LMFDB - Embedded newform 189.3.k.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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([2, 1]))

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

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	189.19
Dual form			189.3.k.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91801 - 3.32210i) q^{2} +(-5.35756 + 9.27956i) q^{4} -0.216546i q^{5} +(6.73498 + 1.90790i) q^{7} +25.7594 q^{8} +O(q^{10})$	\(q+(-1.91801 - 3.32210i) q^{2} +(-5.35756 + 9.27956i) q^{4} -0.216546i q^{5} +(6.73498 + 1.90790i) q^{7} +25.7594 q^{8} +(-0.719386 + 0.415338i) q^{10} -4.44949 q^{11} +(14.9299 - 8.61978i) q^{13} +(-6.57956 - 26.0336i) q^{14} +(-27.9766 - 48.4569i) q^{16} +(4.66285 - 2.69210i) q^{17} +(-6.88143 - 3.97300i) q^{19} +(2.00945 + 1.16016i) q^{20} +(8.53419 + 14.7817i) q^{22} +19.0646 q^{23} +24.9531 q^{25} +(-57.2715 - 33.0657i) q^{26} +(-53.7875 + 52.2760i) q^{28} +(-3.57302 + 6.18865i) q^{29} +(-20.0333 - 11.5662i) q^{31} +(-55.8003 + 96.6489i) q^{32} +(-17.8868 - 10.3270i) q^{34} +(0.413147 - 1.45843i) q^{35} +(5.16805 - 8.95133i) q^{37} +30.4811i q^{38} -5.57808i q^{40} +(-3.32321 + 1.91866i) q^{41} +(30.1335 - 52.1928i) q^{43} +(23.8384 - 41.2893i) q^{44} +(-36.5662 - 63.3346i) q^{46} +(42.4184 - 24.4902i) q^{47} +(41.7199 + 25.6993i) q^{49} +(-47.8604 - 82.8967i) q^{50} +184.724i q^{52} +(-25.0404 - 43.3713i) q^{53} +0.963519i q^{55} +(173.489 + 49.1462i) q^{56} +27.4124 q^{58} +(75.2337 + 43.4362i) q^{59} +(35.6207 - 20.5656i) q^{61} +88.7368i q^{62} +204.290 q^{64} +(-1.86658 - 3.23301i) q^{65} +(-32.1806 + 55.7384i) q^{67} +57.6923i q^{68} +(-5.63747 + 1.42478i) q^{70} +11.8036 q^{71} +(-27.7422 + 16.0170i) q^{73} -39.6496 q^{74} +(73.7353 - 42.5711i) q^{76} +(-29.9672 - 8.48917i) q^{77} +(-7.26004 - 12.5748i) q^{79} +(-10.4931 + 6.05821i) q^{80} +(12.7479 + 7.36003i) q^{82} +(-94.9566 - 54.8232i) q^{83} +(-0.582963 - 1.00972i) q^{85} -231.186 q^{86} -114.616 q^{88} +(111.515 + 64.3830i) q^{89} +(116.998 - 29.5693i) q^{91} +(-102.140 + 176.911i) q^{92} +(-162.718 - 93.9453i) q^{94} +(-0.860336 + 1.49015i) q^{95} +(63.3289 + 36.5629i) q^{97} +(5.35626 - 187.889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.91801	−	3.32210i	−0.959007	−	1.66105i	−0.724920	−	0.688833i	$-0.758123\pi$
$2$	−1.91801	−	3.32210i	−0.959007	−	1.66105i	−0.234087	−	0.972216i	$-0.575210\pi$
$3$		0			0
$3$		0			0
$4$	−5.35756	+	9.27956i	−1.33939	+	2.31989i
$5$		−	0.216546i		−	0.0433092i	−0.999766	−	0.0216546i	$-0.993107\pi$
$5$		−	0.216546i		−	0.0433092i	0.999766	−	0.0216546i	$-0.00689340\pi$
$6$		0			0
$7$	6.73498	+	1.90790i	0.962140	+	0.272557i
$7$	6.73498	+	1.90790i	0.962140	+	0.272557i
$8$	25.7594			3.21992
$9$		0			0
$10$	−0.719386	+	0.415338i	−0.0719386	+	0.0415338i
$11$	−4.44949			−0.404499			−0.202250	−	0.979334i	$-0.564825\pi$
$11$	−4.44949			−0.404499			−0.202250	+	0.979334i	$0.564825\pi$
$12$		0			0
$13$	14.9299	−	8.61978i	1.14845	−	0.663060i	0.199944	−	0.979807i	$-0.435924\pi$
$13$	14.9299	−	8.61978i	1.14845	−	0.663060i	0.948510	+	0.316747i	$0.102591\pi$
$14$	−6.57956	−	26.0336i	−0.469969	−	1.85954i
$15$		0			0
$16$	−27.9766	−	48.4569i	−1.74854	−	3.02856i
$17$	4.66285	−	2.69210i	0.274285	−	0.158359i	−0.356548	−	0.934277i	$-0.616046\pi$
$17$	4.66285	−	2.69210i	0.274285	−	0.158359i	0.630834	+	0.775918i	$0.282713\pi$
$18$		0			0
$19$	−6.88143	−	3.97300i	−0.362181	−	0.209105i	0.307856	−	0.951433i	$-0.400388\pi$
$19$	−6.88143	−	3.97300i	−0.362181	−	0.209105i	−0.670037	+	0.742328i	$0.733722\pi$
$20$	2.00945	+	1.16016i	0.100472	+	0.0580078i
$21$		0			0
$22$	8.53419	+	14.7817i	0.387918	+	0.671893i
$23$	19.0646			0.828897			0.414449	−	0.910073i	$-0.363974\pi$
$23$	19.0646			0.828897			0.414449	+	0.910073i	$0.363974\pi$
$24$		0			0
$25$	24.9531			0.998124
$26$	−57.2715	−	33.0657i	−2.20275	−	1.27176i
$27$		0			0
$28$	−53.7875	+	52.2760i	−1.92098	+	1.86700i
$29$	−3.57302	+	6.18865i	−0.123208	+	0.213402i	−0.921031	−	0.389490i	$-0.872651\pi$
$29$	−3.57302	+	6.18865i	−0.123208	+	0.213402i	0.797823	+	0.602891i	$0.205985\pi$
$30$		0			0
$31$	−20.0333	−	11.5662i	−0.646236	−	0.373104i	0.140777	−	0.990041i	$-0.455040\pi$
$31$	−20.0333	−	11.5662i	−0.646236	−	0.373104i	−0.787013	+	0.616937i	$0.788373\pi$
$32$	−55.8003	+	96.6489i	−1.74376	+	3.02028i
$33$		0			0
$34$	−17.8868	−	10.3270i	−0.526083	−	0.303734i
$35$	0.413147	−	1.45843i	0.0118042	−	0.0416695i
$36$		0			0
$37$	5.16805	−	8.95133i	0.139677	−	0.241928i	−0.787697	−	0.616062i	$-0.788727\pi$
$37$	5.16805	−	8.95133i	0.139677	−	0.241928i	0.927374	+	0.374135i	$0.122060\pi$
$38$			30.4811i			0.802133i
$39$		0			0
$40$		−	5.57808i		−	0.139452i
$41$	−3.32321	+	1.91866i	−0.0810540	+	0.0467965i	−0.539979	−	0.841678i	$-0.681568\pi$
$41$	−3.32321	+	1.91866i	−0.0810540	+	0.0467965i	0.458925	+	0.888475i	$0.348235\pi$
$42$		0			0
$43$	30.1335	−	52.1928i	0.700779	−	1.21379i	−0.267414	−	0.963582i	$-0.586169\pi$
$43$	30.1335	−	52.1928i	0.700779	−	1.21379i	0.968193	−	0.250204i	$-0.0804976\pi$
$44$	23.8384	−	41.2893i	0.541782	−	0.938394i
$45$		0			0
$46$	−36.5662	−	63.3346i	−0.794918	−	1.37684i
$47$	42.4184	−	24.4902i	0.902518	−	0.521069i	0.0245019	−	0.999700i	$-0.492200\pi$
$47$	42.4184	−	24.4902i	0.902518	−	0.521069i	0.878016	+	0.478631i	$0.158867\pi$
$48$		0			0
$49$	41.7199	+	25.6993i	0.851426	+	0.524475i
$50$	−47.8604	−	82.8967i	−0.957208	−	1.65793i
$51$		0			0
$52$			184.724i			3.55238i
$53$	−25.0404	−	43.3713i	−0.472461	−	0.818326i	0.527043	−	0.849839i	$-0.323301\pi$
$53$	−25.0404	−	43.3713i	−0.472461	−	0.818326i	−0.999503	+	0.0315128i	$0.989967\pi$
$54$		0			0
$55$			0.963519i			0.0175185i
$56$	173.489	+	49.1462i	3.09801	+	0.877611i
$57$		0			0
$58$	27.4124			0.472628
$59$	75.2337	+	43.4362i	1.27515	+	0.736207i	0.975952	−	0.217985i	$-0.0699484\pi$
$59$	75.2337	+	43.4362i	1.27515	+	0.736207i	0.299196	+	0.954192i	$0.403282\pi$
$60$		0			0
$61$	35.6207	−	20.5656i	0.583946	−	0.337141i	−0.178754	−	0.983894i	$-0.557207\pi$
$61$	35.6207	−	20.5656i	0.583946	−	0.337141i	0.762700	+	0.646752i	$0.223873\pi$
$62$			88.7368i			1.43124i
$63$		0			0
$64$	204.290			3.19203
$65$	−1.86658	−	3.23301i	−0.0287166	−	0.0497386i
$66$		0			0
$67$	−32.1806	+	55.7384i	−0.480307	+	0.831916i	−0.999745	−	0.0225922i	$-0.992808\pi$
$67$	−32.1806	+	55.7384i	−0.480307	+	0.831916i	0.519438	+	0.854508i	$0.326141\pi$
$68$			57.6923i			0.848416i
$69$		0			0
$70$	−5.63747	+	1.42478i	−0.0805353	+	0.0203540i
$71$	11.8036			0.166247			0.0831237	−	0.996539i	$-0.473510\pi$
$71$	11.8036			0.166247			0.0831237	+	0.996539i	$0.473510\pi$
$72$		0			0
$73$	−27.7422	+	16.0170i	−0.380030	+	0.219411i	−0.677831	−	0.735217i	$-0.737080\pi$
$73$	−27.7422	+	16.0170i	−0.380030	+	0.219411i	0.297801	+	0.954628i	$0.403747\pi$
$74$	−39.6496			−0.535805
$75$		0			0
$76$	73.7353	−	42.5711i	0.970202	−	0.560146i
$77$	−29.9672	−	8.48917i	−0.389185	−	0.110249i
$78$		0			0
$79$	−7.26004	−	12.5748i	−0.0918992	−	0.159174i	0.816411	−	0.577471i	$-0.195960\pi$
$79$	−7.26004	−	12.5748i	−0.0918992	−	0.159174i	−0.908310	+	0.418297i	$0.862627\pi$
$80$	−10.4931	+	6.05821i	−0.131164	+	0.0757277i
