LMFDB - Embedded newform 184.4.i.a.25.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(9,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 10])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.9"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [90,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8563514411$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$9$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	184.25
Dual form			184.4.i.a.81.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.978797 - 6.80768i) q^{3} +(-0.683572 - 0.200715i) q^{5} +(16.8123 - 19.4024i) q^{7} +(-19.4802 + 5.71990i) q^{9} +(15.5835 - 10.0149i) q^{11} +(-26.7041 - 30.8182i) q^{13} +(-0.697325 + 4.85000i) q^{15} +(-0.485449 + 1.06298i) q^{17} +(10.2971 + 22.5474i) q^{19} +(-148.541 - 95.4616i) q^{21} +(-97.0007 + 52.5153i) q^{23} +(-104.730 - 67.3057i) q^{25} +(-19.1351 - 41.9001i) q^{27} +(-36.0087 + 78.8481i) q^{29} +(-7.68183 + 53.4283i) q^{31} +(-83.4315 - 96.2851i) q^{33} +(-15.3867 + 9.88846i) q^{35} +(-49.4724 + 14.5264i) q^{37} +(-183.663 + 211.958i) q^{39} +(-12.3721 - 3.63277i) q^{41} +(-17.1107 - 119.007i) q^{43} +14.4642 q^{45} +440.460 q^{47} +(-44.9864 - 312.887i) q^{49} +(7.71161 + 2.26433i) q^{51} +(298.542 - 344.536i) q^{53} +(-12.6626 + 3.71808i) q^{55} +(143.417 - 92.1685i) q^{57} +(-28.8535 - 33.2988i) q^{59} +(126.095 - 877.009i) q^{61} +(-216.526 + 474.127i) q^{63} +(12.0685 + 26.4264i) q^{65} +(-211.202 - 135.731i) q^{67} +(452.452 + 608.948i) q^{69} +(538.204 + 345.883i) q^{71} +(271.204 + 593.853i) q^{73} +(-355.687 + 778.845i) q^{75} +(67.6809 - 470.731i) q^{77} +(840.560 + 970.058i) q^{79} +(-727.663 + 467.641i) q^{81} +(727.514 - 213.617i) q^{83} +(0.545196 - 0.629190i) q^{85} +(572.018 + 167.960i) q^{87} +(64.8654 + 451.149i) q^{89} -1046.90 q^{91} +371.242 q^{93} +(-2.51318 - 17.4796i) q^{95} +(-501.787 - 147.338i) q^{97} +(-246.286 + 284.229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 2 q^{3} - 87 q^{7} - 113 q^{9} - 6 q^{11} - 8 q^{13} - 6 q^{15} + 306 q^{17} + 275 q^{19} + 350 q^{21} - 23 q^{23} - 289 q^{25} + 511 q^{27} + 309 q^{29} - 314 q^{31} - 1444 q^{33} - 1895 q^{35}+ \cdots + 5967 q^{99}+O(q^{100}) $ 90 * q - 2 * q^3 - 87 * q^7 - 113 * q^9 - 6 * q^11 - 8 * q^13 - 6 * q^15 + 306 * q^17 + 275 * q^19 + 350 * q^21 - 23 * q^23 - 289 * q^25 + 511 * q^27 + 309 * q^29 - 314 * q^31 - 1444 * q^33 - 1895 * q^35 - 130 * q^37 + 1850 * q^39 + 927 * q^41 + 1007 * q^43 - 960 * q^45 + 756 * q^47 + 164 * q^49 + 3505 * q^51 + 1267 * q^53 - 2849 * q^55 - 3214 * q^57 - 467 * q^59 - 37 * q^61 + 5838 * q^63 - 2590 * q^65 - 3217 * q^67 - 2046 * q^69 - 508 * q^71 + 2716 * q^73 + 2855 * q^75 - 2245 * q^77 + 270 * q^79 - 2319 * q^81 + 820 * q^83 + 2470 * q^85 - 3545 * q^87 - 457 * q^89 - 10990 * q^91 + 3734 * q^93 - 5437 * q^95 + 1853 * q^97 + 5967 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.978797	−	6.80768i	−0.188370	−	1.31014i	−0.836229	−	0.548380i	$-0.815245\pi$
$3$	−0.978797	−	6.80768i	−0.188370	−	1.31014i	0.647860	−	0.761760i	$-0.275664\pi$
$4$		0			0
$5$	−0.683572	−	0.200715i	−0.0611405	−	0.0179525i	0.251019	−	0.967982i	$-0.419234\pi$
$5$	−0.683572	−	0.200715i	−0.0611405	−	0.0179525i	−0.312160	+	0.950030i	$0.601052\pi$
$6$		0			0
$7$	16.8123	−	19.4024i	0.907777	−	1.04763i	−0.0908821	−	0.995862i	$-0.528969\pi$
$7$	16.8123	−	19.4024i	0.907777	−	1.04763i	0.998659	−	0.0517688i	$-0.0164859\pi$
$8$		0			0
$9$	−19.4802	+	5.71990i	−0.721489	+	0.211848i
$10$		0			0
$11$	15.5835	−	10.0149i	0.427146	−	0.274510i	−0.309355	−	0.950947i	$-0.600113\pi$
$11$	15.5835	−	10.0149i	0.427146	−	0.274510i	0.736501	+	0.676437i	$0.236477\pi$
$12$		0			0
$13$	−26.7041	−	30.8182i	−0.569722	−	0.657495i	0.395640	−	0.918405i	$-0.370523\pi$
$13$	−26.7041	−	30.8182i	−0.569722	−	0.657495i	−0.965363	+	0.260911i	$0.915977\pi$
$14$		0			0
$15$	−0.697325	+	4.85000i	−0.0120032	+	0.0834843i
$16$		0			0
$17$	−0.485449	+	1.06298i	−0.00692580	+	0.0151654i	−0.913063	−	0.407818i	$-0.866290\pi$
$17$	−0.485449	+	1.06298i	−0.00692580	+	0.0151654i	0.906137	+	0.422983i	$0.139017\pi$
$18$		0			0
$19$	10.2971	+	22.5474i	0.124332	+	0.272249i	0.961555	−	0.274613i	$-0.0885496\pi$
$19$	10.2971	+	22.5474i	0.124332	+	0.272249i	−0.837223	+	0.546862i	$0.815822\pi$
$20$		0			0
$21$	−148.541	−	95.4616i	−1.54354	−	0.991972i
$22$		0			0
$23$	−97.0007	+	52.5153i	−0.879393	+	0.476096i
$23$	−97.0007	+	52.5153i	−0.879393	+	0.476096i
$24$		0			0
$25$	−104.730	−	67.3057i	−0.837838	−	0.538446i
$26$		0			0
$27$	−19.1351	−	41.9001i	−0.136391	−	0.298655i
$28$		0			0
$29$	−36.0087	+	78.8481i	−0.230574	+	0.504887i	−0.989188	−	0.146654i	$-0.953150\pi$
$29$	−36.0087	+	78.8481i	−0.230574	+	0.504887i	0.758614	+	0.651541i	$0.225877\pi$
$30$		0			0
$31$	−7.68183	+	53.4283i	−0.0445064	+	0.309549i	0.955393	+	0.295339i	$0.0954324\pi$
$31$	−7.68183	+	53.4283i	−0.0445064	+	0.309549i	−0.999899	+	0.0142101i	$0.995477\pi$
$32$		0			0
$33$	−83.4315	−	96.2851i	−0.440108	−	0.507912i
$34$		0			0
$35$	−15.3867	+	9.88846i	−0.0743095	+	0.0477558i
$36$		0			0
$37$	−49.4724	+	14.5264i	−0.219817	+	0.0645439i	−0.389786	−	0.920905i	$-0.627451\pi$
$37$	−49.4724	+	14.5264i	−0.219817	+	0.0645439i	0.169970	+	0.985449i	$0.445633\pi$
$38$		0			0
$39$	−183.663	+	211.958i	−0.754091	+	0.870268i
$40$		0			0
$41$	−12.3721	−	3.63277i	−0.0471267	−	0.0138376i	0.258084	−	0.966122i	$-0.416909\pi$
$41$	−12.3721	−	3.63277i	−0.0471267	−	0.0138376i	−0.305211	+	0.952285i	$0.598727\pi$
$42$		0			0
$43$	−17.1107	−	119.007i	−0.0606826	−	0.422057i	−0.997406	−	0.0719854i	$-0.977066\pi$
$43$	−17.1107	−	119.007i	−0.0606826	−	0.422057i	0.936723	−	0.350071i	$-0.113843\pi$
$44$		0			0
$45$	14.4642			0.0479154
$46$		0			0
$47$	440.460			1.36697			0.683486	−	0.729964i	$-0.260463\pi$
$47$	440.460			1.36697			0.683486	+	0.729964i	$0.260463\pi$
$48$		0			0
$49$	−44.9864	−	312.887i	−0.131156	−	0.912208i
$50$		0			0
$51$	7.71161	+	2.26433i	0.0211734	+	0.00621706i
$52$		0			0
$53$	298.542	−	344.536i	0.773734	−	0.892936i	−0.222907	−	0.974840i	$-0.571555\pi$
$53$	298.542	−	344.536i	0.773734	−	0.892936i	0.996640	+	0.0819037i	$0.0261000\pi$
$54$		0			0
$55$	−12.6626	+	3.71808i	−0.0310441	+	0.00911537i
$56$		0			0
$57$	143.417	−	92.1685i	0.333264	−	0.214176i
$58$		0			0
$59$	−28.8535	−	33.2988i	−0.0636680	−	0.0734768i	0.723022	−	0.690825i	$-0.242752\pi$
$59$	−28.8535	−	33.2988i	−0.0636680	−	0.0734768i	−0.786690	+	0.617348i	$0.788207\pi$
$60$		0			0
$61$	126.095	−	877.009i	0.264669	−	1.84081i	−0.231809	−	0.972761i	$-0.574464\pi$
$61$	126.095	−	877.009i	0.264669	−	1.84081i	0.496477	−	0.868050i	$-0.334627\pi$
$62$		0			0
$63$	−216.526	+	474.127i	−0.433012	+	0.948164i
$64$		0			0
$65$	12.0685	+	26.4264i	0.0230295	+	0.0504275i
$66$		0			0
$67$	−211.202	−	135.731i	−0.385111	−	0.247496i	0.333733	−	0.942668i	$-0.391692\pi$
$67$	−211.202	−	135.731i	−0.385111	−	0.247496i	−0.718843	+	0.695172i	$0.755328\pi$
