LMFDB - Embedded newform 189.4.s.a.17.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (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			17.18
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16085 + 1.82492i) q^{2} +(2.66064 + 4.60836i) q^{4} +12.2314 q^{5} +(4.78838 - 17.8905i) q^{7} -9.77690i q^{8} +O(q^{10})$	\(q+(3.16085 + 1.82492i) q^{2} +(2.66064 + 4.60836i) q^{4} +12.2314 q^{5} +(4.78838 - 17.8905i) q^{7} -9.77690i q^{8} +(38.6615 + 22.3212i) q^{10} +10.0114i q^{11} +(57.0263 + 32.9241i) q^{13} +(47.7841 - 47.8109i) q^{14} +(39.1271 - 67.7702i) q^{16} +(38.6818 - 66.9989i) q^{17} +(-104.262 + 60.1959i) q^{19} +(32.5432 + 56.3665i) q^{20} +(-18.2699 + 31.6444i) q^{22} +122.606i q^{23} +24.6062 q^{25} +(120.168 + 208.136i) q^{26} +(95.1861 - 25.5337i) q^{28} +(50.3417 - 29.0648i) q^{29} +(-174.476 + 100.734i) q^{31} +(179.613 - 103.700i) q^{32} +(244.535 - 141.182i) q^{34} +(58.5684 - 218.826i) q^{35} +(82.9121 + 143.608i) q^{37} -439.410 q^{38} -119.585i q^{40} +(112.422 - 194.721i) q^{41} +(152.402 + 263.969i) q^{43} +(-46.1360 + 26.6366i) q^{44} +(-223.746 + 387.539i) q^{46} +(-11.2933 + 19.5606i) q^{47} +(-297.143 - 171.333i) q^{49} +(77.7763 + 44.9042i) q^{50} +350.397i q^{52} +(-360.132 - 207.922i) q^{53} +122.453i q^{55} +(-174.914 - 46.8155i) q^{56} +212.163 q^{58} +(-180.334 - 312.348i) q^{59} +(-635.689 - 367.015i) q^{61} -735.324 q^{62} +130.940 q^{64} +(697.509 + 402.707i) q^{65} +(55.6457 + 96.3811i) q^{67} +411.673 q^{68} +(584.464 - 584.792i) q^{70} +455.487i q^{71} +(-662.747 - 382.637i) q^{73} +605.230i q^{74} +(-554.808 - 320.319i) q^{76} +(179.109 + 47.9383i) q^{77} +(21.5683 - 37.3573i) q^{79} +(478.578 - 828.921i) q^{80} +(710.697 - 410.321i) q^{82} +(200.064 + 346.522i) q^{83} +(473.131 - 819.488i) q^{85} +1112.49i q^{86} +97.8802 q^{88} +(-347.632 - 602.117i) q^{89} +(862.094 - 862.577i) q^{91} +(-565.012 + 326.210i) q^{92} +(-71.3928 + 41.2186i) q^{94} +(-1275.27 + 736.277i) q^{95} +(-955.178 + 551.472i) q^{97} +(-626.554 - 1083.82i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	3.16085	+	1.82492i	1.11753	+	0.645205i	0.940769	−	0.339049i	$-0.110105\pi$
$2$	3.16085	+	1.82492i	1.11753	+	0.645205i	0.176759	+	0.984254i	$0.443439\pi$
$3$		0			0
$3$		0			0
$4$	2.66064	+	4.60836i	0.332580	+	0.576045i
$5$	12.2314			1.09401			0.547003	−	0.837131i	$-0.315769\pi$
$5$	12.2314			1.09401			0.547003	+	0.837131i	$0.315769\pi$
$6$		0			0
$7$	4.78838	−	17.8905i	0.258548	−	0.965998i
$7$	4.78838	−	17.8905i	0.258548	−	0.965998i
$8$		−	9.77690i		−	0.432082i
$9$		0			0
$10$	38.6615	+	22.3212i	1.22258	+	0.705858i
$11$			10.0114i			0.274413i	0.990542	+	0.137206i	$0.0438124\pi$
$11$			10.0114i			0.274413i	−0.990542	+	0.137206i	$0.956188\pi$
$12$		0			0
$13$	57.0263	+	32.9241i	1.21663	+	0.702424i	0.964196	−	0.265189i	$-0.0854345\pi$
$13$	57.0263	+	32.9241i	1.21663	+	0.702424i	0.252437	+	0.967613i	$0.418768\pi$
$14$	47.7841	−	47.8109i	0.912202	−	0.912714i
$15$		0			0
$16$	39.1271	−	67.7702i	0.611361	−	1.05891i
$17$	38.6818	−	66.9989i	0.551866	−	0.955860i	−0.446274	−	0.894896i	$-0.647249\pi$
$17$	38.6818	−	66.9989i	0.551866	−	0.955860i	0.998140	−	0.0609637i	$-0.0194174\pi$
$18$		0			0
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.972864	−	0.231378i	$-0.925677\pi$
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.286053	+	0.958214i	$0.592343\pi$
$20$	32.5432	+	56.3665i	0.363844	+	0.630196i
$21$		0			0
$22$	−18.2699	+	31.6444i	−0.177053	+	0.306664i
$23$			122.606i			1.11153i	0.831341	+	0.555763i	$0.187574\pi$
$23$			122.606i			1.11153i	−0.831341	+	0.555763i	$0.812426\pi$
$24$		0			0
$25$	24.6062			0.196849
$26$	120.168	+	208.136i	0.906415	+	1.56996i
$27$		0			0
$28$	95.1861	−	25.5337i	0.642446	−	0.172336i
$29$	50.3417	−	29.0648i	0.322352	−	0.186110i	−0.330088	−	0.943950i	$-0.607078\pi$
$29$	50.3417	−	29.0648i	0.322352	−	0.186110i	0.652441	+	0.757840i	$0.273745\pi$
$30$		0			0
$31$	−174.476	+	100.734i	−1.01087	+	0.583624i	−0.911445	−	0.411421i	$-0.865033\pi$
$31$	−174.476	+	100.734i	−1.01087	+	0.583624i	−0.0994218	+	0.995045i	$0.531699\pi$
$32$	179.613	−	103.700i	0.992233	−	0.572866i
$33$		0			0
$34$	244.535	−	141.182i	1.23345	−	0.712134i
$35$	58.5684	−	218.826i	0.282853	−	1.05681i
$36$		0			0
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	0.989315	−	0.145794i	$-0.0465737\pi$
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	−0.620919	+	0.783875i	$0.713240\pi$
$38$	−439.410			−1.87583
$39$		0			0
$40$		−	119.585i		−	0.472700i
$41$	112.422	−	194.721i	0.428228	−	0.741713i	−0.568487	−	0.822692i	$-0.692471\pi$
$41$	112.422	−	194.721i	0.428228	−	0.741713i	0.996716	+	0.0809786i	$0.0258046\pi$
$42$		0			0
$43$	152.402	+	263.969i	0.540492	+	0.936159i	0.998876	+	0.0474048i	$0.0150951\pi$
$43$	152.402	+	263.969i	0.540492	+	0.936159i	−0.458384	+	0.888754i	$0.651572\pi$
$44$	−46.1360	+	26.6366i	−0.158074	+	0.0912641i
$45$		0			0
$46$	−223.746	+	387.539i	−0.717163	+	1.24216i
$47$	−11.2933	+	19.5606i	−0.0350489	+	0.0607064i	−0.883018	−	0.469340i	$-0.844492\pi$
$47$	−11.2933	+	19.5606i	−0.0350489	+	0.0607064i	0.847969	+	0.530046i	$0.177825\pi$
$48$		0			0
$49$	−297.143	−	171.333i	−0.866306	−	0.499514i
$50$	77.7763	+	44.9042i	0.219985	+	0.127008i
$51$		0			0
$52$			350.397i			0.934447i
$53$	−360.132	−	207.922i	−0.933358	−	0.538875i	−0.0454860	−	0.998965i	$-0.514484\pi$
$53$	−360.132	−	207.922i	−0.933358	−	0.538875i	−0.887872	+	0.460090i	$0.847817\pi$
$54$		0			0
$55$			122.453i			0.300209i
$56$	−174.914	−	46.8155i	−0.417391	−	0.111714i
$57$		0			0
$58$	212.163			0.480317
$59$	−180.334	−	312.348i	−0.397924	−	0.689225i	0.595545	−	0.803322i	$-0.296936\pi$
$59$	−180.334	−	312.348i	−0.397924	−	0.689225i	−0.993470	+	0.114096i	$0.963603\pi$
$60$		0			0
$61$	−635.689	−	367.015i	−1.33429	−	0.770353i	−0.348336	−	0.937370i	$-0.613253\pi$
$61$	−635.689	−	367.015i	−1.33429	−	0.770353i	−0.985954	+	0.167017i	$0.946586\pi$
$62$	−735.324			−1.50623
$63$		0			0
$64$	130.940			0.255742
$65$	697.509	+	402.707i	1.33100	+	0.768456i
$66$		0			0
$67$	55.6457	+	96.3811i	0.101466	+	0.175744i	0.912289	−	0.409548i	$-0.134313\pi$
$67$	55.6457	+	96.3811i	0.101466	+	0.175744i	−0.810823	+	0.585291i	$0.800980\pi$
$68$	411.673			0.734158
$69$		0			0
$70$	584.464	−	584.792i	0.997955	−	0.998514i
$71$			455.487i			0.761358i	0.924707	+	0.380679i	$0.124310\pi$
$71$			455.487i			0.761358i	−0.924707	+	0.380679i	$0.875690\pi$
$72$		0			0
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.136438	−	0.990649i	$-0.543565\pi$
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.926146	+	0.377166i	$0.876899\pi$
$74$			605.230i			0.950765i
$75$		0			0
$76$	−554.808	−	320.319i	−0.837380	−	0.483462i
$77$	179.109	+	47.9383i	0.265082	+	0.0709490i
$78$		0			0
$79$	21.5683	−	37.3573i	0.0307167	−	0.0532029i	−0.850258	−	0.526366i	$-0.823554\pi$
$79$	21.5683	−	37.3573i	0.0307167	−	0.0532029i	0.880975	+	0.473163i	$0.156888\pi$
$80$	478.578	−	828.921i	0.668833	−	1.15845i
$81$		0			0
$82$	710.697	−	410.321i	0.957115	−	0.552590i
