LMFDB - Embedded newform 76.5.j.a.41.7

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			41.7
Character	$\chi$	$=$	76.41
Dual form			76.5.j.a.13.7

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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	0.764423	+	0.644714i	$0.223024\pi$
$3$	5.33930	+	14.6696i	0.593256	+	1.62996i	−0.171168	+	0.985242i	$0.554754\pi$
$4$		0			0
$5$	−7.24101	+	41.0658i	−0.289640	+	1.64263i	0.398583	+	0.917132i	$0.369502\pi$
$5$	−7.24101	+	41.0658i	−0.289640	+	1.64263i	−0.688223	+	0.725499i	$0.741609\pi$
$6$		0			0
$7$	−15.7120	−	27.2140i	−0.320654	−	0.555389i	0.659969	−	0.751293i	$-0.270569\pi$
$7$	−15.7120	−	27.2140i	−0.320654	−	0.555389i	−0.980623	+	0.195904i	$0.937236\pi$
$8$		0			0
$9$	−124.640	+	104.585i	−1.53876	+	1.29117i
$10$		0			0
$11$	89.7471	−	155.447i	0.741712	−	1.28468i	−0.210004	−	0.977701i	$-0.567348\pi$
$11$	89.7471	−	155.447i	0.741712	−	1.28468i	0.951715	−	0.306982i	$-0.0993190\pi$
$12$		0			0
$13$	34.6560	−	95.2165i	0.205065	−	0.563411i	−0.793941	−	0.607995i	$-0.791974\pi$
$13$	34.6560	−	95.2165i	0.205065	−	0.563411i	0.999006	+	0.0445838i	$0.0141962\pi$
$14$		0			0
$15$	−641.081	+	113.040i	−2.84925	+	0.502399i
$16$		0			0
$17$	−2.64161	−	2.21657i	−0.00914052	−	0.00766981i	0.638206	−	0.769866i	$-0.279677\pi$
$17$	−2.64161	−	2.21657i	−0.00914052	−	0.00766981i	−0.647346	+	0.762196i	$0.724121\pi$
$18$		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	0.386040	+	0.922482i	$0.373843\pi$
$23$	179.219	+	1016.40i	0.338788	+	1.92137i	−0.0472516	+	0.998883i	$0.515046\pi$
$24$		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	0.985689	−	0.168575i	$-0.0539164\pi$
$29$	545.399	+	649.981i	0.648512	+	0.772867i	−0.337177	+	0.941441i	$0.609472\pi$
$30$		0			0
$31$	−974.956	+	562.891i	−1.01452	+	0.585735i	−0.912513	−	0.409048i	$-0.865861\pi$
$31$	−974.956	+	562.891i	−1.01452	+	0.585735i	−0.102010	+	0.994783i	$0.532527\pi$
$32$		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	$0.0103491\pi$
$37$			89.0040i			0.0650139i	−0.999472	+	0.0325069i	$0.989651\pi$
$38$		0			0
$39$	1581.83			1.03999
$40$		0			0
$41$	−344.404	−	946.243i	−0.204881	−	0.562905i	0.794112	−	0.607771i	$-0.207936\pi$
$41$	−344.404	−	946.243i	−0.204881	−	0.562905i	−0.998993	+	0.0448660i	$0.985714\pi$
$42$		0			0
$43$	−83.5286	+	473.714i	−0.0451750	+	0.256200i	−0.999028	−	0.0440728i	$-0.985967\pi$
$43$	−83.5286	+	473.714i	−0.0451750	+	0.256200i	0.953853	+	0.300273i	$0.0970778\pi$
$44$		0			0
$45$	−3392.35	−	5875.73i	−1.67524	−	2.90159i
$46$		0			0
$47$	2550.07	−	2139.76i	1.15440	−	0.968656i	0.154586	−	0.987979i	$-0.450596\pi$
$47$	2550.07	−	2139.76i	1.15440	−	0.968656i	0.999813	+	0.0193232i	$0.00615114\pi$
$48$		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	−0.0259511	−	0.999663i	$-0.508261\pi$
$53$	819.014	−	144.414i	0.291568	−	0.0514113i	0.317519	+	0.948252i	$0.397150\pi$
$54$		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	−0.945699	−	0.325044i	$-0.894621\pi$
$59$	−1606.04	+	1914.01i	−0.461374	+	0.549844i	0.484325	+	0.874888i	$0.339065\pi$
$60$		0			0
$61$	−369.330	−	2094.57i	−0.0992555	−	0.562906i	−0.993360	−	0.115048i	$-0.963298\pi$
$61$	−369.330	−	2094.57i	−0.0992555	−	0.562906i	0.894104	−	0.447859i	$-0.147813\pi$
$62$		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	0.883788	−	0.467888i	$-0.154985\pi$
$67$	1209.96	+	1441.98i	0.269540	+	0.321225i	−0.614248	+	0.789113i	$0.710541\pi$
$68$		0			0
$69$	−13953.3	+	8055.95i	−2.93075	+	1.69207i
$70$		0			0
$71$	−1305.86	−	230.258i	−0.259048	−	0.0456771i	0.0426159	−	0.999092i	$-0.486431\pi$
$71$	−1305.86	−	230.258i	−0.259048	−	0.0456771i	−0.301664	+	0.953414i	$0.597542\pi$
$72$		0			0
$73$	278.093	−	101.218i	0.0521849	−	0.0189937i	−0.315796	−	0.948827i	$-0.602271\pi$
$73$	278.093	−	101.218i	0.0521849	−	0.0189937i	0.367981	+	0.929833i	$0.380049\pi$
