LMFDB - Embedded newform 76.4.i.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	76.5
Dual form			76.4.i.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53481 + 8.70432i) q^{3} +(10.3935 + 8.72119i) q^{5} +(-7.14447 - 12.3746i) q^{7} +(-48.0379 - 17.4843i) q^{9} +O(q^{10})$	\(q+(-1.53481 + 8.70432i) q^{3} +(10.3935 + 8.72119i) q^{5} +(-7.14447 - 12.3746i) q^{7} +(-48.0379 - 17.4843i) q^{9} +(-27.3840 + 47.4304i) q^{11} +(0.390254 + 2.21324i) q^{13} +(-91.8641 + 77.0831i) q^{15} +(62.4092 - 22.7151i) q^{17} +(59.5540 - 57.5528i) q^{19} +(118.678 - 43.1952i) q^{21} +(-125.557 + 105.355i) q^{23} +(10.2599 + 58.1866i) q^{25} +(106.597 - 184.632i) q^{27} +(250.133 + 91.0409i) q^{29} +(50.4297 + 87.3468i) q^{31} +(-370.820 - 311.155i) q^{33} +(33.6650 - 190.924i) q^{35} -28.5238 q^{37} -19.8637 q^{39} +(27.3749 - 155.251i) q^{41} +(329.060 + 276.114i) q^{43} +(-346.798 - 600.671i) q^{45} +(417.292 + 151.882i) q^{47} +(69.4131 - 120.227i) q^{49} +(101.933 + 578.093i) q^{51} +(12.2204 - 10.2541i) q^{53} +(-698.265 + 254.148i) q^{55} +(409.554 + 606.709i) q^{57} +(545.747 - 198.636i) q^{59} +(-516.139 + 433.092i) q^{61} +(126.843 + 719.365i) q^{63} +(-15.2460 + 26.4068i) q^{65} +(-814.086 - 296.303i) q^{67} +(-724.338 - 1254.59i) q^{69} +(-636.938 - 534.454i) q^{71} +(-116.434 + 660.331i) q^{73} -522.222 q^{75} +782.576 q^{77} +(164.407 - 932.400i) q^{79} +(386.145 + 324.014i) q^{81} +(-45.7947 - 79.3188i) q^{83} +(846.753 + 308.193i) q^{85} +(-1176.35 + 2037.50i) q^{87} +(-26.1986 - 148.580i) q^{89} +(24.5998 - 20.6416i) q^{91} +(-837.695 + 304.896i) q^{93} +(1120.90 - 78.7937i) q^{95} +(955.664 - 347.833i) q^{97} +(2144.76 - 1799.66i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	−1.53481	+	8.70432i	−0.295374	+	1.67515i	0.370306	+	0.928910i	$0.379253\pi$
$3$	−1.53481	+	8.70432i	−0.295374	+	1.67515i	−0.665680	+	0.746237i	$0.731858\pi$
$4$		0			0
$5$	10.3935	+	8.72119i	0.929624	+	0.780047i	0.975750	−	0.218889i	$-0.0702431\pi$
$5$	10.3935	+	8.72119i	0.929624	+	0.780047i	−0.0461260	+	0.998936i	$0.514688\pi$
$6$		0			0
$7$	−7.14447	−	12.3746i	−0.385765	−	0.668165i	0.606110	−	0.795381i	$-0.292729\pi$
$7$	−7.14447	−	12.3746i	−0.385765	−	0.668165i	−0.991875	+	0.127216i	$0.959396\pi$
$8$		0			0
$9$	−48.0379	−	17.4843i	−1.77918	−	0.647569i
$10$		0			0
$11$	−27.3840	+	47.4304i	−0.750598	+	1.30007i	0.196936	+	0.980416i	$0.436901\pi$
$11$	−27.3840	+	47.4304i	−0.750598	+	1.30007i	−0.947533	+	0.319657i	$0.896432\pi$
$12$		0			0
$13$	0.390254	+	2.21324i	0.00832592	+	0.0472186i	0.988688	−	0.149989i	$-0.0479238\pi$
$13$	0.390254	+	2.21324i	0.00832592	+	0.0472186i	−0.980362	+	0.197208i	$0.936813\pi$
$14$		0			0
$15$	−91.8641	+	77.0831i	−1.58128	+	1.32685i
$16$		0			0
$17$	62.4092	−	22.7151i	0.890380	−	0.324072i	0.143989	−	0.989579i	$-0.454007\pi$
$17$	62.4092	−	22.7151i	0.890380	−	0.324072i	0.746391	+	0.665508i	$0.231785\pi$
$18$		0			0
$19$	59.5540	−	57.5528i	0.719085	−	0.694922i
$19$	59.5540	−	57.5528i	0.719085	−	0.694922i
$20$		0			0
$21$	118.678	−	43.1952i	1.23322	−	0.448855i
$22$		0			0
$23$	−125.557	+	105.355i	−1.13828	+	0.955132i	−0.999381	−	0.0351744i	$-0.988801\pi$
$23$	−125.557	+	105.355i	−1.13828	+	0.955132i	−0.138901	+	0.990306i	$0.544357\pi$
$24$		0			0
$25$	10.2599	+	58.1866i	0.0820789	+	0.465493i
$26$		0			0
$27$	106.597	−	184.632i	0.759801	−	1.31601i
$28$		0			0
$29$	250.133	+	91.0409i	1.60167	+	0.582961i	0.979769	−	0.200134i	$-0.0641376\pi$
$29$	250.133	+	91.0409i	1.60167	+	0.582961i	0.621903	+	0.783094i	$0.286360\pi$
$30$		0			0
$31$	50.4297	+	87.3468i	0.292176	+	0.506063i	0.974324	−	0.225151i	$-0.0722875\pi$
$31$	50.4297	+	87.3468i	0.292176	+	0.506063i	−0.682148	+	0.731214i	$0.738954\pi$
$32$		0			0
$33$	−370.820	−	311.155i	−1.95611	−	1.64137i
$34$		0			0
$35$	33.6650	−	190.924i	0.162583	−	0.922057i
$36$		0			0
$37$	−28.5238			−0.126737			−0.0633687	−	0.997990i	$-0.520184\pi$
$37$	−28.5238			−0.126737			−0.0633687	+	0.997990i	$0.520184\pi$
$38$		0			0
$39$	−19.8637			−0.0815574
$40$		0			0
$41$	27.3749	−	155.251i	0.104274	−	0.591367i	−0.887234	−	0.461320i	$-0.847376\pi$
$41$	27.3749	−	155.251i	0.104274	−	0.591367i	0.991508	−	0.130047i	$-0.0415129\pi$
$42$		0			0
$43$	329.060	+	276.114i	1.16700	+	0.979232i	0.999977	−	0.00672039i	$-0.00213918\pi$
$43$	329.060	+	276.114i	1.16700	+	0.979232i	0.167026	+	0.985952i	$0.446584\pi$
$44$		0			0
$45$	−346.798	−	600.671i	−1.14883	−	1.98984i
$46$		0			0
$47$	417.292	+	151.882i	1.29507	+	0.471367i	0.895388	−	0.445287i	$-0.146898\pi$
$47$	417.292	+	151.882i	1.29507	+	0.471367i	0.399682	+	0.916654i	$0.369121\pi$
$48$		0			0
$49$	69.4131	−	120.227i	0.202371	−	0.350516i
$50$		0			0
$51$	101.933	+	578.093i	0.279873	+	1.58724i
$52$		0			0
$53$	12.2204	−	10.2541i	0.0316718	−	0.0265758i	−0.626814	−	0.779169i	$-0.715642\pi$
$53$	12.2204	−	10.2541i	0.0316718	−	0.0265758i	0.658486	+	0.752593i	$0.271197\pi$
$54$		0			0
$55$	−698.265	+	254.148i	−1.71189	+	0.623078i
$56$		0			0
$57$	409.554	+	606.709i	0.951697	+	1.40984i
$58$		0			0
$59$	545.747	−	198.636i	1.20424	−	0.438308i	0.339538	−	0.940592i	$-0.389729\pi$
$59$	545.747	−	198.636i	1.20424	−	0.438308i	0.864702	+	0.502285i	$0.167507\pi$
$60$		0			0
$61$	−516.139	+	433.092i	−1.08336	+	0.909045i	−0.996195	−	0.0871494i	$-0.972224\pi$
$61$	−516.139	+	433.092i	−1.08336	+	0.909045i	−0.0871621	+	0.996194i	$0.527780\pi$
$62$		0			0
$63$	126.843	+	719.365i	0.253663	+	1.43859i
$64$		0			0
$65$	−15.2460	+	26.4068i	−0.0290928	+	0.0503902i
$66$		0			0
$67$	−814.086	−	296.303i	−1.48442	−	0.540286i	−0.532449	−	0.846462i	$-0.678728\pi$
$67$	−814.086	−	296.303i	−1.48442	−	0.540286i	−0.951975	+	0.306176i	$0.900950\pi$
$68$		0			0
$69$	−724.338	−	1254.59i	−1.26377	−	2.18891i
$70$		0			0
$71$	−636.938	−	534.454i	−1.06466	−	0.893353i	−0.0700986	−	0.997540i	$-0.522331\pi$
$71$	−636.938	−	534.454i	−1.06466	−	0.893353i	−0.994558	+	0.104187i	$0.966776\pi$
$72$		0			0
$73$	−116.434	+	660.331i	−0.186679	+	1.05871i	0.737100	+	0.675784i	$0.236195\pi$
$73$	−116.434	+	660.331i	−0.186679	+	1.05871i	−0.923779	+	0.382926i	$0.874916\pi$
$74$		0			0
$75$	−522.222			−0.804013
$76$		0			0
$77$	782.576			1.15822
$78$		0			0
$79$	164.407	−	932.400i	0.234142	−	1.32789i	−0.610270	−	0.792194i	$-0.708939\pi$
$79$	164.407	−	932.400i	0.234142	−	1.32789i	0.844412	−	0.535694i	$-0.179950\pi$
$80$		0			0
$81$	386.145	+	324.014i	0.529691	+	0.444463i
$82$		0			0
$83$	−45.7947	−	79.3188i	−0.0605618	−	0.104896i	0.834155	−	0.551530i	$-0.185956\pi$
$83$	−45.7947	−	79.3188i	−0.0605618	−	0.104896i	−0.894717	+	0.446634i	$0.852623\pi$
$84$		0			0
