LMFDB - Embedded newform 360.4.m.c.179.31

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			179.31
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.778894 + 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 - 0.469176i) q^{5} +17.5697 q^{7} +(16.8033 - 15.1542i) q^{8} +O(q^{10})$	\(q+(-0.778894 + 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 - 0.469176i) q^{5} +17.5697 q^{7} +(16.8033 - 15.1542i) q^{8} +(9.97636 - 30.0079i) q^{10} -1.21111i q^{11} +2.29803 q^{13} +(-13.6849 + 47.7731i) q^{14} +(28.1171 + 57.4928i) q^{16} -38.9371 q^{17} +101.821 q^{19} +(73.8229 + 50.4993i) q^{20} +(3.29309 + 0.943328i) q^{22} +79.2103i q^{23} +(124.560 + 10.4819i) q^{25} +(-1.78992 + 6.24849i) q^{26} +(-119.239 - 74.4204i) q^{28} -188.490 q^{29} +195.204i q^{31} +(-178.227 + 31.6716i) q^{32} +(30.3279 - 105.873i) q^{34} +(-196.262 - 8.24327i) q^{35} -377.761 q^{37} +(-79.3074 + 276.857i) q^{38} +(-194.811 + 161.396i) q^{40} +205.009i q^{41} -396.636i q^{43} +(-5.12994 + 8.21938i) q^{44} +(-215.378 - 61.6965i) q^{46} +429.604i q^{47} -34.3070 q^{49} +(-125.520 + 330.522i) q^{50} +(-15.5959 - 9.73382i) q^{52} +65.4197i q^{53} +(-0.568225 + 13.5287i) q^{55} +(295.229 - 266.253i) q^{56} +(146.814 - 512.518i) q^{58} +354.000i q^{59} +595.183i q^{61} +(-530.772 - 152.043i) q^{62} +(52.7031 - 509.280i) q^{64} +(-25.6701 - 1.07818i) q^{65} -31.8435i q^{67} +(264.252 + 164.927i) q^{68} +(175.281 - 527.228i) q^{70} -86.9186 q^{71} -320.319i q^{73} +(294.236 - 1027.16i) q^{74} +(-691.020 - 431.284i) q^{76} -21.2788i q^{77} +518.092i q^{79} +(-287.108 - 655.415i) q^{80} +(-557.433 - 159.680i) q^{82} -520.655 q^{83} +(434.947 + 18.2684i) q^{85} +(1078.48 + 308.938i) q^{86} +(-18.3534 - 20.3507i) q^{88} -40.5337i q^{89} +40.3755 q^{91} +(335.514 - 537.572i) q^{92} +(-1168.12 - 334.616i) q^{94} +(-1137.39 - 47.7718i) q^{95} +1551.48i q^{97} +(26.7215 - 93.2830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.342688\pi$
$7$	17.5697			0.948673			0.474336	+	0.880344i	$0.342688\pi$
$8$	16.8033	−	15.1542i	0.742609	−	0.669725i
$9$		0			0
$10$	9.97636	−	30.0079i	0.315480	−	0.948932i
$11$		−	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	$-0.492196\pi$
$13$	2.29803			0.0490275			0.0245138	+	0.999699i	$0.492196\pi$
$14$	−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	$-0.589590\pi$
$17$	−38.9371			−0.555508			−0.277754	+	0.960652i	$0.589590\pi$
$18$		0			0
$19$	101.821			1.22943			0.614716	−	0.788748i	$-0.289270\pi$
$19$	101.821			1.22943			0.614716	+	0.788748i	$0.289270\pi$
$20$	73.8229	+	50.4993i	0.825365	+	0.564600i
$21$		0			0
$22$	3.29309	+	0.943328i	0.0319132	+	0.00914173i
$23$			79.2103i			0.718108i	0.933317	+	0.359054i	$0.116901\pi$
$23$			79.2103i			0.718108i	−0.933317	+	0.359054i	$0.883099\pi$
$24$		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	$-0.816998\pi$
$37$	−377.761			−1.67847			−0.839237	+	0.543766i	$0.816998\pi$
$38$	−79.3074	+	276.857i	−0.338562	+	1.18190i
$39$		0			0
$40$	−194.811	+	161.396i	−0.770059	+	0.637972i
$41$			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	$-0.751695\pi$
$43$		−	396.636i		−	1.40666i	0.710863	−	0.703331i	$-0.248305\pi$
$44$	−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	$0.232268\pi$
