LMFDB - Embedded newform 76.5.j.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	76.13
Dual form			76.5.j.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +O(q^{10})$	\(q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +(89.7471 + 155.447i) q^{11} +(34.6560 + 95.2165i) q^{13} +(-641.081 - 113.040i) q^{15} +(-2.64161 + 2.21657i) q^{17} +(145.418 - 330.416i) q^{19} +(315.328 + 375.793i) q^{21} +(179.219 - 1016.40i) q^{23} +(-1046.66 + 380.953i) q^{25} +(-1104.62 + 637.755i) q^{27} +(545.399 - 649.981i) q^{29} +(-974.956 - 562.891i) q^{31} +(2759.53 - 486.579i) q^{33} +(1231.34 + 448.170i) q^{35} -89.0040i q^{37} +1581.83 q^{39} +(-344.404 + 946.243i) q^{41} +(-83.5286 - 473.714i) q^{43} +(-3392.35 + 5875.73i) q^{45} +(2550.07 + 2139.76i) q^{47} +(706.764 + 1224.15i) q^{49} +(18.4119 + 50.5863i) q^{51} +(819.014 + 144.414i) q^{53} +(5733.68 - 4811.13i) q^{55} +(-4070.64 - 3897.42i) q^{57} +(-1606.04 - 1914.01i) q^{59} +(-369.330 + 2094.57i) q^{61} +(4804.53 - 1748.70i) q^{63} +(3659.20 - 2112.64i) q^{65} +(1209.96 - 1441.98i) q^{67} +(-13953.3 - 8055.95i) q^{69} +(-1305.86 + 230.258i) q^{71} +(278.093 + 101.218i) q^{73} +17388.1i q^{75} -5640.44 q^{77} +(3934.97 - 10811.2i) q^{79} +(1169.16 + 6630.64i) q^{81} +(-4761.55 + 8247.25i) q^{83} +(110.153 + 92.4296i) q^{85} +(-6622.92 - 11471.2i) q^{87} +(3530.74 + 9700.62i) q^{89} +(-3135.74 - 552.916i) q^{91} +(-13463.0 + 11296.8i) q^{93} +(-14621.8 - 3579.18i) q^{95} +(2269.14 + 2704.25i) q^{97} +(5071.34 - 28761.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	5.33930	−	14.6696i	0.593256	−	1.62996i	−0.171168	−	0.985242i	$-0.554754\pi$
$3$	5.33930	−	14.6696i	0.593256	−	1.62996i	0.764423	−	0.644714i	$-0.223024\pi$
$4$		0			0
$5$	−7.24101	−	41.0658i	−0.289640	−	1.64263i	−0.688223	−	0.725499i	$-0.741609\pi$
$5$	−7.24101	−	41.0658i	−0.289640	−	1.64263i	0.398583	−	0.917132i	$-0.369502\pi$
$6$		0			0
$7$	−15.7120	+	27.2140i	−0.320654	+	0.555389i	−0.980623	−	0.195904i	$-0.937236\pi$
$7$	−15.7120	+	27.2140i	−0.320654	+	0.555389i	0.659969	+	0.751293i	$0.270569\pi$
$8$		0			0
$9$	−124.640	−	104.585i	−1.53876	−	1.29117i
$10$		0			0
$11$	89.7471	+	155.447i	0.741712	+	1.28468i	0.951715	+	0.306982i	$0.0993190\pi$
$11$	89.7471	+	155.447i	0.741712	+	1.28468i	−0.210004	+	0.977701i	$0.567348\pi$
$12$		0			0
$13$	34.6560	+	95.2165i	0.205065	+	0.563411i	0.999006	−	0.0445838i	$-0.0141962\pi$
$13$	34.6560	+	95.2165i	0.205065	+	0.563411i	−0.793941	+	0.607995i	$0.791974\pi$
$14$		0			0
$15$	−641.081	−	113.040i	−2.84925	−	0.502399i
$16$		0			0
$17$	−2.64161	+	2.21657i	−0.00914052	+	0.00766981i	−0.647346	−	0.762196i	$-0.724121\pi$
$17$	−2.64161	+	2.21657i	−0.00914052	+	0.00766981i	0.638206	+	0.769866i	$0.279677\pi$
$18$		0			0
$19$	145.418	−	330.416i	0.402821	−	0.915279i
$19$	145.418	−	330.416i	0.402821	−	0.915279i
$20$		0			0
$21$	315.328	+	375.793i	0.715030	+	0.852139i
$22$		0			0
$23$	179.219	−	1016.40i	0.338788	−	1.92137i	−0.0472516	−	0.998883i	$-0.515046\pi$
$23$	179.219	−	1016.40i	0.338788	−	1.92137i	0.386040	−	0.922482i	$-0.373843\pi$
$24$		0			0
$25$	−1046.66	+	380.953i	−1.67465	+	0.609525i
$26$		0			0
$27$	−1104.62	+	637.755i	−1.51526	+	0.874835i
$28$		0			0
$29$	545.399	−	649.981i	0.648512	−	0.772867i	−0.337177	−	0.941441i	$-0.609472\pi$
$29$	545.399	−	649.981i	0.648512	−	0.772867i	0.985689	+	0.168575i	$0.0539164\pi$
$30$		0			0
$31$	−974.956	−	562.891i	−1.01452	−	0.585735i	−0.102010	−	0.994783i	$-0.532527\pi$
$31$	−974.956	−	562.891i	−1.01452	−	0.585735i	−0.912513	+	0.409048i	$0.865861\pi$
$32$		0			0
$33$	2759.53	−	486.579i	2.53400	−	0.446813i
$34$		0			0
$35$	1231.34	+	448.170i	1.00517	+	0.365853i
$36$		0			0
$37$		−	89.0040i		−	0.0650139i	−0.999472	−	0.0325069i	$-0.989651\pi$
$37$		−	89.0040i		−	0.0650139i	0.999472	−	0.0325069i	$-0.0103491\pi$
$38$		0			0
$39$	1581.83			1.03999
$40$		0			0
$41$	−344.404	+	946.243i	−0.204881	+	0.562905i	−0.998993	−	0.0448660i	$-0.985714\pi$
$41$	−344.404	+	946.243i	−0.204881	+	0.562905i	0.794112	+	0.607771i	$0.207936\pi$
$42$		0			0
$43$	−83.5286	−	473.714i	−0.0451750	−	0.256200i	0.953853	−	0.300273i	$-0.0970778\pi$
$43$	−83.5286	−	473.714i	−0.0451750	−	0.256200i	−0.999028	+	0.0440728i	$0.985967\pi$
$44$		0			0
$45$	−3392.35	+	5875.73i	−1.67524	+	2.90159i
$46$		0			0
$47$	2550.07	+	2139.76i	1.15440	+	0.968656i	0.999813	−	0.0193232i	$-0.00615114\pi$
$47$	2550.07	+	2139.76i	1.15440	+	0.968656i	0.154586	+	0.987979i	$0.450596\pi$
$48$		0			0
$49$	706.764	+	1224.15i	0.294362	+	0.509850i
$50$		0			0
$51$	18.4119	+	50.5863i	0.00707879	+	0.0194488i
$52$		0			0
$53$	819.014	+	144.414i	0.291568	+	0.0514113i	0.317519	−	0.948252i	$-0.397150\pi$
$53$	819.014	+	144.414i	0.291568	+	0.0514113i	−0.0259511	+	0.999663i	$0.508261\pi$
$54$		0			0
$55$	5733.68	−	4811.13i	1.89543	−	1.59045i
$56$		0			0
$57$	−4070.64	−	3897.42i	−1.25289	−	1.19957i
$58$		0			0
$59$	−1606.04	−	1914.01i	−0.461374	−	0.549844i	0.484325	−	0.874888i	$-0.339065\pi$
$59$	−1606.04	−	1914.01i	−0.461374	−	0.549844i	−0.945699	+	0.325044i	$0.894621\pi$
$60$		0			0
$61$	−369.330	+	2094.57i	−0.0992555	+	0.562906i	0.894104	+	0.447859i	$0.147813\pi$
$61$	−369.330	+	2094.57i	−0.0992555	+	0.562906i	−0.993360	+	0.115048i	$0.963298\pi$
$62$		0			0
$63$	4804.53	−	1748.70i	1.21051	−	0.440591i
$64$		0			0
$65$	3659.20	−	2112.64i	0.866082	−	0.500033i
$66$		0			0
$67$	1209.96	−	1441.98i	0.269540	−	0.321225i	−0.614248	−	0.789113i	$-0.710541\pi$
$67$	1209.96	−	1441.98i	0.269540	−	0.321225i	0.883788	+	0.467888i	$0.154985\pi$
$68$		0			0
$69$	−13953.3	−	8055.95i	−2.93075	−	1.69207i
$70$		0			0
$71$	−1305.86	+	230.258i	−0.259048	+	0.0456771i	−0.301664	−	0.953414i	$-0.597542\pi$
$71$	−1305.86	+	230.258i	−0.259048	+	0.0456771i	0.0426159	+	0.999092i	$0.486431\pi$
$72$		0			0
$73$	278.093	+	101.218i	0.0521849	+	0.0189937i	0.367981	−	0.929833i	$-0.380049\pi$
$73$	278.093	+	101.218i	0.0521849	+	0.0189937i	−0.315796	+	0.948827i	$0.602271\pi$
$74$		0			0
$75$			17388.1i			3.09122i
$76$		0			0
$77$	−5640.44			−0.951330
$78$		0			0
$79$	3934.97	−	10811.2i	0.630503	−	1.73229i	−0.0491834	−	0.998790i	$-0.515662\pi$
$79$	3934.97	−	10811.2i	0.630503	−	1.73229i	0.679686	−	0.733503i	$-0.262116\pi$
$80$		0			0
$81$	1169.16	+	6630.64i	0.178199	+	1.01061i
$82$		0			0
$83$	−4761.55	+	8247.25i	−0.691182	+	1.19716i	0.280269	+	0.959921i	$0.409576\pi$
$83$	−4761.55	+	8247.25i	−0.691182	+	1.19716i	−0.971451	+	0.237241i	$0.923757\pi$
$84$		0			0
$85$	110.153	+	92.4296i	0.0152461	+	0.0127930i
$86$		0			0
$87$	−6622.92	−	11471.2i	−0.875006	−	1.51555i
