LMFDB - Embedded newform 76.5.j.a.41.3

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			41.3
Character	$\chi$	$=$	76.41
Dual form			76.5.j.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28730 - 6.28431i) q^{3} +(-2.03045 + 11.5152i) q^{5} +(38.6373 + 66.9218i) q^{7} +(27.7888 - 23.3175i) q^{9} +O(q^{10})$	\(q+(-2.28730 - 6.28431i) q^{3} +(-2.03045 + 11.5152i) q^{5} +(38.6373 + 66.9218i) q^{7} +(27.7888 - 23.3175i) q^{9} +(79.3551 - 137.447i) q^{11} +(65.1618 - 179.031i) q^{13} +(77.0097 - 13.5789i) q^{15} +(343.501 + 288.231i) q^{17} +(-191.484 - 306.031i) q^{19} +(332.182 - 395.879i) q^{21} +(99.9867 + 567.053i) q^{23} +(458.830 + 167.000i) q^{25} +(-679.220 - 392.148i) q^{27} +(447.390 + 533.179i) q^{29} +(533.474 - 308.001i) q^{31} +(-1045.27 - 184.309i) q^{33} +(-849.072 + 309.037i) q^{35} +2288.40i q^{37} -1274.13 q^{39} +(-792.647 - 2177.78i) q^{41} +(465.909 - 2642.30i) q^{43} +(212.083 + 367.339i) q^{45} +(-1399.04 + 1173.94i) q^{47} +(-1785.19 + 3092.03i) q^{49} +(1025.65 - 2817.94i) q^{51} +(-1889.93 + 333.245i) q^{53} +(1421.61 + 1192.87i) q^{55} +(-1485.21 + 1903.33i) q^{57} +(-1322.44 + 1576.02i) q^{59} +(228.828 + 1297.75i) q^{61} +(2634.13 + 958.747i) q^{63} +(1929.27 + 1113.87i) q^{65} +(-3218.45 - 3835.60i) q^{67} +(3334.84 - 1925.37i) q^{69} +(-4665.83 - 822.711i) q^{71} +(6554.25 - 2385.55i) q^{73} -3265.41i q^{75} +12264.3 q^{77} +(-2018.56 - 5545.94i) q^{79} +(-400.563 + 2271.71i) q^{81} +(2417.78 + 4187.71i) q^{83} +(-4016.51 + 3370.26i) q^{85} +(2327.35 - 4031.08i) q^{87} +(-1672.93 + 4596.33i) q^{89} +(14498.7 - 2556.52i) q^{91} +(-3155.80 - 2648.03i) q^{93} +(3912.82 - 1583.61i) q^{95} +(42.3160 - 50.4302i) q^{97} +(-999.747 - 5669.85i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.28730	−	6.28431i	−0.254145	−	0.698257i	−0.999501	−	0.0315905i	$-0.989943\pi$
$3$	−2.28730	−	6.28431i	−0.254145	−	0.698257i	0.745356	−	0.666667i	$-0.232279\pi$
$4$		0			0
$5$	−2.03045	+	11.5152i	−0.0812179	+	0.460610i	0.916891	+	0.399138i	$0.130691\pi$
$5$	−2.03045	+	11.5152i	−0.0812179	+	0.460610i	−0.998109	+	0.0614718i	$0.980421\pi$
$6$		0			0
$7$	38.6373	+	66.9218i	0.788517	+	1.36575i	0.926876	+	0.375369i	$0.122484\pi$
$7$	38.6373	+	66.9218i	0.788517	+	1.36575i	−0.138359	+	0.990382i	$0.544183\pi$
$8$		0			0
$9$	27.7888	−	23.3175i	0.343071	−	0.287871i
$10$		0			0
$11$	79.3551	−	137.447i	0.655827	−	1.13593i	−0.325858	−	0.945419i	$-0.605653\pi$
$11$	79.3551	−	137.447i	0.655827	−	1.13593i	0.981686	−	0.190508i	$-0.0610134\pi$
$12$		0			0
$13$	65.1618	−	179.031i	0.385573	−	1.05935i	−0.583400	−	0.812185i	$-0.698278\pi$
$13$	65.1618	−	179.031i	0.385573	−	1.05935i	0.968973	−	0.247168i	$-0.0794999\pi$
$14$		0			0
$15$	77.0097	−	13.5789i	0.342265	−	0.0603506i
$16$		0			0
$17$	343.501	+	288.231i	1.18858	+	0.997340i	0.999883	+	0.0153052i	$0.00487200\pi$
$17$	343.501	+	288.231i	1.18858	+	0.997340i	0.188701	+	0.982035i	$0.439572\pi$
$18$		0			0
$19$	−191.484	−	306.031i	−0.530427	−	0.847731i
$19$	−191.484	−	306.031i	−0.530427	−	0.847731i
$20$		0			0
$21$	332.182	−	395.879i	0.753248	−	0.897686i
$22$		0			0
$23$	99.9867	+	567.053i	0.189011	+	1.07193i	0.920693	+	0.390287i	$0.127624\pi$
$23$	99.9867	+	567.053i	0.189011	+	1.07193i	−0.731682	+	0.681646i	$0.761265\pi$
$24$		0			0
$25$	458.830	+	167.000i	0.734128	+	0.267201i
$26$		0			0
$27$	−679.220	−	392.148i	−0.931715	−	0.537926i
$28$		0			0
$29$	447.390	+	533.179i	0.531974	+	0.633982i	0.963368	−	0.268181i	$-0.0864226\pi$
$29$	447.390	+	533.179i	0.531974	+	0.633982i	−0.431394	+	0.902164i	$0.641978\pi$
$30$		0			0
$31$	533.474	−	308.001i	0.555124	−	0.320501i	−0.196062	−	0.980591i	$-0.562815\pi$
$31$	533.474	−	308.001i	0.555124	−	0.320501i	0.751186	+	0.660090i	$0.229482\pi$
$32$		0			0
$33$	−1045.27	−	184.309i	−0.959844	−	0.169246i
$34$		0			0
$35$	−849.072	+	309.037i	−0.693120	+	0.252275i
$36$		0			0
$37$			2288.40i			1.67159i	0.549043	+	0.835794i	$0.314992\pi$
$37$			2288.40i			1.67159i	−0.549043	+	0.835794i	$0.685008\pi$
$38$		0			0
$39$	−1274.13			−0.837692
$40$		0			0
$41$	−792.647	−	2177.78i	−0.471533	−	1.29553i	−0.916520	−	0.399989i	$-0.869014\pi$
$41$	−792.647	−	2177.78i	−0.471533	−	1.29553i	0.444987	−	0.895537i	$-0.353208\pi$
$42$		0			0
$43$	465.909	−	2642.30i	0.251979	−	1.42904i	−0.551730	−	0.834023i	$-0.686032\pi$
$43$	465.909	−	2642.30i	0.251979	−	1.42904i	0.803709	−	0.595022i	$-0.202857\pi$
$44$		0			0
$45$	212.083	+	367.339i	0.104733	+	0.181402i
$46$		0			0
$47$	−1399.04	+	1173.94i	−0.633338	+	0.531433i	−0.901964	−	0.431811i	$-0.857875\pi$
$47$	−1399.04	+	1173.94i	−0.633338	+	0.531433i	0.268626	+	0.963244i	$0.413430\pi$
$48$		0			0
$49$	−1785.19	+	3092.03i	−0.743517	+	1.28781i
$50$		0			0
$51$	1025.65	−	2817.94i	0.394327	−	1.08341i
$52$		0			0
$53$	−1889.93	+	333.245i	−0.672812	+	0.118635i	−0.499609	−	0.866251i	$-0.666523\pi$
$53$	−1889.93	+	333.245i	−0.672812	+	0.118635i	−0.173203	+	0.984886i	$0.555412\pi$
$54$		0			0
$55$	1421.61	+	1192.87i	0.469954	+	0.394338i
$56$		0			0
$57$	−1485.21	+	1903.33i	−0.457129	+	0.585821i
$58$		0			0
$59$	−1322.44	+	1576.02i	−0.379902	+	0.452750i	−0.921783	−	0.387705i	$-0.873268\pi$
$59$	−1322.44	+	1576.02i	−0.379902	+	0.452750i	0.541881	+	0.840455i	$0.317712\pi$
$60$		0			0
$61$	228.828	+	1297.75i	0.0614964	+	0.348763i	0.999994	+	0.00347754i	$0.00110694\pi$
$61$	228.828	+	1297.75i	0.0614964	+	0.348763i	−0.938498	+	0.345286i	$0.887782\pi$
$62$		0			0
$63$	2634.13	+	958.747i	0.663677	+	0.241559i
$64$		0			0
$65$	1929.27	+	1113.87i	0.456633	+	0.263637i
$66$		0			0
$67$	−3218.45	−	3835.60i	−0.716964	−	0.854445i	0.277368	−	0.960764i	$-0.410538\pi$
$67$	−3218.45	−	3835.60i	−0.716964	−	0.854445i	−0.994332	+	0.106319i	$0.966094\pi$
$68$		0			0
$69$	3334.84	−	1925.37i	0.700449	−	0.404404i
$70$		0			0
$71$	−4665.83	−	822.711i	−0.925576	−	0.163204i	−0.309508	−	0.950897i	$-0.600164\pi$
$71$	−4665.83	−	822.711i	−0.925576	−	0.163204i	−0.616068	+	0.787693i	$0.711275\pi$
$72$		0			0
$73$	6554.25	−	2385.55i	1.22992	−	0.447655i	0.356351	−	0.934352i	$-0.384021\pi$
$73$	6554.25	−	2385.55i	1.22992	−	0.447655i	0.873571	+	0.486698i	$0.161799\pi$
$74$		0			0
$75$		−	3265.41i		−	0.580517i
$76$		0			0
$77$	12264.3			2.06852
$78$		0			0
$79$	−2018.56	−	5545.94i	−0.323435	−	0.888630i	−0.989731	−	0.142943i	$-0.954344\pi$
$79$	−2018.56	−	5545.94i	−0.323435	−	0.888630i	0.666296	−	0.745687i	$-0.267879\pi$
$80$		0			0
$81$	−400.563	+	2271.71i	−0.0610521	+	0.346244i
$82$		0			0
$83$	2417.78	+	4187.71i	0.350962	+	0.607884i	0.986418	−	0.164253i	$-0.0525214\pi$
$83$	2417.78	+	4187.71i	0.350962	+	0.607884i	−0.635457	+	0.772137i	$0.719188\pi$
