LMFDB - Embedded newform 189.4.i.a.143.2

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			143.2
Character	$\chi$	$=$	189.143
Dual form			189.4.i.a.152.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.07706i q^{2} -17.7766 q^{4} +(-4.21335 + 7.29774i) q^{5} +(-4.29909 + 18.0144i) q^{7} +49.6363i q^{8} +O(q^{10})$	\(q-5.07706i q^{2} -17.7766 q^{4} +(-4.21335 + 7.29774i) q^{5} +(-4.29909 + 18.0144i) q^{7} +49.6363i q^{8} +(37.0511 + 21.3915i) q^{10} +(39.7187 - 22.9316i) q^{11} +(18.3978 - 10.6219i) q^{13} +(91.4601 + 21.8268i) q^{14} +109.794 q^{16} +(8.26439 - 14.3143i) q^{17} +(-49.7708 + 28.7352i) q^{19} +(74.8990 - 129.729i) q^{20} +(-116.425 - 201.654i) q^{22} +(167.733 + 96.8406i) q^{23} +(26.9953 + 46.7573i) q^{25} +(-53.9283 - 93.4065i) q^{26} +(76.4231 - 320.234i) q^{28} +(47.1761 + 27.2371i) q^{29} +294.064i q^{31} -160.341i q^{32} +(-72.6748 - 41.9588i) q^{34} +(-113.351 - 107.275i) q^{35} +(185.255 + 320.871i) q^{37} +(145.890 + 252.689i) q^{38} +(-362.233 - 209.135i) q^{40} +(-166.132 - 287.749i) q^{41} +(104.372 - 180.777i) q^{43} +(-706.062 + 407.645i) q^{44} +(491.666 - 851.590i) q^{46} -419.964 q^{47} +(-306.036 - 154.891i) q^{49} +(237.390 - 137.057i) q^{50} +(-327.049 + 188.822i) q^{52} +(275.842 + 159.258i) q^{53} +386.475i q^{55} +(-894.167 - 213.391i) q^{56} +(138.285 - 239.516i) q^{58} +298.099 q^{59} +226.114i q^{61} +1492.98 q^{62} +64.2925 q^{64} +179.016i q^{65} -99.7298 q^{67} +(-146.913 + 254.460i) q^{68} +(-544.640 + 575.488i) q^{70} -176.132i q^{71} +(142.398 + 82.2136i) q^{73} +(1629.08 - 940.551i) q^{74} +(884.753 - 510.813i) q^{76} +(242.344 + 814.092i) q^{77} +374.441 q^{79} +(-462.600 + 801.247i) q^{80} +(-1460.92 + 843.462i) q^{82} +(-457.551 + 792.502i) q^{83} +(69.6416 + 120.623i) q^{85} +(-917.816 - 529.901i) q^{86} +(1138.24 + 1971.49i) q^{88} +(-67.8208 - 117.469i) q^{89} +(112.254 + 377.089i) q^{91} +(-2981.71 - 1721.49i) q^{92} +2132.18i q^{94} -484.285i q^{95} +(-377.173 - 217.761i) q^{97} +(-786.391 + 1553.76i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	5.07706i		−	1.79501i	−0.441001	−	0.897506i	$-0.645377\pi$
$2$		−	5.07706i		−	1.79501i	0.441001	−	0.897506i	$-0.354623\pi$
$3$		0			0
$3$		0			0
$4$	−17.7766			−2.22207
$5$	−4.21335	+	7.29774i	−0.376854	+	0.652730i	−0.990603	−	0.136772i	$-0.956327\pi$
$5$	−4.21335	+	7.29774i	−0.376854	+	0.652730i	0.613749	+	0.789501i	$0.289661\pi$
$6$		0			0
$7$	−4.29909	+	18.0144i	−0.232129	+	0.972685i
$7$	−4.29909	+	18.0144i	−0.232129	+	0.972685i
$8$			49.6363i			2.19363i
$9$		0			0
$10$	37.0511	+	21.3915i	1.17166	+	0.676457i
$11$	39.7187	−	22.9316i	1.08869	−	0.628557i	0.155465	−	0.987841i	$-0.450312\pi$
$11$	39.7187	−	22.9316i	1.08869	−	0.628557i	0.933228	+	0.359284i	$0.116979\pi$
$12$		0			0
$13$	18.3978	−	10.6219i	0.392509	−	0.226615i	−0.290738	−	0.956803i	$-0.593901\pi$
$13$	18.3978	−	10.6219i	0.392509	−	0.226615i	0.683247	+	0.730188i	$0.260567\pi$
$14$	91.4601	+	21.8268i	1.74598	+	0.416675i
$15$		0			0
$16$	109.794			1.71553
$17$	8.26439	−	14.3143i	0.117906	−	0.204220i	−0.801031	−	0.598622i	$-0.795715\pi$
$17$	8.26439	−	14.3143i	0.117906	−	0.204220i	0.918938	+	0.394402i	$0.129048\pi$
$18$		0			0
$19$	−49.7708	+	28.7352i	−0.600958	+	0.346963i	−0.769418	−	0.638745i	$-0.779454\pi$
$19$	−49.7708	+	28.7352i	−0.600958	+	0.346963i	0.168461	+	0.985708i	$0.446120\pi$
$20$	74.8990	−	129.729i	0.837396	−	1.45041i
$21$		0			0
$22$	−116.425	−	201.654i	−1.12827	−	1.95422i
$23$	167.733	+	96.8406i	1.52064	+	0.877942i	0.999704	+	0.0243457i	$0.00775024\pi$
$23$	167.733	+	96.8406i	1.52064	+	0.877942i	0.520936	+	0.853596i	$0.325583\pi$
$24$		0			0
$25$	26.9953	+	46.7573i	0.215963	+	0.374058i
$26$	−53.9283	−	93.4065i	−0.406777	−	0.704559i
$27$		0			0
$28$	76.4231	−	320.234i	0.515808	−	2.16138i
$29$	47.1761	+	27.2371i	0.302082	+	0.174407i	0.643378	−	0.765549i	$-0.277532\pi$
$29$	47.1761	+	27.2371i	0.302082	+	0.174407i	−0.341296	+	0.939956i	$0.610866\pi$
$30$		0			0
$31$			294.064i			1.70372i	0.523766	+	0.851862i	$0.324527\pi$
$31$			294.064i			1.70372i	−0.523766	+	0.851862i	$0.675473\pi$
$32$		−	160.341i		−	0.885765i
$33$		0			0
$34$	−72.6748	−	41.9588i	−0.366577	−	0.211644i
$35$	−113.351	−	107.275i	−0.547422	−	0.518078i
$36$		0			0
$37$	185.255	+	320.871i	0.823128	+	1.42570i	0.903342	+	0.428921i	$0.141106\pi$
$37$	185.255	+	320.871i	0.823128	+	1.42570i	−0.0802142	+	0.996778i	$0.525560\pi$
$38$	145.890	+	252.689i	0.622803	+	1.07873i
$39$		0			0
$40$	−362.233	−	209.135i	−1.43185	−	0.826679i
$41$	−166.132	−	287.749i	−0.632815	−	1.09607i	−0.986974	−	0.160883i	$-0.948566\pi$
$41$	−166.132	−	287.749i	−0.632815	−	1.09607i	0.354158	−	0.935186i	$-0.384767\pi$
$42$		0			0
$43$	104.372	−	180.777i	0.370152	−	0.641121i	−0.619437	−	0.785046i	$-0.712639\pi$
$43$	104.372	−	180.777i	0.370152	−	0.641121i	0.989589	+	0.143925i	$0.0459724\pi$
$44$	−706.062	+	407.645i	−2.41915	+	1.39670i
$45$		0			0
$46$	491.666	−	851.590i	1.57592	−	2.72957i
$47$	−419.964			−1.30336			−0.651681	−	0.758493i	$-0.725936\pi$
$47$	−419.964			−1.30336			−0.651681	+	0.758493i	$0.725936\pi$
$48$		0			0
$49$	−306.036	−	154.891i	−0.892232	−	0.451577i
$50$	237.390	−	137.057i	0.671439	−	0.387656i
$51$		0			0
$52$	−327.049	+	188.822i	−0.872183	+	0.503555i
$53$	275.842	+	159.258i	0.714903	+	0.412750i	0.812874	−	0.582440i	$-0.197902\pi$
$53$	275.842	+	159.258i	0.714903	+	0.412750i	−0.0979707	+	0.995189i	$0.531235\pi$
$54$		0			0
$55$			386.475i			0.947497i
$56$	−894.167	−	213.391i	−2.13371	−	0.509206i
$57$		0			0
$58$	138.285	−	239.516i	0.313063	−	0.542241i
$59$	298.099			0.657783			0.328891	−	0.944368i	$-0.393325\pi$
$59$	298.099			0.657783			0.328891	+	0.944368i	$0.393325\pi$
$60$		0			0
$61$			226.114i			0.474605i	0.971436	+	0.237303i	$0.0762633\pi$
$61$			226.114i			0.474605i	−0.971436	+	0.237303i	$0.923737\pi$
$62$	1492.98			3.05821
$63$		0			0
$64$	64.2925			0.125571
$65$			179.016i			0.341603i
$66$		0			0
$67$	−99.7298			−0.181850			−0.0909249	−	0.995858i	$-0.528982\pi$
$67$	−99.7298			−0.181850			−0.0909249	+	0.995858i	$0.528982\pi$
$68$	−146.913	+	254.460i	−0.261996	+	0.453791i
$69$		0			0
$70$	−544.640	+	575.488i	−0.929956	+	0.982629i
$71$		−	176.132i		−	0.294409i	−0.989106	−	0.147204i	$-0.952973\pi$
$71$		−	176.132i		−	0.294409i	0.989106	−	0.147204i	$-0.0470275\pi$
$72$		0			0
$73$	142.398	+	82.2136i	0.228307	+	0.131813i	0.609791	−	0.792562i	$-0.291253\pi$
$73$	142.398	+	82.2136i	0.228307	+	0.131813i	−0.381484	+	0.924376i	$0.624587\pi$
$74$	1629.08	−	940.551i	2.55915	−	1.47752i
$75$		0			0
$76$	884.753	−	510.813i	1.33537	−	0.770977i
$77$	242.344	+	814.092i	0.358671	+	1.20486i
$78$		0			0
$79$	374.441			0.533265			0.266633	−	0.963798i	$-0.414089\pi$
$79$	374.441			0.533265			0.266633	+	0.963798i	$0.414089\pi$
$80$	−462.600	+	801.247i	−0.646504	+	1.11978i
$81$		0			0
$82$	−1460.92	+	843.462i	−1.96746	+	1.13591i
$83$	−457.551	+	792.502i	−0.605094	+	1.04805i	0.386943	+	0.922104i	$0.373531\pi$
$83$	−457.551	+	792.502i	−0.605094	+	1.04805i	−0.992037	+	0.125950i	$0.959802\pi$