$81$		0			0
$82$	12.7479	+	7.36003i	0.155463	+	0.0897564i
$83$	−94.9566	−	54.8232i	−1.14406	−	0.660521i	−0.196624	−	0.980479i	$-0.562998\pi$
$83$	−94.9566	−	54.8232i	−1.14406	−	0.660521i	−0.947432	+	0.319958i	$0.896331\pi$
$84$		0			0
$85$	−0.582963	−	1.00972i	−0.00685839	−	0.0118791i
$86$	−231.186			−2.68821
$87$		0			0
$88$	−114.616			−1.30246
$89$	111.515	+	64.3830i	1.25297	+	0.723405i	0.971699	−	0.236222i	$-0.0759094\pi$
$89$	111.515	+	64.3830i	1.25297	+	0.723405i	0.281275	+	0.959627i	$0.409243\pi$
$90$		0			0
$91$	116.998	−	29.5693i	1.28569	−	0.324938i
$92$	−102.140	+	176.911i	−1.11022	+	1.92295i
$93$		0			0
$94$	−162.718	−	93.9453i	−1.73104	−	0.999418i
$95$	−0.860336	+	1.49015i	−0.00905616	+	0.0156857i
$96$		0			0
$97$	63.3289	+	36.5629i	0.652875	+	0.376938i	0.789557	−	0.613677i	$-0.210310\pi$
$97$	63.3289	+	36.5629i	0.652875	+	0.376938i	−0.136682	+	0.990615i	$0.543644\pi$
$98$	5.35626	−	187.889i	0.0546557	−	1.91724i
$99$		0			0
$100$	−133.688	+	231.554i	−1.33688	+	2.31554i
$101$			8.68191i			0.0859595i	0.999076	+	0.0429797i	$0.0136851\pi$
$101$			8.68191i			0.0859595i	−0.999076	+	0.0429797i	$0.986315\pi$
$102$		0			0
$103$			121.454i			1.17917i	0.807708	+	0.589583i	$0.200708\pi$
$103$			121.454i			1.17917i	−0.807708	+	0.589583i	$0.799292\pi$
$104$	384.585	−	222.040i	3.69793	−	2.13500i
$105$		0			0
$106$	−96.0558	+	166.373i	−0.906186	+	1.56956i
$107$	−94.5629	+	163.788i	−0.883766	+	1.53073i	−0.0366442	+	0.999328i	$0.511667\pi$
$107$	−94.5629	+	163.788i	−0.883766	+	1.53073i	−0.847122	+	0.531399i	$0.821667\pi$
$108$		0			0
$109$	−58.4112	−	101.171i	−0.535883	−	0.928176i	−0.999120	−	0.0419419i	$-0.986646\pi$
$109$	−58.4112	−	101.171i	−0.535883	−	0.928176i	0.463237	−	0.886234i	$-0.346688\pi$
$110$	3.20090	−	1.84804i	0.0290991	−	0.0168004i
$111$		0			0
$112$	−95.9710	−	379.732i	−0.856884	−	3.39047i
$113$	−0.633432	−	1.09714i	−0.00560559	−	0.00970917i	0.863209	−	0.504847i	$-0.168451\pi$
$113$	−0.633432	−	1.09714i	−0.00560559	−	0.00970917i	−0.868815	+	0.495138i	$0.835118\pi$
$114$		0			0
$115$		−	4.12837i		−	0.0358988i
$116$	−38.2853	−	66.3121i	−0.330046	−	0.571656i
$117$		0			0
$118$		−	333.245i		−	2.82411i
$119$	36.5405	−	9.23499i	0.307063	−	0.0776050i
$120$		0			0
$121$	−101.202			−0.836380
$122$	−136.642	−	78.8903i	−1.12002	−	0.646642i
$123$		0			0
$124$	214.659	−	123.934i	1.73112	−	0.999464i
$125$		−	10.8171i		−	0.0865371i
$126$		0			0
$127$	−92.8864			−0.731389			−0.365694	−	0.930735i	$-0.619168\pi$
$127$	−92.8864			−0.731389			−0.365694	+	0.930735i	$0.619168\pi$
$128$	−168.630	−	292.076i	−1.31742	−	2.28185i
$129$		0			0
$130$	−7.16025	+	12.4019i	−0.0550788	+	0.0953993i
$131$			174.694i			1.33354i	0.745264	+	0.666769i	$0.232323\pi$
$131$			174.694i			1.33354i	−0.745264	+	0.666769i	$0.767677\pi$
$132$		0			0
$133$	−38.7662	−	39.8871i	−0.291475	−	0.299903i
$134$	246.891			1.84247
$135$		0			0
$136$	120.112	−	69.3468i	0.883177	−	0.509903i
$137$	−24.0716			−0.175705			−0.0878527	−	0.996133i	$-0.528000\pi$
$137$	−24.0716			−0.175705			−0.0878527	+	0.996133i	$0.528000\pi$
$138$		0			0
$139$	−153.847	+	88.8239i	−1.10682	+	0.639021i	−0.938003	−	0.346627i	$-0.887327\pi$
$139$	−153.847	+	88.8239i	−1.10682	+	0.639021i	−0.168814	+	0.985648i	$0.553994\pi$
$140$	11.3201	+	11.6474i	0.0808581	+	0.0831961i
$141$		0			0
$142$	−22.6394	−	39.2126i	−0.159432	−	0.276145i
$143$	−66.4305	+	38.3537i	−0.464549	+	0.268207i
$144$		0			0
$145$	1.34013	+	0.773722i	0.00924225	+	0.00533601i
$146$	106.420	+	61.4416i	0.728904	+	0.420833i
$147$		0			0
$148$	55.3763	+	95.9145i	0.374164	+	0.648071i
$149$	102.143			0.685521			0.342760	−	0.939423i	$-0.388638\pi$
$149$	102.143			0.685521			0.342760	+	0.939423i	$0.388638\pi$
$150$		0			0
$151$	−133.141			−0.881730			−0.440865	−	0.897573i	$-0.645328\pi$
$151$	−133.141			−0.881730			−0.440865	+	0.897573i	$0.645328\pi$
$152$	−177.261	−	102.342i	−1.16619	−	0.673302i
$153$		0			0
$154$	29.2757	+	115.836i	0.190102	+	0.752185i
$155$	−2.50462	+	4.33813i	−0.0161588	+	0.0279879i
$156$		0			0
$157$	87.6068	+	50.5798i	0.558005	+	0.322164i	0.752344	−	0.658770i	$-0.228923\pi$
$157$	87.6068	+	50.5798i	0.558005	+	0.322164i	−0.194339	+	0.980934i	$0.562256\pi$
$158$	−27.8497	+	48.2371i	−0.176264	+	0.305298i
$159$		0			0
$160$	20.9289	+	12.0833i	0.130806	+	0.0755207i
$161$	128.400	+	36.3734i	0.797515	+	0.225921i
$162$		0			0
$163$	−83.7340	+	145.032i	−0.513706	+	0.889764i	0.486168	+	0.873865i	$0.338394\pi$
$163$	−83.7340	+	145.032i	−0.513706	+	0.889764i	−0.999874	+	0.0158987i	$0.994939\pi$
$164$		−	41.1173i		−	0.250715i
$165$		0			0
$166$			420.607i			2.53378i
$167$	−103.598	+	59.8122i	−0.620346	+	0.358157i	−0.777004	−	0.629496i	$-0.783261\pi$
$167$	−103.598	+	59.8122i	−0.620346	+	0.358157i	0.156657	+	0.987653i	$0.449928\pi$
$168$		0			0
$169$	64.1014	−	111.027i	0.379298	−	0.656963i
$170$	−2.23626	+	3.87332i	−0.0131545	+	0.0227842i
$171$		0			0
$172$	322.884	+	559.252i	1.87723	+	3.25146i
$173$	190.599	−	110.043i	1.10173	−	0.636084i	0.165055	−	0.986284i	$-0.447220\pi$
$173$	190.599	−	110.043i	1.10173	−	0.636084i	0.936675	+	0.350200i	$0.113886\pi$
$174$		0			0
$175$	168.059	+	47.6080i	0.960335	+	0.272045i
$176$	124.482	+	215.609i	0.707282	+	1.22505i
$177$		0			0
$178$		−	493.950i		−	2.77500i
$179$	−81.8994	−	141.854i	−0.457538	−	0.792480i	0.541292	−	0.840835i	$-0.317935\pi$
$179$	−81.8994	−	141.854i	−0.457538	−	0.792480i	−0.998830	+	0.0483550i	$0.984602\pi$
$180$		0			0
$181$		−	152.286i		−	0.841359i	−0.907209	−	0.420680i	$-0.861792\pi$
$181$		−	152.286i		−	0.841359i	0.907209	−	0.420680i	$-0.138208\pi$
$182$	−322.637	−	331.965i	−1.77273	−	1.82398i
$183$		0			0
$184$	491.093			2.66898
$185$	−1.93837	−	1.11912i	−0.0104777	−	0.00604930i
$186$		0			0
$187$	−20.7473	+	11.9785i	−0.110948	+	0.0640560i
$188$			524.832i			2.79166i
$189$		0			0
$190$	6.60054			0.0347397
$191$	6.15506	+	10.6609i	0.0322254	+	0.0558161i	0.881688	−	0.471832i	$-0.156407\pi$
$191$	6.15506	+	10.6609i	0.0322254	+	0.0558161i	−0.849463	+	0.527648i	$0.823074\pi$
$192$		0			0
$193$	134.599	−	233.132i	0.697402	−	1.20794i	−0.271963	−	0.962308i	$-0.587673\pi$
$193$	134.599	−	233.132i	0.697402	−	1.20794i	0.969364	−	0.245627i	$-0.0789940\pi$
$194$		−	280.513i		−	1.44594i
$195$		0			0
$196$	−461.995	+	249.457i	−2.35712	+	1.27274i
$197$	−302.183			−1.53392			−0.766962	−	0.641692i	$-0.778233\pi$
$197$	−302.183			−1.53392			−0.766962	+	0.641692i	$0.778233\pi$
$198$		0			0
$199$	−83.0117	+	47.9268i	−0.417144	+	0.240838i	−0.693855	−	0.720115i	$-0.744089\pi$
$199$	−83.0117	+	47.9268i	−0.417144	+	0.240838i	0.276710	+	0.960953i	$0.410756\pi$
$200$	642.776			3.21388
$201$		0			0
$202$	28.8421	−	16.6520i	0.142783	−	0.0824358i
$203$	−35.8715	+	34.8635i	−0.176707	+	0.171741i
$204$		0			0
$205$	0.415477	+	0.719628i	0.00202672	+	0.00351038i
$206$	403.482	−	232.951i	1.95865	−	1.13083i
$207$		0			0
$208$	−835.376	−	482.304i	−4.01623	−	2.31877i
$209$	30.6189	+	17.6778i	0.146502	+	0.0845829i
$210$		0			0
$211$	−45.2108	−	78.3074i	−0.214269	−	0.371125i	0.738777	−	0.673950i	$-0.235404\pi$
$211$	−45.2108	−	78.3074i	−0.214269	−	0.371125i	−0.953046	+	0.302825i	$0.902070\pi$
