LMFDB - Embedded newform 60.4.e.a.11.1

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			11.1
Character	$\chi$	$=$	60.11
Dual form			60.4.e.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81775 - 0.245521i) q^{2} +(-1.56674 - 4.95432i) q^{3} +(7.87944 + 1.38363i) q^{4} -5.00000i q^{5} +(3.19829 + 14.3447i) q^{6} -5.80602i q^{7} +(-21.8626 - 5.83329i) q^{8} +(-22.0907 + 15.5243i) q^{9} +O(q^{10})$	\(q+(-2.81775 - 0.245521i) q^{2} +(-1.56674 - 4.95432i) q^{3} +(7.87944 + 1.38363i) q^{4} -5.00000i q^{5} +(3.19829 + 14.3447i) q^{6} -5.80602i q^{7} +(-21.8626 - 5.83329i) q^{8} +(-22.0907 + 15.5243i) q^{9} +(-1.22760 + 14.0888i) q^{10} -27.6534 q^{11} +(-5.49005 - 41.2051i) q^{12} -70.9938 q^{13} +(-1.42550 + 16.3599i) q^{14} +(-24.7716 + 7.83369i) q^{15} +(60.1711 + 21.8045i) q^{16} -89.8477i q^{17} +(66.0575 - 38.3198i) q^{18} +68.6836i q^{19} +(6.91816 - 39.3972i) q^{20} +(-28.7649 + 9.09652i) q^{21} +(77.9204 + 6.78948i) q^{22} +73.5156 q^{23} +(5.35291 + 117.454i) q^{24} -25.0000 q^{25} +(200.043 + 17.4304i) q^{26} +(111.522 + 85.1219i) q^{27} +(8.03340 - 45.7482i) q^{28} +18.2580i q^{29} +(71.7236 - 15.9914i) q^{30} -277.129i q^{31} +(-164.194 - 76.2128i) q^{32} +(43.3257 + 137.004i) q^{33} +(-22.0595 + 253.168i) q^{34} -29.0301 q^{35} +(-195.542 + 91.7571i) q^{36} -26.7188 q^{37} +(16.8632 - 193.533i) q^{38} +(111.229 + 351.726i) q^{39} +(-29.1665 + 109.313i) q^{40} -364.526i q^{41} +(83.2858 - 18.5693i) q^{42} -425.377i q^{43} +(-217.893 - 38.2621i) q^{44} +(77.6213 + 110.453i) q^{45} +(-207.149 - 18.0496i) q^{46} -80.9735 q^{47} +(13.7541 - 332.269i) q^{48} +309.290 q^{49} +(70.4438 + 6.13801i) q^{50} +(-445.135 + 140.768i) q^{51} +(-559.392 - 98.2293i) q^{52} +610.822i q^{53} +(-293.343 - 267.233i) q^{54} +138.267i q^{55} +(-33.8682 + 126.935i) q^{56} +(340.281 - 107.609i) q^{57} +(4.48270 - 51.4464i) q^{58} -522.866 q^{59} +(-206.025 + 27.4503i) q^{60} +372.807 q^{61} +(-68.0408 + 780.880i) q^{62} +(90.1342 + 128.259i) q^{63} +(443.945 + 255.062i) q^{64} +354.969i q^{65} +(-88.4436 - 396.681i) q^{66} -369.392i q^{67} +(124.316 - 707.949i) q^{68} +(-115.180 - 364.220i) q^{69} +(81.7996 + 7.12749i) q^{70} +985.949 q^{71} +(573.517 - 210.539i) q^{72} -2.29153 q^{73} +(75.2871 + 6.56003i) q^{74} +(39.1684 + 123.858i) q^{75} +(-95.0328 + 541.189i) q^{76} +160.556i q^{77} +(-227.059 - 1018.39i) q^{78} -175.997i q^{79} +(109.022 - 300.856i) q^{80} +(246.995 - 685.882i) q^{81} +(-89.4986 + 1027.14i) q^{82} +207.291 q^{83} +(-239.238 + 31.8754i) q^{84} -449.238 q^{85} +(-104.439 + 1198.61i) q^{86} +(90.4559 - 28.6054i) q^{87} +(604.575 + 161.311i) q^{88} -186.234i q^{89} +(-191.599 - 330.288i) q^{90} +412.192i q^{91} +(579.262 + 101.719i) q^{92} +(-1372.99 + 434.188i) q^{93} +(228.163 + 19.8807i) q^{94} +343.418 q^{95} +(-120.335 + 932.875i) q^{96} -1245.71 q^{97} +(-871.502 - 75.9371i) q^{98} +(610.882 - 429.299i) 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 $

$2$	−2.81775	−	0.245521i	−0.996225	−	0.0868046i
$2$	−2.81775	−	0.245521i	−0.996225	−	0.0868046i
$3$	−1.56674	−	4.95432i	−0.301519	−	0.953460i
$3$	−1.56674	−	4.95432i	−0.301519	−	0.953460i
$4$	7.87944	+	1.38363i	0.984930	+	0.172954i
$5$		−	5.00000i		−	0.447214i
$5$		−	5.00000i		−	0.447214i
$6$	3.19829	+	14.3447i	0.217616	+	0.976034i
$7$		−	5.80602i		−	0.313496i	−0.987639	−	0.156748i	$-0.949899\pi$
$7$		−	5.80602i		−	0.313496i	0.987639	−	0.156748i	$-0.0501010\pi$
$8$	−21.8626	−	5.83329i	−0.966199	−	0.257798i
$9$	−22.0907	+	15.5243i	−0.818173	+	0.574972i
$10$	−1.22760	+	14.0888i	−0.0388202	+	0.445526i
$11$	−27.6534			−0.757984			−0.378992	−	0.925400i	$-0.623729\pi$
$11$	−27.6534			−0.757984			−0.378992	+	0.925400i	$0.623729\pi$
$12$	−5.49005	−	41.2051i	−0.132070	−	0.991240i
$13$	−70.9938			−1.51463			−0.757313	−	0.653052i	$-0.773488\pi$
$13$	−70.9938			−1.51463			−0.757313	+	0.653052i	$0.773488\pi$
$14$	−1.42550	+	16.3599i	−0.0272129	+	0.312313i
$15$	−24.7716	+	7.83369i	−0.426400	+	0.134843i
$16$	60.1711	+	21.8045i	0.940174	+	0.340695i
$17$		−	89.8477i		−	1.28184i	−0.767608	−	0.640919i	$-0.778553\pi$
$17$		−	89.8477i		−	1.28184i	0.767608	−	0.640919i	$-0.221447\pi$
$18$	66.0575	−	38.3198i	0.864995	−	0.501781i
$19$			68.6836i			0.829321i	0.909976	+	0.414661i	$0.136100\pi$
$19$			68.6836i			0.829321i	−0.909976	+	0.414661i	$0.863900\pi$
$20$	6.91816	−	39.3972i	0.0773474	−	0.440474i
$21$	−28.7649	+	9.09652i	−0.298906	+	0.0945249i
$22$	77.9204	+	6.78948i	0.755123	+	0.0657965i
$23$	73.5156			0.666481			0.333241	−	0.942842i	$-0.391858\pi$
$23$	73.5156			0.666481			0.333241	+	0.942842i	$0.391858\pi$
$24$	5.35291	+	117.454i	0.0455274	+	0.998963i
$25$	−25.0000			−0.200000
$26$	200.043	+	17.4304i	1.50891	+	0.131477i
$27$	111.522	+	85.1219i	0.794908	+	0.606730i
$28$	8.03340	−	45.7482i	0.0542203	−	0.308771i
$29$			18.2580i			0.116911i	0.998290	+	0.0584555i	$0.0186176\pi$
$29$			18.2580i			0.116911i	−0.998290	+	0.0584555i	$0.981382\pi$
$30$	71.7236	−	15.9914i	0.436496	−	0.0973208i
$31$		−	277.129i		−	1.60561i	−0.596244	−	0.802803i	$-0.703341\pi$
$31$		−	277.129i		−	1.60561i	0.596244	−	0.802803i	$-0.296659\pi$
$32$	−164.194	−	76.2128i	−0.907051	−	0.421020i
$33$	43.3257	+	137.004i	0.228546	+	0.722707i
$34$	−22.0595	+	253.168i	−0.111270	+	1.27700i
$35$	−29.0301			−0.140200
$36$	−195.542	+	91.7571i	−0.905287	+	0.424801i
$37$	−26.7188			−0.118718			−0.0593588	−	0.998237i	$-0.518906\pi$
$37$	−26.7188			−0.118718			−0.0593588	+	0.998237i	$0.518906\pi$
$38$	16.8632	−	193.533i	0.0719889	−	0.826191i
$39$	111.229	+	351.726i	0.456688	+	1.44414i
$40$	−29.1665	+	109.313i	−0.115291	+	0.432097i
$41$		−	364.526i		−	1.38852i	−0.719724	−	0.694261i	$-0.755732\pi$
$41$		−	364.526i		−	1.38852i	0.719724	−	0.694261i	$-0.244268\pi$
$42$	83.2858	−	18.5693i	0.305983	−	0.0682217i
$43$		−	425.377i		−	1.50859i	−0.656536	−	0.754295i	$-0.727979\pi$
$43$		−	425.377i		−	1.50859i	0.656536	−	0.754295i	$-0.272021\pi$
$44$	−217.893	−	38.2621i	−0.746561	−	0.131096i
$45$	77.6213	+	110.453i	0.257135	+	0.365898i
$46$	−207.149	−	18.0496i	−0.663966	−	0.0578537i
$47$	−80.9735			−0.251302			−0.125651	−	0.992074i	$-0.540102\pi$
$47$	−80.9735			−0.251302			−0.125651	+	0.992074i	$0.540102\pi$
$48$	13.7541	−	332.269i	0.0413591	−	0.999144i
$49$	309.290			0.901720
$50$	70.4438	+	6.13801i	0.199245	+	0.0173609i
$51$	−445.135	+	140.768i	−1.22218	+	0.386498i
$52$	−559.392	−	98.2293i	−1.49180	−	0.261961i
$53$			610.822i			1.58307i	0.611121	+	0.791537i	$0.290719\pi$
$53$			610.822i			1.58307i	−0.611121	+	0.791537i	$0.709281\pi$
$54$	−293.343	−	267.233i	−0.739240	−	0.673442i
$55$			138.267i			0.338981i
$56$	−33.8682	+	126.935i	−0.0808185	+	0.302899i
$57$	340.281	−	107.609i	0.790725	−	0.250056i
$58$	4.48270	−	51.4464i	0.0101484	−	0.116470i
$59$	−522.866			−1.15375			−0.576876	−	0.816832i	$-0.695728\pi$
$59$	−522.866			−1.15375			−0.576876	+	0.816832i	$0.695728\pi$
$60$	−206.025	+	27.4503i	−0.443296	+	0.0590636i
$61$	372.807			0.782509			0.391254	−	0.920283i	$-0.372041\pi$
$61$	372.807			0.782509			0.391254	+	0.920283i	$0.372041\pi$
$62$	−68.0408	+	780.880i	−0.139374	+	1.59955i
$63$	90.1342	+	128.259i	0.180251	+	0.256494i
$64$	443.945	+	255.062i	0.867081	+	0.498168i
$65$			354.969i			0.677362i
$66$	−88.4436	−	396.681i	−0.164949	−	0.739818i
$67$		−	369.392i		−	0.673559i	−0.941584	−	0.336779i	$-0.890662\pi$
$67$		−	369.392i		−	0.673559i	0.941584	−	0.336779i	$-0.109338\pi$
$68$	124.316	−	707.949i	0.221699	−	1.26252i
$69$	−115.180	−	364.220i	−0.200957	−	0.635463i
$70$	81.7996	+	7.12749i	0.139670	+	0.0121700i
$71$	985.949			1.64804			0.824019	−	0.566563i	$-0.191727\pi$
$71$	985.949			1.64804			0.824019	+	0.566563i	$0.191727\pi$
$72$	573.517	−	210.539i	0.938744	−	0.344615i
$73$	−2.29153			−0.00367401			−0.00183701	−	0.999998i	$-0.500585\pi$
$73$	−2.29153			−0.00367401			−0.00183701	+	0.999998i	$0.500585\pi$
$74$	75.2871	+	6.56003i	0.118269	+	0.0103052i
$75$	39.1684	+	123.858i	0.0603038	+	0.190692i
$76$	−95.0328	+	541.189i	−0.143434	+	0.816823i
$77$			160.556i			0.237625i
$78$	−227.059	−	1018.39i	−0.329607	−	1.47833i
$79$		−	175.997i		−	0.250649i	−0.992116	−	0.125324i	$-0.960003\pi$