$88$		0			0
$89$	3530.74	+	9700.62i	0.445744	+	1.22467i	0.935661	+	0.352901i	$0.114805\pi$
$89$	3530.74	+	9700.62i	0.445744	+	1.22467i	−0.489917	+	0.871769i	$0.662973\pi$
$90$		0			0
$91$	−3135.74	−	552.916i	−0.378667	−	0.0667692i
$92$		0			0
$93$	−13463.0	+	11296.8i	−1.55659	+	1.30614i
$94$		0			0
$95$	−14621.8	−	3579.18i	−1.62014	−	0.396585i
$96$		0			0
$97$	2269.14	+	2704.25i	0.241167	+	0.287411i	0.873028	−	0.487670i	$-0.162153\pi$
$97$	2269.14	+	2704.25i	0.241167	+	0.287411i	−0.631861	+	0.775082i	$0.717709\pi$
$98$		0			0
$99$	5071.34	−	28761.0i	0.517431	−	2.93450i
$100$		0			0
$101$	13748.2	−	5003.95i	1.34773	−	0.490535i	0.435495	−	0.900191i	$-0.356573\pi$
$101$	13748.2	−	5003.95i	1.34773	−	0.490535i	0.912240	+	0.409656i	$0.134351\pi$
$102$		0			0
$103$	4736.29	−	2734.50i	0.446441	−	0.257753i	−0.259885	−	0.965640i	$-0.583685\pi$
$103$	4736.29	−	2734.50i	0.446441	−	0.257753i	0.706326	+	0.707887i	$0.250351\pi$
$104$		0			0
$105$	13149.0	−	15670.3i	1.19265	−	1.42134i
$106$		0			0
$107$	18084.6	+	10441.2i	1.57958	+	0.911972i	0.994917	+	0.100697i	$0.0321072\pi$
$107$	18084.6	+	10441.2i	1.57958	+	0.911972i	0.584665	+	0.811275i	$0.301226\pi$
$108$		0			0
$109$	11960.7	−	2109.00i	1.00671	−	0.177510i	0.354103	−	0.935206i	$-0.384786\pi$
$109$	11960.7	−	2109.00i	1.00671	−	0.177510i	0.652607	+	0.757696i	$0.273675\pi$
$110$		0			0
$111$	−1305.65	−	475.219i	−0.105970	−	0.0385698i
$112$		0			0
$113$			12893.0i			1.00971i	0.863205	+	0.504854i	$0.168454\pi$
$113$			12893.0i			1.00971i	−0.863205	+	0.504854i	$0.831546\pi$
$114$		0			0
$115$	−43037.1			−3.25422
$116$		0			0
$117$	5638.72	−	15492.3i	0.411916	−	1.13173i
$118$		0			0
$119$	−18.8169	−	106.716i	−0.00132878	−	0.00753590i
$120$		0			0
$121$	−8788.58	+	15222.3i	−0.600272	+	1.03970i
$122$		0			0
$123$	12042.1	+	10104.6i	0.795964	+	0.667893i
$124$		0			0
$125$	10192.0	+	17653.0i	0.652286	+	1.12979i
$126$		0			0
$127$	1344.04	+	3692.72i	0.0833306	+	0.228949i	0.974359	−	0.224998i	$-0.0722377\pi$
$127$	1344.04	+	3692.72i	0.0833306	+	0.228949i	−0.891029	+	0.453947i	$0.850015\pi$
$128$		0			0
$129$	−7395.18	−	1303.97i	−0.444395	−	0.0783589i
$130$		0			0
$131$	12566.9	−	10544.8i	0.732292	−	0.614466i	−0.198464	−	0.980108i	$-0.563595\pi$
$131$	12566.9	−	10544.8i	0.732292	−	0.614466i	0.930755	+	0.365643i	$0.119151\pi$
$132$		0			0
$133$	6707.13	+	9148.92i	0.379169	+	0.517210i
$134$		0			0
$135$	34188.5	+	40744.3i	1.87591	+	2.23563i
$136$		0			0
$137$	−2132.93	+	12096.4i	−0.113641	+	0.644490i	0.873773	+	0.486334i	$0.161666\pi$
$137$	−2132.93	+	12096.4i	−0.113641	+	0.644490i	−0.987414	+	0.158156i	$0.949445\pi$
$138$		0			0
$139$	−10258.7	+	3733.87i	−0.530963	+	0.193255i	−0.593568	−	0.804784i	$-0.702281\pi$
$139$	−10258.7	+	3733.87i	−0.530963	+	0.193255i	0.0626054	+	0.998038i	$0.480059\pi$
$140$		0			0
$141$	45005.0	−	25983.7i	2.26372	−	1.30696i
$142$		0			0
$143$	−11690.8	+	13932.6i	−0.571706	+	0.681332i
$144$		0			0
$145$	−30641.2	−	17690.7i	−1.45737	−	0.841413i
$146$		0			0
$147$	21731.4	−	3831.84i	1.00567	−	0.177326i
$148$		0			0
$149$	−16333.5	−	5944.92i	−0.735711	−	0.267777i	−0.0531308	−	0.998588i	$-0.516920\pi$
$149$	−16333.5	−	5944.92i	−0.735711	−	0.267777i	−0.682580	+	0.730811i	$0.739142\pi$
$150$		0			0
$151$		−	21119.7i		−	0.926262i	−0.886290	−	0.463131i	$-0.846726\pi$
$151$		−	21119.7i		−	0.926262i	0.886290	−	0.463131i	$-0.153274\pi$
$152$		0			0
$153$	561.070			0.0239681
$154$		0			0
$155$	−16055.9	+	44113.3i	−0.668300	+	1.83614i
$156$		0			0
$157$	−2180.35	−	12365.4i	−0.0884561	−	0.501659i	−0.996557	−	0.0829083i	$-0.973579\pi$
$157$	−2180.35	−	12365.4i	−0.0884561	−	0.501659i	0.908101	−	0.418751i	$-0.137532\pi$
$158$		0			0
$159$	6491.46	−	11243.5i	0.256772	−	0.444743i
$160$		0			0
$161$	24844.5	+	20847.0i	0.958470	+	0.804252i
$162$		0			0
$163$	7477.22	+	12950.9i	0.281426	+	0.487445i	0.971736	−	0.236069i	$-0.0758591\pi$
$163$	7477.22	+	12950.9i	0.281426	+	0.487445i	−0.690310	+	0.723514i	$0.742526\pi$
$164$		0			0
$165$	−39963.5	−	109799.i	−1.46790	−	4.03301i
$166$		0			0
$167$	−22290.5	−	3930.42i	−0.799258	−	0.140931i	−0.240921	−	0.970545i	$-0.577449\pi$
$167$	−22290.5	−	3930.42i	−0.799258	−	0.140931i	−0.558337	+	0.829614i	$0.688560\pi$
$168$		0			0
$169$	14013.8	−	11759.0i	0.490664	−	0.411716i
$170$		0			0
$171$	−52681.4	+	25974.3i	−1.80163	+	0.888283i
$172$		0			0
$173$	4516.54	+	5382.60i	0.150908	+	0.179846i	0.836203	−	0.548421i	$-0.184771\pi$
$173$	4516.54	+	5382.60i	0.150908	+	0.179846i	−0.685294	+	0.728266i	$0.740326\pi$
$174$		0			0
$175$	6077.88	−	34469.4i	0.198461	−	1.12553i
$176$		0			0
$177$	−36652.9	+	13340.6i	−1.16994	+	0.425822i
$178$		0			0
$179$	34046.8	−	19656.9i	1.06260	−	0.613493i	0.136451	−	0.990647i	$-0.456431\pi$
$179$	34046.8	−	19656.9i	1.06260	−	0.613493i	0.926151	+	0.377154i	$0.123097\pi$
$180$		0			0
$181$	−40789.7	+	48611.3i	−1.24507	+	1.48382i	−0.431755	+	0.901991i	$0.642106\pi$
$181$	−40789.7	+	48611.3i	−1.24507	+	1.48382i	−0.813314	+	0.581825i	$0.802339\pi$
$182$		0			0
$183$	28754.6	+	16601.5i	0.858629	+	0.495729i
$184$		0			0
$185$	−3655.02	+	644.478i	−0.106794	+	0.0188306i
$186$		0			0
$187$	−581.636	−	211.698i	−0.0166329	−	0.00605388i
$188$		0			0
$189$		−	40081.7i		−	1.12208i
$190$		0			0
$191$	22006.1			0.603220			0.301610	−	0.953431i	$-0.402476\pi$
$191$	22006.1			0.603220			0.301610	+	0.953431i	$0.402476\pi$
$192$		0			0
$193$	−3866.00	+	10621.8i	−0.103788	+	0.285155i	−0.980707	−	0.195483i	$-0.937373\pi$
$193$	−3866.00	+	10621.8i	−0.103788	+	0.285155i	0.876919	+	0.480638i	$0.159595\pi$
$194$		0			0
$195$	−11454.0	−	64959.0i	−0.301224	−	1.70832i
$196$		0			0
$197$	−21154.9	+	36641.4i	−0.545103	+	0.944146i	0.453497	+	0.891258i	$0.350176\pi$
$197$	−21154.9	+	36641.4i	−0.545103	+	0.944146i	−0.998600	+	0.0528886i	$0.983157\pi$
$198$		0			0
$199$	−20672.4	−	17346.2i	−0.522018	−	0.438025i	0.343316	−	0.939220i	$-0.388450\pi$
$199$	−20672.4	−	17346.2i	−0.522018	−	0.438025i	−0.865335	+	0.501194i	$0.832894\pi$
$200$		0			0
$201$	−14692.9	−	25448.9i	−0.363677	−	0.629907i
$202$		0			0
$203$	9119.28	+	25055.0i	0.221294	+	0.607999i
$204$		0			0
$205$	41352.1	+	7291.48i	0.983987	+	0.173503i
$206$		0			0
$207$	−128638.	+	107940.i	−3.00213	+	2.51909i
$208$		0			0
$209$	64412.8	−	7049.07i	1.47462	−	0.161376i
$210$		0			0
$211$	−21018.7	−	25049.1i	−0.472107	−	0.562635i	0.476466	−	0.879193i	$-0.341917\pi$
$211$	−21018.7	−	25049.1i	−0.472107	−	0.562635i	−0.948573	+	0.316558i	$0.897473\pi$
$212$		0			0
$213$	−3594.58	+	20385.9i	−0.0792298	+	0.449335i
$214$		0			0
