LMFDB - Embedded newform 189.4.s.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (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			17.12
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.223110 + 0.128812i) q^{2} +(-3.96681 - 6.87072i) q^{4} -6.38772 q^{5} +(-1.54394 - 18.4558i) q^{7} -4.10490i q^{8} +O(q^{10})$	\(q+(0.223110 + 0.128812i) q^{2} +(-3.96681 - 6.87072i) q^{4} -6.38772 q^{5} +(-1.54394 - 18.4558i) q^{7} -4.10490i q^{8} +(-1.42516 - 0.822818i) q^{10} +61.0818i q^{11} +(8.78677 + 5.07304i) q^{13} +(2.03287 - 4.31654i) q^{14} +(-31.2058 + 54.0500i) q^{16} +(-22.5082 + 38.9853i) q^{17} +(-69.6373 + 40.2051i) q^{19} +(25.3389 + 43.8883i) q^{20} +(-7.86810 + 13.6279i) q^{22} -27.6800i q^{23} -84.1970 q^{25} +(1.30694 + 2.26369i) q^{26} +(-120.680 + 83.8187i) q^{28} +(-48.9383 + 28.2545i) q^{29} +(92.1526 - 53.2043i) q^{31} +(-42.3642 + 24.4590i) q^{32} +(-10.0436 + 5.79867i) q^{34} +(9.86226 + 117.890i) q^{35} +(95.6403 + 165.654i) q^{37} -20.7157 q^{38} +26.2210i q^{40} +(15.0856 - 26.1289i) q^{41} +(-185.062 - 320.536i) q^{43} +(419.676 - 242.300i) q^{44} +(3.56553 - 6.17569i) q^{46} +(-248.041 + 429.620i) q^{47} +(-338.232 + 56.9893i) q^{49} +(-18.7852 - 10.8456i) q^{50} -80.4953i q^{52} +(-601.424 - 347.232i) q^{53} -390.174i q^{55} +(-75.7592 + 6.33772i) q^{56} -14.5581 q^{58} +(317.670 + 550.221i) q^{59} +(647.712 + 373.957i) q^{61} +27.4135 q^{62} +486.690 q^{64} +(-56.1274 - 32.4052i) q^{65} +(-82.3930 - 142.709i) q^{67} +357.143 q^{68} +(-12.9854 + 27.5729i) q^{70} -278.490i q^{71} +(-313.876 - 181.216i) q^{73} +49.2787i q^{74} +(552.477 + 318.973i) q^{76} +(1127.31 - 94.3066i) q^{77} +(-278.740 + 482.792i) q^{79} +(199.334 - 345.256i) q^{80} +(6.73147 - 3.88641i) q^{82} +(-514.684 - 891.459i) q^{83} +(143.776 - 249.028i) q^{85} -95.3530i q^{86} +250.735 q^{88} +(-730.130 - 1264.62i) q^{89} +(80.0608 - 169.999i) q^{91} +(-190.182 + 109.802i) q^{92} +(-110.681 + 63.9015i) q^{94} +(444.824 - 256.819i) q^{95} +(878.164 - 507.008i) q^{97} +(-82.8039 - 30.8537i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.223110	+	0.128812i	0.0788812	+	0.0455421i	0.538922	−	0.842356i	$-0.318832\pi$
$2$	0.223110	+	0.128812i	0.0788812	+	0.0455421i	−0.460041	+	0.887898i	$0.652165\pi$
$3$		0			0
$3$		0			0
$4$	−3.96681	−	6.87072i	−0.495852	−	0.858841i
$5$	−6.38772			−0.571335			−0.285668	−	0.958329i	$-0.592215\pi$
$5$	−6.38772			−0.571335			−0.285668	+	0.958329i	$0.592215\pi$
$6$		0			0
$7$	−1.54394	−	18.4558i	−0.0833649	−	0.996519i
$7$	−1.54394	−	18.4558i	−0.0833649	−	0.996519i
$8$		−	4.10490i		−	0.181413i
$9$		0			0
$10$	−1.42516	−	0.822818i	−0.0450676	−	0.0260198i
$11$			61.0818i			1.67426i	0.547004	+	0.837130i	$0.315768\pi$
$11$			61.0818i			1.67426i	−0.547004	+	0.837130i	$0.684232\pi$
$12$		0			0
$13$	8.78677	+	5.07304i	0.187462	+	0.108231i	0.590794	−	0.806822i	$-0.298815\pi$
$13$	8.78677	+	5.07304i	0.187462	+	0.108231i	−0.403332	+	0.915054i	$0.632148\pi$
$14$	2.03287	−	4.31654i	0.0388076	−	0.0824032i
$15$		0			0
$16$	−31.2058	+	54.0500i	−0.487590	+	0.844531i
$17$	−22.5082	+	38.9853i	−0.321120	+	0.556196i	−0.980719	−	0.195421i	$-0.937393\pi$
$17$	−22.5082	+	38.9853i	−0.321120	+	0.556196i	0.659599	+	0.751617i	$0.270726\pi$
$18$		0			0
$19$	−69.6373	+	40.2051i	−0.840837	+	0.485457i	−0.857549	−	0.514403i	$-0.828014\pi$
$19$	−69.6373	+	40.2051i	−0.840837	+	0.485457i	0.0167118	+	0.999860i	$0.494680\pi$
$20$	25.3389	+	43.8883i	0.283298	+	0.490686i
$21$		0			0
$22$	−7.86810	+	13.6279i	−0.0762493	+	0.132068i
$23$		−	27.6800i		−	0.250943i	−0.992097	−	0.125471i	$-0.959956\pi$
$23$		−	27.6800i		−	0.250943i	0.992097	−	0.125471i	$-0.0400444\pi$
$24$		0			0
$25$	−84.1970			−0.673576
$26$	1.30694	+	2.26369i	0.00985817	+	0.0170749i
$27$		0			0
$28$	−120.680	+	83.8187i	−0.814514	+	0.565723i
$29$	−48.9383	+	28.2545i	−0.313366	+	0.180922i	−0.648432	−	0.761273i	$-0.724575\pi$
$29$	−48.9383	+	28.2545i	−0.313366	+	0.180922i	0.335066	+	0.942195i	$0.391241\pi$
$30$		0			0
$31$	92.1526	−	53.2043i	0.533906	−	0.308251i	−0.208699	−	0.977980i	$-0.566923\pi$
$31$	92.1526	−	53.2043i	0.533906	−	0.308251i	0.742606	+	0.669729i	$0.233590\pi$
$32$	−42.3642	+	24.4590i	−0.234031	+	0.135118i
$33$		0			0
$34$	−10.0436	+	5.79867i	−0.0506607	+	0.0292489i
$35$	9.86226	+	117.890i	0.0476293	+	0.569347i
$36$		0			0
$37$	95.6403	+	165.654i	0.424951	+	0.736036i	0.996416	−	0.0845902i	$-0.0269581\pi$
$37$	95.6403	+	165.654i	0.424951	+	0.736036i	−0.571465	+	0.820626i	$0.693625\pi$
$38$	−20.7157			−0.0884349
$39$		0			0
$40$			26.2210i			0.103647i
$41$	15.0856	−	26.1289i	0.0574626	−	0.0995282i	−0.835863	−	0.548938i	$-0.815032\pi$
$41$	15.0856	−	26.1289i	0.0574626	−	0.0995282i	0.893326	+	0.449410i	$0.148366\pi$
$42$		0			0
$43$	−185.062	−	320.536i	−0.656317	−	1.13678i	−0.981562	−	0.191145i	$-0.938780\pi$
$43$	−185.062	−	320.536i	−0.656317	−	1.13678i	0.325244	−	0.945630i	$-0.394553\pi$
$44$	419.676	−	242.300i	1.43792	−	0.830185i
$45$		0			0
$46$	3.56553	−	6.17569i	0.0114285	−	0.0197947i
$47$	−248.041	+	429.620i	−0.769798	+	1.33333i	0.167874	+	0.985808i	$0.446310\pi$
$47$	−248.041	+	429.620i	−0.769798	+	1.33333i	−0.937672	+	0.347521i	$0.887024\pi$
$48$		0			0
$49$	−338.232	+	56.9893i	−0.986101	+	0.166149i
$50$	−18.7852	−	10.8456i	−0.0531325	−	0.0306760i
$51$		0			0
$52$		−	80.4953i		−	0.214667i
$53$	−601.424	−	347.232i	−1.55871	−	0.899924i	−0.997380	−	0.0723355i	$-0.976955\pi$
$53$	−601.424	−	347.232i	−1.55871	−	0.899924i	−0.561335	−	0.827589i	$-0.689712\pi$
$54$		0			0
$55$		−	390.174i		−	0.956564i
$56$	−75.7592	+	6.33772i	−0.180781	+	0.0151235i
$57$		0			0
$58$	−14.5581			−0.0329582
$59$	317.670	+	550.221i	0.700968	+	1.21411i	0.968127	+	0.250460i	$0.0805818\pi$
$59$	317.670	+	550.221i	0.700968	+	1.21411i	−0.267159	+	0.963653i	$0.586085\pi$
$60$		0			0
$61$	647.712	+	373.957i	1.35952	+	0.784922i	0.989560	−	0.144124i	$-0.0460363\pi$
$61$	647.712	+	373.957i	1.35952	+	0.784922i	0.369965	+	0.929046i	$0.379370\pi$
$62$	27.4135			0.0561536
$63$		0			0
$64$	486.690			0.950566
$65$	−56.1274	−	32.4052i	−0.107104	−	0.0618365i
$66$		0			0
$67$	−82.3930	−	142.709i	−0.150237	−	0.260219i	0.781077	−	0.624434i	$-0.214670\pi$
$67$	−82.3930	−	142.709i	−0.150237	−	0.260219i	−0.931315	+	0.364216i	$0.881337\pi$
$68$	357.143			0.636912
$69$		0			0
$70$	−12.9854	+	27.5729i	−0.0221722	+	0.0470799i
$71$		−	278.490i		−	0.465502i	−0.972536	−	0.232751i	$-0.925227\pi$
$71$		−	278.490i		−	0.465502i	0.972536	−	0.232751i	$-0.0747728\pi$
$72$		0			0
$73$	−313.876	−	181.216i	−0.503238	−	0.290545i	0.226812	−	0.973939i	$-0.427170\pi$
$73$	−313.876	−	181.216i	−0.503238	−	0.290545i	−0.730050	+	0.683394i	$0.760503\pi$
$74$			49.2787i			0.0774125i
$75$		0			0
$76$	552.477	+	318.973i	0.833861	+	0.481430i
$77$	1127.31	−	94.3066i	1.66843	−	0.139575i
$78$		0			0
$79$	−278.740	+	482.792i	−0.396971	+	0.687574i	−0.993351	−	0.115129i	$-0.963272\pi$
$79$	−278.740	+	482.792i	−0.396971	+	0.687574i	0.596380	+	0.802702i	$0.296605\pi$
$80$	199.334	−	345.256i	0.278577	−	0.482510i
$81$		0			0
$82$	6.73147	−	3.88641i	0.00906544	−	0.00523393i