$74$		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	0.679686	+	0.733503i	$0.262116\pi$
$79$	3934.97	+	10811.2i	0.630503	+	1.73229i	−0.0491834	+	0.998790i	$0.515662\pi$
$80$		0			0
$81$	1169.16	−	6630.64i	0.178199	−	1.01061i
$82$		0			0
$83$	−4761.55	−	8247.25i	−0.691182	−	1.19716i	−0.971451	−	0.237241i	$-0.923757\pi$
$83$	−4761.55	−	8247.25i	−0.691182	−	1.19716i	0.280269	−	0.959921i	$-0.409576\pi$
$84$		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	−0.489917	−	0.871769i	$-0.662973\pi$
$89$	3530.74	−	9700.62i	0.445744	−	1.22467i	0.935661	−	0.352901i	$-0.114805\pi$
$90$		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	−0.631861	−	0.775082i	$-0.717709\pi$
$97$	2269.14	−	2704.25i	0.241167	−	0.287411i	0.873028	+	0.487670i	$0.162153\pi$
$98$		0			0
$99$	5071.34	+	28761.0i	0.517431	+	2.93450i
$100$		0			0
$101$	13748.2	+	5003.95i	1.34773	+	0.490535i	0.912240	−	0.409656i	$-0.134351\pi$
$101$	13748.2	+	5003.95i	1.34773	+	0.490535i	0.435495	+	0.900191i	$0.356573\pi$
$102$		0			0
$103$	4736.29	+	2734.50i	0.446441	+	0.257753i	0.706326	−	0.707887i	$-0.250351\pi$
$103$	4736.29	+	2734.50i	0.446441	+	0.257753i	−0.259885	+	0.965640i	$0.583685\pi$
$104$		0			0
$105$	13149.0	+	15670.3i	1.19265	+	1.42134i
$106$		0			0
$107$	18084.6	−	10441.2i	1.57958	−	0.911972i	0.584665	−	0.811275i	$-0.301226\pi$
$107$	18084.6	−	10441.2i	1.57958	−	0.911972i	0.994917	−	0.100697i	$-0.0321072\pi$
$108$		0			0
$109$	11960.7	+	2109.00i	1.00671	+	0.177510i	0.652607	−	0.757696i	$-0.273675\pi$
$109$	11960.7	+	2109.00i	1.00671	+	0.177510i	0.354103	+	0.935206i	$0.384786\pi$
$110$		0			0
$111$	−1305.65	+	475.219i	−0.105970	+	0.0385698i
$112$		0			0
$113$		−	12893.0i		−	1.00971i	−0.863205	−	0.504854i	$-0.831546\pi$
$113$		−	12893.0i		−	1.00971i	0.863205	−	0.504854i	$-0.168454\pi$
$114$		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	−0.891029	−	0.453947i	$-0.850015\pi$
$127$	1344.04	−	3692.72i	0.0833306	−	0.228949i	0.974359	+	0.224998i	$0.0722377\pi$
$128$		0			0
$129$	−7395.18	+	1303.97i	−0.444395	+	0.0783589i
$130$		0			0
$131$	12566.9	+	10544.8i	0.732292	+	0.614466i	0.930755	−	0.365643i	$-0.119151\pi$
$131$	12566.9	+	10544.8i	0.732292	+	0.614466i	−0.198464	+	0.980108i	$0.563595\pi$
$132$		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	−0.987414	−	0.158156i	$-0.949445\pi$
$137$	−2132.93	−	12096.4i	−0.113641	−	0.644490i	0.873773	−	0.486334i	$-0.161666\pi$
$138$		0			0
$139$	−10258.7	−	3733.87i	−0.530963	−	0.193255i	0.0626054	−	0.998038i	$-0.480059\pi$
$139$	−10258.7	−	3733.87i	−0.530963	−	0.193255i	−0.593568	+	0.804784i	$0.702281\pi$
$140$		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	−0.682580	−	0.730811i	$-0.739142\pi$
$149$	−16333.5	+	5944.92i	−0.735711	+	0.267777i	−0.0531308	+	0.998588i	$0.516920\pi$
$150$		0			0
$151$			21119.7i			0.926262i	0.886290	+	0.463131i	$0.153274\pi$
$151$			21119.7i			0.926262i	−0.886290	+	0.463131i	$0.846726\pi$
$152$		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	0.908101	+	0.418751i	$0.137532\pi$
$157$	−2180.35	+	12365.4i	−0.0884561	+	0.501659i	−0.996557	+	0.0829083i	$0.973579\pi$
$158$		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	−0.690310	−	0.723514i	$-0.742526\pi$
$163$	7477.22	−	12950.9i	0.281426	−	0.487445i	0.971736	+	0.236069i	$0.0758591\pi$
$164$		0			0
$165$	−39963.5	+	109799.i	−1.46790	+	4.03301i
$166$		0			0
$167$	−22290.5	+	3930.42i	−0.799258	+	0.140931i	−0.558337	−	0.829614i	$-0.688560\pi$
$167$	−22290.5	+	3930.42i	−0.799258	+	0.140931i	−0.240921	+	0.970545i	$0.577449\pi$
$168$		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	−0.685294	−	0.728266i	$-0.740326\pi$
$173$	4516.54	−	5382.60i	0.150908	−	0.179846i	0.836203	+	0.548421i	$0.184771\pi$
$174$		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	0.926151	−	0.377154i	$-0.123097\pi$
$179$	34046.8	+	19656.9i	1.06260	+	0.613493i	0.136451	+	0.990647i	$0.456431\pi$
$180$		0			0
