LMFDB - Embedded newform 189.4.o.a.62.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

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, 3]))

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

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (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			62.17
Character	$\chi$	$=$	189.62
Dual form			189.4.o.a.125.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.28475 + 1.89645i) q^{2} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(-13.5672 + 12.6068i) q^{7} -6.12125i q^{8} +O(q^{10})$	\(q+(3.28475 + 1.89645i) q^{2} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(-13.5672 + 12.6068i) q^{7} -6.12125i q^{8} -75.6753i q^{10} +(-31.1676 - 17.9946i) q^{11} +(-6.59980 + 3.81040i) q^{13} +(-68.4731 + 15.6805i) q^{14} +(37.1532 - 64.3512i) q^{16} -21.4747 q^{17} -97.3022i q^{19} +(63.7074 - 110.345i) q^{20} +(-68.2518 - 118.216i) q^{22} +(35.6964 - 20.6094i) q^{23} +(-136.537 + 236.489i) q^{25} -28.9050 q^{26} +(-113.043 - 34.7800i) q^{28} +(51.8612 + 29.9421i) q^{29} +(-61.1449 + 35.3020i) q^{31} +(201.669 - 116.434i) q^{32} +(-70.5390 - 40.7257i) q^{34} +(353.175 + 108.661i) q^{35} +355.309 q^{37} +(184.529 - 319.614i) q^{38} +(-105.768 + 61.0649i) q^{40} +(7.30794 + 12.6577i) q^{41} +(-48.8575 + 84.6237i) q^{43} -229.832i q^{44} +156.339 q^{46} +(-234.897 + 406.853i) q^{47} +(25.1387 - 342.078i) q^{49} +(-896.982 + 517.873i) q^{50} +(-42.1472 - 24.3337i) q^{52} -710.531i q^{53} +718.049i q^{55} +(77.1691 + 83.0483i) q^{56} +(113.568 + 196.705i) q^{58} +(232.735 + 403.109i) q^{59} +(-542.558 - 313.246i) q^{61} -267.794 q^{62} +288.792 q^{64} +(131.678 + 76.0243i) q^{65} +(-262.327 - 454.364i) q^{67} +(-68.5700 - 118.767i) q^{68} +(954.021 + 1026.70i) q^{70} +115.729i q^{71} -708.180i q^{73} +(1167.10 + 673.827i) q^{74} +(538.135 - 310.692i) q^{76} +(649.711 - 148.786i) q^{77} +(128.747 - 222.997i) q^{79} -1482.55 q^{80} +55.4366i q^{82} +(200.583 - 347.420i) q^{83} +(214.229 + 371.056i) q^{85} +(-320.970 + 185.312i) q^{86} +(-110.149 + 190.784i) q^{88} -977.834 q^{89} +(41.5042 - 134.899i) q^{91} +(227.962 + 131.614i) q^{92} +(-1543.16 + 890.942i) q^{94} +(-1681.26 + 970.677i) q^{95} +(521.193 + 300.911i) q^{97} +(731.308 - 1075.97i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	3.28475	+	1.89645i	1.16134	+	0.670497i	0.951624	−	0.307266i	$-0.0994141\pi$
$2$	3.28475	+	1.89645i	1.16134	+	0.670497i	0.209712	+	0.977763i	$0.432747\pi$
$3$		0			0
$3$		0			0
$4$	3.19307	+	5.53055i	0.399133	+	0.691319i
$5$	−9.97590	−	17.2788i	−0.892272	−	1.54546i	−0.837145	−	0.546981i	$-0.815777\pi$
$5$	−9.97590	−	17.2788i	−0.892272	−	1.54546i	−0.0551264	−	0.998479i	$-0.517556\pi$
$6$		0			0
$7$	−13.5672	+	12.6068i	−0.732561	+	0.680702i
$7$	−13.5672	+	12.6068i	−0.732561	+	0.680702i
$8$		−	6.12125i		−	0.270523i
$9$		0			0
$10$		−	75.6753i		−	2.39306i
$11$	−31.1676	−	17.9946i	−0.854307	−	0.493234i	0.00779501	−	0.999970i	$-0.497519\pi$
$11$	−31.1676	−	17.9946i	−0.854307	−	0.493234i	−0.862102	+	0.506735i	$0.830852\pi$
$12$		0			0
$13$	−6.59980	+	3.81040i	−0.140804	+	0.0812934i	−0.568747	−	0.822512i	$-0.692572\pi$
$13$	−6.59980	+	3.81040i	−0.140804	+	0.0812934i	0.427943	+	0.903806i	$0.359238\pi$
$14$	−68.4731	+	15.6805i	−1.30716	+	0.299343i
$15$		0			0
$16$	37.1532	−	64.3512i	0.580519	−	1.00549i
$17$	−21.4747			−0.306375			−0.153187	−	0.988197i	$-0.548954\pi$
$17$	−21.4747			−0.306375			−0.153187	+	0.988197i	$0.548954\pi$
$18$		0			0
$19$		−	97.3022i		−	1.17488i	−0.809269	−	0.587438i	$-0.800136\pi$
$19$		−	97.3022i		−	1.17488i	0.809269	−	0.587438i	$-0.199864\pi$
$20$	63.7074	−	110.345i	0.712271	−	1.23369i
$21$		0			0
$22$	−68.2518	−	118.216i	−0.661424	−	1.14562i
$23$	35.6964	−	20.6094i	0.323618	−	0.186841i	−0.329386	−	0.944195i	$-0.606842\pi$
$23$	35.6964	−	20.6094i	0.323618	−	0.186841i	0.653004	+	0.757354i	$0.273508\pi$
$24$		0			0
$25$	−136.537	+	236.489i	−1.09230	+	1.89191i
$26$	−28.9050			−0.218028
$27$		0			0
$28$	−113.043	−	34.7800i	−0.762971	−	0.234743i
$29$	51.8612	+	29.9421i	0.332082	+	0.191728i	0.656765	−	0.754095i	$-0.271924\pi$
$29$	51.8612	+	29.9421i	0.332082	+	0.191728i	−0.324683	+	0.945823i	$0.605258\pi$
$30$		0			0
$31$	−61.1449	+	35.3020i	−0.354256	+	0.204530i	−0.666558	−	0.745453i	$-0.732233\pi$
$31$	−61.1449	+	35.3020i	−0.354256	+	0.204530i	0.312302	+	0.949983i	$0.398900\pi$
$32$	201.669	−	116.434i	1.11407	−	0.643211i
$33$		0			0
$34$	−70.5390	−	40.7257i	−0.355804	−	0.205423i
$35$	353.175	+	108.661i	1.70564	+	0.524773i
$36$		0			0
$37$	355.309			1.57872			0.789358	−	0.613933i	$-0.210414\pi$
$37$	355.309			1.57872			0.789358	+	0.613933i	$0.210414\pi$
$38$	184.529	−	319.614i	0.787752	−	1.36443i
$39$		0			0
$40$	−105.768	+	61.0649i	−0.418083	+	0.241380i
$41$	7.30794	+	12.6577i	0.0278368	+	0.0482147i	0.879608	−	0.475699i	$-0.157805\pi$
$41$	7.30794	+	12.6577i	0.0278368	+	0.0482147i	−0.851771	+	0.523914i	$0.824471\pi$
$42$		0			0
$43$	−48.8575	+	84.6237i	−0.173272	+	0.300116i	−0.939562	−	0.342379i	$-0.888767\pi$
$43$	−48.8575	+	84.6237i	−0.173272	+	0.300116i	0.766290	+	0.642495i	$0.222101\pi$
$44$		−	229.832i		−	0.787465i
$45$		0			0
$46$	156.339			0.501106
$47$	−234.897	+	406.853i	−0.729005	+	1.26267i	0.228299	+	0.973591i	$0.426684\pi$
$47$	−234.897	+	406.853i	−0.729005	+	1.26267i	−0.957304	+	0.289083i	$0.906650\pi$
$48$		0			0
$49$	25.1387	−	342.078i	0.0732907	−	0.997311i
$50$	−896.982	+	517.873i	−2.53705	+	1.46477i
$51$		0			0
$52$	−42.1472	−	24.3337i	−0.112399	−	0.0648938i
$53$		−	710.531i		−	1.84149i	−0.390167	−	0.920744i	$-0.627583\pi$
$53$		−	710.531i		−	1.84149i	0.390167	−	0.920744i	$-0.372417\pi$
$54$		0			0
$55$			718.049i			1.76040i
$56$	77.1691	+	83.0483i	0.184146	+	0.198175i
$57$		0			0
$58$	113.568	+	196.705i	0.257106	+	0.445321i
$59$	232.735	+	403.109i	0.513551	+	0.889497i	0.999876	+	0.0157191i	$0.00500375\pi$
$59$	232.735	+	403.109i	0.513551	+	0.889497i	−0.486325	+	0.873778i	$0.661663\pi$
$60$		0			0
$61$	−542.558	−	313.246i	−1.13881	−	0.657492i	−0.192674	−	0.981263i	$-0.561716\pi$
$61$	−542.558	−	313.246i	−1.13881	−	0.657492i	−0.946136	+	0.323771i	$0.895049\pi$
$62$	−267.794			−0.548547
$63$		0			0
$64$	288.792			0.564047
$65$	131.678	+	76.0243i	0.251271	+	0.145072i
$66$		0			0
$67$	−262.327	−	454.364i	−0.478334	−	0.828498i	0.521358	−	0.853338i	$-0.325426\pi$
$67$	−262.327	−	454.364i	−0.478334	−	0.828498i	−0.999691	+	0.0248401i	$0.992092\pi$
$68$	−68.5700	−	118.767i	−0.122284	−	0.211803i
$69$		0			0
$70$	954.021	+	1026.70i	1.62896	+	1.75306i
$71$			115.729i			0.193443i	0.995311	+	0.0967216i	$0.0308356\pi$
$71$			115.729i			0.193443i	−0.995311	+	0.0967216i	$0.969164\pi$
$72$		0			0
$73$		−	708.180i		−	1.13543i	−0.823226	−	0.567714i	$-0.807828\pi$
$73$		−	708.180i		−	1.13543i	0.823226	−	0.567714i	$-0.192172\pi$
$74$	1167.10	+	673.827i	1.83342	+	1.05852i
$75$		0			0
$76$	538.135	−	310.692i	0.812215	−	0.468933i
$77$	649.711	−	148.786i	0.961577	−	0.220204i
$78$		0			0
$79$	128.747	−	222.997i	0.183357	−	0.317584i	−0.759665	−	0.650315i	$-0.774637\pi$