$85$	846.753	+	308.193i	1.08051	+	0.393273i
$86$		0			0
$87$	−1176.35	+	2037.50i	−1.44964	+	2.51084i
$88$		0			0
$89$	−26.1986	−	148.580i	−0.0312028	−	0.176960i	0.965224	−	0.261426i	$-0.0841927\pi$
$89$	−26.1986	−	148.580i	−0.0312028	−	0.176960i	−0.996426	+	0.0844660i	$0.973082\pi$
$90$		0			0
$91$	24.5998	−	20.6416i	0.0283380	−	0.0237784i
$92$		0			0
$93$	−837.695	+	304.896i	−0.934031	+	0.339959i
$94$		0			0
$95$	1120.90	−	78.7937i	1.21055	−	0.0850954i
$96$		0			0
$97$	955.664	−	347.833i	1.00034	−	0.364094i	0.210624	−	0.977567i	$-0.432450\pi$
$97$	955.664	−	347.833i	1.00034	−	0.364094i	0.789715	+	0.613473i	$0.210228\pi$
$98$		0			0
$99$	2144.76	−	1799.66i	2.17733	−	1.82700i
$100$		0			0
$101$	−53.5152	−	303.500i	−0.0527224	−	0.299004i	0.947033	−	0.321137i	$-0.104065\pi$
$101$	−53.5152	−	303.500i	−0.0527224	−	0.299004i	−0.999755	+	0.0221337i	$0.992954\pi$
$102$		0			0
$103$	−106.317	+	184.146i	−0.101706	+	0.176160i	−0.912388	−	0.409328i	$-0.865763\pi$
$103$	−106.317	+	184.146i	−0.101706	+	0.176160i	0.810682	+	0.585487i	$0.199097\pi$
$104$		0			0
$105$	1610.19	+	586.062i	1.49656	+	0.544703i
$106$		0			0
$107$	−293.853	−	508.968i	−0.265494	−	0.459849i	0.702199	−	0.711981i	$-0.252202\pi$
$107$	−293.853	−	508.968i	−0.265494	−	0.459849i	−0.967693	+	0.252132i	$0.918868\pi$
$108$		0			0
$109$	−583.913	−	489.961i	−0.513107	−	0.430548i	0.349114	−	0.937080i	$-0.386483\pi$
$109$	−583.913	−	489.961i	−0.513107	−	0.430548i	−0.862221	+	0.506532i	$0.830927\pi$
$110$		0			0
$111$	43.7785	−	248.280i	0.0374349	−	0.212304i
$112$		0			0
$113$	1281.80			1.06710			0.533549	−	0.845769i	$-0.320858\pi$
$113$	1281.80			1.06710			0.533549	+	0.845769i	$0.320858\pi$
$114$		0			0
$115$	−2223.80			−1.80322
$116$		0			0
$117$	19.9501	−	113.143i	0.0157640	−	0.0894020i
$118$		0			0
$119$	−726.971	−	610.001i	−0.560011	−	0.469905i
$120$		0			0
$121$	−834.263	−	1444.99i	−0.626794	−	1.08564i
$122$		0			0
$123$	1309.34	+	476.559i	0.959827	+	0.349349i
$124$		0			0
$125$	447.165	−	774.512i	0.319965	−	0.554196i
$126$		0			0
$127$	−264.164	−	1498.15i	−0.184573	−	1.04676i	−0.926503	−	0.376287i	$-0.877201\pi$
$127$	−264.164	−	1498.15i	−0.184573	−	1.04676i	0.741930	−	0.670477i	$-0.233911\pi$
$128$		0			0
$129$	−2908.43	+	2440.46i	−1.98506	+	1.66566i
$130$		0			0
$131$	982.701	−	357.674i	0.655412	−	0.238550i	0.00715775	−	0.999974i	$-0.497722\pi$
$131$	982.701	−	357.674i	0.655412	−	0.238550i	0.648254	+	0.761424i	$0.275499\pi$
$132$		0			0
$133$	−1137.67	−	325.772i	−0.741720	−	0.212391i
$134$		0			0
$135$	2718.13	−	989.317i	1.73288	−	0.630717i
$136$		0			0
$137$	−324.378	+	272.186i	−0.202288	+	0.169740i	−0.738304	−	0.674468i	$-0.764373\pi$
$137$	−324.378	+	272.186i	−0.202288	+	0.169740i	0.536016	+	0.844208i	$0.319929\pi$
$138$		0			0
$139$	−160.633	−	910.994i	−0.0980194	−	0.555896i	−0.993780	−	0.111359i	$-0.964480\pi$
$139$	−160.633	−	910.994i	−0.0980194	−	0.555896i	0.895761	−	0.444536i	$-0.146632\pi$
$140$		0			0
$141$	−1962.49	+	3399.13i	−1.17214	+	2.03020i
$142$		0			0
$143$	−115.662	−	42.0973i	−0.0676371	−	0.0246179i
$144$		0			0
$145$	1805.77	+	3127.69i	1.03422	+	1.79131i
$146$		0			0
$147$	939.959	+	788.719i	0.527391	+	0.442534i
$148$		0			0
$149$	21.7534	−	123.369i	0.0119604	−	0.0678310i	−0.978243	−	0.207461i	$-0.933480\pi$
$149$	21.7534	−	123.369i	0.0119604	−	0.0678310i	0.990204	+	0.139630i	$0.0445912\pi$
$150$		0			0
$151$	1123.19			0.605326			0.302663	−	0.953098i	$-0.402124\pi$
$151$	1123.19			0.605326			0.302663	+	0.953098i	$0.402124\pi$
$152$		0			0
$153$	−3395.16			−1.79400
$154$		0			0
$155$	−237.627	+	1347.65i	−0.123140	+	0.698359i
$156$		0			0
$157$	389.548	+	326.869i	0.198021	+	0.166159i	0.736406	−	0.676539i	$-0.236521\pi$
$157$	389.548	+	326.869i	0.198021	+	0.166159i	−0.538386	+	0.842699i	$0.680966\pi$
$158$		0			0
$159$	70.4994	+	122.109i	0.0351633	+	0.0609046i
$160$		0			0
$161$	2200.76	+	801.013i	1.07729	+	0.392103i
$162$		0			0
$163$	−1928.13	+	3339.61i	−0.926519	+	1.60478i	−0.137419	+	0.990513i	$0.543881\pi$
$163$	−1928.13	+	3339.61i	−0.926519	+	1.60478i	−0.789100	+	0.614265i	$0.789453\pi$
$164$		0			0
$165$	−1140.48	−	6467.99i	−0.538099	−	3.05171i
$166$		0			0
$167$	1588.69	−	1333.07i	0.736148	−	0.617701i	−0.195652	−	0.980673i	$-0.562682\pi$
$167$	1588.69	−	1333.07i	0.736148	−	0.617701i	0.931800	+	0.362972i	$0.118238\pi$
$168$		0			0
$169$	2059.76	−	749.691i	0.937532	−	0.341234i
$170$		0			0
$171$	−3867.12	+	1723.45i	−1.72939	+	0.770734i
$172$		0			0
$173$	−2216.27	+	806.658i	−0.973990	+	0.354503i	−0.779501	−	0.626401i	$-0.784527\pi$
$173$	−2216.27	+	806.658i	−0.973990	+	0.354503i	−0.194489	+	0.980905i	$0.562305\pi$
$174$		0			0
$175$	646.734	−	542.674i	0.279363	−	0.234413i
$176$		0			0
$177$	891.372	+	5055.22i	0.378529	+	2.14674i
$178$		0			0
$179$	797.557	−	1381.41i	0.333029	−	0.576824i	−0.650075	−	0.759870i	$-0.725263\pi$
$179$	797.557	−	1381.41i	0.333029	−	0.576824i	0.983104	+	0.183046i	$0.0585959\pi$
$180$		0			0
$181$	333.610	+	121.424i	0.137000	+	0.0498641i	0.409610	−	0.912261i	$-0.365665\pi$
$181$	333.610	+	121.424i	0.137000	+	0.0498641i	−0.272610	+	0.962125i	$0.587887\pi$
$182$		0			0
$183$	−2977.60	−	5157.35i	−1.20279	−	2.08329i
$184$		0			0
$185$	−296.462	−	248.761i	−0.117818	−	0.0988611i
$186$		0			0
$187$	−631.625	+	3582.12i	−0.247000	+	1.40081i
$188$		0			0
$189$	−3046.32			−1.17242
$190$		0			0
$191$	−627.091			−0.237564			−0.118782	−	0.992920i	$-0.537899\pi$
$191$	−627.091			−0.237564			−0.118782	+	0.992920i	$0.537899\pi$
$192$		0			0
$193$	−631.558	+	3581.74i	−0.235547	+	1.33585i	0.605912	+	0.795532i	$0.292808\pi$
$193$	−631.558	+	3581.74i	−0.235547	+	1.33585i	−0.841459	+	0.540321i	$0.818303\pi$
$194$		0			0
$195$	−206.454	−	173.235i	−0.0758177	−	0.0636186i
$196$		0			0
$197$	938.661	+	1625.81i	0.339476	+	0.587990i	0.984334	−	0.176312i	$-0.0564169\pi$
$197$	938.661	+	1625.81i	0.339476	+	0.587990i	−0.644858	+	0.764302i	$0.723084\pi$
$198$		0			0
$199$	−4179.74	−	1521.30i	−1.48892	−	0.541921i	−0.535752	−	0.844376i	$-0.679972\pi$
$199$	−4179.74	−	1521.30i	−1.48892	−	0.541921i	−0.953164	+	0.302455i	$0.902194\pi$
$200$		0			0
$201$	3828.58	−	6631.29i	1.34352	−	2.32704i
$202$		0			0
$203$	−660.473	−	3745.73i	−0.228355	−	1.29507i
$204$		0			0
$205$	1638.49	−	1374.86i	0.558230	−	0.468410i
$206$		0			0
$207$	7873.56	−	2865.74i	2.64372	−	0.962236i
$208$		0			0
$209$	1098.93	+	4400.69i	0.363705	+	1.45647i
$210$		0			0
$211$	3677.12	−	1338.36i	1.19973	−	0.436667i	0.336601	−	0.941647i	$-0.390723\pi$
$211$	3677.12	−	1338.36i	1.19973	−	0.436667i	0.863131	+	0.504981i	$0.168500\pi$
$212$		0			0
