LMFDB - Embedded newform 76.5.j.a.53.3

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			53.3
Character	$\chi$	$=$	76.53
Dual form			76.5.j.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.57540 + 1.15942i) q^{3} +(15.2328 - 12.7819i) q^{5} +(-12.2068 + 21.1429i) q^{7} +(-34.2234 + 12.4563i) q^{9} +O(q^{10})$	\(q+(-6.57540 + 1.15942i) q^{3} +(15.2328 - 12.7819i) q^{5} +(-12.2068 + 21.1429i) q^{7} +(-34.2234 + 12.4563i) q^{9} +(29.7884 + 51.5951i) q^{11} +(-294.353 - 51.9023i) q^{13} +(-85.3424 + 101.707i) q^{15} +(-410.296 - 149.336i) q^{17} +(-296.839 + 205.445i) q^{19} +(55.7514 - 153.176i) q^{21} +(206.115 + 172.951i) q^{23} +(-39.8671 + 226.097i) q^{25} +(678.958 - 391.997i) q^{27} +(213.999 + 587.957i) q^{29} +(-287.088 - 165.751i) q^{31} +(-255.691 - 304.721i) q^{33} +(84.3004 + 478.091i) q^{35} -1580.58i q^{37} +1995.66 q^{39} +(-526.177 + 92.7792i) q^{41} +(627.564 - 526.589i) q^{43} +(-362.105 + 627.184i) q^{45} +(-655.645 + 238.635i) q^{47} +(902.486 + 1563.15i) q^{49} +(2871.00 + 506.236i) q^{51} +(2059.40 - 2454.30i) q^{53} +(1113.24 + 405.187i) q^{55} +(1713.64 - 1695.04i) q^{57} +(-64.7073 + 177.782i) q^{59} +(-2557.13 - 2145.68i) q^{61} +(154.398 - 875.634i) q^{63} +(-5147.23 + 2971.76i) q^{65} +(2383.52 + 6548.66i) q^{67} +(-1555.82 - 898.251i) q^{69} +(-3042.63 - 3626.06i) q^{71} +(-235.676 - 1336.58i) q^{73} -1532.90i q^{75} -1454.49 q^{77} +(2334.45 - 411.626i) q^{79} +(-1750.10 + 1468.51i) q^{81} +(-6430.23 + 11137.5i) q^{83} +(-8158.75 + 2969.54i) q^{85} +(-2088.82 - 3617.94i) q^{87} +(-11328.8 - 1997.58i) q^{89} +(4690.48 - 5589.90i) q^{91} +(2079.90 + 757.020i) q^{93} +(-1895.73 + 6923.66i) q^{95} +(4016.29 - 11034.7i) q^{97} +(-1662.15 - 1394.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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
$3$	−6.57540	+	1.15942i	−0.730600	+	0.128825i	−0.526560	−	0.850138i	$-0.676518\pi$
$3$	−6.57540	+	1.15942i	−0.730600	+	0.128825i	−0.204040	+	0.978963i	$0.565407\pi$
$4$		0			0
$5$	15.2328	−	12.7819i	0.609313	−	0.511274i	−0.285111	−	0.958495i	$-0.592030\pi$
$5$	15.2328	−	12.7819i	0.609313	−	0.511274i	0.894424	+	0.447220i	$0.147586\pi$
$6$		0			0
$7$	−12.2068	+	21.1429i	−0.249119	+	0.431487i	−0.963282	−	0.268493i	$-0.913474\pi$
$7$	−12.2068	+	21.1429i	−0.249119	+	0.431487i	0.714163	+	0.699980i	$0.246808\pi$
$8$		0			0
$9$	−34.2234	+	12.4563i	−0.422512	+	0.153782i
$10$		0			0
$11$	29.7884	+	51.5951i	0.246186	+	0.426406i	0.962464	−	0.271408i	$-0.0874894\pi$
$11$	29.7884	+	51.5951i	0.246186	+	0.426406i	−0.716279	+	0.697814i	$0.754156\pi$
$12$		0			0
$13$	−294.353	−	51.9023i	−1.74173	−	0.307114i	−0.789787	−	0.613382i	$-0.789809\pi$
$13$	−294.353	−	51.9023i	−1.74173	−	0.307114i	−0.951946	+	0.306267i	$0.900920\pi$
$14$		0			0
$15$	−85.3424	+	101.707i	−0.379299	+	0.452032i
$16$		0			0
$17$	−410.296	−	149.336i	−1.41971	−	0.516732i	−0.485746	−	0.874100i	$-0.661452\pi$
$17$	−410.296	−	149.336i	−1.41971	−	0.516732i	−0.933964	+	0.357368i	$0.883674\pi$
$18$		0			0
$19$	−296.839	+	205.445i	−0.822269	+	0.569099i
$19$	−296.839	+	205.445i	−0.822269	+	0.569099i
$20$		0			0
$21$	55.7514	−	153.176i	0.126420	−	0.347337i
$22$		0			0
$23$	206.115	+	172.951i	0.389632	+	0.326940i	0.816470	−	0.577388i	$-0.195928\pi$
$23$	206.115	+	172.951i	0.389632	+	0.326940i	−0.426838	+	0.904328i	$0.640372\pi$
$24$		0			0
$25$	−39.8671	+	226.097i	−0.0637873	+	0.361756i
$26$		0			0
$27$	678.958	−	391.997i	0.931355	−	0.537718i
$28$		0			0
$29$	213.999	+	587.957i	0.254457	+	0.699116i	0.999485	+	0.0320826i	$0.0102140\pi$
$29$	213.999	+	587.957i	0.254457	+	0.699116i	−0.745028	+	0.667033i	$0.767564\pi$
$30$		0			0
$31$	−287.088	−	165.751i	−0.298739	−	0.172477i	0.343137	−	0.939285i	$-0.388510\pi$
$31$	−287.088	−	165.751i	−0.298739	−	0.172477i	−0.641876	+	0.766808i	$0.721844\pi$
$32$		0			0
$33$	−255.691	−	304.721i	−0.234795	−	0.279817i
$34$		0			0
$35$	84.3004	+	478.091i	0.0688167	+	0.390279i
$36$		0			0
$37$		−	1580.58i		−	1.15455i	−0.816549	−	0.577276i	$-0.804116\pi$
$37$		−	1580.58i		−	1.15455i	0.816549	−	0.577276i	$-0.195884\pi$
$38$		0			0
$39$	1995.66			1.31207
$40$		0			0
$41$	−526.177	+	92.7792i	−0.313014	+	0.0551929i	−0.327948	−	0.944696i	$-0.606357\pi$
$41$	−526.177	+	92.7792i	−0.313014	+	0.0551929i	0.0149342	+	0.999888i	$0.495246\pi$
$42$		0			0
$43$	627.564	−	526.589i	0.339407	−	0.284797i	−0.457113	−	0.889409i	$-0.651116\pi$
$43$	627.564	−	526.589i	0.339407	−	0.284797i	0.796520	+	0.604612i	$0.206672\pi$
$44$		0			0
$45$	−362.105	+	627.184i	−0.178817	+	0.309720i
$46$		0			0
$47$	−655.645	+	238.635i	−0.296806	+	0.108029i	−0.486131	−	0.873886i	$-0.661592\pi$
$47$	−655.645	+	238.635i	−0.296806	+	0.108029i	0.189325	+	0.981914i	$0.439370\pi$
$48$		0			0
$49$	902.486	+	1563.15i	0.375879	+	0.651042i
$50$		0			0
$51$	2871.00	+	506.236i	1.10381	+	0.194631i
$52$		0			0
$53$	2059.40	−	2454.30i	0.733144	−	0.873727i	−0.262693	−	0.964880i	$-0.584611\pi$
$53$	2059.40	−	2454.30i	0.733144	−	0.873727i	0.995837	+	0.0911521i	$0.0290549\pi$
$54$		0			0
$55$	1113.24	+	405.187i	0.368014	+	0.133946i
$56$		0			0
$57$	1713.64	−	1695.04i	0.527436	−	0.521712i
$58$		0			0
$59$	−64.7073	+	177.782i	−0.0185887	+	0.0510721i	−0.948640	−	0.316358i	$-0.897540\pi$
$59$	−64.7073	+	177.782i	−0.0185887	+	0.0510721i	0.930051	+	0.367430i	$0.119762\pi$
$60$		0			0
$61$	−2557.13	−	2145.68i	−0.687215	−	0.576642i	0.230890	−	0.972980i	$-0.425836\pi$
$61$	−2557.13	−	2145.68i	−0.687215	−	0.576642i	−0.918105	+	0.396338i	$0.870281\pi$
$62$		0			0
$63$	154.398	−	875.634i	0.0389009	−	0.220618i
$64$		0			0
$65$	−5147.23	+	2971.76i	−1.21828	+	0.703374i
$66$		0			0
$67$	2383.52	+	6548.66i	0.530968	+	1.45882i	0.857921	+	0.513782i	$0.171756\pi$
$67$	2383.52	+	6548.66i	0.530968	+	1.45882i	−0.326952	+	0.945041i	$0.606022\pi$
$68$		0			0
$69$	−1555.82	−	898.251i	−0.326783	−	0.188668i
$70$		0			0
$71$	−3042.63	−	3626.06i	−0.603576	−	0.719314i	0.374578	−	0.927196i	$-0.377788\pi$
$71$	−3042.63	−	3626.06i	−0.603576	−	0.719314i	−0.978154	+	0.207881i	$0.933343\pi$
$72$		0			0
$73$	−235.676	−	1336.58i	−0.0442252	−	0.250813i	0.954678	−	0.297641i	$-0.0961999\pi$
$73$	−235.676	−	1336.58i	−0.0442252	−	0.250813i	−0.998903	+	0.0468278i	$0.985089\pi$
$74$		0			0
$75$		−	1532.90i		−	0.272516i
$76$		0			0
$77$	−1454.49			−0.245318
$78$		0			0
$79$	2334.45	−	411.626i	0.374050	−	0.0659552i	0.0165371	−	0.999863i	$-0.494736\pi$
$79$	2334.45	−	411.626i	0.374050	−	0.0659552i	0.357513	+	0.933908i	$0.383625\pi$
$80$		0			0
$81$	−1750.10	+	1468.51i	−0.266742	+	0.223824i
$82$		0			0
$83$	−6430.23	+	11137.5i	−0.933406	+	1.61671i	−0.155954	+	0.987764i	$0.549845\pi$
