LMFDB - Embedded newform 189.3.j.b.44.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.j (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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.11
Character	$\chi$	$=$	189.44
Dual form			189.3.j.b.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.87176i q^{2} -4.24700 q^{4} +(6.53753 - 3.77444i) q^{5} +(2.05575 - 6.69133i) q^{7} -0.709334i q^{8} +O(q^{10})$	\(q+2.87176i q^{2} -4.24700 q^{4} +(6.53753 - 3.77444i) q^{5} +(2.05575 - 6.69133i) q^{7} -0.709334i q^{8} +(10.8393 + 18.7742i) q^{10} +(13.1630 + 7.59968i) q^{11} +(4.30409 - 7.45491i) q^{13} +(19.2159 + 5.90361i) q^{14} -14.9510 q^{16} +(4.60986 - 2.66151i) q^{17} +(-0.417241 + 0.722683i) q^{19} +(-27.7649 + 16.0301i) q^{20} +(-21.8244 + 37.8010i) q^{22} +(-33.8873 + 19.5648i) q^{23} +(15.9929 - 27.7005i) q^{25} +(21.4087 + 12.3603i) q^{26} +(-8.73076 + 28.4181i) q^{28} +(-12.5660 + 7.25497i) q^{29} +12.7419 q^{31} -45.7729i q^{32} +(7.64320 + 13.2384i) q^{34} +(-11.8165 - 51.5041i) q^{35} +(-11.7490 + 20.3498i) q^{37} +(-2.07537 - 1.19822i) q^{38} +(-2.67734 - 4.63730i) q^{40} +(13.4288 + 7.75311i) q^{41} +(0.448287 + 0.776457i) q^{43} +(-55.9034 - 32.2759i) q^{44} +(-56.1855 - 97.3162i) q^{46} +2.35402i q^{47} +(-40.5478 - 27.5114i) q^{49} +(79.5491 + 45.9277i) q^{50} +(-18.2795 + 31.6610i) q^{52} +(31.4529 - 18.1593i) q^{53} +114.738 q^{55} +(-4.74639 - 1.45821i) q^{56} +(-20.8345 - 36.0864i) q^{58} +48.6111i q^{59} -29.6074 q^{61} +36.5917i q^{62} +71.6450 q^{64} -64.9823i q^{65} +92.5333 q^{67} +(-19.5781 + 11.3034i) q^{68} +(147.907 - 33.9343i) q^{70} -15.1629i q^{71} +(-46.8054 - 81.0693i) q^{73} +(-58.4398 - 33.7402i) q^{74} +(1.77203 - 3.06924i) q^{76} +(77.9118 - 72.4551i) q^{77} -82.1651 q^{79} +(-97.7425 + 56.4316i) q^{80} +(-22.2651 + 38.5642i) q^{82} +(-127.067 + 73.3621i) q^{83} +(20.0914 - 34.7993i) q^{85} +(-2.22980 + 1.28737i) q^{86} +(5.39071 - 9.33699i) q^{88} +(-92.3105 - 53.2955i) q^{89} +(-41.0351 - 44.1255i) q^{91} +(143.920 - 83.0920i) q^{92} -6.76019 q^{94} +6.29942i q^{95} +(-26.0332 - 45.0908i) q^{97} +(79.0060 - 116.444i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) $ 22 * q - 24 * q^4 - 12 * q^5	$ 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) $ 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			2.87176i			1.43588i	0.696105	+	0.717940i	$0.254915\pi$
$2$			2.87176i			1.43588i	−0.696105	+	0.717940i	$0.745085\pi$
$3$		0			0
$3$		0			0
$4$	−4.24700			−1.06175
$5$	6.53753	−	3.77444i	1.30751	−	0.754889i	0.325827	−	0.945430i	$-0.394357\pi$
$5$	6.53753	−	3.77444i	1.30751	−	0.754889i	0.981679	+	0.190541i	$0.0610241\pi$
$6$		0			0
$7$	2.05575	−	6.69133i	0.293678	−	0.955904i
$7$	2.05575	−	6.69133i	0.293678	−	0.955904i
$8$		−	0.709334i		−	0.0886668i
$9$		0			0
$10$	10.8393	+	18.7742i	1.08393	+	1.87742i
$11$	13.1630	+	7.59968i	1.19664	+	0.690880i	0.959804	−	0.280670i	$-0.0905567\pi$
$11$	13.1630	+	7.59968i	1.19664	+	0.690880i	0.236835	+	0.971550i	$0.423890\pi$
$12$		0			0
$13$	4.30409	−	7.45491i	0.331084	−	0.573455i	−0.651641	−	0.758528i	$-0.725919\pi$
$13$	4.30409	−	7.45491i	0.331084	−	0.573455i	0.982725	+	0.185073i	$0.0592522\pi$
$14$	19.2159	+	5.90361i	1.37256	+	0.421687i
$15$		0			0
$16$	−14.9510			−0.934436
$17$	4.60986	−	2.66151i	0.271168	−	0.156559i	−0.358250	−	0.933626i	$-0.616626\pi$
$17$	4.60986	−	2.66151i	0.271168	−	0.156559i	0.629419	+	0.777066i	$0.283293\pi$
$18$		0			0
$19$	−0.417241	+	0.722683i	−0.0219601	+	0.0380360i	−0.876797	−	0.480861i	$-0.840324\pi$
$19$	−0.417241	+	0.722683i	−0.0219601	+	0.0380360i	0.854837	+	0.518897i	$0.173657\pi$
$20$	−27.7649	+	16.0301i	−1.38825	+	0.801504i
$21$		0			0
$22$	−21.8244	+	37.8010i	−0.992020	+	1.71823i
$23$	−33.8873	+	19.5648i	−1.47336	+	0.850646i	−0.999550	−	0.0299810i	$-0.990455\pi$
$23$	−33.8873	+	19.5648i	−1.47336	+	0.850646i	−0.473811	+	0.880627i	$0.657122\pi$
$24$		0			0
$25$	15.9929	−	27.7005i	0.639715	−	1.10802i
$26$	21.4087	+	12.3603i	0.823412	+	0.475397i
$27$		0			0
$28$	−8.73076	+	28.4181i	−0.311813	+	1.01493i
$29$	−12.5660	+	7.25497i	−0.433309	+	0.250171i	−0.700755	−	0.713402i	$-0.747154\pi$
$29$	−12.5660	+	7.25497i	−0.433309	+	0.250171i	0.267446	+	0.963573i	$0.413820\pi$
$30$		0			0
$31$	12.7419			0.411029			0.205515	−	0.978654i	$-0.434113\pi$
$31$	12.7419			0.411029			0.205515	+	0.978654i	$0.434113\pi$
$32$		−	45.7729i		−	1.43040i
$33$		0			0
$34$	7.64320	+	13.2384i	0.224800	+	0.389365i
$35$	−11.8165	−	51.5041i	−0.337616	−	1.47155i
$36$		0			0
$37$	−11.7490	+	20.3498i	−0.317540	+	0.549995i	−0.979974	−	0.199125i	$-0.936190\pi$
$37$	−11.7490	+	20.3498i	−0.317540	+	0.549995i	0.662434	+	0.749120i	$0.269523\pi$
$38$	−2.07537	−	1.19822i	−0.0546151	−	0.0315320i
$39$		0			0
$40$	−2.67734	−	4.63730i	−0.0669336	−	0.115932i
$41$	13.4288	+	7.75311i	0.327531	+	0.189100i	0.654744	−	0.755850i	$-0.272776\pi$
$41$	13.4288	+	7.75311i	0.327531	+	0.189100i	−0.327213	+	0.944951i	$0.606110\pi$
$42$		0			0
$43$	0.448287	+	0.776457i	0.0104253	+	0.0180571i	0.871191	−	0.490944i	$-0.163348\pi$
$43$	0.448287	+	0.776457i	0.0104253	+	0.0180571i	−0.860766	+	0.509001i	$0.830015\pi$
$44$	−55.9034	−	32.2759i	−1.27053	−	0.733542i
$45$		0			0
$46$	−56.1855	−	97.3162i	−1.22142	−	2.11557i
$47$			2.35402i			0.0500856i	0.999686	+	0.0250428i	$0.00797220\pi$
$47$			2.35402i			0.0500856i	−0.999686	+	0.0250428i	$0.992028\pi$
$48$		0			0
$49$	−40.5478	−	27.5114i	−0.827506	−	0.561456i
$50$	79.5491	+	45.9277i	1.59098	+	0.918553i
$51$		0			0
$52$	−18.2795	+	31.6610i	−0.351529	+	0.608866i
$53$	31.4529	−	18.1593i	0.593451	−	0.342629i	−0.173010	−	0.984920i	$-0.555349\pi$
$53$	31.4529	−	18.1593i	0.593451	−	0.342629i	0.766461	+	0.642291i	$0.222016\pi$
$54$		0			0
$55$	114.738			2.08615
$56$	−4.74639	−	1.45821i	−0.0847570	−	0.0260395i
$57$		0			0
$58$	−20.8345	−	36.0864i	−0.359216	−	0.622180i
$59$			48.6111i			0.823917i	0.911203	+	0.411958i	$0.135155\pi$
$59$			48.6111i			0.823917i	−0.911203	+	0.411958i	$0.864845\pi$
$60$		0			0
$61$	−29.6074			−0.485367			−0.242683	−	0.970106i	$-0.578028\pi$
$61$	−29.6074			−0.485367			−0.242683	+	0.970106i	$0.578028\pi$
$62$			36.5917i			0.590189i
$63$		0			0
$64$	71.6450			1.11945
$65$		−	64.9823i		−	0.999727i
$66$		0			0
$67$	92.5333			1.38109			0.690547	−	0.723287i	$-0.257370\pi$
$67$	92.5333			1.38109			0.690547	+	0.723287i	$0.257370\pi$
$68$	−19.5781	+	11.3034i	−0.287913	+	0.166227i
$69$		0			0
$70$	147.907	−	33.9343i	2.11296	−	0.484776i
$71$		−	15.1629i		−	0.213562i	−0.994283	−	0.106781i	$-0.965946\pi$
$71$		−	15.1629i		−	0.213562i	0.994283	−	0.106781i	$-0.0340544\pi$
$72$		0			0
$73$	−46.8054	−	81.0693i	−0.641170	−	1.11054i	−0.985172	−	0.171570i	$-0.945116\pi$
$73$	−46.8054	−	81.0693i	−0.641170	−	1.11054i	0.344002	−	0.938969i	$-0.388217\pi$
$74$	−58.4398	−	33.7402i	−0.789726	−	0.455949i
$75$		0			0
$76$	1.77203	−	3.06924i	0.0233161	−	0.0403847i
$77$	77.9118	−	72.4551i	1.01184	−	0.940976i
$78$		0			0
$79$	−82.1651			−1.04006			−0.520032	−	0.854147i	$-0.674080\pi$
$79$	−82.1651			−1.04006			−0.520032	+	0.854147i	$0.674080\pi$
$80$	−97.7425	+	56.4316i	−1.22178	+	0.705395i
$81$		0			0
