LMFDB - Embedded newform 189.4.o.a.62.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.3
Character	$\chi$	$=$	189.62
Dual form			189.4.o.a.125.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.92583 - 2.26658i) q^{2} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(2.53789 + 18.3455i) q^{7} -20.6235i q^{8} +O(q^{10})$	\(q+(-3.92583 - 2.26658i) q^{2} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(2.53789 + 18.3455i) q^{7} -20.6235i q^{8} +0.623335i q^{10} +(-8.78077 - 5.06958i) q^{11} +(13.1146 - 7.57170i) q^{13} +(31.6183 - 77.7738i) q^{14} +(3.45316 - 5.98105i) q^{16} -88.2223 q^{17} -66.1014i q^{19} +(0.862814 - 1.49444i) q^{20} +(22.9812 + 39.8046i) q^{22} +(49.7310 - 28.7122i) q^{23} +(62.4905 - 108.237i) q^{25} -68.6473 q^{26} +(-183.458 + 142.696i) q^{28} +(-102.744 - 59.3195i) q^{29} +(-266.140 + 153.656i) q^{31} +(-169.997 + 98.1477i) q^{32} +(346.345 + 199.963i) q^{34} +(2.01016 - 1.56353i) q^{35} -337.159 q^{37} +(-149.824 + 259.503i) q^{38} +(-2.45592 + 1.41793i) q^{40} +(220.622 + 382.129i) q^{41} +(46.7113 - 80.9064i) q^{43} -127.241i q^{44} -260.314 q^{46} +(-155.927 + 270.073i) q^{47} +(-330.118 + 93.1181i) q^{49} +(-490.654 + 283.279i) q^{50} +(164.581 + 95.0209i) q^{52} -321.580i q^{53} +1.39419i q^{55} +(378.350 - 52.3403i) q^{56} +(268.904 + 465.756i) q^{58} +(-287.300 - 497.619i) q^{59} +(-634.571 - 366.369i) q^{61} +1393.09 q^{62} +834.587 q^{64} +(-1.80333 - 1.04115i) q^{65} +(31.6068 + 54.7445i) q^{67} +(-553.572 - 958.815i) q^{68} +(-11.4354 + 1.58196i) q^{70} -621.395i q^{71} -95.2953i q^{73} +(1323.63 + 764.196i) q^{74} +(718.401 - 414.769i) q^{76} +(70.7195 - 173.954i) q^{77} +(425.124 - 736.337i) q^{79} -0.949659 q^{80} -2000.23i q^{82} +(70.1533 - 121.509i) q^{83} +(6.06554 + 10.5058i) q^{85} +(-366.761 + 211.750i) q^{86} +(-104.553 + 181.090i) q^{88} -1223.70 q^{89} +(172.190 + 221.378i) q^{91} +(624.098 + 360.323i) q^{92} +(1224.28 - 706.841i) q^{94} +(-7.87159 + 4.54466i) q^{95} +(671.481 + 387.680i) q^{97} +(1507.05 + 382.673i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−3.92583	−	2.26658i	−1.38799	−	0.801356i	−0.394901	−	0.918724i	$-0.629221\pi$
$2$	−3.92583	−	2.26658i	−1.38799	−	0.801356i	−0.993089	+	0.117368i	$0.962554\pi$
$3$		0			0
$3$		0			0
$4$	6.27474	+	10.8682i	0.784343	+	1.35852i
$5$	−0.0687529	−	0.119084i	−0.00614945	−	0.0106512i	0.862934	−	0.505316i	$-0.168624\pi$
$5$	−0.0687529	−	0.119084i	−0.00614945	−	0.0106512i	−0.869084	+	0.494665i	$0.835291\pi$
$6$		0			0
$7$	2.53789	+	18.3455i	0.137033	+	0.990566i
$7$	2.53789	+	18.3455i	0.137033	+	0.990566i
$8$		−	20.6235i		−	0.911439i
$9$		0			0
$10$			0.623335i			0.0197116i
$11$	−8.78077	−	5.06958i	−0.240682	−	0.138958i	0.374808	−	0.927102i	$-0.377709\pi$
$11$	−8.78077	−	5.06958i	−0.240682	−	0.138958i	−0.615490	+	0.788145i	$0.711042\pi$
$12$		0			0
$13$	13.1146	−	7.57170i	0.279794	−	0.161539i	−0.353536	−	0.935421i	$-0.615021\pi$
$13$	13.1146	−	7.57170i	0.279794	−	0.161539i	0.633330	+	0.773882i	$0.281687\pi$
$14$	31.6183	−	77.7738i	0.603595	−	1.48471i
$15$		0			0
$16$	3.45316	−	5.98105i	0.0539556	−	0.0934538i
$17$	−88.2223			−1.25865			−0.629325	−	0.777142i	$-0.716669\pi$
$17$	−88.2223			−1.25865			−0.629325	+	0.777142i	$0.716669\pi$
$18$		0			0
$19$		−	66.1014i		−	0.798142i	−0.916920	−	0.399071i	$-0.869333\pi$
$19$		−	66.1014i		−	0.798142i	0.916920	−	0.399071i	$-0.130667\pi$
$20$	0.862814	−	1.49444i	0.00964655	−	0.0167083i
$21$		0			0
$22$	22.9812	+	39.8046i	0.222709	+	0.385744i
$23$	49.7310	−	28.7122i	0.450854	−	0.260300i	−0.257337	−	0.966322i	$-0.582845\pi$
$23$	49.7310	−	28.7122i	0.450854	−	0.260300i	0.708191	+	0.706021i	$0.249512\pi$
$24$		0			0
$25$	62.4905	−	108.237i	0.499924	−	0.865894i
$26$	−68.6473			−0.517802
$27$		0			0
$28$	−183.458	+	142.696i	−1.23822	+	0.963106i
$29$	−102.744	−	59.3195i	−0.657902	−	0.379840i	0.133575	−	0.991039i	$-0.457354\pi$
$29$	−102.744	−	59.3195i	−0.657902	−	0.379840i	−0.791477	+	0.611199i	$0.790688\pi$
$30$		0			0
$31$	−266.140	+	153.656i	−1.54194	+	0.890238i	−0.543221	+	0.839590i	$0.682796\pi$
$31$	−266.140	+	153.656i	−1.54194	+	0.890238i	−0.998717	+	0.0506486i	$0.983871\pi$
$32$	−169.997	+	98.1477i	−0.939109	+	0.542195i
$33$		0			0
$34$	346.345	+	199.963i	1.74699	+	1.00863i
$35$	2.01016	−	1.56353i	0.00970800	−	0.00755100i
$36$		0			0
$37$	−337.159			−1.49807			−0.749035	−	0.662531i	$-0.769482\pi$
$37$	−337.159			−1.49807			−0.749035	+	0.662531i	$0.769482\pi$
$38$	−149.824	+	259.503i	−0.639596	+	1.10781i
$39$		0			0
$40$	−2.45592	+	1.41793i	−0.00970788	+	0.00560485i
$41$	220.622	+	382.129i	0.840376	+	1.45557i	0.889577	+	0.456785i	$0.150999\pi$
$41$	220.622	+	382.129i	0.840376	+	1.45557i	−0.0492008	+	0.998789i	$0.515667\pi$
$42$		0			0
$43$	46.7113	−	80.9064i	0.165661	−	0.286933i	−0.771229	−	0.636558i	$-0.780358\pi$
$43$	46.7113	−	80.9064i	0.165661	−	0.286933i	0.936890	+	0.349625i	$0.113691\pi$
$44$		−	127.241i		−	0.435962i
$45$		0			0
$46$	−260.314			−0.834373
$47$	−155.927	+	270.073i	−0.483921	+	0.838176i	−0.999829	−	0.0184681i	$-0.994121\pi$
$47$	−155.927	+	270.073i	−0.483921	+	0.838176i	0.515909	+	0.856644i	$0.327454\pi$
$48$		0			0
$49$	−330.118	+	93.1181i	−0.962444	+	0.271481i
$50$	−490.654	+	283.279i	−1.38778	+	0.801235i
$51$		0			0
$52$	164.581	+	95.0209i	0.438909	+	0.253404i
$53$		−	321.580i		−	0.833441i	−0.909035	−	0.416721i	$-0.863179\pi$
$53$		−	321.580i		−	0.833441i	0.909035	−	0.416721i	$-0.136821\pi$
$54$		0			0
$55$			1.39419i			0.00341805i
$56$	378.350	−	52.3403i	0.902841	−	0.124898i
$57$		0			0
$58$	268.904	+	465.756i	0.608774	+	1.05443i
$59$	−287.300	−	497.619i	−0.633955	−	1.09804i	−0.986736	−	0.162336i	$-0.948097\pi$
$59$	−287.300	−	497.619i	−0.633955	−	1.09804i	0.352781	−	0.935706i	$-0.385236\pi$
$60$		0			0
$61$	−634.571	−	366.369i	−1.33194	−	0.768997i	−0.346344	−	0.938107i	$-0.612577\pi$
$61$	−634.571	−	366.369i	−1.33194	−	0.768997i	−0.985597	+	0.169111i	$0.945910\pi$
$62$	1393.09			2.85359
$63$		0			0
$64$	834.587			1.63005
$65$	−1.80333	−	1.04115i	−0.00344116	−	0.00198676i
$66$		0			0
$67$	31.6068	+	54.7445i	0.0576325	+	0.0998225i	0.893402	−	0.449258i	$-0.148311\pi$
$67$	31.6068	+	54.7445i	0.0576325	+	0.0998225i	−0.835770	+	0.549080i	$0.814978\pi$
$68$	−553.572	−	958.815i	−0.987213	−	1.70990i
$69$		0			0
$70$	−11.4354	+	1.58196i	−0.0195256	+	0.00270115i
$71$		−	621.395i		−	1.03868i	−0.854569	−	0.519338i	$-0.826178\pi$
$71$		−	621.395i		−	1.03868i	0.854569	−	0.519338i	$-0.173822\pi$
$72$		0			0
$73$		−	95.2953i		−	0.152787i	−0.997078	−	0.0763937i	$-0.975659\pi$
$73$		−	95.2953i		−	0.152787i	0.997078	−	0.0763937i	$-0.0243406\pi$
$74$	1323.63	+	764.196i	2.07930	+	1.20049i
$75$		0			0
$76$	718.401	−	414.769i	1.08429	−	0.626017i
$77$	70.7195	−	173.954i	0.104665	−	0.257453i
$78$		0			0
$79$	425.124	−	736.337i	0.605446	−	1.04866i	−0.386535	−	0.922275i	$-0.626328\pi$
$79$	425.124	−	736.337i	0.605446	−	1.04866i	0.991981	−	0.126388i	$-0.0403385\pi$
$80$	−0.949659			−0.00132719
$81$		0			0
$82$		−	2000.23i		−	2.69376i
$83$	70.1533	−	121.509i	0.0927750	−	0.160691i	−0.815903	−	0.578189i	$-0.803760\pi$