$79$	128.747	−	222.997i	0.183357	−	0.317584i	0.943022	+	0.332731i	$0.107970\pi$
$80$	−1482.55			−2.07192
$81$		0			0
$82$			55.4366i			0.0746579i
$83$	200.583	−	347.420i	0.265263	−	0.459449i	−0.702370	−	0.711812i	$-0.747875\pi$
$83$	200.583	−	347.420i	0.265263	−	0.459449i	0.967632	+	0.252364i	$0.0812079\pi$
$84$		0			0
$85$	214.229	+	371.056i	0.273370	+	0.473490i
$86$	−320.970	+	185.312i	−0.402454	+	0.232357i
$87$		0			0
$88$	−110.149	+	190.784i	−0.133431	+	0.231110i
$89$	−977.834			−1.16461			−0.582304	−	0.812971i	$-0.697849\pi$
$89$	−977.834			−1.16461			−0.582304	+	0.812971i	$0.697849\pi$
$90$		0			0
$91$	41.5042	−	134.899i	0.0478112	−	0.155398i
$92$	227.962	+	131.614i	0.258334	+	0.149149i
$93$		0			0
$94$	−1543.16	+	890.942i	−1.69324	+	0.977592i
$95$	−1681.26	+	970.677i	−1.81573	+	1.04831i
$96$		0			0
$97$	521.193	+	300.911i	0.545558	+	0.314978i	0.747328	−	0.664455i	$-0.231336\pi$
$97$	521.193	+	300.911i	0.545558	+	0.314978i	−0.201770	+	0.979433i	$0.564670\pi$
$98$	731.308	−	1075.97i	0.753809	−	1.10907i
$99$		0			0
$100$	−1743.89			−1.74389
$101$	212.644	−	368.310i	0.209494	−	0.362853i	−0.742062	−	0.670332i	$-0.766152\pi$
$101$	212.644	−	368.310i	0.209494	−	0.362853i	0.951555	+	0.307478i	$0.0994851\pi$
$102$		0			0
$103$	657.161	−	379.412i	0.628660	−	0.362957i	−0.151573	−	0.988446i	$-0.548434\pi$
$103$	657.161	−	379.412i	0.628660	−	0.362957i	0.780233	+	0.625489i	$0.215101\pi$
$104$	23.3244	+	40.3990i	0.0219918	+	0.0380909i
$105$		0			0
$106$	1347.49	−	2333.92i	1.23471	−	2.13859i
$107$			866.455i			0.782835i	0.920213	+	0.391418i	$0.128015\pi$
$107$			866.455i			0.782835i	−0.920213	+	0.391418i	$0.871985\pi$
$108$		0			0
$109$	−94.9205			−0.0834104			−0.0417052	−	0.999130i	$-0.513279\pi$
$109$	−94.9205			−0.0834104			−0.0417052	+	0.999130i	$0.513279\pi$
$110$	−1361.75	+	2358.61i	−1.18034	+	2.04441i
$111$		0			0
$112$	307.195	+	1341.45i	0.259172	+	1.13174i
$113$	1432.66	−	827.148i	1.19269	−	0.688597i	0.233771	−	0.972292i	$-0.424893\pi$
$113$	1432.66	−	827.148i	1.19269	−	0.688597i	0.958915	+	0.283694i	$0.0915601\pi$
$114$		0			0
$115$	−712.208	−	411.194i	−0.577511	−	0.333426i
$116$			382.428i			0.306100i
$117$		0			0
$118$			1765.48i			1.37734i
$119$	291.351	−	270.726i	0.224438	−	0.208550i
$120$		0			0
$121$	−17.8889	−	30.9845i	−0.0134402	−	0.0232791i
$122$	−1188.11	−	2057.87i	−0.881693	−	1.52714i
$123$		0			0
$124$	−390.479	−	225.443i	−0.282791	−	0.163269i
$125$	2954.35			2.11396
$126$		0			0
$127$	−280.600			−0.196057			−0.0980284	−	0.995184i	$-0.531254\pi$
$127$	−280.600			−0.196057			−0.0980284	+	0.995184i	$0.531254\pi$
$128$	−664.740	−	383.788i	−0.459026	−	0.265019i
$129$		0			0
$130$	288.353	+	499.442i	0.194540	+	0.336954i
$131$	1095.66	+	1897.74i	0.730751	+	1.26570i	0.956563	+	0.291527i	$0.0941632\pi$
$131$	1095.66	+	1897.74i	0.730751	+	1.26570i	−0.225812	+	0.974171i	$0.572503\pi$
$132$		0			0
$133$	1226.67	+	1320.12i	0.799741	+	0.860669i
$134$		−	1989.96i		−	1.28289i
$135$		0			0
$136$			131.452i			0.0828815i
$137$	−985.315	−	568.872i	−0.614461	−	0.354759i	0.160248	−	0.987077i	$-0.448770\pi$
$137$	−985.315	−	568.872i	−0.614461	−	0.354759i	−0.774709	+	0.632318i	$0.782104\pi$
$138$		0			0
$139$	1842.29	−	1063.64i	1.12418	−	0.649044i	0.181713	−	0.983352i	$-0.441836\pi$
$139$	1842.29	−	1063.64i	1.12418	−	0.649044i	0.942464	+	0.334308i	$0.108502\pi$
$140$	526.755	+	2300.21i	0.317992	+	1.38860i
$141$		0			0
$142$	−219.474	+	380.140i	−0.129703	+	0.224652i
$143$	274.266			0.160387
$144$		0			0
$145$		−	1194.80i		−	0.684293i
$146$	1343.03	−	2326.20i	0.761301	−	1.31861i
$147$		0			0
$148$	1134.53	+	1965.06i	0.630118	+	1.09140i
$149$	362.688	−	209.398i	0.199413	−	0.115131i	−0.396969	−	0.917832i	$-0.629938\pi$
$149$	362.688	−	209.398i	0.199413	−	0.115131i	0.596382	+	0.802701i	$0.296605\pi$
$150$		0			0
$151$	475.546	−	823.669i	0.256287	−	0.443902i	−0.708957	−	0.705252i	$-0.750834\pi$
$151$	475.546	−	823.669i	0.256287	−	0.443902i	0.965244	+	0.261349i	$0.0841674\pi$
$152$	−595.611			−0.317832
$153$		0			0
$154$	2416.30	+	743.422i	1.26436	+	0.389004i
$155$	1219.95	+	704.339i	0.632186	+	0.364993i
$156$		0			0
$157$	−1885.26	+	1088.45i	−0.958343	+	0.553300i	−0.895663	−	0.444734i	$-0.853298\pi$
$157$	−1885.26	+	1088.45i	−0.958343	+	0.553300i	−0.0626806	+	0.998034i	$0.519965\pi$
$158$	845.807	−	488.327i	0.425878	−	0.245881i
$159$		0			0
$160$	−4023.66	−	2323.06i	−1.98811	−	1.14784i
$161$	−224.484	+	729.628i	−0.109887	+	0.357160i
$162$		0			0
$163$	−382.330			−0.183720			−0.0918601	−	0.995772i	$-0.529281\pi$
$163$	−382.330			−0.183720			−0.0918601	+	0.995772i	$0.529281\pi$
$164$	−46.6695	+	80.8339i	−0.0222212	+	0.0384882i
$165$		0			0
$166$	1317.73	−	760.792i	0.616118	−	0.355716i
$167$	−123.092	−	213.202i	−0.0570370	−	0.0987909i	0.836097	−	0.548582i	$-0.184832\pi$
$167$	−123.092	−	213.202i	−0.0570370	−	0.0987909i	−0.893134	+	0.449791i	$0.851499\pi$
$168$		0			0
$169$	−1069.46	+	1852.36i	−0.486783	+	0.843132i
$170$			1625.10i			0.733174i
$171$		0			0
$172$	−624.021			−0.276635
$173$	1988.82	−	3444.74i	0.874031	−	1.51387i	0.0162391	−	0.999868i	$-0.494831\pi$
$173$	1988.82	−	3444.74i	0.874031	−	1.51387i	0.857792	−	0.513998i	$-0.171836\pi$
$174$		0			0
$175$	−1128.94	−	4929.80i	−0.487655	−	2.12947i
$176$	−2315.95	+	1337.11i	−0.991882	+	0.572663i
$177$		0			0
$178$	−3211.94	−	1854.42i	−1.35250	−	0.780867i
$179$		−	1454.87i		−	0.607498i	−0.952752	−	0.303749i	$-0.901762\pi$
$179$		−	1454.87i		−	0.607498i	0.952752	−	0.303749i	$-0.0982384\pi$
$180$		0			0
$181$		−	735.896i		−	0.302203i	−0.988518	−	0.151101i	$-0.951718\pi$
$181$		−	735.896i		−	0.302203i	0.988518	−	0.151101i	$-0.0482820\pi$
$182$	392.160	−	364.398i	0.159719	−	0.148412i
$183$		0			0
$184$	−126.155	−	218.507i	−0.0505449	−	0.0875463i
$185$	−3544.53	−	6139.31i	−1.40864	−	2.43984i
$186$		0			0
$187$	669.313	+	386.428i	0.261738	+	0.151115i
$188$	−3000.17			−1.16388
$189$		0			0
$190$	−7363.38			−2.81155
$191$	−2390.26	−	1380.02i	−0.905515	−	0.522799i	−0.0265297	−	0.999648i	$-0.508446\pi$
$191$	−2390.26	−	1380.02i	−0.905515	−	0.522799i	−0.878985	+	0.476849i	$0.841779\pi$
$192$		0			0
$193$	−616.442	−	1067.71i	−0.229909	−	0.398214i	0.727872	−	0.685713i	$-0.240510\pi$
$193$	−616.442	−	1067.71i	−0.229909	−	0.398214i	−0.957781	+	0.287499i	$0.907176\pi$
$194$	1141.33	+	1976.84i	0.422384	+	0.731590i
$195$		0			0
$196$	1972.15	−	953.245i	0.718713	−	0.347393i
$197$		−	497.068i		−	0.179770i	−0.995952	−	0.0898849i	$-0.971350\pi$
$197$		−	497.068i		−	0.179770i	0.995952	−	0.0898849i	$-0.0286499\pi$
$198$		0			0
$199$		−	4502.53i		−	1.60390i	−0.597391	−	0.801950i	$-0.703796\pi$
$199$		−	4502.53i		−	1.60390i	0.597391	−	0.801950i	$-0.296204\pi$
$200$	1447.61	+	835.778i	0.511807	+	0.295492i
$201$		0			0
$202$	1396.96	−	806.538i	0.486585	−	0.280930i
$203$	−1081.09	+	247.572i	−0.373780	+	0.0855967i
$204$		0			0
$205$	145.807	−	252.544i	0.0496759	−	0.0860413i
$206$	2878.15			0.973447
$207$		0			0
$208$			566.274i			0.188769i
$209$	−1750.91	+	3032.67i	−0.579489	+	1.00371i
$210$		0			0
$211$	1714.83	+	2970.17i	0.559495	+	0.969074i	0.997539	+	0.0701201i	$0.0223383\pi$