$82$	−22.2651	+	38.5642i	−0.271525	+	0.470295i
$83$	−127.067	+	73.3621i	−1.53093	+	0.883881i	−0.531607	+	0.846991i	$0.678412\pi$
$83$	−127.067	+	73.3621i	−1.53093	+	0.883881i	−0.999319	+	0.0368900i	$0.988255\pi$
$84$		0			0
$85$	20.0914	−	34.7993i	0.236370	−	0.409404i
$86$	−2.22980	+	1.28737i	−0.0259279	+	0.0149695i
$87$		0			0
$88$	5.39071	−	9.33699i	0.0612581	−	0.106102i
$89$	−92.3105	−	53.2955i	−1.03720	−	0.598826i	−0.118159	−	0.992995i	$-0.537699\pi$
$89$	−92.3105	−	53.2955i	−1.03720	−	0.598826i	−0.919038	+	0.394169i	$0.871033\pi$
$90$		0			0
$91$	−41.0351	−	44.1255i	−0.450936	−	0.484896i
$92$	143.920	−	83.0920i	1.56434	−	0.903174i
$93$		0			0
$94$	−6.76019			−0.0719169
$95$			6.29942i			0.0663097i
$96$		0			0
$97$	−26.0332	−	45.0908i	−0.268383	−	0.464854i	0.700061	−	0.714083i	$-0.253156\pi$
$97$	−26.0332	−	45.0908i	−0.268383	−	0.464854i	−0.968445	+	0.249229i	$0.919823\pi$
$98$	79.0060	−	116.444i	0.806184	−	1.18820i
$99$		0			0
$100$	−67.9218	+	117.644i	−0.679218	+	1.17644i
$101$	79.2124	+	45.7333i	0.784281	+	0.452805i	0.837945	−	0.545754i	$-0.183757\pi$
$101$	79.2124	+	45.7333i	0.784281	+	0.452805i	−0.0536643	+	0.998559i	$0.517090\pi$
$102$		0			0
$103$	−9.71277	−	16.8230i	−0.0942987	−	0.163330i	0.815017	−	0.579437i	$-0.196728\pi$
$103$	−9.71277	−	16.8230i	−0.0942987	−	0.163330i	−0.909316	+	0.416107i	$0.863394\pi$
$104$	−5.28803	−	3.05304i	−0.0508464	−	0.0293562i
$105$		0			0
$106$	52.1493	+	90.3252i	0.491974	+	0.852124i
$107$	94.9880	+	54.8414i	0.887738	+	0.512536i	0.873202	−	0.487358i	$-0.162039\pi$
$107$	94.9880	+	54.8414i	0.887738	+	0.512536i	0.0145363	+	0.999894i	$0.495373\pi$
$108$		0			0
$109$	−33.2718	−	57.6285i	−0.305246	−	0.528702i	0.672070	−	0.740488i	$-0.265405\pi$
$109$	−33.2718	−	57.6285i	−0.305246	−	0.528702i	−0.977316	+	0.211786i	$0.932072\pi$
$110$			329.501i			2.99546i
$111$		0			0
$112$	−30.7354	+	100.042i	−0.274423	+	0.893231i
$113$	−136.951	−	79.0689i	−1.21196	−	0.699725i	−0.248773	−	0.968562i	$-0.580027\pi$
$113$	−136.951	−	79.0689i	−1.21196	−	0.699725i	−0.963186	+	0.268837i	$0.913361\pi$
$114$		0			0
$115$	−147.693	+	255.812i	−1.28429	+	2.22445i
$116$	53.3677	−	30.8119i	0.460066	−	0.265619i
$117$		0			0
$118$	−139.599			−1.18305
$119$	−8.33230	−	36.3175i	−0.0700193	−	0.305189i
$120$		0			0
$121$	55.0102	+	95.2804i	0.454630	+	0.787442i
$122$		−	85.0253i		−	0.696928i
$123$		0			0
$124$	−54.1149			−0.436411
$125$		−	52.7346i		−	0.421876i
$126$		0			0
$127$	1.39373			0.0109742			0.00548712	−	0.999985i	$-0.498253\pi$
$127$	1.39373			0.0109742			0.00548712	+	0.999985i	$0.498253\pi$
$128$			22.6554i			0.176996i
$129$		0			0
$130$	186.613			1.43549
$131$	−67.4799	+	38.9596i	−0.515114	+	0.297401i	−0.734933	−	0.678139i	$-0.762787\pi$
$131$	−67.4799	+	38.9596i	−0.515114	+	0.297401i	0.219819	+	0.975541i	$0.429453\pi$
$132$		0			0
$133$	3.97797	+	4.27755i	0.0299096	+	0.0321621i
$134$			265.734i			1.98309i
$135$		0			0
$136$	−1.88790	−	3.26993i	−0.0138816	−	0.0240436i
$137$	−181.021	−	104.512i	−1.32132	−	0.762865i	−0.337381	−	0.941368i	$-0.609541\pi$
$137$	−181.021	−	104.512i	−1.32132	−	0.762865i	−0.983939	+	0.178503i	$0.942875\pi$
$138$		0			0
$139$	−95.9201	+	166.138i	−0.690073	+	1.19524i	0.281741	+	0.959490i	$0.409088\pi$
$139$	−95.9201	+	166.138i	−0.690073	+	1.19524i	−0.971814	+	0.235750i	$0.924245\pi$
$140$	50.1849	+	218.738i	0.358464	+	1.56241i
$141$		0			0
$142$	43.5443			0.306650
$143$	113.310	−	65.4195i	0.792376	−	0.457479i
$144$		0			0
$145$	−54.7669	+	94.8591i	−0.377703	+	0.654201i
$146$	232.812	−	134.414i	1.59460	−	0.920643i
$147$		0			0
$148$	49.8979	−	86.4257i	0.337148	−	0.583957i
$149$	−66.5560	+	38.4261i	−0.446684	+	0.257893i	−0.706429	−	0.707784i	$-0.749695\pi$
$149$	−66.5560	+	38.4261i	−0.446684	+	0.257893i	0.259745	+	0.965677i	$0.416362\pi$
$150$		0			0
$151$	40.3574	−	69.9011i	0.267268	−	0.462921i	−0.700888	−	0.713272i	$-0.747213\pi$
$151$	40.3574	−	69.9011i	0.267268	−	0.462921i	0.968155	+	0.250351i	$0.0805459\pi$
$152$	0.512624	+	0.295964i	0.00337253	+	0.00194713i
$153$		0			0
$154$	208.074	+	223.744i	1.35113	+	1.45288i
$155$	83.3006	−	48.0936i	0.537423	−	0.310282i
$156$		0			0
$157$	216.878			1.38139			0.690694	−	0.723148i	$-0.257305\pi$
$157$	216.878			1.38139			0.690694	+	0.723148i	$0.257305\pi$
$158$		−	235.958i		−	1.49341i
$159$		0			0
$160$	−172.767	−	299.242i	−1.07980	−	1.87026i
$161$	61.2511	+	266.972i	0.380442	+	1.65821i
$162$		0			0
$163$	125.344	−	217.102i	0.768982	−	1.33192i	−0.169133	−	0.985593i	$-0.554097\pi$
$163$	125.344	−	217.102i	0.768982	−	1.33192i	0.938115	−	0.346323i	$-0.112570\pi$
$164$	−57.0321	−	32.9275i	−0.347757	−	0.200777i
$165$		0			0
$166$	−210.678	−	364.906i	−1.26915	−	2.19823i
$167$	134.712	+	77.7761i	0.806660	+	0.465725i	0.845795	−	0.533509i	$-0.179127\pi$
$167$	134.712	+	77.7761i	0.806660	+	0.465725i	−0.0391347	+	0.999234i	$0.512460\pi$
$168$		0			0
$169$	47.4495	+	82.1850i	0.280766	+	0.486302i
$170$	99.9354	+	57.6977i	0.587855	+	0.339398i
$171$		0			0
$172$	−1.90388	−	3.29761i	−0.0110691	−	0.0191722i
$173$		−	63.6335i		−	0.367824i	−0.982943	−	0.183912i	$-0.941124\pi$
$173$		−	63.6335i		−	0.367824i	0.982943	−	0.183912i	$-0.0588761\pi$
$174$		0			0
$175$	−152.476	−	163.959i	−0.871289	−	0.936907i
$176$	−196.800	−	113.623i	−1.11818	−	0.645583i
$177$		0			0
$178$	153.052	−	265.094i	0.859842	−	1.48929i
$179$	−192.374	+	111.067i	−1.07472	+	0.620488i	−0.929466	−	0.368908i	$-0.879732\pi$
$179$	−192.374	+	111.067i	−1.07472	+	0.620488i	−0.145250	+	0.989395i	$0.546399\pi$
$180$		0			0
$181$	107.156			0.592024			0.296012	−	0.955184i	$-0.404343\pi$
$181$	107.156			0.592024			0.296012	+	0.955184i	$0.404343\pi$
$182$	126.718	−	117.843i	0.696252	−	0.647489i
$183$		0			0
$184$	13.8780	+	24.0374i	0.0754240	+	0.130638i
$185$			177.383i			0.958829i
$186$		0			0
$187$	80.9063			0.432654
$188$		−	9.99754i		−	0.0531784i
$189$		0			0
$190$	−18.0904			−0.0952127
$191$		−	18.8994i		−	0.0989499i	−0.998775	−	0.0494749i	$-0.984245\pi$
$191$		−	18.8994i		−	0.0989499i	0.998775	−	0.0494749i	$-0.0157548\pi$
$192$		0			0
$193$	−66.7243			−0.345722			−0.172861	−	0.984946i	$-0.555301\pi$
$193$	−66.7243			−0.345722			−0.172861	+	0.984946i	$0.555301\pi$
$194$	129.490	−	74.7611i	0.667474	−	0.385366i
$195$		0			0
$196$	172.207	+	116.841i	0.878606	+	0.596127i
$197$		−	173.048i		−	0.878418i	−0.898385	−	0.439209i	$-0.855259\pi$
$197$		−	173.048i		−	0.878418i	0.898385	−	0.439209i	$-0.144741\pi$
$198$		0			0
$199$	143.738	+	248.961i	0.722300	+	1.25106i	0.960076	+	0.279740i	$0.0902482\pi$
$199$	143.738	+	248.961i	0.722300	+	1.25106i	−0.237776	+	0.971320i	$0.576418\pi$
$200$	−19.6489	−	11.3443i	−0.0982445	−	0.0567215i
$201$		0			0
$202$	−131.335	+	227.479i	−0.650173	+	1.12613i
$203$	22.7129	+	98.9974i	0.111886	+	0.487672i
$204$		0			0
$205$	117.055			0.570999
$206$	48.3116	−	27.8927i	0.234522	−	0.135402i
$207$		0			0
$208$	−64.3504	+	111.458i	−0.309377	+	0.535857i
$209$	−10.9843	+	6.34180i	−0.0525566	+	0.0303435i
$210$		0			0
$211$	−198.426	+	343.684i	−0.940407	+	1.62883i	−0.175709	+	0.984442i	$0.556222\pi$
$211$	−198.426	+	343.684i	−0.940407	+	1.62883i	−0.764697	+	0.644390i	$0.777111\pi$
