LMFDB - Embedded newform 462.4.e.b.307.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,4,Mod(307,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.307");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	462.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:	$27.2588824227$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.19
Character	$\chi$	$=$	462.307
Dual form			462.4.e.b.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +6.45926i q^{5} +6.00000 q^{6} +(17.9060 + 4.73009i) q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +6.45926i q^{5} +6.00000 q^{6} +(17.9060 + 4.73009i) q^{7} -8.00000i q^{8} -9.00000 q^{9} -12.9185 q^{10} +(23.5058 - 27.9012i) q^{11} +12.0000i q^{12} -11.2199 q^{13} +(-9.46017 + 35.8121i) q^{14} +19.3778 q^{15} +16.0000 q^{16} +34.2568 q^{17} -18.0000i q^{18} -57.3519 q^{19} -25.8370i q^{20} +(14.1903 - 53.7181i) q^{21} +(55.8024 + 47.0116i) q^{22} +14.1561 q^{23} -24.0000 q^{24} +83.2780 q^{25} -22.4398i q^{26} +27.0000i q^{27} +(-71.6242 - 18.9203i) q^{28} +21.4030i q^{29} +38.7556i q^{30} -160.754i q^{31} +32.0000i q^{32} +(-83.7036 - 70.5174i) q^{33} +68.5137i q^{34} +(-30.5529 + 115.660i) q^{35} +36.0000 q^{36} +269.410 q^{37} -114.704i q^{38} +33.6597i q^{39} +51.6741 q^{40} -87.1714 q^{41} +(107.436 + 28.3805i) q^{42} +199.059i q^{43} +(-94.0232 + 111.605i) q^{44} -58.1333i q^{45} +28.3123i q^{46} +114.665i q^{47} -48.0000i q^{48} +(298.253 + 169.394i) q^{49} +166.556i q^{50} -102.770i q^{51} +44.8796 q^{52} +539.539 q^{53} -54.0000 q^{54} +(180.221 + 151.830i) q^{55} +(37.8407 - 143.248i) q^{56} +172.056i q^{57} -42.8060 q^{58} +83.8122i q^{59} -77.5111 q^{60} +513.540 q^{61} +321.509 q^{62} +(-161.154 - 42.5708i) q^{63} -64.0000 q^{64} -72.4723i q^{65} +(141.035 - 167.407i) q^{66} +746.287 q^{67} -137.027 q^{68} -42.4684i q^{69} +(-231.320 - 61.1057i) q^{70} +432.685 q^{71} +72.0000i q^{72} +1066.43 q^{73} +538.821i q^{74} -249.834i q^{75} +229.408 q^{76} +(552.871 - 388.416i) q^{77} -67.3194 q^{78} +922.115i q^{79} +103.348i q^{80} +81.0000 q^{81} -174.343i q^{82} -994.942 q^{83} +(-56.7610 + 214.872i) q^{84} +221.274i q^{85} -398.117 q^{86} +64.2090 q^{87} +(-223.210 - 188.046i) q^{88} -788.857i q^{89} +116.267 q^{90} +(-200.904 - 53.0711i) q^{91} -56.6245 q^{92} -482.263 q^{93} -229.331 q^{94} -370.451i q^{95} +96.0000 q^{96} +977.250i q^{97} +(-338.789 + 596.505i) q^{98} +(-211.552 + 251.111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 96 q^{4} + 144 q^{6} - 36 q^{7} - 216 q^{9}+O(q^{10}) $ 24 * q - 96 * q^4 + 144 * q^6 - 36 * q^7 - 216 * q^9	$ 24 q - 96 q^{4} + 144 q^{6} - 36 q^{7} - 216 q^{9} - 56 q^{10} - 28 q^{11} + 32 q^{14} + 84 q^{15} + 384 q^{16} + 204 q^{17} + 244 q^{19} - 48 q^{21} - 64 q^{22} + 56 q^{23} - 576 q^{24} - 1096 q^{25} + 144 q^{28} + 96 q^{33} + 16 q^{35} + 864 q^{36} - 696 q^{37} + 224 q^{40} - 1276 q^{41} - 216 q^{42} + 112 q^{44} + 836 q^{49} + 168 q^{53} - 1296 q^{54} - 712 q^{55} - 128 q^{56} - 336 q^{58} - 336 q^{60} - 616 q^{61} + 1048 q^{62} + 324 q^{63} - 1536 q^{64} - 168 q^{66} - 1544 q^{67} - 816 q^{68} - 168 q^{70} - 944 q^{71} - 2212 q^{73} - 976 q^{76} - 1888 q^{77} + 1944 q^{81} + 236 q^{83} + 192 q^{84} - 336 q^{86} + 504 q^{87} + 256 q^{88} + 504 q^{90} - 508 q^{91} - 224 q^{92} - 1572 q^{93} - 584 q^{94} + 2304 q^{96} - 2008 q^{98} + 252 q^{99}+O(q^{100}) $ 24 * q - 96 * q^4 + 144 * q^6 - 36 * q^7 - 216 * q^9 - 56 * q^10 - 28 * q^11 + 32 * q^14 + 84 * q^15 + 384 * q^16 + 204 * q^17 + 244 * q^19 - 48 * q^21 - 64 * q^22 + 56 * q^23 - 576 * q^24 - 1096 * q^25 + 144 * q^28 + 96 * q^33 + 16 * q^35 + 864 * q^36 - 696 * q^37 + 224 * q^40 - 1276 * q^41 - 216 * q^42 + 112 * q^44 + 836 * q^49 + 168 * q^53 - 1296 * q^54 - 712 * q^55 - 128 * q^56 - 336 * q^58 - 336 * q^60 - 616 * q^61 + 1048 * q^62 + 324 * q^63 - 1536 * q^64 - 168 * q^66 - 1544 * q^67 - 816 * q^68 - 168 * q^70 - 944 * q^71 - 2212 * q^73 - 976 * q^76 - 1888 * q^77 + 1944 * q^81 + 236 * q^83 + 192 * q^84 - 336 * q^86 + 504 * q^87 + 256 * q^88 + 504 * q^90 - 508 * q^91 - 224 * q^92 - 1572 * q^93 - 584 * q^94 + 2304 * q^96 - 2008 * q^98 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.00000			−0.500000
$5$			6.45926i			0.577734i	0.957369	+	0.288867i	$0.0932785\pi$
$5$			6.45926i			0.577734i	−0.957369	+	0.288867i	$0.906721\pi$
$6$	6.00000			0.408248
$7$	17.9060	+	4.73009i	0.966835	+	0.255401i
$7$	17.9060	+	4.73009i	0.966835	+	0.255401i
$8$		−	8.00000i		−	0.353553i
$9$	−9.00000			−0.333333
$10$	−12.9185			−0.408519
$11$	23.5058	−	27.9012i	0.644297	−	0.764776i
$11$	23.5058	−	27.9012i	0.644297	−	0.764776i
$12$			12.0000i			0.288675i
$13$	−11.2199			−0.239372			−0.119686	−	0.992812i	$-0.538189\pi$
$13$	−11.2199			−0.239372			−0.119686	+	0.992812i	$0.538189\pi$
$14$	−9.46017	+	35.8121i	−0.180596	+	0.683656i
$15$	19.3778			0.333555
$16$	16.0000			0.250000
$17$	34.2568			0.488735			0.244368	−	0.969683i	$-0.421420\pi$
$17$	34.2568			0.488735			0.244368	+	0.969683i	$0.421420\pi$
$18$		−	18.0000i		−	0.235702i
$19$	−57.3519			−0.692496			−0.346248	−	0.938143i	$-0.612544\pi$
$19$	−57.3519			−0.692496			−0.346248	+	0.938143i	$0.612544\pi$
$20$		−	25.8370i		−	0.288867i
$21$	14.1903	−	53.7181i	0.147456	−	0.558203i
$22$	55.8024	+	47.0116i	0.540778	+	0.455587i
$23$	14.1561			0.128337			0.0641687	−	0.997939i	$-0.479560\pi$
$23$	14.1561			0.128337			0.0641687	+	0.997939i	$0.479560\pi$
$24$	−24.0000			−0.204124
$25$	83.2780			0.666224
$26$		−	22.4398i		−	0.169262i
$27$			27.0000i			0.192450i
$28$	−71.6242	−	18.9203i	−0.483418	−	0.127700i
$29$			21.4030i			0.137050i	0.997649	+	0.0685248i	$0.0218292\pi$
$29$			21.4030i			0.137050i	−0.997649	+	0.0685248i	$0.978171\pi$
$30$			38.7556i			0.235859i
$31$		−	160.754i		−	0.931365i	−0.884952	−	0.465683i	$-0.845809\pi$
$31$		−	160.754i		−	0.931365i	0.884952	−	0.465683i	$-0.154191\pi$
$32$			32.0000i			0.176777i
$33$	−83.7036	−	70.5174i	−0.441543	−	0.371985i
$34$			68.5137i			0.345588i
$35$	−30.5529	+	115.660i	−0.147554	+	0.558573i
$36$	36.0000			0.166667
$37$	269.410			1.19705			0.598524	−	0.801105i	$-0.295754\pi$
$37$	269.410			1.19705			0.598524	+	0.801105i	$0.295754\pi$
$38$		−	114.704i		−	0.489669i
$39$			33.6597i			0.138202i
$40$	51.6741			0.204260
$41$	−87.1714			−0.332046			−0.166023	−	0.986122i	$-0.553093\pi$
$41$	−87.1714			−0.332046			−0.166023	+	0.986122i	$0.553093\pi$
$42$	107.436	+	28.3805i	0.394709	+	0.104267i
$43$			199.059i			0.705957i	0.935631	+	0.352978i	$0.114831\pi$
$43$			199.059i			0.705957i	−0.935631	+	0.352978i	$0.885169\pi$
$44$	−94.0232	+	111.605i	−0.322148	+	0.382388i
$45$		−	58.1333i		−	0.192578i
$46$			28.3123i			0.0907482i
$47$			114.665i			0.355866i	0.984043	+	0.177933i	$0.0569410\pi$
$47$			114.665i			0.355866i	−0.984043	+	0.177933i	$0.943059\pi$
$48$		−	48.0000i		−	0.144338i
$49$	298.253	+	169.394i	0.869541	+	0.493861i
$50$			166.556i			0.471091i
$51$		−	102.770i		−	0.282171i
$52$	44.8796			0.119686
$53$	539.539			1.39833			0.699163	−	0.714962i	$-0.253556\pi$
$53$	539.539			1.39833			0.699163	+	0.714962i	$0.253556\pi$
$54$	−54.0000			−0.136083
$55$	180.221	+	151.830i	0.441837	+	0.372232i
$56$	37.8407	−	143.248i	0.0902978	−	0.341828i
$57$			172.056i			0.399813i
$58$	−42.8060			−0.0969087
