LMFDB - Embedded newform 189.3.j.b.116.1

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			116.1
Character	$\chi$	$=$	189.116
Dual form			189.3.j.b.44.11

$q$-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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.745085\pi$
$2$		−	2.87176i		−	1.43588i	0.696105	−	0.717940i	$-0.254915\pi$
$3$		0			0
$3$		0			0
$4$	−4.24700			−1.06175
$5$	6.53753	+	3.77444i	1.30751	+	0.754889i	0.981679	−	0.190541i	$-0.0610241\pi$
$5$	6.53753	+	3.77444i	1.30751	+	0.754889i	0.325827	+	0.945430i	$0.394357\pi$
$6$		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	0.236835	−	0.971550i	$-0.423890\pi$
$11$	13.1630	−	7.59968i	1.19664	−	0.690880i	0.959804	+	0.280670i	$0.0905567\pi$
$12$		0			0
$13$	4.30409	+	7.45491i	0.331084	+	0.573455i	0.982725	−	0.185073i	$-0.0592522\pi$
$13$	4.30409	+	7.45491i	0.331084	+	0.573455i	−0.651641	+	0.758528i	$0.725919\pi$
$14$	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	0.629419	−	0.777066i	$-0.283293\pi$
$17$	4.60986	+	2.66151i	0.271168	+	0.156559i	−0.358250	+	0.933626i	$0.616626\pi$
$18$		0			0
$19$	−0.417241	−	0.722683i	−0.0219601	−	0.0380360i	0.854837	−	0.518897i	$-0.173657\pi$
$19$	−0.417241	−	0.722683i	−0.0219601	−	0.0380360i	−0.876797	+	0.480861i	$0.840324\pi$
$20$	−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	−0.473811	−	0.880627i	$-0.657122\pi$
$23$	−33.8873	−	19.5648i	−1.47336	−	0.850646i	−0.999550	+	0.0299810i	$0.990455\pi$
$24$		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	0.267446	−	0.963573i	$-0.413820\pi$
$29$	−12.5660	−	7.25497i	−0.433309	−	0.250171i	−0.700755	+	0.713402i	$0.747154\pi$
$30$		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	0.662434	−	0.749120i	$-0.269523\pi$
$37$	−11.7490	−	20.3498i	−0.317540	−	0.549995i	−0.979974	+	0.199125i	$0.936190\pi$
$38$	−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	−0.327213	−	0.944951i	$-0.606110\pi$
$41$	13.4288	−	7.75311i	0.327531	−	0.189100i	0.654744	+	0.755850i	$0.272776\pi$
$42$		0			0
$43$	0.448287	−	0.776457i	0.0104253	−	0.0180571i	−0.860766	−	0.509001i	$-0.830015\pi$
$43$	0.448287	−	0.776457i	0.0104253	−	0.0180571i	0.871191	+	0.490944i	$0.163348\pi$
$44$	−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	$-0.992028\pi$
$47$		−	2.35402i		−	0.0500856i	0.999686	−	0.0250428i	$-0.00797220\pi$
$48$		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	0.766461	−	0.642291i	$-0.222016\pi$
$53$	31.4529	+	18.1593i	0.593451	+	0.342629i	−0.173010	+	0.984920i	$0.555349\pi$
$54$		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	$-0.864845\pi$
$59$		−	48.6111i		−	0.823917i	0.911203	−	0.411958i	$-0.135155\pi$
$60$		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	$0.0340544\pi$
$71$			15.1629i			0.213562i	−0.994283	+	0.106781i	$0.965946\pi$
$72$		0			0
$73$	−46.8054	+	81.0693i	−0.641170	+	1.11054i	0.344002	+	0.938969i	$0.388217\pi$
$73$	−46.8054	+	81.0693i	−0.641170	+	1.11054i	−0.985172	+	0.171570i	$0.945116\pi$
$74$	−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	−0.999319	−	0.0368900i	$-0.988255\pi$
$83$	−127.067	−	73.3621i	−1.53093	−	0.883881i	−0.531607	−	0.846991i	$-0.678412\pi$
$84$		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	−0.919038	−	0.394169i	$-0.871033\pi$