$213$	5629.64	−	4723.83i	1.81097	−	1.51958i
$214$		0			0
$215$	1012.04	+	5739.59i	0.321027	+	1.82063i
$216$		0			0
$217$	720.587	−	1248.09i	0.225422	−	0.390443i
$218$		0			0
$219$	−5569.02	−	2026.96i	−1.71836	−	0.625430i
$220$		0			0
$221$	74.6293	+	129.262i	0.0227154	+	0.0393443i
$222$		0			0
$223$	1394.44	+	1170.07i	0.418738	+	0.351362i	0.827683	−	0.561196i	$-0.189659\pi$
$223$	1394.44	+	1170.07i	0.418738	+	0.351362i	−0.408945	+	0.912559i	$0.634103\pi$
$224$		0			0
$225$	524.493	−	2974.55i	0.155405	−	0.881347i
$226$		0			0
$227$	−3000.00			−0.877167			−0.438583	−	0.898691i	$-0.644520\pi$
$227$	−3000.00			−0.877167			−0.438583	+	0.898691i	$0.644520\pi$
$228$		0			0
$229$	−2579.61			−0.744389			−0.372195	−	0.928155i	$-0.621395\pi$
$229$	−2579.61			−0.744389			−0.372195	+	0.928155i	$0.621395\pi$
$230$		0			0
$231$	−1201.10	+	6811.79i	−0.342107	+	1.94018i
$232$		0			0
$233$	−246.160	−	206.553i	−0.0692125	−	0.0580762i	0.607525	−	0.794300i	$-0.292162\pi$
$233$	−246.160	−	206.553i	−0.0692125	−	0.0580762i	−0.676738	+	0.736224i	$0.736607\pi$
$234$		0			0
$235$	3012.54	+	5217.87i	0.836239	+	1.44841i
$236$		0			0
$237$	7863.57	+	2862.11i	2.15525	+	0.784446i
$238$		0			0
$239$	729.946	−	1264.30i	0.197558	−	0.342180i	−0.750178	−	0.661236i	$-0.770032\pi$
$239$	729.946	−	1264.30i	0.197558	−	0.342180i	0.947736	+	0.319056i	$0.103366\pi$
$240$		0			0
$241$	−515.037	−	2920.92i	−0.137662	−	0.780718i	−0.972969	−	0.230935i	$-0.925822\pi$
$241$	−515.037	−	2920.92i	−0.137662	−	0.780718i	0.835308	−	0.549783i	$-0.185290\pi$
$242$		0			0
$243$	996.562	−	836.214i	0.263084	−	0.220754i
$244$		0			0
$245$	1769.97	−	644.216i	0.461548	−	0.167990i
$246$		0			0
$247$	150.619	+	109.347i	0.0388003	+	0.0281684i
$248$		0			0
$249$	760.702	−	276.873i	0.193605	−	0.0704663i
$250$		0			0
$251$	−83.0577	+	69.6937i	−0.0208867	+	0.0175260i	−0.653171	−	0.757210i	$-0.726562\pi$
$251$	−83.0577	+	69.6937i	−0.0208867	+	0.0175260i	0.632285	+	0.774736i	$0.282117\pi$
$252$		0			0
$253$	−1558.78	−	8840.27i	−0.387350	−	2.19677i
$254$		0			0
$255$	−3982.21	+	6897.40i	−0.977945	+	1.69385i
$256$		0			0
$257$	−6216.13	−	2262.49i	−1.50876	−	0.549144i	−0.550450	−	0.834868i	$-0.685544\pi$
$257$	−6216.13	−	2262.49i	−1.50876	−	0.549144i	−0.958312	+	0.285724i	$0.907766\pi$
$258$		0			0
$259$	203.787	+	352.970i	0.0488909	+	0.0846814i
$260$		0			0
$261$	−10424.0	−	8746.82i	−2.47215	−	2.07438i
$262$		0			0
$263$	483.308	−	2740.97i	0.113316	−	0.642645i	−0.874255	−	0.485468i	$-0.838649\pi$
$263$	483.308	−	2740.97i	0.113316	−	0.642645i	0.987570	−	0.157178i	$-0.0502395\pi$
$264$		0			0
$265$	216.441			0.0501732
$266$		0			0
$267$	1333.50			0.305650
$268$		0			0
$269$	−1144.80	+	6492.51i	−0.259479	+	1.47158i	0.524828	+	0.851208i	$0.324130\pi$
$269$	−1144.80	+	6492.51i	−0.259479	+	1.47158i	−0.784307	+	0.620372i	$0.786981\pi$
$270$		0			0
$271$	403.343	+	338.445i	0.0904108	+	0.0758637i	0.686873	−	0.726778i	$-0.258983\pi$
$271$	403.343	+	338.445i	0.0904108	+	0.0758637i	−0.596462	+	0.802641i	$0.703427\pi$
$272$		0			0
$273$	141.916	+	245.805i	0.0314620	+	0.0544938i
$274$		0			0
$275$	−3040.77	−	1106.75i	−0.666783	−	0.242689i
$276$		0			0
$277$	125.371	−	217.150i	0.0271943	−	0.0471020i	−0.852108	−	0.523366i	$-0.824676\pi$
$277$	125.371	−	217.150i	0.0271943	−	0.0471020i	0.879302	+	0.476264i	$0.158009\pi$
$278$		0			0
$279$	−895.333	−	5077.68i	−0.192122	−	1.08958i
$280$		0			0
$281$	−4042.87	+	3392.37i	−0.858282	+	0.720184i	−0.961597	−	0.274465i	$-0.911499\pi$
$281$	−4042.87	+	3392.37i	−0.858282	+	0.720184i	0.103315	+	0.994649i	$0.467055\pi$
$282$		0			0
$283$	2884.16	−	1049.75i	0.605815	−	0.220499i	−0.0208559	−	0.999782i	$-0.506639\pi$
$283$	2884.16	−	1049.75i	0.605815	−	0.220499i	0.626671	+	0.779284i	$0.284417\pi$
$284$		0			0
$285$	−1034.52	+	9877.64i	−0.215017	+	2.05299i
$286$		0			0
$287$	−2116.74	+	770.430i	−0.435356	+	0.158457i
$288$		0			0
$289$	−384.643	+	322.754i	−0.0782908	+	0.0656938i
$290$		0			0
$291$	1560.89	+	8852.26i	0.314437	+	1.78326i
$292$		0			0
$293$	148.646	−	257.463i	0.0296383	−	0.0513350i	−0.850826	−	0.525448i	$-0.823898\pi$
$293$	148.646	−	257.463i	0.0296383	−	0.0513350i	0.880464	+	0.474113i	$0.157231\pi$
$294$		0			0
$295$	7404.56	+	2695.04i	1.46139	+	0.531903i
$296$		0			0
$297$	5838.10	+	10111.9i	1.14061	+	1.97559i
$298$		0			0
$299$	−282.175	−	236.773i	−0.0545772	−	0.0457957i
$300$		0			0
$301$	1065.84	−	6044.67i	0.204099	−	1.15750i
$302$		0			0
$303$	2723.90			0.516448
$304$		0			0
$305$	−9141.57			−1.71621
$306$		0			0
$307$	820.526	−	4653.44i	0.152540	−	0.865100i	−0.808460	−	0.588552i	$-0.799698\pi$
$307$	820.526	−	4653.44i	0.152540	−	0.865100i	0.961000	−	0.276548i	$-0.0891905\pi$
$308$		0			0
$309$	−1439.69	−	1208.04i	−0.265052	−	0.222405i
$310$		0			0
$311$	−428.047	−	741.400i	−0.0780461	−	0.135180i	0.824361	−	0.566065i	$-0.191535\pi$
$311$	−428.047	−	741.400i	−0.0780461	−	0.135180i	−0.902407	+	0.430885i	$0.858201\pi$
$312$		0			0
$313$	4341.13	+	1580.04i	0.783945	+	0.285333i	0.702817	−	0.711371i	$-0.251925\pi$
$313$	4341.13	+	1580.04i	0.783945	+	0.285333i	0.0811285	+	0.996704i	$0.474148\pi$
$314$		0			0
$315$	−4955.37	+	8582.95i	−0.886360	+	1.53522i
$316$		0			0
$317$	1176.01	+	6669.51i	0.208364	+	1.18169i	0.892057	+	0.451923i	$0.149262\pi$
$317$	1176.01	+	6669.51i	0.208364	+	1.18169i	−0.683692	+	0.729770i	$0.739627\pi$
$318$		0			0
$319$	−11167.7	+	9370.84i	−1.96010	+	1.64472i
$320$		0			0
$321$	4881.23	−	1776.62i	0.848735	−	0.308914i
$322$		0			0
$323$	2409.40	−	4944.60i	0.415055	−	0.851779i
$324$		0			0
$325$	−124.777	+	45.4151i	−0.0212965	+	0.00775131i
$326$		0			0
$327$	5160.97	−	4330.57i	0.872790	−	0.732358i
$328$		0			0
$329$	−1101.85	−	6248.93i	−0.184642	−	1.04716i
$330$		0			0
$331$	5209.24	−	9022.67i	0.865033	−	1.49828i	−0.00198153	−	0.999998i	$-0.500631\pi$
$331$	5209.24	−	9022.67i	0.865033	−	1.49828i	0.867014	−	0.498283i	$-0.166036\pi$
$332$		0			0
$333$	1370.22	+	498.720i	0.225489	+	0.0820711i
$334$		0			0
$335$	−5877.09	−	10179.4i	−0.958507	−	1.66018i
$336$		0			0
$337$	3769.83	+	3163.26i	0.609364	+	0.511317i	0.894440	−	0.447188i	$-0.147574\pi$
$337$	3769.83	+	3163.26i	0.609364	+	0.511317i	−0.285076	+	0.958505i	$0.592019\pi$
$338$		0			0
$339$	−1967.32	+	11157.2i	−0.315192	+	1.78755i
$340$		0			0
$341$	−5523.86			−0.877225
$342$		0			0
$343$	−6884.79			−1.08380
$344$		0			0
$345$	3413.10	−	19356.7i	0.532624	−	3.02066i
$346$		0			0
$347$	6760.90	+	5673.07i	1.04595	+	0.877655i	0.992662	−	0.120925i	$-0.0385859\pi$
$347$	6760.90	+	5673.07i	1.04595	+	0.877655i	0.0532864	+	0.998579i	$0.483030\pi$