$84$		0			0
$85$	69.6416	+	120.623i	0.0888669	+	0.153922i
$86$	−917.816	−	529.901i	−1.15082	−	0.664427i
$87$		0			0
$88$	1138.24	+	1971.49i	1.37883	+	2.38820i
$89$	−67.8208	−	117.469i	−0.0807751	−	0.139907i	0.822808	−	0.568319i	$-0.192406\pi$
$89$	−67.8208	−	117.469i	−0.0807751	−	0.139907i	−0.903583	+	0.428413i	$0.859073\pi$
$90$		0			0
$91$	112.254	+	377.089i	0.129312	+	0.434392i
$92$	−2981.71	−	1721.49i	−3.37897	−	1.95085i
$93$		0			0
$94$			2132.18i			2.33955i
$95$		−	484.285i		−	0.523017i
$96$		0			0
$97$	−377.173	−	217.761i	−0.394805	−	0.227941i	0.289435	−	0.957198i	$-0.406533\pi$
$97$	−377.173	−	217.761i	−0.394805	−	0.227941i	−0.684240	+	0.729257i	$0.739866\pi$
$98$	−786.391	+	1553.76i	−0.810587	+	1.60157i
$99$		0			0
$100$	−479.884	−	831.184i	−0.479884	−	0.831184i
$101$	18.8554	+	32.6586i	0.0185761	+	0.0321747i	0.875164	−	0.483826i	$-0.160753\pi$
$101$	18.8554	+	32.6586i	0.0185761	+	0.0321747i	−0.856588	+	0.516001i	$0.827420\pi$
$102$		0			0
$103$	604.583	+	349.056i	0.578363	+	0.333918i	0.760482	−	0.649359i	$-0.224963\pi$
$103$	604.583	+	349.056i	0.578363	+	0.333918i	−0.182120	+	0.983276i	$0.558296\pi$
$104$	527.234	+	913.196i	0.497111	+	0.861021i
$105$		0			0
$106$	808.561	−	1400.47i	0.740891	−	1.28326i
$107$	385.161	−	222.373i	0.347990	−	0.200912i	−0.315810	−	0.948822i	$-0.602276\pi$
$107$	385.161	−	222.373i	0.347990	−	0.200912i	0.663799	+	0.747911i	$0.268943\pi$
$108$		0			0
$109$	−699.211	+	1211.07i	−0.614425	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$109$	−699.211	+	1211.07i	−0.614425	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$110$	1962.16			1.70077
$111$		0			0
$112$	−472.014	+	1977.87i	−0.398225	+	1.66867i
$113$	683.731	−	394.752i	0.569203	−	0.328630i	−0.187628	−	0.982240i	$-0.560080\pi$
$113$	683.731	−	394.752i	0.569203	−	0.328630i	0.756831	+	0.653611i	$0.226747\pi$
$114$		0			0
$115$	−1413.43	+	816.047i	−1.14612	+	0.661711i
$116$	−838.629	−	484.182i	−0.671248	−	0.387545i
$117$		0			0
$118$		−	1513.47i		−	1.18073i
$119$	222.335	+	210.417i	0.171272	+	0.162091i
$120$		0			0
$121$	386.215	−	668.944i	0.290169	−	0.502587i
$122$	1147.99			0.851922
$123$		0			0
$124$		−	5227.45i		−	3.78580i
$125$	−1508.30			−1.07925
$126$		0			0
$127$	−1173.39			−0.819851			−0.409926	−	0.912119i	$-0.634445\pi$
$127$	−1173.39			−0.819851			−0.409926	+	0.912119i	$0.634445\pi$
$128$		−	1609.14i		−	1.11117i
$129$		0			0
$130$	908.876			0.613182
$131$	−472.439	+	818.288i	−0.315093	+	0.545757i	−0.979457	−	0.201652i	$-0.935369\pi$
$131$	−472.439	+	818.288i	−0.315093	+	0.545757i	0.664364	+	0.747409i	$0.268702\pi$
$132$		0			0
$133$	−303.677	−	1020.12i	−0.197986	−	0.665083i
$134$			506.335i			0.326423i
$135$		0			0
$136$	710.511	+	410.214i	0.447984	+	0.258644i
$137$	−1134.04	+	654.737i	−0.707207	+	0.408306i	−0.810026	−	0.586394i	$-0.800547\pi$
$137$	−1134.04	+	654.737i	−0.707207	+	0.408306i	0.102819	+	0.994700i	$0.467214\pi$
$138$		0			0
$139$	2249.02	−	1298.47i	1.37237	−	0.792339i	0.381145	−	0.924515i	$-0.375530\pi$
$139$	2249.02	−	1298.47i	1.37237	−	0.792339i	0.991226	+	0.132177i	$0.0421967\pi$
$140$	2014.99	+	1906.97i	1.21641	+	1.15121i
$141$		0			0
$142$	−894.233			−0.528467
$143$	487.156	−	843.779i	0.284881	−	0.493429i
$144$		0			0
$145$	−397.539	+	229.519i	−0.227681	+	0.131452i
$146$	417.403	−	722.964i	0.236607	−	0.409815i
$147$		0			0
$148$	−3293.20	−	5703.99i	−1.82905	−	3.16800i
$149$	−80.9078	−	46.7122i	−0.0444848	−	0.0256833i	0.477593	−	0.878581i	$-0.341509\pi$
$149$	−80.9078	−	46.7122i	−0.0444848	−	0.0256833i	−0.522077	+	0.852898i	$0.674843\pi$
$150$		0			0
$151$	−942.299	−	1632.11i	−0.507836	−	0.879597i	−0.999959	−	0.00907165i	$-0.997112\pi$
$151$	−942.299	−	1632.11i	−0.507836	−	0.879597i	0.492123	−	0.870526i	$-0.336221\pi$
$152$	−1426.31	−	2470.43i	−0.761110	−	1.31828i
$153$		0			0
$154$	4133.20	−	1230.40i	2.16274	−	0.643819i
$155$	−2146.00	−	1239.00i	−1.11207	−	0.642055i
$156$		0			0
$157$		−	1763.74i		−	0.896570i	−0.893891	−	0.448285i	$-0.852035\pi$
$157$		−	1763.74i		−	0.896570i	0.893891	−	0.448285i	$-0.147965\pi$
$158$		−	1901.06i		−	0.957218i
$159$		0			0
$160$	1170.12	+	675.571i	0.578165	+	0.333804i
$161$	−2465.62	+	2605.28i	−1.20695	+	1.27531i
$162$		0			0
$163$	115.138	+	199.426i	0.0553273	+	0.0958296i	0.892363	−	0.451319i	$-0.149046\pi$
$163$	115.138	+	199.426i	0.0553273	+	0.0958296i	−0.837035	+	0.547149i	$0.815713\pi$
$164$	2953.25	+	5115.19i	1.40616	+	2.43554i
$165$		0			0
$166$	4023.58	+	2323.02i	1.88127	+	1.08615i
$167$	−1568.86	−	2717.35i	−0.726960	−	1.25913i	−0.958162	−	0.286226i	$-0.907599\pi$
$167$	−1568.86	−	2717.35i	−0.726960	−	1.25913i	0.231202	−	0.972906i	$-0.425734\pi$
$168$		0			0
$169$	−872.849	+	1511.82i	−0.397291	+	0.688128i
$170$	612.409	−	353.575i	0.276292	−	0.159517i
$171$		0			0
$172$	−1855.37	+	3213.59i	−0.822503	+	1.42462i
$173$	2161.08			0.949735			0.474867	−	0.880057i	$-0.342496\pi$
$173$	2161.08			0.949735			0.474867	+	0.880057i	$0.342496\pi$
$174$		0			0
$175$	−958.359	+	285.290i	−0.413972	+	0.123234i
$176$	4360.87	−	2517.75i	1.86769	−	1.07831i
$177$		0			0
$178$	−596.398	+	344.330i	−0.251134	+	0.144992i
$179$	698.619	+	403.348i	0.291717	+	0.168423i	0.638716	−	0.769443i	$-0.279466\pi$
$179$	698.619	+	403.348i	0.291717	+	0.168423i	−0.346999	+	0.937865i	$0.612799\pi$
$180$		0			0
$181$			1428.18i			0.586497i	0.956036	+	0.293248i	$0.0947363\pi$
$181$			1428.18i			0.586497i	−0.956036	+	0.293248i	$0.905264\pi$
$182$	1914.50	−	569.921i	0.779739	−	0.232117i
$183$		0			0
$184$	−4806.81	+	8325.63i	−1.92588	+	3.33573i
$185$	−3122.18			−1.24079
$186$		0			0
$187$		−	758.062i		−	0.296444i
$188$	7465.51			2.89616
$189$		0			0
$190$	−2458.75			−0.938823
$191$		−	1034.45i		−	0.391884i	−0.980615	−	0.195942i	$-0.937224\pi$
$191$		−	1034.45i		−	0.391884i	0.980615	−	0.195942i	$-0.0627765\pi$
$192$		0			0
$193$	1514.47			0.564839			0.282419	−	0.959291i	$-0.408863\pi$
$193$	1514.47			0.564839			0.282419	+	0.959291i	$0.408863\pi$
$194$	−1105.59	+	1914.93i	−0.409157	+	0.708680i
$195$		0			0
$196$	5440.26	+	2753.43i	1.98260	+	1.00344i
$197$		−	634.886i		−	0.229613i	−0.993388	−	0.114806i	$-0.963375\pi$
$197$		−	634.886i		−	0.229613i	0.993388	−	0.114806i	$-0.0366248\pi$
$198$		0			0
$199$	2459.80	+	1420.16i	0.876233	+	0.505893i	0.869414	−	0.494084i	$-0.164496\pi$
$199$	2459.80	+	1420.16i	0.876233	+	0.505893i	0.00681818	+	0.999977i	$0.497830\pi$
$200$	−2320.86	+	1339.95i	−0.820547	+	0.473743i
$201$		0			0
$202$	165.810	−	95.7302i	0.0577541	−	0.0333443i
$203$	−693.474	+	732.753i	−0.239765	+	0.253346i
$204$		0			0
$205$	2799.89			0.953915
$206$	1772.18	−	3069.51i	0.599387	−	1.03817i
$207$		0			0
$208$	2019.96	−	1166.23i	0.673361	−	0.388765i
$209$	−1317.89	+	2282.64i	−0.436172	+	0.755473i
$210$		0			0
$211$	−1160.55	−	2010.12i	−0.378650	−	0.655842i	0.612216	−	0.790691i	$-0.290278\pi$
$211$	−1160.55	−	2010.12i	−0.378650	−	0.655842i	−0.990866	+	0.134849i	$0.956945\pi$
$212$	−4903.53	−	2831.06i	−1.58857	−	0.917159i