$59$			83.8122i			0.184939i	0.995716	+	0.0924696i	$0.0294761\pi$
$59$			83.8122i			0.184939i	−0.995716	+	0.0924696i	$0.970524\pi$
$60$	−77.5111			−0.166777
$61$	513.540			1.07790			0.538951	−	0.842337i	$-0.318821\pi$
$61$	513.540			1.07790			0.538951	+	0.842337i	$0.318821\pi$
$62$	321.509			0.658575
$63$	−161.154	−	42.5708i	−0.322278	−	0.0851336i
$64$	−64.0000			−0.125000
$65$		−	72.4723i		−	0.138294i
$66$	141.035	−	167.407i	0.263033	−	0.312218i
$67$	746.287			1.36080			0.680399	−	0.732842i	$-0.261807\pi$
$67$	746.287			1.36080			0.680399	+	0.732842i	$0.261807\pi$
$68$	−137.027			−0.244368
$69$		−	42.4684i		−	0.0740956i
$70$	−231.320	−	61.1057i	−0.394971	−	0.104336i
$71$	432.685			0.723243			0.361621	−	0.932325i	$-0.382223\pi$
$71$	432.685			0.723243			0.361621	+	0.932325i	$0.382223\pi$
$72$			72.0000i			0.117851i
$73$	1066.43			1.70981			0.854906	−	0.518782i	$-0.173615\pi$
$73$	1066.43			1.70981			0.854906	+	0.518782i	$0.173615\pi$
$74$			538.821i			0.846441i
$75$		−	249.834i		−	0.384644i
$76$	229.408			0.346248
$77$	552.871	−	388.416i	0.818253	−	0.574858i
$78$	−67.3194			−0.0977234
$79$			922.115i			1.31324i	0.754221	+	0.656620i	$0.228015\pi$
$79$			922.115i			1.31324i	−0.754221	+	0.656620i	$0.771985\pi$
$80$			103.348i			0.144433i
$81$	81.0000			0.111111
$82$		−	174.343i		−	0.234792i
$83$	−994.942			−1.31577			−0.657886	−	0.753118i	$-0.728549\pi$
$83$	−994.942			−1.31577			−0.657886	+	0.753118i	$0.728549\pi$
$84$	−56.7610	+	214.872i	−0.0737278	+	0.279101i
$85$			221.274i			0.282359i
$86$	−398.117			−0.499187
$87$	64.2090			0.0791256
$88$	−223.210	−	188.046i	−0.270389	−	0.227793i
$89$		−	788.857i		−	0.939535i	−0.882790	−	0.469768i	$-0.844338\pi$
$89$		−	788.857i		−	0.939535i	0.882790	−	0.469768i	$-0.155662\pi$
$90$	116.267			0.136173
$91$	−200.904	−	53.0711i	−0.231434	−	0.0611359i
$92$	−56.6245			−0.0641687
$93$	−482.263			−0.537724
$94$	−229.331			−0.251635
$95$		−	370.451i		−	0.400078i
$96$	96.0000			0.102062
$97$			977.250i			1.02294i	0.859303	+	0.511468i	$0.170898\pi$
$97$			977.250i			1.02294i	−0.859303	+	0.511468i	$0.829102\pi$
$98$	−338.789	+	596.505i	−0.349212	+	0.614858i
$99$	−211.552	+	251.111i	−0.214766	+	0.254925i
$100$	−333.112			−0.333112
$101$	−574.164			−0.565658			−0.282829	−	0.959170i	$-0.591273\pi$
$101$	−574.164			−0.565658			−0.282829	+	0.959170i	$0.591273\pi$
$102$	205.541			0.199525
$103$		−	506.732i		−	0.484755i	−0.970182	−	0.242378i	$-0.922073\pi$
$103$		−	506.732i		−	0.484755i	0.970182	−	0.242378i	$-0.0779273\pi$
$104$			89.7592i			0.0846309i
$105$	346.979	+	91.6586i	0.322493	+	0.0851901i
$106$			1079.08i			0.988766i
$107$			465.895i			0.420932i	0.977601	+	0.210466i	$0.0674982\pi$
$107$			465.895i			0.420932i	−0.977601	+	0.210466i	$0.932502\pi$
$108$		−	108.000i		−	0.0962250i
$109$			3.71651i			0.00326585i	0.999999	+	0.00163292i	$0.000519776\pi$
$109$			3.71651i			0.00326585i	−0.999999	+	0.00163292i	$0.999480\pi$
$110$	−303.660	+	360.442i	−0.263208	+	0.312426i
$111$		−	808.231i		−	0.691116i
$112$	286.497	+	75.6814i	0.241709	+	0.0638502i
$113$	20.7571			0.0172802			0.00864012	−	0.999963i	$-0.497250\pi$
$113$	20.7571			0.0172802			0.00864012	+	0.999963i	$0.497250\pi$
$114$	−344.111			−0.282710
$115$			91.4382i			0.0741448i
$116$		−	85.6120i		−	0.0685248i
$117$	100.979			0.0797908
$118$	−167.624			−0.130772
$119$	613.404	+	162.038i	0.472527	+	0.124823i
$120$		−	155.022i		−	0.117929i
$121$	−225.955	−	1311.68i	−0.169763	−	0.985485i
$122$			1027.08i			0.762192i
$123$			261.514i			0.191707i
$124$			643.017i			0.465683i
$125$			1345.32i			0.962634i
$126$	85.1416	−	322.309i	0.0601985	−	0.227885i
$127$		−	1320.60i		−	0.922709i	−0.887216	−	0.461354i	$-0.847364\pi$
$127$		−	1320.60i		−	0.922709i	0.887216	−	0.461354i	$-0.152636\pi$
$128$		−	128.000i		−	0.0883883i
$129$	597.176			0.407584
$130$	144.945			0.0977883
$131$	−2524.30			−1.68358			−0.841789	−	0.539806i	$-0.818497\pi$
$131$	−2524.30			−1.68358			−0.841789	+	0.539806i	$0.818497\pi$
$132$	334.814	+	282.070i	0.220772	+	0.185992i
$133$	−1026.95	−	271.279i	−0.669530	−	0.176864i
$134$			1492.57i			0.962229i
$135$	−174.400			−0.111185
$136$		−	274.055i		−	0.172794i
$137$	742.692			0.463157			0.231578	−	0.972816i	$-0.425611\pi$
$137$	742.692			0.463157			0.231578	+	0.972816i	$0.425611\pi$
$138$	84.9368			0.0523935
$139$	400.915			0.244641			0.122321	−	0.992491i	$-0.460966\pi$
$139$	400.915			0.244641			0.122321	+	0.992491i	$0.460966\pi$
$140$	122.211	−	462.639i	0.0737768	−	0.279287i
$141$	343.996			0.205459
$142$			865.370i			0.511410i
$143$	−263.733	+	313.049i	−0.154227	+	0.183066i
$144$	−144.000			−0.0833333
$145$	−138.248			−0.0791782
$146$			2132.86i			1.20902i
$147$	508.183	−	894.758i	0.285131	−	0.502030i
$148$	−1077.64			−0.598524
$149$			1285.17i			0.706614i	0.935507	+	0.353307i	$0.114943\pi$
$149$			1285.17i			0.706614i	−0.935507	+	0.353307i	$0.885057\pi$
$150$	499.668			0.271985
$151$		−	2490.17i		−	1.34203i	−0.741442	−	0.671017i	$-0.765858\pi$
$151$		−	2490.17i		−	1.34203i	0.741442	−	0.671017i	$-0.234142\pi$
$152$			458.815i			0.244834i
$153$	−308.311			−0.162912
$154$	776.831	+	1105.74i	0.406486	+	0.578592i
$155$	1038.35			0.538081
$156$		−	134.639i		−	0.0691008i
$157$			1707.03i			0.867742i	0.900975	+	0.433871i	$0.142853\pi$
$157$			1707.03i			0.867742i	−0.900975	+	0.433871i	$0.857147\pi$
$158$	−1844.23			−0.928601
$159$		−	1618.62i		−	0.807324i
$160$	−206.696			−0.102130
$161$	253.480	+	66.9598i	0.124081	+	0.0327774i
$162$			162.000i			0.0785674i
$163$	3617.14			1.73814			0.869069	−	0.494691i	$-0.164719\pi$
$163$	3617.14			1.73814			0.869069	+	0.494691i	$0.164719\pi$
$164$	348.685			0.166023
$165$	455.490	−	540.663i	0.214908	−	0.255095i
$166$		−	1989.88i		−	0.930391i
$167$	−1730.10			−0.801674			−0.400837	−	0.916149i	$-0.631281\pi$
$167$	−1730.10			−0.801674			−0.400837	+	0.916149i	$0.631281\pi$
$168$	−429.745	−	113.522i	−0.197354	−	0.0521335i
$169$	−2071.11			−0.942701
$170$	−442.548			−0.199658
$171$	516.167			0.230832
$172$		−	796.234i		−	0.352978i
$173$	−3267.81			−1.43611			−0.718055	−	0.695987i	$-0.754967\pi$
$173$	−3267.81			−1.43611			−0.718055	+	0.695987i	$0.754967\pi$
$174$			128.418i			0.0559503i
$175$	1491.18	+	393.912i	0.644129	+	0.170154i
$176$	376.093	−	446.419i	0.161074	−	0.191194i
$177$	251.437			0.106775
$178$	1577.71			0.664352
$179$	1651.20			0.689477			0.344739	−	0.938699i	$-0.387968\pi$
$179$	1651.20			0.689477			0.344739	+	0.938699i	$0.387968\pi$
$180$			232.533i			0.0962890i
$181$			216.093i			0.0887407i	0.999015	+	0.0443704i	$0.0141282\pi$
$181$			216.093i			0.0887407i	−0.999015	+	0.0443704i	$0.985872\pi$
$182$	106.142	−	401.808i	0.0432296	−	0.163648i
$183$		−	1540.62i		−	0.622327i
$184$		−	113.249i		−	0.0453741i
$185$			1740.19i			0.691575i
$186$		−	964.526i		−	0.380228i
$187$	805.234	−	955.807i	0.314891	−	0.373773i
$188$		−	458.662i		−	0.177933i
$189$	−127.712	+	483.463i	−0.0491519	+	0.186068i
$190$	740.902			0.282898
$191$	−4125.32			−1.56282			−0.781408	−	0.624021i	$-0.785498\pi$
$191$	−4125.32			−1.56282			−0.781408	+	0.624021i	$0.785498\pi$
$192$			192.000i			0.0721688i
$193$		−	2163.39i		−	0.806860i	−0.915010	−	0.403430i	$-0.867818\pi$
$193$		−	2163.39i		−	0.806860i	0.915010	−	0.403430i	$-0.132182\pi$
$194$	−1954.50			−0.723324