$83$	200.064	+	346.522i	0.264577	+	0.458262i	0.967453	−	0.253051i	$-0.0814342\pi$
$83$	200.064	+	346.522i	0.264577	+	0.458262i	−0.702875	+	0.711313i	$0.748101\pi$
$84$		0			0
$85$	473.131	−	819.488i	0.603745	−	1.04572i
$86$			1112.49i			1.39491i
$87$		0			0
$88$	97.8802			0.118569
$89$	−347.632	−	602.117i	−0.414033	−	0.717127i	0.581293	−	0.813694i	$-0.302547\pi$
$89$	−347.632	−	602.117i	−0.414033	−	0.717127i	−0.995326	+	0.0965674i	$0.969214\pi$
$90$		0			0
$91$	862.094	−	862.577i	0.993099	−	0.993656i
$92$	−565.012	+	326.210i	−0.640289	+	0.369671i
$93$		0			0
$94$	−71.3928	+	41.2186i	−0.0783362	+	0.0452274i
$95$	−1275.27	+	736.277i	−1.37726	+	0.795163i
$96$		0			0
$97$	−955.178	+	551.472i	−0.999831	+	0.577253i	−0.908198	−	0.418540i	$-0.862542\pi$
$97$	−955.178	+	551.472i	−0.999831	+	0.577253i	−0.0916328	+	0.995793i	$0.529209\pi$
$98$	−626.554	−	1083.82i	−0.645832	−	1.11717i
$99$		0			0
$100$	65.4681	+	113.394i	0.0654681	+	0.113394i
$101$	704.387			0.693951			0.346976	−	0.937874i	$-0.387209\pi$
$101$	704.387			0.693951			0.346976	+	0.937874i	$0.387209\pi$
$102$		0			0
$103$			1038.72i			0.993672i	0.867845	+	0.496836i	$0.165505\pi$
$103$			1038.72i			0.993672i	−0.867845	+	0.496836i	$0.834495\pi$
$104$	321.896	−	557.540i	0.303505	−	0.525686i
$105$		0			0
$106$	−758.882	−	1314.42i	−0.695369	−	1.20442i
$107$	−50.4942	+	29.1528i	−0.0456211	+	0.0263394i	−0.522637	−	0.852555i	$-0.675052\pi$
$107$	−50.4942	+	29.1528i	−0.0456211	+	0.0263394i	0.477016	+	0.878895i	$0.341718\pi$
$108$		0			0
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	−0.992551	−	0.121827i	$-0.961125\pi$
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	0.601781	+	0.798661i	$0.294458\pi$
$110$	−223.466	+	387.054i	−0.193697	+	0.335493i
$111$		0			0
$112$	−1025.09	−	1024.51i	−0.864838	−	0.864353i
$113$	2032.03	+	1173.20i	1.69166	+	0.976681i	0.953179	+	0.302407i	$0.0977901\pi$
$113$	2032.03	+	1173.20i	1.69166	+	0.976681i	0.738481	+	0.674274i	$0.235543\pi$
$114$		0			0
$115$			1499.64i			1.21602i
$116$	267.882	+	154.662i	0.214416	+	0.123793i
$117$		0			0
$118$		−	1316.38i		−	1.02697i
$119$	−1013.42	−	1012.86i	−0.780675	−	0.780238i
$120$		0			0
$121$	1230.77			0.924698
$122$	−1339.54	−	2320.16i	−0.994071	−	1.72178i
$123$		0			0
$124$	−928.437	−	536.033i	−0.672388	−	0.388203i
$125$	−1227.95			−0.878652
$126$		0			0
$127$	−1026.54			−0.717251			−0.358625	−	0.933482i	$-0.616754\pi$
$127$	−1026.54			−0.717251			−0.358625	+	0.933482i	$0.616754\pi$
$128$	−1023.03	−	590.644i	−0.706434	−	0.407860i
$129$		0			0
$130$	1469.81	+	2545.79i	0.991624	+	1.71754i
$131$	1431.15			0.954506			0.477253	−	0.878766i	$-0.341632\pi$
$131$	1431.15			0.954506			0.477253	+	0.878766i	$0.341632\pi$
$132$		0			0
$133$	577.689	+	2153.55i	0.376632	+	1.40403i
$134$			406.195i			0.261865i
$135$		0			0
$136$	−655.042	−	378.189i	−0.413010	−	0.238451i
$137$			2527.45i			1.57616i	0.615571	+	0.788081i	$0.288925\pi$
$137$			2527.45i			1.57616i	−0.615571	+	0.788081i	$0.711075\pi$
$138$		0			0
$139$	−247.028	−	142.622i	−0.150739	−	0.0870290i	0.422734	−	0.906254i	$-0.361071\pi$
$139$	−247.028	−	142.622i	−0.150739	−	0.0870290i	−0.573472	+	0.819225i	$0.694404\pi$
$140$	1164.26	−	312.311i	0.702840	−	0.188537i
$141$		0			0
$142$	−831.226	+	1439.73i	−0.491232	+	0.850839i
$143$	−329.616	+	570.911i	−0.192754	+	0.333860i
$144$		0			0
$145$	615.748	−	355.502i	0.352656	−	0.203606i
$146$	−1396.56	−	2418.91i	−0.791645	−	1.37117i
$147$		0			0
$148$	−441.198	+	764.177i	−0.245042	+	0.424425i
$149$		−	1884.28i		−	1.03601i	−0.855376	−	0.518007i	$-0.826674\pi$
$149$		−	1884.28i		−	1.03601i	0.855376	−	0.518007i	$-0.173326\pi$
$150$		0			0
$151$	−400.447			−0.215814			−0.107907	−	0.994161i	$-0.534415\pi$
$151$	−400.447			−0.215814			−0.107907	+	0.994161i	$0.534415\pi$
$152$	588.529	+	1019.36i	0.314053	+	0.543955i
$153$		0			0
$154$	478.652	+	478.384i	0.250460	+	0.250320i
$155$	−2134.08	+	1232.11i	−1.10589	+	0.638489i
$156$		0			0
$157$	1698.99	−	980.915i	0.863659	−	0.498634i	−0.00157672	−	0.999999i	$-0.500502\pi$
$157$	1698.99	−	980.915i	0.863659	−	0.498634i	0.865236	+	0.501365i	$0.167169\pi$
$158$	136.348	−	78.7205i	0.0686536	−	0.0396372i
$159$		0			0
$160$	2196.92	−	1268.39i	1.08551	−	0.626719i
$161$	2193.49	+	587.084i	1.07373	+	0.287383i
$162$		0			0
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	0.999575	+	0.0291623i	$0.00928395\pi$
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	−0.474532	+	0.880238i	$0.657383\pi$
$164$	1196.46			0.569680
$165$		0			0
$166$			1460.40i			0.682827i
$167$	−724.771	+	1255.34i	−0.335835	+	0.581683i	−0.983645	−	0.180119i	$-0.942352\pi$
$167$	−724.771	+	1255.34i	−0.335835	+	0.581683i	0.647810	+	0.761802i	$0.275685\pi$
$168$		0			0
$169$	1069.50	+	1852.42i	0.486798	+	0.843160i
$170$	2990.99	−	1726.85i	1.34940	−	0.779079i
$171$		0			0
$172$	−810.975	+	1404.65i	−0.359513	+	0.622695i
$173$	922.964	−	1598.62i	0.405617	−	0.702549i	−0.588776	−	0.808296i	$-0.700390\pi$
$173$	922.964	−	1598.62i	0.405617	−	0.702549i	0.994393	+	0.105747i	$0.0337235\pi$
$174$		0			0
$175$	117.824	−	440.218i	0.0508951	−	0.190156i
$176$	678.472	+	391.716i	0.290578	+	0.167765i
$177$		0			0
$178$		−	2537.60i		−	1.06855i
$179$	−389.538	−	224.900i	−0.162656	−	0.0939096i	0.416462	−	0.909153i	$-0.363270\pi$
$179$	−389.538	−	224.900i	−0.162656	−	0.0939096i	−0.579118	+	0.815243i	$0.696603\pi$
$180$		0			0
$181$		−	3067.12i		−	1.25954i	−0.776781	−	0.629771i	$-0.783149\pi$
$181$		−	3067.12i		−	1.25954i	0.776781	−	0.629771i	$-0.216851\pi$
$182$	4299.08	−	1153.23i	1.75093	−	0.469686i
$183$		0			0
$184$	1198.71			0.480271
$185$	1014.13	+	1756.52i	0.403028	+	0.698064i
$186$		0			0
$187$	670.751	+	387.258i	0.262300	+	0.151439i
$188$	−120.189			−0.0466261
$189$		0			0
$190$	−5374.58			−2.05217
$191$	4503.79	+	2600.27i	1.70619	+	0.985071i	0.939170	+	0.343452i	$0.111596\pi$
$191$	4503.79	+	2600.27i	1.70619	+	0.985071i	0.767023	+	0.641619i	$0.221737\pi$
$192$		0			0
$193$	−1188.11	−	2057.87i	−0.443119	−	0.767505i	0.554800	−	0.831984i	$-0.312795\pi$
$193$	−1188.11	−	2057.87i	−0.443119	−	0.767505i	−0.997919	+	0.0644786i	$0.979462\pi$
$194$	−4025.56			−1.48979
$195$		0			0
$196$	−1.02330	−	1825.20i	−0.000372923	−	0.665159i
$197$			148.115i			0.0535672i	0.999641	+	0.0267836i	$0.00852651\pi$
$197$			148.115i			0.0535672i	−0.999641	+	0.0267836i	$0.991473\pi$
$198$		0			0
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	0.212803	−	0.977095i	$-0.431741\pi$
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	−0.739788	+	0.672840i	$0.765074\pi$
$200$		−	240.572i		−	0.0850551i
$201$		0			0
$202$	2226.46	+	1285.45i	0.775510	+	0.447741i
$203$	−278.930	−	1039.81i	−0.0964386	−	0.359510i
$204$		0			0
$205$	1375.07	−	2381.70i	0.468484	−	0.811439i
$206$	−1895.58	+	3283.24i	−0.641122	+	1.11046i
$207$		0			0
$208$	4462.55	−	2576.45i	1.48761	−	0.858869i
$209$	−602.643	−	1043.81i	−0.199453	−	0.345463i
$210$		0			0
$211$	545.976	−	945.659i	0.178135	−	0.308540i	−0.763106	−	0.646273i	$-0.776327\pi$
$211$	545.976	−	945.659i	0.178135	−	0.308540i	0.941242	+	0.337733i	$0.109660\pi$