$212$	−133.581	+	77.1228i	−0.630097	+	0.363787i
$213$		0			0
$214$	−157.491	+	272.783i	−0.735940	+	1.27469i
$215$	5.86138	+	3.38407i	0.0272623	+	0.0157399i
$216$		0			0
$217$	26.1941	−	85.2603i	0.120710	−	0.392905i
$218$	165.495	−	95.5487i	0.759153	−	0.438297i
$219$		0			0
$220$	−487.294			−2.21497
$221$		−	45.8215i		−	0.207337i
$222$		0			0
$223$	−221.175	−	383.086i	−0.991816	−	1.71787i	−0.606481	−	0.795098i	$-0.707419\pi$
$223$	−221.175	−	383.086i	−0.991816	−	1.71787i	−0.385335	−	0.922777i	$-0.625914\pi$
$224$	−306.282	−	94.0976i	−1.36733	−	0.420079i
$225$		0			0
$226$	227.067	−	393.291i	1.00472	−	1.74023i
$227$	19.5806	+	11.3049i	0.0862583	+	0.0498012i	0.542509	−	0.840050i	$-0.317475\pi$
$227$	19.5806	+	11.3049i	0.0862583	+	0.0498012i	−0.456250	+	0.889851i	$0.650808\pi$
$228$		0			0
$229$	37.6161	+	65.1531i	0.164263	+	0.284511i	0.936393	−	0.350953i	$-0.114142\pi$
$229$	37.6161	+	65.1531i	0.164263	+	0.284511i	−0.772131	+	0.635464i	$0.780809\pi$
$230$	−734.629	−	424.138i	−3.19404	−	1.84408i
$231$		0			0
$232$	5.14620	+	8.91347i	0.0221819	+	0.0384201i
$233$	176.604	+	101.963i	0.757959	+	0.437608i	0.828562	−	0.559897i	$-0.189159\pi$
$233$	176.604	+	101.963i	0.757959	+	0.437608i	−0.0706034	+	0.997504i	$0.522492\pi$
$234$		0			0
$235$	8.88513	+	15.3895i	0.0378091	+	0.0654872i
$236$		−	206.451i		−	0.874794i
$237$		0			0
$238$	104.295	−	23.9284i	0.438215	−	0.100539i
$239$	206.615	+	119.289i	0.864498	+	0.499118i	0.865516	−	0.500881i	$-0.166991\pi$
$239$	206.615	+	119.289i	0.864498	+	0.499118i	−0.00101792	+	0.999999i	$0.500324\pi$
$240$		0			0
$241$	178.663	−	309.453i	0.741340	−	1.28404i	−0.210546	−	0.977584i	$-0.567524\pi$
$241$	178.663	−	309.453i	0.741340	−	1.28404i	0.951886	−	0.306454i	$-0.0991425\pi$
$242$	−273.622	+	157.976i	−1.13067	+	0.652793i
$243$		0			0
$244$	125.743			0.515339
$245$	−368.923	−	26.8109i	−1.50581	−	0.109432i
$246$		0			0
$247$	3.59169	+	6.22100i	0.0145413	+	0.0251862i
$248$		−	9.03828i		−	0.0364447i
$249$		0			0
$250$	151.441			0.605764
$251$		−	257.530i		−	1.02602i	−0.858384	−	0.513008i	$-0.828531\pi$
$251$		−	257.530i		−	1.02602i	0.858384	−	0.513008i	$-0.171469\pi$
$252$		0			0
$253$	−594.746			−2.35078
$254$			4.00245i			0.0157577i
$255$		0			0
$256$	221.519			0.865309
$257$	−36.4327	+	21.0344i	−0.141761	+	0.0818459i	−0.569203	−	0.822197i	$-0.692748\pi$
$257$	−36.4327	+	21.0344i	−0.141761	+	0.0818459i	0.427442	+	0.904043i	$0.359415\pi$
$258$		0			0
$259$	112.014	+	120.450i	0.432488	+	0.465059i
$260$			275.980i			1.06146i
$261$		0			0
$262$	−111.882	−	193.786i	−0.427032	−	0.739642i
$263$	347.913	+	200.868i	1.32286	+	0.763755i	0.984184	−	0.177147i	$-0.0566867\pi$
$263$	347.913	+	200.868i	1.32286	+	0.763755i	0.338679	+	0.940902i	$0.390020\pi$
$264$		0			0
$265$	137.083	−	237.434i	0.517294	−	0.895979i
$266$	−12.2841	+	11.4238i	−0.0461809	+	0.0429465i
$267$		0			0
$268$	−392.989			−1.46638
$269$	317.698	−	183.423i	1.18103	−	0.681871i	0.224781	−	0.974409i	$-0.427833\pi$
$269$	317.698	−	183.423i	1.18103	−	0.681871i	0.956254	+	0.292539i	$0.0945000\pi$
$270$		0			0
$271$	−50.7938	+	87.9774i	−0.187431	+	0.324640i	−0.944393	−	0.328819i	$-0.893349\pi$
$271$	−50.7938	+	87.9774i	−0.187431	+	0.324640i	0.756962	+	0.653459i	$0.226683\pi$
$272$	−68.9220	+	39.7921i	−0.253390	+	0.146295i
$273$		0			0
$274$	300.135	−	519.849i	1.09538	−	1.89726i
$275$	421.029	−	243.081i	1.53101	−	0.883932i
$276$		0			0
$277$	−46.9665	+	81.3484i	−0.169554	+	0.293676i	−0.938263	−	0.345922i	$-0.887566\pi$
$277$	−46.9665	+	81.3484i	−0.169554	+	0.293676i	0.768709	+	0.639599i	$0.220899\pi$
$278$	−477.110	−	275.459i	−1.71622	−	0.990861i
$279$		0			0
$280$	−36.5336	+	8.38189i	−0.130477	+	0.0299353i
$281$	−75.0040	+	43.3036i	−0.266918	+	0.154105i	−0.627486	−	0.778628i	$-0.715916\pi$
$281$	−75.0040	+	43.3036i	−0.266918	+	0.154105i	0.360568	+	0.932733i	$0.382583\pi$
$282$		0			0
$283$	120.582			0.426084			0.213042	−	0.977043i	$-0.431663\pi$
$283$	120.582			0.426084			0.213042	+	0.977043i	$0.431663\pi$
$284$			64.3970i			0.226750i
$285$		0			0
$286$	187.869	+	325.399i	0.656885	+	1.13776i
$287$	79.4848	−	73.9180i	0.276950	−	0.257554i
$288$		0			0
$289$	−130.333	+	225.743i	−0.450978	+	0.781118i
$290$	−272.413	−	157.277i	−0.939354	−	0.542336i
$291$		0			0
$292$	198.783	+	344.302i	0.680763	+	1.17912i
$293$	142.031	+	82.0014i	0.484746	+	0.279868i	0.722392	−	0.691483i	$-0.243042\pi$
$293$	142.031	+	82.0014i	0.484746	+	0.279868i	−0.237646	+	0.971352i	$0.576376\pi$
$294$		0			0
$295$	183.480	+	317.796i	0.621966	+	1.07728i
$296$	14.4348	+	8.33395i	0.0487663	+	0.0281552i
$297$		0			0
$298$	−110.351	−	191.133i	−0.370304	−	0.641385i
$299$			336.836i			1.12654i
$300$		0			0
$301$	6.11709	−	1.40344i	0.0203226	−	0.00466259i
$302$	200.739	+	115.897i	0.664699	+	0.383764i
$303$		0			0
$304$	6.23817	−	10.8048i	0.0205203	−	0.0355422i
$305$	−193.559	+	111.751i	−0.634620	+	0.366398i
$306$		0			0
$307$	395.153			1.28714			0.643572	−	0.765386i	$-0.277452\pi$
$307$	395.153			1.28714			0.643572	+	0.765386i	$0.277452\pi$
$308$	−330.892	+	307.717i	−1.07432	+	0.999082i
$309$		0			0
$310$	138.113	+	239.219i	0.445527	+	0.771675i
$311$			317.877i			1.02211i	0.859547	+	0.511056i	$0.170746\pi$
$311$			317.877i			1.02211i	−0.859547	+	0.511056i	$0.829254\pi$
$312$		0			0
$313$	19.8956			0.0635643			0.0317822	−	0.999495i	$-0.489882\pi$
$313$	19.8956			0.0635643			0.0317822	+	0.999495i	$0.489882\pi$
$314$			622.821i			1.98351i
$315$		0			0
$316$	348.955			1.10429
$317$			55.4193i			0.174824i	0.996172	+	0.0874121i	$0.0278597\pi$
$317$			55.4193i			0.174824i	−0.996172	+	0.0874121i	$0.972140\pi$
$318$		0			0
$319$	−220.542			−0.691353
$320$	468.381	−	270.420i	1.46369	−	0.845063i
$321$		0			0
$322$	−766.678	+	175.899i	−2.38099	+	0.546269i
$323$			4.44196i			0.0137522i
$324$		0			0
$325$	−137.670	−	238.451i	−0.423599	−	0.733695i
$326$	623.466	+	359.958i	1.91247	+	1.10417i
$327$		0			0
$328$	5.49955	−	9.52549i	0.0167669	−	0.0290411i
$329$	15.7515	+	4.83927i	0.0478770	+	0.0147090i
$330$		0			0
$331$	35.8578			0.108332			0.0541658	−	0.998532i	$-0.482750\pi$
$331$	35.8578			0.108332			0.0541658	+	0.998532i	$0.482750\pi$
$332$	539.654	−	311.569i	1.62546	−	0.938461i
$333$		0			0
$334$	−223.354	+	386.861i	−0.668726	+	1.15827i
$335$	604.940	−	349.262i	1.80579	−	1.04257i
$336$		0			0
$337$	211.555	−	366.423i	0.627758	−	1.08731i	−0.360242	−	0.932859i	$-0.617306\pi$
$337$	211.555	−	366.423i	0.627758	−	1.08731i	0.988001	−	0.154450i	$-0.0493607\pi$
$338$	−236.016	+	136.264i	−0.698271	+	0.403147i
$339$		0			0
$340$	−85.3283	+	147.793i	−0.250966	+	0.434685i
$341$	167.722	+	96.8344i	0.491854	+	0.283972i
$342$		0			0
$343$	−267.444	+	214.762i	−0.779719	+	0.626129i
$344$	0.550767	−	0.317986i	0.00160107	−	0.000924377i
$345$		0			0
$346$	182.740			0.528150
$347$			111.732i			0.321994i	0.986955	+	0.160997i	$0.0514709\pi$
$347$			111.732i			0.321994i	−0.986955	+	0.160997i	$0.948529\pi$
$348$		0			0
$349$	192.127	+	332.774i	0.550508	+	0.953507i	0.998238	+	0.0593385i	$0.0188991\pi$
$349$	192.127	+	332.774i	0.550508	+	0.953507i	−0.447730	+	0.894169i	$0.647768\pi$
$350$	470.850	−	437.873i	1.34529	−	1.25107i