$89$	−92.3105	+	53.2955i	−1.03720	+	0.598826i	−0.118159	+	0.992995i	$0.537699\pi$
$90$		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	−0.968445	−	0.249229i	$-0.919823\pi$
$97$	−26.0332	+	45.0908i	−0.268383	+	0.464854i	0.700061	+	0.714083i	$0.253156\pi$
$98$	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	−0.0536643	−	0.998559i	$-0.517090\pi$
$101$	79.2124	−	45.7333i	0.784281	−	0.452805i	0.837945	+	0.545754i	$0.183757\pi$
$102$		0			0
$103$	−9.71277	+	16.8230i	−0.0942987	+	0.163330i	−0.909316	−	0.416107i	$-0.863394\pi$
$103$	−9.71277	+	16.8230i	−0.0942987	+	0.163330i	0.815017	+	0.579437i	$0.196728\pi$
$104$	−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	0.0145363	−	0.999894i	$-0.495373\pi$
$107$	94.9880	−	54.8414i	0.887738	−	0.512536i	0.873202	+	0.487358i	$0.162039\pi$
$108$		0			0
$109$	−33.2718	+	57.6285i	−0.305246	+	0.528702i	−0.977316	−	0.211786i	$-0.932072\pi$
$109$	−33.2718	+	57.6285i	−0.305246	+	0.528702i	0.672070	+	0.740488i	$0.265405\pi$
$110$		−	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	−0.963186	−	0.268837i	$-0.913361\pi$
$113$	−136.951	+	79.0689i	−1.21196	+	0.699725i	−0.248773	+	0.968562i	$0.580027\pi$
$114$		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	0.219819	−	0.975541i	$-0.429453\pi$
$131$	−67.4799	−	38.9596i	−0.515114	−	0.297401i	−0.734933	+	0.678139i	$0.762787\pi$
$132$		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	−0.983939	−	0.178503i	$-0.942875\pi$
$137$	−181.021	+	104.512i	−1.32132	+	0.762865i	−0.337381	+	0.941368i	$0.609541\pi$
$138$		0			0
$139$	−95.9201	−	166.138i	−0.690073	−	1.19524i	−0.971814	−	0.235750i	$-0.924245\pi$
$139$	−95.9201	−	166.138i	−0.690073	−	1.19524i	0.281741	−	0.959490i	$-0.409088\pi$
$140$	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	0.259745	−	0.965677i	$-0.416362\pi$
$149$	−66.5560	−	38.4261i	−0.446684	−	0.257893i	−0.706429	+	0.707784i	$0.749695\pi$
$150$		0			0
$151$	40.3574	+	69.9011i	0.267268	+	0.462921i	0.968155	−	0.250351i	$-0.0805459\pi$
$151$	40.3574	+	69.9011i	0.267268	+	0.462921i	−0.700888	+	0.713272i	$0.747213\pi$
$152$	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	0.938115	+	0.346323i	$0.112570\pi$
$163$	125.344	+	217.102i	0.768982	+	1.33192i	−0.169133	+	0.985593i	$0.554097\pi$
$164$	−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	−0.0391347	−	0.999234i	$-0.512460\pi$
$167$	134.712	−	77.7761i	0.806660	−	0.465725i	0.845795	+	0.533509i	$0.179127\pi$
$168$		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	$0.0588761\pi$
$173$			63.6335i			0.367824i	−0.982943	+	0.183912i	$0.941124\pi$
$174$		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	−0.145250	−	0.989395i	$-0.546399\pi$
$179$	−192.374	−	111.067i	−1.07472	−	0.620488i	−0.929466	+	0.368908i	$0.879732\pi$
$180$		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	$0.0157548\pi$
$191$			18.8994i			0.0989499i	−0.998775	+	0.0494749i	$0.984245\pi$
$192$		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	$0.144741\pi$
$197$			173.048i			0.878418i	−0.898385	+	0.439209i	$0.855259\pi$
$198$		0			0
$199$	143.738	−	248.961i	0.722300	−	1.25106i	−0.237776	−	0.971320i	$-0.576418\pi$