$195$	−217.417			−0.0798438
$196$	−1193.01	−	677.577i	−0.434770	−	0.246930i
$197$		−	3402.60i		−	1.23058i	−0.788299	−	0.615292i	$-0.789038\pi$
$197$		−	3402.60i		−	1.23058i	0.788299	−	0.615292i	$-0.210962\pi$
$198$	−502.222	−	423.104i	−0.180259	−	0.151862i
$199$		−	5464.36i		−	1.94652i	−0.229702	−	0.973261i	$-0.573775\pi$
$199$		−	5464.36i		−	1.94652i	0.229702	−	0.973261i	$-0.426225\pi$
$200$		−	666.224i		−	0.235546i
$201$		−	2238.86i		−	0.785657i
$202$		−	1148.33i		−	0.399980i
$203$	−101.238	+	383.243i	−0.0350026	+	0.132504i
$204$			411.082i			0.141086i
$205$		−	563.062i		−	0.191834i
$206$	1013.46			0.342774
$207$	−127.405			−0.0427791
$208$	−179.518			−0.0598431
$209$	−1348.10	+	1600.19i	−0.446173	+	0.529604i
$210$	−183.317	+	693.959i	−0.0602385	+	0.228037i
$211$		−	2559.86i		−	0.835204i	−0.908630	−	0.417602i	$-0.862871\pi$
$211$		−	2559.86i		−	0.835204i	0.908630	−	0.417602i	$-0.137129\pi$
$212$	−2158.15			−0.699163
$213$		−	1298.05i		−	0.417565i
$214$	−931.790			−0.297644
$215$	−1285.77			−0.407855
$216$	216.000			0.0680414
$217$	760.382	−	2878.47i	0.237871	−	0.900477i
$218$	−7.43303			−0.00230930
$219$		−	3199.29i		−	0.987161i
$220$	−720.885	−	607.320i	−0.220918	−	0.186116i
$221$	−384.358			−0.116990
$222$	1616.46			0.488693
$223$			1114.73i			0.334745i	0.985894	+	0.167373i	$0.0535283\pi$
$223$			1114.73i			0.334745i	−0.985894	+	0.167373i	$0.946472\pi$
$224$	−151.363	+	572.993i	−0.0451489	+	0.170914i
$225$	−749.502			−0.222075
$226$			41.5142i			0.0122190i
$227$	−1184.90			−0.346452			−0.173226	−	0.984882i	$-0.555419\pi$
$227$	−1184.90			−0.346452			−0.173226	+	0.984882i	$0.555419\pi$
$228$		−	688.223i		−	0.199906i
$229$			1748.58i			0.504583i	0.967651	+	0.252292i	$0.0811842\pi$
$229$			1748.58i			0.504583i	−0.967651	+	0.252292i	$0.918816\pi$
$230$	−182.876			−0.0524283
$231$	−1165.25	−	1658.61i	−0.331894	−	0.472419i
$232$	171.224			0.0484544
$233$			2219.29i			0.623993i	0.950083	+	0.311996i	$0.100998\pi$
$233$			2219.29i			0.623993i	−0.950083	+	0.311996i	$0.899002\pi$
$234$			201.958i			0.0564206i
$235$	−740.654			−0.205596
$236$		−	335.249i		−	0.0924696i
$237$	2766.34			0.758200
$238$	−324.076	+	1226.81i	−0.0882634	+	0.334127i
$239$		−	3962.82i		−	1.07253i	−0.844051	−	0.536263i	$-0.819835\pi$
$239$		−	3962.82i		−	1.07253i	0.844051	−	0.536263i	$-0.180165\pi$
$240$	310.045			0.0833887
$241$	2419.52			0.646702			0.323351	−	0.946279i	$-0.395191\pi$
$241$	2419.52			0.646702			0.323351	+	0.946279i	$0.395191\pi$
$242$	2623.36	−	451.910i	0.696843	−	0.120041i
$243$		−	243.000i		−	0.0641500i
$244$	−2054.16			−0.538951
$245$	−1094.16	+	1926.49i	−0.285320	+	0.502363i
$246$	−523.028			−0.135557
$247$	643.483			0.165764
$248$	−1286.03			−0.329287
$249$			2984.83i			0.759661i
$250$	−2690.64			−0.680685
$251$			5773.92i			1.45198i	0.687706	+	0.725989i	$0.258618\pi$
$251$			5773.92i			1.45198i	−0.687706	+	0.725989i	$0.741382\pi$
$252$	644.617	+	170.283i	0.161139	+	0.0425668i
$253$	332.751	−	394.973i	0.0826873	−	0.0981492i
$254$	2641.19			0.652454
$255$	663.821			0.163020
$256$	256.000			0.0625000
$257$			2093.34i			0.508088i	0.967193	+	0.254044i	$0.0817609\pi$
$257$			2093.34i			0.508088i	−0.967193	+	0.254044i	$0.918239\pi$
$258$			1194.35i			0.288206i
$259$	4824.07	+	1274.33i	1.15735	+	0.305727i
$260$			289.889i			0.0691468i
$261$		−	192.627i		−	0.0456832i
$262$		−	5048.59i		−	1.19047i
$263$		−	2269.07i		−	0.532003i	−0.963973	−	0.266002i	$-0.914297\pi$
$263$		−	2269.07i		−	0.532003i	0.963973	−	0.266002i	$-0.0857026\pi$
$264$	−564.139	+	669.629i	−0.131517	+	0.156109i
$265$			3485.02i			0.807861i
$266$	542.559	−	2053.89i	0.125062	−	0.473429i
$267$	−2366.57			−0.542441
$268$	−2985.15			−0.680399
$269$		−	4896.79i		−	1.10990i	−0.831885	−	0.554949i	$-0.812738\pi$
$269$		−	4896.79i		−	1.10990i	0.831885	−	0.554949i	$-0.187262\pi$
$270$		−	348.800i		−	0.0786196i
$271$	−365.586			−0.0819475			−0.0409738	−	0.999160i	$-0.513046\pi$
$271$	−365.586			−0.0819475			−0.0409738	+	0.999160i	$0.513046\pi$
$272$	548.109			0.122184
$273$	−159.213	+	602.712i	−0.0352968	+	0.133618i
$274$			1485.38i			0.327501i
$275$	1957.51	−	2323.56i	0.429246	−	0.509512i
$276$			169.874i			0.0370478i
$277$			3379.62i			0.733075i	0.930403	+	0.366537i	$0.119457\pi$
$277$			3379.62i			0.733075i	−0.930403	+	0.366537i	$0.880543\pi$
$278$			801.829i			0.172987i
$279$			1446.79i			0.310455i
$280$	925.278	+	244.423i	0.197486	+	0.0521681i
$281$			575.018i			0.122074i	0.998136	+	0.0610369i	$0.0194407\pi$
$281$			575.018i			0.122074i	−0.998136	+	0.0610369i	$0.980559\pi$
$282$			687.993i			0.145281i
$283$	−6975.07			−1.46511			−0.732553	−	0.680710i	$-0.761671\pi$
$283$	−6975.07			−1.46511			−0.732553	+	0.680710i	$0.761671\pi$
$284$	−1730.74			−0.361621
$285$	−1111.35			−0.230985
$286$	−626.098	−	527.465i	−0.129447	−	0.109055i
$287$	−1560.89	−	412.328i	−0.321034	−	0.0848047i
$288$		−	288.000i		−	0.0589256i
$289$	−3739.47			−0.761138
$290$		−	276.495i		−	0.0559874i
$291$	2931.75			0.590592
$292$	−4265.72			−0.854906
$293$	491.206			0.0979406			0.0489703	−	0.998800i	$-0.484406\pi$
$293$	491.206			0.0979406			0.0489703	+	0.998800i	$0.484406\pi$
$294$	1789.52	+	1016.37i	0.354989	+	0.201618i
$295$	−541.365			−0.106846
$296$		−	2155.28i		−	0.423220i
$297$	753.333	+	634.657i	0.147181	+	0.123995i
$298$	−2570.35			−0.499652
$299$	−158.830			−0.0307204
$300$			999.335i			0.192322i
$301$	−941.564	+	3564.35i	−0.180302	+	0.682544i
$302$	4980.34			0.948961
$303$			1722.49i			0.326583i
$304$	−917.630			−0.173124
$305$			3317.09i			0.622741i
$306$		−	616.623i		−	0.115196i
$307$	2418.20			0.449557			0.224779	−	0.974410i	$-0.427834\pi$
$307$	2418.20			0.449557			0.224779	+	0.974410i	$0.427834\pi$
$308$	−2211.48	+	1553.66i	−0.409127	+	0.287429i
$309$	−1520.20			−0.279874
$310$			2076.71i			0.380481i
$311$		−	2211.77i		−	0.403274i	−0.979460	−	0.201637i	$-0.935374\pi$
$311$		−	2211.77i		−	0.403274i	0.979460	−	0.201637i	$-0.0646261\pi$
$312$	269.278			0.0488617
$313$		−	4891.25i		−	0.883291i	−0.897190	−	0.441645i	$-0.854395\pi$
$313$		−	4891.25i		−	0.883291i	0.897190	−	0.441645i	$-0.145605\pi$
$314$	−3414.05			−0.613586
$315$	274.976	−	1040.94i	0.0491845	−	0.186191i
$316$		−	3688.46i		−	0.656620i
$317$	3508.99			0.621718			0.310859	−	0.950456i	$-0.399383\pi$
$317$	3508.99			0.621718			0.310859	+	0.950456i	$0.399383\pi$
$318$	3237.23			0.570865
$319$	597.170	+	503.095i	0.104812	+	0.0883006i
$320$		−	413.393i		−	0.0722167i
$321$	1397.68			0.243025
$322$	−133.920	+	506.961i	−0.0231772	+	0.0877386i
$323$	−1964.69			−0.338447
$324$	−324.000			−0.0555556
$325$	−934.370			−0.159476
$326$			7234.29i			1.22905i
$327$	11.1495			0.00188554
$328$			697.371i			0.117396i
$329$	−542.378	+	2053.20i	−0.0908883	+	0.344063i
$330$	1081.33	+	910.980i	0.180379	+	0.151963i
$331$	286.857			0.0476347			0.0238174	−	0.999716i	$-0.492418\pi$
$331$	286.857			0.0476347			0.0238174	+	0.999716i	$0.492418\pi$
$332$	3979.77			0.657886
$333$	−2424.69			−0.399016
$334$		−	3460.21i		−	0.566869i
$335$			4820.46i			0.786179i
$336$	227.044	−	859.490i	0.0368639	−	0.139551i
$337$			6980.37i			1.12832i	0.825665	+	0.564161i	$0.190800\pi$
$337$			6980.37i			1.12832i	−0.825665	+	0.564161i	$0.809200\pi$
$338$		−	4142.23i		−	0.666590i
$339$		−	62.2714i		−	0.00997675i
