i			1.41444i
$342$		0			0
$343$	−87.8333			−0.256074
$344$		0			0
$345$	391.784	+	226.196i	1.13561	+	0.655642i
$346$		0			0
$347$	11.4958	−	19.9113i	0.0331290	−	0.0573812i	−0.848986	−	0.528416i	$-0.822786\pi$
$347$	11.4958	−	19.9113i	0.0331290	−	0.0573812i	0.882115	+	0.471035i	$0.156119\pi$
$348$		0			0
$349$	293.319			0.840454			0.420227	−	0.907419i	$-0.361950\pi$
$349$	293.319			0.840454			0.420227	+	0.907419i	$0.361950\pi$
$350$		0			0
$351$	95.7022	+	165.761i	0.272656	+	0.472254i
$352$		0			0
$353$	−165.632			−0.469212			−0.234606	−	0.972091i	$-0.575380\pi$
$353$	−165.632			−0.469212			−0.234606	+	0.972091i	$0.575380\pi$
$354$		0			0
$355$	87.2234	−	50.3585i	0.245700	−	0.141855i
$356$		0			0
$357$	−370.162	+	213.713i	−1.03687	+	0.598636i
$358$		0			0
$359$	−9.85859	+	17.0756i	−0.0274613	+	0.0475643i	−0.879429	−	0.476029i	$-0.842076\pi$
$359$	−9.85859	+	17.0756i	−0.0274613	+	0.0475643i	0.851968	+	0.523594i	$0.175409\pi$
$360$		0			0
$361$	15.7538	−	360.656i	0.0436393	−	0.999047i
$362$		0			0
$363$	4.27165	+	2.46624i	0.0117676	+	0.00679404i
$364$		0			0
$365$	206.099	+	356.974i	0.564656	+	0.978012i
$366$		0			0
$367$	−121.600	−	210.618i	−0.331336	−	0.573890i	0.651438	−	0.758702i	$-0.274166\pi$
$367$	−121.600	−	210.618i	−0.331336	−	0.573890i	−0.982774	+	0.184811i	$0.940833\pi$
$368$		0			0
$369$			524.895i			1.42248i
$370$		0			0
$371$	510.894	−	294.965i	1.37707	−	0.795053i
$372$		0			0
$373$		−	73.0173i		−	0.195757i	−0.995198	−	0.0978785i	$-0.968794\pi$
$373$		−	73.0173i		−	0.195757i	0.995198	−	0.0978785i	$-0.0312056\pi$
$374$		0			0
$375$	149.718	+	86.4399i	0.399249	+	0.230506i
$376$		0			0
$377$	0.441755	−	0.765142i	0.00117176	−	0.00202956i
$378$		0			0
$379$		−	235.324i		−	0.620908i	−0.950588	−	0.310454i	$-0.899519\pi$
$379$		−	235.324i		−	0.620908i	0.950588	−	0.310454i	$-0.100481\pi$
$380$		0			0
$381$	−1267.42			−3.32657
$382$		0			0
$383$	−396.137	−	228.710i	−1.03430	−	0.597153i	−0.116086	−	0.993239i	$-0.537035\pi$
$383$	−396.137	−	228.710i	−1.03430	−	0.597153i	−0.918213	+	0.396086i	$0.870368\pi$
$384$		0			0
$385$	383.430	−	664.120i	0.995922	−	1.72499i
$386$		0			0
$387$	1047.74			2.70734
$388$		0			0
$389$	245.683	+	425.536i	0.631577	+	1.09392i	0.987229	+	0.159305i	$0.0509253\pi$
$389$	245.683	+	425.536i	0.631577	+	1.09392i	−0.355653	+	0.934618i	$0.615741\pi$
$390$		0			0
$391$	93.5141			0.239167
$392$		0			0
$393$	946.438	−	546.426i	2.40824	−	1.39040i
$394$		0			0
$395$	6.28528	−	3.62881i	0.0159121	−	0.00918685i
$396$		0			0
$397$	−238.283	+	412.719i	−0.600210	+	1.03959i	0.392579	+	0.919718i	$0.371583\pi$
$397$	−238.283	+	412.719i	−0.600210	+	1.03959i	−0.992789	+	0.119876i	$0.961750\pi$
$398$		0			0
$399$	1039.25	−	254.292i	2.60463	−	0.637323i
$400$		0			0
$401$	141.299	+	81.5790i	0.352366	+	0.203439i	0.665727	−	0.746195i	$-0.268122\pi$
$401$	141.299	+	81.5790i	0.352366	+	0.203439i	−0.313361	+	0.949634i	$0.601455\pi$
$402$		0			0
$403$	−65.0947	−	112.747i	−0.161525	−	0.279770i
$404$		0			0
$405$	550.151	+	952.889i	1.35840	+	2.35281i
$406$		0			0
$407$			401.774i			0.987159i
$408$		0			0
$409$	−181.889	+	105.014i	−0.444716	+	0.256757i	−0.705596	−	0.708614i	$-0.749321\pi$
$409$	−181.889	+	105.014i	−0.444716	+	0.256757i	0.260880	+	0.965371i	$0.415987\pi$
$410$		0			0
$411$		−	1145.32i		−	2.78667i
$412$		0			0
$413$	−555.431	−	320.678i	−1.34487	−	0.776461i
$414$		0			0
$415$	−431.847	+	747.980i	−1.04059	+	1.80236i
$416$		0			0
$417$		−	28.1152i		−	0.0674226i
$418$		0			0
$419$	67.8186			0.161858			0.0809291	−	0.996720i	$-0.474211\pi$
$419$	67.8186			0.161858			0.0809291	+	0.996720i	$0.474211\pi$
$420$		0			0
$421$	−381.747	−	220.402i	−0.906762	−	0.523519i	−0.0273742	−	0.999625i	$-0.508715\pi$
$421$	−381.747	−	220.402i	−0.906762	−	0.523519i	−0.879388	+	0.476106i	$0.842048\pi$
$422$		0			0
$423$	−653.481	+	1131.86i	−1.54487	+	2.67580i
$424$		0			0
$425$	−154.026			−0.362413
$426$		0			0
$427$	−180.060	−	311.873i	−0.421686	−	0.730382i
$428$		0			0
$429$	−179.535			−0.418497
$430$		0			0
