LMFDB - Embedded newform 189.4.i.a.143.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(143,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("189.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.7
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41653i q^{2} +2.16037 q^{4} +(5.35965 - 9.28319i) q^{5} +(3.86176 + 18.1132i) q^{7} -24.5529i q^{8} +O(q^{10})$	\(q-2.41653i q^{2} +2.16037 q^{4} +(5.35965 - 9.28319i) q^{5} +(3.86176 + 18.1132i) q^{7} -24.5529i q^{8} +(-22.4331 - 12.9518i) q^{10} +(22.6226 - 13.0611i) q^{11} +(29.8910 - 17.2576i) q^{13} +(43.7711 - 9.33207i) q^{14} -42.0498 q^{16} +(2.29830 - 3.98078i) q^{17} +(6.74409 - 3.89370i) q^{19} +(11.5788 - 20.0551i) q^{20} +(-31.5627 - 54.6682i) q^{22} +(33.9149 + 19.5808i) q^{23} +(5.04824 + 8.74381i) q^{25} +(-41.7035 - 72.2327i) q^{26} +(8.34283 + 39.1311i) q^{28} +(-210.884 - 121.754i) q^{29} -311.124i q^{31} -94.8081i q^{32} +(-9.61969 - 5.55393i) q^{34} +(188.846 + 61.2308i) q^{35} +(-28.3008 - 49.0184i) q^{37} +(-9.40926 - 16.2973i) q^{38} +(-227.929 - 131.595i) q^{40} +(148.047 + 256.425i) q^{41} +(-60.7001 + 105.136i) q^{43} +(48.8731 - 28.2169i) q^{44} +(47.3176 - 81.9564i) q^{46} -225.820 q^{47} +(-313.174 + 139.897i) q^{49} +(21.1297 - 12.1992i) q^{50} +(64.5757 - 37.2828i) q^{52} +(-307.128 - 177.321i) q^{53} -280.013i q^{55} +(444.730 - 94.8173i) q^{56} +(-294.222 + 509.607i) q^{58} +271.148 q^{59} +749.933i q^{61} -751.841 q^{62} -565.506 q^{64} -369.979i q^{65} +994.849 q^{67} +(4.96519 - 8.59996i) q^{68} +(147.966 - 456.352i) q^{70} +1139.11i q^{71} +(1074.95 + 620.624i) q^{73} +(-118.455 + 68.3898i) q^{74} +(14.5697 - 8.41184i) q^{76} +(323.942 + 359.327i) q^{77} +433.603 q^{79} +(-225.373 + 390.357i) q^{80} +(619.659 - 357.760i) q^{82} +(492.785 - 853.528i) q^{83} +(-24.6362 - 42.6712i) q^{85} +(254.064 + 146.684i) q^{86} +(-320.689 - 555.449i) q^{88} +(75.6350 + 131.004i) q^{89} +(428.022 + 474.777i) q^{91} +(73.2687 + 42.3017i) q^{92} +545.701i q^{94} -83.4756i q^{95} +(-781.452 - 451.172i) q^{97} +(338.067 + 756.794i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	$ 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) $ 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.41653i		−	0.854373i	−0.904163	−	0.427187i	$-0.859505\pi$
$2$		−	2.41653i		−	0.854373i	0.904163	−	0.427187i	$-0.140495\pi$
$3$		0			0
$3$		0			0
$4$	2.16037			0.270046
$5$	5.35965	−	9.28319i	0.479382	−	0.830314i	−0.520338	−	0.853960i	$-0.674194\pi$
$5$	5.35965	−	9.28319i	0.479382	−	0.830314i	0.999720	+	0.0236463i	$0.00752754\pi$
$6$		0			0
$7$	3.86176	+	18.1132i	0.208515	+	0.978019i
$7$	3.86176	+	18.1132i	0.208515	+	0.978019i
$8$		−	24.5529i		−	1.08509i
$9$		0			0
$10$	−22.4331	−	12.9518i	−0.709398	−	0.409571i
$11$	22.6226	−	13.0611i	0.620088	−	0.358008i	−0.156816	−	0.987628i	$-0.550123\pi$
$11$	22.6226	−	13.0611i	0.620088	−	0.358008i	0.776903	+	0.629620i	$0.216789\pi$
$12$		0			0
$13$	29.8910	−	17.2576i	0.637714	−	0.368184i	−0.146019	−	0.989282i	$-0.546646\pi$
$13$	29.8910	−	17.2576i	0.637714	−	0.368184i	0.783733	+	0.621097i	$0.213313\pi$
$14$	43.7711	−	9.33207i	0.835593	−	0.178150i
$15$		0			0
$16$	−42.0498			−0.657029
$17$	2.29830	−	3.98078i	0.0327895	−	0.0567930i	−0.849165	−	0.528128i	$-0.822894\pi$
$17$	2.29830	−	3.98078i	0.0327895	−	0.0567930i	0.881954	+	0.471335i	$0.156228\pi$
$18$		0			0
$19$	6.74409	−	3.89370i	0.0814316	−	0.0470146i	−0.458731	−	0.888575i	$-0.651696\pi$
$19$	6.74409	−	3.89370i	0.0814316	−	0.0470146i	0.540163	+	0.841560i	$0.318363\pi$
$20$	11.5788	−	20.0551i	0.129455	−	0.224223i
$21$		0			0
$22$	−31.5627	−	54.6682i	−0.305872	−	0.529786i
$23$	33.9149	+	19.5808i	0.307467	+	0.177516i	0.645792	−	0.763513i	$-0.276527\pi$
$23$	33.9149	+	19.5808i	0.307467	+	0.177516i	−0.338325	+	0.941029i	$0.609860\pi$
$24$		0			0
$25$	5.04824	+	8.74381i	0.0403859	+	0.0699505i
$26$	−41.7035	−	72.2327i	−0.314567	−	0.544846i
$27$		0			0
$28$	8.34283	+	39.1311i	0.0563088	+	0.264110i
$29$	−210.884	−	121.754i	−1.35035	−	0.779624i	−0.362050	−	0.932159i	$-0.617923\pi$
$29$	−210.884	−	121.754i	−1.35035	−	0.779624i	−0.988298	+	0.152535i	$0.951256\pi$
$30$		0			0
$31$		−	311.124i		−	1.80256i	−0.433232	−	0.901282i	$-0.642627\pi$
$31$		−	311.124i		−	1.80256i	0.433232	−	0.901282i	$-0.357373\pi$
$32$		−	94.8081i		−	0.523746i
$33$		0			0
$34$	−9.61969	−	5.55393i	−0.0485224	−	0.0280144i
$35$	188.846	+	61.2308i	0.912021	+	0.295711i
$36$		0			0
$37$	−28.3008	−	49.0184i	−0.125747	−	0.217799i	0.796278	−	0.604931i	$-0.206799\pi$
$37$	−28.3008	−	49.0184i	−0.125747	−	0.217799i	−0.922024	+	0.387132i	$0.873466\pi$
$38$	−9.40926	−	16.2973i	−0.0401680	−	0.0695730i
$39$		0			0
$40$	−227.929	−	131.595i	−0.900968	−	0.520174i
$41$	148.047	+	256.425i	0.563928	+	0.976752i	0.997149	+	0.0754640i	$0.0240438\pi$
$41$	148.047	+	256.425i	0.563928	+	0.976752i	−0.433221	+	0.901288i	$0.642623\pi$
$42$		0			0
$43$	−60.7001	+	105.136i	−0.215271	+	0.372861i	−0.953357	−	0.301847i	$-0.902397\pi$
$43$	−60.7001	+	105.136i	−0.215271	+	0.372861i	0.738085	+	0.674708i	$0.235730\pi$
$44$	48.8731	−	28.2169i	0.167452	−	0.0966786i
$45$		0			0
$46$	47.3176	−	81.9564i	0.151665	−	0.262692i
$47$	−225.820			−0.700834			−0.350417	−	0.936594i	$-0.613960\pi$
$47$	−225.820			−0.700834			−0.350417	+	0.936594i	$0.613960\pi$
$48$		0			0
$49$	−313.174	+	139.897i	−0.913043	+	0.407864i
$50$	21.1297	−	12.1992i	0.0597638	−	0.0345047i
$51$		0			0
$52$	64.5757	−	37.2828i	0.172212	−	0.0994268i
$53$	−307.128	−	177.321i	−0.795987	−	0.459563i	0.0460792	−	0.998938i	$-0.485327\pi$
$53$	−307.128	−	177.321i	−0.795987	−	0.459563i	−0.842066	+	0.539375i	$0.818661\pi$
$54$		0			0
$55$		−	280.013i		−	0.686490i
$56$	444.730	−	94.8173i	1.06124	−	0.226259i
$57$		0			0
$58$	−294.222	+	509.607i	−0.666090	+	1.15370i
$59$	271.148			0.598313			0.299157	−	0.954204i	$-0.403295\pi$
$59$	271.148			0.598313			0.299157	+	0.954204i	$0.403295\pi$
$60$		0			0
$61$			749.933i			1.57408i	0.616899	+	0.787042i	$0.288389\pi$
$61$			749.933i			1.57408i	−0.616899	+	0.787042i	$0.711611\pi$
$62$	−751.841			−1.54006
$63$		0			0
$64$	−565.506			−1.10450
$65$		−	369.979i		−	0.706004i
$66$		0			0
$67$	994.849			1.81403			0.907016	−	0.421096i	$-0.138354\pi$
$67$	994.849			1.81403			0.907016	+	0.421096i	$0.138354\pi$
$68$	4.96519	−	8.59996i	0.00885467	−	0.0153367i
$69$		0			0
$70$	147.966	−	456.352i	0.252648	−	0.779207i
$71$			1139.11i			1.90405i	0.306018	+	0.952026i	$0.401003\pi$
$71$			1139.11i			1.90405i	−0.306018	+	0.952026i	$0.598997\pi$
$72$		0			0
$73$	1074.95	+	620.624i	1.72348	+	0.995049i	0.911430	+	0.411455i	$0.134979\pi$
$73$	1074.95	+	620.624i	1.72348	+	0.995049i	0.812045	+	0.583594i	$0.198354\pi$
$74$	−118.455	+	68.3898i	−0.186082	+	0.107434i
$75$		0			0
$76$	14.5697	−	8.41184i	0.0219903	−	0.0126961i
$77$	323.942	+	359.327i	0.479436	+	0.531807i
$78$		0			0
$79$	433.603			0.617521			0.308761	−	0.951140i	$-0.400086\pi$
$79$	433.603			0.617521			0.308761	+	0.951140i	$0.400086\pi$
$80$	−225.373	+	390.357i	−0.314968	+	0.545540i
$81$		0			0
$82$	619.659	−	357.760i	0.834511	−	0.481805i
$83$	492.785	−	853.528i	0.651689	−	1.12876i	−0.331024	−	0.943622i	$-0.607394\pi$