$199$	143.738	−	248.961i	0.722300	−	1.25106i	0.960076	−	0.279740i	$-0.0902482\pi$
$200$	−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	−0.764697	−	0.644390i	$-0.777111\pi$
$211$	−198.426	−	343.684i	−0.940407	−	1.62883i	−0.175709	−	0.984442i	$-0.556222\pi$
$212$	−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	−0.385335	+	0.922777i	$0.625914\pi$
$223$	−221.175	+	383.086i	−0.991816	+	1.71787i	−0.606481	+	0.795098i	$0.707419\pi$
$224$	−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	−0.456250	−	0.889851i	$-0.650808\pi$
$227$	19.5806	−	11.3049i	0.0862583	−	0.0498012i	0.542509	+	0.840050i	$0.317475\pi$
$228$		0			0
$229$	37.6161	−	65.1531i	0.164263	−	0.284511i	−0.772131	−	0.635464i	$-0.780809\pi$
$229$	37.6161	−	65.1531i	0.164263	−	0.284511i	0.936393	+	0.350953i	$0.114142\pi$
$230$	−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	−0.0706034	−	0.997504i	$-0.522492\pi$
$233$	176.604	−	101.963i	0.757959	−	0.437608i	0.828562	+	0.559897i	$0.189159\pi$
$234$		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	−0.00101792	−	0.999999i	$-0.500324\pi$
$239$	206.615	−	119.289i	0.864498	−	0.499118i	0.865516	+	0.500881i	$0.166991\pi$
$240$		0			0
$241$	178.663	+	309.453i	0.741340	+	1.28404i	0.951886	+	0.306454i	$0.0991425\pi$
$241$	178.663	+	309.453i	0.741340	+	1.28404i	−0.210546	+	0.977584i	$0.567524\pi$
$242$	−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	$0.171469\pi$
$251$			257.530i			1.02602i	−0.858384	+	0.513008i	$0.828531\pi$
$252$		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	0.427442	−	0.904043i	$-0.359415\pi$
$257$	−36.4327	−	21.0344i	−0.141761	−	0.0818459i	−0.569203	+	0.822197i	$0.692748\pi$
$258$		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	0.338679	−	0.940902i	$-0.390020\pi$
$263$	347.913	−	200.868i	1.32286	−	0.763755i	0.984184	+	0.177147i	$0.0566867\pi$
$264$		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	0.956254	−	0.292539i	$-0.0945000\pi$
$269$	317.698	+	183.423i	1.18103	+	0.681871i	0.224781	+	0.974409i	$0.427833\pi$
$270$		0			0
$271$	−50.7938	−	87.9774i	−0.187431	−	0.324640i	0.756962	−	0.653459i	$-0.226683\pi$
$271$	−50.7938	−	87.9774i	−0.187431	−	0.324640i	−0.944393	+	0.328819i	$0.893349\pi$
$272$	−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	0.768709	−	0.639599i	$-0.220899\pi$
$277$	−46.9665	−	81.3484i	−0.169554	−	0.293676i	−0.938263	+	0.345922i	$0.887566\pi$
$278$	−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	0.360568	−	0.932733i	$-0.382583\pi$
$281$	−75.0040	−	43.3036i	−0.266918	−	0.154105i	−0.627486	+	0.778628i	$0.715916\pi$
$282$		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	−0.237646	−	0.971352i	$-0.576376\pi$
$293$	142.031	−	82.0014i	0.484746	−	0.279868i	0.722392	+	0.691483i	$0.243042\pi$
$294$		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	$-0.829254\pi$
$311$		−	317.877i		−	1.02211i	0.859547	−	0.511056i	$-0.170746\pi$
$312$		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	$-0.972140\pi$
$317$		−	55.4193i		−	0.174824i	0.996172	−	0.0874121i	$-0.0278597\pi$
$318$		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	0.988001	+	0.154450i	$0.0493607\pi$
$337$	211.555	+	366.423i	0.627758	+	1.08731i	−0.360242	+	0.932859i	$0.617306\pi$