$83$	70.1533	−	121.509i	0.0927750	−	0.160691i	0.908678	+	0.417498i	$0.137093\pi$
$84$		0			0
$85$	6.06554	+	10.5058i	0.00774000	+	0.0134061i
$86$	−366.761	+	211.750i	−0.459871	+	0.265506i
$87$		0			0
$88$	−104.553	+	181.090i	−0.126652	+	0.219367i
$89$	−1223.70			−1.45744			−0.728720	−	0.684812i	$-0.759884\pi$
$89$	−1223.70			−1.45744			−0.728720	+	0.684812i	$0.759884\pi$
$90$		0			0
$91$	172.190	+	221.378i	0.198357	+	0.255019i
$92$	624.098	+	360.323i	0.707247	+	0.408330i
$93$		0			0
$94$	1224.28	−	706.841i	1.34335	−	0.775586i
$95$	−7.87159	+	4.54466i	−0.00850114	+	0.00490813i
$96$		0			0
$97$	671.481	+	387.680i	0.702872	+	0.405803i	0.808416	−	0.588611i	$-0.200325\pi$
$97$	671.481	+	387.680i	0.702872	+	0.405803i	−0.105544	+	0.994415i	$0.533658\pi$
$98$	1507.05	+	382.673i	1.55341	+	0.394447i
$99$		0			0
$100$	1568.45			1.56845
$101$	−263.211	+	455.895i	−0.259312	+	0.449141i	−0.966058	−	0.258326i	$-0.916829\pi$
$101$	−263.211	+	455.895i	−0.259312	+	0.449141i	0.706746	+	0.707467i	$0.250162\pi$
$102$		0			0
$103$	−378.997	+	218.814i	−0.362560	+	0.209324i	−0.670203	−	0.742178i	$-0.733793\pi$
$103$	−378.997	+	218.814i	−0.362560	+	0.209324i	0.307643	+	0.951502i	$0.400460\pi$
$104$	−156.155	−	270.468i	−0.147233	−	0.255015i
$105$		0			0
$106$	−728.886	+	1262.47i	−0.667883	+	1.15681i
$107$			1443.67i			1.30434i	0.758071	+	0.652172i	$0.226142\pi$
$107$			1443.67i			1.30434i	−0.758071	+	0.652172i	$0.773858\pi$
$108$		0			0
$109$	−1201.61			−1.05590			−0.527950	−	0.849276i	$-0.677039\pi$
$109$	−1201.61			−1.05590			−0.527950	+	0.849276i	$0.677039\pi$
$110$	3.16005	−	5.47336i	0.00273908	−	0.00474422i
$111$		0			0
$112$	118.489	+	48.1708i	0.0999660	+	0.0406403i
$113$	−404.622	+	233.609i	−0.336846	+	0.194478i	−0.658877	−	0.752251i	$-0.728968\pi$
$113$	−404.622	+	233.609i	−0.336846	+	0.194478i	0.322030	+	0.946729i	$0.395635\pi$
$114$		0			0
$115$	−6.83830	−	3.94810i	−0.00554500	−	0.00320141i
$116$		−	1488.86i		−	1.19170i
$117$		0			0
$118$			2604.75i			2.03209i
$119$	−223.899	−	1618.49i	−0.172477	−	1.24678i
$120$		0			0
$121$	−614.099	−	1063.65i	−0.461381	−	0.799136i
$122$	1660.81	+	2876.61i	1.23248	+	2.13472i
$123$		0			0
$124$	−3339.91	−	1928.30i	−2.41882	−	1.39650i
$125$	−34.3739			−0.0245959
$126$		0			0
$127$	1185.39			0.828237			0.414119	−	0.910223i	$-0.364090\pi$
$127$	1185.39			0.828237			0.414119	+	0.910223i	$0.364090\pi$
$128$	−1916.47	−	1106.47i	−1.32339	−	0.764058i
$129$		0			0
$130$	4.71970	+	8.17477i	0.00318420	+	0.00551519i
$131$	−693.151	−	1200.57i	−0.462297	−	0.800722i	0.536778	−	0.843723i	$-0.319641\pi$
$131$	−693.151	−	1200.57i	−0.462297	−	0.800722i	−0.999075	+	0.0430017i	$0.986308\pi$
$132$		0			0
$133$	1212.67	−	167.758i	0.790613	−	0.109372i
$134$		−	286.557i		−	0.184737i
$135$		0			0
$136$			1819.45i			1.14718i
$137$	801.189	+	462.566i	0.499636	+	0.288465i	0.728563	−	0.684978i	$-0.240188\pi$
$137$	801.189	+	462.566i	0.499636	+	0.288465i	−0.228927	+	0.973444i	$0.573522\pi$
$138$		0			0
$139$	−2339.20	+	1350.54i	−1.42740	+	0.824107i	−0.996915	−	0.0784926i	$-0.974989\pi$
$139$	−2339.20	+	1350.54i	−1.42740	+	0.824107i	−0.430481	+	0.902600i	$0.641656\pi$
$140$	29.6060	+	12.0361i	0.0178726	+	0.00726595i
$141$		0			0
$142$	−1408.44	+	2439.49i	−0.832350	+	1.44167i
$143$	−153.541			−0.0897886
$144$		0			0
$145$			16.3136i			0.00934322i
$146$	−215.994	+	374.113i	−0.122437	+	0.212067i
$147$		0			0
$148$	−2115.58	−	3664.30i	−1.17500	−	2.03516i
$149$	2532.14	−	1461.93i	1.39222	−	0.803798i	0.398659	−	0.917099i	$-0.369476\pi$
$149$	2532.14	−	1461.93i	1.39222	−	0.803798i	0.993561	+	0.113301i	$0.0361425\pi$
$150$		0			0
$151$	359.334	−	622.384i	0.193657	−	0.335423i	−0.752803	−	0.658246i	$-0.771299\pi$
$151$	359.334	−	622.384i	0.193657	−	0.335423i	0.946459	+	0.322823i	$0.104632\pi$
$152$	−1363.24			−0.727458
$153$		0			0
$154$	−671.913	+	522.622i	−0.351586	+	0.273468i
$155$	36.5957	+	21.1286i	0.0189641	+	0.0109489i
$156$		0			0
$157$	1417.53	−	818.411i	0.720581	−	0.416028i	−0.0943856	−	0.995536i	$-0.530089\pi$
$157$	1417.53	−	818.411i	0.720581	−	0.416028i	0.814966	+	0.579508i	$0.196755\pi$
$158$	−3337.93	+	1927.15i	−1.68070	+	0.970355i
$159$		0			0
$160$	23.3756	+	13.4959i	0.0115500	+	0.00666840i
$161$	652.953	+	839.474i	0.319627	+	0.410931i
$162$		0			0
$163$	−2008.88			−0.965321			−0.482661	−	0.875808i	$-0.660330\pi$
$163$	−2008.88			−0.965321			−0.482661	+	0.875808i	$0.660330\pi$
$164$	−2768.70	+	4795.52i	−1.31829	+	2.28334i
$165$		0			0
$166$	−550.820	+	318.016i	−0.257541	+	0.148692i
$167$	83.5889	+	144.780i	0.0387323	+	0.0670864i	0.884742	−	0.466082i	$-0.154335\pi$
$167$	83.5889	+	144.780i	0.0387323	+	0.0670864i	−0.846009	+	0.533168i	$0.821001\pi$
$168$		0			0
$169$	−983.839	+	1704.06i	−0.447810	+	0.775630i
$170$		−	54.9920i		−	0.0248100i
$171$		0			0
$172$	1172.41			0.519739
$173$	473.704	−	820.479i	0.208179	−	0.360577i	−0.742962	−	0.669334i	$-0.766580\pi$
$173$	473.704	−	820.479i	0.208179	−	0.360577i	0.951141	+	0.308757i	$0.0999129\pi$
$174$		0			0
$175$	2144.26	+	871.730i	0.926232	+	0.376552i
$176$	−60.6428	+	35.0121i	−0.0259723	+	0.0149951i
$177$		0			0
$178$	4804.04	+	2773.61i	2.02291	+	1.16793i
$179$		−	2369.02i		−	0.989214i	−0.869117	−	0.494607i	$-0.835312\pi$
$179$		−	2369.02i		−	0.989214i	0.869117	−	0.494607i	$-0.164688\pi$
$180$		0			0
$181$			1499.79i			0.615904i	0.951402	+	0.307952i	$0.0996437\pi$
$181$			1499.79i			0.615904i	−0.951402	+	0.307952i	$0.900356\pi$
$182$	−174.220	−	1259.37i	−0.0709562	−	0.512917i
$183$		0			0
$184$	−592.147	−	1025.63i	−0.237248	−	0.410926i
$185$	23.1806	+	40.1501i	0.00921230	+	0.0159562i
$186$		0			0
$187$	774.659	+	447.250i	0.302934	+	0.174899i
$188$	−3913.61			−1.51824
$189$		0			0
$190$	41.2033			0.0157326
$191$	685.886	+	395.997i	0.259838	+	0.150017i	0.624260	−	0.781216i	$-0.285400\pi$
$191$	685.886	+	395.997i	0.259838	+	0.150017i	−0.364423	+	0.931234i	$0.618734\pi$
$192$		0			0
$193$	2170.01	+	3758.56i	0.809330	+	1.40180i	0.913329	+	0.407223i	$0.133503\pi$
$193$	2170.01	+	3758.56i	0.809330	+	1.40180i	−0.103999	+	0.994577i	$0.533164\pi$
$194$	−1757.41	−	3043.93i	−0.650386	−	1.12650i
$195$		0			0
$196$	−3083.43	−	3003.49i	−1.12370	−	1.09457i
$197$		−	986.827i		−	0.356896i	−0.983949	−	0.178448i	$-0.942892\pi$
$197$		−	986.827i		−	0.356896i	0.983949	−	0.178448i	$-0.0571076\pi$
$198$		0			0
$199$		−	1621.78i		−	0.577714i	−0.957372	−	0.288857i	$-0.906725\pi$
$199$		−	1621.78i		−	0.577714i	0.957372	−	0.288857i	$-0.0932752\pi$
$200$	−2232.22	−	1288.77i	−0.789210	−	0.455651i
$201$		0			0
$202$	2066.64	−	1193.18i	0.719844	−	0.415602i
$203$	827.494	−	2035.45i	0.286102	−	0.703746i
$204$		0			0
$205$	30.3369	−	52.5450i	0.0103357	−	0.0179020i
$206$	1983.84			0.670973
$207$		0			0
$208$		−	104.585i		−	0.0348638i
$209$	−335.106	+	580.421i	−0.110908	+	0.192098i
$210$		0			0
$211$	181.071	+	313.625i	0.0590780	+	0.102326i	0.894052	−	0.447964i	$-0.147851\pi$
$211$	181.071	+	313.625i	0.0590780	+	0.102326i	−0.834974	+	0.550290i	$0.814517\pi$
$212$	3494.99	−	2017.83i	1.13225	−	0.653704i
$213$		0			0
$214$	3272.19	−	5667.60i	1.04524	−	1.81042i