$83$	492.785	−	853.528i	0.651689	−	1.12876i	0.982713	−	0.185136i	$-0.0592724\pi$
$84$		0			0
$85$	−24.6362	−	42.6712i	−0.0314373	−	0.0544511i
$86$	254.064	+	146.684i	0.318563	+	0.183922i
$87$		0			0
$88$	−320.689	−	555.449i	−0.388472	−	0.672853i
$89$	75.6350	+	131.004i	0.0900819	+	0.156027i	0.907545	−	0.419954i	$-0.137954\pi$
$89$	75.6350	+	131.004i	0.0900819	+	0.156027i	−0.817463	+	0.575980i	$0.804620\pi$
$90$		0			0
$91$	428.022	+	474.777i	0.493064	+	0.546924i
$92$	73.2687	+	42.3017i	0.0830303	+	0.0479376i
$93$		0			0
$94$			545.701i			0.598774i
$95$		−	83.4756i		−	0.0901517i
$96$		0			0
$97$	−781.452	−	451.172i	−0.817984	−	0.472263i	0.0317367	−	0.999496i	$-0.489896\pi$
$97$	−781.452	−	451.172i	−0.817984	−	0.472263i	−0.849721	+	0.527233i	$0.823230\pi$
$98$	338.067	+	756.794i	0.348468	+	0.780079i
$99$		0			0
$100$	10.9061	+	18.8899i	0.0109061	+	0.0188899i
$101$	139.325	+	241.319i	0.137261	+	0.237743i	0.926459	−	0.376396i	$-0.122837\pi$
$101$	139.325	+	241.319i	0.137261	+	0.237743i	−0.789198	+	0.614139i	$0.789503\pi$
$102$		0			0
$103$	1115.66	+	644.128i	1.06728	+	0.616192i	0.927436	−	0.373982i	$-0.122008\pi$
$103$	1115.66	+	644.128i	1.06728	+	0.616192i	0.139841	+	0.990174i	$0.455341\pi$
$104$	−423.723	−	733.910i	−0.399514	−	0.691979i
$105$		0			0
$106$	−428.501	+	742.185i	−0.392638	+	0.680070i
$107$	−1405.87	+	811.679i	−1.27019	+	0.733346i	−0.975024	−	0.222100i	$-0.928709\pi$
$107$	−1405.87	+	811.679i	−1.27019	+	0.733346i	−0.295168	+	0.955445i	$0.595376\pi$
$108$		0			0
$109$	−426.818	+	739.271i	−0.375062	+	0.649627i	−0.990336	−	0.138686i	$-0.955712\pi$
$109$	−426.818	+	739.271i	−0.375062	+	0.649627i	0.615274	+	0.788313i	$0.289045\pi$
$110$	−676.660			−0.586518
$111$		0			0
$112$	−162.386	−	761.656i	−0.137001	−	0.642587i
$113$	−1119.93	+	646.595i	−0.932342	+	0.538288i	−0.887551	−	0.460709i	$-0.847595\pi$
$113$	−1119.93	+	646.595i	−0.932342	+	0.538288i	−0.0447903	+	0.998996i	$0.514262\pi$
$114$		0			0
$115$	363.544	−	209.892i	0.294788	−	0.170196i
$116$	−455.586	−	263.033i	−0.364656	−	0.210534i
$117$		0			0
$118$		−	655.238i		−	0.511183i
$119$	80.9800	+	26.2568i	0.0623818	+	0.0202265i
$120$		0			0
$121$	−324.313	+	561.726i	−0.243661	+	0.422033i
$122$	1812.24			1.34486
$123$		0			0
$124$		−	672.143i		−	0.486776i
$125$	1448.14			1.03621
$126$		0			0
$127$	−2072.04			−1.44775			−0.723873	−	0.689933i	$-0.757640\pi$
$127$	−2072.04			−1.44775			−0.723873	+	0.689933i	$0.757640\pi$
$128$			608.098i			0.419912i
$129$		0			0
$130$	−894.066			−0.603191
$131$	−8.86851	+	15.3607i	−0.00591485	+	0.0102448i	−0.868968	−	0.494869i	$-0.835216\pi$
$131$	−8.86851	+	15.3607i	−0.00591485	+	0.0102448i	0.863053	+	0.505114i	$0.168549\pi$
$132$		0			0
$133$	96.5714	+	107.120i	0.0629609	+	0.0698384i
$134$		−	2404.09i		−	1.54986i
$135$		0			0
$136$	−97.7396	−	56.4300i	−0.0616257	−	0.0355796i
$137$	−1736.41	+	1002.51i	−1.08286	+	0.625187i	−0.931665	−	0.363318i	$-0.881644\pi$
$137$	−1736.41	+	1002.51i	−1.08286	+	0.625187i	−0.151190	+	0.988505i	$0.548311\pi$
$138$		0			0
$139$	618.188	−	356.911i	0.377223	−	0.217790i	−0.299386	−	0.954132i	$-0.596782\pi$
$139$	618.188	−	356.911i	0.377223	−	0.217790i	0.676609	+	0.736342i	$0.263449\pi$
$140$	407.977	+	132.281i	0.246288	+	0.0798558i
$141$		0			0
$142$	2752.70			1.62677
$143$	450.808	−	780.822i	0.263626	−	0.456613i
$144$		0			0
$145$	−2260.53	+	1305.11i	−1.29466	+	0.747475i
$146$	1499.76	−	2597.66i	0.850143	−	1.47249i
$147$		0			0
$148$	−61.1402	−	105.898i	−0.0339574	−	0.0588159i
$149$	1390.01	+	802.522i	0.764255	+	0.441243i	0.830821	−	0.556539i	$-0.187871\pi$
$149$	1390.01	+	802.522i	0.764255	+	0.441243i	−0.0665666	+	0.997782i	$0.521204\pi$
$150$		0			0
$151$	−556.394	−	963.702i	−0.299859	−	0.519370i	0.676245	−	0.736677i	$-0.263606\pi$
$151$	−556.394	−	963.702i	−0.299859	−	0.519370i	−0.976103	+	0.217307i	$0.930273\pi$
$152$	−95.6016	−	165.587i	−0.0510152	−	0.0883609i
$153$		0			0
$154$	868.326	−	782.816i	0.454362	−	0.409617i
$155$	−2888.22	−	1667.52i	−1.49669	−	0.864117i
$156$		0			0
$157$			172.991i			0.0879377i	0.999033	+	0.0439688i	$0.0140002\pi$
$157$			172.991i			0.0879377i	−0.999033	+	0.0439688i	$0.986000\pi$
$158$		−	1047.82i		−	0.527594i
$159$		0			0
$160$	−880.122	−	508.139i	−0.434873	−	0.251074i
$161$	−223.699	+	689.922i	−0.109503	+	0.337723i
$162$		0			0
$163$	−1100.08	−	1905.39i	−0.528617	−	0.915591i	−0.999443	−	0.0333655i	$-0.989377\pi$
$163$	−1100.08	−	1905.39i	−0.528617	−	0.915591i	0.470826	−	0.882226i	$-0.343956\pi$
$164$	319.836	+	553.973i	0.152287	+	0.263768i
$165$		0			0
$166$	−2062.58	−	1190.83i	−0.964381	−	0.556785i
$167$	68.4457	+	118.551i	0.0317155	+	0.0549328i	0.881447	−	0.472282i	$-0.156570\pi$
$167$	68.4457	+	118.551i	0.0317155	+	0.0549328i	−0.849732	+	0.527215i	$0.823236\pi$
$168$		0			0
$169$	−502.851	+	870.963i	−0.228881	+	0.396433i
$170$	−103.116	+	59.5343i	−0.0465216	+	0.0268592i
$171$		0			0
$172$	−131.135	+	227.132i	−0.0581332	+	0.100690i
$173$	1491.93			0.655663			0.327831	−	0.944736i	$-0.393682\pi$
$173$	1491.93			0.655663			0.327831	+	0.944736i	$0.393682\pi$
$174$		0			0
$175$	−138.883	+	125.206i	−0.0599918	+	0.0540840i
$176$	−951.276	+	549.219i	−0.407415	+	0.235221i
$177$		0			0
$178$	316.575	−	182.774i	0.133305	−	0.0769636i
$179$	589.130	+	340.135i	0.245998	+	0.142027i	0.617930	−	0.786233i	$-0.287971\pi$
$179$	589.130	+	340.135i	0.245998	+	0.142027i	−0.371932	+	0.928260i	$0.621305\pi$
$180$		0			0
$181$		−	2275.25i		−	0.934355i	−0.884164	−	0.467177i	$-0.845271\pi$
$181$		−	2275.25i		−	0.934355i	0.884164	−	0.467177i	$-0.154729\pi$
$182$	1147.31	−	1034.33i	0.467277	−	0.421261i
$183$		0			0
$184$	480.764	−	832.708i	0.192622	−	0.333630i
$185$	−606.730			−0.241122
$186$		0			0
$187$		−	120.074i		−	0.0469555i
$188$	−487.854			−0.189258
$189$		0			0
$190$	−201.721			−0.0770232
$191$			3347.97i			1.26833i	0.773198	+	0.634164i	$0.218656\pi$
$191$			3347.97i			1.26833i	−0.773198	+	0.634164i	$0.781344\pi$
$192$		0			0
$193$	2064.88			0.770121			0.385060	−	0.922891i	$-0.374181\pi$
$193$	2064.88			0.770121			0.385060	+	0.922891i	$0.374181\pi$
$194$	−1090.27	+	1888.40i	−0.403489	+	0.698864i
$195$		0			0
$196$	−676.571	+	302.230i	−0.246564	+	0.110142i
$197$		−	2890.54i		−	1.04539i	−0.852519	−	0.522696i	$-0.824926\pi$
$197$		−	2890.54i		−	1.04539i	0.852519	−	0.522696i	$-0.175074\pi$
$198$		0			0
$199$	1007.22	+	581.519i	0.358794	+	0.207150i	0.668552	−	0.743666i	$-0.266915\pi$
$199$	1007.22	+	581.519i	0.358794	+	0.207150i	−0.309758	+	0.950816i	$0.600248\pi$
$200$	214.686	−	123.949i	0.0759029	−	0.0438225i
$201$		0			0
$202$	583.154	−	336.684i	0.203122	−	0.117272i
$203$	1390.96	−	4289.95i	0.480918	−	1.48323i
$204$		0			0
$205$	3173.92			1.08135
$206$	1556.56	−	2696.03i	0.526458	−	0.911853i
$207$		0			0
$208$	−1256.91	+	725.679i	−0.418996	+	0.241908i
$209$	101.712	−	176.171i	0.0336632	−	0.0583063i
$210$		0			0
$211$	−540.323	−	935.867i	−0.176291	−	0.305345i	0.764316	−	0.644841i	$-0.223077\pi$
$211$	−540.323	−	935.867i	−0.176291	−	0.305345i	−0.940607	+	0.339497i	$0.889743\pi$
$212$	−663.510	−	383.078i	−0.214953	−	0.124103i
$213$		0			0
$214$	1961.45	+	3397.33i	0.626551	+	1.08522i