$213$		0			0
$214$	−1129.00	−	1955.48i	−0.360639	−	0.624646i
$215$	879.509	+	1523.35i	0.278986	+	0.483218i
$216$		0			0
$217$	−5297.38	−	1264.21i	−1.65719	−	0.395484i
$218$	6148.67	+	3549.94i	1.91028	+	1.10290i
$219$		0			0
$220$		−	6870.21i		−	2.10541i
$221$		−	351.136i		−	0.106878i
$222$		0			0
$223$	3372.66	+	1947.21i	1.01278	+	0.584729i	0.912004	−	0.410180i	$-0.134534\pi$
$223$	3372.66	+	1947.21i	1.01278	+	0.584729i	0.100776	+	0.994909i	$0.467868\pi$
$224$	2888.43	+	689.319i	0.861570	+	0.205612i
$225$		0			0
$226$	−2004.18	−	3471.34i	−0.589895	−	1.02173i
$227$	−1710.90	−	2963.36i	−0.500248	−	0.866455i	−1.00000		0.000286256i	$-0.999909\pi$
$227$	−1710.90	−	2963.36i	−0.500248	−	0.866455i	0.499752	−	0.866168i	$-0.333424\pi$
$228$		0			0
$229$	234.052	+	135.130i	0.0675398	+	0.0389941i	0.533390	−	0.845870i	$-0.320918\pi$
$229$	234.052	+	135.130i	0.0675398	+	0.0389941i	−0.465850	+	0.884864i	$0.654251\pi$
$230$	4143.12	+	7176.10i	1.18778	+	2.05729i
$231$		0			0
$232$	−1351.95	+	2341.64i	−0.382585	+	0.662657i
$233$	1577.64	−	910.849i	0.443581	−	0.256102i	−0.261534	−	0.965194i	$-0.584228\pi$
$233$	1577.64	−	910.849i	0.443581	−	0.256102i	0.705115	+	0.709093i	$0.250895\pi$
$234$		0			0
$235$	1769.45	−	3064.79i	0.491177	−	0.850743i
$236$	−5299.18			−1.46164
$237$		0			0
$238$	1068.30	−	1128.81i	0.290956	−	0.307436i
$239$	3946.04	−	2278.25i	1.06798	−	0.616600i	0.140353	−	0.990101i	$-0.455176\pi$
$239$	3946.04	−	2278.25i	1.06798	−	0.616600i	0.927630	+	0.373501i	$0.121843\pi$
$240$		0			0
$241$	−2475.41	+	1429.18i	−0.661640	+	0.381998i	−0.792902	−	0.609350i	$-0.791431\pi$
$241$	−2475.41	+	1429.18i	−0.661640	+	0.381998i	0.131261	+	0.991348i	$0.458097\pi$
$242$	−3396.27	−	1960.84i	−0.902151	−	0.520857i
$243$		0			0
$244$		−	4019.53i		−	1.05461i
$245$	2419.79	−	1580.76i	0.630999	−	0.412208i
$246$		0			0
$247$	−610.447	+	1057.32i	−0.157254	+	0.272372i
$248$	−14596.2			−3.73735
$249$		0			0
$250$			7657.74i			1.93727i
$251$	1571.15			0.395100			0.197550	−	0.980293i	$-0.436702\pi$
$251$	1571.15			0.395100			0.197550	+	0.980293i	$0.436702\pi$
$252$		0			0
$253$	8882.83			2.20735
$254$			5957.35i			1.47164i
$255$		0			0
$256$	−7655.37			−1.86899
$257$	912.366	−	1580.26i	0.221447	−	0.383557i	−0.733801	−	0.679365i	$-0.762255\pi$
$257$	912.366	−	1580.26i	0.221447	−	0.383557i	0.955247	+	0.295808i	$0.0955888\pi$
$258$		0			0
$259$	−6576.72	+	1957.80i	−1.57783	+	0.469698i
$260$		−	3182.29i		−	0.759067i
$261$		0			0
$262$	4154.50	+	2398.60i	0.979640	+	0.565596i
$263$	−2843.13	+	1641.48i	−0.666598	+	0.384860i	−0.794786	−	0.606889i	$-0.792417\pi$
$263$	−2843.13	+	1641.48i	−0.666598	+	0.384860i	0.128189	+	0.991750i	$0.459084\pi$
$264$		0			0
$265$	−2324.44	+	1342.02i	−0.538828	+	0.311092i
$266$	−5179.24	+	1541.79i	−1.19383	+	0.355387i
$267$		0			0
$268$	1772.85			0.404083
$269$	−2659.87	+	4607.02i	−0.602880	+	1.04422i	0.389502	+	0.921026i	$0.372647\pi$
$269$	−2659.87	+	4607.02i	−0.602880	+	1.04422i	−0.992383	+	0.123194i	$0.960686\pi$
$270$		0			0
$271$	−4679.27	+	2701.58i	−1.04888	+	0.605569i	−0.922335	−	0.386392i	$-0.873721\pi$
$271$	−4679.27	+	2701.58i	−1.04888	+	0.605569i	−0.126542	+	0.991961i	$0.540388\pi$
$272$	907.380	−	1571.63i	0.202272	−	0.350345i
$273$		0			0
$274$	3324.14	+	5757.58i	0.732915	+	1.26945i
$275$	2144.44	+	1238.09i	0.470234	+	0.271490i
$276$		0			0
$277$	−4148.78	−	7185.89i	−0.899913	−	1.55870i	−0.827604	−	0.561313i	$-0.810296\pi$
$277$	−4148.78	−	7185.89i	−0.899913	−	1.55870i	−0.0723092	−	0.997382i	$-0.523037\pi$
$278$	−6592.43	−	11418.4i	−1.42226	−	2.46342i
$279$		0			0
$280$	5324.71	−	5626.30i	1.13647	−	1.20084i
$281$	−1777.79	−	1026.41i	−0.377416	−	0.217901i	0.299277	−	0.954166i	$-0.403254\pi$
$281$	−1777.79	−	1026.41i	−0.377416	−	0.217901i	−0.676694	+	0.736265i	$0.736588\pi$
$282$		0			0
$283$		−	5066.48i		−	1.06421i	−0.846679	−	0.532104i	$-0.821401\pi$
$283$		−	5066.48i		−	1.06421i	0.846679	−	0.532104i	$-0.178599\pi$
$284$			3131.02i			0.654197i
$285$		0			0
$286$	−4283.92	−	2473.32i	−0.885712	−	0.511366i
$287$	5897.83	−	1755.70i	1.21302	−	0.361101i
$288$		0			0
$289$	2319.90	+	4018.18i	0.472196	+	0.817868i
$290$	1165.28	+	2018.33i	0.235958	+	0.408691i
$291$		0			0
$292$	−2531.35	−	1461.48i	−0.507315	−	0.292898i
$293$	−326.783	−	566.006i	−0.0651566	−	0.112855i	0.831607	−	0.555365i	$-0.187421\pi$
$293$	−326.783	−	566.006i	−0.0651566	−	0.112855i	−0.896763	+	0.442510i	$0.854088\pi$
$294$		0			0
$295$	−1256.00	+	2175.45i	−0.247888	+	0.429354i
$296$	−15926.8	+	9195.36i	−3.12746	+	1.80564i
$297$		0			0
$298$	−237.161	+	410.774i	−0.0461018	+	0.0798507i
$299$	4114.54			0.795820
$300$		0			0
$301$	2807.88	+	2657.37i	0.537686	+	0.508864i
$302$	−8286.32	+	4784.11i	−1.57889	+	0.911572i
$303$		0			0
$304$	−5464.53	+	3154.95i	−1.03096	+	0.595225i
$305$	−1650.12	−	952.697i	−0.309789	−	0.178857i
$306$		0			0
$307$		−	3994.22i		−	0.742547i	−0.928524	−	0.371274i	$-0.878921\pi$
$307$		−	3994.22i		−	0.742547i	0.928524	−	0.371274i	$-0.121079\pi$
$308$	−4308.04	−	14471.8i	−0.796992	−	2.67729i
$309$		0			0
$310$	−6290.46	+	10895.4i	−1.15250	+	1.99618i
$311$	10244.3			1.86785			0.933923	−	0.357475i	$-0.116362\pi$
$311$	10244.3			1.86785			0.933923	+	0.357475i	$0.116362\pi$
$312$		0			0
$313$			661.051i			0.119376i	0.998217	+	0.0596882i	$0.0190106\pi$
$313$			661.051i			0.119376i	−0.998217	+	0.0596882i	$0.980989\pi$
$314$	−8954.61			−1.60936
$315$		0			0
$316$	−6656.29			−1.18495
$317$			3338.77i			0.591558i	0.955256	+	0.295779i	$0.0955792\pi$
$317$			3338.77i			0.591558i	−0.955256	+	0.295779i	$0.904421\pi$
$318$		0			0
$319$	2498.36			0.438499
$320$	−270.887	+	469.190i	−0.0473220	+	0.0819641i
$321$		0			0
$322$	13227.1	+	12518.1i	2.28919	+	2.16648i
$323$			949.914i			0.163637i
$324$		0			0
$325$	993.307	+	573.486i	0.169535	+	0.0978808i
$326$	1012.50	−	584.565i	0.172015	−	0.0993131i
$327$		0			0
$328$	14282.8	−	8246.16i	2.40437	−	1.38817i
$329$	1805.46	−	7565.38i	0.302548	−	1.26776i
$330$		0			0
$331$	10822.5			1.79716			0.898579	−	0.438813i	$-0.144601\pi$
$331$	10822.5			1.79716			0.898579	+	0.438813i	$0.144601\pi$
$332$	8133.70	−	14088.0i	1.34456	−	2.32885i
$333$		0			0
$334$	−13796.2	+	7965.22i	−2.26016	+	1.30490i
$335$	420.197	−	727.802i	0.0685308	−	0.118699i
$336$		0			0
$337$	1245.55	+	2157.35i	0.201333	+	0.348720i	0.948958	−	0.315402i	$-0.102139\pi$
$337$	1245.55	+	2157.35i	0.201333	+	0.348720i	−0.747625	+	0.664121i	$0.768806\pi$
$338$	7675.60	+	4431.51i	1.23520	+	0.713143i
$339$		0			0
$340$	−1237.99	−	2144.26i	−0.197469	−	0.342026i
$341$	6743.36	+	11679.8i	1.07089	+	1.85483i
$342$		0			0
$343$	4105.94	−	4847.15i	0.646355	−	0.763037i
$344$	8973.09	+	5180.62i	1.40639	+	0.811977i
$345$		0			0
$346$		−	10972.0i		−	1.70479i
$347$			1235.59i			0.191153i	0.995422	+	0.0955766i	$0.0304695\pi$
$347$			1235.59i			0.191153i	−0.995422	+	0.0955766i	$0.969531\pi$
$348$		0			0
$349$	−6094.84	−	3518.86i	−0.934812	−	0.539714i	−0.0464817	−	0.998919i	$-0.514801\pi$
$349$	−6094.84	−	3518.86i	−0.934812	−	0.539714i	−0.888330	+	0.459205i	$0.848134\pi$