$212$	536.622			2.53124
$213$		0			0
$214$	725.492			3.39015
$215$	−11.3021	−	6.52529i	−0.0525680	−	0.0303502i
$216$		0			0
$217$	−112.857	−	116.120i	−0.520077	−	0.535115i
$218$	−224.067	+	388.096i	−1.02783	+	1.78026i
$219$		0			0
$220$	−8.94103	−	5.16211i	−0.0406410	−	0.0234641i
$221$	46.4106	−	80.3856i	0.210003	−	0.363736i
$222$		0			0
$223$	204.519	+	118.079i	0.917128	+	0.529504i	0.882718	−	0.469904i	$-0.155711\pi$
$223$	204.519	+	118.079i	0.917128	+	0.529504i	0.0344100	+	0.999408i	$0.489045\pi$
$224$	−560.210	+	544.467i	−2.50094	+	2.43066i
$225$		0			0
$226$	−2.42986	+	4.20865i	−0.0107516	+	0.0186223i
$227$		−	88.9796i		−	0.391981i	−0.980606	−	0.195990i	$-0.937208\pi$
$227$		−	88.9796i		−	0.391981i	0.980606	−	0.195990i	$-0.0627921\pi$
$228$		0			0
$229$		−	49.5079i		−	0.216192i	−0.994140	−	0.108096i	$-0.965525\pi$
$229$		−	49.5079i		−	0.216192i	0.994140	−	0.108096i	$-0.0344753\pi$
$230$	−13.7148	+	7.91826i	−0.0596297	+	0.0344272i
$231$		0			0
$232$	−92.0387	+	159.416i	−0.396718	+	0.687136i
$233$	65.4443	−	113.353i	0.280877	−	0.486493i	−0.690724	−	0.723119i	$-0.742708\pi$
$233$	65.4443	−	113.353i	0.280877	−	0.486493i	0.971601	+	0.236625i	$0.0760414\pi$
$234$		0			0
$235$	−5.30326	−	9.18552i	−0.0225671	−	0.0390873i
$236$	−806.138	+	465.424i	−3.41584	+	1.97213i
$237$		0			0
$238$	−100.765	−	103.678i	−0.423381	−	0.435622i
$239$	25.0661	+	43.4158i	0.104879	+	0.181656i	0.913689	−	0.406415i	$-0.133221\pi$
$239$	25.0661	+	43.4158i	0.104879	+	0.181656i	−0.808810	+	0.588070i	$0.799888\pi$
$240$		0			0
$241$			297.883i			1.23603i	0.786166	+	0.618015i	$0.212063\pi$
$241$			297.883i			1.23603i	−0.786166	+	0.618015i	$0.787937\pi$
$242$	194.107	+	336.203i	0.802095	+	1.38927i
$243$		0			0
$244$			440.726i			1.80625i
$245$	5.56507	−	9.03426i	0.0227146	−	0.0368745i
$246$		0			0
$247$	−136.985			−0.554597
$248$	−516.045	−	297.939i	−2.08083	−	1.20137i
$249$		0			0
$250$	−35.9356	+	20.7474i	−0.143742	+	0.0829897i
$251$		−	450.825i		−	1.79612i	−0.439876	−	0.898059i	$-0.644978\pi$
$251$		−	450.825i		−	1.79612i	0.439876	−	0.898059i	$-0.355022\pi$
$252$		0			0
$253$	−84.8280			−0.335288
$254$	178.157	+	308.578i	0.701407	+	1.21487i
$255$		0			0
$256$	−238.290	+	412.731i	−0.930821	+	1.61223i
$257$		−	413.145i		−	1.60757i	−0.594922	−	0.803784i	$-0.702817\pi$
$257$		−	413.145i		−	1.60757i	0.594922	−	0.803784i	$-0.297183\pi$
$258$		0			0
$259$	51.8849	−	50.4269i	0.200328	−	0.194698i
$260$	40.0012			0.153851
$261$		0			0
$262$	580.349	−	335.065i	2.21507	−	1.27887i
$263$	−448.072			−1.70370			−0.851848	−	0.523789i	$-0.824518\pi$
$263$	−448.072			−1.70370			−0.851848	+	0.523789i	$0.824518\pi$
$264$		0			0
$265$	−9.39187	+	5.42240i	−0.0354410	+	0.0204619i
$266$	−58.1547	+	205.289i	−0.218627	+	0.771764i
$267$		0			0
$268$	−344.818	−	597.243i	−1.28664	−	2.22852i
$269$	−438.590	+	253.220i	−1.63044	+	0.941338i	−0.646489	+	0.762923i	$0.723763\pi$
$269$	−438.590	+	253.220i	−1.63044	+	0.941338i	−0.983955	+	0.178414i	$0.942903\pi$
$270$		0			0
$271$	313.473	+	180.984i	1.15673	+	0.667837i	0.950518	−	0.310671i	$-0.100554\pi$
$271$	313.473	+	180.984i	1.15673	+	0.667837i	0.206210	+	0.978508i	$0.433887\pi$
$272$	−260.902	−	150.632i	−0.959197	−	0.553792i
$273$		0			0
$274$	46.1698	+	79.9684i	0.168503	+	0.291855i
$275$	−111.029			−0.403741
$276$		0			0
$277$	−85.4610			−0.308523			−0.154262	−	0.988030i	$-0.549300\pi$
$277$	−85.4610			−0.308523			−0.154262	+	0.988030i	$0.549300\pi$
$278$	590.163	+	340.731i	2.12289	+	1.22565i
$279$		0			0
$280$	10.6424	−	37.5683i	0.0380086	−	0.134172i
$281$	100.522	−	174.109i	0.357729	−	0.619605i	−0.629852	−	0.776715i	$-0.716884\pi$
$281$	100.522	−	174.109i	0.357729	−	0.619605i	0.987581	+	0.157110i	$0.0502177\pi$
$282$		0			0
$283$	−40.7414	−	23.5220i	−0.143962	−	0.0831168i	0.426289	−	0.904587i	$-0.359821\pi$
$283$	−40.7414	−	23.5220i	−0.143962	−	0.0831168i	−0.570251	+	0.821470i	$0.693154\pi$
$284$	−63.2383	+	109.532i	−0.222670	+	0.385676i
$285$		0			0
$286$	254.829	+	147.126i	0.891011	+	0.514426i
$287$	−26.0424	+	6.58177i	−0.0907400	+	0.0229330i
$288$		0			0
$289$	−130.005	+	225.176i	−0.449845	+	0.779154i
$290$		−	5.93604i		−	0.0204691i
$291$		0			0
$292$		−	343.247i		−	1.17550i
$293$	418.946	−	241.878i	1.42985	−	0.825524i	0.432741	−	0.901518i	$-0.357546\pi$
$293$	418.946	−	241.878i	1.42985	−	0.825524i	0.997108	+	0.0759945i	$0.0242132\pi$
$294$		0			0
$295$	9.40593	−	16.2915i	0.0318845	−	0.0552256i
$296$	133.126	−	230.581i	0.449749	−	0.778988i
$297$		0			0
$298$	−195.911	−	339.328i	−0.657419	−	1.13868i
$299$	284.633	−	164.333i	0.951950	−	0.549609i
$300$		0			0
$301$	302.527	−	294.026i	1.00507	−	0.976829i
$302$	255.367	+	442.308i	0.845585	+	1.46460i
$303$		0			0
$304$			444.604i			1.46251i
$305$	−4.45340	−	7.71351i	−0.0146013	−	0.0252902i
$306$		0			0
$307$			53.9925i			0.175871i	0.996126	+	0.0879356i	$0.0280270\pi$
$307$			53.9925i			0.175871i	−0.996126	+	0.0879356i	$0.971973\pi$
$308$	239.327	−	232.602i	0.777035	−	0.755200i
$309$		0			0
$310$	19.2156			0.0619858
$311$	−128.833	−	74.3816i	−0.414253	−	0.239169i	0.278362	−	0.960476i	$-0.410208\pi$
$311$	−128.833	−	74.3816i	−0.414253	−	0.239169i	−0.692616	+	0.721307i	$0.743542\pi$
$312$		0			0
$313$	−379.730	+	219.237i	−1.21320	+	0.700439i	−0.963454	−	0.267873i	$-0.913679\pi$
$313$	−379.730	+	219.237i	−1.21320	+	0.700439i	−0.249742	+	0.968312i	$0.580346\pi$
$314$		−	388.051i		−	1.23583i
$315$		0			0
$316$	155.584			0.492355
$317$	175.901	+	304.669i	0.554893	+	0.961102i	0.997912	+	0.0645901i	$0.0205740\pi$
$317$	175.901	+	304.669i	0.554893	+	0.961102i	−0.443019	+	0.896512i	$0.646093\pi$
$318$		0			0
$319$	15.8981	−	27.5363i	0.0498374	−	0.0863208i
$320$		−	44.2382i		−	0.138244i
$321$		0			0
$322$	−125.437	−	496.322i	−0.389556	−	1.54137i
$323$	−42.7828			−0.132455
$324$		0			0
$325$	372.548	−	215.090i	1.14630	−	0.661817i
$326$	642.412			1.97059
$327$		0			0
$328$	−85.6038	+	49.4234i	−0.260987	+	0.150681i
$329$	332.412	−	84.0115i	1.01037	−	0.255354i
$330$		0			0
$331$	−11.4830	−	19.8891i	−0.0346918	−	0.0600879i	0.848158	−	0.529743i	$-0.177712\pi$
$331$	−11.4830	−	19.8891i	−0.0346918	−	0.0600879i	−0.882850	+	0.469655i	$0.844378\pi$
$332$	1017.47	−	587.437i	3.06467	−	1.76939i
$333$		0			0
$334$	397.404	+	229.441i	1.18983	+	0.686950i
$335$	12.0699	+	6.96857i	0.0360296	+	0.0208017i
$336$		0			0
$337$	−27.9036	−	48.3305i	−0.0828000	−	0.143414i	0.821652	−	0.569990i	$-0.193053\pi$
$337$	−27.9036	−	48.3305i	−0.0828000	−	0.143414i	−0.904452	+	0.426576i	$0.859720\pi$
$338$	−491.789			−1.45500
$339$		0			0
$340$	12.4930			0.0367442
$341$	89.1381	+	51.4639i	0.261402	+	0.150921i
$342$		0			0
$343$	231.951	+	252.681i	0.676241	+	0.736680i
$344$	776.220	−	1344.45i	2.25645	−	3.90829i
$345$		0			0
$346$	−731.144	−	422.126i	−2.11313	−	1.22002i
$347$	−27.5470	+	47.7128i	−0.0793862	+	0.137501i	−0.902985	−	0.429672i	$-0.858629\pi$
$347$	−27.5470	+	47.7128i	−0.0793862	+	0.137501i	0.823599	+	0.567172i	$0.191963\pi$
$348$		0			0
$349$	−253.798	−	146.530i	−0.727213	−	0.419857i	0.0901884	−	0.995925i	$-0.471253\pi$
