LMFDB - Embedded newform 60.4.e.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.e (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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29793 - 1.64910i) q^{2} +(5.00938 + 1.38062i) q^{3} +(2.56093 - 7.57903i) q^{4} +5.00000i q^{5} +(13.7880 - 5.08841i) q^{6} +0.228949i q^{7} +(-6.61376 - 21.6393i) q^{8} +(23.1878 + 13.8321i) q^{9} +O(q^{10})$	\(q+(2.29793 - 1.64910i) q^{2} +(5.00938 + 1.38062i) q^{3} +(2.56093 - 7.57903i) q^{4} +5.00000i q^{5} +(13.7880 - 5.08841i) q^{6} +0.228949i q^{7} +(-6.61376 - 21.6393i) q^{8} +(23.1878 + 13.8321i) q^{9} +(8.24551 + 11.4896i) q^{10} -57.2431 q^{11} +(23.2924 - 34.4306i) q^{12} +21.7463 q^{13} +(0.377561 + 0.526109i) q^{14} +(-6.90310 + 25.0469i) q^{15} +(-50.8833 - 38.8187i) q^{16} +57.8356i q^{17} +(76.0943 - 6.45383i) q^{18} -77.1177i q^{19} +(37.8951 + 12.8046i) q^{20} +(-0.316092 + 1.14689i) q^{21} +(-131.540 + 94.3996i) q^{22} -88.7394 q^{23} +(-3.25519 - 117.530i) q^{24} -25.0000 q^{25} +(49.9713 - 35.8618i) q^{26} +(97.0595 + 101.304i) q^{27} +(1.73521 + 0.586323i) q^{28} +259.258i q^{29} +(25.4421 + 68.9398i) q^{30} +130.711i q^{31} +(-180.942 - 5.29082i) q^{32} +(-286.752 - 79.0309i) q^{33} +(95.3768 + 132.902i) q^{34} -1.14475 q^{35} +(164.216 - 140.318i) q^{36} +117.207 q^{37} +(-127.175 - 177.211i) q^{38} +(108.935 + 30.0233i) q^{39} +(108.196 - 33.0688i) q^{40} -476.410i q^{41} +(1.16499 + 3.15675i) q^{42} -375.822i q^{43} +(-146.595 + 433.847i) q^{44} +(-69.1605 + 115.939i) q^{45} +(-203.917 + 146.340i) q^{46} +28.9897 q^{47} +(-201.300 - 264.708i) q^{48} +342.948 q^{49} +(-57.4482 + 41.2275i) q^{50} +(-79.8491 + 289.721i) q^{51} +(55.6906 - 164.815i) q^{52} -302.739i q^{53} +(390.096 + 72.7277i) q^{54} -286.215i q^{55} +(4.95430 - 1.51422i) q^{56} +(106.470 - 386.312i) q^{57} +(427.543 + 595.757i) q^{58} +353.325 q^{59} +(172.153 + 116.462i) q^{60} +593.338 q^{61} +(215.556 + 300.365i) q^{62} +(-3.16685 + 5.30883i) q^{63} +(-424.516 + 286.234i) q^{64} +108.731i q^{65} +(-789.266 + 291.276i) q^{66} -687.633i q^{67} +(438.338 + 148.113i) q^{68} +(-444.529 - 122.515i) q^{69} +(-2.63055 + 1.88780i) q^{70} +522.657 q^{71} +(145.958 - 593.249i) q^{72} -1160.42 q^{73} +(269.333 - 193.286i) q^{74} +(-125.234 - 34.5155i) q^{75} +(-584.477 - 197.493i) q^{76} -13.1058i q^{77} +(299.837 - 110.654i) q^{78} +884.113i q^{79} +(194.094 - 254.416i) q^{80} +(346.346 + 641.471i) q^{81} +(-785.648 - 1094.75i) q^{82} -390.888 q^{83} +(7.88286 + 5.33279i) q^{84} -289.178 q^{85} +(-619.769 - 863.611i) q^{86} +(-357.937 + 1298.72i) q^{87} +(378.592 + 1238.70i) q^{88} +269.922i q^{89} +(32.2692 + 380.472i) q^{90} +4.97879i q^{91} +(-227.255 + 672.558i) q^{92} +(-180.463 + 654.783i) q^{93} +(66.6162 - 47.8070i) q^{94} +385.588 q^{95} +(-899.103 - 276.316i) q^{96} +318.435 q^{97} +(788.068 - 565.555i) q^{98} +(-1327.34 - 791.792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	$ 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) $ 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	2.29793	−	1.64910i	0.812440	−	0.583045i
$2$	2.29793	−	1.64910i	0.812440	−	0.583045i
$3$	5.00938	+	1.38062i	0.964056	+	0.265701i
$3$	5.00938	+	1.38062i	0.964056	+	0.265701i
$4$	2.56093	−	7.57903i	0.320116	−	0.947378i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	13.7880	−	5.08841i	0.938152	−	0.346223i
$7$			0.228949i			0.0123621i	0.999981	+	0.00618106i	$0.00196750\pi$
$7$			0.228949i			0.0123621i	−0.999981	+	0.00618106i	$0.998032\pi$
$8$	−6.61376	−	21.6393i	−0.292289	−	0.956330i
$9$	23.1878	+	13.8321i	0.858806	+	0.512300i
$10$	8.24551	+	11.4896i	0.260746	+	0.363334i
$11$	−57.2431			−1.56904			−0.784520	−	0.620104i	$-0.787090\pi$
$11$	−57.2431			−1.56904			−0.784520	+	0.620104i	$0.787090\pi$
$12$	23.2924	−	34.4306i	0.560329	−	0.828270i
$13$	21.7463			0.463948			0.231974	−	0.972722i	$-0.425482\pi$
$13$	21.7463			0.463948			0.231974	+	0.972722i	$0.425482\pi$
$14$	0.377561	+	0.526109i	0.00720767	+	0.0100435i
$15$	−6.90310	+	25.0469i	−0.118825	+	0.431139i
$16$	−50.8833	−	38.8187i	−0.795051	−	0.606542i
$17$			57.8356i			0.825129i	0.910928	+	0.412565i	$0.135367\pi$
$17$			57.8356i			0.825129i	−0.910928	+	0.412565i	$0.864633\pi$
$18$	76.0943	−	6.45383i	0.996423	−	0.0845102i
$19$		−	77.1177i		−	0.931158i	−0.885006	−	0.465579i	$-0.845846\pi$
$19$		−	77.1177i		−	0.931158i	0.885006	−	0.465579i	$-0.154154\pi$
$20$	37.8951	+	12.8046i	0.423680	+	0.143160i
$21$	−0.316092	+	1.14689i	−0.00328462	+	0.0119178i
$22$	−131.540	+	94.3996i	−1.27475	+	0.914821i
$23$	−88.7394			−0.804498			−0.402249	−	0.915530i	$-0.631771\pi$
$23$	−88.7394			−0.804498			−0.402249	+	0.915530i	$0.631771\pi$
$24$	−3.25519	−	117.530i	−0.0276859	−	0.999617i
$25$	−25.0000			−0.200000
$26$	49.9713	−	35.8618i	0.376930	−	0.270503i
$27$	97.0595	+	101.304i	0.691819	+	0.722071i
$28$	1.73521	+	0.586323i	0.0117116	+	0.00395731i
$29$			259.258i			1.66011i	0.557685	+	0.830053i	$0.311690\pi$
$29$			259.258i			1.66011i	−0.557685	+	0.830053i	$0.688310\pi$
$30$	25.4421	+	68.9398i	0.154835	+	0.419555i
$31$			130.711i			0.757305i	0.925539	+	0.378652i	$0.123612\pi$
$31$			130.711i			0.757305i	−0.925539	+	0.378652i	$0.876388\pi$
$32$	−180.942	−	5.29082i	−0.999573	−	0.0292279i
$33$	−286.752	−	79.0309i	−1.51264	−	0.416895i
$34$	95.3768	+	132.902i	0.481088	+	0.670368i
$35$	−1.14475			−0.00552850
$36$	164.216	−	140.318i	0.760260	−	0.649619i
$37$	117.207			0.520776			0.260388	−	0.965504i	$-0.416150\pi$
$37$	117.207			0.520776			0.260388	+	0.965504i	$0.416150\pi$
$38$	−127.175	−	177.211i	−0.542907	−	0.756510i
$39$	108.935	+	30.0233i	0.447272	+	0.123271i
$40$	108.196	−	33.0688i	0.427684	−	0.130716i
$41$		−	476.410i		−	1.81470i	−0.420376	−	0.907350i	$-0.638102\pi$
$41$		−	476.410i		−	1.81470i	0.420376	−	0.907350i	$-0.361898\pi$
$42$	1.16499	+	3.15675i	0.00428004	+	0.0115975i
$43$		−	375.822i		−	1.33284i	−0.745575	−	0.666422i	$-0.767825\pi$
$43$		−	375.822i		−	1.33284i	0.745575	−	0.666422i	$-0.232175\pi$
$44$	−146.595	+	433.847i	−0.502275	+	1.48647i
$45$	−69.1605	+	115.939i	−0.229108	+	0.384070i
$46$	−203.917	+	146.340i	−0.653606	+	0.469059i
$47$	28.9897			0.0899699			0.0449849	−	0.998988i	$-0.485676\pi$
$47$	28.9897			0.0899699			0.0449849	+	0.998988i	$0.485676\pi$
$48$	−201.300	−	264.708i	−0.605315	−	0.795986i
$49$	342.948			0.999847
$50$	−57.4482	+	41.2275i	−0.162488	+	0.116609i
$51$	−79.8491	+	289.721i	−0.219237	+	0.795471i
$52$	55.6906	−	164.815i	0.148517	−	0.439534i
$53$		−	302.739i		−	0.784612i	−0.919835	−	0.392306i	$-0.871677\pi$
$53$		−	302.739i		−	0.784612i	0.919835	−	0.392306i	$-0.128323\pi$
$54$	390.096	+	72.7277i	0.983061	+	0.183278i
$55$		−	286.215i		−	0.701696i
$56$	4.95430	−	1.51422i	0.0118223	−	0.00361332i
$57$	106.470	−	386.312i	0.247409	−	0.897688i
$58$	427.543	+	595.757i	0.967917	+	1.34874i
$59$	353.325			0.779645			0.389823	−	0.920890i	$-0.372536\pi$
$59$	353.325			0.779645			0.389823	+	0.920890i	$0.372536\pi$
$60$	172.153	+	116.462i	0.370414	+	0.250587i
$61$	593.338			1.24540			0.622698	−	0.782462i	$-0.286036\pi$
$61$	593.338			1.24540			0.622698	+	0.782462i	$0.286036\pi$
$62$	215.556	+	300.365i	0.441543	+	0.615264i
$63$	−3.16685	+	5.30883i	−0.00633311	+	0.0106167i
$64$	−424.516	+	286.234i	−0.829134	+	0.559050i
$65$			108.731i			0.207484i
$66$	−789.266	+	291.276i	−1.47200	+	0.543237i
$67$		−	687.633i		−	1.25385i	−0.779081	−	0.626923i	$-0.784314\pi$
$67$		−	687.633i		−	1.25385i	0.779081	−	0.626923i	$-0.215686\pi$
$68$	438.338	+	148.113i	0.781710	+	0.264137i
$69$	−444.529	−	122.515i	−0.775580	−	0.213755i
$70$	−2.63055	+	1.88780i	−0.00449158	+	0.00322337i
$71$	522.657			0.873634			0.436817	−	0.899550i	$-0.356106\pi$
$71$	522.657			0.873634			0.436817	+	0.899550i	$0.356106\pi$
$72$	145.958	−	593.249i	0.238908	−	0.971042i
$73$	−1160.42			−1.86051			−0.930256	−	0.366911i	$-0.880415\pi$
$73$	−1160.42			−1.86051			−0.930256	+	0.366911i	$0.880415\pi$
$74$	269.333	−	193.286i	0.423099	−	0.303636i
$75$	−125.234	−	34.5155i	−0.192811	−	0.0531401i
$76$	−584.477	−	197.493i	−0.882159	−	0.298079i
$77$		−	13.1058i		−	0.0193966i
$78$	299.837	−	110.654i	0.435254	−	0.160629i
$79$			884.113i			1.25912i	0.776952	+	0.629560i	$0.216765\pi$
$79$			884.113i			1.25912i	−0.776952	+	0.629560i	$0.783235\pi$
$80$	194.094	−	254.416i	0.271254	−	0.355558i