$431$	−219.620	+	126.798i	−0.509559	+	0.294194i	−0.732652	−	0.680603i	$-0.761718\pi$
$431$	−219.620	+	126.798i	−0.509559	+	0.294194i	0.223094	+	0.974797i	$0.428384\pi$
$432$		0			0
$433$	−112.770	+	65.1081i	−0.260440	+	0.150365i	−0.624535	−	0.780997i	$-0.714712\pi$
$433$	−112.770	+	65.1081i	−0.260440	+	0.150365i	0.364095	+	0.931362i	$0.381378\pi$
$434$		0			0
$435$	5.44308	−	9.42768i	0.0125128	−	0.0216728i
$436$		0			0
$437$	−224.727	−	65.5043i	−0.514249	−	0.149895i
$438$		0			0
$439$	−52.9141	−	30.5499i	−0.120533	−	0.0695898i	0.438521	−	0.898721i	$-0.355502\pi$
$439$	−52.9141	−	30.5499i	−0.120533	−	0.0695898i	−0.559054	+	0.829131i	$0.688836\pi$
$440$		0			0
$441$	597.275	+	1034.51i	1.35437	+	2.34583i
$442$		0			0
$443$	362.639	+	628.110i	0.818599	+	1.41785i	0.906715	+	0.421744i	$0.138582\pi$
$443$	362.639	+	628.110i	0.818599	+	1.41785i	−0.0881161	+	0.996110i	$0.528085\pi$
$444$		0			0
$445$		−	573.889i		−	1.28964i
$446$		0			0
$447$	493.190	−	284.743i	1.10333	−	0.637010i
$448$		0			0
$449$			754.314i			1.67999i	0.542596	+	0.839994i	$0.317442\pi$
$449$			754.314i			1.67999i	−0.542596	+	0.839994i	$0.682558\pi$
$450$		0			0
$451$	−241.633	−	139.507i	−0.535771	−	0.309328i
$452$		0			0
$453$	678.731	−	1175.60i	1.49830	−	2.59513i
$454$		0			0
$455$			206.991i			0.454925i
$456$		0			0
$457$	607.195			1.32865			0.664327	−	0.747442i	$-0.268718\pi$
$457$	607.195			1.32865			0.664327	+	0.747442i	$0.268718\pi$
$458$		0			0
$459$	422.189	+	243.751i	0.919802	+	0.531048i
$460$		0			0
$461$	349.326	−	605.050i	0.757756	−	1.31247i	−0.186236	−	0.982505i	$-0.559629\pi$
$461$	349.326	−	605.050i	0.757756	−	1.31247i	0.943992	−	0.329967i	$-0.107038\pi$
$462$		0			0
$463$	−404.516			−0.873685			−0.436842	−	0.899538i	$-0.643903\pi$
$463$	−404.516			−0.873685			−0.436842	+	0.899538i	$0.643903\pi$
$464$		0			0
$465$	−802.063	−	1389.21i	−1.72487	−	2.98756i
$466$		0			0
$467$	535.061			1.14574			0.572870	−	0.819646i	$-0.305830\pi$
$467$	535.061			1.14574			0.572870	+	0.819646i	$0.305830\pi$
$468$		0			0
$469$	−287.668	+	166.085i	−0.613364	+	0.354126i
$470$		0			0
$471$	158.470	−	91.4927i	0.336454	−	0.194252i
$472$		0			0
$473$	−278.468	+	482.321i	−0.588728	+	1.01971i
$474$		0			0
$475$	370.144	+	107.891i	0.779251	+	0.227139i
$476$		0			0
$477$	−1028.23	−	593.649i	−2.15562	−	1.24455i
$478$		0			0
$479$	392.623	+	680.043i	0.819672	+	1.41971i	0.905924	+	0.423440i	$0.139178\pi$
$479$	392.623	+	680.043i	0.819672	+	1.41971i	−0.0862524	+	0.996273i	$0.527489\pi$
$480$		0			0
$481$	−54.2234	−	93.9177i	−0.112731	−	0.195255i
$482$		0			0
$483$		−	693.748i		−	1.43633i
$484$		0			0
$485$	168.148	−	97.0805i	0.346698	−	0.200166i
$486$		0			0
$487$			500.456i			1.02763i	0.857901	+	0.513815i	$0.171768\pi$
$487$			500.456i			1.02763i	−0.857901	+	0.513815i	$0.828232\pi$
$488$		0			0
$489$	1369.69	+	790.793i	2.80101	+	1.61716i
$490$		0			0
$491$	303.560	−	525.782i	0.618249	−	1.07084i	−0.371556	−	0.928410i	$-0.621176\pi$
$491$	303.560	−	525.782i	0.618249	−	1.07084i	0.989805	−	0.142428i	$-0.0454909\pi$
$492$		0			0
$493$		−	2.25028i		−	0.00456446i
$494$		0			0
$495$	−1543.39			−3.11796
$496$		0			0
$497$	−133.758	−	77.2251i	−0.269130	−	0.155382i
$498$		0			0
$499$	−23.3896	+	40.5120i	−0.0468729	+	0.0811863i	−0.888510	−	0.458857i	$-0.848259\pi$
$499$	−23.3896	+	40.5120i	−0.0468729	+	0.0811863i	0.841637	+	0.540044i	$0.181592\pi$
$500$		0			0
$501$	−700.719			−1.39864
$502$		0			0
$503$	128.217	+	222.078i	0.254904	+	0.441507i	0.964870	−	0.262730i	$-0.0846227\pi$
$503$	128.217	+	222.078i	0.254904	+	0.441507i	−0.709965	+	0.704237i	$0.751289\pi$
$504$		0			0
$505$	6.43700			0.0127465
$506$		0			0
$507$	−756.604	+	436.825i	−1.49231	+	0.861588i
$508$		0			0
$509$	−74.2315	+	42.8576i	−0.145838	+	0.0841996i	−0.571143	−	0.820850i	$-0.693500\pi$
$509$	−74.2315	+	42.8576i	−0.145838	+	0.0841996i	0.425305	+	0.905050i	$0.360167\pi$
$510$		0			0
$511$	316.055	−	547.423i	0.618502	−	1.07128i
$512$		0			0
$513$	−843.834	−	881.498i	−1.64490	−	1.71832i