$349$	−253.798	−	146.530i	−0.727213	−	0.419857i	−0.817402	+	0.576068i	$0.804586\pi$
$350$	−164.181	−	649.620i	−0.469087	−	1.85606i
$351$		0			0
$352$	248.283	−	430.039i	0.705349	−	1.22170i
$353$			189.862i			0.537852i	0.963161	+	0.268926i	$0.0866687\pi$
$353$			189.862i			0.537852i	−0.963161	+	0.268926i	$0.913331\pi$
$354$		0			0
$355$		−	2.55601i		−	0.00720004i
$356$	−1194.89	+	689.871i	−3.35644	+	1.93784i
$357$		0			0
$358$	−314.168	+	544.156i	−0.877565	+	1.51999i
$359$	−203.897	+	353.160i	−0.567959	+	0.983734i	0.428809	+	0.903395i	$0.358933\pi$
$359$	−203.897	+	353.160i	−0.567959	+	0.983734i	−0.996768	+	0.0803384i	$0.974400\pi$
$360$		0			0
$361$	−148.931	−	257.955i	−0.412550	−	0.714558i
$362$	−505.909	+	292.087i	−1.39754	+	0.806869i
$363$		0			0
$364$	−352.434	+	1244.11i	−0.968226	+	3.41789i
$365$	3.46841	+	6.00746i	0.00950249	+	0.0164588i
$366$		0			0
$367$			418.942i			1.14153i	0.821113	+	0.570765i	$0.193353\pi$
$367$			418.942i			1.14153i	−0.821113	+	0.570765i	$0.806647\pi$
$368$	−533.364	−	923.813i	−1.44936	−	2.51036i
$369$		0			0
$370$			8.58595i			0.0232053i
$371$	−85.8988	−	339.879i	−0.231533	−	0.916116i
$372$		0			0
$373$	−322.093			−0.863520			−0.431760	−	0.901989i	$-0.642107\pi$
$373$	−322.093			−0.863520			−0.431760	+	0.901989i	$0.642107\pi$
$374$	79.5873	+	45.9498i	0.212800	+	0.122860i
$375$		0			0
$376$	1092.67	−	630.853i	2.90604	−	1.67780i
$377$			123.195i			0.326776i
$378$		0			0
$379$	−191.824			−0.506131			−0.253066	−	0.967449i	$-0.581439\pi$
$379$	−191.824			−0.506131			−0.253066	+	0.967449i	$0.581439\pi$
$380$	−9.21859	−	15.9671i	−0.0242595	−	0.0420186i
$381$		0			0
$382$	23.6110	−	40.8954i	0.0618088	−	0.107056i
$383$			653.441i			1.70611i	0.521819	+	0.853056i	$0.325254\pi$
$383$			653.441i			1.70611i	−0.521819	+	0.853056i	$0.674746\pi$
$384$		0			0
$385$	−1.83829	+	6.48928i	−0.00477479	+	0.0168553i
$386$	−1032.65			−2.67525
$387$		0			0
$388$	−678.576	+	391.776i	−1.74891	+	1.00973i
$389$	−358.510			−0.921620			−0.460810	−	0.887499i	$-0.652441\pi$
$389$	−358.510			−0.921620			−0.460810	+	0.887499i	$0.652441\pi$
$390$		0			0
$391$	88.8956	−	51.3239i	0.227354	−	0.131263i
$392$	1074.68	+	661.997i	2.74152	+	1.68877i
$393$		0			0
$394$	579.591	+	1003.88i	1.47104	+	2.54792i
$395$	−2.72301	+	1.57213i	−0.00689369	+	0.00398008i
$396$		0			0
$397$	357.921	+	206.646i	0.901564	+	0.520518i	0.877707	−	0.479197i	$-0.159072\pi$
$397$	357.921	+	206.646i	0.901564	+	0.520518i	0.0238567	+	0.999715i	$0.492405\pi$
$398$	318.435	+	183.849i	0.800089	+	0.461931i
$399$		0			0
$400$	−698.103	−	1209.15i	−1.74526	−	3.02287i
$401$	142.265			0.354775			0.177387	−	0.984141i	$-0.443235\pi$
$401$	142.265			0.354775			0.177387	+	0.984141i	$0.443235\pi$
$402$		0			0
$403$	−398.794			−0.989563
$404$	−80.5643	−	46.5138i	−0.199417	−	0.115133i
$405$		0			0
$406$	184.622	+	52.3000i	0.454734	+	0.128818i
$407$	−22.9952	+	39.8289i	−0.0564993	+	0.0978596i
$408$		0			0
$409$	−67.1314	−	38.7583i	−0.164135	−	0.0947636i	0.415682	−	0.909510i	$-0.363543\pi$
$409$	−67.1314	−	38.7583i	−0.164135	−	0.0947636i	−0.579818	+	0.814746i	$0.696876\pi$
$410$	1.59378	−	2.76051i	0.00388727	−	0.00673296i
$411$		0			0
$412$	−1127.04	−	650.697i	−2.73553	−	1.57936i
$413$	423.826	+	436.080i	1.02621	+	1.05588i
$414$		0			0
$415$	−11.8717	+	20.5624i	−0.0286066	+	0.0495481i
$416$			1923.95i			4.62487i
$417$		0			0
$418$		−	135.625i		−	0.324462i
$419$	−579.375	+	334.502i	−1.38276	+	0.798335i	−0.992485	−	0.122364i	$-0.960952\pi$
$419$	−579.375	+	334.502i	−1.38276	+	0.798335i	−0.390272	+	0.920700i	$0.627619\pi$
$420$		0			0
$421$	224.704	−	389.199i	0.533738	−	0.924462i	−0.465485	−	0.885056i	$-0.654120\pi$
$421$	224.704	−	389.199i	0.533738	−	0.924462i	0.999223	−	0.0394062i	$-0.0125466\pi$
$422$	−173.430	+	300.390i	−0.410972	+	0.711824i
$423$		0			0
$424$	−645.025	−	1117.22i	−1.52129	−	2.63494i
$425$	116.353	−	67.1763i	0.273771	−	0.158062i
$426$		0			0
$427$	279.142	−	70.5484i	0.653728	−	0.165219i
$428$	−1013.25	−	1755.01i	−2.36741	−	4.10048i
$429$		0			0
$430$			50.0624i			0.116424i
$431$	−184.361	−	319.323i	−0.427753	−	0.740889i	0.568920	−	0.822393i	$-0.307361\pi$
$431$	−184.361	−	319.323i	−0.427753	−	0.740889i	−0.996673	+	0.0815032i	$0.974028\pi$
$432$		0			0
$433$		−	67.7473i		−	0.156460i	−0.996935	−	0.0782302i	$-0.975073\pi$
$433$		−	67.7473i		−	0.156460i	0.996935	−	0.0782302i	$-0.0249269\pi$
$434$	−169.301	+	597.641i	−0.390094	+	1.37705i
$435$		0			0
$436$	1251.77			2.87102
$437$	−131.192	−	75.7437i	−0.300211	−	0.173327i
$438$		0			0
$439$	117.191	−	67.6602i	0.266950	−	0.154123i	−0.360551	−	0.932740i	$-0.617411\pi$
$439$	117.191	−	67.6602i	0.266950	−	0.154123i	0.627501	+	0.778616i	$0.284078\pi$
$440$			24.8196i			0.0564082i
$441$		0			0
$442$	−356.065			−0.805577
$443$	−305.064	−	528.386i	−0.688632	−	1.19275i	−0.972281	−	0.233817i	$-0.924878\pi$
$443$	−305.064	−	528.386i	−0.688632	−	1.19275i	0.283649	−	0.958928i	$-0.408455\pi$
$444$		0			0
$445$	13.9419	−	24.1480i	0.0313301	−	0.0542652i
$446$		−	905.912i		−	2.03119i
$447$		0			0
$448$	1375.89	+	389.764i	3.07118	+	0.870010i
$449$	724.781			1.61421			0.807105	−	0.590408i	$-0.201033\pi$
$449$	724.781			1.61421			0.807105	+	0.590408i	$0.201033\pi$
$450$		0			0
$451$	14.7866	−	8.53705i	0.0327863	−	0.0189292i
$452$	13.5746			0.0300323
$453$		0			0
$454$	−295.599	+	170.664i	−0.651099	+	0.375912i
$455$	−6.40312	−	25.3355i	−0.0140728	−	0.0556824i
$456$		0			0
$457$	−163.923	−	283.922i	−0.358693	−	0.621274i	0.629050	−	0.777365i	$-0.283444\pi$
$457$	−163.923	−	283.922i	−0.358693	−	0.621274i	−0.987743	+	0.156091i	$0.950111\pi$
$458$	−164.470	+	94.9568i	−0.359105	+	0.207329i
$459$		0			0
$460$	38.3094	+	22.1180i	0.0832813	+	0.0480825i
$461$	−14.8524	−	8.57502i	−0.0322177	−	0.0186009i	0.483805	−	0.875176i	$-0.339255\pi$
$461$	−14.8524	−	8.57502i	−0.0322177	−	0.0186009i	−0.516022	+	0.856575i	$0.672588\pi$
$462$		0			0
$463$	114.904	+	199.020i	0.248173	+	0.429848i	0.963019	−	0.269434i	$-0.0868365\pi$
$463$	114.904	+	199.020i	0.248173	+	0.429848i	−0.714846	+	0.699282i	$0.753503\pi$
$464$	399.843			0.861732
$465$		0			0
$466$	−502.093			−1.07745
$467$	249.369	+	143.973i	0.533981	+	0.308294i	0.742636	−	0.669695i	$-0.233575\pi$
$467$	249.369	+	143.973i	0.533981	+	0.308294i	−0.208655	+	0.977989i	$0.566909\pi$
$468$		0			0
$469$	−323.078	+	314.000i	−0.688867	+	0.669509i
$470$	−20.3435	+	35.2359i	−0.0432839	+	0.0749700i
$471$		0			0
$472$	1937.97	+	1118.89i	4.10587	+	2.37053i
$473$	−134.079	+	232.231i	−0.283465	+	0.490975i
$474$		0			0
$475$	−171.713	−	99.1386i	−0.361501	−	0.208713i
$476$	−110.071	+	388.556i	−0.231241	+	0.816295i
$477$		0			0
$478$	96.1543	−	166.544i	0.201160	−	0.348419i
$479$			794.476i			1.65861i	0.558793	+	0.829307i	$0.311265\pi$
$479$			794.476i			1.65861i	−0.558793	+	0.829307i	$0.688735\pi$
$480$		0			0
$481$		−	178.190i		−	0.370457i
$482$	989.598	−	571.344i	2.05311	−	1.18536i
$483$		0			0
$484$	542.195	−	939.110i	1.12024	−	1.94031i
$485$	7.91755	−	13.7136i	0.0163248	−	0.0282755i
$486$		0			0
$487$	270.679	+	468.830i	0.555809	+	0.962689i	0.997840	+	0.0656896i	$0.0209247\pi$
