LMFDB - Embedded newform 360.4.m.c.179.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.33
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.778894 - 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 + 0.469176i) q^{5} -17.5697 q^{7} +(-16.8033 + 15.1542i) q^{8} +O(q^{10})$	\(q+(0.778894 - 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 + 0.469176i) q^{5} -17.5697 q^{7} +(-16.8033 + 15.1542i) q^{8} +(-7.42491 + 30.7387i) q^{10} -1.21111i q^{11} -2.29803 q^{13} +(-13.6849 + 47.7731i) q^{14} +(28.1171 + 57.4928i) q^{16} +38.9371 q^{17} +101.821 q^{19} +(77.7975 + 44.1311i) q^{20} +(-3.29309 - 0.943328i) q^{22} -79.2103i q^{23} +(124.560 - 10.4819i) q^{25} +(-1.78992 + 6.24849i) q^{26} +(119.239 + 74.4204i) q^{28} -188.490 q^{29} +195.204i q^{31} +(178.227 - 31.6716i) q^{32} +(30.3279 - 105.873i) q^{34} +(196.262 - 8.24327i) q^{35} +377.761 q^{37} +(79.3074 - 276.857i) q^{38} +(180.591 - 177.163i) q^{40} +205.009i q^{41} +396.636i q^{43} +(-5.12994 + 8.21938i) q^{44} +(-215.378 - 61.6965i) q^{46} -429.604i q^{47} -34.3070 q^{49} +(68.5180 - 346.851i) q^{50} +(15.5959 + 9.73382i) q^{52} -65.4197i q^{53} +(0.568225 + 13.5287i) q^{55} +(295.229 - 266.253i) q^{56} +(-146.814 + 512.518i) q^{58} +354.000i q^{59} +595.183i q^{61} +(530.772 + 152.043i) q^{62} +(52.7031 - 509.280i) q^{64} +(25.6701 - 1.07818i) q^{65} +31.8435i q^{67} +(-264.252 - 164.927i) q^{68} +(130.453 - 540.069i) q^{70} -86.9186 q^{71} +320.319i q^{73} +(294.236 - 1027.16i) q^{74} +(-691.020 - 431.284i) q^{76} +21.2788i q^{77} +518.092i q^{79} +(-341.057 - 629.031i) q^{80} +(557.433 + 159.680i) q^{82} +520.655 q^{83} +(-434.947 + 18.2684i) q^{85} +(1078.48 + 308.938i) q^{86} +(18.3534 + 20.3507i) q^{88} -40.5337i q^{89} +40.3755 q^{91} +(-335.514 + 537.572i) q^{92} +(-1168.12 - 334.616i) q^{94} +(-1137.39 + 47.7718i) q^{95} -1551.48i q^{97} +(-26.7215 + 93.2830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.778894	−	2.71907i	0.275381	−	0.961335i
$2$	0.778894	−	2.71907i	0.275381	−	0.961335i
$3$		0			0
$3$		0			0
$4$	−6.78665	−	4.23573i	−0.848331	−	0.529467i
$5$	−11.1705	+	0.469176i	−0.999119	+	0.0419644i
$5$	−11.1705	+	0.469176i	−0.999119	+	0.0419644i
$6$		0			0
$7$	−17.5697			−0.948673			−0.474336	−	0.880344i	$-0.657312\pi$
$7$	−17.5697			−0.948673			−0.474336	+	0.880344i	$0.657312\pi$
$8$	−16.8033	+	15.1542i	−0.742609	+	0.669725i
$9$		0			0
$10$	−7.42491	+	30.7387i	−0.234796	+	0.972045i
$11$		−	1.21111i		−	0.0331967i	−0.999862	−	0.0165983i	$-0.994716\pi$
$11$		−	1.21111i		−	0.0331967i	0.999862	−	0.0165983i	$-0.00528366\pi$
$12$		0			0
$13$	−2.29803			−0.0490275			−0.0245138	−	0.999699i	$-0.507804\pi$
$13$	−2.29803			−0.0490275			−0.0245138	+	0.999699i	$0.507804\pi$
$14$	−13.6849	+	47.7731i	−0.261246	+	0.911992i
$15$		0			0
$16$	28.1171	+	57.4928i	0.439330	+	0.898326i
$17$	38.9371			0.555508			0.277754	−	0.960652i	$-0.410410\pi$
$17$	38.9371			0.555508			0.277754	+	0.960652i	$0.410410\pi$
$18$		0			0
$19$	101.821			1.22943			0.614716	−	0.788748i	$-0.289270\pi$
$19$	101.821			1.22943			0.614716	+	0.788748i	$0.289270\pi$
$20$	77.7975	+	44.1311i	0.869802	+	0.493400i
$21$		0			0
$22$	−3.29309	−	0.943328i	−0.0319132	−	0.00914173i
$23$		−	79.2103i		−	0.718108i	−0.933317	−	0.359054i	$-0.883099\pi$
$23$		−	79.2103i		−	0.718108i	0.933317	−	0.359054i	$-0.116901\pi$
$24$		0			0
$25$	124.560	−	10.4819i	0.996478	−	0.0838549i
$26$	−1.78992	+	6.24849i	−0.0135012	+	0.0471319i
$27$		0			0
$28$	119.239	+	74.4204i	0.804788	+	0.502290i
$29$	−188.490			−1.20696			−0.603479	−	0.797379i	$-0.706219\pi$
$29$	−188.490			−1.20696			−0.603479	+	0.797379i	$0.706219\pi$
$30$		0			0
$31$			195.204i			1.13096i	0.824763	+	0.565478i	$0.191308\pi$
$31$			195.204i			1.13096i	−0.824763	+	0.565478i	$0.808692\pi$
$32$	178.227	−	31.6716i	0.984575	−	0.174962i
$33$		0			0
$34$	30.3279	−	105.873i	0.152976	−	0.534029i
$35$	196.262	−	8.24327i	0.947837	−	0.0398105i
$36$		0			0
$37$	377.761			1.67847			0.839237	−	0.543766i	$-0.183002\pi$
$37$	377.761			1.67847			0.839237	+	0.543766i	$0.183002\pi$
$38$	79.3074	−	276.857i	0.338562	−	1.18190i
$39$		0			0
$40$	180.591	−	177.163i	0.713850	−	0.700299i
$41$			205.009i			0.780903i	0.920623	+	0.390452i	$0.127681\pi$
$41$			205.009i			0.780903i	−0.920623	+	0.390452i	$0.872319\pi$
$42$		0			0
$43$			396.636i			1.40666i	0.710863	+	0.703331i	$0.248305\pi$
$43$			396.636i			1.40666i	−0.710863	+	0.703331i	$0.751695\pi$
$44$	−5.12994	+	8.21938i	−0.0175765	+	0.0281618i
$45$		0			0
$46$	−215.378	−	61.6965i	−0.690343	−	0.197753i
$47$		−	429.604i		−	1.33328i	−0.745380	−	0.666639i	$-0.767732\pi$
$47$		−	429.604i		−	1.33328i	0.745380	−	0.666639i	$-0.232268\pi$
$48$		0			0
$49$	−34.3070			−0.100020
$50$	68.5180	−	346.851i	0.193798	−	0.981041i
$51$		0			0
$52$	15.5959	+	9.73382i	0.0415916	+	0.0259584i
$53$		−	65.4197i		−	0.169549i	−0.996400	−	0.0847745i	$-0.972983\pi$
$53$		−	65.4197i		−	0.169549i	0.996400	−	0.0847745i	$-0.0270170\pi$
$54$		0			0
$55$	0.568225	+	13.5287i	0.00139308	+	0.0331675i
$56$	295.229	−	266.253i	0.704493	−	0.635350i
$57$		0			0
$58$	−146.814	+	512.518i	−0.332373	+	1.16029i
$59$			354.000i			0.781134i	0.920575	+	0.390567i	$0.127721\pi$
$59$			354.000i			0.781134i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$			595.183i			1.24927i	0.780918	+	0.624634i	$0.214752\pi$
$61$			595.183i			1.24927i	−0.780918	+	0.624634i	$0.785248\pi$
$62$	530.772	+	152.043i	1.08723	+	0.311444i
$63$		0			0
$64$	52.7031	−	509.280i	0.102936	−	0.994688i
$65$	25.6701	−	1.07818i	0.0489843	−	0.00205741i
$66$		0			0
$67$			31.8435i			0.0580642i	0.999578	+	0.0290321i	$0.00924251\pi$
$67$			31.8435i			0.0580642i	−0.999578	+	0.0290321i	$0.990757\pi$
$68$	−264.252	−	164.927i	−0.471255	−	0.294123i
$69$		0			0
$70$	130.453	−	540.069i	0.222745	−	0.922152i
$71$	−86.9186			−0.145286			−0.0726432	−	0.997358i	$-0.523143\pi$
$71$	−86.9186			−0.145286			−0.0726432	+	0.997358i	$0.523143\pi$
$72$		0			0
$73$			320.319i			0.513568i	0.966469	+	0.256784i	$0.0826629\pi$
$73$			320.319i			0.513568i	−0.966469	+	0.256784i	$0.917337\pi$
$74$	294.236	−	1027.16i	0.462219	−	1.61358i
$75$		0			0
$76$	−691.020	−	431.284i	−1.04297	−	0.650944i
$77$			21.2788i			0.0314928i
$78$		0			0
$79$			518.092i			0.737847i	0.929460	+	0.368924i	$0.120274\pi$
$79$			518.092i			0.737847i	−0.929460	+	0.368924i	$0.879726\pi$
$80$	−341.057	−	629.031i	−0.476641	−	0.879098i
$81$		0			0
$82$	557.433	+	159.680i	0.750710	+	0.215046i
$83$	520.655			0.688545			0.344273	−	0.938870i	$-0.388126\pi$
$83$	520.655			0.688545			0.344273	+	0.938870i	$0.388126\pi$
$84$		0			0
$85$	−434.947	+	18.2684i	−0.555019	+	0.0233116i