$351$		0			0
$352$	347.860	−	602.511i	0.988238	−	1.71168i
$353$	−417.207	−	240.874i	−1.18189	−	0.682363i	−0.225438	−	0.974258i	$-0.572381\pi$
$353$	−417.207	−	240.874i	−1.18189	−	0.682363i	−0.956451	+	0.291894i	$0.905715\pi$
$354$		0			0
$355$	−57.2316	−	99.1281i	−0.161216	−	0.279234i
$356$	392.043	+	226.346i	1.10124	+	0.635804i
$357$		0			0
$358$	−318.958	−	552.452i	−0.890945	−	1.54316i
$359$	89.8795	+	51.8919i	0.250361	+	0.144546i	0.619929	−	0.784658i	$-0.287161\pi$
$359$	89.8795	+	51.8919i	0.250361	+	0.144546i	−0.369569	+	0.929203i	$0.620495\pi$
$360$		0			0
$361$	180.152	+	312.032i	0.499036	+	0.864355i
$362$			307.727i			0.850075i
$363$		0			0
$364$	174.276	+	187.401i	0.478781	+	0.514839i
$365$	−611.983	−	353.329i	−1.67667	−	0.968024i
$366$		0			0
$367$	−289.156	+	500.833i	−0.787891	+	1.36467i	0.139365	+	0.990241i	$0.455494\pi$
$367$	−289.156	+	500.833i	−0.787891	+	1.36467i	−0.927256	+	0.374427i	$0.877839\pi$
$368$	506.648	−	292.514i	1.37676	−	0.794874i
$369$		0			0
$370$	−509.402			−1.37676
$371$	−56.8509	−	247.793i	−0.153237	−	0.667905i
$372$		0			0
$373$	−77.6054	−	134.416i	−0.208057	−	0.360366i	0.743045	−	0.669241i	$-0.233381\pi$
$373$	−77.6054	−	134.416i	−0.208057	−	0.360366i	−0.951103	+	0.308875i	$0.900047\pi$
$374$			232.344i			0.621239i
$375$		0			0
$376$	1.66979			0.00444093
$377$			124.904i			0.331311i
$378$		0			0
$379$	−288.168			−0.760338			−0.380169	−	0.924917i	$-0.624134\pi$
$379$	−288.168			−0.760338			−0.380169	+	0.924917i	$0.624134\pi$
$380$		−	26.7537i		−	0.0704044i
$381$		0			0
$382$	54.2746			0.142080
$383$	9.58788	−	5.53557i	0.0250336	−	0.0144532i	−0.487431	−	0.873162i	$-0.662066\pi$
$383$	9.58788	−	5.53557i	0.0250336	−	0.0144532i	0.512465	+	0.858708i	$0.328733\pi$
$384$		0			0
$385$	235.873	−	767.752i	0.612657	−	1.99416i
$386$		−	191.616i		−	0.496415i
$387$		0			0
$388$	110.563	+	191.501i	0.284956	+	0.493559i
$389$	−338.537	−	195.455i	−0.870276	−	0.502454i	−0.00283618	−	0.999996i	$-0.500903\pi$
$389$	−338.537	−	195.455i	−0.870276	−	0.502454i	−0.867440	+	0.497542i	$0.834236\pi$
$390$		0			0
$391$	−104.144	+	180.383i	−0.266353	+	0.461336i
$392$	−19.5148	+	28.7620i	−0.0497825	+	0.0733723i
$393$		0			0
$394$	496.953			1.26130
$395$	−537.157	+	310.128i	−1.35989	+	0.785133i
$396$		0			0
$397$	246.403	−	426.782i	0.620662	−	1.07502i	−0.368701	−	0.929548i	$-0.620197\pi$
$397$	246.403	−	426.782i	0.620662	−	1.07502i	0.989363	−	0.145469i	$-0.0464693\pi$
$398$	−714.956	+	412.780i	−1.79637	+	1.03714i
$399$		0			0
$400$	−239.109	+	414.149i	−0.597772	+	1.03537i
$401$	−42.7138	+	24.6608i	−0.106518	+	0.0614983i	−0.552313	−	0.833637i	$-0.686255\pi$
$401$	−42.7138	+	24.6608i	−0.106518	+	0.0614983i	0.445794	+	0.895135i	$0.352921\pi$
$402$		0			0
$403$	54.8424	−	94.9898i	0.136085	−	0.235707i
$404$	−336.415	−	194.229i	−0.832711	−	0.480766i
$405$		0			0
$406$	−284.297	+	65.2260i	−0.700238	+	0.160655i
$407$	−309.304	+	178.577i	−0.759960	+	0.438763i
$408$		0			0
$409$	−39.8004			−0.0973115			−0.0486557	−	0.998816i	$-0.515494\pi$
$409$	−39.8004			−0.0973115			−0.0486557	+	0.998816i	$0.515494\pi$
$410$			336.153i			0.819885i
$411$		0			0
$412$	41.2502	+	71.4474i	0.100122	+	0.173416i
$413$	325.273	+	99.9321i	0.787585	+	0.241966i
$414$		0			0
$415$	−553.803	+	959.214i	−1.33446	+	2.31136i
$416$	−341.233	−	197.011i	−0.820272	−	0.473584i
$417$		0			0
$418$	−18.2121	−	31.5443i	−0.0435697	−	0.0754649i
$419$	56.6016	+	32.6790i	0.135087	+	0.0779928i	0.566021	−	0.824391i	$-0.308482\pi$
$419$	56.6016	+	32.6790i	0.135087	+	0.0779928i	−0.430933	+	0.902384i	$0.641816\pi$
$420$		0			0
$421$	33.2471	+	57.5856i	0.0789717	+	0.136783i	0.902807	−	0.430047i	$-0.141503\pi$
$421$	33.2471	+	57.5856i	0.0789717	+	0.136783i	−0.823835	+	0.566830i	$0.808170\pi$
$422$	−986.977	−	569.831i	−2.33881	−	1.35031i
$423$		0			0
$424$	−12.8810	−	22.3106i	−0.0303798	−	0.0526194i
$425$		−	170.260i		−	0.400613i
$426$		0			0
$427$	−60.8653	+	198.113i	−0.142542	+	0.463964i
$428$	−403.414	−	232.911i	−0.942557	−	0.544186i
$429$		0			0
$430$	−9.71824	+	16.8325i	−0.0226006	+	0.0391453i
$431$	−36.0005	+	20.7849i	−0.0835278	+	0.0482248i	−0.541182	−	0.840905i	$-0.682023\pi$
$431$	−36.0005	+	20.7849i	−0.0835278	+	0.0482248i	0.457654	+	0.889130i	$0.348690\pi$
$432$		0			0
$433$	576.422			1.33123			0.665615	−	0.746295i	$-0.268169\pi$
$433$	576.422			1.33123			0.665615	+	0.746295i	$0.268169\pi$
$434$	244.847	+	75.2233i	0.564164	+	0.173326i
$435$		0			0
$436$	141.306	+	244.749i	0.324095	+	0.561350i
$437$		−	32.6531i		−	0.0747210i
$438$		0			0
$439$	553.849			1.26162			0.630808	−	0.775939i	$-0.282724\pi$
$439$	553.849			1.26162			0.630808	+	0.775939i	$0.282724\pi$
$440$		−	81.3878i		−	0.184972i
$441$		0			0
$442$	131.588			0.297711
$443$			720.218i			1.62577i	0.582421	+	0.812887i	$0.302105\pi$
$443$			720.218i			1.62577i	−0.582421	+	0.812887i	$0.697895\pi$
$444$		0			0
$445$	−804.644			−1.80819
$446$	1100.13	−	635.161i	2.46666	−	1.42413i
$447$		0			0
$448$	147.284	−	479.400i	0.328759	−	1.07009i
$449$		−	204.358i		−	0.455141i	−0.973762	−	0.227571i	$-0.926922\pi$
$449$		−	204.358i		−	0.455141i	0.973762	−	0.227571i	$-0.0730783\pi$
$450$		0			0
$451$	117.842	+	204.109i	0.261291	+	0.452569i
$452$	581.633	+	335.806i	1.28680	+	0.742933i
$453$		0			0
$454$	−32.4649	+	56.2308i	−0.0715086	+	0.123856i
$455$	−434.818	−	133.587i	−0.955644	−	0.293598i
$456$		0			0
$457$	−409.228			−0.895465			−0.447733	−	0.894167i	$-0.647768\pi$
$457$	−409.228			−0.895465			−0.447733	+	0.894167i	$0.647768\pi$
$458$	−187.104	+	108.025i	−0.408524	+	0.235861i
$459$		0			0
$460$	627.252	−	1086.43i	1.36359	−	2.36181i
$461$	69.6371	−	40.2050i	0.151057	−	0.0872125i	−0.422567	−	0.906332i	$-0.638871\pi$
$461$	69.6371	−	40.2050i	0.151057	−	0.0872125i	0.573623	+	0.819119i	$0.305537\pi$
$462$		0			0
$463$	217.055	−	375.951i	0.468802	−	0.811989i	−0.530562	−	0.847646i	$-0.678019\pi$
$463$	217.055	−	375.951i	0.468802	−	0.811989i	0.999364	+	0.0356574i	$0.0113525\pi$
$464$	187.873	−	108.469i	0.404900	−	0.233769i
$465$		0			0
$466$	−292.812	+	507.166i	−0.628352	+	1.08834i
$467$	−573.856	−	331.316i	−1.22881	−	0.709456i	−0.262033	−	0.965059i	$-0.584393\pi$
$467$	−573.856	−	331.316i	−1.22881	−	0.709456i	−0.966782	+	0.255603i	$0.917726\pi$
$468$		0			0
$469$	190.225	−	619.171i	0.405597	−	1.32019i
$470$	−44.1949	+	25.5159i	−0.0940317	+	0.0542893i
$471$		0			0
$472$	34.4815			0.0730540
$473$			13.6274i			0.0288105i
$474$		0			0
$475$	13.3458	+	23.1156i	0.0280964	+	0.0486643i
$476$	35.3873	+	154.241i	0.0743431	+	0.324035i
$477$		0			0
$478$	−342.570	+	593.349i	−0.716674	+	1.24132i
$479$	249.851	+	144.252i	0.521610	+	0.301152i	0.737593	−	0.675245i	$-0.235962\pi$
$479$	249.851	+	144.252i	0.521610	+	0.301152i	−0.215983	+	0.976397i	$0.569296\pi$
$480$		0			0
$481$	101.137	+	175.175i	0.210265	+	0.364189i
$482$	888.675	+	513.077i	1.84372	+	1.06447i
$483$		0			0
$484$	−233.628	−	404.656i	−0.482703	−	0.836067i
$485$	−340.386	−	196.522i	−0.701826	−	0.405199i
$486$		0			0
$487$	−290.844	−	503.756i	−0.597215	−	1.03441i	−0.993230	−	0.116163i	$-0.962940\pi$
$487$	−290.844	−	503.756i	−0.597215	−	1.03441i	0.396015	−	0.918244i	$-0.370393\pi$