$487$	270.679	+	468.830i	0.555809	+	0.962689i	−0.442031	+	0.897000i	$0.645742\pi$
$488$	917.567	−	529.757i	1.88026	−	1.08557i
$489$		0			0
$490$	−40.6866	−	1.15987i	−0.0830338	−	0.00236709i
$491$	138.981	+	240.722i	0.283057	+	0.490269i	0.972136	−	0.234417i	$-0.0753181\pi$
$491$	138.981	+	240.722i	0.283057	+	0.490269i	−0.689079	+	0.724686i	$0.741985\pi$
$492$		0			0
$493$			38.4757i			0.0780440i
$494$	262.740	+	455.079i	0.531863	+	0.921213i
$495$		0			0
$496$			1294.34i			2.60955i
$497$	79.4968	+	22.5200i	0.159953	+	0.0453118i
$498$		0			0
$499$	−484.244			−0.970429			−0.485215	−	0.874395i	$-0.661259\pi$
$499$	−484.244			−0.970429			−0.485215	+	0.874395i	$0.661259\pi$
$500$	100.378	+	57.9534i	0.200756	+	0.115907i
$501$		0			0
$502$	−1497.69	+	864.690i	−2.98344	+	1.72249i
$503$			328.342i			0.652768i	0.945237	+	0.326384i	$0.105830\pi$
$503$			328.342i			0.652768i	−0.945237	+	0.326384i	$0.894170\pi$
$504$		0			0
$505$	1.88003			0.00372283
$506$	162.701	+	281.807i	0.321544	+	0.556930i
$507$		0			0
$508$	497.644	−	861.945i	0.979614	−	1.69674i
$509$			168.117i			0.330288i	0.986269	+	0.165144i	$0.0528089\pi$
$509$			168.117i			0.330288i	−0.986269	+	0.165144i	$0.947191\pi$
$510$		0			0
$511$	−217.402	+	54.9447i	−0.425444	+	0.107524i
$512$	479.134			0.935808
$513$		0			0
$514$	−1372.51	+	792.418i	−2.67025	+	1.54167i
$515$	26.3004			0.0510687
$516$		0			0
$517$	−188.740	+	108.969i	−0.365068	+	0.210772i
$518$	−267.039	−	75.6473i	−0.515520	−	0.146037i
$519$		0			0
$520$	−48.0819	−	83.2802i	−0.0924651	−	0.160154i
$521$	418.280	−	241.494i	0.802841	−	0.463520i	−0.0416227	−	0.999133i	$-0.513253\pi$
$521$	418.280	−	241.494i	0.802841	−	0.463520i	0.844464	+	0.535613i	$0.179919\pi$
$522$		0			0
$523$	421.384	+	243.286i	0.805705	+	0.465174i	0.845462	−	0.534036i	$-0.179325\pi$
$523$	421.384	+	243.286i	0.805705	+	0.465174i	−0.0397574	+	0.999209i	$0.512658\pi$
$524$	−1621.08	−	935.930i	−3.09366	−	1.78613i
$525$		0			0
$526$	859.409	+	1488.54i	1.63386	+	2.82992i
$527$	−124.550			−0.236338
$528$		0			0
$529$	−165.540			−0.312929
$530$	36.0275	+	20.8005i	0.0679764	+	0.0392462i
$531$		0			0
$532$	577.827	−	146.036i	1.08614	−	0.274504i
$533$	−33.0768	+	57.2908i	−0.0620578	+	0.107487i
$534$		0			0
$535$	35.4676	+	20.4772i	0.0662945	+	0.0382752i
$536$	−828.951	+	1435.79i	−1.54655	+	2.67870i
$537$		0			0
$538$	1682.44	+	971.358i	3.12722	+	1.80550i
$539$	−185.632	−	114.349i	−0.344401	−	0.212150i
$540$		0			0
$541$	434.207	−	752.069i	0.802602	−	1.39015i	−0.115297	−	0.993331i	$-0.536782\pi$
$541$	434.207	−	752.069i	0.802602	−	1.39015i	0.917898	−	0.396816i	$-0.129885\pi$
$542$		−	1388.52i		−	2.56184i
$543$		0			0
$544$			600.880i			1.10456i
$545$	−21.9082	+	12.6487i	−0.0401985	+	0.0232086i
$546$		0			0
$547$	224.548	−	388.928i	0.410507	−	0.711020i	−0.584438	−	0.811438i	$-0.698685\pi$
$547$	224.548	−	388.928i	0.410507	−	0.711020i	0.994945	+	0.100419i	$0.0320183\pi$
$548$	128.965	−	223.374i	0.235338	−	0.407617i
$549$		0			0
$550$	212.955	+	368.848i	0.387190	+	0.670633i
$551$	49.1750	−	28.3912i	0.0892468	−	0.0515266i
$552$		0			0
$553$	−24.9049	−	98.5421i	−0.0450359	−	0.178195i
$554$	163.915	+	283.910i	0.295876	+	0.512472i
$555$		0			0
$556$		−	1903.52i		−	3.42359i
$557$	230.561	+	399.343i	0.413933	+	0.716953i	0.995316	−	0.0966773i	$-0.0308215\pi$
$557$	230.561	+	399.343i	0.413933	+	0.716953i	−0.581383	+	0.813630i	$0.697488\pi$
$558$		0			0
$559$		−	1038.98i		−	1.85864i
$560$	−82.2295	+	20.7821i	−0.146838	+	0.0371109i
$561$		0			0
$562$	−771.210			−1.37226
$563$	611.178	+	352.864i	1.08557	+	0.626756i	0.932395	−	0.361442i	$-0.117715\pi$
$563$	611.178	+	352.864i	1.08557	+	0.626756i	0.153179	+	0.988198i	$0.451049\pi$
$564$		0			0
$565$	−0.237580	+	0.137167i	−0.000420496	+	0.000242774i
$566$			180.462i			0.318838i
$567$		0			0
$568$	304.052			0.535303
$569$	−86.8202	−	150.377i	−0.152584	−	0.264283i	0.779593	−	0.626287i	$-0.215426\pi$
$569$	−86.8202	−	150.377i	−0.152584	−	0.264283i	−0.932177	+	0.362004i	$0.882093\pi$
$570$		0			0
$571$	−456.905	+	791.383i	−0.800185	+	1.38596i	0.119310	+	0.992857i	$0.461932\pi$
$571$	−456.905	+	791.383i	−0.800185	+	1.38596i	−0.919494	+	0.393103i	$0.871401\pi$
$572$		−	821.928i		−	1.43694i
$573$		0			0
$574$	71.8149	+	73.8914i	0.125113	+	0.128731i
$575$	475.722			0.827342
$576$		0			0
$577$	−151.096	+	87.2355i	−0.261865	+	0.151188i	−0.625185	−	0.780476i	$-0.714977\pi$
$577$	−151.096	+	87.2355i	−0.261865	+	0.151188i	0.363320	+	0.931664i	$0.381643\pi$
$578$	997.407			1.72562
$579$		0			0
$580$	−14.3596	+	8.29052i	−0.0247579	+	0.0142940i
$581$	−534.934	−	550.401i	−0.920712	−	0.947333i
$582$		0			0
$583$	111.417	+	192.980i	0.191110	+	0.331012i
$584$	−714.622	+	412.587i	−1.22367	+	0.706485i
$585$		0			0
$586$	−1607.09	−	927.853i	−2.74247	−	1.58337i
$587$	674.901	+	389.654i	1.14975	+	0.663807i	0.948825	−	0.315801i	$-0.102273\pi$
$587$	674.901	+	389.654i	1.14975	+	0.663807i	0.200921	+	0.979607i	$0.435606\pi$
$588$		0			0
$589$	91.9053	+	159.185i	0.156036	+	0.270262i
$590$	−72.1628			−0.122310
$591$		0			0
$592$	−578.338			−0.976922
$593$	−957.562	−	552.849i	−1.61478	−	0.932291i	−0.988242	−	0.152897i	$-0.951140\pi$
$593$	−957.562	−	552.849i	−1.61478	−	0.932291i	−0.626534	−	0.779394i	$-0.715527\pi$
$594$		0			0
$595$	−1.99980	−	7.91268i	−0.00336101	−	0.0132986i
$596$	−547.235	+	947.838i	−0.918179	+	1.59033i
$597$		0			0
$598$	−1091.86	−	630.386i	−1.82585	−	1.05416i
$599$	401.941	−	696.183i	0.671021	−	1.16224i	−0.306594	−	0.951840i	$-0.599190\pi$
$599$	401.941	−	696.183i	0.671021	−	1.16224i	0.977615	−	0.210402i	$-0.0674772\pi$
$600$		0			0
$601$	714.013	+	412.236i	1.18804	+	0.685916i	0.957861	−	0.287231i	$-0.0927349\pi$
$601$	714.013	+	412.236i	1.18804	+	0.685916i	0.230181	+	0.973148i	$0.426068\pi$
$602$	−1557.03	−	441.079i	−2.58643	−	0.732689i
$603$		0			0
$604$	713.312	−	1235.49i	1.18098	−	2.04552i
$605$			21.9149i			0.0362229i
$606$		0			0
$607$		−	1110.30i		−	1.82915i	−0.404414	−	0.914576i	$-0.632525\pi$
$607$		−	1110.30i		−	1.82915i	0.404414	−	0.914576i	$-0.367475\pi$
$608$	767.972	−	443.389i	1.26311	−	0.729258i
$609$		0			0
$610$	−17.0834	+	29.5893i	−0.0280055	+	0.0485070i
$611$	422.201	−	731.274i	0.691001	−	1.19685i
$612$		0			0
$613$	423.537	+	733.587i	0.690925	+	1.19672i	0.971535	+	0.236895i	$0.0761298\pi$
$613$	423.537	+	733.587i	0.690925	+	1.19672i	−0.280610	+	0.959822i	$0.590537\pi$
$614$	179.368	−	103.558i	0.292131	−	0.168662i
$615$		0			0
$616$	−771.937	−	218.676i	−1.25314	−	0.354993i
$617$	−69.2750	−	119.988i	−0.112277	−	0.194470i	0.804411	−	0.594073i	$-0.202481\pi$
$617$	−69.2750	−	119.988i	−0.112277	−	0.194470i	−0.916688	+	0.399604i	$0.869148\pi$
$618$		0			0
$619$		−	266.433i		−	0.430425i	−0.976567	−	0.215213i	$-0.930956\pi$
$619$		−	266.433i		−	0.430425i	0.976567	−	0.215213i	$-0.0690445\pi$
$620$	−26.8373	−	46.4835i	−0.0432859	−	0.0749735i
$621$		0			0
$622$			570.660i			0.917460i
$623$	628.213	+	646.377i	1.00837	+	1.03752i
$624$		0			0
$625$	621.485			0.994376
$626$	1456.66	+	841.001i	2.32693	+	1.34345i
$627$		0			0
$628$	−938.717	+	541.968i	−1.49477	+	0.863007i
$629$		−	55.6516i		−	0.0884764i