$84$		0			0
$85$	−4016.51	+	3370.26i	−0.555919	+	0.466471i
$86$		0			0
$87$	2327.35	−	4031.08i	0.307484	−	0.532578i
$88$		0			0
$89$	−1672.93	+	4596.33i	−0.211202	+	0.580271i	−0.999381	−	0.0351738i	$-0.988802\pi$
$89$	−1672.93	+	4596.33i	−0.211202	+	0.580271i	0.788180	+	0.615445i	$0.211024\pi$
$90$		0			0
$91$	14498.7	−	2556.52i	1.75084	−	0.308721i
$92$		0			0
$93$	−3155.80	−	2648.03i	−0.364874	−	0.306166i
$94$		0			0
$95$	3912.82	−	1583.61i	0.433553	−	0.175469i
$96$		0			0
$97$	42.3160	−	50.4302i	0.00449740	−	0.00535979i	−0.763791	−	0.645464i	$-0.776664\pi$
$97$	42.3160	−	50.4302i	0.00449740	−	0.00535979i	0.768288	+	0.640104i	$0.221109\pi$
$98$		0			0
$99$	−999.747	−	5669.85i	−0.102005	−	0.578497i
$100$		0			0
$101$	−4545.64	−	1654.48i	−0.445607	−	0.162188i	0.109464	−	0.993991i	$-0.465087\pi$
$101$	−4545.64	−	1654.48i	−0.445607	−	0.162188i	−0.555071	+	0.831803i	$0.687309\pi$
$102$		0			0
$103$	−9097.21	−	5252.27i	−0.857499	−	0.495077i	0.00567497	−	0.999984i	$-0.498194\pi$
$103$	−9097.21	−	5252.27i	−0.857499	−	0.495077i	−0.863174	+	0.504907i	$0.831527\pi$
$104$		0			0
$105$	3884.17	+	4628.97i	0.352306	+	0.419862i
$106$		0			0
$107$	−15452.5	+	8921.49i	−1.34968	+	0.779237i	−0.988204	−	0.153145i	$-0.951060\pi$
$107$	−15452.5	+	8921.49i	−1.34968	+	0.779237i	−0.361475	+	0.932382i	$0.617727\pi$
$108$		0			0
$109$	6680.09	+	1177.88i	0.562250	+	0.0991399i	0.447548	−	0.894260i	$-0.352297\pi$
$109$	6680.09	+	1177.88i	0.562250	+	0.0991399i	0.114702	+	0.993400i	$0.463409\pi$
$110$		0			0
$111$	14381.1	−	5234.27i	1.16720	−	0.424826i
$112$		0			0
$113$			9283.02i			0.726996i	0.931595	+	0.363498i	$0.118418\pi$
$113$			9283.02i			0.726996i	−0.931595	+	0.363498i	$0.881582\pi$
$114$		0			0
$115$	−6732.77			−0.509094
$116$		0			0
$117$	−2363.79	−	6494.45i	−0.172678	−	0.474429i
$118$		0			0
$119$	−6017.01	+	34124.2i	−0.424900	+	2.40973i
$120$		0			0
$121$	−5273.97	−	9134.78i	−0.360219	−	0.623918i
$122$		0			0
$123$	−11872.8	+	9962.48i	−0.784773	+	0.658502i
$124$		0			0
$125$	−6508.71	+	11273.4i	−0.416557	+	0.721498i
$126$		0			0
$127$	1182.46	−	3248.78i	0.0733126	−	0.201425i	−0.897624	−	0.440763i	$-0.854708\pi$
$127$	1182.46	−	3248.78i	0.0733126	−	0.201425i	0.970936	+	0.239338i	$0.0769303\pi$
$128$		0			0
$129$	−17670.7	+	3115.83i	−1.06188	+	0.187238i
$130$		0			0
$131$	−12314.9	−	10333.5i	−0.717612	−	0.602148i	0.209112	−	0.977892i	$-0.432943\pi$
$131$	−12314.9	−	10333.5i	−0.717612	−	0.602148i	−0.926723	+	0.375744i	$0.877387\pi$
$132$		0			0
$133$	13081.7	−	24638.7i	0.739538	−	1.39288i
$134$		0			0
$135$	5894.80	−	7025.15i	0.323446	−	0.385468i
$136$		0			0
$137$	−2118.53	−	12014.8i	−0.112874	−	0.640140i	−0.987781	−	0.155849i	$-0.950189\pi$
$137$	−2118.53	−	12014.8i	−0.112874	−	0.640140i	0.874907	−	0.484291i	$-0.160922\pi$
$138$		0			0
$139$	−7828.89	−	2849.48i	−0.405201	−	0.147481i	0.131376	−	0.991333i	$-0.458061\pi$
$139$	−7828.89	−	2849.48i	−0.405201	−	0.147481i	−0.536577	+	0.843852i	$0.680283\pi$
$140$		0			0
$141$	10577.4	+	6106.88i	0.532037	+	0.307171i
$142$		0			0
$143$	−19436.3	−	23163.3i	−0.950478	−	1.13274i
$144$		0			0
$145$	−7048.09	+	4069.22i	−0.335224	+	0.193542i
$146$		0			0
$147$	23514.6	+	4146.25i	1.08818	+	0.191876i
$148$		0			0
$149$	−19199.2	+	6987.94i	−0.864791	+	0.314758i	−0.736056	−	0.676921i	$-0.763314\pi$
$149$	−19199.2	+	6987.94i	−0.864791	+	0.314758i	−0.128735	+	0.991679i	$0.541092\pi$
$150$		0			0
$151$			32736.5i			1.43575i	0.696172	+	0.717875i	$0.254885\pi$
$151$			32736.5i			1.43575i	−0.696172	+	0.717875i	$0.745115\pi$
$152$		0			0
$153$	16266.3			0.694874
$154$		0			0
$155$	2463.52	+	6768.47i	0.102540	+	0.281726i
$156$		0			0
$157$	2557.89	−	14506.5i	0.103772	−	0.588523i	−0.887931	−	0.459976i	$-0.847858\pi$
$157$	2557.89	−	14506.5i	0.103772	−	0.588523i	0.991704	−	0.128546i	$-0.0410311\pi$
$158$		0			0
$159$	6417.06	+	11114.7i	0.253829	+	0.439645i
$160$		0			0
$161$	−34085.0	+	28600.7i	−1.31496	+	1.10338i
$162$		0			0
$163$	4902.49	−	8491.36i	0.184519	−	0.319597i	−0.758895	−	0.651213i	$-0.774261\pi$
$163$	4902.49	−	8491.36i	0.184519	−	0.319597i	0.943414	+	0.331616i	$0.107594\pi$
$164$		0			0
$165$	4244.73	−	11662.3i	0.155913	−	0.428368i
$166$		0			0
$167$	28741.8	−	5067.95i	1.03058	−	0.181719i	0.367308	−	0.930099i	$-0.380280\pi$
$167$	28741.8	−	5067.95i	1.03058	−	0.181719i	0.663269	+	0.748381i	$0.269168\pi$
$168$		0			0
$169$	−5926.92	−	4973.28i	−0.207518	−	0.174128i
$170$		0			0
$171$	−12457.0	−	4039.27i	−0.426011	−	0.138137i
$172$		0			0
$173$	27666.0	−	32971.0i	0.924388	−	1.10164i	−0.0701785	−	0.997534i	$-0.522357\pi$
$173$	27666.0	−	32971.0i	0.924388	−	1.10164i	0.994566	−	0.104108i	$-0.0331987\pi$
$174$		0			0
$175$	6551.99	+	37158.2i	0.213942	+	1.21333i
$176$		0			0
$177$	12929.0	+	4705.79i	0.412686	+	0.150206i
$178$		0			0
$179$	53187.6	+	30707.9i	1.65998	+	0.958392i	0.972719	+	0.231986i	$0.0745223\pi$
$179$	53187.6	+	30707.9i	1.65998	+	0.958392i	0.687265	+	0.726407i	$0.258811\pi$
$180$		0			0
$181$	7862.80	+	9370.52i	0.240005	+	0.286027i	0.872579	−	0.488473i	$-0.162446\pi$
$181$	7862.80	+	9370.52i	0.240005	+	0.286027i	−0.632574	+	0.774500i	$0.718002\pi$
$182$		0			0
$183$	7632.06	−	4406.37i	0.227898	−	0.131577i
$184$		0			0
$185$	−26351.5	−	4646.49i	−0.769950	−	0.135763i
$186$		0			0
$187$	66875.1	−	24340.5i	1.91241	−	0.696060i
$188$		0			0
$189$		−	60606.2i		−	1.69665i
$190$		0			0
$191$	−34351.9			−0.941638			−0.470819	−	0.882230i	$-0.656042\pi$
$191$	−34351.9			−0.941638			−0.470819	+	0.882230i	$0.656042\pi$
$192$		0			0
$193$	−18862.0	−	51823.0i	−0.506377	−	1.39126i	−0.884950	−	0.465687i	$-0.845807\pi$
$193$	−18862.0	−	51823.0i	−0.506377	−	1.39126i	0.378573	−	0.925571i	$-0.376415\pi$
$194$		0			0
$195$	2587.05	−	14671.9i	0.0680356	−	0.385849i
$196$		0			0
$197$	−1530.25	−	2650.47i	−0.0394303	−	0.0682953i	0.845637	−	0.533759i	$-0.179221\pi$
$197$	−1530.25	−	2650.47i	−0.0394303	−	0.0682953i	−0.885067	+	0.465464i	$0.845888\pi$
$198$		0			0
$199$	22659.0	−	19013.2i	0.572183	−	0.480119i	−0.310186	−	0.950676i	$-0.600391\pi$
$199$	22659.0	−	19013.2i	0.572183	−	0.480119i	0.882370	+	0.470557i	$0.155947\pi$
$200$		0			0
$201$	−16742.6	+	28999.0i	−0.414409	+	0.717778i
$202$		0			0
$203$	−18395.3	+	50540.8i	−0.446391	+	1.22645i
$204$		0			0
$205$	26687.1	−	4705.65i	0.635029	−	0.111973i
$206$		0			0
$207$	16000.8	+	13426.2i	0.373422	+	0.313339i
$208$		0			0
$209$	−57258.3	+	2033.84i	−1.31083	+	0.0465613i
$210$		0			0
$211$	7223.13	−	8608.19i	0.162241	−	0.193351i	−0.678799	−	0.734324i	$-0.737499\pi$
$211$	7223.13	−	8608.19i	0.162241	−	0.193351i	0.841040	+	0.540973i	$0.181944\pi$