$215$	−18848.6	+	6860.33i	−0.407758	+	0.148412i
$216$		0			0
$217$	30637.1	−	17688.3i	0.650621	−	0.375636i
$218$		0			0
$219$	2969.65	−	3539.09i	0.0619179	−	0.0737909i
$220$		0			0
$221$	−302.602	−	174.707i	−0.00619566	−	0.00357707i
$222$		0			0
$223$	24173.3	−	4262.40i	0.486100	−	0.0857126i	0.0747734	−	0.997201i	$-0.476177\pi$
$223$	24173.3	−	4262.40i	0.486100	−	0.0857126i	0.411327	+	0.911488i	$0.365066\pi$
$224$		0			0
$225$	170297.	+	61983.1i	3.36390	+	1.22436i
$226$		0			0
$227$			72453.9i			1.40608i	0.711150	+	0.703040i	$0.248175\pi$
$227$			72453.9i			1.40608i	−0.711150	+	0.703040i	$0.751825\pi$
$228$		0			0
$229$	−59643.4			−1.13734			−0.568671	−	0.822565i	$-0.692542\pi$
$229$	−59643.4			−1.13734			−0.568671	+	0.822565i	$0.692542\pi$
$230$		0			0
$231$	−30116.0	+	82743.0i	−0.564382	+	1.55063i
$232$		0			0
$233$	−11025.2	−	62527.0i	−0.203083	−	1.15174i	−0.900427	−	0.435007i	$-0.856746\pi$
$233$	−11025.2	−	62527.0i	−0.203083	−	1.15174i	0.697344	−	0.716737i	$-0.254365\pi$
$234$		0			0
$235$	69405.9	−	120215.i	1.25678	−	2.17682i
$236$		0			0
$237$	−137587.	−	115449.i	−2.44951	−	2.05538i
$238$		0			0
$239$	−32898.7	−	56982.2i	−0.575947	−	0.997570i	−0.995938	−	0.0900414i	$-0.971300\pi$
$239$	−32898.7	−	56982.2i	−0.575947	−	0.997570i	0.419991	−	0.907528i	$-0.362033\pi$
$240$		0			0
$241$	19008.1	+	52224.2i	0.327268	+	0.899161i	0.988800	+	0.149245i	$0.0476842\pi$
$241$	19008.1	+	52224.2i	0.327268	+	0.899161i	−0.661532	+	0.749917i	$0.730094\pi$
$242$		0			0
$243$	1764.73	+	311.170i	0.0298859	+	0.00526968i
$244$		0			0
$245$	45153.0	−	37887.9i	0.752237	−	0.631202i
$246$		0			0
$247$	36500.7	+	2395.35i	0.598283	+	0.0392623i
$248$		0			0
$249$	95560.5	+	113885.i	1.54127	+	1.83682i
$250$		0			0
$251$	4921.92	−	27913.6i	0.0781244	−	0.443066i	−0.920505	−	0.390730i	$-0.872222\pi$
$251$	4921.92	−	27913.6i	0.0781244	−	0.443066i	0.998630	−	0.0523352i	$-0.0166664\pi$
$252$		0			0
$253$	174081.	−	63360.1i	2.71963	−	0.989863i
$254$		0			0
$255$	1944.05	−	1122.40i	0.0298969	−	0.0172610i
$256$		0			0
$257$	2843.15	−	3388.34i	0.0430461	−	0.0513004i	−0.744092	−	0.668077i	$-0.767118\pi$
$257$	2843.15	−	3388.34i	0.0430461	−	0.0513004i	0.787138	+	0.616777i	$0.211562\pi$
$258$		0			0
$259$	2422.16	+	1398.43i	0.0361080	+	0.0208469i
$260$		0			0
$261$	−135957.	+	23972.8i	−1.99581	+	0.351915i
$262$		0			0
$263$	37875.5	+	13785.5i	0.547579	+	0.199302i	0.600970	−	0.799271i	$-0.294781\pi$
$263$	37875.5	+	13785.5i	0.547579	+	0.199302i	−0.0533918	+	0.998574i	$0.517003\pi$
$264$		0			0
$265$		−	34679.2i		−	0.493829i
$266$		0			0
$267$	161156.			2.26060
$268$		0			0
$269$	−23225.6	+	63811.9i	−0.320969	+	0.881854i	0.669338	+	0.742958i	$0.266578\pi$
$269$	−23225.6	+	63811.9i	−0.320969	+	0.881854i	−0.990307	+	0.138896i	$0.955644\pi$
$270$		0			0
$271$	9398.41	+	53301.1i	0.127972	+	0.725767i	0.979498	+	0.201454i	$0.0645667\pi$
$271$	9398.41	+	53301.1i	0.127972	+	0.725767i	−0.851526	+	0.524313i	$0.824322\pi$
$272$		0			0
$273$	−24853.7	+	43047.9i	−0.333477	+	0.577600i
$274$		0			0
$275$	−153152.	−	128510.i	−2.02516	−	1.69931i
$276$		0			0
$277$	−11644.8	−	20169.4i	−0.151766	−	0.262866i	0.780111	−	0.625641i	$-0.215163\pi$
$277$	−11644.8	−	20169.4i	−0.151766	−	0.262866i	−0.931877	+	0.362775i	$0.881829\pi$
$278$		0			0
$279$	62648.2	+	172124.i	0.804822	+	2.21123i
$280$		0			0
$281$	134068.	+	23639.8i	1.69790	+	0.299385i	0.936959	−	0.349438i	$-0.113628\pi$
$281$	134068.	+	23639.8i	1.69790	+	0.299385i	0.760939	+	0.648824i	$0.224739\pi$
$282$		0			0
$283$	−71245.6	+	59782.1i	−0.889580	+	0.746446i	−0.968126	−	0.250464i	$-0.919417\pi$
$283$	−71245.6	+	59782.1i	−0.889580	+	0.746446i	0.0785460	+	0.996910i	$0.474972\pi$
$284$		0			0
$285$	−130575.	+	195385.i	−1.60757	+	2.40548i
$286$		0			0
$287$	−20339.8	−	24240.0i	−0.246935	−	0.294286i
$288$		0			0
$289$	−14501.2	+	82240.4i	−0.173623	+	0.984668i
$290$		0			0
$291$	51785.9	−	18848.5i	0.611542	−	0.222583i
$292$		0			0
$293$	−66295.4	+	38275.7i	−0.772233	+	0.445849i	−0.833670	−	0.552262i	$-0.813765\pi$
$293$	−66295.4	+	38275.7i	−0.772233	+	0.445849i	0.0614379	+	0.998111i	$0.480431\pi$
$294$		0			0
$295$	−66970.9	+	79812.8i	−0.769559	+	0.917125i
$296$		0			0
$297$	−198274.	−	114473.i	−2.24777	−	1.29775i
$298$		0			0
$299$	102989.	−	18159.8i	1.15199	−	0.203127i
$300$		0			0
$301$	14204.1	+	5169.86i	0.156776	+	0.0570619i
$302$		0			0
$303$		−	228399.i		−	2.48776i
$304$		0			0
$305$	88689.7			0.953396
$306$		0			0
$307$	8430.56	−	23162.8i	0.0894499	−	0.245762i	−0.886899	−	0.461964i	$-0.847145\pi$
$307$	8430.56	−	23162.8i	0.0894499	−	0.245762i	0.976349	+	0.216202i	$0.0693671\pi$
$308$		0			0
$309$	−14825.5	−	84079.9i	−0.155272	−	0.880593i
$310$		0			0
$311$	−42271.8	+	73217.0i	−0.437049	+	0.756992i	−0.997460	−	0.0712230i	$-0.977310\pi$
$311$	−42271.8	+	73217.0i	−0.437049	+	0.756992i	0.560411	+	0.828215i	$0.310643\pi$
$312$		0			0
$313$	−71271.8	−	59804.1i	−0.727493	−	0.610439i	0.201954	−	0.979395i	$-0.435271\pi$
$313$	−71271.8	−	59804.1i	−0.727493	−	0.610439i	−0.929447	+	0.368956i	$0.879715\pi$
$314$		0			0
$315$	−106602.	−	184639.i	−1.07434	−	1.86081i
$316$		0			0
$317$	3915.26	+	10757.1i	0.0389621	+	0.107047i	0.957648	−	0.287941i	$-0.0929708\pi$
$317$	3915.26	+	10757.1i	0.0389621	+	0.107047i	−0.918686	+	0.394989i	$0.870749\pi$
$318$		0			0
$319$	149985.	+	26446.4i	1.47390	+	0.259888i
$320$		0			0
$321$	249727.	−	209546.i	2.42357	−	2.03362i
$322$		0			0
$323$	348.252	+	1195.16i	0.00333802	+	0.0114557i
$324$		0			0
$325$	−72546.0	−	86457.0i	−0.686826	−	0.818528i
$326$		0			0
$327$	32923.7	−	186720.i	0.307903	−	1.74620i
$328$		0			0
$329$	−98298.3	+	35777.7i	−0.908143	+	0.330537i
$330$		0			0
$331$	−15831.7	+	9140.42i	−0.144501	+	0.0834277i	−0.570507	−	0.821292i	$-0.693253\pi$
$331$	−15831.7	+	9140.42i	−0.144501	+	0.0834277i	0.426006	+	0.904720i	$0.359920\pi$
$332$		0			0
$333$	−9308.49	+	11093.4i	−0.0839442	+	0.100041i
$334$		0			0
$335$	−67977.4	−	39246.8i	−0.605724	−	0.349715i
$336$		0			0
$337$	−221765.	+	39103.2i	−1.95269	+	0.344313i	−0.953633	+	0.300972i	$0.902689\pi$
$337$	−221765.	+	39103.2i	−1.95269	+	0.344313i	−0.999060	+	0.0433406i	$0.986200\pi$
$338$		0			0
$339$	189135.	+	68839.4i	1.64578	+	0.599015i
$340$		0			0
$341$		−	202071.i		−	1.73779i
$342$		0			0
$343$	−119868.			−1.01886
$344$		0			0
$345$	−229788.	+	631337.i	−1.93059	+	5.30424i
$346$		0			0
$347$	−18415.0	−	104437.i	−0.152937	−	0.867349i	−0.960648	−	0.277770i	$-0.910405\pi$
$347$	−18415.0	−	104437.i	−0.152937	−	0.867349i	0.807711	−	0.589579i	$-0.200706\pi$
$348$		0			0