$211$	1714.83	+	2970.17i	0.559495	+	0.969074i	−0.438043	+	0.898954i	$0.644328\pi$
$212$	3929.63	−	2268.77i	1.27306	−	0.734999i
$213$		0			0
$214$	−1643.19	+	2846.09i	−0.524889	+	0.909134i
$215$	1949.59			0.618424
$216$		0			0
$217$	384.522	−	1249.79i	0.120290	−	0.390974i
$218$	−311.790	−	180.012i	−0.0968675	−	0.0559265i
$219$		0			0
$220$	−3971.21	+	2292.78i	−1.21700	+	0.702632i
$221$	141.729	−	81.8270i	0.0431389	−	0.0249063i
$222$		0			0
$223$	2145.46	+	1238.68i	0.644263	+	0.371965i	0.786255	−	0.617903i	$-0.212017\pi$
$223$	2145.46	+	1238.68i	0.644263	+	0.371965i	−0.141992	+	0.989868i	$0.545351\pi$
$224$	−1268.23	+	4122.07i	−0.378292	+	1.22954i
$225$		0			0
$226$	6274.59			1.84681
$227$	84.0252	−	145.536i	0.0245681	−	0.0425531i	−0.853480	−	0.521126i	$-0.825512\pi$
$227$	84.0252	−	145.536i	0.0245681	−	0.0425531i	0.878048	+	0.478573i	$0.158846\pi$
$228$		0			0
$229$	989.455	−	571.262i	0.285524	−	0.164847i	−0.350397	−	0.936601i	$-0.613953\pi$
$229$	989.455	−	571.262i	0.285524	−	0.164847i	0.635922	+	0.771754i	$0.280620\pi$
$230$	−1559.62	−	2701.34i	−0.447123	−	0.774439i
$231$		0			0
$232$	183.283	−	317.455i	0.0518669	−	0.0898361i
$233$			2181.50i			0.613370i	0.951811	+	0.306685i	$0.0992198\pi$
$233$			2181.50i			0.613370i	−0.951811	+	0.306685i	$0.900780\pi$
$234$		0			0
$235$	9373.23			2.60188
$236$	−1486.28	+	2574.31i	−0.409951	+	0.710056i
$237$		0			0
$238$	1470.44	−	336.734i	0.400480	−	0.0917111i
$239$	1654.14	−	955.020i	0.447689	−	0.258473i	−0.259165	−	0.965833i	$-0.583447\pi$
$239$	1654.14	−	955.020i	0.447689	−	0.258473i	0.706854	+	0.707360i	$0.250114\pi$
$240$		0			0
$241$	1962.89	+	1133.28i	0.524651	+	0.302907i	0.738836	−	0.673886i	$-0.235376\pi$
$241$	1962.89	+	1133.28i	0.524651	+	0.302907i	−0.214184	+	0.976793i	$0.568709\pi$
$242$		−	135.702i		−	0.0360464i
$243$		0			0
$244$		−	4000.86i		−	1.04971i
$245$	−6161.46	+	2978.17i	−1.60670	+	0.776604i
$246$		0			0
$247$	370.760	+	642.176i	0.0955098	+	0.165428i
$248$	216.092	+	374.283i	0.0553302	+	0.0958346i
$249$		0			0
$250$	9704.31	+	5602.79i	2.45502	+	1.41741i
$251$	−315.743			−0.0794004			−0.0397002	−	0.999212i	$-0.512640\pi$
$251$	−315.743			−0.0794004			−0.0397002	+	0.999212i	$0.512640\pi$
$252$		0			0
$253$	−1483.43			−0.368626
$254$	−921.702	−	532.145i	−0.227688	−	0.131456i
$255$		0			0
$256$	−2610.84	−	4522.11i	−0.637412	−	1.10403i
$257$	2047.88	+	3547.03i	0.497055	+	0.860924i	0.999994	−	0.00339730i	$-0.00108139\pi$
$257$	2047.88	+	3547.03i	0.497055	+	0.860924i	−0.502939	+	0.864322i	$0.667748\pi$
$258$		0			0
$259$	−4820.56	+	4479.30i	−1.15651	+	1.07463i
$260$			971.003i			0.231612i
$261$		0			0
$262$			8311.48i			1.95987i
$263$	−4270.21	−	2465.41i	−1.00119	−	0.578036i	−0.0925883	−	0.995704i	$-0.529514\pi$
$263$	−4270.21	−	2465.41i	−1.00119	−	0.578036i	−0.908600	+	0.417668i	$0.862847\pi$
$264$		0			0
$265$	−12277.1	+	7088.18i	−2.84595	+	1.64311i
$266$	1525.75	+	6662.58i	0.351691	+	1.53575i
$267$		0			0
$268$	1675.26	−	2901.63i	0.381838	−	0.661362i
$269$	−5506.26			−1.24804			−0.624019	−	0.781409i	$-0.714501\pi$
$269$	−5506.26			−1.24804			−0.624019	+	0.781409i	$0.714501\pi$
$270$		0			0
$271$			7622.48i			1.70861i	0.519774	+	0.854304i	$0.326016\pi$
$271$			7622.48i			1.70861i	−0.519774	+	0.854304i	$0.673984\pi$
$272$	−797.852	+	1381.92i	−0.177856	+	0.308056i
$273$		0			0
$274$	−2157.68	−	3737.21i	−0.475730	−	0.823989i
$275$	8511.06	−	4913.86i	1.86631	−	1.07752i
$276$		0			0
$277$	−1811.14	+	3136.99i	−0.392856	+	0.680446i	−0.992825	−	0.119577i	$-0.961846\pi$
$277$	−1811.14	+	3136.99i	−0.392856	+	0.680446i	0.599969	+	0.800023i	$0.295179\pi$
$278$	8068.60			1.74073
$279$		0			0
$280$	665.140	−	2161.87i	0.141963	−	0.461416i
$281$	1888.83	+	1090.51i	0.400989	+	0.231511i	0.686911	−	0.726742i	$-0.258966\pi$
$281$	1888.83	+	1090.51i	0.400989	+	0.231511i	−0.285922	+	0.958253i	$0.592300\pi$
$282$		0			0
$283$	1985.61	−	1146.39i	0.417075	−	0.240799i	−0.276750	−	0.960942i	$-0.589257\pi$
$283$	1985.61	−	1146.39i	0.417075	−	0.240799i	0.693825	+	0.720143i	$0.255924\pi$
$284$	−640.043	+	369.529i	−0.133731	+	0.0772096i
$285$		0			0
$286$	900.897	+	520.133i	0.186263	+	0.107539i
$287$	−258.721	−	79.6005i	−0.0532120	−	0.0163717i
$288$		0			0
$289$	−4451.84			−0.906134
$290$	2265.88	−	3924.61i	0.458817	−	0.794694i
$291$		0			0
$292$	3916.63	−	2261.27i	0.784943	−	0.453187i
$293$	273.105	+	473.031i	0.0544537	+	0.0943166i	0.891967	−	0.452100i	$-0.149325\pi$
$293$	273.105	+	473.031i	0.0544537	+	0.0943166i	−0.837514	+	0.546416i	$0.815992\pi$
$294$		0			0
$295$	4643.48	−	8042.75i	0.916455	−	1.58735i
$296$		−	2174.94i		−	0.427080i
$297$		0			0
$298$	1588.45			0.308780
$299$	−157.060	+	272.035i	−0.0303779	+	0.0526161i
$300$		0			0
$301$	−403.971	−	1764.04i	−0.0773572	−	0.337800i
$302$	3124.10	−	1803.70i	0.595271	−	0.343680i
$303$		0			0
$304$	−6261.52	−	3615.09i	−1.18132	−	0.682038i
$305$			12499.6i			2.34665i
$306$		0			0
$307$			6193.21i			1.15135i	0.817677	+	0.575677i	$0.195261\pi$
$307$			6193.21i			1.15135i	−0.817677	+	0.575677i	$0.804739\pi$
$308$	2897.44	+	3118.18i	0.536028	+	0.576866i
$309$		0			0
$310$	2671.49	+	4627.16i	0.489453	+	0.847758i
$311$	2335.25	+	4044.78i	0.425788	+	0.737486i	0.996494	−	0.0836685i	$-0.0266637\pi$
$311$	2335.25	+	4044.78i	0.425788	+	0.737486i	−0.570706	+	0.821155i	$0.693330\pi$
$312$		0			0
$313$	2218.64	+	1280.93i	0.400655	+	0.231318i	0.686767	−	0.726878i	$-0.259029\pi$
$313$	2218.64	+	1280.93i	0.400655	+	0.231318i	−0.286112	+	0.958196i	$0.592363\pi$
$314$	−8256.81			−1.48394
$315$		0			0
$316$	1644.40			0.292736
$317$	−2351.36	−	1357.56i	−0.416611	−	0.240530i	0.277015	−	0.960865i	$-0.410655\pi$
$317$	−2351.36	−	1357.56i	−0.416611	−	0.240530i	−0.693626	+	0.720335i	$0.743988\pi$
$318$		0			0
$319$	−1077.59	−	1866.44i	−0.189133	−	0.327589i
$320$	−2880.96	−	4989.97i	−0.503283	−	0.871712i
$321$		0			0
$322$	−2121.08	+	1970.93i	−0.367091	+	0.341104i
$323$			2089.53i			0.359953i
$324$		0			0
$325$		−	2081.04i		−	0.355186i
$326$	−1255.86	−	725.070i	−0.213361	−	0.123184i
$327$		0			0
$328$	77.4810	−	44.7337i	0.0130432	−	0.00753050i
$329$	−1942.21	−	8481.16i	−0.325463	−	1.42122i
$330$		0			0
$331$	−2272.97	+	3936.89i	−0.377443	+	0.653750i	−0.990689	−	0.136142i	$-0.956530\pi$
$331$	−2272.97	+	3936.89i	−0.377443	+	0.653750i	0.613247	+	0.789891i	$0.289863\pi$
$332$	2561.90			0.423501
$333$		0			0
$334$		−	933.756i		−	0.152973i
$335$	−5233.90	+	9065.38i	−0.853607	+	1.47849i
$336$		0			0
$337$	3627.36	+	6282.78i	0.586336	+	1.01556i	0.994707	+	0.102747i	$0.0327634\pi$
$337$	3627.36	+	6282.78i	0.586336	+	1.01556i	−0.408372	+	0.912816i	$0.633903\pi$
$338$	−7025.83	+	4056.37i	−1.13064	+	0.652773i
$339$		0			0
$340$	−1368.10	+	2369.61i	−0.218222	+	0.377971i
$341$	2540.98			0.403525
$342$		0			0
$343$	3971.43	+	4957.96i	0.625181	+	0.780480i
$344$	518.003	+	299.069i	0.0811885	+	0.0468742i
$345$		0			0
$346$	13065.6	−	7543.41i	2.03009	−	1.17207i
$347$	7611.25	−	4394.36i	1.17750	−	0.679832i	0.222067	−	0.975031i	$-0.428720\pi$
$347$	7611.25	−	4394.36i	1.17750	−	0.679832i	0.955436	+	0.295200i	$0.0953862\pi$