$83$	−6430.23	+	11137.5i	−0.933406	+	1.61671i	−0.777452	+	0.628942i	$0.783488\pi$
$84$		0			0
$85$	−8158.75	+	2969.54i	−1.12924	+	0.411009i
$86$		0			0
$87$	−2088.82	−	3617.94i	−0.275970	−	0.477994i
$88$		0			0
$89$	−11328.8	−	1997.58i	−1.43023	−	0.252188i	−0.595724	−	0.803189i	$-0.703135\pi$
$89$	−11328.8	−	1997.58i	−1.43023	−	0.252188i	−0.834505	+	0.551001i	$0.814246\pi$
$90$		0			0
$91$	4690.48	−	5589.90i	0.566415	−	0.675027i
$92$		0			0
$93$	2079.90	+	757.020i	0.240478	+	0.0875269i
$94$		0			0
$95$	−1895.73	+	6923.66i	−0.210053	+	0.767164i
$96$		0			0
$97$	4016.29	−	11034.7i	0.426856	−	1.17278i	−0.520855	−	0.853645i	$-0.674387\pi$
$97$	4016.29	−	11034.7i	0.426856	−	1.17278i	0.947711	−	0.319131i	$-0.103391\pi$
$98$		0			0
$99$	−1662.15	−	1394.71i	−0.169590	−	0.142303i
$100$		0			0
$101$	−1707.31	+	9682.66i	−0.167367	+	0.949187i	0.779223	+	0.626747i	$0.215614\pi$
$101$	−1707.31	+	9682.66i	−0.167367	+	0.949187i	−0.946590	+	0.322440i	$0.895497\pi$
$102$		0			0
$103$	8407.53	−	4854.09i	0.792491	−	0.457545i	−0.0483479	−	0.998831i	$-0.515396\pi$
$103$	8407.53	−	4854.09i	0.792491	−	0.457545i	0.840839	+	0.541286i	$0.182062\pi$
$104$		0			0
$105$	−1108.62	−	3045.90i	−0.100555	−	0.276272i
$106$		0			0
$107$	1216.67	+	702.446i	0.106269	+	0.0613544i	0.552192	−	0.833717i	$-0.313791\pi$
$107$	1216.67	+	702.446i	0.106269	+	0.0613544i	−0.445924	+	0.895071i	$0.647125\pi$
$108$		0			0
$109$	5481.58	+	6532.69i	0.461374	+	0.549844i	0.945699	−	0.325044i	$-0.105379\pi$
$109$	5481.58	+	6532.69i	0.461374	+	0.549844i	−0.484325	+	0.874888i	$0.660935\pi$
$110$		0			0
$111$	1832.56	+	10393.0i	0.148735	+	0.843517i
$112$		0			0
$113$		−	11158.3i		−	0.873860i	−0.899495	−	0.436930i	$-0.856066\pi$
$113$		−	11158.3i		−	0.873860i	0.899495	−	0.436930i	$-0.143934\pi$
$114$		0			0
$115$	5350.36			0.404564
$116$		0			0
$117$	10720.3	−	1890.27i	0.783131	−	0.138087i
$118$		0			0
$119$	8165.80	−	6851.92i	0.576640	−	0.483858i
$120$		0			0
$121$	5545.80	−	9605.60i	0.378785	−	0.656076i
$122$		0			0
$123$	3352.26	−	1220.12i	0.221578	−	0.0806478i
$124$		0			0
$125$	8496.73	+	14716.8i	0.543791	+	0.941873i
$126$		0			0
$127$	−2765.05	−	487.552i	−0.171433	−	0.0302283i	0.0872726	−	0.996184i	$-0.472185\pi$
$127$	−2765.05	−	487.552i	−0.171433	−	0.0302283i	−0.258706	+	0.965956i	$0.583296\pi$
$128$		0			0
$129$	−3515.95	+	4190.14i	−0.211282	+	0.251796i
$130$		0			0
$131$	9397.73	+	3420.49i	0.547621	+	0.199318i	0.600989	−	0.799257i	$-0.294773\pi$
$131$	9397.73	+	3420.49i	0.547621	+	0.199318i	−0.0533681	+	0.998575i	$0.516996\pi$
$132$		0			0
$133$	−720.226	−	8783.86i	−0.0407161	−	0.496572i
$134$		0			0
$135$	5332.00	−	14649.6i	0.292565	−	0.803817i
$136$		0			0
$137$	−12348.0	−	10361.2i	−0.657892	−	0.552037i	0.251562	−	0.967841i	$-0.419056\pi$
$137$	−12348.0	−	10361.2i	−0.657892	−	0.552037i	−0.909454	+	0.415804i	$0.863500\pi$
$138$		0			0
$139$	−5509.82	+	31247.8i	−0.285173	+	1.61730i	0.419495	+	0.907758i	$0.362207\pi$
$139$	−5509.82	+	31247.8i	−0.285173	+	1.61730i	−0.704668	+	0.709538i	$0.748904\pi$
$140$		0			0
$141$	4034.45	−	2329.29i	0.202930	−	0.117162i
$142$		0			0
$143$	−6090.40	−	16733.2i	−0.297834	−	0.818292i
$144$		0			0
$145$	10775.0	+	6220.94i	0.512484	+	0.295883i
$146$		0			0
$147$	−7746.56	−	9231.99i	−0.358488	−	0.427229i
$148$		0			0
$149$	4148.58	+	23527.8i	0.186865	+	1.05976i	0.923536	+	0.383511i	$0.125285\pi$
$149$	4148.58	+	23527.8i	0.186865	+	1.05976i	−0.736672	+	0.676251i	$0.763604\pi$
$150$		0			0
$151$		−	19229.0i		−	0.843341i	−0.906749	−	0.421671i	$-0.861444\pi$
$151$		−	19229.0i		−	0.843341i	0.906749	−	0.421671i	$-0.138556\pi$
$152$		0			0
$153$	15901.9			0.679308
$154$		0			0
$155$	−6491.77	+	1144.67i	−0.270209	+	0.0476451i
$156$		0			0
$157$	9263.80	−	7773.25i	0.375829	−	0.315358i	−0.435233	−	0.900318i	$-0.643334\pi$
$157$	9263.80	−	7773.25i	0.375829	−	0.315358i	0.811062	+	0.584960i	$0.198890\pi$
$158$		0			0
$159$	−10695.8	+	18525.7i	−0.423078	+	0.732792i
$160$		0			0
$161$	−6172.71	+	2246.68i	−0.238135	+	0.0866742i
$162$		0			0
$163$	−21787.7	−	37737.5i	−0.820044	−	1.42036i	−0.905649	−	0.424029i	$-0.860616\pi$
$163$	−21787.7	−	37737.5i	−0.820044	−	1.42036i	0.0856049	−	0.996329i	$-0.472718\pi$
$164$		0			0
$165$	−7789.80	−	1373.55i	−0.286127	−	0.0504519i
$166$		0			0
$167$	−18788.6	+	22391.4i	−0.673692	+	0.802875i	−0.989282	−	0.146021i	$-0.953353\pi$
$167$	−18788.6	+	22391.4i	−0.673692	+	0.802875i	0.315589	+	0.948896i	$0.397798\pi$
$168$		0			0
$169$	57111.1	+	20786.7i	1.99962	+	0.727802i
$170$		0			0
$171$	7599.77	−	10728.6i	0.259901	−	0.366901i
$172$		0			0
$173$	−7796.40	+	21420.4i	−0.260497	+	0.715708i	0.738638	+	0.674103i	$0.235470\pi$
$173$	−7796.40	+	21420.4i	−0.260497	+	0.715708i	−0.999134	+	0.0416056i	$0.986753\pi$
$174$		0			0
$175$	−4293.69	−	3602.84i	−0.140202	−	0.117644i
$176$		0			0
$177$	219.353	−	1244.01i	0.00700158	−	0.0397079i
$178$		0			0
$179$	−40189.9	+	23203.6i	−1.25433	+	0.724186i	−0.971966	−	0.235123i	$-0.924451\pi$
$179$	−40189.9	+	23203.6i	−1.25433	+	0.724186i	−0.282361	+	0.959308i	$0.591117\pi$
$180$		0			0
$181$	−329.458	−	905.180i	−0.0100564	−	0.0276298i	0.934563	−	0.355798i	$-0.115791\pi$
$181$	−329.458	−	905.180i	−0.0100564	−	0.0276298i	−0.944619	+	0.328168i	$0.893569\pi$
$182$		0			0
$183$	19301.9	+	11144.0i	0.576365	+	0.332765i
$184$		0			0
$185$	−20202.8	−	24076.7i	−0.590293	−	0.703484i
$186$		0			0
$187$	−4517.10	−	25617.7i	−0.129174	−	0.732584i
$188$		0			0
$189$			19140.2i			0.535824i
$190$		0			0
$191$	−59657.6			−1.63530			−0.817652	−	0.575712i	$-0.804725\pi$
$191$	−59657.6			−1.63530			−0.817652	+	0.575712i	$0.804725\pi$
$192$		0			0
$193$	−18750.1	+	3306.14i	−0.503371	+	0.0887579i	−0.419567	−	0.907724i	$-0.637818\pi$
$193$	−18750.1	+	3306.14i	−0.503371	+	0.0887579i	−0.0838041	+	0.996482i	$0.526707\pi$
$194$		0			0
$195$	30399.6	−	25508.3i	0.799463	−	0.670830i
$196$		0			0
$197$	−20357.7	+	35260.6i	−0.524562	+	0.908568i	0.475029	+	0.879970i	$0.342438\pi$
$197$	−20357.7	+	35260.6i	−0.524562	+	0.908568i	−0.999591	+	0.0285981i	$0.990896\pi$
$198$		0			0
$199$	−50685.1	+	18447.9i	−1.27989	+	0.465843i	−0.890397	−	0.455185i	$-0.849573\pi$
$199$	−50685.1	+	18447.9i	−1.27989	+	0.465843i	−0.389497	+	0.921028i	$0.627351\pi$
$200$		0			0
$201$	−23265.2	−	40296.6i	−0.575858	−	0.997415i
$202$		0			0
$203$	−15043.3	−	2652.55i	−0.365050	−	0.0643681i
$204$		0			0
$205$	−6829.27	+	8138.81i	−0.162505	+	0.193666i
$206$		0			0
$207$	−9208.32	−	3351.55i	−0.214902	−	0.0782178i
$208$		0			0
$209$	−19442.3	−	9195.56i	−0.445098	−	0.210516i
$210$		0			0
$211$	2915.07	−	8009.09i	0.0654763	−	0.179895i	−0.902640	−	0.430397i	$-0.858374\pi$
