LMFDB - Embedded newform 189.4.i.a.143.15

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			143.15
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83815i q^{2} +4.62119 q^{4} +(-0.207277 + 0.359014i) q^{5} +(5.26194 - 17.7570i) q^{7} +23.1997i q^{8} +O(q^{10})$	\(q+1.83815i q^{2} +4.62119 q^{4} +(-0.207277 + 0.359014i) q^{5} +(5.26194 - 17.7570i) q^{7} +23.1997i q^{8} +(-0.659923 - 0.381007i) q^{10} +(42.9636 - 24.8051i) q^{11} +(-1.43477 + 0.828367i) q^{13} +(32.6401 + 9.67225i) q^{14} -5.67501 q^{16} +(-20.6496 + 35.7662i) q^{17} +(130.814 - 75.5256i) q^{19} +(-0.957866 + 1.65907i) q^{20} +(45.5955 + 78.9737i) q^{22} +(-114.013 - 65.8253i) q^{23} +(62.4141 + 108.104i) q^{25} +(-1.52267 - 2.63733i) q^{26} +(24.3164 - 82.0587i) q^{28} +(136.539 + 78.8310i) q^{29} -18.4071i q^{31} +175.166i q^{32} +(-65.7437 - 37.9571i) q^{34} +(5.28434 + 5.56973i) q^{35} +(173.836 + 301.092i) q^{37} +(138.828 + 240.457i) q^{38} +(-8.32901 - 4.80876i) q^{40} +(-16.9818 - 29.4134i) q^{41} +(29.5623 - 51.2034i) q^{43} +(198.543 - 114.629i) q^{44} +(120.997 - 209.573i) q^{46} -216.532 q^{47} +(-287.624 - 186.873i) q^{49} +(-198.712 + 114.727i) q^{50} +(-6.63037 + 3.82805i) q^{52} +(174.040 + 100.482i) q^{53} +20.5661i q^{55} +(411.957 + 122.075i) q^{56} +(-144.903 + 250.980i) q^{58} -299.637 q^{59} +80.4280i q^{61} +33.8351 q^{62} -367.382 q^{64} -0.686806i q^{65} -257.576 q^{67} +(-95.4259 + 165.282i) q^{68} +(-10.2380 + 9.71343i) q^{70} -1032.80i q^{71} +(-711.100 - 410.554i) q^{73} +(-553.454 + 319.537i) q^{74} +(604.518 - 349.019i) q^{76} +(-214.392 - 893.429i) q^{77} +105.318 q^{79} +(1.17630 - 2.03741i) q^{80} +(54.0663 - 31.2152i) q^{82} +(245.110 - 424.542i) q^{83} +(-8.56037 - 14.8270i) q^{85} +(94.1196 + 54.3400i) q^{86} +(575.470 + 996.743i) q^{88} +(-754.828 - 1307.40i) q^{89} +(7.15964 + 29.8361i) q^{91} +(-526.875 - 304.191i) q^{92} -398.020i q^{94} +62.6189i q^{95} +(-1087.14 - 627.661i) q^{97} +(343.501 - 528.697i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.83815i			0.649885i	0.945734	+	0.324943i	$0.105345\pi$
$2$			1.83815i			0.649885i	−0.945734	+	0.324943i	$0.894655\pi$
$3$		0			0
$3$		0			0
$4$	4.62119			0.577649
$5$	−0.207277	+	0.359014i	−0.0185394	+	0.0321112i	−0.875146	−	0.483858i	$-0.839235\pi$
$5$	−0.207277	+	0.359014i	−0.0185394	+	0.0321112i	0.856607	+	0.515970i	$0.172568\pi$
$6$		0			0
$7$	5.26194	−	17.7570i	0.284118	−	0.958789i
$7$	5.26194	−	17.7570i	0.284118	−	0.958789i
$8$			23.1997i			1.02529i
$9$		0			0
$10$	−0.659923	−	0.381007i	−0.0208686	−	0.0120485i
$11$	42.9636	−	24.8051i	1.17764	−	0.679910i	0.222172	−	0.975008i	$-0.428686\pi$
$11$	42.9636	−	24.8051i	1.17764	−	0.679910i	0.955467	+	0.295098i	$0.0953522\pi$
$12$		0			0
$13$	−1.43477	+	0.828367i	−0.0306104	+	0.0176729i	−0.515227	−	0.857054i	$-0.672292\pi$
$13$	−1.43477	+	0.828367i	−0.0306104	+	0.0176729i	0.484617	+	0.874727i	$0.338959\pi$
$14$	32.6401	+	9.67225i	0.623103	+	0.184644i
$15$		0			0
$16$	−5.67501			−0.0886721
$17$	−20.6496	+	35.7662i	−0.294604	+	0.510269i	−0.974893	−	0.222675i	$-0.928521\pi$
$17$	−20.6496	+	35.7662i	−0.294604	+	0.510269i	0.680289	+	0.732944i	$0.261854\pi$
$18$		0			0
$19$	130.814	−	75.5256i	1.57952	−	0.911935i	0.584592	−	0.811327i	$-0.301255\pi$
$19$	130.814	−	75.5256i	1.57952	−	0.911935i	0.994926	−	0.100608i	$-0.0320787\pi$
$20$	−0.957866	+	1.65907i	−0.0107093	+	0.0185490i
$21$		0			0
$22$	45.5955	+	78.9737i	0.441863	+	0.765330i
$23$	−114.013	−	65.8253i	−1.03362	−	0.596762i	−0.115602	−	0.993296i	$-0.536880\pi$
$23$	−114.013	−	65.8253i	−1.03362	−	0.596762i	−0.918020	+	0.396534i	$0.870213\pi$
$24$		0			0
$25$	62.4141	+	108.104i	0.499313	+	0.864835i
$26$	−1.52267	−	2.63733i	−0.0114854	−	0.0198932i
$27$		0			0
$28$	24.3164	−	82.0587i	0.164121	−	0.553844i
$29$	136.539	+	78.8310i	0.874300	+	0.504777i	0.868775	−	0.495207i	$-0.164908\pi$
$29$	136.539	+	78.8310i	0.874300	+	0.504777i	0.00552512	+	0.999985i	$0.498241\pi$
$30$		0			0
$31$		−	18.4071i		−	0.106646i	−0.998577	−	0.0533229i	$-0.983019\pi$
$31$		−	18.4071i		−	0.106646i	0.998577	−	0.0533229i	$-0.0169813\pi$
$32$			175.166i			0.967664i
$33$		0			0
$34$	−65.7437	−	37.9571i	−0.331616	−	0.191459i
$35$	5.28434	+	5.56973i	0.0255205	+	0.0268988i
$36$		0			0
$37$	173.836	+	301.092i	0.772390	+	1.33782i	0.936250	+	0.351335i	$0.114272\pi$
$37$	173.836	+	301.092i	0.772390	+	1.33782i	−0.163860	+	0.986484i	$0.552395\pi$
$38$	138.828	+	240.457i	0.592653	+	1.02651i
$39$		0			0
$40$	−8.32901	−	4.80876i	−0.0329233	−	0.0190083i
$41$	−16.9818	−	29.4134i	−0.0646857	−	0.112039i	0.831869	−	0.554972i	$-0.187271\pi$
$41$	−16.9818	−	29.4134i	−0.0646857	−	0.112039i	−0.896555	+	0.442933i	$0.853938\pi$
$42$		0			0
$43$	29.5623	−	51.2034i	0.104842	−	0.181592i	−0.808832	−	0.588040i	$-0.799900\pi$
$43$	29.5623	−	51.2034i	0.104842	−	0.181592i	0.913674	+	0.406449i	$0.133233\pi$
$44$	198.543	−	114.629i	0.680262	−	0.392749i
$45$		0			0
$46$	120.997	−	209.573i	0.387827	−	0.671736i
$47$	−216.532			−0.672011			−0.336005	−	0.941860i	$-0.609076\pi$
$47$	−216.532			−0.672011			−0.336005	+	0.941860i	$0.609076\pi$
$48$		0			0
$49$	−287.624	−	186.873i	−0.838554	−	0.544819i
$50$	−198.712	+	114.727i	−0.562043	+	0.324496i
$51$		0			0
$52$	−6.63037	+	3.82805i	−0.0176821	+	0.0102087i
$53$	174.040	+	100.482i	0.451062	+	0.260421i	0.708278	−	0.705933i	$-0.249472\pi$
$53$	174.040	+	100.482i	0.451062	+	0.260421i	−0.257217	+	0.966354i	$0.582805\pi$
$54$		0			0
$55$			20.5661i			0.0504205i
$56$	411.957	+	122.075i	0.983038	+	0.291304i
$57$		0			0
$58$	−144.903	+	250.980i	−0.328047	+	0.568195i
$59$	−299.637			−0.661177			−0.330588	−	0.943775i	$-0.607247\pi$
$59$	−299.637			−0.661177			−0.330588	+	0.943775i	$0.607247\pi$
$60$		0			0
$61$			80.4280i			0.168816i	0.996431	+	0.0844078i	$0.0268998\pi$
$61$			80.4280i			0.168816i	−0.996431	+	0.0844078i	$0.973100\pi$
$62$	33.8351			0.0693075
$63$		0			0
$64$	−367.382			−0.717543
$65$		−	0.686806i		−	0.00131058i
$66$		0			0
$67$	−257.576			−0.469670			−0.234835	−	0.972035i	$-0.575455\pi$
$67$	−257.576			−0.469670			−0.234835	+	0.972035i	$0.575455\pi$
$68$	−95.4259	+	165.282i	−0.170178	+	0.294756i
$69$		0			0
$70$	−10.2380	+	9.71343i	−0.0174811	+	0.0165854i
$71$		−	1032.80i		−	1.72635i	−0.504902	−	0.863177i	$-0.668471\pi$
$71$		−	1032.80i		−	1.72635i	0.504902	−	0.863177i	$-0.331529\pi$
$72$		0			0
$73$	−711.100	−	410.554i	−1.14011	−	0.658243i	−0.193652	−	0.981070i	$-0.562033\pi$
$73$	−711.100	−	410.554i	−1.14011	−	0.658243i	−0.946458	+	0.322828i	$0.895367\pi$
$74$	−553.454	+	319.537i	−0.869428	+	0.501965i
$75$		0			0
$76$	604.518	−	349.019i	0.912407	−	0.526779i
$77$	−214.392	−	893.429i	−0.317302	−	1.32228i
$78$		0			0
$79$	105.318			0.149990			0.0749948	−	0.997184i	$-0.476106\pi$
$79$	105.318			0.149990			0.0749948	+	0.997184i	$0.476106\pi$
$80$	1.17630	−	2.03741i	0.00164393	−	0.00284737i
$81$		0			0
$82$	54.0663	−	31.2152i	0.0728125	−	0.0420383i
$83$	245.110	−	424.542i	0.324148	−	0.561441i	−0.657192	−	0.753724i	$-0.728256\pi$
$83$	245.110	−	424.542i	0.324148	−	0.561441i	0.981340	+	0.192283i	$0.0615891\pi$