$348$		0			0
$349$	−6314.40	−	3645.62i	−0.968487	−	0.559156i	−0.0697122	−	0.997567i	$-0.522208\pi$
$349$	−6314.40	−	3645.62i	−0.968487	−	0.559156i	−0.898775	+	0.438411i	$0.855541\pi$
$350$	5640.84	−	18334.1i	0.861474	−	2.80000i
$351$		0			0
$352$	−8380.70			−1.26901
$353$	5012.28	−	8681.52i	0.755741	−	1.30898i	−0.189264	−	0.981926i	$-0.560610\pi$
$353$	5012.28	−	8681.52i	0.755741	−	1.30898i	0.945005	−	0.327056i	$-0.106057\pi$
$354$		0			0
$355$	1999.65	−	1154.50i	0.298959	−	0.172604i
$356$	−3122.29	−	5407.96i	−0.464834	−	0.805116i
$357$		0			0
$358$	2759.09	−	4778.89i	0.407326	−	0.705509i
$359$			11205.2i			1.64732i	0.567083	+	0.823660i	$0.308072\pi$
$359$			11205.2i			1.64732i	−0.567083	+	0.823660i	$0.691928\pi$
$360$		0			0
$361$	−2608.72			−0.380336
$362$	1395.59	−	2417.24i	0.202626	−	0.350959i
$363$		0			0
$364$	878.590	−	201.200i	0.126513	−	0.0289718i
$365$	−12236.5	+	7064.73i	−1.75476	+	1.01311i
$366$		0			0
$367$	−2597.53	−	1499.68i	−0.369455	−	0.213305i	0.303766	−	0.952747i	$-0.401756\pi$
$367$	−2597.53	−	1499.68i	−0.369455	−	0.213305i	−0.673220	+	0.739442i	$0.735089\pi$
$368$		−	3062.81i		−	0.433859i
$369$		0			0
$370$		−	26888.1i		−	3.77797i
$371$	8957.50	+	9639.92i	1.25350	+	1.34900i
$372$		0			0
$373$	−2052.54	−	3555.11i	−0.284924	−	0.493503i	0.687667	−	0.726026i	$-0.258635\pi$
$373$	−2052.54	−	3555.11i	−0.284924	−	0.493503i	−0.972591	+	0.232524i	$0.925302\pi$
$374$	1465.68	+	2538.64i	0.202644	+	0.350989i
$375$		0			0
$376$	2490.45	+	1437.86i	0.341583	+	0.197213i
$377$	−456.365			−0.0623449
$378$		0			0
$379$	−2051.20			−0.278002			−0.139001	−	0.990292i	$-0.544389\pi$
$379$	−2051.20			−0.278002			−0.139001	+	0.990292i	$0.544389\pi$
$380$	−10736.8	−	6198.87i	−1.44943	−	0.836830i
$381$		0			0
$382$	−5234.28	−	9066.04i	−0.701071	−	1.21429i
$383$	−2786.12	−	4825.70i	−0.371708	−	0.643817i	0.618120	−	0.786083i	$-0.287894\pi$
$383$	−2786.12	−	4825.70i	−0.371708	−	0.643817i	−0.989828	+	0.142266i	$0.954561\pi$
$384$		0			0
$385$	−9052.28	−	9741.93i	−1.19830	−	1.28960i
$386$		−	4676.21i		−	0.616614i
$387$		0			0
$388$			3843.31i			0.502873i
$389$	−1483.30	−	856.385i	−0.193333	−	0.111621i	0.400209	−	0.916424i	$-0.368937\pi$
$389$	−1483.30	−	856.385i	−0.193333	−	0.111621i	−0.593542	+	0.804803i	$0.702271\pi$
$390$		0			0
$391$	−766.569	+	442.579i	−0.0991485	+	0.0572434i
$392$	−2093.94	−	153.880i	−0.269796	−	0.0198269i
$393$		0			0
$394$	942.667	−	1632.75i	0.120535	−	0.208773i
$395$	−5137.48			−0.654417
$396$		0			0
$397$		−	5977.49i		−	0.755672i	−0.925872	−	0.377836i	$-0.876668\pi$
$397$		−	5977.49i		−	0.755672i	0.925872	−	0.377836i	$-0.123332\pi$
$398$	8538.84	−	14789.7i	1.07541	−	1.86267i
$399$		0			0
$400$	10145.6	+	17572.7i	1.26820	+	2.19658i
$401$	−2620.36	+	1512.86i	−0.326320	+	0.188401i	−0.654206	−	0.756316i	$-0.726997\pi$
$401$	−2620.36	+	1512.86i	−0.326320	+	0.188401i	0.327886	+	0.944717i	$0.393664\pi$
$402$		0			0
$403$	269.030	−	465.973i	0.0332539	−	0.0575974i
$404$	2715.94			0.334463
$405$		0			0
$406$	−4020.61	−	1237.02i	−0.491476	−	0.151212i
$407$	−11074.1	−	6393.65i	−1.34871	−	0.778676i
$408$		0			0
$409$	−9538.96	+	5507.32i	−1.15323	+	0.665818i	−0.949672	−	0.313245i	$-0.898584\pi$
$409$	−9538.96	+	5507.32i	−1.15323	+	0.665818i	−0.203558	+	0.979063i	$0.565250\pi$
$410$	957.877	−	553.030i	0.115381	−	0.0666152i
$411$		0			0
$412$	4196.72	+	2422.98i	0.501838	+	0.289736i
$413$	−8239.47	−	2535.03i	−0.981690	−	0.302035i
$414$		0			0
$415$	−8003.98			−0.946746
$416$	−887.316	+	1536.88i	−0.104578	+	0.181134i
$417$		0			0
$418$	−11502.6	+	6641.05i	−1.34596	+	0.777092i
$419$	5849.85	+	10132.2i	0.682062	+	1.18137i	0.974351	+	0.225036i	$0.0722499\pi$
$419$	5849.85	+	10132.2i	0.682062	+	1.18137i	−0.292289	+	0.956330i	$0.594417\pi$
$420$		0			0
$421$	3481.75	−	6030.57i	0.403064	−	0.698128i	−0.591030	−	0.806650i	$-0.701278\pi$
$421$	3481.75	−	6030.57i	0.403064	−	0.698128i	0.994094	+	0.108522i	$0.0346117\pi$
$422$			13008.3i			1.50056i
$423$		0			0
$424$	−4349.33			−0.498166
$425$	2932.09	−	5078.53i	0.334652	−	0.579635i
$426$		0			0
$427$	11310.0	−	2590.03i	1.28180	−	0.293537i
$428$	−4791.98	+	2766.65i	−0.541189	+	0.312456i
$429$		0			0
$430$	6403.93	+	3697.31i	0.718197	+	0.414651i
$431$		−	12686.3i		−	1.41781i	−0.705305	−	0.708904i	$-0.749190\pi$
$431$		−	12686.3i		−	1.41781i	0.705305	−	0.708904i	$-0.250810\pi$
$432$		0			0
$433$			12891.4i			1.43077i	0.698730	+	0.715385i	$0.253749\pi$
$433$			12891.4i			1.43077i	−0.698730	+	0.715385i	$0.746251\pi$
$434$	3633.23	−	3376.02i	0.401844	−	0.373397i
$435$		0			0
$436$	−303.088	−	524.963i	−0.0332919	−	0.0576632i
$437$	−2005.34	−	3473.34i	−0.219515	−	0.380212i
$438$		0			0
$439$	−10467.6	−	6043.45i	−1.13802	−	0.657035i	−0.192078	−	0.981380i	$-0.561523\pi$
$439$	−10467.6	−	6043.45i	−1.13802	−	0.657035i	−0.945939	+	0.324345i	$0.894856\pi$
$440$	4395.36			0.476228
$441$		0			0
$442$	620.724			0.0667983
$443$	8703.97	+	5025.24i	0.933495	+	0.538953i	0.887915	−	0.460007i	$-0.152153\pi$
$443$	8703.97	+	5025.24i	0.933495	+	0.538953i	0.0455796	+	0.998961i	$0.485487\pi$
$444$		0			0
$445$	9754.77	+	16895.8i	1.03915	+	1.79986i
$446$	4698.20	+	8137.53i	0.498803	+	0.863953i
$447$		0			0
$448$	−3918.10	+	3640.73i	−0.413199	+	0.383947i
$449$		−	10044.6i		−	1.05575i	−0.849321	−	0.527877i	$-0.822988\pi$
$449$		−	10044.6i		−	1.05575i	0.849321	−	0.527877i	$-0.177012\pi$
$450$		0			0
$451$		−	526.014i		−	0.0549202i
$452$	9149.17	+	5282.27i	0.952081	+	0.549684i
$453$		0			0
$454$	552.004	−	318.700i	0.0570635	−	0.0329456i
$455$	−2744.92	+	628.596i	−0.282822	+	0.0647671i
$456$		0			0
$457$	7705.51	−	13346.3i	0.788727	−	1.36612i	−0.138020	−	0.990430i	$-0.544074\pi$
$457$	7705.51	−	13346.3i	0.788727	−	1.36612i	0.926747	−	0.375686i	$-0.122593\pi$
$458$	4333.49			0.442119
$459$		0			0
$460$		−	5251.88i		−	0.532326i
$461$	2887.34	−	5001.02i	0.291707	−	0.505251i	−0.682506	−	0.730880i	$-0.739110\pi$
$461$	2887.34	−	5001.02i	0.291707	−	0.505251i	0.974214	+	0.225628i	$0.0724434\pi$
$462$		0			0
$463$	−4764.84	−	8252.94i	−0.478274	−	0.828395i	0.521416	−	0.853303i	$-0.325404\pi$
$463$	−4764.84	−	8252.94i	−0.478274	−	0.828395i	−0.999690	+	0.0249078i	$0.992071\pi$
$464$	3853.62	−	2224.89i	0.385560	−	0.222603i
$465$		0			0
$466$	−4137.12	+	7165.70i	−0.411263	+	0.712328i
$467$	8268.97			0.819363			0.409681	−	0.912229i	$-0.365640\pi$
$467$	8268.97			0.819363			0.409681	+	0.912229i	$0.365640\pi$
$468$		0			0
$469$	9287.11	+	2857.35i	0.914368	+	0.281323i
$470$	30788.8	+	17775.9i	3.02166	+	1.74456i
$471$		0			0
$472$	2467.53	−	1424.63i	0.240630	−	0.138928i
$473$	3045.54	−	1758.34i	0.296055	−	0.170928i
$474$		0			0
$475$	23010.9	+	13285.4i	2.22277	+	1.28332i
$476$	2427.57	+	746.888i	0.233755	+	0.0719192i
$477$		0			0
$478$	7244.60			0.693222
$479$	−7295.72	+	12636.6i	−0.695929	+	1.20538i	0.273938	+	0.961747i	$0.411674\pi$
$479$	−7295.72	+	12636.6i	−0.695929	+	1.20538i	−0.969867	+	0.243637i	$0.921660\pi$
$480$		0			0
$481$	−2344.97	+	1353.87i	−0.222290	+	0.128339i
$482$	4298.41	+	7445.06i	0.406197	+	0.703554i