$514$		0			0
$515$	5.00997	+	2.89251i	0.00972810	+	0.00561652i
$516$		0			0
$517$	−347.364	−	601.653i	−0.671885	−	1.16374i
$518$		0			0
$519$	282.045	+	488.517i	0.543440	+	0.941266i
$520$		0			0
$521$		−	783.314i		−	1.50348i	−0.659458	−	0.751741i	$-0.729214\pi$
$521$		−	783.314i		−	1.50348i	0.659458	−	0.751741i	$-0.270786\pi$
$522$		0			0
$523$	−532.622	+	307.509i	−1.01840	+	0.587972i	−0.913639	−	0.406526i	$-0.866740\pi$
$523$	−532.622	+	307.509i	−1.01840	+	0.587972i	−0.104758	+	0.994498i	$0.533407\pi$
$524$		0			0
$525$			1142.66i			2.17650i
$526$		0			0
$527$	−287.164	−	165.794i	−0.544904	−	0.314600i
$528$		0			0
$529$	188.609	−	326.681i	0.356540	−	0.617545i
$530$		0			0
$531$			1290.80i			2.43089i
$532$		0			0
$533$	75.3114			0.141297
$534$		0			0
$535$	444.618	+	256.700i	0.831062	+	0.479814i
$536$		0			0
$537$	706.720	−	1224.08i	1.31605	−	2.27947i
$538$		0			0
$539$	−634.976			−1.17806
$540$		0			0
$541$	100.734	+	174.477i	0.186200	+	0.322509i	0.943980	−	0.330002i	$-0.107049\pi$
$541$	100.734	+	174.477i	0.186200	+	0.322509i	−0.757780	+	0.652510i	$0.773716\pi$
$542$		0			0
$543$	−859.547			−1.58296
$544$		0			0
$545$	−762.583	+	440.278i	−1.39924	+	0.807849i
$546$		0			0
$547$	−170.320	+	98.3344i	−0.311371	+	0.179770i	−0.647540	−	0.762031i	$-0.724202\pi$
$547$	−170.320	+	98.3344i	−0.311371	+	0.179770i	0.336169	+	0.941802i	$0.390869\pi$
$548$		0			0
$549$	−362.391	+	627.679i	−0.660092	+	1.14331i
$550$		0			0
$551$	−1.57626	+	5.40771i	−0.00286073	+	0.00981436i
$552$		0			0
$553$	−9.63852	−	5.56480i	−0.0174295	−	0.0100629i
$554$		0			0
$555$	−668.113	−	1157.20i	−1.20381	−	2.08505i
$556$		0			0
$557$	545.560	+	944.937i	0.979461	+	1.69648i	0.664352	+	0.747420i	$0.268708\pi$
$557$	545.560	+	944.937i	0.979461	+	1.69648i	0.315109	+	0.949056i	$0.397959\pi$
$558$		0			0
$559$		−	150.328i		−	0.268924i
$560$		0			0
$561$	−396.008	+	228.636i	−0.705897	+	0.407550i
$562$		0			0
$563$		−	462.607i		−	0.821683i	−0.911707	−	0.410841i	$-0.865235\pi$
$563$		−	462.607i		−	0.821683i	0.911707	−	0.410841i	$-0.134765\pi$
$564$		0			0
$565$	853.285	+	492.644i	1.51024	+	0.871936i
$566$		0			0
$567$	843.660	−	1461.26i	1.48794	−	2.57718i
$568$		0			0
$569$			314.149i			0.552107i	0.961142	+	0.276053i	$0.0890267\pi$
$569$			314.149i			0.552107i	−0.961142	+	0.276053i	$0.910973\pi$
$570$		0			0
$571$	339.220			0.594081			0.297041	−	0.954865i	$-0.404000\pi$
$571$	339.220			0.594081			0.297041	+	0.954865i	$0.404000\pi$
$572$		0			0
$573$	131.361	+	75.8411i	0.229251	+	0.132358i
$574$		0			0
$575$	124.998	−	216.503i	0.217388	−	0.376527i
$576$		0			0
$577$	−799.877			−1.38627			−0.693134	−	0.720809i	$-0.743771\pi$
$577$	−799.877			−1.38627			−0.693134	+	0.720809i	$0.743771\pi$
$578$		0			0
$579$	−582.601	−	1009.09i	−1.00622	−	1.74282i
$580$		0			0
$581$	1324.48			2.27965
$582$		0			0
$583$	546.567	−	315.561i	0.937508	−	0.541270i
$584$		0			0
$585$	360.780	−	208.296i	0.616717	−	0.356062i
$586$		0			0
$587$	−17.4317	+	30.1927i	−0.0296963	+	0.0514356i	−0.880492	−	0.474062i	$-0.842787\pi$
$587$	−17.4317	+	30.1927i	−0.0296963	+	0.0514356i	0.850795	+	0.525497i	$0.176121\pi$
$588$		0			0
$589$	573.959	+	599.577i	0.974464	+	1.01796i
$590$		0			0
$591$	784.887	+	453.155i	1.32807	+	0.766760i
$592$		0			0
$593$	468.980	+	812.298i	0.790860	+	1.36981i	0.925435	+	0.378907i	$0.123700\pi$
$593$	468.980	+	812.298i	0.790860	+	1.36981i	−0.134574	+	0.990904i	$0.542967\pi$
$594$		0			0
$595$	263.600	+	456.569i	0.443026	+	0.767343i
$596$		0			0
$597$		−	930.214i		−	1.55815i
$598$		0			0
$599$	−336.116	+	194.057i	−0.561128	+	0.323968i	−0.753598	−	0.657335i	$-0.771684\pi$
$599$	−336.116	+	194.057i	−0.561128	+	0.323968i	0.192470	+	0.981303i	$0.438350\pi$
$600$		0			0
$601$		−	546.854i		−	0.909906i	−0.890515	−	0.454953i	$-0.849656\pi$
$601$		−	546.854i		−	0.909906i	0.890515	−	0.454953i	$-0.150344\pi$
$602$		0			0
$603$	578.963	+	334.264i	0.960137	+	0.554335i
$604$		0			0
$605$	3.04193	−	5.26878i	0.00502798	−	0.00870872i
$606$		0			0