$215$	650.662	+	1126.98i	0.206394	+	0.357486i
$216$		0			0
$217$	5635.44	−	1201.49i	1.76294	−	0.375863i
$218$	1786.47	+	1031.42i	0.555024	+	0.320443i
$219$		0			0
$220$		−	604.932i		−	0.185384i
$221$		−	158.653i		−	0.0482903i
$222$		0			0
$223$	−5362.37	−	3095.96i	−1.61027	−	0.929691i	−0.989306	−	0.145854i	$-0.953407\pi$
$223$	−5362.37	−	3095.96i	−1.61027	−	0.929691i	−0.620966	−	0.783838i	$-0.713259\pi$
$224$	1717.28	−	366.126i	0.512233	−	0.109209i
$225$		0			0
$226$	1562.52	+	2706.36i	0.459899	+	0.796568i
$227$	27.5147	+	47.6568i	0.00804499	+	0.0139343i	0.870020	−	0.493017i	$-0.164106\pi$
$227$	27.5147	+	47.6568i	0.00804499	+	0.0139343i	−0.861975	+	0.506951i	$0.830773\pi$
$228$		0			0
$229$	1253.93	+	723.959i	0.361844	+	0.208911i	0.669889	−	0.742461i	$-0.266341\pi$
$229$	1253.93	+	723.959i	0.361844	+	0.208911i	−0.308045	+	0.951372i	$0.599675\pi$
$230$	−507.211	−	878.516i	−0.145411	−	0.251859i
$231$		0			0
$232$	−2989.40	+	5177.80i	−0.845965	+	1.46525i
$233$	−1409.38	+	813.703i	−0.396271	+	0.228787i	−0.684874	−	0.728662i	$-0.740143\pi$
$233$	−1409.38	+	813.703i	−0.396271	+	0.228787i	0.288602	+	0.957449i	$0.406809\pi$
$234$		0			0
$235$	−1210.32	+	2096.33i	−0.335967	+	0.581912i
$236$	585.780			0.161572
$237$		0			0
$238$	63.4503	−	195.691i	0.0172810	−	0.0532973i
$239$	−1829.22	+	1056.10i	−0.495073	+	0.285830i	−0.726676	−	0.686980i	$-0.758936\pi$
$239$	−1829.22	+	1056.10i	−0.495073	+	0.285830i	0.231604	+	0.972810i	$0.425603\pi$
$240$		0			0
$241$	−1901.69	+	1097.94i	−0.508293	+	0.293463i	−0.732132	−	0.681163i	$-0.761474\pi$
$241$	−1901.69	+	1097.94i	−0.508293	+	0.293463i	0.223839	+	0.974626i	$0.428141\pi$
$242$	1357.43	+	783.712i	0.360574	+	0.208177i
$243$		0			0
$244$			1620.13i			0.425076i
$245$	−379.807	+	3657.05i	−0.0990408	+	0.953635i
$246$		0			0
$247$	134.392	−	232.774i	0.0346200	−	0.0599637i
$248$	−7638.98			−1.95595
$249$		0			0
$250$		−	3499.48i		−	0.885306i
$251$	3257.57			0.819188			0.409594	−	0.912268i	$-0.365670\pi$
$251$	3257.57			0.819188			0.409594	+	0.912268i	$0.365670\pi$
$252$		0			0
$253$	1022.99			0.254209
$254$			5007.15i			1.23692i
$255$		0			0
$256$	−3054.56			−0.745741
$257$	1043.73	−	1807.79i	0.253330	−	0.438781i	−0.711110	−	0.703080i	$-0.751807\pi$
$257$	1043.73	−	1807.79i	0.253330	−	0.438781i	0.964441	+	0.264299i	$0.0851407\pi$
$258$		0			0
$259$	778.588	−	701.914i	0.186792	−	0.168397i
$260$		−	799.291i		−	0.190654i
$261$		0			0
$262$	37.1197	+	21.4310i	0.00875290	+	0.00505349i
$263$	−1541.36	+	889.907i	−0.361386	+	0.208646i	−0.669689	−	0.742642i	$-0.733572\pi$
$263$	−1541.36	+	889.907i	−0.361386	+	0.208646i	0.308302	+	0.951288i	$0.400239\pi$
$264$		0			0
$265$	−3292.20	+	1900.75i	−0.763163	+	0.440613i
$266$	258.860	−	233.368i	0.0596681	−	0.0537921i
$267$		0			0
$268$	2149.24			0.489873
$269$	−1531.88	+	2653.29i	−0.347213	+	0.601390i	−0.985753	−	0.168198i	$-0.946205\pi$
$269$	−1531.88	+	2653.29i	−0.347213	+	0.601390i	0.638540	+	0.769588i	$0.279538\pi$
$270$		0			0
$271$	110.943	−	64.0531i	0.0248683	−	0.0143577i	−0.487514	−	0.873115i	$-0.662096\pi$
$271$	110.943	−	64.0531i	0.0248683	−	0.0143577i	0.512383	+	0.858757i	$0.328763\pi$
$272$	−96.6433	+	167.391i	−0.0215436	+	0.0373146i
$273$		0			0
$274$	2422.61	+	4196.08i	0.534143	+	0.925163i
$275$	228.409	+	131.872i	0.0500856	+	0.0289170i
$276$		0			0
$277$	2481.22	+	4297.60i	0.538202	+	0.932194i	0.999001	+	0.0446890i	$0.0142297\pi$
$277$	2481.22	+	4297.60i	0.538202	+	0.932194i	−0.460799	+	0.887505i	$0.652437\pi$
$278$	−862.487	−	1493.87i	−0.186074	−	0.322290i
$279$		0			0
$280$	1503.39	−	4636.70i	0.320875	−	0.989629i
$281$	−3651.52	−	2108.21i	−0.775201	−	0.447563i	0.0595257	−	0.998227i	$-0.481041\pi$
$281$	−3651.52	−	2108.21i	−0.775201	−	0.447563i	−0.834727	+	0.550664i	$0.814374\pi$
$282$		0			0
$283$		−	2902.34i		−	0.609633i	−0.952411	−	0.304817i	$-0.901405\pi$
$283$		−	2902.34i		−	0.609633i	0.952411	−	0.304817i	$-0.0985952\pi$
$284$			2460.90i			0.514182i
$285$		0			0
$286$	−1886.88	−	1089.39i	−0.390118	−	0.225235i
$287$	−4072.94	+	3671.85i	−0.837694	+	0.755200i
$288$		0			0
$289$	2445.94	+	4236.48i	0.497850	+	0.862301i
$290$	3153.85	+	5462.63i	0.638623	+	1.10613i
$291$		0			0
$292$	2322.30	+	1340.78i	0.465418	+	0.268709i
$293$	184.087	+	318.848i	0.0367047	+	0.0635744i	0.883794	−	0.467876i	$-0.154981\pi$
$293$	184.087	+	318.848i	0.0367047	+	0.0635744i	−0.847089	+	0.531450i	$0.821647\pi$
$294$		0			0
$295$	1453.26	−	2517.12i	0.286820	−	0.496788i
$296$	−1203.54	+	694.865i	−0.236333	+	0.136447i
$297$		0			0
$298$	1939.32	−	3359.00i	0.376986	−	0.652959i
$299$	1351.67			0.261435
$300$		0			0
$301$	−2138.75	−	693.462i	−0.409553	−	0.132792i
$302$	−2328.82	+	1344.54i	−0.443736	+	0.256191i
$303$		0			0
$304$	−283.588	+	163.730i	−0.0535029	+	0.0308899i
$305$	6961.78	+	4019.38i	1.30698	+	0.754588i
$306$		0			0
$307$			860.553i			0.159982i	0.996796	+	0.0799908i	$0.0254891\pi$
$307$			860.553i			0.159982i	−0.996796	+	0.0799908i	$0.974511\pi$
$308$	699.834	+	776.280i	0.129470	+	0.143613i
$309$		0			0
$310$	−4029.61	+	6979.49i	−0.738278	+	1.27874i
$311$	−4650.54			−0.847936			−0.423968	−	0.905677i	$-0.639363\pi$
$311$	−4650.54			−0.847936			−0.423968	+	0.905677i	$0.639363\pi$
$312$		0			0
$313$		−	4106.63i		−	0.741598i	−0.928713	−	0.370799i	$-0.879084\pi$
$313$		−	4106.63i		−	0.741598i	0.928713	−	0.370799i	$-0.120916\pi$
$314$	418.039			0.0751316
$315$		0			0
$316$	936.744			0.166759
$317$		−	4725.10i		−	0.837186i	−0.908174	−	0.418593i	$-0.862523\pi$
$317$		−	4725.10i		−	0.837186i	0.908174	−	0.418593i	$-0.137477\pi$
$318$		0			0
$319$	−6360.97			−1.11645
$320$	−3030.91	+	5249.70i	−0.529479	+	0.917084i
$321$		0			0
$322$	1667.22	+	540.575i	0.288542	+	0.0935561i
$323$		−	35.7957i		−	0.00616633i
$324$		0			0
$325$	301.794	+	174.241i	0.0515094	+	0.0297389i
$326$	−4604.43	+	2658.37i	−0.782257	+	0.451636i
$327$		0			0
$328$	6295.96	−	3634.98i	1.05987	−	0.611915i
$329$	−872.062	−	4090.31i	−0.146135	−	0.685429i
$330$		0			0
$331$	−1185.45			−0.196852			−0.0984262	−	0.995144i	$-0.531381\pi$
$331$	−1185.45			−0.196852			−0.0984262	+	0.995144i	$0.531381\pi$
$332$	1064.60	−	1843.94i	0.175986	−	0.304817i
$333$		0			0
$334$	286.483	−	165.401i	0.0469332	−	0.0270969i
$335$	5332.05	−	9235.37i	0.869614	−	1.50622i
$336$		0			0
$337$	−3299.99	−	5715.76i	−0.533419	−	0.923908i	−0.999238	−	0.0390284i	$-0.987574\pi$
$337$	−3299.99	−	5715.76i	−0.533419	−	0.923908i	0.465819	−	0.884880i	$-0.345760\pi$
$338$	2104.71	+	1215.16i	0.338702	+	0.195550i
$339$		0			0
$340$	−53.2234	−	92.1856i	−0.00848954	−	0.0147043i
$341$	−4063.64	−	7038.42i	−0.645332	−	1.11775i
$342$		0			0
$343$	−3743.39	−	5132.32i	−0.589282	−	0.807927i
$344$	2581.38	+	1490.36i	0.404589	+	0.233590i
$345$		0			0
$346$		−	3605.31i		−	0.560181i
$347$		−	2622.46i		−	0.405709i	−0.979209	−	0.202855i	$-0.934978\pi$
$347$		−	2622.46i		−	0.405709i	0.979209	−	0.202855i	$-0.0650219\pi$
$348$		0			0
$349$	6093.48	+	3518.07i	0.934603	+	0.539593i	0.888264	−	0.459333i	$-0.151911\pi$
$349$	6093.48	+	3518.07i	0.934603	+	0.539593i	0.0463383	+	0.998926i	$0.485245\pi$
$350$	302.565	+	335.615i	0.0462079	+	0.0512554i
$351$		0			0
$352$	−1238.30	−	2144.80i	−0.187505	−	0.324768i