$350$	1448.44	+	4865.65i	0.221206	+	0.743085i
$351$		0			0
$352$	−3676.86	−	6368.51i	−0.556754	−	0.964326i
$353$	−3813.71	−	6605.53i	−0.575023	−	0.995969i	−0.996039	−	0.0889157i	$-0.971660\pi$
$353$	−3813.71	−	6605.53i	−0.575023	−	0.995969i	0.421016	−	0.907053i	$-0.361673\pi$
$354$		0			0
$355$	1285.36	+	742.106i	0.192169	+	0.110949i
$356$	1205.62	+	2088.20i	0.179488	+	0.310883i
$357$		0			0
$358$	2047.82	−	3546.93i	0.302321	−	0.523635i
$359$	11281.0	−	6513.10i	1.65847	−	0.957517i	0.685045	−	0.728501i	$-0.259783\pi$
$359$	11281.0	−	6513.10i	1.65847	−	0.957517i	0.973423	−	0.229016i	$-0.0735508\pi$
$360$		0			0
$361$	−1778.08	+	3079.73i	−0.259233	+	0.449005i
$362$	7250.97			1.05277
$363$		0			0
$364$	−1995.49	−	6703.35i	−0.287341	−	0.965249i
$365$	−1199.95	+	692.789i	−0.172077	+	0.0993486i
$366$		0			0
$367$	9550.68	−	5514.09i	1.35842	−	0.784286i	0.369012	−	0.929425i	$-0.379696\pi$
$367$	9550.68	−	5514.09i	1.35842	−	0.784286i	0.989411	+	0.145139i	$0.0463629\pi$
$368$	18416.0	+	10632.5i	2.60870	+	1.50614i
$369$		0			0
$370$			15851.5i			2.22724i
$371$	−4054.80	+	4284.47i	−0.567425	+	0.599564i
$372$		0			0
$373$	−4204.44	+	7282.31i	−0.583640	+	1.01089i	0.411403	+	0.911453i	$0.365039\pi$
$373$	−4204.44	+	7282.31i	−0.583640	+	1.01089i	−0.995043	+	0.0994410i	$0.968295\pi$
$374$	−3848.73			−0.532121
$375$		0			0
$376$		−	20845.4i		−	2.85910i
$377$	1157.24			0.158093
$378$		0			0
$379$	2248.22			0.304706			0.152353	−	0.988326i	$-0.451315\pi$
$379$	2248.22			0.304706			0.152353	+	0.988326i	$0.451315\pi$
$380$			8608.93i			1.16218i
$381$		0			0
$382$	−5251.95			−0.703437
$383$	−2155.02	+	3732.61i	−0.287511	+	0.497983i	−0.973215	−	0.229897i	$-0.926161\pi$
$383$	−2155.02	+	3732.61i	−0.287511	+	0.497983i	0.685704	+	0.727880i	$0.259494\pi$
$384$		0			0
$385$	−6962.11	−	1661.49i	−0.921616	−	0.219942i
$386$		−	7689.06i		−	1.01389i
$387$		0			0
$388$	6704.84	+	3871.04i	0.877285	+	0.506501i
$389$	−9261.67	+	5347.22i	−1.20716	+	0.696954i	−0.962138	−	0.272564i	$-0.912128\pi$
$389$	−9261.67	+	5347.22i	−1.20716	+	0.696954i	−0.245022	+	0.969518i	$0.578795\pi$
$390$		0			0
$391$	2772.42	−	1600.66i	0.358586	−	0.207030i
$392$	7688.21	−	15190.5i	0.990595	−	1.95723i
$393$		0			0
$394$	−3223.36			−0.412158
$395$	−1577.65	+	2732.58i	−0.200963	+	0.348078i
$396$		0			0
$397$	−800.610	+	462.232i	−0.101213	+	0.0584352i	−0.549752	−	0.835328i	$-0.685278\pi$
$397$	−800.610	+	462.232i	−0.101213	+	0.0584352i	0.448539	+	0.893763i	$0.351944\pi$
$398$	7210.26	−	12488.5i	0.908085	−	1.57285i
$399$		0			0
$400$	2963.92	+	5133.66i	0.370490	+	0.641708i
$401$	−1867.45	−	1078.17i	−0.232558	−	0.134268i	0.379193	−	0.925317i	$-0.376202\pi$
$401$	−1867.45	−	1078.17i	−0.232558	−	0.134268i	−0.611752	+	0.791050i	$0.709535\pi$
$402$		0			0
$403$	3123.53	+	5410.12i	0.386090	+	0.668728i
$404$	−335.185	−	580.557i	−0.0412774	−	0.0714945i
$405$		0			0
$406$	3720.23	+	3520.81i	0.454759	+	0.430382i
$407$	14716.2	+	8496.38i	1.79227	+	1.03477i
$408$		0			0
$409$			12912.7i			1.56110i	0.625091	+	0.780552i	$0.285062\pi$
$409$			12912.7i			1.56110i	−0.625091	+	0.780552i	$0.714938\pi$
$410$		−	14215.2i		−	1.71229i
$411$		0			0
$412$	−10747.4	−	6205.02i	−1.28516	−	0.741989i
$413$	−1281.56	+	5370.07i	−0.152691	+	0.639815i
$414$		0			0
$415$	−3855.65	−	6678.18i	−0.456064	−	0.789926i
$416$	−1703.13	−	2949.90i	−0.200728	−	0.347671i
$417$		0			0
$418$	11589.1	+	6690.99i	1.35608	+	0.782935i
$419$	3818.83	+	6614.40i	0.445255	+	0.771204i	0.998070	−	0.0620997i	$-0.0197797\pi$
$419$	3818.83	+	6614.40i	0.445255	+	0.771204i	−0.552815	+	0.833304i	$0.686446\pi$
$420$		0			0
$421$	1244.97	−	2156.36i	0.144124	−	0.249631i	−0.784922	−	0.619595i	$-0.787297\pi$
$421$	1244.97	−	2156.36i	0.144124	−	0.249631i	0.929046	+	0.369964i	$0.120630\pi$
$422$	−10205.5	+	5892.16i	−1.17724	+	0.679682i
$423$		0			0
$424$	−7904.96	+	13691.8i	−0.905421	+	1.56824i
$425$	892.400			0.101854
$426$		0			0
$427$	−4073.30	−	972.084i	−0.461641	−	0.110170i
$428$	−6846.83	+	3953.02i	−0.773258	+	0.446440i
$429$		0			0
$430$	7734.16	−	4465.32i	0.867382	−	0.500784i
$431$	−4029.69	−	2326.54i	−0.450356	−	0.260013i	0.257624	−	0.966245i	$-0.417060\pi$
$431$	−4029.69	−	2326.54i	−0.450356	−	0.260013i	−0.707981	+	0.706232i	$0.750394\pi$
$432$		0			0
$433$		−	1454.90i		−	0.161474i	−0.996735	−	0.0807370i	$-0.974273\pi$
$433$		−	1454.90i		−	0.161474i	0.996735	−	0.0807370i	$-0.0257274\pi$
$434$	−6418.47	+	26895.1i	−0.709899	+	2.97467i
$435$		0			0
$436$	12429.6	−	21528.7i	1.36530	−	2.36476i
$437$	−11130.9			−1.21845
$438$		0			0
$439$		−	2997.90i		−	0.325927i	−0.986632	−	0.162964i	$-0.947895\pi$
$439$		−	2997.90i		−	0.325927i	0.986632	−	0.162964i	$-0.0521054\pi$
$440$	−19183.2			−2.07846
$441$		0			0
$442$	−1782.74			−0.191847
$443$		−	14462.1i		−	1.55105i	−0.631318	−	0.775524i	$-0.717486\pi$
$443$		−	14462.1i		−	1.55105i	0.631318	−	0.775524i	$-0.282514\pi$
$444$		0			0
$445$	1143.01			0.121762
$446$	9886.09	−	17123.2i	1.04960	−	1.81795i
$447$		0			0
$448$	−276.399	+	1158.19i	−0.0291487	+	0.122141i
$449$		−	18618.7i		−	1.95695i	−0.206375	−	0.978473i	$-0.566167\pi$
$449$		−	18618.7i		−	1.95695i	0.206375	−	0.978473i	$-0.433833\pi$
$450$		0			0
$451$	−13197.1	−	7619.33i	−1.37788	−	0.795522i
$452$	−12154.4	+	7017.34i	−1.26481	+	0.730239i
$453$		0			0
$454$	−15045.2	+	8686.34i	−1.55530	+	0.897951i
$455$	−3224.86	−	769.606i	−0.332272	−	0.0792960i
$456$		0			0
$457$	4177.80			0.427635			0.213818	−	0.976874i	$-0.431410\pi$
$457$	4177.80			0.427635			0.213818	+	0.976874i	$0.431410\pi$
$458$	686.065	−	1188.30i	0.0699950	−	0.121235i
$459$		0			0
$460$	25126.0	−	14506.5i	2.54675	−	1.47037i
$461$	1118.11	−	1936.62i	0.112962	−	0.195656i	−0.804001	−	0.594628i	$-0.797299\pi$
$461$	1118.11	−	1936.62i	0.112962	−	0.195656i	0.916963	+	0.398972i	$0.130633\pi$
$462$		0			0
$463$	−7627.68	−	13211.5i	−0.765634	−	1.32612i	−0.939911	−	0.341420i	$-0.889092\pi$
$463$	−7627.68	−	13211.5i	−0.765634	−	1.32612i	0.174277	−	0.984697i	$-0.444241\pi$
$464$	5179.64	+	2990.47i	0.518231	+	0.299201i
$465$		0			0
$466$	−4624.44	−	8009.76i	−0.459706	−	0.796234i
$467$	5708.66	+	9887.69i	0.565665	+	0.979760i	0.996988	+	0.0775623i	$0.0247137\pi$
$467$	5708.66	+	9887.69i	0.565665	+	0.979760i	−0.431323	+	0.902198i	$0.641953\pi$
$468$		0			0
$469$	428.748	−	1796.57i	0.0422126	−	0.176883i
$470$	−15560.1	−	8983.63i	−1.52709	−	0.881668i
$471$		0			0
$472$			14796.5i			1.44293i
$473$		−	9573.62i		−	0.930646i
$474$		0			0
$475$	−2687.16	−	1551.43i	−0.259569	−	0.149862i
$476$	−3952.35	−	3740.48i	−0.380579	−	0.360178i
$477$		0			0
$478$	−11566.8	−	20034.3i	−1.10681	−	1.91704i
$479$	−1186.31	−	2054.75i	−0.113161	−	0.196000i	0.803882	−	0.594788i	$-0.202764\pi$
$479$	−1186.31	−	2054.75i	−0.113161	−	0.196000i	−0.917043	+	0.398788i	$0.869431\pi$
$480$		0			0
$481$	6816.55	+	3935.54i	0.646170	+	0.373067i
$482$	7256.04	+	12567.8i	0.685692	+	1.18765i
$483$		0			0
$484$	−6865.58	+	11891.5i	−0.644776	+	1.11679i