$488$			21.0015i			0.0430359i
$489$		0			0
$490$	76.9945	−	1059.46i	0.157132	−	2.16216i
$491$	−49.4611	−	28.5564i	−0.100735	−	0.0581597i	0.448786	−	0.893639i	$-0.351857\pi$
$491$	−49.4611	−	28.5564i	−0.100735	−	0.0581597i	−0.549521	+	0.835480i	$0.685190\pi$
$492$		0			0
$493$	−38.6183	+	66.8888i	−0.0783332	+	0.135677i
$494$	−17.8652	+	10.3145i	−0.0361644	+	0.0208795i
$495$		0			0
$496$	−190.504			−0.384081
$497$	−101.460	−	31.1711i	−0.204145	−	0.0627186i
$498$		0			0
$499$	−454.716	−	787.591i	−0.911254	−	1.57834i	−0.812295	−	0.583247i	$-0.801782\pi$
$499$	−454.716	−	787.591i	−0.911254	−	1.57834i	−0.0989598	−	0.995091i	$-0.531552\pi$
$500$			223.964i			0.447928i
$501$		0			0
$502$	739.565			1.47324
$503$		−	399.576i		−	0.794386i	−0.917735	−	0.397193i	$-0.869984\pi$
$503$		−	399.576i		−	0.794386i	0.917735	−	0.397193i	$-0.130016\pi$
$504$		0			0
$505$	690.471			1.36727
$506$		−	1707.97i		−	3.37543i
$507$		0			0
$508$	−5.91917			−0.0116519
$509$	345.084	−	199.234i	0.677964	−	0.391423i	−0.121123	−	0.992637i	$-0.538650\pi$
$509$	345.084	−	199.234i	0.677964	−	0.391423i	0.799088	+	0.601215i	$0.205316\pi$
$510$		0			0
$511$	−638.682	+	146.532i	−1.24987	+	0.286756i
$512$			726.771i			1.41947i
$513$		0			0
$514$	−60.4058	−	104.626i	−0.117521	−	0.203552i
$515$	−126.995	−	73.3206i	−0.246592	−	0.142370i
$516$		0			0
$517$	−17.8898	+	30.9861i	−0.0346031	+	0.0599343i
$518$	−345.904	+	321.678i	−0.667769	+	0.621001i
$519$		0			0
$520$	−46.0942			−0.0886426
$521$	−45.9947	+	26.5550i	−0.0882815	+	0.0509693i	−0.543491	−	0.839415i	$-0.682898\pi$
$521$	−45.9947	+	26.5550i	−0.0882815	+	0.0509693i	0.455209	+	0.890384i	$0.349564\pi$
$522$		0			0
$523$	321.356	−	556.605i	0.614447	−	1.06425i	−0.376034	−	0.926606i	$-0.622712\pi$
$523$	321.356	−	556.605i	0.614447	−	1.06425i	0.990481	−	0.137648i	$-0.0439542\pi$
$524$	286.588	−	165.461i	0.546923	−	0.315766i
$525$		0			0
$526$	−576.844	+	999.123i	−1.09666	+	1.89947i
$527$	58.7385	−	33.9127i	0.111458	−	0.0643504i
$528$		0			0
$529$	501.067	−	867.873i	0.947196	−	1.64059i
$530$	681.855	+	393.669i	1.28652	+	0.742772i
$531$		0			0
$532$	−16.8945	−	18.1668i	−0.0317565	−	0.0341481i
$533$	115.597	−	66.7402i	0.216881	−	0.125216i
$534$		0			0
$535$	827.983			1.54763
$536$		−	65.6371i		−	0.122457i
$537$		0			0
$538$	526.747	+	912.353i	0.979084	+	1.69582i
$539$	−324.654	−	670.283i	−0.602327	−	1.24357i
$540$		0			0
$541$	−142.169	+	246.244i	−0.262790	+	0.455165i	−0.966982	−	0.254844i	$-0.917976\pi$
$541$	−142.169	+	246.244i	−0.262790	+	0.455165i	0.704192	+	0.710009i	$0.251309\pi$
$542$	−252.650	−	145.868i	−0.466144	−	0.269128i
$543$		0			0
$544$	−121.825	−	211.007i	−0.223943	−	0.387881i
$545$	−435.031	−	251.165i	−0.798223	−	0.460854i
$546$		0			0
$547$	−106.336	−	184.180i	−0.194399	−	0.336708i	0.752305	−	0.658816i	$-0.228942\pi$
$547$	−106.336	−	184.180i	−0.194399	−	0.336708i	−0.946703	+	0.322107i	$0.895609\pi$
$548$	768.797	+	443.865i	1.40291	+	0.809972i
$549$		0			0
$550$	698.071	+	1209.09i	1.26922	+	2.19835i
$551$		−	12.1083i		−	0.0219751i
$552$		0			0
$553$	−168.911	+	549.794i	−0.305444	+	0.994202i
$554$	−233.613	−	134.877i	−0.421684	−	0.243459i
$555$		0			0
$556$	407.373	−	705.591i	0.732685	−	1.26905i
$557$	588.247	−	339.625i	1.05610	−	0.609739i	0.131749	−	0.991283i	$-0.457941\pi$
$557$	588.247	−	339.625i	1.05610	−	0.609739i	0.924351	+	0.381544i	$0.124607\pi$
$558$		0			0
$559$	7.71789			0.0138066
$560$	176.669	+	770.036i	0.315480	+	1.37506i
$561$		0			0
$562$	−124.357	−	215.393i	−0.221277	−	0.383262i
$563$		−	534.661i		−	0.949665i	−0.880076	−	0.474832i	$-0.842509\pi$
$563$		−	534.661i		−	0.949665i	0.880076	−	0.474832i	$-0.157491\pi$
$564$		0			0
$565$	−1193.76			−2.11286
$566$			346.282i			0.611805i
$567$		0			0
$568$	−10.7556			−0.0189359
$569$		−	506.885i		−	0.890835i	−0.895323	−	0.445417i	$-0.853055\pi$
$569$		−	506.885i		−	0.890835i	0.895323	−	0.445417i	$-0.146945\pi$
$570$		0			0
$571$	18.3305			0.0321025			0.0160512	−	0.999871i	$-0.494891\pi$
$571$	18.3305			0.0321025			0.0160512	+	0.999871i	$0.494891\pi$
$572$	−481.227	+	277.837i	−0.841306	+	0.485728i
$573$		0			0
$574$	212.275	+	228.261i	0.369816	+	0.397668i
$575$			1251.59i			2.17668i
$576$		0			0
$577$	−117.796	−	204.029i	−0.204153	−	0.353604i	0.745709	−	0.666271i	$-0.232111\pi$
$577$	−117.796	−	204.029i	−0.204153	−	0.353604i	−0.949863	+	0.312668i	$0.898777\pi$
$578$	−648.280	−	374.284i	−1.12159	−	0.647551i
$579$		0			0
$580$	232.595	−	402.867i	0.401026	−	0.694598i
$581$	229.673	+	1001.06i	0.395306	+	1.72300i
$582$		0			0
$583$	552.021			0.946862
$584$	−57.5053	+	33.2007i	−0.0984679	+	0.0568505i
$585$		0			0
$586$	−235.488	+	407.878i	−0.401857	+	0.696037i
$587$	42.7089	−	24.6580i	0.0727580	−	0.0420068i	−0.463180	−	0.886264i	$-0.653292\pi$
$587$	42.7089	−	24.6580i	0.0727580	−	0.0420068i	0.535938	+	0.844258i	$0.319958\pi$
$588$		0			0
$589$	−5.31645	+	9.20837i	−0.00902624	+	0.0156339i
$590$	−912.635	+	526.910i	−1.54684	+	0.893068i
$591$		0			0
$592$	175.659	−	304.249i	0.296720	−	0.513935i
$593$	19.7883	+	11.4248i	0.0333698	+	0.0192661i	0.516592	−	0.856232i	$-0.327200\pi$
$593$	19.7883	+	11.4248i	0.0333698	+	0.0192661i	−0.483222	+	0.875498i	$0.660534\pi$
$594$		0			0
$595$	−191.551	−	205.977i	−0.321935	−	0.346180i
$596$	282.663	−	163.196i	0.474268	−	0.273818i
$597$		0			0
$598$	−967.312			−1.61758
$599$		−	690.372i		−	1.15254i	−0.817259	−	0.576271i	$-0.804507\pi$
$599$		−	690.372i		−	1.15254i	0.817259	−	0.576271i	$-0.195493\pi$
$600$		0			0
$601$	242.122	+	419.367i	0.402865	+	0.697783i	0.994070	−	0.108738i	$-0.0346810\pi$
$601$	242.122	+	419.367i	0.402865	+	0.697783i	−0.591205	+	0.806521i	$0.701348\pi$
$602$	4.03034	+	17.5668i	0.00669493	+	0.0291808i
$603$		0			0
$604$	−171.398	+	296.870i	−0.283772	+	0.491507i
$605$	719.261	+	415.266i	1.18886	+	0.686390i
$606$		0			0
$607$	354.147	+	613.400i	0.583437	+	1.01054i	0.995068	+	0.0991927i	$0.0316260\pi$
$607$	354.147	+	613.400i	0.583437	+	1.01054i	−0.411631	+	0.911351i	$0.635041\pi$
$608$	33.0793	+	19.0984i	0.0544068	+	0.0314118i
$609$		0			0
$610$	−320.923	−	555.855i	−0.526104	−	0.911238i
$611$	17.5490	+	10.1319i	0.0287218	+	0.0165825i
$612$		0			0
$613$	491.502	+	851.306i	0.801798	+	1.38875i	0.918432	+	0.395579i	$0.129456\pi$
$613$	491.502	+	851.306i	0.801798	+	1.38875i	−0.116634	+	0.993175i	$0.537211\pi$
$614$			1134.78i			1.84818i
$615$		0			0
$616$	−51.3949	−	55.2655i	−0.0834333	−	0.0897168i
$617$	−7.63528	−	4.40823i	−0.0123748	−	0.00714462i	0.493800	−	0.869576i	$-0.335608\pi$
$617$	−7.63528	−	4.40823i	−0.0123748	−	0.00714462i	−0.506175	+	0.862431i	$0.668941\pi$
$618$		0			0
$619$	65.4219	−	113.314i	0.105690	−	0.183060i	−0.808330	−	0.588730i	$-0.799628\pi$
$619$	65.4219	−	113.314i	0.105690	−	0.183060i	0.914020	+	0.405670i	$0.132962\pi$
$620$	−353.778	+	204.254i	−0.570610	+	0.329442i
$621$		0			0
$622$	−912.866			−1.46763
$623$	−546.385	+	508.118i	−0.877023	+	0.815599i
$624$		0			0
$625$	200.778	+	347.758i	0.321245	+	0.556412i
$626$			57.1355i			0.0912707i
$627$		0			0
$628$	−921.081			−1.46669
$629$			125.080i			0.198855i
$630$		0			0
$631$	287.127			0.455034			0.227517	−	0.973774i	$-0.426939\pi$