$211$	2915.07	−	8009.09i	0.0654763	−	0.179895i	0.968116	+	0.250502i	$0.0805958\pi$
$212$		0			0
$213$	24210.6	+	20315.1i	0.533638	+	0.447776i
$214$		0			0
$215$	2828.79	−	16042.9i	0.0611961	−	0.347060i
$216$		0			0
$217$	7008.88	−	4046.58i	0.148843	−	0.0859347i
$218$		0			0
$219$	3099.33	+	8515.34i	0.0646218	+	0.177547i
$220$		0			0
$221$	113021.	+	65252.7i	2.31406	+	1.33602i
$222$		0			0
$223$	34972.8	+	41678.9i	0.703267	+	0.838121i	0.992892	−	0.119019i	$-0.0379749\pi$
$223$	34972.8	+	41678.9i	0.703267	+	0.838121i	−0.289625	+	0.957140i	$0.593531\pi$
$224$		0			0
$225$	−1451.95	−	8234.43i	−0.0286805	−	0.162655i
$226$		0			0
$227$		−	98514.8i		−	1.91183i	−0.293638	−	0.955917i	$-0.594866\pi$
$227$		−	98514.8i		−	1.91183i	0.293638	−	0.955917i	$-0.405134\pi$
$228$		0			0
$229$	66558.7			1.26921			0.634606	−	0.772836i	$-0.281163\pi$
$229$	66558.7			1.26921			0.634606	+	0.772836i	$0.281163\pi$
$230$		0			0
$231$	9563.86	−	1686.37i	0.179229	−	0.0316030i
$232$		0			0
$233$	2315.37	−	1942.83i	0.0426490	−	0.0357868i	−0.621214	−	0.783641i	$-0.713360\pi$
$233$	2315.37	−	1942.83i	0.0426490	−	0.0357868i	0.663863	+	0.747854i	$0.268916\pi$
$234$		0			0
$235$	−6937.12	+	12015.4i	−0.125616	+	0.217573i
$236$		0			0
$237$	−14872.7	+	5413.22i	−0.264785	+	0.0963737i
$238$		0			0
$239$	3285.25	+	5690.23i	0.0575139	+	0.0996170i	0.893349	−	0.449364i	$-0.148349\pi$
$239$	3285.25	+	5690.23i	0.0575139	+	0.0996170i	−0.835835	+	0.548981i	$0.815016\pi$
$240$		0			0
$241$	−56846.0	−	10023.5i	−0.978736	−	0.172578i	−0.338676	−	0.940903i	$-0.609979\pi$
$241$	−56846.0	−	10023.5i	−0.978736	−	0.172578i	−0.640059	+	0.768325i	$0.721090\pi$
$242$		0			0
$243$	−31014.3	+	36961.3i	−0.525229	+	0.625944i
$244$		0			0
$245$	33727.4	+	12275.8i	0.561889	+	0.204511i
$246$		0			0
$247$	98038.5	−	45066.6i	1.60695	−	0.738688i
$248$		0			0
$249$	29368.3	−	80688.8i	0.473675	−	1.30141i
$250$		0			0
$251$	51553.1	+	43258.2i	0.818290	+	0.686627i	0.952571	−	0.304316i	$-0.0984280\pi$
$251$	51553.1	+	43258.2i	0.818290	+	0.686627i	−0.134281	+	0.990943i	$0.542872\pi$
$252$		0			0
$253$	−2783.59	+	15786.5i	−0.0434874	+	0.246629i
$254$		0			0
$255$	50204.1	−	28985.4i	0.772074	−	0.445757i
$256$		0			0
$257$	−34927.0	−	95961.1i	−0.528804	−	1.45288i	−0.860480	−	0.509484i	$-0.829836\pi$
$257$	−34927.0	−	95961.1i	−0.528804	−	1.45288i	0.331676	−	0.943393i	$-0.392386\pi$
$258$		0			0
$259$	33418.0	+	19293.9i	0.498174	+	0.287621i
$260$		0			0
$261$	−14647.5	−	17456.3i	−0.215022	−	0.256254i
$262$		0			0
$263$	20006.1	+	113460.i	0.289234	+	1.64033i	0.689756	+	0.724042i	$0.257718\pi$
$263$	20006.1	+	113460.i	0.289234	+	1.64033i	−0.400521	+	0.916287i	$0.631171\pi$
$264$		0			0
$265$		−	63708.9i		−	0.907211i
$266$		0			0
$267$	76807.7			1.07741
$268$		0			0
$269$	−108216.	+	19081.4i	−1.49550	+	0.263697i	−0.860753	−	0.509023i	$-0.830007\pi$
$269$	−108216.	+	19081.4i	−1.49550	+	0.263697i	−0.634747	+	0.772720i	$0.718896\pi$
$270$		0			0
$271$	−17187.3	+	14421.9i	−0.234029	+	0.196373i	−0.752259	−	0.658868i	$-0.771036\pi$
$271$	−17187.3	+	14421.9i	−0.234029	+	0.196373i	0.518230	+	0.855241i	$0.326591\pi$
$272$		0			0
$273$	−24360.7	+	42194.0i	−0.326863	+	0.566143i
$274$		0			0
$275$	−12853.1	+	4678.14i	−0.169958	+	0.0618598i
$276$		0			0
$277$	−16344.8	−	28310.1i	−0.213020	−	0.368962i	0.739638	−	0.673005i	$-0.234997\pi$
$277$	−16344.8	−	28310.1i	−0.213020	−	0.368962i	−0.952658	+	0.304043i	$0.901663\pi$
$278$		0			0
$279$	11889.8	+	2096.49i	0.152745	+	0.0269330i
$280$		0			0
$281$	−19282.5	+	22980.0i	−0.244203	+	0.291030i	−0.874198	−	0.485569i	$-0.838612\pi$
$281$	−19282.5	+	22980.0i	−0.244203	+	0.291030i	0.629995	+	0.776599i	$0.283057\pi$
$282$		0			0
$283$	−53491.0	−	19469.1i	−0.667894	−	0.243094i	−0.0142533	−	0.999898i	$-0.504537\pi$
$283$	−53491.0	−	19469.1i	−0.667894	−	0.243094i	−0.653641	+	0.756805i	$0.726759\pi$
$284$		0			0
$285$	4437.75	−	47723.8i	0.0546353	−	0.587550i
$286$		0			0
$287$	4461.34	−	12257.4i	0.0541628	−	0.148811i
$288$		0			0
$289$	82061.0	+	68857.3i	0.982519	+	0.824431i
$290$		0			0
$291$	−13614.9	+	77213.8i	−0.160778	+	0.911820i
$292$		0			0
$293$	65869.1	−	38029.6i	0.767267	−	0.442982i	−0.0646316	−	0.997909i	$-0.520587\pi$
$293$	65869.1	−	38029.6i	0.767267	−	0.442982i	0.831899	+	0.554927i	$0.187254\pi$
$294$		0			0
$295$	1286.71	+	3535.20i	0.0147855	+	0.0406228i
$296$		0			0
$297$	40450.2	+	23353.9i	0.458572	+	0.264757i
$298$		0			0
$299$	−51694.1	−	61606.6i	−0.578227	−	0.689104i
$300$		0			0
$301$	3473.02	+	19696.5i	0.0383331	+	0.217398i
$302$		0			0
$303$		−	65646.8i		−	0.715037i
$304$		0			0
$305$	−66378.1			−0.713551
$306$		0			0
$307$	−118511.	+	20896.6i	−1.25742	+	0.221717i	−0.762367	−	0.647145i	$-0.775963\pi$
$307$	−118511.	+	20896.6i	−1.25742	+	0.221717i	−0.495054	+	0.868862i	$0.664852\pi$
$308$		0			0
$309$	−49655.0	+	41665.5i	−0.520051	+	0.436375i
$310$		0			0
$311$	−5143.09	+	8908.09i	−0.0531745	+	0.0921009i	−0.891387	−	0.453242i	$-0.850267\pi$
$311$	−5143.09	+	8908.09i	−0.0531745	+	0.0921009i	0.838213	+	0.545343i	$0.183601\pi$
$312$		0			0
$313$	−143463.	+	52216.2i	−1.46437	+	0.532987i	−0.946566	−	0.322511i	$-0.895473\pi$
$313$	−143463.	+	52216.2i	−1.46437	+	0.532987i	−0.517805	+	0.855498i	$0.673251\pi$
$314$		0			0
$315$	−8840.31	−	15311.9i	−0.0890936	−	0.154315i
$316$		0			0
$317$	−86169.8	−	15194.1i	−0.857505	−	0.151201i	−0.272425	−	0.962177i	$-0.587826\pi$
$317$	−86169.8	−	15194.1i	−0.857505	−	0.151201i	−0.585080	+	0.810976i	$0.698937\pi$
$318$		0			0
$319$	−23961.0	+	28555.6i	−0.235463	+	0.280614i
$320$		0			0
$321$	−8814.55	−	3208.23i	−0.0855441	−	0.0311355i
$322$		0			0
$323$	152472.	−	39964.6i	1.46145	−	0.383063i
$324$		0			0
$325$	23470.0	−	64483.2i	0.222201	−	0.610492i
$326$		0			0
$327$	−43617.7	−	36599.6i	−0.407913	−	0.342280i
$328$		0			0
$329$	2957.92	−	16775.2i	0.0273271	−	0.154980i
$330$		0			0
$331$	−17082.7	+	9862.72i	−0.155920	+	0.0900204i	−0.575930	−	0.817499i	$-0.695360\pi$
$331$	−17082.7	+	9862.72i	−0.155920	+	0.0900204i	0.420010	+	0.907519i	$0.362027\pi$
$332$		0			0
$333$	19688.2	+	54093.0i	0.177549	+	0.487812i
$334$		0			0
$335$	120012.	+	69288.8i	1.06938	+	0.617409i
$336$		0			0
$337$	−21146.2	−	25201.0i	−0.186197	−	0.221901i	0.664869	−	0.746960i	$-0.268487\pi$
$337$	−21146.2	−	25201.0i	−0.186197	−	0.221901i	−0.851065	+	0.525060i	$0.824043\pi$
$338$		0			0
$339$	12937.2	+	73370.5i	0.112575	+	0.638443i
$340$		0			0
$341$		−	19749.8i		−	0.169846i
$342$		0			0
$343$	−102683.			−0.872793
$344$		0			0
$345$	−35180.8	+	6203.32i	−0.295575	+	0.0521178i
$346$		0			0