$79$		−	175.997i		−	0.250649i	0.992116	−	0.125324i	$-0.0399971\pi$
$80$	109.022	−	300.856i	0.152363	−	0.420459i
$81$	246.995	−	685.882i	0.338814	−	0.940854i
$82$	−89.4986	+	1027.14i	−0.120530	+	1.38328i
$83$	207.291			0.274135			0.137067	−	0.990562i	$-0.456232\pi$
$83$	207.291			0.274135			0.137067	+	0.990562i	$0.456232\pi$
$84$	−239.238	+	31.8754i	−0.310750	+	0.0414034i
$85$	−449.238			−0.573256
$86$	−104.439	+	1198.61i	−0.130953	+	1.50290i
$87$	90.4559	−	28.6054i	0.111470	−	0.0352509i
$88$	604.575	+	161.311i	0.732363	+	0.195406i
$89$		−	186.234i		−	0.221807i	−0.993831	−	0.110903i	$-0.964626\pi$
$89$		−	186.234i		−	0.221807i	0.993831	−	0.110903i	$-0.0353744\pi$
$90$	−191.599	−	330.288i	−0.224403	−	0.386837i
$91$			412.192i			0.474829i
$92$	579.262	+	101.719i	0.656437	+	0.115271i
$93$	−1372.99	+	434.188i	−1.53088	+	0.484121i
$94$	228.163	+	19.8807i	0.250354	+	0.0218142i
$95$	343.418			0.370884
$96$	−120.335	+	932.875i	−0.127933	+	0.991783i
$97$	−1245.71			−1.30395			−0.651975	−	0.758241i	$-0.726059\pi$
$97$	−1245.71			−1.30395			−0.651975	+	0.758241i	$0.726059\pi$
$98$	−871.502	−	75.9371i	−0.898317	−	0.0782735i
$99$	610.882	−	429.299i	0.620162	−	0.435820i
$100$	−196.986	−	34.5908i	−0.196986	−	0.0345908i
$101$		−	1247.27i		−	1.22879i	−0.788999	−	0.614394i	$-0.789401\pi$
$101$		−	1247.27i		−	1.22879i	0.788999	−	0.614394i	$-0.210599\pi$
$102$	1288.84	−	287.359i	1.25112	−	0.278949i
$103$			502.605i			0.480807i	0.970673	+	0.240403i	$0.0772797\pi$
$103$			502.605i			0.480807i	−0.970673	+	0.240403i	$0.922720\pi$
$104$	1552.11	+	414.128i	1.46343	+	0.390467i
$105$	45.4826	+	143.825i	0.0422728	+	0.133675i
$106$	149.969	−	1721.15i	0.137418	−	1.57710i
$107$	−1179.61			−1.06577			−0.532885	−	0.846188i	$-0.678892\pi$
$107$	−1179.61			−1.06577			−0.532885	+	0.846188i	$0.678892\pi$
$108$	760.957	+	825.019i	0.677992	+	0.735069i
$109$	266.282			0.233993			0.116996	−	0.993132i	$-0.462673\pi$
$109$	266.282			0.233993			0.116996	+	0.993132i	$0.462673\pi$
$110$	33.9474	−	389.602i	0.0294251	−	0.337701i
$111$	41.8614	+	132.374i	0.0357956	+	0.113193i
$112$	126.597	−	349.355i	0.106806	−	0.294741i
$113$			1751.95i			1.45849i	0.684250	+	0.729247i	$0.260130\pi$
$113$			1751.95i			1.45849i	−0.684250	+	0.729247i	$0.739870\pi$
$114$	−985.247	+	219.670i	−0.809446	+	0.180474i
$115$		−	367.578i		−	0.298060i
$116$	−25.2623	+	143.862i	−0.0202202	+	0.115149i
$117$	1568.30	−	1102.13i	1.23923	−	0.870868i
$118$	1473.31	+	128.374i	1.14940	+	0.100151i
$119$	−521.658			−0.401851
$120$	587.268	−	26.7645i	0.446750	−	0.0203605i
$121$	−566.288			−0.425461
$122$	−1050.48	−	91.5317i	−0.779555	−	0.0679254i
$123$	−1805.98	+	571.116i	−1.32390	+	0.418665i
$124$	383.444	−	2183.62i	0.277696	−	1.58141i
$125$			125.000i			0.0894427i
$126$	−222.485	−	383.532i	−0.157306	−	0.271172i
$127$			1098.73i			0.767689i	0.923398	+	0.383844i	$0.125400\pi$
$127$			1098.73i			0.767689i	−0.923398	+	0.383844i	$0.874600\pi$
$128$	−1188.30	−	827.698i	−0.820565	−	0.571554i
$129$	−2107.46	+	666.454i	−1.43838	+	0.454868i
$130$	87.1522	−	1000.21i	0.0587981	−	0.674805i
$131$	−982.649			−0.655377			−0.327689	−	0.944786i	$-0.606270\pi$
$131$	−982.649			−0.655377			−0.327689	+	0.944786i	$0.606270\pi$
$132$	151.819	+	1139.46i	0.100107	+	0.751344i
$133$	398.779			0.259989
$134$	−90.6934	+	1040.86i	−0.0584680	+	0.671016i
$135$	425.610	−	557.612i	0.271338	−	0.355494i
$136$	−524.108	+	1964.30i	−0.330455	+	1.23851i
$137$		−	2089.52i		−	1.30306i	−0.758622	−	0.651531i	$-0.774127\pi$
$137$		−	2089.52i		−	1.30306i	0.758622	−	0.651531i	$-0.225873\pi$
$138$	235.124	+	1054.56i	0.145037	+	0.650509i
$139$		−	1812.09i		−	1.10575i	−0.833264	−	0.552876i	$-0.813530\pi$
$139$		−	1812.09i		−	1.10575i	0.833264	−	0.552876i	$-0.186470\pi$
$140$	−228.741	−	40.1670i	−0.138087	−	0.0242481i
$141$	126.864	+	401.169i	0.0757723	+	0.239607i
$142$	−2778.16	−	242.071i	−1.64182	−	0.143057i
$143$	1963.22			1.14806
$144$	−1667.72	+	452.436i	−0.965115	+	0.261827i
$145$	91.2898			0.0522842
$146$	6.45695	+	0.562617i	0.00366014	+	0.000318921i
$147$	−484.576	−	1532.32i	−0.271886	−	0.859754i
$148$	−210.530	−	36.9690i	−0.116929	−	0.0205327i
$149$			492.456i			0.270762i	0.990794	+	0.135381i	$0.0432258\pi$
$149$			492.456i			0.270762i	−0.990794	+	0.135381i	$0.956774\pi$
$150$	−79.9572	−	358.618i	−0.0435232	−	0.195207i
$151$			1160.38i			0.625367i	0.949857	+	0.312684i	$0.101228\pi$
$151$			1160.38i			0.625367i	−0.949857	+	0.312684i	$0.898772\pi$
$152$	400.652	−	1501.60i	0.213797	−	0.801289i
$153$	1394.82	+	1984.79i	0.737022	+	1.04877i
$154$	39.4199	−	452.408i	0.0206269	−	0.236728i
$155$	−1385.64			−0.718049
$156$	389.760	+	2925.31i	0.200037	+	1.50136i
$157$	−155.686			−0.0791410			−0.0395705	−	0.999217i	$-0.512599\pi$
$157$	−155.686			−0.0791410			−0.0395705	+	0.999217i	$0.512599\pi$
$158$	−43.2110	+	495.917i	−0.0217575	+	0.249703i
$159$	3026.21	−	956.998i	1.50940	−	0.477326i
$160$	−381.064	+	820.969i	−0.188286	+	0.405646i
$161$		−	426.834i		−	0.208939i
$162$	−864.369	+	1872.00i	−0.419205	+	0.907892i
$163$			2711.05i			1.30273i	0.758763	+	0.651367i	$0.225804\pi$
$163$			2711.05i			1.30273i	−0.758763	+	0.651367i	$0.774196\pi$
$164$	504.369	−	2872.26i	0.240150	−	1.36760i
$165$	685.020	−	216.628i	0.323205	−	0.102209i
$166$	−584.096	−	50.8943i	−0.273100	−	0.0237962i
$167$	3886.56			1.80091			0.900453	−	0.434954i	$-0.143235\pi$
$167$	3886.56			1.80091			0.900453	+	0.434954i	$0.143235\pi$
$168$	681.938	−	31.0791i	0.313171	−	0.0142726i
$169$	2843.12			1.29409
$170$	1265.84	+	110.297i	0.571092	+	0.0497613i
$171$	−1066.26	−	1517.27i	−0.476837	−	0.678528i
$172$	588.565	−	3351.73i	0.260917	−	1.48586i
$173$		−	2163.48i		−	0.950788i	−0.879773	−	0.475394i	$-0.842306\pi$
$173$		−	2163.48i		−	0.950788i	0.879773	−	0.475394i	$-0.157694\pi$
$174$	−261.905	+	58.3942i	−0.114109	+	0.0254417i
$175$			145.151i			0.0626992i
$176$	−1663.94	−	602.969i	−0.712636	−	0.258241i
$177$	819.193	+	2590.45i	0.347878	+	1.10006i
$178$	−45.7243	+	524.762i	−0.0192538	+	0.220969i
$179$	−1551.01			−0.647641			−0.323820	−	0.946119i	$-0.604967\pi$
$179$	−1551.01			−0.647641			−0.323820	+	0.946119i	$0.604967\pi$
$180$	458.785	+	977.710i	0.189977	+	0.404856i
$181$	3110.41			1.27732			0.638660	−	0.769489i	$-0.279489\pi$
$181$	3110.41			1.27732			0.638660	+	0.769489i	$0.279489\pi$
$182$	101.202	−	1161.45i	0.0412174	−	0.473037i
$183$	−584.090	−	1847.01i	−0.235941	−	0.746091i
$184$	−1607.24	−	428.838i	−0.643954	−	0.171817i
$185$			133.594i			0.0530921i
$186$	3975.34	−	886.338i	1.56713	−	0.349406i
$187$			2484.60i			0.971613i
$188$	−638.026	−	112.038i	−0.247515	−	0.0434637i
$189$	494.220	−	647.502i	0.190207	−	0.249200i
$190$	−967.667	−	84.3162i	−0.369484	−	0.0321944i
$191$	−768.326			−0.291069			−0.145534	−	0.989353i	$-0.546490\pi$
$191$	−768.326			−0.291069			−0.145534	+	0.989353i	$0.546490\pi$
$192$	568.113	−	2599.06i	0.213542	−	0.976934i
$193$	1117.62			0.416829			0.208415	−	0.978041i	$-0.433170\pi$
$193$	1117.62			0.416829			0.208415	+	0.978041i	$0.433170\pi$
$194$	3510.11	+	305.848i	1.29903	+	0.113189i
$195$	1758.63	−	556.144i	0.645837	−	0.204237i
$196$	2437.03	+	427.944i	0.888131	+	0.155956i
$197$			2963.17i			1.07166i	0.844326	+	0.535831i	$0.180001\pi$
$197$			2963.17i			1.07166i	−0.844326	+	0.535831i	$0.819999\pi$
$198$	−1826.72	+	1059.67i	−0.655652	+	0.380342i
$199$			3683.95i			1.31230i	0.754629	+	0.656152i	$0.227817\pi$
$199$			3683.95i			1.31230i	−0.754629	+	0.656152i	$0.772183\pi$
$200$	546.565	+	145.832i	0.193240	+	0.0515595i
$201$	−1830.09	+	578.741i	−0.642212	+	0.203091i
$202$	−306.229	+	3514.48i	−0.106665	+	1.22415i
$203$	106.006			0.0366511
$204$	−3702.18	+	493.268i	−1.27061	+	0.169293i
$205$	−1822.63			−0.620966
$206$	123.400	−	1416.21i	0.0417363	−	0.478992i
$207$	−1624.01	+	1141.28i	−0.545297	+	0.383208i
$208$	−4271.78	−	1547.98i	−1.42401	−	0.516026i
$209$		−	1899.34i		−	0.628612i
$210$	−92.8467	−	416.429i	−0.0305097	−	0.136840i
$211$		−	1996.57i		−	0.651419i	−0.945470	−	0.325709i	$-0.894397\pi$
$211$		−	1996.57i		−	0.651419i	0.945470	−	0.325709i	$-0.105603\pi$
$212$	−845.153	+	4812.94i	−0.273799	+	1.55922i