$83$	−514.684	−	891.459i	−0.680650	−	1.17892i	−0.974783	−	0.223156i	$-0.928364\pi$
$83$	−514.684	−	891.459i	−0.680650	−	1.17892i	0.294133	−	0.955765i	$-0.404969\pi$
$84$		0			0
$85$	143.776	−	249.028i	0.183467	−	0.317775i
$86$		−	95.3530i		−	0.119560i
$87$		0			0
$88$	250.735			0.303732
$89$	−730.130	−	1264.62i	−0.869591	−	1.50618i	−0.862415	−	0.506201i	$-0.831049\pi$
$89$	−730.130	−	1264.62i	−0.869591	−	1.50618i	−0.00717569	−	0.999974i	$-0.502284\pi$
$90$		0			0
$91$	80.0608	−	169.999i	0.0922269	−	0.195833i
$92$	−190.182	+	109.802i	−0.215520	+	0.124431i
$93$		0			0
$94$	−110.681	+	63.9015i	−0.121445	+	0.0701164i
$95$	444.824	−	256.819i	0.480400	−	0.277359i
$96$		0			0
$97$	878.164	−	507.008i	0.919217	−	0.530710i	0.0358320	−	0.999358i	$-0.488592\pi$
$97$	878.164	−	507.008i	0.919217	−	0.530710i	0.883385	+	0.468647i	$0.155259\pi$
$98$	−82.8039	−	30.8537i	−0.0853516	−	0.0318030i
$99$		0			0
$100$	333.994	+	578.494i	0.333994	+	0.578494i
$101$	−143.704			−0.141575			−0.0707875	−	0.997491i	$-0.522551\pi$
$101$	−143.704			−0.141575			−0.0707875	+	0.997491i	$0.522551\pi$
$102$		0			0
$103$		−	546.960i		−	0.523239i	−0.965171	−	0.261619i	$-0.915744\pi$
$103$		−	546.960i		−	0.523239i	0.965171	−	0.261619i	$-0.0842565\pi$
$104$	20.8243	−	36.0688i	0.0196346	−	0.0340080i
$105$		0			0
$106$	−89.4556	−	154.942i	−0.0819689	−	0.141974i
$107$	−1153.06	+	665.722i	−1.04178	+	0.601475i	−0.920338	−	0.391123i	$-0.872087\pi$
$107$	−1153.06	+	665.722i	−1.04178	+	0.601475i	−0.121447	+	0.992598i	$0.538753\pi$
$108$		0			0
$109$	527.013	−	912.813i	0.463107	−	0.802125i	−0.536007	−	0.844214i	$-0.680068\pi$
$109$	527.013	−	912.813i	0.463107	−	0.802125i	0.999114	+	0.0420888i	$0.0134013\pi$
$110$	50.2592	−	87.0515i	0.0435639	−	0.0754549i
$111$		0			0
$112$	1045.71	+	492.477i	0.882239	+	0.415488i
$113$	−804.987	−	464.760i	−0.670149	−	0.386911i	0.125984	−	0.992032i	$-0.459791\pi$
$113$	−804.987	−	464.760i	−0.670149	−	0.386911i	−0.796133	+	0.605122i	$0.793125\pi$
$114$		0			0
$115$			176.812i			0.143373i
$116$	388.258	+	224.161i	0.310766	+	0.179421i
$117$		0			0
$118$			163.679i			0.127694i
$119$	754.257	+	355.216i	0.581030	+	0.273635i
$120$		0			0
$121$	−2399.99			−1.80315
$122$	96.3405	+	166.867i	0.0714940	+	0.123831i
$123$		0			0
$124$	−731.105	−	422.103i	−0.529477	−	0.305694i
$125$	1336.29			0.956173
$126$		0			0
$127$	−1387.22			−0.969259			−0.484629	−	0.874720i	$-0.661046\pi$
$127$	−1387.22			−0.969259			−0.484629	+	0.874720i	$0.661046\pi$
$128$	447.499	+	258.363i	0.309013	+	0.178409i
$129$		0			0
$130$	−8.34838	−	14.4598i	−0.00563232	−	0.00975547i
$131$	−392.756			−0.261949			−0.130974	−	0.991386i	$-0.541811\pi$
$131$	−392.756			−0.261949			−0.130974	+	0.991386i	$0.541811\pi$
$132$		0			0
$133$	849.533	+	1223.14i	0.553864	+	0.797440i
$134$		−	42.4530i		−	0.0273685i
$135$		0			0
$136$	160.031	+	92.3939i	0.100901	+	0.0582552i
$137$			2081.76i			1.29822i	0.760693	+	0.649112i	$0.224859\pi$
$137$			2081.76i			1.29822i	−0.760693	+	0.649112i	$0.775141\pi$
$138$		0			0
$139$	1088.49	+	628.441i	0.664206	+	0.383479i	0.793878	−	0.608078i	$-0.208059\pi$
$139$	1088.49	+	628.441i	0.664206	+	0.383479i	−0.129672	+	0.991557i	$0.541392\pi$
$140$	770.871	−	535.411i	0.465361	−	0.323218i
$141$		0			0
$142$	35.8730	−	62.1338i	0.0211999	−	0.0367194i
$143$	−309.871	+	536.712i	−0.181208	+	0.313861i
$144$		0			0
$145$	312.604	−	180.482i	0.179037	−	0.103367i
$146$	−46.6858	−	80.8622i	−0.0264640	−	0.0458370i
$147$		0			0
$148$	758.775	−	1314.24i	0.421425	−	0.729930i
$149$			3007.64i			1.65366i	0.562453	+	0.826830i	$0.309858\pi$
$149$			3007.64i			1.65366i	−0.562453	+	0.826830i	$0.690142\pi$
$150$		0			0
$151$	−2870.22			−1.54686			−0.773428	−	0.633884i	$-0.781460\pi$
$151$	−2870.22			−1.54686			−0.773428	+	0.633884i	$0.781460\pi$
$152$	165.038	+	285.854i	0.0880681	+	0.152538i
$153$		0			0
$154$	263.662	+	124.171i	0.137964	+	0.0649740i
$155$	−588.645	+	339.855i	−0.305040	+	0.176115i
$156$		0			0
$157$	−794.753	+	458.851i	−0.404001	+	0.233250i	−0.688209	−	0.725512i	$-0.741603\pi$
$157$	−794.753	+	458.851i	−0.404001	+	0.233250i	0.284208	+	0.958763i	$0.408269\pi$
$158$	−124.379	+	71.8103i	−0.0626271	+	0.0361577i
$159$		0			0
$160$	270.611	−	156.237i	0.133710	−	0.0771977i
$161$	−510.857	+	42.7363i	−0.250069	+	0.0209198i
$162$		0			0
$163$	−806.536	−	1396.96i	−0.387563	−	0.671279i	0.604558	−	0.796561i	$-0.293350\pi$
$163$	−806.536	−	1396.96i	−0.387563	−	0.671279i	−0.992121	+	0.125282i	$0.960016\pi$
$164$	−239.366			−0.113972
$165$		0			0
$166$		−	265.191i		−	0.123993i
$167$	922.384	−	1597.62i	0.427402	−	0.740282i	−0.569239	−	0.822172i	$-0.692762\pi$
$167$	922.384	−	1597.62i	0.427402	−	0.740282i	0.996641	+	0.0818896i	$0.0260955\pi$
$168$		0			0
$169$	−1047.03	−	1813.51i	−0.476572	−	0.825447i
$170$	64.1557	−	37.0403i	0.0289442	−	0.0167110i
$171$		0			0
$172$	−1468.21	+	2543.02i	−0.650872	+	1.12734i
$173$	−1002.90	+	1737.08i	−0.440747	+	0.763396i	−0.997745	−	0.0671176i	$-0.978620\pi$
$173$	−1002.90	+	1737.08i	−0.440747	+	0.763396i	0.556998	+	0.830514i	$0.311953\pi$
$174$		0			0
$175$	129.995	+	1553.92i	0.0561526	+	0.671231i
$176$	−3301.47	−	1906.10i	−1.41396	−	0.816352i
$177$		0			0
$178$		−	376.199i		−	0.158412i
$179$	−1424.92	−	822.678i	−0.594992	−	0.343519i	0.172077	−	0.985083i	$-0.444952\pi$
$179$	−1424.92	−	822.678i	−0.594992	−	0.343519i	−0.767069	+	0.641565i	$0.778286\pi$
$180$		0			0
$181$			3394.40i			1.39394i	0.717099	+	0.696971i	$0.245469\pi$
$181$			3394.40i			1.39394i	−0.717099	+	0.696971i	$0.754531\pi$
$182$	39.7604	−	27.6157i	0.0161936	−	0.0112473i
$183$		0			0
$184$	−113.624			−0.0455242
$185$	−610.924	−	1058.15i	−0.242789	−	0.420523i
$186$		0			0
$187$	−2381.30	−	1374.84i	−0.931217	−	0.537638i
$188$	3935.73			1.52682
$189$		0			0
$190$	132.326			0.0505260
$191$	−98.1081	−	56.6427i	−0.0371668	−	0.0214582i	0.481301	−	0.876555i	$-0.340164\pi$
$191$	−98.1081	−	56.6427i	−0.0371668	−	0.0214582i	−0.518468	+	0.855097i	$0.673498\pi$
$192$		0			0
$193$	437.900	+	758.465i	0.163320	+	0.282878i	0.936057	−	0.351847i	$-0.114446\pi$
$193$	437.900	+	758.465i	0.163320	+	0.282878i	−0.772737	+	0.634726i	$0.781113\pi$
$194$	261.236			0.0966786
$195$		0			0
$196$	1733.26	+	2097.84i	0.631656	+	0.764518i
$197$			1004.09i			0.363140i	0.983378	+	0.181570i	$0.0581179\pi$
$197$			1004.09i			0.363140i	−0.983378	+	0.181570i	$0.941882\pi$
$198$		0			0
$199$	1451.86	+	838.230i	0.517183	+	0.298596i	0.735781	−	0.677219i	$-0.236815\pi$
$199$	1451.86	+	838.230i	0.517183	+	0.298596i	−0.218598	+	0.975815i	$0.570148\pi$
$200$			345.620i			0.122195i
$201$		0			0
$202$	−32.0618	−	18.5109i	−0.0111676	−	0.00644762i
$203$	597.017	+	859.571i	0.206416	+	0.297192i
$204$		0			0
$205$	−96.3623	+	166.904i	−0.0328304	+	0.0568640i
$206$	70.4553	−	122.032i	0.0238294	−	0.0412737i
$207$		0			0
$208$	−548.396	+	316.616i	−0.182810	+	0.105545i
$209$	−2455.80	−	4253.57i	−0.812782	−	1.40778i
$210$		0			0
$211$	1528.10	−	2646.75i	0.498572	−	0.863552i	−0.501427	−	0.865200i	$-0.667191\pi$
$211$	1528.10	−	2646.75i	0.498572	−	0.863552i	0.999999	+	0.00164804i	$0.000524587\pi$