$631$	287.127			0.455034			0.227517	+	0.973774i	$0.426939\pi$
$632$			58.2825i			0.0922192i
$633$		0			0
$634$	−159.151			−0.251026
$635$	9.11154	−	5.26055i	0.0143489	−	0.00828433i
$636$		0			0
$637$	−379.616	+	183.869i	−0.595944	+	0.288648i
$638$		−	633.342i		−	0.992700i
$639$		0			0
$640$	85.5117	+	148.111i	0.133612	+	0.231423i
$641$	391.499	+	226.032i	0.610763	+	0.352624i	0.773264	−	0.634084i	$-0.218623\pi$
$641$	391.499	+	226.032i	0.610763	+	0.352624i	−0.162501	+	0.986708i	$0.551956\pi$
$642$		0			0
$643$	409.902	−	709.971i	0.637484	−	1.10415i	−0.348499	−	0.937309i	$-0.613309\pi$
$643$	409.902	−	709.971i	0.637484	−	1.10415i	0.985983	−	0.166845i	$-0.0533580\pi$
$644$	−260.134	−	1133.83i	−0.403934	−	1.76060i
$645$		0			0
$646$	−12.7562			−0.0197465
$647$	776.946	−	448.570i	1.20084	−	0.693308i	0.240101	−	0.970748i	$-0.422819\pi$
$647$	776.946	−	448.570i	1.20084	−	0.693308i	0.960743	+	0.277440i	$0.0894860\pi$
$648$		0			0
$649$	−369.428	+	639.869i	−0.569227	+	0.985931i
$650$	684.773	−	395.354i	1.05350	−	0.608237i
$651$		0			0
$652$	−532.337	+	922.035i	−0.816468	+	1.41416i
$653$	−472.144	+	272.592i	−0.723038	+	0.417446i	−0.815870	−	0.578236i	$-0.803741\pi$
$653$	−472.144	+	272.592i	−0.723038	+	0.417446i	0.0928321	+	0.995682i	$0.470408\pi$
$654$		0			0
$655$	−294.101	+	509.399i	−0.449010	+	0.777708i
$656$	−200.773	−	115.917i	−0.306057	−	0.176702i
$657$		0			0
$658$	−13.8972	+	45.2346i	−0.0211204	+	0.0687457i
$659$	826.994	−	477.465i	1.25492	−	0.724530i	0.282839	−	0.959167i	$-0.408724\pi$
$659$	826.994	−	477.465i	1.25492	−	0.724530i	0.972083	+	0.234638i	$0.0753904\pi$
$660$		0			0
$661$	724.955			1.09676			0.548378	−	0.836231i	$-0.315246\pi$
$661$	724.955			1.09676			0.548378	+	0.836231i	$0.315246\pi$
$662$			102.975i			0.155551i
$663$		0			0
$664$	52.0383	+	90.1329i	0.0783709	+	0.135742i
$665$	42.1515	+	12.9500i	0.0633857	+	0.0194737i
$666$		0			0
$667$	283.885	−	491.703i	0.425614	−	0.737185i
$668$	−572.123	−	330.316i	−0.856472	−	0.494484i
$669$		0			0
$670$	1003.00	+	1737.24i	1.49701	+	2.59290i
$671$	−389.723	−	225.007i	−0.580809	−	0.335330i
$672$		0			0
$673$	−282.956	−	490.093i	−0.420439	−	0.728222i	0.575543	−	0.817771i	$-0.304791\pi$
$673$	−282.956	−	490.093i	−0.420439	−	0.728222i	−0.995982	+	0.0895494i	$0.971457\pi$
$674$	1052.28	+	607.534i	1.56125	+	0.901385i
$675$		0			0
$676$	−201.518	−	349.040i	−0.298104	−	0.516331i
$677$		−	874.549i		−	1.29180i	−0.763421	−	0.645901i	$-0.776482\pi$
$677$		−	874.549i		−	1.29180i	0.763421	−	0.645901i	$-0.223518\pi$
$678$		0			0
$679$	−355.235	+	81.5014i	−0.523174	+	0.120031i
$680$	−24.6844	−	14.2515i	−0.0363006	−	0.0209581i
$681$		0			0
$682$	−278.085	+	481.658i	−0.407749	+	0.706243i
$683$	−1052.67	+	607.762i	−1.54125	+	0.889842i	−0.542491	+	0.840062i	$0.682519\pi$
$683$	−1052.67	+	607.762i	−1.54125	+	0.889842i	−0.998760	+	0.0497801i	$0.984148\pi$
$684$		0			0
$685$	−1577.91			−2.30351
$686$	−616.746	−	768.034i	−0.899047	−	1.11958i
$687$		0			0
$688$	−6.70233	−	11.6088i	−0.00974176	−	0.0168732i
$689$		−	312.638i		−	0.453756i
$690$		0			0
$691$	304.388			0.440504			0.220252	−	0.975443i	$-0.429312\pi$
$691$	304.388			0.440504			0.220252	+	0.975443i	$0.429312\pi$
$692$			270.252i			0.390537i
$693$		0			0
$694$	−320.867			−0.462344
$695$			1448.18i			2.08371i
$696$		0			0
$697$	82.5398			0.118421
$698$	−955.647	+	551.743i	−1.36912	+	0.790463i
$699$		0			0
$700$	647.565	+	696.333i	0.925092	+	0.994762i
$701$		−	135.215i		−	0.192889i	−0.995338	−	0.0964447i	$-0.969253\pi$
$701$		−	135.215i		−	0.192889i	0.995338	−	0.0964447i	$-0.0307471\pi$
$702$		0			0
$703$	−9.80431	−	16.9816i	−0.0139464	−	0.0241559i
$704$	943.065	+	544.479i	1.33958	+	0.773407i
$705$		0			0
$706$	691.733	−	1198.12i	0.979792	−	1.69705i
$707$	468.857	−	436.020i	0.663164	−	0.616719i
$708$		0			0
$709$	97.4709			0.137477			0.0687383	−	0.997635i	$-0.478103\pi$
$709$	97.4709			0.137477			0.0687383	+	0.997635i	$0.478103\pi$
$710$	284.672	−	164.355i	0.400946	−	0.231487i
$711$		0			0
$712$	−37.8043	+	65.4790i	−0.0530960	+	0.0919650i
$713$	−431.789	+	249.294i	−0.605595	+	0.349640i
$714$		0			0
$715$	493.844	−	855.363i	0.690691	−	1.19631i
$716$	817.014	−	471.703i	1.14108	−	0.658803i
$717$		0			0
$718$	−149.021	+	258.112i	−0.207550	+	0.359488i
$719$	489.105	+	282.385i	0.680257	+	0.392747i	0.799952	−	0.600064i	$-0.204858\pi$
$719$	489.105	+	282.385i	0.680257	+	0.392747i	−0.119695	+	0.992811i	$0.538192\pi$
$720$		0			0
$721$	−132.535	+	30.4075i	−0.183821	+	0.0421741i
$722$	−896.081	+	517.353i	−1.24111	+	0.716555i
$723$		0			0
$724$	−455.093			−0.628582
$725$			464.111i			0.640153i
$726$		0			0
$727$	−119.623	−	207.192i	−0.164543	−	0.284996i	0.771950	−	0.635683i	$-0.219282\pi$
$727$	−119.623	−	207.192i	−0.164543	−	0.284996i	−0.936493	+	0.350687i	$0.885948\pi$
$728$	−31.2998	+	29.1076i	−0.0429942	+	0.0399830i
$729$		0			0
$730$	1014.68	−	1757.47i	1.38997	−	2.40749i
$731$	4.13309	+	2.38624i	0.00565402	+	0.00326435i
$732$		0			0
$733$	−438.033	−	758.695i	−0.597589	−	1.03505i	−0.993176	−	0.116626i	$-0.962792\pi$
$733$	−438.033	−	758.695i	−0.597589	−	1.03505i	0.395587	−	0.918429i	$-0.370541\pi$
$734$	−1438.27	−	830.387i	−1.95950	−	1.13132i
$735$		0			0
$736$	895.541	+	1551.12i	1.21677	+	2.10750i
$737$	1218.02	+	703.224i	1.65267	+	0.954170i
$738$		0			0
$739$	−409.279	−	708.893i	−0.553829	−	0.959259i	−0.997994	−	0.0633143i	$-0.979833\pi$
$739$	−409.279	−	708.893i	−0.553829	−	0.959259i	0.444165	−	0.895945i	$-0.353500\pi$
$740$		−	753.348i		−	1.01804i
$741$		0			0
$742$	711.601	−	163.262i	0.959031	−	0.220030i
$743$	872.271	+	503.606i	1.17399	+	0.677801i	0.954615	−	0.297841i	$-0.0962666\pi$
$743$	872.271	+	503.606i	1.17399	+	0.677801i	0.219370	+	0.975642i	$0.429600\pi$
$744$		0			0
$745$	−290.074	+	502.424i	−0.389362	+	0.674394i
$746$	386.012	−	222.864i	0.517442	−	0.298745i
$747$		0			0
$748$	−343.609			−0.459371
$749$	562.233	−	522.856i	0.750645	−	0.698072i
$750$		0			0
$751$	−57.2003	−	99.0738i	−0.0761655	−	0.131922i	0.825427	−	0.564509i	$-0.190934\pi$
$751$	−57.2003	−	99.0738i	−0.0761655	−	0.131922i	−0.901593	+	0.432586i	$0.857601\pi$
$752$		−	35.1949i		−	0.0468018i
$753$		0			0
$754$	−358.695			−0.475723
$755$		−	609.308i		−	0.807030i
$756$		0			0
$757$	967.771			1.27843			0.639215	−	0.769028i	$-0.279259\pi$
$757$	967.771			1.27843			0.639215	+	0.769028i	$0.279259\pi$
$758$		−	827.549i		−	1.09175i
$759$		0			0
$760$	4.46840			0.00587947
$761$	−990.841	+	572.063i	−1.30203	+	0.751725i	−0.980751	−	0.195262i	$-0.937444\pi$
$761$	−990.841	+	572.063i	−1.30203	+	0.751725i	−0.321274	+	0.946986i	$0.604111\pi$
$762$		0			0
$763$	−454.010	+	104.163i	−0.595033	+	0.136518i
$764$			80.2659i			0.105060i
$765$		0			0
$766$	15.8968	+	27.5341i	0.0207530	+	0.0359453i
$767$	362.391	+	209.227i	0.472479	+	0.272786i
$768$		0			0
$769$	−289.247	+	500.990i	−0.376134	+	0.651483i	−0.990496	−	0.137541i	$-0.956080\pi$
$769$	−289.247	+	500.990i	−0.376134	+	0.651483i	0.614362	+	0.789024i	$0.289413\pi$
$770$	2204.80	+	677.370i	2.86337	+	0.879701i
$771$		0			0
$772$	283.378			0.367071
$773$	−1199.50	+	692.532i	−1.55175	+	0.895901i	−0.553747	+	0.832685i	$0.686802\pi$