$340$		−	885.095i		−	0.141179i
$341$	−4485.24	−	3778.66i	−0.712285	−	0.600076i
$342$			1032.33i			0.163223i
$343$	4539.27	+	4443.94i	0.714570	+	0.699563i
$344$	1592.47			0.249593
$345$	274.315			0.0428075
$346$		−	6535.62i		−	1.01548i
$347$			7282.70i			1.12667i	0.826228	+	0.563337i	$0.190483\pi$
$347$			7282.70i			1.12667i	−0.826228	+	0.563337i	$0.809517\pi$
$348$	−256.836			−0.0395628
$349$	5379.22			0.825052			0.412526	−	0.910946i	$-0.364647\pi$
$349$	5379.22			0.825052			0.412526	+	0.910946i	$0.364647\pi$
$350$	−787.824	+	2982.36i	−0.120317	+	0.455468i
$351$		−	302.937i		−	0.0460672i
$352$	892.839	+	752.186i	0.135194	+	0.113897i
$353$			4065.02i			0.612915i	0.951884	+	0.306458i	$0.0991438\pi$
$353$			4065.02i			0.612915i	−0.951884	+	0.306458i	$0.900856\pi$
$354$			502.873i			0.0755011i
$355$			2794.82i			0.417842i
$356$			3155.43i			0.469768i
$357$	486.113	−	1840.21i	0.0720668	−	0.272813i
$358$			3302.40i			0.487534i
$359$			7673.27i			1.12808i	0.825748	+	0.564039i	$0.190753\pi$
$359$			7673.27i			1.12808i	−0.825748	+	0.564039i	$0.809247\pi$
$360$	−465.067			−0.0680866
$361$	−3569.76			−0.520449
$362$	−432.186			−0.0627492
$363$	−3935.04	+	677.864i	−0.568970	+	0.0980128i
$364$	803.616	+	212.284i	0.115717	+	0.0305679i
$365$			6888.36i			0.987817i
$366$	3081.24			0.440052
$367$		−	514.173i		−	0.0731324i	−0.999331	−	0.0365662i	$-0.988358\pi$
$367$		−	514.173i		−	0.0731324i	0.999331	−	0.0365662i	$-0.0116420\pi$
$368$	226.498			0.0320843
$369$	784.542			0.110682
$370$	−3480.38			−0.489017
$371$	9661.00	+	2552.06i	1.35195	+	0.357134i
$372$	1929.05			0.268862
$373$			7095.33i			0.984940i	0.870330	+	0.492470i	$0.163906\pi$
$373$			7095.33i			0.984940i	−0.870330	+	0.492470i	$0.836094\pi$
$374$	1911.61	+	1610.47i	0.264297	+	0.222661i
$375$	4035.96			0.555777
$376$	917.324			0.125817
$377$		−	240.140i		−	0.0328059i
$378$	−966.926	−	255.425i	−0.131570	−	0.0347556i
$379$	8668.91			1.17491			0.587457	−	0.809256i	$-0.300129\pi$
$379$	8668.91			1.17491			0.587457	+	0.809256i	$0.300129\pi$
$380$			1481.80i			0.200039i
$381$	−3961.79			−0.532726
$382$		−	8250.64i		−	1.10508i
$383$		−	10606.8i		−	1.41510i	−0.706665	−	0.707549i	$-0.749801\pi$
$383$		−	10606.8i		−	1.41510i	0.706665	−	0.707549i	$-0.250199\pi$
$384$	−384.000			−0.0510310
$385$	2508.88	+	3571.14i	0.332115	+	0.472733i
$386$	4326.78			0.570536
$387$		−	1791.53i		−	0.235319i
$388$		−	3909.00i		−	0.511468i
$389$	−12134.0			−1.58153			−0.790767	−	0.612117i	$-0.790318\pi$
$389$	−12134.0			−1.58153			−0.790767	+	0.612117i	$0.790318\pi$
$390$		−	434.834i		−	0.0564581i
$391$	484.944			0.0627230
$392$	1355.15	−	2386.02i	0.174606	−	0.307429i
$393$			7572.89i			0.972014i
$394$	6805.19			0.870154
$395$	−5956.18			−0.758703
$396$	846.209	−	1004.44i	0.107383	−	0.127463i
$397$		−	8375.83i		−	1.05887i	−0.848351	−	0.529434i	$-0.822404\pi$
$397$		−	8375.83i		−	1.05887i	0.848351	−	0.529434i	$-0.177596\pi$
$398$	10928.7			1.37640
$399$	−813.838	+	3080.84i	−0.102112	+	0.386553i
$400$	1332.45			0.166556
$401$	−3985.50			−0.496325			−0.248162	−	0.968718i	$-0.579827\pi$
$401$	−3985.50			−0.496325			−0.248162	+	0.968718i	$0.579827\pi$
$402$	4477.72			0.555543
$403$			1803.65i			0.222943i
$404$	2296.65			0.282829
$405$			523.200i			0.0641926i
$406$	−766.486	−	202.476i	−0.0936948	−	0.0247506i
$407$	6332.70	−	7516.87i	0.771254	−	0.915473i
$408$	−822.164			−0.0997627
$409$	616.533			0.0745369			0.0372685	−	0.999305i	$-0.488134\pi$
$409$	616.533			0.0745369			0.0372685	+	0.999305i	$0.488134\pi$
$410$	1126.12			0.135647
$411$		−	2228.08i		−	0.267404i
$412$			2026.93i			0.242378i
$413$	−396.439	+	1500.74i	−0.0472336	+	0.178806i
$414$		−	254.810i		−	0.0302494i
$415$		−	6426.59i		−	0.760166i
$416$		−	359.037i		−	0.0423155i
$417$		−	1202.74i		−	0.141244i
$418$	−3200.37	−	2696.20i	−0.374487	−	0.315492i
$419$			4371.15i			0.509653i	0.966987	+	0.254827i	$0.0820184\pi$
$419$			4371.15i			0.509653i	−0.966987	+	0.254827i	$0.917982\pi$
$420$	−1387.92	−	366.634i	−0.161246	−	0.0425951i
$421$	−12534.8			−1.45108			−0.725542	−	0.688178i	$-0.758411\pi$
$421$	−12534.8			−1.45108			−0.725542	+	0.688178i	$0.758411\pi$
$422$	5119.72			0.590578
$423$		−	1031.99i		−	0.118622i
$424$		−	4316.31i		−	0.494383i
$425$	2852.84			0.325607
$426$	2596.11			0.295263
$427$	9195.47	+	2429.09i	1.04215	+	0.275297i
$428$		−	1863.58i		−	0.210466i
$429$	939.146	+	791.198i	0.105693	+	0.0890429i
$430$		−	2571.54i		−	0.288397i
$431$			5630.70i			0.629283i	0.949211	+	0.314642i	$0.101884\pi$
$431$			5630.70i			0.629283i	−0.949211	+	0.314642i	$0.898116\pi$
$432$			432.000i			0.0481125i
$433$			12086.3i			1.34141i	0.741725	+	0.670704i	$0.234008\pi$
$433$			12086.3i			1.34141i	−0.741725	+	0.670704i	$0.765992\pi$
$434$	5756.95	+	1520.76i	0.636733	+	0.168200i
$435$			414.743i			0.0457136i
$436$		−	14.8661i		−	0.00163292i
$437$	−811.881			−0.0888731
$438$	6398.59			0.698028
$439$	−2445.21			−0.265840			−0.132920	−	0.991127i	$-0.542435\pi$
$439$	−2445.21			−0.265840			−0.132920	+	0.991127i	$0.542435\pi$
$440$	1214.64	−	1441.77i	0.131604	−	0.156213i
$441$	−2684.27	−	1524.55i	−0.289847	−	0.164620i
$442$		−	768.716i		−	0.0827242i
$443$	2436.92			0.261358			0.130679	−	0.991425i	$-0.458284\pi$
$443$	2436.92			0.261358			0.130679	+	0.991425i	$0.458284\pi$
$444$			3232.92i			0.345558i
$445$	5095.43			0.542801
$446$	−2229.47			−0.236701
$447$	3855.52			0.407964
$448$	−1145.99	−	302.726i	−0.120854	−	0.0319251i
$449$	2525.93			0.265493			0.132746	−	0.991150i	$-0.457620\pi$
$449$	2525.93			0.265493			0.132746	+	0.991150i	$0.457620\pi$
$450$		−	1499.00i		−	0.157030i
$451$	−2049.03	+	2432.19i	−0.213936	+	0.253941i
$452$	−83.0285			−0.00864012
$453$	−7470.50			−0.774823
$454$		−	2369.80i		−	0.244979i
$455$	342.800	−	1297.69i	0.0353203	−	0.133707i
$456$	1376.45			0.141355
$457$		−	3952.31i		−	0.404554i	−0.979328	−	0.202277i	$-0.935166\pi$
$457$		−	3952.31i		−	0.404554i	0.979328	−	0.202277i	$-0.0648341\pi$
$458$	−3497.16			−0.356794
$459$			924.934i			0.0940572i
$460$		−	365.753i		−	0.0370724i
$461$	1817.22			0.183593			0.0917966	−	0.995778i	$-0.470739\pi$
$461$	1817.22			0.183593			0.0917966	+	0.995778i	$0.470739\pi$
$462$	3317.23	−	2330.49i	0.334050	−	0.234685i
$463$	−2118.94			−0.212690			−0.106345	−	0.994329i	$-0.533915\pi$
$463$	−2118.94			−0.212690			−0.106345	+	0.994329i	$0.533915\pi$
$464$			342.448i			0.0342624i
$465$		−	3115.06i		−	0.310661i
$466$	−4438.57			−0.441229
$467$		−	13601.2i		−	1.34772i	−0.738857	−	0.673862i	$-0.764634\pi$
$467$		−	13601.2i		−	1.34772i	0.738857	−	0.673862i	$-0.235366\pi$
$468$	−403.916			−0.0398954
$469$	13363.0	+	3530.00i	1.31567	+	0.347549i
$470$		−	1481.31i		−	0.145378i
$471$	5121.08			0.500991
$472$	670.498			0.0653859
$473$	5553.97	+	4679.03i	0.539899	+	0.454846i
$474$			5532.69i			0.536128i
$475$	−4776.15			−0.461357
$476$	−2453.62	−	648.151i	−0.236263	−	0.0624117i
$477$	−4855.85			−0.466109
$478$	7925.65			0.758391
$479$	1699.19			0.162083			0.0810417	−	0.996711i	$-0.474175\pi$
$479$	1699.19			0.162083			0.0810417	+	0.996711i	$0.474175\pi$
$480$			620.089i			0.0589647i
$481$	−3022.76			−0.286540
$482$			4839.04i			0.457287i
$483$	200.879	−	760.441i	0.0189241	−	0.0716382i
$484$	903.819	+	5246.72i	0.0848816	+	0.492742i