$84$		0			0
$85$	−8.56037	−	14.8270i	−0.0109236	−	0.0189202i
$86$	94.1196	+	54.3400i	0.118014	+	0.0681352i
$87$		0			0
$88$	575.470	+	996.743i	0.697105	+	1.20742i
$89$	−754.828	−	1307.40i	−0.899007	−	1.55713i	−0.828766	−	0.559596i	$-0.810956\pi$
$89$	−754.828	−	1307.40i	−0.899007	−	1.55713i	−0.0702410	−	0.997530i	$-0.522377\pi$
$90$		0			0
$91$	7.15964	+	29.8361i	0.00824763	+	0.0343701i
$92$	−526.875	−	304.191i	−0.597071	−	0.344719i
$93$		0			0
$94$		−	398.020i		−	0.436730i
$95$			62.6189i			0.0676269i
$96$		0			0
$97$	−1087.14	−	627.661i	−1.13796	−	0.657003i	−0.192037	−	0.981388i	$-0.561510\pi$
$97$	−1087.14	−	627.661i	−1.13796	−	0.657003i	−0.945925	+	0.324384i	$0.894843\pi$
$98$	343.501	−	528.697i	0.354070	−	0.544964i
$99$		0			0
$100$	288.428	+	499.571i	0.288428	+	0.499571i
$101$	600.746	+	1040.52i	0.591846	+	1.02511i	0.993984	+	0.109529i	$0.0349342\pi$
$101$	600.746	+	1040.52i	0.591846	+	1.02511i	−0.402137	+	0.915579i	$0.631733\pi$
$102$		0			0
$103$	190.013	+	109.704i	0.181773	+	0.104946i	0.588125	−	0.808770i	$-0.299866\pi$
$103$	190.013	+	109.704i	0.181773	+	0.104946i	−0.406353	+	0.913716i	$0.633200\pi$
$104$	−19.2179	−	33.2863i	−0.0181199	−	0.0313845i
$105$		0			0
$106$	−184.702	+	319.913i	−0.169243	+	0.293138i
$107$	165.493	−	95.5472i	0.149521	−	0.0863261i	−0.423373	−	0.905956i	$-0.639154\pi$
$107$	165.493	−	95.5472i	0.149521	−	0.0863261i	0.572894	+	0.819629i	$0.305821\pi$
$108$		0			0
$109$	−761.102	+	1318.27i	−0.668810	+	1.15841i	0.309427	+	0.950923i	$0.399863\pi$
$109$	−761.102	+	1318.27i	−0.668810	+	1.15841i	−0.978237	+	0.207490i	$0.933470\pi$
$110$	−37.8036			−0.0327675
$111$		0			0
$112$	−29.8616	+	100.771i	−0.0251933	+	0.0850178i
$113$	−1363.73	+	787.351i	−1.13530	+	0.655467i	−0.945263	−	0.326310i	$-0.894195\pi$
$113$	−1363.73	+	787.351i	−1.13530	+	0.655467i	−0.190039	+	0.981777i	$0.560861\pi$
$114$		0			0
$115$	47.2644	−	27.2881i	0.0383255	−	0.0221272i
$116$	630.974	+	364.293i	0.505039	+	0.291584i
$117$		0			0
$118$		−	550.779i		−	0.429689i
$119$	526.444	+	554.875i	0.405538	+	0.427440i
$120$		0			0
$121$	565.083	−	978.752i	0.424555	−	0.735351i
$122$	−147.839			−0.109711
$123$		0			0
$124$		−	85.0630i		−	0.0616039i
$125$	−103.567			−0.0741066
$126$		0			0
$127$	84.3766			0.0589544			0.0294772	−	0.999565i	$-0.490616\pi$
$127$	84.3766			0.0589544			0.0294772	+	0.999565i	$0.490616\pi$
$128$			726.023i			0.501344i
$129$		0			0
$130$	1.26245			0.000851727
$131$	−396.233	+	686.295i	−0.264267	+	0.457724i	−0.967371	−	0.253363i	$-0.918463\pi$
$131$	−396.233	+	686.295i	−0.264267	+	0.457724i	0.703104	+	0.711087i	$0.251797\pi$
$132$		0			0
$133$	−652.774	−	2720.28i	−0.425584	−	1.77352i
$134$		−	473.464i		−	0.305232i
$135$		0			0
$136$	−829.764	−	479.064i	−0.523174	−	0.302055i
$137$	587.944	−	339.450i	0.366653	−	0.211687i	−0.305342	−	0.952243i	$-0.598771\pi$
$137$	587.944	−	339.450i	0.366653	−	0.211687i	0.671995	+	0.740556i	$0.265438\pi$
$138$		0			0
$139$	−2217.73	+	1280.41i	−1.35328	+	0.781314i	−0.988707	−	0.149863i	$-0.952117\pi$
$139$	−2217.73	+	1280.41i	−1.35328	+	0.781314i	−0.364568	+	0.931177i	$0.618783\pi$
$140$	24.4200	+	25.7388i	0.0147419	+	0.0155380i
$141$		0			0
$142$	1898.45			1.12193
$143$	−41.0954	+	71.1794i	−0.0240320	+	0.0416246i
$144$		0			0
$145$	−56.6028	+	32.6797i	−0.0324180	+	0.0187165i
$146$	754.661	−	1307.11i	0.427782	−	0.740940i
$147$		0			0
$148$	803.329	+	1391.41i	0.446170	+	0.772790i
$149$	2041.86	+	1178.87i	1.12266	+	0.648167i	0.942078	−	0.335394i	$-0.108869\pi$
$149$	2041.86	+	1178.87i	1.12266	+	0.648167i	0.180580	+	0.983560i	$0.442203\pi$
$150$		0			0
$151$	−296.427	−	513.427i	−0.159754	−	0.276703i	0.775026	−	0.631930i	$-0.217737\pi$
$151$	−296.427	−	513.427i	−0.159754	−	0.276703i	−0.934780	+	0.355227i	$0.884404\pi$
$152$	1752.17	+	3034.85i	0.934999	+	1.61947i
$153$		0			0
$154$	1642.26	−	394.086i	0.859331	−	0.206210i
$155$	6.60842	+	3.81537i	0.00342452	+	0.00197715i
$156$		0			0
$157$			1862.93i			0.946995i	0.880795	+	0.473498i	$0.157009\pi$
$157$			1862.93i			0.946995i	−0.880795	+	0.473498i	$0.842991\pi$
$158$			193.590i			0.0974760i
$159$		0			0
$160$	−62.8870	−	36.3078i	−0.0310728	−	0.0179399i
$161$	−1768.79	+	1678.16i	−0.865840	+	0.821475i
$162$		0			0
$163$	1052.23	+	1822.52i	0.505627	+	0.875771i	0.999979	+	0.00650957i	$0.00207207\pi$
$163$	1052.23	+	1822.52i	0.505627	+	0.875771i	−0.494352	+	0.869262i	$0.664595\pi$
$164$	−78.4763	−	135.925i	−0.0373657	−	0.0647192i
$165$		0			0
$166$	780.374	+	450.549i	0.364872	+	0.210659i
$167$	−970.922	−	1681.69i	−0.449893	−	0.779238i	0.548485	−	0.836160i	$-0.315205\pi$
$167$	−970.922	−	1681.69i	−0.449893	−	0.779238i	−0.998379	+	0.0569221i	$0.981871\pi$
$168$		0			0
$169$	−1097.13	+	1900.28i	−0.499375	+	0.864943i
$170$	27.2543	−	15.7353i	0.0122959	−	0.00709906i
$171$		0			0
$172$	136.613	−	236.621i	0.0605619	−	0.104896i
$173$	430.049			0.188994			0.0944971	−	0.995525i	$-0.469876\pi$
$173$	430.049			0.188994			0.0944971	+	0.995525i	$0.469876\pi$
$174$		0			0
$175$	2248.03	−	539.450i	0.971058	−	0.233020i
$176$	−243.819	+	140.769i	−0.104424	+	0.0602890i
$177$		0			0
$178$	2403.20	−	1387.49i	1.01195	−	0.584251i
$179$	−316.818	−	182.915i	−0.132291	−	0.0763783i	0.432394	−	0.901685i	$-0.357669\pi$
$179$	−316.818	−	182.915i	−0.132291	−	0.0763783i	−0.564685	+	0.825307i	$0.691002\pi$
$180$		0			0
$181$		−	3311.27i		−	1.35980i	−0.733303	−	0.679902i	$-0.762022\pi$
$181$		−	3311.27i		−	1.35980i	0.733303	−	0.679902i	$-0.237978\pi$
$182$	−54.8434	+	13.1605i	−0.0223366	+	0.00536001i
$183$		0			0
$184$	1527.13	−	2645.06i	0.611854	−	1.05976i
$185$	−144.128			−0.0572786
$186$		0			0
$187$			2048.86i			0.801217i
$188$	−1000.64			−0.388187
$189$		0			0
$190$	−115.103			−0.0439497
$191$			4007.12i			1.51804i	0.651069	+	0.759019i	$0.274321\pi$
$191$			4007.12i			1.51804i	−0.651069	+	0.759019i	$0.725679\pi$
$192$		0			0
$193$	2336.92			0.871582			0.435791	−	0.900048i	$-0.356469\pi$
$193$	2336.92			0.871582			0.435791	+	0.900048i	$0.356469\pi$
$194$	1153.74	−	1998.33i	0.426977	−	0.739545i
$195$		0			0
$196$	−1329.17	−	863.576i	−0.484390	−	0.314714i
$197$		−	337.074i		−	0.121906i	−0.998141	−	0.0609531i	$-0.980586\pi$
$197$		−	337.074i		−	0.121906i	0.998141	−	0.0609531i	$-0.0194140\pi$
$198$		0			0
$199$	4282.30	+	2472.39i	1.52545	+	0.880719i	0.999545	+	0.0301752i	$0.00960652\pi$
$199$	4282.30	+	2472.39i	1.52545	+	0.880719i	0.525905	+	0.850543i	$0.323727\pi$
$200$	−2507.99	+	1447.99i	−0.886707	+	0.511941i
$201$		0			0
$202$	−1912.64	+	1104.26i	−0.666203	+	0.384632i
$203$	2118.26	−	2009.73i	0.732379	−	0.694853i
$204$		0			0
$205$	14.0798			0.00479694
$206$	−201.653	+	349.274i	−0.0682032	+	0.118131i
$207$		0			0
$208$	8.14236	−	4.70100i	0.00271429	−	0.00156709i
$209$	3746.84	−	6489.71i	1.24007	−	2.14786i
$210$		0			0
$211$	−600.104	−	1039.41i	−0.195795	−	0.339128i	0.751366	−	0.659886i	$-0.229396\pi$
$211$	−600.104	−	1039.41i	−0.195795	−	0.339128i	−0.947161	+	0.320758i	$0.896062\pi$
$212$	804.274	+	464.348i	0.260555	+	0.150432i
$213$		0			0
$214$	175.630	+	304.201i	0.0561021	+	0.0971716i