$347$	161308.	−	135354.i	1.33967	−	1.12412i	0.357959	−	0.933737i	$-0.383473\pi$
$347$	161308.	−	135354.i	1.33967	−	1.12412i	0.981711	−	0.190379i	$-0.0609716\pi$
$348$		0			0
$349$	−104498.	+	180996.i	−0.857942	+	1.48600i	0.0159471	+	0.999873i	$0.494924\pi$
$349$	−104498.	+	180996.i	−0.857942	+	1.48600i	−0.873889	+	0.486126i	$0.838410\pi$
$350$		0			0
$351$	−220199.	+	80145.8i	−1.78731	+	0.650529i
$352$		0			0
$353$	−39476.7	−	68375.7i	−0.316805	−	0.548722i	0.663015	−	0.748606i	$-0.269277\pi$
$353$	−39476.7	−	68375.7i	−0.316805	−	0.548722i	−0.979819	+	0.199884i	$0.935943\pi$
$354$		0			0
$355$	−92695.6	−	16344.7i	−0.735534	−	0.129694i
$356$		0			0
$357$	−45749.1	+	54521.7i	−0.358960	+	0.427792i
$358$		0			0
$359$	215635.	+	78484.7i	1.67313	+	0.608970i	0.992343	−	0.123510i	$-0.0394153\pi$
$359$	215635.	+	78484.7i	1.67313	+	0.608970i	0.680788	+	0.732480i	$0.261637\pi$
$360$		0			0
$361$	45905.8	−	121968.i	0.352252	−	0.935905i
$362$		0			0
$363$	−25328.9	+	69590.6i	−0.192222	+	0.528126i
$364$		0			0
$365$	−20674.0	−	17347.6i	−0.155181	−	0.130213i
$366$		0			0
$367$	23042.5	−	130680.i	0.171079	−	0.970237i	−0.771494	−	0.636237i	$-0.780490\pi$
$367$	23042.5	−	130680.i	0.171079	−	0.970237i	0.942573	−	0.334001i	$-0.108399\pi$
$368$		0			0
$369$	16851.9	−	9729.45i	0.123765	−	0.0714555i
$370$		0			0
$371$	26752.1	+	73500.9i	0.194362	+	0.534004i
$372$		0			0
$373$	155610.	+	89841.3i	1.11846	+	0.645741i	0.941006	−	0.338389i	$-0.109882\pi$
$373$	155610.	+	89841.3i	1.11846	+	0.645741i	0.177450	+	0.984130i	$0.443215\pi$
$374$		0			0
$375$	−72932.3	−	86917.4i	−0.518630	−	0.618079i
$376$		0			0
$377$	−32474.8	−	184174.i	−0.228488	−	1.29582i
$378$		0			0
$379$			45074.6i			0.313800i	0.987614	+	0.156900i	$0.0501501\pi$
$379$			45074.6i			0.313800i	−0.987614	+	0.156900i	$0.949850\pi$
$380$		0			0
$381$	18746.6			0.129143
$382$		0			0
$383$	61031.2	−	10761.4i	0.416058	−	0.0733623i	0.0382994	−	0.999266i	$-0.487806\pi$
$383$	61031.2	−	10761.4i	0.416058	−	0.0733623i	0.377759	+	0.925904i	$0.376695\pi$
$384$		0			0
$385$	−22156.0	+	18591.1i	−0.149475	+	0.125425i
$386$		0			0
$387$	−14918.0	+	25838.8i	−0.0996070	+	0.172524i
$388$		0			0
$389$	−30999.0	+	11282.7i	−0.204856	+	0.0745615i	−0.442410	−	0.896813i	$-0.645876\pi$
$389$	−30999.0	+	11282.7i	−0.204856	+	0.0745615i	0.237554	+	0.971374i	$0.423654\pi$
$390$		0			0
$391$	−58740.6	−	101742.i	−0.384224	−	0.665496i
$392$		0			0
$393$	−65759.6	−	11595.2i	−0.425769	−	0.0750746i
$394$		0			0
$395$	30298.9	−	36108.8i	0.194192	−	0.231430i
$396$		0			0
$397$	166267.	+	60516.1i	1.05493	+	0.383964i	0.810522	−	0.585708i	$-0.199184\pi$
$397$	166267.	+	60516.1i	1.05493	+	0.383964i	0.244410	+	0.969672i	$0.421406\pi$
$398$		0			0
$399$	14920.0	+	56922.3i	0.0937178	+	0.357550i
$400$		0			0
$401$	16319.1	−	44836.3i	0.101486	−	0.278831i	−0.878550	−	0.477650i	$-0.841489\pi$
$401$	16319.1	−	44836.3i	0.101486	−	0.278831i	0.980036	+	0.198820i	$0.0637108\pi$
$402$		0			0
$403$	75902.4	+	63689.7i	0.467354	+	0.392156i
$404$		0			0
$405$	−7888.69	+	44739.0i	−0.0480944	+	0.272757i
$406$		0			0
$407$	81550.3	−	47083.1i	0.492308	−	0.284234i
$408$		0			0
$409$	−45717.6	−	125608.i	−0.273298	−	0.750880i	−0.998082	−	0.0619041i	$-0.980283\pi$
$409$	−45717.6	−	125608.i	−0.273298	−	0.750880i	0.724784	−	0.688976i	$-0.241940\pi$
$410$		0			0
$411$	93205.9	+	53812.4i	0.551772	+	0.318566i
$412$		0			0
$413$	−2968.95	−	3538.25i	−0.0174061	−	0.0207438i
$414$		0			0
$415$	44407.2	+	251846.i	0.257844	+	1.46231i
$416$		0			0
$417$		−	211855.i		−	1.21833i
$418$		0			0
$419$	270011.			1.53799			0.768996	−	0.639254i	$-0.220757\pi$
$419$	270011.			1.53799			0.768996	+	0.639254i	$0.220757\pi$
$420$		0			0
$421$	227518.	−	40117.5i	1.28366	−	0.226344i	0.510128	−	0.860099i	$-0.329598\pi$
$421$	227518.	−	40117.5i	1.28366	−	0.226344i	0.773534	+	0.633755i	$0.218487\pi$
$422$		0			0
$423$	19465.9	−	16333.8i	0.108791	−	0.0912867i
$424$		0			0
$425$	50121.7	−	86813.3i	0.277490	−	0.480627i
$426$		0			0
$427$	76580.3	−	27873.0i	0.420012	−	0.152872i
$428$		0			0
$429$	59447.7	+	102967.i	0.323014	+	0.559476i
$430$		0			0
$431$	185848.	+	32770.0i	1.00047	+	0.176409i	0.649812	−	0.760095i	$-0.274848\pi$
$431$	185848.	+	32770.0i	1.00047	+	0.176409i	0.350656	+	0.936504i	$0.385959\pi$
$432$		0			0
$433$	14284.9	−	17024.1i	0.0761906	−	0.0908004i	−0.726603	−	0.687058i	$-0.758902\pi$
$433$	14284.9	−	17024.1i	0.0761906	−	0.0908004i	0.802793	+	0.596258i	$0.203346\pi$
$434$		0			0
$435$	−78062.5	−	28412.4i	−0.412538	−	0.150152i
$436$		0			0
$437$	−96715.1	−	8993.37i	−0.506444	−	0.0470933i
$438$		0			0
$439$	90345.3	−	248222.i	0.468788	−	1.28798i	−0.449928	−	0.893065i	$-0.648550\pi$
$439$	90345.3	−	248222.i	0.468788	−	1.28798i	0.918716	−	0.394920i	$-0.129228\pi$
$440$		0			0
$441$	−50357.3	−	42254.8i	−0.258932	−	0.217270i
$442$		0			0
$443$	−49365.9	+	279968.i	−0.251547	+	1.42659i	0.553235	+	0.833025i	$0.313393\pi$
$443$	−49365.9	+	279968.i	−0.251547	+	1.42659i	−0.804783	+	0.593570i	$0.797718\pi$
$444$		0			0
$445$	−198103.	+	114375.i	−1.00039	+	0.577578i
$446$		0			0
$447$	−54557.2	−	149895.i	−0.273047	−	0.750190i
$448$		0			0
$449$	195311.	+	112763.i	0.968799	+	0.559336i	0.898870	−	0.438216i	$-0.144389\pi$
$449$	195311.	+	112763.i	0.968799	+	0.559336i	0.0699288	+	0.997552i	$0.477723\pi$
$450$		0			0
$451$	−20460.9	−	24384.4i	−0.100594	−	0.119883i
$452$		0			0
$453$	22294.5	+	126439.i	0.108643	+	0.616145i
$454$		0			0
$455$		−	145103.i		−	0.700896i
$456$		0			0
$457$	4647.16			0.0222513			0.0111256	−	0.999938i	$-0.496459\pi$
$457$	4647.16			0.0222513			0.0111256	+	0.999938i	$0.496459\pi$
$458$		0			0
$459$	−337113.	+	59442.1i	−1.60011	+	0.282143i
$460$		0			0
$461$	95361.0	−	80017.4i	0.448713	−	0.376515i	−0.390245	−	0.920711i	$-0.627610\pi$
$461$	95361.0	−	80017.4i	0.448713	−	0.376515i	0.838958	+	0.544196i	$0.183165\pi$
$462$		0			0
$463$	−161098.	+	279029.i	−0.751497	+	1.30163i	0.195601	+	0.980684i	$0.437334\pi$
$463$	−161098.	+	279029.i	−0.751497	+	1.30163i	−0.947097	+	0.320947i	$0.895999\pi$
$464$		0			0
$465$	41358.8	−	15053.4i	0.191277	−	0.0696190i
$466$		0			0
$467$	−158430.	−	274410.i	−0.726449	−	1.25825i	−0.958375	−	0.285512i	$-0.907836\pi$
$467$	−158430.	−	274410.i	−0.726449	−	1.25825i	0.231926	−	0.972733i	$-0.425497\pi$
$468$		0			0
$469$	−167553.	−	29544.0i	−0.761737	−	0.134315i
$470$		0			0
$471$	−51900.8	+	61852.9i	−0.233955	+	0.278816i
$472$		0			0
$473$	45863.6	+	16693.0i	0.204996	+	0.0746125i
$474$		0			0
$475$	−34616.4	−	75305.0i	−0.153425	−	0.333762i
$476$		0			0
$477$	−39908.3	+	109647.i	−0.175399	+	0.481904i
$478$		0			0
$479$	−196084.	−	164534.i	−0.854615	−	0.717107i	0.106186	−	0.994346i	$-0.466136\pi$