$212$			5509.62i			1.78492i
$213$		0			0
$214$	−343.013			−0.109570
$215$	1182.12	+	2047.50i	0.374977	+	0.649480i
$216$		0			0
$217$	−1124.21	−	1618.60i	−0.351687	−	0.506351i
$218$	235.163	−	135.772i	0.0730608	−	0.0421817i
$219$		0			0
$220$	−2680.78	+	1547.75i	−0.821536	+	0.474314i
$221$	−395.549	+	228.370i	−0.120396	+	0.0695106i
$222$		0			0
$223$	3580.72	−	2067.33i	1.07526	−	0.620801i	0.145645	−	0.989337i	$-0.453474\pi$
$223$	3580.72	−	2067.33i	1.07526	−	0.620801i	0.929613	+	0.368536i	$0.120141\pi$
$224$	516.818	+	744.101i	0.154158	+	0.221953i
$225$		0			0
$226$	−119.734	−	207.385i	−0.0352414	−	0.0610400i
$227$	4441.16			1.29855			0.649274	−	0.760555i	$-0.275073\pi$
$227$	4441.16			1.29855			0.649274	+	0.760555i	$0.275073\pi$
$228$		0			0
$229$		−	1299.87i		−	0.375099i	−0.982255	−	0.187549i	$-0.939946\pi$
$229$		−	1299.87i		−	0.375099i	0.982255	−	0.187549i	$-0.0600545\pi$
$230$	−22.7756	+	39.4486i	−0.00652948	+	0.0113094i
$231$		0			0
$232$	115.982	+	200.887i	0.0328215	+	0.0568485i
$233$	−1741.16	+	1005.26i	−0.489559	+	0.282647i	−0.724392	−	0.689389i	$-0.757879\pi$
$233$	−1741.16	+	1005.26i	−0.489559	+	0.282647i	0.234832	+	0.972036i	$0.424546\pi$
$234$		0			0
$235$	1584.42	−	2744.29i	0.439813	−	0.761778i
$236$	2520.28	−	4365.25i	0.695153	−	1.20404i
$237$		0			0
$238$	122.526	+	176.410i	0.0333705	+	0.0480460i
$239$	−4499.21	−	2597.62i	−1.21770	−	0.703038i	−0.253273	−	0.967395i	$-0.581507\pi$
$239$	−4499.21	−	2597.62i	−1.21770	−	0.703038i	−0.964425	+	0.264356i	$0.914840\pi$
$240$		0			0
$241$			6739.77i			1.80144i	0.434402	+	0.900719i	$0.356960\pi$
$241$			6739.77i			1.80144i	−0.434402	+	0.900719i	$0.643040\pi$
$242$	−535.460	−	309.148i	−0.142234	−	0.0821190i
$243$		0			0
$244$		−	5933.67i		−	1.55682i
$245$	2160.54	−	364.032i	0.563394	−	0.0949271i
$246$		0			0
$247$	−815.849			−0.210167
$248$	−218.398	−	378.277i	−0.0559206	−	0.0968574i
$249$		0			0
$250$	298.140	+	172.131i	0.0754241	+	0.0435461i
$251$	1818.28			0.457246			0.228623	−	0.973515i	$-0.426578\pi$
$251$	1818.28			0.457246			0.228623	+	0.973515i	$0.426578\pi$
$252$		0			0
$253$	1690.75			0.420144
$254$	−309.502	−	178.691i	−0.0764563	−	0.0441421i
$255$		0			0
$256$	−1880.20	−	3256.60i	−0.459033	−	0.795068i
$257$	464.053			0.112634			0.0563168	−	0.998413i	$-0.482064\pi$
$257$	464.053			0.112634			0.0563168	+	0.998413i	$0.482064\pi$
$258$		0			0
$259$	2909.61	−	2020.88i	0.698048	−	0.484831i
$260$			514.182i			0.122647i
$261$		0			0
$262$	−87.6278	−	50.5919i	−0.0206628	−	0.0119297i
$263$		−	376.510i		−	0.0882759i	−0.999025	−	0.0441380i	$-0.985946\pi$
$263$		−	376.510i		−	0.0882759i	0.999025	−	0.0441380i	$-0.0140541\pi$
$264$		0			0
$265$	3841.73	+	2218.02i	0.890549	+	0.514159i
$266$	31.9838	+	382.324i	0.00737237	+	0.0881271i
$267$		0			0
$268$	−653.675	+	1132.20i	−0.148991	+	0.258060i
$269$	−1998.09	+	3460.80i	−0.452885	+	0.784419i	−0.998564	−	0.0535750i	$-0.982938\pi$
$269$	−1998.09	+	3460.80i	−0.452885	+	0.784419i	0.545679	+	0.837994i	$0.316272\pi$
$270$		0			0
$271$	−729.622	+	421.248i	−0.163548	+	0.0944242i	−0.579540	−	0.814944i	$-0.696768\pi$
$271$	−729.622	+	421.248i	−0.163548	+	0.0944242i	0.415992	+	0.909368i	$0.363434\pi$
$272$	−1404.77	−	2433.13i	−0.313150	−	0.542391i
$273$		0			0
$274$	−268.157	+	464.461i	−0.0591238	+	0.102405i
$275$		−	5142.90i		−	1.12774i
$276$		0			0
$277$	4166.18			0.903687			0.451844	−	0.892097i	$-0.350766\pi$
$277$	4166.18			0.903687			0.451844	+	0.892097i	$0.350766\pi$
$278$	161.902	+	280.422i	0.0349289	+	0.0604986i
$279$		0			0
$280$	483.929	−	40.4836i	0.103287	−	0.00864056i
$281$	4478.35	−	2585.58i	0.950733	−	0.548906i	0.0574244	−	0.998350i	$-0.481711\pi$
$281$	4478.35	−	2585.58i	0.950733	−	0.548906i	0.893309	+	0.449444i	$0.148378\pi$
$282$		0			0
$283$	5213.04	−	3009.75i	1.09499	−	0.632195i	0.160092	−	0.987102i	$-0.448821\pi$
$283$	5213.04	−	3009.75i	1.09499	−	0.632195i	0.934901	+	0.354907i	$0.115488\pi$
$284$	−1913.43	+	1104.72i	−0.399792	+	0.230820i
$285$		0			0
$286$	−138.270	+	79.8304i	−0.0285877	+	0.0165051i
$287$	−505.521	−	238.074i	−0.103972	−	0.0489654i
$288$		0			0
$289$	1443.26	+	2499.80i	0.293764	+	0.508814i
$290$	92.9933			0.0188302
$291$		0			0
$292$			2875.40i			0.576268i
$293$	2243.89	−	3886.53i	0.447404	−	0.774926i	−0.550812	−	0.834629i	$-0.685682\pi$
$293$	2243.89	−	3886.53i	0.447404	−	0.774926i	0.998216	+	0.0597027i	$0.0190153\pi$
$294$		0			0
$295$	−2029.19	−	3514.66i	−0.400488	−	0.693665i
$296$	679.993	−	392.594i	0.133526	−	0.0770914i
$297$		0			0
$298$	−387.421	+	671.033i	−0.0753111	+	0.130443i
$299$	140.422	−	243.218i	0.0271599	−	0.0470424i
$300$		0			0
$301$	−5630.03	+	3910.35i	−1.07810	+	0.748800i
$302$	−640.374	−	369.720i	−0.122018	−	0.0704471i
$303$		0			0
$304$		−	5018.53i		−	0.946816i
$305$	−4137.40	−	2388.73i	−0.776744	−	0.448454i
$306$		0			0
$307$			263.461i			0.0489789i	0.999700	+	0.0244895i	$0.00779602\pi$
$307$			263.461i			0.0489789i	−0.999700	+	0.0244895i	$0.992204\pi$
$308$	−5119.80	−	7371.36i	−0.947167	−	1.36371i
$309$		0			0
$310$	−175.110			−0.0320825
$311$	−2426.23	−	4202.36i	−0.442377	−	0.766219i	0.555489	−	0.831524i	$-0.312531\pi$
$311$	−2426.23	−	4202.36i	−0.442377	−	0.766219i	−0.997865	+	0.0653054i	$0.979198\pi$
$312$		0			0
$313$	2371.65	+	1369.27i	0.428286	+	0.247271i	0.698616	−	0.715497i	$-0.253800\pi$
$313$	2371.65	+	1369.27i	0.428286	+	0.247271i	−0.270330	+	0.962768i	$0.587133\pi$
$314$	−236.423			−0.0424908
$315$		0			0
$316$	4422.84			0.787355
$317$	6423.47	+	3708.59i	1.13810	+	0.657083i	0.945959	−	0.324285i	$-0.105124\pi$
$317$	6423.47	+	3708.59i	1.13810	+	0.657083i	0.192141	+	0.981367i	$0.438457\pi$
$318$		0			0
$319$	−1725.84	−	2989.24i	−0.302910	−	0.524656i
$320$	−3108.84			−0.543092
$321$		0			0
$322$	−119.482	−	56.2699i	−0.0206785	−	0.00973850i
$323$		−	3619.78i		−	0.623560i
$324$		0			0
$325$	−739.820	−	427.135i	−0.126270	−	0.0729021i
$326$		−	415.568i		−	0.0706017i
$327$		0			0
$328$	−107.257	−	61.9247i	−0.0180557	−	0.0104244i
$329$	8311.93	+	3914.49i	1.39286	+	0.655966i
$330$		0			0
$331$	−2086.06	+	3613.16i	−0.346406	+	0.599992i	−0.985608	−	0.169046i	$-0.945931\pi$
$331$	−2086.06	+	3613.16i	−0.346406	+	0.599992i	0.639203	+	0.769038i	$0.279265\pi$
$332$	−4083.31	+	7072.51i	−0.675003	+	1.16914i
$333$		0			0
$334$	411.585	−	237.629i	0.0674280	−	0.0389296i
$335$	526.303	+	911.584i	0.0858359	+	0.148672i
$336$		0			0
$337$	−528.671	+	915.685i	−0.0854556	+	0.148013i	−0.905585	−	0.424164i	$-0.860568\pi$
$337$	−528.671	+	915.685i	−0.0854556	+	0.148013i	0.820130	+	0.572178i	$0.193901\pi$
$338$		−	539.481i		−	0.0868163i
$339$		0			0
$340$	−2281.33			−0.363890
$341$	3249.82	+	5628.85i	0.516092	+	0.893898i
$342$		0			0
$343$	1573.99	+	6154.36i	0.247777	+	0.968817i
$344$	−1315.77	+	759.660i	−0.206225	+	0.119064i
$345$		0			0
$346$	−447.514	+	258.373i	−0.0695333	+	0.0401451i
$347$	4140.17	−	2390.33i	0.640507	−	0.369797i	−0.144303	−	0.989534i	$-0.546094\pi$
$347$	4140.17	−	2390.33i	0.640507	−	0.369797i	0.784810	+	0.619736i	$0.212761\pi$
$348$		0			0