$212$		0			0
$213$	5501.99	+	31203.3i	0.121272	+	0.687767i
$214$		0			0
$215$	29480.8	+	10730.1i	0.637767	+	0.232128i
$216$		0			0
$217$	41224.0	+	23800.7i	0.875449	+	0.505441i
$218$		0			0
$219$	−29983.1	−	35732.5i	−0.625156	−	0.745032i
$220$		0			0
$221$	73985.4	−	42715.5i	1.51482	−	0.874582i
$222$		0			0
$223$	−32675.5	−	5761.57i	−0.657072	−	0.115859i	−0.164835	−	0.986321i	$-0.552709\pi$
$223$	−32675.5	−	5761.57i	−0.657072	−	0.115859i	−0.492236	+	0.870462i	$0.663820\pi$
$224$		0			0
$225$	16644.3	−	6058.05i	0.328777	−	0.119665i
$226$		0			0
$227$			37637.2i			0.730408i	0.930928	+	0.365204i	$0.119001\pi$
$227$			37637.2i			0.730408i	−0.930928	+	0.365204i	$0.880999\pi$
$228$		0			0
$229$	−83612.9			−1.59442			−0.797209	−	0.603703i	$-0.793691\pi$
$229$	−83612.9			−1.59442			−0.797209	+	0.603703i	$0.793691\pi$
$230$		0			0
$231$	−28052.1	−	77072.6i	−0.525704	−	1.44436i
$232$		0			0
$233$	−15577.1	+	88342.4i	−0.286930	+	1.62726i	0.411379	+	0.911465i	$0.365047\pi$
$233$	−15577.1	+	88342.4i	−0.286930	+	1.62726i	−0.698309	+	0.715797i	$0.746064\pi$
$234$		0			0
$235$	−10677.5	−	18493.9i	−0.193345	−	0.334883i
$236$		0			0
$237$	−30235.4	+	25370.5i	−0.538293	+	0.451681i
$238$		0			0
$239$	−24342.8	+	42162.9i	−0.426161	+	0.738133i	−0.996528	−	0.0832570i	$-0.973468\pi$
$239$	−24342.8	+	42162.9i	−0.426161	+	0.738133i	0.570367	+	0.821390i	$0.306801\pi$
$240$		0			0
$241$	5701.60	−	15665.0i	0.0981664	−	0.269710i	−0.880883	−	0.473335i	$-0.843050\pi$
$241$	5701.60	−	15665.0i	0.0981664	−	0.269710i	0.979049	+	0.203625i	$0.0652723\pi$
$242$		0			0
$243$	−47370.5	+	8352.70i	−0.802224	+	0.141454i
$244$		0			0
$245$	−31980.8	−	26835.1i	−0.532791	−	0.447065i
$246$		0			0
$247$	−67266.3	+	14340.0i	−1.10256	+	0.235048i
$248$		0			0
$249$	20786.7	−	24772.6i	0.335264	−	0.399552i
$250$		0			0
$251$	11781.3	+	66815.0i	0.187002	+	1.06054i	0.923357	+	0.383943i	$0.125434\pi$
$251$	11781.3	+	66815.0i	0.187002	+	1.06054i	−0.736355	+	0.676595i	$0.763455\pi$
$252$		0			0
$253$	85874.2	+	31255.6i	1.34160	+	0.488301i
$254$		0			0
$255$	30366.7	+	17532.2i	0.467001	+	0.269623i
$256$		0			0
$257$	14598.8	+	17398.2i	0.221030	+	0.263413i	0.865152	−	0.501509i	$-0.167222\pi$
$257$	14598.8	+	17398.2i	0.221030	+	0.263413i	−0.644122	+	0.764923i	$0.722777\pi$
$258$		0			0
$259$	−153144.	+	88417.8i	−2.28297	+	1.31808i
$260$		0			0
$261$	24864.8	+	4384.34i	0.365010	+	0.0643611i
$262$		0			0
$263$	−41218.9	+	15002.5i	−0.595916	+	0.216896i	−0.622329	−	0.782756i	$-0.713814\pi$
$263$	−41218.9	+	15002.5i	−0.595916	+	0.216896i	0.0264136	+	0.999651i	$0.491591\pi$
$264$		0			0
$265$		−	22439.6i		−	0.319539i
$266$		0			0
$267$	32711.3			0.458854
$268$		0			0
$269$	−20443.1	−	56166.9i	−0.282515	−	0.776204i	−0.997061	−	0.0766150i	$-0.975589\pi$
$269$	−20443.1	−	56166.9i	−0.282515	−	0.776204i	0.714546	−	0.699589i	$-0.246633\pi$
$270$		0			0
$271$	6645.37	−	37687.8i	0.0904859	−	0.513171i	−0.905552	−	0.424236i	$-0.860543\pi$
$271$	6645.37	−	37687.8i	0.0904859	−	0.513171i	0.996037	−	0.0889346i	$-0.0283462\pi$
$272$		0			0
$273$	−49229.0	−	85267.1i	−0.660534	−	1.14408i
$274$		0			0
$275$	59364.2	−	49812.5i	0.784981	−	0.658677i
$276$		0			0
$277$	2220.77	−	3846.49i	0.0289431	−	0.0501308i	−0.851191	−	0.524856i	$-0.824119\pi$
$277$	2220.77	−	3846.49i	0.0289431	−	0.0501308i	0.880134	+	0.474725i	$0.157453\pi$
$278$		0			0
$279$	7642.75	−	20998.3i	0.0981841	−	0.269759i
$280$		0			0
$281$	−115129.	+	20300.3i	−1.45805	+	0.257093i	−0.845769	−	0.533549i	$-0.820858\pi$
$281$	−115129.	+	20300.3i	−1.45805	+	0.257093i	−0.612278	+	0.790642i	$0.709747\pi$
$282$		0			0
$283$	−46915.8	−	39367.1i	−0.585796	−	0.491541i	0.301049	−	0.953609i	$-0.402663\pi$
$283$	−46915.8	−	39367.1i	−0.585796	−	0.491541i	−0.886845	+	0.462067i	$0.847108\pi$
$284$		0			0
$285$	−18901.7	−	20967.2i	−0.232708	−	0.258137i
$286$		0			0
$287$	115115.	−	137189.i	1.39755	−	1.66554i
$288$		0			0
$289$	20412.2	+	115763.i	0.244395	+	1.38604i
$290$		0			0
$291$	−413.709	−	150.578i	−0.00488550	−	0.00177818i
$292$		0			0
$293$	132814.	+	76680.1i	1.54706	+	0.893197i	0.998364	+	0.0571772i	$0.0182100\pi$
$293$	132814.	+	76680.1i	1.54706	+	0.893197i	0.548699	+	0.836020i	$0.315123\pi$
$294$		0			0
$295$	−15463.1	−	18428.3i	−0.177686	−	0.211758i
$296$		0			0
$297$	−107799.	+	62237.9i	−1.22209	+	0.705573i
$298$		0			0
$299$	108035.	+	19049.5i	1.20843	+	0.213079i
$300$		0			0
$301$	194829.	−	70912.0i	2.15041	−	0.782685i
$302$		0			0
$303$			32350.5i			0.352367i
$304$		0			0
$305$	−15408.5			−0.165638
$306$		0			0
$307$	10545.7	+	28974.0i	0.111892	+	0.307420i	0.982982	−	0.183704i	$-0.0588086\pi$
$307$	10545.7	+	28974.0i	0.111892	+	0.307420i	−0.871090	+	0.491123i	$0.836586\pi$
$308$		0			0
$309$	−12198.9	+	69183.2i	−0.127762	+	0.724576i
$310$		0			0
$311$	−66618.9	−	115387.i	−0.688774	−	1.19299i	−0.972235	−	0.234008i	$-0.924816\pi$
$311$	−66618.9	−	115387.i	−0.688774	−	1.19299i	0.283460	−	0.958984i	$-0.408518\pi$
$312$		0			0
$313$	−129680.	+	108815.i	−1.32369	+	1.11070i	−0.338176	+	0.941083i	$0.609810\pi$
$313$	−129680.	+	108815.i	−1.32369	+	1.11070i	−0.985509	+	0.169621i	$0.945746\pi$
$314$		0			0
$315$	−16388.7	+	28386.0i	−0.165167	+	0.286077i
$316$		0			0
$317$	−5024.10	+	13803.6i	−0.0499965	+	0.137364i	−0.962178	−	0.272423i	$-0.912175\pi$
$317$	−5024.10	+	13803.6i	−0.0499965	+	0.137364i	0.912181	+	0.409787i	$0.134397\pi$
$318$		0			0
$319$	108787.	−	19182.0i	1.06904	−	0.188501i
$320$		0			0
$321$	91409.9	+	76702.0i	0.887122	+	0.744383i
$322$		0			0
$323$	22432.7	−	160313.i	0.215019	−	1.53661i
$324$		0			0
$325$	59796.4	−	71262.5i	0.566120	−	0.674675i
$326$		0			0
$327$	−7877.23	−	44674.0i	−0.0736678	−	0.417791i
$328$		0			0
$329$	−132617.	−	48268.7i	−1.22520	−	0.445937i
$330$		0			0
$331$	69493.7	+	40122.2i	0.634292	+	0.366209i	0.782412	−	0.622761i	$-0.213989\pi$
$331$	69493.7	+	40122.2i	0.634292	+	0.366209i	−0.148120	+	0.988969i	$0.547322\pi$
$332$		0			0
$333$	53360.0	+	63591.9i	0.481202	+	0.573474i
$334$		0			0
$335$	50702.8	−	29273.3i	0.451796	−	0.260845i
$336$		0			0
$337$	199558.	+	35187.5i	1.75715	+	0.309834i	0.957027	−	0.289998i	$-0.0936546\pi$
$337$	199558.	+	35187.5i	1.75715	+	0.309834i	0.800126	+	0.599832i	$0.204766\pi$
$338$		0			0
$339$	58337.4	−	21233.1i	0.507630	−	0.184762i
$340$		0			0
$341$		−	97766.0i		−	0.840773i
$342$		0			0
$343$	−90362.7			−0.768070
$344$		0			0
$345$	15399.9	+	42310.8i	0.129384	+	0.355478i
$346$		0			0
$347$	−22885.2	+	129789.i	−0.190062	+	1.07790i	0.729214	+	0.684285i	$0.239886\pi$
$347$	−22885.2	+	129789.i	−0.190062	+	1.07790i	−0.919277	+	0.393612i	$0.871225\pi$