$479$	−196084.	−	164534.i	−0.854615	−	0.717107i	−0.960801	+	0.277239i	$0.910581\pi$
$480$		0			0
$481$	−82035.9	+	465249.i	−0.354580	+	2.01092i
$482$		0			0
$483$	37983.2	−	21929.6i	0.162816	−	0.0940018i
$484$		0			0
$485$	−79864.0	−	219424.i	−0.339522	−	0.932828i
$486$		0			0
$487$	−304583.	−	175851.i	−1.28424	−	0.741458i	−0.306622	−	0.951831i	$-0.599199\pi$
$487$	−304583.	−	175851.i	−1.28424	−	0.741458i	−0.977621	+	0.210374i	$0.932532\pi$
$488$		0			0
$489$	187017.	+	222878.i	0.782101	+	0.932072i
$490$		0			0
$491$	18194.7	+	103187.i	0.0754714	+	0.428019i	0.999009	+	0.0445113i	$0.0141731\pi$
$491$	18194.7	+	103187.i	0.0754714	+	0.428019i	−0.923538	+	0.383508i	$0.874716\pi$
$492$		0			0
$493$		−	273194.i		−	1.12403i
$494$		0			0
$495$	−43146.2			−0.176089
$496$		0			0
$497$	113806.	−	20067.1i	0.460737	−	0.0812404i
$498$		0			0
$499$	−27491.7	+	23068.3i	−0.110408	+	0.0926433i	−0.696320	−	0.717731i	$-0.745181\pi$
$499$	−27491.7	+	23068.3i	−0.110408	+	0.0926433i	0.585912	+	0.810374i	$0.300736\pi$
$500$		0			0
$501$	97581.6	−	169016.i	0.388770	−	0.673369i
$502$		0			0
$503$	−106076.	+	38608.5i	−0.419257	+	0.152597i	−0.543030	−	0.839713i	$-0.682723\pi$
$503$	−106076.	+	38608.5i	−0.419257	+	0.152597i	0.123772	+	0.992311i	$0.460501\pi$
$504$		0			0
$505$	97755.1	+	169317.i	0.383316	+	0.663922i
$506$		0			0
$507$	−399629.	−	70465.4i	−1.55468	−	0.274132i
$508$		0			0
$509$	−254469.	+	303264.i	−0.982198	+	1.17054i	0.00315251	+	0.999995i	$0.498997\pi$
$509$	−254469.	+	303264.i	−0.982198	+	1.17054i	−0.985350	+	0.170543i	$0.945448\pi$
$510$		0			0
$511$	31136.1	+	11332.6i	0.119240	+	0.0433998i
$512$		0			0
$513$	−121008.	+	255848.i	−0.459809	+	0.972183i
$514$		0			0
$515$	66026.2	−	181405.i	0.248944	−	0.683968i
$516$		0			0
$517$	−31843.0	−	26719.5i	−0.119133	−	0.0999648i
$518$		0			0
$519$	26429.2	−	149887.i	0.0981181	−	0.556455i
$520$		0			0
$521$	−179689.	+	103743.i	−0.661981	+	0.382195i	−0.793032	−	0.609181i	$-0.791498\pi$
$521$	−179689.	+	103743.i	−0.661981	+	0.382195i	0.131050	+	0.991376i	$0.458165\pi$
$522$		0			0
$523$	96198.8	+	264304.i	0.351695	+	0.966275i	0.981826	+	0.189785i	$0.0607792\pi$
$523$	96198.8	+	264304.i	0.351695	+	0.966275i	−0.630130	+	0.776489i	$0.716999\pi$
$524$		0			0
$525$	32410.0	+	18711.9i	0.117587	+	0.0678890i
$526$		0			0
$527$	93038.8	+	110879.i	0.334999	+	0.399236i
$528$		0			0
$529$	−36022.5	−	204294.i	−0.128725	−	0.730035i
$530$		0			0
$531$		−	6890.32i		−	0.0244371i
$532$		0			0
$533$	159697.			0.562138
$534$		0			0
$535$	27511.9	−	4851.10i	0.0961199	−	0.0169485i
$536$		0			0
$537$	237362.	−	199170.i	0.823118	−	0.690678i
$538$		0			0
$539$	−53767.3	+	93127.7i	−0.185072	+	0.320554i
$540$		0			0
$541$	163782.	−	59611.8i	0.559592	−	0.203675i	−0.0467110	−	0.998908i	$-0.514874\pi$
$541$	163782.	−	59611.8i	0.559592	−	0.203675i	0.606303	+	0.795233i	$0.292652\pi$
$542$		0			0
$543$	3215.81	+	5569.94i	0.0109066	+	0.0188908i
$544$		0			0
$545$	167000.	+	29446.6i	0.562242	+	0.0991384i
$546$		0			0
$547$	221287.	−	263719.i	0.739572	−	0.881388i	−0.256802	−	0.966464i	$-0.582669\pi$
$547$	221287.	−	263719.i	0.739572	−	0.881388i	0.996374	+	0.0850760i	$0.0271133\pi$
$548$		0			0
$549$	114241.	+	41580.3i	0.379033	+	0.137957i
$550$		0			0
$551$	−184316.	−	130564.i	−0.607099	−	0.430050i
$552$		0			0
$553$	−19793.3	+	54381.6i	−0.0647243	+	0.177829i
$554$		0			0
$555$	160756.	+	134891.i	0.521894	+	0.437921i
$556$		0			0
$557$	1249.81	−	7088.01i	0.00402840	−	0.0228462i	−0.982727	−	0.185060i	$-0.940752\pi$
$557$	1249.81	−	7088.01i	0.00402840	−	0.0228462i	0.986756	+	0.162213i	$0.0518633\pi$
$558$		0			0
$559$	−212056.	+	122431.i	−0.678622	+	0.391802i
$560$		0			0
$561$	59403.5	+	163210.i	0.188750	+	0.518585i
$562$		0			0
$563$	−325316.	−	187822.i	−1.02634	−	0.592555i	−0.110403	−	0.993887i	$-0.535214\pi$
$563$	−325316.	−	187822.i	−1.02634	−	0.592555i	−0.915933	+	0.401332i	$0.868547\pi$
$564$		0			0
$565$	−142624.	−	169973.i	−0.446782	−	0.532454i
$566$		0			0
$567$	−9685.27	−	54927.9i	−0.0301263	−	0.170855i
$568$		0			0
$569$			326284.i			1.00779i	0.863764	+	0.503896i	$0.168101\pi$
$569$			326284.i			1.00779i	−0.863764	+	0.503896i	$0.831899\pi$
$570$		0			0
$571$	−646431.			−1.98267			−0.991334	−	0.131368i	$-0.958063\pi$
$571$	−646431.			−1.98267			−0.991334	+	0.131368i	$0.958063\pi$
$572$		0			0
$573$	392272.	−	69168.2i	1.19475	−	0.210667i
$574$		0			0
$575$	−47321.1	+	39707.1i	−0.143126	+	0.120097i
$576$		0			0
$577$	−119252.	+	206551.i	−0.358192	+	0.620406i	−0.987659	−	0.156621i	$-0.949940\pi$
$577$	−119252.	+	206551.i	−0.358192	+	0.620406i	0.629467	+	0.777027i	$0.283273\pi$
$578$		0			0
$579$	119456.	−	43478.5i	0.356329	−	0.129693i
$580$		0			0
$581$	−156986.	−	271907.i	−0.465058	−	0.805505i
$582$		0			0
$583$	187976.	+	33145.3i	0.553052	+	0.0975180i
$584$		0			0
$585$	139139.	−	165819.i	0.406571	−	0.484533i
$586$		0			0
$587$	406109.	+	147811.i	1.17860	+	0.428975i	0.855707	−	0.517461i	$-0.173123\pi$
$587$	406109.	+	147811.i	1.17860	+	0.428975i	0.322892	+	0.946436i	$0.395345\pi$
$588$		0			0
$589$	119272.	−	9779.60i	0.343801	−	0.0281897i
$590$		0			0
$591$	92978.4	−	255456.i	0.266199	−	0.731377i
$592$		0			0
$593$	−147770.	−	123993.i	−0.420219	−	0.352606i	0.408027	−	0.912970i	$-0.366217\pi$
$593$	−147770.	−	123993.i	−0.420219	−	0.352606i	−0.828246	+	0.560364i	$0.810661\pi$
$594$		0			0
$595$	36807.9	−	208748.i	0.103970	−	0.589642i
$596$		0			0
$597$	311886.	−	180067.i	0.875079	−	0.505227i
$598$		0			0
$599$	163761.	+	449930.i	0.456412	+	1.25398i	0.928138	+	0.372237i	$0.121409\pi$
$599$	163761.	+	449930.i	0.456412	+	1.25398i	−0.471726	+	0.881745i	$0.656369\pi$
$600$		0			0
$601$	171295.	+	98897.1i	0.474237	+	0.273801i	0.718012	−	0.696031i	$-0.245052\pi$
$601$	171295.	+	98897.1i	0.474237	+	0.273801i	−0.243775	+	0.969832i	$0.578386\pi$
$602$		0			0
$603$	−163144.	−	194428.i	−0.448681	−	0.534717i
$604$		0			0
$605$	−38299.3	−	217206.i	−0.104636	−	0.593418i
$606$		0			0
$607$			69856.4i			0.189596i	0.995497	+	0.0947979i	$0.0302205\pi$
$607$			69856.4i			0.189596i	−0.995497	+	0.0947979i	$0.969780\pi$
$608$		0			0
$609$	101991.			0.274998
$610$		0			0
$611$	205377.	−	36213.4i	0.550134	−	0.0970034i
$612$		0			0
$613$	58868.5	−	49396.5i	0.156661	−	0.131455i	−0.561088	−	0.827756i	$-0.689617\pi$
$613$	58868.5	−	49396.5i	0.156661	−	0.131455i	0.717749	+	0.696302i	$0.245173\pi$
$614$		0			0
$615$	35468.9	−	61433.9i	0.0937772	−	0.162427i
$616$		0			0
$617$	−188604.	+	68646.4i	−0.495429	+	0.180321i	−0.577637	−	0.816294i	$-0.696025\pi$
$617$	−188604.	+	68646.4i	−0.495429	+	0.180321i	0.0822078	+	0.996615i	$0.473803\pi$