$349$	−2180.04	+	1258.65i	−0.334370	+	0.193048i	−0.657780	−	0.753211i	$-0.728504\pi$
$349$	−2180.04	+	1258.65i	−0.334370	+	0.193048i	0.323410	+	0.946259i	$0.395171\pi$
$350$	−171.161	+	363.440i	−0.0261399	+	0.0555048i
$351$		0			0
$352$	−1494.00	−	2587.68i	−0.226223	−	0.391829i
$353$	6005.81			0.905544			0.452772	−	0.891626i	$-0.350435\pi$
$353$	6005.81			0.905544			0.452772	+	0.891626i	$0.350435\pi$
$354$		0			0
$355$			1778.92i			0.265958i
$356$	−5792.58	+	10033.0i	−0.862377	+	1.49368i
$357$		0			0
$358$	−211.942	−	367.095i	−0.0312891	−	0.0541943i
$359$	5772.63	−	3332.83i	0.848656	−	0.489972i	−0.0115408	−	0.999933i	$-0.503674\pi$
$359$	5772.63	−	3332.83i	0.848656	−	0.489972i	0.860197	+	0.509961i	$0.170340\pi$
$360$		0			0
$361$	−196.595	+	340.513i	−0.0286624	+	0.0496447i
$362$	−437.241	+	757.323i	−0.0634830	+	0.109956i
$363$		0			0
$364$	−1485.60	+	124.280i	−0.213920	+	0.0178957i
$365$	2004.95	+	1157.56i	0.287518	+	0.165998i
$366$		0			0
$367$		−	1609.91i		−	0.228982i	−0.993424	−	0.114491i	$-0.963476\pi$
$367$		−	1609.91i		−	0.228982i	0.993424	−	0.114491i	$-0.0365237\pi$
$368$	1496.10	+	863.777i	0.211929	+	0.122357i
$369$		0			0
$370$		−	314.778i		−	0.0442285i
$371$	−5479.88	+	11635.9i	−0.766850	+	1.62831i
$372$		0			0
$373$	5211.06			0.723373			0.361687	−	0.932300i	$-0.382201\pi$
$373$	5211.06			0.723373			0.361687	+	0.932300i	$0.382201\pi$
$374$	−354.193	−	613.481i	−0.0489703	−	0.0848191i
$375$		0			0
$376$	1763.55	+	1018.18i	0.241883	+	0.139651i
$377$	−573.346			−0.0783257
$378$		0			0
$379$	−9946.69			−1.34809			−0.674046	−	0.738689i	$-0.735445\pi$
$379$	−9946.69			−1.34809			−0.674046	+	0.738689i	$0.735445\pi$
$380$	−3529.07	−	2037.51i	−0.476414	−	0.275058i
$381$		0			0
$382$	−14.5926	−	25.2751i	−0.00195451	−	0.00338530i
$383$	−14449.0			−1.92770			−0.963848	−	0.266452i	$-0.914149\pi$
$383$	−14449.0			−1.92770			−0.963848	+	0.266452i	$0.914149\pi$
$384$		0			0
$385$	−7200.96	+	602.405i	−0.953234	+	0.0797439i
$386$			225.628i			0.0297517i
$387$		0			0
$388$	−6967.03	−	4022.42i	−0.911591	−	0.526307i
$389$			9079.32i			1.18339i	0.806161	+	0.591696i	$0.201542\pi$
$389$			9079.32i			1.18339i	−0.806161	+	0.591696i	$0.798458\pi$
$390$		0			0
$391$	1079.12	+	623.028i	0.139574	+	0.0805828i
$392$	233.935	+	1388.41i	0.0301416	+	0.178891i
$393$		0			0
$394$	−129.340	+	224.023i	−0.0165381	+	0.0286449i
$395$	1780.51	−	3083.94i	0.226803	−	0.392835i
$396$		0			0
$397$	1879.14	−	1084.92i	0.237559	−	0.137155i	−0.376495	−	0.926419i	$-0.622871\pi$
$397$	1879.14	−	1084.92i	0.237559	−	0.137155i	0.614055	+	0.789264i	$0.289537\pi$
$398$	215.949	+	374.035i	0.0271973	+	0.0471072i
$399$		0			0
$400$	2627.43	−	4550.84i	0.328429	−	0.568855i
$401$			301.096i			0.0374963i	0.999824	+	0.0187482i	$0.00596808\pi$
$401$			301.096i			0.0374963i	−0.999824	+	0.0187482i	$0.994032\pi$
$402$		0			0
$403$	1079.63			0.133450
$404$	570.047	+	987.351i	0.0702003	+	0.121590i
$405$		0			0
$406$	22.4769	+	268.682i	0.00274756	+	0.0328435i
$407$	−10118.4	+	5841.88i	−1.23232	+	0.711478i
$408$		0			0
$409$	−3938.78	+	2274.06i	−0.476186	+	0.274926i	−0.718826	−	0.695190i	$-0.755320\pi$
$409$	−3938.78	+	2274.06i	−0.476186	+	0.274926i	0.242639	+	0.970117i	$0.421987\pi$
$410$	−42.9987	+	24.8253i	−0.00517941	+	0.00299033i
$411$		0			0
$412$	−3758.01	+	2169.69i	−0.449379	+	0.259449i
$413$	9664.29	−	6712.36i	1.15145	−	0.799743i
$414$		0			0
$415$	3287.66	+	5694.40i	0.388879	+	0.673559i
$416$	−496.326			−0.0584961
$417$		0			0
$418$		−	1265.35i		−	0.148063i
$419$	−687.732	+	1191.19i	−0.0801859	+	0.138886i	−0.903330	−	0.428947i	$-0.858885\pi$
$419$	−687.732	+	1191.19i	−0.0801859	+	0.138886i	0.823144	+	0.567833i	$0.192218\pi$
$420$		0			0
$421$	−1505.07	−	2606.85i	−0.174234	−	0.301782i	0.765662	−	0.643243i	$-0.222412\pi$
$421$	−1505.07	−	2606.85i	−0.174234	−	0.301782i	−0.939896	+	0.341461i	$0.889078\pi$
$422$	681.868	−	393.676i	0.0786559	−	0.0454120i
$423$		0			0
$424$	−1425.35	+	2468.78i	−0.163258	+	0.282771i
$425$	1895.12	−	3282.45i	0.216299	−	0.374640i
$426$		0			0
$427$	5901.64	−	12531.4i	0.668853	−	1.42023i
$428$	9147.99	+	5281.59i	1.03314	+	0.596485i
$429$		0			0
$430$			609.089i			0.0683090i
$431$	−2888.94	−	1667.93i	−0.322867	−	0.186407i	0.329803	−	0.944050i	$-0.393018\pi$
$431$	−2888.94	−	1667.93i	−0.322867	−	0.186407i	−0.652670	+	0.757643i	$0.726351\pi$
$432$		0			0
$433$			3574.98i			0.396772i	0.980124	+	0.198386i	$0.0635700\pi$
$433$			3574.98i			0.396772i	−0.980124	+	0.198386i	$0.936430\pi$
$434$	−42.3248	−	505.938i	−0.00468124	−	0.0559581i
$435$		0			0
$436$	−8362.25			−0.918530
$437$	1112.88	+	1927.56i	0.121822	+	0.211002i
$438$		0			0
$439$	−5246.27	−	3028.94i	−0.570367	−	0.329301i	0.186929	−	0.982373i	$-0.440147\pi$
$439$	−5246.27	−	3028.94i	−0.570367	−	0.329301i	−0.757296	+	0.653072i	$0.773480\pi$
$440$	−1601.62			−0.173533
$441$		0			0
$442$	−117.668			−0.0126626
$443$	−13774.2	−	7952.52i	−1.47727	−	0.852902i	−0.477599	−	0.878578i	$-0.658493\pi$
$443$	−13774.2	−	7952.52i	−1.47727	−	0.852902i	−0.999670	+	0.0256763i	$0.991826\pi$
$444$		0			0
$445$	4663.87	+	8078.05i	0.496828	+	0.860531i
$446$	1065.19			0.113090
$447$		0			0
$448$	−751.420	−	8982.24i	−0.0792438	−	0.947257i
$449$			3388.65i			0.356169i	0.984015	+	0.178085i	$0.0569901\pi$
$449$			3388.65i			0.356169i	−0.984015	+	0.178085i	$0.943010\pi$
$450$		0			0
$451$	1596.00	+	921.453i	0.166636	+	0.0962073i
$452$			7374.46i			0.767402i
$453$		0			0
$454$	990.867	+	572.077i	0.102431	+	0.0591386i
$455$	−511.406	+	1085.91i	−0.0526925	+	0.111886i
$456$		0			0
$457$	−1140.74	+	1975.82i	−0.116765	+	0.202243i	−0.918484	−	0.395458i	$-0.870586\pi$
$457$	−1140.74	+	1975.82i	−0.116765	+	0.202243i	0.801719	+	0.597701i	$0.203919\pi$
$458$	167.439	−	290.013i	0.0170828	−	0.0295882i
$459$		0			0
$460$	1214.83	−	701.382i	0.123134	−	0.0710915i
$461$	2730.79	+	4729.87i	0.275891	+	0.477856i	0.970359	−	0.241666i	$-0.0776939\pi$
$461$	2730.79	+	4729.87i	0.275891	+	0.477856i	−0.694469	+	0.719523i	$0.744361\pi$
$462$		0			0
$463$	−5628.16	+	9748.26i	−0.564931	+	0.978488i	0.432126	+	0.901813i	$0.357764\pi$
$463$	−5628.16	+	9748.26i	−0.564931	+	0.978488i	−0.997056	+	0.0766749i	$0.975570\pi$
$464$		−	3526.81i		−	0.352863i
$465$		0			0
$466$	−517.960			−0.0514894
$467$	−8118.96	−	14062.5i	−0.804498	−	1.39343i	−0.916629	−	0.399738i	$-0.869101\pi$
$467$	−8118.96	−	14062.5i	−0.804498	−	1.39343i	0.112131	−	0.993693i	$-0.464232\pi$
$468$		0			0
$469$	−2506.59	+	1740.96i	−0.246788	+	0.171407i
$470$	706.998	−	408.185i	0.0693859	−	0.0400600i
$471$		0			0
$472$	2258.60	−	1304.00i	0.220255	−	0.127164i
$473$	19578.9	−	11303.9i	1.90326	−	1.09885i
$474$		0			0
$475$	5863.25	−	3385.15i	0.566367	−	0.326992i
$476$	−551.408	−	6591.37i	−0.0530961	−	0.634695i
$477$		0			0
$478$	−669.212	−	1159.11i	−0.0640356	−	0.110913i
$479$	6266.51			0.597754			0.298877	−	0.954292i	$-0.403388\pi$
$479$	6266.51			0.597754			0.298877	+	0.954292i	$0.403388\pi$
$480$		0			0
$481$			1940.75i			0.183972i
$482$	−868.166	+	1503.71i	−0.0820412	+	0.142100i
$483$		0			0
$484$	9520.30	+	16489.6i	0.894093	+	1.54861i