$86$	1078.48	+	308.938i	1.35227	+	0.387368i
$87$		0			0
$88$	18.3534	+	20.3507i	0.0222327	+	0.0246522i
$89$		−	40.5337i		−	0.0482760i	−0.999709	−	0.0241380i	$-0.992316\pi$
$89$		−	40.5337i		−	0.0482760i	0.999709	−	0.0241380i	$-0.00768412\pi$
$90$		0			0
$91$	40.3755			0.0465111
$92$	−335.514	+	537.572i	−0.380214	+	0.609193i
$93$		0			0
$94$	−1168.12	−	334.616i	−1.28173	−	0.367159i
$95$	−1137.39	+	47.7718i	−1.22835	+	0.0515924i
$96$		0			0
$97$		−	1551.48i		−	1.62401i	−0.583648	−	0.812007i	$-0.698375\pi$
$97$		−	1551.48i		−	1.62401i	0.583648	−	0.812007i	$-0.301625\pi$
$98$	−26.7215	+	93.2830i	−0.0275437	+	0.0961532i
$99$		0			0
$100$	−889.741	−	456.465i	−0.889741	−	0.456465i
$101$	324.477			0.319669			0.159835	−	0.987144i	$-0.448904\pi$
$101$	324.477			0.319669			0.159835	+	0.987144i	$0.448904\pi$
$102$		0			0
$103$	144.808			0.138528			0.0692638	−	0.997598i	$-0.477935\pi$
$103$	144.808			0.138528			0.0692638	+	0.997598i	$0.477935\pi$
$104$	38.6145	−	34.8247i	0.0364083	−	0.0328350i
$105$		0			0
$106$	−177.881	−	50.9551i	−0.162993	−	0.0466905i
$107$	1541.44			1.39267			0.696337	−	0.717715i	$-0.254812\pi$
$107$	1541.44			1.39267			0.696337	+	0.717715i	$0.254812\pi$
$108$		0			0
$109$			1287.14i			1.13106i	0.824726	+	0.565532i	$0.191329\pi$
$109$			1287.14i			1.13106i	−0.824726	+	0.565532i	$0.808671\pi$
$110$	37.2280	+	8.99239i	0.0322687	+	0.00779446i
$111$		0			0
$112$	−494.009	−	1010.13i	−0.416781	−	0.852217i
$113$	−1770.49			−1.47392			−0.736962	−	0.675934i	$-0.763740\pi$
$113$	−1770.49			−1.47392			−0.736962	+	0.675934i	$0.763740\pi$
$114$		0			0
$115$	37.1636	+	884.818i	0.0301350	+	0.717476i
$116$	1279.22	+	798.395i	1.02390	+	0.639044i
$117$		0			0
$118$	962.550	+	275.729i	0.750931	+	0.215109i
$119$	−684.112			−0.526995
$120$		0			0
$121$	1329.53			0.998898
$122$	1618.34	+	463.584i	1.20096	+	0.344024i
$123$		0			0
$124$	826.832	−	1324.78i	0.598804	−	0.959426i
$125$	−1386.48	+	175.528i	−0.992081	+	0.125598i
$126$		0			0
$127$	1812.73			1.26656			0.633281	−	0.773922i	$-0.281708\pi$
$127$	1812.73			1.26656			0.633281	+	0.773922i	$0.281708\pi$
$128$	−1343.72	−	539.979i	−0.927882	−	0.372874i
$129$		0			0
$130$	17.0626	−	70.6385i	0.0115115	−	0.0476569i
$131$			1129.86i			0.753563i	0.926302	+	0.376781i	$0.122969\pi$
$131$			1129.86i			0.753563i	−0.926302	+	0.376781i	$0.877031\pi$
$132$		0			0
$133$	−1788.95			−1.16633
$134$	86.5846	+	24.8027i	0.0558192	+	0.0159898i
$135$		0			0
$136$	−654.273	+	590.059i	−0.412525	+	0.372038i
$137$	−2163.98			−1.34950			−0.674749	−	0.738047i	$-0.735748\pi$
$137$	−2163.98			−1.34950			−0.674749	+	0.738047i	$0.735748\pi$
$138$		0			0
$139$	2331.53			1.42272			0.711360	−	0.702828i	$-0.248080\pi$
$139$	2331.53			1.42272			0.711360	+	0.702828i	$0.248080\pi$
$140$	−1366.88	−	775.368i	−0.825158	−	0.468075i
$141$		0			0
$142$	−67.7004	+	236.337i	−0.0400091	+	0.139669i
$143$			2.78316i			0.00162755i
$144$		0			0
$145$	2105.53	−	88.4352i	1.20590	−	0.0506493i
$146$	870.968	+	249.495i	0.493711	+	0.141427i
$147$		0			0
$148$	−2563.73	−	1600.09i	−1.42390	−	0.888696i
$149$	−1321.10			−0.726366			−0.363183	−	0.931718i	$-0.618310\pi$
$149$	−1321.10			−0.726366			−0.363183	+	0.931718i	$0.618310\pi$
$150$		0			0
$151$			2875.03i			1.54945i	0.632299	+	0.774725i	$0.282112\pi$
$151$			2875.03i			1.54945i	−0.632299	+	0.774725i	$0.717888\pi$
$152$	−1710.92	+	1543.00i	−0.912988	+	0.823383i
$153$		0			0
$154$	57.8585	+	16.5739i	0.0302751	+	0.00867251i
$155$	−91.5850	−	2180.52i	−0.0474599	−	1.12996i
$156$		0			0
$157$	−1062.67			−0.540192			−0.270096	−	0.962833i	$-0.587055\pi$
$157$	−1062.67			−0.540192			−0.270096	+	0.962833i	$0.587055\pi$
$158$	1408.73	+	403.539i	0.709318	+	0.203189i
$159$		0			0
$160$	−1976.03	+	437.407i	−0.976366	+	0.216125i
$161$			1391.70i			0.681250i
$162$		0			0
$163$			1304.06i			0.626636i	0.949648	+	0.313318i	$0.101441\pi$
$163$			1304.06i			0.626636i	−0.949648	+	0.313318i	$0.898559\pi$
$164$	868.363	−	1391.32i	0.413462	−	0.662464i
$165$		0			0
$166$	405.535	−	1415.69i	0.189612	−	0.661923i
$167$			2529.54i			1.17211i	0.810272	+	0.586054i	$0.199319\pi$
$167$			2529.54i			1.17211i	−0.810272	+	0.586054i	$0.800681\pi$
$168$		0			0
$169$	−2191.72			−0.997596
$170$	−289.105	+	1196.88i	−0.130431	+	0.539979i
$171$		0			0
$172$	1680.04	−	2691.83i	0.744780	−	1.19331i
$173$			887.010i			0.389816i	0.980822	+	0.194908i	$0.0624408\pi$
$173$			887.010i			0.389816i	−0.980822	+	0.194908i	$0.937559\pi$
$174$		0			0
$175$	−2188.47	+	184.163i	−0.945331	+	0.0795508i
$176$	69.6302	−	34.0530i	0.0298214	−	0.0145843i
$177$		0			0
$178$	−110.214	−	31.5715i	−0.0464095	−	0.0132943i
$179$			3554.35i			1.48416i	0.670311	+	0.742080i	$0.266161\pi$
$179$			3554.35i			1.48416i	−0.670311	+	0.742080i	$0.733839\pi$
$180$		0			0
$181$			1122.19i			0.460840i	0.973091	+	0.230420i	$0.0740099\pi$
$181$			1122.19i			0.460840i	−0.973091	+	0.230420i	$0.925990\pi$
$182$	31.4483	−	109.784i	0.0128083	−	0.0447127i
$183$		0			0
$184$	1200.37	+	1331.00i	0.480935	+	0.533274i
$185$	−4219.78	+	177.236i	−1.67700	+	0.0704361i
$186$		0			0
$187$		−	47.1572i		−	0.0184410i
$188$	−1819.69	+	2915.57i	−0.705927	+	1.13106i
$189$		0			0
$190$	−756.008	+	3129.83i	−0.288666	+	1.19506i
$191$	1665.96			0.631122			0.315561	−	0.948905i	$-0.397807\pi$
$191$	1665.96			0.631122			0.315561	+	0.948905i	$0.397807\pi$
$192$		0			0
$193$		−	4819.74i		−	1.79758i	−0.438381	−	0.898789i	$-0.644448\pi$
$193$		−	4819.74i		−	1.79758i	0.438381	−	0.898789i	$-0.355552\pi$
$194$	−4218.59	−	1208.44i	−1.56122	−	0.447222i
$195$		0			0
$196$	232.830	+	145.315i	0.0848504	+	0.0529575i
$197$			3923.54i			1.41899i	0.704712	+	0.709493i	$0.251076\pi$
$197$			3923.54i			1.41899i	−0.704712	+	0.709493i	$0.748924\pi$
$198$		0			0
$199$		−	841.566i		−	0.299784i	−0.988702	−	0.149892i	$-0.952107\pi$
$199$		−	841.566i		−	0.299784i	0.988702	−	0.149892i	$-0.0478926\pi$
$200$	−1934.17	+	2063.73i	−0.683834	+	0.729638i
$201$		0			0
$202$	252.733	−	882.273i	0.0880308	−	0.307310i
$203$	3311.71			1.14501
$204$		0			0
$205$	−96.1854	−	2290.05i	−0.0327701	−	0.780215i
$206$	112.790	−	393.742i	0.0381478	−	0.133171i
$207$		0			0
$208$	−64.6139	−	132.120i	−0.0215393	−	0.0440427i
$209$		−	123.316i		−	0.0408131i
$210$		0			0
$211$	−1483.70			−0.484086			−0.242043	−	0.970266i	$-0.577817\pi$
$211$	−1483.70			−0.484086			−0.242043	+	0.970266i	$0.577817\pi$
$212$	−277.100	+	443.981i	−0.0897705	+	0.143834i
$213$		0			0
$214$	1200.62	−	4191.27i	0.383516	−	1.33883i
$215$	−186.092	−	4430.62i	−0.0590297	−	1.40542i
$216$		0			0
$217$		−	3429.67i		−	1.07291i
$218$	3499.83	+	1002.55i	1.08733	+	0.311473i
$219$		0			0
$220$	53.4476	−	94.2214i	0.0163793	−	0.0288746i