$338$	−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	$-0.948529\pi$
$347$		−	111.732i		−	0.321994i	0.986955	−	0.160997i	$-0.0514709\pi$
$348$		0			0
$349$	192.127	−	332.774i	0.550508	−	0.953507i	−0.447730	−	0.894169i	$-0.647768\pi$
$349$	192.127	−	332.774i	0.550508	−	0.953507i	0.998238	−	0.0593385i	$-0.0188991\pi$
$350$	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	−0.956451	−	0.291894i	$-0.905715\pi$
$353$	−417.207	+	240.874i	−1.18189	+	0.682363i	−0.225438	+	0.974258i	$0.572381\pi$
$354$		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	−0.369569	−	0.929203i	$-0.620495\pi$
$359$	89.8795	−	51.8919i	0.250361	−	0.144546i	0.619929	+	0.784658i	$0.287161\pi$
$360$		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	−0.927256	−	0.374427i	$-0.877839\pi$
$367$	−289.156	−	500.833i	−0.787891	−	1.36467i	0.139365	−	0.990241i	$-0.455494\pi$
$368$	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	−0.951103	−	0.308875i	$-0.900047\pi$
$373$	−77.6054	+	134.416i	−0.208057	+	0.360366i	0.743045	+	0.669241i	$0.233381\pi$
$374$		−	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	0.512465	−	0.858708i	$-0.328733\pi$
$383$	9.58788	+	5.53557i	0.0250336	+	0.0144532i	−0.487431	+	0.873162i	$0.662066\pi$
$384$		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	−0.867440	−	0.497542i	$-0.834236\pi$
$389$	−338.537	+	195.455i	−0.870276	+	0.502454i	−0.00283618	+	0.999996i	$0.500903\pi$
$390$		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	0.989363	+	0.145469i	$0.0464693\pi$
$397$	246.403	+	426.782i	0.620662	+	1.07502i	−0.368701	+	0.929548i	$0.620197\pi$
$398$	−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	0.445794	−	0.895135i	$-0.352921\pi$
$401$	−42.7138	−	24.6608i	−0.106518	−	0.0614983i	−0.552313	+	0.833637i	$0.686255\pi$
$402$		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	−0.430933	−	0.902384i	$-0.641816\pi$
$419$	56.6016	−	32.6790i	0.135087	−	0.0779928i	0.566021	+	0.824391i	$0.308482\pi$
$420$		0			0
$421$	33.2471	−	57.5856i	0.0789717	−	0.136783i	−0.823835	−	0.566830i	$-0.808170\pi$
$421$	33.2471	−	57.5856i	0.0789717	−	0.136783i	0.902807	+	0.430047i	$0.141503\pi$
$422$	−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	0.457654	−	0.889130i	$-0.348690\pi$
$431$	−36.0005	−	20.7849i	−0.0835278	−	0.0482248i	−0.541182	+	0.840905i	$0.682023\pi$
$432$		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	$-0.697895\pi$
$443$		−	720.218i		−	1.62577i	0.582421	−	0.812887i	$-0.302105\pi$
$444$		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	$0.0730783\pi$
$449$			204.358i			0.455141i	−0.973762	+	0.227571i	$0.926922\pi$
$450$		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	0.573623	−	0.819119i	$-0.305537\pi$
$461$	69.6371	+	40.2050i	0.151057	+	0.0872125i	−0.422567	+	0.906332i	$0.638871\pi$
$462$		0			0
$463$	217.055	+	375.951i	0.468802	+	0.811989i	0.999364	−	0.0356574i	$-0.0113525\pi$
$463$	217.055	+	375.951i	0.468802	+	0.811989i	−0.530562	+	0.847646i	$0.678019\pi$
$464$	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	−0.966782	−	0.255603i	$-0.917726\pi$
$467$	−573.856	+	331.316i	−1.22881	+	0.709456i	−0.262033	+	0.965059i	$0.584393\pi$