$485$	3178.32	−	1835.01i	0.297567	−	0.171801i
$486$		0			0
$487$	9743.51	−	16876.3i	0.906613	−	1.57030i	0.0878768	−	0.996131i	$-0.471992\pi$
$487$	9743.51	−	16876.3i	0.906613	−	1.57030i	0.818737	−	0.574169i	$-0.194675\pi$
$488$	−11223.4			−1.04111
$489$		0			0
$490$	−8025.61	−	12285.4i	−0.739919	−	1.13265i
$491$	10982.0	−	6340.45i	1.00939	−	0.582771i	0.0983757	−	0.995149i	$-0.468635\pi$
$491$	10982.0	−	6340.45i	1.00939	−	0.582771i	0.911012	+	0.412379i	$0.135302\pi$
$492$		0			0
$493$	779.763	−	450.196i	0.0712348	−	0.0411274i
$494$	5368.10	+	3099.28i	0.488912	+	0.282273i
$495$		0			0
$496$			32286.5i			2.92279i
$497$	3172.91	+	757.207i	0.286367	+	0.0683408i
$498$		0			0
$499$	5906.36	−	10230.1i	0.529870	−	0.917761i	−0.469523	−	0.882920i	$-0.655574\pi$
$499$	5906.36	−	10230.1i	0.529870	−	0.917761i	0.999393	−	0.0348413i	$-0.0110926\pi$
$500$	26812.4			2.39818
$501$		0			0
$502$		−	7976.82i		−	0.709209i
$503$	−12272.4			−1.08787			−0.543934	−	0.839128i	$-0.683066\pi$
$503$	−12272.4			−1.08787			−0.543934	+	0.839128i	$0.683066\pi$
$504$		0			0
$505$	−317.778			−0.0280019
$506$		−	45098.7i		−	3.96222i
$507$		0			0
$508$	20858.8			1.82177
$509$	−1255.40	+	2174.41i	−0.109321	+	0.189350i	−0.915495	−	0.402328i	$-0.868201\pi$
$509$	−1255.40	+	2174.41i	−0.109321	+	0.189350i	0.806174	+	0.591678i	$0.201534\pi$
$510$		0			0
$511$	−2093.21	+	2211.77i	−0.181210	+	0.191473i
$512$			25993.7i			2.24369i
$513$		0			0
$514$	−8023.10	−	4632.14i	−0.688490	−	0.397500i
$515$	−5094.64	+	2941.39i	−0.435916	+	0.251676i
$516$		0			0
$517$	−16680.4	+	9630.43i	−1.41896	+	0.819238i
$518$	9939.87	+	33390.4i	0.843113	+	2.83222i
$519$		0			0
$520$	−8885.69			−0.749352
$521$	−4026.54	+	6974.18i	−0.338591	+	0.586457i	−0.984168	−	0.177238i	$-0.943284\pi$
$521$	−4026.54	+	6974.18i	−0.338591	+	0.586457i	0.645577	+	0.763695i	$0.276617\pi$
$522$		0			0
$523$	−16819.4	+	9710.66i	−1.40623	+	0.811888i	−0.995022	−	0.0996530i	$-0.968227\pi$
$523$	−16819.4	+	9710.66i	−1.40623	+	0.811888i	−0.411209	+	0.911541i	$0.634893\pi$
$524$	8398.34	−	14546.4i	0.700159	−	1.21271i
$525$		0			0
$526$	8333.92	+	14434.8i	0.690829	+	1.19655i
$527$	4209.34	+	2430.26i	0.347935	+	0.200880i
$528$		0			0
$529$	12672.7	+	21949.7i	1.04156	+	1.80404i
$530$	6813.51	+	11801.3i	0.558415	+	0.967203i
$531$		0			0
$532$	5398.33	+	18134.3i	0.439939	+	1.47786i
$533$	−6112.90	−	3529.29i	−0.496772	−	0.286811i
$534$		0			0
$535$			3747.74i			0.302857i
$536$		−	4950.22i		−	0.398912i
$537$		0			0
$538$	23390.1	+	13504.3i	1.87439	+	1.08218i
$539$	−15707.2	+	865.819i	−1.25521	+	0.0691901i
$540$		0			0
$541$	−926.844	−	1605.34i	−0.0736564	−	0.127577i	0.826845	−	0.562430i	$-0.190133\pi$
$541$	−926.844	−	1605.34i	−0.0736564	−	0.127577i	−0.900501	+	0.434854i	$0.856800\pi$
$542$	13716.1	+	23757.0i	1.08700	+	1.88275i
$543$		0			0
$544$	−2295.17	−	1325.12i	−0.180891	−	0.104437i
$545$	−5892.04	−	10205.3i	−0.463096	−	0.802106i
$546$		0			0
$547$	3484.25	−	6034.90i	0.272351	−	0.471725i	−0.697113	−	0.716962i	$-0.745532\pi$
$547$	3484.25	−	6034.90i	0.272351	−	0.471725i	0.969463	+	0.245236i	$0.0788655\pi$
$548$	20159.3	−	11639.0i	1.57146	−	0.907286i
$549$		0			0
$550$	6285.87	−	10887.4i	0.487328	−	0.844076i
$551$	−3130.65			−0.242051
$552$		0			0
$553$	−1609.76	+	6745.33i	−0.123786	+	0.518699i
$554$	−36483.2	+	21063.6i	−2.79788	+	1.61536i
$555$		0			0
$556$	−39979.9	+	23082.4i	−3.04951	+	1.76063i
$557$	−2067.96	−	1193.94i	−0.157311	−	0.0908237i	0.419278	−	0.907858i	$-0.362283\pi$
$557$	−2067.96	−	1193.94i	−0.157311	−	0.0908237i	−0.576589	+	0.817034i	$0.695617\pi$
$558$		0			0
$559$		−	4434.52i		−	0.335528i
$560$	−12445.2	−	11778.1i	−0.939118	−	0.888778i
$561$		0			0
$562$	−5211.13	+	9025.94i	−0.391136	+	0.677467i
$563$	−8134.02			−0.608895			−0.304448	−	0.952529i	$-0.598472\pi$
$563$	−8134.02			−0.608895			−0.304448	+	0.952529i	$0.598472\pi$
$564$		0			0
$565$			6652.92i			0.495381i
$566$	−25722.8			−1.91027
$567$		0			0
$568$	8742.53			0.645825
$569$			4591.35i			0.338277i	0.985592	+	0.169138i	$0.0540985\pi$
$569$			4591.35i			0.338277i	−0.985592	+	0.169138i	$0.945902\pi$
$570$		0			0
$571$	−3691.67			−0.270563			−0.135281	−	0.990807i	$-0.543194\pi$
$571$	−3691.67			−0.270563			−0.135281	+	0.990807i	$0.543194\pi$
$572$	−8659.96	+	14999.5i	−0.633027	+	1.09643i
$573$		0			0
$574$	−8913.81	−	29943.7i	−0.648180	−	2.17739i
$575$			10457.0i			0.758410i
$576$		0			0
$577$	8679.71	+	5011.23i	0.626241	+	0.361560i	0.779295	−	0.626657i	$-0.215577\pi$
$577$	8679.71	+	5011.23i	0.626241	+	0.361560i	−0.153054	+	0.988218i	$0.548911\pi$
$578$	20400.6	−	11778.3i	1.46808	−	0.847598i
$579$		0			0
$580$	7066.88	−	4080.06i	0.505924	−	0.292095i
$581$	−12309.4	−	11649.5i	−0.878966	−	0.831850i
$582$		0			0
$583$	14608.1			1.03775
$584$	−4080.77	+	7068.11i	−0.289150	+	0.500823i
$585$		0			0
$586$	−2873.65	+	1659.10i	−0.202575	+	0.116957i
$587$	7147.37	−	12379.6i	0.502561	−	0.870462i	−0.497434	−	0.867502i	$-0.665724\pi$
$587$	7147.37	−	12379.6i	0.502561	−	0.870462i	0.999996	−	0.00295997i	$-0.000942190\pi$
$588$		0			0
$589$	−8449.98	−	14635.8i	−0.591130	−	1.02387i
$590$	11044.9	+	6376.77i	0.770697	+	0.444962i
$591$		0			0
$592$	20339.9	+	35229.7i	1.41210	+	2.44583i
$593$	1519.45	+	2631.76i	0.105221	+	0.182249i	0.913829	−	0.406100i	$-0.133112\pi$
$593$	1519.45	+	2631.76i	0.105221	+	0.182249i	−0.808607	+	0.588349i	$0.799778\pi$
$594$		0			0
$595$	−2472.34	+	735.981i	−0.170346	+	0.0507097i
$596$	1438.26	+	830.382i	0.0988483	+	0.0570701i
$597$		0			0
$598$		−	20889.8i		−	1.42851i
$599$			16067.1i			1.09597i	0.836488	+	0.547985i	$0.184605\pi$
$599$			16067.1i			1.09597i	−0.836488	+	0.547985i	$0.815395\pi$
$600$		0			0
$601$	15122.2	+	8730.80i	1.02637	+	0.592573i	0.915942	−	0.401311i	$-0.131445\pi$
$601$	15122.2	+	8730.80i	1.02637	+	0.592573i	0.110425	+	0.993884i	$0.464779\pi$
$602$	13491.6	−	14255.8i	0.913417	−	0.965154i
$603$		0			0
$604$	16750.8	+	29013.3i	1.12845	+	1.95453i
$605$	3254.52	+	5636.99i	0.218703	+	0.378804i
$606$		0			0
$607$	−14270.2	−	8238.89i	−0.954215	−	0.550916i	−0.0598272	−	0.998209i	$-0.519055\pi$
$607$	−14270.2	−	8238.89i	−0.954215	−	0.550916i	−0.894388	+	0.447293i	$0.852388\pi$
$608$	4607.41	+	7980.27i	0.307328	+	0.532307i
$609$		0			0
$610$	−4836.90	+	8377.77i	−0.321050	+	0.556075i
$611$	−7726.39	+	4460.83i	−0.511581	+	0.295362i
$612$		0			0
$613$	−4806.63	+	8325.33i	−0.316701	+	0.548543i	−0.979798	−	0.199991i	$-0.935909\pi$
$613$	−4806.63	+	8325.33i	−0.316701	+	0.548543i	0.663096	+	0.748534i	$0.269242\pi$
$614$	−20278.9			−1.33288
$615$		0			0
$616$	−40408.5	+	12029.1i	−2.64303	+	0.786793i
$617$	−10457.7	+	6037.77i	−0.682353	+	0.393957i	−0.800741	−	0.599011i	$-0.795561\pi$
$617$	−10457.7	+	6037.77i	−0.682353	+	0.393957i	0.118388	+	0.992967i	$0.462227\pi$
$618$		0			0
$619$	−21528.6	+	12429.5i	−1.39791	+	0.807085i	−0.994174	−	0.107789i	$-0.965623\pi$
$619$	−21528.6	+	12429.5i	−1.39791	+	0.807085i	−0.403739	+	0.914874i	$0.632289\pi$
$620$	38148.6	+	22025.1i	2.47110	+	1.42669i
$621$		0			0