$607$			781.345i			1.28722i	0.765352	+	0.643612i	$0.222565\pi$
$607$			781.345i			1.28722i	−0.765352	+	0.643612i	$0.777435\pi$
$608$		0			0
$609$	−16.6940			−0.0274121
$610$		0			0
$611$	162.398	+	93.7607i	0.265791	+	0.153454i
$612$		0			0
$613$	−156.608	+	271.253i	−0.255478	+	0.442501i	−0.965025	−	0.262157i	$-0.915566\pi$
$613$	−156.608	+	271.253i	−0.255478	+	0.442501i	0.709547	+	0.704658i	$0.248900\pi$
$614$		0			0
$615$	927.947			1.50886
$616$		0			0
$617$	−37.3161	−	64.6334i	−0.0604799	−	0.104754i	0.834200	−	0.551462i	$-0.185930\pi$
$617$	−37.3161	−	64.6334i	−0.0604799	−	0.104754i	−0.894680	+	0.446708i	$0.852596\pi$
$618$		0			0
$619$	310.448			0.501532			0.250766	−	0.968048i	$-0.419318\pi$
$619$	310.448			0.501532			0.250766	+	0.968048i	$0.419318\pi$
$620$		0			0
$621$	−685.247	+	395.628i	−1.10346	+	0.637081i
$622$		0			0
$623$	−762.157	+	440.031i	−1.22337	+	0.706310i
$624$		0			0
$625$	360.267	−	624.002i	0.576428	−	0.998402i
$626$		0			0
$627$	1111.81	−	272.047i	1.77323	−	0.433887i
$628$		0			0
$629$	−239.206	−	138.106i	−0.380295	−	0.219564i
$630$		0			0
$631$	254.604	+	440.987i	0.403493	+	0.698870i	0.994145	−	0.108056i	$-0.0344627\pi$
$631$	254.604	+	440.987i	0.403493	+	0.698870i	−0.590652	+	0.806926i	$0.701129\pi$
$632$		0			0
$633$	441.968	+	765.511i	0.698211	+	1.20934i
$634$		0			0
$635$			1563.28i			2.46186i
$636$		0			0
$637$	148.431	−	85.6964i	0.233015	−	0.134531i
$638$		0			0
$639$			310.848i			0.486460i
$640$		0			0
$641$	−871.393	−	503.099i	−1.35943	−	0.784866i	−0.369881	−	0.929079i	$-0.620602\pi$
$641$	−871.393	−	503.099i	−1.35943	−	0.784866i	−0.989547	+	0.144213i	$0.953935\pi$
$642$		0			0
$643$	4.70269	−	8.14530i	0.00731367	−	0.0126677i	−0.862345	−	0.506320i	$-0.831005\pi$
$643$	4.70269	−	8.14530i	0.00731367	−	0.0126677i	0.869659	+	0.493653i	$0.164339\pi$
$644$		0			0
$645$		−	1852.27i		−	2.87173i
$646$		0			0
$647$	591.348			0.913985			0.456993	−	0.889470i	$-0.348927\pi$
$647$	591.348			0.913985			0.456993	+	0.889470i	$0.348927\pi$
$648$		0			0
$649$	−594.214	−	343.069i	−0.915583	−	0.528612i
$650$		0			0
$651$	−1229.97	+	2130.37i	−1.88935	+	3.27246i
$652$		0			0
$653$	485.763			0.743895			0.371947	−	0.928254i	$-0.378690\pi$
$653$	485.763			0.743895			0.371947	+	0.928254i	$0.378690\pi$
$654$		0			0
$655$	−673.978	−	1167.36i	−1.02897	−	1.78224i
$656$		0			0
$657$	−1272.19			−1.93636
$658$		0			0
$659$	127.933	−	73.8620i	0.194132	−	0.112082i	−0.399784	−	0.916610i	$-0.630915\pi$
$659$	127.933	−	73.8620i	0.194132	−	0.112082i	0.593915	+	0.804528i	$0.297581\pi$
$660$		0			0
$661$	978.163	−	564.743i	1.47982	−	0.854376i	0.480084	−	0.877222i	$-0.340606\pi$
$661$	978.163	−	564.743i	1.47982	−	0.854376i	0.999739	+	0.0228458i	$0.00727268\pi$
$662$		0			0
$663$	61.7133	−	106.891i	0.0930820	−	0.161223i
$664$		0			0
$665$	−313.651	−	1281.84i	−0.471656	−	1.92758i
$666$		0			0
$667$	3.16305	+	1.82619i	0.00474221	+	0.00273792i
$668$		0			0
$669$	−333.708	−	577.999i	−0.498816	−	0.863975i
$670$		0			0
$671$	−192.633	−	333.649i	−0.287083	−	0.497242i
$672$		0			0
$673$			525.774i			0.781239i	0.920552	+	0.390620i	$0.127739\pi$
$673$			525.774i			0.781239i	−0.920552	+	0.390620i	$0.872261\pi$
$674$		0			0
$675$	1128.66	−	651.632i	1.67209	−	0.965381i
$676$		0			0
$677$		−	454.871i		−	0.671892i	−0.941881	−	0.335946i	$-0.890944\pi$
$677$		−	454.871i		−	0.671892i	0.941881	−	0.335946i	$-0.109056\pi$
$678$		0			0
$679$	−257.857	−	148.874i	−0.379760	−	0.219254i
$680$		0			0
$681$	−1143.30	+	1980.25i	−1.67885	+	2.90785i
$682$		0			0
$683$		−	27.9478i		−	0.0409191i	−0.999791	−	0.0204596i	$-0.993487\pi$
$683$		−	27.9478i		−	0.0409191i	0.999791	−	0.0204596i	$-0.00651293\pi$
$684$		0			0
$685$	−1412.67			−2.06230
$686$		0			0
$687$	−2135.80	−	1233.11i	−3.10888	−	1.79491i
$688$		0			0
$689$	−85.1761	+	147.529i	−0.123623	+	0.214121i
$690$		0			0
$691$	−33.1540			−0.0479798			−0.0239899	−	0.999712i	$-0.507637\pi$
$691$	−33.1540			−0.0479798			−0.0239899	+	0.999712i	$0.507637\pi$
$692$		0			0
$693$	1183.40	+	2049.71i	1.70765	+	2.95773i