$47$			429.604i			1.33328i	−0.745380	+	0.666639i	$0.767732\pi$
$48$		0			0
$49$	−34.3070			−0.100020
$50$	−125.520	+	330.522i	−0.355024	+	0.934857i
$51$		0			0
$52$	−15.5959	−	9.73382i	−0.0415916	−	0.0259584i
$53$			65.4197i			0.169549i	0.996400	+	0.0847745i	$0.0270170\pi$
$53$			65.4197i			0.169549i	−0.996400	+	0.0847745i	$0.972983\pi$
$54$		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	$-0.990757\pi$
$67$		−	31.8435i		−	0.0580642i	0.999578	−	0.0290321i	$-0.00924251\pi$
$68$	264.252	+	164.927i	0.471255	+	0.294123i
$69$		0			0
$70$	175.281	−	527.228i	0.299287	−	0.900226i
$71$	−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	$-0.917337\pi$
$73$		−	320.319i		−	0.513568i	0.966469	−	0.256784i	$-0.0826629\pi$
$74$	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	$0.879726\pi$
$80$	−287.108	−	655.415i	−0.401246	−	0.915970i
$81$		0			0
$82$	−557.433	−	159.680i	−0.750710	−	0.215046i
$83$	−520.655			−0.688545			−0.344273	−	0.938870i	$-0.611874\pi$
$83$	−520.655			−0.688545			−0.344273	+	0.938870i	$0.611874\pi$
$84$		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	$0.301625\pi$
$97$			1551.48i			1.62401i	−0.583648	+	0.812007i	$0.698375\pi$
$98$	26.7215	−	93.2830i	0.0275437	−	0.0961532i
$99$		0			0
$100$	−800.945	−	598.738i	−0.800945	−	0.598738i
$101$	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	$-0.522065\pi$
$103$	−144.808			−0.138528			−0.0692638	+	0.997598i	$0.522065\pi$
$104$	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	$-0.745188\pi$
$107$	−1541.44			−1.39267			−0.696337	+	0.717715i	$0.745188\pi$
$108$		0			0
$109$			1287.14i			1.13106i	0.824726	+	0.565532i	$0.191329\pi$
$109$			1287.14i			1.13106i	−0.824726	+	0.565532i	$0.808671\pi$
$110$	−36.3429	−	12.0825i	−0.0315014	−	0.0104729i
$111$		0			0
$112$	494.009	+	1010.13i	0.416781	+	0.852217i
$113$	1770.49			1.47392			0.736962	−	0.675934i	$-0.236260\pi$
$113$	1770.49			1.47392			0.736962	+	0.675934i	$0.236260\pi$
$114$		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	$-0.718292\pi$
$127$	−1812.73			−1.26656			−0.633281	+	0.773922i	$0.718292\pi$
$128$	1343.72	+	539.979i	0.927882	+	0.372874i
$129$		0			0
$130$	22.9259	−	68.9589i	0.0154672	−	0.0465238i
$131$			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	$-0.264252\pi$
$137$	2163.98			1.34950			0.674749	+	0.738047i	$0.264252\pi$
$138$		0			0
$139$	2331.53			1.42272			0.711360	−	0.702828i	$-0.248080\pi$
$139$	2331.53			1.42272			0.711360	+	0.702828i	$0.248080\pi$
$140$	1297.04	+	887.256i	0.783001	+	0.535620i
$141$		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	$-0.412945\pi$
$157$	1062.67			0.540192			0.270096	+	0.962833i	$0.412945\pi$
$158$	−1408.73	−	403.539i	−0.709318	−	0.203189i
$159$		0			0
$160$	2005.74	−	270.167i	0.991050	−	0.133491i
$161$			1391.70i			0.681250i
$162$		0			0
$163$		−	1304.06i		−	0.626636i	−0.949648	−	0.313318i	$-0.898559\pi$
$163$		−	1304.06i		−	0.626636i	0.949648	−	0.313318i	$-0.101441\pi$
$164$	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	$-0.800681\pi$
$167$		−	2529.54i		−	1.17211i	0.810272	−	0.586054i	$-0.199319\pi$
$168$		0			0
$169$	−2191.72			−0.997596
$170$	−388.450	+	1168.42i	−0.175252	+	0.527139i
$171$		0			0
$172$	−1680.04	+	2691.83i	−0.744780	+	1.19331i