$212$		−	2212.82i		−	0.716875i
$213$		0			0
$214$	−212.806			−0.0679772
$215$	1864.09	+	3228.70i	0.591301	+	1.02416i
$216$		0			0
$217$	966.726	+	3603.83i	0.302422	+	1.12739i
$218$	−2811.22	+	1623.06i	−0.873393	+	0.504254i
$219$		0			0
$220$	−564.306	+	325.802i	−0.172934	+	0.0998435i
$221$	4411.76	−	2547.13i	1.34284	−	0.775288i
$222$		0			0
$223$	1063.36	−	613.931i	0.319317	−	0.184358i	−0.331771	−	0.943360i	$-0.607646\pi$
$223$	1063.36	−	613.931i	0.319317	−	0.184358i	0.651088	+	0.759002i	$0.274313\pi$
$224$	−995.188	−	3709.93i	−0.296847	−	1.10661i
$225$		0			0
$226$	4281.96	+	7416.58i	1.26032	+	2.18294i
$227$	2263.45			0.661809			0.330905	−	0.943664i	$-0.392646\pi$
$227$	2263.45			0.661809			0.330905	+	0.943664i	$0.392646\pi$
$228$		0			0
$229$			5152.41i			1.48682i	0.668839	+	0.743408i	$0.266792\pi$
$229$			5152.41i			1.48682i	−0.668839	+	0.743408i	$0.733208\pi$
$230$	−2736.71	+	4740.12i	−0.784580	+	1.35893i
$231$		0			0
$232$	−284.164	−	492.186i	−0.0804149	−	0.139283i
$233$	361.488	−	208.705i	0.101639	−	0.0586812i	−0.448319	−	0.893874i	$-0.647977\pi$
$233$	361.488	−	208.705i	0.101639	−	0.0586812i	0.549958	+	0.835192i	$0.314644\pi$
$234$		0			0
$235$	−138.132	+	239.252i	−0.0383437	+	0.0664132i
$236$	959.609	−	1662.09i	0.264683	−	0.458445i
$237$		0			0
$238$	−1354.90	−	5050.89i	−0.369013	−	1.37563i
$239$	−4832.69	−	2790.15i	−1.30795	−	0.755146i	−0.326198	−	0.945302i	$-0.605767\pi$
$239$	−4832.69	−	2790.15i	−1.30795	−	0.755146i	−0.981754	+	0.190155i	$0.939101\pi$
$240$		0			0
$241$			2773.85i			0.741409i	0.928751	+	0.370704i	$0.120884\pi$
$241$			2773.85i			0.741409i	−0.928751	+	0.370704i	$0.879116\pi$
$242$	3890.28	+	2246.06i	1.03338	+	0.596620i
$243$		0			0
$244$		−	3905.98i		−	1.02481i
$245$	−3634.46	−	2095.64i	−0.947744	−	0.546472i
$246$		0			0
$247$	−7927.59			−2.04219
$248$	984.866	+	1705.84i	0.252174	+	0.436778i
$249$		0			0
$250$	−3881.37	−	2240.91i	−0.981918	−	0.566911i
$251$	−3751.34			−0.943357			−0.471678	−	0.881771i	$-0.656352\pi$
$251$	−3751.34			−0.943357			−0.471678	+	0.881771i	$0.656352\pi$
$252$		0			0
$253$	−1227.45			−0.305017
$254$	−3244.74	−	1873.35i	−0.801548	−	0.462774i
$255$		0			0
$256$	−2679.51	−	4641.05i	−0.654178	−	1.13307i
$257$	−7511.72			−1.82322			−0.911612	−	0.411052i	$-0.865161\pi$
$257$	−7511.72			−1.82322			−0.911612	+	0.411052i	$0.865161\pi$
$258$		0			0
$259$	2966.24	−	795.692i	0.711633	−	0.190895i
$260$			4285.83i			1.02229i
$261$		0			0
$262$	4523.65	+	2611.73i	1.06669	+	0.615852i
$263$		−	5534.91i		−	1.29771i	−0.760913	−	0.648854i	$-0.775248\pi$
$263$		−	5534.91i		−	1.29771i	0.760913	−	0.648854i	$-0.224752\pi$
$264$		0			0
$265$	−4404.91	−	2543.17i	−1.02110	−	0.589532i
$266$	−2104.06	+	7861.28i	−0.484993	+	1.81205i
$267$		0			0
$268$	−296.106	+	512.870i	−0.0674908	+	0.116898i
$269$	411.958	−	713.532i	0.0933737	−	0.161728i	−0.815555	−	0.578680i	$-0.803568\pi$
$269$	411.958	−	713.532i	0.0933737	−	0.161728i	0.908929	+	0.416952i	$0.136902\pi$
$270$		0			0
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	−0.858043	−	0.513577i	$-0.828320\pi$
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	0.0157492	+	0.999876i	$0.494987\pi$
$272$	−3027.02	−	5242.95i	−0.674779	−	1.16875i
$273$		0			0
$274$	−4612.38	+	7988.87i	−1.01695	+	1.76141i
$275$			246.341i			0.0540180i
$276$		0			0
$277$	−2642.56			−0.573199			−0.286599	−	0.958051i	$-0.592525\pi$
$277$	−2642.56			−0.573199			−0.286599	+	0.958051i	$0.592525\pi$
$278$	−520.546	−	901.612i	−0.112303	−	0.194515i
$279$		0			0
$280$	−2139.44	−	572.618i	−0.456628	−	0.122216i
$281$	3315.71	−	1914.33i	0.703910	−	0.406403i	−0.104892	−	0.994484i	$-0.533450\pi$
$281$	3315.71	−	1914.33i	0.703910	−	0.406403i	0.808802	+	0.588081i	$0.200116\pi$
$282$		0			0
$283$	6229.03	−	3596.33i	1.30840	−	0.755406i	0.326572	−	0.945172i	$-0.394106\pi$
$283$	6229.03	−	3596.33i	1.30840	−	0.755406i	0.981829	+	0.189766i	$0.0607731\pi$
$284$	−2099.05	+	1211.89i	−0.438576	+	0.253212i
$285$		0			0
$286$	−2083.73	+	1203.04i	−0.430816	+	0.248732i
$287$	−2945.34	−	2943.69i	−0.605776	−	0.605437i
$288$		0			0
$289$	−536.069	−	928.499i	−0.109112	−	0.188988i
$290$	2595.05			0.525470
$291$		0			0
$292$		−	4072.23i		−	0.816128i
$293$	1871.73	−	3241.93i	0.373199	−	0.646400i	−0.616856	−	0.787076i	$-0.711594\pi$
$293$	1871.73	−	3241.93i	0.373199	−	0.646400i	0.990056	+	0.140675i	$0.0449274\pi$
$294$		0			0
$295$	−2205.74	−	3820.45i	−0.435332	−	0.754017i
$296$	1404.04	−	810.623i	0.275703	−	0.159177i
$297$		0			0
$298$	3438.65	−	5955.92i	0.668442	−	1.15778i
$299$	−4036.69	+	6991.76i	−0.780763	+	1.35232i
$300$		0			0
$301$	5452.30	−	1462.58i	1.04407	−	0.280072i
$302$	−1265.75	−	730.781i	−0.241178	−	0.139244i
$303$		0			0
$304$			9421.17i			1.77744i
$305$	−7775.35	−	4489.10i	−1.45972	−	0.842771i
$306$		0			0
$307$		−	4199.35i		−	0.780682i	−0.920670	−	0.390341i	$-0.872357\pi$
$307$		−	4199.35i		−	0.780682i	0.920670	−	0.390341i	$-0.127643\pi$
$308$	255.627	+	952.944i	0.0472912	+	0.176296i
$309$		0			0
$310$	−8994.02			−1.64783
$311$	−1241.68	−	2150.64i	−0.226395	−	0.392128i	0.730342	−	0.683082i	$-0.239361\pi$
$311$	−1241.68	−	2150.64i	−0.226395	−	0.392128i	−0.956737	+	0.290954i	$0.906027\pi$
$312$		0			0
$313$	−710.623	−	410.278i	−0.128328	−	0.0740904i	0.434462	−	0.900690i	$-0.356939\pi$
$313$	−710.623	−	410.278i	−0.128328	−	0.0740904i	−0.562790	+	0.826600i	$0.690272\pi$
$314$	7160.35			1.28688
$315$		0			0
$316$	229.541			0.0408630
$317$	3579.71	+	2066.74i	0.634247	+	0.366183i	0.782395	−	0.622782i	$-0.213998\pi$
$317$	3579.71	+	2066.74i	0.634247	+	0.366183i	−0.148148	+	0.988965i	$0.547331\pi$
$318$		0			0
$319$	290.979	+	503.990i	0.0510711	+	0.0884577i
$320$	1601.57			0.279783
$321$		0			0
$322$	5861.90	+	5858.61i	1.01451	+	1.01394i
$323$			9313.95i			1.60446i
$324$		0			0
$325$	1403.20	+	810.137i	0.239494	+	0.138272i
$326$			7975.88i			1.35504i
$327$		0			0
$328$	−1903.76	−	1099.14i	−0.320481	−	0.185030i
$329$	295.872	+	295.707i	0.0495805	+	0.0495527i
$330$		0			0
$331$	4444.19	−	7697.57i	0.737991	−	1.27824i	−0.215408	−	0.976524i	$-0.569108\pi$
$331$	4444.19	−	7697.57i	0.737991	−	1.27824i	0.953399	−	0.301713i	$-0.0975584\pi$
$332$	−1064.60	+	1843.94i	−0.175986	+	0.304817i
$333$		0			0
$334$	−4581.78	+	2645.29i	−0.750610	+	0.433365i
$335$	680.622	+	1178.87i	0.111004	+	0.192265i
$336$		0			0
$337$	1800.32	−	3118.24i	0.291007	−	0.504040i	−0.683041	−	0.730380i	$-0.739343\pi$
$337$	1800.32	−	3118.24i	0.291007	−	0.504040i	0.974048	+	0.226341i	$0.0726763\pi$
$338$			7806.96i			1.25634i
$339$		0			0
$340$	5035.32			0.803173
$341$	−1008.49	−	1746.75i	−0.160154	−	0.277395i
$342$		0			0
$343$	−4488.08	+	4495.64i	−0.706512	+	0.707701i
$344$	2580.80	−	1490.02i	0.404498	−	0.233537i
$345$		0			0
$346$	5834.70	−	3368.66i	0.906576	−	0.523412i
$347$	8104.74	−	4679.27i	1.25385	−	0.723909i	0.281976	−	0.959421i	$-0.409010\pi$
$347$	8104.74	−	4679.27i	1.25385	−	0.723909i	0.971871	+	0.235512i	$0.0756767\pi$
$348$		0			0
$349$	−3496.96	+	2018.97i	−0.536355	+	0.309665i	−0.743601	−	0.668624i	$-0.766884\pi$