$81$	346.346	+	641.471i	0.475097	+	0.879933i
$82$	−785.648	−	1094.75i	−1.05805	−	1.47433i
$83$	−390.888			−0.516934			−0.258467	−	0.966020i	$-0.583217\pi$
$83$	−390.888			−0.516934			−0.258467	+	0.966020i	$0.583217\pi$
$84$	7.88286	+	5.33279i	0.0102392	+	0.00692685i
$85$	−289.178			−0.369009
$86$	−619.769	−	863.611i	−0.777109	−	1.08286i
$87$	−357.937	+	1298.72i	−0.441091	+	1.60043i
$88$	378.592	+	1238.70i	0.458614	+	1.50052i
$89$			269.922i			0.321479i	0.986997	+	0.160740i	$0.0513879\pi$
$89$			269.922i			0.321479i	−0.986997	+	0.160740i	$0.948612\pi$
$90$	32.2692	+	380.472i	0.0377941	+	0.445614i
$91$			4.97879i			0.00573538i
$92$	−227.255	+	672.558i	−0.257533	+	0.762164i
$93$	−180.463	+	654.783i	−0.201216	+	0.730084i
$94$	66.6162	−	47.8070i	0.0730951	−	0.0524565i
$95$	385.588			0.416427
$96$	−899.103	−	276.316i	−0.955878	−	0.293764i
$97$	318.435			0.333322			0.166661	−	0.986014i	$-0.446701\pi$
$97$	318.435			0.333322			0.166661	+	0.986014i	$0.446701\pi$
$98$	788.068	−	565.555i	0.812315	−	0.582956i
$99$	−1327.34	−	791.792i	−1.34750	−	0.803819i
$100$	−64.0232	+	189.476i	−0.0640232	+	0.189476i
$101$		−	3.67697i		−	0.00362250i	−0.999998	−	0.00181125i	$-0.999423\pi$
$101$		−	3.67697i		−	0.00362250i	0.999998	−	0.00181125i	$-0.000576539\pi$
$102$	294.291	+	797.436i	0.285678	+	0.774097i
$103$		−	61.6111i		−	0.0589390i	−0.999566	−	0.0294695i	$-0.990618\pi$
$103$		−	61.6111i		−	0.0589390i	0.999566	−	0.0294695i	$-0.00938180\pi$
$104$	−143.824	−	470.573i	−0.135607	−	0.443687i
$105$	−5.73447	−	1.58046i	−0.00532979	−	0.00146893i
$106$	−499.248	−	695.672i	−0.457464	−	0.637450i
$107$	−721.388			−0.651768			−0.325884	−	0.945410i	$-0.605662\pi$
$107$	−721.388			−0.651768			−0.325884	+	0.945410i	$0.605662\pi$
$108$	1016.35	−	476.185i	0.905537	−	0.424267i
$109$	192.798			0.169419			0.0847097	−	0.996406i	$-0.473004\pi$
$109$	192.798			0.169419			0.0847097	+	0.996406i	$0.473004\pi$
$110$	−471.998	−	657.702i	−0.409120	−	0.570085i
$111$	587.134	+	161.818i	0.502057	+	0.138370i
$112$	8.88752	−	11.6497i	0.00749814	−	0.00982851i
$113$			1460.88i			1.21617i	0.793870	+	0.608087i	$0.208063\pi$
$113$			1460.88i			1.21617i	−0.793870	+	0.608087i	$0.791937\pi$
$114$	−392.406	−	1063.30i	−0.322388	−	0.873568i
$115$		−	443.697i		−	0.359782i
$116$	1964.93	+	663.942i	1.57275	+	0.531427i
$117$	504.247	+	300.796i	0.398442	+	0.237681i
$118$	811.916	−	582.670i	0.633415	−	0.454568i
$119$	−13.2414			−0.0102003
$120$	587.652	−	16.2759i	0.447042	−	0.0123815i
$121$	1945.77			1.46188
$122$	1363.45	−	978.475i	1.01181	−	0.726123i
$123$	657.741	−	2386.52i	0.482167	−	1.74947i
$124$	990.665	+	334.743i	0.717454	+	0.242426i
$125$		−	125.000i		−	0.0894427i
$126$	1.47760	+	17.4218i	0.00104472	+	0.0123179i
$127$			742.981i			0.519125i	0.965726	+	0.259563i	$0.0835784\pi$
$127$			742.981i			0.519125i	−0.965726	+	0.259563i	$0.916422\pi$
$128$	−503.479	+	1357.81i	−0.347669	+	0.937617i
$129$	518.868	−	1882.64i	0.354138	−	1.28494i
$130$	179.309	+	249.856i	0.120973	+	0.168568i
$131$	−442.767			−0.295303			−0.147652	−	0.989039i	$-0.547171\pi$
$131$	−442.767			−0.295303			−0.147652	+	0.989039i	$0.547171\pi$
$132$	−1333.33	+	1970.91i	−0.879178	+	1.29959i
$133$	17.6560			0.0115111
$134$	−1133.98	−	1580.13i	−0.731049	−	1.01867i
$135$	−506.519	+	485.297i	−0.322920	+	0.309391i
$136$	1251.52	−	382.511i	0.789096	−	0.241177i
$137$			199.114i			0.124171i	0.998071	+	0.0620855i	$0.0197752\pi$
$137$			199.114i			0.124171i	−0.998071	+	0.0620855i	$0.980225\pi$
$138$	−1223.54	+	451.543i	−0.754741	+	0.278535i
$139$			353.631i			0.215789i	0.994162	+	0.107894i	$0.0344108\pi$
$139$			353.631i			0.215789i	−0.994162	+	0.107894i	$0.965589\pi$
$140$	−2.93162	+	8.67607i	−0.00176976	+	0.00523758i
$141$	145.221	+	40.0238i	0.0867360	+	0.0239050i
$142$	1201.03	−	861.915i	0.709775	−	0.509368i
$143$	−1244.82			−0.727953
$144$	−642.926	−	1603.94i	−0.372063	−	0.928207i
$145$	−1296.29			−0.742422
$146$	−2666.57	+	1913.66i	−1.51155	+	1.08476i
$147$	1717.95	+	473.480i	0.963908	+	0.265660i
$148$	300.159	−	888.315i	0.166709	−	0.493372i
$149$		−	1547.43i		−	0.850810i	−0.905003	−	0.425405i	$-0.860132\pi$
$149$		−	1547.43i		−	0.850810i	0.905003	−	0.425405i	$-0.139868\pi$
$150$	−344.699	+	127.210i	−0.187630	+	0.0692445i
$151$			2778.94i			1.49766i	0.662760	+	0.748832i	$0.269385\pi$
$151$			2778.94i			1.49766i	−0.662760	+	0.748832i	$0.730615\pi$
$152$	−1668.77	+	510.037i	−0.890494	+	0.272168i
$153$	−799.988	+	1341.08i	−0.422714	+	0.708626i
$154$	−21.6127	−	30.1161i	−0.0113091	−	0.0157586i
$155$	−653.557			−0.338677
$156$	506.523	−	748.736i	0.259963	−	0.384274i
$157$	−1581.39			−0.803879			−0.401940	−	0.915666i	$-0.631664\pi$
$157$	−1581.39			−0.803879			−0.401940	+	0.915666i	$0.631664\pi$
$158$	1457.99	+	2031.63i	0.734124	+	1.02296i
$159$	417.968	−	1516.54i	0.208472	−	0.756409i
$160$	26.4541	−	904.710i	0.0130711	−	0.447023i
$161$		−	20.3168i		−	0.00994529i
$162$	1853.73	+	902.895i	0.899029	+	0.437890i
$163$			494.355i			0.237552i	0.992921	+	0.118776i	$0.0378970\pi$
$163$			494.355i			0.237552i	−0.992921	+	0.118776i	$0.962103\pi$
$164$	−3610.72	−	1220.05i	−1.71921	−	0.580915i
$165$	395.155	−	1433.76i	0.186441	−	0.676474i
$166$	−898.232	+	644.614i	−0.419978	+	0.301396i
$167$	2339.49			1.08404			0.542020	−	0.840365i	$-0.317660\pi$
$167$	2339.49			1.08404			0.542020	+	0.840365i	$0.317660\pi$
$168$	26.9085	−	0.745274i	0.0123574	−	0.000342257i
$169$	−1724.10			−0.784752
$170$	−664.510	+	476.884i	−0.299798	+	0.215149i
$171$	1066.70	−	1788.19i	0.477033	−	0.799685i
$172$	−2848.36	−	962.454i	−1.26271	−	0.426665i
$173$		−	2229.83i		−	0.979947i	−0.871737	−	0.489974i	$-0.837006\pi$
$173$		−	2229.83i		−	0.979947i	0.871737	−	0.489974i	$-0.162994\pi$
$174$	1319.21	+	3574.65i	0.574766	+	1.55743i
$175$		−	5.72374i		−	0.00247242i
$176$	2912.71	+	2222.10i	1.24747	+	0.951689i
$177$	1769.94	+	487.808i	0.751621	+	0.207152i
$178$	445.128	+	620.260i	0.187437	+	0.261182i
$179$	2128.21			0.888660			0.444330	−	0.895863i	$-0.353442\pi$
$179$	2128.21			0.888660			0.444330	+	0.895863i	$0.353442\pi$
$180$	701.589	+	821.081i	0.290518	+	0.339999i
$181$	−4714.17			−1.93592			−0.967960	−	0.251106i	$-0.919206\pi$
$181$	−4714.17			−1.93592			−0.967960	+	0.251106i	$0.919206\pi$
$182$	8.21054	+	11.4409i	0.00334399	+	0.00465965i
$183$	2972.26	+	819.175i	1.20063	+	0.330903i
$184$	586.901	+	1920.26i	0.235146	+	0.769365i
$185$			586.035i			0.232898i
$186$	665.113	+	1802.24i	0.262196	+	0.710467i
$187$		−	3310.69i		−	1.29466i
$188$	74.2406	−	219.714i	0.0288008	−	0.0852355i
$189$	−23.1935	+	22.2217i	−0.00892632	+	0.00855234i
$190$	886.053	−	635.874i	0.338321	−	0.242796i
$191$	−3615.45			−1.36966			−0.684829	−	0.728704i	$-0.740123\pi$
$191$	−3615.45			−1.36966			−0.684829	+	0.728704i	$0.740123\pi$
$192$	−2521.74	+	847.758i	−0.947871	+	0.318654i
$193$	1087.66			0.405654			0.202827	−	0.979215i	$-0.434987\pi$
$193$	1087.66			0.405654			0.202827	+	0.979215i	$0.434987\pi$
$194$	731.741	−	525.132i	0.270804	−	0.194342i
$195$	−150.117	+	544.676i	−0.0551286	+	0.200026i
$196$	878.265	−	2599.21i	0.320067	−	0.947234i
$197$		−	1845.81i		−	0.667555i	−0.942652	−	0.333777i	$-0.891677\pi$
$197$		−	1845.81i		−	0.667555i	0.942652	−	0.333777i	$-0.108323\pi$
$198$	−4355.87	+	369.437i	−1.56343	+	0.132600i
$199$			3007.15i			1.07121i	0.844468	+	0.535606i	$0.179917\pi$
$199$			3007.15i			1.07121i	−0.844468	+	0.535606i	$0.820083\pi$
$200$	165.344	+	540.982i	0.0584579	+	0.191266i
$201$	949.360	−	3444.61i	0.333148	−	1.20878i
$202$	−6.06370	−	8.44941i	−0.00211208	−	0.00294306i
$203$	−59.3571			−0.0205224
$204$	1991.31	+	1347.13i	0.683430	+	0.462344i
$205$	2382.05			0.811558
$206$	−101.603	−	141.578i	−0.0343641	−	0.0478844i
$207$	−2057.67	−	1227.45i	−0.690908	−	0.412144i
$208$	−1106.52	−	844.161i	−0.368863	−	0.281404i
$209$			4414.45i			1.46102i
$210$	−15.7837	+	5.82495i	−0.00518658	+	0.00191409i
$211$		−	2538.35i		−	0.828187i	−0.910234	−	0.414093i	$-0.864099\pi$
$211$		−	2538.35i		−	0.828187i	0.910234	−	0.414093i	$-0.135901\pi$
$212$	−2294.47	−	775.294i	−0.743324	−	0.251167i
$213$	2618.19	+	721.591i	0.842232	+	0.232125i
$214$	−1657.70	+	1189.64i	−0.529522	+	0.380010i
$215$	1879.11			0.596066
$216$	1550.21	−	2770.30i	0.488327	−	0.872661i
$217$	−29.9263			−0.00936189
$218$	443.036	−	317.944i	0.137643	−	0.0987792i