$773$	−1199.50	+	692.532i	−1.55175	+	0.895901i	−0.998000	+	0.0632163i	$0.979864\pi$
$774$		0			0
$775$	203.780	−	352.957i	0.262942	−	0.455428i
$776$	−31.9845	+	18.4662i	−0.0412171	+	0.0237967i
$777$		0			0
$778$	561.299	−	972.198i	0.721464	−	1.24961i
$779$	−11.2061	+	6.46984i	−0.0143852	+	0.00830531i
$780$		0			0
$781$	115.233	−	199.590i	0.147546	−	0.255557i
$782$	−518.015	−	299.076i	−0.662424	−	0.382450i
$783$		0			0
$784$	606.229	+	411.322i	0.773252	+	0.524645i
$785$	1417.84	−	818.593i	1.80617	−	1.04279i
$786$		0			0
$787$	−478.039			−0.607419			−0.303710	−	0.952765i	$-0.598225\pi$
$787$	−478.039			−0.607419			−0.303710	+	0.952765i	$0.598225\pi$
$788$			734.937i			0.932661i
$789$		0			0
$790$	−890.612	−	1542.59i	−1.12736	−	1.95264i
$791$	−810.613	+	753.841i	−1.02480	+	0.953023i
$792$		0			0
$793$	−127.433	+	220.720i	−0.160697	+	0.278336i
$794$	1225.62	+	707.609i	1.54360	+	0.891195i
$795$		0			0
$796$	−610.454	−	1057.34i	−0.766902	−	1.32831i
$797$	740.008	+	427.244i	0.928491	+	0.536065i	0.886334	−	0.463046i	$-0.153244\pi$
$797$	740.008	+	427.244i	0.928491	+	0.536065i	0.0421573	+	0.999111i	$0.486577\pi$
$798$		0			0
$799$	6.26524	+	10.8517i	0.00784136	+	0.0135816i
$800$	−1267.93	−	732.041i	−1.58491	−	0.915051i
$801$		0			0
$802$	−70.8200	−	122.664i	−0.0883042	−	0.152947i
$803$		−	1422.82i		−	1.77189i
$804$		0			0
$805$	1408.10	+	1514.15i	1.74919	+	1.88093i
$806$	272.788	+	157.494i	0.338447	+	0.195402i
$807$		0			0
$808$	32.4402	−	56.1881i	0.0401488	−	0.0695397i
$809$	−852.105	+	491.963i	−1.05328	+	0.608113i	−0.923566	−	0.383439i	$-0.874740\pi$
$809$	−852.105	+	491.963i	−1.05328	+	0.608113i	−0.129716	+	0.991551i	$0.541406\pi$
$810$		0			0
$811$	846.271			1.04349			0.521745	−	0.853101i	$-0.325281\pi$
$811$	846.271			1.04349			0.521745	+	0.853101i	$0.325281\pi$
$812$	−96.4618	−	420.442i	−0.118795	−	0.517786i
$813$		0			0
$814$	−512.829	−	888.247i	−0.630012	−	1.09121i
$815$		−	1892.42i		−	2.32199i
$816$		0			0
$817$	−0.748176			−0.000915761
$818$		−	114.297i		−	0.139728i
$819$		0			0
$820$	−497.132			−0.606258
$821$			1001.35i			1.21967i	0.792529	+	0.609835i	$0.208764\pi$
$821$			1001.35i			1.21967i	−0.792529	+	0.609835i	$0.791236\pi$
$822$		0			0
$823$	844.673			1.02633			0.513167	−	0.858289i	$-0.328472\pi$
$823$	844.673			1.02633			0.513167	+	0.858289i	$0.328472\pi$
$824$	−11.9331	+	6.88960i	−0.0144820	+	0.00836117i
$825$		0			0
$826$	−286.981	+	934.105i	−0.347435	+	1.13088i
$827$		−	389.098i		−	0.470493i	−0.971936	−	0.235246i	$-0.924410\pi$
$827$		−	389.098i		−	0.470493i	0.971936	−	0.235246i	$-0.0755897\pi$
$828$		0			0
$829$	−701.276	−	1214.65i	−0.845930	−	1.46519i	−0.884811	−	0.465950i	$-0.845713\pi$
$829$	−701.276	−	1214.65i	−0.845930	−	1.46519i	0.0388805	−	0.999244i	$-0.487621\pi$
$830$	−2754.63	−	1590.39i	−3.31883	−	1.91613i
$831$		0			0
$832$	308.367	−	534.107i	0.370633	−	0.641956i
$833$	−260.142	−	18.9054i	−0.312295	−	0.0226956i
$834$		0			0
$835$	1174.25			1.40628
$836$	46.6504	−	26.9336i	0.0558020	−	0.0322173i
$837$		0			0
$838$	−93.8461	+	162.546i	−0.111988	+	0.193969i
$839$	−511.858	+	295.521i	−0.610081	+	0.352230i	−0.772997	−	0.634409i	$-0.781243\pi$
$839$	−511.858	+	295.521i	−0.610081	+	0.352230i	0.162916	+	0.986640i	$0.447910\pi$
$840$		0			0
$841$	−315.231	+	545.996i	−0.374829	+	0.649222i
$842$	−165.372	+	95.4776i	−0.196404	+	0.113394i
$843$		0			0
$844$	842.715	−	1459.63i	0.998477	−	1.72941i
$845$	620.406	+	358.191i	0.734208	+	0.423895i
$846$		0			0
$847$	750.640	−	172.219i	0.886234	−	0.203328i
$848$	−470.252	+	271.500i	−0.554542	+	0.320165i
$849$		0			0
$850$	488.947			0.575232
$851$		−	919.467i		−	1.08045i
$852$		0			0
$853$	658.680	+	1140.87i	0.772192	+	1.33748i	0.936359	+	0.351043i	$0.114173\pi$
$853$	658.680	+	1140.87i	0.772192	+	1.33748i	−0.164168	+	0.986432i	$0.552494\pi$
$854$	−568.932	−	174.790i	−0.666197	−	0.204673i
$855$		0			0
$856$	38.9009	−	67.3783i	0.0454449	−	0.0787129i
$857$	614.692	+	354.893i	0.717260	+	0.414110i	0.813744	−	0.581224i	$-0.197426\pi$
$857$	614.692	+	354.893i	0.717260	+	0.414110i	−0.0964831	+	0.995335i	$0.530759\pi$
$858$		0			0
$859$	−285.323	−	494.193i	−0.332157	−	0.575312i	0.650778	−	0.759268i	$-0.274443\pi$
$859$	−285.323	−	494.193i	−0.332157	−	0.575312i	−0.982934	+	0.183956i	$0.941110\pi$
$860$	−24.8933	−	14.3722i	−0.0289457	−	0.0167118i
$861$		0			0
$862$	−59.6892	−	103.385i	−0.0692450	−	0.119936i
$863$	−98.2922	−	56.7490i	−0.113896	−	0.0657579i	0.441970	−	0.897030i	$-0.354280\pi$
$863$	−98.2922	−	56.7490i	−0.113896	−	0.0657579i	−0.555866	+	0.831272i	$0.687613\pi$
$864$		0			0
$865$	−240.181	−	416.006i	−0.277666	−	0.480932i
$866$			1655.35i			1.91149i
$867$		0			0
$868$	−111.247	+	362.101i	−0.128164	+	0.417167i
$869$	−1081.54	−	624.428i	−1.24458	−	0.718560i
$870$		0			0
$871$	398.272	−	689.828i	0.457259	−	0.791995i
$872$	−40.8779	+	23.6009i	−0.0468783	+	0.0270652i
$873$		0			0
$874$	93.7717			0.107290
$875$	−352.864	−	108.409i	−0.403274	−	0.123896i
$876$		0			0
$877$	489.772	+	848.310i	0.558463	+	0.967286i	0.997625	+	0.0688781i	$0.0219420\pi$
$877$	489.772	+	848.310i	0.558463	+	0.967286i	−0.439162	+	0.898408i	$0.644725\pi$
$878$			1590.52i			1.81153i
$879$		0			0
$880$	−1715.45			−1.94937
$881$		−	1090.83i		−	1.23817i	−0.785322	−	0.619087i	$-0.787503\pi$
$881$		−	1090.83i		−	1.23817i	0.785322	−	0.619087i	$-0.212497\pi$
$882$		0			0
$883$	−1432.47			−1.62228			−0.811138	−	0.584855i	$-0.801152\pi$
$883$	−1432.47			−1.62228			−0.811138	+	0.584855i	$0.801152\pi$
$884$			194.604i			0.220140i
$885$		0			0
$886$	−2068.29			−2.33442
$887$	8.27405	−	4.77703i	0.00932813	−	0.00538560i	−0.495329	−	0.868706i	$-0.664952\pi$
$887$	8.27405	−	4.77703i	0.00932813	−	0.00538560i	0.504657	+	0.863320i	$0.331619\pi$
$888$		0			0
$889$	2.86515	−	9.32590i	0.00322289	−	0.0104903i
$890$		−	2310.74i		−	2.59634i
$891$		0			0
$892$	939.330	+	1626.97i	1.05306	+	1.82396i
$893$	−1.70121	−	0.982196i	−0.00190505	−	0.00109988i
$894$		0			0
$895$	−838.435	+	1452.21i	−0.936798	+	1.62258i
$896$	151.595	+	46.5738i	0.169191	+	0.0519797i
$897$		0			0
$898$	586.868			0.653528
$899$	−160.114	+	92.4421i	−0.178103	+	0.102828i
$900$		0			0
$901$	96.6624	−	167.424i	0.107283	−	0.185820i
$902$	−586.151	+	338.415i	−0.649835	+	0.375182i
$903$		0			0
$904$	−56.0863	+	97.1443i	−0.0620424	+	0.107461i
$905$	700.538	−	404.456i	0.774075	−	0.446912i
$906$		0			0
$907$	362.720	−	628.249i	0.399911	−	0.692667i	−0.593803	−	0.804610i	$-0.702374\pi$
$907$	362.720	−	628.249i	0.399911	−	0.692667i	0.993715	+	0.111943i	$0.0357075\pi$
$908$	−83.1590	−	48.0119i	−0.0915848	−	0.0528765i
$909$		0			0
$910$	383.630	−	1248.69i	0.421572	−	1.37219i
$911$	−1178.77	+	680.563i	−1.29393	+	0.747051i	−0.979348	−	0.202180i	$-0.935197\pi$
$911$	−1178.77	+	680.563i	−1.29393	+	0.747051i	−0.314581	+	0.949231i	$0.601864\pi$
$912$		0			0
$913$	−2230.11			−2.44262
$914$		−	1175.20i		−	1.28578i
$915$		0			0
$916$	−159.756	−	276.705i	−0.174406	−	0.302080i
$917$	121.970	+	531.622i	0.133009	+	0.579740i
$918$		0			0
$919$	−797.621	+	1381.52i	−0.867923	+	1.50329i	−0.00380700	+	0.999993i	$0.501212\pi$