$349$	−3496.96	+	2018.97i	−0.536355	+	0.309665i	0.207245	+	0.978289i	$0.433550\pi$
$350$	1175.78	−	1176.44i	0.179566	−	0.179667i
$351$		0			0
$352$	1038.18	+	1798.18i	0.157202	+	0.272282i
$353$	4358.17			0.657117			0.328558	−	0.944484i	$-0.393437\pi$
$353$	4358.17			0.657117			0.328558	+	0.944484i	$0.393437\pi$
$354$		0			0
$355$			5571.23i			0.832930i
$356$	1849.85	−	3204.03i	0.275398	−	0.477003i
$357$		0			0
$358$	−820.847	−	1421.75i	−0.121182	−	0.209893i
$359$	3099.17	−	1789.31i	0.455621	−	0.263053i	−0.254580	−	0.967052i	$-0.581937\pi$
$359$	3099.17	−	1789.31i	0.455621	−	0.263053i	0.710201	+	0.703999i	$0.248604\pi$
$360$		0			0
$361$	3817.59	−	6612.26i	0.556581	−	0.964026i
$362$	5597.23	−	9694.68i	0.812662	−	1.40757i
$363$		0			0
$364$	6268.78	+	1677.83i	0.902675	+	0.241600i
$365$	−8106.29	−	4680.17i	−1.16247	−	0.671154i
$366$		0			0
$367$		−	10258.5i		−	1.45910i	−0.683926	−	0.729551i	$-0.739729\pi$
$367$		−	10258.5i		−	1.45910i	0.683926	−	0.729551i	$-0.260271\pi$
$368$	8309.02	+	4797.22i	1.17700	+	0.679544i
$369$		0			0
$370$			7402.79i			1.04014i
$371$	−5444.30	+	5447.35i	−0.761870	+	0.762297i
$372$		0			0
$373$	9853.78			1.36785			0.683927	−	0.729551i	$-0.260271\pi$
$373$	9853.78			1.36785			0.683927	+	0.729551i	$0.260271\pi$
$374$	1413.43	+	2448.13i	0.195419	+	0.338475i
$375$		0			0
$376$	191.242	+	110.413i	0.0262302	+	0.0151440i
$377$	3827.73			0.522913
$378$		0			0
$379$	−11181.0			−1.51538			−0.757688	−	0.652617i	$-0.773671\pi$
$379$	−11181.0			−1.51538			−0.757688	+	0.652617i	$0.773671\pi$
$380$	−6786.06	−	3917.93i	−0.916099	−	0.528910i
$381$		0			0
$382$	9490.53	+	16438.1i	1.27115	+	2.20169i
$383$	8990.60			1.19947			0.599737	−	0.800198i	$-0.295272\pi$
$383$	8990.60			1.19947			0.599737	+	0.800198i	$0.295272\pi$
$384$		0			0
$385$	2190.74	+	586.350i	0.290002	+	0.0776186i
$386$		−	8672.81i		−	1.14361i
$387$		0			0
$388$	−5082.76	−	2934.53i	−0.665047	−	0.383965i
$389$		−	1888.31i		−	0.246121i	−0.992399	−	0.123061i	$-0.960729\pi$
$389$		−	1888.31i		−	0.246121i	0.992399	−	0.123061i	$-0.0392709\pi$
$390$		0			0
$391$	8214.46	+	4742.62i	1.06246	+	0.613414i
$392$	−1675.11	+	2905.14i	−0.215831	+	0.374315i
$393$		0			0
$394$	−270.297	+	468.168i	−0.0345618	+	0.0598629i
$395$	263.809	−	456.931i	0.0336043	−	0.0582043i
$396$		0			0
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.204984	−	0.978765i	$-0.434286\pi$
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.950128	+	0.311861i	$0.100952\pi$
$398$	−3117.38	−	5399.47i	−0.392614	−	0.680027i
$399$		0			0
$400$	962.768	−	1667.56i	0.120346	−	0.208445i
$401$			2064.71i			0.257124i	0.991701	+	0.128562i	$0.0410361\pi$
$401$			2064.71i			0.257124i	−0.991701	+	0.128562i	$0.958964\pi$
$402$		0			0
$403$	−13266.3			−1.63981
$404$	1874.12	+	3246.07i	0.230794	+	0.399747i
$405$		0			0
$406$	1015.92	−	3795.72i	0.124185	−	0.463986i
$407$	−1437.71	+	830.064i	−0.175098	+	0.101093i
$408$		0			0
$409$	−124.596	+	71.9353i	−0.0150632	+	0.00869676i	−0.507513	−	0.861644i	$-0.669435\pi$
$409$	−124.596	+	71.9353i	−0.0150632	+	0.00869676i	0.492449	+	0.870341i	$0.336102\pi$
$410$	8692.80	−	5018.79i	1.04709	−	0.604537i
$411$		0			0
$412$	−4786.80	+	2763.66i	−0.572399	+	0.330475i
$413$	−6451.59	+	1730.64i	−0.768673	+	0.206196i
$414$		0			0
$415$	2447.06	+	4238.43i	0.289449	+	0.501341i
$416$	13656.9			1.60958
$417$		0			0
$418$		−	4399.09i		−	0.514753i
$419$	−1974.15	+	3419.34i	−0.230176	+	0.398677i	−0.957860	−	0.287236i	$-0.907264\pi$
$419$	−1974.15	+	3419.34i	−0.230176	+	0.398677i	0.727684	+	0.685913i	$0.240597\pi$
$420$		0			0
$421$	5518.29	+	9557.95i	0.638824	+	1.10648i	0.985691	+	0.168561i	$0.0539120\pi$
$421$	5518.29	+	9557.95i	0.638824	+	1.10648i	−0.346868	+	0.937914i	$0.612755\pi$
$422$	3451.50	−	1992.72i	0.398143	−	0.229868i
$423$		0			0
$424$	−2032.84	+	3520.98i	−0.232838	+	0.403287i
$425$	951.812	−	1648.59i	0.108634	−	0.188160i
$426$		0			0
$427$	−9610.03	+	9615.42i	−1.08914	+	1.08975i
$428$	−268.694	−	155.130i	−0.0303453	−	0.0175199i
$429$		0			0
$430$			13607.2i			1.52604i
$431$	−1481.18	−	855.162i	−0.165536	−	0.0955724i	0.414943	−	0.909847i	$-0.363801\pi$
$431$	−1481.18	−	855.162i	−0.165536	−	0.0955724i	−0.580479	+	0.814275i	$0.697135\pi$
$432$		0			0
$433$		−	11599.1i		−	1.28734i	−0.765303	−	0.643670i	$-0.777411\pi$
$433$		−	11599.1i		−	1.28734i	0.765303	−	0.643670i	$-0.222589\pi$
$434$	−3521.01	+	13155.3i	−0.389433	+	1.45502i
$435$		0			0
$436$	−4732.67			−0.519849
$437$	−7380.37	−	12783.2i	−0.807897	−	1.39932i
$438$		0			0
$439$	−3706.44	−	2139.92i	−0.402959	−	0.232648i	0.284801	−	0.958587i	$-0.408072\pi$
$439$	−3706.44	−	2139.92i	−0.402959	−	0.232648i	−0.687760	+	0.725938i	$0.741406\pi$
$440$	1197.21			0.129715
$441$		0			0
$442$	18593.2			2.00088
$443$	−8038.03	−	4640.76i	−0.862073	−	0.497718i	0.00263274	−	0.999997i	$-0.499162\pi$
$443$	−8038.03	−	4640.76i	−0.862073	−	0.497718i	−0.864706	+	0.502278i	$0.832495\pi$
$444$		0			0
$445$	−4252.02	−	7364.71i	−0.452955	−	0.784541i
$446$	4481.49			0.475795
$447$		0			0
$448$	626.989	−	2342.58i	0.0661216	−	0.247046i
$449$		−	6876.47i		−	0.722763i	−0.932418	−	0.361382i	$-0.882305\pi$
$449$		−	6876.47i		−	0.722763i	0.932418	−	0.361382i	$-0.117695\pi$
$450$		0			0
$451$	1949.42	+	1125.50i	0.203536	+	0.117511i
$452$			12485.8i			1.29930i
$453$		0			0
$454$	7154.43	+	4130.61i	0.739590	+	0.427003i
$455$	10544.6	−	10550.5i	1.08646	−	1.08707i
$456$		0			0
$457$	5580.75	−	9666.14i	0.571239	−	0.989416i	−0.425200	−	0.905100i	$-0.639796\pi$
$457$	5580.75	−	9666.14i	0.571239	−	0.989416i	0.996439	−	0.0843160i	$-0.0268705\pi$
$458$	−9402.71	+	16286.0i	−0.959301	+	1.66156i
$459$		0			0
$460$	−6910.87	+	3989.99i	−0.700480	+	0.404422i
$461$	−193.554	−	335.245i	−0.0195547	−	0.0338697i	0.856082	−	0.516839i	$-0.172892\pi$
$461$	−193.554	−	335.245i	−0.0195547	−	0.0338697i	−0.875637	+	0.482970i	$0.839558\pi$
$462$		0			0
$463$	−2485.01	+	4304.16i	−0.249435	+	0.432033i	−0.963369	−	0.268179i	$-0.913578\pi$
$463$	−2485.01	+	4304.16i	−0.249435	+	0.432033i	0.713934	+	0.700213i	$0.246911\pi$
$464$		−	4548.89i		−	0.455122i
$465$		0			0
$466$	1523.48			0.151446
$467$	4548.20	+	7877.72i	0.450676	+	0.780594i	0.998428	−	0.0560470i	$-0.0178497\pi$
$467$	4548.20	+	7877.72i	0.450676	+	0.780594i	−0.547752	+	0.836641i	$0.684516\pi$
$468$		0			0
$469$	1990.76	−	534.021i	0.196002	−	0.0525774i
$470$	−873.231	+	504.160i	−0.0857003	+	0.0494791i
$471$		0			0
$472$	−3053.80	+	1763.11i	−0.297802	+	0.171936i
$473$	−2642.69	+	1525.76i	−0.256894	+	0.148318i
$474$		0			0
$475$	−2565.50	+	1481.19i	−0.247817	+	0.143077i
$476$	1971.25	−	7365.06i	0.189815	−	0.709195i
$477$		0			0
$478$	−10183.6	−	17638.5i	−0.974449	−	1.68779i
$479$	−13858.1			−1.32191			−0.660953	−	0.750427i	$-0.729848\pi$
$479$	−13858.1			−1.32191			−0.660953	+	0.750427i	$0.729848\pi$
$480$		0			0
$481$			10919.2i			1.03508i
$482$	−5062.05	+	8767.72i	−0.478361	+	0.828545i
$483$		0			0
$484$	3274.64	+	5671.84i	0.307536	+	0.532667i
$485$	−11683.1	+	6745.26i	−1.09382	+	0.631518i