$215$	12.2551	+	21.2265i	0.00388741	+	0.00673320i
$216$		0			0
$217$	−326.856	−	96.8573i	−0.102251	−	0.0303000i
$218$	−2423.18	−	1399.02i	−0.752836	−	0.434650i
$219$		0			0
$220$			95.0398i			0.0291254i
$221$		−	68.4219i		−	0.0208260i
$222$		0			0
$223$	−1065.22	−	615.003i	−0.319875	−	0.184680i	0.331462	−	0.943469i	$-0.392458\pi$
$223$	−1065.22	−	615.003i	−0.319875	−	0.184680i	−0.651337	+	0.758789i	$0.725792\pi$
$224$	3110.43	+	921.713i	0.927786	+	0.274931i
$225$		0			0
$226$	−1447.27	−	2506.75i	−0.425978	−	0.737816i
$227$	−911.928	−	1579.51i	−0.266638	−	0.461830i	0.701354	−	0.712813i	$-0.252579\pi$
$227$	−911.928	−	1579.51i	−0.266638	−	0.461830i	−0.967991	+	0.250983i	$0.919246\pi$
$228$		0			0
$229$	−4440.87	−	2563.94i	−1.28149	−	0.739869i	−0.304369	−	0.952554i	$-0.598446\pi$
$229$	−4440.87	−	2563.94i	−1.28149	−	0.739869i	−0.977121	+	0.212685i	$0.931779\pi$
$230$	50.1597	+	86.8792i	0.0143802	+	0.0249072i
$231$		0			0
$232$	−1828.85	+	3167.67i	−0.517544	+	0.896412i
$233$	−3036.86	+	1753.33i	−0.853869	+	0.492981i	−0.861954	−	0.506986i	$-0.830760\pi$
$233$	−3036.86	+	1753.33i	−0.853869	+	0.492981i	0.00808557	+	0.999967i	$0.497426\pi$
$234$		0			0
$235$	44.8822	−	77.7382i	0.0124587	−	0.0215791i
$236$	−1384.68			−0.381928
$237$		0			0
$238$	−1019.95	+	967.684i	−0.277787	+	0.263553i
$239$	−3414.05	+	1971.10i	−0.924002	+	0.533473i	−0.884910	−	0.465763i	$-0.845780\pi$
$239$	−3414.05	+	1971.10i	−0.924002	+	0.533473i	−0.0390925	+	0.999236i	$0.512447\pi$
$240$		0			0
$241$	−885.315	+	511.137i	−0.236631	+	0.136619i	−0.613627	−	0.789596i	$-0.710290\pi$
$241$	−885.315	+	511.137i	−0.236631	+	0.136619i	0.376996	+	0.926215i	$0.376957\pi$
$242$	1799.10	+	1038.71i	0.477894	+	0.275912i
$243$		0			0
$244$			371.673i			0.0975162i
$245$	126.708	−	64.5266i	0.0330411	−	0.0168263i
$246$		0			0
$247$	−125.126	+	216.725i	−0.0322331	+	0.0558294i
$248$	427.040			0.109343
$249$		0			0
$250$		−	190.372i		−	0.0481608i
$251$	−646.886			−0.162674			−0.0813369	−	0.996687i	$-0.525919\pi$
$251$	−646.886			−0.162674			−0.0813369	+	0.996687i	$0.525919\pi$
$252$		0			0
$253$	−6531.20			−1.62298
$254$			155.097i			0.0383136i
$255$		0			0
$256$	−4273.60			−1.04336
$257$	−594.642	+	1029.95i	−0.144330	+	0.249987i	−0.929123	−	0.369772i	$-0.879436\pi$
$257$	−594.642	+	1029.95i	−0.144330	+	0.249987i	0.784793	+	0.619758i	$0.212769\pi$
$258$		0			0
$259$	6261.22	−	1502.48i	1.50214	−	0.360461i
$260$		−	3.17386i		−	0.000757056i
$261$		0			0
$262$	−1261.52	−	728.336i	−0.297468	−	0.171743i
$263$	−4129.05	+	2383.91i	−0.968093	+	0.558928i	−0.898654	−	0.438658i	$-0.855454\pi$
$263$	−4129.05	+	2383.91i	−0.968093	+	0.558928i	−0.0694383	+	0.997586i	$0.522121\pi$
$264$		0			0
$265$	−72.1490	+	41.6553i	−0.0167248	+	0.00965608i
$266$	5000.30	−	1199.90i	1.15259	−	0.276581i
$267$		0			0
$268$	−1190.31			−0.271304
$269$	2176.22	−	3769.33i	0.493259	−	0.854350i	−0.506711	−	0.862116i	$-0.669139\pi$
$269$	2176.22	−	3769.33i	0.493259	−	0.854350i	0.999970	+	0.00776629i	$0.00247211\pi$
$270$		0			0
$271$	−476.614	+	275.173i	−0.106835	+	0.0616811i	−0.552465	−	0.833536i	$-0.686313\pi$
$271$	−476.614	+	275.173i	−0.106835	+	0.0616811i	0.445631	+	0.895217i	$0.352979\pi$
$272$	117.187	−	202.974i	0.0261231	−	0.0452466i
$273$		0			0
$274$	623.960	+	1080.73i	0.137572	+	0.238282i
$275$	5363.07	+	3096.37i	1.17602	+	0.678975i
$276$		0			0
$277$	728.078	+	1261.07i	0.157928	+	0.273539i	0.934121	−	0.356956i	$-0.116185\pi$
$277$	728.078	+	1261.07i	0.157928	+	0.273539i	−0.776194	+	0.630495i	$0.782852\pi$
$278$	−2353.58	−	4076.52i	−0.507764	−	0.879473i
$279$		0			0
$280$	−129.216	+	122.595i	−0.0275790	+	0.0261659i
$281$	−6158.20	−	3555.44i	−1.30736	−	0.754803i	−0.325702	−	0.945472i	$-0.605601\pi$
$281$	−6158.20	−	3555.44i	−1.30736	−	0.754803i	−0.981654	+	0.190670i	$0.938934\pi$
$282$		0			0
$283$		−	2719.57i		−	0.571242i	−0.958343	−	0.285621i	$-0.907800\pi$
$283$		−	2719.57i		−	0.571242i	0.958343	−	0.285621i	$-0.0921998\pi$
$284$		−	4772.78i		−	0.997227i
$285$		0			0
$286$	−130.839	−	75.5397i	−0.0270512	−	0.0156180i
$287$	−611.651	+	146.775i	−0.125800	+	0.0301877i
$288$		0			0
$289$	1603.69	+	2777.67i	0.326417	+	0.565371i
$290$	−60.0702	−	104.045i	−0.0121636	−	0.0210680i
$291$		0			0
$292$	−3286.13	−	1897.25i	−0.658583	−	0.380233i
$293$	2004.64	+	3472.14i	0.399701	+	0.692302i	0.993689	−	0.112172i	$-0.0357808\pi$
$293$	2004.64	+	3472.14i	0.399701	+	0.692302i	−0.593988	+	0.804474i	$0.702447\pi$
$294$		0			0
$295$	62.1078	−	107.574i	0.0122578	−	0.0212312i
$296$	−6985.25	+	4032.93i	−1.37165	+	0.791924i
$297$		0			0
$298$	−2166.94	+	3753.26i	−0.421234	+	0.729599i
$299$	218.110			0.0421861
$300$		0			0
$301$	−753.664	−	794.367i	−0.144321	−	0.152115i
$302$	943.758	−	544.879i	0.179825	−	0.103822i
$303$		0			0
$304$	−742.372	+	428.609i	−0.140059	+	0.0808632i
$305$	−28.8748	−	16.6709i	−0.00542087	−	0.00312974i
$306$		0			0
$307$		−	3968.59i		−	0.737783i	−0.929473	−	0.368891i	$-0.879737\pi$
$307$		−	3968.59i		−	0.737783i	0.929473	−	0.368891i	$-0.120263\pi$
$308$	−990.748	−	4128.71i	−0.183289	−	0.763815i
$309$		0			0
$310$	−7.01324	+	12.1473i	−0.00128492	+	0.00222555i
$311$	4775.19			0.870662			0.435331	−	0.900270i	$-0.356631\pi$
$311$	4775.19			0.870662			0.435331	+	0.900270i	$0.356631\pi$
$312$		0			0
$313$			9619.62i			1.73717i	0.495544	+	0.868583i	$0.334969\pi$
$313$			9619.62i			1.73717i	−0.495544	+	0.868583i	$0.665031\pi$
$314$	−3424.36			−0.615438
$315$		0			0
$316$	486.694			0.0866414
$317$		−	8978.58i		−	1.59081i	−0.606077	−	0.795406i	$-0.707258\pi$
$317$		−	8978.58i		−	1.59081i	0.606077	−	0.795406i	$-0.292742\pi$
$318$		0			0
$319$	7821.63			1.37281
$320$	76.1497	−	131.895i	0.0133028	−	0.0230411i
$321$		0			0
$322$	−3084.71	−	3251.31i	−0.533864	−	0.562696i
$323$			6238.30i			1.07464i
$324$		0			0
$325$	−179.100	−	103.404i	−0.0305683	−	0.0176486i
$326$	−3350.07	+	1934.16i	−0.569151	+	0.328599i
$327$		0			0
$328$	682.381	−	393.973i	0.114873	−	0.0663217i
$329$	−1139.38	+	3844.97i	−0.190930	+	0.644317i
$330$		0			0
$331$	−1143.07			−0.189814			−0.0949072	−	0.995486i	$-0.530255\pi$
$331$	−1143.07			−0.189814			−0.0949072	+	0.995486i	$0.530255\pi$
$332$	1132.70	−	1961.89i	0.187244	−	0.324316i
$333$		0			0
$334$	3091.20	−	1784.70i	0.506415	−	0.292379i
$335$	53.3895	−	92.4733i	0.00870740	−	0.0150817i
$336$		0			0
$337$	2865.89	+	4963.87i	0.463250	+	0.802372i	0.999121	−	0.0419278i	$-0.0133499\pi$
$337$	2865.89	+	4963.87i	0.463250	+	0.802372i	−0.535871	+	0.844300i	$0.680017\pi$
$338$	−3493.01	−	2016.69i	−0.562114	−	0.324537i
$339$		0			0
$340$	−39.5591	−	68.5184i	−0.00630999	−	0.0109292i
$341$	−456.591	−	790.838i	−0.0725096	−	0.125590i
$342$		0			0
$343$	−4831.77	+	4124.03i	−0.760615	+	0.649204i
$344$	1187.90	+	685.835i	0.186184	+	0.107493i
$345$		0			0
$346$			790.495i			0.122825i
$347$		−	3185.69i		−	0.492844i	−0.969163	−	0.246422i	$-0.920745\pi$
$347$		−	3185.69i		−	0.492844i	0.969163	−	0.246422i	$-0.0792550\pi$
$348$		0			0
$349$	−6403.54	−	3697.08i	−0.982159	−	0.567050i	−0.0792376	−	0.996856i	$-0.525249\pi$
$349$	−6403.54	−	3697.08i	−0.982159	−	0.567050i	−0.902921	+	0.429806i	$0.858582\pi$