$694$		0			0
$695$	−34.6782			−0.0498966
$696$		0			0
$697$	166.118	−	95.9080i	0.238332	−	0.137601i
$698$		0			0
$699$	−480.192	+	277.239i	−0.686970	+	0.396622i
$700$		0			0
$701$	423.602	−	733.701i	0.604283	−	1.04665i	−0.387882	−	0.921709i	$-0.626793\pi$
$701$	423.602	−	733.701i	0.604283	−	1.04665i	0.992164	−	0.124939i	$-0.0398736\pi$
$702$		0			0
$703$	478.104	+	499.444i	0.680091	+	0.710446i
$704$		0			0
$705$	2000.99	+	1155.27i	2.83828	+	1.63868i
$706$		0			0
$707$	−4.93559	−	8.54870i	−0.00698104	−	0.0120915i
$708$		0			0
$709$	−213.473	−	369.746i	−0.301090	−	0.521503i	0.675293	−	0.737550i	$-0.264017\pi$
$709$	−213.473	−	369.746i	−0.301090	−	0.521503i	−0.976383	+	0.216046i	$0.930684\pi$
$710$		0			0
$711$			22.3996i			0.0315043i
$712$		0			0
$713$	466.091	−	269.098i	0.653704	−	0.377416i
$714$		0			0
$715$			221.444i			0.309712i
$716$		0			0
$717$	328.445	+	189.628i	0.458082	+	0.264474i
$718$		0			0
$719$	310.101	−	537.111i	0.431295	−	0.747025i	−0.565690	−	0.824618i	$-0.691390\pi$
$719$	310.101	−	537.111i	0.431295	−	0.747025i	0.996985	+	0.0775929i	$0.0247234\pi$
$720$		0			0
$721$		−	8.87137i		−	0.0123043i
$722$		0			0
$723$	242.095			0.334847
$724$		0			0
$725$	−5.20982	−	3.00789i	−0.00718596	−	0.00414881i
$726$		0			0
$727$	157.808	−	273.331i	0.217067	−	0.375971i	−0.736843	−	0.676064i	$-0.763684\pi$
$727$	157.808	−	273.331i	0.217067	−	0.375971i	0.953910	+	0.300093i	$0.0970177\pi$
$728$		0			0
$729$	−242.029			−0.332002
$730$		0			0
$731$	−191.441	−	331.586i	−0.261889	−	0.453606i
$732$		0			0
$733$	−443.219			−0.604664			−0.302332	−	0.953203i	$-0.597765\pi$
$733$	−443.219			−0.604664			−0.302332	+	0.953203i	$0.597765\pi$
$734$		0			0
$735$	1828.88	−	1055.91i	2.48828	−	1.43661i
$736$		0			0
$737$	−307.754	+	177.682i	−0.417576	+	0.241088i
$738$		0			0
$739$	−586.867	+	1016.48i	−0.794137	+	1.37549i	0.129249	+	0.991612i	$0.458743\pi$
$739$	−586.867	+	1016.48i	−0.794137	+	1.37549i	−0.923386	+	0.383873i	$0.874590\pi$
$740$		0			0
$741$	−223.180	+	213.644i	−0.301187	+	0.288318i
$742$		0			0
$743$	176.759	+	102.052i	0.237900	+	0.137351i	0.614211	−	0.789142i	$-0.289474\pi$
$743$	176.759	+	102.052i	0.237900	+	0.137351i	−0.376311	+	0.926493i	$0.622808\pi$
$744$		0			0
$745$	−351.211	−	608.315i	−0.471424	−	0.816531i
$746$		0			0
$747$	−1332.83	−	2308.53i	−1.78424	−	3.09040i
$748$		0			0
$749$		−	787.304i		−	1.05114i
$750$		0			0
$751$	−954.158	+	550.883i	−1.27052	+	0.733533i	−0.975085	−	0.221831i	$-0.928797\pi$
$751$	−954.158	+	550.883i	−1.27052	+	0.733533i	−0.295431	+	0.955364i	$0.595463\pi$
$752$		0			0
$753$			101.103i			0.134268i
$754$		0			0
$755$	−1450.01	−	837.166i	−1.92055	−	1.10883i
$756$		0			0
$757$	−315.092	+	545.756i	−0.416238	+	0.720945i	−0.995558	−	0.0941551i	$-0.969985\pi$
$757$	−315.092	+	545.756i	−0.416238	+	0.720945i	0.579319	+	0.815101i	$0.303318\pi$
$758$		0			0
$759$		−	742.188i		−	0.977850i
$760$		0			0
$761$	−51.0716			−0.0671111			−0.0335556	−	0.999437i	$-0.510683\pi$
$761$	−51.0716			−0.0671111			−0.0335556	+	0.999437i	$0.510683\pi$
$762$		0			0
$763$	1169.43	+	675.169i	1.53267	+	0.884887i
$764$		0			0
$765$	530.525	−	918.896i	0.693496	−	1.20117i
$766$		0			0
$767$	185.203			0.241464
$768$		0			0
$769$	453.707	+	785.843i	0.589996	+	1.02190i	0.994232	+	0.107248i	$0.0342038\pi$
$769$	453.707	+	785.843i	0.589996	+	1.02190i	−0.404237	+	0.914654i	$0.632463\pi$
$770$		0			0
$771$	607.775			0.788294
$772$		0			0
$773$	−888.342	+	512.884i	−1.14921	+	0.663499i	−0.948695	−	0.316192i	$-0.897596\pi$
$773$	−888.342	+	512.884i	−1.14921	+	0.663499i	−0.200518	+	0.979690i	$0.564262\pi$
$774$		0			0
$775$	−767.692	+	443.227i	−0.990570	+	0.571906i
$776$		0			0
$777$	−1024.56	+	1774.58i	−1.31860	+	2.28389i
$778$		0			0
$779$	−466.383	+	114.118i	−0.598695	+	0.146493i
$780$		0			0
$781$	−143.097	−	82.6172i	−0.183223	−	0.105784i
$782$		0			0
$783$	9.52018	+	16.4894i	0.0121586	+	0.0210593i
$784$		0			0
$785$	−112.850	−	195.462i	−0.143758	−	0.248996i
$786$		0			0