$219$	−5813.01	−	1602.11i	−1.79364	−	0.494339i
$220$	−2169.23	−	732.977i	−0.664771	−	0.224624i
$221$			1257.71i			0.382817i
$222$	1616.05	−	596.397i	0.488567	−	0.180304i
$223$			4213.99i			1.26542i	0.774388	+	0.632711i	$0.218058\pi$
$223$			4213.99i			1.26542i	−0.774388	+	0.632711i	$0.781942\pi$
$224$	1.21133	−	41.4266i	0.000361319	−	0.0123568i
$225$	−579.694	−	345.803i	−0.171761	−	0.102460i
$226$	2409.13	+	3356.98i	0.709085	+	0.988068i
$227$	−3320.68			−0.970930			−0.485465	−	0.874256i	$-0.661350\pi$
$227$	−3320.68			−0.970930			−0.485465	+	0.874256i	$0.661350\pi$
$228$	−2655.20	−	1796.26i	−0.771251	−	0.521755i
$229$	2833.32			0.817602			0.408801	−	0.912623i	$-0.365947\pi$
$229$	2833.32			0.817602			0.408801	+	0.912623i	$0.365947\pi$
$230$	−731.701	−	1019.58i	−0.209769	−	0.292301i
$231$	18.0941	−	65.6518i	0.00515370	−	0.0186994i
$232$	5610.16	−	1714.67i	1.58761	−	0.485232i
$233$		−	3507.19i		−	0.986109i	−0.869998	−	0.493055i	$-0.835880\pi$
$233$		−	3507.19i		−	0.986109i	0.869998	−	0.493055i	$-0.164120\pi$
$234$	1654.77	−	140.347i	0.462288	−	0.0392083i
$235$			144.949i			0.0402358i
$236$	904.842	−	2677.86i	0.249577	−	0.738619i
$237$	−1220.62	+	4428.86i	−0.334549	+	1.21386i
$238$	−30.4278	+	21.8365i	−0.00828716	+	0.00594726i
$239$	6795.89			1.83929			0.919643	−	0.392754i	$-0.128478\pi$
$239$	6795.89			1.83929			0.919643	+	0.392754i	$0.128478\pi$
$240$	1323.54	−	1006.50i	0.355976	−	0.270705i
$241$	−893.259			−0.238755			−0.119377	−	0.992849i	$-0.538090\pi$
$241$	−893.259			−0.238755			−0.119377	+	0.992849i	$0.538090\pi$
$242$	4471.23	−	3208.77i	1.18769	−	0.852345i
$243$	849.349	+	3691.55i	0.224221	+	0.974538i
$244$	1519.50	−	4496.93i	0.398672	−	1.17986i
$245$			1714.74i			0.447145i
$246$	−2424.17	−	6568.72i	−0.628290	−	1.70247i
$247$		−	1677.02i		−	0.432009i
$248$	2828.50	−	864.493i	0.724233	−	0.221352i
$249$	−1958.11	−	539.668i	−0.498353	−	0.137350i
$250$	−206.138	−	287.241i	−0.0521492	−	0.0726668i
$251$	1159.27			0.291524			0.145762	−	0.989320i	$-0.453437\pi$
$251$	1159.27			0.291524			0.145762	+	0.989320i	$0.453437\pi$
$252$	32.1257	+	37.5972i	0.00803066	+	0.00939842i
$253$	5079.72			1.26229
$254$	1225.25	+	1707.31i	0.302673	+	0.421758i
$255$	−1448.60	−	399.245i	−0.355745	−	0.0980459i
$256$	1082.22	+	3950.45i	0.264213	+	0.964464i
$257$		−	283.707i		−	0.0688606i	−0.999407	−	0.0344303i	$-0.989038\pi$
$257$		−	283.707i		−	0.0688606i	0.999407	−	0.0344303i	$-0.0109617\pi$
$258$	−1912.34	−	5181.82i	−0.461461	−	1.25041i
$259$			26.8345i			0.00643789i
$260$	824.077	+	278.453i	0.196566	+	0.0664190i
$261$	−3586.09	+	6011.62i	−0.850473	+	1.42571i
$262$	−1017.45	+	730.167i	−0.239916	+	0.172175i
$263$	−6489.72			−1.52157			−0.760786	−	0.649003i	$-0.775186\pi$
$263$	−6489.72			−1.52157			−0.760786	+	0.649003i	$0.775186\pi$
$264$	186.337	+	6727.80i	0.0434403	+	1.56844i
$265$	1513.70			0.350889
$266$	40.5723	−	29.1166i	0.00935206	−	0.00671148i
$267$	−372.659	+	1352.14i	−0.0854172	+	0.309924i
$268$	−5211.59	−	1760.98i	−1.18787	−	0.401376i
$269$			5899.83i			1.33724i	0.743602	+	0.668622i	$0.233116\pi$
$269$			5899.83i			1.33724i	−0.743602	+	0.668622i	$0.766884\pi$
$270$	−363.639	+	1950.48i	−0.0819642	+	0.439638i
$271$		−	4161.66i		−	0.932852i	−0.884560	−	0.466426i	$-0.845541\pi$
$271$		−	4161.66i		−	0.932852i	0.884560	−	0.466426i	$-0.154459\pi$
$272$	2245.10	−	2942.87i	0.500476	−	0.656020i
$273$	−6.87383	+	24.9407i	−0.00152389	+	0.00552922i
$274$	328.359	+	457.549i	0.0723974	+	0.100882i
$275$	1431.08			0.313808
$276$	−2066.96	+	3055.35i	−0.450783	+	0.666341i
$277$	−2466.81			−0.535078			−0.267539	−	0.963547i	$-0.586210\pi$
$277$	−2466.81			−0.535078			−0.267539	+	0.963547i	$0.586210\pi$
$278$	583.174	+	812.618i	0.125815	+	0.175315i
$279$	−1808.01	+	3030.91i	−0.387967	+	0.650378i
$280$	7.57108	+	24.7715i	0.00161592	+	0.00528707i
$281$			965.966i			0.205070i	0.994729	+	0.102535i	$0.0326954\pi$
$281$			965.966i			0.205070i	−0.994729	+	0.102535i	$0.967305\pi$
$282$	399.709	−	147.512i	0.0844055	−	0.0311496i
$283$		−	1894.36i		−	0.397907i	−0.980009	−	0.198954i	$-0.936246\pi$
$283$		−	1894.36i		−	0.397907i	0.980009	−	0.198954i	$-0.0637543\pi$
$284$	1338.49	−	3961.23i	0.279664	−	0.827662i
$285$	1931.56	+	532.351i	0.401458	+	0.110645i
$286$	−2860.51	+	2052.84i	−0.591418	+	0.424430i
$287$	109.074			0.0224335
$288$	−4122.46	−	2625.49i	−0.843466	−	0.537182i
$289$	1568.04			0.319161
$290$	−2978.78	+	2137.72i	−0.603173	+	0.432866i
$291$	1595.16	+	439.638i	0.321341	+	0.0885638i
$292$	−2971.76	+	8794.88i	−0.595580	+	1.76261i
$293$		−	7890.46i		−	1.57326i	−0.617424	−	0.786631i	$-0.711824\pi$
$293$		−	7890.46i		−	1.57326i	0.617424	−	0.786631i	$-0.288176\pi$
$294$	4728.55	−	1745.06i	0.938009	−	0.346170i
$295$			1766.63i			0.348668i
$296$	−775.178	−	2536.27i	−0.152217	−	0.498034i
$297$	−5555.98	−	5798.94i	−1.08549	−	1.13296i
$298$	−2551.88	−	3555.89i	−0.496061	−	0.691232i
$299$	−1929.75			−0.373245
$300$	−582.311	+	860.764i	−0.112066	+	0.165654i
$301$	86.0443			0.0164768
$302$	4582.76	+	6385.81i	0.873206	+	1.21676i
$303$	5.07650	−	18.4193i	0.000962500	−	0.00349229i
$304$	−2993.61	+	3924.00i	−0.564787	+	0.740318i
$305$			2966.69i			0.556958i
$306$	373.261	+	4400.96i	0.0697318	+	0.822178i
$307$			7876.14i			1.46422i	0.681188	+	0.732109i	$0.261464\pi$
$307$			7876.14i			1.46422i	−0.681188	+	0.732109i	$0.738536\pi$
$308$	−99.3290	−	33.5630i	−0.0183760	−	0.00620918i
$309$	85.0615	−	308.633i	0.0156601	−	0.0568205i
$310$	−1501.83	+	1077.78i	−0.275155	+	0.197464i
$311$	−1002.79			−0.182840			−0.0914199	−	0.995812i	$-0.529141\pi$
$311$	−1002.79			−0.182840			−0.0914199	+	0.995812i	$0.529141\pi$
$312$	−70.7882	−	2555.85i	−0.0128448	−	0.463770i
$313$	−1190.57			−0.215001			−0.107500	−	0.994205i	$-0.534285\pi$
$313$	−1190.57			−0.215001			−0.107500	+	0.994205i	$0.534285\pi$
$314$	−3633.93	+	2607.88i	−0.653103	+	0.468698i
$315$	−26.5441	−	15.8343i	−0.00474791	−	0.00283225i
$316$	6700.71	+	2264.15i	1.19286	+	0.403065i
$317$		−	1369.48i		−	0.242642i	−0.992613	−	0.121321i	$-0.961287\pi$
$317$		−	1369.48i		−	0.242642i	0.992613	−	0.121321i	$-0.0387130\pi$
$318$	−1540.46	−	4174.16i	−0.271650	−	0.736085i
$319$		−	14840.7i		−	2.60477i
$320$	−1431.17	−	2122.58i	−0.250015	−	0.370800i
$321$	−3613.71	−	995.963i	−0.628341	−	0.173175i
$322$	−33.5045	−	46.6866i	−0.00579855	−	0.00807995i
$323$	4460.15			0.768326
$324$	5748.70	−	982.200i	0.985716	−	0.168416i
$325$	−543.656			−0.0927896
$326$	815.242	+	1135.99i	0.138503	+	0.192996i
$327$	965.800	+	266.181i	0.163330	+	0.0450148i
$328$	−10309.2	+	3150.86i	−1.73545	+	0.530418i
$329$			6.63718i			0.00111222i
$330$	−1456.38	−	3946.33i	−0.242943	−	0.658298i
$331$		−	4268.29i		−	0.708781i	−0.935097	−	0.354391i	$-0.884688\pi$
$331$		−	4268.29i		−	0.708781i	0.935097	−	0.354391i	$-0.115312\pi$
$332$	−1001.04	+	2962.55i	−0.165479	+	0.489732i
$333$	2717.77	+	1621.22i	0.447246	+	0.266794i
$334$	5375.97	−	3858.05i	0.880718	−	0.632045i
$335$	3438.16			0.560737
$336$	60.6048	−	46.0875i	0.00984007	−	0.00748297i
$337$	3005.85			0.485873			0.242937	−	0.970042i	$-0.421889\pi$
$337$	3005.85			0.485873			0.242937	+	0.970042i	$0.421889\pi$
$338$	−3961.86	+	2843.22i	−0.637564	+	0.457546i
$339$	−2016.92	+	7318.08i	−0.323138	+	1.17246i
$340$	−740.565	+	2191.69i	−0.118126	+	0.349591i
$341$		−	7482.32i		−	1.18824i
$342$	−497.704	−	5868.22i	−0.0786923	−	0.927827i
$343$			157.047i			0.0247223i
$344$	−8132.52	+	2485.60i	−1.27464	+	0.389576i
$345$	612.577	−	2222.65i	0.0955943	−	0.346850i
$346$	−3677.22	−	5123.99i	−0.571354	−	0.796148i
$347$	671.091			0.103822			0.0519108	−	0.998652i	$-0.483469\pi$
$347$	671.091			0.103822			0.0519108	+	0.998652i	$0.483469\pi$
$348$	8926.41	+	6038.76i	1.37502	+	0.930205i
$349$	−7541.48			−1.15669			−0.578347	−	0.815791i	$-0.696302\pi$
$349$	−7541.48			−1.15669			−0.578347	+	0.815791i	$0.696302\pi$
$350$	−9.43902	−	13.1527i	−0.00144153	−	0.00200869i
$351$	2110.68	+	2202.98i	0.320968	+	0.335004i
$352$	10357.7	+	302.863i	1.56837	+	0.0458598i
$353$			3942.47i			0.594437i	0.954809	+	0.297219i	$0.0960590\pi$
$353$			3942.47i			0.594437i	−0.954809	+	0.297219i	$0.903941\pi$
$354$	4871.64	−	1797.87i	0.731426	−	0.269931i
$355$			2613.29i			0.390701i
$356$	2045.74	+	691.250i	0.304562	+	0.102911i
$357$	−66.3314	−	18.2814i	−0.00983370	−	0.00271024i