$483$		0			0
$484$	114.241	−	197.871i	0.0107288	−	0.0185829i
$485$		−	12007.4i		−	1.12418i
$486$		0			0
$487$	−14380.5			−1.33807			−0.669036	−	0.743230i	$-0.733293\pi$
$487$	−14380.5			−1.33807			−0.669036	+	0.743230i	$0.733293\pi$
$488$	−1917.45	+	3321.13i	−0.177867	+	0.308075i
$489$		0			0
$490$	−25886.8	−	1902.38i	−2.38663	−	0.175389i
$491$	512.614	−	295.958i	0.0471160	−	0.0272024i	−0.476257	−	0.879306i	$-0.658007\pi$
$491$	512.614	−	295.958i	0.0471160	−	0.0272024i	0.523373	+	0.852104i	$0.324673\pi$
$492$		0			0
$493$	−1113.70	−	642.997i	−0.101742	−	0.0587406i
$494$			2812.52i			0.256156i
$495$		0			0
$496$			5246.33i			0.474934i
$497$	−1458.96	−	1570.12i	−0.131677	−	0.141709i
$498$		0			0
$499$	2075.90	+	3595.56i	0.186232	+	0.322564i	0.943991	−	0.329971i	$-0.107039\pi$
$499$	2075.90	+	3595.56i	0.186232	+	0.322564i	−0.757759	+	0.652535i	$0.773706\pi$
$500$	9433.44	+	16339.2i	0.843752	+	1.46142i
$501$		0			0
$502$	−1037.14	−	598.791i	−0.0922105	−	0.0532378i
$503$	13272.2			1.17650			0.588248	−	0.808681i	$-0.299818\pi$
$503$	13272.2			1.17650			0.588248	+	0.808681i	$0.299818\pi$
$504$		0			0
$505$	−8485.25			−0.747701
$506$	−4872.69	−	2813.25i	−0.428098	−	0.247163i
$507$		0			0
$508$	−895.974	−	1551.87i	−0.0782528	−	0.135538i
$509$	−7547.02	−	13071.8i	−0.657202	−	1.13831i	−0.981337	−	0.192296i	$-0.938407\pi$
$509$	−7547.02	−	13071.8i	−0.657202	−	1.13831i	0.324135	−	0.946011i	$-0.394927\pi$
$510$		0			0
$511$	8927.86	+	9608.03i	0.772887	+	0.831769i
$512$		−	13664.7i		−	1.17949i
$513$		0			0
$514$			15534.8i			1.33310i
$515$	−13111.5	−	7569.95i	−1.12187	−	0.647713i
$516$		0			0
$517$	14642.3	−	8453.75i	1.24559	−	0.719140i
$518$	−24329.1	+	5571.44i	−2.06363	+	0.472577i
$519$		0			0
$520$	465.364	−	806.033i	0.0392453	−	0.0679748i
$521$	5002.27			0.420640			0.210320	−	0.977633i	$-0.432549\pi$
$521$	5002.27			0.420640			0.210320	+	0.977633i	$0.432549\pi$
$522$		0			0
$523$			909.042i			0.0760031i	0.999278	+	0.0380016i	$0.0120992\pi$
$523$			909.042i			0.0760031i	−0.999278	+	0.0380016i	$0.987901\pi$
$524$	−6997.04	+	12119.2i	−0.583334	+	1.01036i
$525$		0			0
$526$	−9351.05	−	16196.5i	−0.775143	−	1.34259i
$527$	1313.07	−	758.099i	0.108535	−	0.0626628i
$528$		0			0
$529$	−5234.01	+	9065.57i	−0.430181	+	0.745095i
$530$	−53769.6			−4.40680
$531$		0			0
$532$	−3384.17	+	10999.4i	−0.275794	+	0.896398i
$533$	−96.4619	−	55.6923i	−0.00783908	−	0.00452589i
$534$		0			0
$535$	14971.3	−	8643.67i	1.20984	−	0.698502i
$536$	−2781.27	+	1605.77i	−0.224128	+	0.129400i
$537$		0			0
$538$	−18086.7	−	10442.4i	−1.44939	−	0.836807i
$539$	−6939.06	+	10209.4i	−0.554520	+	0.815860i
$540$		0			0
$541$	21816.1			1.73373			0.866865	−	0.498544i	$-0.166132\pi$
$541$	21816.1			1.73373			0.866865	+	0.498544i	$0.166132\pi$
$542$	−14455.7	+	25038.0i	−1.14562	+	1.98427i
$543$		0			0
$544$	−4330.77	+	2500.37i	−0.341324	+	0.197063i
$545$	946.918	+	1640.11i	0.0744248	+	0.128907i
$546$		0			0
$547$	3976.21	−	6887.00i	0.310805	−	0.538330i	−0.667732	−	0.744402i	$-0.732735\pi$
$547$	3976.21	−	6887.00i	0.310805	−	0.538330i	0.978537	+	0.206072i	$0.0660680\pi$
$548$		−	7265.78i		−	0.566385i
$549$		0			0
$550$	37275.6			2.88989
$551$	2913.43	−	5046.21i	0.225257	−	0.390156i
$552$		0			0
$553$	1064.53	+	4648.54i	0.0818596	+	0.357461i
$554$	−11898.3	+	6869.49i	−0.912474	+	0.526817i
$555$		0			0
$556$	11765.1	+	6792.57i	0.897393	+	0.518110i
$557$			16793.7i			1.27750i	0.769413	+	0.638752i	$0.220549\pi$
$557$			16793.7i			1.27750i	−0.769413	+	0.638752i	$0.779451\pi$
$558$		0			0
$559$		−	744.667i		−	0.0563436i
$560$	20114.0	−	18690.1i	1.51781	−	1.41036i
$561$		0			0
$562$	4136.22	+	7164.14i	0.310455	+	0.537724i
$563$	−3810.86	−	6600.60i	−0.285273	−	0.494107i	0.687403	−	0.726277i	$-0.258751\pi$
$563$	−3810.86	−	6600.60i	−0.285273	−	0.494107i	−0.972675	+	0.232170i	$0.925418\pi$
$564$		0			0
$565$	−28584.2	−	16503.1i	−2.12840	−	1.22883i
$566$	8696.32			0.645819
$567$		0			0
$568$	708.403			0.0523309
$569$	2201.40	+	1270.98i	0.162193	+	0.0936420i	0.578899	−	0.815399i	$-0.303482\pi$
$569$	2201.40	+	1270.98i	0.162193	+	0.0936420i	−0.416707	+	0.909041i	$0.636816\pi$
$570$		0			0
$571$	−2123.22	−	3677.53i	−0.155611	−	0.269527i	0.777670	−	0.628673i	$-0.216401\pi$
$571$	−2123.22	−	3677.53i	−0.155611	−	0.269527i	−0.933281	+	0.359146i	$0.883068\pi$
$572$	875.751	+	1516.84i	0.0640157	+	0.110878i
$573$		0			0
$574$	−698.877	−	752.121i	−0.0508198	−	0.0546915i
$575$			11255.8i			0.816345i
$576$		0			0
$577$		−	26192.0i		−	1.88975i	−0.327426	−	0.944877i	$-0.606181\pi$
$577$		−	26192.0i		−	1.88975i	0.327426	−	0.944877i	$-0.393819\pi$
$578$	−14623.2	−	8442.70i	−1.05233	−	0.607561i
$579$		0			0
$580$	6607.89	−	3815.07i	0.473065	−	0.273124i
$581$	1658.49	+	7242.22i	0.118426	+	0.517139i
$582$		0			0
$583$	−12785.7	+	22145.5i	−0.908285	+	1.57320i
$584$	−4334.94			−0.307160
$585$		0			0
$586$			2071.72i			0.146044i
$587$	1377.78	−	2386.39i	0.0968777	−	0.167797i	−0.813513	−	0.581547i	$-0.802448\pi$
$587$	1377.78	−	2386.39i	0.0968777	−	0.167797i	0.910391	+	0.413750i	$0.135781\pi$
$588$		0			0
$589$	3434.97	+	5949.53i	0.240298	+	0.416208i
$590$	30505.4	−	17612.3i	2.12862	−	1.22896i
$591$		0			0
$592$	13200.9	−	22864.6i	0.916474	−	1.58738i
$593$	−14044.3			−0.972567			−0.486284	−	0.873801i	$-0.661648\pi$
$593$	−14044.3			−0.972567			−0.486284	+	0.873801i	$0.661648\pi$
$594$		0			0
$595$	−7584.31	−	2333.46i	−0.522565	−	0.160777i
$596$	2316.17	+	1337.24i	0.159185	+	0.0919053i
$597$		0			0
$598$	−1031.80	+	595.713i	−0.0705579	+	0.0407366i
$599$	10357.8	−	5980.08i	0.706524	−	0.407912i	−0.103248	−	0.994656i	$-0.532924\pi$
$599$	10357.8	−	5980.08i	0.706524	−	0.407912i	0.809773	+	0.586744i	$0.199590\pi$
$600$		0			0
$601$	21071.9	+	12165.9i	1.43019	+	0.825718i	0.997134	−	0.0756510i	$-0.0241035\pi$
$601$	21071.9	+	12165.9i	1.43019	+	0.825718i	0.433051	+	0.901369i	$0.357437\pi$
$602$	2018.48	−	6560.56i	0.136656	−	0.444167i
$603$		0			0
$604$	6073.80			0.409171
$605$	−356.915	+	618.196i	−0.0239846	+	0.0415425i
$606$		0			0
$607$	8989.19	−	5189.91i	0.601087	−	0.347038i	−0.168382	−	0.985722i	$-0.553854\pi$
$607$	8989.19	−	5189.91i	0.601087	−	0.347038i	0.769469	+	0.638684i	$0.220521\pi$
$608$	−11329.2	−	19622.8i	−0.755693	−	1.30890i
$609$		0			0
$610$	−23705.0	+	41058.2i	−1.57342	+	2.72524i
$611$		−	3580.20i		−	0.237053i
$612$		0			0
$613$	−7728.54			−0.509222			−0.254611	−	0.967044i	$-0.581947\pi$
$613$	−7728.54			−0.509222			−0.254611	+	0.967044i	$0.581947\pi$
$614$	−11745.1	+	20343.2i	−0.771979	+	1.33711i
$615$		0			0
$616$	−910.753	−	3977.04i	−0.0595703	−	0.260129i
$617$	−6665.11	+	3848.10i	−0.434890	+	0.251084i	−0.701428	−	0.712741i	$-0.747454\pi$
$617$	−6665.11	+	3848.10i	−0.434890	+	0.251084i	0.266538	+	0.963825i	$0.414120\pi$
$618$		0			0
$619$	25350.2	+	14635.9i	1.64606	+	0.950352i	0.978617	+	0.205689i	$0.0659436\pi$
$619$	25350.2	+	14635.9i	1.64606	+	0.950352i	0.667441	+	0.744663i	$0.267390\pi$
$620$			8996.01i			0.582723i
$621$		0			0
$622$			17714.8i			1.14196i
$623$	13266.5	−	12327.3i	0.853147	−	0.792751i
$624$		0			0