$181$	−40789.7	−	48611.3i	−1.24507	−	1.48382i	−0.813314	−	0.581825i	$-0.802339\pi$
$181$	−40789.7	−	48611.3i	−1.24507	−	1.48382i	−0.431755	−	0.901991i	$-0.642106\pi$
$182$		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	0.876919	−	0.480638i	$-0.159595\pi$
$193$	−3866.00	−	10621.8i	−0.103788	−	0.285155i	−0.980707	+	0.195483i	$0.937373\pi$
$194$		0			0
$195$	−11454.0	+	64959.0i	−0.301224	+	1.70832i
$196$		0			0
$197$	−21154.9	−	36641.4i	−0.545103	−	0.944146i	−0.998600	−	0.0528886i	$-0.983157\pi$
$197$	−21154.9	−	36641.4i	−0.545103	−	0.944146i	0.453497	−	0.891258i	$-0.350176\pi$
$198$		0			0
$199$	−20672.4	+	17346.2i	−0.522018	+	0.438025i	−0.865335	−	0.501194i	$-0.832894\pi$
$199$	−20672.4	+	17346.2i	−0.522018	+	0.438025i	0.343316	+	0.939220i	$0.388450\pi$
$200$		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	−0.948573	−	0.316558i	$-0.897473\pi$
$211$	−21018.7	+	25049.1i	−0.472107	+	0.562635i	0.476466	+	0.879193i	$0.341917\pi$
$212$		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	0.411327	−	0.911488i	$-0.365066\pi$
$223$	24173.3	+	4262.40i	0.486100	+	0.0857126i	0.0747734	+	0.997201i	$0.476177\pi$
$224$		0			0
$225$	170297.	−	61983.1i	3.36390	−	1.22436i
$226$		0			0
$227$		−	72453.9i		−	1.40608i	−0.711150	−	0.703040i	$-0.751825\pi$
$227$		−	72453.9i		−	1.40608i	0.711150	−	0.703040i	$-0.248175\pi$
$228$		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	0.697344	+	0.716737i	$0.254365\pi$
$233$	−11025.2	+	62527.0i	−0.203083	+	1.15174i	−0.900427	+	0.435007i	$0.856746\pi$
$234$		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	0.419991	+	0.907528i	$0.362033\pi$
$239$	−32898.7	+	56982.2i	−0.575947	+	0.997570i	−0.995938	+	0.0900414i	$0.971300\pi$
$240$		0			0
$241$	19008.1	−	52224.2i	0.327268	−	0.899161i	−0.661532	−	0.749917i	$-0.730094\pi$
$241$	19008.1	−	52224.2i	0.327268	−	0.899161i	0.988800	−	0.149245i	$-0.0476842\pi$
$242$		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	0.998630	+	0.0523352i	$0.0166664\pi$
$251$	4921.92	+	27913.6i	0.0781244	+	0.443066i	−0.920505	+	0.390730i	$0.872222\pi$
$252$		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	0.787138	−	0.616777i	$-0.211562\pi$
$257$	2843.15	+	3388.34i	0.0430461	+	0.0513004i	−0.744092	+	0.668077i	$0.767118\pi$
$258$		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	−0.0533918	−	0.998574i	$-0.517003\pi$
$263$	37875.5	−	13785.5i	0.547579	−	0.199302i	0.600970	+	0.799271i	$0.294781\pi$
$264$		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	−0.990307	−	0.138896i	$-0.955644\pi$
$269$	−23225.6	−	63811.9i	−0.320969	−	0.881854i	0.669338	−	0.742958i	$-0.266578\pi$
$270$		0			0
$271$	9398.41	−	53301.1i	0.127972	−	0.725767i	−0.851526	−	0.524313i	$-0.824322\pi$
$271$	9398.41	−	53301.1i	0.127972	−	0.725767i	0.979498	−	0.201454i	$-0.0645667\pi$
$272$		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	−0.931877	−	0.362775i	$-0.881829\pi$
$277$	−11644.8	+	20169.4i	−0.151766	+	0.262866i	0.780111	+	0.625641i	$0.215163\pi$
$278$		0			0
$279$	62648.2	−	172124.i	0.804822	−	2.21123i
$280$		0			0
$281$	134068.	−	23639.8i	1.69790	−	0.299385i	0.760939	−	0.648824i	$-0.224739\pi$
$281$	134068.	−	23639.8i	1.69790	−	0.299385i	0.936959	+	0.349438i	$0.113628\pi$
$282$		0			0
$283$	−71245.6	−	59782.1i	−0.889580	−	0.746446i	0.0785460	−	0.996910i	$-0.474972\pi$
$283$	−71245.6	−	59782.1i	−0.889580	−	0.746446i	−0.968126	+	0.250464i	$0.919417\pi$
$284$		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	0.0614379	−	0.998111i	$-0.480431\pi$
$293$	−66295.4	−	38275.7i	−0.772233	−	0.445849i	−0.833670	+	0.552262i	$0.813765\pi$
$294$		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	0.976349	−	0.216202i	$-0.0693671\pi$
$307$	8430.56	+	23162.8i	0.0894499	+	0.245762i	−0.886899	+	0.461964i	$0.847145\pi$
$308$		0			0
$309$	−14825.5	+	84079.9i	−0.155272	+	0.880593i
$310$		0			0
$311$	−42271.8	−	73217.0i	−0.437049	−	0.756992i	0.560411	−	0.828215i	$-0.310643\pi$