$468$		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	−0.215983	−	0.976397i	$-0.569296\pi$
$479$	249.851	−	144.252i	0.521610	−	0.301152i	0.737593	+	0.675245i	$0.235962\pi$
$480$		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	0.396015	+	0.918244i	$0.370393\pi$
$487$	−290.844	+	503.756i	−0.597215	+	1.03441i	−0.993230	+	0.116163i	$0.962940\pi$
$488$		−	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	−0.549521	−	0.835480i	$-0.685190\pi$
$491$	−49.4611	+	28.5564i	−0.100735	+	0.0581597i	0.448786	+	0.893639i	$0.351857\pi$
$492$		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	−0.0989598	+	0.995091i	$0.531552\pi$
$499$	−454.716	+	787.591i	−0.911254	+	1.57834i	−0.812295	+	0.583247i	$0.801782\pi$
$500$		−	223.964i		−	0.447928i
$501$		0			0
$502$	739.565			1.47324
$503$			399.576i			0.794386i	0.917735	+	0.397193i	$0.130016\pi$
$503$			399.576i			0.794386i	−0.917735	+	0.397193i	$0.869984\pi$
$504$		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	0.799088	−	0.601215i	$-0.205316\pi$
$509$	345.084	+	199.234i	0.677964	+	0.391423i	−0.121123	+	0.992637i	$0.538650\pi$
$510$		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	0.455209	−	0.890384i	$-0.349564\pi$
$521$	−45.9947	−	26.5550i	−0.0882815	−	0.0509693i	−0.543491	+	0.839415i	$0.682898\pi$
$522$		0			0
$523$	321.356	+	556.605i	0.614447	+	1.06425i	0.990481	+	0.137648i	$0.0439542\pi$
$523$	321.356	+	556.605i	0.614447	+	1.06425i	−0.376034	+	0.926606i	$0.622712\pi$
$524$	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	0.704192	−	0.710009i	$-0.251309\pi$
$541$	−142.169	−	246.244i	−0.262790	−	0.455165i	−0.966982	+	0.254844i	$0.917976\pi$
$542$	−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	−0.946703	−	0.322107i	$-0.895609\pi$
$547$	−106.336	+	184.180i	−0.194399	+	0.336708i	0.752305	+	0.658816i	$0.228942\pi$
$548$	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	0.924351	−	0.381544i	$-0.124607\pi$
$557$	588.247	+	339.625i	1.05610	+	0.609739i	0.131749	+	0.991283i	$0.457941\pi$
$558$		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	$0.157491\pi$
$563$			534.661i			0.949665i	−0.880076	+	0.474832i	$0.842509\pi$
$564$		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	$0.146945\pi$
$569$			506.885i			0.890835i	−0.895323	+	0.445417i	$0.853055\pi$
$570$		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	−0.949863	−	0.312668i	$-0.898777\pi$
$577$	−117.796	+	204.029i	−0.204153	+	0.353604i	0.745709	+	0.666271i	$0.232111\pi$
$578$	−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	0.535938	−	0.844258i	$-0.319958\pi$
$587$	42.7089	+	24.6580i	0.0727580	+	0.0420068i	−0.463180	+	0.886264i	$0.653292\pi$
$588$		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	−0.483222	−	0.875498i	$-0.660534\pi$
$593$	19.7883	−	11.4248i	0.0333698	−	0.0192661i	0.516592	+	0.856232i	$0.327200\pi$
$594$		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	$0.195493\pi$
$599$			690.372i			1.15254i	−0.817259	+	0.576271i	$0.804507\pi$
$600$		0			0
$601$	242.122	−	419.367i	0.402865	−	0.697783i	−0.591205	−	0.806521i	$-0.701348\pi$
$601$	242.122	−	419.367i	0.402865	−	0.697783i	0.994070	+	0.108738i	$0.0346810\pi$
$602$	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	−0.411631	−	0.911351i	$-0.635041\pi$