$221$	−89.4785			−0.0272352
$222$		0			0
$223$	650.939			0.195471			0.0977356	−	0.995212i	$-0.468840\pi$
$223$	650.939			0.195471			0.0977356	+	0.995212i	$0.468840\pi$
$224$	−3131.39	+	556.458i	−0.934039	+	0.165982i
$225$		0			0
$226$	−1379.02	+	4814.07i	−0.405891	+	1.41694i
$227$	5495.17			1.60673			0.803363	−	0.595489i	$-0.203042\pi$
$227$	5495.17			1.60673			0.803363	+	0.595489i	$0.203042\pi$
$228$		0			0
$229$		−	450.867i		−	0.130105i	−0.997882	−	0.0650527i	$-0.979278\pi$
$229$		−	450.867i		−	0.130105i	0.997882	−	0.0650527i	$-0.0207216\pi$
$230$	2434.83	+	588.130i	0.698033	+	0.168609i
$231$		0			0
$232$	3167.26	−	2856.41i	0.896298	−	0.808331i
$233$	−4370.89			−1.22895			−0.614477	−	0.788935i	$-0.710633\pi$
$233$	−4370.89			−1.22895			−0.614477	+	0.788935i	$0.710633\pi$
$234$		0			0
$235$	201.560	+	4798.88i	0.0559503	+	1.33210i
$236$	1499.45	−	2402.47i	0.413584	−	0.662660i
$237$		0			0
$238$	−532.851	+	1860.15i	−0.145124	+	0.506619i
$239$	2751.80			0.744767			0.372384	−	0.928079i	$-0.378541\pi$
$239$	2751.80			0.744767			0.372384	+	0.928079i	$0.378541\pi$
$240$		0			0
$241$	−1897.47			−0.507166			−0.253583	−	0.967314i	$-0.581609\pi$
$241$	−1897.47			−0.507166			−0.253583	+	0.967314i	$0.581609\pi$
$242$	1035.57	−	3615.09i	0.275077	−	0.960276i
$243$		0			0
$244$	2521.03	−	4039.29i	0.661445	−	1.05979i
$245$	383.226	−	16.0960i	0.0999323	−	0.00419730i
$246$		0			0
$247$	−233.986			−0.0602761
$248$	−2958.15	−	3280.07i	−0.757431	−	0.839858i
$249$		0			0
$250$	−602.646	+	3906.64i	−0.152459	+	0.988310i
$251$		−	5338.02i		−	1.34236i	−0.741294	−	0.671181i	$-0.765787\pi$
$251$		−	5338.02i		−	1.34236i	0.741294	−	0.671181i	$-0.234213\pi$
$252$		0			0
$253$	−95.9325			−0.0238388
$254$	1411.92	−	4928.92i	0.348787	−	1.21759i
$255$		0			0
$256$	−2514.85	+	3233.07i	−0.613978	+	0.789324i
$257$	1852.77			0.449699			0.224850	−	0.974393i	$-0.427811\pi$
$257$	1852.77			0.449699			0.224850	+	0.974393i	$0.427811\pi$
$258$		0			0
$259$	−6637.13			−1.59232
$260$	−178.781	−	101.414i	−0.0426443	−	0.0241902i
$261$		0			0
$262$	3072.18	+	880.045i	0.724426	+	0.207517i
$263$		−	3052.14i		−	0.715602i	−0.933798	−	0.357801i	$-0.883527\pi$
$263$		−	3052.14i		−	0.715602i	0.933798	−	0.357801i	$-0.116473\pi$
$264$		0			0
$265$	30.6934	+	730.771i	0.00711502	+	0.169400i
$266$	−1393.40	+	4864.28i	−0.321185	+	1.12123i
$267$		0			0
$268$	134.881	−	216.111i	0.0307431	−	0.0492577i
$269$	7379.13			1.67254			0.836270	−	0.548318i	$-0.184732\pi$
$269$	7379.13			1.67254			0.836270	+	0.548318i	$0.184732\pi$
$270$		0			0
$271$		−	7809.43i		−	1.75051i	−0.483660	−	0.875256i	$-0.660693\pi$
$271$		−	7809.43i		−	1.75051i	0.483660	−	0.875256i	$-0.339307\pi$
$272$	1094.80	+	2238.60i	0.244052	+	0.499027i
$273$		0			0
$274$	−1685.51	+	5884.01i	−0.371626	+	1.29732i
$275$	−12.6947	−	150.856i	−0.00278370	−	0.0330798i
$276$		0			0
$277$	7318.70			1.58750			0.793751	−	0.608243i	$-0.208125\pi$
$277$	7318.70			1.58750			0.793751	+	0.608243i	$0.208125\pi$
$278$	1816.02	−	6339.60i	0.391790	−	1.36771i
$279$		0			0
$280$	−3172.93	+	3112.70i	−0.677210	+	0.664354i
$281$		−	6414.07i		−	1.36168i	−0.732433	−	0.680839i	$-0.761615\pi$
$281$		−	6414.07i		−	1.36168i	0.732433	−	0.680839i	$-0.238385\pi$
$282$		0			0
$283$			3993.09i			0.838744i	0.907814	+	0.419372i	$0.137750\pi$
$283$			3993.09i			0.838744i	−0.907814	+	0.419372i	$0.862250\pi$
$284$	589.886	+	368.164i	0.123251	+	0.0769243i
$285$		0			0
$286$	7.56761	+	2.16779i	0.00156462	+	0.000448197i
$287$		−	3601.94i		−	0.740821i
$288$		0			0
$289$	−3396.90			−0.691411
$290$	1399.52	−	5793.96i	0.283389	−	1.17322i
$291$		0			0
$292$	1356.78	−	2173.89i	0.271917	−	0.435676i
$293$		−	4615.85i		−	0.920345i	−0.887830	−	0.460172i	$-0.847788\pi$
$293$		−	4615.85i		−	0.920345i	0.887830	−	0.460172i	$-0.152212\pi$
$294$		0			0
$295$	−166.088	−	3954.36i	−0.0327798	−	0.780446i
$296$	−6347.64	+	5724.65i	−1.24645	+	1.12412i
$297$		0			0
$298$	−1029.00	+	3592.15i	−0.200027	+	0.698281i
$299$			182.027i			0.0352071i
$300$		0			0
$301$		−	6968.76i		−	1.33446i
$302$	7817.41	+	2239.35i	1.48954	+	0.426689i
$303$		0			0
$304$	2862.90	+	5853.95i	0.540127	+	1.10443i
$305$	−279.246	−	6648.48i	−0.0524248	−	1.24817i
$306$		0			0
$307$			2911.30i			0.541226i	0.962688	+	0.270613i	$0.0872264\pi$
$307$			2911.30i			0.541226i	−0.962688	+	0.270613i	$0.912774\pi$
$308$	90.1313	−	144.412i	0.0166744	−	0.0267163i
$309$		0			0
$310$	−6000.32	−	1449.37i	−1.09934	−	0.265545i
$311$	−4970.69			−0.906308			−0.453154	−	0.891432i	$-0.649701\pi$
$311$	−4970.69			−0.906308			−0.453154	+	0.891432i	$0.649701\pi$
$312$		0			0
$313$			6615.49i			1.19466i	0.801995	+	0.597331i	$0.203772\pi$
$313$			6615.49i			1.19466i	−0.801995	+	0.597331i	$0.796228\pi$
$314$	−827.706	+	2889.46i	−0.148758	+	0.519305i
$315$		0			0
$316$	2194.50	−	3516.11i	0.390665	−	0.625938i
$317$			5469.03i			0.968994i	0.874793	+	0.484497i	$0.160997\pi$
$317$			5469.03i			0.968994i	−0.874793	+	0.484497i	$0.839003\pi$
$318$		0			0
$319$			228.283i			0.0400670i
$320$	−349.777	+	5713.64i	−0.0611035	+	0.998131i
$321$		0			0
$322$	3784.12	+	1083.99i	0.654909	+	0.187603i
$323$	3964.60			0.682960
$324$		0			0
$325$	−286.242	+	24.0876i	−0.0488548	+	0.00411120i
$326$	3545.82	+	1015.72i	0.602408	+	0.172564i
$327$		0			0
$328$	−3106.74	−	3444.83i	−0.522991	−	0.579906i
$329$			7547.99i			1.26485i
$330$		0			0
$331$	4228.59			0.702189			0.351094	−	0.936340i	$-0.385810\pi$
$331$	4228.59			0.702189			0.351094	+	0.936340i	$0.385810\pi$
$332$	−3533.50	−	2205.35i	−0.584114	−	0.364562i
$333$		0			0
$334$	6878.00	+	1970.25i	1.12679	+	0.322776i
$335$	−14.9402	−	355.708i	−0.00243663	−	0.0580131i
$336$		0			0
$337$		−	9248.58i		−	1.49496i	−0.664283	−	0.747481i	$-0.731263\pi$
$337$		−	9248.58i		−	1.49496i	0.664283	−	0.747481i	$-0.268737\pi$
$338$	−1707.12	+	5959.43i	−0.274719	+	0.959024i
$339$		0			0
$340$	3029.21	+	1718.34i	0.483182	+	0.274088i
$341$	236.414			0.0375440
$342$		0			0
$343$	6629.16			1.04356
$344$	−6010.69	−	6664.80i	−0.942077	−	1.04460i
$345$		0			0
$346$	2411.84	+	690.888i	0.374744	+	0.107348i
$347$	8335.00			1.28947			0.644735	−	0.764406i	$-0.276968\pi$
$347$	8335.00			1.28947			0.644735	+	0.764406i	$0.276968\pi$
$348$		0			0
$349$			416.687i			0.0639104i	0.999489	+	0.0319552i	$0.0101734\pi$
$349$			416.687i			0.0639104i	−0.999489	+	0.0319552i	$0.989827\pi$
$350$	−1203.84	+	6094.05i	−0.183851	+	0.930687i
$351$		0			0
$352$	−38.3578	−	215.853i	−0.00580817	−	0.0326846i
$353$	−2913.16			−0.439241			−0.219620	−	0.975585i	$-0.570482\pi$
$353$	−2913.16			−0.439241			−0.219620	+	0.975585i	$0.570482\pi$
$354$		0			0
$355$	970.923	−	40.7801i	0.145158	−	0.00609686i