$311$	−42271.8	−	73217.0i	−0.437049	−	0.756992i	−0.997460	+	0.0712230i	$0.977310\pi$
$312$		0			0
$313$	−71271.8	+	59804.1i	−0.727493	+	0.610439i	−0.929447	−	0.368956i	$-0.879715\pi$
$313$	−71271.8	+	59804.1i	−0.727493	+	0.610439i	0.201954	+	0.979395i	$0.435271\pi$
$314$		0			0
$315$	−106602.	+	184639.i	−1.07434	+	1.86081i
$316$		0			0
$317$	3915.26	−	10757.1i	0.0389621	−	0.107047i	−0.918686	−	0.394989i	$-0.870749\pi$
$317$	3915.26	−	10757.1i	0.0389621	−	0.107047i	0.957648	+	0.287941i	$0.0929708\pi$
$318$		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	0.426006	−	0.904720i	$-0.359920\pi$
$331$	−15831.7	−	9140.42i	−0.144501	−	0.0834277i	−0.570507	+	0.821292i	$0.693253\pi$
$332$		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	−0.999060	−	0.0433406i	$-0.986200\pi$
$337$	−221765.	−	39103.2i	−1.95269	−	0.344313i	−0.953633	−	0.300972i	$-0.902689\pi$
$338$		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	0.807711	+	0.589579i	$0.200706\pi$
$347$	−18415.0	+	104437.i	−0.152937	+	0.867349i	−0.960648	+	0.277770i	$0.910405\pi$
$348$		0			0
$349$	−22498.0	−	38967.7i	−0.184711	−	0.319929i	0.758768	−	0.651361i	$-0.225802\pi$
$349$	−22498.0	−	38967.7i	−0.184711	−	0.319929i	−0.943479	+	0.331432i	$0.892468\pi$
$350$		0			0
$351$	−99006.7	+	83076.5i	−0.803619	+	0.674316i
$352$		0			0
$353$	4393.73	−	7610.16i	0.0352601	−	0.0610724i	−0.847857	−	0.530225i	$-0.822107\pi$
$353$	4393.73	−	7610.16i	0.0352601	−	0.0610724i	0.883117	+	0.469153i	$0.155441\pi$
$354$		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	0.646635	−	0.762799i	$-0.276176\pi$
$359$	993.881	+	833.965i	0.00771162	+	0.00647081i	−0.638924	+	0.769270i	$0.720620\pi$
$360$		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	0.163681	−	0.986513i	$-0.447663\pi$
$367$	−46474.5	−	16915.3i	−0.345051	−	0.125588i	−0.508732	+	0.860925i	$0.669885\pi$
$368$		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	−0.131746	−	0.991284i	$-0.542058\pi$
$373$	91944.6	−	53084.2i	0.660858	−	0.381547i	0.792604	+	0.609737i	$0.208725\pi$
$374$		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	$-0.726713\pi$
$379$		−	217444.i		−	1.51380i	0.653531	−	0.756900i	$-0.273287\pi$
$380$		0			0
$381$	61346.9			0.422613
$382$		0			0
$383$	22149.4	+	60855.1i	0.150996	+	0.414858i	0.992011	−	0.126154i	$-0.0402635\pi$
$383$	22149.4	+	60855.1i	0.150996	+	0.414858i	−0.841015	+	0.541012i	$0.818041\pi$
$384$		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	−0.758671	−	0.651474i	$-0.774151\pi$
$389$	−37654.1	+	31595.5i	−0.248836	+	0.208798i	0.509835	+	0.860272i	$0.329706\pi$
$390$		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	0.0800945	−	0.996787i	$-0.474478\pi$
$397$	−139900.	−	117390.i	−0.887641	−	0.744819i	−0.967736	+	0.251968i	$0.918922\pi$
$398$		0			0
$399$	170022.	+	49542.1i	1.06797	+	0.311192i
$400$		0			0
$401$	48668.5	−	58000.9i	0.302663	−	0.360700i	−0.593180	−	0.805070i	$-0.702128\pi$
$401$	48668.5	−	58000.9i	0.302663	−	0.360700i	0.895843	+	0.444370i	$0.146572\pi$
$402$		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	0.793088	−	0.609107i	$-0.208472\pi$
$409$	9286.85	+	11067.6i	0.0555164	+	0.0661619i	−0.737572	+	0.675269i	$0.764028\pi$
$410$		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	0.964132	+	0.265424i	$0.0855121\pi$
$421$	70218.5	+	192924.i	0.396175	+	1.08848i	−0.567956	+	0.823059i	$0.692266\pi$
$422$		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	−1.00000		0.000615630i	$-0.999804\pi$
$431$	−43386.3	+	119203.i	−0.233560	+	0.641700i	0.766440	+	0.642316i	$0.222026\pi$
$432$		0			0
$433$	193290.	−	34082.3i	1.03094	−	0.181783i	0.367510	−	0.930020i	$-0.380210\pi$
$433$	193290.	−	34082.3i	1.03094	−	0.181783i	0.663432	+	0.748237i	$0.269099\pi$
$434$		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	0.270352	−	0.962762i	$-0.412860\pi$