$607$	354.147	−	613.400i	0.583437	−	1.01054i	0.995068	−	0.0991927i	$-0.0316260\pi$
$608$	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	−0.116634	−	0.993175i	$-0.537211\pi$
$613$	491.502	−	851.306i	0.801798	−	1.38875i	0.918432	−	0.395579i	$-0.129456\pi$
$614$		−	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	−0.506175	−	0.862431i	$-0.668941\pi$
$617$	−7.63528	+	4.40823i	−0.0123748	+	0.00714462i	0.493800	+	0.869576i	$0.335608\pi$
$618$		0			0
$619$	65.4219	+	113.314i	0.105690	+	0.183060i	0.914020	−	0.405670i	$-0.132962\pi$
$619$	65.4219	+	113.314i	0.105690	+	0.183060i	−0.808330	+	0.588730i	$0.799628\pi$
$620$	−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	−0.162501	−	0.986708i	$-0.551956\pi$
$641$	391.499	−	226.032i	0.610763	−	0.352624i	0.773264	+	0.634084i	$0.218623\pi$
$642$		0			0
$643$	409.902	+	709.971i	0.637484	+	1.10415i	0.985983	+	0.166845i	$0.0533580\pi$
$643$	409.902	+	709.971i	0.637484	+	1.10415i	−0.348499	+	0.937309i	$0.613309\pi$
$644$	−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	0.960743	−	0.277440i	$-0.0894860\pi$
$647$	776.946	+	448.570i	1.20084	+	0.693308i	0.240101	+	0.970748i	$0.422819\pi$
$648$		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	0.0928321	−	0.995682i	$-0.470408\pi$
$653$	−472.144	−	272.592i	−0.723038	−	0.417446i	−0.815870	+	0.578236i	$0.803741\pi$
$654$		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	0.972083	−	0.234638i	$-0.0753904\pi$
$659$	826.994	+	477.465i	1.25492	+	0.724530i	0.282839	+	0.959167i	$0.408724\pi$
$660$		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	−0.995982	−	0.0895494i	$-0.971457\pi$
$673$	−282.956	+	490.093i	−0.420439	+	0.728222i	0.575543	+	0.817771i	$0.304791\pi$
$674$	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	$0.223518\pi$
$677$			874.549i			1.29180i	−0.763421	+	0.645901i	$0.776482\pi$
$678$		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	−0.998760	−	0.0497801i	$-0.984148\pi$
$683$	−1052.67	−	607.762i	−1.54125	−	0.889842i	−0.542491	−	0.840062i	$-0.682519\pi$
$684$		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	$0.0307471\pi$
$701$			135.215i			0.192889i	−0.995338	+	0.0964447i	$0.969253\pi$
$702$		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	−0.119695	−	0.992811i	$-0.538192\pi$
$719$	489.105	−	282.385i	0.680257	−	0.392747i	0.799952	+	0.600064i	$0.204858\pi$
$720$		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	−0.936493	−	0.350687i	$-0.885948\pi$
$727$	−119.623	+	207.192i	−0.164543	+	0.284996i	0.771950	+	0.635683i	$0.219282\pi$
$728$	−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	0.395587	+	0.918429i	$0.370541\pi$
$733$	−438.033	+	758.695i	−0.597589	+	1.03505i	−0.993176	+	0.116626i	$0.962792\pi$
$734$	−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	0.444165	+	0.895945i	$0.353500\pi$
$739$	−409.279	+	708.893i	−0.553829	+	0.959259i	−0.997994	+	0.0633143i	$0.979833\pi$
$740$			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	0.219370	−	0.975642i	$-0.429600\pi$
$743$	872.271	−	503.606i	1.17399	−	0.677801i	0.954615	+	0.297841i	$0.0962666\pi$
$744$		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	−0.901593	−	0.432586i	$-0.857601\pi$