$213$	−1544.72	−	4884.71i	−0.496914	−	1.57134i
$214$	3323.85	+	289.619i	1.06175	+	0.0925138i
$215$	−2126.88			−0.674662
$216$	−1941.63	−	2511.53i	−0.611625	−	0.791147i
$217$	−1609.02			−0.503351
$218$	−750.316	−	65.3777i	−0.233109	−	0.0203116i
$219$	3.59022	+	11.3530i	0.00110778	+	0.00350302i
$220$	−191.311	+	1089.47i	−0.0586280	+	0.333872i
$221$			6378.63i			1.94151i
$222$	−85.4546	−	383.274i	−0.0258348	−	0.115872i
$223$		−	2934.14i		−	0.881096i	−0.897729	−	0.440548i	$-0.854784\pi$
$223$		−	2934.14i		−	0.881096i	0.897729	−	0.440548i	$-0.145216\pi$
$224$	−442.494	+	953.313i	−0.131988	+	0.284357i
$225$	552.267	−	388.106i	0.163635	−	0.114994i
$226$	430.140	−	4936.57i	0.126604	−	1.45299i
$227$	300.433			0.0878435			0.0439217	−	0.999035i	$-0.486015\pi$
$227$	300.433			0.0878435			0.0439217	+	0.999035i	$0.486015\pi$
$228$	2830.12	−	377.077i	0.822057	−	0.109529i
$229$	−1878.85			−0.542173			−0.271087	−	0.962555i	$-0.587383\pi$
$229$	−1878.85			−0.542173			−0.271087	+	0.962555i	$0.587383\pi$
$230$	−90.2480	+	1035.74i	−0.0258729	+	0.296934i
$231$	795.449	−	251.550i	0.226566	−	0.0716483i
$232$	106.504	−	399.166i	0.0301394	−	0.112959i
$233$		−	4503.18i		−	1.26615i	−0.774090	−	0.633075i	$-0.781792\pi$
$233$		−	4503.18i		−	1.26615i	0.774090	−	0.633075i	$-0.218208\pi$
$234$	−4689.68	+	2720.47i	−1.31014	+	0.760011i
$235$			404.868i			0.112386i
$236$	−4119.89	−	723.454i	−1.13636	−	0.199546i
$237$	−871.948	+	275.742i	−0.238984	+	0.0755753i
$238$	1469.90	+	128.078i	0.400334	+	0.0348825i
$239$	−4174.35			−1.12977			−0.564887	−	0.825168i	$-0.691080\pi$
$239$	−4174.35			−1.12977			−0.564887	+	0.825168i	$0.691080\pi$
$240$	−1661.35	−	68.7706i	−0.446831	−	0.0184963i
$241$	−4815.57			−1.28713			−0.643564	−	0.765392i	$-0.722545\pi$
$241$	−4815.57			−1.28713			−0.643564	+	0.765392i	$0.722545\pi$
$242$	1595.66	+	139.035i	0.423855	+	0.0369320i
$243$	−3785.06	−	149.096i	−0.999225	−	0.0393603i
$244$	2937.51	+	515.827i	0.770716	+	0.135338i
$245$		−	1546.45i		−	0.403262i
$246$	5229.02	−	1165.86i	1.35524	−	0.302164i
$247$		−	4876.11i		−	1.25611i
$248$	−1616.57	+	6058.75i	−0.413922	+	1.55134i
$249$	−324.771	−	1026.99i	−0.0826568	−	0.261377i
$250$	30.6901	−	352.219i	0.00776404	−	0.0891051i
$251$	2938.85			0.739038			0.369519	−	0.929223i	$-0.379522\pi$
$251$	2938.85			0.739038			0.369519	+	0.929223i	$0.379522\pi$
$252$	532.744	+	1135.32i	0.133173	+	0.283804i
$253$	−2032.96			−0.505182
$254$	269.761	−	3095.95i	0.0666389	−	0.764791i
$255$	703.839	+	2225.67i	0.172847	+	0.546577i
$256$	3145.13	+	2624.00i	0.767854	+	0.640625i
$257$			1023.87i			0.248512i	0.992250	+	0.124256i	$0.0396543\pi$
$257$			1023.87i			0.248512i	−0.992250	+	0.124256i	$0.960346\pi$
$258$	6101.91	−	1360.48i	1.47244	−	0.328293i
$259$			155.130i			0.0372175i
$260$	−491.147	+	2796.96i	−0.117152	+	0.667154i
$261$	−283.441	−	403.330i	−0.0672206	−	0.0956534i
$262$	2768.86	+	241.260i	0.652903	+	0.0568898i
$263$	6175.08			1.44780			0.723900	−	0.689905i	$-0.242348\pi$
$263$	6175.08			1.44780			0.723900	+	0.689905i	$0.242348\pi$
$264$	−148.026	−	3247.99i	−0.0345090	−	0.757198i
$265$	3054.11			0.707972
$266$	−1123.66	−	97.9084i	−0.259007	−	0.0225682i
$267$	−922.665	+	291.780i	−0.211484	+	0.0668789i
$268$	511.103	−	2910.60i	0.116495	−	0.663408i
$269$			5725.35i			1.29770i	0.760918	+	0.648848i	$0.224749\pi$
$269$			5725.35i			1.29770i	−0.760918	+	0.648848i	$0.775251\pi$
$270$	−1336.17	+	1466.72i	−0.301172	+	0.330598i
$271$		−	267.687i		−	0.0600030i	−0.999550	−	0.0300015i	$-0.990449\pi$
$271$		−	267.687i		−	0.0600030i	0.999550	−	0.0300015i	$-0.00955120\pi$
$272$	1959.08	−	5406.24i	0.436716	−	1.20515i
$273$	2042.13	−	645.797i	0.452731	−	0.143170i
$274$	−513.020	+	5887.74i	−0.113112	+	1.29814i
$275$	691.336			0.151597
$276$	−403.605	−	3029.22i	−0.0880223	−	0.660643i
$277$	−1367.64			−0.296656			−0.148328	−	0.988938i	$-0.547389\pi$
$277$	−1367.64			−0.296656			−0.148328	+	0.988938i	$0.547389\pi$
$278$	−444.906	+	5106.02i	−0.0959844	+	1.10158i
$279$	4302.22	+	6121.96i	0.923180	+	1.31366i
$280$	634.674	+	169.341i	0.135461	+	0.0361431i
$281$		−	917.488i		−	0.194778i	−0.995246	−	0.0973892i	$-0.968951\pi$
$281$		−	917.488i		−	0.194778i	0.995246	−	0.0973892i	$-0.0310492\pi$
$282$	−258.977	−	1161.54i	−0.0546874	−	0.245280i
$283$		−	5302.11i		−	1.11370i	−0.830612	−	0.556851i	$-0.812009\pi$
$283$		−	5302.11i		−	1.11370i	0.830612	−	0.556851i	$-0.187991\pi$
$284$	7768.73	+	1364.19i	1.62320	+	0.285035i
$285$	−538.046	−	1701.41i	−0.111828	−	0.353623i
$286$	−5531.87	−	482.011i	−1.14373	−	0.0996571i
$287$	−2116.45			−0.435296
$288$	4810.30	−	865.393i	0.984200	−	0.177062i
$289$	−3159.60			−0.643111
$290$	−257.232	−	22.4135i	−0.0520868	−	0.00453851i
$291$	1951.71	+	6171.67i	0.393165	+	1.24326i
$292$	−18.0559	−	3.17063i	−0.00361864	−	0.000635435i
$293$		−	2468.87i		−	0.492262i	−0.969237	−	0.246131i	$-0.920841\pi$
$293$		−	2468.87i		−	0.492262i	0.969237	−	0.246131i	$-0.0791594\pi$
$294$	989.199	+	4436.68i	0.196229	+	0.880110i
$295$			2614.33i			0.515973i
$296$	584.143	+	155.859i	0.114705	+	0.0306051i
$297$	−3083.98	−	2353.91i	−0.602527	−	0.459892i
$298$	120.908	−	1387.62i	0.0235034	−	0.269740i
$299$	−5219.16			−1.00947
$300$	137.251	+	1030.13i	0.0264140	+	0.198248i
$301$	−2469.75			−0.472937
$302$	284.897	−	3269.66i	0.0542848	−	0.623007i
$303$	−6179.36	+	1954.14i	−1.17160	+	0.370503i
$304$	−1497.61	+	4132.77i	−0.282546	+	0.779706i
$305$		−	1864.03i		−	0.349948i
$306$	−3442.94	−	5935.11i	−0.643202	−	1.10878i
$307$		−	1268.25i		−	0.235775i	−0.993027	−	0.117887i	$-0.962388\pi$
$307$		−	1268.25i		−	0.235775i	0.993027	−	0.117887i	$-0.0376122\pi$
$308$	−222.151	+	1265.09i	−0.0410981	+	0.234044i
$309$	2490.07	−	787.450i	0.458430	−	0.144972i
$310$	3904.40	+	340.204i	0.715339	+	0.0623300i
$311$	5041.29			0.919181			0.459590	−	0.888131i	$-0.347996\pi$
$311$	5041.29			0.919181			0.459590	+	0.888131i	$0.347996\pi$
$312$	−380.023	−	8338.48i	−0.0689570	−	1.51306i
$313$	6982.28			1.26090			0.630450	−	0.776230i	$-0.282870\pi$
$313$	6982.28			1.26090			0.630450	+	0.776230i	$0.282870\pi$
$314$	438.686	+	38.2242i	0.0788422	+	0.00686980i
$315$	641.295	−	450.671i	0.114708	−	0.0806109i
$316$	243.515	−	1386.76i	0.0433507	−	0.246871i
$317$			241.385i			0.0427683i	0.999771	+	0.0213842i	$0.00680731\pi$
$317$			241.385i			0.0427683i	−0.999771	+	0.0213842i	$0.993193\pi$
$318$	−8762.08	+	1953.59i	−1.54513	+	0.344502i
$319$		−	504.895i		−	0.0886166i
$320$	1275.31	−	2219.73i	0.222787	−	0.387770i
$321$	1848.14	+	5844.18i	0.321350	+	1.01617i
$322$	−104.796	+	1202.71i	−0.0181369	+	0.208150i
$323$	6171.06			1.06306
$324$	2895.19	−	5062.62i	0.496432	−	0.868076i
$325$	1774.85			0.302925
$326$	665.618	−	7639.05i	0.113083	−	1.29782i
$327$	−417.194	−	1319.25i	−0.0705531	−	0.223103i
$328$	−2126.39	+	7969.48i	−0.357957	+	1.34159i
$329$			470.134i			0.0787822i
$330$	−1983.40	+	442.218i	−0.330857	+	0.0737676i
$331$			1362.75i			0.226295i	0.993578	+	0.113148i	$0.0360933\pi$
$331$			1362.75i			0.226295i	−0.993578	+	0.113148i	$0.963907\pi$
$332$	1633.34	+	286.815i	0.270004	+	0.0474127i
$333$	590.237	−	414.790i	0.0971315	−	0.0682593i
$334$	−10951.4	−	954.231i	−1.79411	−	0.156327i
$335$	−1846.96			−0.301225
$336$	−1929.16	−	79.8568i	−0.313228	−	0.0129659i
$337$	7393.00			1.19502			0.597511	−	0.801861i	$-0.296156\pi$
$337$	7393.00			1.19502			0.597511	+	0.801861i	$0.296156\pi$
$338$	−8011.21	−	698.045i	−1.28921	−	0.112333i
$339$	8679.74	−	2744.85i	1.39062	−	0.439763i
$340$	−3539.75	−	621.580i	−0.564617	−	0.0991468i
$341$			7663.56i			1.21702i
$342$	2631.94	+	4537.07i	0.416138	+	0.717359i
$343$		−	3787.21i		−	0.596181i
$344$	−2481.35	+	9299.84i	−0.388911	+	1.45760i
$345$	−1821.10	+	575.899i	−0.284188	+	0.0898705i
$346$	−531.179	+	6096.15i	−0.0825328	+	0.947199i
$347$	−2556.03			−0.395432			−0.197716	−	0.980259i	$-0.563352\pi$
$347$	−2556.03			−0.395432			−0.197716	+	0.980259i	$0.563352\pi$
$348$	752.321	−	100.237i	0.115887	−	0.0154404i
$349$	3542.43			0.543330			0.271665	−	0.962392i	$-0.412426\pi$
$349$	3542.43			0.543330			0.271665	+	0.962392i	$0.412426\pi$
$350$	35.6375	−	408.998i	0.00544258	−	0.0624625i