$439$	225781.	−	269075.i	1.17154	−	1.39619i	0.901189	−	0.433427i	$-0.142696\pi$
$440$		0			0
$441$	39937.1	+	226495.i	0.205352	+	1.16461i
$442$		0			0
$443$	−244865.	−	89123.5i	−1.24773	−	0.454135i	−0.368093	−	0.929789i	$-0.619989\pi$
$443$	−244865.	−	89123.5i	−1.24773	−	0.454135i	−0.879632	+	0.475654i	$0.842211\pi$
$444$		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	−0.720112	−	0.693858i	$-0.755909\pi$
$449$	−96621.1	+	55784.2i	−0.479269	+	0.276706i	0.240843	+	0.970564i	$0.422576\pi$
$450$		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	−0.911778	−	0.410684i	$-0.865290\pi$
$461$	18165.3	−	103020.i	0.0854752	−	0.484754i	0.997253	−	0.0740701i	$-0.0235989\pi$
$462$		0			0
$463$	94892.9	+	164359.i	0.442661	+	0.766712i	0.997886	−	0.0649884i	$-0.0207011\pi$
$463$	94892.9	+	164359.i	0.442661	+	0.766712i	−0.555225	+	0.831700i	$0.687368\pi$
$464$		0			0
$465$	561397.	−	471068.i	2.59635	−	2.17860i
$466$		0			0
$467$	−33851.6	+	58632.8i	−0.155219	+	0.268848i	−0.933139	−	0.359516i	$-0.882942\pi$
$467$	−33851.6	+	58632.8i	−0.155219	+	0.268848i	0.777919	+	0.628364i	$0.216275\pi$
$468$		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	0.987821	+	0.155597i	$0.0497300\pi$
$479$	25878.7	+	146765.i	0.112790	+	0.639664i	−0.875031	+	0.484068i	$0.839159\pi$
$480$		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	−0.728138	−	0.685431i	$-0.759614\pi$
$487$	−118254.	+	68274.0i	−0.498606	+	0.287871i	0.229531	+	0.973301i	$0.426281\pi$
$488$		0			0
$489$	229908.	+	40539.0i	0.961472	+	0.169533i
$490$		0			0
$491$	−73321.2	+	26686.7i	−0.304135	+	0.110696i	−0.489580	−	0.871959i	$-0.662850\pi$
$491$	−73321.2	+	26686.7i	−0.304135	+	0.110696i	0.185445	+	0.982655i	$0.440627\pi$
$492$		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	−0.948021	−	0.318207i	$-0.896919\pi$
$499$	12863.5	−	72952.8i	0.0516606	−	0.292982i	0.999682	+	0.0252254i	$0.00803034\pi$
$500$		0			0
$501$	−176673.	−	306007.i	−0.703875	−	1.21915i
$502$		0			0
$503$	75126.9	−	63039.0i	0.296934	−	0.249157i	−0.482133	−	0.876098i	$-0.660138\pi$
$503$	75126.9	−	63039.0i	0.296934	−	0.249157i	0.779067	+	0.626941i	$0.215693\pi$
$504$		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	0.546917	−	0.837187i	$-0.315801\pi$
$509$	349030.	−	61543.4i	1.34719	−	0.237545i	0.800269	+	0.599642i	$0.204690\pi$
$510$		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	0.774278	−	0.632845i	$-0.218113\pi$
$521$	166490.	+	96123.3i	0.613358	+	0.354122i	−0.160921	+	0.986967i	$0.551446\pi$
$522$		0			0
$523$	174605.	+	208086.i	0.638341	+	0.760745i	0.984107	−	0.177576i	$-0.0568255\pi$
$523$	174605.	+	208086.i	0.638341	+	0.760745i	−0.345766	+	0.938321i	$0.612381\pi$
$524$		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	−0.872751	−	0.488165i	$-0.837666\pi$
$541$	−159088.	+	133491.i	−0.543554	+	0.456096i	0.329197	+	0.944261i	$0.393222\pi$
$542$		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	0.705833	−	0.708378i	$-0.250573\pi$
$547$	482139.	−	85014.1i	1.61138	−	0.284130i	0.905546	+	0.424248i	$0.139462\pi$
$548$		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	0.677143	−	0.735851i	$-0.263218\pi$
$557$	224269.	+	81627.3i	0.722869	+	0.263103i	0.0457256	+	0.998954i	$0.485440\pi$
$558$		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	0.251704	−	0.967804i	$-0.419009\pi$
$563$	385339.	−	222476.i	1.21570	−	0.701884i	0.963995	+	0.265920i	$0.0856756\pi$
$564$		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	$0.191255\pi$
$569$			366070.i			1.13068i	−0.824859	+	0.565339i	$0.808745\pi$
$570$		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	−0.993091	−	0.117351i	$-0.962560\pi$
$577$	−199149.	−	344937.i	−0.598174	−	1.03607i	0.394917	−	0.918717i	$-0.370774\pi$
$578$		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	0.440896	−	0.897558i	$-0.354661\pi$
$587$	−126273.	−	105955.i	−0.366465	−	0.307501i	−0.807361	+	0.590057i	$0.799105\pi$