$68$		0			0
$69$	452.452	+	608.948i	0.789403	+	1.06245i
$70$		0			0
$71$	538.204	+	345.883i	0.899621	+	0.578151i	0.906678	−	0.421824i	$-0.138610\pi$
$71$	538.204	+	345.883i	0.899621	+	0.578151i	−0.00705689	+	0.999975i	$0.502246\pi$
$72$		0			0
$73$	271.204	+	593.853i	0.434822	+	0.952127i	0.992520	+	0.122083i	$0.0389574\pi$
$73$	271.204	+	593.853i	0.434822	+	0.952127i	−0.557698	+	0.830044i	$0.688315\pi$
$74$		0			0
$75$	−355.687	+	778.845i	−0.547616	+	1.19911i
$76$		0			0
$77$	67.6809	−	470.731i	0.100168	−	0.696685i
$78$		0			0
$79$	840.560	+	970.058i	1.19709	+	1.38152i	0.905154	+	0.425083i	$0.139755\pi$
$79$	840.560	+	970.058i	1.19709	+	1.38152i	0.291939	+	0.956437i	$0.405699\pi$
$80$		0			0
$81$	−727.663	+	467.641i	−0.998166	+	0.641482i
$82$		0			0
$83$	727.514	−	213.617i	0.962109	−	0.282501i	0.237289	−	0.971439i	$-0.423741\pi$
$83$	727.514	−	213.617i	0.962109	−	0.282501i	0.724820	+	0.688938i	$0.241923\pi$
$84$		0			0
$85$	0.545196	−	0.629190i	0.000695703	−	0.000802885i
$86$		0			0
$87$	572.018	+	167.960i	0.704905	+	0.206979i
$88$		0			0
$89$	64.8654	+	451.149i	0.0772553	+	0.537322i	0.991291	+	0.131689i	$0.0420400\pi$
$89$	64.8654	+	451.149i	0.0772553	+	0.537322i	−0.914036	+	0.405634i	$0.867051\pi$
$90$		0			0
$91$	−1046.90			−1.20599
$92$		0			0
$93$	371.242			0.413935
$94$		0			0
$95$	−2.51318	−	17.4796i	−0.00271418	−	0.0188775i
$96$		0			0
$97$	−501.787	−	147.338i	−0.525245	−	0.154226i	0.00835115	−	0.999965i	$-0.497342\pi$
$97$	−501.787	−	147.338i	−0.525245	−	0.154226i	−0.533597	+	0.845739i	$0.679160\pi$
$98$		0			0
$99$	−246.286	+	284.229i	−0.250027	+	0.288546i
$100$		0			0
$101$	−774.256	+	227.342i	−0.762785	+	0.223974i	−0.639912	−	0.768448i	$-0.721029\pi$
$101$	−774.256	+	227.342i	−0.762785	+	0.223974i	−0.122874	+	0.992422i	$0.539211\pi$
$102$		0			0
$103$	1086.98	−	698.560i	1.03984	−	0.668264i	0.0948919	−	0.995488i	$-0.469749\pi$
$103$	1086.98	−	698.560i	1.03984	−	0.668264i	0.944947	+	0.327224i	$0.106113\pi$
$104$		0			0
$105$	82.3780	+	95.0693i	0.0765645	+	0.0883601i
$106$		0			0
$107$	256.832	−	1786.31i	0.232046	−	1.61391i	−0.457184	−	0.889372i	$-0.651142\pi$
$107$	256.832	−	1786.31i	0.232046	−	1.61391i	0.689230	−	0.724543i	$-0.257949\pi$
$108$		0			0
$109$	32.0286	−	70.1328i	0.0281448	−	0.0616285i	−0.895038	−	0.445991i	$-0.852851\pi$
$109$	32.0286	−	70.1328i	0.0281448	−	0.0616285i	0.923182	+	0.384362i	$0.125579\pi$
$110$		0			0
$111$	147.315	+	322.574i	0.125968	+	0.275832i
$112$		0			0
$113$	9.36050	+	6.01563i	0.00779258	+	0.00500799i	0.544531	−	0.838741i	$-0.316708\pi$
$113$	9.36050	+	6.01563i	0.00779258	+	0.00500799i	−0.536739	+	0.843749i	$0.680344\pi$
$114$		0			0
$115$	76.8476	−	16.4285i	0.0623137	−	0.0133215i
$116$		0			0
$117$	696.479	+	447.600i	0.550337	+	0.353680i
$118$		0			0
$119$	12.4629	+	27.2900i	0.00960064	+	0.0210225i
$120$		0			0
$121$	−410.370	+	898.585i	−0.308317	+	0.675120i
$122$		0			0
$123$	−12.6210	+	87.7809i	−0.00925200	+	0.0643491i
$124$		0			0
$125$	116.399	+	134.331i	0.0832883	+	0.0961198i
$126$		0			0
$127$	1263.84	−	812.222i	0.883054	−	0.567505i	−0.0186653	−	0.999826i	$-0.505942\pi$
$127$	1263.84	−	812.222i	0.883054	−	0.567505i	0.901720	+	0.432321i	$0.142305\pi$
$128$		0			0
$129$	−793.416	+	232.968i	−0.541522	+	0.159005i
$130$		0			0
$131$	787.483	−	908.804i	0.525212	−	0.606127i	−0.429716	−	0.902964i	$-0.641386\pi$
$131$	787.483	−	908.804i	0.525212	−	0.606127i	0.954928	+	0.296837i	$0.0959319\pi$
$132$		0			0
$133$	610.591	+	179.286i	0.398082	+	0.116887i
$134$		0			0
$135$	4.67027	+	32.4824i	0.00297743	+	0.0207085i
$136$		0			0
$137$	703.671			0.438823			0.219411	−	0.975632i	$-0.429586\pi$
$137$	703.671			0.438823			0.219411	+	0.975632i	$0.429586\pi$
$138$		0			0
$139$	−1086.49			−0.662984			−0.331492	−	0.943458i	$-0.607552\pi$
$139$	−1086.49			−0.662984			−0.331492	+	0.943458i	$0.607552\pi$
$140$		0			0
$141$	−431.121	−	2998.51i	−0.257496	−	1.79092i
$142$		0			0
$143$	−724.786	−	212.816i	−0.423844	−	0.124452i
$144$		0			0
$145$	40.4405	−	46.6708i	0.0231614	−	0.0267297i
$146$		0			0
$147$	−2086.01	+	612.507i	−1.17041	+	0.343665i
$148$		0			0
$149$	−35.3064	+	22.6901i	−0.0194122	+	0.0124754i	−0.550311	−	0.834960i	$-0.685491\pi$
$149$	−35.3064	+	22.6901i	−0.0194122	+	0.0124754i	0.530899	+	0.847435i	$0.321854\pi$
$150$		0			0
$151$	−2081.98	−	2402.73i	−1.12205	−	1.29491i	−0.950842	−	0.309675i	$-0.899780\pi$
$151$	−2081.98	−	2402.73i	−1.12205	−	1.29491i	−0.171204	−	0.985236i	$-0.554766\pi$
$152$		0			0
$153$	3.37647	−	23.4839i	0.00178413	−	0.0124089i
$154$		0			0
$155$	15.9749	−	34.9802i	0.00827831	−	0.0181270i
$156$		0			0
$157$	−249.366	−	546.035i	−0.126761	−	0.277569i	0.835602	−	0.549336i	$-0.185119\pi$
$157$	−249.366	−	546.035i	−0.126761	−	0.277569i	−0.962363	+	0.271767i	$0.912392\pi$
$158$		0			0
$159$	−2637.70	−	1695.15i	−1.31562	−	0.845497i
$160$		0			0
$161$	−611.879	+	2764.95i	−0.299520	+	1.35347i
$162$		0			0
$163$	−828.989	−	532.759i	−0.398352	−	0.256005i	0.326093	−	0.945338i	$-0.394268\pi$
$163$	−828.989	−	532.759i	−0.398352	−	0.256005i	−0.724445	+	0.689332i	$0.757904\pi$
$164$		0			0
$165$	37.7056	+	82.5637i	0.0177902	+	0.0389550i
$166$		0			0
$167$	−258.828	+	566.755i	−0.119933	+	0.262616i	−0.960071	−	0.279756i	$-0.909746\pi$
$167$	−258.828	+	566.755i	−0.119933	+	0.262616i	0.840139	+	0.542372i	$0.182474\pi$
$168$		0			0
$169$	76.0143	−	528.691i	0.0345992	−	0.240642i
$170$		0			0
$171$	−329.558	−	380.330i	−0.147380	−	0.170085i
$172$		0			0
$173$	3131.80	−	2012.69i	1.37634	−	0.884518i	0.377203	−	0.926130i	$-0.376886\pi$
$173$	3131.80	−	2012.69i	1.37634	−	0.884518i	0.999134	+	0.0416123i	$0.0132494\pi$
$174$		0			0
$175$	−3066.63	+	900.445i	−1.32466	+	0.388956i
$176$		0			0
$177$	−198.446	+	229.019i	−0.0842717	+	0.0972547i
$178$		0			0
$179$	4474.65	+	1313.88i	1.86844	+	0.548624i	0.998456	+	0.0555460i	$0.0176900\pi$
$179$	4474.65	+	1313.88i	1.86844	+	0.548624i	0.869985	+	0.493078i	$0.164128\pi$
$180$		0			0
$181$	633.260	+	4404.42i	0.260055	+	1.80872i	0.532371	+	0.846511i	$0.321301\pi$
$181$	633.260	+	4404.42i	0.260055	+	1.80872i	−0.272316	+	0.962208i	$0.587790\pi$
$182$		0			0
$183$	−6093.82			−2.46157
$184$		0			0
$185$	36.7336			0.0145984
$186$		0			0
$187$	3.08070	+	21.4268i	0.00120472	+	0.00837904i
$188$		0			0
$189$	−1134.67	−	333.168i	−0.436693	−	0.128224i
$190$		0			0
$191$	−263.606	+	304.218i	−0.0998633	+	0.115248i	−0.803481	−	0.595330i	$-0.797021\pi$
$191$	−263.606	+	304.218i	−0.0998633	+	0.115248i	0.703618	+	0.710579i	$0.251567\pi$
$192$		0			0
$193$	−4032.26	+	1183.98i	−1.50388	+	0.441578i	−0.926940	−	0.375210i	$-0.877571\pi$
$193$	−4032.26	+	1183.98i	−1.50388	+	0.441578i	−0.576937	+	0.816788i	$0.695752\pi$
$194$		0			0
$195$	168.090	−	108.025i	0.0617290	−	0.0396708i
$196$		0			0
$197$	990.187	+	1142.74i	0.358111	+	0.413282i	0.906006	−	0.423265i	$-0.139116\pi$