$349$	−22498.0	+	38967.7i	−0.184711	+	0.319929i	−0.943479	−	0.331432i	$-0.892468\pi$
$349$	−22498.0	+	38967.7i	−0.184711	+	0.319929i	0.758768	+	0.651361i	$0.225802\pi$
$350$		0			0
$351$	−99006.7	−	83076.5i	−0.803619	−	0.674316i
$352$		0			0
$353$	4393.73	+	7610.16i	0.0352601	+	0.0610724i	0.883117	−	0.469153i	$-0.155441\pi$
$353$	4393.73	+	7610.16i	0.0352601	+	0.0610724i	−0.847857	+	0.530225i	$0.822107\pi$
$354$		0			0
$355$	18911.5	+	51958.8i	0.150061	+	0.412290i
$356$		0			0
$357$	−1665.95	−	293.752i	−0.0130715	−	0.00230486i
$358$		0			0
$359$	993.881	−	833.965i	0.00771162	−	0.00647081i	−0.638924	−	0.769270i	$-0.720620\pi$
$359$	993.881	−	833.965i	0.00771162	−	0.00647081i	0.646635	+	0.762799i	$0.276176\pi$
$360$		0			0
$361$	−88028.0	−	96097.0i	−0.675471	−	0.737387i
$362$		0			0
$363$	176380.	+	210201.i	1.33855	+	1.59523i
$364$		0			0
$365$	2142.91	−	12153.0i	0.0160849	−	0.0912219i
$366$		0			0
$367$	−46474.5	+	16915.3i	−0.345051	+	0.125588i	−0.508732	−	0.860925i	$-0.669885\pi$
$367$	−46474.5	+	16915.3i	−0.345051	+	0.125588i	0.163681	+	0.986513i	$0.447663\pi$
$368$		0			0
$369$	141889.	−	81919.9i	1.04207	−	0.601640i
$370$		0			0
$371$	−16798.5	+	20019.6i	−0.122046	+	0.145448i
$372$		0			0
$373$	91944.6	+	53084.2i	0.660858	+	0.381547i	0.792604	−	0.609737i	$-0.208725\pi$
$373$	91944.6	+	53084.2i	0.660858	+	0.381547i	−0.131746	+	0.991284i	$0.542058\pi$
$374$		0			0
$375$	313381.	−	55257.5i	2.22848	−	0.392942i
$376$		0			0
$377$	80790.3	+	29405.3i	0.568429	+	0.206891i
$378$		0			0
$379$			217444.i			1.51380i	0.653531	+	0.756900i	$0.273287\pi$
$379$			217444.i			1.51380i	−0.653531	+	0.756900i	$0.726713\pi$
$380$		0			0
$381$	61346.9			0.422613
$382$		0			0
$383$	22149.4	−	60855.1i	0.150996	−	0.414858i	−0.841015	−	0.541012i	$-0.818041\pi$
$383$	22149.4	−	60855.1i	0.150996	−	0.414858i	0.992011	+	0.126154i	$0.0402635\pi$
$384$		0			0
$385$	40842.5	+	231629.i	0.275544	+	1.56269i
$386$		0			0
$387$	−39132.4	+	67779.4i	−0.261285	+	0.452560i
$388$		0			0
$389$	−37654.1	−	31595.5i	−0.248836	−	0.208798i	0.509835	−	0.860272i	$-0.329706\pi$
$389$	−37654.1	−	31595.5i	−0.248836	−	0.208798i	−0.758671	+	0.651474i	$0.774151\pi$
$390$		0			0
$391$	1779.50	+	3082.19i	0.0116398	+	0.0201607i
$392$		0			0
$393$	−87590.5	−	240653.i	−0.567116	−	1.55814i
$394$		0			0
$395$	−472465.	−	83308.4i	−3.02814	−	0.533942i
$396$		0			0
$397$	−139900.	+	117390.i	−0.887641	+	0.744819i	−0.967736	−	0.251968i	$-0.918922\pi$
$397$	−139900.	+	117390.i	−0.887641	+	0.744819i	0.0800945	+	0.996787i	$0.474478\pi$
$398$		0			0
$399$	170022.	−	49542.1i	1.06797	−	0.311192i
$400$		0			0
$401$	48668.5	+	58000.9i	0.302663	+	0.360700i	0.895843	−	0.444370i	$-0.146572\pi$
$401$	48668.5	+	58000.9i	0.302663	+	0.360700i	−0.593180	+	0.805070i	$0.702128\pi$
$402$		0			0
$403$	19808.5	−	112340.i	0.121967	−	0.691708i
$404$		0			0
$405$	263827.	−	96025.1i	1.60845	−	0.585430i
$406$		0			0
$407$	13835.4	−	7987.85i	0.0835221	−	0.0482215i
$408$		0			0
$409$	9286.85	−	11067.6i	0.0555164	−	0.0661619i	−0.737572	−	0.675269i	$-0.764028\pi$
$409$	9286.85	−	11067.6i	0.0555164	−	0.0661619i	0.793088	+	0.609107i	$0.208472\pi$
$410$		0			0
$411$	166062.	+	95875.7i	0.983072	+	0.567577i
$412$		0			0
$413$	77322.1	−	13634.0i	0.453319	−	0.0799323i
$414$		0			0
$415$	373158.	+	135819.i	2.16669	+	0.788611i
$416$		0			0
$417$			170428.i			0.980096i
$418$		0			0
$419$	216261.			1.23183			0.615915	−	0.787813i	$-0.288787\pi$
$419$	216261.			1.23183			0.615915	+	0.787813i	$0.288787\pi$
$420$		0			0
$421$	70218.5	−	192924.i	0.396175	−	1.08848i	−0.567956	−	0.823059i	$-0.692266\pi$
$421$	70218.5	−	192924.i	0.396175	−	1.08848i	0.964132	−	0.265424i	$-0.0855121\pi$
$422$		0			0
$423$	−94052.5	−	533398.i	−0.525641	−	2.98106i
$424$		0			0
$425$	1920.46	−	3326.33i	0.0106323	−	0.0184157i
$426$		0			0
$427$	−51198.9	−	42961.0i	−0.280805	−	0.235623i
$428$		0			0
$429$	141964.	+	245890.i	0.771374	+	1.33606i
$430$		0			0
$431$	−43386.3	−	119203.i	−0.233560	−	0.641700i	0.766440	−	0.642316i	$-0.222026\pi$
$431$	−43386.3	−	119203.i	−0.233560	−	0.641700i	−1.00000		0.000615630i	$0.999804\pi$
$432$		0			0
$433$	193290.	+	34082.3i	1.03094	+	0.181783i	0.663432	−	0.748237i	$-0.269099\pi$
$433$	193290.	+	34082.3i	1.03094	+	0.181783i	0.367510	+	0.930020i	$0.380210\pi$
$434$		0			0
$435$	−423119.	+	355039.i	−2.23606	+	1.87628i
$436$		0			0
$437$	−309773.	−	207020.i	−1.62211	−	1.08405i
$438$		0			0
$439$	225781.	+	269075.i	1.17154	+	1.39619i	0.901189	+	0.433427i	$0.142696\pi$
$439$	225781.	+	269075.i	1.17154	+	1.39619i	0.270352	+	0.962762i	$0.412860\pi$
$440$		0			0
$441$	39937.1	−	226495.i	0.205352	−	1.16461i
$442$		0			0
$443$	−244865.	+	89123.5i	−1.24773	+	0.454135i	−0.879632	−	0.475654i	$-0.842211\pi$
$443$	−244865.	+	89123.5i	−1.24773	+	0.454135i	−0.368093	+	0.929789i	$0.619989\pi$
$444$		0			0
$445$	372797.	−	215235.i	1.88258	−	1.08691i
$446$		0			0
$447$	−174419.	+	207865.i	−0.872929	+	1.04032i
$448$		0			0
$449$	−96621.1	−	55784.2i	−0.479269	−	0.276706i	0.240843	−	0.970564i	$-0.422576\pi$
$449$	−96621.1	−	55784.2i	−0.479269	−	0.276706i	−0.720112	+	0.693858i	$0.755909\pi$
$450$		0			0
$451$	−178000.	+	31386.1i	−0.875116	+	0.154307i
$452$		0			0
$453$	−309818.	−	112764.i	−1.50977	−	0.549510i
$454$		0			0
$455$			132775.i			0.641350i
$456$		0			0
$457$	−170845.			−0.818032			−0.409016	−	0.912527i	$-0.634128\pi$
$457$	−170845.			−0.818032			−0.409016	+	0.912527i	$0.634128\pi$
$458$		0			0
$459$	1504.36	−	4133.18i	0.00714044	−	0.0196182i
$460$		0			0
$461$	18165.3	+	103020.i	0.0854752	+	0.484754i	0.997253	+	0.0740701i	$0.0235989\pi$
$461$	18165.3	+	103020.i	0.0854752	+	0.484754i	−0.911778	+	0.410684i	$0.865290\pi$
$462$		0			0
$463$	94892.9	−	164359.i	0.442661	−	0.766712i	−0.555225	−	0.831700i	$-0.687368\pi$
$463$	94892.9	−	164359.i	0.442661	−	0.766712i	0.997886	+	0.0649884i	$0.0207011\pi$
$464$		0			0
$465$	561397.	+	471068.i	2.59635	+	2.17860i
$466$		0			0
$467$	−33851.6	−	58632.8i	−0.155219	−	0.268848i	0.777919	−	0.628364i	$-0.216275\pi$
$467$	−33851.6	−	58632.8i	−0.155219	−	0.268848i	−0.933139	+	0.359516i	$0.882942\pi$
$468$		0			0
$469$	20231.1	+	55584.4i	0.0919758	+	0.252701i
$470$		0			0
$471$	−193037.	−	34037.7i	−0.870160	−	0.153433i
$472$		0			0
$473$	66140.8	−	55498.7i	0.295629	−	0.248062i
$474$		0			0
$475$	−26330.7	+	401230.i	−0.116701	+	1.77831i
$476$		0			0
$477$	−86978.0	−	103656.i	−0.382272	−	0.455574i
$478$		0			0
$479$	25878.7	−	146765.i	0.112790	−	0.639664i	−0.875031	−	0.484068i	$-0.839159\pi$