$618$		0			0
$619$	284865.	+	493401.i	0.743461	+	1.28771i	0.950910	+	0.309467i	$0.100150\pi$
$619$	284865.	+	493401.i	0.743461	+	1.28771i	−0.207449	+	0.978246i	$0.566516\pi$
$620$		0			0
$621$	207740.	+	36630.2i	0.538688	+	0.0949852i
$622$		0			0
$623$	180524.	−	215140.i	0.465113	−	0.554300i
$624$		0			0
$625$	182700.	+	66497.2i	0.467711	+	0.170233i
$626$		0			0
$627$	138503.	+	37922.7i	0.352308	+	0.0964636i
$628$		0			0
$629$	−236037.	+	648507.i	−0.596594	+	1.63913i
$630$		0			0
$631$	7556.90	+	6340.99i	0.0189795	+	0.0159257i	0.652228	−	0.758023i	$-0.273834\pi$
$631$	7556.90	+	6340.99i	0.0189795	+	0.0159257i	−0.633249	+	0.773949i	$0.718279\pi$
$632$		0			0
$633$	−9881.86	+	56042.8i	−0.0246622	+	0.139866i
$634$		0			0
$635$	−48351.3	+	27915.6i	−0.119911	+	0.0692309i
$636$		0			0
$637$	−184518.	−	506959.i	−0.454737	−	1.24938i
$638$		0			0
$639$	149297.	+	86196.4i	0.365635	+	0.211100i
$640$		0			0
$641$	−37756.3	−	44996.2i	−0.0918911	−	0.109512i	0.718139	−	0.695899i	$-0.244994\pi$
$641$	−37756.3	−	44996.2i	−0.0918911	−	0.109512i	−0.810031	+	0.586388i	$0.800550\pi$
$642$		0			0
$643$	−68197.8	−	386769.i	−0.164948	−	0.935469i	−0.949118	−	0.314922i	$-0.898022\pi$
$643$	−68197.8	−	386769.i	−0.164948	−	0.935469i	0.784169	−	0.620547i	$-0.213089\pi$
$644$		0			0
$645$			108768.i			0.261446i
$646$		0			0
$647$	672112.			1.60558			0.802792	−	0.596259i	$-0.203347\pi$
$647$	672112.			1.60558			0.802792	+	0.596259i	$0.203347\pi$
$648$		0			0
$649$	−11100.2	+	1957.27i	−0.0263537	+	0.00464687i
$650$		0			0
$651$	−41394.5	+	34734.1i	−0.0976745	+	0.0819586i
$652$		0			0
$653$	61917.6	−	107244.i	0.145207	−	0.251506i	−0.784243	−	0.620454i	$-0.786948\pi$
$653$	61917.6	−	107244.i	0.145207	−	0.251506i	0.929450	+	0.368948i	$0.120282\pi$
$654$		0			0
$655$	186874.	−	68016.6i	0.435579	−	0.158538i
$656$		0			0
$657$	24714.6	+	42806.9i	0.0572562	+	0.0991706i
$658$		0			0
$659$	181548.	+	32011.8i	0.418042	+	0.0737122i	0.378713	−	0.925514i	$-0.376367\pi$
$659$	181548.	+	32011.8i	0.418042	+	0.0737122i	0.0393294	+	0.999226i	$0.487478\pi$
$660$		0			0
$661$	201313.	−	239916.i	0.460754	−	0.549106i	−0.484777	−	0.874638i	$-0.661099\pi$
$661$	201313.	−	239916.i	0.460754	−	0.549106i	0.945531	+	0.325532i	$0.105544\pi$
$662$		0			0
$663$	−818813.	−	298024.i	−1.86276	−	0.677991i
$664$		0			0
$665$	−123245.	−	124597.i	−0.278693	−	0.281750i
$666$		0			0
$667$	−57579.5	+	158198.i	−0.129424	+	0.355591i
$668$		0			0
$669$	−278283.	−	233508.i	−0.621778	−	0.521734i
$670$		0			0
$671$	34534.0	−	195852.i	0.0767011	−	0.434993i
$672$		0			0
$673$	194799.	−	112467.i	0.430088	−	0.248311i	−0.269296	−	0.963057i	$-0.586791\pi$
$673$	194799.	−	112467.i	0.430088	−	0.248311i	0.699384	+	0.714746i	$0.253458\pi$
$674$		0			0
$675$	61561.3	+	169138.i	0.135114	+	0.371223i
$676$		0			0
$677$	−654034.	−	377607.i	−1.42700	−	0.823877i	−0.430114	−	0.902775i	$-0.641527\pi$
$677$	−654034.	−	377607.i	−1.42700	−	0.823877i	−0.996883	+	0.0788975i	$0.974860\pi$
$678$		0			0
$679$	184278.	+	219614.i	0.399700	+	0.476344i
$680$		0			0
$681$	114220.	+	647775.i	0.246291	+	1.39679i
$682$		0			0
$683$			393871.i			0.844330i	0.906519	+	0.422165i	$0.138730\pi$
$683$			393871.i			0.844330i	−0.906519	+	0.422165i	$0.861270\pi$
$684$		0			0
$685$	−320530.			−0.683104
$686$		0			0
$687$	−437650.	+	77169.5i	−0.927286	+	0.163506i
$688$		0			0
$689$	−733575.	+	615542.i	−1.54528	+	1.29664i
$690$		0			0
$691$	377450.	−	653763.i	0.790503	−	1.36919i	−0.135152	−	0.990825i	$-0.543152\pi$
$691$	377450.	−	653763.i	0.790503	−	1.36919i	0.925656	−	0.378367i	$-0.123514\pi$
$692$		0			0
$693$	49777.7	−	18117.6i	0.103650	−	0.0377254i
$694$		0			0
$695$	315474.	+	546417.i	0.653122	+	1.13124i
$696$		0			0
$697$	229744.	+	40510.0i	0.472909	+	0.0833867i
$698$		0			0
$699$	−12971.9	+	15459.4i	−0.0265492	+	0.0316401i
$700$		0			0
$701$	−789803.	−	287465.i	−1.60725	−	0.584990i	−0.626355	−	0.779538i	$-0.715454\pi$
$701$	−789803.	−	287465.i	−1.60725	−	0.584990i	−0.980893	+	0.194548i	$0.937676\pi$
$702$		0			0
$703$	324723.	+	469179.i	0.657055	+	0.949353i
$704$		0			0
$705$	31683.4	−	87049.4i	0.0637461	−	0.175141i
$706$		0			0
$707$	−183878.	−	154292.i	−0.367867	−	0.308677i
$708$		0			0
$709$	41164.2	−	233454.i	0.0818892	−	0.464417i	−0.916095	−	0.400960i	$-0.868676\pi$
$709$	41164.2	−	233454.i	0.0818892	−	0.464417i	0.997985	−	0.0634565i	$-0.0202124\pi$
$710$		0			0
$711$	−74765.5	+	43165.9i	−0.147898	+	0.0853889i
$712$		0			0
$713$	−30506.6	−	83816.1i	−0.0600087	−	0.164873i
$714$		0			0
$715$	−306656.	−	177048.i	−0.599846	−	0.346321i
$716$		0			0
$717$	−28199.2	−	33606.5i	−0.0548528	−	0.0653710i
$718$		0			0
$719$	39743.6	+	225397.i	0.0768793	+	0.436004i	0.998815	+	0.0486618i	$0.0154957\pi$
$719$	39743.6	+	225397.i	0.0768793	+	0.436004i	−0.921936	+	0.387342i	$0.873393\pi$
$720$		0			0
$721$			237012.i			0.455933i
$722$		0			0
$723$	385406.			0.737297
$724$		0			0
$725$	−141467.	+	24944.4i	−0.269140	+	0.0474567i
$726$		0			0
$727$	−487960.	+	409447.i	−0.923242	+	0.774692i	−0.974592	−	0.223989i	$-0.928092\pi$
$727$	−487960.	+	409447.i	−0.923242	+	0.774692i	0.0513496	+	0.998681i	$0.483648\pi$
$728$		0			0
$729$	253603.	−	439254.i	0.477199	−	0.826534i
$730$		0			0
$731$	−336126.	+	122340.i	−0.629023	+	0.228946i
$732$		0			0
$733$	−204157.	−	353610.i	−0.379975	−	0.658137i	0.611083	−	0.791567i	$-0.290734\pi$
$733$	−204157.	−	353610.i	−0.379975	−	0.658137i	−0.991058	+	0.133430i	$0.957401\pi$
$734$		0			0
$735$	−236004.	−	41613.9i	−0.436862	−	0.0770306i
$736$		0			0
$737$	−266877.	+	318052.i	−0.491334	+	0.585549i
$738$		0			0
$739$	−499421.	−	181774.i	−0.914487	−	0.332846i	−0.158444	−	0.987368i	$-0.550648\pi$
$739$	−499421.	−	181774.i	−0.914487	−	0.332846i	−0.756043	+	0.654522i	$0.772870\pi$
$740$		0			0
$741$	−592391.	+	409999.i	−1.07888	+	0.746700i
$742$		0			0
$743$	−37442.9	+	102874.i	−0.0678253	+	0.186349i	−0.968975	−	0.247160i	$-0.920503\pi$
$743$	−37442.9	+	102874.i	−0.0678253	+	0.186349i	0.901149	+	0.433509i	$0.142725\pi$
$744$		0			0
$745$	363923.	+	305368.i	0.655688	+	0.550188i
$746$		0			0
$747$	81332.6	−	461260.i	0.145755	−	0.826618i
$748$		0			0
$749$	−29703.5	+	17149.3i	−0.0529472	+	0.0305691i
$750$		0			0
$751$	254343.	+	698802.i	0.450962	+	1.23901i	0.932048	+	0.362335i	$0.118020\pi$
$751$	254343.	+	698802.i	0.450962	+	1.23901i	−0.481085	+	0.876674i	$0.659757\pi$
$752$		0			0
$753$	−389137.	−	224668.i	−0.686297	−	0.396234i
$754$		0			0
$755$	−245783.	−	292912.i	−0.431179	−	0.513859i
$756$		0			0
$757$	−89008.1	−	504790.i	−0.155324	−	0.880885i	−0.958489	−	0.285129i	$-0.907964\pi$