$215$	−12.8462			−0.00407489
$216$		0			0
$217$	−3494.33	−	4492.51i	−1.09314	−	1.40540i
$218$	4717.30	+	2723.53i	1.46558	+	0.846151i
$219$		0			0
$220$	−15.1523	+	8.74820i	−0.00464350	+	0.00268093i
$221$	−1157.00	+	667.993i	−0.352163	+	0.203321i
$222$		0			0
$223$	−115.589	−	66.7354i	−0.0347104	−	0.0200401i	0.482544	−	0.875872i	$-0.339713\pi$
$223$	−115.589	−	66.7354i	−0.0347104	−	0.0200401i	−0.517255	+	0.855831i	$0.673046\pi$
$224$	−2232.01	−	2869.60i	−0.665769	−	0.855951i
$225$		0			0
$226$	2117.97			0.623385
$227$	1770.11	−	3065.91i	0.517560	−	0.896439i	−0.482232	−	0.876043i	$-0.660174\pi$
$227$	1770.11	−	3065.91i	0.517560	−	0.896439i	0.999792	−	0.0203961i	$-0.00649274\pi$
$228$		0			0
$229$	−2093.97	+	1208.96i	−0.604251	+	0.348865i	−0.770712	−	0.637183i	$-0.780099\pi$
$229$	−2093.97	+	1208.96i	−0.604251	+	0.348865i	0.166461	+	0.986048i	$0.446766\pi$
$230$	17.8973	+	30.9991i	0.00513093	+	0.00888704i
$231$		0			0
$232$	−1223.38	+	2118.95i	−0.346201	+	0.599638i
$233$			4957.61i			1.39392i	0.717110	+	0.696960i	$0.245465\pi$
$233$			4957.61i			1.39392i	−0.717110	+	0.696960i	$0.754535\pi$
$234$		0			0
$235$	42.8817			0.0119034
$236$	3605.47	−	6244.86i	0.994475	−	1.72248i
$237$		0			0
$238$	−2789.44	+	6861.38i	−0.759715	+	1.86873i
$239$	1649.02	−	952.059i	0.446301	−	0.257672i	−0.259966	−	0.965618i	$-0.583711\pi$
$239$	1649.02	−	952.059i	0.446301	−	0.257672i	0.706267	+	0.707946i	$0.250378\pi$
$240$		0			0
$241$	3592.48	+	2074.12i	0.960216	+	0.554381i	0.896240	−	0.443570i	$-0.146288\pi$
$241$	3592.48	+	2074.12i	0.960216	+	0.554381i	0.0639765	+	0.997951i	$0.479622\pi$
$242$			5567.61i			1.47892i
$243$		0			0
$244$		−	9195.50i		−	2.41263i
$245$	33.7854	+	32.9095i	0.00881009	+	0.00858168i
$246$		0			0
$247$	−500.500	−	866.891i	−0.128931	−	0.223316i
$248$	3168.92	+	5488.73i	0.811398	+	1.40538i
$249$		0			0
$250$	134.946	+	77.9110i	0.0341389	+	0.0197101i
$251$	4077.88			1.02547			0.512737	−	0.858546i	$-0.328632\pi$
$251$	4077.88			1.02547			0.512737	+	0.858546i	$0.328632\pi$
$252$		0			0
$253$	−582.235			−0.144683
$254$	−4653.62	−	2686.77i	−1.14958	−	0.663713i
$255$		0			0
$256$	1677.47	+	2905.46i	0.409538	+	0.709341i
$257$	3830.27	+	6634.22i	0.929671	+	1.61024i	0.783871	+	0.620924i	$0.213242\pi$
$257$	3830.27	+	6634.22i	0.929671	+	1.61024i	0.145801	+	0.989314i	$0.453424\pi$
$258$		0			0
$259$	−855.674	−	6185.36i	−0.205286	−	1.48394i
$260$		−	26.1319i		−	0.00623319i
$261$		0			0
$262$			6284.32i			1.48186i
$263$	−2695.92	−	1556.49i	−0.632083	−	0.364933i	0.149475	−	0.988765i	$-0.452242\pi$
$263$	−2695.92	−	1556.49i	−0.632083	−	0.364933i	−0.781558	+	0.623832i	$0.785575\pi$
$264$		0			0
$265$	−38.2949	+	22.1096i	−0.00887711	+	0.00512520i
$266$	−5140.96	−	2090.01i	−1.18501	−	0.481755i
$267$		0			0
$268$	−396.648	+	687.015i	−0.0904073	+	0.156590i
$269$	−4950.54			−1.12208			−0.561040	−	0.827789i	$-0.689599\pi$
$269$	−4950.54			−1.12208			−0.561040	+	0.827789i	$0.689599\pi$
$270$		0			0
$271$			2802.02i			0.628084i	0.949409	+	0.314042i	$0.101683\pi$
$271$			2802.02i			0.628084i	−0.949409	+	0.314042i	$0.898317\pi$
$272$	−304.646	+	527.662i	−0.0679112	+	0.117626i
$273$		0			0
$274$	−2096.88	−	3631.91i	−0.462326	−	0.800773i
$275$	−1097.43	+	633.601i	−0.240645	+	0.138937i
$276$		0			0
$277$	−179.305	+	310.565i	−0.0388930	+	0.0673647i	−0.884817	−	0.465939i	$-0.845716\pi$
$277$	−179.305	+	310.565i	−0.0388930	+	0.0673647i	0.845924	+	0.533304i	$0.179050\pi$
$278$	12244.4			2.64161
$279$		0			0
$280$	−32.2455	−	41.4567i	−0.00688228	−	0.00884825i
$281$	−3092.08	−	1785.21i	−0.656434	−	0.378993i	0.134483	−	0.990916i	$-0.457063\pi$
$281$	−3092.08	−	1785.21i	−0.656434	−	0.378993i	−0.790917	+	0.611923i	$0.790396\pi$
$282$		0			0
$283$	−626.874	+	361.926i	−0.131674	+	0.0760221i	−0.564390	−	0.825508i	$-0.690889\pi$
$283$	−626.874	+	361.926i	−0.131674	+	0.0760221i	0.432716	+	0.901530i	$0.357555\pi$
$284$	6753.43	−	3899.10i	1.41106	−	0.814679i
$285$		0			0
$286$	602.776	+	348.013i	0.124626	+	0.0719526i
$287$	−6450.45	+	5017.24i	−1.32668	+	1.03191i
$288$		0			0
$289$	2870.17			0.584199
$290$	36.9759	−	64.0442i	0.00748725	−	0.0129683i
$291$		0			0
$292$	1035.69	−	597.954i	0.207565	−	0.119838i
$293$	4746.65	+	8221.43i	0.946424	+	1.63925i	0.752876	+	0.658163i	$0.228666\pi$
$293$	4746.65	+	8221.43i	0.946424	+	1.63925i	0.193548	+	0.981091i	$0.438000\pi$
$294$		0			0
$295$	−39.5055	+	68.4255i	−0.00779694	+	0.0135047i
$296$			6953.40i			1.36540i
$297$		0			0
$298$	−13254.3			−2.57651
$299$	434.800	−	753.096i	0.0840975	−	0.145661i
$300$		0			0
$301$	1602.82	+	651.613i	0.306927	+	0.124779i
$302$	−2821.36	+	1628.91i	−0.537587	+	0.310376i
$303$		0			0
$304$	−395.355	−	228.259i	−0.0745894	−	0.0430642i
$305$			100.756i			0.0189156i
$306$		0			0
$307$		−	1940.82i		−	0.360809i	−0.983593	−	0.180405i	$-0.942259\pi$
$307$		−	1940.82i		−	0.360809i	0.983593	−	0.180405i	$-0.0577407\pi$
$308$	2334.31	−	322.925i	0.431849	−	0.0597414i
$309$		0			0
$310$	−95.7790	−	165.894i	−0.0175480	−	0.0303940i
$311$	−33.9077	−	58.7299i	−0.00618241	−	0.0107082i	0.862918	−	0.505345i	$-0.168635\pi$
$311$	−33.9077	−	58.7299i	−0.00618241	−	0.0107082i	−0.869100	+	0.494636i	$0.835301\pi$
$312$		0			0
$313$	5279.91	+	3048.36i	0.953477	+	0.550490i	0.894159	−	0.447749i	$-0.147774\pi$
$313$	5279.91	+	3048.36i	0.953477	+	0.550490i	0.0593176	+	0.998239i	$0.481108\pi$
$314$	−7419.97			−1.33354
$315$		0			0
$316$	10670.2			1.89951
$317$	−4423.92	−	2554.15i	−0.783823	−	0.452541i	0.0539602	−	0.998543i	$-0.482816\pi$
$317$	−4423.92	−	2554.15i	−0.783823	−	0.452541i	−0.837784	+	0.546002i	$0.816149\pi$
$318$		0			0
$319$	601.450	+	1041.74i	0.105563	+	0.182841i
$320$	−57.3803	−	99.3856i	−0.0100239	−	0.0173619i
$321$		0			0
$322$	−660.649	−	4775.60i	−0.114337	−	0.826502i
$323$			5831.62i			1.00458i
$324$		0			0
$325$		−	1892.64i		−	0.323030i
$326$	7886.50	+	4553.27i	1.33986	+	0.773566i
$327$		0			0
$328$	7880.85	−	4550.01i	1.32667	−	0.765952i
$329$	−5350.37	−	2175.15i	−0.896582	−	0.364498i
$330$		0			0
$331$	1118.47	−	1937.25i	0.185730	−	0.321694i	−0.758092	−	0.652147i	$-0.773868\pi$
$331$	1118.47	−	1937.25i	0.185730	−	0.321694i	0.943822	+	0.330454i	$0.107202\pi$
$332$	1760.78			0.291070
$333$		0			0
$334$		−	757.842i		−	0.124154i
$335$	4.34611	−	7.52769i	0.000708816	−	0.00122771i
$336$		0			0
$337$	−2759.92	−	4780.32i	−0.446120	−	0.772703i	0.552009	−	0.833838i	$-0.313861\pi$
$337$	−2759.92	−	4780.32i	−0.446120	−	0.772703i	−0.998129	+	0.0611353i	$0.980528\pi$
$338$	7724.76	−	4459.89i	1.24311	−	0.717711i
$339$		0			0
$340$	−76.1194	+	131.843i	−0.0121416	+	0.0210299i
$341$	3115.88			0.494822
$342$		0			0
$343$	−2546.11	−	5819.87i	−0.400807	−	0.916162i
$344$	−1668.57	−	963.352i	−0.261522	−	0.150990i
$345$		0			0
$346$	−3719.36	+	2147.37i	−0.577901	+	0.333651i
$347$	7532.59	−	4348.94i	1.16533	−	0.672805i	0.212757	−	0.977105i	$-0.431756\pi$
$347$	7532.59	−	4348.94i	1.16533	−	0.672805i	0.952576	+	0.304300i	$0.0984225\pi$
$348$		0			0
$349$	−3108.44	−	1794.66i	−0.476764	−	0.275260i	0.242303	−	0.970201i	$-0.422097\pi$
$349$	−3108.44	−	1794.66i	−0.476764	−	0.275260i	−0.719067	+	0.694941i	$0.755431\pi$