$350$	991.591	+	4132.22i	0.151436	+	0.631076i
$351$		0			0
$352$	4345.00	+	7525.77i	0.657925	+	1.13956i
$353$	5544.94	+	9604.11i	0.836055	+	1.44809i	0.893169	+	0.449721i	$0.148477\pi$
$353$	5544.94	+	9604.11i	0.836055	+	1.44809i	−0.0571144	+	0.998368i	$0.518190\pi$
$354$		0			0
$355$	370.791	+	214.076i	0.0554353	+	0.0320056i
$356$	−3488.21	−	6041.75i	−0.519311	−	0.899472i
$357$		0			0
$358$	336.226	−	582.360i	0.0496371	−	0.0859740i
$359$	8302.65	−	4793.54i	1.22060	−	0.704716i	0.255558	−	0.966794i	$-0.417741\pi$
$359$	8302.65	−	4793.54i	1.22060	−	0.704716i	0.965047	+	0.262077i	$0.0844076\pi$
$360$		0			0
$361$	7978.74	−	13819.6i	1.16325	−	2.01481i
$362$	6086.62			0.883717
$363$		0			0
$364$	33.0861	+	137.879i	0.00476424	+	0.0198539i
$365$	294.789	−	170.197i	0.0422739	−	0.0244068i
$366$		0			0
$367$	10066.1	−	5811.67i	1.43173	−	0.826612i	0.434481	−	0.900681i	$-0.356932\pi$
$367$	10066.1	−	5811.67i	1.43173	−	0.826612i	0.997253	+	0.0740684i	$0.0235983\pi$
$368$	647.024	+	373.559i	0.0916534	+	0.0529161i
$369$		0			0
$370$		−	264.930i		−	0.0372245i
$371$	2700.05	−	2561.71i	0.377843	−	0.358483i
$372$		0			0
$373$	1951.28	−	3379.72i	0.270867	−	0.469156i	−0.698217	−	0.715886i	$-0.746023\pi$
$373$	1951.28	−	3379.72i	0.270867	−	0.469156i	0.969084	+	0.246731i	$0.0793563\pi$
$374$	−3766.12			−0.520699
$375$		0			0
$376$		−	5023.49i		−	0.689007i
$377$	−261.204			−0.0356835
$378$		0			0
$379$	−699.252			−0.0947709			−0.0473855	−	0.998877i	$-0.515089\pi$
$379$	−699.252			−0.0947709			−0.0473855	+	0.998877i	$0.515089\pi$
$380$			289.374i			0.0390647i
$381$		0			0
$382$	−7365.70			−0.986550
$383$	−5079.23	+	8797.49i	−0.677641	+	1.17371i	0.298048	+	0.954551i	$0.403664\pi$
$383$	−5079.23	+	8797.49i	−0.677641	+	1.17371i	−0.975689	+	0.219158i	$0.929669\pi$
$384$		0			0
$385$	365.192	+	108.217i	0.0483426	+	0.0143254i
$386$			4295.62i			0.566428i
$387$		0			0
$388$	−5023.89	−	2900.54i	−0.657343	−	0.379517i
$389$	4121.08	−	2379.30i	0.537139	−	0.310117i	−0.206780	−	0.978387i	$-0.566298\pi$
$389$	4121.08	−	2379.30i	0.537139	−	0.310117i	0.743918	+	0.668270i	$0.232965\pi$
$390$		0			0
$391$	4708.64	−	2718.53i	0.609018	−	0.351617i
$392$	4335.39	−	6672.79i	0.558598	−	0.859762i
$393$		0			0
$394$	619.594			0.0792251
$395$	−21.8299	+	37.8106i	−0.00278072	+	0.00481635i
$396$		0			0
$397$	6232.29	−	3598.21i	0.787883	−	0.454885i	−0.0513336	−	0.998682i	$-0.516347\pi$
$397$	6232.29	−	3598.21i	0.787883	−	0.454885i	0.839217	+	0.543797i	$0.183014\pi$
$398$	−4544.63	+	7871.53i	−0.572366	+	0.991367i
$399$		0			0
$400$	−354.201	−	613.494i	−0.0442751	−	0.0766867i
$401$	−5831.21	−	3366.65i	−0.726177	−	0.419258i	0.0908451	−	0.995865i	$-0.471043\pi$
$401$	−5831.21	−	3366.65i	−0.726177	−	0.419258i	−0.817022	+	0.576607i	$0.804377\pi$
$402$		0			0
$403$	15.2479	+	26.4101i	0.00188474	+	0.00326447i
$404$	2776.17	+	4808.46i	0.341880	+	0.592153i
$405$		0			0
$406$	3694.18	+	3893.69i	0.451575	+	0.475963i
$407$	14937.2	+	8624.01i	1.81919	+	1.05031i
$408$		0			0
$409$			10901.2i			1.31792i	0.752178	+	0.658960i	$0.229003\pi$
$409$			10901.2i			1.31792i	−0.752178	+	0.658960i	$0.770997\pi$
$410$			25.8807i			0.00311746i
$411$		0			0
$412$	878.089	+	506.965i	0.105001	+	0.0606223i
$413$	−1576.67	+	5320.66i	−0.187852	+	0.633929i
$414$		0			0
$415$	101.611	+	175.996i	0.0120190	+	0.0208175i
$416$	−145.102	−	251.324i	−0.0171014	−	0.0296206i
$417$		0			0
$418$	11929.1	+	6887.26i	1.39586	+	0.805902i
$419$	8088.59	+	14009.8i	0.943087	+	1.63347i	0.759538	+	0.650463i	$0.225425\pi$
$419$	8088.59	+	14009.8i	0.943087	+	1.63347i	0.183549	+	0.983011i	$0.441241\pi$
$420$		0			0
$421$	2966.25	−	5137.69i	0.343387	−	0.594764i	−0.641672	−	0.766979i	$-0.721759\pi$
$421$	2966.25	−	5137.69i	0.343387	−	0.594764i	0.985059	+	0.172215i	$0.0550924\pi$
$422$	1910.60	−	1103.08i	0.220394	−	0.127245i
$423$		0			0
$424$	−2331.15	+	4037.68i	−0.267007	+	0.462469i
$425$	−5155.31			−0.588398
$426$		0			0
$427$	1428.16	+	423.207i	0.161859	+	0.0479636i
$428$	764.773	−	441.542i	0.0863708	−	0.0498662i
$429$		0			0
$430$	−39.0176	+	22.5268i	−0.00437581	+	0.00252637i
$431$	5735.59	+	3311.44i	0.641006	+	0.370085i	0.785002	−	0.619493i	$-0.212662\pi$
$431$	5735.59	+	3311.44i	0.641006	+	0.370085i	−0.143996	+	0.989578i	$0.545995\pi$
$432$		0			0
$433$			9664.86i			1.07266i	0.844007	+	0.536332i	$0.180191\pi$
$433$			9664.86i			1.07266i	−0.844007	+	0.536332i	$0.819809\pi$
$434$	178.039	−	600.812i	0.0196915	−	0.0664513i
$435$		0			0
$436$	−3517.20	+	6091.97i	−0.386338	+	0.669157i
$437$	−19886.0			−2.17683
$438$		0			0
$439$		−	5639.26i		−	0.613092i	−0.951856	−	0.306546i	$-0.900827\pi$
$439$		−	5639.26i		−	0.613092i	0.951856	−	0.306546i	$-0.0991733\pi$
$440$	−477.126			−0.0516957
$441$		0			0
$442$	125.770			0.0135345
$443$			8525.26i			0.914328i	0.889382	+	0.457164i	$0.151135\pi$
$443$			8525.26i			0.914328i	−0.889382	+	0.457164i	$0.848865\pi$
$444$		0			0
$445$	625.833			0.0666682
$446$	1130.47	−	1958.03i	0.120021	−	0.207882i
$447$		0			0
$448$	−1933.14	+	6523.61i	−0.203867	+	0.687972i
$449$		−	12740.7i		−	1.33914i	−0.742751	−	0.669568i	$-0.766479\pi$
$449$		−	12740.7i		−	1.33914i	0.742751	−	0.669568i	$-0.233521\pi$
$450$		0			0
$451$	−1459.20	−	842.470i	−0.152353	−	0.0879609i
$452$	−6302.07	+	3638.50i	−0.655806	+	0.378630i
$453$		0			0
$454$	2903.37	−	1676.26i	0.300137	−	0.173284i
$455$	−12.1956	−	3.61393i	−0.00125657	−	0.000372360i
$456$		0			0
$457$	−13100.6			−1.34096			−0.670481	−	0.741926i	$-0.733912\pi$
$457$	−13100.6			−1.34096			−0.670481	+	0.741926i	$0.733912\pi$
$458$	4712.91	−	8163.01i	0.480830	−	0.832821i
$459$		0			0
$460$	218.418	−	126.104i	0.0221387	−	0.0127818i
$461$	5864.00	−	10156.8i	0.592438	−	1.02613i	−0.401465	−	0.915874i	$-0.631499\pi$
$461$	5864.00	−	10156.8i	0.592438	−	1.02613i	0.993903	−	0.110258i	$-0.0351678\pi$
$462$		0			0
$463$	−3831.27	−	6635.96i	−0.384567	−	0.666089i	0.607142	−	0.794593i	$-0.292316\pi$
$463$	−3831.27	−	6635.96i	−0.384567	−	0.666089i	−0.991709	+	0.128504i	$0.958982\pi$
$464$	−774.862	−	447.367i	−0.0775260	−	0.0447596i
$465$		0			0
$466$	−3222.89	−	5582.22i	−0.320381	−	0.554917i
$467$	−7179.19	−	12434.7i	−0.711378	−	1.23214i	−0.964340	−	0.264666i	$-0.914738\pi$
$467$	−7179.19	−	12434.7i	−0.711378	−	1.23214i	0.252962	−	0.967476i	$-0.418595\pi$
$468$		0			0
$469$	−1355.35	+	4573.78i	−0.133442	+	0.450315i
$470$	142.895	+	82.5003i	0.0140239	+	0.00809671i
$471$		0			0
$472$		−	6951.49i		−	0.677898i
$473$		−	2933.18i		−	0.285132i
$474$		0			0
$475$	16329.3	+	9427.73i	1.57735	+	0.910681i
$476$	2432.80	+	2564.19i	0.234259	+	0.246910i
$477$		0			0
$478$	−3623.19	−	6275.54i	−0.346696	−	0.600495i
$479$	8731.73	+	15123.8i	0.832908	+	1.44264i	0.895723	+	0.444613i	$0.146659\pi$
$479$	8731.73	+	15123.8i	0.832908	+	1.44264i	−0.0628152	+	0.998025i	$0.520008\pi$
$480$		0			0
$481$	−498.830	−	288.000i	−0.0472863	−	0.0273007i
$482$	−939.547	−	1627.34i	−0.0887867	−	0.153783i
$483$		0			0
$484$	2611.36	−	4523.00i	0.245244	−	0.424775i
$485$	450.678	−	260.199i	0.0421943	−	0.0243609i
$486$		0			0