$173$		−	887.010i		−	0.389816i	−0.980822	−	0.194908i	$-0.937559\pi$
$173$		−	887.010i		−	0.389816i	0.980822	−	0.194908i	$-0.0624408\pi$
$174$		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
$190$	1015.80	−	3055.42i	0.387862	−	1.16665i
$191$	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	$0.355552\pi$
$193$			4819.74i			1.79758i	−0.438381	+	0.898789i	$0.644448\pi$
$194$	−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	$-0.748924\pi$
$197$		−	3923.54i		−	1.41899i	0.704712	−	0.709493i	$-0.251076\pi$
$198$		0			0
$199$		−	841.566i		−	0.299784i	−0.988702	−	0.149892i	$-0.952107\pi$
$199$		−	841.566i		−	0.299784i	0.988702	−	0.149892i	$-0.0478926\pi$
$200$	2251.86	−	1711.47i	0.796153	−	0.605095i
$201$		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
$220$	61.1603	−	89.4077i	0.0187428	−	0.0273994i
$221$	−89.4785			−0.0272352
$222$		0			0
$223$	−650.939			−0.195471			−0.0977356	−	0.995212i	$-0.531160\pi$
$223$	−650.939			−0.195471			−0.0977356	+	0.995212i	$0.531160\pi$
$224$	−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	$-0.796958\pi$
$227$	−5495.17			−1.60673			−0.803363	+	0.595489i	$0.796958\pi$
$228$		0			0
$229$		−	450.867i		−	0.130105i	−0.997882	−	0.0650527i	$-0.979278\pi$
$229$		−	450.867i		−	0.130105i	0.997882	−	0.0650527i	$-0.0207216\pi$
$230$	2376.93	+	790.230i	0.681436	+	0.226549i
$231$		0			0
$232$	−3167.26	+	2856.41i	−0.896298	+	0.808331i
$233$	4370.89			1.22895			0.614477	−	0.788935i	$-0.289367\pi$
$233$	4370.89			1.22895			0.614477	+	0.788935i	$0.289367\pi$
$234$		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
$250$	1557.19	−	3633.20i	0.393942	−	0.919136i
$251$		−	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	$-0.572189\pi$
$257$	−1852.77			−0.449699			−0.224850	+	0.974393i	$0.572189\pi$
$258$		0			0
$259$	−6637.13			−1.59232
$260$	169.647	+	116.049i	0.0404656	+	0.0276809i
$261$		0			0
$262$	−3072.18	−	880.045i	−0.724426	−	0.207517i
$263$			3052.14i			0.715602i	0.933798	+	0.357801i	$0.116473\pi$
$263$			3052.14i			0.715602i	−0.933798	+	0.357801i	$0.883527\pi$
$264$		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	$-0.791875\pi$
$277$	−7318.70			−1.58750			−0.793751	+	0.608243i	$0.791875\pi$
$278$	−1816.02	+	6339.60i	−0.391790	+	1.36771i
$279$		0			0
$280$	−3422.77	+	2835.67i	−0.730534	+	0.605227i
$281$		−	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	$-0.862250\pi$
$283$		−	3993.09i		−	0.838744i	0.907814	−	0.419372i	$-0.137750\pi$
$284$	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
$290$	−1880.45	+	5656.20i	−0.380771	+	1.14532i
$291$		0			0
$292$	−1356.78	+	2173.89i	−0.271917	+	0.435676i
$293$			4615.85i			0.920345i	0.887830	+	0.460172i	$0.152212\pi$
$293$			4615.85i			0.920345i	−0.887830	+	0.460172i	$0.847788\pi$
$294$		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	$-0.912774\pi$
$307$		−	2911.30i		−	0.541226i	0.962688	−	0.270613i	$-0.0872264\pi$
$308$	−90.1313	+	144.412i	−0.0166744	+	0.0267163i
$309$		0			0
$310$	5857.65	+	1947.42i	1.07320	+	0.356794i
$311$	−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	$-0.796228\pi$
$313$		−	6615.49i		−	1.19466i	0.801995	−	0.597331i	$-0.203772\pi$
$314$	−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	$-0.839003\pi$