$625$	−12405.2	−	21486.4i	−0.793931	−	1.37513i
$626$	4858.46	+	8415.10i	0.310197	+	0.537276i
$627$		0			0
$628$	−12039.5	−	6951.01i	−0.765014	−	0.441681i
$629$	−7630.15			−0.483679
$630$		0			0
$631$	−16177.9			−1.02065			−0.510326	−	0.859981i	$-0.670475\pi$
$631$	−16177.9			−1.02065			−0.510326	+	0.859981i	$0.670475\pi$
$632$	−1365.02	−	788.094i	−0.0859138	−	0.0496024i
$633$		0			0
$634$	−5149.09	−	8918.49i	−0.322550	−	0.558673i
$635$	2799.24	+	4848.42i	0.174936	+	0.302998i
$636$		0			0
$637$	1137.54	+	2353.43i	0.0707551	+	0.146384i
$638$		−	8174.41i		−	0.507254i
$639$		0			0
$640$			15314.5i			0.945875i
$641$	23508.3	+	13572.5i	1.44855	+	0.836321i	0.998395	−	0.0566298i	$-0.0180355\pi$
$641$	23508.3	+	13572.5i	1.44855	+	0.836321i	0.450155	+	0.892951i	$0.351369\pi$
$642$		0			0
$643$	−18843.1	+	10879.1i	−1.15567	+	0.667229i	−0.950263	−	0.311447i	$-0.899186\pi$
$643$	−18843.1	+	10879.1i	−1.15567	+	0.667229i	−0.205411	+	0.978676i	$0.565853\pi$
$644$	−4752.04	+	1088.23i	−0.290771	+	0.0665874i
$645$		0			0
$646$	−3962.70	+	6863.60i	−0.241347	+	0.418026i
$647$	24932.0			1.51496			0.757478	−	0.652860i	$-0.226431\pi$
$647$	24932.0			1.51496			0.757478	+	0.652860i	$0.226431\pi$
$648$		0			0
$649$		−	16751.9i		−	1.01320i
$650$	3946.60	−	6835.72i	0.238152	−	0.412491i
$651$		0			0
$652$	−1220.80	−	2114.50i	−0.0733288	−	0.127009i
$653$	−838.558	+	484.142i	−0.0502531	+	0.0290137i	−0.524916	−	0.851154i	$-0.675903\pi$
$653$	−838.558	+	484.142i	−0.0502531	+	0.0290137i	0.474663	+	0.880168i	$0.342570\pi$
$654$		0			0
$655$	21860.4	−	37863.3i	1.30406	−	2.25869i
$656$	1086.05			0.0646391
$657$		0			0
$658$	9704.44	−	31541.8i	0.574952	−	1.86874i
$659$	3413.73	+	1970.92i	0.201791	+	0.116504i	0.597491	−	0.801876i	$-0.296165\pi$
$659$	3413.73	+	1970.92i	0.201791	+	0.116504i	−0.395700	+	0.918380i	$0.629498\pi$
$660$		0			0
$661$	−2506.55	+	1447.16i	−0.147494	+	0.0851555i	−0.571931	−	0.820302i	$-0.693805\pi$
$661$	−2506.55	+	1447.16i	−0.147494	+	0.0851555i	0.424437	+	0.905457i	$0.360472\pi$
$662$	−14932.3	+	8621.15i	−0.876675	+	0.506149i
$663$		0			0
$664$	−2126.64	−	1227.82i	−0.124292	−	0.0717598i
$665$	10572.9	−	34364.7i	0.616543	−	2.00392i
$666$		0			0
$667$	2468.35			0.143291
$668$	786.084	−	1361.54i	0.0455307	−	0.0788615i
$669$		0			0
$670$	−34384.1	+	19851.7i	−1.98265	+	1.14468i
$671$	11273.5	+	19526.2i	0.648595	+	1.12340i
$672$		0			0
$673$	−6948.10	+	12034.5i	−0.397964	+	0.689293i	−0.993475	−	0.114054i	$-0.963616\pi$
$673$	−6948.10	+	12034.5i	−0.397964	+	0.689293i	0.595511	+	0.803347i	$0.296950\pi$
$674$			27516.5i			1.57255i
$675$		0			0
$676$	−13659.4			−0.777165
$677$	4561.28	−	7900.37i	0.258943	−	0.448502i	−0.707016	−	0.707197i	$-0.749959\pi$
$677$	4561.28	−	7900.37i	0.258943	−	0.448502i	0.965959	+	0.258695i	$0.0832926\pi$
$678$		0			0
$679$	−10864.7	+	2488.04i	−0.614060	+	0.140622i
$680$	2271.32	−	1311.35i	0.128090	−	0.0739529i
$681$		0			0
$682$	8346.50	+	4818.85i	0.468628	+	0.270562i
$683$			5500.02i			0.308129i	0.988061	+	0.154065i	$0.0492364\pi$
$683$			5500.02i			0.308129i	−0.988061	+	0.154065i	$0.950764\pi$
$684$		0			0
$685$			22700.0i			1.26617i
$686$	3642.63	+	23817.3i	0.202735	+	1.32558i
$687$		0			0
$688$	3630.43	+	6288.08i	0.201175	+	0.348446i
$689$	2707.41	+	4689.36i	0.149701	+	0.259290i
$690$		0			0
$691$	−9079.68	−	5242.16i	−0.499866	−	0.288598i	0.228792	−	0.973475i	$-0.426522\pi$
$691$	−9079.68	−	5242.16i	−0.499866	−	0.288598i	−0.728658	+	0.684877i	$0.759856\pi$
$692$	25401.8			1.39542
$693$		0			0
$694$	33334.8			1.82330
$695$	−36756.9	−	21221.6i	−2.00614	−	1.15825i
$696$		0			0
$697$	−156.935	−	271.820i	−0.00852849	−	0.0147718i
$698$	−13827.5	−	23949.9i	−0.749825	−	1.29874i
$699$		0			0
$700$	23659.7	−	21984.8i	1.27751	−	1.18707i
$701$		−	15162.7i		−	0.816955i	−0.912768	−	0.408477i	$-0.866060\pi$
$701$		−	15162.7i		−	0.816955i	0.912768	−	0.408477i	$-0.133940\pi$
$702$		0			0
$703$		−	34572.4i		−	1.85480i
$704$	−9000.94	−	5196.69i	−0.481869	−	0.278207i
$705$		0			0
$706$	32928.2	−	19011.1i	1.75534	−	1.01345i
$707$	1758.21	+	7677.69i	0.0935282	+	0.408415i
$708$		0			0
$709$	1871.41	−	3241.38i	0.0991289	−	0.171696i	−0.812195	−	0.583385i	$-0.801728\pi$
$709$	1871.41	−	3241.38i	0.0991289	−	0.171696i	0.911324	+	0.411689i	$0.135061\pi$
$710$	8757.80			0.462922
$711$		0			0
$712$			5985.56i			0.315054i
$713$	−1455.10	+	2520.31i	−0.0764293	+	0.132379i
$714$		0			0
$715$	−2736.05	−	4738.98i	−0.143109	−	0.247871i
$716$	8046.24	−	4645.50i	0.419975	−	0.242473i
$717$		0			0
$718$	−21250.1	+	36806.3i	−1.10452	+	1.91309i
$719$	24366.5			1.26386			0.631931	−	0.775024i	$-0.282262\pi$
$719$	24366.5			1.26386			0.631931	+	0.775024i	$0.282262\pi$
$720$		0			0
$721$	−4132.68	+	13432.2i	−0.213466	+	0.693818i
$722$	−8569.01	−	4947.32i	−0.441697	−	0.255014i
$723$		0			0
$724$	4069.91	−	2349.77i	0.208919	−	0.120619i
$725$	−14162.0	+	8176.42i	−0.725466	+	0.418848i
$726$		0			0
$727$	−20385.8	−	11769.7i	−1.03998	−	0.600433i	−0.120153	−	0.992755i	$-0.538339\pi$
$727$	−20385.8	−	11769.7i	−1.03998	−	0.600433i	−0.919828	+	0.392322i	$0.871672\pi$
$728$	−825.748	−	254.057i	−0.0420388	−	0.0129340i
$729$		0			0
$730$	−53591.7			−2.71715
$731$	1049.20	−	1817.27i	0.0530862	−	0.0919481i
$732$		0			0
$733$	−11851.1	+	6842.23i	−0.597176	+	0.344780i	−0.767930	−	0.640534i	$-0.778713\pi$
$733$	−11851.1	+	6842.23i	−0.597176	+	0.344780i	0.170754	+	0.985314i	$0.445380\pi$
$734$	−5688.16	−	9852.18i	−0.286040	−	0.495437i
$735$		0			0
$736$	4799.24	−	8312.53i	0.240356	−	0.416310i
$737$			18881.9i			0.943722i
$738$		0			0
$739$	12978.1			0.646017			0.323009	−	0.946396i	$-0.395306\pi$
$739$	12978.1			0.646017			0.323009	+	0.946396i	$0.395306\pi$
$740$	22635.8	−	39206.4i	1.12447	−	1.94764i
$741$		0			0
$742$	11141.5	+	48652.2i	0.551236	+	2.40712i
$743$	24571.4	−	14186.3i	1.21324	−	0.700464i	0.249775	−	0.968304i	$-0.419643\pi$
$743$	24571.4	−	14186.3i	1.21324	−	0.700464i	0.963463	+	0.267840i	$0.0863099\pi$
$744$		0			0
$745$	−7236.27	−	4177.86i	−0.355861	−	0.205456i
$746$		−	15570.2i		−	0.764163i
$747$		0			0
$748$			4935.56i			0.241259i
$749$	−10923.2	−	11755.4i	−0.532877	−	0.573474i
$750$		0			0
$751$	13262.7	+	22971.6i	0.644423	+	1.11617i	0.984434	+	0.175752i	$0.0562358\pi$
$751$	13262.7	+	22971.6i	0.644423	+	1.11617i	−0.340011	+	0.940421i	$0.610431\pi$
$752$	17454.3	+	30231.8i	0.846402	+	1.46601i
$753$		0			0
$754$	−1499.05	−	865.475i	−0.0724033	−	0.0418021i
$755$	−18976.0			−0.914711
$756$		0			0
$757$	15064.7			0.723296			0.361648	−	0.932315i	$-0.382214\pi$
$757$	15064.7			0.723296			0.361648	+	0.932315i	$0.382214\pi$
$758$	−6737.68	−	3890.00i	−0.322854	−	0.186400i
$759$		0			0
$760$	5941.75	+	10291.4i	0.283592	+	0.491196i
$761$	−2369.82	−	4104.66i	−0.112886	−	0.195524i	0.804047	−	0.594566i	$-0.202676\pi$
$761$	−2369.82	−	4104.66i	−0.112886	−	0.195524i	−0.916933	+	0.399042i	$0.869343\pi$
$762$		0			0
$763$	1287.81	−	1196.64i	0.0611032	−	0.0567776i
$764$		−	17626.0i		−	0.834667i
$765$		0			0
$766$		−	21135.0i		−	0.996917i
$767$	−3072.01	−	1773.63i	−0.144621	−	0.0834967i
$768$		0			0