$919$	−797.621	+	1381.52i	−0.867923	+	1.50329i	−0.864116	+	0.503293i	$0.832122\pi$
$920$	181.456	+	104.764i	0.197235	+	0.113874i
$921$		0			0
$922$	115.459	+	199.981i	0.125227	+	0.216899i
$923$	−113.038	−	65.2627i	−0.122468	−	0.0707071i
$924$		0			0
$925$	375.799	+	650.904i	0.406270	+	0.703680i
$926$	1079.64	+	623.330i	1.16592	+	0.673143i
$927$		0			0
$928$	332.081	+	575.181i	0.357846	+	0.619808i
$929$			299.558i			0.322452i	0.986918	+	0.161226i	$0.0515448\pi$
$929$			299.558i			0.322452i	−0.986918	+	0.161226i	$0.948455\pi$
$930$		0			0
$931$	36.8002	−	17.8243i	0.0395276	−	0.0191454i
$932$	−750.040	−	433.036i	−0.804764	−	0.464631i
$933$		0			0
$934$	951.460	−	1647.98i	1.01869	−	1.76443i
$935$	528.928	−	305.377i	0.565698	−	0.326606i
$936$		0			0
$937$	610.588			0.651642			0.325821	−	0.945432i	$-0.394359\pi$
$937$	610.588			0.651642			0.325821	+	0.945432i	$0.394359\pi$
$938$	1778.11	+	546.281i	1.89564	+	0.582389i
$939$		0			0
$940$	−37.7352	−	65.3592i	−0.0401438	−	0.0695311i
$941$			1710.95i			1.81822i	0.416553	+	0.909112i	$0.363238\pi$
$941$			1710.95i			1.81822i	−0.416553	+	0.909112i	$0.636762\pi$
$942$		0			0
$943$	−606.754			−0.643429
$944$		−	726.783i		−	0.769897i
$945$		0			0
$946$	−39.1345			−0.0413684
$947$		−	865.629i		−	0.914075i	−0.889447	−	0.457038i	$-0.848910\pi$
$947$		−	865.629i		−	0.914075i	0.889447	−	0.457038i	$-0.151090\pi$
$948$		0			0
$949$	−805.820			−0.849125
$950$	−66.3823	+	38.3259i	−0.0698761	+	0.0403430i
$951$		0			0
$952$	−25.7613	+	5.91039i	−0.0270601	+	0.00620839i
$953$			893.350i			0.937408i	0.883355	+	0.468704i	$0.155279\pi$
$953$			893.350i			0.937408i	−0.883355	+	0.468704i	$0.844721\pi$
$954$		0			0
$955$	−71.3348	−	123.556i	−0.0746962	−	0.129378i
$956$	−877.495	−	506.622i	−0.917882	−	0.529939i
$957$		0			0
$958$	−414.256	+	717.513i	−0.432418	+	0.748970i
$959$	−1071.46	+	996.420i	−1.11727	+	1.03902i
$960$		0			0
$961$	−798.644			−0.831055
$962$	−503.061	+	290.442i	−0.522932	+	0.301915i
$963$		0			0
$964$	−758.782	+	1314.25i	−0.787118	+	1.36333i
$965$	−436.212	+	251.847i	−0.452033	+	0.260982i
$966$		0			0
$967$	−564.254	+	977.317i	−0.583510	+	1.01067i	0.411550	+	0.911387i	$0.364988\pi$
$967$	−564.254	+	977.317i	−0.583510	+	1.01067i	−0.995059	+	0.0992813i	$0.968346\pi$
$968$	67.5857	−	39.0206i	0.0698199	−	0.0403106i
$969$		0			0
$970$	564.363	−	977.505i	0.581818	−	1.00774i
$971$	−773.591	−	446.633i	−0.796695	−	0.459972i	0.0456189	−	0.998959i	$-0.485474\pi$
$971$	−773.591	−	446.633i	−0.796695	−	0.459972i	−0.842314	+	0.538987i	$0.818807\pi$
$972$		0			0
$973$	914.500	+	983.372i	0.939877	+	1.01066i
$974$	1446.67	−	835.234i	1.48528	−	0.857529i
$975$		0			0
$976$	442.659			0.453544
$977$			61.5411i			0.0629899i	0.999504	+	0.0314949i	$0.0100268\pi$
$977$			61.5411i			0.0629899i	−0.999504	+	0.0314949i	$0.989973\pi$
$978$		0			0
$979$	−810.057	−	1403.06i	−0.827434	−	1.43316i
$980$	1566.82	+	113.866i	1.59879	+	0.116190i
$981$		0			0
$982$	82.0071	−	142.040i	0.0835103	−	0.144644i
$983$	−1152.76	−	665.547i	−1.17270	−	0.677057i	−0.218384	−	0.975863i	$-0.570078\pi$
$983$	−1152.76	−	665.547i	−1.17270	−	0.677057i	−0.954314	+	0.298806i	$0.903412\pi$
$984$		0			0
$985$	−653.161	−	1131.31i	−0.663108	−	1.14854i
$986$	−192.089	−	110.902i	−0.194816	−	0.112477i
$987$		0			0
$988$	−15.2539	−	26.4206i	−0.0154392	−	0.0267415i
$989$	−30.3825	−	17.5413i	−0.0307204	−	0.0177365i
$990$		0			0
$991$	408.799	+	708.061i	0.412512	+	0.714492i	0.995164	−	0.0982303i	$-0.0313182\pi$
$991$	408.799	+	708.061i	0.412512	+	0.714492i	−0.582652	+	0.812722i	$0.697985\pi$
$992$		−	583.235i		−	0.587938i
$993$		0			0
$994$	89.5160	−	291.369i	0.0900563	−	0.293128i
$995$	1879.38	+	1085.06i	1.88882	+	1.09051i
$996$		0			0
$997$	−782.249	+	1354.90i	−0.784603	+	1.35897i	0.144633	+	0.989485i	$0.453800\pi$
$997$	−782.249	+	1354.90i	−0.784603	+	1.35897i	−0.929236	+	0.369487i	$0.879534\pi$
$998$	2261.77	−	1305.83i	2.26630	−	1.30845i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.b.44.11		22
3.2	odd	2		63.3.j.b.23.1	yes	22
7.4	even	3		189.3.n.b.179.1		22
9.2	odd	6		189.3.n.b.170.1		22
9.7	even	3		63.3.n.b.2.11	yes	22
21.2	odd	6		441.3.r.g.50.1		22
21.5	even	6		441.3.r.f.50.1		22
21.11	odd	6		63.3.n.b.32.11	yes	22
21.17	even	6		441.3.n.f.410.11		22
21.20	even	2		441.3.j.f.275.1		22
63.11	odd	6	inner	189.3.j.b.116.1		22
63.16	even	3		441.3.r.g.344.1		22
63.25	even	3		63.3.j.b.11.11	✓	22
63.34	odd	6		441.3.n.f.128.11		22
63.52	odd	6		441.3.j.f.263.11		22
63.61	odd	6		441.3.r.f.344.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.11	✓	22	63.25	even	3
63.3.j.b.23.1	yes	22	3.2	odd	2
63.3.n.b.2.11	yes	22	9.7	even	3
63.3.n.b.32.11	yes	22	21.11	odd	6
189.3.j.b.44.11		22	1.1	even	1	trivial
189.3.j.b.116.1		22	63.11	odd	6	inner
189.3.n.b.170.1		22	9.2	odd	6
189.3.n.b.179.1		22	7.4	even	3
441.3.j.f.263.11		22	63.52	odd	6
441.3.j.f.275.1		22	21.20	even	2
441.3.n.f.128.11		22	63.34	odd	6
441.3.n.f.410.11		22	21.17	even	6
441.3.r.f.50.1		22	21.5	even	6
441.3.r.f.344.1		22	63.61	odd	6
441.3.r.g.50.1		22	21.2	odd	6
441.3.r.g.344.1		22	63.16	even	3

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.87176i q^{2} -4.24700 q^{4} +(6.53753 - 3.77444i) q^{5} +(2.05575 - 6.69133i) q^{7} -0.709334i q^{8} +O(q^{10})\)	\(q+2.87176i q^{2} -4.24700 q^{4} +(6.53753 - 3.77444i) q^{5} +(2.05575 - 6.69133i) q^{7} -0.709334i q^{8} +(10.8393 + 18.7742i) q^{10} +(13.1630 + 7.59968i) q^{11} +(4.30409 - 7.45491i) q^{13} +(19.2159 + 5.90361i) q^{14} -14.9510 q^{16} +(4.60986 - 2.66151i) q^{17} +(-0.417241 + 0.722683i) q^{19} +(-27.7649 + 16.0301i) q^{20} +(-21.8244 + 37.8010i) q^{22} +(-33.8873 + 19.5648i) q^{23} +(15.9929 - 27.7005i) q^{25} +(21.4087 + 12.3603i) q^{26} +(-8.73076 + 28.4181i) q^{28} +(-12.5660 + 7.25497i) q^{29} +12.7419 q^{31} -45.7729i q^{32} +(7.64320 + 13.2384i) q^{34} +(-11.8165 - 51.5041i) q^{35} +(-11.7490 + 20.3498i) q^{37} +(-2.07537 - 1.19822i) q^{38} +(-2.67734 - 4.63730i) q^{40} +(13.4288 + 7.75311i) q^{41} +(0.448287 + 0.776457i) q^{43} +(-55.9034 - 32.2759i) q^{44} +(-56.1855 - 97.3162i) q^{46} +2.35402i q^{47} +(-40.5478 - 27.5114i) q^{49} +(79.5491 + 45.9277i) q^{50} +(-18.2795 + 31.6610i) q^{52} +(31.4529 - 18.1593i) q^{53} +114.738 q^{55} +(-4.74639 - 1.45821i) q^{56} +(-20.8345 - 36.0864i) q^{58} +48.6111i q^{59} -29.6074 q^{61} +36.5917i q^{62} +71.6450 q^{64} -64.9823i q^{65} +92.5333 q^{67} +(-19.5781 + 11.3034i) q^{68} +(147.907 - 33.9343i) q^{70} -15.1629i q^{71} +(-46.8054 - 81.0693i) q^{73} +(-58.4398 - 33.7402i) q^{74} +(1.77203 - 3.06924i) q^{76} +(77.9118 - 72.4551i) q^{77} -82.1651 q^{79} +(-97.7425 + 56.4316i) q^{80} +(-22.2651 + 38.5642i) q^{82} +(-127.067 + 73.3621i) q^{83} +(20.0914 - 34.7993i) q^{85} +(-2.22980 + 1.28737i) q^{86} +(5.39071 - 9.33699i) q^{88} +(-92.3105 - 53.2955i) q^{89} +(-41.0351 - 44.1255i) q^{91} +(143.920 - 83.0920i) q^{92} -6.76019 q^{94} +6.29942i q^{95} +(-26.0332 - 45.0908i) q^{97} +(79.0060 - 116.444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) 22 * q - 24 * q^4 - 12 * q^5	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Introduction

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