$317$		−	5469.03i		−	0.968994i	0.874793	−	0.484497i	$-0.160997\pi$
$318$		0			0
$319$			228.283i			0.0400670i
$320$	−827.661	+	5664.18i	−0.144587	+	0.989492i
$321$		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	$0.268737\pi$
$337$			9248.58i			1.49496i	−0.664283	+	0.747481i	$0.731263\pi$
$338$	1707.12	−	5959.43i	0.274719	−	0.959024i
$339$		0			0
$340$	−2874.45	−	1966.30i	−0.458497	−	0.313640i
$341$	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	$-0.723032\pi$
$347$	−8335.00			−1.28947			−0.644735	+	0.764406i	$0.723032\pi$
$348$		0			0
$349$			416.687i			0.0639104i	0.999489	+	0.0319552i	$0.0101734\pi$
$349$			416.687i			0.0639104i	−0.999489	+	0.0319552i	$0.989827\pi$
$350$	−2205.34	+	5807.16i	−0.336801	+	0.886874i
$351$		0			0
$352$	38.3578	+	215.853i	0.00580817	+	0.0326846i
$353$	2913.16			0.439241			0.219620	−	0.975585i	$-0.429518\pi$
$353$	2913.16			0.439241			0.219620	+	0.975585i	$0.429518\pi$
$354$		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	$-0.601525\pi$
$367$	−4409.25			−0.627142			−0.313571	+	0.949565i	$0.601525\pi$
$368$	−4554.03	+	2227.17i	−0.645095	+	0.315487i
$369$		0			0
$370$	−3768.68	+	11335.8i	−0.529525	+	1.59276i
$371$			1149.40i			0.160846i
$372$		0			0
$373$	12639.7			1.75458			0.877291	−	0.479958i	$-0.159348\pi$
$373$	12639.7			1.75458			0.877291	+	0.479958i	$0.159348\pi$
$374$	−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	$0.662358\pi$
$380$	7516.68	+	5141.87i	1.01473	+	0.694138i
$381$		0			0
$382$	−1297.60	+	4529.85i	−0.173799	+	0.606720i
$383$		−	6011.54i		−	0.802024i	−0.916073	−	0.401012i	$-0.868658\pi$
$383$		−	6011.54i		−	0.802024i	0.916073	−	0.401012i	$-0.131342\pi$
$384$		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	$-0.582148\pi$
$397$	−4037.67			−0.510440			−0.255220	+	0.966883i	$0.582148\pi$
$398$	2288.27	+	655.491i	0.288193	+	0.0825548i
$399$		0			0
$400$	2899.63	+	7456.01i	0.362454	+	0.932002i
$401$		−	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	$0.617948\pi$
$410$	6151.88	+	2045.24i	0.741024	+	0.246359i
$411$		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
$430$	−11902.2	−	3956.98i	−1.33483	−	0.443774i
$431$	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	$-0.862493\pi$
$433$		−	7544.72i		−	0.837359i	0.908134	−	0.418679i	$-0.137507\pi$
$434$	−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	$0.784805\pi$
$440$	195.468	+	235.938i	0.0211786	+	0.0255634i
$441$		0			0
$442$	69.6943	−	243.298i	0.00750005	−	0.0261821i
$443$	8190.22			0.878396			0.439198	−	0.898390i	$-0.355263\pi$
$443$	8190.22			0.878396			0.439198	+	0.898390i	$0.355263\pi$
$444$		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	$-0.930718\pi$
$457$		−	4219.29i		−	0.431882i	0.976406	−	0.215941i	$-0.0692819\pi$
$458$	1225.94	+	351.178i	0.125075	+	0.0358285i
$459$		0			0
$460$	−4000.07	+	5847.53i	−0.405444	+	0.592701i
$461$	−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	$-0.586361\pi$
$463$	−5339.85			−0.535991			−0.267996	+	0.963420i	$0.586361\pi$
$464$	−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	$-0.156227\pi$
$467$	17801.3			1.76391			0.881956	+	0.471332i	$0.156227\pi$
$468$		0			0
$469$		−	559.480i		−	0.0550839i
$470$	12891.5	+	4285.88i	1.26519	+	0.420623i
$471$		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	$-0.493224\pi$