$348$		0			0
$349$	−40374.8	−	69931.2i	−0.331482	−	0.574143i	0.651321	−	0.758802i	$-0.274215\pi$
$349$	−40374.8	−	69931.2i	−0.331482	−	0.574143i	−0.982803	+	0.184659i	$0.940882\pi$
$350$		0			0
$351$	−114466.	+	96048.2i	−0.929097	+	0.779605i
$352$		0			0
$353$	67250.4	−	116481.i	0.539691	−	0.934773i	−0.459229	−	0.888318i	$-0.651874\pi$
$353$	67250.4	−	116481.i	0.539691	−	0.934773i	0.998920	−	0.0464551i	$-0.0147924\pi$
$354$		0			0
$355$	18947.4	−	52057.7i	0.150347	−	0.413074i
$356$		0			0
$357$	228210.	−	40239.5i	1.79060	−	0.315730i
$358$		0			0
$359$	−96425.6	−	80910.7i	−0.748175	−	0.627794i	0.186844	−	0.982390i	$-0.440174\pi$
$359$	−96425.6	−	80910.7i	−0.748175	−	0.627794i	−0.935020	+	0.354596i	$0.884618\pi$
$360$		0			0
$361$	−56988.6	+	117200.i	−0.437294	+	0.899319i
$362$		0			0
$363$	−45342.7	+	54037.3i	−0.344107	+	0.410091i
$364$		0			0
$365$	14162.1	+	80317.5i	0.106302	+	0.602871i
$366$		0			0
$367$	102088.	+	37157.1i	0.757955	+	0.275873i	0.691949	−	0.721946i	$-0.256752\pi$
$367$	102088.	+	37157.1i	0.757955	+	0.275873i	0.0660056	+	0.997819i	$0.478974\pi$
$368$		0			0
$369$	−72807.1	−	42035.2i	−0.534714	−	0.308717i
$370$		0			0
$371$	−95323.1	−	113602.i	−0.692549	−	0.825348i
$372$		0			0
$373$	−202445.	+	116882.i	−1.45509	+	0.840096i	−0.998763	−	0.0497171i	$-0.984168\pi$
$373$	−202445.	+	116882.i	−1.45509	+	0.840096i	−0.456325	+	0.889813i	$0.650835\pi$
$374$		0			0
$375$	85733.0	+	15117.0i	0.609657	+	0.107499i
$376$		0			0
$377$	124608.	−	45353.7i	0.876726	−	0.319102i
$378$		0			0
$379$		−	127119.i		−	0.884979i	−0.896774	−	0.442490i	$-0.854095\pi$
$379$		−	127119.i		−	0.884979i	0.896774	−	0.442490i	$-0.145905\pi$
$380$		0			0
$381$	−23121.0			−0.159278
$382$		0			0
$383$	−48655.0	−	133679.i	−0.331688	−	0.911306i	−0.987673	−	0.156532i	$-0.949969\pi$
$383$	−48655.0	−	133679.i	−0.331688	−	0.911306i	0.655985	−	0.754774i	$-0.272254\pi$
$384$		0			0
$385$	−24902.0	+	141226.i	−0.168001	+	0.952782i
$386$		0			0
$387$	−48665.0	−	84290.2i	−0.324934	−	0.562801i
$388$		0			0
$389$	−58248.9	+	48876.7i	−0.384936	+	0.323000i	−0.814637	−	0.579972i	$-0.803064\pi$
$389$	−58248.9	+	48876.7i	−0.384936	+	0.323000i	0.429700	+	0.902971i	$0.358619\pi$
$390$		0			0
$391$	−129097.	+	223602.i	−0.844427	+	1.46259i
$392$		0			0
$393$	−36770.7	+	101027.i	−0.238077	+	0.654110i
$394$		0			0
$395$	67961.4	−	11983.4i	0.435580	−	0.0768046i
$396$		0			0
$397$	−112650.	−	94524.9i	−0.714746	−	0.599743i	0.211180	−	0.977447i	$-0.432269\pi$
$397$	−112650.	−	94524.9i	−0.714746	−	0.599743i	−0.925926	+	0.377704i	$0.876714\pi$
$398$		0			0
$399$	−184759.	−	25853.3i	−1.16054	−	0.162394i
$400$		0			0
$401$	110099.	−	131211.i	0.684692	−	0.815984i	−0.306011	−	0.952028i	$-0.598995\pi$
$401$	110099.	−	131211.i	0.684692	−	0.815984i	0.990703	+	0.136044i	$0.0434390\pi$
$402$		0			0
$403$	−20379.6	−	115578.i	−0.125483	−	0.711649i
$404$		0			0
$405$	−25345.9	−	9225.16i	−0.154525	−	0.0562424i
$406$		0			0
$407$	314535.	+	181597.i	1.89880	+	1.09627i
$408$		0			0
$409$	−151405.	−	180438.i	−0.905097	−	1.07865i	−0.996563	−	0.0828441i	$-0.973600\pi$
$409$	−151405.	−	180438.i	−0.905097	−	1.07865i	0.0914657	−	0.995808i	$-0.470845\pi$
$410$		0			0
$411$	−70658.9	+	40794.9i	−0.418296	+	0.241503i
$412$		0			0
$413$	−156566.	−	27606.8i	−0.917903	−	0.161851i
$414$		0			0
$415$	−53131.7	+	19338.3i	−0.308501	+	0.112285i
$416$		0			0
$417$			55716.8i			0.320416i
$418$		0			0
$419$	−28749.7			−0.163759			−0.0818795	−	0.996642i	$-0.526092\pi$
$419$	−28749.7			−0.163759			−0.0818795	+	0.996642i	$0.526092\pi$
$420$		0			0
$421$	7598.61	+	20877.0i	0.0428716	+	0.117789i	0.959281	−	0.282453i	$-0.0911482\pi$
$421$	7598.61	+	20877.0i	0.0428716	+	0.117789i	−0.916409	+	0.400242i	$0.868926\pi$
$422$		0			0
$423$	−11504.4	+	65244.5i	−0.0642957	+	0.364639i
$424$		0			0
$425$	109474.	+	189614.i	0.606082	+	1.04976i
$426$		0			0
$427$	−78006.4	+	65455.1i	−0.427833	+	0.358995i
$428$		0			0
$429$	−101109.	+	175125.i	−0.549381	+	0.951557i
$430$		0			0
$431$	−68732.4	+	188841.i	−0.370005	+	1.01658i	0.605354	+	0.795956i	$0.293031\pi$
$431$	−68732.4	+	188841.i	−0.370005	+	1.01658i	−0.975359	+	0.220623i	$0.929191\pi$
$432$		0			0
$433$	−273497.	+	48224.8i	−1.45873	+	0.257214i	−0.846046	−	0.533111i	$-0.821023\pi$
$433$	−273497.	+	48224.8i	−1.45873	+	0.257214i	−0.612688	+	0.790325i	$0.709912\pi$
$434$		0			0
$435$	41693.4	+	34984.9i	0.220337	+	0.184885i
$436$		0			0
$437$	154390.	−	139181.i	0.808454	−	0.728813i
$438$		0			0
$439$	447.225	−	532.982i	0.00232058	−	0.00276556i	−0.764883	−	0.644169i	$-0.777203\pi$
$439$	447.225	−	532.982i	0.00232058	−	0.00276556i	0.767203	+	0.641404i	$0.221648\pi$
$440$		0			0
$441$	22490.5	+	127550.i	0.115644	+	0.655847i
$442$		0			0
$443$	117220.	+	42664.7i	0.597303	+	0.217401i	0.622939	−	0.782271i	$-0.285939\pi$
$443$	117220.	+	42664.7i	0.597303	+	0.217401i	−0.0256353	+	0.999671i	$0.508161\pi$
$444$		0			0
$445$	−49531.1	−	28596.8i	−0.250125	−	0.144410i
$446$		0			0
$447$	87828.9	+	104670.i	0.439564	+	0.523852i
$448$		0			0
$449$	66839.9	−	38590.0i	0.331545	−	0.191418i	−0.324982	−	0.945720i	$-0.605358\pi$
$449$	66839.9	−	38590.0i	0.331545	−	0.191418i	0.656527	+	0.754302i	$0.272025\pi$
$450$		0			0
$451$	−362230.	−	63870.9i	−1.78087	−	0.314015i
$452$		0			0
$453$	205727.	−	74878.4i	1.00252	−	0.364888i
$454$		0			0
$455$			172147.i			0.831529i
$456$		0			0
$457$	203300.			0.973432			0.486716	−	0.873560i	$-0.338195\pi$
$457$	203300.			0.973432			0.486716	+	0.873560i	$0.338195\pi$
$458$		0			0
$459$	−120283.	−	330475.i	−0.570926	−	1.56861i
$460$		0			0
$461$	41048.6	−	232798.i	0.193151	−	1.09541i	−0.721877	−	0.692022i	$-0.756720\pi$
$461$	41048.6	−	232798.i	0.193151	−	1.09541i	0.915028	−	0.403391i	$-0.132169\pi$
$462$		0			0
$463$	65503.2	+	113455.i	0.305563	+	0.529250i	0.977386	−	0.211461i	$-0.0678220\pi$
$463$	65503.2	+	113455.i	0.305563	+	0.529250i	−0.671824	+	0.740711i	$0.734489\pi$
$464$		0			0
$465$	36900.4	−	30963.1i	0.170657	−	0.143198i
$466$		0			0
$467$	75152.4	−	130168.i	0.344595	−	0.596856i	−0.640685	−	0.767804i	$-0.721350\pi$
$467$	75152.4	−	130168.i	0.344595	−	0.596856i	0.985280	+	0.170948i	$0.0546829\pi$
$468$		0			0
$469$	132333.	−	363582.i	0.601621	−	1.65294i
$470$		0			0
$471$	−97014.0	+	17106.2i	−0.437313	+	0.0771101i
$472$		0			0
$473$	−326205.	−	273718.i	−1.45803	−	1.22344i
$474$		0			0
$475$	−36751.4	−	172394.i	−0.162887	−	0.764073i
$476$		0			0
$477$	−44748.3	+	53328.9i	−0.196671	+	0.234383i
$478$		0			0
$479$	−607.917	−	3447.67i	−0.00264956	−	0.0150264i	0.983454	−	0.181156i	$-0.0579840\pi$