$348$		0			0
$349$	−3856.08	−	6678.93i	−0.591436	−	1.02440i	−0.994039	−	0.109023i	$-0.965228\pi$
$349$	−3856.08	−	6678.93i	−0.591436	−	1.02440i	0.402603	−	0.915375i	$-0.368106\pi$
$350$		0			0
$351$	450.234	+	163.872i	0.0684664	+	0.0249197i
$352$		0			0
$353$	−1681.42	+	2912.31i	−0.253522	+	0.439113i	−0.964493	−	0.264108i	$-0.914922\pi$
$353$	−1681.42	+	2912.31i	−0.253522	+	0.439113i	0.710971	+	0.703221i	$0.248256\pi$
$354$		0			0
$355$	−1958.94	−	11109.7i	−0.292873	−	1.66096i
$356$		0			0
$357$	6425.40	−	5391.55i	0.952572	−	0.799303i
$358$		0			0
$359$	−6323.00	+	2301.38i	−0.929568	+	0.338335i	−0.762038	−	0.647532i	$-0.775801\pi$
$359$	−6323.00	+	2301.38i	−0.929568	+	0.338335i	−0.167530	+	0.985867i	$0.553579\pi$
$360$		0			0
$361$	234.355	−	6855.00i	0.0341675	−	0.999416i
$362$		0			0
$363$	13858.0	−	5043.92i	2.00374	−	0.729303i
$364$		0			0
$365$	−6969.03	+	5847.71i	−0.999385	+	0.838584i
$366$		0			0
$367$	1303.89	+	7394.72i	0.185456	+	1.05177i	0.925368	+	0.379071i	$0.123756\pi$
$367$	1303.89	+	7394.72i	0.185456	+	1.05177i	−0.739911	+	0.672704i	$0.765133\pi$
$368$		0			0
$369$	−4029.48	+	6979.27i	−0.568473	+	0.984624i
$370$		0			0
$371$	−214.199	−	77.9621i	−0.0299748	−	0.0109100i
$372$		0			0
$373$	−1652.72	−	2862.60i	−0.229423	−	0.397372i	0.728215	−	0.685349i	$-0.240350\pi$
$373$	−1652.72	−	2862.60i	−0.229423	−	0.397372i	−0.957637	+	0.287978i	$0.907017\pi$
$374$		0			0
$375$	6055.29	+	5080.99i	0.833850	+	0.699684i
$376$		0			0
$377$	−103.880	+	589.132i	−0.0141912	+	0.0804824i
$378$		0			0
$379$	3712.23			0.503126			0.251563	−	0.967841i	$-0.419056\pi$
$379$	3712.23			0.503126			0.251563	+	0.967841i	$0.419056\pi$
$380$		0			0
$381$	13445.8			1.80800
$382$		0			0
$383$	−1072.88	+	6084.58i	−0.143137	+	0.811770i	0.825707	+	0.564099i	$0.190776\pi$
$383$	−1072.88	+	6084.58i	−0.143137	+	0.811770i	−0.968844	+	0.247671i	$0.920335\pi$
$384$		0			0
$385$	8133.71	+	6824.99i	1.07671	+	0.903464i
$386$		0			0
$387$	−10979.7	−	19017.3i	−1.44219	−	2.49794i
$388$		0			0
$389$	4213.26	+	1533.50i	0.549154	+	0.199876i	0.601671	−	0.798744i	$-0.294502\pi$
$389$	4213.26	+	1533.50i	0.549154	+	0.199876i	−0.0525166	+	0.998620i	$0.516724\pi$
$390$		0			0
$391$	−5442.78	+	9427.16i	−0.703972	+	1.21932i
$392$		0			0
$393$	1605.05	+	9102.70i	0.206016	+	1.16837i
$394$		0			0
$395$	9840.40	−	8257.08i	1.25348	−	1.05179i
$396$		0			0
$397$	−7551.71	+	2748.60i	−0.954684	+	0.347476i	−0.771948	−	0.635686i	$-0.780717\pi$
$397$	−7551.71	+	2748.60i	−0.954684	+	0.347476i	−0.182736	+	0.983162i	$0.558495\pi$
$398$		0			0
$399$	4581.73	−	9402.68i	0.574871	−	1.17976i
$400$		0			0
$401$	8134.61	−	2960.76i	1.01303	−	0.368711i	0.218431	−	0.975852i	$-0.429906\pi$
$401$	8134.61	−	2960.76i	1.01303	−	0.368711i	0.794594	+	0.607141i	$0.207684\pi$
$402$		0			0
$403$	−173.639	+	145.700i	−0.0214630	+	0.0180096i
$404$		0			0
$405$	1187.61	+	6735.28i	0.145711	+	0.826368i
$406$		0			0
$407$	781.094	−	1352.90i	0.0951288	−	0.164768i
$408$		0			0
$409$	7075.28	+	2575.19i	0.855379	+	0.311332i	0.732231	−	0.681056i	$-0.238479\pi$
$409$	7075.28	+	2575.19i	0.855379	+	0.311332i	0.123147	+	0.992388i	$0.460701\pi$
$410$		0			0
$411$	−1871.33	−	3241.25i	−0.224589	−	0.389000i
$412$		0			0
$413$	−6357.10	−	5334.24i	−0.757416	−	0.635547i
$414$		0			0
$415$	215.786	−	1223.79i	0.0255242	−	0.144755i
$416$		0			0
$417$	8176.13			0.960160
$418$		0			0
$419$	4384.25			0.511180			0.255590	−	0.966785i	$-0.417730\pi$
$419$	4384.25			0.511180			0.255590	+	0.966785i	$0.417730\pi$
$420$		0			0
$421$	508.349	−	2882.99i	0.0588490	−	0.333749i	−0.941142	−	0.338012i	$-0.890246\pi$
$421$	508.349	−	2882.99i	0.0588490	−	0.333749i	0.999991	+	0.00426241i	$0.00135677\pi$
$422$		0			0
$423$	−17390.3	−	14592.2i	−1.99892	−	1.67729i
$424$		0			0
$425$	1962.02	+	3398.33i	0.223934	+	0.387866i
$426$		0			0
$427$	9046.87	+	3292.79i	1.02531	+	0.373183i
$428$		0			0
$429$	543.947	−	942.144i	0.0612168	−	0.106031i
$430$		0			0
$431$	1694.52	+	9610.13i	0.189379	+	1.07402i	0.920199	+	0.391452i	$0.128027\pi$
$431$	1694.52	+	9610.13i	0.189379	+	1.07402i	−0.730820	+	0.682571i	$0.760862\pi$
$432$		0			0
$433$	−6304.54	+	5290.14i	−0.699715	+	0.587131i	−0.921693	−	0.387921i	$-0.873193\pi$
$433$	−6304.54	+	5290.14i	−0.699715	+	0.587131i	0.221977	+	0.975052i	$0.428749\pi$
$434$		0			0
$435$	−29995.9	+	10917.6i	−3.30619	+	1.20336i
$436$		0			0
$437$	−1413.96	+	13500.5i	−0.154780	+	1.47784i
$438$		0			0
$439$	−8867.30	+	3227.43i	−0.964039	+	0.350882i	−0.775615	−	0.631206i	$-0.782560\pi$
$439$	−8867.30	+	3227.43i	−0.964039	+	0.350882i	−0.188424	+	0.982088i	$0.560338\pi$
$440$		0			0
$441$	−5436.55	+	4561.81i	−0.587037	+	0.492582i
$442$		0			0
$443$	−2064.94	−	11710.9i	−0.221464	−	1.25598i	−0.869331	−	0.494230i	$-0.835450\pi$
$443$	−2064.94	−	11710.9i	−0.221464	−	1.25598i	0.647868	−	0.761753i	$-0.275661\pi$
$444$		0			0
$445$	1023.50	−	1772.75i	0.109030	−	0.188846i
$446$		0			0
$447$	1040.46	+	378.696i	0.110094	+	0.0400710i
$448$		0			0
$449$	−4117.59	−	7131.87i	−0.432786	−	0.749608i	0.564326	−	0.825552i	$-0.309136\pi$
$449$	−4117.59	−	7131.87i	−0.432786	−	0.749608i	−0.997112	+	0.0759444i	$0.975803\pi$
$450$		0			0
$451$	6613.96	+	5549.78i	0.690553	+	0.579443i
$452$		0			0
$453$	−1723.89	+	9776.64i	−0.178797	+	1.01401i
$454$		0			0
$455$	435.697			0.0448919
$456$		0			0
$457$	−8667.64			−0.887211			−0.443605	−	0.896222i	$-0.646301\pi$
$457$	−8667.64			−0.887211			−0.443605	+	0.896222i	$0.646301\pi$
$458$		0			0
$459$	2458.72	−	13944.1i	0.250028	−	1.41798i
$460$		0			0
$461$	361.032	+	302.942i	0.0364750	+	0.0306061i	0.660843	−	0.750524i	$-0.270199\pi$
$461$	361.032	+	302.942i	0.0364750	+	0.0306061i	−0.624368	+	0.781130i	$0.714643\pi$
$462$		0			0
$463$	−1111.02	−	1924.35i	−0.111520	−	0.193158i	0.804863	−	0.593460i	$-0.202239\pi$
$463$	−1111.02	−	1924.35i	−0.111520	−	0.193158i	−0.916383	+	0.400302i	$0.868905\pi$
$464$		0			0
$465$	−11365.6	−	4136.76i	−1.13348	−	0.412554i
$466$		0			0
$467$	6179.54	−	10703.3i	0.612323	−	1.06058i	−0.378524	−	0.925591i	$-0.623568\pi$
$467$	6179.54	−	10703.3i	0.612323	−	1.06058i	0.990848	−	0.134984i	$-0.0430983\pi$
$468$		0			0
$469$	2149.58	+	12190.9i	0.211639	+	1.20026i
$470$		0			0
$471$	−3443.06	+	2889.07i	−0.336831	+	0.282635i
$472$		0			0
$473$	−22107.2	+	8046.35i	−2.14902	+	0.782181i
$474$		0			0
$475$	3959.82	+	2874.76i	0.382503	+	0.277691i
$476$		0			0
$477$	−766.330	+	278.921i	−0.0735594	+	0.0267734i
$478$		0			0
$479$	9729.41	−	8163.94i	0.928075	−	0.778747i	−0.0473959	−	0.998876i	$-0.515092\pi$
$479$	9729.41	−	8163.94i	0.928075	−	0.778747i	0.975471	+	0.220129i	$0.0706478\pi$