$356$	−171.690	+	275.088i	−0.0255605	+	0.0409541i
$357$		0			0
$358$	9664.51	+	2768.46i	1.42678	+	0.408709i
$359$	10877.9			1.59920			0.799600	−	0.600532i	$-0.205045\pi$
$359$	10877.9			1.59920			0.799600	+	0.600532i	$0.205045\pi$
$360$		0			0
$361$	3508.42			0.511505
$362$	3051.32	+	874.070i	0.443021	+	0.126906i
$363$		0			0
$364$	−274.015	−	171.020i	−0.0394568	−	0.0246261i
$365$	−150.286	−	3578.12i	−0.0215516	−	0.513116i
$366$		0			0
$367$	4409.25			0.627142			0.313571	−	0.949565i	$-0.398475\pi$
$367$	4409.25			0.627142			0.313571	+	0.949565i	$0.398475\pi$
$368$	4554.03	−	2227.17i	0.645095	−	0.315487i
$369$		0			0
$370$	−2804.84	+	11611.9i	−0.394099	+	1.63155i
$371$			1149.40i			0.160846i
$372$		0			0
$373$	−12639.7			−1.75458			−0.877291	−	0.479958i	$-0.840652\pi$
$373$	−12639.7			−1.75458			−0.877291	+	0.479958i	$0.840652\pi$
$374$	−128.223	−	36.7304i	−0.0177280	−	0.00507831i
$375$		0			0
$376$	6510.28	+	7218.77i	0.892931	+	0.990105i
$377$	433.156			0.0591742
$378$		0			0
$379$	−7204.70			−0.976466			−0.488233	−	0.872713i	$-0.662358\pi$
$379$	−7204.70			−0.976466			−0.488233	+	0.872713i	$0.662358\pi$
$380$	7921.38	+	4493.45i	1.06936	+	0.606603i
$381$		0			0
$382$	1297.60	−	4529.85i	0.173799	−	0.606720i
$383$			6011.54i			0.802024i	0.916073	+	0.401012i	$0.131342\pi$
$383$			6011.54i			0.802024i	−0.916073	+	0.401012i	$0.868658\pi$
$384$		0			0
$385$	−9.98351	−	237.695i	−0.00132158	−	0.0314651i
$386$	−13105.2	−	3754.07i	−1.72808	−	0.495018i
$387$		0			0
$388$	−6571.67	+	10529.4i	−0.859861	+	1.37770i
$389$	3831.34			0.499374			0.249687	−	0.968327i	$-0.419672\pi$
$389$	3831.34			0.499374			0.249687	+	0.968327i	$0.419672\pi$
$390$		0			0
$391$		−	3084.22i		−	0.398915i
$392$	576.472	−	519.894i	0.0742761	−	0.0669862i
$393$		0			0
$394$	10668.4	+	3056.02i	1.36412	+	0.390762i
$395$	−243.077	−	5787.34i	−0.0309633	−	0.737197i
$396$		0			0
$397$	4037.67			0.510440			0.255220	−	0.966883i	$-0.417852\pi$
$397$	4037.67			0.510440			0.255220	+	0.966883i	$0.417852\pi$
$398$	−2288.27	−	655.491i	−0.288193	−	0.0825548i
$399$		0			0
$400$	4104.90	+	6866.57i	0.513112	+	0.858322i
$401$		−	323.101i		−	0.0402367i	−0.999798	−	0.0201183i	$-0.993596\pi$
$401$		−	323.101i		−	0.0402367i	0.999798	−	0.0201183i	$-0.00640429\pi$
$402$		0			0
$403$		−	448.584i		−	0.0554480i
$404$	−2202.11	−	1374.40i	−0.271185	−	0.169254i
$405$		0			0
$406$	2579.47	−	9004.77i	0.315313	−	1.10074i
$407$		−	457.510i		−	0.0557198i
$408$		0			0
$409$	−5990.60			−0.724245			−0.362123	−	0.932130i	$-0.617948\pi$
$409$	−5990.60			−0.724245			−0.362123	+	0.932130i	$0.617948\pi$
$410$	−6301.72	−	1522.17i	−0.759073	−	0.183353i
$411$		0			0
$412$	−982.759	−	613.367i	−0.117517	−	0.0733457i
$413$		−	6219.66i		−	0.741040i
$414$		0			0
$415$	−5815.97	+	244.279i	−0.687939	+	0.0288944i
$416$	−409.571	+	72.7821i	−0.0482713	+	0.00857797i
$417$		0			0
$418$	−335.304	−	96.0501i	−0.0392351	−	0.0112391i
$419$			9453.16i			1.10219i	0.834443	+	0.551094i	$0.185790\pi$
$419$			9453.16i			1.10219i	−0.834443	+	0.551094i	$0.814210\pi$
$420$		0			0
$421$		−	6916.63i		−	0.800703i	−0.916362	−	0.400352i	$-0.868888\pi$
$421$		−	6916.63i		−	0.800703i	0.916362	−	0.400352i	$-0.131112\pi$
$422$	−1155.65	+	4034.28i	−0.133308	+	0.465369i
$423$		0			0
$424$	991.381	+	1099.27i	0.113551	+	0.125909i
$425$	4850.00	−	408.133i	0.553551	−	0.0465820i
$426$		0			0
$427$		−	10457.2i		−	1.18515i
$428$	−10461.2	−	6529.11i	−1.18145	−	0.737374i
$429$		0			0
$430$	−12192.1	−	2944.99i	−1.36734	−	0.330279i
$431$	2603.76			0.290995			0.145497	−	0.989359i	$-0.453522\pi$
$431$	2603.76			0.290995			0.145497	+	0.989359i	$0.453522\pi$
$432$		0			0
$433$			7544.72i			0.837359i	0.908134	+	0.418679i	$0.137507\pi$
$433$			7544.72i			0.837359i	−0.908134	+	0.418679i	$0.862493\pi$
$434$	−9325.49	−	2671.35i	−1.03142	−	0.295458i
$435$		0			0
$436$	5452.00	−	8735.39i	0.598861	−	0.959517i
$437$		−	8065.23i		−	0.882866i
$438$		0			0
$439$			11510.9i			1.25144i	0.780046	+	0.625722i	$0.215195\pi$
$439$			11510.9i			1.25144i	−0.780046	+	0.625722i	$0.784805\pi$
$440$	−214.564	−	218.716i	−0.0232476	−	0.0236975i
$441$		0			0
$442$	−69.6943	+	243.298i	−0.00750005	+	0.0261821i
$443$	−8190.22			−0.878396			−0.439198	−	0.898390i	$-0.644737\pi$
$443$	−8190.22			−0.878396			−0.439198	+	0.898390i	$0.644737\pi$
$444$		0			0
$445$	19.0175	+	452.782i	0.00202587	+	0.0482335i
$446$	507.013	−	1769.95i	0.0538290	−	0.187913i
$447$		0			0
$448$	−925.975	+	8947.88i	−0.0976523	+	0.943633i
$449$			12273.8i			1.29006i	0.764159	+	0.645028i	$0.223154\pi$
$449$			12273.8i			1.29006i	−0.764159	+	0.645028i	$0.776846\pi$
$450$		0			0
$451$	248.289			0.0259234
$452$	12015.7	+	7499.31i	1.25038	+	0.780394i
$453$		0			0
$454$	4280.15	−	14941.7i	0.442462	−	1.54460i
$455$	−451.015	+	18.9432i	−0.0464701	+	0.00195181i
$456$		0			0
$457$			4219.29i			0.431882i	0.976406	+	0.215941i	$0.0692819\pi$
$457$			4219.29i			0.431882i	−0.976406	+	0.215941i	$0.930718\pi$
$458$	−1225.94	−	351.178i	−0.125075	−	0.0358285i
$459$		0			0
$460$	3495.64	−	6162.36i	0.354315	−	0.624612i
$461$	−11984.7			−1.21081			−0.605406	−	0.795916i	$-0.706989\pi$
$461$	−11984.7			−1.21081			−0.605406	+	0.795916i	$0.706989\pi$
$462$		0			0
$463$	5339.85			0.535991			0.267996	−	0.963420i	$-0.413639\pi$
$463$	5339.85			0.535991			0.267996	+	0.963420i	$0.413639\pi$
$464$	−5299.81	−	10836.8i	−0.530254	−	1.08424i
$465$		0			0
$466$	−3404.46	+	11884.7i	−0.338430	+	1.18144i
$467$	−17801.3			−1.76391			−0.881956	−	0.471332i	$-0.843773\pi$
$467$	−17801.3			−1.76391			−0.881956	+	0.471332i	$0.843773\pi$
$468$		0			0
$469$		−	559.480i		−	0.0550839i
$470$	13205.5	+	3189.77i	1.29601	+	0.313049i
$471$		0			0
$472$	−5364.57	−	5948.38i	−0.523145	−	0.580077i
$473$	480.370			0.0466965
$474$		0			0
$475$	12682.7	−	1067.27i	1.22510	−	0.103094i
$476$	4642.82	+	2897.71i	0.447066	+	0.279026i
$477$		0			0
$478$	2143.37	−	7482.34i	0.205095	−	0.715971i
$479$	2854.90			0.272325			0.136163	−	0.990686i	$-0.456523\pi$
$479$	2854.90			0.272325			0.136163	+	0.990686i	$0.456523\pi$
$480$		0			0
$481$	−868.105			−0.0822914
$482$	−1477.93	+	5159.36i	−0.139664	+	0.487557i
$483$		0			0
$484$	−9023.07	−	5631.55i	−0.847396	−	0.528883i
$485$	727.919	+	17330.8i	0.0681508	+	1.62258i
$486$		0			0
$487$	−457.529			−0.0425721			−0.0212861	−	0.999773i	$-0.506776\pi$
$487$	−457.529			−0.0425721			−0.0212861	+	0.999773i	$0.506776\pi$
$488$	−9019.49	−	10001.0i	−0.836666	−	0.927717i
$489$		0			0
$490$	254.727	−	1054.55i	0.0234844	−	0.0972243i
$491$		−	9459.38i		−	0.869442i	−0.900565	−	0.434721i	$-0.856847\pi$
$491$		−	9459.38i		−	0.869442i	0.900565	−	0.434721i	$-0.143153\pi$
$492$		0			0