$358$	4890.48	−	3509.64i	0.721983	−	0.518129i
$359$	5686.63			0.836014			0.418007	−	0.908444i	$-0.362729\pi$
$359$	5686.63			0.836014			0.418007	+	0.908444i	$0.362729\pi$
$360$	2966.24	+	729.792i	0.434263	+	0.106843i
$361$	911.866			0.132944
$362$	−10832.8	+	7774.14i	−1.57282	+	1.12873i
$363$	9747.09	+	2686.37i	1.40934	+	0.388424i
$364$	37.7344	+	12.7503i	0.00543357	+	0.00183599i
$365$		−	5802.12i		−	0.832046i
$366$	8180.93	−	3019.15i	1.16837	−	0.431184i
$367$		−	3385.19i		−	0.481486i	−0.970589	−	0.240743i	$-0.922609\pi$
$367$		−	3385.19i		−	0.481486i	0.970589	−	0.240743i	$-0.0773911\pi$
$368$	4515.35	+	3444.75i	0.639617	+	0.487962i
$369$	6589.75	−	11046.9i	0.929671	−	1.55848i
$370$	966.431	+	1346.66i	0.135790	+	0.189216i
$371$	69.3120			0.00969946
$372$	4500.46	+	3044.58i	0.627253	+	0.424340i
$373$	8746.73			1.21418			0.607089	−	0.794634i	$-0.292337\pi$
$373$	8746.73			1.21418			0.607089	+	0.794634i	$0.292337\pi$
$374$	−5459.66	−	7607.72i	−0.754846	−	1.05183i
$375$	172.578	−	626.172i	0.0237650	−	0.0862278i
$376$	−191.731	−	627.316i	−0.0262973	−	0.0860409i
$377$			5637.90i			0.770203i
$378$	−16.6510	+	89.3122i	−0.00226570	+	0.0121527i
$379$			2190.54i			0.296888i	0.988921	+	0.148444i	$0.0474265\pi$
$379$			2190.54i			0.296888i	−0.988921	+	0.148444i	$0.952573\pi$
$380$	987.464	−	2922.38i	0.133305	−	0.394514i
$381$	−1025.77	+	3721.87i	−0.137932	+	0.500465i
$382$	−8308.04	+	5962.24i	−1.11276	+	0.798573i
$383$	−8538.26			−1.13912			−0.569562	−	0.821948i	$-0.692887\pi$
$383$	−8538.26			−1.13912			−0.569562	+	0.821948i	$0.692887\pi$
$384$	−4396.74	+	6106.70i	−0.584298	+	0.811539i
$385$	65.5289			0.00867444
$386$	2499.36	−	1793.66i	0.329570	−	0.236515i
$387$	5198.41	−	8714.48i	0.682817	−	1.14466i
$388$	815.491	−	2413.43i	0.106702	−	0.315782i
$389$		−	2657.71i		−	0.346404i	−0.984886	−	0.173202i	$-0.944589\pi$
$389$		−	2657.71i		−	0.346404i	0.984886	−	0.173202i	$-0.0554114\pi$
$390$	553.269	+	1499.18i	0.0718356	+	0.194652i
$391$		−	5132.30i		−	0.663815i
$392$	−2268.17	−	7421.14i	−0.292245	−	0.956184i
$393$	−2217.99	−	611.293i	−0.284689	−	0.0784622i
$394$	−3043.92	−	4241.53i	−0.389215	−	0.542348i
$395$	−4420.56			−0.563095
$396$	−9400.24	+	8032.22i	−1.19288	+	1.01928i
$397$	2636.32			0.333282			0.166641	−	0.986018i	$-0.446708\pi$
$397$	2636.32			0.333282			0.166641	+	0.986018i	$0.446708\pi$
$398$	4959.10	+	6910.21i	0.624565	+	0.870295i
$399$	88.4459	+	24.3763i	0.0110973	+	0.00305850i
$400$	1272.08	+	970.468i	0.159010	+	0.121308i
$401$			930.551i			0.115884i	0.998320	+	0.0579420i	$0.0184539\pi$
$401$			930.551i			0.115884i	−0.998320	+	0.0579420i	$0.981546\pi$
$402$	−3498.96	−	9481.06i	−0.434110	−	1.17630i
$403$			2842.48i			0.351350i
$404$	−27.8679	−	9.41646i	−0.00343188	−	0.00115962i
$405$	−3207.36	+	1731.73i	−0.393518	+	0.212470i
$406$	−136.398	+	97.8858i	−0.0166732	+	0.0119655i
$407$	−6709.29			−0.817118
$408$	6797.45	−	188.266i	0.824813	−	0.0228445i
$409$	1844.98			0.223053			0.111526	−	0.993761i	$-0.464426\pi$
$409$	1844.98			0.223053			0.111526	+	0.993761i	$0.464426\pi$
$410$	5473.77	−	3928.24i	0.659342	−	0.473175i
$411$	−274.901	+	997.437i	−0.0329923	+	0.119708i
$412$	−466.952	−	157.782i	−0.0558376	−	0.0188673i
$413$			80.8937i			0.00963806i
$414$	−6752.57	+	572.709i	−0.801620	+	0.0679882i
$415$		−	1954.44i		−	0.231180i
$416$	−3934.81	−	115.056i	−0.463750	−	0.0135603i
$417$	−488.231	+	1771.47i	−0.0573351	+	0.208032i
$418$	7279.88	+	10144.1i	0.851843	+	1.18699i
$419$	−3898.38			−0.454531			−0.227266	−	0.973833i	$-0.572979\pi$
$419$	−3898.38			−0.454531			−0.227266	+	0.973833i	$0.572979\pi$
$420$	−26.6639	+	39.4143i	−0.00309778	+	0.00457910i
$421$	−1228.68			−0.142238			−0.0711192	−	0.997468i	$-0.522657\pi$
$421$	−1228.68			−0.142238			−0.0711192	+	0.997468i	$0.522657\pi$
$422$	−4186.00	−	5832.95i	−0.482870	−	0.672852i
$423$	672.207	+	400.989i	0.0772667	+	0.0460916i
$424$	−6551.06	+	2002.24i	−0.750348	+	0.229334i
$425$		−	1445.89i		−	0.165026i
$426$	7206.38	−	2659.50i	0.819602	−	0.302472i
$427$			135.845i			0.0153957i
$428$	−1847.42	+	5467.42i	−0.208642	+	0.617471i
$429$	−6235.79	−	1718.63i	−0.701787	−	0.193417i
$430$	4318.06	−	3098.84i	0.484268	−	0.347534i
$431$	−9125.77			−1.01989			−0.509946	−	0.860207i	$-0.670334\pi$
$431$	−9125.77			−1.01989			−0.509946	+	0.860207i	$0.670334\pi$
$432$	−1006.22	−	8922.39i	−0.112065	−	0.993701i
$433$	−12158.7			−1.34945			−0.674724	−	0.738070i	$-0.735737\pi$
$433$	−12158.7			−1.34945			−0.674724	+	0.738070i	$0.735737\pi$
$434$	−68.7684	+	49.3515i	−0.00760597	+	0.00545841i
$435$	−6493.62	−	1789.69i	−0.715736	−	0.197262i
$436$	493.743	−	1461.22i	0.0542339	−	0.160504i
$437$			6843.38i			0.749114i
$438$	−15999.9	+	5904.71i	−1.74544	+	0.644151i
$439$			5218.06i			0.567299i	0.958928	+	0.283650i	$0.0915453\pi$
$439$			5218.06i			0.567299i	−0.958928	+	0.283650i	$0.908455\pi$
$440$	−6193.49	+	1892.96i	−0.671053	+	0.205098i
$441$	7952.19	+	4743.69i	0.858675	+	0.512222i
$442$	2074.09	+	2890.12i	0.223200	+	0.311016i
$443$	2691.98			0.288713			0.144357	−	0.989526i	$-0.453889\pi$
$443$	2691.98			0.288713			0.144357	+	0.989526i	$0.453889\pi$
$444$	2730.04	−	4035.50i	0.291806	−	0.431343i
$445$	−1349.61			−0.143770
$446$	6949.29	+	9683.43i	0.737799	+	1.02808i
$447$	2136.42	−	7751.68i	0.226061	−	0.820228i
$448$	−65.5331	−	97.1928i	−0.00691104	−	0.0102498i
$449$			6289.65i			0.661085i	0.943791	+	0.330542i	$0.107232\pi$
$449$			6289.65i			0.661085i	−0.943791	+	0.330542i	$0.892768\pi$
$450$	−1902.36	+	161.346i	−0.199285	+	0.0169020i
$451$			27271.1i			2.84734i
$452$	11072.0	+	3741.20i	1.15218	+	0.389317i
$453$	−3836.67	+	13920.8i	−0.397930	+	1.44383i
$454$	−7630.67	+	5476.13i	−0.788822	+	0.566096i
$455$	−24.8940			−0.00256494
$456$	−9063.67	+	251.033i	−0.930801	+	0.0257800i
$457$	8051.24			0.824117			0.412058	−	0.911157i	$-0.364810\pi$
$457$	8051.24			0.824117			0.412058	+	0.911157i	$0.364810\pi$
$458$	6510.76	−	4672.43i	0.664253	−	0.476699i
$459$	−5858.97	+	5613.50i	−0.595802	+	0.570840i
$460$	−3362.79	−	1136.28i	−0.340850	−	0.115172i
$461$		−	4985.15i		−	0.503647i	−0.967773	−	0.251824i	$-0.918970\pi$
$461$		−	4985.15i		−	0.503647i	0.967773	−	0.251824i	$-0.0810303\pi$
$462$	−66.6875	−	180.702i	−0.00671555	−	0.0181970i
$463$		−	16925.5i		−	1.69891i	−0.527660	−	0.849456i	$-0.676931\pi$
$463$		−	16925.5i		−	1.69891i	0.527660	−	0.849456i	$-0.323069\pi$
$464$	10064.1	−	13191.9i	1.00692	−	1.31987i
$465$	−3273.91	−	902.314i	−0.326504	−	0.0899867i
$466$	−5783.71	−	8059.25i	−0.574946	−	0.801154i
$467$	12000.7			1.18914			0.594569	−	0.804045i	$-0.297323\pi$
$467$	12000.7			1.18914			0.594569	+	0.804045i	$0.297323\pi$
$468$	3571.09	−	3051.38i	0.352721	−	0.301390i
$469$	157.433			0.0155002
$470$	239.035	+	333.081i	0.0234593	+	0.0326891i
$471$	−7921.81	−	2183.31i	−0.774984	−	0.213591i
$472$	−2336.81	−	7645.71i	−0.227882	−	0.745598i
$473$			21513.2i			2.09129i
$474$	4498.73	+	12190.1i	0.435936	+	1.18125i
$475$			1927.94i			0.186232i
$476$	−33.9104	+	100.357i	−0.00326529	+	0.00966358i
$477$	4187.52	−	7019.85i	0.401957	−	0.673830i
$478$	15616.5	−	11207.1i	1.49431	−	1.07239i
$479$	8467.89			0.807741			0.403870	−	0.914816i	$-0.367665\pi$
$479$	8467.89			0.807741			0.403870	+	0.914816i	$0.367665\pi$
$480$	1381.58	−	4495.51i	0.131375	−	0.427482i
$481$	2548.81			0.241613
$482$	−2052.64	+	1473.07i	−0.193974	+	0.139205i
$483$	28.0498	−	101.775i	0.00264247	−	0.00958781i
$484$	4982.98	−	14747.0i	0.467973	−	1.38496i
$485$			1592.18i			0.149066i
$486$	8039.47	+	7082.24i	0.750366	+	0.661022i
$487$			16143.9i			1.50215i	0.660215	+	0.751076i	$0.270465\pi$
$487$			16143.9i			1.50215i	−0.660215	+	0.751076i	$0.729535\pi$
$488$	−3924.20	−	12839.4i	−0.364016	−	1.19101i
$489$	−682.517	+	2476.41i	−0.0631176	+	0.229013i
$490$	2827.78	+	3940.34i	0.260706	+	0.363279i
$491$	6839.84			0.628672			0.314336	−	0.949312i	$-0.398218\pi$
$491$	6839.84			0.628672			0.314336	+	0.949312i	$0.398218\pi$
$492$	−16403.0	−	11096.7i	−1.50306	−	1.01683i
$493$	−14994.4			−1.36980
$494$	−2765.58	−	3853.67i	−0.251881	−	0.350981i
$495$	3958.96	−	6636.70i	0.359479	−	0.602621i
$496$	5074.05	−	6651.02i	0.459337	−	0.602096i
$497$			119.662i			0.0108000i
$498$	−5389.55	+	1989.00i	−0.484963	+	0.178974i
$499$			3835.92i			0.344127i	0.985086	+	0.172064i	$0.0550435\pi$
$499$			3835.92i			0.344127i	−0.985086	+	0.172064i	$0.944957\pi$