$485$	−6312.31			−0.590984
$486$	486.000			0.0453609
$487$	−4363.09			−0.405976			−0.202988	−	0.979181i	$-0.565065\pi$
$487$	−4363.09			−0.405976			−0.202988	+	0.979181i	$0.565065\pi$
$488$		−	4108.32i		−	0.381096i
$489$		−	10851.4i		−	1.00351i
$490$	−3852.98	−	2188.32i	−0.355224	−	0.201752i
$491$		−	4458.94i		−	0.409835i	−0.978779	−	0.204918i	$-0.934307\pi$
$491$		−	4458.94i		−	0.409835i	0.978779	−	0.204918i	$-0.0656926\pi$
$492$		−	1046.06i		−	0.0958534i
$493$			733.199i			0.0669810i
$494$			1286.97i			0.117213i
$495$	−1621.99	−	1366.47i	−0.147279	−	0.124077i
$496$		−	2572.07i		−	0.232841i
$497$	7747.67	+	2046.64i	0.699257	+	0.184717i
$498$	−5969.65			−0.537161
$499$	−6331.69			−0.568027			−0.284013	−	0.958820i	$-0.591666\pi$
$499$	−6331.69			−0.568027			−0.284013	+	0.958820i	$0.591666\pi$
$500$		−	5381.29i		−	0.481317i
$501$			5190.31i			0.462846i
$502$	−11547.8			−1.02670
$503$	−70.5402			−0.00625295			−0.00312647	−	0.999995i	$-0.500995\pi$
$503$	−70.5402			−0.00625295			−0.00312647	+	0.999995i	$0.500995\pi$
$504$	−340.566	+	1289.23i	−0.0300993	+	0.113943i
$505$		−	3708.67i		−	0.326800i
$506$	789.947	+	665.503i	0.0694020	+	0.0584688i
$507$			6213.34i			0.544269i
$508$			5282.39i			0.461354i
$509$		−	15982.7i		−	1.39179i	−0.718143	−	0.695896i	$-0.755008\pi$
$509$		−	15982.7i		−	1.39179i	0.718143	−	0.695896i	$-0.244992\pi$
$510$			1327.64i			0.115273i
$511$	19095.6	+	5044.31i	1.65311	+	0.436687i
$512$			512.000i			0.0441942i
$513$		−	1548.50i		−	0.133271i
$514$	−4186.67			−0.359273
$515$	3273.11			0.280060
$516$	−2388.70			−0.203792
$517$	3199.31	+	2695.30i	0.272157	+	0.229283i
$518$	−2548.67	+	9648.14i	−0.216182	+	0.818369i
$519$			9803.43i			0.829138i
$520$	−579.778			−0.0488941
$521$		−	1010.25i		−	0.0849515i	−0.999097	−	0.0424758i	$-0.986475\pi$
$521$		−	1010.25i		−	0.0849515i	0.999097	−	0.0424758i	$-0.0135245\pi$
$522$	385.254			0.0323029
$523$	10171.9			0.850453			0.425226	−	0.905087i	$-0.360194\pi$
$523$	10171.9			0.850453			0.425226	+	0.905087i	$0.360194\pi$
$524$	10097.2			0.841789
$525$	1181.74	−	4473.54i	0.0982385	−	0.371888i
$526$	4538.14			0.376183
$527$		−	5506.93i		−	0.455191i
$528$	−1339.26	−	1128.28i	−0.110386	−	0.0929962i
$529$	−11966.6			−0.983530
$530$	−6970.04			−0.571244
$531$		−	754.310i		−	0.0616464i
$532$	4107.78	+	1085.12i	0.334765	+	0.0884320i
$533$	978.054			0.0794826
$534$		−	4733.14i		−	0.383564i
$535$	−3009.34			−0.243187
$536$		−	5970.29i		−	0.481115i
$537$		−	4953.60i		−	0.398070i
$538$	9793.57			0.784816
$539$	11737.0	−	4339.86i	0.937935	−	0.346811i
$540$	697.600			0.0555925
$541$			15686.7i			1.24662i	0.781974	+	0.623311i	$0.214213\pi$
$541$			15686.7i			1.24662i	−0.781974	+	0.623311i	$0.785787\pi$
$542$		−	731.173i		−	0.0579457i
$543$	648.279			0.0512345
$544$			1096.22i			0.0863970i
$545$	−24.0059			−0.00188679
$546$	−1205.42	−	318.427i	−0.0944824	−	0.0249586i
$547$			3768.33i			0.294556i	0.989095	+	0.147278i	$0.0470512\pi$
$547$			3768.33i			0.294556i	−0.989095	+	0.147278i	$0.952949\pi$
$548$	−2970.77			−0.231578
$549$	−4621.86			−0.359301
$550$	4647.11	+	3915.03i	0.360279	+	0.303523i
$551$		−	1227.50i		−	0.0949063i
$552$	−339.747			−0.0261967
$553$	−4361.68	+	16511.4i	−0.335403	+	1.26969i
$554$	−6759.24			−0.518362
$555$	5220.57			0.399281
$556$	−1603.66			−0.122321
$557$			2539.00i			0.193143i	0.995326	+	0.0965717i	$0.0307877\pi$
$557$			2539.00i			0.193143i	−0.995326	+	0.0965717i	$0.969212\pi$
$558$	−2893.58			−0.219525
$559$		−	2233.42i		−	0.168987i
$560$	−488.846	+	1850.56i	−0.0368884	+	0.139643i
$561$	−2867.42	−	2415.70i	−0.215798	−	0.181802i
$562$	−1150.04			−0.0863192
$563$	−5870.85			−0.439479			−0.219740	−	0.975559i	$-0.570521\pi$
$563$	−5870.85			−0.439479			−0.219740	+	0.975559i	$0.570521\pi$
$564$	−1375.99			−0.102730
$565$			134.076i			0.00998337i
$566$		−	13950.1i		−	1.03599i
$567$	1450.39	+	383.137i	0.107426	+	0.0283779i
$568$		−	3461.48i		−	0.255705i
$569$		−	12490.2i		−	0.920242i	−0.887856	−	0.460121i	$-0.847806\pi$
$569$		−	12490.2i		−	0.920242i	0.887856	−	0.460121i	$-0.152194\pi$
$570$		−	2222.70i		−	0.163331i
$571$		−	21440.2i		−	1.57136i	−0.618635	−	0.785679i	$-0.712314\pi$
$571$		−	21440.2i		−	1.57136i	0.618635	−	0.785679i	$-0.287686\pi$
$572$	1054.93	−	1252.20i	0.0771134	−	0.0915331i
$573$			12376.0i			0.902292i
$574$	824.656	−	3121.79i	0.0599660	−	0.227005i
$575$	1178.89			0.0855014
$576$	576.000			0.0416667
$577$			6285.44i			0.453494i	0.973954	+	0.226747i	$0.0728091\pi$
$577$			6285.44i			0.453494i	−0.973954	+	0.226747i	$0.927191\pi$
$578$		−	7478.94i		−	0.538206i
$579$	−6490.16			−0.465841
$580$	552.990			0.0395891
$581$	−17815.5	−	4706.16i	−1.27213	−	0.336049i
$582$			5863.50i			0.417612i
$583$	12682.3	−	15053.8i	0.900938	−	1.06941i
$584$		−	8531.45i		−	0.604510i
$585$			652.250i			0.0460978i
$586$			982.413i			0.0692544i
$587$			1852.69i			0.130270i	0.997876	+	0.0651351i	$0.0207478\pi$
$587$			1852.69i			0.130270i	−0.997876	+	0.0651351i	$0.979252\pi$
$588$	−2032.73	+	3579.03i	−0.142565	+	0.251015i
$589$			9219.56i			0.644967i
$590$		−	1082.73i		−	0.0755513i
$591$	−10207.8			−0.710478
$592$	4310.56			0.299262
$593$	−19779.8			−1.36974			−0.684872	−	0.728663i	$-0.740142\pi$
$593$	−19779.8			−1.36974			−0.684872	+	0.728663i	$0.740142\pi$
$594$	−1269.31	+	1506.67i	−0.0876777	+	0.104073i
$595$	−1046.64	+	3962.14i	−0.0721147	+	0.272995i
$596$		−	5140.69i		−	0.353307i
$597$	−16393.1			−1.12382
$598$		−	317.661i		−	0.0217226i
$599$	10805.1			0.737036			0.368518	−	0.929621i	$-0.379865\pi$
$599$	10805.1			0.737036			0.368518	+	0.929621i	$0.379865\pi$
$600$	−1998.67			−0.135992
$601$	22136.4			1.50244			0.751218	−	0.660054i	$-0.229467\pi$
$601$	22136.4			1.50244			0.751218	+	0.660054i	$0.229467\pi$
$602$	−7128.70	−	1883.13i	−0.482632	−	0.127493i
$603$	−6716.58			−0.453599
$604$			9960.67i			0.671017i
$605$	8472.49	−	1459.50i	0.569348	−	0.0980779i
$606$	−3444.98			−0.230929
$607$	−15414.8			−1.03076			−0.515378	−	0.856963i	$-0.672348\pi$
$607$	−15414.8			−1.03076			−0.515378	+	0.856963i	$0.672348\pi$
$608$		−	1835.26i		−	0.122417i
$609$	1149.73	+	303.714i	0.0765015	+	0.0202087i
$610$	−6634.18			−0.440344
$611$		−	1286.54i		−	0.0851844i
$612$	1233.25			0.0814559
$613$			4056.94i			0.267305i	0.991028	+	0.133653i	$0.0426706\pi$
$613$			4056.94i			0.267305i	−0.991028	+	0.133653i	$0.957329\pi$
$614$			4836.40i			0.317885i
$615$	−1689.19			−0.110755
$616$	−3107.33	−	4422.97i	−0.203243	−	0.289296i
$617$	15308.9			0.998885			0.499443	−	0.866347i	$-0.333538\pi$
$617$	15308.9			0.998885			0.499443	+	0.866347i	$0.333538\pi$
$618$		−	3040.39i		−	0.197901i
$619$			16951.0i			1.10068i	0.834941	+	0.550339i	$0.185502\pi$
$619$			16951.0i			1.10068i	−0.834941	+	0.550339i	$0.814498\pi$
$620$	−4153.42			−0.269041
$621$			382.216i			0.0246985i
$622$	4423.54			0.285158
$623$	3731.36	−	14125.3i	0.239958	−	0.908376i
$624$			538.555i			0.0345504i
$625$	1719.96			0.110078
$626$	9782.51			0.624581
$627$	4800.56	+	4044.31i	0.305767	+	0.257598i
$628$		−	6828.11i		−	0.433871i
$629$	9229.14			0.585040
$630$	2081.88	+	549.952i	0.131657	+	0.0347787i
$631$	−23446.5			−1.47922			−0.739612	−	0.673034i	$-0.764991\pi$
$631$	−23446.5			−1.47922			−0.739612	+	0.673034i	$0.764991\pi$
$632$	7376.92			0.464301