$479$	−607.917	−	3447.67i	−0.00264956	−	0.0150264i	−0.986104	+	0.166130i	$0.946873\pi$
$480$		0			0
$481$	409695.	+	149117.i	1.77080	+	0.644519i
$482$		0			0
$483$	257698.	+	148782.i	1.10463	+	0.637759i
$484$		0			0
$485$	494.796	+	589.675i	0.00210350	+	0.00250686i
$486$		0			0
$487$	291020.	−	168020.i	1.22706	−	0.708442i	0.260644	−	0.965435i	$-0.416065\pi$
$487$	291020.	−	168020.i	1.22706	−	0.708442i	0.966413	+	0.256993i	$0.0827319\pi$
$488$		0			0
$489$	−64575.9	−	11386.5i	−0.270055	−	0.0476180i
$490$		0			0
$491$	5044.74	−	1836.14i	0.0209255	−	0.00761626i	−0.331536	−	0.943443i	$-0.607567\pi$
$491$	5044.74	−	1836.14i	0.0209255	−	0.00761626i	0.352462	+	0.935826i	$0.385345\pi$
$492$		0			0
$493$			312099.i			1.28410i
$494$		0			0
$495$	67319.6			0.274746
$496$		0			0
$497$	−125218.	−	344033.i	−0.506936	−	1.39280i
$498$		0			0
$499$	−55118.2	+	312591.i	−0.221357	+	1.25538i	0.648171	+	0.761495i	$0.275534\pi$
$499$	−55118.2	+	312591.i	−0.221357	+	1.25538i	−0.869528	+	0.493884i	$0.835577\pi$
$500$		0			0
$501$	−97589.7	−	169030.i	−0.388802	−	0.673425i
$502$		0			0
$503$	166647.	−	139833.i	0.658659	−	0.552681i	−0.251025	−	0.967980i	$-0.580768\pi$
$503$	166647.	−	139833.i	0.658659	−	0.552681i	0.909685	+	0.415300i	$0.136323\pi$
$504$		0			0
$505$	28281.4	−	48984.8i	0.110897	−	0.192078i
$506$		0			0
$507$	−17697.0	+	48622.0i	−0.0688467	+	0.189155i
$508$		0			0
$509$	141631.	−	24973.3i	0.546666	−	0.0963919i	0.106507	−	0.994312i	$-0.466033\pi$
$509$	141631.	−	24973.3i	0.546666	−	0.0963919i	0.440159	+	0.897920i	$0.354922\pi$
$510$		0			0
$511$	412884.	+	346451.i	1.58120	+	1.32678i
$512$		0			0
$513$	10050.6	+	282952.i	0.0381907	+	1.07517i
$514$		0			0
$515$	78952.6	−	94092.1i	0.297682	−	0.354763i
$516$		0			0
$517$	50332.9	+	285452.i	0.188309	+	1.06795i
$518$		0			0
$519$	−270481.	−	98447.0i	−1.00416	−	0.365484i
$520$		0			0
$521$	−147332.	−	85062.1i	−0.542777	−	0.313372i	0.203427	−	0.979090i	$-0.434792\pi$
$521$	−147332.	−	85062.1i	−0.542777	−	0.313372i	−0.746204	+	0.665718i	$0.768125\pi$
$522$		0			0
$523$	79213.6	+	94403.1i	0.289599	+	0.345130i	0.891154	−	0.453701i	$-0.149897\pi$
$523$	79213.6	+	94403.1i	0.289599	+	0.345130i	−0.601555	+	0.798831i	$0.705452\pi$
$524$		0			0
$525$	218527.	−	126167.i	0.792842	−	0.457748i
$526$		0			0
$527$	272024.	+	47965.2i	0.979460	+	0.172705i
$528$		0			0
$529$	−48586.8	+	17684.1i	−0.173623	+	0.0631935i
$530$		0			0
$531$			74631.8i			0.264688i
$532$		0			0
$533$	−441540.			−1.55423
$534$		0			0
$535$	−71357.7	−	196054.i	−0.249306	−	0.684963i
$536$		0			0
$537$	71321.7	−	404485.i	0.247328	−	1.40267i
$538$		0			0
$539$	283327.	+	490737.i	0.975238	+	1.68916i
$540$		0			0
$541$	−222820.	+	186969.i	−0.761308	+	0.638813i	−0.938467	−	0.345369i	$-0.887754\pi$
$541$	−222820.	+	186969.i	−0.761308	+	0.638813i	0.177159	+	0.984182i	$0.443309\pi$
$542$		0			0
$543$	40902.7	−	70845.5i	0.138724	−	0.240277i
$544$		0			0
$545$	−27127.2	+	74531.3i	−0.0913296	+	0.250926i
$546$		0			0
$547$	186506.	−	32886.0i	0.623329	−	0.109910i	0.146942	−	0.989145i	$-0.453057\pi$
$547$	186506.	−	32886.0i	0.623329	−	0.109910i	0.476388	+	0.879235i	$0.341946\pi$
$548$		0			0
$549$	36619.2	+	30727.1i	0.121496	+	0.101948i
$550$		0			0
$551$	77501.0	−	239011.i	0.255272	−	0.787252i
$552$		0			0
$553$	293153.	−	349366.i	0.958613	−	1.14243i
$554$		0			0
$555$	31074.0	+	176229.i	0.100881	+	0.572127i
$556$		0			0
$557$	−177494.	−	64602.5i	−0.572101	−	0.208228i	0.0397378	−	0.999210i	$-0.487348\pi$
$557$	−177494.	−	64602.5i	−0.572101	−	0.208228i	−0.611839	+	0.790982i	$0.709570\pi$
$558$		0			0
$559$	−442694.	−	255589.i	−1.41671	−	0.817936i
$560$		0			0
$561$	−305927.	−	364590.i	−0.972058	−	1.15845i
$562$		0			0
$563$	238656.	−	137788.i	0.752931	−	0.434705i	−0.0738207	−	0.997272i	$-0.523519\pi$
$563$	238656.	−	137788.i	0.752931	−	0.434705i	0.826752	+	0.562566i	$0.190186\pi$
$564$		0			0
$565$	−106896.	−	18848.7i	−0.334862	−	0.0590452i
$566$		0			0
$567$	−167503.	+	60966.2i	−0.521023	+	0.189637i
$568$		0			0
$569$			201455.i			0.622233i	0.950372	+	0.311116i	$0.100703\pi$
$569$			201455.i			0.622233i	−0.950372	+	0.311116i	$0.899297\pi$
$570$		0			0
$571$	206021.			0.631885			0.315943	−	0.948778i	$-0.397679\pi$
$571$	206021.			0.631885			0.315943	+	0.948778i	$0.397679\pi$
$572$		0			0
$573$	78573.2	+	215878.i	0.239312	+	0.657506i
$574$		0			0
$575$	−48821.1	+	276878.i	−0.147663	+	0.837439i
$576$		0			0
$577$	51593.6	+	89362.8i	0.154969	+	0.268414i	0.933048	−	0.359753i	$-0.117139\pi$
$577$	51593.6	+	89362.8i	0.154969	+	0.268414i	−0.778079	+	0.628167i	$0.783806\pi$
$578$		0			0
$579$	−282529.	+	237070.i	−0.842763	+	0.707162i
$580$		0			0
$581$	−186833.	+	323604.i	−0.553478	+	0.958653i
$582$		0			0
$583$	−104172.	+	286210.i	−0.306488	+	0.842068i
$584$		0			0
$585$	79584.8	−	14032.9i	0.232551	−	0.0410050i
$586$		0			0
$587$	101118.	+	84847.8i	0.293461	+	0.246243i	0.777616	−	0.628739i	$-0.216429\pi$
$587$	101118.	+	84847.8i	0.293461	+	0.246243i	−0.484155	+	0.874982i	$0.660873\pi$
$588$		0			0
$589$	−196410.	−	104282.i	−0.566151	−	0.300593i
$590$		0			0
$591$	−13156.2	+	15679.0i	−0.0376666	+	0.0448894i
$592$		0			0
$593$	−87272.3	−	494946.i	−0.248180	−	1.40750i	−0.812990	−	0.582278i	$-0.802161\pi$
$593$	−87272.3	−	494946.i	−0.248180	−	1.40750i	0.564809	−	0.825221i	$-0.308950\pi$
$594$		0			0
$595$	−380731.	−	138575.i	−1.07543	−	0.391426i
$596$		0			0
$597$	−171313.	−	98907.5i	−0.480664	−	0.277511i
$598$		0			0
$599$	−68182.5	−	81256.7i	−0.190029	−	0.226467i	0.662615	−	0.748960i	$-0.269447\pi$
$599$	−68182.5	−	81256.7i	−0.190029	−	0.226467i	−0.852644	+	0.522493i	$0.825002\pi$
$600$		0			0
$601$	−370588.	+	213959.i	−1.02599	+	0.592355i	−0.915833	−	0.401559i	$-0.868468\pi$
$601$	−370588.	+	213959.i	−1.02599	+	0.592355i	−0.110156	+	0.993914i	$0.535135\pi$
$602$		0			0
$603$	−178874.	−	31540.3i	−0.491940	−	0.0867422i
$604$		0			0
$605$	115898.	−	42183.3i	0.316639	−	0.115247i
$606$		0			0
$607$		−	158805.i		−	0.431009i	−0.976503	−	0.215504i	$-0.930860\pi$
$607$		−	158805.i		−	0.431009i	0.976503	−	0.215504i	$-0.0691395\pi$
$608$		0			0
$609$	359690.			0.969825
$610$		0			0
$611$	119006.	+	326967.i	0.318778	+	0.875835i
$612$		0			0
$613$	32986.8	−	187077.i	0.0877848	−	0.497852i	−0.908936	−	0.416935i	$-0.863104\pi$
$613$	32986.8	−	187077.i	0.0877848	−	0.497852i	0.996721	−	0.0809167i	$-0.0257848\pi$
$614$		0			0
$615$	−90613.3	−	156947.i	−0.239575	−	0.414956i
$616$		0			0
$617$	−98890.7	+	82979.1i	−0.259768	+	0.217971i	−0.763365	−	0.645968i	$-0.776454\pi$
$617$	−98890.7	+	82979.1i	−0.259768	+	0.217971i	0.503597	+	0.863939i	$0.332010\pi$