$588$		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	0.964009	+	0.265870i	$0.0856593\pi$
$593$	52420.3	+	297290.i	0.149070	+	0.845417i	−0.814939	+	0.579547i	$0.803230\pi$
$594$		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	0.724950	−	0.688802i	$-0.241863\pi$
$599$	−28443.5	−	33897.6i	−0.0792736	−	0.0944747i	−0.804223	+	0.594327i	$0.797418\pi$
$600$		0			0
$601$	157578.	−	90977.5i	0.436260	−	0.251875i	−0.265750	−	0.964042i	$-0.585620\pi$
$601$	157578.	−	90977.5i	0.436260	−	0.251875i	0.702010	+	0.712167i	$0.252286\pi$
$602$		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	$-0.866251\pi$
$607$		−	300602.i		−	0.815859i	0.913013	−	0.407929i	$-0.133749\pi$
$608$		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	−0.842083	−	0.539348i	$-0.818671\pi$
$613$	50234.3	−	284893.i	0.133684	−	0.758159i	0.975767	−	0.218812i	$-0.0702180\pi$
$614$		0			0
$615$	327754.	+	567687.i	0.866559	+	1.50092i
$616$		0			0
$617$	341235.	−	286330.i	0.896362	−	0.752137i	−0.0731138	−	0.997324i	$-0.523294\pi$
$617$	341235.	−	286330.i	0.896362	−	0.752137i	0.969476	+	0.245186i	$0.0788492\pi$
$618$		0			0
$619$	7560.10	−	13094.5i	0.0197309	−	0.0341749i	−0.855991	−	0.516990i	$-0.827052\pi$
$619$	7560.10	−	13094.5i	0.0197309	−	0.0341749i	0.875722	+	0.482815i	$0.160386\pi$
$620$		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	0.826117	+	0.563498i	$0.190545\pi$
$631$	96573.5	+	547695.i	0.242549	+	1.37556i	−0.583568	+	0.812064i	$0.698344\pi$
$632$		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	0.642400	−	0.766369i	$-0.277939\pi$
$641$	404284.	+	71286.3i	0.983945	+	0.173496i	0.341545	+	0.939865i	$0.389050\pi$
$642$		0			0
$643$	−536898.	+	195415.i	−1.29858	+	0.472646i	−0.896535	−	0.442973i	$-0.853924\pi$
$643$	−536898.	+	195415.i	−1.29858	+	0.472646i	−0.402048	+	0.915619i	$0.631702\pi$
$644$		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	0.834282	−	0.551338i	$-0.185883\pi$
$653$	−25726.1	−	44559.0i	−0.0603321	−	0.104498i	−0.894614	+	0.446840i	$0.852549\pi$
$654$		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	−0.998270	−	0.0587880i	$-0.981276\pi$
$659$	−85016.0	+	233580.i	−0.195763	+	0.537854i	0.802508	+	0.596642i	$0.203499\pi$
$660$		0			0
$661$	46683.4	−	8231.55i	0.106846	−	0.0188399i	−0.119969	−	0.992778i	$-0.538280\pi$
$661$	46683.4	−	8231.55i	0.106846	−	0.0188399i	0.226816	+	0.973938i	$0.427169\pi$
$662$		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	−0.139807	−	0.990179i	$-0.544648\pi$
$673$	−483380.	−	279079.i	−1.06723	−	0.616166i	−0.927424	+	0.374013i	$0.877982\pi$
$674$		0			0
$675$	913211.	+	1.08832e6i	2.00430	+	2.38864i
$676$		0			0
$677$	−473966.	+	273645.i	−1.03412	+	0.597049i	−0.918162	−	0.396206i	$-0.870327\pi$
$677$	−473966.	+	273645.i	−1.03412	+	0.597049i	−0.115957	+	0.993254i	$0.536993\pi$
$678$		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	$-0.923108\pi$
$683$		−	223188.i		−	0.478442i	0.970965	−	0.239221i	$-0.0768921\pi$
$684$		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	0.786588	−	0.617478i	$-0.211846\pi$
$691$	−67543.4	−	116989.i	−0.141458	−	0.245012i	−0.928046	+	0.372466i	$0.878512\pi$
$692$		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	0.906361	−	0.422504i	$-0.138849\pi$
$701$	318263.	+	267054.i	0.647664	+	0.543455i	−0.258697	+	0.965959i	$0.583293\pi$
$702$		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	0.366830	−	0.930288i	$-0.380443\pi$
$709$	25063.6	+	9122.40i	0.0498599	+	0.0181475i	−0.316970	+	0.948436i	$0.602665\pi$
$710$		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	−0.523812	−	0.851834i	$-0.675491\pi$
$719$	−195167.	+	71035.1i	−0.377528	+	0.137409i	0.146285	+	0.989243i	$0.453269\pi$
$720$		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	−0.762083	−	0.647479i	$-0.775823\pi$
$727$	92752.4	−	526025.i	0.175492	−	0.995262i	0.937575	−	0.347783i	$-0.113065\pi$