$487$	−1345.48	+	2330.44i	−0.125194	+	0.216842i	−0.921809	−	0.387645i	$-0.873289\pi$
$487$	−1345.48	+	2330.44i	−0.125194	+	0.216842i	0.796615	+	0.604487i	$0.206622\pi$
$488$	−1865.90			−0.173085
$489$		0			0
$490$	118.610	+	232.908i	0.0109352	+	0.0214729i
$491$	5823.37	−	3362.13i	0.535245	−	0.309024i	−0.207905	−	0.978149i	$-0.566664\pi$
$491$	5823.37	−	3362.13i	0.535245	−	0.309024i	0.743149	+	0.669125i	$0.233331\pi$
$492$		0			0
$493$	−5638.96	+	3255.66i	−0.515144	+	0.297419i
$494$	−398.373	−	230.001i	−0.0362827	−	0.0209478i
$495$		0			0
$496$			104.461i			0.00945651i
$497$	−18339.5	−	5434.55i	−1.65521	−	0.490488i
$498$		0			0
$499$	−101.373	+	175.583i	−0.00909435	+	0.0157519i	−0.870537	−	0.492103i	$-0.836228\pi$
$499$	−101.373	+	175.583i	−0.00909435	+	0.0157519i	0.861442	+	0.507855i	$0.169562\pi$
$500$	−478.604			−0.0428076
$501$		0			0
$502$		−	1189.08i		−	0.105719i
$503$	−7820.60			−0.693247			−0.346624	−	0.938004i	$-0.612672\pi$
$503$	−7820.60			−0.693247			−0.346624	+	0.938004i	$0.612672\pi$
$504$		0			0
$505$	−498.083			−0.0438899
$506$		−	12005.4i		−	1.05475i
$507$		0			0
$508$	389.921			0.0340550
$509$	−4922.62	+	8526.23i	−0.428667	+	0.742472i	−0.996755	−	0.0804953i	$-0.974350\pi$
$509$	−4922.62	+	8526.23i	−0.428667	+	0.742472i	0.568088	+	0.822968i	$0.307683\pi$
$510$		0			0
$511$	−11032.0	+	10466.7i	−0.955042	+	0.906106i
$512$		−	2047.34i		−	0.176719i
$513$		0			0
$514$	−1893.21	−	1093.04i	−0.162463	−	0.0937978i
$515$	−78.7708	+	45.4783i	−0.00673991	+	0.00389129i
$516$		0			0
$517$	−9303.02	+	5371.10i	−0.791386	+	0.456907i
$518$	2761.78	+	11509.1i	0.234258	+	0.976216i
$519$		0			0
$520$	15.9337			0.00134373
$521$	3985.06	−	6902.32i	0.335103	−	0.580415i	−0.648402	−	0.761298i	$-0.724562\pi$
$521$	3985.06	−	6902.32i	0.335103	−	0.580415i	0.983505	+	0.180883i	$0.0578957\pi$
$522$		0			0
$523$	−4651.74	+	2685.68i	−0.388922	+	0.224544i	−0.681693	−	0.731638i	$-0.738756\pi$
$523$	−4651.74	+	2685.68i	−0.388922	+	0.224544i	0.292771	+	0.956183i	$0.405423\pi$
$524$	−1831.07	+	3171.50i	−0.152654	+	0.264404i
$525$		0			0
$526$	−4381.99	−	7589.83i	−0.363239	−	0.629149i
$527$	658.353	+	380.100i	0.0544181	+	0.0314183i
$528$		0			0
$529$	2582.44	+	4472.91i	0.212249	+	0.367627i
$530$	−76.5687	−	132.621i	−0.00627535	−	0.0108692i
$531$		0			0
$532$	−3016.60	−	12571.0i	−0.245838	−	1.02447i
$533$	48.7302	+	28.1344i	0.00396011	+	0.00228637i
$534$		0			0
$535$			79.2189i			0.00640174i
$536$		−	5975.68i		−	0.481548i
$537$		0			0
$538$	6928.60	+	4000.23i	0.555229	+	0.320562i
$539$	−16992.8	−	894.205i	−1.35794	−	0.0714585i
$540$		0			0
$541$	−2172.50	−	3762.88i	−0.172649	−	0.299037i	0.766696	−	0.642010i	$-0.221899\pi$
$541$	−2172.50	−	3762.88i	−0.172649	−	0.299037i	−0.939345	+	0.342973i	$0.888566\pi$
$542$	−505.810	−	876.089i	−0.0400856	−	0.0694303i
$543$		0			0
$544$	−6265.02	−	3617.11i	−0.493769	−	0.285078i
$545$	−315.518	−	546.493i	−0.0247987	−	0.0429526i
$546$		0			0
$547$	4859.25	−	8416.46i	0.379829	−	0.657883i	−0.611208	−	0.791470i	$-0.709316\pi$
$547$	4859.25	−	8416.46i	0.379829	−	0.657883i	0.991037	+	0.133587i	$0.0426495\pi$
$548$	2717.00	−	1568.66i	0.211797	−	0.122281i
$549$		0			0
$550$	−5691.60	+	9858.15i	−0.441256	+	0.764278i
$551$	23815.0			1.84130
$552$		0			0
$553$	554.176	−	1870.13i	0.0426148	−	0.143808i
$554$	−2318.04	+	1338.32i	−0.177769	+	0.102635i
$555$		0			0
$556$	−10248.6	+	5917.00i	−0.781718	+	0.451325i
$557$	13997.2	+	8081.28i	1.06478	+	0.614749i	0.926749	−	0.375680i	$-0.122591\pi$
$557$	13997.2	+	8081.28i	1.06478	+	0.614749i	0.138026	+	0.990429i	$0.455924\pi$
$558$		0			0
$559$			97.9537i			0.00741145i
$560$	−29.9887	−	31.6083i	−0.00226295	−	0.00238517i
$561$		0			0
$562$	6535.43	−	11319.7i	0.490535	−	0.849632i
$563$	−14273.7			−1.06850			−0.534249	−	0.845327i	$-0.679405\pi$
$563$	−14273.7			−1.06850			−0.534249	+	0.845327i	$0.679405\pi$
$564$		0			0
$565$		−	652.798i		−	0.0486078i
$566$	4998.98			0.371242
$567$		0			0
$568$	23960.7			1.77001
$569$		−	12206.0i		−	0.899300i	−0.893205	−	0.449650i	$-0.851549\pi$
$569$		−	12206.0i		−	0.899300i	0.893205	−	0.449650i	$-0.148451\pi$
$570$		0			0
$571$	−18732.1			−1.37288			−0.686438	−	0.727188i	$-0.740827\pi$
$571$	−18732.1			−1.37288			−0.686438	+	0.727188i	$0.740827\pi$
$572$	−189.910	+	328.934i	−0.0138821	+	0.0240444i
$573$		0			0
$574$	−269.795	−	1124.31i	−0.0196185	−	0.0817557i
$575$		−	16433.7i		−	1.19188i
$576$		0			0
$577$	−14902.3	−	8603.86i	−1.07520	−	0.620768i	−0.145604	−	0.989343i	$-0.546513\pi$
$577$	−14902.3	−	8603.86i	−1.07520	−	0.620768i	−0.929598	+	0.368574i	$0.879846\pi$
$578$	−5105.78	+	2947.82i	−0.367426	+	0.212134i
$579$		0			0
$580$	−261.573	+	151.019i	−0.0187262	+	0.0108116i
$581$	−6248.86	−	6586.33i	−0.446207	−	0.470305i
$582$		0			0
$583$	9969.87			0.708250
$584$	9524.72	−	16497.3i	0.674890	−	1.16894i
$585$		0			0
$586$	−6382.32	+	3684.83i	−0.449917	+	0.259759i
$587$	−8021.17	+	13893.1i	−0.564002	+	0.976880i	0.433140	+	0.901327i	$0.357406\pi$
$587$	−8021.17	+	13893.1i	−0.564002	+	0.976880i	−0.997142	+	0.0755529i	$0.975928\pi$
$588$		0			0
$589$	−1390.21	−	2407.92i	−0.0972541	−	0.168449i
$590$	197.737	+	114.164i	0.0137978	+	0.00796618i
$591$		0			0
$592$	−986.520	−	1708.70i	−0.0684894	−	0.118627i
$593$	−7608.23	−	13177.8i	−0.526868	−	0.912562i	−0.999510	−	0.0313075i	$-0.990033\pi$
$593$	−7608.23	−	13177.8i	−0.526868	−	0.912562i	0.472642	−	0.881255i	$-0.343300\pi$
$594$		0			0
$595$	−308.328	+	73.9880i	−0.0212440	+	0.00509783i
$596$	9435.85	+	5447.79i	0.648502	+	0.374413i
$597$		0			0
$598$			400.920i			0.0274161i
$599$		−	25030.0i		−	1.70734i	−0.520815	−	0.853670i	$-0.674372\pi$
$599$		−	25030.0i		−	1.70734i	0.520815	−	0.853670i	$-0.325628\pi$
$600$		0			0
$601$	4104.86	+	2369.94i	0.278604	+	0.160852i	0.632791	−	0.774323i	$-0.281909\pi$
$601$	4104.86	+	2369.94i	0.278604	+	0.160852i	−0.354187	+	0.935174i	$0.615243\pi$
$602$	1460.17	−	1385.35i	0.0988571	−	0.0937918i
$603$		0			0
$604$	−1369.85	−	2372.65i	−0.0922820	−	0.159837i
$605$	234.257	+	405.745i	0.0157420	+	0.0272659i
$606$		0			0
$607$	−9191.69	−	5306.82i	−0.614628	−	0.354855i	0.160147	−	0.987093i	$-0.448803\pi$
$607$	−9191.69	−	5306.82i	−0.614628	−	0.354855i	−0.774774	+	0.632238i	$0.782137\pi$
$608$	13229.5	+	22914.2i	0.882447	+	1.52844i
$609$		0			0
$610$	30.6436	−	53.0763i	0.00203397	−	0.00352294i
$611$	310.675	−	179.368i	0.0205705	−	0.0118764i
$612$		0			0
$613$	6179.57	−	10703.3i	0.407163	−	0.705226i	−0.587408	−	0.809291i	$-0.699852\pi$
$613$	6179.57	−	10703.3i	0.407163	−	0.705226i	0.994571	+	0.104065i	$0.0331849\pi$
$614$	7294.87			0.479474
$615$		0			0
$616$	20727.3	−	4973.83i	1.35572	−	0.325327i
$617$	13982.2	−	8072.63i	0.912322	−	0.526729i	0.0311444	−	0.999515i	$-0.490085\pi$
$617$	13982.2	−	8072.63i	0.912322	−	0.526729i	0.881177	+	0.472786i	$0.156752\pi$
$618$		0			0
$619$	−5823.81	+	3362.38i	−0.378156	+	0.218329i	−0.677016	−	0.735968i	$-0.736727\pi$
$619$	−5823.81	+	3362.38i	−0.378156	+	0.218329i	0.298860	+	0.954297i	$0.403394\pi$
$620$	30.5388	+	17.6316i	0.00197817	+	0.00114210i
$621$		0			0
$622$			8777.52i			0.565830i