$493$	−7339.27			−0.670475
$494$	−182.251	+	636.224i	−0.0165989	+	0.0579455i
$495$		0			0
$496$	−11222.8	+	5488.58i	−1.01597	+	0.496864i
$497$	1527.13			0.137829
$498$		0			0
$499$	−14875.1			−1.33447			−0.667234	−	0.744848i	$-0.732522\pi$
$499$	−14875.1			−1.33447			−0.667234	+	0.744848i	$0.732522\pi$
$500$	10153.0	+	4681.49i	0.908113	+	0.418725i
$501$		0			0
$502$	−14514.4	−	4157.75i	−1.29046	−	0.369661i
$503$			17690.4i			1.56815i	0.620669	+	0.784073i	$0.286861\pi$
$503$			17690.4i			1.56815i	−0.620669	+	0.784073i	$0.713139\pi$
$504$		0			0
$505$	−3624.56	+	152.237i	−0.319388	+	0.0134147i
$506$	−74.7213	+	260.847i	−0.00656476	+	0.0229171i
$507$		0			0
$508$	−12302.3	−	7678.22i	−1.07446	−	0.670603i
$509$	6504.69			0.566435			0.283217	−	0.959056i	$-0.408598\pi$
$509$	6504.69			0.566435			0.283217	+	0.959056i	$0.408598\pi$
$510$		0			0
$511$		−	5627.89i		−	0.487208i
$512$	6832.13	+	9356.27i	0.589727	+	0.807603i
$513$		0			0
$514$	1443.11	−	5037.81i	0.123839	−	0.432312i
$515$	−1617.57	+	67.9404i	−0.138405	+	0.00581322i
$516$		0			0
$517$	−520.298			−0.0442605
$518$	−5169.63	+	18046.8i	−0.438495	+	1.53076i
$519$		0			0
$520$	−415.004	+	407.125i	−0.0349983	+	0.0343339i
$521$		−	20972.3i		−	1.76356i	−0.471661	−	0.881780i	$-0.656345\pi$
$521$		−	20972.3i		−	1.76356i	0.471661	−	0.881780i	$-0.343655\pi$
$522$		0			0
$523$		−	8886.01i		−	0.742941i	−0.928445	−	0.371470i	$-0.878854\pi$
$523$		−	8886.01i		−	0.742941i	0.928445	−	0.371470i	$-0.121146\pi$
$524$	4785.80	−	7667.99i	0.398986	−	0.639270i
$525$		0			0
$526$	−8298.98	−	2377.30i	−0.687933	−	0.197063i
$527$			7600.68i			0.628256i
$528$		0			0
$529$	5892.73			0.484320
$530$	2010.92	+	485.736i	0.164809	+	0.0398095i
$531$		0			0
$532$	12141.0	+	7577.52i	0.989433	+	0.617532i
$533$		−	471.116i		−	0.0382857i
$534$		0			0
$535$	−17218.6	+	723.205i	−1.39145	+	0.0584427i
$536$	−482.561	−	535.077i	−0.0388871	−	0.0431190i
$537$		0			0
$538$	5747.56	−	20064.3i	0.460585	−	1.60787i
$539$			41.5496i			0.00332035i
$540$		0			0
$541$			10773.5i			0.856174i	0.903737	+	0.428087i	$0.140812\pi$
$541$			10773.5i			0.856174i	−0.903737	+	0.428087i	$0.859188\pi$
$542$	−21234.3	−	6082.72i	−1.68283	−	0.482057i
$543$		0			0
$544$	6939.65	−	1233.20i	0.546939	−	0.0971929i
$545$	−603.897	−	14378.0i	−0.0474644	−	1.13007i
$546$		0			0
$547$		−	7179.60i		−	0.561202i	−0.959824	−	0.280601i	$-0.909466\pi$
$547$		−	7179.60i		−	0.561202i	0.959824	−	0.280601i	$-0.0905338\pi$
$548$	14686.2	+	9166.04i	1.14482	+	0.714514i
$549$		0			0
$550$	−420.074	−	82.9829i	−0.0325673	−	0.00643346i
$551$	−19192.2			−1.48387
$552$		0			0
$553$		−	9102.70i		−	0.699975i
$554$	5700.50	−	19900.0i	0.437168	−	1.52612i
$555$		0			0
$556$	−15823.3	−	9875.75i	−1.20694	−	0.753283i
$557$			8222.38i			0.625482i	0.949838	+	0.312741i	$0.101247\pi$
$557$			8222.38i			0.625482i	−0.949838	+	0.312741i	$0.898753\pi$
$558$		0			0
$559$		−	911.480i		−	0.0689651i
$560$	5992.25	+	11051.9i	0.452176	+	0.833976i
$561$		0			0
$562$	−17440.3	−	4995.88i	−1.30903	−	0.374980i
$563$	−8460.61			−0.633343			−0.316672	−	0.948535i	$-0.602565\pi$
$563$	−8460.61			−0.633343			−0.316672	+	0.948535i	$0.602565\pi$
$564$		0			0
$565$	19777.2	−	830.671i	1.47263	−	0.0618524i
$566$	10857.5	+	3110.20i	0.806314	+	0.230974i
$567$		0			0
$568$	1460.52	−	1317.18i	0.107891	−	0.0973020i
$569$			23847.3i			1.75700i	0.477745	+	0.878499i	$0.341454\pi$
$569$			23847.3i			1.75700i	−0.477745	+	0.878499i	$0.658546\pi$
$570$		0			0
$571$	14897.6			1.09185			0.545925	−	0.837834i	$-0.316178\pi$
$571$	14897.6			1.09185			0.545925	+	0.837834i	$0.316178\pi$
$572$	11.7887	−	18.8884i	0.000861734	−	0.00138070i
$573$		0			0
$574$	−9793.91	−	2805.53i	−0.712178	−	0.204008i
$575$	−830.271	−	9866.42i	−0.0602169	−	0.715579i
$576$		0			0
$577$			16102.6i			1.16180i	0.813975	+	0.580900i	$0.197299\pi$
$577$			16102.6i			1.16180i	−0.813975	+	0.580900i	$0.802701\pi$
$578$	−2645.83	+	9236.40i	−0.190401	+	0.664678i
$579$		0			0
$580$	−14664.1	−	8318.28i	−1.04982	−	0.595514i
$581$	−9147.72			−0.653204
$582$		0			0
$583$	−79.2306			−0.00562846
$584$	−4854.16	−	5382.42i	−0.343950	−	0.381380i
$585$		0			0
$586$	−12550.8	−	3595.26i	−0.884760	−	0.253445i
$587$	−18547.3			−1.30414			−0.652068	−	0.758161i	$-0.726098\pi$
$587$	−18547.3			−1.30414			−0.652068	+	0.758161i	$0.726098\pi$
$588$		0			0
$589$			19875.8i			1.39044i
$590$	−10881.5	−	2628.42i	−0.759297	−	0.183407i
$591$		0			0
$592$	10621.6	+	21718.6i	0.737405	+	1.50782i
$593$	17876.4			1.23793			0.618966	−	0.785418i	$-0.287552\pi$
$593$	17876.4			1.23793			0.618966	+	0.785418i	$0.287552\pi$
$594$		0			0
$595$	7641.86	−	320.969i	0.526531	−	0.0221150i
$596$	8965.82	+	5595.81i	0.616198	+	0.384586i
$597$		0			0
$598$	494.945	+	141.780i	0.0338458	+	0.00969535i
$599$	−13964.6			−0.952553			−0.476277	−	0.879296i	$-0.658014\pi$
$599$	−13964.6			−0.952553			−0.476277	+	0.879296i	$0.658014\pi$
$600$		0			0
$601$	9775.07			0.663450			0.331725	−	0.943376i	$-0.392369\pi$
$601$	9775.07			0.663450			0.331725	+	0.943376i	$0.392369\pi$
$602$	−18948.5	−	5427.93i	−1.28286	−	0.367485i
$603$		0			0
$604$	12177.9	−	19511.8i	0.820382	−	1.31445i
$605$	−14851.5	+	623.785i	−0.998018	+	0.0419182i
$606$		0			0
$607$	−26752.6			−1.78889			−0.894444	−	0.447180i	$-0.852428\pi$
$607$	−26752.6			−1.78889			−0.894444	+	0.447180i	$0.852428\pi$
$608$	18147.2	−	3224.81i	1.21047	−	0.215104i
$609$		0			0
$610$	−18295.2	−	4419.18i	−1.21434	−	0.293323i
$611$			987.240i			0.0653674i
$612$		0			0
$613$	−2985.70			−0.196723			−0.0983617	−	0.995151i	$-0.531360\pi$
$613$	−2985.70			−0.196723			−0.0983617	+	0.995151i	$0.531360\pi$
$614$	7916.01	+	2267.59i	0.520300	+	0.149043i
$615$		0			0
$616$	−322.462	−	357.555i	−0.0210915	−	0.0233868i
$617$	18951.1			1.23654			0.618269	−	0.785966i	$-0.287834\pi$
$617$	18951.1			1.23654			0.618269	+	0.785966i	$0.287834\pi$
$618$		0			0
$619$	−5709.25			−0.370717			−0.185359	−	0.982671i	$-0.559345\pi$
$619$	−5709.25			−0.370717			−0.185359	+	0.982671i	$0.559345\pi$
$620$	−8614.56	+	15186.4i	−0.558015	+	0.983709i
$621$		0			0
$622$	−3871.64	+	13515.6i	−0.249580	+	0.871266i
$623$			712.164i			0.0457981i
$624$		0			0
$625$	15405.3	−	2611.24i	0.985937	−	0.167119i
$626$	17988.0	+	5152.77i	1.14847	+	0.328987i
$627$		0			0
$628$	7211.95	+	4501.17i	0.458261	+	0.286013i
$629$	14708.9			0.932406
$630$		0			0
$631$			22893.9i			1.44436i	0.691706	+	0.722180i	$0.256860\pi$
$631$			22893.9i			1.44436i	−0.691706	+	0.722180i	$0.743140\pi$
$632$	−7851.25	−	8705.67i	−0.494155	−	0.547932i
$633$		0			0
$634$	14870.7	+	4259.80i	0.931528	+	0.266842i
$635$	−20249.0	+	850.488i	−1.26545	+	0.0531505i
$636$		0			0