$751$	−57.2003	+	99.0738i	−0.0761655	+	0.131922i	0.825427	+	0.564509i	$0.190934\pi$
$752$			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	−0.321274	−	0.946986i	$-0.604111\pi$
$761$	−990.841	−	572.063i	−1.30203	−	0.751725i	−0.980751	+	0.195262i	$0.937444\pi$
$762$		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	0.614362	−	0.789024i	$-0.289413\pi$
$769$	−289.247	−	500.990i	−0.376134	−	0.651483i	−0.990496	+	0.137541i	$0.956080\pi$
$770$	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	−0.998000	−	0.0632163i	$-0.979864\pi$
$773$	−1199.50	−	692.532i	−1.55175	−	0.895901i	−0.553747	−	0.832685i	$-0.686802\pi$
$774$		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	0.0421573	−	0.999111i	$-0.486577\pi$
$797$	740.008	−	427.244i	0.928491	−	0.536065i	0.886334	+	0.463046i	$0.153244\pi$
$798$		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	−0.129716	−	0.991551i	$-0.541406\pi$
$809$	−852.105	−	491.963i	−1.05328	−	0.608113i	−0.923566	+	0.383439i	$0.874740\pi$
$810$		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	$-0.791236\pi$
$821$		−	1001.35i		−	1.21967i	0.792529	−	0.609835i	$-0.208764\pi$
$822$		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	$0.0755897\pi$
$827$			389.098i			0.470493i	−0.971936	+	0.235246i	$0.924410\pi$
$828$		0			0
$829$	−701.276	+	1214.65i	−0.845930	+	1.46519i	0.0388805	+	0.999244i	$0.487621\pi$
$829$	−701.276	+	1214.65i	−0.845930	+	1.46519i	−0.884811	+	0.465950i	$0.845713\pi$
$830$	−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	0.162916	−	0.986640i	$-0.447910\pi$
$839$	−511.858	−	295.521i	−0.610081	−	0.352230i	−0.772997	+	0.634409i	$0.781243\pi$
$840$		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	−0.164168	−	0.986432i	$-0.552494\pi$
$853$	658.680	−	1140.87i	0.772192	−	1.33748i	0.936359	−	0.351043i	$-0.114173\pi$
$854$	−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	−0.0964831	−	0.995335i	$-0.530759\pi$
$857$	614.692	−	354.893i	0.717260	−	0.414110i	0.813744	+	0.581224i	$0.197426\pi$
$858$		0			0
$859$	−285.323	+	494.193i	−0.332157	+	0.575312i	−0.982934	−	0.183956i	$-0.941110\pi$
$859$	−285.323	+	494.193i	−0.332157	+	0.575312i	0.650778	+	0.759268i	$0.274443\pi$
$860$	−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	−0.555866	−	0.831272i	$-0.687613\pi$
$863$	−98.2922	+	56.7490i	−0.113896	+	0.0657579i	0.441970	+	0.897030i	$0.354280\pi$
$864$		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	−0.439162	−	0.898408i	$-0.644725\pi$
$877$	489.772	−	848.310i	0.558463	−	0.967286i	0.997625	−	0.0688781i	$-0.0219420\pi$
$878$		−	1590.52i		−	1.81153i
$879$		0			0
$880$	−1715.45			−1.94937
$881$			1090.83i			1.23817i	0.785322	+	0.619087i	$0.212497\pi$
$881$			1090.83i			1.23817i	−0.785322	+	0.619087i	$0.787503\pi$
$882$		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	0.504657	−	0.863320i	$-0.331619\pi$
$887$	8.27405	+	4.77703i	0.00932813	+	0.00538560i	−0.495329	+	0.868706i	$0.664952\pi$
$888$		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	0.993715	−	0.111943i	$-0.0357075\pi$
$907$	362.720	+	628.249i	0.399911	+	0.692667i	−0.593803	+	0.804610i	$0.702374\pi$
$908$	−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	−0.314581	−	0.949231i	$-0.601864\pi$