$197$	990.187	+	1142.74i	0.358111	+	0.413282i	−0.547895	+	0.836547i	$0.684571\pi$
$198$		0			0
$199$	105.127	−	731.174i	0.0374485	−	0.260460i	−0.962493	−	0.271308i	$-0.912544\pi$
$199$	105.127	−	731.174i	0.0374485	−	0.260460i	0.999941	+	0.0108477i	$0.00345298\pi$
$200$		0			0
$201$	−717.291	+	1570.65i	−0.251711	+	0.551169i
$202$		0			0
$203$	924.453	+	2024.27i	0.319625	+	0.699881i
$204$		0			0
$205$	7.72805	+	4.96652i	0.00263293	+	0.00169208i
$206$		0			0
$207$	1589.21	−	1577.84i	0.533612	−	0.529796i
$208$		0			0
$209$	386.275	+	248.244i	0.127843	+	0.0821598i
$210$		0			0
$211$	−1703.75	−	3730.68i	−0.555880	−	1.21721i	−0.953981	−	0.299866i	$-0.903058\pi$
$211$	−1703.75	−	3730.68i	−0.555880	−	1.21721i	0.398102	−	0.917341i	$-0.369669\pi$
$212$		0			0
$213$	1827.87	−	4002.47i	0.587997	−	1.28753i
$214$		0			0
$215$	−12.1902	+	84.7844i	−0.00386680	+	0.0268942i
$216$		0			0
$217$	907.488	+	1047.30i	0.283891	+	0.327627i
$218$		0			0
$219$	3777.31	−	2427.53i	1.16551	−	0.749029i
$220$		0			0
$221$	45.7227	−	13.4254i	0.0139169	−	0.00408638i
$222$		0			0
$223$	3596.29	−	4150.34i	1.07993	−	1.24631i	0.112376	−	0.993666i	$-0.464154\pi$
$223$	3596.29	−	4150.34i	1.07993	−	1.24631i	0.967559	−	0.252645i	$-0.0813006\pi$
$224$		0			0
$225$	2425.14	+	712.084i	0.718559	+	0.210988i
$226$		0			0
$227$	610.429	+	4245.63i	0.178483	+	1.24138i	0.860275	+	0.509830i	$0.170292\pi$
$227$	610.429	+	4245.63i	0.178483	+	1.24138i	−0.681793	+	0.731545i	$0.738799\pi$
$228$		0			0
$229$	−687.818			−0.198481			−0.0992407	−	0.995063i	$-0.531641\pi$
$229$	−687.818			−0.198481			−0.0992407	+	0.995063i	$0.531641\pi$
$230$		0			0
$231$	−3270.83			−0.931624
$232$		0			0
$233$	256.528	+	1784.19i	0.0721276	+	0.501658i	0.993577	+	0.113160i	$0.0360971\pi$
$233$	256.528	+	1784.19i	0.0721276	+	0.501658i	−0.921449	+	0.388499i	$0.872994\pi$
$234$		0			0
$235$	−301.086	−	88.4069i	−0.0835774	−	0.0245405i
$236$		0			0
$237$	5781.11	−	6671.76i	1.58449	−	1.82860i
$238$		0			0
$239$	3178.66	−	933.340i	0.860296	−	0.252606i	0.178313	−	0.983974i	$-0.442936\pi$
$239$	3178.66	−	933.340i	0.860296	−	0.252606i	0.681983	+	0.731368i	$0.261118\pi$
$240$		0			0
$241$	−3764.70	+	2419.43i	−1.00625	+	0.646677i	−0.936420	−	0.350882i	$-0.885882\pi$
$241$	−3764.70	+	2419.43i	−1.00625	+	0.646677i	−0.0698291	+	0.997559i	$0.522245\pi$
$242$		0			0
$243$	3081.34	+	3556.05i	0.813448	+	0.938769i
$244$		0			0
$245$	−32.0497	+	222.911i	−0.00835747	+	0.0581275i
$246$		0			0
$247$	419.897	−	919.446i	0.108168	−	0.236854i
$248$		0			0
$249$	−2166.33	−	4743.60i	−0.551347	−	1.20728i
$250$		0			0
$251$	2670.94	+	1716.51i	0.671667	+	0.431654i	0.831526	−	0.555486i	$-0.187468\pi$
$251$	2670.94	+	1716.51i	0.671667	+	0.431654i	−0.159859	+	0.987140i	$0.551104\pi$
$252$		0			0
$253$	−985.676	+	1789.83i	−0.244936	+	0.444765i
$254$		0			0
$255$	−4.81696	−	3.09567i	−0.00118294	−	0.000760229i
$256$		0			0
$257$	2155.46	+	4719.79i	0.523166	+	1.14557i	0.968227	+	0.250074i	$0.0804548\pi$
$257$	2155.46	+	4719.79i	0.523166	+	1.14557i	−0.445061	+	0.895500i	$0.646818\pi$
$258$		0			0
$259$	−549.896	+	1204.10i	−0.131926	+	0.288878i
$260$		0			0
$261$	250.453	−	1741.94i	0.0593972	−	0.413117i
$262$		0			0
$263$	4637.62	+	5352.10i	1.08733	+	1.25485i	0.964970	+	0.262362i	$0.0845014\pi$
$263$	4637.62	+	5352.10i	1.08733	+	1.25485i	0.122362	+	0.992486i	$0.460953\pi$
$264$		0			0
$265$	−273.228	+	175.593i	−0.0633369	+	0.0407042i
$266$		0			0
$267$	3007.79	−	883.167i	0.689415	−	0.202430i
$268$		0			0
$269$	3296.31	−	3804.15i	0.747137	−	0.862242i	−0.247151	−	0.968977i	$-0.579494\pi$
$269$	3296.31	−	3804.15i	0.747137	−	0.862242i	0.994287	+	0.106735i	$0.0340397\pi$
$270$		0			0
$271$	2733.40	+	802.599i	0.612702	+	0.179905i	0.573337	−	0.819319i	$-0.305648\pi$
$271$	2733.40	+	802.599i	0.612702	+	0.179905i	0.0393645	+	0.999225i	$0.487467\pi$
$272$		0			0
$273$	1024.71	+	7126.99i	0.227172	+	1.58002i
$274$		0			0
$275$	−2306.12			−0.505688
$276$		0			0
$277$	891.602			0.193398			0.0966988	−	0.995314i	$-0.469172\pi$
$277$	891.602			0.193398			0.0966988	+	0.995314i	$0.469172\pi$
$278$		0			0
$279$	−155.961	−	1084.73i	−0.0334665	−	0.232764i
$280$		0			0
$281$	−8921.67	−	2619.64i	−1.89403	−	0.556137i	−0.992303	−	0.123830i	$-0.960482\pi$
$281$	−8921.67	−	2619.64i	−1.89403	−	0.556137i	−0.901726	−	0.432307i	$-0.857700\pi$
$282$		0			0
$283$	−3832.96	+	4423.48i	−0.805110	+	0.929146i	−0.998650	−	0.0519462i	$-0.983458\pi$
$283$	−3832.96	+	4423.48i	−0.805110	+	0.929146i	0.193540	+	0.981092i	$0.438003\pi$
$284$		0			0
$285$	−116.535	+	34.2179i	−0.0242209	+	0.00711190i
$286$		0			0
$287$	−278.487	+	178.973i	−0.0572772	+	0.0368098i
$288$		0			0
$289$	3216.44	+	3711.97i	0.654679	+	0.755540i
$290$		0			0
$291$	−511.883	+	3560.22i	−0.103117	+	0.717196i
$292$		0			0
$293$	−1107.98	+	2426.13i	−0.220917	+	0.483741i	−0.987345	−	0.158590i	$-0.949305\pi$
$293$	−1107.98	+	2426.13i	−0.220917	+	0.483741i	0.766428	+	0.642331i	$0.222032\pi$
$294$		0			0
$295$	13.0399	+	28.5534i	0.00257360	+	0.00563541i
$296$		0			0
$297$	−717.819	−	461.314i	−0.140243	−	0.0901285i
$298$		0			0
$299$	4208.75	+	1587.01i	0.814041	+	0.306954i
$300$		0			0
$301$	−2596.69	−	1668.79i	−0.497246	−	0.319560i
$302$		0			0
$303$	2305.51	+	5048.37i	0.437123	+	0.957165i
$304$		0			0
$305$	−262.224	+	574.190i	−0.0492291	+	0.107797i
$306$		0			0
$307$	445.905	−	3101.34i	0.0828963	−	0.576557i	−0.905464	−	0.424424i	$-0.860477\pi$
$307$	445.905	−	3101.34i	0.0828963	−	0.576557i	0.988360	−	0.152133i	$-0.0486142\pi$
$308$		0			0
$309$	−5819.51	−	6716.07i	−1.07139	−	1.23645i
$310$		0			0
$311$	2060.32	−	1324.09i	0.375660	−	0.241422i	−0.339163	−	0.940728i	$-0.610144\pi$
$311$	2060.32	−	1324.09i	0.375660	−	0.241422i	0.714823	+	0.699306i	$0.246507\pi$
$312$		0			0
$313$	2933.92	−	861.475i	0.529823	−	0.155570i	−0.00586994	−	0.999983i	$-0.501868\pi$
$313$	2933.92	−	861.475i	0.529823	−	0.155570i	0.535693	+	0.844413i	$0.320050\pi$
$314$		0			0
$315$	243.176	−	280.640i	0.0434965	−	0.0501976i
$316$		0			0
$317$	4018.10	+	1179.82i	0.711920	+	0.209039i	0.617588	−	0.786502i	$-0.288110\pi$
$317$	4018.10	+	1179.82i	0.711920	+	0.209039i	0.0943327	+	0.995541i	$0.469928\pi$
$318$		0			0
$319$	228.515	+	1589.35i	0.0401077	+	0.278955i
$320$		0			0
$321$	−12412.0			−2.15816
$322$		0			0
$323$	−28.9662			−0.00498986
$324$		0			0
$325$	722.475	+	5024.92i	0.123310	+	0.857638i
$326$		0			0
$327$	−508.792	−	149.395i	−0.0860435	−	0.0252647i
$328$		0			0
$329$	7405.13	−	8545.98i	1.24091	−	1.43208i
$330$		0			0
$331$	−9921.53	+	2913.23i	−1.64754	+	0.483762i	−0.968225	−	0.250081i	$-0.919543\pi$
$331$	−9921.53	+	2913.23i	−1.64754	+	0.483762i	−0.679318	+	0.733844i	$0.737724\pi$
$332$		0			0
$333$	880.642	−	565.954i	0.144922	−	0.0931354i
$334$		0			0
$335$	117.128	+	135.173i	0.0191027	+	0.0220457i
$336$		0			0
$337$	693.640	−	4824.37i	0.112122	−	0.779823i	−0.853728	−	0.520719i	$-0.825664\pi$