$486$		0			0
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	−0.895980	−	0.444094i	$-0.853526\pi$
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	0.832587	+	0.553894i	$0.186859\pi$
$488$	−3588.27	+	6215.07i	−0.332856	+	0.576523i
$489$		0			0
$490$	−7663.61	−	13256.6i	−0.706544	−	1.22219i
$491$	15324.0	+	8847.30i	1.40847	+	0.813183i	0.995241	−	0.0974422i	$-0.0310661\pi$
$491$	15324.0	+	8847.30i	1.40847	+	0.813183i	0.413233	+	0.910625i	$0.364399\pi$
$492$		0			0
$493$		−	4497.12i		−	0.410832i
$494$	−25057.9	−	14467.2i	−2.28220	−	1.31763i
$495$		0			0
$496$			15765.7i			1.42722i
$497$	8148.91	+	2181.05i	0.735470	+	0.196848i
$498$		0			0
$499$	−14157.8			−1.27012			−0.635059	−	0.772464i	$-0.719024\pi$
$499$	−14157.8			−1.27012			−0.635059	+	0.772464i	$0.719024\pi$
$500$	−3267.14	−	5658.85i	−0.292222	−	0.506143i
$501$		0			0
$502$	−11857.4	−	6845.88i	−1.05423	−	0.608659i
$503$	5337.01			0.473093			0.236546	−	0.971620i	$-0.423985\pi$
$503$	5337.01			0.473093			0.236546	+	0.971620i	$0.423985\pi$
$504$		0			0
$505$	8615.60			0.759187
$506$	−3879.79	−	2240.00i	−0.340865	−	0.196799i
$507$		0			0
$508$	−2731.25	−	4730.67i	−0.238543	−	0.413169i
$509$	1521.38			0.132483			0.0662417	−	0.997804i	$-0.478899\pi$
$509$	1521.38			0.132483			0.0662417	+	0.997804i	$0.478899\pi$
$510$		0			0
$511$	−10019.1	+	10024.7i	−0.867353	+	0.867839i
$512$		−	10109.2i		−	0.872595i
$513$		0			0
$514$	−23743.4	−	13708.3i	−2.03750	−	1.17635i
$515$			12705.0i			1.08708i
$516$		0			0
$517$	−195.828	−	113.061i	−0.0166586	−	0.00961786i
$518$	10827.9	+	2898.07i	0.918437	+	0.245819i
$519$		0			0
$520$	3937.23	−	6819.47i	0.332036	−	0.575103i
$521$	8290.88	−	14360.2i	0.697178	−	1.20755i	−0.272262	−	0.962223i	$-0.587772\pi$
$521$	8290.88	−	14360.2i	0.697178	−	1.20755i	0.969441	−	0.245325i	$-0.0788948\pi$
$522$		0			0
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	−0.125009	−	0.992156i	$-0.539896\pi$
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	0.796727	+	0.604339i	$0.206563\pi$
$524$	3807.78	+	6595.26i	0.317449	+	0.549838i
$525$		0			0
$526$	10100.8	−	17495.0i	0.837288	−	1.45023i
$527$			15586.3i			1.28833i
$528$		0			0
$529$	−2865.21			−0.235491
$530$	−9282.16	−	16077.2i	−0.760738	−	1.31764i
$531$		0			0
$532$	−8387.31	+	8392.01i	−0.683526	+	0.683910i
$533$	12822.0	−	7402.79i	1.04199	−	0.601596i
$534$		0			0
$535$	−617.613	+	356.579i	−0.0499098	+	0.0288154i
$536$	942.309	−	544.042i	0.0759357	−	0.0438415i
$537$		0			0
$538$	2604.27	−	1503.58i	0.208695	−	0.120490i
$539$	1715.28	−	2974.81i	0.137073	−	0.237725i
$540$		0			0
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	0.999995	−	0.00324160i	$-0.00103183\pi$
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	−0.502805	+	0.864400i	$0.667699\pi$
$542$	−15836.5			−1.25505
$543$		0			0
$544$		−	16045.2i		−	1.26458i
$545$	−5439.21	+	9420.99i	−0.427505	+	0.740460i
$546$		0			0
$547$	4213.76	+	7298.44i	0.329373	+	0.570491i	0.982388	−	0.186854i	$-0.0598292\pi$
$547$	4213.76	+	7298.44i	0.329373	+	0.570491i	−0.653014	+	0.757346i	$0.726496\pi$
$548$	−11647.4	+	6724.61i	−0.907940	+	0.524199i
$549$		0			0
$550$	−449.553	+	778.648i	−0.0348527	+	0.0603666i
$551$	−3499.16	+	6060.73i	−0.270543	+	0.468595i
$552$		0			0
$553$	−565.066	−	564.749i	−0.0434522	−	0.0434278i
$554$	−8352.73	−	4822.45i	−0.640566	−	0.369831i
$555$		0			0
$556$		−	1517.86i		−	0.115776i
$557$	−17760.6	−	10254.1i	−1.35106	−	0.780035i	−0.362662	−	0.931921i	$-0.618132\pi$
$557$	−17760.6	−	10254.1i	−1.35106	−	0.780035i	−0.988398	+	0.151886i	$0.951465\pi$
$558$		0			0
$559$			20070.9i			1.51862i
$560$	−12538.2	−	12531.2i	−0.946138	−	0.945607i
$561$		0			0
$562$	13973.9			1.04885
$563$	−2255.95	−	3907.43i	−0.168876	−	0.292502i	0.769149	−	0.639069i	$-0.220680\pi$
$563$	−2255.95	−	3907.43i	−0.168876	−	0.292502i	−0.938025	+	0.346568i	$0.887347\pi$
$564$		0			0
$565$	24854.5	+	14349.8i	1.85069	+	1.06849i
$566$	26252.0			1.94957
$567$		0			0
$568$	4453.25			0.328969
$569$	11133.3	+	6427.82i	0.820268	+	0.473582i	0.850509	−	0.525960i	$-0.176294\pi$
$569$	11133.3	+	6427.82i	0.820268	+	0.473582i	−0.0302406	+	0.999543i	$0.509627\pi$
$570$		0			0
$571$	−3099.39	−	5368.30i	−0.227155	−	0.393444i	0.729809	−	0.683651i	$-0.239609\pi$
$571$	−3099.39	−	5368.30i	−0.227155	−	0.393444i	−0.956964	+	0.290208i	$0.906276\pi$
$572$	−3507.95			−0.256424
$573$		0			0
$574$	−3937.78	−	14679.5i	−0.286341	−	1.06744i
$575$			3016.86i			0.218803i
$576$		0			0
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.943908	−	0.330209i	$-0.107119\pi$
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.185985	+	0.982553i	$0.440452\pi$
$578$		−	3913.12i		−	0.281599i
$579$		0			0
$580$	3276.56	+	1891.72i	0.234572	+	0.135430i
$581$	7157.45	−	1919.98i	0.511086	−	0.137099i
$582$		0			0
$583$	2081.59	−	3605.42i	0.147874	−	0.256126i
$584$	−3741.00	+	6479.61i	−0.265075	+	0.459123i
$585$		0			0
$586$	11832.5	−	6831.49i	0.834122	−	0.481580i
$587$	2442.51	+	4230.56i	0.171743	+	0.297468i	0.939029	−	0.343837i	$-0.111727\pi$
$587$	2442.51	+	4230.56i	0.171743	+	0.297468i	−0.767286	+	0.641305i	$0.778393\pi$
$588$		0			0
$589$	12127.5	−	21005.5i	0.848398	−	1.46947i
$590$		−	16101.1i		−	1.12351i
$591$		0			0
$592$	12976.4			0.900893
$593$	1304.78	+	2259.95i	0.0903557	+	0.156501i	0.907661	−	0.419704i	$-0.137866\pi$
$593$	1304.78	+	2259.95i	0.0903557	+	0.156501i	−0.817305	+	0.576205i	$0.804533\pi$
$594$		0			0
$595$	−12395.5	−	12388.6i	−0.854063	−	0.853585i
$596$	8683.43	−	5013.38i	0.596791	−	0.344557i
$597$		0			0
$598$	−25518.7	+	14733.3i	−1.74505	+	1.00750i
$599$	−13896.7	+	8023.27i	−0.947920	+	0.547282i	−0.892434	−	0.451177i	$-0.851004\pi$
$599$	−13896.7	+	8023.27i	−0.947920	+	0.547282i	−0.0554860	+	0.998459i	$0.517671\pi$
$600$		0			0
$601$	6848.07	−	3953.74i	0.464790	−	0.268347i	−0.249266	−	0.968435i	$-0.580189\pi$
$601$	6848.07	−	3953.74i	0.464790	−	0.268347i	0.714056	+	0.700088i	$0.246856\pi$
$602$	19903.0	+	5327.01i	1.34748	+	0.360652i
$603$		0			0
$604$	−1065.44	−	1845.40i	−0.0717753	−	0.124318i
$605$	15054.0			1.01162
$606$		0			0
$607$		−	3703.30i		−	0.247632i	−0.992305	−	0.123816i	$-0.960487\pi$
$607$		−	3703.30i		−	0.247632i	0.992305	−	0.123816i	$-0.0395132\pi$
$608$	−12484.6	+	21624.0i	−0.832759	+	1.44238i
$609$		0			0
$610$	−16384.5	−	28378.7i	−1.08752	−	1.88364i
$611$	−1288.03	+	743.644i	−0.0852833	+	0.0492383i
$612$		0			0
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	−0.980704	−	0.195498i	$-0.937368\pi$
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	0.659658	+	0.751566i	$0.270701\pi$
$614$	7663.46	−	13273.5i	0.503700	−	0.872435i
$615$		0			0
$616$	468.688	−	1751.13i	0.0306558	−	0.114537i
$617$	22722.4	+	13118.8i	1.48261	+	0.855985i	0.999805	−	0.0197440i	$-0.00628512\pi$
$617$	22722.4	+	13118.8i	1.48261	+	0.855985i	0.482804	+	0.875729i	$0.339618\pi$
$618$		0			0
$619$		−	5165.08i		−	0.335383i	−0.985839	−	0.167692i	$-0.946369\pi$
$619$		−	5165.08i		−	0.335383i	0.985839	−	0.167692i	$-0.0536313\pi$
$620$	−11356.0	−	6556.41i	−0.735596	−	0.424697i