$637$	78.8384			0.00490375
$638$	620.716	+	177.808i	0.0385179	+	0.0110337i
$639$		0			0
$640$	15263.3	+	5401.39i	0.942712	+	0.333607i
$641$			21664.2i			1.33492i	0.744645	+	0.667461i	$0.232619\pi$
$641$			21664.2i			1.33492i	−0.744645	+	0.667461i	$0.767381\pi$
$642$		0			0
$643$		−	30691.8i		−	1.88237i	−0.337886	−	0.941187i	$-0.609712\pi$
$643$		−	30691.8i		−	1.88237i	0.337886	−	0.941187i	$-0.390288\pi$
$644$	5894.86	−	9444.97i	0.360699	−	0.577925i
$645$		0			0
$646$	3088.00	−	10780.0i	0.188074	−	0.656553i
$647$		−	18491.6i		−	1.12362i	−0.827268	−	0.561808i	$-0.810106\pi$
$647$		−	18491.6i		−	1.12362i	0.827268	−	0.561808i	$-0.189894\pi$
$648$		0			0
$649$	428.733			0.0259311
$650$	−157.456	+	797.072i	−0.00950145	+	0.0480980i
$651$		0			0
$652$	5523.64	−	8850.18i	0.331783	−	0.531595i
$653$		−	16257.8i		−	0.974301i	−0.873318	−	0.487151i	$-0.838036\pi$
$653$		−	16257.8i		−	0.974301i	0.873318	−	0.487151i	$-0.161964\pi$
$654$		0			0
$655$	−530.106	−	12621.1i	−0.0316228	−	0.752899i
$656$	−11786.5	+	5764.27i	−0.701505	+	0.343075i
$657$		0			0
$658$	20523.5	+	5879.09i	1.21594	+	0.348314i
$659$			26760.0i			1.58183i	0.611929	+	0.790913i	$0.290394\pi$
$659$			26760.0i			1.58183i	−0.611929	+	0.790913i	$0.709606\pi$
$660$		0			0
$661$			8913.33i			0.524491i	0.965001	+	0.262245i	$0.0844630\pi$
$661$			8913.33i			0.524491i	−0.965001	+	0.262245i	$0.915537\pi$
$662$	3293.63	−	11497.8i	0.193369	−	0.675039i
$663$		0			0
$664$	−8748.73	+	7890.08i	−0.511320	+	0.461136i
$665$	19983.5	−	839.334i	1.16530	−	0.0489443i
$666$		0			0
$667$			14930.4i			0.866727i
$668$	10714.5	−	17167.1i	0.620592	−	0.994335i
$669$		0			0
$670$	−978.829	−	236.435i	−0.0564410	−	0.0136333i
$671$	720.832			0.0414716
$672$		0			0
$673$			31805.2i			1.82169i	0.412744	+	0.910847i	$0.364570\pi$
$673$			31805.2i			1.82169i	−0.412744	+	0.910847i	$0.635430\pi$
$674$	−25147.5	−	7203.67i	−1.43716	−	0.411684i
$675$		0			0
$676$	14874.4	+	9283.53i	0.846292	+	0.528194i
$677$		−	13746.1i		−	0.780362i	−0.920738	−	0.390181i	$-0.872412\pi$
$677$		−	13746.1i		−	0.780362i	0.920738	−	0.390181i	$-0.127588\pi$
$678$		0			0
$679$			27259.0i			1.54066i
$680$	7031.71	−	6898.22i	0.396549	−	0.389021i
$681$		0			0
$682$	184.141	−	642.824i	0.0103389	−	0.0360924i
$683$	4786.94			0.268180			0.134090	−	0.990969i	$-0.457189\pi$
$683$	4786.94			0.268180			0.134090	+	0.990969i	$0.457189\pi$
$684$		0			0
$685$	24172.7	−	1015.29i	1.34831	−	0.0566309i
$686$	5163.41	−	18025.1i	0.287376	−	1.00321i
$687$		0			0
$688$	−22803.7	+	11152.3i	−1.26364	+	0.617989i
$689$			150.336i			0.00831256i
$690$		0			0
$691$	8377.79			0.461225			0.230612	−	0.973046i	$-0.425927\pi$
$691$	8377.79			0.461225			0.230612	+	0.973046i	$0.425927\pi$
$692$	3757.14	−	6019.83i	0.206394	−	0.330693i
$693$		0			0
$694$	6492.09	−	22663.4i	0.355095	−	1.23961i
$695$	−26044.4	+	1093.90i	−1.42147	+	0.0597036i
$696$		0			0
$697$			7982.46i			0.433798i
$698$	1133.00	+	324.555i	0.0614393	+	0.0175997i
$699$		0			0
$700$	15632.5	+	8019.94i	0.844073	+	0.433036i
$701$	16788.3			0.904543			0.452271	−	0.891880i	$-0.350614\pi$
$701$	16788.3			0.904543			0.452271	+	0.891880i	$0.350614\pi$
$702$		0			0
$703$	38463.8			2.06357
$704$	−616.795	−	63.8293i	−0.0330204	−	0.00341713i
$705$		0			0
$706$	−2269.05	+	7921.08i	−0.120958	+	0.422258i
$707$	−5700.94			−0.303262
$708$		0			0
$709$			24847.5i			1.31617i	0.752943	+	0.658086i	$0.228634\pi$
$709$			24847.5i			1.31617i	−0.752943	+	0.658086i	$0.771366\pi$
$710$	645.363	−	2671.77i	0.0341127	−	0.141225i
$711$		0			0
$712$	614.255	+	681.101i	0.0323317	+	0.0358502i
$713$	15462.2			0.812150
$714$		0			0
$715$	−1.30579	−	31.0893i	−6.82992e−5	−	0.00162612i
$716$	15055.3	−	24122.1i	0.785813	−	1.25906i
$717$		0			0
$718$	8472.73	−	29577.7i	0.440389	−	1.53737i
$719$	25349.7			1.31486			0.657430	−	0.753516i	$-0.271644\pi$
$719$	25349.7			1.31486			0.657430	+	0.753516i	$0.271644\pi$
$720$		0			0
$721$	−2544.22			−0.131417
$722$	2732.69	−	9539.62i	0.140859	−	0.491728i
$723$		0			0
$724$	4753.31	−	7615.93i	0.243999	−	0.390944i
$725$	−23478.3	+	1975.73i	−1.20271	+	0.101209i
$726$		0			0
$727$	−18469.7			−0.942233			−0.471116	−	0.882071i	$-0.656149\pi$
$727$	−18469.7			−0.942233			−0.471116	+	0.882071i	$0.656149\pi$
$728$	−678.443	+	611.857i	−0.0345395	+	0.0311496i
$729$		0			0
$730$	−9846.20	−	2378.34i	−0.499211	−	0.120584i
$731$			15443.9i			0.781412i
$732$		0			0
$733$	−9953.90			−0.501576			−0.250788	−	0.968042i	$-0.580690\pi$
$733$	−9953.90			−0.501576			−0.250788	+	0.968042i	$0.580690\pi$
$734$	3434.34	−	11989.1i	0.172703	−	0.602894i
$735$		0			0
$736$	−2508.71	−	14117.4i	−0.125642	−	0.707032i
$737$	38.5660			0.00192754
$738$		0			0
$739$	23550.8			1.17230			0.586150	−	0.810203i	$-0.300643\pi$
$739$	23550.8			1.17230			0.586150	+	0.810203i	$0.300643\pi$
$740$	29388.9	+	16671.0i	1.45994	+	0.828160i
$741$		0			0
$742$	3125.30	+	895.263i	0.154627	+	0.0442940i
$743$			22216.4i			1.09696i	0.836164	+	0.548480i	$0.184793\pi$
$743$			22216.4i			1.09696i	−0.836164	+	0.548480i	$0.815207\pi$
$744$		0			0
$745$	14757.3	−	619.827i	0.725726	−	0.0304815i
$746$	−9845.00	+	34368.2i	−0.483178	+	1.68674i
$747$		0			0
$748$	−199.745	+	320.039i	−0.00976391	+	0.0156441i
$749$	−27082.5			−1.32119
$750$		0			0
$751$		−	1554.76i		−	0.0755444i	−0.999286	−	0.0377722i	$-0.987974\pi$
$751$		−	1554.76i		−	0.0755444i	0.999286	−	0.0377722i	$-0.0120261\pi$
$752$	24699.1	−	12079.2i	1.19772	−	0.585750i
$753$		0			0
$754$	337.383	−	1177.78i	0.0162954	−	0.0568862i
$755$	−1348.90	−	32115.5i	−0.0650217	−	1.54808i
$756$		0			0
$757$	13835.7			0.664287			0.332144	−	0.943229i	$-0.392228\pi$
$757$	13835.7			0.664287			0.332144	+	0.943229i	$0.392228\pi$
$758$	−5611.70	+	19590.1i	−0.268900	+	0.938711i
$759$		0			0
$760$	18387.9	−	18038.8i	0.877631	−	0.860970i
$761$			23563.7i			1.12245i	0.827664	+	0.561224i	$0.189670\pi$
$761$			23563.7i			1.12245i	−0.827664	+	0.561224i	$0.810330\pi$
$762$		0			0
$763$		−	22614.7i		−	1.07301i
$764$	−11306.3	−	7056.55i	−0.535401	−	0.334158i
$765$		0			0
$766$	16345.8	+	4682.36i	0.771014	+	0.220862i
$767$		−	813.502i		−	0.0382971i
$768$		0			0
$769$	−23989.8			−1.12496			−0.562480	−	0.826811i	$-0.690153\pi$
$769$	−23989.8			−1.12496			−0.562480	+	0.826811i	$0.690153\pi$
$770$	−654.084	−	157.993i	−0.0306124	−	0.00739439i
$771$		0			0
$772$	−20415.1	+	32709.9i	−0.951757	+	1.52494i
$773$		−	32032.6i		−	1.49047i	−0.666802	−	0.745235i	$-0.732337\pi$
$773$		−	32032.6i		−	1.49047i	0.666802	−	0.745235i	$-0.267663\pi$
$774$		0			0
$775$	2046.10	+	24314.6i	0.0948362	+	1.12697i
$776$	23511.4	+	26070.1i	1.08764	+	1.20601i
$777$		0			0
$778$	2984.21	−	10417.7i	0.137518	−	0.480066i