$480$		0			0
$481$	−11.1315	−	63.1300i	−0.00105520	−	0.00598436i
$482$		0			0
$483$	−10350.0	+	17926.8i	−0.975035	+	1.68881i
$484$		0			0
$485$	12966.2	+	4719.32i	1.21395	+	0.441842i
$486$		0			0
$487$	−4414.72	−	7646.52i	−0.410781	−	0.711493i	0.584195	−	0.811614i	$-0.301410\pi$
$487$	−4414.72	−	7646.52i	−0.410781	−	0.711493i	−0.994975	+	0.100121i	$0.968077\pi$
$488$		0			0
$489$	−26109.8	−	21908.7i	−2.41457	−	2.02606i
$490$		0			0
$491$	−1441.14	+	8173.09i	−0.132459	+	0.751215i	0.844136	+	0.536129i	$0.180114\pi$
$491$	−1441.14	+	8173.09i	−0.132459	+	0.751215i	−0.976595	+	0.215085i	$0.930997\pi$
$492$		0			0
$493$	17678.6			1.61502
$494$		0			0
$495$	37986.8			3.44925
$496$		0			0
$497$	−2063.07	+	11700.2i	−0.186200	+	1.05599i
$498$		0			0
$499$	3181.81	+	2669.86i	0.285446	+	0.239517i	0.774256	−	0.632873i	$-0.218124\pi$
$499$	3181.81	+	2669.86i	0.285446	+	0.239517i	−0.488810	+	0.872390i	$0.662569\pi$
$500$		0			0
$501$	9165.14	+	15874.5i	0.817302	+	1.41561i
$502$		0			0
$503$	6311.01	+	2297.02i	0.559432	+	0.203616i	0.606232	−	0.795288i	$-0.292680\pi$
$503$	6311.01	+	2297.02i	0.559432	+	0.203616i	−0.0468004	+	0.998904i	$0.514902\pi$
$504$		0			0
$505$	2090.67	−	3621.15i	0.184225	−	0.319087i
$506$		0			0
$507$	3364.22	+	19079.4i	0.294695	+	1.67130i
$508$		0			0
$509$	2025.69	−	1699.75i	0.176399	−	0.148016i	−0.550314	−	0.834958i	$-0.685492\pi$
$509$	2025.69	−	1699.75i	0.176399	−	0.148016i	0.726712	+	0.686942i	$0.241047\pi$
$510$		0			0
$511$	9003.18	−	3276.89i	0.779407	−	0.283681i
$512$		0			0
$513$	−4277.78	−	17130.5i	−0.368165	−	1.47433i
$514$		0			0
$515$	−2710.97	+	986.714i	−0.231961	+	0.0844268i
$516$		0			0
$517$	−18630.9	+	15633.2i	−1.58489	+	1.32988i
$518$		0			0
$519$	−3619.86	−	20529.2i	−0.306154	−	1.73629i
$520$		0			0
$521$	9565.95	−	16568.7i	0.804399	−	1.39326i	−0.112296	−	0.993675i	$-0.535821\pi$
$521$	9565.95	−	16568.7i	0.804399	−	1.39326i	0.916696	−	0.399586i	$-0.130846\pi$
$522$		0			0
$523$	3157.03	+	1149.06i	0.263953	+	0.0960709i	0.470606	−	0.882343i	$-0.344035\pi$
$523$	3157.03	+	1149.06i	0.263953	+	0.0960709i	−0.206654	+	0.978414i	$0.566257\pi$
$524$		0			0
$525$	3731.00	+	6462.28i	0.310160	+	0.537213i
$526$		0			0
$527$	5131.37	+	4305.73i	0.424148	+	0.355902i
$528$		0			0
$529$	2552.16	−	14474.0i	0.209761	−	1.18961i
$530$		0			0
$531$	−29689.5			−2.42639
$532$		0			0
$533$	354.290			0.0287917
$534$		0			0
$535$	1384.65	−	7852.72i	0.111894	−	0.634584i
$536$		0			0
$537$	10800.1	+	9062.39i	0.867896	+	0.728252i
$538$		0			0
$539$	3801.61	+	6584.58i	0.303798	+	0.526193i
$540$		0			0
$541$	−16478.0	−	5997.50i	−1.30951	−	0.476623i	−0.409428	−	0.912343i	$-0.634272\pi$
$541$	−16478.0	−	5997.50i	−1.30951	−	0.476623i	−0.900082	+	0.435720i	$0.856494\pi$
$542$		0			0
$543$	−1568.94	+	2717.49i	−0.123996	+	0.214767i
$544$		0			0
$545$	−1795.86	−	10184.8i	−0.141149	−	0.800496i
$546$		0			0
$547$	8382.75	−	7033.96i	0.655248	−	0.549818i	−0.253410	−	0.967359i	$-0.581552\pi$
$547$	8382.75	−	7033.96i	0.655248	−	0.549818i	0.908658	+	0.417541i	$0.137108\pi$
$548$		0			0
$549$	32366.5	−	11780.5i	2.51616	−	0.915806i
$550$		0			0
$551$	20136.1	−	8973.99i	1.55685	−	0.693838i
$552$		0			0
$553$	−12712.7	+	4627.03i	−0.977572	+	0.355807i
$554$		0			0
$555$	2620.31	−	2198.70i	0.200407	−	0.168162i
$556$		0			0
$557$	1003.23	+	5689.58i	0.0763161	+	0.432810i	0.998895	+	0.0470011i	$0.0149664\pi$
$557$	1003.23	+	5689.58i	0.0763161	+	0.432810i	−0.922579	+	0.385809i	$0.873922\pi$
$558$		0			0
$559$	−482.689	+	836.042i	−0.0365216	+	0.0632573i
$560$		0			0
$561$	−30210.5	−	10995.7i	−2.27360	−	0.827523i
$562$		0			0
$563$	11369.7	+	19692.8i	0.851108	+	1.47416i	0.880209	+	0.474586i	$0.157402\pi$
$563$	11369.7	+	19692.8i	0.851108	+	1.47416i	−0.0291005	+	0.999576i	$0.509264\pi$
$564$		0			0
$565$	13322.4	+	11178.9i	0.991999	+	0.832386i
$566$		0			0
$567$	1250.74	−	7093.29i	0.0926385	−	0.525379i
$568$		0			0
$569$	16103.2			1.18643			0.593216	−	0.805043i	$-0.297858\pi$
$569$	16103.2			1.18643			0.593216	+	0.805043i	$0.297858\pi$
$570$		0			0
$571$	−21556.7			−1.57990			−0.789948	−	0.613173i	$-0.789893\pi$
$571$	−21556.7			−1.57990			−0.789948	+	0.613173i	$0.789893\pi$
$572$		0			0
$573$	962.464	−	5458.40i	0.0701702	−	0.397955i
$574$		0			0
$575$	−7418.45	−	6224.82i	−0.538036	−	0.451466i
$576$		0			0
$577$	−10071.9	−	17445.0i	−0.726684	−	1.25865i	−0.958277	−	0.285841i	$-0.907727\pi$
$577$	−10071.9	−	17445.0i	−0.726684	−	1.25865i	0.231593	−	0.972813i	$-0.425606\pi$
$578$		0			0
$579$	−30207.3	−	10994.6i	−2.16818	−	0.789151i
$580$		0			0
$581$	−654.358	+	1133.38i	−0.0467252	+	0.0809305i
$582$		0			0
$583$	151.715	+	860.418i	0.0107777	+	0.0611233i
$584$		0			0
$585$	1194.09	−	1001.96i	0.0843923	−	0.0708136i
$586$		0			0
$587$	1947.13	−	708.698i	0.136911	−	0.0498315i	−0.272656	−	0.962112i	$-0.587902\pi$
$587$	1947.13	−	708.698i	0.136911	−	0.0498315i	0.409567	+	0.912280i	$0.365680\pi$
$588$		0			0
$589$	8030.34	+	2299.48i	0.561773	+	0.160863i
$590$		0			0
$591$	−15592.2	+	5675.10i	−1.08524	+	0.394996i
$592$		0			0
$593$	328.969	−	276.038i	0.0227810	−	0.0191156i	−0.631326	−	0.775518i	$-0.717489\pi$
$593$	328.969	−	276.038i	0.0227810	−	0.0191156i	0.654107	+	0.756402i	$0.273045\pi$
$594$		0			0
$595$	−2235.84	−	12680.1i	−0.154051	−	0.873669i
$596$		0			0
$597$	19657.0	−	34046.9i	1.34758	−	2.33408i
$598$		0			0
$599$	−2583.77	−	940.415i	−0.176244	−	0.0641474i	0.252391	−	0.967625i	$-0.418783\pi$
$599$	−2583.77	−	940.415i	−0.176244	−	0.0641474i	−0.428635	+	0.903478i	$0.641005\pi$
$600$		0			0
$601$	2698.54	+	4674.02i	0.183155	+	0.317233i	0.942953	−	0.332926i	$-0.108036\pi$
$601$	2698.54	+	4674.02i	0.183155	+	0.317233i	−0.759799	+	0.650159i	$0.774702\pi$
$602$		0			0
$603$	33926.3	+	28467.5i	2.29118	+	1.92253i
$604$		0			0
$605$	3931.07	−	22294.2i	0.264167	−	1.49816i
$606$		0			0
$607$	181.459			0.0121337			0.00606687	−	0.999982i	$-0.498069\pi$
$607$	181.459			0.0121337			0.00606687	+	0.999982i	$0.498069\pi$
$608$		0			0
$609$	33617.7			2.23688
$610$		0			0
$611$	−173.301	+	982.839i	−0.0114746	+	0.0650759i
$612$		0			0
$613$	−9101.95	−	7637.44i	−0.599713	−	0.503219i	0.291640	−	0.956528i	$-0.405799\pi$
$613$	−9101.95	−	7637.44i	−0.599713	−	0.503219i	−0.891353	+	0.453309i	$0.850243\pi$
$614$		0			0
$615$	9452.43	+	16372.1i	0.619770	+	1.07347i
$616$		0			0
$617$	−5234.42	−	1905.17i	−0.341539	−	0.124310i	0.165555	−	0.986201i	$-0.447058\pi$
$617$	−5234.42	−	1905.17i	−0.341539	−	0.124310i	−0.507095	+	0.861890i	$0.669281\pi$
$618$		0			0
$619$	−1686.87	+	2921.75i	−0.109533	+	0.189717i	−0.915581	−	0.402133i	$-0.868269\pi$