$769$	17949.9	−	10363.4i	0.841730	−	0.485973i	−0.0161222	−	0.999870i	$-0.505132\pi$
$769$	17949.9	−	10363.4i	0.841730	−	0.485973i	0.857852	+	0.513897i	$0.171799\pi$
$770$	−11259.4	−	49167.1i	−0.526962	−	2.30111i
$771$		0			0
$772$	3936.68	−	6818.53i	0.183529	−	0.317881i
$773$	−10493.9			−0.488279			−0.244139	−	0.969740i	$-0.578505\pi$
$773$	−10493.9			−0.488279			−0.244139	+	0.969740i	$0.578505\pi$
$774$		0			0
$775$		−	19280.2i		−	0.893631i
$776$	1841.95	−	3190.35i	0.0852089	−	0.147586i
$777$		0			0
$778$	−3248.19	−	5626.02i	−0.149683	−	0.259258i
$779$	1231.62	−	711.078i	0.0566464	−	0.0327048i
$780$		0			0
$781$	2082.49	−	3606.98i	0.0954128	−	0.165260i
$782$	−3357.32			−0.153526
$783$		0			0
$784$	−21079.1	−	14327.0i	−0.960237	−	0.652650i
$785$	37614.3	+	21716.6i	1.71021	+	0.987388i
$786$		0			0
$787$	−6470.70	+	3735.86i	−0.293082	+	0.169211i	−0.639331	−	0.768932i	$-0.720789\pi$
$787$	−6470.70	+	3735.86i	−0.293082	+	0.169211i	0.346249	+	0.938143i	$0.387455\pi$
$788$	2749.06	−	1587.17i	0.124278	−	0.0717521i
$789$		0			0
$790$	−16875.4	−	9743.00i	−0.759998	−	0.438785i
$791$	−9009.57	+	29283.3i	−0.404985	+	1.31630i
$792$		0			0
$793$	4774.37			0.213799
$794$	11336.0	−	19634.6i	0.506676	−	0.877589i
$795$		0			0
$796$	24901.5	−	14376.9i	1.10881	−	0.640170i
$797$	−26.6623	−	46.1805i	−0.00118498	−	0.00205244i	0.865432	−	0.501026i	$-0.167044\pi$
$797$	−26.6623	−	46.1805i	−0.00118498	−	0.00205244i	−0.866617	+	0.498973i	$0.833711\pi$
$798$		0			0
$799$	5044.33	−	8737.04i	0.223349	−	0.386851i
$800$			63590.0i			2.81031i
$801$		0			0
$802$	−11476.3			−0.505290
$803$	−12743.4	+	22072.2i	−0.560031	+	0.970003i
$804$		0			0
$805$	14846.5	−	3399.89i	0.650026	−	0.148858i
$806$	1767.39	−	1020.40i	0.0772378	−	0.0445933i
$807$		0			0
$808$	−2254.51	−	1301.64i	−0.0981603	−	0.0566729i
$809$		−	2578.18i		−	0.112045i	−0.998430	−	0.0560223i	$-0.982158\pi$
$809$		−	2578.18i		−	0.112045i	0.998430	−	0.0560223i	$-0.0178418\pi$
$810$		0			0
$811$			3556.10i			0.153973i	0.997032	+	0.0769863i	$0.0245298\pi$
$811$			3556.10i			0.153973i	−0.997032	+	0.0769863i	$0.975470\pi$
$812$	−4821.19	−	5188.49i	−0.208363	−	0.224237i
$813$		0			0
$814$	−24250.5	−	42003.1i	−1.04420	−	1.80861i
$815$	3814.08	+	6606.19i	0.163928	+	0.283932i
$816$		0			0
$817$	8234.08	+	4753.95i	0.352600	+	0.203574i
$818$	−41777.5			−1.78572
$819$		0			0
$820$	1862.28			0.0793093
$821$	−28617.2	−	16522.1i	−1.21650	−	0.702347i	−0.252333	−	0.967640i	$-0.581198\pi$
$821$	−28617.2	−	16522.1i	−1.21650	−	0.702347i	−0.964168	+	0.265293i	$0.914531\pi$
$822$		0			0
$823$	9921.48	+	17184.5i	0.420220	+	0.727843i	0.995961	−	0.0897898i	$-0.0286195\pi$
$823$	9921.48	+	17184.5i	0.420220	+	0.727843i	−0.575741	+	0.817632i	$0.695286\pi$
$824$	−2322.47	−	4022.64i	−0.0981883	−	0.170067i
$825$		0			0
$826$	−22257.1	−	23952.7i	−0.937557	−	1.00898i
$827$		−	16163.8i		−	0.679648i	−0.940489	−	0.339824i	$-0.889632\pi$
$827$		−	16163.8i		−	0.679648i	0.940489	−	0.339824i	$-0.110368\pi$
$828$		0			0
$829$			30024.8i			1.25791i	0.777443	+	0.628954i	$0.216517\pi$
$829$			30024.8i			1.25791i	−0.777443	+	0.628954i	$0.783483\pi$
$830$	−26291.1	−	15179.2i	−1.09949	−	0.634791i
$831$		0			0
$832$	−1905.97	+	1100.41i	−0.0794202	+	0.0458533i
$833$	−539.846	+	7346.00i	−0.0224544	+	0.305551i
$834$		0			0
$835$	−2455.92	+	4253.77i	−0.101785	+	0.176297i
$836$	−22363.1			−0.925174
$837$		0			0
$838$			44375.9i			1.82928i
$839$	−5951.06	+	10307.5i	−0.244879	+	0.424143i	−0.962098	−	0.272706i	$-0.912082\pi$
$839$	−5951.06	+	10307.5i	−0.244879	+	0.424143i	0.717219	+	0.696848i	$0.245415\pi$
$840$		0			0
$841$	−10401.4	−	18015.8i	−0.426481	−	0.738686i
$842$	22873.4	−	13206.0i	0.936186	−	0.540507i
$843$		0			0
$844$	−10951.1	+	18967.9i	−0.446626	+	0.773579i
$845$	42675.4			1.73737
$846$		0			0
$847$	633.316	+	194.852i	0.0256919	+	0.00790459i
$848$	−45723.5	−	26398.5i	−1.85159	−	1.06902i
$849$		0			0
$850$	19262.4	−	11121.1i	0.777287	−	0.448767i
$851$	12683.3	−	7322.69i	0.510902	−	0.294969i
$852$		0			0
$853$	−28403.7	−	16398.9i	−1.14012	−	0.658251i	−0.193662	−	0.981068i	$-0.562037\pi$
$853$	−28403.7	−	16398.9i	−1.14012	−	0.658251i	−0.946461	+	0.322818i	$0.895370\pi$
$854$	42062.5	+	12941.3i	1.68542	+	0.518551i
$855$		0			0
$856$	5303.78			0.211775
$857$	−3583.64	+	6207.05i	−0.142841	+	0.247408i	−0.928565	−	0.371169i	$-0.878957\pi$
$857$	−3583.64	+	6207.05i	−0.142841	+	0.247408i	0.785724	+	0.618577i	$0.212291\pi$
$858$		0			0
$859$	28909.1	−	16690.7i	1.14827	−	0.662956i	0.199808	−	0.979835i	$-0.435968\pi$
$859$	28909.1	−	16690.7i	1.14827	−	0.662956i	0.948466	+	0.316879i	$0.102635\pi$
$860$	6225.18	+	10782.3i	0.246833	+	0.427528i
$861$		0			0
$862$	24058.9	−	41671.2i	0.950637	−	1.64655i
$863$			10473.7i			0.413127i	0.978433	+	0.206564i	$0.0662280\pi$
$863$			10473.7i			0.413127i	−0.978433	+	0.206564i	$0.933772\pi$
$864$		0			0
$865$	−79361.2			−3.11949
$866$	−24448.0	+	42345.2i	−0.959328	+	1.66160i
$867$		0			0
$868$	8139.83	−	1864.04i	0.318299	−	0.0728915i
$869$	−8025.48	+	4633.51i	−0.313286	+	0.180876i
$870$		0			0
$871$	3462.61	+	1999.14i	0.134703	+	0.0777707i
$872$			581.032i			0.0225645i
$873$		0			0
$874$		−	15212.1i		−	0.588738i
$875$	−40082.3	+	37244.8i	−1.54861	+	1.43898i
$876$		0			0
$877$	−8766.80	−	15184.5i	−0.337553	−	0.584659i	0.646419	−	0.762983i	$-0.276266\pi$
$877$	−8766.80	−	15184.5i	−0.337553	−	0.584659i	−0.983972	+	0.178324i	$0.942933\pi$
$878$	−22922.2	−	39702.5i	−0.881080	−	1.52607i
$879$		0			0
$880$	46207.3	+	26677.8i	1.77006	+	1.02194i
$881$	6138.62			0.234751			0.117375	−	0.993088i	$-0.462552\pi$
$881$	6138.62			0.234751			0.117375	+	0.993088i	$0.462552\pi$
$882$		0			0
$883$	27717.1			1.05635			0.528173	−	0.849137i	$-0.322877\pi$
$883$	27717.1			1.05635			0.528173	+	0.849137i	$0.322877\pi$
$884$	905.098	+	522.558i	0.0344363	+	0.0198818i
$885$		0			0
$886$	19060.3	+	33013.3i	0.722734	+	1.25181i
$887$	−24730.2	−	42833.9i	−0.936142	−	1.62145i	−0.772585	−	0.634912i	$-0.781036\pi$
$887$	−24730.2	−	42833.9i	−0.936142	−	1.62145i	−0.163557	−	0.986534i	$-0.552297\pi$
$888$		0			0
$889$	3806.96	−	3537.46i	0.143624	−	0.133456i
$890$			73997.9i			2.78698i
$891$		0			0
$892$			15820.8i			0.593855i
$893$	39587.7	+	22856.0i	1.48349	+	0.856491i
$894$		0			0
$895$	−25138.4	+	14513.6i	−0.938864	+	0.542053i
$896$	13857.0	−	3173.29i	0.516663	−	0.118317i
$897$		0			0
$898$	19049.1	−	32994.0i	0.707881	−	1.22609i
$899$	−4228.07			−0.156856
$900$		0			0
$901$			15258.4i			0.564186i
$902$	997.560	−	1727.82i	0.0368238	−	0.0637808i
$903$		0			0
$904$	−5063.17	−	8769.67i	−0.186282	−	0.322649i
$905$	−12715.4	+	7341.23i	−0.467043	+	0.269647i
$906$		0			0
$907$	10676.2	−	18491.7i	0.390846	−	0.676965i	−0.601716	−	0.798710i	$-0.705516\pi$
$907$	10676.2	−	18491.7i	0.390846	−	0.676965i	0.992561	+	0.121746i	$0.0388493\pi$
$908$	1073.19			0.0392237
$909$		0			0
$910$	−10208.5	−	3140.84i	−0.371877	−	0.114415i
$911$	35324.0	+	20394.3i	1.28467	+	0.741707i	0.977699	−	0.210011i	$-0.0673500\pi$
$911$	35324.0	+	20394.3i	1.28467	+	0.741707i	0.306975	+	0.951718i	$0.400683\pi$
$912$		0			0