$350$	−6442.14	−	8282.38i	−0.983848	−	1.26489i
$351$		0			0
$352$	1990.27			0.301369
$353$	−2114.60	+	3662.59i	−0.318834	+	0.552237i	−0.980245	−	0.197786i	$-0.936625\pi$
$353$	−2114.60	+	3662.59i	−0.318834	+	0.552237i	0.661411	+	0.750024i	$0.269958\pi$
$354$		0			0
$355$	−73.9979	+	42.7227i	−0.0110631	+	0.00638729i
$356$	−7678.41	−	13299.4i	−1.14313	−	1.97996i
$357$		0			0
$358$	−5369.58	+	9300.38i	−0.792712	+	1.37302i
$359$		−	5830.19i		−	0.857119i	−0.903513	−	0.428560i	$-0.859021\pi$
$359$		−	5830.19i		−	0.857119i	0.903513	−	0.428560i	$-0.140979\pi$
$360$		0			0
$361$	2489.60			0.362969
$362$	3399.39	−	5887.92i	0.493559	−	0.854868i
$363$		0			0
$364$	−1325.52	+	3260.48i	−0.190869	+	0.469494i
$365$	−11.3481	+	6.55183i	−0.00162736	+	0.000939558i
$366$		0			0
$367$	−6038.16	−	3486.13i	−0.858826	−	0.495844i	0.00479270	−	0.999989i	$-0.498474\pi$
$367$	−6038.16	−	3486.13i	−0.858826	−	0.495844i	−0.863619	+	0.504145i	$0.831808\pi$
$368$		−	396.591i		−	0.0561787i
$369$		0			0
$370$		−	210.163i		−	0.0295293i
$371$	5899.56	−	816.136i	0.825579	−	0.114209i
$372$		0			0
$373$	2583.05	+	4473.98i	0.358567	+	0.621056i	0.987722	−	0.156224i	$-0.0499321\pi$
$373$	2583.05	+	4473.98i	0.358567	+	0.621056i	−0.629155	+	0.777280i	$0.716599\pi$
$374$	−2027.45	−	3511.65i	−0.280313	−	0.485516i
$375$		0			0
$376$	5569.86	+	3215.76i	0.763946	+	0.441064i
$377$	−1796.60			−0.245436
$378$		0			0
$379$	12063.2			1.63494			0.817472	−	0.575969i	$-0.195375\pi$
$379$	12063.2			1.63494			0.817472	+	0.575969i	$0.195375\pi$
$380$	−98.7844	−	57.0332i	−0.0133356	−	0.00769932i
$381$		0			0
$382$	−1795.11	−	3109.23i	−0.240435	−	0.416445i
$383$	−106.285	−	184.092i	−0.0141800	−	0.0245604i	0.858848	−	0.512230i	$-0.171180\pi$
$383$	−106.285	−	184.092i	−0.0141800	−	0.0245604i	−0.873028	+	0.487670i	$0.837847\pi$
$384$		0			0
$385$	−25.5772	+	3.53831i	−0.00338581	+	0.000468388i
$386$		−	19674.0i		−	2.59424i
$387$		0			0
$388$			9730.36i			1.27316i
$389$	−12010.6	−	6934.30i	−1.56545	−	0.903812i	−0.996689	−	0.0813080i	$-0.974090\pi$
$389$	−12010.6	−	6934.30i	−1.56545	−	0.903812i	−0.568759	−	0.822504i	$-0.692576\pi$
$390$		0			0
$391$	−4387.38	+	2533.06i	−0.567467	+	0.327627i
$392$	1920.42	+	6808.20i	0.247439	+	0.877209i
$393$		0			0
$394$	−2236.72	+	3874.11i	−0.286001	+	0.495368i
$395$	−116.914			−0.0148926
$396$		0			0
$397$			13097.7i			1.65581i	0.560869	+	0.827905i	$0.310467\pi$
$397$			13097.7i			1.65581i	−0.560869	+	0.827905i	$0.689533\pi$
$398$	−3675.89	+	6366.83i	−0.462954	+	0.801861i
$399$		0			0
$400$	−431.579	−	747.518i	−0.0539474	−	0.0934397i
$401$	−10477.0	+	6048.87i	−1.30472	+	0.753282i	−0.981210	−	0.192941i	$-0.938197\pi$
$401$	−10477.0	+	6048.87i	−1.30472	+	0.753282i	−0.323513	+	0.946224i	$0.604864\pi$
$402$		0			0
$403$	−2326.87	+	4030.26i	−0.287617	+	0.498167i
$404$	−6606.33			−0.813558
$405$		0			0
$406$	−7862.10	+	6115.24i	−0.961058	+	0.747523i
$407$	2960.51	+	1709.25i	0.360558	+	0.208168i
$408$		0			0
$409$	12143.5	−	7011.04i	1.46811	−	0.847613i	0.468747	−	0.883332i	$-0.344706\pi$
$409$	12143.5	−	7011.04i	1.46811	−	0.847613i	0.999362	+	0.0357194i	$0.0113723\pi$
$410$	−238.194	+	137.522i	−0.0286917	+	0.0165651i
$411$		0			0
$412$	−4756.22	−	2746.00i	−0.568743	−	0.328364i
$413$	8399.95	−	6533.59i	1.00081	−	0.778443i
$414$		0			0
$415$	−19.2930			−0.00228206
$416$	−1486.29	+	2574.33i	−0.175172	+	0.303406i
$417$		0			0
$418$	2631.14	−	1519.09i	0.307878	−	0.177754i
$419$	4578.14	+	7929.57i	0.533787	+	0.924546i	0.999221	+	0.0394632i	$0.0125648\pi$
$419$	4578.14	+	7929.57i	0.533787	+	0.924546i	−0.465434	+	0.885082i	$0.654102\pi$
$420$		0			0
$421$	−6878.44	+	11913.8i	−0.796281	+	1.37920i	0.125741	+	0.992063i	$0.459869\pi$
$421$	−6878.44	+	11913.8i	−0.796281	+	1.37920i	−0.922022	+	0.387137i	$0.873464\pi$
$422$		−	1641.65i		−	0.189370i
$423$		0			0
$424$	−6632.11			−0.759631
$425$	−5513.06	+	9548.90i	−0.629230	+	1.08986i
$426$		0			0
$427$	5110.78	−	12571.4i	0.579222	−	1.42475i
$428$	−15690.1	+	9058.66i	−1.77198	+	1.02305i
$429$		0			0
$430$	50.4318	+	29.1168i	0.00565590	+	0.00326544i
$431$			14429.5i			1.61263i	0.591487	+	0.806314i	$0.298541\pi$
$431$			14429.5i			1.61263i	−0.591487	+	0.806314i	$0.701459\pi$
$432$		0			0
$433$			11861.6i			1.31647i	0.752814	+	0.658233i	$0.228696\pi$
$433$			11861.6i			1.31647i	−0.752814	+	0.658233i	$0.771304\pi$
$434$	3535.52	+	25557.0i	0.391037	+	2.82667i
$435$		0			0
$436$	−7539.77	−	13059.3i	−0.828187	−	1.43446i
$437$	−1897.92	−	3287.29i	−0.207757	−	0.359845i
$438$		0			0
$439$	−1856.80	−	1072.02i	−0.201868	−	0.116549i	0.395658	−	0.918398i	$-0.370516\pi$
$439$	−1856.80	−	1072.02i	−0.201868	−	0.116549i	−0.597527	+	0.801849i	$0.703850\pi$
$440$	28.7532			0.00311535
$441$		0			0
$442$	6056.23			0.651731
$443$	3418.13	+	1973.46i	0.366592	+	0.211652i	0.671969	−	0.740580i	$-0.265449\pi$
$443$	3418.13	+	1973.46i	0.366592	+	0.211652i	−0.305376	+	0.952232i	$0.598782\pi$
$444$		0			0
$445$	84.1330	+	145.723i	0.00896244	+	0.0155234i
$446$	302.522	+	523.983i	0.0321184	+	0.0556308i
$447$		0			0
$448$	2118.09	+	15311.0i	0.223372	+	1.61468i
$449$			1118.30i			0.117541i	0.998272	+	0.0587706i	$0.0187180\pi$
$449$			1118.30i			0.117541i	−0.998272	+	0.0587706i	$0.981282\pi$
$450$		0			0
$451$		−	4473.85i		−	0.467107i
$452$	−5077.80	−	2931.67i	−0.528406	−	0.305075i
$453$		0			0
$454$	−13898.3	+	8024.16i	−1.43673	+	0.829499i
$455$	14.5239	−	35.7254i	0.00149646	−	0.00368095i
$456$		0			0
$457$	−153.625	+	266.087i	−0.0157249	+	0.0272363i	−0.873781	−	0.486320i	$-0.838339\pi$
$457$	−153.625	+	266.087i	−0.0157249	+	0.0272363i	0.858056	+	0.513556i	$0.171672\pi$
$458$	10960.8			1.11826
$459$		0			0
$460$		−	99.0931i		−	0.0100440i
$461$	−37.5737	+	65.0796i	−0.00379606	+	0.00657497i	−0.867917	−	0.496709i	$-0.834542\pi$
$461$	−37.5737	+	65.0796i	−0.00379606	+	0.00657497i	0.864121	+	0.503284i	$0.167875\pi$
$462$		0			0
$463$	−8234.32	−	14262.3i	−0.826525	−	1.43158i	−0.900748	−	0.434342i	$-0.856981\pi$
$463$	−8234.32	−	14262.3i	−0.826525	−	1.43158i	0.0742230	−	0.997242i	$-0.476352\pi$
$464$	−709.585	+	409.679i	−0.0709950	+	0.0409890i
$465$		0			0
$466$	11236.8	−	19462.7i	1.11703	−	1.93475i
$467$	−8886.59			−0.880561			−0.440281	−	0.897860i	$-0.645121\pi$
$467$	−8886.59			−0.880561			−0.440281	+	0.897860i	$0.645121\pi$
$468$		0			0
$469$	−924.103	+	718.779i	−0.0909832	+	0.0707679i
$470$	−168.346	−	97.1947i	−0.0165218	−	0.00953885i
$471$		0			0
$472$	−10262.6	+	5925.14i	−1.00080	+	0.577811i
$473$	−820.323	+	473.613i	−0.0797431	+	0.0460397i
$474$		0			0
$475$	−7154.60	−	4130.71i	−0.691107	−	0.399011i
$476$	16185.1	−	12589.0i	1.55849	−	1.21221i
$477$		0			0
$478$	−8631.66			−0.825948
$479$	7210.06	−	12488.2i	0.687758	−	1.19123i	−0.284803	−	0.958586i	$-0.591928\pi$
$479$	7210.06	−	12488.2i	0.687758	−	1.19123i	0.972561	−	0.232646i	$-0.0747385\pi$
$480$		0			0
$481$	−4421.69	+	2552.86i	−0.419151	+	0.241997i
$482$	−9402.31	−	16285.3i	−0.888513	−	1.53895i
$483$		0			0
$484$	7706.62	−	13348.3i	0.723762	−	1.25359i
$485$		−	106.616i		−	0.00998186i
$486$		0			0