$485$	−5609.47	+	3238.63i	−0.525181	+	0.303214i
$486$		0			0
$487$	262.826	−	455.227i	0.0244554	−	0.0423580i	−0.853539	−	0.521029i	$-0.825548\pi$
$487$	262.826	−	455.227i	0.0244554	−	0.0423580i	0.877994	+	0.478671i	$0.158882\pi$
$488$	1535.05	−	2658.79i	0.142395	−	0.246635i
$489$		0			0
$490$	528.928	+	197.085i	0.0487644	+	0.0181702i
$491$	13426.5	+	7751.78i	1.23407	+	0.712491i	0.967876	−	0.251429i	$-0.0809004\pi$
$491$	13426.5	+	7751.78i	1.23407	+	0.712491i	0.266194	+	0.963919i	$0.414234\pi$
$492$		0			0
$493$		−	2543.83i		−	0.232390i
$494$	−182.024	−	105.092i	−0.0165782	−	0.00957144i
$495$		0			0
$496$			6641.13i			0.601200i
$497$	−5139.75	+	429.972i	−0.463882	+	0.0388066i
$498$		0			0
$499$	9320.68			0.836175			0.418087	−	0.908407i	$-0.362701\pi$
$499$	9320.68			0.836175			0.418087	+	0.908407i	$0.362701\pi$
$500$	−5300.82	−	9181.30i	−0.474120	−	0.821200i
$501$		0			0
$502$	405.676	+	234.217i	0.0360681	+	0.0208239i
$503$	−1065.29			−0.0944311			−0.0472155	−	0.998885i	$-0.515035\pi$
$503$	−1065.29			−0.0944311			−0.0472155	+	0.998885i	$0.515035\pi$
$504$		0			0
$505$	917.941			0.0808868
$506$	377.222	+	217.789i	0.0331414	+	0.0191342i
$507$		0			0
$508$	5502.84	+	9531.21i	0.480609	+	0.832439i
$509$	9387.36			0.817460			0.408730	−	0.912655i	$-0.365972\pi$
$509$	9387.36			0.817460			0.408730	+	0.912655i	$0.365972\pi$
$510$		0			0
$511$	−2859.88	+	6072.61i	−0.247581	+	0.525707i
$512$		−	5102.59i		−	0.440439i
$513$		0			0
$514$	103.535	+	59.7758i	0.00888467	+	0.00512957i
$515$			3493.83i			0.298945i
$516$		0			0
$517$	−26241.9	−	15150.8i	−2.23234	−	1.28884i
$518$	909.477	−	76.0833i	0.0771431	−	0.00645349i
$519$		0			0
$520$	−133.020	+	230.397i	−0.0112179	+	0.0194300i
$521$	−10087.0	+	17471.2i	−0.848216	+	1.46915i	0.0345837	+	0.999402i	$0.488989\pi$
$521$	−10087.0	+	17471.2i	−0.848216	+	1.46915i	−0.882799	+	0.469751i	$0.844344\pi$
$522$		0			0
$523$	13914.0	−	8033.23i	1.16332	−	0.671642i	0.211221	−	0.977438i	$-0.432256\pi$
$523$	13914.0	−	8033.23i	1.16332	−	0.671642i	0.952097	+	0.305797i	$0.0989227\pi$
$524$	1557.99	+	2698.52i	0.129888	+	0.224972i
$525$		0			0
$526$	48.4991	−	84.0029i	0.00402027	−	0.00696331i
$527$			4790.14i			0.395942i
$528$		0			0
$529$	11400.8			0.937028
$530$	571.418	+	989.725i	0.0468317	+	0.0811149i
$531$		0			0
$532$	5033.90	−	10688.9i	0.410239	−	0.871093i
$533$	265.106	−	153.059i	0.0215442	−	0.0124385i
$534$		0			0
$535$	7365.46	−	4252.45i	0.595208	−	0.343644i
$536$	−585.805	+	338.215i	−0.0472070	+	0.0272550i
$537$		0			0
$538$	−891.588	+	514.759i	−0.0714482	+	0.0412506i
$539$	−3481.01	−	20659.9i	−0.278177	−	1.65099i
$540$		0			0
$541$	−12174.8	−	21087.4i	−0.967535	−	1.67582i	−0.702645	−	0.711541i	$-0.747998\pi$
$541$	−12174.8	−	21087.4i	−0.967535	−	1.67582i	−0.264890	−	0.964279i	$-0.585336\pi$
$542$	−217.048			−0.0172011
$543$		0			0
$544$		−	2202.11i		−	0.173556i
$545$	−3366.41	+	5830.79i	−0.264589	+	0.458282i
$546$		0			0
$547$	5442.16	+	9426.10i	0.425393	+	0.736802i	0.996457	−	0.0841031i	$-0.0268025\pi$
$547$	5442.16	+	9426.10i	0.425393	+	0.736802i	−0.571064	+	0.820906i	$0.693469\pi$
$548$	14303.2	−	8257.96i	1.11497	−	0.643727i
$549$		0			0
$550$	662.470	−	1147.43i	0.0513597	−	0.0889576i
$551$	2271.95	−	3935.14i	0.175660	−	0.304251i
$552$		0			0
$553$	9340.66	+	4398.96i	0.718274	+	0.338269i
$554$	929.515	+	536.656i	0.0712839	+	0.0411558i
$555$		0			0
$556$		−	9971.63i		−	0.760596i
$557$	−21701.2	−	12529.2i	−1.65082	−	0.953104i	−0.976734	−	0.214455i	$-0.931203\pi$
$557$	−21701.2	−	12529.2i	−1.65082	−	0.953104i	−0.674090	−	0.738649i	$-0.735464\pi$
$558$		0			0
$559$		−	3755.31i		−	0.284137i
$560$	−6679.73	−	3145.81i	−0.504054	−	0.237383i
$561$		0			0
$562$	1332.22			0.0999933
$563$	−8948.10	−	15498.6i	−0.669836	−	1.16019i	−0.977950	−	0.208840i	$-0.933031\pi$
$563$	−8948.10	−	15498.6i	−0.669836	−	1.16019i	0.308114	−	0.951349i	$-0.400302\pi$
$564$		0			0
$565$	5142.04	+	2968.76i	0.382880	+	0.221056i
$566$	1550.77			0.115166
$567$		0			0
$568$	−1143.17			−0.0844480
$569$	−764.970	−	441.656i	−0.0563607	−	0.0325399i	0.471555	−	0.881837i	$-0.343693\pi$
$569$	−764.970	−	441.656i	−0.0563607	−	0.0325399i	−0.527916	+	0.849297i	$0.677026\pi$
$570$		0			0
$571$	−5229.75	−	9058.20i	−0.383290	−	0.663877i	0.608241	−	0.793753i	$-0.291876\pi$
$571$	−5229.75	−	9058.20i	−0.383290	−	0.663877i	−0.991530	+	0.129876i	$0.958542\pi$
$572$	4916.80			0.359408
$573$		0			0
$574$	−82.1198	−	118.234i	−0.00597145	−	0.00859756i
$575$			2330.58i			0.169029i
$576$		0			0
$577$	17098.4	+	9871.79i	1.23365	+	0.712249i	0.967789	−	0.251762i	$-0.0810099\pi$
$577$	17098.4	+	9871.79i	1.23365	+	0.712249i	0.265863	+	0.964011i	$0.414343\pi$
$578$			743.640i			0.0535145i
$579$		0			0
$580$	−2480.08	−	1431.88i	−0.177552	−	0.102509i
$581$	−15657.9	+	10875.3i	−1.11807	+	0.776561i
$582$		0			0
$583$	21209.6	−	36736.0i	1.50671	−	2.60969i
$584$	−743.874	+	1288.43i	−0.0527084	+	0.0912937i
$585$		0			0
$586$	1001.27	−	578.082i	0.0705835	−	0.0407514i
$587$	−4130.99	−	7155.09i	−0.290467	−	0.503104i	0.683453	−	0.729995i	$-0.260477\pi$
$587$	−4130.99	−	7155.09i	−0.290467	−	0.503104i	−0.973920	+	0.226890i	$0.927144\pi$
$588$		0			0
$589$	−4278.17	+	7410.01i	−0.299285	+	0.518377i
$590$		−	1045.54i		−	0.0729562i
$591$		0			0
$592$	−11938.1			−0.828807
$593$	13435.3	+	23270.7i	0.930392	+	1.61149i	0.782652	+	0.622460i	$0.213867\pi$
$593$	13435.3	+	23270.7i	0.930392	+	1.61149i	0.147741	+	0.989026i	$0.452800\pi$
$594$		0			0
$595$	−4817.98	−	2269.02i	−0.331963	−	0.156337i
$596$	20664.6	−	11930.7i	1.42023	−	0.819970i
$597$		0			0
$598$	62.6590	−	36.1762i	0.00428481	−	0.00247384i
$599$	14454.8	−	8345.50i	0.985991	−	0.569262i	0.0819174	−	0.996639i	$-0.473896\pi$
$599$	14454.8	−	8345.50i	0.985991	−	0.569262i	0.904074	+	0.427377i	$0.140562\pi$
$600$		0			0
$601$	−16426.9	+	9484.10i	−1.11492	+	0.643702i	−0.940100	−	0.340898i	$-0.889269\pi$
$601$	−16426.9	+	9484.10i	−1.11492	+	0.643702i	−0.174824	+	0.984600i	$0.555936\pi$
$602$	−1759.82	+	147.219i	−0.119144	+	0.00996713i
$603$		0			0
$604$	11385.6	+	19720.5i	0.767012	+	1.32850i
$605$	15330.5			1.03020
$606$		0			0
$607$			5154.91i			0.344698i	0.985036	+	0.172349i	$0.0551356\pi$
$607$			5154.91i			0.344698i	−0.985036	+	0.172349i	$0.944864\pi$
$608$	1966.75	−	3406.52i	0.131188	−	0.227224i
$609$		0			0
$610$	−615.397	−	1065.90i	−0.0408470	−	0.0707491i
$611$	−4358.96	+	2516.65i	−0.288616	+	0.166633i
$612$		0			0
$613$	4050.42	−	7015.53i	0.266876	−	0.462242i	−0.701178	−	0.712987i	$-0.747342\pi$
$613$	4050.42	−	7015.53i	0.266876	−	0.462242i	0.968053	+	0.250744i	$0.0806754\pi$
$614$	−33.9371	+	58.7808i	−0.00223060	+	0.00386352i
$615$		0			0
$616$	−387.119	−	4627.51i	−0.0253206	−	0.302675i
$617$	6750.27	+	3897.27i	0.440447	+	0.254292i	0.703787	−	0.710411i	$-0.251491\pi$
$617$	6750.27	+	3897.27i	0.440447	+	0.254292i	−0.263340	+	0.964703i	$0.584824\pi$
$618$		0			0
$619$			17518.1i			1.13750i	0.822510	+	0.568750i	$0.192573\pi$
$619$			17518.1i			1.13750i	−0.822510	+	0.568750i	$0.807427\pi$
$620$	4670.09	+	2696.28i	0.302509	+	0.174654i