$623$	−27187.4	+	6524.04i	−1.74838	+	0.419551i
$624$		0			0
$625$	−7780.29	+	13475.9i	−0.497939	+	0.862455i
$626$	−17682.3			−1.12896
$627$		0			0
$628$			8608.98i			0.547031i
$629$	−14358.6			−0.910196
$630$		0			0
$631$	15753.1			0.993855			0.496928	−	0.867792i	$-0.334461\pi$
$631$	15753.1			0.993855			0.496928	+	0.867792i	$0.334461\pi$
$632$			2443.34i			0.153783i
$633$		0			0
$634$	16504.0			1.03384
$635$	−17.4893	+	30.2924i	−0.00109298	+	0.00189310i
$636$		0			0
$637$	567.475	+	29.8620i	0.0352970	+	0.00185742i
$638$			14377.3i			0.892170i
$639$		0			0
$640$	−260.653	−	150.488i	−0.0160987	−	0.00929462i
$641$	11961.1	−	6905.76i	0.737030	−	0.425525i	−0.0839584	−	0.996469i	$-0.526756\pi$
$641$	11961.1	−	6905.76i	0.737030	−	0.425525i	0.820989	+	0.570945i	$0.193423\pi$
$642$		0			0
$643$	12084.2	−	6976.82i	0.741142	−	0.427899i	−0.0813422	−	0.996686i	$-0.525921\pi$
$643$	12084.2	−	6976.82i	0.741142	−	0.427899i	0.822484	+	0.568788i	$0.192587\pi$
$644$	−8173.92	+	7755.10i	−0.500152	+	0.474524i
$645$		0			0
$646$	−11466.9			−0.698392
$647$	−7274.72	+	12600.2i	−0.442038	+	0.765633i	−0.997841	−	0.0656817i	$-0.979078\pi$
$647$	−7274.72	+	12600.2i	−0.442038	+	0.765633i	0.555802	+	0.831314i	$0.312411\pi$
$648$		0			0
$649$	−12873.5	+	7432.52i	−0.778627	+	0.449541i
$650$	190.072	−	329.214i	0.0114696	−	0.0198659i
$651$		0			0
$652$	4862.57	+	8422.22i	0.292075	+	0.505889i
$653$	1585.21	+	915.223i	0.0949987	+	0.0548475i	0.546747	−	0.837298i	$-0.315866\pi$
$653$	1585.21	+	915.223i	0.0949987	+	0.0548475i	−0.451748	+	0.892146i	$0.649199\pi$
$654$		0			0
$655$	−164.260	−	284.506i	−0.00979872	−	0.0169719i
$656$	96.3720	+	166.921i	0.00573582	+	0.00993473i
$657$		0			0
$658$	−7067.65	−	2094.36i	−0.418732	−	0.124083i
$659$	−8381.93	−	4839.31i	−0.495468	−	0.286059i	0.231372	−	0.972865i	$-0.425679\pi$
$659$	−8381.93	−	4839.31i	−0.495468	−	0.286059i	−0.726840	+	0.686807i	$0.759012\pi$
$660$		0			0
$661$			11941.2i			0.702661i	0.936252	+	0.351330i	$0.114271\pi$
$661$			11941.2i			0.702661i	−0.936252	+	0.351330i	$0.885729\pi$
$662$		−	2101.13i		−	0.123358i
$663$		0			0
$664$	9849.25	+	5686.47i	0.575640	+	0.332346i
$665$	1111.92	+	329.497i	0.0648400	+	0.0192140i
$666$		0			0
$667$	−10378.1	−	17975.5i	−0.602464	−	1.04350i
$668$	−4486.82	−	7771.40i	−0.259881	−	0.450126i
$669$		0			0
$670$	169.980	+	98.1380i	0.00980135	+	0.00565881i
$671$	1995.02	+	3455.48i	0.114779	+	0.198804i
$672$		0			0
$673$	215.515	−	373.284i	0.0123440	−	0.0213804i	−0.859787	−	0.510652i	$-0.829404\pi$
$673$	215.515	−	373.284i	0.0123440	−	0.0213804i	0.872131	+	0.489272i	$0.162737\pi$
$674$	−9124.36	+	5267.95i	−0.521450	+	0.301059i
$675$		0			0
$676$	−5070.04	+	8781.57i	−0.288464	+	0.499634i
$677$	15806.0			0.897301			0.448650	−	0.893707i	$-0.351905\pi$
$677$	15806.0			0.897301			0.448650	+	0.893707i	$0.351905\pi$
$678$		0			0
$679$	−16865.9	+	16001.7i	−0.953243	+	0.904400i
$680$	343.982	−	198.598i	0.0193987	−	0.0111998i
$681$		0			0
$682$	1453.68	−	839.283i	0.0816192	−	0.0471229i
$683$	27402.6	+	15820.9i	1.53518	+	0.886338i	0.999111	+	0.0421653i	$0.0134256\pi$
$683$	27402.6	+	15820.9i	1.53518	+	0.886338i	0.536072	+	0.844173i	$0.319908\pi$
$684$		0			0
$685$			281.440i			0.0156982i
$686$	−7580.60	−	8881.52i	−0.421908	−	0.494312i
$687$		0			0
$688$	−167.766	+	290.580i	−0.00929655	+	0.0161021i
$689$	−332.945			−0.0184096
$690$		0			0
$691$		−	15356.2i		−	0.845407i	−0.906268	−	0.422703i	$-0.861081\pi$
$691$		−	15356.2i		−	0.845407i	0.906268	−	0.422703i	$-0.138919\pi$
$692$	1987.34			0.109172
$693$		0			0
$694$	5855.79			0.320292
$695$		−	1061.59i		−	0.0579404i
$696$		0			0
$697$	1402.67			0.0762267
$698$	6795.80	−	11770.7i	0.368517	−	0.638290i
$699$		0			0
$700$	10388.6	−	2492.90i	0.560931	−	0.134604i
$701$			7678.12i			0.413693i	0.978373	+	0.206846i	$0.0663200\pi$
$701$			7678.12i			0.413693i	−0.978373	+	0.206846i	$0.933680\pi$
$702$		0			0
$703$	45480.4	+	26258.1i	2.44001	+	1.40874i
$704$	−15784.1	+	9112.93i	−0.845006	+	0.487864i
$705$		0			0
$706$	−17653.8	+	10192.4i	−0.941092	+	0.543339i
$707$	21637.7	−	5192.30i	1.15102	−	0.276204i
$708$		0			0
$709$	−16034.9			−0.849371			−0.424686	−	0.905341i	$-0.639615\pi$
$709$	−16034.9			−0.849371			−0.424686	+	0.905341i	$0.639615\pi$
$710$	−393.505	+	681.570i	−0.0207999	+	0.0360266i
$711$		0			0
$712$	30331.3	−	17511.8i	1.59651	−	0.921744i
$713$	−1211.66	+	2098.65i	−0.0636422	+	0.110231i
$714$		0			0
$715$	−17.0363	−	29.5077i	−0.000891077	−	0.00154339i
$716$	−1464.08	−	845.286i	−0.0764179	−	0.0441199i
$717$		0			0
$718$	8811.25	+	15261.5i	0.457985	+	0.793253i
$719$	9585.35	+	16602.3i	0.497181	+	0.861143i	0.999995	−	0.00325214i	$-0.00103519\pi$
$719$	9585.35	+	16602.3i	0.497181	+	0.861143i	−0.502814	+	0.864395i	$0.667702\pi$
$720$		0			0
$721$	2947.86	−	2796.82i	0.152266	−	0.144464i
$722$	25402.5	+	14666.2i	1.30940	+	0.755980i
$723$		0			0
$724$		−	15302.0i		−	0.785490i
$725$			19680.6i			1.00817i
$726$		0			0
$727$	−13432.8	−	7755.44i	−0.685276	−	0.395644i	0.116564	−	0.993183i	$-0.462812\pi$
$727$	−13432.8	−	7755.44i	−0.685276	−	0.395644i	−0.801840	+	0.597539i	$0.796145\pi$
$728$	−692.189	+	166.101i	−0.0352393	+	0.00845622i
$729$		0			0
$730$	312.847	+	541.868i	0.0158616	+	0.0274732i
$731$	1220.90	+	2114.66i	0.0617737	+	0.106995i
$732$		0			0
$733$	−17635.0	−	10181.6i	−0.888629	−	0.513050i	−0.0151352	−	0.999885i	$-0.504818\pi$
$733$	−17635.0	−	10181.6i	−0.888629	−	0.513050i	−0.873494	+	0.486835i	$0.838151\pi$
$734$	10682.7	+	18503.0i	0.537203	+	0.930463i
$735$		0			0
$736$	11530.3	−	19971.1i	0.577465	−	1.00020i
$737$	−11066.4	+	6389.18i	−0.553101	+	0.319333i
$738$		0			0
$739$	1493.90	−	2587.52i	0.0743629	−	0.128800i	−0.826446	−	0.563016i	$-0.809641\pi$
$739$	1493.90	−	2587.52i	0.0743629	−	0.128800i	0.900809	+	0.434215i	$0.142974\pi$
$740$	−666.046			−0.0330869
$741$		0			0
$742$	4708.81	+	4963.11i	0.232973	+	0.245555i
$743$	−4165.48	+	2404.94i	−0.205675	+	0.118747i	−0.599300	−	0.800525i	$-0.704554\pi$
$743$	−4165.48	+	2404.94i	−0.205675	+	0.118747i	0.393625	+	0.919271i	$0.371221\pi$
$744$		0			0
$745$	−846.462	+	488.705i	−0.0416268	+	0.0240333i
$746$	6212.43	+	3586.75i	0.304897	+	0.176033i
$747$		0			0
$748$			9468.18i			0.462822i
$749$	−825.822	−	3441.42i	−0.0402869	−	0.167886i
$750$		0			0
$751$	1125.06	−	1948.66i	0.0546657	−	0.0946838i	−0.837398	−	0.546594i	$-0.815924\pi$
$751$	1125.06	−	1948.66i	0.0546657	−	0.0946838i	0.892063	+	0.451910i	$0.149257\pi$
$752$	1228.82			0.0595886
$753$		0			0
$754$		−	480.133i		−	0.0231902i
$755$	245.770			0.0118470
$756$		0			0
$757$	−16948.7			−0.813754			−0.406877	−	0.913483i	$-0.633382\pi$
$757$	−16948.7			−0.813754			−0.406877	+	0.913483i	$0.633382\pi$
$758$		−	1285.33i		−	0.0615902i
$759$		0			0
$760$	−1452.74			−0.0693373
$761$	12064.6	−	20896.5i	0.574692	−	0.995396i	−0.421383	−	0.906883i	$-0.638455\pi$
$761$	12064.6	−	20896.5i	0.574692	−	0.995396i	0.996075	−	0.0885135i	$-0.0282116\pi$
$762$		0			0
$763$	19403.6	+	20451.6i	0.920654	+	0.970375i
$764$			18517.7i			0.876893i
$765$		0			0
$766$	−16171.1	−	9336.40i	−0.762776	−	0.440389i