$337$	693.640	−	4824.37i	0.112122	−	0.779823i	0.965850	−	0.259104i	$-0.0834271\pi$
$338$		0			0
$339$	31.7905	−	69.6114i	0.00509328	−	0.0111527i
$340$		0			0
$341$	415.370	+	909.534i	0.0659635	+	0.144440i
$342$		0			0
$343$	580.867	+	373.301i	0.0914399	+	0.0587648i
$344$		0			0
$345$	−187.058	−	507.074i	−0.0291910	−	0.0791302i
$346$		0			0
$347$	−7037.06	−	4522.44i	−1.08867	−	0.699647i	−0.132127	−	0.991233i	$-0.542181\pi$
$347$	−7037.06	−	4522.44i	−1.08867	−	0.699647i	−0.956545	+	0.291586i	$0.905817\pi$
$348$		0			0
$349$	871.815	+	1909.01i	0.133717	+	0.292799i	0.964632	−	0.263600i	$-0.0849099\pi$
$349$	871.815	+	1909.01i	0.133717	+	0.292799i	−0.830915	+	0.556399i	$0.812183\pi$
$350$		0			0
$351$	−780.299	+	1708.62i	−0.118659	+	0.259827i
$352$		0			0
$353$	594.996	−	4138.29i	0.0897122	−	0.623962i	−0.894513	−	0.447042i	$-0.852477\pi$
$353$	594.996	−	4138.29i	0.0897122	−	0.623962i	0.984225	−	0.176920i	$-0.0566135\pi$
$354$		0			0
$355$	−298.478	−	344.461i	−0.0446241	−	0.0514989i
$356$		0			0
$357$	173.583	−	111.555i	0.0257339	−	0.0165382i
$358$		0			0
$359$	3161.77	−	928.379i	0.464824	−	0.136485i	−0.0409307	−	0.999162i	$-0.513032\pi$
$359$	3161.77	−	928.379i	0.464824	−	0.136485i	0.505755	+	0.862677i	$0.331214\pi$
$360$		0			0
$361$	4089.33	−	4719.34i	0.596200	−	0.688051i
$362$		0			0
$363$	6518.95	+	1914.14i	0.942579	+	0.276766i
$364$		0			0
$365$	−66.1921	−	460.376i	−0.00949220	−	0.0660197i
$366$		0			0
$367$	−7706.16			−1.09607			−0.548036	−	0.836455i	$-0.684624\pi$
$367$	−7706.16			−1.09607			−0.548036	+	0.836455i	$0.684624\pi$
$368$		0			0
$369$	261.789			0.0369328
$370$		0			0
$371$	−1665.65	−	11584.8i	−0.233090	−	1.62117i
$372$		0			0
$373$	5030.83	+	1477.18i	0.698355	+	0.205056i	0.611592	−	0.791173i	$-0.290529\pi$
$373$	5030.83	+	1477.18i	0.698355	+	0.205056i	0.0867631	+	0.996229i	$0.472348\pi$
$374$		0			0
$375$	800.555	−	923.890i	0.110241	−	0.127225i
$376$		0			0
$377$	3391.54	−	995.845i	0.463324	−	0.136044i
$378$		0			0
$379$	−6847.52	+	4400.64i	−0.928057	+	0.596426i	−0.914985	−	0.403488i	$-0.867798\pi$
$379$	−6847.52	+	4400.64i	−0.928057	+	0.596426i	−0.0130723	+	0.999915i	$0.504161\pi$
$380$		0			0
$381$	−6766.40	−	7808.84i	−0.909851	−	1.05002i
$382$		0			0
$383$	−1822.14	+	12673.3i	−0.243099	+	1.69079i	0.393284	+	0.919417i	$0.371339\pi$
$383$	−1822.14	+	12673.3i	−0.243099	+	1.69079i	−0.636383	+	0.771374i	$0.719570\pi$
$384$		0			0
$385$	−140.747	+	308.194i	−0.0186316	+	0.0407975i
$386$		0			0
$387$	1014.03	+	2220.41i	0.133194	+	0.291654i
$388$		0			0
$389$	−9969.32	−	6406.89i	−1.29939	−	0.835070i	−0.306249	−	0.951952i	$-0.599074\pi$
$389$	−9969.32	−	6406.89i	−1.29939	−	0.835070i	−0.993146	+	0.116881i	$0.962710\pi$
$390$		0			0
$391$	−8.73412	−	128.604i	−0.00112968	−	0.0166337i
$392$		0			0
$393$	−6957.64	−	4471.40i	−0.893044	−	0.573925i
$394$		0			0
$395$	−379.878	−	831.818i	−0.0483893	−	0.105958i
$396$		0			0
$397$	3494.46	−	7651.80i	0.441768	−	0.967337i	−0.549502	−	0.835492i	$-0.685183\pi$
$397$	3494.46	−	7651.80i	0.441768	−	0.967337i	0.991270	−	0.131845i	$-0.0420900\pi$
$398$		0			0
$399$	622.875	−	4332.19i	0.0781523	−	0.543561i
$400$		0			0
$401$	676.080	+	780.238i	0.0841941	+	0.0971652i	0.796283	−	0.604924i	$-0.206796\pi$
$401$	676.080	+	780.238i	0.0841941	+	0.0971652i	−0.712089	+	0.702089i	$0.752251\pi$
$402$		0			0
$403$	1851.70	−	1190.02i	0.228883	−	0.147094i
$404$		0			0
$405$	591.273	−	173.613i	0.0725446	−	0.0213010i
$406$		0			0
$407$	−625.473	+	721.835i	−0.0761758	+	0.0879116i
$408$		0			0
$409$	−7219.15	−	2119.73i	−0.872773	−	0.256269i	−0.185479	−	0.982648i	$-0.559384\pi$
$409$	−7219.15	−	2119.73i	−0.872773	−	0.256269i	−0.687294	+	0.726379i	$0.741202\pi$
$410$		0			0
$411$	−688.751	−	4790.37i	−0.0826608	−	0.574919i
$412$		0			0
$413$	−1131.17			−0.134773
$414$		0			0
$415$	−540.185			−0.0638955
$416$		0			0
$417$	1063.45	+	7396.47i	0.124886	+	0.868601i
$418$		0			0
$419$	11816.4	+	3469.62i	1.37773	+	0.404539i	0.884980	−	0.465629i	$-0.154172\pi$
$419$	11816.4	+	3469.62i	1.37773	+	0.404539i	0.492755	+	0.870168i	$0.335990\pi$
$420$		0			0
$421$	4949.48	−	5712.01i	0.572977	−	0.661250i	−0.393103	−	0.919494i	$-0.628598\pi$
$421$	4949.48	−	5712.01i	0.572977	−	0.661250i	0.966080	+	0.258244i	$0.0831439\pi$
$422$		0			0
$423$	−8580.24	+	2519.39i	−0.986255	+	0.289591i
$424$		0			0
$425$	122.386	−	78.6526i	0.0139684	−	0.00897696i
$426$		0			0
$427$	−14896.1	−	17191.0i	−1.68823	−	1.94832i
$428$		0			0
$429$	−739.368	+	5142.42i	−0.0832099	+	0.578737i
$430$		0			0
$431$	2336.39	−	5115.99i	0.261114	−	0.571760i	−0.732984	−	0.680246i	$-0.761873\pi$
$431$	2336.39	−	5115.99i	0.261114	−	0.571760i	0.994098	+	0.108486i	$0.0346002\pi$
$432$		0			0
$433$	3100.74	+	6789.68i	0.344139	+	0.753559i	0.999999	−	0.00132331i	$-0.000421224\pi$
$433$	3100.74	+	6789.68i	0.344139	+	0.753559i	−0.655860	+	0.754882i	$0.727694\pi$
$434$		0			0
$435$	−357.303	−	229.625i	−0.0393825	−	0.0253096i
$436$		0			0
$437$	−2182.91	−	1646.36i	−0.238953	−	0.180220i
$438$		0			0
$439$	5820.25	+	3740.45i	0.632768	+	0.406655i	0.817334	−	0.576165i	$-0.195451\pi$
$439$	5820.25	+	3740.45i	0.632768	+	0.406655i	−0.184565	+	0.982820i	$0.559088\pi$
$440$		0			0
$441$	2666.03	+	5837.79i	0.287877	+	0.630363i
$442$		0			0
$443$	−2657.74	+	5819.63i	−0.285040	+	0.624151i	−0.996943	−	0.0781263i	$-0.975106\pi$
$443$	−2657.74	+	5819.63i	−0.285040	+	0.624151i	0.711903	+	0.702278i	$0.247834\pi$
$444$		0			0
$445$	46.2121	−	321.412i	0.00492284	−	0.0342391i
$446$		0			0
$447$	189.025	+	218.146i	0.0200012	+	0.0230827i
$448$		0			0
$449$	−13422.5	+	8626.10i	−1.41079	+	0.906661i	−0.999987	−	0.00506191i	$-0.998389\pi$
$449$	−13422.5	+	8626.10i	−1.41079	+	0.906661i	−0.410805	+	0.911723i	$0.634752\pi$
$450$		0			0
$451$	−229.182	+	67.2940i	−0.0239286	+	0.00702606i
$452$		0			0
$453$	−14319.2	+	16525.2i	−1.48515	+	1.71396i
$454$		0			0
$455$	715.634	+	210.129i	0.0737350	+	0.0216506i
$456$		0			0
$457$	841.013	+	5849.37i	0.0860851	+	0.598735i	0.986507	+	0.163718i	$0.0523487\pi$
$457$	841.013	+	5849.37i	0.0860851	+	0.598735i	−0.900422	+	0.435017i	$0.856742\pi$
$458$		0			0
$459$	53.8283			0.00547383
$460$		0			0
$461$	12168.4			1.22937			0.614686	−	0.788772i	$-0.289283\pi$
$461$	12168.4			1.22937			0.614686	+	0.788772i	$0.289283\pi$
$462$		0			0
$463$	−991.879	−	6898.67i	−0.0995606	−	0.692459i	−0.977073	−	0.212905i	$-0.931708\pi$
$463$	−991.879	−	6898.67i	−0.0995606	−	0.692459i	0.877512	−	0.479554i	$-0.159202\pi$
$464$		0			0
$465$	−253.771	−	74.5138i	−0.0253082	−	0.00743117i
$466$		0			0
$467$	−2092.75	+	2415.16i	−0.207368	+	0.239316i	−0.849901	−	0.526943i	$-0.823338\pi$
$467$	−2092.75	+	2415.16i	−0.207368	+	0.239316i	0.642533	+	0.766258i	$0.277884\pi$
$468$		0			0
$469$	−6184.29	+	1815.87i	−0.608879	+	0.178783i
$470$		0			0
$471$	−3473.15	+	2232.06i	−0.339776	+	0.218361i
$472$		0			0
$473$	−1458.49	−	1683.19i	−0.141779	−	0.163622i