$487$	5047.02			0.469615			0.234807	−	0.972042i	$-0.424554\pi$
$487$	5047.02			0.469615			0.234807	+	0.972042i	$0.424554\pi$
$488$	−7555.83	+	13087.1i	−0.700894	+	1.21398i
$489$		0			0
$490$	−58.0438	−	205.774i	−0.00535133	−	0.0189713i
$491$	−1213.61	+	700.678i	−0.111547	+	0.0644015i	−0.554735	−	0.832027i	$-0.687181\pi$
$491$	−1213.61	+	700.678i	−0.111547	+	0.0644015i	0.443189	+	0.896428i	$0.353847\pi$
$492$		0			0
$493$	9064.35	+	5233.30i	0.828068	+	0.478085i
$494$			4537.69i			0.413280i
$495$		0			0
$496$			2122.39i			0.192133i
$497$	11399.8	−	1577.04i	1.02888	−	0.142333i
$498$		0			0
$499$	4556.45	+	7892.00i	0.408767	+	0.708005i	0.994752	−	0.102317i	$-0.0326257\pi$
$499$	4556.45	+	7892.00i	0.408767	+	0.708005i	−0.585985	+	0.810322i	$0.699292\pi$
$500$	−215.687	−	373.581i	−0.0192916	−	0.0334141i
$501$		0			0
$502$	−16009.1	−	9242.84i	−1.42335	−	0.821769i
$503$	6606.33			0.585610			0.292805	−	0.956172i	$-0.405411\pi$
$503$	6606.33			0.585610			0.292805	+	0.956172i	$0.405411\pi$
$504$		0			0
$505$	72.3862			0.00637850
$506$	2285.75	+	1319.68i	0.200819	+	0.115943i
$507$		0			0
$508$	7438.00	+	12883.0i	0.649622	+	1.12518i
$509$	−2008.77	−	3479.30i	−0.174926	−	0.302981i	0.765210	−	0.643781i	$-0.222635\pi$
$509$	−2008.77	−	3479.30i	−0.174926	−	0.302981i	−0.940136	+	0.340801i	$0.889302\pi$
$510$		0			0
$511$	1748.25	−	241.850i	0.151346	−	0.0209370i
$512$			2495.14i			0.215372i
$513$		0			0
$514$		−	34726.4i		−	2.97999i
$515$	52.1143	+	30.0882i	0.00445909	+	0.00257446i
$516$		0			0
$517$	2738.32	−	1580.97i	0.232942	−	0.134489i
$518$	−10660.4	+	26222.1i	−0.904228	+	2.22420i
$519$		0			0
$520$	−21.4722	+	37.1910i	−0.00181081	+	0.00313641i
$521$	1142.40			0.0960645			0.0480323	−	0.998846i	$-0.484705\pi$
$521$	1142.40			0.0960645			0.0480323	+	0.998846i	$0.484705\pi$
$522$		0			0
$523$		−	6315.64i		−	0.528038i	−0.964518	−	0.264019i	$-0.914952\pi$
$523$		−	6315.64i		−	0.528038i	0.964518	−	0.264019i	$-0.0850481\pi$
$524$	8698.69	−	15066.6i	0.725199	−	1.25608i
$525$		0			0
$526$	7055.82	+	12221.0i	0.584883	+	1.01305i
$527$	23479.4	−	13555.9i	1.94076	−	1.12050i
$528$		0			0
$529$	−4434.72	+	7681.16i	−0.364487	+	0.631311i
$530$	200.452			0.0164285
$531$		0			0
$532$	9432.40	+	12126.8i	0.768696	+	0.988279i
$533$	5786.73	+	3340.97i	0.470265	+	0.271508i
$534$		0			0
$535$	171.917	−	99.2566i	0.0138928	−	0.00802100i
$536$	1129.02	−	651.842i	0.0909821	−	0.0525285i
$537$		0			0
$538$	19434.9	+	11220.8i	1.55744	+	0.899186i
$539$	3370.76	+	855.911i	0.269367	+	0.0683983i
$540$		0			0
$541$	727.024			0.0577767			0.0288884	−	0.999583i	$-0.490803\pi$
$541$	727.024			0.0577767			0.0288884	+	0.999583i	$0.490803\pi$
$542$	6351.00	−	11000.3i	0.503319	−	0.871774i
$543$		0			0
$544$	14997.5	−	8658.82i	1.18201	−	0.682433i
$545$	82.6139	+	143.092i	0.00649320	+	0.0112465i
$546$		0			0
$547$	455.248	−	788.513i	0.0355850	−	0.0616351i	−0.847684	−	0.530501i	$-0.822004\pi$
$547$	455.248	−	788.513i	0.0355850	−	0.0616351i	0.883269	+	0.468866i	$0.155337\pi$
$548$			11609.9i			0.905022i
$549$		0			0
$550$	5744.43			0.445351
$551$	−3921.10	+	6791.55i	−0.303166	+	0.525099i
$552$		0			0
$553$	14587.4	+	5930.39i	1.12174	+	0.456032i
$554$	1407.84	−	812.815i	0.107966	−	0.0623343i
$555$		0			0
$556$	−29355.7	−	16948.5i	−2.23913	−	1.29276i
$557$		−	2329.01i		−	0.177169i	−0.996069	−	0.0885847i	$-0.971766\pi$
$557$		−	2329.01i		−	0.177169i	0.996069	−	0.0885847i	$-0.0282344\pi$
$558$		0			0
$559$		−	1414.74i		−	0.107043i
$560$	−2.41013	−	17.4220i	−0.000181869	−	0.00131467i
$561$		0			0
$562$	8092.65	+	14016.9i	0.607416	+	1.05208i
$563$	−6684.01	−	11577.0i	−0.500350	−	0.866632i	−1.00000		0.000404657i	$-0.999871\pi$
$563$	−6684.01	−	11577.0i	−0.500350	−	0.866632i	0.499650	−	0.866228i	$-0.333462\pi$
$564$		0			0
$565$	55.6379	+	32.1225i	0.00414284	+	0.00239187i
$566$	3281.33			0.243683
$567$		0			0
$568$	−12815.4			−0.946691
$569$	−6678.40	−	3855.77i	−0.492044	−	0.284082i	0.233378	−	0.972386i	$-0.425022\pi$
$569$	−6678.40	−	3855.77i	−0.492044	−	0.284082i	−0.725422	+	0.688304i	$0.758355\pi$
$570$		0			0
$571$	−5367.85	−	9297.39i	−0.393411	−	0.681408i	0.599486	−	0.800385i	$-0.295372\pi$
$571$	−5367.85	−	9297.39i	−0.393411	−	0.681408i	−0.992897	+	0.118978i	$0.962038\pi$
$572$	−963.432	−	1668.71i	−0.0704250	−	0.121980i
$573$		0			0
$574$	36695.3	−	5076.37i	2.66835	−	0.369135i
$575$		−	7176.97i		−	0.520522i
$576$		0			0
$577$		−	2233.10i		−	0.161118i	−0.996750	−	0.0805590i	$-0.974329\pi$
$577$		−	2233.10i		−	0.161118i	0.996750	−	0.0805590i	$-0.0256705\pi$
$578$	−11267.8	−	6505.47i	−0.810863	−	0.468152i
$579$		0			0
$580$	−177.299	+	102.363i	−0.0126930	+	0.00732829i
$581$	2407.19	+	978.624i	0.171888	+	0.0698798i
$582$		0			0
$583$	−1630.27	+	2823.72i	−0.115813	+	0.200594i
$584$	−1965.32			−0.139256
$585$		0			0
$586$		−	43034.6i		−	3.03369i
$587$	6194.97	−	10730.0i	0.435594	−	0.754471i	−0.561750	−	0.827307i	$-0.689872\pi$
$587$	6194.97	−	10730.0i	0.435594	−	0.754471i	0.997344	+	0.0728359i	$0.0232049\pi$
$588$		0			0
$589$	10156.9	+	17592.2i	0.710537	+	1.23069i
$590$	310.183	−	179.084i	0.0216441	−	0.0124962i
$591$		0			0
$592$	−1164.26	+	2016.56i	−0.0808292	+	0.140000i
$593$	−16050.0			−1.11146			−0.555729	−	0.831363i	$-0.687561\pi$
$593$	−16050.0			−1.11146			−0.555729	+	0.831363i	$0.687561\pi$
$594$		0			0
$595$	−177.341	+	137.938i	−0.0122190	+	0.00950407i
$596$	31777.0	+	18346.5i	2.18395	+	1.26091i
$597$		0			0
$598$	−3413.90	+	1971.02i	−0.233453	+	0.134784i
$599$	14534.4	−	8391.43i	0.991417	−	0.572395i	0.0857192	−	0.996319i	$-0.472681\pi$
$599$	14534.4	−	8391.43i	0.991417	−	0.572395i	0.905697	+	0.423925i	$0.139348\pi$
$600$		0			0
$601$	6341.34	+	3661.18i	0.430397	+	0.248490i	0.699516	−	0.714617i	$-0.253399\pi$
$601$	6341.34	+	3661.18i	0.430397	+	0.248490i	−0.269119	+	0.963107i	$0.586732\pi$
$602$	−4815.46	−	6191.04i	−0.326019	−	0.419149i
$603$		0			0
$604$	9018.90			0.607573
$605$	−84.4422	+	146.258i	−0.00567448	+	0.00982849i
$606$		0			0
$607$	−7505.80	+	4333.47i	−0.501896	+	0.289770i	−0.729496	−	0.683985i	$-0.760245\pi$
$607$	−7505.80	+	4333.47i	−0.501896	+	0.289770i	0.227600	+	0.973755i	$0.426912\pi$
$608$	6487.70	+	11237.0i	0.432749	+	0.749543i
$609$		0			0
$610$	228.371	−	395.550i	0.0151581	−	0.0262547i
$611$			4722.53i			0.312689i
$612$		0			0
$613$	5674.74			0.373900			0.186950	−	0.982369i	$-0.440140\pi$
$613$	5674.74			0.373900			0.186950	+	0.982369i	$0.440140\pi$
$614$	−4399.02	+	7619.32i	−0.289136	+	0.500799i
$615$		0			0
$616$	−3587.54	−	1458.48i	−0.234653	−	0.0953962i
$617$	3264.02	−	1884.48i	0.212973	−	0.122960i	−0.389719	−	0.920934i	$-0.627428\pi$
$617$	3264.02	−	1884.48i	0.212973	−	0.122960i	0.602693	+	0.797974i	$0.294095\pi$
$618$		0			0
$619$	−14473.4	−	8356.19i	−0.939795	−	0.542591i	−0.0498991	−	0.998754i	$-0.515890\pi$
$619$	−14473.4	−	8356.19i	−0.939795	−	0.542591i	−0.889896	+	0.456163i	$0.849223\pi$
$620$			530.305i			0.0343509i
$621$		0			0
$622$			307.418i			0.0198172i
$623$	−3105.63	−	22449.5i	−0.199718	−	1.44369i
$624$		0			0
$625$	−7808.95	−	13525.5i	−0.499773	−	0.865632i
$626$	−13818.7	−	23934.7i	−0.882277	−	1.52815i