$353$	5225.72	+	9051.21i	0.787923	+	1.36472i	0.927237	+	0.374475i	$0.122177\pi$
$353$	5225.72	+	9051.21i	0.787923	+	1.36472i	−0.139314	+	0.990248i	$0.544490\pi$
$354$		0			0
$355$	10574.6	+	6105.24i	1.58096	+	0.912768i
$356$	163.400	+	283.016i	0.0243263	+	0.0421344i
$357$		0			0
$358$	821.946	−	1423.65i	0.121344	−	0.210174i
$359$	9887.03	−	5708.28i	1.45353	−	0.839197i	0.454852	−	0.890567i	$-0.349692\pi$
$359$	9887.03	−	5708.28i	1.45353	−	0.839197i	0.998680	+	0.0513705i	$0.0163589\pi$
$360$		0			0
$361$	−3399.18	+	5887.55i	−0.495579	+	0.858368i
$362$	−5498.22			−0.798288
$363$		0			0
$364$	924.685	+	1025.69i	0.133150	+	0.147695i
$365$	11522.7	−	6652.66i	1.65241	−	0.954017i
$366$		0			0
$367$	−6570.38	+	3793.41i	−0.934526	+	0.539549i	−0.888240	−	0.459380i	$-0.848072\pi$
$367$	−6570.38	+	3793.41i	−0.934526	+	0.539549i	−0.0462857	+	0.998928i	$0.514738\pi$
$368$	−1426.12	−	823.368i	−0.202015	−	0.116633i
$369$		0			0
$370$			1466.18i			0.206009i
$371$	2025.78	−	6247.83i	0.283486	−	0.874316i
$372$		0			0
$373$	1072.47	−	1857.56i	0.148874	−	0.257858i	−0.781937	−	0.623357i	$-0.785768\pi$
$373$	1072.47	−	1857.56i	0.148874	−	0.257858i	0.930812	+	0.365499i	$0.119102\pi$
$374$	−290.163			−0.0401175
$375$		0			0
$376$			5544.52i			0.760471i
$377$	−8404.70			−1.14818
$378$		0			0
$379$	1473.32			0.199682			0.0998408	−	0.995003i	$-0.468167\pi$
$379$	1473.32			0.199682			0.0998408	+	0.995003i	$0.468167\pi$
$380$		−	180.338i		−	0.0243451i
$381$		0			0
$382$	8090.48			1.08363
$383$	6321.90	−	10949.9i	0.843431	−	1.46087i	−0.0435459	−	0.999051i	$-0.513865\pi$
$383$	6321.90	−	10949.9i	0.843431	−	1.46087i	0.886977	−	0.461814i	$-0.152801\pi$
$384$		0			0
$385$	5071.92	−	1081.34i	0.671400	−	0.143144i
$386$		−	4989.85i		−	0.657971i
$387$		0			0
$388$	−1688.23	−	974.698i	−0.220894	−	0.127533i
$389$	−7322.70	+	4227.76i	−0.954436	+	0.551044i	−0.894456	−	0.447156i	$-0.852437\pi$
$389$	−7322.70	+	4227.76i	−0.954436	+	0.551044i	−0.0599797	+	0.998200i	$0.519104\pi$
$390$		0			0
$391$	155.893	−	90.0051i	0.0201634	−	0.0116413i
$392$	3434.88	+	7689.31i	0.442571	+	0.990737i
$393$		0			0
$394$	−6985.08			−0.893155
$395$	2323.96	−	4025.22i	0.296029	−	0.512737i
$396$		0			0
$397$	−8524.29	+	4921.50i	−1.07764	+	0.622174i	−0.930258	−	0.366906i	$-0.880417\pi$
$397$	−8524.29	+	4921.50i	−1.07764	+	0.622174i	−0.147379	+	0.989080i	$0.547084\pi$
$398$	1405.26	−	2433.98i	0.176983	−	0.306544i
$399$		0			0
$400$	−212.278	−	367.676i	−0.0265347	−	0.0459595i
$401$	−2044.96	−	1180.66i	−0.254665	−	0.147031i	0.367234	−	0.930129i	$-0.380305\pi$
$401$	−2044.96	−	1180.66i	−0.254665	−	0.147031i	−0.621898	+	0.783098i	$0.713638\pi$
$402$		0			0
$403$	−5369.25	−	9299.82i	−0.663676	−	1.14952i
$404$	300.994	+	521.337i	0.0370669	+	0.0642017i
$405$		0			0
$406$	−10366.8	−	3361.31i	−1.26723	−	0.410884i
$407$	−1280.47	−	739.282i	−0.155948	−	0.0900364i
$408$		0			0
$409$		−	4905.18i		−	0.593021i	−0.955030	−	0.296511i	$-0.904177\pi$
$409$		−	4905.18i		−	0.593021i	0.955030	−	0.296511i	$-0.0958230\pi$
$410$		−	7669.88i		−	0.923874i
$411$		0			0
$412$	2410.24	+	1391.56i	0.288214	+	0.166400i
$413$	1047.11	+	4911.35i	0.124758	+	0.585162i
$414$		0			0
$415$	−5282.31	−	9149.23i	−0.624815	−	1.08221i
$416$	−1636.16	−	2833.91i	−0.192835	−	0.334000i
$417$		0			0
$418$	−425.723	−	245.792i	−0.0498153	−	0.0287609i
$419$	5174.25	+	8962.06i	0.603290	+	1.04493i	0.992319	+	0.123704i	$0.0394772\pi$
$419$	5174.25	+	8962.06i	0.603290	+	1.04493i	−0.389029	+	0.921225i	$0.627189\pi$
$420$		0			0
$421$	1438.21	−	2491.05i	0.166494	−	0.288376i	−0.770691	−	0.637209i	$-0.780089\pi$
$421$	1438.21	−	2491.05i	0.166494	−	0.288376i	0.937185	+	0.348833i	$0.113422\pi$
$422$	−2261.55	+	1305.71i	−0.260878	+	0.150618i
$423$		0			0
$424$	−4353.73	+	7540.88i	−0.498669	+	0.863720i
$425$	46.4096			0.00529693
$426$		0			0
$427$	−13583.7	+	2896.06i	−1.53948	+	0.328221i
$428$	−3037.20	+	1753.53i	−0.343011	+	0.198037i
$429$		0			0
$430$	2723.38	−	1572.35i	0.305426	−	0.176338i
$431$	5858.22	+	3382.24i	0.654711	+	0.377998i	0.790259	−	0.612773i	$-0.209946\pi$
$431$	5858.22	+	3382.24i	0.654711	+	0.377998i	−0.135548	+	0.990771i	$0.543279\pi$
$432$		0			0
$433$		−	10320.4i		−	1.14542i	−0.819756	−	0.572712i	$-0.805891\pi$
$433$		−	10320.4i		−	1.14542i	0.819756	−	0.572712i	$-0.194109\pi$
$434$	−2903.43	−	13618.2i	−0.321127	−	1.50621i
$435$		0			0
$436$	−922.086	+	1597.10i	−0.101284	+	0.175429i
$437$	304.967			0.0333834
$438$		0			0
$439$		−	6549.31i		−	0.712031i	−0.934480	−	0.356015i	$-0.884135\pi$
$439$		−	6549.31i		−	0.712031i	0.934480	−	0.356015i	$-0.115865\pi$
$440$	−6875.12			−0.744906
$441$		0			0
$442$	−383.390			−0.0412579
$443$		−	17407.0i		−	1.86689i	−0.358720	−	0.933445i	$-0.616787\pi$
$443$		−	17407.0i		−	1.86689i	0.358720	−	0.933445i	$-0.383213\pi$
$444$		0			0
$445$	1621.51			0.172735
$446$	−7481.50	+	12958.3i	−0.794303	+	1.37577i
$447$		0			0
$448$	−2183.85	−	10243.1i	−0.230306	−	1.08023i
$449$			8031.38i			0.844152i	0.906560	+	0.422076i	$0.138699\pi$
$449$			8031.38i			0.844152i	−0.906560	+	0.422076i	$0.861301\pi$
$450$		0			0
$451$	6698.41	+	3867.33i	0.699369	+	0.403781i
$452$	−2419.47	+	1396.88i	−0.251775	+	0.145363i
$453$		0			0
$454$	115.164	−	66.4901i	0.0119051	−	0.00687342i
$455$	6701.49	−	1428.77i	0.690485	−	0.147213i
$456$		0			0
$457$	10210.7			1.04516			0.522580	−	0.852590i	$-0.324970\pi$
$457$	10210.7			1.04516			0.522580	+	0.852590i	$0.324970\pi$
$458$	1749.47	−	3030.17i	0.178488	−	0.309150i
$459$		0			0
$460$	785.390	−	453.445i	0.0796065	−	0.0459608i
$461$	−8240.35	+	14272.7i	−0.832519	+	1.44197i	0.0635154	+	0.997981i	$0.479769\pi$
$461$	−8240.35	+	14272.7i	−0.832519	+	1.44197i	−0.896034	+	0.443984i	$0.853565\pi$
$462$		0			0
$463$	−1041.49	−	1803.91i	−0.104540	−	0.181069i	0.809010	−	0.587795i	$-0.200004\pi$
$463$	−1041.49	−	1803.91i	−0.104540	−	0.181069i	−0.913550	+	0.406726i	$0.866670\pi$
$464$	8867.62	+	5119.72i	0.887217	+	0.512235i
$465$		0			0
$466$	1966.34	+	3405.80i	0.195470	+	0.338564i
$467$	−3810.55	−	6600.06i	−0.377583	−	0.653993i	0.613127	−	0.789984i	$-0.289911\pi$
$467$	−3810.55	−	6600.06i	−0.377583	−	0.653993i	−0.990710	+	0.135992i	$0.956578\pi$
$468$		0			0
$469$	3841.87	+	18019.9i	0.378254	+	1.77416i
$470$	5065.85	+	2924.77i	0.497170	+	0.287041i
$471$		0			0
$472$		−	6657.46i		−	0.649226i
$473$			3171.25i			0.308275i
$474$		0			0
$475$	68.0916	+	39.3127i	0.00657739	+	0.00379746i
$476$	174.947	+	56.7243i	0.0168460	+	0.00546209i
$477$		0			0
$478$	2552.10	+	4420.37i	0.244206	+	0.422977i
$479$	−3418.25	−	5920.58i	−0.326062	−	0.564756i	0.655665	−	0.755052i	$-0.272389\pi$
$479$	−3418.25	−	5920.58i	−0.326062	−	0.564756i	−0.981727	+	0.190296i	$0.939055\pi$
$480$		0			0
$481$	−1691.88	−	976.807i	−0.160381	−	0.0925958i
$482$	2653.21	+	4595.49i	0.250727	+	0.434272i
$483$		0			0
$484$	−700.636	+	1213.54i	−0.0657997	+	0.113968i
$485$	−8376.63	+	4836.25i	−0.784254	+	0.452789i
$486$		0			0
$487$	9331.03	−	16161.8i	0.868233	−	1.50382i	0.00443162	−	0.999990i	$-0.498589\pi$
$487$	9331.03	−	16161.8i	0.868233	−	1.50382i	0.863801	−	0.503833i	$-0.168077\pi$
$488$	18413.0			1.70803
$489$		0			0