$474$		0			0
$475$	439.161	−	3054.44i	0.0424213	−	0.295047i
$476$		0			0
$477$	−3844.94	+	8419.25i	−0.369073	+	0.808157i
$478$		0			0
$479$	6377.61	+	13965.0i	0.608352	+	1.33210i	0.923696	+	0.383127i	$0.125153\pi$
$479$	6377.61	+	13965.0i	0.608352	+	1.33210i	−0.315344	+	0.948977i	$0.602120\pi$
$480$		0			0
$481$	1768.79	+	1136.74i	0.167672	+	0.107756i
$482$		0			0
$483$	19421.8	+	1459.15i	1.82965	+	0.137461i
$484$		0			0
$485$	313.435	+	201.432i	0.0293450	+	0.0188589i
$486$		0			0
$487$	607.933	+	1331.19i	0.0565669	+	0.123864i	0.935805	−	0.352519i	$-0.114675\pi$
$487$	607.933	+	1331.19i	0.0565669	+	0.123864i	−0.879238	+	0.476383i	$0.841948\pi$
$488$		0			0
$489$	−2815.44	+	6164.96i	−0.260365	+	0.570121i
$490$		0			0
$491$	1731.48	−	12042.7i	0.159146	−	1.10689i	−0.741065	−	0.671433i	$-0.765679\pi$
$491$	1731.48	−	12042.7i	0.159146	−	1.10689i	0.900211	−	0.435453i	$-0.143412\pi$
$492$		0			0
$493$	−66.3339	−	76.5534i	−0.00605989	−	0.00699349i
$494$		0			0
$495$	225.403	−	144.858i	0.0204669	−	0.0131533i
$496$		0			0
$497$	15759.4	−	4627.37i	1.42234	−	0.417638i
$498$		0			0
$499$	11454.6	−	13219.3i	1.02761	−	1.18592i	0.0452374	−	0.998976i	$-0.485596\pi$
$499$	11454.6	−	13219.3i	1.02761	−	1.18592i	0.982370	−	0.186946i	$-0.0598590\pi$
$500$		0			0
$501$	4111.63	+	1207.28i	0.366655	+	0.107660i
$502$		0			0
$503$	−1218.45	−	8474.50i	−0.108008	−	0.751211i	−0.969792	−	0.243935i	$-0.921562\pi$
$503$	−1218.45	−	8474.50i	−0.108008	−	0.751211i	0.861784	−	0.507276i	$-0.169348\pi$
$504$		0			0
$505$	574.890			0.0506580
$506$		0			0
$507$	−3673.57			−0.321792
$508$		0			0
$509$	2142.89	+	14904.1i	0.186605	+	1.29787i	0.840720	+	0.541470i	$0.182132\pi$
$509$	2142.89	+	14904.1i	0.186605	+	1.29787i	−0.654115	+	0.756395i	$0.726959\pi$
$510$		0			0
$511$	16081.7	+	4722.02i	1.39220	+	0.408786i
$512$		0			0
$513$	747.703	−	862.896i	0.0643507	−	0.0742647i
$514$		0			0
$515$	−883.241	+	259.343i	−0.0755733	+	0.0221903i
$516$		0			0
$517$	6863.92	−	4411.17i	0.583897	−	0.375248i
$518$		0			0
$519$	−16767.1	−	19350.3i	−1.41810	−	1.63658i
$520$		0			0
$521$	267.676	−	1861.73i	0.0225088	−	0.156552i	−0.975467	−	0.220145i	$-0.929347\pi$
$521$	267.676	−	1861.73i	0.0225088	−	0.156552i	0.997976	+	0.0635930i	$0.0202560\pi$
$522$		0			0
$523$	−5130.00	+	11233.1i	−0.428908	+	0.939179i	0.564594	+	0.825369i	$0.309033\pi$
$523$	−5130.00	+	11233.1i	−0.428908	+	0.939179i	−0.993503	+	0.113810i	$0.963695\pi$
$524$		0			0
$525$	9131.56	+	19995.3i	0.759112	+	1.66222i
$526$		0			0
$527$	−53.0643	−	34.1024i	−0.00438618	−	0.00281883i
$528$		0			0
$529$	6651.28	−	10188.1i	0.546665	−	0.837351i
$530$		0			0
$531$	752.538	+	483.627i	0.0615016	+	0.0395247i
$532$		0			0
$533$	218.430	+	478.295i	0.0177509	+	0.0388691i
$534$		0			0
$535$	−534.102	+	1169.52i	−0.0431612	+	0.0945098i
$536$		0			0
$537$	4564.67	−	31748.0i	0.366816	−	2.55126i
$538$		0			0
$539$	−3834.59	−	4425.35i	−0.306433	−	0.353643i
$540$		0			0
$541$	785.258	−	504.655i	0.0624046	−	0.0401050i	−0.509067	−	0.860727i	$-0.670009\pi$
$541$	785.258	−	504.655i	0.0624046	−	0.0401050i	0.571471	+	0.820622i	$0.306373\pi$
$542$		0			0
$543$	29364.1	−	8622.07i	2.32069	−	0.681415i
$544$		0			0
$545$	−35.9706	+	41.5122i	−0.00282717	+	0.00326273i
$546$		0			0
$547$	−16192.1	−	4754.44i	−1.26568	−	0.371637i	−0.421073	−	0.907027i	$-0.638347\pi$
$547$	−16192.1	−	4754.44i	−1.26568	−	0.371637i	−0.844605	+	0.535390i	$0.820165\pi$
$548$		0			0
$549$	2560.05	+	17805.6i	0.199017	+	1.38419i
$550$		0			0
$551$	−2148.60			−0.166123
$552$		0			0
$553$	32953.2			2.53402
$554$		0			0
$555$	−35.9547	−	250.071i	−0.00274990	−	0.0191260i
$556$		0			0
$557$	−10549.5	−	3097.61i	−0.802505	−	0.235637i	−0.145339	−	0.989382i	$-0.546427\pi$
$557$	−10549.5	−	3097.61i	−0.802505	−	0.235637i	−0.657167	+	0.753745i	$0.728245\pi$
$558$		0			0
$559$	−3210.66	+	3705.30i	−0.242928	+	0.280354i
$560$		0			0
$561$	142.851	−	41.9449i	0.0107508	−	0.00315671i
$562$		0			0
$563$	−4019.27	+	2583.03i	−0.300874	+	0.193360i	−0.682363	−	0.731013i	$-0.739048\pi$
$563$	−4019.27	+	2583.03i	−0.300874	+	0.193360i	0.381489	+	0.924373i	$0.375411\pi$
$564$		0			0
$565$	−5.19115	−	5.99091i	−0.000386537	−	0.000446087i
$566$		0			0
$567$	−3160.32	+	21980.5i	−0.234076	+	1.62803i
$568$		0			0
$569$	−1392.02	+	3048.10i	−0.102560	+	0.224575i	−0.953955	−	0.299950i	$-0.903030\pi$
$569$	−1392.02	+	3048.10i	−0.102560	+	0.224575i	0.851395	+	0.524525i	$0.175757\pi$
$570$		0			0
$571$	−2903.31	−	6357.37i	−0.212784	−	0.465933i	0.772901	−	0.634526i	$-0.218805\pi$
$571$	−2903.31	−	6357.37i	−0.212784	−	0.465933i	−0.985686	+	0.168593i	$0.946077\pi$
$572$		0			0
$573$	2329.04	+	1496.78i	0.169803	+	0.109126i
$574$		0			0
$575$	13693.4	+	1028.78i	0.993141	+	0.0746143i
$576$		0			0
$577$	6819.92	+	4382.89i	0.492057	+	0.316226i	0.763032	−	0.646361i	$-0.223710\pi$
$577$	6819.92	+	4382.89i	0.492057	+	0.316226i	−0.270975	+	0.962586i	$0.587346\pi$
$578$		0			0
$579$	12006.9	+	26291.5i	0.861814	+	1.88711i
$580$		0			0
$581$	8086.47	−	17706.9i	0.577424	−	1.26438i
$582$		0			0
$583$	1201.84	−	8358.95i	0.0853773	−	0.593812i
$584$		0			0
$585$	−386.253	−	445.760i	−0.0272985	−	0.0315041i
$586$		0			0
$587$	−17748.7	+	11406.4i	−1.24798	+	0.802029i	−0.986592	−	0.163204i	$-0.947817\pi$
$587$	−17748.7	+	11406.4i	−1.24798	+	0.802029i	−0.261390	+	0.965233i	$0.584181\pi$
$588$		0			0
$589$	−1283.77	+	376.949i	−0.0898079	+	0.0263700i
$590$		0			0
$591$	6810.20	−	7859.39i	0.474000	−	0.547025i
$592$		0			0
$593$	−1304.30	−	382.978i	−0.0903226	−	0.0265211i	0.236259	−	0.971690i	$-0.424079\pi$
$593$	−1304.30	−	382.978i	−0.0903226	−	0.0265211i	−0.326582	+	0.945169i	$0.605897\pi$
$594$		0			0
$595$	−3.04180	−	21.1562i	−0.000209583	−	0.00145768i
$596$		0			0
$597$	−5080.50			−0.348293
$598$		0			0
$599$	−24090.0			−1.64322			−0.821612	−	0.570047i	$-0.806925\pi$
$599$	−24090.0			−1.64322			−0.821612	+	0.570047i	$0.806925\pi$
$600$		0			0
$601$	3345.58	+	23269.0i	0.227070	+	1.57931i	0.710354	+	0.703844i	$0.248535\pi$
$601$	3345.58	+	23269.0i	0.227070	+	1.57931i	−0.483284	+	0.875464i	$0.660556\pi$
$602$		0			0
$603$	4890.62	+	1436.02i	0.330284	+	0.0969803i
$604$		0			0
$605$	460.877	−	531.880i	0.0309707	−	0.0357421i
$606$		0			0
$607$	−4709.91	+	1382.96i	−0.314941	+	0.0924752i	−0.435383	−	0.900245i	$-0.643387\pi$
$607$	−4709.91	+	1382.96i	−0.314941	+	0.0924752i	0.120442	+	0.992720i	$0.461569\pi$
$608$		0			0
$609$	12875.7	−	8274.73i	0.856734	−	0.550589i
$610$		0			0
$611$	−11762.1	−	13574.2i	−0.778795	−	0.898777i
$612$		0			0
$613$	−2826.48	+	19658.6i	−0.186233	+	1.29528i	0.655423	+	0.755262i	$0.272490\pi$
$613$	−2826.48	+	19658.6i	−0.186233	+	1.29528i	−0.841656	+	0.540014i	$0.818419\pi$
$614$		0			0
$615$	26.2463	−	57.4714i	0.00172090	−	0.00376824i
$616$		0			0
$617$	−1440.37	−	3153.96i	−0.0939821	−	0.205792i	0.856802	−	0.515645i	$-0.172448\pi$