$913$	−12503.4	+	7218.81i	−0.453232	+	0.261673i
$914$	50621.4	−	29226.3i	1.83195	−	1.05768i
$915$		0			0
$916$	6318.79	+	3648.16i	0.227924	+	0.131592i
$917$	−38789.4	−	11934.3i	−1.39688	−	0.429777i
$918$		0			0
$919$	37868.9			1.35928			0.679641	−	0.733545i	$-0.262136\pi$
$919$	37868.9			1.35928			0.679641	+	0.733545i	$0.262136\pi$
$920$	−2517.02	+	4359.60i	−0.0901996	+	0.156230i
$921$		0			0
$922$	18968.4	−	10951.4i	0.677540	−	0.391178i
$923$	−440.972	−	763.786i	−0.0157257	−	0.0272376i
$924$		0			0
$925$	−48512.9	+	84026.9i	−1.72443	+	2.98680i
$926$		−	36145.2i		−	1.28273i
$927$		0			0
$928$	13945.1			0.493286
$929$	21195.0	−	36710.7i	0.748530	−	1.29649i	−0.199998	−	0.979796i	$-0.564094\pi$
$929$	21195.0	−	36710.7i	0.748530	−	1.29649i	0.948527	−	0.316695i	$-0.102573\pi$
$930$		0			0
$931$	−33284.9	−	2446.05i	−1.17172	−	0.0861076i
$932$	−12064.9	+	6965.69i	−0.424034	+	0.244816i
$933$		0			0
$934$	27161.5	+	15681.7i	0.951555	+	0.549380i
$935$		−	15419.9i		−	0.539341i
$936$		0			0
$937$		−	28387.3i		−	0.989725i	−0.868971	−	0.494863i	$-0.835218\pi$
$937$		−	28387.3i		−	0.989725i	0.868971	−	0.494863i	$-0.164782\pi$
$938$	25087.0	+	26998.3i	0.873262	+	0.939792i
$939$		0			0
$940$	29929.4	+	51839.2i	1.03850	+	1.79873i
$941$	7205.30	+	12479.9i	0.249613	+	0.432343i	0.963419	−	0.268001i	$-0.0863632\pi$
$941$	7205.30	+	12479.9i	0.249613	+	0.432343i	−0.713805	+	0.700344i	$0.753030\pi$
$942$		0			0
$943$	521.735	+	301.224i	0.0180170	+	0.0104021i
$944$	34587.4			1.19250
$945$		0			0
$946$	13338.5			0.458426
$947$	27439.3	+	15842.1i	0.941561	+	0.543611i	0.890449	−	0.455082i	$-0.150390\pi$
$947$	27439.3	+	15842.1i	0.941561	+	0.543611i	0.0511119	+	0.998693i	$0.483723\pi$
$948$		0			0
$949$	2698.45	+	4673.85i	0.0923028	+	0.159873i
$950$	50390.2	+	87278.3i	1.72092	+	2.98072i
$951$		0			0
$952$	−1657.18	−	1783.43i	−0.0564176	−	0.0607158i
$953$		−	24370.5i		−	0.828370i	−0.910193	−	0.414185i	$-0.864067\pi$
$953$		−	24370.5i		−	0.828370i	0.910193	−	0.414185i	$-0.135933\pi$
$954$		0			0
$955$			55067.7i			1.86592i
$956$	10563.6	+	6098.88i	0.357375	+	0.206331i
$957$		0			0
$958$	−47929.3	+	27672.0i	−1.61641	+	0.933237i
$959$	20539.6	−	4703.63i	0.691615	−	0.158382i
$960$		0			0
$961$	−12403.0	+	21482.7i	−0.416335	+	0.721113i
$962$	−10270.2			−0.344204
$963$		0			0
$964$			14474.5i			0.483602i
$965$	−12299.1	+	21302.7i	−0.410283	+	0.710630i
$966$		0			0
$967$	9567.67	+	16571.7i	0.318175	+	0.551096i	0.980107	−	0.198468i	$-0.0635967\pi$
$967$	9567.67	+	16571.7i	0.318175	+	0.551096i	−0.661932	+	0.749564i	$0.730263\pi$
$968$	−189.663	+	109.502i	−0.00629753	+	0.00363588i
$969$		0			0
$970$	22771.5	−	39441.4i	0.753762	−	1.30555i
$971$	15282.0			0.505070			0.252535	−	0.967588i	$-0.418736\pi$
$971$	15282.0			0.505070			0.252535	+	0.967588i	$0.418736\pi$
$972$		0			0
$973$	−11585.6	+	37656.0i	−0.381723	+	1.24069i
$974$	−47236.2	−	27271.9i	−1.55395	−	0.897173i
$975$		0			0
$976$	−40315.5	+	23276.2i	−1.32220	+	0.763373i
$977$	−11983.9	+	6918.89i	−0.392424	+	0.226566i	−0.683210	−	0.730222i	$-0.739417\pi$
$977$	−11983.9	+	6918.89i	−0.392424	+	0.226566i	0.290786	+	0.956788i	$0.406083\pi$
$978$		0			0
$979$	30476.7	+	17595.7i	0.994933	+	0.574425i
$980$	−36144.9	−	24566.8i	−1.17817	−	0.800773i
$981$		0			0
$982$	2245.08			0.0729566
$983$	23671.0	−	40999.4i	0.768044	−	1.33029i	−0.170578	−	0.985344i	$-0.554563\pi$
$983$	23671.0	−	40999.4i	0.768044	−	1.33029i	0.938622	−	0.344947i	$-0.112103\pi$
$984$		0			0
$985$	−8588.73	+	4958.71i	−0.277827	+	0.160404i
$986$	−2438.83	−	4224.17i	−0.0787708	−	0.136435i
$987$		0			0
$988$	−2367.72	+	4101.02i	−0.0762423	+	0.132055i
$989$			4027.69i			0.129498i
$990$		0			0
$991$	13576.2			0.435177			0.217589	−	0.976041i	$-0.430181\pi$
$991$	13576.2			0.435177			0.217589	+	0.976041i	$0.430181\pi$
$992$	−8220.68	+	14238.6i	−0.263112	+	0.455723i
$993$		0			0
$994$	−1814.69	−	7924.30i	−0.0579058	−	0.252861i
$995$	−77798.2	+	44916.8i	−2.47876	+	1.43111i
$996$		0			0
$997$	−14126.1	−	8155.72i	−0.448725	−	0.259071i	0.258567	−	0.965993i	$-0.416750\pi$
$997$	−14126.1	−	8155.72i	−0.448725	−	0.259071i	−0.707292	+	0.706922i	$0.750083\pi$
$998$			15747.4i			0.499473i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.62.17		44
3.2	odd	2		63.4.o.a.20.6	yes	44
7.6	odd	2	inner	189.4.o.a.62.18		44
9.2	odd	6		567.4.c.c.566.2		44
9.4	even	3		63.4.o.a.41.5	yes	44
9.5	odd	6	inner	189.4.o.a.125.18		44
9.7	even	3		567.4.c.c.566.43		44
21.20	even	2		63.4.o.a.20.5	✓	44
63.13	odd	6		63.4.o.a.41.6	yes	44
63.20	even	6		567.4.c.c.566.44		44
63.34	odd	6		567.4.c.c.566.1		44
63.41	even	6	inner	189.4.o.a.125.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.5	✓	44	21.20	even	2
63.4.o.a.20.6	yes	44	3.2	odd	2
63.4.o.a.41.5	yes	44	9.4	even	3
63.4.o.a.41.6	yes	44	63.13	odd	6
189.4.o.a.62.17		44	1.1	even	1	trivial
189.4.o.a.62.18		44	7.6	odd	2	inner
189.4.o.a.125.17		44	63.41	even	6	inner
189.4.o.a.125.18		44	9.5	odd	6	inner
567.4.c.c.566.1		44	63.34	odd	6
567.4.c.c.566.2		44	9.2	odd	6
567.4.c.c.566.43		44	9.7	even	3
567.4.c.c.566.44		44	63.20	even	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.28475 + 1.89645i) q^{2} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(-13.5672 + 12.6068i) q^{7} -6.12125i q^{8} +O(q^{10})\)	\(q+(3.28475 + 1.89645i) q^{2} +(3.19307 + 5.53055i) q^{4} +(-9.97590 - 17.2788i) q^{5} +(-13.5672 + 12.6068i) q^{7} -6.12125i q^{8} -75.6753i q^{10} +(-31.1676 - 17.9946i) q^{11} +(-6.59980 + 3.81040i) q^{13} +(-68.4731 + 15.6805i) q^{14} +(37.1532 - 64.3512i) q^{16} -21.4747 q^{17} -97.3022i q^{19} +(63.7074 - 110.345i) q^{20} +(-68.2518 - 118.216i) q^{22} +(35.6964 - 20.6094i) q^{23} +(-136.537 + 236.489i) q^{25} -28.9050 q^{26} +(-113.043 - 34.7800i) q^{28} +(51.8612 + 29.9421i) q^{29} +(-61.1449 + 35.3020i) q^{31} +(201.669 - 116.434i) q^{32} +(-70.5390 - 40.7257i) q^{34} +(353.175 + 108.661i) q^{35} +355.309 q^{37} +(184.529 - 319.614i) q^{38} +(-105.768 + 61.0649i) q^{40} +(7.30794 + 12.6577i) q^{41} +(-48.8575 + 84.6237i) q^{43} -229.832i q^{44} +156.339 q^{46} +(-234.897 + 406.853i) q^{47} +(25.1387 - 342.078i) q^{49} +(-896.982 + 517.873i) q^{50} +(-42.1472 - 24.3337i) q^{52} -710.531i q^{53} +718.049i q^{55} +(77.1691 + 83.0483i) q^{56} +(113.568 + 196.705i) q^{58} +(232.735 + 403.109i) q^{59} +(-542.558 - 313.246i) q^{61} -267.794 q^{62} +288.792 q^{64} +(131.678 + 76.0243i) q^{65} +(-262.327 - 454.364i) q^{67} +(-68.5700 - 118.767i) q^{68} +(954.021 + 1026.70i) q^{70} +115.729i q^{71} -708.180i q^{73} +(1167.10 + 673.827i) q^{74} +(538.135 - 310.692i) q^{76} +(649.711 - 148.786i) q^{77} +(128.747 - 222.997i) q^{79} -1482.55 q^{80} +55.4366i q^{82} +(200.583 - 347.420i) q^{83} +(214.229 + 371.056i) q^{85} +(-320.970 + 185.312i) q^{86} +(-110.149 + 190.784i) q^{88} -977.834 q^{89} +(41.5042 - 134.899i) q^{91} +(227.962 + 131.614i) q^{92} +(-1543.16 + 890.942i) q^{94} +(-1681.26 + 970.677i) q^{95} +(521.193 + 300.911i) q^{97} +(731.308 - 1075.97i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

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