$500$	−947.378	−	320.116i	−0.0847361	−	0.0286321i
$501$	11719.4	+	3229.94i	1.04508	+	0.288030i
$502$	2663.92	−	1911.76i	0.236846	−	0.169972i
$503$	−4049.88			−0.358997			−0.179498	−	0.983758i	$-0.557447\pi$
$503$	−4049.88			−0.358997			−0.179498	+	0.983758i	$0.557447\pi$
$504$	135.824	+	33.4171i	0.0120041	+	0.00295341i
$505$	18.3849			0.00162003
$506$	11672.8	−	8376.97i	1.02553	−	0.735971i
$507$	−8636.67	−	2380.33i	−0.756545	−	0.208509i
$508$	5631.07	+	1902.72i	0.491808	+	0.166180i
$509$		−	16263.7i		−	1.41626i	−0.706081	−	0.708131i	$-0.749539\pi$
$509$		−	16263.7i		−	1.41626i	0.706081	−	0.708131i	$-0.250461\pi$
$510$	−3987.18	+	1471.46i	−0.346187	+	0.127759i
$511$		−	265.679i		−	0.0229999i
$512$	9001.54	+	7293.15i	0.776984	+	0.629521i
$513$	7812.31	−	7485.00i	0.672363	−	0.644193i
$514$	−467.862	−	651.939i	−0.0401489	−	0.0559451i
$515$	308.055			0.0263583
$516$	−12939.8	−	8753.81i	−1.10396	−	0.746831i
$517$	−1659.46			−0.141166
$518$	44.2528	+	61.6637i	0.00375358	+	0.00523040i
$519$	3078.55	−	11170.1i	0.260373	−	0.944724i
$520$	2352.87	−	719.122i	0.198423	−	0.0606454i
$521$			2254.17i			0.189553i	0.995499	+	0.0947764i	$0.0302136\pi$
$521$			2254.17i			0.189553i	−0.995499	+	0.0947764i	$0.969786\pi$
$522$	1673.21	+	19728.1i	0.140296	+	1.65417i
$523$		−	13463.0i		−	1.12561i	−0.826589	−	0.562805i	$-0.809722\pi$
$523$		−	13463.0i		−	1.12561i	0.826589	−	0.562805i	$-0.190278\pi$
$524$	−1133.89	+	3355.74i	−0.0945313	+	0.279764i
$525$	7.90231	−	28.6724i	0.000656924	−	0.00238355i
$526$	−14912.9	+	10702.2i	−1.23618	+	0.887145i
$527$	−7559.77			−0.624875
$528$	11523.0	+	15152.7i	0.949763	+	1.24893i
$529$	−4292.32			−0.352784
$530$	3478.36	−	2496.24i	0.285076	−	0.204584i
$531$	8192.83	+	4887.24i	0.669564	+	0.399412i
$532$	45.2159	−	133.816i	0.00368488	−	0.0109053i
$533$		−	10360.1i		−	0.841927i
$534$	1373.47	+	3721.67i	0.111303	+	0.301596i
$535$		−	3606.94i		−	0.291480i
$536$	−14879.9	+	4547.83i	−1.19909	+	0.366486i
$537$	10661.0	+	2938.26i	0.856718	+	0.236118i
$538$	9729.41	+	13557.4i	0.779674	+	1.08643i
$539$	−19631.4			−1.56880
$540$	2380.92	+	5081.73i	0.189738	+	0.404968i
$541$	13062.7			1.03810			0.519049	−	0.854745i	$-0.326286\pi$
$541$	13062.7			1.03810			0.519049	+	0.854745i	$0.326286\pi$
$542$	−6863.00	−	9563.18i	−0.543895	−	0.757885i
$543$	−23615.1	−	6508.48i	−1.86633	−	0.514375i
$544$	305.998	−	10464.9i	0.0241168	−	0.824777i
$545$			963.991i			0.0757667i
$546$	25.3342	+	68.6475i	0.00198572	+	0.00538066i
$547$			17735.1i			1.38628i	0.720801	+	0.693142i	$0.243774\pi$
$547$			17735.1i			1.38628i	−0.720801	+	0.693142i	$0.756226\pi$
$548$	1509.09	+	509.916i	0.117637	+	0.0397492i
$549$	13758.2	+	8207.12i	1.06955	+	0.638017i
$550$	3288.51	−	2359.99i	0.254950	−	0.182964i
$551$	19993.4			1.54582
$552$	288.864	+	10429.6i	0.0222733	+	0.804189i
$553$	−202.417			−0.0155654
$554$	−5668.56	+	4068.03i	−0.434718	+	0.311975i
$555$	−809.092	+	2935.67i	−0.0618811	+	0.224527i
$556$	2680.18	+	905.625i	0.204433	+	0.0690774i
$557$		−	18970.1i		−	1.44307i	−0.692380	−	0.721533i	$-0.743438\pi$
$557$		−	18970.1i		−	1.44307i	0.692380	−	0.721533i	$-0.256562\pi$
$558$	843.589	+	9946.39i	0.0640000	+	0.754596i
$559$		−	8172.72i		−	0.618371i
$560$	58.2485	+	44.4376i	0.00439544	+	0.00335327i
$561$	4570.80	−	16584.5i	0.343992	−	1.24812i
$562$	1592.98	+	2219.72i	0.119565	+	0.166607i
$563$	13017.9			0.974489			0.487244	−	0.873266i	$-0.338002\pi$
$563$	13017.9			0.974489			0.487244	+	0.873266i	$0.338002\pi$
$564$	675.241	−	998.132i	0.0504127	−	0.0745194i
$565$	−7304.38			−0.543889
$566$	−3123.98	−	4353.09i	−0.231998	−	0.323276i
$567$	−146.865	+	79.2957i	−0.0108778	+	0.00587320i
$568$	−3456.73	−	11309.9i	−0.255354	−	0.835482i
$569$			4738.08i			0.349087i	0.984649	+	0.174544i	$0.0558450\pi$
$569$			4738.08i			0.349087i	−0.984649	+	0.174544i	$0.944155\pi$
$570$	5316.48	−	1962.03i	0.390672	−	0.144176i
$571$		−	16398.1i		−	1.20182i	−0.799317	−	0.600909i	$-0.794805\pi$
$571$		−	16398.1i		−	1.20182i	0.799317	−	0.600909i	$-0.205195\pi$
$572$	−3187.90	+	9434.54i	−0.233030	+	0.689647i
$573$	−18111.2	−	4991.56i	−1.32043	−	0.363919i
$574$	250.643	−	179.874i	0.0182259	−	0.0130798i
$575$	2218.49			0.160900
$576$	−13802.8	+	765.168i	−0.998467	+	0.0553507i
$577$	−15441.6			−1.11411			−0.557055	−	0.830476i	$-0.688069\pi$
$577$	−15441.6			−1.11411			−0.557055	+	0.830476i	$0.688069\pi$
$578$	3603.24	−	2585.86i	0.259299	−	0.186086i
$579$	5448.49	+	1501.64i	0.391073	+	0.107783i
$580$	−3319.71	+	9824.63i	−0.237661	+	0.703354i
$581$		−	89.4936i		−	0.00639040i
$582$	4390.58	−	1620.33i	0.312707	−	0.115404i
$583$			17329.7i			1.23109i
$584$	7674.76	+	25110.7i	0.543808	+	1.77926i
$585$	−1503.98	+	2521.24i	−0.106294	+	0.178189i
$586$	−13012.2	−	18131.7i	−0.917283	−	1.27818i
$587$	8969.18			0.630661			0.315330	−	0.948982i	$-0.397885\pi$
$587$	8969.18			0.630661			0.315330	+	0.948982i	$0.397885\pi$
$588$	7988.08	−	11807.9i	0.560243	−	0.828144i
$589$	10080.2			0.705171
$590$	2913.35	+	4059.58i	0.203289	+	0.283272i
$591$	2548.36	−	9246.35i	0.177370	−	0.643560i
$592$	−5963.88	−	4549.82i	−0.414044	−	0.315873i
$593$		−	23461.9i		−	1.62473i	−0.583147	−	0.812367i	$-0.698179\pi$
$593$		−	23461.9i		−	1.62473i	0.583147	−	0.812367i	$-0.301821\pi$
$594$	−22330.3	−	4163.16i	−1.54246	−	0.287570i
$595$		−	66.2072i		−	0.00456173i
$596$	−11728.0	−	3962.87i	−0.806039	−	0.272358i
$597$	−4151.73	+	15064.0i	−0.284622	+	1.03271i
$598$	−4434.42	+	3182.35i	−0.303239	+	0.217619i
$599$	20679.5			1.41058			0.705292	−	0.708917i	$-0.250816\pi$
$599$	20679.5			1.41058			0.705292	+	0.708917i	$0.250816\pi$
$600$	81.3797	+	2938.26i	0.00553719	+	0.199923i
$601$	−6106.70			−0.414472			−0.207236	−	0.978291i	$-0.566447\pi$
$601$	−6106.70			−0.414472			−0.207236	+	0.978291i	$0.566447\pi$
$602$	197.723	−	141.896i	0.0133864	−	0.00960671i
$603$	9511.41	−	15944.7i	0.642346	−	1.07681i
$604$	21061.7	+	7116.68i	1.41885	+	0.479426i
$605$			9728.84i			0.653775i
$606$	−18.7099	−	50.6980i	−0.00125419	−	0.00339846i
$607$		−	7949.25i		−	0.531549i	−0.964035	−	0.265775i	$-0.914372\pi$
$607$		−	7949.25i		−	0.531549i	0.964035	−	0.265775i	$-0.0856277\pi$
$608$	−408.016	+	13953.8i	−0.0272158	+	0.930760i
$609$	−297.342	−	81.9496i	−0.0197847	−	0.00545282i
$610$	4892.38	+	6817.24i	0.324732	+	0.452495i
$611$	630.418			0.0417414
$612$	8115.36	+	9497.54i	0.536020	+	0.627313i
$613$	−21910.3			−1.44364			−0.721818	−	0.692082i	$-0.756693\pi$
$613$	−21910.3			−1.44364			−0.721818	+	0.692082i	$0.756693\pi$
$614$	12988.5	+	18098.8i	0.853705	+	1.18959i
$615$	11932.6	+	3288.70i	0.782387	+	0.215632i
$616$	−283.599	+	86.6784i	−0.0185496	+	0.00566943i
$617$		−	8096.89i		−	0.528312i	−0.964480	−	0.264156i	$-0.914907\pi$
$617$		−	8096.89i		−	0.528312i	0.964480	−	0.264156i	$-0.0850933\pi$
$618$	−313.503	−	849.492i	−0.0204060	−	0.0552938i
$619$			397.882i			0.0258356i	0.999917	+	0.0129178i	$0.00411197\pi$
$619$			397.882i			0.0258356i	−0.999917	+	0.0129178i	$0.995888\pi$
$620$	−1673.71	+	4953.32i	−0.108416	+	0.320855i
$621$	−8613.00	−	8989.64i	−0.556566	−	0.580905i
$622$	−2304.34	+	1653.71i	−0.148546	+	0.106604i
$623$	−61.7984			−0.00397416
$624$	−4377.52	−	5756.41i	−0.280835	−	0.369296i
$625$	625.000			0.0400000
$626$	−2735.85	+	1963.38i	−0.174675	+	0.125355i
$627$	−6094.68	+	22113.7i	−0.388195	+	1.40851i
$628$	−4049.84	+	11985.4i	−0.257335	+	0.761578i
$629$			6778.74i			0.429708i
$630$	−87.1088	+	7.38801i	−0.00550873	+	0.000467215i
$631$			24459.5i			1.54313i	0.636148	+	0.771567i	$0.280527\pi$
$631$			24459.5i			1.54313i	−0.636148	+	0.771567i	$0.719473\pi$
$632$	19131.6	−	5847.31i	1.20413	−	0.368027i
$633$	3504.50	−	12715.6i	0.220050	−	0.798418i
$634$	−2258.40	−	3146.95i	−0.141471	−	0.197132i
$635$	−3714.90			−0.232160
$636$	−10423.5	−	7051.53i	−0.649871	−	0.439641i
$637$	7457.83			0.463877
$638$	−24473.9	−	34102.9i	−1.51870	−	2.11622i
$639$	12119.3	+	7229.45i	0.750282	+	0.447563i
$640$	−6789.07	−	2517.39i	−0.419315	−	0.155482i
$641$			16377.9i			1.00919i	0.863357	+	0.504594i	$0.168358\pi$
$641$			16377.9i			1.00919i	−0.863357	+	0.504594i	$0.831642\pi$
$642$	−9946.47	+	3670.72i	−0.611458	+	0.225657i
$643$			9971.27i			0.611553i	0.952103	+	0.305776i	$0.0989160\pi$
$643$			9971.27i			0.611553i	−0.952103	+	0.305776i	$0.901084\pi$
$644$	−153.982	−	52.0300i	−0.00942195	−	0.00318365i