$633$	−7679.58			−0.482205
$634$			7017.98i			0.439621i
$635$	8530.08			0.533080
$636$			6474.46i			0.403662i
$637$	−3346.36	−	1900.59i	−0.208144	−	0.118217i
$638$	−1006.19	+	1194.34i	−0.0624380	+	0.0741134i
$639$	−3894.16			−0.241081
$640$	826.785			0.0510649
$641$	−23151.6			−1.42657			−0.713287	−	0.700872i	$-0.752794\pi$
$641$	−23151.6			−1.42657			−0.713287	+	0.700872i	$0.752794\pi$
$642$			2795.37i			0.171845i
$643$			27583.2i			1.69172i	0.533408	+	0.845858i	$0.320911\pi$
$643$			27583.2i			1.69172i	−0.533408	+	0.845858i	$0.679089\pi$
$644$	−1013.92	−	267.839i	−0.0620405	−	0.0163887i
$645$			3857.31i			0.235475i
$646$		−	3929.39i		−	0.239318i
$647$		−	12975.9i		−	0.788462i	−0.919011	−	0.394231i	$-0.871011\pi$
$647$		−	12975.9i		−	0.788462i	0.919011	−	0.394231i	$-0.128989\pi$
$648$		−	648.000i		−	0.0392837i
$649$	2338.46	+	1970.07i	0.141437	+	0.119156i
$650$		−	1868.74i		−	0.112766i
$651$	−8635.42	−	2281.15i	−0.519891	−	0.137335i
$652$	−14468.6			−0.869069
$653$	−30695.0			−1.83949			−0.919747	−	0.392511i	$-0.871606\pi$
$653$	−30695.0			−1.83949			−0.919747	+	0.392511i	$0.871606\pi$
$654$			22.2991i			0.00133328i
$655$		−	16305.1i		−	0.972660i
$656$	−1394.74			−0.0830115
$657$	−9597.88			−0.569938
$658$	−4106.41	−	1084.76i	−0.243290	−	0.0642677i
$659$		−	2571.82i		−	0.152024i	−0.997107	−	0.0760121i	$-0.975781\pi$
$659$		−	2571.82i		−	0.152024i	0.997107	−	0.0760121i	$-0.0242188\pi$
$660$	−1821.96	+	2162.65i	−0.107454	+	0.127547i
$661$			23895.1i			1.40607i	0.711157	+	0.703033i	$0.248172\pi$
$661$			23895.1i			1.40607i	−0.711157	+	0.703033i	$0.751828\pi$
$662$			573.714i			0.0336828i
$663$			1153.07i			0.0675441i
$664$			7959.53i			0.465196i
$665$	1752.26	−	6633.31i	0.102180	−	0.386810i
$666$		−	4849.39i		−	0.282147i
$667$			302.984i			0.0175886i
$668$	6920.42			0.400837
$669$	3344.20			0.193265
$670$	−9640.92			−0.555912
$671$	12071.2	−	14328.4i	0.694489	−	0.824354i
$672$	1718.98	+	454.088i	0.0986772	+	0.0260667i
$673$		−	8328.94i		−	0.477053i	−0.971136	−	0.238527i	$-0.923336\pi$
$673$		−	8328.94i		−	0.477053i	0.971136	−	0.238527i	$-0.0766644\pi$
$674$	−13960.7			−0.797845
$675$			2248.50i			0.128215i
$676$	8284.46			0.471350
$677$	−1178.06			−0.0668782			−0.0334391	−	0.999441i	$-0.510646\pi$
$677$	−1178.06			−0.0668782			−0.0334391	+	0.999441i	$0.510646\pi$
$678$	124.543			0.00705462
$679$	−4622.48	+	17498.7i	−0.261258	+	0.989010i
$680$	1770.19			0.0998290
$681$			3554.70i			0.200024i
$682$	7557.32	−	8970.48i	0.424318	−	0.503662i
$683$	−21234.4			−1.18962			−0.594811	−	0.803866i	$-0.702773\pi$
$683$	−21234.4			−1.18962			−0.594811	+	0.803866i	$0.702773\pi$
$684$	−2064.67			−0.115416
$685$			4797.24i			0.267581i
$686$	−8887.88	+	9078.54i	−0.494666	+	0.505278i
$687$	5245.74			0.291321
$688$			3184.94i			0.176489i
$689$	−6053.57			−0.334721
$690$			548.629i			0.0302695i
$691$		−	14874.1i		−	0.818869i	−0.912339	−	0.409435i	$-0.865726\pi$
$691$		−	14874.1i		−	0.818869i	0.912339	−	0.409435i	$-0.134274\pi$
$692$	13071.2			0.718055
$693$	−4975.84	+	3495.74i	−0.272751	+	0.191619i
$694$	−14565.4			−0.796678
$695$			2589.61i			0.141338i
$696$		−	513.672i		−	0.0279751i
$697$	−2986.21			−0.162283
$698$			10758.4i			0.583400i
$699$	6657.86			0.360262
$700$	−5964.71	−	1575.65i	−0.322064	−	0.0850770i
$701$			12323.3i			0.663972i	0.943284	+	0.331986i	$0.107719\pi$
$701$			12323.3i			0.663972i	−0.943284	+	0.331986i	$0.892281\pi$
$702$	605.875			0.0325745
$703$	−15451.2			−0.828951
$704$	−1504.37	+	1785.68i	−0.0805371	+	0.0955969i
$705$			2221.96i			0.118701i
$706$	−8130.04			−0.433396
$707$	−10281.0	−	2715.84i	−0.546898	−	0.144469i
$708$	−1005.75			−0.0533874
$709$	15693.8			0.831302			0.415651	−	0.909524i	$-0.363554\pi$
$709$	15693.8			0.831302			0.415651	+	0.909524i	$0.363554\pi$
$710$	−5589.65			−0.295459
$711$		−	8299.03i		−	0.437747i
$712$	−6310.85			−0.332176
$713$		−	2275.66i		−	0.119529i
$714$	3680.42	+	972.227i	0.192908	+	0.0509589i
$715$	−2022.06	−	1703.52i	−0.105763	−	0.0891021i
$716$	−6604.80			−0.344739
$717$	−11888.5			−0.619223
$718$	−15346.5			−0.797671
$719$		−	16156.7i		−	0.838029i	−0.907980	−	0.419014i	$-0.862376\pi$
$719$		−	16156.7i		−	0.838029i	0.907980	−	0.419014i	$-0.137624\pi$
$720$		−	930.134i		−	0.0481445i
$721$	2396.89	−	9073.57i	0.123807	−	0.468679i
$722$		−	7139.52i		−	0.368013i
$723$		−	7258.57i		−	0.373373i
$724$		−	864.372i		−	0.0443704i
$725$			1782.40i			0.0913057i
$726$	−1355.73	−	7870.08i	−0.0693055	−	0.402323i
$727$		−	19081.8i		−	0.973458i	−0.873553	−	0.486729i	$-0.838190\pi$
$727$		−	19081.8i		−	0.973458i	0.873553	−	0.486729i	$-0.161810\pi$
$728$	−424.569	+	1607.23i	−0.0216148	+	0.0818241i
$729$	−729.000			−0.0370370
$730$	−13776.7			−0.698492
$731$			6819.11i			0.345026i
$732$			6162.48i			0.311164i
$733$	−14202.4			−0.715657			−0.357828	−	0.933787i	$-0.616483\pi$
$733$	−14202.4			−0.715657			−0.357828	+	0.933787i	$0.616483\pi$
$734$	1028.35			0.0517124
$735$	5779.47	+	3282.49i	0.290040	+	0.164730i
$736$			452.996i			0.0226870i
$737$	17542.1	−	20822.3i	0.876757	−	1.04070i
$738$			1569.08i			0.0782640i
$739$		−	22213.0i		−	1.10571i	−0.833278	−	0.552854i	$-0.813539\pi$
$739$		−	22213.0i		−	1.10571i	0.833278	−	0.552854i	$-0.186461\pi$
$740$		−	6960.76i		−	0.345788i
$741$		−	1930.45i		−	0.0957041i
$742$	−5104.13	+	19322.0i	−0.252532	+	0.955974i
$743$		−	24337.5i		−	1.20169i	−0.799366	−	0.600844i	$-0.794831\pi$
$743$		−	24337.5i		−	1.20169i	0.799366	−	0.600844i	$-0.205169\pi$
$744$			3858.10i			0.190114i
$745$	−8301.27			−0.408235
$746$	−14190.7			−0.696457
$747$	8954.48			0.438591
$748$	−3220.94	+	3823.23i	−0.157445	+	0.186886i
$749$	−2203.72	+	8342.33i	−0.107506	+	0.406972i
$750$			8071.93i			0.392994i
$751$	8200.74			0.398468			0.199234	−	0.979952i	$-0.436155\pi$
$751$	8200.74			0.398468			0.199234	+	0.979952i	$0.436155\pi$
$752$			1834.65i			0.0889664i
$753$	17321.8			0.838300
$754$	480.279			0.0231973
$755$	16084.6			0.775338
$756$	510.849	−	1933.85i	0.0245759	−	0.0930338i
$757$	−477.727			−0.0229370			−0.0114685	−	0.999934i	$-0.503651\pi$
$757$	−477.727			−0.0229370			−0.0114685	+	0.999934i	$0.503651\pi$
$758$			17337.8i			0.830789i
$759$	−1184.92	−	998.254i	−0.0566665	−	0.0477396i
$760$	−2963.61			−0.141449
$761$	31513.1			1.50111			0.750557	−	0.660805i	$-0.229785\pi$
$761$	31513.1			1.50111			0.750557	+	0.660805i	$0.229785\pi$
$762$		−	7923.58i		−	0.376694i
$763$	−17.5794	+	66.5480i	−0.000834100	+	0.00315754i
$764$	16501.3			0.781408
$765$		−	1991.46i		−	0.0941196i
$766$	21213.6			1.00062
$767$		−	940.364i		−	0.0442694i
$768$		−	768.000i		−	0.0360844i
$769$	−1216.60			−0.0570505			−0.0285253	−	0.999593i	$-0.509081\pi$
$769$	−1216.60			−0.0570505			−0.0285253	+	0.999593i	$0.509081\pi$
$770$	−7142.27	+	5017.76i	−0.334272	+	0.234841i
$771$	6280.01			0.293345
$772$			8653.55i			0.403430i
$773$		−	13551.6i		−	0.630554i	−0.949000	−	0.315277i	$-0.897903\pi$
$773$		−	13551.6i		−	0.630554i	0.949000	−	0.315277i	$-0.102097\pi$
$774$	3583.05			0.166396
$775$		−	13387.3i		−	0.620498i
$776$	7818.00			0.361662
$777$	3823.00	−	14472.2i	0.176512	−	0.668195i
$778$		−	24267.9i		−	1.11831i
$779$	4999.44			0.229940
$780$	869.667			0.0399219
$781$	10170.6	−	12072.4i	0.465983	−	0.553118i
$782$			969.889i			0.0443518i
$783$	−577.881			−0.0263752