$630$		0			0
$631$	−336.916			−0.533940			−0.266970	−	0.963705i	$-0.586022\pi$
$631$	−336.916			−0.533940			−0.266970	+	0.963705i	$0.586022\pi$
$632$	−187.014	−	323.918i	−0.295908	−	0.512528i
$633$		0			0
$634$	674.761	−	1168.72i	1.06429	−	1.84341i
$635$			20.1142i			0.0316758i
$636$		0			0
$637$	844.396	+	24.0717i	1.32558	+	0.0377891i
$638$	−121.971			−0.191178
$639$		0			0
$640$	−63.2479	+	36.5162i	−0.0988248	+	0.0570565i
$641$	−329.423			−0.513920			−0.256960	−	0.966422i	$-0.582721\pi$
$641$	−329.423			−0.513920			−0.256960	+	0.966422i	$0.582721\pi$
$642$		0			0
$643$	−83.9635	+	48.4763i	−0.130581	+	0.0753909i	−0.563867	−	0.825865i	$-0.690687\pi$
$643$	−83.9635	+	48.4763i	−0.130581	+	0.0753909i	0.433287	+	0.901256i	$0.357354\pi$
$644$	−1025.44	+	996.622i	−1.59230	+	1.54755i
$645$		0			0
$646$	82.0580	+	142.129i	0.127025	+	0.220013i
$647$	−256.523	+	148.104i	−0.396481	+	0.228908i	−0.684964	−	0.728577i	$-0.740182\pi$
$647$	−256.523	+	148.104i	−0.396481	+	0.228908i	0.288484	+	0.957485i	$0.406849\pi$
$648$		0			0
$649$	−334.752	−	193.269i	−0.515796	−	0.297795i
$650$	−1429.10	−	825.093i	−2.19862	−	1.26937i
$651$		0			0
$652$	−897.219	−	1554.03i	−1.37610	−	2.38348i
$653$	255.473			0.391230			0.195615	−	0.980681i	$-0.437330\pi$
$653$	255.473			0.391230			0.195615	+	0.980681i	$0.437330\pi$
$654$		0			0
$655$	37.8291			0.0577544
$656$	185.944	+	107.355i	0.283452	+	0.163651i
$657$		0			0
$658$	−916.664	−	943.169i	−1.39311	−	1.43339i
$659$	232.879	−	403.358i	0.353382	−	0.612075i	−0.633458	−	0.773777i	$-0.718365\pi$
$659$	232.879	−	403.358i	0.353382	−	0.612075i	0.986840	+	0.161702i	$0.0516983\pi$
$660$		0			0
$661$	778.126	+	449.251i	1.17719	+	0.679654i	0.955364	−	0.295432i	$-0.0954635\pi$
$661$	778.126	+	449.251i	1.17719	+	0.679654i	0.221831	+	0.975085i	$0.428797\pi$
$662$	−44.0490	+	76.2951i	−0.0665393	+	0.115249i
$663$		0			0
$664$	−2446.02	−	1412.21i	−3.68377	−	2.12682i
$665$	−8.63738	+	8.39466i	−0.0129885	+	0.0126236i
$666$		0			0
$667$	−68.1183	+	117.984i	−0.102126	+	0.176888i
$668$		−	1281.79i		−	1.91885i
$669$		0			0
$670$		−	53.4632i		−	0.0797959i
$671$	−158.494	+	91.5066i	−0.236206	+	0.136373i
$672$		0			0
$673$	119.363	−	206.742i	0.177359	−	0.307195i	−0.763616	−	0.645671i	$-0.776578\pi$
$673$	119.363	−	206.742i	0.177359	−	0.307195i	0.940975	+	0.338475i	$0.109911\pi$
$674$	−107.039	+	185.397i	−0.158812	+	0.275070i
$675$		0			0
$676$	686.853	+	1189.66i	1.01606	+	1.75986i
$677$	−766.619	+	442.607i	−1.13238	+	0.653778i	−0.944531	−	0.328421i	$-0.893483\pi$
$677$	−766.619	+	442.607i	−1.13238	+	0.653778i	−0.187845	+	0.982199i	$0.560150\pi$
$678$		0			0
$679$	356.760	+	367.076i	0.525420	+	0.540612i
$680$	−15.0167	−	26.0098i	−0.0220835	−	0.0382497i
$681$		0			0
$682$		−	394.834i		−	0.578935i
$683$	−634.213	−	1098.49i	−0.928569	−	1.60833i	−0.785718	−	0.618585i	$-0.787706\pi$
$683$	−634.213	−	1098.49i	−0.928569	−	1.60833i	−0.142851	−	0.989744i	$-0.545627\pi$
$684$		0			0
$685$			5.21261i			0.00760965i
$686$	394.547	−	1255.21i	0.575142	−	1.82975i
$687$		0			0
$688$	−3372.13			−4.90136
$689$	−747.702	−	431.686i	−1.08520	−	0.626540i
$690$		0			0
$691$	269.030	−	155.325i	0.389335	−	0.224782i	−0.292537	−	0.956254i	$-0.594500\pi$
$691$	269.030	−	155.325i	0.389335	−	0.224782i	0.681872	+	0.731472i	$0.261166\pi$
$692$			2358.24i			3.40786i
$693$		0			0
$694$	211.342			0.304528
$695$	19.2344	+	33.3150i	0.0276755	+	0.0479353i
$696$		0			0
$697$	−10.3304	+	17.8928i	−0.0148213	+	0.0256712i
$698$			1124.19i			1.61058i
$699$		0			0
$700$	−1342.16	+	1304.45i	−1.91738	+	1.86350i
$701$	701.901			1.00129			0.500643	−	0.865654i	$-0.333097\pi$
$701$	701.901			1.00129			0.500643	+	0.865654i	$0.333097\pi$
$702$		0			0
$703$	−71.1272	+	41.0653i	−0.101177	+	0.0584144i
$704$	−908.988			−1.29118
$705$		0			0
$706$	630.739	−	364.158i	0.893398	−	0.515804i
$707$	−16.5642	+	58.4725i	−0.0234288	+	0.0827050i
$708$		0			0
$709$	192.709	+	333.782i	0.271804	+	0.470779i	0.969324	−	0.245787i	$-0.0790463\pi$
$709$	192.709	+	333.782i	0.271804	+	0.470779i	−0.697520	+	0.716566i	$0.745713\pi$
$710$	−8.49132	+	4.90247i	−0.0119596	+	0.00690489i
$711$		0			0
$712$	2872.55	+	1658.47i	4.03448	+	2.32931i
$713$	−381.928	−	220.506i	−0.535663	−	0.309265i
$714$		0			0
$715$	8.30532	+	14.3852i	0.0116158	+	0.0201192i
$716$	1755.12			2.45129
$717$		0			0
$718$	1564.31			2.17871
$719$	−272.086	−	157.089i	−0.378424	−	0.218483i	0.298709	−	0.954344i	$-0.403444\pi$
$719$	−272.086	−	157.089i	−0.378424	−	0.218483i	−0.677132	+	0.735861i	$0.736777\pi$
$720$		0			0
$721$	−231.722	+	817.991i	−0.321389	+	1.13452i
$722$	−571.302	+	989.524i	−0.791277	+	1.37053i
$723$		0			0
$724$	1413.15	+	815.881i	1.95186	+	1.12691i
$725$	−89.1579	+	154.426i	−0.122976	+	0.213001i
$726$		0			0
$727$	528.017	+	304.851i	0.726295	+	0.419327i	0.817065	−	0.576545i	$-0.195599\pi$
$727$	528.017	+	304.851i	0.726295	+	0.419327i	−0.0907700	+	0.995872i	$0.528933\pi$
$728$	3013.80	−	761.687i	4.13983	−	1.04627i
$729$		0			0
$730$	13.3049	−	23.0448i	0.0182259	−	0.0315682i
$731$		−	324.490i		−	0.443898i
$732$		0			0
$733$		−	294.374i		−	0.401602i	−0.979632	−	0.200801i	$-0.935646\pi$
$733$		−	294.374i		−	0.401602i	0.979632	−	0.200801i	$-0.0643544\pi$
$734$	1391.77	−	803.536i	1.89614	−	1.09474i
$735$		0			0
$736$	−1063.81	+	1842.58i	−1.44540	+	2.50350i
$737$	143.187	−	248.008i	0.194284	−	0.336509i
$738$		0			0
$739$	−98.9144	−	171.325i	−0.133849	−	0.231833i	0.791308	−	0.611418i	$-0.209400\pi$
$739$	−98.9144	−	171.325i	−0.133849	−	0.231833i	−0.925157	+	0.379584i	$0.876067\pi$
$740$	20.7699	−	11.9915i	0.0280674	−	0.0162047i
$741$		0			0
$742$	−964.357	+	937.257i	−1.29967	+	1.26315i
$743$	−488.580	−	846.245i	−0.657577	−	1.13896i	−0.981241	−	0.192785i	$-0.938248\pi$
$743$	−488.580	−	846.245i	−0.657577	−	1.13896i	0.323664	−	0.946172i	$-0.395085\pi$
$744$		0			0
$745$		−	22.1185i		−	0.0296893i
$746$	617.779	+	1070.02i	0.828121	+	1.43435i
$747$		0			0
$748$		−	256.701i		−	0.343184i
$749$	−949.370	+	922.691i	−1.26752	+	1.23190i
$750$		0			0
$751$	1205.90			1.60573			0.802864	−	0.596162i	$-0.203308\pi$
$751$	1205.90			1.60573			0.802864	+	0.596162i	$0.203308\pi$
$752$	−2373.44	−	1370.31i	−3.15617	−	1.82222i
$753$		0			0
$754$	409.264	−	236.289i	0.542791	−	0.313381i
$755$			28.8312i			0.0381870i
$756$		0			0
$757$	−1037.16			−1.37010			−0.685048	−	0.728498i	$-0.740219\pi$
$757$	−1037.16			−1.37010			−0.685048	+	0.728498i	$0.740219\pi$
$758$	367.921	+	637.257i	0.485383	+	0.840709i
$759$		0			0
$760$	−22.1617	+	38.3852i	−0.0291601	+	0.0505068i
$761$		−	424.556i		−	0.557893i	−0.960307	−	0.278946i	$-0.910015\pi$
$761$		−	424.556i		−	0.557893i	0.960307	−	0.278946i	$-0.0899852\pi$
$762$		0			0
$763$	−200.374	−	792.828i	−0.262614	−	1.03909i
$764$	−131.904			−0.172650
$765$		0			0
$766$	2170.79	−	1253.31i	2.83394	−	1.63617i
$767$	1497.64			1.95260
$768$		0			0
$769$	−1247.99	+	720.527i	−1.62287	+	0.936967i	−0.636728	+	0.771089i	$0.719713\pi$
$769$	−1247.99	+	720.527i	−1.62287	+	0.936967i	−0.986146	+	0.165878i	$0.946954\pi$
$770$	25.0839	−	6.33953i	0.0325765	−	0.00823316i
$771$		0			0