$767$	429.912	−	248.210i	0.0202389	−	0.0116849i
$768$		0			0
$769$	33734.0	−	19476.3i	1.58190	−	0.913308i	0.587314	−	0.809359i	$-0.300185\pi$
$769$	33734.0	−	19476.3i	1.58190	−	0.913308i	0.994583	−	0.103949i	$-0.0331480\pi$
$770$	−198.920	+	671.279i	−0.00930985	+	0.0314172i
$771$		0			0
$772$	10799.4			0.503469
$773$	−9505.37	+	16463.8i	−0.442283	+	0.766056i	−0.997858	−	0.0654098i	$-0.979165\pi$
$773$	−9505.37	+	16463.8i	−0.442283	+	0.766056i	0.555576	+	0.831466i	$0.312498\pi$
$774$		0			0
$775$	1989.89	−	1148.86i	0.0922310	−	0.0532496i
$776$	14561.5	−	25221.3i	0.673619	−	1.16674i
$777$		0			0
$778$	4373.53	+	7575.17i	0.201540	+	0.349078i
$779$	−4442.93	−	2565.13i	−0.204345	−	0.117978i
$780$		0			0
$781$	−25618.7	−	44373.0i	−1.17377	−	2.03302i
$782$	4997.08	+	8655.20i	0.228511	+	0.395792i
$783$		0			0
$784$	1632.27	+	1060.51i	0.0743563	+	0.0483102i
$785$	−668.819	−	386.143i	−0.0304091	−	0.0175567i
$786$		0			0
$787$		−	1983.51i		−	0.0898404i	−0.998991	−	0.0449202i	$-0.985697\pi$
$787$		−	1983.51i		−	0.0898404i	0.998991	−	0.0449202i	$-0.0143034\pi$
$788$		−	1557.68i		−	0.0704191i
$789$		0			0
$790$	−69.5016	−	40.1268i	−0.00313007	−	0.00180715i
$791$	6805.13	+	28358.8i	0.305895	+	1.27474i
$792$		0			0
$793$	−66.6239	−	115.396i	−0.00298346	−	0.00516751i
$794$	6614.07	+	11455.9i	0.295623	+	0.512034i
$795$		0			0
$796$	19789.4	+	11425.4i	0.881175	+	0.508746i
$797$	1555.18	+	2693.65i	0.0691182	+	0.119716i	0.898513	−	0.438946i	$-0.144648\pi$
$797$	1555.18	+	2693.65i	0.0691182	+	0.119716i	−0.829395	+	0.558662i	$0.811315\pi$
$798$		0			0
$799$	4471.31	−	7744.54i	0.197977	−	0.342906i
$800$	−18936.2	+	10932.8i	−0.836870	+	0.483167i
$801$		0			0
$802$	6188.42	−	10718.7i	0.272470	−	0.471932i
$803$	−40735.3			−1.79018
$804$		0			0
$805$	−235.853	−	982.864i	−0.0103264	−	0.0430328i
$806$	−48.5458	+	28.0279i	−0.00212153	+	0.00122487i
$807$		0			0
$808$	−24139.8	+	13937.1i	−1.05103	+	0.606815i
$809$	−1302.95	−	752.256i	−0.0566244	−	0.0326921i	0.471421	−	0.881909i	$-0.343741\pi$
$809$	−1302.95	−	752.256i	−0.0566244	−	0.0326921i	−0.528045	+	0.849216i	$0.677075\pi$
$810$		0			0
$811$			28460.1i			1.23227i	0.787642	+	0.616133i	$0.211302\pi$
$811$			28460.1i			1.23227i	−0.787642	+	0.616133i	$0.788698\pi$
$812$	9788.91	−	9287.34i	0.423058	−	0.401381i
$813$		0			0
$814$	−15852.3	+	27456.9i	−0.682581	+	1.18227i
$815$	−872.413			−0.0374961
$816$		0			0
$817$		−	8930.84i		−	0.382436i
$818$	−20038.1			−0.856497
$819$		0			0
$820$	65.0653			0.00277095
$821$		−	22614.3i		−	0.961319i	−0.876907	−	0.480660i	$-0.840397\pi$
$821$		−	22614.3i		−	0.961319i	0.876907	−	0.480660i	$-0.159603\pi$
$822$		0			0
$823$	26069.3			1.10415			0.552076	−	0.833794i	$-0.313836\pi$
$823$	26069.3			1.10415			0.552076	+	0.833794i	$0.313836\pi$
$824$	−2545.11	+	4408.25i	−0.107601	+	0.186370i
$825$		0			0
$826$	−9780.19	−	2898.17i	−0.411981	−	0.122082i
$827$		−	37100.7i		−	1.56000i	−0.625782	−	0.779998i	$-0.715220\pi$
$827$		−	37100.7i		−	1.56000i	0.625782	−	0.779998i	$-0.284780\pi$
$828$		0			0
$829$	6606.87	+	3814.48i	0.276799	+	0.159810i	0.631973	−	0.774990i	$-0.282245\pi$
$829$	6606.87	+	3814.48i	0.276799	+	0.159810i	−0.355175	+	0.934800i	$0.615579\pi$
$830$	−323.507	+	186.777i	−0.0135290	+	0.00781098i
$831$		0			0
$832$	527.110	−	304.327i	0.0219642	−	0.0126811i
$833$	12623.1	−	6428.36i	0.525045	−	0.267382i
$834$		0			0
$835$	804.998			0.0333630
$836$	17314.9	−	29990.2i	0.716324	−	1.24071i
$837$		0			0
$838$	−25752.2	+	14868.1i	−1.06157	+	0.612898i
$839$	10297.8	−	17836.3i	0.423741	−	0.733942i	−0.572561	−	0.819862i	$-0.694050\pi$
$839$	10297.8	−	17836.3i	0.423741	−	0.733942i	0.996302	+	0.0859208i	$0.0273832\pi$
$840$		0			0
$841$	234.138	+	405.540i	0.00960017	+	0.0166280i
$842$	9443.86	+	5452.41i	0.386528	+	0.223162i
$843$		0			0
$844$	−2773.20	−	4803.32i	−0.113101	−	0.195897i
$845$	−454.818	−	787.768i	−0.0185162	−	0.0320711i
$846$		0			0
$847$	−14406.3	−	15184.3i	−0.584423	−	0.615985i
$848$	−987.681	−	570.238i	−0.0399966	−	0.0230920i
$849$		0			0
$850$		−	9476.24i		−	0.382391i
$851$		−	45771.1i		−	1.84373i
$852$		0			0
$853$	25770.4	+	14878.6i	1.03442	+	0.597224i	0.918248	−	0.396005i	$-0.129604\pi$
$853$	25770.4	+	14878.6i	1.03442	+	0.597224i	0.116174	+	0.993229i	$0.462937\pi$
$854$	−777.920	+	2625.18i	−0.0311708	+	0.105189i
$855$		0			0
$856$	2216.66	+	3839.38i	0.0885094	+	0.153303i
$857$	−5862.26	−	10153.7i	−0.233665	−	0.404720i	0.725219	−	0.688519i	$-0.241739\pi$
$857$	−5862.26	−	10153.7i	−0.233665	−	0.404720i	−0.958884	+	0.283799i	$0.908405\pi$
$858$		0			0
$859$	24749.2	+	14288.9i	0.983040	+	0.567558i	0.903186	−	0.429248i	$-0.141221\pi$
$859$	24749.2	+	14288.9i	0.983040	+	0.567558i	0.0798532	+	0.996807i	$0.474555\pi$
$860$	56.6334	+	98.0920i	0.00224556	+	0.00388943i
$861$		0			0
$862$	−6086.94	+	10542.9i	−0.240513	+	0.416580i
$863$	20733.1	−	11970.2i	0.817800	−	0.472157i	−0.0318572	−	0.999492i	$-0.510142\pi$
$863$	20733.1	−	11970.2i	0.817800	−	0.472157i	0.849657	+	0.527335i	$0.176809\pi$
$864$		0			0
$865$	−89.1391	+	154.394i	−0.00350384	+	0.00606883i
$866$	−17765.5			−0.697109
$867$		0			0
$868$	−1510.47	−	447.596i	−0.0590651	−	0.0175028i
$869$	4524.84	−	2612.42i	0.176634	−	0.101979i
$870$		0			0
$871$	369.563	−	213.367i	0.0143768	−	0.00830043i
$872$	−30583.4	−	17657.3i	−1.18771	−	0.685725i
$873$		0			0
$874$		−	36553.5i		−	1.41469i
$875$	−544.964	+	1839.05i	−0.0210550	+	0.0710527i
$876$		0			0
$877$	474.216	−	821.366i	0.0182590	−	0.0316255i	−0.856752	−	0.515729i	$-0.827521\pi$
$877$	474.216	−	821.366i	0.0182590	−	0.0316255i	0.875011	+	0.484104i	$0.160854\pi$
$878$	10365.8			0.398439
$879$		0			0
$880$		−	116.713i		−	0.00447089i
$881$	−39460.9			−1.50905			−0.754524	−	0.656273i	$-0.772132\pi$
$881$	−39460.9			−1.50905			−0.754524	+	0.656273i	$0.772132\pi$
$882$		0			0
$883$	−34371.8			−1.30997			−0.654984	−	0.755643i	$-0.727325\pi$
$883$	−34371.8			−1.30997			−0.654984	+	0.755643i	$0.727325\pi$
$884$		−	316.191i		−	0.0120301i
$885$		0			0
$886$	−15670.7			−0.594208
$887$	−13107.3	+	22702.6i	−0.496168	+	0.859389i	−0.999990	−	0.00441892i	$-0.998593\pi$
$887$	−13107.3	+	22702.6i	−0.496168	+	0.859389i	0.503822	+	0.863807i	$0.331927\pi$
$888$		0			0
$889$	443.985	−	1498.28i	0.0167500	−	0.0565249i
$890$			1150.38i			0.0433267i
$891$		0			0
$892$	−4922.58	−	2842.05i	−0.184776	−	0.106680i
$893$	−28325.5	+	16353.8i	−1.06145	+	0.612830i
$894$		0			0
$895$	131.338	−	75.8281i	0.00490520	−	0.00283202i
$896$	12892.0	+	3820.29i	0.480683	+	0.142441i
$897$		0			0
$898$	23419.4			0.870284
$899$	1451.05	−	2513.30i	0.0538324	−	0.0932404i
$900$		0			0
$901$	−7187.73	+	4149.84i	−0.265769	+	0.153442i
$902$	1548.59	−	2682.24i	0.0571645	−	0.0990118i
$903$		0			0
$904$	−18266.3	−	31638.1i	−0.672044	−	1.16401i
$905$	1188.79	+	686.349i	0.0436649	+	0.0252100i
$906$		0			0
$907$	12932.4	+	22399.5i	0.473443	+	0.820027i	0.999538	−	0.0303990i	$-0.00967779\pi$
$907$	12932.4	+	22399.5i	0.473443	+	0.820027i	−0.526095	+	0.850426i	$0.676344\pi$
$908$	−4214.20	−	7299.20i	−0.154023	−	0.266776i
$909$		0			0
$910$	6.64296	−	22.4174i	0.000241991	−	0.000816627i