$619$	−1686.87	+	2921.75i	−0.109533	+	0.189717i	0.806048	+	0.591850i	$0.201602\pi$
$620$		0			0
$621$	6067.83	+	34412.4i	0.392099	+	2.22370i
$622$		0			0
$623$	−1651.44	+	1385.72i	−0.106201	+	0.0891135i
$624$		0			0
$625$	18342.4	−	6676.09i	1.17391	−	0.427270i
$626$		0			0
$627$	−39991.7	+	2811.21i	−2.54723	+	0.179057i
$628$		0			0
$629$	−1780.15	+	647.921i	−0.112844	+	0.0410720i
$630$		0			0
$631$	−18426.1	+	15461.3i	−1.16249	+	0.975445i	−0.999937	−	0.0112545i	$-0.996418\pi$
$631$	−18426.1	+	15461.3i	−1.16249	+	0.975445i	−0.162554	+	0.986700i	$0.551973\pi$
$632$		0			0
$633$	6005.87	+	34061.0i	0.377112	+	2.13871i
$634$		0			0
$635$	10320.0	−	17874.8i	0.644942	−	1.11707i
$636$		0			0
$637$	293.180	+	106.709i	0.0182358	+	0.00663729i
$638$		0			0
$639$	21252.5	+	36810.5i	1.31571	+	2.27887i
$640$		0			0
$641$	9375.88	+	7867.30i	0.577730	+	0.484773i	0.884201	−	0.467107i	$-0.154704\pi$
$641$	9375.88	+	7867.30i	0.577730	+	0.484773i	−0.306471	+	0.951880i	$0.599148\pi$
$642$		0			0
$643$	−1127.22	+	6392.78i	−0.0691340	+	0.392079i	0.930531	+	0.366212i	$0.119346\pi$
$643$	−1127.22	+	6392.78i	−0.0691340	+	0.392079i	−0.999665	+	0.0258664i	$0.991766\pi$
$644$		0			0
$645$	−51512.5			−3.14465
$646$		0			0
$647$	−32046.9			−1.94729			−0.973643	−	0.228077i	$-0.926756\pi$
$647$	−32046.9			−1.94729			−0.973643	+	0.228077i	$0.926756\pi$
$648$		0			0
$649$	−5523.34	+	31324.4i	−0.334068	+	1.89459i
$650$		0			0
$651$	9757.84	+	8187.80i	0.587465	+	0.492942i
$652$		0			0
$653$	5819.36	+	10079.4i	0.348743	+	0.604041i	0.986026	−	0.166589i	$-0.0532752\pi$
$653$	5819.36	+	10079.4i	0.348743	+	0.604041i	−0.637283	+	0.770630i	$0.719942\pi$
$654$		0			0
$655$	13333.1	+	4852.83i	0.795367	+	0.289490i
$656$		0			0
$657$	17138.7	−	29685.1i	1.01772	−	1.76275i
$658$		0			0
$659$	−3446.69	−	19547.1i	−0.203739	−	1.15546i	−0.899412	−	0.437102i	$-0.856005\pi$
$659$	−3446.69	−	19547.1i	−0.203739	−	1.15546i	0.695673	−	0.718359i	$-0.255106\pi$
$660$		0			0
$661$	5383.22	−	4517.06i	0.316767	−	0.265799i	−0.470515	−	0.882392i	$-0.655932\pi$
$661$	5383.22	−	4517.06i	0.316767	−	0.265799i	0.787282	+	0.616593i	$0.211488\pi$
$662$		0			0
$663$	−1239.68	+	451.206i	−0.0726170	+	0.0264304i
$664$		0			0
$665$	−8983.30	−	13307.8i	−0.523846	−	0.776020i
$666$		0			0
$667$	−40997.6	+	14921.9i	−2.37996	+	0.866234i
$668$		0			0
$669$	−12324.9	+	10341.8i	−0.712268	+	0.597664i
$670$		0			0
$671$	−6407.80	−	36340.4i	−0.368659	−	2.09077i
$672$		0			0
$673$	−285.983	+	495.337i	−0.0163801	+	0.0283712i	−0.874099	−	0.485747i	$-0.838548\pi$
$673$	−285.983	+	495.337i	−0.0163801	+	0.0283712i	0.857719	+	0.514119i	$0.171881\pi$
$674$		0			0
$675$	11836.8	+	4308.23i	0.674958	+	0.245665i
$676$		0			0
$677$	4188.57	+	7254.82i	0.237784	+	0.411854i	0.960078	−	0.279732i	$-0.0902456\pi$
$677$	4188.57	+	7254.82i	0.237784	+	0.411854i	−0.722294	+	0.691586i	$0.756912\pi$
$678$		0			0
$679$	−11132.0	−	9340.86i	−0.629171	−	0.527937i
$680$		0			0
$681$	4604.42	−	26112.9i	0.259092	−	1.46938i
$682$		0			0
$683$	13972.5			0.782783			0.391392	−	0.920224i	$-0.371994\pi$
$683$	13972.5			0.782783			0.391392	+	0.920224i	$0.371994\pi$
$684$		0			0
$685$	−5745.22			−0.320458
$686$		0			0
$687$	3959.20	−	22453.7i	0.219873	−	1.24696i
$688$		0			0
$689$	27.4639	+	23.0450i	0.00151857	+	0.00127423i
$690$		0			0
$691$	11088.0	+	19204.9i	0.610428	+	1.05729i	0.991168	+	0.132610i	$0.0423359\pi$
$691$	11088.0	+	19204.9i	0.610428	+	1.05729i	−0.380740	+	0.924682i	$0.624331\pi$
$692$		0			0
$693$	−37593.3	−	13682.8i	−2.06068	−	0.750025i
$694$		0			0
$695$	6275.41	−	10869.3i	0.342504	−	0.593234i
$696$		0			0
$697$	−1818.09	−	10310.9i	−0.0988020	−	0.560334i
$698$		0			0
$699$	2175.71	−	1825.64i	0.117730	−	0.0987869i
$700$		0			0
$701$	14167.1	−	5156.41i	0.763317	−	0.277825i	0.0691186	−	0.997608i	$-0.477981\pi$
$701$	14167.1	−	5156.41i	0.763317	−	0.277825i	0.694198	+	0.719784i	$0.255759\pi$
$702$		0			0
$703$	−1698.71	+	1641.62i	−0.0911350	+	0.0880726i
$704$		0			0
$705$	−50041.6	+	18213.7i	−2.67330	+	0.973002i
$706$		0			0
$707$	−3373.35	+	2830.58i	−0.179445	+	0.150572i
$708$		0			0
$709$	−4736.71	−	26863.2i	−0.250904	−	1.42295i	−0.806372	−	0.591409i	$-0.798572\pi$
$709$	−4736.71	−	26863.2i	−0.250904	−	1.42295i	0.555468	−	0.831538i	$-0.312539\pi$
$710$		0			0
$711$	−24200.2	+	41915.9i	−1.27648	+	2.21093i
$712$		0			0
$713$	−15534.2	−	5654.00i	−0.815935	−	0.296976i
$714$		0			0
$715$	−834.990	−	1446.25i	−0.0436739	−	0.0756455i
$716$		0			0
$717$	9884.57	+	8294.14i	0.514848	+	0.432009i
$718$		0			0
$719$	−3999.36	+	22681.5i	−0.207442	+	1.17646i	0.686107	+	0.727500i	$0.259318\pi$
$719$	−3999.36	+	22681.5i	−0.207442	+	1.17646i	−0.893550	+	0.448964i	$0.851793\pi$
$720$		0			0
$721$	3038.30			0.156938
$722$		0			0
$723$	26215.1			1.34848
$724$		0			0
$725$	−2731.03	+	15488.4i	−0.139901	+	0.793415i
$726$		0			0
$727$	−4783.57	−	4013.89i	−0.244034	−	0.204769i	0.512564	−	0.858649i	$-0.328696\pi$
$727$	−4783.57	−	4013.89i	−0.244034	−	0.204769i	−0.756598	+	0.653880i	$0.773140\pi$
$728$		0			0
$729$	12554.2	+	21744.5i	0.637818	+	1.10473i
$730$		0			0
$731$	26808.3	+	9757.43i	1.35642	+	0.493696i
$732$		0			0
$733$	11129.2	−	19276.3i	0.560800	−	0.971334i	−0.436627	−	0.899643i	$-0.643827\pi$
$733$	11129.2	−	19276.3i	0.560800	−	0.971334i	0.997427	−	0.0716916i	$-0.0228397\pi$
$734$		0			0
$735$	2890.90	+	16395.1i	0.145078	+	0.822780i
$736$		0			0
$737$	36346.7	−	30498.5i	1.81662	−	1.52432i
$738$		0			0
$739$	−4323.94	+	1573.78i	−0.215235	+	0.0783391i	−0.447387	−	0.894340i	$-0.647645\pi$
$739$	−4323.94	+	1573.78i	−0.215235	+	0.0783391i	0.232152	+	0.972679i	$0.425423\pi$
$740$		0			0
$741$	−1182.96	+	1143.21i	−0.0586467	+	0.0566760i
$742$		0			0
$743$	8083.67	−	2942.22i	0.399140	−	0.145275i	−0.134648	−	0.990894i	$-0.542990\pi$
$743$	8083.67	−	2942.22i	0.399140	−	0.145275i	0.533788	+	0.845618i	$0.320768\pi$
$744$		0			0
$745$	1302.02	−	1092.53i	0.0640301	−	0.0537276i
$746$		0			0
$747$	813.043	+	4611.00i	0.0398229	+	0.225847i
$748$		0			0
$749$	−4198.85	+	7272.62i	−0.204837	+	0.354787i
$750$		0			0
$751$	−8843.85	−	3218.90i	−0.429716	−	0.156404i	0.118102	−	0.993001i	$-0.462319\pi$
$751$	−8843.85	−	3218.90i	−0.429716	−	0.156404i	−0.547818	+	0.836598i	$0.684541\pi$
$752$		0			0
$753$	−479.159	−	829.928i	−0.0231893	−	0.0401650i
$754$		0			0
$755$	11673.9	+	9795.59i	0.562726	+	0.472183i
$756$		0			0
$757$	−4798.88	+	27215.8i	−0.230407	+	1.30670i	0.621666	+	0.783282i	$0.286456\pi$
$757$	−4798.88	+	27215.8i	−0.230407	+	1.30670i	−0.852073	+	0.523422i	$0.824655\pi$
$758$		0			0