$622$		−	52010.9i		−	3.35281i
$623$	2407.70	−	716.739i	0.154835	−	0.0460923i
$624$		0			0
$625$	2980.59	−	5162.53i	0.190758	−	0.330402i
$626$	3356.20			0.214282
$627$		0			0
$628$			31353.2i			1.99224i
$629$	6124.08			0.388208
$630$		0			0
$631$	15977.9			1.00803			0.504017	−	0.863694i	$-0.331855\pi$
$631$	15977.9			1.00803			0.504017	+	0.863694i	$0.331855\pi$
$632$			18585.9i			1.16979i
$633$		0			0
$634$	16951.1			1.06185
$635$	4943.89	−	8563.06i	0.308964	−	0.535141i
$636$		0			0
$637$	−7275.61	+	401.049i	−0.452543	+	0.0249453i
$638$		−	12684.3i		−	0.787112i
$639$		0			0
$640$	11743.1	+	6779.88i	0.725291	+	0.418747i
$641$	2384.63	−	1376.77i	0.146938	−	0.0848347i	−0.424728	−	0.905321i	$-0.639630\pi$
$641$	2384.63	−	1376.77i	0.146938	−	0.0848347i	0.571667	+	0.820486i	$0.306297\pi$
$642$		0			0
$643$	17064.4	−	9852.16i	1.04659	−	0.604248i	0.124896	−	0.992170i	$-0.460140\pi$
$643$	17064.4	−	9852.16i	1.04659	−	0.604248i	0.921692	+	0.387922i	$0.126807\pi$
$644$	43830.3	−	46312.9i	2.68192	−	2.83382i
$645$		0			0
$646$	4822.78			0.293730
$647$	12081.7	−	20926.1i	0.734126	−	1.27154i	−0.220980	−	0.975278i	$-0.570925\pi$
$647$	12081.7	−	20926.1i	0.734126	−	1.27154i	0.955106	−	0.296265i	$-0.0957413\pi$
$648$		0			0
$649$	11840.1	−	6835.88i	0.716124	−	0.413454i
$650$	2911.62	−	5043.08i	0.175697	−	0.304317i
$651$		0			0
$652$	−2046.77	−	3545.11i	−0.122941	−	0.212940i
$653$	−1757.49	−	1014.69i	−0.105323	−	0.0608082i	0.446413	−	0.894827i	$-0.352701\pi$
$653$	−1757.49	−	1014.69i	−0.105323	−	0.0608082i	−0.551736	+	0.834019i	$0.686034\pi$
$654$		0			0
$655$	−3981.10	−	6895.47i	−0.237488	−	0.411341i
$656$	−18240.3	−	31593.1i	−1.08561	−	1.88034i
$657$		0			0
$658$	−38409.9	−	9166.45i	−2.27565	−	0.543078i
$659$	−22266.8	−	12855.8i	−1.31623	−	0.759923i	−0.333107	−	0.942889i	$-0.608097\pi$
$659$	−22266.8	−	12855.8i	−1.31623	−	0.759923i	−0.983119	+	0.182966i	$0.941430\pi$
$660$		0			0
$661$			15918.2i			0.936681i	0.883548	+	0.468341i	$0.155148\pi$
$661$			15918.2i			0.936681i	−0.883548	+	0.468341i	$0.844852\pi$
$662$		−	54946.6i		−	3.22592i
$663$		0			0
$664$	−39336.9	−	22711.2i	−2.29905	−	1.32735i
$665$	8724.10	+	2081.99i	0.508731	+	0.121408i
$666$		0			0
$667$	5275.32	+	9137.11i	0.306238	+	0.530420i
$668$	27889.0	+	48305.2i	1.61536	+	2.79788i
$669$		0			0
$670$	−3695.10	−	2133.37i	−0.213066	−	0.123014i
$671$	5185.15	+	8980.94i	0.298317	+	0.516700i
$672$		0			0
$673$	6087.69	−	10544.2i	0.348682	−	0.603935i	−0.637333	−	0.770588i	$-0.719963\pi$
$673$	6087.69	−	10544.2i	0.348682	−	0.603935i	0.986016	+	0.166653i	$0.0532959\pi$
$674$	10953.0	−	6323.73i	0.625956	−	0.361396i
$675$		0			0
$676$	15516.3	−	26874.9i	0.882809	−	1.52907i
$677$	−9317.57			−0.528956			−0.264478	−	0.964392i	$-0.585200\pi$
$677$	−9317.57			−0.528956			−0.264478	+	0.964392i	$0.585200\pi$
$678$		0			0
$679$	5544.32	−	5858.36i	0.313360	−	0.331109i
$680$	−5987.26	+	3456.75i	−0.337649	+	0.194942i
$681$		0			0
$682$	59299.3	−	34236.4i	3.32945	−	1.92226i
$683$	−3212.24	−	1854.59i	−0.179960	−	0.103900i	0.407314	−	0.913288i	$-0.366466\pi$
$683$	−3212.24	−	1854.59i	−0.179960	−	0.103900i	−0.587274	+	0.809388i	$0.699799\pi$
$684$		0			0
$685$		−	11034.5i		−	0.615487i
$686$	−24609.3	−	20846.1i	−1.36966	−	1.16022i
$687$		0			0
$688$	11459.4	−	19848.2i	0.635006	−	1.09986i
$689$	6766.51			0.374141
$690$		0			0
$691$			5266.38i			0.289931i	0.989437	+	0.144966i	$0.0463072\pi$
$691$			5266.38i			0.289931i	−0.989437	+	0.144966i	$0.953693\pi$
$692$	−38416.6			−2.11038
$693$		0			0
$694$	6273.19			0.343123
$695$			21883.7i			1.19438i
$696$		0			0
$697$	−5491.91			−0.298452
$698$	−17865.5	+	30943.9i	−0.968793	+	1.67800i
$699$		0			0
$700$	17036.3	−	5071.48i	0.919875	−	0.273834i
$701$			20150.6i			1.08570i	0.839829	+	0.542851i	$0.182655\pi$
$701$			20150.6i			1.08570i	−0.839829	+	0.542851i	$0.817345\pi$
$702$		0			0
$703$	−18440.6	−	10646.7i	−0.989330	−	0.571190i
$704$	2553.61	−	1474.33i	0.136709	−	0.0789287i
$705$		0			0
$706$	−33536.7	+	19362.4i	−1.78778	+	1.03217i
$707$	−669.385	+	199.267i	−0.0356079	+	0.0106000i
$708$		0			0
$709$	−6869.50			−0.363878			−0.181939	−	0.983310i	$-0.558237\pi$
$709$	−6869.50			−0.363878			−0.181939	+	0.983310i	$0.558237\pi$
$710$	3767.72	−	6525.88i	0.199155	−	0.344946i
$711$		0			0
$712$	5830.72	−	3366.37i	0.306904	−	0.177191i
$713$	−28477.3	+	49324.2i	−1.49577	+	2.59075i
$714$		0			0
$715$	4105.12	+	7110.28i	0.214717	+	0.371901i
$716$	−12419.1	−	7170.15i	−0.648215	−	0.374247i
$717$		0			0
$718$	−33067.4	−	57274.5i	−1.71875	−	2.97697i
$719$	−17274.8	−	29920.8i	−0.896023	−	1.55196i	−0.832533	−	0.553976i	$-0.813110\pi$
$719$	−17274.8	−	29920.8i	−0.896023	−	1.55196i	−0.0634907	−	0.997982i	$-0.520223\pi$
$720$		0			0
$721$	−8887.19	+	9390.56i	−0.459052	+	0.485053i
$722$	15636.0	+	9027.43i	0.805970	+	0.465327i
$723$		0			0
$724$		−	25388.2i		−	1.30324i
$725$			2941.10i			0.150662i
$726$		0			0
$727$	17074.5	+	9857.94i	0.871054	+	0.502903i	0.867698	−	0.497091i	$-0.165598\pi$
$727$	17074.5	+	9857.94i	0.871054	+	0.502903i	0.00335586	+	0.999994i	$0.498932\pi$
$728$	−18717.3	+	5571.88i	−0.952896	+	0.283664i
$729$		0			0
$730$	3517.34	+	6092.20i	0.178332	+	0.308880i
$731$	−1725.14	−	2988.02i	−0.0872865	−	0.151185i
$732$		0			0
$733$	−572.664	−	330.628i	−0.0288565	−	0.0166603i	0.485502	−	0.874235i	$-0.338637\pi$
$733$	−572.664	−	330.628i	−0.0288565	−	0.0166603i	−0.514359	+	0.857575i	$0.671970\pi$
$734$	−27995.4	−	48489.4i	−1.40780	−	2.43839i
$735$		0			0
$736$	15527.5	−	26894.4i	0.777649	−	1.34693i
$737$	−3961.13	+	2286.96i	−0.197979	+	0.114303i
$738$		0			0
$739$	−7494.18	+	12980.3i	−0.373042	+	0.646128i	−0.990032	−	0.140843i	$-0.955019\pi$
$739$	−7494.18	+	12980.3i	−0.373042	+	0.646128i	0.616990	+	0.786971i	$0.288352\pi$
$740$	55501.6			2.75713
$741$		0			0
$742$	21752.5	+	20586.5i	1.07623	+	1.01854i
$743$	20594.5	−	11890.2i	1.01688	−	0.587094i	0.103679	−	0.994611i	$-0.466939\pi$
$743$	20594.5	−	11890.2i	1.01688	−	0.587094i	0.913198	+	0.407517i	$0.133605\pi$
$744$		0			0
$745$	681.786	−	393.630i	0.0335285	−	0.0193577i
$746$	36972.7	+	21346.2i	1.81457	+	1.04764i
$747$		0			0
$748$			13475.7i			0.658719i
$749$	2350.06	+	7894.43i	0.114645	+	0.385122i
$750$		0			0
$751$	−16200.6	+	28060.3i	−0.787175	+	1.36343i	0.140515	+	0.990078i	$0.455124\pi$
$751$	−16200.6	+	28060.3i	−0.787175	+	1.36343i	−0.927691	+	0.373349i	$0.878209\pi$
$752$	−46109.4			−2.23596
$753$		0			0
$754$		−	5875.40i		−	0.283779i
$755$	15880.9			0.765519
$756$		0			0
$757$	13584.0			0.652202			0.326101	−	0.945335i	$-0.394265\pi$
$757$	13584.0			0.652202			0.326101	+	0.945335i	$0.394265\pi$
$758$		−	11414.4i		−	0.546950i
$759$		0			0
$760$	24038.1			1.14731
$761$	6400.03	−	11085.2i	0.304863	−	0.528038i	−0.672368	−	0.740217i	$-0.734723\pi$
$761$	6400.03	−	11085.2i	0.304863	−	0.528038i	0.977231	+	0.212179i	$0.0680559\pi$
$762$		0			0
$763$	−18810.7	−	17802.3i	−0.892520	−	0.844677i
$764$			18388.9i			0.870795i
$765$		0			0
$766$	18950.7	+	10941.2i	0.893886	+	0.516085i