$772$	1442.24	+	2498.03i	1.86818	+	3.23579i
$773$	274.651	−	158.570i	0.355306	−	0.205136i	−0.311714	−	0.950176i	$-0.600903\pi$
$773$	274.651	−	158.570i	0.355306	−	0.205136i	0.667020	+	0.745040i	$0.267570\pi$
$774$		0			0
$775$	−499.893	−	288.614i	−0.645024	−	0.372405i
$776$	1631.31	+	941.838i	2.10221	+	1.21371i
$777$		0			0
$778$	687.628	+	1191.01i	0.883840	+	1.53086i
$779$	30.4913			0.0391416
$780$		0			0
$781$	−52.5199			−0.0672470
$782$	−341.006	−	196.880i	−0.436069	−	0.251765i
$783$		0			0
$784$	78.1276	−	2740.59i	0.0996525	−	3.49565i
$785$	10.9528	−	18.9709i	0.0139527	−	0.0241667i
$786$		0			0
$787$	−1078.90	−	622.903i	−1.37090	−	0.791490i	−0.379860	−	0.925044i	$-0.624028\pi$
$787$	−1078.90	−	622.903i	−1.37090	−	0.791490i	−0.991042	+	0.133553i	$0.957361\pi$
$788$	1618.96	−	2804.13i	2.05452	−	3.55854i
$789$		0			0
$790$	10.4455	+	6.03074i	0.0132222	+	0.00763384i
$791$	−2.17293	−	8.59771i	−0.00274706	−	0.0108694i
$792$		0			0
$793$	354.542	−	614.086i	0.447090	−	0.774383i
$794$		−	1585.40i		−	1.99672i
$795$		0			0
$796$		−	1027.08i		−	1.29031i
$797$	111.463	−	64.3530i	0.139853	−	0.0807440i	−0.428441	−	0.903570i	$-0.640937\pi$
$797$	111.463	−	64.3530i	0.139853	−	0.0807440i	0.568294	+	0.822826i	$0.307604\pi$
$798$		0			0
$799$	131.860	−	228.389i	0.165032	−	0.285843i
$800$	−1392.39	+	2411.69i	−1.74049	+	3.01461i
$801$		0			0
$802$	−272.866	−	472.617i	−0.340231	−	0.589298i
$803$	123.439	−	71.2674i	0.153722	−	0.0887514i
$804$		0			0
$805$	7.87650	−	27.8045i	0.00978447	−	0.0345397i
$806$	764.892	+	1324.83i	0.948998	+	1.64371i
$807$		0			0
$808$			223.640i			0.276783i
$809$	517.683	+	896.653i	0.639904	+	1.10835i	0.985453	+	0.169946i	$0.0543594\pi$
$809$	517.683	+	896.653i	0.639904	+	1.10835i	−0.345549	+	0.938401i	$0.612307\pi$
$810$		0			0
$811$		−	1195.01i		−	1.47350i	−0.676165	−	0.736751i	$-0.736359\pi$
$811$		−	1195.01i		−	1.47350i	0.676165	−	0.736751i	$-0.263641\pi$
$812$	−131.334	−	519.655i	−0.161741	−	0.639969i
$813$		0			0
$814$	176.421			0.216733
$815$	31.4060	+	18.1322i	0.0385349	+	0.0222482i
$816$		0			0
$817$	−414.723	+	239.441i	−0.507617	+	0.293073i
$818$			297.356i			0.363516i
$819$		0			0
$820$	−8.90377			−0.0108583
$821$	−633.626	−	1097.47i	−0.771773	−	1.33675i	−0.936590	−	0.350427i	$-0.886037\pi$
$821$	−633.626	−	1097.47i	−0.771773	−	1.33675i	0.164817	−	0.986324i	$-0.447297\pi$
$822$		0			0
$823$	−296.052	+	512.778i	−0.359723	+	0.623059i	−0.987914	−	0.155000i	$-0.950462\pi$
$823$	−296.052	+	512.778i	−0.359723	+	0.623059i	0.628191	+	0.778059i	$0.283796\pi$
$824$			3128.58i			3.79682i
$825$		0			0
$826$	635.797	−	2244.40i	0.769730	−	2.71719i
$827$	265.260			0.320749			0.160375	−	0.987056i	$-0.448730\pi$
$827$	265.260			0.320749			0.160375	+	0.987056i	$0.448730\pi$
$828$		0			0
$829$	449.714	−	259.643i	0.542478	−	0.313200i	−0.203605	−	0.979053i	$-0.565266\pi$
$829$	449.714	−	259.643i	0.542478	−	0.313200i	0.746083	+	0.665853i	$0.231932\pi$
$830$	91.0806			0.109736
$831$		0			0
$832$	3050.03	−	1760.94i	3.66590	−	2.11651i
$833$	263.719	+	7.51797i	0.316589	+	0.00902517i
$834$		0			0
$835$	12.9521	+	22.4337i	0.0155115	+	0.0268667i
$836$	−328.085	+	189.420i	−0.392446	+	0.226579i
$837$		0			0
$838$	2222.50	+	1283.16i	2.65215	+	1.53122i
$839$	469.432	+	271.026i	0.559513	+	0.323035i	0.752950	−	0.658078i	$-0.228630\pi$
$839$	469.432	+	271.026i	0.559513	+	0.323035i	−0.193437	+	0.981113i	$0.561963\pi$
$840$		0			0
$841$	394.967	+	684.103i	0.469640	+	0.813440i
$842$	−1723.94			−2.04744
$843$		0			0
$844$	968.878			1.14796
$845$	−24.0424	−	13.8809i	−0.0284525	−	0.0164271i
$846$		0			0
$847$	−681.593	−	193.083i	−0.804715	−	0.227961i
$848$	−1401.09	+	2426.76i	−1.65223	+	2.86175i
$849$		0			0
$850$	−446.332	−	257.690i	−0.525097	−	0.303165i
$851$	98.5270	−	170.654i	0.115778	−	0.200533i
$852$		0			0
$853$	168.797	+	97.4552i	0.197887	+	0.114250i	0.595669	−	0.803230i	$-0.296887\pi$
$853$	168.797	+	97.4552i	0.197887	+	0.114250i	−0.397783	+	0.917480i	$0.630220\pi$
$854$	−769.767	−	792.023i	−0.901366	−	0.927428i
$855$		0			0
$856$	−2435.88	+	4219.07i	−2.84566	+	4.92882i
$857$			1323.66i			1.54453i	0.635300	+	0.772265i	$0.280876\pi$
$857$			1323.66i			1.54453i	−0.635300	+	0.772265i	$0.719124\pi$
$858$		0			0
$859$		−	480.658i		−	0.559555i	−0.960065	−	0.279778i	$-0.909739\pi$
$859$		−	480.658i		−	0.559555i	0.960065	−	0.279778i	$-0.0902607\pi$
$860$	121.104	−	69.9192i	0.140818	−	0.0813014i
$861$		0			0
$862$	−707.216	+	1224.93i	−0.820436	+	1.42104i
$863$	−620.991	+	1075.59i	−0.719572	+	1.24634i	0.241597	+	0.970377i	$0.422329\pi$
$863$	−620.991	+	1075.59i	−0.719572	+	1.24634i	−0.961169	+	0.275959i	$0.911005\pi$
$864$		0			0
$865$	−23.8293	−	41.2735i	−0.0275483	−	0.0477150i
$866$	−225.063	+	129.940i	−0.259888	+	0.150047i
$867$		0			0
$868$	1682.18	−	425.142i	1.93799	−	0.489795i
$869$	32.3035	+	55.9513i	0.0371732	+	0.0643858i
$870$		0			0
$871$			1109.56i			1.27389i
$872$	−1504.64	−	2606.11i	−1.72550	−	2.98865i
$873$		0			0
$874$			581.110i			0.664886i
$875$	20.6380	−	72.8532i	0.0235863	−	0.0832608i
$876$		0			0
$877$	−1041.91			−1.18804			−0.594019	−	0.804451i	$-0.702459\pi$
$877$	−1041.91			−1.18804			−0.594019	+	0.804451i	$0.702459\pi$
$878$	−449.548	−	259.546i	−0.512013	−	0.295611i
$879$		0			0
$880$	46.6891	−	26.9560i	0.0530558	−	0.0306318i
$881$		−	332.498i		−	0.377409i	−0.982034	−	0.188705i	$-0.939571\pi$
$881$		−	332.498i		−	0.377409i	0.982034	−	0.188705i	$-0.0604289\pi$
$882$		0			0
$883$	−651.814			−0.738181			−0.369091	−	0.929393i	$-0.620331\pi$
$883$	−651.814			−0.738181			−0.369091	+	0.929393i	$0.620331\pi$
$884$	497.295	+	861.341i	0.562551	+	0.974367i
$885$		0			0
$886$	−1170.23	+	2026.90i	−1.32081	+	2.28770i
$887$			842.321i			0.949629i	0.880086	+	0.474815i	$0.157485\pi$
$887$			842.321i			0.949629i	−0.880086	+	0.474815i	$0.842515\pi$
$888$		0			0
$889$	−625.588	−	177.218i	−0.703698	−	0.199345i
$890$	−106.963			−0.120183
$891$		0			0
$892$	−2191.45	+	1265.23i	−2.45678	+	1.41842i
$893$	−389.199			−0.435833
$894$		0			0
$895$	−30.7179	+	17.7350i	−0.0343216	+	0.0198156i
$896$	−578.470	−	2288.86i	−0.645614	−	2.55453i
$897$		0			0
$898$	−1390.14	−	2407.79i	−1.54804	−	2.68128i
$899$	143.159	−	82.6528i	0.159242	−	0.0919386i
$900$		0			0
$901$	−233.520	−	134.823i	−0.259178	−	0.149637i
$902$	−56.7219	−	32.7484i	−0.0628845	−	0.0363064i
$903$		0			0
$904$	−16.3168	−	28.2615i	−0.0180496	−	0.0312628i
$905$	−32.9769			−0.0364385
$906$		0			0
$907$	−719.847			−0.793658			−0.396829	−	0.917893i	$-0.629889\pi$
$907$	−719.847			−0.793658			−0.396829	+	0.917893i	$0.629889\pi$
$908$	825.691	+	476.713i	0.909352	+	0.525015i
$909$		0			0
$910$	−71.8857	+	69.8656i	−0.0789952	+	0.0767754i
$911$	−178.178	+	308.613i	−0.195585	+	0.338763i	−0.947092	−	0.320962i	$-0.895994\pi$
$911$	−178.178	+	308.613i	−0.195585	+	0.338763i	0.751507	+	0.659725i	$0.229327\pi$
$912$		0			0
$913$	422.509	+	243.935i	0.462770	+	0.267180i
$914$	−628.812	+	1089.13i	−0.687978	+	1.19161i
$915$		0			0
$916$	459.411	+	265.241i	0.501540	+	0.289565i
$917$	−333.297	+	1176.56i	−0.363465	+	1.28305i
$918$		0			0
$919$	125.952	−	218.156i	0.137054	−	0.237384i	−0.789326	−	0.613974i	$-0.789570\pi$