$645$	9413.18	+	2594.34i	0.574641	+	0.158375i
$646$	10249.1	−	7355.24i	0.624218	−	0.447969i
$647$	−8134.31			−0.494270			−0.247135	−	0.968981i	$-0.579489\pi$
$647$	−8134.31			−0.494270			−0.247135	+	0.968981i	$0.579489\pi$
$648$	11590.3	−	11737.2i	0.702641	−	0.711545i
$649$	−20225.4			−1.22329
$650$	−1249.28	+	896.544i	−0.0753860	+	0.0541006i
$651$	−149.912	−	41.3169i	−0.00902538	−	0.00248746i
$652$	3746.73	+	1266.01i	0.225051	+	0.0760441i
$653$			26326.4i			1.57769i	0.614591	+	0.788846i	$0.289321\pi$
$653$			26326.4i			1.57769i	−0.614591	+	0.788846i	$0.710679\pi$
$654$	2658.30	−	981.037i	0.158941	−	0.0586568i
$655$		−	2213.83i		−	0.132064i
$656$	−18493.6	+	24241.3i	−1.10069	+	1.44278i
$657$	−26907.7	−	16051.1i	−1.59782	−	0.953141i
$658$	10.9454	+	15.2518i	0.000648473	+	0.000903610i
$659$	−27981.8			−1.65404			−0.827022	−	0.562170i	$-0.809967\pi$
$659$	−27981.8			−1.65404			−0.827022	+	0.562170i	$0.809967\pi$
$660$	−9854.55	−	6666.65i	−0.581194	−	0.393180i
$661$	19315.6			1.13660			0.568298	−	0.822823i	$-0.307602\pi$
$661$	19315.6			1.13660			0.568298	+	0.822823i	$0.307602\pi$
$662$	−7038.85	−	9808.22i	−0.413252	−	0.575842i
$663$	−1736.42	+	6300.34i	−0.101715	+	0.369057i
$664$	2585.24	+	8458.53i	0.151094	+	0.494360i
$665$			88.2802i			0.00514791i
$666$	8918.79	−	756.434i	0.518913	−	0.0440109i
$667$		−	23006.4i		−	1.33555i
$668$	5991.26	−	17731.0i	0.347019	−	1.02700i
$669$	−5817.91	+	21109.5i	−0.336224	+	1.21994i
$670$	7900.64	−	5669.88i	0.455565	−	0.326935i
$671$	−33964.5			−1.95408
$672$	63.2624	−	205.849i	0.00363155	−	0.0118167i
$673$	22871.2			1.30998			0.654992	−	0.755636i	$-0.272672\pi$
$673$	22871.2			1.30998			0.654992	+	0.755636i	$0.272672\pi$
$674$	6907.23	−	4956.96i	0.394743	−	0.283286i
$675$	−2426.49	−	2532.59i	−0.138364	−	0.144414i
$676$	−4415.30	+	13067.0i	−0.251212	+	0.743457i
$677$		−	8049.33i		−	0.456958i	−0.973549	−	0.228479i	$-0.926625\pi$
$677$		−	8049.33i		−	0.456958i	0.973549	−	0.228479i	$-0.0733753\pi$
$678$	7433.54	+	20142.5i	0.421067	+	1.14096i
$679$			72.9056i			0.00412056i
$680$	1912.55	+	6257.61i	0.107857	+	0.352894i
$681$	−16634.5	−	4584.59i	−0.936030	−	0.257977i
$682$	−12339.1	−	17193.8i	−0.692799	−	0.965374i
$683$	−3935.14			−0.220460			−0.110230	−	0.993906i	$-0.535159\pi$
$683$	−3935.14			−0.220460			−0.110230	+	0.993906i	$0.535159\pi$
$684$	−10821.0	−	12664.0i	−0.604898	−	0.707922i
$685$	−995.569			−0.0555310
$686$	258.987	+	360.883i	0.0144142	+	0.0200854i
$687$	14193.2	+	3911.74i	0.788214	+	0.217237i
$688$	−14588.9	+	19123.1i	−0.808427	+	1.05968i
$689$		−	6583.44i		−	0.364019i
$690$	−2257.71	−	6117.68i	−0.124565	−	0.337531i
$691$		−	20215.6i		−	1.11294i	−0.830869	−	0.556468i	$-0.812156\pi$
$691$		−	20215.6i		−	1.11294i	0.830869	−	0.556468i	$-0.187844\pi$
$692$	−16899.9	−	5710.44i	−0.928381	−	0.313697i
$693$	181.280	−	303.894i	0.00993690	−	0.0166580i
$694$	1542.12	−	1106.70i	0.0843487	−	0.0605327i
$695$	−1768.16			−0.0965036
$696$	30470.8	−	843.935i	1.65947	−	0.0459616i
$697$	27553.5			1.49736
$698$	−17329.8	+	12436.7i	−0.939743	+	0.674405i
$699$	4842.09	−	17568.8i	0.262010	−	0.950664i
$700$	−43.3804	−	14.6581i	−0.00234232	−	0.000791462i
$701$			665.960i			0.0358815i	0.999839	+	0.0179408i	$0.00571103\pi$
$701$			665.960i			0.0358815i	−0.999839	+	0.0179408i	$0.994289\pi$
$702$	8483.12	+	1581.56i	0.456089	+	0.0850313i
$703$		−	9038.73i		−	0.484925i
$704$	24300.6	−	16384.9i	1.30094	−	0.877172i
$705$	−200.119	+	726.103i	−0.0106907	+	0.0387895i
$706$	6501.53	+	9059.50i	0.346584	+	0.482944i
$707$	0.841841			4.47817e−5
$708$	8229.81	−	12165.2i	0.436858	−	0.645757i
$709$	30035.9			1.59101			0.795503	−	0.605949i	$-0.207207\pi$
$709$	30035.9			1.59101			0.795503	+	0.605949i	$0.207207\pi$
$710$	4309.57	+	6005.14i	0.227796	+	0.317421i
$711$	−12229.1	+	20500.6i	−0.645047	+	1.08134i
$712$	5840.91	−	1785.20i	0.307440	−	0.0939650i
$713$		−	11599.2i		−	0.609250i
$714$	−182.573	+	67.3779i	−0.00956947	+	0.00353159i
$715$		−	6224.11i		−	0.325550i
$716$	5450.21	−	16129.8i	0.284475	−	0.841898i
$717$	34043.2	+	9382.54i	1.77317	+	0.488699i
$718$	13067.5	−	9377.84i	0.679211	−	0.487434i
$719$	7654.14			0.397012			0.198506	−	0.980100i	$-0.436391\pi$
$719$	7654.14			0.397012			0.198506	+	0.980100i	$0.436391\pi$
$720$	8019.71	−	3214.63i	0.415107	−	0.166392i
$721$	14.1058			0.000728611
$722$	2095.40	−	1503.76i	0.108009	−	0.0775127i
$723$	−4474.67	−	1233.25i	−0.230173	−	0.0634372i
$724$	−12072.7	+	35728.8i	−0.619719	+	1.83405i
$725$		−	6481.46i		−	0.332021i
$726$	26828.2	−	9900.87i	1.37147	−	0.506137i
$727$		−	14810.2i		−	0.755545i	−0.925898	−	0.377772i	$-0.876690\pi$
$727$		−	14810.2i		−	0.755545i	0.925898	−	0.377772i	$-0.123310\pi$
$728$	107.737	−	32.9285i	0.00548491	−	0.00167639i
$729$	−841.915	+	19665.0i	−0.0427737	+	0.999085i
$730$	−9568.28	−	13332.8i	−0.485121	−	0.675987i
$731$	21735.9			1.09977
$732$	13820.3	−	20429.0i	0.697831	−	1.03153i
$733$	4598.62			0.231724			0.115862	−	0.993265i	$-0.463037\pi$
$733$	4598.62			0.231724			0.115862	+	0.993265i	$0.463037\pi$
$734$	−5582.52	−	7778.91i	−0.280728	−	0.391178i
$735$	−2367.40	+	8589.77i	−0.118807	+	0.431073i
$736$	16056.7	+	469.504i	0.804154	+	0.0235138i
$737$			39362.2i			1.96733i
$738$	−3074.67	−	36252.1i	−0.153361	−	1.80821i
$739$			25698.2i			1.27919i	0.768711	+	0.639597i	$0.220899\pi$
$739$			25698.2i			1.27919i	−0.768711	+	0.639597i	$0.779101\pi$
$740$	4441.57	+	1500.79i	0.220643	+	0.0745544i
$741$	2315.33	−	8400.83i	0.114785	−	0.416481i
$742$	159.274	−	114.302i	0.00788022	−	0.00565522i
$743$	−19187.9			−0.947421			−0.473711	−	0.880681i	$-0.657086\pi$
$743$	−19187.9			−0.947421			−0.473711	+	0.880681i	$0.657086\pi$
$744$	15362.6	−	425.490i	0.757015	−	0.0209667i
$745$	7737.17			0.380494
$746$	20099.3	−	14424.2i	0.986446	−	0.707921i
$747$	−9063.82	−	5406.80i	−0.443946	−	0.264825i
$748$	−25091.8	−	8478.44i	−1.22653	−	0.414442i
$749$		−	165.161i		−	0.00805723i
$750$	−636.051	−	1723.50i	−0.0309671	−	0.0839109i
$751$		−	1567.14i		−	0.0761462i	−0.999275	−	0.0380731i	$-0.987878\pi$
$751$		−	1567.14i		−	0.0761462i	0.999275	−	0.0380731i	$-0.0121220\pi$
$752$	−1475.09	−	1125.34i	−0.0715307	−	0.0545705i
$753$	5807.23	+	1600.51i	0.281046	+	0.0774582i
$754$	9297.47	+	12955.5i	0.449063	+	0.625743i
$755$	−13894.7			−0.669775
$756$	109.022	+	232.692i	0.00524484	+	0.0111943i
$757$	−21515.7			−1.03302			−0.516512	−	0.856280i	$-0.672770\pi$
$757$	−21515.7			−1.03302			−0.516512	+	0.856280i	$0.672770\pi$
$758$	3612.43	+	5033.71i	0.173099	+	0.241204i
$759$	25446.2	+	7013.16i	1.21692	+	0.335391i
$760$	−2550.19	−	8343.85i	−0.121717	−	0.398241i
$761$			6568.94i			0.312909i	0.987685	+	0.156455i	$0.0500065\pi$
$761$			6568.94i			0.312909i	−0.987685	+	0.156455i	$0.949994\pi$
$762$	3780.59	+	10244.2i	0.179733	+	0.487018i
$763$			44.1411i			0.00209438i
$764$	−9258.91	+	27401.6i	−0.438450	+	1.29758i
$765$	−6705.40	−	3999.94i	−0.316907	−	0.189043i
$766$	−19620.3	+	14080.5i	−0.925470	+	0.664161i
$767$	7683.51			0.361715
$768$	−32.8323	+	21283.4i	−0.00154262	+	0.999999i
$769$	12276.5			0.575685			0.287842	−	0.957678i	$-0.407062\pi$
$769$	12276.5			0.575685			0.287842	+	0.957678i	$0.407062\pi$
$770$	150.580	−	108.064i	0.00704746	−	0.00505759i
$771$	391.692	−	1421.20i	0.0182963	−	0.0663855i
$772$	2785.41	−	8243.39i	0.129857	−	0.384308i
$773$			18877.9i			0.878384i	0.898393	+	0.439192i	$0.144735\pi$
$773$			18877.9i			0.878384i	−0.898393	+	0.439192i	$0.855265\pi$
$774$	−2425.49	−	28597.9i	−0.112639	−	1.32808i
$775$		−	3267.78i		−	0.151461i
$776$	−2106.05	−	6890.71i	−0.0974265	−	0.318766i
$777$	−37.0482	+	134.424i	−0.00171055	+	0.00620648i
$778$	−4382.83	−	6107.22i	−0.201969	−	0.281433i
$779$	−36739.6			−1.68977
$780$	3743.68	+	2532.62i	0.171853	+	0.116259i
$781$	−29918.5			−1.37077
$782$	−8463.68	−	11793.6i	−0.387034	−	0.539309i
$783$	−26263.9	+	25163.5i	−1.19871	+	1.14849i
$784$	−17450.3	−	13312.8i	−0.794930	−	0.606450i
$785$		−	7906.97i		−	0.359506i
$786$	−6104.85	+	2252.98i	−0.277039	+	0.102241i
$787$		−	42886.2i		−	1.94248i	−0.238111	−	0.971238i	$-0.576528\pi$
$787$		−	42886.2i		−	1.94248i	0.238111	−	0.971238i	$-0.423472\pi$
$788$	−13989.4	−	4726.98i	−0.632427	−	0.213695i
$789$	−32509.5	−	8959.84i	−1.46688	−	0.404282i
$790$	−10158.1	+	7289.96i	−0.457481	+	0.328310i
$791$	−334.467			−0.0150345