$621$		0			0
$622$		−	9063.81i		−	0.584286i
$623$	−12436.8	+	3336.17i	−0.799791	+	0.214544i
$624$		0			0
$625$	−18095.3			−1.15810
$626$	−1497.45	−	2593.65i	−0.0956070	−	0.165596i
$627$		0			0
$628$	9040.81	+	5219.72i	0.574471	+	0.331671i
$629$	12828.8			0.813221
$630$		0			0
$631$	1350.06			0.0851743			0.0425871	−	0.999093i	$-0.486440\pi$
$631$	1350.06			0.0851743			0.0425871	+	0.999093i	$0.486440\pi$
$632$	−365.239	−	210.871i	−0.0229880	−	0.0132721i
$633$		0			0
$634$	7543.27	+	13065.3i	0.472526	+	0.818439i
$635$	−12556.0			−0.784677
$636$		0			0
$637$	−11303.9	−	19553.7i	−0.703106	−	1.21624i
$638$			2124.05i			0.131805i
$639$		0			0
$640$	−12513.0	−	7224.38i	−0.772843	−	0.446201i
$641$			18082.9i			1.11424i	0.830431	+	0.557122i	$0.188094\pi$
$641$			18082.9i			1.11424i	−0.830431	+	0.557122i	$0.811906\pi$
$642$		0			0
$643$	−16884.0	−	9748.00i	−1.03552	−	0.597859i	−0.116961	−	0.993137i	$-0.537315\pi$
$643$	−16884.0	−	9748.00i	−1.03552	−	0.597859i	−0.918562	+	0.395277i	$0.870649\pi$
$644$	3130.58	+	11670.4i	0.191556	+	0.714096i
$645$		0			0
$646$	−16997.2	+	29440.0i	−1.03521	+	1.79303i
$647$	−8503.93	+	14729.2i	−0.516730	+	0.895002i	0.483082	+	0.875575i	$0.339517\pi$
$647$	−8503.93	+	14729.2i	−0.516730	+	0.895002i	−0.999811	+	0.0194267i	$0.993816\pi$
$648$		0			0
$649$	3127.04	−	1805.40i	0.189132	−	0.109196i
$650$	2956.86	+	5121.44i	0.178427	+	0.309045i
$651$		0			0
$652$	−5814.22	+	10070.5i	−0.349237	+	0.604896i
$653$		−	4331.50i		−	0.259578i	−0.991542	−	0.129789i	$-0.958570\pi$
$653$		−	4331.50i		−	0.259578i	0.991542	−	0.129789i	$-0.0414301\pi$
$654$		0			0
$655$	17504.9			1.04424
$656$	−8797.50	−	15237.7i	−0.523604	−	0.906909i
$657$		0			0
$658$	395.568	+	1474.63i	0.0234359	+	0.0873661i
$659$	−2674.86	+	1544.33i	−0.158115	+	0.0912875i	−0.576970	−	0.816766i	$-0.695765\pi$
$659$	−2674.86	+	1544.33i	−0.158115	+	0.0912875i	0.418855	+	0.908053i	$0.362432\pi$
$660$		0			0
$661$	−19561.4	+	11293.8i	−1.15106	+	0.664564i	−0.949145	−	0.314839i	$-0.898050\pi$
$661$	−19561.4	+	11293.8i	−1.15106	+	0.664564i	−0.201914	+	0.979403i	$0.564716\pi$
$662$	28094.8	−	16220.6i	1.64945	−	0.952311i
$663$		0			0
$664$	3387.91	−	1956.01i	0.198007	−	0.114319i
$665$	7065.92	+	26340.8i	0.412037	+	1.53602i
$666$		0			0
$667$	3563.52	+	6172.19i	0.206866	+	0.358303i
$668$	−7713.41			−0.446768
$669$		0			0
$670$			4968.31i			0.286482i
$671$	3674.33	−	6364.12i	0.211395	−	0.366146i
$672$		0			0
$673$	3978.45	+	6890.88i	0.227872	+	0.394686i	0.957177	−	0.289502i	$-0.0934898\pi$
$673$	3978.45	+	6890.88i	0.227872	+	0.394686i	−0.729305	+	0.684189i	$0.760156\pi$
$674$	11381.0	−	6570.85i	0.650418	−	0.375519i
$675$		0			0
$676$	−5691.08	+	9857.24i	−0.323798	+	0.560835i
$677$	5552.77	−	9617.67i	0.315229	−	0.545993i	−0.664257	−	0.747504i	$-0.731252\pi$
$677$	5552.77	−	9617.67i	0.315229	−	0.545993i	0.979486	+	0.201511i	$0.0645853\pi$
$678$		0			0
$679$	5292.38	+	19729.3i	0.299121	+	1.11508i
$680$	−8012.05	−	4625.76i	−0.451836	−	0.260867i
$681$		0			0
$682$		−	7361.60i		−	0.413329i
$683$	−16295.7	−	9408.31i	−0.912938	−	0.527085i	−0.0315626	−	0.999502i	$-0.510048\pi$
$683$	−16295.7	−	9408.31i	−0.912938	−	0.527085i	−0.881375	+	0.472417i	$0.843382\pi$
$684$		0			0
$685$			30914.1i			1.72433i
$686$	−22390.3	+	6019.65i	−1.24616	+	0.335031i
$687$		0			0
$688$	23852.3			1.32174
$689$	−13691.3	−	23714.1i	−0.757037	−	1.31123i
$690$		0			0
$691$	−12726.4	−	7347.58i	−0.700629	−	0.404508i	0.106953	−	0.994264i	$-0.465891\pi$
$691$	−12726.4	−	7347.58i	−0.700629	−	0.404508i	−0.807582	+	0.589756i	$0.799224\pi$
$692$	9822.69			0.539599
$693$		0			0
$694$	34157.1			1.86828
$695$	−3021.49	−	1744.46i	−0.164909	−	0.0952103i
$696$		0			0
$697$	−8697.38	−	15064.3i	−0.472649	−	0.818653i
$698$	−14737.8			−0.799190
$699$		0			0
$700$	2342.17	−	628.285i	0.126465	−	0.0339242i
$701$			2167.47i			0.116782i	0.998294	+	0.0583910i	$0.0185970\pi$
$701$			2167.47i			0.116782i	−0.998294	+	0.0583910i	$0.981403\pi$
$702$		0			0
$703$	−17289.2	−	9981.93i	−0.927560	−	0.535527i
$704$			1310.89i			0.0701788i
$705$		0			0
$706$	13775.5	+	7953.30i	0.734346	+	0.423975i
$707$	3372.87	−	12601.9i	0.179420	−	0.670356i
$708$		0			0
$709$	−17149.1	+	29703.1i	−0.908388	+	1.57337i	−0.0920850	+	0.995751i	$0.529353\pi$
$709$	−17149.1	+	29703.1i	−0.908388	+	1.57337i	−0.816303	+	0.577623i	$0.803980\pi$
$710$	−10167.0	+	17609.8i	−0.537411	+	0.930823i
$711$		0			0
$712$	−5886.84	+	3398.77i	−0.309858	+	0.178896i
$713$	−12350.6	−	21391.8i	−0.648714	−	1.12361i
$714$		0			0
$715$	−4031.65	+	6983.02i	−0.210874	+	0.365245i
$716$		−	2393.51i		−	0.124930i
$717$		0			0
$718$	13061.3			0.678893
$719$	7330.37	+	12696.6i	0.380218	+	0.658557i	0.991093	−	0.133170i	$-0.0425157\pi$
$719$	7330.37	+	12696.6i	0.380218	+	0.658557i	−0.610875	+	0.791727i	$0.709182\pi$
$720$		0			0
$721$	18583.3	+	4973.79i	0.959885	+	0.256912i
$722$	24133.6	−	13933.6i	1.24399	−	0.718218i
$723$		0			0
$724$	14134.4	−	8160.48i	0.725552	−	0.418898i
$725$	1238.72	−	715.173i	0.0634549	−	0.0366357i
$726$		0			0
$727$	−9274.34	+	5354.55i	−0.473131	+	0.273162i	−0.717550	−	0.696507i	$-0.754736\pi$
$727$	−9274.34	+	5354.55i	−0.473131	+	0.273162i	0.244418	+	0.969670i	$0.421403\pi$
$728$	−8433.33	−	8428.61i	−0.429341	−	0.429100i
$729$		0			0
$730$	−17081.8	−	29586.6i	−0.866064	−	1.50007i
$731$	23580.8			1.19312
$732$		0			0
$733$			15214.2i			0.766644i	0.923615	+	0.383322i	$0.125220\pi$
$733$			15214.2i			0.766644i	−0.923615	+	0.383322i	$0.874780\pi$
$734$	18720.9	−	32425.6i	0.941421	−	1.63059i
$735$		0			0
$736$	12714.2	+	22021.7i	0.636755	+	1.10289i
$737$	−964.907	+	557.089i	−0.0482263	+	0.0278435i
$738$		0			0
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	−0.720462	−	0.693495i	$-0.756070\pi$
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	0.960815	+	0.277191i	$0.0894035\pi$
$740$	−5396.45	+	9346.92i	−0.268078	+	0.464324i
$741$		0			0
$742$	−27149.5	+	7282.86i	−1.34325	+	0.360326i
$743$	4935.72	+	2849.64i	0.243706	+	0.140704i	0.616879	−	0.787058i	$-0.288397\pi$
$743$	4935.72	+	2849.64i	0.243706	+	0.140704i	−0.373173	+	0.927762i	$0.621730\pi$
$744$		0			0
$745$		−	23047.3i		−	1.13341i
$746$	31146.3	+	17982.3i	1.52861	+	0.882546i
$747$		0			0
$748$			4121.41i			0.201462i
$749$	279.775	+	1042.96i	0.0136485	+	0.0508799i
$750$		0			0
$751$	34815.7			1.69167			0.845833	−	0.533448i	$-0.179104\pi$
$751$	34815.7			1.69167			0.845833	+	0.533448i	$0.179104\pi$
$752$	883.748	+	1530.70i	0.0428550	+	0.0742271i
$753$		0			0
$754$	12098.9	+	6985.29i	0.584370	+	0.337386i
$755$	−4898.01			−0.236102
$756$		0			0
$757$	−12225.4			−0.586976			−0.293488	−	0.955963i	$-0.594816\pi$
$757$	−12225.4			−0.586976			−0.293488	+	0.955963i	$0.594816\pi$
$758$	−35341.3	−	20404.3i	−1.69348	−	0.977728i
$759$		0			0
$760$	7198.51	+	12468.2i	0.343576	+	0.595091i
$761$	−11388.4			−0.542482			−0.271241	−	0.962512i	$-0.587434\pi$
$761$	−11388.4			−0.542482			−0.271241	+	0.962512i	$0.587434\pi$
$762$		0			0
$763$	11650.5	+	11644.0i	0.552787	+	0.552477i
$764$			27673.4i			1.31046i