$487$	457.529			0.0425721			0.0212861	+	0.999773i	$0.493224\pi$
$488$	9019.49	+	10001.0i	0.836666	+	0.927717i
$489$		0			0
$490$	−342.259	+	1029.48i	−0.0315545	+	0.0949126i
$491$		−	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	$0.732522\pi$
$500$	8666.03	+	7063.99i	0.775113	+	0.631822i
$501$		0			0
$502$	14514.4	+	4157.75i	1.29046	+	0.369661i
$503$		−	17690.4i		−	1.56815i	−0.620669	−	0.784073i	$-0.713139\pi$
$503$		−	17690.4i		−	1.56815i	0.620669	−	0.784073i	$-0.286861\pi$
$504$		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
$520$	−447.682	+	370.891i	−0.0377541	+	0.0312782i
$521$		−	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	$0.121146\pi$
$523$			8886.01i			0.742941i	−0.928445	+	0.371470i	$0.878854\pi$
$524$	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
$530$	1963.11	+	652.651i	0.160890	+	0.0534893i
$531$		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	$0.0905338\pi$
$547$			7179.60i			0.561202i	−0.959824	+	0.280601i	$0.909466\pi$
$548$	−14686.2	−	9166.04i	−1.14482	−	0.714514i
$549$		0			0
$550$	400.299	+	152.018i	0.0310342	+	0.0117856i
$551$	−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	$-0.898753\pi$
$557$		−	8222.38i		−	0.625482i	0.949838	−	0.312741i	$-0.101247\pi$
$558$		0			0
$559$		−	911.480i		−	0.0689651i
$560$	−5044.39	−	11515.4i	−0.380651	−	0.868956i
$561$		0			0
$562$	17440.3	+	4995.88i	1.30903	+	0.374980i
$563$	8460.61			0.633343			0.316672	−	0.948535i	$-0.397435\pi$
$563$	8460.61			0.633343			0.316672	+	0.948535i	$0.397435\pi$
$564$		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	$-0.802701\pi$
$577$		−	16102.6i		−	1.16180i	0.813975	−	0.580900i	$-0.197299\pi$
$578$	2645.83	−	9236.40i	0.190401	−	0.664678i
$579$		0			0
$580$	−13914.9	−	9518.64i	−0.996181	−	0.681448i
$581$	−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	$-0.273902\pi$
$587$	18547.3			1.30414			0.652068	+	0.758161i	$0.273902\pi$
$588$		0			0
$589$			19875.8i			1.39044i
$590$	10622.8	+	3531.63i	0.741243	+	0.246432i
$591$		0			0
$592$	−10621.6	−	21718.6i	−0.737405	−	1.50782i
$593$	−17876.4			−1.23793			−0.618966	−	0.785418i	$-0.712448\pi$
$593$	−17876.4			−1.23793			−0.618966	+	0.785418i	$0.712448\pi$
$594$		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	$-0.147572\pi$
$607$	26752.6			1.78889			0.894444	+	0.447180i	$0.147572\pi$
$608$	−18147.2	+	3224.81i	−1.21047	+	0.215104i
$609$		0			0
$610$	17860.2	+	5937.75i	1.18547	+	0.394119i
$611$			987.240i			0.0653674i
$612$		0			0
$613$	2985.70			0.196723			0.0983617	−	0.995151i	$-0.468640\pi$
$613$	2985.70			0.196723			0.0983617	+	0.995151i	$0.468640\pi$
$614$	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	$-0.712166\pi$
$617$	−18951.1			−1.23654			−0.618269	+	0.785966i	$0.712166\pi$
$618$		0			0
$619$	−5709.25			−0.370717			−0.185359	−	0.982671i	$-0.559345\pi$
$619$	−5709.25			−0.370717			−0.185359	+	0.982671i	$0.559345\pi$
$620$	−9857.67	+	14410.5i	−0.638538	+	0.933452i
$621$		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
$640$	−14756.6	−	6662.27i	−0.911417	−	0.411483i
$641$			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	$0.390288\pi$
$643$			30691.8i			1.88237i	−0.337886	+	0.941187i	$0.609712\pi$