$757$	−89008.1	−	504790.i	−0.155324	−	0.880885i	0.803166	−	0.595756i	$-0.203147\pi$
$758$		0			0
$759$		−	107030.i		−	0.185790i
$760$		0			0
$761$	−894191.			−1.54405			−0.772024	−	0.635593i	$-0.780756\pi$
$761$	−894191.			−1.54405			−0.772024	+	0.635593i	$0.780756\pi$
$762$		0			0
$763$	−205033.	+	36152.8i	−0.352187	+	0.0621001i
$764$		0			0
$765$	242231.	−	203256.i	0.413911	−	0.347313i
$766$		0			0
$767$	28274.1	−	48972.1i	0.0480615	−	0.0832450i
$768$		0			0
$769$	671793.	−	244513.i	1.13601	−	0.413474i	0.295540	−	0.955330i	$-0.404500\pi$
$769$	671793.	−	244513.i	1.13601	−	0.413474i	0.840471	+	0.541856i	$0.182278\pi$
$770$		0			0
$771$	340918.	+	590488.i	0.573511	+	0.993350i
$772$		0			0
$773$	17858.0	+	3148.84i	0.0298864	+	0.00526977i	0.188571	−	0.982059i	$-0.439614\pi$
$773$	17858.0	+	3148.84i	0.0298864	+	0.00526977i	−0.158685	+	0.987329i	$0.550725\pi$
$774$		0			0
$775$	48921.1	−	58302.0i	0.0814504	−	0.0970688i
$776$		0			0
$777$	−242107.	−	88119.7i	−0.401019	−	0.145959i
$778$		0			0
$779$	137129.	−	135641.i	0.225972	−	0.223520i
$780$		0			0
$781$	96451.9	−	265000.i	0.158128	−	0.434453i
$782$		0			0
$783$	375773.	+	315311.i	0.612918	+	0.514299i
$784$		0			0
$785$	41757.3	−	236817.i	0.0677630	−	0.384303i
$786$		0			0
$787$	864510.	−	499125.i	1.39579	−	0.805860i	0.401843	−	0.915709i	$-0.368370\pi$
$787$	864510.	−	499125.i	1.39579	−	0.805860i	0.993948	+	0.109848i	$0.0350365\pi$
$788$		0			0
$789$	−263096.	−	722849.i	−0.422629	−	1.16116i
$790$		0			0
$791$	235919.	+	136208.i	0.377059	+	0.217695i
$792$		0			0
$793$	641331.	+	764309.i	1.01985	+	1.21541i
$794$		0			0
$795$	73865.4	+	418912.i	0.116871	+	0.662809i
$796$		0			0
$797$			1.11913e6i			1.76183i	0.473275	+	0.880915i	$0.343072\pi$
$797$			1.11913e6i			1.76183i	−0.473275	+	0.880915i	$0.656928\pi$
$798$		0			0
$799$	304645.			0.477200
$800$		0			0
$801$	412595.	−	72751.5i	0.643070	−	0.113391i
$802$		0			0
$803$	61940.8	−	51974.5i	0.0960607	−	0.0806045i
$804$		0			0
$805$	−65311.0	+	113122.i	−0.100785	+	0.174564i
$806$		0			0
$807$	689439.	−	250935.i	1.05864	−	0.385314i
$808$		0			0
$809$	−236932.	−	410379.i	−0.362015	−	0.627029i	0.626277	−	0.779601i	$-0.284578\pi$
$809$	−236932.	−	410379.i	−0.362015	−	0.627029i	−0.988292	+	0.152572i	$0.951245\pi$
$810$		0			0
$811$	573604.	+	101142.i	0.872109	+	0.153776i	0.591753	−	0.806120i	$-0.298436\pi$
$811$	573604.	+	101142.i	0.872109	+	0.153776i	0.280356	+	0.959896i	$0.409547\pi$
$812$		0			0
$813$	96292.4	−	114757.i	0.145684	−	0.173619i
$814$		0			0
$815$	−814244.	−	296361.i	−1.22586	−	0.446175i
$816$		0			0
$817$	−78100.6	+	285242.i	−0.117007	+	0.427336i
$818$		0			0
$819$	−90894.9	+	249732.i	−0.135510	+	0.372311i
$820$		0			0
$821$	567201.	+	475938.i	0.841493	+	0.706096i	0.957899	−	0.287105i	$-0.0926930\pi$
$821$	567201.	+	475938.i	0.841493	+	0.706096i	−0.116406	+	0.993202i	$0.537137\pi$
$822$		0			0
$823$	223865.	−	1.26960e6i	0.330511	−	1.87442i	−0.137205	−	0.990543i	$-0.543812\pi$
$823$	223865.	−	1.26960e6i	0.330511	−	1.87442i	0.467716	−	0.883879i	$-0.345077\pi$
$824$		0			0
$825$	79090.3	−	45662.8i	0.116203	−	0.0670896i
$826$		0			0
$827$	180552.	+	496063.i	0.263993	+	0.725314i	0.998889	+	0.0471339i	$0.0150088\pi$
$827$	180552.	+	496063.i	0.263993	+	0.725314i	−0.734896	+	0.678180i	$0.762769\pi$
$828$		0			0
$829$	−570413.	−	329328.i	−0.830005	−	0.479203i	0.0238496	−	0.999716i	$-0.492408\pi$
$829$	−570413.	−	329328.i	−0.830005	−	0.479203i	−0.853854	+	0.520512i	$0.825741\pi$
$830$		0			0
$831$	140297.	+	167200.i	0.203164	+	0.242121i
$832$		0			0
$833$	−136852.	−	776129.i	−0.197225	−	1.11852i
$834$		0			0
$835$			581237.i			0.833644i
$836$		0			0
$837$	−259895.			−0.370977
$838$		0			0
$839$	38822.3	−	6845.42i	0.0551515	−	0.00972470i	−0.146004	−	0.989284i	$-0.546641\pi$
$839$	38822.3	−	6845.42i	0.0551515	−	0.00972470i	0.201156	+	0.979559i	$0.435530\pi$
$840$		0			0
$841$	241911.	−	202988.i	0.342030	−	0.286997i
$842$		0			0
$843$	100147.	−	173459.i	0.140923	−	0.244086i
$844$		0			0
$845$	1.13566e6	−	413345.i	1.59050	−	0.578895i
$846$		0			0
$847$	135393.	+	234508.i	0.188725	+	0.326882i
$848$		0			0
$849$	374298.	+	65998.8i	0.519280	+	0.0915631i
$850$		0			0
$851$	273364.	−	325783.i	0.377470	−	0.449851i
$852$		0			0
$853$	675109.	+	245720.i	0.927846	+	0.337708i	0.761356	−	0.648335i	$-0.224534\pi$
$853$	675109.	+	245720.i	0.927846	+	0.337708i	0.166491	+	0.986043i	$0.446756\pi$
$854$		0			0
$855$	−21364.9	−	260565.i	−0.0292259	−	0.356438i
$856$		0			0
$857$	−439145.	+	1.20654e6i	−0.597924	+	1.64278i	0.157479	+	0.987522i	$0.449663\pi$
$857$	−439145.	+	1.20654e6i	−0.597924	+	1.64278i	−0.755403	+	0.655261i	$0.772559\pi$
$858$		0			0
$859$	−219214.	−	183942.i	−0.297086	−	0.249284i	0.482044	−	0.876147i	$-0.339894\pi$
$859$	−219214.	−	183942.i	−0.297086	−	0.249284i	−0.779130	+	0.626862i	$0.784339\pi$
$860$		0			0
$861$	−15123.6	+	85770.1i	−0.0204009	+	0.115699i
$862$		0			0
$863$	−719645.	+	415487.i	−0.966266	+	0.557874i	−0.898096	−	0.439800i	$-0.855049\pi$
$863$	−719645.	+	415487.i	−0.966266	+	0.557874i	−0.0681701	+	0.997674i	$0.521716\pi$
$864$		0			0
$865$	155032.	+	425946.i	0.207199	+	0.569276i
$866$		0			0
$867$	−619419.	−	357621.i	−0.824036	−	0.475757i
$868$		0			0
$869$	90777.5	+	108184.i	0.120209	+	0.143260i
$870$		0			0
$871$	−361704.	−	2.05133e6i	−0.476779	−	2.70395i
$872$		0			0
$873$			427672.i			0.561154i
$874$		0			0
$875$	−414873.			−0.541875
$876$		0			0
$877$	249893.	−	44062.8i	0.324903	−	0.0572892i	−0.00881769	−	0.999961i	$-0.502807\pi$
$877$	249893.	−	44062.8i	0.324903	−	0.0572892i	0.333721	+	0.942672i	$0.391696\pi$
$878$		0			0
$879$	−389024.	+	326430.i	−0.503499	+	0.422486i
$880$		0			0
$881$	753241.	−	1.30465e6i	0.970470	−	1.68090i	0.276331	−	0.961063i	$-0.410881\pi$
$881$	753241.	−	1.30465e6i	0.970470	−	1.68090i	0.694139	−	0.719841i	$-0.255785\pi$
$882$		0			0
$883$	−510968.	+	185977.i	−0.655349	+	0.238527i	−0.648227	−	0.761447i	$-0.724489\pi$
$883$	−510968.	+	185977.i	−0.655349	+	0.238527i	−0.00712173	+	0.999975i	$0.502267\pi$
$884$		0			0
$885$	−12559.4	−	21753.5i	−0.0160355	−	0.0277743i
$886$		0			0
$887$	896515.	+	158080.i	1.13949	+	0.200923i	0.711382	−	0.702805i	$-0.248069\pi$
$887$	896515.	+	158080.i	1.13949	+	0.200923i	0.428107	+	0.903728i	$0.359181\pi$
$888$		0			0
$889$	44060.7	−	52509.5i	0.0557504	−	0.0664407i
$890$		0			0
$891$	−127900.	−	46551.9i	−0.161108	−	0.0586384i
$892$		0			0
$893$	145595.	−	205535.i	0.182575	−	0.257741i
$894$		0			0
$895$	−315620.	+	867158.i	−0.394020	+	1.08256i
$896$		0			0
$897$	411337.	+	345153.i	0.511226	+	0.428970i
$898$		0			0
$899$	36017.6	−	204266.i	0.0445651	−	0.252742i