$728$		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	−0.996686	−	0.0813395i	$-0.974080\pi$
$733$	−229907.	+	398210.i	−0.427901	+	0.741147i	0.568785	+	0.822486i	$0.307414\pi$
$734$		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	0.990501	−	0.137504i	$-0.0439081\pi$
$739$	560912.	+	470661.i	1.02708	+	0.861826i	0.0365835	+	0.999331i	$0.488353\pi$
$740$		0			0
$741$	230027.	+	522661.i	0.418931	+	0.951883i
$742$		0			0
$743$	291541.	−	347445.i	0.528107	−	0.629373i	−0.434371	−	0.900734i	$-0.643029\pi$
$743$	291541.	−	347445.i	0.528107	−	0.629373i	0.962478	+	0.271361i	$0.0874737\pi$
$744$		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	0.892767	−	0.450519i	$-0.148761\pi$
$751$	165853.	+	197656.i	0.294065	+	0.350453i	−0.598702	+	0.800972i	$0.704317\pi$
$752$		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	−0.827392	−	0.561625i	$-0.810176\pi$
$757$	−630471.	+	229473.i	−1.10020	+	0.400442i	−0.272813	+	0.962067i	$0.587954\pi$
$758$		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	−0.213616	+	0.976918i	$0.568524\pi$
$769$	−717195.	+	601798.i	−1.21279	+	1.01765i	−0.999170	+	0.0407312i	$0.987031\pi$
$770$		0			0
$771$	−34525.2	+	59799.3i	−0.0580800	+	0.100598i
$772$		0			0
$773$	199327.	−	547647.i	0.333586	−	0.916519i	−0.653586	−	0.756853i	$-0.726736\pi$
$773$	199327.	−	547647.i	0.333586	−	0.916519i	0.987171	−	0.159666i	$-0.0510418\pi$
$774$		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	0.999321	−	0.0368482i	$-0.0117318\pi$
$787$	908658.	+	524614.i	1.46707	+	0.847013i	0.467749	+	0.883861i	$0.345065\pi$
$788$		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	$-0.838856\pi$
$797$		−	616025.i		−	0.969799i	0.874570	−	0.484900i	$-0.161144\pi$
$798$		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	−0.841700	−	0.539945i	$-0.818445\pi$
$809$	30601.0	−	53002.5i	0.0467561	−	0.0809840i	0.888456	+	0.458961i	$0.151778\pi$
$810$		0			0
$811$	185309.	−	509132.i	0.281744	−	0.774085i	−0.715411	−	0.698704i	$-0.753760\pi$
$811$	185309.	−	509132.i	0.281744	−	0.774085i	0.997155	−	0.0753812i	$-0.0240174\pi$
$812$		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	−0.411426	−	0.911443i	$-0.634969\pi$
$821$	−226844.	−	1.28650e6i	−0.336544	−	1.90864i	0.0748821	−	0.997192i	$-0.476142\pi$
$822$		0			0
$823$	−778911.	−	283500.i	−1.14997	−	0.418556i	−0.304469	−	0.952522i	$-0.598479\pi$
$823$	−778911.	−	283500.i	−1.14997	−	0.418556i	−0.845506	+	0.533966i	$0.820701\pi$
$824$		0			0
$825$	−2.70292e6	−	1.56053e6i	−3.97123	−	2.29279i
$826$		0			0
$827$	−773049.	−	921284.i	−1.13031	−	1.34705i	−0.930106	−	0.367290i	$-0.880286\pi$
$827$	−773049.	−	921284.i	−1.13031	−	1.34705i	−0.200199	−	0.979755i	$-0.564159\pi$
$828$		0			0
$829$	85456.8	−	49338.5i	0.124348	−	0.0717921i	−0.436536	−	0.899687i	$-0.643795\pi$
$829$	85456.8	−	49338.5i	0.124348	−	0.0717921i	0.560884	+	0.827895i	$0.310462\pi$
$830$		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	0.871392	+	0.490587i	$0.163218\pi$
$839$	365483.	+	1.00416e6i	0.519210	+	1.42652i	−0.352182	+	0.935931i	$0.614560\pi$
$840$		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	0.620459	−	0.784239i	$-0.286946\pi$
$853$	−32104.5	−	26938.9i	−0.0441233	−	0.0370238i	−0.664583	+	0.747215i	$0.731391\pi$
$854$		0			0
$855$	1.44812e6	−	1.97532e6i	1.98095	−	2.70213i
$856$		0			0
$857$	−633608.	+	755105.i	−0.862699	+	1.02812i	0.136598	+	0.990627i	$0.456383\pi$
$857$	−633608.	+	755105.i	−0.862699	+	1.02812i	−0.999297	+	0.0374978i	$0.988061\pi$
$858$		0			0
$859$	−153699.	−	871671.i	−0.208298	−	1.18132i	−0.892165	−	0.451710i	$-0.850814\pi$
$859$	−153699.	−	871671.i	−0.208298	−	1.18132i	0.683867	−	0.729607i	$-0.260297\pi$
$860$		0			0
$861$	−464192.	−	168952.i	−0.626169	−	0.227907i
$862$		0			0
$863$	1.16431e6	+	672218.i	1.56332	+	0.902585i	0.996917	+	0.0784590i	$0.0250000\pi$
$863$	1.16431e6	+	672218.i	1.56332	+	0.902585i	0.566406	+	0.824126i	$0.308333\pi$