$792$	−8355.11	+	33959.4i	−0.374856	+	1.52360i
$793$	12902.9			0.577799
$794$	6058.07	−	4347.56i	0.270772	−	0.194319i
$795$	7582.68	+	2089.84i	0.338277	+	0.0932314i
$796$	22791.3	+	7701.10i	1.01484	+	0.342912i
$797$			7388.90i			0.328392i	0.986428	+	0.164196i	$0.0525029\pi$
$797$			7388.90i			0.328392i	−0.986428	+	0.164196i	$0.947497\pi$
$798$	243.441	−	89.8412i	0.0107991	−	0.00398540i
$799$			1676.64i			0.0742368i
$800$	4523.55	+	132.271i	0.199915	+	0.00584559i
$801$	−3733.59	+	6258.88i	−0.164694	+	0.276088i
$802$	1534.57	+	2138.34i	0.0675657	+	0.0941488i
$803$	66426.2			2.91922
$804$	−23675.6	−	16016.6i	−1.03852	−	0.702566i
$805$	101.584			0.00444767
$806$	4687.54	+	6531.81i	0.204853	+	0.285451i
$807$	−8145.42	+	29554.5i	−0.355307	+	1.28918i
$808$	−79.5670	+	24.3186i	−0.00346430	+	0.00105882i
$809$		−	13228.2i		−	0.574882i	−0.957798	−	0.287441i	$-0.907195\pi$
$809$		−	13228.2i		−	0.574882i	0.957798	−	0.287441i	$-0.0928045\pi$
$810$	−4514.47	+	9268.64i	−0.195830	+	0.402058i
$811$		−	4361.33i		−	0.188837i	−0.995533	−	0.0944186i	$-0.969901\pi$
$811$		−	4361.33i		−	0.188837i	0.995533	−	0.0944186i	$-0.0300992\pi$
$812$	−152.009	+	449.869i	−0.00656956	+	0.0194425i
$813$	5745.67	−	20847.3i	0.247859	−	0.899321i
$814$	−15417.4	+	11064.3i	−0.663859	+	0.476417i
$815$	−2471.78			−0.106236
$816$	15309.6	−	11642.3i	0.656791	−	0.499463i
$817$	−28982.5			−1.24109
$818$	4239.63	−	3042.56i	0.181217	−	0.130050i
$819$	−68.8672	+	115.447i	−0.00293824	+	0.00492558i
$820$	6100.26	−	18053.6i	0.259793	−	0.768853i
$821$		−	1863.03i		−	0.0791965i	−0.999216	−	0.0395982i	$-0.987392\pi$
$821$		−	1863.03i		−	0.0791965i	0.999216	−	0.0395982i	$-0.0126078\pi$
$822$	1013.17	+	2745.37i	0.0429908	+	0.116491i
$823$			32302.6i			1.36816i	0.729405	+	0.684082i	$0.239797\pi$
$823$			32302.6i			1.36816i	−0.729405	+	0.684082i	$0.760203\pi$
$824$	−1333.22	+	407.481i	−0.0563652	+	0.0172273i
$825$	7168.81	+	1975.77i	0.302528	+	0.0833789i
$826$	133.402	+	185.888i	0.00561943	+	0.00783034i
$827$	−1818.09			−0.0764464			−0.0382232	−	0.999269i	$-0.512170\pi$
$827$	−1818.09			−0.0764464			−0.0382232	+	0.999269i	$0.512170\pi$
$828$	−14572.4	+	12451.7i	−0.611627	+	0.522617i
$829$	−13254.4			−0.555300			−0.277650	−	0.960682i	$-0.589556\pi$
$829$	−13254.4			−0.555300			−0.277650	+	0.960682i	$0.589556\pi$
$830$	−3223.07	−	4491.16i	−0.134788	−	0.187820i
$831$	−12357.2	−	3405.73i	−0.515845	−	0.142170i
$832$	−9231.64	+	6224.51i	−0.384675	+	0.259370i
$833$			19834.6i			0.825003i
$834$	1799.42	+	4875.86i	0.0747109	+	0.202443i
$835$			11697.4i			0.484798i
$836$	33457.2	+	11305.1i	1.38414	+	0.467697i
$837$	−13241.6	+	12686.8i	−0.546828	+	0.523918i
$838$	−8958.20	+	6428.83i	−0.369279	+	0.265012i
$839$	12276.7			0.505170			0.252585	−	0.967575i	$-0.418719\pi$
$839$	12276.7			0.505170			0.252585	+	0.967575i	$0.418719\pi$
$840$	3.72637	+	134.543i	0.000153062	+	0.00552638i
$841$	−42825.9			−1.75595
$842$	−2823.42	+	2026.22i	−0.115560	+	0.0829314i
$843$	−1333.63	+	4838.89i	−0.0544872	+	0.197699i
$844$	−19238.2	−	6500.54i	−0.784606	−	0.265116i
$845$		−	8620.50i		−	0.350952i
$846$	2205.95	−	187.095i	0.0896480	−	0.00760337i
$847$			445.483i			0.0180720i
$848$	−11751.9	+	15404.4i	−0.475900	+	0.623807i
$849$	2615.39	−	9489.55i	0.105724	−	0.383605i
$850$	−2384.42	−	3322.55i	−0.0962176	−	0.134074i
$851$	−10400.9			−0.418963
$852$	12174.0	−	17995.4i	0.489522	−	0.723605i
$853$	45559.3			1.82875			0.914374	−	0.404870i	$-0.132683\pi$
$853$	45559.3			1.82875			0.914374	+	0.404870i	$0.132683\pi$
$854$	224.021	+	312.161i	0.00897641	+	0.0125081i
$855$	8940.93	+	5333.50i	0.357630	+	0.213335i
$856$	4771.08	+	15610.3i	0.190505	+	0.623305i
$857$		−	31339.9i		−	1.24919i	−0.780951	−	0.624593i	$-0.785265\pi$
$857$		−	31339.9i		−	1.24919i	0.780951	−	0.624593i	$-0.214735\pi$
$858$	−17163.6	+	6334.17i	−0.682931	+	0.252034i
$859$		−	13141.9i		−	0.521997i	−0.965339	−	0.260999i	$-0.915948\pi$
$859$		−	13141.9i		−	0.521997i	0.965339	−	0.260999i	$-0.0840518\pi$
$860$	4812.27	−	14241.8i	0.190810	−	0.564700i
$861$	546.392	+	150.589i	0.0216272	+	0.00596060i
$862$	−20970.4	+	15049.3i	−0.828600	+	0.594643i
$863$	32243.9			1.27184			0.635919	−	0.771756i	$-0.280621\pi$
$863$	32243.9			1.27184			0.635919	+	0.771756i	$0.280621\pi$
$864$	−17026.2	−	18843.6i	−0.670419	−	0.741983i
$865$	11149.2			0.438246
$866$	−27939.8	+	20051.0i	−1.09634	+	0.786789i
$867$	7854.91	+	2164.87i	0.307689	+	0.0848014i
$868$	−76.6391	+	226.812i	−0.00299689	+	0.00886925i
$869$		−	50609.3i		−	1.97561i
$870$	−17873.2	+	6596.07i	−0.696505	+	0.257043i
$871$		−	14953.4i		−	0.581720i
$872$	−1275.12	−	4172.01i	−0.0495195	−	0.162021i
$873$	7383.81	+	4404.63i	0.286259	+	0.170761i
$874$	11285.4	+	15725.6i	0.436768	+	0.608610i
$875$	28.6187			0.00110570
$876$	−27029.1	+	39954.0i	−1.04250	+	1.54101i
$877$	−6634.43			−0.255449			−0.127724	−	0.991810i	$-0.540767\pi$
$877$	−6634.43			−0.255449			−0.127724	+	0.991810i	$0.540767\pi$
$878$	8605.11	+	11990.7i	0.330761	+	0.460896i
$879$	10893.7	−	39526.3i	0.418016	−	1.51671i
$880$	−11110.5	+	14563.6i	−0.425608	+	0.557884i
$881$		−	4909.32i		−	0.187740i	−0.995584	−	0.0938701i	$-0.970076\pi$
$881$		−	4909.32i		−	0.187740i	0.995584	−	0.0938701i	$-0.0299239\pi$
$882$	26096.4	−	2213.33i	0.996270	−	0.0844972i
$883$		−	26840.7i		−	1.02295i	−0.859299	−	0.511473i	$-0.829100\pi$
$883$		−	26840.7i		−	1.02295i	0.859299	−	0.511473i	$-0.170900\pi$
$884$	9532.20	+	3220.90i	0.362673	+	0.122546i
$885$	−2439.04	+	8849.71i	−0.0926412	+	0.336135i
$886$	6185.97	−	4439.35i	0.234562	−	0.168333i
$887$	26485.8			1.00260			0.501300	−	0.865273i	$-0.332855\pi$
$887$	26485.8			1.00260			0.501300	+	0.865273i	$0.332855\pi$
$888$	−381.531	−	13775.4i	−0.0144182	−	0.520576i
$889$	−170.105			−0.00641748
$890$	−3101.30	+	2225.64i	−0.116804	+	0.0838243i
$891$	−19825.9	−	36719.8i	−0.745446	−	1.38065i
$892$	31937.9	+	10791.7i	1.19883	+	0.405082i
$893$		−	2235.62i		−	0.0837762i
$894$	−7873.98	−	21336.0i	−0.294570	−	0.798190i
$895$			10641.1i			0.397421i
$896$	−310.871	−	115.271i	−0.0115909	−	0.00429793i
$897$	−9666.85	−	2664.25i	−0.359829	−	0.0991714i
$898$	10372.3	+	14453.2i	0.385442	+	0.537091i
$899$	−33888.0			−1.25721
$900$	−4105.40	+	3507.94i	−0.152052	+	0.129924i
$901$	17509.1			0.647406
$902$	44972.9	+	62667.1i	1.66013	+	2.31329i
$903$	431.028	+	118.794i	0.0158845	+	0.00437789i
$904$	31612.3	−	9661.88i	1.16306	−	0.355475i
$905$		−	23570.8i		−	0.865769i
$906$	14140.4	+	38316.0i	0.518525	+	1.40504i
$907$			10971.0i			0.401639i	0.979628	+	0.200819i	$0.0643604\pi$
$907$			10971.0i			0.401639i	−0.979628	+	0.200819i	$0.935640\pi$
$908$	−8504.02	+	25167.5i	−0.310810	+	0.919838i
$909$	50.8603	−	85.2608i	0.00185581	−	0.00311102i
$910$	−57.2045	+	41.0527i	−0.00208386	+	0.00149548i
$911$	24590.7			0.894320			0.447160	−	0.894454i	$-0.352436\pi$
$911$	24590.7			0.894320			0.447160	+	0.894454i	$0.352436\pi$
$912$	−20413.7	+	15523.8i	−0.741189	+	0.563644i
$913$	22375.6			0.811090
$914$	18501.2	−	13277.3i	0.669545	−	0.480497i
$915$	−4095.88	+	14861.3i	−0.147984	+	0.536939i
$916$	7255.93	−	21473.8i	0.261728	−	0.774579i
$917$		−	101.371i		−	0.00365057i
$918$	−4206.25	+	22561.4i	−0.151228	+	0.811153i
$919$			11889.9i			0.426781i	0.976967	+	0.213391i	$0.0684507\pi$
$919$			11889.9i			0.426781i	−0.976967	+	0.213391i	$0.931549\pi$
$920$	−9601.28	+	2934.50i	−0.344071	+	0.105161i
$921$	−10874.0	+	39454.6i	−0.389043	+	1.41159i
$922$	−8221.01	−	11455.5i	−0.293649	−	0.409183i
$923$	11365.8			0.405321
$924$	−451.239	−	305.265i	−0.0160657	−	0.0108685i
$925$	−2930.17			−0.104155
$926$	−27911.9	−	38893.6i	−0.990542	−	1.38026i
$927$	852.211	−	1428.62i	0.0301945	−	0.0506172i
$928$	1371.69	−	46910.7i	0.0485215	−	1.65940i
$929$		−	28847.8i		−	1.01880i	−0.860530	−	0.509400i	$-0.829867\pi$
$929$		−	28847.8i		−	1.01880i	0.860530	−	0.509400i	$-0.170133\pi$
$930$	−9011.22	+	3325.57i	−0.317731	+	0.117258i
$931$		−	26447.3i		−	0.931016i
$932$	−26581.1	−	8981.66i	−0.934218	−	0.315669i
$933$	−5023.37	−	1384.48i	−0.176268	−	0.0485806i
$934$	27576.8	−	19790.4i	0.966103	−	0.693321i
$935$	16553.4			0.578990
$936$	3174.05	−	12900.9i	0.110841	−	0.450513i
$937$	27252.7			0.950169			0.475084	−	0.879940i	$-0.342418\pi$
$937$	27252.7			0.950169			0.475084	+	0.879940i	$0.342418\pi$
$938$	361.770	−	259.623i	0.0125930	−	0.00903731i