$621$		0			0
$622$		−	1250.12i		−	0.0805870i
$623$	−22212.3	+	15427.6i	−1.42844	+	0.992126i
$624$		0			0
$625$	1988.76			0.127281
$626$	352.758	+	610.995i	0.0225225	+	0.0390100i
$627$		0			0
$628$	6305.28	+	3640.35i	0.400650	+	0.231315i
$629$	−8610.77			−0.545841
$630$		0			0
$631$	8636.00			0.544839			0.272420	−	0.962179i	$-0.412176\pi$
$631$	8636.00			0.544839			0.272420	+	0.962179i	$0.412176\pi$
$632$	1981.81	+	1144.20i	0.124735	+	0.0720155i
$633$		0			0
$634$	955.425	+	1654.84i	0.0598498	+	0.103663i
$635$	8861.18			0.553772
$636$		0			0
$637$	−3261.08	−	1215.12i	−0.202839	−	0.0755803i
$638$		−	889.237i		−	0.0551806i
$639$		0			0
$640$	−2858.50	−	1650.35i	−0.176550	−	0.101931i
$641$		−	15365.3i		−	0.946791i	−0.880850	−	0.473396i	$-0.843028\pi$
$641$		−	15365.3i		−	0.946791i	0.880850	−	0.473396i	$-0.156972\pi$
$642$		0			0
$643$	6869.74	+	3966.25i	0.421332	+	0.243256i	0.695647	−	0.718384i	$-0.255118\pi$
$643$	6869.74	+	3966.25i	0.421332	+	0.243256i	−0.274315	+	0.961640i	$0.588451\pi$
$644$	2320.10	+	3340.43i	0.141964	+	0.204397i
$645$		0			0
$646$	466.273	−	807.608i	0.0283982	−	0.0491872i
$647$	9673.35	−	16754.7i	0.587788	−	1.01808i	−0.406734	−	0.913547i	$-0.633332\pi$
$647$	9673.35	−	16754.7i	0.587788	−	1.01808i	0.994522	−	0.104531i	$-0.0333343\pi$
$648$		0			0
$649$	−33608.5	+	19403.9i	−2.03274	+	1.17360i
$650$	−110.041	−	190.596i	−0.00664023	−	0.0115012i
$651$		0			0
$652$	−6398.76	+	11083.0i	−0.384348	+	0.665710i
$653$		−	19303.6i		−	1.15683i	−0.815743	−	0.578414i	$-0.803672\pi$
$653$		−	19303.6i		−	1.15683i	0.815743	−	0.578414i	$-0.196328\pi$
$654$		0			0
$655$	2508.82			0.149661
$656$	941.512	+	1630.75i	0.0560364	+	0.0970579i
$657$		0			0
$658$	1350.24	+	1944.04i	0.0799966	+	0.115177i
$659$	−6426.97	+	3710.61i	−0.379908	+	0.219340i	−0.677778	−	0.735266i	$-0.737057\pi$
$659$	−6426.97	+	3710.61i	−0.379908	+	0.219340i	0.297870	+	0.954606i	$0.403724\pi$
$660$		0			0
$661$	−12251.0	+	7073.14i	−0.720893	+	0.416208i	−0.815081	−	0.579347i	$-0.803308\pi$
$661$	−12251.0	+	7073.14i	−0.720893	+	0.416208i	0.0941886	+	0.995554i	$0.469974\pi$
$662$	−930.840	+	537.421i	−0.0546498	+	0.0315521i
$663$		0			0
$664$	−3659.35	+	2112.73i	−0.213871	+	0.123478i
$665$	−5426.58	−	7813.06i	−0.316442	−	0.455605i
$666$		0			0
$667$	782.086	+	1354.61i	0.0454011	+	0.0786369i
$668$	−14635.7			−0.847713
$669$		0			0
$670$			271.178i			0.0156366i
$671$	−22841.9	+	39563.4i	−1.31416	+	2.27620i
$672$		0			0
$673$	4164.46	+	7213.05i	0.238526	+	0.413139i	0.960292	−	0.278998i	$-0.0900024\pi$
$673$	4164.46	+	7213.05i	0.238526	+	0.413139i	−0.721766	+	0.692138i	$0.756669\pi$
$674$	−235.903	+	136.199i	−0.0134817	+	0.00778365i
$675$		0			0
$676$	−8306.74	+	14387.7i	−0.472618	+	0.818599i
$677$	2239.79	−	3879.44i	0.127153	−	0.220235i	−0.795420	−	0.606059i	$-0.792750\pi$
$677$	2239.79	−	3879.44i	0.127153	−	0.220235i	0.922572	+	0.385824i	$0.126083\pi$
$678$		0			0
$679$	−10713.1	−	15424.4i	−0.605493	−	0.871775i
$680$	−1022.23	−	590.187i	−0.0576483	−	0.0332833i
$681$		0			0
$682$			1674.47i			0.0940156i
$683$	2140.00	+	1235.53i	0.119890	+	0.0692184i	0.558746	−	0.829339i	$-0.311283\pi$
$683$	2140.00	+	1235.53i	0.119890	+	0.0692184i	−0.438856	+	0.898557i	$0.644616\pi$
$684$		0			0
$685$		−	13297.7i		−	0.741721i
$686$	−441.585	+	1575.85i	−0.0245770	+	0.0877057i
$687$		0			0
$688$	23100.0			1.28006
$689$	−3523.05	−	6102.10i	−0.194800	−	0.337404i
$690$		0			0
$691$	−20070.0	−	11587.4i	−1.10492	−	0.637926i	−0.167412	−	0.985887i	$-0.553541\pi$
$691$	−20070.0	−	11587.4i	−1.10492	−	0.637926i	−0.937509	+	0.347961i	$0.886874\pi$
$692$	15913.3			0.874181
$693$		0			0
$694$	1231.62			0.0673653
$695$	−6952.98	−	4014.30i	−0.379484	−	0.219095i
$696$		0			0
$697$	679.097	+	1176.23i	0.0369048	+	0.0639210i
$698$	−648.518			−0.0351673
$699$		0			0
$700$	10160.9	−	7057.28i	0.548637	−	0.381057i
$701$			21807.9i			1.17500i	0.809225	+	0.587498i	$0.199887\pi$
$701$			21807.9i			1.17500i	−0.809225	+	0.587498i	$0.800113\pi$
$702$		0			0
$703$	−13320.3	−	7690.46i	−0.714628	−	0.412591i
$704$			29727.9i			1.59149i
$705$		0			0
$706$	1339.95	+	773.623i	0.0714304	+	0.0412404i
$707$	221.870	+	2652.17i	0.0118024	+	0.141082i
$708$		0			0
$709$	−6487.34	+	11236.4i	−0.343635	+	0.595193i	−0.985105	−	0.171955i	$-0.944992\pi$
$709$	−6487.34	+	11236.4i	−0.343635	+	0.595193i	0.641470	+	0.767148i	$0.278325\pi$
$710$	−229.147	+	396.893i	−0.0121123	+	0.0209791i
$711$		0			0
$712$	−5191.14	+	2997.11i	−0.273239	+	0.157755i
$713$	−1472.70	−	2550.79i	−0.0773534	−	0.133980i
$714$		0			0
$715$	1979.37	−	3428.37i	0.103530	−	0.179320i
$716$			13053.6i			0.681337i
$717$		0			0
$718$	1717.24			0.0892574
$719$	8416.91	+	14578.5i	0.436575	+	0.756171i	0.997423	−	0.0717486i	$-0.0228579\pi$
$719$	8416.91	+	14578.5i	0.436575	+	0.756171i	−0.560847	+	0.827919i	$0.689525\pi$
$720$		0			0
$721$	−10094.6	+	844.474i	−0.521417	+	0.0436197i
$722$	−87.7246	+	50.6478i	−0.00452184	+	0.00261069i
$723$		0			0
$724$	23322.0	−	13464.9i	1.19717	−	0.691189i
$725$	4120.45	−	2378.95i	0.211076	−	0.121865i
$726$		0			0
$727$	−28354.9	+	16370.7i	−1.44653	+	0.835152i	−0.998272	−	0.0587547i	$-0.981287\pi$
$727$	−28354.9	+	16370.7i	−1.44653	+	0.835152i	−0.448253	+	0.893907i	$0.647954\pi$
$728$	−697.830	−	328.641i	−0.0355265	−	0.0167311i
$729$		0			0
$730$	298.216	+	516.525i	0.0151198	+	0.0261883i
$731$	16661.6			0.843027
$732$		0			0
$733$		−	7405.70i		−	0.373173i	−0.982439	−	0.186586i	$-0.940258\pi$
$733$		−	7405.70i		−	0.373173i	0.982439	−	0.186586i	$-0.0597424\pi$
$734$	207.376	−	359.186i	0.0104283	−	0.0180624i
$735$		0			0
$736$	677.025	+	1172.64i	0.0339069	+	0.0587285i
$737$	8716.91	−	5032.71i	0.435674	−	0.251536i
$738$		0			0
$739$	6333.95	−	10970.7i	0.315288	−	0.546095i	−0.664210	−	0.747546i	$-0.731232\pi$
$739$	6333.95	−	10970.7i	0.315288	−	0.546095i	0.979499	+	0.201450i	$0.0645655\pi$
$740$	−4846.84	+	8394.98i	−0.240775	+	0.417035i
$741$		0			0
$742$	−2721.46	+	1890.20i	−0.134647	+	0.0935192i
$743$	−16940.8	−	9780.78i	−0.836471	−	0.482937i	0.0195919	−	0.999808i	$-0.493763\pi$
$743$	−16940.8	−	9780.78i	−0.836471	−	0.482937i	−0.856063	+	0.516871i	$0.827097\pi$
$744$		0			0
$745$		−	19211.9i		−	0.944794i
$746$	1162.64	+	671.249i	0.0570605	+	0.0329439i
$747$		0			0
$748$			21815.0i			1.06636i
$749$	14066.7	+	20252.9i	0.686229	+	0.988017i
$750$		0			0
$751$	−2326.49			−0.113042			−0.0565211	−	0.998401i	$-0.518001\pi$
$751$	−2326.49			−0.113042			−0.0565211	+	0.998401i	$0.518001\pi$
$752$	−15480.6	−	26813.2i	−0.750692	−	1.30024i
$753$		0			0
$754$	−127.919	−	73.8540i	−0.00617843	−	0.00356712i
$755$	18334.2			0.883774
$756$		0			0
$757$	5811.77			0.279039			0.139519	−	0.990219i	$-0.455444\pi$
$757$	5811.77			0.279039			0.139519	+	0.990219i	$0.455444\pi$
$758$	−2219.20	−	1281.26i	−0.106339	−	0.0613950i
$759$		0			0
$760$	−1054.22	−	1825.96i	−0.0503164	−	0.0871506i
$761$	−26599.4			−1.26705			−0.633526	−	0.773721i	$-0.718393\pi$
$761$	−26599.4			−1.26705			−0.633526	+	0.773721i	$0.718393\pi$
$762$		0			0
$763$	−17660.4	−	8317.11i	−0.837939	−	0.394626i
$764$			898.765i			0.0425604i