$490$	8837.39	+	917.817i	0.814760	+	0.0846178i
$491$	−8389.01	+	4843.40i	−0.771061	+	0.445172i	−0.833253	−	0.552892i	$-0.813524\pi$
$491$	−8389.01	+	4843.40i	−0.771061	+	0.445172i	0.0621920	+	0.998064i	$0.480191\pi$
$492$		0			0
$493$	−969.349	+	559.654i	−0.0885544	+	0.0511269i
$494$	−562.505	−	324.762i	−0.0512314	−	0.0295784i
$495$		0			0
$496$			13082.7i			1.18434i
$497$	−20632.9	+	4398.98i	−1.86220	+	0.397024i
$498$		0			0
$499$	2074.80	−	3593.65i	0.186134	−	0.322393i	−0.757824	−	0.652459i	$-0.773738\pi$
$499$	2074.80	−	3593.65i	0.186134	−	0.322393i	0.943958	+	0.330066i	$0.107071\pi$
$500$	3128.52			0.279823
$501$		0			0
$502$		−	7872.03i		−	0.699892i
$503$	−11384.6			−1.00917			−0.504586	−	0.863362i	$-0.668355\pi$
$503$	−11384.6			−1.00917			−0.504586	+	0.863362i	$0.668355\pi$
$504$		0			0
$505$	2986.94			0.263202
$506$		−	2472.09i		−	0.217189i
$507$		0			0
$508$	−4476.37			−0.390958
$509$	−1010.10	+	1749.54i	−0.0879605	+	0.152352i	−0.906649	−	0.421886i	$-0.861368\pi$
$509$	−1010.10	+	1749.54i	−0.0879605	+	0.152352i	0.818688	+	0.574238i	$0.194702\pi$
$510$		0			0
$511$	−7090.26	+	21867.5i	−0.613806	+	1.89308i
$512$			12246.2i			1.05705i
$513$		0			0
$514$	−4368.58	−	2522.20i	−0.374883	−	0.216439i
$515$	11959.1	−	6904.61i	1.02327	−	0.590783i
$516$		0			0
$517$	−5108.63	+	2949.47i	−0.434579	+	0.250904i
$518$	−1696.20	−	1881.48i	−0.143874	−	0.159590i
$519$		0			0
$520$	−9084.04			−0.766080
$521$	−5932.30	+	10275.0i	−0.498846	+	0.864027i	−0.999999	−	0.00133177i	$-0.999576\pi$
$521$	−5932.30	+	10275.0i	−0.498846	+	0.864027i	0.501153	+	0.865359i	$0.332909\pi$
$522$		0			0
$523$	5064.90	−	2924.22i	0.423466	−	0.244488i	−0.273093	−	0.961988i	$-0.588047\pi$
$523$	5064.90	−	2924.22i	0.423466	−	0.244488i	0.696559	+	0.717499i	$0.254713\pi$
$524$	−19.1593	+	33.1848i	−0.00159728	+	0.00276658i
$525$		0			0
$526$	2150.49	+	3724.76i	0.178262	+	0.308759i
$527$	−1238.52	−	715.058i	−0.102373	−	0.0591051i
$528$		0			0
$529$	−5316.69	−	9208.77i	−0.436976	−	0.756865i
$530$	4593.23	+	7955.71i	0.376448	+	0.652026i
$531$		0			0
$532$	208.630	+	231.420i	0.0170024	+	0.0188596i
$533$	8850.55	+	5109.87i	0.719249	+	0.415259i
$534$		0			0
$535$			17401.3i			1.40621i
$536$		−	24426.4i		−	1.96839i
$537$		0			0
$538$	6411.76	+	3701.83i	0.513812	+	0.296649i
$539$	−5257.57	+	7255.25i	−0.420148	+	0.579788i
$540$		0			0
$541$	−5802.24	−	10049.8i	−0.461105	−	0.798657i	0.537911	−	0.843001i	$-0.319213\pi$
$541$	−5802.24	−	10049.8i	−0.461105	−	0.798657i	−0.999016	+	0.0443443i	$0.985880\pi$
$542$	−154.786	−	268.098i	−0.0122669	−	0.0212468i
$543$		0			0
$544$	−377.410	−	217.898i	−0.0297451	−	0.0171733i
$545$	4575.20	+	7924.47i	0.359596	+	0.622839i
$546$		0			0
$547$	−2895.79	+	5015.65i	−0.226353	+	0.392055i	−0.956724	−	0.290995i	$-0.906014\pi$
$547$	−2895.79	+	5015.65i	−0.226353	+	0.392055i	0.730372	+	0.683050i	$0.239347\pi$
$548$	−3751.28	+	2165.80i	−0.292421	+	0.168829i
$549$		0			0
$550$	318.672	−	551.957i	0.0247059	−	0.0427918i
$551$	−1896.29			−0.146615
$552$		0			0
$553$	1674.47	+	7853.93i	0.128763	+	0.603948i
$554$	10385.3	−	5995.95i	0.796441	−	0.459826i
$555$		0			0
$556$	1335.52	−	771.060i	0.101868	−	0.0588134i
$557$	5630.99	+	3251.06i	0.428353	+	0.247310i	0.698645	−	0.715469i	$-0.253787\pi$
$557$	5630.99	+	3251.06i	0.428353	+	0.247310i	−0.270292	+	0.962779i	$0.587120\pi$
$558$		0			0
$559$			4190.15i			0.317038i
$560$	−7940.93	−	2574.75i	−0.599224	−	0.194291i
$561$		0			0
$562$	−5094.55	+	8824.02i	−0.382386	+	0.662311i
$563$	−5027.14			−0.376321			−0.188160	−	0.982138i	$-0.560252\pi$
$563$	−5027.14			−0.376321			−0.188160	+	0.982138i	$0.560252\pi$
$564$		0			0
$565$			13862.1i			1.03218i
$566$	−7013.60			−0.520854
$567$		0			0
$568$	27968.4			2.06607
$569$			892.534i			0.0657592i	0.999459	+	0.0328796i	$0.0104678\pi$
$569$			892.534i			0.0657592i	−0.999459	+	0.0328796i	$0.989532\pi$
$570$		0			0
$571$	17418.8			1.27663			0.638313	−	0.769777i	$-0.279632\pi$
$571$	17418.8			1.27663			0.638313	+	0.769777i	$0.279632\pi$
$572$	973.912	−	1686.87i	0.0711911	−	0.123307i
$573$		0			0
$574$	8873.15	+	9842.40i	0.645223	+	0.715704i
$575$			395.394i			0.0286766i
$576$		0			0
$577$	5638.05	+	3255.13i	0.406785	+	0.234858i	0.689407	−	0.724374i	$-0.257871\pi$
$577$	5638.05	+	3255.13i	0.406785	+	0.234858i	−0.282622	+	0.959231i	$0.591204\pi$
$578$	10237.6	−	5910.68i	0.736727	−	0.425349i
$579$		0			0
$580$	−4883.57	+	2819.53i	−0.349619	+	0.201853i
$581$	17363.1	+	5629.77i	1.23983	+	0.402000i
$582$		0			0
$583$	−9264.04			−0.658109
$584$	15238.1	−	26393.2i	1.07972	−	1.87013i
$585$		0			0
$586$	770.507	−	444.852i	0.0543163	−	0.0313595i
$587$	2173.87	−	3765.25i	0.152854	−	0.264750i	−0.779422	−	0.626500i	$-0.784487\pi$
$587$	2173.87	−	3765.25i	0.152854	−	0.264750i	0.932275	+	0.361749i	$0.117820\pi$
$588$		0			0
$589$	−1211.42	−	2098.25i	−0.0847468	−	0.146786i
$590$	−6082.70	−	3511.85i	−0.424442	−	0.245052i
$591$		0			0
$592$	1190.04	+	2061.22i	0.0826191	+	0.143100i
$593$	7744.80	+	13414.4i	0.536325	+	0.928942i	0.999098	+	0.0424652i	$0.0135212\pi$
$593$	7744.80	+	13414.4i	0.536325	+	0.928942i	−0.462773	+	0.886477i	$0.653145\pi$
$594$		0			0
$595$	677.771	−	611.026i	0.0466990	−	0.0421002i
$596$	3002.93	+	1733.74i	0.206384	+	0.119156i
$597$		0			0
$598$		−	3266.35i		−	0.223363i
$599$		−	12787.6i		−	0.872268i	−0.899882	−	0.436134i	$-0.856347\pi$
$599$		−	12787.6i		−	0.872268i	0.899882	−	0.436134i	$-0.143653\pi$
$600$		0			0
$601$	14961.0	+	8637.74i	1.01543	+	0.586258i	0.912776	−	0.408460i	$-0.133934\pi$
$601$	14961.0	+	8637.74i	1.01543	+	0.586258i	0.102652	+	0.994717i	$0.467267\pi$
$602$	−1675.77	+	5168.35i	−0.113454	+	0.349911i
$603$		0			0
$604$	−1202.02	−	2081.95i	−0.0809757	−	0.140254i
$605$	3476.41	+	6021.31i	0.233613	+	0.404630i
$606$		0			0
$607$	−8907.33	−	5142.65i	−0.595614	−	0.343878i	0.171700	−	0.985149i	$-0.445074\pi$
$607$	−8907.33	−	5142.65i	−0.595614	−	0.343878i	−0.767314	+	0.641272i	$0.778407\pi$
$608$	−369.155	−	639.395i	−0.0246237	−	0.0426495i
$609$		0			0
$610$	9712.97	−	16823.4i	0.644699	−	1.11665i
$611$	−6749.99	+	3897.11i	−0.446932	+	0.258036i
$612$		0			0
$613$	12096.2	−	20951.3i	0.797002	−	1.38045i	−0.124558	−	0.992212i	$-0.539751\pi$
$613$	12096.2	−	20951.3i	0.797002	−	1.38045i	0.921560	−	0.388236i	$-0.126916\pi$
$614$	2079.55			0.136684
$615$		0			0
$616$	8822.52	−	7953.70i	0.577061	−	0.520233i
$617$	−2592.10	+	1496.55i	−0.169132	+	0.0976481i	−0.582176	−	0.813063i	$-0.697799\pi$
$617$	−2592.10	+	1496.55i	−0.169132	+	0.0976481i	0.413045	+	0.910711i	$0.364465\pi$
$618$		0			0
$619$	5723.97	−	3304.74i	0.371674	−	0.214586i	−0.302516	−	0.953144i	$-0.597826\pi$
$619$	5723.97	−	3304.74i	0.371674	−	0.214586i	0.674189	+	0.738559i	$0.264493\pi$
$620$	−6239.63	−	3602.45i	−0.404177	−	0.233352i
$621$		0			0
$622$			11238.2i			0.724454i
$623$	−2080.81	+	1875.89i	−0.133813	+	0.120636i
$624$		0			0
$625$	7130.50	−	12350.4i	0.456352	−	0.790425i
$626$	−9923.80			−0.633602
$627$		0			0
$628$			373.725i			0.0237472i
$629$	−260.175			−0.0164926
$630$		0			0
$631$	−17308.9			−1.09201			−0.546005	−	0.837782i	$-0.683852\pi$
$631$	−17308.9			−1.09201			−0.546005	+	0.837782i	$0.683852\pi$