$939$	−5964.03	−	1643.73i	−0.207273	−	0.0571258i
$940$	1098.57	+	371.203i	0.0381185	+	0.0128801i
$941$			14420.4i			0.499567i	0.968302	+	0.249784i	$0.0803595\pi$
$941$			14420.4i			0.499567i	−0.968302	+	0.249784i	$0.919640\pi$
$942$	−21804.2	+	8046.79i	−0.754161	+	0.278321i
$943$			42276.3i			1.45992i
$944$	−17978.4	−	13715.6i	−0.619858	−	0.472888i
$945$	−111.109	−	115.967i	−0.00382472	−	0.00399197i
$946$	35477.5	+	49435.8i	1.21931	+	1.69904i
$947$	−17702.9			−0.607464			−0.303732	−	0.952757i	$-0.598233\pi$
$947$	−17702.9			−0.607464			−0.303732	+	0.952757i	$0.598233\pi$
$948$	30440.5	+	20593.1i	1.04289	+	0.705521i
$949$	−25234.9			−0.863181
$950$	3179.37	+	4430.27i	0.108581	+	0.151302i
$951$	1890.73	−	6860.22i	0.0644700	−	0.233920i
$952$	87.5756	+	286.535i	0.00298145	+	0.00975489i
$953$			6694.50i			0.227551i	0.993506	+	0.113776i	$0.0362945\pi$
$953$			6694.50i			0.227551i	−0.993506	+	0.113776i	$0.963706\pi$
$954$	−1953.83	−	23036.7i	−0.0663077	−	0.781805i
$955$		−	18077.2i		−	0.612530i
$956$	17403.8	−	51506.2i	0.588785	−	1.74250i
$957$	20489.4	−	74342.9i	0.692089	−	2.51114i
$958$	19458.6	−	13964.4i	0.656240	−	0.470949i
$959$	−45.5870			−0.00153502
$960$	−4238.79	−	12608.7i	−0.142507	−	0.423901i
$961$	12705.5			0.426489
$962$	5856.98	−	4203.25i	0.196296	−	0.140871i
$963$	−16727.4	−	9978.31i	−0.559743	−	0.333901i
$964$	−2287.57	+	6770.03i	−0.0764292	+	0.226191i
$965$			5438.29i			0.181414i
$966$	−103.380	−	280.128i	−0.00344328	−	0.00933020i
$967$			20929.0i			0.696001i	0.937494	+	0.348000i	$0.113139\pi$
$967$			20929.0i			0.696001i	−0.937494	+	0.348000i	$0.886861\pi$
$968$	−12868.8	−	42105.0i	−0.427294	−	1.39804i
$969$	22342.6	+	6157.77i	0.740709	+	0.204145i
$970$	2625.66	+	3658.71i	0.0869123	+	0.121107i
$971$	44371.6			1.46648			0.733241	−	0.679969i	$-0.238007\pi$
$971$	44371.6			1.46648			0.733241	+	0.679969i	$0.238007\pi$
$972$	30153.4	+	3016.55i	0.995033	+	0.0995432i
$973$	−80.9637			−0.00266760
$974$	26622.9	+	37097.4i	0.875823	+	1.22041i
$975$	−2723.38	−	750.583i	−0.0894544	−	0.0246543i
$976$	−30191.0	−	23032.6i	−0.990154	−	0.755386i
$977$			44186.1i			1.44692i	0.690368	+	0.723458i	$0.257449\pi$
$977$			44186.1i			1.44692i	−0.690368	+	0.723458i	$0.742551\pi$
$978$	2515.48	+	6816.16i	0.0822457	+	0.222860i
$979$		−	15451.1i		−	0.504413i
$980$	12996.0	+	4391.32i	0.423616	+	0.143138i
$981$	4470.56	+	2666.81i	0.145499	+	0.0867936i
$982$	15717.5	−	11279.6i	0.510758	−	0.366544i
$983$	−47946.8			−1.55571			−0.777856	−	0.628442i	$-0.783693\pi$
$983$	−47946.8			−1.55571			−0.777856	+	0.628442i	$0.783693\pi$
$984$	−55992.6	+	1550.80i	−1.81400	+	0.0502417i
$985$	9229.03			0.298540
$986$	−34456.0	+	24727.2i	−1.11288	+	0.798657i
$987$	−9.16343	+	33.2482i	−0.000295517	+	0.00107224i
$988$	−12710.2	−	4294.73i	−0.409276	−	0.138293i
$989$			33350.2i			1.07227i
$990$	−1847.19	−	21779.4i	−0.0593004	−	0.699186i
$991$			29612.3i			0.949209i	0.880199	+	0.474605i	$0.157409\pi$
$991$			29612.3i			0.949209i	−0.880199	+	0.474605i	$0.842591\pi$
$992$	691.571	−	23651.2i	0.0221345	−	0.756981i
$993$	5892.89	−	21381.5i	0.188324	−	0.683305i
$994$	197.335	+	274.975i	0.00629687	+	0.00877432i
$995$	−15035.8			−0.479061
$996$	−9104.73	+	13458.5i	−0.289653	+	0.428161i
$997$	−50768.6			−1.61270			−0.806348	−	0.591442i	$-0.798559\pi$
$997$	−50768.6			−1.61270			−0.806348	+	0.591442i	$0.798559\pi$
$998$	6325.82	+	8814.67i	0.200642	+	0.279583i
$999$	11376.0	+	11873.5i	0.360283	+	0.376037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.19	yes	24
3.2	odd	2	inner	60.4.e.a.11.6	yes	24
4.3	odd	2	inner	60.4.e.a.11.5	✓	24
8.3	odd	2		960.4.h.d.191.22		24
8.5	even	2		960.4.h.d.191.3		24
12.11	even	2	inner	60.4.e.a.11.20	yes	24
24.5	odd	2		960.4.h.d.191.21		24
24.11	even	2		960.4.h.d.191.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.5	✓	24	4.3	odd	2	inner
60.4.e.a.11.6	yes	24	3.2	odd	2	inner
60.4.e.a.11.19	yes	24	1.1	even	1	trivial
60.4.e.a.11.20	yes	24	12.11	even	2	inner
960.4.h.d.191.3		24	8.5	even	2
960.4.h.d.191.4		24	24.11	even	2
960.4.h.d.191.21		24	24.5	odd	2
960.4.h.d.191.22		24	8.3	odd	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29793 - 1.64910i) q^{2} +(5.00938 + 1.38062i) q^{3} +(2.56093 - 7.57903i) q^{4} +5.00000i q^{5} +(13.7880 - 5.08841i) q^{6} +0.228949i q^{7} +(-6.61376 - 21.6393i) q^{8} +(23.1878 + 13.8321i) q^{9} +O(q^{10})\)	\(q+(2.29793 - 1.64910i) q^{2} +(5.00938 + 1.38062i) q^{3} +(2.56093 - 7.57903i) q^{4} +5.00000i q^{5} +(13.7880 - 5.08841i) q^{6} +0.228949i q^{7} +(-6.61376 - 21.6393i) q^{8} +(23.1878 + 13.8321i) q^{9} +(8.24551 + 11.4896i) q^{10} -57.2431 q^{11} +(23.2924 - 34.4306i) q^{12} +21.7463 q^{13} +(0.377561 + 0.526109i) q^{14} +(-6.90310 + 25.0469i) q^{15} +(-50.8833 - 38.8187i) q^{16} +57.8356i q^{17} +(76.0943 - 6.45383i) q^{18} -77.1177i q^{19} +(37.8951 + 12.8046i) q^{20} +(-0.316092 + 1.14689i) q^{21} +(-131.540 + 94.3996i) q^{22} -88.7394 q^{23} +(-3.25519 - 117.530i) q^{24} -25.0000 q^{25} +(49.9713 - 35.8618i) q^{26} +(97.0595 + 101.304i) q^{27} +(1.73521 + 0.586323i) q^{28} +259.258i q^{29} +(25.4421 + 68.9398i) q^{30} +130.711i q^{31} +(-180.942 - 5.29082i) q^{32} +(-286.752 - 79.0309i) q^{33} +(95.3768 + 132.902i) q^{34} -1.14475 q^{35} +(164.216 - 140.318i) q^{36} +117.207 q^{37} +(-127.175 - 177.211i) q^{38} +(108.935 + 30.0233i) q^{39} +(108.196 - 33.0688i) q^{40} -476.410i q^{41} +(1.16499 + 3.15675i) q^{42} -375.822i q^{43} +(-146.595 + 433.847i) q^{44} +(-69.1605 + 115.939i) q^{45} +(-203.917 + 146.340i) q^{46} +28.9897 q^{47} +(-201.300 - 264.708i) q^{48} +342.948 q^{49} +(-57.4482 + 41.2275i) q^{50} +(-79.8491 + 289.721i) q^{51} +(55.6906 - 164.815i) q^{52} -302.739i q^{53} +(390.096 + 72.7277i) q^{54} -286.215i q^{55} +(4.95430 - 1.51422i) q^{56} +(106.470 - 386.312i) q^{57} +(427.543 + 595.757i) q^{58} +353.325 q^{59} +(172.153 + 116.462i) q^{60} +593.338 q^{61} +(215.556 + 300.365i) q^{62} +(-3.16685 + 5.30883i) q^{63} +(-424.516 + 286.234i) q^{64} +108.731i q^{65} +(-789.266 + 291.276i) q^{66} -687.633i q^{67} +(438.338 + 148.113i) q^{68} +(-444.529 - 122.515i) q^{69} +(-2.63055 + 1.88780i) q^{70} +522.657 q^{71} +(145.958 - 593.249i) q^{72} -1160.42 q^{73} +(269.333 - 193.286i) q^{74} +(-125.234 - 34.5155i) q^{75} +(-584.477 - 197.493i) q^{76} -13.1058i q^{77} +(299.837 - 110.654i) q^{78} +884.113i q^{79} +(194.094 - 254.416i) q^{80} +(346.346 + 641.471i) q^{81} +(-785.648 - 1094.75i) q^{82} -390.888 q^{83} +(7.88286 + 5.33279i) q^{84} -289.178 q^{85} +(-619.769 - 863.611i) q^{86} +(-357.937 + 1298.72i) q^{87} +(378.592 + 1238.70i) q^{88} +269.922i q^{89} +(32.2692 + 380.472i) q^{90} +4.97879i q^{91} +(-227.255 + 672.558i) q^{92} +(-180.463 + 654.783i) q^{93} +(66.6162 - 47.8070i) q^{94} +385.588 q^{95} +(-899.103 - 276.316i) q^{96} +318.435 q^{97} +(788.068 - 565.555i) q^{98} +(-1327.34 - 791.792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9	\( 24 q + 6 q^{4} + 30 q^{6} + 20 q^{9} - 30 q^{10} - 188 q^{12} + 72 q^{13} + 306 q^{16} + 256 q^{18} - 68 q^{21} - 300 q^{22} - 434 q^{24} - 600 q^{25} + 300 q^{28} - 40 q^{30} + 848 q^{33} - 468 q^{34} - 294 q^{36} + 504 q^{37} - 210 q^{40} - 228 q^{42} - 220 q^{45} + 684 q^{46} + 1212 q^{48} - 2256 q^{49} + 576 q^{52} - 1054 q^{54} + 1416 q^{57} + 3108 q^{58} + 490 q^{60} + 1992 q^{61} - 1842 q^{64} - 472 q^{66} - 1548 q^{69} + 540 q^{70} + 312 q^{72} - 2304 q^{73} - 420 q^{76} - 2792 q^{78} + 3840 q^{81} + 600 q^{82} - 176 q^{84} + 240 q^{85} - 372 q^{88} - 1170 q^{90} - 4384 q^{93} + 1044 q^{94} - 3846 q^{96} - 2448 q^{97}+O(q^{100}) \) 24 * q + 6 * q^4 + 30 * q^6 + 20 * q^9 - 30 * q^10 - 188 * q^12 + 72 * q^13 + 306 * q^16 + 256 * q^18 - 68 * q^21 - 300 * q^22 - 434 * q^24 - 600 * q^25 + 300 * q^28 - 40 * q^30 + 848 * q^33 - 468 * q^34 - 294 * q^36 + 504 * q^37 - 210 * q^40 - 228 * q^42 - 220 * q^45 + 684 * q^46 + 1212 * q^48 - 2256 * q^49 + 576 * q^52 - 1054 * q^54 + 1416 * q^57 + 3108 * q^58 + 490 * q^60 + 1992 * q^61 - 1842 * q^64 - 472 * q^66 - 1548 * q^69 + 540 * q^70 + 312 * q^72 - 2304 * q^73 - 420 * q^76 - 2792 * q^78 + 3840 * q^81 + 600 * q^82 - 176 * q^84 + 240 * q^85 - 372 * q^88 - 1170 * q^90 - 4384 * q^93 + 1044 * q^94 - 3846 * q^96 - 2448 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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