$784$	4772.04	+	2710.31i	0.217385	+	0.123465i
$785$	−11026.1			−0.501324
$786$	−15145.8			−0.687318
$787$	−14150.7			−0.640936			−0.320468	−	0.947259i	$-0.603840\pi$
$787$	−14150.7			−0.640936			−0.320468	+	0.947259i	$0.603840\pi$
$788$			13610.4i			0.615292i
$789$	−6807.21			−0.307152
$790$		−	11912.4i		−	0.536484i
$791$	371.678	+	98.1830i	0.0167071	+	0.00441338i
$792$	2008.89	+	1692.42i	0.0901297	+	0.0759311i
$793$	−5761.87			−0.258020
$794$	16751.7			0.748733
$795$	10455.1			0.466419
$796$			21857.4i			0.973261i
$797$		−	4236.84i		−	0.188302i	−0.995558	−	0.0941510i	$-0.969986\pi$
$797$		−	4236.84i		−	0.188302i	0.995558	−	0.0941510i	$-0.0300136\pi$
$798$	−6161.67	−	1627.68i	−0.273334	−	0.0722044i
$799$			3928.08i			0.173924i
$800$			2664.89i			0.117773i
$801$			7099.71i			0.313178i
$802$		−	7970.99i		−	0.350954i
$803$	25067.3	−	29754.7i	1.10163	−	1.30762i
$804$			8955.44i			0.392828i
$805$	−432.511	+	1637.30i	−0.0189366	+	0.0716858i
$806$	−3607.29			−0.157645
$807$	−14690.4			−0.640799
$808$			4593.31i			0.199990i
$809$			41975.8i			1.82422i	0.409949	+	0.912108i	$0.365546\pi$
$809$			41975.8i			1.82422i	−0.409949	+	0.912108i	$0.634454\pi$
$810$	−1046.40			−0.0453911
$811$	15302.5			0.662567			0.331284	−	0.943531i	$-0.392518\pi$
$811$	15302.5			0.662567			0.331284	+	0.943531i	$0.392518\pi$
$812$	404.952	−	1532.97i	0.0175013	−	0.0662522i
$813$			1096.76i			0.0473124i
$814$	15033.7	+	12665.4i	0.647337	+	0.545359i
$815$			23364.1i			1.00418i
$816$		−	1644.33i		−	0.0705429i
$817$		−	11416.4i		−	0.488872i
$818$			1233.07i			0.0527056i
$819$	1808.14	+	477.640i	0.0771445	+	0.0203786i
$820$			2252.25i			0.0959170i
$821$		−	21462.1i		−	0.912343i	−0.889892	−	0.456171i	$-0.849220\pi$
$821$		−	21462.1i		−	0.912343i	0.889892	−	0.456171i	$-0.150780\pi$
$822$	4456.15			0.189083
$823$	2509.62			0.106294			0.0531469	−	0.998587i	$-0.483075\pi$
$823$	2509.62			0.106294			0.0531469	+	0.998587i	$0.483075\pi$
$824$	−4053.86			−0.171387
$825$	−6970.67	−	5872.54i	−0.294167	−	0.247825i
$826$	−3001.49	−	792.878i	−0.126435	−	0.0333992i
$827$		−	41288.7i		−	1.73609i	−0.496482	−	0.868047i	$-0.665375\pi$
$827$		−	41288.7i		−	1.73609i	0.496482	−	0.868047i	$-0.334625\pi$
$828$	509.621			0.0213896
$829$			26471.7i			1.10905i	0.832168	+	0.554524i	$0.187100\pi$
$829$			26471.7i			1.10905i	−0.832168	+	0.554524i	$0.812900\pi$
$830$	12853.2			0.537518
$831$	10138.9			0.423241
$832$	718.074			0.0299215
$833$	10217.2	+	5802.91i	0.424975	+	0.241367i
$834$	2405.49			0.0998744
$835$		−	11175.2i		−	0.463154i
$836$	5392.41	−	6400.75i	0.223087	−	0.264802i
$837$	4340.37			0.179241
$838$	−8742.30			−0.360379
$839$			17402.7i			0.716101i	0.933702	+	0.358051i	$0.116558\pi$
$839$			17402.7i			0.716101i	−0.933702	+	0.358051i	$0.883442\pi$
$840$	733.269	−	2775.83i	0.0301193	−	0.114018i
$841$	23930.9			0.981217
$842$		−	25069.5i		−	1.02607i
$843$	1725.05			0.0704793
$844$			10239.4i			0.417602i
$845$		−	13377.9i		−	0.544630i
$846$	2063.98			0.0838783
$847$	2158.41	−	24555.8i	0.0875605	−	0.996159i
$848$	8632.62			0.349582
$849$			20925.2i			0.845880i
$850$			5705.68i			0.230239i
$851$	3813.81			0.153626
$852$			5192.22i			0.208782i
$853$	14588.7			0.585589			0.292795	−	0.956175i	$-0.405415\pi$
$853$	14588.7			0.585589			0.292795	+	0.956175i	$0.405415\pi$
$854$	−4858.18	+	18390.9i	−0.194664	+	0.736914i
$855$			3334.06i			0.133359i
$856$	3727.16			0.148822
$857$	−16804.4			−0.669810			−0.334905	−	0.942252i	$-0.608704\pi$
$857$	−16804.4			−0.669810			−0.334905	+	0.942252i	$0.608704\pi$
$858$	−1582.40	+	1878.29i	−0.0629628	+	0.0747364i
$859$		−	41528.8i		−	1.64953i	−0.565479	−	0.824763i	$-0.691309\pi$
$859$		−	41528.8i		−	1.64953i	0.565479	−	0.824763i	$-0.308691\pi$
$860$	5143.08			0.203928
$861$	−1236.98	+	4682.68i	−0.0489620	+	0.185349i
$862$	−11261.4			−0.444970
$863$	35866.9			1.41474			0.707371	−	0.706843i	$-0.249881\pi$
$863$	35866.9			1.41474			0.707371	+	0.706843i	$0.249881\pi$
$864$	−864.000			−0.0340207
$865$		−	21107.6i		−	0.829689i
$866$	−24172.6			−0.948519
$867$			11218.4i			0.439443i
$868$	−3041.53	+	11513.9i	−0.118936	+	0.450238i
$869$	25728.1	+	21675.0i	1.00433	+	0.846117i
$870$	−829.486			−0.0323244
$871$	−8373.26			−0.325737
$872$	29.7321			0.00115465
$873$		−	8795.25i		−	0.340978i
$874$		−	1623.76i		−	0.0628428i
$875$	−6363.49	+	24089.4i	−0.245857	+	0.930708i
$876$			12797.2i			0.493580i
$877$			41450.3i			1.59598i	0.602668	+	0.797992i	$0.294104\pi$
$877$			41450.3i			1.59598i	−0.602668	+	0.797992i	$0.705896\pi$
$878$		−	4890.42i		−	0.187977i
$879$		−	1473.62i		−	0.0565460i
$880$	2883.54	+	2429.28i	0.110459	+	0.0930580i
$881$		−	137.771i		−	0.00526857i	−0.999997	−	0.00263429i	$-0.999161\pi$
$881$		−	137.771i		−	0.00526857i	0.999997	−	0.00263429i	$-0.000838520\pi$
$882$	3049.10	−	5368.55i	0.116404	−	0.204953i
$883$	−5743.33			−0.218889			−0.109444	−	0.993993i	$-0.534907\pi$
$883$	−5743.33			−0.218889			−0.109444	+	0.993993i	$0.534907\pi$
$884$	1537.43			0.0584949
$885$			1624.09i			0.0616874i
$886$			4873.83i			0.184808i
$887$	−39717.1			−1.50346			−0.751731	−	0.659470i	$-0.770781\pi$
$887$	−39717.1			−1.50346			−0.751731	+	0.659470i	$0.770781\pi$
$888$	−6465.85			−0.244346
$889$	6246.54	−	23646.7i	0.235660	−	0.892107i
$890$			10190.9i			0.383819i
$891$	1903.97	−	2260.00i	0.0715885	−	0.0849751i
$892$		−	4458.94i		−	0.167373i
$893$		−	6576.28i		−	0.246435i
$894$			7711.04i			0.288474i
$895$			10665.5i			0.398334i
$896$	605.451	−	2291.97i	0.0225744	−	0.0854570i
$897$			476.491i			0.0177364i
$898$			5051.87i			0.187732i
$899$	3440.63			0.127643
$900$	2998.01			0.111037
$901$	18482.9			0.683412
$902$	−4864.37	−	4098.06i	−0.179563	−	0.151276i
$903$	10693.1	+	2824.69i	0.394067	+	0.104097i
$904$		−	166.057i		−	0.00610948i
$905$	−1395.80			−0.0512685
$906$		−	14941.0i		−	0.547883i
$907$	23546.7			0.862024			0.431012	−	0.902346i	$-0.358157\pi$
$907$	23546.7			0.862024			0.431012	+	0.902346i	$0.358157\pi$
$908$	4739.60			0.173226
$909$	5167.47			0.188553
$910$	2595.38	+	685.600i	0.0945452	+	0.0249752i
$911$	45813.3			1.66615			0.833074	−	0.553161i	$-0.186579\pi$
$911$	45813.3			1.66615			0.833074	+	0.553161i	$0.186579\pi$
$912$			2752.89i			0.0999532i
$913$	−23386.9	+	27760.1i	−0.847747	+	1.00627i
$914$	7904.61			0.286063
$915$	9951.27			0.359540
$916$		−	6994.33i		−	0.252292i
$917$	−45200.1	−	11940.1i	−1.62774	−	0.429987i
$918$	−1849.87			−0.0665085
$919$			46113.0i			1.65520i	0.561319	+	0.827600i	$0.310294\pi$
$919$			46113.0i			1.65520i	−0.561319	+	0.827600i	$0.689706\pi$
$920$	731.505			0.0262142
$921$		−	7254.60i		−	0.259552i
$922$			3634.44i			0.129820i
$923$	−4854.68			−0.173124
$924$	4660.99	+	6634.45i	0.165947	+	0.236209i
$925$	22435.9			0.797502
$926$		−	4237.88i		−	0.150394i
$927$			4560.59i			0.161585i
$928$	−684.896			−0.0242272
$929$			19640.7i			0.693639i	0.937932	+	0.346820i	$0.112738\pi$
$929$			19640.7i			0.693639i	−0.937932	+	0.346820i	$0.887262\pi$
$930$	6230.12			0.219671
$931$	−17105.3	−	9715.08i	−0.602154	−	0.341997i
$932$		−	8877.15i		−	0.311996i
$933$	−6635.32			−0.232830
$934$	27202.4			0.952985
$935$	6173.81	+	5201.22i	0.215941	+	0.181923i
$936$		−	807.833i		−	0.0282103i
$937$	−3650.66			−0.127280			−0.0636402	−	0.997973i	$-0.520271\pi$