$644$	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	$0.189894\pi$
$647$			18491.6i			1.12362i	−0.827268	+	0.561808i	$0.810106\pi$
$648$		0			0
$649$	428.733			0.0259311
$650$	−288.448	+	759.548i	−0.0174059	+	0.0458337i
$651$		0			0
$652$	−5523.64	+	8850.18i	−0.331783	+	0.531595i
$653$			16257.8i			0.974301i	0.873318	+	0.487151i	$0.161964\pi$
$653$			16257.8i			0.974301i	−0.873318	+	0.487151i	$0.838036\pi$
$654$		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
$670$	−955.556	−	317.682i	−0.0550990	−	0.0183181i
$671$	720.832			0.0414716
$672$		0			0
$673$		−	31805.2i		−	1.82169i	−0.412744	−	0.910847i	$-0.635430\pi$
$673$		−	31805.2i		−	1.82169i	0.412744	−	0.910847i	$-0.364570\pi$
$674$	−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	$0.127588\pi$
$677$			13746.1i			0.780362i	−0.920738	+	0.390181i	$0.872412\pi$
$678$		0			0
$679$			27259.0i			1.54066i
$680$	7585.39	−	6284.28i	0.427774	−	0.354399i
$681$		0			0
$682$	−184.141	+	642.824i	−0.0103389	+	0.0360924i
$683$	−4786.94			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$683$	−4786.94			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$684$		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
$700$	−14072.3	−	10519.6i	−0.759834	−	0.568007i
$701$	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	$0.771366\pi$
$710$	−867.131	+	2608.24i	−0.0458350	+	0.137867i
$711$		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	$-0.343851\pi$
$727$	18469.7			0.942233			0.471116	+	0.882071i	$0.343851\pi$
$728$	678.443	−	611.857i	0.0345395	−	0.0311496i
$729$		0			0
$730$	−9612.09	−	3195.61i	−0.487341	−	0.162021i
$731$			15443.9i			0.781412i
$732$		0			0
$733$	9953.90			0.501576			0.250788	−	0.968042i	$-0.419310\pi$
$733$	9953.90			0.501576			0.250788	+	0.968042i	$0.419310\pi$
$734$	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	$0.300643\pi$
$740$	−27887.4	−	19076.7i	−1.38535	−	0.947666i
$741$		0			0
$742$	−3125.30	−	895.263i	−0.154627	−	0.0442940i
$743$		−	22216.4i		−	1.09696i	−0.836164	−	0.548480i	$-0.815207\pi$
$743$		−	22216.4i		−	1.09696i	0.836164	−	0.548480i	$-0.184793\pi$
$744$		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	$-0.607772\pi$
$757$	−13835.7			−0.664287			−0.332144	+	0.943229i	$0.607772\pi$
$758$	5611.70	−	19590.1i	0.268900	−	0.938711i
$759$		0			0
$760$	−19835.8	+	16433.4i	−0.946736	+	0.784344i
$761$			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	$0.690153\pi$
$770$	−638.532	−	212.285i	−0.0298845	−	0.00993535i
$771$		0			0
$772$	20415.1	−	32709.9i	0.951757	−	1.52494i
$773$			32032.6i			1.49047i	0.666802	+	0.745235i	$0.267663\pi$
$773$			32032.6i			1.49047i	−0.666802	+	0.745235i	$0.732337\pi$
$774$		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	$-0.732695\pi$
$787$		−	32873.6i		−	1.48897i	0.667640	−	0.744485i	$-0.267305\pi$
$788$	−16619.0	+	26627.7i	−0.751306	+	1.20377i
$789$		0			0
$790$	15546.8	+	5168.67i	0.700167	+	0.232776i
$791$	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	$-0.864604\pi$
$797$		−	18569.4i		−	0.825298i	0.910890	−	0.412649i	$-0.135396\pi$
$798$		0			0
$799$		−	16727.5i		−	0.740647i
$800$	−22531.9	+	2076.85i	−0.995779	+	0.0917846i
$801$		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
$820$	−10352.8	+	15134.4i	−0.440898	+	0.644530i