$351$	−7917.41	−	6043.13i	−1.20399	−	0.918970i
$352$	4540.52	+	2107.55i	0.687530	+	0.319127i
$353$		−	4637.94i		−	0.699299i	−0.936881	−	0.349649i	$-0.886301\pi$
$353$		−	4637.94i		−	0.699299i	0.936881	−	0.349649i	$-0.113699\pi$
$354$	−1672.27	−	7500.36i	−0.251075	−	1.12610i
$355$		−	4929.75i		−	0.737025i
$356$	257.680	−	1467.42i	0.0383623	−	0.218464i
$357$	817.301	+	2584.46i	0.121166	+	0.383149i
$358$	4370.35	+	380.804i	0.645196	+	0.0562182i
$359$	−10403.5			−1.52947			−0.764733	−	0.644347i	$-0.777129\pi$
$359$	−10403.5			−1.52947			−0.764733	+	0.644347i	$0.777129\pi$
$360$	−1052.69	−	2867.58i	−0.154116	−	0.419819i
$361$	2141.56			0.312226
$362$	−8764.36	−	763.669i	−1.27250	−	0.110877i
$363$	887.225	+	2805.58i	0.128284	+	0.405660i
$364$	−570.322	+	3247.84i	−0.0821236	+	0.467673i
$365$			11.4576i			0.00164307i
$366$	1192.34	+	5347.81i	0.170286	+	0.763755i
$367$			582.188i			0.0828065i	0.999143	+	0.0414032i	$0.0131828\pi$
$367$			582.188i			0.0828065i	−0.999143	+	0.0414032i	$0.986817\pi$
$368$	4423.52	+	1602.97i	0.626608	+	0.227067i
$369$	5658.99	+	8052.62i	0.798361	+	1.13605i
$370$	32.8001	−	376.435i	0.00460864	−	0.0528917i
$371$	3546.45			0.496287
$372$	−11419.1	+	1521.45i	−1.59154	+	0.212053i
$373$	−4607.12			−0.639538			−0.319769	−	0.947496i	$-0.603605\pi$
$373$	−4607.12			−0.639538			−0.319769	+	0.947496i	$0.603605\pi$
$374$	610.019	−	7000.97i	0.0843405	−	0.967945i
$375$	619.291	−	195.842i	0.0852801	−	0.0269687i
$376$	1770.29	+	472.342i	0.242808	+	0.0647851i
$377$		−	1296.20i		−	0.177076i
$378$	−1551.56	+	1703.16i	−0.211121	+	0.231749i
$379$		−	6738.28i		−	0.913251i	−0.889659	−	0.456625i	$-0.849058\pi$
$379$		−	6738.28i		−	0.913251i	0.889659	−	0.456625i	$-0.150942\pi$
$380$	2705.94	+	475.164i	0.365295	+	0.0641458i
$381$	5443.46	−	1721.42i	0.731961	−	0.231473i
$382$	2164.95	+	188.640i	0.289970	+	0.0252661i
$383$	−8080.66			−1.07807			−0.539037	−	0.842282i	$-0.681212\pi$
$383$	−8080.66			−1.07807			−0.539037	+	0.842282i	$0.681212\pi$
$384$	−2238.92	+	7184.03i	−0.297538	+	0.954710i
$385$	802.782			0.106269
$386$	−3149.18	−	274.399i	−0.415256	−	0.0361827i
$387$	6603.66	+	9396.86i	0.867398	+	1.23429i
$388$	−9815.53	−	1723.61i	−1.28430	−	0.225523i
$389$		−	4461.03i		−	0.581448i	−0.956807	−	0.290724i	$-0.906104\pi$
$389$		−	4461.03i		−	0.581448i	0.956807	−	0.290724i	$-0.0938962\pi$
$390$	−5091.93	+	1135.29i	−0.661128	+	0.147405i
$391$		−	6605.21i		−	0.854322i
$392$	−6761.88	−	1804.18i	−0.871241	−	0.232461i
$393$	1539.55	+	4868.36i	0.197609	+	0.624876i
$394$	727.520	−	8349.48i	0.0930252	−	1.06762i
$395$	−879.987			−0.112094
$396$	5407.40	−	2537.40i	0.686192	−	0.321992i
$397$	6579.96			0.831836			0.415918	−	0.909402i	$-0.363460\pi$
$397$	6579.96			0.831836			0.415918	+	0.909402i	$0.363460\pi$
$398$	904.486	−	10380.5i	0.113914	−	1.30735i
$399$	−624.782	−	1975.68i	−0.0783915	−	0.247889i
$400$	−1504.28	−	545.112i	−0.188035	−	0.0681390i
$401$		−	12288.2i		−	1.53028i	−0.643863	−	0.765141i	$-0.722669\pi$
$401$		−	12288.2i		−	1.53028i	0.643863	−	0.765141i	$-0.277331\pi$
$402$	5298.83	−	1181.42i	0.657417	−	0.146577i
$403$			19674.4i			2.43189i
$404$	1725.76	−	9827.76i	0.212524	−	1.21027i
$405$	−3429.41	−	1234.98i	−0.420762	−	0.151522i
$406$	−298.699	−	26.0267i	−0.0365128	−	0.00318149i
$407$	738.867			0.0899860
$408$	10552.9	−	480.946i	1.28051	−	0.0583588i
$409$	−11825.8			−1.42970			−0.714848	−	0.699280i	$-0.753504\pi$
$409$	−11825.8			−1.42970			−0.714848	+	0.699280i	$0.753504\pi$
$410$	5135.72	+	447.493i	0.618622	+	0.0539027i
$411$	−10352.2	+	3273.73i	−1.24242	+	0.392898i
$412$	−695.420	+	3960.24i	−0.0831574	+	0.473561i
$413$			3035.77i			0.361696i
$414$	4856.26	−	2817.10i	0.576503	−	0.334428i
$415$		−	1036.46i		−	0.122597i
$416$	11656.7	+	5410.64i	1.37384	+	0.637689i
$417$	−8977.69	+	2839.07i	−1.05429	+	0.333405i
$418$	−466.326	+	5351.86i	−0.0545664	+	0.626239i
$419$	15752.4			1.83665			0.918326	−	0.395824i	$-0.129541\pi$
$419$	15752.4			1.83665			0.918326	+	0.395824i	$0.129541\pi$
$420$	159.377	+	1196.19i	0.0185162	+	0.138972i
$421$	695.890			0.0805596			0.0402798	−	0.999188i	$-0.487175\pi$
$421$	695.890			0.0805596			0.0402798	+	0.999188i	$0.487175\pi$
$422$	−490.198	+	5625.83i	−0.0565462	+	0.648960i
$423$	1788.76	−	1257.05i	0.205609	−	0.144492i
$424$	3563.11	−	13354.2i	0.408113	−	1.52956i
$425$			2246.19i			0.256368i
$426$	3153.35	+	14143.2i	0.358639	+	1.60854i
$427$		−	2164.53i		−	0.245313i
$428$	−9294.68	−	1632.15i	−1.04971	−	0.184329i
$429$	−3075.85	−	9726.44i	−0.346162	−	1.09463i
$430$	5993.03	+	522.194i	0.672115	+	0.0585638i
$431$	−2738.25			−0.306025			−0.153013	−	0.988224i	$-0.548898\pi$
$431$	−2738.25			−0.306025			−0.153013	+	0.988224i	$0.548898\pi$
$432$	4854.39	+	7553.57i	0.540641	+	0.841253i
$433$	−10462.7			−1.16121			−0.580607	−	0.814184i	$-0.697185\pi$
$433$	−10462.7			−1.16121			−0.580607	+	0.814184i	$0.697185\pi$
$434$	4533.81	+	395.047i	0.501451	+	0.0436932i
$435$	−143.027	−	452.279i	−0.0157647	−	0.0498509i
$436$	2098.15	+	368.436i	0.230466	+	0.0404699i
$437$			5049.32i			0.552727i
$438$	−7.32896	−	32.8713i	−0.000799523	−	0.00358596i
$439$			5176.74i			0.562807i	0.959590	+	0.281404i	$0.0907999\pi$
$439$			5176.74i			0.562807i	−0.959590	+	0.281404i	$0.909200\pi$
$440$	806.553	−	3022.88i	0.0873884	−	0.327523i
$441$	−6832.42	+	4801.50i	−0.737763	+	0.518464i
$442$	1566.08	−	17973.4i	0.168532	−	1.93418i
$443$	−203.945			−0.0218729			−0.0109365	−	0.999940i	$-0.503481\pi$
$443$	−203.945			−0.0218729			−0.0109365	+	0.999940i	$0.503481\pi$
$444$	146.688	+	1100.95i	0.0156791	+	0.117678i
$445$	−931.171			−0.0991949
$446$	−720.391	+	8267.67i	−0.0764832	+	0.877770i
$447$	2439.78	−	771.549i	0.258161	−	0.0816398i
$448$	1480.89	−	2577.56i	0.156173	−	0.271826i
$449$		−	6685.44i		−	0.702684i	−0.936247	−	0.351342i	$-0.885725\pi$
$449$		−	6685.44i		−	0.702684i	0.936247	−	0.351342i	$-0.114275\pi$
$450$	−1651.44	+	957.994i	−0.172999	+	0.100356i
$451$			10080.4i			1.05248i
$452$	−2424.06	+	13804.4i	−0.252252	+	1.43651i
$453$	5748.90	−	1818.01i	0.596263	−	0.188560i
$454$	−846.547	−	73.7626i	−0.0875119	−	0.00762522i
$455$	2060.96			0.212350
$456$	−8067.14	+	367.657i	−0.828461	+	0.0377568i
$457$	−1879.27			−0.192360			−0.0961801	−	0.995364i	$-0.530662\pi$
$457$	−1879.27			−0.192360			−0.0961801	+	0.995364i	$0.530662\pi$
$458$	5294.12	+	461.296i	0.540127	+	0.0470632i
$459$	7648.00	−	10020.0i	0.777730	−	1.01894i
$460$	508.593	−	2896.31i	0.0515506	−	0.293568i
$461$		−	6621.36i		−	0.668953i	−0.942404	−	0.334477i	$-0.891440\pi$
$461$		−	6621.36i		−	0.668953i	0.942404	−	0.334477i	$-0.108560\pi$
$462$	−2303.14	+	513.506i	−0.231930	+	0.0517109i
$463$		−	9275.47i		−	0.931032i	−0.885039	−	0.465516i	$-0.845869\pi$
$463$		−	9275.47i		−	0.931032i	0.885039	−	0.465516i	$-0.154131\pi$
$464$	−398.105	+	1098.60i	−0.0398310	+	0.109917i
$465$	2170.94	+	6864.93i	0.216505	+	0.684631i
$466$	−1105.62	+	12688.8i	−0.109908	+	1.26137i
$467$	12203.2			1.20920			0.604599	−	0.796530i	$-0.293334\pi$
$467$	12203.2			1.20920			0.604599	+	0.796530i	$0.293334\pi$
$468$	13882.3	−	6514.19i	1.37117	−	0.643415i
$469$	−2144.70			−0.211158
$470$	99.4033	−	1140.82i	0.00975560	−	0.111962i
$471$	243.920	+	771.321i	0.0238625	+	0.0754578i
$472$	11431.2	+	3050.03i	1.11475	+	0.297434i
$473$			11763.1i			1.14349i
$474$	2524.63	−	562.890i	0.244642	−	0.0545451i
$475$		−	1717.09i		−	0.165864i
$476$	−4110.37	−	721.782i	−0.395795	−	0.0695017i
$477$	−9482.56	−	13493.5i	−0.910224	−	1.29523i
$478$	11762.3	+	1024.89i	1.12551	+	0.0980697i
$479$	−8641.38			−0.824289			−0.412145	−	0.911118i	$-0.635220\pi$
$479$	−8641.38			−0.824289			−0.412145	+	0.911118i	$0.635220\pi$
$480$	4664.37	+	601.673i	0.443539	+	0.0572135i
$481$	1896.87			0.179813
$482$	13569.1	+	1182.32i	1.28227	+	0.111729i
$483$	−2114.67	+	668.736i	−0.199215	+	0.0629991i
$484$	−4462.03	−	783.534i	−0.419049	−	0.0735851i
$485$			6228.57i			0.583144i
$486$	10628.7	+	1349.43i	0.992037	+	0.125949i
$487$			10391.9i			0.966948i	0.875359	+	0.483474i	$0.160625\pi$
$487$			10391.9i			0.966948i	−0.875359	+	0.483474i	$0.839375\pi$
$488$	−8150.52	−	2174.69i	−0.756059	−	0.201729i