$618$		0			0
$619$	156923.	−	271799.i	0.409549	−	0.709359i	−0.585290	−	0.810824i	$-0.699020\pi$
$619$	156923.	−	271799.i	0.409549	−	0.709359i	0.994839	+	0.101465i	$0.0323528\pi$
$620$		0			0
$621$	154456.	−	424363.i	0.400516	−	1.10041i
$622$		0			0
$623$	−372232.	+	65634.6i	−0.959042	+	0.169105i
$624$		0			0
$625$	117175.	+	98321.8i	0.299969	+	0.251704i
$626$		0			0
$627$	143748.	+	355177.i	0.365652	+	0.903462i
$628$		0			0
$629$	−659590.	+	786068.i	−1.66714	+	1.98682i
$630$		0			0
$631$	−102049.	−	578750.i	−0.256301	−	1.45356i	−0.792710	−	0.609599i	$-0.791330\pi$
$631$	−102049.	−	578750.i	−0.256301	−	1.45356i	0.536408	−	0.843959i	$-0.319781\pi$
$632$		0			0
$633$	−70618.1	−	25702.9i	−0.176242	−	0.0641467i
$634$		0			0
$635$	35009.6	+	20212.8i	0.0868239	+	0.0501278i
$636$		0			0
$637$	437243.	+	521085.i	1.07757	+	1.28419i
$638$		0			0
$639$	−148841.	+	85933.5i	−0.364520	+	0.210456i
$640$		0			0
$641$	242434.	+	42747.6i	0.590034	+	0.104039i	0.460690	−	0.887561i	$-0.347602\pi$
$641$	242434.	+	42747.6i	0.590034	+	0.104039i	0.129344	+	0.991600i	$0.458713\pi$
$642$		0			0
$643$	−448205.	+	163133.i	−1.08406	+	0.394567i	−0.821419	−	0.570325i	$-0.806817\pi$
$643$	−448205.	+	163133.i	−1.08406	+	0.394567i	−0.262646	+	0.964892i	$0.584595\pi$
$644$		0			0
$645$		−	209809.i		−	0.504319i
$646$		0			0
$647$	104424.			0.249454			0.124727	−	0.992191i	$-0.460195\pi$
$647$	104424.			0.249454			0.124727	+	0.992191i	$0.460195\pi$
$648$		0			0
$649$	111677.	+	306831.i	0.265140	+	0.728467i
$650$		0			0
$651$	55279.2	−	313504.i	0.130437	−	0.739744i
$652$		0			0
$653$	−136854.	−	237038.i	−0.320945	−	0.555893i	0.659738	−	0.751495i	$-0.270667\pi$
$653$	−136854.	−	237038.i	−0.320945	−	0.555893i	−0.980683	+	0.195602i	$0.937334\pi$
$654$		0			0
$655$	143997.	−	120828.i	0.335638	−	0.281634i
$656$		0			0
$657$	126509.	−	219120.i	0.293084	−	0.507636i
$658$		0			0
$659$	−169164.	+	464776.i	−0.389528	+	1.07022i	0.577687	+	0.816258i	$0.303955\pi$
$659$	−169164.	+	464776.i	−0.389528	+	1.07022i	−0.967215	+	0.253960i	$0.918267\pi$
$660$		0			0
$661$	123889.	−	21845.0i	0.283550	−	0.0499975i	−0.0300643	−	0.999548i	$-0.509571\pi$
$661$	123889.	−	21845.0i	0.283550	−	0.0499975i	0.313614	+	0.949550i	$0.398460\pi$
$662$		0			0
$663$	−437664.	−	367244.i	−0.995667	−	0.835464i
$664$		0			0
$665$	257159.	+	200666.i	0.581511	+	0.453765i
$666$		0			0
$667$	−257607.	+	307005.i	−0.579038	+	0.690070i
$668$		0			0
$669$	38531.3	+	218522.i	0.0860916	+	0.488250i
$670$		0			0
$671$	196530.	+	71531.2i	0.436501	+	0.158873i
$672$		0			0
$673$	365687.	+	211130.i	0.807383	+	0.466143i	0.846046	−	0.533110i	$-0.178977\pi$
$673$	365687.	+	211130.i	0.807383	+	0.466143i	−0.0386634	+	0.999252i	$0.512310\pi$
$674$		0			0
$675$	−246158.	−	293359.i	−0.540263	−	0.643861i
$676$		0			0
$677$	−553872.	+	319778.i	−1.20846	+	0.697704i	−0.962422	−	0.271557i	$-0.912461\pi$
$677$	−553872.	+	319778.i	−1.20846	+	0.697704i	−0.246036	+	0.969261i	$0.579128\pi$
$678$		0			0
$679$	5009.86	+	883.373i	0.0108664	+	0.00191604i
$680$		0			0
$681$	236524.	−	86087.6i	0.510012	−	0.185629i
$682$		0			0
$683$			23651.0i			0.0507000i	0.999679	+	0.0253500i	$0.00807003\pi$
$683$			23651.0i			0.0507000i	−0.999679	+	0.0253500i	$0.991930\pi$
$684$		0			0
$685$	142655.			0.304022
$686$		0			0
$687$	191248.	+	525450.i	0.405213	+	1.11331i
$688$		0			0
$689$	−63490.0	+	360070.i	−0.133742	+	0.758487i
$690$		0			0
$691$	−263775.	−	456872.i	−0.552430	−	0.956837i	−0.998098	−	0.0616392i	$-0.980367\pi$
$691$	−263775.	−	456872.i	−0.552430	−	0.956837i	0.445668	−	0.895198i	$-0.352966\pi$
$692$		0			0
$693$	340809.	−	285973.i	0.709651	−	0.595468i
$694$		0			0
$695$	48708.7	−	84365.9i	0.100841	−	0.174661i
$696$		0			0
$697$	355429.	−	976534.i	0.731624	−	2.01012i
$698$		0			0
$699$	590801.	−	104174.i	1.20917	−	0.213209i
$700$		0			0
$701$	77321.9	+	64880.8i	0.157350	+	0.132032i	0.718064	−	0.695978i	$-0.245029\pi$
$701$	77321.9	+	64880.8i	0.157350	+	0.132032i	−0.560714	+	0.828010i	$0.689473\pi$
$702$		0			0
$703$	700322.	−	438193.i	1.41706	−	0.886656i
$704$		0			0
$705$	−91799.1	+	109402.i	−0.184697	+	0.220113i
$706$		0			0
$707$	−64910.7	−	368127.i	−0.129861	−	0.736476i
$708$		0			0
$709$	241224.	+	87798.4i	0.479875	+	0.174660i	0.570621	−	0.821214i	$-0.306703\pi$
$709$	241224.	+	87798.4i	0.479875	+	0.174660i	−0.0907454	+	0.995874i	$0.528925\pi$
$710$		0			0
$711$	−185411.	−	107047.i	−0.366772	−	0.211756i
$712$		0			0
$713$	227993.	+	271712.i	0.448480	+	0.534478i
$714$		0			0
$715$	306196.	−	176782.i	0.598945	−	0.345801i
$716$		0			0
$717$	320644.	+	56538.2i	0.623713	+	0.109978i
$718$		0			0
$719$	82282.6	−	29948.4i	0.159166	−	0.0579317i	−0.261208	−	0.965282i	$-0.584121\pi$
$719$	82282.6	−	29948.4i	0.159166	−	0.0579317i	0.420374	+	0.907351i	$0.361899\pi$
$720$		0			0
$721$		−	811735.i		−	1.56151i
$722$		0			0
$723$	−111485.			−0.213275
$724$		0			0
$725$	116235.	+	319353.i	0.221137	+	0.607568i
$726$		0			0
$727$	5021.81	−	28480.1i	0.00950148	−	0.0538856i	−0.979688	−	0.200526i	$-0.935735\pi$
$727$	5021.81	−	28480.1i	0.00950148	−	0.0538856i	0.989190	+	0.146640i	$0.0468460\pi$
$728$		0			0
$729$	254265.	+	440400.i	0.478445	+	0.828690i
$730$		0			0
$731$	921635.	−	773343.i	1.72474	−	1.44723i
$732$		0			0
$733$	−239223.	+	414347.i	−0.445241	+	0.771180i	−0.998069	−	0.0621152i	$-0.980215\pi$
$733$	−239223.	+	414347.i	−0.445241	+	0.771180i	0.552828	+	0.833295i	$0.313549\pi$
$734$		0			0
$735$	−95490.2	+	262357.i	−0.176760	+	0.485644i
$736$		0			0
$737$	−782593.	+	137992.i	−1.44079	+	0.254050i
$738$		0			0
$739$	−547603.	−	459493.i	−1.00271	−	0.841376i	−0.0153548	−	0.999882i	$-0.504888\pi$
$739$	−547603.	−	459493.i	−1.00271	−	0.841376i	−0.987358	+	0.158506i	$0.949332\pi$
$740$		0			0
$741$	243976.	+	389923.i	0.444335	+	0.710137i
$742$		0			0
$743$	59406.1	−	70797.5i	0.107610	−	0.128245i	−0.709551	−	0.704654i	$-0.751102\pi$
$743$	59406.1	−	70797.5i	0.107610	−	0.128245i	0.817161	+	0.576409i	$0.195547\pi$
$744$		0			0
$745$	−41484.9	−	235272.i	−0.0747441	−	0.423895i
$746$		0			0
$747$	164834.	+	59994.7i	0.295397	+	0.107516i
$748$		0			0
$749$	−1.19408e6	−	689405.i	−2.12849	−	1.22888i
$750$		0			0
$751$	486298.	+	579548.i	0.862229	+	1.02757i	0.999315	+	0.0370059i	$0.0117820\pi$
$751$	486298.	+	579548.i	0.862229	+	1.02757i	−0.137086	+	0.990559i	$0.543774\pi$
$752$		0			0
$753$	392939.	−	226863.i	0.693003	−	0.400105i
$754$		0			0
$755$	−376969.	−	66469.8i	−0.661321	−	0.116609i
$756$		0			0
$757$	−451854.	+	164461.i	−0.788509	+	0.286994i	−0.704716	−	0.709490i	$-0.748926\pi$