$632$		−	10646.2i		−	0.670069i
$633$		0			0
$634$	−11418.4			−0.715270
$635$	−11105.4	+	19235.1i	−0.694023	+	1.20208i
$636$		0			0
$637$	−6946.79	+	9586.30i	−0.432091	+	0.596269i
$638$			15371.5i			0.953861i
$639$		0			0
$640$	5645.09	+	3259.19i	0.348659	+	0.201298i
$641$	−21963.3	+	12680.5i	−1.35335	+	0.781357i	−0.988717	−	0.149794i	$-0.952139\pi$
$641$	−21963.3	+	12680.5i	−1.35335	+	0.781357i	−0.364633	+	0.931151i	$0.618806\pi$
$642$		0			0
$643$	−10112.2	+	5838.27i	−0.620195	+	0.358070i	−0.776945	−	0.629568i	$-0.783232\pi$
$643$	−10112.2	+	5838.27i	−0.620195	+	0.358070i	0.156750	+	0.987638i	$0.449898\pi$
$644$	−483.272	+	1490.49i	−0.0295708	+	0.0912010i
$645$		0			0
$646$	−86.5014			−0.00526835
$647$	5873.10	−	10172.5i	0.356871	−	0.618118i	−0.630566	−	0.776136i	$-0.717177\pi$
$647$	5873.10	−	10172.5i	0.356871	−	0.618118i	0.987436	+	0.158018i	$0.0505103\pi$
$648$		0			0
$649$	6134.07	−	3541.51i	0.371006	−	0.214201i
$650$	421.059	−	729.296i	0.0254082	−	0.0440082i
$651$		0			0
$652$	−2376.57	−	4116.34i	−0.142751	−	0.247252i
$653$	−5975.62	−	3450.03i	−0.358107	−	0.206753i	0.310143	−	0.950690i	$-0.399623\pi$
$653$	−5975.62	−	3450.03i	−0.358107	−	0.206753i	−0.668250	+	0.743937i	$0.732956\pi$
$654$		0			0
$655$	95.0643	+	164.656i	0.00567094	+	0.00982236i
$656$	−6225.35	−	10782.6i	−0.370517	−	0.641754i
$657$		0			0
$658$	−9884.37	+	2107.37i	−0.585612	+	0.124854i
$659$	4602.35	+	2657.17i	0.272052	+	0.157069i	0.629820	−	0.776741i	$-0.283129\pi$
$659$	4602.35	+	2657.17i	0.272052	+	0.157069i	−0.357768	+	0.933811i	$0.616462\pi$
$660$		0			0
$661$			18583.4i			1.09351i	0.837293	+	0.546754i	$0.184137\pi$
$661$			18583.4i			1.09351i	−0.837293	+	0.546754i	$0.815863\pi$
$662$			2864.68i			0.168185i
$663$		0			0
$664$	−20956.6	−	12099.3i	−1.22481	−	0.707143i
$665$	1512.01	−	322.363i	0.0881701	−	0.0187980i
$666$		0			0
$667$	−4768.06	−	8258.52i	−0.276792	−	0.479417i
$668$	147.868	+	256.115i	0.00856465	+	0.0148344i
$669$		0			0
$670$	−22317.6	−	12885.1i	−1.28687	−	0.742975i
$671$	9794.99	+	16965.4i	0.563534	+	0.976070i
$672$		0			0
$673$	5147.44	−	8915.63i	0.294828	−	0.510657i	−0.680117	−	0.733104i	$-0.738071\pi$
$673$	5147.44	−	8915.63i	0.294828	−	0.510657i	0.974945	+	0.222447i	$0.0714043\pi$
$674$	−13812.3	+	7974.54i	−0.789363	+	0.455739i
$675$		0			0
$676$	−1086.34	+	1881.60i	−0.0618084	+	0.107055i
$677$	5268.21			0.299075			0.149538	−	0.988756i	$-0.452222\pi$
$677$	5268.21			0.299075			0.149538	+	0.988756i	$0.452222\pi$
$678$		0			0
$679$	5154.37	−	15896.9i	0.291320	−	0.898478i
$680$	−1047.70	+	604.890i	−0.0590845	+	0.0341125i
$681$		0			0
$682$	−17008.6	+	9819.91i	−0.954974	+	0.551355i
$683$	15591.8	+	9001.90i	0.873502	+	0.504317i	0.868510	−	0.495671i	$-0.165078\pi$
$683$	15591.8	+	9001.90i	0.873502	+	0.504317i	0.00499159	+	0.999988i	$0.498411\pi$
$684$		0			0
$685$			21492.5i			1.19881i
$686$	−12402.4	+	9046.02i	−0.690271	+	0.503467i
$687$		0			0
$688$	2552.43	−	4420.93i	0.141440	−	0.244980i
$689$	−12240.5			−0.676816
$690$		0			0
$691$		−	10326.6i		−	0.568513i	−0.958748	−	0.284257i	$-0.908253\pi$
$691$		−	10326.6i		−	0.568513i	0.958748	−	0.284257i	$-0.0917468\pi$
$692$	3223.13			0.177059
$693$		0			0
$694$	−6337.26			−0.346627
$695$		−	7651.68i		−	0.417618i
$696$		0			0
$697$	1361.03			0.0739636
$698$	8501.53	−	14725.1i	0.461014	−	0.798499i
$699$		0			0
$700$	−300.039	+	270.492i	−0.0162006	+	0.0146052i
$701$		−	26276.7i		−	1.41577i	−0.706326	−	0.707887i	$-0.749649\pi$
$701$		−	26276.7i		−	1.41577i	0.706326	−	0.707887i	$-0.250351\pi$
$702$		0			0
$703$	−381.726	−	220.390i	−0.0204795	−	0.0118238i
$704$	−12793.2	+	7386.15i	−0.684889	+	0.395421i
$705$		0			0
$706$	21872.5	−	12628.1i	1.16598	−	0.673181i
$707$	−3833.00	+	3455.54i	−0.203897	+	0.183817i
$708$		0			0
$709$	−12951.2			−0.686025			−0.343012	−	0.939331i	$-0.611447\pi$
$709$	−12951.2			−0.686025			−0.343012	+	0.939331i	$0.611447\pi$
$710$	14753.5	−	25553.8i	0.779844	−	1.35073i
$711$		0			0
$712$	3216.52	−	1857.06i	0.169303	−	0.0977473i
$713$	6092.05	−	10551.7i	0.319984	−	0.554229i
$714$		0			0
$715$	−4832.35	−	8369.87i	−0.252755	−	0.437784i
$716$	1272.74	+	734.817i	0.0664309	+	0.0383539i
$717$		0			0
$718$	−13794.3	−	23892.3i	−0.716987	−	1.24186i
$719$	−6027.33	−	10439.6i	−0.312631	−	0.541492i	0.666300	−	0.745684i	$-0.267877\pi$
$719$	−6027.33	−	10439.6i	−0.312631	−	0.541492i	−0.978931	+	0.204191i	$0.934544\pi$
$720$		0			0
$721$	−7358.78	+	22695.7i	−0.380104	+	1.17230i
$722$	14227.5	+	8214.22i	0.733367	+	0.423410i
$723$		0			0
$724$		−	4915.39i		−	0.252319i
$725$		−	2458.57i		−	0.125943i
$726$		0			0
$727$	24377.4	+	14074.3i	1.24361	+	0.718000i	0.969828	−	0.243791i	$-0.0783910\pi$
$727$	24377.4	+	14074.3i	1.24361	+	0.718000i	0.273785	+	0.961791i	$0.411724\pi$
$728$	11657.1	−	10509.2i	0.593464	−	0.535021i
$729$		0			0
$730$	−16076.4	−	27845.1i	−0.815087	−	1.41177i
$731$	279.014	+	483.267i	0.0141173	+	0.0244518i
$732$		0			0
$733$	−5289.89	−	3054.12i	−0.266557	−	0.153897i	0.360765	−	0.932657i	$-0.382516\pi$
$733$	−5289.89	−	3054.12i	−0.266557	−	0.153897i	−0.627322	+	0.778760i	$0.715849\pi$
$734$	9166.90	+	15877.5i	0.460976	+	0.798434i
$735$		0			0
$736$	1856.42	−	3215.41i	0.0929733	−	0.161035i
$737$	22506.0	−	12993.9i	1.12486	−	0.649437i
$738$		0			0
$739$	−8878.08	+	15377.3i	−0.441929	+	0.765443i	−0.997833	−	0.0658036i	$-0.979039\pi$
$739$	−8878.08	+	15377.3i	−0.441929	+	0.765443i	0.555904	+	0.831247i	$0.312372\pi$
$740$	−1310.76			−0.0651142
$741$		0			0
$742$	−15098.1	−	4895.37i	−0.746992	−	0.242203i
$743$	8335.34	−	4812.41i	0.411567	−	0.237618i	−0.279896	−	0.960030i	$-0.590300\pi$
$743$	8335.34	−	4812.41i	0.411567	−	0.237618i	0.691463	+	0.722412i	$0.256967\pi$
$744$		0			0
$745$	14899.9	−	8602.48i	0.732740	−	0.423048i
$746$	−4488.87	−	2591.65i	−0.220307	−	0.127194i
$747$		0			0
$748$		−	259.404i		−	0.0126802i
$749$	−20131.2	−	22330.2i	−0.982081	−	1.08936i
$750$		0			0
$751$	8094.83	−	14020.7i	0.393322	−	0.681253i	−0.599564	−	0.800327i	$-0.704659\pi$
$751$	8094.83	−	14020.7i	0.393322	−	0.681253i	0.992885	+	0.119074i	$0.0379926\pi$
$752$	9495.69			0.460468
$753$		0			0
$754$			20310.2i			0.980975i
$755$	−11928.3			−0.574987
$756$		0			0
$757$	−16960.5			−0.814318			−0.407159	−	0.913357i	$-0.633481\pi$
$757$	−16960.5			−0.814318			−0.407159	+	0.913357i	$0.633481\pi$
$758$		−	3560.32i		−	0.170603i
$759$		0			0
$760$	−2049.56			−0.0978231
$761$	693.400	−	1201.00i	0.0330299	−	0.0572094i	−0.849038	−	0.528332i	$-0.822818\pi$
$761$	693.400	−	1201.00i	0.0330299	−	0.0572094i	0.882068	+	0.471122i	$0.156151\pi$
$762$		0			0
$763$	−15038.8	−	4876.14i	−0.713554	−	0.231361i
$764$			7232.86i			0.342507i
$765$		0			0
$766$	−26460.7	−	15277.1i	−1.24812	−	0.720605i
$767$	8104.89	−	4679.36i	0.381553	−	0.220289i
$768$		0			0
$769$	18569.7	−	10721.2i	0.870795	−	0.502754i	0.00318241	−	0.999995i	$-0.498987\pi$
$769$	18569.7	−	10721.2i	0.870795	−	0.502754i	0.867612	+	0.497241i	$0.165654\pi$
$770$	−2613.10	−	12256.5i	−0.122298	−	0.573626i
$771$		0			0
$772$	4460.90			0.207968
$773$	6650.89	−	11519.7i	0.309464	−	0.536008i	−0.668781	−	0.743459i	$-0.733184\pi$