$627$		0			0
$628$	17789.3	+	10270.6i	1.13036	+	0.652616i
$629$	29744.9			1.88554
$630$		0			0
$631$	−19529.4			−1.23210			−0.616049	−	0.787708i	$-0.711268\pi$
$631$	−19529.4			−1.23210			−0.616049	+	0.787708i	$0.711268\pi$
$632$	−15185.9	−	8767.56i	−0.955793	−	0.551827i
$633$		0			0
$634$	11578.4	+	20054.3i	0.725292	+	1.25624i
$635$	−81.4988	−	141.160i	−0.00509320	−	0.00882168i
$636$		0			0
$637$	−3624.29	+	3720.76i	−0.225431	+	0.231431i
$638$		−	5452.93i		−	0.338375i
$639$		0			0
$640$			304.293i			0.0187941i
$641$	15018.7	+	8671.07i	0.925436	+	0.534301i	0.885365	−	0.464896i	$-0.153908\pi$
$641$	15018.7	+	8671.07i	0.925436	+	0.534301i	0.0400707	+	0.999197i	$0.487242\pi$
$642$		0			0
$643$	−247.186	+	142.713i	−0.0151603	+	0.00875278i	−0.507561	−	0.861616i	$-0.669453\pi$
$643$	−247.186	+	142.713i	−0.0151603	+	0.00875278i	0.492401	+	0.870369i	$0.336119\pi$
$644$	−5026.43	+	12363.9i	−0.307561	+	0.756530i
$645$		0			0
$646$	13217.8	−	22893.9i	0.805027	−	1.39435i
$647$	−24266.2			−1.47450			−0.737252	−	0.675617i	$-0.763877\pi$
$647$	−24266.2			−1.47450			−0.737252	+	0.675617i	$0.763877\pi$
$648$		0			0
$649$			5825.97i			0.352372i
$650$	−4289.81	+	7430.17i	−0.258862	+	0.448362i
$651$		0			0
$652$	−12605.2	−	21832.8i	−0.757143	−	1.31141i
$653$	−19796.2	+	11429.4i	−1.18635	+	0.684939i	−0.957475	−	0.288517i	$-0.906838\pi$
$653$	−19796.2	+	11429.4i	−1.18635	+	0.684939i	−0.228875	+	0.973456i	$0.573505\pi$
$654$		0			0
$655$	−95.3123	+	165.086i	−0.00568574	+	0.00984799i
$656$	3047.38			0.181372
$657$		0			0
$658$	16074.5	+	20666.3i	0.952354	+	1.22440i
$659$	2687.96	+	1551.89i	0.158889	+	0.0917346i	0.577336	−	0.816506i	$-0.304092\pi$
$659$	2687.96	+	1551.89i	0.158889	+	0.0917346i	−0.418447	+	0.908241i	$0.637426\pi$
$660$		0			0
$661$	−20614.8	+	11901.9i	−1.21304	+	0.700351i	−0.963421	−	0.267993i	$-0.913640\pi$
$661$	−20614.8	+	11901.9i	−1.21304	+	0.700351i	−0.249622	+	0.968343i	$0.580306\pi$
$662$	−8781.83	+	5070.19i	−0.515582	+	0.297672i
$663$		0			0
$664$	−2505.94	−	1446.81i	−0.146460	−	0.0845588i
$665$	−103.352	−	132.875i	−0.00602677	−	0.00774836i
$666$		0			0
$667$	−6812.78			−0.395490
$668$	−1049.00	+	1816.92i	−0.0607589	+	0.105237i
$669$		0			0
$670$	−34.1242	+	19.7016i	−0.00196766	+	0.00113603i
$671$	3714.68	+	6434.01i	0.213716	+	0.370167i
$672$		0			0
$673$	7675.47	−	13294.3i	0.439625	−	0.761453i	−0.558035	−	0.829817i	$-0.688445\pi$
$673$	7675.47	−	13294.3i	0.439625	−	0.761453i	0.997660	+	0.0683640i	$0.0217779\pi$
$674$			25022.3i			1.43000i
$675$		0			0
$676$	−24693.3			−1.40495
$677$	−7096.57	+	12291.6i	−0.402871	+	0.697793i	−0.994071	−	0.108732i	$-0.965321\pi$
$677$	−7096.57	+	12291.6i	−0.402871	+	0.697793i	0.591200	+	0.806525i	$0.298654\pi$
$678$		0			0
$679$	−5408.05	+	13302.6i	−0.305658	+	0.751850i
$680$	216.667	−	125.093i	0.0122188	−	0.00705454i
$681$		0			0
$682$	−12232.4	−	7062.38i	−0.686808	−	0.396529i
$683$		−	2156.60i		−	0.120820i	−0.998174	−	0.0604100i	$-0.980759\pi$
$683$		−	2156.60i		−	0.120820i	0.998174	−	0.0604100i	$-0.0192408\pi$
$684$		0			0
$685$		−	127.211i		−	0.00709560i
$686$	−3195.61	+	28618.8i	−0.177856	+	1.59281i
$687$		0			0
$688$	−322.603	−	558.765i	−0.0178766	−	0.0309633i
$689$	−2434.91	−	4217.38i	−0.134634	−	0.233192i
$690$		0			0
$691$	2822.31	+	1629.46i	0.155377	+	0.0897071i	0.575673	−	0.817680i	$-0.304740\pi$
$691$	2822.31	+	1629.46i	0.155377	+	0.0897071i	−0.420295	+	0.907387i	$0.638074\pi$
$692$	11889.5			0.653136
$693$		0			0
$694$	−39428.9			−2.15663
$695$	321.653	+	185.706i	0.0175554	+	0.0101356i
$696$		0			0
$697$	−19463.8	−	33712.3i	−1.05774	−	1.83206i
$698$	8135.45	+	14091.0i	0.441163	+	0.764116i
$699$		0			0
$700$	3980.56	+	28774.0i	0.214930	+	1.55365i
$701$		−	23138.1i		−	1.24667i	−0.781956	−	0.623334i	$-0.785778\pi$
$701$		−	23138.1i		−	1.24667i	0.781956	−	0.623334i	$-0.214222\pi$
$702$		0			0
$703$			22286.7i			1.19567i
$704$	−7328.32	−	4231.00i	−0.392324	−	0.226509i
$705$		0			0
$706$	16603.1	−	9585.79i	0.885078	−	0.511000i
$707$	−9031.65	−	3671.74i	−0.480439	−	0.195318i
$708$		0			0
$709$	3118.01	−	5400.55i	0.165161	−	0.286067i	−0.771551	−	0.636167i	$-0.780519\pi$
$709$	3118.01	−	5400.55i	0.165161	−	0.286067i	0.936712	+	0.350100i	$0.113852\pi$
$710$	387.337			0.0204740
$711$		0			0
$712$			25237.0i			1.32837i
$713$	−8823.59	+	15282.9i	−0.463459	+	0.802734i
$714$		0			0
$715$	10.5564	+	18.2842i	0.000552150	+	0.000956352i
$716$	25747.0	−	14865.0i	1.34387	−	0.775883i
$717$		0			0
$718$	−13214.6	+	22888.3i	−0.686858	+	1.18967i
$719$	−26084.5			−1.35297			−0.676486	−	0.736455i	$-0.736498\pi$
$719$	−26084.5			−1.35297			−0.676486	+	0.736455i	$0.736498\pi$
$720$		0			0
$721$	−4976.12	−	6397.58i	−0.257032	−	0.330455i
$722$	−9773.76	−	5642.88i	−0.503797	−	0.290867i
$723$		0			0
$724$	−16300.0	+	9410.81i	−0.836719	+	0.483080i
$725$	−12841.1	+	7413.82i	−0.657802	+	0.379782i
$726$		0			0
$727$	5419.16	+	3128.75i	0.276459	+	0.159614i	0.631819	−	0.775116i	$-0.282309\pi$
$727$	5419.16	+	3128.75i	0.276459	+	0.159614i	−0.355360	+	0.934729i	$0.615642\pi$
$728$	4565.59	−	3551.17i	0.232434	−	0.180790i
$729$		0			0
$730$	59.4009			0.00301168
$731$	−4120.98	+	7137.75i	−0.208509	+	0.361148i
$732$		0			0
$733$	5690.16	−	3285.22i	0.286727	−	0.165542i	−0.349738	−	0.936848i	$-0.613729\pi$
$733$	5690.16	−	3285.22i	0.286727	−	0.165542i	0.636465	+	0.771306i	$0.280396\pi$
$734$	15803.2	+	27371.9i	0.794695	+	1.37645i
$735$		0			0
$736$	−5636.08	+	9761.97i	−0.282267	+	0.488901i
$737$		−	640.932i		−	0.0320339i
$738$		0			0
$739$	22303.3			1.11020			0.555101	−	0.831783i	$-0.312680\pi$
$739$	22303.3			1.11020			0.555101	+	0.831783i	$0.312680\pi$
$740$	−290.905	+	503.863i	−0.0144512	+	0.0250302i
$741$		0			0
$742$	−25010.5	−	10167.8i	−1.23742	−	0.503061i
$743$	−20415.4	+	11786.8i	−1.00803	+	0.581988i	−0.910615	−	0.413256i	$-0.864391\pi$
$743$	−20415.4	+	11786.8i	−1.00803	+	0.581988i	−0.0974173	+	0.995244i	$0.531058\pi$
$744$		0			0
$745$	−348.183	−	201.024i	−0.0171228	−	0.00988583i
$746$		−	23418.8i		−	1.14936i
$747$		0			0
$748$			11225.5i			0.548724i
$749$	−26484.9	+	3663.88i	−1.29204	+	0.178739i
$750$		0			0
$751$	87.9670	+	152.363i	0.00427425	+	0.00740322i	0.868155	−	0.496294i	$-0.165306\pi$
$751$	87.9670	+	152.363i	0.00427425	+	0.00740322i	−0.863880	+	0.503697i	$0.831973\pi$
$752$	1076.88	+	1865.21i	0.0522205	+	0.0904485i
$753$		0			0
$754$	7053.13	+	4072.13i	0.340663	+	0.196682i
$755$	−98.8209			−0.00476352
$756$		0			0
$757$	6273.79			0.301221			0.150611	−	0.988593i	$-0.451876\pi$
$757$	6273.79			0.301221			0.150611	+	0.988593i	$0.451876\pi$
$758$	−47357.9	−	27342.1i	−2.26928	−	1.31017i
$759$		0			0
$760$	93.7269	+	162.340i	0.00447346	+	0.00774827i
$761$	482.344	+	835.445i	0.0229763	+	0.0397961i	0.877285	−	0.479970i	$-0.159352\pi$
$761$	482.344	+	835.445i	0.0229763	+	0.0397961i	−0.854309	+	0.519766i	$0.826019\pi$
$762$		0			0
$763$	−3049.55	−	22044.1i	−0.144693	−	1.04594i
$764$			9939.11i			0.470660i
$765$		0			0
$766$			963.616i			0.0454528i
$767$	−7535.64	−	4350.70i	−0.354754	−	0.204817i
$768$		0			0