$757$	−451854.	+	164461.i	−0.788509	+	0.286994i	−0.0837927	+	0.996483i	$0.526703\pi$
$758$		0			0
$759$		−	611151.i		−	1.06088i
$760$		0			0
$761$	738590.			1.27536			0.637682	−	0.770299i	$-0.279893\pi$
$761$	738590.			1.27536			0.637682	+	0.770299i	$0.279893\pi$
$762$		0			0
$763$	179275.	+	492554.i	0.307943	+	0.846067i
$764$		0			0
$765$	−33027.9	+	187310.i	−0.0564362	+	0.320066i
$766$		0			0
$767$	195984.	+	339454.i	0.333142	+	0.577019i
$768$		0			0
$769$	468069.	−	392756.i	0.791511	−	0.664157i	−0.154608	−	0.987976i	$-0.549411\pi$
$769$	468069.	−	392756.i	0.791511	−	0.664157i	0.946119	+	0.323819i	$0.104967\pi$
$770$		0			0
$771$	75943.7	−	131538.i	0.127757	−	0.221281i
$772$		0			0
$773$	−60864.5	+	167224.i	−0.101860	+	0.279859i	−0.980146	−	0.198277i	$-0.936465\pi$
$773$	−60864.5	+	167224.i	−0.101860	+	0.279859i	0.878286	+	0.478136i	$0.158688\pi$
$774$		0			0
$775$	296210.	−	52229.9i	0.493170	−	0.0869592i
$776$		0			0
$777$	905932.	+	760168.i	1.50056	+	1.25912i
$778$		0			0
$779$	−514688.	+	659585.i	−0.848143	+	1.08692i
$780$		0			0
$781$	−483337.	+	576018.i	−0.792406	+	0.944352i
$782$		0			0
$783$	−94791.4	−	537589.i	−0.154613	−	0.876853i
$784$		0			0
$785$	161852.	+	58909.4i	0.262651	+	0.0955972i
$786$		0			0
$787$	−415176.	−	239702.i	−0.670321	−	0.387010i	0.125877	−	0.992046i	$-0.459825\pi$
$787$	−415176.	−	239702.i	−0.670321	−	0.387010i	−0.796198	+	0.605036i	$0.793159\pi$
$788$		0			0
$789$	188560.	+	224717.i	0.302898	+	0.360980i
$790$		0			0
$791$	−621236.	+	358671.i	−0.992896	+	0.573249i
$792$		0			0
$793$	247248.	+	43596.4i	0.393175	+	0.0693274i
$794$		0			0
$795$	−141018.	+	51326.2i	−0.223120	+	0.0812091i
$796$		0			0
$797$			242438.i			0.381667i	0.981622	+	0.190833i	$0.0611190\pi$
$797$			242438.i			0.381667i	−0.981622	+	0.190833i	$0.938881\pi$
$798$		0			0
$799$	−818937.			−1.28279
$800$		0			0
$801$	60686.5	+	166735.i	0.0945861	+	0.259873i
$802$		0			0
$803$	192226.	−	1.09017e6i	0.298113	−	1.69068i
$804$		0			0
$805$	−260136.	−	450569.i	−0.401429	−	0.695296i
$806$		0			0
$807$	−306211.	+	256941.i	−0.470190	+	0.394536i
$808$		0			0
$809$	579718.	−	1.00410e6i	0.885768	−	1.53419i	0.0409364	−	0.999162i	$-0.486966\pi$
$809$	579718.	−	1.00410e6i	0.885768	−	1.53419i	0.844831	−	0.535033i	$-0.179701\pi$
$810$		0			0
$811$	−126174.	+	346659.i	−0.191835	+	0.527061i	−0.997901	−	0.0647646i	$-0.979370\pi$
$811$	−126174.	+	346659.i	−0.191835	+	0.527061i	0.806066	+	0.591826i	$0.201593\pi$
$812$		0			0
$813$	−252042.	+	44441.8i	−0.381322	+	0.0672373i
$814$		0			0
$815$	87825.9	+	73694.6i	0.132223	+	0.110948i
$816$		0			0
$817$	−897840.	+	363377.i	−1.34510	+	0.544394i
$818$		0			0
$819$	343290.	−	409117.i	0.511792	−	0.609930i
$820$		0			0
$821$	162294.	+	920417.i	0.240778	+	1.36552i	0.830096	+	0.557620i	$0.188285\pi$
$821$	162294.	+	920417.i	0.240778	+	1.36552i	−0.589318	+	0.807901i	$0.700603\pi$
$822$		0			0
$823$	−821423.	−	298973.i	−1.21274	−	0.441401i	−0.345085	−	0.938571i	$-0.612150\pi$
$823$	−821423.	−	298973.i	−1.21274	−	0.441401i	−0.867653	+	0.497171i	$0.834372\pi$
$824$		0			0
$825$	−448821.	−	259127.i	−0.659425	−	0.380719i
$826$		0			0
$827$	−24737.0	−	29480.4i	−0.0361689	−	0.0431045i	0.747657	−	0.664085i	$-0.231179\pi$
$827$	−24737.0	−	29480.4i	−0.0361689	−	0.0431045i	−0.783826	+	0.620981i	$0.786734\pi$
$828$		0			0
$829$	1.05216e6	−	607466.i	1.53100	−	0.883921i	0.531679	−	0.846946i	$-0.321561\pi$
$829$	1.05216e6	−	607466.i	1.53100	−	0.883921i	0.999316	−	0.0369746i	$-0.0117721\pi$
$830$		0			0
$831$	−29252.1	−	5157.94i	−0.0423599	−	0.00746920i
$832$		0			0
$833$	−1.50443e6	+	547569.i	−2.16812	+	0.789130i
$834$		0			0
$835$			341259.i			0.489453i
$836$		0			0
$837$	−483129.			−0.689623
$838$		0			0
$839$	345872.	+	950276.i	0.491351	+	1.34998i	0.899444	+	0.437035i	$0.143972\pi$
$839$	345872.	+	950276.i	0.491351	+	1.34998i	−0.408093	+	0.912940i	$0.633806\pi$
$840$		0			0
$841$	38696.3	−	219458.i	0.0547113	−	0.310283i
$842$		0			0
$843$	390908.	+	677073.i	0.550072	+	0.952753i
$844$		0			0
$845$	69302.8	−	58152.0i	0.0970594	−	0.0814425i
$846$		0			0
$847$	407544.	−	705887.i	0.568078	−	0.983939i
$848$		0			0
$849$	−140084.	+	384878.i	−0.194345	+	0.533959i
$850$		0			0
$851$	−1.29765e6	+	228810.i	−1.79183	+	0.315948i
$852$		0			0
$853$	716054.	+	600841.i	0.984120	+	0.825774i	0.984706	−	0.174226i	$-0.0557422\pi$
$853$	716054.	+	600841.i	0.984120	+	0.825774i	−0.000586269		1.00000i	$0.500187\pi$
$854$		0			0
$855$	71806.5	−	135244.i	0.0982271	−	0.185006i
$856$		0			0
$857$	−54370.9	+	64796.7i	−0.0740295	+	0.0882250i	−0.801788	−	0.597608i	$-0.796118\pi$
$857$	−54370.9	+	64796.7i	−0.0740295	+	0.0882250i	0.727759	+	0.685833i	$0.240562\pi$
$858$		0			0
$859$	80318.4	+	455508.i	0.108850	+	0.617319i	0.989612	+	0.143761i	$0.0459196\pi$
$859$	80318.4	+	455508.i	0.108850	+	0.617319i	−0.880762	+	0.473558i	$0.842969\pi$
$860$		0			0
$861$	−1.12544e6	−	409627.i	−1.51816	−	0.552564i
$862$		0			0
$863$	793201.	+	457955.i	1.06503	+	0.614895i	0.926819	−	0.375508i	$-0.122532\pi$
$863$	793201.	+	457955.i	1.06503	+	0.614895i	0.138210	+	0.990403i	$0.455865\pi$
$864$		0			0
$865$	323495.	+	385527.i	0.432350	+	0.515255i
$866$		0			0
$867$	680803.	−	393062.i	0.905697	−	0.522905i
$868$		0			0
$869$	−922456.	−	162654.i	−1.22154	−	0.215390i
$870$		0			0
$871$	−896411.	+	326267.i	−1.18160	+	0.430068i
$872$		0			0
$873$		−	2388.10i		−	0.00313346i
$874$		0			0
$875$	−1.00592e6			−1.31385
$876$		0			0
$877$	−156587.	−	430218.i	−0.203590	−	0.559358i	0.795313	−	0.606199i	$-0.207307\pi$
$877$	−156587.	−	430218.i	−0.203590	−	0.559358i	−0.998902	+	0.0468416i	$0.985084\pi$
$878$		0			0
$879$	178096.	−	1.01003e6i	0.230503	−	1.30725i
$880$		0			0
$881$	−436910.	−	756750.i	−0.562912	−	0.974991i	−0.997241	−	0.0742372i	$-0.976348\pi$
$881$	−436910.	−	756750.i	−0.562912	−	0.974991i	0.434329	−	0.900754i	$-0.356986\pi$
$882$		0			0
$883$	959270.	−	804923.i	1.23032	−	1.03236i	0.232106	−	0.972690i	$-0.425438\pi$
$883$	959270.	−	804923.i	1.23032	−	1.03236i	0.998218	−	0.0596742i	$-0.0190062\pi$
$884$		0			0
$885$	−80440.1	+	139326.i	−0.102704	+	0.177888i
$886$		0			0
$887$	453842.	−	1.24692e6i	0.576843	−	1.58486i	−0.216627	−	0.976254i	$-0.569506\pi$
$887$	453842.	−	1.24692e6i	0.576843	−	1.58486i	0.793470	−	0.608609i	$-0.208272\pi$
$888$		0			0
$889$	263101.	−	46391.9i	0.332904	−	0.0587000i
$890$		0			0
$891$	280453.	+	235328.i	0.353268	+	0.296427i
$892$		0			0
$893$	627155.	+	203360.i	0.786452	+	0.255013i
$894$		0			0
$895$	−461603.	+	550117.i	−0.576265	+	0.686766i
$896$		0			0
$897$	−127396.	−	722499.i	−0.158333	−	0.897950i
$898$		0			0
$899$	402891.	+	146640.i	0.498504	+	0.181440i