$911$	−21902.9	−	12645.6i	−0.796570	−	0.459900i	0.0457002	−	0.998955i	$-0.485448\pi$
$911$	−21902.9	−	12645.6i	−0.796570	−	0.459900i	−0.842270	+	0.539055i	$0.818781\pi$
$912$		0			0
$913$		−	24319.8i		−	0.881566i
$914$		−	24080.9i		−	0.871472i
$915$		0			0
$916$	−20522.1	−	11848.5i	−0.740252	−	0.427385i
$917$	10101.6	+	10647.2i	0.363778	+	0.383424i
$918$		0			0
$919$	−2197.32	−	3805.87i	−0.0788715	−	0.136609i	0.823892	−	0.566747i	$-0.191798\pi$
$919$	−2197.32	−	3805.87i	−0.0788715	−	0.136609i	−0.902763	+	0.430138i	$0.858465\pi$
$920$	633.076	+	1096.52i	0.0226868	+	0.0392947i
$921$		0			0
$922$	18669.7	+	10778.9i	0.666868	+	0.385017i
$923$	855.540	+	1481.84i	0.0305097	+	0.0528443i
$924$		0			0
$925$	−21699.6	+	37584.8i	−0.771328	+	1.33598i
$926$	12197.9	−	7042.46i	0.432881	−	0.249924i
$927$		0			0
$928$	−13808.5	+	23917.0i	−0.488455	+	0.846029i
$929$	5602.71			0.197868			0.0989338	−	0.995094i	$-0.468457\pi$
$929$	5602.71			0.197868			0.0989338	+	0.995094i	$0.468457\pi$
$930$		0			0
$931$	−51739.0	−	2722.64i	−1.82135	−	0.0958443i
$932$	−14033.9	+	8102.49i	−0.493237	+	0.284770i
$933$		0			0
$934$	22856.9	−	13196.5i	0.800751	−	0.462314i
$935$	−735.570	−	424.681i	−0.0257280	−	0.0148541i
$936$		0			0
$937$			1117.11i			0.0389481i	0.999810	+	0.0194740i	$0.00619917\pi$
$937$			1117.11i			0.0389481i	−0.999810	+	0.0194740i	$0.993801\pi$
$938$	−8407.31	−	2491.34i	−0.292653	−	0.0867218i
$939$		0			0
$940$	207.409	−	359.243i	0.00719675	−	0.0124651i
$941$	53232.7			1.84414			0.922070	−	0.387023i	$-0.126497\pi$
$941$	53232.7			1.84414			0.922070	+	0.387023i	$0.126497\pi$
$942$		0			0
$943$			4471.33i			0.154408i
$944$	1700.44			0.0586279
$945$		0			0
$946$	5391.63			0.185303
$947$		−	21584.8i		−	0.740667i	−0.928899	−	0.370333i	$-0.879243\pi$
$947$		−	21584.8i		−	0.740667i	0.928899	−	0.370333i	$-0.120757\pi$
$948$		0			0
$949$	1360.36			0.0465322
$950$	−17329.6	+	30015.7i	−0.591838	+	1.02509i
$951$		0			0
$952$	−12872.9	+	12213.3i	−0.438250	+	0.415795i
$953$			27626.3i			0.939040i	0.882922	+	0.469520i	$0.155573\pi$
$953$			27626.3i			0.939040i	−0.882922	+	0.469520i	$0.844427\pi$
$954$		0			0
$955$	−1438.61	−	830.584i	−0.0487460	−	0.0281435i
$956$	−15777.0	+	9108.85i	−0.533749	+	0.308160i
$957$		0			0
$958$	−27799.8	+	16050.2i	−0.937549	+	0.541294i
$959$	−2933.89	−	12226.3i	−0.0987907	−	0.411687i
$960$		0			0
$961$	29452.2			0.988627
$962$	529.387	−	916.926i	0.0177423	−	0.0307306i
$963$		0			0
$964$	−4091.21	+	2362.06i	−0.136690	+	0.0789179i
$965$	−484.390	+	838.988i	−0.0161586	+	0.0279875i
$966$		0			0
$967$	1972.99	+	3417.31i	0.0656122	+	0.113644i	0.896965	−	0.442101i	$-0.145767\pi$
$967$	1972.99	+	3417.31i	0.0656122	+	0.113644i	−0.831353	+	0.555744i	$0.812433\pi$
$968$	22706.7	+	13109.7i	0.753949	+	0.435293i
$969$		0			0
$970$	478.286	+	828.415i	0.0158318	+	0.0274215i
$971$	−1848.32	−	3201.38i	−0.0610869	−	0.105806i	0.833865	−	0.551969i	$-0.186123\pi$
$971$	−1848.32	−	3201.38i	−0.0610869	−	0.105806i	−0.894951	+	0.446163i	$0.852790\pi$
$972$		0			0
$973$	11066.6	+	46117.7i	0.364625	+	1.51949i
$974$	−4283.70	−	2473.19i	−0.140923	−	0.0813617i
$975$		0			0
$976$		−	456.430i		−	0.0149692i
$977$			34033.9i			1.11447i	0.830354	+	0.557237i	$0.188138\pi$
$977$			34033.9i			1.11447i	−0.830354	+	0.557237i	$0.811862\pi$
$978$		0			0
$979$	−64860.3	−	37447.1i	−2.11741	−	1.22249i
$980$	585.541	−	298.190i	0.0190861	−	0.00971973i
$981$		0			0
$982$	6180.10	+	10704.2i	0.200830	+	0.347848i
$983$	9810.49	+	16992.3i	0.318317	+	0.551342i	0.980137	−	0.198321i	$-0.0635489\pi$
$983$	9810.49	+	16992.3i	0.318317	+	0.551342i	−0.661820	+	0.749663i	$0.730216\pi$
$984$		0			0
$985$	121.014	+	69.8676i	0.00391455	+	0.00226007i
$986$	−5984.40	−	10365.3i	−0.193288	−	0.334785i
$987$		0			0
$988$	−578.231	+	1001.53i	−0.0186194	+	0.0322498i
$989$	−6740.95	+	3891.89i	−0.216734	+	0.125131i
$990$		0			0
$991$	10727.8	−	18581.1i	0.343874	−	0.595607i	−0.641275	−	0.767311i	$-0.721594\pi$
$991$	10727.8	−	18581.1i	0.343874	−	0.595607i	0.985149	+	0.171704i	$0.0549274\pi$
$992$	3224.30			0.103197
$993$		0			0
$994$	9989.53	−	33710.8i	0.318761	−	1.07570i
$995$	−1775.24	+	1024.94i	−0.0565618	+	0.0326560i
$996$		0			0
$997$	30039.1	−	17343.1i	0.954209	−	0.550913i	0.0598233	−	0.998209i	$-0.480946\pi$
$997$	30039.1	−	17343.1i	0.954209	−	0.550913i	0.894386	+	0.447296i	$0.147613\pi$
$998$	−322.749	−	186.339i	−0.0102369	−	0.00591028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.15		44
3.2	odd	2		63.4.i.a.38.8	yes	44
7.5	odd	6		189.4.s.a.89.15		44
9.4	even	3		63.4.s.a.59.8	yes	44
9.5	odd	6		189.4.s.a.17.15		44
21.5	even	6		63.4.s.a.47.8	yes	44
63.5	even	6	inner	189.4.i.a.152.8		44
63.40	odd	6		63.4.i.a.5.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.15	✓	44	63.40	odd	6
63.4.i.a.38.8	yes	44	3.2	odd	2
63.4.s.a.47.8	yes	44	21.5	even	6
63.4.s.a.59.8	yes	44	9.4	even	3
189.4.i.a.143.15		44	1.1	even	1	trivial
189.4.i.a.152.8		44	63.5	even	6	inner
189.4.s.a.17.15		44	9.5	odd	6
189.4.s.a.89.15		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)

\(f(q)\)	\(=\)	\(q+1.83815i q^{2} +4.62119 q^{4} +(-0.207277 + 0.359014i) q^{5} +(5.26194 - 17.7570i) q^{7} +23.1997i q^{8} +O(q^{10})\)	\(q+1.83815i q^{2} +4.62119 q^{4} +(-0.207277 + 0.359014i) q^{5} +(5.26194 - 17.7570i) q^{7} +23.1997i q^{8} +(-0.659923 - 0.381007i) q^{10} +(42.9636 - 24.8051i) q^{11} +(-1.43477 + 0.828367i) q^{13} +(32.6401 + 9.67225i) q^{14} -5.67501 q^{16} +(-20.6496 + 35.7662i) q^{17} +(130.814 - 75.5256i) q^{19} +(-0.957866 + 1.65907i) q^{20} +(45.5955 + 78.9737i) q^{22} +(-114.013 - 65.8253i) q^{23} +(62.4141 + 108.104i) q^{25} +(-1.52267 - 2.63733i) q^{26} +(24.3164 - 82.0587i) q^{28} +(136.539 + 78.8310i) q^{29} -18.4071i q^{31} +175.166i q^{32} +(-65.7437 - 37.9571i) q^{34} +(5.28434 + 5.56973i) q^{35} +(173.836 + 301.092i) q^{37} +(138.828 + 240.457i) q^{38} +(-8.32901 - 4.80876i) q^{40} +(-16.9818 - 29.4134i) q^{41} +(29.5623 - 51.2034i) q^{43} +(198.543 - 114.629i) q^{44} +(120.997 - 209.573i) q^{46} -216.532 q^{47} +(-287.624 - 186.873i) q^{49} +(-198.712 + 114.727i) q^{50} +(-6.63037 + 3.82805i) q^{52} +(174.040 + 100.482i) q^{53} +20.5661i q^{55} +(411.957 + 122.075i) q^{56} +(-144.903 + 250.980i) q^{58} -299.637 q^{59} +80.4280i q^{61} +33.8351 q^{62} -367.382 q^{64} -0.686806i q^{65} -257.576 q^{67} +(-95.4259 + 165.282i) q^{68} +(-10.2380 + 9.71343i) q^{70} -1032.80i q^{71} +(-711.100 - 410.554i) q^{73} +(-553.454 + 319.537i) q^{74} +(604.518 - 349.019i) q^{76} +(-214.392 - 893.429i) q^{77} +105.318 q^{79} +(1.17630 - 2.03741i) q^{80} +(54.0663 - 31.2152i) q^{82} +(245.110 - 424.542i) q^{83} +(-8.56037 - 14.8270i) q^{85} +(94.1196 + 54.3400i) q^{86} +(575.470 + 996.743i) q^{88} +(-754.828 - 1307.40i) q^{89} +(7.15964 + 29.8361i) q^{91} +(-526.875 - 304.191i) q^{92} -398.020i q^{94} +62.6189i q^{95} +(-1087.14 - 627.661i) q^{97} +(343.501 - 528.697i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 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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