$900$		0			0
$901$	−1.21148e6	+	699448.i	−1.49234	+	0.861600i
$902$		0			0
$903$	−45673.0	−	125486.i	−0.0560124	−	0.153893i
$904$		0			0
$905$	−16588.5	−	9577.35i	−0.0202539	−	0.0116936i
$906$		0			0
$907$	82230.3	+	97998.2i	0.0999579	+	0.119125i	0.813704	−	0.581279i	$-0.197448\pi$
$907$	82230.3	+	97998.2i	0.0999579	+	0.119125i	−0.713746	+	0.700404i	$0.753003\pi$
$908$		0			0
$909$	−62180.1	−	352641.i	−0.0752529	−	0.426781i
$910$		0			0
$911$			61177.7i			0.0737151i	0.999321	+	0.0368576i	$0.0117348\pi$
$911$			61177.7i			0.0737151i	−0.999321	+	0.0368576i	$0.988265\pi$
$912$		0			0
$913$	−766187.			−0.919164
$914$		0			0
$915$	436463.	−	76960.1i	0.521321	−	0.0919229i
$916$		0			0
$917$	−187036.	+	156941.i	−0.222426	+	0.186638i
$918$		0			0
$919$	216234.	−	374528.i	0.256031	−	0.443459i	−0.709144	−	0.705064i	$-0.750918\pi$
$919$	216234.	−	374528.i	0.256031	−	0.443459i	0.965175	+	0.261605i	$0.0842517\pi$
$920$		0			0
$921$	755027.	−	274807.i	0.890109	−	0.323973i
$922$		0			0
$923$	707405.	+	1.22526e6i	0.830357	+	1.43822i
$924$		0			0
$925$	357366.	+	63013.2i	0.417666	+	0.0736458i
$926$		0			0
$927$	−227271.	+	270851.i	−0.264475	+	0.315189i
$928$		0			0
$929$	598590.	+	217869.i	0.693582	+	0.252443i	0.664668	−	0.747139i	$-0.268573\pi$
$929$	598590.	+	217869.i	0.693582	+	0.252443i	0.0289140	+	0.999582i	$0.490795\pi$
$930$		0			0
$931$	−589035.	−	278593.i	−0.679582	−	0.321419i
$932$		0			0
$933$	23489.6	−	64537.3i	0.0269844	−	0.0741391i
$934$		0			0
$935$	−396250.	−	332494.i	−0.453259	−	0.380330i
$936$		0			0
$937$	−120994.	+	686188.i	−0.137811	+	0.781563i	0.835050	+	0.550173i	$0.185438\pi$
$937$	−120994.	+	686188.i	−0.137811	+	0.781563i	−0.972861	+	0.231390i	$0.925673\pi$
$938$		0			0
$939$	882786.	−	509677.i	1.00121	−	0.578048i
$940$		0			0
$941$	−360657.	−	990897.i	−0.407300	−	1.11905i	−0.958604	−	0.284744i	$-0.908091\pi$
$941$	−360657.	−	990897.i	−0.407300	−	1.11905i	0.551303	−	0.834305i	$-0.314131\pi$
$942$		0			0
$943$	−124500.	−	71879.8i	−0.140005	−	0.0808321i
$944$		0			0
$945$	244647.	+	291559.i	0.273953	+	0.326484i
$946$		0			0
$947$	16148.0	+	91580.0i	0.0180061	+	0.102118i	0.992486	−	0.122356i	$-0.0390449\pi$
$947$	16148.0	+	91580.0i	0.0180061	+	0.102118i	−0.974480	+	0.224473i	$0.927934\pi$
$948$		0			0
$949$			405660.i			0.450432i
$950$		0			0
$951$	584218.			0.645972
$952$		0			0
$953$	−578425.	+	101992.i	−0.636885	+	0.112300i	−0.482762	−	0.875752i	$-0.660366\pi$
$953$	−578425.	+	101992.i	−0.636885	+	0.112300i	−0.154123	+	0.988052i	$0.549255\pi$
$954$		0			0
$955$	−908753.	+	762534.i	−0.996412	+	0.836089i
$956$		0			0
$957$	124445.	−	215545.i	0.135880	−	0.235350i
$958$		0			0
$959$	369795.	−	134594.i	0.402090	−	0.146349i
$960$		0			0
$961$	−406814.	−	704623.i	−0.440503	−	0.762974i
$962$		0			0
$963$	−50388.6	−	8884.88i	−0.0543350	−	0.00958073i
$964$		0			0
$965$	−243358.	+	290023.i	−0.261331	+	0.311442i
$966$		0			0
$967$	−476721.	−	173512.i	−0.509814	−	0.185557i	0.0742891	−	0.997237i	$-0.476331\pi$
$967$	−476721.	−	173512.i	−0.509814	−	0.185557i	−0.584103	+	0.811680i	$0.698553\pi$
$968$		0			0
$969$	−956230.	+	439563.i	−1.01839	+	0.468137i
$970$		0			0
$971$	−174080.	+	478282.i	−0.184634	+	0.507278i	−0.997132	−	0.0756867i	$-0.975885\pi$
$971$	−174080.	+	478282.i	−0.184634	+	0.507278i	0.812498	+	0.582964i	$0.198107\pi$
$972$		0			0
$973$	−593410.	−	497930.i	−0.626800	−	0.525947i
$974$		0			0
$975$	−79561.3	+	451214.i	−0.0836937	+	0.474650i
$976$		0			0
$977$	−738321.	+	426270.i	−0.773492	+	0.446576i	−0.834119	−	0.551585i	$-0.814023\pi$
$977$	−738321.	+	426270.i	−0.773492	+	0.446576i	0.0606267	+	0.998161i	$0.480690\pi$
$978$		0			0
$979$	−234403.	−	644018.i	−0.244567	−	0.671943i
$980$		0			0
$981$	−268972.	−	155291.i	−0.279492	−	0.161365i
$982$		0			0
$983$	−751613.	−	895737.i	−0.777834	−	0.926987i	0.220999	−	0.975274i	$-0.429068\pi$
$983$	−751613.	−	895737.i	−0.777834	−	0.926987i	−0.998833	+	0.0482873i	$0.984624\pi$
$984$		0			0
$985$	140591.	+	797329.i	0.144905	+	0.821798i
$986$		0			0
$987$			113733.i			0.116749i
$988$		0			0
$989$	220425.			0.225356
$990$		0			0
$991$	−583461.	+	102880.i	−0.594107	+	0.104757i	−0.462614	−	0.886560i	$-0.653088\pi$
$991$	−583461.	+	102880.i	−0.594107	+	0.104757i	−0.131493	+	0.991317i	$0.541977\pi$
$992$		0			0
$993$	100891.	−	84657.4i	0.102318	−	0.0858552i
$994$		0			0
$995$	−536279.	+	928862.i	−0.541682	+	0.938221i
$996$		0			0
$997$	618338.	−	225057.i	0.622065	−	0.226413i	−0.0117090	−	0.999931i	$-0.503727\pi$
$997$	618338.	−	225057.i	0.622065	−	0.226413i	0.633774	+	0.773518i	$0.281505\pi$
$998$		0			0
$999$	−619583.	−	1.07315e6i	−0.620824	−	1.07530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.53.3	yes	42
19.14	odd	18	inner	76.5.j.a.33.3	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.3	✓	42	19.14	odd	18	inner
76.5.j.a.53.3	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)

\(f(q)\)	\(=\)	\(q+(-6.57540 + 1.15942i) q^{3} +(15.2328 - 12.7819i) q^{5} +(-12.2068 + 21.1429i) q^{7} +(-34.2234 + 12.4563i) q^{9} +O(q^{10})\)	\(q+(-6.57540 + 1.15942i) q^{3} +(15.2328 - 12.7819i) q^{5} +(-12.2068 + 21.1429i) q^{7} +(-34.2234 + 12.4563i) q^{9} +(29.7884 + 51.5951i) q^{11} +(-294.353 - 51.9023i) q^{13} +(-85.3424 + 101.707i) q^{15} +(-410.296 - 149.336i) q^{17} +(-296.839 + 205.445i) q^{19} +(55.7514 - 153.176i) q^{21} +(206.115 + 172.951i) q^{23} +(-39.8671 + 226.097i) q^{25} +(678.958 - 391.997i) q^{27} +(213.999 + 587.957i) q^{29} +(-287.088 - 165.751i) q^{31} +(-255.691 - 304.721i) q^{33} +(84.3004 + 478.091i) q^{35} -1580.58i q^{37} +1995.66 q^{39} +(-526.177 + 92.7792i) q^{41} +(627.564 - 526.589i) q^{43} +(-362.105 + 627.184i) q^{45} +(-655.645 + 238.635i) q^{47} +(902.486 + 1563.15i) q^{49} +(2871.00 + 506.236i) q^{51} +(2059.40 - 2454.30i) q^{53} +(1113.24 + 405.187i) q^{55} +(1713.64 - 1695.04i) q^{57} +(-64.7073 + 177.782i) q^{59} +(-2557.13 - 2145.68i) q^{61} +(154.398 - 875.634i) q^{63} +(-5147.23 + 2971.76i) q^{65} +(2383.52 + 6548.66i) q^{67} +(-1555.82 - 898.251i) q^{69} +(-3042.63 - 3626.06i) q^{71} +(-235.676 - 1336.58i) q^{73} -1532.90i q^{75} -1454.49 q^{77} +(2334.45 - 411.626i) q^{79} +(-1750.10 + 1468.51i) q^{81} +(-6430.23 + 11137.5i) q^{83} +(-8158.75 + 2969.54i) q^{85} +(-2088.82 - 3617.94i) q^{87} +(-11328.8 - 1997.58i) q^{89} +(4690.48 - 5589.90i) q^{91} +(2079.90 + 757.020i) q^{93} +(-1895.73 + 6923.66i) q^{95} +(4016.29 - 11034.7i) q^{97} +(-1662.15 - 1394.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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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