$900$		0			0
$901$	−745243.	−	430266.i	−0.918012	−	0.530014i
$902$		0			0
$903$	−891267.	−	1.06217e6i	−1.09303	−	1.30262i
$904$		0			0
$905$	−123869.	+	71515.7i	−0.151239	+	0.0873181i
$906$		0			0
$907$	−414291.	−	73050.7i	−0.503606	−	0.0887993i	−0.0839270	−	0.996472i	$-0.526746\pi$
$907$	−414291.	−	73050.7i	−0.503606	−	0.0887993i	−0.419679	+	0.907673i	$0.637857\pi$
$908$		0			0
$909$	−164896.	+	60017.2i	−0.199564	+	0.0726354i
$910$		0			0
$911$			1.34150e6i			1.61642i	0.588898	+	0.808208i	$0.299562\pi$
$911$			1.34150e6i			1.61642i	−0.588898	+	0.808208i	$0.700438\pi$
$912$		0			0
$913$	767451.			0.920681
$914$		0			0
$915$	35244.0	+	96832.0i	0.0420962	+	0.115658i
$916$		0			0
$917$	215717.	−	1.22339e6i	0.256535	−	1.45488i
$918$		0			0
$919$	653377.	+	1.13168e6i	0.773629	+	1.33996i	0.935562	+	0.353162i	$0.114894\pi$
$919$	653377.	+	1.13168e6i	0.773629	+	1.33996i	−0.161933	+	0.986802i	$0.551773\pi$
$920$		0			0
$921$	157961.	−	132545.i	0.186221	−	0.156258i
$922$		0			0
$923$	−451325.	+	781717.i	−0.529768	+	0.917585i
$924$		0			0
$925$	−382164.	+	1.04999e6i	−0.446649	+	1.22716i
$926$		0			0
$927$	−375270.	+	66170.3i	−0.436701	+	0.0770022i
$928$		0			0
$929$	1.08100e6	+	907070.i	1.25255	+	1.05102i	0.996434	+	0.0843710i	$0.0268881\pi$
$929$	1.08100e6	+	907070.i	1.25255	+	1.05102i	0.256118	+	0.966645i	$0.417556\pi$
$930$		0			0
$931$	1.28809e6	−	45753.7i	1.48610	−	0.0527869i
$932$		0			0
$933$	−572753.	+	682580.i	−0.657967	+	0.784134i
$934$		0			0
$935$	144501.	+	819505.i	0.165290	+	0.937408i
$936$		0			0
$937$	293229.	+	106727.i	0.333985	+	0.121561i	0.503569	−	0.863955i	$-0.332020\pi$
$937$	293229.	+	106727.i	0.333985	+	0.121561i	−0.169584	+	0.985516i	$0.554242\pi$
$938$		0			0
$939$	980443.	+	566059.i	1.11196	+	0.641993i
$940$		0			0
$941$	535358.	+	638014.i	0.604595	+	0.720529i	0.978340	−	0.207003i	$-0.0663709\pi$
$941$	535358.	+	638014.i	0.604595	+	0.720529i	−0.373745	+	0.927531i	$0.621926\pi$
$942$		0			0
$943$	1.15566e6	−	667221.i	1.29959	−	0.750320i
$944$		0			0
$945$	697895.	+	123058.i	0.781495	+	0.137799i
$946$		0			0
$947$	−557287.	+	202836.i	−0.621411	+	0.226175i	−0.633489	−	0.773752i	$-0.718378\pi$
$947$	−557287.	+	202836.i	−0.621411	+	0.226175i	0.0120779	+	0.999927i	$0.496155\pi$
$948$		0			0
$949$		−	1.32886e6i		−	1.47552i
$950$		0			0
$951$	98237.7			0.108622
$952$		0			0
$953$	−42293.0	−	116199.i	−0.0465675	−	0.127943i	0.914229	−	0.405198i	$-0.132798\pi$
$953$	−42293.0	−	116199.i	−0.0465675	−	0.127943i	−0.960796	+	0.277255i	$0.910575\pi$
$954$		0			0
$955$	69749.8	−	395571.i	0.0764779	−	0.433728i
$956$		0			0
$957$	−369374.	−	639774.i	−0.403313	−	0.698558i
$958$		0			0
$959$	722196.	−	605995.i	0.785268	−	0.658918i
$960$		0			0
$961$	−272031.	+	471171.i	−0.294558	+	0.510190i
$962$		0			0
$963$	−221378.	+	608231.i	−0.238716	+	0.655867i
$964$		0			0
$965$	635053.	−	111977.i	0.681954	−	0.120247i
$966$		0			0
$967$	−1.02135e6	−	857018.i	−1.09225	−	0.916510i	−0.0953735	−	0.995442i	$-0.530405\pi$
$967$	−1.02135e6	−	857018.i	−1.09225	−	0.916510i	−0.996880	+	0.0789320i	$0.974849\pi$
$968$		0			0
$969$	−1.05877e6	+	225712.i	−1.12760	+	0.240384i
$970$		0			0
$971$	55943.1	−	66670.3i	0.0593346	−	0.0707122i	−0.735561	−	0.677459i	$-0.763081\pi$
$971$	55943.1	−	66670.3i	0.0593346	−	0.0707122i	0.794895	+	0.606747i	$0.207526\pi$
$972$		0			0
$973$	−111795.	−	634020.i	−0.118085	−	0.669695i
$974$		0			0
$975$	−584609.	−	212780.i	−0.614973	−	0.223832i
$976$		0			0
$977$	−1.16020e6	−	669842.i	−1.21547	−	0.701751i	−0.251523	−	0.967851i	$-0.580932\pi$
$977$	−1.16020e6	−	669842.i	−1.21547	−	0.701751i	−0.963945	+	0.266100i	$0.914265\pi$
$978$		0			0
$979$	498997.	+	594681.i	0.520634	+	0.620467i
$980$		0			0
$981$	213097.	−	123031.i	0.221431	−	0.127843i
$982$		0			0
$983$	902579.	+	159149.i	0.934067	+	0.164701i	0.619913	−	0.784671i	$-0.287168\pi$
$983$	902579.	+	159149.i	0.934067	+	0.164701i	0.314154	+	0.949372i	$0.398279\pi$
$984$		0			0
$985$	33627.9	−	12239.6i	0.0346599	−	0.0126152i
$986$		0			0
$987$			943813.i			0.968839i
$988$		0			0
$989$	1.54491e6			1.57947
$990$		0			0
$991$	375939.	+	1.03288e6i	0.382798	+	1.05173i	0.970173	+	0.242414i	$0.0779392\pi$
$991$	375939.	+	1.03288e6i	0.382798	+	1.05173i	−0.587375	+	0.809315i	$0.699839\pi$
$992$		0			0
$993$	93187.4	−	528492.i	0.0945058	−	0.535969i
$994$		0			0
$995$	172933.	+	299530.i	0.174676	+	0.302547i
$996$		0			0
$997$	977356.	−	820099.i	0.983246	−	0.825042i	−0.00132954	−	0.999999i	$-0.500423\pi$
$997$	977356.	−	820099.i	0.983246	−	0.825042i	0.984576	+	0.174957i	$0.0559788\pi$
$998$		0			0
$999$	897393.	−	1.55433e6i	0.899191	−	1.55744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.41.3	yes	42
19.13	odd	18	inner	76.5.j.a.13.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.3	✓	42	19.13	odd	18	inner
76.5.j.a.41.3	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)

\(f(q)\)	\(=\)	\(q+(-2.28730 - 6.28431i) q^{3} +(-2.03045 + 11.5152i) q^{5} +(38.6373 + 66.9218i) q^{7} +(27.7888 - 23.3175i) q^{9} +O(q^{10})\)	\(q+(-2.28730 - 6.28431i) q^{3} +(-2.03045 + 11.5152i) q^{5} +(38.6373 + 66.9218i) q^{7} +(27.7888 - 23.3175i) q^{9} +(79.3551 - 137.447i) q^{11} +(65.1618 - 179.031i) q^{13} +(77.0097 - 13.5789i) q^{15} +(343.501 + 288.231i) q^{17} +(-191.484 - 306.031i) q^{19} +(332.182 - 395.879i) q^{21} +(99.9867 + 567.053i) q^{23} +(458.830 + 167.000i) q^{25} +(-679.220 - 392.148i) q^{27} +(447.390 + 533.179i) q^{29} +(533.474 - 308.001i) q^{31} +(-1045.27 - 184.309i) q^{33} +(-849.072 + 309.037i) q^{35} +2288.40i q^{37} -1274.13 q^{39} +(-792.647 - 2177.78i) q^{41} +(465.909 - 2642.30i) q^{43} +(212.083 + 367.339i) q^{45} +(-1399.04 + 1173.94i) q^{47} +(-1785.19 + 3092.03i) q^{49} +(1025.65 - 2817.94i) q^{51} +(-1889.93 + 333.245i) q^{53} +(1421.61 + 1192.87i) q^{55} +(-1485.21 + 1903.33i) q^{57} +(-1322.44 + 1576.02i) q^{59} +(228.828 + 1297.75i) q^{61} +(2634.13 + 958.747i) q^{63} +(1929.27 + 1113.87i) q^{65} +(-3218.45 - 3835.60i) q^{67} +(3334.84 - 1925.37i) q^{69} +(-4665.83 - 822.711i) q^{71} +(6554.25 - 2385.55i) q^{73} -3265.41i q^{75} +12264.3 q^{77} +(-2018.56 - 5545.94i) q^{79} +(-400.563 + 2271.71i) q^{81} +(2417.78 + 4187.71i) q^{83} +(-4016.51 + 3370.26i) q^{85} +(2327.35 - 4031.08i) q^{87} +(-1672.93 + 4596.33i) q^{89} +(14498.7 - 2556.52i) q^{91} +(-3155.80 - 2648.03i) q^{93} +(3912.82 - 1583.61i) q^{95} +(42.3160 - 50.4302i) q^{97} +(-999.747 - 5669.85i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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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