$479$	25878.7	−	146765.i	0.112790	−	0.639664i	0.987821	−	0.155597i	$-0.0497300\pi$
$480$		0			0
$481$	8474.65	−	3084.52i	0.0366296	−	0.0133321i
$482$		0			0
$483$	438470.	−	253151.i	1.87951	−	1.08514i
$484$		0			0
$485$	94621.5	−	112765.i	0.402259	−	0.479394i
$486$		0			0
$487$	−118254.	−	68274.0i	−0.498606	−	0.287871i	0.229531	−	0.973301i	$-0.426281\pi$
$487$	−118254.	−	68274.0i	−0.498606	−	0.287871i	−0.728138	+	0.685431i	$0.759614\pi$
$488$		0			0
$489$	229908.	−	40539.0i	0.961472	−	0.169533i
$490$		0			0
$491$	−73321.2	−	26686.7i	−0.304135	−	0.110696i	0.185445	−	0.982655i	$-0.440627\pi$
$491$	−73321.2	−	26686.7i	−0.304135	−	0.110696i	−0.489580	+	0.871959i	$0.662850\pi$
$492$		0			0
$493$			2925.91i			0.0120384i
$494$		0			0
$495$	−1.21782e6			−4.97017
$496$		0			0
$497$	14251.4	−	39155.5i	0.0576961	−	0.158519i
$498$		0			0
$499$	12863.5	+	72952.8i	0.0516606	+	0.292982i	0.999682	−	0.0252254i	$-0.00803034\pi$
$499$	12863.5	+	72952.8i	0.0516606	+	0.292982i	−0.948021	+	0.318207i	$0.896919\pi$
$500$		0			0
$501$	−176673.	+	306007.i	−0.703875	+	1.21915i
$502$		0			0
$503$	75126.9	+	63039.0i	0.296934	+	0.249157i	0.779067	−	0.626941i	$-0.215693\pi$
$503$	75126.9	+	63039.0i	0.296934	+	0.249157i	−0.482133	+	0.876098i	$0.660138\pi$
$504$		0			0
$505$	−305042.	−	528349.i	−1.19613	−	2.07175i
$506$		0			0
$507$	−97676.0	−	268362.i	−0.379990	−	1.04401i
$508$		0			0
$509$	349030.	+	61543.4i	1.34719	+	0.237545i	0.800269	−	0.599642i	$-0.204690\pi$
$509$	349030.	+	61543.4i	1.34719	+	0.237545i	0.546917	+	0.837187i	$0.315801\pi$
$510$		0			0
$511$	−7123.95	+	5977.70i	−0.0272822	+	0.0228925i
$512$		0			0
$513$	50091.6	+	457726.i	0.190340	+	1.73929i
$514$		0			0
$515$	−146590.	−	174699.i	−0.552700	−	0.658683i
$516$		0			0
$517$	−103757.	+	588437.i	−0.388184	+	2.20150i
$518$		0			0
$519$	103076.	−	37516.5i	0.382668	−	0.139280i
$520$		0			0
$521$	166490.	−	96123.3i	0.613358	−	0.354122i	−0.160921	−	0.986967i	$-0.551446\pi$
$521$	166490.	−	96123.3i	0.613358	−	0.354122i	0.774278	+	0.632845i	$0.218113\pi$
$522$		0			0
$523$	174605.	−	208086.i	0.638341	−	0.760745i	−0.345766	−	0.938321i	$-0.612381\pi$
$523$	174605.	−	208086.i	0.638341	−	0.760745i	0.984107	+	0.177576i	$0.0568255\pi$
$524$		0			0
$525$	−473201.	−	273202.i	−1.71683	−	0.991211i
$526$		0			0
$527$	3823.15	−	674.124i	0.0137657	−	0.00242727i
$528$		0			0
$529$	−737989.	−	268606.i	−2.63717	−	0.959853i
$530$		0			0
$531$			406530.i			1.44179i
$532$		0			0
$533$	−102034.			−0.359161
$534$		0			0
$535$	297824.	−	818264.i	1.04052	−	2.85881i
$536$		0			0
$537$	−106573.	−	604408.i	−0.369573	−	2.09595i
$538$		0			0
$539$	−126860.	+	219728.i	−0.436664	+	0.756324i
$540$		0			0
$541$	−159088.	−	133491.i	−0.543554	−	0.456096i	0.329197	−	0.944261i	$-0.393222\pi$
$541$	−159088.	−	133491.i	−0.543554	−	0.456096i	−0.872751	+	0.488165i	$0.837666\pi$
$542$		0			0
$543$	495320.	+	857919.i	1.67991	+	2.90969i
$544$		0			0
$545$	−173215.	−	475905.i	−0.583168	−	1.60224i
$546$		0			0
$547$	482139.	+	85014.1i	1.61138	+	0.284130i	0.905546	−	0.424248i	$-0.139462\pi$
$547$	482139.	+	85014.1i	1.61138	+	0.284130i	0.705833	+	0.708378i	$0.250573\pi$
$548$		0			0
$549$	265094.	−	222441.i	0.879540	−	0.738022i
$550$		0			0
$551$	−135453.	−	274727.i	−0.446154	−	0.904896i
$552$		0			0
$553$	232391.	+	276953.i	0.759922	+	0.905640i
$554$		0			0
$555$	−10061.0	+	57058.8i	−0.0326629	+	0.185241i
$556$		0			0
$557$	224269.	−	81627.3i	0.722869	−	0.263103i	0.0457256	−	0.998954i	$-0.485440\pi$
$557$	224269.	−	81627.3i	0.722869	−	0.263103i	0.677143	+	0.735851i	$0.263218\pi$
$558$		0			0
$559$	42210.6	−	24370.3i	0.135082	−	0.0779898i
$560$		0			0
$561$	−6211.06	+	7402.05i	−0.0197351	+	0.0235194i
$562$		0			0
$563$	385339.	+	222476.i	1.21570	+	0.701884i	0.963995	−	0.265920i	$-0.0856756\pi$
$563$	385339.	+	222476.i	1.21570	+	0.701884i	0.251704	+	0.967804i	$0.419009\pi$
$564$		0			0
$565$	529460.	−	93358.0i	1.65858	−	0.292452i
$566$		0			0
$567$	−198817.	−	72363.3i	−0.618424	−	0.225088i
$568$		0			0
$569$		−	366070.i		−	1.13068i	−0.824859	−	0.565339i	$-0.808745\pi$
$569$		−	366070.i		−	1.13068i	0.824859	−	0.565339i	$-0.191255\pi$
$570$		0			0
$571$	−144578.			−0.443435			−0.221718	−	0.975111i	$-0.571166\pi$
$571$	−144578.			−0.443435			−0.221718	+	0.975111i	$0.571166\pi$
$572$		0			0
$573$	117497.	−	322820.i	0.357864	−	0.983222i
$574$		0			0
$575$	199620.	+	1.13210e6i	0.603765	+	3.42412i
$576$		0			0
$577$	−199149.	+	344937.i	−0.598174	+	1.03607i	0.394917	+	0.918717i	$0.370774\pi$
$577$	−199149.	+	344937.i	−0.598174	+	1.03607i	−0.993091	+	0.117351i	$0.962560\pi$
$578$		0			0
$579$	135175.	+	113426.i	0.403218	+	0.338340i
$580$		0			0
$581$	−149627.	−	259162.i	−0.443260	−	0.767749i
$582$		0			0
$583$	51055.4	+	140274.i	0.150212	+	0.412704i
$584$		0			0
$585$	−677032.	−	119379.i	−1.97832	−	0.348832i
$586$		0			0
$587$	−126273.	+	105955.i	−0.366465	+	0.307501i	−0.807361	−	0.590057i	$-0.799105\pi$
$587$	−126273.	+	105955.i	−0.366465	+	0.307501i	0.440896	+	0.897558i	$0.354661\pi$
$588$		0			0
$589$	−327765.	+	240286.i	−0.944782	+	0.692625i
$590$		0			0
$591$	424562.	+	505973.i	1.21553	+	1.44861i
$592$		0			0
$593$	52420.3	−	297290.i	0.149070	−	0.845417i	−0.814939	−	0.579547i	$-0.803230\pi$
$593$	52420.3	−	297290.i	0.149070	−	0.845417i	0.964009	−	0.265870i	$-0.0856593\pi$
$594$		0			0
$595$	−4246.12	+	1545.46i	−0.0119938	+	0.00436540i
$596$		0			0
$597$	−364839.	+	210640.i	−1.02365	+	0.591006i
$598$		0			0
$599$	−28443.5	+	33897.6i	−0.0792736	+	0.0944747i	−0.804223	−	0.594327i	$-0.797418\pi$
$599$	−28443.5	+	33897.6i	−0.0792736	+	0.0944747i	0.724950	+	0.688802i	$0.241863\pi$
$600$		0			0
$601$	157578.	+	90977.5i	0.436260	+	0.251875i	0.702010	−	0.712167i	$-0.252286\pi$
$601$	157578.	+	90977.5i	0.436260	+	0.251875i	−0.265750	+	0.964042i	$0.585620\pi$
$602$		0			0
$603$	−301619.	+	53183.6i	−0.829515	+	0.146266i
$604$		0			0
$605$	688753.	+	250686.i	1.88171	+	0.684886i
$606$		0			0
$607$			300602.i			0.815859i	0.913013	+	0.407929i	$0.133749\pi$
$607$			300602.i			0.815859i	−0.913013	+	0.407929i	$0.866251\pi$
$608$		0			0
$609$	416238.			1.12230
$610$		0			0
$611$	−115366.	+	316964.i	−0.309025	+	0.849039i
$612$		0			0
$613$	50234.3	+	284893.i	0.133684	+	0.758159i	0.975767	+	0.218812i	$0.0702180\pi$
$613$	50234.3	+	284893.i	0.133684	+	0.758159i	−0.842083	+	0.539348i	$0.818671\pi$
$614$		0			0
$615$	327754.	−	567687.i	0.866559	−	1.50092i
$616$		0			0
$617$	341235.	+	286330.i	0.896362	+	0.752137i	0.969476	−	0.245186i	$-0.0788492\pi$
$617$	341235.	+	286330.i	0.896362	+	0.752137i	−0.0731138	+	0.997324i	$0.523294\pi$