$759$	79340.9			3.79433
$760$		0			0
$761$	13417.7			0.639147			0.319574	−	0.947561i	$-0.396460\pi$
$761$	13417.7			0.639147			0.319574	+	0.947561i	$0.396460\pi$
$762$		0			0
$763$	−1891.32	+	10726.2i	−0.0897382	+	0.508931i
$764$		0			0
$765$	−35287.7	−	29609.9i	−1.66775	−	1.39941i
$766$		0			0
$767$	652.608	+	1130.35i	0.0307227	+	0.0532132i
$768$		0			0
$769$	−36360.7	−	13234.2i	−1.70507	−	0.620596i	−0.708686	−	0.705524i	$-0.750712\pi$
$769$	−36360.7	−	13234.2i	−1.70507	−	0.620596i	−0.996387	+	0.0849278i	$0.972934\pi$
$770$		0			0
$771$	29234.0	−	50634.7i	1.36555	−	2.36520i
$772$		0			0
$773$	2202.43	+	12490.6i	0.102479	+	0.581185i	0.992197	+	0.124676i	$0.0397892\pi$
$773$	2202.43	+	12490.6i	0.102479	+	0.581185i	−0.889719	+	0.456509i	$0.849100\pi$
$774$		0			0
$775$	−4565.01	+	3830.50i	−0.211587	+	0.177543i
$776$		0			0
$777$	−3385.14	+	1232.09i	−0.156295	+	0.0568867i
$778$		0			0
$779$	−7304.82	−	10821.3i	−0.335972	−	0.497706i
$780$		0			0
$781$	42791.3	−	15574.7i	1.96055	−	0.713583i
$782$		0			0
$783$	43472.4	−	36477.7i	1.98414	−	1.66489i
$784$		0			0
$785$	1198.08	+	6794.64i	0.0544729	+	0.308931i
$786$		0			0
$787$	525.634	−	910.425i	0.0238079	−	0.0412365i	−0.853876	−	0.520477i	$-0.825754\pi$
$787$	525.634	−	910.425i	0.0238079	−	0.0412365i	0.877684	+	0.479240i	$0.159088\pi$
$788$		0			0
$789$	23116.5	+	8413.73i	1.04305	+	0.379641i
$790$		0			0
$791$	−9157.81	−	15861.8i	−0.411649	−	0.712997i
$792$		0			0
$793$	−1159.96	−	973.323i	−0.0519438	−	0.0435860i
$794$		0			0
$795$	−332.196	+	1883.97i	−0.0148198	+	0.0840474i
$796$		0			0
$797$	−37739.5			−1.67729			−0.838646	−	0.544676i	$-0.816652\pi$
$797$	−37739.5			−1.67729			−0.838646	+	0.544676i	$0.816652\pi$
$798$		0			0
$799$	29492.9			1.30586
$800$		0			0
$801$	−1339.29	+	7595.52i	−0.0590782	+	0.335049i
$802$		0			0
$803$	−28131.3	−	23605.0i	−1.23628	−	1.03736i
$804$		0			0
$805$	15887.9	+	27518.6i	0.695620	+	1.20485i
$806$		0			0
$807$	−54755.8	−	19929.5i	−2.38847	−	0.869332i
$808$		0			0
$809$	−17945.3	+	31082.2i	−0.779882	+	1.35080i	0.152127	+	0.988361i	$0.451388\pi$
$809$	−17945.3	+	31082.2i	−0.779882	+	1.35080i	−0.932009	+	0.362435i	$0.881946\pi$
$810$		0			0
$811$	−4966.82	−	28168.2i	−0.215054	−	1.21963i	−0.880813	−	0.473464i	$-0.843003\pi$
$811$	−4966.82	−	28168.2i	−0.215054	−	1.21963i	0.665759	−	0.746166i	$-0.268108\pi$
$812$		0			0
$813$	−3564.98	+	2991.38i	−0.153788	+	0.129043i
$814$		0			0
$815$	−49165.4	+	17894.7i	−2.11312	+	0.769111i
$816$		0			0
$817$	35487.9	−	2494.62i	1.51966	−	0.106825i
$818$		0			0
$819$	−1542.63	+	561.470i	−0.0658165	+	0.0239552i
$820$		0			0
$821$	−5457.40	+	4579.30i	−0.231991	+	0.194663i	−0.751371	−	0.659880i	$-0.770607\pi$
$821$	−5457.40	+	4579.30i	−0.231991	+	0.194663i	0.519380	+	0.854543i	$0.326163\pi$
$822$		0			0
$823$	−3358.69	−	19048.1i	−0.142256	−	0.806772i	−0.969530	−	0.244974i	$-0.921221\pi$
$823$	−3358.69	−	19048.1i	−0.142256	−	0.806772i	0.827274	−	0.561799i	$-0.189890\pi$
$824$		0			0
$825$	14300.5	−	24769.2i	0.603490	−	1.04528i
$826$		0			0
$827$	6048.91	+	2201.62i	0.254343	+	0.0925731i	0.466045	−	0.884761i	$-0.345679\pi$
$827$	6048.91	+	2201.62i	0.254343	+	0.0925731i	−0.211702	+	0.977334i	$0.567901\pi$
$828$		0			0
$829$	−20139.7	−	34883.0i	−0.843765	−	1.46144i	−0.886689	−	0.462366i	$-0.847001\pi$
$829$	−20139.7	−	34883.0i	−0.843765	−	1.46144i	0.0429239	−	0.999078i	$-0.486333\pi$
$830$		0			0
$831$	1697.72	+	1424.55i	0.0708703	+	0.0594672i
$832$		0			0
$833$	1601.05	−	9080.00i	0.0665943	−	0.377675i
$834$		0			0
$835$	28138.1			1.16618
$836$		0			0
$837$	21502.6			0.887981
$838$		0			0
$839$	−4747.86	+	26926.5i	−0.195369	+	1.10799i	0.716524	+	0.697562i	$0.245732\pi$
$839$	−4747.86	+	26926.5i	−0.195369	+	1.10799i	−0.911893	+	0.410429i	$0.865379\pi$
$840$		0			0
$841$	35594.9	+	29867.6i	1.45946	+	1.22464i
$842$		0			0
$843$	−23323.2	−	40397.0i	−0.952900	−	1.65047i
$844$		0			0
$845$	27946.3	+	10171.6i	1.13773	+	0.414100i
$846$		0			0
$847$	−11920.7	+	20647.3i	−0.483590	+	0.837603i
$848$		0			0
$849$	4710.72	+	26715.8i	0.190426	+	1.07996i
$850$		0			0
$851$	3581.37	−	3005.12i	0.144263	−	0.121051i
$852$		0			0
$853$	13111.8	−	4772.29i	0.526305	−	0.191559i	−0.0651825	−	0.997873i	$-0.520763\pi$
$853$	13111.8	−	4772.29i	0.526305	−	0.191559i	0.591488	+	0.806314i	$0.298541\pi$
$854$		0			0
$855$	−55223.5	−	15813.2i	−2.20889	−	0.632514i
$856$		0			0
$857$	−20354.9	+	7408.59i	−0.811332	+	0.295301i	−0.714174	−	0.699968i	$-0.753197\pi$
$857$	−20354.9	+	7408.59i	−0.811332	+	0.295301i	−0.0971580	+	0.995269i	$0.530975\pi$
$858$		0			0
$859$	−960.157	+	805.668i	−0.0381375	+	0.0320012i	−0.661657	−	0.749806i	$-0.730147\pi$
$859$	−960.157	+	805.668i	−0.0381375	+	0.0320012i	0.623520	+	0.781808i	$0.285702\pi$
$860$		0			0
$861$	−3457.29	−	19607.2i	−0.136845	−	0.776089i
$862$		0			0
$863$	−9183.65	+	15906.5i	−0.362242	+	0.627422i	−0.988330	−	0.152331i	$-0.951322\pi$
$863$	−9183.65	+	15906.5i	−0.362242	+	0.627422i	0.626087	+	0.779753i	$0.284655\pi$
$864$		0			0
$865$	−30069.9	−	10944.5i	−1.18197	−	0.430203i
$866$		0			0
$867$	−2219.00	−	3843.42i	−0.0869218	−	0.150553i
$868$		0			0
$869$	39722.0	+	33330.7i	1.55060	+	1.30111i
$870$		0			0
$871$	338.089	−	1917.40i	0.0131524	−	0.0745908i
$872$		0			0
$873$	−51989.7			−2.01556
$874$		0			0
$875$	−12779.0			−0.493726
$876$		0			0
$877$	680.769	−	3860.83i	0.0262120	−	0.148656i	−0.968893	−	0.247481i	$-0.920397\pi$
$877$	680.769	−	3860.83i	0.0262120	−	0.148656i	0.995105	+	0.0988250i	$0.0315084\pi$
$878$		0			0
$879$	2012.90	+	1689.02i	0.0772393	+	0.0648114i
$880$		0			0
$881$	7242.98	+	12545.2i	0.276983	+	0.479749i	0.970634	−	0.240563i	$-0.0773320\pi$
$881$	7242.98	+	12545.2i	0.276983	+	0.479749i	−0.693650	+	0.720312i	$0.743999\pi$
$882$		0			0
$883$	27016.6	+	9833.25i	1.02965	+	0.374762i	0.800948	−	0.598734i	$-0.204329\pi$
$883$	27016.6	+	9833.25i	1.02965	+	0.374762i	0.228703	+	0.973496i	$0.426552\pi$
$884$		0			0
$885$	−34823.1	+	60315.3i	−1.32267	+	2.29094i
$886$		0			0
$887$	−1028.95	−	5835.44i	−0.0389499	−	0.220896i	0.959120	−	0.283001i	$-0.0913299\pi$
$887$	−1028.95	−	5835.44i	−0.0389499	−	0.220896i	−0.998070	+	0.0621046i	$0.980219\pi$
$888$		0			0
$889$	−16651.6	+	13972.4i	−0.628209	+	0.527130i
$890$		0			0
$891$	−25942.3	+	9442.22i	−0.975420	+	0.355024i
$892$		0			0
$893$	33592.6	−	14971.1i	1.25883	−	0.561019i
$894$		0			0
$895$	20337.0	−	7402.05i	0.759541	−	0.276450i
$896$		0			0
$897$	2494.03	−	2092.74i	0.0928353	−	0.0778981i
$898$		0			0
$899$	4661.99	+	26439.5i	0.172954	+	0.980874i
$900$		0			0
$901$	529.743	−	917.541i	0.0195874	−	0.0339264i