$937$	−3650.66			−0.127280			−0.0636402	+	0.997973i	$0.520271\pi$
$938$	−7060.00	+	26726.1i	−0.245754	+	0.930317i
$939$	−14673.8			−0.509968
$940$	2962.62			0.102798
$941$	−53220.5			−1.84372			−0.921859	−	0.387525i	$-0.873330\pi$
$941$	−53220.5			−1.84372			−0.921859	+	0.387525i	$0.873330\pi$
$942$			10242.2i			0.354254i
$943$	−1234.01			−0.0426139
$944$			1341.00i			0.0462348i
$945$	−3122.81	−	824.927i	−0.107498	−	0.0283967i
$946$	−9358.06	+	11107.9i	−0.321625	+	0.381766i
$947$	24663.2			0.846300			0.423150	−	0.906060i	$-0.360924\pi$
$947$	24663.2			0.846300			0.423150	+	0.906060i	$0.360924\pi$
$948$	−11065.4			−0.379100
$949$	−11965.3			−0.409282
$950$		−	9552.30i		−	0.326229i
$951$		−	10527.0i		−	0.358949i
$952$	1296.30	−	4907.23i	0.0441317	−	0.167063i
$953$		−	30839.6i		−	1.04826i	−0.851638	−	0.524131i	$-0.824390\pi$
$953$		−	30839.6i		−	1.04826i	0.851638	−	0.524131i	$-0.175610\pi$
$954$		−	9711.69i		−	0.329589i
$955$		−	26646.5i		−	0.902891i
$956$			15851.3i			0.536263i
$957$	1509.28	−	1791.51i	0.0509804	−	0.0605134i
$958$			3398.38i			0.114610i
$959$	13298.7	+	3513.00i	0.447796	+	0.118291i
$960$	−1240.18			−0.0416943
$961$	3949.06			0.132559
$962$		−	6045.51i		−	0.202615i
$963$		−	4193.05i		−	0.140311i
$964$	−9678.09			−0.323351
$965$	13973.9			0.466151
$966$	1520.88	+	401.759i	0.0506559	+	0.0133813i
$967$		−	3291.48i		−	0.109459i	−0.998501	−	0.0547295i	$-0.982570\pi$
$967$		−	3291.48i		−	0.109459i	0.998501	−	0.0547295i	$-0.0174297\pi$
$968$	−10493.4	+	1807.64i	−0.348422	+	0.0600203i
$969$			5894.08i			0.195403i
$970$		−	12624.6i		−	0.417889i
$971$			54931.4i			1.81548i	0.419531	+	0.907741i	$0.362195\pi$
$971$			54931.4i			1.81548i	−0.419531	+	0.907741i	$0.637805\pi$
$972$			972.000i			0.0320750i
$973$	7178.79	+	1896.36i	0.236528	+	0.0624815i
$974$		−	8726.18i		−	0.287069i
$975$			2803.11i			0.0920732i
$976$	8216.64			0.269476
$977$	50926.7			1.66764			0.833822	−	0.552033i	$-0.186148\pi$
$977$	50926.7			1.66764			0.833822	+	0.552033i	$0.186148\pi$
$978$	21702.9			0.709592
$979$	−22010.1	−	18542.7i	−0.718534	−	0.605340i
$980$	4376.65	−	7705.96i	0.142660	−	0.251182i
$981$		−	33.4486i		−	0.00108862i
$982$	8917.88			0.289797
$983$			32188.5i			1.04441i	0.852821	+	0.522204i	$0.174890\pi$
$983$			32188.5i			1.04441i	−0.852821	+	0.522204i	$0.825110\pi$
$984$	2092.11			0.0677786
$985$	21978.3			0.710950
$986$	−1466.40			−0.0473627
$987$	6159.61	+	1627.13i	0.198645	+	0.0524744i
$988$	−2573.93			−0.0828822
$989$			2817.90i			0.0906006i
$990$	2732.94	−	3243.98i	0.0877359	−	0.104142i
$991$	−9826.54			−0.314985			−0.157493	−	0.987520i	$-0.550341\pi$
$991$	−9826.54			−0.314985			−0.157493	+	0.987520i	$0.550341\pi$
$992$	5144.14			0.164644
$993$		−	860.572i		−	0.0275019i
$994$	−4093.27	+	15495.3i	−0.130614	+	0.494449i
$995$	35295.7			1.12457
$996$		−	11939.3i		−	0.379831i
$997$	3830.39			0.121675			0.0608373	−	0.998148i	$-0.480623\pi$
$997$	3830.39			0.121675			0.0608373	+	0.998148i	$0.480623\pi$
$998$		−	12663.4i		−	0.401656i
$999$			7274.08i			0.230372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.4.e.b.307.19	yes	24
7.6	odd	2		462.4.e.a.307.18	yes	24
11.10	odd	2		462.4.e.a.307.7	✓	24
77.76	even	2	inner	462.4.e.b.307.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.e.a.307.7	✓	24	11.10	odd	2
462.4.e.a.307.18	yes	24	7.6	odd	2
462.4.e.b.307.6	yes	24	77.76	even	2	inner
462.4.e.b.307.19	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	462.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +6.45926i q^{5} +6.00000 q^{6} +(17.9060 + 4.73009i) q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +6.45926i q^{5} +6.00000 q^{6} +(17.9060 + 4.73009i) q^{7} -8.00000i q^{8} -9.00000 q^{9} -12.9185 q^{10} +(23.5058 - 27.9012i) q^{11} +12.0000i q^{12} -11.2199 q^{13} +(-9.46017 + 35.8121i) q^{14} +19.3778 q^{15} +16.0000 q^{16} +34.2568 q^{17} -18.0000i q^{18} -57.3519 q^{19} -25.8370i q^{20} +(14.1903 - 53.7181i) q^{21} +(55.8024 + 47.0116i) q^{22} +14.1561 q^{23} -24.0000 q^{24} +83.2780 q^{25} -22.4398i q^{26} +27.0000i q^{27} +(-71.6242 - 18.9203i) q^{28} +21.4030i q^{29} +38.7556i q^{30} -160.754i q^{31} +32.0000i q^{32} +(-83.7036 - 70.5174i) q^{33} +68.5137i q^{34} +(-30.5529 + 115.660i) q^{35} +36.0000 q^{36} +269.410 q^{37} -114.704i q^{38} +33.6597i q^{39} +51.6741 q^{40} -87.1714 q^{41} +(107.436 + 28.3805i) q^{42} +199.059i q^{43} +(-94.0232 + 111.605i) q^{44} -58.1333i q^{45} +28.3123i q^{46} +114.665i q^{47} -48.0000i q^{48} +(298.253 + 169.394i) q^{49} +166.556i q^{50} -102.770i q^{51} +44.8796 q^{52} +539.539 q^{53} -54.0000 q^{54} +(180.221 + 151.830i) q^{55} +(37.8407 - 143.248i) q^{56} +172.056i q^{57} -42.8060 q^{58} +83.8122i q^{59} -77.5111 q^{60} +513.540 q^{61} +321.509 q^{62} +(-161.154 - 42.5708i) q^{63} -64.0000 q^{64} -72.4723i q^{65} +(141.035 - 167.407i) q^{66} +746.287 q^{67} -137.027 q^{68} -42.4684i q^{69} +(-231.320 - 61.1057i) q^{70} +432.685 q^{71} +72.0000i q^{72} +1066.43 q^{73} +538.821i q^{74} -249.834i q^{75} +229.408 q^{76} +(552.871 - 388.416i) q^{77} -67.3194 q^{78} +922.115i q^{79} +103.348i q^{80} +81.0000 q^{81} -174.343i q^{82} -994.942 q^{83} +(-56.7610 + 214.872i) q^{84} +221.274i q^{85} -398.117 q^{86} +64.2090 q^{87} +(-223.210 - 188.046i) q^{88} -788.857i q^{89} +116.267 q^{90} +(-200.904 - 53.0711i) q^{91} -56.6245 q^{92} -482.263 q^{93} -229.331 q^{94} -370.451i q^{95} +96.0000 q^{96} +977.250i q^{97} +(-338.789 + 596.505i) q^{98} +(-211.552 + 251.111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} + 144 q^{6} - 36 q^{7} - 216 q^{9}+O(q^{10}) \) 24 * q - 96 * q^4 + 144 * q^6 - 36 * q^7 - 216 * q^9	\( 24 q - 96 q^{4} + 144 q^{6} - 36 q^{7} - 216 q^{9} - 56 q^{10} - 28 q^{11} + 32 q^{14} + 84 q^{15} + 384 q^{16} + 204 q^{17} + 244 q^{19} - 48 q^{21} - 64 q^{22} + 56 q^{23} - 576 q^{24} - 1096 q^{25} + 144 q^{28} + 96 q^{33} + 16 q^{35} + 864 q^{36} - 696 q^{37} + 224 q^{40} - 1276 q^{41} - 216 q^{42} + 112 q^{44} + 836 q^{49} + 168 q^{53} - 1296 q^{54} - 712 q^{55} - 128 q^{56} - 336 q^{58} - 336 q^{60} - 616 q^{61} + 1048 q^{62} + 324 q^{63} - 1536 q^{64} - 168 q^{66} - 1544 q^{67} - 816 q^{68} - 168 q^{70} - 944 q^{71} - 2212 q^{73} - 976 q^{76} - 1888 q^{77} + 1944 q^{81} + 236 q^{83} + 192 q^{84} - 336 q^{86} + 504 q^{87} + 256 q^{88} + 504 q^{90} - 508 q^{91} - 224 q^{92} - 1572 q^{93} - 584 q^{94} + 2304 q^{96} - 2008 q^{98} + 252 q^{99}+O(q^{100}) \) 24 * q - 96 * q^4 + 144 * q^6 - 36 * q^7 - 216 * q^9 - 56 * q^10 - 28 * q^11 + 32 * q^14 + 84 * q^15 + 384 * q^16 + 204 * q^17 + 244 * q^19 - 48 * q^21 - 64 * q^22 + 56 * q^23 - 576 * q^24 - 1096 * q^25 + 144 * q^28 + 96 * q^33 + 16 * q^35 + 864 * q^36 - 696 * q^37 + 224 * q^40 - 1276 * q^41 - 216 * q^42 + 112 * q^44 + 836 * q^49 + 168 * q^53 - 1296 * q^54 - 712 * q^55 - 128 * q^56 - 336 * q^58 - 336 * q^60 - 616 * q^61 + 1048 * q^62 + 324 * q^63 - 1536 * q^64 - 168 * q^66 - 1544 * q^67 - 816 * q^68 - 168 * q^70 - 944 * q^71 - 2212 * q^73 - 976 * q^76 - 1888 * q^77 + 1944 * q^81 + 236 * q^83 + 192 * q^84 - 336 * q^86 + 504 * q^87 + 256 * q^88 + 504 * q^90 - 508 * q^91 - 224 * q^92 - 1572 * q^93 - 584 * q^94 + 2304 * q^96 - 2008 * q^98 + 252 * q^99

Introduction

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