$767$	5484.35	−	3166.39i	0.258186	−	0.149064i
$768$		0			0
$769$	−20477.1	+	11822.5i	−0.960238	+	0.554393i	−0.896246	−	0.443557i	$-0.853716\pi$
$769$	−20477.1	+	11822.5i	−0.960238	+	0.554393i	−0.0639914	+	0.997950i	$0.520383\pi$
$770$	−8435.51	+	35347.1i	−0.394798	+	1.65431i
$771$		0			0
$772$	−26922.1			−1.25511
$773$	5212.32	−	9028.01i	0.242528	−	0.420071i	−0.718906	−	0.695108i	$-0.755357\pi$
$773$	5212.32	−	9028.01i	0.242528	−	0.420071i	0.961434	+	0.275037i	$0.0886900\pi$
$774$		0			0
$775$	−13749.6	+	7938.36i	−0.637292	+	0.367941i
$776$	10808.8	−	18721.4i	0.500019	−	0.866058i
$777$		0			0
$778$	27148.2	+	47022.1i	1.25104	+	2.16687i
$779$	16537.0	+	9547.65i	0.760590	+	0.439127i
$780$		0			0
$781$	−4038.98	−	6995.72i	−0.185053	−	0.320521i
$782$	−8126.64	−	14075.7i	−0.371621	−	0.643667i
$783$		0			0
$784$	−33600.8	−	17006.1i	−1.53065	−	0.774694i
$785$	12871.3	+	7431.25i	0.585218	+	0.337876i
$786$		0			0
$787$			18164.5i			0.822740i	0.911468	+	0.411370i	$0.134950\pi$
$787$			18164.5i			0.822740i	−0.911468	+	0.411370i	$0.865050\pi$
$788$			11286.1i			0.510216i
$789$		0			0
$790$	13873.5	+	8009.85i	0.624805	+	0.360731i
$791$	4171.79	+	14014.1i	0.187524	+	0.629940i
$792$		0			0
$793$	2401.77	+	4159.99i	0.107553	+	0.186287i
$794$	2346.78	+	4064.75i	0.104892	+	0.181678i
$795$		0			0
$796$	−43726.7	−	25245.6i	−1.94705	−	1.12413i
$797$	14273.1	+	24721.7i	0.634353	+	1.09873i	0.986652	+	0.162844i	$0.0520668\pi$
$797$	14273.1	+	24721.7i	0.634353	+	1.09873i	−0.352299	+	0.935888i	$0.614600\pi$
$798$		0			0
$799$	−3470.74	+	6011.50i	−0.153675	+	0.266172i
$800$	7497.09	−	4328.44i	0.331328	−	0.191292i
$801$		0			0
$802$	−5473.94	+	9481.15i	−0.241012	+	0.417445i
$803$	7541.15			0.331409
$804$		0			0
$805$	−8624.09	−	28970.4i	−0.377589	−	1.26841i
$806$	27467.5	−	15858.4i	1.20037	−	0.693037i
$807$		0			0
$808$	−1621.05	+	935.913i	−0.0705796	+	0.0407491i
$809$	−13928.5	−	8041.64i	−0.605317	−	0.349480i	0.165814	−	0.986157i	$-0.446975\pi$
$809$	−13928.5	−	8041.64i	−0.605317	−	0.349480i	−0.771130	+	0.636677i	$0.780308\pi$
$810$		0			0
$811$			27967.7i			1.21095i	0.795866	+	0.605473i	$0.207016\pi$
$811$			27967.7i			1.21095i	−0.795866	+	0.605473i	$0.792984\pi$
$812$	12327.6	−	13025.8i	0.532775	−	0.562952i
$813$		0			0
$814$	43136.6	−	74714.9i	1.85742	−	3.21714i
$815$	−1940.48			−0.0834011
$816$		0			0
$817$			11996.5i			0.513716i
$818$	65558.6			2.80220
$819$		0			0
$820$	−49772.4			−2.11967
$821$			5041.38i			0.214306i	0.994243	+	0.107153i	$0.0341735\pi$
$821$			5041.38i			0.214306i	−0.994243	+	0.107153i	$0.965826\pi$
$822$		0			0
$823$	23037.4			0.975740			0.487870	−	0.872916i	$-0.337774\pi$
$823$	23037.4			0.975740			0.487870	+	0.872916i	$0.337774\pi$
$824$	−17325.9	+	30009.3i	−0.732493	+	1.26872i
$825$		0			0
$826$	27264.2	+	6506.54i	1.14848	+	0.274082i
$827$		−	20530.9i		−	0.863277i	−0.902047	−	0.431638i	$-0.857936\pi$
$827$		−	20530.9i		−	0.863277i	0.902047	−	0.431638i	$-0.142064\pi$
$828$		0			0
$829$	−4622.95	−	2669.06i	−0.193681	−	0.111822i	0.400023	−	0.916505i	$-0.369002\pi$
$829$	−4622.95	−	2669.06i	−0.193681	−	0.111822i	−0.593705	+	0.804683i	$0.702335\pi$
$830$	−33905.6	+	19575.4i	−1.41793	+	0.818640i
$831$		0			0
$832$	1182.84	−	682.911i	0.0492878	−	0.0284564i
$833$	−4746.36	+	3100.62i	−0.197421	+	0.128968i
$834$		0			0
$835$	26440.7			1.09583
$836$	23427.5	−	40577.6i	0.969206	−	1.67871i
$837$		0			0
$838$	33581.7	−	19388.4i	1.38432	−	0.799239i
$839$	20068.0	−	34758.8i	0.825773	−	1.43028i	−0.0755533	−	0.997142i	$-0.524072\pi$
$839$	20068.0	−	34758.8i	0.825773	−	1.43028i	0.901327	−	0.433140i	$-0.142594\pi$
$840$		0			0
$841$	−10710.8	−	18551.6i	−0.439164	−	0.760655i
$842$	−10948.0	−	6320.81i	−0.448090	−	0.258705i
$843$		0			0
$844$	20630.5	+	35733.1i	0.841388	+	1.45733i
$845$	−7355.24	−	12739.6i	−0.299441	−	0.518647i
$846$		0			0
$847$	10390.2	+	9833.27i	0.421503	+	0.398908i
$848$	30285.8	+	17485.5i	1.22644	+	0.708084i
$849$		0			0
$850$		−	4530.77i		−	0.182828i
$851$			71760.8i			2.89063i
$852$		0			0
$853$	−5640.90	−	3256.78i	−0.226425	−	0.130727i	0.382497	−	0.923957i	$-0.375064\pi$
$853$	−5640.90	−	3256.78i	−0.226425	−	0.130727i	−0.608922	+	0.793230i	$0.708398\pi$
$854$	−4935.33	+	20680.4i	−0.197756	+	0.828652i
$855$		0			0
$856$	11037.7	+	19117.9i	0.440727	+	0.763362i
$857$	−14192.9	−	24582.9i	−0.565719	−	0.979854i	−0.996982	−	0.0776282i	$-0.975265\pi$
$857$	−14192.9	−	24582.9i	−0.565719	−	0.979854i	0.431263	−	0.902226i	$-0.358068\pi$
$858$		0			0
$859$	38570.8	+	22268.9i	1.53204	+	0.884521i	0.999268	+	0.0382602i	$0.0121816\pi$
$859$	38570.8	+	22268.9i	1.53204	+	0.884521i	0.532768	+	0.846261i	$0.321152\pi$
$860$	−15634.6	−	27080.0i	−0.619927	−	1.07374i
$861$		0			0
$862$	−11812.0	+	20459.0i	−0.466727	+	0.808395i
$863$	−433.875	+	250.498i	−0.0171139	+	0.00988071i	−0.508533	−	0.861043i	$-0.669812\pi$
$863$	−433.875	+	250.498i	−0.0171139	+	0.00988071i	0.491419	+	0.870923i	$0.336479\pi$
$864$		0			0
$865$	−9105.40	+	15771.0i	−0.357911	+	0.619920i
$866$	−7386.64			−0.289848
$867$		0			0
$868$	94169.3	+	22473.3i	3.68239	+	0.878794i
$869$	14872.3	−	8586.53i	0.580562	−	0.335188i
$870$		0			0
$871$	−1834.80	+	1059.32i	−0.0713777	+	0.0412099i
$872$	−60113.0	−	34706.2i	−2.33450	−	1.34782i
$873$		0			0
$874$			56512.4i			2.18714i
$875$	6484.33	−	27171.1i	0.250526	−	1.04977i
$876$		0			0
$877$	15066.8	−	26096.4i	0.580124	−	1.00480i	−0.415341	−	0.909666i	$-0.636338\pi$
$877$	15066.8	−	26096.4i	0.580124	−	1.00480i	0.995464	−	0.0951376i	$-0.0303291\pi$
$878$	−15220.5			−0.585044
$879$		0			0
$880$			42432.6i			1.62546i
$881$	−6217.46			−0.237766			−0.118883	−	0.992908i	$-0.537931\pi$
$881$	−6217.46			−0.237766			−0.118883	+	0.992908i	$0.537931\pi$
$882$		0			0
$883$	9681.01			0.368960			0.184480	−	0.982836i	$-0.440940\pi$
$883$	9681.01			0.368960			0.184480	+	0.982836i	$0.440940\pi$
$884$			6241.99i			0.237490i
$885$		0			0
$886$	−73424.9			−2.78415
$887$	−32.1571	+	55.6977i	−0.00121728	+	0.00210840i	−0.866633	−	0.498945i	$-0.833721\pi$
$887$	−32.1571	+	55.6977i	−0.00121728	+	0.00210840i	0.865416	+	0.501054i	$0.167054\pi$
$888$		0			0
$889$	5044.49	−	21137.8i	0.190311	−	0.797457i
$890$		−	5803.14i		−	0.218564i
$891$		0			0
$892$	−59954.3	−	34614.6i	−2.25047	−	1.29931i
$893$	20901.9	−	12067.7i	0.783265	−	0.452218i
$894$		0			0
$895$	−5887.06	+	3398.89i	−0.219869	+	0.126941i
$896$	28987.7	+	6917.85i	1.08081	+	0.257934i
$897$		0			0
$898$	−94528.1			−3.51274
$899$	−8009.46	+	13872.8i	−0.297142	+	0.514664i
$900$		0			0
$901$	4559.34	−	2632.34i	0.168583	−	0.0973316i
$902$	−38683.8	+	67002.3i	−1.42797	+	2.47332i
$903$		0			0
$904$	19594.0	+	33937.8i	0.720893	+	1.24862i
$905$	−10422.5	−	6017.43i	−0.382824	−	0.221024i
$906$		0			0
$907$	370.358	+	641.479i	0.0135585	+	0.0234840i	0.872725	−	0.488212i	$-0.162351\pi$
$907$	370.358	+	641.479i	0.0135585	+	0.0234840i	−0.859167	+	0.511696i	$0.829017\pi$
$908$	30413.9	+	52678.4i	1.11159	+	1.92532i
$909$		0			0
$910$	−3907.34	+	16372.8i	−0.142337	+	0.596433i