$773$	6650.89	−	11519.7i	0.309464	−	0.536008i	0.978245	+	0.207452i	$0.0665170\pi$
$774$		0			0
$775$	2720.41	−	1570.63i	0.126090	−	0.0727983i
$776$	−11077.6	+	19186.9i	−0.512450	+	0.887589i
$777$		0			0
$778$	10216.5	+	17695.5i	0.470797	+	0.815444i
$779$	1996.88	+	1152.90i	0.0918431	+	0.0530257i
$780$		0			0
$781$	14878.1	+	25769.6i	0.681665	+	1.18068i
$782$	−217.500	−	376.722i	−0.00994603	−	0.0172270i
$783$		0			0
$784$	13168.9	−	5882.66i	0.599895	−	0.267979i
$785$	1605.91	+	927.174i	0.0730159	+	0.0421557i
$786$		0			0
$787$			29326.5i			1.32831i	0.747596	+	0.664154i	$0.231208\pi$
$787$			29326.5i			1.32831i	−0.747596	+	0.664154i	$0.768792\pi$
$788$		−	6244.63i		−	0.282304i
$789$		0			0
$790$	−9727.08	−	5615.93i	−0.438068	−	0.252919i
$791$	−16036.8	−	17788.6i	−0.720863	−	0.799607i
$792$		0			0
$793$	12942.0	+	22416.3i	0.579553	+	1.00382i
$794$	11893.0	+	20599.2i	0.531569	+	0.920704i
$795$		0			0
$796$	2175.97	+	1256.30i	0.0968909	+	0.0559400i
$797$	−20376.9	−	35293.9i	−0.905632	−	1.56860i	−0.820067	−	0.572268i	$-0.806064\pi$
$797$	−20376.9	−	35293.9i	−0.905632	−	1.56860i	−0.0855648	−	0.996333i	$-0.527269\pi$
$798$		0			0
$799$	−519.003	+	898.939i	−0.0229800	+	0.0398025i
$800$	828.985	−	478.614i	0.0366363	−	0.0211520i
$801$		0			0
$802$	−2853.10	+	4941.72i	−0.125619	+	0.217579i
$803$	32424.3			1.42494
$804$		0			0
$805$	5205.73	+	5774.38i	0.227923	+	0.252820i
$806$	−22473.3	+	12975.0i	−0.982120	+	0.567027i
$807$		0			0
$808$	5925.06	−	3420.84i	0.257974	−	0.148941i
$809$	30238.0	+	17457.9i	1.31410	+	0.758698i	0.982773	−	0.184817i	$-0.0591692\pi$
$809$	30238.0	+	17457.9i	1.31410	+	0.758698i	0.331331	+	0.943515i	$0.392502\pi$
$810$		0			0
$811$		−	29989.5i		−	1.29849i	−0.760581	−	0.649243i	$-0.775086\pi$
$811$		−	29989.5i		−	1.29849i	0.760581	−	0.649243i	$-0.224914\pi$
$812$	3004.99	−	9267.88i	0.129870	−	0.400541i
$813$		0			0
$814$	−1786.50	+	3094.31i	−0.0769247	+	0.133238i
$815$	−23584.1			−1.01364
$816$		0			0
$817$			945.392i			0.0404836i
$818$	−11853.5			−0.506662
$819$		0			0
$820$	6856.84			0.292014
$821$			13054.3i			0.554931i	0.960736	+	0.277466i	$0.0894944\pi$
$821$			13054.3i			0.554931i	−0.960736	+	0.277466i	$0.910506\pi$
$822$		0			0
$823$	−435.216			−0.0184334			−0.00921670	−	0.999958i	$-0.502934\pi$
$823$	−435.216			−0.0184334			−0.00921670	+	0.999958i	$0.502934\pi$
$824$	15815.2	−	27392.7i	0.668627	−	1.15810i
$825$		0			0
$826$	11868.4	−	2530.37i	0.499946	−	0.106589i
$827$		−	11735.6i		−	0.493453i	−0.969085	−	0.246726i	$-0.920645\pi$
$827$		−	11735.6i		−	0.493453i	0.969085	−	0.246726i	$-0.0793549\pi$
$828$		0			0
$829$	−27253.5	−	15734.8i	−1.14180	−	0.659220i	−0.194926	−	0.980818i	$-0.562447\pi$
$829$	−27253.5	−	15734.8i	−1.14180	−	0.659220i	−0.946876	+	0.321598i	$0.895780\pi$
$830$	−22109.4	+	12764.9i	−0.924613	+	0.533826i
$831$		0			0
$832$	−16903.5	+	9759.27i	−0.704357	+	0.406661i
$833$	−162.867	+	1568.20i	−0.00677434	+	0.0652281i
$834$		0			0
$835$	1467.38			0.0608153
$836$	219.737	−	380.595i	0.00909061	−	0.0157454i
$837$		0			0
$838$	21657.1	−	12503.7i	0.892759	−	0.515435i
$839$	−2421.48	+	4194.13i	−0.0996410	+	0.172583i	−0.911536	−	0.411220i	$-0.865103\pi$
$839$	−2421.48	+	4194.13i	−0.0996410	+	0.172583i	0.811895	+	0.583803i	$0.198436\pi$
$840$		0			0
$841$	17453.4	+	30230.2i	0.715626	+	1.23950i
$842$	−6019.70	−	3475.47i	−0.246381	−	0.142248i
$843$		0			0
$844$	−1167.30	−	2021.82i	−0.0476067	−	0.0824572i
$845$	5390.21	+	9336.12i	0.219443	+	0.380086i
$846$		0			0
$847$	−11427.1	−	3705.08i	−0.463564	−	0.150305i
$848$	12914.7	+	7456.30i	0.522986	+	0.301946i
$849$		0			0
$850$		−	112.150i		−	0.00452556i
$851$		−	2216.60i		−	0.0892882i
$852$		0			0
$853$	−6882.39	−	3973.55i	−0.276258	−	0.159498i	0.355470	−	0.934688i	$-0.384321\pi$
$853$	−6882.39	−	3973.55i	−0.276258	−	0.159498i	−0.631728	+	0.775190i	$0.717654\pi$
$854$	6998.43	+	32825.4i	0.280423	+	1.31529i
$855$		0			0
$856$	19929.1	+	34518.1i	0.795749	+	1.37828i
$857$	17425.1	+	30181.1i	0.694550	+	1.20300i	0.970332	+	0.241776i	$0.0777300\pi$
$857$	17425.1	+	30181.1i	0.694550	+	1.20300i	−0.275782	+	0.961220i	$0.588937\pi$
$858$		0			0
$859$	5651.27	+	3262.76i	0.224469	+	0.129597i	0.608018	−	0.793923i	$-0.291965\pi$
$859$	5651.27	+	3262.76i	0.224469	+	0.129597i	−0.383549	+	0.923521i	$0.625298\pi$
$860$	1405.67	+	2434.69i	0.0557360	+	0.0965377i
$861$		0			0
$862$	8173.31	−	14156.6i	0.322951	−	0.559368i
$863$	36921.8	−	21316.8i	1.45635	−	0.840825i	0.457523	−	0.889198i	$-0.348737\pi$
$863$	36921.8	−	21316.8i	1.45635	−	0.840825i	0.998829	+	0.0483726i	$0.0154035\pi$
$864$		0			0
$865$	7996.25	−	13849.9i	0.314313	−	0.544406i
$866$	−24939.7			−0.978620
$867$		0			0
$868$	12174.6	−	2595.65i	0.476076	−	0.101500i
$869$	9809.22	−	5663.36i	0.382917	−	0.221077i
$870$		0			0
$871$	29737.1	−	17168.7i	1.15683	−	0.667898i
$872$	18151.2	+	10479.6i	0.704906	+	0.406978i
$873$		0			0
$874$		−	736.962i		−	0.0285219i
$875$	5592.37	+	26230.4i	0.216065	+	1.01343i
$876$		0			0
$877$	−12267.9	+	21248.6i	−0.472357	+	0.818146i	−0.999500	−	0.0316308i	$-0.989930\pi$
$877$	−12267.9	+	21248.6i	−0.472357	+	0.818146i	0.527143	+	0.849777i	$0.323263\pi$
$878$	−15826.6			−0.608340
$879$		0			0
$880$			11774.5i			0.451043i
$881$	2108.51			0.0806328			0.0403164	−	0.999187i	$-0.487163\pi$
$881$	2108.51			0.0806328			0.0403164	+	0.999187i	$0.487163\pi$
$882$		0			0
$883$	20470.1			0.780153			0.390077	−	0.920782i	$-0.372449\pi$
$883$	20470.1			0.780153			0.390077	+	0.920782i	$0.372449\pi$
$884$		−	342.749i		−	0.0130406i
$885$		0			0
$886$	−42064.6			−1.59502
$887$	−24283.5	+	42060.3i	−0.919234	+	1.59216i	−0.118652	+	0.992936i	$0.537857\pi$
$887$	−24283.5	+	42060.3i	−0.919234	+	1.59216i	−0.800582	+	0.599224i	$0.795476\pi$
$888$		0			0
$889$	−8001.72	−	37531.2i	−0.301877	−	1.41592i
$890$		−	3918.43i		−	0.147580i
$891$		0			0
$892$	−11584.7	−	6688.43i	−0.434848	−	0.251060i
$893$	−1522.95	+	879.275i	−0.0570701	+	0.0329494i
$894$		0			0
$895$	6315.07	−	3646.01i	0.235854	−	0.136170i
$896$	−11014.6	+	2348.33i	−0.410682	+	0.0875582i
$897$		0			0
$898$	19408.1			0.721221
$899$	−37880.5	+	65610.9i	−1.40532	+	2.43409i
$900$		0			0
$901$	−1411.75	+	815.073i	−0.0521999	+	0.0301377i
$902$	9345.52	−	16186.9i	0.344980	−	0.597523i
$903$		0			0
$904$	15875.8	+	27497.6i	0.584093	+	1.01168i
$905$	−21121.6	−	12194.6i	−0.775808	−	0.447913i
$906$		0			0
$907$	996.506	+	1726.00i	0.0364812	+	0.0631873i	0.883690	−	0.468074i	$-0.155052\pi$
$907$	996.506	+	1726.00i	0.0364812	+	0.0631873i	−0.847208	+	0.531261i	$0.821718\pi$
$908$	59.4419	+	102.956i	0.00217252	+	0.00376291i
$909$		0			0
$910$	−3452.67	−	16194.4i	−0.125775	−	0.589932i
$911$	−6123.30	−	3535.29i	−0.222694	−	0.128572i	0.384503	−	0.923124i	$-0.374373\pi$
$911$	−6123.30	−	3535.29i	−0.222694	−	0.128572i	−0.607197	+	0.794551i	$0.707706\pi$
$912$		0			0
$913$		−	25745.3i		−	0.933238i
$914$		−	24674.6i		−	0.892956i
$915$		0			0
$916$	2708.96	+	1564.02i	0.0977147	+	0.0564156i
$917$	−312.479	−	101.317i	−0.0112530	−	0.00364863i
$918$		0			0
$919$	8935.60	+	15476.9i	0.320738	+	0.555535i	0.980641	−	0.195817i	$-0.0627357\pi$
$919$	8935.60	+	15476.9i	0.320738	+	0.555535i	−0.659902	+	0.751351i	$0.729402\pi$