$765$		0			0
$766$	28417.9	+	16407.1i	1.34045	+	0.773906i
$767$		−	23749.4i		−	1.11805i
$768$		0			0
$769$	5063.88	+	2923.63i	0.237462	+	0.137099i	0.614010	−	0.789299i	$-0.289556\pi$
$769$	5063.88	+	2923.63i	0.237462	+	0.137099i	−0.376548	+	0.926397i	$0.622889\pi$
$770$	5854.57	+	5851.29i	0.274005	+	0.273852i
$771$		0			0
$772$	6322.26	−	10950.5i	0.294745	−	0.510513i
$773$	2151.82	−	3727.06i	0.100124	−	0.173419i	−0.811612	−	0.584197i	$-0.801410\pi$
$773$	2151.82	−	3727.06i	0.100124	−	0.173419i	0.911735	+	0.410778i	$0.134743\pi$
$774$		0			0
$775$	−4293.20	+	2478.68i	−0.198989	+	0.114886i
$776$	5391.69	+	9338.68i	0.249421	+	0.432009i
$777$		0			0
$778$	3446.01	−	5968.66i	0.158799	−	0.275047i
$779$			27069.4i			1.24501i
$780$		0			0
$781$	−4560.05			−0.208926
$782$	17309.8	+	29981.4i	0.791555	+	1.37101i
$783$		0			0
$784$	−23237.6	+	13433.6i	−1.05857	+	0.611955i
$785$	20781.0	−	11997.9i	0.944848	−	0.545509i
$786$		0			0
$787$	24548.4	−	14173.0i	1.11189	−	0.641949i	0.172571	−	0.984997i	$-0.444793\pi$
$787$	24548.4	−	14173.0i	1.11189	−	0.641949i	0.939318	+	0.343048i	$0.111459\pi$
$788$	−682.566	+	394.080i	−0.0308571	+	0.0178154i
$789$		0			0
$790$	1667.72	−	962.859i	0.0751074	−	0.0433633i
$791$	30719.2	−	30736.5i	1.38085	−	1.38162i
$792$		0			0
$793$	−24167.3	−	41859.0i	−1.08223	−	1.87447i
$794$	38508.1			1.72116
$795$		0			0
$796$		−	9089.98i		−	0.404756i
$797$	−4002.70	+	6932.88i	−0.177896	+	0.308124i	−0.941160	−	0.337963i	$-0.890262\pi$
$797$	−4002.70	+	6932.88i	−0.177896	+	0.308124i	0.763264	+	0.646087i	$0.223596\pi$
$798$		0			0
$799$	873.691	+	1513.28i	0.0386846	+	0.0670036i
$800$	4419.60	−	2551.65i	0.195320	−	0.112768i
$801$		0			0
$802$	−3767.92	+	6526.23i	−0.165898	+	0.287343i
$803$	3830.72	−	6635.00i	0.168348	−	0.291587i
$804$		0			0
$805$	26829.3	+	7180.83i	1.17467	+	0.314399i
$806$	−41932.8	−	24209.9i	−1.83253	−	1.05801i
$807$		0			0
$808$		−	6886.72i		−	0.299844i
$809$	9857.91	+	5691.47i	0.428412	+	0.247344i	0.698670	−	0.715444i	$-0.253776\pi$
$809$	9857.91	+	5691.47i	0.428412	+	0.247344i	−0.270258	+	0.962788i	$0.587109\pi$
$810$		0			0
$811$			3510.72i			0.152008i	0.997108	+	0.0760038i	$0.0242161\pi$
$811$			3510.72i			0.152008i	−0.997108	+	0.0760038i	$0.975784\pi$
$812$	4049.70	−	4051.97i	0.175021	−	0.175119i
$813$		0			0
$814$	−6059.18			−0.260902
$815$	13364.4	+	23147.9i	0.574400	+	0.994890i
$816$		0			0
$817$	−31779.6	−	18348.0i	−1.36087	−	0.785697i
$818$	−525.104			−0.0224448
$819$		0			0
$820$	14634.3			0.623233
$821$	−11046.2	−	6377.52i	−0.469567	−	0.271105i	0.246491	−	0.969145i	$-0.420722\pi$
$821$	−11046.2	−	6377.52i	−0.469567	−	0.271105i	−0.716058	+	0.698040i	$0.754056\pi$
$822$		0			0
$823$	4835.76	+	8375.78i	0.204817	+	0.354753i	0.950074	−	0.312024i	$-0.101007\pi$
$823$	4835.76	+	8375.78i	0.204817	+	0.354753i	−0.745258	+	0.666777i	$0.767674\pi$
$824$	10155.5			0.429348
$825$		0			0
$826$	−23550.8	−	6303.33i	−0.992053	−	0.265522i
$827$		−	41804.8i		−	1.75779i	−0.477011	−	0.878897i	$-0.658280\pi$
$827$		−	41804.8i		−	1.75779i	0.477011	−	0.878897i	$-0.341720\pi$
$828$		0			0
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	0.743465	−	0.668775i	$-0.233181\pi$
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	−0.207444	+	0.978247i	$0.566515\pi$
$830$			17862.7i			0.747017i
$831$		0			0
$832$	7467.01	+	4311.08i	0.311144	+	0.179639i
$833$	−22973.2	+	13280.8i	−0.955551	+	0.552402i
$834$		0			0
$835$	−8864.93	+	15354.5i	−0.367406	+	0.636365i
$836$	3206.83	−	5554.39i	0.132668	−	0.229788i
$837$		0			0
$838$	−12480.0	+	7205.33i	−0.514457	+	0.297022i
$839$	746.315	+	1292.66i	0.0307100	+	0.0531912i	0.880972	−	0.473169i	$-0.156890\pi$
$839$	746.315	+	1292.66i	0.0307100	+	0.0531912i	−0.850262	+	0.526360i	$0.823557\pi$
$840$		0			0
$841$	−10505.0	+	18195.1i	−0.430726	+	0.746039i
$842$			40281.6i			1.64869i
$843$		0			0
$844$	5810.58			0.236977
$845$	13081.4	+	22657.6i	0.532560	+	0.922422i
$846$		0			0
$847$	5893.41	−	22019.2i	0.239079	−	0.893256i
$848$	−28181.9	+	16270.8i	−1.14124	+	0.658894i
$849$		0			0
$850$	6017.06	−	3473.95i	0.242804	−	0.140183i
$851$	−17607.2	+	10165.5i	−0.709244	+	0.409482i
$852$		0			0
$853$	3660.40	−	2113.34i	0.146928	−	0.0848291i	−0.424734	−	0.905318i	$-0.639632\pi$
$853$	3660.40	−	2113.34i	0.146928	−	0.0848291i	0.571662	+	0.820489i	$0.306299\pi$
$854$	−47923.2	+	12855.4i	−1.92025	+	0.515107i
$855$		0			0
$856$	285.025	+	493.677i	0.0113808	+	0.0197121i
$857$	−6728.80			−0.268205			−0.134102	−	0.990967i	$-0.542815\pi$
$857$	−6728.80			−0.268205			−0.134102	+	0.990967i	$0.542815\pi$
$858$		0			0
$859$		−	39541.8i		−	1.57060i	−0.619113	−	0.785302i	$-0.712508\pi$
$859$		−	39541.8i		−	1.57060i	0.619113	−	0.785302i	$-0.287492\pi$
$860$	−9919.32	+	17180.8i	−0.393309	+	0.681232i
$861$		0			0
$862$	−3121.20	−	5406.07i	−0.123328	−	0.213610i
$863$	22905.9	−	13224.7i	0.903508	−	0.521640i	0.0251711	−	0.999683i	$-0.491987\pi$
$863$	22905.9	−	13224.7i	0.903508	−	0.521640i	0.878337	+	0.478043i	$0.158654\pi$
$864$		0			0
$865$	11289.1	−	19553.3i	0.443747	−	0.768592i
$866$	21167.4	−	36663.1i	0.830599	−	1.43864i
$867$		0			0
$868$	−14035.6	+	14043.5i	−0.548848	+	0.549156i
$869$	373.998	+	215.928i	0.0145996	+	0.00842906i
$870$		0			0
$871$			7328.34i			0.285088i
$872$	7530.49	+	4347.73i	0.292448	+	0.168845i
$873$		0			0
$874$		−	53874.2i		−	2.08504i
$875$	−5879.91	+	21968.7i	−0.227174	+	0.848776i
$876$		0			0
$877$	2426.36			0.0934234			0.0467117	−	0.998908i	$-0.485126\pi$
$877$	2426.36			0.0934234			0.0467117	+	0.998908i	$0.485126\pi$
$878$	−7810.34	−	13527.9i	−0.300212	−	0.519982i
$879$		0			0
$880$	8298.64	+	4791.22i	0.317894	+	0.183536i
$881$	−22112.5			−0.845616			−0.422808	−	0.906219i	$-0.638956\pi$
$881$	−22112.5			−0.845616			−0.422808	+	0.906219i	$0.638956\pi$
$882$		0			0
$883$	−50385.7			−1.92029			−0.960144	−	0.279506i	$-0.909829\pi$
$883$	−50385.7			−1.92029			−0.960144	+	0.279506i	$0.909829\pi$
$884$	23476.2	+	13554.0i	0.893201	+	0.515690i
$885$		0			0
$886$	−16938.0	−	29337.5i	−0.642261	−	1.11243i
$887$	−10325.0			−0.390845			−0.195422	−	0.980719i	$-0.562608\pi$
$887$	−10325.0			−0.390845			−0.195422	+	0.980719i	$0.562608\pi$
$888$		0			0
$889$	−4915.47	+	18365.4i	−0.185444	+	0.692863i
$890$		−	31038.3i		−	1.16900i
$891$		0			0
$892$	5658.42	+	3266.89i	0.212397	+	0.122627i
$893$		−	2719.24i		−	0.101899i
$894$		0			0
$895$	−4764.58	−	2750.83i	−0.177947	−	0.102738i
$896$	−15465.6	+	15474.3i	−0.576639	+	0.576963i
$897$		0			0
$898$	12549.0	−	21735.5i	0.466331	−	0.807708i
$899$	−5855.63	+	10142.2i	−0.217237	+	0.376266i
$900$		0			0
$901$	−27861.2	+	16085.6i	−1.03018	+	0.594773i
$902$	4107.88	+	7115.06i	0.151638	+	0.262645i
$903$		0			0
$904$	11470.2	−	19867.0i	0.422006	−	0.730936i
$905$		−	37515.0i		−	1.37795i
$906$		0			0
$907$	−4878.45			−0.178596			−0.0892979	−	0.996005i	$-0.528462\pi$
$907$	−4878.45			−0.178596			−0.0892979	+	0.996005i	$0.528462\pi$
$908$	6022.23	+	10430.8i	0.220104	+	0.381232i
$909$		0			0
$910$	52583.6	−	14105.5i	1.91553	−	0.513839i