$489$	13431.4	−	4247.50i	1.24210	−	0.392799i
$490$	−379.685	+	4357.51i	−0.0350050	+	0.401739i
$491$	−3786.89			−0.348065			−0.174032	−	0.984740i	$-0.555680\pi$
$491$	−3786.89			−0.348065			−0.174032	+	0.984740i	$0.555680\pi$
$492$	−15020.3	+	2001.27i	−1.37636	+	0.183382i
$493$	1640.43			0.149861
$494$	−1197.19	+	13739.7i	−0.109036	+	1.25137i
$495$	−2146.49	−	3054.41i	−0.194904	−	0.277345i
$496$	6042.65	−	16675.2i	0.547022	−	1.50955i
$497$		−	5724.45i		−	0.516653i
$498$	662.978	+	2973.54i	0.0596561	+	0.267565i
$499$		−	13264.6i		−	1.18999i	−0.803730	−	0.594994i	$-0.797154\pi$
$499$		−	13264.6i		−	1.18999i	0.803730	−	0.594994i	$-0.202846\pi$
$500$	−172.954	+	984.930i	−0.0154695	+	0.0880948i
$501$	−6089.22	−	19255.3i	−0.543007	−	1.71709i
$502$	−8280.95	−	721.548i	−0.736249	−	0.0641520i
$503$	9843.04			0.872523			0.436262	−	0.899820i	$-0.356302\pi$
$503$	9843.04			0.872523			0.436262	+	0.899820i	$0.356302\pi$
$504$	−1222.39	−	3329.85i	−0.108035	−	0.294292i
$505$	−6236.33			−0.549531
$506$	5728.37	+	499.133i	0.503275	+	0.0438521i
$507$	−4454.43	−	14085.8i	−0.390194	−	1.23387i
$508$	−1520.24	+	8657.37i	−0.132775	+	0.756120i
$509$			5302.71i			0.461766i	0.972982	+	0.230883i	$0.0741614\pi$
$509$			5302.71i			0.461766i	−0.972982	+	0.230883i	$0.925839\pi$
$510$	−1436.79	−	6444.20i	−0.124750	−	0.559517i
$511$			13.3047i			0.00115179i
$512$	−8217.94	−	8165.97i	−0.709346	−	0.704860i
$513$	−5846.48	+	7659.77i	−0.503174	+	0.659234i
$514$	251.382	−	2885.02i	0.0215720	−	0.247574i
$515$	2513.02			0.215023
$516$	−17527.7	+	2335.34i	−1.49538	+	0.199240i
$517$	2239.20			0.190483
$518$	38.0877	−	437.118i	0.00323065	−	0.0370770i
$519$	−10718.6	+	3389.61i	−0.906539	+	0.286680i
$520$	2070.64	−	7760.54i	0.174622	−	0.654466i
$521$		−	5895.86i		−	0.495782i	−0.968788	−	0.247891i	$-0.920262\pi$
$521$		−	5895.86i		−	0.495782i	0.968788	−	0.247891i	$-0.0797375\pi$
$522$	699.641	+	1206.08i	0.0586637	+	0.101127i
$523$			20434.3i			1.70847i	0.519886	+	0.854236i	$0.325974\pi$
$523$			20434.3i			1.70847i	−0.519886	+	0.854236i	$0.674026\pi$
$524$	−7742.72	−	1359.62i	−0.645501	−	0.113350i
$525$	719.123	−	227.413i	0.0597812	−	0.0189050i
$526$	−17399.8	−	1516.11i	−1.44234	−	0.125676i
$527$	−24899.4			−2.05813
$528$	−380.348	+	9188.38i	−0.0313495	+	0.757335i
$529$	−6762.45			−0.555803
$530$	−8605.73	−	749.847i	−0.705300	−	0.0614553i
$531$	11550.5	−	8117.10i	0.943968	−	0.663375i
$532$	3142.15	+	551.763i	0.256071	+	0.0449661i
$533$			25879.1i			2.10309i
$534$	2671.48	−	595.631i	0.216491	−	0.0482686i
$535$			5898.06i			0.476627i
$536$	−2154.77	+	8075.87i	−0.173642	+	0.650792i
$537$	2430.02	+	7684.19i	0.195276	+	0.617500i
$538$	1405.69	−	16132.6i	0.112646	−	1.29280i
$539$	−8552.93			−0.683489
$540$	4125.09	−	3804.79i	0.328733	−	0.303207i
$541$	6210.29			0.493533			0.246766	−	0.969075i	$-0.420632\pi$
$541$	6210.29			0.493533			0.246766	+	0.969075i	$0.420632\pi$
$542$	−65.7226	+	754.274i	−0.00520854	+	0.0597765i
$543$	−4873.19	−	15410.0i	−0.385136	−	1.21787i
$544$	−6847.55	+	14752.4i	−0.539680	+	1.16269i
$545$		−	1331.41i		−	0.104645i
$546$	−5912.78	+	1318.31i	−0.463450	+	0.103330i
$547$			7119.29i			0.556488i	0.960510	+	0.278244i	$0.0897523\pi$
$547$			7119.29i			0.556488i	−0.960510	+	0.278244i	$0.910248\pi$
$548$	2891.12	−	16464.2i	0.225370	−	1.28343i
$549$	−8235.55	+	5787.55i	−0.640227	+	0.449921i
$550$	−1948.01	−	169.737i	−0.151025	−	0.0131593i
$551$	−1254.02			−0.0969568
$552$	393.522	+	8634.68i	0.0303432	+	0.665790i
$553$	−1021.84			−0.0785773
$554$	3853.68	+	335.785i	0.295536	+	0.0257511i
$555$	661.869	−	209.307i	0.0506212	−	0.0160083i
$556$	2507.27	−	14278.3i	0.191244	−	1.08909i
$557$		−	11276.2i		−	0.857786i	−0.903355	−	0.428893i	$-0.858904\pi$
$557$		−	11276.2i		−	0.857786i	0.903355	−	0.428893i	$-0.141096\pi$
$558$	−10619.5	−	18306.4i	−0.805663	−	1.38884i
$559$			30199.1i			2.28495i
$560$	−1746.78	−	632.987i	−0.131812	−	0.0477653i
$561$	12309.5	−	3892.71i	0.926394	−	0.292960i
$562$	−225.262	+	2585.25i	−0.0169077	+	0.194043i
$563$	−2262.67			−0.169378			−0.0846892	−	0.996407i	$-0.526990\pi$
$563$	−2262.67			−0.169378			−0.0846892	+	0.996407i	$0.526990\pi$
$564$	444.549	+	3336.52i	0.0331895	+	0.249101i
$565$	8759.76			0.652258
$566$	−1301.78	+	14940.0i	−0.0966745	+	1.10950i
$567$	−3982.25	−	1434.06i	−0.294954	−	0.106217i
$568$	−21555.4	−	5751.33i	−1.59233	−	0.424860i
$569$			13730.3i			1.01161i	0.862648	+	0.505804i	$0.168804\pi$
$569$			13730.3i			1.01161i	−0.862648	+	0.505804i	$0.831196\pi$
$570$	1098.35	+	4926.24i	0.0807102	+	0.361995i
$571$			3653.95i			0.267799i	0.990995	+	0.133899i	$0.0427499\pi$
$571$			3653.95i			0.267799i	−0.990995	+	0.133899i	$0.957250\pi$
$572$	15469.1	+	2716.38i	1.13076	+	0.198562i
$573$	1203.76	+	3806.54i	0.0877626	+	0.277522i
$574$	5963.62	+	519.631i	0.433653	+	0.0377857i
$575$	−1837.89			−0.133296
$576$	−13766.7	+	1257.44i	−0.995855	+	0.0909604i
$577$	23382.9			1.68708			0.843539	−	0.537069i	$-0.180468\pi$
$577$	23382.9			1.68708			0.843539	+	0.537069i	$0.180468\pi$
$578$	8902.97	+	775.748i	0.640683	+	0.0558250i
$579$	−1751.02	−	5537.06i	−0.125682	−	0.397430i
$580$	719.312	+	126.311i	0.0514962	+	0.00904275i
$581$		−	1203.54i		−	0.0859402i
$582$	−3984.15	−	17869.4i	−0.283760	−	1.27270i
$583$		−	16891.3i		−	1.19994i
$584$	50.0987	+	13.3671i	0.00354983	+	0.000947151i
$585$	−5510.63	−	7841.51i	−0.389464	−	0.554199i
$586$	−606.158	+	6956.66i	−0.0427306	+	0.490404i
$587$	8003.27			0.562743			0.281372	−	0.959599i	$-0.409211\pi$
$587$	8003.27			0.562743			0.281372	+	0.959599i	$0.409211\pi$
$588$	−1698.02	−	12744.3i	−0.119090	−	0.893822i
$589$	19034.2			1.33156
$590$	641.871	−	7366.53i	0.0447889	−	0.514026i
$591$	14680.5	−	4642.51i	1.02179	−	0.323126i
$592$	−1607.70	−	582.591i	−0.111615	−	0.0404465i
$593$		−	4544.68i		−	0.314718i	−0.987541	−	0.157359i	$-0.949702\pi$
$593$		−	4544.68i		−	0.314718i	0.987541	−	0.157359i	$-0.0502980\pi$
$594$	8111.95	+	7389.92i	0.560332	+	0.510458i
$595$			2608.29i			0.179713i
$596$	−681.377	+	3880.27i	−0.0468293	+	0.266682i
$597$	18251.5	−	5771.79i	1.25123	−	0.395684i
$598$	14706.3	+	1281.41i	1.00566	+	0.0876267i
$599$	24458.6			1.66837			0.834183	−	0.551488i	$-0.185940\pi$
$599$	24458.6			1.66837			0.834183	+	0.551488i	$0.185940\pi$
$600$	−133.823	−	2936.34i	−0.00910548	−	0.199793i
$601$	8847.09			0.600466			0.300233	−	0.953866i	$-0.402935\pi$
$601$	8847.09			0.600466			0.300233	+	0.953866i	$0.402935\pi$
$602$	6959.14	+	606.374i	0.471152	+	0.0410531i
$603$	5734.54	+	8160.12i	0.387278	+	0.551088i
$604$	−1605.54	+	9143.15i	−0.108160	+	0.615943i
$605$			2831.44i			0.190272i
$606$	17891.7	−	3989.12i	1.19934	−	0.267404i
$607$		−	25038.0i		−	1.67424i	−0.547021	−	0.837119i	$-0.684238\pi$
$607$		−	25038.0i		−	1.67424i	0.547021	−	0.837119i	$-0.315762\pi$
$608$	5234.58	−	11277.4i	0.349161	−	0.752237i
$609$	−166.084	−	525.189i	−0.0110510	−	0.0349454i
$610$	−457.659	+	5252.38i	−0.0303771	+	0.348628i
$611$	5748.62			0.380629
$612$	8244.16	+	17569.0i	0.544527	+	1.16043i
$613$	−8235.80			−0.542644			−0.271322	−	0.962489i	$-0.587461\pi$
$613$	−8235.80			−0.542644			−0.271322	+	0.962489i	$0.587461\pi$
$614$	−311.382	+	3573.62i	−0.0204664	+	0.234885i
$615$	2855.58	+	9029.90i	0.187233	+	0.592066i
$616$	936.573	−	3510.18i	0.0612591	−	0.229593i
$617$		−	13354.0i		−	0.871333i	−0.900108	−	0.435667i	$-0.856513\pi$
$617$		−	13354.0i		−	0.871333i	0.900108	−	0.435667i	$-0.143487\pi$
$618$	−7209.72	+	1607.47i	−0.469284	+	0.104631i
$619$		−	4166.44i		−	0.270539i	−0.990809	−	0.135269i	$-0.956810\pi$
$619$		−	4166.44i		−	0.270539i	0.990809	−	0.135269i	$-0.0431900\pi$
$620$	−10918.1	−	1917.22i	−0.707228	−	0.124189i
$621$	8198.65	+	6257.79i	0.529791	+	0.404374i
$622$	−14205.1	−	1237.74i	−0.915711	−	0.0797891i
$623$	−1081.28			−0.0695355
$624$	−976.458	+	23589.1i	−0.0626436	+	1.51333i
$625$	625.000			0.0400000
$626$	−19674.3	−	1714.29i	−1.25614	−	0.109452i
$627$	−9409.93	+	2975.76i	−0.599357	+	0.189538i
$628$	−1226.72	−	215.413i	−0.0779483	−	0.0136877i
$629$			2400.63i			0.152177i
$630$	−1917.66	+	1112.43i	−0.121272	+	0.0703495i
$631$			49.3032i			0.00311050i	0.999999	+	0.00155525i	$0.000495052\pi$