$765$		0			0
$766$	−3223.70	−	1861.21i	−0.152059	−	0.0877913i
$767$			6446.22i			0.303467i
$768$		0			0
$769$	−5505.13	−	3178.39i	−0.258153	−	0.149045i	0.365339	−	0.930875i	$-0.380953\pi$
$769$	−5505.13	−	3178.39i	−0.258153	−	0.149045i	−0.623492	+	0.781830i	$0.714287\pi$
$770$	−1684.20	−	793.171i	−0.0788239	−	0.0371220i
$771$		0			0
$772$	3474.14	−	6017.38i	0.161965	−	0.280531i
$773$	−3466.39	+	6003.96i	−0.161290	+	0.279363i	−0.935332	−	0.353772i	$-0.884899\pi$
$773$	−3466.39	+	6003.96i	−0.161290	+	0.279363i	0.774041	+	0.633135i	$0.218232\pi$
$774$		0			0
$775$	−7758.97	+	4479.64i	−0.359626	+	0.207630i
$776$	−2081.22	−	3604.78i	−0.0962776	−	0.166758i
$777$		0			0
$778$	−1169.53	+	2025.68i	−0.0538942	+	0.0933474i
$779$			2426.07i			0.111583i
$780$		0			0
$781$	17010.7			0.779372
$782$	160.507	+	278.007i	0.00733982	+	0.0127129i
$783$		0			0
$784$	7474.53	−	20059.8i	0.340494	−	0.913805i
$785$	5076.66	−	2931.01i	0.230820	−	0.133264i
$786$		0			0
$787$	−28847.2	+	16655.0i	−1.30660	+	0.754365i	−0.981527	−	0.191325i	$-0.938722\pi$
$787$	−28847.2	+	16655.0i	−1.30660	+	0.754365i	−0.325071	+	0.945689i	$0.605388\pi$
$788$	6898.84	−	3983.05i	0.311879	−	0.180064i
$789$		0			0
$790$	794.500	−	458.705i	0.0357810	−	0.0206582i
$791$	−7334.66	+	15574.2i	−0.329697	+	0.700071i
$792$		0			0
$793$	3794.20	+	6571.74i	0.169907	+	0.294287i
$794$	559.004			0.0249853
$795$		0			0
$796$		−	13300.4i		−	0.592237i
$797$	−17597.8	+	30480.4i	−0.782117	+	1.35467i	0.148589	+	0.988899i	$0.452527\pi$
$797$	−17597.8	+	30480.4i	−0.782117	+	1.35467i	−0.930706	+	0.365768i	$0.880806\pi$
$798$		0			0
$799$	−11165.9	−	19339.9i	−0.494395	−	0.856318i
$800$	3566.94	−	2059.37i	0.157638	−	0.0910123i
$801$		0			0
$802$	−38.7850	+	67.1775i	−0.00170766	+	0.00295776i
$803$	11069.0	−	19172.1i	0.486447	−	0.842551i
$804$		0			0
$805$	3263.21	−	272.988i	0.142873	−	0.0119522i
$806$	240.876	+	139.070i	0.0105267	+	0.00607758i
$807$		0			0
$808$			589.890i			0.0256835i
$809$	−17121.2	−	9884.94i	−0.744067	−	0.429587i	0.0794792	−	0.996837i	$-0.474674\pi$
$809$	−17121.2	−	9884.94i	−0.744067	−	0.429587i	−0.823546	+	0.567249i	$0.808008\pi$
$810$		0			0
$811$		−	20597.9i		−	0.891848i	−0.895071	−	0.445924i	$-0.852875\pi$
$811$		−	20597.9i		−	0.891848i	0.895071	−	0.445924i	$-0.147125\pi$
$812$	3537.62	−	7511.70i	0.152889	−	0.324642i
$813$		0			0
$814$	−3010.03			−0.129609
$815$	5151.93	+	8923.40i	0.221428	+	0.383525i
$816$		0			0
$817$	25774.4	+	14880.9i	1.10371	+	0.637228i
$818$	−1171.71			−0.0500829
$819$		0			0
$820$	1529.01			0.0651161
$821$	3722.39	+	2149.12i	0.158237	+	0.0913581i	0.577027	−	0.816725i	$-0.304213\pi$
$821$	3722.39	+	2149.12i	0.158237	+	0.0913581i	−0.418791	+	0.908083i	$0.637546\pi$
$822$		0			0
$823$	4809.41	+	8330.14i	0.203700	+	0.352819i	0.949718	−	0.313107i	$-0.101370\pi$
$823$	4809.41	+	8330.14i	0.203700	+	0.352819i	−0.746018	+	0.665926i	$0.768037\pi$
$824$	−2245.22			−0.0949221
$825$		0			0
$826$	3020.83	−	252.711i	0.127250	−	0.0106452i
$827$			28304.7i			1.19015i	0.803672	+	0.595073i	$0.202877\pi$
$827$			28304.7i			1.19015i	−0.803672	+	0.595073i	$0.797123\pi$
$828$		0			0
$829$	24753.6	+	14291.5i	1.03707	+	0.598750i	0.919001	−	0.394256i	$-0.128998\pi$
$829$	24753.6	+	14291.5i	1.03707	+	0.598750i	0.118065	+	0.993006i	$0.462331\pi$
$830$			1693.97i			0.0708415i
$831$		0			0
$832$	4276.43	+	2469.00i	0.178195	+	0.102881i
$833$	5391.26	−	14468.8i	0.224245	−	0.601819i
$834$		0			0
$835$	−5891.93	+	10205.1i	−0.244190	+	0.422949i
$836$	−19483.4	+	33746.3i	−0.806039	+	1.39610i
$837$		0			0
$838$	−306.879	+	177.177i	−0.0126503	+	0.00730366i
$839$	−16920.3	−	29306.9i	−0.696251	−	1.20594i	−0.969757	−	0.244072i	$-0.921517\pi$
$839$	−16920.3	−	29306.9i	−0.696251	−	1.20594i	0.273506	−	0.961870i	$-0.411817\pi$
$840$		0			0
$841$	−10597.9	+	18356.0i	−0.434535	+	0.752636i
$842$		−	775.486i		−	0.0317399i
$843$		0			0
$844$	−24246.8			−0.988872
$845$	6688.13	+	11584.2i	0.272282	+	0.471607i
$846$		0			0
$847$	3705.44	+	44293.7i	0.150319	+	1.79687i
$848$	37535.8	−	21671.3i	1.52003	−	0.877588i
$849$		0			0
$850$	845.641	−	488.231i	0.0341238	−	0.0197014i
$851$	4585.31	−	2647.33i	0.184703	−	0.106638i
$852$		0			0
$853$	20134.3	−	11624.6i	0.808191	−	0.466609i	−0.0381363	−	0.999273i	$-0.512142\pi$
$853$	20134.3	−	11624.6i	0.808191	−	0.466609i	0.846327	+	0.532663i	$0.178809\pi$
$854$	2930.91	−	2035.67i	0.117440	−	0.0815683i
$855$		0			0
$856$	2732.72	+	4733.22i	0.109115	+	0.188993i
$857$	21596.9			0.860836			0.430418	−	0.902630i	$-0.358366\pi$
$857$	21596.9			0.860836			0.430418	+	0.902630i	$0.358366\pi$
$858$		0			0
$859$			13653.1i			0.542302i	0.962537	+	0.271151i	$0.0874043\pi$
$859$			13653.1i			0.542302i	−0.962537	+	0.271151i	$0.912596\pi$
$860$	9378.53	−	16244.1i	0.371866	−	0.644092i
$861$		0			0
$862$	−429.701	−	744.264i	−0.0169787	−	0.0294080i
$863$	9232.02	−	5330.11i	0.364150	−	0.210242i	−0.306750	−	0.951790i	$-0.599241\pi$
$863$	9232.02	−	5330.11i	0.364150	−	0.210242i	0.670900	+	0.741548i	$0.265908\pi$
$864$		0			0
$865$	6406.26	−	11096.0i	0.251814	−	0.436155i
$866$	−460.501	+	797.612i	−0.0180698	+	0.0312979i
$867$		0			0
$868$	−6661.47	+	14144.8i	−0.260490	+	0.553118i
$869$	−29489.8	−	17025.9i	−1.15118	−	0.664632i
$870$		0			0
$871$		−	1671.93i		−	0.0650416i
$872$	−3747.00	−	2163.33i	−0.145516	−	0.0840134i
$873$		0			0
$874$			573.411i			0.0221921i
$875$	−2063.16	−	24662.3i	−0.0797113	−	0.952845i
$876$		0			0
$877$	−1529.03			−0.0588729			−0.0294364	−	0.999567i	$-0.509371\pi$
$877$	−1529.03			−0.0588729			−0.0294364	+	0.999567i	$0.509371\pi$
$878$	−780.330	−	1351.57i	−0.0299941	−	0.0519514i
$879$		0			0
$880$	21088.9	+	12175.7i	0.807847	+	0.466411i
$881$	22496.2			0.860292			0.430146	−	0.902759i	$-0.358462\pi$
$881$	22496.2			0.860292			0.430146	+	0.902759i	$0.358462\pi$
$882$		0			0
$883$	−1745.87			−0.0665381			−0.0332691	−	0.999446i	$-0.510592\pi$
$883$	−1745.87			−0.0665381			−0.0332691	+	0.999446i	$0.510592\pi$
$884$	3138.14	+	1811.80i	0.119397	+	0.0689339i
$885$		0			0
$886$	−2048.77	−	3548.57i	−0.0776858	−	0.134556i
$887$	−9173.02			−0.347238			−0.173619	−	0.984813i	$-0.555546\pi$
$887$	−9173.02			−0.347238			−0.173619	+	0.984813i	$0.555546\pi$
$888$		0			0
$889$	2141.78	+	25602.2i	0.0808022	+	0.965885i
$890$			2403.06i			0.0905063i
$891$		0			0
$892$	−28408.1	−	16401.4i	−1.06634	−	0.615650i
$893$		−	39890.1i		−	1.49482i
$894$		0			0
$895$	9101.99	+	5255.04i	0.339940	+	0.196264i
$896$	4077.39	−	8657.84i	0.152027	−	0.322810i
$897$		0			0
$898$	−436.500	+	756.040i	−0.0162207	+	0.0280951i
$899$	−3006.53	+	5207.46i	−0.111539	+	0.193191i
$900$		0			0
$901$	27073.9	−	15631.1i	1.00107	−	0.577968i
$902$	237.389	+	411.170i	0.00876296	+	0.0151779i
$903$		0			0
$904$	−1907.79	+	3304.39i	−0.0701905	+	0.121574i
$905$		−	21682.5i		−	0.796408i
$906$		0			0
$907$	14441.4			0.528688			0.264344	−	0.964429i	$-0.414845\pi$
$907$	14441.4			0.528688			0.264344	+	0.964429i	$0.414845\pi$
$908$	−17617.3	−	30514.0i	−0.643887	−	1.11525i
$909$		0			0
$910$	−253.978	+	176.401i	−0.00925197	+	0.00642598i