$911$	−1178.77	−	680.563i	−1.29393	−	0.747051i	−0.979348	+	0.202180i	$0.935197\pi$
$912$		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	−0.864116	−	0.503293i	$-0.832122\pi$
$919$	−797.621	−	1381.52i	−0.867923	−	1.50329i	−0.00380700	−	0.999993i	$-0.501212\pi$
$920$	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	$-0.948455\pi$
$929$		−	299.558i		−	0.322452i	0.986918	−	0.161226i	$-0.0515448\pi$
$930$		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	$-0.636762\pi$
$941$		−	1710.95i		−	1.81822i	0.416553	−	0.909112i	$-0.363238\pi$
$942$		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	$0.151090\pi$
$947$			865.629i			0.914075i	−0.889447	+	0.457038i	$0.848910\pi$
$948$		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	$-0.844721\pi$
$953$		−	893.350i		−	0.937408i	0.883355	−	0.468704i	$-0.155279\pi$
$954$		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	−0.995059	−	0.0992813i	$-0.968346\pi$
$967$	−564.254	−	977.317i	−0.583510	−	1.01067i	0.411550	−	0.911387i	$-0.364988\pi$
$968$	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	−0.842314	−	0.538987i	$-0.818807\pi$
$971$	−773.591	+	446.633i	−0.796695	+	0.459972i	0.0456189	+	0.998959i	$0.485474\pi$
$972$		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	$-0.989973\pi$
$977$		−	61.5411i		−	0.0629899i	0.999504	−	0.0314949i	$-0.0100268\pi$
$978$		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	−0.954314	−	0.298806i	$-0.903412\pi$
$983$	−1152.76	+	665.547i	−1.17270	+	0.677057i	−0.218384	+	0.975863i	$0.570078\pi$
$984$		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	−0.582652	−	0.812722i	$-0.697985\pi$
$991$	408.799	−	708.061i	0.412512	−	0.714492i	0.995164	+	0.0982303i	$0.0313182\pi$
$992$			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	−0.929236	−	0.369487i	$-0.879534\pi$
$997$	−782.249	−	1354.90i	−0.784603	−	1.35897i	0.144633	−	0.989485i	$-0.453800\pi$
$998$	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.116.1		22
3.2	odd	2		63.3.j.b.11.11	✓	22
7.2	even	3		189.3.n.b.170.1		22
9.4	even	3		63.3.n.b.32.11	yes	22
9.5	odd	6		189.3.n.b.179.1		22
21.2	odd	6		63.3.n.b.2.11	yes	22
21.5	even	6		441.3.n.f.128.11		22
21.11	odd	6		441.3.r.g.344.1		22
21.17	even	6		441.3.r.f.344.1		22
21.20	even	2		441.3.j.f.263.11		22
63.4	even	3		441.3.r.g.50.1		22
63.13	odd	6		441.3.n.f.410.11		22
63.23	odd	6	inner	189.3.j.b.44.11		22
63.31	odd	6		441.3.r.f.50.1		22
63.40	odd	6		441.3.j.f.275.1		22
63.58	even	3		63.3.j.b.23.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.11	✓	22	3.2	odd	2
63.3.j.b.23.1	yes	22	63.58	even	3
63.3.n.b.2.11	yes	22	21.2	odd	6
63.3.n.b.32.11	yes	22	9.4	even	3
189.3.j.b.44.11		22	63.23	odd	6	inner
189.3.j.b.116.1		22	1.1	even	1	trivial
189.3.n.b.170.1		22	7.2	even	3
189.3.n.b.179.1		22	9.5	odd	6
441.3.j.f.263.11		22	21.20	even	2
441.3.j.f.275.1		22	63.40	odd	6
441.3.n.f.128.11		22	21.5	even	6
441.3.n.f.410.11		22	63.13	odd	6
441.3.r.f.50.1		22	63.31	odd	6
441.3.r.f.344.1		22	21.17	even	6
441.3.r.g.50.1		22	63.4	even	3
441.3.r.g.344.1		22	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
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

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