$631$			49.3032i			0.00311050i	−0.999999	+	0.00155525i	$0.999505\pi$
$632$	−1026.64	+	3847.76i	−0.0646166	+	0.242177i
$633$	−9891.64	+	3128.10i	−0.621102	+	0.196415i
$634$	59.2651	−	680.164i	0.00371249	−	0.0426069i
$635$	5493.65			0.343321
$636$	25169.0	−	3353.45i	1.56921	−	0.209077i
$637$	−21957.7			−1.36577
$638$	−123.962	+	1422.67i	−0.00769233	+	0.0882821i
$639$	−21780.3	+	15306.1i	−1.34838	+	0.947576i
$640$	−4138.49	+	5941.52i	−0.255607	+	0.366968i
$641$			8803.55i			0.542464i	0.962514	+	0.271232i	$0.0874310\pi$
$641$			8803.55i			0.542464i	−0.962514	+	0.271232i	$0.912569\pi$
$642$	−3772.74	−	16921.2i	−0.231928	−	1.04023i
$643$		−	20483.5i		−	1.25628i	−0.778099	−	0.628141i	$-0.783816\pi$
$643$		−	20483.5i		−	1.25628i	0.778099	−	0.628141i	$-0.216184\pi$
$644$	590.580	−	3363.21i	0.0361368	−	0.205790i
$645$	3332.27	+	10537.3i	0.203423	+	0.643263i
$646$	−17388.5	−	1515.12i	−1.05904	−	0.0922782i
$647$	13597.2			0.826213			0.413106	−	0.910683i	$-0.364444\pi$
$647$	13597.2			0.826213			0.413106	+	0.910683i	$0.364444\pi$
$648$	−9400.90	+	13554.4i	−0.569911	+	0.821706i
$649$	14459.0			0.874524
$650$	−5001.07	−	435.761i	−0.301782	−	0.0262953i
$651$	2520.91	+	7971.59i	0.151770	+	0.479925i
$652$	−3751.09	+	21361.5i	−0.225313	+	1.28310i
$653$			308.154i			0.0184671i	0.999957	+	0.00923354i	$0.00293917\pi$
$653$			308.154i			0.0184671i	−0.999957	+	0.00923354i	$0.997061\pi$
$654$	851.646	+	3819.74i	0.0509205	+	0.228385i
$655$			4913.24i			0.293094i
$656$	7948.30	−	21933.9i	0.473062	−	1.30545i
$657$	50.6213	−	35.5742i	0.00300598	−	0.00211245i
$658$	115.428	−	1324.72i	0.00683866	−	0.0784848i
$659$	10034.0			0.593127			0.296563	−	0.955013i	$-0.404159\pi$
$659$	10034.0			0.593127			0.296563	+	0.955013i	$0.404159\pi$
$660$	5697.31	−	759.094i	0.336011	−	0.0447692i
$661$	−18731.2			−1.10221			−0.551104	−	0.834437i	$-0.685793\pi$
$661$	−18731.2			−1.10221			−0.551104	+	0.834437i	$0.685793\pi$
$662$	334.584	−	3839.90i	0.0196435	−	0.225441i
$663$	31601.8	−	9993.64i	1.85115	−	0.585401i
$664$	−4531.93	−	1209.19i	−0.264869	−	0.0706713i
$665$		−	1993.89i		−	0.116271i
$666$	−1764.98	+	1023.86i	−0.102690	+	0.0595702i
$667$			1342.25i			0.0779190i
$668$	30623.9	+	5377.57i	1.77377	+	0.311474i
$669$	−14536.7	+	4597.02i	−0.840090	+	0.265667i
$670$	5204.28	+	453.467i	0.300088	+	0.0261477i
$671$	−10309.4			−0.593129
$672$	5416.29	+	698.666i	0.310920	+	0.0401066i
$673$	2749.59			0.157487			0.0787435	−	0.996895i	$-0.474909\pi$
$673$	2749.59			0.157487			0.0787435	+	0.996895i	$0.474909\pi$
$674$	−20831.6	−	1815.13i	−1.19051	−	0.103733i
$675$	−2788.06	−	2128.05i	−0.158982	−	0.121346i
$676$	22402.2	+	3933.84i	1.27459	+	0.223819i
$677$			17574.5i			0.997702i	0.866688	+	0.498851i	$0.166245\pi$
$677$			17574.5i			0.997702i	−0.866688	+	0.498851i	$0.833755\pi$
$678$	−25131.3	+	5603.25i	−1.42354	+	0.317392i
$679$			7232.65i			0.408783i
$680$	9821.51	+	2620.54i	0.553879	+	0.147784i
$681$	−470.700	−	1488.44i	−0.0264865	−	0.0837553i
$682$	1881.56	−	21594.0i	0.105643	−	1.21243i
$683$	−28547.9			−1.59935			−0.799675	−	0.600433i	$-0.794995\pi$
$683$	−28547.9			−1.59935			−0.799675	+	0.600433i	$0.794995\pi$
$684$	−6302.21	−	13430.5i	−0.352297	−	0.750774i
$685$	−10447.6			−0.582747
$686$	−929.839	+	10671.4i	−0.0517513	+	0.593931i
$687$	2943.66	+	9308.42i	0.163475	+	0.516941i
$688$	9275.12	−	25595.4i	0.513969	−	1.41834i
$689$		−	43364.6i		−	2.39777i
$690$	5272.81	−	1175.62i	0.290916	−	0.0648625i
$691$		−	835.522i		−	0.0459982i	−0.999735	−	0.0229991i	$-0.992679\pi$
$691$		−	835.522i		−	0.0459982i	0.999735	−	0.0229991i	$-0.00732148\pi$
$692$	2993.46	−	17047.0i	0.164443	−	0.936460i
$693$	−2492.52	−	3546.80i	−0.136628	−	0.194418i
$694$	7202.26	+	627.558i	0.393940	+	0.0343253i
$695$	−9060.45			−0.494507
$696$	−2144.46	+	97.7331i	−0.116790	+	0.00532265i
$697$	−32751.8			−1.77986
$698$	−9981.70	−	869.740i	−0.541279	−	0.0471636i
$699$	−22310.2	+	7055.30i	−1.20722	+	0.381768i
$700$	−200.835	+	1143.71i	−0.0108441	+	0.0617543i
$701$		−	23220.9i		−	1.25113i	−0.780173	−	0.625564i	$-0.784869\pi$
$701$		−	23220.9i		−	1.25113i	0.780173	−	0.625564i	$-0.215131\pi$
$702$	20825.6	+	18971.9i	1.11967	+	1.02001i
$703$		−	1835.15i		−	0.0984550i
$704$	−12276.6	−	7053.33i	−0.657233	−	0.377603i
$705$	2005.85	−	634.321i	0.107155	−	0.0338864i
$706$	−1138.71	+	13068.5i	−0.0607024	+	0.696659i
$707$	−7241.66			−0.385220
$708$	2870.56	+	21544.7i	0.152376	+	1.14364i
$709$	−13434.1			−0.711605			−0.355802	−	0.934561i	$-0.615792\pi$
$709$	−13434.1			−0.711605			−0.355802	+	0.934561i	$0.615792\pi$
$710$	−1210.35	+	13890.8i	−0.0639772	+	0.734243i
$711$	2732.23	+	3887.90i	0.144116	+	0.205074i
$712$	−1086.36	+	4071.56i	−0.0571812	+	0.214309i
$713$		−	20373.3i		−	1.07011i
$714$	−1668.41	−	7483.03i	−0.0874492	−	0.392221i
$715$		−	9816.11i		−	0.513429i
$716$	−12221.1	−	2146.02i	−0.637881	−	0.112012i
$717$	6540.11	+	20681.1i	0.340648	+	1.07720i
$718$	29314.6	+	2554.29i	1.52369	+	0.132765i
$719$	−1580.82			−0.0819953			−0.0409976	−	0.999159i	$-0.513054\pi$
$719$	−1580.82			−0.0819953			−0.0409976	+	0.999159i	$0.513054\pi$
$720$	2262.18	+	8338.59i	0.117092	+	0.431613i
$721$	2918.13			0.150731
$722$	−6034.38	−	525.797i	−0.311047	−	0.0271027i
$723$	7544.73	+	23857.9i	0.388094	+	1.22723i
$724$	24508.3	+	4303.66i	1.25807	+	0.220917i
$725$		−	456.449i		−	0.0233822i
$726$	−1811.15	−	8123.25i	−0.0925870	−	0.415264i
$727$			5738.76i			0.292763i	0.989228	+	0.146381i	$0.0467627\pi$
$727$			5738.76i			0.292763i	−0.989228	+	0.146381i	$0.953237\pi$
$728$	2404.44	−	9011.58i	0.122410	−	0.458779i
$729$	5191.52	+	18986.0i	0.263757	+	0.964589i
$730$	2.81308	−	32.2847i	0.000142626	−	0.00163687i
$731$	−38219.1			−1.93377
$732$	−2046.73	−	15361.5i	−0.103346	−	0.775654i
$733$	37406.6			1.88492			0.942458	−	0.334325i	$-0.108508\pi$
$733$	37406.6			1.88492			0.942458	+	0.334325i	$0.108508\pi$
$734$	142.939	−	1640.46i	0.00718799	−	0.0824939i
$735$	−7661.62	+	2422.88i	−0.384494	+	0.121591i
$736$	−12070.8	−	5602.84i	−0.604533	−	0.280602i
$737$			10215.0i			0.510547i
$738$	−13968.5	−	24079.7i	−0.696733	−	1.20106i
$739$		−	22977.2i		−	1.14375i	−0.820342	−	0.571873i	$-0.806217\pi$
$739$		−	22977.2i		−	1.14375i	0.820342	−	0.571873i	$-0.193783\pi$
$740$	−184.845	+	1052.65i	−0.00918249	+	0.0522920i
$741$	−24157.9	+	7639.59i	−1.19765	+	0.378741i
$742$	−9993.01	−	870.726i	−0.494414	−	0.0430800i
$743$	−13441.0			−0.663662			−0.331831	−	0.943339i	$-0.607666\pi$
$743$	−13441.0			−0.663662			−0.331831	+	0.943339i	$0.607666\pi$
$744$	32549.8	−	1483.44i	1.60394	−	0.0730991i
$745$	2462.28			0.121088
$746$	12981.7	+	1131.14i	0.637124	+	0.0555149i
$747$	−4579.21	+	3218.05i	−0.224290	+	0.157620i
$748$	−3437.76	+	19577.2i	−0.168044	+	0.956971i
$749$			6848.85i			0.334114i
$750$	−1793.09	+	399.786i	−0.0872992	+	0.0194642i
$751$		−	39327.0i		−	1.91087i	−0.295204	−	0.955434i	$-0.595388\pi$
$751$		−	39327.0i		−	1.91087i	0.295204	−	0.955434i	$-0.404612\pi$
$752$	−4872.27	−	1765.59i	−0.236268	−	0.0856174i
$753$	−4604.41	−	14560.0i	−0.222834	−	0.704644i
$754$	−318.244	+	3652.38i	−0.0153711	+	0.176408i
$755$	5801.90			0.279673
$756$	4790.08	−	4418.14i	0.230441	−	0.212548i
$757$	−16046.9			−0.770453			−0.385226	−	0.922822i	$-0.625877\pi$
$757$	−16046.9			−0.770453			−0.385226	+	0.922822i	$0.625877\pi$
$758$	−1654.39	+	18986.8i	−0.0792744	+	0.909803i
$759$	3185.11	+	10071.9i	0.152322	+	0.481671i
$760$	−7508.01	−	2003.26i	−0.358348	−	0.0956130i
$761$			21727.3i			1.03497i	0.855691	+	0.517486i	$0.173132\pi$
$761$			21727.3i			1.03497i	−0.855691	+	0.517486i	$0.826868\pi$
$762$	−15761.0	+	3514.05i	−0.749291	+	0.167061i
$763$		−	1546.04i		−	0.0733557i
$764$	−6053.98	−	1063.08i	−0.286682	−	0.0503415i
$765$	9923.97	−	6974.09i	0.469022	−	0.329606i
$766$	22769.3	+	1983.97i	1.07400	+	0.0935818i
$767$	37120.2			1.74750
$768$	8072.56	−	19693.1i	0.379288	−	0.925279i
$769$	−1213.18			−0.0568900			−0.0284450	−	0.999595i	$-0.509056\pi$
$769$	−1213.18			−0.0568900			−0.0284450	+	0.999595i	$0.509056\pi$
$770$	−2262.04	−	197.100i	−0.105868	−	0.00922464i
$771$	5072.60	−	1604.14i	0.236946	−	0.0749309i