$919$	125.952	−	218.156i	0.137054	−	0.237384i	0.926380	+	0.376590i	$0.122903\pi$
$920$		−	106.344i		−	0.115591i
$921$		0			0
$922$			65.7881i			0.0713537i
$923$	176.226	−	101.744i	0.190928	−	0.110232i
$924$		0			0
$925$	128.959	−	223.363i	0.139415	−	0.241474i
$926$	440.775	−	763.445i	0.475999	−	0.824455i
$927$		0			0
$928$	−398.751	−	690.657i	−0.429688	−	0.744242i
$929$	−225.282	+	130.066i	−0.242499	+	0.140007i	−0.616325	−	0.787492i	$-0.711379\pi$
$929$	−225.282	+	130.066i	−0.242499	+	0.140007i	0.373826	+	0.927499i	$0.378046\pi$
$930$		0			0
$931$	−184.989	−	342.601i	−0.198699	−	0.367992i
$932$	701.244	+	1214.59i	0.752407	+	1.30321i
$933$		0			0
$934$		−	1104.57i		−	1.18262i
$935$	2.59389	+	4.49275i	0.00277421	+	0.00480508i
$936$		0			0
$937$			1274.73i			1.36044i	0.733008	+	0.680220i	$0.238116\pi$
$937$			1274.73i			1.36044i	−0.733008	+	0.680220i	$0.761884\pi$
$938$	1662.81	+	471.043i	1.77271	+	0.502178i
$939$		0			0
$940$	113.650			0.120904
$941$	−1120.44	−	646.884i	−1.19069	−	0.687443i	−0.232224	−	0.972662i	$-0.574600\pi$
$941$	−1120.44	−	646.884i	−1.19069	−	0.687443i	−0.958462	+	0.285219i	$0.907934\pi$
$942$		0			0
$943$	−63.3558	+	36.5785i	−0.0671854	+	0.0387895i
$944$		−	4860.79i		−	5.14914i
$945$		0			0
$946$	1028.66			1.08738
$947$	−237.044	−	410.572i	−0.250310	−	0.433550i	0.713301	−	0.700858i	$-0.247199\pi$
$947$	−237.044	−	410.572i	−0.250310	−	0.433550i	−0.963611	+	0.267308i	$0.913866\pi$
$948$		0			0
$949$	−276.126	+	478.264i	−0.290965	+	0.503966i
$950$			760.597i			0.800628i
$951$		0			0
$952$	941.259	−	237.887i	0.988717	−	0.249882i
$953$	140.452			0.147379			0.0736893	−	0.997281i	$-0.476523\pi$
$953$	140.452			0.147379			0.0736893	+	0.997281i	$0.476523\pi$
$954$		0			0
$955$	2.30857	−	1.33285i	0.00241735	−	0.00139566i
$956$	−537.172			−0.561896
$957$		0			0
$958$	2639.33	−	1523.82i	2.75504	−	1.59062i
$959$	−162.122	−	45.9262i	−0.169053	−	0.0478897i
$960$		0			0
$961$	−212.944	−	368.830i	−0.221586	−	0.383798i
$962$	−591.965	+	341.771i	−0.615348	+	0.355271i
$963$		0			0
$964$	−2764.23	−	1595.93i	−2.86745	−	1.65553i
$965$	−50.4836	−	29.1467i	−0.0523147	−	0.0302039i
$966$		0			0
$967$	577.643	+	1000.51i	0.597356	+	1.03465i	0.993210	+	0.116337i	$0.0371153\pi$
$967$	577.643	+	1000.51i	0.597356	+	1.03465i	−0.395854	+	0.918313i	$0.629551\pi$
$968$	−2606.90			−2.69308
$969$		0			0
$970$	−60.7439			−0.0626226
$971$	−645.071	−	372.432i	−0.664337	−	0.383555i	0.129590	−	0.991568i	$-0.458634\pi$
$971$	−645.071	−	372.432i	−0.664337	−	0.383555i	−0.793928	+	0.608012i	$0.791967\pi$
$972$		0			0
$973$	−1205.63	+	304.702i	−1.23908	+	0.313157i
$974$	1038.33	−	1798.44i	1.06605	−	1.84645i
$975$		0			0
$976$	−1993.09	−	1150.71i	−2.04210	−	1.17901i
$977$	−720.133	+	1247.31i	−0.737086	+	1.27667i	0.216716	+	0.976235i	$0.430466\pi$
$977$	−720.133	+	1247.31i	−0.737086	+	1.27667i	−0.953802	+	0.300436i	$0.902868\pi$
$978$		0			0
$979$	−496.184	−	286.472i	−0.506827	−	0.292617i
$980$	54.0188	+	100.043i	0.0551212	+	0.102085i
$981$		0			0
$982$	533.135	−	923.417i	0.542907	−	0.940343i
$983$		−	586.281i		−	0.596421i	−0.954500	−	0.298210i	$-0.903610\pi$
$983$		−	586.281i		−	0.596421i	0.954500	−	0.298210i	$-0.0963897\pi$
$984$		0			0
$985$			65.4365i			0.0664330i
$986$	127.820	−	73.7969i	0.129635	−	0.0748447i
$987$		0			0
$988$	733.908	−	1271.17i	0.742821	−	1.28660i
$989$	574.485	−	995.036i	0.580874	−	1.00610i
$990$		0			0
$991$	−390.134	−	675.732i	−0.393677	−	0.681868i	0.599254	−	0.800559i	$-0.295464\pi$
$991$	−390.134	−	675.732i	−0.393677	−	0.681868i	−0.992931	+	0.118690i	$0.962130\pi$
$992$	2235.73	−	1290.80i	2.25376	−	1.30121i
$993$		0			0
$994$	−77.6623	−	307.290i	−0.0781311	−	0.309145i
$995$	10.3784	+	17.9758i	0.0104305	+	0.0180662i
$996$		0			0
$997$			215.003i			0.215650i	0.994170	+	0.107825i	$0.0343886\pi$
$997$			215.003i			0.215650i	−0.994170	+	0.107825i	$0.965611\pi$
$998$	928.787	+	1608.71i	0.930649	+	1.61193i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.19.1		28
3.2	odd	2		63.3.k.a.61.14	yes	28
7.3	odd	6		189.3.t.a.73.14		28
9.4	even	3		189.3.t.a.145.14		28
9.5	odd	6		63.3.t.a.40.1	yes	28
21.2	odd	6		441.3.l.a.97.14		28
21.5	even	6		441.3.l.b.97.14		28
21.11	odd	6		441.3.t.a.178.1		28
21.17	even	6		63.3.t.a.52.1	yes	28
21.20	even	2		441.3.k.b.313.14		28
63.5	even	6		441.3.l.a.391.14		28
63.23	odd	6		441.3.l.b.391.14		28
63.31	odd	6	inner	189.3.k.a.10.1		28
63.32	odd	6		441.3.k.b.31.14		28
63.41	even	6		441.3.t.a.166.1		28
63.59	even	6		63.3.k.a.31.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.14	✓	28	63.59	even	6
63.3.k.a.61.14	yes	28	3.2	odd	2
63.3.t.a.40.1	yes	28	9.5	odd	6
63.3.t.a.52.1	yes	28	21.17	even	6
189.3.k.a.10.1		28	63.31	odd	6	inner
189.3.k.a.19.1		28	1.1	even	1	trivial
189.3.t.a.73.14		28	7.3	odd	6
189.3.t.a.145.14		28	9.4	even	3
441.3.k.b.31.14		28	63.32	odd	6
441.3.k.b.313.14		28	21.20	even	2
441.3.l.a.97.14		28	21.2	odd	6
441.3.l.a.391.14		28	63.5	even	6
441.3.l.b.97.14		28	21.5	even	6
441.3.l.b.391.14		28	63.23	odd	6
441.3.t.a.166.1		28	63.41	even	6
441.3.t.a.178.1		28	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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91801 - 3.32210i) q^{2} +(-5.35756 + 9.27956i) q^{4} -0.216546i q^{5} +(6.73498 + 1.90790i) q^{7} +25.7594 q^{8} +O(q^{10})\)	\(q+(-1.91801 - 3.32210i) q^{2} +(-5.35756 + 9.27956i) q^{4} -0.216546i q^{5} +(6.73498 + 1.90790i) q^{7} +25.7594 q^{8} +(-0.719386 + 0.415338i) q^{10} -4.44949 q^{11} +(14.9299 - 8.61978i) q^{13} +(-6.57956 - 26.0336i) q^{14} +(-27.9766 - 48.4569i) q^{16} +(4.66285 - 2.69210i) q^{17} +(-6.88143 - 3.97300i) q^{19} +(2.00945 + 1.16016i) q^{20} +(8.53419 + 14.7817i) q^{22} +19.0646 q^{23} +24.9531 q^{25} +(-57.2715 - 33.0657i) q^{26} +(-53.7875 + 52.2760i) q^{28} +(-3.57302 + 6.18865i) q^{29} +(-20.0333 - 11.5662i) q^{31} +(-55.8003 + 96.6489i) q^{32} +(-17.8868 - 10.3270i) q^{34} +(0.413147 - 1.45843i) q^{35} +(5.16805 - 8.95133i) q^{37} +30.4811i q^{38} -5.57808i q^{40} +(-3.32321 + 1.91866i) q^{41} +(30.1335 - 52.1928i) q^{43} +(23.8384 - 41.2893i) q^{44} +(-36.5662 - 63.3346i) q^{46} +(42.4184 - 24.4902i) q^{47} +(41.7199 + 25.6993i) q^{49} +(-47.8604 - 82.8967i) q^{50} +184.724i q^{52} +(-25.0404 - 43.3713i) q^{53} +0.963519i q^{55} +(173.489 + 49.1462i) q^{56} +27.4124 q^{58} +(75.2337 + 43.4362i) q^{59} +(35.6207 - 20.5656i) q^{61} +88.7368i q^{62} +204.290 q^{64} +(-1.86658 - 3.23301i) q^{65} +(-32.1806 + 55.7384i) q^{67} +57.6923i q^{68} +(-5.63747 + 1.42478i) q^{70} +11.8036 q^{71} +(-27.7422 + 16.0170i) q^{73} -39.6496 q^{74} +(73.7353 - 42.5711i) q^{76} +(-29.9672 - 8.48917i) q^{77} +(-7.26004 - 12.5748i) q^{79} +(-10.4931 + 6.05821i) q^{80} +(12.7479 + 7.36003i) q^{82} +(-94.9566 - 54.8232i) q^{83} +(-0.582963 - 1.00972i) q^{85} -231.186 q^{86} -114.616 q^{88} +(111.515 + 64.3830i) q^{89} +(116.998 - 29.5693i) q^{91} +(-102.140 + 176.911i) q^{92} +(-162.718 - 93.9453i) q^{94} +(-0.860336 + 1.49015i) q^{95} +(63.3289 + 36.5629i) q^{97} +(5.35626 - 187.889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more