$779$			20874.1i			0.960068i
$780$		0			0
$781$			105.268i			0.00482303i
$782$	−8386.20	−	2402.28i	−0.383491	−	0.109854i
$783$		0			0
$784$	−964.615	−	1972.41i	−0.0439420	−	0.0898509i
$785$	11870.5	−	498.578i	0.539716	−	0.0226688i
$786$		0			0
$787$			32873.6i			1.48897i	0.667640	+	0.744485i	$0.267305\pi$
$787$			32873.6i			1.48897i	−0.667640	+	0.744485i	$0.732695\pi$
$788$	16619.0	−	26627.7i	0.751306	−	1.20377i
$789$		0			0
$790$	−15925.5	−	3846.79i	−0.717220	−	0.173244i
$791$	31106.9			1.39827
$792$		0			0
$793$		−	1367.75i		−	0.0612485i
$794$	3144.92	−	10978.7i	0.140565	−	0.490704i
$795$		0			0
$796$	−3564.65	+	5711.41i	−0.158726	+	0.254316i
$797$			18569.4i			0.825298i	0.910890	+	0.412649i	$0.135396\pi$
$797$			18569.4i			0.825298i	−0.910890	+	0.412649i	$0.864604\pi$
$798$		0			0
$799$		−	16727.5i		−	0.740647i
$800$	21868.0	−	5813.15i	0.966436	−	0.256907i
$801$		0			0
$802$	−878.533	−	251.662i	−0.0386809	−	0.0110804i
$803$	387.942			0.0170488
$804$		0			0
$805$	−652.952	−	15546.0i	−0.0285882	−	0.680650i
$806$	−1219.73	−	349.399i	−0.0533041	−	0.0152693i
$807$		0			0
$808$	−5452.28	+	4917.17i	−0.237389	+	0.214091i
$809$		−	12596.0i		−	0.547405i	−0.961814	−	0.273702i	$-0.911752\pi$
$809$		−	12596.0i		−	0.547405i	0.961814	−	0.273702i	$-0.0882484\pi$
$810$		0			0
$811$	−23294.9			−1.00862			−0.504312	−	0.863522i	$-0.668254\pi$
$811$	−23294.9			−1.00862			−0.504312	+	0.863522i	$0.668254\pi$
$812$	−22475.4	−	14027.5i	−0.971346	−	0.606243i
$813$		0			0
$814$	−1244.00	−	356.352i	−0.0535654	−	0.0153442i
$815$	−611.833	−	14567.0i	−0.0262964	−	0.626084i
$816$		0			0
$817$			40385.7i			1.72940i
$818$	−4666.05	+	16288.8i	−0.199443	+	0.696242i
$819$		0			0
$820$	−9047.27	+	15949.2i	−0.385298	+	0.679231i
$821$	−1847.19			−0.0785229			−0.0392614	−	0.999229i	$-0.512501\pi$
$821$	−1847.19			−0.0785229			−0.0392614	+	0.999229i	$0.512501\pi$
$822$		0			0
$823$	46776.9			1.98122			0.990608	−	0.136729i	$-0.0436591\pi$
$823$	46776.9			1.98122			0.990608	+	0.136729i	$0.0436591\pi$
$824$	−2433.25	+	2194.44i	−0.102872	+	0.0927754i
$825$		0			0
$826$	−16911.7	−	4844.46i	−0.712388	−	0.204068i
$827$	−11543.9			−0.485392			−0.242696	−	0.970102i	$-0.578032\pi$
$827$	−11543.9			−0.485392			−0.242696	+	0.970102i	$0.578032\pi$
$828$		0			0
$829$		−	42223.8i		−	1.76899i	−0.466548	−	0.884496i	$-0.654502\pi$
$829$		−	42223.8i		−	1.76899i	0.466548	−	0.884496i	$-0.345498\pi$
$830$	−3865.81	+	16004.3i	−0.161668	+	0.669297i
$831$		0			0
$832$	−121.113	+	1170.34i	−0.00504668	+	0.0487671i
$833$	−1335.82			−0.0555621
$834$		0			0
$835$	−1186.80	−	28256.2i	−0.0491868	−	1.17107i
$836$	−522.333	+	836.902i	−0.0216092	+	0.0346230i
$837$		0			0
$838$	25703.8	+	7363.01i	1.05957	+	0.303522i
$839$	−21486.3			−0.884137			−0.442069	−	0.896981i	$-0.645755\pi$
$839$	−21486.3			−0.884137			−0.442069	+	0.896981i	$0.645755\pi$
$840$		0			0
$841$	11139.6			0.456748
$842$	−18806.8	−	5387.33i	−0.769744	−	0.220498i
$843$		0			0
$844$	10069.3	+	6284.56i	0.410665	+	0.256307i
$845$	24482.6	−	1028.30i	0.996718	−	0.0418635i
$846$		0			0
$847$	−23359.4			−0.947627
$848$	3761.17	−	1839.42i	0.152310	−	0.0744880i
$849$		0			0
$850$	2667.89	−	13505.4i	0.107656	−	0.544976i
$851$		−	29922.6i		−	1.20533i
$852$		0			0
$853$	−41043.4			−1.64748			−0.823740	−	0.566967i	$-0.808117\pi$
$853$	−41043.4			−1.64748			−0.823740	+	0.566967i	$0.808117\pi$
$854$	−28433.7	−	8145.02i	−1.13932	−	0.326366i
$855$		0			0
$856$	−25901.2	+	23359.2i	−1.03421	+	0.932710i
$857$	11059.4			0.440819			0.220409	−	0.975407i	$-0.429261\pi$
$857$	11059.4			0.440819			0.220409	+	0.975407i	$0.429261\pi$
$858$		0			0
$859$	−9970.32			−0.396022			−0.198011	−	0.980200i	$-0.563448\pi$
$859$	−9970.32			−0.396022			−0.198011	+	0.980200i	$0.563448\pi$
$860$	−17504.0	+	30857.3i	−0.694047	+	1.22352i
$861$		0			0
$862$	2028.06	−	7079.80i	0.0801344	−	0.279744i
$863$			39264.2i			1.54875i	0.632728	+	0.774374i	$0.281935\pi$
$863$			39264.2i			1.54875i	−0.632728	+	0.774374i	$0.718065\pi$
$864$		0			0
$865$	−416.164	−	9908.34i	−0.0163584	−	0.389473i
$866$	20514.6	+	5876.54i	0.804982	+	0.230592i
$867$		0			0
$868$	−14527.1	+	23275.9i	−0.568069	+	0.910181i
$869$	627.467			0.0244941
$870$		0			0
$871$		−	73.1772i		−	0.00284675i
$872$	−19505.6	−	21628.3i	−0.757503	−	0.839938i
$873$		0			0
$874$	−21929.9	−	6281.97i	−0.848730	−	0.243124i
$875$	24359.9	−	3083.97i	0.941160	−	0.119151i
$876$		0			0
$877$	−18829.4			−0.725000			−0.362500	−	0.931984i	$-0.618077\pi$
$877$	−18829.4			−0.725000			−0.362500	+	0.931984i	$0.618077\pi$
$878$	31298.8	+	8965.75i	1.20306	+	0.344624i
$879$		0			0
$880$	−761.827	+	413.057i	−0.0291832	+	0.0158229i
$881$		−	47636.4i		−	1.82169i	−0.412748	−	0.910845i	$-0.635431\pi$
$881$		−	47636.4i		−	1.82169i	0.412748	−	0.910845i	$-0.364569\pi$
$882$		0			0
$883$			16281.8i			0.620528i	0.950650	+	0.310264i	$0.100418\pi$
$883$			16281.8i			0.620528i	−0.950650	+	0.310264i	$0.899582\pi$
$884$	607.259	+	379.007i	0.0231044	+	0.0144201i
$885$		0			0
$886$	−6379.32	+	22269.8i	−0.241893	+	0.844433i
$887$		−	26169.5i		−	0.990626i	−0.868715	−	0.495313i	$-0.835053\pi$
$887$		−	26169.5i		−	0.990626i	0.868715	−	0.495313i	$-0.164947\pi$
$888$		0			0
$889$	−31849.0			−1.20155
$890$	1245.96	+	300.959i	0.0469265	+	0.0113350i
$891$		0			0
$892$	−4417.69	−	2757.20i	−0.165824	−	0.103495i
$893$		−	43742.4i		−	1.63918i
$894$		0			0
$895$	−1667.62	−	39703.8i	−0.0622819	−	1.48285i
$896$	23608.6	+	9487.24i	0.880256	+	0.353735i
$897$		0			0
$898$	33373.2	+	9559.97i	1.24018	+	0.355257i
$899$		−	36794.1i		−	1.36502i
$900$		0			0
$901$		−	2547.26i		−	0.0941858i
$902$	193.391	−	675.113i	0.00713881	−	0.0249211i
$903$		0			0
$904$	29750.1	−	26830.2i	1.09455	−	0.987125i
$905$	−526.506	−	12535.5i	−0.0193389	−	0.460434i
$906$		0			0
$907$		−	26934.6i		−	0.986053i	−0.870014	−	0.493026i	$-0.835891\pi$
$907$		−	26934.6i		−	0.986053i	0.870014	−	0.493026i	$-0.164109\pi$
$908$	−37293.8	−	23276.1i	−1.36304	−	0.850708i
$909$		0			0
$910$	−299.785	+	1241.09i	−0.0109206	+	0.0452108i
$911$	801.496			0.0291490			0.0145745	−	0.999894i	$-0.495361\pi$
$911$	801.496			0.0291490			0.0145745	+	0.999894i	$0.495361\pi$
$912$		0			0
$913$		−	630.570i		−	0.0228574i
$914$	11472.5	+	3286.38i	0.415184	+	0.118932i
$915$		0			0
$916$	−1909.75	+	3059.88i	−0.0688865	+	0.110372i
$917$		−	19851.3i		−	0.714884i
$918$		0			0
$919$		−	10268.4i		−	0.368578i	−0.982872	−	0.184289i	$-0.941002\pi$
$919$		−	10268.4i		−	0.368578i	0.982872	−	0.184289i	$-0.0589982\pi$
$920$	−14033.1	−	14304.7i	−0.502890	−	0.512622i
$921$		0			0
$922$	−9334.84	+	32587.3i	−0.333435	+	1.16400i
$923$	199.741			0.00712303
$924$		0			0