$821$	−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	$-0.956341\pi$
$823$	−46776.9			−1.98122			−0.990608	+	0.136729i	$0.956341\pi$
$824$	−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	$-0.421968\pi$
$827$	11543.9			0.485392			0.242696	+	0.970102i	$0.421968\pi$
$828$		0			0
$829$		−	42223.8i		−	1.76899i	−0.466548	−	0.884496i	$-0.654502\pi$
$829$		−	42223.8i		−	1.76899i	0.466548	−	0.884496i	$-0.345498\pi$
$830$	−5194.24	+	15623.7i	−0.217222	+	0.653383i
$831$		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
$850$	4887.38	−	12869.6i	0.197218	−	0.519321i
$851$		−	29922.6i		−	1.20533i
$852$		0			0
$853$	41043.4			1.64748			0.823740	−	0.566967i	$-0.191883\pi$
$853$	41043.4			1.64748			0.823740	+	0.566967i	$0.191883\pi$
$854$	−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	$-0.570739\pi$
$857$	−11059.4			−0.440819			−0.220409	+	0.975407i	$0.570739\pi$
$858$		0			0
$859$	−9970.32			−0.396022			−0.198011	−	0.980200i	$-0.563448\pi$
$859$	−9970.32			−0.396022			−0.198011	+	0.980200i	$0.563448\pi$
$860$	20029.9	−	29280.8i	0.794201	−	1.16101i
$861$		0			0
$862$	−2028.06	+	7079.80i	−0.0801344	+	0.279744i
$863$		−	39264.2i		−	1.54875i	−0.632728	−	0.774374i	$-0.718065\pi$
$863$		−	39264.2i		−	1.54875i	0.632728	−	0.774374i	$-0.281935\pi$
$864$		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	$-0.381923\pi$
$877$	18829.4			0.725000			0.362500	+	0.931984i	$0.381923\pi$
$878$	−31298.8	−	8965.75i	−1.20306	−	0.344624i
$879$		0			0
$880$	−793.780	+	347.720i	−0.0304072	+	0.0133200i
$881$		−	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	$-0.899582\pi$
$883$		−	16281.8i		−	0.620528i	0.950650	−	0.310264i	$-0.100418\pi$
$884$	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	$0.164947\pi$
$887$			26169.5i			0.990626i	−0.868715	+	0.495313i	$0.835053\pi$
$888$		0			0
$889$	−31849.0			−1.20155
$890$	−1216.33	−	404.379i	−0.0458107	−	0.0152301i
$891$		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	$0.164109\pi$
$907$			26934.6i			0.986053i	−0.870014	+	0.493026i	$0.835891\pi$
$908$	37293.8	+	23276.1i	1.36304	+	0.850708i
$909$		0			0
$910$	402.801	−	1211.58i	0.0146733	−	0.0441358i
$911$	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	$-0.0589982\pi$
$920$	−12784.2	−	15431.1i	−0.458133	−	0.552986i
$921$		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	$0.103981\pi$
$937$			18407.4i			0.641775i	−0.947117	+	0.320887i	$0.896019\pi$
$938$	1521.26	+	435.776i	0.0529541	+	0.0151691i
$939$		0			0
$940$	−21694.7	+	31714.6i	−0.752769	+	1.10044i
$941$	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	$-0.419333\pi$
$947$	14613.0			0.501436			0.250718	+	0.968060i	$0.419333\pi$
$948$		0			0
$949$		−	736.101i		−	0.0251790i
$950$	−12780.5	+	33653.9i	−0.436478	+	1.14934i
$951$		0			0
$952$	−11495.3	+	10367.1i	−0.391351	+	0.352942i
$953$	17273.6			0.587144			0.293572	−	0.955937i	$-0.405156\pi$
$953$	17273.6			0.587144			0.293572	+	0.955937i	$0.405156\pi$
$954$		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	$-0.453966\pi$
$967$	8667.36			0.288235			0.144118	+	0.989561i	$0.453966\pi$
$968$	22340.6	−	20148.0i	0.741790	−	0.668987i
$969$		0			0
$970$	46556.7	+	15478.2i	1.54108	+	0.512344i
$971$			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	$-0.403334\pi$