$772$	8806.22	+	1546.38i	0.410548	+	0.0720923i
$773$		−	11190.6i		−	0.520694i	−0.965515	−	0.260347i	$-0.916163\pi$
$773$		−	11190.6i		−	0.520694i	0.965515	−	0.260347i	$-0.0838369\pi$
$774$	−16300.3	−	28099.3i	−0.756982	−	1.30492i
$775$			6928.22i			0.321121i
$776$	27234.5	+	7266.62i	1.25987	+	0.336155i
$777$	768.566	−	243.048i	0.0354854	−	0.0112218i
$778$	−1095.28	+	12570.1i	−0.0504724	+	0.579254i
$779$	25037.0			1.15153
$780$	14626.5	−	1948.80i	0.671428	−	0.0894593i
$781$	−27264.9			−1.24919
$782$	−1621.71	+	18611.8i	−0.0741591	+	0.851097i
$783$	−1554.15	+	2036.17i	−0.0709334	+	0.0929334i
$784$	18610.3	+	6743.91i	0.847774	+	0.307212i
$785$			778.432i			0.0353929i
$786$	−3142.79	−	14095.8i	−0.142621	−	0.639671i
$787$			22315.6i			1.01075i	0.862899	+	0.505377i	$0.168647\pi$
$787$			22315.6i			1.01075i	−0.862899	+	0.505377i	$0.831353\pi$
$788$	−4099.94	+	23348.1i	−0.185348	+	1.05551i
$789$	−9674.72	−	30593.3i	−0.436539	−	1.38042i
$790$	2479.58	+	216.055i	0.111670	+	0.00973024i
$791$	10171.9			0.457232
$792$	−15859.7	+	5822.12i	−0.711553	+	0.261212i
$793$	−26467.0			−1.18521
$794$	−18540.7	−	1615.52i	−0.828696	−	0.0722072i
$795$	−4784.99	−	15131.1i	−0.213467	−	0.675023i
$796$	−5097.23	+	29027.5i	−0.226968	+	1.29253i
$797$		−	879.892i		−	0.0391058i	−0.999809	−	0.0195529i	$-0.993776\pi$
$797$		−	879.892i		−	0.0391058i	0.999809	−	0.0195529i	$-0.00622429\pi$
$798$	1275.41	+	5720.37i	0.0565777	+	0.253758i
$799$			7275.28i			0.322129i
$800$	4104.84	+	1905.32i	0.181410	+	0.0842041i
$801$	2891.15	+	4114.04i	0.127533	+	0.181476i
$802$	−3017.00	+	34625.1i	−0.132836	+	1.52451i
$803$	63.3685			0.00278484
$804$	−15220.8	+	2027.98i	−0.667659	+	0.0889570i
$805$	−2134.17			−0.0934404
$806$	4830.48	−	55437.7i	0.211100	−	2.42272i
$807$	28365.2	−	8970.11i	1.23730	−	0.391280i
$808$	−7275.67	+	27268.5i	−0.316779	+	1.18725i
$809$			18762.5i			0.815396i	0.913117	+	0.407698i	$0.133668\pi$
$809$			18762.5i			0.815396i	−0.913117	+	0.407698i	$0.866332\pi$
$810$	9360.01	+	4321.84i	0.406021	+	0.187474i
$811$			4479.95i			0.193973i	0.995286	+	0.0969867i	$0.0309204\pi$
$811$			4479.95i			0.193973i	−0.995286	+	0.0969867i	$0.969080\pi$
$812$	835.269	+	146.673i	0.0360988	+	0.00633895i
$813$	−1326.21	+	419.395i	−0.0572104	+	0.0180920i
$814$	−2081.94	−	181.407i	−0.0896463	−	0.00781120i
$815$	13555.2			0.582600
$816$	−29853.6	−	1235.78i	−1.28074	−	0.0530157i
$817$	29216.4			1.25111
$818$	33322.0	+	2903.47i	1.42430	+	0.124104i
$819$	−6398.97	−	9105.59i	−0.273014	−	0.388492i
$820$	−14361.3	−	2521.85i	−0.611608	−	0.107398i
$821$			33949.1i			1.44316i	0.692333	+	0.721578i	$0.256583\pi$
$821$			33949.1i			1.44316i	−0.692333	+	0.721578i	$0.743417\pi$
$822$	29973.6	−	6682.88i	1.27183	−	0.283567i
$823$			8395.58i			0.355591i	0.984067	+	0.177796i	$0.0568966\pi$
$823$			8395.58i			0.355591i	−0.984067	+	0.177796i	$0.943103\pi$
$824$	2931.84	−	10988.2i	0.123951	−	0.464555i
$825$	−1083.14	−	3425.10i	−0.0457093	−	0.144541i
$826$	745.344	−	8554.05i	0.0313969	−	0.360331i
$827$	−41042.4			−1.72574			−0.862868	−	0.505429i	$-0.831334\pi$
$827$	−41042.4			−1.72574			−0.862868	+	0.505429i	$0.831334\pi$
$828$	−14375.4	+	6745.58i	−0.603357	+	0.283122i
$829$	23994.1			1.00525			0.502623	−	0.864506i	$-0.332369\pi$
$829$	23994.1			1.00525			0.502623	+	0.864506i	$0.332369\pi$
$830$	−254.472	+	2920.48i	−0.0106420	+	0.122134i
$831$	2142.74	+	6775.75i	0.0894474	+	0.282850i
$832$	−31517.4	−	18107.8i	−1.31330	−	0.754538i
$833$		−	27789.0i		−	1.15586i
$834$	25993.9	−	5795.59i	1.07925	−	0.240629i
$835$		−	19432.8i		−	0.805390i
$836$	2627.98	−	14965.7i	0.108721	−	0.619139i
$837$	23589.7	−	30906.1i	0.974170	−	1.27631i
$838$	−44386.5	−	3867.55i	−1.82972	−	0.159430i
$839$	32441.7			1.33494			0.667468	−	0.744638i	$-0.267378\pi$
$839$	32441.7			1.33494			0.667468	+	0.744638i	$0.267378\pi$
$840$	−155.395	−	3409.69i	−0.00638292	−	0.140054i
$841$	24055.6			0.986332
$842$	−1960.84	−	170.855i	−0.0802555	−	0.00699295i
$843$	−4545.53	+	1437.46i	−0.185714	+	0.0587294i
$844$	2762.51	−	15731.8i	0.112665	−	0.641602i
$845$		−	14215.6i		−	0.578736i
$846$	−5348.91	+	3102.89i	−0.217375	+	0.126099i
$847$			3287.88i			0.133380i
$848$	−13318.7	+	36753.9i	−0.539345	+	1.48836i
$849$	−26268.4	+	8307.01i	−1.06187	+	0.335802i
$850$	551.486	−	6329.21i	0.0222539	−	0.255400i
$851$	−1964.25			−0.0791231
$852$	−5412.91	−	40626.1i	−0.217657	−	1.63360i
$853$	34328.3			1.37793			0.688967	−	0.724792i	$-0.258064\pi$
$853$	34328.3			1.37793			0.688967	+	0.724792i	$0.258064\pi$
$854$	−531.436	+	6099.09i	−0.0212943	+	0.244387i
$855$	−7586.34	+	5331.31i	−0.303447	+	0.213248i
$856$	25789.4	+	6881.02i	1.02975	+	0.274753i
$857$			17468.4i			0.696277i	0.937443	+	0.348138i	$0.113186\pi$
$857$			17468.4i			0.696277i	−0.937443	+	0.348138i	$0.886814\pi$
$858$	6278.95	+	28161.9i	0.249837	+	1.12055i
$859$		−	49441.1i		−	1.96380i	−0.189389	−	0.981902i	$-0.560651\pi$
$859$		−	49441.1i		−	1.96380i	0.189389	−	0.981902i	$-0.439349\pi$
$860$	−16758.7	−	2942.83i	−0.664495	−	0.116685i
$861$	3315.92	+	10485.6i	0.131250	+	0.415037i
$862$	7715.71	+	672.297i	0.304870	+	0.0265644i
$863$	21826.5			0.860931			0.430466	−	0.902607i	$-0.358349\pi$
$863$	21826.5			0.860931			0.430466	+	0.902607i	$0.358349\pi$
$864$	−11823.9	−	22475.9i	−0.465576	−	0.885008i
$865$	−10817.4			−0.425205
$866$	29481.3	+	2568.81i	1.15683	+	0.100799i
$867$	4950.27	+	15653.7i	0.193910	+	0.613181i
$868$	−12678.2	−	2226.29i	−0.495766	−	0.0870566i
$869$			4866.93i			0.189988i
$870$	291.971	+	1309.53i	0.0113779	+	0.0510312i
$871$			26224.6i			1.02019i
$872$	−5821.61	−	1553.30i	−0.226083	−	0.0603227i
$873$	27518.7	−	19338.8i	1.06686	−	0.749735i
$874$	1239.71	−	14227.7i	0.0479793	−	0.550641i
$875$	725.753			0.0280399
$876$	12.5806	+	94.4225i	0.000485227	+	0.00364183i
$877$	−27627.7			−1.06376			−0.531882	−	0.846818i	$-0.678515\pi$
$877$	−27627.7			−1.06376			−0.531882	+	0.846818i	$0.678515\pi$
$878$	1271.00	−	14586.8i	0.0488543	−	0.560683i
$879$	−12231.6	+	3868.07i	−0.469352	+	0.148426i
$880$	−3014.84	+	8319.69i	−0.115489	+	0.318701i
$881$			34438.1i			1.31697i	0.752595	+	0.658484i	$0.228802\pi$
$881$			34438.1i			1.31697i	−0.752595	+	0.658484i	$0.771198\pi$
$882$	20430.9	−	11851.9i	0.779983	−	0.452466i
$883$			36676.2i			1.39780i	0.715221	+	0.698898i	$0.246326\pi$
$883$			36676.2i			1.39780i	−0.715221	+	0.698898i	$0.753674\pi$
$884$	−8825.67	+	50260.0i	−0.335791	+	1.91225i
$885$	12952.2	−	4095.97i	0.491960	−	0.155576i
$886$	574.665	+	50.0726i	0.0217904	+	0.00189867i
$887$	−6157.49			−0.233087			−0.116544	−	0.993186i	$-0.537181\pi$
$887$	−6157.49			−0.233087			−0.116544	+	0.993186i	$0.537181\pi$
$888$	−143.023	−	3138.22i	−0.00540490	−	0.118595i
$889$	6379.25			0.240667
$890$	2623.81	+	228.622i	0.0988205	+	0.00861058i
$891$	−6830.26	+	18967.0i	−0.256815	+	0.713152i
$892$	4059.77	−	23119.4i	0.152389	−	0.867818i
$893$		−	5561.56i		−	0.208410i
$894$	−7064.14	+	1575.01i	−0.264273	+	0.0589221i
$895$			7755.03i			0.289634i
$896$	−4805.64	+	6899.33i	−0.179180	+	0.257244i
$897$	8177.05	+	25857.4i	0.304374	+	0.962490i
$898$	−1641.41	+	18837.9i	−0.0609963	+	0.700032i
$899$	5059.81			0.187713
$900$	4888.55	−	2293.93i	0.181057	−	0.0849602i
$901$	54881.0			2.02925
$902$	2474.94	−	28404.0i	0.0913598	−	1.04850i
$903$	3869.45	+	12235.9i	0.142599	+	0.450926i
$904$	10219.7	−	38302.2i	0.375996	−	1.40920i
$905$		−	15552.0i		−	0.571235i
$906$	−16645.3	+	3711.23i	−0.610380	+	0.136090i
$907$		−	46057.8i		−	1.68613i	−0.537809	−	0.843067i	$-0.680748\pi$
$907$		−	46057.8i		−	1.68613i	0.537809	−	0.843067i	$-0.319252\pi$
$908$	2367.25	+	415.689i	0.0865197	+	0.0151929i
$909$	19362.9	+	27552.9i	0.706519	+	1.00536i
$910$	−5807.27	−	506.008i	−0.211549	−	0.0184330i
$911$	4675.89			0.170054			0.0850269	−	0.996379i	$-0.472902\pi$
$911$	4675.89			0.170054			0.0850269	+	0.996379i	$0.472902\pi$
$912$	22821.5	+	944.683i	0.828612	+	0.0343000i
$913$	−5732.32			−0.207790
$914$	5295.32	+	461.400i	0.191634	+	0.0166978i
$915$	−9235.03	+	2920.45i	−0.333662	+	0.105516i
$916$	−14804.3	−	2599.63i	−0.534003	−	0.0937710i
$917$			5705.28i			0.205458i
$918$	−24010.3	+	26356.2i	−0.863244	+	0.947587i