$902$		0			0
$903$	50978.8	+	18554.8i	1.87870	+	0.683792i
$904$		0			0
$905$	2408.42	+	4171.50i	0.0884625	+	0.153222i
$906$		0			0
$907$	−3122.97	−	2620.48i	−0.114329	−	0.0959336i	0.583831	−	0.811875i	$-0.301553\pi$
$907$	−3122.97	−	2620.48i	−0.114329	−	0.0959336i	−0.698160	+	0.715942i	$0.745998\pi$
$908$		0			0
$909$	−2735.74	+	15515.2i	−0.0998227	+	0.566123i
$910$		0			0
$911$	−1486.15			−0.0540488			−0.0270244	−	0.999635i	$-0.508603\pi$
$911$	−1486.15			−0.0540488			−0.0270244	+	0.999635i	$0.508603\pi$
$912$		0			0
$913$	5016.17			0.181830
$914$		0			0
$915$	14030.5	−	79571.1i	0.506924	−	2.87491i
$916$		0			0
$917$	−11446.9	−	9605.13i	−0.412226	−	0.345899i
$918$		0			0
$919$	11418.4	+	19777.2i	0.409856	+	0.709891i	0.994873	−	0.101129i	$-0.0322456\pi$
$919$	11418.4	+	19777.2i	0.409856	+	0.709891i	−0.585017	+	0.811021i	$0.698912\pi$
$920$		0			0
$921$	39245.6	+	14284.2i	1.40411	+	0.511055i
$922$		0			0
$923$	934.307	−	1618.27i	0.0333186	−	0.0577096i
$924$		0			0
$925$	−292.650	−	1659.70i	−0.0104025	−	0.0589953i
$926$		0			0
$927$	8326.89	−	6987.09i	0.295028	−	0.247558i
$928$		0			0
$929$	−21994.4	+	8005.32i	−0.776764	+	0.282719i	−0.699823	−	0.714317i	$-0.746738\pi$
$929$	−21994.4	+	8005.32i	−0.776764	+	0.282719i	−0.0769414	+	0.997036i	$0.524515\pi$
$930$		0			0
$931$	−2785.57	−	11154.9i	−0.0980596	−	0.392683i
$932$		0			0
$933$	7110.35	−	2587.96i	0.249499	−	0.0908102i
$934$		0			0
$935$	−37805.2	+	31722.3i	−1.32231	+	1.10955i
$936$		0			0
$937$	7469.73	+	42363.0i	0.260433	+	1.47699i	0.781732	+	0.623614i	$0.214336\pi$
$937$	7469.73	+	42363.0i	0.260433	+	1.47699i	−0.521299	+	0.853374i	$0.674553\pi$
$938$		0			0
$939$	−20416.0	+	35361.5i	−0.709531	+	1.22894i
$940$		0			0
$941$	13057.0	+	4752.35i	0.452333	+	0.164636i	0.558133	−	0.829752i	$-0.311518\pi$
$941$	13057.0	+	4752.35i	0.452333	+	0.164636i	−0.105800	+	0.994387i	$0.533740\pi$
$942$		0			0
$943$	12919.3	+	22376.9i	0.446141	+	0.772738i
$944$		0			0
$945$	−31662.0	−	26567.5i	−1.08991	−	0.914542i
$946$		0			0
$947$	−1816.44	+	10301.5i	−0.0623297	+	0.353490i	0.937653	+	0.347573i	$0.112994\pi$
$947$	−1816.44	+	10301.5i	−0.0623297	+	0.353490i	−0.999982	+	0.00591606i	$0.998117\pi$
$948$		0			0
$949$	−1506.91			−0.0515451
$950$		0			0
$951$	−59858.5			−2.04106
$952$		0			0
$953$	2451.73	−	13904.4i	0.0833361	−	0.472622i	−0.914367	−	0.404886i	$-0.867311\pi$
$953$	2451.73	−	13904.4i	0.0833361	−	0.472622i	0.997703	−	0.0677364i	$-0.0215777\pi$
$954$		0			0
$955$	−6517.68	−	5468.98i	−0.220845	−	0.185311i
$956$		0			0
$957$	−64426.5	−	111590.i	−2.17619	−	3.76927i
$958$		0			0
$959$	5685.70	+	2069.43i	0.191450	+	0.0696822i
$960$		0			0
$961$	9809.19	−	16990.0i	0.329267	−	0.570307i
$962$		0			0
$963$	5217.09	+	29587.6i	0.174578	+	0.990079i
$964$		0			0
$965$	−37801.2	+	31718.9i	−1.26100	+	1.05810i
$966$		0			0
$967$	−45505.0	+	16562.4i	−1.51328	+	0.550788i	−0.959459	−	0.281848i	$-0.909053\pi$
$967$	−45505.0	+	16562.4i	−1.51328	+	0.550788i	−0.553820	+	0.832637i	$0.686830\pi$
$968$		0			0
$969$	39341.4	+	28561.2i	1.30426	+	0.946871i
$970$		0			0
$971$	4394.93	−	1599.63i	0.145252	−	0.0528676i	−0.268371	−	0.963316i	$-0.586485\pi$
$971$	4394.93	−	1599.63i	0.145252	−	0.0528676i	0.413623	+	0.910448i	$0.364263\pi$
$972$		0			0
$973$	−10125.5	+	8496.34i	−0.333618	+	0.279938i
$974$		0			0
$975$	−203.799	−	1155.80i	−0.00669414	−	0.0379644i
$976$		0			0
$977$	21220.8	−	36755.5i	0.694896	−	1.20360i	−0.275319	−	0.961353i	$-0.588784\pi$
$977$	21220.8	−	36755.5i	0.694896	−	1.20360i	0.970216	−	0.242243i	$-0.0778831\pi$
$978$		0			0
$979$	7764.62	+	2826.09i	0.253481	+	0.0922597i
$980$		0			0
$981$	19483.3	+	33746.0i	0.634101	+	1.09829i
$982$		0			0
$983$	−22136.0	−	18574.3i	−0.718240	−	0.602675i	0.208658	−	0.977989i	$-0.433090\pi$
$983$	−22136.0	−	18574.3i	−0.718240	−	0.602675i	−0.926898	+	0.375314i	$0.877535\pi$
$984$		0			0
$985$	−4423.00	+	25084.1i	−0.143075	+	0.811417i
$986$		0			0
$987$	56083.8			1.80868
$988$		0			0
$989$	−70405.8			−2.26367
$990$		0			0
$991$	9128.59	−	51770.8i	0.292613	−	1.65949i	−0.384137	−	0.923276i	$-0.625501\pi$
$991$	9128.59	−	51770.8i	0.292613	−	1.65949i	0.676750	−	0.736213i	$-0.263388\pi$
$992$		0			0
$993$	70541.1	+	59191.0i	2.25433	+	1.89161i
$994$		0			0
$995$	−30174.6	−	52264.0i	−0.961408	−	1.66521i
$996$		0			0
$997$	−25708.2	−	9357.02i	−0.816637	−	0.297232i	−0.100274	−	0.994960i	$-0.531972\pi$
$997$	−25708.2	−	9357.02i	−0.816637	−	0.297232i	−0.716363	+	0.697728i	$0.754194\pi$
$998$		0			0
$999$	−3040.55	+	5266.39i	−0.0962952	+	0.166788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.5.1	✓	30
19.2	odd	18		1444.4.a.k.1.14		15
19.4	even	9	inner	76.4.i.a.61.1	yes	30
19.17	even	9		1444.4.a.j.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.5.1	✓	30	1.1	even	1	trivial
76.4.i.a.61.1	yes	30	19.4	even	9	inner
1444.4.a.j.1.2		15	19.17	even	9
1444.4.a.k.1.14		15	19.2	odd	18

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53481 + 8.70432i) q^{3} +(10.3935 + 8.72119i) q^{5} +(-7.14447 - 12.3746i) q^{7} +(-48.0379 - 17.4843i) q^{9} +O(q^{10})\)	\(q+(-1.53481 + 8.70432i) q^{3} +(10.3935 + 8.72119i) q^{5} +(-7.14447 - 12.3746i) q^{7} +(-48.0379 - 17.4843i) q^{9} +(-27.3840 + 47.4304i) q^{11} +(0.390254 + 2.21324i) q^{13} +(-91.8641 + 77.0831i) q^{15} +(62.4092 - 22.7151i) q^{17} +(59.5540 - 57.5528i) q^{19} +(118.678 - 43.1952i) q^{21} +(-125.557 + 105.355i) q^{23} +(10.2599 + 58.1866i) q^{25} +(106.597 - 184.632i) q^{27} +(250.133 + 91.0409i) q^{29} +(50.4297 + 87.3468i) q^{31} +(-370.820 - 311.155i) q^{33} +(33.6650 - 190.924i) q^{35} -28.5238 q^{37} -19.8637 q^{39} +(27.3749 - 155.251i) q^{41} +(329.060 + 276.114i) q^{43} +(-346.798 - 600.671i) q^{45} +(417.292 + 151.882i) q^{47} +(69.4131 - 120.227i) q^{49} +(101.933 + 578.093i) q^{51} +(12.2204 - 10.2541i) q^{53} +(-698.265 + 254.148i) q^{55} +(409.554 + 606.709i) q^{57} +(545.747 - 198.636i) q^{59} +(-516.139 + 433.092i) q^{61} +(126.843 + 719.365i) q^{63} +(-15.2460 + 26.4068i) q^{65} +(-814.086 - 296.303i) q^{67} +(-724.338 - 1254.59i) q^{69} +(-636.938 - 534.454i) q^{71} +(-116.434 + 660.331i) q^{73} -522.222 q^{75} +782.576 q^{77} +(164.407 - 932.400i) q^{79} +(386.145 + 324.014i) q^{81} +(-45.7947 - 79.3188i) q^{83} +(846.753 + 308.193i) q^{85} +(-1176.35 + 2037.50i) q^{87} +(-26.1986 - 148.580i) q^{89} +(24.5998 - 20.6416i) q^{91} +(-837.695 + 304.896i) q^{93} +(1120.90 - 78.7937i) q^{95} +(955.664 - 347.833i) q^{97} +(2144.76 - 1799.66i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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