$911$	6737.06	−	3889.65i	0.245015	−	0.141460i	−0.372464	−	0.928046i	$-0.621487\pi$
$911$	6737.06	−	3889.65i	0.245015	−	0.141460i	0.617480	+	0.786587i	$0.288154\pi$
$912$		0			0
$913$	54451.9	−	31437.8i	1.97382	−	1.13958i
$914$	−509.020	+	293.883i	−0.0184211	+	0.0106354i
$915$		0			0
$916$	−8931.03	+	5156.33i	−0.322150	+	0.185993i
$917$	606.392	+	7248.63i	0.0218373	+	0.261037i
$918$		0			0
$919$	−18628.7	−	32265.9i	−0.668667	−	1.15817i	−0.978277	−	0.207302i	$-0.933532\pi$
$919$	−18628.7	−	32265.9i	−0.668667	−	1.15817i	0.309610	−	0.950864i	$-0.399801\pi$
$920$	725.797			0.0260096
$921$		0			0
$922$			1407.04i			0.0502585i
$923$	1412.79	−	2447.03i	0.0503820	−	0.0872642i
$924$		0			0
$925$	−8052.63	−	13947.6i	−0.286237	−	0.495776i
$926$	−2511.39	+	1449.95i	−0.0891248	+	0.0514562i
$927$		0			0
$928$	1382.15	−	2393.96i	0.0488916	−	0.0846827i
$929$	2514.38	−	4355.04i	0.0887989	−	0.153804i	−0.818205	−	0.574927i	$-0.805030\pi$
$929$	2514.38	−	4355.04i	0.0887989	−	0.153804i	0.907004	+	0.421123i	$0.138364\pi$
$930$		0			0
$931$	21262.3	−	17567.3i	0.748491	−	0.618414i
$932$	13813.7	+	7975.37i	0.485498	+	0.280302i
$933$		0			0
$934$		−	4183.29i		−	0.146554i
$935$	15211.1	+	8782.11i	0.532037	+	0.307172i
$936$		0			0
$937$		−	4765.66i		−	0.166155i	−0.996543	−	0.0830776i	$-0.973525\pi$
$937$		−	4765.66i		−	0.166155i	0.996543	−	0.0830776i	$-0.0264749\pi$
$938$	−783.503	+	65.5448i	−0.0272732	+	0.00228157i
$939$		0			0
$940$	−25140.4			−0.872328
$941$	10316.7	+	17869.1i	0.357402	+	0.619039i	0.987526	−	0.157456i	$-0.0503292\pi$
$941$	10316.7	+	17869.1i	0.357402	+	0.619039i	−0.630124	+	0.776495i	$0.716996\pi$
$942$		0			0
$943$	−723.250	−	417.569i	−0.0249759	−	0.0144198i
$944$	−39652.5			−1.36714
$945$		0			0
$946$	5824.33			0.200175
$947$	−17146.1	−	9899.28i	−0.588355	−	0.339687i	0.176092	−	0.984374i	$-0.443654\pi$
$947$	−17146.1	−	9899.28i	−0.588355	−	0.339687i	−0.764447	+	0.644687i	$0.776988\pi$
$948$		0			0
$949$	−1838.64	−	3184.61i	−0.0628921	−	0.108932i
$950$	1744.20			0.0595676
$951$		0			0
$952$	1458.12	−	3096.15i	0.0496408	−	0.105406i
$953$		−	14437.1i		−	0.490726i	−0.969431	−	0.245363i	$-0.921093\pi$
$953$		−	14437.1i		−	0.490726i	0.969431	−	0.245363i	$-0.0789072\pi$
$954$		0			0
$955$	626.687	+	361.818i	0.0212347	+	0.0122599i
$956$			41217.1i			1.39441i
$957$		0			0
$958$	1398.12	+	807.205i	0.0471516	+	0.0272230i
$959$	38420.5	−	3214.11i	1.29371	−	0.108226i
$960$		0			0
$961$	−9234.10	+	15993.9i	−0.309963	+	0.536871i
$962$	−249.993	+	433.000i	−0.00837847	+	0.0145119i
$963$		0			0
$964$	46307.1	−	26735.4i	1.54715	−	0.893246i
$965$	−2797.18	−	4844.87i	−0.0933104	−	0.161618i
$966$		0			0
$967$	24854.3	−	43049.0i	0.826537	−	1.43160i	−0.0742011	−	0.997243i	$-0.523641\pi$
$967$	24854.3	−	43049.0i	0.826537	−	1.43160i	0.900739	−	0.434362i	$-0.143026\pi$
$968$			9851.70i			0.327113i
$969$		0			0
$970$	−1668.70			−0.0552359
$971$	−25649.0	−	44425.3i	−0.847698	−	1.46826i	−0.883258	−	0.468888i	$-0.844655\pi$
$971$	−25649.0	−	44425.3i	−0.847698	−	1.46826i	0.0355601	−	0.999368i	$-0.488678\pi$
$972$		0			0
$973$	9917.81	−	21059.2i	0.326773	−	0.693863i
$974$	117.278	−	67.7104i	0.00385814	−	0.00222750i
$975$		0			0
$976$	−40424.7	+	23339.2i	−1.32578	+	0.765440i
$977$	−8697.33	+	5021.41i	−0.284803	+	0.164431i	−0.635596	−	0.772022i	$-0.719245\pi$
$977$	−8697.33	+	5021.41i	−0.284803	+	0.164431i	0.350793	+	0.936453i	$0.385912\pi$
$978$		0			0
$979$	77245.4	−	44597.6i	2.52173	−	1.45592i
$980$	−11071.6	−	13400.4i	−0.360887	−	0.436796i
$981$		0			0
$982$	1997.05	+	3458.99i	0.0648966	+	0.112404i
$983$	−7076.64			−0.229613			−0.114807	−	0.993388i	$-0.536625\pi$
$983$	−7076.64			−0.229613			−0.114807	+	0.993388i	$0.536625\pi$
$984$		0			0
$985$		−	6413.86i		−	0.207475i
$986$	327.677	−	567.554i	0.0105835	−	0.0183312i
$987$		0			0
$988$	3236.32	+	5605.48i	0.104212	+	0.180500i
$989$	−8872.46	+	5122.52i	−0.285266	+	0.164698i
$990$		0			0
$991$	−13272.9	+	22989.4i	−0.425457	+	0.736913i	−0.996463	−	0.0840327i	$-0.973220\pi$
$991$	−13272.9	+	22989.4i	−0.425457	+	0.736913i	0.571006	+	0.820946i	$0.306553\pi$
$992$	−2602.65	+	4507.92i	−0.0833005	+	0.144281i
$993$		0			0
$994$	−1202.11	−	566.133i	−0.0383589	−	0.0180650i
$995$	−9274.06	−	5354.38i	−0.295485	−	0.170598i
$996$		0			0
$997$			27496.8i			0.873451i	0.899595	+	0.436726i	$0.143862\pi$
$997$			27496.8i			0.873451i	−0.899595	+	0.436726i	$0.856138\pi$
$998$	2079.54	+	1200.62i	0.0659584	+	0.0380811i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.12		44
3.2	odd	2		63.4.s.a.59.11	yes	44
7.5	odd	6		189.4.i.a.152.11		44
9.2	odd	6		189.4.i.a.143.12		44
9.7	even	3		63.4.i.a.38.11	yes	44
21.5	even	6		63.4.i.a.5.12	✓	44
63.47	even	6	inner	189.4.s.a.89.12		44
63.61	odd	6		63.4.s.a.47.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.12	✓	44	21.5	even	6
63.4.i.a.38.11	yes	44	9.7	even	3
63.4.s.a.47.11	yes	44	63.61	odd	6
63.4.s.a.59.11	yes	44	3.2	odd	2
189.4.i.a.143.12		44	9.2	odd	6
189.4.i.a.152.11		44	7.5	odd	6
189.4.s.a.17.12		44	1.1	even	1	trivial
189.4.s.a.89.12		44	63.47	even	6	inner

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.223110 + 0.128812i) q^{2} +(-3.96681 - 6.87072i) q^{4} -6.38772 q^{5} +(-1.54394 - 18.4558i) q^{7} -4.10490i q^{8} +O(q^{10})\)	\(q+(0.223110 + 0.128812i) q^{2} +(-3.96681 - 6.87072i) q^{4} -6.38772 q^{5} +(-1.54394 - 18.4558i) q^{7} -4.10490i q^{8} +(-1.42516 - 0.822818i) q^{10} +61.0818i q^{11} +(8.78677 + 5.07304i) q^{13} +(2.03287 - 4.31654i) q^{14} +(-31.2058 + 54.0500i) q^{16} +(-22.5082 + 38.9853i) q^{17} +(-69.6373 + 40.2051i) q^{19} +(25.3389 + 43.8883i) q^{20} +(-7.86810 + 13.6279i) q^{22} -27.6800i q^{23} -84.1970 q^{25} +(1.30694 + 2.26369i) q^{26} +(-120.680 + 83.8187i) q^{28} +(-48.9383 + 28.2545i) q^{29} +(92.1526 - 53.2043i) q^{31} +(-42.3642 + 24.4590i) q^{32} +(-10.0436 + 5.79867i) q^{34} +(9.86226 + 117.890i) q^{35} +(95.6403 + 165.654i) q^{37} -20.7157 q^{38} +26.2210i q^{40} +(15.0856 - 26.1289i) q^{41} +(-185.062 - 320.536i) q^{43} +(419.676 - 242.300i) q^{44} +(3.56553 - 6.17569i) q^{46} +(-248.041 + 429.620i) q^{47} +(-338.232 + 56.9893i) q^{49} +(-18.7852 - 10.8456i) q^{50} -80.4953i q^{52} +(-601.424 - 347.232i) q^{53} -390.174i q^{55} +(-75.7592 + 6.33772i) q^{56} -14.5581 q^{58} +(317.670 + 550.221i) q^{59} +(647.712 + 373.957i) q^{61} +27.4135 q^{62} +486.690 q^{64} +(-56.1274 - 32.4052i) q^{65} +(-82.3930 - 142.709i) q^{67} +357.143 q^{68} +(-12.9854 + 27.5729i) q^{70} -278.490i q^{71} +(-313.876 - 181.216i) q^{73} +49.2787i q^{74} +(552.477 + 318.973i) q^{76} +(1127.31 - 94.3066i) q^{77} +(-278.740 + 482.792i) q^{79} +(199.334 - 345.256i) q^{80} +(6.73147 - 3.88641i) q^{82} +(-514.684 - 891.459i) q^{83} +(143.776 - 249.028i) q^{85} -95.3530i q^{86} +250.735 q^{88} +(-730.130 - 1264.62i) q^{89} +(80.0608 - 169.999i) q^{91} +(-190.182 + 109.802i) q^{92} +(-110.681 + 63.9015i) q^{94} +(444.824 - 256.819i) q^{95} +(878.164 - 507.008i) q^{97} +(-82.8039 - 30.8537i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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