$787$		−	451.238i		−	0.573364i	−0.958026	−	0.286682i	$-0.907448\pi$
$787$		−	451.238i		−	0.573364i	0.958026	−	0.286682i	$-0.0925524\pi$
$788$		0			0
$789$	−457.668	+	264.235i	−0.580061	+	0.334898i
$790$		0			0
$791$		−	1510.95i		−	1.91017i
$792$		0			0
$793$	90.0587	+	51.9954i	0.113567	+	0.0655680i
$794$		0			0
$795$	−1049.50	+	1817.78i	−1.32012	+	2.28652i
$796$		0			0
$797$		−	749.743i		−	0.940707i	−0.882478	−	0.470353i	$-0.844126\pi$
$797$		−	749.743i		−	0.940707i	0.882478	−	0.470353i	$-0.155874\pi$
$798$		0			0
$799$	477.612			0.597762
$800$		0			0
$801$	1533.92	+	885.612i	1.91501	+	1.10563i
$802$		0			0
$803$	338.123	−	585.646i	0.421075	−	0.729323i
$804$		0			0
$805$	−855.689			−1.06297
$806$		0			0
$807$	635.184	+	1100.17i	0.787093	+	1.36328i
$808$		0			0
$809$	−1088.11			−1.34500			−0.672501	−	0.740097i	$-0.734780\pi$
$809$	−1088.11			−1.34500			−0.672501	+	0.740097i	$0.734780\pi$
$810$		0			0
$811$	241.170	−	139.239i	0.297373	−	0.171689i	−0.343889	−	0.939010i	$-0.611744\pi$
$811$	241.170	−	139.239i	0.297373	−	0.171689i	0.641262	+	0.767322i	$0.278411\pi$
$812$		0			0
$813$	272.213	−	157.163i	0.334826	−	0.193312i
$814$		0			0
$815$	975.387	−	1689.42i	1.19679	−	2.07291i
$816$		0			0
$817$	227.791	+	930.944i	0.278814	+	1.13947i
$818$		0			0
$819$	−553.258	−	319.424i	−0.675529	−	0.390017i
$820$		0			0
$821$	350.562	+	607.191i	0.426993	+	0.739574i	0.996604	−	0.0823402i	$-0.0262394\pi$
$821$	350.562	+	607.191i	0.426993	+	0.739574i	−0.569611	+	0.821915i	$0.692906\pi$
$822$		0			0
$823$	−235.695	−	408.235i	−0.286385	−	0.496033i	0.686559	−	0.727074i	$-0.259120\pi$
$823$	−235.695	−	408.235i	−0.286385	−	0.496033i	−0.972944	+	0.231041i	$0.925787\pi$
$824$		0			0
$825$			1222.45i			1.48175i
$826$		0			0
$827$	835.101	−	482.146i	1.00980	−	0.583006i	0.0986637	−	0.995121i	$-0.468543\pi$
$827$	835.101	−	482.146i	1.00980	−	0.583006i	0.911132	+	0.412115i	$0.135210\pi$
$828$		0			0
$829$		−	75.3930i		−	0.0909445i	−0.998966	−	0.0454722i	$-0.985521\pi$
$829$		−	75.3930i		−	0.0909445i	0.998966	−	0.0454722i	$-0.0144793\pi$
$830$		0			0
$831$	1032.75	+	596.260i	1.24278	+	0.717522i
$832$		0			0
$833$	218.266	−	378.048i	0.262024	−	0.453840i
$834$		0			0
$835$			864.288i			1.03508i
$836$		0			0
$837$	2805.69			3.35207
$838$		0			0
$839$	−865.359	−	499.615i	−1.03142	−	0.595489i	−0.114027	−	0.993478i	$-0.536375\pi$
$839$	−865.359	−	499.615i	−1.03142	−	0.595489i	−0.917390	+	0.397989i	$0.869708\pi$
$840$		0			0
$841$	−420.456	+	728.251i	−0.499948	+	0.865935i
$842$		0			0
$843$	1447.67			1.71729
$844$		0			0
$845$	538.793	+	933.217i	0.637625	+	1.10440i
$846$		0			0
$847$	−9.32964			−0.0110149
$848$		0			0
$849$	576.226	−	332.684i	0.678711	−	0.391854i
$850$		0			0
$851$	388.250	−	224.157i	0.456228	−	0.263404i
$852$		0			0
$853$	563.381	−	975.805i	0.660470	−	1.14397i	−0.320022	−	0.947410i	$-0.603690\pi$
$853$	563.381	−	975.805i	0.660470	−	1.14397i	0.980492	−	0.196558i	$-0.0629763\pi$
$854$		0			0
$855$	−1918.58	+	1836.61i	−2.24396	+	2.14808i
$856$		0			0
$857$	−1351.51	−	780.295i	−1.57702	−	0.910495i	−0.995272	−	0.0971295i	$-0.969034\pi$
$857$	−1351.51	−	780.295i	−1.57702	−	0.910495i	−0.581752	−	0.813366i	$-0.697633\pi$
$858$		0			0
$859$	−614.769	−	1064.81i	−0.715680	−	1.23959i	−0.962697	−	0.270583i	$-0.912784\pi$
$859$	−614.769	−	1064.81i	−0.715680	−	1.23959i	0.247016	−	0.969011i	$-0.420550\pi$
$860$		0			0
$861$	−711.507	−	1232.37i	−0.826373	−	1.43132i
$862$		0			0
$863$			310.818i			0.360160i	0.983652	+	0.180080i	$0.0576356\pi$
$863$			310.818i			0.360160i	−0.983652	+	0.180080i	$0.942364\pi$
$864$		0			0
$865$	602.551	−	347.883i	0.696591	−	0.402177i
$866$		0			0
$867$			1262.50i			1.45617i
$868$		0			0
$869$	−10.3115	−	5.95336i	−0.0118660	−	0.00685081i
$870$		0			0
$871$	47.9599	−	83.0689i	0.0550630	−	0.0953719i
$872$		0			0
$873$			599.249i			0.686425i
$874$		0			0
$875$	−326.998			−0.373711
$876$		0			0
$877$	1386.34	+	800.404i	1.58078	+	0.912661i	0.994746	+	0.102371i	$0.0326427\pi$
$877$	1386.34	+	800.404i	1.58078	+	0.912661i	0.586029	+	0.810290i	$0.300691\pi$