$618$		0			0
$619$	7560.10	+	13094.5i	0.0197309	+	0.0341749i	0.875722	−	0.482815i	$-0.160386\pi$
$619$	7560.10	+	13094.5i	0.0197309	+	0.0341749i	−0.855991	+	0.516990i	$0.827052\pi$
$620$		0			0
$621$	450246.	+	1.23704e6i	1.16753	+	3.20775i
$622$		0			0
$623$	−319468.	−	56330.8i	−0.823097	−	0.145134i
$624$		0			0
$625$	117857.	−	98893.6i	0.301713	−	0.253168i
$626$		0			0
$627$	240512.	−	982548.i	0.611790	−	2.49930i
$628$		0			0
$629$	197.284	+	235.114i	0.000498644	+	0.000594261i
$630$		0			0
$631$	96573.5	−	547695.i	0.242549	−	1.37556i	−0.583568	−	0.812064i	$-0.698344\pi$
$631$	96573.5	−	547695.i	0.242549	−	1.37556i	0.826117	−	0.563498i	$-0.190545\pi$
$632$		0			0
$633$	−479685.	+	174591.i	−1.19715	+	0.435727i
$634$		0			0
$635$	141912.	−	81933.0i	0.351943	−	0.203194i
$636$		0			0
$637$	−92065.8	+	109720.i	−0.226892	+	0.270400i
$638$		0			0
$639$	186843.	+	107874.i	0.457589	+	0.264189i
$640$		0			0
$641$	404284.	−	71286.3i	0.983945	−	0.173496i	0.341545	−	0.939865i	$-0.389050\pi$
$641$	404284.	−	71286.3i	0.983945	−	0.173496i	0.642400	+	0.766369i	$0.277939\pi$
$642$		0			0
$643$	−536898.	−	195415.i	−1.29858	−	0.472646i	−0.402048	−	0.915619i	$-0.631702\pi$
$643$	−536898.	−	195415.i	−1.29858	−	0.472646i	−0.896535	+	0.442973i	$0.853924\pi$
$644$		0			0
$645$			313131.i			0.752674i
$646$		0			0
$647$	256568.			0.612907			0.306453	−	0.951886i	$-0.400858\pi$
$647$	256568.			0.612907			0.306453	+	0.951886i	$0.400858\pi$
$648$		0			0
$649$	153388.	−	421431.i	0.364169	−	1.00055i
$650$		0			0
$651$	−95900.3	−	543878.i	−0.226286	−	1.28333i
$652$		0			0
$653$	−25726.1	+	44559.0i	−0.0603321	+	0.104498i	−0.894614	−	0.446840i	$-0.852549\pi$
$653$	−25726.1	+	44559.0i	−0.0603321	+	0.104498i	0.834282	+	0.551338i	$0.185883\pi$
$654$		0			0
$655$	−524029.	−	439713.i	−1.22144	−	1.02491i
$656$		0			0
$657$	−24075.6	−	41700.1i	−0.0557758	−	0.0966066i
$658$		0			0
$659$	−85016.0	−	233580.i	−0.195763	−	0.537854i	0.802508	−	0.596642i	$-0.203499\pi$
$659$	−85016.0	−	233580.i	−0.195763	−	0.537854i	−0.998270	+	0.0587880i	$0.981276\pi$
$660$		0			0
$661$	46683.4	+	8231.55i	0.106846	+	0.0188399i	0.226816	−	0.973938i	$-0.427169\pi$
$661$	46683.4	+	8231.55i	0.106846	+	0.0188399i	−0.119969	+	0.992778i	$0.538280\pi$
$662$		0			0
$663$	−4178.57	+	3506.24i	−0.00950607	+	0.00797654i
$664$		0			0
$665$	327141.	−	341681.i	0.739762	−	0.772640i
$666$		0			0
$667$	−562896.	−	670833.i	−1.26525	−	1.50787i
$668$		0			0
$669$	66540.6	−	377371.i	0.148674	−	0.843171i
$670$		0			0
$671$	−358740.	+	130571.i	−0.796774	+	0.290002i
$672$		0			0
$673$	−483380.	+	279079.i	−1.06723	+	0.616166i	−0.927424	−	0.374013i	$-0.877982\pi$
$673$	−483380.	+	279079.i	−1.06723	+	0.616166i	−0.139807	+	0.990179i	$0.544648\pi$
$674$		0			0
$675$	913211.	−	1.08832e6i	2.00430	−	2.38864i
$676$		0			0
$677$	−473966.	−	273645.i	−1.03412	−	0.597049i	−0.115957	−	0.993254i	$-0.536993\pi$
$677$	−473966.	−	273645.i	−1.03412	−	0.597049i	−0.918162	+	0.396206i	$0.870327\pi$
$678$		0			0
$679$	−109246.	+	19263.1i	−0.236956	+	0.0417817i
$680$		0			0
$681$	1.06287e6	+	386853.i	2.29185	+	0.834165i
$682$		0			0
$683$			223188.i			0.478442i	0.970965	+	0.239221i	$0.0768921\pi$
$683$			223188.i			0.478442i	−0.970965	+	0.239221i	$0.923108\pi$
$684$		0			0
$685$	512194.			1.09157
$686$		0			0
$687$	−318454.	+	874945.i	−0.674735	+	1.85382i
$688$		0			0
$689$	14633.1	+	82988.5i	0.0308246	+	0.174815i
$690$		0			0
$691$	−67543.4	+	116989.i	−0.141458	+	0.245012i	−0.928046	−	0.372466i	$-0.878512\pi$
$691$	−67543.4	+	116989.i	−0.141458	+	0.245012i	0.786588	+	0.617478i	$0.211846\pi$
$692$		0			0
$693$	703022.	+	589906.i	1.46387	+	1.22833i
$694$		0			0
$695$	227618.	+	394246.i	0.471235	+	0.816202i
$696$		0			0
$697$	−1187.64	−	3263.00i	−0.00244466	−	0.00671664i
$698$		0			0
$699$	−976113.	−	172115.i	−1.99777	−	0.352261i
$700$		0			0
$701$	318263.	−	267054.i	0.647664	−	0.543455i	−0.258697	−	0.965959i	$-0.583293\pi$
$701$	318263.	−	267054.i	0.647664	−	0.543455i	0.906361	+	0.422504i	$0.138849\pi$
$702$		0			0
$703$	−29408.3	−	12942.8i	−0.0595058	−	0.0261889i
$704$		0			0
$705$	−1.39292e6	−	1.66002e6i	−2.80252	−	3.33991i
$706$		0			0
$707$	−79835.1	+	452768.i	−0.159719	+	0.905809i
$708$		0			0
$709$	25063.6	−	9122.40i	0.0498599	−	0.0181475i	−0.316970	−	0.948436i	$-0.602665\pi$
$709$	25063.6	−	9122.40i	0.0498599	−	0.0181475i	0.366830	+	0.930288i	$0.380443\pi$
$710$		0			0
$711$	−1.62115e6	+	935970.i	−3.20688	+	1.85150i
$712$		0			0
$713$	−746855.	+	890067.i	−1.46912	+	1.75083i
$714$		0			0
$715$	656805.	+	379206.i	1.28477	+	0.741760i
$716$		0			0
$717$	−1.01156e6	+	178366.i	−1.96768	+	0.346955i
$718$		0			0
$719$	−195167.	−	71035.1i	−0.377528	−	0.137409i	0.146285	−	0.989243i	$-0.453269\pi$
$719$	−195167.	−	71035.1i	−0.377528	−	0.137409i	−0.523812	+	0.851834i	$0.675491\pi$
$720$		0			0
$721$			171858.i			0.330598i
$722$		0			0
$723$	867598.			1.65975
$724$		0			0
$725$	−323235.	+	888080.i	−0.614953	+	1.68957i
$726$		0			0
$727$	92752.4	+	526025.i	0.175492	+	0.995262i	0.937575	+	0.347783i	$0.113065\pi$
$727$	92752.4	+	526025.i	0.175492	+	0.995262i	−0.762083	+	0.647479i	$0.775823\pi$
$728$		0			0
$729$	−258697.	+	448076.i	−0.486783	+	0.843133i
$730$		0			0
$731$	1270.67	+	1066.22i	0.00237793	+	0.00199532i
$732$		0			0
$733$	−229907.	−	398210.i	−0.427901	−	0.741147i	0.568785	−	0.822486i	$-0.307414\pi$
$733$	−229907.	−	398210.i	−0.427901	−	0.741147i	−0.996686	+	0.0813395i	$0.974080\pi$
$734$		0			0
$735$	−314715.	−	864672.i	−0.582563	−	1.60058i
$736$		0			0
$737$	332741.	+	58671.3i	0.612593	+	0.108017i
$738$		0			0
$739$	560912.	−	470661.i	1.02708	−	0.861826i	0.0365835	−	0.999331i	$-0.488353\pi$
$739$	560912.	−	470661.i	1.02708	−	0.861826i	0.990501	+	0.137504i	$0.0439081\pi$
$740$		0			0
$741$	230027.	−	522661.i	0.418931	−	0.951883i
$742$		0			0
$743$	291541.	+	347445.i	0.528107	+	0.629373i	0.962478	−	0.271361i	$-0.0874737\pi$
$743$	291541.	+	347445.i	0.528107	+	0.629373i	−0.434371	+	0.900734i	$0.643029\pi$
$744$		0			0
$745$	−125862.	+	713796.i	−0.226767	+	1.28606i
$746$		0			0
$747$	1.45602e6	−	529947.i	2.60931	−	0.949710i
$748$		0			0
$749$	−568293.	+	328104.i	−1.01300	+	0.584854i
$750$		0			0
$751$	165853.	−	197656.i	0.294065	−	0.350453i	−0.598702	−	0.800972i	$-0.704317\pi$
$751$	165853.	−	197656.i	0.294065	−	0.350453i	0.892767	+	0.450519i	$0.148761\pi$
$752$		0			0
$753$	−383202.	−	221242.i	−0.675830	−	0.390191i
$754$		0			0
$755$	−867298.	+	152928.i	−1.52151	+	0.268283i
$756$		0			0