$911$	−26279.5	+	15172.5i	−0.955741	+	0.551797i	−0.894860	−	0.446348i	$-0.852724\pi$
$911$	−26279.5	+	15172.5i	−0.955741	+	0.551797i	−0.0608814	+	0.998145i	$0.519391\pi$
$912$		0			0
$913$	−3469.16	+	2002.92i	−0.125753	+	0.0726035i
$914$	35279.8	−	20368.8i	1.27675	−	0.737133i
$915$		0			0
$916$	−23744.1	+	13708.7i	−0.856472	+	0.494484i
$917$	6852.90	−	25604.1i	0.246786	−	0.922052i
$918$		0			0
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	−0.999961	−	0.00880146i	$-0.997198\pi$
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	0.492358	−	0.870393i	$-0.336135\pi$
$920$	14661.8			0.525419
$921$		0			0
$922$		−	1412.88i		−	0.0504671i
$923$	−14996.5	+	25974.7i	−0.534796	+	0.926293i
$924$		0			0
$925$	2040.15	+	3533.64i	0.0725185	+	0.125606i
$926$	−15709.5	+	9069.87i	−0.557500	+	0.321873i
$927$		0			0
$928$	6028.03	−	10440.9i	0.213232	−	0.369329i
$929$	10855.5	−	18802.2i	0.383376	−	0.664026i	−0.608167	−	0.793809i	$-0.708095\pi$
$929$	10855.5	−	18802.2i	0.383376	−	0.664026i	0.991542	+	0.129783i	$0.0414281\pi$
$930$		0			0
$931$	41294.4	−	23.1518i	1.45367	−	0.000815004i
$932$	1923.57	+	1110.58i	0.0676060	+	0.0390323i
$933$		0			0
$934$			33200.3i			1.16311i
$935$	8204.20	+	4736.70i	0.286958	+	0.165675i
$936$		0			0
$937$			6528.34i			0.227611i	0.993503	+	0.113805i	$0.0363041\pi$
$937$			6528.34i			0.227611i	−0.993503	+	0.113805i	$0.963696\pi$
$938$	7267.04	+	1945.01i	0.252961	+	0.0677047i
$939$		0			0
$940$	−1470.08			−0.0510093
$941$	−1498.33	−	2595.18i	−0.0519066	−	0.0899049i	0.838905	−	0.544278i	$-0.183196\pi$
$941$	−1498.33	−	2595.18i	−0.0519066	−	0.0899049i	−0.890811	+	0.454374i	$0.849863\pi$
$942$		0			0
$943$	23873.9	+	13783.6i	0.824434	+	0.475987i
$944$	−28223.9			−0.973102
$945$		0			0
$946$	−11137.5			−0.382782
$947$	−4997.80	−	2885.48i	−0.171496	−	0.0990133i	0.411795	−	0.911277i	$-0.364902\pi$
$947$	−4997.80	−	2885.48i	−0.171496	−	0.0990133i	−0.583291	+	0.812263i	$0.698235\pi$
$948$		0			0
$949$	−25196.0	−	43640.7i	−0.861850	−	1.49277i
$950$	−10812.2			−0.369257
$951$		0			0
$952$	−9902.59	+	9908.14i	−0.337127	+	0.337316i
$953$			38807.0i			1.31908i	0.751670	+	0.659540i	$0.229249\pi$
$953$			38807.0i			1.31908i	−0.751670	+	0.659540i	$0.770751\pi$
$954$		0			0
$955$	55087.5	+	31804.8i	1.86659	+	1.07767i
$956$		−	29694.3i		−	1.00458i
$957$		0			0
$958$	−43803.3	−	25289.9i	−1.47727	−	0.852900i
$959$	45217.4	+	12102.4i	1.52257	+	0.407514i
$960$		0			0
$961$	5399.17	−	9351.64i	0.181235	−	0.313908i
$962$	−19926.7	+	34514.0i	−0.667840	+	1.15673i
$963$		0			0
$964$	−12782.9	+	7380.21i	−0.427085	+	0.246577i
$965$	−14532.2	−	25170.5i	−0.484775	−	0.839656i
$966$		0			0
$967$	−27150.0	+	47025.2i	−0.902880	+	1.56383i	−0.0791416	+	0.996863i	$0.525218\pi$
$967$	−27150.0	+	47025.2i	−0.902880	+	1.56383i	−0.823738	+	0.566970i	$0.808115\pi$
$968$		−	12033.1i		−	0.399545i
$969$		0			0
$970$	−49238.1			−1.62984
$971$	−17624.4	−	30526.3i	−0.582485	−	1.00889i	−0.995184	−	0.0980262i	$-0.968747\pi$
$971$	−17624.4	−	30526.3i	−0.582485	−	1.00889i	0.412699	−	0.910868i	$-0.364586\pi$
$972$		0			0
$973$	−3734.45	+	3736.54i	−0.123043	+	0.123112i
$974$	−4306.94	+	2486.61i	−0.141687	+	0.0818031i
$975$		0			0
$976$	−49745.4	+	28720.5i	−1.63147	+	0.941928i
$977$	−42809.1	+	24715.8i	−1.40183	+	0.809344i	−0.994580	−	0.103975i	$-0.966844\pi$
$977$	−42809.1	+	24715.8i	−1.40183	+	0.809344i	−0.407245	+	0.913319i	$0.633511\pi$
$978$		0			0
$979$	6028.02	−	3480.28i	0.196789	−	0.113616i
$980$	−12.5163	−	22324.6i	−0.000407980	−	0.727688i
$981$		0			0
$982$	32291.1	+	55929.9i	1.04934	+	1.81751i
$983$	−42847.4			−1.39026			−0.695128	−	0.718886i	$-0.744652\pi$
$983$	−42847.4			−1.39026			−0.695128	+	0.718886i	$0.744652\pi$
$984$		0			0
$985$			1811.64i			0.0586029i
$986$	8206.87	−	14214.7i	0.265071	−	0.459116i
$987$		0			0
$988$	−21092.4	−	36533.2i	−0.679190	−	1.17639i
$989$	−32364.1	+	18685.4i	−1.04057	+	0.600771i
$990$		0			0
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	−0.517178	−	0.855878i	$-0.673018\pi$
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	0.999801	+	0.0199505i	$0.00635086\pi$
$992$	−20892.2	+	36186.3i	−0.668677	+	1.15818i
$993$		0			0
$994$	21777.2	+	21765.0i	0.694901	+	0.694512i
$995$	−18094.8	−	10447.0i	−0.576525	−	0.332857i
$996$		0			0
$997$		−	7200.82i		−	0.228738i	−0.993438	−	0.114369i	$-0.963515\pi$
$997$		−	7200.82i		−	0.228738i	0.993438	−	0.114369i	$-0.0364847\pi$
$998$	−44750.5	−	25836.7i	−1.41939	−	0.819487i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.18		44
3.2	odd	2		63.4.s.a.59.5	yes	44
7.5	odd	6		189.4.i.a.152.5		44
9.2	odd	6		189.4.i.a.143.18		44
9.7	even	3		63.4.i.a.38.5	yes	44
21.5	even	6		63.4.i.a.5.18	✓	44
63.47	even	6	inner	189.4.s.a.89.18		44
63.61	odd	6		63.4.s.a.47.5	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.18	✓	44	21.5	even	6
63.4.i.a.38.5	yes	44	9.7	even	3
63.4.s.a.47.5	yes	44	63.61	odd	6
63.4.s.a.59.5	yes	44	3.2	odd	2
189.4.i.a.143.18		44	9.2	odd	6
189.4.i.a.152.5		44	7.5	odd	6
189.4.s.a.17.18		44	1.1	even	1	trivial
189.4.s.a.89.18		44	63.47	even	6	inner

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.16085 + 1.82492i) q^{2} +(2.66064 + 4.60836i) q^{4} +12.2314 q^{5} +(4.78838 - 17.8905i) q^{7} -9.77690i q^{8} +O(q^{10})\)	\(q+(3.16085 + 1.82492i) q^{2} +(2.66064 + 4.60836i) q^{4} +12.2314 q^{5} +(4.78838 - 17.8905i) q^{7} -9.77690i q^{8} +(38.6615 + 22.3212i) q^{10} +10.0114i q^{11} +(57.0263 + 32.9241i) q^{13} +(47.7841 - 47.8109i) q^{14} +(39.1271 - 67.7702i) q^{16} +(38.6818 - 66.9989i) q^{17} +(-104.262 + 60.1959i) q^{19} +(32.5432 + 56.3665i) q^{20} +(-18.2699 + 31.6444i) q^{22} +122.606i q^{23} +24.6062 q^{25} +(120.168 + 208.136i) q^{26} +(95.1861 - 25.5337i) q^{28} +(50.3417 - 29.0648i) q^{29} +(-174.476 + 100.734i) q^{31} +(179.613 - 103.700i) q^{32} +(244.535 - 141.182i) q^{34} +(58.5684 - 218.826i) q^{35} +(82.9121 + 143.608i) q^{37} -439.410 q^{38} -119.585i q^{40} +(112.422 - 194.721i) q^{41} +(152.402 + 263.969i) q^{43} +(-46.1360 + 26.6366i) q^{44} +(-223.746 + 387.539i) q^{46} +(-11.2933 + 19.5606i) q^{47} +(-297.143 - 171.333i) q^{49} +(77.7763 + 44.9042i) q^{50} +350.397i q^{52} +(-360.132 - 207.922i) q^{53} +122.453i q^{55} +(-174.914 - 46.8155i) q^{56} +212.163 q^{58} +(-180.334 - 312.348i) q^{59} +(-635.689 - 367.015i) q^{61} -735.324 q^{62} +130.940 q^{64} +(697.509 + 402.707i) q^{65} +(55.6457 + 96.3811i) q^{67} +411.673 q^{68} +(584.464 - 584.792i) q^{70} +455.487i q^{71} +(-662.747 - 382.637i) q^{73} +605.230i q^{74} +(-554.808 - 320.319i) q^{76} +(179.109 + 47.9383i) q^{77} +(21.5683 - 37.3573i) q^{79} +(478.578 - 828.921i) q^{80} +(710.697 - 410.321i) q^{82} +(200.064 + 346.522i) q^{83} +(473.131 - 819.488i) q^{85} +1112.49i q^{86} +97.8802 q^{88} +(-347.632 - 602.117i) q^{89} +(862.094 - 862.577i) q^{91} +(-565.012 + 326.210i) q^{92} +(-71.3928 + 41.2186i) q^{94} +(-1275.27 + 736.277i) q^{95} +(-955.178 + 551.472i) q^{97} +(-626.554 - 1083.82i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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