$878$		0			0
$879$	322.989	−	559.433i	0.367450	−	0.636442i
$880$		0			0
$881$	851.795			0.966850			0.483425	−	0.875386i	$-0.339393\pi$
$881$	851.795			0.966850			0.483425	+	0.875386i	$0.339393\pi$
$882$		0			0
$883$	−295.515	−	511.847i	−0.334672	−	0.579668i	0.648750	−	0.761002i	$-0.275292\pi$
$883$	−295.515	−	511.847i	−0.334672	−	0.579668i	−0.983422	+	0.181333i	$0.941959\pi$
$884$		0			0
$885$	2281.97			2.57850
$886$		0			0
$887$	1320.49	−	762.387i	1.48872	−	0.859512i	0.488802	−	0.872395i	$-0.337434\pi$
$887$	1320.49	−	762.387i	1.48872	−	0.859512i	0.999917	+	0.0128829i	$0.00410087\pi$
$888$		0			0
$889$	2076.12	−	1198.65i	2.33535	−	1.34831i
$890$		0			0
$891$	902.568	−	1563.29i	1.01298	−	1.75454i
$892$		0			0
$893$	−1147.76	−	334.555i	−1.28529	−	0.374642i
$894$		0			0
$895$	−1509.81	−	871.690i	−1.68694	−	0.973955i
$896$		0			0
$897$	100.166	+	173.492i	0.111668	+	0.193414i
$898$		0			0
$899$	−6.47543	−	11.2158i	−0.00720293	−	0.0124758i
$900$		0			0
$901$			433.883i			0.481557i
$902$		0			0
$903$	−2459.92	+	1420.23i	−2.72416	+	1.57279i
$904$		0			0
$905$			1060.19i			1.17148i
$906$		0			0
$907$	−56.8668	−	32.8321i	−0.0626977	−	0.0361986i	0.468323	−	0.883557i	$-0.344858\pi$
$907$	−56.8668	−	32.8321i	−0.0626977	−	0.0361986i	−0.531021	+	0.847359i	$0.678192\pi$
$908$		0			0
$909$	−9.93343	+	17.2052i	−0.0109279	+	0.0189276i
$910$		0			0
$911$			870.826i			0.955901i	0.878387	+	0.477951i	$0.158620\pi$
$911$			870.826i			0.955901i	−0.878387	+	0.477951i	$0.841380\pi$
$912$		0			0
$913$	1416.96			1.55198
$914$		0			0
$915$	1109.66	+	640.660i	1.21274	+	0.700175i
$916$		0			0
$917$	−1033.55	+	1790.16i	−1.12710	+	1.95219i
$918$		0			0
$919$	1437.73			1.56445			0.782223	−	0.622999i	$-0.214086\pi$
$919$	1437.73			1.56445			0.782223	+	0.622999i	$0.214086\pi$
$920$		0			0
$921$	−1303.18	−	2257.17i	−1.41496	−	2.45078i
$922$		0			0
$923$	44.6001			0.0483208
$924$		0			0
$925$	−639.481	+	369.205i	−0.691331	+	0.399140i
$926$		0			0
$927$	−15.4625	+	8.92731i	−0.0166802	+	0.00963032i
$928$		0			0
$929$	−754.935	+	1307.59i	−0.812631	+	1.40752i	0.0983848	+	0.995148i	$0.468632\pi$
$929$	−754.935	+	1307.59i	−0.812631	+	1.40752i	−0.911016	+	0.412370i	$0.864701\pi$
$930$		0			0
$931$	−789.336	+	755.610i	−0.847837	+	0.811611i
$932$		0			0
$933$	−2115.51	−	1221.39i	−2.26743	−	1.30910i
$934$		0			0
$935$	282.006	+	488.449i	0.301611	+	0.522405i
$936$		0			0
$937$	−427.373	−	740.231i	−0.456107	−	0.790001i	0.542644	−	0.839963i	$-0.317423\pi$
$937$	−427.373	−	740.231i	−0.456107	−	0.790001i	−0.998751	+	0.0499617i	$0.984090\pi$
$938$		0			0
$939$			1230.86i			1.31082i
$940$		0			0
$941$	738.469	−	426.355i	0.784770	−	0.453087i	−0.0533481	−	0.998576i	$-0.516989\pi$
$941$	738.469	−	426.355i	0.784770	−	0.453087i	0.838118	+	0.545489i	$0.183656\pi$
$942$		0			0
$943$			311.333i			0.330152i
$944$		0			0
$945$	−3863.19	−	2230.41i	−4.08803	−	2.36022i
$946$		0			0
$947$	675.755	−	1170.44i	0.713574	−	1.23595i	−0.249933	−	0.968263i	$-0.580409\pi$
$947$	675.755	−	1170.44i	0.713574	−	1.23595i	0.963507	−	0.267683i	$-0.0862581\pi$
$948$		0			0
$949$			182.532i			0.192342i
$950$		0			0
$951$	−1818.64			−1.91235
$952$		0			0
$953$	−1137.22	−	656.574i	−1.19330	−	0.688955i	−0.234250	−	0.972176i	$-0.575263\pi$
$953$	−1137.22	−	656.574i	−1.19330	−	0.688955i	−0.959054	+	0.283222i	$0.908597\pi$
$954$		0			0
$955$	93.5447	−	162.024i	0.0979525	−	0.169659i
$956$		0			0
$957$	−17.8596			−0.0186621
$958$		0			0
$959$	1083.17	+	1876.11i	1.12948	+	1.95632i
$960$		0			0
$961$	−947.371			−0.985818
$962$		0			0
$963$	−1372.25	+	792.268i	−1.42497	+	0.822708i
$964$		0			0
$965$	−1244.65	+	718.597i	−1.28979	+	0.744660i
$966$		0			0
$967$	−301.262	+	521.802i	−0.311543	+	0.539609i	−0.978697	−	0.205312i	$-0.934179\pi$
$967$	−301.262	+	521.802i	−0.311543	+	0.539609i	0.667153	+	0.744920i	$0.267513\pi$
$968$		0			0
$969$	−220.204	+	755.459i	−0.227249	+	0.779628i
$970$		0			0
$971$	1583.76	+	914.384i	1.63106	+	0.941693i	0.983767	+	0.179452i	$0.0574324\pi$