$769$	382.458	−	220.812i	0.0179347	−	0.0103546i	−0.491006	−	0.871156i	$-0.663371\pi$
$769$	382.458	−	220.812i	0.0179347	−	0.0103546i	0.508941	+	0.860802i	$0.330037\pi$
$770$	108.432	+	44.0820i	0.00507481	+	0.00206312i
$771$		0			0
$772$	−27232.5	+	47168.0i	−1.26958	+	2.19898i
$773$	−6634.17			−0.308686			−0.154343	−	0.988017i	$-0.549326\pi$
$773$	−6634.17			−0.308686			−0.154343	+	0.988017i	$0.549326\pi$
$774$		0			0
$775$			38408.1i			1.78021i
$776$	7995.32	−	13848.3i	0.369865	−	0.640625i
$777$		0			0
$778$	31434.2	+	54445.7i	1.44855	+	2.50896i
$779$	25259.3	−	14583.4i	1.16176	−	0.670740i
$780$		0			0
$781$	−3150.21	+	5456.33i	−0.144332	+	0.249991i
$782$	22965.5			1.05018
$783$		0			0
$784$	−583.006	+	2296.00i	−0.0265582	+	0.104592i
$785$	−194.919	−	112.536i	−0.00886235	−	0.00511668i
$786$		0			0
$787$	6336.06	−	3658.13i	0.286984	−	0.165690i	−0.349597	−	0.936900i	$-0.613682\pi$
$787$	6336.06	−	3658.13i	0.286984	−	0.165690i	0.636581	+	0.771210i	$0.280348\pi$
$788$	10725.0	−	6192.09i	0.484851	−	0.279929i
$789$		0			0
$790$	458.985	+	264.995i	0.0206708	+	0.0119343i
$791$	−5312.57	−	6830.14i	−0.238803	−	0.307019i
$792$		0			0
$793$	−11096.2			−0.496893
$794$	29687.0	−	51419.4i	1.32689	−	2.29825i
$795$		0			0
$796$	17625.8	−	10176.3i	0.784837	−	0.453126i
$797$	−14429.9	−	24993.3i	−0.641322	−	1.11080i	−0.985138	−	0.171765i	$-0.945053\pi$
$797$	−14429.9	−	24993.3i	−0.641322	−	1.11080i	0.343816	−	0.939037i	$-0.388280\pi$
$798$		0			0
$799$	13756.2	−	23826.5i	0.609087	−	1.05497i
$800$			24533.2i			1.08423i
$801$		0			0
$802$	54840.9			2.41459
$803$	−483.107	+	836.766i	−0.0212310	+	0.0367731i
$804$		0			0
$805$	55.0751	−	135.472i	0.00241136	−	0.00593139i
$806$	18269.8	−	10548.1i	0.798418	−	0.460967i
$807$		0			0
$808$	9402.16	+	5428.34i	0.409365	+	0.236347i
$809$			9191.53i			0.399452i	0.979852	+	0.199726i	$0.0640053\pi$
$809$			9191.53i			0.399452i	−0.979852	+	0.199726i	$0.935995\pi$
$810$		0			0
$811$		−	31228.1i		−	1.35212i	−0.736848	−	0.676058i	$-0.763687\pi$
$811$		−	31228.1i		−	1.35212i	0.736848	−	0.676058i	$-0.236313\pi$
$812$	27313.9	−	3778.57i	1.18046	−	0.163303i
$813$		0			0
$814$	−7748.31	−	13420.5i	−0.333634	−	0.577871i
$815$	138.116	+	239.224i	0.00593619	+	0.0102818i
$816$		0			0
$817$	−5348.03	−	3087.68i	−0.229013	−	0.132221i
$818$	−63564.3			−2.71696
$819$		0			0
$820$	761.424			0.0324269
$821$	18611.4	+	10745.3i	0.791160	+	0.456776i	0.840371	−	0.542012i	$-0.182337\pi$
$821$	18611.4	+	10745.3i	0.791160	+	0.456776i	−0.0492107	+	0.998788i	$0.515671\pi$
$822$		0			0
$823$	−13576.6	−	23515.4i	−0.575032	−	0.995984i	−0.996038	−	0.0889267i	$-0.971656\pi$
$823$	−13576.6	−	23515.4i	−0.575032	−	0.995984i	0.421006	−	0.907058i	$-0.361677\pi$
$824$	4512.71	+	7816.25i	0.190786	+	0.330451i
$825$		0			0
$826$	−47785.6	+	6610.59i	−2.01292	+	0.278465i
$827$			14491.9i			0.609349i	0.952457	+	0.304675i	$0.0985477\pi$
$827$			14491.9i			0.609349i	−0.952457	+	0.304675i	$0.901452\pi$
$828$		0			0
$829$		−	12056.9i		−	0.505129i	−0.967580	−	0.252565i	$-0.918726\pi$
$829$		−	12056.9i		−	0.505129i	0.967580	−	0.252565i	$-0.0812741\pi$
$830$	75.7409	+	43.7290i	0.00316748	+	0.00182874i
$831$		0			0
$832$	10945.2	−	6319.24i	0.456080	−	0.263318i
$833$	29123.8	−	8215.09i	1.21138	−	0.341700i
$834$		0			0
$835$	11.4940	−	19.9081i	0.000476365	−	0.000825088i
$836$	−8410.82			−0.347960
$837$		0			0
$838$		−	41506.8i		−	1.71101i
$839$	15546.1	−	26926.7i	0.639704	−	1.10800i	−0.345794	−	0.938311i	$-0.612390\pi$
$839$	15546.1	−	26926.7i	0.639704	−	1.10800i	0.985498	−	0.169689i	$-0.0542764\pi$
$840$		0			0
$841$	−5156.89	−	8932.00i	−0.211443	−	0.366231i
$842$	54007.1	−	31181.0i	2.21046	−	1.27621i
$843$		0			0
$844$	−2272.35	+	3935.83i	−0.0926749	+	0.160518i
$845$	270.567			0.0110151
$846$		0			0
$847$	17954.7	−	13965.4i	0.728373	−	0.566537i
$848$	−1923.38	−	1110.47i	−0.0778883	−	0.0449688i
$849$		0			0
$850$	43286.6	−	24991.5i	1.74673	−	1.00847i
$851$	−16767.2	+	9680.57i	−0.675410	+	0.389948i
$852$		0			0
$853$	−33795.3	−	19511.7i	−1.35654	−	0.783198i	−0.367384	−	0.930070i	$-0.619746\pi$
$853$	−33795.3	−	19511.7i	−1.35654	−	0.783198i	−0.989156	+	0.146871i	$0.953080\pi$
$854$	−48558.0	+	37769.0i	−1.94569	+	1.51338i
$855$		0			0
$856$	29773.6			1.18883
$857$	−8986.51	+	15565.1i	−0.358195	+	0.620412i	−0.987659	−	0.156617i	$-0.949941\pi$
$857$	−8986.51	+	15565.1i	−0.358195	+	0.620412i	0.629464	+	0.777030i	$0.283274\pi$
$858$		0			0
$859$	−16462.0	+	9504.31i	−0.653870	+	0.377512i	−0.789937	−	0.613187i	$-0.789887\pi$
$859$	−16462.0	+	9504.31i	−0.653870	+	0.377512i	0.136067	+	0.990700i	$0.456554\pi$
$860$	−80.6063	−	139.614i	−0.00319611	−	0.00553582i
$861$		0			0
$862$	32705.5	−	56647.6i	1.29229	−	2.23831i
$863$		−	5497.42i		−	0.216842i	−0.994105	−	0.108421i	$-0.965421\pi$
$863$		−	5497.42i		−	0.216842i	0.994105	−	0.108421i	$-0.0345794\pi$
$864$		0			0
$865$	−130.274			−0.00512075
$866$	26885.1	−	46566.4i	1.05496	−	1.82724i
$867$		0			0
$868$	26899.4	−	66166.4i	1.05187	−	2.58737i
$869$	−7465.83	+	4310.40i	−0.291440	+	0.168263i
$870$		0			0
$871$	829.018	+	478.634i	0.0322505	+	0.0186198i
$872$			24781.3i			0.962388i
$873$		0			0
$874$			17207.1i			0.665948i
$875$	−87.2372	−	630.607i	−0.00337046	−	0.0243639i
$876$		0			0
$877$	9852.44	+	17064.9i	0.379354	+	0.657060i	0.990968	−	0.134096i	$-0.0428130\pi$
$877$	9852.44	+	17064.9i	0.379354	+	0.657060i	−0.611615	+	0.791156i	$0.709480\pi$
$878$	4859.65	+	8417.15i	0.186794	+	0.323537i
$879$		0			0
$880$	8.33873	+	4.81437i	0.000319430	+	0.000184423i
$881$	−16133.0			−0.616952			−0.308476	−	0.951232i	$-0.599819\pi$
$881$	−16133.0			−0.616952			−0.308476	+	0.951232i	$0.599819\pi$
$882$		0			0
$883$	21767.7			0.829605			0.414803	−	0.909911i	$-0.363851\pi$
$883$	21767.7			0.829605			0.414803	+	0.909911i	$0.363851\pi$
$884$	−14519.7	−	8382.96i	−0.552433	−	0.318947i
$885$		0			0
$886$	−8945.99	−	15494.9i	−0.339217	−	0.587542i
$887$	9673.92	+	16755.7i	0.366199	+	0.634275i	0.988968	−	0.148131i	$-0.0473256\pi$
$887$	9673.92	+	16755.7i	0.366199	+	0.634275i	−0.622769	+	0.782406i	$0.713992\pi$
$888$		0			0
$889$	3008.39	+	21746.6i	0.113496	+	0.820424i
$890$		−	762.776i		−	0.0287284i
$891$		0			0
$892$		−	1674.99i		−	0.0628731i
$893$	17852.2	+	10307.0i	0.668983	+	0.386238i
$894$		0			0
$895$	−282.112	+	162.877i	−0.0105363	+	0.00608312i
$896$	15435.1	−	37966.8i	0.575502	−	1.41560i
$897$		0			0
$898$	2534.72	−	4390.26i	0.0941923	−	0.163146i
$899$	36459.1			1.35259
$900$		0			0
$901$			28370.5i			1.04901i
$902$	−10140.3	+	17563.6i	−0.374319	+	0.648340i
$903$		0			0
$904$	4817.83	+	8344.73i	0.177255	+	0.307015i
$905$	178.601	−	103.115i	0.00656009	−	0.00378747i
$906$		0			0
$907$	−11279.6	+	19536.8i	−0.412935	+	0.715225i	−0.995209	−	0.0977677i	$-0.968830\pi$
$907$	−11279.6	+	19536.8i	−0.412935	+	0.715225i	0.582274	+	0.812993i	$0.302163\pi$
$908$	44427.8			1.62378
$909$		0			0
$910$	−137.992	+	107.332i	−0.00502682	+	0.00390992i
$911$	−8494.79	−	4904.47i	−0.308941	−	0.178367i	0.337512	−	0.941321i	$-0.390415\pi$
$911$	−8494.79	−	4904.47i	−0.308941	−	0.178367i	−0.646452	+	0.762954i	$0.723748\pi$
$912$		0			0