$925$	47053.8	−	3959.64i	1.67256	−	0.140748i
$926$	4159.18	−	14519.4i	0.147602	−	0.515267i
$927$		0			0
$928$	−33594.1	+	5969.78i	−1.18834	+	0.211172i
$929$			11407.5i			0.402872i	0.979502	+	0.201436i	$0.0645608\pi$
$929$			11407.5i			0.402872i	−0.979502	+	0.201436i	$0.935439\pi$
$930$		0			0
$931$	−3493.16			−0.122968
$932$	29663.7	+	18513.9i	1.04256	+	0.650690i
$933$		0			0
$934$	−13865.3	+	48403.0i	−0.485747	+	1.69571i
$935$	22.1250	+	526.769i	0.000773867	+	0.0184248i
$936$		0			0
$937$		−	18407.4i		−	0.641775i	−0.947117	−	0.320887i	$-0.896019\pi$
$937$		−	18407.4i		−	0.641775i	0.947117	−	0.320887i	$-0.103981\pi$
$938$	−1521.26	−	435.776i	−0.0529541	−	0.0151691i
$939$		0			0
$940$	18958.9	−	33422.1i	0.657840	−	1.15969i
$941$	18620.6			0.645072			0.322536	−	0.946557i	$-0.395465\pi$
$941$	18620.6			0.645072			0.322536	+	0.946557i	$0.395465\pi$
$942$		0			0
$943$	16238.8			0.560773
$944$	−20352.5	+	9953.47i	−0.701712	+	0.343176i
$945$		0			0
$946$	374.158	−	1306.16i	0.0128593	−	0.0448910i
$947$	−14613.0			−0.501436			−0.250718	−	0.968060i	$-0.580667\pi$
$947$	−14613.0			−0.501436			−0.250718	+	0.968060i	$0.580667\pi$
$948$		0			0
$949$		−	736.101i		−	0.0251790i
$950$	6976.54	−	35316.5i	0.238262	−	1.20612i
$951$		0			0
$952$	11495.3	−	10367.1i	0.391351	−	0.352942i
$953$	−17273.6			−0.587144			−0.293572	−	0.955937i	$-0.594844\pi$
$953$	−17273.6			−0.587144			−0.293572	+	0.955937i	$0.594844\pi$
$954$		0			0
$955$	−18609.6	+	781.627i	−0.630567	+	0.0264847i
$956$	−18675.5	−	11655.9i	−0.631809	−	0.394329i
$957$		0			0
$958$	2223.67	−	7762.67i	0.0749931	−	0.261796i
$959$	38020.4			1.28023
$960$		0			0
$961$	−8313.57			−0.279063
$962$	−676.162	+	2360.43i	−0.0226615	+	0.0791096i
$963$		0			0
$964$	12877.5	+	8037.20i	0.430245	+	0.268528i
$965$	2261.31	+	53838.9i	0.0754343	+	1.79599i
$966$		0			0
$967$	−8667.36			−0.288235			−0.144118	−	0.989561i	$-0.546034\pi$
$967$	−8667.36			−0.288235			−0.144118	+	0.989561i	$0.546034\pi$
$968$	−22340.6	+	20148.0i	−0.741790	+	0.668987i
$969$		0			0
$970$	47690.7	+	11519.6i	1.57861	+	0.381312i
$971$			17837.4i			0.589524i	0.955571	+	0.294762i	$0.0952404\pi$
$971$			17837.4i			0.589524i	−0.955571	+	0.294762i	$0.904760\pi$
$972$		0			0
$973$	−40964.3			−1.34970
$974$	−356.367	+	1244.05i	−0.0117235	+	0.0409261i
$975$		0			0
$976$	−34218.7	+	16734.8i	−1.12225	+	0.548841i
$977$	−18264.1			−0.598077			−0.299038	−	0.954241i	$-0.596666\pi$
$977$	−18264.1			−0.598077			−0.299038	+	0.954241i	$0.596666\pi$
$978$		0			0
$979$	−49.0909			−0.00160261
$980$	−2669.00	−	1514.01i	−0.0869980	−	0.0493501i
$981$		0			0
$982$	−25720.7	−	7367.86i	−0.835825	−	0.239428i
$983$			13106.5i			0.425261i	0.977133	+	0.212630i	$0.0682030\pi$
$983$			13106.5i			0.425261i	−0.977133	+	0.212630i	$0.931797\pi$
$984$		0			0
$985$	−1840.83	−	43827.8i	−0.0595469	−	1.41774i
$986$	−5716.52	+	19956.0i	−0.184636	+	0.644551i
$987$		0			0
$988$	1587.98	+	991.103i	0.0511340	+	0.0319142i
$989$	31417.7			1.01014
$990$		0			0
$991$		−	17141.8i		−	0.549473i	−0.961520	−	0.274736i	$-0.911409\pi$
$991$		−	17141.8i		−	0.549473i	0.961520	−	0.274736i	$-0.0885905\pi$
$992$	6182.41	+	34790.6i	0.197875	+	1.11351i
$993$		0			0
$994$	1189.47	−	4152.37i	0.0379555	−	0.132500i
$995$	394.843	+	9400.71i	0.0125803	+	0.299520i
$996$		0			0
$997$	32317.1			1.02657			0.513286	−	0.858218i	$-0.328428\pi$
$997$	32317.1			1.02657			0.513286	+	0.858218i	$0.328428\pi$
$998$	−11586.1	+	40446.3i	−0.367487	+	1.28287i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.33	yes	64
3.2	odd	2	inner	360.4.m.c.179.32	yes	64
4.3	odd	2		1440.4.m.c.719.4		64
5.4	even	2	inner	360.4.m.c.179.31	yes	64
8.3	odd	2	inner	360.4.m.c.179.36	yes	64
8.5	even	2		1440.4.m.c.719.61		64
12.11	even	2		1440.4.m.c.719.62		64
15.14	odd	2	inner	360.4.m.c.179.34	yes	64
20.19	odd	2		1440.4.m.c.719.1		64
24.5	odd	2		1440.4.m.c.719.3		64
24.11	even	2	inner	360.4.m.c.179.29	✓	64
40.19	odd	2	inner	360.4.m.c.179.30	yes	64
40.29	even	2		1440.4.m.c.719.64		64
60.59	even	2		1440.4.m.c.719.63		64
120.29	odd	2		1440.4.m.c.719.2		64
120.59	even	2	inner	360.4.m.c.179.35	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.29	✓	64	24.11	even	2	inner
360.4.m.c.179.30	yes	64	40.19	odd	2	inner
360.4.m.c.179.31	yes	64	5.4	even	2	inner
360.4.m.c.179.32	yes	64	3.2	odd	2	inner
360.4.m.c.179.33	yes	64	1.1	even	1	trivial
360.4.m.c.179.34	yes	64	15.14	odd	2	inner
360.4.m.c.179.35	yes	64	120.59	even	2	inner
360.4.m.c.179.36	yes	64	8.3	odd	2	inner
1440.4.m.c.719.1		64	20.19	odd	2
1440.4.m.c.719.2		64	120.29	odd	2
1440.4.m.c.719.3		64	24.5	odd	2
1440.4.m.c.719.4		64	4.3	odd	2
1440.4.m.c.719.61		64	8.5	even	2
1440.4.m.c.719.62		64	12.11	even	2
1440.4.m.c.719.63		64	60.59	even	2
1440.4.m.c.719.64		64	40.29	even	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.778894 - 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 + 0.469176i) q^{5} -17.5697 q^{7} +(-16.8033 + 15.1542i) q^{8} +O(q^{10})\)	\(q+(0.778894 - 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 + 0.469176i) q^{5} -17.5697 q^{7} +(-16.8033 + 15.1542i) q^{8} +(-7.42491 + 30.7387i) q^{10} -1.21111i q^{11} -2.29803 q^{13} +(-13.6849 + 47.7731i) q^{14} +(28.1171 + 57.4928i) q^{16} +38.9371 q^{17} +101.821 q^{19} +(77.7975 + 44.1311i) q^{20} +(-3.29309 - 0.943328i) q^{22} -79.2103i q^{23} +(124.560 - 10.4819i) q^{25} +(-1.78992 + 6.24849i) q^{26} +(119.239 + 74.4204i) q^{28} -188.490 q^{29} +195.204i q^{31} +(178.227 - 31.6716i) q^{32} +(30.3279 - 105.873i) q^{34} +(196.262 - 8.24327i) q^{35} +377.761 q^{37} +(79.3074 - 276.857i) q^{38} +(180.591 - 177.163i) q^{40} +205.009i q^{41} +396.636i q^{43} +(-5.12994 + 8.21938i) q^{44} +(-215.378 - 61.6965i) q^{46} -429.604i q^{47} -34.3070 q^{49} +(68.5180 - 346.851i) q^{50} +(15.5959 + 9.73382i) q^{52} -65.4197i q^{53} +(0.568225 + 13.5287i) q^{55} +(295.229 - 266.253i) q^{56} +(-146.814 + 512.518i) q^{58} +354.000i q^{59} +595.183i q^{61} +(530.772 + 152.043i) q^{62} +(52.7031 - 509.280i) q^{64} +(25.6701 - 1.07818i) q^{65} +31.8435i q^{67} +(-264.252 - 164.927i) q^{68} +(130.453 - 540.069i) q^{70} -86.9186 q^{71} +320.319i q^{73} +(294.236 - 1027.16i) q^{74} +(-691.020 - 431.284i) q^{76} +21.2788i q^{77} +518.092i q^{79} +(-341.057 - 629.031i) q^{80} +(557.433 + 159.680i) q^{82} +520.655 q^{83} +(-434.947 + 18.2684i) q^{85} +(1078.48 + 308.938i) q^{86} +(18.3534 + 20.3507i) q^{88} -40.5337i q^{89} +40.3755 q^{91} +(-335.514 + 537.572i) q^{92} +(-1168.12 - 334.616i) q^{94} +(-1137.39 + 47.7718i) q^{95} -1551.48i q^{97} +(-26.7215 + 93.2830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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