$617$	−1440.37	−	3153.96i	−0.0939821	−	0.205792i	−0.950785	+	0.309853i	$0.899720\pi$
$618$		0			0
$619$	−104.102	−	66.9020i	−0.00675960	−	0.00434413i	0.537257	−	0.843419i	$-0.319461\pi$
$619$	−104.102	−	66.9020i	−0.00675960	−	0.00434413i	−0.544016	+	0.839075i	$0.683097\pi$
$620$		0			0
$621$	4056.52	+	3059.45i	0.262130	+	0.197700i
$622$		0			0
$623$	9843.90	+	6326.29i	0.633046	+	0.406834i
$624$		0			0
$625$	6411.90	+	14040.1i	0.410362	+	0.898566i
$626$		0			0
$627$	1311.88	−	2872.62i	0.0835590	−	0.182969i
$628$		0			0
$629$	8.57496	−	59.6402i	0.000543571	−	0.00378062i
$630$		0			0
$631$	−19973.2	−	23050.3i	−1.26009	−	1.45423i	−0.836116	−	0.548553i	$-0.815179\pi$
$631$	−19973.2	−	23050.3i	−1.26009	−	1.45423i	−0.423978	−	0.905672i	$-0.639367\pi$
$632$		0			0
$633$	−23729.7	+	15250.1i	−1.49000	+	0.957565i
$634$		0			0
$635$	−1026.95	+	301.541i	−0.0641785	+	0.0188445i
$636$		0			0
$637$	−8441.31	+	9741.79i	−0.525050	+	0.605940i
$638$		0			0
$639$	−12462.7	−	3659.39i	−0.771547	−	0.226546i
$640$		0			0
$641$	−3211.80	−	22338.5i	−0.197907	−	1.37647i	−0.810344	−	0.585954i	$-0.800720\pi$
$641$	−3211.80	−	22338.5i	−0.197907	−	1.37647i	0.612438	−	0.790519i	$-0.290189\pi$
$642$		0			0
$643$	3572.97			0.219136			0.109568	−	0.993979i	$-0.465053\pi$
$643$	3572.97			0.219136			0.109568	+	0.993979i	$0.465053\pi$
$644$		0			0
$645$	589.117			0.0359635
$646$		0			0
$647$	906.620	+	6305.68i	0.0550895	+	0.383156i	0.998649	+	0.0519542i	$0.0165450\pi$
$647$	906.620	+	6305.68i	0.0550895	+	0.383156i	−0.943560	+	0.331202i	$0.892546\pi$
$648$		0			0
$649$	−783.124	−	229.946i	−0.0473657	−	0.0139078i
$650$		0			0
$651$	6241.42	−	7202.98i	0.375761	−	0.433651i
$652$		0			0
$653$	−9108.84	+	2674.60i	−0.545875	+	0.160283i	−0.543031	−	0.839713i	$-0.682723\pi$
$653$	−9108.84	+	2674.60i	−0.545875	+	0.160283i	−0.00284408	+	0.999996i	$0.500905\pi$
$654$		0			0
$655$	−720.712	+	463.173i	−0.0429932	+	0.0276301i
$656$		0			0
$657$	−8679.88	−	10017.1i	−0.515425	−	0.594832i
$658$		0			0
$659$	−2586.71	+	17990.9i	−0.152904	+	1.06347i	0.758416	+	0.651771i	$0.225974\pi$
$659$	−2586.71	+	17990.9i	−0.152904	+	1.06347i	−0.911320	+	0.411700i	$0.864935\pi$
$660$		0			0
$661$	−6117.04	+	13394.4i	−0.359947	+	0.788175i	0.639859	+	0.768492i	$0.278993\pi$
$661$	−6117.04	+	13394.4i	−0.359947	+	0.788175i	−0.999806	+	0.0196823i	$0.993735\pi$
$662$		0			0
$663$	−136.149	−	298.125i	−0.00797526	−	0.0174634i
$664$		0			0
$665$	−381.397	−	245.109i	−0.0222405	−	0.0142931i
$666$		0			0
$667$	−647.863	−	9539.33i	−0.0376093	−	0.553769i
$668$		0			0
$669$	−31774.2	−	20420.1i	−1.83627	−	1.18010i
$670$		0			0
$671$	−6818.17	−	14929.7i	−0.392269	−	0.858950i
$672$		0			0
$673$	10790.6	−	23628.2i	0.618051	−	1.35334i	−0.298877	−	0.954292i	$-0.596612\pi$
$673$	10790.6	−	23628.2i	0.618051	−	1.35334i	0.916928	−	0.399052i	$-0.130661\pi$
$674$		0			0
$675$	−816.098	+	5676.09i	−0.0465358	+	0.323663i
$676$		0			0
$677$	−18220.0	−	21027.0i	−1.03435	−	1.19370i	−0.980776	−	0.195135i	$-0.937486\pi$
$677$	−18220.0	−	21027.0i	−1.03435	−	1.19370i	−0.0535695	−	0.998564i	$-0.517060\pi$
$678$		0			0
$679$	−11294.9	+	7258.79i	−0.638377	+	0.410260i
$680$		0			0
$681$	28305.4	−	8311.21i	1.59275	−	0.467675i
$682$		0			0
$683$	274.245	−	316.496i	0.0153641	−	0.0177312i	−0.748015	−	0.663681i	$-0.768993\pi$
$683$	274.245	−	316.496i	0.0153641	−	0.0177312i	0.763380	+	0.645950i	$0.223539\pi$
$684$		0			0
$685$	−481.010	−	141.237i	−0.0268299	−	0.00787796i
$686$		0			0
$687$	673.234	+	4682.44i	0.0373879	+	0.260038i
$688$		0			0
$689$	−18590.3			−1.02791
$690$		0			0
$691$	19726.7			1.08602			0.543008	−	0.839727i	$-0.317285\pi$
$691$	19726.7			1.08602			0.543008	+	0.839727i	$0.317285\pi$
$692$		0			0
$693$	1374.10	+	9557.06i	0.0753213	+	0.523871i
$694$		0			0
$695$	742.693	+	218.074i	0.0405352	+	0.0119022i
$696$		0			0
$697$	9.86758	−	11.3878i	0.000536243	−	0.000618857i
$698$		0			0
$699$	11895.1	−	3492.73i	0.643656	−	0.188994i
$700$		0			0
$701$	−7752.11	+	4981.98i	−0.417679	+	0.268426i	−0.732556	−	0.680706i	$-0.761673\pi$
$701$	−7752.11	+	4981.98i	−0.417679	+	0.268426i	0.314877	+	0.949132i	$0.398037\pi$
$702$		0			0
$703$	−836.953	−	965.895i	−0.0449023	−	0.0518200i
$704$		0			0
$705$	−307.144	+	2136.23i	−0.0164081	+	0.114121i
$706$		0			0
$707$	−8606.01	+	18844.5i	−0.457797	+	1.00244i
$708$		0			0
$709$	9343.62	+	20459.7i	0.494932	+	1.08375i	0.978083	+	0.208213i	$0.0667649\pi$
$709$	9343.62	+	20459.7i	0.494932	+	1.08375i	−0.483151	+	0.875537i	$0.660508\pi$
$710$		0			0
$711$	−21922.9	−	14089.0i	−1.15636	−	0.743149i
$712$		0			0
$713$	−2060.66	−	5586.00i	−0.108236	−	0.293404i
$714$		0			0
$715$	452.728	+	290.951i	0.0236798	+	0.0152181i
$716$		0			0
$717$	−9465.15	−	20725.8i	−0.493002	−	1.07952i
$718$		0			0
$719$	5904.39	−	12928.8i	0.306254	−	0.670603i	−0.692452	−	0.721464i	$-0.743469\pi$
$719$	5904.39	−	12928.8i	0.306254	−	0.670603i	0.998706	+	0.0508615i	$0.0161967\pi$
$720$		0			0
$721$	4720.87	−	32834.4i	0.243848	−	1.69600i
$722$		0			0
$723$	20155.6	+	23260.8i	1.03678	+	1.19651i
$724$		0			0
$725$	9078.10	−	5834.14i	0.465038	−	0.298862i
$726$		0			0
$727$	12029.9	−	3532.31i	0.613708	−	0.180201i	0.0399173	−	0.999203i	$-0.487291\pi$
$727$	12029.9	−	3532.31i	0.613708	−	0.180201i	0.573791	+	0.819002i	$0.305472\pi$
$728$		0			0
$729$	5898.66	−	6807.41i	0.299683	−	0.345852i
$730$		0			0
$731$	134.809	+	39.5835i	0.00682093	+	0.00200280i
$732$		0			0
$733$	4554.45	+	31676.9i	0.229499	+	1.59620i	0.700227	+	0.713921i	$0.253082\pi$
$733$	4554.45	+	31676.9i	0.229499	+	1.59620i	−0.470728	+	0.882278i	$0.656009\pi$
$734$		0			0
$735$	1548.87			0.0777294
$736$		0			0
$737$	−4650.61			−0.232439
$738$		0			0
$739$	539.986	+	3755.68i	0.0268791	+	0.186949i	0.998837	−	0.0482045i	$-0.0153499\pi$
$739$	539.986	+	3755.68i	0.0268791	+	0.186949i	−0.971958	+	0.235153i	$0.924441\pi$
$740$		0			0
$741$	−6670.29	−	1958.57i	−0.330687	−	0.0970985i
$742$		0			0
$743$	3916.38	−	4519.75i	0.193376	−	0.223167i	−0.650779	−	0.759267i	$-0.725558\pi$
$743$	3916.38	−	4519.75i	0.193376	−	0.223167i	0.844155	+	0.536100i	$0.180103\pi$
$744$		0			0
$745$	28.6887	−	8.42377i	0.00141084	−	0.000414259i
$746$		0			0
$747$	−12950.2	+	8322.62i	−0.634304	+	0.407642i
$748$		0			0
$749$	−30340.7	−	35015.0i	−1.48014	−	1.70817i
$750$		0			0
$751$	−3056.99	+	21261.8i	−0.148537	+	1.03310i	0.770081	+	0.637947i	$0.220216\pi$
$751$	−3056.99	+	21261.8i	−0.148537	+	1.03310i	−0.918617	+	0.395148i	$0.870693\pi$
$752$		0			0
$753$	9071.15	−	19863.1i	0.439006	−	0.961288i
$754$		0			0
$755$	940.918	+	2060.32i	0.0453557	+	0.0993151i
$756$		0			0
$757$	2879.65	+	1850.64i	0.138260	+	0.0888541i	0.607942	−	0.793981i	$-0.291995\pi$
$757$	2879.65	+	1850.64i	0.138260	+	0.0888541i	−0.469683	+	0.882835i	$0.655632\pi$
$758$		0			0
$759$	13149.4	+	4958.29i	0.628843	+	0.237120i
$760$		0			0
$761$	−29096.9	−	18699.5i	−1.38602	−	0.890742i	−0.386520	−	0.922281i	$-0.626323\pi$