$913$	−1232.00	+	711.295i	−0.0446585	+	0.0257836i
$914$	1206.21	−	696.407i	0.0436520	−	0.0252025i
$915$		0			0
$916$	−26278.3	−	15171.8i	−0.947881	−	0.547259i
$917$	20266.0	−	15763.2i	0.729818	−	0.567662i
$918$		0			0
$919$	−38354.6			−1.37672			−0.688358	−	0.725371i	$-0.741668\pi$
$919$	−38354.6			−1.37672			−0.688358	+	0.725371i	$0.741668\pi$
$920$	−81.4236	+	141.030i	−0.00291789	+	0.00505393i
$921$		0			0
$922$	295.016	−	170.328i	0.0105378	−	0.00608399i
$923$	−4705.02	−	8149.33i	−0.167787	−	0.290616i
$924$		0			0
$925$	−21069.2	+	36493.0i	−0.748921	+	1.29717i
$926$			74654.8i			2.64936i
$927$		0			0
$928$	23288.3			0.823789
$929$	−1824.39	+	3159.94i	−0.0644310	+	0.111598i	−0.896441	−	0.443162i	$-0.853857\pi$
$929$	−1824.39	+	3159.94i	−0.0644310	+	0.111598i	0.832010	+	0.554760i	$0.187190\pi$
$930$		0			0
$931$	6155.24	+	21821.3i	0.216681	+	0.768167i
$932$	−53880.1	+	31107.7i	−1.89367	+	1.09331i
$933$		0			0
$934$	34887.2	+	20142.1i	1.22221	+	0.705643i
$935$		−	122.999i		−	0.00430213i
$936$		0			0
$937$		−	22851.6i		−	0.796724i	−0.917228	−	0.398362i	$-0.869579\pi$
$937$		−	22851.6i		−	0.796724i	0.917228	−	0.398362i	$-0.130421\pi$
$938$	5257.04	−	727.250i	0.182994	−	0.0253151i
$939$		0			0
$940$	269.072	+	466.046i	0.00933633	+	0.0161710i
$941$	23868.9	+	41342.2i	0.826892	+	1.43222i	0.900465	+	0.434928i	$0.143226\pi$
$941$	23868.9	+	41342.2i	0.826892	+	1.43222i	−0.0735735	+	0.997290i	$0.523440\pi$
$942$		0			0
$943$	21943.5	+	12669.1i	0.757773	+	0.437501i
$944$	−3968.37			−0.136822
$945$		0			0
$946$	4293.93			0.147577
$947$	−40970.4	−	23654.2i	−1.40587	−	0.811679i	−0.410882	−	0.911688i	$-0.634779\pi$
$947$	−40970.4	−	23654.2i	−1.40587	−	0.811679i	−0.994986	+	0.100010i	$0.968113\pi$
$948$		0			0
$949$	−721.548	−	1249.76i	−0.0246812	−	0.0427490i
$950$	18725.2	+	32432.9i	0.639499	+	1.10765i
$951$		0			0
$952$	−33378.9	+	4617.58i	−1.13636	+	0.157202i
$953$		−	29971.1i		−	1.01874i	−0.860548	−	0.509370i	$-0.829879\pi$
$953$		−	29971.1i		−	1.01874i	0.860548	−	0.509370i	$-0.170121\pi$
$954$		0			0
$955$		−	108.904i		−	0.00369009i
$956$	20694.3	+	11947.9i	0.700106	+	0.404206i
$957$		0			0
$958$	−56610.9	+	32684.3i	−1.90920	+	1.10228i
$959$	−6452.70	+	15872.2i	−0.217277	+	0.534452i
$960$		0			0
$961$	32324.7	−	55988.0i	1.08505	−	1.87936i
$962$	23145.1			0.775703
$963$		0			0
$964$			52058.3i			1.73930i
$965$	298.389	−	516.824i	0.00995386	−	0.0172406i
$966$		0			0
$967$	27462.8	+	47567.0i	0.913284	+	1.58185i	0.809395	+	0.587265i	$0.199795\pi$
$967$	27462.8	+	47567.0i	0.913284	+	1.58185i	0.103889	+	0.994589i	$0.466871\pi$
$968$	−21936.2	+	12664.9i	−0.728364	+	0.420521i
$969$		0			0
$970$	−241.654	+	418.558i	−0.00799902	+	0.0138547i
$971$	38391.4			1.26884			0.634418	−	0.772990i	$-0.281240\pi$
$971$	38391.4			1.26884			0.634418	+	0.772990i	$0.281240\pi$
$972$		0			0
$973$	−30712.9	−	39486.3i	−1.01193	−	1.30100i
$974$	−19813.7	−	11439.5i	−0.651821	−	0.376329i
$975$		0			0
$976$	−4382.54	+	2530.26i	−0.143731	+	0.0829834i
$977$	−12928.6	+	7464.33i	−0.423360	+	0.244427i	−0.696514	−	0.717543i	$-0.745266\pi$
$977$	−12928.6	+	7464.33i	−0.423360	+	0.244427i	0.273154	+	0.961970i	$0.411933\pi$
$978$		0			0
$979$	10745.0	+	6203.65i	0.350779	+	0.202522i
$980$	−145.671	+	573.684i	−0.00474826	+	0.0186997i
$981$		0			0
$982$	6352.56			0.206434
$983$	−25253.7	+	43740.8i	−0.819399	+	1.41924i	0.0867264	+	0.996232i	$0.472359\pi$
$983$	−25253.7	+	43740.8i	−0.819399	+	1.41924i	−0.906126	+	0.423009i	$0.860974\pi$
$984$		0			0
$985$	−117.515	+	67.8472i	−0.00380136	+	0.00219471i
$986$	−23723.4	−	41090.1i	−0.766233	−	1.32715i
$987$		0			0
$988$	6281.02	−	10879.0i	0.202253	−	0.350312i
$989$		−	5364.74i		−	0.172486i
$990$		0			0
$991$	−4236.35			−0.135794			−0.0678971	−	0.997692i	$-0.521629\pi$
$991$	−4236.35			−0.135794			−0.0678971	+	0.997692i	$0.521629\pi$
$992$	30161.9	−	52242.0i	0.965365	−	1.67206i
$993$		0			0
$994$	−48328.3	−	19647.4i	−1.54213	−	0.626941i
$995$	−193.127	+	111.502i	−0.00615332	+	0.00355262i
$996$		0			0
$997$	19233.0	+	11104.2i	0.610948	+	0.352731i	0.773336	−	0.633996i	$-0.218586\pi$
$997$	19233.0	+	11104.2i	0.610948	+	0.352731i	−0.162388	+	0.986727i	$0.551920\pi$
$998$		−	41310.1i		−	1.31027i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.62.3		44
3.2	odd	2		63.4.o.a.20.19	✓	44
7.6	odd	2	inner	189.4.o.a.62.4		44
9.2	odd	6		567.4.c.c.566.27		44
9.4	even	3		63.4.o.a.41.20	yes	44
9.5	odd	6	inner	189.4.o.a.125.4		44
9.7	even	3		567.4.c.c.566.18		44
21.20	even	2		63.4.o.a.20.20	yes	44
63.13	odd	6		63.4.o.a.41.19	yes	44
63.20	even	6		567.4.c.c.566.17		44
63.34	odd	6		567.4.c.c.566.28		44
63.41	even	6	inner	189.4.o.a.125.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.19	✓	44	3.2	odd	2
63.4.o.a.20.20	yes	44	21.20	even	2
63.4.o.a.41.19	yes	44	63.13	odd	6
63.4.o.a.41.20	yes	44	9.4	even	3
189.4.o.a.62.3		44	1.1	even	1	trivial
189.4.o.a.62.4		44	7.6	odd	2	inner
189.4.o.a.125.3		44	63.41	even	6	inner
189.4.o.a.125.4		44	9.5	odd	6	inner
567.4.c.c.566.17		44	63.20	even	6
567.4.c.c.566.18		44	9.7	even	3
567.4.c.c.566.27		44	9.2	odd	6
567.4.c.c.566.28		44	63.34	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.92583 - 2.26658i) q^{2} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(2.53789 + 18.3455i) q^{7} -20.6235i q^{8} +O(q^{10})\)	\(q+(-3.92583 - 2.26658i) q^{2} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(2.53789 + 18.3455i) q^{7} -20.6235i q^{8} +0.623335i q^{10} +(-8.78077 - 5.06958i) q^{11} +(13.1146 - 7.57170i) q^{13} +(31.6183 - 77.7738i) q^{14} +(3.45316 - 5.98105i) q^{16} -88.2223 q^{17} -66.1014i q^{19} +(0.862814 - 1.49444i) q^{20} +(22.9812 + 39.8046i) q^{22} +(49.7310 - 28.7122i) q^{23} +(62.4905 - 108.237i) q^{25} -68.6473 q^{26} +(-183.458 + 142.696i) q^{28} +(-102.744 - 59.3195i) q^{29} +(-266.140 + 153.656i) q^{31} +(-169.997 + 98.1477i) q^{32} +(346.345 + 199.963i) q^{34} +(2.01016 - 1.56353i) q^{35} -337.159 q^{37} +(-149.824 + 259.503i) q^{38} +(-2.45592 + 1.41793i) q^{40} +(220.622 + 382.129i) q^{41} +(46.7113 - 80.9064i) q^{43} -127.241i q^{44} -260.314 q^{46} +(-155.927 + 270.073i) q^{47} +(-330.118 + 93.1181i) q^{49} +(-490.654 + 283.279i) q^{50} +(164.581 + 95.0209i) q^{52} -321.580i q^{53} +1.39419i q^{55} +(378.350 - 52.3403i) q^{56} +(268.904 + 465.756i) q^{58} +(-287.300 - 497.619i) q^{59} +(-634.571 - 366.369i) q^{61} +1393.09 q^{62} +834.587 q^{64} +(-1.80333 - 1.04115i) q^{65} +(31.6068 + 54.7445i) q^{67} +(-553.572 - 958.815i) q^{68} +(-11.4354 + 1.58196i) q^{70} -621.395i q^{71} -95.2953i q^{73} +(1323.63 + 764.196i) q^{74} +(718.401 - 414.769i) q^{76} +(70.7195 - 173.954i) q^{77} +(425.124 - 736.337i) q^{79} -0.949659 q^{80} -2000.23i q^{82} +(70.1533 - 121.509i) q^{83} +(6.06554 + 10.5058i) q^{85} +(-366.761 + 211.750i) q^{86} +(-104.553 + 181.090i) q^{88} -1223.70 q^{89} +(172.190 + 221.378i) q^{91} +(624.098 + 360.323i) q^{92} +(1224.28 - 706.841i) q^{94} +(-7.87159 + 4.54466i) q^{95} +(671.481 + 387.680i) q^{97} +(1507.05 + 382.673i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

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