$971$	1583.76	+	914.384i	1.63106	+	0.941693i	0.647293	+	0.762241i	$0.275901\pi$
$972$		0			0
$973$	26.5896	+	46.0545i	0.0273274	+	0.0473325i
$974$		0			0
$975$	−164.981	−	285.756i	−0.169212	−	0.293083i
$976$		0			0
$977$			1382.93i			1.41548i	0.706471	+	0.707742i	$0.250286\pi$
$977$			1382.93i			1.41548i	−0.706471	+	0.707742i	$0.749714\pi$
$978$		0			0
$979$	−815.374	+	470.756i	−0.832864	+	0.480854i
$980$		0			0
$981$		−	2717.70i		−	2.77034i
$982$		0			0
$983$	481.352	+	277.909i	0.489677	+	0.282715i	0.724440	−	0.689338i	$-0.242098\pi$
$983$	481.352	+	277.909i	0.489677	+	0.282715i	−0.234764	+	0.972052i	$0.575432\pi$
$984$		0			0
$985$	558.935	−	968.103i	0.567446	−	0.982846i
$986$		0			0
$987$		−	3543.23i		−	3.58990i
$988$		0			0
$989$	621.449			0.628361
$990$		0			0
$991$	925.405	+	534.283i	0.933809	+	0.539135i	0.888014	−	0.459816i	$-0.152085\pi$
$991$	925.405	+	534.283i	0.933809	+	0.539135i	0.0457948	+	0.998951i	$0.485418\pi$
$992$		0			0
$993$	1560.41	−	2702.71i	1.57141	−	2.72177i
$994$		0			0
$995$	−1147.35			−1.15312
$996$		0			0
$997$	177.830	+	308.011i	0.178365	+	0.308938i	0.941321	−	0.337513i	$-0.109586\pi$
$997$	177.830	+	308.011i	0.178365	+	0.308938i	−0.762955	+	0.646451i	$0.776252\pi$
$998$		0			0
$999$	2337.12			2.33946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.h.a.65.4	✓	8
3.2	odd	2		684.3.y.h.217.1		8
4.3	odd	2		304.3.r.c.65.1		8
19.8	odd	6		1444.3.c.b.721.8		8
19.11	even	3		1444.3.c.b.721.1		8
19.12	odd	6	inner	76.3.h.a.69.4	yes	8
57.50	even	6		684.3.y.h.145.1		8
76.31	even	6		304.3.r.c.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.h.a.65.4	✓	8	1.1	even	1	trivial
76.3.h.a.69.4	yes	8	19.12	odd	6	inner
304.3.r.c.65.1		8	4.3	odd	2
304.3.r.c.145.1		8	76.31	even	6
684.3.y.h.145.1		8	57.50	even	6
684.3.y.h.217.1		8	3.2	odd	2
1444.3.c.b.721.1		8	19.11	even	3
1444.3.c.b.721.8		8	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.72527 + 2.72814i) q^{3} +(3.36497 - 5.82829i) q^{5} -10.3204 q^{7} +(10.3855 + 17.9882i) q^{9} +O(q^{10})\)	\(q+(4.72527 + 2.72814i) q^{3} +(3.36497 - 5.82829i) q^{5} -10.3204 q^{7} +(10.3855 + 17.9882i) q^{9} -11.0410 q^{11} +(2.58092 - 1.49010i) q^{13} +(31.8008 - 18.3602i) q^{15} +(3.79523 - 6.57354i) q^{17} +(-13.7250 + 13.1386i) q^{19} +(-48.7667 - 28.1555i) q^{21} +(6.15997 + 10.6694i) q^{23} +(-10.1460 - 17.5734i) q^{25} +64.2255i q^{27} +(0.256743 - 0.148230i) q^{29} -43.6849i q^{31} +(-52.1718 - 30.1214i) q^{33} +(-34.7278 + 60.1503i) q^{35} -36.3892i q^{37} +16.2607 q^{39} +(21.8850 + 12.6353i) q^{41} +(25.2213 - 43.6845i) q^{43} +139.787 q^{45} +(31.4613 + 54.4925i) q^{47} +57.5107 q^{49} +(35.8670 - 20.7078i) q^{51} +(-49.5033 + 28.5808i) q^{53} +(-37.1526 + 64.3503i) q^{55} +(-100.699 + 24.6397i) q^{57} +(53.8188 + 31.0723i) q^{59} +(17.4470 + 30.2191i) q^{61} +(-107.182 - 185.645i) q^{63} -20.0565i q^{65} +(27.8737 - 16.0929i) q^{67} +67.2210i q^{69} +(12.9605 + 7.48276i) q^{71} +(-30.6243 + 53.0428i) q^{73} -110.719i q^{75} +113.948 q^{77} +(0.933929 + 0.539204i) q^{79} +(-81.7469 + 141.590i) q^{81} -128.336 q^{83} +(-25.5417 - 44.2395i) q^{85} +1.61757 q^{87} +(73.8495 - 42.6371i) q^{89} +(-26.6361 + 15.3784i) q^{91} +(119.178 - 206.423i) q^{93} +(30.3914 + 124.205i) q^{95} +(24.9851 + 14.4252i) q^{97} +(-114.666 - 198.608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9	\( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - q^5 - 12 * q^7 + 16 * q^9 - 10 * q^11 + 9 * q^13 + 33 * q^15 + 23 * q^17 - 33 * q^19 - 31 * q^23 - 73 * q^25 - 105 * q^29 - 111 * q^33 - 68 * q^35 + 234 * q^39 + 18 * q^41 - 41 * q^43 + 200 * q^45 + 107 * q^47 + 312 * q^49 - 9 * q^51 + 39 * q^53 + 70 * q^55 - 381 * q^57 + 348 * q^59 - 45 * q^61 - 358 * q^63 - 432 * q^67 - 243 * q^71 + 16 * q^73 + 544 * q^77 + 75 * q^79 - 68 * q^81 - 82 * q^83 + 109 * q^85 + 414 * q^87 - 213 * q^89 + 222 * q^91 + 288 * q^93 - 385 * q^95 + 144 * q^97 - 388 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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