$761$	−29096.9	−	18699.5i	−1.38602	−	0.890742i	−0.999503	+	0.0315386i	$0.989959\pi$
$762$		0			0
$763$	−822.271	−	1800.52i	−0.0390147	−	0.0854303i
$764$		0			0
$765$	−7.02162	+	15.3752i	−0.000331852	+	0.000726656i
$766$		0			0
$767$	−255.699	+	1778.43i	−0.0120375	+	0.0837227i
$768$		0			0
$769$	−22706.7	−	26204.9i	−1.06479	−	1.22883i	−0.972452	−	0.233105i	$-0.925111\pi$
$769$	−22706.7	−	26204.9i	−1.06479	−	1.22883i	−0.0923378	−	0.995728i	$-0.529434\pi$
$770$		0			0
$771$	30021.1	−	19293.4i	1.40231	−	0.901212i
$772$		0			0
$773$	−23157.0	+	6799.51i	−1.07749	+	0.316380i	−0.771874	−	0.635775i	$-0.780681\pi$
$773$	−23157.0	+	6799.51i	−1.07749	+	0.316380i	−0.305616	+	0.952155i	$0.598862\pi$
$774$		0			0
$775$	4400.55	−	5078.50i	0.203964	−	0.235387i
$776$		0			0
$777$	8735.40	+	2564.94i	0.403321	+	0.118426i
$778$		0			0
$779$	−45.4864	−	316.365i	−0.00209207	−	0.0145507i
$780$		0			0
$781$	11851.1			0.542978
$782$		0			0
$783$	3992.77			0.182235
$784$		0			0
$785$	60.8621	+	423.305i	0.00276721	+	0.0192464i
$786$		0			0
$787$	22168.8	+	6509.36i	1.00411	+	0.294833i	0.742141	−	0.670244i	$-0.233810\pi$
$787$	22168.8	+	6509.36i	1.00411	+	0.294833i	0.261968	+	0.965077i	$0.415629\pi$
$788$		0			0
$789$	31896.1	−	36810.1i	1.43920	−	1.66093i
$790$		0			0
$791$	274.089	−	80.4797i	0.0123205	−	0.00361761i
$792$		0			0
$793$	−30395.1	+	19533.7i	−1.36111	+	0.874733i
$794$		0			0
$795$	1462.82	+	1688.18i	0.0652589	+	0.0753127i
$796$		0			0
$797$	−4821.47	+	33534.0i	−0.214285	+	1.49039i	0.544344	+	0.838862i	$0.316779\pi$
$797$	−4821.47	+	33534.0i	−0.214285	+	1.49039i	−0.758629	+	0.651523i	$0.774130\pi$
$798$		0			0
$799$	−213.821	+	468.202i	−0.00946737	+	0.0207307i
$800$		0			0
$801$	−3844.12	−	8417.44i	−0.169570	−	0.371306i
$802$		0			0
$803$	10173.7	+	6538.24i	0.447101	+	0.287334i
$804$		0			0
$805$	973.229	−	1767.23i	0.0426110	−	0.0773746i
$806$		0			0
$807$	−29123.9	−	18716.8i	−1.27039	−	0.816433i
$808$		0			0
$809$	15844.9	+	34695.4i	0.688598	+	1.50782i	0.853269	+	0.521471i	$0.174617\pi$
$809$	15844.9	+	34695.4i	0.688598	+	1.50782i	−0.164671	+	0.986349i	$0.552656\pi$
$810$		0			0
$811$	8352.81	−	18290.1i	0.361661	−	0.791926i	−0.638098	−	0.769955i	$-0.720279\pi$
$811$	8352.81	−	18290.1i	0.361661	−	0.791926i	0.999759	−	0.0219712i	$-0.00699421\pi$
$812$		0			0
$813$	2788.39	−	19393.7i	0.120287	−	0.836613i
$814$		0			0
$815$	459.741	+	530.569i	0.0197595	+	0.0228037i
$816$		0			0
$817$	2507.12	−	1611.23i	0.107360	−	0.0689959i
$818$		0			0
$819$	20393.9	−	5988.18i	0.870110	−	0.255487i
$820$		0			0
$821$	−13020.5	+	15026.4i	−0.553493	+	0.638765i	−0.961693	−	0.274128i	$-0.911611\pi$
$821$	−13020.5	+	15026.4i	−0.553493	+	0.638765i	0.408201	+	0.912892i	$0.366156\pi$
$822$		0			0
$823$	−3292.84	−	966.864i	−0.139467	−	0.0409511i	0.211254	−	0.977431i	$-0.432245\pi$
$823$	−3292.84	−	966.864i	−0.139467	−	0.0409511i	−0.350721	+	0.936480i	$0.614063\pi$
$824$		0			0
$825$	2257.22	+	15699.3i	0.0952562	+	0.662522i
$826$		0			0
$827$	−43792.0			−1.84135			−0.920676	−	0.390329i	$-0.872361\pi$
$827$	−43792.0			−1.84135			−0.920676	+	0.390329i	$0.872361\pi$
$828$		0			0
$829$	−28166.1			−1.18004			−0.590019	−	0.807390i	$-0.700880\pi$
$829$	−28166.1			−1.18004			−0.590019	+	0.807390i	$0.700880\pi$
$830$		0			0
$831$	−872.697	−	6069.74i	−0.0364302	−	0.253378i
$832$		0			0
$833$	354.433	+	104.071i	0.0147423	+	0.00432874i
$834$		0			0
$835$	290.684	−	335.467i	0.0120473	−	0.0139034i
$836$		0			0
$837$	2385.64	−	700.488i	0.0985184	−	0.0289276i
$838$		0			0
$839$	−16011.3	+	10289.9i	−0.658846	+	0.423415i	−0.826889	−	0.562365i	$-0.809892\pi$
$839$	−16011.3	+	10289.9i	−0.658846	+	0.423415i	0.168043	+	0.985780i	$0.446255\pi$
$840$		0			0
$841$	11051.0	+	12753.5i	0.453114	+	0.522922i
$842$		0			0
$843$	−9101.17	+	63300.0i	−0.371840	+	2.58620i
$844$		0			0
$845$	−158.078	+	346.141i	−0.00643554	+	0.0140919i
$846$		0			0
$847$	10535.4	+	23069.4i	0.427393	+	0.935861i
$848$		0			0
$849$	33865.3	+	21763.9i	1.36897	+	0.879783i
$850$		0			0
$851$	4036.00	−	4007.13i	0.162576	−	0.161413i
$852$		0			0
$853$	21824.4	+	14025.7i	0.876028	+	0.562989i	0.899591	−	0.436733i	$-0.143865\pi$
$853$	21824.4	+	14025.7i	0.876028	+	0.562989i	−0.0235630	+	0.999722i	$0.507501\pi$
$854$		0			0
$855$	148.939	+	326.130i	0.00595742	+	0.0130449i
$856$		0			0
$857$	−12170.4	+	26649.5i	−0.485104	+	1.06223i	0.495925	+	0.868365i	$0.334829\pi$
$857$	−12170.4	+	26649.5i	−0.485104	+	1.06223i	−0.981029	+	0.193863i	$0.937898\pi$
$858$		0			0
$859$	−2342.80	+	16294.6i	−0.0930564	+	0.647222i	0.888898	+	0.458105i	$0.151472\pi$
$859$	−2342.80	+	16294.6i	−0.0930564	+	0.647222i	−0.981955	+	0.189117i	$0.939438\pi$
$860$		0			0
$861$	1490.97	+	1720.67i	0.0590153	+	0.0681073i
$862$		0			0
$863$	−14940.3	+	9601.54i	−0.589308	+	0.378726i	−0.801048	−	0.598601i	$-0.795724\pi$
$863$	−14940.3	+	9601.54i	−0.589308	+	0.378726i	0.211739	+	0.977326i	$0.432087\pi$
$864$		0			0
$865$	−2544.79	+	747.217i	−0.100029	+	0.0293713i
$866$		0			0
$867$	22121.6	−	25529.7i	0.866540	−	1.00004i
$868$		0			0
$869$	22813.9	+	6698.78i	0.890575	+	0.261497i
$870$		0			0
$871$	1456.97	+	10133.4i	0.0566791	+	0.394212i
$872$		0			0
$873$	10617.7			0.411631
$874$		0			0
$875$	4563.28			0.176305
$876$		0			0
$877$	4273.51	+	29722.9i	0.164545	+	1.14444i	0.889931	+	0.456095i	$0.150752\pi$
$877$	4273.51	+	29722.9i	0.164545	+	1.14444i	−0.725386	+	0.688343i	$0.758339\pi$
$878$		0			0
$879$	17600.8	+	5168.06i	0.675382	+	0.198310i
$880$		0			0
$881$	13911.3	−	16054.5i	0.531991	−	0.613950i	−0.424601	−	0.905381i	$-0.639586\pi$
$881$	13911.3	−	16054.5i	0.531991	−	0.613950i	0.956592	+	0.291430i	$0.0941311\pi$
$882$		0			0
$883$	−9508.33	+	2791.90i	−0.362379	+	0.106404i	−0.457853	−	0.889028i	$-0.651381\pi$
$883$	−9508.33	+	2791.90i	−0.362379	+	0.106404i	0.0954740	+	0.995432i	$0.469563\pi$
$884$		0			0
$885$	181.619	−	116.720i	0.00689838	−	0.00443332i
$886$		0			0
$887$	30140.2	+	34783.7i	1.14094	+	1.31671i	0.941582	+	0.336783i	$0.109339\pi$
$887$	30140.2	+	34783.7i	1.14094	+	1.31671i	0.199354	+	0.979928i	$0.436116\pi$
$888$		0			0
$889$	5489.00	−	38176.9i	0.207081	−	1.44028i
$890$		0			0
$891$	−6656.17	+	14575.0i	−0.250269	+	0.548014i
$892$		0			0
$893$	4535.44	+	9931.23i	0.169958	+	0.372157i
$894$		0			0
$895$	−2795.03	−	1796.26i	−0.104388	−	0.0670863i
$896$		0			0
$897$	6684.36	−	30205.2i	0.248812	−	1.12433i
$898$		0			0
$899$	−3936.11	−	2529.58i	−0.146025	−	0.0938446i
$900$		0			0
$901$	221.309	+	484.600i	0.00818300	+	0.0179183i
$902$		0			0
$903$	−8818.98	+	19310.9i	−0.325003	+	0.711656i
$904$		0			0
$905$	451.154	−	3137.85i	0.0165711	−	0.115255i
$906$		0			0
$907$	6878.23	+	7937.90i	0.251806	+	0.290599i	0.867553	−	0.497344i	$-0.165691\pi$
$907$	6878.23	+	7937.90i	0.251806	+	0.290599i	−0.615748	+	0.787943i	$0.711146\pi$
$908$		0			0
$909$	13782.3	−	8857.33i	0.502892	−	0.323189i
$910$		0			0