$757$	−630471.	−	229473.i	−1.10020	−	0.400442i	−0.272813	−	0.962067i	$-0.587954\pi$
$757$	−630471.	−	229473.i	−1.10020	−	0.400442i	−0.827392	+	0.561625i	$0.810176\pi$
$758$		0			0
$759$		−	2.89199e6i		−	5.02011i
$760$		0			0
$761$	723766.			1.24977			0.624884	−	0.780718i	$-0.285146\pi$
$761$	723766.			1.24977			0.624884	+	0.780718i	$0.285146\pi$
$762$		0			0
$763$	−130533.	+	358636.i	−0.224218	+	0.616035i
$764$		0			0
$765$	−4062.71	−	23040.8i	−0.00694214	−	0.0393708i
$766$		0			0
$767$	126586.	−	219254.i	0.215177	−	0.372697i
$768$		0			0
$769$	−717195.	−	601798.i	−1.21279	−	1.01765i	−0.999170	−	0.0407312i	$-0.987031\pi$
$769$	−717195.	−	601798.i	−1.21279	−	1.01765i	−0.213616	−	0.976918i	$-0.568524\pi$
$770$		0			0
$771$	−34525.2	−	59799.3i	−0.0580800	−	0.100598i
$772$		0			0
$773$	199327.	+	547647.i	0.333586	+	0.916519i	0.987171	+	0.159666i	$0.0510418\pi$
$773$	199327.	+	547647.i	0.333586	+	0.916519i	−0.653586	+	0.756853i	$0.726736\pi$
$774$		0			0
$775$	1.23488e6	+	217743.i	2.05600	+	0.362527i
$776$		0			0
$777$	33447.1	−	28065.5i	0.0554009	−	0.0464868i
$778$		0			0
$779$	262571.	+	251398.i	0.432685	+	0.414273i
$780$		0			0
$781$	−152990.	−	182326.i	−0.250819	−	0.298915i
$782$		0			0
$783$	−187932.	+	1.06582e6i	−0.306533	+	1.73844i
$784$		0			0
$785$	−492007.	+	179076.i	−0.798421	+	0.290602i
$786$		0			0
$787$	908658.	−	524614.i	1.46707	−	0.847013i	0.467749	−	0.883861i	$-0.345065\pi$
$787$	908658.	−	524614.i	1.46707	−	0.847013i	0.999321	+	0.0368482i	$0.0117318\pi$
$788$		0			0
$789$	404457.	−	482013.i	0.649708	−	0.774292i
$790$		0			0
$791$	−350870.	−	202575.i	−0.560780	−	0.323767i
$792$		0			0
$793$	−212238.	+	37423.2i	−0.337502	+	0.0595106i
$794$		0			0
$795$	−508730.	−	185162.i	−0.804920	−	0.292967i
$796$		0			0
$797$			616025.i			0.969799i	0.874570	+	0.484900i	$0.161144\pi$
$797$			616025.i			0.969799i	−0.874570	+	0.484900i	$0.838856\pi$
$798$		0			0
$799$	−11479.2			−0.0179812
$800$		0			0
$801$	574470.	−	1.57834e6i	0.895370	−	2.46001i
$802$		0			0
$803$	9224.12	+	52312.6i	0.0143052	+	0.0811288i
$804$		0			0
$805$	676200.	−	1.17121e6i	1.04348	−	1.80736i
$806$		0			0
$807$	812086.	+	681421.i	1.24697	+	1.04633i
$808$		0			0
$809$	30601.0	+	53002.5i	0.0467561	+	0.0809840i	0.888456	−	0.458961i	$-0.151778\pi$
$809$	30601.0	+	53002.5i	0.0467561	+	0.0809840i	−0.841700	+	0.539945i	$0.818445\pi$
$810$		0			0
$811$	185309.	+	509132.i	0.281744	+	0.774085i	0.997155	+	0.0753812i	$0.0240174\pi$
$811$	185309.	+	509132.i	0.281744	+	0.774085i	−0.715411	+	0.698704i	$0.753760\pi$
$812$		0			0
$813$	832086.	+	146719.i	1.25889	+	0.221976i
$814$		0			0
$815$	477697.	−	400836.i	0.719180	−	0.603464i
$816$		0			0
$817$	−168669.	−	41287.6i	−0.252692	−	0.0618551i
$818$		0			0
$819$	333011.	+	396867.i	0.496468	+	0.591667i
$820$		0			0
$821$	−226844.	+	1.28650e6i	−0.336544	+	1.90864i	0.0748821	+	0.997192i	$0.476142\pi$
$821$	−226844.	+	1.28650e6i	−0.336544	+	1.90864i	−0.411426	+	0.911443i	$0.634969\pi$
$822$		0			0
$823$	−778911.	+	283500.i	−1.14997	+	0.418556i	−0.845506	−	0.533966i	$-0.820701\pi$
$823$	−778911.	+	283500.i	−1.14997	+	0.418556i	−0.304469	+	0.952522i	$0.598479\pi$
$824$		0			0
$825$	−2.70292e6	+	1.56053e6i	−3.97123	+	2.29279i
$826$		0			0
$827$	−773049.	+	921284.i	−1.13031	+	1.34705i	−0.200199	+	0.979755i	$0.564159\pi$
$827$	−773049.	+	921284.i	−1.13031	+	1.34705i	−0.930106	+	0.367290i	$0.880286\pi$
$828$		0			0
$829$	85456.8	+	49338.5i	0.124348	+	0.0717921i	0.560884	−	0.827895i	$-0.310462\pi$
$829$	85456.8	+	49338.5i	0.124348	+	0.0717921i	−0.436536	+	0.899687i	$0.643795\pi$
$830$		0			0
$831$	−358053.	+	63134.3i	−0.518495	+	0.0914247i
$832$		0			0
$833$	−4580.42	−	1667.14i	−0.00660108	−	0.00240260i
$834$		0			0
$835$			943837.i			1.35371i
$836$		0			0
$837$	1.43595e6			2.04969
$838$		0			0
$839$	365483.	−	1.00416e6i	0.519210	−	1.42652i	−0.352182	−	0.935931i	$-0.614560\pi$
$839$	365483.	−	1.00416e6i	0.519210	−	1.42652i	0.871392	−	0.490587i	$-0.163218\pi$
$840$		0			0
$841$	−2197.34	−	12461.7i	−0.00310675	−	0.0176192i
$842$		0			0
$843$	1.06261e6	−	1.84050e6i	1.49527	−	2.58989i
$844$		0			0
$845$	−584367.	−	490343.i	−0.818413	−	0.686730i
$846$		0			0
$847$	−276173.	−	478346.i	−0.384959	−	0.666768i
$848$		0			0
$849$	496579.	+	1.36434e6i	0.688926	+	1.89281i
$850$		0			0
$851$	−90463.8	−	15951.2i	−0.124915	−	0.0220259i
$852$		0			0
$853$	−32104.5	+	26938.9i	−0.0441233	+	0.0370238i	−0.664583	−	0.747215i	$-0.731391\pi$
$853$	−32104.5	+	26938.9i	−0.0441233	+	0.0370238i	0.620459	+	0.784239i	$0.286946\pi$
$854$		0			0
$855$	1.44812e6	+	1.97532e6i	1.98095	+	2.70213i
$856$		0			0
$857$	−633608.	−	755105.i	−0.862699	−	1.02812i	−0.999297	−	0.0374978i	$-0.988061\pi$
$857$	−633608.	−	755105.i	−0.862699	−	1.02812i	0.136598	−	0.990627i	$-0.456383\pi$
$858$		0			0
$859$	−153699.	+	871671.i	−0.208298	+	1.18132i	0.683867	+	0.729607i	$0.260297\pi$
$859$	−153699.	+	871671.i	−0.208298	+	1.18132i	−0.892165	+	0.451710i	$0.850814\pi$
$860$		0			0
$861$	−464192.	+	168952.i	−0.626169	+	0.227907i
$862$		0			0
$863$	1.16431e6	−	672218.i	1.56332	−	0.902585i	0.566406	−	0.824126i	$-0.308333\pi$
$863$	1.16431e6	−	672218.i	1.56332	−	0.902585i	0.996917	−	0.0784590i	$-0.0250000\pi$
$864$		0			0
$865$	188337.	−	224451.i	0.251711	−	0.299978i
$866$		0			0
$867$	1.12901e6	+	651833.i	1.50196	+	0.867158i
$868$		0			0
$869$	2.03372e6	−	358600.i	2.69310	−	0.474866i
$870$		0			0
$871$	179233.	+	65235.4i	0.236255	+	0.0859898i
$872$		0			0
$873$		−	574375.i		−	0.753646i
$874$		0			0
$875$	−640546.			−0.836632
$876$		0			0
$877$	−167316.	+	459696.i	−0.217539	+	0.597684i	−0.999677	−	0.0254215i	$-0.991907\pi$
$877$	−167316.	+	459696.i	−0.217539	+	0.597684i	0.782138	+	0.623106i	$0.214129\pi$
$878$		0			0
$879$	207518.	+	1.17689e6i	0.268583	+	1.52321i
$880$		0			0
$881$	67861.2	−	117539.i	0.0874318	−	0.151436i	−0.818993	−	0.573803i	$-0.805467\pi$
$881$	67861.2	−	117539.i	0.0874318	−	0.151436i	0.906425	+	0.422367i	$0.138801\pi$
$882$		0			0
$883$	−1.00739e6	−	845297.i	−1.29203	−	1.08415i	−0.991463	−	0.130387i	$-0.958378\pi$
$883$	−1.00739e6	−	845297.i	−1.29203	−	1.08415i	−0.300571	−	0.953759i	$-0.597177\pi$
$884$		0			0
$885$	813245.	+	1.40858e6i	1.03833	+	1.79844i
$886$		0			0
$887$	139490.	+	383246.i	0.177295	+	0.487114i	0.996228	−	0.0867752i	$-0.0276562\pi$
$887$	139490.	+	383246.i	0.177295	+	0.487114i	−0.818933	+	0.573889i	$0.805434\pi$
$888$		0			0
$889$	−121611.	−	21443.4i	−0.153876	−	0.0271325i
$890$		0			0
$891$	−925782.	+	776823.i	−1.16615	+	0.978513i
$892$		0			0
$893$	1.07784e6	−	531422.i	1.35161	−	0.666402i
$894$		0			0