$864$		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	0.782138	−	0.623106i	$-0.214129\pi$
$877$	−167316.	−	459696.i	−0.217539	−	0.597684i	−0.999677	+	0.0254215i	$0.991907\pi$
$878$		0			0
$879$	207518.	−	1.17689e6i	0.268583	−	1.52321i
$880$		0			0
$881$	67861.2	+	117539.i	0.0874318	+	0.151436i	0.906425	−	0.422367i	$-0.138801\pi$
$881$	67861.2	+	117539.i	0.0874318	+	0.151436i	−0.818993	+	0.573803i	$0.805467\pi$
$882$		0			0
$883$	−1.00739e6	+	845297.i	−1.29203	+	1.08415i	−0.300571	+	0.953759i	$0.597177\pi$
$883$	−1.00739e6	+	845297.i	−1.29203	+	1.08415i	−0.991463	+	0.130387i	$0.958378\pi$
$884$		0			0
$885$	813245.	−	1.40858e6i	1.03833	−	1.79844i
$886$		0			0
$887$	139490.	−	383246.i	0.177295	−	0.487114i	−0.818933	−	0.573889i	$-0.805434\pi$
$887$	139490.	−	383246.i	0.177295	−	0.487114i	0.996228	+	0.0867752i	$0.0276562\pi$
$888$		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	−0.544609	−	0.838690i	$-0.683322\pi$
$907$	−1.10500e6	−	194842.i	−1.34322	−	0.236847i	−0.798614	+	0.601843i	$0.794433\pi$
$908$		0			0
$909$	−2.23691e6	+	814170.i	−2.70721	+	0.985343i
$910$		0			0
$911$			1.01359e6i			1.22130i	0.791899	+	0.610652i	$0.209093\pi$
$911$			1.01359e6i			1.22130i	−0.791899	+	0.610652i	$0.790907\pi$
$912$		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	0.670023	−	0.742340i	$-0.266284\pi$
$919$	−260018.	−	450364.i	−0.307874	−	0.533253i	−0.977897	+	0.209087i	$0.932951\pi$
$920$		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	0.193340	−	0.981132i	$-0.438068\pi$
$929$	−638058.	−	535394.i	−0.739313	−	0.620358i	−0.932653	+	0.360774i	$0.882512\pi$
$930$		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	0.980380	−	0.197117i	$-0.0631580\pi$
$937$	1.40887e6	+	512786.i	1.60469	+	0.584059i	0.624310	+	0.781177i	$0.285380\pi$
$938$		0			0
$939$	−1.25784e6	−	726217.i	−1.42658	−	0.823636i
$940$		0			0
$941$	551535.	+	657294.i	0.622865	+	0.742302i	0.981560	−	0.191153i	$-0.0612227\pi$
$941$	551535.	+	657294.i	0.622865	+	0.742302i	−0.358695	+	0.933455i	$0.616778\pi$
$942$		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	−0.363417	−	0.931626i	$-0.618390\pi$
$947$	−38539.0	+	14027.1i	−0.0429735	+	0.0156411i	0.320444	+	0.947267i	$0.396168\pi$
$948$		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	0.972618	+	0.232409i	$0.0746608\pi$
$953$	342339.	+	940570.i	0.376939	+	1.03563i	−0.595679	+	0.803223i	$0.703117\pi$
$954$		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	0.571079	−	0.820895i	$-0.306525\pi$
$967$	−129208.	−	108418.i	−0.138177	−	0.115944i	−0.709257	+	0.704950i	$0.750969\pi$
$968$		0			0
$969$	19392.0	−	1272.60i	0.0206526	−	0.00135532i
$970$		0			0
$971$	−664896.	+	792392.i	−0.705204	+	0.840430i	−0.993105	−	0.117231i	$-0.962598\pi$
$971$	−664896.	+	792392.i	−0.705204	+	0.840430i	0.287900	+	0.957660i	$0.407043\pi$
$972$		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	0.654400	−	0.756148i	$-0.272921\pi$
$977$	311898.	+	180075.i	0.326756	+	0.188653i	−0.327644	+	0.944801i	$0.606255\pi$
$978$		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	0.476049	−	0.879419i	$-0.342069\pi$
$983$	601620.	+	106082.i	0.622609	+	0.109783i	0.146560	+	0.989202i	$0.453180\pi$
$984$		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	0.999996	+	0.00288150i	$0.000917211\pi$
$991$	231581.	+	636265.i	0.235807	+	0.647874i	−0.764189	+	0.644992i	$0.776861\pi$
$992$		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	−0.380126	−	0.924935i	$-0.624119\pi$
$997$	461965.	−	387635.i	0.464749	−	0.389971i	0.844875	+	0.534964i	$0.179675\pi$
$998$		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.41.7	yes	42
19.13	odd	18	inner	76.5.j.a.13.7	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.7	✓	42	19.13	odd	18	inner
76.5.j.a.41.7	yes	42	1.1	even	1	trivial

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

Related objects

Downloads

Learn more