$911$	29571.9	−	8683.11i	1.07548	−	0.315789i	0.304411	−	0.952541i	$-0.401540\pi$
$911$	29571.9	−	8683.11i	1.07548	−	0.315789i	0.771069	+	0.636751i	$0.219722\pi$
$912$		0			0
$913$	9197.87	−	10614.9i	0.333412	−	0.384778i
$914$		0			0
$915$	4165.56	+	1223.12i	0.150502	+	0.0441914i
$916$		0			0
$917$	−4393.59	−	30558.1i	−0.158222	−	1.10046i
$918$		0			0
$919$	−37778.9			−1.35605			−0.678026	−	0.735038i	$-0.737164\pi$
$919$	−37778.9			−1.35605			−0.678026	+	0.735038i	$0.737164\pi$
$920$		0			0
$921$	−21549.4			−0.770984
$922$		0			0
$923$	−3712.78	−	25823.0i	−0.132403	−	0.920882i
$924$		0			0
$925$	6158.94	+	1808.43i	0.218924	+	0.0642819i
$926$		0			0
$927$	−17178.9	+	19825.5i	−0.608661	+	0.702433i
$928$		0			0
$929$	−9895.21	+	2905.50i	−0.349463	+	0.102612i	−0.451753	−	0.892143i	$-0.649201\pi$
$929$	−9895.21	+	2905.50i	−0.349463	+	0.102612i	0.102290	+	0.994755i	$0.467383\pi$
$930$		0			0
$931$	6591.58	−	4236.15i	0.232041	−	0.149124i
$932$		0			0
$933$	−11030.6	−	12730.0i	−0.387059	−	0.446690i
$934$		0			0
$935$	2.19479	−	15.2651i	7.67671e−5	−	0.000533927i
$936$		0			0
$937$	20168.0	−	44161.7i	0.703158	−	1.53970i	−0.132943	−	0.991124i	$-0.542443\pi$
$937$	20168.0	−	44161.7i	0.703158	−	1.53970i	0.836100	−	0.548577i	$-0.184830\pi$
$938$		0			0
$939$	−8736.36	−	19130.0i	−0.303621	−	0.664838i
$940$		0			0
$941$	31966.3	+	20543.5i	1.10741	+	0.711689i	0.960727	−	0.277495i	$-0.0895041\pi$
$941$	31966.3	+	20543.5i	1.10741	+	0.711689i	0.146682	+	0.989184i	$0.453141\pi$
$942$		0			0
$943$	1390.88	−	297.343i	0.0480309	−	0.0102681i
$944$		0			0
$945$	708.755	+	455.489i	0.0243977	+	0.0156794i
$946$		0			0
$947$	−11627.6	−	25460.9i	−0.398994	−	0.873674i	−0.997371	−	0.0724599i	$-0.976915\pi$
$947$	−11627.6	−	25460.9i	−0.398994	−	0.873674i	0.598378	−	0.801214i	$-0.295812\pi$
$948$		0			0
$949$	11059.2	−	24216.3i	0.378291	−	0.828341i
$950$		0			0
$951$	4098.94	−	28508.7i	0.139766	−	0.972091i
$952$		0			0
$953$	23815.9	+	27485.0i	0.809520	+	0.934236i	0.998863	−	0.0476751i	$-0.0151812\pi$
$953$	23815.9	+	27485.0i	0.809520	+	0.934236i	−0.189343	+	0.981911i	$0.560636\pi$
$954$		0			0
$955$	241.255	−	155.045i	0.00817469	−	0.00525356i
$956$		0			0
$957$	10596.2	−	3111.31i	0.357915	−	0.105093i
$958$		0			0
$959$	11830.3	−	13652.9i	0.398353	−	0.459724i
$960$		0			0
$961$	25788.7	+	7572.24i	0.865653	+	0.254179i
$962$		0			0
$963$	5214.36	+	36266.7i	0.174486	+	1.21358i
$964$		0			0
$965$	2993.98			0.0998753
$966$		0			0
$967$	34760.8			1.15598			0.577990	−	0.816044i	$-0.303837\pi$
$967$	34760.8			1.15598			0.577990	+	0.816044i	$0.303837\pi$
$968$		0			0
$969$	28.3521	+	197.193i	0.000939938	+	0.00653741i
$970$		0			0
$971$	−19123.1	−	5615.05i	−0.632018	−	0.185577i	−0.0499947	−	0.998749i	$-0.515920\pi$
$971$	−19123.1	−	5615.05i	−0.632018	−	0.185577i	−0.582023	+	0.813172i	$0.697739\pi$
$972$		0			0
$973$	−18266.3	+	21080.5i	−0.601841	+	0.694562i
$974$		0			0
$975$	33500.9	−	9836.76i	1.10040	−	0.323106i
$976$		0			0
$977$	6391.96	−	4107.87i	0.209311	−	0.134516i	−0.431785	−	0.901976i	$-0.642116\pi$
$977$	6391.96	−	4107.87i	0.209311	−	0.134516i	0.641097	+	0.767460i	$0.278480\pi$
$978$		0			0
$979$	5529.05	+	6380.87i	0.180500	+	0.208308i
$980$		0			0
$981$	−222.770	+	1549.40i	−0.00725026	+	0.0504267i
$982$		0			0
$983$	2932.27	−	6420.78i	0.0951423	−	0.208333i	−0.856077	−	0.516849i	$-0.827105\pi$
$983$	2932.27	−	6420.78i	0.0951423	−	0.208333i	0.951219	+	0.308516i	$0.0998323\pi$
$984$		0			0
$985$	−447.500	−	979.888i	−0.0144757	−	0.0316973i
$986$		0			0
$987$	−65426.4	−	42047.0i	−2.10998	−	1.35600i
$988$		0			0
$989$	7909.45	+	10645.2i	0.254303	+	0.342263i
$990$		0			0
$991$	14445.9	+	9283.83i	0.463057	+	0.297589i	0.751291	−	0.659971i	$-0.229432\pi$
$991$	14445.9	+	9283.83i	0.463057	+	0.297589i	−0.288234	+	0.957560i	$0.593068\pi$
$992$		0			0
$993$	29543.5	+	64691.2i	0.944143	+	2.06738i
$994$		0			0
$995$	−218.619	+	478.710i	−0.00696553	+	0.0152524i
$996$		0			0
$997$	−893.647	+	6215.45i	−0.0283873	+	0.197438i	−0.999080	−	0.0428864i	$-0.986345\pi$
$997$	−893.647	+	6215.45i	−0.0283873	+	0.197438i	0.970693	+	0.240324i	$0.0772537\pi$
$998$		0			0
$999$	1555.32	+	1794.93i	0.0492574	+	0.0568460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.i.a.25.2	✓	90
23.12	even	11	inner	184.4.i.a.81.2	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.i.a.25.2	✓	90	1.1	even	1	trivial
184.4.i.a.81.2	yes	90	23.12	even	11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978797 - 6.80768i) q^{3} +(-0.683572 - 0.200715i) q^{5} +(16.8123 - 19.4024i) q^{7} +(-19.4802 + 5.71990i) q^{9} +(15.5835 - 10.0149i) q^{11} +(-26.7041 - 30.8182i) q^{13} +(-0.697325 + 4.85000i) q^{15} +(-0.485449 + 1.06298i) q^{17} +(10.2971 + 22.5474i) q^{19} +(-148.541 - 95.4616i) q^{21} +(-97.0007 + 52.5153i) q^{23} +(-104.730 - 67.3057i) q^{25} +(-19.1351 - 41.9001i) q^{27} +(-36.0087 + 78.8481i) q^{29} +(-7.68183 + 53.4283i) q^{31} +(-83.4315 - 96.2851i) q^{33} +(-15.3867 + 9.88846i) q^{35} +(-49.4724 + 14.5264i) q^{37} +(-183.663 + 211.958i) q^{39} +(-12.3721 - 3.63277i) q^{41} +(-17.1107 - 119.007i) q^{43} +14.4642 q^{45} +440.460 q^{47} +(-44.9864 - 312.887i) q^{49} +(7.71161 + 2.26433i) q^{51} +(298.542 - 344.536i) q^{53} +(-12.6626 + 3.71808i) q^{55} +(143.417 - 92.1685i) q^{57} +(-28.8535 - 33.2988i) q^{59} +(126.095 - 877.009i) q^{61} +(-216.526 + 474.127i) q^{63} +(12.0685 + 26.4264i) q^{65} +(-211.202 - 135.731i) q^{67} +(452.452 + 608.948i) q^{69} +(538.204 + 345.883i) q^{71} +(271.204 + 593.853i) q^{73} +(-355.687 + 778.845i) q^{75} +(67.6809 - 470.731i) q^{77} +(840.560 + 970.058i) q^{79} +(-727.663 + 467.641i) q^{81} +(727.514 - 213.617i) q^{83} +(0.545196 - 0.629190i) q^{85} +(572.018 + 167.960i) q^{87} +(64.8654 + 451.149i) q^{89} -1046.90 q^{91} +371.242 q^{93} +(-2.51318 - 17.4796i) q^{95} +(-501.787 - 147.338i) q^{97} +(-246.286 + 284.229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 2 q^{3} - 87 q^{7} - 113 q^{9} - 6 q^{11} - 8 q^{13} - 6 q^{15} + 306 q^{17} + 275 q^{19} + 350 q^{21} - 23 q^{23} - 289 q^{25} + 511 q^{27} + 309 q^{29} - 314 q^{31} - 1444 q^{33} - 1895 q^{35}+ \cdots + 5967 q^{99}+O(q^{100}) \) 90 * q - 2 * q^3 - 87 * q^7 - 113 * q^9 - 6 * q^11 - 8 * q^13 - 6 * q^15 + 306 * q^17 + 275 * q^19 + 350 * q^21 - 23 * q^23 - 289 * q^25 + 511 * q^27 + 309 * q^29 - 314 * q^31 - 1444 * q^33 - 1895 * q^35 - 130 * q^37 + 1850 * q^39 + 927 * q^41 + 1007 * q^43 - 960 * q^45 + 756 * q^47 + 164 * q^49 + 3505 * q^51 + 1267 * q^53 - 2849 * q^55 - 3214 * q^57 - 467 * q^59 - 37 * q^61 + 5838 * q^63 - 2590 * q^65 - 3217 * q^67 - 2046 * q^69 - 508 * q^71 + 2716 * q^73 + 2855 * q^75 - 2245 * q^77 + 270 * q^79 - 2319 * q^81 + 820 * q^83 + 2470 * q^85 - 3545 * q^87 - 457 * q^89 - 10990 * q^91 + 3734 * q^93 - 5437 * q^95 + 1853 * q^97 + 5967 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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