$895$	−1.05376e6	−	1.25582e6i	−1.31552	−	1.56777i
$896$		0			0
$897$	283494.	−	1.60777e6i	0.352337	−	1.99820i
$898$		0			0
$899$	−897609.	+	326703.i	−1.11063	+	0.404235i
$900$		0			0
$901$	−2483.62	+	1433.92i	−0.00305940	+	0.00176634i
$902$		0			0
$903$	151680.	−	180765.i	0.186017	−	0.221686i
$904$		0			0
$905$	2.29162e6	+	1.32307e6i	2.79799	+	1.61542i
$906$		0			0
$907$	−1.10500e6	+	194842.i	−1.34322	+	0.236847i	−0.798614	−	0.601843i	$-0.794433\pi$
$907$	−1.10500e6	+	194842.i	−1.34322	+	0.236847i	−0.544609	+	0.838690i	$0.683322\pi$
$908$		0			0
$909$	−2.23691e6	−	814170.i	−2.70721	−	0.985343i
$910$		0			0
$911$		−	1.01359e6i		−	1.22130i	−0.791899	−	0.610652i	$-0.790907\pi$
$911$		−	1.01359e6i		−	1.22130i	0.791899	−	0.610652i	$-0.209093\pi$
$912$		0			0
$913$	−1.70934e6			−2.05063
$914$		0			0
$915$	473541.	−	1.30104e6i	0.565607	−	1.55399i
$916$		0			0
$917$	89517.0	+	507676.i	0.106455	+	0.603737i
$918$		0			0
$919$	−260018.	+	450364.i	−0.307874	+	0.533253i	−0.977897	−	0.209087i	$-0.932951\pi$
$919$	−260018.	+	450364.i	−0.307874	+	0.533253i	0.670023	+	0.742340i	$0.266284\pi$
$920$		0			0
$921$	−294776.	−	247346.i	−0.347514	−	0.291599i
$922$		0			0
$923$	−67180.2	−	116360.i	−0.0788566	−	0.136584i
$924$		0			0
$925$	33906.3	+	93156.9i	0.0396275	+	0.108876i
$926$		0			0
$927$	−876318.	−	154518.i	−1.01977	−	0.179813i
$928$		0			0
$929$	−638058.	+	535394.i	−0.739313	+	0.620358i	−0.932653	−	0.360774i	$-0.882512\pi$
$929$	−638058.	+	535394.i	−0.739313	+	0.620358i	0.193340	+	0.981132i	$0.438068\pi$
$930$		0			0
$931$	507255.	−	55511.8i	0.585231	−	0.0640451i
$932$		0			0
$933$	848362.	+	1.01104e6i	0.974581	+	1.16146i
$934$		0			0
$935$	−4481.92	+	25418.2i	−0.00512674	+	0.0290752i
$936$		0			0
$937$	1.40887e6	−	512786.i	1.60469	−	0.584059i	0.624310	−	0.781177i	$-0.285380\pi$
$937$	1.40887e6	−	512786.i	1.60469	−	0.584059i	0.980380	+	0.197117i	$0.0631580\pi$
$938$		0			0
$939$	−1.25784e6	+	726217.i	−1.42658	+	0.823636i
$940$		0			0
$941$	551535.	−	657294.i	0.622865	−	0.742302i	−0.358695	−	0.933455i	$-0.616778\pi$
$941$	551535.	−	657294.i	0.622865	−	0.742302i	0.981560	+	0.191153i	$0.0612227\pi$
$942$		0			0
$943$	900040.	+	519638.i	1.01213	+	0.584356i
$944$		0			0
$945$	−1.64599e6	+	290232.i	−1.84316	+	0.324999i
$946$		0			0
$947$	−38539.0	−	14027.1i	−0.0429735	−	0.0156411i	0.320444	−	0.947267i	$-0.396168\pi$
$947$	−38539.0	−	14027.1i	−0.0429735	−	0.0156411i	−0.363417	+	0.931626i	$0.618390\pi$
$948$		0			0
$949$			29986.9i			0.0332965i
$950$		0			0
$951$	178707.			0.197597
$952$		0			0
$953$	342339.	−	940570.i	0.376939	−	1.03563i	−0.595679	−	0.803223i	$-0.703117\pi$
$953$	342339.	−	940570.i	0.376939	−	1.03563i	0.972618	−	0.232409i	$-0.0746608\pi$
$954$		0			0
$955$	−159346.	−	903697.i	−0.174717	−	0.990868i
$956$		0			0
$957$	1.18878e6	−	2.05902e6i	1.29800	−	2.24821i
$958$		0			0
$959$	−295680.	−	248105.i	−0.321503	−	0.269773i
$960$		0			0
$961$	171933.	+	297796.i	0.186171	+	0.322458i
$962$		0			0
$963$	−1.16207e6	−	3.19277e6i	−1.25308	−	3.44282i
$964$		0			0
$965$	464185.	+	81848.3i	0.498467	+	0.0878931i
$966$		0			0
$967$	−129208.	+	108418.i	−0.138177	+	0.115944i	−0.709257	−	0.704950i	$-0.750969\pi$
$967$	−129208.	+	108418.i	−0.138177	+	0.115944i	0.571079	+	0.820895i	$0.306525\pi$
$968$		0			0
$969$	19392.0	+	1272.60i	0.0206526	+	0.00135532i
$970$		0			0
$971$	−664896.	−	792392.i	−0.705204	−	0.840430i	0.287900	−	0.957660i	$-0.407043\pi$
$971$	−664896.	−	792392.i	−0.705204	−	0.840430i	−0.993105	+	0.117231i	$0.962598\pi$
$972$		0			0
$973$	59571.8	−	337848.i	0.0629238	−	0.356859i
$974$		0			0
$975$	−1.65563e6	+	602602.i	−1.74163	+	0.633901i
$976$		0			0
$977$	311898.	−	180075.i	0.326756	−	0.188653i	−0.327644	−	0.944801i	$-0.606255\pi$
$977$	311898.	−	180075.i	0.326756	−	0.188653i	0.654400	+	0.756148i	$0.272921\pi$
$978$		0			0
$979$	−1.19105e6	+	1.41944e6i	−1.24270	+	1.48099i
$980$		0			0
$981$	−1.71135e6	−	988048.i	−1.77828	−	1.02669i
$982$		0			0
$983$	601620.	−	106082.i	0.622609	−	0.109783i	0.146560	−	0.989202i	$-0.453180\pi$
$983$	601620.	−	106082.i	0.622609	−	0.109783i	0.476049	+	0.879419i	$0.342069\pi$
$984$		0			0
$985$	1.65789e6	+	603423.i	1.70877	+	0.621941i
$986$		0			0
$987$			1.63303e6i			1.67633i
$988$		0			0
$989$	−496454.			−0.507559
$990$		0			0
$991$	231581.	−	636265.i	0.235807	−	0.647874i	−0.764189	−	0.644992i	$-0.776861\pi$
$991$	231581.	−	636265.i	0.235807	−	0.647874i	0.999996	−	0.00288150i	$-0.000917211\pi$
$992$		0			0
$993$	49556.3	+	281048.i	0.0502575	+	0.285024i
$994$		0			0
$995$	−562648.	+	974535.i	−0.568317	+	0.984354i
$996$		0			0
$997$	461965.	+	387635.i	0.464749	+	0.389971i	0.844875	−	0.534964i	$-0.179675\pi$
$997$	461965.	+	387635.i	0.464749	+	0.389971i	−0.380126	+	0.924935i	$0.624119\pi$
$998$		0			0
$999$	56762.7	+	98315.9i	0.0568764	+	0.0985129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.13.7	✓	42
19.3	odd	18	inner	76.5.j.a.41.7	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.7	✓	42	1.1	even	1	trivial
76.5.j.a.41.7	yes	42	19.3	odd	18	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +O(q^{10})\)	\(q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +(89.7471 + 155.447i) q^{11} +(34.6560 + 95.2165i) q^{13} +(-641.081 - 113.040i) q^{15} +(-2.64161 + 2.21657i) q^{17} +(145.418 - 330.416i) q^{19} +(315.328 + 375.793i) q^{21} +(179.219 - 1016.40i) q^{23} +(-1046.66 + 380.953i) q^{25} +(-1104.62 + 637.755i) q^{27} +(545.399 - 649.981i) q^{29} +(-974.956 - 562.891i) q^{31} +(2759.53 - 486.579i) q^{33} +(1231.34 + 448.170i) q^{35} -89.0040i q^{37} +1581.83 q^{39} +(-344.404 + 946.243i) q^{41} +(-83.5286 - 473.714i) q^{43} +(-3392.35 + 5875.73i) q^{45} +(2550.07 + 2139.76i) q^{47} +(706.764 + 1224.15i) q^{49} +(18.4119 + 50.5863i) q^{51} +(819.014 + 144.414i) q^{53} +(5733.68 - 4811.13i) q^{55} +(-4070.64 - 3897.42i) q^{57} +(-1606.04 - 1914.01i) q^{59} +(-369.330 + 2094.57i) q^{61} +(4804.53 - 1748.70i) q^{63} +(3659.20 - 2112.64i) q^{65} +(1209.96 - 1441.98i) q^{67} +(-13953.3 - 8055.95i) q^{69} +(-1305.86 + 230.258i) q^{71} +(278.093 + 101.218i) q^{73} +17388.1i q^{75} -5640.44 q^{77} +(3934.97 - 10811.2i) q^{79} +(1169.16 + 6630.64i) q^{81} +(-4761.55 + 8247.25i) q^{83} +(110.153 + 92.4296i) q^{85} +(-6622.92 - 11471.2i) q^{87} +(3530.74 + 9700.62i) q^{89} +(-3135.74 - 552.916i) q^{91} +(-13463.0 + 11296.8i) q^{93} +(-14621.8 - 3579.18i) q^{95} +(2269.14 + 2704.25i) q^{97} +(5071.34 - 28761.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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