$920$	−5153.46	−	8926.05i	−0.184679	−	0.319873i
$921$		0			0
$922$	34490.5	+	19913.1i	1.23198	+	0.711282i
$923$	19658.3	+	34049.2i	0.701042	+	1.21424i
$924$		0			0
$925$	285.739	−	494.914i	0.0101568	−	0.0175921i
$926$	−4359.21	+	2516.79i	−0.154700	+	0.0893163i
$927$		0			0
$928$	−11543.2	+	19993.5i	−0.408325	+	0.707239i
$929$	−4376.92			−0.154577			−0.0772885	−	0.997009i	$-0.524626\pi$
$929$	−4376.92			−0.154577			−0.0772885	+	0.997009i	$0.524626\pi$
$930$		0			0
$931$	−1567.35	+	2162.89i	−0.0551750	+	0.0761393i
$932$	−3044.77	+	1757.90i	−0.107012	+	0.0617832i
$933$		0			0
$934$	−15949.3	+	9208.32i	−0.558754	+	0.322597i
$935$	−1114.67	−	643.555i	−0.0389878	−	0.0225096i
$936$		0			0
$937$			17609.3i			0.613948i	0.951718	+	0.306974i	$0.0993165\pi$
$937$			17609.3i			0.613948i	−0.951718	+	0.306974i	$0.900684\pi$
$938$	43545.6	−	9284.00i	1.51579	−	0.323170i
$939$		0			0
$940$	−2614.73	+	4528.85i	−0.0907267	+	0.157143i
$941$	−17934.4			−0.621302			−0.310651	−	0.950524i	$-0.600547\pi$
$941$	−17934.4			−0.621302			−0.310651	+	0.950524i	$0.600547\pi$
$942$		0			0
$943$			11595.5i			0.400425i
$944$	−11401.7			−0.393109
$945$		0			0
$946$	7663.43			0.263382
$947$			29359.9i			1.00747i	0.863860	+	0.503733i	$0.168040\pi$
$947$			29359.9i			1.00747i	−0.863860	+	0.503733i	$0.831960\pi$
$948$		0			0
$949$	42841.9			1.46545
$950$	95.0005	−	164.546i	0.00324444	−	0.00561954i
$951$		0			0
$952$	644.679	−	1988.29i	0.0219476	−	0.0676900i
$953$		−	38731.1i		−	1.31650i	−0.752800	−	0.658249i	$-0.771297\pi$
$953$		−	38731.1i		−	1.31650i	0.752800	−	0.658249i	$-0.228703\pi$
$954$		0			0
$955$	31079.9	+	17944.0i	1.05311	+	0.608014i
$956$	−3951.79	+	2281.57i	−0.133693	+	0.0771874i
$957$		0			0
$958$	−14307.3	+	8260.31i	−0.482513	+	0.278579i
$959$	−24864.3	−	27580.3i	−0.837237	−	0.928692i
$960$		0			0
$961$	−67007.1			−2.24924
$962$	−2360.49	+	4088.48i	−0.0791114	+	0.137025i
$963$		0			0
$964$	−4108.35	+	2371.96i	−0.137263	+	0.0792486i
$965$	11067.0	−	19168.7i	0.369182	−	0.639442i
$966$		0			0
$967$	−26793.9	−	46408.3i	−0.891037	−	1.54332i	−0.838634	−	0.544695i	$-0.816645\pi$
$967$	−26793.9	−	46408.3i	−0.891037	−	1.54332i	−0.0524027	−	0.998626i	$-0.516688\pi$
$968$	13792.0	+	7962.81i	0.457946	+	0.264395i
$969$		0			0
$970$	11686.9	+	20242.4i	0.386851	+	0.670045i
$971$	−24550.2	−	42522.1i	−0.811382	−	1.40536i	−0.911897	−	0.410420i	$-0.865382\pi$
$971$	−24550.2	−	42522.1i	−0.811382	−	1.40536i	0.100514	−	0.994936i	$-0.467951\pi$
$972$		0			0
$973$	8852.09	+	9819.04i	0.291660	+	0.323519i
$974$	−39055.6	−	22548.7i	−1.28483	−	0.741795i
$975$		0			0
$976$		−	31534.6i		−	1.03422i
$977$			30678.4i			1.00459i	0.864695	+	0.502297i	$0.167512\pi$
$977$			30678.4i			1.00459i	−0.864695	+	0.502297i	$0.832488\pi$
$978$		0			0
$979$	3422.12	+	1975.76i	0.111717	+	0.0645001i
$980$	−820.524	+	7900.59i	−0.0267456	+	0.257525i
$981$		0			0
$982$	11704.2	+	20272.3i	0.380343	+	0.658774i
$983$	8917.17	+	15445.0i	0.289332	+	0.501138i	0.973651	−	0.228045i	$-0.0732334\pi$
$983$	8917.17	+	15445.0i	0.289332	+	0.501138i	−0.684318	+	0.729183i	$0.739900\pi$
$984$		0			0
$985$	−26833.4	−	15492.3i	−0.868003	−	0.501142i
$986$	1352.42	+	2342.46i	0.0436814	+	0.0756585i
$987$		0			0
$988$	290.336	−	502.877i	0.00934901	−	0.0161930i
$989$	−4117.27	+	2377.11i	−0.132378	+	0.0764283i
$990$		0			0
$991$	−17209.5	+	29807.8i	−0.551643	+	0.955474i	0.446513	+	0.894777i	$0.352666\pi$
$991$	−17209.5	+	29807.8i	−0.551643	+	0.955474i	−0.998156	+	0.0606970i	$0.980668\pi$
$992$	−29497.1			−0.944086
$993$		0			0
$994$	10630.3	+	49860.1i	0.339207	+	1.59101i
$995$	10796.7	−	6233.48i	0.343999	−	0.198608i
$996$		0			0
$997$	−10457.0	+	6037.37i	−0.332174	+	0.191781i	−0.656806	−	0.754060i	$-0.728093\pi$
$997$	−10457.0	+	6037.37i	−0.332174	+	0.191781i	0.324632	+	0.945840i	$0.394760\pi$
$998$	−8684.18	−	5013.81i	−0.275444	−	0.159028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.7		44
3.2	odd	2		63.4.i.a.38.16	yes	44
7.5	odd	6		189.4.s.a.89.7		44
9.4	even	3		63.4.s.a.59.16	yes	44
9.5	odd	6		189.4.s.a.17.7		44
21.5	even	6		63.4.s.a.47.16	yes	44
63.5	even	6	inner	189.4.i.a.152.16		44
63.40	odd	6		63.4.i.a.5.7	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.7	✓	44	63.40	odd	6
63.4.i.a.38.16	yes	44	3.2	odd	2
63.4.s.a.47.16	yes	44	21.5	even	6
63.4.s.a.59.16	yes	44	9.4	even	3
189.4.i.a.143.7		44	1.1	even	1	trivial
189.4.i.a.152.16		44	63.5	even	6	inner
189.4.s.a.17.7		44	9.5	odd	6
189.4.s.a.89.7		44	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.41653i q^{2} +2.16037 q^{4} +(5.35965 - 9.28319i) q^{5} +(3.86176 + 18.1132i) q^{7} -24.5529i q^{8} +O(q^{10})\)	\(q-2.41653i q^{2} +2.16037 q^{4} +(5.35965 - 9.28319i) q^{5} +(3.86176 + 18.1132i) q^{7} -24.5529i q^{8} +(-22.4331 - 12.9518i) q^{10} +(22.6226 - 13.0611i) q^{11} +(29.8910 - 17.2576i) q^{13} +(43.7711 - 9.33207i) q^{14} -42.0498 q^{16} +(2.29830 - 3.98078i) q^{17} +(6.74409 - 3.89370i) q^{19} +(11.5788 - 20.0551i) q^{20} +(-31.5627 - 54.6682i) q^{22} +(33.9149 + 19.5808i) q^{23} +(5.04824 + 8.74381i) q^{25} +(-41.7035 - 72.2327i) q^{26} +(8.34283 + 39.1311i) q^{28} +(-210.884 - 121.754i) q^{29} -311.124i q^{31} -94.8081i q^{32} +(-9.61969 - 5.55393i) q^{34} +(188.846 + 61.2308i) q^{35} +(-28.3008 - 49.0184i) q^{37} +(-9.40926 - 16.2973i) q^{38} +(-227.929 - 131.595i) q^{40} +(148.047 + 256.425i) q^{41} +(-60.7001 + 105.136i) q^{43} +(48.8731 - 28.2169i) q^{44} +(47.3176 - 81.9564i) q^{46} -225.820 q^{47} +(-313.174 + 139.897i) q^{49} +(21.1297 - 12.1992i) q^{50} +(64.5757 - 37.2828i) q^{52} +(-307.128 - 177.321i) q^{53} -280.013i q^{55} +(444.730 - 94.8173i) q^{56} +(-294.222 + 509.607i) q^{58} +271.148 q^{59} +749.933i q^{61} -751.841 q^{62} -565.506 q^{64} -369.979i q^{65} +994.849 q^{67} +(4.96519 - 8.59996i) q^{68} +(147.966 - 456.352i) q^{70} +1139.11i q^{71} +(1074.95 + 620.624i) q^{73} +(-118.455 + 68.3898i) q^{74} +(14.5697 - 8.41184i) q^{76} +(323.942 + 359.327i) q^{77} +433.603 q^{79} +(-225.373 + 390.357i) q^{80} +(619.659 - 357.760i) q^{82} +(492.785 - 853.528i) q^{83} +(-24.6362 - 42.6712i) q^{85} +(254.064 + 146.684i) q^{86} +(-320.689 - 555.449i) q^{88} +(75.6350 + 131.004i) q^{89} +(428.022 + 474.777i) q^{91} +(73.2687 + 42.3017i) q^{92} +545.701i q^{94} -83.4756i q^{95} +(-781.452 - 451.172i) q^{97} +(338.067 + 756.794i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) 44 * q - 162 * q^4 + 3 * q^5 + 5 * q^7 - 6 * q^10 - 9 * q^11 - 36 * q^13 - 54 * q^14 + 526 * q^16 + 72 * q^17 - 6 * q^19 - 24 * q^20 + 14 * q^22 + 285 * q^23 - 349 * q^25 + 96 * q^26 - 156 * q^28 + 132 * q^29 + 24 * q^34 - 765 * q^35 + 82 * q^37 + 873 * q^38 + 420 * q^40 - 618 * q^41 + 82 * q^43 - 603 * q^44 + 266 * q^46 + 402 * q^47 - 79 * q^49 + 1845 * q^50 + 189 * q^52 - 564 * q^53 - 66 * q^56 + 269 * q^58 - 1494 * q^59 + 2904 * q^62 - 1144 * q^64 - 590 * q^67 - 3504 * q^68 - 105 * q^70 - 6 * q^73 - 1515 * q^74 - 144 * q^76 + 4443 * q^77 + 1102 * q^79 + 4239 * q^80 + 18 * q^82 - 1830 * q^83 - 237 * q^85 - 1209 * q^86 - 623 * q^88 - 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 792 * q^97 - 5667 * q^98

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