$911$	21092.1	+	12177.5i	0.767082	+	0.442875i	0.831833	−	0.555027i	$-0.187292\pi$
$911$	21092.1	+	12177.5i	0.767082	+	0.442875i	−0.0647510	+	0.997901i	$0.520625\pi$
$912$		0			0
$913$			41969.5i			1.52135i
$914$		−	21211.0i		−	0.767611i
$915$		0			0
$916$	−4160.65	−	2402.15i	−0.150078	−	0.0866478i
$917$	−12709.9	−	12028.6i	−0.457707	−	0.433172i
$918$		0			0
$919$	12770.3	+	22118.8i	0.458382	+	0.793941i	0.998876	−	0.0474073i	$-0.0150959\pi$
$919$	12770.3	+	22118.8i	0.458382	+	0.793941i	−0.540494	+	0.841348i	$0.681763\pi$
$920$	−40505.5	−	70157.6i	−1.45155	−	2.51416i
$921$		0			0
$922$	−9832.35	−	5676.71i	−0.351205	−	0.202768i
$923$	−1870.86	−	3240.43i	−0.0667175	−	0.115558i
$924$		0			0
$925$	−10002.0	+	17324.0i	−0.355530	+	0.615795i
$926$	−67075.8	+	38726.2i	−2.38040	+	1.37432i
$927$		0			0
$928$	4367.21	−	7564.23i	0.154484	−	0.267573i
$929$	47720.2			1.68531			0.842653	−	0.538457i	$-0.180992\pi$
$929$	47720.2			1.68531			0.842653	+	0.538457i	$0.180992\pi$
$930$		0			0
$931$	19682.4	−	1084.94i	0.692874	−	0.0381929i
$932$	−28045.0	+	16191.8i	−0.985669	+	0.569076i
$933$		0			0
$934$	50200.4	−	28983.2i	1.75868	−	1.01538i
$935$	5532.14	+	3193.98i	0.193498	+	0.111716i
$936$		0			0
$937$		−	54541.0i		−	1.90158i	−0.309841	−	0.950788i	$-0.600276\pi$
$937$		−	54541.0i		−	1.90158i	0.309841	−	0.950788i	$-0.399724\pi$
$938$	−9121.30	−	2176.78i	−0.317506	−	0.0757722i
$939$		0			0
$940$	−31454.8	+	54481.4i	−1.09143	+	1.89041i
$941$	−43643.3			−1.51194			−0.755968	−	0.654609i	$-0.772833\pi$
$941$	−43643.3			−1.51194			−0.755968	+	0.654609i	$0.772833\pi$
$942$		0			0
$943$		−	64353.2i		−	2.22230i
$944$	32729.5			1.12845
$945$		0			0
$946$	−48605.9			−1.67052
$947$		−	4033.11i		−	0.138393i	−0.997603	−	0.0691966i	$-0.977956\pi$
$947$		−	4033.11i		−	0.138393i	0.997603	−	0.0691966i	$-0.0220436\pi$
$948$		0			0
$949$	3493.07			0.119484
$950$	−7876.71	+	13642.9i	−0.269004	+	0.465929i
$951$		0			0
$952$	−10444.3	+	11035.9i	−0.355569	+	0.375708i
$953$			40892.4i			1.38996i	0.719028	+	0.694981i	$0.244587\pi$
$953$			40892.4i			1.38996i	−0.719028	+	0.694981i	$0.755413\pi$
$954$		0			0
$955$	7549.12	+	4358.48i	0.255794	+	0.147683i
$956$	−70147.0	+	40499.4i	−2.37313	+	1.37013i
$957$		0			0
$958$	−10432.1	+	6022.98i	−0.351823	+	0.203125i
$959$	−6919.35	−	23243.8i	−0.232990	−	0.782670i
$960$		0			0
$961$	−56682.7			−1.90268
$962$	19981.0	−	34608.0i	0.669659	−	1.15988i
$963$		0			0
$964$	44004.3	−	25405.9i	1.47021	−	0.848827i
$965$	−6380.99	+	11052.2i	−0.212862	+	0.368687i
$966$		0			0
$967$	−9795.27	−	16965.9i	−0.325744	−	0.564206i	0.655918	−	0.754832i	$-0.272282\pi$
$967$	−9795.27	−	16965.9i	−0.325744	−	0.564206i	−0.981663	+	0.190626i	$0.938948\pi$
$968$	33203.9	+	19170.3i	1.10249	+	0.636525i
$969$		0			0
$970$	−9316.44	−	16136.5i	−0.308384	−	0.534137i
$971$	−16147.0	−	27967.4i	−0.533657	−	0.924321i	−0.999227	−	0.0393099i	$-0.987484\pi$
$971$	−16147.0	−	27967.4i	−0.533657	−	0.924321i	0.465570	−	0.885011i	$-0.345849\pi$
$972$		0			0
$973$	13722.4	+	46097.0i	0.452129	+	1.51881i
$974$	−85681.8	−	49468.4i	−2.81871	−	1.62738i
$975$		0			0
$976$			24825.9i			0.814199i
$977$		−	24429.7i		−	0.799973i	−0.916521	−	0.399987i	$-0.869015\pi$
$977$		−	24429.7i		−	0.799973i	0.916521	−	0.399987i	$-0.130985\pi$
$978$		0			0
$979$	−5387.50	−	3110.48i	−0.175879	−	0.101544i
$980$	−43015.6	+	28100.5i	−1.40212	+	0.915955i
$981$		0			0
$982$	−32190.8	−	55756.2i	−1.04608	−	1.81186i
$983$	−467.204	−	809.221i	−0.0151592	−	0.0262565i	0.858346	−	0.513071i	$-0.171492\pi$
$983$	−467.204	−	809.221i	−0.0151592	−	0.0262565i	−0.873505	+	0.486814i	$0.838159\pi$
$984$		0			0
$985$	4633.23	+	2675.00i	0.149875	+	0.0865305i
$986$	−2285.67	−	3958.91i	−0.0738243	−	0.127867i
$987$		0			0
$988$	10851.6	−	18795.6i	0.349430	−	0.605231i
$989$	35013.1	−	20214.8i	1.12573	−	0.649943i
$990$		0			0
$991$	−4956.45	+	8584.83i	−0.158877	+	0.275183i	−0.934464	−	0.356058i	$-0.884121\pi$
$991$	−4956.45	+	8584.83i	−0.158877	+	0.275183i	0.775587	+	0.631241i	$0.217454\pi$
$992$	47150.4			1.50910
$993$		0			0
$994$	3844.39	−	16109.0i	0.122673	−	0.514032i
$995$	−20728.0	+	11967.3i	−0.660423	+	0.381295i
$996$		0			0
$997$	14635.2	−	8449.65i	0.464897	−	0.268408i	−0.249204	−	0.968451i	$-0.580169\pi$
$997$	14635.2	−	8449.65i	0.464897	−	0.268408i	0.714101	+	0.700043i	$0.246836\pi$
$998$	−51939.0	−	29987.0i	−1.64739	−	0.951123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.i.a.143.2		44
3.2	odd	2		63.4.i.a.38.21	yes	44
7.5	odd	6		189.4.s.a.89.2		44
9.4	even	3		63.4.s.a.59.21	yes	44
9.5	odd	6		189.4.s.a.17.2		44
21.5	even	6		63.4.s.a.47.21	yes	44
63.5	even	6	inner	189.4.i.a.152.21		44
63.40	odd	6		63.4.i.a.5.2	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.2	✓	44	63.40	odd	6
63.4.i.a.38.21	yes	44	3.2	odd	2
63.4.s.a.47.21	yes	44	21.5	even	6
63.4.s.a.59.21	yes	44	9.4	even	3
189.4.i.a.143.2		44	1.1	even	1	trivial
189.4.i.a.152.21		44	63.5	even	6	inner
189.4.s.a.17.2		44	9.5	odd	6
189.4.s.a.89.2		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)

\(f(q)\)	\(=\)	\(q-5.07706i q^{2} -17.7766 q^{4} +(-4.21335 + 7.29774i) q^{5} +(-4.29909 + 18.0144i) q^{7} +49.6363i q^{8} +O(q^{10})\)	\(q-5.07706i q^{2} -17.7766 q^{4} +(-4.21335 + 7.29774i) q^{5} +(-4.29909 + 18.0144i) q^{7} +49.6363i q^{8} +(37.0511 + 21.3915i) q^{10} +(39.7187 - 22.9316i) q^{11} +(18.3978 - 10.6219i) q^{13} +(91.4601 + 21.8268i) q^{14} +109.794 q^{16} +(8.26439 - 14.3143i) q^{17} +(-49.7708 + 28.7352i) q^{19} +(74.8990 - 129.729i) q^{20} +(-116.425 - 201.654i) q^{22} +(167.733 + 96.8406i) q^{23} +(26.9953 + 46.7573i) q^{25} +(-53.9283 - 93.4065i) q^{26} +(76.4231 - 320.234i) q^{28} +(47.1761 + 27.2371i) q^{29} +294.064i q^{31} -160.341i q^{32} +(-72.6748 - 41.9588i) q^{34} +(-113.351 - 107.275i) q^{35} +(185.255 + 320.871i) q^{37} +(145.890 + 252.689i) q^{38} +(-362.233 - 209.135i) q^{40} +(-166.132 - 287.749i) q^{41} +(104.372 - 180.777i) q^{43} +(-706.062 + 407.645i) q^{44} +(491.666 - 851.590i) q^{46} -419.964 q^{47} +(-306.036 - 154.891i) q^{49} +(237.390 - 137.057i) q^{50} +(-327.049 + 188.822i) q^{52} +(275.842 + 159.258i) q^{53} +386.475i q^{55} +(-894.167 - 213.391i) q^{56} +(138.285 - 239.516i) q^{58} +298.099 q^{59} +226.114i q^{61} +1492.98 q^{62} +64.2925 q^{64} +179.016i q^{65} -99.7298 q^{67} +(-146.913 + 254.460i) q^{68} +(-544.640 + 575.488i) q^{70} -176.132i q^{71} +(142.398 + 82.2136i) q^{73} +(1629.08 - 940.551i) q^{74} +(884.753 - 510.813i) q^{76} +(242.344 + 814.092i) q^{77} +374.441 q^{79} +(-462.600 + 801.247i) q^{80} +(-1460.92 + 843.462i) q^{82} +(-457.551 + 792.502i) q^{83} +(69.6416 + 120.623i) q^{85} +(-917.816 - 529.901i) q^{86} +(1138.24 + 1971.49i) q^{88} +(-67.8208 - 117.469i) q^{89} +(112.254 + 377.089i) q^{91} +(-2981.71 - 1721.49i) q^{92} +2132.18i q^{94} -484.285i q^{95} +(-377.173 - 217.761i) q^{97} +(-786.391 + 1553.76i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) 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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