$977$	18264.1			0.598077			0.299038	+	0.954241i	$0.403334\pi$
$978$		0			0
$979$	−49.0909			−0.00160261
$980$	−2532.64	−	1732.48i	−0.0825533	−	0.0564715i
$981$		0			0
$982$	25720.7	+	7367.86i	0.835825	+	0.239428i
$983$		−	13106.5i		−	0.425261i	−0.977133	−	0.212630i	$-0.931797\pi$
$983$		−	13106.5i		−	0.425261i	0.977133	−	0.212630i	$-0.0682030\pi$
$984$		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	$-0.671572\pi$
$997$	−32317.1			−1.02657			−0.513286	+	0.858218i	$0.671572\pi$
$998$	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.179.31	yes	64
3.2	odd	2	inner	360.4.m.c.179.34	yes	64
4.3	odd	2		1440.4.m.c.719.1		64
5.4	even	2	inner	360.4.m.c.179.33	yes	64
8.3	odd	2	inner	360.4.m.c.179.30	yes	64
8.5	even	2		1440.4.m.c.719.64		64
12.11	even	2		1440.4.m.c.719.63		64
15.14	odd	2	inner	360.4.m.c.179.32	yes	64
20.19	odd	2		1440.4.m.c.719.4		64
24.5	odd	2		1440.4.m.c.719.2		64
24.11	even	2	inner	360.4.m.c.179.35	yes	64
40.19	odd	2	inner	360.4.m.c.179.36	yes	64
40.29	even	2		1440.4.m.c.719.61		64
60.59	even	2		1440.4.m.c.719.62		64
120.29	odd	2		1440.4.m.c.719.3		64
120.59	even	2	inner	360.4.m.c.179.29	✓	64

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

\(f(q)\)	\(=\)	\(q+(-0.778894 + 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 - 0.469176i) q^{5} +17.5697 q^{7} +(16.8033 - 15.1542i) q^{8} +O(q^{10})\)	\(q+(-0.778894 + 2.71907i) q^{2} +(-6.78665 - 4.23573i) q^{4} +(-11.1705 - 0.469176i) q^{5} +17.5697 q^{7} +(16.8033 - 15.1542i) q^{8} +(9.97636 - 30.0079i) q^{10} -1.21111i q^{11} +2.29803 q^{13} +(-13.6849 + 47.7731i) q^{14} +(28.1171 + 57.4928i) q^{16} -38.9371 q^{17} +101.821 q^{19} +(73.8229 + 50.4993i) q^{20} +(3.29309 + 0.943328i) q^{22} +79.2103i q^{23} +(124.560 + 10.4819i) q^{25} +(-1.78992 + 6.24849i) q^{26} +(-119.239 - 74.4204i) q^{28} -188.490 q^{29} +195.204i q^{31} +(-178.227 + 31.6716i) q^{32} +(30.3279 - 105.873i) q^{34} +(-196.262 - 8.24327i) q^{35} -377.761 q^{37} +(-79.3074 + 276.857i) q^{38} +(-194.811 + 161.396i) q^{40} +205.009i q^{41} -396.636i q^{43} +(-5.12994 + 8.21938i) q^{44} +(-215.378 - 61.6965i) q^{46} +429.604i q^{47} -34.3070 q^{49} +(-125.520 + 330.522i) q^{50} +(-15.5959 - 9.73382i) q^{52} +65.4197i q^{53} +(-0.568225 + 13.5287i) q^{55} +(295.229 - 266.253i) q^{56} +(146.814 - 512.518i) q^{58} +354.000i q^{59} +595.183i q^{61} +(-530.772 - 152.043i) q^{62} +(52.7031 - 509.280i) q^{64} +(-25.6701 - 1.07818i) q^{65} -31.8435i q^{67} +(264.252 + 164.927i) q^{68} +(175.281 - 527.228i) q^{70} -86.9186 q^{71} -320.319i q^{73} +(294.236 - 1027.16i) q^{74} +(-691.020 - 431.284i) q^{76} -21.2788i q^{77} +518.092i q^{79} +(-287.108 - 655.415i) q^{80} +(-557.433 - 159.680i) q^{82} -520.655 q^{83} +(434.947 + 18.2684i) q^{85} +(1078.48 + 308.938i) q^{86} +(-18.3534 - 20.3507i) q^{88} -40.5337i q^{89} +40.3755 q^{91} +(335.514 - 537.572i) q^{92} +(-1168.12 - 334.616i) q^{94} +(-1137.39 - 47.7718i) q^{95} +1551.48i q^{97} +(26.7215 - 93.2830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 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

Fields

Representations

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Database

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