$919$			166.886i			0.00599029i	0.999996	+	0.00299515i	$0.000953386\pi$
$919$			166.886i			0.00599029i	−0.999996	+	0.00299515i	$0.999047\pi$
$920$	−2144.19	+	8036.21i	−0.0768390	+	0.287985i
$921$	−6283.33	+	1987.02i	−0.224802	+	0.0710906i
$922$	−1625.68	+	18657.3i	−0.0580683	+	0.666428i
$923$	−69996.3			−2.49616
$924$	6615.74	−	881.463i	0.235543	−	0.0313831i
$925$	667.971			0.0237435
$926$	−2277.32	+	26136.0i	−0.0808179	+	0.927518i
$927$	−7802.56	−	11102.9i	−0.276451	−	0.393383i
$928$	1391.49	−	2997.84i	0.0492219	−	0.106044i
$929$			33064.7i			1.16773i	0.811852	+	0.583863i	$0.198460\pi$
$929$			33064.7i			1.16773i	−0.811852	+	0.583863i	$0.801540\pi$
$930$	−4431.69	−	19876.7i	−0.156259	−	0.700841i
$931$			21243.2i			0.747816i
$932$	6230.74	−	35482.5i	0.218986	−	1.24707i
$933$	−7898.38	−	24976.2i	−0.277150	−	0.876402i
$934$	−34385.5	−	2996.13i	−1.20463	−	0.104964i
$935$	12423.0			0.434518
$936$	−40716.1	+	14947.0i	−1.42185	+	0.521963i
$937$	5952.16			0.207523			0.103761	−	0.994602i	$-0.466912\pi$
$937$	5952.16			0.207523			0.103761	+	0.994602i	$0.466912\pi$
$938$	6043.23	+	526.568i	0.210361	+	0.0183295i
$939$	−10939.4	−	34592.5i	−0.380185	−	1.20222i
$940$	−560.188	+	3190.13i	−0.0194376	+	0.110692i
$941$		−	5231.57i		−	0.181237i	−0.995886	−	0.0906186i	$-0.971116\pi$
$941$		−	5231.57i		−	0.181237i	0.995886	−	0.0906186i	$-0.0288844\pi$
$942$	−497.930	−	2233.28i	−0.0172223	−	0.0772443i
$943$		−	26798.4i		−	0.925424i
$944$	−31461.4	−	11400.8i	−1.08473	−	0.393077i
$945$	−3237.51	−	2471.10i	−0.111446	−	0.0850633i
$946$	2888.09	−	33145.6i	0.0992599	−	1.13917i
$947$	−13903.3			−0.477081			−0.238540	−	0.971133i	$-0.576669\pi$
$947$	−13903.3			−0.477081			−0.238540	+	0.971133i	$0.576669\pi$
$948$	−7251.99	+	966.235i	−0.248453	+	0.0331032i
$949$	162.684			0.00556475
$950$	−421.581	+	4838.33i	−0.0143978	+	0.165238i
$951$	1195.90	−	378.188i	0.0407779	−	0.0128955i
$952$	11404.8	+	3042.98i	0.388268	+	0.103596i
$953$			16469.4i			0.559808i	0.960028	+	0.279904i	$0.0903027\pi$
$953$			16469.4i			0.559808i	−0.960028	+	0.279904i	$0.909697\pi$
$954$	23406.6	+	40349.4i	0.794356	+	1.36935i
$955$			3841.63i			0.130170i
$956$	−32891.5	−	5775.76i	−1.11275	−	0.195399i
$957$	−2501.41	+	791.038i	−0.0844924	+	0.0267196i
$958$	24349.2	+	2121.64i	0.821178	+	0.0715521i
$959$	−12131.8			−0.408505
$960$	−12995.3	−	2840.56i	−0.436898	−	0.0954988i
$961$	−47009.4			−1.57797
$962$	−5344.92	−	465.721i	−0.179134	−	0.0156086i
$963$	26058.4	−	18312.6i	0.871984	−	0.612788i
$964$	−37944.0	−	6662.97i	−1.26773	−	0.222614i
$965$		−	5588.10i		−	0.186412i
$966$	6122.81	−	1365.14i	0.203932	−	0.0454685i
$967$			6660.73i			0.221504i	0.993848	+	0.110752i	$0.0353260\pi$
$967$			6660.73i			0.221504i	−0.993848	+	0.110752i	$0.964674\pi$
$968$	12380.5	+	3303.33i	0.411080	+	0.109683i
$969$	−9668.44	−	30573.5i	−0.320531	−	1.01358i
$970$	1529.24	−	17550.6i	0.0506196	−	0.580943i
$971$	30462.3			1.00678			0.503389	−	0.864060i	$-0.332086\pi$
$971$	30462.3			1.00678			0.503389	+	0.864060i	$0.332086\pi$
$972$	−29617.9	−	6411.93i	−0.977359	−	0.211587i
$973$	−10521.0			−0.346649
$974$	2551.43	−	29281.9i	0.0839356	−	0.963298i
$975$	−2780.72	−	8793.16i	−0.0913377	−	0.288827i
$976$	22432.2	+	8128.86i	0.735694	+	0.266597i
$977$			5485.47i			0.179627i	0.995959	+	0.0898136i	$0.0286271\pi$
$977$			5485.47i			0.179627i	−0.995959	+	0.0898136i	$0.971373\pi$
$978$	−38889.2	+	8670.70i	−1.27151	+	0.283495i
$979$			5150.01i			0.168126i
$980$	2139.72	−	12185.2i	0.0697457	−	0.397184i
$981$	−5882.35	+	4133.83i	−0.191446	+	0.134539i
$982$	10670.5	+	929.759i	0.346751	+	0.0302136i
$983$	−15377.0			−0.498932			−0.249466	−	0.968384i	$-0.580255\pi$
$983$	−15377.0			−0.498932			−0.249466	+	0.968384i	$0.580255\pi$
$984$	42814.9	−	1951.27i	1.38708	−	0.0632157i
$985$	14815.9			0.479261
$986$	−4622.34	−	402.761i	−0.149295	−	0.0130086i
$987$	2329.20	−	736.577i	0.0751157	−	0.0237543i
$988$	6746.75	−	38421.0i	0.217250	−	1.23718i
$989$		−	31271.9i		−	1.00545i
$990$	5298.36	+	9133.58i	0.170094	+	0.293216i
$991$		−	12717.9i		−	0.407665i	−0.979006	−	0.203832i	$-0.934660\pi$
$991$		−	12717.9i		−	0.407665i	0.979006	−	0.203832i	$-0.0653398\pi$
$992$	−21120.8	+	45502.8i	−0.675993	+	1.45637i
$993$	6751.53	−	2135.08i	0.215764	−	0.0682323i
$994$	−1405.47	+	16130.1i	−0.0448479	+	0.514703i
$995$	18419.8			0.586880
$996$	−1138.04	−	8541.46i	−0.0362050	−	0.271734i
$997$	−6526.82			−0.207329			−0.103664	−	0.994612i	$-0.533057\pi$
$997$	−6526.82			−0.207329			−0.103664	+	0.994612i	$0.533057\pi$
$998$	−3256.73	+	37376.3i	−0.103296	+	1.18550i
$999$	−2979.75	−	2274.36i	−0.0943695	−	0.0720296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.e.a.11.1	✓	24
3.2	odd	2	inner	60.4.e.a.11.24	yes	24
4.3	odd	2	inner	60.4.e.a.11.23	yes	24
8.3	odd	2		960.4.h.d.191.11		24
8.5	even	2		960.4.h.d.191.14		24
12.11	even	2	inner	60.4.e.a.11.2	yes	24
24.5	odd	2		960.4.h.d.191.12		24
24.11	even	2		960.4.h.d.191.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.e.a.11.1	✓	24	1.1	even	1	trivial
60.4.e.a.11.2	yes	24	12.11	even	2	inner
60.4.e.a.11.23	yes	24	4.3	odd	2	inner
60.4.e.a.11.24	yes	24	3.2	odd	2	inner
960.4.h.d.191.11		24	8.3	odd	2
960.4.h.d.191.12		24	24.5	odd	2
960.4.h.d.191.13		24	24.11	even	2
960.4.h.d.191.14		24	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81775 - 0.245521i) q^{2} +(-1.56674 - 4.95432i) q^{3} +(7.87944 + 1.38363i) q^{4} -5.00000i q^{5} +(3.19829 + 14.3447i) q^{6} -5.80602i q^{7} +(-21.8626 - 5.83329i) q^{8} +(-22.0907 + 15.5243i) q^{9} +O(q^{10})\)	\(q+(-2.81775 - 0.245521i) q^{2} +(-1.56674 - 4.95432i) q^{3} +(7.87944 + 1.38363i) q^{4} -5.00000i q^{5} +(3.19829 + 14.3447i) q^{6} -5.80602i q^{7} +(-21.8626 - 5.83329i) q^{8} +(-22.0907 + 15.5243i) q^{9} +(-1.22760 + 14.0888i) q^{10} -27.6534 q^{11} +(-5.49005 - 41.2051i) q^{12} -70.9938 q^{13} +(-1.42550 + 16.3599i) q^{14} +(-24.7716 + 7.83369i) q^{15} +(60.1711 + 21.8045i) q^{16} -89.8477i q^{17} +(66.0575 - 38.3198i) q^{18} +68.6836i q^{19} +(6.91816 - 39.3972i) q^{20} +(-28.7649 + 9.09652i) q^{21} +(77.9204 + 6.78948i) q^{22} +73.5156 q^{23} +(5.35291 + 117.454i) q^{24} -25.0000 q^{25} +(200.043 + 17.4304i) q^{26} +(111.522 + 85.1219i) q^{27} +(8.03340 - 45.7482i) q^{28} +18.2580i q^{29} +(71.7236 - 15.9914i) q^{30} -277.129i q^{31} +(-164.194 - 76.2128i) q^{32} +(43.3257 + 137.004i) q^{33} +(-22.0595 + 253.168i) q^{34} -29.0301 q^{35} +(-195.542 + 91.7571i) q^{36} -26.7188 q^{37} +(16.8632 - 193.533i) q^{38} +(111.229 + 351.726i) q^{39} +(-29.1665 + 109.313i) q^{40} -364.526i q^{41} +(83.2858 - 18.5693i) q^{42} -425.377i q^{43} +(-217.893 - 38.2621i) q^{44} +(77.6213 + 110.453i) q^{45} +(-207.149 - 18.0496i) q^{46} -80.9735 q^{47} +(13.7541 - 332.269i) q^{48} +309.290 q^{49} +(70.4438 + 6.13801i) q^{50} +(-445.135 + 140.768i) q^{51} +(-559.392 - 98.2293i) q^{52} +610.822i q^{53} +(-293.343 - 267.233i) q^{54} +138.267i q^{55} +(-33.8682 + 126.935i) q^{56} +(340.281 - 107.609i) q^{57} +(4.48270 - 51.4464i) q^{58} -522.866 q^{59} +(-206.025 + 27.4503i) q^{60} +372.807 q^{61} +(-68.0408 + 780.880i) q^{62} +(90.1342 + 128.259i) q^{63} +(443.945 + 255.062i) q^{64} +354.969i q^{65} +(-88.4436 - 396.681i) q^{66} -369.392i q^{67} +(124.316 - 707.949i) q^{68} +(-115.180 - 364.220i) q^{69} +(81.7996 + 7.12749i) q^{70} +985.949 q^{71} +(573.517 - 210.539i) q^{72} -2.29153 q^{73} +(75.2871 + 6.56003i) q^{74} +(39.1684 + 123.858i) q^{75} +(-95.0328 + 541.189i) q^{76} +160.556i q^{77} +(-227.059 - 1018.39i) q^{78} -175.997i q^{79} +(109.022 - 300.856i) q^{80} +(246.995 - 685.882i) q^{81} +(-89.4986 + 1027.14i) q^{82} +207.291 q^{83} +(-239.238 + 31.8754i) q^{84} -449.238 q^{85} +(-104.439 + 1198.61i) q^{86} +(90.4559 - 28.6054i) q^{87} +(604.575 + 161.311i) q^{88} -186.234i q^{89} +(-191.599 - 330.288i) q^{90} +412.192i q^{91} +(579.262 + 101.719i) q^{92} +(-1372.99 + 434.188i) q^{93} +(228.163 + 19.8807i) q^{94} +343.418 q^{95} +(-120.335 + 932.875i) q^{96} -1245.71 q^{97} +(-871.502 - 75.9371i) q^{98} +(610.882 - 429.299i) 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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